text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
|---|---|---|
Welcome to Sportsplex of Halfmoon Sportsplex of Halfmoon Online - Schedules, standings, team payment and more!
Email - We'll need your email address so we can properly link it to a Sportsplex of Halfmoon Online account.
New to Sportsplex of Halfmoon Online? | {
"redpajama_set_name": "RedPajamaC4"
} | 5,273 |
The Last Zombie: Inferno Vol. 2
The Last Zombie: Inferno
Doctor Ian Scott and his team of soldiers and scientists make their way across the wastelands of a post-zombie apocalyptic America. Infected with the virus that caused the zombie outbreak, Ian struggles to stay alive long enough to see his wife again. As if that wasn't enough, the team find themselves caught between a raging, state-wide wildfire and the radioactive destruction of a nuclear reactor meltdown.
Action/Adventure Zombies Post-Apocalyptic Horror
Continuing AP's popular new series! The Last zombie: Inferno picks up where the last series left off, as Doctor Ian Scott and his team of soldiers and scientists make their way across the wastelands of a post-zombie apocalyptic America. Infected with the virus that caused the zombie outbreak, Ian struggles to stay alive long enough to see his wife again. As if that weren't enough, the team find th
The Last Zombie: Neverland
Lost somewhere between Missouri and Iowa (after surviving the events of The Last Zombie: Inferno), the team stops to repair their vehicles and scavenge supplies. But they soon learn that they aren't the only scavengers in town when a horde of ravenous, swarming rats attack the convoy!
The Last Zombie: Before the After
Shocker Award recipient and two-time Bram Stoker Award winner, Brian Keene is known worldwide for his novels and short stories of the shambling undead! Keene teams up with A.P. powerhouse Joseph Wight (Twilight X, How to Draw (and Fight) Zombies) to tell a terror-tinged tale for the ages! Follow the frantic journey of a man seeking his one ray of hope in a post-apocalyptic nightmare United States
The Last Zombie: The End
The Last Zombie
Shocker Award recipient and two-time Bram Stoker Award winner, Brian Keene is known worldwide for his novels and short stories of the shambling undead! Keene teams up with A.P. powerhouse Joseph Wight (Twilight X, How to Draw (and Fight) Zombies) to tell a terror-tinged tale for the ages! Follow the frantic journey of a man seeking his one ray of hope in a post-apocalyptic nightmare United Stat | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,859 |
S.H.E's Hebe "flying solo" releasing individual album
S.H.E's Hebe is finally "flying solo" releasing her individual album which has been in production for two years, however H.I.M are trying to be mysterious. Online, there has been a 30 second preview clip circulating, which doesn't reveal the girl's eyes, nor is there a name attached to this clip, but as soon as fans heard it, they knew who that unique singing voice belonged it.
This clip called "A girl who loves singing, a song about love" has been circulating online. Its simple shots show a girl with long flowing hair, but doesn't show her face yet her graceful vocals have attracted lots of attention. Even though fans have already discovered who this mysterious person is, H.I.M are still persistent, "We've seen this clip and think this girl sings really well, we believe that with her talents, she will be a real competitor among this summer's female singers."
H.I.M. has been deliberately using these tactics to create suspense and anticipation for their "half-new artist" but as soon as fans heard her pronounce "shi jie" (meaning: world), they were immediately certain that it was Hebe. Netizens have been searching all over the internet and have now gathered that the song is called "Love?", the album will be released at the beginning of September, Golden Melody Best Album Cover Designer Nie Yong Zhen designed the cover, the album will come with a 330 The Wall Concert DVD as well as many other details. In regards to this, H.I.M continues to deny everything.
S.H.E are still continuing their world tour but H.I.M has already made many plans for them as they all continue their individual pursuits, Ella is acting, Selina is hosting while it has been rumoured since 2008 that Hebe will be releasing a solo album. Each has their own arena but they have no plans to disband and fly solo.
English Lyric for "A girl who loves singing, a song about love"
I love you, you love her, she loves her, she loves him
You love me, I love him, he loves him, he loves her
Eh, how come in this world, nobody loves anymore?
How come in this world, everyone is unhappy?
How come in this world, everyone loves somebody else,
But not themselves?
純誼 said...
馥甄 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,781 |
Over 170 years ago on the Galapagos Islands, Charles Darwin made an interesting observation. The animals he saw on this remote outpost were not quite like the ones he had seen throughout South America during the survey expedition of the HMS Beagle. In fact, and more importantly, he noticed a tortoise or finch on one island was not quite like a tortoise or a finch on another island. They had adapted to their environment.
We all have seminal moments in our lives – events that prove to be major influences and shift our perspective or open our minds to new ways of thinking. Some moments become shared touchstones. Where were you when Neil Armstrong set foot on the moon? What were you doing when you heard about the airplanes crashing into the World Trade Center? Others – like the teenager who hears Nirvana playing on the radio and ditches his trombone in favor of an electric guitar – are more personal.
Seemingly everyone I talk to these days is in transition, trying to reconcile past experiences and skills with current and future market needs. Few planned on careers where it seems the most important skill is the ability to acquire new skills.
In a networked, cloud-based world where nothing is fixed or permanent, how do communicators and marketers determine what will endure? How do our skills apply? Perhaps we should be asking: How will we adapt?
Everything is measured in terms of individual perception. To me, that little puppy is cute and cuddly; to you, it's smelly and sheds all over the furniture; to another, it may look like dinner. If we accept that premise, then our real value is an ability to make ideas and information accessible to each individual in our audience. Fortunately, we have more and better tools to do this than ever before.
The theory of evolution was not new when Darwin published The Origin of Species. He was recognized for synthesizing his experiences and insights with existing thought and making the principle of natural selection accessible to the public.
Similarly, the concept of creating adaptive or fluid websites is not new. With the explosion of mobile devices, web designers and developers debated the merits of various screen resolutions and wrestled with the lack of standards across multiple web browsers. The response has ranged from building a dizzying array of mobile apps to creating and maintaining separate mobile-friendly websites to doing nothing at all.
In the article Responsive Web Design, and subsequent book, Ethan Marcotte gives name to a better way forward. Responsive designs automatically deliver the best site for your users based on what you know about them – one site serving all audiences better.
Rather than quarantining our content into disparate, device-specific experiences, we can use [technology] to progressively enhance our work within different viewing contexts.
Responsive websites use new technologies and better browser support to rearrange, resize, add or subtract content to fit the device. Additionally, it forces the web team – designers, writers and developers – to rethink how that content is edited, organized and delivered.
Successful marketers have always aimed to serve an audience's needs – to quickly respond with interest and enthusiasm. Responsive web designs not only meet your users' need for relevant information any time, anywhere, on any device, but essentially eliminate the need to create and maintain separate apps and sites.
I believe this represents a seminal moment. If simplicity is the ultimate sophistication, as Leonardo da Vinci once wrote, then the tools we use are finally getting sophisticated enough to make our lives simpler – and that's an adaptation we can all embrace.
The web is an amazingly flexible medium that can be updated at a second's notice, yet many people seem to forget this when launching a site. A website needs to be functional and well designed when it is unveiled, but waiting for perfection is a trap that can delay a launch indefinitely. Here is how to avoid that trap.
Websites often get delayed because the scope of the site is too big to execute given the manpower. Don't plan for content that no one has time to write or interactive features no one has time to build. Distinguish between functionality and features that are necessary and those that are simply nice to have.
For example, many organizations struggle with how to integrate social media into their website. While social media is an attractive feature, it adds little value if no one has the time to sustain it. Instead of setting up blogs, a YouTube channel, and an account on every networking site, determine how many channels you realistically have the time and passion to maintain. One well-maintained social media channel will be more effective than half a dozen that are not.
Sites can be delayed by endless hypothetical questions. A common one I hear is: What if members of my audience are using a dial-up connection or an outdated browser? Yes, it's possible that someone will want to access your site on Netscape, but frankly the number of people fitting this profile is statistically insignificant.
Be as thorough as possible when planning for the ways different people will be accessing your site. Make sure it is easily accessible from multiple browsers, screen readers for the visually impaired, and for smart phone users. However, it is impossible to prepare for every scenario. Inevitably, some people will encounter a few bugs.
Encourage people to report problems by including a link to your webmaster in the footer of your site. If enough people have the same problem, they will identify where the site needs improvements. Don't waste time worrying about hypothetical scenarios. Wait and troubleshoot the real ones.
You may think your site won't be perfect until that interactive slideshow is finished, or until you have time to write a great blog. Get over it. Don't delay releasing new content or a more user-friendly interface just because a few bells and whistles aren't ready. In fact, adding features at a later date can be to your advantage. New features draw the attention of search engines and give users a reason to return to your site after the redesign.
A good website is always evolving. Regularly adding new features and content should be the goal, not a reason to delay launching. If your organization's website is perfect when you launch it, you've waited too long.
Website projects often start with a lot of enthusiasm. People are tempted to jump right to the "fun" parts of web design, getting excited about the potential new look, features and functionality. This is like picking out drapes and paint chips for a new house before a blueprint has been made.
The first thing you need to know is what content your visitors are looking at. Your web host should be able to provide statistics on web page views and how people find your site. Google Analytics can also be installed on sites for free. Often, people are surprised to find which pages are being looked at and which are not. Ultimately, a thorough website content audit will answer two questions: What's there? And, is it any good?
Website statistics only provide information about existing content. Focus groups or one-on-one interviews can help identify needs that are currently unmet, or features that are difficult for your visitors to find or use. Focus on understanding your user's needs rather than on current habits. Ask why they visit your site, what other sites they visit, and what needs are met there. What are they not finding on the web? Can you fill that need?
Users can also help you organize the site. Find out what categories they want to see in the main navigation, and what information they would expect to find in each category. While no two people will organize a website exactly the same way, look for patterns that will help you choose the best path to information.
Make time for usability testing. You don't need video cameras, statistically valid samples, or white lab coats. Conducting a web usability test can be as simple as sitting with a test subject at a computer. Ask them to articulate their needs. Ask them to perform tasks. Then watch and listen.
It's important to conduct usability tests early (and often) in your project. As web usability consultant Steve Krug says in his book Don't Make Me Think, "Testing one user early is better than testing 50 near the end." This allows for an iterative process in which your design continually moves closer and closer to the ideal solution.
By employing a process that includes data analysis, insights from your site's users, and usability testing throughout, your new website will have a solid foundation. This provides the best chance of building a successful website, one which meets your audience's needs.
The shopping experience at my local "super" retailer often goes something likes this: I walk into the store hoping for a quick trip to pick up a roll of masking tape. After half an hour searching in "Office Supplies," an employee finally takes me to find it in the hardware section.
When we've conducted web usability tests, we have seen a lot of people with experiences similar to my shopping trip. They enter a website with a specific task, then get frustrated when the information they seek is not in the expected section.
92% of prospective students will be disappointed or walk away if they can't find what they're looking for.
65% said that they would be more interested in a college because of a good web experience.
In our research, we have found web users overwhelmingly prefer indexed navigation. The idea is similar to a sitemap, but instead of showing the whole site the navigation shows only the most relevant information. Indexed navigation eliminates much of the site users' guessing by showing what kinds of things each category includes.
Indexed navigation (highlighted) is organized by topic and provides users easy access to the information they seek.
When creating an indexed navigation it's important to ask users what information is important to them, and where do they expect to find it. What kind of categories are they looking for in the main navigation? What kind of information do they expect to see under those headings? Does the wording in the navigation reflect what falls in those categories?
The answers to these questions may be surprising. External audiences often view your website differently. What seems obvious or interesting to you may not be important to someone who's visiting your site for the first time.
When organizing a site, it's important to show your users the big picture. The easier it is for people to find what they're looking for, the better the website experience will be.
The online version of your publication is an increasingly important part of the communications mix. Because print and pixels are distinctly different, it's vital to consider how each affects the way your audience consumes information.
An online publication should be more than a way to reduce costs by saving money on printing and mailing. In fact, research published in the March 2010 issue of CASE's Currents magazine found that nearly 75% of respondents did not look at the online edition of their alumni magazine, while 91% always or frequently read the printed version.
People have different expectations when they go online. Readers seek up-to-the-minute information in a media-rich environment that includes video, message boards, and opportunities to connect via social networks. Creating an online publication that delivers relevant content and draws repeat visits takes dedication and time.
Putting a publication on the web offers new opportunities to communicate with people beyond your core audience. The CASE research finds that external searches often spark more interest in your organization and the information and expertise you provide. Online publications must be optimized to help people find you.
Through animation, some online publications try to literally mimic the effect of a printed page being turned. This gimmick not only misses the point, but is not terribly helpful to the reader. Your web interface should focus on delivering content to your readers in a way that advances the story and increases understanding.
The success of your online efforts relies on your ability to adapt to the way people are viewing the written word. Devices like the iPhone and Amazon Kindle enable readers to interact with content in new ways. Recently, Wired magazine unveiled their vision for taking advantage of this new technology.
Each advance in technology requires an understanding of how people will interact with information — both what is possible and what is preferable. The question should not be: How do we make this more like a printed piece? But, how can we leverage the technology to create a more engaging experience for our readers?
The web allows designers to create interactive experiences that are not possible in print. However, it is tempting to let the "experience" get in the way of providing people with information.
Recently, as part of a site redesign, we conducted usability testing on a number of university websites. Many of the home pages featured a large section devoted to creating an interactive experience, with beautiful slide shows or video and elegant navigation. However, none of our test subjects explored these features, skipping straight to the main navigation.
This reinforced our belief that most web users, even first-time visitors, have a goal in mind when they enter a site. Users are usually looking for the fastest way to obtain specific information.
In my own experience, MySpace is a site where my need for information trumps my design sensibilities. I frequently use the music section of MySpace to get information on my favorite artists. These pages are usually a cluttered mess, with distracting backgrounds and poor visual hierarchy. But despite these disadvantages, I find myself turning almost exclusively to MySpace for information rather than to the artists' official .com websites.
Why? Even with the less-satisfying visual experience, actual content is fairly straightforward and easy to find on MySpace pages.
When using the web to find information about an artist, I am usually looking for one of two things – music to listen to or tour dates. On an artist's .com site, I am never sure what to expect. Often these sites require waiting for Flash to load and have cumbersome animated menus. Also, custom music players necessitate a learning curve for each one.
MySpace Music pages, on the other hand, have a predictable and basic layout with a limited number of options. While the components of each page may vary somewhat, everything is on one page. Once you've seen a few MySpace pages, the consistency of the available options makes finding information easy.
While including animation and interactive features can supplement the web experience, it's easy to get carried away. When designing a site, I always try to remember that the users' primary need is information.
Because it appears to affect relatively few people, web accessibility isn't often top-of-mind during the design and coding process. I've found, however, that considering accessibility earlier in the process can help improve the web experience for all users.
Earlier in my career, I was more focused on the way a site appeared than how the code was organized. When I started incorporating accessibility guidelines into my work, I discovered sites could be built more efficiently without sacrificing visual appeal.
There are many advantages to designing an accessible website. Most importantly, it is highly beneficial to site navigation. Sometimes the most visually logical way to create navigation makes for unnecessarily complicated code. Because accessible menus generally operate on less code, site users experience no lag time when waiting for a hover state or a dropdown menu to appear.
Accessible websites make your site more visible to search engines because images with text require a live text equivalent. Additionally, because they follow standard coding protocols, accessible websites are easier to manage and update.
Focusing on web accessibility earlier in the process means all content is properly coded, leading to simpler sites with cleaner typography. The result: Websites that work better for all users because both the design and production were considered, together, early in the process. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,578 |
\section{Introduction}
\label{S:1}
Rare-earth based perovskite manganates have been in the centre of research intrigue due to their rich inter-related structural\cite{abdel2012rare}, electronic\cite{Kalashnikova2003} and magnetic properties\cite{wood1973magnetic,serrao2007multiferroic}, which account for their giant magnetoresistance\cite{diehl1997potential}, colossal magnetoresistance\cite{millis1997electron}, magnetocapacinatce\cite{goto2004ferroelectricity} and high magnetocaloric\cite{elghoul2018rare,sande2001large} and magnetodielectric effects\cite{lorenz2004large} to name a few. The underlying physics which drives the unusual but rich physical properties of the manganites results from the array of different complex interactions like double exchange (DE)\cite{Rama_DE}, super exchange (SE)\cite{BIRSAN_SE}, electron-phonon interaction\cite{Edwards_EP}, electron-electron interaction\cite{Varshney2010} etc. The manganates have the empirical formula of ABO$_3$, where A and B mainly belong to large rare-earth and transition metal cations respectively. The structure of these perovskites are mostly deviated from high symmetry with the tilting and the distortion of the BO$_6$ octahedra being the main structural characteristics which affect their physical properties. The tunable cation-cation ordering (long-range and short-range) at the transition metal site actively modulated by chemical doping at these active sites. Thus the combination of structural deviations and cation-cation ordering modulate the observed exotic properties in these perovskites which range from structural phase transitions\cite{Sangeeta2018}, magnetic phase transitions\cite{Troyanchuk2003} and electronic metal insulator transitions\cite{Rusydi2008} which have direct implications on their magneto-dielectric\cite{lorenz2004large}, magneto-caloric effect\cite{sande2001large} and magneto-resistive effects\cite{TOKURA19991} which are useful for switchable spintronics applications\cite{Volkov_2012}. The hexagonal perovskite manganites belong to multiferroic group of materials which show the electric ($\sim$ 900 K) and magnetic ( $\sim$ 100 K) ordering simultaneously\cite{Fukumura_2007,Fiebig2006}.
\begin{figure*}
\centering
\includegraphics[scale=0.65]{Figure/Spin_95.pdf}
\caption{The magnetic spin structure of LAM95 unit cell (a) For R-3c and (b) Pnma space group}
\label{fig:1}
\end{figure*}
Among the rare-earth manganites, LaMnO$_3$ is highly studied material, which takes part as a parent compound due to its highly enriched and intense properties. Previous studies shows that it belongs to the orthorhombic centrosymmetric space group\cite{Iliev1998,NORBY1995191}. The MnO$_6$ octahedra becomes tilted and distorted due to orthorhombic distortion of this material\cite{PRADO1999418}. This leads to the cooperative John-Teller effect of this material which lifts the degeneracy of d-orbital of Mn$^{3+}$-ion [t$_{2g}^3(d_{XY}^1, d_{YZ}^1, d_{XZ}^1)$ and e$_g^1(d_{Z^2}^1, d_{X^2+Y^2}^0)$]. The spins (S=2) of the magnetic Mn$^{3+}$-ions are ferromagnetically aligned through the O$^{2-}$ due the Hund rule and the orbital ordering in the Basal plane. Now, the perpendicular planes show the antiferromagnetic alignment with this plane due to cooperative John-Teller distortion\cite{pavarini2010}, which forms the A-type anti-ferromagnetism of this material\cite{rodriguez1998neutron}. A study shows that the system becomes ferromagnetic instead of antiferromagnetic if the cooperative JT distortion is absent\cite{coey1999,chukalkin2006structure}. Later, it is studied that the doping of divalent atom in the La-site removes the JT distortion and the system shows the ferromagnetic behaviour at low temperatures\cite{mahendiran1996structure}. The doping of this cations generates the Mn$^{4+}$-ion in the material due to the charge neutrality. Now the e$_g$ electron of Mn$^{3+}$ is hopped towards the empty e$_g$-orbital of Mn$^{4+}$ through the O$^{2-}$ induces the ferromagnetism in the system; this whole process is called the double exchange (DE) mechanism\cite{skumryev1999weak}. So, the Mn$^{4+}$ is mainly responsible for FM transition in LaMnO$_3$.
During the synthesis of LaMnO$_3$, the uncontrolled sintering and annealing create some vacancy of the cationic sites which produces some extra amount of non-stoichiometric oxygen (3+$\delta$) to balance the charge neutrality\cite{wang2010effect}. As a result of this procedure, the system creates some Mn$^{4+}$-ion, which is called the self-doping\cite{chandra2012evidence}. This generates the DE ferromagnetic interaction in the materials. If the system crosses the certain limit of self doping, it becomes fully ferromagnetic. So, the lower value of $\delta$ enhances the super-exchange (SE) which creates the canted A-AFM magnetic structure. The DE interaction (FM) wins the competition for higher $\delta$ values. If the $\delta \ge 0.1$, the crystal structure changes from orthorhombic to rhombohedral\cite{chandra2012evidence}.
In case of magnetic cations (M = Fe, Ni, Co) doping in the Mn site lead to the Orthorhombic crystal structure with ferromagnetic transition\cite{bhat2021study,hebert2002induced,de2005effect}. The exchange interactions between Mn$^{3+}$ and M$^{3+}$ are responsible for the ferromagnetic behaviour of these materials. But doping of the non-magnetic tetravalent Ti$^{4+}$-ion shows the Rhombohedral R-3c structure and the material creates Mn$^{2+}$-ion for the charge neutrality\cite{yang2005structural}. The DE interaction between Mn$^{3+}$ and Mn$^{2+}$ generates the ferromagnetism in this material. In this context, we have studied the effect of non-magnetic trivalent Al-doping in Mn-site of LaMnO$_3$. The detailed structural properties have studied through X-ray diffraction and X-ray Photo-electron Spectroscopy (XPS) method, which supports the presence of Mn$^{4+}$ state in this sample. The detailed magnetic analysis have performed through the M-T and M-H curves and the DFT calculations with the magnetic Monte-Carlo simulations.
\section{Experimental Details}
\label{S:2}
\begin{figure*}
\centering
\includegraphics[scale=0.65]{Figure/XRD_all_figure.pdf}
\caption{The XRD data and the Rietveld refinement of LaAl$_{x}$Mn$_{1-x}$O$_3$ [x= (a) 0.05, (b) 0.15, (c) 0.25]. (d) The zoomed view of main perovskite peaks of these materials and the 4$^{th}$ one is for the LaAl$_{0.5}$Mn$_{0.5}$O$_3$, taken from our previous study.}
\label{fig:2}
\end{figure*}
Al doped LaMnO$_3$ is prepared through sol-gel citrate method. Firstly all the nitrates La(NO$_3$)$_3$.$6$H$_2$O, Mn(NO$_3$)$_3$.$9$H$_2$O, and Al(NO$_3$)$_2$.$6$H$_2$O were taken with calculated stoichiometric ratio in a de-ionised water medium with appropriate molar ratio of citric acid and ethylene glycol. Then, the solution is stirred and heated to achieve a gel and and fluffy ash-like powder. The obtained powder is calcined and sintered at 1173 K and 1223 K to get the final material. LaAl$_{x}$Mn$_{1-x}$O$_3$ (x= 0.05, 0.15, 0.25) are prepared with the help of above described method. The room temperature X-ray diffraction (XRD) pattern of these materials are obtained from X-ray powder diffractometer (Rigaku Miniflex II, Cu-K$\alpha: \lambda$=1.54 \AA), where the range of 2$\theta$ is 10\textdegree~ to 80\textdegree~ at a scanning rate of 0.02\textdegree~ per step. We get the crystal structure and the lattice parameters from the Rietveld refinement analysis of the XRD data using the Fullprof suite program~\cite{RODRIGUEZCARVAJAL1993}. The X-ray photoemission spectra of LaAl$_{0.25}$Mn$_{0.75}$O$_3$ are taken by X-ray photoelectron spectroscopy (XPS). The magnetic properties are taken from the vibrating sample magnetometer (VSM;Lakeshore).
\begin{table}[ht]
\centering
\caption{Atomic coordinates and lattice parameters of LaAl$_{x}$Mn$_{1-x}$O$_3$ (x= 0.05, 0.15, 0.25) determined from Rietveld Refinement method.}
\label{tab:1}
\begin{tabular}{c c c c c c c c c}
\hline
\hline
Sample & Atom & x & y & z & lattice & Reliability & Occu- & Wickoff\\
& & & & & parameters (\AA) & factors & pancy & site\\
\hline
LAM95 & La & 0.000 & 0.000 & 0.250 & a = 5.505 & $\chi^2$=1.23 & 1.00 & 6a\\
& Mn & 0.000 & 0.000 & 0.000 & b = 5.505 & R$_p$=7.90 & 0.991 & 6b\\
& Al & 0.0000 & 0.0000 & 0.000 & c = 13.311 & R$_{wp}$=10.3 & 0.021 & 6b\\
& O & 0.456 & 0.000 & 0.250 & $\gamma$=120\textdegree & R$_{exp}$=8.67 & 1.128 & 18e\\
\hline
LAM85 & La & 0.000 & 0.000 & 0.250 & a = 5.486 & $\chi^2$=1.18 & 1.00 & 6a\\
& Mn & 0.000 & 0.000 & 0.000 & b = 5.486 & R$_p$=7.53 & 0.933 & 6b\\
& Al & 0.0000 & 0.0000 & 0.000 & c = 13.288 & R$_{wp}$=9.74 & 0.054 & 6b\\
& O & 0.451 & 0.000 & 0.250 & $\gamma$=120\textdegree & R$_{exp}$=8.44 & 1.161 & 18e\\
\hline
LAM75 & La & 0.000 & 0.000 & 0.250 & a = 5.471 & $\chi^2$=1.16 & 1.00 & 6a\\
& Mn & 0.000 & 0.000 & 0.000 & b = 5.471 & R$_p$=7.46 & 0.891 & 6b\\
& Al & 0.0000 & 0.0000 & 0.000 & c = 13.275 & R$_{wp}$=9.67 & 0.055 & 6b\\
& O & 0.452 & 0.000 & 0.250 & $\gamma$=120\textdegree & R$_{exp}$=8.97 & 1.184 & 18e\\
\hline
\hline
\end{tabular}
\end{table}
\section{Computational details}
\subsection{Ab-initio Calculations}
The electronic and magnetic properties of Al doped LaMnO$_3$ have been thoroughly investigated through full-potential linearized augmented plane wave (FPLAPW) method as implemented in WIEN2K\cite{BLAHA1990,Blaha2020}. The crystal structure of LaMnO$_3$ is being optimized through spin-polarized general gradient approximation (GGA) with Coulomb repulsion U (GGA+U) method. We have taken five magnetic spin configurations for the optimization process such as ferromagnetic (FM), non-magnetic (NM) and three antiferromagnetic (AFM) [A-AFM, C-AFM, G-AFM]. Now we have made the supercell for the other three Al-doped systems. In the supercell, we have replaced the Mn through the Al atoms in appropriate percentage. The all the structures is being optimized through the above described process. The Hubbard parameter $U_{eff}$ for Mn-d orbital are fixed to 3 eV for all structures. The self consistent criteria for energy and charge convergence have been set to $10^{-4}$ Ry and $10^{-3}$ e, respectively.
\begin{figure*}
\centering
\includegraphics[scale=0.56]{Figure/XPS.pdf}
\caption{(a)The whole XPS spectra of LaAl$_{0.25}$Mn$_{0.75}$O$_3$ and fitted data are shown for (b) La and (c) Mn atom}
\label{fig:3}
\end{figure*}
\subsection{Monte Carlo Simulations}
Monte-Carlo simulation is a very useful technique to study the magnetic properties theoretically\cite{masrour2015,bhowmik2021phase,BHOWMIKLaMn2Si2,BHOWMIK2021412659}. We have used the anisotropic Ising model for this simulation\cite{BhowmikPr2CrMnO6}. The anisotropy comes from the two types of Mn ions, Mn$^{3+}$ and Mn$^{4+}$, which is verified by XPS spectra, discussed later. So, the Hamiltonian, we have taken for the computation of the magnetic properties, is described in the following.
\begin{equation}
H = - J_{1}\sum_{<i,j>}{S_iS_j} - J_{2}\sum_{<i,k>}{S_iS_k} -\Delta\sum_{i}{S_i^2} -h\sum_{i}{S_i}
\end{equation}Where h and $\Delta$ are the external field and the anisotropic constant, respectively. $J{_{1}}$ and $J{_{2}}$ are the interaction constants for the nearest neighbour (NN) and next nearest neighbour (NNN) interaction, respectively. Due to the two type of Mn-ions, we have used two spins value S = 2 and 1.5 for Mn$^{3+}$ and Mn$^{4+}$, respectively. The value of these constants are determined from the first principle calculations described in later part of this article.
The single flip standard sampling method with periodic boundary condition is applied to the whole lattice size (L=30) in all three Cartesian directions. 10$^6$ MCS steps are used for the lattice equilibrium and the next 10$^7$ steps for the average of the magnetization and other observable. The physical quantities, which have been measured using MCS, are described as follows \cite{book}.
\section{Results and Discussions}
\subsection{Crystallographic Information }
\begin{figure*}
\centering
\includegraphics[scale=0.65]{Figure/Magnetic_Expt_Final.pdf}
\caption{(a) The M vs T curve for LaAl$_{x}$Mn$_{1-x}$O$_3$ (x= 0.05, 0.15, 0.25). (inset) The inverse susceptibility and its linear fitted curve with respect to the temperature in the paramagnetic region. (b) The magnetic hysteresis for these materials and its zoomed view at origin (inset). }
\label{fig:4}
\end{figure*}
The crystal structure of these materials are determined from XRD, described in Figure 2 (a-d). The main peak near 32\textdegree~as well as next to this splitted into two parts, which indicates that it might be fitted with the Rhombohedral symmetry. However, we have performed the Rietveld refinement of these diffraction pattern with the pseudo-voigt function in Fullprof suite programme. The refinement suggests that these three samples crystallizing with the R$\Bar{3}$c (space group 167) symmetry. The lattice parameter, atomic coordinates and the goodness of fit ($\chi^2$) are given in table 1. Figure 2(d) represents the zoomed view of main peaks and next two other peaks of LaAl$_{x}$Mn$_{1-x}$O$_3$ (x= 0.05, 0.15, 0.25). The splitting of main peaks are going to abolish with higher Al concentration. For 75\% Mn, the 32\textdegree~peak almost marges into one peak. From our previous study of LaAl$_{0.5}$Mn$_{0.5}$O$_3$, there is no sign of splitting of peaks (Figure 2(d-d))\cite{HALDER202021021}. This 50\% Al-doped material's symmetry also completely changes to Monoclinic P2$_1$/n. So, this material have a structural phase transition from R$\Bar{3}$c to P2$_1$/n with increasing Al-concentration.
The surface elemental composition and oxidation states of LaAl$_{0.25}$Mn$_{0.75}$O$_3$ are investigated using X-ray photoelectron spectroscopy (XPS) in a wide energy window of 0-1200 eV. The survey spectrum of LaAl$_{0.25}$Mn$_{0.75}$O$_3$ in figure 3(a) shows the presence of La(3d), Al(2p), Mn(2p) and O(1s). The high resolution core level XPS spectra for La 3d and Mn 2p in are presented in figure 3(b), and figure 3(c), respectively showing their formal oxidation valence states. The XPS spectra of La-3d in figure 3(b) shows two sets of spin-orbit split peaks (834.6 eV; 838.1 eV) corresponding to La 3d$_{5/2}$ and (851.4 eV; 855.0 eV) corresponding to La 3d$_{3/2}$ respectively, which are known-markers for the +3 oxidation state for La. The core-level XPS spectra of Mn-2p, shown in figure 3(c) demonstrates a mixed or variable oxidation state for Mn. The double splitting of individual peaks corresponding to Mn 2p${_3/2}$ at $\sim$643 ev and Mn 2p$_{1/2}$ at $\sim$653 eV marks the presence of two oxidation states for Mn, namely Mn$^{3+}$ and Mn$^{4+}$. The lower binding energies corresponding to 642.2 eV and 652.6 eV mark the presence of the Mn$^{3+}$ state whereas the higher binding energies at 644.8 eV and 654.8 eV correspond to the Mn$^{4+}$ oxidation state. In addition, satellite peaks for 2p$_{3/2}$ and 2p$_{1/2}$ occur at 529.7 eV, and 531.2 eV, respectively. The system has 30\% of Mn$^{4+}$ state in the Mn-site, which means the excess of non-stoichiometric oxygen ($\delta$) is 0.3. The presence of heterogeneous oxidation states of Mn is important to gain insights into the intriguing magnetic landscape of the materials which will be discussed in the subsequent sections.
\begin{figure*}
\centering
\includegraphics[scale=0.60]{Figure/EnergyVsVolume_Pnma.pdf}
\caption{The energy with respect to the volume for different spin configurations of LaAl$_{x}$Mn$_{1-x}$O$_3$ [x= (a) 0.0, (b) 0.05, (c) 0.15, (d) 0.25].}
\label{fig:5}
\end{figure*}
\subsection{Magnetic Properties}
The temperature dependency of magnetization is plotted in Figure 4(a). The value of magnetization decreases gradually with increasing temperature for all three materials. The magnetic moment should be decreased with the decreasing Mn concentration. But we have seen that the value of magnetization for x=0.15 is greater than the x=0.05. This happens due the increasing percentage of Mn$^{4+}$ ion in the x=0.15 sample. The magnetization vs Temperature plot clearly indicates the ferromagnetic transition of these materials. The transition temperatures are T$^{0.05}_C$ = 135 K, T$^{0.15}_C$ = 110 K and T$^{0.25}_C$ = 85 K which are determined from the minimum point of 1st derivative of M-T curve.
\begin{figure*}
\centering
\includegraphics[scale=0.60]{Figure/EnergyVsVolume_R-3c.pdf}
\caption{The energy with respect to the volume for different spin configurations of LaAl$_{x}$Mn$_{1-x}$O$_3$ [x= (a) 0.0, (b) 0.05, (c) 0.15, (d) 0.25].}
\label{fig:6}
\end{figure*}
The inverse of the dc susceptibility is plotted in the inset of Figure 4(a). The linear part (paramagnetic region) of this curve is fitted through Curie-Weiss law, $\chi = C/(T-\Theta_{CW})$. The positive value of $\Theta_{CW}$ indicates the ferromagnetic ordering of these materials at lower temperatures. The effective magnetic moments are 3.76 $\mu_B$/FU, 3.51 $\mu_B$/FU and 3.32 $\mu_B$/FU, calculated from the Curie constant C. The spin only moment value of Mn$^{3+}$ is 4.9 $\mu_B$. So, the theoretical magnetic moments for x=0.05, 0.15 and 0.25 are 4.66 $\mu_B$/FU, 4.17 $\mu_B$/FU and 3.68 $\mu_B$/FU, respectively. It is clearly seen that there is a difference between experimental and theoretical moment value. In the octahedral environment the d-orbital of Mn$^{3+}$ ion is separated to e$_g$ and t$_{2g}$ due to the crystal field effect. This discrepancy of the moment arises due to the much stronger crystal field interaction than the spin-orbit interaction. But with lower Mn-concentration this difference in the moment is small due to the presence of extra Mn$^{4+}$ in the system, which is proved from the XPS data previously. In this case, the crystal field interaction creates less impact because there is no e$_g$ electron in Mn$^{4+}$-ion. The origin of ferromagnetic character of these material are mainly due to the double exchange interaction (DE) between Mn$^{3+}$ and Mn$^{4+}$ through the O$^{2-}$-ion. One t$_{2g}$ electron of Mn$^{3+}$ transfers through O$^{2-}$-ion to Mn$^{4+}$, creates the ferromagnetism in these materials.
\begin{table}[ht]
\centering
\caption{Calculated magnetic moments of each atoms, interstitial and cell for Al doped LaMnO$_3$ in $\mu_B$ unit}
\label{tab:2}
\begin{tabular}{c c c c c c c c c}
\hline
Symmetry & Materials & $\mu_{La}$ & $\mu_{Al}$ & $\mu_{Mn^1}$ & $\mu_{Mn^2}$ & $\mu_{O}$ & $\mu_{int}$ & $\mu_{cell}$ \\
\hline
Pnma & LAM95 & 0.01 & 0.007 & 3.23 & -3.24 & -0.06 & -0.51 & 3.99 \\
& LAM85 & 0.01 & 0.006 & 3.37 & 3.40 & 0.02 & 3.23 & 27.98 \\
& LAM75 & 0.02 & 0.003 & 2.86 & 3.01 & 0.04 & 2.44 & 11.99 \\
\hline
R-3c & LAM95 & 0.01 & 0.008 & 2.96 & 2.58 & 0.05 & 2.51 & 30.00\\
& LAM85 & 0.01 & 0.009 & 3.76 & 3.68 & -0.02 & 1.83 & 28.00\\
& LAM75 & 0.01 & 0.015 & 3.70 & 3.69 & -0.01 & 0.76 & 12.00\\
\hline
\hline
\end{tabular}
\end{table}
Figure 4(b) and its inset figure represent the magnetic hysteresis loop and its zoomed view of these three materials at 80 K. For x=0.05, the loop behaves like ferromagnet as magnetization saturates in high 10 kG magnetic field. The value of coercivity H$_C$ = 333 Oe and the remanent magnetization M$_r$ = 0.25 $\mu_B$/f.u. suggest the ferromagnetic behaviour of this material. In case of x=0.15, the curve also saturates at high field and coercivity H$_C$ = 78.15 Oe and the remanent magnetization M$_r$ = 0.11 $\mu_B$/f.u., which indicates the ferromagnetic character of this material. But for x=0.25 sample, we have seen the paramagnetic type behaviour at 80 K.
\subsection{Electronic and Magnetic Structure: DFT}
The electronic and magnetic structure of the material play a crucial role for different transport properties of the materials. To know the better physics of the material, the first principle density functional theory is most accurate tool in this regards. The crystal structure should be optimized to get accurate results. The minimization of the energy with respect to the volume is a best way to achieve a optimized structure. However, we have taken the atomic coordinates and lattice parameters of the Rhombohedral R-3c LaMnO$_3$ and optimized this structure through the WIEN2K structure optimization. We have used four different spin configurations (FM, A-AFM, C-AFM and G-AFM). Among these we have seen that FM has the lowest energy, so the LaMnO$_3$ is ferromagnetic (Figure 5). Then we have introduced the Al-atom by replacing some Mn-ion with appropriate proportion 5\%, 15\% and 25\% in the B-site of the perovskites. All the structures have shown the ferromagnetic in the ground state.
But, in literature, we have seen that the Orthorhombic Pnma LaMnO$_3$ shows the A-type antiferromagnetic spin configuration in the ground state. So, we have taken this structure and optimized for four different spin configurations. The result of this study shows that the A-AFM has the lowest energy among them. So, the structural symmetry has responsible for the magnetic structure in this case. The superexchange interaction through Mn$^{+3}$-O-Mn$^{+3}$ causes the antiferromagnetic interaction of this material. In the orthorhombic structure, there is very less amount of Mn$^{4+}$. So, the superexchange interaction has dominated over the ferromagnetic DE interaction (Mn$^{+3}$-O-Mn$^{+4}$). Now, for the 5\% Al-doped LaMnO$_3$ (Pnma), shows the A-AFM magnetic structure in the ground state. But the other two materials have shown the FM ground state. The doping of non magnetic Al-atom (above 5\%) breaks the superexchange AFM interaction between NN Mn$^{+3}$-ions.
\begin{figure*} \centering \includegraphics[scale=0.7]{Figure/Dos_pnma_r-3c.pdf} \caption{The DOS and PDOS curve for (a,b) Pnma LaAl$_{x}$Mn$_{1-x}$O$_3$ [x= 0.05, 0.25] and (c,d) R-3c LaAl$_{x}$Mn$_{1-x}$O$_3$ (x= 0.05, 0.25). The Fermi energy (E$_F$) is set to zero, shown with the vertical dotted line.} \label{fig:7}\end{figure*}
The bond lengths of Mn-O in MnO$_6$ octahedra derived from DFT are 1.69 \AA, 2.09 \AA, and 2.24 \AA for Pnma LAM95 structure. Whereas these bond lengths become 1.91 \AA, 1.96 \AA, and 2.18 \AA for Pnma LAM85. So, clearly the John-Teller effect is dominated in the 1st case which leads to the antiferromagnetic ground state of 0.05\% Al doped LaMnO$_3$. The John-Teller effect lifting the degeneracy of e$_g$ orbital and the system shows the orbital ordering, which is responsible for long range AFM ordering of Mn-ions here. This is called the cooperative John-Teller effect. In the second case, the cooperative JT effect disappears which means the system is no longer antiferromagnetic. For, LaGa$_{1-x}$Mn$_x$O$_3$, the antiferromagnetic state is progressively destroyed above the 30\% of Ga-doped LaMnO$_3$ and the compound becomes ferromagnetic just like our case\cite{NOGINOVA2005288}.
The Total DOS and the partial DOS of Al-doped LaMnO$_3$ (x=0.05 and 0.25) are shown in figure 6(a-d). Figure 6(a) represents the DOS of Pnma LAM95. In the TDOS, we see a symmetric states for up and down spin configuration, which proves the antiferromagnetic character present here. But for 25\% Al-doped compound, we clearly a asymmetric Total DOS, which confirms the ferromagnetic ground state. For Pnma space group, it shows some gap in the Fermi level for both spins, which indicate the semiconducting behaviour of these compounds. But for R-3c space group, there is no gap in the up-spin states whereas in down-spin it creates some gap for all compounds, which support the half-metallic behaviour of these materials. It also shows the asymmetric DOS in the TDOS for up and down spins because of the ferromagnetic ground state of these compounds. The U-value for Mn is taken to 4 eV for all calculations.
\begin{figure*}
\centering
\includegraphics[scale=0.65]{Figure/Magnetic_MCS.pdf}
\caption{The magnetic properties are shown for LaAl$_{x}$Mn$_{1-x}$O$_3$ (x= 0.05, 0.15, 0.25) from the Monte-Carlo simulation (a) The Magnetization vs Temperature curve, (b) The magnetic susceptibility (c) The specific heat curve and (d) The magnetic hysteresis curve with respect to external magnetic field.}
\label{fig:8}
\end{figure*}
\subsection{Magnetic properties: Monte-Carlo Simulation}
Now, we have studied the magnetic properties of Al-doped LaMnO$_3$ from the Monte-Carlo simulation. The magnetic properties of these materials arise from the Mn-atom, which is situated at the corner-site of the unit cell. The interaction between two nearest neighbour Mn-ion must be ferromagnetic for these case. So, the interaction constant is a very important parameter to determine the magnetic state. We have calculated the nn and nnn interaction constants $J_1$ and $J_2$ from our DFT data.
The constants are calculated from the following equation\cite{jebari2021,SIDIAHMED2017191,hamid2020}, \begin{equation}J_{1} = \frac{E_{A-AFM}-E_{FM}}{2*Z*(S_1.S_2)}
\end{equation}
\begin{equation}J_{2} = \frac{E_{C-AFM}-E_{G-AFM}}{2*Z*(S_1.S_2)}
\end{equation}
And the magnetic anisotropic constants are determined from this equation, \begin{equation}
\Delta = \frac{E_a}{\sum_i(S_i)^2}
\end{equation}
Where, $E_{FM,AFM}$ stands for the minimum energy of different spin configuration. The Z, $S_1$ and $S_2$ are co-ordination number and the spin of two types of Mn ions. $E_a$ is the magnetic an-isotropic energy, calculated from this literature\cite{Larson2003}. The value of nn interaction constants ($J_1$) are 0.69 meV, 0.52 meV, and 0.56 meV respectively for x=0.05, 0.15, and 0.25 samples. Whereas the nnn interaction constants ($J_2$) are 0.008 meV, 0.08 meV, and 0.01 meV respectively. The anisotropic constants are 0.017 meV, 0.013 meV, and 0.01 meV rexpectively. The experimental magnetic data shows a long range ferromagnetism for all three cases. From the DFT calculations, we have seen that the ferromagnetic configuration has the minimum energy for the Rhombohedral R-3c space group.
Figure 8(a-c) and 8(d) represent the temperature-dependent magnetic properties and magnetic hysteresis loop, derived with the help of these interaction constants from the Monte-Carlo simulation. The value of magnetization decreases sharply with increasing temperature for all three materials. The magnetization curves follow the experimental DC-magnetization. The magnetization for x=0.05 is lesser than the x=0.15 curve as the experimental one. The presence of higher percentage of Mn$^{4+}$-ion in x=0.15 material means the more amount of double exchange interaction, which increases the magnetization. Now the transition temperature of this ferromagnetism are determined from the magnetic susceptibility and specific heat curve, displayed in figure 8(b) and 8(c). The critical temperatures are 140 K, 110 K and 87 K for x=0.05, 0.15 and 0.25 respectively. From the hysteresis curve, we have seen that the saturation magnetization (M$_S$) of x=0.15 is larger than the x=0.05 material.
\section{Conclusions}
We have synthesized the LaAl$_{x}$Mn$_{1-x}$O$_3$ (x= 0.05, 0.15, 0.25) in sol-gel procedure. The XRD data confirm the R-3c symmetry of the all compounds. The mixed valance of Mn-ions (Mn$^{3+}$ and Mn$^{4+}$) are present of 25\% Al doped material. For balancing the extra oxygen (3+$\delta$), the system introduces the Mn$^{4+}$-ion which is responsible for the ferromagnetic DE interaction. As a result, the experimental magnetic study shows the ferromagnetic transition of these materials. We have performed the DFT calculations to see the magnetic ground state. We have seen the cooperative John-Teller effect for Pnma space group is responsible for antiferromagnetic state of 5\% Al-doped compound. For higher Al-concentrations, the JT-effect is vanishes and the systems shows the ferromagnetic behaviour. We have performed the Monte Carlo simulation through the anisotropic Ising model to analyze the origin of magnetic transition. The interaction constants are calculated from the DFT calculations. It shows the ferromagnetic behaviour for all the compounds and the critical temperatures are 140 K, 110 K and 87 K for x=0.05, 0.15 and 0.25 respectively.
\section{Acknowledgement}
T.K Bhowmik would like to thank Department of Science and Technology (DST), Government of India for providing the financial support in the form of DST-INSPIRE fellowship (IF160418).
\bibliographystyle{model1-num-names.bst}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 733 |
\section{Introduction}
\label{Intro}It is well known that the variety of bright solitons, supported
by the balance between the self-focusing nonlinearity and diffraction (in
optics) or kinetic energy (in matter waves), can be greatly expanded if a
spatially periodic (alias lattice) potential is introduced, in the form of
photonic lattices acting on optical waves \cite{phot-latt}, or optical
lattices acting on matter waves in atomic Bose-Einstein condensates (BECs)
\cite{opt-latt}. In particular, periodic potentials make it possible to
create \textit{gap solitons} in media with self-defocusing nonlinearity, due
to its interplay with the effective negative mass of collective excitations,
see original works \cite{Dark}-\cite{Oberthaler} and books \cite{JYang,DPeli}%
. In addition to the fundamental solitons, the analysis addressed patterns
such as nonlinear Bloch states \cite{Kiv2003,BlochW}, domain walls \cite%
{DomWalls05}, and gap waves, i.e., broad modes with sharp edges \cite%
{gapwave}.
The spectral bandgap structure induced by lattice potentials gives rise to
many families of gap solitons, classified by the number of a bandgap in
which they reside. Further, the oscillatory shape of fundamental gap
solitons opens the way to build various two- and multi-soliton bound states
through the effective interaction potential induced by their overlapping
tails. The variety of the gap-soliton families include both stable and
unstable solutions. A specific possibility, revealed in work \cite{Thaw} and
further analyzed in Refs. \cite{sub}-\cite{China}, is the existence of
\textit{subfundamental solitons} (SFSs) in the second finite bandgap (in Ref.
\cite{China} SFSs were called ``second-family fundamental gap solitons"). They
feature a dipole (antisymmetric) shape, which is squeezed, essentially, into
a single cell of the lattice potential. The name ``subfundamental'' implies that the
soliton's norm (in terms of BEC; or the total power, in terms of optics)
is smaller than the norm of a stable fundamental soliton (FS) existing at
the same value of the chemical potential (or propagation constant, in the
optics model) in the second finite bandgap. SFSs have a small stability
region \cite{China}, while unstable ones spontaneously rearrange
into stable FSs belonging to the first
finite bandgap. Partial stabilization of SFSs was also demonstrated in a model
which includes, in addition to the local nonlinearity, long-range
dipole-dipole interactions \cite{subDD}.
Apart from the linear spatially periodic potentials induced by lattice
structures, the formation of solitons may be facilitated by
nonlinear-lattice \textit{pseudopotentials} \cite{pseudo}, which are induced
by spatially periodic modulation of the coefficient in front of the cubic
term in the respective Gross-Pitaevskii/nonlinear Schr\"{o}dinger equation
(GPE/NLSE) \cite{RMP}. This structure can be created in BEC by means of the
Feshbach resonance controlled by magnetic or optical fields \cite{FR-Randy}-%
\cite{FR-Tom}. Experimentally, the possibility of the periodic modulation of
the nonlinearity on a submicron scale was demonstrated in Ref. \cite%
{experiment-inhom-Feshbach}. The spatial profile of the nonlinearity may
also be ``painted" by a fast moving laser beam \cite{painting}, or imposed
by an optical-flux lattice \cite{Cooper}. Another approach relies on the use
of a magnetic lattice, into which the atomic condensate is loaded \cite%
{magn-latt}, or of concentrators of the magnetic field \cite{concentrator}.
In optics, spatial modulation of the Kerr coefficient can be achieved by
means of an inhomogeneous density of resonant nonlinearity-enhancing dopants
implanted into the waveguide \cite{Kip}. Alternatively, a spatially periodic
distribution of resonance detuning can be superimposed on a uniform dopant
density. A review of results for solitons supported by nonlinear lattices
was given in Ref. \cite{RMP}.
In the one-dimensional setting, a generic form of the scaled GPE/NLSE for
the mean-field amplitude, $\Psi (x,t)$, including both a linear periodic
potential, $U(x)$, and a periodic pseudopotential induced by modulation
function $P(x)$, both with period $L$, is \cite{HS}
\begin{equation}
i\Psi _{t}+\Psi _{xx}-U(x)\Psi +P(x)|\Psi |^{2}\Psi =0. \label{UP}
\end{equation}%
The prototypical examples of both periodic potentials are provided by
functions%
\begin{equation}
\left\{ U(x),P(x)\right\} =\left\{ A_{U},A_{P}\right\} +\left\{
B_{U},B_{P}\right\} \cos (2x), \label{cos}
\end{equation}%
where the period is scaled to be $L=\pi $. Equation (\ref{UP}) is written in
terms of BEC; in optics, Eq. (\ref{UP}) models the light propagation in
planar waveguides, with transverse coordinate $x$, $t$ being replaced by the
propagation distance, $z$. In the former case, the model can be implemented
in a cigar-shaped BEC trap with the transverse confinement strength subject
to periodic modulation along the axial direction, $x$ \cite{De Nicola,Luca}.
Similarly, the optics realization is possible in the planar waveguides with
the thickness (in direction $y$) subject to the same modulation along $x$.
It is also relevant to mention that, while we here consider the simplest
cubic form of the local nonlinearity in Eq. (\ref{UP}), strong transverse
confinement applied to the BEC with a relatively high atomic density gives
rise to the one-dimensional equation with nonpolynomial nonlinearity \cite%
{Luca}, which may be a subject for a separate work. \textcolor{black}{It is important for the what follows that Eq.~(\ref{UP}) conserves the quantities $N$ and $E$,
\begin{eqnarray}
&&N=\int_{-\infty}^\infty |\Psi|^2~dx,\label{N_cons}\\[2mm]
&&E = \int \limits_{-\infty}^{+\infty}\left( | \Psi_x |^2 +U(x) | \Psi |^2 -\frac12 P(x) | \Psi |^4\right)~dx \label{E_cons}
\end{eqnarray}
having in BEC context the sence of the number of particles and the energy correspondingly.}
The objective of the present work is to generate new types of solitons in
the model based on Eq. (\ref{UP}), and identify \emph{stable solitons} among
them. To this end, we develop a procedure which makes it possible to predict
an infinite number of different families of stationary soliton solutions
(starting from the SF and DS families), by means of a \textit{coding
technique }\cite{AlfAvr}. Actual results are produced, with the help of
numerical calculations, for the model with the pseudopotential only \cite%
{Malomed}, i.e., Eq. (\ref{UP}) with $U=0$, where effects produced by the
periodic modulation of the nonlinearity are not obscured by the
linear-lattice potential. Keeping in mind the prototypical $\cos (2x)$
modulation function in Eq. (\ref{cos}), we assume that $P(x)$ in Eq. (\ref%
{UP}) is an even $\pi $-periodic function, which takes both positive and
negative local values. In particular, while FSs supported by nonlinear
lattices have been already studied in detail \cite{Malomed}, a possibility
of the existence and stability of the single-cell DSs in the same setting was not
considered previously. We demonstrate that this class of solitons is also
supported by the nonlinear lattice. It is composed of two branches, one of
which is \emph{stable}, on the contrary to the chiefly unstable SFS
family in the models with linear lattices. Another difference is that
the single-cell DSs are not subfundamental, as their norm exceeds that
of the SFs existing at the same value of the soliton frequency. We also show that, in addition to
the SFs and DSs, there exist a plethora of solitons in the model with
periodic pseudopotential. While most of them are unstable, we have found
some stable bound states of fundamental solitons.
The rest of the paper is structured as follows. Stationary soliton solutions
are produced in Section II. Results of the stability analysis are summarized
in Section III. Section IV is focused on the new class of the single-cell DSs,
including both numerical results and analytical approximations, based on the
variational approximation (VA) and Vakhitov-Kolokolov (VK) \cite{Vakh}
stability criterion. The paper is concluded by Section V.
\section{Stationary modes}
\label{StatMod}
Stationary solutions to Eq. (\ref{UP}) with chemical potential $\omega $ (in
the optics model, $-\omega $ is the propagation constant) are sought for in
the usual form, $\Psi (t,x)=u(x)\exp \left( -i\omega t\right) $, where $u(x)$
is determined by equation
\begin{equation}
u_{xx}+Q(x)u+P(x)u^{3}=0,\quad Q(x)=\omega -U(x).
\label{eq:stationary}
\end{equation}%
Solitons are selected by the localization
condition,
\begin{equation}
\lim\limits_{x\rightarrow \pm \infty }u(x)=0, \label{Local}
\end{equation}%
which implies that the function $u(x)$ is real (see, e.g., Ref. \cite{AKS}).
Therefore, we focus our attention on real solutions to Eq. (\ref%
{eq:stationary}).
For the analysis of stationary modes we apply the approach developed
previously for the usual model, with the uniform nonlinearity and a linear
lattice potential, i.e., $P(x)=-1$ and $U(x)$ a bounded periodic function
\cite{AlfAvr}. This approach makes use of the fact that the ``most common"
solutions of equation
\begin{equation}
u_{xx}+Q(x)u-u^{3}=0 \label{eq:old}
\end{equation}%
are singular, i.e., they diverge at some finite value of $x = x_0$ ($\lim
\limits_{x \to x_0} u(x) = \infty$), as
\begin{equation}
u(x)\approx \pm \sqrt{2}\left( x-x_{0}\right) ^{-1}. \label{diverging}
\end{equation}
Then, it was shown that, under certain conditions imposed on $Q(x)$,
nonsingular solutions can be described using methods of symbolic dynamics.
More precisely, under these conditions there exists one-to-one
correspondence between all solutions of Eq. (\ref{eq:old}) and bi-infinite
sequences of symbols of some finite alphabet, which are called \textit{codes}
of the solutions.
As shown below, this approach can be extended for Eq.~(\ref{eq:stationary}),
which combines the periodic lattice potential and periodic modulation of the
nonlinearity coefficient, that represents the nonlinear-lattice
pseudopotential.
\subsection{The coding procedure}
\label{Coding}
Assume that $Q(x)$ and $P(x)$ in Eq. (\ref{eq:stationary}) are even $\pi $%
-periodic functions. We call a solution $u(x)$ of Eq.(\ref{eq:stationary})
singular if $u(x)$ diverges at finite $x_{0}$ as per Eq. (\ref{diverging}).
In this case, one may also say that solution $u(x)$ \textit{collapses} at
point $x=x_{0}$.
Define \textit{Poincar\'{e} map} $T:\mathbb{R}^{2}\rightarrow \mathbb{R}^{2}$
associated with Eq.(\ref{eq:stationary}) as follows:
\begin{equation}
T%
\begin{pmatrix}
u_{0} \\
u_{0}^{\prime }%
\end{pmatrix}%
=%
\begin{pmatrix}
u(\pi ) \\
u_{x}(\pi )%
\end{pmatrix}%
\end{equation}%
where $u(x)$ is a solution of the Cauchy problem for Eq. (\ref{eq:stationary}%
) with initial conditions%
\begin{equation}
u(0)=u_{0},\quad u_x(0)=u_{0}^{\prime }. \label{initial}
\end{equation}
We call an \textit{orbit} a sequence of points $\{p_{n}\}$, $p_{n}\in
\mathbb{R}^{2}$ (the sequence may be finite, infinite or bi-infinite), such
that $Tp_{n}=p_{n+1}$.
Define sets $\mathcal{U}_{L}^{+}\in \mathbb{R}^{2}$ and $\mathcal{U}%
_{L}^{-}\in \mathbb{R}^{2}$, $L>0$ as follows: $p=(u_{0},u_{0}^{\prime })\in
\mathcal{U}_{L}^{+}$ if and only if solutions of the Cauchy problem for Eq. (%
\ref{eq:stationary}) with initial conditions (\ref{initial}) does not
collapse on interval $[0,L]$. Similarly, we define $\mathcal{U}_{L}^{-}$ as
the set of initial conditions $u(0)=u_{0}$, $u_{x}(0)=u_{0}^{\prime }$ such
that the corresponding solution of the Cauchy problem for Eq.(\ref%
{eq:stationary}) does not collapse on interval $[-L,0]$. It is easy to show
that Poincar\'{e} map $T$ is defined only on set $\mathcal{U}_{\pi }^{+}$
and transforms it into $\mathcal{U}_{\pi }^{-}$. Accordingly, inverse map $%
T^{-1}$ is defined only on $\mathcal{U}_{\pi }^{-}$ and transforms this set
into {\color{black} $\mathcal{U}_{\pi }^{+}$}.
Next, consider the following sets:
\begin{eqnarray}
&&\Delta _{0}=\mathcal{U}_{\pi }^{+}\cap \mathcal{U}_{\pi }^{-}, \\
&&\Delta _{n+1}^{+}=T\Delta _{n}^{+}\cap \Delta _{0},\quad n=0,1,\ldots , \\
&&\Delta _{n+1}^{-}=T^{-1}\Delta _{n}^{-}\cap \Delta _{0},\quad n=0,1,\ldots
,
\end{eqnarray}%
Evidently, $\Delta _{0}$ consists of points that have $T$-image and $T$%
-pre-image. The following statements are valid:
\begin{eqnarray}
&&\{p\in \Delta _{n}^{+}\}\quad \Leftrightarrow \quad \{Tp,T^{2}p,\ldots
,T^{n}p\in \Delta _{0}\}; \\
&&\{p\in \Delta _{n}^{-}\}\quad \Leftrightarrow \quad
\{T^{-1}p,T^{-2}p,\ldots ,T^{-n}p\in \Delta _{0}\}.
\end{eqnarray}%
Sets $\Delta _{n}^{\pm }$ are nested in the following sense:
\begin{eqnarray}
&&\ldots \subset \Delta _{n+1}^{+}\subset \Delta _{n}^{+}\ldots \subset
\Delta _{1}^{+}\subset \Delta _{0} \\
&&\ldots \subset \Delta _{n+1}^{-}\subset \Delta _{n}^{-}\ldots \subset
\Delta _{1}^{-}\subset \Delta _{0}.
\end{eqnarray}%
Now, we define sets
\begin{equation}
\Delta ^{+}=\bigcap_{n=1}^{\infty }\Delta _{n}^{+},\quad \Delta
^{-}=\bigcap_{n=1}^{\infty }\Delta _{n}^{-}.
\end{equation}%
Consider set $\Delta =\Delta ^{+}\cap \Delta ^{-}$. It is is invariant with
respect to the action of the $T$ map. Orbits generated by points from $%
\Delta $ are in one-to-one correspondence with non-collapsing solutions of
Eq. (\ref{eq:stationary}). Therefore, the numerical study of sets $\Delta
_{n}^{\pm }$ allows one to predict and compute bounded solutions of Eq. (\ref%
{eq:stationary}).
There are several restrictions for $Q(x)$ and $P(x)$ for this approach to be
applicable. In Ref. \cite{AlfLeb}, the following statements were proved.
\begin{ntheorem}
Suppose that $Q(x), P(x) \in C^1(\mathbb{R})$ and for each $x \in \mathbb{R}$
\begin{itemize}
\item[a)] there exists ${\widetilde{P}}$ such that $P(x) > 0$, $|P^{\prime
}(x)| \le \widetilde{P}$;
\item[b)] there exist $Q_0, \widetilde{Q}$, such that $Q(x) \ge Q_0$, $%
|Q^{\prime }(x)| \le \widetilde{Q}$;
\end{itemize}
then the solution to the Cauchy problem for Eq.(\ref{eq:stationary}) with
arbitrary initial conditions (\ref{initial}) can be continued onto the whole
real axis $\mathbb{R}$. \label{prop:nonsingular}
\end{ntheorem}
\begin{ntheorem}
Suppose that $\forall {x\in \mathbb{R}}$ conditions $P(x)<0$, $Q(x)<0$
holds, then all solutions of Eq. (\ref{eq:stationary}) are singular, except
the trivial zero solution. \label{prop:singular}
\end{ntheorem}
In particular, this implies that, if $P(x)$ and $Q(x)$ are bounded and
periodic, and $P(x)>0$ for all $x\in \mathbb{R}$, then all solutions of Eq. (%
\ref{eq:stationary}) are non-singular, and the present approach cannot be
applied. In the case of $P(x)<0$, $Q(x)<0$, Eq. (\ref{eq:stationary}) has no
non-singular solutions, except for the zero state, therefore the approach
cannot be used either. However, it follows from Proposition 2 of Ref. \cite%
{AlfLeb} that, if $P(x)$ is a sign-alternating function, the collapsing
behavior is \textit{generic} for solutions of Eq. (\ref{eq:stationary}), and
the application of the approach is reasonable for finding non-collapsing
solutions.
In Ref. \cite{AlfAvr} the case of $P(x)=-1$ in Eq. (\ref{eq:stationary}) was
considered from a more abstract viewpoint. It was shown that if
\begin{itemize}
\item[a)] the $\Delta _{0}$ set consist of a finite number $N$ of connected
components, {\color{black} $\Delta_{0}=\bigcup_{k=1}^{N} D_k$}, and each of the components $%
D_{k}$ is a curvilinear quadrangle, whose boundaries satisfy special
conditions of smoothness and monotonicity;
\item[b)] all the sets $TD_{k}\cap D_{m}$ and $T^{-1}D_{k}\cap D_{m}$, $%
k,m=1,\dots ,N$, are non-empty, and the action of $T$ on curves lying in $%
D_{k}$ preserves the monotony property;
\item[c)] areas of sets $\Delta _{n}^{\pm }$ vanish at $n\rightarrow \infty $%
;
\end{itemize}
then orbits of the Poincar\'{e} map $T$ acting on the $\Delta _{0}$ set are
in one-to-one correspondence with bi-infinite sequences of symbols of some $%
N $-symbol alphabet.
This result can be commented as follows. Let symbols of the alphabet be the
numbers $1,\dots ,N$. Denote the connected components of $\Delta _{0}$ by $%
D_{k}$, $k=1,\ldots ,N$. Then for each non-collapsing solution $u(x)$ there
exist an unique orbit $\{p_{k}\}$, $k=0,\pm 1,\pm 2,\ldots $, $p_{k}\in
\Delta $, and the corresponding unique bi-infinite sequence $\ldots \alpha
_{-1},\alpha _{0},\alpha _{1},\ldots $, $\alpha _{k}\in \{1,\ldots ,N\}$
such that
\begin{eqnarray}
\ldots,~&p_{-1}=T^{-1}p_{0}\in D_{\alpha _{-1}},\quad
p_{0}\in D_{\alpha_{0}},\nonumber\\
&p_{1}=Tp_{0}\in D_{\alpha _{1}},\ldots\label{Seq}
\end{eqnarray}%
On the contrary, for each bi-infinite sequence of numbers $\{1,\ldots ,N\}$
there exists an unique orbit $\{p_{k}\}$, $k=0,\pm 1,\pm 2,\ldots $, $%
p_{k}\in \Delta $, that satisfies condition (\ref{Seq}) and corresponds to an
unique solution $u(x)$. The check of conditions (a),(b) and (c) was carried
out in Ref. \cite{AlfAvr} numerically, using some auxiliary statements.
In what follows below, we apply this approach to Eq. (\ref{eq:stationary})
with $U(x)=0$, i.e., $Q(x)=\omega $, when the linear potential is absent,
and only the pseudopotential is present in Eq. (\ref{eq:stationary}),
induced by the modulation function taken as
\begin{equation}
P(x)=\alpha +\cos (2x), \label{NP}
\end{equation}%
This is a new setting for which the present method was not elaborated
previously.
\subsection{Numerical results}
\label{NumSteady}
According to what was said above [Eq. (\ref{NP})], we now focus on the
following version of Eq. (\ref{eq:stationary}):
\begin{equation}
u_{xx}+\omega u+(\alpha +\cos 2x)u^{3}=0. \label{eq:current}
\end{equation}%
Due to Theorem \ref{prop:nonsingular} we impose restriction $\alpha \in
(-1,1)$ in Eq. (\ref{eq:current}) for the approach to be applied, i.e., the
nonlinearity coefficient (\ref{NP}) must be a sign-changing function of $x$.
Another restriction, $\omega <0$, comes from the obvious condition of the
soliton localization, given by Eq. (\ref{Local}).
\textit{Sets $\mathcal{U}_{\pi }^{\pm }$.} The set $\mathcal{U}_{\pi }^{+}$
was found by scanning the plane $(u,u^{\prime })$ of initial data by means
of the following procedure. The Cauchy problem for Eq. (\ref{eq:current})
was solved numerically, taking as initial conditions $u(0)=n\Delta u$, $u_x(0)=m\Delta u^{\prime }$, $m,n=-L,\ldots ,L$ where spacings $\Delta u$ and $\Delta u^{\prime }$ are
small enough (typical values were $\Delta u=\Delta
u^{\prime }=0.01$). If the absolute value of the solution of the Cauchy
problem exceeds, in interval $[0;\pi ]$, some sufficiently large value $%
u_{\infty }$, it is assumed that the collapse occurs. The corresponding
point is marked {\color{black} white}, otherwise, it is {\color{black} grey}. The computations were
actually performed for $u_{\infty }=10^{5}$ and further checked for $%
u_{\infty }=10^{7}$, the results obtained for both cases agreeing very well.
Since Eq.(\ref{eq:current}) is invariant with respect to inversion $x\to-x$,
the set $\mathcal{U}_{\pi }^{-}$ is the reflection of $\mathcal{U}_{\pi }^{+}
$ with respect to the $u$-axis. The numerical results allow us to conjecture
that, for $\alpha \in (-1;1)$, $\mathcal{U}_{\pi }^{\pm }$ \textit{are
unbounded spirals with infinite number of rotations around the origin}, see
Fig. \ref{pic:spirals}.
\textit{Set $\Delta _{0}$.} Some examples of set $\Delta _{0}$ are displayed
in Fig.~\ref{pic:spirals}. Panel (A) of Fig. \ref{pic:spirals} corresponds
to the case of $\omega =-1$, $\alpha =-1.1$, when $\Delta _{0}$ consists of
only one connected component situated in the origin. This fact agrees with
Theorem \ref{prop:singular}. If $\alpha \in (-1;1)$, then, presumably, $%
\Delta _{0}$ is unbounded and consists of an infinite number of connected
components that are situated along the $u$ and $u^{\prime }$ axes [panels
(B)-(F) of Fig. \ref{pic:spirals}]. The connected components can be
enumerated by symbols $\{A_{k}\},k=\pm 1,\pm 2,\dots $ (the components along
$u$ axis) and $\{B_{k}\},k=\pm 1,\pm 2,\dots $ (the components along $%
u^{\prime }$ axis). The central connected component is denoted $O$.
\begin{figure
\includegraphics[scale=0.45]{Figure01.eps}
\caption{$\mathcal{U}_{\protect\pi }^{+}$ (dark grey color), $\mathcal{U}_{%
\protect\pi }^{-}$ (light grey color) and their intersection $\Delta _{0}$ {\color{black} (black color)}
in the model based on Eq. (\protect\ref{eq:current}), at different values of
parameters $\protect\omega $ and $\protect\alpha $: A) $\protect\omega =-1$,
$\protect\alpha =-1.1$; B) $\protect\omega =-1$, $\protect\alpha =-0.3$; C) $%
\protect\omega =-1$, $\protect\alpha =0.15$; D) $\protect\omega =-1$, $%
\protect\alpha =0.5$; E) $\protect\omega =-0.7$, $\protect\alpha =0.55$; F) $%
\protect\omega =-1.5$, $\protect\alpha =0$.}
\label{pic:spirals}
\end{figure}
The basic assumption for the applicability of the coding approach is that
the the connected components are curvilinear quadrangles with opposite sides
lying on the boundaries of $\mathcal{U}_{\pi }^{+}$ and $\mathcal{U}_{\pi
}^{-}$. Due to geometric properties of the spirals, it is quite natural to
assume that all connected components $\{A_{k}\},\{B_{k}\},k=\pm 1,\pm
2,\dots $ satisfy this condition. However, central connected component $O$
may be such a curvilinear quadrangle (cases A, B, F in Fig. \ref{pic:spirals}%
), or may be not (cases C, D, E in Fig. \ref{pic:spirals}), depending on
values of $\omega $ and $\alpha $.
\textit{Coding.} Assume that the parameters $\omega $ and $\alpha $ are such
that all connected components in $\Delta _{0}$ are curvilinear quadrangles.
Then, our numerical study indicates that $T^{-1}A_{k}$, $T^{-1}B_{k}$, $%
k=1,2,\ldots $, and $T^{-1}O$ are infinite curvilinear strips situated
inside $\mathcal{U}_{\pi }^{+}$ and crossing all the connected components.
Similarly, $TA_{k}$, $TB_{k}$, $k=1,2,\ldots $, and $TO$ are also
curvilinear strips situated inside the $\mathcal{U}_{\pi }^{-}$ set, that
also cross all the connected components. $T$-pre-images of the sets
\begin{eqnarray*}
&&T^{-1}Z\cap A_{l},\quad T^{-1}Z\cap B_{l},\quad T^{-1}Z\cap O,\quad l=\pm
1,\pm 2,\ldots , \\
&&Z\in \{O,A_{k},B_{k},k=\pm 1,\pm 2,\ldots \},
\end{eqnarray*}%
are infinite curvilinear strips belonging to $T^{-1}Z$. Similar statement
are also valid for $T$-images of $TZ\cap A_{l}$, $TZ\cap B_{l}$, $TZ\cap O$ $%
l=\pm 1,\pm 2,\ldots $ which are placed inside $TZ$, with $Z\in
\{O,A_{k},B_{k},k=\pm 1,\pm 2,\ldots \}$. Therefore the situation is similar
to one considered in Ref.\cite{AlfAvr} and we conjecture that the dynamics
of $T$ is similar to dynamics of the Poincar\'{e} map from Ref.\cite{AlfAvr}%
, and that \textit{there is one-to-one correspondence between all
nonsingular solutions of Eq.(\ref{eq:current}) and bi-infinite sequences $%
\{\ldots Z_{-1},Z_{0},Z_{1},\ldots \}$ based on the infinite alphabet of
symbols $Z_{m}\in \{O,A_{k},B_{k},k=\pm 1,\pm 2,\ldots \}$}. The orbit
corresponding to code $\{\ldots ,Z_{-1},Z_{0},Z_{1},\ldots \}$ visits
successively connected components $Z_{m}$, $m=\ldots ,-1,0,1,\ldots $. Note
that the orbit corresponding to the soliton solution starts and ends in the
central connected component, therefore it has the code of the form $\{\ldots
,O,O,Z_{1},Z_{2},\ldots ,Z_{N},O,O,\ldots \}$ where symbols $Z_{1}$ and $%
Z_{N}$ are different from $O$.
\textit{Solitons.} Regardless of whether the coding conjecture is true or
false generically, it might be used for the prediction of possible shapes of
nonlinear modes. Specifically, the location of the connected components in
the plane of $(u,u^{\prime })$, and the order in which the orbit visits
them, yields comprehensive information about the nonlinear mode. In the
present model, the predicted nonlinear modes were found numerically in
\textit{all} the cases considered. Some of soliton solutions of Eq.(\ref%
{eq:current}) and their codes are shown in Fig. \ref{pic:coding} for $\omega
=-1$, $\alpha =-0.1$. The soliton in panel (B) is the FS, cf. Ref. \cite%
{Malomed}, with code {\color{black} $\{\dots, O,A_{1},O,\dots \}$, or $\{\dots,O,A_{-1},O,\dots \}$}%
, which is its symmetric counterpart. Another particular solution,
shown in panel G, represents the above-mentioned DSs (\textit{dipole solitons}),
which are essentially confined to
a single cell of the nonlinear lattice. This solution corresponds
to code {\color{black} $\{\dots, O,B_{-1},O,\dots, \}$}, and its symmetric counterpart is {\color{black} $\{\dots,O,B_{1},O,\dots \}$}. The DSs are similar to the
(mostly unstable) SFSs reported in Refs. \cite{Thaw}-\cite{China} in
models with the linear lattice potential, as both soliton species feature
the antisymmetric profile squeezed into a single cell of the underlying lattice
(the linear one, in the case of the SFSs, and the nonlinear lattice,
as concerns the DSs). The area of the localization of
the soliton corresponding to code $\{\ldots ,O,Z_{1},Z_{2},\ldots
,Z_{N},O,\ldots \}$, where the symbols $Z_{1}$ and $Z_{N}$ are different
from $O$, is $N\pi $, i.e., it extends over $N$ periods of the underlying
nonlinear lattice. In particular, the solitons with codes $\{\ldots
,O,O,Z,O,O,\ldots \}$, $Z\neq O$ (named \textit{elementary solitons }in what
follows below), are localized, essentially, in one period of the lattice.
\begin{figure
\includegraphics[scale=0.4]{Figure02_signed.eps}
\caption{Numerically found solutions of Eq. (\protect\ref{eq:current}) and
their codes for parameters $\protect\omega =-1$, $\protect\alpha =-0.1$; A) $%
\mathcal{U}_{\protect\pi }^{\pm }$ sets; {\color{black} B)-J) the profiles of solitons together with their codes}
}
\label{pic:coding}
\end{figure}
\section{The linear-stability analysis}
\label{LinStab}
As said above, stability is a critically important issue for solitons
supported by lattice potentials. Here, we address the
stability of solitons produced by Eqs. (\ref{UP}), (\ref{eq:current}). It
has been shown in Sect. \ref{StatMod} that there exist a great variety of
shapes of such modes. Thus, adopting the nonlinear lattice as given by Eq. (%
\ref{NP}), we aim to study the linear stability of solitons generated by
equation
\begin{equation}
i\Psi _{t}+\Psi _{xx}+(\alpha +\cos 2x)|\Psi |^{2}\Psi =0
\label{eq:stability}
\end{equation}
Following the well-established approach, (see, e.g., Ref. \cite{JYang}), we
consider small perturbations around a stationary solution $\Psi
_{0}(x,t)=u(x)e^{-i\omega t}$ in the form of
\begin{equation}
\Psi (t,x)=\left[ u(x)+\widetilde{U}(t,x)\right] e^{-i\omega t},~\left\vert
\widetilde{U}(t,x)\right\vert \ll 1,
\end{equation}%
where $u(x)$ is a localized solution of Eq. (\ref{eq:current}), and the
perturbation satisfies the linear equation
\begin{equation}
i\widetilde{U}_{t}+\widetilde{U}_{xx}+\omega \widetilde{U}+(\alpha +\cos
2x)u^{2}(2\widetilde{U}+\widetilde{U}^{\ast })=0, \label{linear}
\end{equation}%
where asterisk means complex conjugate. Seeking solutions to Eq. (\ref%
{linear}) as
\begin{equation}
\widetilde{U}(t,x)=(v(x)+w(x))e^{\lambda t}+(v^{\ast }(x)-w^{\ast
}(x))e^{\lambda ^{\ast }t},
\end{equation}%
we arrive at the eigenvalue problem
\begin{equation}
LY=\lambda Y, \label{eq:eigproblem}
\end{equation}%
\begin{equation}
L=i%
\begin{pmatrix}
0 & L_{0} \\
L_{1} & 0%
\end{pmatrix}%
,~~~Y=%
\begin{pmatrix}
v \\
w%
\end{pmatrix}%
, \label{Y}
\end{equation}%
where
\begin{eqnarray*}
&&L_{0}=\partial _{xx}+G_{0}(x),\quad G_{0}(x)=\omega +(\alpha +\cos
2x)u^{2},\\
&&L_{1}=\partial _{xx}+G_{1}(x),\quad G_{1}(x)=\omega +3(\alpha +\cos
2x)u^{2}.
\end{eqnarray*}%
The soliton is linearly unstable if the spectrum produced by Eq. (\ref%
{eq:eigproblem}) contains at least one eigenvalue $\lambda $ with a non-zero
real part, $\Re (\lambda )>0$. Otherwise, the solitons are linearly stable.
Equation (\ref{eq:eigproblem}) generates the spectrum consisting of
continuous and discrete parts. It is easy to show that the continuous
spectrum is represented by two rays, $[-i\omega ;+i\infty )$ and $(-i\infty
;i\omega ]$, if $\omega <0$, and by the whole imaginary axis, if $\omega >0$%
. The discrete spectrum includes zero eigenvalue $\lambda =0$. Other
eigenvalues of the discrete spectrum appear in quadruples, since if $\lambda
$ is an eigenvalue then $-\lambda $, $\lambda ^{\ast }$ and $-\lambda ^{\ast
}$ are eigenvalues too.
To find discrete eigenvalues numerically, the Fourier Collocation Method (FCM)
\cite{JYang} was used. This method is very efficient to find
{\it exponential instabilities}, that appears due to real eigenvalues. However it
is known that it can miss the situations of weak {\it oscillatory instabilities}
caused by quartets of complex eigenvalues with small real parts (see e.g. \cite{Egor})
where more sophisticated methods, such as Evans function method, \cite{PelKiv}, must be applied. With the help of FCM, a great number of stationary solutions of Eq.(\ref{eq:stability}%
), represented by different codes, were analyzed. Due the infinite number of
essentially different solutions, it is not possible to perform a
comprehensive stability analysis of all localized solutions, even of all
elementary solitons. However, we observed that a majority of the solitons
are linearly unstable, thus being physically irrelevant solutions. \emph{%
Stable solitons} can be categorized as follows:
a) Among the elementary solitons, it was found that FS and DS are \textit{%
linearly stable}, under some restrictions on $\omega $ and $\alpha $. Other
elementary solitons were found to be unstable. Note that
FSs are considered as stable solutions in models with linear lattice potentials, see Ref. \cite{Malomed}
and references therein, while the SFSs are chiefly unstable in that case, having a small stability
region \cite{China} (strictly speaking, FSs in models with linear lattice potentials may also feature a very weak oscillatory instability, having at the same time great lifetime, see \cite{Egor}). Therefore, \emph{stable} DSs supported by the nonlinear
pseudopotential, whose shape is very similar to that of the \emph{chiefly unstable} SFSs in
the systems with linear lattice potentials, deserve a detailed consideration, which is given in Sect. %
\ref{SFS}. It includes not only numerical results, but also analytical ones
based on VA.
b) There are stable bound states of FSs -- for instance, with codes {\color{black} $\{\dots
,O,A_{1},A_{-1},A_{1},O,\dots \}$, $\{\dots ,O,A_{1},O,A_{-1},O,\dots \}$}.
However, other bound states of these modes may be unstable.
Stability spectra for some solitons and their bound states are shown in Fig.%
\ref{pic:stability}. These example adequately represent the generic
situation.
\begin{figure*}[tbp]
\subfloat[][$\{\dots,O,A_1,O,\dots\}$]{\includegraphics[width=0.5%
\textwidth]{Figure03_a.eps}} \subfloat[][$\{\dots,O,B_{-1},O,\dots\}$]{%
\includegraphics[width=0.5\textwidth]{Figure03_b.eps}} \vfill
\subfloat[][$\{\dots,O,A_1,A_{-1},A_1,O,\dots\}$]{\includegraphics[width=0.5%
\textwidth]{Figure03_c.eps}} \subfloat[][$\{\dots,O,A_1,A_1,A_1,O,\dots\}$]{%
\includegraphics[width=0.5\textwidth]{Figure03_d.eps}} \vfill
\subfloat[][$\{\dots,O,A_1,A_1,O,\dots\}$]{\includegraphics[width=0.5%
\textwidth]{Figure03_e.eps}} \subfloat[][$\{\dots,O,A_1,O,A_{-1},O,\dots\}$]{%
\includegraphics[width=0.5\textwidth]{Figure03_f.eps}} \vfill
\subfloat[][$\{\dots,O,A_1,B_1,A_{-1},O,\dots\}$]{\includegraphics[width=0.5%
\textwidth]{Figure03_g.eps}} \subfloat[][$\{\dots,O,A_1,B_{-1},A_{-1},O,%
\dots\}$]{\includegraphics[width=0.5\textwidth]{Figure03_h.eps}}
\caption{Localized solutions, their codes, and linear-stability spectra for $%
\protect\omega =-1$, $\protect\alpha =-0.2$.}
\label{pic:stability}
\end{figure*}
\section{Dipole solitons (DSs)}
\label{SFS}
\subsection{The variational approximation}
\label{SFS_VA}
Some general features of soliton solutions of Eq. (\ref{eq:current}) can be
obtained by means of the VA, using the fact that Eq. (\ref{eq:current}) for
the stationary states can be derived from Lagrangian
\begin{equation}
L=\int_{-\infty }^{+\infty }\left\{ \frac{1}{2}\left( u^{\prime }\right)
^{2}-\frac{1}{2}\omega u^{2}-\frac{1}{4}\left[ \alpha +\cos \left( 2x\right) %
\right] u^{4}\right\}~dx . \label{eq:lagrangian}
\end{equation}%
In Ref. \cite{Malomed}, VA was successfully applied for analysis of FS. In
that study, the soliton was assumed to be bell-shaped, and the following
ansatz was used
\begin{equation}
u(x)=A\exp \left( -\frac{x^{2}}{2W^{2}}\right) ,
\end{equation}%
The VA had yielded correct predictions for the existence of the minimal norm
\begin{equation}
N= \int_{-\infty }^{+\infty }u^{2}(x)dx=\sqrt{\pi }A^{2}W.
\end{equation}%
for the FS, and the existence of an amplitude threshold for stable solitons.
A similar analysis for the DS may be based on the simplest spatially odd
ansatz:
\begin{equation}
u(x)=Ax\exp \left( -\frac{x^{2}}{2W^{2}}\right) , \label{eq:ansatz}
\end{equation}%
The maximum value of $u(x)$, which is $\sqrt{e}AW$, is situated at $x_{\max
}=W$, therefore $W$ may be regarded as the half-width of the DS. Norm $N$
of ansatz (\ref{eq:ansatz}) is
\begin{equation}
N=\frac{\sqrt{\pi }}{2}A^{2}W^{3}. \label{eq:norm}
\end{equation}%
Equation (\ref{eq:norm}) makes it possible to eliminate the amplitude $A$ in
favor of the norm:%
\begin{equation}
A^{2}=\frac{2}{\sqrt{\pi }}\frac{N}{W^{3}}. \label{eq:amplitude}
\end{equation}
The substitution of ansatz (\ref{eq:ansatz}) into Lagrangian (\ref%
{eq:lagrangian}) and calculation of the integrals yields the following
effective Lagrangian:
\begin{eqnarray}
&&L_{\mathrm{eff}}=-\frac{\omega }{2}N+\frac{3N}{4W^{2}}-\frac{3\alpha N^{2}}{%
16\sqrt{2\pi }W}-\nonumber\\[2mm]
&&-\frac{N^{2}e^{-W^{2}/2}}{16\sqrt{2\pi }W}\left(
3-6W^{2}+W^{4}\right) , \label{eq:leff}
\end{eqnarray}%
where Eq. (\ref{eq:amplitude}) was used to eliminate $A^{2}$. The
Euler-Lagrange (variational) equations following from the effective
Lagrangian are
\begin{eqnarray}
\partial L_{\mathrm{eff}}/\partial W &=&0, \label{eq:dw} \\
\partial L_{\mathrm{eff}}/\partial N &=&0, \label{eq:dn}
\end{eqnarray}%
with $W$ and $N$ treated as free variational parameters for given $\omega $.$%
\allowbreak $
Hereafter, we consider the case $\alpha =0$ in more detail. Equation (\ref%
{eq:dw}) implies the following relation between $N$ and $W$:
\begin{equation}
N=\frac{48\sqrt{\pi /2}\exp \left( W^{2}/2\right) }{W\left(
3+9W^{2}-9W^{4}+W^{6}\right) }. \label{eq:N(W)}
\end{equation}%
This relation is plotted in Fig. \ref{pic:N(W)},\textcolor{black}{ (left panel, thin dashed line),} where it attains a minimum
value,
\begin{equation}
N_{\min }^{(\mathrm{VA})}\approx 19.41 \label{min-VA}
\end{equation}%
at $W=W_{0}\approx 0.806$.
An essential feature of the dependence is that it predicts the existence of
a minimum norm necessary for the DS to exist. Furthermore, it follows from
Eq.(\ref{eq:N(W)}) that the range of the variation of $W$ predicted by the
VA is \emph{finite}:
\textcolor{black}{\begin{equation}
0<W<W^*_{VA}\approx 1.21. \label{eq:wmax}
\end{equation}
}
\begin{figure}[tbp]
\center{\includegraphics[width=0.45\textwidth]{Figure04_05.eps}}
\caption{\textcolor{black}{Left panel: the relation between the norm and width of the DS, as predicted by the variational approximation, (thin dashed line, $\alpha=0$). Bold line shows the same relation for numerically computed DS. Right panel: the magnification of the bold line in small rectangle in the left panel}}
\label{pic:N(W)}
\end{figure}
The second variational equation, Eq.(\ref{eq:dn}), yields, after additional
algebraic manipulations, a monotonic dependence $\omega $ on $W$:
\begin{equation}
\omega =\frac{3}{2}\cdot\frac{-9+33W^{2}-13W^{4}+W^{6}}{W^{2}\left(
3+9W^{2}-9W^{4}+W^{6}\right) }. \label{eq:omega}
\end{equation}%
It may be combined with Eq. (\ref{eq:N(W)}) to apply the VK stability
criterion \cite{Vakh}, $dN/d\omega \equiv \left( d\omega /dW\right)
^{-1}dN/dW<0$. Because it follows from Eq. (\ref{eq:omega}) that $d\omega
/dW $ is always positive, the VK criterion predicts that stable is the left
branch in Fig. \ref{pic:N(W)}, with $dN/dW<0$, which corresponds to interval%
\begin{equation}
0<W<W_{0}\approx 0.806, \label{eq:stab}
\end{equation}%
while the right branch, with $dN/dW>0$, i.e., $W>W_{0}$ is unstable.
Note that Eq. (\ref{eq:omega}) is compatible with the above-mentioned
localization condition, $\omega <0$, at $0<W<0.556$, while the fact that the
VA predicts $\omega >0$ at $W>0.556$ is a manifestation of its inaccuracy.
It is worthy to note that the predicted stability region tends to have $%
\omega <0$, i.e., the stability is predicted in the region where the VA is
more accurate.
To summarize, the predictions of VA are:
\noindent (i) the existence of the minimal norm of the DS;
\noindent (ii) the existence of its maximum width;
\noindent (iii) the existence of the maximum width of DSs to be stable.
\noindent In what follows below we show that these predictions qualitatively
agree with results of numerical computation. The application of the VA to
more complex solitons is much more cumbersome and is not presented here.
\subsection{Numerical results for stationary dipole solitons}
\label{The dipole-soliton_profile}
The numerical computation of DS profiles was carried out by dint of the
shooting method. The results can be summarized as follows.
(1) The DS family of may be parameterized by $\omega $ or by $W$, which is
here defined as the distance of maxima of the wave field from the central
point. The amplitude and norm of the DS grow as the soliton shrinks (i.e.,
when $W$ tends to zero), and in this limit $\omega $ tends to $-\infty $.
Examples of DS profiles for $\alpha =0$ and $\omega =-15$ (thin line), $%
\omega =-7$ (dash line), and $\omega =-1$ (thick line) are depicted in Fig. %
\ref{pic:Profiles}. \textcolor{black}{The dependence of norm $N$ on $W$ is also shown in Fig. \ref{pic:N(W)} (bold line in the left panel and the right panel). It is seen in Fig. \ref{pic:N(W)} that this dependence agrees well with VA results at the interval left to $W_{\rm comp}^*$, the
maximum width of DS. Also it follows from
Fig. \ref{pic:N(W)} that there is a minimum norm $N_{\min }$ necessary for the existence of the DS, hence the above-mentioned prediction (i) of the VA holds.}
(2) The DS exists for $\omega <\omega ^{\ast }$. At {\color{black} $\omega =\omega ^{\ast
} \approx 0.265$ }, the DS family, coded by $\{\ldots, O,B_{\pm 1},O,\ldots, \}$, undergoes a
saddle-node bifurcation and annihilates with the family coded by {\color{black} $\{\dots,
O,A_{\mp 1},B_{\pm 1},A_{\pm 1},O,\dots \}$} (see Fig.~\ref{pic:Bifur}). This
implies that width $W$ of the DSs is bounded from above, hence prediction (ii)
of VA, concerning the existence of the maximum width of the DS, holds too.
\textcolor{black}{However the estimation of VA for the greatest width of the dipol soliton, $W_{VA}^*$, is quite rough when compared with computed value $W_{\rm comp}^*$, see Fig. \ref{pic:N(W)}.}
Note that the panel A in Fig. \ref{pic:Bifur} also demonstrates that,
although the single-cell DS is very similar, in its shape, to the SFS in
systems with linear lattice potentials, the DS in the present model is not
subfundamental, as its norm is \emph{higher} than that of the FS existing
at the same $\omega$. \textcolor{black}{The panel B of Fig. \ref{pic:Bifur}
presents the dependence of energy $E$ versus the norm $N$. It follows
from Fig. \ref{pic:Bifur} that the energy for the branch coded by $\{\dots,
O,A_{\mp 1},B_{\pm 1},A_{\pm 1},O,\dots \}$ is greater than the
energy of the DS branch.}
Thus, the predictions of the VA qualitatively agree with the numerical
results, although the accuracy of the VA is rather low, as ansatz (\ref%
{eq:ansatz}) is not accurate enough. For instance, the VA-predicted minimum
norm, given by Eq. (\ref{min-VA}), is smaller than the respective numerical
value,
\begin{equation}
N_{\min }^{\mathrm{(num)}}\approx 27.5, \label{min-num}
\end{equation}
by $\approx 30\%$. The ansatz may be improved by adding more terms to it,
but then the VA becomes too cumbersome.
\begin{figure}[tbp]
\centerline{\includegraphics[scale=0.8]{Figure06.eps}}
\caption{Numerically found profiles of the dipole solitons for $%
\protect\omega =-15$ (thin line), $\protect\omega =-7$ (dash line), and $%
\protect\omega =-1$ (thick line), with $\protect\alpha =0$ in Eq. (\protect
\ref{eq:current}).}
\label{pic:Profiles}
\end{figure}
\subsection{Evolution of dipole solitons}
\label{SFS_evolution}To check the above-mentioned prediction (iii) of the VA
concerning the stability of the DSs, we have performed simulations of the
evolution of these solitons in the framework of Eq. (\ref{UP}), with $U(x)=0$
and $P(x)$ corresponding to Eq. (\ref{eq:current}). The simulations were run
by means of the Trofimov-Peskov finite-difference numerical scheme \cite%
{Trofimov}. The
scheme is implicit, its realization implying iterations for the calculation
of values in each temporal layer, but it allows running computation with
larger temporal steps. In order to reveal instability (if it is), the
soliton profile was perturbed in initial moment with small spatial
perturbation. A finite spatial domain $[-4\pi, 4\pi]$ was used, with
reflection of radiation from boundaries eliminated by means of absorbing
boundary conditions.
\begin{figure}[tbp]
\centerline{\includegraphics[scale=0.45]{Figure07_renew.eps}}
\caption{\textcolor{black}{A: The bifurcation diagram for solitons in Eq. (\protect\ref%
{eq:current}) with $\protect\alpha =0$: the family of single-cell dipole
solitons corresponding to code $\{\ldots, O,B_{\pm 1},O,\ldots \}$ coalesces at $%
\protect\omega =\protect\omega ^{\ast }$ with family $\{\dots, O,A_{\mp
1},B_{\pm 1},A_{\pm 1},O,\dots \}$. The bottom branch (dashed line) represents fundamental solitons, showing that, on the contrary to the
SFSs in models with linear lattice potentials, the norm of the dipole solitons
is higher than the norm of the fundamental solitons at the same value of $\omega$.
B: Dependence of the energy $E$ on $N$ for the dipole-soliton branch. Two profiles of solitons coexisting at $\protect\omega = -0.8$ are displayed in the right panels (a) and (b), the corresponding points are marked in panels A and B
}}
\label{pic:Bifur}
\end{figure}
\begin{figure*}[tbp]
\subfloat[][$\omega =
-0.3$]{\includegraphics[width=0.5\textwidth]{Figure08_a.eps}} %
\subfloat[][$\omega =
-0.7$]{\includegraphics[width=0.5\textwidth]{Figure08_b.eps}} \vfill
\subfloat[][$\omega =
-1.2$]{\includegraphics[width=0.5\textwidth]{Figure08_c.eps}} %
\subfloat[][$\omega =
-1.4$]{\includegraphics[width=0.5\textwidth]{Figure08_d.eps}}
\caption{Typical examples of dipole solitons, their linear-stability
spectra, and unstable and stable temporal evolution, for $\protect\alpha =0$
in Eq. (\protect\ref{eq:current}). Additional examples of the evolution are
shown below in the lower panel of Fig. \protect\ref{pic:N(omega)}.}
\label{pic:sfs}
\end{figure*}
Typical results of the simulations are presented in Fig. \ref{pic:sfs}, for $%
\alpha =0$ in Eq. (\ref{eq:current}). One can conclude that the VA\
prediction (iii), based on the VK criterion, is generally valid. The results are
summarized in the $\left( \omega ,N\right) $ plane, as shown in Fig. \ref%
{pic:N(omega)}. The DS is stable for the values of omega corresponding to
the slope of the $N(\omega)$ curve situated left to the minimum point $%
\omega _{\min }\approx -0.66$ and transforms into FS at the slope right to
this point. The border between the stability and instability regions in the
top panel of Fig. \ref{pic:N(omega)} is fuzzy. Within this ``fuzzy area''
the evolution of initial DS profile strongly depends on the type of imposed
perturbation and parameters of the numerical method.
\begin{figure}[tbp]
\center{\includegraphics[scale=0.4]{Figure09.eps}}
\caption{The upper panel: the $N(\protect\omega )$ curve for the
dipole solitons at $\protect\alpha =0$ in Eq. (\protect\ref%
{eq:current}). The lower panel displays typical examples of the stable and
unstable evolution of the dipole solitons for $\protect\omega =-1.4$
and $\protect\omega =-0.4$, respectively. In the latter case, the unstable
dipole soliton transforms into a fundamental soliton corresponding
to $\protect\omega \approx -13.96$ and amplitude $\approx 5.43$. In ``fuzzy area''
the simulation is very sensitive to the type of initial perturbation and the parameters of
the numerical method.}
\label{pic:N(omega)}
\end{figure}
\section{Conclusion}
\label{Discuss}The mathematical issue considered in this work is the
classification of families of solitons and their bound states in the model
of the nonlinear lattice, which is represented by the periodically varying
nonlinearity coefficient. A condition necessary for the existence of the
infinite variety of the bound states is that the local coefficient must
assume both positive and negative values. Then, the analysis is performed
for the physically relevant problem, which may find direct applications to
Bose-Einstein condensates and planar waveguides in nonlinear optics: finding
two branches of the DSs (\textit{dipole solitons}), whose
antisymmetric profile is confined, essentially, to a single cell of the
nonlinear lattice. The shape of these solitons is very similar to that of
the \textit{subfundamental solitons}, which are known in models with usual linear
lattice potentials, where they are chiefly unstable. An essential
finding reported here is that one of two branches of the single-cell DS, family which satisfies
the VK (Vakhitov-Kolokolov) criterion, is \emph{completely stable}. Also it was found that DSs belonging to the unstable branch evolve into stable FSs.
These results were obtained by means of numerical methods and also, in a
qualitatively correct form, with the help of the VA (variational
approximation). Besides that, it was found that particular species of FS
bound states are stable too.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,604 |
Holger Heinrich Herwig (* 25. September 1941 in Hamburg) ist ein kanadischer Militärhistoriker deutscher Abstammung.
Leben
Herwig studierte an der University of British Columbia (BA 1965) und der State University of New York (MA 1967 und Ph.D. 1970).
1971/72 war er Visiting Assistant Professor an der Indiana University. Von 1971 bis 1989 unterrichtete er an der Vanderbilt University, zuletzt als Professor. 1985/86 war er Visiting Professor of Strategy am Naval War College.
Danach wurde er Professor of History an der University of Calgary. Von 1991 bis 1996 war er Head of the Department of History. Außerdem ist er seit 2001 Inhaber des Canada Research Chair in the Centre for Military and Strategic Studies. 1998 war er Andrea and Charles Bronfman Distinguished Visiting Professor of Judaic Studies am College of William & Mary. 2010 hielt er die Harmon Memorial Lecture in Military History an der United States Air Force Academy in Colorado Springs.
Er ist u. a. Fellow der Royal Society of Canada und wurde mit mehreren Stipendien ausgezeichnet wie durch die Alexander von Humboldt-Stiftung, die National Endowment for the Humanities und die Rockefeller Foundation. Außerdem ist er Mitglied der Atlantik-Brücke.
Herwig ist Autor mehrerer Bücher und Fachaufsätze, vor allem zum Ersten Weltkrieg. Er beschäftigte sich insbesondere mit dem Ausbruch des Ersten Weltkriegs und auch mit der Geschichtsschreibung zu seiner Entstehung.
Er war beratend für den Discovery Channel und andere historische TV-Produktionen (u. a. Deadly Seas, Murder in Normandy, Forced March to Freedom) tätig.
1999 erhielt er den Norman B. Tomlinson, Jr., Book Prize der Western Front Association (heute: World War One Historical Association) für sein Buch The First World War: Germany and Austria-Hungary 1914–1918, erschienen bei Edward Arnold (heute: Taylor & Francis).
Schriften (Auswahl)
(Übersicht)
The German Naval Officer Corps (1973); das Buch erschien 1977 in überarbeiteter Form in deutscher Übersetzung unter dem Titel "Das Elitekorps des Kaisers. Die Marineoffiziere im Wilhelminischen Deutschland." ISBN 3-7672-0514-9
Politics of Frustration (1976)
"Luxury" Fleet (1980)
mit Neil M. Heyman: Biographical Dictionary of World War I (1982)
Germany's Vision of Empire in Venezuela 1871-1914 (1986)
(ed.): Wolfgang Wegener: The Naval Strategy of the World War (1989)
The Outbreak of World War I (5th ed., 1991)
The First World War (1997)
mit David J. Bercuson: Deadly Seas (1997)
mit William F. Sater: The Grand Illusion (1999)
mit David J. Bercuson: The Destruction of the Bismarck (2001)
mit David J. Bercuson: Bismarck (2002)
World History of Warfare (2003)
mit Richard F. Hamilton: The Origins of World War I (2003)
mit Richard F. Hamilton: Decisions for War, 1914-1917 (2005)
mit David J. Bercuson: One Christmas in Washington (2006)
mit Michael Keren: War Memory and Popular Culture (2009)
The Marne, 1914 (2009)
mit Richard F. Hamilton: War Planning 1914 (2009)
(neuere Beiträge)
Marne 1914: Eine Schlacht, die die Welt veränderte? (= Zeitalter der Weltkriege. Band 13). Ferdinand Schöningh, Paderborn 2016, ISBN 978-3-506-78195-6.
The Demon of Geopolitics. How Karl Haushofer «educated» Hitler and Hess. Rowman & Littlefield, Lanham, Maryland, USA 2016.
Weblinks
Holger H. Herwig an der University of Calgary
Fußnoten
Militärhistoriker
Hochschullehrer (University of Calgary)
Hochschullehrer (Vanderbilt University)
Mitglied der Royal Society of Canada
Kanadier
Deutscher
Geboren 1941
Mann | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,807 |
Konarak-e Pain (, also Romanized as Konarak-e Pā'īn, Kanārak-e Pā'īn, and Konrok Pā'īn; also known as Konarak-e Soflá and Kanārak) is a village in Gandoman Rural District, Gandoman District, Borujen County, Chaharmahal and Bakhtiari Province, Iran. At the 2006 census, its population was 382, in 81 families. The village is populated by Lurs.
References
Populated places in Borujen County
Luri settlements in Chaharmahal and Bakhtiari Province | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,382 |
The new Chinese android pill with the company Acer C B1-A71 by using a seven-inch display C rapidly cluttered with rumors. Recently, this device (even now not formally declared by Acer) lit MEIZU MX3 up within the pursuing resources C internet site on the American companys ties FCC and GLBenchmark.With the time of reporting around the specialized features on the device (in addition as part-time), were being the very first pictures that confirm a 7-inch screen measurement in the pill. Externally, the novelty appears to be like very beautiful.
Resolution to this product C 1024600 pixels, dual-core processor running at one.two GHz. The pill has 512 MB of RAM, flash-memory is obtainable 8GB. Graphics accelerator is really a PowerVR SGX 531. The machine provides a slot for microSD, Bluetooth product and receiver GPS. Running technique, which so far is within the unit C Android four.one.2, but nearer with the time it might be up-to-date to Android four.2.The documentation may be study that the pill is current Adapter Wi-Fi, there is no information and facts with regard to the presence of 3G modules and LTE, but that is no ensure that these features are usually not from the plate. Inside the image it is possible to begin to see the SIM-card, that is a clear proof which the phone can operate in cell networks.Having said that, the lower resolution on the screen indicates that Acer B1-A71 will fall within the devices. His closest rivals provide Tablets Amazon Kindle Hearth and also the solution from Google C Nexus 7.It ought to be MEIZU MX3 Smartphone Exynos 5410 Octa Core 5.1 Inch 1080P Gorilla Glass Screen pointed out which the lately introduced another Acer pill together with the screen in 7 inches- Manufacturer Iconia Tab A110. But looking at individuals images and technical specs of the new technique C we are able to conclude that it belongs to your completely diverse design amount. B1-A71 C the finances, but fashionable system.
Today, there have been 9 visitors (78 hits) on this page! | {
"redpajama_set_name": "RedPajamaC4"
} | 8,191 |
\section{Introduction}
Fuzziness has revolutionized many areas such as mathematics, science, engineering, medicine. This concept was initiated by Zadeh \cite{Zadeh}. Not only Zadeh discovered this concept, but he also developed the infrastructure of today's popular forms of use such as relations of similarity, decision making, and fuzzy programming in a short time.\\
Just like in the theory of sets, fuzzy sets(FS) also have led to the emergence of new mathematical concepts, research topics, and the design of engineering applications.
Therefore, the nature of the classical set theory must be well known and understood. In particular, consider the two fundamental laws of Boolean algebra the law of excluded middle and law of contradiction. In logic, the proposition every proposition is either true or false excludes any third, or middle, possibility, which gave this principle the name of the law of excluded middle. When look at the principles of Boolean algebra, there are two items as prediction: "True" or "False". Whether classical, Boolean or crisp, set theory can be defined as a characteristic function of the membership of an element $x$ in a set $A$.
For each elements of universal set $X$, the function that generates the values $0$ and $1$ is called the characteristic function.\\
In some real life problems in expert system, belief system, information fusion and so on , we must consider the truth-membership as well as the falsity-membership for proper description of an object in uncertain, ambiguous environment. Neither the fuzzy sets nor the interval valued fuzzy sets is appropriate for such a situation.
Intuitionistic fuzzy sets introduced by Atanassov \cite{Ata} is appropriate for such a situation. The intuitionistic fuzzy sets can only handle the incomplete
information considering both the truth-membership ( or simply membership ) and falsity-membership ( or non-membership ) values. It does not handle the indeterminate and inconsistent information which exists in belief system.\\
The notion of intuitionistic fuzzy metric space has been introduced by Park \cite{Park}. Furthermore, The concept of intuitionistic fuzzy normed space is given by Saadati and Park \cite{Saad}.
The study of statistical convergence was initiated by Fast\cite{Fast}. Schoenberg \cite{Sch} studied statistical convergence as
a summability method and listed some of the elementary properties of statistical convergence. Both of these mathematicians
mentioned that if a bounded sequence is statistically convergent to $L$ then it is Ces\`{a}ro summable to $L$. Statistical convergence
also arises as an example of "convergence in density" as introduced by Buck\cite{Buck}. In \cite{Zygm}, Zygmund called this concept
"almost convergence" and established relation between statistical convergence and strong summability. The idea of statistical convergence
has been studied in different branches of mathematics such as number theory\cite{ErTe}, trigonometric series\cite{Zygm}, summability theory\cite{FreeSem},
measure theory\cite{Mil}, Hausdorff locally convex topological vector spaces\cite{Maddox}. The concept of $\alpha\beta-$statistical convergence was introduced and studied by Aktu\v{g}lu\cite{Aktuglu}. In \cite{VatanAli}, Karakaya and Karaisa have been extended the concept of $\alpha\beta-$statistical convergence. Also, they have been introduced the concept of weighted $\alpha\beta-$statistical convergence of order $\gamma$, weighted $\alpha\beta-$summmability of order of $\gamma$ and strongly weighted $\alpha\beta-$summable sequences of order $\gamma$, in \cite{VatanAli}. In \cite{Braha}, Braha gave a new weighted equi-statistical convergence and proved the Korovkin type theorems using the new definition.\\
In the present work, we will study Fibonacci statistical convergence, Fibonacci statistically Cauchy and Fibonacci statistical completeness
with respect to the intuitionistic fuzzy normed space.\\
\section{Preliminaries}\label{chap:1}
The Fibonacci numbers are the sequence of numbers $(f_{n})$ for $n=1,2,\ldots$ defined by the linear recurrence equation
\begin{eqnarray*}
f_{n}=f_{n-1}+f_{n-2} \quad n\geq 2,
\end{eqnarray*}
From this definition, it means that the first two numbers in Fibonacci sequence are either $1$ and $1$ (or $0$ and $1$)
depending on the chosen starting point of the sequence and all subsequent number is the sum of the previous two. That is,
we can choose $f_{1}=f_{2}=1$ or $f_{0}=0$, $f_{1}=1$. \\
Some of the fundamental properties of Fibonacci numbers are given as follows:
\begin{eqnarray*}
&&\lim_{n\rightarrow\infty}\frac{f_{n+1}}{f_{n}}=\frac{1+\sqrt{5}}{2}=\alpha, \quad \textrm{(golden ratio)}\\
&&\sum_{k=0}^{n}f_{k}=f_{n+2}-1 \quad (n\in\mathbb{N}),\\
&&\sum_{k}\frac{1}{f_{k}} \quad \textrm{converges},\\
&&f_{n-1}f_{n+1}-f_{n}^{2}=(-1)^{n+1} \quad (n\geq 1) \quad \textrm{(Cassini formula)}
\end{eqnarray*}
It yields $f_{n-1}^{2}+f_{n}f_{n-1}-f_{n}^{2}=(-1)^{n+1}$, if we can substituting for $f_{n+1}$ in Cassini's formula.\\
Let $f_{n}$ be the $n$th Fibonacci number for every $n\in \mathbb{N}$. Then, we define the infinite matrix $\widehat{F}=(\widehat{f}_{nk})$ \cite{Kara1} by
\begin{eqnarray*}
\widehat{f}_{nk}=\left\{\begin{array}{ccl}
-\frac{f_{n+1}}{f_{n}}&, & (k=n-1)\\
\frac{f_{n}}{f_{n+1}}&, & (k=n)\\
0&, & (0\leq k < n-1 \textrm{or} k>n).
\end{array}\right.
\end{eqnarray*}
Let $A$ is a subset of positive integer. We consider the interval $[1,n]$ and select an integer in this interval, randomly. Then,
the ratio of the number of elements of $A$ in $[1,n]$ to the total number of elements in $[1,n]$ is belong to $A$, probably. For
$n\rightarrow \infty$, if this probability exists, that is this probability tends to some limit, then this limit is used to as
the asymptotic density of the set $A$. This mentions us that the asymptotic density is a kind of probability of choosing a number
from the set $A$.\\
Now, we give some definitions and properties of asymptotic density:\\
The set of positive integers will be denoted by $\mathbb{Z^{+}}$. Let $A$ and $B$ be subsets of $\mathbb{Z}^{+}$. If the symmetric
difference $A\Delta B$ is finite, then, we can say $A$ is asymptotically equal to $B$ and denote $A\sim B$. Freedman and Sember
have introduced the concept of a lower asymptotic density and defined a concept of convergence in density, in \cite{FreeSem}.
\begin{defin}\cite{FreeSem}
Let $f$ be a function which defined for all sets of natural numbers and take values in the interval $[0,1]$.
Then, the function $f$ is said to a lower asymptotic density, if the following conditions hold:
\begin{itemize}
\item[i.] $f(A)=f(B)$, if $A\sim B$,
\item[ii.] $f(A)+f(B)\leq f(A\cup B)$, if $A\cap B=\emptyset$,
\item[iii .] $f(A)+f(B)\leq 1+ f(A\cap B)$, for all $A$,
\item[iv.] $f(\mathbb{Z^{+}})=1$.
\end{itemize}
\end{defin}
We can define the upper density based on the definition of lower density as follows:\\
Let $f$ be any density. Then, for any set of natural numbers $A$, the function $\overline{f}$ is said to upper density associated with $f$, if
$\overline{f}(A)=1-f(\mathbb{Z}^{+} \backslash A)$.\\
Consider the set $A\subset \mathbb{Z}^{+}$. If $f(A)=\overline{f}(A)$, then we can say that the set $A$ has natural density
with respect to $f$. The term asymptotic density is often used for the function
\begin{eqnarray*}
d(A)=\liminf_{n\rightarrow\infty}\frac{A(n)}{n},
\end{eqnarray*}
where $A\subset \mathbb{N}$ and $A(n)=\sum_{a\leq n, a\in A}1$. Also the natural density of $A$ is given by $d(A)=\lim_{n}n^{-1}|A(n)|$ where
$|A(n)|$ denotes the number of elements in $A(n)$.\\
\begin{defin}
A real numbers sequence $x=(x_{k})$ is statistically convergent to $L$ provided that for every $\varepsilon >0$ the set
$\{n\in\mathbb{N}: |x_{n}-L|\geq \varepsilon\}$ has natural density zero. The set of all statistical convergent sequence is denoted by $S$.
In this case, we write $S-\lim x=L$ or $x_{k}\rightarrow L(S)$.\\
\end{defin}
\begin{defin}\cite{Fri}
The sequence $x=(x_{k})$ is statistically Cauchy sequence if for every $\varepsilon >0$ there is a positive integer $N=N(\varepsilon)$ such
that
\begin{eqnarray*}
d\left(\{n\in\mathbb{N}: |x_{n}-x_{N(\varepsilon)}|\geq \varepsilon\}\right)=0.
\end{eqnarray*}
\end{defin}
It can be seen from the definition that statistical convergence is a generalization of the usual of notion of convergence that parallels
the usual theory of convergence. Kirisci and Karaisa \cite{KirKar} are defined Fibonacci statistical convergence and Fibonacci Cauchy sequence as follows:\\
\begin{defin}
A sequence $x=(x_{k})$ is said to be Fibonacci statistically
convergence(or $\widehat{F}-$statistically convergence) if there is
a number $L$ such that for every $\epsilon> 0$ the set
$K_{\epsilon}(\widehat{F}):=\{k\leq
n:|\widehat{F}x_{k}-L|\geq\epsilon\}$ has natural density zero,
i.e., $d(K_{\epsilon}(\widehat{F}))=0$. That is
\begin{eqnarray*}
\lim_{n \to \infty}\frac{1}{n}\left|\{k\leq n:
|\widehat{F}x_{k}-L|\geq \epsilon \}\right|=0.
\end{eqnarray*}
\end{defin}
In this case we write $d(\widehat{F})-\lim x_{k}=L$ or $x_{k}\rightarrow L(S(\widehat{F}))$. The set of
$\widehat{F}-$statistically convergent sequences will be denoted by
$S(\widehat{F})$. In the case $L=0$, we will write
$S_{0}(\widehat{F})$.
\begin{defin}
Let $x=(x_{k})\in \omega$. The sequence $x$ is said to be $\widehat{F}-$statistically Cauchy if
there exists a number $N=N(\varepsilon)$ such that
\begin{eqnarray*}
\lim_{n \to \infty}\frac{1}{n}\left|\{k\leq n:
|\widehat{F}x_{k}-\widehat{F}x_{N}|\geq \epsilon \}\right|=0
\end{eqnarray*}
for every $\varepsilon >0$.\\
\end{defin}
In 1965, fuzzy set theory has long been presented to handle vagueness, inexact and imprecise data by Zadeh
\cite{Zadeh}. After Zadeh, fuzzy sets, especially fuzzy numbers have been widely studied and applied to various
fields, such as decision-making, pattern recognition, game theory and so on. In fuzzy sets, the degree
of memberships of the elements in a universe is a single value but, those single values cannot provide any
additional information because, in practice, information regarding elements corresponding to a fuzzy concept
may be incomplete. The fuzzy set theory is not capable of dealing with the lack of knowledge with respect
to degrees of memberships, Atanassov \cite{Ata} proposed the theory of intuitionistic fuzzy sets the extension of
Zadehs fuzzy sets by using a non-membership degree cope with the presence of vagueness and hesitancy
originating from imprecise knowledge or information.\\
\begin{defin}\cite{Schw}
Let $\bigstar$ be a binary operation with $\bigstar: [0,1]\times [0,1] \rightarrow [0,1]$ and given the following
properties:\\
\begin{itemize}
\item $\forall x\in [0,1]$, $x \bigstar 1 = x$, \\
\item $\forall x,y,z,t\in [0,1]$, $x\bigstar y\leq z\bigstar t$ whenever $x\leq y$ and $z\leq t$, \\
\item $\bigstar$ is continuous,\\
\item $\bigstar$ is commutative and associative.\\
\end{itemize}
If these conditions are satisfies, then the operation $\bigstar$ is called a \emph{continuous t-norm}.\\
\end{defin}
\begin{defin}\cite{Schw}
Let $\blacktriangle$ be a binary operation with $\blacktriangle: [0,1]\times [0,1] \rightarrow [0,1]$ and given the following
properties:\\
\begin{itemize}
\item $\forall x\in [0,1]$, $x \blacktriangle 0 = x$, \\
\item $\forall x,y,z,t\in [0,1]$, $x\blacktriangle y\leq z\blacktriangle t$ whenever $x\leq y$ and $z\leq t$, \\
\item $\blacktriangle$ is continuous,\\
\item $\blacktriangle$ is commutative and associative.\\
\end{itemize}
If these conditions are satisfies, then the operation $\blacktriangle$ is called a \emph{continuous t-conorm}.\\
\end{defin}
The concept of intuitionistic fuzzy normed space is given with the continuous t-norm and continuous t-conorm as follows:\\
\begin{defin}\cite{Saad}
Let $X$ be a vector space, $T$ and $U$ be two fuzzy sets on $X \times (0,\infty)$ and, $\bigstar$ and $\blacktriangle$
be a continuous t-norm and a continuous t-conorm, respectively. Consider the following conditions are hold:\\
\begin{itemize}
\item $T(x,t)+U(x,t)\leq 1$,\\
\item $T(x,t)>0$,\\
\item $T(x,t)=1$ if and only if $x=0$,\\
\item $T(\alpha x,t)=T\left(x, \frac{t}{|\alpha|}\right)$ for each $\alpha\neq 0$,\\
\item $T(x,t)\bigstar T(y,s)\leq T(x+y,t+s)$,\\
\item $T(x,.):(0,\infty)\rightarrow [0,1]$ is continuous,\\
\item $\lim_{t\rightarrow\infty} T(x,t)=1$ and $\lim_{t\rightarrow 0} T(x,t)=0$,\\
\item $U(x,t)<1$,\\
\item $U(x,t)=0$ if and only if $x=0$,\\
\item $U(\alpha x,t)=U\left(x, \frac{t}{|\alpha|}\right)$ for each $\alpha\neq 0$,\\
\item $U(x,t)\blacktriangle U(y,s)\geq U(x+y,t+s)$,\\
\item $U(x,.):(0,\infty)\rightarrow [0,1]$ is continuous,\\
\item $\lim_{t\rightarrow\infty} U(x,t)=0$ and $\lim_{t\rightarrow 0} U(x,t)=1$.\\
\end{itemize}
for every $x,y\in X$ and $s,t>0$. Then, the 5-tuple $(X, T,S, \bigstar, \blacktriangle)$
is called \emph{intuitionistic fuzzy normed space}(IFNS). Therefore, $(T,U)$ is called an intuitionistic fuzzy norm(IFN).\\
\end{defin}
The concepts of convergence and Cauchy sequences in IFNS as follows :\\
\begin{defin}\cite{Saad}
Consider the IFNS $(X, T,U, \bigstar, \blacktriangle)$. Let $\varepsilon, t>0$. If there exists $N\in \mathbb{N}$ such that $T(x_{k}-\mathcal{L}, t)>1-\varepsilon$
and $U(x_{k}-\mathcal{L},t)<\varepsilon$ for all $k\geq N$, then, in IFN $(T,U)$, a sequence $x=(x_{k})$ is said to be convergent to $\mathcal{L}\in X$.
It is denoted by $(T,U)-\lim x=\mathcal{L}$.\\
If there exists $N\in \mathbb{N}$ such that $T(x_{k}-x_{m}, t)>1-\varepsilon$
and $U(x_{k}-x_{m},t)<\varepsilon$ for all $k, m\geq N$,then, in IFN $(T,U)$, a sequence $x=(x_{k})$ is called Cauchy sequence.\\
\end{defin}
\section{Method}
In the theory of numbers, there are many different definitions of density. It is well known that the most popular
of these definitions is asymptotic density. But, asymptotic density does not exist for all sequences. New densities
have been defined to fill those gaps and to serve different purposes.\\
The asymptotic density is one of the possibilities to measure how large a subset of the set of natural number. We
know intuitively that positive integers are much more than perfect squares. Because, every perfect square is
positive and many other positive integers exist besides. However, the set of positive integers is not in fact larger
than the set of perfect squares: both sets are infinite and countable and can therefore be put in one-to-one correspondence.
Nevertheless if one goes through the natural numbers, the squares become increasingly scarce. It is precisely in this case,
natural density help us and makes this intuition precise.\\
The Fibonacci Sequence was firstly used in the Theory of Sequence Spaces by Kara and Ba\c{s}ar{\i}r\cite{KaraBas}.
Afterward, Kara\cite{Kara1} defined the Fibonacci
difference matrix $\widehat{F}$ by using the Fibonacci sequence $(f_{n})$ for $n\in \{0,1,\ldots\}$ and
introduced the new sequence spaces
related to the matrix domain of $\widehat{F}$. \\
The concept of the statistical convergence is studied in the intuitionistic fuzzy normed space (\cite{KaSiMuFa}, \cite{KaSiMuFa2}, \cite{Karakus},
\cite{KoDe}, \cite{KuMur}, \cite{MoLo}, \cite{MuMo1}, \cite{MuMo2}). Kirisci and Karaisa \cite{KirKar} defined Fibonacci type statistical convergence and investigated
some fundamental properties. Further, in \cite{KirKar}, various approximation results concerning the classical
Korovkin theorem via Fibonacci type statistical convergence are given.\\
In this paper, by combining the definitions of Fibonacci sequence and statistical convergence with respect to the IFN $(T,U)$,
we will obtain a new concept of statistical convergence in IFNS and so on give a useful characterization for statistical convergence sequences on IFNS.
We will examine some basic properties of new statistical convergence in IFNS. We will see that this new statistical convergence method on IFNS is stronger than
the usual convergence on IFNS.\\
\section{Main Results}
\subsection{Fibonacci Statistical Convergence in IFNS}
Using the definitions and properties of density, statistical convergence, Fibonacci numbers and IFNS in Chapter 2 , we give new definitions as follows:\\
\begin{defin}\label{def:1}
Take an IFNS $(X,T,U,\bigstar,\blacktriangle)$. A sequence $x=(x_{k})$ is said to be Fibonacci statistical convergence with respect to IFN $(T,U)$ (briefly, FSC-IFN),
if there is a number $\mathcal{L}\in X$ such that for every $\varepsilon >0$ and $t>0$, the set
\begin{eqnarray*}
K_{\varepsilon}(\widehat{F}):=\big\{k\leq n: T(\widehat{F}x_{k}-\mathcal{L}, t)\leq 1-\varepsilon \quad \textit{or} \quad U(\widehat{F}x_{k}-\mathcal{L}, t)\geq\varepsilon\big\}
\end{eqnarray*}
has natural density zero, i.e., $d(K_{\varepsilon}(\widehat{F}))=0$. That is,
\begin{eqnarray*}
\lim_{n}\frac{1}{n} \bigg |\big\{k\leq n: T(\widehat{F}x_{k}-\mathcal{L}, t)\leq 1-\varepsilon \quad \textit{or} \quad U(\widehat{F}x_{k}-\mathcal{L}, t)\geq\varepsilon\big\} \bigg|=0.
\end{eqnarray*}
\end{defin}
In this case we write $d(\widehat{F})_{IFN}-\lim x_{k}=\mathcal{L}$ or $x_{k}\rightarrow \mathcal{L}(S(\widehat{F})_{IFN})$. The set of
FSC-IFN will be denoted by
$S(\widehat{F})_{IFN}$. In the case $\mathcal{L}=0$, we will write
$S_{0}(\widehat{F})_{IFN}$.\\
\begin{exmp}\label{exmp:1}
Let $(X,\|.\|)$ be a normed space and for all $a,b\in [0,1]$, $a\bigstar b=ab$ and $a\blacktriangle b=\min\{a+b,1\}$.
For all $x\in X$ and every $t>0$, consider
\begin{eqnarray*}
T(x,t):=\frac{t}{t+\|x\|}, \quad \quad U(x,t):=\frac{\|x\|}{t+\|x\|}.
\end{eqnarray*}
Then, $(X,T,U,\bigstar,\blacktriangle)$ is an IFNS. Define the $\widehat{F}x_{n}=(f_{n+1}^{2})=(1,2^{2},3^{2},5^{2},\cdots)$.
Since $f_{n+1}^{2}\rightarrow \infty$ as $k\rightarrow \infty$ and $\widehat{F}x=(1,0,0,\cdots)$, then $\widehat{F}x \in S$.
Consider
\begin{eqnarray*}
K_{n}(\varepsilon, t)=\{k\leq n: T_{F}(\widehat{F}x_{k},t)\leq 1-\varepsilon \quad \textit{or} \quad U_{F}(\widehat{F}x_{k},t)\geq \varepsilon\}
\end{eqnarray*}
for $\varepsilon \in (0,1)$ and for any $t>0$. When $n$ becomes sufficiently large, the quantity $T(\widehat{F}x_{k}-\mathcal{L}, t)$ becomes less than
$1-\varepsilon$ and similarly the quantity $U(\widehat{F}x_{k}-\mathcal{L}, t)$ becomes greater than $\varepsilon$. So, for $\varepsilon>0$ and $t>0$,
$K_{\varepsilon}(\widehat{F})=0$.
\end{exmp}
The following lemma can be easily get by using the definitions and properties of density given in Chapter 2 and Definition \ref{def:1}.\\
\begin{lem}\label{lem:1}
Take an IFNS $(X,T,U,\bigstar,\blacktriangle)$. For every $\varepsilon >0$ and $t>0$, the following statements are equivalent:
\begin{itemize}
\item[i.] $d(\widehat{F})_{IFN}-\lim x_{k}=\mathcal{L}$.
\item[ii.] $\lim_{n}\frac{1}{n} \bigg |\big\{k\leq n: T(\widehat{F}x_{k}-\mathcal{L}, t)\leq 1-\varepsilon\big\}\bigg|= \lim_{n}\frac{1}{n} \bigg |\big\{U(\widehat{F}x_{k}-\mathcal{L}, t)\geq\varepsilon\big\} \bigg|=0$.
\item[iii.] $\lim_{n}\frac{1}{n} \bigg |\big\{k\leq n: T(\widehat{F}x_{k}-\mathcal{L}, t)> 1-\varepsilon\big\}\bigg|$ and $\lim_{n}\frac{1}{n} \bigg |\big\{k\leq n:U(\widehat{F}x_{k}-\mathcal{L}, t)<\varepsilon\big\} \bigg|=1$.
\item[iv.] $\lim_{n}\frac{1}{n} \bigg |\big\{k\leq n: T(\widehat{F}x_{k}-\mathcal{L}, t)> 1-\varepsilon\big\}\bigg|= \lim_{n}\frac{1}{n} \bigg |\big\{U(\widehat{F}x_{k}-\mathcal{L}, t)<\varepsilon\big\} \bigg|=1$.
\item[v.] $S-\lim T(\widehat{F}x_{k}-\mathcal{L}, t)=1$ and $S-\lim U(\widehat{F}x_{k}-\mathcal{L}, t)=0$.
\end{itemize}
\end{lem}
\begin{thm}
Take an IFNS $(X,T,U,\bigstar,\blacktriangle)$. The $d(\widehat{F})_{IFN}-\lim x_{k}=\mathcal{L}$ is unique,
when a sequence $x=(x_{k})$ is FSC-IFN.
\end{thm}
\begin{proof}
For $\mathcal{L}_{1}\neq \mathcal{L}_{2}$, suppose that $d(\widehat{F})_{IFN}-\lim x_{k}=\mathcal{L}_{1}$ and $d(\widehat{F})_{IFN}-\lim x_{k}=\mathcal{L}_{2}$. Choose $r>0$ such that $(1-r)\bigstar(1-r)>1-\varepsilon$ and $r\blacktriangle r<\varepsilon$, for a given $\varepsilon>0$.
Define the following set, for any $t>0$:\\
\begin{eqnarray*}
&&K_{T,1}(r,t):=\big\{k\in \mathbb{N}: T(\widehat{F}x_{k}-\mathcal{L}_{1}, \frac{t}{2})\leq 1-r\big\},\\
&&K_{T,2}(r,t):=\big\{k\in \mathbb{N}: T(\widehat{F}x_{k}-\mathcal{L}_{2}, \frac{t}{2})\leq 1-r\big\},\\
&&K_{U,1}(r,t):=\big\{k\in \mathbb{N}: U(\widehat{F}x_{k}-\mathcal{L}_{1}, \frac{t}{2})\geq r\big\},\\
&&K_{U,1}(r,t):=\big\{k\in \mathbb{N}: U(\widehat{F}x_{k}-\mathcal{L}_{2}, \frac{t}{2})\geq r\big\}.
\end{eqnarray*}
Then, for all $t>0$ and using the Lemma \ref{lem:1}, we have
\begin{eqnarray*}
d\big(K_{T,1}(\varepsilon,t))=d(K_{U,1}(\varepsilon,t)\big)=0
\end{eqnarray*}
because of $d(\widehat{F})_{IFN}-\lim x_{k}=\mathcal{L}_{1}$.
Similarly, for all $t>0$, we have
\begin{eqnarray*}
d\big(K_{T,2}(\varepsilon,t))=d(K_{U,2}(\varepsilon,t)\big)=0
\end{eqnarray*}
because of $d(\widehat{F})_{IFN}-\lim x_{k}=\mathcal{L}_{2}$.
Let
\begin{eqnarray*}
K_{T,U}(\varepsilon,t):=\big\{K_{T,1}(\varepsilon,t)\cup K_{T,2}(\varepsilon,t)\big\}\cap\big\{K_{U,1}(\varepsilon,t)\cup K_{U,2}(\varepsilon,t)\big\}.
\end{eqnarray*}
Hence reveal that $d(K_{T,U}(\varepsilon,t))=0$ which implies $d(\mathbb{N} / K_{T,U}(\varepsilon,t))=1$.
Then, we have two possible cases, when take $k\in \mathbb{N} / K_{T,U}(\varepsilon,t)$:
\begin{itemize}
\item[i.] $k\in \mathbb{N} / \big(K_{T,1}(\varepsilon,t)\cup K_{T,2}(\varepsilon,t)\big)$,\\
\item[ii.] $k\in \mathbb{N} / \big(K_{U,1}(\varepsilon,t)\cup K_{U,2}(\varepsilon,t)\big)$.
\end{itemize}
Firstly, consider (i). Then, we have
\begin{eqnarray*}
T(\mathcal{L}_{1}-\mathcal{L}_{2},t)\geq T\left(\widehat{F}x_{k}-\mathcal{L}_{1},\frac{t}{2}\right)\bigstar
T\left(\widehat{F}x_{k}-\mathcal{L}_{2},\frac{t}{2}\right)> (1-r)\bigstar (1-r).
\end{eqnarray*}
In this case,
\begin{eqnarray}\label{equ:1}
T(\mathcal{L}_{1}-\mathcal{L}_{2}, t)> 1- \varepsilon,
\end{eqnarray}
because of $(1-r)\blacktriangle (1-r)>1- \varepsilon$.
Using the (\ref{equ:1}), for all $t>0$, we obtain $T(\mathcal{L}_{1}-\mathcal{L}_{2}, t)=1$, where $\varepsilon >0$ is arbitrary.
From here, $\mathcal{L}_{1}=\mathcal{L}_{2}$ is obtained.\\
Moreover, then we can write that
\begin{eqnarray*}
U(\mathcal{L}_{1}-\mathcal{L}_{2},t)\leq U\left(\widehat{F}x_{k}-\mathcal{L}_{1},\frac{t}{2}\right)\blacktriangle
U\left(\widehat{F}x_{k}-\mathcal{L}_{2},\frac{t}{2}\right)< r \blacktriangle r.
\end{eqnarray*}
if we take $k\in \mathbb{N} / \big(K_{U,1}(\varepsilon,t)\cup K_{U,2}(\varepsilon,t)\big)$. Using $r \blacktriangle r< \varepsilon$,
we see that
\begin{eqnarray*}
U(\mathcal{L}_{1}-\mathcal{L}_{2},t)<\varepsilon.
\end{eqnarray*}
For all $t>0$, we obtain $U(\mathcal{L}_{1}-\mathcal{L}_{2}, t)=0$, where $\varepsilon >0$ is arbitrary.
Thus, $\mathcal{L}_{1}=\mathcal{L}_{2}$ and this step completes the proof.\\
\end{proof}
\begin{thm}\label{theo:1}
Take an IFNS $(X,T,U,\bigstar,\blacktriangle)$. If $(T,U)-\lim x=\mathcal{L}$, then
$d(\widehat{F})_{IFN}-\lim x_{k}=\mathcal{L}$.
\end{thm}
\begin{proof}
Let $(T,U)-\lim x=\mathcal{L}$. Then, for every $\varepsilon>0$ and $t>0$, there is a number $N\in \mathbb{N}$ such that
$T(x_{k}-\mathcal{L}, t)>1-\varepsilon$ and $U(x_{k}-\mathcal{L}, t)<\varepsilon$, for all $k\geq N$.
It shows that the set
\begin{eqnarray*}
\big\{k\in \mathbb{N}: T(x_{k}-\mathcal{L}, t)\leq 1-\varepsilon \quad \textit{or} \quad U(x_{k}-\mathcal{L}, t)\geq\varepsilon \big\}
\end{eqnarray*}
has at most finitely many terms. Then,
\begin{eqnarray*}
\lim_{n}\frac{1}{n} \bigg |\{k\leq n: T(\widehat{F}x_{k}-\mathcal{L}, t)\leq 1-\varepsilon \quad \textit{or} \quad U(\widehat{F}x_{k}-\mathcal{L}, t)\geq\varepsilon\} \bigg|=0,
\end{eqnarray*}
because of every finite subset of the natural numbers has density zero. This completes the proof.
\end{proof}
The converse of this theorem need not be true. Example \ref{exmp:1} shows that the converse of
Theorem \ref{theo:1} is not valid.
\begin{thm}\label{theo:2}
Let $(X,T,U,\bigstar,\blacktriangle)$ be an IFNS. $d(\widehat{F})_{IFN}-\lim x_{k}=\mathcal{L}$ if and only if
there exists a increasing index sequence $J=\{j_{1},j_{2},\cdots\}\subseteq \mathbb{N}$, when $d(J)=1$ and $(T,U)-\lim_{n\rightarrow\infty} x_{j_{n}}=\mathcal{L}$.
\end{thm}
\begin{proof}
Assume that $d(\widehat{F})_{IFN}-\lim x_{k}=\mathcal{L}$. For any $t>0$ and $u=1,2,\ldots$
\begin{eqnarray*}
M_{T,U}(u,t)=\bigg \{k\in \mathbb{N}: T(\widehat{F}x_{k}-\mathcal{L}, t)> 1-\frac{1}{u} \quad \textit{or} \quad U(\widehat{F}x_{k}-\mathcal{L}, t)< \frac{1}{u} \bigg\}.
\end{eqnarray*}
and
\begin{eqnarray*}
P_{T,U}(u,t)=\bigg \{k\in \mathbb{N}: T(\widehat{F}x_{k}-\mathcal{L}, t)\leq 1-\frac{1}{u} \quad \textit{or} \quad U(\widehat{F}x_{k}-\mathcal{L}, t)\geq \frac{1}{u} \bigg\}.
\end{eqnarray*}
Then, $d(P_{T,U}(u,t))=0$, since $d(\widehat{F})_{IFN}-\lim x_{k}=\mathcal{L}$. Further, for $t>0$ and $u=1,2,\ldots$,
\begin{eqnarray*}
M_{T,U}(u,t)\supset M_{T,U}(u+1,t).
\end{eqnarray*}
Since $d(\widehat{F})_{IFN}-\lim x_{k}=\mathcal{L}$, it is clear that, for $t>0$ and $u=1,2,\ldots$,
\begin{eqnarray}\label{equ:2}
d(M_{T,U}(u,t))=1.
\end{eqnarray}
Now, we will show that $k\in M_{T,U}(u,t)$, $x_{k}\rightarrow \mathcal{L}(S(\widehat{F})_{IFN})$.
Suppose that for some $k\in M_{T,U}(u,t)$, $x_{k}\nrightarrow \mathcal{L}(S(\widehat{F})_{IFN})$.
Therefore there is $\mu >0$ and a positive integer $N$ such that for all $k\geq N$,
$T(\widehat{F}x_{k}-\mathcal{L}, t)\leq 1-\mu$ or $U(\widehat{F}x_{k}-\mathcal{L}, t)\geq \mu$.
Let $T(\widehat{F}x_{k}-\mathcal{L}, t)> 1-\mu$ or $U(\widehat{F}x_{k}-\mathcal{L}, t)< \mu$, for all $k\geq N$.
Then, $d(\{k\in \mathbb{N}: T(\widehat{F}x_{k}-\mathcal{L}, t)> 1-\mu \quad \textit{and} \quad U(\widehat{F}x_{k}-\mathcal{L}, t)< \mu\})=0$.
Since $\mu>\frac{1}{u}$, we have $d(M_{T,U}(u,t))=0$, which contradicts (\ref{equ:2}). Therefore
$k\in M_{T,U}(u,t)$, $x_{k}\rightarrow \mathcal{L}(S(\widehat{F})_{IFN})$.\\
Suppose that there exists a subset $J=\{j_{1},j_{2},\cdots\}\subseteq \mathbb{N}$ such that $d(J)=1$
and $(T,U)-\lim_{n\rightarrow \infty}x_{j_{n}}=\mathcal{L}$, i.e. there exists $N\in \mathbb{N}$ such that
for every $\mu>0$ and $t>0$, $T(\widehat{F}x_{k}-\mathcal{L}, t)> 1-\mu$ or $U(\widehat{F}x_{k}-\mathcal{L}, t)< \mu$.
Now,
\begin{eqnarray*}
K_{T,U}(\mu, t):=\big \{k\in \mathbb{N}: T(\widehat{F}x_{k}-\mathcal{L}, t)\leq 1-\mu \quad \textit{or} \quad U(\widehat{F}x_{k}-\mathcal{L}, t)\geq \mu \big\}\\
\subseteq \mathbb{N} - \{j_{N+1},j_{N+2},\ldots\}.
\end{eqnarray*}
Therefore $d(M_{T,U}(\mu, t))\leq 1-1=0$. Hence $d(\widehat{F})_{IFN}-\lim x_{k}=\mathcal{L}$.
\end{proof}
\subsection{Fibonacci Statistical Complete IFNS}
\begin{defin}\label{def:2}
Take an IFNS $(X,T,U,\bigstar,\blacktriangle)$. A sequence $x=(x_{k})$ is said to be Fibonacci statistical Cauchy with respect to IFN $(T,U)$ (briefly, $FSCa-IFN$),
if for every $\varepsilon>0$ and $t>0$, there exists $N=N(\varepsilon)$ such that
\begin{eqnarray*}
K_{\varepsilon}(\widehat{F}):=\{k\leq n: T(\widehat{F}x_{k}-\widehat{F}x_{N}, t)\leq 1-\varepsilon \quad \textit{or} \quad U(\widehat{F}x_{k}-\widehat{F}x_{N}, t)\geq\varepsilon\}
\end{eqnarray*}
has natural density zero, i.e., $d(K_{\varepsilon}(\widehat{F}))=0$. That is,
\begin{eqnarray*}
\lim_{n}\frac{1}{n} \bigg |\{k\leq n: T(\widehat{F}x_{k}-\widehat{F}x_{N}, t)\leq 1-\varepsilon \quad \textit{or} \quad U(\widehat{F}x_{k}-\widehat{F}x_{N}, t)\geq\varepsilon\} \bigg|=0.
\end{eqnarray*}
\end{defin}
\begin{thm}\label{theo:3}
Let $(X,T,U,\bigstar,\blacktriangle)$ be an IFNS. If a sequence $x=(x_{k})$ is $FSC-IFN$, then it is
$FSCa-IFN$.
\end{thm}
\begin{proof}
Let $d(\widehat{F})_{IFN}-\lim x_{k}=\mathcal{L}$. For a given $\varepsilon>0$, choose $u>0$
such that $(1-\varepsilon)\bigstar(1-\varepsilon)>1-u$ and $\varepsilon\blacktriangle\varepsilon<u$.
Then, for $t>0$, we have,
\begin{eqnarray}\label{equ:3}
d\left(A(\varepsilon, t)\right)=d(\{k\in \mathbb{N}: T(\widehat{F}x_{k}-\mathcal{L}, t/2))\leq 1-\varepsilon
\quad \textit{or} \quad U(\widehat{F}x_{k}-\mathcal{L}, t/2)\geq \varepsilon\})=0
\end{eqnarray}
which implies that
\begin{eqnarray*}
d\left(A^{C}(\varepsilon, t)\right)=d(\{k\in \mathbb{N}: T(\widehat{F}x_{k}-\mathcal{L}, t/2))> 1-\varepsilon
\quad \textit{and} \quad U(\widehat{F}x_{k}-\mathcal{L}, t/2)< \varepsilon\})=1.
\end{eqnarray*}
Let $q\in A^{C}(\varepsilon, t)$. Then
\begin{eqnarray*}
T(\widehat{F}x_{q}-\mathcal{L}, t)> 1-\varepsilon \quad \textit{and} \quad U(\widehat{F}x_{q}-\mathcal{L}, t)< \varepsilon.
\end{eqnarray*}
Now, let
\begin{eqnarray*}
B(\varepsilon, t)=\left\{ k\in \mathbb{N}:T(\widehat{F}x_{k}-\widehat{F}x_{q}, t)\leq 1-u
\quad \textit{or} \quad U(\widehat{F}x_{k}-\widehat{F}x_{q}, t)\geq u\right\}.
\end{eqnarray*}
We need to show that $B(\varepsilon, t)\subset A(\varepsilon, t)$. Let $k\in B(\varepsilon, t)/A(\varepsilon, t)$.
Then we have
\begin{eqnarray*}
T(\widehat{F}x_{k}-\widehat{F}x_{q}, t)\leq 1-u \quad \textit{and} \quad T(\widehat{F}x_{k}-\mathcal{L}, t/2)>1-\varepsilon,
\end{eqnarray*}
in particular $T(\widehat{F}x_{q}-\mathcal{L}, t/2)>1-\varepsilon$. Then
\begin{eqnarray*}
1-u \geq T(\widehat{F}x_{k}-\widehat{F}x_{q}, t)\geq T(\widehat{F}x_{k}-\mathcal{L}, t/2)\bigstar T(\widehat{F}x_{q}-\mathcal{L}, t/2)>(1-\varepsilon)\bigstar(1-\varepsilon)>1-u,
\end{eqnarray*}
which is not possible. On the other hand,
\begin{eqnarray*}
U(\widehat{F}x_{k}-\widehat{F}x_{q}, t)\geq u \quad \textit{and} \quad U(\widehat{F}x_{k}-\mathcal{L}, t/2)<\varepsilon,
\end{eqnarray*}
in particular $U(\widehat{F}x_{q}-\mathcal{L}, t/2)<\varepsilon$. Then
\begin{eqnarray*}
u\leq U(\widehat{F}x_{k}-\widehat{F}x_{q}, t)\leq U(\widehat{F}x_{k}-\mathcal{L}, t/2)\bigstar U(\widehat{F}x_{q}-\mathcal{L}, t/2)< \varepsilon\blacktriangle\varepsilon<u,
\end{eqnarray*}
which is not possible. Hence $B(\varepsilon, t)\subset A(\varepsilon, t)$. Therefore, by \ref{equ:3} $d(B(\varepsilon,t))=0$. Hence,
$x$ is $FSCa-IFN$.
\end{proof}
\begin{defin}(\cite{Saad})
An IFNS $(X,T,U,\bigstar,\blacktriangle)$ is said to be complete if every Cauchy sequence
is convergent in $(X,T,U,\bigstar,\blacktriangle)$.
\end{defin}
\begin{defin}
An IFNS $(X,T,U,\bigstar,\blacktriangle)$ is said to be statistically $(FSC-IFN)$ complete is every
statistically ($FSC-IFN$, respectively) Cauchy sequence with respect to intuitionistic fuzzy norm $(T,U)$ is statistically
($FSC-IFN$, respecitvely) convergent with respect to to intuitionistic fuzzy norm $(T,U)$.
\end{defin}
\begin{thm}\label{theo:4}
An IFNS $(X,T,U,\bigstar,\blacktriangle)$ is $(FSC-IFN)-$complete.
\end{thm}
\begin{proof}
Let $x=(x_{k})$ be $(FSC-IFN)-$Cauchy but not $(FSC-IFN)-$convergent. For a given $\varepsilon>0$
and $t>0$, choose $u>0$ such that $(1-\varepsilon)\bigstar(1-\varepsilon)>1-u$ and $\varepsilon\blacktriangle\varepsilon<u$.
Now
\begin{eqnarray*}
T(\widehat{F}x_{k}-\widehat{F}x_{N}, t)\geq T(\widehat{F}x_{k}-\mathcal{L}, t/2)\bigstar T(\widehat{F}x_{N}-\mathcal{L}, t/2)>(1-\varepsilon)\bigstar(1-\varepsilon)>1-u
\end{eqnarray*}
and
\begin{eqnarray*}
U(\widehat{F}x_{k}-\widehat{F}x_{N}, t)\leq U(\widehat{F}x_{k}-\mathcal{L}, t/2)\blacktriangle U(\widehat{F}x_{N}-\mathcal{L}, t/2)<\varepsilon \blacktriangle \varepsilon<u,
\end{eqnarray*}
since $x$ is not $(FSC-IFN)-$convergent. Therefore $d(E^{C}(\varepsilon, t))=0$, where
\begin{eqnarray*}
E(\varepsilon,t)=\{k\in \mathbb{N}: U_{x_{k}-x_{N}}(\varepsilon)\leq 1-r\}
\end{eqnarray*}
and so $d(E(\varepsilon,t))=1$, which is a contradiction, since $x$ was $(FSC-IFN)-$Cauchy. So that $x$ must be
$(FSC-IFN)-$convergent. Hence every IFNS is $(FSC-IFN)-$complete.
\end{proof}
We can give following theorem from Theorems \ref{theo:2}, \ref{theo:3}, \ref{theo:4}.
\begin{thm}
Let $(X,T,U,\bigstar,\blacktriangle)$ be an IFNS. Then, for any sequence $x=(x_{k})\in X$,
the following conditions are equivalent:\\
\begin{itemize}
\item [i.] $x$ is $(FSC-IFN)-$convergent.\\
\item[ii.] $x$ is $(FSC-IFN)-$Cauchy.\\
\item[iii.] IFNS $(X,T,U,\bigstar,\blacktriangle)$ is $(FSC-IFN)-$complete.\\
\item[iv.] There exists an increasing index sequence $J=(j_{n})$ of natural numbers such that
$d(K)=1$ and the subsequence $(x_{k_{n}})$ is a $(FSC-IFN)-$Cauchy.
\end{itemize}
\end{thm}
\section{Conclusion}
In this paper, the well-known concept of statistical convergence of real numbers combine
with the definition of Fibonacci numbers is studied in intuitionistic fuzzy normed spaces.
Firstly, the definition of Fibonacci statistical convergence with respect to intuitionistic fuzzy
normed space(FSC-IFN) is given and some properties of FSC-IFN are investigated. After,
the definitions of Fibonacci statistical Cauchy with respect to intuitionistic fuzzy
normed space(FSCa-IFN) and FSC-IFN completeness are given. It shows that an IFNS is (FSC-IFN)-complete.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,026 |
Q: If the sections of a function are $\mathscr{L}^2$, would the function be jointly $\mathscr{L}^2$? Let $(\varOmega,\mathcal{A},\mu)$ and $(\varXi,\mathcal{B},\nu)$ be $\sigma$-finite measure spaces, and $f\colon\varOmega\times\varXi\to\mathbb{R}$ be $\big(\mathcal{A}\otimes\mathcal{B}\big)$-$\mathcal{B}(\mathbb{R})$-measurable. Suppose also that the sections of $f$ are $\mathscr{L}^2$; i.e.,
$$f(\cdot,\xi)\in\mathscr{L}^2(\varOmega,\mu),~\text{for $\nu$-a.e.}~\xi,~\text{and}~f(\omega,\cdot)\in\mathscr{L}^2(\varXi,\nu),~\text{for $\mu$-a.e.}~\omega.$$
Then, is it true that $f\in\mathscr{L}^2(\varOmega\times\varXi,\mu\otimes\nu)$? If not, what restrictions do we need?
A: The answer is no. You cannot conclude that $f\in\mathscr{L}^2(\varOmega\times\varXi,\mu\otimes\nu)$, see this essentially the same question.
One sufficient condition for the claim to hold though is that $f$ be a tensor product: $f(\omega, \xi) = f_1(\omega)f_2(\xi)$. Since the $\mathscr{L}^p$ play nice with tensor products:
$$ \|f_1 \otimes f_2\|_{\mathscr{L}^p(\varOmega\times\varXi,\mu\otimes\nu)} = \|f_1\|_{\mathscr{L}^p(\varOmega,\mu)} \|f_2\|_{\mathscr{L}^p(\varXi,\nu)}.$$
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,112 |
\section{Introduction and summary}
\label{one}
Solving the {\it vacuum Einstein equation} globally, or in other words:
finding a (pseudo-)Riemannian {\it Ricci-flat} metric along a
differentiable manifold i.e., a metric $g$ which satisfies the second order
non-linear partial differential equation
\[{\rm Ric}_g=0\]
over a differentiable manifold $M$, is a century-old evergreen problem
dwelling in the heart of modern differential geometry \cite{bes} and
theoretical physics \cite{wald}. The problem of solvability naturally
splits up into {\it local} and {\it global} solvability and also depends on
the signature of the metric. Let us first consider the {\it Riemannian} case.
Thanks to its non-linearity, solvability of the Ricci-flatness condition is
already locally problematic; nevertheless exploiting its elliptic character
various kinds of local existence results (e.g. \cite{det,gas}) are known
at least for the related but in some sense complementary equation
${\rm Ric}_g=\Lambda g$ (whose solutions are called {\it Einstein
metrics}) with $\Lambda\not=0$. As one expects, in these local
existence problems the dimension of $M$ plays no special role. However
dimensionality issues characteristically enter the
game when one considers global solvability. Finding global
solutions in four dimensions i.e., when $\dim_\R M=4$ is particularly
important from a physical point of view and quite interestingly, from the
mathematical viewpoint, precisely this is the dimension where global
solvability is the most subtle. As it is well-known, if $\dim_\R M<4$ the
vacuum Einstein equation reduces to a full flatness condition on the metric
hence it admits only a ``few'' global solutions; on the contrary, if
$\dim_\R M>4$ there are no (known) obstructions for global solvability hence
apparently there are ``too many'' global solutions. A delicate balance is
achieved if $\dim_\R M=4$: for instance by a classical result \cite{hit0,tho}
we know that a Riemannian Einstein (hence in particular a Ricci-flat) metric
on a compact $M$ can exist only if
its Euler characteristic $\chi (M)$ and signature $\sigma (M)$ obey the
inequality $\chi (M)\geqq\frac{3}{2}\vert\sigma (M)\vert$. This implies
for example that the connected sum of at least five copies
of complex projective spaces cannot be Einstein. However even in four
dimensions if $M$ is non-compact there are no (known) obstruction against
the solvability of the vacuum Einstein equation.
Restricting attention to the four dimensional case from now on, the main
result of the paper---strongly motivated by \cite{che-nem} and considered
as a substantially improved and technically revised and greatly simplified
version of our earlier efforts \cite{ete1, ete2}---can be formulated in the
{\it Riemannian} setting as
\begin{theorem} Let $M$ be a connected, simply connected, oriented, closed
(i.e., compact without boundary), smooth $4$-manifold which is spin (or
equivalently having even intersection form) and take the punctured space
$M^\times:=M\setminus\{{\rm point}\}$. If $X^\times$ is a smooth
$4$-manifold {\it homeomorphic} but not necessarily diffeomorphic to
$M^\times$ such that it carries a smooth structure {\it \`a la} Gompf then
$X^\times$ can be equipped with a complete Ricci-flat Riemannian metric.
\label{fotetel1}
\end{theorem}
\noindent As an extreme but important application of Theorem
\ref{fotetel1} we obtain
\begin{corollary}
Let $R^4$ be the largest member of the Gomp--Taubes radial family of large
exotic $\R^4$'s. Then $R^4$ carries a complete Ricci-flat Riemannian metric.
\label{kovetkezmeny1}
\end{corollary}
\noindent The proof of Theorem \ref{fotetel1} is based on a successive
application of basic results by Gompf \cite{gom1,gom2,gom3}, Penrose
\cite{pen1}, Taubes \cite{tau1,tau2} and Uhlenbeck \cite{uhl} on exotic
smooth structures, twistor theory, self-dual spaces and singularity
removal in Yang--Mills fields, respectively. The idea in the spirit of
twistor theory is to convert the real-analytic problem of solving ${\rm
Ric}_g=0$ on the real $4$-space $M^\times$ into a complex-analytic problem
on a complex $3$-space $Z$ associated to $M^\times$. This is in principle
simple and works as follows. Take an arbitrary oriented and closed smooth
$4$-manifold $M$. In the first step, following Taubes, by connected
summing sufficiently (but finitely) many complex projective spaces to $M$,
we construct a space $\overline{X}_M\cong M\#\C P^2\#\dots\#\C P^2$ which
(with respect to its induced orientation) carries a self-dual metric
$\overline{\gamma}$. Then, in the second step following Penrose, we
observe that $\overline{Z}$, the {\it twistor space} of
$(\overline{X}_M,\overline{\gamma})$, is a complex $3$-manifold. Let
$X_M\subset\overline{X}_M$ be the open space obtained by deleting
carefully choosen closed subsets, homeomorphic to a projective line, from
every $\C P^2$ factor of $\overline{X}_M$ and put
$\gamma:=\overline{\gamma}\vert_{X_M}$ and $Z:=\overline{Z}\vert_{X_M}$.
Making use of $Z$ we can conformally rescale the incomplete self-dual
space $(X_M,\gamma )$ to a complete Ricci-flat one $(X_M,g)$ if $M$ is
connected, simply connected and spin. In the third and last step, by the
aid of Uhlenbeck's singularity removal theorem, we remove (or fill in) the
extra $\C P^2\setminus\C P^1=\R^4$'s along $X_M$ to obtain an open smooth
space $X^\times$ which is homeomorphic to the punctured space $M^\times$
however is not necessarily diffeomorphic to it by results of Gompf. The
result is a connected, simply connected, open, complete, Ricci-flat
Riemannian spin $4$-manifold $(X^\times, g)$.
By the conformal invariance of self-duality this technical condition in
fact survives the whole procedure. Taking into account that a complete
Ricci-flat and self-dual metric on a simply connected $4$-manifold always
induces a hyper--K\"ahler structure on it \cite[Chapter 13]{bes}, we can
re-formulate the result of our construction as
\begin{theorem}
The complete Ricci-flat metric of Theorem \ref{fotetel1} on
$X^\times$ with its fixed orientation is self-dual as well consequently
$X^\times$ carries a hyper-K\"ahler structure, too.
\label{fotetel2}
\end{theorem}
\noindent In this way we obtain
\begin{corollary}
The space $R^4$ of Corollary \ref{kovetkezmeny1} carries a hyper-K\"ahler
structure.
\label{kovetkezmeny2}
\end{corollary}
Next let consider the analogous problem in {\it Lorentzian} signature.
Surely the most productive---and both mathematically and physically
extraordinary important---presently known method to find global solutions of
the Lorentzian vacuum Einstein equation is based on the {\it initial
value formulation} \cite[Chapter 10]{wald} which exploits the hyperbolic
character of the Ricci-flatness condition (far from being complete, just for
recent results cf. eg. \cite{car-sch,cor,ise-maz-pol, maz-pol-uhl}) and the
references therein). In this approach one starts with an appropriate
initial value data set, subject to the (simpler) vacuum constraint equations,
on a {\it three} dimensional manifold $\Sigma$ and obtains solutions of the
original vacuum Einstein equation on a {\it four} dimensional manifold $M$
which is {\it always diffeomorphic} to the smooth product $\Sigma\times\R$
(with the unique smooth structures on the factors) \cite{ber-san, che-nem}.
It is worth calling attention that even if the initial value formulation
produces an abundance of solutions from the viewpoint of
{\it global analysis} and {\it theoretical physics}, it is quite inproductive
from the viewpoint of (low dimensional) {\it differential topology}.
To illustrate this, suppose we want to find spaces $(M,g)$ satisfying
${\rm Ric}_g=0$ over a connected and simply connected, open four-manifold $M$.
If the initial value formulation is applied, and if in this case
we impose a further condition that the corresponding Cauchy surface $\Sigma$ be
compact, then by the Poincar\'e--Hamilton--Perelman theorem $\Sigma$ must
be homeomorphic hence diffeomorphic to the three-sphere $S^3$ consequently $M$
is uniquely fixed to be $S^3\times\R$ up to diffeomorphisms (but of course
this unique $M$ still can carry lot of non-isometric Ricci-flat metrics $g$).
However in sharp contrast to this differentio-topological
rigidity of initial value formulation in the simply connected setting we
obtain
\begin{theorem} Consider the space $X^\times$ as in Theorem \ref{fotetel1}
or equivalently, in Theorem \ref{fotetel2}. Then there exists a smooth
Lorentzian metric $g_L$ on $X^\times$ such that $(X^\times, g_L)$ is, a
perhaps incomplete, Ricci-flat Lorentzian $4$-manifold.
\label{lorentztetel}
\end{theorem}
\noindent To make a comparison, let us indicate the ``size'' of the set of
non-isometric solutions to the Lorentzian vacuum Einstein equation
provided by Theorem \ref{lorentztetel}.
By the fundamental classification result of Freedman \cite{fre},
connected and simply connected, oriented, closed topological four-manifolds
are topologically classified by their intersection form
$Q_M: H_2(M;\Z)\times H_2(M;\Z)\rightarrow H_4(M;\Z)\cong\Z$. By
assumptions in our theorems here, $M$ is spin and smooth hence $Q_M$ must be
even hence indefinite taking into account the other fundamental result in
this field by Donaldson \cite{don}. Therefore if $\sigma (M)$
denotes the signature and $b_2(M)$ the second Betti number of $M$ then its
intersection form looks like
\[Q_M=\frac{1}{8}\sigma (M)\left(\begin{smallmatrix}
2 & 0 &-1 & 0 & 0 & 0 & 0 & 0\\
0 & 2 & 0 &-1 & 0 & 0 & 0 & 0\\
-1& 0 & 2 &-1 & 0 & 0 & 0 & 0\\
0 &-1 &-1 & 2 &-1 & 0 & 0 & 0\\
0 & 0 & 0 &-1 & 2 &-1 & 0 & 0\\
0 & 0 & 0 & 0 &-1 & 2 &-1 & 0\\
0 & 0 & 0 & 0 & 0 &-1 & 2 &-1\\
0 & 0 & 0 & 0 & 0 & 0 &-1 & 2
\end{smallmatrix}\right)\oplus
\frac{1}{2}\left(b_2(M)-\sigma (M)\right)
\left(\begin{smallmatrix}0 &1\\1&0\end{smallmatrix}\right)\]
hence the simplest examples for $M$ are $S^4$, $S^2\times S^2$, the $K3$
surfaces, etc. Consequently, unlike the initial value formulation in the
simply connected case, the set of solutions provided by Theorem
\ref{lorentztetel} already contains many topologically different underlying
spaces. But even more, most of these compact $M$'s
themselves carry countable infinitely many different smooth structures, too.
Finally, passing to the non-compact punctured spaces $M^\times$, the
cardinality of the inequivalent smooth structures $X^\times$ underlying
the Ricci-flat solutions in Theorem \ref{fotetel1} already reaches that of the
continuum in ZFC set theory by a theorem of Gompf \cite{gom3} (recalled as
Theorem \ref{gompftetel} here). Therefore the set of
non-isometric Ricci-flat spaces exhibited in Theorem \ref{lorentztetel} is
huge indeed. These solutions are not accessible within the initial value
formulation because they, compared to the time evolution of typical initial
data sets, are ``too long'' in an appropriate sense
(cf. \cite[Section 5]{ete2}). Informally speaking, the vacuum Einstein
equation is more tractable in Riemannian signature because of the elliptic
nature of the Ricci-flatness condition in contrast to its
hyperbolic character in Lorentzian signature: meanwhile solutions in
Riemannian signature are protected by elliptic regularity hence ``extend
well'', the regularity profiles of Lorentzian initial data sets quickly get
destroyed during their hyperbolic time evolution.
The paper is organized as follows. Section \ref{two} contains the
collection of the required background material with rapid discussions of
these results from our viewpoint. Sections \ref{three} and
\ref{four}, respectively, contain the construction in the simpler non-exoting
setting i.e., when $X^\times$ is not only homeomorphic but even diffeomorphic
to $M^\times\subset M$ and then in the exotic setting with appropriate
modifications. In Section \ref{five} we prove Theorem \ref{lorentztetel}
by simply recalling \cite[Lemma 4.2]{ete2}. Finally
in Section \ref{six} a physical interpretation of these Lorentzian Ricci-flat
solutions is discussed. This interpretation places these solutions into
the realm of the {\it strong cosmic censorship conjecture} and gravitational
{\it topology change} processes.
\section{Background material}
\label{two}
Let us begin with recalling all the powerful results, techniques, tools
to be used during the construction of Riemannian Ricci-flat metrics
in this paper.
{\it Construction of self-dual spaces}.
It is well-known that the Fubini--Study metric on the complex projective
space $\C P^2$ with orientation inherited from its complex structure is
self-dual (or half-conformally flat) i.e., the anti-self-dual part $W^-$ of its
Weyl tensor vanishes; consequently the oppositely oriented complex projective
plane $(\C P^2)^{op}$ is anti-self-dual. A powerful generalization of
this latter classical fact is Taubes' construction of an abundance of
anti-self-dual $4$-manifolds; firstly we exhibit his result but now in an
orientation-reversed form:
\begin{theorem} {\rm (Taubes \cite[Theorem 1.1]{tau2})} Let $M$ be a
connected, compact, oriented smooth
$4$-manifold. Let $\C P^2$ denote the complex projective plane with its
usual orientation and let $\#$ denote the operation of taking the connected
sum of manifolds. Then there exists a natural number $k_M\geqq 0$ such
that for all $k\geqq k_M$ the modified compact manifold
\[M\#\underbrace{\C P^2\#\dots\#\C P^2}_{k}\]
admits a self-dual Riemannian metric. $\Diamond$
\label{taubestetel}
\end{theorem}
\noindent Let us roughly summarize how Taubes' construction works
(\cite[Section 2]{tau2}). Take an arbitrary connected,
oriented, closed Riemannian $4$-manifold $(M,g)$ and consider the
density of the anti-self-dual part of the Weyl curvature of $g$
i.e., the pointwise norm $\vert W^-_g\vert_g$ along $M$. If it happens that
somewhere around a point $p\in M$ this curvature density is large then take a
$\C P^2$ with its usual Fubini--Study metric having zero anti-self-dual Weyl
tensor and glue it to a ball $B^4_\varepsilon (p)\subset M$ of sufficiently
small radius about the point. The result is a Riemannian metric on $M\#\C P^2$
having a bit smaller anti-self-dual Weyl tensor: this is because while
$W^-_g$ is unchanged on $M\setminus \overline{B}^4_\varepsilon (p)$ it
is killed in the bulk of $B^4_\varepsilon (p)$ except possibly along an annulus
where $g$ and the Fubini--Study metric of $\C P^2$ have been glued together.
Repeating this procedure, without doing connected summing on any previously
added $\C P^2$ factor, probably very (but surely finitely) many times one
comes up with a metric $\overline{\gamma}'$ on
$\overline{X}_M:=M\#\C P^2\#\dots\#\C P^2$ (regarding the specific notation
cf. Sections \ref{three} and \ref{four} below) whose
$W^-_{\overline{\gamma}'}$ is already arbitrarily small in e.g. the original
$L^2$-norm. Then, by the aid of the implicit
function theorem, one perturbs this metric with a small symmetric tensor
field $h$ on $\overline{X}_M$ into a new one
$\overline{\gamma}:=\overline{\gamma}'+h$ which is already self-dual i.e.
having $W^-_{\overline{\gamma}}=0$ along $\overline{X}_M$. For further
rather technical details we refer to \cite[Section 2]{tau2}.
{\it Tools from twistor theory}. Let us now
recall Penrose' twistor method \cite{pen1} to solve the Riemannian vacuum
Einstein equation (for a very clear introduction cf. \cite[Chapter 13]{bes},
\cite{hit1,hit2}). Consider the bundle of unit-length anti-self-dual $2$-forms
$S(\wedge^-\overline{X}_M)$ over a compact oriented space
$(\overline{X}_M,\overline{\gamma})$ which is self-dual with respect to its
orientation. Since in $4$ dimensions $\wedge^-\overline{X}_M$
is a rank $3$ real vector bundle over $\overline{X}_M$, its
unit-sphere bundle $S(\wedge^-\overline{X}_M)$ is the total space of
a smooth $S^2$-fibration
$\overline{p}:S(\wedge^-\overline{X}_M)\rightarrow\overline{X}_M$.
The Levi--Civita connection of the metric $\overline{\gamma}$ on
$\overline{X}_M$ can be used to furnish the real $6$-manifold
$S(\wedge^-\overline{X}_M)$ with a canonical almost complex structure; the
fundamental observation of twistor theory is that this almost complex
structure is integrable because $\overline{\gamma}$ is self-dual
\cite[Theorem 13.46]{bes}. The resulting complex $3$-manifold
$\overline{Z}\cong S(\wedge^-\overline{X}_M)$ is called the
{\it twistor space} while the smooth fibration $\overline{p}:\overline{Z}
\rightarrow\overline{X}_M$ the {\it twistor fibration} of
$(\overline{X}_M,\overline{\gamma})$. The most
important property of a twistor space of this kind is that its twistor
fibers $\overline{p}^{-1}(x)\subset\overline{Z}$ for all
$x\in\overline{X}_M$ fit into
a locally complete complex $4$-paremeter family $\overline{X}_M^\C$ of
projective lines $Y\subset\overline{Z}$ each with normal bundle $H\oplus H$,
with $H$ being the dual of the tautological line bundle over $Y\cong\C P^1$.
Moreover, there exists a real structure $\overline{\tau}
:\overline{Z}\rightarrow \overline{Z}$ defined by
taking the antipodal maps along the twistor fibers
$Y_x:=\overline{p}^{-1}(x)\subset\overline{Z}$ for all
$x\in\overline{X}_M\subset\overline{X}_M^\C$ which are
therefore called {\it real lines} among all the lines $Y$ in $\overline{Z}$.
In other words, $\overline{Z}$ is fibered exactly by the real lines $Y_x$ for
all $x\in\overline{X}_M$. Hence the real $4$ dimensional self-dual geometry
has been encoded into a $3$ dimensional complex analytic structure in the
sense that one can recover $(\overline{X}_M,\overline{\gamma})$ just from
$\overline{Z}$ up to conformal equivalence.
One can go further and raise the question how to recover precisely
$(\overline{X}_M,\overline{\gamma})$ itself from its conformal
class, or more interestingly to us: how to get a Ricci-flat Riemannian
$4$-manifold $(X_M,g)$ i.e., a solution of the (self-dual)
Riemannian vacuum Einstein equation. Not surprisingly, to get the
latter stronger structure, one has to specify further data on the twistor
space. A fundamental result of twistor theory \cite{pen1} is that a
solution of the $4$ dimensional (self-dual) Riemannian vacuum Einstein
equation is equivalent to the following set of data (cf.
\cite{hit1,hit2}):
\begin{itemize}
\item[$*$] A complex $3$-manifold $Z$, the total space of
a holomorphic fibration $\pi:Z\rightarrow\C P^1$;
\item[$*$] A complex $4$-paremeter family of holomorphically
embedded complex projective lines $Y\subset Z$, each with normal
bundle $NY\cong H\oplus H$ (here $H$ is the dual of the tautological
bundle i.e., the unique holomorphic line bundle on $Y\cong\C P^1$ with
$\langle c_1(H), [Y]\rangle =1$);
\item[$*$] A non-vanishing holomorphic section $s$ of
$K_Z\otimes\pi^*H^4$ (here $K_Z$ is the canonical bundle of $Z$);
\item[$*$] A real structure $\tau :Z\rightarrow Z$ such that it
coincides with the antipodal map $u\mapsto -\overline{u}^{-1}$ of $\C P^1$
upon restricting to the $\tau$-invariant elements $Y\subset Z$
(called real lines) from the family; moreover these real lines are both
sections of $\pi$ and comprise a fibration of $Z$.
\end{itemize}
\noindent These data allow one to construct a Ricci-flat
and self-dual (i.e., the Ricci and the anti-self-dual Weyl part of
the curvature tensor vanishes) solution $(X_M,g)$ of the
{\it Riemannian} Einstein's vacuum equation with vanishing cosmological
constant as follows. The holomorphic lines $Y\subset Z$ form a locally
complete family and fit together into a complex $4$-manifold
$X_M^\C$. This space carries a natural complex conformal structure
by declaring two nearby points $y_1,y_2\in X_M^\C$ to be
null-separated if the corresponding lines intersect i.e.,
$Y_1\cap Y_2\not=\emptyset$ in $Z$. Infinitesimally this intersection
condition means that on every tangent space $T_yX_M^\C\cong\C^4$ a null cone is
specified: using the identification $T_yX_M^\C\cong H^0(Y_y;\co(NY_y))
\cong H^0(\C P^1; \co (H\oplus H))$ given by $(a,b,c,d)\mapsto (au+b,cu+d)$,
a tangent vector at $y$ is null if and only if its corresponding holomorphic
sections have a common zero i.e. $ad-bc=0$ which is an equation of a cone.
Restricting the complex conformal structure to the real lines singled out
by $\tau$ and parameterized by an embedded real
$4$-manifold $X_M\subset X_M^\C$ we obtain the real
conformal class $[g]$ of a Riemannian metric on $X_M$.
The isomorphism $s:\pi^*H^{-4}\cong K_Z$ is essentially uniquely
fixed by its compatibility with $\tau$ and gives rise to a volume form on
$X_M$ this way fixing the metric $g$ in the conformal class. Given the
conformal class, it is already meaningful to talk about the
unit-sphere bundle of anti-self-dual $2$-forms $S(\wedge^-X_M)$ over $X_M$
with its induced orientation from the twistor space and $Z$
can be identified with the total space of $S(\wedge^-X_M)$. This way we
obtain a smooth twistor fibration $p:Z\rightarrow X_M$ whose fibers are
$\C P^1$'s hence $\pi :Z\rightarrow\C P^1$ can be regarded as a parallel
translation along this bundle over $X_M$ with respect to a
flat connection which is nothing but the induced connection of $g$ on
$\wedge^-X_M$, cf. \cite{leb}. Knowing the decomposition of the Riemannian
curvature into irreducible components over an oriented Riemannian $4$-manifold
\cite{sin-tho}, this partial flatness of $S(\wedge^-X_M)$ implies that $g$ is
Ricci-flat and self-dual. Finally note that, compared with the bare twistor
space $\overline{Z}$ of a self-dual manifold
$(\overline{X}_M,\overline{\gamma})$ above, the essential new
requirement for constructing a self-dual {\it Ricci-flat} space $(X_M,g)$
is the existence of a holomorphic map $\pi$ from the
twistor space $Z$ into $\C P^1$ which is compatible with the real
structure in the above sense. We conclude our summary of the
non-linear graviton construction by referring to \cite{hit1, hit2, hug-tod,
leb, war-wel} or \cite[Chapter 13]{bes} for further details.
{\it Removable singularities in Yang--Mills fields}. Next let
us refresh Uhlenbeck's by-now classical singularity removal theorem:
\begin{theorem}{\rm (Uhlenbeck \cite[Theorem 4.1]{uhl} or
\cite[Appendix D]{fre-uhl})}
$*$\:Local version: Let $\nabla^\times$ be a solution of the
${\rm SU}(2)$ Yang--Mills equations in the open punctured $4$-ball
$B^4\setminus\{0\}$ with $\Vert F_{\nabla^\times}\Vert^2_{L^2(B^4)}
=\int_{B^4}\vert F_{\nabla^\times}\vert^2<+\infty$ i.e., having finite energy
and $\nabla^\times =\dd +A^\times$ such that
$A^\times\in L^2_1(B^4\setminus\{0\})$. Then $\nabla^\times$ is $L^2_2$
gauge equivalent to a connection $\nabla$ which extends smoothly across the
singularity to a smooth connection.
$*$\: Global version: Let $(M,g)$ be a connected, closed, oriented
Riemannian $4$-manifold and let $\nabla^\times$ be an
${\rm SU}(2)$ connection on a vector bundle $E^\times$ over
$M^\times:=M\setminus\{{\rm point}\}$ which is a solution of the
${\rm SU}(2)$ Yang--Mills equations and satisfies $\Vert F_{\nabla^\times}
\Vert_{L^2 (M)}<+\infty$ and there is an $L^2_{1,loc}$ gauge for
$\nabla^\times$ around the puncturing of $M$. Then $\nabla^\times$ is
$L^2_{2,loc}$ gauge equivalent to a connection $\nabla$ on a vector
bundle $E$ over $M$ i.e., to a connection which extends across the pointlike
singularity of the original connection. $\Diamond$
\label{uhlenbecktetel}
\end{theorem}
\noindent Locally finite energy i.e., $F_{\nabla^\times}\in L^2_{loc}$
does not guarantee the continuity of the gauge transformation hence the
topology of $E^\times$ can change i.e., $E^\times$ and $E$ can be different;
however if $F_{\nabla^\times}\in L^{2+\varepsilon}_{loc}$ holds then we can
assume continuity. Nevertheless the isomorphism class of $E$ is fully
determined by the smooth connection $\nabla$ via the numerical value of the
integral
$-\infty <\frac{1}{8\pi^2}\int_M{\rm tr} (F_\nabla\wedge F_\nabla )<+\infty$,
the second Chern number of the bundle $E$.
{\it Exotic stuff}. Finally we evoke some results which provide
us with a sort of summary of what is so special in four dimensions (i.e.,
absent in any other ones). First we recall a special class of large exotic
(or fake) $\R^4$'s whose properties we will need here are summarized
as follows:
\begin{theorem} {\rm (Gompf--Taubes, cf. \cite[Lemma 9.4.2, Addendum 9.4.4
and Theorem 9.4.10]{gom-sti})} There exists a pair $(R^4,K)$ consisting of a
differentiable $4$-manifold $R^4$ homeomorphic but not diffeomorphic to the
standard $\R^4$ and a compact oriented smooth $4$-manifold $K\subset R^4$
such that
\begin{itemize}
\item[$*$] $R^4$ cannot be smoothly embedded into the standard
$\R^4$ i.e., $R^4\not\subseteqq\R^4$ but it can be smoothly embedded as a
proper open subset into the complex projective plane i.e.,
$R^4\subsetneqq\C P^2$;
\item[$*$] Take a homeomorphism $f:\R^4\rightarrow R^4$, let
$0\in B^4_t\subset\R^4$ be the standard open $4$-ball of radius $t\in\R_+$
centered at the origin and put $R^4_t:=f(B^4_t)$ and
$R^4_{+\infty}:=R^4$. Then
\[\left\{ R^4_t\:\left\vert\:\mbox{$r\leqq t\leqq +\infty$ such that
$0<r<+\infty$ satisfies $K\subset R^4_r$}\right.\right\}\]
is an uncountable family of nondiffeomorphic exotic $\R^4$'s none of them
admitting a smooth embedding into $\R^4$ i.e., $R^4_t\not\subseteqq\R^4$
for all $r\leqq t\leqq +\infty$. $\Diamond$
\end{itemize}
\label{egzotikusnagycsalad}
\end{theorem}
\noindent
The fact that any member $R^4_t$ in this family is not diffeomorphic to
$\R^4$ implies the counterintuitive phenomenon that
$R^4_t\not\cong W\times\R$ i.e., $R^4_t$ does not admit any {\it smooth}
splitting into a $3$-manifold $W$ and $\R$ (with their unique smooth
structures) in spite of the fact that such {\it continuous} splittings
obviously exist. Indeed, from the contractibility of $R^4_t$ we can see that
$W$ must be a contractible open $3$-manifold (a so-called
{\it Whitehead continuum} \cite{whi}) however, by an early result of
McMillen \cite{mcm} spaces of this kind always satisfy $W\times\R\cong\R^4$
i.e., their product with a line is always diffeomorphic to the standard
$\R^4$. We will call this property of (any) exotic $\R^4$ occasionally below
as ``creased''.
From Theorem \ref{egzotikusnagycsalad} we deduce that for all
$r<t<+\infty$ there is a sequence of smooth proper embeddings
\[R^4_r\subsetneqq R^4_t\subsetneqq R^4_{+\infty}=R^4\subsetneqq\C P^2\]
which are very wild in the following sense. The complement $\C P^2
\setminus R^4$ of the largest member $R^4$ of this family is homeomorphic
to $S^2$ regarded as an only ``continuously embedded projective line'' in
$\C P^2$; therefore we shall denote this complement as $S^2:=\C
P^2\setminus R^4\subset\C P^2$ in order to distinguish it from the
ordinary projective lines $\C P^1=\C P^2\setminus\R^4 \subset\C P^2$. If
$\C P^2=\R^4\cup\C P^1=\C^2\cup\C P^1$ is any holomorphic decomposition
then $R^4\cap\C P^1\not=\emptyset$ (because otherwise $R^4\subseteqq\R^4$
would hold, a contradiction) as well as $S^2\cap \C P^1\not=\emptyset$
(because otherwise $H_2(R^4;\Z )\cong\Z$ would hold since $\C P^1\subset\C
P^2$ represents a generator of $H_2(\C P^2;\Z)\cong\Z$, a contradiction
again). Hence an ordinary projective line $\C P^1$ is always intersected by
both $R^4$ and $S^2$ such that $S^2\cap\C P^1$ in the worst situation is a
Cantor set. These demonstrate that the members of the large radial family
``live somewhere between'' $\R^4$ and its complex projective closure $\C P^2$.
However a more precise identification or location of them is a difficult task
because these large exotic $\R^4$'s---although being honest differentiable
$4$-manifolds---are very transcendental objects, cf. \cite[p. 366]{gom-sti}:
They require infinitely many $3$-handles in any handle decomposition (like any
other known large exotic $\R^4$) and there is presently\footnote{More precisely
in the year 1999, cf. \cite{gom-sti}.} no clue as how one might draw
explicit handle diagrams of them (even after removing their $3$-handles).
We note that the structure of small exotic $\R^4$'s i.e., which admit
smooth embeddings into $\R^4$, is better understood and is quite different, cf.
\cite[Chapter 9]{gom-sti}. For instance, unlike the large case,
in their corresponding radial family certain (but surely not more than
countably many) members are diffeomorphic such that the non-diffeomorphic
small exotic $\R^4$'s are parameterized not by an interval but a Cantor
set only, cf. \cite[Theorem 9.4.12 and its proof]{gom-sti}.
Our last ingredient is the following {\it m\'enagerie} result of Gompf.
\begin{theorem} {\rm (Gompf \cite[Theorem 2.1]{gom3})} Let $X$ be a
connected (possibly non-compact, possibly with boundary) topological
$4$-manifold and let $X^\times:=X\setminus\{{\rm point}\}$ be
the punctured manifold with a single point removed. Then the non-compact
space $X^\times$ admits noncountably many (with the cardinality of the
continuum in ZFC set theory) pairwise non-diffeomorphic smooth
structures. $\Diamond$
\label{gompftetel}
\end{theorem}
\noindent If for instance $M$ is a connected compact smooth
$4$-manifold then Gompf's construction simply goes as follows: Take $R^4$
from Theorem \ref{egzotikusnagycsalad} and put
\[X^\times:=M\#R^4\]
which is a smooth $4$-manifold obviously homeomorphic
to the punctured $M^\times$. More generally, the
construction $X^\times_t:=M^\times\# R^4_t$ produces uncountably many
mutually non-diffeomorphic smooth structures on
the unique topological $4$-manifold underlying $X^\times_t$.
\section{The construction}
\label{three}
\noindent In this section, which serves as a warming-up for the next
one, we construct solutions of the vacuum Einstein equation on punctured
$4$-manifolds carrying their standard smooth structure. We begin with
an application of Theorem \ref{taubestetel} as follows.
\begin{lemma}
Out of any connected, closed (i.e., compact without boundary) oriented
smooth $4$-manifold $M$ one can construct a connected, open (i.e.,
non-compact without boundary) oriented smooth Riemannian $4$-manifold
$(X_M,\gamma)$ which is self-dual but incomplete in general.
\label{kezdolemma}
\end{lemma}
\noindent {\it Proof.} Pick any connected, oriented, closed, smooth
$4$-manifold $M$. Referring to Theorem \ref{taubestetel} let
$k:=\max (1,k_M)\in\N$ be a positive integer, put
\[\overline{X}_M:=M\#\underbrace{\C P^2\#\dots\#\C P^2}_{k}\]
and let $\overline{\gamma}$ be a self-dual metric on it. Then
$(\overline{X}_M,\overline{\gamma})$ is a compact self-dual
manifold. Pick a $\C P^2$ factor within $\overline{X}_M$ and any
(holomorphically embedded) projective line $\C P^1\subset\C P^2$ in that
factor (avoiding its attaching point to $M$); then
$\C P^1=\C P^2\setminus\C^2\cong\C P^2\setminus\R^4$ i.e., the line arises as
the complement of an $\R^4$ in $\C P^2$. Let $K\subset\R^4$ be any connected
compact subset and put
\begin{equation}
X_M:=M\#\underbrace{(\C P^2\setminus\C P^1)\#\dots\#(\C
P^2\setminus\C P^1)}_{k-1}\#_K(\C P^2\setminus\C P^1)
\cong M\#\underbrace{\R^4\#\dots\#\R^4}_{k-1}\#_K\R^4\cong
M^\times\#\underbrace{\R^4\#\dots\#\R^4}_{k-1}
\label{ujsokasag}
\end{equation}
where the operation $\#_K$ means that the attaching point $y_0\in\R^4$
taken to glue a distinguished $\R^4$ with the rest
$M\#\underbrace{\R^4\#\dots\#\R^4}_{k-1}$
satisfies $y_0\in K\subset\R^4$ and $M^\times:=
M\#_K\R^4\cong M\setminus\{{\rm point}\}$ is the punctured space with its
inherited smooth structure from the smooth embedding $M^\times\subset M$.
The result is a connected, open $4$-manifold $X_M$ (see Figure 1).
\vspace{1in}
\centerline{
\begin{tikzpicture}[scale=0.7]
\node at (-0.8,0) {$M$};
\draw [thick] plot [tension=0.8,smooth cycle] coordinates {(0,0)
(2,2) (5,0) (2,-2)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(0.5,0.4) (1.5,0.2)
(2.5,0.4)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(0.8,0.3) (1.5,0.5)
(2.2,0.3)};
\node at (7.2,0) {$X_M$};
\draw [thick] plot [tension=0.8,smooth] coordinates { (8.5,0.2) (9,-0.2)
(9.5,0.2)};
\draw [thick] plot [tension=0.8,smooth] coordinates { (8.7,0) (9,0.1)
(9.3,0)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(8.5,1) (9,1.3) (10,1) (11,0.7) (12,0.9) (12.5,1.3)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(13.1,1.3) (13.4,0.6) (14,0.3)};
\draw plot [tension=0.8,smooth] coordinates
{(12.5,1.3) (12.8,1.4) (13.1,1.3)};
\draw plot [tension=0.8,smooth] coordinates
{(12.5,1.3) (12.8,1.2) (13.1,1.3)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(8.5,-1) (9,-1.3) (10,-1) (11,-0.7) (12,-0.9) (12.5,-1.3)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(13.1,-1.3) (13.4,-0.6) (14,-0.3)};
\draw plot [tension=0.8,smooth] coordinates
{(12.5,-1.3) (12.8,-1.4) (13.1,-1.3)};
\draw plot [tension=0.8,smooth] coordinates
{(12.5,-1.3) (12.8,-1.2) (13.1,-1.3)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(8.5,1) (8,0)
(8.5,-1)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(14,0.3) (15,0.2)
(16,1)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(14,-0.3) (15,-0.2)
(16,-1)};
\draw [gray] plot [tension=0.8,smooth] coordinates {(16,1) (15.8,0) (16,-1)};
\draw [gray] plot [tension=0.8,smooth] coordinates {(16,1) (16.2,0) (16,-1)};
\end{tikzpicture}}
\centerline{Figure 1. Construction of $X_M$ out of $M$. The gray
ellipse represents a distinguished end}
\centerline{diffeomorphic to the complement of a connected compact subset
$K$ in $\R^4$.}
\vspace{0.3in}
\noindent From the proper smooth embedding $X_M\subsetneqq\overline{X}_M$
there exists a restricted self-dual Riemannian metric
$\gamma:=\overline{\gamma}\vert_{X_M}$ on $X_M$ which is however in
general non-complete. $\Diamond$
\vspace{0.1in}
\noindent Next we improve the incomplete
self-dual space $(X_M,\gamma)$ of Lemma \ref{kezdolemma} to a complete
Ricci-flat space $(X_M,g)$ by conformally rescaling $\gamma$
with a suitable positive smooth function $\varphi :X_M\rightarrow\R_+$ which
is a ``multi-task'' function in the sense that it kills both the scalar
curvature and the traceless Ricci tensor of $\gamma$ moreover blows up
sufficiently fast along the $\R^4$ ends of $X_M$ to render the
rescaled metric $g$ complete. Two classical examples serve as a
motivation.
\vspace{0.1in}
\noindent {\it First example}.
First, let $S^4\subset\R^5$ be the standard $4$-sphere equipped with the
standard orientation and round metric inherited from the embedding.
Put $\overline{X}_M:=S^4$ and $\overline{\gamma}:=$the standard
round metric. It is well-known that $(\overline{X}_M,\overline{\gamma})=
(S^4,\overline{\gamma})$ is self-dual and Einstein with non-zero
cosmological constant i.e., not Ricci-flat. Put
$X_M:=S^4\setminus\{\infty\}=\R^4$; then
$\gamma=\overline{\gamma}\vert_{\R^4}$ thus $(X_M,\gamma )=(\R^4,\gamma )$
is an incomplete self-dual space. But setting $\varphi
:\R^4\rightarrow\R_+$ to be $\varphi (x):=(1+\vert x\vert^2)^{-1}$,
then $g:=\varphi^{-2}\gamma$
is nothing but the standard flat metric $\eta$ on $\R^4$ which is of
course complete and Ricci-flat. Hence $(X_M,g)=(\R^4, \eta)$,
the conformal rescaling of $(X_M,\gamma )=(\R^4,\gamma)$, is the
desired complete Ricci-flat space in this simple case. Note that
$(\R^4,\eta )$ is a trivial hyper-K\"ahler space, too.
It is worth working out here how the corresponding holomorphic map
$\pi :Z\rightarrow \C P^1$ over the corresponding twistor space
arises in this situation (see the summary of twistor theory in Section
\ref{two}). Consider the smooth twistor fibration
$\overline{p}:\overline{Z}\rightarrow S^4$. Since $\R^4\subset S^4$ writing
$Z:=\overline{Z}\vert_{\R^4}$ and $p:=\overline{p}\vert_{\R^4}$ we obtain a
restricted fibration $p:Z\rightarrow\R^4$. Unlike the full twistor fibration
over $S^4$, the restricted one is topologically trivial i.e. $Z$ is
homeomorphic to $\R^4\times S^2$ since $\R^4$ is contractible; consequently
$Z$ admits a continuous trivialization over $\R^4$. This is a necessary
topological condition for the existence of the map $\pi$.
Since $\R^4$ with its flat metric is conformally
equivalent to $S^4\setminus\{\infty\}$ with its round metric, $Z$
arises by deleting the twistor line over $\infty\in S^4$ from $\overline{Z}$.
However it is well-known that the twistor space $\overline{Z}$ of the round
$S^4$ is $\C P^3$ consequently the twistor space $Z$ of the flat $\R^4$ is
simply $\C P^3\setminus\C P^1$. More explicitly,
take a homogeneous coordinate system $[z_0:z_1:z_2:z_3]$ on $\C P^3$ and
remove the line $z_0=z_1=0$ from $\C P^3$ to get $Z$. We wish to define
a map $\pi :Z\rightarrow\C P^1$ such that its target space is a twistor
i.e. a real line in $Z$. Any line in $\C P^3\setminus\C P^1$ can be
written as $[z_0:z_1:az_1+bz_0:cz_1+dz_0]$ with $[z_0:z_1]\in\C P^1$ and
$a,b,c,d\in\C$ being some parameters. Note that the case of $a=b=c=d=0$ is
meaningful and $[z_0:z_1:0:0]$ is simply the distinguished line
$[z_0:z_1]$ in $\C P^3\setminus\C P^1$. Thus
\begin{equation}
\mbox{The lines in $Z$}=\{[z_0:z_1:az_1+bz_0:cz_1+dz_0]\:\vert\:
\mbox{$[z_0:z_1]\in\C P^1$ and $a,b,c,d\in\C$}\}\:\:.
\label{H+H}
\end{equation}
The real structure on $\overline{Z}$ is defined by demanding the fibers
of $\overline{p}:\overline{Z}\rightarrow S^4$ to be invariant. Under
$\overline{Z}\cong\C P^3$ it comes from the identification $\C^4\cong\HH^2$
and has the form $[z_0:z_1:z_2:z_3]\mapsto
[\overline{z}_1:-\overline{z}_0:\overline{z}_3:-\overline{z}_2]$. It is
compatible with the antipodal map $[z_0:z_1]\mapsto
[\overline{z}_1:-\overline{z}_0]$ and restricts to a real structure
$\tau:Z\rightarrow Z$. It then follows that the corresponding real lines
have the shape $[z_0:z_1:az_1+\overline{c}z_0:cz_1-\overline{a}z_0]$.
Consequently the twistor fibration $p:Z\rightarrow\R^4$ looks like
$[z_0:z_1:az_1+\overline{c}z_0:cz_1-\overline{a}z_0]\mapsto (a,c)
\in\C^2\cong\R^4$ and in particular the distinguished line is real and can
be identified with the twistor line $p^{-1}(0)$ over the origin. Since every
point $z\in Z$ contained in exactly one real line let us define $\pi
:Z\rightarrow p^{-1}(0)$ by the canonical projection $\pi
([z_0:z_1:az_1+\overline{c}z_0:cz_1-\overline{a}z_0]):=[z_0:z_1]$.
Upon introducing the projective coordinate
$u:=\frac{cz_1-\overline{a}z_0}{az_1+\overline{c}z_0}$ if $(a,c)\not=(0,0)$ or
$u:=\frac{z_1}{z_0}$ if $(a,c)=(0,0)$ along the twistor lines in the
domain of $\pi$ the map looks like
\begin{equation}
\pi (u)=\left\{\begin{array}{ll}\frac{\overline{c}u+\overline{a}}{-au+c}
& \mbox{if $(a,c)\not=(0,0)$}\\
u & \mbox{if $(a,c)=(0,0)$}
\end{array}\right.
\label{alappi}
\end{equation}
which is an obviously holomorphic map since it arises by holomorphic
deformations of $p^{-1}(0)$ within $Z$ moreover it is the identity on
$p^{-1}(0)$. What we only have to check is that $\pi$ is compatible with
the real structure. This means that we have to demonstrate that all real
lines $p^{-1}(x)\subset Z$ are sections of $\pi :Z\rightarrow p^{-1}(0)$
or in other words that $\pi\vert_{p^{-1}(x)}: p^{-1}(x)\rightarrow p^{-1}(0)$
is a holomorphic bijection of $\C P^1$ for every $x\in\R^4$. Assume that
this is not true. Since $\pi\vert_{p^{-1}(x)}$ has the form (\ref{alappi})
we can normalize its coefficients such that $\vert c\vert^2+\vert
a\vert^2=1$. However the assumption implies that this rational function is
constant in $u$ yielding $\vert c\vert^2+\vert a\vert^2=0$, a contradiction.
\vspace{0.1in}
\noindent {\it Second example}. This time put $\overline{X}_M:=\C P^2$ and
$\overline{\gamma}:=$Fubini--Study metric. It is well-known that
$(\overline{X}_M,\overline{\gamma})=(\C P^2,
\overline{\gamma})$ is self-dual and Einstein with non-zero cosmological
constant i.e., not Ricci-flat. Now let $X_M:=\C P^2\setminus\C P^1=\R^4$;
then $\gamma=\overline{\gamma}\vert_{\R^4}$ and $(X_M,\gamma )=(\R^4,\gamma )$
is an incomplete self-dual space.
If $0\not=(z_0,z_1,z_2)\in\C^3$ and $[z_0:z_1:z_2]\in\C P^2$ then take
the projective line $\C P^1\subset\C P^2$ defined by $z_0=0$. Introducing
$w_i=\frac{z_i}{z_0}$ ($i=1,2)$ and $w=(w_1,w_2)\in\C^2=\R^4$, on the
complementum $\C P^2\setminus\C P^1$ the restricted Fubini--Study metric
$\gamma$ looks like
\[\gamma_{ij}(w)=(1+\vert w\vert^2)^{-1}\delta_{ij}-
(1+\vert w\vert^2)^{-2}\overline{w}_iw_j\]
and along this local part it already possesses a K\"ahler potential
$K(w)=\log (1+\vert w\vert^2)$.
This time define $\varphi :\R^4\rightarrow \R_+$ as $\varphi (w):=
{\rm e}^{-\frac{3}{4}K(w)}=(1+\vert w\vert^2)^{-\frac{3}{4}}$ which is a
non-holomorphic function and consider the conformally rescaled (real) metric
$g:=\varphi^{-2}\gamma$. One can check that this is a complete
Ricci-flat metric on $\R^4$. Hence $(X_M,g)=(\R^4,g)$, the conformal
rescaling of $(X_M,\gamma )=(\R^4,\gamma )$ is a complete Ricci-flat space.
It is already not flat but note again that nevertheless $g$ indudes a (not
asymptotically flat in any sense) hyper-K\"ahler structure on $\R^4$
because $g$ is a complete, self-dual, Ricci-flat metric on the simply
connected space $\R^4$.
Again, the corresponding twistor-theoretic map $\pi$ arises as follows.
Consider the smooth twistor fibration $\overline{p}:\overline{Z}
\rightarrow\C P^2$. Since $\R^4\subset\C P^2$, writing
$Z:=\overline{Z}\vert_{\R^4}$ and $p:=\overline{p}\vert_{\R^4}$
we obtain a restricted fibration $p:Z\rightarrow\R^4$.
Unlike the full twistor fibration over $\C P^2$, this restricted one is
topologically trivial i.e., $Z$ is homeomorphic to $\R^4\times S^2$
since $\R^4$ is contractible; consequently $Z$ admits a continuous
trivialization over $\R^4$. This is a necessary topological condition for
the existence of the map $\pi$. It is known that $\overline{Z}
\cong P(T\C P^2)$ i.e., the twistor space of the complex projective space can
be identified with its projective holomorphic tangent bundle. Consequently
$\overline{Z}$ admits a very classical description namely
can be identified with the flag manifold $F_{12}(\C ^3)$ consisting of pairs
$(L,P)$ where $0\in L\subset\C^3$ is a
line (i.e., a point $p\in\C P^2$) and $0\in L\subset P\subset\C^3$ is a
plane containing the line (i.e., a line $p\in\ell\subset\C P^2$ containing
the point). Then in the twistor fibration
$\overline{p}:\overline{Z}\rightarrow\C P^2$ of the complex projective space
$(L,P)\in F_{12}(\C ^3)$ is sent into the point $x\in\C P^2$
provided by the line $X:=L^\perp\cap P\subset\C ^3$ where $L^\perp$ is the
plane perpendicular to the line $L$ in $\C^3$ with respect to the standard
Hermitian scalar product. This is a smooth but not holomorphic fibration
over $\C P^2$ with $\C P^1$'s as fibers since $\overline{p}^{-1}(x)=
\{ (L,P)\:\vert\:L\subset X^\perp\:,\:X\subset P\}=\{(p,\ell )\:\vert\:
x^\perp\cap\ell, x\in\ell\}$ i.e., it consists of
all lines $\ell\subset\C P^2$ through $x\in\C P^2$ (a copy of $\C P^1$)
and a distinguished point $p$ on each given by its intersection with the line
$x^\perp\subset\C P^2$ given by $X^\perp\subset\C^3$.
Consider now the restricted twistor fibration $p:Z\rightarrow\R^4$. Fix a
point $x_0\in\C P^2 \setminus x_0^\perp =\R^4$ with target space
$p^{-1}(x_0)\cong\C P^1$ consisting of terminating pairs
$(p_0,\ell_0)\in p^{-1}(x_0)\subset Z$. Take a starting pair $(p,\ell)\in Z$
over a running point $x\in \C P^2\setminus x^\perp_0$.
Our aim is to construct a holomorphic map which associates to
$(p,\ell)$ another pair $(p_0,\ell_0)$. We construct this
$\pi:Z\rightarrow p^{-1}(x_0)$ very simply as follows.
Consider a starting pair $(p,\ell)$ and take its
line component $\ell\subset\C P^2$. This line has a unique
intersecion $p_0:=x_0^\perp\cap\ell$ with the infinitely distant
projective line. Then, given the target space $p^{-1}(x_0)$, define the
projective line component $\ell_0\subset\C P^2$ in the
terminating pair $(p_0,\ell_0)\in p^{-1}(x_0)$ by taking
the unique projective line $\ell_0$ connecting
$p_0$ with $x_0$. In short,
\begin{eqnarray}
\mbox{$\pi((p,\ell)):=
(p_0,\ell_0)$ where}& &
\mbox{$p_0\in\C P^2$ satisfies $p_0:=x^\perp_0\cap\ell$ and}\nonumber\\
& &\mbox{$\ell_0\subset\C P^2$ satisfies that
$\ell_0$ connects $p_0$ with $x_0$ in $\C P^2$}
\label{pi}
\end{eqnarray}
(see Figure 2 for a construction of this map in projective geometry).
\centerline{
\setlength{\unitlength}{1cm}
\begin{picture}(7,5)
\thicklines
\put(1,1){\circle*{0.2}}
\put(1.2,0.8){$x$}
\put(3,3){\circle*{0.2}}
\put(2.8,2.5){$p_0$}
\put(5,1){\circle*{0.2}}
\put(4.4,0.8){$x_0$}
\put(-0.5,-0.5){\line(1,1){4}}
\put(1.3,1.7){$\ell$}
\put(5.5,0.5){\line(-1,1){3}}
\put(4.6,1.7){$\ell_0$}
\put(-1,3){\line(1,0){6}}
\put(1,3.3){$x^\perp_0$}
\put(0,-0.8){\line(0,1){5}}
\put(0,0){\circle*{0.2}}
\put(-0.4,0.1){$p$}
\put(-0.6,2){$x^\perp$}
\put(7,2){$\C P^2$}
\end{picture}
}
\vspace{0.3in}
\centerline{Figure 2. Construction of the map $\pi : Z\rightarrow \C P^1$
satisfying $\pi((p,\ell))=(p_0,\ell_0)$.}
\vspace{0.3in}
\noindent It is a classical observation that this map is
well-defined on $Z$ and holomorphic; in particular it is the identity on the
target space $p^{-1}(x_0)$ i.e., $\pi((p_0,\ell_0))=(p_0,\ell_0)$.
This globally defined map admits a local description which looks very similar
to the {\it First example}. Given the target point $x_0\in\C
P^2\setminus x_0^\perp\cong\R^4$, its twistor line can be identified
with the infinitely distant line $x^\perp_0\subset\C P^2$ or
equivalently, $x^\perp_0\subset Z$. Likewise, if $x\in\C P^2\setminus
x_0^\perp\cong\R^4$ is a nearby point then its twistor line is
$x^\perp\subset\C P^2$ or equivalently, $x^\perp\subset Z$. In this
picture the map (\ref{pi}) can be described simply as follows:
if $x\in\ell\subset\C P^2$ is a line then $\pi (\ell\cap x^\perp )=
\ell\cap x^\perp_0$ as $\ell$ runs over all possibilities. Pick
homogeneous coordinates $[z_0:z_1:z_2]$ on $\C P^2$ such that
$x_0:=[1:0:0]$ hence $x_0^\perp =\{[0:v_1:v_2]\vert [v_1:v_2]\in\C P^1\}$.
Likewise, if $x=[1:z_1:z_2]$ is the nearby point then
$x^\perp = \{[-\overline{z}_1w_1-\overline{z}_2w_2:w_1:w_2]\vert [w_1:w_2]\in\C
P^1\}$. The affine part of the line $\ell$ connecting $[1:z_1:z_2]$ and
$[0:v_1:v_2]$ is $\{[t:v_1+(z_1-v_1)t: v_2+(z_2-v_2)t]\:\vert\:t\in\C\}$
hence by solving the equation $[t:v_1+(z_1-v_1)t: v_2+(z_2-v_2)t]=
[-\overline{z}_1w_1-\overline{z}_2w_2:w_1:w_2]$
for $[w_1:w_2]$ and upon introducing the projective coordinate
$u:=\frac{w^1}{w^2}$ along $x^\perp\cong \C P^1$ the map (\ref{pi}) takes
the shape
\[\pi (u)=\frac{(1+\vert z_1\vert^2)u-z_1\overline{z}_2}
{-\overline{z}_1z_2u+(1+\vert z_2\vert^2)}\]
hence looks like (\ref{alappi}) indeed.
\begin{remark}\rm It follows from the description (\ref{H+H}) of its
holomorphic lines that the twistor space $Z$ of the flat $\R^4$ can be
globally holomorphically identified with the total space of the bundle
$H\oplus H$ over the distinguished projective line $\C P^1$ parameterized
with $[z_0:z_1]$ in (\ref{H+H}) and the map (\ref{alappi})
is nothing but the projection $\pi :H\oplus H\rightarrow\C P^1$. The point is
that this picture on the twistor space continues to hold true in the generic
case at least locally. Consider a
general twistor space $Z$ with its twistor fibration $p:Z\rightarrow X_M$.
Take $x\in X_M$ and let $Np^{-1}(x)$ be the normal bundle of the twistor
line $p^{-1}(x)\subset Z$. We know (see the summary of twistor theory in
Section \ref{two}) that the holomorphy type of the normal bundle is fixed in
advance and is a very special bundle: it is positive hence admits holomorphic
sections such that they parameterize a locally complete family of projective
lines $Y\subset Z$ which are small holomorphic
deformations of $Y_x=p^{-1}(x)$ inside $Z$ (cf. e.g. \cite[Sections III.1 and
III.2]{gri}) including therefore all nearby real lines as well.
Thus there exist small open neighbourhoods $U_x\subset X_M$ of $x$
and $V_x\subset Np^{-1}(x)$ of the zero section with an injection
$\Psi_x: p^{-1}(U_x)\rightarrow V_x$ that is, $\Psi_x$ maps
injectively the twistor fibers over $U_x$ into the space of holomorphic
sections of $V_x$ such that this map is onto an appropriately defined
subspace of real sections. More explicitly, we know that the normal bundle is
always isomorphic to $H\oplus H$ consequently all small holomorphic
deformations of a given twistor line within $Z$ can be parameterized by
$(a,b,c,d)\in\C^4\cong H^0(\C P^1;\co (H\oplus H))$ such that the twistor
lines satisfy a reality condition implying $ad-bc\not=0$ (because the real
lines never intersect), exactly like in the {\it First example}.
\end{remark}
\noindent We can return now to the much more
general situation set up in Lemma \ref{kezdolemma}; motiveted by
the examples, instead of finding conformal rescalings
$\varphi :X_M\rightarrow\R_+$ directly, we are going to use Penrose'
non-linear graviton construction (i.e., twistor theory \cite{pen1})
to find their holomorphic counterparts $\pi :Z\rightarrow\C P^1$. Consider
the compact self-dual space $(\overline{X}_M,\overline{\gamma})$ from Lemma
\ref{kezdolemma}, take its twistor fibration $\overline{p}:
\overline{Z}\rightarrow\overline{X}_M$ and let $p:Z\rightarrow X_M$
be its restriction induced by the smooth embedding $X_M\subsetneqq
\overline{X}_M$ i.e., $Z:=\overline{Z}\vert_{X_M}$ and
$p:=\overline{p}\vert_{X_M}$. Then $Z$ is a non-compact
complex $3$-manifold already obviously possessing all the required twistor
data except the existence of a holomorphic mapping $\pi :Z\rightarrow\C P^1$.
\begin{lemma} Consider the connected, open, oriented, incomplete,
self-dual space $(X_M,\gamma)$ as in Lemma \ref{kezdolemma}
with its twistor fibration $p:Z\rightarrow X_M$ constructed above.
If $\pi_1(M)=1$ and $M$ is spin (or equivalently, having even
intersection form) then there exists a holomorphic mapping
$\pi :Z\rightarrow\C P^1$.
\label{pilemma}
\end{lemma}
\noindent {\it Proof.} Let $x_0\in X_M$ be a fixed point.
Our aim is to construct a holomorphic map
\begin{equation}
\pi:\:\:Z\longrightarrow p^{-1}(x_0)\cong\C P^1
\label{celfuggveny}
\end{equation}
that we carry out by analytic continuation.
First, put $\pi\vert_{p^{-1}(x_0)}:={\rm Id}_{p^{-1}(x_0)}$. Secondly,
suppose that in $x\in X_M$ the map is already defined i.e. there exists
$\pi\vert_{p^{-1}(x)}: p^{-1}(x)\rightarrow p^{-1}(x_0)$ which is
compatible with the real structure on $Z$ hence is a
holomorphic bijection between the twistor fibers in question or in other
words is a holomorphic bijection of $\C P^1$. Consider a sufficiently small
open neighbourhood $U_x\subset X_M$ of $x$ such that $p^{-1}(U_x)\subset Z$ can
be holomorphically modeled within the neighbourhood $V_x$ of the zero
section of $Np^{-1}(x)$, the normal bundle of the twistor line
$p^{-1}(x)$. Define $\rho_x: p^{-1}(U_x)\rightarrow p^{-1}(x)$ to be the
restriction of the projection $\pi :Np^{-1}(x)\rightarrow p^{-1}(x)$ onto
the image of the twistor lines of $p^{-1}(U_x)$ within $Np^{-1}(x)$.
That is, given a point $z\in p^{-1}(U_x)$ there exists a unique real
line passing through it and $\rho_x(z)\in p^{-1}(x)$ simply arises
by the projection of this line onto the central twistor line $p^{-1}(x)$.
This local map is clearly holomorphic because it stems from holomorphic
deformations of $p^{-1}(x)$ inside $Z$ provided by its locally complete
family of lines.\footnote{For a comparison with the general theory
\cite[Proposition 1.3]{gri} we remark here that although the Griffiths
obstruction groups $H^1( p^{-1}(x); \co ((\pi\vert_{p^{-1}(x)})^*Tp^{-1}(x_0)
\otimes S^kN^*p^{-1}(x)))$ against the extendibility of
$\pi\vert_{p^{-1}(x)}:p^{-1}(x)\rightarrow p^{-1}(x_0)$ to the $k^{\rm th}$
formal neighbourhoud of $p^{-1}(x)\subset Z$ are non-trivial for $k\geqq 4$,
the above construction (or the explicit {\it Second example}) shows that
the corresponding obstruction classes $\omega(\pi_{k-1})$ themselves are
nevertheless trivial. This essentially follows from Kodaira's
integrability condition $H^1(p^{-1}(x);\co (Np^{-1}(x)))=\{0\}$, cf.
\cite[Theorem 3.1]{gri}.} Moreover $\rho_x$ is the identity on $p^{-1}(x)$.
What we have to still check that it is compatible with the real
structure on $Z$ i.e. for every $y\in U_x$ the map $\rho_x$ is a
holomorphic bijection between $p^{-1}(y)$ and $p^{-1}(x)$.
Exploiting the isomorphism $Np^{-1}(x)\cong H\oplus H$ (see the summary of
twistor theory in Section \ref{two}) the map $\rho_x:
p^{-1}(U_x)\rightarrow p^{-1}(x)$ can be described by the projection
$\pi :H\oplus H\rightarrow\C P^1$ therefore, upon introducing the projective
coordinate $u$ along $p^{-1}(y)\cong\C P^1$
\[\rho_x(u)=\left\{\begin{array}{ll}\frac{au+b}{cu+d}
& \mbox{if $(a,b,c,d)\not=(0,0,0,0)$}\\
u & \mbox{if $(a,b,c,d)=(0,0,0,0)$}
\end{array}\right.\]
where $(a,b,c,d)\in H^0(\C P^1;\co (H\oplus H))\cong\C^4$ are the
coefficients of a real line hence satisfy an appropriate reality condition.
Fortunately whatever this reality condition is, we surely know that
$ad-bc\not=0$ because real lines never intersect. However this implies that
the map $u\mapsto \frac{au+b}{cu+d}$ is not constant in $u$ that is, $\rho_x$
is indeed a holomorphic bijection between $p^{-1}(y)$ and $p^{-1}(x)$
for all $y\in U_x$ (such that it is the identity on $p^{-1}(x)$) hence
$\rho_x$ is compatible with the real structure on $p^{-1}(U_x)$ as desired.
Therefore let us define the local extension $\pi\vert_{p^{-1}(U_x)}:p^{-1}(U_x)
\rightarrow p^{-1}(x_0)$ by the composition
$\pi\vert_{p^{-1}(U_x)}:=\pi\vert_{p^{-1}(x)}\circ\rho_x$.
By assumption $\pi\vert_{p^{-1}(x)}$ already possesses all the
required properties hence is compatible with the real structure therefore it
is a holomorphic bijection between the twistor lines $p^{-1}(x)$ and
$p^{-1}(x_0)$; consequently, taking a projective coordinate $v$
along $p^{-1}(x)\cong\C P^1$, we know that
$\pi\vert_{p^{-1}(x)}$ also has the form
$v\mapsto\frac{a_0v+b_0}{c_0v+d_0}$ with some
$a_0,b_0,c_0,d_0\in\C$ satisfying $a_0d_0-b_0c_0\not=0$. Composing the maps
above means that we insert $v=\frac{au+b}{cu+d}$ where $u$ is the projective
coordinate along $p^{-1}(y)\cong\C P^1$ as before; thus the local extension
looks like
\[\pi\vert_{p^{-1}(U_x)}(u)=\frac{a_0\frac{au+b}{cu+d} +b_0}
{c_0\frac{au+b}{cu+d}+d_0}=\frac{(a_0a+b_0c)u+(a_0b+b_0d)}
{(c_0a+d_0c)u+(c_0b+d_0d)}\:\:.\]
Since $(a_0a+b_0c)(c_0b+d_0d)-(a_0b+b_0d)(c_0a+d_0c)=
(a_0d_0-b_0c_0)(ad-bc)\not=0$ it readily follows that it
continues to be compatible with the real structure.
Thirdly, since $M$ is connected, simply connected and spin, $Z$ is
connected, simply connected and $p:Z\rightarrow X_M$ is trivial. These make
sure that $\pi$ extends over $Z$ in a consistent way. $\Diamond$
\begin{remark}\rm Note that the reasons for both the local map $\rho_x$
and the non-local one $\pi\vert_{p^{-1}(x)}$ having the same shape (namely
both are fractional linear transformations of $\C P^1$) are quite different.
Nevertheless it makes possible to regard $\pi :Z\rightarrow\C P^1$ as an
action of ${\rm SL}(2;\C )$ on the target projective line $\C P^1$ via
fractional linear transformations which are in turn ${\rm SO}(3)$
rotations on $S^2$ regarded as the unit sphere in the space of
anti-self-dual $2$-forms provided either by the old or the new metric
$\gamma$ or $g$, respectively.
\end{remark}
\noindent It follows that $\pi :Z\rightarrow\C P^1$ i.e., the map
(\ref{celfuggveny}) constructed in Lemma \ref{pilemma} is compatible with the
real structure $\tau :Z\rightarrow Z$ already fixed by the self-dual structure
in Theorem \ref{taubestetel} therefore twistor theory provides us with a
Ricci-flat (and self-dual) Riemannian metric $g$ on $X_M$. We proceed
further and demonstrate that, unlike $(X_M,\gamma)$, the space $(X_M,g)$ is
complete.
\begin{lemma} The four dimensional connected and simply connected, open,
oriented, Ricci-flat Riemannian spin manifold $(X_M,g)$ is complete.
\label{teljeslemma}
\end{lemma}
\noindent {\it Proof}. Since both $\gamma$ and
this Ricci-flat metric $g$ arise from the same complex structure on
the same twistor space $Z$ we know from twistor theory that these metrics are
in fact conformally equivalent. That is, there exists a smooth non-constant
strictly positive function $\varphi :X_M\rightarrow\R_+$ such that
$\varphi^{-2}\gamma= g$. Our strategy to prove completeness
is to follow Gordon \cite{gor} i.e., to demonstrate that an appropriate
real-valued function on $X_M$, in our case
$\log\varphi^{-1}:X_M\rightarrow\R$, is proper (i.e., the preimages of
compact subsets are compact) with bounded
gradient in modulus with respect to $g$ implying the completeness.
Referring to (\ref{ujsokasag}) the open space $X_M$ arises by deleting
one-one projective line from each $\C P^2$ factor, respectively, of
the closed space $\overline{X}_M$. First we observe that
$\varphi^{-1}:X_M\rightarrow\R_+$ is uniformly divergent along these
projective lines. Assume that $\varphi^{-1}$
extends over $\overline{X}_M\supset X_M$ in a uniform continuous manner i.e.
$\overline{\varphi}^{-1}\in C^0(\overline{X}_M)$ exists. A general
principle based on the twistor construction is that the continuous
extendibility of $\varphi^{-1}$ over $U\subseteqq \overline{X}_M$ implies the
extendibility of $\pi$ i.e. the holomorphic map (\ref{celfuggveny}) over
$\overline{p}^{-1}(U)\subseteqq\overline{Z}$ too in a manner which is
compatible with the real structure on $\overline{p}^{-1}(U)$ i.e. this
extension is a trivialization of the real bundle $S(\wedge^-U)$
(see the summary of twistor theory in Section \ref{two}). Therefore by our
assumption the holomorphic map (\ref{celfuggveny}) extends over $\overline{Z}$
as well. However, since $\C P^2$ is not spin
$\overline{X}_M=M\#\C P^2\#\dots\#\C P^2$ cannot be spin, too; consequently
$S(\wedge^-\overline{X}_M)$ underlying the compact twistor space
$\overline{Z}$ of $(\overline{X}_M,\overline{\gamma})$ is
topologically not trivial hence its globally trivializing map
(\ref{celfuggveny}) cannot extend from $X_M$ to $\overline{X}_M$,
a contradiction. Assume that $\varphi^{-1}$ extends over
at least one point of $\overline{X}_M\setminus X_M$ continuously. It yet
follows that we run into a same type of contradiction. Assume now
that $\varphi^{-1}$ extends over at least one point of
$\overline{X}_M\setminus X_M$ in a discontinuous-but-bounded manner. Then we
proceed as follows. The conformal scaling function satisfies with respect to
$\gamma$ the following equations on $X_M$:
\begin{equation}
\left\{\begin{array}{ll}
\Delta_\gamma\varphi^{-1}+\frac{1}{6}\varphi^{-1}{\rm Scal}_\gamma&=0\:\:\:
\mbox{(vanishing of the scalar curvature of $g$ on $X_M$)};\\
&\\
\nabla^2_\gamma\varphi -\frac{1}{4}\left(\Delta_\gamma\varphi\right)
\gamma+\frac{1}{2}\varphi\:{\rm Ric}^0_\gamma&= 0\:\:\:
\mbox{(vanishing of the traceless Ricci tensor of $g$ on $X_M$)}.
\end{array}\right.
\label{skalazas}
\end{equation}
The Ricci tensor ${\rm Ric}_\gamma$ of $\gamma$ extends smoothly over
$\overline{X}_M$ because it is just the restriction of the Ricci tensor of
the self-dual metric $\overline{\gamma}$ on $\overline{X}_M$. Therefore
both its scalar curvature ${\rm Scal}_\gamma$ and traceless Ricci part ${\rm
Ric}^0_\gamma$ extend. Thus from the first equation of
(\ref{skalazas}) we can see that
$\varphi\Delta_\gamma\varphi^{-1}$ extends smoothly over $\overline{X}_M$.
Likewise, adding
the tracial part to the second equation of (\ref{skalazas}) we get
$\varphi^{-1}\nabla^2_\gamma\varphi =-\frac{1}{2}{\rm Ric}_\gamma$ hence we
conclude that the symmetric tensor field
$\varphi^{-1}\nabla^2_\gamma\varphi$ extends
smoothly over $\overline{X}_M$ so its trace
$\varphi^{-1}\Delta_\gamma\varphi$ as well.
Expanding $\Delta_{\overline{\gamma}}(\varphi\varphi^{-1})=0$ gives
$(\Delta_{\overline{\gamma}}\varphi) \varphi^{-1} +2\:\overline{\gamma}
(\dd\varphi\:,\dd\varphi^{-1})+\varphi\Delta_{\overline{\gamma}}
\varphi^{-1}=0$ hence we obtain the pointwise equality
\begin{equation}
\varphi^2\left\vert\dd\varphi^{-1}\right\vert^2_{\overline{\gamma}}=
\frac{1}{2}\left(\varphi\Delta_{\overline{\gamma}}\varphi^{-1}+
\varphi^{-1}\Delta_{\overline{\gamma}}\varphi\right)
\label{azonossag}
\end{equation}
which demonstrates that $\varphi\left\vert\dd\varphi^{-1}\right\vert_{\overline
{\gamma}}$ extends smoothly over $\overline{X}_M$, too. If $\varphi^{-1}$ was
extendible as a discontinuous bounded function over a point of
$\overline{X}_M\setminus X_M$ then its gradient $\dd\varphi^{-1}$ was
divergent in that point; hence from the extendibility of
$\varphi\vert\dd\varphi^{-1}\vert_{\overline{\gamma}}$ we obtain that
$\varphi$ vanishes hence $\varphi^{-1}$ is unbounded in that point, a
contradiction again. We conclude that
$\varphi^{-1}:X_M\rightarrow\R_+$ is {\it uniformly divergent along the
whole complementum} $\overline{X}_M\setminus X_M$ yielding, on the one
hand, that the function $\log\varphi^{-1}:X_M\rightarrow\R$ is proper.
As a byproduct the inverse of $\varphi^{-1}$ is bounded on $X_M$
i.e., $\vert\varphi\vert\leqq c_1$ with a finite constant.
We already know that $\vert\varphi\Delta_{\gamma}
\varphi^{-1}\vert\leqq c_2$ and $\vert\varphi^{-1}
\Delta_{\gamma}\varphi\vert\leqq c_3$ with other
finite constants as well.
Now writing $\varphi\vert\dd\varphi^{-1}\vert_{\gamma}=
\vert\dd (\log\varphi^{-1})\vert_{\gamma}$ and carefully noticing
that $\vert\xi\vert_g=\varphi\vert\xi\vert_\gamma$ on
$1$-forms we can use (\ref{azonossag}) and the estimates above to come up with
\[\vert\dd (\log \varphi^{-1})\vert_g
\leqq c_1\vert\dd (\log \varphi^{-1})\vert_{\gamma}
\leqq c_1\left(\left\vert\varphi\Delta_\gamma\varphi^{-1}\vert
+\vert\varphi^{-1}\Delta_\gamma\varphi\right\vert\right)^{\frac{1}{2}}\leqq
c_1(c_2+c_3)^{\frac{1}{2}}<+\infty\]
and conclude, on the other hand, that $\log\varphi^{-1}:
X_M\rightarrow\R$ has bounded gradient in modulus with respect to $g$.
Therefore, in light of Gordon's theorem \cite{gor}, the Ricci-flat space
$(X_M,g)$ is complete. $\Diamond$
\vspace{0.1in}
\noindent We want to finish the construction by ending up with an
open space with a single end, hence we want to remove the
extra ``non-distinguished'' $\R^4$'s from $X_M$ in its decomposition
(\ref{ujsokasag}) without destroying completeness and Ricci flatness.
\begin{lemma} Consider the space $(X_M,g)$ as in Lemma
\ref{teljeslemma}. Then the orientation and the complete Ricci-flat
metric $g$ on $X_M$ descend to the punctured space $M^\times\subset M$ with
its inherited smooth structure, rendering it a connected and simply connected,
open, oriented, complete, Ricci-flat Riemannian spin $4$-manifold
$(M^\times, g)$.
\label{levagolemma}
\end{lemma}
\noindent {\it Proof}. It is clear from (\ref{ujsokasag})
that $M^\times$ arises from $X_M$ by filling in the ``centers'' of the
finitely many non-distinguished $\R^4$ summands with one-one point,
respectively (see Figure 3).
\vspace{0.4in}
\centerline{
\begin{tikzpicture}[scale=0.7]
\node at (10.2,0) {$M^\times$};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(11,0) (11.1,0.5) (11.5,1) (12.25,1.4) (13.5,1.5) (14.75,1.2) (16,0.2)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(11,0) (11.1,-0.5) (11.5,-1)
(12.25,-1.4) (13.5,-1.5) (14.75,-1.2) (16,-0.2)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(16,0.2) (17,0.2)
(18,1)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(16,-0.2) (17,-0.2)
(18,-1)};
\draw [gray] plot [tension=0.8,smooth] coordinates {(18,1) (18.3,0)
(18,-1)};
\draw [gray] plot [tension=0.8,smooth] coordinates {(18,1) (17.7,0)
(18,-1)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(11.5,0.4) (12.5,0.2)
(13.5,0.4)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(11.8,0.3) (12.5,0.5)
(13.2,0.3)};
\node at (-2.5,0) {$X_M$};
\draw [thick] plot [tension=0.8,smooth] coordinates { (0.5,0.2) (1,-0.2)
(1.5,0.2)};
\draw [thick] plot [tension=0.8,smooth] coordinates { (0.7,0) (1,0.1) (1.3,0)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(0.5,1) (1,1.3) (2,1) (3,0.7) (4,0.9) (4.5,1.3)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(5.1,1.3) (5.4,0.6) (6,0.3)};
\draw plot [tension=0.8,smooth] coordinates
{(4.5,1.3) (4.8,1.4) (5.1,1.3)};
\draw plot [tension=0.8,smooth] coordinates
{(4.5,1.3) (4.8,1.2) (5.1,1.3)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(0.5,-1) (1,-1.3) (2,-1) (3,-0.7) (4,-0.9) (4.5,-1.3)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(5.1,-1.3) (5.4,-0.6) (6,-0.3)};
\draw plot [tension=0.8,smooth] coordinates
{(4.5,-1.3) (4.8,-1.4) (5.1,-1.3)};
\draw plot [tension=0.8,smooth] coordinates
{(4.5,-1.3) (4.8,-1.2) (5.1,-1.3)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(0.5,1) (0,0) (0.5,-1)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(6,0.3) (7,0.2) (8,1)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(6,-0.3) (7,-0.2) (8,-1)};
\draw [gray] plot [tension=0.8,smooth] coordinates {(8,1) (7.8,0) (8,-1)};
\draw [gray] plot [tension=0.8,smooth] coordinates {(8,1) (8.2,0) (8,-1)};
\end{tikzpicture}
}
\vspace{0.1in}
\centerline{Figure 3. Construction of $M^\times$ out of $X_M$ by
filling in the extra $\R^4$'s.}
\vspace{0.3in}
\noindent Given this set-up, our strategy to prove the lemma is as follows:
First apply Uhlenbeck's singularity removal theorem at each $\R^4$ summand to
get rid of the corresponding singularity of the Levi--Civita connection of
$g$---which is certainly an obstacle against the extension of the
metric over the ``center'' of this $\R^4$ summand in the intermediate
manifold---and in this way extend the connection to $M^\times$. Finally
around each former singular point use a geodesic normal coordinate system
adapted to this extended smooth connection on $M^\times$ to conclude that
the metric $g$ on $X_M$
smoothly extends over the singularities, too. If this procedure works then
the result is a smooth complete Ricci-flat metric on $M^\times$. However,
as we shall see shortly, the non-existence of a spin structure on the
original compact $M$ plays the role of an (and the only one) obstruction
against the feasibility of this procedure.
So let us take a fixed $\R^4$ summand in
$X_M=M^\times\#\R^4\#\dots\#\R^4$. Since $X_M$ locally looks like a
punctured $M$ around this summand i.e., a point $p\in M$ removed, we can
{\it diffeomorphically} model $M^\times\#\R^4\#\dots\#\R^4$ around this
$\R^4$ summand by an open punctured ball in some local modeling $\R^4$.
More precisely let $p\in M$ be a point, $p\in U\subset M$ a neighbourhood
containing the point and consider a local coordinate system
$(U,y_1,\dots,y_4)$ centered at
$p$ i.e., satisfying $y_1(p)=0,\dots, y_4(p)=0$. Identifying this local
coordinate system with $(x_1,\dots,x_4)$ about the origin of the
modeling $\R^4$ implies that $p$ is mapped to $0\in\R^4$ having coordinates
$(x_1,\dots,x_4)=(0,\dots,0)$ and our model for the vicinity of
the given $\R^4$ summand in $X_M$ then looks like
\begin{equation}
\left( B^{4\times}_r(0)\:,\: x_1,\dots, x_4\right)
\label{golyo}
\end{equation}
i.e., a coordinatized open punctured ball $B^{4\times}_r(0):=
B^4_r(0)\setminus\{0\}$ about $0\in\R^4$ of (Euclidean) radius $r>0$. (In
this picture the ``infinity'' of the $\R^4$ summand corresponds to the
the center of the ball.) Consider the restricted tangent bundle
$TB^{4\times}_r(0):=TX_M\vert_{B^{4\times}_r(0)}$; using the
restrictions of the orientation on $X_M$ and the metric $g$, we can render
it a real four-rank ${\rm SO}(4)$ vector bundle over the punctured ball
$B^{4\times}_r(0)$. We claim that $TB^{4\times}_r(0)$ in fact can be
reduced to a complex two-rank ${\rm SU}(2)\subset{\rm SO}(4)$ vector bundle
over the annulus. We can see this by exploiting the so far unmentioned
feature of our construction namely that as a ``byproduct''
the space $(X_M,g)$ of Lemma \ref{teljeslemma} carries a compatible
hyper-K\"ahler structure, too. Since the original compact space
$(\overline{X}_M,\overline{\gamma})$ of Lemma \ref{kezdolemma} was
oriented and self-dual with both properties being conformally invariant,
$(X_M,g)$ is in fact a connected, simply connected, oriented, complete
self-dual and Ricci-flat space or in other words: A hyper-K\"ahler
$4$-manifold \cite[Chapter 13]{bes}. This implies among other things that
the holonomy group of the Levi--Civita connection of $g$ hence the structure
group of $TX_M$ reduces to ${\rm SU}(2)\subset {\rm SO}(4)$. Consider the
Levi--Civita connection of $(X_M,g)$. We can therefore suppose that its
restriction to $TB^{4\times}_r(0)\subset TX_M$ is
an ${\rm SU}(2)$ connection $\nabla^\times$ suffering from a singularity at
the origin. We know moreover that being $\nabla^\times$ self-dual, it solves
the ${\rm SU}(2)$ Yang--Mills equations. Moreover $\nabla^\times$ has
finite energy over $B^{4\times}_r(0)$. This is because $g$ is Ricci-flat
and self-dual so the curvature of $\nabla^\times$ coincides with the
self-dual Weyl component $W^+_g$ of $g$ only; however being conformally
invariant, $W^+_g=W^+_\gamma=W^+_{\overline{\gamma}}\vert_{X_M}$ that is,
the curvature tensor of $\nabla^\times$ is just the restriction of the Weyl
tensor of the original smooth metric $\overline{\gamma}$ on
$\overline{X}_M$. Consequently it is a smooth bounded tensor field on
$B^{4\times}_r(0)$ implying finite local energy. This
also yields that, if $0<r$ is sufficiently small, $\nabla^\times$
admits an $L^2_1$ gauge along $B^{4\times}_r(0)$ as well. Therefore,
by Uhlenbeck's singularity removal theorem (see Theorem \ref{uhlenbecktetel})
there exists an $L^2_2$ gauge transformation on $TB^{4\times}_r(0)$
such that the gauge transformed connection extends across the singularity to
a smooth ${\rm SU}(2)$ connection $\nabla$ on the trivial bundle $TB^4_r(0)$.
Consequently, switching to the global picture, the singularity of the
Levi--Civita connection around the fixed $\R^4$ summand of $X_M$
can be removed hence the corresponding $\R^4$ summand
can be deleted from (\ref{ujsokasag}) according to our original plan.
Repeating this procedure around all the finitely many $\R^4$ summands
of $X_M$ we finally come up with a smooth ${\rm SU}(2)$ connection over
$M^\times$.
However there is an important topological subtlety here. For notational
simplicity suppose that $X_M=M^\times\#\R^4$ i.e., possesses one
non-distinguished $\R^4$ summand only. Then the singularity removal procedure
carried out above convinces us that the original singular Levi--Civita
connection defined on the {\it tangent} bundle $T(M^\times\#\R^4)$, regarded
as an ${\rm SU}(2)$ bundle, indeed extends to a non-singular
${\rm SU}(2)$ connection on {\it some} ${\rm SU}(2)$ bundle $E^\times$ over
$M^\times$ i.e., it indeed smoothly exists somewhere which is however not
necessarily the tangent bundle of $M^\times$. For instance, as we
emphasized in the discussion after Theorem \ref{uhlenbecktetel}, the
singularity-removing-gauge-transformation is not continuous in general
hence the original global vector bundle carrying the singular connection may
change topology during the singularity removal procedure. However, we know
the following two things. On the one hand complex two-rank ${\rm SU}(2)$
vector bundles over $M^\times$, like the $E^\times$ above carrying the
non-singular connection, are classified by various characteristic classes
taking values in the groups $H^i(M^\times;\pi_{i-1}({\rm SU}(2))$
with $i=1,\dots,4$. Knowing the first three homotopy groups of ${\rm SU}(2)$
and taking into account the non-compactness of $M^\times$ these
cohomology groups are all trivial consequently we know that $E^\times$
is necessarily isomorphic to the trivial bundle over $M^\times$. On the
other hand, real rank-four ${\rm SO}(4)$ vector bundles over $M^\times$, like
the tangent bundle $TM^\times$ carrying an orientation and a Riemann
metric, are classified by characteristic classes taking
values in $H^i(M^\times;\pi_{i-1}({\rm SO}(4))$.
Again recalling the first three homotopy groups of the non-simply
connected group ${\rm SO}(4)$ and still keeping in mind that $M^\times$ is
non-compact, the only potentially non-trivial group here is
$H^2(M^\times;\Z_2)$ demonstrating that vector bundles of this type over
$M^\times$ are classified by a single element and this is nothing but their
second Stiefel--Whitney class. Consequently if $M$
is spin or equivalently $w_2(TM)=0\in H^2(M;\Z_2)$ then by the injection
$M^\times\subset M$ we find $w_2(TM^\times )=0
\in H^2(M^\times;\Z_2)$ as well showing that
{\it $TM^\times$ is isomorphic to the trivial bundle}, too. Therefore we
conclude that whenever $M$ is spin, we can identify the vector
bundle $E^\times$ carrying the non-singular ${\rm SU}(2)$ connection over
$M^\times$ with its tangent bundle $TM^\times$.
Having understood this, we can finish the proof by extending the metric
itself through the singularities. Fortunately this is simple. Consider the
restricted connection $\nabla$ about one singular point $p$. This is now
an overall (i.e., including the singular point) smooth connection.
Therefore there exists a $\delta (p)>0$ such that we can
suppose without loss of generality that the coordinate system
(\ref{golyo}) we take about this singular point with
$0<r<\delta (p)$ is a geodesic normal coordinate system
with respect to $\nabla$. This implies that the Christoffel symbols
$\nabla_{\partial_i}\partial_j=\sum\limits_k\Gamma^k_{ij}\partial_k$ all
vanish in the center i.e., $\Gamma_{ij}^k(0,\dots,0)=0$ for all
$i,j,k=1,\dots 4$. Then the well-known compatibility equations
\[\Gamma_{ij}^k=\frac{1}{2}
\sum\limits_{l=1}^4\left(\partial_ig_{lj}+\partial_jg_{li}-
\partial_lg_{ij}\right)g^{lk}\]
imply in a well-known way that in this gauge $g$
extends over the origin, too, such that $g_{ij}(0,\dots,0)=\delta_{ij}$
and $\partial_kg_{ij}(0,\dots,0)=0$ for all $i,j,k=1,\dots,4$. The further
differentiablity i.e., the smoothness of $g$ at the origin follows from
the smoothness of the Christoffel symbols there. That $g$ is
Ricci-flat is a trivial consequence of the same property of the
original metric. $\Diamond$
\section{Construction in the exotic setting}
\label{four}
In this section we shall sink into the bottomless sea of four
dimensionality, called Exotica, and repeat the procedure performed in
Section \ref{three}. That is, we shall construct solutions of
the vacuum Einstein equation on the smooth $4$-manifold $X^\times$ which
is only {\it homeomorphic} but not {\it diffeomorphic} to the punctured
manifold $M^\times$ appeared in Section \ref{three}. This construction
basically goes along the lines of that presented in Section \ref{three}
with minor technical differences. Consequently, those steps which
require new tools will be worked out in detail while those which are
basically the same as the corresponding ones in Section \ref{three} will
be sketched only.
To begin with, we compose Theorems \ref{taubestetel},
\ref{egzotikusnagycsalad} and \ref{gompftetel} together as follows.
\begin{lemma}
Out of any connected, closed (i.e., compact without boundary) oriented
smooth $4$-manifold $M$ one can construct a connected, open (i.e.,
non-compact without boundary) oriented smooth Riemannian $4$-manifold
$(X_M,\gamma)$ which is self-dual but incomplete in general.
\label{egzotikuskezdolemma}
\end{lemma}
\noindent {\it Proof.} Pick any connected, oriented, closed, smooth
$4$-manifold $M$. Referring to Theorem \ref{taubestetel} let
$k:=\max (1,k_M)\in\N$ be a positive integer, put
\[\overline{X}_M:=M\#\underbrace{\C P^2\#\dots\#\C P^2}_{k}\]
and let $\overline{\gamma}$ be a self-dual metric on it. Then
$(\overline{X}_M,\overline{\gamma})$ is a compact self-dual manifold. Pick
one $\C P^2$ factor within $\overline{X}_M$ and denote by
$S^2:=\C P^2\setminus R^4$ the complement of the largest exotic
$\R^4$-space $R^4\subset\C P^2$, considered as an only
``continously embedded projective line'' in that factor, as in the
discussion after Theorem \ref{egzotikusnagycsalad} (we can suppose that the
closed subspace $S^2\subset\C P^2$ avoids the attaching point of $\C P^2$ to
$M$). Let $K\subset R^4$ be the connected compact subset as in part (ii) of
Theorem \ref{egzotikusnagycsalad} and put
\begin{equation}
X_M:=M\#\underbrace{(\C P^2\setminus\C P^1)\#\dots\#
(\C P^2\setminus\C P^1)}_{k-1}\#_K(\C P^2\setminus S^2)\cong
M\#\underbrace{\R^4\#\dots\#\R^4}_{k-1}\#_KR^4\cong
X^\times\#\underbrace{\R^4\#\dots\#\R^4}_{k-1}
\label{egzotikusujsokasag}
\end{equation}
where the operation $\#_K$ means that the attaching point $y_0\in R^4$
used to glue $R^4$ with $M\#\R^4\#\dots\#\R^4$ satisfies
$y_0\in K\subset R^4$ and $X^\times:=M\#_KR^4$ is a smooth manifold
homeomorphic but not diffeomorphic to the puncturation $M^\times$ of the
original manifold (see Theorem \ref{gompftetel}). The result is a
connected, open $4$-manifold $X_M$ (see Figure 4).
\vspace{0.3in}
\centerline{
\begin{tikzpicture}[scale=0.7]
\node at (-0.8,0) {$M$};
\draw [thick] plot [tension=0.8,smooth cycle] coordinates {
(0,0) (2,2) (5,0) (2,-2)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(0.5,0.4) (1.5,0.2)
(2.5,0.4)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(0.8,0.3) (1.5,0.5)
(2.2,0.3)};
\node at (7.5,0) {$X_M$};
\draw [thick] plot [tension=0.8,smooth] coordinates { (9.5,0.2)
(10.2,-0.2) (10.9,0.2)};
\draw [thick] plot [tension=0.8,smooth] coordinates { (9.7,0)
(10.2,0.3) (10.7,0)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(9.5,1) (10,1.3) (11,1) (12,0.7) (13,0.9) (13.5,1.3)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(14.1,1.3) (14.4,0.6) (15,0.3)};
\draw plot [tension=0.8,smooth] coordinates
{(13.5,1.3) (13.8,1.4) (14.1,1.3)};
\draw plot [tension=0.8,smooth] coordinates
{(13.5,1.3) (13.8,1.2) (14.1,1.3)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(9.5,-1) (10,-1.3) (11,-1) (12,-0.7) (13,-0.9) (13.5,-1.3)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(14.1,-1.3) (14.4,-0.6) (15,-0.3)};
\draw plot [tension=0.8,smooth] coordinates
{(13.5,-1.3) (13.8,-1.4) (14.1,-1.3)};
\draw plot [tension=0.8,smooth] coordinates
{(13.5,-1.3) (13.8,-1.2) (14.1,-1.3)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(9.5,1) (9,0)
(9.5,-1)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(15,0.3) (16,0.2)
(17,1)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(15,-0.3) (16,-0.2)
(17,-1)};
\draw[gray] plot coordinates {(17,1) (17.5,0.9) (17,0.7) (17.5,0.6)
(17,0.5) (17.5,0.4) (17,0.3) (17.5,0.2) (17,0.1) (17.5,0) (17,-0.1)
(17.5,-0.2) (17,-0.3) (17.5,-0.4) (17,-0.5) (17.5,-0.6) (17,-0.7)
(17.5,-0.9) (17,-1)};
\end{tikzpicture}
}
\vspace{0.1in}
\centerline{Figure 4. Construction of $X_M$ out of $M$ in the exotic
setting. The gray zig-zag represents a}
\centerline{``creased end'' diffeomorphic to the complement of a connected
compact subset $K$ in the exotic $R^4$.}
\vspace{0.3in}
\noindent From the proper smooth embedding $X_M\subsetneqq\overline{X}_M$
there exists a restricted self-dual Riemannian metric
$\gamma:=\overline{\gamma}\vert_{X_M}$ on $X_M$ which is however in
general non-complete. $\Diamond$
\vspace{0.1in}
\noindent In the case of our situation set up in Lemma
\ref{egzotikuskezdolemma}
twistor theory works as follows. Consider the compact self-dual
space $(\overline{X}_M,\overline{\gamma})$ from Lemma
\ref{egzotikuskezdolemma}, take its twistor fibration $\overline{p}:
\overline{Z}\rightarrow\overline{X}_M$ and let $p:Z\rightarrow X_M$
be its restriction induced by the smooth embedding $X_M\subsetneqq
\overline{X}_M$ i.e., $Z:=\overline{Z}\vert_{X_M}$ and
$p:=\overline{p}\vert_{X_M}$. Then $Z$ is a non-compact
complex $3$-manifold already obviously possessing all the required twistor
data except the existence of a holomorphic mapping $\pi :Z\rightarrow\C P^1$.
\begin{lemma} Consider the connected, open, oriented, incomplete, self-dual
space $(X_M,\gamma)$ as in Lemma
\ref{egzotikuskezdolemma} with its twistor fibration $p:Z\rightarrow X_M$
constructed above. If $\pi_1(M)=1$ and $M$ is spin (or equivalently, having
even intersection form) then there exists a holomorphic mapping
$\pi :Z\rightarrow\C P^1$.
\label{egzotikuspilemma}
\end{lemma}
\noindent {\it Proof.} Let $x_0\in X_M$ be an arbitrary fixed point
of $X_M$ in (\ref{egzotikusujsokasag}). Our aim is to construct a
holomorphic map
\[\pi:\:\:Z\longrightarrow p^{-1}(x_0)\cong\C P^1\]
that we carry out exactly the same way as in the proof of Lemma
\ref{pilemma} hence we do not repeat it here. $\Diamond$
\vspace{0.1in}
\noindent It also follows that $\pi :Z\rightarrow\C P^1$ i.e., the map
constructed in Lemma \ref{egzotikuspilemma} is
compatible with the real structure $\tau :Z\rightarrow Z$ already fixed by
the self-dual structure in Theorem \ref{taubestetel} therefore twistor theory
provides us with a Ricci-flat (and self-dual) Riemannian metric $g$
on $X_M$. We proceed further and demonstrate that, unlike
$(X_M,\gamma)$, the space $(X_M,g)$ is complete.
\begin{lemma} The four dimensional connected and simply connected, open,
oriented, Ricci-flat Riemannian spin manifold $(X_M,g)$ is complete.
\label{egzotikusteljeslemma}
\end{lemma}
\noindent {\it Proof}. The metrics $\gamma$ and $g$ originate from the same
twistor space again hence they are conformally equivalent consequently there
exists a smooth function
$\psi :X_M\rightarrow\R_+$ satisfying $g=\psi^{-2}\gamma$.
Taking into account that the steps in the proof of Lemma \ref{teljeslemma}
have been insensitive for the particular construction of the complementum
$\overline{X}_M\setminus X_M$ we can simply repeat them here. Hence
we find again, on the one hand, that $\psi^{-1}$ blows up
uniformly along the whole $\overline{X}_M\setminus X_M$ this time consisting of
the disjoint union of ``ordinary'' i.e. holomorphically embedded
projective lines $\C P^1=\C P^2\setminus\R^4$ and the distinguished
``continuously embedded projective line'' $S^2=\C P^2\setminus R^4$
in the distinguished factor in (\ref{egzotikusujsokasag}); consequently
$\log\psi^{-1}$ is proper. Moreover, on the other hand, recalling the
steps of Lemma \ref{teljeslemma} we see that $\log\psi^{-1}$ has
bounded gradient in modulus with respect to $g$, too. Consequently $(X_M, g)$
is complete as in the proof of Lemma \ref{teljeslemma} hence the details are
omitted. $\Diamond$
\begin{remark}\rm For clarity we remark that comparing the proofs of
Lemmata \ref{teljeslemma} and \ref{egzotikusteljeslemma} one cannot
conclude that the resulting complete spaces $(X_M,g)$ in the
non-exotic and exotic situations are conformally equivalent. This is because
(see the discussion after Theorem \ref{egzotikusnagycsalad})
the locations of $X_M$ in the two cases within their common
closure $\overline{X}_M$ are different such that even the former cannot be
mapped into the latter by any diffeomorphism of $\overline{X}_M$. Consequently
taking the pointwise product of the scaling function $\varphi^{-2}$ in
Lemma \ref{teljeslemma} with the inverse one $\psi^2$ from Lemma
\ref{egzotikusteljeslemma} to obtain a conformal rescaling
between the corresponding metrics makes no sense.
\end{remark}
\noindent Finally we cut down the standard $\R^4$'s from $X_M$ to
obtain $X^\times$ as in Lemma \ref{levagolemma}.
\begin{lemma} Consider the space $(X_M,g)$ as in Lemma
\ref{egzotikusteljeslemma}. Then the orientation and the complete
Ricci-flat metric $g$ on $X_M$ descend to the punctured space $X^\times$
(which is homeomorphic but not diffeomorphic to the corresponding space
$M^\times$ of Lemma \ref{levagolemma}) with
its inherited smooth structure, rendering it a connected and simply connected,
open, oriented, complete, Ricci-flat Riemannian spin $4$-manifold
$(X^\times, g)$.
\label{egzotikuslevagolemma}
\end{lemma}
\noindent {\it Proof.} Taking into account that filling in the standard
$\R^4$'s in the decomposition (\ref{egzotikusujsokasag}) of $X_M$ is a
completely local procedure (see Figure 5)
\vspace{0.3in}
\centerline{
\begin{tikzpicture}[scale=0.7]
\node at (10.2,0) {$X^\times$};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(11,0) (11.1,0.5) (11.5,1) (12.25,1.4) (13.5,1.5) (14.75,1.2) (16,0.2)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(11,0) (11.1,-0.5) (11.5,-1)
(12.25,-1.4) (13.5,-1.5) (14.75,-1.2) (16,-0.2)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(16,0.2) (17,0.2)
(18,1)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(16,-0.2) (17,-0.2)
(18,-1)};
\draw[gray] plot coordinates {(18,1) (18.5,0.9) (18,0.7) (18.5,0.6)
(18,0.5) (18.5,0.4) (18,0.3) (18.5,0.2) (18,0.1) (18.5,0) (18,-0.1)
(18.5,-0.2) (18,-0.3) (18.5,-0.4) (18,-0.5) (18.5,-0.6) (18,-0.7)
(18.5,-0.9) (18,-1)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(11.5,0.4) (12.5,0.2)
(13.5,0.4)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(11.8,0.3) (12.5,0.5)
(13.2,0.3)};
\node at (-1,0) {$X_M$};
\draw [thick] plot [tension=0.8,smooth] coordinates { (0.5,0.2) (1,-0.2)
(1.5,0.2)};
\draw [thick] plot [tension=0.8,smooth] coordinates { (0.7,0) (1,0.1)
(1.3,0)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(0.5,1) (1,1.3) (2,1) (3,0.7) (4,0.9) (4.5,1.3)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(5.1,1.3) (5.4,0.6) (6,0.3)};
\draw plot [tension=0.8,smooth] coordinates
{(4.5,1.3) (4.8,1.4) (5.1,1.3)};
\draw plot [tension=0.8,smooth] coordinates
{(4.5,1.3) (4.8,1.2) (5.1,1.3)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(0.5,-1) (1,-1.3) (2,-1) (3,-0.7) (4,-0.9) (4.5,-1.3)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(5.1,-1.3) (5.4,-0.6) (6,-0.3)};
\draw plot [tension=0.8,smooth] coordinates
{(4.5,-1.3) (4.8,-1.4) (5.1,-1.3)};
\draw plot [tension=0.8,smooth] coordinates
{(4.5,-1.3) (4.8,-1.2) (5.1,-1.3)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(0.5,1) (0,0)
(0.5,-1)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(6,0.3) (7,0.2) (8,1)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(6,-0.3) (7,-0.2)
(8,-1)};
\draw[gray] plot coordinates {(8,1) (8.5,0.9) (8,0.7) (8.5,0.6)
(8,0.5) (8.5,0.4) (8,0.3) (8.5,0.2) (8,0.1) (8.5,0) (8,-0.1)
(8.5,-0.2) (8,-0.3) (8.5,-0.4) (8,-0.5) (8.5,-0.6) (8,-0.7)
(8.5,-0.9) (8,-1)};
\end{tikzpicture}
}
\vspace{0.1in}
\centerline{Figure 5. Construction of $X^\times$ out of $X_M$ by filling
in the extra $\R^4$'s.}
\vspace{0.3in}
\noindent the proof of this lemma is verbatim the same as the proof of Lemma
\ref{levagolemma} hence is omitted. $\Diamond$
\vspace{0.1in}
\noindent{\it Proof of Theorems \ref{fotetel1} or \ref{fotetel2}}.
Collecting all the ruslts of Sections \ref{three} and
\ref{four} together the desired statements are obtained. $\Diamond$
\begin{remark}\rm Before proceeding further let us note that Theorems
\ref{fotetel1} or \ref{fotetel2} correspond to the case when the
creased end of $X^\times$ is diffeomorphic to the largest member
$R^4=R^4_{+\infty}$ in the radial family of Theorem
\ref{egzotikusnagycsalad} i.e. $X^\times=M\#R^4_{+\infty}$. It would be
interesting to understand whether or not a similar construction works for
the intermediate members of the family i.e. for $X^\times_t=M\#R^4_t$.
\end{remark}
\section{Lorentzian solutions}
\label{five}
In the previous sections we have produced an immense class of Ricci flat
Riemannian spaces $(X^\times ,g)$ which are non-compact but complete. In
this section we convert all of them i.e. the spaces in Theorem \ref{fotetel1}
or equivalently Theorem \ref{fotetel2} into Ricci-flat
Lorentzian ones as formulated in Theorem \ref{lorentztetel} by
(essentially verbatim) recalling \cite[Lemma 4.2]{ete2}. Conversion is
in principle possible because all the underlying manifolds
$X^\times$ are non-compact hence there is no topological obstruction
against Lorentzian structure.
\vspace{0.1in}
\noindent {\it Proof of Theorem \ref{lorentztetel}}. By virtue of its global
triviality (cf. Lemma \ref{levagolemma} or \ref{egzotikuslevagolemma}),
$TX^\times$ admits a nowhere vanishing smooth section
yielding a splitting $TX^\times=L\oplus L^\perp$ into a real line bundle
$L\subset TX^\times$ spanned the section and its $g$-orthogonal complementum
subbundle $L^\perp\subset TX^\times$. Take the
complexification $T^\C X^\times:=TX^\times\otimes_\R\C$ of the real tangent
bundle as well as the complex bilinear extension of the Riemannian Ricci-flat
metric $g$ found on $TX^\times$ to a Ricci-flat metric $g^\C$ on
$T^\C X^\times$. This means that if $v^\C$ is a complexified tangent vector
then both $v^\C\mapsto g^\C(v^\C\:,\:\cdot\:):=g(v^\C\:,\:\cdot\:)$ and
$v^\C\mapsto g^\C(\:\cdot\:,\:v^\C):=g(\:\cdot\:,\:v^\C)$ are declared to be
$\C$-linear and of course ${\rm Ric}_{g^\C}={\rm Ric}_g=0$. There is an
induced splitting
\begin{equation}
T^\C X^\times=L\oplus L^\perp\oplus\sqrt{-1}\:L\oplus\sqrt{-1}\:L^\perp
\label{felbontas}
\end{equation}
over $\R$ of the complexification i.e., if $T^\C X^\times$ is
considered as a real rank-$8$ bundle over $X^\times$. Define a metric on the
real rank-$4$ sub-bundle $L^\perp\oplus\sqrt{-1}\:L\subset T^\C X^\times$ by
taking the restriction $g^\C\vert_{L^\perp\oplus\sqrt{-1}\:L}$. It readily
follows from the orthogonality and reality of the splitting that this is
a non-degenerate real-valued $\R$-bilinear form of Lorentzian type on this
real sub-bundle. To see this, we simply have to observe that taking real vector
fields $v_1,v_2:X^\times\rightarrow L$ and $w_1,w_2:X^\times\rightarrow
L^\perp$ we can exploit the $\C$-bilinearity of $g^\C$ to write
\[g^\C\vert_{L^\perp\oplus\sqrt{-1}\:L}(\sqrt{-1}\:v_1,\sqrt{-1}\:v_1)=
g^\C(\sqrt{-1}\:v_1,\sqrt{-1}\:v_1)=-g^\C(v_1,v_1) =-g(v_1,v_1)\]
and
\[g^\C\vert_{L^\perp\oplus\sqrt{-1}\:L}(\sqrt{-1}\:v_1,w_1)=
g^\C(\sqrt{-1}\:v_1,w_1)=\sqrt{-1}\:g^\C(v_1,w_1)
=\sqrt{-1}g(v_1,w_1)=0\]
and finally
\[g^\C\vert_{L^\perp\oplus\sqrt{-1}\:L}(w_1,w_2)=
g^\C(w_1,w_2)=g(w_1,w_2)\:\:\:.\]
Consider the $\R$-linear bundle isomorphism $W_L:T^\C X^\times
\rightarrow T^\C X^\times$ of the complexified tangent bundle defined by, with
respect to the splitting (\ref{felbontas}), as
\[W_L(v_1,w_1,\sqrt{-1}\:v_2,\sqrt{-1}\:w_2):=
(v_2, w_1,\sqrt{-1}\:v_1,\sqrt{-1}\:w_2)\:\:.\]
Obviously $W_L^2={\rm Id}_{T^\C X^\times}$ or more precisely $W_L$ is a
{\it real reflection} with respect to $g^\C$ making the diagram
\[\xymatrix{
\ar[d] T^\C X^\times\ar[r]^{W_L} & T^\C X^\times\ar[d] \\
X^\times\ar[r]^{{\rm Id}_{X^\times}} & X^\times
}\]
commutative. In particular it maps the real tangent bundle
$TX^\times=L\oplus L^\perp\subset T^\C X^\times$ onto the real bundle
$L^\perp\oplus\sqrt{-1}\:L\subset T^\C X^\times$ and {\it vice versa}.
Consequently with arbitrary two tangent vectors $v,w:X^\times\rightarrow
TX^\times$
\[g_L(v,w):=g^\C(W_Lv\:,\:W_Lw)\]
satisfies $g_L(v,w)=g^\C\vert_{L^\perp\oplus\sqrt{-1}\:L}(W_Lv\:,\:W_Lw)$
i.e., obtain a non-degenerate real-valued $\R$-bilinear form of Lorentzian type
hence a smooth Lorentzian metric $g_L$ on the original real tangent bundle
$TX^\times$.
Concerning the Ricci tensor of $g_L$, the Levi--Civita
connections $\nabla^L$ of $g_L$ and $\nabla^\C$ of $g^\C$ satisfy
\begin{eqnarray}
g_L(\nabla^L_uv,w)+g_L(v,\nabla^L_uw)&=&\dd g_L(v,w)u\nonumber\\
&=&\dd g^\C(W_Lv,W_Lw)u\nonumber\\
&=&g^\C(\nabla^\C_u(W_Lv)\:,\:W_Lw)+g^\C(W_Lv\:,\:\nabla^\C_u(W_Lw))\nonumber\\
&=&g^\C(W^2_L\nabla^\C_u W_Lv\:,\:W_Lw)+g^\C(W_Lv\:,\:W^2_L\nabla^\C_uW_Lw)
\nonumber\\
&=&g_L((W_L\nabla^\C_u W_L)v\:,\:w)+g_L(v\:,\:(W_L\nabla^\C_u W_L)w)\nonumber
\end{eqnarray}
yielding $\nabla^L=W_L\nabla^\C W_L$ (this is an $\R$-linear operator).
Consequently the curvature ${\rm Riem}_{g_L}$ of $g_L$ is
\[{\rm Riem}_{g_L}(v,w)u=\left[\nabla^L_v\:,\nabla^L_w\right]u-
\nabla^L_{[v,w]}u=W_L({\rm Riem}_{g^\C}(v,w)W_Lu)\:\:.\]
Let $\{e_0,e_1,e_2,e_3\}$ be a real orthonormal frame for $g_L$ at
$T_pX^\times$ satisfying $g_L(e_0,e_0)=-1$ and $+1$ for the rest; then
$W_Le_0=\sqrt{-1}\:e_0$ and $W_Le_j=e_j$ for $j=1,2,3$ together
with the definition of $g_L$ imply that
\[g_L({\rm Riem}_{g_L}(e_0,v)w,e_0)=g^\C\left(W_L({\rm
Riem}_{g_L}(e_0,v)w),W_Le_0\right)=g^\C\left({\rm
Riem}_{g^\C}(e_0,v)W_Lw\:,\sqrt{-1}e_0\right)\]
and likewise
\[g_L({\rm Riem}_{g_L}(e_j,v)w\:,\:e_j)=g^\C(W_L({\rm
Riem}_{g_L}(e_j,v)w),W_Le_j)=g^\C({\rm
Riem}_{g^\C}\left(e_j\:,\:v\right)W_Lw\:,e_j)\:\:.\]
Using an orthonormal frame $\{f_1,\dots,f_m\}$ for a metric $h$ of any
signature, its Ricci tensor looks like ${\rm Ric}_h(v,w)=
\sum\limits_{k=1}^mh(f_k,f_k)h({\rm Riem}_h(f_k,v)w\:,\:f_k)$; hence
\begin{eqnarray}
{\rm Ric}_{g_L}(v,w)\!\!\!\!\!\!&=&\!\!\!\!\!\!g_L(e_0,e_0)g_L({\rm
Riem}_{g_L}(e_0,v)w,e_0)+
\sum\limits_{j=1}^3g_L(e_j,e_j)g_L({\rm Riem}_{g_L}(e_j,v)w,e_j)\nonumber\\
\!\!\!\!\!\!&=&\!\!\!\!\!\!g^\C(\sqrt{-1}e_0,\!\sqrt{-1}e_0)g^\C({\rm
Riem}_{g^\C}(e_0,v)W_Lw,\sqrt{-1}e_0)
\!+\!\!\sum\limits_{j=1}^3g^\C(e_j,e_j)g^\C({\rm
Riem}_{g^\C}(\!e_j,v)W_Lw,e_j\!)\nonumber\\
\!\!\!&=&\!\!\!(-\sqrt{-1}\:-1)g^\C(e_0,e_0)g^\C({\rm
Riem}_{g^\C}(e_0,v)W_Lw,e_0)+{\rm Ric}_{g^\C}(v\:,\:W_Lw)\nonumber\\
&=& (-1+\sqrt{-1})g_L({\rm Riem}_{g_L}(e_0,v)w,e_0)\nonumber
\end{eqnarray}
and we also used $\{e_0,e_1,e_2,e_3\}$ as a complex orthonormal
basis for $g^\C$ on $T^\C_pX^\times$ to write
\[\sum_{j=0}^3g^\C(e_j,e_j)g^\C({\rm Riem}_{g^\C}(e_j,v)W_Lw,e_j)=
{\rm Ric}_{g^\C}(v,W_Lw)=0\:\:.\]
Being the left hand side in
${\rm Ric}_{g_L}(v,w)=(-1+\sqrt{-1})g_L({\rm Riem}_{g_L}(e_0,v)w,e_0)$ real,
the right hand side must be real as well for all $v,w\in T_pX^\times$
which is possible if and only if both sides vanish. This demonstrates that
$g_L$ is indeed Ricci-flat. $\Diamond$
\section{Physical interpretation}
\label{six}
In this closing section we discuss the physical interpretation of the
Lorentzian Ricci-flat geometries found in Theorem \ref{lorentztetel}. We
believe that an interpretation is necessary because there are many known
physically irrelevant solutions of the vacuum Einstein equation and our
solutions as presented in Theorem \ref{lorentztetel} are admittedly very
implicit and transcendental hence their physical significance, if any, is
unclear yet. The offered interpretation fits well into the context of the
celebrated {\it strong cosmic censorship conjecture} in its usual broad
formulation (${\bf SCCC}$ for short) which is a hot topic recently (far
from being complete cf. \cite{car-cos-des-hin-jan1,
car-cos-des-hin-jan2,daf-luk,dia-epe-rea-san,dia-rea-san,ete1,ete2,
ge-jia-wan-zha-zho,hod,lun-zie-car-cos-nat,mo-tia-wan-zha-zho}; for
historical accounts see \cite{cha,ise,pen2}) and the so far hypothetical {\it
topology changing} phenomena (again far from being
complete, cf. e.g. \cite{dow,gib,hor}).
The current situation of the ${\bf SCCC}$ can perhaps be best
summarized as a {\it puzzling dichotomy}: although there are some signs or
hints for its (in)validity in {\it physically relevant} situations
(like various black holes in asymptotically flat or de Sitter space-times
filled with vacuum or various matter fields, etc. \cite{car-cos-des-hin-jan1,
car-cos-des-hin-jan2,daf-luk,dia-epe-rea-san,dia-rea-san,ge-jia-wan-zha-zho,hod,
lun-zie-car-cos-nat,mo-tia-wan-zha-zho}), these
are still not sharp enough to decide the status of the ${\bf SCCC}$ in these
important cases. On the other hand there exists an superabundance of
``exotic'' smooth solutions in which the ${\bf SCCC}$
clearly fails \cite{ete1,ete2} (namely the ones exhibited in
Theorem \ref{lorentztetel}) however the physical meaning of these quite
{\it purely mathematical} solutions is not clear yet. The reason for this
latter issue is that, although being smooth solutions of the vacuum
Einstein equation hence apparently relevant, the ${\bf SCCC}$ violating
properties of these ``exotic'' solutions rest neither on some physical
phenomenon nor on standard analytico-geometric properties of Lorentzian
metrics; but rather based on subtle novel differentio-topological features
(often called {\it exotica}) of four dimensional manifolds which have
gradually been recognized in the underlying mathematical model of physical
space-times from the 1980's onwards (cf. \cite[Introduction]{ete2}). Despite
that no {\it a priori} principle has been introduced so
far to exclude these curious and apparently fundamental mathematical
discoveries from the game, they have not found their right places in
theoretical physics yet \cite{ass-bra}.
The aim of this section is an effort to fill in this gap by offering a
plausible and simple physical interpretation of the new ${\bf SCCC}$
violating solutions \cite{ete1,ete2} (i.e. the spaces exhibited in Theorem
\ref{lorentztetel}). As an interesting observation it
will turn out that, meanwhile the aforementioned classical situations in
which ${\bf SCCC}$ breakdown has been examined belong to the well known
static or stationary regime of general relativity, the new ${\bf SCCC}$
violating solutions are related with the yet unexplored deep
dynamical regime of general relativity describing spatial topology changes as
will be explained shortly. We also find that this dynamics appears as a
{\it cosmologial redshift} for late time internal observers within these
space-times. Therefore, quite unsurprisingly, one is tempted to say that as
one moves from the static towards the dynamical regime, ${\bf SCCC}$ violating
phenomena become more and more relevant in general relativity.
Take any connected, simply connected, closed spin $4$-manifold $M$ and
form the connected sum $X^\times:=M\#R^4$ as before (see Figure 5).
It is easy to see (cf. the summary of the exotic stuff
in Section \ref{two}) that $X^\times$ is homeomorphic to the
punctured space $M^\times =M\setminus\{{\rm point}\}$ however cannot be
diffeomorphic to it (with its usual inherited smooth
structure from the smooth embedding $M^\times\subset M$) since $M^\times$ is
diffeomorphic to $M\#\R^4$ meanwhile $X^\times$ by construction is
diffeomorphic to $M\# R^4$ hence the ends of the two open spaces, although
homeomorphic, are not diffeomorphic. Actually, from a general viewpoint,
the appearance of non-compact $4$-manifolds carrying smooth structures like
$X^\times$ i.e. having a ``creased end'' is much more typical.
Theorem \ref{lorentztetel} then says that
$X^\times$ always carries a Ricci-flat Lorentzian metric $g_L$. Having
$X^\times$ a creased end implies that it surely cannot be written as a smooth
product $\Sigma\times\R$ where $\Sigma$ is a $3$-manifold and $\R$ is the real
line (with their unique smooth structures); however the existence of such a
smooth splitting is a necessary condition of global hyperbolicity
\cite{ber-san}. Consequently we arrive at a sort of heavy breakdown of
the ${\bf SCCC}$ (in its usual broad formulation, cf. e.g.
\cite{ete1, ete2}), namely
\vspace{0.1in}
\noindent $\overline{{\bf SCCC}}$. {\it The smooth Ricci-flat Lorentzian
$4$-manifold $(X^\times ,g_L)$ in Theorem \ref{lorentztetel} is not
globally hyperbolic and no (sufficiently large in an appropriate topological
sense) perturbation of it can be globally hyperbolic.}
\vspace{0.1in}
\noindent Furthermore, Theorem \ref{fotetel1} says that $X^\times$
carries a complete Ricci-flat Riemannian metric $g$, too. As a by-product
of the construction we have seen that fixing an appropriate
orientation on $X^\times$ the metric $g$ is self-dual, too. However a
simply-connected, complete Riemannian $4$-manifold which is both
Ricci-flat and self-dual is in fact, as formulated in Theorem \ref{fotetel2},
hyper-K\"ahler (cf. e.g. \cite[Chapter 13]{bes}). Physically speaking the
Riemannian $4$-manifolds $(X^\times, g)$ exhibited in Theorem \ref{fotetel1}
or equiavlently, in Theorem \ref{fotetel2} are therefore examples of
{\it gravitational instantons}. Consequently, even if these Riemannian
(or Euclidean) vacuum spaces might not play any role in classical general
relativity, they are not negligable in any quantum theory perhaps
lurking behind classical general relativity.
After these introductory or general remarks let us move towards
a suggested physical interpretation of the ${\bf SCCC}$ breaking
but otherwise regular geometry $(X^\times, g_L)$. The conversion procedure
in Theorem \ref{lorentztetel} rests on a nowhere-vanishing vector field
\begin{equation}
v\in C^\infty (X^\times; TX^\times\setminus\{0\})
\label{vektormezo}
\end{equation}
along $X^\times$ whose choice was otherwise arbitrary.
Therefore, taking into account the global triviality of the tangent bundle
$TX^\times$ (cf. Lemmata \ref{levagolemma} and \ref{egzotikuslevagolemma}),
we have a great freedom in specifying it what we now exploit as
follows. Consider the original simply connected and closed $M$ used in Theorem
\ref{fotetel1}. Simply connectedness implies the vanishing of the first de
Rham cohomology of $M$ therefore if we put any Riemannian metric onto $M$
and consider the corresponding Laplacian on $1$-forms, its kernel is trivial.
The Hodge decomposition theorem then says that any $1$-form $\xi$ on $M$
uniquely splits as $\xi=\dd f+\dd^*\eta$ where $f$ is a function and
$\eta$ a $2$-form on $M$. The corresponding dual decomposition of a smooth
vector field $v$ on $M$ therefore looks like $v={\rm grad}f+{\rm div}T$
where $T$ is a $(2,0)$-type tensor field.
Motivated by this, consider now the space $X^\times$ of Theorem
\ref{lorentztetel} and recall that it is homeomorphic to $M^\times$
consequently has vanishing first de Rham cohomology, too. Therefore,
as a first and naive choice, we set the nowhere
vanishing vector field (\ref{vektormezo}) used to construct the Ricci-flat
Lorentzian metric $g_L$ on $X^\times$ out of the Ricci-flat Riemannian one
$g$ to be of the form
\begin{equation}
v:={\rm grad} f
\label{szetszedes}
\end{equation}
where $f:X^\times\rightarrow (-\infty ,0]$ is a Morse function
(to be defined shortly) on $X^\times$ such that $f^{-1}(-\infty)$ corresponds
to the creased end of $X^\times$ while $f^{-1}(t)\subset
X^\times$ are compact level sets for all $-\infty <t\leqq 0$ and in
particular the point $f^{-1}(0)$ is the ``top'' of $X^\times$
(see Figure 6).
\vspace{0.1in}
\centerline{
\begin{tikzpicture}[scale=0.6, rotate=-90]
\node at (15,-2) {$f:$};
\node at (15,3) {$\xrightarrow{\hspace{1cm}}$};
\node at (15,7) {$(-\infty ,0]$};
\draw [fill=black] (11.2,5) circle (0.15cm);
\draw [thick] (11.2,5) -- (18.15,5);
\draw [thick] (18.3,5) circle (0.15cm);
\node at (15,0) {$X^\times$};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(11,0) (11.1,0.5) (11.5,1) (12.25,1.4) (13.5,1.5) (14.75,1.2) (16,0.2)};
\draw [thick] plot [tension=0.8,smooth] coordinates
{(11,0) (11.1,-0.5) (11.5,-1)
(12.25,-1.4) (13.5,-1.5) (14.75,-1.2) (16,-0.2)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(16,0.2) (17,0.2)
(18,1)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(16,-0.2) (17,-0.2)
(18,-1)};
\draw [red, thick] plot coordinates {(18,1) (18.5,0.9) (18,0.7) (18.5,0.6)
(18,0.5) (18.5,0.4) (18,0.3) (18.5,0.2) (18,0.1) (18.5,0) (18,-0.1)
(18.5,-0.2) (18,-0.3) (18.5,-0.4) (18,-0.5) (18.5,-0.6) (18,-0.7)
(18.5,-0.9) (18,-1)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(12.2,-0.8)
(11.9,0.1) (12.2,0.8)};
\draw [thick] plot [tension=0.8,smooth] coordinates {(12.1,-0.65)
(12.4,0.1)(12.1,0.7)};
\end{tikzpicture}
}
\vspace{0.1in}
\centerline{Figure 6. The manifold $X^\times$ with a zig-zag
representing its creased end}
\centerline{and a Morse function $f:X^\times\rightarrow (-\infty,0]$ on it.}
\vspace{0.3in}
\noindent Moreover ${\rm grad} f$ in (\ref{szetszedes}) is defined by
$\dd f =g({\rm grad}f\:,\:\cdot\:)$ to be the dual vector field of the
$1$-form $\dd f$ with respect to the original {\it Riemannian} metric $g$ on
$X^\times$. If the choice in (\ref{szetszedes}) is possible then we gain a
very nice picture on the vacuum space-time $(X^\times ,g_L)$. Namely,
${\rm grad}f :X^\times\rightarrow L\subset L\oplus L^\perp =TX^\times$ is a
vector field such that for a generic $t\in (-\infty ,0]$ it does not
vanish and the level set $f^{-1}(t)\subset X^\times$ is a $3$ dimensional
closed (i.e., compact without boundary) submanifold with
$Tf^{-1}(t)=L^\perp\subset L\oplus L^\perp=TX^\times$. Hence with
respect to $g_L$ we find that ${\rm grad}f$
is a timelike and by definition future-directed vector field
$g_L$-orthogonal for the level sets which are spacelike. In other words:
{\it The vector field $v$ in (\ref{vektormezo}) is an infinitesimal
observer in the space-time $(X^\times ,g_L)$. If $v$ has the form
(\ref{szetszedes}) then $v$ can be identified with a global classical
observer in the sense that the level value $t\in (-\infty ,0]$
corresponds to its global classical proper time as moves along its future
directed own timelike curves (i.e., the integral curves of $v={\rm grad}f$)
and the level sets $f^{-1}(t)\subset X^\times$ correspond to its global
classical spacelike submanifolds}. However this picture is too
naive because $f$ may attain critical points i.e., $p\in X^\times$ where
${\rm grad}f(p)=0$ as we know from Morse theory. Hence the nowhere-vanishing
vector field (\ref{vektormezo}) cannot globally look like (\ref{szetszedes}).
{\it A rapid course on Morse theory}. The following things are well
known \cite{gom-sti,mil} but we summarize them here for completeness and
convenience. Let $N$ be a smooth $n$-manifold. The point $p\in N$ is a
{\it critical point} of a smooth function $f:N\rightarrow\R$ iff in a local
coordinate system $(U_p, x_1,\dots,x_n)$ centered at $p$ all the
partial derivatives vanish there i.e., $\partial_if(p)=0$ for all
$i=1,\dots, n$ and it is {\it non-degenerate} iff the
matrix $(\partial^2_{ij}f(p))_{i,j=1,\dots,n}$ is not singular. Moreover
$c\in\R$ is a {\it critical value} iff the level set $f^{-1}(c)\subset N$
contains a critical point. The smooth function $f:N\rightarrow\R$ is a
{\it Morse function} along $N$ iff it admits only non-degenerate
critical points such that each critical value level set contains at most one
critical point. (Being non-degenerate already implies that
the critical points are isolated \cite[Corollary 2.3]{mil}). We shall also
assume below that the
level set $f^{-1}(c)\subset N$ is compact as well, for all $c\in\R$.
We know the following things. If $c\in\R$ is non-critical
then $f^{-1}(c)\subset N$ is a smooth $n-1$ dimensional submanifold. If
$c\in\R$ critical with a single critical point $p\in f^{-1}(c)\subset N$
then (cf. \cite[Lemma 2.2]{mil}) there exists a local coordinate system
$(U_p, y_1,\dots,y_n)$ about $p$ i.e., $y_1(p)=\dots=y_n(p)=0$, in which
\[f\vert_{U_p}(y_1,\dots,y_n)=f(0,\dots,0)-\sum\limits_{i=1}^k
y^2_i+\sum\limits_{i=k+1}^{n}y^2_i\]
and the number $0\leqq k\leqq n$ is called the {\it index} of the critical
point. Therefore a critical point of index $k=0$ is a local minimum while
with index $k=n$ is a local maximum of $f$. Take $c\in\R$, $\varepsilon >0$
and suppose that $[c-\varepsilon,c+\varepsilon]\subset\R$
consists of non-critical values only. Then (cf. \cite[Theorem 3.1]{mil})
$f^{-1}(c-\varepsilon)$ and $f^{-1}(c+\varepsilon)$ are diffeomorphic.
If the only critical value in $[c-\varepsilon,c+\varepsilon]$
is $c$ and its unique critical point $p\in f^{-1}(c)$ is of index $k$ then
(cf. \cite[Theorem 3.2]{mil}) $f^{-1}(c+\varepsilon)$ is obtained from
$f^{-1}(c-\varepsilon)$ by glueing to the boundary of
$f^{-1}((-\infty ,c-\varepsilon ])$ a closed $n$-ball $B^n$ in the form of
a $k$-handle $B^k\times B^{n-k}$. More precisely take an embedding
$\varphi_k: S^{k-1}\times B^{n-k}\rightarrow f^{-1}(c-\varepsilon)$
and glue $B^n$ to $f^{-1}((-\infty, c-\varepsilon])$ by identifying
\[S^{k-1}\times B^{n-k}\subseteqq\partial(B^k\times B^{n-k})=
(S^{k-1}\times B^{n-k})\cup (B^k\times S^{n-k-1})\]
with the image $\varphi _k(S^{k-1}\times B^{n-k})\subseteqq
\partial\left(f^{-1}((-\infty, c-\varepsilon])\right)=f^{-1}(c-\varepsilon )$. Then
after ``smoothing off the corners'' we obtain an $n$ dimensional
manifold-with-boundary $f^{-1}((-\infty, c-\varepsilon])\cup_{\varphi_k}B^n$
and $f^{-1}(c+\varepsilon)$ is diffeomorphic to
$\partial\left(f^{-1}((-\infty, c-\varepsilon])\cup_{\varphi_k}B^n\right)$.
For instance if $k=0$ then $B^n$ is glued along $S^{-1}\times B^n$ where
$S^{-1}=\emptyset$ i.e., it is not glued hence this critical point is a local
minimum; while if $k=n$ then $B^n$ is attached along $S^{n-1}\times B^0$
where $B^0$ is a point i.e., it is attached along its full boundary
$S^{n-1}$ hence this is a local maximum of $f$. Note that replacing the
bottom-up function $f$ with the top-down function $-f$ critical points with
index $k$ and $n-k$ interchange.
Critical points necessarily occur. If $N$ is compact then a fundamental
result of Morse theory (cf. \cite[Theorem 5.2]{mil}) states that if
$m_k(N)$ denotes the number of critical points of index $k$ and $b_k(N)$ the
$k^{{\rm th}}$ Betti number of $N$ then $b_k(N)\leqq m_k(N)<+\infty$.
If $N$ is not compact then in general no such lower bounds exist but some
$m_k(N)$'s can be even infinite. For further details cf.
\cite[Chapter 4]{gom-sti} or \cite{mil}.
Returning to our problem, we therefore correct (\ref{szetszedes}) as
follows. Although critical points of $f$ are unavoidable, they are at least
isolated i.e., for all $p,q\in X^\times$ pairs of critical points there exist
small surrounding open neighbourhoods $U_p,U_q\subset X^\times$ such that
$U_p\cap U_q=\emptyset$. Then taking the union
\[C_f:=\bigcup\limits_{\mbox{$p$ is a critical point of $f$}}U_p\]
which is therefore disjoint and supposing that this set is sharply
concentrated around the critical
points of $f$ in $X^\times$, let us correct (\ref{szetszedes}) to
\[v:={\rm grad}f+w\]
where $w$ is a smooth vector field (of the form $w={\rm div}T$) on
$X^\times$ such that $w(p)\not=0$ in the critical point $p$ but
${\rm supp}\:w\subset C_f$ i.e., $w$ vanishes outside of
$C_f\subset X^\times$. Fortunately this changes our physical picture
on $(X^\times, g_L)$ only locally (i.e. close to a critical point
only). More precisely, the classical observer picture of $v$ breaks down
only in the vicinity of critical points of its Morse function part. Therefore
from now on we suppose: {\it if $v={\rm grad}f+w$ is a non-vanishing
vector field on $X^\times$ then the infinitesimal observer provided by $v$
in the original space-time $(X^\times, g_L)$ gives rise to a global classical
observer in the sense above at least on the open domain
\begin{equation}
(X^\times\setminus\overline{C}_f\:,\:
g_L\vert_{X^\times\setminus\overline{C}_f}\:)\subsetneqq (X^\times, g_L)
\label{megszoritas}
\end{equation}
because $v={\rm grad}f$ along this restriction as before}.
Let us ask ourselves now about the ``experiences'' of this partial global
classical observer, constructed from a Morse function, as it moves in
$(X^\times, g_L)$. That is, consider a Morse function $f$ on $X^\times$ as
above (see Figure 6) with an associated global classical observer
on the restricted domain $X^\times\setminus\overline{C}_f$. This observer has a
global proper time $t\in (-\infty, 0]$ measured by $f$ with the
infinite past $t=-\infty$ being the creased end of $X^\times$ and
also has corresponding global spacelike
$\Sigma_t:=f^{-1}(t)\subset X^\times\setminus\overline{C}_f$ for
appropriate $t$'s which are closed $3$-manifolds. First, fix
$-\infty < K<0$ such that $\Sigma_K$ is a submanifold and consider the
compact part $f^{-1}([K, 0])\subsetneqq X^\times$. As the
observer moves forwards in time i.e., from $t=K$ to $t=0$ along the integral
curves of ${\rm grad}f$ then only finitely many critical points occur. As we
have seen, around these points the spacelike $\Sigma_t$'s change topology by
picking up a $k$-handle according to the index of the critical point.
Now consider the much more interesting non-compact $f^{-1}((-\infty
,K])\subset X^\times$ regime, the downward ``neck'' part in Figure 6.
If $K<0$ is sufficiently small (we mean $\vert K\vert >0$ is
sufficiently large) we can suppose that $f^{-1}((-\infty, K])$ is fully
contained in the exotic but topologically trivial summand $R^4$ of $X^\times$
in its decomposition $X^\times =M\#R^4$. Therefore if $-\infty <t\leqq K$
then $\Sigma_t$ is fully contained in the $R^4$ summand. We can
without loss of generality suppose that $\Sigma_K$ surrounds the
attaching region of $M$ and $R^4$ hence $\Sigma_K$ is diffeomorphic to
$S^3$. Now take an observer in $(X^\times,g_L)$ moving backwards in time along
the integral curves of ${\rm grad} f$ i.e. from $t=K$ downwards $t=-\infty$. A
generic value of $t$
is not critical for $f$ consequently the corresponding spacelike submanifold
$\Sigma_t$ exists. Consider a fixed time $-\infty<t_0<K$ which is a
critical value of $f$. How the corresponding transition between the
$\Sigma_t$'s then looks like? As we have seen, in this moment always a single
$4$-ball $B^4$, attached through its boundary $S^3$ in various ways to
$\Sigma_t$ depending on the index $k$ of the critical point, is going to be
removed from the latter space-time portion $f^{-1}([t_0,K])$. Therefore, as we
move backwards in time provided by $f$ (or move forwards in time provided by
$-f$) and pass through the moment $t_0$ the space $\Sigma_{t_0+\varepsilon}$
undergoes one of the following topological transitions:
\begin{itemize}
\item[$*$] If $k=1$ then at $t_0$ an $S^3$, attached
along two disjoint $B^3$'s to $\Sigma_{t_0+\varepsilon}$, is annihilated
(or equivalently, attached along a thickened $S^2$, is created);
\item[$*$] If $k=2$ then at $t_0$ an $S^3$, attached
along a thickened knot to $\Sigma_{t_0+\varepsilon}$, is annihilated
(or equivalently, attached along a thickened knot, is created);
\item[$*$] If $k=3$ then at $t_0$ an $S^3$, attached
along a thickened $S^2$ to $\Sigma_{t_0+\varepsilon}$, is annihilated
(or equivalently, attached along two disjoint $B^3$'s, is created)
\end{itemize}
and in this way the latter space $\Sigma_{t_0+\varepsilon}$
evolves into to the earlier $\Sigma_{t_0-\varepsilon}$ as we move backwards
in time. Strictly mathematically speaking this $k$-handle attachment is to be
performed ``instantaneosly'' somewhere along the singular level surface
$\Sigma_{t_0}$ carrying a unique critical point $p$ at the moment $t_0$;
however from a physical viewpoint we can rather suppose that it occurs within
the ``non-classical'' (with respect to the observer provided by ${\rm grad}f$)
region $\Sigma_t\cap U_p\subset C_f$ at some unspecified time $t\in
(t_0-\varepsilon ,t_0+\varepsilon)$ such that $\Sigma_{t_0\pm\varepsilon}
\cap U_p$ are still not empty (see Figure 7). Beside the $f$ Morse
function picture, we have formulated all processes in the dual picture of
the reversed Morse function $-f$ as well in order to gain full symmetry in
the formulation. Moreover we note that applying diffeomorphisms on $X^\times$
(or equivalently, modifying $f$) we can assume that along $f^{-1}((-\infty
,K])$ with $K<0$ the $k=0,4$ handle attachment steps corresponding to local
minima and maxima do not occur.
\vspace{0.3in}
\centerline{
\begin{tikzpicture}[scale=0.7, rotate=-90]
\draw [thick, fill=gray] (7.5,2) circle (0.25cm);
\node at (8.2,2) {$\Sigma_{t_0-\varepsilon}\cap U_p$};
\draw [thick] (7.5,-1) circle (1cm);
\draw [thick] (7.5,5) circle (1cm);
\node at (7.5,9) {$\Sigma_{t_0-\varepsilon}$};
\draw [thick, fill=gray] (5,2) circle (0.7cm);
\draw [fill] (5,2) circle (0.1cm);
\node at (6.2,2) {$\Sigma_{t_0}\cap U_p$};
\node at (5,1.5) {$p$};
\def100{100}
\def1.3{1.3}
\pgfmathsetmacro\cc{1.3*1.3}
\draw [thick, rotate=90, xshift=2cm, yshift=-5cm]
(0,0) --
plot[variable=\t,
domain=-45+1/100:45-1/100,
samples=100,
smooth,]
(\t:{\cc*sqrt(2*\cc*cos(2*(\t))})
-- cycle;
\draw [thick, rotate=90, xshift=2cm, yshift=-5cm]
(0,0) --
plot[variable=\t,
domain=180-45+1/100:180+45-1/100,
samples=100,
smooth,]
(\t:{\cc*sqrt(2*\cc*cos(2*\t))})
-- cycle;
\node at (5,9) {$\Sigma_{t_0}$};
\draw [thick] (2,2) circle (1.6cm);
\draw [thick, fill=gray] (2,2) circle (0.25cm);
\node at (2.7,2) {$\Sigma_{t_0+\varepsilon}\cap U_p$};
\node at (2,9) {$\Sigma_{t_0+\varepsilon}$};
\end{tikzpicture}
}
\vspace{0.3in}
\centerline{Figure 7. Topology change about the critical point
$p\in\Sigma_{t_0}\cap U_p\subset X^\times$ about the moment
$t_0\in (-\infty, 0]$.}
\vspace{0.3in}
Taking $-\infty\leftarrow t$ i.e., as moving backwards in time till the
creased end of $X^\times$ in Figure 6, in this process
the collection $\{\Sigma_t\}_{-\infty <t\leqq K}$ of spacelike
submanifolds looks like an evolution (in reversed
time) from $\Sigma_K=S^3$ into a three dimensional ``boiling foam'' limit
$\Sigma_{-\infty}$ or something like that. That is, these spacelike
submanifolds unboundedly continue to switch their topology; or in other
words the spatial oscillation between these states never stops and it is
reasonable to expect that all closed orientable $3$-manifolds
occur as $-\infty\leftarrow t$. Indeed, as
we noted in the Introduction, large exotic $R^4$'s always require
countably infinitely many handles in their handle decomposition therefore
moving backwards in time the $\Sigma_t$'s permanently continue changing their
topological type. Moreover soon or later $\Sigma_t$ very likely can be
arbitrary since the $k=2$ processes above are nothing but surgeries along
knots and all connected, closed, orientable $3$-manifolds arise this way
from $S^3=\Sigma_K$ by the Lickorish--Wallace theorem \cite{lic,wal}. This
``boiling foam'' picture therefore seems to be very weird and dynamical and
the sole ``driving force'' behind this dynamics is the non-standard
smooth structure along the end of $X^\times$. (Exactly the same thing is
responsible for the role of these spaces in $\overline{\bf SCCC}$, too.)
The existence of topologically different Cauchy surfaces in $\R^4$ is
already known to physicists, too \cite{new-cla}.
All the things have described up to this point might seem as mere
mathematical nonsense. However they get even physically interesting if
we recognize that this vivid spatial topology oscillation in $(X^\times,
g_L)$ appears as a cosmological redshift phenomenon to our observer moving in
(\ref{megszoritas}), as it looks back to the early creased end of $X^\times$
at late times. Let $E\in X^\times\setminus\overline{C}_f$ be a
space-time event with a normalized future-directed timelike vector $n_E$
where a photon is emitted; in the geometrical optics approximation this
photon travels along a future-directed null geodesic $\gamma$ in
$(X^\times, g_L)$ till it is received in a later
$R\in X^\times\setminus\overline{C}_f$ with corresponding receiver $n_R$.
Taking any affine parameterization (i.e., $\nabla^L_{\gamma'}\gamma'=0$) the
emitted frequency measured by $n_E$ is $\omega_E=-g_L(\gamma_E',n_E)$ while
$\omega_R=-g_L(\gamma_R',n_R)$ is the frequency measured by the receiver.
Then we define the {\it redshift factor} $z$ in the standard way by the
frequency ratio
\[1+z=\frac{\omega_E}{\omega_R}=\frac{g_L(\gamma_E',n_E)}
{g_L(\gamma_R',n_R)}\]
and say that the photon is {\it redshifted} along $\gamma$ if $z>0$.
We adapt this general framework at least qualitatively to our setup as
follows. Assume that the observer in the above process is given by
$n=\frac{{\rm grad}f}{\vert{\rm grad}f\vert_{g_L}}$. Making use of the
notation in the proof of Theorem \ref{lorentztetel},
${\rm grad} f$ is a section of $L\subset TX^\times$ hence
$W_L{\rm grad}f=\sqrt{-1}\:{\rm grad}f$; moreover if
$\gamma'=\gamma'_L+\gamma'_{L^\perp}$ is
the unique decomposition according to $TX^\times =L\oplus L^\perp$ then
$W_L\gamma' =W_L\gamma'_L+W_L\gamma'_{L^\perp}=
\sqrt{-1}\gamma'_L+\gamma'_{L^\perp}\in \sqrt{-1}\:L\oplus L^\perp$.
Consequently
\[g_L(\gamma'\:,\:n)=\frac{g_L(\gamma'\:,\:{\rm grad}f)}{\vert {\rm
grad}f\vert_{g_L}}=\frac{g^\C(W_L\gamma'\:,\:W_L{\rm grad}f)}{\vert
W_L{\rm grad}f\vert_{g^\C}}=\frac{-g(\gamma'_L\:,\:{\rm grad}f)}
{-\vert {\rm grad}f\vert_g}=\frac{g(\gamma'\:,\:{\rm grad}f)}{\vert
{\rm grad}f\vert_g}\:\:.\]
Moreover
\[\dd g(\gamma'\:,\:{\rm grad}f)\gamma'=-\dd g_L(\gamma'\:,\:{\rm
grad}f)\gamma'=
-g_L(\nabla^L_{\gamma '}\gamma'\:,\:{\rm grad}f)-g_L(\gamma'\:,\:
\nabla^L_{\gamma '}{\rm grad}f)=-{\rm Hess}_f(\gamma',\gamma')\]
where ${\rm Hess}_f(x)=(\partial^2_{ij}f(x))_{i,j=1,\dots,4}$. Consider a
non-critical point $q\in X^\times$ and its open neighbourhood $V_q\subset
X^\times\setminus\overline{C}_f$ i.e. $V_q$ surely does not contain any
critical point of $f$. Then there exists a local coordinate
system $(V_q, t,x_1,x_2,x_3)$ centered at $q$ i.e.
$t(q)=x_i(q)=0$ such that $f\vert_{V_q}(t,x_1,x_2,x_3)=t$ implying
${\rm Hess}_f\vert_{V_q}=0$. Therefore $\dd g(\gamma'\:,\:{\rm grad}f)\gamma'=
\gamma'(g(\gamma'\:,\:{\rm grad}f))=0$ along $V_q$ i.e. if the photon path
$\gamma$ does not intersect any critical point then $g(\gamma'\:,\:{\rm
grad}f)$ is a non-zero constant along the whole $\gamma$. In this situation
we end up with
\[1+z=\frac{\vert {\rm grad}f(R)\vert_g}{\vert {\rm grad}f(E)\vert_g}\:\:.\]
As we emphasized throughout this note, the level surfaces
$f^{-1}(t)\subset X^\times$ attain critical points more and more frequently
as $-\infty\leftarrow t$. Consequently, the earlier space-time event
$E\in f^{-1}(t_E)$ is ``more likely'' to be in the vicinity of a
critical point $p_E\in f^{-1}(t_E)$ satisfying ${\rm grad}f(p_E)=0$ than
the later event $R\in f^{-1}(t_R)$ with $t_R>t_E$. Therefore, acknowledging
that a more careful statistical analysis is surely required, it is reasonable
that ``typically'' $\vert{\rm grad}f(E)\vert_g\approx 0$ meanwhile
$\vert{\rm grad} f(R)\vert_g\approx 1$ implying that the gradient ratio on
the right hand side of $1+z$, when calculated for the ``typical'' early photon
emitting event $E\in X^\times\setminus\overline{C}_f$ and late
photon receiving event $R\in X^\times\setminus\overline{C}_f$, is large
resulting in $z>0$. By the same reasoning this ratio even seems to be capable
to be unbounded hence ``typically'' even $z>2$ seems reasonable which is
exclusively characteristical for {\it cosmological} (i.e., not gravitational
caused by a compact body, etc.) redshift. A cosmological context here is not
surprising since our solutions $(X^\times ,g_L)$ are smooth while it has
been known for a long time that in general relativity the gravitational field
of an isolated massive object cannot be regular everywhere \cite{ein, ein-pau}.
Finally, one may raise the question about the place or role or relevance
of this topology changing phenomenon within the full theory of
(classical or even quantum) general relativity. Regarding
this it is worth calling attention again that the Riemannian solutions
$(X^\times ,g)$ underlying our smooth vacuum space-times $(X^\times
,g_L)$ are not only Ricci-flat but even self-dual (see Theorem
\ref{fotetel2} here). Consequently they are gravitational instantons and
their appearance here looks reasonable for they are expected to generate
these topology changes as tunnelings at the semi-classical (i.e. the leading
term of quantum corrections) level. At first sight
the whole picture presented here strongly resembles the structure of the
vacuum sector of a non-Abelian gauge theory in temporal gauge over Minkowski
space: in analogy with the present situation instantons of the Euclidean
Yang--Mills theory over the Euclidean flat space execute semi-classical
tunnelings between topologically (hence classically) separated classical
vacua along space-like submanifolds in the original Minkowskian
Yang--Mills theory over the Minkowskian flat space.
However there is a subtle difference between the two tunneling processes
which is probably worth recording here. In case of Yang--Mills theory
all the aforementioned topologically different states connected by
(anti)instanton effects are {\it vacua} hence the corresponding
tunneling mechanism is time-symmetric which means that both instantons
and antiinstantons occur and play a role. On the contrary in our
gravitational situation the family $\{\Sigma_t\}_{-\infty <t\leqq 0}$ of
topologically different spatial submanifolds with their corresponding
Riemannian metrics inherited from their embeddings into $(X^\times,g_L)$
and connected by instanton effects are {\it not flat}; rather as
$t\rightarrow 0$ this family looks like a sequence descending from
quite complicated, topologically non-trivial highly curved compact $3$-spaces
($\Sigma_t$'s with $t\ll 0$, the bottom part of Figure 6)
towards topologically trivial $3$-spheres carrying metrics already close
to the standard round metric ($\Sigma_t$'s with $t\lessapprox 0$,
the top of Figure 6). Therefore, as moving {\it forwards} in
time the whole process seems to describe a sort of monotonic decay
mechanism converting the gravitational degrees of freedom into other
ones (like Yang--Mills fields, fermions, etc.) before reaching the
gravitational vacuum (in our spatially compact situation the standard
round $S^3$ plays the role of the flat geometry i.e. the gravitational
vacuum). This process therefore seems to be not reversible and having a
creased end introduces a sort of time direction along the cosmological
space-time $(X^\times, g_L)$. Consequently the gravitational instantons
provided by the spaces $(X^\times, g)$ are asymmetric unlike the
gravitational instanton-antiinstanton pairs considered in \cite[Section
III]{wit}.
Are then $(X^\times, g)$'s physically relevant? Based on cluster
decomposition Witten argues that a non-perturbative
field is still relevant in a quantum theory if it is continuously deformable
to the vacuum in an appropriate configuration space \cite[Section III]{wit}.
Consider the case of traditional general
relativity when space-time is topologically $\R^m$ and in particular the
vacuum is the flat $\R^m$. Then by this argument gravitational
instantons restricted to be exotic $m$-spheres if $m\not=4$. However if $m=4$
we cannot forget about exotic $\R^4$'s. In this exceptional situation we can
follow Gompf \cite[Chapter 9.4]{gom-sti}
and consider the configuration space $\crr_\sim$ of compact equivalence
classes of smooth structures on $\R^4$. The set $\crr_\sim$ can be given the
structure of a connected metrizable topological space with countable basis
in which therefore the vacuum i.e. the standard $\R^4$ is represented by a
point while our gravitational instanton $R^4$ by another point.
Consequently within $\crr_\sim$ the gravitational instanton considered here
is deformable into the vacuum. However the relevance of this purely formal
observation is not clear neither from a physical nor a mathematical viewpoint.
\vspace{0.1in}
\noindent {\bf Acknowledgement}. This paper is dedicated to Roger Penrose, the
laureate of the 2020 Nobel Prize in physics.
The author wishes to thank to I. K\'ad\'ar for the stimulating discussions and
the Referee of JGP for raising lot of excellent clarifying questions.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,026 |
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <Defn.h>
#include <stdio.h>
#include <ctype.h>
#include <limits.h> /* required for MB_LEN_MAX */
#include <wchar.h>
#include <wctype.h>
static void
mbcsToSbcs(const char *in, char *out, const char *encoding, int enc);
#include <R_ext/Riconv.h>
#include <Rmath.h> /* for fround */
#define R_USE_PROTOTYPES 1
#include <R_ext/GraphicsEngine.h>
#include <R_ext/Error.h>
#include <R_ext/RS.h>
#include "Fileio.h"
#include "grDevices.h"
#ifdef HAVE_ERRNO_H
#include <errno.h>
#else
extern int errno;
#endif
#include "zlib.h"
/* from connections.o */
extern gzFile R_gzopen (const char *path, const char *mode);
extern char *R_gzgets(gzFile file, char *buf, int len);
extern int R_gzclose (gzFile file);
#define INVALID_COL 0xff0a0b0c
/* Define this to use hyphen except in -[0-9] */
#undef USE_HYPHEN
/* In ISOLatin1, minus is 45 and hyphen is 173 */
#ifdef USE_HYPHEN
static char PS_hyphen = 173;
#endif
#define USERAFM 999
/* Part 0. AFM File Names */
static const char *CIDBoldFontStr1 =
"16 dict begin\n"
" /basecidfont exch def\n"
" /basefont-H /.basefont-H /Identity-H [ basecidfont ] composefont def\n"
" /basefont-V /.basefont-V /Identity-V [ basecidfont ] composefont def\n"
" /CIDFontName dup basecidfont exch get def\n"
" /CIDFontType 1 def\n"
" /CIDSystemInfo dup basecidfont exch get def\n"
" /FontInfo dup basecidfont exch get def\n"
" /FontMatrix [ 1 0 0 1 0 0 ] def\n"
" /FontBBox [\n"
" basecidfont /FontBBox get cvx exec\n"
" 4 2 roll basecidfont /FontMatrix get transform\n"
" 4 2 roll basecidfont /FontMatrix get transform\n"
" ] def\n"
" /cid 2 string def\n";
static const char *CIDBoldFontStr2 =
" /BuildGlyph {\n"
" gsave\n"
" exch begin\n"
" dup 256 idiv cid exch 0 exch put\n"
" 256 mod cid exch 1 exch put\n"
" rootfont\n"
" /WMode known { rootfont /WMode get 1 eq } { false } ifelse\n"
" { basefont-V } { basefont-H } ifelse setfont\n"
" .03 setlinewidth 1 setlinejoin\n"
" newpath\n"
" 0 0 moveto cid false charpath stroke\n"
" 0 0 moveto cid show\n"
" currentpoint setcharwidth\n"
" end\n"
" grestore\n"
" } bind def\n"
" currentdict\n"
"end\n"
"/CIDFont defineresource pop\n";
/* Part 1. AFM File Parsing. */
/* These are the basic entities in the AFM file */
#define BUFSIZE 512
#define NA_SHORT -30000
typedef struct {
unsigned char c1;
unsigned char c2;
short kern;
} KP;
typedef struct {
short FontBBox[4];
short CapHeight;
short XHeight;
short Descender;
short Ascender;
short StemH;
short StemV;
short ItalicAngle;
struct {
short WX;
short BBox[4];
} CharInfo[256];
KP *KernPairs;
short KPstart[256];
short KPend[256];
short nKP;
short IsFixedPitch;
} FontMetricInfo;
enum {
Empty,
StartFontMetrics,
Comment,
FontName,
EncodingScheme,
FullName,
FamilyName,
Weight,
ItalicAngle,
IsFixedPitch,
UnderlinePosition,
UnderlineThickness,
Version,
Notice,
FontBBox,
CapHeight,
XHeight,
Descender,
Ascender,
StartCharMetrics,
C,
CH,
EndCharMetrics,
StartKernData,
StartKernPairs,
KPX,
EndKernPairs,
EndKernData,
StartComposites,
CC,
EndComposites,
EndFontMetrics,
StdHW,
StdVW,
CharacterSet,
Unknown
};
static const struct {
const char *keyword;
const int code;
}
KeyWordDictionary[] = {
{ "StartFontMetrics", StartFontMetrics },
{ "Comment", Comment },
{ "FontName", FontName },
{ "EncodingScheme", EncodingScheme },
{ "FullName", FullName },
{ "FamilyName", FamilyName },
{ "Weight", Weight },
{ "ItalicAngle", ItalicAngle },
{ "IsFixedPitch", IsFixedPitch },
{ "UnderlinePosition", UnderlinePosition },
{ "UnderlineThickness", UnderlineThickness },
{ "Version", Version },
{ "Notice", Notice },
{ "FontBBox", FontBBox },
{ "CapHeight", CapHeight },
{ "XHeight", XHeight },
{ "Descender", Descender },
{ "Ascender", Ascender },
{ "StartCharMetrics", StartCharMetrics },
{ "C ", C },
{ "CH ", CH },
{ "EndCharMetrics", EndCharMetrics },
{ "StartKernData", StartKernData },
{ "StartKernPairs", StartKernPairs },
{ "KPX ", KPX },
{ "EndKernPairs", EndKernPairs },
{ "EndKernData", EndKernData },
{ "StartComposites", StartComposites },
{ "CC ", CC },
{ "EndComposites", EndComposites },
{ "EndFontMetrics", EndFontMetrics },
{ "StdHW", StdHW },
{ "StdVW", StdVW },
{ "CharacterSet", CharacterSet},
{ NULL, Unknown },
};
static int MatchKey(char const * l, char const * k)
{
while (*k)
if (*k++ != *l++) return 0;
return 1;
}
static int KeyType(const char * const s)
{
int i;
if (*s == '\n')
return Empty;
for (i = 0; KeyWordDictionary[i].keyword; i++)
if (MatchKey(s, KeyWordDictionary[i].keyword))
return KeyWordDictionary[i].code;
// printf("Unknown %s\n", s); // not needed, PR#15057 found it annoying
return Unknown;
}
static char *SkipToNextItem(char *p)
{
while (!isspace((int)*p)) p++;
while (isspace((int)*p)) p++;
return p;
}
static char *SkipToNextKey(char *p)
{
while (*p != ';') p++;
p++;
while (isspace((int)*p)) p++;
return p;
}
static int GetFontBBox(const char *buf, FontMetricInfo *metrics)
{
if (sscanf(buf, "FontBBox %hd %hd %hd %hd",
&(metrics->FontBBox[0]),
&(metrics->FontBBox[1]),
&(metrics->FontBBox[2]),
&(metrics->FontBBox[3])) != 4) return 0;
#ifdef DEBUG_PS2
Rprintf("FontBBox %d %d %d %d\n",
(metrics->FontBBox[0]),
(metrics->FontBBox[1]),
(metrics->FontBBox[2]),
(metrics->FontBBox[3]));
#endif
return 1;
}
/* The longest named Adobe glyph is 39 chars:
whitediamondcontainingblacksmalldiamond
*/
typedef struct {
char cname[40];
} CNAME;
/* If reencode > 0, remap to new encoding */
static int GetCharInfo(char *buf, FontMetricInfo *metrics,
CNAME *charnames, CNAME *encnames,
int reencode)
{
char *p = buf, charname[40];
int nchar, nchar2 = -1, i;
short WX;
if (!MatchKey(buf, "C ")) return 0;
p = SkipToNextItem(p);
sscanf(p, "%d", &nchar);
if ((nchar < 0 || nchar > 255) && !reencode) return 1;
p = SkipToNextKey(p);
if (!MatchKey(p, "WX")) return 0;
p = SkipToNextItem(p);
sscanf(p, "%hd", &WX);
p = SkipToNextKey(p);
if (!MatchKey(p, "N ")) return 0;
p = SkipToNextItem(p);
if(reencode) {
sscanf(p, "%s", charname);
#ifdef DEBUG_PS2
Rprintf("char name %s\n", charname);
#endif
/* a few chars appear twice in ISOLatin1 */
nchar = nchar2 = -1;
for (i = 0; i < 256; i++)
if(!strcmp(charname, encnames[i].cname)) {
strcpy(charnames[i].cname, charname);
if(nchar == -1) nchar = i; else nchar2 = i;
}
if (nchar == -1) return 1;
} else {
sscanf(p, "%s", charnames[nchar].cname);
}
metrics->CharInfo[nchar].WX = WX;
p = SkipToNextKey(p);
if (!MatchKey(p, "B ")) return 0;
p = SkipToNextItem(p);
sscanf(p, "%hd %hd %hd %hd",
&(metrics->CharInfo[nchar].BBox[0]),
&(metrics->CharInfo[nchar].BBox[1]),
&(metrics->CharInfo[nchar].BBox[2]),
&(metrics->CharInfo[nchar].BBox[3]));
#ifdef DEBUG_PS2
Rprintf("nchar = %d %d %d %d %d %d\n", nchar,
metrics->CharInfo[nchar].WX,
metrics->CharInfo[nchar].BBox[0],
metrics->CharInfo[nchar].BBox[1],
metrics->CharInfo[nchar].BBox[2],
metrics->CharInfo[nchar].BBox[3]);
#endif
if (nchar2 > 0) {
metrics->CharInfo[nchar2].WX = WX;
sscanf(p, "%hd %hd %hd %hd",
&(metrics->CharInfo[nchar2].BBox[0]),
&(metrics->CharInfo[nchar2].BBox[1]),
&(metrics->CharInfo[nchar2].BBox[2]),
&(metrics->CharInfo[nchar2].BBox[3]));
#ifdef DEBUG_PS2
Rprintf("nchar = %d %d %d %d %d %d\n", nchar2,
metrics->CharInfo[nchar2].WX,
metrics->CharInfo[nchar2].BBox[0],
metrics->CharInfo[nchar2].BBox[1],
metrics->CharInfo[nchar2].BBox[2],
metrics->CharInfo[nchar2].BBox[3]);
#endif
}
return 1;
}
static int GetKPX(char *buf, int nkp, FontMetricInfo *metrics,
CNAME *charnames)
{
char *p = buf, c1[50], c2[50];
int i, done = 0;
p = SkipToNextItem(p);
sscanf(p, "%s %s %hd", c1, c2, &(metrics->KernPairs[nkp].kern));
if (streql(c1, "space") || streql(c2, "space")) return 0;
for(i = 0; i < 256; i++) {
if (!strcmp(c1, charnames[i].cname)) {
metrics->KernPairs[nkp].c1 = (unsigned char) i;
done++;
break;
}
}
for(i = 0; i < 256; i++)
if (!strcmp(c2, charnames[i].cname)) {
metrics->KernPairs[nkp].c2 = (unsigned char) i;
done++;
break;
}
return (done==2);
}
/* Encode File Parsing. */
/* Statics here are OK, as all the calls are in one initialization
so no concurrency (until threads?) */
typedef struct {
/* Probably can make buf and p0 local variables. Only p needs to be
stored across calls. Need to investigate this more closely. */
char buf[1000];
char *p;
char *p0;
} EncodingInputState;
/* read in the next encoding item, separated by white space. */
static int GetNextItem(FILE *fp, char *dest, int c, EncodingInputState *state)
{
if (c < 0) state->p = NULL;
while (1) {
if (feof(fp)) { state->p = NULL; return 1; }
if (!state->p || *state->p == '\n' || *state->p == '\0') {
state->p = fgets(state->buf, 1000, fp);
}
/* check for incomplete encoding file */
if(!state->p) return 1;
while (isspace((int)* state->p)) state->p++;
if (state->p == '\0' || *state->p == '%'|| *state->p == '\n') { state->p = NULL; continue; }
state->p0 = state->p;
while (!isspace((int)*state->p)) state->p++;
if (state->p != '\0') *state->p++ = '\0';
if(c == 45) strcpy(dest, "/minus"); else strcpy(dest, state->p0);
break;
}
return 0;
}
/*
* Convert the encoding file name into a name to be used with iconv()
* in mbcsToSbcs()
*
* FIXME: Doesn't trim path/to/encfile (i.e., doesn't handle
* custom encoding file selected by user).
* Also assumes that encpath has ".enc" suffix supplied
* (not required by R interface)
*/
static int pathcmp(const char *encpath, const char *comparison) {
char pathcopy[PATH_MAX];
char *p1, *p2;
strcpy(pathcopy, encpath);
/*
* Strip path/to/encfile/
*/
p1 = &(pathcopy[0]);
while ((p2 = strchr(p1, FILESEP[0]))) {
p1 = p2 + sizeof(char);
}
/*
* Strip suffix
*/
p2 = (strchr(p1, '.'));
if (p2)
*p2 = '\0';
return strcmp(p1, comparison);
}
static void seticonvName(const char *encpath, char *convname)
{
/*
* Default to "latin1"
*/
char *p;
strcpy(convname, "latin1");
if(pathcmp(encpath, "ISOLatin1")==0)
strcpy(convname, "latin1");
else if(pathcmp(encpath, "ISOLatin2")==0)
strcpy(convname, "latin2");
else if(pathcmp(encpath, "ISOLatin7")==0)
strcpy(convname, "latin7");
else if(pathcmp(encpath, "ISOLatin9")==0)
strcpy(convname, "latin-9");
else if (pathcmp(encpath, "WinAnsi")==0)
strcpy(convname, "CP1252");
else {
/*
* Last resort = trim .enc off encpath to produce convname
*/
strcpy(convname, encpath);
p = strrchr(convname, '.');
if(p) *p = '\0';
}
}
/* Load encoding array from a file: defaults to the R_HOME/library/grDevices/afm directory */
/*
* encpath gives the file to read from
* encname is filled with the encoding name from the file
* encconvname is filled with a "translation" of the encoding name into
* one that can be used with iconv()
* encnames is filled with the character names from the file
* enccode is filled with the raw source of the file
*/
static int
LoadEncoding(const char *encpath, char *encname,
char *encconvname, CNAME *encnames,
char *enccode, Rboolean isPDF)
{
char buf[BUFSIZE];
int i;
FILE *fp;
EncodingInputState state;
state.p = state.p0 = NULL;
seticonvName(encpath, encconvname);
if(strchr(encpath, FILESEP[0])) strcpy(buf, encpath);
else snprintf(buf, BUFSIZE,"%s%slibrary%sgrDevices%senc%s%s",
R_Home, FILESEP, FILESEP, FILESEP, FILESEP, encpath);
#ifdef DEBUG_PS
Rprintf("encoding path is %s\n", buf);
#endif
if (!(fp = R_fopen(R_ExpandFileName(buf), "r"))) {
strcat(buf, ".enc");
if (!(fp = R_fopen(R_ExpandFileName(buf), "r"))) return 0;
}
if (GetNextItem(fp, buf, -1, &state)) return 0; /* encoding name */
strcpy(encname, buf+1);
if (!isPDF) snprintf(enccode, 5000, "/%s [\n", encname);
else enccode[0] = '\0';
if (GetNextItem(fp, buf, 0, &state)) { fclose(fp); return 0;} /* [ */
for(i = 0; i < 256; i++) {
if (GetNextItem(fp, buf, i, &state)) { fclose(fp); return 0; }
strcpy(encnames[i].cname, buf+1);
strcat(enccode, " /"); strcat(enccode, encnames[i].cname);
if(i%8 == 7) strcat(enccode, "\n");
}
if (GetNextItem(fp, buf, 0, &state)) { fclose(fp); return 0;} /* ] */
fclose(fp);
if (!isPDF) strcat(enccode,"]\n");
return 1;
}
/* Load font metrics from a file: defaults to the
R_HOME/library/grDevices/afm directory */
static int
PostScriptLoadFontMetrics(const char * const fontpath,
FontMetricInfo *metrics,
char *fontname,
CNAME *charnames,
CNAME *encnames,
int reencode)
{
char buf[BUFSIZE], *p, truth[10];
int mode, i = 0, j, ii, nKPX=0;
gzFile fp;
if(strchr(fontpath, FILESEP[0])) strcpy(buf, fontpath);
else
snprintf(buf, BUFSIZE,"%s%slibrary%sgrDevices%safm%s%s.gz",
R_Home, FILESEP, FILESEP, FILESEP, FILESEP, fontpath);
#ifdef DEBUG_PS
Rprintf("afmpath is %s\n", buf);
Rprintf("reencode is %d\n", reencode);
#endif
if (!(fp = R_gzopen(R_ExpandFileName(buf), "rb"))) {
/* try uncompressed version */
snprintf(buf, BUFSIZE,"%s%slibrary%sgrDevices%safm%s%s",
R_Home, FILESEP, FILESEP, FILESEP, FILESEP, fontpath);
if (!(fp = R_gzopen(R_ExpandFileName(buf), "rb"))) {
warning(_("afm file '%s' could not be opened"),
R_ExpandFileName(buf));
return 0;
}
}
metrics->KernPairs = NULL;
metrics->CapHeight = metrics->XHeight = metrics->Descender =
metrics->Ascender = metrics->StemH = metrics->StemV = NA_SHORT;
metrics->IsFixedPitch = -1;
metrics->ItalicAngle = 0;
mode = 0;
for (ii = 0; ii < 256; ii++) {
charnames[ii].cname[0] = '\0';
metrics->CharInfo[ii].WX = NA_SHORT;
for(j = 0; j < 4; j++) metrics->CharInfo[ii].BBox[j] = 0;
}
while (R_gzgets(fp, buf, BUFSIZE)) {
switch(KeyType(buf)) {
case StartFontMetrics:
mode = StartFontMetrics;
break;
case EndFontMetrics:
mode = 0;
break;
case FontBBox:
if (!GetFontBBox(buf, metrics)) {
warning("'FontBBox' could not be parsed");
goto pserror;
}
break;
case C:
if (mode != StartFontMetrics) goto pserror;
if (!GetCharInfo(buf, metrics, charnames, encnames, reencode)) {
warning("'CharInfo' could not be parsed");
goto pserror;
}
break;
case StartKernData:
mode = StartKernData;
break;
case StartKernPairs:
if(mode != StartKernData) goto pserror;
p = SkipToNextItem(buf);
sscanf(p, "%d", &nKPX);
if(nKPX > 0) {
/* nPKX == 0 should not happen, but has */
metrics->KernPairs = (KP *) malloc(nKPX * sizeof(KP));
if (!metrics->KernPairs) goto pserror;
}
break;
case KPX:
if(mode != StartKernData || i >= nKPX) goto pserror;
if (GetKPX(buf, i, metrics, charnames)) i++;
break;
case EndKernData:
mode = 0;
break;
case Unknown:
warning(_("unknown AFM entity encountered"));
break;
case FontName:
p = SkipToNextItem(buf);
sscanf(p, "%[^\n\f\r]", fontname);
break;
case CapHeight:
p = SkipToNextItem(buf);
sscanf(p, "%hd", &metrics->CapHeight);
break;
case XHeight:
p = SkipToNextItem(buf);
sscanf(p, "%hd", &metrics->XHeight);
break;
case Ascender:
p = SkipToNextItem(buf);
sscanf(p, "%hd", &metrics->Ascender);
break;
case Descender:
p = SkipToNextItem(buf);
sscanf(p, "%hd", &metrics->Descender);
break;
case StdHW:
p = SkipToNextItem(buf);
sscanf(p, "%hd", &metrics->StemH);
break;
case StdVW:
p = SkipToNextItem(buf);
sscanf(p, "%hd", &metrics->StemV);
break;
case ItalicAngle:
p = SkipToNextItem(buf);
sscanf(p, "%hd", &metrics->ItalicAngle);
break;
case IsFixedPitch:
p = SkipToNextItem(buf);
sscanf(p, "%[^\n\f\r]", truth);
metrics->IsFixedPitch = strcmp(truth, "true") == 0;
break;
case Empty:
default:
break;
}
}
metrics->nKP = (short) i;
R_gzclose(fp);
/* Make an index for kern-pair searches: relies on having contiguous
blocks by first char for efficiency, but works in all cases. */
{
short ind, tmp;
for (j = 0; j < 256; j++) {
metrics->KPstart[j] = (short) i;
metrics->KPend[j] = 0;
}
for (j = 0; j < i; j++) {
ind = metrics->KernPairs[j].c1;
tmp = metrics->KPstart[ind];
if(j < tmp) metrics->KPstart[ind] = (short) j;
tmp = metrics->KPend[ind];
if(j > tmp) metrics->KPend[ind] = (short) j;
}
}
return 1;
pserror:
R_gzclose(fp);
return 0;
}
extern int Ri18n_wcwidth(wchar_t c);
static double
PostScriptStringWidth(const unsigned char *str, int enc,
FontMetricInfo *metrics,
Rboolean useKerning,
int face, const char *encoding)
{
int sum = 0, i;
short wx;
const unsigned char *p = NULL, *str1 = str;
unsigned char p1, p2;
int status;
if(!metrics && (face % 5) != 0) {
/* This is the CID font case, and should only happen for
non-symbol fonts. So we assume monospaced with multipliers.
We need to remap even if we are in a SBCS, should we get to here */
size_t ucslen;
ucslen = mbcsToUcs2((char *)str, NULL, 0, enc);
if (ucslen != (size_t)-1) {
/* We convert the characters but not the terminator here */
R_CheckStack2(ucslen * sizeof(ucs2_t));
ucs2_t ucs2s[ucslen];
status = (int) mbcsToUcs2((char *)str, ucs2s, (int) ucslen, enc);
if (status >= 0)
for(i = 0 ; i < ucslen ; i++) {
wx = (short)(500 * Ri18n_wcwidth(ucs2s[i]));
/* printf("width for U+%04x is %d\n", ucs2s[i], wx); */
sum += wx;
}
else
warning(_("invalid string in '%s'"), "PostScriptStringWidth");
return 0.001 * sum;
} else {
warning(_("invalid string in '%s'"), "PostScriptStringWidth");
return 0.0;
}
} else
if(!strIsASCII((char *) str) &&
/*
* Every fifth font is a symbol font:
* see postscriptFonts()
*/
(face % 5) != 0) {
R_CheckStack2(strlen((char *)str)+1);
char buff[strlen((char *)str)+1];
/* Output string cannot be longer */
mbcsToSbcs((char *)str, buff, encoding, enc);
str1 = (unsigned char *)buff;
}
/* safety */
if(!metrics) return 0.0;
/* Now we know we have an 8-bit encoded string in the encoding to
be used for output. */
for (p = str1; *p; p++) {
#ifdef USE_HYPHEN
if (*p == '-' && !isdigit(p[1]))
wx = metrics->CharInfo[(int)PS_hyphen].WX;
else
#endif
wx = metrics->CharInfo[*p].WX;
if(wx == NA_SHORT)
warning(_("font width unknown for character 0x%x"), *p);
else sum += wx;
if(useKerning) {
/* check for kerning adjustment */
p1 = p[0]; p2 = p[1];
for (i = metrics->KPstart[p1]; i < metrics->KPend[p1]; i++)
/* second test is a safety check: should all start with p1 */
if(metrics->KernPairs[i].c2 == p2 &&
metrics->KernPairs[i].c1 == p1) {
sum += metrics->KernPairs[i].kern;
break;
}
}
}
return 0.001 * sum;
}
/* Be careful about the assumptions here. In an 8-bit locale 0 <= c < 256
and it is in the encoding in use. As it is not going to be
re-encoded when text is output, it is correct not to re-encode here.
When called in an MBCS locale and font != 5, chars < 128 are sent
as is (we assume that is ASCII) and others are re-encoded to
Unicode in GEText (and interpreted as Unicode in GESymbol).
*/
# ifdef WORDS_BIGENDIAN
static const char UCS2ENC[] = "UCS-2BE";
# else
static const char UCS2ENC[] = "UCS-2LE";
# endif
static void
PostScriptMetricInfo(int c, double *ascent, double *descent, double *width,
FontMetricInfo *metrics,
Rboolean isSymbol,
const char *encoding)
{
Rboolean Unicode = mbcslocale;
if (c == 0) {
*ascent = 0.001 * metrics->FontBBox[3];
*descent = -0.001 * metrics->FontBBox[1];
*width = 0.001 * (metrics->FontBBox[2] - metrics->FontBBox[0]);
return;
}
if (c < 0) { Unicode = TRUE; c = -c; }
/* We don't need the restriction to 65536 here any more as we could
convert from UCS4ENC, but there are few language chars above 65536. */
if(Unicode && !isSymbol && c >= 128 && c < 65536) { /* Unicode */
void *cd = NULL;
const char *i_buf; char *o_buf, out[2];
size_t i_len, o_len, status;
unsigned short w[2];
if ((void*)-1 == (cd = Riconv_open(encoding, UCS2ENC)))
error(_("unknown encoding '%s' in 'PostScriptMetricInfo'"),
encoding);
/* Here we use terminated strings, but could use one char */
w[0] = (unsigned short) c; w[1] = 0;
i_buf = (char *)w;
i_len = 4;
o_buf = out;
o_len = 2;
status = Riconv(cd, &i_buf, (size_t *)&i_len,
(char **)&o_buf, (size_t *)&o_len);
Riconv_close(cd);
if (status == (size_t)-1) {
*ascent = 0;
*descent = 0;
*width = 0;
warning(_("font metrics unknown for Unicode character U+%04x"), c);
return;
} else {
c = out[0] & 0xff;
}
}
if (c > 255) { /* Unicode */
*ascent = 0;
*descent = 0;
*width = 0;
warning(_("font metrics unknown for Unicode character U+%04x"), c);
} else {
short wx;
*ascent = 0.001 * metrics->CharInfo[c].BBox[3];
*descent = -0.001 * metrics->CharInfo[c].BBox[1];
wx = metrics->CharInfo[c].WX;
if(wx == NA_SHORT) {
warning(_("font metrics unknown for character 0x%x"), c);
wx = 0;
}
*width = 0.001 * wx;
}
}
static void
PostScriptCIDMetricInfo(int c, double *ascent, double *descent, double *width)
{
/* calling in a SBCS is probably not intentional, but we should try to
cope sensibly. */
if(!mbcslocale && c > 0) {
if (c > 255)
error(_("invalid character (%04x) sent to 'PostScriptCIDMetricInfo' in a single-byte locale"),
c);
else {
/* convert to UCS-2 to use wcwidth. */
char str[2]={0,0};
ucs2_t out;
str[0] = (char) c;
if(mbcsToUcs2(str, &out, 1, CE_NATIVE) == (size_t)-1)
error(_("invalid character sent to 'PostScriptCIDMetricInfo' in a single-byte locale"));
c = out;
}
}
/* Design values for all CJK fonts */
*ascent = 0.880;
*descent = -0.120;
if (c == 0 || c > 65535) *width = 1.; else *width = 0.5*Ri18n_wcwidth(c);
}
/*******************************************************
* Data structures and functions for loading Type 1 fonts into an R session.
*
* Used by PostScript, XFig and PDF drivers.
*
* The idea is that font information is only loaded once for each font
* within an R session. Also, each encoding is only loaded once per
* session. A global list of loaded fonts and a global list of
* loaded encodings are maintained. Devices maintain their own list
* of fonts and encodings used on the device; the elements of these
* lists are just pointers to the elements of the global lists.
*
* Cleaning up device lists just involves free'ing the lists themselves.
* When the R session closes, the actual font and encoding information
* is unloaded using the global lists.
*/
/*
* Information about one Type 1 font
*/
typedef struct CIDFontInfo {
char name[50];
} CIDFontInfo, *cidfontinfo;
typedef struct T1FontInfo {
char name[50];
FontMetricInfo metrics;
CNAME charnames[256];
} Type1FontInfo, *type1fontinfo;
/*
* Information about a font encoding
*/
typedef struct EncInfo {
char encpath[PATH_MAX];
char name[100]; /* Name written to PostScript/PDF file */
char convname[50]; /* Name used in mbcsToSbcs() with iconv() */
CNAME encnames[256];
char enccode[5000];
} EncodingInfo, *encodinginfo;
/*
* Information about a font family
* (5 fonts representing plain, bold, italic, bolditalic, and symbol)
*
* The name is a graphics engine font family name
* (distinct from the Type 1 font name)
*/
typedef struct CIDFontFamily {
char fxname[50];
cidfontinfo cidfonts[4];
type1fontinfo symfont;
char cmap[50];
char encoding[50];
} CIDFontFamily, *cidfontfamily;
typedef struct T1FontFamily {
char fxname[50];
type1fontinfo fonts[5];
encodinginfo encoding;
} Type1FontFamily, *type1fontfamily;
/*
* A list of Type 1 font families
*
* Used to keep track of fonts currently loaded in the session
* AND by each device to keep track of fonts currently used on the device.
*/
typedef struct CIDFontList {
cidfontfamily cidfamily;
struct CIDFontList *next;
} CIDFontList, *cidfontlist;
typedef struct T1FontList {
type1fontfamily family;
struct T1FontList *next;
} Type1FontList, *type1fontlist;
/*
* Same as type 1 font list, but for encodings.
*/
typedef struct EncList {
encodinginfo encoding;
struct EncList *next;
} EncodingList, *encodinglist;
/*
* Various constructors and destructors
*/
static cidfontinfo makeCIDFont()
{
cidfontinfo font = (CIDFontInfo *) malloc(sizeof(CIDFontInfo));
if (!font)
warning(_("failed to allocate CID font info"));
return font;
}
static type1fontinfo makeType1Font()
{
type1fontinfo font = (Type1FontInfo *) malloc(sizeof(Type1FontInfo));
/*
* Initialise font->metrics.KernPairs to NULL
* so that we know NOT to free it if we fail to
* load this font and have to
* bail out and free this type1fontinfo
*/
font->metrics.KernPairs = NULL;
if (!font)
warning(_("failed to allocate Type 1 font info"));
return font;
}
static void freeCIDFont(cidfontinfo font)
{
free(font);
}
static void freeType1Font(type1fontinfo font)
{
if (font->metrics.KernPairs)
free(font->metrics.KernPairs);
free(font);
}
static encodinginfo makeEncoding()
{
encodinginfo encoding = (EncodingInfo *) malloc(sizeof(EncodingInfo));
if (!encoding)
warning(_("failed to allocate encoding info"));
return encoding;
}
static void freeEncoding(encodinginfo encoding)
{
free(encoding);
}
static cidfontfamily makeCIDFontFamily()
{
cidfontfamily family = (CIDFontFamily *) malloc(sizeof(CIDFontFamily));
if (family) {
int i;
for (i = 0; i < 4; i++)
family->cidfonts[i] = NULL;
family->symfont = NULL;
} else
warning(_("failed to allocate CID font family"));
return family;
}
static type1fontfamily makeFontFamily()
{
type1fontfamily family = (Type1FontFamily *) malloc(sizeof(Type1FontFamily));
if (family) {
int i;
for (i = 0; i < 5; i++)
family->fonts[i] = NULL;
family->encoding = NULL;
} else
warning(_("failed to allocate Type 1 font family"));
return family;
}
/*
* Frees a font family, including fonts, but NOT encoding
*
* Used by global font list to free all fonts loaded in session
* (should not be used by devices; else may free fonts more than once)
*
* Encodings are freed using the global encoding list
* (to ensure that each encoding is only freed once)
*/
static void freeCIDFontFamily(cidfontfamily family)
{
int i;
for (i = 0; i < 4; i++)
if (family->cidfonts[i])
freeCIDFont(family->cidfonts[i]);
if (family->symfont)
freeType1Font(family->symfont);
free(family);
}
static void freeFontFamily(type1fontfamily family)
{
int i;
for (i=0; i<5; i++)
if (family->fonts[i])
freeType1Font(family->fonts[i]);
free(family);
}
static cidfontlist makeCIDFontList()
{
cidfontlist fontlist = (CIDFontList *) malloc(sizeof(CIDFontList));
if (fontlist) {
fontlist->cidfamily = NULL;
fontlist->next = NULL;
} else
warning(_("failed to allocate font list"));
return fontlist;
}
static type1fontlist makeFontList()
{
type1fontlist fontlist = (Type1FontList *) malloc(sizeof(Type1FontList));
if (fontlist) {
fontlist->family = NULL;
fontlist->next = NULL;
} else
warning(_("failed to allocate font list"));
return fontlist;
}
/*
* Just free the Type1FontList structure, do NOT free elements it points to
*
* Used by both global font list and devices to free the font lists
* (global font list separately takes care of the fonts pointed to)
*/
static void freeCIDFontList(cidfontlist fontlist) {
/*
* These will help to find any errors if attempt to
* use freed font list.
*/
fontlist->cidfamily = NULL;
fontlist->next = NULL;
free(fontlist);
}
static void freeFontList(type1fontlist fontlist) {
/*
* These will help to find any errors if attempt to
* use freed font list.
*/
fontlist->family = NULL;
fontlist->next = NULL;
free(fontlist);
}
static void freeDeviceCIDFontList(cidfontlist fontlist) {
if (fontlist) {
if (fontlist->next)
freeDeviceCIDFontList(fontlist->next);
freeCIDFontList(fontlist);
}
}
static void freeDeviceFontList(type1fontlist fontlist) {
if (fontlist) {
if (fontlist->next)
freeDeviceFontList(fontlist->next);
freeFontList(fontlist);
}
}
static encodinglist makeEncList()
{
encodinglist enclist = (EncodingList *) malloc(sizeof(EncodingList));
if (enclist) {
enclist->encoding = NULL;
enclist->next = NULL;
} else
warning(_("failed to allocated encoding list"));
return enclist;
}
static void freeEncList(encodinglist enclist)
{
enclist->encoding = NULL;
enclist->next = NULL;
free(enclist);
}
static void freeDeviceEncList(encodinglist enclist) {
if (enclist) {
if (enclist->next)
freeDeviceEncList(enclist->next);
freeEncList(enclist);
}
}
/*
* Global list of fonts and encodings that have been loaded this session
*/
static cidfontlist loadedCIDFonts = NULL;
static type1fontlist loadedFonts = NULL;
static encodinglist loadedEncodings = NULL;
/*
* There are separate PostScript and PDF font databases at R level
* so MUST have separate C level records too
* (because SAME device-independent font family name could map
* to DIFFERENT font for PostScript and PDF)
*/
static cidfontlist PDFloadedCIDFonts = NULL;
static type1fontlist PDFloadedFonts = NULL;
static encodinglist PDFloadedEncodings = NULL;
/*
* Names of R level font databases
*/
static char PostScriptFonts[] = ".PostScript.Fonts";
static char PDFFonts[] = ".PDF.Fonts";
/*
* Free the above globals
*
* NOTE that freeing the font families does NOT free the encodings
* Hence we free all encodings first.
*/
/* NB this is exported, and was at some point used by KillAllDevices
in src/main/graphics.c. That would be a problem now it is in a
separate DLL.
*/
#if 0
void freeType1Fonts()
{
encodinglist enclist = loadedEncodings;
type1fontlist fl = loadedFonts;
cidfontlist cidfl = loadedCIDFonts;
type1fontlist pdffl = PDFloadedFonts;
cidfontlist pdfcidfl = PDFloadedCIDFonts;
while (enclist) {
enclist = enclist->next;
freeEncoding(loadedEncodings->encoding);
freeEncList(loadedEncodings);
loadedEncodings = enclist;
}
while (fl) {
fl = fl->next;
freeFontFamily(loadedFonts->family);
freeFontList(loadedFonts);
loadedFonts = fl;
}
while (cidfl) {
cidfl = cidfl->next;
freeCIDFontFamily(loadedCIDFonts->cidfamily);
freeCIDFontList(loadedCIDFonts);
loadedCIDFonts = cidfl;
}
while (pdffl) {
pdffl = pdffl->next;
freeFontFamily(PDFloadedFonts->family);
freeFontList(PDFloadedFonts);
PDFloadedFonts = pdffl;
}
while (pdfcidfl) {
pdfcidfl = pdfcidfl->next;
freeCIDFontFamily(PDFloadedCIDFonts->cidfamily);
freeCIDFontList(PDFloadedCIDFonts);
PDFloadedCIDFonts = pdfcidfl;
}
}
#endif
/*
* Given a path to an encoding file,
* find an EncodingInfo that corresponds
*/
static encodinginfo
findEncoding(const char *encpath, encodinglist deviceEncodings, Rboolean isPDF)
{
encodinglist enclist = isPDF ? PDFloadedEncodings : loadedEncodings;
encodinginfo encoding = NULL;
int found = 0;
/*
* "default" is a special encoding which means use the
* default (FIRST) encoding set up ON THIS DEVICE.
*/
if (!strcmp(encpath, "default")) {
found = 1;
encoding = deviceEncodings->encoding;
} else {
while (enclist && !found) {
found = !strcmp(encpath, enclist->encoding->encpath);
if (found)
encoding = enclist->encoding;
enclist = enclist->next;
}
}
return encoding;
}
/*
* Find an encoding in device encoding list
*/
static encodinginfo
findDeviceEncoding(const char *encpath, encodinglist enclist, int *index)
{
encodinginfo encoding = NULL;
int found = 0;
*index = 0;
while (enclist && !found) {
found = !strcmp(encpath, enclist->encoding->encpath);
if (found)
encoding = enclist->encoding;
enclist = enclist->next;
*index = *index + 1;
}
return encoding;
}
/*
* Utility to avoid string overrun
*/
static void safestrcpy(char *dest, const char *src, int maxlen)
{
if (strlen(src) < maxlen)
strcpy(dest, src);
else {
warning(_("truncated string which was too long for copy"));
strncpy(dest, src, maxlen-1);
dest[maxlen-1] = '\0';
}
}
/*
* Add an encoding to the list of loaded encodings ...
*
* ... and return the new encoding
*/
static encodinginfo addEncoding(const char *encpath, Rboolean isPDF)
{
encodinginfo encoding = makeEncoding();
if (encoding) {
if (LoadEncoding(encpath,
encoding->name,
encoding->convname,
encoding->encnames,
encoding->enccode,
isPDF)) {
encodinglist newenc = makeEncList();
if (!newenc) {
freeEncoding(encoding);
encoding = NULL;
} else {
encodinglist enclist =
isPDF ? PDFloadedEncodings : loadedEncodings;
safestrcpy(encoding->encpath, encpath, PATH_MAX);
newenc->encoding = encoding;
if (!enclist) {
if(isPDF) PDFloadedEncodings = newenc;
else loadedEncodings = newenc;
} else {
while (enclist->next)
enclist = enclist->next;
enclist->next = newenc;
}
}
} else {
warning(_("failed to load encoding file '%s'"), encpath);
freeEncoding(encoding);
encoding = NULL;
}
} else
encoding = NULL;
return encoding;
}
/*
* Add an encoding to a list of device encodings ...
*
* ... and return the new list
*/
static encodinglist addDeviceEncoding(encodinginfo encoding,
encodinglist devEncs)
{
encodinglist newenc = makeEncList();
if (!newenc) {
devEncs = NULL;
} else {
encodinglist enclist = devEncs;
newenc->encoding = encoding;
if (!devEncs)
devEncs = newenc;
else {
while (enclist->next)
enclist = enclist->next;
enclist->next = newenc;
}
}
return devEncs;
}
/*
* Given a graphics engine font family name,
* find a Type1FontFamily that corresponds
*
* If get fxname match, check whether the encoding in the
* R database is "default"
* (i.e., the graphics engine font family encoding is unspecified)
* If it is "default" then check that the loaded encoding is the
* same as the encoding we want. A matching encoding is defined
* as one which leads to the same iconvname (see seticonvName()).
* This could perhaps be made more rigorous by actually looking inside
* the relevant encoding file for the encoding name.
*
* If the encoding we want is NULL, then we just don't care.
*
* Returns NULL if can't find font in loadedFonts
*/
static const char *getFontEncoding(const char *family, const char *fontdbname);
static type1fontfamily
findLoadedFont(const char *name, const char *encoding, Rboolean isPDF)
{
type1fontlist fontlist;
type1fontfamily font = NULL;
char *fontdbname;
int found = 0;
if (isPDF) {
fontlist = PDFloadedFonts;
fontdbname = PDFFonts;
} else {
fontlist = loadedFonts;
fontdbname = PostScriptFonts;
}
while (fontlist && !found) {
found = !strcmp(name, fontlist->family->fxname);
if (found) {
font = fontlist->family;
if (encoding) {
char encconvname[50];
const char *encname = getFontEncoding(name, fontdbname);
seticonvName(encoding, encconvname);
if (!strcmp(encname, "default") &&
strcmp(fontlist->family->encoding->convname,
encconvname)) {
font = NULL;
found = 0;
}
}
}
fontlist = fontlist->next;
}
return font;
}
SEXP Type1FontInUse(SEXP name, SEXP isPDF)
{
if (!isString(name) || LENGTH(name) > 1)
error(_("invalid font name or more than one font name"));
return ScalarLogical(
findLoadedFont(CHAR(STRING_ELT(name, 0)), NULL, asLogical(isPDF))
!= NULL);
}
static cidfontfamily findLoadedCIDFont(const char *family, Rboolean isPDF)
{
cidfontlist fontlist;
cidfontfamily font = NULL;
int found = 0;
if (isPDF) {
fontlist = PDFloadedCIDFonts;
} else {
fontlist = loadedCIDFonts;
}
while (fontlist && !found) {
found = !strcmp(family, fontlist->cidfamily->cidfonts[0]->name);
if (found)
font = fontlist->cidfamily;
fontlist = fontlist->next;
}
#ifdef PS_DEBUG
if(found)
Rprintf("findLoadedCIDFont found = %s\n",family);
#endif
return font;
}
SEXP CIDFontInUse(SEXP name, SEXP isPDF)
{
if (!isString(name) || LENGTH(name) > 1)
error(_("invalid font name or more than one font name"));
return ScalarLogical(
findLoadedCIDFont(CHAR(STRING_ELT(name, 0)), asLogical(isPDF))
!= NULL);
}
/*
* Find a font in device font list
*/
static cidfontfamily
findDeviceCIDFont(const char *name, cidfontlist fontlist, int *index)
{
cidfontfamily font = NULL;
int found = 0;
*index = 0;
/*
* If the graphics engine font family is ""
* just use the default font that was loaded when the device
* was created.
* This will (MUST) be the first font in the device
*/
#ifdef DEBUG_PS
Rprintf("findDeviceCIDFont=%s\n", name);
Rprintf("? cidfontlist %s\n", (fontlist) ? "found" : "not found");
#endif
if (strlen(name) > 0) {
while (fontlist && !found) {
#ifdef DEBUG_PS
Rprintf("findDeviceCIDFont=%s\n", name);
Rprintf("findDeviceCIDFont fontlist->cidfamily->name=%s\n",
fontlist->cidfamily->fxname);
#endif
found = !strcmp(name, fontlist->cidfamily->fxname);
if (found)
font = fontlist->cidfamily;
fontlist = fontlist->next;
*index = *index + 1;
}
} else {
font = fontlist->cidfamily;
*index = 1;
}
#ifdef DEBUG_PS
Rprintf("findDeviceCIDFont find index=%d\n", *index);
Rprintf("findDeviceCIDFont find font=%s\n", (font) ? "Found" : "NULL");
#endif
return font;
}
/*
* Must only be called once a device has at least one font added
* (i.e., after the default font has been added)
*/
static type1fontfamily
findDeviceFont(const char *name, type1fontlist fontlist, int *index)
{
type1fontfamily font = NULL;
int found = 0;
*index = 0;
/*
* If the graphics engine font family is ""
* just use the default font that was loaded when the device
* was created.
* This will (MUST) be the first font in the device
*/
if (strlen(name) > 0) {
while (fontlist && !found) {
found = !strcmp(name, fontlist->family->fxname);
if (found)
font = fontlist->family;
fontlist = fontlist->next;
*index = *index + 1;
}
} else {
font = fontlist->family;
*index = 1;
}
return font;
}
/*
* Get an R-level font database
*/
static SEXP getFontDB(const char *fontdbname) {
SEXP graphicsNS, PSenv;
SEXP fontdb;
PROTECT(graphicsNS = R_FindNamespace(ScalarString(mkChar("grDevices"))));
PROTECT(PSenv = findVar(install(".PSenv"), graphicsNS));
/* under lazy loading this will be a promise on first use */
if(TYPEOF(PSenv) == PROMSXP) {
PROTECT(PSenv);
PSenv = eval(PSenv, graphicsNS);
UNPROTECT(1);
}
PROTECT(fontdb = findVar(install(fontdbname), PSenv));
UNPROTECT(3);
return fontdb;
}
/*
* Get an R-level font object
*/
static SEXP getFont(const char *family, const char *fontdbname) {
int i, nfonts;
SEXP result = R_NilValue;
int found = 0;
SEXP fontdb = getFontDB(fontdbname);
SEXP fontnames;
PROTECT(fontnames = getAttrib(fontdb, R_NamesSymbol));
nfonts = LENGTH(fontdb);
for (i=0; i<nfonts && !found; i++) {
const char *fontFamily = CHAR(STRING_ELT(fontnames, i));
if (strcmp(family, fontFamily) == 0) {
found = 1;
result = VECTOR_ELT(fontdb, i);
}
}
if (!found)
warning(_("font family '%s' not found in PostScript font database"),
family);
UNPROTECT(1);
return result;
}
/*
* Get the path to the afm file for a user-specifed font
* given a graphics engine font family and the face
* index (0..4)
*
* Do this by looking up the font name in the PostScript
* font database
*/
static const char*
fontMetricsFileName(const char *family, int faceIndex,
const char *fontdbname)
{
int i, nfonts;
const char *result = NULL;
int found = 0;
SEXP fontdb = getFontDB(fontdbname);
SEXP fontnames;
PROTECT(fontnames = getAttrib(fontdb, R_NamesSymbol));
nfonts = LENGTH(fontdb);
for (i = 0; i < nfonts && !found; i++) {
const char *fontFamily = CHAR(STRING_ELT(fontnames, i));
if (strcmp(family, fontFamily) == 0) {
found = 1;
/* 1 means vector of font afm file paths */
result = CHAR(STRING_ELT(VECTOR_ELT(VECTOR_ELT(fontdb, i), 1),
faceIndex));
}
}
if (!found)
warning(_("font family '%s' not found in PostScript font database"),
family);
UNPROTECT(1);
return result;
}
static const char *getFontType(const char *family, const char *fontdbname)
{
return CHAR(STRING_ELT(getAttrib(getFont(family, fontdbname),
R_ClassSymbol), 0));
}
static Rboolean isType1Font(const char *family, const char *fontdbname,
type1fontfamily defaultFont)
{
/*
* If family is "" then we're referring to the default device
* font, so the test is just whether the default font is
* type1
*
* If loading font, send NULL for defaultFont
*/
if (strlen(family) == 0) {
if (defaultFont)
return TRUE;
else
return FALSE;
} else
return !strcmp(getFontType(family, fontdbname),
"Type1Font");
}
static Rboolean isCIDFont(const char *family, const char *fontdbname,
cidfontfamily defaultCIDFont) {
/*
* If family is "" then we're referring to the default device
* font, so the test is just whether the default font is
* type1
*
* If loading font, send NULL for defaultCIDFont
*/
if (strlen(family) == 0) {
if (defaultCIDFont)
return TRUE;
else
return FALSE;
} else
return !strcmp(getFontType(family, fontdbname),
"CIDFont");
}
/*
* Get encoding name from font database
*/
static const char *getFontEncoding(const char *family, const char *fontdbname)
{
SEXP fontnames;
int i, nfonts;
const char *result = NULL;
int found = 0;
SEXP fontdb = getFontDB(fontdbname);
PROTECT(fontnames = getAttrib(fontdb, R_NamesSymbol));
nfonts = LENGTH(fontdb);
for (i=0; i<nfonts && !found; i++) {
const char *fontFamily = CHAR(STRING_ELT(fontnames, i));
if (strcmp(family, fontFamily) == 0) {
found = 1;
/* 2 means 'encoding' element */
result = CHAR(STRING_ELT(VECTOR_ELT(VECTOR_ELT(fontdb, i), 2), 0));
}
}
if (!found)
warning(_("font encoding for family '%s' not found in font database"),
family);
UNPROTECT(1);
return result;
}
/*
* Get Font name from font database
*/
static const char *getFontName(const char *family, const char *fontdbname)
{
SEXP fontnames;
int i, nfonts;
const char *result = NULL;
int found = 0;
SEXP fontdb = getFontDB(fontdbname);
PROTECT(fontnames = getAttrib(fontdb, R_NamesSymbol));
nfonts = LENGTH(fontdb);
for (i=0; i<nfonts && !found; i++) {
const char *fontFamily = CHAR(STRING_ELT(fontnames, i));
if (strcmp(family, fontFamily) == 0) {
found = 1;
/* 0 means 'family' element */
result = CHAR(STRING_ELT(VECTOR_ELT(VECTOR_ELT(fontdb, i), 0), 0));
}
}
if (!found)
warning(_("font CMap for family '%s' not found in font database"),
family);
UNPROTECT(1);
return result;
}
/*
* Get CMap name from font database
*/
static const char *getFontCMap(const char *family, const char *fontdbname)
{
SEXP fontnames;
int i, nfonts;
const char *result = NULL;
int found = 0;
SEXP fontdb = getFontDB(fontdbname);
PROTECT(fontnames = getAttrib(fontdb, R_NamesSymbol));
nfonts = LENGTH(fontdb);
for (i=0; i<nfonts && !found; i++) {
const char *fontFamily = CHAR(STRING_ELT(fontnames, i));
if (strcmp(family, fontFamily) == 0) {
found = 1;
/* 2 means 'cmap' element */
result = CHAR(STRING_ELT(VECTOR_ELT(VECTOR_ELT(fontdb, i), 2), 0));
}
}
if (!found)
warning(_("font CMap for family '%s' not found in font database"),
family);
UNPROTECT(1);
return result;
}
/*
* Get Encoding name from CID font in font database
*/
static const char *
getCIDFontEncoding(const char *family, const char *fontdbname)
{
SEXP fontnames;
int i, nfonts;
const char *result = NULL;
int found = 0;
SEXP fontdb = getFontDB(fontdbname);
PROTECT(fontnames = getAttrib(fontdb, R_NamesSymbol));
nfonts = LENGTH(fontdb);
for (i=0; i<nfonts && !found; i++) {
const char *fontFamily = CHAR(STRING_ELT(fontnames, i));
if (strcmp(family, fontFamily) == 0) {
found = 1;
/* 3 means 'encoding' element */
result = CHAR(STRING_ELT(VECTOR_ELT(VECTOR_ELT(fontdb, i), 3), 0));
}
}
if (!found)
warning(_("font encoding for family '%s' not found in font database"),
family);
UNPROTECT(1);
return result;
}
/*
* Get Encoding name from CID font in font database
*/
static const char *getCIDFontPDFResource(const char *family)
{
SEXP fontnames;
int i, nfonts;
const char *result = NULL;
int found = 0;
SEXP fontdb = getFontDB(PDFFonts);
PROTECT(fontnames = getAttrib(fontdb, R_NamesSymbol));
nfonts = LENGTH(fontdb);
for (i=0; i<nfonts && !found; i++) {
const char *fontFamily = CHAR(STRING_ELT(fontnames, i));
if (strcmp(family, fontFamily) == 0) {
found = 1;
/* 4 means 'pdfresource' element */
result = CHAR(STRING_ELT(VECTOR_ELT(VECTOR_ELT(fontdb, i), 4), 0));
}
}
if (!found)
warning(_("font encoding for family '%s' not found in font database"),
family);
UNPROTECT(1);
return result;
}
/*
* Add a graphics engine font family/encoding to the list of loaded fonts ...
*
* ... and return the new font
*/
static cidfontfamily addLoadedCIDFont(cidfontfamily font, Rboolean isPDF)
{
cidfontlist newfont = makeCIDFontList();
if (!newfont) {
freeCIDFontFamily(font);
font = NULL;
} else {
cidfontlist fontlist;
if (isPDF)
fontlist = PDFloadedCIDFonts;
else
fontlist = loadedCIDFonts;
newfont->cidfamily = font;
if (!fontlist) {
if (isPDF)
PDFloadedCIDFonts = newfont;
else
loadedCIDFonts = newfont;
} else {
while (fontlist->next)
fontlist = fontlist->next;
fontlist->next = newfont;
}
}
return font;
}
static type1fontfamily addLoadedFont(type1fontfamily font,
Rboolean isPDF)
{
type1fontlist newfont = makeFontList();
if (!newfont) {
freeFontFamily(font);
font = NULL;
} else {
type1fontlist fontlist;
if (isPDF)
fontlist = PDFloadedFonts;
else
fontlist = loadedFonts;
newfont->family = font;
if (!fontlist) {
if (isPDF)
PDFloadedFonts = newfont;
else
loadedFonts = newfont;
} else {
while (fontlist->next)
fontlist = fontlist->next;
fontlist->next = newfont;
}
}
return font;
}
/*
* Add a font from a graphics engine font family name
*/
static cidfontfamily addCIDFont(const char *name, Rboolean isPDF)
{
cidfontfamily fontfamily = makeCIDFontFamily();
char *fontdbname;
if (isPDF)
fontdbname = PDFFonts;
else
fontdbname = PostScriptFonts;
if (fontfamily) {
int i;
const char *cmap = getFontCMap(name, fontdbname);
if (!cmap) {
freeCIDFontFamily(fontfamily);
fontfamily = NULL;
} else {
/*
* Set the name of the font
*/
safestrcpy(fontfamily->fxname, name, 50);
/*
* Get the font CMap
*/
safestrcpy(fontfamily->cmap, cmap, 50);
/*
* Get the font Encoding (name)
*
* If we have got here then we know there is a
* match in the font database because we already
* have the CMap => don't need to check for failure
*/
safestrcpy(fontfamily->encoding,
getCIDFontEncoding(name, fontdbname), 50);
/*
* Load font info
*/
for(i = 0; i < 4; i++) {
fontfamily->cidfonts[i] = makeCIDFont();
/*
* Use name from R object font database.
*/
safestrcpy(fontfamily->cidfonts[i]->name,
getFontName(name, fontdbname), 50);
}
/*
* Load the (Type 1!) symbol font
*
* Gratuitous loop of length 1 so "break" jumps to end of loop
*/
for (i = 0; i < 1; i++) {
type1fontinfo font = makeType1Font();
const char *afmpath = fontMetricsFileName(name, 4, fontdbname);
if (!font) {
freeCIDFontFamily(fontfamily);
fontfamily = NULL;
break;
}
if (!afmpath) {
freeCIDFontFamily(fontfamily);
fontfamily = NULL;
break;
}
fontfamily->symfont = font;
if (!PostScriptLoadFontMetrics(afmpath,
&(fontfamily->symfont->metrics),
fontfamily->symfont->name,
fontfamily->symfont->charnames,
/*
* Reencode all but
* symbol face
*/
NULL, 0)) {
warning(_("cannot load afm file '%s'"), afmpath);
freeCIDFontFamily(fontfamily);
fontfamily = NULL;
break;
}
}
/*
* Add font
*/
if (fontfamily)
fontfamily = addLoadedCIDFont(fontfamily, isPDF);
}
} else
fontfamily = NULL;
#ifdef DEBUG_PS
Rprintf("%d fontfamily = %s\n", __LINE__, (fontfamily) ? "set" : "null");
Rprintf("%d addCIDFont = %s\n", __LINE__, fontfamily->fxname);
#endif
return fontfamily;
}
static type1fontfamily addFont(const char *name, Rboolean isPDF,
encodinglist deviceEncodings)
{
type1fontfamily fontfamily = makeFontFamily();
char *fontdbname;
if (isPDF)
fontdbname = PDFFonts;
else
fontdbname = PostScriptFonts;
if (fontfamily) {
int i;
encodinginfo encoding;
const char *encpath = getFontEncoding(name, fontdbname);
if (!encpath) {
freeFontFamily(fontfamily);
fontfamily = NULL;
} else {
/*
* Set the name of the font
*/
safestrcpy(fontfamily->fxname, name, 50);
/*
* Find or add encoding
*/
if (!(encoding = findEncoding(encpath, deviceEncodings, isPDF)))
encoding = addEncoding(encpath, isPDF);
if (!encoding) {
freeFontFamily(fontfamily);
fontfamily = NULL;
} else {
/*
* Load font info
*/
fontfamily->encoding = encoding;
for(i = 0; i < 5 ; i++) {
type1fontinfo font = makeType1Font();
const char *afmpath = fontMetricsFileName(name, i, fontdbname);
if (!font) {
freeFontFamily(fontfamily);
fontfamily = NULL;
break;
}
if (!afmpath) {
freeFontFamily(fontfamily);
fontfamily = NULL;
break;
}
fontfamily->fonts[i] = font;
if (!PostScriptLoadFontMetrics(afmpath,
&(fontfamily->fonts[i]->metrics),
fontfamily->fonts[i]->name,
fontfamily->fonts[i]->charnames,
/*
* Reencode all but
* symbol face
*/
encoding->encnames,
(i < 4)?1:0)) {
warning(_("cannot load afm file '%s'"), afmpath);
freeFontFamily(fontfamily);
fontfamily = NULL;
break;
}
}
/*
* Add font
*/
if (fontfamily)
fontfamily = addLoadedFont(fontfamily, isPDF);
}
}
} else
fontfamily = NULL;
return fontfamily;
}
/*
* Add a default font family/encoding to the list of loaded fonts ...
*
* ... using a set of AFM paths ...
*
* ... and return the new font
*/
static type1fontfamily
addDefaultFontFromAFMs(const char *encpath, const char **afmpaths,
Rboolean isPDF,
encodinglist deviceEncodings)
{
encodinginfo encoding;
type1fontfamily fontfamily = makeFontFamily();
if (fontfamily) {
int i;
if (!(encoding = findEncoding(encpath, deviceEncodings, isPDF)))
encoding = addEncoding(encpath, isPDF);
if (!encoding) {
freeFontFamily(fontfamily);
fontfamily = NULL;
} else {
/*
* This is the device default font, so set the
* graphics engine font family name to ""
*/
fontfamily->fxname[0] ='\0';
/*
* Load font info
*/
fontfamily->encoding = encoding;
for(i = 0; i < 5 ; i++) {
type1fontinfo font = makeType1Font();
if (!font) {
freeFontFamily(fontfamily);
fontfamily = NULL;
break;
}
fontfamily->fonts[i] = font;
if (!PostScriptLoadFontMetrics(afmpaths[i],
&(fontfamily->fonts[i]->metrics),
fontfamily->fonts[i]->name,
fontfamily->fonts[i]->charnames,
/*
* Reencode all but
* symbol face
*/
encoding->encnames,
(i < 4)?1:0)) {
warning(_("cannot load afm file '%s'"), afmpaths[i]);
freeFontFamily(fontfamily);
fontfamily = NULL;
break;
}
}
/*
* Add font
*/
if (fontfamily)
fontfamily = addLoadedFont(fontfamily, isPDF);
}
} else
fontfamily = NULL;
return fontfamily;
}
/*
* Add a graphics engine font family/encoding to a list of device fonts ...
*
* ... and return the new font list
*/
static cidfontlist addDeviceCIDFont(cidfontfamily font,
cidfontlist devFonts,
int *index)
{
cidfontlist newfont = makeCIDFontList();
*index = 0;
if (!newfont) {
devFonts = NULL;
} else {
cidfontlist fontlist = devFonts;
newfont->cidfamily = font;
*index = 1;
if (!devFonts) {
devFonts = newfont;
} else {
while (fontlist->next) {
fontlist = fontlist->next;
*index = *index + 1;
}
fontlist->next = newfont;
}
}
return devFonts;
}
static type1fontlist addDeviceFont(type1fontfamily font,
type1fontlist devFonts,
int *index)
{
type1fontlist newfont = makeFontList();
*index = 0;
if (!newfont) {
devFonts = NULL;
} else {
type1fontlist fontlist = devFonts;
newfont->family = font;
*index = 1;
if (!devFonts) {
devFonts = newfont;
} else {
while (fontlist->next) {
fontlist = fontlist->next;
*index = *index + 1;
}
fontlist->next = newfont;
}
}
return devFonts;
}
/*
***********************************************************
*/
/* Part 2. Device Driver State. */
typedef struct {
char filename[PATH_MAX];
int open_type;
char papername[64]; /* paper name */
int paperwidth; /* paper width in big points (1/72 in) */
int paperheight; /* paper height in big points */
Rboolean landscape; /* landscape mode */
int pageno; /* page number */
int fileno; /* file number */
int maxpointsize;
double width; /* plot width in inches */
double height; /* plot height in inches */
double pagewidth; /* page width in inches */
double pageheight; /* page height in inches */
Rboolean pagecentre;/* centre image on page? */
Rboolean printit; /* print page at close? */
char command[2*PATH_MAX];
char title[1024];
char colormodel[30];
FILE *psfp; /* output file */
Rboolean onefile; /* EPSF header etc*/
Rboolean paperspecial; /* suppress %%Orientation */
Rboolean warn_trans; /* have we warned about translucent cols? */
Rboolean useKern;
Rboolean fillOddEven; /* polygon fill mode */
/* This group of variables track the current device status.
* They should only be set by routines that emit PostScript code. */
struct {
double lwd; /* line width */
int lty; /* line type */
R_GE_lineend lend;
R_GE_linejoin ljoin;
double lmitre;
int font;
int cidfont;
int fontsize; /* font size in points */
rcolor col; /* color */
rcolor fill; /* fill color */
} current;
/*
* Fonts and encodings used on the device
*/
type1fontlist fonts;
cidfontlist cidfonts;
encodinglist encodings;
/*
* These next two just record the default device font
*/
type1fontfamily defaultFont;
cidfontfamily defaultCIDFont;
}
PostScriptDesc;
/* Part 3. Graphics Support Code. */
static const char * const TypeFaceDef[] = { "R", "B", "I", "BI", "S" };
static void specialCaseCM(FILE *fp, type1fontfamily family, int familynum)
{
fprintf(fp, "%% begin encoding\n");
fprintf(fp, "/SymbolEncoding [\n");
fprintf(fp, " /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef\n");
fprintf(fp, " /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef\n");
fprintf(fp, " /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef\n");
fprintf(fp, " /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef\n");
fprintf(fp, " /space /exclam /universal /numbersign /existential /percent /ampersand /suchthat\n");
fprintf(fp, " /parenleft /parenright /asteriskmath /plus /comma /minus /period /slash\n");
fprintf(fp, " /zero /one /two /three /four /five /six /seven\n");
fprintf(fp, " /eight /nine /colon /semicolon /less /equal /greater /question\n");
fprintf(fp, " /congruent /Alpha /Beta /Chi /Delta /Epsilon /Phi /Gamma\n");
fprintf(fp, " /Eta /Iota /theta1 /Kappa /Lambda /Mu /Nu /Omicron\n");
fprintf(fp, " /Pi /Theta /Rho /Sigma /Tau /Upsilon /sigma1 /Omega\n");
fprintf(fp, " /Xi /Psi /Zeta /bracketleft /therefore /bracketright /perpendicular /underscore\n");
fprintf(fp, " /radicalex /alpha /beta /chi /delta /epsilon /phi /gamma\n");
fprintf(fp, " /eta /iota /phi1 /kappa /lambda /mu /nu /omicron\n");
fprintf(fp, " /pi /theta /rho /sigma /tau /upsilon /omega1 /omega\n");
fprintf(fp, " /xi /psi /zeta /braceleft /bar /braceright /similar /.notdef\n");
fprintf(fp, " /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef\n");
fprintf(fp, " /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef\n");
fprintf(fp, " /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef\n");
fprintf(fp, " /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef\n");
fprintf(fp, " /Euro /Upsilon1 /minute /lessequal /fraction /infinity /florin /club\n");
fprintf(fp, " /diamond /heart /spade /arrowboth /arrowleft /arrowup /arrowright /arrowdown\n");
fprintf(fp, " /degree /plusminus /second /greaterequal /multiply /proportional /partialdiff /bullet\n");
fprintf(fp, " /divide /notequal /equivalence /approxequal /ellipsis /arrowvertex /arrowhorizex /carriagereturn\n");
fprintf(fp, " /aleph /Ifraktur /Rfraktur /weierstrass /circlemultiply /circleplus /emptyset /intersection\n");
fprintf(fp, " /union /propersuperset /reflexsuperset /notsubset /propersubset /reflexsubset /element /notelement\n");
fprintf(fp, " /angle /gradient /registerserif /copyrightserif /trademarkserif /product /radical /dotmath\n");
fprintf(fp, " /logicalnot /logicaland /logicalor /arrowdblboth /arrowdblleft /arrowdblup /arrowdblright /arrowdbldown\n");
fprintf(fp, " /lozenge /angleleft /registersans /copyrightsans /trademarksans /summation /parenlefttp /parenleftex\n");
fprintf(fp, " /parenleftbt /bracketlefttp /bracketleftex /bracketleftbt /bracelefttp /braceleftmid /braceleftbt /braceex\n");
fprintf(fp, " /.notdef /angleright /integral /integraltp /integralex /integralbt /parenrighttp /parenrightex\n");
fprintf(fp, " /parenrightbt /bracketrighttp /bracketrightex /bracketrightbt /bracerighttp /bracerightmid /bracerightbt /.notdef\n");
fprintf(fp, "] def\n");
fprintf(fp, "%% end encoding\n");
fprintf(fp, "/mergefonts\n");
fprintf(fp, "{ /targetencoding exch def\n");
fprintf(fp, " /fontarray exch def\n");
fprintf(fp, " fontarray 0 get dup maxlength dict begin\n");
fprintf(fp, " { 1 index /FID ne { def } { pop pop } ifelse } forall\n");
fprintf(fp, " %% Create a new dictionary\n");
fprintf(fp, " /CharStrings 256 dict def\n");
fprintf(fp, " %% Add a definition of .notdef\n");
fprintf(fp, " fontarray\n");
fprintf(fp, " { /CharStrings get dup /.notdef known\n");
fprintf(fp, " { /.notdef get /result exch def exit }\n");
fprintf(fp, " { pop } ifelse\n");
fprintf(fp, " } forall\n");
fprintf(fp, " CharStrings /.notdef result put\n");
fprintf(fp, " %% Add in the other definitions\n");
fprintf(fp, " targetencoding\n");
fprintf(fp, " { /code exch def\n");
fprintf(fp, " %% Check that it is not a .notdef\n");
fprintf(fp, " code /.notdef eq\n");
fprintf(fp, " { /.notdef }\n");
fprintf(fp, " { fontarray\n");
fprintf(fp, " { /CharStrings get dup code known\n");
fprintf(fp, " { code get /result exch def /found true def exit }\n");
fprintf(fp, " { pop /found false def } ifelse\n");
fprintf(fp, " } forall\n");
fprintf(fp, " %% define character if it was found and accumulate encoding\n");
fprintf(fp, " found { CharStrings code result put code } { /.notdef } ifelse\n");
fprintf(fp, " } ifelse\n");
fprintf(fp, " } forall\n");
fprintf(fp, " %% grab new encoding off of stack\n");
fprintf(fp, " 256 array astore /Encoding exch def\n");
fprintf(fp, " %% Undefine some local variables\n");
fprintf(fp, " currentdict /fontarray undef\n");
fprintf(fp, " currentdict /targetencoding undef\n");
fprintf(fp, " currentdict /code undef\n");
fprintf(fp, " currentdict /result undef\n");
fprintf(fp, " currentdict /found undef\n");
fprintf(fp, " %% Leave new font on the stack\n");
fprintf(fp, " currentdict\n");
fprintf(fp, " end\n");
fprintf(fp, "} def\n");
fprintf(fp, "%%%%IncludeResource: font %s\n",
family->fonts[0]->name);
fprintf(fp, "%%%%IncludeResource: font CMSY10\n");
fprintf(fp, "[ /%s findfont /CMSY10 findfont ] %s mergefonts\n",
family->fonts[0]->name, family->encoding->name);
fprintf(fp, "/Font%d exch definefont pop\n",
(familynum - 1)*5 + 1);
fprintf(fp, "%%%%IncludeResource: font %s\n",
family->fonts[1]->name);
fprintf(fp, "%%%%IncludeResource: font CMBSY10\n");
fprintf(fp, "[ /%s findfont /CMBSY10 findfont ] %s mergefonts\n",
family->fonts[1]->name, family->encoding->name);
fprintf(fp, "/Font%d exch definefont pop\n",
(familynum - 1)*5 + 2);
fprintf(fp, "%%%%IncludeResource: font %s\n",
family->fonts[2]->name);
fprintf(fp, "[ /%s findfont /CMSY10 findfont ] %s mergefonts\n",
family->fonts[2]->name, family->encoding->name);
fprintf(fp, "/Font%d exch definefont pop\n",
(familynum - 1)*5 + 3);
fprintf(fp, "%%%%IncludeResource: font %s\n",
family->fonts[3]->name);
fprintf(fp, "[ /%s findfont /CMBSY10 findfont ] %s mergefonts\n",
family->fonts[3]->name, family->encoding->name);
fprintf(fp, "/Font%d exch definefont pop\n",
(familynum - 1)*5 + 4);
fprintf(fp, "%%%%IncludeResource: font CMMI10\n");
fprintf(fp, "[ /CMR10 findfont /CMSY10 findfont /CMMI10 findfont ] SymbolEncoding mergefonts\n");
fprintf(fp, "/Font%d exch definefont pop\n",
(familynum - 1)*5 + 5);
}
static void PSEncodeFonts(FILE *fp, PostScriptDesc *pd)
{
type1fontlist fonts = pd->fonts;
int familynum = 1;
int haveWrittenDefaultEnc = 0;
cidfontlist cidfonts = pd->cidfonts;
int cidfamilynum = 1;
while (fonts) {
int dontcare;
/*
* Has the encoding already been used on the device?
*/
encodinginfo encoding =
findDeviceEncoding(fonts->family->encoding->encpath,
pd->encodings, &dontcare);
/*
* If we've added the encoding to the device then it has been
* written to file ...
*
* ... UNLESS this is the default encoding for the device, in
* which case it has been added, but not written to file.
*
* Use haveWrittenDefaultEnc to make sure we only do it once.
*/
if (!encoding ||
(encoding == pd->encodings->encoding && !haveWrittenDefaultEnc)) {
/*
* Don't need to add default encoding again.
*/
if (encoding != pd->encodings->encoding) {
/*
* The encoding should have been loaded when the
* font was loaded
*/
encoding = findEncoding(fonts->family->encoding->encpath,
pd->encodings, FALSE);
if (!encoding)
warning(_("corrupt loaded encodings; encoding not recorded"));
else {
/*
* Record encoding on device's list of encodings so
* don't write same encoding more than once
*/
encodinglist enclist = addDeviceEncoding(encoding,
pd->encodings);
if (enclist)
pd->encodings = enclist;
else
warning(_("failed to record device encoding"));
}
} else {
/*
* Make sure we only write default encoding once.
*/
haveWrittenDefaultEnc = 1;
}
/*
* Include encoding unless it is ISOLatin1Encoding,
* which is predefined
*/
if (strcmp(fonts->family->encoding->name, "ISOLatin1Encoding"))
fprintf(fp, "%% begin encoding\n%s def\n%% end encoding\n",
fonts->family->encoding->enccode);
}
if(strcmp(fonts->family->fonts[4]->name,
"CMSY10 CMBSY10 CMMI10") == 0) {
/* use different ps fragment for CM fonts */
specialCaseCM(fp, fonts->family, familynum);
} else {
int i;
for (i = 0; i < 4 ; i++) {
fprintf(fp, "%%%%IncludeResource: font %s\n",
fonts->family->fonts[i]->name);
fprintf(fp, "/%s findfont\n",
fonts->family->fonts[i]->name);
fprintf(fp, "dup length dict begin\n");
fprintf(fp, " {1 index /FID ne {def} {pop pop} ifelse} forall\n");
fprintf(fp, " /Encoding %s def\n",
fonts->family->encoding->name);
fprintf(fp, " currentdict\n");
fprintf(fp, " end\n");
fprintf(fp, "/Font%d exch definefont pop\n",
(familynum - 1)*5 + i + 1);
}
fprintf(fp, "%%%%IncludeResource: font %s\n",
fonts->family->fonts[4]->name);
fprintf(fp, "/%s findfont\n",
fonts->family->fonts[4]->name);
fprintf(fp, "dup length dict begin\n");
fprintf(fp, " {1 index /FID ne {def} {pop pop} ifelse} forall\n");
fprintf(fp, " currentdict\n");
fprintf(fp, " end\n");
fprintf(fp, "/Font%d exch definefont pop\n",
(familynum - 1)*5 + 5);
}
familynum++;
fonts = fonts->next;
}
while(cidfonts) {
int i;
char *name = cidfonts->cidfamily->cidfonts[0]->name;
fprintf(fp, "%%%%IncludeResource: CID fake Bold font %s\n", name);
fprintf(fp, "/%s-Bold\n/%s /CIDFont findresource\n", name, name);
fprintf(fp, "%s", CIDBoldFontStr1);
fprintf(fp, "%s", CIDBoldFontStr2);
for (i = 0; i < 4 ; i++) {
char *fmt = NULL /* -Wall */;
fprintf(fp, "%%%%IncludeResource: CID font %s-%s\n", name,
cidfonts->cidfamily->cmap);
switch(i) {
case 0: fmt = "/%s-%s findfont\n";
break;
case 1: fmt = "/%s-Bold-%s findfont\n";
break;
case 2: fmt = "/%s-%s findfont [1 0 .3 1 0 0] makefont\n";
break;
case 3: fmt = "/%s-Bold-%s findfont [1 0 .3 1 0 0] makefont\n";
break;
default:
break;
}
fprintf(fp, fmt, name, cidfonts->cidfamily->cmap);
fprintf(fp, "dup length dict begin\n");
fprintf(fp, " {1 index /FID ne {def} {pop pop} ifelse} forall\n");
fprintf(fp, " currentdict\n");
fprintf(fp, " end\n");
fprintf(fp, "/Font%d exch definefont pop\n",
(familynum - 1)*5 + (cidfamilynum - 1)*5 + i + 1);
}
/*
* Symbol font
*/
fprintf(fp, "%%%%IncludeResource: font %s\n",
cidfonts->cidfamily->symfont->name);
fprintf(fp, "/%s findfont\n",
cidfonts->cidfamily->symfont->name);
fprintf(fp, "dup length dict begin\n");
fprintf(fp, " {1 index /FID ne {def} {pop pop} ifelse} forall\n");
fprintf(fp, " currentdict\n");
fprintf(fp, " end\n");
fprintf(fp, "/Font%d exch definefont pop\n",
(familynum - 1)*5 + (cidfamilynum - 1)*5 + 5);
cidfamilynum++;
cidfonts = cidfonts->next;
}
}
/* The variables "paperwidth" and "paperheight" give the dimensions */
/* of the (unrotated) printer page in points whereas the graphics */
/* region box is for the rotated page. */
static void PSFileHeader(FILE *fp,
const char *papername, double paperwidth,
double paperheight, Rboolean landscape,
int EPSFheader, Rboolean paperspecial,
double left, double bottom, double right, double top,
const char *title,
PostScriptDesc *pd)
{
int i;
SEXP prolog;
type1fontlist fonts = pd->fonts;
int firstfont = 1;
if(EPSFheader)
fprintf(fp, "%%!PS-Adobe-3.0 EPSF-3.0\n");
else
fprintf(fp, "%%!PS-Adobe-3.0\n");
/*
* DocumentNeededResources names all fonts
*/
while (fonts) {
for (i=0; i<5; i++)
if (firstfont) {
fprintf(fp, "%%%%DocumentNeededResources: font %s\n",
fonts->family->fonts[0]->name);
firstfont = 0;
} else
fprintf(fp, "%%%%+ font %s\n", fonts->family->fonts[i]->name);
fonts = fonts->next;
}
if(!EPSFheader)
fprintf(fp, "%%%%DocumentMedia: %s %.0f %.0f 0 () ()\n",
papername, paperwidth, paperheight);
fprintf(fp, "%%%%Title: %s\n", title);
fprintf(fp, "%%%%Creator: R Software\n");
fprintf(fp, "%%%%Pages: (atend)\n");
if (!EPSFheader && !paperspecial) { /* gs gets confused by this */
if (landscape)
fprintf(fp, "%%%%Orientation: Landscape\n");
else
fprintf(fp, "%%%%Orientation: Portrait\n");
}
fprintf(fp, "%%%%BoundingBox: %.0f %.0f %.0f %.0f\n",
left, bottom, right, top);
fprintf(fp, "%%%%EndComments\n");
fprintf(fp, "%%%%BeginProlog\n");
fprintf(fp, "/bp { gs");
if (streql(pd->colormodel, "srgb")) fprintf(fp, " sRGB");
if (landscape)
fprintf(fp, " %.2f 0 translate 90 rotate", paperwidth);
fprintf(fp, " gs } def\n");
prolog = findVar(install(".ps.prolog"), R_GlobalEnv);
if(prolog == R_UnboundValue) {
/* if no object is visible, look in the graphics namespace */
SEXP graphicsNS = R_FindNamespace(ScalarString(mkChar("grDevices")));
prolog = findVar(install(".ps.prolog"), graphicsNS);
/* under lazy loading this will be a promise on first use */
if(TYPEOF(prolog) == PROMSXP) {
PROTECT(prolog);
prolog = eval(prolog, graphicsNS);
UNPROTECT(1);
}
}
if(!isString(prolog))
error(_("object '.ps.prolog' is not a character vector"));
fprintf(fp, "%% begin .ps.prolog\n");
for (i = 0; i < length(prolog); i++)
fprintf(fp, "%s\n", CHAR(STRING_ELT(prolog, i)));
fprintf(fp, "%% end .ps.prolog\n");
if (streql(pd->colormodel, "srgb+gray") || streql(pd->colormodel, "srgb")) {
SEXP graphicsNS = R_FindNamespace(ScalarString(mkChar("grDevices")));
prolog = findVar(install(".ps.prolog.srgb"), graphicsNS);
/* under lazy loading this will be a promise on first use */
if(TYPEOF(prolog) == PROMSXP) {
PROTECT(prolog);
prolog = eval(prolog, graphicsNS);
UNPROTECT(1);
}
for (i = 0; i < length(prolog); i++)
fprintf(fp, "%s\n", CHAR(STRING_ELT(prolog, i)));
}
if (streql(pd->colormodel, "srgb+gray"))
fprintf(fp, "/srgb { sRGB setcolor } bind def\n");
else if (streql(pd->colormodel, "srgb"))
fprintf(fp, "/srgb { setcolor } bind def\n");
PSEncodeFonts(fp, pd);
fprintf(fp, "%%%%EndProlog\n");
}
static void PostScriptFileTrailer(FILE *fp, int pageno)
{
fprintf(fp, "ep\n");
fprintf(fp, "%%%%Trailer\n");
fprintf(fp, "%%%%Pages: %d\n", pageno);
fprintf(fp, "%%%%EOF\n");
}
static void PostScriptStartPage(FILE *fp, int pageno)
{
fprintf(fp, "%%%%Page: %d %d\n", pageno, pageno);
fprintf(fp, "bp\n");
}
static void PostScriptEndPage(FILE *fp)
{
fprintf(fp, "ep\n");
}
static void PostScriptSetClipRect(FILE *fp, double x0, double x1,
double y0, double y1)
{
fprintf(fp, "%.2f %.2f %.2f %.2f cl\n", x0, y0, x1, y1);
}
static void PostScriptSetLineWidth(FILE *fp, double linewidth)
{
/* Must not allow line width to be zero */
if (linewidth < .01)
linewidth = .01;
fprintf(fp, "%.2f setlinewidth\n", linewidth);
}
static void PostScriptSetLineEnd(FILE *fp, R_GE_lineend lend)
{
int lineend = 1; /* -Wall */
switch (lend) {
case GE_ROUND_CAP:
lineend = 1;
break;
case GE_BUTT_CAP:
lineend = 0;
break;
case GE_SQUARE_CAP:
lineend = 2;
break;
default:
error(_("invalid line end"));
}
fprintf(fp, "%1d setlinecap\n", lineend);
}
static void PostScriptSetLineJoin(FILE *fp, R_GE_linejoin ljoin)
{
int linejoin = 1; /* -Wall */
switch (ljoin) {
case GE_ROUND_JOIN:
linejoin = 1;
break;
case GE_MITRE_JOIN:
linejoin = 0;
break;
case GE_BEVEL_JOIN:
linejoin = 2;
break;
default:
error(_("invalid line join"));
}
fprintf(fp, "%1d setlinejoin\n", linejoin);
}
static void PostScriptSetLineMitre(FILE *fp, double linemitre)
{
if (linemitre < 1)
error(_("invalid line mitre"));
fprintf(fp, "%.2f setmiterlimit\n", linemitre);
}
static void PostScriptSetFont(FILE *fp, int fontnum, double size)
{
fprintf(fp, "/Font%d findfont %.0f s\n", fontnum, size);
}
static void
PostScriptSetLineTexture(FILE *fp, const char *dashlist, int nlty,
double lwd, int lend)
{
/* use same macro for Postscript and PDF */
/* Historically the adjustment was 1 to allow for round end caps.
As from 2.11.0, no adjustment is done for butt endcaps.
The + 1 adjustment on the 'off' segments seems wrong, but it
has been left in for back-compatibility
*/
#define PP_SetLineTexture(_CMD_, adj) \
double dash[8], a = adj; \
int i; \
Rboolean allzero = TRUE; \
for (i = 0; i < nlty; i++) { \
dash[i] = lwd * \
((i % 2) ? (dashlist[i] + a) \
: ((nlty == 1 && dashlist[i] == 1.) ? 1. : dashlist[i] - a) ); \
if (dash[i] < 0) dash[i] = 0; \
if (dash[i] > .01) allzero = FALSE; \
} \
fprintf(fp,"["); \
if (!allzero) { \
for (i = 0; i < nlty; i++) { \
fprintf(fp," %.2f", dash[i]); \
} \
} \
fprintf(fp,"] 0 %s\n", _CMD_)
PP_SetLineTexture("setdash", (lend == GE_BUTT_CAP) ? 0. : 1.);
}
static void PostScriptMoveTo(FILE *fp, double x, double y)
{
fprintf(fp, "%.2f %.2f m\n", x, y);
}
static void PostScriptRLineTo(FILE *fp, double x0, double y0,
double x1, double y1)
{
double x = fround(x1, 2) - fround(x0, 2),
y = fround(y1, 2) - fround(y0, 2);
/* Warning: some machines seem to compute these differently from
others, and we do want to diff the output. x and y should be
above around 0.01 or negligible (1e-14), and it is the latter case
we are watching out for here.
*/
if(fabs(x) < 0.005) fprintf(fp, "0"); else fprintf(fp, "%.2f", x);
if(fabs(y) < 0.005) fprintf(fp, " 0"); else fprintf(fp, " %.2f", y);
fprintf(fp, " l\n");
}
static void PostScriptStartPath(FILE *fp)
{
fprintf(fp, "np\n");
}
static void PostScriptEndPath(FILE *fp)
{
fprintf(fp, "o\n");
}
static void PostScriptRectangle(FILE *fp, double x0, double y0,
double x1, double y1)
{
fprintf(fp, "%.2f %.2f %.2f %.2f r ", x0, y0, x1-x0, y1-y0);
}
static void PostScriptCircle(FILE *fp, double x, double y, double r)
{
fprintf(fp, "%.2f %.2f %.2f c ", x, y, r);
}
static void PostScriptWriteString(FILE *fp, const char *str, size_t nb)
{
size_t i;
fputc('(', fp);
for (i = 0 ; i < nb && *str; i++, str++)
switch(*str) {
case '\n':
fprintf(fp, "\\n");
break;
case '\\':
fprintf(fp, "\\\\");
break;
case '-':
#ifdef USE_HYPHEN
if (!isdigit((int)str[1]))
fputc(PS_hyphen, fp);
else
#endif
fputc(*str, fp);
break;
case '(':
case ')':
fprintf(fp, "\\%c", *str);
break;
default:
fputc(*str, fp);
break;
}
fputc(')', fp);
}
static FontMetricInfo *metricInfo(const char *, int, PostScriptDesc *);
static void PostScriptText(FILE *fp, double x, double y,
const char *str, size_t nb, double xc, double rot,
const pGEcontext gc,
pDevDesc dd)
{
int face = gc->fontface;
if(face < 1 || face > 5) face = 1;
fprintf(fp, "%.2f %.2f ", x, y);
PostScriptWriteString(fp, str, nb);
if(xc == 0) fprintf(fp, " 0");
else if(xc == 0.5) fprintf(fp, " .5");
else if(xc == 1) fprintf(fp, " 1");
else fprintf(fp, " %.2f", xc);
if(rot == 0) fprintf(fp, " 0");
else if(rot == 90) fprintf(fp, " 90");
else fprintf(fp, " %.2f", rot);
fprintf(fp, " t\n");
}
static void PostScriptText2(FILE *fp, double x, double y,
const char *str, size_t nb,
Rboolean relative, double rot,
const pGEcontext gc,
pDevDesc dd)
{
int face = gc->fontface;
if(face < 1 || face > 5) face = 1;
if(relative) {
fprintf(fp, "\n%.3f ", x);
PostScriptWriteString(fp, str, nb);
fprintf(fp, " tb");
} else {
fprintf(fp, "%.2f %.2f ", x, y);
PostScriptWriteString(fp, str, nb);
if(rot == 0) fprintf(fp, " 0");
else if(rot == 90) fprintf(fp, " 90");
else fprintf(fp, " %.2f", rot);
fprintf(fp, " ta");
}
}
static void PostScriptHexText(FILE *fp, double x, double y,
const char *str, size_t strlen,
double xc, double rot)
{
unsigned char *p = (unsigned char *)str;
size_t i;
fprintf(fp, "%.2f %.2f ", x, y);
fprintf(fp, "<");
for(i = 0; i < strlen; i++) fprintf(fp, "%02x", *p++);
fprintf(fp, ">");
if(xc == 0) fprintf(fp, " 0");
else if(xc == 0.5) fprintf(fp, " .5");
else if(xc == 1) fprintf(fp, " 1");
else fprintf(fp, " %.2f", xc);
if(rot == 0) fprintf(fp, " 0");
else if(rot == 90) fprintf(fp, " 90");
else fprintf(fp, " %.2f", rot);
fprintf(fp, " t\n");
}
static void
PostScriptTextKern(FILE *fp, double x, double y,
const char *str, double xc, double rot,
const pGEcontext gc,
pDevDesc dd)
{
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
int face = gc->fontface;
FontMetricInfo *metrics;
size_t i, n, nout = 0;
int j, w;
unsigned char p1, p2;
double fac = 0.001 * floor(gc->cex * gc->ps + 0.5);
Rboolean relative = FALSE;
Rboolean haveKerning = FALSE;
if(face < 1 || face > 5) {
warning(_("attempt to use invalid font %d replaced by font 1"), face);
face = 1;
}
/* check if this is T1 -- should be, but be safe*/
if(!isType1Font(gc->fontfamily, PostScriptFonts, pd->defaultFont)) {
PostScriptText(fp, x, y, str, strlen(str), xc, rot, gc, dd);
return;
}
metrics = metricInfo(gc->fontfamily, face, pd);
n = strlen(str);
if (n < 1) return;
/* First check for any kerning */
for(i = 0; i < n-1; i++) {
p1 = str[i];
p2 = str[i+1];
#ifdef USE_HYPHEN
if (p1 == '-' && !isdigit((int)p2))
p1 = (unsigned char)PS_hyphen;
#endif
for (j = metrics->KPstart[p1]; j < metrics->KPend[p1]; j++)
if(metrics->KernPairs[j].c2 == p2 &&
metrics->KernPairs[j].c1 == p1) {
haveKerning = TRUE;
break;
}
}
if(haveKerning) {
/* We have to start at the left edge, as we are going
to do this in pieces */
if (xc != 0) {
double rot1 = rot * M_PI/180.;
int w = 0; short wx;
for(i = 0; i < n; i++) {
unsigned char p1 = str[i];
wx = metrics->CharInfo[(int)p1].WX;
w += (wx == NA_SHORT) ? 0 : wx;
}
x -= xc*fac*cos(rot1)*w;
y -= xc*fac*sin(rot1)*w;
}
for(i = 0; i < n-1; i++) {
p1 = str[i];
p2 = str[i+1];
#ifdef USE_HYPHEN
if (p1 == '-' && !isdigit((int)p2))
p1 = (unsigned char)PS_hyphen;
#endif
for (j = metrics->KPstart[p1]; j < metrics->KPend[p1]; j++)
if(metrics->KernPairs[j].c2 == p2 &&
metrics->KernPairs[j].c1 == p1) {
PostScriptText2(fp, x, y, str+nout, i+1-nout,
relative, rot, gc, dd);
nout = i+1;
w = metrics->KernPairs[j].kern;
x = fac*w; y = 0;
relative = TRUE;
break;
}
}
PostScriptText2(fp, x, y, str+nout, n-nout, relative, rot, gc, dd);
fprintf(fp, " gr\n");
} else
PostScriptText(fp, x, y, str, strlen(str), xc, rot, gc, dd);
}
/* Device Driver Actions */
static void PS_Circle(double x, double y, double r,
const pGEcontext gc,
pDevDesc dd);
static void PS_Clip(double x0, double x1, double y0, double y1,
pDevDesc dd);
static void PS_Close(pDevDesc dd);
static void PS_Line(double x1, double y1, double x2, double y2,
const pGEcontext gc,
pDevDesc dd);
static void PS_MetricInfo(int c,
const pGEcontext gc,
double* ascent, double* descent,
double* width, pDevDesc dd);
static void PS_NewPage(const pGEcontext gc,
pDevDesc dd);
static Rboolean PS_Open(pDevDesc, PostScriptDesc*);
static void PS_Polygon(int n, double *x, double *y,
const pGEcontext gc,
pDevDesc dd);
static void PS_Polyline(int n, double *x, double *y,
const pGEcontext gc,
pDevDesc dd);
static void PS_Rect(double x0, double y0, double x1, double y1,
const pGEcontext gc,
pDevDesc dd);
static void PS_Path(double *x, double *y,
int npoly, int *nper,
Rboolean winding,
const pGEcontext gc,
pDevDesc dd);
static void PS_Raster(unsigned int *raster, int w, int h,
double x, double y, double width, double height,
double rot, Rboolean interpolate,
const pGEcontext gc, pDevDesc dd);
static void PS_Size(double *left, double *right,
double *bottom, double *top,
pDevDesc dd);
static double PS_StrWidth(const char *str,
const pGEcontext gc,
pDevDesc dd);
static void PS_Text(double x, double y, const char *str,
double rot, double hadj,
const pGEcontext gc,
pDevDesc dd);
static double PS_StrWidthUTF8(const char *str,
const pGEcontext gc,
pDevDesc dd);
static void PS_TextUTF8(double x, double y, const char *str,
double rot, double hadj,
const pGEcontext gc,
pDevDesc dd);
/* PostScript Support (formerly in PostScript.c) */
static void PostScriptSetCol(FILE *fp, double r, double g, double b,
PostScriptDesc *pd)
{
const char *mm = pd->colormodel;
if(r == g && g == b &&
!(streql(mm, "cmyk") || streql(mm, "srgb")
|| streql(mm, "rgb-nogray")) ) { /* grey */
if(r == 0) fprintf(fp, "0");
else if (r == 1) fprintf(fp, "1");
else fprintf(fp, "%.4f", r);
fprintf(fp," setgray");
} else {
if(strcmp(mm, "gray") == 0) {
fprintf(fp, "%.4f setgray", 0.213*r + 0.715*g + 0.072*b);
// error(_("only gray colors are allowed in this color model"));
} else if(strcmp(mm, "cmyk") == 0) {
double c = 1.0-r, m=1.0-g, y=1.0-b, k=c;
k = fmin2(k, m);
k = fmin2(k, y);
if(k == 1.0) c = m = y = 0.0;
else { c = (c-k)/(1-k); m = (m-k)/(1-k); y = (y-k)/(1-k); }
/* else {c /= (1.-k); m /= (1.-k); y /= (1.-k);} */
if(c == 0) fprintf(fp, "0");
else if (c == 1) fprintf(fp, "1");
else fprintf(fp, "%.4f", c);
if(m == 0) fprintf(fp, " 0");
else if (m == 1) fprintf(fp, " 1");
else fprintf(fp, " %.4f", m);
if(y == 0) fprintf(fp, " 0");
else if (y == 1) fprintf(fp, " 1");
else fprintf(fp, " %.4f", y);
if(k == 0) fprintf(fp, " 0");
else if (k == 1) fprintf(fp, " 1");
else fprintf(fp, " %.4f", k);
fprintf(fp," setcmykcolor\n");
} else {
if(r == 0) fprintf(fp, "0");
else if (r == 1) fprintf(fp, "1");
else fprintf(fp, "%.4f", r);
if(g == 0) fprintf(fp, " 0");
else if (g == 1) fprintf(fp, " 1");
else fprintf(fp, " %.4f", g);
if(b == 0) fprintf(fp, " 0");
else if (b == 1) fprintf(fp, " 1");
else fprintf(fp, " %.4f", b);
if (streql(mm, "srgb+gray") || streql(mm, "srgb"))
fprintf(fp," srgb");
else fprintf(fp," rgb");
}
}
}
static void PostScriptSetFill(FILE *fp, double r, double g, double b,
PostScriptDesc *pd)
{
fprintf(fp,"/bg { ");
PostScriptSetCol(fp, r, g, b, pd);
fprintf(fp, " } def\n");
}
/* Driver Support Routines */
static void SetColor(int, pDevDesc);
static void SetFill(int, pDevDesc);
static void SetFont(int, int, pDevDesc);
static void SetLineStyle(const pGEcontext, pDevDesc dd);
static void Invalidate(pDevDesc);
static void PS_cleanup(int stage, pDevDesc dd, PostScriptDesc *pd);
Rboolean
PSDeviceDriver(pDevDesc dd, const char *file, const char *paper,
const char *family, const char **afmpaths, const char *encoding,
const char *bg, const char *fg, double width, double height,
Rboolean horizontal, double ps,
Rboolean onefile, Rboolean pagecentre, Rboolean printit,
const char *cmd, const char *title, SEXP fonts,
const char *colormodel, int useKern, Rboolean fillOddEven)
{
/* If we need to bail out with some sort of "error"
then we must free(dd) */
double xoff, yoff, pointsize;
rcolor setbg, setfg;
encodinginfo enc;
encodinglist enclist;
type1fontfamily font;
cidfontfamily cidfont = NULL;
int gotFont;
PostScriptDesc *pd;
/* Check and extract the device parameters */
if(strlen(file) > PATH_MAX - 1) {
free(dd);
error(_("filename too long in %s()"), "postscript");
}
/* allocate new postscript device description */
if (!(pd = (PostScriptDesc *) malloc(sizeof(PostScriptDesc)))) {
free(dd);
error(_("memory allocation problem in %s()"), "postscript");
}
/* from here on, if need to bail out with "error", must also */
/* free(pd) */
/* initialise postscript device description */
strcpy(pd->filename, file);
strcpy(pd->papername, paper);
strncpy(pd->title, title, 1024);
if (streql(colormodel, "grey")) strcpy(pd->colormodel, "grey");
else strncpy(pd->colormodel, colormodel, 30);
pd->useKern = (useKern != 0);
pd->fillOddEven = fillOddEven;
if(strlen(encoding) > PATH_MAX - 1) {
PS_cleanup(1, dd, pd);
error(_("encoding path is too long in %s()"), "postscript");
}
/*
* Load the default encoding AS THE FIRST ENCODING FOR THIS DEVICE.
*
* encpath MUST NOT BE "default"
*/
pd->encodings = NULL;
if (!(enc = findEncoding(encoding, pd->encodings, FALSE)))
enc = addEncoding(encoding, 0);
if (enc && (enclist = addDeviceEncoding(enc, pd->encodings))) {
pd->encodings = enclist;
} else {
PS_cleanup(1, dd, pd);
error(_("failed to load encoding file in %s()"), "postscript");
}
/*****************************
* Load fonts
*****************************/
pd->fonts = NULL;
pd->cidfonts = NULL;
gotFont = 0;
/*
* If user specified afms then assume the font hasn't been loaded
* Could lead to redundant extra loading of a font, but not often(?)
*/
if (!strcmp(family, "User")) {
font = addDefaultFontFromAFMs(encoding, afmpaths, 0, pd->encodings);
} else {
/*
* Otherwise, family is a device-independent font family.
* One of the elements of postscriptFonts().
* NOTE this is the first font loaded on this device!
*/
/*
* Check first whether this font has been loaded
* in this R session
*/
font = findLoadedFont(family, encoding, FALSE);
cidfont = findLoadedCIDFont(family, FALSE);
if (!(font || cidfont)) {
/*
* If the font has not been loaded yet, load it.
*
* The family SHOULD be in the font database to get this far.
* (checked at R level in postscript() in postscript.R)
*/
if (isType1Font(family, PostScriptFonts, NULL)) {
font = addFont(family, FALSE, pd->encodings);
} else if (isCIDFont(family, PostScriptFonts, NULL)) {
cidfont = addCIDFont(family, FALSE);
} else {
/*
* Should NOT get here.
* AND if we do, we should free
*/
PS_cleanup(3, dd, pd);
error(_("invalid font type"));
}
}
}
if (font || cidfont) {
/*
* At this point the font is loaded, so add it to the
* device's list of fonts.
*
* If the user specified a vector of AFMs, it is a Type 1 font
*/
if (!strcmp(family, "User") ||
isType1Font(family, PostScriptFonts, NULL)) {
pd->fonts = addDeviceFont(font, pd->fonts, &gotFont);
pd->defaultFont = pd->fonts->family;
pd->defaultCIDFont = NULL;
} else /* (isCIDFont(family, PostScriptFonts)) */ {
pd->cidfonts = addDeviceCIDFont(cidfont, pd->cidfonts, &gotFont);
pd->defaultFont = NULL;
pd->defaultCIDFont = pd->cidfonts->cidfamily;
}
}
if (!gotFont) {
PS_cleanup(3, dd, pd);
error(_("failed to initialise default PostScript font"));
}
/*
* Load the font names sent in via the fonts arg
* NOTE that these are the font names specified at the
* R-level, NOT the translated font names.
*/
if (!isNull(fonts)) {
int i, dontcare, gotFonts = 0, nfonts = LENGTH(fonts);
type1fontlist fontlist;
cidfontlist cidfontlist;
for (i = 0; i < nfonts; i++) {
int index, cidindex;
const char *name = CHAR(STRING_ELT(fonts, i));
/*
* Check first whether this device is already
* using this font.
*/
if (findDeviceFont(name, pd->fonts, &index) ||
findDeviceCIDFont(name, pd->cidfonts, &cidindex))
gotFonts++;
else {
/*
* Check whether the font is loaded and, if not,
* load it.
*/
font = findLoadedFont(name, encoding, FALSE);
cidfont = findLoadedCIDFont(name, FALSE);
if (!(font || cidfont)) {
if (isType1Font(name, PostScriptFonts, NULL)) {
font = addFont(name, FALSE, pd->encodings);
} else if (isCIDFont(name, PostScriptFonts, NULL)) {
cidfont = addCIDFont(name, FALSE);
} else {
/*
* Should NOT get here.
*/
PS_cleanup(4, dd, pd);
error(_("invalid font type"));
}
}
/*
* Once the font is loaded, add it to the device's
* list of fonts.
*/
if (font || cidfont) {
if (isType1Font(name, PostScriptFonts, NULL)) {
if ((fontlist = addDeviceFont(font, pd->fonts,
&dontcare))) {
pd->fonts = fontlist;
gotFonts++;
}
} else /* (isCIDFont(family, PostScriptFonts)) */ {
if ((cidfontlist = addDeviceCIDFont(cidfont,
pd->cidfonts,
&dontcare))) {
pd->cidfonts = cidfontlist;
gotFonts++;
}
}
}
}
}
if (gotFonts < nfonts) {
PS_cleanup(4, dd, pd);
error(_("failed to initialise additional PostScript fonts"));
}
}
/*****************************
* END Load fonts
*****************************/
setbg = R_GE_str2col(bg);
setfg = R_GE_str2col(fg);
pd->width = width;
pd->height = height;
pd->landscape = horizontal;
pointsize = floor(ps);
if(R_TRANSPARENT(setbg) && R_TRANSPARENT(setfg)) {
PS_cleanup(4, dd, pd);
error(_("invalid foreground/background color (postscript)"));
}
pd->printit = printit;
if(strlen(cmd) > 2*PATH_MAX - 1) {
PS_cleanup(4, dd, pd);
error(_("'command' is too long"));
}
strcpy(pd->command, cmd);
if (printit && strlen(cmd) == 0) {
PS_cleanup(4, dd, pd);
error(_("'postscript(print.it=TRUE)' used with an empty 'print' command"));
}
strcpy(pd->command, cmd);
/* Deal with paper and plot size and orientation */
pd->paperspecial = FALSE;
if(!strcmp(pd->papername, "Default") ||
!strcmp(pd->papername, "default")) {
SEXP s = STRING_ELT(GetOption1(install("papersize")), 0);
if(s != NA_STRING && strlen(CHAR(s)) > 0)
strcpy(pd->papername, CHAR(s));
else strcpy(pd->papername, "a4");
}
if(!strcmp(pd->papername, "A4") ||
!strcmp(pd->papername, "a4")) {
pd->pagewidth = 21.0 / 2.54;
pd->pageheight = 29.7 /2.54;
}
else if(!strcmp(pd->papername, "Letter") ||
!strcmp(pd->papername, "letter") ||
!strcmp(pd->papername, "US") ||
!strcmp(pd->papername, "us")) {
pd->pagewidth = 8.5;
pd->pageheight = 11.0;
}
else if(!strcmp(pd->papername, "Legal") ||
!strcmp(pd->papername, "legal")) {
pd->pagewidth = 8.5;
pd->pageheight = 14.0;
}
else if(!strcmp(pd->papername, "Executive") ||
!strcmp(pd->papername, "executive")) {
pd->pagewidth = 7.25;
pd->pageheight = 10.5;
}
else if(!strcmp(pd->papername, "special")) {
if(pd->landscape) {
pd->pagewidth = height;
pd->pageheight = width;
} else {
pd->pagewidth = width;
pd->pageheight = height;
}
pd->paperspecial = TRUE;
}
else {
PS_cleanup(4, dd, pd);
error(_("invalid page type '%s' (postscript)"), pd->papername);
}
pd->pagecentre = pagecentre;
pd->paperwidth = (int)(72 * pd->pagewidth);
pd->paperheight = (int)(72 * pd->pageheight);
pd->onefile = onefile;
if(pd->landscape) {
double tmp;
tmp = pd->pagewidth;
pd->pagewidth = pd->pageheight;
pd->pageheight = tmp;
}
if(strcmp(pd->papername, "special"))
{
if(pd->width < 0.1 || pd->width > pd->pagewidth-0.5)
pd->width = pd->pagewidth-0.5;
if(pd->height < 0.1 || pd->height > pd->pageheight-0.5)
pd->height = pd->pageheight-0.5;
}
if(pagecentre)
{
xoff = (pd->pagewidth - pd->width)/2.0;
yoff = (pd->pageheight - pd->height)/2.0;
} else {
xoff = yoff = 0.0;
}
pd->maxpointsize = (int)(72.0 * ((pd->pageheight > pd->pagewidth) ?
pd->pageheight : pd->pagewidth));
pd->pageno = pd->fileno = 0;
pd->warn_trans = FALSE;
/* Base Pointsize */
/* Nominal Character Sizes in Pixels */
/* Only right for 12 point font. */
/* Max pointsize suggested by Peter Dalgaard */
if(pointsize < 6.0) pointsize = 6.0;
if(pointsize > pd->maxpointsize) pointsize = pd->maxpointsize;
dd->startps = pointsize;
dd->startfont = 1;
dd->startlty = 0;
dd->startfill = setbg;
dd->startcol = setfg;
dd->startgamma = 1;
/* Set graphics parameters that must be set by device driver. */
/* Page dimensions in points. */
dd->left = 72 * xoff; /* left */
dd->right = 72 * (xoff + pd->width); /* right */
dd->bottom = 72 * yoff; /* bottom */
dd->top = 72 * (yoff + pd->height); /* top */
dd->cra[0] = 0.9 * pointsize;
dd->cra[1] = 1.2 * pointsize;
/* Character Addressing Offsets */
/* These offsets should center a single */
/* plotting character over the plotting point. */
/* Pure guesswork and eyeballing ... */
dd->xCharOffset = 0.4900;
dd->yCharOffset = 0.3333;
dd->yLineBias = 0.2;
/* Inches per Raster Unit */
/* We use points (72 dots per inch) */
dd->ipr[0] = 1.0/72.0;
dd->ipr[1] = 1.0/72.0;
/* GREset(.) dd->gp.mkh = dd->gp.cra[0] * dd->gp.ipr[0]; */
dd->canClip = TRUE;
dd->canHAdj = 2;
dd->canChangeGamma = FALSE;
/* Start the driver */
PS_Open(dd, pd);
dd->close = PS_Close;
dd->size = PS_Size;
dd->newPage = PS_NewPage;
dd->clip = PS_Clip;
dd->text = PS_Text;
dd->strWidth = PS_StrWidth;
dd->metricInfo = PS_MetricInfo;
dd->rect = PS_Rect;
dd->path = PS_Path;
dd->raster = PS_Raster;
dd->circle = PS_Circle;
dd->line = PS_Line;
dd->polygon = PS_Polygon;
dd->polyline = PS_Polyline;
/* dd->locator = PS_Locator;
dd->mode = PS_Mode; */
dd->hasTextUTF8 = TRUE;
dd->textUTF8 = PS_TextUTF8;
dd->strWidthUTF8 = PS_StrWidthUTF8;
dd->useRotatedTextInContour = TRUE;
dd->haveTransparency = 1;
dd->haveTransparentBg = 2;
dd->haveRaster = 3; /* non-missing colours */
dd->deviceSpecific = (void *) pd;
dd->displayListOn = FALSE;
return TRUE;
}
static void CheckAlpha(int color, PostScriptDesc *pd)
{
unsigned int alpha = R_ALPHA(color);
if (alpha > 0 && alpha < 255 && !pd->warn_trans) {
warning(_("semi-transparency is not supported on this device: reported only once per page"));
pd->warn_trans = TRUE;
}
}
static void SetColor(int color, pDevDesc dd)
{
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
if(color != pd->current.col) {
PostScriptSetCol(pd->psfp,
R_RED(color)/255.0,
R_GREEN(color)/255.0,
R_BLUE(color)/255.0, pd);
fprintf(pd->psfp, "\n");
pd->current.col = color;
}
}
static void SetFill(int color, pDevDesc dd)
{
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
if(color != pd->current.fill) {
PostScriptSetFill(pd->psfp,
R_RED(color)/255.0,
R_GREEN(color)/255.0,
R_BLUE(color)/255.0, pd);
pd->current.fill = color;
}
}
/* Note that the line texture is scaled by the line width. */
static void SetLineStyle(const pGEcontext gc, pDevDesc dd)
{
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
char dashlist[8];
int i;
int newlty = gc->lty;
double newlwd = gc->lwd;
R_GE_lineend newlend = gc->lend;
R_GE_linejoin newljoin = gc->ljoin;
double newlmitre = gc->lmitre;
if (pd->current.lty != newlty || pd->current.lwd != newlwd) {
pd->current.lwd = newlwd;
pd->current.lty = newlty;
PostScriptSetLineWidth(pd->psfp, newlwd * 0.75);
/* process lty : */
for(i = 0; i < 8 && newlty & 15 ; i++) {
dashlist[i] = newlty & 15;
newlty = newlty >> 4;
}
PostScriptSetLineTexture(pd->psfp, dashlist, i, newlwd * 0.75, newlend);
}
if (pd->current.lend != newlend) {
pd->current.lend = newlend;
PostScriptSetLineEnd(pd->psfp, newlend);
}
if (pd->current.ljoin != newljoin) {
pd->current.ljoin = newljoin;
PostScriptSetLineJoin(pd->psfp, newljoin);
}
if (pd->current.lmitre != newlmitre) {
pd->current.lmitre = newlmitre;
PostScriptSetLineMitre(pd->psfp, newlmitre);
}
}
static void SetFont(int font, int size, pDevDesc dd)
{
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
if(size < 1 || size > pd->maxpointsize)
size = 10;
if (size != pd->current.fontsize || font != pd->current.font) {
PostScriptSetFont(pd->psfp, font, size);
pd->current.fontsize = size;
pd->current.font = font;
}
}
static void PS_cleanup(int stage, pDevDesc dd, PostScriptDesc *pd)
{
switch (stage) {
case 4: /* Allocated fonts */
freeDeviceFontList(pd->fonts);
freeDeviceCIDFontList(pd->cidfonts);
case 3: /* Allocated encodings */
freeDeviceEncList(pd->encodings);
case 1: /* Allocated PDFDesc */
free(pd);
free(dd);
}
}
static Rboolean PS_Open(pDevDesc dd, PostScriptDesc *pd)
{
char buf[512];
if (strlen(pd->filename) == 0) {
if(strlen(pd->command) == 0) return FALSE;
errno = 0;
pd->psfp = R_popen(pd->command, "w");
pd->open_type = 1;
if (!pd->psfp || errno != 0) {
PS_cleanup(4, dd, pd);
error(_("cannot open 'postscript' pipe to '%s'"), pd->command);
return FALSE;
}
} else if (pd->filename[0] == '|') {
errno = 0;
pd->psfp = R_popen(pd->filename + 1, "w");
pd->open_type = 1;
if (!pd->psfp || errno != 0) {
PS_cleanup(4, dd, pd);
error(_("cannot open 'postscript' pipe to '%s'"),
pd->filename + 1);
return FALSE;
}
} else {
snprintf(buf, 512, pd->filename, pd->fileno + 1); /* file 1 to start */
pd->psfp = R_fopen(R_ExpandFileName(buf), "w");
pd->open_type = 0;
}
if (!pd->psfp) {
PS_cleanup(4, dd, pd);
error(_("cannot open file '%s'"), buf);
return FALSE;
}
if(pd->landscape)
PSFileHeader(pd->psfp,
pd->papername,
pd->paperwidth,
pd->paperheight,
pd->landscape,
!(pd->onefile),
pd->paperspecial,
dd->bottom,
dd->left,
dd->top,
dd->right,
pd->title,
pd);
else
PSFileHeader(pd->psfp,
pd->papername,
pd->paperwidth,
pd->paperheight,
pd->landscape,
!(pd->onefile),
pd->paperspecial,
dd->left,
dd->bottom,
dd->right,
dd->top,
pd->title,
pd);
return TRUE;
}
/* The driver keeps track of the current values of colors, fonts and
line parameters, to save emitting some PostScript. In some cases,
the state becomes unknown, notably after changing the clipping and
at the start of a new page, so we have the following routine to
invalidate the saved values, which in turn causes the parameters to
be set before usage.
Called at the start of each page and by PS_Clip (since that
does a grestore).
*/
static void Invalidate(pDevDesc dd)
{
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
pd->current.font = -1;
pd->current.fontsize = -1;
pd->current.lwd = -1;
pd->current.lty = -1;
pd->current.lend = 0;
pd->current.ljoin = 0;
pd->current.lmitre = 0;
pd->current.col = INVALID_COL;
pd->current.fill = INVALID_COL;
}
static void PS_Clip(double x0, double x1, double y0, double y1, pDevDesc dd)
{
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
PostScriptSetClipRect(pd->psfp, x0, x1, y0, y1);
/* clipping does grestore so invalidate monitor variables */
Invalidate(dd);
}
static void PS_Size(double *left, double *right,
double *bottom, double *top,
pDevDesc dd)
{
*left = dd->left;
*right = dd->right;
*bottom = dd->bottom;
*top = dd->top;
}
static void PostScriptClose(pDevDesc dd);
static void PS_NewPage(const pGEcontext gc,
pDevDesc dd)
{
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
if(pd->onefile) {
if(++pd->pageno > 1) PostScriptEndPage(pd->psfp);
} else if(pd->pageno > 0) {
PostScriptClose(dd);
pd->fileno++;
PS_Open(dd, pd);
pd->pageno = 1;
} else pd->pageno++;
PostScriptStartPage(pd->psfp, pd->pageno);
Invalidate(dd);
CheckAlpha(gc->fill, pd);
if(R_OPAQUE(gc->fill)) {
/*
* Override some gc settings
*/
gc->col = R_TRANWHITE;
PS_Rect(0, 0, 72.0 * pd->pagewidth, 72.0 * pd->pageheight, gc, dd);
}
pd->warn_trans = FALSE;
}
#ifdef Win32
#include "run.h" /* for runcmd */
#endif
static void PostScriptClose(pDevDesc dd)
{
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
PostScriptFileTrailer(pd->psfp, pd->pageno);
if(pd->open_type == 1)
pclose(pd->psfp);
else {
fclose(pd->psfp);
if (pd->printit) {
char buff[3*PATH_MAX+ 10];
int err = 0;
/* This should not be possible: the command is limited
to 2*PATH_MAX */
if(strlen(pd->command) + strlen(pd->filename) > 3*PATH_MAX) {
warning(_("error from postscript() in running:\n %s"),
pd->command);
return;
}
strcpy(buff, pd->command);
strcat(buff, " ");
strcat(buff, pd->filename);
/* Rprintf("buff is %s\n", buff); */
#ifdef Unix
err = R_system(buff);
#endif
#ifdef Win32
err = Rf_runcmd(buff, CE_NATIVE, 0, 0, NULL, NULL, NULL);
#endif
if (err)
warning(_("error from postscript() in running:\n %s"),
buff);
}
}
}
static void PS_Close(pDevDesc dd)
{
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
PostScriptClose(dd);
freeDeviceCIDFontList(pd->cidfonts);
freeDeviceFontList(pd->fonts);
freeDeviceEncList(pd->encodings);
pd->cidfonts = NULL;
pd->fonts = NULL;
pd->encodings = NULL;
free(pd);
}
static FontMetricInfo
*CIDsymbolmetricInfo(const char *family, PostScriptDesc *pd)
{
FontMetricInfo *result = NULL;
int fontIndex;
cidfontfamily fontfamily;
fontfamily = findDeviceCIDFont(family, pd->cidfonts, &fontIndex);
if (fontfamily) {
/* (Type 1!) symbol font */
result = &(fontfamily->symfont->metrics);
} else
error(_("CID family '%s' not included in postscript() device"),
family);
return result;
}
static FontMetricInfo *metricInfo(const char *family, int face,
PostScriptDesc *pd) {
FontMetricInfo *result = NULL;
int fontIndex;
type1fontfamily fontfamily = findDeviceFont(family, pd->fonts, &fontIndex);
if (fontfamily) {
if(face < 1 || face > 5) {
warning(_("attempt to use invalid font %d replaced by font 1"),
face);
face = 1;
}
result = &(fontfamily->fonts[face-1]->metrics);
} else
error(_("family '%s' not included in postscript() device"), family);
return result;
}
static char *convname(const char *family, PostScriptDesc *pd) {
char *result = NULL;
int fontIndex;
type1fontfamily fontfamily = findDeviceFont(family, pd->fonts, &fontIndex);
if (fontfamily)
result = fontfamily->encoding->convname;
else
error(_("family '%s' not included in postscript() device"), family);
return result;
}
static double PS_StrWidth(const char *str,
const pGEcontext gc,
pDevDesc dd)
{
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
int face = gc->fontface;
if(face < 1 || face > 5) face = 1;
if (isType1Font(gc->fontfamily, PostScriptFonts, pd->defaultFont)) {
return floor(gc->cex * gc->ps + 0.5) *
PostScriptStringWidth((const unsigned char *)str, CE_NATIVE,
metricInfo(gc->fontfamily, face, pd),
pd->useKern, face,
convname(gc->fontfamily, pd));
} else { /* cidfont(gc->fontfamily, PostScriptFonts) */
if (face < 5) {
return floor(gc->cex * gc->ps + 0.5) *
PostScriptStringWidth((const unsigned char *)str, CE_NATIVE,
NULL, FALSE, face, NULL);
} else {
return floor(gc->cex * gc->ps + 0.5) *
PostScriptStringWidth((const unsigned char *)str, CE_NATIVE,
/* Send symbol face metric info */
CIDsymbolmetricInfo(gc->fontfamily, pd),
FALSE, face, NULL);
}
}
}
static double PS_StrWidthUTF8(const char *str,
const pGEcontext gc,
pDevDesc dd)
{
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
int face = gc->fontface;
if(face < 1 || face > 5) face = 1;
if (isType1Font(gc->fontfamily, PostScriptFonts, pd->defaultFont)) {
return floor(gc->cex * gc->ps + 0.5) *
PostScriptStringWidth((const unsigned char *)str, CE_UTF8,
metricInfo(gc->fontfamily, face, pd),
pd->useKern, face,
convname(gc->fontfamily, pd));
} else { /* cidfont(gc->fontfamily, PostScriptFonts) */
if (face < 5) {
return floor(gc->cex * gc->ps + 0.5) *
PostScriptStringWidth((const unsigned char *)str, CE_UTF8,
NULL, FALSE, face, NULL);
} else {
return floor(gc->cex * gc->ps + 0.5) *
PostScriptStringWidth((const unsigned char *)str, CE_UTF8,
/* Send symbol face metric info */
CIDsymbolmetricInfo(gc->fontfamily, pd),
FALSE, face, NULL);
}
}
}
static void PS_MetricInfo(int c,
const pGEcontext gc,
double* ascent, double* descent,
double* width, pDevDesc dd)
{
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
int face = gc->fontface;
if(face < 1 || face > 5) face = 1;
if (isType1Font(gc->fontfamily, PostScriptFonts, pd->defaultFont)) {
PostScriptMetricInfo(c, ascent, descent, width,
metricInfo(gc->fontfamily, face, pd),
face == 5, convname(gc->fontfamily, pd));
} else { /* cidfont(gc->fontfamily, PostScriptFonts) */
if (face < 5) {
PostScriptCIDMetricInfo(c, ascent, descent, width);
} else {
PostScriptMetricInfo(c, ascent, descent, width,
CIDsymbolmetricInfo(gc->fontfamily, pd),
TRUE, "");
}
}
*ascent = floor(gc->cex * gc->ps + 0.5) * *ascent;
*descent = floor(gc->cex * gc->ps + 0.5) * *descent;
*width = floor(gc->cex * gc->ps + 0.5) * *width;
}
static void PS_Rect(double x0, double y0, double x1, double y1,
const pGEcontext gc,
pDevDesc dd)
{
int code;
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
/* code is set as follows */
/* code == 0, nothing to draw */
/* code == 1, outline only */
/* code == 2, fill only */
/* code == 3, outline and fill */
CheckAlpha(gc->fill, pd);
CheckAlpha(gc->col, pd);
code = 2 * (R_OPAQUE(gc->fill)) + (R_OPAQUE(gc->col));
if (code) {
if(code & 2)
SetFill(gc->fill, dd);
if(code & 1) {
SetColor(gc->col, dd);
SetLineStyle(gc, dd);
}
PostScriptRectangle(pd->psfp, x0, y0, x1, y1);
fprintf(pd->psfp, "p%d\n", code);
}
}
typedef rcolor * rcolorPtr;
static void PS_imagedata(rcolorPtr raster,
int w, int h,
PostScriptDesc *pd)
{
/* Each original byte is translated to two hex digits
(representing a number between 0 and 255) */
for (int i = 0; i < w*h; i++)
fprintf(pd->psfp, "%02x%02x%02x",
R_RED(raster[i]), R_GREEN(raster[i]), R_BLUE(raster[i]));
}
static void PS_grayimagedata(rcolorPtr raster,
int w, int h,
PostScriptDesc *pd)
{
/* Weights as in PDF gray conversion */
for (int i = 0; i < w*h; i++) {
double r = 0.213 * R_RED(raster[i]) + 0.715 * R_GREEN(raster[i])
+ 0.072 * R_BLUE(raster[i]);
fprintf(pd->psfp, "%02x", (int)(r+0.49));
}
}
/* Could support 'colormodel = "cmyk"' */
static void PS_writeRaster(unsigned int *raster, int w, int h,
double x, double y,
double width, double height,
double rot,
Rboolean interpolate,
pDevDesc dd)
{
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
/* This takes the simple approach of creating an inline
* image.
* There is no support for semitransparent images, not even
* for transparent pixels (missing values in image(useRaster = TRUE) ).
*
* The version in R < 2.13.2 used colorimage, hence the DeviceRGB
* colour space.
*/
/* Now we are using level-2 features, there are other things we could do
(a) encode the data more compactly, e.g. using
/DataSource currentfile /ASCII85Decode filter /FlateDecode filter def
(b) add a mask with ImageType 3: see PLRM 3rd ed section 4.10.6.
(c) interpolation (done but disabled, as at least ghostscript
seems to ignore the request, and Mac preview always
interpolates.)
(d) sRGB colorspace (done)
*/
/* Save graphics state */
fprintf(pd->psfp, "gsave\n");
/* set the colour space: this form of the image operator uses the
current colour space. */
if (streql(pd->colormodel, "srgb+gray"))
fprintf(pd->psfp, "sRGB\n");
else if (streql(pd->colormodel, "srgb")) /* set for page */ ;
else if (streql(pd->colormodel, "gray"))
fprintf(pd->psfp, "/DeviceGray setcolorspace\n");
else
fprintf(pd->psfp, "/DeviceRGB setcolorspace\n");
/* translate */
fprintf(pd->psfp, "%.2f %.2f translate\n", x, y);
/* rotate */
if (rot != 0.0) fprintf(pd->psfp, "%.2f rotate\n", rot);
/* scale */
fprintf(pd->psfp, "%.2f %.2f scale\n", width, height);
/* write dictionary */
fprintf(pd->psfp, "8 dict dup begin\n");
fprintf(pd->psfp, " /ImageType 1 def\n");
fprintf(pd->psfp, " /Width %d def\n", w);
fprintf(pd->psfp, " /Height %d def\n", h);
fprintf(pd->psfp, " /BitsPerComponent 8 def\n");
if (interpolate)
fprintf(pd->psfp, " /Interpolate true def\n");
if (streql(pd->colormodel, "gray"))
fprintf(pd->psfp, " /Decode [0 1] def\n");
else
fprintf(pd->psfp, " /Decode [0 1 0 1 0 1] def\n");
fprintf(pd->psfp, " /DataSource currentfile /ASCIIHexDecode filter def\n");
fprintf(pd->psfp, " /ImageMatrix [%d 0 0 %d 0 %d] def\n", w, -h, h);
fprintf(pd->psfp, "end\n");
fprintf(pd->psfp, "image\n");
/* now the data */
if (streql(pd->colormodel, "gray"))
PS_grayimagedata(raster, w, h, pd);
else
PS_imagedata(raster, w, h, pd);
fprintf(pd->psfp, ">\n");
/* Restore graphics state */
fprintf(pd->psfp, "grestore\n");
}
/* see comments above */
#define OLD 1
static void PS_Raster(unsigned int *raster, int w, int h,
double x, double y,
double width, double height,
double rot,
Rboolean interpolate,
const pGEcontext gc, pDevDesc dd)
{
#ifdef OLD
if (interpolate) {
/* Generate a new raster
* which is interpolated from the original
* Assume a resolution for the new raster of 72 dpi
* Ideally would allow user to set this.
*/
const void *vmax;
vmax = vmaxget();
int newW = (int) width;
int newH = (int) height;
unsigned int *newRaster =
(unsigned int *) R_alloc(newW * newH, sizeof(unsigned int));
R_GE_rasterInterpolate(raster, w, h,
newRaster, newW, newH);
PS_writeRaster(newRaster, newW, newH,
x, y, width, height, rot, FALSE, dd);
vmaxset(vmax);
} else {
PS_writeRaster(raster, w, h,
x, y, width, height, rot, FALSE, dd);
}
#else
PS_writeRaster(raster, w, h,
x, y, width, height, rot, interpolate, dd);
#endif
}
static void PS_Circle(double x, double y, double r,
const pGEcontext gc,
pDevDesc dd)
{
int code;
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
/* code is set as follows */
/* code == 0, nothing to draw */
/* code == 1, outline only */
/* code == 2, fill only */
/* code == 3, outline and fill */
CheckAlpha(gc->fill, pd);
CheckAlpha(gc->col, pd);
code = 2 * (R_OPAQUE(gc->fill)) + (R_OPAQUE(gc->col));
if (code) {
if(code & 2)
SetFill(gc->fill, dd);
if(code & 1) {
SetColor(gc->col, dd);
SetLineStyle(gc, dd);
}
PostScriptCircle(pd->psfp, x, y, r);
fprintf(pd->psfp, "p%d\n", code);
}
}
static void PS_Line(double x1, double y1, double x2, double y2,
const pGEcontext gc,
pDevDesc dd)
{
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
CheckAlpha(gc->col, pd);
/* FIXME : clip to the device extents here */
if(R_OPAQUE(gc->col)) {
SetColor(gc->col, dd);
SetLineStyle(gc, dd);
PostScriptStartPath(pd->psfp);
PostScriptMoveTo(pd->psfp, x1, y1);
PostScriptRLineTo(pd->psfp, x1, y1, x2, y2);
/* fprintf(pd->psfp, "%.2f %.2f rl\n", x2 - x1, y2 - y1);*/
PostScriptEndPath(pd->psfp);
}
}
static void PS_Polygon(int n, double *x, double *y,
const pGEcontext gc,
pDevDesc dd)
{
PostScriptDesc *pd;
int i, code;
pd = (PostScriptDesc *) dd->deviceSpecific;
/* code is set as follows */
/* code == 0, nothing to draw */
/* code == 1, outline only */
/* code == 2, fill only */
/* code == 3, outline and fill */
/* code == 6, eofill only */
/* code == 7, outline and eofill */
CheckAlpha(gc->fill, pd);
CheckAlpha(gc->col, pd);
code = 2 * (R_OPAQUE(gc->fill)) + (R_OPAQUE(gc->col));
if (code) {
if(code & 2) {
SetFill(gc->fill, dd);
if (pd->fillOddEven) code |= 4;
}
if(code & 1) {
SetColor(gc->col, dd);
SetLineStyle(gc, dd);
}
fprintf(pd->psfp, "np\n");
fprintf(pd->psfp, " %.2f %.2f m\n", x[0], y[0]);
for(i = 1 ; i < n ; i++)
if (i % 100 == 0)
fprintf(pd->psfp, "%.2f %.2f lineto\n", x[i], y[i]);
else
PostScriptRLineTo(pd->psfp, x[i-1], y[i-1], x[i], y[i]);
fprintf(pd->psfp, "cp p%d\n", code);
}
}
static void PS_Path(double *x, double *y,
int npoly, int *nper,
Rboolean winding,
const pGEcontext gc,
pDevDesc dd)
{
PostScriptDesc *pd;
int i, j, index, code;
pd = (PostScriptDesc *) dd->deviceSpecific;
/* code is set as follows */
/* code == 0, nothing to draw */
/* code == 1, outline only */
/* code == 2, fill only */
/* code == 3, outline and fill */
/* code == 6, eofill only */
/* code == 7, outline and eofill */
CheckAlpha(gc->fill, pd);
CheckAlpha(gc->col, pd);
code = 2 * (R_OPAQUE(gc->fill)) + (R_OPAQUE(gc->col));
if (code) {
if(code & 2) {
SetFill(gc->fill, dd);
if (!winding) code |= 4;
}
if(code & 1) {
SetColor(gc->col, dd);
SetLineStyle(gc, dd);
}
fprintf(pd->psfp, "np\n");
index = 0;
for (i = 0; i < npoly; i++) {
fprintf(pd->psfp, " %.2f %.2f m\n", x[index], y[index]);
index++;
for(j = 1; j < nper[i]; j++) {
if (j % 100 == 0)
fprintf(pd->psfp, "%.2f %.2f lineto\n",
x[index], y[index]);
else
PostScriptRLineTo(pd->psfp, x[index-1], y[index-1],
x[index], y[index]);
index++;
}
fprintf(pd->psfp, "cp\n");
}
fprintf(pd->psfp, "p%d\n", code);
}
}
static void PS_Polyline(int n, double *x, double *y,
const pGEcontext gc,
pDevDesc dd)
{
PostScriptDesc *pd;
int i;
pd = (PostScriptDesc*) dd->deviceSpecific;
CheckAlpha(gc->col, pd);
if(R_OPAQUE(gc->col)) {
SetColor(gc->col, dd);
SetLineStyle(gc, dd);
fprintf(pd->psfp, "np\n");
fprintf(pd->psfp, "%.2f %.2f m\n", x[0], y[0]);
for(i = 1 ; i < n ; i++) {
/* split up solid lines (only) into chunks of size 1000 */
if(gc->lty == 0 && i%1000 == 0)
fprintf(pd->psfp, "currentpoint o m\n");
if (i % 100 == 0)
fprintf(pd->psfp, "%.2f %.2f lineto\n", x[i], y[i]);
else
PostScriptRLineTo(pd->psfp, x[i-1], y[i-1], x[i], y[i]);
}
fprintf(pd->psfp, "o\n");
}
}
static int translateFont(char *family, int style, PostScriptDesc *pd)
{
int result = style;
type1fontfamily fontfamily;
int fontIndex;
if(style < 1 || style > 5) {
warning(_("attempt to use invalid font %d replaced by font 1"), style);
style = 1;
}
fontfamily = findDeviceFont(family, pd->fonts, &fontIndex);
if (fontfamily) {
result = (fontIndex - 1)*5 + style;
} else {
warning(_("family '%s' not included in postscript() device"), family);
}
return result;
}
static int numFonts(type1fontlist fonts) {
int i = 0;
while (fonts) {
i++;
fonts = fonts->next;
}
return i;
}
static int translateCIDFont(char *family, int style, PostScriptDesc *pd)
{
int result = style;
cidfontfamily fontfamily;
int fontIndex;
if(style < 1 || style > 5) {
warning(_("attempt to use invalid font %d replaced by font 1"), style);
style = 1;
}
fontfamily = findDeviceCIDFont(family, pd->cidfonts, &fontIndex);
if (fontfamily) {
/*
* CID fonts all listed after all Type 1 fonts.
*/
result = (numFonts(pd->fonts)*5) + (fontIndex - 1)*5 + style;
} else {
warning(_("family '%s' not included in postscript() device"), family);
}
return result;
}
static void drawSimpleText(double x, double y, const char *str,
double rot, double hadj,
int font,
const pGEcontext gc,
pDevDesc dd) {
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
SetFont(font,
(int)floor(gc->cex * gc->ps + 0.5),dd);
CheckAlpha(gc->col, pd);
if(R_OPAQUE(gc->col)) {
SetColor(gc->col, dd);
if(pd->useKern)
PostScriptTextKern(pd->psfp, x, y, str, hadj, rot, gc, dd);
else
PostScriptText(pd->psfp, x, y, str, strlen(str), hadj, rot, gc, dd);
}
}
/* <FIXME> it would make sense to cache 'cd' here, but we would also
need to know if the current locale's charset changes. However,
currently this is only called in a UTF-8 locale.
*/
static void mbcsToSbcs(const char *in, char *out, const char *encoding,
int enc)
{
void *cd = NULL;
const char *i_buf; char *o_buf;
size_t i_len, o_len, status;
#if 0
if(enc != CE_UTF8 &&
( !strcmp(encoding, "latin1") || !strcmp(encoding, "ISOLatin1")) ) {
mbcsToLatin1(in, out); /* more tolerant */
return;
}
#endif
if ((void*)-1 ==
(cd = Riconv_open(encoding, (enc == CE_UTF8) ? "UTF-8" : "")))
error(_("unknown encoding '%s' in 'mbcsToSbcs'"), encoding);
i_buf = (char *) in;
i_len = strlen(in)+1; /* include terminator */
o_buf = (char *) out;
o_len = i_len; /* must be the same or fewer chars */
next_char:
status = Riconv(cd, &i_buf, &i_len, &o_buf, &o_len);
/* libiconv 1.13 gives EINVAL on \xe0 in UTF-8 (as used in fBasics) */
if(status == (size_t) -1 && (errno == EILSEQ || errno == EINVAL)) {
warning(_("conversion failure on '%s' in 'mbcsToSbcs': dot substituted for <%02x>"),
in, (unsigned char) *i_buf),
*o_buf++ = '.'; i_buf++; o_len--; i_len--;
if(i_len > 0) goto next_char;
}
Riconv_close(cd);
if (status == (size_t)-1) /* internal error? */
error("conversion failure from %s to %s on '%s' in 'mbcsToSbcs'",
(enc == CE_UTF8) ? "UTF-8" : "native", encoding, in);
}
static void PS_Text0(double x, double y, const char *str, int enc,
double rot, double hadj,
const pGEcontext gc,
pDevDesc dd)
{
const char *str1 = str;
char *buff;
PostScriptDesc *pd = (PostScriptDesc *) dd->deviceSpecific;
if (gc->fontface == 5) {
if (isCIDFont(gc->fontfamily, PostScriptFonts, pd->defaultCIDFont)) {
drawSimpleText(x, y, str, rot, hadj,
translateCIDFont(gc->fontfamily, gc->fontface, pd),
gc, dd);
return;
} else {
drawSimpleText(x, y, str, rot, hadj,
translateFont(gc->fontfamily, gc->fontface, pd),
gc, dd);
return;
}
}
/* No symbol fonts from now on */
if (isCIDFont(gc->fontfamily, PostScriptFonts, pd->defaultCIDFont)) {
/* NB, we could be in a SBCS here */
size_t ucslen;
int fontIndex;
/*
* CID convert optimize PS encoding == locale encode case
*/
cidfontfamily cidfont = findDeviceCIDFont(gc->fontfamily,
pd->cidfonts,
&fontIndex);
if(!cidfont)
error(_("family '%s' not included in postscript() device"),
gc->fontfamily);
if (!dd->hasTextUTF8 &&
!strcmp(locale2charset(NULL), cidfont->encoding)) {
SetFont(translateCIDFont(gc->fontfamily, gc->fontface, pd),
(int)floor(gc->cex * gc->ps + 0.5),dd);
CheckAlpha(gc->col, pd);
if(R_OPAQUE(gc->col)) {
SetColor(gc->col, dd);
PostScriptHexText(pd->psfp, x, y, str, strlen(str), hadj, rot);
}
return;
}
/*
* CID convert PS encoding != locale encode case
*/
ucslen = (dd->hasTextUTF8) ? Rf_utf8towcs(NULL, str, 0) : mbstowcs(NULL, str, 0);
if (ucslen != (size_t)-1) {
void *cd;
const char *i_buf; char *o_buf;
size_t nb, i_len, o_len, buflen = ucslen * sizeof(ucs2_t);
size_t status;
cd = (void*) Riconv_open(cidfont->encoding,
(enc == CE_UTF8) ? "UTF-8" : "");
if(cd == (void*)-1) {
warning(_("failed open converter to encoding '%s'"),
cidfont->encoding);
return;
}
R_CheckStack2(buflen);
unsigned char buf[buflen];
i_buf = (char *)str;
o_buf = (char *)buf;
i_len = strlen(str); /* do not include terminator */
nb = o_len = buflen;
status = Riconv(cd, &i_buf, (size_t *)&i_len,
(char **)&o_buf, (size_t *)&o_len);
Riconv_close(cd);
if(status == (size_t)-1)
warning(_("failed in text conversion to encoding '%s'"),
cidfont->encoding);
else {
SetFont(translateCIDFont(gc->fontfamily, gc->fontface, pd),
(int)floor(gc->cex * gc->ps + 0.5), dd);
CheckAlpha(gc->col, pd);
if(R_OPAQUE(gc->col)) {
SetColor(gc->col, dd);
PostScriptHexText(pd->psfp, x, y, (char *)buf,
nb - o_len, hadj, rot);
}
}
return;
} else {
warning(_("invalid string in '%s'"), "PS_Text");
return;
}
}
/* Now using single-byte non-symbol font.
Was utf8locale, but it is not entirely obvious that only UTF-8
needs re-encoding, although we don't have any other MBCSs that
can sensibly be mapped to a SBCS.
It would be perverse (but possible) to write English in a
CJK MBCS.
*/
if((enc == CE_UTF8 || mbcslocale) && !strIsASCII(str)) {
R_CheckStack2(strlen(str)+1);
buff = alloca(strlen(str)+1); /* Output string cannot be longer */
mbcsToSbcs(str, buff, convname(gc->fontfamily, pd), enc);
str1 = buff;
}
drawSimpleText(x, y, str1, rot, hadj,
translateFont(gc->fontfamily, gc->fontface, pd),
gc, dd);
}
static void PS_Text(double x, double y, const char *str,
double rot, double hadj,
const pGEcontext gc,
pDevDesc dd)
{
PS_Text0(x, y, str, CE_NATIVE, rot, hadj, gc, dd);
}
static void PS_TextUTF8(double x, double y, const char *str,
double rot, double hadj,
const pGEcontext gc,
pDevDesc dd)
{
PS_Text0(x, y, str, CE_UTF8, rot, hadj, gc, dd);
}
/***********************************************************************
XFig driver shares font handling
************************************************************************/
typedef struct {
char filename[PATH_MAX];
char papername[64]; /* paper name */
int paperwidth; /* paper width in big points (1/72 in) */
int paperheight; /* paper height in big points */
Rboolean landscape; /* landscape mode */
int pageno; /* page number */
int fontnum; /* font number in XFig */
int maxpointsize;
double width; /* plot width in inches */
double height; /* plot height in inches */
double pagewidth; /* page width in inches */
double pageheight; /* page height in inches */
Rboolean pagecentre; /* centre image on page? */
double lwd; /* current line width */
int lty; /* current line type */
rcolor col; /* current color */
rcolor fill; /* current fill color */
rcolor bg; /* background color */
int XFigColors[534];
int nXFigColors;
FILE *psfp; /* output file */
FILE *tmpfp; /* temp file */
char tmpname[PATH_MAX];
Rboolean onefile;
Rboolean warn_trans; /* have we warned about translucent cols? */
int ymax; /* used to invert coord system */
char encoding[50]; /* for writing text */
Rboolean textspecial; /* use textspecial flag in xfig for latex integration */
Rboolean defaultfont; /* use the default font in xfig */
/*
* Fonts and encodings used on the device
*
* ASSUME ONLY ONE (DEFAULT) FOR NOW
*/
type1fontlist fonts;
encodinglist encodings;
} XFigDesc;
static void
XF_FileHeader(FILE *fp, const char *papername, Rboolean landscape,
Rboolean onefile)
{
fprintf(fp, "#FIG 3.2\n");
fprintf(fp, landscape ? "Landscape\n" : "Portrait\n");
fprintf(fp, "Flush Left\nInches\n");
/* Fix */fprintf(fp, "%s\n", papername);
fprintf(fp, "100.0\n");
fprintf(fp, onefile ? "Multiple\n" : "Single\n");
fprintf(fp, "-2\n"); /* no background */
fprintf(fp, "1200 2\n"); /* coordinate system */
fprintf(fp, "# End of XFig header\n");
}
static void XF_FileTrailer(FILE *fp)
{
fprintf(fp, "# end of XFig file\n");
}
static void XF_EndPage(FILE *fp)
{
fprintf(fp, "# end of XFig page\n");
}
static void XF_WriteString(FILE *fp, const char *str)
{
unsigned int c;
for ( ; *str; str++) {
c = (unsigned char)*str;
if (c > 127) {
fprintf(fp, "\\%o", c);
} else {
switch(*str) {
case '\n':
fprintf(fp, "\\n");
break;
case '\\':
fprintf(fp, "\\\\");
break;
default:
fputc(*str, fp);
break;
}
}
}
}
static void XF_CheckAlpha(int color, XFigDesc *pd)
{
unsigned int alpha = R_ALPHA(color);
if (alpha > 0 && alpha < 255 && !pd->warn_trans) {
warning(_("semi-transparency is not supported on this device: reported only once per page"));
pd->warn_trans = TRUE;
}
}
static int XF_SetColor(int color, XFigDesc *pd)
{
int i;
if(!R_OPAQUE(color)) return -1;
color = color & 0xffffff;
for (i = 0; i < pd->nXFigColors; i++)
if(color == pd->XFigColors[i]) return i;
if(pd->nXFigColors == 534)
error(_("ran out of colors in xfig()"));
/* new colour */
fprintf(pd->psfp, "0 %d #%02x%02x%02x\n", pd->nXFigColors,
R_RED(color), R_GREEN(color), R_BLUE(color));
pd->XFigColors[pd->nXFigColors] = color;
return pd->nXFigColors++;
}
static void XFconvert(double *x, double *y, XFigDesc *pd)
{
(*x) *= 16.667;
(*y) = pd->ymax - 16.667*(*y);
}
static int XF_SetLty(int lty)
{
switch(lty) {
case LTY_BLANK:
return -1;
case LTY_SOLID:
return 0;
case LTY_DASHED:
return 1;
case LTY_DOTTED:
return 2;
case LTY_DOTDASH:
return 3;
default:
warning(_("unimplemented line texture %08x: using Dash-double-dotted"),
lty);
return 4;
}
}
/* Device Driver Actions */
static void XFig_Circle(double x, double y, double r,
const pGEcontext gc,
pDevDesc dd);
static void XFig_Clip(double x0, double x1, double y0, double y1,
pDevDesc dd);
static void XFig_Close(pDevDesc dd);
static void XFig_Line(double x1, double y1, double x2, double y2,
const pGEcontext gc,
pDevDesc dd);
static void XFig_MetricInfo(int c,
const pGEcontext gc,
double* ascent, double* descent,
double* width, pDevDesc dd);
static void XFig_NewPage(const pGEcontext gc, pDevDesc dd);
static void XFig_Polygon(int n, double *x, double *y,
const pGEcontext gc,
pDevDesc dd);
static void XFig_Polyline(int n, double *x, double *y,
const pGEcontext gc,
pDevDesc dd);
static void XFig_Rect(double x0, double y0, double x1, double y1,
const pGEcontext gc,
pDevDesc dd);
static void XFig_Size(double *left, double *right,
double *bottom, double *top,
pDevDesc dd);
static double XFig_StrWidth(const char *str,
const pGEcontext gc,
pDevDesc dd);
static void XFig_Text(double x, double y, const char *str,
double rot, double hadj,
const pGEcontext gc,
pDevDesc dd);
static Rboolean XFig_Open(pDevDesc, XFigDesc*);
/*
* Values taken from FIG format definition
*/
static int XFigBaseNum(const char *name)
{
int i;
if (!strcmp(name, "Times"))
i = 0;
else if (!strcmp(name, "AvantGarde"))
i = 4;
else if (!strcmp(name, "Bookman"))
i = 8;
else if (!strcmp(name, "Courier"))
i = 12;
else if (!strcmp(name, "Helvetica"))
i = 16;
else if (!strcmp(name, "Helvetica-Narrow"))
i = 20;
else if (!strcmp(name, "NewCenturySchoolbook"))
i = 24;
else if (!strcmp(name, "Palatino"))
i = 28;
else {
warning(_("unknown postscript font family '%s', using Helvetica"),
name);
i = 16;
}
return i;
}
static void XF_resetColors(XFigDesc *pd)
{
int i;
for(i = 0; i < 32; i++) pd->XFigColors[i] = 0;
pd->XFigColors[7] = 0xffffff; /* white */
pd->nXFigColors = 32;
}
/* Driver Support Routines */
static Rboolean
XFigDeviceDriver(pDevDesc dd, const char *file, const char *paper,
const char *family,
const char *bg, const char *fg,
double width, double height,
Rboolean horizontal, double ps,
Rboolean onefile, Rboolean pagecentre,
Rboolean defaultfont, Rboolean textspecial,
const char *encoding)
{
/* If we need to bail out with some sort of "error" */
/* then we must free(dd) */
int gotFont;
double xoff, yoff, pointsize;
XFigDesc *pd;
type1fontfamily font;
encodinginfo enc;
encodinglist enclist;
/* Check and extract the device parameters */
if(strlen(file) > PATH_MAX - 1) {
free(dd);
error(_("filename too long in %s()"), "xfig");
}
/* allocate new xfig device description */
if (!(pd = (XFigDesc *) malloc(sizeof(XFigDesc)))) {
free(dd);
error(_("memory allocation problem in %s()"), "xfig");
return FALSE;
}
/* from here on, if need to bail out with "error", must also */
/* free(pd) */
/* initialize xfig device description */
strcpy(pd->filename, file);
strcpy(pd->papername, paper);
pd->fontnum = XFigBaseNum(family);
/* this might have changed the family, so update */
if(pd->fontnum == 16) family = "Helvetica";
pd->bg = R_GE_str2col(bg);
pd->col = R_GE_str2col(fg);
pd->fill = R_TRANWHITE;
pd->width = width;
pd->height = height;
pd->landscape = horizontal;
pd->textspecial = textspecial;
pd->defaultfont = defaultfont;
pointsize = floor(ps);
if(R_TRANSPARENT(pd->bg) && R_TRANSPARENT(pd->col)) {
free(dd);
free(pd);
error(_("invalid foreground/background color (xfig)"));
}
pd->warn_trans = FALSE;
/*
* Load the default encoding AS THE FIRST ENCODING FOR THIS DEVICE.
*/
pd->encodings = NULL;
if (!(enc = findEncoding("ISOLatin1.enc", pd->encodings, FALSE)))
enc = addEncoding("ISOLatin1.enc", 0);
if (enc && (enclist = addDeviceEncoding(enc, pd->encodings))) {
pd->encodings = enclist;
} else {
free(dd);
free(pd);
error(_("failed to load encoding file in %s()"), "xfig");
}
/* Load default font */
pd->fonts = NULL;
gotFont = 0;
font = findLoadedFont(family, "ISOLatin1.enc", FALSE);
if (!font) {
/*
* If the font has not been loaded yet, load it.
*
* The family SHOULD be in the font database to get this far.
* (checked at R level in postscript() in postscript.R)
*/
if (isType1Font(family, PostScriptFonts, NULL)) {
font = addFont(family, FALSE, pd->encodings);
} else {
error(_("only Type 1 fonts supported for XFig"));
}
}
if (font) {
/*
* At this point the font is loaded, so add it to the
* device's list of fonts.
*/
pd->fonts = addDeviceFont(font, pd->fonts, &gotFont);
}
if (!gotFont) {
free(dd);
free(pd);
error(_("failed to initialise default XFig font"));
}
/* Deal with paper and plot size and orientation */
if(!strcmp(pd->papername, "Default") ||
!strcmp(pd->papername, "default")) {
SEXP s = STRING_ELT(GetOption1(install("papersize")), 0);
if(s != NA_STRING && strlen(CHAR(s)) > 0)
strcpy(pd->papername, CHAR(s));
else strcpy(pd->papername, "A4");
}
if(!strcmp(pd->papername, "A4") ||
!strcmp(pd->papername, "a4")) {
strcpy(pd->papername, "A4");
pd->pagewidth = 21.0 / 2.54;
pd->pageheight = 29.7 / 2.54;
}
else if(!strcmp(pd->papername, "Letter") ||
!strcmp(pd->papername, "letter")) {
strcpy(pd->papername, "Letter");
pd->pagewidth = 8.5;
pd->pageheight = 11.0;
}
else if(!strcmp(pd->papername, "Legal") ||
!strcmp(pd->papername, "legal")) {
strcpy(pd->papername, "Legal");
pd->pagewidth = 8.5;
pd->pageheight = 14.0;
}
else {
freeDeviceFontList(pd->fonts);
freeDeviceEncList(pd->encodings);
pd->fonts = NULL;
pd->encodings = NULL;
free(dd);
free(pd);
error(_("invalid page type '%s' (xfig)"), pd->papername);
}
pd->pagecentre = pagecentre;
pd->paperwidth = (int)(72 * pd->pagewidth);
pd->paperheight = (int)(72 * pd->pageheight);
if(!onefile) {
char *p = strrchr(pd->filename, '%');
if(!p)
warning(_("xfig(%s, onefile=FALSE) will only return the last plot"), pd->filename);
}
if(pd->landscape) {
double tmp;
tmp = pd->pagewidth;
pd->pagewidth = pd->pageheight;
pd->pageheight = tmp;
}
if(pd->width < 0.1 || pd->width > pd->pagewidth-0.5)
pd->width = pd->pagewidth-0.5;
if(pd->height < 0.1 || pd->height > pd->pageheight-0.5)
pd->height = pd->pageheight-0.5;
if(pagecentre) {
xoff = (pd->pagewidth - pd->width)/2.0;
yoff = (pd->pageheight - pd->height)/2.0;
} else {
xoff = yoff = 0.0;
}
if(pagecentre)
pd->ymax = (int)(1200.0 * pd->pageheight);
else
pd->ymax = (int)(1200.0 * pd->height);
pd->onefile = onefile;
pd->maxpointsize = (int)(72.0 * ((pd->pageheight > pd->pagewidth) ?
pd->pageheight : pd->pagewidth));
pd->pageno = 0;
/* Base Pointsize */
/* Nominal Character Sizes in Pixels */
/* Only right for 12 point font. */
/* Max pointsize suggested by Peter Dalgaard */
if(pointsize < 6.0) pointsize = 6.0;
if(pointsize > pd->maxpointsize) pointsize = pd->maxpointsize;
dd->startps = pointsize;
dd->startlty = LTY_SOLID;
dd->startfont = 1;
dd->startfill = pd->bg;
dd->startcol = pd->col;
dd->startgamma = 1;
/* Set graphics parameters that must be set by device driver. */
/* Page dimensions in points. */
dd->left = 72 * xoff; /* left */
dd->right = 72 * (xoff + pd->width); /* right */
dd->bottom = 72 * yoff; /* bottom */
dd->top = 72 * (yoff + pd->height); /* top */
dd->cra[0] = 0.9 * pointsize;
dd->cra[1] = 1.2 * pointsize;
/* Character Addressing Offsets */
/* These offsets should center a single */
/* plotting character over the plotting point. */
/* Pure guesswork and eyeballing ... */
dd->xCharOffset = 0.4900;
dd->yCharOffset = 0.3333;
dd->yLineBias = 0.2;
/* Inches per Raster Unit */
/* 1200 dpi */
dd->ipr[0] = 1.0/72.0;
dd->ipr[1] = 1.0/72.0;
dd->canClip = FALSE;
dd->canHAdj = 1; /* 0, 0.5, 1 */
dd->canChangeGamma = FALSE;
strncpy(pd->encoding, encoding, 50);
XF_resetColors(pd);
/* Start the driver */
XFig_Open(dd, pd);
dd->close = XFig_Close;
dd->size = XFig_Size;
dd->newPage = XFig_NewPage;
dd->clip = XFig_Clip;
dd->text = XFig_Text;
dd->strWidth = XFig_StrWidth;
dd->metricInfo = XFig_MetricInfo;
dd->rect = XFig_Rect;
/* dd->path = XFig_Path;
dd->raster = XFig_Raster;
dd->cap = XFig_Cap; */
dd->circle = XFig_Circle;
dd->line = XFig_Line;
dd->polygon = XFig_Polygon;
dd->polyline = XFig_Polyline;
/* dd->locator = XFig_Locator;
dd->mode = XFig_Mode; */
dd->hasTextUTF8 = FALSE;
dd->useRotatedTextInContour = FALSE; /* maybe */
dd->haveTransparency = 1;
dd->haveTransparentBg = 1;
dd->haveRaster = 1;
dd->haveCapture = 1;
dd->haveLocator = 1;
dd->deviceSpecific = (void *) pd;
dd->displayListOn = FALSE;
return 1;
}
static void XFig_cleanup(pDevDesc dd, XFigDesc *pd)
{
freeDeviceFontList(pd->fonts);
freeDeviceEncList(pd->encodings);
pd->fonts = NULL;
pd->encodings = NULL;
free(dd);
free(pd);
}
static Rboolean XFig_Open(pDevDesc dd, XFigDesc *pd)
{
char buf[512], *tmp;
if (strlen(pd->filename) == 0) {
XFig_cleanup(dd, pd);
error(_("empty file name"));
return FALSE;
} else {
snprintf(buf, 512, pd->filename, pd->pageno + 1); /* page 1 to start */
pd->psfp = R_fopen(R_ExpandFileName(buf), "w");
}
if (!pd->psfp) {
XFig_cleanup(dd, pd);
error(_("cannot open file '%s'"), buf);
return FALSE;
}
/* assume tmpname is less than PATH_MAX */
tmp = R_tmpnam("Rxfig", R_TempDir);
strcpy(pd->tmpname, tmp);
free(tmp);
pd->tmpfp = R_fopen(pd->tmpname, "w");
if (!pd->tmpfp) {
fclose(pd->psfp);
XFig_cleanup(dd, pd);
error(_("cannot open file '%s'"), pd->tmpname);
return FALSE;
}
XF_FileHeader(pd->psfp, pd->papername, pd->landscape, pd->onefile);
pd->pageno = 0;
return TRUE;
}
static void XFig_Clip(double x0, double x1, double y0, double y1,
pDevDesc dd)
{
}
static void XFig_Size(double *left, double *right,
double *bottom, double *top,
pDevDesc dd)
{
*left = dd->left;
*right = dd->right;
*bottom = dd->bottom;
*top = dd->top;
}
#define CHUNK 10000
static void XFig_NewPage(const pGEcontext gc,
pDevDesc dd)
{
char buf[PATH_MAX];
XFigDesc *pd = (XFigDesc *) dd->deviceSpecific;
pd->pageno++;
if(pd->onefile) {
fprintf(pd->tmpfp, "#Start of page %d\n", pd->pageno);
if(pd->pageno > 1) XF_EndPage(pd->tmpfp);
} else {
char buffer[CHUNK];
size_t nread, res;
if(pd->pageno == 1) return;
XF_FileTrailer(pd->tmpfp);
fclose(pd->tmpfp);
pd->tmpfp = R_fopen(pd->tmpname, "r");
while(1) {
nread = fread(buffer, 1, CHUNK, pd->tmpfp);
if(nread > 0) {
res = fwrite(buffer, 1, nread, pd->psfp);
if(res != nread) error(_("write failed"));
}
if(nread < CHUNK) break;
}
fclose(pd->tmpfp);
fclose(pd->psfp);
snprintf(buf, PATH_MAX, pd->filename, pd->pageno);
pd->psfp = R_fopen(R_ExpandFileName(buf), "w");
pd->tmpfp = R_fopen(pd->tmpname, "w");
XF_FileHeader(pd->psfp, pd->papername, pd->landscape, pd->onefile);
XF_resetColors(pd);
}
XF_CheckAlpha(gc->fill, pd);
if(R_OPAQUE(gc->fill)) {
FILE *fp = pd->tmpfp;
int cbg = XF_SetColor(gc->fill, pd);
int ix0, iy0, ix1, iy1;
double x0 = 0.0, y0 = 0.0, x1 = 72.0 * pd->pagewidth,
y1 = 72.0 * pd->pageheight;
XFconvert(&x0, &y0, pd); XFconvert(&x1, &y1, pd);
ix0 = (int)x0; iy0 = (int)y0; ix1 = (int)x1; iy1 = (int)y1;
fprintf(fp, "2 2 "); /* Polyline */
fprintf(fp, "%d %d ", 0, 0); /* style, thickness */
fprintf(fp, "%d %d ", cbg, cbg); /* pen colour fill colour */
fprintf(fp, "200 0 20 4.0 0 0 -1 0 0 ");
fprintf(fp, "%d\n", 5); /* number of points */
fprintf(fp, "%d %d ", ix0, iy0);
fprintf(fp, "%d %d ", ix0, iy1);
fprintf(fp, "%d %d ", ix1, iy1);
fprintf(fp, "%d %d ", ix1, iy0);
fprintf(fp, "%d %d\n", ix0, iy0);
}
pd->warn_trans = FALSE;
}
#ifdef HAVE_UNISTD_H
#include <unistd.h>
#endif
static void XFig_Close(pDevDesc dd)
{
char buf[CHUNK];
size_t nread, res;
XFigDesc *pd = (XFigDesc *) dd->deviceSpecific;
XF_FileTrailer(pd->tmpfp);
fclose(pd->tmpfp);
pd->tmpfp = R_fopen(pd->tmpname, "r");
while(1) {
nread = fread(buf, 1, CHUNK, pd->tmpfp);
if(nread > 0) {
res = fwrite(buf, 1, nread, pd->psfp);
if(res != nread) error(_("write failed"));
}
if(nread < CHUNK) break;
}
fclose(pd->tmpfp);
unlink(pd->tmpname);
fclose(pd->psfp);
free(pd);
}
static void XFig_Rect(double x0, double y0, double x1, double y1,
const pGEcontext gc,
pDevDesc dd)
{
XFigDesc *pd = (XFigDesc *) dd->deviceSpecific;
FILE *fp = pd->tmpfp;
int ix0, iy0, ix1, iy1;
int cbg = XF_SetColor(gc->fill, pd), cfg = XF_SetColor(gc->col, pd), cpen,
dofill, lty = XF_SetLty(gc->lty), lwd = (int)(gc->lwd*0.833 + 0.5);
if(lty < 0) return;
XF_CheckAlpha(gc->col, pd);
XF_CheckAlpha(gc->fill, pd);
cpen = (R_OPAQUE(gc->col))? cfg: -1;
dofill = (R_OPAQUE(gc->fill))? 20: -1;
XFconvert(&x0, &y0, pd);
XFconvert(&x1, &y1, pd);
ix0 = (int)x0; iy0 = (int)y0; ix1 = (int)x1; iy1 = (int)y1;
fprintf(fp, "2 2 "); /* Polyline */
fprintf(fp, "%d %d ", lty, lwd>0?lwd:1); /* style, thickness */
fprintf(fp, "%d %d ", cpen, cbg); /* pen colour fill colour */
fprintf(fp, "100 0 %d ", dofill); /* depth, pen style, area fill */
fprintf(fp, "%.2f 0 0 -1 0 0 ", 4.0*lwd); /* style value, join .... */
fprintf(fp, "%d\n", 5); /* number of points */
fprintf(fp, " %d %d ", ix0, iy0);
fprintf(fp, " %d %d ", ix0, iy1);
fprintf(fp, " %d %d ", ix1, iy1);
fprintf(fp, " %d %d ", ix1, iy0);
fprintf(fp, " %d %d\n", ix0, iy0);
}
static void XFig_Circle(double x, double y, double r,
const pGEcontext gc,
pDevDesc dd)
{
XFigDesc *pd = (XFigDesc *) dd->deviceSpecific;
FILE *fp = pd->tmpfp;
int ix, iy, ir;
int cbg = XF_SetColor(gc->fill, pd), cfg = XF_SetColor(gc->col, pd), cpen,
dofill, lty = XF_SetLty(gc->lty), lwd = (int)(gc->lwd*0.833 + 0.5);
if(lty < 0) return;
XF_CheckAlpha(gc->col, pd);
XF_CheckAlpha(gc->fill, pd);
cpen = (R_OPAQUE(gc->col))? cfg: -1;
dofill = (R_OPAQUE(gc->fill))? 20: -1;
XFconvert(&x, &y, pd);
ix = (int)x; iy = (int)y; ir = (int)(16.667*r);
fprintf(fp, "1 3 "); /* Circle + radius */
fprintf(fp, "%d %d ", lty, lwd>0?lwd:1); /* style, thickness */
fprintf(fp, "%d %d ", cpen, cbg); /* pen colour fill colour */
fprintf(fp, "100 0 %d ", dofill); /* depth, pen style, area fill */
fprintf(fp, "%.2f 1 0 ", 4.0*lwd); /* style value, direction, x, angle */
fprintf(fp, " %d %d %d %d %d %d %d %d \n",
ix, iy, ir, ir, ix, iy, ix+ir, iy);
}
static void XFig_Line(double x1, double y1, double x2, double y2,
const pGEcontext gc,
pDevDesc dd)
{
XFigDesc *pd = (XFigDesc *) dd->deviceSpecific;
FILE *fp = pd->tmpfp;
int lty = XF_SetLty(gc->lty), lwd = (int)(gc->lwd*0.833 + 0.5);
if(lty < 0) return;
XFconvert(&x1, &y1, pd);
XFconvert(&x2, &y2, pd);
XF_CheckAlpha(gc->col, pd);
if(R_OPAQUE(gc->col)) {
fprintf(fp, "2 1 "); /* Polyline */
fprintf(fp, "%d %d ", lty, lwd>0?lwd:1); /* style, thickness */
fprintf(fp, "%d %d ", XF_SetColor(gc->col, pd), 7);
/* pen colour fill colour */
fprintf(fp, "100 0 -1 "); /* depth, pen style, area fill */
fprintf(fp, "%.2f 0 0 -1 0 0 ", 4.0*lwd); /* style value, join .... */
fprintf(fp, "%d\n", 2); /* number of points */
fprintf(fp, "%d %d %d %d\n", (int)x1, (int)y1, (int)x2, (int)y2);
}
}
static void XFig_Polygon(int n, double *x, double *y,
const pGEcontext gc,
pDevDesc dd)
{
XFigDesc *pd = (XFigDesc *) dd->deviceSpecific;
FILE *fp = pd->tmpfp;
double xx, yy;
int i;
int cbg = XF_SetColor(gc->fill, pd), cfg = XF_SetColor(gc->col, pd), cpen,
dofill, lty = XF_SetLty(gc->lty), lwd = (int)(gc->lwd*0.833 + 0.5);
if(lty < 0) return;
XF_CheckAlpha(gc->col, pd);
XF_CheckAlpha(gc->fill, pd);
cpen = (R_OPAQUE(gc->col))? cfg: -1;
dofill = (R_OPAQUE(gc->fill))? 20: -1;
fprintf(fp, "2 3 "); /* Polyline */
fprintf(fp, "%d %d ", lty, lwd>0?lwd:1); /* style, thickness */
fprintf(fp, "%d %d ", cpen, cbg); /* pen colour fill colour */
fprintf(fp, "100 0 %d ", dofill); /* depth, pen style, area fill */
fprintf(fp, "%.2f 0 0 -1 0 0 ", 4.0*lwd); /* style value, join .... */
fprintf(fp, "%d\n", n+1); /* number of points */
/* close the path */
for(i = 0 ; i <= n ; i++) {
xx = x[i%n];
yy = y[i%n];
XFconvert(&xx, &yy, pd);
fprintf(fp, " %d %d\n", (int)xx, (int)yy);
}
}
static void XFig_Polyline(int n, double *x, double *y,
const pGEcontext gc,
pDevDesc dd)
{
XFigDesc *pd = (XFigDesc*) dd->deviceSpecific;
FILE *fp = pd->tmpfp;
double xx, yy;
int i, lty = XF_SetLty(gc->lty), lwd = (int)(gc->lwd*0.833 + 0.5);
XF_CheckAlpha(gc->col, pd);
if(R_OPAQUE(gc->col) && lty >= 0) {
fprintf(fp, "2 1 "); /* Polyline */
fprintf(fp, "%d %d ", lty, lwd>0?lwd:1); /* style, thickness */
fprintf(fp, "%d %d ", XF_SetColor(gc->col, pd), 7); /* pen colour fill colour */
fprintf(fp, "100 0 -1 "); /* depth, pen style, area fill */
fprintf(fp, "%.2f 0 0 -1 0 0 ", 4.0*lwd); /* style value, join .... */
fprintf(fp, "%d\n", n); /* number of points */
for(i = 0 ; i < n ; i++) {
xx = x[i];
yy = y[i];
XFconvert(&xx, &yy, pd);
fprintf(fp, " %d %d\n", (int)xx, (int)yy);
}
}
}
static const int styles[4] = {0,2,1,3};
static void XFig_Text(double x, double y, const char *str,
double rot, double hadj,
const pGEcontext gc,
pDevDesc dd)
{
XFigDesc *pd = (XFigDesc *) dd->deviceSpecific;
FILE *fp = pd->tmpfp;
int fontnum, style = gc->fontface;
double size = floor(gc->cex * gc->ps + 0.5);
const char *str1 = str;
char *buf;
if(style < 1 || style > 5) {
warning(_("attempt to use invalid font %d replaced by font 1"), style);
style = 1;
}
if(style == 5) fontnum = 32;
else fontnum = pd->fontnum + styles[style-1];
/*
* xfig -international hoge.fig
* mapping multibyte(EUC only) string Times{Romani,Bold} font Only
*/
if ( mbcslocale && style != 5 )
if (!strncmp("EUC", locale2charset(NULL), 3))
fontnum = ((style & 1) ^ 1 ) << 1 ;
XFconvert(&x, &y, pd);
XF_CheckAlpha(gc->col, pd);
if(R_OPAQUE(gc->col)) {
fprintf(fp, "4 %d ", (int)floor(2*hadj)); /* Text, how justified */
fprintf(fp, "%d 100 0 ", XF_SetColor(gc->col, pd));
/* color, depth, pen_style */
fprintf(fp, "%d %d %.4f %d ", pd->defaultfont?-1:fontnum, (int)size, rot * DEG2RAD,pd->textspecial?6:4);
/* font pointsize angle flags (Postscript font) */
fprintf(fp, "%d %d ", (int)(size*12),
(int)(16.667*XFig_StrWidth(str, gc, dd) +0.5));
fprintf(fp, "%d %d ", (int)x, (int)y);
if(strcmp(pd->encoding, "none") != 0) {
/* reencode the text */
void *cd;
const char *i_buf; char *o_buf;
size_t i_len, o_len, status;
size_t buflen = MB_LEN_MAX*strlen(str) + 1;
cd = (void*)Riconv_open(pd->encoding, "");
if(cd == (void*)-1) {
warning(_("unable to use encoding '%s'"), pd->encoding);
} else {
R_CheckStack2(buflen);
buf = (char *) alloca(buflen);
i_buf = (char *) str;
o_buf = buf;
i_len = strlen(str) + 1; /* including terminator */
o_len = buflen;
status = Riconv(cd, &i_buf, &i_len, &o_buf, &o_len);
Riconv_close(cd);
if(status == (size_t)-1)
warning(_("failed in text conversion to encoding '%s'"),
pd->encoding);
else str1 = buf;
}
}
XF_WriteString(fp, str1);
fprintf(fp, "\\001\n");
}
}
static double XFig_StrWidth(const char *str,
const pGEcontext gc,
pDevDesc dd)
{
XFigDesc *pd = (XFigDesc *) dd->deviceSpecific;
int face = gc->fontface;
if(face < 1 || face > 5) face = 1;
return floor(gc->cex * gc->ps + 0.5) *
PostScriptStringWidth((const unsigned char *)str, CE_NATIVE,
&(pd->fonts->family->fonts[face-1]->metrics),
FALSE, face, "latin1");
}
static void XFig_MetricInfo(int c,
const pGEcontext gc,
double* ascent, double* descent,
double* width, pDevDesc dd)
{
XFigDesc *pd = (XFigDesc *) dd->deviceSpecific;
int face = gc->fontface;
if(face < 1 || face > 5) face = 1;
PostScriptMetricInfo(c, ascent, descent, width,
&(pd->fonts->family->fonts[face-1]->metrics),
face == 5, "");
*ascent = floor(gc->cex * gc->ps + 0.5) * *ascent;
*descent = floor(gc->cex * gc->ps + 0.5) * *descent;
*width = floor(gc->cex * gc->ps + 0.5) * *width;
}
/***********************************************************************
PDF driver also shares font handling
************************************************************************/
typedef struct {
rcolorPtr raster;
int w;
int h;
Rboolean interpolate;
int nobj; /* The object number when written out */
int nmaskobj; /* The mask object number */
} rasterImage;
typedef struct {
char filename[PATH_MAX];
int open_type;
char cmd[PATH_MAX];
char papername[64]; /* paper name */
int paperwidth; /* paper width in big points (1/72 in) */
int paperheight; /* paper height in big points */
int pageno; /* page number */
int fileno; /* file number */
int maxpointsize;
double width; /* plot width in inches */
double height; /* plot height in inches */
double pagewidth; /* page width in inches */
double pageheight; /* page height in inches */
Rboolean pagecentre; /* centre image on page? */
Rboolean onefile; /* one file or one file per page? */
FILE *pdffp; /* output file */
FILE *mainfp;
FILE *pipefp;
/* This group of variables track the current device status.
* They should only be set by routines that emit PDF. */
struct {
double lwd; /* line width */
int lty; /* line type */
R_GE_lineend lend;
R_GE_linejoin ljoin;
double lmitre;
int fontsize; /* font size in points */
rcolor col; /* color */
rcolor fill; /* fill color */
rcolor bg; /* color */
int srgb_fg, srgb_bg; /* Are stroke and fill colorspaces set? */
} current;
/*
* This is a record of the alpha transparency levels used during
* drawing to the device.
* Only allow 256 different alpha levels
* (because R uses 8-bit alpha channel).
* "alphas" is a record of alphas used so far (unused set to -1)
* There are separate alpha levels for stroking and filling
* (i.e., col and fill)
*/
short colAlpha[256];
short fillAlpha[256];
Rboolean usedAlpha;
/*
* What version of PDF are we trying to work with?
* This is used (so far) for implementing transparency and CID fonts
* Alphas are only used if version is at least 1.4
*/
int versionMajor;
int versionMinor;
int nobjs; /* number of objects */
int *pos; /* object positions */
int max_nobjs; /* current allocation size */
int *pageobj; /* page object numbers */
int pagemax;
int startstream; /* position of start of current stream */
Rboolean inText;
char title[1024];
char colormodel[30];
Rboolean dingbats, useKern;
Rboolean fillOddEven; /* polygon fill mode */
Rboolean useCompression;
char tmpname[PATH_MAX]; /* used before compression */
/*
* Fonts and encodings used on the device
*/
type1fontlist fonts;
cidfontlist cidfonts;
encodinglist encodings;
/*
* These next two just record the default device font
*/
type1fontfamily defaultFont;
cidfontfamily defaultCIDFont;
/* Record if fonts are used */
Rboolean fontUsed[100];
/* Raster images used on the device */
rasterImage *rasters;
int numRasters; /* number in use */
int writtenRasters; /* number written out */
int maxRasters; /* size of array allocated */
/* Soft masks for raster images */
int *masks;
int numMasks;
/* Is the device "offline" (does not write out to a file) */
Rboolean offline;
}
PDFDesc;
/* Macro for driver actions to check for "offline" device and bail out */
#define PDF_checkOffline() if (pd->offline) return
/* Device Driver Actions */
static Rboolean PDF_Open(pDevDesc, PDFDesc*);
static void PDF_Circle(double x, double y, double r,
const pGEcontext gc,
pDevDesc dd);
static void PDF_Clip(double x0, double x1, double y0, double y1,
pDevDesc dd);
static void PDF_Close(pDevDesc dd);
static void PDF_Line(double x1, double y1, double x2, double y2,
const pGEcontext gc,
pDevDesc dd);
void PDF_MetricInfo(int c,
const pGEcontext gc,
double* ascent, double* descent,
double* width, pDevDesc dd);
static void PDF_NewPage(const pGEcontext gc, pDevDesc dd);
static void PDF_Polygon(int n, double *x, double *y,
const pGEcontext gc,
pDevDesc dd);
static void PDF_Polyline(int n, double *x, double *y,
const pGEcontext gc,
pDevDesc dd);
static void PDF_Rect(double x0, double y0, double x1, double y1,
const pGEcontext gc,
pDevDesc dd);
static void PDF_Path(double *x, double *y,
int npoly, int *nper,
Rboolean winding,
const pGEcontext gc,
pDevDesc dd);
static void PDF_Raster(unsigned int *raster, int w, int h,
double x, double y, double width, double height,
double rot, Rboolean interpolate,
const pGEcontext gc, pDevDesc dd);
static void PDF_Size(double *left, double *right,
double *bottom, double *top,
pDevDesc dd);
double PDF_StrWidth(const char *str,
const pGEcontext gc,
pDevDesc dd);
static void PDF_Text(double x, double y, const char *str,
double rot, double hadj,
const pGEcontext gc,
pDevDesc dd);
static double PDF_StrWidthUTF8(const char *str,
const pGEcontext gc,
pDevDesc dd);
static void PDF_TextUTF8(double x, double y, const char *str,
double rot, double hadj,
const pGEcontext gc,
pDevDesc dd);
/***********************************************************************
* Some stuff for recording raster images
*/
/* Detect an image by non-NULL rasters[] */
static rasterImage* initRasterArray(int numRasters)
{
int i;
/* why not use calloc? */
rasterImage* rasters = malloc(numRasters*sizeof(rasterImage));
if (rasters) {
for (i = 0; i < numRasters; i++) {
rasters[i].raster = NULL;
}
} /* else error thrown in PDFDeviceDriver */
return rasters;
}
/* Add a raster (by making a copy)
* Return value indicates whether the image is semi-transparent
*/
static int addRaster(rcolorPtr raster, int w, int h,
Rboolean interpolate, PDFDesc *pd)
{
int i, alpha = 0;
rcolorPtr newRaster;
if (pd->numRasters == pd->maxRasters) {
int new = 2*pd->maxRasters;
void *tmp;
/* Do it this way so previous pointer is retained if it fails */
tmp = realloc(pd->masks, new*sizeof(int));
if(!tmp) error(_("failed to increase 'maxRaster'"));
pd->masks = tmp;
tmp = realloc(pd->rasters, new*sizeof(rasterImage));
if(!tmp) error(_("failed to increase 'maxRaster'"));
pd->rasters = tmp;
for (i = pd->maxRasters; i < new; i++) {
pd->rasters[i].raster = NULL;
pd->masks[i] = -1;
}
pd->maxRasters = new;
}
newRaster = malloc(w*h*sizeof(rcolor));
if (!newRaster)
error(_("unable to allocate raster image"));
for (i = 0; i < w*h; i++) {
newRaster[i] = raster[i];
if (!alpha && R_ALPHA(raster[i]) < 255) alpha = 1;
}
pd->rasters[pd->numRasters].raster = newRaster;
pd->rasters[pd->numRasters].w = w;
pd->rasters[pd->numRasters].h = h;
pd->rasters[pd->numRasters].interpolate = interpolate;
pd->rasters[pd->numRasters].nobj = -1; /* not yet written out */
pd->rasters[pd->numRasters].nmaskobj = -1; /* not yet written out */
/* If any of the pixels are not opaque, we need to add
* a mask as well */
if (alpha)
pd->masks[pd->numRasters] = pd->numMasks++;
pd->numRasters++;
return alpha;
}
static void killRasterArray(rasterImage *rasters, int numRasters) {
int i;
for (i = 0; i < numRasters; i++)
if (rasters[i].raster != NULL) free(rasters[i].raster);
}
/* Detect a mask by masks[] >= 0 */
static int* initMaskArray(int numRasters) {
int i;
int* masks = malloc(numRasters*sizeof(int));
if (masks) {
for (i = 0; i < numRasters; i++) masks[i] = -1;
} /* else error thrown in PDFDeviceDriver */
return masks;
}
static void writeRasterXObject(rasterImage raster, int n,
int mask, int maskObj, PDFDesc *pd)
{
Bytef *buf, *buf2, *p;
uLong inlen;
if (streql(pd->colormodel, "gray")) {
inlen = raster.w * raster.h;
p = buf = Calloc(inlen, Bytef);
for(int i = 0; i < raster.w * raster.h; i++) {
double r = 0.213 * R_RED(raster.raster[i])
+ 0.715 * R_GREEN(raster.raster[i])
+ 0.072 * R_BLUE(raster.raster[i]);
*p++ = (Bytef)(r + 0.49);
}
} else {
inlen = 3 * raster.w * raster.h;
p = buf = Calloc(inlen, Bytef);
for(int i = 0; i < raster.w * raster.h; i++) {
*p++ = R_RED(raster.raster[i]);
*p++ = R_GREEN(raster.raster[i]);
*p++ = R_BLUE(raster.raster[i]);
}
}
uLong outlen = inlen;
if (pd->useCompression) {
outlen = (int)(1.001*inlen + 20);
buf2 = Calloc(outlen, Bytef);
int res = compress(buf2, &outlen, buf, inlen);
if(res != Z_OK) error("internal error %d in writeRasterXObject", res);
Free(buf);
buf = buf2;
}
fprintf(pd->pdffp, "%d 0 obj <<\n", n);
fprintf(pd->pdffp, " /Type /XObject\n");
fprintf(pd->pdffp, " /Subtype /Image\n");
fprintf(pd->pdffp, " /Width %d\n", raster.w);
fprintf(pd->pdffp, " /Height %d\n", raster.h);
if (streql(pd->colormodel, "gray"))
fprintf(pd->pdffp, " /ColorSpace /DeviceGray\n");
else if (streql(pd->colormodel, "srgb"))
fprintf(pd->pdffp, " /ColorSpace 5 0 R\n"); /* sRGB */
else
fprintf(pd->pdffp, " /ColorSpace /DeviceRGB\n");
fprintf(pd->pdffp, " /BitsPerComponent 8\n");
fprintf(pd->pdffp, " /Length %u\n", (unsigned)
(pd->useCompression ? outlen : 2 * outlen + 1));
if (raster.interpolate)
fprintf(pd->pdffp, " /Interpolate true\n");
if (pd->useCompression)
fprintf(pd->pdffp, " /Filter /FlateDecode\n");
else
fprintf(pd->pdffp, " /Filter /ASCIIHexDecode\n");
if (mask >= 0)
fprintf(pd->pdffp, " /SMask %d 0 R\n", maskObj);
fprintf(pd->pdffp, " >>\nstream\n");
if (pd->useCompression) {
size_t res = fwrite(buf, 1, outlen, pd->pdffp);
if(res != outlen) error(_("write failed"));
} else {
for(int i = 0; i < outlen; i++)
fprintf(pd->pdffp, "%02x", buf[i]);
fprintf(pd->pdffp, ">\n");
}
Free(buf);
fprintf(pd->pdffp, "endstream\nendobj\n");
}
static void writeMaskXObject(rasterImage raster, int n, PDFDesc *pd)
{
Bytef *buf, *buf2, *p;
uLong inlen = raster.w * raster.h, outlen = inlen;
p = buf = Calloc(outlen, Bytef);
for(int i = 0; i < raster.w * raster.h; i++)
*p++ = R_ALPHA(raster.raster[i]);
if (pd->useCompression) {
outlen = (uLong)(1.001*inlen + 20);
buf2 = Calloc(outlen, Bytef);
int res = compress(buf2, &outlen, buf, inlen);
if(res != Z_OK) error("internal error %d in writeRasterXObject", res);
Free(buf);
buf = buf2;
}
fprintf(pd->pdffp, "%d 0 obj <<\n", n);
fprintf(pd->pdffp, " /Type /XObject\n");
fprintf(pd->pdffp, " /Subtype /Image\n");
fprintf(pd->pdffp, " /Width %d\n", raster.w);
fprintf(pd->pdffp, " /Height %d\n", raster.h);
/* This is not a mask but a 'soft mask' */
fprintf(pd->pdffp, " /ColorSpace /DeviceGray\n");
fprintf(pd->pdffp, " /BitsPerComponent 8\n");
fprintf(pd->pdffp, " /Length %u\n", (unsigned)
(pd->useCompression ? outlen : 2 * outlen + 1));
if (raster.interpolate)
fprintf(pd->pdffp, " /Interpolate true\n");
if (pd->useCompression)
fprintf(pd->pdffp, " /Filter /FlateDecode\n");
else
fprintf(pd->pdffp, " /Filter /ASCIIHexDecode\n");
fprintf(pd->pdffp, " >>\nstream\n");
if (pd->useCompression) {
size_t res = fwrite(buf, 1, outlen, pd->pdffp);
if(res != outlen) error(_("write failed"));
} else {
for(int i = 0; i < outlen; i++)
fprintf(pd->pdffp, "%02x", buf[i]);
fprintf(pd->pdffp, ">\n");
}
Free(buf);
fprintf(pd->pdffp, "endstream\nendobj\n");
}
/***********************************************************************
* Some stuff for fonts
*/
/*
* Add a graphics engine font family to the list of fonts used on a
* PDF device ...
*
* ... AND add the font encoding to the list of encodings used on the
* device (if necessary)
*/
/*
* Differs from addDeviceFont (used in PostScript device)
* because we do not need to immediately write font
* information to file. In PDF, the font information is
* all written at the end as part of the file footer.
*/
static Rboolean addPDFDeviceCIDfont(cidfontfamily family,
PDFDesc *pd,
int *fontIndex)
{
Rboolean result = FALSE;
cidfontlist fontlist = addDeviceCIDFont(family, pd->cidfonts, fontIndex);
if (fontlist) {
pd->cidfonts = fontlist;
result = TRUE;
}
return result;
}
static Rboolean addPDFDevicefont(type1fontfamily family,
PDFDesc *pd,
int *fontIndex)
{
Rboolean result = FALSE;
type1fontlist fontlist = addDeviceFont(family, pd->fonts, fontIndex);
if (fontlist) {
int dontcare;
encodinginfo encoding =
findDeviceEncoding(family->encoding->encpath,
pd->encodings, &dontcare);
if (encoding) {
pd->fonts = fontlist;
result = TRUE;
} else {
/*
* The encoding should have been loaded when the font was loaded
*/
encoding = findEncoding(family->encoding->encpath,
pd->encodings, TRUE);
if (!encoding) {
warning(_("corrupt loaded encodings; font not added"));
} else {
encodinglist enclist = addDeviceEncoding(encoding,
pd->encodings);
if (enclist) {
pd->fonts = fontlist;
pd->encodings = enclist;
result = TRUE;
} else
warning(_("failed to record device encoding; font not added"));
}
}
}
return result;
}
static void PDFcleanup(int stage, PDFDesc *pd) {
switch (stage) {
case 6: /* Allocated masks */
free(pd->masks);
case 5: /* Allocated rasters */
free(pd->rasters);
case 4: /* Allocated fonts */
freeDeviceFontList(pd->fonts);
freeDeviceCIDFontList(pd->cidfonts);
freeDeviceEncList(pd->encodings);
pd->fonts = NULL;
pd->cidfonts = NULL;
pd->encodings = NULL;
case 3: /* Allocated pageobj */
free(pd->pageobj);
case 2: /* Allocated pos */
free(pd->pos);
case 1: /* Allocated PDFDesc */
free(pd);
}
}
Rboolean
PDFDeviceDriver(pDevDesc dd, const char *file, const char *paper,
const char *family, const char **afmpaths,
const char *encoding,
const char *bg, const char *fg, double width, double height,
double ps, int onefile, int pagecentre,
const char *title, SEXP fonts,
int versionMajor, int versionMinor,
const char *colormodel, int dingbats, int useKern,
Rboolean fillOddEven, Rboolean useCompression)
{
/* If we need to bail out with some sort of "error" */
/* then we must free(dd) */
int i, gotFont;
double xoff = 0.0, yoff = 0.0, pointsize;
rcolor setbg, setfg;
encodinginfo enc;
encodinglist enclist;
type1fontfamily font;
cidfontfamily cidfont = NULL;
PDFDesc *pd;
/* Check and extract the device parameters */
/* 'file' could be NULL */
if(file && strlen(file) > PATH_MAX - 1) {
/* not yet created PDFcleanup(0, pd); */
free(dd);
error(_("filename too long in %s()"), "pdf");
}
/* allocate new PDF device description */
if (!(pd = (PDFDesc *) malloc(sizeof(PDFDesc)))) {
free(dd);
error(_("memory allocation problem in %s()"), "pdf");
}
/* from here on, if need to bail out with "error", must also
free(pd) */
pd->versionMajor = versionMajor;
pd->versionMinor = versionMinor;
/* This is checked at the start of every page. We typically have
three objects per page plus one or two for each raster image,
so this is an ample initial allocation.
*/
pd->max_nobjs = 2000;
pd->pos = (int *) calloc(pd->max_nobjs, sizeof(int));
if(!pd->pos) {
PDFcleanup(1, pd);
free(dd);
error("cannot allocate pd->pos");
}
/* This one is dynamic: initial allocation */
pd->pagemax = 100;
pd->pageobj = (int *) calloc(pd->pagemax, sizeof(int));
if(!pd->pageobj) {
PDFcleanup(2, pd);
free(dd);
error("cannot allocate pd->pageobj");
}
/* initialize PDF device description */
/* 'file' could be NULL */
if (file)
strcpy(pd->filename, file);
else
strcpy(pd->filename, "nullPDF");
strcpy(pd->papername, paper);
strncpy(pd->title, title, 1024);
memset(pd->fontUsed, 0, 100*sizeof(Rboolean));
if (streql(colormodel, "grey")) strcpy(pd->colormodel, "gray");
else strncpy(pd->colormodel, colormodel, 30);
pd->dingbats = (dingbats != 0);
pd->useKern = (useKern != 0);
pd->fillOddEven = fillOddEven;
pd->useCompression = useCompression;
if(useCompression && pd->versionMajor == 1 && pd->versionMinor < 2) {
pd->versionMinor = 2;
warning(_("increasing the PDF version to 1.2"));
}
pd->width = width;
pd->height = height;
if (file)
pd->offline = FALSE;
else
pd->offline = TRUE;
if(strlen(encoding) > PATH_MAX - 1) {
PDFcleanup(3, pd);
free(dd);
error(_("encoding path is too long in %s()"), "pdf");
}
/*
* Load the default encoding AS THE FIRST ENCODING FOR THIS DEVICE.
*
* encpath MUST NOT BE "default"
*/
pd->encodings = NULL;
if (!(enc = findEncoding(encoding, pd->encodings, TRUE)))
enc = addEncoding(encoding, 1);
if (enc && (enclist = addDeviceEncoding(enc,
pd->encodings))) {
pd->encodings = enclist;
} else {
PDFcleanup(3, pd);
free(dd);
error(_("failed to load default encoding"));
}
/*****************************
* Load fonts
*****************************/
pd->fonts = NULL;
pd->cidfonts = NULL;
gotFont = 0;
/*
* If user specified afms then assume the font hasn't been loaded
* Could lead to redundant extra loading of a font, but not often(?)
*/
if (!strcmp(family, "User")) {
font = addDefaultFontFromAFMs(encoding, afmpaths, 0, pd->encodings);
} else {
/*
* Otherwise, family is a device-independent font family.
* One of the elements of pdfFonts().
* NOTE this is the first font loaded on this device!
*/
/*
* Check first whether this font has been loaded
* in this R session
*/
font = findLoadedFont(family, encoding, TRUE);
cidfont = findLoadedCIDFont(family, TRUE);
if (!(font || cidfont)) {
/*
* If the font has not been loaded yet, load it.
*
* The family SHOULD be in the font database to get this far.
* (checked at R level in postscript() in postscript.R)
*/
if (isType1Font(family, PDFFonts, NULL)) {
font = addFont(family, TRUE, pd->encodings);
} else if (isCIDFont(family, PDFFonts, NULL)) {
cidfont = addCIDFont(family, TRUE);
} else {
/*
* Should NOT get here.
*/
error(_("invalid font type"));
}
}
}
if (font || cidfont) {
/*
* At this point the font is loaded, so add it to the
* device's list of fonts.
*/
if (!strcmp(family, "User") ||
isType1Font(family, PDFFonts, NULL)) {
addPDFDevicefont(font, pd, &gotFont);
pd->defaultFont = pd->fonts->family;
pd->defaultCIDFont = NULL;
} else /* (isCIDFont(family, PDFFonts)) */ {
addPDFDeviceCIDfont(cidfont, pd, &gotFont);
pd->defaultFont = NULL;
pd->defaultCIDFont = pd->cidfonts->cidfamily;
}
}
if (!gotFont) {
PDFcleanup(3, pd);
free(dd);
error(_("failed to initialise default PDF font"));
}
/*
* Load the font names sent in via the fonts arg
* NOTE that these are the font names specified at the
* R-level, NOT the translated font names.
*/
if (!isNull(fonts)) {
int i, dontcare, gotFonts = 0, nfonts = LENGTH(fonts);
for (i = 0; i < nfonts; i++) {
int index, cidindex;
const char *name = CHAR(STRING_ELT(fonts, i));
if (findDeviceFont(name, pd->fonts, &index) ||
findDeviceCIDFont(name, pd->cidfonts, &cidindex))
gotFonts++;
else {
/*
* Check whether the font is loaded and, if not,
* load it.
*/
font = findLoadedFont(name, encoding, TRUE);
cidfont = findLoadedCIDFont(name, TRUE);
if (!(font || cidfont)) {
if (isType1Font(name, PDFFonts, NULL)) {
font = addFont(name, TRUE, pd->encodings);
} else if (isCIDFont(name, PDFFonts, NULL)) {
cidfont = addCIDFont(name, TRUE);
} else {
/*
* Should NOT get here.
*/
error(_("invalid font type"));
}
}
/*
* Once the font is loaded, add it to the device's
* list of fonts.
*/
if (font || cidfont) {
if (isType1Font(name, PDFFonts, NULL)) {
if (addPDFDevicefont(font, pd, &dontcare)) {
gotFonts++;
}
} else /* (isCIDFont(family, PDFFonts)) */ {
if (addPDFDeviceCIDfont(cidfont, pd, &dontcare)) {
gotFonts++;
}
}
}
}
}
if (gotFonts < nfonts) {
PDFcleanup(4, pd);
free(dd);
error(_("failed to initialise additional PDF fonts"));
}
}
/*****************************
* END Load fonts
*****************************/
pd->numRasters = pd->writtenRasters = 0;
pd->maxRasters = 64; /* dynamic */
pd->rasters = initRasterArray(pd->maxRasters);
if (!pd->rasters) {
PDFcleanup(4, pd);
free(dd);
error(_("failed to allocate rasters"));
}
pd->numMasks = 0;
pd->masks = initMaskArray(pd->maxRasters);
if (!pd->masks) {
PDFcleanup(5, pd);
free(dd);
error(_("failed to allocate masks"));
}
setbg = R_GE_str2col(bg);
setfg = R_GE_str2col(fg);
/*
* Initialise all alphas to -1
*/
pd->usedAlpha = FALSE;
for (i = 0; i < 256; i++) {
pd->colAlpha[i] = -1;
pd->fillAlpha[i] = -1;
}
/* Deal with paper and plot size and orientation */
if(!strcmp(pd->papername, "Default") ||
!strcmp(pd->papername, "default")) {
SEXP s = STRING_ELT(GetOption1(install("papersize")), 0);
if(s != NA_STRING && strlen(CHAR(s)) > 0)
strcpy(pd->papername, CHAR(s));
else strcpy(pd->papername, "a4");
}
if(!strcmp(pd->papername, "A4") ||
!strcmp(pd->papername, "a4")) {
pd->pagewidth = 21.0 / 2.54;
pd->pageheight = 29.7 /2.54;
}
else if(!strcmp(pd->papername, "A4r") ||
!strcmp(pd->papername, "a4r")) {
pd->pageheight = 21.0 / 2.54;
pd->pagewidth = 29.7 /2.54;
}
else if(!strcmp(pd->papername, "Letter") ||
!strcmp(pd->papername, "letter") ||
!strcmp(pd->papername, "US") ||
!strcmp(pd->papername, "us")) {
pd->pagewidth = 8.5;
pd->pageheight = 11.0;
}
else if(!strcmp(pd->papername, "USr") ||
!strcmp(pd->papername, "usr")) {
pd->pageheight = 8.5;
pd->pagewidth = 11.0;
}
else if(!strcmp(pd->papername, "Legal") ||
!strcmp(pd->papername, "legal")) {
pd->pagewidth = 8.5;
pd->pageheight = 14.0;
}
else if(!strcmp(pd->papername, "Executive") ||
!strcmp(pd->papername, "executive")) {
pd->pagewidth = 7.25;
pd->pageheight = 10.5;
}
else if(!strcmp(pd->papername, "special")) {
pd->pagewidth = width;
pd->pageheight = height;
}
else {
PDFcleanup(6, pd);
free(dd);
error(_("invalid paper type '%s' (pdf)"), pd->papername);
}
pd->pagecentre = pagecentre;
pd->paperwidth = (int)(72 * pd->pagewidth);
pd->paperheight = (int)(72 * pd->pageheight);
if(strcmp(pd->papername, "special"))
{
if(pd->width < 0.1 || pd->width > pd->pagewidth-0.5)
pd->width = pd->pagewidth-0.5;
if(pd->height < 0.1 || pd->height > pd->pageheight-0.5)
pd->height = pd->pageheight-0.5;
}
if(pagecentre)
{
xoff = (pd->pagewidth - pd->width)/2.0;
yoff = (pd->pageheight - pd->height)/2.0;
} else {
xoff = yoff = 0.0;
}
pointsize = floor(ps);
if(R_TRANSPARENT(setbg) && R_TRANSPARENT(setfg)) {
PDFcleanup(6, pd);
free(dd);
error(_("invalid foreground/background color (pdf)"));
}
pd->onefile = onefile;
pd->maxpointsize = (int)(72.0 * ((pd->pageheight > pd->pagewidth) ?
pd->pageheight : pd->pagewidth));
pd->pageno = pd->fileno = 0;
/* Base Pointsize */
/* Nominal Character Sizes in Pixels */
/* Only right for 12 point font. */
/* Max pointsize suggested by Peter Dalgaard */
if(pointsize < 6.0) pointsize = 6.0;
if(pointsize > pd->maxpointsize) pointsize = pd->maxpointsize;
dd->startps = pointsize;
dd->startlty = 0;
dd->startfont = 1;
dd->startfill = setbg;
dd->startcol = setfg;
dd->startgamma = 1;
/* Set graphics parameters that must be set by device driver. */
/* Page dimensions in points. */
dd->left = 72 * xoff; /* left */
dd->right = 72 * (xoff + pd->width); /* right */
dd->bottom = 72 * yoff; /* bottom */
dd->top = 72 * (yoff + pd->height); /* top */
dd->cra[0] = 0.9 * pointsize;
dd->cra[1] = 1.2 * pointsize;
/* Character Addressing Offsets */
/* These offsets should center a single */
/* plotting character over the plotting point. */
/* Pure guesswork and eyeballing ... */
dd->xCharOffset = 0.4900;
dd->yCharOffset = 0.3333;
dd->yLineBias = 0.2;
/* Inches per Raster Unit */
/* 1200 dpi */
dd->ipr[0] = 1.0/72.0;
dd->ipr[1] = 1.0/72.0;
dd->canClip = TRUE;
dd->canHAdj = 0;
dd->canChangeGamma = FALSE;
/* Start the driver */
PDF_Open(dd, pd); /* errors on failure */
dd->close = PDF_Close;
dd->size = PDF_Size;
dd->newPage = PDF_NewPage;
dd->clip = PDF_Clip;
dd->text = PDF_Text;
dd->strWidth = PDF_StrWidth;
dd->metricInfo = PDF_MetricInfo;
dd->rect = PDF_Rect;
dd->path = PDF_Path;
dd->raster = PDF_Raster;
dd->circle = PDF_Circle;
dd->line = PDF_Line;
dd->polygon = PDF_Polygon;
dd->polyline = PDF_Polyline;
/* dd->locator = PDF_Locator;
dd->mode = PDF_Mode; */
dd->hasTextUTF8 = TRUE;
dd->textUTF8 = PDF_TextUTF8;
dd->strWidthUTF8 = PDF_StrWidthUTF8;
dd->useRotatedTextInContour = TRUE;
dd->haveTransparency = 2;
dd->haveTransparentBg = 3;
dd->haveRaster = 2;
dd->deviceSpecific = (void *) pd;
dd->displayListOn = FALSE;
return TRUE;
}
/* Called at the start of a page and when clipping is reset */
static void PDF_Invalidate(pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
pd->current.fontsize = -1;
pd->current.lwd = -1;
pd->current.lty = -1;
pd->current.lend = 0;
pd->current.ljoin = 0;
pd->current.lmitre = 0;
/* page starts with black as the default fill and stroke colours */
pd->current.col = INVALID_COL;
pd->current.fill = INVALID_COL;
pd->current.bg = INVALID_COL;
pd->current.srgb_fg = pd->current.srgb_bg = 0;
}
/*
* Search through the alphas used so far and return
* existing index if there is one.
* Otherwise, add alpha to the list and return new index
*/
static int alphaIndex(int alpha, short *alphas) {
int i, found = 0;
for (i = 0; i < 256 && !found; i++) {
if (alphas[i] < 0) {
alphas[i] = (short) alpha;
found = 1;
}
else if (alpha == alphas[i])
found = 1;
}
if (!found)
error(_("invalid 'alpha' value in PDF"));
return i;
}
/*
* colAlpha graphics state parameter dictionaries are named
* /GS1 to /GS256
* fillAlpha graphics state parameter dictionaries are named
* /GS257 to /GS512
*/
static int colAlphaIndex(int alpha, PDFDesc *pd) {
return alphaIndex(alpha, pd->colAlpha);
}
static int fillAlphaIndex(int alpha, PDFDesc *pd) {
return alphaIndex(alpha, pd->fillAlpha) + 256;
}
/*
* Does the version support alpha transparency?
* As from R 2.4.0 bump the version number so it does.
*/
static void alphaVersion(PDFDesc *pd) {
if(pd->versionMajor == 1 && pd->versionMinor < 4) {
pd->versionMinor = 4;
warning(_("increasing the PDF version to 1.4"));
}
pd->usedAlpha = TRUE;
}
/*
* Do we need to bother with semi-transparency?
*/
static int semiTransparent(int col)
{
return !(R_OPAQUE(col) || R_TRANSPARENT(col));
}
static void PDF_SetLineColor(int color, pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
if(color != pd->current.col) {
unsigned int alpha = R_ALPHA(color);
if (0 < alpha && alpha < 255) alphaVersion(pd);
if (pd->usedAlpha) {
/*
* Apply graphics state parameter dictionary
* to set alpha
*/
fprintf(pd->pdffp, "/GS%i gs\n", colAlphaIndex(alpha, pd));
}
if(streql(pd->colormodel, "gray")) {
double r = R_RED(color)/255.0, g = R_GREEN(color)/255.0,
b = R_BLUE(color)/255.0;
/* weights from C-9 of
http://www.faqs.org/faqs/graphics/colorspace-faq/
Those from C-11 might be more appropriate.
*/
fprintf(pd->pdffp, "%.3f G\n", (0.213*r+0.715*g+0.072*b));
} else if(streql(pd->colormodel, "cmyk")) {
double r = R_RED(color)/255.0, g = R_GREEN(color)/255.0,
b = R_BLUE(color)/255.0;
double c = 1.0-r, m = 1.0-g, y = 1.0-b, k = c;
k = fmin2(k, m);
k = fmin2(k, y);
if(k == 1.0) c = m = y = 0.0;
else { c = (c-k)/(1-k); m = (m-k)/(1-k); y = (y-k)/(1-k); }
fprintf(pd->pdffp, "%.3f %.3f %.3f %.3f K\n", c, m, y, k);
} else if(streql(pd->colormodel, "rgb")) {
fprintf(pd->pdffp, "%.3f %.3f %.3f RG\n",
R_RED(color)/255.0,
R_GREEN(color)/255.0,
R_BLUE(color)/255.0);
} else {
if (!streql(pd->colormodel, "srgb"))
warning(_("unknown 'colormodel', using 'srgb'"));
if (!pd->current.srgb_bg) {
fprintf(pd->pdffp, "/sRGB CS\n");
pd->current.srgb_bg = 1;
}
fprintf(pd->pdffp, "%.3f %.3f %.3f SCN\n",
R_RED(color)/255.0,
R_GREEN(color)/255.0,
R_BLUE(color)/255.0);
}
pd->current.col = color;
}
}
static void PDF_SetFill(int color, pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
if(color != pd->current.fill) {
unsigned int alpha = R_ALPHA(color);
if (0 < alpha && alpha < 255) alphaVersion(pd);
if (pd->usedAlpha) {
/*
* Apply graphics state parameter dictionary
* to set alpha
*/
fprintf(pd->pdffp, "/GS%i gs\n", fillAlphaIndex(alpha, pd));
}
if(streql(pd->colormodel, "gray")) {
double r = R_RED(color)/255.0, g = R_GREEN(color)/255.0,
b = R_BLUE(color)/255.0;
fprintf(pd->pdffp, "%.3f g\n", (0.213*r+0.715*g+0.072*b));
} else if(streql(pd->colormodel, "cmyk")) {
double r = R_RED(color)/255.0, g = R_GREEN(color)/255.0,
b = R_BLUE(color)/255.0;
double c = 1.0-r, m = 1.0-g, y = 1.0-b, k = c;
k = fmin2(k, m);
k = fmin2(k, y);
if(k == 1.0) c = m = y = 0.0;
else { c = (c-k)/(1-k); m = (m-k)/(1-k); y = (y-k)/(1-k); }
fprintf(pd->pdffp, "%.3f %.3f %.3f %.3f k\n", c, m, y, k);
} else if(streql(pd->colormodel, "rgb")) {
fprintf(pd->pdffp, "%.3f %.3f %.3f rg\n",
R_RED(color)/255.0,
R_GREEN(color)/255.0,
R_BLUE(color)/255.0);
} else {
if (!streql(pd->colormodel, "srgb"))
warning(_("unknown 'colormodel', using 'srgb'"));
if (!pd->current.srgb_fg) {
fprintf(pd->pdffp, "/sRGB cs\n");
pd->current.srgb_fg = 1;
}
fprintf(pd->pdffp, "%.3f %.3f %.3f scn\n",
R_RED(color)/255.0,
R_GREEN(color)/255.0,
R_BLUE(color)/255.0);
}
pd->current.fill = color;
}
}
static void PDFSetLineEnd(FILE *fp, R_GE_lineend lend)
{
int lineend = 1; /* -Wall */
switch (lend) {
case GE_ROUND_CAP:
lineend = 1;
break;
case GE_BUTT_CAP:
lineend = 0;
break;
case GE_SQUARE_CAP:
lineend = 2;
break;
default:
error(_("invalid line end"));
}
fprintf(fp, "%1d J\n", lineend);
}
static void PDFSetLineJoin(FILE *fp, R_GE_linejoin ljoin)
{
int linejoin = 1; /* -Wall */
switch (ljoin) {
case GE_ROUND_JOIN:
linejoin = 1;
break;
case GE_MITRE_JOIN:
linejoin = 0;
break;
case GE_BEVEL_JOIN:
linejoin = 2;
break;
default:
error(_("invalid line join"));
}
fprintf(fp, "%1d j\n", linejoin);
}
/* Note that the line texture is scaled by the line width.*/
static void PDFSetLineTexture(FILE *fp, const char *dashlist, int nlty,
double lwd, int lend)
{
PP_SetLineTexture("d", (lend == GE_BUTT_CAP) ? 0. : 1.);
}
static void PDF_SetLineStyle(const pGEcontext gc, pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
char dashlist[8];
int i;
int newlty = gc->lty;
double linewidth;
double newlwd = gc->lwd;
R_GE_lineend newlend = gc->lend;
R_GE_linejoin newljoin = gc->ljoin;
double newlmitre = gc->lmitre;
if (pd->current.lty != newlty || pd->current.lwd != newlwd ||
pd->current.lend != newlend) {
pd->current.lwd = newlwd;
pd->current.lty = newlty;
linewidth = newlwd * 0.75;
/* Must not allow line width to be zero */
if (linewidth < .01)
linewidth = .01;
fprintf(pd->pdffp, "%.2f w\n", linewidth);
/* process lty : */
for(i = 0; i < 8 && newlty & 15 ; i++) {
dashlist[i] = newlty & 15;
newlty = newlty >> 4;
}
PDFSetLineTexture(pd->pdffp, dashlist, i, newlwd * 0.75, newlend);
}
if (pd->current.lend != newlend) {
pd->current.lend = newlend;
PDFSetLineEnd(pd->pdffp, newlend);
}
if (pd->current.ljoin != newljoin) {
pd->current.ljoin = newljoin;
PDFSetLineJoin(pd->pdffp, newljoin);
}
if (pd->current.lmitre != newlmitre) {
pd->current.lmitre = newlmitre;
fprintf(pd->pdffp, "%.2f M\n", newlmitre);
}
}
/* This was an optimization that has effectively been disabled in
2.8.0, to avoid repeatedly going in and out of text mode. Howver,
Acrobat puts all text rendering calls in BT...ET into a single
transparency group, and other viewers do not. So for consistent
rendering we put each text() call into a separate group.
*/
static void texton(PDFDesc *pd)
{
fprintf(pd->pdffp, "BT\n");
pd->inText = TRUE;
}
static void textoff(PDFDesc *pd)
{
fprintf(pd->pdffp, "ET\n");
pd->inText = FALSE;
}
static void PDF_Encodings(PDFDesc *pd)
{
encodinglist enclist = pd->encodings;
while (enclist) {
encodinginfo encoding = enclist->encoding;
pd->pos[++pd->nobjs] = (int) ftell(pd->pdffp);
fprintf(pd->pdffp, "%d 0 obj\n<<\n/Type /Encoding ", pd->nobjs);
if (strcmp(encoding->name, "WinAnsiEncoding") == 0 ||
strcmp(encoding->name, "MacRomanEncoding") == 0 ||
strcmp(encoding->name, "PDFDocEncoding") == 0) {
fprintf(pd->pdffp, "/BaseEncoding /%s\n", encoding->name);
fprintf(pd->pdffp, "/Differences [ 45/minus ]\n");
} else if (strcmp(encoding->name, "ISOLatin1Encoding") == 0) {
fprintf(pd->pdffp, "/BaseEncoding /WinAnsiEncoding\n");
fprintf(pd->pdffp, "/Differences [ 45/minus 96/quoteleft\n144/dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent\n/dieresis /.notdef /ring /cedilla /.notdef /hungarumlaut /ogonek /caron /space]\n");
} else {
int enc_first;
int c = 0;
int len;
char buf[128];
for(enc_first=0;encoding->enccode[enc_first]!='[' &&
encoding->enccode[enc_first]!='\0' ;enc_first++);
if (enc_first >= strlen(encoding->enccode))
enc_first=0;
fprintf(pd->pdffp, "/BaseEncoding /PDFDocEncoding\n");
fprintf(pd->pdffp, "/Differences [\n");
while(encoding->enccode[enc_first]) {
switch (encoding->enccode[enc_first]) {
case ' ':
case '\t':
case '\n':
case '[':
case ']':
enc_first++;
continue;
}
for(len=0;
(encoding->enccode[enc_first+len]!=' ') &&
(encoding->enccode[enc_first+len]!=']') &&
(encoding->enccode[enc_first+len]!='\t') &&
(encoding->enccode[enc_first+len]!='\0') &&
(encoding->enccode[enc_first+len]!='\n') ;
len++);
memcpy(buf,encoding->enccode + enc_first , len);
buf[len]='\0';
fprintf(pd->pdffp, " %d%s", c, buf);
if ( (c+1) % 8 == 0 ) fprintf(pd->pdffp, "\n");
c++;
enc_first+=len;
}
fprintf(pd->pdffp, "\n]\n");
}
fprintf(pd->pdffp, ">>\nendobj\n");
enclist = enclist->next;
}
}
/* Read sRGB profile from icc/srgb.flate
* HexCode original from
* http://code.google.com/p/ghostscript/source/browse/trunk/gs/iccprofiles/srgb.icc
*/
#define BUFSIZE2 10000
static void PDFwritesRGBcolorspace(PDFDesc *pd)
{
char buf[BUFSIZE2];
FILE *fp;
snprintf(buf, BUFSIZE2, "%s%slibrary%sgrDevices%sicc%s%s",
R_Home, FILESEP, FILESEP, FILESEP, FILESEP,
pd->useCompression ? "srgb.flate" : "srgb");
if (!(fp = R_fopen(R_ExpandFileName(buf), "rb")))
error(_("failed to load sRGB colorspace file"));
size_t res = fread(buf, 1, BUFSIZE2, fp);
res = fwrite(buf, 1, res, pd->pdffp);
fclose(fp);
}
#include <time.h>
#include <Rversion.h>
static void PDF_startfile(PDFDesc *pd)
{
struct tm *ltm;
time_t ct;
pd->nobjs = 0;
pd->pageno = 0;
/*
* I destroy it when I open in Japanese environment carelessly
*/
fprintf(pd->pdffp, "%%PDF-%i.%i\n%%\x81\xe2\x81\xe3\x81\xcf\x81\xd3\x5c\x72\n",
pd->versionMajor, pd->versionMinor);
pd->pos[++pd->nobjs] = (int) ftell(pd->pdffp);
/* Object 1 is Info node. Date format is from the PDF manual */
ct = time(NULL);
ltm = localtime(&ct);
fprintf(pd->pdffp,
"1 0 obj\n<<\n/CreationDate (D:%04d%02d%02d%02d%02d%02d)\n",
1900 + ltm->tm_year, ltm->tm_mon+1, ltm->tm_mday,
ltm->tm_hour, ltm->tm_min, ltm->tm_sec);
fprintf(pd->pdffp,
"/ModDate (D:%04d%02d%02d%02d%02d%02d)\n",
1900 + ltm->tm_year, ltm->tm_mon+1, ltm->tm_mday,
ltm->tm_hour, ltm->tm_min, ltm->tm_sec);
fprintf(pd->pdffp, "/Title (%s)\n", pd->title);
fprintf(pd->pdffp, "/Producer (R %s.%s)\n/Creator (R)\n>>\nendobj\n",
R_MAJOR, R_MINOR);
/* Object 2 is the Catalog, pointing to pages list in object 3 (at end) */
pd->pos[++pd->nobjs] = (int) ftell(pd->pdffp);
fprintf(pd->pdffp, "2 0 obj\n<< /Type /Catalog /Pages 3 0 R >>\nendobj\n");
/* Objects at the end */
pd->nobjs += 2;
if (streql(pd->colormodel, "srgb")) pd->nobjs += 2;
}
static const char *Base14[] =
{
"Courier", "Courier-Oblique", "Courier-Bold", "Courier-BoldOblique",
"Helvetica", "Helvetica-Oblique", "Helvetica-Bold",
"Helvetica-BoldOblique", "Symbol", "Times-Roman", "Times-Italic",
"Times-Bold", "Times-BoldItalic", "ZapfDingbats"
};
static int isBase14(const char *name)
{
int i;
for(i = 0; i < 14; i++)
if(strcmp(name, Base14[i]) == 0) return 1;
return 0;
}
static const char *KnownSanSerif[] =
{
"AvantGarde", "Helvetica-Narrow", "URWGothic", "NimbusSan"
};
static int isSans(const char *name)
{
int i;
for(i = 0; i < 4; i++)
if(strncmp(name, KnownSanSerif[i], strlen(KnownSanSerif[i])) == 0)
return 1;
return 0;
}
#define boldslant(x) ((x==3)?",BoldItalic":((x==2)?",Italic":((x==1)?",Bold":"")))
#if defined(BUFSIZ) && (BUFSIZ > 512)
/* OS's buffer size in stdio.h, probably.
Windows has 512, Solaris 1024, glibc 8192
*/
# define APPENDBUFSIZE BUFSIZ
#else
# define APPENDBUFSIZE 512
#endif
static void PDF_endfile(PDFDesc *pd)
{
int i, startxref, tempnobj, nenc, nfonts, cidnfonts, firstencobj;
int nraster, nmask;
/* object 3 lists all the pages */
pd->pos[3] = (int) ftell(pd->pdffp);
fprintf(pd->pdffp, "3 0 obj\n<< /Type /Pages /Kids [ ");
for(i = 0; i < pd->pageno; i++)
fprintf(pd->pdffp, "%d 0 R ", pd->pageobj[i]);
fprintf(pd->pdffp,
"] /Count %d /MediaBox [0 0 %d %d] >>\nendobj\n",
pd->pageno,
(int) (0.5 + pd->paperwidth), (int) (0.5 + pd->paperheight));
/* Object 4 is the standard resources dict for each page */
/* Count how many images and masks */
nraster = pd->numRasters;
nmask = pd->numMasks;
if(pd->nobjs + nraster + nmask + 500 >= pd->max_nobjs) {
int new = pd->nobjs + nraster + nmask + 500;
void *tmp = realloc(pd->pos, new * sizeof(int));
if(!tmp)
error("unable to increase object limit: please shutdown the pdf device");
pd->pos = (int *) tmp;
pd->max_nobjs = new;
}
pd->pos[4] = (int) ftell(pd->pdffp);
/* The resource dictionary for each page */
/* ProcSet is regarded as obsolete as from PDF 1.4 */
if (nraster > 0) {
if (nmask > 0) {
fprintf(pd->pdffp,
"4 0 obj\n<<\n/ProcSet [/PDF /Text /ImageC /ImageB]\n/Font <<");
} else {
fprintf(pd->pdffp,
"4 0 obj\n<<\n/ProcSet [/PDF /Text /ImageC]\n/Font <<");
}
} else {
/* fonts */
fprintf(pd->pdffp,
"4 0 obj\n<<\n/ProcSet [/PDF /Text]\n/Font <<");
}
/* Count how many encodings will be included:
* fonts come after encodings */
nenc = 0;
if (pd->encodings) {
encodinglist enclist = pd->encodings;
while (enclist) {
nenc++;
enclist = enclist->next;
}
}
/* Should be a default text font at least, plus possibly others */
tempnobj = pd->nobjs + nenc;
/* Dingbats always F1 */
if(pd->fontUsed[1]) fprintf(pd->pdffp, " /F1 %d 0 R ", ++tempnobj);
nfonts = 2;
if (pd->fonts) {
type1fontlist fontlist = pd->fonts;
while (fontlist) {
for (i = 0; i < 5; i++) {
if(nfonts >= 100 || pd->fontUsed[nfonts]) {
fprintf(pd->pdffp, "/F%d %d 0 R ", nfonts, ++tempnobj);
/* Allow for the font descriptor object, if present */
if(!isBase14(fontlist->family->fonts[i]->name)) tempnobj++;
}
nfonts++;
}
fontlist = fontlist->next;
}
}
cidnfonts = 0;
if (pd->cidfonts) {
cidfontlist fontlist = pd->cidfonts;
while (fontlist) {
for (i = 0; i < 5; i++) {
fprintf(pd->pdffp, "/F%d %d 0 R ",
1000 + cidnfonts + 1, ++tempnobj);
cidnfonts++;
}
fontlist = fontlist->next;
}
}
fprintf(pd->pdffp, ">>\n");
if (nraster > 0) {
/* image XObjects */
fprintf(pd->pdffp, "/XObject <<\n");
for (i = 0; i < nraster; i++) {
fprintf(pd->pdffp, " /Im%d %d 0 R\n", i, pd->rasters[i].nobj);
if (pd->masks[i] >= 0)
fprintf(pd->pdffp, " /Mask%d %d 0 R\n",
pd->masks[i], pd->rasters[i].nmaskobj);
}
fprintf(pd->pdffp, ">>\n");
}
/* graphics state parameter dictionaries */
fprintf(pd->pdffp, "/ExtGState << ");
for (i = 0; i < 256 && pd->colAlpha[i] >= 0; i++)
fprintf(pd->pdffp, "/GS%i %d 0 R ", i + 1, ++tempnobj);
for (i = 0; i < 256 && pd->fillAlpha[i] >= 0; i++)
fprintf(pd->pdffp, "/GS%i %d 0 R ", i + 257, ++tempnobj);
/* Special state to set AIS if we have soft masks */
if (nmask > 0)
fprintf(pd->pdffp, "/GSais %d 0 R ", ++tempnobj);
fprintf(pd->pdffp, ">>\n");
if (streql(pd->colormodel, "srgb")) {
/* Objects 5 and 6 are the sRGB color space, if required */
fprintf(pd->pdffp, "/ColorSpace << /sRGB 5 0 R >>\n");
fprintf(pd->pdffp, ">>\nendobj\n");
pd->pos[5] = (int) ftell(pd->pdffp);
fprintf(pd->pdffp, "5 0 obj\n[/ICCBased 6 0 R]\nendobj\n");
pd->pos[6] = (int) ftell(pd->pdffp);
fprintf(pd->pdffp, "6 0 obj\n");
PDFwritesRGBcolorspace(pd);
fprintf(pd->pdffp, "endobj\n");
} else {
fprintf(pd->pdffp, ">>\nendobj\n");
}
if(tempnobj >= pd->max_nobjs) {
int new = tempnobj + 500;
void *tmp = realloc(pd->pos, new * sizeof(int));
if(!tmp)
error("unable to increase object limit: please shutdown the pdf device");
pd->pos = (int *) tmp;
pd->max_nobjs = new;
}
/*
* Write out objects representing the encodings
*/
firstencobj = pd->nobjs;
PDF_Encodings(pd);
/*
* Write out objects representing the fonts
*/
if (pd->fontUsed[1]) {
pd->pos[++pd->nobjs] = (int) ftell(pd->pdffp);
fprintf(pd->pdffp, "%d 0 obj\n<< /Type /Font /Subtype /Type1 /Name /F1 /BaseFont /ZapfDingbats >>\nendobj\n", pd->nobjs);
}
nfonts = 2;
if (pd->fonts) {
type1fontlist fontlist = pd->fonts;
while (fontlist) {
FontMetricInfo *metrics;
/*
* Find the index of the device encoding
* This really should be there
*/
int encIndex;
encodinginfo encoding =
findDeviceEncoding(fontlist->family->encoding->encpath,
pd->encodings, &encIndex);
if (!encoding)
error(_("corrupt encodings in PDF device"));
for (i = 0; i < 5; i++) {
if (nfonts >= 100 || pd->fontUsed[nfonts]) {
type1fontinfo fn = fontlist->family->fonts[i];
int base = isBase14(fn->name);
metrics = &fn->metrics;
pd->pos[++pd->nobjs] = (int) ftell(pd->pdffp);
fprintf(pd->pdffp, "%d 0 obj\n<< /Type /Font /Subtype /Type1 /Name /F%d /BaseFont /%s\n",
pd->nobjs,
nfonts,
fn->name);
if (!base) {
int ii, first, last, tmp;
for(first = 1, ii = 0; ii < 255; ii++)
if(metrics->CharInfo[ii].WX != NA_SHORT) {
first = ii;
break;
}
for(last = 255, ii = 254; ii >= 0; ii--)
if(metrics->CharInfo[ii].WX != NA_SHORT) {
last = ii + 1;
break;
}
fprintf(pd->pdffp,
"/FirstChar %d /LastChar %d /Widths [\n",
first, last);
for (ii = first; ii <= last; ii++) {
tmp = metrics->CharInfo[ii].WX;
fprintf(pd->pdffp, " %d", tmp==NA_SHORT ? 0 : tmp);
if ((ii + 1) % 15 == 0) fprintf(pd->pdffp, "\n");
}
fprintf(pd->pdffp, "]\n");
fprintf(pd->pdffp, "/FontDescriptor %d 0 R\n",
pd->nobjs + 1);
}
if(i < 4)
fprintf(pd->pdffp, "/Encoding %d 0 R ",
/* Encodings come after dingbats font which is
* object 5 */
encIndex + firstencobj);
fprintf(pd->pdffp, ">>\nendobj\n");
if(!base) {
/* write font descriptor */
int flags = 32 /*bit 6, non-symbolic*/ +
((i==2 || i==3) ? 64/* italic */: 0) +
(metrics->IsFixedPitch > 0 ? 1 : 0) +
(isSans(fn->name) ? 0 : 2);
/* <FIXME> we have no real way to know
if this is serif or not */
pd->pos[++pd->nobjs] = (int) ftell(pd->pdffp);
fprintf(pd->pdffp,
"%d 0 obj <<\n"
" /Type /FontDescriptor\n"
" /FontName /%s\n"
" /Flags %d\n"
" /FontBBox [%d %d %d %d]\n"
" /CapHeight %d\n /Ascent %d\n /Descent %d\n"
" /ItalicAngle %d\n /XHeight %d\n /StemV %d\n"
">>\nendobj\n",
pd->nobjs,
fn->name,
(i == 4) ? 4 : flags,
metrics->FontBBox[0], metrics->FontBBox[1],
metrics->FontBBox[2], metrics->FontBBox[3],
metrics->CapHeight, metrics->Ascender,
metrics->Descender,
metrics->ItalicAngle, metrics->XHeight,
(metrics->StemV != NA_SHORT) ? metrics->StemV :
(i==2 || i==3) ? 140 : 83);
}
}
nfonts++;
}
fontlist = fontlist->next;
}
}
cidnfonts = 0;
if (pd->cidfonts) {
cidfontlist fontlist = pd->cidfonts;
if(pd->versionMajor == 1 && pd->versionMinor < 3) {
pd->versionMinor = 3;
warning(_("increasing the PDF version to 1.3"));
}
while (fontlist) {
for (i = 0; i < 4; i++) {
pd->pos[++pd->nobjs] = (int) ftell(pd->pdffp);
fprintf(pd->pdffp,
/** format **/
"%d 0 obj\n"
"<<\n"
" /Type /Font\n"
" /Subtype /Type0\n"
" /Name /F%d\n"
" /BaseFont /%s%s\n"
" /DescendantFonts [\n"
" <<\n"
" /Type /Font\n"
" /Subtype /CIDFontType0\n"
" /BaseFont /%s%s\n"
" %s"
" >>\n"
" ]\n"
" /Encoding /%s\n"
">>\n"
"endobj\n",
/** vararg **/
pd->nobjs, /* pdf objnum */
1000 + cidnfonts + 1, /* - face */
fontlist->cidfamily->cidfonts[i]->name,/* /BaseFont*/
boldslant(i), /* - boldslant */
fontlist->cidfamily->cidfonts[i]->name,/* /BaseFont*/
boldslant(i), /* - boldslant */
/* Resource */
/*
* Pull the resource out of R object
* Hopefully one day this will be unnecessary
*/
getCIDFontPDFResource(fontlist->cidfamily->fxname),
fontlist->cidfamily->cmap /* /Encoding */
);
cidnfonts++;
}
/* Symbol face does not use encoding */
pd->pos[++pd->nobjs] = (int) ftell(pd->pdffp);
fprintf(pd->pdffp, "%d 0 obj\n<<\n/Type /Font\n/Subtype /Type1\n/Name /F%d\n/BaseFont /%s\n>>\nendobj\n",
pd->nobjs,
1000 + cidnfonts + 1,
fontlist->cidfamily->symfont->name);
cidnfonts++;
fontlist = fontlist->next;
}
}
/*
* Write out objects representing the graphics state parameter
* dictionaries for alpha transparency
*/
for (i = 0; i < 256 && pd->colAlpha[i] >= 0; i++) {
pd->pos[++pd->nobjs] = (int) ftell(pd->pdffp);
fprintf(pd->pdffp,
"%d 0 obj\n<<\n/Type /ExtGState\n/CA %1.3f >>\nendobj\n",
pd->nobjs, pd->colAlpha[i]/255.0);
}
for (i = 0; i < 256 && pd->fillAlpha[i] >= 0; i++) {
pd->pos[++pd->nobjs] = (int) ftell(pd->pdffp);
fprintf(pd->pdffp,
"%d 0 obj\n<<\n/Type /ExtGState\n/ca %1.3f\n>>\nendobj\n",
pd->nobjs, pd->fillAlpha[i]/255.0);
}
if (nmask > 0) {
pd->pos[++pd->nobjs] = (int) ftell(pd->pdffp);
fprintf(pd->pdffp,
"%d 0 obj\n<<\n/Type /ExtGState\n/AIS false\n>>\nendobj\n",
pd->nobjs);
}
/* write out xref table */
startxref = (int) ftell(pd->pdffp);
/* items here must be exactly 20 bytes including terminator */
fprintf(pd->pdffp, "xref\n0 %d\n", pd->nobjs+1);
fprintf(pd->pdffp, "0000000000 65535 f \n");
for(i = 1; i <= pd->nobjs; i++)
fprintf(pd->pdffp, "%010d 00000 n \n", pd->pos[i]);
fprintf(pd->pdffp,
"trailer\n<< /Size %d /Info 1 0 R /Root 2 0 R >>\nstartxref\n%d\n",
pd->nobjs+1, startxref);
fprintf(pd->pdffp, "%%%%EOF\n");
/* now seek back and update the header */
rewind(pd->pdffp);
fprintf(pd->pdffp, "%%PDF-%i.%i\n", pd->versionMajor, pd->versionMinor);
fclose(pd->pdffp);
if (pd->open_type == 1) {
char buf[APPENDBUFSIZE];
size_t nc;
pd->pdffp = R_fopen(pd->filename, "rb");
while((nc = fread(buf, 1, APPENDBUFSIZE, pd->pdffp))) {
if(nc != fwrite(buf, 1, nc, pd->pipefp))
error("write error");
if (nc < APPENDBUFSIZE) break;
}
fclose(pd->pdffp);
pclose(pd->pipefp);
unlink(pd->filename);
}
}
static Rboolean PDF_Open(pDevDesc dd, PDFDesc *pd)
{
char buf[512];
if (pd->offline)
return TRUE;
if (pd->filename[0] == '|') {
strncpy(pd->cmd, pd->filename + 1, PATH_MAX);
char *tmp = R_tmpnam("Rpdf", R_TempDir);
strncpy(pd->filename, tmp, PATH_MAX);
free(tmp);
errno = 0;
pd->pipefp = R_popen(pd->cmd, "w");
if (!pd->pipefp || errno != 0) {
PDFcleanup(6, pd);
error(_("cannot open 'pdf' pipe to '%s'"), pd->cmd);
return FALSE;
}
pd->open_type = 1;
if (!pd->onefile) {
pd->onefile = TRUE;
warning(_("file = \"|cmd\" implies 'onefile = TRUE'"));
}
} else pd->open_type = 0;
snprintf(buf, 512, pd->filename, pd->fileno + 1); /* file 1 to start */
/* NB: this must be binary to get tell positions and line endings right,
as well as allowing binary streams */
pd->mainfp = R_fopen(R_ExpandFileName(buf), "wb");
if (!pd->mainfp) {
PDFcleanup(6, pd);
free(dd);
error(_("cannot open file '%s'"), buf);
}
pd->pdffp = pd->mainfp;
PDF_startfile(pd);
return TRUE;
}
static void pdfClip(double x0, double x1, double y0, double y1, PDFDesc *pd)
{
if(x0 != 0.0 || y0 != 0.0 || x1 != 72*pd->width || y1 != 72*pd->height)
fprintf(pd->pdffp, "Q q %.2f %.2f %.2f %.2f re W n\n",
x0, y0, x1 - x0, y1 - y0);
else fprintf(pd->pdffp, "Q q\n");
}
static void PDF_Clip(double x0, double x1, double y0, double y1, pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
PDF_checkOffline();
if(pd->inText) textoff(pd);
pdfClip(x0, x1, y0, y1, pd);
PDF_Invalidate(dd);
}
static void PDF_Size(double *left, double *right,
double *bottom, double *top,
pDevDesc dd)
{
*left = dd->left;
*right = dd->right;
*bottom = dd->bottom;
*top = dd->top;
}
static void PDF_endpage(PDFDesc *pd)
{
if(pd->inText) textoff(pd);
fprintf(pd->pdffp, "Q\n");
if (pd->useCompression) {
fflush(pd->pdffp);
fseek(pd->pdffp, 0, SEEK_END);
unsigned int len = (unsigned int) ftell(pd->pdffp);
fseek(pd->pdffp, 0, SEEK_SET);
Bytef *buf = Calloc(len, Bytef);
uLong outlen = (uLong)(1.001*len + 20);
Bytef *buf2 = Calloc(outlen, Bytef);
size_t res = fread(buf, 1, len, pd->pdffp);
if (res < len) error("internal read error in PDF_endpage");
fclose(pd->pdffp);
unlink(pd->tmpname);
pd->pdffp = pd->mainfp;
int res2 = compress(buf2, &outlen, buf, len);
if(res2 != Z_OK)
error("internal compression error %d in PDF_endpage", res2);
fprintf(pd->pdffp, "%d 0 obj\n<<\n/Length %d /Filter /FlateDecode\n>>\nstream\n",
pd->nobjs, (int) outlen);
size_t nwrite = fwrite(buf2, 1, outlen, pd->pdffp);
if(nwrite != outlen) error(_("write failed"));
Free(buf); Free(buf2);
fprintf(pd->pdffp, "endstream\nendobj\n");
} else {
int here = (int) ftell(pd->pdffp);
fprintf(pd->pdffp, "endstream\nendobj\n");
pd->pos[++pd->nobjs] = (int) ftell(pd->pdffp);
fprintf(pd->pdffp, "%d 0 obj\n%d\nendobj\n", pd->nobjs,
here - pd->startstream);
}
if(pd->nobjs + 2*(pd->numRasters-pd->writtenRasters) + 500
>= pd->max_nobjs) {
int new = pd->nobjs + 2*(pd->numRasters-pd->writtenRasters) + 2000;
void *tmp = realloc(pd->pos, new * sizeof(int));
if(!tmp)
error("unable to increase object limit: please shutdown the pdf device");
pd->pos = (int *) tmp;
pd->max_nobjs = new;
}
/* Write out any new rasters */
for (int i = pd->writtenRasters; i < pd->numRasters; i++) {
pd->pos[++pd->nobjs] = (int) ftell(pd->pdffp);
pd->rasters[i].nobj = pd->nobjs;
writeRasterXObject(pd->rasters[i], pd->nobjs,
pd->masks[i], pd->nobjs+1, pd);
if (pd->masks[i] >= 0) {
pd->pos[++pd->nobjs] = (int) ftell(pd->pdffp);
pd->rasters[i].nmaskobj = pd->nobjs;
writeMaskXObject(pd->rasters[i], pd->nobjs, pd);
}
free(pd->rasters[i].raster);
pd->rasters[i].raster = NULL;
pd->writtenRasters = pd->numRasters;
}
}
#define R_VIS(col) (R_ALPHA(col) > 0)
static void PDF_NewPage(const pGEcontext gc,
pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
char buf[512];
PDF_checkOffline();
if(pd->pageno >= pd->pagemax) {
void * tmp = realloc(pd->pageobj, 2*pd->pagemax * sizeof(int));
if(!tmp)
error("unable to increase page limit: please shutdown the pdf device");
pd->pageobj = (int *) tmp;
pd->pagemax *= 2;
}
if(pd->nobjs + 500 >= pd->max_nobjs) {
int new = pd->max_nobjs + 2000;
void *tmp = realloc(pd->pos, new * sizeof(int));
if(!tmp)
error("unable to increase object limit: please shutdown the pdf device");
pd->pos = (int *) tmp;
pd->max_nobjs = new;
}
if(pd->pageno > 0) {
PDF_endpage(pd);
if(!pd->onefile) {
PDF_endfile(pd);
pd->fileno++;
snprintf(buf, 512, pd->filename, pd->fileno + 1); /* file 1 to start */
pd->mainfp = R_fopen(R_ExpandFileName(buf), "wb");
if (!pd->mainfp)
error(_("cannot open 'pdf' file argument '%s'\n please shut down the PDF device"), buf);
pd->pdffp = pd->mainfp;
PDF_startfile(pd);
}
}
pd->pos[++pd->nobjs] = (int) ftell(pd->pdffp);
pd->pageobj[pd->pageno++] = pd->nobjs;
fprintf(pd->pdffp, "%d 0 obj\n<< /Type /Page /Parent 3 0 R /Contents %d 0 R /Resources 4 0 R >>\nendobj\n",
pd->nobjs, pd->nobjs+1);
pd->pos[++pd->nobjs] = (int) ftell(pd->pdffp);
if (pd->useCompression) {
char *tmp = R_tmpnam("pdf", R_TempDir);
/* assume tmpname is less than PATH_MAX */
strcpy(pd->tmpname, tmp);
pd->pdffp = fopen(tmp, "w+b");
free(tmp);
if(! pd->pdffp) error("cannot open file '%s', reason %s",
tmp, strerror(errno));
} else {
fprintf(pd->pdffp, "%d 0 obj\n<<\n/Length %d 0 R\n>>\nstream\n",
pd->nobjs, pd->nobjs + 1);
pd->startstream = (int) ftell(pd->pdffp);
}
/*
* Line end/join/mitre now controlled by user
* Same old defaults
* .. but they are still needed because SetXXX produces the corresponding
* command only if the value changes - so we have to define base defaults
* according to the values reset by Invalidate. I'm pretty sure about j/J
* but not so about M because Invalidate uses 0 yet the default used to be
* 10.
*
* fprintf(pd->pdffp, "1 J 1 j 10 M q\n");
*/
fprintf(pd->pdffp, "1 J 1 j q\n");
PDF_Invalidate(dd);
if(R_VIS(gc->fill)) {
PDF_SetFill(gc->fill, dd);
fprintf(pd->pdffp, "0 0 %.2f %.2f re f\n",
72.0 * pd->width, 72.0 * pd->height);
}
pd->inText = FALSE;
}
static void PDF_Close(pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
if (!pd->offline) {
if(pd->pageno > 0) PDF_endpage(pd);
PDF_endfile(pd);
/* may no longer be needed */
killRasterArray(pd->rasters, pd->maxRasters);
}
PDFcleanup(6, pd); /* which frees masks and rasters */
}
static void PDF_Rect(double x0, double y0, double x1, double y1,
const pGEcontext gc,
pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
int code;
PDF_checkOffline();
code = 2 * (R_VIS(gc->fill)) + (R_VIS(gc->col));
if (code) {
if(pd->inText) textoff(pd);
if(code & 2)
PDF_SetFill(gc->fill, dd);
if(code & 1) {
PDF_SetLineColor(gc->col, dd);
PDF_SetLineStyle(gc, dd);
}
fprintf(pd->pdffp, "%.2f %.2f %.2f %.2f re", x0, y0, x1-x0, y1-y0);
switch(code) {
case 1: fprintf(pd->pdffp, " S\n"); break;
case 2: fprintf(pd->pdffp, " f\n"); break;
case 3: fprintf(pd->pdffp, " B\n"); break;
}
}
}
#ifdef SIMPLE_RASTER
/* Maybe reincoporate this simpler approach as an alternative
* (for opaque raster images) because it has the advantage of
* NOT keeping the raster in memory until the PDF file is complete
*/
static void PDF_Raster(unsigned int *raster,
int w, int h,
double x, double y,
double width, double height,
double rot, Rboolean interpolate,
const pGEcontext gc, pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
double angle, cosa, sina;
PDF_checkOffline();
/* This takes the simple approach of creating an inline
* image. This is not recommended for larger images
* because it makes more work for the PDF viewer.
* It also does not allow for semitransparent images.
*/
if(pd->inText) textoff(pd);
/* Save graphics state */
fprintf(pd->pdffp, "q\n");
/* translate */
fprintf(pd->pdffp,
"1 0 0 1 %.2f %.2f cm\n",
x, y);
/* rotate */
angle = rot*M_PI/180;
cosa = cos(angle);
sina = sin(angle);
fprintf(pd->pdffp,
"%.2f %.2f %.2f %.2f 0 0 cm\n",
cosa, sina, -sina, cosa);
/* scale */
fprintf(pd->pdffp,
"%.2f 0 0 %.2f 0 0 cm\n",
width, height);
/* Begin image */
fprintf(pd->pdffp, "BI\n");
/* Image characteristics */
/* Use ASCIIHexDecode filter for now, just because
* it's easier to implement */
fprintf(pd->pdffp,
" /W %d\n /H %d\n /CS /RGB\n /BPC 8\n /F [/AHx]\n",
w, h);
if (interpolate) {
fprintf(pd->pdffp, " /I true\n");
}
/* Begin image data */
fprintf(pd->pdffp, "ID\n");
/* The image stream */
PDF_imagedata(raster, w, h, pd);
/* End image */
fprintf(pd->pdffp, "EI\n");
/* Restore graphics state */
fprintf(pd->pdffp, "Q\n");
}
#else
static void PDF_Raster(unsigned int *raster,
int w, int h,
double x, double y,
double width, double height,
double rot, Rboolean interpolate,
const pGEcontext gc, pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
double angle, cosa, sina;
int alpha;
PDF_checkOffline();
/* Record the raster so can write it out when page is finished */
alpha = addRaster(raster, w, h, interpolate, pd);
if(pd->inText) textoff(pd);
/* Save graphics state */
fprintf(pd->pdffp, "q\n");
/* Need to set AIS graphics state parameter ? */
if (alpha) fprintf(pd->pdffp, "/GSais gs\n");
/* translate */
fprintf(pd->pdffp,
"1 0 0 1 %.2f %.2f cm\n",
x, y);
/* rotate */
angle = rot*M_PI/180;
cosa = cos(angle);
sina = sin(angle);
fprintf(pd->pdffp,
"%.2f %.2f %.2f %.2f 0 0 cm\n",
cosa, sina, -sina, cosa);
/* scale */
fprintf(pd->pdffp,
"%.2f 0 0 %.2f 0 0 cm\n",
width, height);
/* Refer to XObject which will be written to file when page is finished */
fprintf(pd->pdffp, "/Im%d Do\n", pd->numRasters - 1);
/* Restore graphics state */
fprintf(pd->pdffp, "Q\n");
}
#endif
/* r is in device coords */
static void PDF_Circle(double x, double y, double r,
const pGEcontext gc,
pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
int code, tr;
double xx, yy, a;
PDF_checkOffline();
if (r <= 0.0) return; /* since PR#14797 use 0-sized pch=1, but now
GECircle omits such circles */
code = 2 * (R_VIS(gc->fill)) + (R_VIS(gc->col));
if (code) {
if(code & 2)
PDF_SetFill(gc->fill, dd);
if(code & 1) {
PDF_SetLineColor(gc->col, dd);
PDF_SetLineStyle(gc, dd);
}
}
if (code) {
if (semiTransparent(gc->col) || semiTransparent(gc->fill)
|| r > 10 || !pd->dingbats) {
/*
* Due to possible bug in Acrobat Reader for rendering
* semi-transparent text, only ever draw Bezier curves
* regardless of circle size. Otherwise use font up to 20pt
*/
{
/* Use four Bezier curves, hand-fitted to quadrants */
double s = 0.55 * r;
if(pd->inText) textoff(pd);
fprintf(pd->pdffp, " %.2f %.2f m\n", x - r, y);
fprintf(pd->pdffp, " %.2f %.2f %.2f %.2f %.2f %.2f c\n",
x - r, y + s, x - s, y + r, x, y + r);
fprintf(pd->pdffp, " %.2f %.2f %.2f %.2f %.2f %.2f c\n",
x + s, y + r, x + r, y + s, x + r, y);
fprintf(pd->pdffp, " %.2f %.2f %.2f %.2f %.2f %.2f c\n",
x + r, y - s, x + s, y - r, x, y - r);
fprintf(pd->pdffp, " %.2f %.2f %.2f %.2f %.2f %.2f c\n",
x - s, y - r, x - r, y - s, x - r, y);
switch(code) {
case 1: fprintf(pd->pdffp, "S\n"); break;
case 2: fprintf(pd->pdffp, "f\n"); break;
case 3: fprintf(pd->pdffp, "B\n"); break;
}
}
} else {
pd->fontUsed[1] = TRUE;
/* Use char 108 in Dingbats, which is a solid disc
afm is C 108 ; WX 791 ; N a71 ; B 35 -14 757 708 ;
so diameter = 0.722 * size
centre = (0.396, 0.347) * size
*/
a = 2./0.722 * r;
xx = x - 0.396*a;
yy = y - 0.347*a;
tr = (R_OPAQUE(gc->fill)) +
2 * (R_OPAQUE(gc->col)) - 1;
if(!pd->inText) texton(pd);
fprintf(pd->pdffp,
"/F1 1 Tf %d Tr %.2f 0 0 %.2f %.2f %.2f Tm",
tr, a, a, xx, yy);
fprintf(pd->pdffp, " (l) Tj 0 Tr\n");
textoff(pd); /* added in 2.8.0 */
}
}
}
static void PDF_Line(double x1, double y1, double x2, double y2,
const pGEcontext gc,
pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
PDF_checkOffline();
if(!R_VIS(gc->col)) return;
PDF_SetLineColor(gc->col, dd);
PDF_SetLineStyle(gc, dd);
if(pd->inText) textoff(pd);
fprintf(pd->pdffp, "%.2f %.2f m %.2f %.2f l S\n", x1, y1, x2, y2);
}
static void PDF_Polygon(int n, double *x, double *y,
const pGEcontext gc,
pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
double xx, yy;
int i, code;
PDF_checkOffline();
code = 2 * (R_VIS(gc->fill)) + (R_VIS(gc->col));
if (code) {
if(pd->inText) textoff(pd);
if(code & 2)
PDF_SetFill(gc->fill, dd);
if(code & 1) {
PDF_SetLineColor(gc->col, dd);
PDF_SetLineStyle(gc, dd);
}
xx = x[0];
yy = y[0];
fprintf(pd->pdffp, "%.2f %.2f m\n", xx, yy);
for(i = 1 ; i < n ; i++) {
xx = x[i];
yy = y[i];
fprintf(pd->pdffp, "%.2f %.2f l\n", xx, yy);
}
if (pd->fillOddEven) {
switch(code) {
case 1: fprintf(pd->pdffp, "s\n"); break;
case 2: fprintf(pd->pdffp, "h f*\n"); break;
case 3: fprintf(pd->pdffp, "b*\n"); break;
}
} else {
switch(code) {
case 1: fprintf(pd->pdffp, "s\n"); break;
case 2: fprintf(pd->pdffp, "h f\n"); break;
case 3: fprintf(pd->pdffp, "b\n"); break;
}
}
}
}
static void PDF_Path(double *x, double *y,
int npoly, int *nper,
Rboolean winding,
const pGEcontext gc,
pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
double xx, yy;
int i, j, index, code;
PDF_checkOffline();
code = 2 * (R_VIS(gc->fill)) + (R_VIS(gc->col));
if (code) {
if(pd->inText) textoff(pd);
if(code & 2)
PDF_SetFill(gc->fill, dd);
if(code & 1) {
PDF_SetLineColor(gc->col, dd);
PDF_SetLineStyle(gc, dd);
}
index = 0;
for (i=0; i < npoly; i++) {
xx = x[index];
yy = y[index];
index++;
fprintf(pd->pdffp, "%.2f %.2f m\n", xx, yy);
for(j=1; j < nper[i]; j++) {
xx = x[index];
yy = y[index];
index++;
fprintf(pd->pdffp, "%.2f %.2f l\n", xx, yy);
}
if (i < npoly - 1)
fprintf(pd->pdffp, "h\n");
}
if (winding) {
switch(code) {
case 1: fprintf(pd->pdffp, "s\n"); break;
case 2: fprintf(pd->pdffp, "h f\n"); break;
case 3: fprintf(pd->pdffp, "b\n"); break;
}
} else {
switch(code) {
case 1: fprintf(pd->pdffp, "s\n"); break;
case 2: fprintf(pd->pdffp, "h f*\n"); break;
case 3: fprintf(pd->pdffp, "b*\n"); break;
}
}
}
}
static void PDF_Polyline(int n, double *x, double *y,
const pGEcontext gc,
pDevDesc dd)
{
PDFDesc *pd = (PDFDesc*) dd->deviceSpecific;
double xx, yy;
int i;
PDF_checkOffline();
if(pd->inText) textoff(pd);
if(R_VIS(gc->col)) {
PDF_SetLineColor(gc->col, dd);
PDF_SetLineStyle(gc, dd);
xx = x[0];
yy = y[0];
fprintf(pd->pdffp, "%.2f %.2f m\n", xx, yy);
for(i = 1 ; i < n ; i++) {
xx = x[i];
yy = y[i];
fprintf(pd->pdffp, "%.2f %.2f l\n", xx, yy);
}
fprintf(pd->pdffp, "S\n");
}
}
static int PDFfontNumber(const char *family, int face, PDFDesc *pd)
{
/* DingBats is font 1 */
int num = 1;
if (strlen(family) > 0) {
int fontIndex, cidfontIndex;
/*
* Try to find font in already loaded fonts
*/
type1fontfamily fontfamily = findDeviceFont(family, pd->fonts,
&fontIndex);
cidfontfamily cidfontfamily = findDeviceCIDFont(family, pd->cidfonts,
&cidfontIndex);
if (fontfamily)
num = (fontIndex - 1)*5 + 1 + face;
else if (cidfontfamily)
/*
* Use very high font number for CID fonts to avoid
* Type 1 fonts
*/
num = 1000 + (cidfontIndex - 1)*5 + face;
else {
/*
* Check whether the font is loaded and, if not,
* load it.
*/
fontfamily = findLoadedFont(family,
pd->encodings->encoding->encpath,
TRUE);
cidfontfamily = findLoadedCIDFont(family, TRUE);
if (!(fontfamily || cidfontfamily)) {
if (isType1Font(family, PDFFonts, NULL)) {
fontfamily = addFont(family, TRUE, pd->encodings);
} else if (isCIDFont(family, PDFFonts, NULL)) {
cidfontfamily = addCIDFont(family, TRUE);
} else {
/*
* Should NOT get here.
*/
error(_("invalid font type"));
}
}
/*
* Once the font is loaded, add it to the device's
* list of fonts.
*/
if (fontfamily || cidfontfamily) {
if (isType1Font(family, PDFFonts, NULL)) {
if (addPDFDevicefont(fontfamily, pd, &fontIndex)) {
num = (fontIndex - 1)*5 + 1 + face;
} else {
fontfamily = NULL;
}
} else /* (isCIDFont(family, PDFFonts)) */ {
if (addPDFDeviceCIDfont(cidfontfamily, pd,
&cidfontIndex)) {
num = 1000 + (cidfontIndex - 1)*5 + face;
} else {
cidfontfamily = NULL;
}
}
}
}
if (!(fontfamily || cidfontfamily))
error(_("failed to find or load PDF font"));
} else {
if (isType1Font(family, PDFFonts, pd->defaultFont))
num = 1 + face;
else
num = 1000 + face;
}
if(num < 100) pd->fontUsed[num] = TRUE;
return num;
}
/* added for 2.9.0 (donated by Ei-ji Nakama) : */
static void PDFWriteT1KerningString(FILE *fp, const char *str,
FontMetricInfo *metrics,
const pGEcontext gc)
{
unsigned char p1, p2;
size_t i, n;
int j, ary_buf[128], *ary;
Rboolean haveKerning = FALSE;
n = strlen(str);
if (n < 1) return;
if(n > sizeof(ary_buf)/sizeof(int))
ary = Calloc(n, int);
else ary = ary_buf;
for(i = 0; i < n-1; i++) {
ary[i] = 0.;
p1 = str[i];
p2 = str[i+1];
#ifdef USE_HYPHEN
if (p1 == '-' && !isdigit((int)p2))
p1 = (unsigned char)PS_hyphen;
#endif
for (j = metrics->KPstart[p1]; j < metrics->KPend[p1]; j++)
if(metrics->KernPairs[j].c2 == p2 &&
metrics->KernPairs[j].c1 == p1) {
ary[i] += metrics->KernPairs[j].kern;
haveKerning = TRUE;
break;
}
}
ary[i] = 0;
if(haveKerning) {
fputc('[', fp); fputc('(', fp);
for(i = 0; str[i]; i++) {
switch(str[i]) {
case '\n':
fprintf(fp, "\\n");
break;
case '\\':
fprintf(fp, "\\\\");
break;
case '-':
#ifdef USE_HYPHEN
if (!isdigit((int)str[i+1]))
fputc(PS_hyphen, fp);
else
#endif
fputc(str[i], fp);
break;
case '(':
case ')':
fprintf(fp, "\\%c", str[i]);
break;
default:
fputc(str[i], fp);
break;
}
if( ary[i] != 0 && str[i+1] ) fprintf(fp, ") %d (", -ary[i]);
}
fprintf(fp, ")] TJ\n");
} else {
PostScriptWriteString(fp, str, strlen(str));
fprintf(fp, " Tj\n");
}
if(ary != ary_buf) Free(ary);
}
static FontMetricInfo *PDFmetricInfo(const char *, int, PDFDesc *);
static void PDFSimpleText(double x, double y, const char *str,
double rot, double hadj,
int font,
const pGEcontext gc,
pDevDesc dd) {
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
int size = (int)floor(gc->cex * gc->ps + 0.5);
int face = gc->fontface;
double a, b, bm, rot1;
if(!R_VIS(gc->col)) return;
if(face < 1 || face > 5) {
warning(_("attempt to use invalid font %d replaced by font 1"), face);
face = 1;
}
rot1 = rot * DEG2RAD;
a = size * cos(rot1);
b = size * sin(rot1);
bm = -b;
/* avoid printing -0.00 on rotated text */
if(fabs(a) < 0.01) a = 0.0;
if(fabs(b) < 0.01) {b = 0.0; bm = 0.0;}
if(!pd->inText) texton(pd);
PDF_SetFill(gc->col, dd);
fprintf(pd->pdffp, "/F%d 1 Tf %.2f %.2f %.2f %.2f %.2f %.2f Tm ",
font,
a, b, bm, a, x, y);
if (pd->useKern &&
isType1Font(gc->fontfamily, PDFFonts, pd->defaultFont)) {
PDFWriteT1KerningString(pd->pdffp, str,
PDFmetricInfo(gc->fontfamily, face, pd), gc);
} else {
PostScriptWriteString(pd->pdffp, str, strlen(str));
fprintf(pd->pdffp, " Tj\n");
}
textoff(pd); /* added in 2.8.0 */
}
static char *PDFconvname(const char *family, PDFDesc *pd);
static void PDF_Text0(double x, double y, const char *str, int enc,
double rot, double hadj,
const pGEcontext gc,
pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
int size = (int) floor(gc->cex * gc->ps + 0.5);
int face = gc->fontface;
double a, b, bm, rot1;
char *buff;
const char *str1;
PDF_checkOffline();
if(!R_VIS(gc->col)) return;
if(face < 1 || face > 5) {
warning(_("attempt to use invalid font %d replaced by font 1"), face);
face = 1;
}
if (face == 5) {
PDFSimpleText(x, y, str, rot, hadj,
PDFfontNumber(gc->fontfamily, face, pd),
gc, dd);
return;
}
rot1 = rot * DEG2RAD;
a = size * cos(rot1);
b = size * sin(rot1);
bm = -b;
/* avoid printing -0.00 on rotated text */
if(fabs(a) < 0.01) a = 0.0;
if(fabs(b) < 0.01) {b = 0.0; bm = 0.0;}
if(!pd->inText) texton(pd);
if(isCIDFont(gc->fontfamily, PDFFonts, pd->defaultCIDFont) && face != 5) {
/* NB we could be in a SBCS here */
size_t ucslen;
unsigned char *p;
int fontIndex;
/*
* CID convert optimize PDF encoding == locale encode case
*/
cidfontfamily cidfont = findDeviceCIDFont(gc->fontfamily,
pd->cidfonts,
&fontIndex);
if (!cidfont) {
int dontcare;
/*
* Try to load the font
*/
cidfont = addCIDFont(gc->fontfamily, 1);
if (cidfont) {
if (!addPDFDeviceCIDfont(cidfont, pd, &dontcare)) {
cidfont = NULL;
}
}
}
if (!cidfont)
error(_("failed to find or load PDF CID font"));
if(!dd->hasTextUTF8 &&
!strcmp(locale2charset(NULL), cidfont->encoding)) {
PDF_SetFill(gc->col, dd);
fprintf(pd->pdffp,
"/F%d 1 Tf %.2f %.2f %.2f %.2f %.2f %.2f Tm ",
PDFfontNumber(gc->fontfamily, face, pd),
a, b, bm, a, x, y);
fprintf(pd->pdffp, "<");
p = (unsigned char *) str;
while(*p)
fprintf(pd->pdffp, "%02x", *p++);
fprintf(pd->pdffp, ">");
fprintf(pd->pdffp, " Tj\n");
return;
}
/*
* CID convert PDF encoding != locale encode case
*/
ucslen = (dd->hasTextUTF8) ? Rf_utf8towcs(NULL, str, 0): mbstowcs(NULL, str, 0);
if (ucslen != (size_t)-1) {
void *cd;
const char *i_buf; char *o_buf;
size_t i, nb, i_len, o_len, buflen = ucslen*sizeof(ucs2_t);
size_t status;
cd = (void*)Riconv_open(cidfont->encoding,
(enc == CE_UTF8) ? "UTF-8": "");
if(cd == (void*)-1) return;
R_CheckStack2(buflen);
unsigned char buf[buflen];
i_buf = (char *)str;
o_buf = (char *)buf;
i_len = strlen(str); /* no terminator,
as output a byte at a time */
nb = o_len = buflen;
status = Riconv(cd, &i_buf, (size_t *)&i_len,
(char **)&o_buf, (size_t *)&o_len);
Riconv_close(cd);
if(status == (size_t)-1)
warning(_("failed in text conversion to encoding '%s'"),
cidfont->encoding);
else {
unsigned char *p;
PDF_SetFill(gc->col, dd);
fprintf(pd->pdffp,
"/F%d 1 Tf %.2f %.2f %.2f %.2f %.2f %.2f Tm <",
PDFfontNumber(gc->fontfamily, face, pd),
a, b, bm, a, x, y);
for(i = 0, p = buf; i < nb - o_len; i++)
fprintf(pd->pdffp, "%02x", *p++);
fprintf(pd->pdffp, "> Tj\n");
}
return;
} else {
warning(_("invalid string in '%s'"), "PDF_Text");
return;
}
}
PDF_SetFill(gc->col, dd);
fprintf(pd->pdffp, "/F%d 1 Tf %.2f %.2f %.2f %.2f %.2f %.2f Tm ",
PDFfontNumber(gc->fontfamily, face, pd),
a, b, bm, a, x, y);
if((enc == CE_UTF8 || mbcslocale) && !strIsASCII(str) && face < 5) {
/* face 5 handled above */
R_CheckStack2(strlen(str)+1);
buff = alloca(strlen(str)+1); /* Output string cannot be longer */
mbcsToSbcs(str, buff, PDFconvname(gc->fontfamily, pd), enc);
str1 = buff;
} else str1 = str;
if (pd->useKern &&
isType1Font(gc->fontfamily, PDFFonts, pd->defaultFont)) {
PDFWriteT1KerningString(pd->pdffp, str1,
PDFmetricInfo(gc->fontfamily, face, pd), gc);
} else{
PostScriptWriteString(pd->pdffp, str1, strlen(str1));
fprintf(pd->pdffp, " Tj\n");
}
textoff(pd); /* added in 2.8.0 */
}
static void PDF_Text(double x, double y, const char *str,
double rot, double hadj,
const pGEcontext gc,
pDevDesc dd)
{
PDF_Text0(x, y, str, CE_NATIVE, rot, hadj, gc, dd);
}
static void PDF_TextUTF8(double x, double y, const char *str,
double rot, double hadj,
const pGEcontext gc,
pDevDesc dd)
{
PDF_Text0(x, y, str, CE_UTF8, rot, hadj, gc, dd);
}
static FontMetricInfo
*PDFCIDsymbolmetricInfo(const char *family, PDFDesc *pd)
{
FontMetricInfo *result = NULL;
if (strlen(family) > 0) {
int dontcare;
/*
* Find the family in pd->cidfonts
*/
cidfontfamily fontfamily = findDeviceCIDFont(family,
pd->cidfonts,
&dontcare);
if (fontfamily)
result = &(fontfamily->symfont->metrics);
else {
/*
* Try to load the font
*/
fontfamily = addCIDFont(family, 1);
if (fontfamily) {
if (addPDFDeviceCIDfont(fontfamily, pd, &dontcare)) {
result = &(fontfamily->symfont->metrics);
} else {
fontfamily = NULL;
}
}
}
if (!fontfamily)
error(_("failed to find or load PDF CID font"));
} else {
result = &(pd->cidfonts->cidfamily->symfont->metrics);
}
return result;
}
static FontMetricInfo
*PDFmetricInfo(const char *family, int face, PDFDesc *pd)
{
FontMetricInfo *result = NULL;
if (strlen(family) > 0) {
int dontcare;
/*
* Find the family in pd->fonts
*/
type1fontfamily fontfamily = findDeviceFont(family, pd->fonts,
&dontcare);
if (fontfamily)
result = &(fontfamily->fonts[face-1]->metrics);
else {
/*
* Check whether the font is loaded and, if not,
* load it.
*/
fontfamily = findLoadedFont(family,
pd->encodings->encoding->encpath,
TRUE);
if (!fontfamily) {
fontfamily = addFont(family, TRUE, pd->encodings);
}
/*
* Once the font is loaded, add it to the device's
* list of fonts.
*/
if (fontfamily) {
int dontcare;
if (addPDFDevicefont(fontfamily, pd, &dontcare)) {
result = &(fontfamily->fonts[face-1]->metrics);
} else {
fontfamily = NULL;
}
}
}
if (!fontfamily)
error(_("failed to find or load PDF font"));
} else {
result = &(pd->fonts->family->fonts[face-1]->metrics);
}
return result;
}
static char
*PDFconvname(const char *family, PDFDesc *pd)
{
char *result = (pd->fonts) ? pd->fonts->family->encoding->convname : "latin1";
/* pd->fonts is NULL when CIDfonts are used */
if (strlen(family) > 0) {
int dontcare;
/*
* Find the family in pd->fonts
*/
type1fontfamily fontfamily = findDeviceFont(family, pd->fonts,
&dontcare);
if (fontfamily)
result = fontfamily->encoding->convname;
else {
/*
* Check whether the font is loaded and, if not,
* load it.
*/
fontfamily = findLoadedFont(family,
pd->encodings->encoding->encpath,
TRUE);
if (!fontfamily) {
fontfamily = addFont(family, TRUE, pd->encodings);
}
/*
* Once the font is loaded, add it to the device's
* list of fonts.
*/
if (fontfamily) {
int dontcare;
if (addPDFDevicefont(fontfamily, pd, &dontcare)) {
result = fontfamily->encoding->convname;
} else {
fontfamily = NULL;
}
}
}
if (!fontfamily)
error(_("failed to find or load PDF font"));
}
return result;
}
double PDF_StrWidth(const char *str,
const pGEcontext gc,
pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
if(gc->fontface < 1 || gc->fontface > 5) gc->fontface = 1;
if (isType1Font(gc->fontfamily, PDFFonts, pd->defaultFont)) {
return floor(gc->cex * gc->ps + 0.5) *
PostScriptStringWidth((const unsigned char *)str, CE_NATIVE,
PDFmetricInfo(gc->fontfamily,
gc->fontface, pd),
pd->useKern, gc->fontface,
PDFconvname(gc->fontfamily, pd));
} else { /* cidfont(gc->fontfamily) */
if (gc->fontface < 5) {
return floor(gc->cex * gc->ps + 0.5) *
PostScriptStringWidth((const unsigned char *)str, CE_NATIVE,
NULL, FALSE, gc->fontface, NULL);
} else {
return floor(gc->cex * gc->ps + 0.5) *
PostScriptStringWidth((const unsigned char *)str, CE_NATIVE,
PDFCIDsymbolmetricInfo(gc->fontfamily,
pd),
FALSE, gc->fontface, NULL);
}
}
}
static double PDF_StrWidthUTF8(const char *str,
const pGEcontext gc,
pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
int face = gc->fontface;
if(gc->fontface < 1 || gc->fontface > 5) gc->fontface = 1;
if (isType1Font(gc->fontfamily, PDFFonts, pd->defaultFont)) {
return floor(gc->cex * gc->ps + 0.5) *
PostScriptStringWidth((const unsigned char *)str, CE_UTF8,
PDFmetricInfo(gc->fontfamily,
gc->fontface, pd),
pd->useKern, gc->fontface,
PDFconvname(gc->fontfamily, pd));
} else { /* cidfont(gc->fontfamily) */
if (face < 5) {
return floor(gc->cex * gc->ps + 0.5) *
PostScriptStringWidth((const unsigned char *)str, CE_UTF8,
NULL, FALSE, gc->fontface, NULL);
} else {
return floor(gc->cex * gc->ps + 0.5) *
PostScriptStringWidth((const unsigned char *)str, CE_UTF8,
PDFCIDsymbolmetricInfo(gc->fontfamily,
pd),
FALSE, gc->fontface, NULL);
}
}
}
void PDF_MetricInfo(int c,
const pGEcontext gc,
double* ascent, double* descent,
double* width, pDevDesc dd)
{
PDFDesc *pd = (PDFDesc *) dd->deviceSpecific;
int face = gc->fontface;
if(gc->fontface < 1 || gc->fontface > 5) gc->fontface = 1;
if (isType1Font(gc->fontfamily, PDFFonts, pd->defaultFont)) {
PostScriptMetricInfo(c, ascent, descent, width,
PDFmetricInfo(gc->fontfamily,
gc->fontface, pd),
face == 5, PDFconvname(gc->fontfamily, pd));
} else { /* cidfont(gc->fontfamily) */
if (face < 5) {
PostScriptCIDMetricInfo(c, ascent, descent, width);
} else {
PostScriptMetricInfo(c, ascent, descent, width,
PDFCIDsymbolmetricInfo(gc->fontfamily, pd),
TRUE, "");
}
}
*ascent = floor(gc->cex * gc->ps + 0.5) * *ascent;
*descent = floor(gc->cex * gc->ps + 0.5) * *descent;
*width = floor(gc->cex * gc->ps + 0.5) * *width;
}
/* PostScript Device Driver Parameters:
* ------------------------
* file = output filename
* paper = paper type
* family = typeface = "family"
* encoding = char encoding file name
* cidfamily = char encoding file name for CID fonts
* bg = background color
* fg = foreground color
* width = width in inches
* height = height in inches
* horizontal = {TRUE: landscape; FALSE: portrait}
* ps = pointsize
* onefile = {TRUE: normal; FALSE: single EPSF page}
* pagecentre = centre plot region on paper?
* printit = 'print' after closing device?
* command = 'print' command
* title = character string
* fonts
* colorModel
* useKerning
* fillOddEven
*/
SEXP PostScript(SEXP args)
{
pGEDevDesc gdd;
const void *vmax;
const char *file, *paper, *family=NULL, *bg, *fg, *cmd;
const char *afms[5];
const char *encoding, *title, call[] = "postscript", *colormodel;
int i, horizontal, onefile, pagecentre, printit, useKern;
double height, width, ps;
SEXP fam, fonts;
Rboolean fillOddEven;
vmax = vmaxget();
args = CDR(args); /* skip entry point name */
file = translateChar(asChar(CAR(args))); args = CDR(args);
paper = CHAR(asChar(CAR(args))); args = CDR(args);
/* 'family' can be either one string or a 5-vector of afmpaths. */
fam = CAR(args); args = CDR(args);
if(length(fam) == 1)
family = CHAR(asChar(fam));
else if(length(fam) == 5) {
if(!isString(fam)) error(_("invalid 'family' parameter in %s"), call);
family = "User";
for(i = 0; i < 5; i++) afms[i] = CHAR(STRING_ELT(fam, i));
} else
error(_("invalid 'family' parameter in %s"), call);
encoding = CHAR(asChar(CAR(args))); args = CDR(args);
bg = CHAR(asChar(CAR(args))); args = CDR(args);
fg = CHAR(asChar(CAR(args))); args = CDR(args);
width = asReal(CAR(args)); args = CDR(args);
height = asReal(CAR(args)); args = CDR(args);
horizontal = asLogical(CAR(args));args = CDR(args);
if(horizontal == NA_LOGICAL)
horizontal = 1;
ps = asReal(CAR(args)); args = CDR(args);
onefile = asLogical(CAR(args)); args = CDR(args);
pagecentre = asLogical(CAR(args));args = CDR(args);
printit = asLogical(CAR(args)); args = CDR(args);
cmd = CHAR(asChar(CAR(args))); args = CDR(args);
title = translateChar(asChar(CAR(args))); args = CDR(args);
fonts = CAR(args); args = CDR(args);
if (!isNull(fonts) && !isString(fonts))
error(_("invalid 'fonts' parameter in %s"), call);
colormodel = CHAR(asChar(CAR(args))); args = CDR(args);
useKern = asLogical(CAR(args)); args = CDR(args);
if (useKern == NA_LOGICAL) useKern = 1;
fillOddEven = asLogical(CAR(args));
if (fillOddEven == NA_LOGICAL)
error(_("invalid value of '%s'"), "fillOddEven");
R_GE_checkVersionOrDie(R_GE_version);
R_CheckDeviceAvailable();
BEGIN_SUSPEND_INTERRUPTS {
pDevDesc dev;
if (!(dev = (pDevDesc) calloc(1, sizeof(DevDesc))))
return 0;
if(!PSDeviceDriver(dev, file, paper, family, afms, encoding, bg, fg,
width, height, (double)horizontal, ps, onefile,
pagecentre, printit, cmd, title, fonts,
colormodel, useKern, fillOddEven)) {
/* we no longer get here: error is thrown in PSDeviceDriver */
error(_("unable to start %s() device"), "postscript");
}
gdd = GEcreateDevDesc(dev);
GEaddDevice2(gdd, "postscript");
} END_SUSPEND_INTERRUPTS;
vmaxset(vmax);
return R_NilValue;
}
/* XFig Device Driver Parameters:
* ------------------------
* file = output filename
* paper = paper type
* family = typeface = "family"
* bg = background color
* fg = foreground color
* width = width in inches
* height = height in inches
* horizontal = {TRUE: landscape; FALSE: portrait}
* ps = pointsize
* onefile = {TRUE: normal; FALSE: single EPSF page}
* pagecentre = centre plot region on paper?
* defaultfont = {TRUE: use xfig default font; FALSE: use R font}
* textspecial = {TRUE: use textspecial; FALSE: use standard font}
*
* encoding
*/
SEXP XFig(SEXP args)
{
pGEDevDesc gdd;
const void *vmax;
const char *file, *paper, *family, *bg, *fg, *encoding;
int horizontal, onefile, pagecentre, defaultfont, textspecial;
double height, width, ps;
vmax = vmaxget();
args = CDR(args); /* skip entry point name */
file = translateChar(asChar(CAR(args))); args = CDR(args);
paper = CHAR(asChar(CAR(args))); args = CDR(args);
family = CHAR(asChar(CAR(args))); args = CDR(args);
bg = CHAR(asChar(CAR(args))); args = CDR(args);
fg = CHAR(asChar(CAR(args))); args = CDR(args);
width = asReal(CAR(args)); args = CDR(args);
height = asReal(CAR(args)); args = CDR(args);
horizontal = asLogical(CAR(args));args = CDR(args);
if(horizontal == NA_LOGICAL)
horizontal = 1;
ps = asReal(CAR(args)); args = CDR(args);
onefile = asLogical(CAR(args)); args = CDR(args);
pagecentre = asLogical(CAR(args));args = CDR(args);
defaultfont = asLogical(CAR(args)); args = CDR(args);
textspecial = asLogical(CAR(args)); args = CDR(args);
encoding = CHAR(asChar(CAR(args)));
R_GE_checkVersionOrDie(R_GE_version);
R_CheckDeviceAvailable();
BEGIN_SUSPEND_INTERRUPTS {
pDevDesc dev;
if (!(dev = (pDevDesc) calloc(1, sizeof(DevDesc))))
return 0;
if(!XFigDeviceDriver(dev, file, paper, family, bg, fg, width, height,
(double) horizontal, ps, onefile, pagecentre, defaultfont, textspecial,
encoding)) {
/* we no longer get here: error is thrown in XFigDeviceDriver */
error(_("unable to start %s() device"), "xfig");
}
gdd = GEcreateDevDesc(dev);
GEaddDevice2(gdd, "xfig");
} END_SUSPEND_INTERRUPTS;
vmaxset(vmax);
return R_NilValue;
}
/* PDF Device Driver Parameters:
* ------------------------
* file = output filename
* paper = paper type
* family = typeface = "family"
* encoding = char encoding file name
* cidfamily = char encoding file name for CID fonts
* bg = background color
* fg = foreground color
* width = width in inches
* height = height in inches
* ps = pointsize
* onefile = {TRUE: normal; FALSE: single page per file}
* title
* fonts
* versionMajor
* versionMinor
* colormodel
* useDingbats
* forceLetterSpacing
* fillOddEven
*/
SEXP PDF(SEXP args)
{
pGEDevDesc gdd;
const void *vmax;
const char *file, *paper, *encoding, *family = NULL /* -Wall */,
*bg, *fg, *title, call[] = "PDF", *colormodel;
const char *afms[5];
double height, width, ps;
int i, onefile, pagecentre, major, minor, dingbats, useKern, useCompression;
SEXP fam, fonts;
Rboolean fillOddEven;
vmax = vmaxget();
args = CDR(args); /* skip entry point name */
if (isNull(CAR(args)))
file = NULL;
else
file = translateChar(asChar(CAR(args))); args = CDR(args);
paper = CHAR(asChar(CAR(args))); args = CDR(args);
fam = CAR(args); args = CDR(args);
if(length(fam) == 1)
family = CHAR(asChar(fam));
else if(length(fam) == 5) {
if(!isString(fam)) error(_("invalid 'family' parameter in %s"), call);
family = "User";
for(i = 0; i < 5; i++) afms[i] = CHAR(STRING_ELT(fam, i));
} else
error(_("invalid 'family' parameter in %s"), call);
encoding = CHAR(asChar(CAR(args))); args = CDR(args);
bg = CHAR(asChar(CAR(args))); args = CDR(args);
fg = CHAR(asChar(CAR(args))); args = CDR(args);
width = asReal(CAR(args)); args = CDR(args);
height = asReal(CAR(args)); args = CDR(args);
ps = asReal(CAR(args)); args = CDR(args);
onefile = asLogical(CAR(args)); args = CDR(args);
pagecentre = asLogical(CAR(args));args = CDR(args);
title = translateChar(asChar(CAR(args))); args = CDR(args);
fonts = CAR(args); args = CDR(args);
if (!isNull(fonts) && !isString(fonts))
error(_("invalid 'fonts' parameter in %s"), call);
major = asInteger(CAR(args)); args = CDR(args);
minor = asInteger(CAR(args)); args = CDR(args);
colormodel = CHAR(asChar(CAR(args))); args = CDR(args);
dingbats = asLogical(CAR(args)); args = CDR(args);
if (dingbats == NA_LOGICAL) dingbats = 1;
useKern = asLogical(CAR(args)); args = CDR(args);
if (useKern == NA_LOGICAL) useKern = 1;
fillOddEven = asLogical(CAR(args)); args = CDR(args);
if (fillOddEven == NA_LOGICAL)
error(_("invalid value of '%s'"), "fillOddEven");
useCompression = asLogical(CAR(args)); args = CDR(args);
if (useCompression == NA_LOGICAL)
error(_("invalid value of '%s'"), "useCompression");
R_GE_checkVersionOrDie(R_GE_version);
R_CheckDeviceAvailable();
BEGIN_SUSPEND_INTERRUPTS {
pDevDesc dev;
if (!(dev = (pDevDesc) calloc(1, sizeof(DevDesc))))
return 0;
if(!PDFDeviceDriver(dev, file, paper, family, afms, encoding, bg, fg,
width, height, ps, onefile, pagecentre,
title, fonts, major, minor, colormodel,
dingbats, useKern, fillOddEven,
useCompression)) {
/* we no longer get here: error is thrown in PDFDeviceDriver */
error(_("unable to start %s() device"), "pdf");
}
gdd = GEcreateDevDesc(dev);
GEaddDevice2(gdd, "pdf");
} END_SUSPEND_INTERRUPTS;
vmaxset(vmax);
return R_NilValue;
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,189 |
Off-Topic General Discussion NO iDEVICE HELP QUESTIONS IN HERE!
New Members Come Introduce Yourself in Here.
Which games do you play on your mobile phone?
Looking for games related ICO projects!
sexual health affected by energy drinks??
Totally Stupid but really funny JB song.
How Can I transfer data from iphone 4S to Iphone X?
business modem for residential service?? | {
"redpajama_set_name": "RedPajamaC4"
} | 4,262 |
Company Week Cover Story
by legacyzoom@gmail.com | Sep 5, 2019 | Media
Owner and CEO Katie Hedrick expects sales at her family-run manufacturing company to top $1 million in 2017.
Successful businesses are more often than not built on strong partnerships. In the case of Colorado Tech Shop, it's the cooperative collaboration between Hedrick and her husband, Iain Ramsay, the company's president, forming that foundation.
"I have been an entrepreneur since I was 20," Hedrick explains. "And Iain has over a decade of experience in operations management and manufacturing. Together, we have the perfect melding of skills. While I excel at the big picture and have been great at steering the ship towards our long-range goals, he is the perfect first mate and excels at all the day-to-day minutiae that makes a company run smoothly."
And Colorado Tech Shop is certainly running smoothly. Since the company's founding in 2015, Hedrick and her team have tripled their staff, doubled their factory and office space, and moved from Boulder to Longmont.
"The rent is vastly cheaper here than in Boulder," Hedrick says of their 4,800-square-foot facility on the south side of Longmont. "Plus, it has really become a hotbed for manufacturing and innovation. We now feel that we're right in the middle of the action."
As an all-inclusive shop offering engineering and design work, board layout, prototyping, and full assembly as well as fulfillment, warranty, inspection, and shipping, there's plenty of action to be found. Hedrick estimates that manufacturing makes up more than 50 percent of the company's business, but the specific services requested by each customer depends on the maturity of their organization. "If the customer's business is more mature, we do more manufacturing work," she explains. "If the business is a lot younger, we might be doing more design work, prototyping and things like that."
The healthcare industry is currently Colorado Tech Shop's biggest source of customers. However, they're also making a splash within the cannabis industry — they manufacture ExtractCraft's extraction machine — and the entertainment industry. "We have a client that makes a product for the 10-pin bowling industry," says Hedrick, noting that she hopes to do more work with companies within the wearable technology industry this year.
"We're starting to specialize in it and want to make wearable technology a much bigger part of our business," she says. "I think it's a huge, up-and-coming industry that will become really popular. Right now, we're in the process of working with a company that makes smart clothing. The circuitry is built right into the fabric."
She expects Colorado Tech Shop's sales to exceed $1 million in 2017 and says the market for their services is growing because "The hunger for American-made products is increasing and sourcing local is becoming really important to a lot of people."
Some of the company's customers are actually reshoring manufacturing after overseas disappointments. "It's a whole different ballgame to deal with Chinese manufacturers when you don't know if they're subbing out important parts and it takes so long to get the product here," she explains.
"Then, if something is wrong, it's a big deal to fix it. When they work with us, it's so much easier. We talk customers through every step of the process, have an open-door policy and, because of our unique size, we have the ability to change things on the fly, do so quickly, and do so cost-effectively."
And there's also appeal based on the bottom line, she adds. "We run a pretty lean operation, which means we don't have a big overhead and can pass those savings on to the customer. While we can't compete with China, obviously, we're not that far off — and you don't have the headache of manufacturing overseas."
Challenges: "I'm sure every company says this, but finding the right staff is one of our biggest challenges," Hedrick says. "And it's not just finding staff with the particular skills we need, but also people who meld well with the rest of the team." Colorado Tech Shop tripled the size of its staff in its first eight months of business, and Hedrick expects to add at least three more employees in 2017.
"Our office culture really sets us apart as a company to work for," she continues. "We make sure employees know that they're valued and appreciated, and we want to build a strong team that feels like family. Happy employees are going to be loyal and do their best for you. Our current team is amazing in that way. They'll stay extra or come in early at the drop of a hat. They're really dedicated."
Opportunities: Hedrick and her team are currently working to form a business partnership that will enable them to develop their own product for sale. "It's going to be an electronic sports target that uses ultrasonic and laser technology to actually pinpoint the location where the bullet passes through," she explains. "We see it as new technology that can be used for training law enforcement and even in sports-shooting competitions and at shooting ranges."
Additionally, Colorado Tech Shop is beginning to put infrastructure in place to create their own business accelerator. "This will involve creating a framework and network of people so that we can bring new inventors and entrepreneurs on board and offer them everything from legal counseling and marketing to manufacturing," Hedrick explains. She's already forging connections with accelerators and incubators in Longmont and the surrounding area. "It's going to be a great opportunity because we'll get to help people starting from the very beginning and moving on to the development, prototyping, and manufacturing of new products."
Needs: "We know we need to invest in a second pick-and-place machine soon," Hedrick muses. "Ours is running full-time right now. And we also need another reflow oven. We've joked about having a keg and beer tap added to our office. And a fireman's pole would be really fun!"
3 Days & Times You're Available
# of People Attending
Type of Project Type of Project Product Design PCBA Proto Box Build
Project Deadline
Notes on Budget
1500 Kansas Avenue Building 3, Suites D-F
Longmont, CO 80501 1500 Kansas Avenue Building 3, Suites D-F Longmont, CO 80501
contact@coloradotechshop.com
8am - 5pm M - Th
About Services Media Contact
Download CTS Brochure
Certifcations
Let's Build Together
Product Design PCBA Proto Box Build | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,142 |
Diese Liste zeigt die Wappen der Samtgemeinden, Gemeinden und vormals selbstständigen Gemeinden im Landkreis Grafschaft Bentheim in Niedersachsen.
Samtgemeindewappen
Wappen der Städte und Gemeinden
Folgende Gemeinden führen kein Wappen:
Wappen ehemaliger Gemeinden
Bentheim
Wappen
Bentheim
Wappen Bentheim | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,638 |
Q: Is there a way to extract the 'NAME of the company' 'TITLE of the job' and 'LOCATION of the job' from each line of string below From each line of string below, I want to extract company name, job title and location of the job. Is there a way to do so? as the pattern is not consistent. Thanks.
"Jerry (YC S17) Is Hiring Senior Software Dev, Data Engineer (Toronto/Remote)"
"Iris Automation Is Hiring an Account Executive for B2B Flying Vehicle Software"
"Strikingly (YC W13) is hiring in our Shanghai office"
"BuildZoom (YC W13) is hiring help make remodeling cheaper"
"EquipmentShare (YC W15) Is Looking for an Experienced React Native Dev"
"Saleswhale (YC S16) AI Assistant Startup Is Hiring Customer Success Managers"
"Streak (YC S11) is profitable, well funded and hiring in Vancouver"
"Tesorio (YC S15) Is Hiring Engineering Managers, Senior Python Engineer"
"Checkr (YC S14) is hiring engineers to build the future of online trust"
"Rescale Is Hiring a Senior DevOps Engineer in San Francisco"
"Tremendous.com is hiring its first engineer"
"Remix is looking for a front-end engineer to help build better public transit"
"Atomwise (YC W15) Is Hiring a Senior Machine Learning Research Scientist in SF"
"Confident Cannabis (YC S15) Is Hiring Engineers"
"WaystoCap (YC W17) is hiring a software engineer in Spain"
"Smarking (YC W15) Is Hiring a Customer Service Manager"
"Sunsama (YC W19) Is Hiring a Senior Full Stack Engineer (RN/GraphQL/Node)"
"Pachyderm Raised $10M and Is Looking for a Senior Full-Stack Engineer"
"Picktrace (YC S15) is hiring a senior Android engineer"
"Segment is hiring engineers to create our developer platform"
"XIX Is Hiring a Senior Front End Engineer"
"Athelas (YC S16) is hiring software engineers"
"Dyneti (YC W19) is hiring software engineers"
"ZeroCater (YC W11) Is Hiring a Principal Engineer in SF: Must Love Food"
"Mux is looking for developers who want to help developers build better video"
"Munich, Germany: Demodesk (YC W19) Is Hiring Software Engineers"
"New Story (YC Nonprofit) Hiring a JavaScript Software Engineer"
"Quit Genius (YC W18) Is Hiring a Product Manager in London"
"Flexport is hiring senior engineers in SF Come get to know us"
"OneSignal Is Hiring Ruby on Rails and DevOps Engineers in San Mateo"
************* This is what I want **************
Example 1
"Jerry (YC S17) Is Hiring Senior Software Dev, Data Engineer (Toronto/Remote)"
Company Name: Jerry
Job Title: Senior Software Dev, Data Engineer
Location: Toronto/Remote
Example 2
"Remix is looking for a front-end engineer to help build better public transit"
Company Name: Remix
Job Title: front-end engineer
Location:
Example 3
"Munich, Germany: Demodesk (YC W19) Is Hiring Software Engineers"
Company Name: Demodesk
Job Title: Software engineer
Location: Munich, Germany
A: *
*Gather a large corpus of examples such as these. 100,000 or so would probably do, but if you can get a million samples, that would be better.
*Split them manually. If you can afford it, it will be much faster if you distribute the work out to interns/mechanical turk/etc.
*Train a ML model on your dataset. Don't forget to take a random selection of samples for training/testing. Aim for upwards of 90% accuracy, but also try not to overfit your data.
A: As per my knowledge, if the pattern is not consistent than we can not extract and fetch data from the any string.
its can be only done by human being as they have understanding skill, or you need to implement ML.
A: We can use this models SPACY, CRF, StanfordNLP and LSTM easily. Train 70% and test on 30% data. I prefer Bidirectional-LSTM is best for this.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,138 |
Do you already have basic knowledge of wine, or are you a professional in the restaurant industry? One of the few specialized wine training programs offered in French in Canada, the Découverte du vin 1 (Wine Discovery 1) program will teach you the basics of French winemaking and how to make excellent wine and food pairings.
Thanks to advice from experienced professors and through many tastings and sessions with wine producers, wine consultants and restaurant staff can improve their wine recommendations and soundly guide customers in their wine choices. The relevance and quality of this program make it a gateway to an exciting career. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,945 |
Published 04/19/2019 02:19:55 pm at 04/19/2019 02:19:55 pm in Best Ratchet Screwdriver.
best ratchet screwdriver universal metal hose ratchet screwdriver handle 180 degree rotation screwdriver with bits multi function combo 3 ratchet screwdriver screwdriver best stubby ratchet screwdriver craftsman.
best ratchet screwdriver ukc,best quality ratchet screwdriver snap-on,best ratchet screwdriver kit,best stubby ratchet screwdriver set,best ratchet screwdriver ukulele,best stubby ratchet screwdriver as seen on tv,best ratchet screwdriver uke,best stubby ratchet screwdriver review,best quality ratchet screwdriver mechanism,best quality ratchet screwdriver,best ratchet screwdriver 2018 ford. | {
"redpajama_set_name": "RedPajamaC4"
} | 290 |
package org.apache.causeway.core.metamodel.facets.value.semantics;
import java.time.format.FormatStyle;
import java.util.Optional;
import org.apache.causeway.applib.annotation.ValueSemantics;
import org.apache.causeway.core.metamodel.facetapi.FacetHolder;
import org.apache.causeway.core.metamodel.facets.objectvalue.temporalformat.TimeFormatStyleFacet;
import org.apache.causeway.core.metamodel.facets.objectvalue.temporalformat.TimeFormatStyleFacetAbstract;
public class TimeFormatStyleFacetFromValueSemanticsAnnotation
extends TimeFormatStyleFacetAbstract {
public static Optional<TimeFormatStyleFacet> create(
final Optional<ValueSemantics> valueSemanticsIfAny,
final FacetHolder holder) {
return valueSemanticsIfAny
.map(ValueSemantics::timeFormatStyle)
.map(timeFormatStyle->
new TimeFormatStyleFacetFromValueSemanticsAnnotation(timeFormatStyle, holder));
}
private TimeFormatStyleFacetFromValueSemanticsAnnotation(
final FormatStyle timeFormatStyle, final FacetHolder holder) {
super(timeFormatStyle, holder);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,694 |
The Church without a Protector
Without a Christian king to defend Her - a King Ælfred, Prince Vladimir, etc. - the Church is at the mercy of her enemies, just as she was in her infancy before the first Christian Emperor, Constantine the Great.
Father Andrew Phillips's essay on the conflict between Orthodox Christian Greece and the EU, 'The Fate of Christian Europe Hangs in the Balance in Greece' (posted 30 Dec. 2013), offers yet more striking proof of this, and is something all Christians in the Western world (including the South) should pay careful attention to. For we may soon come under the same persecution for our faith, so long as the godless, corporate-bankster Elite are in power in the Western nations, so long as we reject the monarchic principle in government for a national democracy, which weakens, not strengthens, the powers of good in a country.
Greece had the misfortune of being the first Orthodox country to be betrayed by its political elite and sold for a mess of pottage to the EU. Current events in Greece point to the fate that awaits all the other Orthodox countries, Cyprus, Bulgaria, Romania and others, which have already taken or still in their folly wish to take, that same path of apostasy. Thus:
Greece's international creditors are setting it ever more anti-Christian ultimatums: it has been decreed by EU order that priests must no longer visit schools and groups of school pupils have been banned from attending services; Sundays will now be desecrated and businesses opened; priests have lost 20% of their paid leave; the number of ordinations allowed has been cut; the mention of religion has been removed from passports; a mosque must be built in Athens; certain Church properties may be privatised or else auctioned off by order of EU bureaucrats and their atheist quislings in the Greek government; laws on 'free unions' and others forbidding 'insulting language', the latter including calls to patriotism and quotations from the Gospels, are under discussion.
Little wonder that some bishops are preparing their flock to 'to resist Antichrist' in a new wave of persecution. Metropolitan Nicholas of Phtiotidis has spoken clearly of a possible popular revolt. Metropolitan Kosmas has said that if the law on same sex unions is passed, then the people must protest and become confessors of Christ. Like the Patriarchate of Antioch in Syria, today the Church of Greece has to stop compromising the Faith and stand up and be counted. The easy, consumerist times of previous years, when decadent practices were introduced from Western Europe and gradually everything was allowed – the Catholic calendar was introduced, the Liturgy was abbreviated, confession before communion was no longer obligatory, seating was introduced in all the churches, little girls were allowed to serve in the altar – are over. In reality the Church is not Consumerism, for the Church is the ascetic principle, not the rationalist and secularist one.
Greeks are finally waking up to the fact that their obsessive dream of 'Europe' has turned out to be a nightmare – just as their ignored monastic elders had forewarned. A wave of new barbarianism, this time of the liberal sort, is unfurling on Greece and massive immigration is destroying what remains of the local, Orthodox way of life and culture. Greece is entering the spiritual winter of Western Europe, as anti-EU Greek politicians are removed by 'auditors' from Brussels, Berlin and Paris. Only the Church of Greece remains independent from EU tyranny. Metropolitan Seraphim of Piraeus has threatened to excommunicate any politician who votes for laws which trample underfoot traditional moral standards. Many Church figures are finally asking that Greece leave the EU. It is no longer an economic struggle, but a spiritual, moral and cultural one.
Resistance now is vital for the future of European history. Given the apostasy of Protestants (and they are often in the forefront of the new decadence in any case) and the open abandonment of the Christian cause by most Roman Catholics (they see the EU has a pro-Cathoolic project and its flag as a Catholic banner), the struggle for Christ against those who are preparing the coming of Antichrist is now concentrated on the Orthodox world. Orthodox resistance to the Babylon of Brussels and its globalist 'liberal' project may be severely repressed, individual bishops and theologians may be 'removed', using contemporary technological controls. Other Local Orthodox Churches, already compromised by calendar change, should look carefully – they will be next to have to submit to the 'New World Order', that is, the restoration of the Old Pagan Order.
Resistance by Greece to the ethnocentric atheism of Western Europe is vital. Geopolitically, Greece is the key. If it falls, then the rest of the Balkans will also fall. And the EU tyrants know this. For if Greece is after all corageous and does choose freedom from the EU, then all the Balkans will also look north to Russia and the developing Eurasian Union, as the German Foreign Minister Joschka Fischer has already pointed out and as was evident when bankrupt Cyprus almost chose Russia instead of the EU to come to its rescue.
Let us pray for courage in the Church of Greece.
Source: http://www.events.orthodoxengland.org.uk/the-fate-of-christian-europe-hangs-in-the-balance-in-greece/, accessed 13 Jan. 2014. Reprinted in full with the kind permission of the author.
Remembering Lee - III
Satanic Acts at the Grammys?
An Urgent Plea from the Tenth Amendment Center
Remembering Lee - II
Remembering Lee
' . . . large-scale, uncontrolled experiment . . ....
Tradition and Self-Denial
True Christian Culture
A Time for Choosing
Wisdom from an African Saint
Northern Racism
Beyond Agrarianism
Getting Off to a Good Start | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,566 |
\section{Introduction}
CLIC~\cite{clicrep2000} is based on a two-beam scheme in which the rf power used to accelerate the main beam (at 12 GHz) is produced by a second beam (the drive beam, DB) running parallel to the main one~\cite{braun98} through so-called Power Extraction and Transfer Structure (PETS). This drive beam has a high current but relatively low energy and is decelerated for producing the rf power.
The CLIC Drive Beam Linac (DBL) will consist of about 750 structures which are low frequency (1 GHz) and will be almost fully loaded transferring more than 95\% of their input power to the beam. The average energy gain per structure will be $\Delta E \approx 3.4$ MeV~\cite{personal_com}. The initial beam energy is assumed to be $E_{0} =50$ MeV, the final beam energy $E_{f} =2.4$ GeV, the bunch charge $q =$ 8.4 nC, initial bunch length $\sigma_{z,0} = 3$ mm and the transverse normalized emittances are $\epsilon_{N,x} =\epsilon_{N,y}=50~\mu$m \cite{clicparms}. The beam pulse consists of 24 $\times$ 24 sub-trains of about 120 bunches each. The first sub-train fills odd buckets, the immediately following second sub-train fills even buckets; this pattern is then repeated. After DBL, 24 sub-trains will be merged into a signle sub-train using delay loop (DL), combiner ring one (CR1) and combiner ring two (CR2)\cite{clicparms}. At the end of CLIC DB complex initial train with 140 $\mu$s length will be transformed to 24 trains, each has 240 ns and 100 A pulse current.
In this study, we discuss major transverse instabilities driven by wakefields in accelerating sections based on different lattice types. The linac will be seperated into two section with a bunch compressor which reduces the initial bunch length $\sigma_{z,0} = 3$ mm to the final value of $\sigma_{z,f} = 1$ mm. In order to define longitudinal tolerances four different bunch compressor have been taken into account with neglecting the imperfections on bunch compressor sections. Also coherent synchrotron radiation has not been included. Additionally, in all calculations we have used simulation code PLACET \cite{schulte_placet} and we have taken into account only two sub-trains 15 bunches each. As it is seen later, the multi-bunch effects reach steady state condition within this length for a sub-train.
\subsection{ Layout of DBL }{\label{sec:layout}}
In CLIC 1\% luminosity loss requires $\delta\sigma_{\phi}\le 0.2^{\circ}$ bunch phase and $\delta\sigma_{z}\le 1~\%$ bunch length jitter in the PETS \cite{schulte_phase,eadli}. Therefore bunch energy jitter and bunch phase-length coupling in DBL are of concern. If the full bunch compression is performed in front of PETS one needs $R_{56} \approx -60$ cm for a chirp of 0.5\% energy spread per $3$ mm bunch length. In that case, for getting acceptable beam phase jitter one would need $3 \times 10^{-5}$ beam energy jitter. In order to avoid the strong coupling between energy jitter induced in the drive beam accelerator and beam phase jitter transformed in the bunch compressor, we propose that the bunches are accelerated to 300 MeV in first stage of drive beam linac (DBL1) and compressed from 3 mm to length of 1 mm, which is the length required in PETS, and then accelerated to their final energy of $E_{f} =2.4$GeV (see Fig. \ref{fig:dbalayout}).
\begin{figure}[]
\begin{center}
\includegraphics[width=0.8\columnwidth]{f1_baseline}
\caption{\label{fig:dbalayout} Basic layout of CLIC drive beam linac }
\end{center}
\end{figure}
\subsection{ Accelerating Structure
\begin{wrapfigure}{r}{0.55\columnwidth}
\centerline{\includegraphics[width=0.5\columnwidth]{f2_3mm_wks}}
\caption{\label{fig:wakes} Wake potentials of a Gaussian bunch with 3 mm bunch
length }
\end{wrapfigure}
The accelerating structure, which will be fed with 15 MW input power, will consist of 19 cell in a length of 2.4 m. It will be same Slotted Iris Constant Aperture (SICA) structure like in CTF3 \cite{jensen_1q,personal_com}. Short range wake longitudinal and transverse potentials of the structure have been calculated using ABCI code \cite{abci} for a Gaussian bunch. In order to compute non-Gaussian bunch wake especially in DBL2, short range wake functions of the structure have been obtained with numerical fitting of Karl Bane's expressions \cite{bane1,bane2} to ABCI results. Figure \ref{fig:wakes} shows computed wake potentials of a Gaussian bunch using Bane's formulas and ABCI code.
The long-range transverse wakefields used in calculations have been obtained by scaling lowest four dipole modes of 3 GHz CTF3 structure to 1 GHz \cite{ctf3des}. However the loss and damping factors used in the simulation are 50\% larger than in ref \cite{clicparms} and almost perfect compensation of the long-range longitudinal wakefields is predicted \cite{personal_com}.
\section { Lattices
Three different lattices were investigated with taking into account their cost. One consists of simple FODO-cells, with one structure between each pair of quadrupoles. The other lattice is based on doublets in which two structures are placed in one cell. The last one is the triplet which houses two structures similar to doublet (see Fig. \ref{fig:lattices}). Since transverse deflection caused by wakefields requires small betatron functions especially when the beam energy is small \cite{schulte_multi,avni} we have optimized lattices for minimum integration and the best phase advance along the beamline. With constant quadrupole spacing and with constant phase advance per cell, the strengths of quadrupoles reach to high values by the end of beamline (e.g. $\sim$ 0.65 T pole tip field for 22 cm quadrupole length).
\begin{figure}[h]
\includegraphics[width=\columnwidth]{f3_all_beta}
\caption{\label{fig:lattices} Sketch of the lattice cells and betatron functions along the cells.
a)FODO, b)Doublet, c)Triplet. Strength of quadrupoles are scaled with energy. }
\end{figure}
In the FODO lattice, the length of each quadrupole is 20 cm, the spacing between quadrupoles is 2.9 m and the phase advance is $\mu_{x,y}= 103^{\circ}$ per cell. The doublet lattice has phase advance of $\mu_{x,y}= 58^{\circ}$, the doublet spacing is 5.4 m, the distance between two quadrupoles is 40 cm and the length of each quadrupole is 20 cm. In triplet, the distance between triplets is 5.4 m, the distances between quadrupoles in triples are 40 cm and one has $\mu_{x}= 46^{\circ}$ and $\mu_{x}= 49^{\circ}$ phase advances. For triplet, the lengths of central and outer quadrupoles are chosen 22 cm and 16 cm, respectively, also the strength of central one is larger than outer ones in order to have equal horizontal and vertical betatron functions inside the structure (see Fig. \ref{fig:lattices}). The lengths of the lattices are comparable but, obviously, triplet would have more cost due to one more quadrupole for each accelerating structure.
In all following calculations tracking has been started and finished at the middle of the distance between two quadrupoles for FODO, it is middle of the distance between doublets and triplets for other relevant types of lattices. This choice gives availability to align all quadrupoles in misalignment studies since the alignment is performed respect to the following BPM after quadrupole. However the minimum transverse acceptances are 5.33$\sigma$, 6.20$\sigma$ and 5.04$\sigma$ for the FODO, doublet and triplet lattice, respectively.
\section { Transverse Beam Jitter}{\label{jitter}}
Since we can not estimate the transverse jitter of the incoming beam, only the jitter amplification is calculated. The normalized amplification factor $Amp$ for a slice, that has $\Delta x_{0}$ initial offset, is defined as:
\begin{equation}{\label{equ:2} }
Amp_x = \frac{1} {x_{N}(0)}
\sqrt{ x_{N}^2(L) + {x'}_{N}^2(L) }
\end{equation}
Here, $L$ is length of beamline, $x_{N}(0)$, $ x_{N}(L)$ and ${x'}_{N}(L)$ are initial position, final position and final angle of the center of the slice in normalized coordinates, respectively. Equivalently one can define $Amp_y$ and the maximum amplification factor $Amp_{max}$ is the maximum of $Amp_x$ and $Amp_y$ over all slices. For a slice with nominal energy and without wakefield effects, one has $Amp_{x,y}=1$. In order to check the amplification of bunches in a train, we use the method in Ref. \cite{schulte_multi,avni}.
\begin{figure}[h!]
\includegraphics[width=\columnwidth]{f4_allamps}
\caption{\label{fig:pointamp} The normalized amplitudes of the point-like bunches with constant charge at the end of perfectly aligned DBL for an offset incoming train, a)FODO, b)Doublet, c)Triplet. }
\end{figure}
The impact of an initial offset of a train of point like bunches with constant charge is shown in Fig. \ref{fig:pointamp}. We assumed all bunches have the nominal Twiss parameters and the same initial offset at the entrance of beamline. In calculation we have used two sub-trains of 15 bunches each and for checking the worst case we take into account full bunch charge at sub-train switching point. As it can be seen on the figure the amplification of bunches of a single sub-train reaches steady state rapidly within this sub-train length and the agreement between the simulation and the simple analytic model is very good. Since the distance between bunches at switching point from odd buckets to even (or v.v.) is half of the others, the amplification at that point is slightly high due to strong kick caused by closer bunches. FODO lattice compensates transverse deflections and worst one occurs on triplet. The maximum amplification factor, $Amp_{max}$, for point-like bunch case for FODO, doublet and triplet lattices are 2.03, 2.65 and 3.67, respectively. In case of half bunch charge at sub-train switching point the amplification factors will decrease to 1.41, 1.77 and 2.34 for FODO, doublet and triplet lattices, respectively \cite{avni}.
For multi-particle case of bunches, there is additional transverse kick due to short range wake fields. On the other hand the energy difference of particles within a bunch will force them to advance in phase with respect to the reference one, thus some compensating of the kicks of long range wakefields occurs \cite{mosnier,bane1986}. Therefore the amplification factor will not be as high as point-like bunches case. Fig. \ref{fig:multiamp} shows PLACET results for final offset of a train at the end of perfectly aligned DBL1 and DBL2. Similar to point-like bunches case, all bunches have nominal Twiss parameters at the entrance of beamline and train consists of two sub-trains 15 bunches each. Switching point from even to odd buckets the bunches are kicked significantly; the maximum amplification for FODO, doublet and triplet lattices are 1.55, 2.15 and 2.70, respectively. Without knowledge of the acceptance downstream and the size of the incoming beam jitter, it is not possible to decide whether the amplification is acceptable. For all types of lattices within the linac that has $5\sigma$ minimum acceptance, even a large incoming jitter of $\Delta x_0=\sigma$ does not lead to beam loss.
\begin{figure}[h!]
\centerline{\includegraphics[width=0.7\columnwidth]{f5_multi_amps}}
\caption{\label{fig:multiamp} The normalized final offset of the bunches with constant charge at the end of the DBL1 (I, top) and DBL2 (II, bottom) for an offset incoming train, a)FODO, b)Doublet, c)Triplet. Group of red dots shows first bunch and blue dots show trailing bunches. }
\end{figure}
\section { Alignment
All elements on beamline may be scattered around a straight line. To align the beamline and compute the emittance growth caused by the miss-alignment, two different routines based on the beam have been taken into account. First one-to-one correction: each quadrupole is moved transversely in order to bring the average beam position to zero in the beam position monitor (BPM) located after quadrupole. Second wakefield-free steering: two or more beams with different energy and charge from the nominal one are steered to follow the same trajectory in order to remove dispersion and wakefield effect from the lattice during one-to-one correction is applied to nominal beam \cite{wkfresteering}.
In order to have better comparison between lattices we have used one BPM after each quadrupole at an appropriate location and have simulated 100 different beamlines, the elements of which are scattered with a normal distribution. In calculation following assumptions have been considered:
\vspace{-\topsep}
\begin{itemize}
\item all quadrupoles have $\sigma_{x,y}=300$ $\mu$m position errors $\sigma_{x',y'}=300$ $\mu$rad angle errors and $\sigma_{\theta}=1$ mrad roll errors;
\vspace{-\topsep}
\item all BPMs and accelerating structures have only $\sigma_{x,y}=300$ $\mu$m position errors;
\vspace{-\topsep}
\item the beamline on bunch compression section is perfectly aligned;
\vspace{-\topsep}
\item accelerating structures are perfectly straight (no tilting effect);
\vspace{-\topsep}
\item the beam is injected without any offset to DBL1 and DBL2;
\vspace{-\topsep}
\item the resolution of BPMs are $10$ $\mu$m;
\vspace{-\topsep}
\item each of two test beams used for wakefield-free steering consists of single bunch and they have $E_{in,1}$ = 40 MeV and $E_{in,2}$ = 60 MeV initial energies, $Q_1$ = 9 nC and $Q_2$ = 8 nC charges, $V_{1}$ = 0.93$V_{0}$ and $V_{2}$ = 1.05$V_{0}$ accelerating gradients, respectively, where $V_{0}$ is nominal gradient for actual beam.
\end{itemize}
\begin{wrapfigure}{r}{0.65\columnwidth}
\includegraphics[width=0.6\columnwidth]{f6_emittance}
\caption{\label{fig:emitt} Emittance growth along the beamline. a)wakefield-free steering, b)
one-to-one correction}
\end{wrapfigure}
Fig. \ref{fig:emitt} shows PLACET results for emittance growth along the beamline based on lattices considered. The growth is quite small for all lattice types and for both correction routines. Since the FODO type of lattice has weakest quadrupoles, the growth on it is smallest and is about 5\%. The emittance growth would be higher due to the fact that the bunch compression section will also be misaligned and the beam will have offset at the entrance of DBL2. However the static imperfections errors given above could be improved somewhat if necessary.
\section {Impact of the Energy and Gradient Errors
Although CLIC DB has very tight tolerances concerning error of incoming beam energy and structure gradients \cite{schulte_phase}, during commissioning large energy and gradient errors may occur. Any error of incoming beam energy or variation of the gradient will lead quadrupole strengths not to be adapted to the beam energy. These situations can cause beam amplification to grow, eventually, beam losses especially in DBL1 where the beam energy is low. On the other hand one can also define the tolerances for the RF and incoming beam for the real operation according the acceptable errors \cite{schulte_phase} at the end of DBL using different bunch compressors.
\subsection{Transverse Stability}
In order to check the amplification we have simulated train of two sub-trains 15 bunches each on perfectly aligned beamline of the lattice types considered. We assume the beam has the nominal Twiss parameters and offset of $\Delta x_0=\Delta y_0=\sigma$ at the entrance of beamline. Fig. \ref{fig:eg_amp} a shows the amplification as a function of the deviation from the nominal initial beam energy (a) and the nominal accelerating gradient (b). As it was discussed in section \ref{jitter} minimum amplification is obtained with FODO lattice for nominal case. FODO lattice is more sensitive to initial beam energy variations than the others especially while the beam energy is much lower than the nominal value. The gradient variation more or less does not change the amplification for all lattices and doublet lattice seems more stable for both energy and gradient variations. Gradient errors below -15\% cause amplification to increase rapidly for FODO type of lattice. This result can be explained as: towards the end of DBL1 the beam, that is accelerated to lower energy than the nominal by low gradient structures, will be over focused by quadrupoles which are adapted to nominal energy. Thus, the betatron functions will grow rapidly as a result of large phase advance. This situation is not the same for doublet and triplet lattice because of small phase advance per cell.
\begin{figure}[h!]
\includegraphics[width=\columnwidth]{f7_e_g_amp}
\caption{\label{fig:eg_amp} Amplification of the beam in DBL1, a) for different initial beam energy, b) for different accelerating gradient}
\end{figure}
Another crucial subject would be the acceptance of the lattice in DBL1. The acceptance in normalized coordinates defined as, the beam any particle of which has initial positions $x_0$, $x'_0$, $y_0$ and $y'_0$, that fulfills
\begin{equation}{\label{equ:5} }
Ar_N \geq \sqrt{ {x}_N^2 + {x'}_{N}^2 + y_N^2 + {y'}_{N}^2 }
\end{equation}
will pass through the accelerator. In simulations, we have considered two cases: perfectly aligned beamline and beamline the elements of which are scattered with a normal distribution of $\sigma = 300~\mu$m. For miss-aligned case we have simulated 20 different machines and applied one-to-one correction. Additionally, for both case we assumed the beam which has nominal Twiss parameters, has offset $\Delta x_0=\Delta y_0=500 \mu$m at the entrance of beamline and computed the unnormalized acceptance. However we have neglected initial beam angle with expecting that it will transform same as offset under first order approximation.
\begin{figure}[h!]
\includegraphics[width=\columnwidth]{f8_e_g_accpt}
\caption{\label{fig:egaccpt} Acceptance of the lattices, a) for different initial beam energy, b) for different accelerating gradient}
\end{figure}
Fig. \ref{fig:egaccpt} shows the acceptance of the lattices as a function of initial beam energy error (a) and accelerating gradient error (b). The acceptance is highest for doublet and it is less sensitive to the energy errors in doublet and triplet. For FODO the acceptance is reasonable around nominal beam energy, but it is very sensitive to the energy errors due to the same reason explained in amplification calculation. For all lattices the size of the acceptance for perfect and miss-aligned machines are close to each other. All lattices are less sensitive to the gradient error and the acceptance is highest for doublet lattice similar to energy error case. For FODO lattice beam loss starts when the accelerating gradient is below -15\% of the nominal gradient.
\subsection{Longitudinal Stability }
As it has been discussed in section \ref{sec:layout}, compressing the bunch before the main part of the acceleration one can afford having a strong bunch energy chirp and small $R_{56}$, thus a weak coupling between beam energy jitter and beam phase jitter can be obtained. Assuming additional improvement by factor 10 for the tolerance of the phase using feed forward system before PETS the energy error in DBL1 relaxes up to $1 \times 10^{-3}$ \cite{schulte_phase}. In the second stage of the drive beam linac (DBL2), the large relative energy spread will be reduced below 0.4\% which is acceptable in the PETS. In order to reduce significant impact of coherent synchrotron radiation, the bunches are uncompressed to 2 mm before they enter the delay loop and re-compressed behind the combiner rings to the final required length of 1 mm. To avoid an energy jitter from DBL2 turning into beam phase jitter the sum of all $R_{56}$ of all elements after DBL has to be zero.
Under first order approximation the error of beam phase ($\delta \sigma_{\phi}$) or error of bunch length ($\delta \sigma $) of a beam in a magnetic chicane will be proportional to jitter of the beam energy ($\delta \sigma \approx R_{56} \delta E $). Several quantities such as error of charge ($\delta Q$), incoming beam phase ($\delta \sigma_{in}$)) and energy ($\delta E_{in}$) of incoming bunch or error of phase ($\delta \phi_{RF}$) and gradient ($\delta G$) of linac can cause jitter on relative energy spread. The bunch compressor should compensate large errors of these quantities as well as errors caused by beam loading. Currently we have taken into account single bunch case and studied four types of compressors which have -10 cm, -12 cm, -14 cm and +26 cm compressing factors in order to define longitudinal tolerances with neglecting the imperfections on bunch compressor sections.
\begin{figure}[h!]
\includegraphics[width=\columnwidth]{f9_e_q_in_dph_dz_out}
\caption{\label{fig:bef_sz} Energy error of incoming bunch vs. phase jitter of outgoing bunch (a), and charge error of incoming bunch vs. bunch length variation of outgoing bunch (b). Gray areas show acceptable tolerances. }
\end{figure}
Left hand side of Fig. \ref{fig:bef_sz} shows phase jitter of the outgoing bunch as a function of deviation from nominal initial beam energy. As it can be seen on the figure largest incoming beam energy error is accepted by the bunch compressor that has $R_{56}$=-10. Right hand side of the Fig. \ref{fig:bef_sz} shows bunch length variation as function of the deviation from the nominal bunch charge. Similarly largest charge error (current error) is compensated by by the bunch compressor that has $R_{56}$=-10 while smallest errors are accepted by the compressor with $R_{56}$=+26 cm.
\begin{figure}[h!]
\includegraphics[width=\columnwidth]{f10_g_ph_lin_dph_dz_out}
\caption{\label{fig:lf_sz} Gradient error of linac vs. phase jitter of outgoing bunch (a), RF error of linac vs. bunch length variation of outgoing bunch (b). Gray areas show acceptable tolerances.}
\end{figure}
Left hand side of the Fig. \ref{fig:lf_sz} shows phase jitter of the outgoing bunch as a function of linac gradient error in DBL1 and right hand side shows bunch length variation as function of phase error of linac in DBL1. Similarly to initial bunch energy and charge error cases largest errors are accepted by the bunch compressor that has $R_{56}$=-10cm.
\section { Conclusion
The lattice has to prevent a large amplification of any transverse jitter of the incoming beam. It should also have a large energy acceptance and allow easy correction of static errors of the beam line. Three type of lattice have been studied for finding a compromise between lattices for the CLIC DBL.
The calculations show that if one uses FODO type of lattice the effects of transverse wakefields will be significantly smaller than using doublet or triplet types. For both alignment routines, triplet type of lattice gives largest emittance growth. Although FODO and doublet type of lattices have same number of quadrupoles, FODO gives smallest emittance growth. On the other hand, smallest sensitivity to energy errors can be obtained with doublet type of lattice while FODO type of lattice yields largest. Nevertheless, too large errors should not be important since the energy of the beam has to be controlled very accurately because of the tight tolerance of energy error in bunch compressor.
The FODO lattice has as many magnets as the doublet solution but fewer than the triplet design. It performs best in terms of jitter amplification and emittance growth in presence of static imperfections. The energy bandwidth is smaller than it is in the other designs but we consider the first two points more important. In particular the jitter amplification is very important since this can lead to losses further downstream. This will be a change compared to the CTF3 design, which is based on triplets \cite{ctf3des}.
FODO lattice will bring out other advantages such as easy operation. One can also consider using four structures in one FODO-cell after 1.5 GeV. For example, if one uses 30\% weaker and 40\% shorter quadrupoles after 1.5 GeV the integral increases from 11.28 m$^2$/MeV to 12.439 m$^2$/MeV and beamline shortens from 2.35km to 2.21km. In that case the maximum amplification factor of a train of point-like bunches will be 2.22 which is still better than doublet case mentioned above \cite{avni}.
One can also improve the triplet lattice with using single accelerating structure in one triplet-cell as it is in CTF3 design. In that case the maximum amplification factor of a train of point-like bunches can be calculated as 2.58 for the constant bunch charge condition considered in section \ref{jitter}. On the other hand using single structure per cell would increase the length of beamline from 2,55km to 3.25km.
\begin{wraptable}{l}{0.5\columnwidth}
\centerline{
\begin{tabular}{|l|c|c|}
\hline
{\bf Parameter} & {\bf Value} & {\bf Unit} \\
\hline
Initial energy error & 1 & \% \\
\hline
RF power error & 0.2 & \% \\
\hline
Beam current error & 0.1 & \% \\
\hline
RF phase error & 0.05 & deg \\
\hline
\end{tabular}
}
\caption{The tolerances in DBL1.}
\label{tab:limits}
\end{wraptable}
As it can be seen on figures \ref{fig:bef_sz} and \ref{fig:lf_sz} above, larger longitudinal errors can be compensated by chicane that has $R_{56}= -10$ cm. In order to compress the bunches from 3 mm to 1 mm with that bunch compressor one can easily calculate a chirp about 2\% energy spread per $3$ mm bunch length which means the RF will be operated at about 25$\circ$ off-crest phase. Thus relative gradient reduction comes out for this compressor while the compressor with $R_{56}= +26$ cm allows RF to be used more efficient. Calculated longitudinal tolerances of DBA1 is summarized as in Table \ref{tab:limits}. Additionally to the table the tolerance of accelerating power amplitude will be half of klystron power and the phase error of the incoming beam will be two times of the RF phase error.
\section{Acknowledgments}
Author would like to thank Dr. Daniel Schulte for his support during the study of beam dynamics for CLIC Drive Beam Linac.
This work is partially supported by State Planning Organization (SPO) of Turkey and CERN.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,472 |
{"url":"https:\/\/economics.stackexchange.com\/questions\/22467\/quarterly-gdp-growth-terminology-yoy-vs-qoq","text":"# Quarterly GDP growth terminology: YoY vs QoQ\n\nQuarterly GDP growth can be calculated either in terms of YoY change or \u2014 in the case of seasonally adjusted data \u2014 in terms of QoQ change. (A third option would be to annualize the QoQ rate.)\n\nTo start with a current example: In the U.S., GDP in Q1 2018 grew by 2.9% compared to Q1 2017 (= YoY), whereas it grew by 0.7% compared to Q4 2017 (= QoQ).\n\nIn Q4 2017, however, YoY growth was at 2.6%, whereas QoQ growth was at 0.7%. So GDP growth in Q1 2018 was higher compared to the previous quarter in terms of YoY (2.6% -> 2.9%), whereas it was slightly lower compared to the previous quarter in terms of QoQ (0.7% -> 0.6%).\n\nNow in judging an economy's growth momentum, analysts typically focus on changes in QoQ growth rates - in the example above coming to a conclusion like \"growth in the U.S. slightly lost momentum in Q1 2018\".\n\nMy question is: Is there a different term to express changes in the YoY rate? To stay with the example above, if I comment on the fact that the U.S. YoY rate is up to 2.9% from 2.6%, concluding that there was a \u201cstrengthening of growth momentum\u201d might be misleading (especially given the diverging picture based on changes in the QoQ rate).\n\n\u2022 There are many correct ways to say it. It should definitely be clear whether you're referring to YoY growth or the (annualized) growth rate in Q1 2018 compared to Q4 2017. If it arises many times in the text, then you could define some shorthand that would be used, unless using different indicators which could require to be more explicit each time. Jun 15 '18 at 17:29\n\nI have to highlight a flaw in the premise of your question.\n\nFor the quarterly NIPA statistics published and reported by the Bureau of Economic Statistics (bea.gov) under the U.S. Dept. of Commerce, the real growth rate shown in Table 1.1.1 in an annualized statistic based on the estimate of the QoQ level change in the real\/constant-dollar value of the economy.\n\nCurrent dollar quarterly values are given in Table 1.1.5. Real dollar quarterly values are given in Table 1.1.6. The growth rate reported in Table 1.1.1 is calculated from the values in Table 1.1.6 as follows: $$100\\% * \\left( \\left( \\frac{V_{q}}{V_{q-1}} \\right)^4 - 1 \\right).$$\n\nThis gives you the annualized growth rate.\n\nThe annual growth rate is YoY: $$100\\% * \\left( \\left( \\frac{V_{q}}{V_{q-4}} \\right) - 1 \\right).$$\n\nAnd the quarterly growth rate is QoQ: $$100\\% * \\left( \\left( \\frac{V_{q}}{V_{q-1}} \\right) - 1 \\right).$$\n\nAs long as you clearly label what you are doing, there\u2019s probably a lot of ways of phrasing the change in the year-on-year growth rate. However, anyone with experience will take those changes with a large grain of salt, as a result of \u201cbase effects.\u201d\n\nFor relatively low growth rates, the annual rate of change is roughly equal to the sum of non-annualised quarterly growth rates over the last four quarters (or the average of annualised growth rates for 4 quarters). The change in the annual growth rate on quarter is therefore driven by the difference between the latest quarter, and the quarter that dropped out of the annual average. If that previous period was abnormally low, the current annual growth rate will jump higher, even if the quarterly growth rate is unchanged.\n\nSince that hardly represents new information about the economy, that jump is not providing a lot of new information - we knew about that weak quarter for a long time.\n\nYear-on-year changes are a great for time series plots, but you need to dig further if you want to discuss acceleration\/deceleration.\n\n\u2022 First of all, many thanks for your response! You say that \"For relatively low growth rates, the annual rate of change is roughly equal to the sum of non-annualised quarterly growth rates over the last four quarters (...) The change in the annual growth rate on quarter is therefore driven by the difference between the latest quarter, and the quarter that dropped out of the annual average.\" Just to clarify: \"Annual rate of change\" and \"annual growth rate\" here refers to YoY growth in a certain quarter, right? (and not to, say, growth in full year 2018 compared to full year 2017) Jun 18 '18 at 8:05\n\u2022 Yes, that\u2019s quarter versus the quarter 4 quarters ago. A full year versus full year would be the percentage change of the 4 quarter moving average. Jun 18 '18 at 13:36\n\u2022 Can you recommend any literature that specifically addresses things like these and related topics? Oct 22 '18 at 7:48\n\u2022 @Thorsten The sort of observations I gave are what I picked up when creating charts for publication in industry. At most, the definitions might appear in a book on econometrics, but it would jump to more complicated things immediately. So there\u2019s no particular books I used to pick it up. Oct 23 '18 at 11:56","date":"2022-01-25 11:08:15","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\": 0, \"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\": 3, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.41326257586479187, \"perplexity\": 1038.0772426953672}, \"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-2022-05\/segments\/1642320304810.95\/warc\/CC-MAIN-20220125100035-20220125130035-00242.warc.gz\"}"} | null | null |
Getting equipment, spares and needed consumables to assets across the globe can be a daunting task. We have experience and know-how in working in logistically challenged regions in the world and understand the importance of knowing how to navigate through subjects like end-user agreements, ITAR and goods and services embargoes.
Identifying the proper requirements is amplified when working in 'hard to reach' areas and is an area in which we excel. We also provide support on the receiving end through inventory control practices. We have multiple logistics partners - both foreign and domestic - that can provide just about any needed part to meet our client's needs.
We can provide technical advice and the correct level of oversight rigor on just about any major industrial repair. We have multiple decades of experience of planning and executing overhaul periods of all marine equipment, including widespread hull replacement, shaft repairs, propeller repairs, engine overhauls, stern tube replacements, tank repairs, and HVAC modernization. We also specialize in preparing vessels for delivery and heavy-lift.
Additionally, we have qualified engineers experienced in marine coatings who have experience with R&D projects involving Naval Research Laboratories test and evaluations of new generation coatings in conjunction with leading coatings suppliers.
Our employees possess licenses such as Professional Engineer, and are USCG-qualified, engineering-department crew members for any tonnage, any horsepower, steam, diesel or gas turbine plants, and any combination thereof. Our employees are experienced on nearly every type of major commercial application, and have served as active-duty officers or performed as Port Engineers for nearly every type of US Navy vessel in the current fleet.
Our operational background and ability enables us to operate and/or train in multiple plant designs in great detail, complimenting our extensive abilities in the repair and modernization arena. We leverage experiences such as training foreign Navies to operate newly delivered vessels to demonstrate our mission reach. | {
"redpajama_set_name": "RedPajamaC4"
} | 5,931 |
This story is supported by City of Sydney
Foley Street Creative Spaces · The Tribe
I recently spent a week in sunny Sydney, and was truly inspired (and a little bit jealous) to get a first-hand look at one of City of Sydney's newest creative initiatives.
Foley Street in Darlinghurst is part of the Oxford st and Foley st Creative Spaces Program, aimed at fostering the creative community by providing affordable retail and work spaces for artists and designers. Just metres from Oxford Street, this enclave is a bustling little precinct of five neighbouring shopfronts, each leased to a different creative tenant.
Today, we meet with one of the lucky program participants – founder and director of The Tribe, Jess Polaschek.
Founder and director of The Tribe, Jess Polaschek, in her Foley street store. Jess established her handcrafted homewares, accessories and art hub in 2014, and was accepted into City of Sydney's Foley Street Creative Space Program at the start of last year. Photo – Nikki To for The Design Files.
The Tribe's Foley street showroom. Photo – Nikki To for The Design Files.
Jess styled the space to feel light and uncluttered, while being super fun and inspiring – 'I wanted the space to be a bit of an assault on the senses, but still have a reference to a traditional gallery space,' she tells. Photo – Nikki To for The Design Files.
<span class="s1″>Jess feels strongly about stocking original artwork works with authenticity. </span>Photo – <a href="http://nikkito.com/" target="_blank" rel="noopener noreferrer">Nikki To</a> for The Design Files.
I'm a proud Melbournian, but DAMN sometimes Sydney gets me a little… how can I say… distracted!?
Usually, it's the balmy weather and sparkling water that beckons me… but on this occasion it's something a little less glamorous. It's the council. City of Sydney are just SO GOOD at supporting creative businesses and start-ups, I'm beginning to think Melbourne could lift its game.
Case in point – Foley Street in Darlinghurst. This amazing little enclave is part of the Oxford st and Foley st Creative Space Program, which provides affordable studio and retail spaces for artists and designers. It's a sweet little laneway of five neighbouring shopfronts, each inhabited by a different creative business. We recently popped by and met a few of the inspiring creatives based here.
JESS POLASCHEK – THE TRIBE
With a background in design and visual communications, Jess Polaschek is the founder and director of The Tribe – a store, gallery and creative community supporting a diverse range of Australian makers and artists. Aside from simply stocking their work, The Tribe hosts regular events, workshops and exhibitions with her artists, and even provides an area on site for small businesses and students to do photo shoots!
Tell us about The Tribe?
I launched The Tribe as an online store in 2014, and it has developed from there. The name was inspired by the idea of forming a strong group, a family of like-minded creative thinkers and engagers, whether you shop with us, exhibit with us, attend a workshop, or help out creatively, I want you to feel like an important part of a community. Each member of our tribe is as important as the next, and they are all doing great things for our creative small business community.
How would you describe your offering at The Tribe?
Well made, eclectic, colourful, original, and fun! We believe art and design should be inclusive and have a sense of joy about it. There is enough serious, minimal design out there, The Tribe is all about inspiring happiness and creating connections!
Product wise, we stock a range of prints and offbeat homewares, everything has a story behind it. Affordable art prints are the area we are growing at the moment, we offer a diverse range from digitally printed, open edition, through to signed and numbered, limited edition, hand screen-printed works.
We support artists and designers at differing stages of their careers. We have the wonderfully fun products of Georgia Perry and Ahoy Trader, who are both quite established as brands, colourful designs from the currently booming conservationists Eggpicnic, as well as the very original cardboard art of Jeff McCann. We also champion the work of emerging artists like Le Riquiqui with her colourful, abstract, modernist prints and Earlies with his surf culture inspired screen prints.
What influences the pieces you decide to stock, and do you have any criteria for making your selections?
Firstly the work needs to be on brand for us, it needs to encapsulate that sense of joy and personality. Secondly, authenticity is a big factor for me. Imitation is not the highest form of flattery, and we try and work with people who are making every effort to be original, while still maintaining a high standard of finish and presentation.
I also love working with multi-faceted businesses and artists, the people that excite me the most are those who can create original artworks, produce high-quality prints or products and also run workshops or engage in events with us, all under one cohesive brand and distinctive look.
When did you become a part of the Oxford Street and Foley Street Creative Spaces Program, and what impact has this had on your business?
I found out The Tribe had been accepted into the program over New Years 2015/16, it was a fantastic way to start the year!
The initial application itself was the first way the program impacted my business, having to go through that kind of process is an incredibly helpful thing for a small business, I had to really think about what The Tribe's goals were, and it helped clarify a lot of ideas for me around what we stood for.
Once accepted, the program's impact only increased. Working with a city council and everything that comes along with that has been a fantastic learning curve, and having their support and mentorship has been invaluable.
The exciting part is the future impacts the program will have, the next three years is a chance for The Tribe to really thrive and experiment, take risks, become more involved in the local creative community and leverage the subsidised rent and support of the City of Sydney for the benefit of our whole Tribe.
The connections I have made through this program have had the biggest personal impact on The Tribe, we are now working with several artists we met through the creative spaces initiative, and all of my laneway neighbours are the bee's knees. It is so important to surround yourself with a community of likeminded people, and I couldn't have asked for a better bunch of creative legends to share this little slice of Sydney with for the next three years.
What are your hopes for the small business?
To survive and thrive, continue to build and help promote high quality locally designed goods and artworks, but most importantly become known as a place for connections. I want to build a strong community of creative folks who are into collaboration and sharing their passions and processes with others.
Our mission has also become a lot about education – many people have forgotten what goes into creating something, people have been conditioned to expect rock bottom prices and mass manufacturing, this disconnect people have with how things are made and the costs associated with ethical and local production is upsetting. I hope we continue to challenge these perceptions and help encourage people to really understand the value of supporting small business and the arts… all while surrounding themselves with colour and fun, of course!
Visit The Tribe at 21 Foley Street, Darlinghurst, Sydney.
Foley Street is part of the City of Sydney's Creative Spaces program which aims to foster the creative community by providing more affordable spaces for artists and designers. To find out about the types of spaces available, go here.
An Eclectic + Colourful Indoor Plant Haven On Victoria's Coast
Plant nursery Arizona Living in Torquay is filled with locally grown cacti, succulents and indoor plants, alongside vibrant homewares!
Bonnie & Neil's Sunny New Collection Is Inspired By Mediterranean Beach Clubs
Bonnie & Neil are bringing the colours of the Italian coast and Grecian-style prints to our home with their new summer collection! | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,044 |
Rishi Sunak will face an "ungovernable" Tory party, warns a Johnson supporter
Rishi Sunak's hopes of a gradual rise to power took a hit after Boris Johnson's supporters warned he would face an "ungovernable" conservative parliamentary party, while Penny Mordaunt's campaign insisted he stay in. race.
The former chancellor could be appointed successor to Liz Truss as party leader, and therefore prime minister, as early as 2pm on Monday if Mordaunt, the leader of the municipalities, fails to collect the necessary 100 nominations from parliamentarians.
Sunak, who has more than 160 nominations, became the very likely winner after Johnson announced Sunday night that he would not be running. The former prime minister said he had more than 100 MPs supporting him, but others were skeptical.
Christopher Chope, the Christchurch MP and Johnson's supporter, warned on Monday that Sunak was seen as undermining Johnson and Truss, and therefore could not expect loyalty from Conservative MPs. To get a mandate, Chope said, Sunak had to hold a general election.
"We have a parliamentary party that is completely torn apart and is ungovernable," Chope told BBC Radio 4's Today program. to guarantee him his support in the event that he is elected leader of the party and of the country.
"Unless we can have someone as our leader in parliament who demands the support and respect of the parliamentary party, we are in fact ungovernable.
Watch: Boris Johnson withdraws from the race for 10 Downing Street
"Unlike Boris, who had a mandate, we now have the prospect of having a Conservative party leader who does not have a mandate from the country and will not even have a mandate from the members."
Asked if he would support Sunak if we won, Chope replied: "I supported Boris Johnson and I supported Liz Truss, and I saw before my eyes their authority undermined by the people who now wish to take control and inherit the crown.
"Respect is a mutual thing. If the people who are now seeking the crown want to have the respect that comes with having a mandate, then what I'm saying is that the best way to get that respect is to win a mandate with people, which is why I think a ' general election is essentially the only answer.
"Otherwise we will go from bad to worse. We will have constant rebellions as we try to change policies ".
Related: "Such a Disappointment of Democracy": Uproar over UK Early General Elections
Mordaunt is stuck on around 30 publicly declared MP nominations, though her team hopes to be encouraged by some Johnson supporters moving in with her.
Mordaunt supporters on Sunday swore she was still in the running and on Monday morning they released details of a poll which they claimed showed she was the best placed candidate to unite the nation.
The Deltapoll poll of 4,000 voters found that Mordaunt was more attractive to voters in the seats earned by the Tories in 2019 than Sunak or Johnson. She also found that she was considered more trustworthy, "pointing out that she is the only candidate who can unite the country and restore confidence in the government," she claimed in her campaign.
Owen Farrell in doubt about clash with Argentina due to concussion protocols
Japan steps up its push to gain public membership of digital IDs
Athena Strand's mother says her 'princess' was kidnapped by a 'cruel monster'
Martin Lewis demonstrates a quick trick to check if your phone is out of contract
Oat milk producers accused of hypocrisy for selling by-products as animal feed | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,534 |
Q: Are XML Comments Necessary Documentation? I used to be a fan of requiring XML comments for documentation. I've since changed my mind for two main reasons:
*
*Like good code, methods should be self-explanatory.
*In practice, most XML comments are useless noise that provide no additional value.
Many times we simply use GhostDoc to generate generic comments, and this is what I mean by useless noise:
/// <summary>
/// Gets or sets the unit of measure.
/// </summary>
/// <value>
/// The unit of measure.
/// </value>
public string UnitOfMeasure { get; set; }
To me, that's obvious. Having said that, if there were special instructions to include, then we should absolutely use XML comments.
I like this excerpt from this article:
Sometimes, you will need to write comments. But, it should be the exception not the rule. Comments should only be used when they are expressing something that cannot be expressed in code. If you want to write elegant code, strive to eliminate comments and instead write self-documenting code.
Am I wrong to think we should only be using XML comments when the code isn't enough to explain itself on its own?
I believe this is a good example where XML comments make pretty code look ugly. It takes a class like this...
public class RawMaterialLabel : EntityBase
{
public long Id { get; set; }
public string ManufacturerId { get; set; }
public string PartNumber { get; set; }
public string Quantity { get; set; }
public string UnitOfMeasure { get; set; }
public string LotNumber { get; set; }
public string SublotNumber { get; set; }
public int LabelSerialNumber { get; set; }
public string PurchaseOrderNumber { get; set; }
public string PurchaseOrderLineNumber { get; set; }
public DateTime ManufacturingDate { get; set; }
public string LastModifiedUser { get; set; }
public DateTime LastModifiedTime { get; set; }
public Binary VersionNumber { get; set; }
public ICollection<LotEquipmentScan> LotEquipmentScans { get; private set; }
}
... And turns it into this:
/// <summary>
/// Container for properties of a raw material label
/// </summary>
public class RawMaterialLabel : EntityBase
{
/// <summary>
/// Gets or sets the id.
/// </summary>
/// <value>
/// The id.
/// </value>
public long Id { get; set; }
/// <summary>
/// Gets or sets the manufacturer id.
/// </summary>
/// <value>
/// The manufacturer id.
/// </value>
public string ManufacturerId { get; set; }
/// <summary>
/// Gets or sets the part number.
/// </summary>
/// <value>
/// The part number.
/// </value>
public string PartNumber { get; set; }
/// <summary>
/// Gets or sets the quantity.
/// </summary>
/// <value>
/// The quantity.
/// </value>
public string Quantity { get; set; }
/// <summary>
/// Gets or sets the unit of measure.
/// </summary>
/// <value>
/// The unit of measure.
/// </value>
public string UnitOfMeasure { get; set; }
/// <summary>
/// Gets or sets the lot number.
/// </summary>
/// <value>
/// The lot number.
/// </value>
public string LotNumber { get; set; }
/// <summary>
/// Gets or sets the sublot number.
/// </summary>
/// <value>
/// The sublot number.
/// </value>
public string SublotNumber { get; set; }
/// <summary>
/// Gets or sets the label serial number.
/// </summary>
/// <value>
/// The label serial number.
/// </value>
public int LabelSerialNumber { get; set; }
/// <summary>
/// Gets or sets the purchase order number.
/// </summary>
/// <value>
/// The purchase order number.
/// </value>
public string PurchaseOrderNumber { get; set; }
/// <summary>
/// Gets or sets the purchase order line number.
/// </summary>
/// <value>
/// The purchase order line number.
/// </value>
public string PurchaseOrderLineNumber { get; set; }
/// <summary>
/// Gets or sets the manufacturing date.
/// </summary>
/// <value>
/// The manufacturing date.
/// </value>
public DateTime ManufacturingDate { get; set; }
/// <summary>
/// Gets or sets the last modified user.
/// </summary>
/// <value>
/// The last modified user.
/// </value>
public string LastModifiedUser { get; set; }
/// <summary>
/// Gets or sets the last modified time.
/// </summary>
/// <value>
/// The last modified time.
/// </value>
public DateTime LastModifiedTime { get; set; }
/// <summary>
/// Gets or sets the version number.
/// </summary>
/// <value>
/// The version number.
/// </value>
public Binary VersionNumber { get; set; }
/// <summary>
/// Gets the lot equipment scans.
/// </summary>
/// <value>
/// The lot equipment scans.
/// </value>
public ICollection<LotEquipmentScan> LotEquipmentScans { get; private set; }
}
A: The comments that look useless to users who can read the code become rather useful to users who have no access to the source. This happens when the class is used as an external API by people outside your organization: the HTMLs generated from your XML docs is their only way to learn about your classes.
That said, a comment that reiterates the method name with added spaces between the words remains useless. If your class is going to be used outside of your organization, you need to document at lest the valid ranges for your values. For example, you should say that setting UnitOfMeasure to null is illegal, that the value supplied to the setter must not contain spaces at the beginning or at the end of the string, and so on. You should also document the range of LabelSerialNumber if it differs from that of a plain Int32: perhaps it does not allow negative numbers*, or does not allow more than seven digits. Your internal users may take it for granted, because they look at serial numbers day in and day out, but the external users may be genuinely surprised to see an exception from what looks like an innocent setter.
* ...in which case uint may be a better choice
A: If your comments only look like this:
/// <summary>
/// Gets or sets the sublot number.
/// </summary>
/// <value>
/// The sublot number.
/// </value>
Then yes, they are not all that useful. If they read something like this:
/// <summary>
/// Gets or sets the sublot number.
/// Note that the sublot number is only used by the legacy inventory system.
/// Latest version of the online inventory system does not use this, so you can leave it null.
/// Some vendors require it but if you don't set it they'll send a request for it specifically.
/// </summary>
/// <value>
/// The sublot number.
/// </value>
Then I'd say they have value. So to answer your question: Comments are necessary when they say something that the code does not say.
An exception: it is good to have comments on anything that is publicly accessible if you're writing a library/API that will be available to the public. I hate using a library and seeing a function named getAPCDGFSocket() with no explanation of what an APCDGFSocket is (I'd be happy with something as simple as This gets the Async Process Coordinator Data Generator File Socket). So in that case, I'd say use some tool to generate all comments and then manually tweak the ones that need it (and please make sure your cryptic acronyms are explained).
Also, getters/setters are generally bad examples for "are comments necessary?" because they are usually quite obvious and comments aren't necessary. Comments are more important on functions that perform some algorithm where some explanation of why things are being done they way they are could make the code much more understandable and also make it easier for future programmers to work with.
...and finally, I'm pretty sure that this question is relevant for all styles of comments, not just those that are formatted using XML (which you are using because you're working in a .NET environment).
A: You are absolutely right about avoiding such useless comments. They make reading the code more difficult instead of making it easier, and are taking too much space.
In my practice people who write comments with getters/setters, tend to omit comments when those are really necessary (like building a 20-line sql-query for a component with no documentation).
I write comments when there are some other obvious solutions _ I indicate why exactly this approach has been used. Or when its hard to get the idea without knowing all of the details _ I briefly list the details that are necessary to understand the code.
The example you bring is more of writing comments to say that one writes comments rather than making others' (and theirs also) life easier.
BTW you can improve your ability of writing comments by returning to your old code and trying to comprehend it (you might even not recognize your own code in 2-3 months _ its absolutely like reading someone else's code). If you do this painlessly, than everything's just fine.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,226 |
Industry News / Member News
UNIFI Communications acquires WIS Telecom to accelerate growth of UNIFI'S global carrier business
by Telecom Council · Published November 22, 2016 · Updated February 7, 2019
NEW YORK, NY, USA – November 22, 2016 – UNIFI Communications, Inc., a leading US-based international telecommunications carrier, announced today that it has acquired 100% of WIS Telecom S.p.A. and its subsidiary, WIS Telecom S.A., from Libero Acquisition S.a.r.l., an investment vehicle of Orascom TMT Investments S.à r.l. ("OTMTI"), majority-owned by Mr. Naguib Sawris of Cairo, Egypt.
"This acquisition will be highly synergistic for us," said Adrian Shatku, UNIFI's founder and CEO, "because UNIFI and WIS have similar core businesses, networks, geographic compliments and customers, and combining the two will expand our footprint, yield operating cost savings and enable provision of higher quality services to the wholesale voice market. Overall, it will greatly accelerate the growth of our business."
Mr. Shatku noted that WIS is ranked by Telegeography as the 15th largest international carrier worldwide, the company offers a comprehensive portfolio of international voice, data and IP solutions to meet the needs of both fixed and mobile operators, on a network that includes more than 150 interconnections with mobile operators and Tier-1 carriers in 70 countries. WIS services are supported by an international backbone connecting voice switches to the major telehouses in the United States, United Kingdom, Hong Kong, Italy, Greece, Germany, France and Belgium. WIS also owns a submarine cable between Italy and Greece.
"This transaction comes as part of our strategy to divest non-core assets and consolidate our operations within our new areas of focus. After the merger with Vimplecom, our business has shifted from voice and mobile communication and related operations to focus on technology and online solutions," commented Naguib Sawiris on this move. He added, "I am delighted to have the opportunity to transfer ownership of WIS to a company such as UNIFI who will help WIS achieve its full potential while taking good care of its employees and customers, and I look forward to continuing a strong business relationship with UNIFI and Mr. Shatku in the future."
About UNIFI Communications
UNIFI Communications, headquartered in New York City, USA, is an international voice carrier and a leading provider of enhanced telecommunication services and solutions. Service offerings include highly competitive wholesale voice termination services, pre-paid calling services partnerships (co-branding, marketing, and sales of partner services), and network infrastructure development services.
For more information, visit www.unificom.com.
About WIS Telecom
WIS TELECOM, headquartered in Rome, Italy, with additional offices in Milan, Italy, and Nivelles, Belgium, was formerly known as WIND International Services S.p.A. The company primarily operates in South and Eastern Europe and the MENA region (Middle East and North Africa), where it is an undisputed leader in international telecom services.
For more information, visit wis-telecom.com.
About OTMTI
Orascom TMT Investments S.ὰ r.l "OTMTI", (formerly Weather Investments II S.à r.l.) is a company incorporated under the laws of Luxembourg, with Mr. Naguib Sawiris as chairman.
It is a renowned investor and strategic shareholder in telecommunication and technology companies with roots dating back to 1997 with the creation of the mobile telecommunications group, Orascom Telecom Holding S.A.E. (OTH) in Cairo. OTMTI holds a number of leading companies in this field under its umbrella spanning Europe, Asia, North Africa and the United States. The portfolio companies cover telecom infrastructure, cloud computing, digital content and services, technology development and hosting; including but not limited to OTMT, Supernap, Italia Online, DADA, IntY Cascade, and WIS.
For more information, visit www.otmtinvestments.com
UNIFI Media Contact: OTMTI Media Contact:
Brian Shatku Manal Abdel-Hamid
UNIFI Communications, Inc. Orascom TMT Investments S.ὰ r.l
Tel: +1 212 845 9095, ext. 112 M: +20122 215 6333
Email: marketing@unificom.com Email: mabdelhamid@otmtinvestments.com
Debrief: Wrap up on yesterday's NFV Deep Dive
Breaking Down the True IP Communications Story
by Telecom Council · Published November 3, 2015 · Last modified March 5, 2019
The Ultimate Exchange: Creating Boundless Opportunities when Real Time Communications Meets the Internet of Things
by Telecom Council · Published September 16, 2016 · Last modified February 7, 2019 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,981 |
This is a placeholder page for Tracy Cop, which means this person is not currently on this site. We do suggest using the tools below to find Tracy Cop.
You are visiting the placeholder page for Tracy Cop. This page is here because someone used our placeholder utility to look for Tracy Cop. We created this page automatically in hopes Tracy Cop would find it. If you are not Tracy Cop, but are an alumni of Mcpherson High School, register on this site for free now. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,258 |
Q: Prompt only once for username and password for svn export in makefile I want to write a Makefile to export several files from an svn repository, but to prompt for username and password only once. The files are located in different directories in the same repository. I'm using svn+ssh.
A: SVN client will prompt you for the password only once and will then cache it by default. The next time you attempt to access the repository that's using the same authentication realm the cached password will be reused and you will not get an authentication prompt. Read SVNBook | Client Credentials.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,131 |
{"url":"https:\/\/www.lessonplanet.com\/teachers\/writing-lowercase-e-and-s","text":"# Writing Lowercase e and s\n\nGet familiar with the letters e and s. Two lovely snails need your class to trace the letters on their backs. After that, they can trace and then copy each letter for good measure.\n\nCCSS: Designed\nConcepts\n\nResource Details","date":"2018-09-25 09:57:19","metadata":"{\"extraction_info\": {\"found_math\": false, \"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\": 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\": 0.8233629465103149, \"perplexity\": 4724.678169885602}, \"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-2018-39\/segments\/1537267161350.69\/warc\/CC-MAIN-20180925083639-20180925104039-00223.warc.gz\"}"} | null | null |
Ksar Astour (en arabe : قصر أستور) est un village fortifié dans la province de Zagora, région de Draa-Tafilalet au sud-est du Maroc .
Notes et références
Voir aussi
Village au Maroc
Ksar au Maroc | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,562 |
Q: How can I generate a pdf using CakePhp v3.x I'm using CakePHP v3.x, how can I generate a PDF file?
There is the possibility to generate an "only for download" or "only for print" file? (which doesn't need to be saved on server)
A: How can I generate a pdf using CakePhp v3.x?
Here's a plugin for this: https://github.com/FriendsOfCake/CakePdf
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,693 |
{"url":"http:\/\/math.stackexchange.com\/questions\/456990\/permutation-and-combination-problem","text":"# permutation and combination problem\n\nlet us consider this problem:\n\nChelsea has a bookshelf consisting of ten classics: four Russian novels, three British novels, two French novels, and a German novel. If she wants to make sure that the novels are always grouped according to country, how many ways can she arrange the novels?\n\nmy attempt is following because these novels should be arranged according to country,it means that i should multiply number of arrangement of Russian novels together by number of British novels arrangement by French and one German Novels number of arrangement,which means that\n\n$4!*3!*2!*1!=288$\n\nbut in answer there is $24*288=6912$ where $24$ comes from?does it means that there is $24$ ways first book i could choose? $4*3*2*1=24$?\n\n-\n\nConsider the big group. So you have Russian, British, French, and German. You can arrange them $4!$ ways. For each type of book, you can arrange them $4!$, $3!$, $2!$, and $1!$ ways (which is what is in your attempt.)\nSo the final answer is $4!4!3!2!1!=6912$.\nit means that $4!$ is related to number of country,not number of books right? \u2013\u00a0dato datuashvili Aug 1 '13 at 6:01\nyes, $4!$ refers to the country, and the order matters. \u2013\u00a0vantonio1992 Aug 1 '13 at 12:02","date":"2016-05-24 22:01:56","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\": 0.4816291034221649, \"perplexity\": 1327.4063817683434}, \"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-2016-22\/segments\/1464049273667.68\/warc\/CC-MAIN-20160524002113-00200-ip-10-185-217-139.ec2.internal.warc.gz\"}"} | null | null |
<?xml version="1.0" encoding="UTF-8"?>
<project version="4">
<component name="ProjectModuleManager">
<modules>
<module fileurl="file://$PROJECT_DIR$/HttpClientWithJSoup.iml" filepath="$PROJECT_DIR$/HttpClientWithJSoup.iml" />
<module fileurl="file://$PROJECT_DIR$/app/app.iml" filepath="$PROJECT_DIR$/app/app.iml" />
</modules>
</component>
</project> | {
"redpajama_set_name": "RedPajamaGithub"
} | 8,789 |
\section*{Introduction}
This is an elementary introduction to the representation
theory of finite semigroups.
As the title suggests, it is not necessarily intended for semigroup
theorists.
We start with a quick primer on the semigroups that will interest us
-- the inverse and regular monoids -- and spend a certain amount of
energy selling these objects to the general mathematical
public.
Section \ref{section:representations} introduces
from scratch
linear actions of semigroups on vector spaces, where the emphasis is
on those aspects of the theory that are in common with group
representations. By this point the symmetric group $S_{\kern-.3mm n}$ will have
appeared a number of times,
so we divert to describe
its ``atomic'' representations. There are two fundamental
constructions, reduction and induction, that connect group theory and
semigroup theory, at least when it comes to representations. These are
described in Sections
\ref{section:reduction}-\ref{section:induction}.
Section \ref{section:clifford:munn} contains, what is, from the point
of view of these notes, the
fundamental theorem
of semigroup representation theory: the Clifford-Munn
correspondence.
It gives a mechanism for producing the atomic
representations of semigroups using only knowledge from group
theory. The last section is essentially a gratuitous excuse to draw
pictures of our favourite polytope, the permutohedron, dressed up as a
worked example of the representations of an interesting Renner monoid.
Throughout, three running examples, $S_{\kern-.3mm n}$ (a group), $I_n$ (an
inverse monoid) and $T_n$ (a regular monoid) are used as
illustration.
By the end of Section \ref{section:induction} the emphasis
will have completely moved to inverse monoids. We also start with
actions on vector spaces over an arbitrary field $k$, but in later
sections we
retreat to the relative safety of representations over $\ams{C}}\def\Q{\ams{Q}}\def\F{\ams{F}}\def\K{\ams{K}$. We borrow
heavily from a number of sources
-- full attributions are given in the Notes and References section at
the end.
\section{Semigroups}
\label{section:semigroup_basics}
A semigroup is a set equipped with an associative multiplication. This
leaves us with quite a bit of scope! In this section we feel our way towards a
manageable class of semigroups to study. Our guiding principle will
be the role of inverses in semigroup theory.
We start with three finite examples that are the most typical of their
type. Throughout, we write $[n]$ for the set $\{1,2,\ldots,n\}$.
\begin{description}
\item[--] \emph{The symmetric group $S_{\kern-.3mm n}$}: consisting of all
bijections $g:[n]\rightarrow [n]$ with multiplication the usual
composition of maps.
\item[--] \emph{The symmetric inverse monoid $I_n$}: consisting of all
\emph{partial\/} bijections $s:[n]\rightarrow [n]$, i.e. bijections $s:X\rightarrow Y$
where $X,Y\subseteq [n]$. The multiplication is composition of partial
maps as shown in Figure \ref{fig:partialmapcomposition}.
\begin{figure}[h]
\centering
\begin{pspicture}(0,0)(12,6.5)
\rput(6,3.25){\BoxedEPSF{fig4.eps scaled 450}}
\rput(4.1,3.1){${\red st}$}\rput(4.7,5.9){${\red \text{dom}\,(st)}$}
\rput(4.4,1.5){${\red \text{im}\,(st)}$}
\rput(8,6.1){$\text{im}\,\,t$}\rput(10.5,4.5){$\text{dom}\,\,s$}
\rput(5.7,5.4){$t$}\rput(7.5,3.1){$s$}
\end{pspicture}
\caption{composition of partial maps of $[n]$.}
\label{fig:partialmapcomposition}
\end{figure}
All our functions, actions, etc, will be on the left,
so the partial map $st$ has domain the $t$-preimage of $\text{im}\,
t\cap\text{dom}\, s$ and image the $s$-image of $\text{im}\, t\cap \text{dom}\, s$, and is the usual
composition of $t$ followed by $s$ between these two sets.
If
$\text{im}\, t\cap \text{dom}\, s$ is empty, then $st$ is the unique bijection
$\varnothing\rightarrow\varnothing$, which we will call the zero map
$0$.
\item[--] \emph{The full transformation monoid $T_n$}: consisting of all mappings
$s:[n]\rightarrow [n]$ with multiplication the usual composition of maps.
\end{description}
\paragraph{Inverses in semigroup theory.} Naively, a semigroup is a
group, except without inverses. But to completely rule out inverses in a
semigroup is unnecessarily defeatist.
The elements of $S_{\kern-.3mm n}$ are ``global'' symmetries of the set $[n]$ -- with
global inverses -- while the elements of $I_n$ are ``local'' symmetries
of $[n]$, with local inverses to match.
Our three running examples motivate
three ways in which inverses arise:
\smallskip
(i). The symmetric group $S_{\kern-.3mm n}$ is a group, obviously, so for every
$g\inS_{\kern-.3mm n}$ there is a unique
$h\inS_{\kern-.3mm n}$ with $gh=\id=hg$. Write $h=g^{-1}$ as usual.
\smallskip
(ii). If $s:X\rightarrow Y$ is an element of $I_n$ then there is a unique
$X\leftarrow Y:t$, that is the inverse of $s$, but only defined on the set
$Y$. Indeed, $st=\id_Y$ and $ts=\id_X$, where $\id_X:X\rightarrow X$ and
$\id_Y:Y\rightarrow Y$ are partial identities, and in particular,
idempotents (i.e: $\id_X\id_X=\id_X$ and $\id_Y\id_Y=\id_Y$).
As a working definition of the local inverse of $s$, we could
take it to be an element $t$ such that $st$ and $ts$ are idempotents,
but not necessarily the global idempotent $\id$. It
turns out that this isn't quite satisfactory, as any map defined
on some subset of the image of $s$, and equal to the inverse of $s$ on this
subset, also has this property.
Instead, we have $s\,\id_X =s=\id_Y s$. Together with $st=\id_Y$ and
$ts=\id_X$ we get that $t$ satisfies $sts=s$; similarly
$tst=t$.
A semigroup with the property that for every $s$
there is a \emph{unique\/} $s^*$ satisfying
\begin{equation}\label{eq:inverse_semigroup}
ss^*s=s\text{ and }s^*ss^*=s^*
\end{equation}
is called an inverse semigroup; a semigroup with an
identity $\id$ is a monoid, and an inverse semigroup with an identity
$\id$ is an \emph{inverse monoid\/}. $I_n$ is thus the most inverse
monoid-like of the inverse monoids. We will sometimes call $s^*$ an
inverse ``in the sense of semigroup theory'' and reserve the notation
$s^{-1}$ for inverses in a group.
\smallskip
(iii). Definition (\ref{eq:inverse_semigroup}) of inverses opens up new
possibilities. The element $s\in T_n$ shown on the left of Figure
\ref{fig:inverses_in_Tn} has \emph{kernel\/} the
partition of $[n]$ whose blocks are the \emph{fibers\/} of $s$: the
$s$-preimages of a point in the image of $s$.
\begin{figure}
\centering
\begin{pspicture}(0,0)(14,3.5)
\rput(0,0.35){
\rput(3.5,1.5){\BoxedEPSF{fig10c.eps scaled 450}}
\rput(10.5,1.5){\BoxedEPSF{fig11c.eps scaled 450}}
\rput(0.3,1.5){$s$}
\rput(0.85,3){$1$}\rput(6.5,3){$n$}
\rput(0.9,0.05){$1$}\rput(6.55,0.05){$n$}
\rput(3.5,3){{\cyan fibers/kernel of $s$}}
\rput(7.3,1.5){$t$}
\rput(7.8,2.9){$1$}\rput(13.4,2.9){$n$}
\rput(7.8,0.05){$1$}\rput(13.4,0.05){$n$}
\rput(10.5,0){{\red fibers/kernel of $t$}}
\rput(10.2,2.9){$x$}\rput(8.5,0.05){$sx$}
}
\end{pspicture}
\caption{inverses in $T_n$.}
\label{fig:inverses_in_Tn}
\end{figure}
Now construct an element $t\in T_n$ in the following way:
\begin{description}
\item[--] partition the image copy of $[n]$ so that each block of the
partition
contains exactly one element of the image of $s$; this partition
will be the kernel of $t$.
\item[--] For each block in this new kernel choose an $x$ in the domain
copy of $[n]$ such that the
block contains the point $sx$; then
define $t$ so that it maps this block to $x$; see the right of
Figure \ref{fig:inverses_in_Tn}.
\end{description}
The $t$ just constructed satisfies $sts=s$ and $tst=t$; conversely,
any $t$ satisfying these relations
must come about in this way.
But this $t$ is clearly not
unique -- there is choice in the partition of the image $[n]$ and for each block
of this partition, choice in the
$x$ so that the block is labelled by $sx$.
A monoid with the property that for every $s$
there is \emph{some\/} $t$ satisfying
$sts=s$ and $tst=t$
is called a \emph{regular monoid\/}.
\emph{From now on:} $S$ will be a finite regular monoid.
\paragraph{The structure of semigroups: Green's relations.} These allow
us to draw strategic pictures of semigroups. Define an equivalence relation
$\LL$ on $S$ by $s\LL t$ when $S\kern-0.5mm s=S\kern-0.35mm
t$, where $S\kern-0.5mm s=\{rs\,:\,r\in
S\}$ is a left ideal (hence the ``$\LL$''). Dually, define $s\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q t$
when $sS=tS$.
In $S_{\kern-.3mm n}$, and indeed any group, these relations are trivial: any two
elements are $\LL$ and $\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$-related. In $I_n$ and $T_n$ they take a particularly
simple form:
\begin{description}
\item[--] $s\LL t$ when the fibers of $s$ are equal to the
fibers of $t$ (or $s$ and $t$ have the same kernel). In $I_n$ this
is equivalent to $\text{dom}\, s=\text{dom}\, t$.
\item[--] $s\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q t$ when $\text{im}\, s=\text{im}\, t$.
\end{description}
If we consider the equivalence relation $\langle\LL,\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q\rangle$
generated by $\LL$ and $\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$, then something very nice happens.
The
$\LL$-class of any element $t$ that is $\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$-related to $s$ intersects the
$\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$-class of any element $r$ that is $\LL$-related to $s$. It is particularly
easy to see for $I_n$ as on the left of Figure
\ref{fig:LR_commute}. The
$\langle\LL,\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q\rangle$-classes are thus partitioned into $\LL$-classes and
partitioned into $\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$-classes, with any $\LL$-class intersecting any
$\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$-class and vice-versa. Semigroup theorists call this grid an
``eggbox'' -- see the right of Figure \ref{fig:LR_commute}.
\begin{figure}[t]
\centering
\begin{pspicture}(0,0)(14,7)
\rput(0,1){
\rput(3.5,2.5){\BoxedEPSF{fig6.eps scaled 450}}
\rput(2.3,3.65){$X\stackrel{s}{\rightarrow}Y$}\rput(4.6,3.65){$W\stackrel{t}{\rightarrow}Y$}
\rput(2.3,1.45){$X\stackrel{r}{\rightarrow}Z$}\rput(4.6,1.45){$W\stackrel{q}{\rightarrow}Z$}
\rput(0.55,3.65){$\text{im}\,=Y$}\rput(0.55,1.45){$\text{im}\,=Z$}
\rput(2.3,4.95){$\text{dom}\,=X$}\rput(4.6,4.95){$\text{dom}\,=W$}
\rput(4.6,0.05){${\red \LL_t}$}\rput(6.1,1.45){${\red \mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q_r}$}
}
\rput(10,4){\BoxedEPSF{fig9d.eps scaled 450}}
\rput(8,6.2){$\langle\LL,\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q\rangle$-class eggbox:}
\rput(4.1,-0.1){\rput{90}(5.9,.8){$\left\{\begin{array}{c}
\vrule width 0 mm height 50 mm depth 0 pt\end{array}\right.$}}
\rput(12.8,3.4){$\left.\begin{array}{c}
\vrule width 0 mm height 50 mm depth 0 pt\end{array}\right\}$}
\rput(10,0.4){$\LL$-classes $=$ domain sets of size $m$}
\rput(0,0.4){
\rput(13.7,3.4){$\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$-classes}
\rput(13.7,3.1){$=$}
\rput(13.7,2.8){image sets}
\rput(13.7,2.5){of size $m$}
}
\rput(8.5,0.85){$X$}\rput(12.6,3.2){$Y$}
\rput(11.6,6.7){$=$ all bijections $X\stackrel{s}{\rightarrow}Y$}
\end{pspicture}
\caption{In the symmetric inverse monoid $I_n$, the
$\LL$-class $\LL_t$ of any element $t$ that is $\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$-related to $s$ intersects the
$\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$-class $\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q_r$ of any element $r$ that is $\LL$-related to $s$
\emph{(left)\/} and an eggbox grid of a $\langle\LL,\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q\rangle$-class
\emph{(right)} partitioned into mutually intersecting $\LL$ and $\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$-classes.}
\label{fig:LR_commute}
\end{figure}
Moreover, pursuing the ideal theme, define a relation $\mathscr J$ on $S$
by $s\mathscr J t$ when $S\kern-0.5mm sS=S\kern-0.35mm tS$. Again,
this has a simple form in
$I_n$ and $T_n$, with $s\mathscr J t$ when $\text{im}\, s$ and $\text{im}\, t$ are sets of
the same size. But the $\langle\LL,\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q\rangle$-class of $I_n$ in
Figure \ref{fig:LR_commute} consists precisely of those partial
bijections whose image has the fixed size $|\text{im}\, s\,|=|Y|$. Thus
$\mathscr J=\langle\LL,\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q\rangle$ in $I_n$, and in general for any finite $S$.
Our final relation is $\HH=\LL\cap\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$, so that $s\HH t$ when they
are both $\LL$ and $\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$-related. In $I_n$ and $T_n$
a pair $s\HH t$ means that $s$ and $t$ have the same fibers (or
domains in $I_n$) and the same
images. The $\HH$-classes are thus the small boxes in the eggbox grid
with one marked on the right of Figure \ref{fig:LR_commute}.
Write $\LL_s,\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q_s,\mathscr J_s$ and $\HH_s$ for the equivalence class of
$s\in S$ under these relations.
The $\mathscr J$-classes
are not just floating around in the ether in a disembodied fashion. They
can be compared to each other; in other words, they
form a poset. This is what we mean by ``strategic picture''.
Again we can see this quite naturally by looking at
$I_n$ and $T_n$, where the $\mathscr J$-classes are parametrised by the
possible sizes of the images: by $\{0,\ldots,n\}$ in
$I_n$ and by $\{1,\ldots,n\}$ in $T_n$.
Indeed, $S\kern-0.5mm sS$ consists of the maps having image size $\leq
|\text{im}\, s\,|$, so that $S\kern-0.5mm sS\subseteq S\kern-0.35mm tS$ exactly
when $|\text{im}\, s\,|\leq|\text{im}\, t\,|$. We will write $\mathscr J_m$ for the
$\mathscr J$-class consisting of those
maps with image size $m$.
In general, define a partial order on
the
$\mathscr J$-classes of a semigroup $S$ by $\mathscr J_s\leq\mathscr J_t$ whenever
$S\kern-0.5mm sS\subseteq S\kern-0.35mm tS$.
\begin{figure}[t]
\centering
\begin{pspicture}(0,0)(14,9)
\rput(0,-0.5){
\rput(3.5,5){\BoxedEPSF{fig3.eps scaled 450}}
\rput(10.5,5){\BoxedEPSF{fig2.eps scaled 450}}
\rput(4,8.9){$\mathscr J_5$}\rput(4.5,8){$\mathscr J_4$}\rput(5,6.1){$\mathscr J_3$}
\rput(5,3.9){$\mathscr J_2$}\rput(4.5,2){$\mathscr J_1$}\rput(4,1.1){$\mathscr J_0$}
\rput(10,8.6){$\mathscr J_5$}\rput(9,7.7){$\mathscr J_4$}\rput(7.5,6){$\mathscr J_3$}
\rput(8.5,3.5){$\mathscr J_2$}\rput(10,1.8){$\mathscr J_1$}
}
\end{pspicture}
\caption{The $\HH$-classes containing idempotents in $I_5$
\emph{(left)} and $T_5$ \emph{(right)}.}
\label{fig:Tn_Hclasses_idempotents}
\end{figure}
\paragraph{Idempotents.} An idempotent is an element $e$
with the property that $e^2=e$. In a group there is precisely one: the identity
$\id$. But in $I_n$ there are others, and in $T_n$ even more again.
The idempotents in $I_n$ are the maps $\id_X:X\rightarrow X$
that are the identity on some $X\subseteq [n]$; they are the \emph{partial
identities\/}. In the eggbox on the right of Figure \ref{fig:LR_commute},
$\id_X$ lives on the
diagonal in the row and
column labelled by $X$.
Moreover, $\id_X$ is the only
idempotent in its
row and column. In fact, this is true for any inverse semigroup: each
$\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$-class and each $\LL$-class contains a unique idempotent.
To find idempotents in $T_n$, fix any partition of $[n]$; this will be
the fibers/kernel of $e$. In each fiber fix a point, and then define $e$
to map each fiber to the point chosen in it -- see Figure
\ref{fig:Tn_idempotents}. (A slicker way to say it is that $e$
restricts to the identity on its image.)
\begin{figure}[b]
\centering
\begin{pspicture}(0,0)(14,3)
\rput(7,1.5){\BoxedEPSF{fig12b.eps scaled 450}}
\rput(3.5,2.9){$1$}\rput(10.9,2.9){$n$}
\rput(3.5,0.1){$1$}\rput(10.9,0.1){$n$}
\rput(3,1.5){$e$}
\end{pspicture}
\caption{An idempotent in $T_n$.}
\label{fig:Tn_idempotents}
\end{figure}
If the fibers -- and hence the $\LL$-class -- are fixed, there is still
wiggle-room in the
choice of point in each one. So a given $\LL$-class may contain several
idempotents. Dually, fixing some image points (and hence the
$\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$-class) there are many partitions of $[n]$ with a unique image
point in each block of the partition, and so several idempotents in a
given $\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$-class. This behaviour is typical of regular, non-inverse
semigroups. Figure
\ref{fig:Tn_Hclasses_idempotents} compares the
$\HH$-classes containing idempotents in $I_5$ and $T_5$.
In any case, in both $I_n$ and $T_n$ -- and in a regular monoid in
general -- each $\HH$-class contains at most one idempotent.
\begin{figure}
\centering
\begin{pspicture}(0,0)(14,7.5)
\rput(7,3.75){\BoxedEPSF{fig9c.eps scaled 450}}
\rput(7.95,3.85){${\scriptstyle s}$}
\rput(-7.5,-0.7){
\rput(9.6,7.9){$n$}\rput(9.4,6.7){$n-1$}
\rput(9.4,4.5){$m$}\rput(9.4,2.4){$1$}\rput(9.4,1.2){$0$}
}
\rput(0.9,2.5){$\red S\kern-0.5mmsS$}
\psline[linewidth=0.75pt,linecolor=red]{->}(1.2,2.5)(2,2.5)
\rput(4.8,3.8){$\mathscr J_m$}\rput(4.8,1.35){$\mathscr J_1$}
\rput(4.8,0.725){$0$}\rput(4.8,5.95){$\mathscr J_{n-1}$}
\rput(4.8,6.85){$S_{\kern-.3mm n}$}
\rput(9.7,0.55){$=$ all bijections $X\stackrel{s}{\rightarrow}Y$}
\rput(7.95,1.45){$X$}\rput(12.15,3.85){$Y$}
\rput(7.35,6.25){$S_{\kern-.3mm m}$}\rput(7.95,5.65){$S_{\kern-.3mm m}$}
\rput(8.6,5.05){$S_{\kern-.3mm m}$}\rput(9.2,4.45){$S_{\kern-.3mm m}$}
\rput(9.8,3.825){$S_{\kern-.3mm m}$}\rput(10.425,3.2){$S_{\kern-.3mm m}$}
\rput(11.05,2.6){$S_{\kern-.3mm m}$}\rput(11.63,2){$S_{\kern-.3mm m}$}
\rput(9.5,7){domains of size $m$}
\rput(-2.85,-2.8){\rput{90}(9.5,7){images of size $m$}}
\end{pspicture}
\caption{Strategic picture of $I_n$. The $\mathscr J$-class poset
\emph{(left)\/}, the stacked eggboxes \emph{(middle)\/} and the
eggbox picture of the $\mathscr J$-class $\mathscr J_m$ \emph{(right)\/}; there
are $\binom{n}{m}$ rows and columns with the maximal subgroups
$\congS_{\kern-.3mm m}$ down the diagonal.}
\label{fig:In_stategic_picture}
\end{figure}
\paragraph{Subgroups.} In any monoid the \emph{units\/} are the elements
that have inverses in the sense of group theory, and these form a
subgroup. In our three examples $S_{\kern-.3mm n},I_n$ and $T_n$, these are the
bijections $[n]\rightarrow [n]$, so the group of units is $S_{\kern-.3mm n}$
with identity $\id:[n]\rightarrow [n]$. In $S_{\kern-.3mm n}$ this is the whole story,
but in $I_n$ there are other subgroups, \emph{disjoint from the units\/}, and in $T_n$ even
more again.
For $X\subseteq [n]$ fixed, the bijections $X\rightarrow X$ form a subgroup of
$I_n$ isomorphic to $S_{\kern-.3mm m}$, where $m=|X|$. This subgroup is precisely the
diagonal $\HH$-class containing the idempotent $\id_X:X\rightarrow X$.
In general, if
$\HH_e$ is the $\HH$-class containing the idempotent $e$, then this is
a subgroup of $S$ with identity $e$. Moreover, any subgroup of $S$ is a
subgroup of an $\HH_e$ for some $e$, hence these are \emph{maximal
subgroups\/} of $S$. We write $G_e$ for $\HH_e$ from now on, to
stress its group structure.
$T_n$ has many more $\HH$-classes containing idempotents, hence many
more maximal subgroups. The $\HH$-class containing the idempotent $e$
on the left of
Figure \ref{fig:Tn_maximal_subgroup} consists of the maps with fibers
$X_1,\ldots,X_m$ and image points $y_1,\ldots,y_m$,
\begin{figure}[h]
\centering
\begin{pspicture}(0,0)(14,3)
\rput(3.5,1.5){\BoxedEPSF{fig13b2.eps scaled 450}}
\rput(1.6,2.95){$X_1$}\rput(3.5,2.95){$X_2$}
\rput(1.25,0.1){$y_1$}\rput(3.1,0.1){$y_2$}
\rput(5.6,1.5){$e$}
\rput(10.5,1.5){\BoxedEPSF{fig13c2.eps scaled 450}}
\rput(7,0){
\rput(1.6,2.95){$X_1$}\rput(3.5,2.95){$X_2$}
\rput(1.25,0.1){$y_1$}\rput(3.1,0.1){$y_2$}
}
\end{pspicture}
\caption{Maximal subgroup of $T_n$ with identity the idempotent $e$
\emph{(left)\/} and a typical element \emph{(right)\/}.}
\label{fig:Tn_maximal_subgroup}
\end{figure}
and where these maps give a bijection
$\{X_1,\ldots,X_m\}\rightarrow\{y_1,\ldots,y_m\}$. The maximal subgroups of
$T_n$ are thus symmetric groups $S_{\kern-.3mm m}$ as well, but in a slightly
different way to $I_n$.
Figure \ref{fig:Tn_Hclasses_idempotents} therefore also shows these
$S_{\kern-.3mm m}$ subgroups (shaded), for $0\leq m\leq 5$, in $I_5$ and $T_5$.
\begin{figure}[t]
\centering
\begin{pspicture}(0,0)(14,6.5)
\rput(0,0.25){
\rput(7,3){\BoxedEPSF{fig5.eps scaled 450}}
\rput(0,-0.55){
\rput(5.4,5.3){$X\stackrel{e}{\rightarrow}X$}
\rput(5.4,1.9){$X\stackrel{s}{\rightarrow}Y$}
\rput(8.65,5.3){$Z\stackrel{t}{\rightarrow}X$}
\rput*(4.1,3.5){${\red s(-)}$}
\rput*(7,6.4){${\red (-)t}$}
\rput(5.4,4.4){$G_e$}
\rput(3.95,5.3){$\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q_e$}
\rput(5.4,6.6){$\LL_e$}
\rput(5.4,2.6){$\HH_s$}
\rput(8.6,4.4){$\HH_t$}
\rput(7,6){{\red bijection}}
\rput(3.1,3.5){{\red bijection}}
}
}
\end{pspicture}
\caption{Green's lemma.}
\label{fig:Green_lemma}
\end{figure}
\paragraph{The strategic picture for $I_n$:}
is given in Figure
\ref{fig:In_stategic_picture}.
The $\mathscr J$-class poset is on the left -- the image sizes $\{0,\ldots,n\}$
with their usual total order -- and the stacked eggboxes are in the
middle. The maximal $\mathscr J$-class consists of all the bijections with
image size $n$, so is the symmetric group $S_{\kern-.3mm n}$, and the minimal $\mathscr J$-class
has single element the zero map $0:\varnothing\rightarrow\varnothing$.
The class $\mathscr J_m$ has rows and columns indexed by the $\binom{n}{m}$
subsets of size $m$, with the blue box in Figure \ref{fig:In_stategic_picture}
containing the bijections
$s:X\rightarrow Y$. The idempotents $\id_X:X\rightarrow X$ lie down the
diagonal, with the maximal subgroups consisting of all the bijections
$X\rightarrow X$ for fixed $|X|=m$, and thus $\congS_{\kern-.3mm m}$.
\paragraph{Green's lemma.} The maximal subgroups can be used to parametrise the
$\LL$ and $\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$ classes containing them -- indeed, the
$\HH$-classes in $\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q_e$ are like right cosets of the subgroup $G_e$
and the $\HH$-classes in $\LL_e$ are like left cosets.
It is easy to
see in $I_n$: let $e$ be the idempotent
$\id_X:X\rightarrow X$, contained in the maximal subgroup $G_e$ of all
bijections $X\rightarrow X$ (see Figure \ref{fig:Green_lemma}). An $s\in\LL_e$
is a bijection $s:X\rightarrow Y$. For any $g\in G_e$, the composition
$$
X\stackrel{g}{\rightarrow}X\stackrel{s}{\rightarrow}Y
$$
is a bijection $X\rightarrow Y$, and all such bijections arise in this way via
some $g$. Put another way, left multiplication by $s$ is a bijection
$s(-):G_e\rightarrow\HH_s$.
Thus:
\begin{equation}
\label{eq:1}
\text{every element of the $\HH$-class $\HH_s$ can be uniquely
expressed as $sg$ for some $g\in G_e$}
\end{equation}
(so $\HH_s=sG_e$ is the
left coset in $\LL_e$ of the maximal subgroup $G_e$).
Dually, if $t\in\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q_e$ is
some bijection $t:Z\rightarrow X$ then every element of $\HH_t$ has a unique
expression as $gt$ for some $g\in G_e$, and so $\HH_t$ is the right
coset $G_et$ of $G_e$ in $\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q_e$. These observations are called
Green's lemma.
\begin{figure}
\centering
\begin{pspicture}(0,0)(14,7)
\rput(0,0){
\rput(7,3.5){\BoxedEPSF{fig1.eps scaled 450}}
\rput(5.4,5.3){$X\stackrel{e}{\rightarrow}X$}
\rput(8.65,1.9){$Y\stackrel{f}{\rightarrow}Y$}
\rput(8.65,5.3){$Y\stackrel{s^*}{\rightarrow}X$}
\rput(5.4,1.9){$X\stackrel{s}{\rightarrow}Y$}
\rput*(7.025,3.5){${\red\cong}$}
\rput*(7,6.4){${\red (-)s}$}
\rput*(7,0.6){${\red (-)s^*}$}
\rput*(4.1,3.5){${\red s(-)}$}
\rput*(9.9,3.5){${\red s^*(-)}$}
\rput(5.4,4.4){$G_e$}\rput(8.6,2.6){$G_f$}
\rput(7.4,4){${\red s^*(-)s}$}
\rput(6.7,3){${\red s(-)s^*}$}
}
\end{pspicture}
\caption{Maximal subgroups are isomorphic.}
\label{fig:maximal_subgroups_isomorphic}
\end{figure}
An important consequence is that the maximal
subgroups in a fixed $\mathscr J$-class are isomorphic.
Again we see it in $I_n$; let $e=\id_X$ and $f=\id_Y$ be idempotents in
the $\mathscr J$-class
$\mathscr J_e=\mathscr J_f$ and
let $G_e,G_f$ be the corresponding maximal subgroups -- see Figure
\ref{fig:maximal_subgroups_isomorphic}. Somewhat incidentally,
$G_e\congS_{\kern-.3mm m}\cong G_f$ with $|X|=m=|Y|$, but this isomorphism
also arises naturally as follows.
``Complete the square'' of $\HH$-classes that has the maximal
subgroups at its diagonal corners, and fix a representative $s:X\rightarrow Y$
of the $\HH$-class lying the the same column as $G_e$ and row as
$G_f$. The inverse $s^*:Y\rightarrow X$ then lies in the diagonally
opposite $\HH$-class.
Any $h:Y\rightarrow Y$ in the group $G_f$ can now
be decomposed as:
$$
Y\stackrel{h}{\rightarrow}Y=Y\stackrel{s^*}{\rightarrow}X\stackrel{g}{\rightarrow}X\stackrel{s}{\rightarrow}Y
$$
for some $g\in G_e$, and the map $g\mapsto sgs^*$ is a
homomorphism $G_e\rightarrow G_f$ with inverse the map $h\mapsto s^*hs$.
\paragraph{The inverse monoids $S\kern-1pt(G,L)$.}
Mathematics contains many examples of a group
acting on a poset or a lattice -- we now describe an
inverse monoid that wraps up the group, the lattice and the
action into a single object. It turns out that many naturally occurring
inverse monoids arise this way. It is also a
particularly useful format for understanding
their representations -- we will find it essential for the examples of
\S\ref{section:sexy:example}.
Let $G$ be a finite group and
$L$ a finite lattice -- a poset in which every pair of elements $a,b$ has a
greatest lower bound, or \emph{meet\/} $a\wedge b$, and a least upper
bound, or \emph{join\/} $a\vee b$. Suppose that $G$ acts on $L$:
each $g\in G$ gives rise to a poset map $a\mapsto g\cdot a$, so that if $a\leq
b$ in $L$ then $g\cdot a\leq g\cdot b$. As this must also be true for $g^{-1}$, we
have $a\leq b$ iff $g\cdot a\leq g\cdot b$.
We form a semigroup $S\kern-1pt(G,L)$ out of this input data: the elements
have \emph{expressions\/} of the form $g_a$ where $g\in G$ and $a\in L$. Two
different expressions can represent the same element:
\begin{equation}
\label{eq:12}
g_a=h_b\text{ in }S\kern-1pt(G,L)
\text{ iff }
a=b\text{ and }
g^{-1}h\cdot c=c
\text{ for all }
c\leq a
\end{equation}
Finally, the product is given by
\begin{equation}
\label{eq:13}
g_ah_b=(gh)_{h^{-1}\cdot a\wedge b}
\end{equation}
where $gh$ is the product of $g$ and $h$ in $G$. If it seems a little
mysterious, you can think of $g_a$ as the element of the symmetric
inverse monoid on the set $L$ and having domain the interval $L_{\leq
a}=\{c\in L:c\leq a\}$ with effect the restriction of $g$ to this
interval. Then (\ref{eq:13}) is just the composition of
partial bijections for $I_{L}$ and (\ref{eq:12}) warns us that
different elements of $G$ can restrict to the same partial bijection
in $S\kern-1pt(G,L)$.
As $L$ is a finite lattice it has a maximum $\mathbf{1}=\bigvee_{a\in L} a$
and a minimum $\mathbf{0}=\bigwedge_{a\in L}a$, hence $S\kern-1pt(G,L)$ has an identity
$\id_{\mathbf{1}}$, where $\id$ is the identity in $G$, and a zero $g_{\mathbf{0}}$,
for any $g\in G$ (as $g\cdot\mathbf{0}=\mathbf{0}=h\cdot\mathbf{0}$ for any other $h$, we have
by (\ref{eq:12}) that $g_{\mathbf{0}}=h_{\mathbf{0}}$). More significantly, $g_a$ has the
semigroup inverse $g_a^*=g^{-1}_{g\cdot a}$ so that $S\kern-1pt(G,L)$ is an inverse
monoid.
The Green's relation structure follows the dictates of the symmetric
inverse monoid on $L$: we have $g_a\LL h_b$ exactly when $a=b$ and
$g_a\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q h_b$ when $g\cdot a=h\cdot b$. In particular the $\LL$-class of $g_a$
consists of all the $h_a$ as $h\in G$ varies, and the $\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$-class of all
the $h_{h^{-1}\cdot a}$.
The $\HH$-class of $g_a$ consists of the $h_a$ for those $h\in G$ such
that $h\cdot a=g\cdot a$. The $\mathscr J$-classes correspond to the orbits of the
$G$-action on $L$; if $\{a_1,\ldots,a_m\}$ is an orbit, then the
eggbox decomposition of the corresponding $\mathscr J$-class has rows and
columns indexed by the $a_i$ and the
$\mathscr J$-class consists of all the $g_a$ where $g\in G$ and $a$ is one of the $a_i$.
To complete the strategic picture, let $\mathscr J_1$ and $\mathscr J_2$ be
$\mathscr J$-classes corresponding to the $G$-orbits $\{a_1,\ldots,a_m\}$ and
$\{b_1,\ldots,b_\ell\}$. Then $\mathscr J_1\leq\mathscr J_2$ exactly when $a_i\leq b_j$
in $L$ for some $a_i$ and some $b_j$ (or equivalently
$a_i\leq b_j$ for any $a_i$ and some $b_j$, or, any $b_j$ and some
$a_i$).
The idempotents of $S\kern-1pt(G,L)$ are the $\id_a$ for $\id$ the
identity of $G$, and the units are the $g_{\mathbf{1}}$ with $\mathbf{1}$ the maximum of
$L$. By (\ref{eq:12})-(\ref{eq:13}) the units form an isomorphic copy of $G$ in $S\kern-1pt(G,L)$.
The maximal subgroup $G_a$ containing the idempotent $\id_a$ consists of the
$g_a$ with $g\cdot a=a$, subject to our running ambiguity
(\ref{eq:12}). It turns out that the ambiguity can be easily ironed out:
let $G^a$ be those elements of $G$ with $g\cdot a=a$ and let
$G^{\leq a}$ be those elements of $G$ with $g\cdot c=c$ for all $c\leq
a$. Then $G^{\leq a}$ is a normal subgroup of $G^a$ and there is an isomorphism
\begin{equation}
\label{eq:17}
G_a\cong G^a/G^{\leq a}
\end{equation}
from the maximal subgroup $G_a$ to this
sub-quotient of the group of units $G$.
Let $s=g_a$ be an element in the $\LL$-class of the maximal subgroup
$G_a$ and $s(-):G_a\rightarrow\HH_s$ the bijection promised by
Green's lemma. We can make the decomposition (\ref{eq:1}) quite
explicit: if $t=h_a$ is another element of $\HH_s$ then
\begin{equation}
\label{eq:14}
t=s\cdot g^{-1}_{b}h_a
\end{equation}
where $b=g\cdot a$ and
$g^{-1}_{b}h_a\in G_a$.
\begin{example}
We can shoehorn $I_n$ into this setting: $G=S_{\kern-.3mm n}$ and $L$ is the
lattice of subsets of $[n]$ ordered by inclusion with $S_{\kern-.3mm n}$ acting on
$L$ in the obvious way. We leave the reader to show that
$S\kern-1pt(S_{\kern-.3mm n},L)\cong I_n$ via the map that sends $g_a$ to the partial
permutation obtained by restricting $g$ to the subset $a$.
\end{example}
\begin{vexercise}
\label{exercise:sgl:order}
If $[G:H]$ is the index of the subgroup $H$ in $G$, show that
${\displaystyle |S\kern-1pt(G,L)|=\sum_{a\in L}[G:G^{\leq a}]}.$
Hence $|I_n|=\sum_{X\subseteq [n]}[S_{\kern-.3mm n}:S_{\kern-.3mm X}]$, where $S_{\kern-.3mm X}$ is the
symmetric group on the set $X$.
\end{vexercise}
\begin{figure}
\centering
\begin{pspicture}(0,0)(14,13)
\rput(0,3){
\rput(1,9){(a).}
\rput(3,4.75){\BoxedEPSF{Pi4.eps scaled 450}}
}
\rput(-1,-2){
\rput(7,4){(b).}
\rput(8.5,4.75){\BoxedEPSF{fig9a.eps scaled 450}}
\rput(8.5,2.5){$\{a,b,c,d\}$}
\rput(9.25,4.3){$\{ab,c,d\}$}
\rput(6.6,5.5){$\{abc,d\}$}
\rput(10.4,5.5){$\{ab,cd\}$}
\rput(8.5,7){$\{abcd\}$}
}
\rput(8,3){
\rput(3,4.75){\BoxedEPSF{Jclass4.eps scaled 450}}
\rput(3.1,9.1,){$\{abcd\}$}
\rput(3.1,9.4){$S_{\kern-.3mm 4}$}
\rput(0,8){(c).}
\rput(0.25,7){$\{abc,d\}$}
\rput(0.25,4.8){$S_{\kern-.3mm 3}\timesS_{\kern-.3mm 1}$}
\rput(3.1,4.2){$\{ab,c,d\}$}
\rput(5,3){$S_{\kern-.3mm 2}\timesS_{\kern-.3mm 1}\timesS_{\kern-.3mm 1}$}
\rput(3.1,0.2){$\{a,b,c,d\}$}
\rput(3.1,-0.2){$S_{\kern-.3mm 1}\timesS_{\kern-.3mm 1}\timesS_{\kern-.3mm 1}\timesS_{\kern-.3mm 1}$}
\rput(6,4.9){$S_{\kern-.3mm 2}\timesS_{\kern-.3mm 2}$}
}
\end{pspicture}
\caption{Strategic picture of $S\kern-1pt(G,L)$ when $G=S_{\kern-.3mm 4}$ and
$L=\Pi(4)$ from Example \ref{exercise:partition}: (a). the partition
lattice $\Pi(4)$; (b). the poset of
$\mathscr J$-classes labelled by the type of partitions; (c).
the strategic picture.}
\label{fig:S(G,L)}
\end{figure}
\begin{example}
\label{exercise:partition}
An important lattice in combinatorics is the \emph{partition
lattice\/} $\Pi(n)$, having elements
the partitions
$\Lambda=\{\Lambda_1,\ldots,\Lambda_p\}$ of $[n]$ ordered by
$\{\Lambda_1,\ldots,\Lambda_p\}\leq\{\Delta_1,\ldots,\Delta_q\}$ iff
each $\Lambda_i$ is a subset of some $\Delta_j$. The symmetric group
$S_{\kern-.3mm n}$
acts on $\Pi(n)$ via $g\cdot
\{\Lambda_1,\ldots,\Lambda_p\}=\{g\Lambda_1,\ldots,g\Lambda_p\}$.
The resulting $S\kern-1pt(G,L)$ is called the monoid of uniform block
permutations and the strategic picture, when $n=4$, is in Figure \ref{fig:S(G,L)}.
The $\mathscr J$-class poset is the poset of partitions
$\lambda=\{\lambda_1,\ldots,\lambda_p\}$ of the integer $n$ (see the
beginning of the Interlude),
and the corresponding maximal subgroup is isomorphic to the Young subgroup
$S_{\kern-1pt\lambda_1}\times\cdots\times
S_{\kern-1pt\lambda_p}$. In particular, the order of the monoid of
uniform block permutations is
$\sum_{\Lambda\in\Pi(n)}[S_{\kern-.3mm n}:S_{\lambda_1}\times\cdots\times S_{\lambda_p}]$.
\end{example}
\section{Representations}
\label{section:representations}
This section contains the basics of representation theory that are
common to all
finite regular monoids. The theme is the extent to which
representations can be decomposed into ``atomic'' pieces. These can
then be reassembled to get a handle on the sociology of the
representations of a semigroup. It turns out
that this is almost always possible for groups and inverse monoids,
but less so for regular, non-inverse monoids.
Throughout, $k$ is a field and $V$ a finite dimensional vector space over
$k$. Let $End(V)$ be the monoid, under composition, of all vector space
homomorphisms (or linear
maps) $V\rightarrow V$.
An \emph{$S$-action on $V$\/} or \emph{linear representation of $S$\/}
is a monoid homomorphism
$$
\varphi:S\rightarrow End(V).
$$
We adopt the convention that all monoid homomorphisms send $1$'s to $1$'s,
so that $\varphi(1_S)$ is the identity homomorpism $\id:V\rightarrow V$. In
particular
$\text{im}\,\varphi\not=\{0\}$, and so our representations are not
\emph{null\/}. If $S$ is a group then necessarily
$\text{im}\,\varphi\subset GL(V)$, the group of vector space isomorphisms
(or invertible linear maps) $V\rightarrow V$. The notion of a semigroup representation is thus
a straight generalisation of that of a group representation.
We will identify $s\in S$ and $\varphi(s)\in
End(V)$, so that if $v\in V$, we just write $s\cdot v$, or even $sv$, for the effect
of the linear map $\varphi(s)$ on the vector $v$. Mostly we will just write
$V$ for an $S$-representation without explicit reference to the
action.
The following representation of our three running examples $S_{\kern-.3mm n},I_n$
and $T_n$ will turn out to display the full range of possible behaviours:
\begin{example}[mapping representations]
\label{example:mapping:representation}
Fix a basis $\{v_1,\ldots,v_n\}$ for the space $V$ and for $s\in
S_{\kern-.3mm n},I_n$ or $T_n$ define
\begin{equation}
\label{eq:2}
s\cdot v_i=v_{s(i)}
\quad (s\in S_{\kern-.3mm n}, T_n)
\quad
\text{ or }
\quad
s\cdot v_i
=
\left\{\begin{array}{ll}
v_{s(i)}, &\text{ if }i\in\text{dom}\, s\\
0,&\text{else.}
\end{array}\right.
\quad (s\in I_n)
\end{equation}
and then extend linearly. To analyse the structure of the mapping
representations, we need to know how to decompose representations in general.
\end{example}
\paragraph{Sub-representations and reducibility.} These allow
us to understand representations in the large. If $V$ is a
representation and $U$ is a subspace left invariant
by the $S$-action, i.e. $SU=U$, then we call $U$ an
\emph{($S$-)subrepresentation\/} of
$V$. The quotient space $V/U$ then carries an $S$-action via
$s\cdot(v+U)=sv+U$, well-defined, as $sU=U$. There is then a 1-1
correspondence between the subrepresentations of $V/U$ and the
subrepresentations $W$ of $V$ such that $U\subseteq W\subseteq V$.
If $V$ has a proper, non-zero subrepresentation $U$, then call $V$
\emph{reducible\/}; $V$ is \emph{irreducible\/} if the only
subrepresentations are
$\{0\}$ and $V$.
A subrepresentation $U$ of $V$ is \emph{maximal\/} when $U\not=V$ but
for any subrepresentation $W$ of $V$ with $U\subseteq W\subseteq V$ we
have either $W=U$ or $W=V$. Because of the 1-1 correspondence
mentioned above, $U$
is maximal exactly when $V/U$ is irreducible.
If $U,W$ are subrepresentations of $V$ such that $V=U\oplus W$ as
vector spaces, then the representation $V$ is the \emph{(internal)
direct sum\/} of $U$ and $W$. Externally, if $U$ and $W$ are
arbitrary $S$-representations then the vector space direct sum
$U\oplus W$ carries an $S$-action via $s\cdot(u+w)=su+sw$, and
$U\oplus W$ is the \emph{(external) direct sum\/} of $U$ and $W$.
\begin{example}[the permuting coordinates and reflectional representations of
$S_{\kern-.3mm n}$]
\label{example:permutation:representation}
The $S_{\kern-.3mm n}$-action in (\ref{eq:2}) is by ``permuting coordinates''
(or more accurately, permuting basis vectors). In particular,
for $(i,j)\inS_{\kern-.3mm n}$ the resulting
isomorphism $V\rightarrow V$ is the reflection in the hyperplane with
equation $x_i-x_j=0$.
As $S_{\kern-.3mm n}$ is generated by the transpositions, its image in $GL(V)$
is generated by reflections, i.e: is a \emph{reflection group\/}.
\begin{figure}
\centering
\begin{pspicture}(0,0)(14,4)
\rput(1.5,0){
\rput(0,2){\BoxedEPSF{symmetric.group3.eps scaled 225}}
\rput(0.5,2.5){${\red s=(1,2,3)}$}
\rput(1.05,0.45){$v_1$}\rput(1.95,1.8){$v_2$}\rput(-0.6,3.85){$v_3$}
}
\rput(0,0){
\rput(5.75,2){\BoxedEPSF{symmetric.group2.eps scaled 225}}
\rput(6.85,2.3){$U$}
}
\rput(0,0){
\rput(9,2){\BoxedEPSF{symmetric.group1.eps scaled 225}}
\rput(9.5,2.5){$W+\frac{1}{n}u$}
}
\rput(12.5,0){
\rput(0,2){\BoxedEPSF{symmetric.group4.eps scaled 225}}
\rput(0.1,2.5){${\red s=[1,2,3]}$}
\rput(-0.3,-0.175){\rput(1.05,0.45){$v_1$}
\rput(1.95,1.8){$v_2$}
\rput(-0.6,3.85){$v_3$}
\rput(-1.3,3.85){$0$}}
}
\end{pspicture}
\caption{\emph{From left to right}: Permutation action of $S_{\kern-.3mm n}$; the
line $U$ which is the $k$-span of $u=v_1+\cdots+v_n$; the (affine)
hyperplane $W+\frac{1}{n}u$ coming from the reflectional representation; the partial
reflection action of $I_n$. The pictures are for $n=3$
and the notation for partial
permutations is described in the Notes and References section.}
\label{fig:reflection_rep_Sn}
\end{figure}
The vector $u=v_1+\cdots+v_n$ is fixed by any permutation
in $S_{\kern-.3mm n}$, so that if
$U$ is the $k$-span of $u$ then
$S_{\kern-.3mm n} U=U$, a subrepresentation. As each vector in $U$ is fixed by
every element of $S_{\kern-.3mm n}$,
this is the \emph{trivial
representation\/} of $S_{\kern-.3mm n}$ (see Figure \ref{fig:reflection_rep_Sn}).
Thus if $n>1$ then the permuting coordinates representation $V$ is
reducible. Moreover, as $U$ is $1$-dimensional it has only the two
subspaces, $S_{\kern-.3mm n}$-invariant or otherwise, namely $\{0\}$ and $U$.
Hence $U$ is irreducible. When $n=1$ we have $V=U$ is irreducible.
Now let $W$ be the hyperplane with equation $x_1+x_2+\cdots+x_n=0$,
that is, the
set of
points whose coordinates with respect to the $v_i$ sum to
$0$. Permuting the coordinates of such
a vector doesn't change the
fact that they add to $0$, hence $W$ is also a
subrepresentation of $V$. Figure \ref{fig:reflection_rep_Sn} has the
plane $W$ when $n=3$, shifted off the origin to make it easier to
see. For reasons that are maybe a little obscure at the moment, $W$ is
called the \emph{reflectional representation\/} of $S_{\kern-.3mm n}$.
Moreover, if the characteristic $\text{char}(k)$ of the
field does not divide $\dim V=n$, then $W$ is irreducible.
For suppose that $X\not=\{0\}$ is a $S_{\kern-.3mm n}$-invariant subspace of $W$
and let
$v\in X$ with $v\not=0$.
If all the coordinates of $v$ are equal to some $\lambda\in k$, then these
sum to $0$ to give
$n\lambda=0$, hence -- by the restriction on the characteristic --
we must have $\lambda=0$, hence $v=0$, a contradiction. The vector $v$ must
therefore have two
coordinates that are different. For each $1\leq i <n$ we can engineer a $g_i\inS_{\kern-.3mm n}$
such that in the vector
$g_i\cdot v$ it is the $i$-th and $(i+1)$-st coordinates that are different.
Then $(i,i+1)g_i\cdot
v-g_i\cdot v$ is a non-zero multiple of $v_i-v_{i+1}$. As $X$ is
$S_{\kern-.3mm n}$-invariant we conclude that for each $1\leq i <n$
the vector $v_i-v_{i+1}$ is an element of $X$. But these vectors form a basis
for $W$, so $X=W$, and $W$ is irreducible as claimed.
The permuting coordinates representation of $S_{\kern-.3mm n}$ can thus be decomposed
$V=U\oplus W$ into the trivial and reflectional representations, with
both of these
irreducible.
\end{example}
\begin{example}[the partial reflectional representation of $I_n$]
\label{example:partial:reflection:representation}
The $I_n$-action (\ref{eq:2}) is by partial permutations of
coordinates and
the image of $I_n$ in $End(V)$ is a \emph{reflection monoid\/}.
Assume that $n>1$.
The line $U$ spanned by $u=v_1+\cdots+v_n$ is no longer $I_n$-invariant:
if $s\in I_n$ is the partial identity with domain $\{1\}$
then $s\cdot u=v_1\not\in U$. Similarly $W$ is not
$I_n$-invariant.
In fact, $V$ itself is irreducible: for suppose $U$ is an
$I_n$-invariant subspace containing $0\not=v\in U$ with
$v=\sum \lambda_iv_i$ and $\lambda_j\not=0$ for
some $j$. For each $1\leq i\leq n$ let $s_i\in I_n$ be the partial
permutation shown in Figure \ref{fig:In_irreducible}.
\begin{figure}[h]
\centering
\begin{pspicture}(0,0)(14,3)
\rput(7,1.5){\BoxedEPSF{fig17a.eps scaled 450}}
\rput(4.2,2.9){$1$}\rput(7.5,2.9){$j$}\rput(9.85,2.9){$n$}
\rput(4.2,0.1){$1$}\rput(6,0.1){$i$}\rput(9.85,0.1){$n$}
\rput(8,1.5){${\red s_i=[j,i]}$}
\end{pspicture}
\caption{$s_i\in I_n$ for $1\leq i\leq n$; the notation $[j,i]$ is
explained in the Notes and References section.}
\label{fig:In_irreducible}
\end{figure}
Then $s_i\cdot v=\lambda_jv_i$, hence
$v_i\in U$ for all
$i$, and so $U=V$.
\end{example}
\begin{example}[the mapping representation of $T_n$]
\label{example:mapping:representation:T_n}
Again suppose that $n>1$. The hyperplane $W$ goes back to being a
subrepresentation of $V$: if $w\in W$ with $w=\sum \lambda_i
v_i$ where $\sum\lambda_i=0$, then $sw$ for $s\in T_n$ is shown in
Figure \ref{fig:Tn_mapping_rep}. In particular the non-zero
coordinates of $sw$ are sums of the coordinates of $w$, and so still
sum to $0$:
\begin{figure}[h]
\centering
\begin{pspicture}(0,0)(14,4)
\rput(0,0.5){
\rput(7,1.5){\BoxedEPSF{fig10d.eps scaled 450}}
\rput(3.5,3){$w=$}
\rput(4.5,3){$\lambda_1$}
\rput(5.25,3){$\lambda_2$}
\rput(6,3){$\lambda_3$}
\rput(6.8,3){$\lambda_4$}
\rput(7.6,3){$\lambda_5$}
\rput(8.55,3){$\lambda_6$}
\rput(9.45,3){$\lambda_7$}
\rput(3.5,0){$s\cdot w=$}
\rput(4.75,0){$\lambda_4+\lambda_5$}
\rput(5.6,0){$0$}
\rput(6.8,0){$\lambda_1+\lambda_2+\lambda_3$}
\rput(8.85,0){$\lambda_6+\lambda_7$}
\rput(8,0){$0$
}
\end{pspicture}
\caption{The hyperplane $W$ is a $T_n$-subrepresentation.}
\label{fig:Tn_mapping_rep}
\end{figure}
i.e. $sw=\sum\mu_i v_i$ where
$\mu_i=\sum \lambda_{ij}$, the sum over the $j$ in the
fiber of $i$. As $\sum\mu_i=\sum\lambda_i=0$, we get $sw\in W$.
If $S$ is any monoid, $V$ an $S$-representation and $T$ a submonoid of $S$, then
it is easy to see that restricting the $S$-action to $T$
makes $V$ into a $T$-representation. This observation gives that
$W$ is irreducible: if $X$ is a subrepresentation of $W$ then
it is an $S_{\kern-.3mm n}$-subrepresentation
of the $S_n$-representation $W$. The irreducibility of this
-- when $\text{char}(k)$ does not divide $n$ -- then gives $X=\{0\}$ or
$W$.
Just as for $I_n$, the line $U$ spanned by $v_1+\cdots+ v_n$ is not a
subrepresentation: for
example when $s$ is the constant map in $T_n$ that
sends all of $[n]$ to $1$, then $su=nv_1\not\in U$.
In fact, when $n>2$ we claim that there are \emph{no\/}
$1$-dimensional subrepresentations of the $T_n$-mapping representation
$V$. For, suppose that
$v\not=0$
so that $v=\sum\lambda_iv_i$ with
$\lambda_j\not=0$ for some $j$. If $s_1,s_2\in T_n$ are given by
Figure \ref{fig:Tn_elements}, where
everything apart from $j$ is sent to $n$, with $s_i$ sending $j$ to $i$,
then
$$
s_1(v)=\lambda_jv_1+\biggl(\sum_{i\not=j}\lambda_i\biggr)v_n
\quad
\text{ and }
\quad
s_2(v)=\lambda_jv_2+\biggl(\sum_{i\not=j}\lambda_i\biggr)v_n.
$$
As these are independent, any non-trivial $T_n$-invariant subspace
must be at least $2$-dimensional, and the claim follows.
\begin{figure}[h]
\centering
\begin{pspicture}(0,0)(14,3)
\rput(3.5,1.5){\BoxedEPSF{fig16a.eps scaled 450}}
\rput(0.65,2.9){$1$}\rput(4,2.9){$j$}\rput(6.35,2.9){$n$}
\rput(7.6,2.9){$1$}\rput(10.95,2.9){$j$}\rput(13.3,2.9){$n$}
\rput(0.65,0.1){$1$}\rput(6.35,0.1){$n$}
\rput(8.35,0.1){$2$}\rput(13.3,0.1){$n$}
\rput(10.5,1.5){\BoxedEPSF{fig16b.eps scaled 450}}
\rput(0.65,1.5){$s_1$}\rput(7.6,1.5){$s_2$}
\end{pspicture}
\caption{The $s_1$ and $s_2$ in $T_n$ for Example
\ref{example:mapping:representation:T_n}.}
\label{fig:Tn_elements}
\end{figure}
\end{example}
\paragraph{Semisimplicity.}
If $S$ is a finite regular monoid and $k$ a field, then the pair
$(S,k)$ is \emph{semisimple\/} when every $S$-representation $V$
over $k$ can be
decomposed
$$V=\bigoplus V_i$$
with the $V_i$ irreducible
subrepresentations of $V$.
Such a decomposition is then unique in the following sense: a
\emph{morphism\/} $q:V\rightarrow U$ of
$S$-representations is a linear map that
commutes with the $S$-actions on $V$ and $U$, i.e. for all $s\in S$ the diagram
$$
\begin{pspicture}(0,0)(14,2)
\rput(5,0){
\rput(1,2){$V$}
\psline[linewidth=0.5pt]{->}(1.25,2)(2.75,2)
\rput(2,2.2){${\scriptstyle s\cdot (-)}$}
\rput(3,2){$V$}
\psline[linewidth=0.5pt]{->}(1,1.7)(1,0.3)
\psline[linewidth=0.5pt]{->}(3,1.7)(3,0.3)
\rput(0.8,1){${\scriptstyle q}$}\rput(3.2,1){${\scriptstyle q}$}
\rput(1,0){$U$}
\psline[linewidth=0.5pt]{->}(1.25,0)(2.75,0)
\rput(2,0.2){${\scriptstyle s\cdot (-)}$}
\rput(3,0){$U$}
}
\end{pspicture}
$$
commutes, where the top $s\cdot(-)$ is the $S$-action on $V$
and the bottom is the $S$-action on $U$. Call $q$ an
\emph{isomorphism\/} if it is a bijective morphism. Uniqueness then
means:
\begin{theorem}[Jordan-H\"{o}lder]
\label{theorem:JordanHolder}
Let $V$ be an $S$-representation and $V=\bigoplus V_i$ with the
subrepresentations $V_i$ irreducible. If $W$ is an irreducible
subrepresentation of $V$ then $W$ is isomorphic to one of the $V_i$.
\end{theorem}
We saw at the end of Example \ref{example:permutation:representation} that
the reflectional representation of $S_n$ can be so decomposed, and indeed:
\begin{theorem}[Mashke]
\label{theorem:Mashke}
If $S$ is a finite group then $(S,k)$ is semisimple if and only if
the characteristic
$\text{char}(k)$ does not divide the order of $S$.
\end{theorem}
In particular, $(S_{\kern-.3mm n},k)$ is semisimple exactly when $\text{char}(k)$ doesn't
divide $n!$, so that characteristic $0$ representations can always be
decomposed. The situation for inverse monoids is almost as good:
\begin{theorem}[Munn-Oganesyan]
\label{theorem: Munn:Oganesyan}
If $S$ is a finite inverse monoid then $(S,k)$ is semisimple if
and only if $\text{char}(k)$ does not divide the order of any
subgroup of $S$.
\end{theorem}
As any subgroup of $S$ is in turn a subgroup of a maximal subgroup $G_e$ for
some idempotent $e$, it suffices that the characteristic does not
divide the order of any $G_e$.
For our model inverse monoid $I_n$, we have already seen that
the maximal subgroups
are isomorphic to $S_{\kern-.3mm m}$ for $1\leq m\leq
n$. The pair $(I_n,k)$ is thus semisimple when the
characteristic of $k$ does not divide $m!$ for any $m\leq n$,
i.e. when it does not divide $n!$ We therefore get the same condition for
the semisimplicity of $I_n$ and $S_{\kern-.3mm n}$ representations.
For $T_n$ things are not so good.
If the mapping representation $V$ of $T_n$
is decomposable $V=\bigoplus V_i$ with the $V_i$
irreducible, then by Theorem
\ref{theorem:JordanHolder}, one of the $V_i$ is isomorphic to the
representation on the hyperplane $W$ with equation $x_1+\cdots
x_n=0$ that we saw above. The
decomposition of $V$ must then be $V\cong
W\oplus W'$ with $W'$ a $1$-dimensional subrepresentation. But we have
seen for $n>2$ that there are no $1$-dimensional subrepresentations of
$V$, and so no such decomposition of $V$ can exist when $n>2$.
Thus the pair $(T_n,k)$ is not semisimple, when $n>2$,
for \emph{any\/} $k$ whose characteristic does not divide $n$. In
particular, not even for $k$ of characteristic $0$.
\paragraph{Here then is what we have learned from the three examples:}
in characteristic $0$ the partial permuting coordinates (or
reflectional)
representation of $I_n$ is ``atomic''; the permuting coordinates representation
of $S_{\kern-.3mm n}$ is not atomic but can be decomposed into
pieces that are; the mapping representation of $T_n$ is not atomic and
cannot even be decomposed into atomic pieces.
\section*{Interlude: the symmetric group}
The moral of \S\S\ref{section:reduction}-\ref{section:clifford:munn}
is that the representations of a
(finite regular) monoid $S$ are largely driven by the representations
of its maximal subgroups. In every example that
we have seen so far these maximal subgroups have been symmetric
groups, or products of symmetric groups. It seems reasonable then to
understand better the representations of the symmetric
group, at least when $k=\ams{C}}\def\Q{\ams{Q}}\def\F{\ams{F}}\def\K{\ams{K}$.
We do this in a completely self-contained-tailored-to-$S_{\kern-.3mm n}$
way, without any reference to the general theory of
representations of finite groups. This will make it seem a little like
pulling a rabbit out of a hat; the reader who is interested in the
broader context of these facts should consult the Notes and References
at the end.
By Theorem \ref{theorem:Mashke}, any $S_{\kern-.3mm n}$-representation over $\ams{C}}\def\Q{\ams{Q}}\def\F{\ams{F}}\def\K{\ams{K}$
is a direct sum of irreducible representations; we will thus content
ourselves with describing just these. Despite the comments in the previous
paragraph, we allow ourselves one general fact: the irreducible
representations over $\ams{C}}\def\Q{\ams{Q}}\def\F{\ams{F}}\def\K{\ams{K}$ of a finite group are in 1-1 correspondence
with the conjugacy classes of the group. For $S_{\kern-.3mm n}$, these in turn
are in 1-1 correspondence with the possible cycle structures of
permutations of degree $n$ and \emph{these in turn\/} with the
partitions of the integer $n$: the integer
sequences $\lambda_1\geq\ldots\geq\lambda_p>0$ with
$\sum\lambda_i=n$. Write $\lambda=\{\lambda_1,\ldots,\lambda_p\}\vdash n$.
Fix $\lambda=\{\lambda_1,\ldots,\lambda_p\}\vdash n$ a partition of
$n$. A Young diagram of shape $\lambda$ illustrates the structure of
$\lambda$, as on the
left of Figure \ref{fig:Young:diagram}, and a \emph{tableau\/} $T$ is a Young
diagram filled with entries from $[n]$ with no repeats allowed -- as in the
middle of Figure \ref{fig:Young:diagram}. The
tableau is standard, or $T$ is a \emph{standard tableau\/}, when
the entries increase along the rows and down the columns. Finally, a tableau $T$
yields a \emph{tabloid\/} $\{T\}$, which is just a tableau where we no
longer care about the ordering in the rows -- see the right of Figure
\ref{fig:Young:diagram}.
\begin{figure}
\centering
\begin{pspicture}(0,0)(14,2.5)
\rput(3,1.25){\BoxedEPSF{tableau3.eps scaled 450}}
\rput(1.1,2.1){$\lambda_1$}\rput(1.1,1.5){$\lambda_2$}
\rput(1.1,1.1){$\vdots$}\rput(1.1,0.5){$\lambda_p$}
\rput(7,1.25){\BoxedEPSF{tableau3.eps scaled 450}}
\rput(5.65,2.05){$2$}\rput(6.15,2.05){$3$}\rput(6.7,2.05){$12$}
\rput(7.25,2.05){$7$}\rput(7.8,2.05){$13$}\rput(8.35,2.05){$15$}
\rput(5.65,1.55){$5$}\rput(6.15,1.55){$1$}\rput(6.7,1.55){$10$}
\rput(7.25,1.55){$14$}
\rput(5.65,1){$4$}\rput(6.15,1){$9$}\rput(6.7,1){$11$}\rput(7.25,1){$16$}
\rput(5.65,0.45){$6$}\rput(6.15,0.45){$8$}
\rput(11,1.25){\BoxedEPSF{tableau4.eps scaled 450}}
\rput(4,0){
\rput(5.65,2.05){$2$}\rput(6.15,2.05){$7$}\rput(6.7,2.05){$12$}
\rput(7.25,2.05){$3$}\rput(7.8,2.05){$13$}\rput(8.35,2.05){$15$}
\rput(5.65,1.55){$1$}\rput(6.15,1.55){$10$}\rput(6.7,1.55){$5$}
\rput(7.25,1.55){$14$}
\rput(5.65,1){$16$}\rput(6.15,1){$11$}\rput(6.7,1){$9$}\rput(7.25,1){$4$}
\rput(5.65,0.45){$8$}\rput(6.15,0.45){$6$}
}
\end{pspicture}
\caption{A Young diagram \emph{(left)}, a tableau $T$
\emph{(middle)} and the resulting tabloid $\{T\}$ \emph{(right)}
corresponding to a partition
$\lambda=\{\lambda_1,\ldots,\lambda_p\}\vdash n$.}
\label{fig:Young:diagram}
\end{figure}
The symmetric group $S_{\kern-.3mm n}$ acts on the set of tableau of shape
$\lambda$, via $g:T\mapsto gT$ for $g\inS_{\kern-.3mm n}$, where $gT$ is the
tableau that has $g(i)$ in the box in which $T$ has $i$. This action
extends to the set of tabloids of shape $\lambda$ via
$g\cdot\{T\}=\{gT\}$. For a tableau $T$, the column group $c_T$ is
defined
$$
c_T=\{g\inS_{\kern-.3mm n}:g\text{ preserves each column of }T\}\subseteqS_{\kern-.3mm n}
$$
Let $M^\lambda$ be the $\ams{C}}\def\Q{\ams{Q}}\def\F{\ams{F}}\def\K{\ams{K}$-vector space with basis the tabloids
$\{T\}$ of the fixed shape $\lambda$. Via the action above, $S_{\kern-.3mm n}$
acts on $M^\lambda$ by permuting the basis vectors. For the partition
$\lambda=\{n-1,1\}$ we will see below that $M^\lambda$ is the
permuting coordinates representation of
\S\ref{section:representations}. Now we have other representations of $S_{\kern-.3mm n}$.
In any case, the $M^\lambda$ are in general reducible -- much like the
permuting coordinates representation -- and we will pass to a
particular subrepresentation.
If $T$ is a tableau then let $v_T\in M^\lambda$ be the vector
\begin{equation}
\label{eq:19}
v_T=\sum_{h\in c_T}\text{sign}(h)\, h\cdot\{T\}
\end{equation}
where $\text{sign}(h)=1$ or $-1$ depending on whether $h$ is an even
or odd permutation.
We will see below that in general
the vectors $v_T$, as $T$ ranges over the tableau of
shape $\lambda$, are \emph{not\/} independent. (The $v_T$ for $T$
standard \emph{are\/} an
independent subset, although we won't need this fact here.)
In any case, let
\begin{equation}
\label{eq:15}
S^\lambda:=\text{ the subspace of }M^\lambda\text{ spanned by the }v_T.
\end{equation}
It turns out that $S^\lambda$ is an irreducible subrepresentation of
$M^\lambda$, and
as $\lambda$ varies over the partitions of $n$, the $S^\lambda$ --
called \emph{Specht\/} representations -- give a
complete and non-redundant list of the irreducible
$S_{\kern-.3mm n}$-representations over $\ams{C}}\def\Q{\ams{Q}}\def\F{\ams{F}}\def\K{\ams{K}$.
\begin{example}
\label{symmetric:example:trivial}
If $\lambda=\BoxedEPSF{tableau5.eps scaled 200}$
then there is a single tabloid:
$$
\begin{pspicture}(0,0)(14,1)
\rput(4.8,0.5){$T=$}
\rput(7,0.5){\BoxedEPSF{tableau5b.eps scaled 450}}
\rput(5.65,0.5){$1$}\rput(6.2,0.5){$2$}
\rput(6.75,0.5){$3$}\rput(8.35,0.5){$n$}
\end{pspicture}
$$
and the column group $c_T$ is trivial. There is thus just one vector
$v_T=\{T\}$ in the $1$-dimensional space $M^\lambda$, with
$g\cdot\{T\}=\{T\}$ for all $g\inS_{\kern-.3mm n}$, so that $M^\lambda=S^\lambda$ is the
trivial $1$-dimensional representation of $S_{\kern-.3mm n}$.
\end{example}
\begin{example}
\label{symmetric:example:sign}
At the other extreme we have:
$$
\begin{pspicture}(0,0)(14,3)
\rput(0,0){
\rput(6.15,1.5){$\lambda=$}
\rput(7,1.5){\BoxedEPSF{tableau6.eps scaled 400}}
}
\end{pspicture}
$$
For any tableau of this shape the column
group $c_T$ is the full symmetric group $S_{\kern-.3mm n}$,
and upto sign, there is just one of the vectors
$$
v_T=\sum_{h\inS_{\kern-.3mm n}}\text{sign}(h)\, h\cdot\{T\}=A-B,
$$
where $A$ is the sum of those terms with $h$ even and $B$ the sum
involving those with $h$ odd. An even permutation $g\inS_{\kern-.3mm n}$
preserves both summands and an odd one swaps them over, so that
$$
g\cdot v_T
=\left\{
\begin{array}{ll}
A-B=v_T, & g\text{ even},\\
B-A=-v_T, & g\text{ odd}.\\
\end{array}\right.
=\text{sign}(g)\cdot v_T
$$
The resulting Specht representation $S^\lambda$ is
thus $1$-dimensional (hence irreducible) but
not
the trivial representation; it is called the \emph{sign representation\/} of
$S_{\kern-.3mm n}$.
\end{example}
\begin{figure}
\centering
\begin{pspicture}(0,0)(14,3)
\rput(2,2){$\mathlarger{\mathlarger{S}}^{\BoxedEPSF{tableau5a.eps
scaled 80}}$}
\rput(2,1.5){$1$-dimensional}
\rput(2,1.1){trivial representation}
\rput(5,2){$\mathlarger{\mathlarger{S}}^{\BoxedEPSF{tableau6a.eps
scaled 80}}$}
\rput(5,1.5){$1$-dimensional}
\rput(5,1.1){sign representation}
\rput(8.5,2){$\mathlarger{\mathlarger{S}}^{\BoxedEPSF{tableau1a.eps
scaled 80}}$}
\rput(8.5,1.5){$2$-dimensional}
\rput(8.5,1.1){reflectional representation}
\rput(12,1.5){$\BoxedEPSF{S3_reflectional.eps scaled 400}$}
\rput(13.15,0.9){${\red 1}$}\rput(10.85,0.9){${\red
2}$}\rput(12,2.8){${\red 3}$}
\rput(13.8,1.5){$v_1-v_2$}
\rput(11.1,0.2){$v_2-v_3$}
\rput(11.1,2.8){$v_1-v_3$}
\end{pspicture}
\caption{The three irreducible $S_{\kern-.3mm 3}$ representations over $\ams{C}}\def\Q{\ams{Q}}\def\F{\ams{F}}\def\K{\ams{K}$: the
trivial representation, the sign representation and the
reflectional representation. The last corresponds to
the symmetries of an equilateral triangle.}
\label{fig:symmetric:three}
\end{figure}
\begin{example}
\label{symmetric:example:reflectional}
If now
$\lambda=\BoxedEPSF{tableau1.eps scaled 200}$
then $M^\lambda$ is an $n$-dimensional space with
basis the tabloids:
$$
\begin{pspicture}(0,0)(14,2)
\rput(2,0){
\rput(-1.5,0){
\rput(1.75,1){$v_1=$}
\rput(2.65,1.3){$2$}\rput(3.2,1.3){$3$}\rput(5.35,1.3){$n$}
\rput(2.65,0.75){$1$}
\rput(4,1){\BoxedEPSF{tableau2a.eps scaled 450}}
}
\rput(5,1){$\cdots$}
\rput(4.25,0){
\rput(1.75,1){$v_n=$}
\rput(2.65,1.3){$2$}\rput(3.2,1.3){$3$}\rput(5.15,1.3){$n-1$}
\rput(2.65,0.75){$n$}
\rput(4,1){\BoxedEPSF{tableau2a.eps scaled 450}}
}}
\rput(6.3,1){,}
\rput(7.5,1,1){,}
\end{pspicture}
$$
and the $S_{\kern-.3mm n}$-action is $g\cdot v_i=v_{g\cdot i}$; it is
thus the permuting coordinates representation of Example
\ref{example:mapping:representation}.
If
$$
\begin{pspicture}(0,0)(14,1.75)
\rput(-1.8,-0.125){
\rput(1.75,1){$T=$}
\rput(2.65,1.3){$i$}\rput(2.65,0.75){$j$}
\rput(4,1){\BoxedEPSF{tableau1.eps scaled 450}}
\rput(6.5,1){then}
\rput(1,0){
\rput(6.8,1){$v_T=$}
\rput(9,1){\BoxedEPSF{tableau2.eps scaled 450}}
\rput(7.65,1.3){$j$}\rput(7.65,0.75){$i$}
\rput(11,1){$-$}
\rput(13,1){\BoxedEPSF{tableau2.eps scaled 450}}
\rput(11.65,1.3){$i$}\rput(11.65,0.75){$j$}
}
}
\end{pspicture}
$$
i.e. $v_T=v_i-v_j\in M^\lambda$, and the $v_T$, as $T$ ranges over the
tableau of shape $\lambda$, give the vectors
$\{v_i-v_j\}_{1\leq i\not=j\leq n}$, which span the hyperplane in
$M^\lambda$ having equation $\sum x_i=0$ (and as promised, the
$v_T$, as $T$ ranges over all tableau, form a dependent set). The restriction of the
$S_{\kern-.3mm n}$-action on $M^\lambda$ to this hyperplane then gives that $S^\lambda$
the reflectional
representation of Example \ref{example:permutation:representation}.
\end{example}
When $n=3$ the possible $\lambda$ are
$\begin{pspicture}(0,0)(0.15,0.1)
\BoxedEPSF{tableau5a.eps scaled 150}
\end{pspicture}$,
$\begin{pspicture}(0,0)(0.15,0.1)
\BoxedEPSF{tableau6a.eps scaled 150}
\end{pspicture}$ and
$\begin{pspicture}(0,0)(0.15,0.1)
\BoxedEPSF{tableau1a.eps scaled 150}
\end{pspicture}$ and the $S^\lambda$ are the
three examples in Figure \ref{fig:symmetric:three}.
\begin{vexercise}
\label{exercise:exterior:powers;reflectional}
Show that the exterior power $\bigwedge^p S^{\BoxedEPSF{tableau1.eps scaled 100}}\cong
S^{\BoxedEPSF{tableau7.eps scaled 100}}$, where there are $n-p$ boxes
in the first row of the Young
diagram of the second Specht representation. (The exterior powers of the reflectional
representation are thus also irreducible).
\end{vexercise}
\section{Reduction}
\label{section:reduction}
This section and the next give two constructions for shuttling back
and forth between representations of a finite regular monoid $S$ and
representations of the maximal subgroups $G_e$ of $S$. The first of
these -- reduction -- squashes $S$-representations down to
$G_e$-representations; the second, induction, blows up
$G_e$-representations into $S$-representations. In Section
\ref{section:clifford:munn} we will see that with a little care in the
choice of $e$, these constructions turn out to be inverses of each
other. Throughout, the underlying field $k=\ams{C}}\def\Q{\ams{Q}}\def\F{\ams{F}}\def\K{\ams{K}$.
We start with two examples that illustrate all the key features:
\begin{example}
\label{example:I_n:reduction}
Let $S=I_n$, the symmetric invere monoid, and let $V$ be the partial
reflectional representation of Example
\ref{example:partial:reflection:representation}; we saw in that
example that $V$ is irreducible with basis $\{v_1,\ldots,v_n\}$.
Now let $e$ be an idempotent in the $\mathscr J$-class $\mathscr J_m$ in the
strategic picture for $I_n$ of Figure
\ref{fig:In_stategic_picture}. This idempotent is the identity map
$\id_X:X\rightarrow X$ on some subset $X\subseteq [n]$ of size $m$ and is the
identity of the maximal subgroup $G_e$ consisting of all bijections
$X\rightarrow X$, which in turn is a copy of the symmetric group $S_{\kern-.3mm m}$.
To squash $V$ down to a representation of $G_e\congS_{\kern-.3mm m}$, we take its
image under $e$: let $eV:=e\cdot V=\{ev\,:\,v\in V\}$. Then,
as $e\cdot v_i\not=0$ exactly when $i\in\text{dom}\,(e)=X$,
in which case $e\cdot v_i=v_i$, the
space
$eV$ has basis the $v_i$ for $i\in X$. Define an action of $G_e$ on
$eV$ by:
\begin{equation}
\label{eq:8}
g\cdot(ev)=(ge)\cdot v,
\quad\quad
(g\in G_e)
\end{equation}
observing, as $e$ is an identity for $G_e$, that $(ge)\cdot
v=(eg)\cdot v=e\cdot(gv)\in eV$. Indeed, $eV$ with this action is just
the
permuting coordinates
representation of $S_{\kern-.3mm m}$ given in Example
\ref{example:permutation:representation}.
We saw there that this representation is reducible when $m\geq 2$,
irreducible when $m=1$, and if $e\in \mathscr J_0$ is the zero map then $eV=0$.
Upto isomorphism of representations, $eV$ doesn't depend on the choice
of the idempotent $e$ in $\mathscr J_m$. For suppose that $f=\id_Y:Y\rightarrow Y$ is
another idempotent in $\mathscr J_m$, with $Y$ a subset of size $m$, and $f$
the identity of the maximal subgroup $G_f$. We know from Figure
\ref{fig:maximal_subgroups_isomorphic} that $G_f\cong S_Y\cong
S_X\cong G_e$ via the map $h\mapsto s^*hs$, where $s$ is some
bijection $X\rightarrow Y$ and $s^*$ is its semigroup inverse. Defining a
$G_f$-action on $fV$ as in (\ref{eq:8}) gives a
representation of $G_f$.
\begin{figure}
\centering
\begin{pspicture}(0,0)(14,5.5)
\rput(-4.8,0){
\rput(6.4,4){
\rput(0,0){$V=$ partial reflectional}
\rput(0,-0.35){representation of $I_n$}
}
\rput(6.4,2.9){
\rput(-0.2,0){$eV=$ permuting coordinates}
\rput(0,-0.35){representation of $S_{\kern-.3mm m}$}
\rput(0,-0.7){($0\leq m\leq n$)}
}
\rput(-1.5,-1.75){
\rput(10,4.5){\BoxedEPSF{fig15.eps scaled 450}}
\rput(10.6,6.7){$n$}\rput(10.9,5.95){$n-1$}
\rput(10.6,3.7){$2$}\rput(10.6,2.9){${\red 1}$}\rput(10.6,2.1){$0$}
\rput(11.3,5.2){$\left.\begin{array}{c}
\vrule width 0 mm height 34 mm depth 0 pt\end{array}\right\}$}
\rput(12,2.9){{\red $eV$ irreducible}}
\rput(-0.8,0){\rput{90}(12.4,5.25){$eV$ reducible}}
\rput(9,2.9){${\red \mathscr J_V}$}
\rput(12,2.1){$eV=0$}
}}
\rput(2.5,0.2){
\rput(6.4,4){
\rput(0,0){$W=$ hyperplane from}
\rput(0,-0.35){Example \ref{example:mapping:representation:T_n}}
\rput(0,-0.7){representation of $T_n$}
}
\rput(6.4,2.7){
\rput(-0.2,0){$eW=$ reflectional}
\rput(0,-0.35){representation of $S_{\kern-.3mm m}$}
\rput(0,-0.7){($1\leq m\leq n$)}
}
\rput(-1.5,-1.75){
\rput(10,4.5){\BoxedEPSF{fig15.eps scaled 450}}
\rput(10.6,6.7){$n$}\rput(10.9,5.95){$n-1$}
\rput(10.6,3.7){$3$}\rput(10.6,2.9){${\red 2}$}\rput(10.6,2.1){$1$}
\rput(11.3,5.2){$\left.\begin{array}{c}
\vrule width 0 mm height 34 mm depth 0 pt\end{array}\right\}$}
\rput(12,2.9){{\red $eW$ irreducible}}
\rput(-0.8,0){\rput{90}(12.4,5.25){$eW$ irreducible}}
\rput(9,2.9){${\red \mathscr J_W}$}
\rput(12,2.1){$eW=0$}
}}
\end{pspicture}
\caption{Reducing irreducible representations of $I_n$
\emph{(left)} and $T_n$
\emph{(right)}. The apexes $\mathscr J_V$, in red, are at the bottom of the red intervals.}
\label{fig:I_n:reduction}
\end{figure}
The spaces $fV$ and $eV$ are incidentally isomorphic as they both have
dimension $m$; but the map $f\cdot v\mapsto (s^*f)\cdot v$ naturally
gives an
isomorphism $fV\rightarrow eV$ that respects the actions of $G_f$ and $G_e$:
firstly $s^*f=es^*$, so that $(s^*f)\cdot v=(es^*)\cdot
v=e\cdot(s^*v)\in eV$. Then
$$
\begin{pspicture}(0,0)(14,2.5)
\rput(5,0.25){
\rput(1,2){$fV$}
\psline[linewidth=0.5pt]{->}(1.3,2)(2.7,2)
\rput(2,2.2){${\scriptstyle h(-)}$}
\rput(3,2){$fV$}
\psline[linewidth=0.5pt]{->}(1,1.7)(1,0.3)
\psline[linewidth=0.5pt]{->}(3,1.7)(3,0.3)
\rput(0.8,1){${\scriptstyle\cong}$}\rput(3.2,1){${\scriptstyle\cong}$}
\rput(1,0){$eV$}
\psline[linewidth=0.5pt]{->}(1.3,0)(2.7,0)
\rput(2,0.2){${\scriptstyle s^*hs(-)}$}
\rput(3,0){$eV$}
}
\end{pspicture}
$$
commutes, and so the representations $fV$ and $eV$ are indeed
isomorphic as claimed.
The results of the example are summarised on the left of Figure
\ref{fig:I_n:reduction}.
\end{example}
\begin{example}
\label{example:T_n:reduction}
The calculations, if not necessarily the results, are similar for the
mapping representation of $T_n$ from Example
\ref{example:mapping:representation:T_n}. Now $V$ is reducible, so we
start instead with the hyperplane $W$ consisting of the $w=\sum \lambda_i
v_i$ with $\sum\lambda_i=0$; this is an irreducible representation of $T_n$.
Let $e$ be the idempotent in $\mathscr J_m$ (the maps $[n]\rightarrow [n]$ having
image size $m$) given in Figure \ref{fig:T_n:reduction:idempotent}.
\begin{figure}[h]
\centering
\begin{pspicture}(0,0)(14,3)
\rput(7,1.5){\BoxedEPSF{fig18a.eps scaled 450}}
\rput(4.2,2.9){$1$}\rput(5,2.9){$2$}\rput(7.5,2.9){$m-1$}\rput(9.9,2.9){$n$}
\rput(4.2,0.1){$1$}\rput(5,0.1){$2$}\rput(7.5,0.1){$m-1$}
\rput(8.35,0.1){$m$}\rput(9.9,0.1){$n$}
\end{pspicture}
\caption{$e\in\mathscr J_m\subset T_n$ for Example \ref{example:T_n:reduction}.}
\label{fig:T_n:reduction:idempotent}
\end{figure}
Then the maximal subgroup $G_e$ consists of all bijections from
the fibres of $e$ to the image of $e$ -- again, isomorphic to the
symmetric group $S_{\kern-.3mm m}$. The space $eV$ has basis $\{v_1,\ldots,v_m\}$
and the subspace $eW$ is the hyperplane in $eV$ whose coordinates add to $0$
with respect to this basis. Via the action (\ref{eq:8}) the space
$eV$ is again the permuting coordinates representation of $S_{\kern-.3mm m}$ and
$eW$ is now
the reflectional representation -- see Figure \ref{fig:I_n:reduction} (right).
\end{example}
\paragraph{The general picture is as follows:} let $S$ be a finite regular monoid
and $V$ an \emph{irreducible\/} representation of $S$. Choose an
idempotent in each $\mathscr J$-class of $S$; the spaces $eV$, equipped with the action
(\ref{eq:8}), are then representations of the maximal subgroups $G_e$
for the various choices of $e$.
It doesn't matter, upto
isomorphism of the resulting representations, which
idempotent in a given $\mathscr J$-class is chosen.
In particular, whether $eV=0$, or not, is a property of the $\mathscr J$-class
containing $e$. The $\mathscr J$-classes for which
$eV\not=0$ form an \emph{interval\/} in the poset of $\mathscr J$-classes:
there is a
$\mathscr J$-class $\mathscr J_V$ such that
$$
eV\not=0\text{ exactly when }e\in\mathscr J_s\text{ with }\mathscr J_s\geq\mathscr J_V.
$$
The $\mathscr J$-class $\mathscr J_V$ is called the \emph{apex\/} of the
representation $V$, although ``trough'' would probably be a better
name.
Figure \ref{fig:reduction:general} shows the idea for the $\mathscr J$-class
poset of Figure \ref{fig:S(G,L)} (left and middle) and generically (right).
\paragraph{} In Example \ref{example:I_n:reduction}, the partial reflectional
representation has apex the $\mathscr J$-class $\mathscr J_1$ consisting of the
partial bijections on sets of size $1$; the interval of $\mathscr J$-classes
$\geq\mathscr J_1$ is marked on the left in Figure
\ref{fig:I_n:reduction}. For the irreducible representation $W$ of $T_n$ in
Example \ref{example:T_n:reduction}, the apex is the $\mathscr J$-class
$\mathscr J_2$ of maps with image size $2$ -- see the right of Figure
\ref{fig:I_n:reduction}.
In both examples, starting with an irreducible $S$-representation $V$,
we get an irreducible $G_e$-representation \emph{when $e$ is in the
apex $\mathscr J$-class $\mathscr J_V$\/}.
If $f$ is an idempotent lying in a $\mathscr J$-class strictly greater
than $\mathscr J_V$, then the resulting $G_f$-representation may or may not
be irreducible.
\begin{definitionnumberless}[reduced representations]
\label{definition:reduced:representation}
Let $V$ be an irreducible representation of $S$ with apex $\mathscr J_V$ and
$e\in\mathscr J_V$ an idempotent. Then the reduced $G_e$-representation is
given by
\begin{equation}
\label{eq:9}
V\downarrow G_e:=eV
\end{equation}
together with the $G_e$-action (\ref{eq:8}).
\end{definitionnumberless}
\begin{figure}
\centering
\begin{pspicture}(0,0)(14,5.5)
\rput(0,0){
\rput(2.5,2.75){\BoxedEPSF{Jclass3.eps scaled 450}}
\rput(2.6,4.975){${\scriptstyle e_1}$}
\rput(1.375,3.9){${\scriptstyle e_2}$}
\rput(4,3.05){${\scriptstyle e_3}$}
\rput(2.775,1.55){${\scriptstyle e_4}$}
\rput(2.65,0.425){${\scriptstyle e_5}$}
}
\rput(0,0){
\rput(7,2.75){\BoxedEPSF{fig9e.eps scaled 450}}
\rput(6.7,4.7){${e_1V\not=0}$}
\rput(6.3,3.25){${e_2V=0}$}
\rput(8.65,3.25){${\red e_3V\not=0}$}
\rput(7.45,2){${e_4V=0}$}
\rput(6.7,0.25){${e_5V=0}$}
}
\rput(0,0){
\rput(11.5,2.75){\BoxedEPSF{fig19.eps scaled 450}}
\rput(11.5,0.7){$\mathscr J$-class poset}
\rput(11.5,1.95){${\red \mathscr J_V}$}\rput(11.5,1.6){{\red apex}}
\rput*(12.675,2.3){{\red $eV$ irreducible}}
\rput(10.3,2.5){$eV=0$}\rput(11.5,4){$eV\not=0$}
\rput(13,5.5){{\red interval}}\rput(13,5.2){${\red \geq \mathscr J_V}$}
}
\end{pspicture}
\caption{Schematic of reduction: the example of Figure
\ref{fig:S(G,L)}
\emph{(left and middle\/)} and the generic set-up \emph{(right)\/.}
}
\label{fig:reduction:general}
\end{figure}
\begin{vexercise}
\label{exercise:reduction:I_n}
We can verify the general picture for $I_n$ and then for
inverse monoids of the form $S=S\kern-1pt(G,L)$. The reader
might want to leave this exercise until after they have read
\S\ref{section:clifford:munn}.
\begin{enumerate}
\item Let $S=I_n$ and let $V$ be a representation of $S$. Let
$I$ be the set of $\mathscr J$-classes $\mathscr J_e$ such that $eV\not=0$.
Show that $I\not=\varnothing$ and if $\mathscr J_e\in
I$ and $\mathscr J_e\leq \mathscr J_f$ in the $\mathscr J$-class poset, then
$\mathscr J_f\in I$. Hence $I$ forms a (closed) interval in the $\mathscr J$-class
poset. Denote the minimum element by $\mathscr J_v$.
\item Let $e$ be an idempotent in this minimal $\mathscr J$-class $\mathscr J_V$
and let $T=\{s_i\}$ be a collection of representatives for the
$\HH$-classes in the $\LL$-class $\LL_e$. Suppose that we have
$0\not=eW\not=eV$ with $eW$ a $G_e\congS_{\kern-.3mm m}$-subrepresentation of
$eV$, and consider the subspace
\begin{equation}
\label{eq:22}
U=\sum_{s_i\in T} s_i e W
\end{equation}
of $V$. Show that $U$ is an $I_n$-subrepresentation of $V$.
\item If now $V$ is an irreducible $I_n$-representation, then use
the arguments of \S\ref{section:clifford:munn}
(about the composition $\text{Irr}_m(I_n)\rightarrow\text{Irr}(S_{\kern-.3mm m})\rightarrow\text{Irr}_m(I_n)$)
to show that $V=\bigoplus_{s_i\in
T}s_ieV$. Deduce that $0\not=U\not=V$ for the $U$ of
(\ref{eq:22}) and hence that $eV$ is
irreducible as a $S_{\kern-.3mm m}$-representation.
\item Repeat the whole thing for an inverse monoid of the form
$S=S\kern-1pt(G,L)$.
\end{enumerate}
\end{vexercise}
\section{Induction}
\label{section:induction}
Induction is the opposite of reduction: it takes as
input a representation of a maximal subgroup and spits out a
representation of the whole semigroup.
We start with the general construction when $k=\ams{C}}\def\Q{\ams{Q}}\def\F{\ams{F}}\def\K{\ams{K}$. Let $e$ be an idempotent in
the semigroup
$S$, with $G_e$ the maximal subgroup having identity $e$, and let $V$
be a representation of the group $G_e$.
The induction of $V$ to an $S$-representation is controlled by the
$\HH$-classes that are in the $\LL$-class $\LL_e$ containing
$G_e$. Choose a transversal for these $\HH$-classes, i.e. a set
$T=\{s_i\}$ with exactly one $s_i$ in each $\HH$-class of $\LL_e$; choose
$e$ itself as the representative in the $\HH$-class $G_e$. The transversal is just
scaffolding for the construction -- the
resulting $S$-representation is independent of the choice of $T$.
For each $s_i\in T$, let $V_i$ be an isomorphic copy of the space $V$
having the
elements
$$
V_i=\{s_i\otimes v : v\in V\}
$$
and vector space operations given by $\lambda(s_i\otimes v)+\mu (s_i\otimes
u)=s_i\otimes (\lambda
v+\mu u)$. The ``$s_i\,\otimes$" notation is just a device to tell us
which particular copy of $V$ we are working in; other than that it serves no
purpose and just comes along for the ride in the vector space
operation on $V_i$ (although see the comments in the Note and References section)
Let $U$ be the space
\begin{equation}
\label{eq:5}
U=\bigoplus_{s_i\in T} V_i
\end{equation}
and define an $S$-action on $U$ by
\begin{equation}
\label{eq:4}
t\cdot(s_i\otimes v)
=
\left\{
\begin{array}{ll}
s_j\otimes g\cdot v, &\text{ if }ts_i\in\LL_e,\text{ hence }ts_i=s_jg\\
0, &\text{ if }ts_i\not\in \LL_e,
\end{array}
\right.
\end{equation}
for $t\in S$.
The action of $t$ thus kills the vector $s_i\otimes v$, unless $ts_i$
is also in the $\LL$-class $\LL_e$, in which case by
(\ref{eq:1}) there are unique $s_j\in T$ and $g\in G_e$ with
$ts_i=s_jg$. The vector $v$ is then moved in $V$ by the action of $g$,
with the resulting image
transferred to the corresponding element of $V_j$ -- see Figure
\ref{fig:induction}.
\begin{figure}
\centering
\begin{pspicture}(0,0)(14,8.5)
\rput(0,0){
\rput(7,4.25){\BoxedEPSF{fig20.eps scaled 550}}
\rput(11,1){$G_e$-representation}
\rput(11.5,6){$S$-representation}
\rput(11.5,5.6){$U=\bigoplus_T V_i$}
\rput(10.2,5.75){$\left.\begin{array}{c}
\vrule width 0 mm height 45 mm depth 0 pt\end{array}\right\}$}
}
\rput(5.55,0.6){${\blue v}$}
\rput(8.6,0.9){${\blue g\cdot v}$}
\rput(5.45,3.9){${\blue s_i\otimes v}$}
\rput(5.45,6.5){${\blue s_j\otimes v}$}
\rput(8.45,4.3){${\blue s_i\otimes g\cdot v}$}
\rput(8.45,6.9){${\blue s_j\otimes g\cdot v}$}
\rput(7.2,2.1){${\red g}$}\rput(7.8,8){${\red t}$}
\rput(4,0.2){$V$}\rput(4,3.6){$V_i$}\rput(4,6.2){$V_j$}
\end{pspicture}
\caption{Schematic of the first step of induction.}
\label{fig:induction}
\end{figure}
\begin{example}[trivial $S_{\kern-.4mm 1}$ to trivial $I_n$]
\label{induction:example:trivial:to:trivial}
Let $S=I_n$ and $e$ be the zero map $0:\varnothing\rightarrow\varnothing$. The
subgroup $G_e$ is the trivial group (or $S_{\kern-.4mm 1}$!) with the single
element $0$. If $V$ is the trivial representation of $S_{\kern-.4mm
1}$ then (slightly confusingly)
$0\cdot v=v$ for all $v\in V$, and the transversal $T$ consists of the
one element $\{0\}$, so $U=V_0$ is a single copy of $V$. Finally, for any
$t\in I_n$ we have $t\cdot(0\otimes v)=0\otimes 0\cdot v=0\otimes v$,
and so $U$ is the trivial $1$-dimensional representation of $I_n$.
\end{example}
\begin{example}
At the opposite end of the strategic picture for $I_n$ we have the
idempotent $e=\id:[n]\rightarrow[n]$, the identity of the group of units
$S_{\kern-.3mm n}$. If $V$ is any representation of $S_n$, then again we have a
transversal $T$
containing the single element $\{e\}$ and so $U=V_e$. Moreover $t\cdot U=0$
unless $t\inS_{\kern-.3mm n}$ is also a unit, in which case it has effect
that of the representation $V$.
Every $S_{\kern-.3mm n}$-representation is thus
also an $I_n$-representation, just by making that part of $I_n$ not in
$S_{\kern-.3mm n}$ (i.e. the stacked $\mathscr J$-classes $0,\mathscr J_1,\ldots,\mathscr J_{n-1}$ in
the middle of Figure \ref{fig:In_stategic_picture})
act as the zero map. It is easy to check that in general any
$G$-representation is also an $S$-representation in this way, when
$G$ is the group
of units of $S$.
\end{example}
\begin{example}[trivial $S_{\kern-.4mm 1}$ to partial reflectional
$I_n$]
\label{example:induction100}
Moving up one rung from the bottom in the strategic picture for $I_n$
in Figure \ref{fig:In_stategic_picture},
let $e$ be the partial identity $1\mapsto 1$ with domain and image
$\{1\}$, so that $G_e$ is again the trivial group $\{e\}$. Also again, let
$V$ be the trivial $1$-dimensional representation of $G_e$, with basis
vector $v$, and action $e\cdot v=v$.
\begin{figure}
\centering
\begin{pspicture}(0,0)(14,5.5)
\rput(0,0){
\rput(5.5,2.75){\BoxedEPSF{fig9f.eps scaled 450}}
\rput(1.6,0.2){$0$}\rput(1.6,1.35){$1$}
\rput(1.6,3.6){$n-1$}\rput(1.6,4.8){$n$}
\rput(5.65,4.5){${\scriptstyle 1}$}
\rput(5.15,1.6){${\scriptstyle i}$}
\rput(5.15,4){${\scriptstyle 1}$}
\rput(8.7,4.5){${\scriptstyle j}$}
\rput(5.65,4.1){${\scriptstyle 1\stackrel{e}{\rightarrow}1}$}
\rput(8.7,1.6){${\scriptstyle j\rightarrow i}$}
\rput(11.25,4.1){${\scriptstyle 1\stackrel{e}{\rightarrow}1}$}
\rput(11.25,1.65){${\scriptstyle 1\stackrel{s_i}{\rightarrow}i}$}
\rput(5.6,0){
\rput(5.65,4.5){${\scriptstyle 1}$}
\rput(5.15,1.6){${\scriptstyle i}$}
\rput(5.15,4){${\scriptstyle 1}$}
}
\rput(12.75,4){$G_e=\{e\}$}
\rput(13,3){$V$ $1$-dimensional}
\rput(13,2.65){basis $v$}
\rput(13,2.3){$e\cdot v=v$}
}
\end{pspicture}
\caption{The trivial representation of the subgroup $G_e$, where
$e:1\mapsto 1$, induces up to the partial reflectional representation
of $I_n$.}
\label{fig:induction:trivial:to:partial:permutation}
\end{figure}
The $\mathscr J$-class containing the subgroup $G_e$ consists of all the bijections
with domain and image of size $1$ (Figure
\ref{fig:induction:trivial:to:partial:permutation}) and $\LL_e$ is the
column of all the maps with domain $1$. There is no choice for the
representatives $T$: they are the partial bijections $s_i:1\mapsto i$.
The copy $V_i$ of $V$ has basis the vector $s_i\otimes v$, and so the space
$U$ of (\ref{eq:5}) is
$n$-dimensional with basis $\{s_i\otimes v\}_{1\leq i\leq n}$.
For the $I_n$-action, we have $ts_i\in\LL_e$ when it has domain $1$, and this
is exactly when $i$ lies in the domain of $t$, in which case
$ts_i=s_{t(i)}=s_{t(i)}e$. Thus
$$
t\cdot(s_i\otimes v)
=
\left\{
\begin{array}{ll}
s_{t(i)}\otimes v, &\text{ if }i\in\text{dom}\,(t),\\
0, &\text{ else.}
\end{array}
\right.
$$
Replacing $s_i\otimes v$ by $v_i$ we get the formula (\ref{eq:2}), and
so $U$ is the partial reflectional representation of $I_n$.
\end{example}
In Examples
\ref{induction:example:trivial:to:trivial}-\ref{example:induction100} an
irreducible $G_e$-representation $V$ becomes an irreducible
$S$-representation $U$. We are not always so lucky:
\begin{example}[trivial $S_{\kern-.4mm 1}$ to mapping $T_n$]
\label{induction:example200}
This is very similar to Example \ref{example:induction100}.
Let $S$ be the full transformation monoid $T_n$, with strategic
picture on the left of Figure
\ref{fig:induction:trivial:to:nonirreducible:Tn}.
\begin{figure}
\centering
\begin{pspicture}(0,0)(14,5.5)
\rput(0,0.25){
\rput(5.5,2.75){\BoxedEPSF{fig9h.eps scaled 450}}
\rput(2.7,0.2){$1$}\rput(2.7,1.35){$2$}
\rput(2.7,3.6){$n-1$}\rput(2.7,4.8){$n$}
\rput(0.35,0){
\rput(5.65,4.5){${\scriptstyle 1}$}
\rput(5.15,1.6){${\scriptstyle i}$}
\rput(5.15,4){${\scriptstyle 1}$}
}
\rput(6,4){$e_1$}\rput(6,1.6){$e_i$}
\rput(6.6,2.5){$\mathscr J_1$}
\rput(8.35,4.35){${\scriptstyle 1}$}
\rput(10.3,4.35){${\scriptstyle n}$}
\rput(8.35,2.95){${\scriptstyle 1}$}
\rput(10.3,2.95){${\scriptstyle n}$}
\rput(8.35,2.35){${\scriptstyle 1}$}
\rput(10.3,2.35){${\scriptstyle n}$}
\rput(8.35,0.95){${\scriptstyle 1}$}
\rput(9.1,0.95){${\scriptstyle i}$}
\rput(10.3,0.95){${\scriptstyle n}$}
\rput(10.75,3.5){${\cyan e_1}$}
\rput(10.75,1.5){${\cyan e_i}$}
\rput(-0.5,-0.5){
\rput(12.75,4){$G_{e_1}=\{e_1\}$}
\rput(13,3){$V$ $1$-dimensional}
\rput(13,2.65){basis $v$}
\rput(13,2.3){$e_1\cdot v=v$}
}
}
\end{pspicture}
\caption{An irreducible $V$ doesn't necessarily give an irreducible
$U$: the trivial representation of the subgroup $G_{e_1}$, where
$e_1$ is the constant map $[n]\mapsto 1$, induces up to the mapping
representation
of $T_n$.}
\label{fig:induction:trivial:to:nonirreducible:Tn}
\end{figure}
The $\mathscr J$-class at the bottom consists of the maps with image size $1$
-- the constant maps. There is a single $\LL$-class and $n$
$\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$-classes, each containing the single constant map $e_i:[n]\mapsto
i$ for $1\leq i\leq n$. These are all idempotents, so that every
$\HH$-class in this $\mathscr J$-class is a maximal subgroup. (You can see this in Figure
\ref{fig:Tn_Hclasses_idempotents}, where every box of $\mathscr J_1$ is a maximal
subgroup). In anycase, there is no choice once again for $T$, which
must be the $\{e_i\}_{1\leq i\leq n}$.
Let $e_1$ be the constant map $e:[n]\mapsto 1$ and $V$ be the
trivial $G_{e_1}$-representation with basis the vector $v$. For each $i$,
the space $V_i$ has basis the vector $e_i\otimes v$ and the $U$ of
(\ref{eq:5}) is $n$-dimensional with basis $\{e_i\otimes v\}_{1\leq
i\leq n}$.
For any $t\in T_n$ we have $t\cdot e_i=e_{t(i)}=e_{t(i)}e_1$, so that
(\ref{eq:4}) becomes
$t\cdot(e_i\otimes v)=e_{t(i)}\otimes v$, and once again we have the
formula (\ref{eq:2}), after replacing $e_i\otimes v$ with $v_i$. The
space $U$ thus carries the mapping representation of $T_n$, which is
reducible, even though the seeding representation $V$ of the
subgroup $G_{e_1}\cong S_{\kern-.4mm 1}$ is irreducible.
Before leaving the example we observe something for
later on: the $\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$-class $\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q_e$ contains just the single element
$\{e_1\}$ with $e_1\cdot(e_i\otimes v)=e_1\otimes v$ for all $i$. Suppose
that $u\in U$ is a vector that is annihilated by $e_1$, i.e.
$$
u=\sum \lambda_i (e_i\otimes v)\text{ with }e_1\cdot u=0.
$$
Then
$$
e_1\cdot u=0
\Leftrightarrow
\biggl(\sum \lambda_i\biggr)(e_1\otimes v)=0
\Leftrightarrow
\sum \lambda_i=0,
$$
so that, after replacing $e_i\otimes v$ with $v_i$,
the set of such annihilated vectors is the hyperplane $W$ consisting
of the $w=\sum \lambda_iv_i$ where $\sum\lambda_i=0$.
These annihilated vectors thus form a subrepresentation of $U$. Even
more is true: $U$ is the $n$-dimensional mapping representation and
$W\subset U$ is $(n-1)$-dimensional, so the quotient representation
$U/W$ is $1$-dimensional, hence irreducible.
In particular, $W$ is a maximal subrepresentation of $U$.
\end{example}
\paragraph{Returning to generalities,} let $V$ be
a representation of the maximal
subgroup $G_e$ and $U$ the space given in (\ref{eq:5}). As in the
example just done, consider the vectors in $U$ that are annihilated by
the elements of the $\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q$-class $\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q_e$:
\begin{equation}
\label{eq:6}
\text{Ann}_{e}(U):=\{u\in U: s\cdot u=0\text{ for all }s\in\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q_e\}.
\end{equation}
\begin{definitionnumberless}[induced representations]
\label{definition:induced:representation}
Let $V$ be a representation of the maximal subgroup $G_e$ of $S$ and
$U$ be the $S$-representation given by (\ref{eq:5}) and (\ref{eq:4}). Then
the $S$-representation induced by $V$ is the quotient
\begin{equation}
\label{eq:7}
V\uparrow S:=U/\text{Ann}_{e}(U)
\end{equation}
\end{definitionnumberless}
As in Example
\ref{induction:example200}, if $V$ is irreducible, then
$\text{Ann}_{e}(U)$ is a maximal subrepresentation of
$U$, and $V\uparrow S$ is irreducible. The construction depends
only on the $\mathscr J$-class of $e$: if $e$ and $f$ lie in the same
$\mathscr J$-class then the resulting
induced representations are isomorphic.
\begin{example}
\label{example:inversesemigroup:annihilator}
We can verify some of these general claims in the setting of $I_n$. In the
Exercise following, we do this for an inverse monoid of
the form $S\kern-1pt(G,L)$.
Suppose that $|X|=m$ and $V$ is
a representation of the maximal subgroup $G_e\congS_{\kern-.3mm m}$, with $e$ the partial
identity $X\rightarrow X$, and let $U$ be the $I_n$-representation described
in (\ref{eq:5})-(\ref{eq:4}).
We show first that the annihilator
$\text{Ann}_{e}(U)$ is trivial.
To see this, let $T=\{s_i\}$ be the
transversal used for the induction and
$u=\sum_i s_i\otimes v_i\in \text{Ann}_{e}(U)$.
Fix an $s_j:X\rightarrow Y\in T$ with $s_j^*:Y\rightarrow X$ the semigroup
inverse of $s_j$ -- see Figure
\ref{fig:induction:zeroannihilator}. Then for any $i$ we have:
$$
s_j^*s_i\in\LL_e
\Leftrightarrow
\text{dom}\,(s_j^*s_i)=X
\Leftrightarrow
\text{im}\,(s_i)=\text{dom}\,(s_j^*)
\Leftrightarrow
\text{im}\,(s_i)=Y
\Leftrightarrow
s_i=s_j.
$$
Thus, on the one hand, by (\ref{eq:4}):
$$
s_j^*\cdot u=s_j^*\cdot(s_j\otimes v_j)=e\otimes v_j,
$$
while on the other, $s_j^*\in\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q_e$ and $u\in \text{Ann}_{e}(U)$ gives
$s_j^*\cdot u=0$. The conclusion
is that $v_j=0$ and hence $s_j\otimes v_j=0$. Letting $j$ vary we see
that $u=0$ and hence $\text{Ann}_{e}(U)=0$ as claimed.
\begin{figure}
\centering
\begin{pspicture}(0,0)(14,5.5)
\rput(3.5,0.25){
\rput(3.5,2.5){\BoxedEPSF{fig14.eps scaled 450}}
\rput(2.3,3.65){$X\stackrel{e}{\rightarrow}X$}\rput(4.6,3.65){$Y\stackrel{s_j^*}{\rightarrow}X$}
\rput(2.3,1.45){$X\stackrel{s_j}{\rightarrow}Y$}
\rput(0.55,3.65){$\text{im}\,=X$}\rput(0.55,1.45){$\text{im}\,=Y$}
\rput(2.3,4.95){$\text{dom}\,=X$}\rput(4.6,4.95){$\text{dom}\,=Y$}
\rput(5.6,3.65){$\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q_e$}\rput(2.3,0.45){$\LL_e$}
}
\end{pspicture}
\caption{$\text{Ann}_{e}(U)=0$ in $I_n$.}
\label{fig:induction:zeroannihilator}
\end{figure}
The annihilator is then certainly an $I_n$-subrepresentation of
$U$, albeit for trivial reasons! Suppose now that $V$ is an
\emph{irreducible\/} $S_{\kern-.3mm m}$-representation. We
claim that the annihilator is a maximal subrepresentation, or
equivalently, that $U$ is an irreducible $I_n$-representation. Let $u$
be a non-zero vector in $U=\bigoplus_T s_i\otimes V$ with
$u=\sum_i s_i\otimes v_i$ and $s_j\otimes v_j\not=0$ for some $j$ (so
that in particular, $v_j\not=0$). Let $W=I_n\cdot u\subset U$ be the
set (hence subspace -- Exercise) of all images of $u$ under the elements of
$I_n$.
We claim that $W=U$. We have $s_j^*\cdot u\in W$, where as above
$$
s_j^*\cdot u=e\otimes v_j
$$
with $0\not=e\otimes v_j\in V$. On the one hand, we have
$S_{\kern-.3mm m}\cdot(e\otimes v_j)\subseteq W$ (as $S_{\kern-.3mm m}\subset I_n$), while on
the other $S_{\kern-.3mm m}\cdot(e\otimes v_j)$ is a non-zero
$S_{\kern-.3mm m}$-subrepresentation of the irreducible $S_{\kern-.3mm m}$-representation
$V$. The conclusion is that $S_{\kern-.3mm m}\cdot(e\otimes v_j)=V$, and hence
$V\subseteq W$. For any $s_i\in T$ we have by the definition of the action
in (\ref{eq:4}) that
$$
s_i\cdot(e\otimes v)=s_i\otimes v
$$
and so $s_i\cdot V=s_i\otimes V$. Thus, as soon as we have $V\subseteq
W$ then we have $s_i\otimes V\subseteq W$ for each $s_i$, and thus
$U\subseteq W$.
This proves the claim, and so the $I_n$-representation $U$ is irreducible.
To summarise: if $V$ is an irreducible $S_{\kern-.3mm m}$-representation then the
induced representation $V\uparrow I_n$ is the space $U$, and this in
turn is an irreducible $I_n$-representation.
\end{example}
\begin{vexercise}
\label{exercise:sgl:ann}
Let $S$ be an inverse monoid of the form $S=S\kern-1pt(G,L)$ and $V$ an
irreducible representation of the maximal subgroup $G_e$. Let $U$ be the
$S$-representation given by (\ref{eq:5})-(\ref{eq:4}).
\begin{enumerate}
\item Show that $\text{Ann}_{e}(U)=0$ (\emph{hint :\/} prove
the following fact first: if the finite group $G$ acts on the
lattice $L$, and if $a,b$ lie in the same $G$-orbit with $a\leq
b$, then $a=b$; in other words, distinct elements of $L$ in the same
$G$-orbit are not comparable.)
\item Mimic the argument above for $I_n$ to show that $U$ is irreducible.
\end{enumerate}
\end{vexercise}
\paragraph{Here is how induction works for an inverse monoid of the form
$S=S\kern-1pt(G,L)$.}
\label{example:induction:sgl}
Let $e=\id_a$ be an idempotent and $V$ a
representation of the maximal subgroup $G_a$ given in (\ref{eq:17}).
The $\HH$-classes in $\LL_e$ are parametrised by the $G$-orbit of $a$,
say $G\cdot a=\{a,b,\ldots\}$; let
$\alpha}\def\ww{\omega}\def\bb{\beta}\def\ss{\sigma=\id,\bb,\ldots$ be elements of $G$ such that
$$
\alpha}\def\ww{\omega}\def\bb{\beta}\def\ss{\sigma:a\mapsto a, \bb:a\mapsto b,\ldots
$$
We then take our transversal $T$ to be
$\alpha}\def\ww{\omega}\def\bb{\beta}\def\ss{\sigma_a,\bb_a,\ldots$
In light of
Exercise \ref{exercise:sgl:ann},
the
induced representation is carried by the space
$$
V\uparrow S=\bigoplus_{\bb_a\in T}b\otimes V
$$
where (after simplifying notation a little) $b\otimes V=\{b\otimes
v:v\in V\}$ and, as usual, the vector space
operations happen in the ``$v$'' coordinate, with the ``$b\,\otimes$"
just a label for the copy of $V$.
Suppose that $s=g_c$ is some element of $S$. To understand the action
in (\ref{eq:4}) we need to compute products like $s\,\bb_a$: as
$s\,\bb_a=g_c\bb_a=(g\bb)_{\bb^{-1}\cdot c\wedge a}$, we have that
$s\,\bb_a$ lies in $\LL_e$ exactly when
$$
\bb^{-1}\cdot c\wedge a=a
\Leftrightarrow
a\leq \bb^{-1}\cdot c
\Leftrightarrow
b\leq c
$$
(recall that $\bb\in G$ sends $a$ to $b$). Moreover, if $b\leq c$, then
$s\,\bb_a$ lies in the $\HH$-class $\HH_d$, where $d=g\cdot b$. The
description (\ref{eq:14}) gives the element
$\delta_d^{-1}s\,\bb_a=(\delta^{-1}g\bb)_a$ of $G_a$ and
$$
s\,\bb_a=\delta_a\cdot (\delta^{-1}g\bb)_a
$$
Thus, for $b\otimes v$ an element of $V\uparrow S$ and for
$g_c$ an element of $S=S\kern-1pt(G,L)$ we have the action:
\begin{equation}
\label{eq:18}
g_c\cdot(b\otimes v)
=
\left\{
\begin{array}{ll}
d\otimes h\cdot v, &\text{ if }b\leq c\\
0, &\text{ if }b\not\leq c,
\end{array}
\right.
\end{equation}
where $d=g\cdot b$ and $h=(\delta^{-1}g\bb)_a$ with $\delta:a\mapsto
d$ one of the elements of $G$ chosen above.
We can say more. If $s$ lies in the $\mathscr J$-class $\mathscr J_c$ with
$\mathscr J_a\not\leq\mathscr J_c$, then for any $b$ in the $G$-orbit of $a$ we have
$b\not\leq c$ in $L$, hence $s\cdot(b\otimes v)=0$, and so $s\cdot
V\uparrow S=0$. On the other hand, if $s=\id_c\in\mathscr J_c$ with
$a\leq c$ and if $a\otimes v\not=0$
in $V\uparrow S$, then $s\cdot(a\otimes v)=a\otimes v$, and so $s\cdot
V\uparrow S\not=0$. The conclusion is that $s\cdot V\uparrow S\not= 0$
precisely for those $s$ lying in the $\mathscr J$-classes that are
$\geq\mathscr J_a$ in the $\mathscr J$-class poset. In particular, the apex of $V\uparrow S$, for
$V$ a representation of $G_a$, is $\mathscr J_a$.
\begin{example}
\label{example:Tn:induction}
We return to $T_n$ and Example \ref{induction:example200} where
$e_1:[n]\mapsto 1$
is our idempotent, $V$ is the trivial
representation of $G_{e_1}\cong S_{\kern-.4mm 1}$ and $U$ the mapping
representation of $T_n$. We saw at the end
of Example \ref{induction:example200}
that $\text{Ann}_{e}(U)$
is the hyperplane $W$ in $U$ consisting of the $w=\sum \lambda_iv_i$
with $\sum\lambda_i=0$. The induced representation $V\uparrow T_n=U/W$
is thus $1$-dimensional, and as $v_i-v_j\in W$
we have $v_i+W=v_j+W$ for all $i$ and $j$. Taking $v_1+W$ to be the
basis vector for $V\uparrow T_n$, we have for any $t\in T_n$ that:
$$
t\cdot(v_1+W)=t(v_1)+W=v_{t(1)}+W=v_1+W,
$$
so that $V\uparrow T_n$ is the trivial representation.
\end{example}
\section{The Clifford-Munn correspondence}
\label{section:clifford:munn}
Induction creates irreducible representations of a (finite regular)
monoid out of irreducible representations of its maximal
subgroups. With a little care in the accounting, this process gives a
1-1 correspondence between the irreducible $S$-representations and the
irreducibles of a certain collection of maximal subgroups.
This bijection
is called the
\emph{Clifford-Munn correspondence\/}.
The bijection comes about by showing that reduction
is the inverse of
induction; for us, this is the principal purpose of reduction.
The apex of an $S$-representation $V$
tells us the ``right'' maximal subgroup to reduce to.
Figure \ref{fig:CM:correspondence} illustrates the correspondence, where as
usual, the strategic picture of $S$ drives the whole process. Let $\text{Irr}(S)$ be
the set of isomorphism classes of irreducible $S$-representations and
$E=\{e_i\}$ be a set of
idempotents in 1-1 corrrespondence with the $\mathscr J$-classes of $S$.
For $e\in E$ let
$$
\text{Irr}_e(S)=\{V\in\text{Irr}(S):\mathscr J_V=\mathscr J_e\},
$$
be the irreducible $S$-representations $V$ whose apex $\mathscr J_V$ is the
$\mathscr J$-class $\mathscr J_e$ containing $e$. Every irreducible $V$ has a
uniquely determined apex --
the set of $S$-irreducibles $\text{Irr}(S)$ is thus partitioned into the
$\text{Irr}_e(S)$ as $e$ ranges over $E$.
Finally, let $\text{Irr}(G_e)$ be the irreducible representations of the
maximal subgroup $G_e$.
\begin{theorem}[Clifford-Munn correspondence]
\label{theorem:CM}
For a fixed $e\in E$, the maps:
$$
\begin{pspicture}(0,0)(14,1)
\rput(0,-0.35){
\rput(5.5,0.75){$\text{Irr}_e(S)$}
\psline[linewidth=0.5pt]{->}(6.2,0.9)(7.8,0.9)
\rput(7,1.1){${\scriptstyle V\rightarrow V\downarrow G_e}$}
\rput(8.5,0.75){$\text{Irr}(G_e)$}
\psline[linewidth=0.5pt]{<-}(6.2,0.6)(7.8,0.6)
\rput(7,0.4){${\scriptstyle V\uparrow S \leftarrow V}$}
}
\end{pspicture}
$$
are mutual inverses, inducing a bijection
$\text{Irr}(S)\rightleftarrows\bigcup_{e\in T}\text{Irr}(G_e)$.
\end{theorem}
\begin{figure}
\centering
\begin{pspicture}(0,0)(14,6)
\rput(0,0.25){
\rput(0,0.25){
\rput(4.5,1.65){\BoxedEPSF{fig9a.eps scaled 250}}
\rput(4.5,0.25){$\mathscr J$-classes}
}
\rput(2,3){\BoxedEPSF{CM1.eps scaled 450}}
\rput(2,3.6){$\text{Irr}(S)$}
\psline[linewidth=0.5pt]{<->}(3.8,3.5)(5.2,3.5)
\rput(4.5,3.65){${\scriptstyle\text{partition}}$}
\rput(7,3){\BoxedEPSF{CM2.eps scaled 450}}
\rput(7.1,4.8){${\scriptstyle e_1}$}
\rput(6.05,4.1){${\scriptstyle e_2}$}
\rput(7.85,3.775){${\scriptstyle e_3}$}
\rput(6.965,2.275){${\scriptstyle e_4}$}
\rput(7.1,1.1){${\scriptstyle e_5}$}
\rput(6.2,3.4){${\scriptstyle\text{Irr}_{e_2}(S)}$}
\rput(7.8,3.3){${\scriptstyle\text{Irr}_{e_3}(S)}$}
\rput(7,1.675){${\scriptstyle\text{Irr}_{e_4}(S)}$}
\psline[linewidth=0.5pt]{<->}(8.75,3.5)(10.15,3.5)
\rput(9.45,3.65){${\scriptstyle\text{1-1}}$}
\rput(9.45,3.35){${\scriptstyle\text{correspondence}}$}
\rput(12.1,3){\BoxedEPSF{CM3.eps scaled 450}}
\rput(12.2,5.2){${\scriptstyle e_1}$}
\rput(11,4.15){${\scriptstyle e_2}$}
\rput(13.1,3.8){${\scriptstyle e_3}$}
\rput(12.1,2.1){${\scriptstyle e_4}$}
\rput(12.25,0.7){${\scriptstyle e_5}$}
\rput(11,5){${\scriptstyle\text{Irr}(G_{e_2})}$}
\rput(13.5,4.8){${\scriptstyle\text{Irr}(G_{e_3})}$}
\rput(0.1,-1){\rput{90}(11,3){${\scriptstyle\text{Irr}(G_{e_4})}$}}
}
\end{pspicture}
\caption{Schematic of the Clifford-Munn correspondence: the
irreducibles of $S$ \emph{(left)} partitioned into their various
apexes \emph{(middle)} which in turn are in 1-1 correspondence with
the irreducibles of the corresponding maximal subgroups \emph{(right)}.}
\label{fig:CM:correspondence}
\end{figure}
\paragraph{} We will prove the correspondence in the context of the symmetric inverse
monoid $I_n$ when $k=\ams{C}}\def\Q{\ams{Q}}\def\F{\ams{F}}\def\K{\ams{K}$.
Exercise \ref{exercise:CMP} at the end of the section asks for a
proof for an inverse monoid of the form $S=S\kern-1pt(G,L)$.
Fix then, in $I_n$, the $\mathscr J$-class
$\mathscr J_m$ for some $0\leq m\leq n$ and the idempotent
$e=\id:[m]\rightarrow [m]$. The maximal subgroup
$G_e$ is isomorphic to $S_{\kern-.3mm m}$ and consists of all partial bijections $[m]\rightarrow[m]$. As
we have a nice total order on the $\mathscr J$-classes, we write
$\text{Irr}_m(I_n)$ for $\text{Irr}_e(I_n)$.
\paragraph{The map $\text{Irr}_m(I_n)\rightarrow\text{Irr}(S_{\kern-.3mm m})$ given by $V\mapsto
V\downarrowS_{\kern-.3mm m}$:} as $V\in\text{Irr}_m(I_n)$, it is irreducible
with apex $\mathscr J_m$, and hence $V\downarrowS_{\kern-.3mm m}=eV$ is an irreducible
$S_{\kern-.3mm m}$-representation by
\S\ref{section:reduction}. Thus $V\downarrowS_{\kern-.3mm m}\in\text{Irr}(S_{\kern-.3mm m})$.
\paragraph{The map $\text{Irr}(S_{\kern-.3mm m})\rightarrow\text{Irr}_m(I_n)$ given by $V\mapsto
V\uparrow I_n$:} first, we show that this is indeed a map. For
$V\in\text{Irr}(S_{\kern-.3mm m})$, we saw in Example
\ref{example:inversesemigroup:annihilator} that
$\text{Ann}_{e}(U)=0$ where $U$ is the $I_n$-representation given in
(\ref{eq:5})-(\ref{eq:4})
and that $V\uparrow I_n=U$ is
irreducible. Thus $V\uparrow I_n\in\text{Irr}(I_n)$; we need it to be in
$\text{Irr}_m(I_n)$, i.e. to have apex the $\mathscr J$-class $\mathscr J_m$. The
following essentially repeats the more general arguments immediately
preceding Example \ref{example:Tn:induction}, but in a concrete
setting.
The $\LL$-class $\LL_e$ consists of all the partial bijections with
domain $[m]$. If $Y=\{i_1,\ldots,i_m\}$ is some subset of size $m$,
then let $s_Y:[m]\rightarrow Y$
\begin{figure}
\centering
\begin{pspicture}(0,0)(14,3.5)
\rput(0,0.25){
\rput(-3.5,0){
\rput(7,1.5){\BoxedEPSF{fig17b.eps scaled 450}}
\rput(4.2,2.9){$1$}\rput(5.2,2.9){$2$}
\rput(7.5,2.9){$m$}\rput(9.85,2.9){$n$}
\rput(4.2,0.1){$1$}\rput(5,0.1){$i_1$}
\rput(6,0.1){$i_2$}\rput(8.6,0.1){$i_m$}
\rput(9.85,0.1){$n$}
\rput(9,1.5){${\red s_Y}$}
}
\rput(10.5,1.5){\BoxedEPSF{fig17c.eps scaled 450}}
\rput(7.7,2.9){$1$}
\rput(11,2.9){$m$}\rput(13.35,2.9){$n$}
\rput(7.7,1.8){$1$}
\rput(10,1.8){$\ell$}\rput(13.35,1.8){$n$}
\rput(13,2){${\red s_Y}$}
\rput(13,0.9){${\red f}$}
\rput(7.7,0.1){$1$}
\rput(10,0.1){$\ell$}\rput(13.35,0.1){$n$}
}
\end{pspicture}
\caption{The $s_Y\in\LL_e$ in a transversal $T$ \emph{(left)\/} and
$fs_Y$ \emph{(right)\/}.}
\label{fig:transversal}
\end{figure}
be the map $s_Y:j\mapsto i_j$ given on the left of Figure
\ref{fig:transversal}. We take $T=\{s_Y\}$ to be the transversal used in
the induction process, for $Y$ ranging
over all $m$-subsets of $[n]$. Thus
$$
V\uparrow I_n=U=\bigoplus_{s_Y} V_Y
$$
where $V_Y$ is the vector space consisting of the vectors $s_Y\otimes
v$ for $v\in V$. The $I_n$-action on $U$ is given by (\ref{eq:4}).
We claim the following: if $f$ is an idempotent, then
$f(V\uparrow I_n)\not=0$ exactly when $f$ lies in a $\mathscr J$-class $\mathscr J_\ell$
with $\mathscr J_m\leq\mathscr J_\ell$.
Moreover, $e(V\uparrow I_n)$ is itself isomorphic, as an
$S_{\kern-.3mm m}$-representation, to $V$.
We choose $f$ conveniently in its $\mathscr J$-class $\mathscr J_\ell$:
$f=\id:[\ell]\rightarrow[\ell]$. We have $\mathscr J_\ell<\mathscr J_m$
exactly when $\ell<m$, in which case the right part of Figure
\ref{fig:transversal} shows that $m\not\subseteq\text{dom}\,(fs_Y)$ for any
$m$-subset $Y$. Hence $fs_Y\not\in\LL_e$ (the partial bijections with
domain $[m]$) for any $Y$, and so by (\ref{eq:4})
$$
f\cdot(s_Y\otimes v)=0
$$
for all $Y$ and all $v$. Thus $f(V\uparrow I_n)=0$ when
$\mathscr J_\ell<\mathscr J_m$.
If now $f=e$ then we have
$$
es_Y\in\LL_e\Leftrightarrow\text{dom}\,(e s_Y)=[m]\Leftrightarrow
Y=[m]\Leftrightarrow s_Y=e
$$
in which case
$$
e\cdot(s_Y\otimes v)\not=0\Leftrightarrow s_Y\otimes v=e\otimes v.
$$
The map $e\otimes v\mapsto v$ is then an isomorphism of vector
spaces $e(V\uparrow I_n)\rightarrow V$, and for any $g\inS_{\kern-.3mm m}$ the diagram
$$
\begin{pspicture}(0,0)(14,2)
\rput(5.75,2){$e\otimes v$}
\rput(8.25,2){$e\otimes gv $}
\rput(5.75,0){$v$}
\rput(8.25,0){$gv$}
\psline[linewidth=0.5pt]{->}(6.2,2)(7.7,2)
\psline[linewidth=0.5pt]{->}(6,0)(7.9,0)
\psline[linewidth=0.5pt]{->}(5.75,1.8)(5.75,0.2)
\psline[linewidth=0.5pt]{->}(8.25,1.8)(8.25,0.2)
\rput(7,2.2){${\scriptstyle g(-)}$}
\rput(7,0.2){${\scriptstyle g(-)}$}
\end{pspicture}
$$
commutes. Thus, the $S_{\kern-.3mm m}$-representations $e(V\uparrow I_n)$ and $V$ are
isomorphic as claimed.
Finally, Exercise \ref{exercise:reduction:I_n} part 1 gives that $f(V\uparrow
I_n)\not=0$ when $\mathscr J_\ell>\mathscr J_m$. This establishes all our claims.
In particular, $\mathscr J_m$ is the apex of the $I_n$-representation
$V\uparrow I_n$, and so $V\uparrow I_n$ is indeed in $\text{Irr}_m(I_n)$.
\paragraph{The composition
$\text{Irr}(S_{\kern-.3mm m})\rightarrow\text{Irr}_m(I_n)\rightarrow\text{Irr}(S_{\kern-.3mm m})$:} We have
just seen, for $V$ an irreducible $S_{\kern-.3mm m}$-representation,
that $e(V\uparrow I_n)\cong V$. Thus $(V\uparrow
I_n)\downarrowS_{\kern-.3mm m}\cong V$, and the composition is the identity.
\paragraph{The composition
$\text{Irr}_m(I_n)\rightarrow\text{Irr}(S_{\kern-.3mm m})\rightarrow\text{Irr}_m(I_n)$:} we now
show that $(V\downarrowS_{\kern-.3mm m})\uparrow I_n\cong V$ when $V$ is
an irreducible $I_n$-representation with apex $\mathscr J_V=\mathscr J_m$. The strategy is
to reconstruct the representation $(V\downarrowS_{\kern-.3mm m})\uparrow I_n$ inside $V$.
We have already the idempotent $e=\id:[m]\rightarrow[m]$ and the transversal
$T=\{s_Y\}$ in Figure \ref{fig:transversal}
for the $m$-sized subsets $Y$ of
$[n]$.
Consider now the subspaces $(s_Ye)V$ of $V$ for the various
$Y$. Then:
\begin{description}
\item[--] Each vector space $(s_Ye)V$ is isomorphic to $eV$: the
linear map
$eV\rightarrow(s_Ye)V$ given by
$ev\mapsto (s_Ye)v$ has inverse the map $(s_Ye)v\mapsto
s_Y^*(s_Ye)v=e^2v=ev$, and so is an isomorphism.
\item[--] The sum $\sum_Y (s_Ye)V$ of these spaces is direct: for
which we need to show that for a fixed subset $Y$, the intersection
\begin{equation}
\label{eq:11}
s_YeV\cap \sum_{Z\not=Y}s_ZeV
\end{equation}
is the zero space.
We have just seen that $s_Y^*$ gives an isomorphism $s_YeV\rightarrow eV$, hence
maps the subspace $s_YeV\cap \sum_{Z\not=Y}s_ZeV$ of $s_YeV$ isomorphically onto
its image in $eV$. But
\begin{equation}
\label{eq:10}
s_Y^*\biggl(s_YeV\cap \sum_{Z\not=Y}s_ZeV\biggr)
\subseteq
s_Y^*s_YeV\cap s_Y^*\biggl(\sum_{Z\not=Y}s_ZeV\biggr)
=
eV \cap \sum_{Z\not=Y}s_Y^*s_ZeV
\end{equation}
where $Z\not= Y$ gives that the domain of $s_Y^*s_Ze$ has size
strictly less than $m$, and so $s_Y^*s_Ze$ lies in a $\mathscr J$-class lower
down the strategic picture than $\mathscr J_m$ does. As $\mathscr J_m$ is the
apex of $V$ we have $s_Y^*s_ZeV=0$ for all $Z$, so that the right hand
side of (\ref{eq:10}) is $0$, and hence (\ref{eq:11}) is too.
\item[--] Restricting the $S$-action on $V$ to the subspace
$\bigoplus_Y s_YeV$: if $t\in I_n$ then there are two
possibilities for the product $ts_Y$. Either:
\begin{description}
\item[(i).]$ts_Y\in\LL_e$, in which case by (\ref{eq:1}), there is
a $g\in G_e$ and an $m$-subset $Z$ such that $ts_Y=s_Zg$; or
\item[(ii).] $ts_Y\not\in\LL_e$, and since this $\LL$-class consists
of all partial bijections with domain $[m]$, and
$\text{dom}\,(ts_Y)\subseteq [m]$, we have that $\text{dom}\,(ts_Y)$ is a proper
subset of $[m]$. In particular $ts_Y$ lies in a $\mathscr J$-class
lower down the strategic picture than $\mathscr J_m$.
\end{description}
The $S$-action on $\bigoplus_Y s_Y eV$ is therefore given by
$$
t\cdot(s_Ye)\cdot v
=
\left\{
\begin{array}{ll}
(s_Ze)\cdot (g\cdot v),&\text{ if }ts_Y\in\LL_e,\text{ or}\\
0, &\text{ else.}
\end{array}
\right.
$$
\end{description}
We conclude, first of all, that the subspace $\bigoplus_Y s_YeV$ is
in fact a subrepresentation of $V$; moreover $\bigoplus_Y s_YeV$ contains, by
taking $Y=[m]$, the subspace $eV\not=0$. Thus $\bigoplus_Y s_YeV$ is
a non-zero subrepresentation of the irreducible representation $V$, hence
$$
\bigoplus_Y s_YeV=V.
$$
Finally, if $ts_Y\in\LL_e$ then the diagram
$$
\begin{pspicture}(0,0)(14,2.5)
\rput(0,0.25){
\rput(5.5,2){$(s_Ye)\cdot v$}
\rput(5.5,0){$s_Y\otimes e\cdot v$}
\rput(8.5,2){$(s_Ze)\cdot (g\cdot v)$}
\rput(8.5,0){$s_Z\otimes (eg)\cdot v$}
\psline[linewidth=0.5pt]{->}(6.2,2)(7.4,2)
\psline[linewidth=0.5pt]{->}(6.3,0)(7.5,0)
\psline[linewidth=0.5pt]{->}(5.5,1.8)(5.5,0.2)
\psline[linewidth=0.5pt]{->}(8.5,1.8)(8.5,0.2)
\rput(7,2.2){${\scriptstyle t(-)}$}
\rput(7,0.2){${\scriptstyle t(-)}$}
}
\end{pspicture}
$$
commutes (it trivially commutes if $ts_Y\not\in\LL_e$). Thus
$(V\downarrowS_{\kern-.3mm m})\uparrow I_n\cong V$ as $I_n$-representations, and the
composition $\text{Irr}_m(I_n)\rightarrow\text{Irr}(S_{\kern-.3mm m})\rightarrow\text{Irr}_m(I_n)$
is the identity map.
This completes the proof of the Clifford-Munn correspondence when $S=I_n$.
\begin{vexercise}
\label{exercise:CMP}
Mimic the proof above for an inverse monoid $S$ of the form $S=S\kern-1pt(G,L)$
(\emph{hint:\/} much of the proof can be found scattered among what we
have already said).
\end{vexercise}
\begin{example}[The irreducibles of $I_n$]
\label{induction:specht}
We are finally in a position to describe the irreducible
representations over $\ams{C}}\def\Q{\ams{Q}}\def\F{\ams{F}}\def\K{\ams{K}$ of the symmetric inverse monoid $I_n$.
By Theorem \ref{theorem: Munn:Oganesyan}, every $I_n$-representation
over $\ams{C}}\def\Q{\ams{Q}}\def\F{\ams{F}}\def\K{\ams{K}$ is a direct sum of these.
As we will be
doing things this way in \S\ref{section:sexy:example} -- and this is
sort of a dry run at it --
we will use the $S\kern-1pt(S_{\kern-.3mm n},L)$ description of $I_n$ that we saw at the end of
\S\ref{section:semigroup_basics}, where $L$ is the
lattice of subsets of $[n]$. This allows us to follow the recipe for induction
given at the end of \S\ref{section:induction}.
Fix an $m$ in the range $0\leq m\leq n$, hence a $\mathscr J$-class
corresponding to the $S_{\kern-.3mm n}$-orbit on $L$ consisting of the subsets
of $[n]$ having size
$m$. Let $a=\{1,2,\ldots,m\}$ and $G_a$ the maximal
subgroup containing the idempotent $\id_a$. The elements of $G_a$ are
the $g_a$ where $g\inS_{\kern-.3mm n}$ is such that $g\cdot a=a$ (rather than
being
the bijections $a\rightarrow a$
as they would
be in the ``usual'' way of describing $I_n$). Finally, let $\lambda$ be a
partition of $m$ and $S^\lambda$ be the Specht representation spanned by the
$v_T$ in (\ref{eq:19}) as $T$ ranges over the tableau of shape
$\lambda$.
We will describe the representation $S^\lambda\uparrow I_n$.
The Clifford-Munn correspondence tells us that the $S^\lambda\uparrow
I_n$, as both $\lambda$ and $m$ vary in $\lambda \vdash m$, form a
complete and non-redundant list of the $I_n$-irreducibles over $\ams{C}}\def\Q{\ams{Q}}\def\F{\ams{F}}\def\K{\ams{K}$.
If
$b=\{i_1,\ldots,i_m\}$ is a subset of $[n]$ of size $m$, then let
$\beta$ be an element of $S_{\kern-.3mm n}$ that sends $j\in a$ to $i_j\in b$. We then
take the transversal $T$ needed for induction to be the resulting $\beta_a$ as $b$ ranges
over the subsets of size $m$.
If $T$ is a tableau of shape $\lambda$ filled with entries from $a$, then $\bb\cdot
T$ is a tableau of shape $\lambda$ filled with entries from $b$. Let $S^{\lambda,b}$
be a copy of $S^\lambda$, spanned by the
$$
b\otimes v_T=\sum_{h\in c_{\bb\cdot T}}\text{sign}(h)\, h\cdot\{\bb\cdot
T\},
$$
as $T$ varies over the tableau (on $a$), and
where $c_{\bb\cdot T}$ are those elements of the symmetric group on
the set $b$ preserving the columns of $T$. The vector $b\otimes v_T$
is just the vector $v_T$, but with every occurence of $j\in a$ in a tabloid
replaced by $i_j\in b$, and $S^{\lambda,b}$ is the space spanned by
the $b\otimes v_T$.
The representation $S^\lambda\uparrow I_n$ acts on the space
$$
S^\lambda\uparrow I_n
=
\bigoplus_{|b|=m}
S^{\lambda,b}
$$
To see how, fix an $s=g_c\in I_n$. We saw at the end of \S\ref{section:induction}
that the apex of
$S^\lambda\uparrow I_n$
is the $\mathscr J$-class containing the maximal subgroup $G_a$ that we started with, so
if $|c|< m$ we get $s\cdot S^\lambda\uparrow
I_n=0$.
On the other hand, by (\ref{eq:18}),
if $c$ has size at least $m$, then it will \emph{not\/} kill
those summands $S^{\lambda,b}$ for which $b\subseteq c$. In this case
$s\,\bb_a$ lies in the $\HH$-class labelled by the subset $d=g\cdot
b$, so that for $b\otimes v_T$ spanning $S^{\lambda,b}$ we get
$$
s\cdot(b\otimes v_T)=d\otimes h\cdot v_T
$$
where $h=(\delta^{-1}g\,\bb)_a\in G_a$.
\end{example}
\section{A sexy example}
\label{section:sexy:example}
For the purposes of these notes, ``sexy'' will mean a certain family
of Renner monoids. These encode much of the structure of algebraic
monoids, and are ubiquitous in nature.
We first set the examples up in the form $S\kern-1pt(G,L)$ from Section
\ref{section:semigroup_basics}. As usual $G$ is the
symmetric group $S_{\kern-.3mm n}$, but the lattice is one we haven't seen
before. Let $L_0$ consist of the \emph{ordered\/} partitions of $[n]$,
i.e. the \emph{tuples\/} $\Lambda=(\Lambda_1,\ldots,\Lambda_p)$ with
$\{\Lambda_1,\ldots,\Lambda_p\}$ a partition of $[n]$. Partially order
the ordered partitions via
$(\Lambda_1,\ldots,\Lambda_p)\leq (\Delta_1,\ldots,\Delta_q)$ if and
only if
\begin{align*}
\label{eq:16}
&\text{\textendash}\text{ each }\Lambda_i\subseteq\text{some
}\Delta_j,\text{ and}\\
&\text{\textendash}\text{ if }\Lambda_i\subseteq\Delta_j\text{ and for
}i<k\text{ we have }\Lambda_k\subseteq\Delta_\ell,\text{ then }j\leq\ell.
\end{align*}
$L_0$ then has maximum element the ordered partition $([n])$ with a
single block and \emph{minimal\/} elements the ordered partitions
where every block has size one; these minima are in 1-1 correspondence
with the permutations of $[n]$.
Formally adjoin a minimum
$\mathbf{0}$ to $L_0$ to get the lattice $L$. The $S_{\kern-.3mm n}$-action on $L$ is the
usual $g\cdot
(\Lambda_1,\ldots,\Lambda_p)=(g\cdot\Lambda_1,\ldots,g\cdot\Lambda_p)$
together with $g\cdot\mathbf{0}=\mathbf{0}$.
\paragraph{A short diversion on where the example comes from.} A
linear algebraic group $\ams{G}$, over an algebraically closed field
$k$, is an affine algebraic variety over $k$,
together with a morphism $\varphi:\ams{G}\times \ams{G}\rightarrow \ams{G}$
of varieties, such that the product $gh:=\varphi(g,h)$ gives
$\ams{G}$ the structure of a group. Generalising this idea, a
\emph{linear algebraic monoid\/} $\ams{M}$ arises when
$\varphi:\ams{M}\times\ams{M}\rightarrow\ams{M}$
gives $\ams{M}$ the structure of a monoid.
The canonical examples are $\ams{G}=\gl_nk$, the group of invertible
matrices over $k$, and $\ams{M}=\text{M}}\def\d{\text{D}}\def\su{\text{SU}}\def\sp{\text{Sp}_nk$, the monoid of all
$n\times n$ matrices over $k$ (both under multiplication). In fact
$\gl_nk$ is the group of units
of the monoid $\text{M}}\def\d{\text{D}}\def\su{\text{SU}}\def\sp{\text{Sp}_nk$, and indeed for sensible $\ams{M}$ the group
of units $\ams{G}$ is an algebraic group with Zariski closure
$\overline{\ams{G}}=\ams{M}$.
There is a standard construction of algebraic monoids that
starts with a sensible
algebraic group $\ams{G}_0$ and a sensible representation
$f:\ams{G}_0\rightarrow GL(V)$. The resulting algebraic
monoid is then $\ams{M}=\overline}\def\tl{\tilde}\def\wtl{\widetilde}\def\widehat}\def\ch{\check{\widehat{k^\times f(\ams{G}_0)}\subset\text{M}}\def\d{\text{D}}\def\su{\text{SU}}\def\sp{\text{Sp}_{m}k$ with
group of units
$\ams{G}=k^\times f(\ams{G}_0)$. For example, if $\ams{G}_0=\sl_n, \text{SO}}\def\pso{\text{PSO}}\def\po{\text{PO}}\def\sl{\text{SL}_n$ and
$\sp_n$ and $f$ is the natural representation of $\ams{G}_0$,
then the resulting $\ams{M}$ are the \emph{classical monoids\/}: the general linear monoids
$\text{M}}\def\d{\text{D}}\def\su{\text{SU}}\def\sp{\text{Sp}_n=\overline}\def\tl{\tilde}\def\wtl{\widetilde}\def\widehat}\def\ch{\check{\widehat{k^\times \sl_n}$, the
orthogonal monoids $\text{MSO}}\def\msp{\text{MSp}_n=\overline}\def\tl{\tilde}\def\wtl{\widetilde}\def\widehat}\def\ch{\check{\widehat{k^\times \text{SO}}\def\pso{\text{PSO}}\def\po{\text{PO}}\def\sl{\text{SL}_n}$ and the symplectic
monoids $\msp_n=\overline}\def\tl{\tilde}\def\wtl{\widetilde}\def\widehat}\def\ch{\check{\widehat{k^\times \sp_n}$.
Associated to a (reductive) algebraic group $\ams{G}$ is a finite group --
called the Weyl group -- that encodes much of the structure of
$\ams{G}$; for a (reductive) algebraic monoid $\ams{M}$ there
is a finite inverse monoid $R$ --
called the \emph{Renner monoid\/} -- that plays an analogous role.
For example, the Weyl group of $\gl_nk$ is the symmetric group $S_{\kern-.3mm n}$
and the Renner monoid of $\text{M}}\def\d{\text{D}}\def\su{\text{SU}}\def\sp{\text{Sp}_nk$ is the symmetric inverse monoid
$I_n$. In general the group of units of the Renner monoid $R$ of
$\ams{M}$ is the Weyl group $W$ of the algebraic group of units $\ams{G}$ of $\ams{M}$.
If $R$ is the Renner monoid of the algebraic monoid $\ams{M}$ having
group of units the algebraic group $\ams{G}$, then $R$ is an inverse
monoid of the form
$S\kern-1pt(W,L)$: the group $W$ is the Weyl group of
$\ams{G}$ and the lattice $L$ turns out to be the face lattice of a convex
polytope.
To see what this means, a polytope $P$ in $\R^m$ is the convex hull of a finite set
of points. It has $r$-dimensional faces, for $-1\leq r\leq m$, with
the $0$-dimensional faces being the vertices, $1$-dimensional faces
the edges, and so on, with $P$ itself the unique $m$-dimensional
face; for formal reasons (mainly so that we get a lattice below) we
take the empty set $\varnothing$ to be
the unique face of dimension $-1$. The \emph{face lattice\/} of $P$
consists of the faces ordered by inclusion; it is a lattice with meet
$\ss\wedge\tau$ the intersection and join $\ss\vee\tau$ the smallest
face containing both $\ss$ and $\tau$.
The Renner monoid of $\text{M}}\def\d{\text{D}}\def\su{\text{SU}}\def\sp{\text{Sp}_nk$ has the form $S\kern-1pt(W,L)$ where $W$ is the
symmetric group $S_{\kern-.3mm n}$ and $L$ is the face lattice of an
$(n-1)$-dimensional simplex. If $[n]=\{1,\ldots,n\}$ are the labels of
the vertices of the simplex,
then $L$ is the lattice of subsets of $[n]$ ordered by
inclusion, and the $S_{\kern-.3mm n}$-action on $L$ is the usual one. This is
the description of $I_n$ we gave at the end of
\S\ref{section:semigroup_basics}.
Now to the example we are interested in: let $\ams{G}_0=\sl_n$ and
$V_0$ be the natural
module for $\ams{G}_0$. Let $\bigwedge^p V_0$ be the $p$-th exterior
power of $V_0$
and finally
$$
V=\bigotimes_{p=1}^{n-1}\bigwedge^p V_0,\text{ with }
\dim V:=m=\prod_{p=1}^{n-1}\binom{n}{p}.
$$
If $f:\ams{G}_0\rightarrow GL(V)$ is the corresponding representation
then let $\ams{M}=\overline}\def\tl{\tilde}\def\wtl{\widetilde}\def\widehat}\def\ch{\check{\widehat{k^\times f(\ams{G}_0)}$ and let $R$ be
the Renner monoid of $\ams{M}$. Then $R\congS\kern-1pt(W,L)$ with $W$ the
symmetric group $S_{\kern-.3mm n}$ and $L$ the face lattice of the
$(n-1)$-dimensional permutohedron. This is the polytope in $\R^n$
obtained by taking the convex hull of the $n!$ points arising
from all permutations of the coordinates of the point
$(1,2,\ldots,n)$. As all these points lie in the hyperplane with
equation $x_1+x_2+\cdots+x_n=1+2+\cdots+n$, the polytope is actually
$(n-1)$-dimensional.
\begin{figure}
\centering
\begin{pspicture}(0,0)(14,7)
\rput(2.5,3){\BoxedEPSF{permutohedron5.eps scaled 250}}
\rput(0.75,0.5){
\rput(9.15,3){\BoxedEPSF{permutohedron4a.eps scaled 450}}
\rput(10.05,3.9){$\scriptscriptstyle{{\blue 1,2,3,4}}$}
\rput(9.55,5.5){$\scriptscriptstyle{{\blue 1,3,2,4}}$}
\rput(11.5,4.5){$\scriptscriptstyle{{\blue 1,4,3,2}}$}
\rput(8.75,2.4){$\scriptscriptstyle{{\blue 2,1,3,4}}$}
\rput(6.9,2.55){$\scriptscriptstyle{{\blue 2,3,1,4}}$}
\rput(6.45,4.2){$\scriptscriptstyle{{\blue 3,2,1,4}}$}
\rput(7.75,5.65){$\scriptscriptstyle{{\blue 3,1,2,4}}$}
\rput(10.05,1.15){$\scriptscriptstyle{{\blue 2,1,4,3}}$}
\rput*(9.5,0.1){$\scriptscriptstyle{{\blue 2,4,1,3}}$}
\rput*(10.2,0.5){$\scriptscriptstyle{{\blue 4,2,1,3}}$}
\rput(11.3,2.6){$\scriptscriptstyle{{\blue 1,2,4,3}}$}
\rput*(7.7,0.3){$\scriptscriptstyle{{\blue 2,4,3,1}}$}
\rput*(6.4,1.5){$\scriptscriptstyle{{\blue 2,3,4,1}}$}
\rput*(6,3.1){$\scriptscriptstyle{{\blue 3,2,4,1}}$}
\rput(12,3){$\scriptscriptstyle{{\blue 1,4,2,3}}$}
\rput(10.25,5.8){$\scriptscriptstyle{{\blue 1,3,4,2}}$}
\rput*(8.5,5.9){$\scriptscriptstyle{{\blue 3,1,4,2}}$}
\rput*(11.45,2){$\scriptscriptstyle{{\blue 4,1,2,3}}$}
\rput(9.8,4.7){$\scriptscriptstyle{{\red 1,23,4}}$}
\rput(9.4,3.15){$\scriptscriptstyle{{\red 12,3,4}}$}
\rput(7.85,2.5){$\scriptscriptstyle{{\red 2,13,4}}$}
\rput(6.7,3.45){$\scriptscriptstyle{{\red 23,1,4}}$}
\rput(7.05,4.9){$\scriptscriptstyle{{\red 3,12,4}}$}
\rput(8.65,5.6){$\scriptscriptstyle{{\red 13,2,4}}$}
\rput(9.35,1.85){$\scriptscriptstyle{{\red 2,1,34}}$}
\rput(10.7,3.25){$\scriptscriptstyle{{\red 1,2,34}}$}
\rput(10.65,1.9){$\scriptscriptstyle{{\red 12,4,3}}$}
\rput*(8.5,0.2){$\scriptscriptstyle{{\red 2,4,13}}$}
\rput*(7,0.9){$\scriptscriptstyle{{\red 2,34,1}}$}
\rput*(10.9,1.4){$\scriptscriptstyle{{\red 4,12,3}}$}
\rput(11.75,3.75){$\scriptscriptstyle{{\red 1,4,23}}$}
\rput(10.9,5.15){$\scriptscriptstyle{{\red 1,34,2}}$}
\rput*(6.2,2.35){$\scriptscriptstyle{{\red 23,4,1}}$}
\rput*(9.8,0.7){$\scriptscriptstyle{{\red 2,14,3}}$}
\rput*(6.7,2.1){$\scriptscriptstyle{{\red 2,3,14}}$}
\rput(6.15,3.55){$\scriptscriptstyle{{\red 3,2,14}}$}
\rput(8.15,3.9){$123,4$}
\rput(10.05,2.5){$12,34$}
\rput(10.8,4.2){$1,234$}
}
\end{pspicture}
\caption{The $3$-permutodehron, after identifying the hyperplane
$x_1+x_2+x_2+x_4=10\subset\R^4$ with $\R^3$ \emph{(left)\/}
and part of the lattice of ordered partitions overlaid on the faces
\emph{(right)\/}, with the blocks of the partitions separated by commas.}
\label{fig:permutohedron}
\end{figure}
The face lattice of the permutohedron is isomorphic to the lattice $L$
of ordered
partitions, with $\mathbf{0}$ adjoined, described at the beginning of the section. Figure
\ref{fig:permutohedron} shows the $n=4$ case.
\paragraph{} To describe the irreducible representations over $\ams{C}}\def\Q{\ams{Q}}\def\F{\ams{F}}\def\K{\ams{K}$ of
our Renner monoid, we use the $S\kern-1pt(G,L)$ description from the beginning
of the section, and
start by drilling down a little more into
the structure of the monoid, following
\S\ref{section:semigroup_basics}.
First, we have our usual ambiguity with the elements of $S\kern-1pt(G,L)$,
where $g_a=h_b$ when $a=b$ and $g^{-1}h\cdot c=c$ for all $c\leq
a$. In this case it turns out to disappear. If $a$ is the ordered partition
$(\Lambda_1,\ldots,\Lambda_p)$ and
$c$ is a minimal element $\not=\mathbf{0}$ with the property that $c\leq a$,
then $c$ has the form
$$
c=(\{x_{11},\ldots,x_{1q_1}\},\ldots,\{x_{p1},\ldots,x_{pq_p}\})
$$
where
$\Lambda_1=\{x_{11},\ldots,x_{1q_1}\},\ldots,\Lambda_p=\{x_{p1},\ldots,x_{pq_p}\}$.
If $k$ is an
element of $S_{\kern-.3mm n}$ with $k\cdot c=c$ then $k=\id$. Thus $g_a=h_b$ iff
$a=b$ and $g=h$.
If $(\Lambda_1,\ldots,\Lambda_p)$ is an ordered partition with
$\lambda_i=|\Lambda_i|$, then the ordered tuple
$(\lambda_1,\ldots,\lambda_p)$ is called a \emph{composition\/} of
$n$: namely, the $\lambda_i$ are totally ordered with
$\sum\lambda_i=n$. Call the composition the \emph{type\/} of the
ordered partition. Two ordered partitions are then in the same
$S_{\kern-.3mm n}$-orbit when they have the same type, and the $\mathscr J$-class poset
has elements the compositions ordered by
$(\lambda_1,\ldots,\lambda_p)\leq (\mu_1,\ldots,\mu_q)$ whenever
$$
(\lambda_1,\ldots,\lambda_p)=
(\lambda_{11},\ldots,\lambda_{1m_1},\ldots,\lambda_{p1},\ldots,\lambda_{p,m_p})
$$
with $\mu_i=\lambda_{i1}+\ldots+\lambda_{i,p_i}$. Figure
\ref{fig:permutohedron2} shows this poset when $n=4$.
Fix a composition $(\lambda_1,\ldots,\lambda_p)$ and consider the
$\mathscr J$-class of ordered partitions of this type.
If $a$ is one of them, then the
maximal subgroup is $G_a=\{g_a:g\cdot a=a\}$, and this is isomorphic to
the Young subgroup $S_{\kern-1pt\lambda_1}\times\cdots\times
S_{\kern-1pt\lambda_p}$ of $S_{\kern-.3mm n}$. We saw above that our usual
ambiguity in expressing elements vanishes in $R$; this is why there
is no need to form a quotient when describing $G_a$.
Let
$a=(\Lambda_1,\ldots,\Lambda_p)$ be the ordered partition of type
$(\lambda_1,\ldots,\lambda_p)$
given by:
\begin{equation}
\label{eq:20}
\Lambda_1=\{1,\ldots,\lambda_1\},
\ldots,
\Lambda_p=\{n-\lambda_p+1,\ldots,n\},
\end{equation}
We now describe the irreducible representations of $R$ that arise by
inducing up those of the maximal subgroup $G_a\cong
S_{\kern-1pt\lambda_1}\times\cdots\times
S_{\kern-1pt\lambda_p}$.
Varying the composition produces a complete list of the irreducibles
over $\ams{C}}\def\Q{\ams{Q}}\def\F{\ams{F}}\def\K{\ams{K}$ of the Renner monoid $R$. We borrow one more fact from the
representation theory of finite groups: if $\{V_i\}_{i\in I}$ and
$\{U_j\}_{j\in J}$ are the irreducibles of the groups $G$ and $H$, then the
$\{V_i\otimes U_j\}_{I\times J}$ are the irreducibles of $G\times H$,
with $V_i\otimes U_j$ a $(G\times H)$-representation
via the action $(g,h)\cdot v\otimes u=g\cdot v\otimes h\cdot u$.
\begin{figure}
\centering
\begin{pspicture}(0,0)(4,6)
\rput(2,3){\BoxedEPSF{fig21.eps scaled 450}}
\rput(1.45,1.8){${\scriptstyle (1,1,1,1)}$}
\rput(0.3,3){${\scriptstyle (2,1,1)}$}
\rput(1.5,3){${\scriptstyle (1,2,1)}$}
\rput(2.7,3){${\scriptstyle (1,1,2)}$}
\rput(0.4,4.2){${\scriptstyle (3,1)}$}
\rput(1.6,4.2){${\scriptstyle (2,2)}$}
\rput(2.8,4.2){${\scriptstyle (1,3)}$}
\rput(2,5.7){${\scriptstyle (4)}$}
\rput(2,0.3){${\scriptstyle\mathbf{0}}$}
\end{pspicture}
\caption{The $\mathscr J$-class poset of our Renner monoid $R$ when $n=4$,
corresponding to the poset of compositions of $4$.}
\label{fig:permutohedron2}
\end{figure}
Now fix partitions $\mu_1\vdash\lambda_1,\ldots,\mu_p\vdash\lambda_p$ and
consider the irreducible $(S_{\kern-1pt\lambda_1}\times\cdots\times
S_{\kern-1pt\lambda_p})$-representation
\begin{equation}
\label{eq:21}
S^{\mu_1}\otimes\cdots\otimes S^{\mu_p}
\end{equation}
where $S^{\mu_i}$ is the Specht representation of $S_{\kern-1pt\lambda_i}$
corresponding to the partition $\mu_i\vdash\lambda_i$. The
representation (\ref{eq:21})
is spanned by the vectors
$$
v_{T_1}\otimes\cdots\otimes v_{T_p}
$$
defined in (\ref{eq:19}) and
as the $T_i$ range over the tableau of shape $\mu_i$ filled with the numbers $\Lambda_i$
in (\ref{eq:20}). To describe $S^{\mu_1}\otimes\cdots\otimes
S^{\mu_p}\uparrow R$, let $b=(\Delta_1,\ldots,\Delta_p)$ be another ordered
partition of type $(\lambda_1,\ldots,\lambda_p)$ and let
$\beta\inS_{\kern-.3mm n}$ be such that $\beta:\Lambda_i\mapsto\Delta_i$ in an
order preserving way, i.e. if $x<y\in\Lambda_i$ then
$\beta(x)<\beta(y)\in\Delta_i$. Let $S^{\mu_1,\,\bb}\otimes\cdots\otimes
S^{\mu_p,\,\bb}$ be a copy of (\ref{eq:21}) with spanning vectors of
the form:
$$
\bb\otimes
v_{T_1}\otimes\cdots\otimes v_{T_p},
$$
defined to be $v_{T_1}\otimes\cdots\otimes v_{T_p}$, but with every
occurence of $j$ in a tabloid replaced by $\bb(j)$. (Warning: this
vector is linear in the $v_{T_i}$ coordinates only; the
``$\bb\,\otimes$", as usual, is just notation that comes along for the
ride).
The representation
$S^{\mu_1}\otimes\cdots\otimes
S^{\mu_p}\uparrow R$
is carried by the space
$$
S^{\mu_1}\otimes\cdots\otimes
S^{\mu_p}\uparrow R
=
\bigoplus_{b}
S^{\mu_1,\,\bb}\otimes\cdots\otimes
S^{\mu_p,\,\bb}
$$
with the direct sum over the ordered partitions of type
$(\lambda_1,\ldots,\lambda_p)$. Let $s=g_c\in R$ with
$g\inS_{\kern-.3mm n}$ and $c$ the ordered partition $(\Omega_1,\ldots,\Omega_q)$ of type
$(\omega_1,\ldots,\omega_q)$. If
$(\lambda_1,\ldots,\lambda_p)\not\leq(\omega_1,\ldots,\omega_q)$ then
$$
s\cdot (S^{\mu_1}\otimes\cdots\otimes
S^{\mu_p}\uparrow R)=0.
$$
Otherwise, when
$(\lambda_1,\ldots,\lambda_p)\leq(\omega_1,\ldots,\omega_q)$
we have $s\cdot (S^{\mu_1,\,\bb}\otimes\cdots\otimes
S^{\mu_p,\,\bb})\not=0$ when $b=(\Delta_1,\ldots,\Delta_p)\leq
(\Omega_1,\ldots,\Omega_q)$ and in this case
$$
s\cdot(\bb\otimes
v_{T_1}\otimes\cdots\otimes v_{T_p})
=\delta\otimes h\cdot (v_{T_1}\otimes\cdots\otimes v_{T_p})
$$
where $d=g\cdot b$ and
$h=(\delta^{-1}g\,\bb)_a\in G_a\cong S_{\kern-1pt\lambda_1}\times\cdots\times
S_{\kern-1pt\lambda_p}$.
\section*{Notes and References}
There are numerous books that deal with semigroup representations,
starting with the classic \cite{MR0132791}*{Chapter 5}; more modern sources are
\cite{MR2460611,MR3525092}. The reader who has got this far will see
large overlap with \cite{MR2460611}, making \cite{MR3525092} a good
next step. The original papers of Clifford \cite{MR0006551} and Munn
\cite{MR0066355}-\cite{MR0172953} are still very readable, as is the later reworking by
Rhodes \cite{MR1142387}.
\paragraph{Semigroups.} The standard reference on semigroups is
\cite{Howie95}, where we have followed Chapters 1, 2 and 5; see
also \cite{MR0132791,Lawson98,MR2460611}. The three running examples are very
much in the style of \cite{MR2460611}. For the reader who is wondering
about the ``full'' transformation semigroup, there is a partial
version $PT_n$, which is a sort-of-amalgam of $I_n$ and $T_n$; see
\cite{MR2460611}*{Chapter 2}.
The restriction to finite
regular monoids is purely to make things cleaner. An expert (who
shouldn't be reading this anyway) can make the appropriate
adjustments, especially in Section \ref{section:clifford:munn}. One
convenience that results is that the relation $\langle \LL,\mathcal R}\def\LL{\mathcal L}\def\mathscr P{\mathcal P}\def\QQ{\mathcal Q\rangle$,
usually called $\DD$ by semigroup theorists, coincides with $\mathscr J$. So
all mention of $\DD$ (which gives the eggbox
pictures) has been
merged with $\mathscr J$ (which gives the partial order
on the eggboxes). Figure \ref{fig:Tn_Hclasses_idempotents} is adapted
from a picture by James East.
The inverse monoids $S\kern-1pt(G,L)$ appear in \cite{Everitt10}*{Section 9.2} as monoids of
partial permutations, although they are implicit in the
literature. Their purpose in \cite{Everitt10} is to shed light on the
\emph{factorisable\/}
inverse monoids: these are monoids $S$ with the property that
$S=EG=GE$, where $G$ is the group of units of $S$ and $E$ the
idempotents -- see \cite {Chen74, FitzGerald10}.
Exercise \ref{exercise:sgl:order} can be done by counting the $g_a$,
but bearing in mind the
ambiguity; another way, more natural in this context, is to count up
the entries in the boxes in the strategic picture. The monoid of
uniform block permutations of Example \ref{exercise:partition} first
appears in \cite{FitzGerald03}. The picture of the Hasse diagram for
the partition lattice $\Pi(4)$ in Figure \ref{fig:S(G,L)} is based on
one by Tilman Piesk \cite{Baez15}.
\paragraph{Representations.} There are many books on group
representation theory; we have followed the notation and style
of \cite{MR1153249}*{Part I}. In particular the approach is elementary,
\emph{aka\/} ``module-free''. In this section the representations are
over an arbitrary field $k$; one moral to be extracted at the end is
that in dealing with semigroup representations in characteristic $p>0$,
one needs to be just as careful, if not
more careful, than one does in group representation theory. The
emphasis thus moves to $k=\ams{C}}\def\Q{\ams{Q}}\def\F{\ams{F}}\def\K{\ams{K}$ in later sections. Another omission is
the theory of semigroup characters, which is well developed for the
running examples.
The restriction to monoids (rather than semigroups) and
monoid homomorphisms removes null representations from consideration
-- this makes a number of statements
less cluttered.
The standard reference on reflection groups is \cite{Humphreys90}. A
finite reflection group (acting on a real vector space) can be boiled
down to a very concise piece of combinatorial data called a Coxeter
symbol. Starting from a Coxeter symbol one can construct a
representation of the reflection group, called the reflectional
representation; a fundamental result in the theory of reflection
groups is that the reflectional representation is
irreducible. Starting from the type $A$ Coxeter symbol:
$$
\begin{pspicture}(0,0)(14,1)
\rput(7,0.5){\BoxedEPSF{An.eps scaled 350}}
\rput(4.9,0.9){$s_1$}\rput(6.1,0.9){$s_2$}
\rput(7.8,0.9){$s_{n-2}$}\rput(9.1,0.9){$s_{n-1}$}
\end{pspicture}
$$
this process gives the reflectional representation of Example
\ref{example:permutation:representation}. The elementary argument showing that
this is irreducible was supplied by Michael
Bate.
Munn \cite{MR0081910} extends the cycle notation for permutations in
$S_{\kern-.3mm n}$ to elements $s\in I_n$ in the following neat way: for
$x\in[n]$, repeated application of $s$ either results in a \emph{cycle\/}:
$x,s(x),s^2(x),\ldots,$ $s^{k+1}(x)=x$, in which case we write
$(x,s(x),\ldots,s^k(x))$ as usual; or, $s^{k}(x)$ is the first
iteration of $S$ that does not lie in
the domain of $s$, so that no more applications of $s$ can be made. In
this case we have a \emph{link\/} $[x,s(x),\ldots,s^k(x)]$. Any $s\in
I_n$ can then be written uniquely as a juxtaposition of disjoint cycles and
links; the element $[1,2,3]\in I_3$ on the right of Figure
\ref{fig:reflection_rep_Sn} is an example.
Reflection monoids appear in \cite{Everitt10}, where
$I_n$ is a Boolean monoid of type $A$.
The formulation of semisimplicity suffers a little from the
module-free approach, where it is cleaner to talk in terms of the
semisimplicity of the semigroup algebra $kS$.
We have also avoided the notion of decomposability: the mapping
representation of $T_n$ is thus indecomposable but not irreducible,
\emph{even in characteristic $0$\/}. One imagines that this is the
aspect of the whole thing that group theorists find most distressing.
Theorem
\ref{theorem:JordanHolder} is standard -- we have followed
\cite{MR1984740}*{Theorem 6.1.15}; Theorem \ref{theorem:Mashke} similarly
(see e.g. \cite{MR1984740}*{Theorem 3.1.14});
Theorem \ref{theorem:
Munn:Oganesyan} is
less well known, except to the cognoscenti;
see \cite{MR0132791,MR3525092}. For $I_n$ and
$T_n$ see also \cite{MR2460611}*{Section 11.5}.
\paragraph{Interlude: the symmetric group.} A standard introductory
text to all aspects of the representations of $S_{\kern-.3mm n}$ is
\cite{MR1824028}; for the Young tableau of this section we have
followed \cite{MR1464693}*{Section 7.2}; see also
\cite{MR1153249}*{Chapter 4}. The irreducibles of $S_{\kern-.3mm n}$ are more
commonly called Specht \emph{modules\/} rather than representations;
as we are not mentioning modules, we hope the change of nomenclature
is not too discombobulating. The representation
$S^{\BoxedEPSF{tableau1a.eps
scaled 80}}$
in Figure \ref{fig:symmetric:three} is $S_{\kern-.3mm 3}$ as the symmetries
--
obtained by permuting its three vertices
--
of
the equilateral triangle. In
general
$S^{\BoxedEPSF{tableau1.eps scaled 100}}$ is the representation of $S_{\kern-.3mm n}$ acting as the
symmetries of the regular $(n-1)$-simplex; it is another incarnation
of the reflectional representation of $S_{\kern-.3mm n}$ mentioned in Example
\ref{example:permutation:representation} and
in the notes
to the previous section. The number of irreducible representations of $S_{\kern-.3mm n}$
over $\ams{C}}\def\Q{\ams{Q}}\def\F{\ams{F}}\def\K{\ams{K}$ is equal to the number $p(n)$ of partitions $\lambda\vdash n$;
there is no known closed formula for $p(n)$, but many
weird and wonderful properties are known. To choose just one, there is
the
generating function
$$
\sum_{n=0}^{\infty} p(n)x^n
=
\prod_{k=1}^{\infty}\left(\frac{1}{1-x^k}\right)
$$
Exercise
\ref{exercise:exterior:powers;reflectional} is
\cite{MR1153249}*{Exercise 4.6}.
\paragraph{Reduction.} We have generally followed
\cite{MR2529864}. The philosophy of the Clifford-Munn correspondence described in
Section \ref{section:clifford:munn}
is that knowledge
of group representations yields knowledge of semigroup
representations. The passage from groups to
semigroups is the induction construction of
Section \ref{section:induction}.
The current section is thus a little more perfunctory, as
reduction -- for us -- is merely the inverse construction, its
principal purpose being to establish the Clifford-Munn bijection.
The usual terminology is ``restriction'' in
much of the literature, but we have gone for reduction on two counts:
it is first of all a double restriction -- in that an action of $S$ on
$V$ is being restricted to both a subgroup of
$S$ and a subspace of $V$ -- and secondly, \emph{re}duction seems a
more satisfying counterpoint to
\emph{in}duction.
\paragraph{Induction.} The section is based on
\cite{MR2460611}*{Chapter 11}. Like there we adopt an elementary
approach; for example, in module-theoretic terms the representation $U$ is
$kS\otimes_{kG_e}V$; the notation $s_i\otimes v$ for the elements of
the copy $V_i$ of $V$ is a nod to this. That the construction is
independent of the transversal $T$ is \cite{MR2460611}*{Theorem
11.3.1(ii)}. The general picture is from \cite{MR2529864}*{Theorem 7}. The justification
in Example \ref{example:inversesemigroup:annihilator} that $U$ is an
irreducible $I_n$-representation closely follows \cite{MR2460611}*{Theorem 11.3.1}.
\paragraph{The Clifford-Munn correspondence.} Again we have followed
\cite{MR2460611, MR2529864} for the general picture. The irreducibles
of the symmetric inverse monoid in Example \ref{induction:specht} are a
venerable topic. Munn \cite{MR0081910} took a character-theoretic
approach while Grood \cite{MR1887083} constructed the ``Specht'' representations
for $I_n$ from scratch, and seemingly without reference to the
Clifford-Munn correspondence. Our approach follows
\cite{Majed}, where this and representations of other Boolean reflection monoids are
described.
\paragraph{A sexy example.} For algebraic groups
and Weyl groups see \cite{Humphreys75} and for algebraic monoids and
Renner monoids, the
books of Putcha and Renner \cite{Putcha88, Renner05}. A beautiful
expository article is \cite{Solomon95}; the example in this section is
taken from
\cite{Solomon95}*{Example 5.7}.
The meaning of ``sensible'', when talking about algebraic
groups and monoids, depends on the context. If $\ams{M}$
is irreducible, meaning its underlying variety is irreducible, then
the units $\text{G}$ are a connected algebraic group with
$\overline{\text{G}}=\ams{M}$. If $\text{G}_0$ is connected semisimple and the
representation $f:\text{G}_0\rightarrow GL(V)$ is rational with finite
kernel, then we have the construction for
$\ams{M}=\overline{k^\times f(\ams{G}_0)}$ described.
The Renner monoid of $\text{M}}\def\d{\text{D}}\def\su{\text{SU}}\def\sp{\text{Sp}_nk$ is isomorphic to the symmetric inverse
monoid; in this incarnation,
$I_n$ is called the \emph{Rook monoid\/} and consists of the
$n\times n$ matrices, with $0,1$-entries, such that each row and
column contains \emph{at most\/} one $1$. The name comes about as
the matrices can be identified with
$n\times
n$ chessboards, with rooks in the positions occupied by $1$'s,
and with the property that no two rooks are attacking each
other. Warning: the Renner monoid is not in
general a submonoid of $\ams{M}$, much as the Weyl group is not in general a subgroup
of $\text{G}$; both $\gl_nk$ and $\text{M}}\def\d{\text{D}}\def\su{\text{SU}}\def\sp{\text{Sp}_nk$ are a little special in this
way.
Good references for polytopes are \cite{Grunbaum03, MR1311028} where
one can also find the combinatorial description of the face polytope
of a permutohedron in terms of ordered partitions.
\vspace{1em}
\begin{biblist}
\bib{Majed}{article}{
author={Albaity, Majed},
title={Representations of reflection monoids},
note={(in preparation).}
}
\bib{Baez15}{article}{
author={John Baez},
title={Lattice of partitions},
journal={American Mathematical Society Blogs},
eprint={blogs.ams.org}
}
\bib{Chen74}{article}{
author={Chen, S. Y.},
author={Hsieh, S. C.},
title={Factorizable inverse semigroups},
journal={Semigroup Forum},
volume={8},
date={1974},
number={4},
pages={283--297},
issn={0037-1912},
}
\bib{MR0006551}{article}{
author={Clifford, A. H.},
title={Matrix representations of completely simple semigroups},
journal={Amer. J. Math.},
volume={64},
date={1942},
pages={327--342},
issn={0002-9327},
}
\bib{MR0132791}{book}{
author={Clifford, A. H.},
author={Preston, G. B.},
title={The algebraic theory of semigroups. Vol. I},
series={Mathematical Surveys, No. 7},
publisher={American Mathematical Society, Providence, R.I.},
date={1961},
pages={xv+224},
}
\bib{MR0218472}{book}{
author={Clifford, A. H.},
author={Preston, G. B.},
title={The algebraic theory of semigroups. Vol. II},
series={Mathematical Surveys, No. 7},
publisher={American Mathematical Society, Providence, R.I.},
date={1967},
pages={xv+350},
review={\MR{0218472}},
}
\bib{EverittFountain}{article}{
author={Everitt, Brent},
author={Fountain, John},
title={Partial mirror symmetry, lattice presentations and algebraic
monoids},
journal={Proc. London Math. Soc.},
volume={107},
date={2013},
number={3},
pages={414--450},
}
\bib{Everitt10}{article}{
author={Everitt, Brent},
author={Fountain, John},
title={Partial symmetry, reflection monoids and Coxeter groups},
journal={Adv. Math.},
volume={223},
date={2010},
number={5},
pages={1782--1814},
}
\bib{FitzGerald10}{article}{
author={FitzGerald, D. G.},
title={Factorizable inverse monoids},
journal={Semigroup Forum},
volume={80},
date={2010},
number={3},
pages={484--509},
issn={0037-1912},
}
\bib{FitzGerald03}{article}{
author={FitzGerald, D. G.},
title={A presentation for the monoid of uniform block permutations},
journal={Bull. Austral. Math. Soc.},
volume={68},
date={2003},
number={2},
pages={317--324},
issn={0004-9727},
}
\bib{MR3602826}{article}{
author={Fountain, John},
title={Sandy Green: his impact on semigroup theory},
journal={Semigroup Forum},
volume={94},
date={2017},
number={1},
pages={1--5},
issn={0037-1912},
}
\bib{MR2672169}{article}{
author={Fountain, John},
title={The work of Douglas Munn and its legacy},
journal={Semigroup Forum},
volume={81},
date={2010},
number={1},
pages={2--25},
issn={0037-1912},
}
\bib{MR1464693}{book}{
author={Fulton, William},
title={Young tableaux},
series={London Mathematical Society Student Texts},
volume={35},
note={With applications to representation theory and geometry},
publisher={Cambridge University Press, Cambridge},
date={1997},
pages={x+260},
isbn={0-521-56144-2},
isbn={0-521-56724-6},
}
\bib{MR1153249}{book}{
author={Fulton, William},
author={Harris, Joe},
title={Representation theory},
series={Graduate Texts in Mathematics},
volume={129},
note={A first course;
Readings in Mathematics},
publisher={Springer-Verlag, New York},
date={1991},
pages={xvi+551},
isbn={0-387-97527-6},
isbn={0-387-97495-4},
}
\bib{MR2460611}{book}{
author={Ganyushkin, Olexandr},
author={Mazorchuk, Volodymyr},
title={Classical finite transformation semigroups},
series={Algebra and Applications},
volume={9},
note={An introduction},
publisher={Springer-Verlag London, Ltd., London},
date={2009},
pages={xii+314},
isbn={978-1-84800-280-7},
}
\bib{MR2529864}{article}{
author={Ganyushkin, Olexandr},
author={Mazorchuk, Volodymyr},
author={Steinberg, Benjamin},
title={On the irreducible representations of a finite semigroup},
journal={Proc. Amer. Math. Soc.},
volume={137},
date={2009},
number={11},
pages={3585--3592},
issn={0002-9939},
}
\bib{MR1887083}{article}{
author={Grood, Cheryl},
title={A Specht module analog for the rook monoid},
journal={Electron. J. Combin.},
volume={9},
date={2002},
number={1},
pages={Research Paper 2, 10},
issn={1077-8926},
}
\bib{Grunbaum03}{book}{
author={Gr{\"u}nbaum, Branko},
title={Convex polytopes},
series={Graduate Texts in Mathematics},
volume={221},
edition={2},
note={Prepared and with a preface by Volker Kaibel, Victor Klee and
G\"unter M.\ Ziegler},
publisher={Springer-Verlag},
place={New York},
date={2003},
pages={xvi+468},
isbn={0-387-00424-6},
isbn={0-387-40409-0},
}
\bib{Howie95}{book}{
author={Howie, John M.},
title={Fundamentals of semigroup theory},
series={London Mathematical Society Monographs. New Series},
volume={12},
note={Oxford Science Publications},
publisher={The Clarendon Press, Oxford University Press, New York},
date={1995},
pages={x+351},
}
\bib{Humphreys90}{book}{
author={Humphreys, James E.},
title={Reflection groups and Coxeter groups},
series={Cambridge Studies in Advanced Mathematics},
volume={29},
publisher={Cambridge University Press, Cambridge},
date={1990},
pages={xii+204},
}
\bib{Humphreys75}{book}{
author={Humphreys, James E.},
title={Linear algebraic groups},
note={Graduate Texts in Mathematics, No. 21},
publisher={Springer-Verlag},
place={New York},
date={1975},
pages={xiv+247},
}
\bib{Lawson98}{book}{
author={Lawson, Mark V.},
title={Inverse semigroups},
note={The theory of partial symmetries},
publisher={World Scientific Publishing Co. Inc.},
place={River Edge, NJ},
date={1998},
pages={xiv+411},
isbn={981-02-3316-7},
}
\bib{MR0172953}{article}{
author={Munn, W. D.},
title={Matrix representations of inverse semigroups},
journal={Proc. London Math. Soc. (3)},
volume={14},
date={1964},
pages={165--181},
issn={0024-6115},
}
\bib{MR0153762}{article}{
author={Munn, W. D.},
title={A class of irreducible matrix representations of an arbitrary
inverse semigroup},
journal={Proc. Glasgow Math. Assoc.},
volume={5},
date={1961},
pages={41--48},
}
\bib{MR0133384}{article}{
author={Munn, W. D.},
title={Irreducible matrix representations of semigroups},
journal={Quart. J. Math. Oxford Ser. (2)},
volume={11},
date={1960},
pages={295--309},
issn={0033-5606},
}
\bib{MR0082050}{article}{
author={Munn, W. D.},
title={Matrix representations of semigroups},
journal={Proc. Cambrdige Philos. Soc.},
volume={53},
date={1957},
pages={5--12},
}
\bib{MR0081910}{article}{
author={Munn, W. D.},
title={The characters of the symmetric inverse semigroup},
journal={Proc. Cambridge Philos. Soc.},
volume={53},
date={1957},
pages={13--18},
}
\bib{MR0066355}{article}{
author={Munn, W. D.},
title={On semigroup algebras},
journal={Proc. Cambridge Philos. Soc.},
volume={51},
date={1955},
pages={1--15},
}
\bib{Oganesyan55}{article}{
author={Oganesyan, V. A.},
title={On the semisimplicity of a system algebra},
language={Russian, with Armenian summary},
journal={Akad. Nauk Armyan. SSR. Dokl.},
volume={21},
date={1955},
pages={145--147},
issn={0321-1339},
}
\bib{}{article}{
author={Ponizovskii, J. S.},
title={On matrix representations of semigroups (Russian)},
journal={Mat. Sb.},
volume={38},
date={1956},
pages={241--260},
issn={0037-1912},
}
\bib{MR1407463}{article}{
author={Putcha, Mohan S.},
title={Complex representations of finite monoids},
journal={Proc. London Math. Soc. (3)},
volume={73},
date={1996},
number={3},
pages={623--641},
issn={0024-6115},
}
\bib{Putcha88}{book}{
author={Putcha, Mohan S.},
title={Linear algebraic monoids},
series={London Mathematical Society Lecture Note Series},
volume={133},
publisher={Cambridge University Press},
place={Cambridge},
date={1988},
pages={x+171},
isbn={0-521-35809-4},
}
\bib{Renner05}{book}{
author={Renner, Lex E.},
title={Linear algebraic monoids},
series={Encyclopaedia of Mathematical Sciences},
volume={134},
note={;
Invariant Theory and Algebraic Transformation Groups, V},
publisher={Springer-Verlag},
place={Berlin},
date={2005},
pages={xii+246},
isbn={3-540-24241-4},
}
\bib{MR1142387}{article}{
author={Rhodes, John},
author={Zalcstein, Yechezkel},
title={Elementary representation and character theory of finite
semigroups and its application},
conference={
title={Monoids and semigroups with applications},
address={Berkeley, CA},
date={1989},
},
book={
publisher={World Sci. Publ., River Edge, NJ},
},
date={1991},
pages={334--367},
}
\bib{MR1824028}{book}{
author={Sagan, Bruce E.},
title={The symmetric group},
series={Graduate Texts in Mathematics},
volume={203},
edition={2},
note={Representations, combinatorial algorithms, and symmetric
functions},
publisher={Springer-Verlag, New York},
date={2001},
pages={xvi+238},
isbn={0-387-95067-2},
}
\bib{Solomon95}{article}{
author={Solomon, Louis},
title={An introduction to reductive monoids},
conference={
title={Semigroups, formal languages and groups},
address={York},
date={1993},
},
book={
series={NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.},
volume={466},
publisher={Kluwer Acad. Publ.},
place={Dordrecht},
},
date={1995},
pages={295--352},
}
\bib{MR3525092}{book}{
author={Steinberg, Benjamin},
title={Representation theory of finite monoids},
series={Universitext},
publisher={Springer, Cham},
date={2016},
pages={xxiv+317},
isbn={978-3-319-43930-3},
isbn={978-3-319-43932-7},
}
\bib{MR1984740}{book}{
author={Weintraub, Steven H.},
title={Representation theory of finite groups: algebra and arithmetic},
series={Graduate Studies in Mathematics},
volume={59},
publisher={American Mathematical Society, Providence, RI},
date={2003},
pages={x+212},
isbn={0-8218-3222-0},
}
\bib{MR0283104}{article}{
author={Zalcstein, Yechezkel},
title={Studies in the representation theory of finite semigroups},
journal={Trans. Amer. Math. Soc.},
volume={161},
date={1971},
pages={71--87},
issn={0002-9947},
}
\bib{MR1311028}{book}{
author={Ziegler, G\"{u}nter M.},
title={Lectures on polytopes},
series={Graduate Texts in Mathematics},
volume={152},
publisher={Springer-Verlag, New York},
date={1995},
pages={x+370},
isbn={0-387-94365-X},
review={\MR{1311028}},
doi={10.1007/978-1-4613-8431-1},
}
\end{biblist}
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,652 |
Q: Attiny85 Burn Bootloader Error [Device signature = 0x000000] [SOLVED] I had read in different forums about similar issues and double-check the connections and datasheet. But it's still not working for me. First of all, I will share my build and my configuration. Later the error.
The Connections
simulate this circuit – Schematic created using CircuitLab
The Configuration
I know that it's in Spanish, I apologize for that but it can also be read.
The Previous Steps
I ran without the capacitor the "ArduinoISP" example code added with the plugin: "ATTinyCore" (also I tried to reinstall it but no changes). Later when I load the settings mentioned in the Configuration part and click "Burn Bootloader" it fails...
The Error
I have no clue why this is happening. Maybe a clue could be that before burning the bootloader with these specs I miss-clicked and ran the burn bootloader with this plate:
I don't know if I broke the ATtiny85 doing that. The error:
avrdude: Yikes! Invalid device signature. Double check connections and try again, or use -F to override this check.
Error burning bootloader
My Research
Meanwhile, I asked in Discord's servers with no answer I surfed on forums and I found a youtube video with the same console name error. And suggest connecting Attiny85 Pin Nº1 to GND before the burning:
The Question
What I'm doing wrong? Is my Attiny85 dead?
Update
I will put the output verbose complete error:
avrdude: Version 6.3-20190619
Copyright (c) 2000-2005 Brian Dean, http://www.bdmicro.com/
Copyright (c) 2007-2014 Joerg Wunsch
System wide configuration file is "C:\Users\santa\AppData\Local\Arduino15\packages\arduino\tools\avrdude\6.3.0-arduino17/etc/avrdude.conf"
Using Port : COM3
Using Programmer : stk500v1
Overriding Baud Rate : 19200
AVR Part : ATtiny85
Chip Erase delay : 400000 us
PAGEL : P00
BS2 : P00
RESET disposition : possible i/o
RETRY pulse : SCK
serial program mode : yes
parallel program mode : yes
Timeout : 200
StabDelay : 100
CmdexeDelay : 25
SyncLoops : 32
ByteDelay : 0
PollIndex : 3
PollValue : 0x53
Memory Detail :
Block Poll Page Polled
Memory Type Mode Delay Size Indx Paged Size Size #Pages MinW MaxW ReadBack
----------- ---- ----- ----- ---- ------ ------ ---- ------ ----- ----- ---------
eeprom 65 12 4 0 no 512 4 0 4000 4500 0xff 0xff
flash 65 6 32 0 yes 8192 64 128 30000 30000 0xff 0xff
signature 0 0 0 0 no 3 0 0 0 0 0x00 0x00
lock 0 0 0 0 no 1 0 0 9000 9000 0x00 0x00
lfuse 0 0 0 0 no 1 0 0 9000 9000 0x00 0x00
hfuse 0 0 0 0 no 1 0 0 9000 9000 0x00 0x00
efuse 0 0 0 0 no 1 0 0 9000 9000 0x00 0x00
calibration 0 0 0 0 no 1 0 0 0 0 0x00 0x00
Programmer Type : STK500
Description : Atmel STK500 Version 1.x firmware
Hardware Version: 2
Firmware Version: 1.18
Topcard : Unknown
Vtarget : 0.0 V
Varef : 0.0 V
Oscillator : Off
SCK period : 0.1 us
avrdude: AVR device initialized and ready to accept instructions
Reading | ################################################## | 100% 0.03s
avrdude: Device signature = 0x000000 (retrying)
Reading | ################################################## | 100% 0.02s
avrdude: Device signature = 0x000000 (retrying)
An error occurred while uploading the sketch
Reading | ################################################## | 100% 0.03s
avrdude: Device signature = 0x000000
avrdude: Yikes! Invalid device signature.
Double check connections and try again, or use -F to override
this check.
avrdude done. Thank you.
I will hightlight some stuff that could give a clue:
avrdude: Device signature = 0x000000
Also, I saw:
Vtarget : 0.0 V
So in theory no voltage in the Attiny?
Error Solved!
Thanks all for helping with dm and collaborating. It was just a dumb error haha. In fact with Arduino Mega the attiny setup are different. Because intead of using
10->reset| 11->mosi | 12->miso | 13->Sck
they changed to:
10->reset| 51->mosi | 50->miso | 52->Sck
I made a fast draw in ASCII for how to plug in the Attiny85 using an Arduino Mega 2560:
----Mistake: referential**-----
A: [Solved]
As I added in the thread, I could solve the problem. Thanks so much for helping.
Solution:
In Arduino Mega the ATTiny setup uses different pins. Because intead of using:
10->reset| 11->mosi | 12->miso | 13->Sck
it uses:
10->reset| 51->mosi | 50->miso | 52->Sck
More info here, I highly recommend visiting this website before buying components.
I made a simple draft in ASCII for being more intuitive:
----Mistake: referential**-----
A: If you've programmed ATTinyCore with Micronucleus bootloader, it disables RESET via fuses and you no longer can use ISP to program it. From this description, part "Disabling reset":
Disabling Reset
Because a board running the Micronucleus bootloader
can be reprogrammed without the use of the RESET pin, it is practical
to use them with reset configured to act as an I/O pin. This is,
obviously, of particular utility on the ATtiny85, where available pins
are at a premium, but may be used on any part (except the ATtiny841,
in the current version of this core). Because this requires changing
the fuses, it can only be enabled with an ISP programmer. Once reset
as been disabled, it can no longer be programmed via ISP. Only HVSP or
parallel programming (depending on the part - each part supports one
or the other, never both), wherein 12v is applied to the reset pin
under specific conditions, can be used to unset this fuse or to
unbrick a part where reset is disabled and the bootloader is no longer
functioning. Note that the bootloader can still be upgraded over USB -
including to a version that only runs upon external reset!
It is designed to use with USB bootloader called micronucleus once burnt. You can assemble a variant of Digispark board and use it via USB now:
Or you can assemble a tool called Fusebit Doctor. Which can reset fuses to default via HVPP/HVSP programming methods.
Ignore VTarget message, ArduinoISP simply doesn't supports reading target voltage so it always shows 0V.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,944 |
November 29, 2018 Larry Noodles Comments 2 comments
Rabbi Daniel Greer's long time friend and personal printer was sentenced today in Federal Court. His guideline numbers were 10-15 months. Because he ratted out his nephew Ira, who went to jail for 6 months, the US Attorney argued that Uncle Lou shouldn't get the guidelines numbers because of his "substantial cooperation" with the Feds. Ira is still sitting in Otisville Federal Prison, he won't be out until April of 2019.
Uncle Lou was represented by legendary New Haven attorney Hugh Keefe. Hugh has the luck of the Irish. I have seen Hugh get all kinds of reprobates out of a jam. Uncle Lou must have paid at least $50K in legal fees to Attorney Keefe. Attorneys get to charge much higher fees in Federal criminal cases. If you get charged with a Federal felony, no matter how small, the Feds will tell you that you are facing up to 30 years in jail. The only way to get that kind of jail time in State Court is if you murder at least ten people. Almost every Federal criminal statute has sentencing limits that are excessive. No President, or Congressman, wants to be seen as lowering these limits, lest they appear soft on crime, and incur the wrath of law enforcement employees and voters. Criminal defense attorneys are thus able to feed off the fear of defendants facing decades in the slammer. Defendants will beg, borrow and steal in order to pay their lawyer.
Lou Goatberg must have told Hugh Keefe that he didn't want to see me at the sentencing. Someone had the time for the sentencing changed at the last minute. Nobody notified Larry Noodles that the time was changed to 2 PM from 3 PM. I arrived after the sentencing hearing was over, but I still got to witness some drama. I watched Lou Goatberg and his supporters leave the courthouse. They were all gathered outside the courthouse on the street in front of the New Haven Green celebrating. Lou proceeded to give hugs to all his fans. I didn't see Senator Leiberman, who wrote letters in support of Lou. I don't know if he attended the hearing but I will find out.
As I was outside I watched Lou's friend, whom I recognized as "Joan," push a very heavy set African American woman in a walker on the sidewalk towards the courthouse. The Black woman was smiling and sitting in the little tiny resting seat attached to the walker. Joan was pushing this heavy woman very quickly on the little wobbly walker, she was practically running down the sidewalk. Joan shouted at pedestrians to get out of the way. There were many people around because they were gathering on the New Haven Green for the Christmas tree lighting ceremony. As Joan quickly pushed this woman in front of the courthouse she hit a crack in the sidewalk, which caused the heavy set woman to go flying off the walker and land on the ground, with Joan tumbling over her. A crowd of people gathered and tried to help them get up. Joan got up but the African American woman didn't move for a while. Neither one of them looked injured. No ambulance arrived. By the time they got up from the ground Lou and his gaggle of fans began descending on the sidewalk. Hugh Keefe and his young blond associate slipped away while Lou held court for his fans in front of the Christmas carolers on the Green. One of Lou's employees wrote in his character letter that Lou was the only Orthodox Jew who sang Christmas carols in the Goat Copy office.
Joan wrote in her character letter the following words about Lou: "He is deeply religious, attuned to the spirit, not just the letter, of the law. When he purchased a motel, he realized that the life style and clientele activities were inconsistent with his values. Although he had a family and children to educate, he sold the motel. It was prosperous; he sold it anyway."
Lou's in laws owned the motel and gave it to Lou and his wife after they got married. Lou must have been renting the motel rooms by the hour. I wonder if Lou rented rooms to chomos and diddlers (child molesters), like the owners of the Branford Motel. Rabbi Daniel Greer "the Goat" used to check into the Branford Motel with teenage boys Avi Hack and Eli Mirlis. This creepy bearded Goat wore a baseball cap and checked in as "Mr. Green." The Goat had a teacher for many years at his elementary school whose name was Mr. Green. Was the Goat trying to pin his crimes on Mr. Green in case he ever got caught? The owners of the Branford Motel must have seen the Goat check in at times with Avi Hack and at other times check in with Eli Mirlis. A creepy bearded old man checking in with a 15 year old boy, without anyone from the motel saying a word to the police. Outrageous.
Joan wrote in her character letter that Lou sold his sleezy motel in order to go into an honest business, ie., printing for child molester Daniel Greer, and committing tax fraud and tax evasion for years with his nephew Ira. Lou's loyal supporters would be the first to condemn drug addicts and prostitutes hanging around the New Haven Green across the street from the Federal Courthouse. Lock them all up. But when it comes to Lou Goatberg, he is no criminal, he is a tzaddik, a saint.
Even Senator Joe Leiberman came to bat for Lou. Has Joe Leiberman ever wrote a letter in support of any of his constituents who didn't pray with Joe in Beaver Hill? Of course not. As a criminal defense attorney I don't know how many complete nobodies I watched get sentenced. Longer sentences always make the prosecutors look good. Another notch on their belt. The common people with no connections get longer sentences than those with the high priced lawyers or friends in politics. A no name lawyer, like myself, standing next to a no name defendant, doesn't have a chance in front of a judge who in many cases is a former prosecutor. The criminal justice system is rigged against minorities and the poor, and does little to solve the problem of crime, which is rooted in homelessness, mental illness, drug addiction and unemployment. The only guy who is trying to end the madness is former public defender and recently elected District Attorney of Philadelphia Larry Krasner. Larry revamped the entire D.A.'s office by firing 30 prosecutors and hiring in experts in homelessness, drug addiction and social work, drawing the ire of the police union. You read about his rational, not radical, approach by clicking this LINK.
You can read Lou's sentence imposed by the Federal Court by clicking this LINK
Thanks to all those who have donated
2 thoughts on "Goatberg Gets 1 Year Probation"
SNITCHES GET STITCHES……IN THIS CASE SNITCHES GETS KISSES AND HUGS…..AND SUPPORT FROM THE JEWISH COMMUNITY…
silly goyim says:
and La Kosher Nostra just keeps on winning. At least the goy Hugh got to wet his beak with that long, strong, yiddish doe.
Happy extra oil day! For such an old religion, that sure is a modern holiday. lmgao | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,803 |
{"url":"https:\/\/nn.labml.ai\/normalization\/deep_norm\/index.html","text":"# DeepNorm\n\nThis is a PyTorch implementation of the DeepNorm from the paper DeepNet: Scaling Transformers to 1,000 Layers.\n\nThe paper proposes a method to stabilize extremely deep transformers through a new normalizing function to replace LayerNorm and a weight initialization scheme. This combines the performance of Post-LayerNorm and the stability of Pre-LayerNorm. Transformers with DeepNorms are supposed to be stable even without a learning rate warm-up.\n\nThe paper first shows that the changes to layer outputs (for the same input) change gradually during stable training; when unstable it changes rapidly during the initial training steps. This happens with initializing weights to small values, and learning rate warm-ups where the training is stable. They use the idea of keeping the changes to layer outputs small to derive the new normalization and weight initialization mechanism.\n\n## Weight Initializations\n\nUsually, the weights are initialized with Xavier or Kaiming initializations. This paper scales (sets the gain) the weights by a constant depending on the size of the transformer.\n\nDeepNorm suggests scaling the weights of the two linear transforms in the Feed-Forward Network, the value projection transform, and the output projection transform of the attention layer. Weights of these transforms are scaled by (has a gain equal to) .\n\nThe scaling is implemented in the\n\n## Normalization Function\n\nwhere is a constant that depends on the depth of the transformer, is Layer Normalization, and is the function of the -th transformer sub-layer (FFN or attention).\n\nThis function is used to replace Post-LayerNorm.\n\n## and constants\n\nWhere is the number of layers in the encoder and is the number of layers in the decoder.\n\nRefer to the paper for derivation.\n\nHere is an experiment implementation that uses DeepNorm.\n\n74from typing import Union, List\n75\n76import torch\n77from torch import nn, Size\n78\n79from labml_nn.normalization.layer_norm import LayerNorm\n81from labml_nn.transformers.feed_forward import FeedForward\n82from labml_nn.transformers.utils import subsequent_mask\n\n## DeepNorm Normalization\n\n85class DeepNorm(nn.Module):\n\u2022 alpha is\n\u2022 normalized_shape is the shape for LayerNorm\n\u2022 eps is for LayerNorm\n\u2022 elementwise_affine is a flag indicating whether to do an elementwise transformation in LayerNorm\n92 def __init__(self, alpha: float, normalized_shape: Union[int, List[int], Size], *,\n93 eps: float = 1e-5,\n94 elementwise_affine: bool = True):\n101 super().__init__()\n102\n103 self.alpha = alpha\n\nInitialize\n\n105 self.layer_norm = LayerNorm(normalized_shape, eps=eps, elementwise_affine=elementwise_affine)\n\u2022 x is the output from the previous layer\n\u2022 gx is the output of the current sub-layer\n107 def forward(self, x: torch.Tensor, gx: torch.Tensor):\n113 return x + self.alpha * gx\n\n## Transformer Decoder Layer with DeepNorm\n\nThis implements a transformer decoder layer with DeepNorm. Encoder layers will have a similar form.\n\n116class DeepNormTransformerLayer(nn.Module):\n\u2022 d_model is the token embedding size\n\u2022 self_attn is the self attention module\n\u2022 feed_forward is the feed forward module\n\u2022 deep_norm_alpha is coefficient in DeepNorm\n\u2022 deep_norm_beta is constant for scaling weights initialization\n123 def __init__(self, *,\n124 d_model: int,\n126 feed_forward: FeedForward,\n127 deep_norm_alpha: float,\n128 deep_norm_beta: float,\n129 ):\n137 super().__init__()\n138\n139 self.self_attn = self_attn\n140 self.feed_forward = feed_forward\n\nDeepNorms after attention and feed forward network\n\n142 self.self_attn_norm = DeepNorm(deep_norm_alpha, [d_model])\n143 self.feed_forward_norm = DeepNorm(deep_norm_alpha, [d_model])\n\nScale weights after initialization\n\n146 with torch.no_grad():\n\nFeed forward network linear transformations\n\n148 feed_forward.layer1.weight *= deep_norm_beta\n149 feed_forward.layer2.weight *= deep_norm_beta\n\nAttention value projection\n\n152 self_attn.value.linear.weight *= deep_norm_beta\n\nAttention output project\n\n154 self_attn.output.weight *= deep_norm_beta\n\nThe mask will be initialized on the first call\n\n157 self.mask = None\n\u2022 x are the embeddings of shape [seq_len, batch_size, d_model]\n159 def forward(self, x: torch.Tensor):\n\n164 if self.mask is None or self.mask.size(0) != len(x):\n\n166 self.mask = subsequent_mask(len(x)).to(x.device)\n169 x = self.self_attn_norm(x, self.self_attn(query=x, key=x, value=x, mask=self.mask))\n171 x = self.feed_forward_norm(x, self.feed_forward(x))\n174 return x","date":"2022-08-15 12:14:49","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\": 0.3774610757827759, \"perplexity\": 14122.804423997264}, \"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\/1659882572174.8\/warc\/CC-MAIN-20220815115129-20220815145129-00192.warc.gz\"}"} | null | null |
Lunar New Year Fireworks Display in Hong Kong is an annual event to celebrate the Chinese New Year in Hong Kong. It is held on The Second Day of Lunar New Year above the sky of Victoria Harbour in the evening.
History
In 1982, to celebrate its 150th anniversary, Jardine Matheson sponsored the first fireworks display event. The event received good public response. Since then, it became an annual event of Chinese New Year as a greeting to Hong Kong citizens.
Other events
Fireworks shows similar to this event are also held in Victoria Harbour on the common calendar's New Year's Eve on December 31 and the anniversary of Hong Kong's handover from the United Kingdom to China that happened on June 30, 1997.
Festivals in Hong Kong
1982 establishments in Hong Kong
Recurring events established in 1982
Annual events in Hong Kong
Fireworks events in Asia
Festivals established in 1982 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,137 |
{"url":"http:\/\/mathoverflow.net\/feeds\/user\/23358","text":"User bidyut sanki - MathOverflow most recent 30 from http:\/\/mathoverflow.net 2013-05-20T02:24:35Z http:\/\/mathoverflow.net\/feeds\/user\/23358 http:\/\/www.creativecommons.org\/licenses\/by-nc\/2.5\/rdf http:\/\/mathoverflow.net\/questions\/126352\/injectivity-radius-of-hyperbolic-surface injectivity radius of hyperbolic surface Bidyut Sanki 2013-04-03T05:36:40Z 2013-04-15T13:56:06Z <p>Given a positive real number $l$. Does there exist a closed hyperbolic surface $X$ so that injectivity radius not less than $l$?<\/p> http:\/\/mathoverflow.net\/questions\/124396\/finite-index-subgroup-of-a-fuchsian-group finite index subgroup of a fuchsian group Bidyut Sanki 2013-03-13T09:46:40Z 2013-03-16T14:28:25Z <p>Given G, a fuchsian group and a finite sub set A of G. Does there exist a finite index subgroup H in G such that inter section of A with H is empty? <\/p> http:\/\/mathoverflow.net\/questions\/118431\/representation-of-teichmuller-space-teichmuller-space representation of teichmuller space Teichmuller space Bidyut Sanki 2013-01-09T09:42:43Z 2013-01-09T14:57:49Z <p>I want to study representation of teichmuller space of surface of genus g in psl(2,R). can you suggest any good references.<\/p> http:\/\/mathoverflow.net\/questions\/118429\/fundamental-group-of-a-compact-manifold fundamental group of a compact manifold Bidyut Sanki 2013-01-09T09:36:49Z 2013-01-09T10:18:52Z <p>why fundamental group of of compact manifold is finitely presented<\/p> http:\/\/mathoverflow.net\/questions\/95724\/uniqueness-of-distance-realizing-geodesic-in-hyperbolic-surface Uniqueness of distance realizing geodesic in hyperbolic surface. Bidyut Sanki 2012-05-02T05:22:59Z 2012-05-02T06:47:32Z <blockquote> <p><strong>Possible Duplicate:<\/strong><br> <a href=\"http:\/\/mathoverflow.net\/questions\/95640\/hyperbolic-surfaces\" rel=\"nofollow\">Hyperbolic surfaces<\/a> <\/p> <\/blockquote> <p>Given a hyperbolic surface S with geodesic boundary. Let a and b be two distinct simple closed geodesic boundaries. Does there exist a unique distance realizing geodesic in S? (1) for S is a pair of pants. (2) S is any hyperbolic surface with boundary. <\/p> http:\/\/mathoverflow.net\/questions\/118429\/fundamental-group-of-a-compact-manifold\/118435#118435 Comment by Bidyut Sanki Bidyut Sanki 2013-01-09T10:29:13Z 2013-01-09T10:29:13Z Thank you very much http:\/\/mathoverflow.net\/questions\/95829\/distance-of-a-point-from-a-geodesic-on-hyperbolic-surface Comment by Bidyut Sanki Bidyut Sanki 2012-05-03T18:43:25Z 2012-05-03T18:43:25Z @ Sam Nead, The motivation is the following: It is wellknown that given a geodesic $\\gamma$ a point $p$ in hyperbolic plane then there is a unique geodesic from p to $\\gamma$ meeting perpendicularly and realizes the distance from p to $\\gamma$. So if we take hyperbolic surface instead of hyperbolic plane then what will happen. @ Anton Petrunin Please provede a proof or reference for your answer. Thanks a lot http:\/\/mathoverflow.net\/questions\/95724\/uniqueness-of-distance-realizing-geodesic-in-hyperbolic-surface\/95728#95728 Comment by Bidyut Sanki Bidyut Sanki 2012-05-02T08:26:32Z 2012-05-02T08:26:32Z well, I have got an example of hyperbolic surface with boundary where more than one (at least two) distance realizing geodesics between two distinct geodesic boundaries will exist. I have a further question: Suppose p and q are two distance realizing geodesics between the boundary geodesics. Is it true that p and q are always disjoint? http:\/\/mathoverflow.net\/questions\/95640\/distance-realizing-geodesics-in-hyperbolic-surfaces Comment by Bidyut Sanki Bidyut Sanki 2012-05-02T05:26:14Z 2012-05-02T05:26:14Z @ Yemon choi.. Sure","date":"2013-05-20 02:24:39","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\": 0.8463370203971863, \"perplexity\": 1693.7985489851037}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"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-2013-20\/segments\/1368698207393\/warc\/CC-MAIN-20130516095647-00092-ip-10-60-113-184.ec2.internal.warc.gz\"}"} | null | null |
The Odisha government has appointed 154 junior lecturers for this.
BHUBANESWAR: Odisha government has decided to upgrade an additional 21 high schools to higher secondary schools for SC and ST students to provide science education to them, official sources said. ST & SC Development, Minorities & Backward Classes Welfare Minister Ramesh Chandra Majhi said the new upgraded higher secondary schools will come up in Gajapati, Kandhamal, Sundergarh, Nabarangpur, Koraput, Rayagada, Malkangiri, Kalahandi, Mayurbhanj and Balangir districts.
These will be science stream higher secondary schools, he said.
"For the current academic session 2018-19, the government has decided to upgrade 21 more high schools to higher secondary schools," Mr Majhi said. Classes in those schools will commence from the current academic year for which the government has appointed 154 junior lecturers.
The state government had earlier upgraded 26 High Schools of Mayurbhanj, Gajapati, Kalahandi, Sambalpur, Keonjhar, Sundargarh, Rayagada, Malkangiri, Nabarangpur districts into higher secondary schools in the science stream till 2017-18.
These schools are run by the SC/ST development department, officials said. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,133 |
roundtheworldflights.com is a tailor-made tour operator, offering luxury holidays and every kind of travel experience imaginable - from tailor-made journeys, round the world trips, luxury beach holidays or private tours.
You can custom design your own eBrochure by selecting only the pages you want to see. Just click on the right to take you through to browse our eBrochures online, and your chosen pages will then be emailed to you via our eBrochure service. There's no waiting. Almost all brochure orders are built and despatched from our servers in less than 15 seconds. And it's free.
roundtheworldflights.com Contact us Hello. Follow us.. No surcharges on UK Debit Cards! | {
"redpajama_set_name": "RedPajamaC4"
} | 5,875 |
\section{Experiments}\label{experiments}
In this section, we conduct extensive experiments to answer the following questions:
\begin{itemize}
\item \textbf{(Q1)} How does our proposed CIN perform in high-order feature interactions learning?
\item \textbf{(Q2)} Is it necessary to combine explicit and implicit high-order feature interactions for recommender systems?
\item \textbf{(Q3)} How does the settings of networks influence the performance of xDeepFM?
\end{itemize}
We will answer these questions after presenting some fundamental experimental settings.
\subsection{Experiment Setup}
\subsubsection{Datasets.} We evaluate our proposed models on the following three datasets:\\
\indent \textbf{1. Criteo Dataset}. It is a famous industry benchmarking dataset for developing models predicting ad click-through rate, and is publicly accessible\footnote{http://labs.criteo.com/2014/02/kaggle-display-advertising-challenge-dataset/}. Given a user and the page he is visiting, the goal is to predict the probability that he will clik on a given ad. \\
\indent \textbf{2. Dianping Dataset}. \textsl{Dianping.com} is the largest consumer review site in China. It provides diverse functions such as reviews, check-ins, and shops' meta information (including geographical messages and shop attributes). We collect 6 months' users check-in activities for restaurant recommendation experiments. Given a user's profile, a restaurant's attributes and the user's last three visited POIs (point of interest), we want to predict the probability that he will visit the restaurant. For each restaurant in a user's check-in instance, we sample four restaurants which are within 3 kilometers as negative instances by POI popularity.\\
\indent \textbf{3. Bing News Dataset}. Bing News\footnote{https://www.bing.com/news} is part of Microsoft's Bing search engine. In order to evaluate the performance of our model in a real commercial dataset, we collect five consecutive days' impression logs on news reading service. We use the first three days' data for training and validation, and the next two days for testing. \\
\indent For the Criteo dataset and the Dianping dataset, we randomly split instances by 8:1:1 for training , validation and test. The characteristics of the three datasets are summarized in Table \ref{tab:datasets}.
\begin{table}[ht]
\centering
\caption{Statistics of the evaluation datasets. M indicates million and K indicates thousand. }
\begin{tabular}{|c|c|c|c|} \hline
Datasest & \#instances & \#fields &\#features (sparse) \\ \hline
Criteo & 45M & 39 & 2.3M \\ \hline
Dianping & 1.2M & 18 & 230K \\ \hline
Bing News & 5M & 45 & 17K \\ \hline
\end{tabular}
\label{tab:datasets}
\end{table}
\subsubsection{Evaluation Metrics.} We use two metrics for model evaluation: \textbf{AUC} (Area Under the ROC curve) and \textbf{Logloss} (cross entropy). These two metrics evaluate the performance from two different angels: AUC measures the probability that a positive instance will be ranked higher than a randomly chosen negative one. It only takes into account the order of predicted instances and is insensitive to class imbalance problem. Logloss, in contrast, measures the distance between the predicted score and the true label for each instance. Sometimes we rely more on Logloss because we need to use the predicted probability to estimate the benefit of a ranking strategy (which is usually adjusted as CTR $\times$ bid).
\subsubsection{Baselines.} We compare our xDeepFM with LR(logistic regression), FM, DNN (plain deep neural network), PNN (choose the better one from iPNN and oPNN) \cite{qu2016product}, Wide \& Deep \cite{cheng2016wide}, DCN (Deep \& Cross Network) \cite{wang2017deep} and DeepFM \cite{guo2017deepfm}. As introduced and discussed in Section \ref{preliminaries}, these models are highly related to our xDeepFM and some of them are state-of-the-art models for recommender systems. Note that the focus of this paper is to learn feature interactions automatically, so we do not include any hand-crafted cross features.
\subsubsection{Reproducibility} We implement our method using Tensorflow\footnote{https://www.tensorflow.org/}. Hyper-parameters of each model are tuned by grid-searching on the validation set, and the best settings for each model will be shown in corresponding sections. Learning rate is set to \textsl{0.001}. For optimization method, we use the Adam \cite{kingma2014adam} with a mini-batch size of 4096. We use a L2 regularization with $\lambda=0.0001$ for DNN, DCN, Wide\&Deep, DeepFM and xDeepFM, and use dropout 0.5 for PNN. The default setting for number of neurons per layer is: (1) 400 for DNN layers; (2) 200 for CIN layers on Criteo dataset, and 100 for CIN layers on Dianping and Bing News datasets. Since we focus on neural networks structures in this paper, we make the dimension of field embedding for all models be a fixed value of 10. We conduct experiments of different settings in parallel with 5 \textsl{Tesla K80 GPUs}.
The source code is available at \textsl{\url{https://github.com/Leavingseason/xDeepFM}}.
\begin{table}[ht]
\centering
\caption{Performance of individual models on the Criteo, Dianping, and Bing News datasets. Column \textsl{Depth} indicates the best network depth for each model. }
\begin{tabular}{c|cc|c} \hline\hline
Model name & AUC & Logloss & Depth \\ \hline
\multicolumn{4}{c}{Criteo}\\ \hline
FM & 0.7900 & 0.4592 & - \\ \hline
DNN & 0.7993 & 0.4491 & 2 \\ \hline
CrossNet & 0.7961 & 0.4508 & 3 \\ \hline
CIN & \textbf{0.8012} & 0.4493 & 3 \\ \hline
\multicolumn{4}{c}{Dianping}\\ \hline
FM & 0.8165 & 0.3558 & - \\ \hline
DNN & 0.8318 & 0.3382 & 3 \\ \hline
CrossNet & 0.8283 & 0.3404 & 2 \\ \hline
CIN & \textbf{0.8576} & \textbf{0.3225} & 2 \\ \hline
\multicolumn{4}{c}{Bing News}\\ \hline
FM & 0.8223 & 0.2779 & - \\ \hline
DNN & 0.8366 & 0.273 & 2 \\ \hline
CrossNet & 0.8304 & 0.2765 & 6 \\ \hline
CIN & \textbf{0.8377} & \textbf{0.2662} & 5 \\ \hline \hline
\end{tabular}
\label{tab:cin}
\end{table}
\begin{table*}[th]
\centering
\caption{Overall performance of different models on Criteo, Dianping and Bing News datasets. The column \textsl{Depth} presents the best setting for network depth with a format of (cross layers, DNN layers).}
{\setlength{\tabcolsep}{1em}{\renewcommand{\arraystretch}{1.1}
\begin{tabular}{c|cc|c||cc|c||cc|c} \hline\hline
& \multicolumn{3}{c||}{Criteo} & \multicolumn{3}{c||}{Dianping} & \multicolumn{3}{c}{Bing News} \\ \hline
Model name & AUC & Logloss & Depth& AUC & Logloss & Depth & AUC & Logloss & Depth \\ \hline
LR & 0.7577 & 0.4854 & -,- & 0.8018 & 0.3608 & -,- & 0.7988 & 0.2950 & -,- \\ \hline
FM & 0.7900 & 0.4592 & -,- & 0.8165 & 0.3558 & -,- & 0.8223 & 0.2779 & -,- \\ \hline
DNN & 0.7993 & 0.4491 & -,2 & 0.8318 & 0.3382 & -,3 & 0.8366 & 0.2730 & -,2 \\ \hline
DCN & 0.8026 & 0.4467 & 2,2 & 0.8391 & 0.3379 & 4,3& 0.8379 & 0.2677 & 2,2 \\ \hline
Wide\&Deep & 0.8000 & 0.4490 & -,3& 0.8361 & 0.3364 & -,2 & 0.8377 & 0.2668 & -,2 \\ \hline
PNN & 0.8038 & 0.4927 & -,2 & 0.8445 & 0.3424 & -,3& 0.8321 & 0.2775 & -,3\\ \hline
DeepFM & 0.8025 & 0.4468 & -,2& 0.8481 & 0.3333 & -,2 & 0.8376 & 0.2671 & -,3 \\ \hline
xDeepFM & \textbf{0.8052} & \textbf{0.4418} & 3,2& \textbf{0.8639} & \textbf{0.3156} & 3,3 & \textbf{0.8400} & \textbf{0.2649} & 3,2 \\ \hline \hline
\end{tabular}
}}
\label{tab:overallperformance}
\end{table*}
\subsection{Performance Comparison among Individual Neural Components (Q1)}
We want to know how CIN performs individually. Note that FM measures 2-order feature interactions explicitly, DNN model high-order feature interactions implicitly, CrossNet tries to model high-order feature interactions with a small number of parameters (which is proven not effective in Section \ref{sec:explicit}), and CIN models high-order feature interactions explicitly. There is no theoretic guarantee of the superiority of one individual model over the others, due to that it really depends on the dataset. For example, if the practical dataset does not require high-order feature interactions, FM may be the best individual model. Thus we do not have any expectation for which model will perform the best in this experiment.
\indent Table \ref{tab:cin} shows the results of individual models on the three practical datasets. Surprisingly, our CIN outperform the other models consistently. On one hand, the results indicate that for practical datasets, higher-order interactions over sparse features are necessary, and this can be verified through the fact that DNN, CrossNet and CIN outperform FM significantly on all the three datasets. On the other hand, CIN is the best individual model, which demonstrates the effectiveness of CIN on modeling explicit high-order feature interactions. Note that a $k$-layer CIN can model $k$-degree feature interactions. It is also interesting to see that it take 5 layers for CIN to yield the best result ON the Bing News dataset.
\subsection{Performance of Integrated Models (Q2)}
xDeepFM integrates CIN and DNN into an end-to-end model. While CIN and DNN covers two distinct properties in learning feature interactions, we are interested to know whether it is indeed necessary and effective to combine them together for jointly explicit and implicit learning. Here we compare several strong baselines which are not limited to individual models, and the results are shown in Table \ref{tab:overallperformance}. We observe that LR is far worse than all the rest models, which demonstrates that factorization-based models are essential for measuring sparse features. Wide\&Deep, DCN, DeepFM and xDeepFM are significantly better than DNN, which directly reflects that, despite their simplicity, incorporating hybrid components are important for boosting the accuracy of predictive systems. Our proposed xDeepFM achieves the best performance on all datasets, which demonstrates that combining explicit and implicit high-order feature interaction is necessary, and xDeepFM is effective in learning this class of combination. Another interesting observation is that, all the neural-based models do not require a very deep network structure for the best performance. Typical settings for the depth hyper-parameter are 2 and 3, and the best depth setting for xDeepFM is 3, which indicates that the interactions we learned are at most 4-order.
\subsection{Hyper-Parameter Study (Q3)}
We study the impact of hyper-parameters on xDeepFM in this section, including (1) the number of hidden layers; (2) the number of neurons per layer; and (3) activation functions. We conduct experiments via holding the best settings for the DNN part while varying the settings for the CIN part.
\begin{figure*}[htbp]
\centering
\begin{subfigure}{.32\textwidth}
\centering
\includegraphics[width=0.85\textwidth,height=.5\textwidth]{materials/auc_depth_network.pdf}
\caption{Number of layers.}
\label{fig:auc_depth}
\end{subfigure} \hfill
\begin{subfigure}{.32\textwidth}
\centering
\includegraphics[width=0.85\textwidth,height=.5\textwidth]{materials/auc_neworksize.pdf}
\caption{Number of neurons per layer.}
\label{fig:auc_size}
\end{subfigure} \hfill
\begin{subfigure}{.32\textwidth}
\centering
\includegraphics[width=0.85\textwidth,height=.5\textwidth]{materials/auc_activation.pdf}
\caption{Activation functions}
\label{fig:auc_activation}
\end{subfigure}
\caption{Impact of network hyper-parameters on AUC performance.}
\label{fig:auc_hyperparameter}
\end{figure*}
\begin{figure*}[htbp]
\centering
\begin{subfigure}{.32\textwidth}
\centering
\includegraphics[width=0.85\textwidth,height=.5\textwidth]{materials/logloss_depth_network.pdf}
\caption{Number of layers.}
\label{fig:logloss_depth}
\end{subfigure} \hfill
\begin{subfigure}{.32\textwidth}
\centering
\includegraphics[width=0.85\textwidth,height=.5\textwidth]{materials/logloss_networksize.pdf}
\caption{Number of neurons per layer.}
\label{fig:logloss_size}
\end{subfigure} \hfill
\begin{subfigure}{.32\textwidth}
\centering
\includegraphics[width=0.85\textwidth,height=.5\textwidth]{materials/logloss_activation.pdf}
\caption{Activation functions}
\label{fig:logloss_activation}
\end{subfigure}
\caption{Impact of network hyper-parameters on Logloss performance.}
\label{fig:logloss_hyperparameter}
\end{figure*}
\\\indent\textbf{Depth of Network}. Figure \ref{fig:auc_depth} and \ref{fig:logloss_depth} demonstrate the impact of number of hidden layers. We can observe that the performance of xDeepFM increases with the depth of network at the beginning. However, model performance degrades when the depth of network is set greater than 3. It is caused by overfitting evidenced by that we notice that the loss of training data still keeps decreasing when we add more hidden layers.
\\\indent\textbf{Number of Neurons per Layer}. Adding the number of neurons per layer indicates increasing the number of feature maps in CIN. As shown in Figure \ref{fig:auc_size} and \ref{fig:logloss_size}, model performance on Bing News dataset increases steadily when we increase the number of neurons from $20$ to $200$, while on Dianping dataset, $100$ is a more suitable setting for the number of neurons per layer. In this experiment we fix the depth of network at 3.
\\\indent\textbf{Activation Function}. Note that we exploit the identity as activation function on neurons of CIN, as shown in Eq. \ref{eq:xk}. A common practice in deep learning literature is to employ non-linear activation functions on hidden neurons. We thus compare the results of different activation functions on CIN (for neurons in DNN, we keep the activation function with \textsl{relu}). As shown in Figure \ref{fig:auc_activation} and \ref{fig:logloss_activation}, identify function is indeed the most suitable one for neurons in CIN.
\section{introduction} \label{introduction}
Features play a central role in the success of many predictive systems. Because using raw features can rarely lead to optimal results, data scientists usually spend a lot of work on the transformation of raw features in order to generate best predictive systems \cite{he2014practical,lian2017restaurant} or to win data mining games \cite{liu2016repeat,Lian:2017:PLJ:3124791.3124794,lian2016cross}. One major type of feature transformation is the cross-product transformation over categorical features \cite{cheng2016wide}. These features are called \textsl{cross features} or \textsl{multi-way features}, they measure the interactions of multiple raw features. For instance, a 3-way feature {\fontfamily{qcr}\selectfont AND(user\_organization=msra, item\_category=deeplearning, time=monday)} has value 1 if the user works at Microsoft Research Asia and is shown a technical article about deep learning on a Monday.\\
\indent There are three major downsides for traditional cross feature engineering. First, obtaining high-quality features comes with a high cost. Because right features are usually task-specific, data scientists need spend a lot of time exploring the potential patterns from the product data before they become domain experts and extract meaningful cross features. Second, in large-scale predictive systems such as web-scale recommender systems, the huge number of raw features makes it infeasible to extract all cross features manually. Third, hand-crafted cross features do not generalize to unseen interactions in the training data. Therefore, learning to interact features without manual engineering is a meaningful task. \\
\indent Factorization Machines (FM) \cite{rendle2010factorization} embed each feature $i$ to a latent factor vector $\mathbf{v}_i = [v_{i1}, v_{i2}, ..., v_{iD}]$, and pairwise feature interactions are modeled as the inner product of latent vectors: $f^{(2)}(i,j)=\langle\mathbf{v}_i, \mathbf{v}_j\rangle x_ix_j$. In this paper we use the term \textsl{bit} to denote a element (such as $v_{i1}$) in latent vectors. The classical FM can be extended to arbitrary higher-order feature interactions \cite{blondel2016higher}, but one major downside is that, \cite{blondel2016higher} proposes to model all feature interactions, including both useful and useless combinations. As revealed in \cite{DBLP:conf/ijcai/XiaoY0ZWC17}, the interactions with useless features may introduce noises and degrade the performance. In recent years, deep neural networks (DNNs) have become successful in computer vision, speech recognition, and natural language processing with their great power of feature representation learning. It is promising to exploit DNNs to learn sophisticated and selective feature interactions. \cite{zhang2016deep} proposes a Factorisation-machine supported Neural Network (FNN) to learn high-order feature interactions. It uses the pre-trained factorization machines for field embedding before applying DNN. \cite{qu2016product} further proposes a Product-based Neural Network (PNN), which introduces a product layer between embedding layer and DNN layer, and does not rely on pre-trained FM. The major downside of FNN and PNN is that they focus more on high-order feature interactions while capture little low-order interactions. The Wide\&Deep \cite{cheng2016wide} and DeepFM \cite{guo2017deepfm} models overcome this problem by introducing hybrid architectures, which contain a shallow component and a deep component with the purpose of learning both memorization and generalization. Therefore they can jointly learn low-order and high-order feature interactions. \\
\indent All the abovementioned models leverage DNNs for learning high-order feature interactions. However, DNNs model high-order feature interactions in an implicit fashion. The final function learned by DNNs can be arbitrary, and there is no theoretical conclusion on what the maximum degree of feature interactions is. In addition, DNNs model feature interactions at the bit-wise level, which is different from the traditional FM framework which models feature interactions at the vector-wise level. Thus, in the field of recommender systems, whether DNNs are indeed the most effective model in representing high-order feature interactions remains an open question. In this paper, we propose a neural network-based model to learn feature interactions in an explicit, vector-wise fashion. Our approach is based on the Deep \& Cross Network (DCN) \cite{wang2017deep}, which aims to efficiently capture feature interactions of bounded degrees. However, we will argue in Section \ref{sec:explicit} that DCN will lead to a special format of interactions. We thus design a novel compressed interaction network (CIN) to replace the cross network in the DCN. CIN learns feature interactions explicitly, and the degree of interactions grows with the depth of the network. Following the spirit of the Wide\&Deep and DeepFM models, we combine the explicit high-order interaction module with implicit interaction module and traditional FM module, and name the joint model eXtreme Deep Factorization Machine (xDeepFM). The new model requires no manual feature engineering and release data scientists from tedious feature searching work. To summarize, we make the following contributions:
\begin{itemize}
\item We propose a novel model, named eXtreme Deep Factorization Machine (xDeepFM), that jointly learns explicit and implicit high-order feature interactions effectively and requires no manual feature engineering.
\item We design a compressed interaction network (CIN) in xDeepFM that learns high-order feature interactions explicitly. We show that the degree of feature interactions increases at each layer, and features interact at the vector-wise level rather than the bit-wise level.
\item We conduct extensive experiments on three real-world dataset, and the results demonstrate that our xDeepFM outperforms several state-of-the-art models significantly.
\end{itemize}
\indent The rest of this paper is organized as follows. Section \ref{preliminaries} provides some preliminary knowledge which is necessary for understanding deep learning-based recommender systems. Section \ref{mymodel} introduces our proposed CIN and xDeepFM model in detail. We will present experimental explorations on multiple datasets in Section \ref{experiments}. Related works are discussed in Section \ref{relatedwork}. Section \ref{conclusions} concludes this paper.
\subsection{CIN Analysis}
We analyze the proposed CIN to study the model complexity and the potential effectiveness.
\subsubsection{Space Complexity}
The $h$-th feature map at the $k$-th layer contains $H_{k-1} \times m$ parameters, which is exactly the size of $\mathbf{W}^{k,h}$. Thus, there are $H_{k} \times H_{k-1} \times m$ parameters at the $k$-th layer. Considering the last regression layer for the output unit, which has $\sum_{k=1}^{T}H_{k}$ parameters, the total number of parameters for CIN is $\sum_{k=1}^{T}H_{k} \times (1 + H_{k-1} \times m)$. Note that CIN is independent of the embedding dimension $D$. In contrast, a plain $T$-layers DNN contains $m \times D \times H_1 + H_T + \sum_{k=2}^{T}H_{k} \times H_{k-1}$ parameters, and the number of parameters will increase with the embedding dimension $D$. \\
\indent Usually $m$ and $H_k$ will not be very large, so the scale of $\mathbf{W}^{k,h}$ is acceptable. When necessary, we can exploit a $L$-order decomposition and replace $\mathbf{W}^{k,h}$ with two smaller matrices $\mathbf{U}^{k,h} \in \mathbb{R}^{H_{k-1} \times L}$ and $\mathbf{V}^{k,h} \in \mathbb{R}^{m\times L}$:
\begin{equation}
\mathbf{W}^{k,h} = \mathbf{U}^{k,h} (\mathbf{V}^{k,h})^T
\end{equation}
where $L\ll H$ and $L\ll m$. Hereafter we assume that each hidden layer has the same number (which is $H$) of feature maps for simplicity. Through the $L$-order decomposition, the space complexity of CIN is reduced from $O(mTH^2)$ to $O(mTHL+TH^2L)$. In contrast, the space complexity of the plain DNN is $O(mDH+TH^2)$, which is sensitive to the dimension (D) of field embedding.
\subsubsection{Time Complexity}\label{sec:time_complexity}
The cost of computing tensor $\mathbf{Z}^{k+1}$ (as shown in Figure \ref{fig:CIN1}) is $O(mHD)$ time. Because we have $H$ feature maps in one hidden layer, computing a $T$-layers CIN takes $O(mH^2DT)$ time. A $T$-layers plain DNN, by contrast, takes $O(mHD + H^2T)$ time. Therefore, the major downside of CIN lies in the time complexity.
\subsubsection{Polynomial Approximation}
Next we examine the high-order interaction properties of CIN. For simplicity, we assume that numbers of feature maps at hidden layers are all equal to the number of fields $m$. Let $[m]$ denote the set of positive integers that are less than or equal to $m$. The $h$-th feature map at the first layer, denoted as $\mathbf{x}^{1}_h\ \in \mathbb{R}^{D}$, is calculated via:
\begin{equation}
\mathbf{x}^{1}_h = \sum_{\substack{i\in [m]\\ j\in [m]}} \mathbf{W}^{1,h}_{i,j}(\mathbf{x}^0_i \circ \mathbf{x}^0_j)
\end{equation}
Therefore, each feature map at the first layer models pair-wise interactions with $O(m^2)$ coefficients. Similarly, the $h$-th feature map at the second layer is:
\begin{equation}
\label{eq:level2}
\begin{split}
\mathbf{x}^{2}_h & = \sum_{\substack{i\in [m]\\ j\in [m]}} \mathbf{W}^{2,h}_{i,j}(\mathbf{x}^1_i \circ \mathbf{x}^0_j) \\
& = \sum_{\substack{i\in [m]\\ j\in [m]}} \sum_{\substack{l\in [m]\\ k\in [m]}} \mathbf{W}^{2,h}_{i,j}\mathbf{W}^{1,i}_{l,k} (\mathbf{x}^0_j \circ \mathbf{x}^0_k \circ \mathbf{x}^0_l)
\end{split}
\end{equation}
Note that all calculations related to the subscript $l$ and $k$ is already finished at the previous hidden layer. We expand the factors in Equation \ref{eq:level2} just for clarity. We can observe that each feature map at the second layer models 3-way interactions with $O(m^2)$ new parameters. \\
\indent A classical $k$-order polynomial has $O(m^k)$ coefficients. We show that CIN approximate this class of polynomial with only $O(km^3)$ parameters in terms of a chain of feature maps. By induction hypothesis, we can prove that the $h$-th feature map at the $k$-th layer is:
\begin{equation}
\label{eq:levelk}
\begin{split}
\mathbf{x}^{k}_h & = \sum_{\substack{i\in [m]\\ j\in [m]}} \mathbf{W}^{k,h}_{i,j}(\mathbf{x}^{k-1}_i \circ \mathbf{x}^0_j) \\
& = \sum_{\substack{i\in [m]\\ j\in [m]}} ... \sum_{\substack{r\in [m]\\ t\in [m]}} \sum_{\substack{l\in [m]\\ s\in [m]}} \mathbf{W}^{k,h}_{i,j}...\mathbf{W}^{1,r}_{l,s} (\underbrace{\mathbf{x}^0_j \circ ... \circ \mathbf{x}^0_s \circ \mathbf{x}^0_l}_{k\ vectors})
\end{split}
\end{equation}
For better illustration, here we borrow the notations from \cite{wang2017deep}. Let $\boldsymbol{\alpha}=[\alpha_1,...,\alpha_m] \in \mathbb{N}^d$ denote a multi-index, and $|\boldsymbol{\alpha}|=\sum_{i=1}^m \alpha_i$. We omit the original superscript from $\mathbf{x}^0_i$, and use $\mathbf{x}_i$ to denote it since we only we the feature maps from the $0$-th layer (which is exactly the field embeddings) for the final expanded expression (refer to Eq. \ref{eq:levelk}). Now a superscript is used to denote the vector operation, such as $\mathbf{x}^3_i=\mathbf{x}_i \circ \mathbf{x}_i \circ \mathbf{x}_i$. Let $VP_k(\mathbf{X})$ denote a multi-vector polynomial of degree $k$:
\begin{equation}
VP_k(\mathbf{X})= \left\{ \left. \sum_{\boldsymbol{\alpha}} w_{\boldsymbol{\alpha}} \mathbf{x}_1^{\alpha_1} \circ \mathbf{x}_2^{\alpha_2} \circ ... \circ \mathbf{x}_m^{\alpha_m} \right| 2 \leqslant |\boldsymbol{\alpha}| \leqslant k \right\}
\end{equation}
Each vector polylnomial in this class has $O(m^k)$ coefficients. Then, our CIN approaches the coefficient $w_{\boldsymbol{\alpha}}$ with:
\begin{equation}
\hat w_{\boldsymbol{\alpha}} = \sum_{i=1}^{m} \sum_{j=1}^{m} \sum_{B\in P_{\boldsymbol{\alpha}}} \prod_{t=2}^{|\boldsymbol{\alpha}|} \mathbf{W}^{t,j}_{i,B_t}
\end{equation}
where, $B=[B_1, B_2, ..., B_{|\boldsymbol{\alpha}|}]$ is a multi-index, and $P_{\boldsymbol{\alpha}}$ is the set of all the permutations of the indices $ (\underbrace{1,...1}_{\alpha_1\ times},...,\underbrace{m,...,m}_{\alpha_m\ times})$.
\section{Our proposed model}\label{mymodel}
\begin{figure*}[htbp]
\centering
\begin{subfigure}{.33\textwidth}
\centering
\includegraphics[width=0.85\textwidth]{materials/CIN_1.pdf}
\caption{Outer products along each dimension for feature interactions. The tensor $\mathbf{Z}^{k+1}$ is an intermediate result for further learning.}
\label{fig:CIN1}
\end{subfigure} \hfill
\begin{subfigure}{.32\textwidth}
\centering
\includegraphics[width=0.85\textwidth]{materials/CIN_2.pdf}
\caption{The $k$-th layer of CIN. It compresses the intermediate tensor $\mathbf{Z}^{k+1}$ to $H_{k+1}$ embedding vectors (aslo known as \textsl{feature maps}).}
\label{fig:CIN2}
\end{subfigure}
\begin{subfigure}{.32\textwidth}
\centering
\includegraphics[width=0.85\textwidth]{materials/CIN_3.pdf}
\caption{An overview of the CIN architecture.}
\label{fig:CIN3}
\end{subfigure}
\caption{Components and architecture of the Compressed Interaction Network (CIN).}
\label{fig:CIN}
\end{figure*}
\subsection{Compressed Interaction Network}
We design a new cross network, named Compressed Interaction Network (CIN), with the following considerations: (1) interactions are applied at vector-wise level, not at bit-wise level; (2) high-order feature interactions is measured explicitly; (3) the complexity of network will not grow exponentially with the degree of interactions.\\
\indent Since an embedding vector is regarded as a unit for vector-wise interactions, hereafter we formulate the output of field embedding as a matrix $\mathbf{X}^0 \in \mathbb{R}^{m\times D}$, where the $i$-th row in $\mathbf{X}^0$ is the embedding vector of the $i$-th field: $\mathbf{X}^0_{i,*} = \mathbf{e}_i$, and $D$ is the dimension of the field embedding. The output of the $k$-th layer in CIN is also a matrix $\mathbf{X}^k \in \mathbb{R}^{H_k\times D}$, where $H_k$ denotes the number of (embedding) feature vectors in the $k$-th layer and we let $H_0=m$. For each layer, $\mathbf{X}^k$ are calculated via:
\begin{equation}
\label{eq:xk}
\mathbf{X}^k_{h,*} = \sum_{i=1}^{H_{k-1}}\sum_{j=1}^{m}\mathbf{W}^{k,h}_{ij}(\mathbf{X}^{k-1}_{i,*}\circ \mathbf{X}^0_{j,*})
\end{equation}
where $1\leq h \leq H_k$, $\mathbf{W}^{k,h}\in \mathbb{R}^{H_{k-1}\times m}$ is the parameter matrix for the $h$-th feature vector, and $\circ$ denotes the Hadamard product, for example, $\langle a_1,a_2,a_3 \rangle \circ \langle b_1,b_2,b_3\rangle = \langle a_1b_1,a_2b_2,a_3b_3\rangle$. Note that $\mathbf{X}^k$ is derived via the interactions between $\mathbf{X}^{k-1}$ and $\mathbf{X}^0$, thus feature interactions are measured explicitly and the degree of interactions increases with the layer depth. The structure of CIN is very similar to the Recurrent Neural Network (RNN), where the outputs of the next hidden layer are dependent on the last hidden layer and an additional input. We hold the structure of embedding vectors at all layers, thus the interactions are applied at the vector-wise level.\\
\indent It is interesting to point out that Equation \ref{eq:xk} has strong connections with the well-known Convolutional Neural Networks (CNNs) in computer vision. As shown in Figure \ref{fig:CIN1}, we introduce an intermediate tensor $\mathbf{Z}^{k+1}$, which is the outer products (along each embedding dimension) of hidden layer $\mathbf{X}^k$ and original feature matrix $\mathbf{X}^0$. Then $\mathbf{Z}^{k+1}$ can be regarded as a special type of image and $\mathbf{W}^{k,h}$ is a filter. We slide the filter across $\mathbf{Z}^{k+1}$ along the embedding dimension (D) as shown in Figure \ref{fig:CIN2}, and get an hidden vector $\mathbf{X}^{k+1}_{i,*}$, which is usually called a \textsl{feature map} in computer vision. Therefore, $\mathbf{X}^k$ is a collection of $H_k$ different \textsl{feature maps}. The term ``\textsl{compressed}" in the name of CIN indicates that the $k$-th hidden layer compress the potential space of $H_{k-1}\times m$ vectors down to $H_k$ vectors.\\
\indent Figure \ref{fig:CIN3} provides an overview of the architecture of CIN. Let T denotes the depth of the network. Every hidden layer $\mathbf{X}^k, k\in [1,T]$ has a connection with output units. We first apply sum pooling on each feature map of the hidden layer:
\begin{equation}
{p}^k_i = \sum_{j=1}^D \mathbf{X}^k_{i,j}
\end{equation}
for $i\in [1,H_k]$. Thus, we have a pooling vector $\mathbf{p}^k = [p^k_1, p^k_2, ..., p^k_{H_k}]$ with length $H_k$ for the $k$-th hidden layer. All pooling vectors from hidden layers are concatenated before connected to output units: $\mathbf{p}^+ = [\mathbf{p}^1,\mathbf{p}^2,...,\mathbf{p}^T] \in \mathbb{R}^{\sum_{i=1}^T H_i}$. If we use CIN directly for binary classification, the output unit is a sigmoid node on $\mathbf{p}^+$:
\begin{equation}
y=\frac{1}{1+exp(\mathbf{p^+}^T\mathbf{w}^{o})}
\end{equation}
where $\mathbf{w}^{o}$ are the regression parameters.
\input{model_analysis.tex}
\subsection{Combination with Implicit Networks}
As discussed in Section \ref{sec:implicit}, plain DNNs learn implicit high-order feature interactions. Since CIN and plain DNNs can complement each other, an intuitive way to make the model stronger is to combine these two structures. The resulting model is very similar to the Wide\&Deep or DeepFM model. The architecture is shown in Figure \ref{fig:xDeepFM}. We name the new model eXtreme Deep Factorization Machine (xDeepFM), considering that on one hand, it includes both low-order and high-order feature interactions; on the other hand, it includes both implicit feature interactions and explicit feature interactions. Its resulting output unit becomes:
\begin{equation}
\hat y=\sigma(\mathbf{w}_{linear}^T\mathbf{a}+\mathbf{w}^T_{dnn}\mathbf{x}^k_{dnn}+\mathbf{w}^T_{cin}\mathbf{p}^+ + b)
\end{equation}
where $\sigma$ is the sigmoid function, $\mathbf{a}$ is the raw features. $\mathbf{x}^k_{dnn}, \mathbf{p}^+$ are the outputs of the plain DNN and CIN, respectively. $\mathbf{w}_*$ and $b$ are learnable parameters. For binary classifications, the loss function is the log loss:
\begin{equation}
\mathcal{L}=-\frac{1}{N}\sum_{i=1}^{N}y_i log \hat y_i + (1-y_i)log(1-\hat y_i)
\end{equation}
where $N$ is the total number of training instances. The optimization process is to minimize the following objective function:
\begin{equation}
\mathcal{J}=\mathcal{L} + \lambda_* ||\Theta||
\end{equation}
where $\lambda_*$ denotes the regularization term and $\Theta$ denotes the set of parameters, including these in linear part, CIN part, and DNN part.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.45\textwidth]{materials/xdeepfm.pdf}
\caption{The architecture of xDeepFM.}
\label{fig:xDeepFM}
\end{figure}
\subsubsection{Relationship with FM and DeepFM}
Suppose all fields are univalent. It's not hard to observe from Figure \ref{fig:xDeepFM} that, when the depth and feature maps of the CIN part are both set to 1, xDeepFM is a generalization of DeepFM by learning the linear regression weights for the FM layer (note that in DeepFM, units of FM layer are directly linked to the output unit without any coefficients). When we further remove the DNN part, and at the same time use a constant \textsl{sum filter} (which simply takes the sum of inputs without any parameter learning) for the feature map, then xDeepFM is downgraded to the traditional FM model.
\section{Preliminaries}\label{preliminaries}
\subsection{Embedding Layer}\label{sec:emb}
In computer vision or natural language understanding, the input data are usually images or textual signals, which are known to be spatially and/or temporally correlated, so DNNs can be applied directly on the raw feature with dense structures. However, in web-scale recommender systems, the input features are sparse, of huge dimension, and present no clear spatial or temporal correlation. Therefore, \textsl{multi-field} categorical form is widely used by related works \cite{guo2017deepfm,shan2016deep,wang2017deep,qu2016product,zhang2016deep}. For example, one input instance \texttt{[user\_id=s02,gender=male,\\ organization=msra,interests=comedy\&rock]} is normally transformed into a high-dimensional sparse features via field-aware one-hot encoding:
\begin{equation*}
[\underbrace{0,1,0,0,...,0}_{user id}]\ [\underbrace{1,0}_{gender}]\ [\underbrace{0,1,0,0,...,0}_{organization}]\ [\underbrace{0,1,0,1,...,0}_{interests}]
\end{equation*}
An embedding layer is applied upon the raw feature input to compress it to a low dimensional, dense real-value vector. If the field is univalent, the feature embedding is used as the field embedding. Take the above instance as an example, the embedding of feature \textsl{male} is taken as the embedding of field \textsl{gender}. If the field is multivalent, the sum of feature embedding is used as the field embedding. The embedding layer is illustrated in Figure \ref{fig:field_embedding}. The result of embedding layer is a wide concatenated vector:
\begin{equation*}
\mathbf{e}=[\mathbf{e}_1,\mathbf{e}_2,...,\mathbf{e}_m]
\end{equation*}
where $m$ denotes the number of fields, and $\mathbf{e_i}\in \mathbb{R}^D$ denotes the embedding of one field. Although the feature lengths of instances can be various, their embeddings are of the same length $m\times D$, where $D$ is the dimension of field embedding.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.4\textwidth]{materials/embedding_layer.pdf}
\caption{The field embedding layer. The dimension of embedding in this example is 4.}
\label{fig:field_embedding}
\end{figure}
\subsection{Implicit High-order Interactions}\label{sec:implicit}
FNN \cite{zhang2016deep}, Deep Crossing \cite{shan2016deep}, and the deep part in Wide\&Deep \cite{cheng2016wide} exploit a feed-forward neural network on the field embedding vector $\mathbf{e}$ to learn high-order feature interactions. The forward process is :
\begin{equation}
\mathbf{x}^1=\sigma (\mathbf{W}^{(1)}\mathbf{e}+\mathbf{b}^1)
\end{equation}
\begin{equation}
\mathbf{x}^k=\sigma (\mathbf{W}^{(k)}\mathbf{x}^{(k-1)}+\mathbf{b}^k)
\end{equation}
where $k$ is the layer depth, $\sigma$ is an activation function, and $\mathbf{x}^k$ is the output of the $k$-th layer. The visual structure is very similar to what is shown in Figure \ref{fig:deepfm}, except that they do not include the \textsl{FM or Product layer}. This architecture models the interaction in a bit-wise fashion. That is to say, even the elements within the same field embedding vector will influence each other.
\iffalse
\begin{figure}[htbp]
\centering
\includegraphics[width=0.4\textwidth]{materials/dnn_structure.pdf}
\caption{The architecture of multi-layer feed-forward neural network for high-order feature interactions.}
\label{fig:dnn_structure}
\end{figure}
\fi
\\
\indent PNN \cite{qu2016product} and DeepFM \cite{guo2017deepfm} modify the above architecture slightly. Besides applying DNNs on the embedding vector $\mathbf{e}$, they add a two-way interaction layer in the architecture. Therefore, both bit-wise and vector-wise interaction is included in their model. The major difference between PNN and DeepFM, is that PNN connects the outputs of product layer to the DNNs, whereas DeepFM connects the FM layer directly to the output unit (refer to Figure \ref{fig:deepfm}).
\begin{figure}[htbp]
\centering
\includegraphics[width=0.48\textwidth]{materials/deepfm.pdf}
\caption{The architecture of DeepFM (with linear part omitted) and PNN. We re-use the symbols in \cite{guo2017deepfm}, where red edges represent \textsl{weight-1 connections} (no parameters) and gray edges represent \textsl{normal connections} (network parameters).}
\label{fig:deepfm}
\end{figure}
\subsection{Explicit High-order Interactions}\label{sec:explicit}
\cite{wang2017deep} proposes the Cross Network (CrossNet) whose architecture is shown in Figure \ref{fig:crossnet}. It aims to explicitly model the high-order feature interactions. Unlike the classical fully-connected feed-forward network, the hidden layers are calculated by the following cross operation:
\begin{equation}
\mathbf{x}_k = \mathbf{x}_0\mathbf{x}_{k-1}^T\mathbf{w}_k + \mathbf{b}_k + \mathbf{x}_{k-1}
\end{equation}
where $\mathbf{w}_k, \mathbf{b}_k, \mathbf{x}_k \in \mathbb{R}^{mD}$ are weights, bias and output of the $k$-th layer, respectively. We argue that the CrossNet learns a special type of high-order feature interactions, where each hidden layer in the CrossNet is a scalar multiple of $\mathbf{x}_{0}$.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.31\textwidth]{materials/crossnet.pdf}
\caption{The architecture of the Cross Network.}
\label{fig:crossnet}
\end{figure}
\begin{theorem}
Consider a $k$-layer cross network with the (i+1)-th layer defined as $\mathbf{x}_{i+1} = \mathbf{x}_0\mathbf{x}_{i}^T\mathbf{w}_{i+1} + \mathbf{x}_{i}$. Then, the output of the cross network $\mathbf{x}_k$ is a scalar multiple of $\mathbf{x}_0$.
\end{theorem}
\begin{proof}
When $k$=1, according to the associative law and distributive law for matrix multiplication, we have:
\begin{equation}
\begin{split}
\mathbf{x}_1 & = \mathbf{x}_0(\mathbf{x}_{0}^T\mathbf{w}_1) + \mathbf{x}_{0} \\
& = \mathbf{x}_0(\mathbf{x}_{0}^T\mathbf{w}_1 + 1) \\
& = \alpha^1 \mathbf{x}_0
\end{split}
\end{equation}
where the scalar $\alpha^1 = \mathbf{x}_{0}^T\mathbf{w}_1 + 1$ is actually a linear regression of $ \mathbf{x}_0$. Thus, $ \mathbf{x}_1$ is a scalar multiple of $\mathbf{x}_0$. Suppose the scalar multiple statement holds for $k$=$i$. For $k$=$i+1$, we have :
\begin{equation}
\begin{split}
\mathbf{x}_{i+1} & = \mathbf{x}_0\mathbf{x}_{i}^T\mathbf{w}_{i+1} + \mathbf{x}_{i} \\
& = \mathbf{x}_0((\alpha^{i}\mathbf{x}_{0})^T\mathbf{w}_{i+1}) + \alpha^{i}\mathbf{x}_{0} \\
& = \alpha^{i+1} \mathbf{x}_0
\end{split}
\end{equation}
where, $\alpha^{i+1} = \alpha^i(\mathbf{x}_{0}^T\mathbf{w}_{i+1}+1)$ is a scalar. Thus $\mathbf{x}_{i+1}$ is still a scalar multiple of $\mathbf{x}_{0}$. By induction hypothesis, the output of cross network $\mathbf{x}_k$ is a scalar multiple of $\mathbf{x}_0$.
\end{proof}
Note that the \textsl{scalar multiple} does not mean $\mathbf{x}_k$ is linear with $\mathbf{x}_0$. The coefficient $\alpha^{i+1}$ is sensitive with $\mathbf{x}_0$. The CrossNet can learn feature interactions very efficiently (the complexity is negligible compared with a DNN model), however the downsides are: (1) the output of CrossNet is limited in a special form, with each hidden layer is a scalar multiple of $\mathbf{x}_{0}$; (2) interactions come in a bit-wise fashion.
\section{related work}\label{relatedwork}
\subsection{Classical Recommender Systems}
\subsubsection{Non-factorization Models}
For web-scale recommender systems (RSs), the input features are usually sparse, categorical-continuous-mixed, and high-dimensional. Linear models, such as logistic regression with \textsl{FTRL} \cite{mcmahan2013ad}, are widely adopted as they are easy to manage, maintain, and deploy. Because linear models lack the ability of learning feature interactions, data scientists have to spend a lot of work on engineering cross features in order to achieve better performance \cite{richardson2007predicting,Lian:2017:PLJ:3124791.3124794}. Considering that some hidden features are hard to design manually, some researchers exploit boosting decision trees to help build feature transformations \cite{he2014practical,ling2017model}.
\subsubsection{Factorization Models}
A major downside of the aforementioned models is that they can not generalize to unseen feature interactions in the training set. Factorization Machines \cite{rendle2010factorization} overcome this problem via embedding each feature into a low dimension latent vector. Matrix factorization (MF) \cite{koren2009matrix}, which only considers IDs as features, can be regarded as a special kind of FM. Recommendations are made via the product of two latent vectors, thus it does not require the co-occurrence of user and item in the training set. MF is the most popular model-based collaborative filtering method in the RS literature \cite{srebro2005maximum,koren2008factorization,lee2013local,pan2008one}. \cite{chen2012svdfeature,menon2010log} extend MF to leveraging side information, in which both a linear model and a MF model are included. On the other hand, for many recommender systems, only implicit feedback datasets such as users' watching history and browsing activities are available. Thus researchers extend the factorization models to a Bayesian Personalized Ranking (BPR) framework \cite{rendle2009bpr,rendle2010pairwise,he2016vbpr,yuan2016lambdafm} for implicit feedback.
\subsection{Recommender Systems with Deep Learning}
Deep learning techniques have achieved great success in computer vision \cite{krizhevsky2012imagenet,he2016deep}, speech recognition \cite{hinton2012deep,amodei2016deep} and natural language understanding \cite{mikolov2010recurrent,cho2014learning}. As a result, an increasing number of researchers are interested in employing DNNs for recommender systems.
\subsubsection{Deep Learning for High-Order Interactions} To avoid manually building up high-order cross features, researchers apply DNNs on field embedding, thus patterns from categorical feature interactions can be learned automatically. Representative models include FNN \cite{zhang2016deep}, PNN \cite{qu2016product}, DeepCross \cite{shan2016deep}, NFM \cite{he2017neural}, DCN \cite{wang2017deep}, Wide\&Deep \cite{cheng2016wide}, and DeepFM \cite{guo2017deepfm}. These models are highly related to our proposed xDeepFM. Since we have reviewed them in Section \ref{introduction} and Section \ref{preliminaries}, we do not further discuss them in detail in this section. We have demonstrated that our proposed xDeepFM has two special properties in comparison with these models: (1) xDeepFM learns high-order feature interactions in both explicit and implicit fashions; (2) xDeepFM learns feature interactions at the vector-wise level rather than at the bit-wise level.
\subsubsection{Deep Learning for Elaborate Representation Learning} We include some other deep learning-based RSs in this section due to that they are less focused on learning feature interactions. Some early work employs deep learning mainly to model auxiliary information, such as visual data \cite{he2016vbpr} and audio data \cite{wang2014improving}. Recently, deep neural networks are used to model the collaborative filtering (CF) in RSs. \cite{he2017neuralwww} proposes a Neural Collaborative Filtering (NCF) so that the inner product in MF can be replaced with an arbitrary function via a neural architecture. \cite{sedhain2015autorec,wu2016collaborative} model CF base on the autoencoder paradigm, and they have empirically demonstrated that autoencoder-based CF outperforms several classical MF models. Autoencoders can be further employed for jointly modeling CF and side information with the purpose of generating better latent factors \cite{dong2017hybrid,wang2015collaborative,zhang2016collaborative}. \cite{elkahky2015multi,lian2017cccfnet} employ neural networks to jointly train multiple domains' latent factors. \cite{chen2017attentive} proposes the Attentive Collaborative Filtering (ACF) to learn more elaborate preference at both item-level and component-level. \cite{zhou2017deep} shows tha traditional RSs can not capture \textsl{interest diversity} and \textsl{local activation} effectively, so they introduce a Deep Interest Network (DIN) to represent users' diverse interests with an attentive activation mechanism.
\section{Conclusions}\label{conclusions}
In this paper, we propose a novel network named Compressed Interaction Network (CIN), which aims to learn high-order feature interactions explicitly. CIN has two special virtues: (1) it can learn certain bounded-degree feature interactions effectively; (2) it learns feature interactions at a vector-wise level. Following the spirit of several popular models, we incorporate a CIN and a DNN in an end-to-end framework, and named the resulting model eXtreme Deep Factorization Machine (xDeepFM). Thus xDeepFM can automatically learn high-order feature interactions in both explicit and implicit fashions, which is of great significance to reducing manual feature engineering work. We conduct comprehensive experiments and the results demonstrate that our xDeepFM outperforms state-of-the-art models consistently on three real-world datasets.\\
\indent There are two directions for future work. First, currently we simply employ a sum pooling for embedding multivalent fields. We can explore the usage of the DIN mechanism \cite{zhou2017deep} to capture the related activation according to the candidate item. Second, as discussed in section \ref{sec:time_complexity}, the time complexity of the CIN module is high. We are interested in developing a distributed version of xDeepFM which can be trained efficiently on a GPU cluster.
\section*{Acknowledgements}
The authors would like to thank the anonymous reviewers for their insightful reviews, which are very helpful on the revision of this paper. This work is supported in part by Youth Innovation Promotion Association of CAS. | {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,337 |
from __future__ import absolute_import, print_function
from __future__ import division, unicode_literals
import six
from qscripts_config import __version__, QScriptsConfig as QScfg
import sys
import os
import argparse
from Qpyl.core.qstructure import QStruct, QStructError
from Qpyl.common import backup_file, init_logger, get_version_full
logger = init_logger('Qpyl')
parser = argparse.ArgumentParser(description="""
Command-line tool for converting atom placeholders to indexes. The
placeholders have the following format: $RESID.ATOM_NAME$
""", add_help=False)
reqarg = parser.add_argument_group("Required")
reqarg.add_argument("pdb",
help="pdb structure file (created with qprep)")
reqarg.add_argument("inp",
help="input/fep file containing the placeholders")
reqarg.add_argument("out",
help="output filename")
optarg = parser.add_argument_group("Optional")
optarg.add_argument("--ignore_errors", action="store_true", default=False,
help="Don't use this unless it's an emergency")
optarg.add_argument("-v", "--version", action="version",
version=get_version_full())
optarg.add_argument("-h", "--help", action="help", help="show this "
"help message and exit")
if len(sys.argv) == 1:
parser.print_help()
sys.exit(1)
args = parser.parse_args()
for k, v in six.iteritems(vars(args)):
if k in ["inp", "pdb"] and not os.path.lexists(v):
print("FATAL! File '{}' doesn't exist.".format(v))
sys.exit(1)
inpstr = open(args.inp, "r").read()
try:
qstruct = QStruct(args.pdb, "pdb", ignore_errors=args.ignore_errors)
outstring = qstruct.convert_placeholders(inpstr)
except QStructError as e:
print("FATAL! Exception raised: {}".format(str(e)))
sys.exit(1)
backup = backup_file(args.out)
if backup:
print("Backed up '{}' to '{}'".format(args.out, backup))
open(args.out, "w").write(outstring)
print("Created file '{}'...".format(args.out))
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,859 |
{"url":"https:\/\/chemistry.stackexchange.com\/questions\/39470\/calculate-the-partial-pressure-of-no2","text":"# Calculate the partial pressure of NO2\n\nCalculate the partial pressure of $\\ce{NO2}$.\n\n$$p_{\\ce{N2}}\/p_{\\ce{O2}}=5$$\n\n$$\\ce{N2(g) + O2(g) <=> 2NO(g)}$$\n\nLet\u2019s assume $K=0.1$\n\n$$K= \\frac{p_{\\ce{NO}}^2}{p_{\\ce{O2}}\\cdot p_{\\ce{N2}}}$$\n\n$$K= \\frac{p_{\\ce{NO}}^2}{p_{\\ce{O2}}\\cdot p_{\\ce{O2}}\\cdot5}$$\n\nBut how do I proceed?\n\nOk. Now you have 3 variables and 2 equations. To solve the problem you need 3 equations.\n\nThird equation you'll get from the partial pressure law:\n\nThe total pressure of an ideal gas mixture is the sum of the partial pressures of each individual gas in the mixture.\n\nTip: suppose total pressure is 1.\n\n\u2022 so? p(o2)+p(N2) =1 Aha so I can choose whatever sum I want? \u2013\u00a0MrGuest Oct 22 '15 at 10:37\n\u2022 Don't forget about NO. \u2013\u00a0Alex Oct 23 '15 at 9:23\n\nWhen applying partial pressures please do not forget the partial pressure that the product itself exerts (NO)\n\nSo we have: p(O2)+ p(N2) + p(NO) = total pressure of the system.","date":"2020-05-26 01:28:38","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\": 0.9006854295730591, \"perplexity\": 950.9642452195757}, \"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\/1590347390437.8\/warc\/CC-MAIN-20200525223929-20200526013929-00479.warc.gz\"}"} | null | null |
Shifting from Experience to Transformation
In this exclusive excerpt, Deepend Group explores the evolution of the Experience Economy and how you can prepare for it
Matt Whale (CMO)
In this exclusive excerpt from Deepend Group's new online book, Indepth: Experience Economy, Matt Whale, managing director of the innovation consultancy, How To Impact, explores the Experience Economy and how innovation platforms can help deliver 'change' for transformation-driven consumers.
"Customers are no longer buying products and services – they are buying experiences delivered via the products and services."
– Gregory Yankelovich, CEO of Customer Experience IQ
If all the articles on the Experience Economy have shown us anything, it is that our interactions with brands are no longer about just using a certain product or service; they span a far greater breadth of engagement.
And while some industries are only now getting to grips with the challenges thrown up by the Experience Economy, others are already thinking ahead to the next stage.
Pine & Gilmore, the academics who defined the Experience Economy, said that the next phase of consumer engagement with brands will be the Transformation Economy:
"With transformations, the economic offering of a company is the individual person or company changed as the result of what the company does. With transformations, the customer is the product! The individual buyer of the transformation essentially says, 'Change me'."
Change here can take different forms – a better sense of identity or purpose, or a physical or mental transformation. Brands take on the role of a coach, enabler or advisor, helping consumers to change themselves in a meaningful, long-term way – beyond the short-term interactions of the Experience Economy, towards self-actualisation – the highest part of Maslow's hierarchy of needs.
One industry struggling to keep up with the changes digital is creating for traditional product cycles is home entertainment. Interestingly, as DVD sales drop and cinema revenues follow suit, the core offer actually remains strong – consumers are consuming more home entertainment than ever, they are just not paying for it in its old format.
Recently, How To Impact conducted the largest insight and user journey innovation research project in Australia in this sector, interacting with people as they acquired, watched, logged and shared entertainment. One of the key traits revealed showcased the move from experiences to transformations: The TV series binge.
In one extreme example, one consumer took a week off work to watch all five (pirated) seasons of Breaking Bad in 7 days. He commented afterwards: "It was a trip - as mind-altering as the ice Walter White was making in the show." He clearly wanted to put himself at the centre of his own transformation.
Generally, it takes a more complex and layered experience to create a transformation. And one of the main reasons to run away from the old way of thinking about the economy is the appalling success rate of old school product or service innovation thinking: The Experience and Transformation Economies require brands to think in terms of multi-element 'innovation platforms'.
An innovation platform is a new solution that brings together five or more types of innovation – not just new product performance or service design, but a connected raft of supporting innovations that make one 'whole' innovation idea with a proven higher success rate.*
Doblin's 10 types of innovation
Today, buying an experience requires an inter-connected family of product, service, process and network innovations.
One of the industries most suited to the Transformation Economy is the weight loss or 'shape management' category. Looking at the history of that sector, there's been a clear progression through the different types of economies to a new status quo that takes a platform approach with the user at the centre.
Product Economy: the first offers were diet products – portion-controlled, low-fat or low-sugar foods, drinks and meal replacements that you bought from a store.In 1963 WeightWatchers was launched, bringing us diet foods.
Service Economy: Jenny Craig brought service into the picture in 1985 by offering a full programme of meals – and formalised a mainstream weight management service – but still based around core product offers. And although WeightWatchers introduced a simple points system so that their products worked in harmony in 1997, the writing was starting to appear on the wall for a product-centric approach.
Experience Economy: Options for losing weight and managing your shape got easier with the arrival of delivery services like Lite'n'Easy and the arrival of the weight/shape management app. Today more than half of all Australians looking to lose weight use two or more weight loss apps. The experience became personal.
Transformation Economy: Michelle Bridges' 12 Week Body Transformation offering and clothing range has evolved shape/weight management beyond its product and service origins. Her brand offers transformation experiences: a greater focus on education, coaching, support and empowerment. This year, Michelle Bridges made the BRW Rich Women list for the first time with a net worth of $53 million.
Bridges isn't alone; she's part of an industry-wide trend, which now extends to the travel space with places like the Golden Door health retreat in the Hunter Valley. The emphasis there is on 'balancing mind, body and spirit to achieve life-long wellness' and providing tools to change. Indeed, according to one recent guest, "Ten years ago this was a fat camp – now it's a change centre".
We've long talked about customer-centric design, so the concept of a Transformation Economy that revolves around the transformation of the customer as a 'product' shouldn't be too alien in principle. The future is open to organisations that have the practical capability and structures to deliver customer-centric transformation platforms. We all need to be agents of change.
*When Doblin undertook its major innovation research exercise and examined nearly 10,000 projects, it found innovation ideas that just focused on just one type of innovation had a success rate of less than 5 per cent. But when innovations were built around a platform of five or more types of innovation they had a 35-70 per cent success rate. The wider the innovation platform, the more of an experience you can build and the better your chances of success.
This exclusive extract is from the newly launched online publication, Indepth: Experience Economy from Deepend Group. The independent, digital communications and innovation consultancy group comprises specialist agencies Deepend (digital), How To Impact (innovation), Nomad (mobile) and History Will Be Kind (PR/social media). | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 108 |
Jakub of Gostynin (; c. 1454 – 16 February 1506) was a Polish philosopher and theologian of the late 15th century, and Rector of the University of Krakow in 1503–1504.
Life
Jakub of Gostynin was one of the chief adherents of the Cologne-style Thomism, a philosophical school that upheld the legacy of work and thought of Thomas Aquinas. Jakub's main work, entitled "Theoremata seu propositiones Auctoris Causarum", was a commentary to Liber de Causis attributed to the Greek philosopher Aristotle. He also wrote a commentary to Metaphysics by Aristotle entitled: "Expositiosuper I–XII libros "Metaphysicae" Aristotelis" as well as to his Physics. He contributed to commentaries by Paul of Venice (Paweł z Wenecji) to On the Soul (or "De Anima") by Aristotle and the theological works of Jan Versor. Jakub of Gostynin is also the author of commentaries on the Gospel of John. He donated his extensive library of manuscripts of philosophy, theology and language to the University of Krakow, the city where he died.
See also
History of philosophy in Poland
References
References
Jakub z Gostynina PEF — Polskie Towarzystwo Tomasza z Akwinu (pdf)
1454 births
1506 deaths
Thomists
15th-century philosophers
Academic staff of Jagiellonian University
15th-century Polish philosophers | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,459 |
\section{Abstract}
We present a reliable estimate on the production rate of $B_c$ mesons
in $1S$ and $2S$ states in
the large transverse momentum region at hadronic colliders
using heavy quark fragmentation
functions derived within the framework of perturbative QCD. We
also present the transverse momentum distribution for the $B_c$ mesons.
The production rate is large enough for the $B_c$ mesons to be identified at
the Tevatron. At the SSC/LHC the rate is so large that their properties can be
studied in details.
\end{abstract}
\section{Introduction}
\label{intro}
Heavy flavor production and decays are very useful for
measuring CKM matrix elements of the standard model and for
testing bound-state models for mesons and
baryons. Ever since the first $B$ meson was discovered, a lot of data have
been coming out from, {\it e.g.},
CLEO, ARGUS, LEP/SLC, FNAL, on the $B_d$ and $B_u$ meson families. From
the recent run at Tevatron the masses and other properties
of the $B_s$ have been measured and confirmed \cite{Bs}.
The next family of $B$ mesons will be the $B_c$ mesons
made up of $\bar bc$.
The $B_c$-meson family
differs from the $J/\psi$ and $\Upsilon$ families and from other $B$ mesons
because it is made up of a pair of heavy quark and antiquark of {\it
different} flavors and masses.
The $J/\psi$ and $\Upsilon$ families have
played important roles in developing heavy quark
bound-state models inspired by QCD.
Being quarkonium systems of different flavors and masses
$\bar b c$ bound-states
provide unique opportunities to test different bound-state
models of QCD. The decays of $B_c$ mesons also provide rich sources to
test the standard model, e.g. the measurement of $|V_{bc}|$, and enables
us to see the interplay between strong and weak interactions.
Since the physics of the $B_c$ mesons is so interesting, one would like to know
how many can be produced in the present colliders (e.g. Tevatron) and in
the future hadronic supercolliders (SSC/LHC). It is the purpose of this
letter to present reliable estimate in the high $p_T$ region,
by using the heavy
quark fragmentation functions $D_{\bar b \to B_c}(z)$ \cite{ours}
which are based on
perturbative QCD. We will summarize some features of these heavy quark
fragmentations in Sec.~II, and present the production rates and the $p_T$
distributions for the $B_c$ mesons in Sec.~III.
Finally we will conclude in Sec.IV.
\section{Heavy Quark Fragmentation}
Previous estimates of $B_c$ meson production have based
on perturbative QCD calculations for $e^+e^-$ colliders \cite{bclep}
and monte carlo studies for both $e^+e^-$ and hadronic colliders \cite{bcmc}.
The monte carlo estimates of the ratio $\sigma(B_c^\pm)/\sigma(b\bar b X)$
are all of the
order $10^{-3}$ for LEP, Tevatron, SSC/LHC, and HERA. This fact leads
us to think that the production mechanisms are all of the same nature.
In the region of large $p_T$, the major mechanism for producing $B_c$ or any
other mesons is heavy quark fragmentation \cite{ours,eric},
in which a $\bar b$ antiquark
is produced at large $p_T$ by a hard-scattering process and it subsequently
fragments into the meson.
The differential cross section for direct production of the
$B_c$ meson at high $p_T$ can be factorized at leading order in $\alpha_s$ as
\begin{equation}
\label{fact}
d\sigma(B_c(p)) = \int_0^1 dz\; d\hat\sigma(\bar b(p/z,\,\mu))
D_{\bar b\to B_c}(z,\,\mu)\,,
\end{equation}
where $z$ is the longitudinal momentum fraction carried by the $B_c$,
and $\mu$ is a factorization scale.
The physical interpretation is as follow: a heavy $\bar b$ antiquark is
produced in a hard process with four-momentum $p/z$, and then it fragments
into the $B_c$ meson with a longitudinal momentum fraction $z$.
The fragmentation function $D_{\bar b\to B_c}(z)$ satisfies the
Altarelli-Parisi evolution equation
\begin{equation}
\label{evol}
\mu \frac{\partial}{\partial \mu} D_{\bar b\to B_c}(z) = \int_z^1
\frac{dy}{y} P_{\bar b \to \bar b}(z/y, \mu) D_{\bar b\to B_c}(y,\mu)\,,
\end{equation}
at leading order in $\alpha_s$.
The factorization for $B_u,\,B_d$, and $B_s$ productions can be described
in the same way as Eqs.~(\ref{fact}) and (\ref{evol}), with the corresponding
fragmentation functions.
These fragmentation functions should be independent of the
hard process by which the $\bar b$ is produced.
The fragmentation of $\bar b$ into $B_u,\,B_d$, and $B_s$ is a soft process,
and can only be described by a phenomenological function \cite{peter}.
However, $\bar b\to B_c$ requires the production of a $c\bar c$ pair and it is
therefore a hard process which can be calculated using perturbative QCD
\cite{ours,eric}. This perturbative QCD approach has been shown valid in
calculating the fragmentation functions for heavy quarkonium productions
\cite{eric},
including the splitting of gluons and charm quarks into $S$-wave charmonium.
The fragmentation functions $D_{\bar b\to B_c}(z)$ derived in
Ref.~\cite{ours} need only the input parameters of
$\alpha_s,\,m_b,\,m_c$, and the radial wave function $R(0)$ of the bound
state at the origin so that it has more predictive power.
The initial fragmentation functions are given by
\begin{eqnarray}
D_{\bar b\rightarrow B_c}(z,\mu_0) & = &
\frac{2\alpha_s(2m_c)^2 |R(0)|^2}
{81\pi m_c^3}\; \frac{rz(1-z)^6}{(1-(1-r)z)^6} \nonumber \\
\label{dz1}
&\times & [ 6 - 18(1-2r)z + (21 -74r+68r^2) z^2 \\
&& -2(1-r)(6-19r+18r^2)z^3 + 3(1-r)^2(1-2r+2r^2)z^4 ]\,, \nonumber
\end{eqnarray}
for the $^1S_0$ $B_c$ state, and
\begin{eqnarray}
D_{\bar b\rightarrow B_c^*}(z,\mu_0) & = &
\frac{2\alpha_s(2m_c)^2 |R(0)|^2}
{27\pi m_c^3}\; \frac{rz(1-z)^6}{(1-(1-r)z)^6} \nonumber \\
\label{dz2}
&\times & [ 2 - 2(3-2r)z + 3(3 - 2r+ 4r^2) z^2 \\
& & -2(1-r)(4-r +2r^2)z^3 + (1-r)^2(3-2r+2r^2)z^4 ]\,, \nonumber
\end{eqnarray}
for the first excited state $B_c^*$ which has the spin-orbital quantum number
$^3S_1$, and $r=m_c/(m_b+m_c)$. Note that the scale
in $\alpha_s$ is set to be $2m_c$.
The perturbative QCD calculation gives directly the fragmentation function at
the scale $\mu_0=2m_c$, which is the minimum virtuality of the
gluon splitting into $c\bar c$.
Using the Heavy Quark Effective Theory methods \cite{jaffe},
it can be shown that the evolution up to the scale $m_b$ is trivial, which
means that higher order radiative corrections will not introduce any logarithm
of $m_b/m_c$. A
convenient choice for the initial scale is $\mu_0=m_b+2m_c$ \cite{ours},
because the
fragmentation functions for $c\to B_c,\,B_c^*$ can then be obtained from
Eqs.~(\ref{dz1}) and (\ref{dz2}) simply by interchanging $m_b$ and $m_c$.
In the factorization scheme of Eq.~(\ref{fact}), all the dependence on the
momentum $p$ is in the hard process $\hat\sigma$.
Large logarithm of $p/\mu$ can be avoided by choosing the factorization scale
$\mu$ to be of order $p$.
The induced large logarithm of order $\mu/m_b$ in $D(z)$ can be solved by
evolving the Eq.~(\ref{evol}).
To leading order in $\alpha_s$ only the $\bar b \to \bar b$ contributes to
the evolution. The fragmentation functions $D_{\bar b\to B_c}(z)$ and
$D_{\bar b\to B_c^*}(z)$ at the initial scale $\mu_0$ and higher scale
have been shown in Fig.~1 of Ref.~\cite{ours}.
\section{Results \& Discussions}
In this section, we use Eq.~(\ref{fact}) to compute the direct production
rates of $B_c$ and $B_c^*$ in hadronic collisions.
Our calculation includes
\begin{equation}
gg \to b\bar b\,,\quad g \bar b \to g\bar b\,,\quad {\rm and}\quad
q\bar q \to b \bar b \,,
\end{equation}
as the hard subprocesses for the inclusive production of the $\bar b$. We
choose the scale $\mu$ for the parton distribution functions and for
$\alpha_s$ to be the transverse mass of the $\bar b$,
$\sqrt{p_{T\bar b}^2 + m_b^2}$.
We use the parameterization of HMRS (set b) \cite{HMRS}
for parton distribution functions.
The running coupling constant $\alpha_s(Q)$ is evaluated at 1-loop by
evolving from the
experimental value $\alpha_s(m_Z)=0.12$ \cite{zlep}, and given by
\begin{equation}
\alpha_s(Q) = \frac{\alpha_s(m_Z)}{1+ 8\pi b_0\alpha_s(m_Z)\log(Q/m_Z)}\,,
\end{equation}
where $b_0 = (33-2n_f)/48\pi^2$, and $n_f$ is the number of active flavors
below the scale $Q$.
The subprocess cross sections are convoluted with $D(z,\mu)$, as is in
Eq.~(\ref{fact}). The functions $D(z,\mu_0)$ at the initial scale $\mu_0$ are
given in Eqs.~(\ref{dz1}) and (\ref{dz2}), and are evolved
to the scale
$\mu$ using Eq.~(\ref{evol}).
For the initial fragmentation functions $D(z,\mu_0)$
we use the input parameters of $m_b=4.9$~GeV, $m_c=1.5$~GeV, and
$|R(0)|^2=(1.18\;{\rm GeV})^3$.
The $p_T$ spectrum for the $B_c$ meson at
Tevatron energy is shown in Fig.~\ref{teva}, with the acceptance cuts
\begin{equation}
p_T(B_c) > 10 \;{\rm GeV}\quad {\rm and }\quad |y(B_c)| < 1\,.
\end{equation}
The corresponding spectrum for the $B_c^*$ is also shown on the same figure.
The shape of the two spectra is very similar, because
$D_{\bar b\to B_c}(z)$ and $D_{\bar b\to B_c^*}(z)$ have similar shapes and
differ primarily by an overall normalization difference of about 50\%.
The corresponding spectra at SSC($\sqrt{s}=40$~TeV) and LHC($\sqrt{s}=14$~TeV)
energies are shown in Fig.~\ref{SSC}, but under slightly different
acceptance requirements
\begin{equation}
p_T(B_c) > 20 \;{\rm GeV}\quad {\rm and }\quad |y(B_c)| < 2.5\,.
\end{equation}
The integrated cross sections versus $p_T^{\rm min}(B_c)$ are also
shown in Fig.~\ref{inte}.
The cross sections at the SSC are about three times as large as those at the
LHC, and about two order of magnitudes larger than those at the Tevatron.
So far we have only estimated the $B_c$ meson productions in $1\,^1S_0$ and
$1\,^3S_1$ states.
Since the annihilation channel for the decay of the excited $B_c$-meson
states is suppressed relative to the
electromagnetic and hadronic transitions, all the
excited states ($1\,^3S_1,\,2S,\,1P,\,2P,\,1D$) below the $BD$ threshold will
decay to the ground state $1\,^1S_0$ by emitting photons or pions. They
therefore all contribute to the inclusive production of $B_c$ mesons.
A simple modification can be made to estimate the
productions in $2\,^1S_0$ and $2\,^3S_1$ states, by multiplying with the factor
$|R_{2S}(0)/R_{1S}(0)|^2 \simeq 0.6$ \cite{eichten}. Therefore, the curves in
Figs.~\ref{teva}, \ref{SSC}, and \ref{inte} can be
multiplied by 0.6 to get the productions for 2S states.
To get
the total inclusive production rate, however, we need to include $P$-wave and
possibly $D$-wave contributions, which have not been calculated. Therefore,
the cross sections presented here are rather conservative to the actual
production rates.
Table~\ref{table1} shows the number of $B_c$
mesons that can be produced inclusively at Tevatron, SSC and LHC, including
the contributions from $1S$ and $2S$ states, with
integrated luminosities of 0.025, 10, and 100
fb$^{-1}$ respectively.
It is also informative to give the ratio $\sigma(B_c)/\sigma(\bar b X)$,
which is simply the fragmentation probability $\int_0^1 dz D_{\bar b\to
B_c}(z)$. Adding the contributions from $1S$ and $2S$ states, the ratio
$\sigma(B_c)/\sigma(\bar b X)$ is about $1.5\times 10^{-3}$, which is
consistent with the monte carlo studies \cite{bcmc}.
The factorization in Eq.~({\ref{fact}) is correct up to the
order $(m_b/p_T)^2$, which explains why we impose a rather high $p_T$ cut on
the $B_c$ mesons.
In the low $p_T$ region, mechanisms other than heavy quark
fragmentation have to be taken into account. For example, production of pairs
of $b\bar b$ and $c\bar c$ followed by recombination of $\bar b$ and $c$ to
form a $B_c$ meson contributes at low $p_T$ region; whereas heavy quark
fragmentation dominates at high $p_T$.
Similar conclusion can be found in the production of $J/\psi$ by
heavy quark fragmentation \cite{sean}, which is dominant over
the process $gg\to\psi g$ in the large $p_T$ region.
There are other uncertainties arising from higher order QCD corrections,
relativistic corrections of the bound state model, and the values of
$\alpha_s$ and $R(0)$ used. But the largest source of uncertainties comes from
the values of $m_b$ and $m_c$ employed
because of the factor $1/m_c^3$ in the
initial fragmentation functions as in Eqs.~(\ref{dz1}) and (\ref{dz2}).
\section{Conclusions}
We have used heavy quark fragmentation functions derived from perturbative QCD
to calculate the production rates and the $p_T$ distributions for
$S$-wave $B_c$ mesons at Tevatron, SSC , and LHC energies.
Imposing cuts of $p_T(B_c)>10$~GeV and $|y(B_c)|<1$ at the Tevatron,
and including the
contributions from 1S and 2S states, about 16000 $B_c^+$ and 16000 $B_c^-$
mesons
should be produced for 25 pb$^{-1}$ integrated luminosities.
The corresponding numbers for SSC and LHC with $p_T(B_c)>20$~GeV and
$|y(B_c)|<2.5$
are $7.1\times 10^7$ and $2.3\times 10^8$
with integrated luminosities of 10 and 100 fb$^{-1}$ respectively.
These $B_c$ mesons can be detected via the decays of the form
$J/\psi + X$, and in particular, via
\begin{equation}
B_c^\pm \quad \rightarrow \psi \ell^\pm \nu_\ell \quad {\rm and} \quad
B_c^\pm \quad \rightarrow \psi \pi^\pm
\end{equation}
with $\psi \rightarrow \ell'^+ \ell'^-$.
The first one has a distinct signature of three charged leptons coming off from
the same secondary vertex and has a combined branching ratio of
about 1\%. The second decay channel has a smaller branching ratio of order
0.2-0.4\%, but it has the advantage that the $B_c$ can be fully reconstructed.
The production rate of $B_c$ mesons given above is large enough that it should
be possible to use these decay modes to identify the $B_c$ mesons at the
Tevatron, and to study its properties in details at the SSC and LHC.
\acknowledgements
Special thanks to Eric Braaten for suggesting the problem, reading the
manuscript, and giving many
valuable comments. Also thanks to E.~Eichten, R.~Oakes and T.~C.~Yuan for
helpful discussions.
This work was supported by the U.~S. Department of Energy, Division of
High Energy Physics, under Grant DE-FG02-91-ER40684.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 647 |
Q: Importing User-Defined Functions Written in F# Using Excel DNA Into VBA Subroutines I am currently using Excel DNA to write functions in F# and import them into Excel as formulas. Whenever selecting a cell, I am able to call any of the functions imported through Excel DNA. However, when attempting to create a new macro, I am only able to call the built-in formulas in my code, not the user defined ones. For example, If I write the following:
Sub a()
Range("A1").Value = ActiveWorkbook.Application.WorksheetFunction.Sum(2, 3)
End Sub
The macro is able to input "5" into cell A1. However, if I have a function written in F# that was imported through Excel DNA , the above logic does not apply since that function is not listed under ActiveWorkbook.Application.WorksheetFunction. Where would the user-defined functions/formulas be located?
A: Have a look at this tutorial. There are a few steps to go through. The tutorial uses C#, but it should work equally well for F#.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,371 |
Q: Regular Expressions and TMatch.Groups.Count I'm porting some classes from the Apache Commons library, and I found the following behaviour strange. I have a regular expression defined as
const
IPV4_REGEX = '^(\d{1,3})\.(\d{1,3})\.(\d{1,3})\.(\d{1,3})$';
and I use it as follows:
ipv4Validator: TRegEx;
ipv4Validator := TRegEx.Create(IPV4_REGEX);
When I use it to match an IP address, the following code returns false - the debugger shows that Match.Groups.Count is 5, which I didn't expect.
var
Match: TMatch;
begin
Match := ipv4Validator.Match(inet4Address);
if Match.Groups.Count <> 4 then
Exit(false);
Is this the correct behaviour of TMatch.Groups.Count?
Just in case, here's the full code of my class. Notice that I have commented the offending line, because it made my tests fail.
unit InetAddressValidator;
interface
uses RegularExpressions;
const
IPV4_REGEX = '^(\d{1,3})\.(\d{1,3})\.(\d{1,3})\.(\d{1,3})$';
type
TInetAddressValidator = class
private
ipv4Validator: TRegEx;
public
constructor Create; overload;
function isValid(const inetAddress: String): Boolean;
function isValidInet4Address(const inet4Address: String): Boolean;
end;
implementation
uses SysUtils;
constructor TInetAddressValidator.Create;
begin
inherited;
ipv4Validator := TRegEx.Create(IPV4_REGEX);
end;
function TInetAddressValidator.isValid(const inetAddress: String): Boolean;
begin
Result := isValidInet4Address(inetAddress);
end;
function TInetAddressValidator.isValidInet4Address(const inet4Address
: String): Boolean;
var
Match: TMatch;
IpSegment: Integer;
i: Integer;
begin
Match := ipv4Validator.Match(inet4Address);
// if Match.Groups.Count <> 4 then
// Exit(false);
IpSegment := 0;
for i := 1 to Match.Groups.Count - 1 do
begin
try
IpSegment := StrToInt(Match.Groups[i].Value);
except
Exit(false);
end;
if IpSegment > 255 then
Exit(false);
end;
Result := true;
end;
end.
A: Match.Groups[0] contains the whole expression, so this is correct.
TGroupcollection constructor:
constructor TGroupCollection.Create(ARegEx: TPerlRegEx;
const AValue: UTF8String; AIndex, ALength: Integer; ASuccess: Boolean);
var
I: Integer;
begin
FRegEx := ARegEx;
/// populate collection;
if ASuccess then
begin
SetLength(FList, FRegEx.GroupCount + 1);
for I := 0 to Length(FList) - 1 do
FList[I] := TGroup.Create(AValue, FRegEx.GroupOffsets[I], FRegEx.GroupLengths[I], ASuccess);
end;
end;
As you can see the internal Flist (TArray<TGroup>) is initiated with the number of groups + 1. FList[0] receives a group with offset 1 and the whole expression length. This behaviour is not documented.
A: Delphi's TRegEx is designed to mimic .NET's Regex class, which also adds the overall regex match to Match.Groups.Count. .NET does this so that the GroupCollection class can implement the ICollection interface.
In Java Matcher.group(0) also returns the overall regex match. Matcher.groupCount() returns the number of groups excluding the overall match. Most regex libraries do it this way.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,399 |
Scorched é um filme independente de comédia criminal de 2003, dirigido por Gavin Grazer, estrelado por Alicia Silverstone, Rachael Leigh Cook, Woody Harrelson e John Cleese. Scorched segue a história de vários funcionários descontentes do banco que tentam roubar o mesmo banco na mesma noite sem saber que outros estão fazendo exatamente a mesma coisa.
O filme teve um desempenho financeiro muito ruim nas bilheterias. Do orçamento inicial de US$7 milhões, Scorched ganhou de volta apenas US$8,000 no final de sua exibição nos cinemas. Foi retirado de sua exibição nos cinemas depois de apenas um fim de semana nos cinemas.
Sinopse
Sheila Rilo (Silverstone) é uma caixa do banco no Desert Savings Bank, em uma pequena cidade deserta. O namorado dela é Rick Becker (Joshua Leonard , o gerente do banco informado por seus superiores de que ele seria demitido se os caixas eletrônicos do banco fossem roubados apenas mais uma vez. Sheila e Rick passaram vários anos em um relacionamento de novo e de novo, no qual ele a usa entre outros encontros. Depois que Sheila paga a maior parte da educação de Rick, ele a deixa como professora. Sheila decide se vingar de Rick roubando o banco e fazendo com que ele seja demitido.
Na mesma noite, Stuart (Paulo Costanzo) e Jason (Woody Harrelson), outros dois caixas do mesmo banco, também decidiram assaltar o banco. O plano de Stuart é roubar US$250.000 do banco e apostar todo o valor em um jogo de roleta em Las Vegas. Stuart, que está desesperado por emoção em sua vida, está seguindo a sugestão de seu amigo Max (David Krumholtz), embora o inteligente Stuart geralmente exija Max de seus esquemas de enriquecer rápido.
Jason é um amante da natureza que vive com um pato órfão. Ele foi promovido a gerente assistente de banco, um cargo com muito mais responsabilidade, mas apenas um aumento de US$0,55 por hora. Ele sente que o banco lhe deve anos de serviço leal e mal pago e decide se vingar roubando o cofre de um milionário local mesquinho, Charles Merchant (Cleese). O comerciante, que ficou rico produzindo comerciais e vendendo vídeos sobre como ficar rico rapidamente no mercado imobiliário, é a pessoa que matou a mãe do pato de Jason, facilitando a decisão de Jason de roubar o cofre do comerciante.
Jason não é o único com um plano de vingança contra o magnata local. Uma funcionária insatisfeita de uma loja de roupas, Shmally (Cook), se vinga contra Merchant na mesma noite, com Carter (Marcus Thomas) ajudando-a a jogar ovos na casa de Merchant. Carter Doleman é amigo e colega de quarto de Shmally e o mais novo funcionário do banco. Devido à sua incapacidade de se vestir bem e sua falta de capacidade de conseguir um emprego por conta própria, Shmally concordou em ajudá-lo. Quando Carter foi chamado para uma entrevista no banco, Shmally fez uma reforma, vestiu-o adequadamente e o treinou sobre como passar na entrevista. Ansioso e empolgado por começar seu primeiro dia de trabalho, Carter hesitante é arrastado para fora da cama por Shmally para que ele possa ajudá-la a cuidar da casa de Merchant.
Elenco e personagens
Marcus Thomas como Carter Doleman, companheiro de quarto de Shmally, o mais novo funcionário do banco
Alicia Silverstone como Sheila Rilo, caixa do banco, namorada de Rick
Rachael Leigh Cook como Shmally, funcionária da loja de roupas, colega de quarto de Carter
Woody Harrelson como Jason "Woods" Valley, gerente assistente e amante da natureza
John Cleese como Charles Merchant, empresário e milionário local, criador de infomerciais
Paulo Costanzo como Stuart "Stu" Stein, caixa do banco, amigo de Max, desesperado por emoção na vida
David Krumholtz como Max, amigo de Stu, cheio de esquemas de enriquecimento rápido
Joshua Leonard como Rick Becker, gerente de banco, namorado de Sheila
Ivan Sergei como Mark, bombeiro, o novo interesse amoroso de Sheila
Wayne Morse como Gavin, companheiro bombeiro de Mark
Canções
Canções incluídas na trilha sonora:
Recepção
Resposta da crítica
O filme recebeu críticas negativas dos críticos. O agregador de críticas Rotten Tomatoes atribui-lhe uma pontuação de 17% com base em críticas de 6 críticos.
Peter Bradshaw, do The Guardian, deu ao filme uma estrela em cinco e chamou Scorched "de uma perda de tempo maior e mais desagradável do que rolar uma enorme bola de esterco sólido por uma colina íngreme", enquanto Angus Wolfe Murray, da Eye for Film, que premiou o filme com a mesma classificação de 1 estrela, o chamou de "desastre absoluto" e concluiu que "um acidente de carro tem mais estilo". Rich Cline do ShadowsontheWall.com admite que Scorched tem um "elenco excelente", que são "artistas talentosos", mas que o filme ainda é uma "bagunça", que é "completamente inútil" e conclui que "enquanto o filme é assistível, nem um único segmento do enredo ganha vida". O crítico Matthew Leyland, do serviço on-line BBCi, deu ao filme duas estrelas em cinco, chamando-o de "farsa de vingança morna" com um "enredo mal cozido" e observando que "tentativas de humor insano se tornam em forma de pêra". Sean Axmaker, do Seattle Post-Intelligencer, chamou o filme de "divertido, mas morno", chamou o roteiro de "preguiçoso" e finalmente concluiu que, com apenas "personagens vagamente agradáveis", Scorched é "agressivamente amável e totalmente imemorável".
Das raras críticas favoráveis, foi a de Duane Byrge, do The Hollywood Reporter, na qual ele chamou o enredo de "um triunfo brutalmente satisfatório do bem sobre o mal" e "um caminhão cheio de risadas" ao concluir que "essa comédia maravilhosamente desobediente deveria sair com uma tonelada de dólares, euros e outras moedas em quadrinhos".
Bilheteria
Scorched foi filmado em seis semanas, terminando a filmagem principal em 23 de junho de 2001, mas não foi lançado nos Estados Unidos até 25 de julho de 2003. O filme sofreu grandes perdas financeiras durante sua exibição nos cinemas, ganhando apenas US$ 8 mil (aproximadamente 0,1%) a partir de um orçamento de produção de US$ 7 milhões. No mercado interno, o filme só foi lançado por três dias em 1 de agosto de 2003 e foi exibido em apenas doze cinemas. Os ganhos do fim de semana de abertura, que também se tornou o último fim de semana do filme, classificaram o filme como o 604º filme de 2003 pelo rendimento bruto interno.
Filmes dos Estados Unidos de 2003
Filmes de comédia dos Estados Unidos
Filmes de comédia da década de 2000
Filmes em língua inglesa da década de 2000
Filmes independentes dos Estados Unidos
Filmes independentes da década de 2000
Filmes sobre vingança
Roubo a banco em filmes | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,148 |
Produced by David Widger
HYACINTH
By George A. Birmingham
1906
CHAPTER I
In the year 1850 or thereabouts religious and charitable society in
England was seized with a desire to convert Irish Roman Catholics to
the Protestant faith. It is clear to everyone with any experience of
missionary societies that, the more remote the field of actual work, the
easier it is to keep alive the interest of subscribers. The mission to
Roman Catholics, therefore, commenced in that western portion of Galway
which the modern tourist knows as Connemara, and the enthusiasm was
immense. Elderly ladies, often with titles, were energetic in the cause
of the new reformation. Young ladies, some of them very attractive,
collected money from their brothers and admirers. States-men and Bishops
headed the subscription-lists, and influential committees earnestly
debated plans for spending the money which poured in. Faith in the
efficacy of money handled by influential committees is one of the
characteristics of the English people, and in this particular case
it seemed as if their faith were to be justified by results. Most
encouraging reports were sent to headquarters from Gonnemara. It
appeared that converts were flocking in, and that the schools of the
missionaries were filled to overflowing. In the matter of education
circumstances favoured the new reformation. The leonine John McHale, the
Papal Archbishop of Tuam, pursued a policy which drove the children of
his flock into the mission schools. The only other kind of education
available was that which some humorous English statesman had called
'national,' and it did not seem to the Archbishop desirable that an
Irish boy should be beaten for speaking his own language, or rewarded
for calling himself 'a happy English child.' He refused to allow the
building of national schools in his diocese, and thus left the cleverer
boys to drift into the mission schools, where they learnt carefully
selected texts of Scripture along with the multiplication-table. The
best of them were pushed on through Dublin University, and crowned the
hopes of their teachers by taking Holy Orders in the Church of England.
There are still to be met with in Galway and Mayo ancient peasants and
broken-down inhabitants of workhouses who speak with a certain pride
of 'my brother the minister.' There are also here and there in English
rectories elderly gentlemen who have almost forgotten the thatched
cottages where they ate their earliest potatoes.
Among these cleverer boys was one AEneas Conneally, who was something
more than clever. He was also religious in an intense and enthusiastic
manner, which puzzled his teachers while it pleased them. His ancestors
had lived for generations on a seaboard farm, watered by salt rain,
swept by misty storms. The famine and the fever that followed it left
him fatherless and brotherless. The emigration schemes robbed him and
his mother of their surviving relations. The mission school and the
missionary's charity effected the half conversion of the mother and a
whole-hearted acceptance of the new faith on the part of AEneas. Unlike
most of his fellows in the college classrooms, he refused to regard an
English curacy as the goal of his ambition. It seemed to him that his
conversion ought not to end in his parading the streets of Liverpool in
a black coat and a white tie. He wanted to return to his people and tell
them in their own tongue the Gospel which he had found so beautiful.
The London committee meditated on his request, and before they arrived
at a conclusion his mother died, having at the last moment made a
tardy submission to the Church she had denied. Her apostasy--so the
missionaries called it--confirmed the resolution of her son, and the
committee at length agreed to allow him to return to his native village
as the first Rector of the newly-created parish of Carrowkeel. He was
provided with all that seemed necessary to insure the success of
his work. They built him a gray house, low and strong, for it had to
withstand the gales which swept in from the Atlantic. They bought him
a field where a cow could graze, and an acre of bog to cut turf from. A
church was built for him, gray and strong, like his house. It was fitted
with comfortable pews, a pulpit, a reading-desk, and a movable table of
wood decently covered with a crimson cloth. Beyond the church stood the
school he had attended as a boy, whitewashed without and draped inside
with maps and illuminated texts. A salary, not princely but sufficient,
was voted to Mr. Conneally, and he was given authority over a
Scripture-reader and a schoolmaster. The whole group of mission
buildings--the rectory, the church, and the school--stood, like types
of the uncompromising spirit of Protestantism, upon the bare hillside,
swept by every storm, battered by the Atlantic spray. Below them
Carrowkeel, the village, cowered in such shelter as the sandhills
afforded. Eastward lonely cottages, faintly smoking dots in the
landscape, straggled away to the rugged bases of the mountains. The
Rev. AEneas Conneally entered upon his mission enthusiastically, and
the London committee awaited results. There were scarcely any results,
certainly none that could be considered satisfactory. The day for making
conversions was past, and the tide had set decisively against the new
reformation. A national school, started by a clearsighted priest, in
spite of his Archbishop, left the mission school almost without pupils.
The Scripture-reader lost heart, and took to seeking encouragement
in the public-house. He found it, and once when exalted--he said,
spiritually--paraded the streets cursing the Virgin Mary. Worse
followed, and the committee in London dismissed the man. A diminishing
income forced on them the necessity of economy, and no successor was
appointed. For a few years Mr. Conneally laboured on. Then a sharp-eyed
inspector from London discovered that the schoolmaster took very little
trouble about teaching, but displayed great talent in prompting his
children at examinations. He, too, was dismissed, and the committee,
still bent on economy, appointed a mistress in his place. She was a
pretty girl, and after she had shivered through the stormy nights of
two winters in the lonely school-house, Mr. Conneally married her.
Afterwards the office of school-teacher was also left vacant. The
whitewashed school fell gradually into decay, and the committee effected
a further saving.
After his marriage Mr. Conneally's missionary enthusiasm began to flag.
His contact with womanhood humanized him. The sternness of the reformer
died in him, and his neighbours, who never could comprehend his
religion, came to understand the man. They learned to look upon him as a
friend, to seek his sympathy and help. In time they learnt to love him.
Two years passed, and a son was born. The village people crowded upon
him with congratulations, and mothers of wide experience praised the boy
till Mrs. Conneally's heart swelled in her with pride. He was christened
Hyacinth, after a great pioneer and leader of the mission work. The
naming was Mr. Conneally's act of contrition for the forsaking of
his enthusiasm, his recognition of the value of a zeal which had not
flagged. Failing the attainment of greatness, the next best thing is to
dedicate a new life to a patron saint who has won the reward of those
who endure to the end. For two years more life in the glebe house was
rapturously happy. Such bliss has in it, no doubt, an element of sin,
and it is not good that it should endure. This was to be seen afterwards
in calmer times, though hardly at the moment when the break came. There
was a hope of a second child, a delightful time of expectation; then an
accident, the blighting of the hope, and in a few days the death of Mrs.
Conneally. Her husband buried her, digging the first grave in the rocky
ground that lay around the little church.
For a time Mr. Conneally was stunned by his sorrow. He stopped working
altogether, ceased to think, even to feel. Men avoided him with
instinctive reverence at first, and afterwards with fear, as he
wandered, muttering to himself, among the sandhills and along the beach.
After a while the power of thought and a sense of the outward things of
life returned to him. He found that an aged crone from the village had
established herself in his house, and was caring for Hyacinth. He let
her stay, and according to her abilities she cooked and washed for him
and the boy, neither asking wages nor taking orders from him, until she
died.
Hyacinth grew and throve amazingly. From morning till evening he was in
the village, among the boats beside the little pier, or in the fields,
when the men worked there. Everyone petted and loved him, from Father
Moran, the priest who had started the national school, down to old
Shamus, the crippled singer of interminable Irish songs and teller of
heroic legends of the past. It was when he heard the boy repeat a story
of Finn MacCool to the old crone in the kitchen that Mr. Conneally awoke
to the idea that he must educate his son. He began, naturally enough,
with Irish, for it was Irish, and not English, that Hyacinth spoke
fluently.
Afterwards the English alphabet followed, though not for the sake of
reading books, for except the Bible and the Prayer-Book Hyacinth was
taught to read no English books. He learned Latin after a fashion, not
with nice attention to complexities of syntax, but as a language meant
to be used, read, and even spoken now and then to Father Moran.
Meanwhile the passage of the years brought changes to Carrowkeel.
The Admiralty established a coastguard station near the village, and
arranged, for the greater security of the Empire, that men in blue-serge
clothes should take it in turns to look at the Atlantic through a
telescope. Then the unquiet spirit of the Congested Districts Board
possessed the place for a while. A young engineer designed a new pier to
shelter fishing-boats. He galvanized the people into unwonted activity,
and, though sceptical of good results, they earned a weekly wage by
building it. Boats came, great able boats, which fought the Atlantic,
and the old curraghs were left to blister in the sun far up on the
beach. Instructors from the Isle of Man taught new ways of catching
mackerel. Green patches between the cottages and the sea, once the
playground of pigs and children, or the marine parade of solemn lines
of geese, were spread with brown nets. On May mornings, if the take was
good, long lines of carts rattled down the road carrying the fish to
the railway at Clifden, and the place bore for a while the appearance
of vitality. A vagrant Englishman discovered that lobsters could be had
almost for the asking in Carrowkeel. The commercial instincts of his
race were aroused in him.
He established a trade between the villagers and the fishmongers of
Manchester. The price of lobsters rose to the unprecedented figure of
four shillings a dozen, and it was supposed that even so the promoter of
the scheme secured a profit.
To AEneas Conneally, growing quietly old, the changes meant very little.
The coastguards, being bound by one of the articles of the British
Constitution, came to church on Sunday mornings with exemplary
regularity, and each man at fixed intervals brought a baby to be
christened and a woman to be churched. Otherwise they hardly affected
Mr. Conneally's life. The great officials who visited Carrowkeel to
survey the benignant activities of the Congested Districts Board
were men whose magnificent intellectual powers raised them above any
recognised form of Christianity. Neither Father Moran's ministrations
nor Mr. Conneally's appealed to them.
The London committee of the mission to Roman Catholics made no inquiry
about what was going on at Carrowkeel. They asked for no statistics,
expected no results, but signed quarterly cheques for Mr. Conneally,
presuming, one may suppose, that if he had ceased to exist they would
somehow have heard of it.
By far the most important event for Hyacinth and his father was the
death of their old housekeeper. In the changed state of society in
Carrowkeel it was found impossible to secure the services of another.
Hyacinth, at this time about fifteen years old, took to the housework
without feeling that he was doing anything strange or unmanly. He was
familiar with the position of 'bachelor boys' who, having grown elderly
under the care of a mother, preferred afterwards the toil of their own
kitchens to the uncertain issue of marrying a girl to 'do for them.'
Life under their altered circumstances was simplified. It seemed
unnecessary to carry a meal from the room it was cooked in to another
for the purpose of eating it, so the front rooms of the house, with
their tattered furniture, were left to moulder quietly in the persistent
damp. One door was felt to be sufficient for the ingress and egress
of two people from a house. The kitchen door, being at the back of the
house, was oftenest the sheltered one, so the front door was bolted, and
the grass grew up to it. One by one, as Hyacinth's education required,
the Latin and Greek books were removed from the forsaken study, and
took their places among the diminishing array of plates and cups on the
kitchen dresser. The spreading and removal of a tablecloth for every
meal came to be regarded as foolish toil. When room was required on the
table for plates, the books and papers were swept on one side. A pile of
potatoes, and the pan, with bacon or a fish perhaps still frizzling in
it, was set in the place left vacant.
Morning and evening AEneas Conneally expected his son to join with him in
prayer. The two knelt together on the earthen floor facing the window,
while the old man meditated aloud on Divine things. There were breaks in
his speech and long silences, so that sometimes it was hard to tell
when his prayer had really ended. These devotions formed a part of
his father's life into which Hyacinth never really entered at all. He
neither rebelled nor mocked. He simply remained outside. So when his
father wandered off to solitary places on the seashore, and sat gazing
into the sunset or a gathering storm, Hyacinth neither followed nor
questioned him. Sometimes on winter nights when the wind howled more
fiercely than usual round the house, the old man would close the book
they read together, and repeat aloud long passages from the Apocalypse.
His voice, weak and wavering at first, would gather strength as he
proceeded, and the young man listened, stirred to vague emotion over the
fall of Babylon the Great.
For the most part Hyacinth's time was his own. Even the hours of study
were uncertain. He read when he liked, and his father seemed content
with long days of idleness followed by others of application. It was,
indeed, only owing to his love of what he read that the boy learned at
all. Often while he tramped from his home to the village at midday his
heart was hot within him with some great thought which had sprung to him
from a hastily construed chorus of Euripides. Sometimes he startled the
fishermen when he went with them at night by chanting Homer's rolling
hexameters through the darkness while the boat lay waiting, borne
gunwale down to the black water with the drag of the net that had been
shot.
There was a tacit understanding that Hyacinth, like his father, was
to take Holy Orders. He matriculated in Trinity College when he was
eighteen, and, as is often done by poorer students, remained at home,
merely passing the required examinations, until he took his degree,
and the time came for his entering the divinity school. Then it became
necessary for him to reside in Dublin, and the first great change in his
life took place.
The night before he left home he and his father sat together in the
kitchen after they had finished their evening meal. For a long time
neither of them spoke. Hyacinth held a book in his hand, but scarcely
attempted to read it. His thoughts wandered from hopeful expectation of
what the future was to bring him and the new life was to mean, to vague
regrets, weighted with misgivings, which would take no certain shape.
There crowded upon him recollections of busy autumn days when the grain
harvest overtook the belated hay-making, and men toiled till late in
the fields; of long nights in the springtime when he tugged at the
fishing-nets, and felt the mackerel slipping and flapping past his
feet in the darkness; of the longer winter nights when he joined the
gatherings of the boys and girls to dance jigs and reels on the earthen
floor of some kitchen. It seemed now that all this was past and over for
him. Holiday time would bring him back to Carrowkeel, but would it be
the same? Would he be the same?
He looked at his father, half hoping for sympathy; but the old man sat
gazing--it seemed to Hyacinth stupidly--into the fire. He wondered if
his father had forgotten that this was their last evening together. Then
suddenly, without raising his eyes, the old man began to speak, and it
appeared that he, too, was thinking of the change.
'I do not know, my son, what they will teach you in their school of
divinity. I have long ago forgotten all I learned there, and I have not
missed the knowledge. It does not seem to me now that what they taught
me has been of any help in getting to know Him.'
He paused for a long time. Hyacinth was familiar enough with his
father's ways of speech to know that the emphatic 'Him' meant the God
whom he worshipped.
'There is, I am sure, only one way in which we can become His friends.
_These are they which have come out of great tribulation!_ You remember
that, Hyacinth? That is the only way. You may be taught truths about
Him, but they matter very little. You have already great thoughts,
burning thoughts, but they will not of themselves bring you to Him. The
other way is the only way. Shall I wish it for you, my son? Shall I give
it to you for my blessing? May great tribulation come upon you in your
life! _Great tribulation!_ See how weak my faith is even now at the very
end. I cannot give you this blessing, although I know very well that it
is the only way. I know this, because I have been along this way myself,
and it has led me to Him.'
Again he paused. It did not seem to Hyacinth to be possible to say
anything. He was not sure in his heart that the friendship of the Man of
Sorrows was so well worth having that he would be content to pay for it
by accepting such a benediction from his father.
'I shall do this for you, Hyacinth: I shall pray that when the choice is
given you, the great choice between what is easy and what is hard, the
right decision may be made for you. I do not know in what form it will
come. Perhaps it will be as it was with me. He made the choice for me,
for indeed I could not have chosen for myself. He set my feet upon the
narrow way, forced me along it for a while, and now at the end I see His
face.'
Hyacinth had heard enough of the brief bliss of his father's married
life to understand. He caught for the first time a glimpse of the
meaning of the solitary life, the long prayers, and the meditations. He
was profoundly moved, but it did not even then seem to him desirable to
choose such a way, or to have such attainment thrust on him.
Next morning the autumn sunlight chased the recollection of his emotion
from his mind. The fishermen stopped his car as he drove through the
street to shake hands with him. Their wives shouted familiar blessings
from the cabin doors. Father Moran came bare-headed to the gate of his
presbytery garden and waved a farewell.
CHAPTER II
There is that about the material fabric, the actual stone and mortar, of
Trinity College, Dublin, which makes a vivid appeal to the imagination
of the common man. The cultured sentimentalist will not indeed be
able to lave his soul in tepid emotion while he walks through these
quadrangles, as he may among the cloisters and chapels of the Oxford
colleges. The amateur of the past cannot here stand at gaze before any
single building as he does before the weather-beaten front of Oriel,
tracing in imagination the footsteps of Newman or Arnold. Yet to the
average man, and far more to the newly emancipated schoolboy, Trinity
College, Dublin, makes an appeal which can hardly be ignored. In Oxford
and Cambridge town and University are mixed together; shops jostle and
elbow colleges in the streets. In Dublin a man leaves the city behind
him when he enters the college, passes completely out of the atmosphere
of the University when he steps on to the pavement. The physical
contrast is striking enough, appealing to the ear and the eye. The
rattle of the traffic, the jangling of cart bells, the inarticulate
babel of voices, suddenly cease when the archway of the great
entrance-gate is passed.
An immense silence takes their place. There is no longer any need for
watchfulness, nor risk of being hustled by the hurrying crowds.
Instead of footway and street crossing there are broad walks, untrodden
stretches of smooth grass. The heavy campanile is in front, and heights
of gray building frown down on each side. It needs no education, not
even any imagination, to appreciate the change. It is not necessary to
know that great scholars inhabited the place, to recall any name or
any man's career. The appeal is not to a recollected impression of the
Middle Ages, or indeed of any past, remote or near. It is the spirit of
scholarship itself, abstract, intangible, which creates this atmosphere.
Knowledge, a severe goddess, awes while she beckons.
Hyacinth Conneally had submitted himself to such emotions time after
time when, fresh from the wilds of Connemara, he made his way to the
examination-hall, an outside student in a borrowed cap and gown. Now,
when for the first time he entered into the actual life of the college,
could look up at windows of rooms that were his own, and reckon on his
privilege of fingering tomes from the shelves of the huge library, the
spirit of the place awed him anew. He neither analyzed nor attempted
an expression of what he felt, but his first night within the walls was
restless because of the inspiration which filled him.
Yet this college does not fail to make an appeal also to the thinking
mind, only it is a strange appeal, tending to sadness. The sudden
silence after the tumult of the streets has come for some minds to
be the symbol of a divorce between the knowledge within and the life
without. And this is not the separation which must always exist between
thought and action, the gulf fixed between the student and the merchant.
It is a real divorce between the nation and the University, between
the two kinds of life which ought, like man and woman, to complete each
other through their very diversity, but here have gone hopelessly apart.
Never once through all the centuries of Ireland's struggle to express
herself has the University felt the throb of her life. It is true
that Ireland's greatest patriots, from Swift to Davis, have been her
children; but she has never understood their spirit, never looked on
them as anything but strangers to her family. They have been to her
stray robber wasps, to be driven from the hive; while to the others they
have seemed cygnets among her duckling brood. It is very wonderful that
the University alone has been able to resist the glamour of Ireland's
past, and has failed to admire the persistency of her nationality.
There has surely been enough in every century that has passed since the
college was founded to win it over from alien thought and the ideals of
the foreigner.
All this Hyacinth came to feel afterwards, and learnt in bitterness of
spirit to be angry at the University's isolation from Irish life. At
first quite other thoughts crowded upon his mind. He felt a rebellion
against his father's estimate of what he was to learn. It seemed to him
that he had come into vital touch with the greatest life of all. He was
to join the ranks of those who besieged the ears of God for knowledge,
and left behind them to successors yet unborn great traditions of the
enigmas they had guessed. In entering upon the study of theology he
seemed to become a soldier in the sacred band, the elite of the army
which won and guarded truth. Already he was convinced that there could
be no greater science than the Divine one, no more inspiring moment in
life than this one when he took his first step towards the knowledge of
God.
He crossed the quadrangle with his mind full of such thoughts,
and joined a group of students round the door of one of the
examination-halls. It did not shock his sense of fitness that some of
his fellow-students in the great science wore shabby clothes, or that
others scorned the use of a razor. Bred as he had been at home, he felt
no incongruity between dirty collars and the study of divinity. It
was not until he caught scraps of conversation that he experienced an
awakening from his dream. One eager group surrounded a foreseeing youth
who had written the dates of the first four General Councils of the
Church upon his shirt-cuff.
'Read them out, like a good man,' said one.
'Hold on a minute,' said another, 'till I see if I have got them right.
I ground them up specially this morning. Nicaea, 318--no, hang it! that's
the number of Bishops who were present; 325 was the date, wasn't it?'
'What was the row about at Chalcedon?' asked a tall, pale youth. 'Didn't
some monk or other go for Cyril of Alexandria?'
'You'll be stuck anyhow, Tommy,' said a neat, dapper little man with a
very ragged gown.
Hyacinth slipped past the group, and approached two better dressed
students who stood apart from the others.
'Is this,' he asked, 'where the entrance examination to the divinity
school is to be held?'
For answer he received a curt 'Yes' and a stare. Apparently his suit of
brown Connemara homespun did not commend him to these aristocrats. They
turned their backs on him, and resumed their conversation.
'She was walking up and down the pier listening to the band with two
of the rankest outsiders you ever set eyes on--medicals out of Paddy
Dunn's. Of course I could do nothing else but break it off.'
'Oh, you were engaged to her, then? I didn't know.'
'Well, I was and I wasn't. Anyhow, I thought it better to have a clear
understanding. She came up to me outside the door of Patrick's on Sunday
afternoon just as if nothing had happened. "Hullo, Bob," says she;
"I haven't seen you for ages." "My name," said I, "is Mr. Banks"--just
like that, as cool as you please. I could see she felt it. "I've called
you Bob," says she, very red in the face, "and you've called me Maimie
ever since we went to Sunday-school together, and I'm not going to begin
calling you Mr. Banks now, my boy-o! so don't you think it!"'
It was a relief to Hyacinth when he was tapped on the arm by a boy with
a very pimply face, who thrust a paper into his hand, and distracted
his attention from the final discomfiture of Maimie, which Mr. Banks was
recounting in a clear, high-pitched voice, as if he wished everyone in
the neighbourhood to hear it.
'I hope you'll come,' said the boy.
'Where?'
'It's all in the paper. The students' prayer-meeting, held every
Wednesday morning at nine o'clock sharp. Special meeting to-morrow.'
Hyacinth was bewildered. There was something quite unfamiliar in this
prompt and business-like advertisement of prayer. The student with the
papers began to be doubtful of him.
'You're not High Church, are you?' he asked. 'We're not. We don't have
printed offices, with verses and responds, and that sort of thing. We
have extempore prayer by members of the union.'
'No; I'm not High Church,' said Hyacinth--'at least, I think not. I
don't really know much about these things. I'll be very glad to go to
your meeting.'
'That's right,' said the other. 'All are welcome. There will be special
prayer to-morrow for the success of the British arms. I suppose you
heard that old Kruger has sent an ultimatum. There will be war at once.'
There was a sudden movement among the students; gowns were pulled
straight and caps adjusted.
'Here he comes,' said someone.
Dr. Henry, the divinity professor, crossed the square rapidly. He was a
middle-aged man, stout, almost ponderous, in figure; but he held himself
rigidly upright, and walked fast across the square. The extreme neatness
of his clothes contrasted with the prevailing shabbiness of the students
and the assistant lecturers who followed him. Yet he did not seem to be
a man who gave to externals more than their due share of consideration.
His broad forehead gave promise of great intellectual power, a promise
half belied by the narrow gray eyes beneath it. These were eyes which
might see keenly, and would certainly see things just as they are,
though they were not likely to catch any glimpse of that greater
world where objects cannot be focussed sharply. Yet in them, an odd
contradiction, there lurked a possibility of humorous twinkling. The
man was capable perhaps of the broad tolerance of the great humorist,
certainly of very acute perception of life's minor incongruities. His
thin lips were habitually pressed together, giving a suggestion of
strength to the set of his mouth. A man with such a mouth can think and
act, but not feel either passionately or enduringly. He will direct men
because he knows his own mind, but is not likely to sway them because
he will always be master of himself, and will not become enslaved to
any great enthusiasm. The students trooped into the hall, and the
examination began. The assistant lecturers helped in the work. Each
student was called up in turn, asked a few questions, and given a
portion of the Greek Testament to translate. For the most part their
capacities were known beforehand. There were some who had won honours
in their University course before entering the divinity school. For
them the examiners were all smiles, and the business of the day was
understood to be perfunctory. Others were recognised as mere pass men,
whom it was necessary to spur to some exertion. A few, like Hyacinth,
were unknown. These were the poorer students who had not been able to
afford to reside at the University sooner than was absolutely necessary.
Their knowledge, generally scanty, was received by the examiners with
undisguised contempt. It fell to Hyacinth's lot to present himself to
Dr. Henry. He did so tremulously.
The professor inquired his name, and looked him over coldly.
'Read for me,' he said, handing him a Greek Testament. The passage
marked was St. Paul's great description of charity. It was very familiar
to Hyacinth, and he read it with a serious feeling for the words. Dr.
Henry, who at first had occupied himself with some figures on a sheet of
paper, looked up and listened attentively.
'Where were you at school,' he asked. 'Who taught you Greek?'
'My father taught me, sir.'
'Ah! You have got a very peculiar pronunciation, and you've made an
extraordinary number of mistakes in accentuation and quantity, but
you've read as if St. Paul meant something. Now translate.'
'You have given me,' he said, when Hyacinth had finished, 'the
Authorized Version word for word. Can you do no better than that?'
'I can do it differently,' said Hyacinth, 'not better.'
'Do you know any Greek outside of the New Testament?'
Hyacinth repeated a few lines from Homer.
'That book of the "Odyssey" is not in the college course,' said Dr.
Henry. 'How did you come to read it?'
Hyacinth had no explanation to give. He had read the book, it seemed,
without being forced, and without hope of getting a prize. He recited it
as if he liked it. The remainder of the examination disclosed the fact
that he was lamentably deficient in the rudiments of Greek grammar, and
had the very vaguest ideas of the history of the Church.
Afterwards Professor Henry discussed the new class with his assistants
as they crossed the square together.
'The usual lot,' said Dr. Spenser--'half a dozen scholars, perhaps one
man among them with real brains. The rest are either idlers or, what is
worse, duffers.'
'I hit on one man with brains,' said Dr. Henry.
'Oh! Thompson, I suppose. I saw that you took him. He did well in his
degree exam.'
'No,' said Dr. Henry; 'the man I mean has more brains than Thompson.
He's a man I never heard of before. His name is Conneally. He looks
as if he came up from the wilds somewhere. He has hands like an
agricultural labourer, and a brogue that I fancy comes from Galway.
But he's a man to keep an eye on. He may do something by-and-by if he
doesn't go off the lines. We must try and lick him into shape a bit.'
Hyacinth Conneally knew extremely little about the politics, foreign or
domestic, of the English nation. His father neither read newspapers nor
cared to discuss such rumours of the doings of Governments as happened
to reach Carrowkeel. On the other hand, he knew a good deal about
the history of Ireland, and the English were still for him the 'new
foreigners' whom Keating describes. His intercourse with the fishermen
and peasants of the Galway seaboard had intensified his vague dislike
of the series of oscillations between bullying and bribery which make up
the story of England's latest attempts to govern Ireland. Without in the
least understanding the reasons for the war in South Africa, he felt
a strong sympathy with the Boers. To him they seemed a small people
doomed, if they failed to defend themselves, to something like the
treatment which Ireland had received.
It was therefore with surprise, almost with horror, that he listened for
the first time to the superlative Imperialism of the Protestant Unionist
party when he attended the prayer-meeting to which he had been invited.
The room was well filled with students, who joined heartily in the
singing of 'Onward, Christian soldiers,' a hymn selected as appropriate
for the occasion. An address by the chairman, a Dublin clergyman,
followed. According to this gentleman the Boers were a psalm-singing
but hypocritical nation addicted to slave-driving. England, on the
other hand, was the pioneer of civilization, and the nursing-mother of
missionary enterprise. It was therefore clear that all good Christians
ought to pray for the success of the British arms. The speech bewildered
rather than irritated Hyacinth. The mind gasps for a time when immersed
suddenly in an entirely new view of things, and requires time to adjust
itself for pleasure or revolt, just as the body does when plunged into
cold water. It had never previously occurred to him that an Irishman
could regard England as anything but a pirate. Anger rapidly succeeded
his surprise while he listened to the prayers which followed. It was
apparently open to any student present to give utterance, as occasion
offered, to his desires, and a large number of young men availed
themselves of the opportunity. Some spoke briefly and haltingly, some
laboriously attempted to adapt the phraseology of the Prayer-Book to the
sentiment of the moment, a few had the gift of rapid and even eloquent
supplication. These last were the hardest to endure. They prefaced their
requests with fantastic eulogies of England's righteousness, designed
apparently for the edification of the audience present in the flesh, for
they invariably began by assuring the Almighty that He was well aware
of the facts, and generally apologized to Him for recapitulating
them. Hyacinth's anger increased as he heard the fervent groans which
expressed the unanimous conviction of the justice of the petitions. No
one seemed to think it possible that the right could be on the other
side.
When the meeting was over, the secretary, whose name, it appeared, was
Mackenzie, greeted Hyacinth warmly.
'Glad to have you with us,' he said. 'I hope you'll always come. I shall
be delighted to propose you as a member of the union. Subscription
one shilling, to defray necessary expenses. In any case, whether you
subscribe or not, we shall be glad to have you with us.'
'I shall never come again,' said Hyacinth.
Mackenzie drew back, astonished.
'Why not? Didn't you like the meeting? I thought it was capital--so
informal and hearty. Didn't you think it was hearty? But perhaps you are
High Church. Are you?'
Hyacinth remembered that this identical question had been put to him the
day before by the pimply-faced boy who distributed leaflets. He wondered
vaguely at the importance which attached to the nickname.
'I am not sure,' he said, 'that I quite know what you mean. You see, I
have only just entered the divinity school, and I hardly know anything
about theology. What is a High Churchman?'
'Oh, it doesn't require any theology to know that. It's the simplest
thing in the world. A High Churchman is--well, of course, a High
Churchman sings Gregorian chants, you know, and puts flowers on
the altar. There's more than that, of course. In fact, a High
Churchman------' He paused and then added with an air of victorious
conviction: 'But anyhow if you were High Church you would be sure to
know it.'
'Ah, well,' said Hyacinth, turning to leave the room, 'I don't know
anything about it, so I suppose I'm not High Church.'
Mackenzie, however, was not going to allow him to escape so easily.
'Hold on a minute. If you're not High Church why won't you come to our
meetings?'
'Because I can't join in your prayers when I am not at all sure that
England ought to win.'
'Good Lord!' said Mackenzie. It is possible to startle even the
secretary of a prayer union into mild profanity. 'You don't mean to tell
me you are a Pro-Boer, and you a divinity student?'
It had not hitherto struck Hyacinth that it was impossible to combine a
sufficient orthodoxy with a doubt about the invariable righteousness of
England's quarrels. Afterwards he came to understand the matter better.
CHAPTER III
Mackenzie was not at heart an ill-natured man, and he would have
repudiated with indignation the charge of being a mischief-maker. He
felt after his conversation with Hyacinth much as most men would if they
discovered an unsuspected case of small-pox among their acquaintances.
His first duty was to warn the society in which he moved of the
existence of a dangerous man, a violent and wicked rebel. He repeated
a slightly exaggerated version of what Hyacinth had said to everyone
he met. The pleasurable sense of personal importance which comes with
having a story to tell grew upon him, and he spent the greater part
of the day in seeking out fresh confidants to swell the chorus of his
commination.
In England at the time public opinion was roused to a fever heat of
patriotic enthusiasm, and the Irish Protestant Unionists were eager to
outdo even the music-halls in Imperialist sentiment, the students of
Trinity College being then, as ever, the 'death or glory' boys of
Irish loyalty. It is easy to imagine how Hyacinth's name was whispered
shudderingly in the reading-room of the library, how his sentiments were
anathematized in the dining-hall at commons, how plots were hatched for
the chastisement of his iniquity over the fire in the evenings, when
pipes were lit and tea was brewed.
At the end of the week Hyacinth was in an exceedingly uncomfortable
position. Outside the lecture-rooms nobody would speak to him. Inside he
found himself the solitary occupant of the bench he sat on--a position
of comparative physical comfort, for the other seats were crowded, but
not otherwise desirable. A great English poet had just composed a poem,
which a musician, no doubt equally eminent, had set to a noble tune.
It embodied an appeal for funds for purposes not clearly specified, and
hazarded the experiment of rhyming 'cook's son' with 'Duke's son,' which
in less fervent times might have provoked the criticism of the captious.
It became the fashion in college to chant this martial ode whenever
Hyacinth was seen approaching. It was thundered out by a choir who
marched in step up and down his staircase. Bars of it were softly
hummed in his ear while he tried to note the important truths which
the lecturers impressed upon their classes. One night five musicians
relieved each other at the task of playing the tune on a concertina
outside his door. They commenced briskly at eight o'clock in the
evening, and the final sleepy version only died away at six the next
morning.
Dr. Henry, who either did not know or chose to ignore the state of
the students' feelings, advised Hyacinth to become a member of the
Theological Debating Society. The election to membership, he said, was
a mere form, and nobody was ever excluded. Hyacinth sent his name to
the secretary, and was blackbeaned by an overwhelming majority of the
members. Shortly afterwards the Lord-lieutenant paid a visit to the
college, and the students seized the chance of displaying their loyalty
to the Throne and Constitution. They assembled outside the library,
which the representative of Queen Victoria was inspecting under the
guidance of the Provost and two of the senior Fellows. It is the nature
of the students of Trinity College to shout while they wait for the
development of interesting events, and on this occasion even the library
walls were insufficient to exclude the noise. The excellent nobleman
inside found himself obliged to cast round for original remarks about
the manuscript of the 'Book of Kells,' while the air was heavy with the
verses which commemorate the departure of 'fifty thousand fighting men'
to Table Bay. When at length he emerged on the library steps the tune
changed, as was right and proper, to 'God save the Queen.' Strangely
enough, Hyacinth had never before heard the national anthem. It is not
played or sung often by the natives of Connemara, and although the ocean
certainly forms part of the British Empire, the Atlantic waves have
not yet learned to beat out this particular melody. So it happened
that Hyacinth, without meaning to be offensive, omitted the ceremony of
removing his hat. A neighbour, joyful at the opportunity, snatched the
offending garment, and skimmed it far over the heads of the crowd. A few
hard kicks awakened Hyacinth more effectually to a sense of his crime,
and it was with a torn coat and many bruises that he escaped in the end
to the shelter of his rooms, less inclined to be loyal than when he left
them.
After a few weeks it became clear that the British armies in South
Africa were not going to reap that rich and unvarying crop of victories
which the valour of the soldiers and the ability of the generals
deserved. The indomitable spirit of the great nation rose to the
occasion, and the position of those who entertained doubts about the
justice of the original quarrel became more than ever unbearable.
Hyacinth took to wandering by himself through parts of the city in which
he was unlikely to meet any of his fellow-students. His soul grew bitter
within him. The course of petty persecution to which he was subjected
hardened his original sentimental sympathy with the Boer cause into a
clearly defined hatred of everything English. When he got clear of the
college and the hateful sound of the 'cook's son, Duke's son' tune, he
tramped along, gloating quietly over the news of the latest 'regrettable
incident.'
He was very lonely and friendless, for not even the discomfiture of his
enemies can make up to a young man for the want of a friend to speak to.
An inexpressible longing for home came over him. There was a shop in a
by-street which exposed photographs of Galway scenery in its windows for
a time. Hyacinth used to go day by day to gaze at them. The modest front
of the Gaelic League Hyce was another haunt of his. He used to stand
Debating his eyes on the Irish titles of the books in the window, and
repeating the words he read aloud to himself until the passers-by turned
to look at him. Once he entered a low-browed, dingy shop merely because
the owner's name was posted over the door in Gaelic characters. It was
one of those shops to be found in the back streets of most large towns
which devote themselves to a composite business, displaying newspapers,
apples, tobacco, and sweets for sale. The afternoon light, already
growing feeble in the open air, had almost deserted the interior of
the shop. At first Hyacinth saw nothing but an untidy red-haired
girl reading in a corner by the Ught of a candle. Ho asked her for
cigarettes. She rose, and laid her book and the candle on the counter.
It was one of O'Growney's Irish primers, dirty and pencilled. Hyacinth's
heart warmed to her at once. Was she not trying to learn the dear Irish
which the barefooted girls far away at home shouted to each other as
they dragged the seaweed up from the shore? Then from the far end of the
shop he heard a man's voice speaking Irish. It was not the soft liquid
tongue of the Connaught peasants, but a language more regular and
formal. The man spoke it as if it were a language he had learned,
comparatively slowly and with effort. Yet the sound of it seemed to
Hyacinth one of the sweetest things he had ever heard. Not even the
shrinking self-distrust which he had been taught by repeated snubbings
and protracted ostracism could prevent him from making himself known to
this stranger.
'The blessing of God upon Ireland!' he said.
There was not a moment's hesitation on the part of the stranger. The
sound of the Gaelic was enough for him. He stretched out both hands to
Hyacinth.
'Is it that you also are one of us--one of the Gaels?' he asked.
Hyacinth seized the outstretched hands and held them tight. The feeling
of offered friendship and companionship warmed him with a sudden glow.
He felt that his eyes were filling with tears, and that his voice would
break if he tried to speak, but he did not care at all. He poured out a
long Gaelic greeting, scarcely knowing what he said. Perhaps neither
the man whose hands he held nor the owner of the shop behind the counter
fully understood him, but they guessed at his feelings.
'Is it that you are a stranger here and lonely? Where is your home? What
name is there on you?'
'Maiseadh, I am a stranger indeed and lonely too,' said Hyacinth.
'You are a stranger no longer, then. We are all of us friends with each
other. You speak our own dear tongue, and that is enough to make us
friends.'
The tobacconist, it appeared, also spoke Irish of a kind. He cast
occasional remarks into the conversation which followed, less, it seemed
to Hyacinth, with a view of giving expression to any thought than for
the sake of airing some phrases which he had somewhat inadequately
learned. Indeed, it struck Hyacinth very soon that his new friend was
getting rather out of his depth in his 'own dear tongue.' At last the
tobacconist said with a smile:
'I'm afraid we must ask Mr. Conneally--didn't you say that Conneally was
your name?--to speak the Beurla. I'm clean beaten with the Gaelic, and
you can't go much further yourself, Cahal. Isn't that the truth, now.'
'And small blame to me,' said Cahal--in English, Charles--Maguire.
'After all, what am I but a learner? And it's clear that Mr. Conneally
has spoken it since ever he spoke at all.'
Hyacinth smiled and nodded. Maguire went on:
'What are you doing this afternoon? What do you say to coming round with
me to see Mary O'Dwyer? It's her "at home" day, and I'm just on my way
there.'
'But,' said Hyacinth, 'I don't know her. I can hardly go to her house,
can I?'
'Oh, I'll introduce you,' said Maguire cheerfully. 'She allows me to
bring anyone I like to see her. She likes to know anyone who loves
Ireland and speaks Gaelic. Perhaps we'll meet Finola too; she's often
there.'
'Meet who?'
'Finola. That's what we call Miss Goold--Augusta Goold, you know. We
call her Finola because she shelters the rest of us under her wings when
the Moyle gets tempestuous. You remember the story?'
'Of course I do,' said Hyacinth, who had learnt the tale of Lir's
daughter as other children do Jack the Giant-Killer. 'And who is Miss
O'Dwyer?'
'Oh, she writes verses. Surely you know them?'
Hyacinth shook his head.
'What a pity! We all admire them immensely. She has something nearly
every week in the _Croppy_. She has just brought out a volume of lyrics.
Her brother worked the publishing of it in New York. He is mixed up with
literary people there. You must have heard of him at all events. He's
Patrick O'Dwyer, one of the few who stood by O'Neill when he fought the
priests. He gave up the Parliamentary people after that. No honest man
could do anything else.'
He conducted Hyacinth to one of the old squares on the north side of the
city. When the tide of fashion set southwards, spreading terraces and
villas from Leeson Street to Killiney, it left behind some of the finest
houses in Dublin. Nowadays for a comparatively low rent it is possible
to live in a splendid house if you do not aspire to the glory of a smart
address. Miss O'Dwyer's house, for instance, boasted a spacious hall and
lofty sitting-rooms, with impressive ceilings and handsome fireplaces;
yet she paid for it little more than half the rent which a cramped villa
in Clyde Road would have cost her. Even so, it was somewhat of a mystery
to her friends how Miss O'Dwyer managed to live there. A solicitor who
had his offices on the ground-floor probably paid the rent of the whole
house; but the profits of verse-making are small, and a poetess, like
meaner women, requires food, clothes, and fire. Indeed, Miss O'Dwyer,
no longer 'M. O'D.,' whose verses adorned the _Croppy_, but 'Miranda,'
served an English paper as Irish correspondent. It was a pity that a
pen certainly capable of better things should have been employed
in describing the newest costume of the Lord Lieutenant's wife at
Punchestown, or the confection of pale-blue tulle which, draped round
Mrs. Chesney, adorned a Castle ball. Miss O'Dwyer herself was heartily
ashamed of the work, but it was, or appeared to her to be, necessary to
live, and even with the aid of occasional remittances from Patrick in
New York, she could scarcely have afforded her friends a cup of tea
without the guineas earned by torturing the English language in a
weekly chronicle of Irish society's clothes. Even with the help of such
earnings, poverty was for ever tapping her on the shoulder, and no one
except Mary herself and her one maid-servant knew how carefully fire
and light had to be economized in the splendid rooms where an extinct
aristocracy had held revels a century before.
Hyacinth and his friend advanced past the solicitor's doors, and up
the broad staircase as far as the drawing-room. For a time they got no
further than the threshold. The opening of the door was greeted with a
long-drawn and emphatic 'Hush!' from the company within. Maguire laid
his hand on Hyacinth's arm, and the two stood still looking into the
room. What was left of the feeble autumn twilight was almost excluded by
half-drawn curtains. No lamp was lit, and the fire cast only fitful rays
here and there through the room. It was with difficulty that Hyacinth
discerned figures in a semicircle, and a slim woman in a white dress
standing apart from the others near the fire. Then he heard a voice,
a singularly sweet voice, as it seemed to him, reciting with steady
emphasis on the syllables which marked the rhythm of the poem:
'Out there in the West, where the heavy gray clouds are
insistent,
Where the sky stoops to gather the earth into mournful
embraces,
Where the country lies saturate, sodden, round saturate
hamlets--
'Out there in the sunset where rages and surges Atlantic,
And the salt is commingled with rain over desolate beaches,
Thy heart, O beloved, is still beating--fitfully, feebly.
'Is beating--ah! not as it beat in the squadrons of Sarafield,
Exultantly, joyously, gladly, expectant of battle,
With throbs like the notes of the drums when men gather for
fighting.
'Beats still; but, ah! not as it beat in the latest Fitzgerald,
Nobly devote to his race's most noble tradition;
Or in Emmet or Davis, or, last on their list, in O'Brien.
'Beats fitfully, feebly. O desolate mother! O Erin!
When shall the pulse of thy life, which but flutters in
Connaucht,
Throb through thy meadows and boglands, and mountains and
cities?'
A subdued murmur of applause greeted the close of the recitation, and
praise more sincere than that with which politeness generally greets the
drawing-room performances of minor poets. Hyacinth joined in neither.
It seemed to him that the verses were too beautiful to speak about, so
sacred that praise was a kind of sacrilege. Perhaps some excuse may be
found for his emotion in the fact that for weeks he had heard no poetry
except the ode about 'wiping something off a slate.' The violence of the
contrast benumbed his critical faculty. So a man who was obliged to gaze
for a long time at the new churches erected in Belfast might afterwards
catch himself in the act of admiring the houses which the Congested
Districts Board builds in Connaught.
'I am afraid I must have bored you.' It was Miss O'Dwyer who greeted
him. 'I didn't see you and Mr. Maguire come in until I had commenced my
poor little poem. I ought to have given you some tea before I inflicted
it on you.'
'Oh,' said Hyacinth, 'it was beautiful. Is it really your own? Did you
write it?'
Miss O'Dwyer flushed. The vehement sincerity of his tone embarrassed
her, though she was accustomed to praise.
'You are very kind,' she said. 'All my friends here are far too kind to
me. But come now, I must give you some tea.'
The tea was nearly stone cold and weak with frequent waterings. The
saucer and spoon, possibly even the cup, had been used by someone else
before. Mr. Maguire secured for himself the last remaining morsel of
cake, leaving Hyacinth the choice between a gingerbread biscuit and
a torn slice of bread and butter. None of these things appeared to
embarrass Miss O'Dwyer. They did not matter in the least to Hyacinth.
'Do you know the West well?' he asked.
'Indeed, I do not. I've always longed to go and spend a whole long
summer there, but I've never had the chance.'
'Then how did you know it was like that? I mean, how did you catch the
spirit of it in your poem?'
'Did I?' she said. 'I am so glad. But I don't deserve any credit for
it. I wrote those verses after I had been looking at one of Jim Tynan's
pictures. You know them, of course? No? Oh, but you must go and see them
at once if you love the West. And you do, don't you?'
'It is my home,' said Hyacinth.
When he had finished his tea she introduced him to some of the people
who were in the room. Afterwards he came to know them, but the memories
which Miss O'Dwyer's verses called up in him made him absent and
preoccupied. He scarcely heard the names she spoke. Soon the party broke
up, and Hyacinth turned to look for Maguire.
'I'm afraid Mr. Maguire has gone,' said Miss O'Dwyer. 'He has a lecture
to attend this afternoon. You must come here again, Mr. Conneally. Come
next Wednesday--every Wednesday, if you like. We can have a talk about
the West. I shall want you to tell me all sorts of things. Perhaps
Finola will be here next week. She very often comes. I shall look
forward to introducing you to her. You are sure to admire her immensely.
We all do.'
'Yes, I've heard of her,' said Hyacinth. 'Mr. Maguire told me who she
was.'
'Oh, but he couldn't have told you half. She is magnificent. All the
rest of us are only little children compared to her. Now be sure you
come and meet her.'
CHAPTER IV
Ever since Pitt and Castlerea perpetrated their Act of Union two
political parties have struggled together in Ireland. Both of them have
been steadily prominent, so prominent that they have sometimes attracted
the attention of the English public, and drawn to their contest a little
quite unintelligent interest. The simplest and most discernible line
of division between them is a religious one. The Protestant party has
hitherto been guided and led by the gentry. It has been steadily loyal
to England and to the English Government. It has not been greatly
concerned about Ireland or Ireland's welfare, but has been consistently
anxious to preserve its own privileges, powers, and property. It has not
come well out of the struggle of the nineteenth century. Its Church has
been disestablished, its privileges and powers abolished, and the last
remnants of its property are being filched from it. It is a curious
piece of irony that this party should have hastened its own defeat
by the very policy adopted to secure victory. No doubt the Irish
aristocracy would have suffered less if they had been seditious instead
of loyal. The Roman Catholic party has been led by ecclesiastics, and
has always included the bulk of the people. Its leaders have not cared
for the welfare of Ireland any more than the Protestant party, but they
have always pretended that they did, being in this respect much wiser
than their opponents. They have pulled the strings of a whole series of
political movements, and made puppets dance on and off the stage as they
chose. Also they have understood how to deal with England. Unlike the
Protestant party, they have never been loyal, because they knew from the
first that England gives most to those who bully or worry her. They have
kept one object steadily in view, an object quite as selfish in reality
as that of the aristocracy--the aggrandisement of their Church. For
this they have been prepared at any time to sacrifice the interests
of Ireland, and are content at the present moment to watch the country
bleeding to death with entire complacency. The leaders of this party
enter upon the twentieth century in sight of their promised land. They
possess all the power and nearly all the wealth of Ireland. If the
Bishops can secure the continuance of English government for the next
half-century Ireland will have become the Church's property. Her
money will go to propagating the faith. Her children will supply the
English-speaking world with a superfluity of priests and nuns.
Outside both parties there have always been a few men united by no ties
of policy or religion, unless, as perhaps we may, we call patriotism
a kind of religion. Other lands have been loved sincerely, devotedly,
passionately, as mothers, wives, and mistresses are loved. Ireland alone
has been loved religiously, as men are taught to love God or the
saints. Her lovers have called themselves Catholic or Protestant: such
distinctions have not mattered to these men. They have scarcely ever
been able to form themselves into a party, never into a strong or a wise
party. They have been violent, desperate, frequently ridiculous, but
always sincere and unselfish. Their great weakness has lain in the fact
that they have had no consistent aim. Some of their leaders have looked
for a return to Ireland's Constitution, and built upon the watchword of
the volunteers, 'The King, the Lords, and the Commons of Ireland.' Some
have dreamed of a complete independence, of an Irish republic shaping
its own world policy. Some have wholly distrusted politics, and given
their strength to the intellectual, spiritual, or material regeneration
of the people. Among these men have been found the sanest practical
reformers and the wildest revolutionary dreamers. On the outskirts of
their company have hung all sorts of people. Parliamentary politicians
have leaned towards them, and been driven straightway out of public
life. Criminals have claimed fellowship with them, and brought
discredit upon honourable men. Poets and men of letters have drawn
their inspiration from their strivings, and in return have decked their
patriotism with imperishable splendour. In the future, no doubt,
the struggle will lie between this party and the hitherto victorious
hierarchy, with England for ally, and the fight seems a wholly unequal
one. It was into an advanced and vehement group of patriots that Mary
O'Dwyer introduced Hyacinth. He became a regular reader of the _Croppy_,
and made the acquaintance of most of the contributors to its pages. He
found them clever, enthusiastic, and agreeable men and women, but, as
he was forced to admit to himself, occasionally reckless. One evening a
discussion took place in Mary O'Dwyer's room which startled and shocked
him. Excitement ran high over the events of the war. The sympathies
of the 'Independent Irelanders,' as they called themselves, fiercely
assertive even in their name, were of course entirely with the Boers,
and they received every report of an English reverse with unmixed
satisfaction.
When Hyacinth entered the room he found four people there. Mary
O'Dwyer herself was making tea at a little table near the fire. Augusta
Goold--the famous Finola--was stretched in a deep chair smoking
a cigarette. She was a remarkable woman both physically and
intellectually. It was her delight to emphasize her splendid figure
by draping it in brilliant reds and yellows. To anyone who cared to
speculate on such a subject it seemed a mystery why her clothes remained
on her when she walked. The laws of gravity seemed to demand that they
should loosen with her movements, become detached, and finally drop
down. Nothing of the sort had ever happened, so it must be presumed that
she had secret and unconventional ways of fastening them. Similarly it
was not easy to see why her hair stayed upon her head. It was arranged
upon no recognised system, and suggested that she had perfected the art,
known generally only to heroines of romances, of twisting her tresses
with a single movement into a loose knot. That she affected white frills
of immense complexity was frequently evident, owing to the difficulty
she experienced in confining her long legs to feminine attitudes.
Her complexion put it in the power of her enemies to accuse her of
familiarity with cosmetics--a slander, for she had been observed to turn
green during an attack of sea-sickness. She had great brilliant eyes,
which were capable of expressing intensity of enthusiasm or hatred,
but no one had ever seen them soften with any emotion like love. Her
attitude towards social conventions was symbolized by her clothes. In
the old days, when the houses of 'society' had still been open to her,
she was accustomed to challenge criticism by fondling a pet monkey
at tea-parties. Since she had lost caste by taking up the cause of
'Independent Ireland' the ape had been discarded, and the same result
achieved by occasional bickerings with the police. She was an able
public speaker, and could convince her audiences for a time of the
reasonableness of opinions which next morning appeared to be the outcome
of delirium. She wrote, not, like Mary O'Dwyer, verse in which any
sentiment may be excused, but incisive and vigorous prose. Occasionally
even the Castle officials got glimmerings of the meaning of one of her
articles, and suppressed the whole issue of the _Croppy_ in which it
appeared.
Near her sat a much less remarkable person--Thomas Grealy, historian
and archaeologist. He had been engaged for many years on a history of
Ireland, but no volume of it had as yet appeared. His friends suspected
that he had got permanently stuck somewhere about the period of the
introduction of Christianity into the island. His essays, published in
the _Croppy_, dwelt with passionate regret on the departed glories
of Tara. He held strong views about the historical reality of the
Tuath-de-Danaan, and got irritated at the most casual mention of Dr.
Petrie's theory of the round towers. He had proved that King Arthur
was an Irishman, with whose reputation Malory and Tennyson had taken
unwarrantable liberties. The name of Dante brought a smile of contempt
to his lips, for he knew that the 'Purgatorio' was stolen shamelessly
from the works of a monk of Cong. He nourished a secret passion for
Finola. He never ventured to declare it, but his imagination endowed
every heroine, from Queen Maev down to the foster daughter of the
Leinster farmer who married King Cormac, with Miss Goold's figure, eyes
and hair. It was perhaps the burning of this passion which rendered him
so cadaverous that his clothes--in other respects also they looked as
if they had been bought in far-off happier days--hung round him like the
covering of a broken-ribbed umbrella.
The fourth person present was Timothy Halloran, who hovered about Mary
O'Dwyer's tea-table. He was what the country people call a 'spoilt
priest.' Destined by simple and pious parents to take Holy Orders, he
got as far as the inside of Maynooth College. While there he had kicked
a fellow-student down the whole length of a long corridor for telling
tales to the authorities. A committee of ecclesiastics considered the
case, and having come to the conclusion that he lacked vocation for
the priesthood, sent him home. Timothy was accustomed to say that his
violence might have been passed over, but that his failure to appreciate
the devotion to duty which inspired the tale-bearer marked him
decisively as unfit for ordination. He never regretted his expulsion,
although he complained bitterly that he had been nearly choked before
they cast him out. He meant, it is to be supposed, that the effort to
instil a proper reverence for dogma had almost destroyed his capacity
for thought, not that the fingers of the reverend professors had
actually closed around his windpipe. His subsequent experiences had
included a period of teaching in an English Board School, a brief, but
not wholly unsatisfactory, career as a political organizer in New
York, and a return to Ireland, where he earned a precarious living as a
journalist.
All four greeted Hyacinth warmly as he entered the room.
'We were just discussing,' said Mary O'Dwyer, 'the failure of our
attempt to organize a field hospital and a staff of nurses for the
Boers. It is a shame to have to admit that the English garrison in
Ireland can raise thousands of pounds for their war funds, and the Irish
can't be got to subscribe a few hundreds.'
'The wealth of the country,' said Grealy, 'is in the hands of a
minority--the so-called Loyalists.'
'Nonsense,' said Finola sharply. 'If you ever gave a thought to anything
more recent than the High-King's Court at Tara you would know that the
landlords are not the wealthy part of the community any longer. There's
many a provincial publican calling himself a Nationalist who could buy
up the nearest landlord and every Protestant in the parish along with
him. I'm a Protestant myself, born and bred among the class you speak
of, and I know.'
'You're quite right, Miss Goold,' said Tim. 'The people could have given
the money if they liked. I attribute the failure of the fund to the
apathy or treachery of the priests, call it which you like. There isn't
a Protestant church in the country where the parsons don't preach "Give
give, give" to their people Sunday after Sunday. And what's the result?
Why, they have raised thousands of pounds.'
'After the poem you published in last week's _Croppy_,' said Hyacinth
to Mary O'Dwyer, 'I made sure the subscriptions would have come in. Your
appeal was one of the most beautiful things I ever read. It would have
touched the heart of a stone.'
'Poetry is all well enough,' said Tim. 'I admire your verses, Mary,
as much as anyone, but we want a collection at every church door after
Mass. That's what we ought to have, but it's exactly what we won't get,
because the priests are West Britons at heart. They would pray for the
Queen and the army to-morrow, like Cardinal Vaughan, if they weren't
afraid.'
'I believe,' said Finola, 'that we went the wrong way about the thing
altogether. We asked for a hospital, and we appealed to the people's
pity for the wounded Boers. Nobody in Ireland cares a pin about
the Boers. Why on earth should we? From all I can hear they are a
narrow-minded, intolerant set of hypocrites. I'd just as soon read the
stuff some fool of an English newspaper man wrote about "our brother the
Boer" as listen to the maudlin sentiment our people talk. We don't want
to help the Boers. We want to hurt the English.'
'And you think----' said Grealy.
'I think,' went on Finola, 'that we ought to have asked for volunteers
to go out and fight, instead of nurses to cocker up the men who are
fools enough to get themselves shot. We'd have got them.'
'You would not,' said Tim. 'The clergy would have been dead against you.
They would have nipped the whole project in the bud without so much as
making a noise in doing it.'
'That's true,' said Grealy. 'Remember, Miss Goold, it was the priests
who cursed Tara, and the monks who broke the power of the Irish Kings. I
haven't worked the thing out yet, but I mean to show----'
Finola interrupted the poor man ruthlessly:
'Let's try it, anyway. Let's preach a crusade.'
'Not the least bit of good,' said Tim. 'Every blackguard in the country
is enlisted already in the Connaught Bangers or the Dublin Fusiliers,
or some confounded Militia regiment. There's nobody left but the nice,
respectable, goody-goody boys who wouldn't leave their mothers or miss
going to confession if you went down on your knees to them.'
'Well, then, the Irish troops ought to shoot their officers, and walk
over to the Boer camp,' said Finola savagely.
Hyacinth half smiled at what seemed to him a monstrous jest. Then, when
he perceived that she was actually in earnest, the smile froze into a
kind of grin. His hands trembled with the violence of his indignation.
'It would be devilish treachery,' he blurted out. 'The name of Irishman
will never be disgraced by such an act.'
Augusta Goold flung her cigarette into the grate, and rose from her
chair. She stood over Hyacinth, her hands clenched and her bosom heaving
rapidly. Her eyes blazed down into his until their scorn cowed him.
'There is no treachery possible for an Irishman,' she said, 'except
the one of fighting for England. Any deed against England--yes, _any_
deed--is glorious, and not shameful.'
Hyacinth was utterly quelled. He ventured upon no reply. Indeed, not
only did her violence render argument undesirable--and it seemed for
the moment that he would find himself in actual grips with a furious
Amazon--but her words carried with them a certain conviction. It
actually seemed to him while she spoke as if a good defence might be
made for Irish soldiers who murdered their officers and deserted to an
enemy in the field. It was not until hours afterwards, when the vivid
impression of Finola's face had faded from his recollection, when he had
begun to forget the flash of her eyes, the poise of her figure, and the
glow of her draperies, that his moral sense was able to reassert itself.
Then he knew that she had spoken wickedly. It might be right for an
Irishman to fight against England when he could. It might be justifiable
to seize the opportunity of England's embarrassment to make a bid for
freedom by striking a blow at the Empire. So far his conscience went
willingly, but that treachery and murder could ever be anything but
horrible he refused altogether to believe.
Another conversation in which he took part about this time helped
Hyacinth still further to understand the position of his new friends.
Tim Halloran and he were smoking and chatting together over the fire
when Maguire joined them.
'What's the matter with you?' asked Halloran. 'You look as if you'd been
at your mother's funeral.'
'You're not so far out in your guess,' said Maguire grimly. 'I spent the
morning at my sister's wedding. Would you like a bit of the cake?' He
produced from his pocket a paper containing crushed fragments of white
sugar and a shapeless mass of citron and currants. 'With the compliments
of the Reverend Mother,' he said. 'Try a bit.'
'What on earth do you mean?' said Hyacinth.
'Oh, I assure you the Sisters of Pity do these things in style,' said
Maguire. 'It's a pretty fancy, that of the wedding-cake, isn't it?
But you're a Protestant, Conneally; you don't understand this delicate
playfulness. I was present to-day at the reception of my only sister
into the Institute of the Catholic Sisters of Pity, founded by Honoria
Kavanagh. I've lost Birdie Maguire, that's all, the little girl that
used to climb on to my knee and kiss me, and instead of her there's a
Sister Monica Mary, who will no doubt pray for my soul when she's let.'
'What was the figure in her case?' asked Tim in a perfectly
matter-of-fact tone.
'Six hundred pounds,' said Maguire. 'It must have put the old man to the
pin of his collar to pay it. The only time he ever talked to me about
his affairs he told me he had got four hundred pounds put by for
Birdie's fortune, and that I was to have my medical course and whatever
the old shop would fetch when he was gone. They must have put the screw
on pretty tight to make him spring the extra two hundred. I dare say I
shall suffer for it in the end. He must have borrowed the money.'
Hyacinth felt intensely curious about this young nun. Like most
Protestants he had grown up to regard monasticism in all its forms as
something remote, partly horrible, wholly unintelligible.
'Why did she do it?' he asked. 'What sort of a girl was she? Do you mind
telling me?'
'Not in the least,' said Maguire. 'Only I'm not sure that I know. Three
years ago--that is, when I left home--she was the last sort of girl you
could imagine going into a convent. She was pretty, fond of nice clothes
and admiration, as keen as every girl ought to be on a dance. I never
supposed she had a thought of religion in her head--I mean, beyond the
usual confessions and attendances at Mass.'
'I suppose,' said Hyacinth, 'your people wanted it.'
'I don't think so,' said Maguire. 'Perhaps my mother did. I don't know.'
'You see, Conneally,' said Tim Halloran, 'it is a sort of hall-mark
of respectability among people like Maguire's to have a girl in a good
convent. A little lower down in the social scale, in the class I come
from, the boys are made priests. A doctor is a more expensive article to
manufacture, so Maguire's father selected that line of life for him. Not
that they could have made a priest of you, Maguire, in any case. You'd
have disgraced Maynooth, as I did.'
'I don't understand,' said Hyacinth. 'I thought a vocation for the life
was necessary.'
'Oh, so it is,' said Tim Halloran, 'but, you see, there's the period of
the novitiate. Given a girl at an impressionable age, the proper convent
atmosphere, and a prize of six hundred pounds for the Order, and it
will go hard with the Reverend Mother if she can't work the girl up to
a vocation. It takes a man a lifetime to make six hundred pounds in
a country shop, but there's many a one who does it by hard work and
self-denial; then down come the nuns and sweep it away, and it's
wasted. It ought to be invested in a local factory or in waterworks, or
gas-works, or fifty other things that would benefit the town it's made
in. It ought to be fructifying and bearing interest; instead of which
off it goes to Munich for stained glass, or to Italy for a marble altar.
Is it any wonder Ireland is crying out with poverty?'
'Yes,' said Maguire, 'and that's not the worst of it. I'd be content to
let them take the damned money and deck their churches with it, but the
girls--there are hundreds of them caught every year for nuns, and swept
out of life. It isn't the Irish convents alone that get them. American
nuns come over and Australian nuns, and they go round and round the
country picking up girls here and there, and carry them off. There,
I don't want to talk too much about it. The money is nothing, but the
girls and boys----'
'It seems strange to me,' said Hyacinth, 'that when you think that way
you should go on belonging to your Church.'
'Desert the Church!' said Maguire. 'We'll never do that. How could we
live without religion? And what other religion is there? I grant you
that your priests wouldn't rob us, but--but think of the cold of it.
You can't realize it, Conneally, but think what it would mean to
a Catholic--a religion without saints, without absolution, without
sacrifice. Besides, what we complain of is not Catholicism. It's a
parasitic growth destroying the true faith, defiling the Church.'
'Yes,' said Tim Halloran, 'and even from my point of view how should we
be the better of a change? Your Church is ruled by old women who think
the name of Englishman the most glorious in the world. You preach
loyalty, and I believe you pray for the Queen in your services. A nice
fool I would feel praying that the Queen should have victory over her
enemies.'
For a long time afterwards this conversation dwelt in Hyacinth's mind.
Tim Halloran he knew to be practically a freethinker, but Maguire
regularly heard Mass on Sundays, and often went to confession. It was a
puzzle how he could do so, feeling as he did about the religious Orders.
So insistent did the problem become to his mind that he found himself
continually leading the conversation round to it from one side or
another. Mary O'Dwyer told him that she also had a sister in a nunnery.
'She teaches girls to make lace, and wonderful work they do. She is
perfectly happy. I think her face is the sweetest and most beautiful
thing I have ever seen. There is not a line on it of care or of
fretfulness. It seems to me as if her whole life might be described as
a quiet smile. I always feel better by the mere recollection of her face
for a long time after I have visited her. Oh, I know it wouldn't do
for me. I couldn't stand it for a week. I should go mad with the quiet
restraint of it all. But my sister is happy. I can't forget that. I
suppose she has a vocation.'
'Vocation,' said Hyacinth thoughtfully. 'Yes, I can understand how that
would make all the difference. But how many of them have the vocation?'
'Don't you think vocation might be learnt? I mean mightn't one grow into
it, if one wished to very much, and if the life was constantly before
one's eyes, beautiful and calm?'
It was almost the same thought which Timothy Halloran had suggested.
Mary O'Dwyer spoke of growing into vocation, Tim of the working of it
up. Was there any difference except a verbal one?
On another occasion he spoke to Dr. Henry about the position of the
Church of Ireland in the country.
'We have proved,' said the professor, 'that the Roman claims have no
support in Scripture, history, or reason. Our books remain unanswered,
because they are unanswerable. We can do no more.'
'We might offer the Irish people a Church which they could join,' said
Hyacinth.
'We do. We offer them the Church of St. Patrick, the ancient, historic
Church of Ireland. We offer them the two Sacraments of the Gospel,
administered by priests duly ordained at the hands of an Episcopate
which goes back in an unbroken line to the Apostles. We present them the
three great creeds for their assent. We use a liturgy that is at once
ancient and pure. The Church of Ireland has all this, is beyond dispute
a branch of the great Catholic Church of Christ.'
'It may be all you say,' said Hyacinth, 'but it is not national. In
sentiment and sympathy it is English and not Irish.'
'I know what you mean,' said Dr. Henry. 'I think I understand how you
feel, but I cannot consent to the conclusion you want to draw. There
is no real meaning in the cry for nationality. It is a sentiment, a
fashion, and will pass. Even if it were genuine and enduring, I hold it
to be better for Ireland to be an integral part of a great Empire than a
contemptible and helpless item among the nations of the world, a prey to
the intrigues of ambitious foreign statesmen.'
Hyacinth sighed and turned to go, but Dr. Henry laid a hand upon his
shoulder and detained him.
'Conneally,' he said kindly, 'let me give you a word of advice. Don't
mix yourself up with your new friends too much. You will ruin your own
prospects in life if you do. There is nothing more fatal to a man among
the people with whom you and I are to live and work than the suspicion
of being tainted with Nationalist ideas. You can't be both a rebel and
a clergyman. You see,' he added with a smile, 'I take enough interest in
you to know who your friends are, and what you are thinking about.'
CHAPTER V
Augusta Goold's scheme for enrolling Irish volunteers to help the Boers
was duly set forth in the next issue of the _Croppy_. It included two
appeals--one for money and one for men. The details were worked out
with the frank contempt for possibility which characterizes some of the
famous suggestions of Dean Swift. She had the same faculty that he had
for bringing absurdities within the range of the commonplace; but there
was this difference between them--Miss Goold quite believed in her own
plans, while the great Dean no doubt grinned over the proof-sheets of
his 'Modest Proposal.'
It happened, most unfortunately, that the appeal synchronized with
another, also for funds, which was issued by Mr. O'Rourke, the leader
of the Parliamentary party. Since the death of John O'Neill the purse
of the party had been getting lean. The old tactics which used to draw
plaudits and dollars from the United States, as well as a tribute from
every parish in Ireland, had lately been unsuccessful. There were still
violent scenes in the House of Commons, but they no longer produced
anything except contemptuous smiles. Members of Parliament still
succeeded occasionally in getting the Chief Secretary to imprison them,
but the glory of martyrdom was harder to win than in the old days.
Latterly things had come to such a pass that even the reduced stipends
offered to the members fell into arrear. The attendance at Westminster
dropped away. The Government could afford to smile at Mr. O'Rourke's
efforts to make himself disagreeable, and the Opposition were frankly
contemptuous of a people who could not profit them by more than a dozen
votes in a critical division. It became impossible to wring even a
modest Land Bill from the Prime Minister, and Mr. Chesney, now much at
ease in the Secretary's office in the Castle, scarcely felt it necessary
to be civil to deputations which wanted railways. It was clear that
something must be done, or Mr. O'Rourke's business would disappear.
He decided to appeal for funds _orbi et urbi_. The world--in this case
North America--was to be visited, exhorted, and, it was hoped, taxed by
some of his most eloquent lieutenants. Even Canada, with its leaven
of Orangemen, was to be honoured with the speeches of an orator of
second-rate powers. The city--Dublin, of course--was the chosen scene of
the leader's personal exertions. Since his revolt against John O'Neill,
O'Rourke had been a little shy of Dublin audiences, but the pressing
nature of the present crisis almost forced him to pay his court to the
capital. He found some comfort in the recollection that during the five
years that had elapsed since O'Neill's death he had missed no public
opportunity of shedding tears beside his tomb. He remembered, too, that
he had put his name down for a large subscription towards the erection
of a statue to the dead leader, a work of art which the existing
generation seemed unlikely to have the pleasure of seeing.
Thus it happened that on the very day of the publication of Miss Goold's
scheme Mr. O'Rourke announced his intention of addressing an appeal for
funds to a public meeting in the Rotunda. Miss Goold was disconcerted
and irritated. She was well aware that Mr. O'Rourke's appeal would give
the respectable Nationalists an excellent excuse for ignoring hers, and
unfortunately the respectable people are just the ones who have most
money. She was confident that she could rely on the extreme section of
the Nationalists, and on that element in the city population which loves
and makes a row, but she could not count on the moneyed classes. They
were, so far as their words went, very enthusiastic for the Boer
cause; but when it came to writing cheques, it was likely that the
counter-attractions of the Parliamentary fund would prove too strong.
Since it seemed that Mr. O'Rourke would certainly spoil her collection,
the obvious thing to do was to try to spoil his. If he afforded people
an excuse for not paying the travelling expenses of her volunteers to
Lorenzo Marques, she would, if possible, suggest a way of escape from
paying for his men's journeys to London. After all, no one really wanted
to subscribe to either fund, and it might be supposed that the public
would very gladly keep their purses shut altogether.
For an Irishman it is quite possible to be genuinely enthusiastic and at
the same time able to see the humorous side of his own enthusiasm. This
is a reason why an Irishman is never a bore unless, to gain his private
ends, he wants to be. Even an Irish advocate of total abstinence, or an
Irish antivaccinationist, if such a thing exists, is not a bore,
because he will always trot out his conscientious objections with a
half-humorous, half-deprecating smile. This same capacity for avoiding
the slavery of serious fanaticism enables an Irishman to cease quite
joyfully from the pursuit of his own particular fad in order to corner
an obnoxious opponent. Thus Augusta Goold and her friends were genuinely
desirous of striking a blow at England, and really believed that their
volunteers might do it; but this did not prevent them from finding
infinite relish in the prospect of watching Mr. O'Rourke squirming on
the horns of a dilemma. They took counsel together, and the result of
their deliberations was peculiar. They proposed to invite Mr. O'Rourke
to join his appeal to theirs, to pool the money which came in, and to
divide it evenly between the volunteers and the members of Parliament.
It was Tim Halloran who hit upon the brilliant idea. Augusta Goold
chuckled over it as she grasped its consequences. Mr. O'Rourke, Tim
argued, would be unwilling to accept the proposal because he wanted all
the money he could get, more than was at all likely to be collected.
He would be equally unwilling to reject it, because he could then be
represented as indifferent to the heroic struggle of the Boers. In
the existing state of Irish and American opinion a suspicion of such
indifference would be quite sufficient to wreck his chances of getting
any money at all.
Of course, the obvious way of making such a proposal would have been by
letter to Mr. O'Rourke. Afterwards the correspondence--he must make a
reply of some sort--could be sent to the press, and sufficient publicity
would be given to the matter. This was what Tim Halloran wanted to do,
but such a course did not commend itself to Augusta Goold. It lacked
dramatic possibilities, and there was always the chance that the leading
papers might refuse to take any notice of the matter, or relegate
the letters to a back page and small print. Besides, a mere newspaper
controversy would not make a strong appeal to the section of the Dublin
populace on whose support she chiefly relied. A much more attractive
plan suggested itself. Augusta Goold, with a few friends to act as
aides-de-camp, would present herself to Mr. O'Rourke at his Rotunda
meeting, and put the proposal to him then and there in the presence of
the audience.
In the meantime the few days before the meeting were occupied in
scattering suggestive seed over the hoardings and blank walls of the
city. One morning people were startled by the sight of an immense
placard which asked in violent red letters, 'What is Ireland going
to do?' Public opinion was divided about the ultimate purpose of the
poster. The majority expected the announcement of a new play or novel;
a few held that a pill or a cocoa would be recommended. Next morning the
question became more explicit, and the hypothesis of the play and the
pill were excluded. 'What,' the new poster ran, 'is Ireland going to do
for the Boers?' The public were not intensely anxious to find an answer
to the conundrum thrust thus forcibly on their attention, but they
became curious to know who the advertisers were who hungered for the
information. Men blessed by Providence with sagacious-looking faces made
the most of their opportunity, and informed their friends that the thing
was a new dodge of O'Rourke's to get money. Their reputation suffered
when the next placard appeared. The advertisers had apparently changed
their minds, for what they now wanted to know was, 'What are the Irish
M.P.'s going to do for the Boers?' Clearly Mr. O'Rourke could have
nothing to gain by insisting on an answer to such a question. The public
were puzzled but pleased. The bill-stickers of the city foresaw
the possibility of realizing a competence, for the next morning the
satisfied inquirers published the result of their investigations. 'The
Em Pees '(it was thus that they now referred to the honourable members
of Parliament) 'are supporting the infamies of England.' It was at
this point that the eye of a Castle official was caught by one of the
placards as he made his way to the Kildare Street Club for luncheon.
He discussed the matter with a colleague, and it occurred to them that
since they were paid for governing Ireland, they ought to give the
public some value for their money, and seize the opportunity of doing
something. They sent a series of telegrams to Mr. Chesney's London
house, which were forwarded by his private secretary to the Riviera.
The replies which followed kept the Castle officials in a state of
pleasurable excitement until quite late in the evening. At about eight
o'clock large numbers of Metropolitan police sallied out of their
barracks and tore down the last batch of placards. Next morning fresh
ones were posted up, each of which bore the single word, 'Why?' The
bill-stickers were highly pleased, and many of them were arrested for
drunkenness. Mr. O'Rourke was much less pleased, for he began to guess
what the answer was likely to be, and how it would affect his chances of
securing a satisfactory collection. The officials were perplexed. They
suspected the 'Why?' of containing within its three letters some hideous
sedition, but it was not possible to deal vigorously with what might,
after all, be only the cunning novelty of some advertising manufacturer.
More telegrams harried Mr. Chesney, but before any definite course of
action had been decided on the morning of the Rotunda meeting arrived,
and with it an answer to the multifarious 'Whys': Because O'Rourke wants
all the money to spend in the London restaurants.' There was a great
deal of laughter, and many people, quite uninterested in politics,
determined to go to the meeting in hopes of more amusement.
When Mr. O'Rourke took the chair the hall was crowded to its utmost
capacity. Under ordinary circumstances this would have augured well for
the success of his appeal, for it showed that the public were at all
events not apathetic. On this particular occasion, however, Mr. O'Rourke
would have been better pleased with a smaller audience. The placards
had shown him that something unpleasant was likely to occur, though they
afforded no hint of the form which the unpleasantness would take. When
he rose to his feet he was greeted with the usual volley of cheers, and
although some rude remarks about the Boers were made in the corners of
the hall, they did not amount to anything like an organized attempt at
interruption. He began his speech cautiously, feeling the pulse of
his audience, and plying them with the well-worn platitudes of the
Nationalist platform. When these evoked the usual enthusiasm he waxed
bolder, and shot out some almost original epigrams directed against the
Government, working up to a really new gibe about officials who sat
like spiders spinning murderous webs in Dublin Castle. The audience
were delighted with this, but their joy reached its height when someone
shouted: 'You might speak better of the men who tore down the placard
on Wednesday.' Mr. O'Rourke ignored the suggestion, and passed on to
sharpen his wit upon the landlords. He described them as 'ill-omened
tax-gatherers who suck the life-blood of the country, and refuse to
disgorge a penny of it for any useful purpose.' Mr. O'Rourke was not a
man who shrank from a mixed metaphor, or paused to consider such trifles
as the unpleasantness which would ensue if anyone who had been sucking
blood were to repent and disgorge it. 'Where,' he went on to ask, 'do
they spend their immense revenues? Is it in Ireland?' Here he made one
of those dramatic pauses for which his oratory was famous. The audience
waited breathlessly for the denunciation which was to follow. They were
treated, unexpectedly, to a well-conceived anticlimax. A voice spoke
softly, but quite clearly, from the back of the hall:
'Bedad, and I shouldn't wonder if it was in the London restaurants.'
A roar of laughter followed. The orator might no doubt have made an
effective reply, but every time he opened his mouth minor wits, rending
like wolves the carcase of the original joke, yelled 'turtle-soup'
at him, or 'champagne and oysters.' He got angry, and consequently
flurried. He tried to quell the tumult by thundering out the
denunciation which he had prepared. But the delight which the audience
took in shrieking the items of their imaginary bill of fare was too much
for him. He forgot what he had meant to say, floundered, attempted to
pull himself together, and brought out the stale jest about providing
each landlord with a single ticket to Holyhead.
'And that same,' said his original tormentor, 'would be cheaper than
giving you a return ticket to London.'
The audience was immensely tickled. So far the entertainment, if not
precisely novel, was better than anything they had hoped for, and
everyone had an agreeable conviction that there was still something
in the way of a sensation in store. Perhaps it was eagerness for the
expected climax which induced them to keep tolerably quiet during the
remainder of Mr. O'Rourke's speech. He set forth at some length the
glorious achievements of his party in the past, and explained the
opportunities of future usefulness which lay to be grasped if only the
necessary funds were provided. He sat down to make way, as he assured
the audience, for certain tried and trusty soldiers of the cause who
were waiting to propose important resolutions. So far as these
warriors were concerned, he might as well have remained standing. Their
resolutions are to this day unproposed and uncommended--a secret joy,
no doubt, to those who framed them, but not endorsed by any popular
approval.
Hyacinth Conneally was not admitted to the secret councils of Augusta
Goold and her friends. He knew no more than the general public what kind
of a coup was meditated, but he gathered from Miss O'Dwyer's nervous
excitement and Tim Halloran's air of immense and mysterious importance
that something quite out of the common was likely to occur. By arriving
an hour and a half before the opening of the meeting he secured a seat
near the platform. He enjoyed the discomfiture of O'Rourke, whom he had
learnt from the pages of the _Croppy_ to despise as a mere windbag, and
to hate as the betrayer of O'Neill. A sudden thrill of excitement went
through him when O'Rourke sat down. The whole audience turned their
faces from the platform towards the door at the far end of the hall, and
Hyacinth, without knowing exactly what he expected, turned too.
There was a swaying visible among the crowd near the door, and almost
immediately it became clear that someone was trying to force a way
through the densely-packed people. Curses were to be heard, and even
cries from those who were being trodden on. At last a way was made.
Augusta Goold, followed by Grealy, Halloran, and Mary O'Dwyer, came
slowly up the hall towards the platform. Those of the audience whose
limbs had not been crushed or their feet mangled in preparation for her
progress cheered her wildly. Indeed, she made a regal appeal to them.
Even amidst a crowd of men her height made her conspicuous, and she had
arrayed herself for the occasion in a magnificent violet robe. It flowed
from her shoulders in spacious folds, and swept behind her, splendidly
contemptuous of the part it played as scavenger amid the accumulated
filth of the floor. Her bare arms shone out of the wide sleeves which
hung around them. Her neck rose strong and stately over the silver clasp
of a cloak which she had thrown back from her shoulders. She wore a hat
which seemed to hold her hair captive from falling loose around her. One
great tress alone escaped from it, and by some cunning manipulation was
made to stand straight out, as if blown by the wind from its fastenings.
In comparison her suite looked commonplace and mean. Poor Miss O'Dwyer
was arrayed--'gowned,' she would have said herself in reporting the
scene--in vesture not wanting in splendour, but which beside Miss
Goold's could not catch the eye. Thomas Grealy, awkward and stooped,
peered through his glasses at the crowd. Tim Halloran walked jauntily,
but his eyes glanced nervously from side to side. He was certainly ill
at ease, possibly frightened, at the position in which he found himself.
A hurried consultation took place among the gentlemen on the platform,
which ended in Mr. O'Rourke stepping forward with a smile and an
outstretched hand to welcome Augusta Goold as she ascended the steps.
The expression of his face belied the smile which he had impressed upon
his lips. His eyes had the same look of furtive malice as a dog's
which wants to bite but fears the stick. Augusta Goold waved aside the
proffered hand, and stepped unaided on to the platform. Mr. O'Rourke
placed a chair for her, but she ignored it and stood, with her followers
behind her, facing the audience. O'Rourke and two of his tried and
trusty members of Parliament approached her. They stood between her
and the audience, and talked to her for some time, apparently very
earnestly. Augusta Goold looked past them, over them, sometimes it
seemed through them, while they spoke, but made them no answer whatever.
At last Mr. O'Rourke shrugged his shoulders, and withdrew to his chair
with a sulky scowl.
'I wish,' said Augusta Goold, 'to ask a simple question of your
chairman.'
Mr. O'Rourke rose.
'This meeting,' he said, 'is convened for the purpose of raising funds
for the carrying on of the national business in the House of Commons. If
Miss Goold's question relates to the business in hand, I shall be most
happy to answer it. If not, I am afraid I cannot allow it to be asked
here. At another time and in another place I shall be prepared to listen
to what Miss Goold has to say, and in the meantime if she will take her
seat on the platform she will be heartily welcome.'
'My question,' said Augusta Goold, 'is intimately connected with the
business of the meeting. It is simply this: Are you, Mr. O'Rourke,
prepared to give any portion of the money entrusted to you by the Irish
people to assist the Boers in their struggle for freedom?'
It was manifestly absurd to ask such a question at all. Mr. O'Rourke
had no intention of collecting money for the Boers, who seemed to have
plenty of their own, and he could not without breach of trust have
applied funds subscribed to feed and clothe members of Parliament to
arming volunteers. Nevertheless, it was an awkward question to answer
in the presence of an audience excited by Augusta Goold's beauty and
splendid audacity. A really strong man, like, for instance, O'Rourke's
predecessor, John O'Neill, might have faced the situation, and won, if
not the immediate cheers, at least the respect of the Irish people. But
Mr. O'Rourke was not a strong man, and besides he was out of temper and
had lost his nerve. He took perhaps the worst course open to him: he
made a speech. He appealed to his past record as a Nationalist, and to
his publicly reiterated expressions of sympathy with the Boer cause.
He asked the audience to trust him to do what was right, but he neither
said Yes nor No to the question he was asked.
Augusta Goold stood calm and impassive while he spoke. A sneer gathered
on her lips and indrawn nostrils as he made his appeal for the people's
confidence. When he had finished she said, very slowly, and with that
extreme distinctness of articulation which women speakers seem to learn
so much more easily than men:
'Are you prepared to give any portion of the money entrusted to you by
the Irish people to assist the Boers in their struggle for freedom?'
Mr. O'Rourke was goaded into attempting another speech, but the audience
was in no mood to listen to him. He was interrupted again and again with
shouts of 'Yes or no!' 'Answer the question!' The bantering tone with
which they had plied him earlier in the evening with suggestions for a
menu had changed now into angry insistence. He passed his hand over his
forehead with a gesture of despair, and sat down. At once the tumult
ceased, and the people waited breathless for Augusta Goold to speak
again.
'Are you prepared'--she seemed to have learnt her question off by
heart--'to give any portion of the money entrusted to you by the Irish
people to assist the Boers in their struggle for freedom?'
Mr. Shea, a red-headed member of Parliament from Co. Limerick, being
himself one of those most deeply interested in the contents of the
party's purse, sprang to his feet. It was clear that he was in a
condition of almost dangerous excitement, for he stammered, as he
shouted to the chairman:
'Sir, is this--this--this woman to be allowed to interrupt the meeting?
I demand her immediate removal.'
Augusta Goold smiled at him. It was really a very gracious, almost a
tender, smile. One might imagine the divine Theodora in her earlier days
smiling with just such an expression on a plebeian lover whose passion
she regarded as creditable to him but hopeless.
'I assure you, Mr. Shea, that I shall not interrupt the business for
more than a minute. Mr. O'Rourke has only got to say one word--either
Yes or No. Are you prepared to give any portion of the funds entrusted
to you by the Irish people to assist the Boers in their struggle for
freedom?'
Mr. Shea was not at all mollified either by the smile or the politeness
of her tone.
'We shall not permit the meeting to be interrupted any more,' he
shouted. 'Either you will withdraw at once, or we shall have you removed
by force.'
She smiled at him again--a pitying smile, as if she regretted the
petulance of his manner, and turned to the chairman.
'Are you prepared to give----'
Then Mr. Shea's feelings became too strong for his self-control. He
sprang forward, apparently with the intention of laying violent hands
upon Augusta Groold. Hyacinth Conneally started up to protect her, and
the same impulse moved a large part of the audience. There was a rush
for the platform, and a fierce, threatening yell. Mr. Shea hung back,
frightened. Augusta Goold held up her hand, and immediately the rush
stopped and the people were silent. She went on with her question,
taking it up at the exact word which Mr. Shea had interrupted, in the
same level and exquisitely irritating tone.
'--Any of the money entrusted to you by the Irish people to assist the
Boers in their struggle for freedom?'
Mr. O'Rourke had sat scowling silently since the failure of his last
attempt to explain himself. This final disjointed repetition of the
galling question roused him to the necessity of doing something. He
was a pitiful sight as he rose and confronted Augusta Goold. There
were blotches of purple red and spaces of pallor on his face; his hands
twisted together; a sweat had broken out from his neck, and made his
collar limp. His words were a stammering mixture of bluster and appeal.
'You mustn't--mustn't--mustn't interrupt the meeting,' So far he tried
to assert himself, then, with a glance at the contemptuous face of the
woman before him, he relapsed into the tone of a schoolboy who begs off
the last strokes of a caning. 'Is this nice conduct? Is it ladylike to
come here and attack us like this? Miss Goold, I'm ashamed of you.'
'I am glad to hear,' said Augusta Goold, departing for the first time
from her question, 'that there is anything left in the world that Mr.
O'Rourke is ashamed of. I didn't think there was.'
It was Mr. Shea and not his leader who resented this last insult. His
lips drew apart, leaving his teeth bare in a ghastly grin. He clenched
his fists, and stood for a moment trembling from head to foot. Then he
leaped forward towards Augusta Goold. The man who stood next Hyacinth
lurched suddenly forward, wrenched his right hand free of the crowd
round him, and flung it back behind his head. Hyacinth saw that he held
a large stone in it.
'You are a cowardly blackguard, Shea,' he yelled--'a damned, cowardly
blackguard! Would you strike a woman?'
Shea turned on the instant, saw the hand stretched back to fling the
stone. He seized the chair behind him--the very chair which, while an
appearance of politeness was still possible, Mr. O'Rourke had offered
to Augusta Goold--and flung it with all his force at the man with the
stone. One of the legs grazed Hyacinth's cheek, scraping the skin
off. The corner of the seat struck the man beside him full across the
forehead just above his eyes. The blood poured out, blinding, and then,
as he gasped, choking him. He reeled and huddled together helplessly.
He could not fall, for the pressure of the crowd round him held him up.
Hyacinth felt his hands groping wildly as if for support, and reached
out his own to grasp him. But the man wanted no help for himself. As
soon as he felt another hand touch his he pressed the stone into it.
'I can't see,' he whispered hoarsely. 'Take it, you, and kill him, kill
him, kill him! smash his skull!'
Hyacinth took the stone. The feel of the man's blood warm on it and the
fierce yelling and stamping of the crowd filled him with a mad lust of
hate against Shea, who stood as if suddenly paralyzed within a few feet
of him. He wrenched his hand free, and with a mighty effort flung the
stone. He saw it strike Shea fair on the forehead. In spite of the
tumult around him, he fancied he heard the dull thud of its impact.
He saw Shea fling up his hands and pitch forward. He saw Augusta Goold
gather her skirts in her hand, and sweep them swiftly aside lest the man
should fall on them. Then the crowd pressing towards the platform swept
him off his feet, and he was tossed helplessly forward. A giddy
sickness seized him. The pressure slackened for an instant, and he fell.
Someone's boot struck him on the head. He felt without any keen regret
that he was likely to be trampled to death. Then he lost consciousness.
CHAPTER VI
Next morning the Dublin daily papers laid themselves out to make the
most of the sensational fight at the Rotunda. Even the habitually
cautious _Irish Times_ felt that the occasion justified the expression
of an opinion, and that there would be no serious risk of alienating the
sympathies of subscribers and advertisers by condemning the bloodshed.
It published an exceedingly dignified and stodgy leading article,
drawing the largest and finest words from the dictionary, and weaving
them with extraordinary art into sentences which would have been
creditable to anyone bent upon imitating the style of Dr. Samuel
Johnson. The British Empire and the whole of civilized Europe were
called upon to witness the unspeakably deplorable consequences which
invariably followed the habitual neglect of the cultivation of the
elementary decencies of public life. The paper disclaimed any sympathy
with either of the belligerent parties, and pointed out with sorrowful
solemnity that if the principles sedulously inculcated upon its readers
in its own columns were persistently flouted and contemned by those who
claimed the position of national representatives, little else except a
repetition at frequent intervals of the painful and humiliating
scenes of the night before could possibly be anticipated by reasonable
observers of the general trend of democratic institutions. The _Daily
Express_ openly exulted over the rioters. Its leading article--the
staff may have danced in a ring round the office table while composing
it--declared that now at length the Irish had proved to the world
that they were all, without a solitary exception, irredeemably
vicious corner-boys. Miss Augusta Goold was warmly praised for having
demonstrated once for all that 'patriotism' ought to be written 'Pat
riotism.' Deep regret was expressed that those who attended the meeting
had not been armed with revolvers instead of stones, and that the
platform had not been defended with Maxim guns instead of comparatively
innocuous wooden chairs. Had modern weapons of precision been used the
_Daily Express_ would have been able to congratulate mankind on getting
rid of quite a considerable number of Irishmen.
The _Freeman's Journal_ and the _Daily Independent_ were awkwardly
situated. Their sympathies were entirely with Mr. O'Rourke, and
they were exceedingly angry with Miss Goold for interfering with the
collection of funds for the Parliamentary party. At the same time,
they felt a difficulty in denouncing her, not for want of suitable
language--the Irish Nationalist press has a superb command of words
which a self-respecting dictionary would hesitate to recognise--but
because they felt that push of the horns of the dilemma on which
O'Roun'y-had been impaled, and they were obliged to sand their
denunciations between layers of stoutest pro-Boer sentiment.
All four papers contained reports of the proceedings which were
practically identical up to a certain point. It was about the
commencement of the actual bloodshed that they differed. The _Irish
Times_ reporter believed that Mr. Shea had begun the fray by striking
Augusta Goold behind the ear with his clenched fist. The _Daily Express_
man claimed to have overheard Mr. O'Rourke urging his friends to brain
a member of the audience with a chair. The _Freeman's Journal_ held that
Augusta Goold's supporters had come into the hall supplied with huge
stones, which, at a given signal, they had flung at the inoffensive
members of Parliament who occupied the platform, adding, as a
corroborative detail, that the lady who accompanied Augusta Goold
had twice kicked the prostrate Mr. Shea in the stomach. The _Daily
Independent_ advanced the ingenious theory that the contest had been
precipitated by a malevolent student of Trinity College, who had flung
an apple of discord--on this occasion a jagged paving-stone of unusual
size--into the midst of a group of ladies and gentlemen who were
peacefully discussing a slight difference of opinion among themselves.
Beyond this point none of the papers gave any account of the
proceedings, all four reporters having recognised that, not being
retained as war correspondents, they were not called upon to risk their
lives on the battlefield. The accounts all closed with the information
that the wounded had been carried to Jervis Street Hospital, and were
under treatment suitable to their injuries. Hyacinth had suffered a
slight concussion of the brain and a flesh wound. Other sufferers were
in the same ward, Mr. Shea himself occupying a bed, so that Hyacinth had
the satisfaction of seeing him stretched out, a melancholy figure,
with a bandage concealing most of his red hair. After the surgeon
had finished his rounds for the morning a police official visited the
sufferers, and made a careful note of their names and addresses. He
inquired in a perfunctory manner whether any of them wished to swear an
information. No one, except Mr. Shea, was sufficiently satisfied with
his own share of the meeting to wish for more fame than was unavoidable.
As no further use was ever made of Mr. Shea's narrative, it may be
presumed that the authorities regarded it as wanting in accuracy.
No blame, however, ought to be attached to the author for any petty
deviation from the truth of which he may have been guilty. No man's mind
is perfectly clear on the morning after he has been struck on the head
with a stone, and perhaps afterwards kicked twice in the stomach by a
lady journalist. Besides, all members of Parliament are, in virtue of
their office, 'honourable gentlemen.'
An excited and sympathetic nurse provided Hyacinth with copies of the
four morning papers, which he read with interest and a good deal of
amusement. Only the account in the _Daily Independent_ caused him any
uneasiness. No doubt, as he fully recognised, the suggestion about
the Trinity student was nothing but a wild guess on the part of the
reporter. It was highly unlikely that anyone would seriously consider a
theory so intrinsically improbable. Still, if the faintest suspicion of
the part he had played reached the ears of the college authorities, he
felt that his career as a divinity student was likely to be an extremely
brief one. His chief fear was that a prolonged absence from college
would give rise to inquiry, and that his bandages would excite suspicion
when he reappeared. Fortunately, the house surgeon decided that he was
sufficiently recovered to be allowed to leave the hospital early in the
afternoon. The boot which had put an end to his share in the riot had
raised its bruise under his hair, so he was able to remove the bandages
from his head as soon as he got into the street. There still remained a
long strip of plaster meant to keep a dressing of iodoform in its place
over the cut on his cheek which Mr. Shea's chair-leg had inflicted.
This he could not get off, and thinking it wiser to make his entry into
college after nightfall, he sought a refuge in Mary O'Dwyer's rooms.
He found the poetess laid on a sofa and clad in a blue dressing-gown.
She stretched a hand of welcome to Hyacinth, and then, before he had
time to take it, began to laugh immoderately. The laughing fit ended in
sobs, and then tears flowed from her eyes, which she mopped convulsively
with an already damp pocket-handkerchief. Before she had recovered
sufficient self-possession to speak, she signed to Hyacinth to fetch a
bottle of smelling-salts from the chimney-piece. He hastened to obey,
and found himself kneeling beside the sofa, holding the bottle to her
nose. After a while she recovered sufficiently to tell him that she had
not slept at all during the night, and felt extremely unwell and quite
unstrung in consequence. Another fit of immoderate and tearful laughter
followed, and Hyacinth, embarrassed and alarmed, fetched a tumbler of
soda-water from the syphon on the sideboard. The lady refused to
swallow any, and, just as he had made up his mind to risk an external
application, recovered again. During the lucid interval which followed
she informed him that his own conduct had been superb and heroic. What
seemed to be an effort to celebrate his achievements in extemporary
verse brought on another fit. Hyacinth determined to risk an appearance
in the college square in broad daylight rather than continue his
ministrations. While he was searching for his hat Miss O'Dwyer became
suddenly quite calm, and began to explain to him how immensely the cause
of Ireland's independence had benefited by the demonstration in the
Rotunda. Hyacinth listened anxiously, waiting for the next explosion,
and experienced very great relief when the door opened and Augusta Goold
walked in.
Unlike Mary O'Dwyer, she was entirely mistress of herself. Her cheeks
were not a shade paler than usual, nor her hand at all less cool and
firm. She stretched herself, after her usual fashion, in the largest
available chair and lit a cigarette.
'You look excited, my dear Mary,' she said--'a little overexcited,
perhaps. Have you had tea? No? Perhaps you will be so kind as to ring
the bell, Mr. Conneally.'
Mary O'Dwyer repeated the information she had given Hyacinth about her
sleepless night, and complimented Augusta Goold on her nerve.
'As for poor little me,' she went on, 'I'm like a--like a--you remember
the kind of thing, don't you?--like a--I'm not sure if I know the name
of the thing myself.'
She relapsed into a weak giggle, and Hyacinth stooped for the bottle of
smelling-salts, which had rolled under the sofa. Augusta Goold was much
less sympathetic. She fixed her with a strong stare of amazement and
disgust. Apparently this treatment was the right one, for the giggling
stopped almost immediately.
'I see you have got some sticking-plaster on your face, Mr. Conneally,'
she said, when Mary O'Dwyer had quieted down.
'Yes,' said Hyacinth, 'and a good-sized bump behind my ear.'
'I suppose this business will be very awkward for you in college. Will
they turn you out?'
'I'm sure they will if they find out that I threw that stone at Shea.'
'You made a very good shot,' said Augusta, smiling at the recollection.
'But how on earth did you come to have a stone that size in the hall
with you?'
Hyacinth told the story of the man who had been felled by the chair and
his murderous bequest.
'That's the proper spirit,' said Augusta. 'I admire that man, and he
couldn't have passed his stone on to better hands than yours. Shea went
down as if he had been shot. I was afraid of my life he would clutch at
my skirts as he fell or squirm up against me after he was down. But he
lay quite still. By the way, Mary, I suppose your dress was ruined?'
Mary O'Dwyer was quite subdued.
'It was torn,' she said meekly enough.
'Have you another one?'
'Of course I have. I've three others, besides some old ones.'
'Well, then, you'd better go and put on one of them. An old one will do.
It's disgusting to see a woman slopping about in a dressing-gown at this
time of day. I'll have tea ready when you come back.'
Miss O'Dwyer obeyed sulkily. She wished very much that Augusta Goold had
stopped at home. It would have been a great deal pleasanter to have gone
on practising hysterics with Hyacinth as a sympathetic spectator. When
the door was shut Augusta Goold turned to Hyacinth again.
'That's the worst of women'--apparently she did not consider herself as
one of the sex--'they are all right at the time (nothing could have
been better than Mary's behaviour at the meeting), but they collapse
afterwards in such idiotic ways. But I want to talk to you about
yourself. I owe you a good turn for what you did last night. Only for
you, I think Shea would have dared to touch me, and then very likely I
should have killed him, and there might have been trouble afterwards.'
She spoke quite calmly, but Hyacinth had very little doubt that she
meant exactly what she said. 'Grealy of course, was useless. One might
have expected him to give utterance to an ancient tribal war-cry, but he
didn't even do that. Tim Halloran got frightened when the row began. I
noticed him dodging about behind Mary and me, and I mean to let him know
what I think about him. It's you I have to thank, and I won't forget it.
If you get into trouble over this business in college, come to me, and
I will see you straight. In fact, if you like to give up the divinity
student business at once, I dare say I can put you in the way of earning
an honester livelihood.'
Hyacinth was gratified at the way Augusta Goold spoke to him. Since
the evening on which he had given his opinion about the morality of
desertion and murder he had been conscious of a coolness in her manner.
Now he had apparently reinstated himself in her good graces. Praise,
even for an act he was secretly ashamed of, and gratitude, though he
by no means recognised that he deserved it, were pleasant to him. He
promised to remember the offer of help, but declined for the present to
commit his future to the keeping of so bloodthirsty a patroness.
Curiously enough, Hyacinth's reception in college was a great deal more
cordial after the Rotunda meeting than it had ever been before. For a
while the battle which had been fought at their doors superseded the
remoter South African warfare as a topic of conversation among the
students. Their sympathies were with Augusta Goold. Even members of the
divinity classes suffered themselves to be lured from their habitual
worship of respectability so far as to express admiration for the
dramatic picturesqueness of the part she played. It is true that the
lady herself was called by names universally resented by women, and that
the broadest slanders were circulated about her character. Still, a halo
of glory hung round her. It was felt that she had done a surprisingly
courageous thing when she faced Mr. O'Rourke on his own platform. Also,
she had behaved with a certain dignity, neither throwing chairs nor
stones at her opponents. Then, she was an undeniably beautiful woman,
a fact which made its inevitable appeal to the young men. The mere
expression of sympathy with this flamboyant and scandal-smeared heroine
brought with it a delightful flavour of gay and worldly vice. It was
pretty well known that Hyacinth was a friend of Miss Goold's, and it
was rumoured that he had earned his piece of sticking-plaster in
her defence. No one knew exactly what he had done or how much he had
suffered, but a great many men were anxious to know. Very much to his
own surprise, he received a number of visitors in his rooms. Men who had
been the foremost of his tormentors came, ostensibly to inquire for his
health, in reality to glean details of the fight at the Rotunda. Certain
medical students of the kind which glory in any kind of row openly
congratulated him on his luck in being present on such an occasion. Men
who claimed to be fast, and tried to impress their acquaintances with
the belief that they indulged habitually in wild scenes of revelry,
courted Hyacinth, and boasted afterwards of their second-hand
acquaintance with Miss Goold. It became the fashion to be seen
arm-in-arm with him in the quadrangle, and to inquire from him in public
for 'Finola.'
This new popularity by no means pleased Hyacinth. He was not at all
proud of his share in the Rotunda meeting, and lived in daily dread of
being recognised as the assailant of Mr. Shea. He knew, too, that he was
making no way with the better class of students. The men whose faces
he liked were more than ever shy of making his acquaintance. The
sub-lecturers and minor professors in the divinity school were coldly
contemptuous in their manner, and it seemed to him that even Dr.
Henry was less friendly. He became desperately anxious to get out of a
position which he found more intolerable than the original isolation. He
applied himself with extreme diligence to his studies, even affecting
an interest, unnatural for the most pious, in the expositions given
by learned doctors of the Thirty-nine Articles. At lectures on Church
history he made notes about the vagaries of heretics so assiduously that
the professor began to hope that there existed one student at least
who took an interest in the Christological controversies of the sixth
century. He never ventured back again to the Wednesday prayer-meeting,
but he performed many attendances beyond the required minimum at the
college chapel. Morning after morning he dragged himself from his
bed and hurried across the dusky quadrangle to take his part in the
mutilated matins with which the college authorities see fit to usher
in the day. He even went to hear the sermons delivered on Friday
afternoons, homilies so painful that the preachers themselves recognise
an extraordinary merit in enduring them, and allow that submission of
the ears to one of them is to be reckoned as equal to two ordinary acts
of devotion.
It is to be hoped that Hyacinth derived some remote benefit from the
discipline to which he subjected himself, for the immediate results were
not satisfactory. He seemed no nearer winning the respect of the more
serious students, and Dr. Henry's manner showed no signs of softening
into friendliness. His surfeit of theology bred in him a dislike of the
subject. The solemn platitudes which were posed as expositions of the
creeds affected his mind much as the expurgated life histories of maiden
aunts do the newly-emancipated school-girl. The relentless closing in of
argument upon a single previously settled doctrine woke in him a desire
to break through at some point and breathe again in the open. He
began to fear that he was becoming hopelessly irreligious. His morning
devotions in the foggy atmosphere of the chapel did not touch the
capacity for enthusiasm within him. The vague splendour of his father's
meditations had left him outside, indeed, but sure that within there
lay a great reality. But now religion had come to seem an altogether
narrower thing, a fenced off, well-ordered garden in which useful
vegetables might be cultivated, but very little inspiring to the soul.
The unwelcome attention of the students whose friendship he did not
desire, and his increasing dislike for the work he was expected to do,
led him to spend more and more of his time with Augusta Goold and her
friends. He found in their society that note of enthusiasm which he
missed in the religion of the college. He responded warmly to their
passionate devotion to the dream of an independent Irish Republic. He
felt less conscious of his want of religion in their company. With the
exception of Augusta Goold herself, the members of the coterie were
professedly Roman Catholics; but this made little or no difference
in their intercourse with him. What he found in their ideals was a
substitute for religion, a space where his enthusiasm might extend
itself. He became, as he realized his own position clearly, very
doubtful whether he ought to continue his college course. It did not
seem likely that he would in the end be able to take Holy Orders, and
to remain in the divinity school without that intention was clearly
foolish. On the other hand, he shrank from inflicting what he knew would
be a painful disappointment on his father. It happened that before the
term ended his connection with the divinity school was cut in a way that
saved him from the responsibility of forming a decision.
He was a regular attendant at the lectures of Dr. Spenser, who had never
from the first disguised his dislike and contempt for Hyacinth. This
gentleman was one day explaining to his class the difference between
evidence which leads to a high degree of probability and a demonstration
which produces absolute certainty. The subject was a dry one, and quite
unsuited to Dr. Spenser, whose heart was set on maintaining a reputation
for caustic wit. He cast about for an illustration which would at once
make clear the distinction and enliven his lecture. His eye lit upon
Hyacinth, upon whose cheek there still burned a long red scar. Dr.
Spenser's face brightened.
'For instance, gentlemen,' he said, 'if I should reason from the fact
that our friend Mr. Conneally affects the society of certain charming
ladies of doubtful reputation, like Miss Goold, to the conclusion that
Mr. Conneally is himself a Nationalist, I should only have arrived at
a probable conclusion. The degree of probability might be very high;
still, I should have no right to regard my conclusion as absolutely
certain.'
The class tittered delightedly. Dr. Spenser proceeded without heeding a
deep flush on Hyacinth's face, which might have warned a wiser man that
an explosion was coming.
'If I should then proceed to reason thus: All Nationalists are rebels
and potential murderers--Mr. Conneally is a Nationalist; therefore Mr.
Conneally is a rebel and potential murderer--I should, assuming the
truth of my minor premise, have arrived at a certainty.'
The syllogism was greeted with loud applause. Hyacinth started to his
feet. For a time he could only gasp for breath to utter a reply, and
Dr. Spenser, secure in the conviction of his own intellectual and social
superiority to the son of a parson from Connemara, determined to pursue
his prey.
'Does Mr. Conneally,' he asked with a simper, 'propose to impugn the
accuracy of my induction or the logic of my deduction?'
The simper and the number of beautiful long words which Dr. Spenser had
succeeded in collecting together into one sentence provoked a sustained
clapping of hands and stamping of feet from the class. Hyacinth rapidly
regained his self-possession, and was surprised at his own coolness when
he replied:
'I should say, sir, that a man who makes an induction holding up a lady
to ridicule is probably a cad, and that the cad who makes a deduction
confusing patriotism with murder is certainly a fool.'
A report of Hyacinth's speech was handed to Dr. Henry, with a
suggestion that expulsion from the divinity school was the only suitable
punishment. Hyacinth did not look forward with any pleasure to the
interview to which he was summoned. He was agreeably surprised when he
entered the professor's room. Dr. Henry offered him a chair.
'I hear,' he said--his tone was severe, but a barely perceptible gleam
of humorous appreciation flashed across his eyes as he spoke--'that you
have been exceedingly insolent to Dr. Spenser.'
'I don't know, sir, whether you heard the whole story, but if you did
you will surely recognise that Dr. Spenser was gratuitously insulting to
me.'
'Quite so,' said Dr. Henry. 'I recognise that, but the question is, What
am I to do with you now? What would you do if you were in my place? I
should like to know your views of the best way out of the situation.'
Hyacinth was silent.
'You see,' Dr. Henry went on, 'we can't have our divinity lecturers
called fools and cads before their classes. I should be afraid myself
to deliver a lecture in your presence if I thought I was liable to that
kind of interruption.'
'I think, sir,' said Hyacinth, 'that the best thing will be for me to
leave the divinity school.'
'I think so, too. But leaving our divinity school need not mean that you
give up the idea of taking Holy Orders. I have a very high opinion of
your abilities, Conneally--so high that I should not like the Church to
lose your services. At the same time, you are not at present the kind
of man whom I could possibly recommend to any Irish Bishop. Your
Nationalist principles are an absolute bar to your working in the Church
of Ireland.'
'I wonder, sir, how you can call our Church the Church of Ireland, and
in the same breath say that there is no room for a Nationalist in her.
Don't the two things contradict each other.'
Dr. Henry's eyes twinkled again. There spread over his mouth a smile of
tolerant amusement.
'My dear boy, I'm not going to let you trap me into a discussion of that
question. Theoretically, I have no doubt you would make out an excellent
case. National Church, National spirit, National politics--Irish Church,
Irish nation, Irish ideas. They all go excellently together, don't they?
And yet the facts are as I state them. A Nationalist clergyman in
the Church of Ireland would be just as impossible as an English
Nonconformist in the Court of Louis Quatorze. After all, in this life
one has got to steer one's course among facts, and they're sharp things
which knock holes in the man who disregards them. Now, what I propose
to you is this: Put off your ordination for three years or so. Take
up schoolmastaring. I will undertake to get you a post in an English
school. Your politics won't matter over there, because no one will in
the least understand what you mean. Work hard, think hard, read hard.
Mix with the bigger world across the Channel. See England and realize
what England is and what her Empire means. Don't be angry with me for
saying that, long before the three years are over, you'll have come to
see that what you call patriotism is nothing else than parochialism of
a particularly narrow and uninstructed kind. Then come back here to me,
and I'll arrange for your ordination. You'll do the best of good work
when you've grown up a bit, and I'll see you a Bishop before I die.'
'I shall always be grateful to you,' said Hyacinth. 'I shall never
forget your kindness, and the way you've treated me; but I can't do what
you ask.'
'Oh, I'm not going to take no for an answer,' said Dr. Henry. 'Go home
to the West and think it over. Talk to your father about your future.
Write to me if you like about your plans, and remember my offer is open
six months or a year hence. You'll be the same man then that you are
now--I mean, in character. I'm not afraid of your turning out badly. You
may think wrong-headedly, but I'm sure you'll not act disgracefully.'
CHAPTER VII
The December afternoon was growing dark when the weary car-horse
surmounted the last hill on the road from Clifden and broke into a
shambling trot down the long straight stretch into Carrowkeel. Soon, as
the distance dwindled, the lights which twinkled here and there in the
village became distinguishable. This--Hyacinth recognised it--was the
great hanging lamp in the window of Rafferty's shop. That, a softer
glow, came from the forge of Killeen, the smith. That, and that, fainter
and more uncertain lights, were from fires seen through the open upper
section of cottage doors. He could almost tell whose the cabins were
where they shone. The scene inside rose to the imagination. A man with
ragged clothes and a half-empty pipe is squeezed into the stone nook
beside the blazing turf. The kettle, hanging from its hook, swings
steaming beside him. The woman of the house, barefooted, sluttish, in
torn crimson petticoat and gray bodice pinned across her breast, moves
the red cinders from the lid of the pot-oven and peers at the browning
cake within. Babies toddle or crawl over the greasy floor. The car
rattled into the village street. Men whom he knew stopped it to speak to
him. Children playing the last of their games in the fading light paused
to stare at him. Father Moran, returning to his presbytery, waved his
hand and shouted a greeting. He passed the last house of the village,
and could see the fishing-boats, dim and naked-looking, riding at their
anchors in the bay. Out beyond them, grim and terrible in the twilight,
lay the hulk where the ice for fish-packing was stored. The thick stump
of her one remaining mast made a blacker bar against the black sky. The
pier was deserted, but he could see the bulky stacks of fish-boxes piled
on it, and hear the water lapping against it. Along its utmost edge lay
a belt of gray white, where the waves broke as they surged round it. He
passed the pier, and there lay before him the long hill that led home.
The church and the ruined school stood out clearly on the skyline. Below
them, less clearly seen, was the rectory, and Hyacinth noted that the
lamp in the kitchen was lit. Then the door was opened, and he saw, plain
against the light, a man's figure, his father's. No doubt the old man
was watching and listening. Perhaps the sound of the wheels reached him
through the evening air, for in a few minutes he came out and walked
down the drive. Hyacinth saw him fumble with the fastening of the
rickety gate, and at last open it slowly and with difficulty. The car
reached a gap in the loose stone wall, a familiar gap, for across it lay
a short cut up a steeper part of the hill, which the road went round.
Hyacinth jumped down and ran up the path. In another minute the
greeting of father and son was accomplished, and the two were walking
hand-in-hand towards the house. Hyacinth noticed that his father
trembled, and that his feet stumbled uncertainly among the loose stones
and stiff weeds.
When they entered the lighted room he saw that his father seemed
older--many years older--than when he had said good-bye to him two
months before. His skin was very transparent, his lips were tremulous,
his eyes, after the first long look at his son, shifted feebly to the
fire, the table, and the floor.
'My dear son,' he said, 'I thank God that I have got you safe home
again. Indeed, it is good to see you again, Hyacinth, for it has been
very lonely while you were away. I have not been able to do very much
lately or to go out to the seashore, as I used to. Perhaps it is only
that I have not cared to. But I have tried hard to get everything ready
for your coming.'
He looked round the room with evident pride as he spoke. Hyacinth
followed his gaze, and it was with a sense of deep shame that he found
himself noticing the squalor of his home. The table was stained, and the
books which littered half of it were thick with dust and grease-spotted.
The earthen floor was damp and pitted here and there, so that the chairs
stood perilously among its inequalities. The fine white powder of turf
ashes lay thick upon the dresser. The whitewash above the fireplace was
blackened by the track of the smoke that had blown out of the chimney
and climbed up to the still blacker rafters of the roof. Hyacinth
remembered how he, and not his father, had been accustomed to clean the
room and wash the cups and plates. He wondered how such matters had been
managed in his absence, and a great sense of compassion filled his eyes
with tears as he thought of the painful struggle which the details
of life must have brought upon his father. He noted the evident
preparations for his coming. There were two eggs lying in a saucer ready
to be boiled, a fresh loaf--and this was not the day they got their
bread--and a small tin of cocoa beside his cup. The hearth was piled
with glowing turf, and the iron tripod with a saucepan on it stood
surrounded with red coals. Some sense of what Hyacinth was feeling
passed into his father's mind.
'Isn't it all right, my son? I tried to make it very nice for you. I
wanted to get Maggie Cassidy up from the village for the day, but her
baby had the chin-cough, and she couldn't come.'
He took Hyacinth's hand and held it while he spoke.
'Perhaps it looks poor to you,' he went on, 'after your college rooms
and the houses your friends live in; but it's your own home, son, isn't
it?'
Hyacinth made a gulp at the emotion which had brought him near to tears.
'It's splendid, father--simply splendid. And now I'm going to boil those
two eggs and make the cocoa, and we'll have a feast. Hallo! you've got
some jam--jam and butter and eggs, and this is the month of December,
when there's hardly a hen laying or a cow milking in the whole parish!'
He held up the jam-pot as he spoke. It was wrapped in dingy red paper,
and had a mouldy damp stain on one side. Hyacinth recognised the mark,
and remembered that he had seen the identical pot on the upper shelf of
Rafferty's shop for years. Its label bore an inscription only vaguely
prophetic of the contents--'Irish Household Jam.'
'That's right, father, you are supporting home manufacture. I declare
I wouldn't have tasted it if it had come from England. You see, I'm a
greater patriot than ever.'
Old Mr. Gonneally smiled in a feeble, wavering way. He seemed scarcely
to understand what was being said to him, but he found a quiet pleasure
in the sound of his son's voice. He settled himself in a chair by the
fireside and watched contentedly while Hyacinth put the eggs into the
saucepan, hung the kettle on its hook, and cut slices of bread. Then the
meal was eaten, Hyacinth after his long drive finding a relish even in
the household jam. He plied his father with questions, and heard what
the old man knew of the gossip of the village--how Thady Durkan had
broken his arm, and talked of giving up the fishing; how the police from
Letter-frack had found, or said they found, a whisky-still behind the
old castle; how a Gaelic League organizer had come round persuading the
people to sing and dance at the Galway Feis.
After supper Hyacinth nerved himself to tell the story of his term in
college, and his determination to leave the divinity school. More than
once he made an effort to begin, but the old man, who brightened a
little during their meal, relapsed again into dreaminess, and did not
seem to be listening to him. They pulled their chairs near to the fire,
and Mr. Conneally sat holding his son's hand fast. Sometimes he stroked
or patted it gently, but otherwise he seemed scarcely to recognise
that he was not alone. His eyes were fixed on the fire, but they stared
strangely, as if they saw something afar off, something not in the
room at all. There was no response in them when Hyacinth spoke, and no
intelligence. From time to time his lips moved slightly as if they were
forming words, but he said nothing. After awhile Hyacinth gave up the
attempt to tell his story, and sat silent for so long that in the end he
was startled when his father spoke.
'Hyacinth, my son, I have somewhat to say unto you.' Before Hyacinth
could reply to him he continued: 'And the young man answered and said
unto him, "Say on." And the old man lifted up his voice and said unto
his son, "He that hath ears to hear, let him hear."'
He spoke as if he were reading out of a book some narrative from the
Bible. Hyacinth realized suddenly that the communication which was to
be made to him had been rehearsed by his father alone, again and again,
that statement, question and reply, would follow each other in
due sequence from the same lips. He felt that his father was still
rehearsing, and had forgotten the real presence of his son. He grasped
the hand that held him and shook it, saying sharply:
'Father, father, I am here. Don't you know me?'
'Yes, yes, my son. Surely I know you. There is something I want to tell
you. I have wanted to tell it to you for many days. I am glad that you
are here now to listen to it.'
He paused, and Hyacinth feared that he would relapse again into dreamy
insensibility; but he did not.
'I think,' he said, 'that I should like to pray before I speak to you.'
He knelt down as Hyacinth had seen him kneel a thousand times before,
facing the eastward-looking window, now a black, uncurtained square in
the whitewashed wall. What he said was almost unintelligible. There was
no petition nor even any sequence of ideas which could be traced.
He poured forth a series of ejaculations expressive of intense and
rapturous delight, very strange to listen to in such a place and from
an old man's lips. Then the language he spoke changed from English
into Gaelic, and there came a kind of hymn of adoration. His sentences
followed each other in metrical balance like the Latin of the old
liturgies, and suited themselves naturally to a subdued melody, half
chant, half cry, like the mourning of the keeners round a grave. At
last, rising from his knees, he spoke, and his voice became wholly
unemotional, devoid of fervour or excitement. He told his story as a man
might relate some quite commonplace incident of daily life.
'One evening I was sitting here by the fire, just as I always sit. I
remember that the lamp was not lit, and that the fire was low, so that
there was not much light in the room. It came into my mind that it was
just out of such gloom that the Lord called "Samuel, Samuel," and I
wished that I was like Samuel, so innocent that I could hear the voice
of the Lord. I do not remember what I thought of after that. Perhaps for
a time I did not think at all. Then I felt that there were arms about my
neck; but not like your arms, Hyacinth, when you were a child and clung
to me. These were arms which held me lovingly, strongly, protectingly,
like--do you remember, Hyacinth?--"His right hand is under my head; His
left hand doth embrace me." I sat quite still, and did not move or speak
or even breathe, lest He should go away from me. Then, after a long
time--I knew afterwards that the time was long, though then it seemed
only a minute for the joy that I had in it--He told me--I do not mean
that I heard a voice or any words; I did not hear, I _felt_ Him tell
me--the things that are to be. The last great fight, the Armageddon,
draweth very near. All that is good is on one side in the fight, and the
Captain over all. What is bad is on the other side--all kinds of tyranny
and greed and lust. I did not hear these words, but I felt the things,
only without any fear, for round me were the everlasting arms. And
the battlefield is Ireland, our dear Ireland which we love. All these
centuries since the great saints died He has kept Ireland to be His
battlefield. I understood then how our people have been saved from
riches and from power and from the opportunities of lust, that our soil
out of all the world might be fit for the feet of the great Captain, for
the marching of His horsemen and His chariots. Not even when I knew all
this did I desire to share in the conflict. I am old and feeble, but
that is not the reason why there was no desire on me, for strength is in
His power to give to whom He wills. I did not desire it, because I was
quite happy, being safe with Him.'
For a long time after he ceased speaking there was silence, for Hyacinth
had no comment to offer. At last the old man spoke again.
'That is all. I have no other word of revelation. But I have wondered
since how men are to be disentangled from their parties and their
churches and their nations, and gathered simply into good and bad. Will
all men who are good just know the Captain when they see Him and range
themselves with Him? But why should we think about such things as these?
Doubtless He can order them. But you, Hyacinth--will you be sure to know
the good side from the bad, the Captain from the enemy?'
For a long time after he had gone to bed Hyacinth lay awake haunted by
his father's prophecy of an Armageddon. There was that in his nature
which responded eagerly to such a call to battle. In the presence of
enthusiasm like his father's or like Augusta Goold's, Hyacinth
caught fire. His mind flamed with the idea of an Independent Ireland
resplendent with her ancient glories. He embraced no less eagerly the
thought of his father's battle and his own part in it. Groping for
points of contact between the two enthusiasms, he caught at the
conception of the Roman Church as the Antichrist and her power in
Ireland as the point round which the fight must rage. Then with a sudden
flash he saw, not Rome, but the British Empire, as the embodiment of
the power of darkness. He had learned to think of it as a force, greedy,
materialistic, tyrannous, grossly hypocritical. What more was required
to satisfy the conception of evil that he sought for? He remembered
all that he had ever heard from Augusta Goold and her friends about the
shameless trickery of English statesmen, about the insatiable greed of
the merchants, about the degraded sensuality of the workers. He recalled
the blatant boastfulness with which English demagogues claimed to be
the sole possessors of enlightened consciences, and the tales of
native races exploited, gin-poisoned, and annihilated by pioneers of
civilization advancing with Bibles in their hands.
But with all his capacity for enthusiasm there was a strain of weakness
in Hyacinth. More than once after the glories of an Independent Ireland
had been preached to him he had found himself growing suddenly cold and
dejected, smitten by an east wind of common-sense. At the time when he
first recognised the loftiness of his father's religion he had revolted
against being called upon to adopt so fantastic a creed. So now, when
his mind grew weary with the endeavour to set an Armageddon in array, he
began to wish for a life of peaceful monotony, a place to be quiet in,
where no high calls or imperious demands would come to threaten him.
He ceased to toss to and fro, and gradually sank into a half-conscious
sleep. It seemed to him at the time that he was still awake, held back
from slumber by the great stillness of the country, that silence which
disturbs ears long accustomed to the continuous roar of towns. Suddenly
he started into perfect wakefulness, and felt that he was in possession
of all his faculties. The room where he lay was quite dark, but he
strained his eyes to see something in it. He listened intently, although
no sound whatever met his ears. A great overmastering fear laid hold on
him. He tried to reason with himself, insisting that there was nothing,
and could be nothing, to be afraid of. Still the fear remained. His
lips grew stiff and painfully hot, and when he tried to moisten them his
tongue was dry and moved across them raspingly. He struggled with the
terror that paralyzed him, and by a great effort raised his hand to his
forehead. It was damp and cold, and the hair above it was damp. He had
no way of knowing how much of the night had passed, or even how long he
lay rigid, unable to breathe without a kind of pain; but suddenly as it
had come the terror left him, left him without any effort on his part or
any reason that he recognised. Then the window of his room shook, and he
heard outside the low moan of the rising wind. Some heavy drops of rain
struck audibly on the roof, and the first gust of the storm carried to
his ears the sound of waves beating on the rocks. His senses strained no
more. His eyes closed, and he sank quietly into a long dreamless sleep.
It was late when he woke, so late that the winter sky was fully lit. The
wind, whose first gusts had lulled him to sleep, had risen to a gale,
and the rain, mixed with salt spray, beat fiercely against his window
and on the roof. He listened, expecting to hear his father moving in the
room below, but within the house there was no sound. He rose, vaguely
anxious, and without waiting to dress went into the kitchen. Everything
lay untouched, just as he had left it the night before. The lamp and
the remnants of the meal were on the table. The two chairs stood side
by side before the hearth, where the fire which he had covered up
smouldered feebly. He turned and went to his father's room. He could
not have explained how it was, but when he opened the door he was not
surprised to see the old man lying quite still, dead, upon the bed. His
face was turned upwards, and on it was that strange look of emotionless
peace which rests very often on the faces of the dead. It seemed
to Hyacinth quite natural that the soul as it departed into unknown
beatitude should have printed this for the last expression on the
earthly habitation which it left behind. He neither wondered nor, at
first, sorrowed very much to see his father dead. His sight was undimmed
and his hands steady when he closed the eyes and composed the limbs of
the body on the bed. Afterwards it seemed strange to him that he should
have dressed quietly, arranged the furniture in the kitchen, and blown
the fire into a blaze before he went down into the village to tell his
news and seek for help.
They buried AEneas Conneally beside his wife in the wind-swept
churchyard. The fishermen carried his coffin into the church and out
again to the grave. Father Moran himself stood by bareheaded while the
clergyman from Clifden read the prayers and sprinkled the coffin-lid
with the clay which symbolized the return of earth to earth and dust to
dust. In the presence of death, and, with the recollection of the simple
goodness of the man who was gone, priest and people alike forgot for an
hour the endless strife between his creed and theirs.
CHAPTER VIII
In Connaught the upper middle classes, clergy, doctors, lawyers, police
officers, bank officials, and so forth, are all strangers in the land.
Each of them looks forward to a promotion which will enable him to move
to some more congenial part of Ireland. A Dublin suburb is the ideal
residence; failing that, the next best thing is a country town within
easy reach of the metropolis. Most of them sooner or later achieve a
promotion, but some of them are so unfortunate as to die in their exile.
In either case their furniture and effects are auctioned. No one ever
removes his goods from Con-naught, because the cost of getting things
to any other part of Ireland is exorbitant, and also because tables
and chairs fetch very high prices at auctions. Thus it happens that a
certain historic interest attaches to the furniture of most middle-class
houses west of the Shannon. The dispensary doctor dines off a table
which once graced the parlour of a parish priest. The inspector
of police boasts of the price he paid for his easy-chair, recently
upholstered, at the auction of a departing bank manager, the same
mahogany frame having once supported the portly person of an old-time
Protestant Archdeacon. It is to be supposed that the furniture
originally imported--no one knows how--into Connaught must have been of
superlative quality. Articles whose pedigree, so to speak, can be traced
for nearly a hundred years are still in daily use, unimpaired by changes
of scene and ownership.
An auction of any importance is a public holiday. Clergy, doctors,
lawyers, and police officers gather to the scene, not unlike those
beasts of prey of whom we read that they readily devour the remains of
a fallen member of their own pack. The natives also collect
together--publicans and shopkeepers in search of bargains in china,
glass, and house-linen; farmers bent on purchasing such outdoor property
as wheelbarrows, scythes, or harness.
When Hyacinth, to use the local expression, 'called an auction' shortly
after his father's death, he was favoured with quite the usual crowd of
would-be buyers. Almost everyone with either money or credit within
a radius of twenty miles came into Carrowkeel for the occasion. The
presiding auctioneer had done his duty beforehand by advertising old Mr.
Conneally's mouldy furniture as 'magnificently upholstered suites,'
and his battered editions of the classics as 'a valuable library
of handsomely bound books.' It is not likely that anyone was really
deceived by these announcements, or expected to find in the little
rectory anything sumptuous or splendid. The people assembled mainly
because they were exceedingly curious to see the inside of a house whose
doors had never been open to them during the lifetime of the owner. It
was always possible, besides, that though the 'magnificently upholstered
suites 'existed only in the auctioneer's imagination, treasures of
silver spoons or candlesticks plated upon copper might be discovered
among the effects of a man who lived as queer a life as Mr. Conneally.
When men and women put themselves to a great deal of inconvenience to
attend an auction, they do not like to return empty-handed. A day is
more obviously wasted if one goes home with nothing to show than if one
brings a table or a bedstead purchased at twice its proper value. Thus
the bidding at Hyacinth's auction was brisk, and the prices such as gave
sincere satisfaction to the auctioneer. Everything was sold except 'the
valuable library.' It was in vain that the auctioneer made personal
appeals to Father Moran and the Rector of Clifden, as presumably the
two most learned gentlemen present. Neither of them wanted the venerable
classics. In fact, neither of them could have read a line of the crooked
Greek type or construed a page of the Latin authors. Even the Irish
books, in spite of the Gaelic revival, found no purchasers. When all was
over, Hyacinth wheeled them away in barrowfuls, wondering greatly what
he was to do with them.
Indeed, the disposal of his library was not the chief of his
perplexities. He wondered also what he was to do with himself. When the
auctioneer sent in his cheque, and the London Committee of the Mission
had paid over certain arrears of salary, Hyacinth found himself the
possessor of nearly two hundred pounds. It seemed to him quite a large
fortune, amply sufficient to start life with, if only some suitable way
of employing brains, energy, and money would suggest itself. In order to
consider the important topic at his leisure, he hired the only lodging
in Carrowkeel--the apartment (it was both bed and sitting room) over Mr.
Rafferty's public-house. The furniture had suffered during the tenancy
of a series of Congested Districts Board officials. An engineer, who
went to sleep in the evenings over the fire, had burnt a round hole in
the hearthrug. An instructor in fish-curing, a hilarious young man,
had cracked the mirror over the mantelpiece, and broken many ornaments,
including the fellow of the large china dog which now mourned its mate
on the sideboard. Other gentlemen had been responsible for dislocating
the legs of two chairs and a disorganization of the handle, which made
it impossible to shut the door from the inside. The chief glory of the
apartment, however, still remained--a handsomely-framed document,
signed by Earl Spencer, then Lord Lieutenant, ordering the arrest of the
present Mr. Rafferty's father as a person dangerous to the Commonwealth.
The first thing which brought Hyacinth's meditations to a definite point
was a letter he received from Dr. Henry.
'I do not know,' the professor wrote, 'and of course I do not wish
to inquire, how you are situated financially; but if, as I suppose is
likely, you are obliged in the near future to earn your living, I may
perhaps be of some help to you..You have taken your B.A. degree, and are
so far qualified either to accept a post as a schoolmaster in an English
preparatory school or to seek ordination from some Bishop. As you are
probably aware, none of our Irish Bishops will accept a man who has
not completed his divinity course. Several English Bishops, however,
especially in the northern province, are willing to ordain men who have
nothing more than a University degree, always supposing that they pass
the required examination. I shall be quite willing to give you a letter
of recommendation to one of these Bishops, and I have no doubt that
a curacy could be found for you in one of the northern manufacturing
towns, where you would have an ample sphere for useful work.'
The letter went on to urge the advisability of Hyacinth's suppressing,
disguising, or modifying his political opinions, which, stated nakedly,
were likely to beget a certain prejudice in the well-balanced episcopal
mind, and in any case would be quite out of place among the operatives
of Yorkshire or Lancashire.
Hyacinth recognised and appreciated Dr. Henry's kindness. He even tried
to bring himself to consider the offer seriously and carefully, but it
was no use. He could not conceive himself as likely to be either useful
or happy amid the hustling commercialism of the Manchester streets or
the staid proprieties of an Anglican vicarage.
After he had spent about a week in his new lodging, Father Moran called
on him. The priest sat beside the fire for more than an hour chatting
in a desultory manner. He drank tea and smoked, and it was not until he
rose to go that the real object of his visit appeared.
'I don't know what you're thinking of doing, Mr. Conneally, and maybe
I've no right to ask.'
'I wouldn't have the least objection to telling you,' said Hyacinth, 'if
I knew myself; but I haven't my mind made up.'
The priest put down his hat again, and settled himself with his back to
the fire and his hands in his pockets. Hyacinth sat down, and during the
pause which followed contemplated the wonderful number and variety of
the stains on the black waistcoat in front of him.
'Then you've given up the idea of finishing your divinity course?' said
the priest. 'I'm not blaming you in the least. There's men that studying
suits, and there's men that it doesn't. I never was much of a one for
books myself.'
He sighed heavily, perhaps at the recollection of his own struggles with
the mysteries of theology in his Maynooth student days. Then he walked
over and closed the door, returned, drew a chair close to Hyacinth, and
spoke in the tone of a man who imparts an important secret.
'Did you hear that Thady Durkan's giving up the fishing? Since he broke
his arm he declares he'll never step aboard the boat again. You know the
St. Bridget. She's not one of the biggest boats, but she's a very lucky
one. She made over five hundred pounds last year, besides the share the
Board took. She was built at Baltimore, and the Board spent over two
hundred pounds on her, nets and gear and all. There's only one year more
of instalments to pay off the price of her, and Thady has the rest of
the men bought out. There's nobody owns a stick or a net or a sail of
her except himself, barring, of course, what's due to the Board.'
Hyacinth was sufficiently acquainted with the system on which the
Congested Districts Board provides the Connaught fishermen with boats
and nets to understand Father Moran's rather involved statement
of Durkan's financial position. He did not yet grasp why all this
information should have been conveyed to him in such a solemn and
mysterious tone.
'You might have the _St. Bridget_,' said the priest, 'for one hundred
and fifty pounds down.'
He paused to let the full glory of the situation lay hold upon Hyacinth.
Perhaps he expected an outburst of delight and surprise, but none came.
'Mind you,' he said, 'there's others looking for her. The men that
worked with Thady are thinking of making him an offer, and I dare say
the Board would be glad enough to have the boat owned among them; but I
can put in a word myself both with Thady and the inspector. Faith, the
times is changed since I was a young man. I can remember when a priest
was no more thought of than a barefooted gossure out of a bog, and now
there isn't a spalpeen of a Government inspector but lifts his hat to me
in the street. Oh, a note from me will go a good way with the Board,
and you'll not miss the chance for want of my good word--I promise you
that.'
'Thank you,' said Hyacinth.
'Mind you, there's a good thing to be made out of her. But sure you know
that as well as I do myself, and maybe better. What do you say now?'
'I'll think it over,' said Hyacinth, 'and whatever comes of it I'll be
greatly obliged to you.'
'Well, don't be delaying too long. And look you here'--his voice sank
almost to a whisper--'don't be talking about what I've said to you.
People are queer, and if Father Joyce down in Clifden came to hear
that I was working for a Protestant he'd be sure to go talking to the
Archbishop, and I'd never get to the end of the fuss that would be
made.'
'Indeed, it's very good of you, especially considering who I am--I mean,
my father being a convert, and----'
'Say no more,' said the priest--'say no more. Your father was a good
man, Catholic or Protestant. I'm not one of these bitter kind of
priests, Mr. Con-neally. I can be a good Catholic without hating my
neighbours. I don't hold with all this bullyragging in newspapers about
"sourfaces" and "saved." Maybe that's the reason that I'm stuck down
here at the other end of nowhere all my life, and never got promotion
or praise. But what do I care as long as they let me alone to do my work
for the people? I'm not afraid to say it to you, Mr. Conneally, for you
won't want to get me into trouble, but it's my belief that there's many
of our priests would rather have grand churches than contented people.
They're fonder of Rome than they are of Ireland.'
'Really, Father Moran,' said Hyacinth, smiling, 'if you go on like this,
I shall expect to hear of your turning Protestant.'
'God forbid, Mr. Conneally! I wish you well. I wish you to be here among
us, and to be prosperous; but the dearest wish of my heart for you is
that I might see you back in the Catholic Church, believing the creed of
your forefathers.'
The priest's suggestion attracted Hyacinth a great deal more than Dr.
Henry's. He liked the sea and the fishing, and he loved the simple
people among whom he had been brought up. His experiences in Dublin had
not encouraged him to be ambitious. Life in the great world--it was thus
that he thought of the bickerings of the Dublin Nationalists and the
schoolboy enthusiasms of college students--was not a very simple
thing. There was a complexity and a confusion in affairs which made
it difficult to hold to any cause devotedly. It seemed to him, looking
back, that Miss Goold's ideals--and she had ideals, as he knew--were
somehow vulgarized in their contact with the actual. He had seen
something of the joy she found in her conflict with O'Rourke, and it did
not seem to him to be pure or ennobling. At one time he was on the verge
of deciding to do what the priest wished. Walking day by day along the
shore or through the fields, he came to think that life might very
well be spent without ambitious or extended hopes in quiet toil and
unexciting pleasures. What held him back was the recollection, which
never ceased to haunt him, of his father's prophecy. The thought of
the great fight, declared to be imminent, stirred in him an emotion so
strong that the peace and monotony he half desired became impossible.
He never made it clear to himself that he either believed or disbelieved
the prediction. He certainly did not expect to see an actual gathering
of armed men, or that Ireland was to be the scene of a battle like those
in South Africa. But there was in him a conviction that Ireland was
awakening out of a long sleep, was stretching her limbs in preparation
for activity. He felt the quiver of a national strenuousness which was
already shaking loose the knots of the old binding-ropes of prejudice
and cowardice. It seemed to him that bone was coming to dry bone, and
that sooner or later--very soon, it was likely--one would breathe on
these, and they would live. That contest should come out of such a
renaissance was inevitable. But what contest? Against whom was the new
Ireland to fight, and who was truly on her side? Here was the puzzle,
insoluble but insistent. It would not let him rest, recurring to his
mind with each fresh recollection of his father's prophecy.
It was while he was wearying himself with this perplexity that he got
a letter from Augusta Goold. It was characteristic of her that she had
written no word of sympathy when she heard of his father's death, and
now, when a letter did come, it contained no allusion to Hyacinth's
affairs. She told him with evident delight that she had enlisted no less
than ten recruits for the Boer army. She had collected sufficient money
to equip them and pay their travelling expenses. It was arranged that
they were to proceed to Paris, and there join a body of volunteers
organized by a French officer, a certain Pierre de Villeneuve, about
whom Miss Goold was enthusiastic. She was in communication with an
Irishman who seemed likely to be a suitable captain for her little band,
and she wanted Hyacinth back in Dublin to help her.
'You know,' she wrote, 'the people I have round me here. Poor old Grealy
is quite impracticable, though he means well. He talks about nothing
but the Fianna and Finn McCool, and can't see that my fellows must have
riding lessons, and must be got somehow to understand the mechanism of
a rifle. Tim Halloran has been in a sulk ever since I told him what I
thought of his conduct at the Rotunda. He never comes near me, and Mary
O'Dwyer told me the other day that he called my volunteers a "pack of
blackguards." I dare say it's perfectly true, but they're a finer kind
of blackguard than the sodden loafers the English recruit for their
miserable army.'
She went on to describe the series of Boer victories which had come one
after another just at Christmas-time. She was confident that the cause
of freedom and nationality would ultimately triumph, and she foresaw the
intervention of some Continental Power. A great blow would be struck at
the already tottering British Empire, and then--the freedom of Ireland.
Hyacinth felt strangely excited as he read her news. The letter seemed
the first clear note of the trumpet summoning him to his father's
Armageddon. Politics and squabbling at home might be inglorious and
degrading, but the actual war which was being waged in South Africa,
the struggle of a people for existence and liberty, could be nothing but
noble. He saw quite clearly what his own next step was to be, and there
was no temptation to hesitate about it. He would place his money at Miss
Goold's disposal, and go himself with her ten volunteers to join the
brigade of the heroic de Villeneuve.
CHAPTER IX
The prospect of joining Augusta Goold's band of volunteers and going to
South Africa to fight afforded Hyacinth great satisfaction. For two days
he lived in an atmosphere of day-dreams and delightful anticipations. He
had no knowledge whatever of the actual conditions of modern warfare.
He understood vaguely that he would be called upon to endure great
hardships. He liked to think of these, picturing himself bravely
cheerful through long periods of hunger, heat, or cold. He had visions
of night watches, of sudden alarms, of heart-stirring skirmishes, of
scouting work, and stealthy approaches to the enemy's lines. He thought
out the details of critical interviews with commanding officers in
which he with some chosen comrade volunteered for incredibly dangerous
enterprises. He conceived of himself as wounded, though not fatally, and
carried to the rear out of some bullet-swept firing-line. He was just
twenty-three years of age. Adventure had its fascination, and the world
was still a place full of splendid possibilities.
At the end of his two days of dreaming he returned, flushed with his
great purposes, to the realities of life. He went to Father Moran to
tell him that he would not buy Durkan's boat. He laughed to himself
at the thought of doing such a thing. Was he to spend his life fishing
mackerel round the rocky islands of Connemara, when he might be fighting
like one of the ancient heroes, giving his strength, perhaps his life,
for a great cause? The priest met him at the presbytery door.
'Come in, Mr. Conneally--come in and sit down. I was expecting you these
two days. What were you doing at all, walking away there along the rocks
by yourself? The people were beginning to say that you were getting to
be like your poor father, and that nobody'd ever get any good out of
you. But I knew you'd come back to me here. I hope now it's to tell me
that you'll buy the boat you've come.'
They entered the house, and the priest opened the door of the little
sitting-room. Hyacinth knew it well. There was the dark mahogany table
with the marks burnt into it where hot dishes were set down, the shabby
arm-chair, the worn cocoanut-matting on the floor, the dozen or so books
in the hanging shelf, the tawdry sacred pictures round the wall. He had
known it all, and it all seemed unchanged since he was a child.
'Sit you down--sit you down,' said the priest. 'And now about the boat.'
'I'm not going in for her,' said Hyacinth. 'I'm as thankful to you for
suggesting it as if I did buy her. I hope you'll understand that, but
I'm not going to buy her.'
He found it difficult to speak of his new plan to Father Moran.
'Do you tell me that, now? I'm sorry for it. And why wouldn't you buy
her? What's there to hinder you?'
Hyacinth hesitated.
'Well, now,' said the priest, 'I can guess. I thought the auction turned
out well for you, but I never heard for certain, and maybe you haven't
got the money for the boat. Whisht now, my son, and let me speak. I'm
thinking the thing might be managed.'
'But, Father Moran------'
'Ah now, will you be quiet when I bid you? I haven't the money myself.
Never a penny have I been able to save all my life, with the calls there
are on me in a parish like this. Sure, you know yourself how it is.
There's one will have a cow that has died on him, and another will be
wanting a lock of potatoes for seed in the springtime; and if it isn't
that, it'll be something else. And who would the creatures go to in
their trouble but the old priest that christened and married the most
of them? But, indeed, thanks be to God, things is improving. The fishing
brings in a lot of money to the men, and there's a better breed of
cattle in the country now, and the pigs fetch a good price since we had
the railway to Clifden, and maybe the last few years I might have saved
a little, but I didn't. Indeed, I don't know where it is the money goes
at all, but someway it's never at rest in my breeches pockets till it's
up and off somewhere. God forgive us! it's more careful we ought to be.'
'But, Father Moran, I don't----'
'Arrah then, will you cease your talking for one minute, and let me get
a word in edgeways for your own good? What was I saying? Oh, I was just
after telling you I hadn't got the money to help you. But maybe I might
manage to get it. The man in the bank in Clifden knows me. I borrowed a
few pounds off him two years ago when the Cassidys' house and three more
beside it got blown away in the big wind. Father Joyce put his name on
the back of the bill along with my own, and trouble enough I had to get
him to do it, for he said I ought to put an appeal in the newspapers,
and I'd get the money given to me. But I never was one to go begging
round the country. I said I'd rather borrow the money and pay it back
like a decent man. And so I did, every penny of it. And I think the bank
will trust me now, with just your name and mine, more especially as
it's to buy a boat we want the money. What do you say to that, now?' He
looked at Hyacinth triumphantly.
'Father Moran, you're too good to me--you're too good altogether. What
did ever I do to deserve such kindness from you? But you're all wrong.
I've got plenty of money.'
'And why in the name of all that's holy didn't you tell me so at once,
and not keep me standing here twisting my brains into hard knots with
thinking out ways of getting what you don't want? If you've got the
money you'll buy the boat. What better could you do with it?'
'But I don't want to buy the boat. I don't want to live here always. I'm
going away out into the world. I want to see things and do things.'
'Out into the world! Will you listen to the boy? Is it America you're
thinking of? Ah, now, there's enough gone out and left us lonely here.
Isn't the best of all the boys and girls going to work for the strangers
in the strange land? and why would you be going after them?'
'I'm not going to America. I'm going to South Africa. I'm going to join
some young Irishmen to fight for the Boers and for freedom.'
'You're going out to fight--to fight for the Boers! What is it that's in
your head at all, Hyacinth Con-neally? Tell me now.'
Again Hyacinth hesitated. Was it possible to give utterance to the
thoughts and hopes which filled his mind? Could he tell anyone about
the furious fancies of the last few days, or of that weird vision of
his father's which lay at the back of what he felt and dreamed? Could
he even speak of the enthusiasm which moved him to devote himself to the
cause of freedom and a threatened nationality? In the presence of a man
of the world the very effort to express himself would have acted as some
corrosive acid, and stained with patches of absurdity the whole fabric
of his dreams. He looked at Father Moran, and saw the priest's eyes lit
with sympathy. He knew that he had a listener who would not scoff, who
might, perhaps, even understand. He began to speak, slowly and haltingly
at first, then more rapidly. At last he poured out with breathless,
incoherent speed the strange story of the Armageddon vision, the hopes
that were in him, the fierce enthusiasm, the passionate love for
Ireland which burnt in his soul. He was not conscious of the gaping
inconsequences of his train of emotion. He did not recognise how
ridiculous it was to connect the Boer War with the Apocalyptic battle
of the saints, or the utter impossibility of getting either one or the
other into any sort of relation with the existing condition of Ireland.
A casual observer might have supposed that Hyacinth had made a mistake
in telling his story to Father Moran. A smile, threatening actual
laughter, hovered visibly round the priest's mouth. His eyes had a
shrewd, searching expression, difficult to interpret. Still, he listened
to the rhapsody without interrupting it, till Hyacinth stopped abruptly,
smitten with sudden self-consciousness, terrified of imminent ridicule.
Nor were the priest's first words reassuring.
'I wouldn't say now, Hyacinth Conneally, but there might be the makings
of a fine man in you yet.'
'I might have known,' said Hyacinth angrily, 'that you'd laugh at me. I
was a fool to tell you at all. But I'm in earnest about what I'm going
to do. Whatever you may think about the rest, there's no laughing at
that.'
'Well, you're just wrong then, for I wasn't laughing nor meaning to
laugh at all. God forbid that I should laugh at you, and I meant it when
I said that there was the makings of a fine man in you. Laugh at you!
It's little you know me. Listen now, till I tell you something; but
don't you be repeating it. This must be between you and me, and go no
further. I was very much of your way of thinking myself once.'
Hyacinth gazed at him in astonishment. The thought of Father Moran,
elderly, rotund, kindly; of Father Moran with sugar-stick in his pocket
for the school-children and a quaint jest on his lips for their mothers;
of Father Moran in his ruffled silk hat and shabby black coat and baggy
trousers--of this Father Moran mounted and armed, facing the British
infantry in South Africa, was wholly grotesque. He laughed aloud.
'It's yourself that has the bad manners to be laughing now,' said
the priest. 'But small blame to you if it was out to the Boers I was
thinking of going. The gray goose out there on the road might laugh--and
she's the solemnest mortal I know--at the notion of me charging along
with maybe a pike in my hand, and the few gray hairs that's left on the
sides of my head blowing about in the breeze I'd make as I went prancing
to and fro. But that's not what I meant when I said that once upon a
time I was something of your way of thinking. And sure enough I was, but
it's a long time ago now.'
He sighed, and for a minute or two he said no more. Hyacinth began
to wonder what he meant, and whether the promised confidence would be
forthcoming at all. Then the priest went on:
'When I was a young man--and it's hard for you to think it, but I was a
fine young man; never a better lad at the hurling than I was, me that's
a doddering old soggarth now--when I was a boy, as I'm telling you,
there was a deal of going to and fro in the country and meetings at
night, and drillings too, and plenty of talk of a rising--no less.
Little good came of it that ever I saw, but I'm not blaming the men that
was in it. They were good men, Hyacinth Conneally--men that would have
given the souls out of their bodies for the sake of Ireland. They would,
sure, for they loved Ireland well. But I had my own share in the doings.
Of course, it was before ever there was a word of my being a priest.
That came after. Thanks be to God for His mercies'--the old man crossed
himself reverently--'He kept me from harm and the sin that might have
been laid on me. But in those days there were great thoughts in me, just
as there are in you to-day. Faith! I'm of opinion that my thoughts were
greater than yours, for I was all for fighting here in Ireland, for the
Poor Old Woman herself, and it's out to some foreign war you'd be
going to fight for people that's not friends of yours by so much as one
heart's drop. Still, the feeling in you is the same as the feeling that
was in me, not a doubt of it. But, indeed, so far as I'm concerned, it's
over and gone. I haven't spoken to a mortal soul about such things these
thirty years, and I wouldn't be doing it now only just to show you that
I'm the last man in Ireland that would laugh at you for what you've told
me.'
'I'm glad I told you what's in my heart,' said Hyacinth; 'I'd like to
think I had your blessing with me when I go.'
'Well, you won't get it,' said Father Moran, 'so I tell you straight.
I'll give you no blessing when you're going away out of the country,
just when there's need of every man in it. I tell you this--and you'll
remember that I know what I'm talking about--it's not men that 'll fight
who will help Ireland to-day, but men that will work.'
'Work!' said Hyacinth--'work! What work is there for a man like me to do
in Ireland?'
'Don't I offer you the chance of buying Thady Durkan's boat? Isn't there
work enough for any man in her?'
'But that's not the sort of work I ought to be doing. What good would
it be to anyone but myself? What good would it be to Ireland if I caught
boatloads of mackerel?'
'Don't be making light of the mackerel, now. He's a good fish if you get
him fresh, and split him down and fry him with a lump of butter in the
pan. There's worse fish than the mackerel, as you'll discover if you go
to South Africa, and find yourself living on a bit of some ancient tough
beast of an ostrich, or whatever it may happen to be that they eat out
there.'
In his exalted mood Hyacinth felt insulted at the praise of the mackerel
and the laughter in the priest's eyes when he suggested a dinner off
ostrich. He held out his hand, and said good-bye.
'Wait, now--wait,' said the priest; 'don't be in such a tearing hurry.
I'll talk as serious as you like, and not hurt your feelings, if you'll
stay for a minute or two. Listen, now. Isn't the language dying on the
people's lips? They're talking the English, more and more of them every
day; and don't you know as well as I do that when they lose their Irish
they'll lose half the good that's in them? What sort will the next
generation of our people be, with their own language gone from them, and
their Irish ways forgotten, and all the old tales and songs and tunes
perished away like the froth of the waves that the storm blew up across
the fields the night your father died? I'll tell you what they'll
be--just sham Englishmen. And the Lord knows the real thing is not the
best kind of man in the world, but the copy of an Englishman! sure,
that's the poorest creature to be found anywhere on the face of God's
good earth. And that's what we'll be, when the Irish is gone from us.
Wouldn't there be work enough for you to do, now, if you were to buy
Thady Durkan's boat, and stay here and help to keep the people to the
old tongue and the old ways?'
Hyacinth shook his head. His mood was altogether too heroic to allow
him to think highly of what the priest said to him. He loved the Irish
language as his native speech--loved it, too, as a symbol, and something
more, perhaps--as an expression of the nationality of Ireland. But it
did not seem to him to be a very essential thing, and to spend his life
talking it and persuading other people to talk it was an obscure kind of
patriotism which made no strong appeal to him--which, indeed, could not
stand compared to the glory of drawing the sword.
'You've listened to what I've told you, Father Moran, and you say that
you understand what I feel, but I don't think you really do, or else you
wouldn't fancy that I could be satisfied to stay here. What is it you
ask of me? To spend my time fishing and talking Irish and dancing jigs.
Ah! it's well enough I'd like to do it. Don't think that such a life
wouldn't be pleasant to me. It would be too pleasant. That's what's the
matter with it. It's a temptation, and not a duty, that you're setting
before me.'
'Maybe it is now--maybe it is. And if it's that way you think of it,
you're right enough to say no to me. But for all that I understand you
well enough. Who's this now coming up to the house to see me?' He went
over to the window and looked out. 'Isn't it a queer life a priest lives
in a place like this, with never a minute of quiet peace from morning to
night but somebody will be coming interrupting and destroying it? First
it's you, Hyacinth Conneally--not that I grudge the time to you when
you're going off so soon--and now it's Michael Kavanagh. Indeed, he's
a decent man too, like yourself. Come in, Michael--come in. Don't be
standing there pulling at the old door-bell. You know as well as myself
it's broken these two years. It's heartbroken the thing is ever since
that congested engineer put up the electric bell for me, and little
use that was, seeing that Biddy O'Halloran--that's my housekeeper, Mr.
Conneally; you remember her--poured a jug of hot water into its inside
the way it wouldn't annoy her with ringing so loud. And why the noise
of it vexed her I couldn't say, for she's as deaf as a post every time
I speak to her. Ah, you're there, Michael, are you? Now, what do you
want?'
A young farmer, black-haired, tall and straight, stood in the doorway
with his hat in his hand. He had brought a paper for Father Moran's
signature. It related to a bull which the Congested Districts Board
proposed to lend to the parish, and of which Kavanagh had been chosen
to be custodian. A long conversation followed, conducted in Irish. The
newly-erected habitation for the animal was discussed; then the best
method of bringing him home from Clifden Station; then the kind of
beast he was likely to turn out to be, and the suitability of particular
breeds of cattle to the coarse, brine-soaked land of Carrowkeel.
Kavanagh related a fearful tale of a lot of 'foreign 'fowls which had
been planted in the neighbourhood by the Board. They were particularly
nice to look at, and settings of their eggs were eagerly booked long
beforehand. Then one by one they sickened and died. Some people thought
they died out of spite, being angered at the way they had been treated
in the train. Kavanagh himself did not think so badly of them. He was of
opinion that their spirits were desolated in them with the way the rain
came through the roof of their house, and that their feet got sore with
walking on the unaccustomed sea-sand. However their death was to be
explained, he hoped that the bull would turn out to be hardier. Father
Moran, on his part, hoped that the roof of the bull's house would
turn out to be sounder. In the end the paper was signed, and Kavanagh
departed.
'Now, there,' said the priest, 'is a fine young man. Only for him, I
don't know how I'd get on in the parish at all. He's got a head on his
shoulders, and a notion of improving himself and his neighbours, and it
would do you good to see him dance a jig. But why need I tell you that
when you've seen him yourself? He is to be the secretary of the Gaelic
League when we get a branch of it started in Carrowkeel. And a good
secretary he'll make, for his heart will be in the work. I dare say,
now, you've heard of the League when you were up in Dublin. Well, you'll
hear more of it. By the time you're back here again---- Now, don't be
saying that you'll not come back. I'll give you a year to get sick of
fighting for the Boers, and then there'll be a hunger on you for the old
place that will bring you back to it in spite of yourself.'
'Good-bye, Father Moran. Whatever happens to me, I'll not forget
Carrowkeel nor you either. You've been good to me, and if I don't take
your advice and stay where I am, it's not through want of gratitude.'
The priest wrung his hand.
'You'll come back. It may be after I'm dead and gone, but back you'll
come. Here or somewhere else in the old country you'll spend your days
working for Ireland, because you'll have learnt that working is better
than fighting.'
CHAPTER X
When Hyacinth got back to Dublin about the middle of February, the
streets were gay with amateur warriors. The fever for volunteering,
which laid hold on the middle classes after the series of regrettable
incidents of the winter, raged violently among the Irish Loyalists.
Nowhere were the recruiting officers more fervently besieged than in
Dublin. Youthful squireens who boasted of being admirable snipe shots,
and possessed a knowledge of all that pertained to horses, struggled
with prim youths out of banks for the privilege of serving as troopers.
The sons of plump graziers in the West made up parties with footmen
out of their landlords' mansions, and arrived in Dublin hopeful of
enlistment. Light-hearted undergraduates of Trinity, drapers' assistants
of dubious character, and the crowd of nondescripts whose time is spent
in preparing for examinations which they fail to pass, leaped at the
opportunity of winning glory and perhaps wealth in South Africa. Those
who were fortunate enough to be selected were sent to the Curragh to
be broken in to their new profession. They were clothed, to their own
intense delight, in that peculiar shade of yellow which is supposed to
be a help to the soldier in his efforts not to be shot. Their legs were
screwed into putties and breeches incredibly tight round the knees,
which expanded rapidly higher up, and hung round their hips in
voluminous folds. Their jackets were covered with a multiplicity of
quaint little pockets, sewed on in unexpected places, and each provided
with a flap which buttoned over it. The name of the artist who designed
this costume has perished, nor does there remain any written record
of the use which these tightly-secured pocket-covers were supposed to
serve. Augusta Goold suggested that perhaps they were meant to prevent
the troopers' money from falling out in the event of any commanding
officer ordering his men to receive the enemy standing on their heads.'
In the light of the intelligence displayed by the English Generals up
to the present,' she said, 'the War Office is quite right to be prepared
for such a thing happening.'
It seemed possible to procure almost any amount of leave from the
Curragh, and the yeomen delighted to spend it in promenading the
fashionable streets of the metropolis. The tea-shops reaped a rich
harvest from the regal way in which they treated their female relatives
and friends. Indeed, their presence must have seriously disorganized the
occupations by which young women earn their living. It was difficult to
imagine that the sick in the hospitals could have been properly looked
after, or the letters of solicitors typewritten, so great was the number
of damsels who attached themselves to these attractive heroes. The
philosophic observer found another curious subject for speculation in
the fact that this parade of military splendour took place in a city
whose population sympathized intensely with the Boer cause, and was
accustomed to receive the news of a British defeat with delight. The
Dublin artisan viewed the yeomen much as the French in Paris must have
looked upon the allied troops who entered their city after Waterloo.
The very name by which they were called had an anti-national sound, and
suggested the performance of other amateur horse-soldiers in Wexford a
century earlier.
The little band whose writings filled the pages of the _Croppy_ were
more than anyone else enraged at the flaunting of Imperialism in their
streets. They had rejoiced quite openly after Christmas, and called
attention every week in prose and poetry to the moribund condition of
the British Empire, even boasting as if they themselves had borne a part
in its humiliation. They were still in a position to assert that the
Boers were victorious, and that the volunteers were likely to do no more
than exhaust the prison accommodation at Pretoria. They could and did
compose biting jests, but their very bitterness witnessed to a deep
disappointment. It was not possible to deny that the despised English
garrison in Ireland was displaying a wholly unlooked-for spirit. No one
could have expected that West Britons and 'Seonini' would have wanted to
fight. Very likely, when the time came, they would run away; but in
the meanwhile here they were, swaggering through the streets of Dublin,
outward and visible signs of a force in the country hostile to the hopes
of the _Croppy_, a force that some day Republican Ireland would have to
reckon with.
Augusta Goold herself was more tolerant and more philosophic than her
friends. She looked at the yeomen with a certain admiration. Their
exuberant youthfulness, their strutting, and their obvious belief in
themselves, made a strong appeal to her imagination.
'Look at that young man,' she said to Hyacinth, pointing out a volunteer
who passed them in the street. 'I happen to know who he is. In fact, I
knew his people very well indeed at one time, and spent a fortnight with
them once when that young man was a toddler, and sometimes sat on my
knee--at least, he may have sat on my knee. There were a good many
children, and at this distance of time I can't be certain which of them
it was that used to worry me most during the hour before dinner. The
father is a landlord in the North, and comes of a fine old family. He's
a strong Protestant, and English, of course, in all his sympathies.
Well, a hundred years or so ago that boy's great-grandfather was
swaggering about these same streets in a uniform, just as his descendant
is doing now. He helped to drag a cannon into the Phoenix Park one day
with a large placard tied over its muzzle--"Our rights or----" Who do
you think he was threatening? Just the same England that this boy is so
keen to fight for to-day!'
'Ah,' said Hyacinth, 'you are thinking of the volunteer movement of
1780.'
'Afterwards,' she went on, 'he was one of the incorruptibles. You'll
see his name on Jonah Barrington's red list. He stood out to the
last against the Union, wouldn't be bribed, and fought two duels with
Castlereagh's bravoes. The curious thing is that the present man is
quite proud of that ancestor in a queer, inconsistent sort of way. Says
the only mark of distinction his family can boast of is that they didn't
get a Union peerage. Strange, isn't it?'
'It is strange,' said Hyacinth. 'The Irish gentry of 1782 were men to be
proud of; yet look at their descendants to-day.'
'It is very sad. Do you know, I sometimes think that Ireland will never
get her freedom till those men take it for her. Almost every struggle
that Ireland ever made was captained by her aristocracy. Think of the
Geraldines and the O'Neills. Think of Sarsfield and the Wild Geese.
Think of the men who wrenched a measure of independence from England in
1782. Think of Lord Edward and Smith O'Brien. No, we may talk and write
and agitate, but we'll _do_ nothing till we get the old families with
us.'
Hyacinth laughed. It seemed to him that Miss Goold was deliberately
talking nonsense, rejoicing in a paradox.
'We are likely to wait, if we wait for them. Look at those.' He waved
his hand towards a group of yeomen who were chatting at the street
corner. 'They are going to stamp out a nation in South Africa. Is it
likely that they will create one here?'
'It is not likely'--she sighed as she spoke--'yet stranger things than
that have happened. Have you ever considered what the present English
policy in Ireland really is? Do you understand that they are trying to
keep us quiet by bribing the priests? They think that the Protestants
are powerless, or that they will be loyal no matter what happens. But
think: These Protestants have been accustomed for generations to regard
themselves as a superior race. They conceive themselves to have a
natural right to govern. Now they are being snubbed and insulted. There
isn't an English official from their Lord Lieutenant down but thinks he
is quite safe in ignoring the Protestants, and is only anxious to
make himself agreeable to the priests. That's the beginning. Very soon
they'll be bullied as well as snubbed. They will stand a good deal of
it, because, like most strong people, they are very stupid and slow at
understanding; but do you suppose they will always stand it?'
'They're English, and not Irish,' said Hyacinth. 'I suppose they like
what their own people do.'
'It's a lie. They are not English, though they say it themselves. In the
end they will find out that they are Irish. Some day a last insult, a
particularly barefaced robbery, or an intolerable oppression, will awake
them. Then they'll turn on the people that betrayed them. They will
discover that Ireland--their Ireland--isn't meant to be a cabbage-garden
for Manchester, nor yet a _creche_ for sucking priests. Ah! it will be
good to be alive when they find themselves. We shall be within reach of
the freedom of Ireland then.'
Hyacinth was amazed at her vehement admiration for the class she was
accustomed to anathematize. He turned her words over and over in his
mind. They recalled, as so many different things seemed to do, his
father's vision of an Armageddon. Amid the confusion of Irish politics
this thought of a Protestant and aristocratic revolt was strangely
attractive; only it seemed to be wholly impossible. He bewildered
himself in the effort to arrange the pieces of the game into some
reasonable order. What was to be thought of a priesthood who, contrary
to all the traditions of their Church, had nursed a revolution against
the rights of property? or of a people, amazingly quick of apprehension,
idealistic of temperament, who time after time submitted themselves
blindfold to the tyranny of a single leader, worshipped a man, and asked
no questions about his policy? How was he to place an aristocracy who
refused to lead, and persisted in whining about their wrongs to the
inattentive shopkeepers of English towns, gentlemen not wanting in
honour and spirit courting a contemptuous bourgeoisie with ridiculous
flatteries? In what reasonable scheme of things was it possible to
place Protestants, blatant in their boasts about liberty, who hugged
subjection to a power which deliberately fostered the growth of
an ecclesiastical tyranny? Where amid this crazy dance of
self-contradictory fanatics and fools was a sane man to find a place on
which to stand? How, above all, was Ireland, a nation, to evolve itself?
He turned with relief from these perplexities to the work that lay
before him. However a man might worry and befog himself over the
confused issues of politics, it was at all events a straightforward
and simple matter to fight, and Hyacinth was going to the front as the
eleventh Irish volunteer.
To do Miss Goold justice, she had been extremely unwilling to enrol him,
and had refused to take a penny of his money. Her conscience, such as
it was after years of patriotic endeavour, rebelled against committing a
young man whom she really liked to the companionship of the men she had
enlisted and the care of their commander, Captain Albert Quinn.
This gentleman, whom she daily expected in Dublin, belonged to County
Mayo. He represented himself as a member of an ancient but impoverished
family, boasted of his military experience, and professed to be
profoundly skilled in all matters relating to horses. Miss Goold's
inquiries elicited the fact that he held an undefined position under
his brother, a respectable manufacturer of woollen goods. His military
experience had been gathered during the few months he held a commission
in the militia battalion of the Connaught Rangers, an honourable
position which he had resigned because his brother officers persistently
misunderstood his methods of winning money at cards. No one, however,
was found to deny that he really did possess a wonderful knowledge of
horses. The worst that Miss Goold's correspondents could suggest with
regard to this third qualification was that he knew too much. None
of these drawbacks to the Captain--he had assumed the title when he
accepted the command of the volunteers--weighed with Miss Goold. Indeed,
she admitted to Mary O'Dwyer, in a moment of frankness, that if her men
weren't more or less blackguards she couldn't expect them to go out
to South Africa. She did not speak equally plainly to Hyacinth. She
recollected that he had displayed a very inconvenient kind of morality
when she first knew him, and she believed him quite capable of breaking
away from her influence altogether if he discovered the kind of men she
was willing to work with.
She did her best to persuade him to give up the idea of joining the
force, by pointing out to him that he was quite unfitted for the work
that would have to be done.
'You know nothing about horses,' she said. 'I don't suppose you've ever
been on the back of one.'
Hyacinth admitted that this was true. The inhabitants of Carrowkeel
rarely ride their shaggy ponies, and when they do it is sitting sideways
just above the creatures' tails, with two creels for turf or seaweed in
the place where the saddle ought to be.
'And I don't suppose you know much about shooting?'
Hyacinth was depressed, for he had never pulled a trigger in his life.
In the West of Ireland a man is not allowed to possess a gun unless
a resident magistrate will certify to his loyalty and harmless-ness.
Therefore, the inhabitants of villages like Carrowkeel are debarred from
shooting either snipe or seals, and the British Empire stands secure.
The difficulty about his horsemanship Hyacinth endeavoured to get over.
He arranged with a car-driver of his acquaintance to teach him to groom
and harness his horses. The man possessed two quadrupeds, which he
described as 'the yellow pony' and 'the little mare.' Hyacinth began
with the yellow pony, the oldest and staidest of the two. The little
mare, who had a temper of her own, gave him more trouble. She disliked
his way of putting the crupper under her tail, and one day, to her
owner's great delight, 'rose the divil on them' when her new groom got
the shaft of the car stuck through her collar.
The want of experience in shooting was more difficult to get over.
Grealy owned an antiquated army rifle, which he lent to Hyacinth.
It was, of course, entirely different from the Mauser, and it was
impossible to get an opportunity for firing it off. However, there was
some comfort to be found in handling the thing, and taking long and
careful aim at a distant church spire through a window.
In the face of such enthusiasm, Miss Goold could not refuse her recruit.
She talked to him freely about her plans, and was eloquent about the
spirit and abilities of M. de Villeneuve, who was to take charge of her
soldiers after they joined him in Paris. On the subject of Captain Quinn
she was much more reticent, and she refused altogether to introduce
Hyacinth to his ten fellow troopers.
'There's not the least necessity,' she said, 'for you to meet them until
the time for starting comes. In fact, I may say it is safer for none of
you to know each other.'
Hyacinth experienced a thrill of agreeable excitement. He felt that he
was engaged in a real conspiracy.
'For fear of informers?' he asked.
'Yes. One never can be quite sure of anyone. Of course, they can every
one of them give information against me. You can yourself, if you like.
But no one can betray anyone else, and as long as the men are safe, it
doesn't matter what happens to me.'
It was one of Miss Goold's weaknesses that she imagined herself to be an
object of hatred and dread to the Government, and nothing irritated her
more than a suspicion that she was not being taken seriously.
The first glimpse that Hyacinth got of the character of the men among
whom he was to serve came to him through Tim Halloran. Tim was still
sore from the scolding he had been given for his conduct at the
Rotunda meeting, and missed no opportunity of scoffing--not, of course,
publicly, but among his friends--at Miss Goold and her volunteers.
Hyacinth avoided him as much as possible, but one evening he walked up
against him on the narrow footway at the corner of George's Street.
Halloran was delighted, and seized him by the arm.
'You're the very man I wanted to see,' he said. 'Have you heard about
Doherty?'
Hyacinth knew no one called Doherty. He said so, and tried to escape,
but Halloran held him fast.
'Not know Doherty! How's that? I thought you were in all dear Finola's
secrets. Faith! I heard you were going out to fight for the Boers
yourself. I didn't believe it, of course. You wouldn't be such a
fool. But I thought you'd know that Doherty is one of the ten precious
recruits, or, rather, _was_ one of them.' He laughed loudly. 'He'll
fight on the other side now, if he fights at all.'
'What do you mean>' asked Hyacinth uneasily.
He was not at all sure what view the authorities in Dublin Castle might
take of recruiting for the Boer service, and Miss Goold's hints about
informers recurred to his mind alarmingly. Perhaps this Doherty was an
informer.
'Well,' said Halloran, 'I was in one of the police-courts this morning
doing my work for the _Evening Star_. You know I report the police news
for that rag, don't you? Well, I do. My column is called "The Doom of
the Disorderly." Rather a good title that for a column of the kind!
There didn't appear to be anything particular on, just a few ordinary
drunks, until this fellow Doherty was brought in. I thought I recognised
him, and when I heard his name I was certain of my man. He hadn't done
anything very bad--assaulted a tram-conductor, or some such trifle--and
would have got off with a fine. However, a military man turned up and
claimed him as a deserter. His real name, it appears, is Johnston. He
deserted six weeks ago from the Dublin Fusiliers.'
'How on earth did he impose on Miss Goold?' asked Hyacinth.
Halloran looked at him curiously.
'Oh, I shouldn't say he exactly imposed upon Finola. She's not precisely
a fool, you know, and she has pretty accurate information about most of
the people she deals with.'
'But surely------'
Halloran shrugged his shoulders.
'My dear fellow, I don't want to shatter your ideal, but the beautiful
Finola wants to work a revolution, and you can't do that sort of thing
without soiling your hands. However, whether he imposed on her or not,
there's no doubt about it that he was a deserter. Why, it appeared that
the fool was tattooed all over the arms and chest, and the military
people had a list of the designs. They had a perfectly plain case, and,
indeed, Doherty made no defence.'
'What will they do with him?' said Hyacinth, still uneasy about the
possibility of Doherty's volunteering information.
'I don't know,' said Halloran. 'I should think the best punishment would
be to send him out to Ladysmith. I dare say the Boers would pass him
in if the circumstances were explained to them. By the way, it would be
rather funny if he met the other nine out there on a kopje, wouldn't it?
He might take them prisoners, or they might capture him. Either way the
situation would have its comic possibilities.'
CHAPTER XI
Miss Goold lived that part of her life which was not spent at political
meetings or in the office of the _Croppy_ in a villa at Killiney. A
house agent would have described it as a most desirable residence,
standing in its own grounds, overlooking the sea. Its windows opened
upon one of the best of the many beautiful views of Dublin Bay. Its
half-acre of pleasure ground--attended to by a jobbing gardener once a
week--was trim and flowery. Its brown gate shone with frequently renewed
paint, and the drive up to the door was neatly raked. Inside
Miss Goold's wants were ministered to by an eminently respectable
man-servant, his wife who cooked, and a maid. The married couple were
fixtures, and had been with Miss Goold since she started housekeeping.
The maids varied. They never quarrelled with their mistress, but they
found it impossible to live with their fellow-servants. Mr. and Mrs.
Ginty were North of Ireland Protestants of the severest type. Ginty
himself was a strong Orangeman, and his wife professed and enforced a
strict code of morals. It did not in the least vex Miss Goold to
know that her servants' quarters were decorated with portraits of the
reigning family in gilt frames, or that King William III. pranced on a
white charger above the kitchen range. Nor had she any objection to her
butler invoking a nightly malediction on the Pope over his tumbler of
whisky-and-water. Unfortunately, her maids--the first three were Roman
Catholics--found that their religious convictions were outraged, and
left, after stormy scenes. The red-haired Protestant from the North who
followed them was indifferent to the eternal destiny of Leo XIII., but
declined to be dictated to by Mrs. Ginty about the conduct of her love
affairs. Miss Goold, to whom the quarrel was referred, pleaded the
damsel's cause, and suggested privately that not even a policeman--she
had a low opinion of the force--could be swept away from the path of
respectability by a passion for so ugly a girl. Mrs. Ginty pointed out
in reply that red hair and freckles were no safeguard when a flirtation
is carried on after dark. There seemed no answer to this, and the maid
returned indignantly to Ballymena. She was succeeded by an anaemic and
wholly incompetent niece of Mrs. Ginty's, who lived in such terror of
her aunt that peace settled upon the household. Miss Goold suspected
that this girl did little or no work--was, in fact, wholly unfit for her
position; but so long as she herself was made comfortable, it did not
seem to matter who tidied away her clothes or dusted her bedroom.
Miss Goold, in fact, had so far mastered the philosophy of life as to
understand that the only real use of money is to purchase comfort and
freedom from minor worries. She had deliberately cut herself adrift from
the social set to which she belonged by birth and education, and so had
little temptation to spend her substance either in giving parties
or enjoying them. The ladies who flutter round the Lord Lieutenant's
hospitable court would as soon have thought of calling on a music-hall
danseuse as on Miss Goold. Their husbands, brothers, and sons took
liberties with her reputation in the smoking-rooms of the Kildare Street
Club, and professed to be in possession of private information about
her life which placed her outside the charity of even their tolerant
morality. The little circle of revolutionary politicians who gathered
round the _Croppy_ were not the sort of people who gave dinner-parties;
and there is, in spite of the Gospel precept, a certain awkwardness
nowadays in continually asking people to dinner who cannot afford a
retributive invitation. Occasionally, however, Miss Goold did entertain
a few of her friends, and it was generally admitted among them that she
not only provided food and drink of great excellence, but arranged the
appointments of her feasts luxuriously.
On the very day after his interview with Tim Halloran Hyacinth received
an invitation to dinner at the Killiney villa. Captain Quinn, the
note informed him, had arrived in Dublin, and was anxious to make the
acquaintance of his future comrade-in-arms. It seemed to Hyacinth,
thinking over the story of Doherty, unlikely that the whole corps would
be asked to meet their Captain round a dinner-table, but he hoped that
some of them would be there. Their presence would reconcile him to the
awkwardness of not possessing a dress-suit. Grealy, who had occasionally
dined at the villa, warned him that a white shirt-front and black
trousers would certainly be expected of him, and Hyacinth made an
unsuccessful effort to hire garments for the night which would fit him.
In the end, since it seemed absurd to purchase even a second-hand suit
for a single evening, he brushed his Sunday clothes and bought a pair of
patent-leather shoes.
He arrived at the platform of Westland Row Station in good time for
the train he meant to catch. He was soon joined by Miss O'Dwyer, who
appeared with her head and neck swathed in a fluffy shawl and the train
of a silk skirt gathered in her hand. The view of several flounces of
nebulous white petticoat confirmed Hyacinth in his conjecture that she
was bound for Miss Goold's party. No one who could be supposed to be a
member of Captain Quinn's corps appeared on the platform, and Hyacinth
became painfully conscious of the shortcomings of his costume. He
thought that even Miss O'Dwyer glanced at it with some contempt. He
wished that, failing a dress-suit, he could have imitated the Imperial
Yeomen who paraded the streets, and donned some kind of uniform. His
discomfort reached a climax when Ginty received them at the door, passed
Miss O'Dwyer on to the incompetent niece, and solemnly extracted the new
shoes from their brown-paper parcel.
Miss Goold stood chatting to Captain Quinn when Hyacinth entered the
drawing-room. She moved forward to meet him, radiant and splendid, he
thought, beyond imagination. The rustle of her draperies, the faint
scent that hung around her, and the glitter of the stones on her throat,
bewildered him.
It was not till after he had been presented to his commander that he was
able to take his eyes off her. Then, in spite of his embarrassment, he
experienced surprise and disappointment. He had formed no clear idea
of what he expected Captain Quinn to be like, but he had a vague mental
picture of a furiously-moustachioed swashbuckler, a man of immense power
and hirsute hands. Instead, there stood before him a slim, small man,
clean shaved, with shiny black hair smoothly brushed. His clothes were
so well cut and his linen so glossy that he seemed fittingly placed even
beside the magnificent Finola. His hand, when Hyacinth shook it, seemed
absurdly small, and his feet, in their neat pumps, were more like a
woman's than a man's. Then, when he turned to resume his conversation
with his hostess, Hyacinth was able to watch his face. He noticed
the man's eyes. They were small and quick, like a bird's, and shifted
rapidly, never resting long on any object. His mouth was seldom closed,
and the lips, like the eyes, moved incessantly, though very slightly.
There were strange lines about the cheeks and jaws, which somehow
suggested that the man had seen a good deal of the evil of the world,
and not altogether unwillingly. His voice was wonderfully soft and
clear, and he spoke without a trace of any provincial accent.
During dinner Captain Quinn took the largest share in the conversation.
It appeared that he was a man of considerable knowledge of the world. He
had been a sailor in his time, and had made two voyages to Melbourne
as apprentice in a large sailing-ship. His stories were interesting and
humorously told; though they all dealt with experiences of his own, he
never allowed himself to figure as anything of a hero. He recounted,
for instance, how one night in Melbourne Docks he had run from a
half-drunken Swede, armed with a knife, and had spent hours dodging
round the deck of a ship and calling for help before he could get his
assailant arrested. His career as an officer in the mercantile navy was
cut short by a period of imprisonment in a small town in Madagascar.
He did not specify his offence, but gave a vivid account of life in the
gaol.
'There were twenty of us altogether,' he said--'nineteen <DW65>s and
myself. There was no nonsense about discipline or work. We just sat
about all day in an open courtyard, with nothing but a big iron gate
between us and liberty. All the same, there was very little chance
of escape. There were always four black soldiers on guard, truculent
scoundrels with curly swords. A sort of missionary man got wind of my
being there, and used to come and visit me. One day he gave me a tract
called "Gideon." I read the thing because I had absolutely nothing else
to read. In the end it turned out an extremely useful tract, for it
occurred to me that the old plan for defeating the Midianites might
work with the four black soldiers. I organized the other prisoners, and
divided them into three bands. We raked up a pretty fair substitute
for pitchers and lamps. Then one night we played off the stratagem, and
flurried the sentries to such an extent that I got clear away. I rather
fancy one or two others got off, too, but I don't know. I got into a
rather disagreeable tramp steamer, and volunteered as stoker. It's so
difficult to get stokers in the tropics that the captain took his risks
and kept me. I must say I was sorry afterwards that I hadn't stayed in
the gaol.'
The story was properly appreciated by the audience, and Hyacinth began
to feel a liking for the Captain.
'Do you know,' said Miss Goold, when their laughter had subsided, 'I
believe I know that identical tract. I once had an evangelical aunt, a
dear old lady who went about her house with a bunch of keys in a small
basket. She used to give me religious literature. I never was reduced to
reading it, but I distinctly remember a picture of Gideon with his mouth
open waving a torch on the front page. Could it have been the same?'
'It must have been,' said the Captain. 'Mine had that picture, too.
Gideon had nothing on but a sort of nightshirt with a belt to it, and
only one sleeve. By the way, if you are up in tracts, perhaps you know
one called "The Rock of Horeb "?'
Miss Goold shook her head.
'Ah, well,' said the Captain, after appealing to Mary O'Dwyer and
Hyacinth, 'it can't be helped, but I must say I should like to meet
someone who had read "The Rock of Horeb." I once sailed from Peru in
an exceedingly ill-found little barque loaded with guano. We had a very
dull time going through the tropics, and absolutely the only thing to
read on board was the first half of "The Rook of Horeb." There were at
least two pages missing. I read it until I nearly knew it off by heart,
and ever since I've been trying to get a complete copy to see how it
ended.'
Some of his stories dealt with more civilized life. He delighted Miss
Goold with an account, not at all unfriendly, of the humours of
the third battalion of the Connaught Rangers. He quoted one of Mary
O'Dwyer's poems to her, and pleased Hyacinth by his enthusiastic
admiration of the Connemara scenery. Good food, good wine, and a
companion like Captain Quinn, gladden the heart, and the little party
was very merry when Ginty deposited coffee and cigarettes and finally
departed.
In Miss Goold's house it was not the custom for the ladies to desert
the dinner-table by themselves. Very often the hostess was the only lady
present, and she had the greatest dislike to leaving a conversation just
when it was likely to become really interesting. Moreover, Miss Goold
smoked, not because it was a smart or emancipated thing to do, but
because she liked it, and--a curious note of femininity about her--she
objected to her drawing-room smelling of tobacco.
When Ginty had disappeared, and the serious business of enjoying the
food was completed, the talk of the party turned on the South African
campaign and the prospects of the Irish volunteers. Captain Quinn
displayed a considerable knowledge of the operations both of the Boers
and the British Generals. For the latter he expressed what appeared to
Hyacinth to be an exaggerated contempt, but the two ladies listened
to it with evident enjoyment. He delighted Miss Goold by his extreme
eagerness to be off.
'I don't see,' he said, 'why we shouldn't start to-morrow.'
'I'm afraid that's out of the question,' said Augusta Goold. 'M. de
Villeneuve arranged to send me a wire when he was ready for our men, and
I can't well send them sooner.'
'Ah,' said the Captain, 'but it seems to me the Frenchman is inclined
to dawdle. Don't you think that if we went over it might hurry him up a
bit?'
She agreed that this was possible, but represented the difficulty of
keeping the men suitably employed in Paris for perhaps three weeks or a
month.
'You see,' she said, 'they are all right here in Dublin, where I can
keep an eye on them. Besides, they have all got some sort of employment
here, and I don't have to pay them. I haven't got money enough to keep
them in Paris, and they won't get anything from Dr. Leyds until you have
them on board the steamer.'
Captain Quinn seemed satisfied, but later on in the evening he returned
to the subject.
'I can't help feeling that it would be better for me, at all events, to
go over to Paris at once. I shouldn't ask to draw any pay at present. I
have enough by me to keep me going for a few weeks.'
'But what about the men? Will you come back for them?'
'No, I think that would be foolish and unnecessary. There is no use in
attracting attention to our movements. We can't have a public send-off,
with cheers and that sort of thing, in any case, or march through the
streets like those ridiculous yeomen. Our fellows have got to slip
away quietly in twos and threes. We can't tell whether we're not being
watched this minute.'
There was a note of sincerity in the Captain's voice which convinced
Hyacinth that he was genuinely frightened at the thought of having a
policeman on his track. Miss Goold, too, looked appropriately solemn at
the suggestion. As a matter of fact, the authorities in Dublin Castle
did occasionally send a detective in plain clothes to walk after her.
It is not conceivable that they suspected her of wanting to blow up
Nelson's pillar or assassinate a judge. Probably they merely wished to
exercise the members of the force, and, in the absence of any actual
crime in the country, felt that no harm could come to anyone through the
'shadowing' of Miss Goold. The plan, though the authorities probably did
not consider this, had the incidental advantage of gratifying the lady
herself. She was perfectly acquainted with most of the officers who were
put on her track, and was always in good spirits when she recognised one
of them waiting for her in Westland Row Station. Captain Quinn kept a
watch on her face with his sharp shifting eyes while he spoke, and he
was quick to realize that he had hit on a way of flattering her.
'You are a person, Miss Goold, of whose actions the Government is bound
to take cognisance. I dare say they have their suspicions of me, and if
you and I are seen together in Dublin during the next week or two there
will certainly be inquiries; whereas, if I go over to Paris at once,
there will be no reason to watch you or anybody else.'
Augusta Goold hesitated.
'What do you say, Mr. Conneally?' she asked.
Hyacinth was puzzled at this extreme eagerness to be off. A suspicion
crossed his mind that the Captain meditated some kind of treachery. He
made what appeared to him to be a brilliant suggestion.
'Let me go with Captain Quinn. I can start to-morrow if necessary. I
should like to see something of Paris; and you know, Miss Goold, I've
plenty of money.'
He thought it likely that the Captain would object to this plan. If
he meditated any kind of crooked dealing when he got to Paris, though
Hyacinth failed to see any motive for treachery, he would not want to be
saddled with a companion. The answer he received surprised him.
'Delightful! I shall be glad to have a friend with me. In the intervals
of military preparation we can have a gay time--not too gay, of course,
Miss Goold. I shall keep Mr. Conneally out of serious mischief. When we
have a little spare cash we may as well enjoy ourselves. We shan't want
to carry money about with us in the Transvaal. We mean to live at the
expense of the English out there.'
Augusta Goold smiled almost maternally at Hyacinth.
'My dear boy,' she said, 'what seems plenty of money to you won't go
very far in Paris. What is it? Let me see, you said two hundred pounds,
and you want to buy your outfit out of that. Keep a little by you in
case of accident.'
'Well,' said the Captain, 'that's settled. And if we are really to start
to-morrow, we ought to get home to-night. Mr. Conneally may be ready
to start at a moment's notice, but he must at least pack up his
tooth-brush. May we see you safe back to town, Miss O'Dwyer? Remember,
we shall expect a valedictory ode in the next number of the _Croppy_.
Write us something that will go to a tune, something with a swing in it,
and we'll sing it beside the camp fires on the veldt. Miss Goold'--he
held out his hand as he spoke--'I'm a plain fellow'--he did not look in
the least as if he thought so--'I've led too rough a life to be any good
at making pretty speeches, but I'm glad I've seen you and talked to you.
If I'm knocked on the head out there I shall go under satisfied, for
I've met a woman fit to be a queen--a woman who is a queen, the queen of
the heart of Ireland.'
It is likely that Augusta Goold, though she was certainly not a fool,
was a little excited by the homage, for she refused to say good-bye,
declaring that she would see the boat off next morning. It was a promise
which would cost her something to keep, for the mail steamer leaves at 8
a.m., and Miss Goold was a lady who appreciated the warmth of her bed in
the mornings, especially during the early days of March, when the wind
is likely to be in the east.
CHAPTER XII
Captain Quinn made himself very agreeable to Mary O'Dwyer during the
short journey back to Dublin. At Westland Row he saw her into a cab,
which he paid for. His last words were a reminder that he would expect
to have her war-song, music and all, sent after him to Paris. Then he
turned to Hyacinth.
'That's all right. We've done with her. It was better to pay the cab for
her, else she might have scrupled about taking one, and we should have
been obliged to go home with her in a beastly tram. Come along. I'm
staying at the Gresham. It's always as well to go to a decent place
if you have any money. You come with me, and we'll have a drink and a
talk.'
There were two priests and a Bishop in earnest conference round the
fire in the hall of the hotel when they entered. When he discovered that
their talk was of the iniquities of the National Board of Education, and
therefore likely to last beyond midnight, Captain Quinn led the way into
the smoking-room, which was unoccupied. A sufficient supply of whisky
and a syphon of soda-water were set before them. The Captain stretched
himself in a comfortable chair, and lit his pipe.
'A fine woman, Miss Goold,' he said meditatively. Hyacinth murmured an
assent.
'A very fine woman, and apparently pretty comfortably off. I wonder why
on earth she does it.'
He looked at Hyacinth as if he expected some sort of explanation to be
forthcoming.
'Does what?' asked Hyacinth at length.
'Oh, all this revolutionary business: the _Croppy_, seditious speeches,
and now this rot about helping the Boers. What does she stand to gain by
it? I don't suppose there's any money in the business, and a woman
like that might get all the notoriety she wants in her own proper set,
without stumping the country and talking rot.'
This way of looking at Augusta Goold's patriotism was new to Hyacinth,
and he resented it.
'I suppose she believes in the principles she professes,' he said.
The Captain looked at him curiously, and then took a drink of his
whisky-and-soda.
'Well,' he said, 'let's suppose she does. After all, her motives are
nothing to us, and she's a damned fine woman, whatever she does it for.'
He drank again.
'It would have been very pleasant, now, if she would have spent the next
few weeks with me in Paris. You won't mind my saying that I'd rather
have had her than you, Conneally, as a companion in a little burst.
However, I saw at once that it wouldn't do. Anyone with an eye in his
head could tell at a glance that she wasn't that sort.'
He sighed. Hyacinth was not quite sure that he understood. The
suggestion was so calmly made and reasoned on that it seemed impossible
that it could be as iniquitous as it appeared.
'There's no one such an utter fool about women,' went on the Captain,
'as your respectable married man, who never does anything wrong himself.
I'd heard of Miss Goold, as everybody has, and listened to discussions
about her character. You know just as well as I do the sort of things
they say about her.'
Hyacinth did know very well, and flared up in defence of his patroness.
'They are vile lies.'
'That's just what I'm saying. Those respectable people who tell the lies
are such fools. They think that every woman who doesn't mew about
at afternoon parties must be a bad one. Now, anyone with a little
experience would know at once that Miss Goold--what's this the other
one called her? Oh yes, Finola--that Finola may be a fool, but she's not
_that_.'
He pulled himself together as he spoke. Evidently he plumed himself, on
his experience and the faculty for judging it had brought him.
'Now, I'd just as soon have asked my sister-in-law to come to Paris with
me for a fortnight as Finola. You don't know Mrs. James Quinn, I think.
That's a pity. She's the most domesticated and virtuous _haus-frau_ in
the world.'
He paused, and then asked Hyacinth, 'Why are you doing it?'
Again Hyacinth was reduced by sheer surprise to a futility.
'Doing what?'
'Oh, going out to fight for the Boers. Now, don't, like a good fellow,
say you're acting on principle. It's all well enough to give Finola
credit for that kind of thing. She is, as we agreed, a splendid woman.
But you mustn't ask me to believe in the whole corps in the same way.'
Hyacinth meditated a reply. It was clearly impossible to assert that
he wanted to fight for liberty, to give his life to the cause of an
oppressed nationality. It would be utterly absurd to tell the story of
his father's vision, and say that he looked on the South African War
as a skirmish preliminary to the Armageddon. Sitting opposite to this
cynical man of the world and listening to his talk, Hyacinth came
himself to disbelieve in principle. He felt that there must be some
baser motive at the bottom of his desire to fight, only, for the life of
him, he could not remember what it was. He could not even imagine a good
reason--good in the estimation of his companion--why anyone should do so
foolish a thing as go out to the Transvaal. The Captain was not at all
impatient. He sat smoking quietly, until there seemed no prospect of
Hyacinth answering; then he said:
'Well, if you don't want to tell me, I don't mind. Only I think you're
foolish. You see, little accidents happen in these affairs. There are
such things as bullets, and one of them might hit you somewhere that
would matter. Then it would be my duty to send home your last words to
your sorrowing relatives, and it would be easier to do that if I knew
exactly what you had done. The death-bed repentance of the prodigal
is always most consoling to the elder brother--much more consoling, in
fact, than the prodigal's return. Now, how the deuce am I to make up a
plausible repentance for you, if I don't know what you've done?'
'But I've not done anything,' said Hyacinth ineffectively.
The Captain ignored him.
'Come, now, it can't be anything very bad at your age. Have you got
into a mess with a girl? Or'--he brightened up at the guess--'are
you hopelessly enamoured of the beautiful Finola? That would be most
suitable. The bold, bad woman sends the minstrel boy to his death,
with his wild harp slung behind him. I could draw tears from the
stoniest-hearted elder brother over that.'
If he could have thought of a crime at the moment, Hyacinth would
probably have confessed it; but he was bewildered, and could hit on
nothing better than:
'I have no elder brother--in fact, no relation of any sort.'
'Lucky man! Now, I have a perfect specimen of a brother--James Quinn,
Esquire, of Ballymoy. He's a churchwarden. Think of that! If it should
be your melancholy duty to send the message home to him--in case that
bullet hits me, I mean--tell him------ Oh, there's no false pride about
me. Fill your glass again. I don't in the least mind your knowing that I
wouldn't go a step to fight for Boer or Briton either if it wasn't for a
little affair connected with some horses and a cheque. You see, the War
Office people sent down a perfect idiot to buy remounts for the cavalry
in Galway and Mayo. He was the sort of idiot that would tempt an
Archbishop to swindle him. I rather overdid it, I'm afraid, and now the
matter is likely to come out.'
For all his boasted powers of observation, Captain Quinn failed to
notice the disgust and alarm on Hyacinth's face.
'I stuck the fool,' he went on, 'with every old screw in the country. I
got broken-winded mares from the ploughs. I collected a regular hospital
of spavined, knock-kneed beasts, and he took them from me without a word
at thirty pounds apiece. It would have been all right if I had gone no
further. But, hang it all! I got to the end of my tether. I declare to
you I don't believe there was another screw left in the whole county of
Mayo, and unless I took to selling him the asses I couldn't go on. Then
I heard of this plan of your friend Finola's, and I determined to make
a little coup and clear. I altered a cheque. The idiot was on his way to
an out-of-the-way corner of Connemara looking for mounted infantry cobs.
I knew he wouldn't see his bank-book for at least a week, so I chanced
it. That's the reason why I am so uncommonly anxious to get clear at
once. If I once get off, it will be next door to impossible to get me
back again. General Joubert will hardly give me up. I'm not the least
afraid of those ridiculous policemen who walk about after Finola. But
I am very much afraid of being tapped on the shoulder for reasons
quite non-political. I can tell you I've been on the jump ever since
yesterday, when I cashed the cheque, and I shan't feel easy till I've
left France behind me. I fancy I'm safe for the present. The idiot is
sure to try fifty ways of getting his accounts straight before he lights
on my little cheque; and when he does, I've covered my tracks pretty
well. My dear brother hasn't the slightest notion what's become of me.
I dare say he'll stop making inquiries as soon as the police begin. Poor
old chap! He'll feel it about the family name, and so on.'
He smiled at his own reflection in the mirror over the chimneypiece. He
was evidently well satisfied with the performance he had narrated. Then
at last Hyacinth found himself able to speak. Again, as when he had
defeated Dr. Spenser in the college lecture-room, his own coolness
surprised him.
'You're an infernal blackguard!' he said.
Captain Quinn looked at him with a surprise that was perfectly genuine.
He doubted if he could have heard correctly.
'What did you say?'
'I said,' repeated Hyacinth, 'you are an infernal blackguard!'
'Did you really suppose that I would be going on this fool of an
expedition if I wasn't?'
'I shall tell Miss Goold the story you have just told me. I shall tell
her to-morrow morning before the boat sails.'
'Very well,' said the Captain; 'but don't suppose for a moment that
you'll shock Finola. She doesn't know this particular story about me,
but I expect she knows another every bit as bad, and I dare say she will
regard the whole thing as a justifiable spoiling of the Egyptians. By
the way '--there was a note of anxiety in his voice--'I hope you won't
find it necessary to repeat anything I've said about the lady herself.
_That_ might irritate her.'
'Is it likely,' said Hyacinth, 'that I would repeat that kind of talk to
any woman?'
'Quite so. I admire your attitude. Such things are entirely unfit for
repetition. But seriously, now, what on earth do you expect to happen
when you tell her? I'm perfectly certain that every single volunteer
she's got is just as great a blackguard--your word, my dear fellow--as I
am, and Finola knows it perfectly well.'
Hyacinth hesitated. The phrase in Miss Goold's letter in which she had
originally described her men as blackguards recurred to his mind. He
remembered the story of Doherty. His anger began to give way to a sick
feeling of disgust.
'Think, now,' said the Captain: 'is it likely that you could enlist a
corps of Sunday-school teachers for this kind of work? I'll give you
credit for the highest motives, though I'm blest if I understand them;
but how can you suppose that there is anyone else in the whole world
that feels the way you feel or wants to act as you are doing?'
'I dare say you are right,' said Hyacinth feebly.
'Of course I'm right--perfectly right.'
Hyacinth tried to lift his glass of whisky-and-water to his lips, but
his hand trembled, and he was obliged to put it down. Captain Quinn
watched him wipe the spilt liquid off his hand, and then settle down in
his chair with his head bowed and his eyes half shut.
'Sit up, man,' he said. 'It's all right. You've done nothing to be
ashamed of, at all events. But look here, you ought not to come with us
at all.
It's no job for a man like you. You back out of it. Don't turn up
to-morrow morning. I'll explain to Finola if she's there, and if not
I'll write her a letter that will set you straight with her. I'm really
sorry for you, Conneally.'
Hyacinth looked up at him.
'I'm sorry I called you a blackguard,' he said. 'You're not any worse
than everyone else in the world.'
'Nonsense,' said Captain Quinn. 'Don't take it like that. From your
point of view you were quite right to call me a blackguard. And, mind
you, there are plenty of people in the world who aren't blackguards.
There's my brother, for instance. He's a bit of a prig--in fact, he's
as priggish as he well can be--but he's never done anything but run
straight. I don't suppose he could go crooked if he tried.'
Hyacinth got up.
'Good-night,' he said, 'and good-bye. I shan't go with you.'
'Wait a minute,' said Captain Quinn. 'I think I've done you one good
turn to-night in stopping you going to South Africa. Now I'll do you
another, and one at the same time to that brother of mine. I left him
in a hurry. I told you that, but I don't think I mentioned that I was in
his employment. He runs a woollen factory down in Mayo. I owned a
share in the business once, but that went long ago, and the whole thing
belongs to James now. I was a sort of clerk and general agent. I wasn't
really the least use, for I never did any work. James was for ever
complaining, but I'm bound to say he stuck to me. I'll give you a letter
to him, and I dare say you may get the job that I've chucked. It's not
much of a thing, but it may suit you for a while. Sit down till I write
my letter.'
Hyacinth obeyed. Since his anger evaporated a sort of numbness had crept
over his mind. He scarcely understood what was said to him. He had a
vague feeling of gratitude towards Captain Quinn, and at the same time
a great desire to get away and be alone. He felt that he required to
adjust his mind to the new thoughts which had been crowded into it. When
he received the letter he put it into his pocket, and rose again to go.
The Captain saw him to the door.
'Good-bye.' Hyacinth heard him, but his voice seemed far off, and his
words meaningless. 'Take my advice and run down to Ballymoy at once.
Don't hang about Finola any more. She's a splendid woman, but she's not
for you. If you married her you'd be perfectly miserable. Not that I
think she'd ever marry you. Still, she might. Women do such odd things.
If by any chance she does, you'll have to be very careful. Give her her
head, and take her easy up to the jumps. Don't try to hustle her, and
for God's sake don't begin sawing at her mouth. I'd very much like to be
here to see you in the character of Mr. Augusta Goold.' He sighed.
'But, of course, I can't. The British Isles will be too hot for me for
a while. However, who can tell what might happen if I win a good medal
from old Kruger, and capture a few British Generals? I might act best
man for you yet, if you'll wait a year or two.'
When Hyacinth got home to his lodgings the first object that met his eye
was Grealy's ancient rifle. He tied a label round its barrel addressed
to the owner. Then he packed his few belongings carefully and strapped
his bag. So far he was sure of himself. He had no doubt whatever that he
must leave Dublin at once. He felt that he could not endure an interview
with Augusta Goold. She might blame him or might pity him. Either would
be intolerable. She might even justify herself to him, might beat him
into submission by sheer force of her beauty and her passion, as she had
done once before. He would run no such risk. He felt that he could not
sacrifice his sense of right and wrong, could not allow himself to be
dragged into the moral chaos in which, it seemed to him now, Miss Goold
lived. He was unconscious of any Divine leading, or even of any direct
reliance on the obligations of honour. He could not himself have told
why he clung with such desperate terror to his plan of escaping from his
surroundings. Simply he could not do certain things or associate as a
friend with people who did them. To get away from Dublin was the first
necessity. For a moment it occurred to him that he might go to Dr.
Henry, tell him the whole story, and ask for advice and help. But that
was impossible. How could he confess the degradation of his ideal?
How could he resist the inevitable reminder that he had been warned
beforehand? Besides, not even now, after all that he had seen, could he
accept Dr. Henry's point of view. He still believed in Ireland, still
hoped to serve her, still looked for the coming of his father's captain
to lead the saints to the final victory. Miss Goold had failed him, but
he was not yet ready to enrol himself a citizen of England.
No, he must leave Dublin. But where to go? His lamp burnt dim and
expired as he sat thinking. His fire had long ago gone out. He shivered
with cold and misery, while the faint light of the dawn stole into his
room. He heard the first twitter of the birds in the convent garden
behind his lodging. Then came the noise of the earliest traffic, the
unnaturally loud rattle of the dust-carts on their rounds. A steamer
hooted far away down the river, and an early bell rang the neighbouring
nuns to prayer. Hyacinth grew desperate. Could he go home, back to the
fishing-boats and simple people of Carrowkeel? A great desire for the
old scenes seized upon him. He fought against it with all his might. He
had rejected the offer of the home life once. Now, no doubt, it would be
closed against him. The boat that might have been his was sold long ago.
He would not go back to confess himself a fool and a failure.
Gradually his mind worked back over the conversation in the hotel with
Captain Quinn. The recollection of the latter part of it, which had
meant nothing at the time, grew clear. He felt for the letter in his
pocket, and drew it out. After all, why should he not offer himself to
James Quinn? Ballymoy was remote enough to be a hiding-place. It was in
County Mayo, the Captain had said. He had never heard of the place, and
it seemed likely that no one else, except its inhabitants, knew of it
either. At least, there was no reason that he could see why he should
not go there. His brain refused to work any longer, either at planning
or remembering. His lips formed the word Ballymoy. He repeated it again
and again. He seemed to go on repeating it in the troubled sleep which
came to him.
CHAPTER XIII
The Irish get credit, even from their enemies, for being a quick-witted,
imaginative, and artistic people, yet they display astonishingly little
taste or originality in their domestic architecture. In Connaught, where
the Celtic genius may be supposed to have the freest opportunity
for expressing itself, the towns are all exactly alike, and their
resemblance consists in the absence of any beauty which can please
the eye. An English country town, although the English bucolic is
notoriously as stupid as an ox, has certain features of its own. So has
a Swiss cottage or a French village. It is possible to represent these
upon Christmas cards or the lids of chocolate-boxes without labelling
them English, Swiss, or French. Any moderately well educated young lady
will recognise them at once, and exclaim without hesitation, 'How truly
English!' or 'How sweetly Swiss!' But no one can depict an Irish town
with any hope of having it recognised unless he idealizes boldly,
introducing a highly-intelligent pig, or a man in knee-breeches kissing
a fancifully-attired colleen. And then, after all, he might as well have
labelled it Irish at once in good plain print, and saved himself the
trouble of drawing the symbolic figures.
To describe Ballymoy, therefore, mountains, rivers, and such like
natural eccentricities being left out of the count, is to describe fifty
other West of Ireland towns. There is a railway-station, bleak, gray,
and windswept, situated, for the benefit of local car-owners, a mile and
a half from the town, and the road which connects the two is execrable.
There is a workhouse, in Ballymoy as everywhere else in this lost land
the most prominent building. There is a convent, immense and wonderfully
white, with rows and rows of staring windows and a far-seen figure of
the Blessed Virgin, poised in a niche above the main door. There is
a Roman Catholic church, gray-walled, gray-roofed, and unspeakably
hideous, but large and, like the workhouse and the convent, obtruding
itself upon the eye. It seems as if the inhabitants of the town must all
of them be forced, and that at no distant date, either into religion
or pauperism, just as small bodies floating in a pond are sucked into
connection with one or other of the logs which lie among them. The shops
in the one tortuous street block the footpaths in front of their doors
with piles of empty packing-cases. The passenger is saluted, here by a
buffet in the face from a waterproof coat suspended outside a draper's,
there by a hot breath of whisky-laden air. Two shops out of every
three are public-houses. These occupy a very beautiful position in the
economic life of the town. Their profits go to build the church, to
pay the priests, and to fill the coffers of the nuns. The making of
the profits fills the workhouse. A little aloof stands the Protestant
church, austere to look upon, expressing in all its lines a grim
reproach of the people's life. Beyond it, among scanty, stooped trees,
is the rectory, gray, as everything else is, wearing, like a decayed
lady, the air of having lived through better days.
Such, save for one feature, is Ballymoy, as the traveller sees it, as
Hyacinth Conneally saw it when he arrived there one gusty afternoon.
The one unusual feature is Mr. James Quinn's woollen mill. It stands,
a gaunt and indeed somewhat dilapidated building, at the bottom of the
street, in the angle where the river turns sharply to flow under the
bridge. The water just above the bridge is swept into a channel and
forced to turn the wheel which works some primitive machinery within.
In the centre of the mill's front is an archway through which carts pass
into the paved square behind. Here is the weighbridge, and here great
bundles of heavy-smelling fleeces are unloaded. Off the square is the
office where Mr. Quinn sits, pays for the wool, and enters the weight
of it in damp ledgers. Here on Saturdays two or three men and a score of
girls receive their wages. The business is a peculiar one. You may bring
your wool to Mr. Quinn in fleeces, just as you sheer it off the sheep's
back. He will pay you for it, more or less, according to the amount
of trouble you have taken with your sheep. This is the way the younger
generation likes to treat its wool. If you are older, and are blessed
with a wife able to card and spin, you deal differently with Mr. Quinn.
For many evenings after the shearing your wife sits by the fireside
with two carding-combs in her hands, and wipes off them wonderfully soft
rolls of wool. Afterwards she fetches the great wheel from its nook, and
you watch her pulling out an endless gray thread while she steps back
and forwards across the floor. The girls watch her, too, but not, as
you do, with sleepy admiration. Their emotion is amused contempt.
Nevertheless, your kitchen wall is gradually decorated with bunches of
great gray balls. When these have accumulated sufficiently, you take
them to Mr. Quinn. A certain number of them become his property. Out of
the rest he will weave what you like--coarse yellow flannel, good for
bawneens, and, when it is dyed crimson, for petticoats; or blankets--not
fluffy like the blankets that are bought in shops, but warm to sleep
under when the winter comes; or perhaps frieze, very thick and rough,
the one fabric that will resist the winter rain.
This portion of his business Mr. Quinn finds to be decreasing year by
year. Fewer and fewer women care to card and spin the wool. The younger
men find it more profitable to sell it at once, and to wear, instead
of the old bawneens, shirts called flannel which are brought over from
cotton-spinning Lancashire, and sold in the shops. The younger women
think that they look prettier in gowns made artfully by the local
dressmaker out of feeble materials got up to catch the eye. If now and
then, for the sake of real warmth, one of them makes a petticoat of the
old crimson flannel, it is kept so short that, save in very heavy rain,
it can be concealed. Unfortunately, while these old-fashioned profits
are vanishing, Mr. Quinn finds it very hard to increase the other branch
of his business. The fabrics which he makes are good, so good that he
finds it difficult to sell them in the teeth of competition. The
country shops are flooded with what he calls 'shoddy.' An army of eager
commercial travellers pushes showy goods on the shopkeepers and the
public at half his price. Even the farmers in remote districts are
beginning to acquire a taste for smartness. Some things in which he used
to do a useful trade are now scarcely worth making. There is hardly
any demand for the checked head-kerchiefs. The women prefer hats and
bonnets, decked with cheap ribbons or artificial flowers; and these
bring no trade to Mr. Quinn's mill. Still, he manages to hold on. The
Lancashire people, though they have invented flannelette, cannot as yet
make a passable imitation of frieze, and there is a Dublin house which
buys annually all the blankets he can turn out. It is true that even
there, and for the best class of customers, prices have to be cut so as
to leave a bare margin of profit. Yet since there is a margin, Mr. Quinn
holds on, though not very hopefully.
Hyacinth left the bulk of his luggage--a packing-case containing the
books which the auctioneer had failed to dispose of in Carrowkeel--at
the station, and walked into Ballymoy carrying his bag. He had little
difficulty in making his way to the mill, and found the owner of it in
his office. It was difficult at first to believe that James Quinn could
be any relation to Captain Albert, the traveller, horse-dealer, soldier,
and thief. This man was tall, though he stooped when he stood to receive
his visitor. His movements were slow. His fair hair lay thin across his
forehead, and was touched above the ears with gray. His blue eyes were
very gentle, and had a way of looking long and steadily at what they
saw. A glance at his face left the impression that life, perhaps by no
very gentle means, had taught him patience.
'This letter will introduce me,' said Hyacinth; 'it is from your
brother, Captain, or Mr. Albert, Quinn.'
James Quinn took the letter, and turned it over slowly. Then, without
opening it, he laid it on the table in front of him. His eyes travelled
from it to Hyacinth's face, and rested there. It was some time before he
spoke, and then it was to correct Hyacinth upon a trivial point.
'My half-brother,' he said. 'My father married twice, and Albert is the
son of his second wife. You may have noticed that he is a great deal
younger than I am.'
'He looks younger, certainly,' said Hyacinth, for the other was waiting
for a reply.
'Nearly twenty years younger. Albert is only just thirty.'
The exact age of the Captain was uninteresting and seemed to be beside
the purpose of the visit. Hyacinth shifted his chair and fidgeted,
uncertain what to do or say next.
'Albert gave you this letter to me. Is he a friend of yours?'
'No.'
James Quinn looked at him again steadily. It seemed--but this may have
been fancy--that there was a kindlier expression in his eyes after the
emphatio repudiation of friendship with Albert. At length he took up the
letter, and read it through slowly.
'Why did my brother give you this letter?'
The question was a puzzling one. Hyacinth had never thought of trying
to understand the Captain's motives. Then the conversation in the hotel
recurred to him.
'He said that he wanted to do a good turn to me and to you also.'
'What had you done for him?'
'Nothing whatever.'
Apparently James Quinn was not in the least vexed at the brevity of
the answers he received, or disturbed because his cross-examination was
obviously disagreeable to Hyacinth.
'In this letter,' he went on, referring to the document as he spoke,
'he describes you as a young man who is "certainly honest, probably
religious, and possibly intelligent." I presume you know my brother, and
if you do, you may be surprised to hear that I am quite prepared to take
his word for all this. I have very seldom known Albert to tell me lies,
and I don't know why he should want to deceive me in this case. Still,
I am a little puzzled to account for his giving you the letter. Can you
add nothing in the way of explanation to what you have said?'
'I don't know that I can,' said Hyacinth.
'Will you tell me how you met my brother, and what he is doing now, or
where he is?'
'I do not think I should be justified in doing so.'
'Ah, well! I can understand that in certain circumstances Albert would
be very grateful to a man who would hold his tongue. He might be quite
willing to do you a good turn if you undertook to answer no questions
about him.'
He smiled as he spoke, a little grimly, but there was laughter lurking
in the corners of his eyes. A Puritan will sometimes smile in such a
way at the thought of a sinful situation, too solemn to be laughed
at openly, but appealing to a not entirely atrophied sense of humour.
Hyacinth felt reassured.
'Indeed,' he said, 'I made no promise of silence. It is only that--well,
I don't think----'
James Quinn waited patiently for the conclusion of the sentence, but
Hyacinth never arrived at it.
'In this letter,' he said at last, 'my brother asks me to give you the
place he lately held in my business. Now, I don't want to press you to
say anything you don't want to, but before we go further I must ask you
this, Were you implicated in the affair yourself?'
'I beg your pardon. I don't quite understand what you mean.'
'Well, I suppose that since my brother is anxious that you should hold
your tongue, he has done something that won't bear talking about. Were
you implicated in--in whatever the trouble was?'
'Certainly not,' said Hyacinth. 'In fact, it was on account of what you
speak of as "trouble" that I declined to have anything more to do with
your brother.'
'That is probably very much to your credit, and, in the light of my
brother's estimate of your character, I may say that I entirely believe
what you say. Am I to understand that you are an applicant for the post
in my business which Albert held, and which this letter tells me I may
consider vacant?'
'That is what brought me down here,' said Hyacinth.
'Have you any other recommendations or testimonials as to character to
show me?'
'No. But there are several people who would answer questions about me if
you wrote to them: Dr. Henry, of Trinity College, would, or Miss Augusta
Goold, or Father Moran, of Carrowkeel, in County Galway.'
'You have given me the most remarkable list of references I ever came
across in my life. I don't suppose anyone ever before was recommended
for a post by a Protestant divinity professor, a notoriously violent
political agitator, a Roman Catholic priest, and a--well, we won't
describe my brother. How do you come to be mixed up with all these
people? Who are you?'
'I am the son of AEneas Conneally, Rector of Carrowkeel, who died last
Christmas.'
'Well,' said James Quinn, 'I suppose if all these people are prepared
to recommend you, your character must be all right. Now, tell me, do you
know what the post is you are applying for?'
'No,' said Hyacinth. 'And I may as well say that I have had no
experience or business training whatever.'
'So I should suppose from the way you have come to me. Well, my brother
was clerk and traveller for my business. He was supposed to help me to
keep accounts and to push the sale of my goods among the shopkeepers
in Connaught. As a matter of fact, he never did either the one or the
other. When he was at home he did nothing. When he was on the road
he bought and sold horses. I paid him eighty pounds a year and his
travelling expenses. I also promised him a percentage on the profits of
the sales he effected. Now, do you think this work would suit you?'
'I might not be able to do it,' said Hyacinth, 'but I should very much
like to be allowed to try. I can understand that I shall be very little
use at first, and I am willing to work without any salary for a time,
perhaps six months, until I have learned something about your business.'
'Come, now, that's a business-like offer. I'll give you a trial, if it
was only for the sake of your list of references. I won't keep you six
months without paying you if you turn out to be any good at all. And I
think there must be something in you, for you've gone about getting this
job in the queerest way I ever heard of. Would you like any time to make
up your mind finally before accepting the post?'
'No,' said Hyacinth; 'I accept at once.'
They walked together through the mill, and looked at the machines and
the workers. The girls smiled when Mr. Quinn stopped to speak to them,
and looked with frank curiosity at Hyacinth. The three or four men who
did the heavier work stopped and chatted for a few minutes when they
came to them. Evidently there was no soreness or distrust here between
the employer and the employed. When they had gone through the rooms
where the work was going on, they climbed a staircase like a ladder, and
came to the loft where the wool was stored. Hyacinth handled it as he
was directed, and endeavoured to appreciate the difference between the
good and the inferior qualities. They passed by an unglazed window at
the back of the mill, and Mr. Quinn pointed out his own house. It stood
among trees and shrubs, now for the most part bare, but giving promise
of shady privacy in summertime. Long windows opened out on to a lawn
stretching down to the watercourse which fed the millwheel. A gravel
path skirted one side of the house leading to a bridge, and thence to
a doorway in a high wall, beyond which lay the road. As they looked
the door opened, and a woman with two little girls came through. They
crossed the bridge, and walked up to the house.
'That is my wife,' said Mr. Quinn, 'and my two little girls.'
He stretched out between the bars of the window, and shouted to them.
All three looked back. Mrs. Quinn waved her hand, and the two children
shouted in reply. Then a light appeared in one of the windows, and
Hyacinth caught a glimpse of a trim maid-servant pulling the curtains
across it.
'We shall be having tea at half-past six,' said Mr. Quinn. 'Will you
come and join us? By the way, where are you staying?'
Hyacinth accepted the invitation, and confessed that he had not as yet
looked for any place to lay his head.
'Ah! Better go to the hotel for to-night. It's not much of a place,
but you will have to learn to put up with that sort of accommodation.
Tomorrow we'll try and find you some decent lodgings.'
The hotel struck even Hyacinth as of inferior quality, though it
boasted great things in the timetable advertisements, and called itself
'Imperial' in large gold letters above its door. A smell of whisky and
tobacco greeted him as he entered, and a waiter with a greasy coat, in
answer to inquiries about a bed, sent him down a dark passage to seek
a lady called Miss Sweeney at the bar. Large leather cases with broad
straps and waterproof-covered baskets blocked the passage, and Hyacinth
stumbled among them for some time before he discovered Miss Sweeney
reading a periodical called _Spicy Bits_ among her whisky-bottles.
She was a young woman of would-be fashionable appearance, and acted
apparently in the double capacity of barmaid and clerk. On hearing that
Hyacinth required, not whisky, but a bedroom, she requested him to go
forward to the office, indicating a glass case at the far end of the bar
counter. Here he repeated his request to her through a small opening in
the glass, and received her assurance, given with great condescension,
that No. 42 was vacant, and, further, that there was a fire in the
commercial room. A boy whom she summoned carried Hyacinth's bag to an
extremely dirty and ill-furnished bedroom, and afterwards conducted
him to the promised fire. Two other guests were seated at it when he
entered, who, after a long stare, made room for him. Apparently there
was no one else stopping in the hotel, and the whole mass of cumbrous
baggage which blocked the passage to the bar must belong to them.
Hyacinth realized, with a feeling of disgust which he could
not account for, that these were two members of his new
profession--fellow-travellers in the voyages of commerce. He
gathered--for they talked loudly, without regarding his presence--that
they represented two Manchester firms which were rivals in the wholesale
drapery business. Very much of what they said was unintelligible to him,
though the words were familiar. He knew that 'lines' could be 'quoted,'
but not apparently in the same sense in which they discussed these
operations, and it puzzled him to hear of muslins being 'done at one and
seven-eighths.' He sat for a time wondering at the waste of money and
energy involved in sending these men to remote corners of Ireland to
search for customers. Then he left them, and made his way down the muddy
street to Mr. Quinn's house.
The room into which he was shown was different from any he had ever
seen. It was lit by a single lamp with a dull glass globe and a turf
fire which burnt brightly. Two straight-backed, leather-covered chairs
stood one on either side of the tiled hearth. Near one stood a little
table covered with neatly-arranged books, and, rising from among them,
a reading-lamp, as yet unlit. Beyond the other was a work-table
strewed with reels and scissors, on which lay a child's frock and some
stockings. The table was laid for tea. On it were plates piled up with
floury scones, delicate beleek saucers full of butter patted thin into
the shapes of shells, and jam in glass dishes cased in silver
filigree. A large home-baked loaf of soda bread on a wooden platter
stood at one end of the table, and near it a sponge-cake. At the other
end was an array of cups and saucers with silver spoons that glittered,
a jug of cream, and one of milk. Two of the cups were larger than the
others, and had those curious bars across them which are designed to
save men from wetting their moustaches when they drink. No room and no
preparation for a meal could have offered a more striking contrast to
Augusta Goold's dining-room, her groups of wineglasses, multiplicity of
heavy-handled knives and forks, and her candles shrouded in silk. Nor
was the dainty neatness less remote from the cracked delf and huddled
sordidness of his old home.
Long before Hyacinth had realized an impression of the scene before him
Mrs. Quinn greeted him, and led him to the fire. Her two little girls,
who lay on the hearthrug with a picture-book between them, were bidden
to make room for him. When her husband appeared she bustled off, and in
a minute or two she and the maid came in bringing toast and tea and hot
water hissing in a silver urn.
As the evening passed Hyacinth began to realize that he had entered into
a home of peace. He felt that these people were neither greatly anxious
to be rich nor much afraid of being poor. They seemed in no way fretted
that there were others higher in the social scale, cleverer or more
brilliant than they were. He understood that they were both of them
religious in a way quite different from any he had known. They neither
spoke of mysteries, like his father, nor were eager about disputings,
like the men who had been his fellow-students. They were living a very
simple life, of which faith and a wide charity formed a part as natural
as eating or sleeping. When the children's bedtime came it seemed to
him a very wonderful thing that they should kneel in turns beside their
father's knee and say their prayers aloud, when he, a stranger, was in
the room. It seemed to him less strange, because then he had been two
hours longer in the company of the Quinns, that before leaving he,
too, should kneel beside his hostess and listen while his new employer
repeated the familiar words of some of the old collects he had heard his
father read in church.
CHAPTER XIV
On Sunday, the third day after his arrival in Ballymoy, Hyacinth went to
church. He could hardly have avoided doing so, even if he had wanted to,
for Mrs. Quinn invited him to share her pew. There was no real necessity
for such hospitality, for the church was never, even under the most
favourable circumstances, more than half full. The four front seats were
reserved for a Mr. Stack, on whose property the town of Ballymoy stood.
But this gentleman preferred to live in Surrey, and even when he came
over to Ireland for the shooting rarely honoured the church with his
presence. A stone tablet, bearing the name of this magnate's father, a
Cork pawnbroker, who had purchased the property for a small sum under
the Encumbered Estates Court Act, adorned the wall beside the pulpit.
The management of the property was in the hands of a Dublin firm, so
the parish was deprived of the privilege of a resident land agent. The
doctor, recently appointed to the district, was a Roman Catholic of
plebeian antecedents, which reduced the resident gentry of Ballymoy
to the Quinns, a bank manager, and the Rector, Canon Beecher. A few
farmers, Mr. Stack's gamekeeper, and the landlady of the Imperial Hotel,
made up the rest of the congregation.
The service was not of a very attractive or inspiriting kind. Canon
Beecher--his title was a purely honorary one, not even involving the
duty of preaching in the unpretending building which, in virtue of
some forgotten history, was dignified with the name of Killinacoff
Cathedral--read slowly with somewhat ponderous emphasis. His thirty
years in Holy Orders had slightly hardened an originally luscious Dublin
brogue, but there remained a certain gentle aspiration of the _d's_ and
_t's_, and a tendency to omit the labial consonants altogether. He read
an immense number of prayers, gathering, as it seemed to Hyacinth, the
longest ones from the four corners of the Prayer-Book. At intervals he
allowed himself to be interrupted with a hymn, but resumed afterwards
the steady flow of supplication. The eldest Miss Beecher--the Canon had
altogether two daughters and three sons--played a harmonium. The other
girl and the three boys, with the assistance of an uncertain bass from
Mr. Quinn, gave utterance to the congregation's praise. Hyacinth tried
to join in the first hymn, which happened to be familiar to him, but
quavered into silence towards the end of the second verse, discovering
that the eyes of Mrs. Beecher from her pew, of the Canon from the
reading-desk, of the vocal Miss Beecher and her brothers, were fixed
upon him. The sermon proved to be long and uninteresting. It was about
Melchizedek, and was so far appropriate to the Priest and King that it
had no recognisable beginning and need not apparently have ever had an
end. Perhaps no one, unless he were specially trained for the purpose,
could have followed right through the quiet meander-ings of the Canon's
thought. This kind of sermon, however, has the one advantage that
the listener can take it up and drop it again at any point without
inconvenience, and Hyacinth was able to give his attention to some
sections of it. There was no attempt at eloquence or any kind of
learning displayed, but he understood, as he listened, where the Quinns
got their religion, or at least how their religion was kept alive.
Certain very simple things were reiterated with a quiet earnestness
which left no doubt that the preacher believed exactly what he said, and
lived by the light of his faith.
One evening shortly afterwards Canon Beecher called upon Hyacinth. The
conversation during the visit resolved itself into a kind of catechism,
which, curiously enough, was quite inoffensive. The Canon learnt by
degrees something of Hyacinth's past life, and his career in Trinity
College. He shook his head gravely over the friendship with Augusta
Goold, whom he evidently regarded as almost beyond the reach of the
grace of God. Hyacinth was forced to admit, with an increasing sense of
shame, that he had never signed a temperance pledge, did not read the
organ of the Church Missionary Society, was not a member of a Young
Men's Christian Association, or even of a Gleaners' Union. He felt, as
he made each confession sorrowfully, that he was losing all hope of the
Canon's friendship, and was most agreeably surprised when the interview
closed with a warm invitation to a mid-day dinner at the Rectory on the
following Sunday. Mrs. Quinn, who took a sort of elder sister's interest
in his goings out and comings in, was delighted when she heard that he
was going to the Rectory, and assured him that he would like both Mrs.
Beecher and the girls. She confided afterwards to her husband that the
influence of a Christian home was likely to be most beneficial to the
'poor boy.'
The Rectory displayed none of the signs of easy comfort which had
charmed Hyacinth in the Quinns' house. The floor of the square hall was
covered with a cheap, well-worn oilcloth. Its walls were damp-stained,
and the only furniture consisted of a wooden chair and a somewhat
rickety table. In the middle of the wall hung a large olive-green card
with silver lettering. 'Christ is the unseen Guest in this house,'
Hyacinth read, 'the Sharer in every pleasure, the Listener to every
conversation.' A fortnight before, he would have turned with disgust
from such an advertisement, but now, since he had known the Quinns
and listened to the Canon's wandering sermons, he looked at it with
different eyes. He felt that the words might actually express a fact,
and that a family might live together as if they believed them to be
true.
'Yes,' said the Canon, who had come in with him, and saw him gaze at it,
'these motto-cards are very nice. I bought several of them last time I
was in Dublin, and I think I have a spare one left which I can give
you if you like. It has silver letters like that one, but printed on a
crimson ground.'
Evidently the design and the colouring were what struck him as
noticeable. The motto itself was a commonplace of Christian living, the
expression of a basal fact, quite naturally hung where it would catch
the eye of chance visitors.
In the drawing-room Mrs. Beecher and her two daughters, still in their
hats and gloves, stood round a turf fire. They made a place at once for
Hyacinth, and one of the girls drew forward a rickety basket-work chair,
covered with faded cretonne. He was formally introduced to them. Miss
Beecher and Miss Elsie Beecher had both, the latter very recently,
reached the dignity of young womanhood, and wore long dresses. The three
boys, who were younger, were made known afterwards.
When they went into the dining-room the Canon selected the soundest of
a miscellaneous collection of chairs for Hyacinth, and seated him beside
Mrs. Beecher. Then the elder girl--Miss Beecher's name, he learnt, was
Marion--entered in a long apron carrying a boiled leg of mutton followed
by her sister with dishes of potatoes and mashed parsnips.
'You see,' said Mrs. Beecher, and there was no note of apology in her
voice as she made the explanation, 'my girls are accustomed to do a good
deal of the house-work. We have only one servant, and she is not very
presentable when she has just cooked the dinner.'
Hyacinth glanced at Marion Beecher, who smiled at him with frank
friendliness, as she took her seat beside her father. He saw suddenly
that the girl was beautiful. He had not noticed this in church. There he
had no opportunity of observing the subtle grace with which she
moved, and the half-light left unrevealed the lustrous purity of her
complexion, the radiant red and white which only the warm damp of the
western seaboard can give or preserve. Her eyes he had seen even in the
church, but now first he realized what unfathomable gentleness and what
a wonder of frank innocence were in them. The Canon looked round the
table at his children, and there was a humorous twinkle in his eye when
he turned to Hyacinth and quoted:
'"Your sons shall grow up as young plants, and your daughters shall be
as the polished corners of the temple."'
Perhaps nine-tenths of civilized mankind would regard five children as
five misfortunes under any circumstances, as quite overwhelming when
they have been showered on a man with a very small income, who is
obliged to live in a remote corner of Ireland. Apparently the Canon
did not look upon himself as an afflicted man at all. There was
an unmistakable sincerity about the way in which he completed his
quotation:
'"Lo! thus shall the man be blessed that feareth the Lord."'
It dawned on Hyacinth that quite possibly the Canon's view of the
situation might be the right one. It was certainly wonderfully pleasant
to see the girls move through the room, and it seemed to him that they
actually realized the almost forgotten ideal of serviceable womanhood.
The talk at dinner turned first on the ailments of an old woman who was
accustomed to clean the church, but was now suspected of being past
her work; then, by an abrupt transition, on the new hat which the
bank-manager's wife had brought home from Dublin; and, finally, the
connection of thought being again far from obvious, on the hymns which
had been sung that morning. It was at this point that Hyacinth was
included in the conversation. Marion Beecher announced that one of the
hymns was a special favourite of hers, because she remembered her mother
singing the younger children to sleep with it when they were babies. She
caught Hyacinth looking at her while she spoke, and said to him:
'Do you sing, Mr. Conneally?'
'I do a little.'
'Oh, then you must come and help us in the choir.' 'Choir' seemed a
grandiose name for the four Beechers and Mr. Quinn, but Marion, who had
little experience of anything better, had no misgivings. 'I hope you
sing tenor. I always long to have a tenor in my choir. Why, we might
have one of Barnby's anthems at Easter, and we haven't been able to sing
one since Mr. Nash left the bank.'
Hyacinth had never sung a part in his life, and could not read music,
but he grew bold, and, professing to have an excellent ear, said he
was willing to learn. The prospect of a long series of choir practices
conducted by Marion Beecher seemed to him just then an extremely
pleasant one.
After dinner, while the two girls cleared away the plates and dishes,
Canon Beecher invited Hyacinth to smoke.
'I never learnt the habit myself,' he said. 'It wasn't so much the
fashion in my young days as it is now, but I have no objection whatever
to the smell.'
Hyacinth lit a cigarette apologetically. It seemed to him almost a
wicked thing to do, but his host evidently wished him to be comfortable.
Their talk after the girls had left the room turned on politics.
Hyacinth's confession of his friendship with Augusta Goold had impressed
the Canon, and he delivered himself of a very kindly little lecture on
the duty of loyalty and the sinfulness of contention with the powers
that be. His way of putting the matter neither irritated Hyacinth, like
the flamboyant Imperialism of the Trinity students, nor drove him into
self-assertion, like Dr. Henry's contemptuous reasonableness. Still, he
felt bound to make some sort of defence of the opinions which were still
his own.
'Surely,' he said, 'there must be some limit to the duty of loyalty. If
a Government has no constitutional right to rule, is a man bound to be
loyal toit?'
'I think,' said the Canon, 'that the question is decided for us. Is it
not, Mr. Conneally? "Render unto Caesar"--you remember the verse. Even if
the Government were as unconstitutional as you appear to think, it would
not be more so than the Roman Government of Judaea when these words were
spoken.'
Hyacinth pondered this answer. It opened up to him an entirely new way
of looking at the subject, and he could see that it might be necessary
for a Christian to acquiesce without an attempt at resistance in any
Government which happened to exist.
He remembered other verses in the New Testament which could be quoted
even more conclusively in favour of this passive obedience. Yet he felt
that there must be a fallacy lurking somewhere. It was, on the face of
it, an obvious absurdity to think that a man, because he happened to
be a Christian, was therefore bound to submit to any form of tyranny or
oppression.
'Suppose,' he said--'I only say suppose--that a Government did immoral
things, that it robbed or allowed evil-disposed people to rob, would it
still be right to be loyal?'
'I think so,' said the Canon quietly.
Hyacinth looked at him in astonishment.
'Do you mean to say that you yourself would be loyal under such
circumstances?'
'I prefer not to discuss the question in that personal way, but the
Church to which you and I belong is loyal still, although the Government
has robbed us of our property and our position, and although it is now
allowing our people to be robbed still further.'
'You mean by the Disestablishment and the Land Acts?'
'Yes. I think it is our great glory that our loyalty is imperishable,
that it survives even such treatment as we have received and are
receiving.'
'That is very beautiful,' said Hyacinth slowly. 'I see that there is a
great nobility in such loyalty, although I do not even wish to share it
myself. You see, I am an Irishman, and I want to see my country great
and free.'
'I suppose,' said the Canon, 'that it is very natural that we should
love the spot on earth in which we live. I think that I love Ireland
too. But we must remember that our citizenship is in heaven, and it
seems to me that any departure from the laws of the King of that country
dishonours us, and even dishonours the earthly country which we call our
own.'
Hyacinth said nothing. There flashed across him a recollection of
Augusta Goold's hope that some final insult would one day goad the
Irish Protestants into disloyalty. Clearly, if Canon Beecher was to be
regarded as a type, she had no conception of the religious spirit of the
Church of Ireland. But was there anyone else like this clergyman? He did
not know, but he guessed that his friends the Quinns would think of the
matter in somewhat the same way. It seemed to him quite possible that in
scattered and remote parishes this strangely unreasonable conception of
Christianity might survive. After a pause the Canon went on:
'You must not think that I do not love Ireland too. I look forward to
seeing her free some day, but with the freedom of the Gospel. It will
not be in my time, I know, but surely it will come to pass. Our people
have still the simple faith of the early ages, and they have many very
beautiful virtues. They only want the dawn of the Dayspring from on
high to shine on them, and then Ireland will be once more the Island of
Saints--_insula sanctorum_.' He dwelt tenderly on the two words. 'I do
not think it will matter much then what earthly Government bears rule
over us. But come, I see that you have finished your smoke, and I must
go to my study to think over my sermon.'
When Hyacinth entered the drawing-room the girls surrounded him, asking
him for answers to a printed list of questions. It appeared that the
committee of a bazaar for some charity in which it was right to be
interested had issued a sort of examination-paper, and promised a prize
to the best answerer. The questions were all of one kind: 'What is the
Modern Athens--the Eternal City--the City of the Tribes? Who was the
Wizard of the North--the Bulwark of the Protestant Faith? The earlier
names on the list presented little difficulty to Hyacinth. Marion
took down his answers, whilst Elsie murmured a pleasant chorus of
astonishment at his cleverness. Suddenly he came to a dead stop. 'Who
was the Martyr of Melanesia?'
'I have never heard of him,' said Hyacinth.
'Never heard of the Martyr of Melanesia!' said Elsie. 'Why, we knew that
at once.'
'Yes,' said Marion, 'there was an article on him in last month's
_Gleaner_. Surely you read the _Gleaner_, Mr. Conneally?'
Hyacinth felt Marion's eyes fixed on him with something of a reproach
in them. He wrestled with a vague recollection of having somewhere
heard the name of the periodical. For a moment he thought of risking
cross-questioning, and saying that he had only missed the last number.
Then he suddenly remembered the card with silver lettering which
hung above his coat in the hall, and told the truth with even a quite
unnecessary aggravation.
'No, I never remember seeing a copy of it in my life. I don't even know
what it is about.'
'Oh!' said the girls, round-eyed with horror. 'Just think! And we all
have collecting-boxes.'
'It is a missionary periodical,' said Marion. 'It has news in it
from every corner of the mission-field, and every month a list of the
stations that specially need our prayers.'
Hyacinth left the Rectory that night with three well-read numbers of the
_Gleaner_ in his pocket.
Afterwards he had many talks with Canon Beecher and the Quinns about
the work of the missionary societies. He learnt, to his surprise, that
really immense sums of money were subscribed every year by members of
the Church of Ireland for the conversion of the heathen in very remote
parts of the world. It could not be denied that these contributions
represented genuine self-denial. Young men went without a sufficiency
of tobacco, and refrained from buying sorely-needed new tennis-racquets.
Ladies, with the smallest means at their command, reared marketable
chickens, and sold their own marmalade and cakes. In such ways, and not
from the superfluity of the rich, many thousands of pounds were gathered
annually. It was still more wonderful to him to discover that large
numbers of young men and women, and these the most able and energetic,
devoted themselves to this foreign service, and that their brothers and
sisters at home were banded together in unions to watch their doings
and to pray for them. He found himself entirely untouched by this
enthusiasm, in spite of the beautiful expression it found in the lives
of his new friends.
But it astonished him greatly that there should be this potent energy
in the Irish Church. The utter helplessness of its Bishops and clergy in
Irish affairs, the total indifference of its people to every effort at
national regeneration, had led him to believe that the Church itself was
moribund. Now he discovered that there was in it an amazing vitality,
a capacity of giving birth to enthusiastic souls. The knowledge brought
with it first of all a feeling of intense irritation. It seemed to him
that all religions were in league against Ireland. The Roman Church
seized the scanty savings of one section of the people, and squandered
them in buying German glass and Italian marble. Were the Protestants
any better, when they spent L20,000 a year on Chinamen and <DW64>s? The
Roman Catholics took the best of their boys and girls to make priests
and nuns of them. The Protestants were doing the same thing when they
shipped off their young men and young women to spend their strength
among savages. Both were robbing Ireland of what Ireland needed
most--money and vitality. He would not say, even to himself, that all
this religious enthusiasm was so much ardour wasted. No doubt the Roman
priest did good work in Chicago, as the Protestant missionary did in
Uganda; only it seemed to him that of all lands Ireland needed most the
service and the prayers of those of her children who had the capacity of
self-forgetfulness. Afterwards, when he thought more deeply, he found a
great hope in the very existence of all this altruistic enthusiasm. He
had a vision of all that might be done for Ireland if only the splendid
energy of her own children could be used in her service. He tried more
than once to explain his point of view. Mr. Quinn met him with blank
disbelief in any possible future for Ireland.
'The country is doomed,' he said. 'The people are lazy, thriftless, and
priest-ridden. The best of them are flying to America, and those that
remain are dying away, drifting into lunatic asylums, hospitals, and
workhouses. There is a curse upon us. In another twenty years there
will be no Irish people--at least, none in Ireland. Then the English and
Scotch will come and make something of the country.'
From Canon Beecher he met with scarcely more sympathy or understanding.
'Yes,' he admitted, 'no doubt we ought to make more efforts than we do
to convert our fellow-countrymen. But it is very difficult to see how we
are to go to work. There is one society which exists for this purpose.
Its friends are full of the very kind of enthusiasm which you describe.
I could point you out plenty of its agents whose whole souls are
in their work, but you know as well as I do how completely they are
failing.'
'But,' said Hyacinth, 'I do not in the least mean that we should start
more missions to Roman Catholics. It does not seem to me to matter much
what kind of religion a man professes, and I should be most unwilling to
uproot anyone's belief. What we ought to do is throw our whole force and
energy into the work of regenerating Ireland. It is possible for us to
do this, and we ought to try.'
'Well, well,' said the Canon, 'I must not let you make me argue with
you, Conneally; but I hope you won't preach these doctrines of yours to
my daughters. I think it is better for them to drop their pennies into
missionary collecting-boxes, and leave the tangled problems of Irish
politics to those better able to understand them than we are.'
CHAPTER XV
There are certain professions, in themselves honest, useful, and even
estimable, for which society has agreed to entertain a feeling of
contempt. It is, for instance, very difficult to think of a curate
as anything except a butt for satirists, or to be respectful to the
profession of tailoring, although many a man for private pecuniary
reasons is meek before the particular individual who makes his clothes.
Yet the novelist and the playwright, who hold the mirror up to modern
humanity, are occasionally kind even to curates and tailors. There is a
youthful athlete in Holy Orders who thrashes, to our immense admiration,
the village bully, bewildering his victim and his admirers with his
mastery of what is described a little vaguely as the 'old Oxford
science.' Once, at least, a glamour of romance has been shed over the
son of a tailor, and it becomes imaginable that even the chalker of
unfinished coats may in the future be posed as heroic. There is still,
however, a profession which no eccentric novelist has ever ventured to
represent as other than entirely contemptible. The commercial traveller
is beneath satire, and outside the region of sympathy. If he appears at
all in fiction or on the stage, he is irredeemably vulgar. He is
never heroic, never even a villain, rarely comic, always, poor man,
objectionable. This is a peculiar thing in the literature of a people
like the English, who are not ashamed to glory in their commercial
success, and are always ready to cheer a politician who professes to
have the interests of trade at heart. Amid the current eulogies of
the working man and the apotheosis of the beings called 'Captains
of Industry,' the bagman surely ought to find at least an apologist.
Without him it seems likely that many articles would fail to find a
place in the windows of the provincial shopkeepers. Without him large
sections of the public would probably remain ignorant for years of new
brands of cigarettes, and dyspeptic people might never come across the
foods which Americans prepare for their use.
Also the individual bagman is often not without his charm. He knows, if
not courts and princes, at least hotels and railway companies. He is on
terms of easy familiarity with every 'boots' in several counties. He can
calculate to a nicety how long a train is likely to be delayed by a fair
'somewhere along the line.' He is also full of information about local
politics. In Connaught, for instance, an experienced member of the
profession will gauge for you the exact strength of the existing League
in any district. He knows what publicans may be regarded as 'priest's
men,' and who have leanings towards independence. His knowledge is
frequently minute, and he can prophesy the result of a District Council
election by reckoning up the number of leading men who read the _United
Irishman_, and weighing them against those who delight in the pages of
the _Leader_. The men who can do these things are themselves local. They
reside in their district, and, as a rule, push the sales and collect the
debts of local brewers and flour-merchants. The representatives of the
larger English firms only make their rounds twice or three times a year,
and are less interesting. They pay the penalty of being cosmopolitan,
and tend to become superficial in their judgment of men and things.
Hyacinth, like most members of the public, was ignorant of the greatness
and interest of his new profession. He entered upon it with some
misgiving, and viewed his trunk of sample blankets and shawls with
disgust. Even a new overcoat, though warm and weatherproof, afforded
him little joy, being itself a sample of Mr. Quinn's frieze. One thought
alone cheered him, and even generated a little enthusiasm for his work.
It occurred to him that in selling the produce of the Ballymoy Mill
he was advancing the industrial revival of Ireland. He knew that
other people, quite heroic figures, were working for the same end. A
Government Board found joyous scope for the energies of its officials in
giving advice to people who wanted to cure fish or make lace. It earned
the blessing which is to rest upon those who are reviled and evil spoken
of, for no one, except literary people, who write for English magazines,
ever had a good word for it. There were also those--their activity
took the form of letters to the newspapers--who desired to utilize the
artistic capacity of the Celt, and to enrich the world with beautiful
fabrics and carpentry. They, too, were workers in the cause of the
revival. Then there were great ladies, the very cream of the Anglo-Irish
aristocracy, who petted tweeds and stockings, and offered magnificent
prizes to industrious cottagers. They earned quite large sums of
money for their proteges by holding sales in places like Belfast and
Manchester, where titles can be judiciously cheapened to a wealthy
bourgeoisie, and the wives of ship-builders and cotton-spinners will
spend cheerfully in return for the privilege of shaking hands with
a Countess. A crowd of minor enthusiasts fostered such industries as
sprigging, and there was one man who believed that the future prosperity
of Ireland might be secured by teaching people to make dolls. It was
altogether a noble army, and even a commercial traveller might hold
his head high in the world if he counted himself one of its soldiers.
Hitherto results have not been at all commensurate with the amount of
printer's ink expended in magazine articles and advertisements. Yet
something has been accomplished. Nunneries here and there have been
induced to accept presents of knitting-machines, and people have
begun to regard as somehow sacred the words 'technical education.'
The National Board of Education has also spent a large sum of money in
reviving among its teachers the almost forgotten art of making paper
boats.
Hyacinth very soon discovered that his patriotic view of this work did
not commend itself to his brother travellers. He found that they had no
feeling but one of contempt for people whom they regarded as meddling
amateurs. Occasionally, when some convent, under a bustling Mother
Superior, advanced from the region of half-charitable sales at
exhibitions into the competition of the open market, contempt became
dislike, and wishes were expressed in quite unsuitable language that the
good ladies would mind their own proper business. Until Hyacinth learnt
to conceal his hopes of Ireland's future as a manufacturing country he
was regarded with suspicion. No one, of course, objected to his making
what use he could of patriotism as an advertisement, but he was given to
understand that, like other advertisements, it could not be quoted
among the initiated without a serious breach of good manners. Even as an
advertisement it was not rated highly.
There was an elderly gentleman, stout and somewhat bibulous, who
superintended the consumption of certain brands of American cigarettes
in the province of Connaught. Hyacinth met him in the exceedingly
dirty Railway Hotel at Knock. Since there were no other guests, and the
evening was wet, the two were thrown upon each other's society in the
commercial-room.
'I don't think,' said Mr. Hollywell, in reply to a remark of Hyacinth's,
'that there's the least use trying to drag patriotic sentiment into
business. Of course, since you represent an Irish house--woollen goods,
I think you said--you're quite right to run the fact for all it's worth.
I don't in the least blame you. Only I don't think you'll find it pays.'
He sipped his whisky-and-water--it was still early, and he had only
arrived at his third glass--and then proceeded to give his personal
experience.
'Now, I work for an American firm. If there was any force in the
patriotic idea I shouldn't sell a single cigarette. My people are in
the big tobacco combine. You must have read the sort of things the
newspapers wrote about us when we started. From any point of view,
British Imperial or Irish National, we should have been boycotted long
ago if patriotism had anything to do with trade. But look at the facts.
Our chief rivals in this district are two Irish firms. They advertise
in Gaelic, which is a mistake to start with, because nobody can read it.
They get the newspaper people to write articles recommending a "great
home industry" to public support. They get local branches of all the
different leagues to pass resolutions pledging their members to smoke
only Irish tobacco. But until quite lately they simply didn't have a
look in.'
'Why?' asked Hyacinth. 'Were your things cheaper or better?'
'No,' said the other, 'I don't think they were either. You see, prices
are bound to come out pretty even in the long run, and I should say
that, if anything, they sold a slightly better article. It's hard to
say exactly why we beat them. When competition is really keen a lot of
little things that you would hardly notice make all the difference.
For one thing, I get a free hand in the matter of subscribing to local
bazaars and race-meetings. I've often taken as much as a pound's worth
of tickets for a five-pound note that some priest was raffling in aid of
a new chapel. It's wonderful the orders you can get from shopkeepers in
that kind of way. Then, we get our things up better. Look at that.'
He handed Hyacinth a highly-glazed packet with a picture of a handsome
brown dog on it.
'Keep it,' said Mr. Hollywell. 'I give away twenty or thirty of
those packets every week. Now look inside. What have you? Oh, H.M.S.
_Majestic_. That's one of a series of photos of "Britain's first line
of defence." Lots of people go on buying those cigarettes just to get
a complete collection of the photos. We supply an album to keep them in
for one and sixpence. There's another of our makes which has pictures
of actresses and pretty women. They are extraordinarily popular. They're
perfectly all right, of course, from the moral point of view, but one in
every ten is in tights or sitting with her legs very much crossed, just
to keep up the expectation. It's very queer the people who go for those
photos. You'd expect it to be young men, but it isn't.'
The subject was not particularly interesting to Hyacinth, but since his
companion was evidently anxious to go on talking, he asked the expected
question.
'Young women,' said Mr. Hollywell. 'I found it out quite by accident. I
got a lot of complaints from one particular town that our cigarettes had
no photos with them. I discovered after a while that a girl in one
of the principal shops had hit on a dodge for getting out the photos
without apparently injuring the packets. The funny thing was that
she never touched the ironclads or the "Types of the soldiers of all
nations," which you might have thought would interest her, but she
collared every single actress, and had duplicates of most of them. And
she wasn't an exception. Most girls goad their young men to buy these
cigarettes and make collections of the photos. Queer, isn't it? I can't
imagine why they do it.'
'You said just now,' said Hyacinth, 'that latterly you hadn't done quite
so well. Did you run out of actresses and battleships?'
'No; but one of the Irish firms took to offering prizes and enclosing
coupons. You collected twenty coupons, and you got a silver-backed
looking-glass--girls again, you see--or two thousand coupons, and you
got a new bicycle. It's an old dodge, of course, but somehow it always
seems to pay. However, all this doesn't matter to you. All I wanted was
to show you that there is no use relying on patriotism. The thing to go
in for in any business is attractive novelties, cheap lines, and, in the
country shops, long credit.'
It was not very long before Hyacinth began to realize the soundness of
Mr. Hollywell's contempt for patriotism. In the town of Clogher he
found the walls placarded with the advertisements of an ultra-patriotic
draper. 'Feach Annseo,' he read, 'The Irish House. Support Home
Manufactures.' Another placard was even more vehement in its appeal.
'Why curse England,' it asked, 'and support her manufactures?' Try
O'Reilly, the one-price man.' The sentiments were so admirable that
Hyacinth followed the advice and tried O'Reilly.
The shop was crowded when he entered, for it was market day in Clogher.
The Irish country-people, whose manners otherwise are the best in
the world, have one really objectionable habit. In the street or in a
crowded building they push their way to the spot they want to reach,
without the smallest regard for the feelings of anyone who happens to
be in the way. Sturdy country-women, carrying baskets which doubled the
passage room they required, hustled Hyacinth into a corner, and for a
time defeated his efforts to emerge. Getting his case of samples safely
between his legs, he amused himself watching the patriot shopkeeper and
his assistants conducting their business. It was perfectly obvious that
in one respect the announcements of the attractive placard departed
from the truth: O'Reilly was not a 'one-price man,' He charged for every
article what he thought his customers were likely to pay. The result was
that every sale involved prolonged bargaining and heated argument. In
most cases no harm was done. The country-women were keenly alive to the
value of their money, and evidently enjoyed the process of beating
down the price by halfpennies until the real value of the article was
reached. Then Mr. O'Reilly and his assistants were accustomed to close
the haggle with a beautiful formula:
'To _you_,' they said, with confidential smiles and flattering emphasis
on the pronoun--'to _you_ the price will be one and a penny; but,
really, there will be no profit on the sale.'
Occasionally with timid and inexperienced customers O'Reilly's method
proved its value. Hyacinth saw him sell a dress-length of serge to a
young woman with a baby in her arms for a penny a yard more than he
had charged a moment before for the same material. Another thing which
struck him as he watched was the small amount of actual cash which was
paid across the counter. Most of the women, even those who seemed quite
poor, had accounts in the shop, and did not shrink from increasing
them. Once or twice a stranger presented some sort of a letter of
introduction, and was at once accommodated with apparently unlimited
credit.
At length there was a lull in the business, and Hyacinth succeeded in
spreading his goods on a vacant counter, and attracting the attention of
Mr. O'Reilly. He began with shawls.
'I hope,' he said, 'that you will give me a good order for these
shawls.'
Mr. O'Reilly fingered them knowingly.
'Price?' he said.
Hyacinth mentioned a sum which left a fair margin of profit for Mr.
Quinn. O'Reilly shook his head and laughed.
'Can't do it.'
Hyacinth reduced his price at once as far as possible.
'No use,' said Mr. O'Reilly.
Compared with the suave oratory to which he treated his customers, this
extreme economy of words was striking.
'See here,' he said, producing a bundle of shawls from a shelf beside
him. 'I get these for twenty-five shillings a dozen less from Thompson
and Taylor of Manchester.'
Hyacinth looked at them curiously. Each bore a prominent label setting
forth a name for the garment in large letters surrounded with wreaths
of shamrocks. 'The Colleen Bawn,' he read, 'Erin's Own,' 'The Kathleen
Mavourneen,' 'The Cruiskeen Lawn.' The appropriateness of this last
title was not obvious to the mere Irishman, but the colour of the
garment was green, so perhaps there was a connection of thought in the
maker's mind between that and 'Lawn.' 'Cruiskeen' he may have taken for
the name of a place.
'Are these,' asked Hyacinth, 'what you advertise as Irish goods?'
Mr. O'Reilly cleared his throat twice before he replied.
'They are got up specially for the Irish market.' In the interests of
his employer Hyacinth kept his temper, but the effort was a severe one.
'These,' he said, 'are half cotton. Mine are pure wool. They are really
far better value even if they were double the price.'
Mr. O'Reilly shrugged his shoulders.
'I don't say they're not, but I should not sell one of yours for every
dozen of the others.'
'Try,' said Hyacinth; 'give them a fair chance. Tell the people that
they will last twice as long. Tell them that they are made in Ireland.'
'That would not be the slightest use. They would simply laugh in my
face. My customers don't care a pin where the goods are made. I have
never in my life been asked for Irish manufacture.'
'Then, why on earth do you stick up those advertisements?' said
Hyacinth, pointing to the 'Feach Annseo' which appeared on a hoarding
across the street.
Mr. O'Reilly was perfectly frank and unashamed.
'The other drapery house in the town is owned by a Scotchman, and of
course it pays more or less to keep on saying that I am Irish. Besides,
I mean to stand for the Urban Council in March, and those sort of ads.
are useful at an election, even if they are no good for business.'
'I'll tell you what I'll do,' said Hyacinth, shirking a discussion on
the morality of advertising: 'I'll let you have a dozen shawls at cost
price, and take back what you can't sell, if you give me your word to do
your best for them.'
Similar discussions followed the display of serges and blankets. It
appeared that nice-looking goods could be sent over from England at
lower prices. It was vain for Hyacinth to press the fact that his things
were better. Mr. O'Reilly admitted as much.
'But what am I to do? The people don't want what is good. They want a
cheap article which looks well, and they don't care a pin whether the
thing is made in England, Ireland, or America. Take my advice,' he added
as Hyacinth left the shop: 'get your boss to do inferior lines--cheap,
cheap and showy.'
So far Mr. Hollywell's opinions were entirely justified. The appeal of
the patriotic press to the public and the shopkeepers on behalf of the
industrial revival of Ireland had certainly not affected the town of
Clogher. Hyacinth was bitterly disappointed; but hope, when it is born
of enthusiasm, dies hard, and he was greatly interested in a speech
which he read one day in the 'Mayo Telegraph'. It had been made at a
meeting of the League by an Ardnaree shopkeeper called Dowling. A trade
rival--the fact of the rivalry was not emphasized--had advertised in
a Scotch paper for a milliner. Dowling was exceedingly indignant. He
quoted emigration statistics showing the number of girls who left Mayo
every year for the United States. He pointed out that all of them might
be employed at home, as milliners or otherwise, if only the public would
boycott shops which sold English goods or employed Scotch milliners.
He more than suspected that the obnoxious advertisement was part of an
organized attempt to effect a new plantation of Connaught--'worse than
Cromwell's was.' The fact that Connaught was the only part of Ireland
which Cromwell did not propose to plant escaped the notice of both
Mr. Dowling and his audience. The speech concluded with a passionate
peroration and a verse, no doubt declaimed soundingly, of 'The West's
Awake.'
Hyacinth made an expedition to Ardnaree, and called hopefully on the
orator. His reception was depressing in the extreme. The shop, which was
large and imposing, was stocked with goods which were obviously English,
and Mr. Dowling curtly refused even to look at the samples of Mr.
Quinn's manufactures. Hyacinth quoted his own speech to the man, and was
amazed at the cynical indifference with which he ignored the dilemma.
'Business is one thing,' he said, 'and politics is something entirely
different.'
Hyacinth lost his temper completely.
'I shall write to the papers,' he said, Vand expose you. I shall have
your speech reprinted, and along with it an account of the way you
conduct your business.'
A mean, hard smile crossed Mr. Dowling's mouth before he answered:
'Perhaps you don't know that my wife is the Archbishop's niece?'
Hyacinth stared at him. For a minute or two he entirely failed to
understand what Mrs. Dowling's relationship to a great ecclesiastic had
to do with the question. At last a light broke on him.
'You mean that an editor wouldn't print my letter because he would be
afraid of offending a Roman Catholic Archbishop?'
The expression 'Roman Catholic' caught Mr. Dowling's attention.
'Are you a Protestant?' he asked. 'You are--a dirty Protestant--and you
dare to come here into my own house, and insult me and trample on my
religious convictions. I'm a Catholic and a member of the League. What
do you mean, you Souper, you Sour-face, by talking to me about Irish
manufactures? Get out of this house, and go to the hell that's waiting
for you!'
As Hyacinth turned to go, there flashed across his mind the recollection
of Miss Goold and her friends who wrote for the _Croppy_.
'There's one paper in Ireland, anyhow,' he said, 'which is not afraid
of your wife nor your Archbishop. I'll write to the _Croppy_, and you'll
see if they won't publish the facts.'
Mr. Dowling grinned.
'I don't care if they do,' he said. 'The priests are dead against the
_Croppy_, and there's hardly a man in the town reads it. Go up there
now to Hely's and try if you can buy a copy. I tell you it isn't on sale
here at all, and whatever they publish will do me no harm.'
When Hyacinth returned to the hotel he found Mr. Holywell seated, with
the inevitable whisky-and-water beside him, in the commercial-room.
'Well, Mr. Conneally,' he said, 'and how is patriotism paying you? Find
people ready to buy what's Irish?'
Hyacinth, boiling over with indignation, related his experience with Mr.
Dowling.
'What did I tell you?' said Mr. Hollywell. 'But anyhow you're just as
well out of a deal with that fellow. I wouldn't care to do business with
him myself. I happen to know, and you may take my word for it '--his
voice sunk to a confidential whisper--'that he's very deep in the books
of two English firms, and that he daren't--simply daren't--place
an order with anyone else. They'd have him in the Bankruptcy Court
to-morrow if he did. I shouldn't feel easy with Mr. Dowling's cheque for
an account until I saw how the clerk took it across the bank counter.
You mark my words, there'll be a fire in that establishment before the
year's out.'
The prophecy was fulfilled, as Hyacinth learnt from the _Mayo
Telegraphy_ and Mr. Dowling's whole stock of goods was consumed. There
were rumours that a sceptical insurance company made difficulties about
paying the compensation demanded; but the inhabitants of Ardnaree marked
their confidence in the husband of an Archbishop's niece by presenting
him with an address of sympathy and a purse containing ten sovereigns.
Most of Hyacinth's business was done with small shopkeepers in remote
districts. The country-people who lived out of reach of such centres
of fashion as Ardnaree and Clogher were sufficiently unsophisticated to
prefer things which were really good. Hats and bonnets were not quite
universal among the women in the mountain districts far back where they
spoke Irish, and Mr. Quinn's head-kerchiefs were still in request. Even
the younger women wanted garments which would keep them warm and dry,
and Hyacinth often returned well satisfied from a tour of the country
shops. Sometimes he doubted whether he ought to trust the people with
more than a few pounds' worth of goods, but he gradually learnt that,
unlike the patriotic Mr. Dowling, they were universally honest. He
discovered, too, that these people, with their imperfect English and
little knowledge of the world, were exceedingly shrewd. They had very
little real confidence in oratorical politicians, and their interest
in public affairs went no further than voting consistently for the
man their priest recommended. But they quickly understood Hyacinth's
arguments when he told them that the support of Irish manufactures would
help to save their sons and daughters from the curse of emigration.
'Faith, sir,' said a shopkeeper who kept a few blankets and tweeds among
his flour-sacks and porter-barrels, 'since you were talking to the boys
last month, I couldn't induce one of them to take the foreign stuff if I
was to offer him a shilling along with it.'
CHAPTER XVI
When he returned to Ballymoy after his interview with Mr. Dowling,
Hyacinth set himself to fulfil his threat of writing to the _Croppy_.
He spent Saturday afternoon and evening in his lodgings with the paper
containing the blatant speech spread out before him. He blew his anger
to a white heat by going over the evidence of the man's grotesque
hypocrisy. He wrote and rewrote his article. It was his first attempt
at expressing thought on paper since the days when he sought to satisfy
examiners with disquisitions on Dryden's dramatic talent and other
topics suited to the undergraduate mind. This was a different business.
It was no longer a question of filling a sheet of foolscap with
grammatical sentences, discovering synonyms for words hard to spell. Now
thoughts were hot in him, and the art lay in finding words which would
blister and scorch. Time after time he tore up a page of bombast or
erased ridiculous flamboyancies. Late at night, with a burning head and
ice-cold feet, he made his last copy, folded it up, and, distrusting the
cooler criticism of the morning, went out and posted it to the _Croppy_.
A letter from Miss Goold overtook him the following Thursday in the
hotel at Clogher.
'I was delighted to hear from you again,' she wrote. 'I was afraid
you had cut me altogether, gone over to the respectable people, and
forgotten poor Ireland. Captain Quinn told me that you and he had
quarrelled, and I gathered that you rather disapproved of him. Well, he
was a bit of a blackguard; but, after all, one doesn't expect a man
who takes on a job of that kind to be anything else. I never thought
it would suit you, and you will do me the justice of remembering that I
never wanted you to volunteer. Now about your article. It was admirable.
These "Cheap Patriots"'--it was thus the article was headed--'are just
the creatures we want to scarify. Dowling and his kind are the worst
enemies Ireland has to-day. We'll publish anything of that kind you send
us, and remember we're not the least afraid of anybody. It's a grand
thing for a paper to be as impecunious as the _Croppy_. No man but
a fool would take a libel action against us with any hope of getting
damages. A jury might value Dowling's character at any fantastic sum
they chose, but it would be a poor penny the _Croppy_ would pay. Still,
we're not so hard up that we can't give our contributors something,
and next week you'll get a small cheque from the office. I hope it may
encourage you to send us more. Don't be afraid to speak out. If anything
peculiarly seditious occurs to you, write it in Irish. I know it's all
the same to you which language you write in. Do us half a column every
fortnight or so on Western life and politics.'
Hyacinth was absurdly elated by Miss Goold's praise. He made up his
mind to contribute regularly to the _Croppy_, and had visions of a great
future as a journalist, or perhaps a literary exponent of the ideas of
Independent Ireland.
Meanwhile, he became very intimate both with the Quinns and with Canon
Beecher's family. Mrs. Quinn was an enthusiastic gardener, and early in
the spring Hyacinth helped her with her flowerbeds. He learnt to plait
the foliage of faded crocuses, and pin them tidily to the ground with
little wooden forks. He gathered suitable earth for the boxes in which
begonias made their earliest sprout-ings, and learned to know the
daffodils and tulips by their names. Later on he helped Mr. Quinn to mow
the grass and mix a potent weed-killer for the gravel walks. There came
to be an understanding that, whenever he was not absent on a journey, he
spent the latter part of the afternoon and the evening with the Quinns.
As the days lengthened the family tea was pushed back to later and later
hours to give more time out of doors.
There is something about the very occupation of gardening which is
deadening to enthusiasm. Perhaps a man learns patience by familiarity
with growing plants. Nature is never in a hurry in a garden, and there
is no use in trying to hustle a flower, whereas a great impatience is
the very life-spirit of enthusiastic patriotism. There has probably
never been a revolutionary gardener, or even a strong Radical who worked
with open-air flowers. Of course, in greenhouses things can be forced,
and the spirit of the ardent reformer may find expression in the nurture
of premature blooms. Perhaps also the constant stooping which gardening
necessitates, especially in the early spring, when the weeds grow
plentifully, tends to destroy the stiff mental independence which must
be the attitude of the militant patriot. It is very difficult for a man
who has stooped long enough to have conquered his early cramps and aches
to face the problems of politics with uncompromising rigidity. Hyacinth
recognised with a curious qualm of disgust that his thoughts turned less
and less to Ireland's wrongs and Ireland's future as he learnt to care
for the flowers and the grass.
No doubt, too, the atmosphere of the Quinns' family life was not
congenial to the spirit of the Irish politician. Mrs. Quinn was totally
uninterested in politics, and except a prejudice in favour of what she
called loyalty, had absolutely no views on any question which did
not directly affect her home and her children. Mr. Quinn had a
coldly-reasonable political and economic creed, which acted on the
luxuriant fancies of Hyacinth's enthusiasm as his weed-killer did on
the tender green of the paths. He declined altogether to see any good in
supporting Irish manufactures simply because they were Irish. The story
of O'Reilly's attitude towards his shawls moved him to no indignation.
'I think he's perfectly right,' he said. 'If a man can buy cheap shawls
in England he would be a fool to pay more for Irish ones. Business can't
be run on those lines. I'm not an object of charity, and if I can't
meet fair competition I must go under, and it's right that I should go
under.'
Hyacinth had no answer to give. He shirked the point at issue, and
attacked Mr. Quinn along another line in the hope of arousing his
indignation.
'But it is not fair competition that you are called upon to face. Do
you call it fair competition when the Government subsidizes a woollen
factory in a convent?'
'Ah!' said Mr. Quinn, 'you are thinking of the four thousand pounds
the Congested Districts Board gave to the convent at Bobeen. But it is
hardly fair to hold the Government responsible for the way that body
wastes eighty thousand pounds a year.'
'The Government is ultimately responsible, and you must admit that,
after such a gift, and in view of the others which will certainly
follow, you are called upon to meet most unfair competition.'
'Yes, I admit that. But isn't that exactly what you want to make
general? There doesn't seem to me any difference between giving a bounty
to one industry and imposing a protective tariff in favour of another;
and if your preference for Irish manufactures means anything, it means
a sort of voluntary protection for every business in the country. If you
object to the Robeen business being subsidized you can't logically try
to insist on mine being protected.'
It was puzzling to have the tables turned on him so adroitly. Hyacinth
was reduced to feeble threat.
'Just wait a while till the nuns get another four thousand pounds, and
perhaps four thousand pounds more after that, and see how it will affect
you.'
Mr. Quinn smiled.
'I'm not much afraid of nuns as trade competitors, or, for the matter of
that, of the Congested Districts Board either. If the Yorkshire people
would only import a few Mother Superiors to manage their factories,
and take the advice of members of our Board in their affairs, I would
cheerfully make them a present of any reasonable subsidy, and beat them
out of the market afterwards.'
There was another influence at work on Hyacinth's mind which had as much
to do with the decay of his patriotism as either the gardening or Mr.
Quinn's logic. Marion Beecher and her sister were very frequently at the
Mill House during the spring and summer. There was one long afternoon
which was spent in the marking out of the tennis-ground. Mr. Quinn had
theories involving calculations with a pencil and pieces of paper about
the surest method of securing right angles at the corners and parallel
lines down the sides of the court. Hyacinth and Marion worked obediently
with a tape measure and the garden line. One of the boys messed
cheerfully with a pail of liquid whitening. Afterwards the gardening was
somewhat deserted, and Hyacinth was instructed in the game. It took
him a long time to learn, and for many afternoons he and Marion were
regularly beaten, but she would not give up hope of him. Often the
excuse of her coming to the Quinns was the necessity of practising some
new hymn or chant for Sunday. Hyacinth worked as hard at the music as at
the tennis under her tuition, and there came a time when he could sing
an easy tenor part with fair accuracy. Then in the early summer, when
the evenings were warm, hymns were sung on the lawn in front of the
house. There seemed no incongruity in Marion Beecher's company in
passing without a break from lawn-tennis to hymn-singing, and Mr. Quinn
was always ready to do his best at the bass with a serious simplicity,
as if it were a perfectly natural and usual thing to close an
afternoon's amusement with 'Rock of Ages.' Hyacinth was not conscious of
any definite change in his attitude towards religion. He still believed
himself to be somehow outside the inner shrine of the life which the
Beechers and the Quinns lived, just as he had been outside his father's
prayers. But he found it increasingly difficult after an hour or two of
companionship with Marion Beecher to get back to the emotions which had
swayed him during the weeks of his intimacy with Miss Goold. To write
for the _Croppy_ after sitting beside Marion in church on Sunday
evenings was like passing suddenly from a quiet wood into a heated
saloon where people wrangled. A wave of the old passionate feeling, when
it returned, affected him as raw spirit would the palate of a boy.
One day early in summer--the short summer of Connaught, which is
glorious in June, and dissolves into windy mist and warm rain in the
middle of July--Hyacinth was invited by Canon Beecher to join a boating
party on the lake. The river, whose one useful function was the turning
of Mr. Quinn's millwheel, wound away afterwards through marshy fields
and groves of willow-trees into the great lake. At its mouth the
Beechers kept their boat, a cumbrous craft, very heavy to row, but safe
and suited to carry a family in comfort. The party started early--Canon
Beecher, Hyacinth, and one of the boys very early, for they had to
walk the two miles which separated Ballymoy from the lake shore. Mrs.
Beecher, the girls, the two other boys, and the baskets of provisions
followed a little later on the Rectory car, packed beyond all
possibility of comfort. The Canon himself pulled an oar untiringly, but
without the faintest semblance of style, and the party rippled with joy
when they discovered that Hyacinth also could row.
'Now,' said Elsie, 'we can go anywhere. We can go on rowing and rowing
all day, and see places we've never seen before.'
'My dear girl,' said her mother, 'remember that Mr. Conneally and your
father aren't machines. You mustn't expect them to go too far.'
'Oh, but,' said Elsie, 'father says he never gets tired if he has only
one oar to pull.'
The Canon was preparing for his toil. The old coat, in colour now almost
olive green, was folded and used as a cushion by Marion in the bow. His
white cuffs, stowed inside his hat, were committed to the care of Mrs.
Beecher. He rolled his gray shirtsleeves up to the elbow, and unbuttoned
his waistcoat.
'Now,' he said, 'I'm ready. If I'm not hurried, I'll pull along all day.
But what about you, Conneally? You're not accustomed to this sort of
thing?'
But Hyacinth for once was self-confident. He might be a poor singer and
a contemptible tennis player, but he knew that nothing which had to do
with boats could come amiss to him. He looked across the sparkling water
of the lake.
'I'll go on as long as you like. You won't tire me when there's no tide
and no waves. This is a very different business from getting out the
sweeps to pull a nobby five miles against the strength of the ebb, with
a heavy ground swell running.'
About eleven o'clock they landed on an island and ate biscuits. The
Canon told Hyacinth the story of the ruin under whose walls they sat.
'It belonged to the Lynotts, the Welshmen of Tyrawley. They were at feud
with the Burkes, and one night in winter----'
The girls wandered away, carrying their biscuits with them. It is
likely that they had heard the story every summer as long as they could
remember. Mrs. Beecher alone still maintained an attitude of admiration
for her husband's antiquarian knowledge, the more creditable because she
must have been familiar with the onset of the MacWilliam Burkes before
even Marion was old enough to listen. To Hyacinth the story was both
new and interesting. It stirred him to think of the Lynotts fighting
hopelessly, or begging mercy in the darkness and the cold just where he
sat now saturate with sunlight and with life. He gazed across the mile
of shining water which separated the castle from the land, and tried to
realize how the Irish servant-girl swam from the island with an infant
Lynott on her back, and saved the name from perishing. How the snow must
have beaten in her face and the lake-waves choked her breath! It was a
great story, but the girls, shouting from the water's edge, reminded him
that he was out to pull an oar, and not to sentimentalize. He and the
Canon rose, half smiling, half sighing, and took their places in the
boat.
They penetrated before luncheon time to a bay hitherto unknown to the
Beechers. A chorus of delight greeted its discovery. The water shone
bright green and very clear above the slabs of white limestone. The
shore far inland was almost verdure-less. Broad flat rocks lay baking
in the sunshine, and only the scantiest grass struggled up between their
edges. Sometimes they overlapped each other, and rose Uke an immense
staircase. Fifty yards or so from the land was a tiny island entirely
overgrown with stunted bushes. The boat was pushed up to it and a
landing-place sought, but the shrubs were too thick, and it was decided
to picnic among the rocks on the land. Then Marion in the bow made a
discovery. A causeway about a foot under water led from the island to
the shore. The whole party leaned over to examine it. Every stone was
visible in the clear water, and it was obvious that it had been planned
and built, and was no merely accidental formation of the rocks. The
Canon had heard of a similar device resorted to by an island hermit
to insure the privacy of his cell. Hyacinth spoke vaguely of the
settlements of primitive communities of lake-dwellers. The three boys
planned an expedition across the causeway after luncheon.
'We'll carry our shoes and stockings with us,' they said, 'and then
explore the island. Perhaps there is a hermit there still, or
a primitive lake-dweller. What is a primitive lake-dweller, Mr.
Conneally?'
Hyacinth was uncertain, but hazarded a suggestion that the lake-dwellers
were the people who buried each other in raths. The Canon, whose
archaeology did not go back beyond St. Patrick, offered no correction.
Tea was made later on in yet another bay, this time on the eastern shore
of the lake. An oak wood grew down almost to the water's edge, and the
branches overhung a sandy beach, more golden than any sea-strand. The
whole party collected dead wood and broken twigs for the fire. Then,
while the girls unpacked the baskets and secured the kettle amidst the
smoke, Hyacinth lay back luxuriously and watched the sun set behind the
round-shouldered mountain opposite. The long, steep <DW72> shone
bright green while the sun still rested in view above the summit; then
suddenly, when the topmost rim of it had dipped out of sight, the whole
mountainside turned purple, and a glory of gold and crimson hung above
it on the motionless streaks of cloud. Slowly the splendour faded, the
purple turned gray, and a faint breeze fluttered across the lake.
The day was the first of many which Hyacinth gave to such expeditions.
The work of Mr. Quinn's office was not so pressing as to necessitate
his spending every day there when he was in Ballymoy, and a holiday
was always obtainable. The lake scenery remained vivid in his memory in
after-years, and had its influence upon him even while he enjoyed it,
unconscious of anything except the present pleasure. There was something
besides the innocent gaiety of the girls and the simple sincerity of the
Canon's platitudes, something about the lake itself, which removed him
to a spiritual region utterly remote from the fiery atmosphere of Miss
Goold's patriotism. Many things which once loomed very large before him
sank to insignificance as he drank to the full of the desolation around
him. The past, in which no doubt men strove and hoped, hated and loved
and feared, had left the just recognisable ruins of some castles and the
causeway built by an unknown hermit or the prehistoric lake-dwellers.
A few thatched cabins, faintly smoking, and here and there a cairn of
stones gathered laboriously off the wretched fields, were the evidences
of present activity. Now and then a man hooted to his dog as it barked
at the sheep on the hillside, or a girl drove a turf-laden donkey inland
from the boggy shore. Otherwise there were no signs of human life. A
deep sense of monotony and inevitableness settled down upon Hyacinth. He
came for the first time under the great enchantment which paralyzes
the spirit and energy of the Celt. He knew himself to be, as his people
were, capable of spasms of enthusiasm, the victim of transitory burnings
of soul. But the curse was upon him--the inevitable curse of feeling too
keenly and seeing too clearly to be strenuous and constant. The flame
would die down, the enthusiasm would vanish--it was vanishing from him,
as he knew well--and leave him, not indeed content with common life, but
patient of it, and to the very end sad with the sense of possibilities
unrealized.
Yet it was not without many struggles and periods of return to the older
emotions that Hyacinth surrendered his enthusiasm. There still recurred
to him memories of his father's vision of an Armageddon and the
conception of his own part in it. Sometimes, waking very early in the
morning, he became vividly conscious of his own feebleness of will and
his falling away from great purposes. The conviction that he was called
to struggle for Ireland's welfare, to sacrifice, if necessary, his life
and happiness for Ireland, was strong in him still. He felt himself
affected profoundly by the influences which surrounded him, but he had
not ceased to believe that the idea of self-sacrificing labour was for
him a high vocation. He writhed, his limbs twisting involuntarily, when
these thoughts beset him, and often he was surprised to discover that he
was actually uttering aloud words of self-reproach.
Then he would write fiercely, brutally, catch at the excuse of some
hypocrisy or corruption, or else denounce selfishness and easy-going
patriotic sentiment, finding subject for his satire in himself. His
articles brought him letters of praise from Miss Goold. 'You have it,'
she wrote once, 'the thing we all seek for, the power of beating red-hot
thought into sword-blades. Write more like the last.' But the praise
always came late. The violent mood, the self-reproach, the bitterness,
were past. His life was wrapt round again with softer influences, and he
read his own words with shame when they reached him in print. Afterwards
for a while, if he wrote at all, it was of the peasant life, of quaint
customs, half-forgotten legends and folklore. These articles appeared
too, but brought no praise from Miss Goold. Once she reproached him when
he lapsed into gentleness for many consecutive weeks.
'You oughtn't to waste yourself. There are fifty men and women can do
the sort of thing you're doing now; we don't want you to take it up.
It's fighting men we need, not maundering sentimentalists.'
CHAPTER XVII
It was during the second year of Hyacinth's residence in Ballymoy that
the station-master at Clogher died. The poor man caught a cold one
February night while waiting for a train which had broken down three
miles outside his station. From the cold came first pneumonia, and then
the end. Now, far to the east of Clogher, on a different branch of the
railway-line, is a town with which the people of Mayo have no connection
whatever. In it is a very flourishing Masonic lodge. Almost every male
Protestant in the town and the neighbourhood belongs to it, and the
Rector of the parish is its chaplain. Among its members at that time was
an intelligent young man who occupied the position of goods clerk on the
railway. The Masonic brethren, as in duty bound, used their influence to
secure his promotion, and brought considerable pressure to bear on the
directors of the company to have him made station-master at Clogher.
It is said with some appearance of truth that no appointment in Ireland
is ever made on account of the fitness of the candidate for the post
to be filled. Whether the Lord Lieutenant has to nominate a Local
Government Board Inspector, or an Urban Council has to select a street
scavenger, the principle acted on is the same. No investigation is made
about the ability or character of a candidate. Questions may be asked
about his political opinions, his religious creed, and sometimes about
the social position of his wife, but no one cares in the least about his
ability. The matter really turns upon the amount of influence which
he can bring to bear. So it happened that John Crawford, Freemason and
Protestant, was appointed station-master at Clogher. Of course, nobody
really cared who got the post except a few seniors of John Crawford's,
who wanted it for themselves. Probably even they would have stopped
grumbling after a month or two if it had not happened that a leading
weekly newspaper, then at the height of its popularity and influence,
was just inaugurating a crusade against Protestants and Freemasons.
The case of John Crawford became the subject of a series of bitter and
vehement articles. It was pointed out that although Roman Catholics were
beyond all question more intelligent, better educated, and more upright
than Protestants, they were condemned by the intolerance of highly-paid
officials to remain hewers of wood and drawers of water. It was shown by
figures which admitted of no controversy that Irish railways, banks, and
trading companies were, without exception, on the verge of bankruptcy,
entirely owing to the apathy of shareholders who allowed their interests
to be sacrificed to the bigotry of directors. It was urged that a
public meeting should be held at Clogher to protest against the new
appointment.
The meeting was convened, and Father Fahey consented to occupy the
chair. He was supported by a dispensary doctor, anxious to propitiate
the Board of Guardians with a view to obtaining a summer holiday; a
leading publican, who had a son at Maynooth; a grazier, who dreaded the
possible partition of his ranch by the Congested Districts Board; and
Mr. O'Reilly, who saw a hope of drawing custom from the counter of his
rival draper, the Scotchman.
Father Fahey opened the proceedings with a speech. He assured his
audience that he was not actuated by any spirit of religious bigotry
or intolerance. He wished well to his Protestant fellow-countrymen,
and hoped that in the bright future which lay before Ireland men of all
creeds would be united in working for the common good of their country.
These sentiments were not received with vociferous applause. The
audience was perfectly well aware that something much more to the point
was coming, and reserved their cheers. Father Fahey did not
disappoint them. He proceeded to show that the appointment of the new
station-master was a deliberate insult to the faith of the inhabitants
of Clogher.
'Are we,' he asked, 'to submit tamely to having the worst evils of the
old ascendancy revived in our midst?'
He was followed by the dispensary doctor, who also began by declaring
his freedom from bigotry. He confused the issue slightly by complaining
that the new station-master was entirely ignorant of the Irish language.
It was perfectly well known that in private life the doctor was in the
habit of expressing the greatest contempt for the Gaelic League, and
that he could not, if his life depended on it, have translated even Mr.
O'Reilly's advertisements; but his speech was greeted with tumultuous
cheers. He proceeded to harrow the feelings of his audience by
describing what he had heard at the railway-station one evening while
waiting for the train. As he paced the platform his attention was
attracted by the sound of a piano in the station-master's house. He
listened, and, to his amazement and disgust, heard the tune of a popular
song, 'a song'--he brought down his fist on the table as he uttered the
awful indictment--'imported from England.'
'I ask,' he went on--'I ask our venerated and beloved parish priest;
I ask you, fathers of innocent families; I ask every right-thinking
patriot in this room, are our ears to be insulted, our morals corrupted,
our intellects depraved, by sounds like these?'
He closed his speech by proposing a resolution requiring the railway
company to withdraw the obnoxious official from their midst.
The oratory of the grazier, who seconded the resolution, was not
inferior. It filled his heart with a sense of shame, so he said, to
think of his cattle, poor, innocent beasts of the field, being
handled by a Protestant. They had been bred, these bullocks of his,
by Catholics, fed by Catholics, were owned by a Catholic, bought with
Catholic money at the fairs, and yet they were told that in all Ireland
no Catholic could be discovered fit to put them into a train.
Neither the resolution itself nor the heart-rending appeal of the
grazier produced the slightest effect on the railway company. John
Crawford continued to sell tickets, even to Father Fahey himself, and
appeared entirely unconcerned by the fuss.
About a fortnight after the meeting Hyacinth spent a night in Clogher.
Mr. Holywell, the cigarette man, happened to be in the hotel, and, as
usual, got through a good deal of desultory conversation while he drank
his whisky-and-water. Quite unexpectedly, and apropos of nothing that
had been said, he plumped out the question:
'What religion are you, Conneally?'
The inquiry was such an unusual one, and came so strangely from Mr.
Holywell, who had always seemed a Gallio in matters spiritual, that
Hyacinth hesitated.
'I'm a Baptist myself,' he went on, apparently with a view to palliating
his inquisitiveness by a show of candour. 'I find it a very convenient
sort of religion in Connaught. There isn't a single place of worship
belonging to my denomination in the whole province, so I'm always able
to get my Sundays to myself. I don't want to convert you to anything or
to argue with you, but I have a fancy that you are a Church of Ireland
Protestant.'
Hyacinth admitted the correctness of the guess, and wondered what was
coming next.
'Ever spend a Sunday here?'
'Never,' said Hyacinth; 'I always get back home for the end of the week
if I can.'
'Ah! Well, do you know, if I were you, I should spend next Sunday here,
and go to Mass.'
'I shall not do anything of the sort.'
'Well, it's your own affair, of course; only I just think I should do it
if I were you. Good-night.'
'Wait a minute,' said Hyacinth. 'I want to know what you mean.'
Mr. Holywell sat down again heavily.
'Been round your customers here lately?'
'No. I only arrived this evening, and have done nothing yet. I mean to
go round them to-morrow.'
'You may just as well go home by the early train for all the good you'll
do.'
Hyacinth restrained himself with an effort. He reflected that he was
more likely to get at the meaning of these mysterious warnings if he
refrained from direct questioning. After a minute of two of silence Mr.
Hollywell went on:
'They had a meeting here a little while ago about the appointment of
a Protestant station-master. They didn't take much by it so far as the
railway company is concerned, but I happen to know that word has gone
round that every shopkeeper in the town is to order his goods as far as
possible from Catholics. Now, everybody knows your boss is a Protestant,
but the people are a little uncertain about you. They've never seen you
at Mass, which is suspicious, but, on the other hand, the way you gas on
about Irish manufactures makes them think you can't be a Protestant.
The proper thing for you to do is to lie low till you've put in an
appearance at Mass, and then go round and try for orders.'
'That's the kind of thing,' said Hyacinth, 'that I couldn't do if I had
no religion at all; but it happens that I have convictions of a sort,
and I don't mean to go against them.'
'Oh, well, as I said before, it's your own affair; only better
Protestants than you have done as much. Why, I do it myself constantly,
and everyone knows that a Baptist is the strongest kind of Protestant
there is.'
This reasoning, curiously enough, proved unconvincing.
'I can't believe,' said Hyacinth, 'that a religious boycott of the kind
is possible. People won't be such fools as to act clean against their
own interests. Considering that nine-tenths of the drapery goods in the
country come from England and are sold by Protestant travellers, I don't
see how the shopkeepers could act as you say.'
'Oh, of course they won't act against their own interests. I've never
come across a religion yet that made men do that. They won't attempt to
boycott the English firms, because, as you say, they couldn't; but they
can boycott you. Everything your boss makes is turned out just as well
and just as cheap, or cheaper, by the nuns at Robeen. Perhaps you didn't
know that these holy ladies have hired a traveller. Well, they have, and
he's a middling smart man, too--quite smart enough to play the trumps
that are put into his hand; and he's got a fine flush of them now. What
with the way that wretched rag of a paper, which started all the fuss,
goes on rampaging, and the amount of feeling that's got up over the
station-master, the peaceablest people in the place would be afraid to
deal with a Protestant at the present moment. The Robeen man has the
game in his own hands, and I'm bound to say he'd be a fool if he didn't
play it for all it's worth. I'd do it myself if I was in his shoes.'
Hyacinth discovered next day that Mr. Holywell had summed up the
situation very accurately. No point-blank questions were asked about his
religion, but he could by no means persuade his customers to give him
even a small order. Every shop-window was filled with goods placarded
ostentatiously as 'made in Robeen.' Every counter had tweeds, blankets,
and flannels from the same factory. No one was in the least uncivil to
him, and no one assigned any plausible reason for refusing to deal with
him. He was simply bowed out as quickly as possible from every shop he
entered.
He returned home disgusted and irritated, and told his tale to his
employer. Mr. Quinn recognised the danger that threatened him. For the
first time, he admitted that his business was being seriously injured
by the competition of Robeen. He took Hyacinth into his confidence more
fully than he had ever done before, and explained what seemed to be a
hopeful plan.
'I may tell you, Conneally, that I have very little capital to fall back
upon in my business. Years ago when things were better than they are
now, I had a few thousands put by, but most of it went on buying my
brother Albert's share of the mill. Lately I have not been able to save,
and at the present moment I can lay hands on very little money. Still, I
have something, and what I mean to do is this: I shall give up all idea
of making a profit for the present. I shall even sell my goods at a
slight loss, and try to beat the nunnery out of the market. I think
this religious animosity will weaken after a while, and if we offer the
cheapest goods we must in the end get back our customers.'
Hyacinth was not so sanguine.
'You forget,' he said, 'that these people have Government money at their
backs, and are likely to get more of it. If you sell at a loss they will
do so, too, and ask for a new grant from the Congested Districts Board
to make good their deficiency.'
Mr. Quinn sighed.
'That is quite possible,' he said. 'But what can I do? I must make a
fight for my business.'
Hyacinth hesitated.
'Perhaps I have no right to make the suggestion, but it seems to me that
you are bound to be beaten. Would it not be better to give in at once?
Don't risk the money you have safe. Keep it, and try to sell the mill
and the business.'
'I shall hold on,' said Mr. Quinn.
'Ought you not to think of your wife? Remember what it will mean to
her if you are beaten in the end, when your savings are gone and your
business unsaleable.'
For a moment there were signs of wavering in Mr. Quinn's face. The
fingers of his hands twisted in and out of each other, and a pitiable
look of great distress came into his eyes. Then he unclasped his hands
and placed them flat on the table before him.
'I shall hold on,' he said. 'I shall not close my mill while I have a
shilling left to pay my workers with.'
'Well,' said Hyacinth, 'it is for you to decide. At least, you can count
on my doing my best, my very best.'
CHAPTER XVIII
Mr. Quinn carried on his struggle for nearly a year, although from the
very first he might have recognised its hopelessness. Time after time
Hyacinth made his tour, and visited the shopkeepers who had once been
his customers. Occasionally he succeeded in obtaining orders, and a
faint gleam of hope encouraged him, but he had no steady success. Mr.
Quinn's original estimate of the situation was so far justified that
after a while the religious animosity died out. Shopkeepers even
explained apologetically that they gave their orders to the Robeen
convent for purely commercial reasons.
'Their goods are cheaper than yours, and that's the truth, Mr.
Conneally.'
Hyacinth recognised that Mr. Quinn was being beaten at his own game. He
had attempted to drive the nuns out of the market by underselling them,
and now it appeared that they, too, were prepared to face a loss. It was
obvious that their losses must be great, much greater than Mr. Quinn's.
Rumours were rife of large loans raised by the Mother Superior, of
mortgages on the factory buildings and the machinery. These stories
brought very little consolation, for, as Hyacinth knew, Mr. Quinn was
very nearly at the end of his resources. He refused to borrow.
'When I am forced to close up,' he said, 'I shall do so with a clear
balance-sheet. I have no wish for bankruptcy.'
'I should like,' said Hyacinth vindictively, 'to see the Reverend Mother
reduced to paying a shilling in the pound.'
'I am afraid,' said Mr. Quinn, 'you won't see that. The convent is a
branch of an immense organization. No doubt, if it comes to a pinch,
funds will be forthcoming.'
'Yes, and they won't draw on their own purse till they have got all
they can out of the Congested Districts Board. I have no doubt they are
counting on another four thousand pounds to start them clear when they
have beaten you.'
One day, quite accidentally, Hyacinth came by a piece of information
about the working of the Robeen factory which startled him. He was
travelling home by rail. It happened to be Friday, and, as usual in
the early summer, the train was crowded with emigrants on their way to
Queenstown. The familiar melancholy crowd waited on every platform.
Old women weeping openly and men with faces ridiculously screwed and
puckered in the effort to restrain the rising tears clung to their sons
and daughters. Pitiful little boxes and carpet bags were piled on
the platform. Friends clung to hands outstretched through the
carriage-windows while the train moved slowly out. Then came the long
mournful wail from those left behind, and the last wavings of farewell.
At the Robeen station the crowd was no less than elsewhere. The
carriages set apart for the emigrants were full, and at the last minute
two girls were hustled into the compartment where Hyacinth sat. A woman,
their mother, mumbled and slobbered over their hands. An old man, too
old to be their father, shouted broken benedictions to them. Two
young men--lovers, perhaps, or brothers--stood red-eyed, desolate and
helpless, without speaking. After the train had started Hyacinth looked
at the girls. One of them, a pretty creature of perhaps eighteen years
old, wept quietly in the corner of the carriage. Beside her lay her
carpet bag and a brown shawl. On her lap was an orange, and she held a
crumpled paper bag of biscuits in her hand. There was nothing unusual
about her. She was just one instance of heartbreak, the heart-break of a
whole nation which loves home as no other people have ever loved it, and
yet are doomed, as it seems inevitably, to leave it. She was just one
more waif thrown into the whirlpool of the great world to toil and
struggle, succeed barrenly or pitifully fail; but through it all,
through even the possible loss of faith and ultimate degradation, fated
to cling to a love for the gray desolate fatherland. The other girl
was different. Hyacinth looked at her with intense interest. She was the
older of the two, and not so pretty as her sister. Her face was thin and
pale, and a broad scar under one ear showed where a surgeon's knife had
cut. She sat with her hands folded on her lap, gazing dry-eyed out of
the window beside her. There was no sign of sorrow on her face, nothing
but a kind of sulky defiance.
After a while she took the paper bag out of her sister's hand, opened
it, and began to eat the gingerbread biscuits it contained. Hyacinth
spoke to her, but she turned her head away, and would not answer him.
His voice seemed to rouse the younger sister, who stopped crying and
looked at him curiously. He tried again, and this time he spoke in
Irish.
At once the younger girl brightened and answered him. Apparently she had
no fear that malice could lurk in the heart of a man who spoke her own
language. In a few minutes she was chatting to him as if he were an old
friend.
He learnt that the two girls were on their way to New York. They had
a sister there who had sent them the price of their tickets. Yes, the
sister was in a situation, was getting good wages, and had clothes 'as
grand as a lady's.' She had sent home a photograph at Christmas-time,
which their mother had shown all round the parish. These two were to get
situations also as soon as they arrived. Oh yes, there was no doubt of
it: Bridgy had promised. There were four of them left at home--three
boys and a girl. No doubt in time they would all follow Bridgy to
America--all but Seumas; he was to have the farm. No, the girls
could not get married, because their father was too poor to give them
fortunes. There was nothing for them but to go to America. But their
mother had not wanted them to go. The clergy and the nuns were against
the girls going. Indeed, they nearly had them persuaded to send Bridgy's
money back.
'But Onny was set on going.'
She glanced at her sister in the corner of the carriage. Hyacinth turned
to her.
'Why do you want to leave Ireland?'
But Onny remained silent, sulky, at it seemed. It was the younger girl
who answered him.
'They say it's a fine life they have out there. There's good money to be
earned, and mightn't we be coming home some day with a fortune?'
'But aren't you sorry to leave Ireland?'
Again he looked at the elder girl, and this time was rewarded with a
flash of defiant bitterness from her eyes.
'Sorry, is it? No, but I'm glad!'
'Onny's always saying that there was nothing to be earned in the
factory. And she got more than the rest of us. Wasn't she the first girl
that Sister Mary Aloysius picked out of the school when the young lady
from England came over to teach us? She was the best worker they had.'
'It's true what she says,' said Onny. 'I was the best worker they had. I
worked for them for three years, and all I was getting at the end of it
was six shillings a week. Why would I be working for that when I might
be getting wages like Bridgy's in America? What sense would there be in
it?'
'But why did you work for such wages?'
'Well, now,' said the younger girl, 'how could we be refusing the
Reverend Mother when she came round the town herself, and gave warning
that we'd all be wanted?'
'There's few,' continued Onny, without noticing her sister, 'that earned
as much as I did. Many a girl works there and has no more than one and
ninepence to take home at the end of the week.'
Hyacinth began to understand how it was that Mr. Quinn was being
hopelessly beaten. This was no struggle between two trade rivals, to be
won by the side with the longer purse. Nor was it simply a fight between
an independent manufacturer and a firm fed with Government bounties. Mr.
Quinn's rival could count on an unlimited supply of labour at starvation
wages, while he had to hire men and women at the market value of their
services. He had been sorry for the two girls when they got into the
train. Now he felt almost glad that they were leaving Ireland. It
appeared that they had certainly chosen the wiser part.
He arrived at home dejected, and sat down beside the fire in his room
to give himself up to complete despair. He found no hope anywhere. Irish
patriotism, so he saw it, was a matter of words and fine phrases. No one
really believed in it or would venture anything for it. Politics was a
game at which sharpers cheated each other and the people. The leaders
were bold only in sordid personal quarrels. The mass of the people were
utterly untouched by the idea of nationality, in earnest about nothing
but huckstering and petty gains. Over all was the grip of a foreign
bureaucracy and a selfish Church tightening slowly, squeezing out the
nation's life, grasping and holding fast its wealth. No man any longer
made any demand except to be allowed to earn what would buy whisky
enough to fuddle him into temporary forgetfulness of the present misery
and the imminent tyranny.
The slatternly maid-servant who brought him his meals and made his bed
tapped at the door.
'Please, sir, Jimmy Loughlin's after coming with a letter from Mr.
Quinn, and he's waiting to know if you'll go.'
Hyacinth read the note, which asked him to call on his employer that
afternoon.
'Tell him I'll be there.'
'Will you have your dinner before you go? The chops is in the pan below.
Or will I keep them till you come back?'
'Oh, I've time enough. Bring them as soon as they're cooked, and for
goodness' sake see that the potatoes are properly boiled.'
He took up a great English weekly paper, with copies of which Canon
Beecher supplied him at irregular intervals, and propped it against
the dish-cover while he ate. The article which caught his attention was
headed 'Angels in Connaught.' It contained an idealized account of the
work of the Robeen nuns, from whose shoulders it seemed to the writer
likely that wings would soon sprout. There was a description of the once
miserable cabins now transformed into homesteads so comfortable that
English labourers would not disdain them. The people shared in the
elevation of their surroundings. Men and women, lately half-naked
savages, starved and ignorant, had risen in the scale of civilization
and intelligence to a level which almost equalled that of a Hampshire
villager. The double stream of emigration to the United States and
migration to the English harvest-fields was stopped. An earthly paradise
had been created in a howling wilderness by the self-denying labours of
the holy ladies, aided by the statesmanlike liberality of the Congested
Districts Board. There was another page of the article, but Hyacinth
could stand no more.
He stood up and glanced at his watch. It was already nearly five
o'clock. He pushed his way down the street, where the country-people,
having completed their week's marketing, were loading donkeys on the
footpath or carts pushed backwards against the kerbstone. Women dragged
their heavily-intoxicated husbands from the public-houses, and girls,
damp and bedraggled, stood in groups waiting for their parents. He
turned into the gloomy archway of the mill, unlocked the iron gate, and
crossed the yard into the Quinns' garden. The lamp burned brightly in
the dining-room, and he could see Mrs Quinn in her chair by the fireside
sewing. Her children sat on the rug at her feet. He saw their faces
turned up to hers, gravely intent. No doubt she was telling them some
story. He stood for a minute and watched them, while the peaceful joy
of the scene entered into his heart. This, no doubt, a home full of such
love and peace, was the best thing life had got to give. It was God's
most precious benediction. 'Lo, thus shall a man be blessed who feareth
the Lord.' He turned and passed on to the door. The servant showed him
in, not, as he expected, to the sitting-room he had just gazed at, but
to Mr. Quinn's study.
It was a desolate chamber. A plain wooden desk like a schoolmaster's
stood in one corner, and upon it a feeble lamp. A bookcase surmounted a
row of cupboards along one wall. Its contents--Hyacinth had often looked
over them--were a many-volumed encyclopaedia, Macaulay's 'History of
England,' Foxe's 'Book of Martyrs,' a series entitled 'Heroes of the
Reformation,' and some bound volumes of a trade journal. Above the
chimneypiece hung two trout-rods, a landing-net, and an old gun. The
grate was tireless. It was a room obviously not loved by its owner.
Neither pleasure nor comfort was looked for in it. It was simply a place
of escape from the attractions of quiet ease when business overflowed
the proper office hours. Mr. Quinn rose from his desk when Hyacinth
entered.
'I am very glad to see you,' he said; 'I want to have a talk with you.'
Hyacinth waited while he arranged and rearranged some papers on the desk
in front of him. Mr. Quinn, although he had specially sent for Hyacinth,
seemed in no hurry to get to the subject of the interview. When he did
speak, it was evident from his tone that the important topic was still
postponed.
'How did you get on this week?'
Hyacinth had nothing good to report. He took from his pocket the
note-book in which he entered his orders, and went over it. It contained
an attenuated list. Moreover, the harvest had been bad, and old debts
very difficult to collect. Mr. Quinn listened, apparently not very
attentively, and when the reading was over said:
'What you report this week is simply a repetition of the story of the last
six months. I did not expect it to be different. It makes the decision
I have to make a little more inevitable, that is all. Mr. Conneally, we
have been very good friends, and since you have been in my employment I
have been satisfied with you in every way. Now I am unable to employ you
any longer. I am giving up my business.'
Hyacinth made an effort to speak, but Mr. Quinn held up his hand and
silenced him.
'This week,' he continued, 'I received news which settled the matter
for me. Jameson and Thorpe, the big drapers in Dublin, were my best
customers for certain goods. Last Monday they wrote that they had an
offer of blankets at a figure a long way below mine. I didn't believe
that articles equal in quality to mine could be produced at the price,
and wrote a hint to that effect. I received--nothing could have been
more courteous--a sample of the blankets offered. Well, I admit that it
was at least equal to what I could supply in every way. I wrote again
asking as a favour to be supplied with the name of the competing firm. I
got the answer to-day. Mr. Thorpe wrote himself. The Robeen convent has
undersold me.'
Hyacinth made another attempt to speak.
'Let me finish,' said Mr. Quinn. 'I had foreseen, of course, that this
was coming. I have no more capital to fall back upon. I do not mean to
run into debt. There is nothing for me but to dismiss my employees and
shut up.'
'Yes,' said Hyacinth. 'And then----'
He knew he had no right to ask a question about the future, but the
thought of Mrs. Quinn and her children as he had seen them in the
dining-room almost forced him to inquire what was to happen to them. A
spasm of extreme pain crossed Mr. Quinn's face.
'You are thinking of my wife. It will be hard--yes, very hard. She loved
this place, her friends here, her garden, and all the quiet, peaceful
life we have lived. Well, there is to be an end of it. But don't look so
desperate.' He forced himself to smile as he spoke. 'We shall not starve
or go to the workhouse. I have a knowledge of woollen goods if I have
nothing else, and I dare say I can get an appointment as foreman or
traveller for some big drapery house. But I may not be reduced to that.
There is a secretary wanted just now in the office of one of the Dublin
charitable societies. I mean to apply for the post. Canon Beecher and
our Bishop are both members of the committee, and I am sure will do
their best for me. The salary is not princely--a hundred and twenty
pounds a year, I think. But there, I ought not to be talking all this
time about myself. I must try and do something for you.'
'Never mind me,' said Hyacinth; 'I shall be all right. But I can't bear
to think of you and Mrs. Quinn. Poverty like that in Dublin! Have you
thought what it means? A shabby little house in a crowded street, off at
the back of somewhere; dirt and stuffiness and vulgarity all around you.
She can't be expected to stand it--or you either.'
'My dear boy,' said Mr. Quinn, 'my wife and I have been trying all our
lives to be Christians. Shall we receive good at the Lord's hand and not
evil also? However it may be with me, I know that she will not fail in
the trial.'
His face lit up as he spoke, and the smile on it was no longer forced,
but clear and brave. Hyacinth knew that he was once again in the
presence of that mysterious power which enables men and women to meet
and conquer loss and pain, against which every kind of misfortune beats
in vain. His eyes filled with tears as he took Mr. Quinn's hand and bade
him good-night.
CHAPTER XIX
Hyacinth had three months' work to do before he actually left Mr.
Quinn's employment. He knew that at the end of that time he would be
left absolutely without income, and that it was necessary for him to
look out for some other situation. He reckoned up the remains of his
original capital, and found himself with little more than a hundred
pounds to fall back upon. Yet he did nothing. From time to time he
bestirred himself, pondered the newspaper advertisements of vacant
situations, and mentally resolved to commence his search at once. Always
some excuse offered itself to justify putting the unpleasant business
off, and he allowed himself to slip back into the quiet routine of life
as if no catastrophe threatened him. He was, indeed, far more troubled
about the Quinns' future than his own, and when, at the end of April,
Canon Beecher returned from Dublin with the news that he had secured the
secretaryship of the Church of Ireland Scriptural Schools Society for
Mr. Quinn, Hyacinth felt that his mind was relieved of a great anxiety.
That no such post had been discovered for him did not cost him a
thought. In spite of his spasmodic efforts to goad himself into a
condition of reasonable anxiety for his future, there remained half
consciously present in his mind a conviction that somehow a way of
getting sufficient food and clothes would offer itself in due time.
The conviction was justified by the event. It was on Saturday evening
that the Canon returned with his good news, and on Sunday morning
Hyacinth received a letter from Miss Goold.
'You have no doubt heard,' she wrote, 'that we have got a new editor
for the Croppy--Patrick O'Dwyer, Mary's brother. Of course, you remember
Mary and her unpoetical hysterics the morning after the Rotunda meeting.
The new editor is a splendid man. He has been on the staff of a New
York paper for the last five years, and thoroughly understands the whole
business. But that's not the best of him. He hates England worse than
I do. I'm only a child beside him, bursting out into fits of temper
now and then, and cooling off again. He hates steadily, quietly, and
intensely. But even that is not all that is to be said. He has got
brains--brains enough, my dear Hyacinth, to make fools of you and me
every day and all day long. He has devised a new policy for Ireland. The
plan is simplicity itself, like all really great plans, and it _must_
succeed. I won't go into it now, because I want you to come up to Dublin
and see O'Dwyer. He tells me that he needs somebody else besides himself
on the staff of the _Croppy_, which, by the way, is to be enlarged and
improved. He wants a man who can write a column a week in Irish, as well
as an article now and then in good strong plain English. I suggested
your name to him, and showed him some of the articles you had written.
He was greatly pleased with the one about O'Dowd's cheap patriotism, and
liked one or two of the others. He just asked one question about you:
"Does Mr. Conneally hate England and the Empire, and everything English,
from the Parliament to the police barrack? It is this hatred which must
animate the work." I said I thought you did. I told him how you had
volunteered to fight for the Boers, and about the day you nearly killed
that blackguard Shea. He seemed to think that was good enough, and asked
me to write to you on the subject. We can't offer you a big salary. The
editor himself is only to get a hundred pounds a year for the present,
and I am guaranteeing another hundred for you. I am confident that I
shan't have to pay it for more than six months. The paper is sure to go
as it never went before, and in a few years we shall be able to treble
O'Dwyer's salary and double yours. Nothing like such a chance has ever
offered itself in Irish history before. Everything goes to show that
this is our opportunity. England is weaker than she has been for
centuries, is clinging desperately to the last tatters of her old
prestige. She hasn't a single statesman capable of thinking or acting
vigorously. Her Parliament is the laughingstock of Europe. Her Irish
policy may be summed up in four words--intrigue with the Vatican. In
Ireland the power of the faithful garrison is gone. The Protestants in
the North are sick of being fooled by one English party after another.
The landlords, or what's left of them, are beginning to discover that
they have been bought and sold. The Bishops, England's last line of
defence, are overreaching themselves, and we are within measurable
distance of the day when the Church will be put into her proper place.
There is not so much as a shoneen publican in a country town left who
believes in the ranting of O'Rourke and his litter of blind whelps.
Ireland is simply crying out for light and leading, and the _Croppy_
is going to give both. You always wanted to serve Ireland. Now I am
offering you the chance. I don't say you ought to thank me, though you
will thank me to the day of your death. I don't say that you have an
opportunity of becoming a great man. I know you, and I know a better way
of making sure of you than that. I say to you, Hyacinth Conneally, that
we want you--just _you_ and nobody else. Ireland wants you.'
The letter, especially the last part of it, was sufficiently ridiculous
to have moved Hyacinth to a smile. But it did no such thing. On the
contrary, its rhetoric excited and touched him. The flattery of the
final sentences elated him. The absurdity of the idea that Ireland
needed him, a fifth-rate office clerk, an out-of-work commercial
traveller who had failed to sell blankets and flannels, did not strike
him at all. The figure of Augusta Goold rose to his mind. She flashed
before him, an Apocalyptic angel, splended and terrible, trumpet-calling
him to the last great fight. He forgot in an instant the Quinns and
their trouble. The years of quietness in Ballymoy, the daily intercourse
with gentle people, the atmosphere of the religion in which he had
lived, fell away from him suddenly.
He sat absorbed in an ecstasy of joyful excitement until the jangling of
Canon Beecher's church bell recalled him to common life again. It speaks
for the strength of the habits he had formed in Ballymoy that he rose
without hesitation and went to take his part in the morning service.
He sat down as usual beside Marion Beecher and her harmonium. He
listened to her playing until her father entered. He found himself
gazing at her when she stood up for the opening words of the service.
He felt himself strangely affected by the gentleness of her face and the
slender beauty of her form. When she knelt down he could not take
his eyes off her. There came over him an inexplicable softening, a
relaxation of the tense excitement of the morning. He thought of her
kneeling there in the faded shabby church Sunday after Sunday for years
and years, when he was working at hot pressure far away. He knew just
how her eyes would look calmly, trustfully up to the God she spoke
to; how her soul would grow in gentleness; how love would be the very
atmosphere around her. And all the while he would struggle and fight,
with no inspiration except a bitter hate. Suddenly there came on him a
feeling that he could not leave her. The very thought of separation
was a fierce pain. A desire of her seized on him like uncontrollable
physical hunger. Wherever he might be, whatever life might have in store
for him, he knew that his heart would go back to her restlessly, and
remain unsatisfied without her. He understood that he loved her. Canon
Beecher's voice came to him as if from an immense distance:
'O God, make speed to save us.'
Then he heard very clearly Marion's sweet voice replying:
'O Lord, make haste to help us.'
There was a faint shuffling, and the congregation rose to their feet.
His eyes were still on Marion, and now his whole body quivered with the
force of his newly-found love. She half turned and looked at him. For
one instant their eyes met, and he saw in hers a flash of recognition,
then a strange look of fear, and she turned away from him, flushed and
trembling. He saw that she had read his heart and knew his love.
'Glory be to the Father, and to the Son, and to the Holy Ghost,' read
the Canon heavily.
Hyacinth's heart swelled in him. His whole being seemed to throb with
exultation, and he responded in a voice he could not recognise for his.
'As it was in the beginning, is now, and ever shall be, world without
end. Amen.'
Marion stood silent. Her head was bowed down, and her hands clasped
tight together.
Of the remainder of the morning's service Hyacinth could never
afterwards remember anything. No doubt Canon Beecher read the Psalms and
lessons and prayers; no doubt he preached. Probably, also, hymns were
sung, and Marion played them, but he could not imagine how. It seemed
quite impossible that she could have touched the keys with her fingers,
or that she could have uttered any sound; yet no one had remarked the
absence of hymns or even noticed any peculiarity in their performance.
Not till after the service was over did he regain full consciousness
of himself and his surroundings; then he became exceedingly alert. He
watched the Canon disappear into the vestry, heard the congregation
trample down the aisle, listened to Marion playing a final voluntary.
It seemed to him as he sat there waiting for her to stop that she played
much longer than usual. He could hear Mrs. Beecher and Mr. Quinn talking
in the porch, and every moment he expected the Canon to appear. At last
the music ceased, and the lid of the harmonium was closed and locked. He
stepped forward and took Marion's hands in his.
'Marion,' he said, 'I love you. It was only this morning that I found
it out, but I know--oh, I know--that I love you far, far more than I can
tell you.'
The hand which lay in his grew cold, and the girl's head was bowed so
that he could not see her face. He felt her tremble.
'Marion, Marion, I love you, love you, love you!'
Then very slowly she raised her head and looked at him. He stooped to
kiss her lips, and felt her face flush and glow when he touched it. Then
she drew her hands from his and fled down the church to her mother.
Hyacinth stood agape with wonder at the words which he had spoken. The
knowledge of his love had come on him like a sudden gust, and he only
half realized what he had done. He walked back to his lodgings, going
over and over the amazing words, recalling with flushed astonishment the
kiss. Then a chilling doubt beset him suddenly. Did Marion know how poor
he was? Never in his life had the fear of poverty or the desire of
gain determined Hyacinth's plans. He knew very well that no such
considerations would have in any way affected his conduct towards
Marion. Once he realized that he loved her, the confession of his
love was quite inevitable. Yet he felt vaguely that he might be judged
blameworthy. He had read a few novels, and he knew that even the writers
whose chief business it is to glorify the passion of love do not dare to
represent it as independent of money. He knew, too, that many penniless
heroes won admiration--he did not in the least understand why they
should--by silently deserting affectionate women. He knew that kisses
were immoral except for those who possessed a modest competence. These
authorized ethics of marriage engagements were wholly incomprehensible
to him, and it in no way disquieted his conscience that he had bound
Marion to him with his kiss; yet he felt that she had a right to know
what income he hoped to earn, and what kind of home he would have to
offer her. A hundred pounds a year might be deemed insufficient, and
he knew that, not being either a raven or a lily, he could not count on
finding food and clothes ready when he wanted them.
The daughters of the Irish Church clergy, even of the dignitaries, are
not brought up in luxury. Still, they are most of them accustomed to a
daily supply of food--plain, perhaps, but sufficient--and will look for
as much in the homes of their husbands. A girl like Marion Beecher does
not expect to secure a position which will enable her to send her own
clothes to a laundress or hire a cook who can make pastry; but it is not
fair to ask her to wash the family's blankets or to boil potatoes for a
pig. Probably her friends would think her lucky in marrying a curate or
a dispensary doctor with one hundred and fifty pounds a year, and
the prospect of one-third as much again after a while. But Hyacinth
remembered that he was poorer than any curate. He determined to put the
matter plainly before Marion without delay.
The Rectory door was opened for him by Elsie Beecher, and, in spite of
her wondering protests, Hyacinth walked into the dining-room and asked
that Marion should be sent to him. The room was empty, as he expected.
He stood and waited for her, deriving faint comfort and courage from the
threadbare carpet, patched tablecloth, and poor crazy chairs. They were
strange properties for a scene with possibilities of deep romance in it,
but they made his confession of poverty easier.
Marion entered at last and stood beside him. He neither took her hand
nor looked at her.
'When I told you to-day that I loved you,' he said, 'I ought to have
told you that I am very poor.'
'I know it,' she said.
'But I am poorer even than you know. I am not in Mr. Quinn's employment
any more. I have no settled income, and only a prospect of earning a
very small one.' He paused. 'I shall have to go away from Ballymoy. I
must live in Dublin. I do not think it is fair to ask you to marry me. I
shall have no more to live upon than----'
She moved a step nearer to him and laid her hand on his arm.
'Look at me,' she said.
He raised his eyes to her face, and saw again there, as he had seen in
church, the wonderful shining of love, which is stronger than all things
and holds poverty and hardship cheap.
'Keep looking at me still,' she said. 'Now tell me: Do you really think
it matters that you are poor? Do you think I care whether you have much
or little? Tell me.'
He could not answer her, although he knew that there was only one answer
to her question.
'Do you think that I love money? Do you doubt that I love you?'
Her voice sunk almost to a whisper as she spoke, and her eyes fell from
looking into his. Just as when he kissed her in the church, she flushed
suddenly, but this time she did not try to escape from him. Instead she
clung to his arm, and hid her face against his shoulder. He put his arms
round her and held her close.
'I know,' he said. 'I was a fool to come here thinking that my being
poor would matter. I might have known. Indeed, I think I did know even
before I spoke to you.'
She had no answer except a long soft laugh, which was half smothered in
his arms.
CHAPTER XX
On Saturday evenings and Sunday afternoons Canon Beecher enjoyed the
privilege of a fire in his study. He was supposed to be engaged at these
seasons in the preparation of his sermons, a serious and exacting work
which demanded solitude and profound quiet. In earlier years he really
had prepared his sermons painfully, but long practice brings to the
preacher a certain fatal facility. Old ideas are not improved by being
clothed in new phrases, and of new ideas--a new idea will occasionally
obtrude itself even on the Christian preacher--the Canon was exceedingly
mistrustful. The study was an unexciting and comparatively comfortable
room. The firelight on winter afternoons played pleasantly on the
dim gold backs of the works of St. Augustine, a fine folio edition
bequeathed to Mrs. Beecher by a scholarly uncle, which reposed
undisturbed along a lower shelf. Adventurous rays occasionally explored
a faded print of the Good Shepherd which hung above the books, and
gleamed upon the handle of the safe where the parish registers and
church plate were stored. The quiet and the process of digesting his
mid-day dinner frequently tempted the Canon to indulge in a series of
pleasant naps on Sunday afternoons.
When Hyacinth tapped at the study door and entered, the room was almost
dark, and the sermon preparation, if proceeding at all, can have got no
further than the preliminary concatenation of ideas. The Canon, however,
was aggressively, perhaps suspiciously, wide awake.
'Who is that?' he asked. 'Oh, Conneally, it is you. I am very glad to
see you. Curiously enough, I thought of going down to call on you this
afternoon. I wanted to have a talk with you. I dare say you have come up
to consult me.'
Hyacinth was astonished. How could anyone have guessed what he came
about? Had Marion told her father already?
'It is a sad business,' the Canon went on--' very distressing and
perplexing indeed. But so far as you personally are concerned,
Conneally, I cannot regard it as an unmixed misfortune. You were meant
for something better, if I may say so, than selling blankets. Now, I
have a plan for your future, which I talked over last week with an old
friend of yours. Now that something has been settled about the Quinns,
we must all give our minds to your affairs.'
Then Hyacinth understood that Canon Beecher expected to be consulted
about his future plans, and even had some scheme of his own in mind.
'Yes,' he replied, 'I shall be very glad of your help and advice,
although I think I have decided about what I am going to do. It was
not on that subject I came to speak to you to-day, but on another, more
important, I think, for you and for me and for Marion.'
'For Marion?'
'I ought to tell you at once that I love your daughter Marion, and I am
sure that she loves me. I want to marry her.'
'My dear boy! I had not the slightest idea of this. It is one of the
most extraordinary things--or perhaps extraordinary is not exactly the
proper word--one of the most surprising things I----'
The Canon stopped abruptly and sat stroking his chin with his forefinger
in the effort to adjust his mind to the new situation presented to it.
It was characteristic of the man that the thought of Hyacinth's poverty
was not the first which presented itself. Indeed, Canon Beecher was one
of those unreasonable Christians who are actually convinced of the truth
of certain paradoxical sayings in the Gospel about wealth and poverty.
He believed that there were things of more importance in life than the
possession of money. Fortunately, such Christians are rare, for their
absurd creed forms a standing menace to the existence of Church and
sect alike. Fortunately also, ecclesiastical authorities have sufficient
wisdom to keep these eccentrics in the background, confining them as far
as possible to remote and obscure places. If ever a few of them escape
into the open and find means of expressing themselves, the whole
machinery of modern religion will become dislocated, and the Church will
very likely relapse into the barbarity of the Apostolic age.
'I believe, Conneally,' said the Canon at last, 'that you are a good
man. I do not merely mean that you are moral and upright, but that you
sincerely desire to follow in the footsteps of the Master.'
He looked as if he wanted some kind of answer, at least a confirmation
of his belief. Fresh from his interview with Marion, and having the
Canon's eyes upon him, it did not seem impossible to Hyacinth to answer
yes. Even the thought of the work he was to engage in with Miss Goold
and Patrick O'Dwyer seemed to offer no ground for hesitation. Was he
not enlisting with them to take part in the great battle? He had
never ceased to believe his father's words: 'And the battlefield is
Ireland--our dear Ireland which we love!' He felt for the moment that
he was altogether prepared to make the confession of faith the Canon
required.
'Yes,' he said, 'I am on His side.'
'And you love Marion? Are you quite sure of that? Are you certain that
this is not a passing fancy?'
This time Hyacinth had no doubt whatever about his answer.
'I am as certain of my love as I am of anything in the world.'
'I am glad. I am very glad that this has happened--for your sake,
because I have always liked you; also for Marion's sake. I shall see you
happy because you love one another, and because you both love the Lord.
I ask no more than those two things. But I must go and tell my wife at
once. She will be glad, too.'
He rose and went to the door. With his hand stretched out to open it he
stopped, struck by a sudden thought.
'By the way, I ought to ask you--if you mean to be married--have you
any--I mean it is necessary--I hope you won't think I am laying undue
stress upon such matters, but I really--I mean we really ought to
consider what you are to live upon.'
It was the prospect of imparting the news to his wife which forced this
speech from him. Mrs. Beecher was, indeed, the least worldly of women.
Did she not marry the Canon, then a mere curate, on the slenderest
income, and bear him successively five babies in defiance of common
prudence? But it had fallen to her lot to order the affairs of the
household, and she had learnt that the people who give you bread and
beef demand, after an interval, more or less money in exchange. It was
likely that, after her first rapture had subsided, she would make some
inquiry about Hyacinth's income and prospects. The Canon felt he ought
to be prepared.
'Of course, I have lost my position with Mr. Quinn. You know that. But I
have an offer of work which I hope will lead on to something better,
and will enable me in a short time to earn enough money to marry on.
You know--or perhaps you don't, for I am afraid I never told you '--he
remembered that he had carefully concealed his connection with the
_Croppy_ from his friends at Ballymoy, and paused--' I have done some
little writing. Oh, nothing very much--not a book, or anything like
that, only a few articles for the press. Well, a friend of mine has got
me the offer of a post in connection with a weekly paper. It is not a
very great thing in itself just now, but it may improve, and there is
always the prospect of picking up other work of the same kind.'
The Canon, who had never seen even an abstract of one of his own sermons
in print, had a proper reverence for the men who guide the world's
thought through the press.
'That is very good, Conneally--very satisfactory indeed. I always knew
you had brains. But why did you never tell me what you were doing? I
should have been deeply interested in anything you wrote.'
Hyacinth's conscience smote him.
'The truth is, that I was sure you wouldn't approve of the paper I
wrote for. It is the _Croppy_, the organ of the extreme left wing of the
Nationalist party. It is Miss Goold--Augusta Goold--who now offers me
work on that paper. She says---- But you had better read what she says
for yourself. Then you will know the worst of it.'
He took the letter from his pocket. The Canon lit a candle and read it
through slowly and attentively. When he had finished he laid it upon the
table and sat down. Hyacinth waited in extreme anxiety for what was to
come.
'I do not like the cause you mean to work for or the people you call
your friends. I would rather see my daughter's husband doing almost
anything else in the world. I would be happier if you proposed to break
stones upon the roadside. You know what my political opinions are.
I regard the _Croppy_ as a disloyal and seditious paper, bent upon
fostering a dangerous spirit.'
Hyacinth listened patiently. He had steeled himself against the hearing
of some such words, and was determined not to be moved to argument or
self-defence except as a last resort.
'I hope,' he said, 'that you will at least give me credit for honestly
acting in accordance with my convictions.'
'I am sure--quite sure--that you are honest, and believe that your cause
is the right one. I recognise, too, though this is a very difficult
thing to do, that you have every right to form and hold your own
political opinions. It seems to me that they are very wrong and very
mischievous, but it is quite possible that I am mistaken and prejudiced.
In any case, I am not called upon to refuse you my affection or to
separate you from my daughter because we differ about politics.'
Hyacinth breathed a great sigh of relief. He looked at the Canon in
wonder and admiration. It had been beyond hope that a man grown gray in
a narrow faith, a faith in which for centuries religion and politics had
been inextricably blended, could have risen in one clear flight above
the mire of prejudice. It seemed, even after he had spoken, impossible
that in Ireland, where political opponents believe each other to be
thieves and murderers, there could be found even one man, and he from
the least emancipated class of all, who could understand and practise
tolerance.
'I say,' went on the Canon, speaking very slowly, and with evident
difficulty, 'that I have no right to put you away from me because of
your political opinions. But there is something here '--he touched Miss
Goold's letter--' from which I must by all means try to save you.
Will you let me speak to you, not as Marion's father, not even as your
friend, but as Christ's ambassador set here to watch for your soul? But
I need not excuse myself for what I am about to say. You will at least
listen to me patiently.'
He took up Miss Goold's letter and searched through it for a short time;
then he read aloud:
'"He just asked one question about you: Does Mr. Conneally hate England
and the Empire and everything English, from the Parliament to the police
barrack? For it is this hatred which must animate our work. I said
I thought you did." Now consider what those words mean. You are to
dedicate your powers, the talents God has given you, to preaching
a gospel of hate. This is not a question of politics. I am ready
to believe that in the contest of which our unhappy country is the
battle-ground a man may be either on your side or mine, and yet be
a follower of Christ. It is impossible to think that anyone can
deliberately, with his eyes open, accept hatred for the inspiration of
his life and still be true to Him.'
Hyacinth was greatly moved by the solemnity with which the Canon spoke.
There was that in him which witnessed to the truth of what he heard. Yet
he refused to be convinced. When he spoke it was clear that he was not
addressing his companion, for his eyes were fixed upon the picture of
the Good Shepherd, faintly illuminated by the candle light. He desired
to order his own thought on the dilemma, to justify, if he could, his
own position to himself. 'It is true that the Gospel of Christ is a
Gospel of love. Yet there are circumstances in which it is wrong to
follow it. Is it possible to rouse our people out of their sordid
apathy, to save Ireland for a place among the nations, except by
preaching a mighty indignation against the tyranny which has crushed us
to the dust?'
He felt that Canon Beecher's eyes never left him for a moment while he
spoke. He looked up, and saw in them an intense pleading. There
stole over him a desire to yield, to submit himself to this appealing
tenderness. He defended himself desperately against his weakness.
'I am not choosing the pleasanter way. It would be easier for me to give
up the fight for Ireland, to desert the beaten side, to forget the lost
cause.' He turned to Canon Beecher, speaking almost fiercely: 'Do you
think it is a small thing for me to surrender your friendship, and
perhaps--perhaps to lose Marion? Is there not _some_ of the nobility of
sacrifice in refusing to listen to you?'
'I cannot argue with you. No doubt you are cleverer than I am. But I
_know_ this--God is love, and only he who dwelleth in love dwelleth in
God.'
'But I do love: I love Ireland.'
'Ah yes; but He says, "Love your enemies."'
'Then,' said Hyacinth, 'I will not have Him for my God.'
Hardly had he spoken than he started and grew suddenly cold. It was no
doubt some trick of memory, but he believed that he heard very faintly
from far off a remembered voice:
'Will you be sure to know the good side from the bad, the Captain from
the enemy.'
They were the last words his father had said to him. They had passed
unregarded when they were spoken, but lingered unthought of in some
recess of his memory. Now they came on him full of meaning, insistent
for an answer.
'You have chosen,' said the Canon.
He had chosen. Could he be sure that he had chosen right, that he knew
the good side from the bad?
'You have chosen, and I have no more to say. Only, before it becomes
impossible for you and me to kneel together, I ask you to let me pray
with you once more. You can do this because you still believe He hears
us, although you have decided to walk no more with Him.'
They knelt together, and Hyacinth, numbly indifferent, felt his hand
grasped and held.
'O Christ,' said Canon Beecher, 'this child of Thine has chosen to live
by hatred rather than by love. Do Thou therefore remove love from him,
lest it prove a hindrance to him on the way on which he goes. Let the
memory of the cross be blotted out from his mind, so that he may do
successfully that which he desires.'
Hyacinth wrenched his hand free from the grasp which held it, and flung
himself forward across the table at which they knelt. Except for his
sobs and his choking efforts to subdue them, there was silence in the
room. Canon Beecher rose from his knees and stood watching him, his lips
moving with unspoken supplication. At last Hyacinth also rose and stood,
calm suddenly.
'You have conquered me,' he said.
'My son, my son, this is joy indeed! All along I knew He could not fail
you. But I have not conquered you. The Lord Jesus has saved you.'
'I do not know,' said Hyacinth slowly, 'whether I have been saved or
lost. I am not sure even now that I know the good side from the bad.
But I do know that I cannot live without the hope of being loved by Him.
Whether it is the better part to which I resign myself I cannot tell.
No doubt He knows. As for me, if I have been forced to make a great
betrayal, if I am to live hereafter very basely--and I think I am--at
least I have not cut myself off from the opportunity of loving Him.'
CHAPTER XXI
Canon Beecher took no notice of Hyacinth's last speech. He had returned
with amazing swiftness and ease from the region of high emotion to the
commonplace. Excursions to the shining peaks of mystical experience are
for most men so rare that the glory leaves them with dazzled eyes, and
they walk stumblingly for a while along the dull roads of the world.
But Canon Beecher, in the course of his pleading with Hyacinth, had been
only in places very well known to him. The presence chamber of the King
was to him also the room of a familiar friend. It was no breathless
descent from the green hill of the cross to the thoroughfare of common
life.
'Now, my dear boy,' he said, 'we really must go and talk to my wife and
Marion. Besides, I must tell you the plan I have made for you--the plan
I was just going to speak about when you put it out of my head with the
news of your love-making.'
For Hyacinth a great effort was necessary before he could get back to
his normal state. His hands were trembling violently. His forehead and
hair were damp with sweat. His whole body was intensely cold. His mind
was confused, and he listened to what was said to him with only the
vaguest apprehension of its meaning. The Canon laid a firm hand upon
his arm, and led him away from the study. In the passage he stopped, and
asked Hyacinth to go back and blow out the candle which still burned on
the study table.
'And just put some turf on the fire,' he added; 'I don't want it to go
out.'
The pause enabled Hyacinth to regain his self-command, and the
performance of the perfectly ordinary acts required of him helped to
bring him back again to common life.
When they entered the drawing-room it was evident that Mrs. Beecher had
already heard the news, and was, in fact, discussing the matter eagerly
with Marion. She sprang up, and hastened across the room to meet them.
'I am so glad,' she said--'so delighted! I am sure you and Marion will
be happy together.'
She took Hyacinth's hands in hers, and held them while she spoke, then
drew nearer to him and looked up in his face expectantly. A fearful
suspicion seized him that on an occasion of the kind she might consider
it right to kiss him. It was with the greatest difficulty that he
suppressed a wholly unreasonable impulse to laugh aloud. Apparently the
need of such affectionate stimulant was strong in Mrs. Beecher. When
Hyacinth hung back, she left him for her husband, put her arms round his
neck, and kissed him heartily on both cheeks.
'Isn't it fortunate,' she said, 'that you saw Dr. Henry last week while
you were in Dublin? You little thought how important that talk with him
was going to turn out--I mean, of course, important for us. It always
was important for Mr.--I mean for Hyacinth.'
The Canon seemed a little embarrassed. He cleared his throat somewhat
unnecessarily, and then said:
'I haven't mentioned that matter yet.'
'Not mentioned Dr. Henry's offer! Then, what have you been talking about
all this time?'
It did not seem necessary to tell Mrs. Beecher all that had been said,
or to repeat the scene in the study for her benefit. The Canon cleared
his throat again.
'I was in Dublin last week attending a meeting of the Scriptural Schools
Society, and I met Dr. Henry. We were talking about the Quinns. I told
you that Mr. Quinn is to be the new secretary of the society, didn't I?
Dr. Henry knows Mr. Quinn slightly, and was greatly interested in him.
Your name naturally was mentioned. Dr. Henry seems to have taken a
warm interest in you when you were in college, and to have a very high
opinion of your abilities. He did not know what had become of you, and
was very pleased to hear that you were a friend of ours.'
Hyacinth knew at once what was coming--knew what Canon Beecher's plan
for his future was, and why he was pleased with it; understood how Mrs.
Beecher came to describe this conversation with Dr. Henry as fortunate.
He waited for the rest of the recital, vaguely surprised at his own want
of feeling.
'I told him,' the Canon went on, eying Hyacinth doubtfully, 'that you
had lost your employment here. I hope you don't object to my
having mentioned that. I am sure you wouldn't if you had heard how
sympathetically he spoke of you. He assured me that he was most anxious
to help you in any way in his power. He just asked one question about
you.' Hyacinth started. Where had he heard those identical words before?
Oh yes, they were in Miss Goold's letter. Patrick O'Dwyer also had just
asked one question about him. He smiled faintly as the Canon went on:
'"Is he fit, spiritually fit, to be ordained? For it is the desire to
serve God which must animate our work." I said I thought you were. I
told him how you sang in our choir here, and how fond you seemed of our
quiet life, and what a good fellow you are. You see, I did not know then
that I was praising the man who is to be my son-in-law. He asked me to
remind you of a promise he had once made, and to say that he was ready
to fufil it. I understood him to mean that he would recommend you to any
Bishop you like for ordination.'
Hyacinth remained silent. He felt that in surrendering his work for the
_Croppy_ he surrendered also his right to make any choice. He was ready
to be shepherded into any position, like a sheep into a pen. And he
had no particular wish to resist. He saw a simple satisfaction in Mrs.
Beecher's face and a beautiful joy in Marion's eyes. It was impossible
for him to disappoint them. He smiled a response to Mrs. Beecher's
kindly triumph.
'Isn't that splendid! Now you and Marion will be able to be married
quite soon, and I do dislike long engagements. Of course, you will be
very poor at first, but no poorer than we were. And Marion is not afraid
of being poor--are you, dear?'
'That is just what I have been saying to him,' said Marion; 'isn't it,
Hyacinth? Of course I am not afraid. I have always said that if I ever
married I should like to marry a clergyman, and if one does that one is
sure to be poor.'
Evidently there was no doubt in either of their minds that Hyacinth
would accept Dr. Henry's offer. Nor had he any doubt himself. The thing
seemed too inevitable to be anything but right. Only on Canon Beecher's
face there lingered a shadow of uncertainty. Hyacinth saw it, and
relieved his mind at once.
'I shall write to Dr. Henry to-night and thank him. I shall ask him to
try and get me a curacy as soon as possible.'
'Thank you,' said the Canon.
'I think,' added Hyacinth, 'that I should prefer getting work in
England.'
'Oh, why,' said Mrs. Beecher. 'Wouldn't it be better to stay in Ireland!
and then we might have Marion somewhere within reach.'
'My dear,' said the Canon, 'we must let Hyacinth decide for himself. I
am sure he knows what is wisest for him to do.'
Hyacinth was not at all sure that he knew what was wisest, and he was
quite certain that he had not decided for himself in any matter of the
slightest importance. He had suggested an English curacy in the vague
hope that it might be easier there to forget his hopes and dreams for
Ireland. It seemed to him, too, that a voluntary exile, of which he
could not think without pain, might be a kind of atonement for the
betrayal of his old enthusiasm.
The Canon followed him to the door when he left.
'My dear boy'--there was a break in his voice as he spoke--' my dear
boy, you have made me very happy. I am sure that you will not enter upon
the work of the ministry from any unworthy motive. The call will become
clearer to you by degrees. I mean the inward call. The outward call, the
leading of circumstance, has already made abundantly plain the way you
ought to walk in. The other will come--the voice which brings assurance
and peace when it speaks.'
Hyacinth looked at him wistfully. There seemed very little possibility
of anything like assurance for him, and only such peace as might be
gained by smothering the cries with which his heart assailed him. The
Canon held his hand and wrung it.
'I can understand why you want to go to England. Your political opinions
will interfere very little with your work there. Here, of course, it
would be different. Yes, your choice is certainly wise, for nothing
must be allowed to hinder your work. "Laying aside every weight," you
remember, "let us run the race." Yes, I understand.'
It was perfectly clear to Hyacinth that the Canon did not understand in
the least. It was not likely that anyone ever would understand.
Gradually his despondency gave way before the crowding in of thoughts of
satisfaction. He was to have Marion, to live with her, to love her, and
be loved by her as long as they both lived. He saw life stretching out
before him, a sunlit, pleasant journey in Marion's company. It did not
seem to him that any trouble could be really bad, any disappointment
intolerable, any toil oppressive with her love for an atmosphere round
him. He believed, too, that the work he was undertaking was a good work,
perhaps the highest and noblest kind of work there is to be done in the
world. From this conviction also came a glow of happiness. Yet there
kept recurring chill shudderings of self-reproach. Something within him
kept whispering that he had bartered his soul for happiness.
'I have chosen the easier and therefore the baser way,' he said. 'I have
shrunk from toil and pain. I have refused to make the sacrifice demanded
of me.'
He went back again to the story of his father's vision. For a moment
it seemed quite clear that he had deliberately refused the call to the
great fight, that he had judged himself unworthy, being cowardly and
selfish in his heart. Then he remembered that the Captain of whom his
father had told him was no one else but Christ, the same Christ of whom
Canon Beecher spoke, the Good Shepherd whose love he had discovered to
be the greatest need of all.
'I must have Him,' he said--'I must have Him--and Marion.'
Again with the renewed decision came a glow of happiness and a sense of
rest, until there rose, as if to smite him, the thought of Ireland--of
Ireland, poor, derided of strangers, deserted by her sons, roped in as
a prize-ring where selfish men struggle ignobly for sordid gains The
children of the land fled from it sick with despair. Its deserted houses
were full of all doleful things. Cormorants and the daughters of the owl
lodged in the lintels of them.
Sullen desolation was on the threshold, while satyrs cried to their
fellows across tracts of brown rush-grown land. Aliens came to hiss and
passed by wagging their hands. Over all was the monotony of the gray
sky, descending and still descending with clouds that came upon the
land, mistily folding it in close embraces of death. Voices sounded far
off and unreal through the gloom. The final convulsive struggles of the
nation's life grew feebler and fewer. Of all causes Ireland's seemed the
most hopelessly lost. Was he, too, going to forsake her? He felt that in
spite of all the good promised him there would always hang over his life
a gloom that oven Marion's love would not disperse, the heavy shadow of
Ireland's Calvary. For Marion there would be no such darkness, nor would
Marion understand it. But surely Christ understood. Words of His crowded
to the memory. 'When He beheld the city He wept over it, saying,
Oh, Jerusalem, Jerusalem!' Most certainly He understood this, as He
understood all human emotion. He, too, had yearned over a nation's fall,
had felt the heartbreak of the patriot.
'I have chosen Him,' he said at last. 'Once having caught a glimpse of
Him, I could not do without Him. He understands it all, and He has given
me Marion.'
CHAPTER XXII
It was a brilliant July day, and the convent at Robeen was decked for a
festival. The occasion was a very great one. Cloth of gold hung in the
chapel, the entrance-hall was splendid with flowers, and the whole
white front of the buildings had put on signs of holiday. Indeed,
this festival was unique, the very greatest day in the history of the
sisterhood. Easter, Christmas, and the saints' days recurred annually
in their proper order, and the emotions they brought with them were no
doubt familiar to holy ladies whose business it was to live in close
touch with the other world. But on this day the great of the earth,
beings much more unapproachable, as a rule, than the saints, were to
visit the convent. Honour was to be paid to ladies whose magnificence
was guaranteed by worldly titles; to the Proconsuls of the far-off
Imperial power, holders of the purse-strings of the richest nation
upon earth; to Judges accustomed to sit in splendid robes and awful
head-dresses, pronouncing the doom of malefactors; to a member of the
Cabinet, a very mighty man, though untitled; and quite possibly--a
glittering hope--to the Lord Lieutenant himself.
It was therefore no wonder that the nuns had decked their convent
with all possible splendour. On each side of the iron gateway was a
flag-post. From the top of one fluttered the green banner of Ireland,
with its gold harp and a great crown over it. From the other hung
the Union Jack, emblem of that marriage of nationalities for whose
consummation eight centuries have not sufficed. It was hoisted upside
down--not with intentional disrespect, but because Sister Gertrude, who
superintended this part of the decorations, had long ago renounced the
world, and did not remember that the tangled crosses had a top or a
bottom to them. Between the posts hung a festoon of signalling flags,
long pointed strips of bunting with red balls or blue on them. The
central streamer just tipped as it fluttered the top of the iron cross
which marked the religious nature of the gateway. The straight gravel
walk inside was covered with red baize, and on each side of it were
planted tapering poles, round which crimson and white muslin circled
in alternate stripes, giving them the appearance of huge old-fashioned
sugar-sticks. These added to the gaiety of the scene, though it cannot
be supposed that they were of any actual use. The most bewildered
visitor was hardly likely to stray off the red baize or miss his way to
the door in front of him. Within the great entrance-hall were palms and
flowering shrubs in pots or tubs. The mosaic flooring, imported from
Italy, and a source of pride to all the Sisters, shone with much washing
and polishing. The Madonna with the blue eyes and the golden crown,
before which even Bishops crossed themselves, was less in evidence than
usual, for the expected guests were mostly heretics. She stood retired
behind the flower-pots, and veiled her benignity with the leaves of
palms.
Right and left of the hall stretched corridors, whose shining parquet
invited the curious to explore the working-rooms and eating-rooms which
lay beyond. The door of the chapel stood open, and offered a vision
of simpering angels crowding the canvas of the altar-piece, a
justly-admired specimen of German religious art. Before it, dimly
seen, two nuns knelt, types of conventual piety, absorbed in spiritual
contemplation amid the tumult of the world's invasion of their
sanctuary. Another door led to the garden. Here a fountain played into a
great stone basin, and neat gravel walks intersected each other at sharp
angles among flower-beds. The grass which lay around the maze of paths
was sacred as a rule, even from the list slippers of the nuns, but
to-day booths stood on it like stalls at a charity bazaar, hung with
tweeds, blankets, and stockings. A tall Calvary lowered incongruously
over one. An inferior Madonna, deposed from her old station in the
entrance-hall, presided in a weather-beaten blue robe over another.
Beyond the garden, blocked off from it by a white wall, lay the factory
itself, the magnet which was drawing the great of the earth to the
nunnery. Here were the workers, all of them bright young women, smiling
pleasantly and well washed for the occasion. They were dressed in neat
violet petticoats and white blouses, with shawls thrown back from their
heads, a glorified presentment of the Mayo woman's working dress. Here
and there, a touch of realism creditable to the Reverend Mother's talent
for stage management, one sat in bare feet--not, of course, dust or mud
stained, as bare feet are apt to be in Connaught, but clean. The careful
observer of detail might have been led to suppose that the Sisters
improved upon the practice of the Holy Father himself, and daily washed
the feet of the poor.
Everywhere fresh-complexioned, gentle-faced nuns flitted silently about.
The brass crosses pendent over their breasts relieved with a single
glitter the sombre folds of their robes. Snowy coifs, which had cost the
industrial schoolgirls of a sister house hours of labour and many tears,
shone, glazed and unwrinkled, round their heads. Even the youngest of
them had acquired the difficult art of walking gracefully with her hands
folded in front of her.
At about two o'clock the visitors began to arrive, although the train
from Dublin which was to bring the very elect was not due for another
half-hour. Lady Geoghegan, grown pleasantly stout and cheerfully
benignant, came by a local train, and rejoiced the eyes of beholders
with a dress made of one of the convent tweeds. Sir Gerald followed
her, awkward and unwilling. He had been dragged with difficulty from his
books and the society of his children, and was doubtful whether a cigar
in a nunnery garden might not be counted sacrilege. With them was
a wonderful person--an English priest: it was thus he described
himself--whom Lady Geoghegan had met in Yorkshire. His charming manners
and good Church principles had won her favour and earned him the holiday
he was enjoying at Clogher House. He was arrayed in a pair of gray
trousers, a white shirt, and a blazer with the arms of Brazenose College
embroidered on the pocket, his sacerdotal character being marked only
by his collar. He leaped gaily from the car which brought them from the
station, and, as he assisted his hostess to alight, amazed the little
crowd around the gate by chaffing the driver in an entirely unknown
tongue. The good man had an ear for music, and plumed himself on his
ability to pick up any dialect he heard--Scotch, Yorkshire, or Irish
brogue. The driver was bewildered, but smiled pleasantly. He realized
that the gentleman was a foreigner, and since the meaning of his speech
was not clear, it was quite likely that he might be hazy about the value
of money and the rates of car hire.
The Duchess of Drummin came in her landau. Like Lady Geoghegan, she
marked the national and industrial nature of the occasion in her attire.
At much personal inconvenience, for the day was warm, she wore a long
cloak of rich brown tweed, adorned with rows of large leather-covered
buttons. Lady Josephine Maguire fluttered after her. She had bidden
her maid disguise a dress, neither Irish nor homespun, with as much
Carrickmacross lace as could be attached to it. Lord Eustace, who
represented his father, appeared in all the glory of a silk hat and a
frock-coat. He eyed Sir Gerald's baggy trousers and shabby wideawake
with contempt, and turned away his eyes from beholding the vanity of
obviously bad form when he came face to face with the English priest in
his blazer.
A smiling nun took charge of each party as it arrived. Lady Geoghegan
plied hers with questions, and received a series of quite uninforming
answers. Her husband followed her, bent principally upon escaping
from the precincts if he could. Already he was bored, and he knew that
speeches from great men were in store for him if he were forced to
linger. The Duchess of Drummin eyed each object presented to her notice
gravely through long-handled glasses, but gave her attendant nun very
little conversational help. Lady Josephine made every effort to be
intelligent, and inquired in a dormitory where the looking-glasses
were. She was amazed to hear that the nuns did, or failed to do, their
hair--the head-dresses concealed the result of their efforts--without
mirrors. Lord Eustace was preoccupied. Amid his unaccustomed
surroundings he walked uncertain whether to keep his hat on his head
or hold it in his hands. The English priest, whose name was Austin, got
detached from Lady Geoghegan, and picked up a stray nun for himself. She
took him, by his own request, straight to the chapel. He crossed himself
with elaborate care on entering, and knelt for a moment before the
altar. The nun was delighted.
'So you, too, are a Catholic?'
'Certainly,' he replied briskly--'an English Catholic.'
'Ah! many of our priests go to England. Perhaps you have met Father
O'Connell. He is on a London mission.'
'No,' said Mr. Austin, 'I do not happen to have met him. My church is in
Yorkshire.'
The nun gazed at him in amazement.
'Your church! Then you are----
'Yes,' he said, 'I am a priest.'
Her eyes slowly travelled over him. They began at the gray trousers,
passed to the blazer, resting a moment on the college arms, which
certainly suggested the ecclesiastical, and remained fixed on his
collar. After all, why should she, a humble nun, doubt his word when he
said he was a priest? Perhaps he might belong to some order of which
she had never heard. Eccentricities of costume might be forced on the
English clergy by Protestant intolerance. She smothered her uncertainty,
and took him at his word. They went together into the garden. Mr. Austin
took off his hat before the tarnished Madonna, and crossed himself
again. The nun's doubts vanished.
'I think,' he said, 'that I should like to buy some of this tweed. Is it
for sale?'
'Oh, certainly. Sister Aloysia will sell it to you. We are so glad, so
very glad, when anyone will buy what our poor workers make. It is all a
help to the good cause.'
'Now this,' said Mr. Austin, fingering a bright-green cloth, 'would make
a nice lady's dress. Don't you think so?'
The nun cast down her eyes.
'I do not know, Father, about dresses. Sister Aloysia, the Reverend
Father wants to buy tweed to make a dress for '--she hesitated; perhaps
it was his niece, but he looked young to have a full-grown niece--'for
his sister.'
Sister Aloysia looked round her, puzzled. She saw no Reverend Father.
'This,' said the other, 'is Father--Father----'
'Austin,' he helped her out.
'Father Austin,' added the nun.
'And you wish,' said Sister Aloysia, 'to buy a dress for your sister?'
'Not for my sister,' said Mr. Austin--'for my wife.'
Both nuns started back as if he had tried to strike them.
'Your wife! Your wife! Then you are a Protestant.'
'Certainly not,' he said. 'I detest all Protestants. I am a Catholic--an
Anglo-Catholic.'
Neither of the nuns had ever heard of an Anglo-Catholic before.
What manner of religion such people might profess was doubtful and
unimportant. One thing was clear--this was not a priest in any sense of
the word which they could recognise. They distrusted him, as a wolf,
not certainly in the clothing, but using the language, of a sheep. The
situation became embarrassing. Mr. Austin prepared to bow himself away.
'I think,' he said, 'I shall ask Lady Geoghegan'--he rolled the title
out emphatically; it formed a salve to his wounded dignity--'I shall ask
Lady Geoghegan to purchase the tweed for me. I must be on the look-out
for a friend who promised to meet me here this afternoon--a young man
whom I contemplate engaging as my curate. I am most particular in the
choice of a curate, and should, of course, prefer a public school
and 'Varsity man. I need scarcely say that I refer only to Oxford and
Cambridge as the Universities. As a rule, I do not care for Irishmen,
but on the recommendation of my friend Dr. Henry, I am willing to
consider this Mr. Conneally.'
It seemed to Mr. Austin that a preference for the English Universities,
the friendship of a distinguished professor, a contempt for the mere
Irishman, and a titled hostess ought to restore the respect he had
forfeited by the mention of his wife. Curiously enough, and this shows
the disadvantage of a monastic seclusion from the world, the nuns
remained unimpressed. The conception of a married priest was too much
for them. As he walked away Mr. Austin heard Sister Aloysia murmur:
'How very indecent!'
Meanwhile, the train from Dublin had arrived, and Mr. Austin, when he
returned after his interview with Hyacinth, found that even the two nuns
he had victimized had forgotten him in the excitement of gazing at
more important visitors. Mr. Justice Saunders, a tall, stout man with a
florid face, made a tour of the factory under the charge of one of the
senior Sisters. He took little notice of what he was shown, being
mainly bent on explaining to his escort how he came to be known in legal
circles as 'Satan Saunders.' Afterwards he added a tale of how he had
once bluffed a crowd in an out-of-the-way country town into giving three
cheers for the Queen.
'You're all loyal here,' he said. 'I saw the Union Jack flying over the
gate as I came in.'
The nun smiled, a slow, enigmatic smile, and the Judge, watching her,
was struck by her innocence and simplicity.'
'Surely,' she said, 'the Church must always be loyal.'
'Well, I'm not so sure of that. I've met a few firebrands of priests in
my time.'
'Oh, those!' she said with a shrug of her shoulders. 'You must not think
of them. It will always be easy to keep them in order when the time
comes. They spring from the cabins. What can you expect of them? But the
Church---- Can the Church fail of respect for the Sovereign?'
Mr. Clifford and Mr. Davis followed Judge Saunders. They were members of
the Congested Districts Board, and it was clear from the manner of
the nun who escorted them that they were guests of very considerable
importance in her estimation. Mr. Clifford was an Englishman who had
been imported to assist in governing Ireland because he was married to
the sister of the Chief Secretary's wife. He was otherwise qualified
for the task by possessing a fair knowledge of the points of a horse. He
believed that he knew Ireland and the Irish people thoroughly.
His colleague, Mr. Davis, was a man of quite a different stamp. The
son of a Presbyterian farmer in County Tyrone, he had joined the Irish
Parliamentary party, and made himself particularly objectionable in
Westminster. He had devoted his talents to discovering and publishing
the principles upon which appointments to lucrative posts are made
by the officials in Dublin Castle. It was found convenient at last to
provide him with a salary and a seat on the Congested Districts Board.
Thus he found himself engaged in ameliorating the lot of the Connaught
peasants. Mr. Clifford used to describe him as 'a bit of a bounder--in
fact, a complete outsider--but no fool.' His estimate of Mr. Clifford
was perhaps less complimentary.
'Every business,' he used to say, 'must have at least one gentleman in
it to do the entertaining and the dining out. We have Mr. Clifford. He's
a first-rate man at one of the Lord Lieutenant's balls.'
A professor from Trinity College was one of the two guests conducted by
the Reverend Mother herself. Nominally this learned gentleman existed
for the purpose of impressing upon the world the beauties of Latin
poetry, but he was best known to fame as an orator on the platforms
of the Primrose League, and a writer of magazine articles on Irish
questions. He was a man who owed his success in life largely to his
faculty for always keeping beside the most important person present. The
Lord Lieutenant, being slightly indisposed, had been unable to make an
early start, so the most honourable stranger was Mr. Chesney, the Chief
Secretary. To him Professor Cairns attached himself, and received a
share of the Reverend Mother's blandishments.
Mr. Chesney himself was dapper and smiling as usual. Even the early
hour at which he had been obliged to leave home had neither ruffled his
temper nor withered the flower in his buttonhole. He spent his money
generously at the various stalls in the garden, addressed friendly
remarks to the women in the factory, and asked the questions with which
Mr. Davis had primed him in the train.
Quite a crowd of minor people followed the great statesman. There were
barristers who hoped to become County Court Judges, and ladies who
enjoyed a novel kind of occasion for displaying their clothes, hoping to
see their names afterwards in the newspaper accounts of the proceedings.
There were a few foremen from leading Dublin shops, who foresaw the
possibility of a fashionable boom in Robeen tweeds and flannels. There
were also reporters from the Dublin papers, and a representative--Miss
O'Dwyer--of a syndicate which supplied ladies' journals with accounts of
the clothes worn at fashionable functions.
The supreme moment of the day arrived when the company assembled to
listen to words of wisdom from the orators selected to address them.
Seats had been provided by carting in forms from the neighbouring
national schools. A handsomely-carved chair of ecclesiastical design
awaited Mr. Chesney.
He opened his speech by assuring his audience that there was no occasion
for him to address them at all, a truth which struck home to the heart
of Sir Gerald, who was trying to arrange himself comfortably at a desk
designed for a class of infants.
'Facts,' Mr. Chesney explained himself, 'are more eloquent than words.
You have seen what I could never have described to you--the contented
workers in this factory and the artistic designs of the fabrics they
weave. Many of you remember what Robeen was a few years ago--a howling
wilderness. We are told on high authority that even the wilderness shall
blossom as a rose.'
He bowed in the direction of the Reverend Mother, possibly with a
feeling that it was suitable to acknowledge her presence when quoting
Holy Writ, possibly with a vague idea that she might consider herself
a spiritual descendant of the Prophet Isaiah. 'You see it now a hive of
happy industry.'
He observed with pleasure that the reporters were busy with their
note-books, and he knew that these editors of public utterance might be
relied on to unravel a tangled metaphor before publishing a speech. He
went on light-heartedly, confident that in the next day's papers his
wilderness would blossom into something else, and that the hive, if
it appeared at all, would be arrived at by some other process than
blossoming. The habit of rolling out agreeable platitudes to audiences
forced to listen is one which grows on public men as dram-drinking does
on the common herd. Mr. Chesney was evidently enjoying himself, and
there seemed no reason why he should ever stop. He could, and perhaps
would, have gone on for hours but for the offensive way in which Judge
Saunders snapped the case of his watch at the end of every period. There
was really no hurry, for the special train which was to bring them back
to Dublin would certainly wait until they were ready for it. Mr. Chesney
felt aggrieved at the repeated interruption, and closed his speech
without giving the audience the benefit of his peroration.
The Judge came next, and began with reminding his hearers that he
was known as 'Satan Saunders.' An account of the origin of the name
followed, and was enjoyed even by those who had listened to the Judge's
oratory before, and therefore knew the story. There was something
piquant, almost _risque_, in the constant repetition of a really wicked
word like 'Satan' in the halls of a nunnery. The audience laughed
reassuringly, and the Judge went on to supply fresh pabulum for mirth by
suggesting that the Reverend Mother should clothe her nuns in their own
tweeds. He was probably right in supposing that the new costumes would
add a gaiety to the religious life. Other jests followed, and he sat
down amid a flutter of applause after promising that when he next
presided over the Winter Assizes in a draughty court-house he would send
for a Robeen blanket and wrap his legs in it.
Mr. Clifford, who followed the Judge, began by wondering whether anyone
present had ever been in Lancashire. After a pause, during which no one
owned to having crossed the Channel, he said that Lancashire was the
home of the modern factory. There every man and woman earned good wages,
wore excellent clothes, and lived in a house fitted with hot and cold
water taps and a gas-meter. It was his hope to see Mayo turned into
another Lancashire. When ladies of undoubted commercial ability, like
the Lady Abbess who presided over the Robeen convent--Lady Abbess
sounded well, and Mr. Clifford was not strong on ecclesiastical
titles--took the matter up, success was assured. All that was required
for the development of the factory system in Mayo was capital, and that
'we, the Congested Districts Board, are in a position to supply.' With
the help of some prompting from Mr. Davis, he proceeded to lay
before the audience a few figures purporting to explain the Board's
expenditure.
Professor Cairns was evidently anxious to follow Mr. Clifford, if only
in the humble capacity of the proposer of a vote of thanks. But Ids
name was not on the programme, and Mr. Chesney was already engaged in a
whispered conversation with the Reverend Mother. Ignoring the professor,
almost rudely, he announced that the company in general was invited to
tea in the dining-room.
The refreshments provided, if not substantial, were admirable in
quality. There happened just then to be a young lady engaged, at the
expense of the County Council, in teaching cookery in a neighbouring
convent. She was sent over to Robeen for the occasion, and made a number
of delightful cakes at extremely small expense. The workers in the
factory had given the butter she required as a thank-offering, and the
necessary eggs came from another convent where the nuns, with financial
assistance from the Congested Districts Board, kept a poultry-farm.
The Reverend Mother dispensed her hospitality with the same air of
generosity with which Mr. Clifford had spoken of providing capital for
the future ecclesiastical factories.
CHAPTER XXIII
The Reverend Mother bowed out the last of her guests, and retired to
her own room well satisfied. She was assured of further support from
the Congested Districts Board, and certain debts which had grown
uncomfortably during her struggle with Mr. Quinn need trouble her no
longer. Her goods would be extensively advertised next morning in the
daily press. Her house would obtain a celebrity likely to attract
the most eligible novices--those, that is to say, who would bring the
largest sums of money as their dowries. There arose before her mind a
vision of almost unbounded wealth and all that might be done with it.
What statues of saints might not Italy supply! French painters and
German organ-builders would compete for the privilege of furnishing the
chapel of her house. Already she foresaw pavements of gorgeous mosaic,
windows radiant with Munich glass, and store of vestments to make
her sacristy famous. Grandiose plans suggested themselves of founding
daughter houses in Melbourne, in Auckland, in Capetown, in Natal. All
things were possible to a well-filled purse. She saw how her Order
might open schools in English towns, where girls could be taught French,
Italian, Latin, music, all the accomplishments dear to middle-class
parents, at ridiculously low fees, or without fees at all. She stirred
involuntarily at the splendour of her visions. The day's weariness
dropped off from her. She rose from her chair and went into the chapel.
She prostrated herself before the altar, and lay passive in a glow of
warm emotion. For God, for the Mother of God, for the Catholic Church,
she had laboured and suffered and dared. Now she was well within sight
of the end, the golden reward, the fulfilment of hopes that had never
been altogether selfish.
Her thoughts, sanctified now by the Presence on the altar, drifted out
again on to the shining sea of the future. What she, a humble nun,
had done others would do. A countless army of missionary men and women
marching from the Irish shore would conquer the world's conquerors,
regain for the Church the Anglo-Saxon race. Once in the far past Irish
men and women had Christianized Europe, and Ireland had won her glorious
title, 'Island of Saints.' Now the great day was to dawn again, the
great race to be reborn. For this end had Ireland been kept faithful and
pure for centuries, just that she might be at last the witness to
the spiritual in a materialized world. For this end had the Church in
Ireland gone through the storm of persecution, suffered the blight of
the world's contempt, that she might emerge in the end entirely fitted
for the bloodless warfare.
'And I am one of the race, a daughter of Ireland. And I am a
worker--nay, one who has accomplished something--in the vineyard of the
Church. Ah, God!'
She was swept forward on a wave of emotion. Thought ceased, expiring
in the ecstasy of a communion which transcended thought. Then suddenly,
sharp as an unexpected pain, an accusation shot across her soul,
shattering the glory of the trance in an instant.
'Who am I that I should boast?'
The long years of introspection, the discipline of hundreds of
heart-searching confessions, the hardly-learned lesson of self-distrust,
made it possible for her to recognise the vain-glory even with the halo
of devotion shining round it. She abased herself in penitence.
'Give me the work, my Lord; give others the glory and the fruit of it.
Let me toil, but withhold the reward from me. May my eyes not see it,
lest I be lifted up! Nay, give me not even work to do, lest I should be
praised or learn to praise myself. "Nunc dimittis servam tuam, Domine,
secundum verbum tuum in pace."'
There stole over her a sense of peace--numb, silent peace--wholly unlike
the satisfaction which had flooded her in her own room or during the
earlier ecstasy before the altar. She raised her eyes slowly till they
rested on the shrine where the body of the sacrifice reposed.
'Quia viderunt oculi mei salutare tuum.'
At last she rose. The lines of care and age gathered again upon her
face. Her eyes gleamed with keen intelligence. She braced herself with
the thought of all that might still lie before her. The advice of Iago,
strangely sanctified, clamoured in her heart--' Put money in thy purse.'
CHAPTER XXIV
The Reverend Mother was not the only person well satisfied with the
day. The Right Hon. T. J. Chesney leant back in his saloon-carriage,
and puffed contentedly at his cigar. It might be his part
occasionally--indeed, frequently--to talk like a fool, but the man was
shrewd enough. It really seemed that he had hit on the true method of
governing Ireland. Nationalist members of Parliament could be muzzled,
not by the foolish old methods of coercion, but by winning the goodwill
of the Bishops. No Irish member, dared open his mouth when a priest
bid him keep it shut, or give a vote contrary to the wishes of the
hierarchy. And the Bishops were reasonable men. They looked at things
from a point of view intelligible to Englishmen. There was no ridiculous
sentimentality about their demands. For so much money they would silence
the clamour of the Parliamentary party; for so much more they would
preach a modified loyalty, would assert before the world that the Irish
people were faithful servants of the Sovereign; for a good lump sum down
they would undertake to play 'God Save the King' or 'Rule, Britannia'
on the organ at Maynooth. Of course, the money must be paid: Mr. Chesney
was beginning to understand that, and felt the drawback. It would have
been much pleasanter and simpler if the Bishops would have been content
with promises. There was a certain difficulty in obtaining the necessary
funds without announcing precisely what they-were for. But, after all,
a man cannot be called a great statesman without doing something to
deserve the title, and British statesmanship is the art of hoodwinking
the taxpayer. That is all--not too difficult a task for a clever man.
Mr. Chesney reckoned on no power in Ireland likely to be seriously
troublesome. The upper classes were either helpless and sulking, or
helpless and smiling artificially. They might grumble in private or
try to make themselves popular by joining the chorus of the Church's
flatterers. Either way their influence was inconsiderable. Was there
anyone else worth considering? The Orangemen were still a noisy faction,
but their organization appeared to be breaking up. They were more bent
on devouring their own leaders than interfering with him. There were a
number of people anxious to revive the Irish language, who at one time
had caused him some little uneasiness. He had found it quite impossible
to understand the Gaelic League, and, being an Englishman, arrived
gradually at the comfortable conclusion that what he could not
understand must be foolish. Now, he had great hopes that the Bishops
might capture the movement.
If once it was safely under the patronage of the Church, he had
nothing more to fear from it No doubt, resolutions would be passed,
but resolutions------ Mr. Chesney smiled. There were, of course, the
impossible people connected with the _Croppy_. Mr. Chesney did not like
them, and in the bottom of his heart was a little nervous about them.
they seemed to be very little afraid of the authority of the Church,
and he doubted if the authority of the state would frighten them at
all. Still, there were very few of them, and their abominable spirit of
independence was spreading slowly, if at all.
'They won't,' he said to himself, 'be of any importance for some years
to come, at all events, and five years hence----'
In five years Mr. Chesney hoped to be Prime Minister, or perhaps to
have migrated to the House of Lords, At least, he expected to be out
of Ireland, Meanwhile, he lighted a fresh cigar. The condition of the
country was extremely satisfactory, and his policy was working out
better than he had hoped.
The other travellers by the special train were equally well pleased,
Ireland, so they understood Mr. Chesney, was to be made happy and
contented, peaceful and prosperous. It followed that there must be
Boards under the control of Dublin Castle--more and more Boards, an
endless procession of them. There is no way devised by the wit of man
for securing prosperity and contentment except the creation of Boards,
If Boards, then necessarily officials--officials with salaries and
travelling allowances. Nice gentlemanly men, with villas at Dalkey and
Killiney, would perform duties not too arduous in connection with the
Boards, and carry out the benevolent policy of the Government. There
was not a man in the train, except the newspaper reporters, who did not
believe in the regeneration of Ireland by Boards, and everyone hoped to
take a share in the good work, with the prospect of a retiring pension
afterwards.
The local magnates--with the exception of Sir Gerald Geoghegan, whose
temper had been bad from the first--also went home content. The minds of
great ladies work somewhat confusedly, for Providence, no doubt wisely,
has denied to most of them the faculty of reason. It was enough for them
to feel that the nuns were 'sweet women,' and that in some way not very
clear Mr. Chesney was getting the better of 'those wretched agitators.'
Only one of all whom the special train had brought down failed to return
in it. Mary O'Dwyer slipped out of the convent before the speeches
began, and wandered away towards the desolate stony hill where the
stream which turns the factory mill took its rise. It grieved her to
miss the cup of tea which a friendly nun had led her to expect; but even
tea might be too dearly purchased, and Miss O'Dwyer had a strong dislike
to listening to what Augusta Goold described as the 'sugared hypocrisies
of professional liars.' Besides, she had her cigarette-case in her
pocket, and a smoke, unattainable for her in the convent or the train,
was much to be desired. She left the road at the foot of the hill, and
picked her way along the rough bohireen which led upwards along the
course of the stream. After awhile even this track disappeared. The
stream tumbled noisily over rocks and stones, the bog-stained water
glowing auburn- in the sunlight. The ling and heather were
springy under her feet, and the air was sweet with the scent of the
bog-myrtle. She spied round her for a rock which cast a shade upon the
kind of heathery bed she had set her heart to find. Her eyes lit upon
a little party--a young man and two girls--encamped with a kettle, a
spirit-stove, and a store of bread-and-butter. Her renunciation of the
convent tea had not been made without a pang. She looked longingly at
the steam which already spouted from the kettle. The young man said
a few words to the girls, then stood up, raised his hat to her, and
beckoned. She approached him, wondering.
'Surely it can't be--I really believe it is----'
'Yes, Miss O'Dwyer, it really is myself, Hyacinth Conneally.'
'My dear boy, you are the last person I expected to meet, though of
course I knew you were somewhere down in these parts.'
'Come and have some tea,' said Hyacinth. 'And let me introduce you to
Miss Beecher and Miss Elsie Beecher.'
Miss O'Dwyer took stock of the two girls. 'They make their own clothes,'
she thought, 'and apparently only see last year's fashion-plates. The
eldest isn't bad-looking. How is it all West of Ireland girls have such
glorious complexions? Her figure wouldn't be bad if her mother bought
her a decent pair of stays. I wonder who they are, and what they are
doing here with Hyacinth. They can't be his sisters.'
While they drank their tea certain glances and smiles gave her an
inkling of the truth. 'I suppose Hyacinth is engaged to the elder one,'
she concluded. 'That kind of girl wouldn't dare to make eyes at a man
unless she had some kind of right to him.'
After tea she produced her cigarette-case.
'I hope you don't mind,' she said to Marion. 'I know it's very shocking,
but I've had a tiring day and an excellent tea, and oh, this heather is
delicious to lie on!' She stretched herself at full length as she spoke.
'I really must smoke, just to arrive at perfect felicity for once in my
life. How happy you people ought to be who always have in a place like
this!'
'Oh,' said Marion, 'it sometimes rains, you know.'
'Ah! and then these sweet spots get boggy, I suppose, and you have to
wear thick, clumping boots.'
Her own were very neat and small, and she knew that they must obtrude
themselves on the eye while she lay prone. Elsie, whose shoes were
patched as well as thick-soled, made an ineffectual attempt to cover
them with her skirt.
'Now,' said Hyacinth, 'tell us what you are doing down here. They
haven't made you an inspectress of boarded-out workhouse children, have
they? or sent you down to improve the breed of hens?'
'No,' said Miss O'Dwyer; 'I have spent the afternoon helping to govern
Ireland.'
Marion and Elsie gazed at her in wonder. A lady who smoked cigarettes
and bore the cares of State upon her shoulders was a novelty to them.
'I have sat in the seats of the mighty,' she said; 'I have breathed the
same air as Mr. Chesney and two members of the C.D.B. Think of that!
Moreover, I might, if I liked, have drunk tea with a Duchess.'
'Oh,' said Hyacinth, 'you were at the convent function, I suppose. I
wonder I didn't see you.'
'What on earth were _you_ doing there? I thought you hated the nuns and
all their ways.'
'Go on about yourself,' said Hyacinth. 'You are not employed by the
Government to inspect infant industries, are you?'
'Oh no; I was one of the representatives of the press. I have notes here
of all the beautiful clothes worn by the wives and daughters of the West
British aristocracy. Listen to this: "Lady Geoghegan was gowned in an
important creation of saffron tweed, the product of the convent looms.
We are much mistaken if this fabric in just this shade is not destined
to play a part in robing the _elegantes_ who will shed a lustre on our
house-parties during the autumn." And this--you must just listen to
this.'
'I won't,' said Hyacinth; 'you can if you like, Marion. I'll shut my
ears.'
'Very well,' said Miss O'Dwyer; 'I'll talk seriously. When are you
coming up to Dublin? You know my brother has taken over the editorship
of the _Croppy_. We are going to make it a great power in the country.
We are coming out with a policy which will sweep the old set of
political talkers out of existence, and dear the country of Mr. Chesney
and the likes of him.' She waved her hand towards the convent. 'Oh, it
is going to be great. It is great already. Why don't you come and help
us?'
Hyacinth looked at her. She had half risen and leaned upon her elbow.
Her face was flushed and her eyes sparkled. There was no doubt about
the genuineness of her enthusiasm. The words of her poem, long since, he
supposed, blotted from his memory, suddenly returned to him:
'O, desolate mother, O, Erin,
When shall the pulse of thy life which but flutters in Connacht
Throb through thy meadows and boglands and mountains and cities?'
Had it come at last, this revival of the nation's vitality? Had it come
just too late for him to share it?
'I shall not help you,' he said sadly; 'I do not suppose that I ever
could have helped you much, but now I shall not even try.'
She looked at him quickly with a startled expression in her eyes. Then
she turned to Marion.
'Are you preventing him?' she said.
'No,' said Hyacinth; 'it is not Marion. But I am going away--going to
England. I am going to be ordained, to become an English curate. Do you
understand? I came here to-day to see the man who is to be my Rector,
and to make final arrangements with him.'
'Oh, Hyacinth!'
For some minutes she said no more. He saw in her face a wondering
sorrow, a pathetic submissive-ness to an unexpected disappointment, like
the look in the face of a dog struck suddenly by the hand of a friend.
He felt that he could have borne her anger better. No doubt if he had
made his confession to Augusta Goold he would have been overwhelmed with
passionate wrath or withered by a superb contemptuous stare. Then he
could have worked himself to anger in return. But this!
'You will never speak to any of us again,' she went on. You will be
ashamed even to read the _Croppy_. You will wear a long black coat and
gray gloves. You will learn to talk about the "Irish Problem" and the
inestimable advantages of belonging to a world-wide Empire, and about
the great heart of the English people. I see it all--all that will
happen to you. Your hair will get quite smooth and sleek. Then you will
become a Vicar of a parish. You will live in a beautiful house, with
Virginia creeper growing over it and plum-trees in the garden. You will
have a nice clean village for a parish, with old women who drop curtsies
to you, and men--such men! stupid as bullocks! I know it all. And you
will be ashamed to call yourself an Irishman. Oh, Hyacinth!'
Miss O'Dwyer's catalogue of catastrophes was curiously mixed. Perhaps
the comedy in it tended to obscure the utter degradation of the ruin
she described. But the freakish incongruity of the speech did not strike
Hyacinth. He found in it only two notes--pity that such a fate awaited
him, and contempt for the man who submitted to it.
'I cannot help myself. Will you not make an effort to understand? I am
trying to; do what is right.'
She shook her head.
'No,' he said, 'I know it is no use. You could not understand even if I
told you all I felt.'
Her eyes filled suddenly with tears. He heard her sob. Then she turned
without a word and left them. He stood watching her till she reached
the road and started on her walk to the railway-station. Then he took
Marion's two hands in his, and held them fast.
'Will _you_ understand?' he asked her.
She looked up at him. Her face was all tenderness. Love shone on
him--trusting, unquestioning, adoring love, love that would be loyal to
the uttermost; but her eyes were full of a dumb wonder.
CHAPTER XXV
One morning near the end of September the _Irish Times_ published a list
of Irish graduates ordained in England on the previous Sunday. Among
other names appeared:
'Hyacinth Conneally, B.A., T.C.D., deacon, by the Bishop of Ripon, for
the curacy of Kirby-Stowell.'
Shortly afterwards the _Croppy_ printed the following verses, signed
'M.O'D.':
'EIRE TO H. C.
'Bight across the low, flat curragh from the sea,
Drifting, driving sweeps the rain,
Where the bogborn, bent, brown rushes grow for me,
Barren grass instead of grain.
'Out across the sad, soaked curragh towards the sea,
Striding, striving go the men,
With their spades and forks and barrows toil for me
That my corn may grow again
'Ah I but safe from blast of wind and bitter sea,
You who loved me---Tusa fein--
Live and feel and work for others, not for me,
Never coming back again.
'Yes, while all across the curragh from the West
Drifts the sea-rain off the sea,
You have chosen. Have you chosen what is best
For yourself, O son, and me?'
Hyacinth read the verses, cut them out of the _Croppy_, and locked them
in the box in which he stored the few papers of interest he possessed.
The sorrowful judgment pronounced on his conduct affected him, but only
in a dull way, like an additional blow upon a limb already bruised to
numbness. He accepted his new duties and performed them without any
feeling of enthusiasm, and after a little while without any definite
hope of doing any good. He got no further in understanding the people he
had to deal with, and he was aware that even those of them who came most
frequently into contact with him regarded him as a stranger. A young
doctor whose wife took a fancy to Marion tried to make friends with him.
The result was unsatisfactory, owing to Hyacinth's irresponsiveness. He
could not, without yawning piteously, spend an evening discussing the
performances of the local cricket club; nor did his conduct improve when
the two ladies suspended their talk and sacrificed an hour to playing
four-handed halma with their husbands. An unmarried solicitor, attracted
by Marion's beauty and friendliness, adopted the habit of calling at
Hyacinth's little house about nine or ten o'clock in the evening. He
was a man full of anecdote and simple mirth, and he often stayed, quite
happily, till midnight. Every week he brought an illustrated paper as
an offering to Marion, and recommended the short stories in it; to
her notice. He often asked Hyacinth's advice and help in solving the
conundrums set by the prize editor. He took a mild interest in politics,
and retailed gossip picked up at the Conservative Club. After a while he
gave up coming to the house. Hyacinth blamed himself for being cold and
unfriendly to the man.
Mr. Austin treated Hyacinth with kindness and some consideration, much
as a wise master treats an upper servant. He was anxious that his curate
should perform many and complicated ceremonies in church, was seriously
intent on the wearing of correctly- stoles, and 'ran,' as he
expressed it himself, a very large number of different organizations, of
each of which the objective appeared to be a tea-party in the parochial
hall. Hyacinth accepted his tuition, bowed low at the times when Mr.
Austin liked to bow, watched for the seasons when stoles bloomed white
and gold, changed to green, or faded down to violet. He tried to
make himself agreeable to the 'united mothers' and the rest when they
assembled for tea-drinking. Mr. Austin asserted that these were the
methods by which the English people were being taught the Catholic
faith. Hyacinth did not doubt it, nor did he permit himself to wonder
whether it was worth while teaching them.
To Marion the new life was full of many delights. The surpliced
choir-boys gratified her aesthetic sense, and she entered herself as one
of a band of volunteers who scrubbed the chancel tiles and polished a
brass cross. She smiled, kissed, and petted Hyacinth out of the fits of
depression which came on him, managed his small income with wonderful
skill, and wrote immensely long letters home to Ballymoy.
CHAPTER XXVI
It is very hard for a poor man to travel from one side of England to the
other side of Ireland, because railway companies, even when, to allure
the public, they advertise extraordinary excursions, charge a great
deal for their tickets. The journey becomes still more difficult of
accomplishment when the poor man is married. Then there are two tickets
to be bought, and very likely most of the money which might have bought
them has been spent securing the safe arrival of a baby--a third person
who in due time will also require a railway-ticket. This was Hyacinth's
case. For two summers he had no holiday at all, and it was only by the
most fortunate of chances that he found himself during the third
summer in a position to go to Ballymoy. He sublet his house to a
freshly-arrived supervisor of Inland Revenue, who wanted six weeks
to look about for a suitable residence. With the nine pounds paid in
advance by this gentleman, Hyacinth and Marion, having with them their
baby, a perambulator, and much other luggage, set off for Ballymoy.
The journey is not a very pleasant one, because it is made over the
lines of three English railway companies, whose trains refuse to connect
with each other at junctions, and because St. George's Channel is
generally rough. The discomfort of third-class carriages is more acutely
felt when the Irish shore is reached, but the misery of having to feed
and tend a year-old child lasts the whole journey through. Therefore,
Marion arrived in Dublin dishevelled, weary, and, for all her natural
placidness, inclined to be cross. The steamer came to port at an hour
which left them just the faint hope of catching the earliest train to
Ballymoy. Disappointment followed the nervous strain of a rush across
Dublin. Two long hours intervened before the next train started, and the
people who keep the refreshment-room in Broadstone Station are not early
risers. Marion, without tea or courage, settled herself and the baby in
the draughty waiting-room.
Hyacinth was also dishevelled, dirty, and tired, having borne his full
share of strife with the child's worst moods. But the sight of Ireland
from the steamer's deck filled him with a strange sense of exultation.
He wished to shout with gladness when the gray dome of the Custom House
rose to view, immense above the low blanket of mist. Even the incredibly
hideous iron grating of the railway viaduct set his pulse beating
joyfully. He drew deep breaths, inhaling various abominable smells
delightedly. The voices of the sleepy porters on the quay roused in him
a craving for the gentle slovenliness of Irish speech. He fussed and
hustled Marion beyond the limits of her endurance, pretending eagerness
to catch the early train, caring in reality not at all whether any train
were caught or missed, filled only with a kind of frenzy to keep moving
somehow further into Ireland. In the cab he gave utterance to ridiculous
pleasantries. He seized the child from Marion, and held him, wailing
piteously, half out of the window, that his eyes might rest on the great
gilt characters which adorn the offices of the Gaelic League. It was
with rapture that he read Irish names, written and spelt in Irish, above
the shops, and saw a banner proclaiming the annual festival of Irish
Ireland hanging ovei the door of the Rotunda. The city had grown more
Irish since he left it. There was no possibility now, even in the early
morning, with few people but scavengers and milkmen in the streets, of
mistaking for an English town.
While Marion sat torpid in the waiting-room, he paced the platform
eagerly from end to end. He saw the train pushed slowly into position
beside the platform, watched porters sweep the accumulated debris of
yesterday's traffic from the floors of the carriages, and rub with
filthy rags the brass doorhandles. Little groups of passengers began to
arrive--first a company of cattle-jobbers, four of them, red-faced men
with keen, crafty eyes, bound for some Western fair; then a laughing
party of tourists, women in short skirts and exaggeratedly protective
veils, men with fierce tweed knickerbockers dragging stuffed hold-alls
and yellow bags. These were evidently English. Their clear high-pitched
voices proclaimed contempt for their surroundings, and left no doubt of
their nationality. One of them addressed a bewildered porter in cheerful
song:
'Are you right there,
Michael? are you right?
Have you got the parcel there for Mrs. White?'
He felt, and his companions sympathized, that he was entering into the
spirit of Irish life. Then, heralded by an obsequious guard, came a
great man, proconsular in mien and gait. Bags and rugs were wheeled
beside him. In his hand was a despatch-box bearing the tremendous
initials of the Local Government Board. He took complete possession of
a first-class smoking carriage, scribbled a telegram, perhaps of
international importance, handed it to the guard for instant despatch,
and lit a finely-odorous cigar. Hyacinth, humbled by the mere view of
this incarnation of the Imperial spirit, went meekly to the waiting-room
to fetch Marion and his child. He led them across the now crowded
platform towards a third-class carriage.
'I will not go with you in your first-class carriage, Father Lavelle; so
that's flat. Nor I won't split the difference and go second either, if
that's what you're going to propose to me. Is it spend what would keep
the family of a poor man in bread and tea for a week, for the sake of
easing my back with a cushion? Get away with you. The plain deal board's
good enough for me. And, moreover, I doubt very much if I've the money
to do it, if I were ever so willing. I'm afraid to look into my purse to
count the few coppers that's left in it after paying that murdering bill
in the hotel you took me to. Gresham, indeed! A place where they're
not ashamed to charge a poor old priest three and sixpence for his
breakfast, and me not able to eat the half of what they put before me.'
Hyacinth turned quickly. Two priests stood together near the bookstall.
The one, a young man, handsome and well-dressed, he did not know. The
other he recognised at once. It seemed to be the same familiarly shabby
black coat which he wore, the same many-stained waistcoat, the identical
silk hat, ruffled and rain-spotted. The same pads of flesh hung flaccid
from his jaws; the red, cracked knuckles of his hands, well remembered,
were enormous still. Only the furrows on the face seemed to be ploughed
deeper and wider, and a few more stiff hairs curled over the general
bushiness of the grizzled eyebrows.
'Father Moran!' cried Hyacinth.
'I am Father Moran. You're right there. But who _you_ are or how you
come to know me is more than I can tell. But wait a minute. I've a sort
of recollection of your voice. Will you speak to me again, and maybe
I'll be able to put a name on you.'
Hyacinth said a few words rapidly in Irish.
'I have you now,' said the priest. 'You're Hyacinth Conneally, the boy
that went out to fight for the Boers. Father Lavelle, this is a friend
of mine that I've known ever since he was born, and I haven't laid eyes
on him these six years or more. You're going West, Mr. Conneally? But of
course you are. Where else would you be going? We'll travel together
and talk. If it's second-class you're going, Father Lavelle will have
to lend me the money to pay the extra on my ticket, so as I can go with
you. Seemingly it's a Protestant minister you've grown into. Well
now, who'd have thought it? And you so set on fighting the battle of
Armageddon and all. It's a come-down for you, so it is. But never mind.
You might have got yourself killed in it. There's many a one killed or
maimed for life in smaller fights than it. It's better to be a minister
any day than a corpse or a <DW36>. And as you are a minister, it's
likely to be third-class you're travelling. Times are changed since
I was young. It was the priests travelled third-class then, if they
travelled at all, and the ministers were cocked up on the cushions,
looking down on the likes of us out of the windows with the little red
curtains half-drawn across them. Now it'll be Father Lavelle there,
with his grand new coat that he says is Irish manufacture--but I
don't believe him--who'll be doing the gentleman. But come along, Mr.
Conneally--come along, and tell me all the battles you fought and the
Generals you made prisoners of, and how it was you took to preaching
afterwards.'
Hyacinth, somewhat shyly, introduced the priest to Marion. Then a
ticket-collector drove them into their carriage and locked the door.
Father Moran began to catechize Hyacinth before the train started, and
drew from him, as they went westwards, the story of his disappointments,
doubts, hopes, veerings, and final despair. Hyacinth spoke unwillingly
at first, giving no more than necessary answers to the questions.
Then, because he found that reticence called down on him fresh and
more detailed inquiries, and also because the priest's evident and
sympathetic interest redeemed a prying curiosity from offensiveness,
he told his tale more freely. Very soon there was no more need of
questioning, and Father Moran's share in the talk took the form of
comments interrupting a narrative.
Of Captain Albert Quinn he said:
'I've heard of him, and a nice kind of a boy he seems to have been. I
suppose he fought when he got there. He's just the sort that would be
splendid at the fighting. Well, God is good, and I suppose it's to
do the fighting for the rest of us that He makes the likes of Captain
Quinn. Did you hear that they wanted to make him a member of Parliament?
Well, they did. Nothing less would please them. But what good would
that be, when he couldn't set foot in the country for fear of being
arrested?'
Later on he was moved to laughter.
'To think of your going on the road with a bag full of blankets and
shawls! I never heard of such a thing, and all the grand notions your
head was full of! Why didn't you come my way? I'd have made Rafferty
give you an order. I'd have bought the makings of a frieze coat from you
myself--I would, indeed.'
Afterwards he became grave again.
'I won't let you say the hard word about the nuns, Mr. Conneally. Don't
do it, now. There's plenty of good convents up and down through the
country--more than ever you'll know of, being the black Protestant you
are. And the ones that ruined your business--supposing they did ruin
it, and I've only your word for that--what right have you to be blaming
them? They were trying to turn an honest penny by an honest trade, and
that's just what you and your friend Mr. Quinn were doing yourselves.'
Hyacinth, conscious of a failure in good taste, shifted his ground, only
to be interrupted again.
'Oh, you may abuse the Congested Districts Board to your heart's
content. I never could see what the Government made all the Boards for
unless it was to keep the people out of mischief. As long as there is
a Board of any kind about the country every blackguard will be so busy
throwing stones at it that he won't have time nor inclination left
to annoy decent people. And I'll say this for the Congested Districts
Board: they mean well. Indeed they do; not a doubt of it. There's one
good thing they did, anyway, if there isn't another, and that's when
they came to Carrowkeel and bought the big Curragh Farm that never
supported a Christian, but two herds and some bullocks ever since the
famine clearances. They fetched the people down off the mountains and
put them on it. Wasn't that a good thing, now? Sure, all Government
Boards do more wrong than right. It's the nature of that sort of
confederation. But it's all the more thankful we ought to be when once
in a while they do something useful.'
Hyacinth came to tell of the choice which Canon Beecher offered him, and
dwelt with tragic emphasis on his own decision. The priest listened, a
smile on his lips, a look of pity which belied the smile in his eyes.
'So you thought Ireland would be lost altogether unless you wrote
articles for Miss Goold in the _Croppy?_ It's no small opinion you have
of yourself, Hyacinth Conneally. And you thought you'd save your soul by
going to preach the Gospel to the English people? Was that it, now?'
'It was not,' said Hyacinth, 'and you know it wasn't.'
'Of course it wasn't. What was I thinking of to forget the young lady
that was in it? A fine wife you've got, any way. God bless her, and make
you a good husband to her! By the looks of her she's better than you
deserve. I suppose it was to get money you went to England, so as to buy
her pretty dresses and a beautiful house to live in? Did you think you'd
grow rich over there?'
'Indeed I did not,' said Hyacinth bitterly. 'I knew we'd never be rich.'
'Well, then, couldn't you as well have been poor in Ireland? And better,
for everybody's poor here. But there, I know well enough it wasn't money
you were after. Don't be getting angry with me, now. It wasn't for the
sake of saving your soul you went, nor to get your nice wife, though a
man might go a long way for the likes of her. I don't know why you went,
and it's my belief you don't know yourself. But you made a mistake,
whatever you did it for, going off on that English mission. Is it a
mission you call it when you're a Protestant? I don't think it is, but
it doesn't matter. You made a mistake. Why don't you come back again?'
'God knows I would if I could. It's hungry I am to get back--just sick
with hunger and the great desire that is on me to be back again in
Ireland.'
'Well, what's to hinder you? Let me tell you this: There's been four
men in your father's place since he died. Never a one of the first three
would stay. They tell me the pay's small, and the place is desolate to
them for the want of Protestants, there being none, you may say, but the
coastguards. After the third of them left it was long enough before they
got the fourth. I hear they went scouring and scraping round the four
coasts of the country with a trawl-net trying to get a man. And now
they've got him he's all for going away. He says there's no work to do,
and no people to preach to. But you'd find work, if you were there. I'd
find you work myself--work for the people you knew since you were born,
that's in the way at last of getting to be the men and women they were
meant to be, and that wants all the help can be got for them. Why don't
you come back?'
'Indeed, Father Moran, I would if I could.' 'If you could! What's the
use of talking? Isn't your wife's father a Canon? And wouldn't that
professor in the college that you used to tell me of do something for
you? What's the good of having fine friends like that if they won't get
you sent to a place like Carrowkeel, that never another minister but
yourself would as much as cat his dinner in twice if he could help it?'
Hyacinth glanced doubtfully at Marion. The child lay quiet in her arms.
She slept uncomfortably. It was clear that she had not cared to listen
to the conversation of the two men.
THE END
End of the Project Gutenberg EBook of Hyacinth, by George A. Birmingham
*** | {
"redpajama_set_name": "RedPajamaBook"
} | 274 |
\section{Introduction}
The study of cosmic rays of ultra-high energies sheds light on the most powerful processes in the Universe.
The fine structures of the primary cosmic ray spectrum and the mass composition yield information on the type of cosmic accelerators and their location.
For example, at energies of about EeV, a transition from galactic to extragalactic cosmic ray sources is expected~\cite{Aloisio2012129}.
To distinguish between galactic and extragalactic sources, the precise determination of fluxes of different primary nuclei is required.
Modern optical detectors, namely, non-imaging air-Cherenkov arrays and fluorescence telescopes reach energy resolutions
of about 10\% and a resolution for the depth of the shower maximum ($X_\mathrm{max}$) of about 20~g/cm\textsuperscript{2}.
However, the duty cycle of such detectors is less than 15\%~\cite{Prosin:2016jev,Porcelli:2015jli}.
Digital radio arrays, as a novel technique, which allows for measurements of air-showers produced by primary cosmic rays with energies above 100~PeV.
A broad description of radio emission from air-showers, the technique of its detection and of historical and modern experiments is given in Ref.~\cite{SchroederReview2016}.
Modern detectors, such as LOFAR~\cite{Buitink:2016nkf}, AERA~\cite{Aab:2015vta} and Tunka-Rex~\cite{Bezyazeekov:2015ica} have already proven the feasibility of this technique, and shown that radio detection has a resolution competitive to optical technique.
Triggered by an external particle array, a radio detector becomes a scalable, cost-effective extension, which provides precise measurements of ultra-high energy cosmic rays around-the-clock.
In the present paper we focus on the setup of Tunka-Rex, discuss the achieved results and prospects of mass-composition studies with radio arrays.
\section{The Tunka Radio Extension}
The Tunka Radio Extension (Tunka-Rex) array has been commissioned in 2012 and originally consisted of 18 antennas distributed over an area of 1 km\textsuperscript{2}~\cite{TunkaRex_NIM_2015}.
The detector layout is mostly determined by the Tunka-133~\cite{Prosin:2016jev} clusters, the original air-Cherenkov array of the TAIGA facility~\cite{Budnev:2016btu} located nearby southern tip of Lake Baikal in Siberia.
At the moment the cosmic-ray detectors of TAIGA consists of Tunka-133, Tunka-Grande~\cite{Budnev:2015cha} and Tunka-Rex.
Tunka-Rex now contains 63 antenna stations including six satellite stations extending the area to 3~km\textsuperscript{2}.
The common layout of the three experiments is shown in Fig.~\ref{fig:layout}.
\begin{figure}[t]
\includegraphics[width=1.0\linewidth]{map}
\caption{Layout of cosmic-ray detectors of the TAIGA~\cite{Budnev:2016btu} facility.
The core consists of 19 clusters, each of them is equipped with 3 Tunka-Rex antenna station, and 6 satellite clusters with one Tunka-Rex antenna station per cluster.
Triangles depict preliminary positions of the antennas deployed in 2016 (precise position measurements will be performed soon).
}
\label{fig:layout}
\end{figure}
Each Tunka-Rex antenna station consists of two perpendicular short aperiodic loaded loop antennas~(SALLA)~\cite{KroemerSALLAIcrc2009,Abreu:2012pi} rotated by an angle of $\pm$45$^\circ$ with respect to magnetic North.
Each antenna contains a low-noise amplifier (LNA) and a load suppressing the downward direction,
which makes the antenna upward-looking and decreases the uncertainty due to ground conditions to the level of only 3\%.
A Tunka-Rex antenna station and the SALLA gain pattern are shown in Fig.~\ref{fig:antenna}.
Before digitalization, the signals are analogically processed with a filter-amplifier with an effective band of 30-76~MHz.
Each Tunka-Rex antenna station is connected either to the Tunka-133 or the Tunka-Grande local data acquisition and shares the same ADC boards.
All clusters are synchronized with the central DAQ via optical fibers.
We have checked the stability of the synchronization with a beacon-based method~\cite{Schroeder2010277,PierreAuger:2016zxi}.
The relative timing is stable to better than a nanosecond during a single run, however, after reset we obtain jumps of about 5~ns.
Taking background into account, the resulting timing uncertainty is about 7~ns.
Depending on the trigger mode, the entire cluster is triggered by air-Cherenkov (clear winter moonless nights) or particle detectors (the rest of the time),
and traces from the Tunka-133 PMTs (when operating), scintillators and antennas are recorded simultaneously in traces of 1024 samples with 5~ns sampling rate and a bitdepth of 12 bits.
As a result, TAIGA features duplex (particles + radio) and triplex (particles + radio + air-Cherenkov) measurements of cosmic rays with energies of $10^{16}$--$10^{18}$~eV.
\begin{figure}[t]
\includegraphics[width=1.0\linewidth]{antenna}
\caption{
\textit{Left: }Gain pattern of the SALLA antennas of Tunka-Rex.
\textit{Right: }A Tunka-Rex antenna station. Two perpendicular SALLAs are mounted on a wooden pole at the height of about 3 m (upper end of SALLA).
}
\label{fig:antenna}
\end{figure}
\subsection{Antenna calibration}
The calibration of the Tunka-Rex antenna was performed in the following way: the directivity of the SALLA antenna was simulated with the NEC2 code~\cite{nec2},
and then normalized to an amplitude calibration made with the commercial reference source VSQ1000+DPA4000 by Schaffner Electrotest GmbH (now Teseq).
The same method was also used to calibrate the LOPES antennas~\cite{LOPES:2015eya}, as well as the LOFAR ones~\cite{Nelles:2015gca}, what makes these three experiments having consistent absolute calibration scale.
The hardware response and temperature dependence of the LNA and filter-amplifier were measured under laboratory conditions, and the calibration of the ADC was done on the board already deployed at the local DAQ of the clusters.
As result, the overall uncertainty on the absolute amplitude reconstruction is 22\%, with a dominating contribution of 16\% from the calibration scale uncertainty of the reference source, and a number of smaller contributions given by environmental conditions, antenna production and deployment.
\section{Event reconstruction}
Since all clusters operate independently, single-cluster events are merged into shower events during offline analysis.
At the first step, only events containing at least three antenna stations of signal-to-noise ratio~(SNR) in power ${S^2/N^2 > 10}$ are selected.
The amplitude of the signal $S$ is defined as the maximum of amplitude of the Hilbert envelope of the vectorial sum of the two measured polarizations inside of the signal window.
The position of the signal window is constant and defined by the hardware delay between the radio signal arrival time and the particle or air-Cherenkov trigger,
while the width of the signal window is defined by timing uncertainties and different shower geometries.
The noise level~$N$ is defined as RMS of the amplitude in a noise window.
An example of radio and air-Cherenkov traces recorded at the same cluster are given in Fig.~\ref{fig:trace-recoldf}.
Since Tunka-Rex is operating close to the threshold, the contribution of the background cannot be neglected.
This contribution is taken into account for the estimation of timing and amplitude uncertainties,
and the measured amplitudes is corrected for a systematic background bias using a function depending on SNR.
\begin{figure*}[t]
\begin{center}
\includegraphics[height=0.26\linewidth]{trace_14_1}~~~~\includegraphics[height=0.26\linewidth]{recoldf}
\caption{\textit{Left: }Example traces recorded by the Tunka-133 local DAQ.
The radio signal is recorded earlier than the PMT pulses, mostly due to longer cables of Tunka-133.
\textit{Right: }Sketch describing the reconstruction of the primary energy and distance to the shower maximum.
The lateral distribution is fitted by a Gaussian-shape function with fixed width.
The primary energy is proportional to the amplitude at~120~m distance, and the distance to the shower maximum is calculated from the slope at~180~m from the shower axis.
}
\label{fig:trace-recoldf}
\end{center}
\end{figure*}
At the next step, the arrival direction is reconstructed with a plane wave front model, and is compared to the one measured by the master detector (Tunka-133/Tunka-Grande).
Since the angular resolution of Tunka-Rex is about 1--2$^\circ$, all events with direction deviating from the master reconstruction by more than 5$^\circ$ are rejected and excluded from analysis.
After the first quality cuts, the position of the shower core is reconstructed.
In the triplex mode, the shower core and axis is taken from the Tunka-133 reconstruction, since it has much larger density than the other cosmic-ray detectors of TAIGA, and the resolution is better than 5~m.
In the duplex mode we plan to combine the reconstructions from Tunka-Rex and Tunka-Grande, since both of them are expected to feature a resolution of about 20-30~m due to their spacing,
and we expect that the combined reconstruction will improve this value.
After the reconstruction of the shower core, the amplitudes from the detector surface are projected to the shower axis forming the lateral distribution.
Any antenna station passed SNR cut appears further on the lateral distribution than two antenna stations without the signal is considered as outlier and rejected as false positive.
To reconstruct the primary energy $E_\mathrm{pr}$ and the depth of the shower maximum $X_\mathrm{max}$, the lateral distribution is corrected to remove the dependence on a geomagnetic and azimuth angles, which is introduced by the interference of the geomagnetic and charge excess effects~\cite{Kostunin:2015taa}.
The resulting distribution is fitted with a lateral distribution function (LDF), containing two free parameters.
These two parameters, namely normalization and slope, are used for the reconstruction of $E_\mathrm{pr}$ and $X_\mathrm{max}$, respectively.
A sketch describing the idea of the LDF approach is given in Fig.~\ref{fig:trace-recoldf}.
Since $X_\mathrm{max}$ is very sensitive to the shape of the LDF, we apply additional quality cuts to select high-quality events:
the event must contain at least one antenna further than 200~m from the shower axis (to increase the sensitivity to the LDF slope), and the resulting fit uncertainty of $X_\mathrm{max}$ must be less than~50~g/cm\textsuperscript{2}.
It is worth noting, that radio technique is sensitive only to electromagnetic component of air-showers,
which means that method have additional uncertainties due to unknown primary particles.
These uncertainties is discussed in section~\ref{sec:syst_unc}.
Up to now, we have finished the reconstruction of measurements during 2012-2014, when Tunka-Rex was operating jointly with Tunka-133.
To compare the reconstructions of the detectors,
we selected events with core positions inside the dense part of detector, i.e. within 500~m radius around the center.
To avoid implicit tuning in the cross-check of Tunka-Rex and Tunka-133, the half of Tunka-133 reconstruction of $E_\mathrm{pr}$ and $X_\mathrm{max}$ was blinded, and opened only after the final reconstruction of Tunka-Rex.
The comparing set includes 148 events with reconstructed energy and 42 events with reconstructed $X_\mathrm{max}$.
The obtained resolution of Tunka-Rex is 15\% for energy and 40~g/cm\textsuperscript{2} for $X_\mathrm{max}$, while no significant absolute shift between the reconstructions of Tunka-Rex and Tunka-133 was observed.
Since all of the high-energy events have passed the quality cuts, we can use them for a mass-composition study.
The mean $X_\mathrm{max}$ value obtained for ${\lg(E_\mathrm{pr}/\mbox{eV}) = 17.9\pm0.1}$ is given in Fig.~\ref{fig:xmax} based on 8 events.
It is worth noting, that these results were obtained with the Tunka-Rex configuration consisting of one antenna per cluster.
Meanwhile, starting from 2016 the array features three antennas per cluster.
To better understand systematic uncertainties, atmospheric effects will have to be taken into account~\cite{Abraham:2009bc}.
For the effective frequencies of Tunka-Rex these uncertainties can be in the order of 2\% and 5~g/cm\textsuperscript{2} for the energy~\cite{Glaser:2016qso} and shower maximum~\cite{Buitink:2016nkf} reconstructions, respectively.
In future, we plan to include Global Data Assimilation System (GDAS) data to our analysis to decrease these uncertainties~\cite{Abreu:2012zg}.
\begin{figure}[t]
\includegraphics[width=1.0\linewidth]{xmax}
\caption{
Mean depth of the shower maximum versus the primary energy reconstructed by modern cosmic-ray experiments: Tunka-133~\cite{Prosin:2016jev}, Auger~\cite{AugerHEATXmaxICRC2015}, LOFAR~\cite{Buitink:2016nkf} and Tunka-Rex.
Errorbars indicate statistic uncertainties only, and all measurements agree within additional systematic uncertainties.
}
\label{fig:xmax}
\end{figure}
\subsection{Energy reconstruction with a single antenna station}
Besides the main goals of energy and shower maximum reconstruction we have shown that a single antenna station can provide useful information when the shower core and axis are known~\cite{HillerArena2016}.
Assuming a mean value for the steepness of the radio LDF of about ${\eta_0^{-1} \approx 120}$~m,
and a threshold of ${S_\mathrm{th} \approx 90}$~{\textmu}V/m,
using reconstructed shower geometry from Tunka-133, we obtained a reliable energy reconstruction using single-antenna events.
Particularly, the number of events was increased by more than three times, while the energy resolution has slightly decreased to 20\%.
This result indicates the feasibility of equipping surface particle detectors with simple radio extensions, which allow for the determination of the electromagnetic energy deposit of high-energy air-showers above $10^{17}$~eV.
\section{The radio amplitude as measure for the absolute energy scale}
The independent energy reconstruction by Tunka-Rex is based on an absolute amplitude calibration of the antennas and on normalization parameters obtained with CoREAS.
As shown above, that the absolute energy scales of Tunka-Rex and Tunka-133 experiments are in very good agreement.
Since the radio emission from air-showers is well understood and its generation and propagation depend weakly on the atmospheric condition, it can be used as universal tool to compare or cross-check the energy scale of experiments located in different places and exploiting different techniques.
To test this statement, we have selected KASCADE-Grande~\cite{Apel2012183} with its radio extension LOPES~\cite{Apel:2014ika} and compared it with Tunka-133 and Tunka-Rex measurement, respectively~\cite{Apel:2016gws}.
Since Tunka-Rex and LOPES were calibrated with the same reference source,
most systematic uncertainties of the amplitude calibration cancel out in the comparison.
We realize this comparison with two different approaches.
The first one is to compare the ratio $\kappa$ of measured radio amplitudes and the energy reconstructed by the master experiment.
Then the relative shift between the masters is defined as ${f_\mathrm{amp} = \kappa_{\mathrm{Tunka-Rex}}/\kappa_{\mathrm{LOPES}}}$.
This method relies only on direct radio measurements,
and the reconstruction procedure are chosen as similar as possible (i.e. the same bandwidth and the same LDF treatment),
moreover, the reconstruction is corrected for the different observation depths and magnetic fields of the two locations.
The second method is implemented via CoREAS simulations: two simulations -- one with proton and one with iron primary were produced for each event, and then the measured and simulated radio amplitudes were compared to each other.
Then, the mean ratios $F^\mathrm{p}$ ($F^\mathrm{Fe}$) between simulated and measured amplitudes are determined, and the scale shift between the master experiments is defined as ${f_\mathrm{sim} = F_{\mathrm{Tunka-Rex}}/F_{\mathrm{LOPES}}}$.
The main uncertainty of these method is given by the hadronic model used in the simulation and uncertainties due to angular dependence of antenna gain.
The result of both methods is that the energy scales of Tunka-133 and KASCADE-Grande are consistent to about 10\% limited by systematic uncertainties of the LOPES experiment, and the mean KASCADE-Grande energy scale is lower than Tunka-133 by about 5\%.
A similar shift is obtained by a straight-forward fit of the energy spectra of Tunka-133 and KASCADE-Grande.
The spectra and results of the scale comparison are given in Fig.~\ref{fig:spec_comparison}.
This result can be applied to study finer features of the energy spectrum with higher accuracy, e.g. it allows to define the positions of knee-like structures with lower uncertainty.
\begin{figure}[t]
\includegraphics[width=1.0\linewidth]{spec_comparison}
\caption{
Energy spectra of cosmic rays from KASCADE-Grande~\cite{Apel2012183} and Tunka-133~\cite{Prosin:2016jev}: normalized flux per energy;
and the results from the comparison of the energy scales between the experiments Tunka-Rex and LOPES (small box) in the energy range of $10^{17}$ to $10^{18}$\,eV.
With a systematic increase of KASCADE-Grande energies by $4\,\%$ (or a corresponding decrease of Tunka-133 energies) the average flux per energy of both experiments can be brought to agreement in this energy range~\cite{Apel:2016gws}.
}
\label{fig:spec_comparison}
\end{figure}
\section{Ongoing activity}
In this section we discuss theoretical work performing in the frame of Tunka-Rex experiment with a purpose of improving the reconstruction of air-shower events.
\subsection{Lateral distribution function}
Hereafter we perform calculations in the frame of the geomagnetic coordinate system based on the shower axis vector $\bm{\hat{\mathrm{V}}}$ and the vector of the Earth's magnetic field $\bm{\hat{\mathrm{B}}}$ (a hat over a vector denotes a unit vector: $\bm{\hat{\mathrm{B}}} = \bm{\mathrm{B}} / |\bm{\mathrm{B}}|$):
\begin{eqnarray}
&& \bm{\hat{\mathrm{e}}}_x = \bm{\hat{\mathrm{V}}} \times \bm{\hat{\mathrm{B}}}\,, \\
&& \bm{\hat{\mathrm{e}}}_y = \bm{\hat{\mathrm{V}}} \times (\bm{\hat{\mathrm{V}}} \times \bm{\hat{\mathrm{B}}})\,, \\
&& \bm{\hat{\mathrm{e}}}_z = \bm{\hat{\mathrm{V}}}\,.
\end{eqnarray}
This way, the shower front is laying in the plane $(\bm{\hat{\mathrm{e}}}_x, \bm{\hat{\mathrm{e}}}_y)$.
Let us also define useful angles: the geomagnetic angle between shower axis and magnetic field $\alpha_{\mathrm g} = \angle(\bm{\mathrm{V}},\bm{\mathrm{B}})$ and the geomagnetic azimuth $\phi_{\mathrm g} = \angle(\bm{\hat{\mathrm{e}}}_x,\bm{\mathrm{r}})$,
where $\bm{\mathrm{r}}$ is the coordinate of an antenna station.
The main parameterization used by Tunka-Rex is the parameterization describing the distribution of radio amplitudes with respect to the shower axis, i.e. the LDF:
\begin{eqnarray}
&&\mathcal{E}(r,\phi_\mathrm{g}) = \mathsf{\hat K}^{-1}(\phi_\mathrm{g})\mathcal{E}_2(r), \\
&&\mathsf{\hat K}(\phi_\mathrm{g}) = \left(\varepsilon^2 + 2\varepsilon\cos\phi_{\mathrm g}\sin\alpha_{\mathrm g} + \sin^2\alpha_{\mathrm g}\right)^{-\frac{1}{2}}, \\
&&\mathcal{E}_2(r) = \mathcal{E}_0\exp\left(a_1(r-r_0) + a_2(r-r_0)^2\right),
\end{eqnarray}
where $\mathcal{E}(r,\phi_\mathrm{g})$ is the amplitude at the antenna station with coordinates $(r,\phi_\mathrm{g})$.
This amplitude is described with two significant terms: first, the azimuthal asymmetry $\varepsilon$ is corrected by the term $\mathsf{\hat K}(\phi_\mathrm{g})$;
second, the lateral distribution $\mathcal{E}_2(r)$,
which is a Gaussian-like function with the normalization $\mathcal{E}_0$, with a width proportional to $a_2$ and the slope proportional to $a_1$.
The maximum of $\mathcal{E}_2(r)$ reflects Cherenkov-like features of the radio emission.
The parameter $r_0$ is arbitrarily chosen in a way to obtain maximum correlation of $\mathcal{E}_0$ and $a_1$ with the primary energy and the distance to the shower maximum, respectively.
\subsection{Estimation of core position}
After the upgrade of Tunka-Rex, we are now implementing an independent reconstruction of the position of shower core with radio standalone.
The position of the core $(x_0,y_0)$ is added to LDF parameters ${r = r(x_0,y_0)}$ and $\phi_\mathrm{g} = \phi_\mathrm{g}(x_0,y_0)$.
Since Tunka-Rex operates near the threshold, currently the core position is reconstructed in three steps:
\begin{enumerate}
\item The initial core position is estimated a center of mass of the radio amplitudes during the arrival-direction reconstruction (requires at least 3 antennas);
\item Parameters $a_1$ and $a_2$ are fixed to default values, and the LDF is fitted with three free parameters: $\mathcal{E}_0$, $x_0$ and $y_0$ (requires at least 4 antennas);
\item The LDF is fitted again including $a_1$ and $a_2$, and the limits for $\mathcal{E}_0$, $x_0$ and $y_0$ are defined from the previous stage (requires at least 6 antennas).
\end{enumerate}
With this procedure we expect to obtain resolutions of about 20-30~m for the dense part of the detector (inner circle of 500~m around the center of the array).
To improve these numbers we plan to apply stricter quality cuts on the signal reconstruction for this particular procedure.
\subsection{Limitation of the one-dimensional approach}
For the time being, all methods for the $X_\mathrm{max}$ reconstruction are based on the simple relation between single parameters of the LDF and $X_\mathrm{max}$ or the distance to $X_\mathrm{max}$.
For example, Tunka-Rex, LOFAR~\cite{Nelles:2014xaa} and AERA use Gaussian-like parameterizations and exploit the correlation of $X_\mathrm{max}$ with the slope and width of LDF, respectively.
In this section we describe the relation between the position of the depth of the shower maximum and the slope of the LDF,
give a more strict consideration of it,
and discuss its possible hidden features.
We use the following assumptions: the distribution of the electrons behaves as Gaisser-Hillas function and the density of the Earth's atmosphere falls exponentially with increasing altitude, namely we use the CORSIKA parameterization of the standard atmosphere~\cite{HeckKnappCapdevielle1998}.
The simple form of the amplitude of the radio signal $\mathcal{E}_\nu(r)$ with frequency $\nu$ at distance $r$ from the shower axis is~\cite{Allan1971}:
\begin{equation}
\label{eq1}
\mathcal{E}_\nu(r) = \kappa \int\limits^{h^\nu_2(r,n_\mathrm{r})}_{h^\nu_1(r,n_\mathrm{r})} \frac{N(h)}{h} \mathrm{d}h\,,
\end{equation}
where $\kappa$ is the normalization coefficient (the dependence on geomagnetic angle $\alpha_\mathrm{g}$ has already been taken into account),
$N(h)$ is the number of electrons at the altitude $h$, and $h^\nu_{1,2}(r,n_\mathrm{r})$ are the integration limits depending on the distance to shower axis $r$ and refractive index $n_\mathrm{r}$.
Assuming that the refractive index $n_\mathrm{r}(h)$ is proportional to the density of the atmosphere, one can recalculate it from the atmospheric parameterization and use it as an input to estimate the integration limits $h^\nu_{1,2}(r,n_\mathrm{r})$ for \textit{vertical} air-showers:
\begin{equation}
h_{1,2}^\nu(r,n_\mathrm{r}) = \left(\frac{r}{r_{1,2}(\nu,n_\mathrm{r})}\right)^{\alpha_{1,2}(\nu,n_\mathrm{r})}\,,
\label{eq:h12par}
\end{equation}
This parameterization is obtained by numerical solution of the equation
\begin{equation}
\Delta t (r,h^\nu) = \Delta t (r,h_c^\nu) + \frac{1}{2\pi\nu}\,,
\end{equation}
where
\begin{equation}
\Delta t (r,h^\nu) = \cos\left(\arctan\left(\frac{r}{h^\nu}\right)\right)\int\limits_0^{h^\nu}\frac{n_\mathrm{r}(h')}{c}\mathrm{d}h' - \frac{h^\nu}{c}\,,
\end{equation}
where $c$ is the velocity of light, and $h_c$ is defined as solution of equation
\begin{equation}
\frac{\partial}{\partial h_c} \Delta t (r,h_c) = 0\,.
\end{equation}
For inclined air-showers everything is scaled by $\cos\theta$ (where $\theta$ is the zenith angle) at first approximation, but here we do not consider these cases.
The curves denoting the behavior of $h^\nu_{1,2}(r,n_\mathrm{r})$ are in Fig~\ref{fig:cr-xmax-geo}.
One can see that for lateral distances far from the Cherenkov bump (${r>100}$~m), the upper limit goes to infinity (becomes higher than the top of the atmosphere) and the lower limit goes to the position of the shower maximum and above.
\begin{figure*}
\begin{center}
\includegraphics[height=0.43\linewidth]{cr}~~~~~\includegraphics[height=0.43\linewidth]{xmax-geo}
\caption{\textit{Left: }Sketch describing the radio emission from air-showers.
The X axis indicates the position of the observing antenna, the Y axis indicates the altitude (the observer is placed on zero altitude),
the colored band indicates possible positions of the shower maximum for typical air-showers (one sigma spread around the mean due to shower-to-shower fluctuations for vertical air-showers of energies $10^{17}$ -- $10^{18}$~eV), and the lines indicate the bounds of the emission region for different frequencies.
These lines are calculated using the atmosphere refractivity $n_\mathrm{r}$ as input.
One can see, that the emission region reduces with increasing frequency and the point of intersection with the shower maximum will define the Cherenkov ring observed for high frequencies.
For lower frequencies one can see the exponential fall-off of amplitudes after the intersection of $h_1$ with the shower maximum line.\hspace{\textwidth}
\textit{Right: }Correlation between the true geometrical distance to the shower maximum and the estimation made with the simplest slope method neglecting particle interactions and propagation constants.
We obtained no difference between slopes of proton and iron induced air-showers.
The dependence is not linear mostly due to the different density of the atmosphere at the different altitudes (i.e. the geometrical mean path length of electron is different); for real data analysis we use a more sophisticaed method tuning all reconstruction constants are tuned against CoREAS simulations to obtain a linear dependence~\cite{Kostunin:2015taa,Bezyazeekov:2015ica}.
}
\label{fig:cr-xmax-geo}
\end{center}
\end{figure*}
In our case, the integration limits in~Eq.~(\ref{eq1}) are as follows: $h^\nu_2(r,n_\mathrm{r})\to\infty$, $h^\nu_1(r,n_\mathrm{r}) > h_\mathrm{max}$, i.e. we integrate over the upper tail of the electron distribution.
This way, the value of the integral~Eq.~(\ref{eq1}) has the following form:
\begin{equation}
\mathcal{E}_\nu(r > r_\mathrm{c}) \propto \exp \left(-\frac{(r/r_1)^{\alpha_1}}{h_\mathrm{max}}f_{\mathrm{int}}(h_\mathrm{max},...)\right)\,.
\end{equation}
As it was expected, we obtained an exponential-like behavior of the LDF, where the exponent is defined by the altitude of the shower maximum $h_\mathrm{max}$.
It is worth noting that the power of $r$ (defined as $\alpha_1 \approx 3/2$, which is obtained from the fit of~Eq.~(\ref{eq:h12par}) to curves shown in Fig.~\ref{fig:cr-xmax-geo}) is between 1 and 2, i.e. both exponential and Gaussian describe the tail of the LDF only approximately.
The term $f_\mathrm{int}$, which includes constants from the interaction models, has weaker dependence on the shower geometry and scales with $h_\mathrm{max}$ due to the non-isotropical atmosphere.
Simplifying ${f_\mathrm{int} = 1}$ one still conserves the correlation between the slope of $\mathcal{E}$ and $h_\mathrm{max}$ (see Fig.~\ref{fig:cr-xmax-geo}),
what means, that the radio signal has a high sensitivity to the position of the shower maximum.
However, this one-dimensional slope method does not give additional information on the type of primary particle, which would go beyond $X_\mathrm{max}$.
One can see from Eq.~(\ref{eq1}), that the height of the shower maximum $h_\mathrm{max}$ is encoded in the slope of the LDF.
what means, that the radio signal has a high sensitivity to the position of the shower maximum.
On the other side, this one-dimensional slope method does not give additional information on the type of primary particle.
\subsection{Systematic uncertainties}
\label{sec:syst_unc}
To study uncertainties given by hadronic interactions and shower-to-shower fluctuations, we performed simulations with recently released CORSIKA~v7.5.
Both, QGSJET-II.04 and EPOS-LHC yield almost the same radio amplitude with a difference less than one given by shower-to-shower fluctuations.
For the detailed study we use QGSJET-II.04, with which we simulated events with parameters similar to the events reconstructed in 2012-2014 with four different primary particles: proton, helium, nitrogen and iron.
The energy resolution (taking noise into account) for each particle is about 10\%, while the shift in the absolute values of the energy is about 12\% between proton and iron.
This is due to the fraction of the primary energy going into the electromagnetic cascade, the same feature is also observed with the optical methods, such as air-Cherenkov and fluorescence.
This shift is much larger, than shower-to shower fluctuations for this particles: 5\% and 1.3\% for proton and iron, respectively.
The reconstruction of the absolute value of the shower maximum is not much affected by the primary composition, since it is reconstructed with the simple slope method, and the one-dimensional slopes are the same for showers of different primary particles with the same shower maxima.
\subsection{Hints from the charge-excess asymmetry}
In the work~\cite{Kostunin:2015taa} it is shown that the charge-excess asymmetry has a non-trivial dependence on the distance to the shower axis,
particularly, the asymmetry features a local maximum depending on the distance to the shower maximum (see Fig.~\ref{fig:asymm_profile}).
This structure was obtained by analyzing the polarization of CoREAS simulations at individual antenna positions.
As it is mentioned above, in the Tunka-Rex reconstruction the LDF is corrected for charge-excess asymmetry~$\varepsilon$.
To show the consistency of the polarization and LDF approaches, we express $\varepsilon$ in terms of the LDF.
Since the Tunka-Rex LDF is azimuthal symmetric, we have used LDF developed for AERA~\cite{Aab:2015vta} experiment.
The expression for asymmetry has the following form:
\begin{equation}
\varepsilon(r) = \sin\alpha_\mathrm{g}\frac{{\mathcal{E}_{\mathrm{2G}}(r)} - \tilde{\mathcal{E}}_{\mathrm{2G}}(r)}{\mathcal{E}_{\mathrm{2G}}(r) + \tilde{\mathcal{E}}_{\mathrm{2G}}(r)}\,,\,\,\,
\label{eq_eps}
\end{equation}
with
\begin{equation}
\begin{cases}
\mathcal{E}_{\mathrm{2G}}(r) = \mathcal{E}_{\mathrm{2G}}(\bm{r}_x) \\
\tilde{\mathcal{E}}_{\mathrm{2G}}(r) = \mathcal{E}_{\mathrm{2G}}(-\bm{r}_x) \\
\end{cases}\,,
\end{equation}
where $\mathcal{E}_{\mathrm{2G}}(r)$ is the AERA parameterization and vector $\bm{r}_x$ is along the Lorentz force (perpendicular to the shower axis and geomagnetic field).
Taking mean values for the parameters of $\mathcal{E}_{\mathrm{2G}}(r)$, one can obtain the corresponding curve $\varepsilon(r)$ and compare it to one obtained with the polarization approach.
The comparison is presented in Fig.~\ref{fig:asymm_profile}.
One can see, that both definitions are in good agreement, which leads to an interesting conclusion: the asymmetry (or charge-excess) information can be extracted from the more simple measurement of the total radio amplitude, instead of precise measurements of the components of the electrical field.
Measuring the amplitude asymmetry requires higher number of stations per events, but lower signal-to-noise ratios.
As it was shown in Ref.~\cite{Kostunin:2015taa}, the behavior of the asymmetry is connected to the distance to the shower maximum,
i.e. an accurate measurement of the asymmetry by either means should be sensitive to the mass composition.
The idea of an one-antenna analysis can be also applied to a polarization study of the asymmetry: knowing the geometry of the air-shower and the behavior of $\varepsilon(r)$ one can study the mean shower maximum via the mean asymmetry.
Finally, the asymmetry contains information not only on the total number of the charge particles, but also on the dynamics of their creation.
\begin{figure}[t]
\includegraphics[width=1.0\linewidth]{asymm_profile}
\caption{
Askaryan asymmetry normalized to the geomagnetic field in the Tunka Valley as a function of the distance to the shower axis.
Points indicate the polarization measurements by LOFAR~\cite{Schellart:2014oaa} (green) and CoREAS simulations~\cite{Kostunin:2015taa} (blue and red).
The black solid line indicates the LDF asymmetry $\varepsilon(r)$ from Eq.~(\ref{eq_eps}).
The blue band is the polarization measurements by AERA~\cite{Aab:2014esa} (with uncertainties), the dashed line is the theoretical prediction for Tunka-Rex~\cite{Kostunin:2015taa}.}
\label{fig:asymm_profile}
\end{figure}
\subsection{Signal recognition with neural networks}
The recognition of the signal and the determination of its amplitude are the most fundamental problems of the basic event reconstruction.
Since the measured signal is a sum of a true radio signal from the air-shower and the background of environment and hardware, the quality of the signal reconstruction is a function of the SNR.
When the SNR is relatively small (conditionally, $\mathrm{SNR}<100$), the influence of the background cannot be neglected.
On average, the amplitude of the measured signal is higher than the amplitude of the true one, and the average fraction between them is expressed as ${\mathcal{E}_\mathrm{t} = \mathcal{E}_\mathrm{m}\sqrt{1 - k/\mathrm{SNR}}}$, where $k$ is a constant, which depends on the definition of SNR.
However, this amplitude can be lower, since the background is uncorrelated with the signal~\cite{Allan:1970xr,Schroeder2012S238}.
In this year we started the investigation of the applicability of neural networks for the signal reconstruction.
We designed a neural network, which gets input traces of 200 counts and predicts the amplitude of the true signal.
We prepared a dataset of about 10000 events, randomly divided in two parts, and used the first one for the training and the second one for the control check.
The control check has shown that the resolution of amplitude reconstruction is about 22\%, which corresponds our standard reconstruction for signals near threshold.
Thus, further investigations are required before this neutral-network approach can be implemented in our standard reconstruction.
\section{Conclusion}
The Tunka Radio Extension is a modern experiment which measures radio emission from air-showers induced by primary cosmic rays with energies above 100~PeV.
Tunka-Rex has proven the feasibility and competitiveness of the radio detection technique.
Operated as a sparse array with spacing of about 200~m between antennas, it has reached a precision of 15\% and 40~g/cm\textsuperscript{2} for the primary energy and the depth of the shower maximum, respectively.
After being upgraded during the last two yeas, Tunka-Rex has now reached triple of its original density and a new trigger from the recently deployed scintillator array Tunka-Grande has been implemented.
This increases the operation time and quality of events, e.g. we now expect more than 1000 events per year instead of about 100 during the first stages of operation.
\section*{Acknowledgements}
The construction of Tunka-Rex was funded by the German Helmholtz association and the Russian Foundation for Basic Research (grant HRJRG-303).
Moreover, this work has been supported by the Helmholtz Alliance for Astroparticle Physics (HAP), by Deutsche Forschungsgemeinschaft (DFG) grant SCHR 1480/1-1, and by the Russian grant RSF 15-12-20022.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,921 |
\section{INTRODUCTION}
In theory of linear algebra, the general problem of the classification of the
\emph{integral matrices} which have simpler decompositions is the key in many
theoretical and applied fields. In this paper, we intend to find the \emph{lower-triangular} decomposition for
some new kind of matrices which we call them \emph{matrices with
vertically recurrence relation} into Toeplitz block matrices.
\\
Fortunately, several interesting classes of the integer-valued Toeplitz matrices can be
nicely factorized into Pascal matrices [3]. The important point in finding this matrix decomposition is the well-known property of the Pascal triangle which is called \emph{the
hockey stick and puck theorem}. Using the generalization of the
above theorem, one can construct a new linearly recurrence
relation which we call it the \emph{generalized hockey stick and puck}
theorem. This later one is the principle of the \emph{multiplicative
decomposition}
of the above matrices .\\
In section $2$, we start by the definition of the matrix with
\emph{vertically-recurrent} relation associated with the sequence
$\Lambda=\{ \lambda_{n} \}_{n\geq 0}$, then we investigate some of
it's properties, specially its multiplicative decomposition and
also we find its inverse matrix. In section $3$, we deal with the
power of this matrix and find it's associated sequence $\Lambda=\{
\lambda_{n} \}_{n\geq 0}$. Furthermore, we present two important
applications of this new kind of matrix for factorization of
\emph{admissible matrices} and in \emph{ladder networks}. Finally, we propose
some open problems and conjectures about these matrices.
\newpage
\section{The Vertically-Recurrent Matrices}
We start by motivating the main idea behind these new \emph{integral} matrices. Consider
the two dimensional
\emph{linear recurrence} relation
among entries of the well-known \emph{Pascal's triangle}, as follows
$$
\begin{array}{ccc}
\overset{\bf u}{\bullet}&&\overset{\bf v}\bullet \\\\
& &\overset{\bf w}\bullet
\end{array}
$$
\begin{center}
Figure 1. $ w=u+v $
\end{center}
Now if we consider the two consecutive columns of the left-justified Pascal's
triangle; i.e,. the $k-1$ and the $k$th columns, we have
$$
\begin{array}{ccc}
\overset{\bf u_l}\bullet&&\\
\overset{\bf u_{l-1}}\bullet&&\overset{\bf v_{l-1}=w_{l-1}}\bullet\\
\overset{\bf u_{l-2}}\bullet&&\overset{\bf v_{l-2}=w_{l-2}}\bullet\\
\vdots &&\vdots\\
\overset{\bf u_2}\bullet&&\overset{\bf v_2=w_2}\bullet\\
\overset{\bf u_1}\bullet&&\overset{\bf v_1=w_1}\bullet\\
&&\overset{\bf w=w_0}\bullet\\
\end{array}
$$
\begin{center}
Figure 2. Hockey Stick and Puck Theorem
\end{center}
Therefore, at any step, after computing the $w_i$'s with respect
to $u_i$'s and $v_i$'s, fix the $u_i$ and just rewrite $v_i$, as
the
next $w_i$, with respect to $u_{i+1}$ and $v_{i+1}$. Continuing this
process until to get the main diagonal. It can be easily seen that $w$ is
expressible as the sum of the entries $u_1,u_2,\ldots,u_l$. More precisely, we have
\begin{eqnarray}
w_0=w&=&u_1+v_1\nonumber\\
w_1=v_1&=&u_2+v_2\nonumber\\
&\vdots&\nonumber\\
w_{l-2}=v_{l-2}&=&u_{l-1}+v_{l-1}\nonumber\\
w_{l-1}=v_{l-1}&=&u_{l}\nonumber
\end{eqnarray}
and consequently,
\begin{equation}\label{2}
w=u_1+u_2+\cdots+u_l.
\end{equation}
Now, if we translate the above relation into the language of recurrence relations, we
obtain
\begin{equation}\label{Vert-Rec1}
a_{n,k}=\sum_{l=k-1}^{n-1}{a_{l,k-1}},\hspace{0.5cm} (n \geq k \geq 1).
\end{equation}
The above equality is known as the \emph{vertically-recurrent} relation.
In special case for the left-justified Pascal's triangle; that is
$a_{n,k} ={n-1 \choose k-1}$,
we get the well-known \emph{hockey stick
and puck} theorem [4] as follows ( see Figure 2 )
\begin{equation}
{n\choose k}=\sum_{l=k-1}^{n-1}{{l\choose k-1}},\hspace{1cm}
(n \geq k \geq 1).
\end{equation}
Thus, it is natural to generalize the relation (\ref{Vert-Rec1}) associated
with an arbitrary sequence $\Lambda=\{\lambda_n \}_{n\geq0 }$,
$\lambda_0=1$, as follows:
\begin{equation}\label{GenVertRec1}
a_{n,k}=\sum_{l=k-1}^{n-1}{\lambda_{n-1-l}a_{l,k-1}},\hspace{1cm}
(n \geq k\geq 1).
\end{equation}
We call the equation (\ref{GenVertRec1}) \emph{the generalized hockey stick and
puck theorem} . Now we are at the position to define our new class of matrices that we call them \emph{vertically-recurrent} matrices.
\\
For combinatorial reasons, we mainly concentrate on the class of matrices in which their associate sequences have only integer values.
\begin{defn}
Suppose $n$ and $k$ are positive integers. We define the
\emph{vertically-recurrent} matrix
$V_{n}[{\bf \Lambda}]$
associated with the sequence
${\bf \Lambda}=\{\lambda_n \}_{n\geq0 }$ , $\lambda_0=1$, of order
$(n+1)\times(n+1)$ in the following form:
$$
(V_{n}[{\bf \Lambda}])_{ij}= \left\{
\begin{array}{ccc}
\lambda_{i} &\hspace{1cm}\mbox{if\ } i\geq0, j=0, \\
a_{i,j}&\hspace{1cm}\mbox{if\ } j\geq i \geq 1,\\
0 &\hspace{.4cm}\mbox{if\ } i<j,
\end{array}
\right.
$$
in which the entries $a_{i,j}$'s satisfy the relation (\ref{GenVertRec1}).
\end{defn}
\begin{exmp}
For ${\bf\Lambda}=\{\lambda_{n}=1\}_{n\geq0}$, we have:\\
$$V_{3}[{\bf \Lambda}]= \left[
\begin{array}{cccc}
1 & 0 & 0 & 0\\ 1 &1& 0 & 0\\ 1 & 2 &1& 0\\1 &3&3&1
\end{array}
\right],
$$
\\
where the above matrix is call the Pascal matrix $P_{n}$, for
$n=3$
(see [5]).
\end{exmp}
\begin{exmp}
For ${\bf\Lambda}=\{\lambda_{n}=2^n\}_{n\geq0}$, we have:\\
$$ V_{3}[{\bf \Lambda}]= \left[
\begin{array}{cccc}
1 & 0 & 0 & 0\\ 2 &1& 0 & 0\\ 4 & 4 &1& 0\\8 &12&6&1
\end{array}
\right].
$$
\\
We note that the above matrix is the
\emph{Pascal functional matrix} $P_n[x]$
for $n=3$ and $x=2$ (see \cite{m4}).
\end{exmp}
Next, we start to obtain a \emph{multiplicative decomposition} of
$V_{n}[{\bf \Lambda}]$. To do this, we first define the lower
triangular \emph{Teoplitz} matrix by $T_n[{\bf
\Lambda}]=[\lambda_{i-j}]_{0\leq i\leq j\leq n}$ and the
Teoplitz-block
matrix $\overline{T}_{k}[{\bf \Lambda}]$, as follows\\
\begin{eqnarray}
\overline{T}_{k}[{\bf \Lambda}]=\left[
\begin{array}{cccc}
I_k&0\\
0&T_{n-k}[{\bf \Lambda}]
\end{array}\right].\nonumber
\end{eqnarray}
By convention, $\overline{T}_{0}[{\bf \Lambda}]= T_n$ and
$\overline{T}_{n}[{\bf \Lambda}]= I_{n+1}$, where $I_{n+1}$ is the
identity matrix of order $n+1$.
\begin{thm}\label{MultDecomp1}
Suppose $n$ is a natural number. Then, we have
$$
V_{n}[{\bf \Lambda}]= T_{n}[{\bf \Lambda}]([1]\oplus V_{n-1}[{\bf
\Lambda}]),
$$
in which the symbol $\oplus$ denotes the direct sum of two
matrices.
\end{thm}
\begin{proof}
For each $i$ and $j$ with $i\geq j\geq0$, since the $(i,j)$-entry
of $[1]\oplus V_{n-1}[{\bf \Lambda}]$ is $(V_{n}[{\bf
\Lambda}])_{i-1,j-1}$, from the definition of matrix product and
the relation (0.4), we get
\begin{eqnarray}
(T_{n}[{\bf \Lambda}]([1]\oplus
V_{n-1}[{\bf \Lambda}]))_{i,j}
&=&\sum_{l=j}^{i}(T_{n}[{\bf \Lambda}])_{i,l}(V_{n}[{\bf \Lambda}])_{l-1,j-1}\nonumber\\
&=&\sum_{l=j-1}^{i-1}(T_{n}[{\bf \Lambda}])_{i,l+1}(V_{n}[{\bf \Lambda}])_{l,j-1}\nonumber\\
&=&\sum_{l=j-1}^{i-1}\lambda_{i-l-1}a_{l,j-1}\nonumber\\
&=&a_{i,j}=(V_{n}[{\bf \Lambda}])_{i,j}\nonumber
\end{eqnarray}
\end{proof}
Now, as an immediate consequence of Theorem \ref{MultDecomp1}, we have the
following results:
\begin{cor}
~\vspace{.2cm}
\begin{itemize}
\item[(i).] $V_{n}[{\bf \Lambda}]=\overline{T}_{n}[{\bf
\Lambda}]\overline{T}_{n-1}[{\bf
\Lambda}]\cdots\overline{T}_{1}[{\bf \Lambda}].$
\item[(ii).]$
V_{n}^{-1}[{\bf\Lambda}]=\overline{T}_{1}^{-1}[{\bf
\Lambda}]\overline{T}_{2}^{-1}[{\bf
\Lambda}]\cdots\overline{T}_{k}^{-1}[{\bf \Lambda}].$
\end{itemize}
\end{cor}
In [3], the Teoplitz matrices with
\emph{integer entries} are
investigated. Considering these matrices, we can calculate the
inverse of $\overline{T}_{n}[{\bf \Lambda}]$ by means of the
Pascal functional matrices [3] in some important special
cases. We leave the general case as an open question.\\
{\bf Case 1}. Let ${\bf\Lambda}=\{\lambda_n=\lambda\}_{n\geq0}$, then we
clearly have
\begin{equation}
\overline{T}_{n}[{\bf\Lambda}]=\lambda S_n[1],
\end{equation}
where
$$
(S_n[x])_{ij}= \left\{
\begin{array}{cc}
x^{i-j} &\hspace{.5cm}\mbox{if\ } i\geq j\geq0, \\
0&\hspace{.1cm}\mbox{if\ } i<j.
\end{array}
\right.
$$
We also have $S_n[x]=P_{n,1}[x]P_n[-x]$, in which the matrices
$P_n[x]$ and $P_{n,1}[x]$ are Pascal functional and Pascal
k-eliminated functional matrices, respectively [5,6]. Thus, we get
$$
T_{n}[{\bf\Lambda}]=\lambda P_{n,1}[1]P_n[-1].
$$
{\bf Case 2}. Let ${\bf\Lambda}=\{\lambda_n=\lambda^{n}\}_{n\geq0}$. Now,
it is clearly the generalization of the above case, since in this
case $T_n[{\bf\Lambda}]=S_n[\lambda]$ and consequently
$$
T_n[{\bf\Lambda}]=
P_{n,1}[\lambda]P_n[-\lambda].
$$
\section{The Powers of Vertically-Recurrent Matrices}
If we consider the Pascal functional matrix for the values
$1,2,\ldots,l$, then we observe that all of these matrices are
\emph{vertically-recurrent}. Indeed, for
$P_n[l]$ in general, the associated sequence is
${\bf\Lambda}=\{\lambda_n=l^n\}_{n\geq0}$. On the other hand, we
know that the Pascal matrix $P_n[x]$ has an exponential property
(see [5]) therefore the matrix $P_n[l]$ is just the $l$-th power
of the matrix $P_n[1]$. For the above reason, the following challenging
question naturally arises in the context of vertically-recurrent matrices.
\begin{quote}
\emph{If the associated sequence of the matrix $V_n[{\bf\Lambda}]$
is ${\bf\Lambda}=\{\lambda_n\}_{n\geq0}$, then what is the
associated sequence of the matrix $(V_n[{\bf\Lambda}])^m$ with
respect to the sequence $\lambda_n$?}
\end{quote}
In general case ${\bf\Lambda}=\{\lambda_n\}_{n\geq0}$, the above
question is a very challenging problem but we have given an affirmative
answer to some special and interesting cases.
\\
{\bf Case1}. Suppose $V_n[{\bf \Lambda}]$ is a matrix with
constant associated sequence
${\bf\Lambda}=\{\lambda_n=\lambda\}_{n\geq0}$. We have the
following interesting result.
\begin{prop}
{Let $V_n[{\bf\Lambda}]$ be a vertically-recurrent matrix
with its associated sequence ${\bf\Lambda}=\{\lambda_n = \lambda \}_{n\geq0}$. Then,
the associated sequence of $(V_n[{\bf\Lambda}])^m$ is
$\lambda^m(\frac{\lambda^m-1}{\lambda-1})^{n}$}
\end{prop}
\begin{proof}
{The above statement is equal to prove that the recurrence
relation for entries of $(V_n[{\bf\Lambda}])^m$ is, as follows: }
\end{proof}
\begin{equation}
a_{n,k}=\lambda^m a_{n-1,k-1}+(\frac{\lambda^m-1}{\lambda-1})^n
a_{n-1,k}.
\end{equation}
Since, considering the above identity and mathematical induction
we are able to prove,
$$
a_{n,k}=\sum_{k-1}^{n-1}\big[\lambda^m(\frac{\lambda^m-1}{\lambda-1})\big]^{n-1-l}a_{l,k-1},
$$
Namely, $\lambda^m(\frac{\lambda^m-1}{\lambda-1})^n$ is the
associated sequence for $(V_n[\Lambda])^m$. For proving the
equivalence statement we just need to consider the following
result from [7].
\begin{lem}
Suppose $\alpha, \alpha', \beta$, $\beta'$ are four real numbers.
Also let $A=[a_{ij}]$, $B=[b_{ij}]$ be two lower triangular
matrices where their entries satisfy the following recurrence relations
respectively,
\begin{eqnarray}
&&\left\{
\begin{array}{cc}
a_{n,k}=\alpha a_{n-1,k-1}+\beta a_{n-1,k},&~~~(n\geq k\geq1),\\
a_{n,0}=1& n\geq 0,\\
a_{n,k}=0 & k>n,
\end{array}
\right.\\
&&\left\{
\begin{array}{cc}
b_{n,k}=\alpha' b_{n-1,k-1}+\beta' b_{n-1,k},&~~~(n\geq k\geq1),\\
b_{n,0}=1&n\geq 0,\\
b_{n,k}=0 &k>n.
\end{array}
\right.
\end{eqnarray}
{\it If $AB=[c_{ij}]$ then, there are real numbers
$\alpha''=\alpha\alpha'$ and $\beta''=\beta+\alpha\beta'$, such
that }
\begin{eqnarray}
\left\{
\begin{array}{cc}
c_{n,k}=\alpha'' c_{n-1,k-1}+\beta'' c_{n-1,k},&(n\geq k\geq1),\\
c_{n,0}=\sum_{i=0}^{n}a_{n,i}&n\geq 0,\\
\hspace{-.8cm}c_{n,k}=0~~~~ &k>n.
\end{array}
\right.
\end{eqnarray}
\end{lem}
\begin{proof}
Let $C=AB=[c_{n,k}]$. By the definition of the product of two matrices, we conclude that
$
c_{n,k} = \sum_{l=k}^{n} a_{n,l} b_{l,k} ~(n\geq k \geq 1)
$
. Hence, this immediately implies that
$
c_{n,0} = \sum_{l=0}^{n} a_{n,l} b_{l,0} =
\sum_{l=0}^{n} a_{n,l} ~ (n\geq 0)
$
and
$
c_{n,k} = 0~(k > n)
$
.
Moreover, we have
\begin{equation}\label{keyrec1}
c_{n-1,k-1} =
\sum_{l=k-1}^{n-1} a_{n-1,l} b_{l,k-1}, ~~~
c_{n-1,k} =
\sum_{l=k}^{n-1} a_{n-1,l} b_{l,k}.
\end{equation}
Put
$
I_{n,k} = \alpha \alpha^{'} c_{n-1,k-1} + (\beta + \alpha \beta^{'})
c_{n-1,k}
$
. Then, we have
\begin{eqnarray}
I_{n,k} & = & \alpha \alpha^{'} \sum_{l=k-1}^{n-1} a_{n-1,l} b_{l,k-1} + (\beta + \alpha \beta^{'})
\sum_{l=k}^{n-1} a_{n-1,l} b_{l,k}, \nonumber\\
& = &
\Bigg[
\alpha \alpha^{'} \sum_{l=k-1}^{n-1} a_{n-1,l} b_{l,k-1}
+ \alpha \beta^{'} \sum_{l=k}^{n-1} a_{n-1,l} b_{l,k}
\Bigg] \nonumber\\
& + & \beta \sum_{l=k}^{n-1} a_{n-1,l} b_{l,k}, \nonumber\\
& = & \alpha
\Bigg[
\sum_{l=k}^{n-1} a_{n-1,l}
\Big( \alpha^{'} b_{l,k-1}
+ \beta^{'} b_{l,k} \Big) + a_{n-1,k-1} b_{k-1,k-1}
\Bigg] \nonumber\\
& + & \beta \sum_{l=k}^{n-1} a_{n-1,l} b_{l,k}, \nonumber\\
& = & \alpha \Bigg[ \sum_{l=k}^{n-1} b_{l+1,k} + a_{n-1,k-1}
a_{n-1,k-1} \Bigg] \nonumber\\
& + & \beta \sum_{l=k+1}^{n} a_{n-1,l} b_{l,k} +
\beta \Big( a_{n-1,k-1} b_{k,k} - a_{n-1,n} b_{n,k} \Big)
\nonumber\\
& = & \sum_{l=k+1}^{n}
\Big(
\alpha a_{n-1,l-1} + \beta a_{n-1,l}
\Big) b_{l,k} +
\Big(
\alpha a_{n-1,l-1} + \beta a_{n-1,k}
\Big) \nonumber\\
& = &
\sum_{l=k+1}^{n} a_{n,l} b_{l,k} + a_{n,k} \nonumber \\
& = & \sum_{l=k}^{n} a_{n,l} b_{l,k}=c_{n,k}, \nonumber
\end{eqnarray}
as required.
\end{proof}
Now the equivalence statement is easily proved considering the
above lemma and the mathematical induction.
\\
{\bf Case2.} $\lambda_n=\lambda^n$. In this case, we use the above
lemma again to obtain the following theorem,
\begin{thm}
{Let $V_n[\Lambda]$ be a matrix with vertically recurrent relation
and it's associated sequence $\lambda_n=\lambda^n$. Then, the
associated sequence of $(V_n[\Lambda])^m$ is}
\end{thm}
\begin{equation}
\lambda_n=(\lambda{m})^n.
\end{equation}
\begin{proof}
Considering the same argument in theorem $0.4$, It is necessary to
prove the following recurrent relation for $(V_n[\Lambda])^m$:
$$
a_{n,k}=a_{n-1,k-1}+(2m)\lambda a_{n-1,k}.
$$
But, applying the lemma $0.5$, it is just necessary to prove the
special case $m=1$. Namely, $$a_{n,k}=a_{n-1,k-1}+2\lambda
a_{n-1,k},$$\\
Now it can be easily seen that,
$$a_{n,k}=\sum_{k-1}^{l-1}(2\lambda)^{n-1-l}a_{l,k-1}$$
\end{proof}
\section{Applications}
In this section, we present two applications of vertically-recurrent matrices in
the area of \emph{integral matrices} and
\emph{electrical engineering}
.
\\
As our first application, we mention an interesting class of integral matrices which are called \emph{admissible matrices}.
To do so, we consider infinite matrices $A=(a_{n,k})$, indexed by
$\{0,1,2,\ldots\}$, and denote it by $r_m=\{a_{m,0},a_{m,0},\ldots\}$
the $m$th row.
\begin{defn}
$A=(a_{n,k})$ is called admissible [8] if
\begin{enumerate}
\item
$a_{n,k}=0$
for $n<k$, $a_{n,n}=1$ for all $n$ (that is, $A$ is lower
triangular with main diagonal equal to $1$).
\item
$r_m.r_n=(a_{m+n,0})$ for all $m,n$, where
$r_m.r_n=\sum_{k}a_{mk}a_{nk}$ is the usual inner product.
\end{enumerate}
\end{defn}
Here, we consider some few examples of these matrices and show
that they are indeed vertically-recurrent matrices.
\\
An interesting theorem in [8], states that all admissible matrices
are characterized by sequence $s_0=b_0$; $s_n=b_n-b_{n-1}, n\geq1$
in which $b_{n}=a_{n+1,n}$. Thus, any sequence
$s=\{s_0,s_1,\ldots,s_n,\ldots\}$ will present an admissible
matrix $A=(a_{n,k})$.
\begin{prop}
Let $A=(a_{n,k})$ ba an \emph{admissible} matrix with $a_{n+1,n} = b_{n}$ for all $n$.
Set $s_{0} = b_{0}$, $s_{1} = b_{1} - b_{0}, \ldots, s_{n} = b_{n} - b_{n-1}, \ldots$. Then, we have
\begin{eqnarray}\label{keyadmis1}
a_{n,k} & = & a_{n-1,k-1} + s_{k} a_{n-1,k} + a_{n-1,k+1} \hspace{0.5cm} (n\geq 1) \nonumber\\
a_{0,0} & = & 1, \hspace{1cm} a_{0,k} = 1 \hspace{0.5cm} \textit{for} ~~~(k>0).
\end{eqnarray}
Conversely, if $a_{n,k}$ is given by
the recursion (\ref{keyadmis1}),
then $(a_{n,k})$ is an \emph{admissible} matrix
with $a_{n+1,n} =
s_{0} + \cdots + s_{n} $.
\end{prop}
For example the corresponding admissible
matrix for sequence $s=\{1,1,1,\ldots\}$ is
$$
\left[
\begin{array}{ccccc}
1 & 0 & 0 & 0&0\\ 1 &1& 0 & 0&0\\ 2 & 2 &1& 0&0\\4
&5&3&1&0\\9&12&9&4&1
\end{array}
\right],
$$
and for the sequence $s=\{1,2,2,\ldots\}$ is
$$
\left[
\begin{array}{ccccc}
1 & 0 & 0 & 0&0\\ 1 &1& 0 & 0&0\\ 2 & 3 &1& 0&0\\5
&9&5&1&0\\14&28&20&7&1
\end{array}
\right].
$$
Clearly the first matrix is a vertically recurrence matrix with
associated sequence $\mathbf{\Lambda}=\{1,1,2,4,9,\ldots\}$ and the second
one with $\mathbf{\Lambda}=\{1,2,5,14,\ldots\}$ and these are just the
first columns of the above matrices.
\section{Ladder Networks}
The transfer ratio $T_k~ (k=0, 1, 2, \ldots, n)$ of the output to
input signal (voltage or current) along the network (Figure $3$) is
determined by a polynomial in $x$ of the corresponding degree, in
which $x$ determined by the product of impedance of a longitudinal
branch and
admittance of transversal branch [9]. \\
It can be determined from a solution of the following recurrence
equation,
\begin{eqnarray}
& & a_{k+1}-(2+x)a_k+a_{k-1}=0; \nonumber\\
& & a_1=(1+x)a_0,
\end{eqnarray}
where $a_0$ denotes a known signal at the input port of the first
cell and $a_k$ is the corresponding signal at the k-port of the
network (e.g., $a_k=V_k$ as shown in Figure $3$).
$$
\unitlength 1mm \linethickness{0.4pt}
\begin{picture}(200.33,35.67)
\put(9.00,10.33){\line(1,0){111.00}}
\put(16.67,12.50){\line(0,-1){2.4}}
\put(14.33,12.67){\framebox(5.00,11.67)[cc]{Y}}
\put(34.33,12.20){\line(0,-1){1.9}}
\put(31.67,12.33){\framebox(5.00,11.67)[cc]{Y}}
\put(51.2,12.50){\line(0,-1){2.4}}
\put(48.67,12.67){\framebox(5.00,11.67)[cc]{Y}}
\put(70.2,12.50){\line(0,-1){2.4}}
\put(67.67,12.67){\framebox(5.00,11.67)[cc]{Y}}
\put(83,12.5){\line(0,-1){1.9}}
\put(80.33,12.33){\framebox(5.00,11.67)[cc]{Y}}
\put(97.8,10.33){\line(0,1){1.7}}
\put(95.00,12.33){\framebox(5.00,11.67)[cc]{Y}}
\put(111.00,10.33){\line(0,1){1.9}}
\put(108.67,12.33){\framebox(5.00,11.67)[cc]{Y}}
\put(119.67,10.33){\line(1,0){16.33}}
\put(127.5,10.33){\line(0,1){1.5}}
\put(125.00,12.00){\framebox(5.00,11.67)[cc]{Y}}
\put(16.67,24.5){\line(0,1){3}} \put(9.3,27.33){\line(1,0){10.8}}
\put(20.33,25.00){\framebox(9.33,4.33)[cc]{Z}}
\put(34.67,27){\line(0,-1){2.8}} \put(30,27.00){\line(1,0){8.5}}
\put(38.67,25){\framebox(8.33,4.33)[cc]{Z}} ~
\put(47.00,27.00){\line(1,0){10.2}}
\put(51,27){\line(0,-1){2.8}}
\put(57.33,25){\framebox(8.33,4.33)[cc]{Z}}
\put(70,27){\line(0,-1){2.6}}
\put(65.67,27){\line(1,0){20}}
\put(86.00,25.00){\framebox(8.33,4.33)[cc]{Z}}
\put(94.33,27.00){\line(1,0){20.00}}
\put(82.67,24){\line(0,1){3}}
\put(114.33,25){\framebox(8.33,4.33)[cc]{Z}}
\put(122.67,27){\line(1,0){14.67}}
\put(8.33,27.3){\circle*{2}}
\put(8.00,10.00){\circle*{2}} \put(136.67,10.00){\circle*{2}}
\put(136.33,27.3){\circle*{2}} \put(97.50,24){\line(0,1){3}}
\put(111.50,24){\line(0,1){3}} \put(127.5,24){\line(0,1){3}}
\put(7.67,12.00){\vector(0,1){12.67}}
\put(39.00,11.00){\vector(0,1){11.33}}
\put(56.00,11.33){\vector(0,1){11.33}}
\put(74.33,11.67){\vector(0,1){11.33}}
\put(102.00,11.67){\vector(0,1){11.33}}
\put(136.67,12.33){\vector(0,1){12.67}}
\put(15.5,28.67){\mbox{$0$}}
\put(33.67,28.33){\mbox{$1$}}
\put(50.00,28.00){\mbox{$2$}}
\put(69.33,27.67){\mbox{$3$}}
\put(77.67,27.67){\mbox{$k-1$}}
\put(97.00,28.00){\mbox{$k$}}
\put(106.33,27.67){\mbox{$n-1$}}
\put(125.67,27.33){\mbox{$n$}}
\put(132.33,15.67){\mbox{$V_n$}}
\put(103.33,15.00){\mbox{$V_k$}}
\put(76.00,14.00){\mbox{$V_3$}}
\put(58.00,13.67){\mbox{$V_2$}}
\put(41.00,12.67){\mbox{$V_1$}}
\put(9.00,13.67){\mbox{$V_0$}}
\end{picture}
$$
\begin{center}
{\bf Figure 3}. Electrical Ladder Network
\end{center}
The ratio $T_k$ follows from the relation
$$
T_k=\frac{a_k}{a_0},~~ k=0, 1, 2, \ldots, n.
$$
It is easy to see that $T_k$ is determined by a polynomial in $x$
of the $k$th degree, so we can write
$$
T_k=\sum_{m=0}^{k}p_{k,m}x^{m},~~ k=0, 1, 2, \ldots, n.
$$
\\
From the direct inspection of the above expression, we have that
\begin{align*}
T_0&=1,\\ T_1&=1+x,\\T_2&=1+3x+x^2,\\T_3&=1+6x+5x^2+x^3,\\
T_4&=1+10x+15x^2+7x^3+x^4,\\T_5&=1+15x+35x^2+28x^3+9x^4+x^5.
\end{align*}
Now, if we define the matrix $MNT$, \emph{modified numerical
triangle} [9], as follows
$$
(MNT)_{ij}=\left\{
\begin{array}{cc}
p_{i,j} & i\geq j\geq0;\\
0& i<j,
\end{array}
\right.
$$
it is not hard to prove (by mathematical induction) that
the entries $p_{n,k}$'s have the
following formula
\begin{equation}
p_{n,k} = {n+k \choose 2k+1}, \hspace{0.5cm} (n \geq k \geq 0).
\end{equation}
Then, we observe that the above array is a vertically-recurrent matrix with associated sequence
$\Lambda=\{\lambda_{n}=n+1\}$.
Indeed, it is equivalent to prove
the following \emph{binomial identity}:
\begin{equation}
{n+k \choose 2k+1} =
\sum_{l=k-1}^{n-1}
{n-l \choose 1}{l+k-1 \choose 2k-1}
\hspace{0.5cm} (n\geq k \geq 1).
\end{equation}
For example
$$
\left[
\begin{array}{cccc}
1 & 0 & 0 & 0\\ 1 &1& 0 & 0\\ 1 & 3 &1& 0\\1 &6&5&1
\end{array}
\right]=\left[
\begin{array}{cccc}
1 & 0 & 0 & 0\\ 1 &1& 0 & 0\\ 1 & 2 &1& 0\\1 &3&3&1
\end{array}
\right]\left[
\begin{array}{cccc}
1 & 0 & 0 & 0\\ 0 &1& 0 & 0\\ 0 & 0 &1& 0\\0 &0&2&1
\end{array}
\right]\left[
\begin{array}{cccc}
1 & 0 & 0 & 0\\ 0 &1& 0 & 0\\ 0 & 0 &1& 0\\0 &0&0&1
\end{array}
\right]
$$
It is interesting to note that one can observe that there is also another modified triangle that
we denote it by
$MNT_{2}$ which can be defined, as follows
\begin{equation}
(MNT_{2})_{ij}=\left\{
\begin{array}{cc}
{i+2j \choose 3j+1} & i\geq j\geq0;\\
0& i<j,
\end{array}
\right.
\end{equation}
Now, it is easy to see that $MNT_{2}$ is also a vertically-recurrent
matrix with associate sequence
$
\mathbf{\Lambda} = \{
\lambda_{n} = {n+2 \choose 2}
\}_{n\geq 0}
$
.
Indeed, this claim is equivalent to prove the following combinatorial
identity:
\begin{equation}
{n+2k \choose 3k+1} =
\sum_{l=k-1}^{n-1}
{n-l+1 \choose 2}
{l+2k-2 \choose 3k-2}
\hspace{0.5cm} (n\geq k \geq 1).
\end{equation}
\section{Open Problems and Conjectures}
Considering the previous discussions, we pose the following open
problems and conjectures.
\begin{oprob}
Consider the matrix with vertically recurrence relation
$V_n[\Lambda]$ with associated sequence
$\Lambda=\{\lambda_n\}_{n\geq0}$. Find the associated sequence of
the matrix $(V_n[\Lambda])^m$ with respect to the sequence
$\lambda_n$.
\end{oprob}
\begin{oprob}
For any matrix with vertically recurrence sequence $V_n[\Lambda]$
with associated sequence $\Lambda=\{\lambda_n\}_{n\geq0}$
($\lambda_n\in \mathbb{Z};\hspace{.5cm}n=0,1,2,\cdots$), find it's
minimal polynomial in the field of $\mathbb{Z}_{p}$ (see [10]).
\end{oprob}
Let $A=[a_{n,k}]$ be an integral arrays (array with only integer entries) which can be defined recursively, as follows
\begin{eqnarray}
&&\left\{
\begin{array}{cc}
a_{n,k}=\alpha a_{n-1,k-1}+\alpha_{n-1} a_{n-1,k},&~~~(n\geq k\geq1),\\
a_{n,0}=1& n\geq 0,\\
a_{n,k}=0 & k>n,
\end{array}
\right.
\end{eqnarray}
We also come up with the following conjectures.
\begin{conj}
The triangular array $A=[a_{n,k}]$ is a vertically-recurrent matrix with associated sequence
$
\lambda_0 =1
$
and
$
\lambda_{i} = \prod_{j=i}^{n} \alpha_{j}
$
.
\end{conj}
\begin{conj}
The \emph{Catalan} array $C_{n}$ is a vertically-recurrent
matrix.
\end{conj}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,662 |
Multiple OHIO Sightings
Upturn in HOTLINE incomings
SUMMARY UPDATE
Kenny Young
In the days after taking a number ofunusual rumors and odd reports of strange activity from the northeasternOhio area in the last week of September, UFO sighting reports have continued.While future updates are pending on a report that North Olmsted policeofficers have taken a sequence of unusual UFO photographs, a femaletalk-show radio host from Case Western Reserve University has reportedhaving several photographs of a two tube-shaped or blimp-like objects seenin the Cleveland area surrounded by approaching jets. One of the objectsreportedly 'vanished' while under observation. Evaluation of these photosare pending.
Separately, incoming UFO sighting reportswere received by the Cincinnati UFO Hotline at a frequency and rate thatwas felt to be of some surprise; one report of a female caller claimingtwo witnesses to mutli-colored, lighted objects visually spied near Westfield,Indiana in late September. Another caller reported three witnesses to anobject near Tiffin, Ohio, while other callers reporting unusual activityin Southern Ohio along the I-75 corridor from Dayton south to Springboro/Franklin.
At 10:22 p.m. on Thursday evening, Oct.7, 2004, a female caller to the Cincinnati UFO Hotline (513-588-4548) soughtto report unusual lights seen near Springboro, Ohio. The witness was contactedaround 10:30 p.m. and said that the sighting took place around 2-hoursearlier, about 8:30 p.m.
She said that while riding as a passengerin a car near Springboro, Ohio, driving on Clearcreek / Franklin Road andcrossing a bridge over Interstate-75, she looked to the south in the vicinityof Middletown and spotted 1 very bright light. She sid this was a hugelight, yellowish orange in color and composed of two smaller lights insideof the bright light. The object hovered for what she thought could havebeen two minutes with no motion detected as she observed it. She said thedriver did not see the object nor did she mention it until the object 'dimmedout' and vanished completely.
"I should think that other people sawthis," she said, while adding that it was seen over I-75 to the south ofher location. The object was seen clearly and estimated to be lower thanan airplane. There were no trees obstructing her view and the object wasseen out over the open highway, causing her to believe there would be otherwitnesses.
The witness thought to have seen thesame thing about a month ago in the same area, and at that point gatheredsome information online about earlier sightings near Springboro.
"This was some kind of huge light andit wasn't a plane," she said. "plane lights just don't 'go out' and thelights were much larger than lights on a plane.
The witness said that she lives nearthe Wright Brothers Airport and easily recognizes airplane headlights.
A second report of UFO activity fromthe Southern Ohio area was received by a man from the Dayton, Ohio area.
A retired policeman contacted the CincinnatiUFO Hotline (513-588-4548) to report a UFO sighting. The 51-year old officer,who had spent 21-years on force, called to report observing a red and bluelight source that had appeared in Dayton, Ohio skies at least 2 nightsin a row.
The object was first seen beginningearly during the morning of October 4 around 2:30 a.m., first observedto the east of his residence. The officer said that the object held a fixedposition in this same location until at least 4:30 a.m. when he quit watching,having gone to bed. The officer said that again the next morning (Oct.5th), the object had reappeared in the same place and at that point, heguessed it to be a star.
However, the officer said that on thethird morning of October 6th, the object was not there in the same locationat the same time of day, nor was it there last night or this evening. Heaffirmed that he has been looking in the same place at the same time ofday.
The retired officer lives on east endof Dayton, the object was viewed on the two consecutive nights in the easternskies from 2:30 a.m., viewed near the WHIO TV tower on Wilmington Pike,to the east of his vantage point.
He characterized the object as a blueand red light source that held an estimated 400 foot elevation. The objectseemed to flicker like a star, but was lower than any other star and muchlarger. He said it almost appeared to rotate. He attempted to view theobject through binoculars on the second night but could not ascertain anydetail, guessing it to be holding position at some distance.
On Sunday, October 10, a man near Ft.Wayne, Indiana videotaped something in the sky The object, according toUFO researcher Roger Sugden, had a sound explanation. It was an airplane.However, an Assistant Professor of Geosciences as IPFW and an astronomerat the Ft. Wayne Astronomical Society weren't so sure, offering quite differentexplanations. Those stories can be viewed at the following links:
https://www.firstcoastnews.com/news/usworld/news-article.aspx?storyid=25686
https://www.wishtv.com/global/story.asp?s=2416065&ClientType=Printable
'UFO' Spotted Near Fort Wayne
Fort Wayne - A resident here got outhis video camera and caught an object moving through the sky at a highrate of speed on Sunday.
Brandon McBroom used the family videocamto tape a strange looking object in the Sunday sky. He pulled overin the Croninger Elementary parking lot and pointed the camera north-northwest.
WANE-TV took the tape around town Mondayto the experts. "That's not a meteor. It's too slow," said Roger Sugden,Assistant State Director with Mutual UFO Network. "High altitude aircraft.If you've seen them at sunset, they're pretty far away. Peopledon't know what they're looking at. You'll see a white line that's movingreal slow, that's the contrail and in front is the aircraft."
But Christopher Crow, Assistant Professorof Geosciences at IPFW, thinks this is a meteor. "Whatever that is,it's coming down at a very fast speed. That's what's causingit to heat up - the friction in the atmosphere to the pointwhere it's creating plasma, giving off flames," said Crow.
"My first inclination is it's not ameteor," said Chris Highland, who is from the Fort Wayne Astronomical Society.His opinion is different from the other two. "I'm more inclinedto think this is space junk, like an empty booster or a fuel tank," saidHighland.
https://kenny.anomalyresponse.com
Cincinnati UFO Hotline 859-801-6767 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,422 |
Thank you for downloading this Touchstone eBook.
* * *
Join our mailing list and get updates on new releases, deals, bonus content and other great books from Touchstone and Simon & Schuster.
CLICK HERE TO SIGN UP
or visit us online to sign up at
eBookNews.SimonandSchuster.com
FOREWORD
by Salma Hayek
WELCOME TO THE JUICE GENERATION!
Juice Generation, the Store
The Green Curve
When to Juice
Lift
Juicing Jargon
Clear
Juicing Jargon
Glow
Nourish
The Sugar Question
Juice Imposters
Ready Made Juices: Our Advisory System
Balance
Juice vs. Blend
Peace, Love and Juice!
THE GREEN CURVE
Adjusting to Greens
Produce Myth Busted
Juice Diy: Getting Your Kitchen Prepped
Spotlight: The Juicer
Shopping For A Juicer? These Questions are Key
Spotlight: The Blender
More Tools of the Trade
Shopping for Produce
Prepping the Produce
The Pulp Predicament
A Greener, Cleaner Kitchen
Sip Tips
PHASE 1: Light Green: Bright and Refreshing
Phase 1 Buying Guide
Phase 1 Juices: Classic Combinations
Sanya's Gold Medal Greens
Celery, Carrot, Spinach
Carrot, Beet, Spinach
Carrot, Orange, Kale
Cucumber, Pineapple, Celery
Cucumber, Watermelon, Lemon
Orange, Pineapple, Beet
Watermelon, Orange, Cucumber
Celery, Pineapple, Ginger
Watermelon, Pineapple, Lime
Orange, Apple, Spinach
Green Apple, Ginger, Orange
Lemons and Limes
Apples
Debra's Green Elixir
Tropical Lust
Red Delicious
Apple Zing
Apple Mint Smoothie
Daily Detox
Pink, White, What's Right?
Citrus Super C
Grapefruit Refreshmint
Grapefruit Moon
Grapefruit Zinger
The Grateful Grapefruit Juice
Why Kale Is King
Michelle's Leafy Green Goodness
Emerald + Orange: Kale + Carrot
TropiKale: Kale + Pineapple
Leaves & Roots: Kale + Carrot + Beet
Hail to Kale
Phase 1 Smoothies: Pure Simplicity
The Essential Components
Peaches and Greens
Clean Green
Tropical Greens
Nuts for Greens
Not Got Milk
Cocoverde
Perfectly Pear
Banana 2.0
Smooth Strawberry
PB Split
Whiz Kids
Kid-Approved Juice Combos
Agua Fresca
Try These Combos
PHASE 2: Medium Green: Take Your Juice to the Next Level
Phase 2 Buying Guide
Drink the Rainbow
Very Veggie
Get Ur Green On
SupaDupa Greens
Paula's Daikon Blues
Sweet Greens
Blake's Intoxicating Detoxification
Juice Boost: Fat is your Friend
Exotic Tastes and Creamy Textures
Coco Love!
Crack that Nut
Kale Kolada
Carrot Creamsicle
Amazon Acaí
Pacific Pineapple
Sweet 'n' Creamy Greens
CocoBliss
Berry Cherry
Mango Tango
Luscious Cup
Fruity Fiesta
Todo Bueno
Hemp Seeds
Hemp Protein Buzz
Acaí
Amazing Green Acaí Bowl
PB Acaí Bowl
Aloha Acaí Bowl
Coco Acaí Bowl
Hemp Acaí Bowl
PHASE 3: Ultra Green: The Full Feel-Good Effect
Phase 3 Buying Guide
Collard Greens
Collard Cooler
Zesty Green
Mega Green
Burdock Beauty
The Detoxifier
Jade Joy
Wild Watercress
The Spice Bazaar
Cayenne Kick
Golden Goddess
Piña Piquante
Pink Himalayan Salt
Salsa Samba
The Lift-Off
Carrot Spice
Ultra Wellness and Superfoods
Nut Milk
Irresistible Brazil Nut Milk
Vanilla Almond Milk
Cinnamon Cashew Milk
Chai Hemp Milk
Ultra Wellness and Superfoods
Hero's Garden
Antioxidant All-Star
Emerald Escape
Island Blue
The Sage's Smoothie
Lynsey's Joyful Almond
The Next Fruit Frontier
All-Star Aronia
Pink Pitaya
Buckthorn Blast
Maca & More: Super Boosters
Maca Master
Queen of Fruits
Drink of the Gods
CLEANSE AND REVIVE
Using Your Juicing Tools for Detoxing and Healing
The Reset
The Green Curve Cleanse
Juice for a Day
The 3-Day Cleanse
Darker Green Juices
Lighter Green Juices
Nut Milks
Coconut Water
Fruit-Based Juices
Juice Farmacy
Michael's Go-to Greens
Hot Stuff!
Cold Warrior
Lemon Lozenge
Ginger Fix
Dr. Bombay
Wheatgrass Rx
Verdant Vista
Gaia's Garden
The Professional
Juice Shots
The Defender
Performance +
Fountain of Youth
Shot of Gold
Vital Shot
Living Juicy: Maintaining A Happy Green Habit for Life
ACKNOWLEDGMENTS
ABOUT ERIC HELMS
## FOREWORD
Growing up in Coatzacoalcos, Veracruz, Mexico, aguas frescas—cooling drinks made of watermelon, cucumber, lime, guanabana, melon, prickly pear, tamarind, rice-based horchatas, hibiscus flower teas, to name a few—were always on the menu, instead of the traditional sodas. Savoring the colors, aromas, and tastes of these fresh-made juices was something I embraced at an early age.
When I moved to California in my midtwenties, I discovered a whole new world of juicing, one devoted to the healing effects of green juices squeezed from buckets of vegetables and tart citrus fruits. Green juicing was still something of a West Coast phenomenon at that time—mainly done by dedicated health nuts—and not nearly as accessible as it is today. But for me, it was love at first sip.
I started buying armfuls of California-grown cucumbers, celery, spinach, lemons, and grapefruits, and my kitchen—always my favorite room in my home—became my laboratory of liquid experiments. I loved the energy, the clarity in body and mind, and the glowing skin that my glasses of liquid green delivered. And, since I do find good meals to be a true source of pleasure—I believe eating well, and with people you love, is about feeding your body, heart, and soul—I used juicing to ensure I covered my nutritional bases every day, and as a tool to restore inner balance if my body needed a break from too much indulgence. I was one of the first people in my circle of friends to do short juice cleanses when I felt the need to get calm, clear, and focused and to give my body a chance to rest and restore. At the beginning, they looked at me a little strangely, but when they saw the results they understood that my homemade juices were key to my preventive healthcare regime: a way to keep equilibrium, take charge of my health, and look my very best.
That's always been what juicing is to me: a tool for staying in balance. Juicing vegetables and fruits, or drinking green smoothies, is not about deprivation or dieting. These are habits that help us add more to our lives: more high-grade, nutrition-rich foods in a busy, fast-paced schedule; more awareness of what our body needs to stay well and not get sick; and perhaps most important, more sensory delight from delicious foods that we otherwise might not try.
They're also life changing. Anyone who has, at the very least, a cheap blender, can begin to drink their way to well-being by tripling or quadrupling their daily dose of fresh vegetables and fruits in about three minutes. This has wonderful effects for everyone, no matter where on the eating spectrum they are. To me, this is what the current juice boom is all about: people of all ages discovering their power to feel and look better by giving their bodies the essential elements they need.
As a mother, I have even more reason to get fruits and vegetables into the juicer. I want my daughter to grow up learning to love all the benefits that nature offers. I am also happy that proceeds from this book are going to Wellness in the Schools, a pioneering nonprofit program that brings chefs and restaurateurs into New York City's public school cafeterias and classrooms, alongside fitness and environmental experts, to combat childhood obesity and give every kid a chance to be their best and brightest self.
When I met Eric Helms fifteen years ago, it was like finding a juicing coconspirator—one who had access to the newest, coolest ingredients on the natural-foods scene. Eventually, we launched a juice-cleanse delivery service using the recipes we'd developed. We called it Cooler Cleanse, and our mission was to give busy people a simple way to recharge and renew themselves, using cold-pressed juices and raw-food meals in moderate cleansing and detox programs.
Eric's book, The Juice Generation, is driven by the same mission of making juicing and blending accessible, exciting, and even more important, a long-term, "happy green habit" that doesn't get dropped after a two-week fling. It confronts the myth that things that are great for us don't always taste good. With its three-phase program of recipes, this book offers an innovative solution; a culinary adventure that tempts you into the world of green and nutrient-dense drinks slowly and deliciously, one step at a time, so your taste buds can adjust from sweet to savory naturally. It could convert anyone from juice skeptic to juice connoisseur!
Juicing and blending help me stay energized and positive, and bring me back to center if I wander a little too far into the tempting pleasures of wine, pasta, and cheese. I hope that you and those you love will enjoy the adventure of drinking your food as much as I have—and that this book gives you the skills and inspiration to make your own kitchen an exciting, colorful, liquid laboratory, too.
Salma Hayek
## WELCOME TO THE JUICE GENERATION!
Do you live juicy? Are you energized and uplifted, with a little extra spring in your step? Does your skin glow? Do your eyes shine? Is your mind clear and your outlook optimistic? Do you feel light and bright inside?
If you answer yes, chances are that you're already a convert to the power of juicing and blending, got a green drink habit going on, and maybe even have a thing for superfood smoothies. The recipes in this book will expand your juice know-how with new flavors and combinations to explore.
But if your life is not as juicy as you'd like it to be, if you find yourself chasing the next latte, cola, or energy drink high, or you feel foggy or dull, get ready to experience the boost you can get from juice in all its splendid forms.
These liquid elixirs, made from armfuls of ripe vegetables and rainbows of lush fruits, are some of the most phenomenal and fast ways to get goodness into your body. They let you cheat, in a good way. With just a few minutes of prep time, they're a shortcut to getting, and exceeding, your RDA (Recommended Dietary Allowance) of greens and fruits. Better yet, you get to take this vitamin bonanza on the go—just add a straw.
Why are these "sunshine foods" so powerful? Fully charged with the vitality of sun and earth and made fresh from whole foods, raw juices and blended drinks enhance your daily diet with easy-to-absorb doses of concentrated plant nutrition—nature's best medicine, rich with antioxidants, minerals, and enzymes. Each drink acts as a delicious, homemade supplement-in-a-cup.
How much of your diet can you say that about? They protect your system against the stress and toxicity you face every day and they're potent antidotes to the fatiguing effects of a time-challenged, fast-paced modern life.
Juices also help you look fantastic. Famed for their rejuvenating properties, they give your skin a vibrant, healthy glow, help your eyes shine bright, help you maintain an ideal weight, and generally contribute to a younger and more vital appearance. And juices and smoothies fit into any dietary regimen with a caloric spectrum that runs from a supremely low 60 calories per 8 ounces of green juice; to a vitamin-stacked 120 calories for a slightly sweet 12-ounce fruit juice; to a rich and filling 400-calorie smoothie plumped with healthy fats. One swig of an emerald-green fruit-and-veggie nectar and you feel it instantly: You're revitalized, inspired, and poised for action.
Now we're inviting you to join the Juice Generation, to learn what making your own plant-filled concoctions can do for you, and for your family and friends. Whether you're a juice virgin, newly juice curious, or already an old pro with the single-auger juicer, we want to get you excited about the endless possibilities of squeezing, crushing, and grinding, and get you skilled in integrating the joys of juicing into your busy life.
For too long, a daily juicing habit has seemed out of reach—a complicated luxury that only devout yogis and the charmed elite manage to pull off. But the tide is changing, and now it's easier and more accessible than ever to integrate a short (and yes that can mean five-minute) juicing or blending ritual into your life. Incorporating these power foods does not require a whole lifestyle change: it's about picking up a few new tools and making this a happy habit—something that fits into the way you already live.
With a little guidance, some practice, and a willingness to try something new, you too can boost your body, mind, and spirit with nutrient-rich cocktails. The door is open—come on in!
## JUICE GENERATION, THE STORE
Fifteen years ago, we started a small juice bar called, appropriately, Juice Generation, in the heart of—some would say the belly of—New York City, in Hell's Kitchen. It was a ballsy move: Back then, people would walk into our oxygenated oasis, look quizzically at our steel juicers, ask, "Where's the food?" and walk out. Public awareness of juicing was still a seed waiting to sprout.
But we persisted, making juices and smoothies fresh-to-order for a small band of loyal customers, because we sensed that the world's busiest city had a deep thirst for fresh-squeezed nourishment on-the-go. Our first fans were Broadway's hard-working actors and dancers, who relied on our juices and blended drinks to sustain them for long hours in rehearsal and on stage. They loved the light and clarifying refreshment they got from green juices and the heartier replenishment of recovery smoothies.
* * *
As foot traffic increased, we began to serve a bigger cross-section of Manhattanites, from harried professionals and fitness instructors, to toddler-toting moms. Our grass-roots education in making liquid foods was earned from the best vantage point possible: behind a counter with a juicer and blender at the ready. Over the years, we've become pretty good at tempting people to take a walk on the raw side through juices and smoothies. We consider these drinks the ultraeasy, liquid aspect of the growing raw-food movement that is inspiring people to try out dishes made from "living" food like fresh greens and sprouted seeds and nuts. (They're just as delicious as a kelp-noodle pad thai or cashew coconut pie, and a lot less intimidating to make!) We also developed creative methods for helping people achieve smart and balanced juicing habits for the long term, like a "scale-up-the-green" ladder of drinks that helps beginners (who typically like sweeter things) introduce the all-important green vegetables into their cups slowly, so that their palates can adjust to the taste. We became international superfruit sleuths, adding yet undiscovered delicacies like pitaya (aka dragonfruit) to our recipes, because we were so excited about their nutritional potential and their unexpected flavor profiles. We even launched a sister company, Cooler Cleanse, offering detoxifying juice cleanses delivered to your door.
At Juice Generation, the store, our ethos is centered on making everything not just healthy but tasty. To us, enjoyment is part of well-being. If you consume healthy foods simply out of principle, and not out of pleasure, something's missing from the equation. You either lose the enthusiasm and drop the habit, or you keep going, but with a feeling of constriction or resentment—a state that is the opposite of vibrant health. Plus, we were motivated by sheer survival. Our Big Apple audience is filled with some of the world's most discerning foodies—chefs, restaurant critics, and the everyday patrons of the city's extraordinary food scene.
Our business has grown significantly since those pioneering Hell's Kitchen days, and now we're witnessing a juice boom in full swing. New York City is hopping with new juice bars, plant-based restaurants, and the latest iteration of this phenomenon: roaming juice trucks that bring their tonics straight to your street. Nationally, juice bars and juice cleansing companies are showing up in surprising pockets of America, and the exotic, food-as-medicine ingredients known as superfoods are filling the shelves in towns that previously had few natural-food options. The movement is taking off internationally, too, and the world of raw food and drink evolves daily online, with aficionados sharing daring new ingredients and exciting recipes that mix savory, sweet, spicy, and tangy with gusto.
Whether you're vegetarian or carnivore; a late-night pizza-eater or a Paleo-perfect fitness buff, getting daily doses of vegetables, fruits, nuts, seeds, sprouts, and superfoods in your drinks improves how you work, play, and live. And that's something to lift up your glass and toast.
I eat a lot at my restaurant, Telepan, and juicing is a way to get a good amount of nutrients into myself before I go in, without filling me up with calories. I've made it part of my daily routine, either by picking up a green juice on my way to work or making juice at home. And it is a great activity to do with the kids I work with at Wellness in the Schools (WITS)—it is a creative way to introduce them to fruit and vegetable combinations they might never have considered before.
—Bill Telepan, celebrated chef; executive chef, Wellness in the Schools
## THE GREEN CURVE
We created this book to distill our fifteen years of wisdom into a field guide you can use to help you find juicing confidence in your own kitchen. We've created what we hope is a foolproof method that takes anyone from beginner to experienced in terms of their skill and taste palate. It's called the Green Curve, and it's based on our many years of seeing how our patrons tastes have naturally expanded and evolved.
This book you're holding is also popping with words of wisdom from the people who've come up alongside us on our fifteen-year journey; a colorful cast of inspiring and aspirational characters who use juices and blended drinks every day to fuel their best lives. You'll hear their tips and insights on getting the most from a juicing and blending habit. They range from well-known actors and entertainers to founders of natural beauty companies; from Olympic sprinters and celebrated dancers to filmmakers and chefs. Each one of this diverse group has their own way of using liquid tools: some are devout green juicers who actually crave bitter leaves; others make luscious smoothies enhanced with healthy fats, and many do both, because they've developed an awareness of the kind of nutritional support their body needs at different times. All of them have mastered the art of finding time in their hectic schedules to treat themselves right by making—and yes, sometimes purchasing—vibrantly-colored liquid elixirs, and they unanimously report they feel more centered, clear, creative, and confident as a result.
* * *
## WHEN TO JUICE
EVERY DAY WE HEAR SOME SIMILAR REFRAINS:
"I'm a working mom. I'm always seeking energy and I'm dying to get off the caffeine-crash roller coaster."
"No matter what I eat, I never seem to be satisfied. I'm always grazing, trying to find the thing that will make me feel complete."
"After a long day on the go, the face I see in the mirror looks tired and blah."
"I run out the door in a rush every morning with no time to make a good breakfast, and I fade by midmorning."
"I go from work to a workout, and then commute home, and if I don't replenish properly, I bonk the next day."
DO YOU RECOGNIZE YOURSELF IN ANY OF THESE?
Drinking juices and blends releases the tremendous healing power of raw and living foods, which is why, when you juice and blend regularly, a range of physical ailments—from joint pain, allergies, gut issues, skin problems, mood imbalances, sleep problems, and more—have a chance to improve. This book is designed to help you lift, clear, glow, nourish, and balance. Here's how.
## LIFT
Running your own business is a 24-hour commitment. Juicing is the way I survive on so many levels: It is the easiest breakfast for me to grab and go and it relieves my mind, knowing I filled my body with the right vitamins and minerals to nourish my cells and have taken care of myself first thing in the morning, so I can go forward into my day facing the unexpected. I drink juice first thing because it's the easiest food to digest and run through the system. It feels like I am watering a plant, filling up my body with its live and vibrant life force. And even though I am super dynamic and results oriented, and accomplish a tremendous amount each day, I seem to have a very Zen energy. Maybe it's the juice and food that I put through my body that manifests in my even mood. Ever seen an aggressive yogi? I doubt it. Food really does make a difference.
—Susan Beischel, founder and designer of the luxury natural clothing line Skin; member of the Council of Fashion Designers of America
* * *
We are obsessed with the quest for more energy. We're doing more than ever before, constantly outputting wattage for a never-slowing juggle of career and kids, personal dreams, and public obligations. We're pushing harder, working longer—resting less and sleeping worse. Which leaves us in a perpetual net deficit of energy. What are we using to prop ourselves up? Surging quantities of caffeine and chemical-laden, sugar-saturated sodas and energy drinks.
Now, we humbly acknowledge the pleasure of a robust macchiato brewed from the finest quality beans, or a delicate oolong steeped to perfection. The problem is when they go from a choice to a dependency. We're relying on these buzzy beverages as liquid life support, but the foundation of energy they provide is rickety. Their initial rush gives way to a crash that undermines us like a trapdoor, and eventually they can take a system-wide toll, acidifying our systems and burning out adrenal glands. Used in this excessive way, caffeine can be dirty energy: destructive and unsustainable.
Juicing provides a different kind of lift: Think of it as clean power—a more sustainable resource. A glass of juice floods your body with a mother lode of components that are essential to life, giving you a boost of vitality in about 20 minutes. The nutrients are rapidly absorbed because juicing and blending breaks down the whole plant food and partially "predigests" it. This saves your body some of the energy needed for breaking down solid foods, meaning you intake more nutrients with less energy expenditure. Better yet, because the foods are still in their raw, uncooked state, their enzymes are intact and able to lend their full power to your cells, assisting your body in performing all the actions it takes to keep you alive. Cells are our tiny energy-producing factories that need oxygen and nutrients and support for detoxification. In return, they make ATP, the energy that supports life. Give them more of what they need—elements rich in oxygen like chlorophyll from green plants and important micronutrients, and it's not surprising that you feel an extra tingle inside. This is one of the reasons that raw food is so important: It literally fires you up.
## JUICING JARGON
Raw food means food that has not been heated above 115°F, which keeps all the bioavailable nutrients intact and in their original state, so you get the richest infusion of nature's bounty.
Living food is a loosely used term that often refers to seeds that are sprouting or just bursting into growth and thus considered ultra full of natural life force. Some people use the term to refer to just-picked vegetables and fruits.
Blending has some other energy benefits. Where juice delivers an instant uplifting boost, partly because there's no tough material for the digestive system to break down, a blended drink has a slower-absorbing quality and the potential to deliver longer-lasting fuel because it contains plenty of fiber, and often, fats and proteins. It is a meal in a cup that has the potential, if you build it right, to carry you all the way from breakfast through to lunch.
We're not going to lie: A raw juice or smoothie won't get you wired like a double latte does. Consider it a different kind of lift, one that nourishes and sustains, perking you up more gently without the jagged takeoff and bumpy landing of caffeine. Some people say that drinking juice feels like "lighting up" their circuitry, and many say their morning habit helps to tone down a reliance on coffee or tea without a great struggle. A green juice or smoothie first thing can help soften the habit of even a hardened espresso denizen.
Juice Smarts: Rethink the four o'clock cookie break. Substitute a fresh juice for a sweet treat at that midafternoon slump and watch how it works wonders. A smart blend of plant power can provide an energizing lift without the big insulin spike and resulting metabolic disruption that comes from ultrasweet treats and wheat-filled baked goods.
## CLEAR
The residue of modern living and eating can show itself in the guise of a foggy mind, a weighed down body, and a dumpy spirit. Luckily, juicing and blending can bring some levity to the situation. Consider it a 21st-century survival tool that can help you stay buoyed, alert, and feeling bright and clear, even in the gunkiest moments.
This clarity is due in large part to the ways that vegetables (particularly green ones) and some fruits (like grapefruits) deliver potent nutrients that support your on-board cleaning crew, your detoxification system—especially the liver, where most of your detoxification occurs. In addition, the load on your digestive system decreases when you periodically have a liquid snack or meal instead of denser food. This diverts energy away from digestion and toward detoxification, the never-ending cleansing the body does to rid itself of the unavoidable by-products of living (called metabolic wastes) and unwanted toxins from outside. Combined with the greater amounts of fiber moving through your intestines and the highly efficient hydration that comes from juices and blendeds, which help your intestines to eliminate more regularly, you get to enjoy the lighter and brighter effects of improved daily cleansing.
Juicing has been a lifesaver for me as I get older playing in the NBA. It's important to have the proper nutrients, and weight management is critical because as you get older, you gain more weight. Juicing has really helped me to be able to stay youthful—and to be able to keep up with the young guys.
—Baron Davis, point guard, New York Knicks
Equally as important, when these liquid treats integrate themselves into your diet they tend to take the place of convenience foods and snacks like gluten-filled breads, breakfast cereal, baked goods, and pasteurized dairy—all things that have notoriously clogging, dulling, and irritating effects. This gradual reduction in toxifying foods helps you achieve an increasingly detoxified state, because you're eliminating the triggers that cause inflammatory and immune responses. That's why with juices in your life you feel energized, more clear and focused, and, often, more optimistic.
Will all this detoxification affect your waistline? Maybe so, because you're replacing toxic foods that puff you up, due to their inflammatory effect, with a lot more healing whole foods that help you run a cleaner engine. That said, health and well-being is the goal, and weight changes are an added bonus.
Juice Smarts: Studies show that when used in conjunction with a low-glycemic diet, green and veggie juices help to enhance weight loss. Low-glycemic indicates foods with carbohydrates that break down slowly, releasing their glucose (sugar) more gradually into the bloodstream, helping create better blood sugar control and blood-lipid levels, and making you feel more full.
JUICY TIP
When you feel weighed down or extra sluggish, try doing one day of a liquid morning and evening—a healthy smoothie in the morning and a juice in the evening, or vice versa. This quick "reset" lightens the load on your digestion and helps you sleep better, too.
WHAT IS PRESSED OR COLD-PRESSED JUICE?
Cold-pressed juices are the turbo-charged model of juicing, developed specifically for use in cleansing and healing programs. They're made using a labor-intensive process involving a hydraulic press that slowly extracts even higher levels of nutrients from the produce than regular domestic blenders, with extremely low exposure to air. Their major benefit is that they create a completely pulp-free elixir, which floods the body with nutrients without any energy expenditure used on digestion, and can retain full nutritional value for at least three days. That's why they first came to fame through use in intensive healing programs for acute health issues, when the body's capacity is unusually compromised and has almost no extra power to digest and absorb.
In the last few years, cold-pressed juices earned cachet for their use in preventive healthcare programs—multiday detoxification and cleansing programs—because they give the digestive system such a profound break and because many say these juices have the most intense flavors due to their extraordinary extraction capacity. Now cold-press juice has become an everyday drink, and many juice boutiques exclusively sell these ultrafine pressed juices, which they make off site every morning and sell in bottles at premium prices (due to the unavoidably slower production). At Juice Generation we offer both made-to-order centrifugal juices and cold-pressed bottled versions because it's a question of taste and price. Not everyone enjoys pulp-free juice (and sometimes you just want to see your juice made to order before your eyes!).
Can you make cold-pressed juices at home? It requires splurging on a specialized and costly professional-grade machine called a Norwalk Juicer. For most people, a good-quality consumer-level juicer, which extracts juice through crushing and grinding fruits and vegetables, suffices. It delivers plenty of raw nutrients at an efficient speed and cost.
## JUICING JARGON
• Enzymes are catalysts that regulate every chemical reaction in our cells, enabling all the activities in our body, including digestion and healing. They're abundant in raw foods and their unique shape is damaged by heat and cooking, which is why it's important, especially as we age, to get lots of raw foods in your diet, to help up the supply of enzymes.
• Vitamins are organic compounds that the body must get from food and the sun. We require 13 of them: Nine are water soluble (eight B vitamins and C) and four are fat soluble (A, C, E, and K). Cooking foods tends to reduce their vitamin content. Some plants, like broccoli, release more vitamins when steamed.
• Minerals are absorbed from the soil by plants and turned into compounds that our tissues can absorb. Plants thus provide us with essential macro minerals like calcium and potassium, as well as trace minerals needed in tiny amounts, like chromium, copper, iron, and zinc.
Antioxidants are molecules that help keep us healthy by neutralizing free radicals—highly reactive molecules that damage and degenerate our tissues and cause our bodies to age. Free radicals are produced by our bodies as waste and also enter us via external pollution and toxicity, and even sunlight! Plants have multiple complexes of different neutralizing antioxidants, including Vitamins A, C, and E, and a host of enzymes.
Phytochemicals are the thousands of miraculous and mysterious substances in plants that give them their color, flavor, and aroma. Some, like beta-carotene, resveratrol, curcumin, and lycopene, have been shown to have potent benefits for health and beauty. Many of them are powerful antioxidants.
Electrolytes are substances that become ions in solution and have the ability to conduct electricity. They need to be in optimal balance for our bodies to work well. Sodium and potassium are two that tend to be out of balance in the Standard American Diet—too much sodium, too little potassium. This causes us to wilt like a plant, and can push blood pressure up. Juicing helps to flood our cells with higher potassium, from vegetables like cucumbers and celery, which helps us excrete sodium and return us to our energized best.
Micronutrients refer to all the organic compounds such as vitamins, minerals, and phytochemicals that our bodies need in tiny amounts in order to run properly. Deprived of enough of these micronutrients, we become susceptible to diseases and DNA damage. Folic acid, iron, zinc, iodine, and magnesium are just a few of these wonder substances that nature provides through food.
Fiber is a carbohydrate that is not digested by the body. It can be soluble or insoluble—both are essential for optimal health. Insoluble fiber—found in dark leafy greens, fruit skin, and seeds and nuts—regulates bowl movements and helps to maintain a healthy pH balance in the intestines, which can prevent colon cancer. Soluble fiber—found in fruit pulps, bananas, some nuts, flaxseeds, beans, avocados, blueberries, cucumbers, and more—helps you feel full longer, which regulates blood sugar levels. Soluble fiber can also lower LDL cholesterol by disrupting the absorption of dietary cholesterol.
Omega-3 and omega-6 fatty acids are essential fatty acids that we do not produce—they can only be obtained from our diet. Omega-3s are made up of two fatty acids, EPA and DHA, which are the basis of the hormones that control immune function, blood clotting, and cell growth. There are limited sources—cold water fish (like salmon), avocados, walnuts, and flaxseeds (vegetarian sources contain ALA, a precursor omega-3 that the body must convert to EPA and DHA). Most people tend to have low levels of this essential fatty acid, which is where blended drinks full of these good plant foods can help.
The best vegetables for skin are made up of mostly water, which instantly hydrates the skin for a gorgeous glow. One of my absolute favorite drinks is the classic, all-green juice of kale, spinach, parsley, cucumber, celery, lemon, and ginger. All of these ingredients benefit the skin with the ultimate hydration and more. Kale has vitamin K, which helps brighten your complexion and reduce dark circles. Kale and spinach also have vitamin A, which encourages your skin to repair itself and retain moisture. Parsley is a natural deodorizer that has many vital vitamins that keep your immune system strong, and you'll rejuvenate and refresh the body and nourish the skin with celery. Cucumbers contain vitamin C and are rich in caffeic acid, which helps soothe the skin. They also contain silica, which contributes to collagen formation. (Try to buy organic cucumber, since silica is mostly on the skin and this can be added to the juice.) Lemon helps in the detoxification process of the body, but it can also be used directly on the skin as a natural exfoliator. Ginger acts as an anti-inflammatory in the body to keep you going during a busy time.
To replenish the skin, coconut water contains vitamins, minerals, and electrolytes that taste delicious! And aloe water is an amazing detoxifier that provides collagen and elastin repair for healthy skin.
—Pat McGrath, makeup artist and beauty guru
## GLOW
Nutraceutical beauty is today's booming trend; it features luxurious face products with active nutrients and supplements from food sources that nourish the skin, give it a radiant look, and help slow aging. Juice is the original nutraceutical, and works from the inside out, helping to diminish wrinkles and develop dewier and clearer skin, brighter, whiter eyes, and a distinctive "juice glow." The rejuvenating effect of consuming vegetables, especially greens, is partly due to their alkalizing effect, which helps to balance out the acidity in our tissues that is a common effect of our modern life and diet and that can lead to skin disorders like acne, rosacea, and a generally dull, dry complexion. Then there are the high levels of naturally occurring antioxidants you consume, which help combat the aging effects of pollution and environmental stress and help create healthy and more vibrant skin.
Add in the fact that the electrolytes in juices deliver hydration that has an undeniably energizing effect on the skin, and we are confident to issue a challenge: Get back to us after a week of juicing and blending your cucumbers, celery, and spinach, and tell us your face doesn't look better. Don't forget to check your hair and nails, too: When they receive good doses of minerals like zinc, copper, thiamin, niacin, and iron, along with good proteins like the sulfur-bearing amino acids methionine, cysteine, and cystine (which are found in spirulina and super seeds like hemp), your locks and talons will get extra strong and shiny.
* * *
## NOURISH
Blended foods pack a lot of nutrient density into a very small package. People think that they need a lot of food to feel good, but it's not about volume, it's about density. In a 16- or 32-ounce blended drink, you are getting so much dense nutrition in a small volume.
—Jason Wrobel, chef and host of the Cooking Channel's How to Live to 100
Everyone knows they're supposed to pack their diets full of plant-based food to stay healthy; the question is, "How on earth do I do that every single day?" Nine daily servings of fruits and vegetables are considered a minimum baseline for health (which means 2 cups fruit and 21/2 cups vegetables, but up that number considerably if you require a caloric intake higher than 2000 calories a day). Blitzing salad bowl–size servings of leaves, stalks, fruits, and roots into liquid form is one way to achieve that goal; reducing them into such a concentrated form delivers a large nutritional punch in a small amount of food.
Think of it as flipping on its head that all-American logic, that size matters and we need to eat massive portions in order to function. So much of the modern diet is super sized but nutritionally empty.
A smartly constructed smoothie packs an abundance of good things into one glass. Think: giant handfuls of fresh vegetables and fruits; nutrient-dense superseeds like hemp and chia, and nuts for good fats and protein; and even functional ingredients (natural ingredients that have specific physical and mental enhancing effects, like turmeric root or cinnamon). These all give you extra help where you need it, like lifting the mood or calming inflammation. It's an exercise in elegant simplicity. Some of nature's greatest foods give their effects in small and potent amounts.
Which is why juicing and blending can help to counter the modern dilemma: We're eating more food than ever before, but our bodies are still deprived of essential nutrients due to the industrialized way that our foods are grown, produced, and processed. If you use the freshest, organic-whenever-possible, and local-whenever-possible produce, which research shows has higher amounts of essential micronutrients, you can replenish some key factors that your diet may be missing, clearing out obstacles to feeling, looking, and performing at your best.
Don't forgo food: Wise juicing and blending means using liquid foods as supplements and enhancements to your diet, not ditching your regular meals. But in the quest to be vital and vibrant, it's not always volume of food we're after; it's nutritional density.
Juice Smarts: One cup of carrot or celery juice provides most of the same nutrients found in about 4 to 5 cups of the same vegetables in whole form. (Different juicers produce different amounts.)
## THE SUGAR QUESTION
Smart juicing means becoming savvy about sugars in your drinks. Successful long-term juicers learn to liquefy greens and vegetables on a daily basis, and to juice sweet-tasting fruits and the sweetest root vegetables, which are higher in natural sugars, in moderation.
"But these are naturally occurring sugars in my pineapple, mango, and beets!" you say. "How can they be bad?" The truth is that ultrasweet fruits and sweet root vegetables are dense sources of polysaccharide carbohydrates, which when digested or broken down in juice turn into glucose and other simple sugars. This isn't too problematic when you eat the whole plant with its fiber intact, because it's a slow process to break down the entire mass and extract the sugar out. But when you juice them and take out the fibers, the sugars are delivered to the bloodstream in a much faster manner, causing a bigger sugar rush and a larger insulin spike (insulin is the hormone that regulates sugars in the blood). The sugars, if not used up right away in vigorous activity, get stored as fat; the insulin spike, if it happens repeatedly, disrupts your metabolism, with weight problems or blood sugar–related illnesses a possible result.
That's why ensuring your liquid meals frequently feature greens and low-sugar fruits like berries or tart green apples is a key to a healthy juicing and blending habit. Getting your greens is at the very heart of the Juice Generation's ethos: They are alkalinizing, anti-inflammatory, chlorophyll-packed gifts from Mother Nature. Adding healthy fats to your drinks, in the form of avocados, seeds, nut butters, or even via flax oil or coconut stirred into fresh-made juice, can also be a tool to slow down the speed of sugars entering your bloodstream and achieve good balance.
If you are overweight or have high blood pressure, diabetes, or high cholesterol, be even more vigilant about limiting your sweet fruits and pure root-vegetable drinks until you normalize these conditions.
## JUICE IMPOSTERS
Supermarket shelves and convenience store coolers are stocked with bottled, packaged, and frozen juices and smoothies. So why bother to make your drinks fresh at home? Because most of these items are juice imposters! Most of the "juice" beverages filling store shelves are several steps away from the raw, whole foods they came from—and the ingredients they contain are not always benign.
Almost all store-bought juices are pasteurized at high heat to kill off any potential pathogens in the juice and give it a long shelf life (up to a year if unopened!). This sterilizing process also, not surprisingly, kills off the fragile enzymes and a lot of the active power of the vitamins and antioxidants. Your fruit or vegetable nectar goes from fresh to, well, somewhat vapid. Pasteurization does enable big food producers to make huge amounts of product and ship it nationwide without fear that contaminants are left in, but the ones who benefit the most from this process are the producers, not the consumers, who are left to guzzle drinks stripped of their best components. We'd rather wash our produce well, juice it fresh and turbo-charged to get all the nutritional and energetic benefits—and watch it degrade naturally like nature intended if we forget to drink it.
* * *
## READY MADE JUICES: OUR ADVISORY SYSTEM
CODE YELLOW: Bottled smoothies and juices with "no added sugars." These convenience-store quick fixes look healthy, with their cute labels covered in fruits (and maybe vegetables), but they're less than fresh. The popular ones may say "all natural," but they're rarely organic. Plus, check the ingredient list and the nutritional content. Each 15-ounce bottle might contain two servings; and if it's a fruit-only juice, the whole bottle may have 50 grams of sugars from carbohydrates. (Compare to an ultra-green juice you make at home that may contain just 2 grams.) Bottled "green" smoothies are often mainly fruit with a touch of green. If you're going to have one, read the fine print, water down if possible, and consume the contents in small increments.
CODE ORANGE: Bottled or frozen juices partly or fully "made from concentrate." This process heats the juice to evaporate water and separate out the pulp, concentrating the flavorings, and then recombines the concentrate and pulp to achieve the concentration and flavor the producer desires. This concentrate is then stored in refrigerated tanks until it can be packaged or reconstituted. Along the way, the heating process pasteurizes the juice. Though many argue there's nothing inherently bad about a concentrate if it has no added sugars or flavorings—again, you're drinking a lot of the quick-hit carbs without the advantages of fresh juice's life force.
CODE RED: "Juice cocktails" or "juice drinks." Three words: Back away slowly. And, when it comes to your kids: Just say no. These beverages may have fruit-derived ingredients, but they're so concentrated and enhanced they are essentially sugar water delivering empty, and damaging, calories. With up to 20 teaspoons of sugar per bottle, they're as bad as the sugariest sodas! (We noticed that a certain grape beverage from one of America's favorite brands has 72 grams of sugar, the same as six scoops of ice-cream; and a canned tea beverage we cannot name, with two fruits in its name, contains 84 grams of sugar!)
STATUS PENDING
Some supermarkets are starting to carry bottles of cold-pressed juice; but they're a different animal from the cold-pressed juices sold in juiceries, which have a three-day life if unopened. The supermarket juices have been pasteurized to survive transit and have a much longer shelf life. This is done through a new process called High Pressure Processing (or High Pressure Pascalization) that, its advocates say, keeps most of the fragile nutrients intact, because the process does not use heat. Rather, it surrounds the packaged juice in water at high pressure.
Yet when you pick up one of these juices, you simply don't know how long it's been on the shelf. Four days? Ten days? Fourteen? HPP is helping large companies ramp up their distribution, but we're not fans. We think it's processed juice masquerading as fresh. Crack one of these beverages open and see: The taste and vibrancy will be different from the juice made right before your eyes. That said, in a pinch, if you're yearning for a juice and there's no made-to-order juicery within reach, these bottles are by far your best bet.
YOUR BEST STRATEGY
Make your own juices and smoothies and watch them come directly from nature's own container: the whole fruit or vegetable in its untouched state.
## BALANCE
Dynamic members of the Juice Generation know that life doesn't have a lot of wiggle room. Staying healthy, with fewer illnesses and colds, is critical when you're juggling many balls in the air. Who's going to catch you if you fall? Juicing mavens use juicing and blending as their secret weapon for staying in balance. It boosts the immune system, making it a preventive healthcare boon. It protects against pain and chronic disease by alkalinizing your blood, which buffers the acidic imbalance from sugars, meat, dairy, and grains that is a major cause of joint and muscle pain and a gateway into degenerative disease.
Juicing and blending also helps create a more balanced relationship to food. Ardent juicers report a reduction in cravings and say their appetite feels under control. At a fundamental level, the body is more nourished, and when it's replete with the nutrients it needs, it sends signals to the brain that it is well fed. Satiety—the happy feeling of having had enough to eat and drink—is increased by consuming vibrant flavors along with healthy fats. Have some almonds with your juice, or put some coconut oil in your smoothie, and it's easier than you can imagine to get that satisfaction.
Even fearsome sugar cravings have a chance to simmer down, or even dissolve, when sugary addictions are replaced with fresh juices or green drinks. Cravings usually come from an overgrowth of candida living in the guts, which feeds on sugar and tells you to consume more. If you ditch 4 o'clock cookies and spontaneous candy attacks in favor of healthier fare, these hungry demons can begin to die off, and bother you less.
Many renowned healing centers and methods use juicing as a tool for more serious conditions: There are green juicing programs designed to reverse type 2 diabetes and cancer patients have found success in a somewhat controversial healing system called Gerson Therapy, which follows a strict regime of using 14 cold-pressed juices a day to help their bodies heal.
## JUICE VS. BLEND
Though some people take sides—juicy fruit and veggie elixirs versus thick, luscious purees—we prefer an equal opportunity approach. We like to juice, blend, and eat our vegetables and fruits—raw and cooked. This is about having more options, not less.
The number one perk of choosing juice over blends: Nutrients are easily absorbed because the foods are virtually predigested; the resulting energetic uplift can have a supercharge effect. The cons are that you've taken the fiber out, which can have your hungry tummy seeking solid food soon after the last sip; and, if you overdo the fruits, you'll get a quick sugar spike, which as a daily habit isn't ideal because it contributes to weight gain and insulin destabilization. If you end up predominantly juicing, be sure your diet is filled with lots of good fiber—don't use the juices as an excuse not to eat vegetables or fiber-rich whole foods. And don't go bananas putting only sweet stuff in your juicer!
The pros of blending are that you leave all the fiber in the drink, which most people don't have enough of in their diets, and you can easily blend in healthy fats and sources of protein to make your drink more of a meal. The cons for some people is the texture—thicker, obviously, which some love but others don't enjoy—and the not-quite-the-same instant infusion to the cells as juice, because of the fiber. (This is why juices, which don't require any work by your digestive system to break down the components, are used in healing and restorative juice-cleansing programs.)
* * *
## PEACE, LOVE AND JUICE!
Slow down. Take a breath. Chop carrots. Juicing is a kind of mindfulness training. The act of handling your food deliberately—washing it, cutting it, and watching it transform with a rush of flavor and aroma and a flood of color—has the power to stop your mind from racing and connect you to the present. Bring your awareness to the tangy, succulent tastes in your mouth as you drink, and you cannot help but grin. It's a moment of respite.
OK, so the whole experience might just last a few minutes—and then it's back to the rat race. But consider it a food meditation of sorts. Anecdotal evidence suggests that the juice habit has a happifying effect—it floods contentment, as well as nutrition, through your veins.
It's also empowering. Making a juice or healthy smoothie is one of the easiest ways to pave your way to your and your family's good health and to getting more intimate with the energy of what you eat. Food's gotten far too hands-off in recent decades: The shift to eating prepared meals, grocery-store dinners, and restaurant food makes everyone feel a little grief. What happened, we find ourselves wondering on our commute or work break, to having the time to cook with joy and love?
We say: It starts with the simple and short act of pulverizing a rainbow of colors, sprinkling in a hint of spice or a splash of citrus, and serving it joyously to yourself or someone you care about. A world of discovery opens up through juicing to deliver that happifying effect: You savor a plethora of natural flavors you have never known before; learn the pleasure of buying produce that's in season from local markets and get to know who grows it; and, by gaining an awareness of what nature's up to month by month, have a new appreciation for your place in the greater whole.
For many people, juicing and blending is a doorway into a bigger lifestyle shift that includes eating consciously, shopping responsibly, and living in a more wakeful way to the natural world. It's a way of getting back to basics and being more attuned to body and soul.
Welcome to the Juice Generation!
## THE GREEN CURVE
I'm a juicing addict! I've been searching for ways to optimize every facet of my mind, body, and physical performance. The benefits of juicing have opened up doors to a sharper mind, a more powerful and explosive body, and an overall feeling of wellness. I'm hooked—and I'm never going back!
—Steve Weatherford, Super Bowl champion and New York Giants punter
The Green Curve is a step-by-step journey into a new food world that is simple, fun, and satisfying while helping you integrate raw juices and sumptuous smoothies into your life at a natural pace.
It's based on years of real-life observations at our stores: First-time customers tend to start with drinks on the sweeter, fruitier side, eyeing the greener drinks from a distance. A few visits later, they get more curious, venture outside their comfort zones, and experiment with one of the sweeter green juices, like a watermelon-kale. (Typical response: "You can't even taste the kale!")
Convinced by the refreshing uplift they've found, they eventually go the whole nine yards and pick up an ultra-green concoction—one of our detoxifying drinks filled with seven kinds of leafy, liquidy greens, with only a splash of lemon added. They might get adventurous and add a shot of wheatgrass—a health elixir bursting with living energy—or green-blue algae full of vitamins, minerals, amino acids, and fatty acids.
Some weeks or months after first coming in, our new recruits discover a new range to their palate that didn't exist before, and they've successfully developed a "happy green habit"—an ingrained desire to give their body what will serve it best. (And it explains why these days, our green drinks outsell fruit-only offerings by ten to one.)
When it comes to getting started in your own kitchen, this unfolding can happen in the same way. There are a couple of other factors to consider as well. Learning to carve out extra time in your day, starting with simple and nonintimidating recipes, and keeping costs within your budget are equally important. The Green Curve addresses all these by guiding you at a comfortable gait from simple juicing and blending recipes to more sophisticated ones. You'll start with basic juice or blended combos with sweeter profiles that you can make easily and quickly from minimal ingredients. You'll progress to recipes with more ingredients and a medium-green profile—half savory, half sweet. Then, if you choose, you'll explore exotic options that throw in exciting new ingredients that tend to have the greenest flavors yet and that might require a few more purchases and prep steps.
Don't worry. This isn't a severe self-help program—30 Days to a Much Improved You, If You Give Up Everything You Love. It's about discovery. A happy green habit that lasts is founded on a genuine love for the flavors, textures, colors, and possibilities of vibrant, plant-based ingredients, and is based on enjoying the process of combining them in exciting new ways. The Green Curve helps you to develop this love by presenting sumptuous treats alongside the good-for-you drinks, and keeping you jazzed with a spectrum of flavors, from sweet to rich to tart to tangy. You'll use old standards in new ways—the cucumber is a lot cooler than you ever realized—and discover some of the new juicing and blending-world trends to impress your friends. (Clue: It's where fresh coconuts meet superfruits.)
WHAT IS GREEN?
The Green Curve is designed to ease you into consuming more of the leafy and dark green plants that pack such extraordinary health power. To us, green is an umbrella word describing all things vibrantly phytonutrient-filled—full of plant power. We use the term a little loosely: It involves all the foods that are actually green—from spinach and celery to kale, watercress, lettuce, and more—as well as ones that are all the other colors of the rainbow: from orange, yellow, and red to purple, blue, and brown. Green means natural; green means plant-based; green means full of earth's powerful energizing and healing power.
Juice Smarts: The more intensely colored a fruit or vegetable is, the more chemically active antioxidants it usually contains. Go bright!
MAKING YOUR WAY UP THE CURVE
The Green Curve rolls out our favorite recipes over three distinct phases that we recommend should last for about three weeks each. This 3 x 3 formula helps you get accustomed to the recipes in each phase at a reasonable pace before moving on to the next level of complexity and flavor intensity.
PHASE 1: You'll aim to make two to three juices or smoothies a week, with at least 30 percent including a handful of leafy greens like spinach or kale.
PHASE 2: You'll aim to make five juices or smoothies a week, at least 50 percent including handfuls of leafy greens.
PHASE 3: You'll aim to have a drink with green vegetables in it every day, with a few non-green elixirs as needed or as treats! That's a 90 percent green rate.
The goal throughout the Green Curve is also to start listening to your body and noticing how different types of things affect you and what you might naturally feel drawn to consume at different moments.
There are no hard and fast rules. If you're ready to dial it up after one week on Phase 1 and dive into the new ingredients of Phase 2, or would rather start at Phase 2 because you're already adept, go ahead; and if you want to linger longer than three weeks, feel free.
## ADJUSTING TO GREENS
WARNING: YOUR PALATE HAS BEEN HIJACKED!
Why can the initial sips of good-for-you drinks be challenging? We'll admit what most juice books don't tell you: Though the greener, more veggie-heavy drinks on the spectrum become second nature when you get in the groove, that initial hit may shock your taste buds. The reality is that green-y, leafy, cruciferous-y, healing-herb–filled drinks are not exactly the mainstay of the Standard American Diet that most of us were raised on, and their flavor profiles are almost the complete opposite of what we recognize as "yummy!" The mind knows they're good for us; the mouth rejects this wisdom.
If this is your experience, it is OK. It is because your palate has been hijacked!
Consider that even the healthiest person is biologically conditioned to crave non-green flavors. Did you know every one of your tongue's 10,000 taste buds is wired to detect sugar, and each hit of the sweet stuff activates our brain's pleasure centers? In fact, the human tongue can detect four flavors—salt, sour, bitter, and sweet—but we're more naturally drawn to sweet because we've evolved from primate ancestors whose entire survival M.O. was to plunder super-ripe sweet fruits in trees—the best source of energy and water for a busy primate.
And since those early days—through no fault of your own—that tendency has become more pronounced, as humans developed agriculture, grains, and the ability to produce dense, carbohydrate-filled food. The natural sweet tooth has gotten more exaggerated. (By the way, if you think the primate diet sounds about right, consider that our chimp friends are always in active mode, swinging on branches, burning through carbohydrates at rapid speed, not perched all day in front of a computer screen, storing up carbs as fat.)
Our pleasure centers are also fired up by fatty, salty things, because we need fat as well as the right amounts of sodium to survive. Now factor in how our taste buds have been taken on a wild ride over the last few decades. Big corporations have figured out how to exploit our natural palate by developing edible products that deliver artificially enhanced instant gratification to our neuro pleasure centers.
The good news is that taste bud preferences can change and palates can transform. When you consume less of the dominant flavor profiles found in sweet and processed foods and gradually add in new flavors found in fresh, green, tart, and leafy ones, a kind of "waking up" occurs. Your palate literally expands. As the loud noise of artificially enhanced foods dies down, you gain a heightened awareness of the subtler yet delightful flavors naturally found in fruits, vegetables, nuts, seeds, and sprouts.
## PRODUCE MYTH BUSTED
MYTH: Fresh vegetables cost more than protein-dense foods.
Fresh veggies and fruits can seem pricier than their meaty counterparts, but USDA studies have found that, pound-for-pound, produce is actually less expensive than most protein-rich foods and processed foods. One of the keys to mastering affordable juicing and blending is to seek out alternative places to buy in volume, and to be flexible according to seasonable availability. When your favorite summer vegetables are out-of-season and getting shipped in from afar, consider switching to a smoothie with frozen fruits.
* * *
GOT TIME TO CHECK EMAIL? YOU'VE GOT TIME TO JUICE.
Buying your ingredients; washing and storing them; chopping and juicing or blending them; and inevitably, cleaning the juicer or blender afterward . . . there's no getting around the fact that juicing and blending involves finding a little extra time. The time factor is why thousands of people bought juicers back in the 80s (along with their roller blades), used them once . . . and then put them in the garage where they're still gathering dust. (And also why the blending trend, with its speedy production and cleanup, is possibly outpacing juicing in its growth.)
Rest assured that things have evolved since those early days: there are juicers on the market that can be cleaned in under 90 seconds; there are after-work farmers' markets and Community Supported Agriculture schemes (CSAs) that make buying your baskets of vegetables and fruits not only affordable, but fun. And with a few expert kitchen tips (like organizing your fridge and washing certain produce in advance), you can streamline the process down to ten minutes—or even five if you're making an ultra simple juice or blended beverage. The Green Curve will get you comfortable carving out a few extra minutes little by little—and not diving in to complex concoctions straight off the bat.
JUICY TIP
When it comes to best price and taste, buying what's in season will reward you most. Get acquainted with the deep flavor of ripe strawberries and tomatoes harvested at their peak, and you might start to question the taste and the sustainability of midwinter versions flown in from afar.
HOW MUCH JUICE IS TOO MUCH JUICE?
The goal of juicing is not to follow a protocol of a specific amount or schedule. The goal is to find what suits you and makes you feel good. Pay attention to your body and don't follow a set of rules that works for someone else. When in doubt, remember less is more. Start with a glass of juice or a small smoothie, and try it out first thing in the morning if you can. Make sure that you keep eating a healthy solid-food diet, even if you occasionally substitute a liquid meal for a plated meal. If you find you want to increase the number of liquid meals in your day, be sure to include lots of green, vegetable-rich drinks, coconut waters, and nut milks, and keep fruits in check.
Though the Green Curve is not a cleanse, some enhanced detoxification may occur, especially if you are also shifting off of irritating or toxifying foods. This could express itself as greater energy and better bowel movements, but also as temporary headaches and fatigue. Many healers say that the three-month mark is when people begin to notice deep and lasting changes from true dietary improvement. Three months happens to be the lifespan of red blood cells, so perhaps putting vibrant foods into your body for that length of time, along with cutting out bad habits, is why 90 days is a marker for a substantial shift. So consider making your Green Curve journey three months of adventure and exploration!
## JUICE DIY: GETTING YOUR KITCHEN PREPPED
Do you need a kitchen remodel to join the juice generation? Not at all. A couple of pieces of equipment—which you may already own—and some savvy shopping skills will get you started. If purchasing a juicer is too much of a leap at first, in Phase 1 you can begin with a blender and acquire a juicer later.
* * *
## SPOTLIGHT: THE JUICER
There are two kinds of juicers for at-home juicing. Centrifugal juicers grind produce to a pulp and release the juice by spinning it through a serrated metal basket at an extremely high speed. Masticating juicers "chew" the produce slowly, by pushing it through a slow-moving drill and squeezing out the juice. Centrifugals tend to be cheaper and are considerably faster at their job. Masticating juicers have their own advantage: Their slower speed means they don't cause as much friction as centrifugal spinners, meaning less heating up of the produce. Heat will speed up the oxidation of the naturally occurring enzymes and nutrients in the produce that occurs when you chop and break down whole food.
Several years ago I started a personal juicing program, which has had a profound effect on maintaining high energy levels, clear skin, and fast-growing, healthy hair. For me, good looks are important. Frequent TV shows, magazine articles, and public appearances require that I look and feel good, and that my appearance personifies everything I write and talk about. My green juice regimen is simple. I put a random combination of vegetables and fruits into my Breville juicer—food that I would enjoy eating whether juiced or not: nothing strong, pungent, or stomach ache–inducing. My mix includes celery, cucumbers, mint, ginger, papaya, carrot, pear, spinach, and orange peel.
—Martha Stewart, business magnate and publisher
A masticator also tends to get more juice out of your vegetables and fruits, especially the essential leafy greens. They can usually extract liquid from delicate plants like wheatgrass and sprouts, where most centrifugals cannot. They are typically more expensive to purchase; however, the benefits reveal themselves over time, when money is saved due to their efficiency with extraction. Other selling points: Many of the "single auger" masticating juicers come apart quickly and are extremely quick to clean. And there are now some vertical masticating juicers that can fit neatly into a snug kitchen corner. The cons: They do juice more slowly, and almost always require that you cut your produce into smaller chunks. If every second counts in your morning, you may want to look for one of the good-quality, speedy centrifugals. When shopping, keep in mind that cheap juicers tend to deliver less volume, and are less durable.
JUICING TIPS
When juicing, keeps these points in mind:
1. Pass your pulp through a second time to extract every ounce of juice from your produce.
2. Centrifugals usually produce more foam in the juice because they are more oxygenated. If foam bothers you, pour juice through a tea strainer and squish it through with a clean finger.
3. Keep a toothbrush by your kitchen sink to clean pulp off your juicer's metal graters.
Juice Smarts: If you don't already own an electric citrus juicer, you don't need a special one for citrus if you have a juicer. (With a citrus juicer, you also won't get the important nutrients from the white citrus pith the way you will by putting the whole peeled fruit through the juicer.)
JUICY TIP
Single gear (or "single auger") masticating juicers tend to be more affordable and easier to clean. Twin-gear (or "titrating") models are for devout juicers: They turn even more slowly and are said by juice aficionados to be the most efficient of all and the closest machine to a hydraulic press, though they are costly and will take a little longer to clean. A third at-home option is one of the new dual-extraction juicers that crushes and presses produce at a low speed. Its proponents say it gets even more nutrients than a masticating juicer and does not aerate the produce at all.
## SHOPPING FOR A JUICER? THESE QUESTIONS ARE KEY
How much do I have to spend right now? Can I afford more upfront and save by getting more out of my produce down the line, or is my budget on the tighter side today?
How long does the juicer take to produce juice—and more critical, to clean? Bothersome cleanup will stop even an enthusiast in their tracks. Check online reviews on every machine to get real-people feedback.
How efficient is the machine at extracting juice? Does it extract a good amount, especially from leaves? Does the pulp come out fairly dry (meaning most of the juice is out) or is it wet and goopy?
How fast or slow does it work, and what are the purported effects on its nutritional quality?
How long is the warranty on the juicer and its parts?
Will it fit on my kitchen counter and how does it look?
* * *
## SPOTLIGHT: THE BLENDER
Chances are you own a basic blender. That will get you started whipping up blended drinks. But bear in mind that a $20 blender might lack the power to grind frozen fruits, and certainly raw nuts, into pureed or ground form. (A burning smell during operation is a sure sign your blender can't handle it.) Medium-price blenders can do a better job with frozen produce and achieve a good consistency.
The true joy of blending is revealed with high-speed blenders, like those by Vitamix, the grandfather of all blenders, and from its newer rival, Blendtec. These (expensive) workhorses of the professional kitchen have become lusted-over items for amateurs because they are true heavy hitters. The consistency they achieve with blended drinks is remarkable (think: as creamy as a milkshake); they grind nuts and water beautifully into nut milks or instantly turn dry nuts into powder for your smoothie; and they liquidize things very quickly without wear and tear on the machine.
Some small, portable high-speed blenders now exist—often sold on late-night infomercials—that can be especially great for making smoothies at work or on the road. They may not stand up to long-term use in the kitchen like a full-size model, but they achieve surprisingly good consistency.
* * *
## MORE TOOLS OF THE TRADE
A FEW SIMPLE KITCHEN INSTRUMENTS WILL MAKE DAILY JUICING AND BLENDING A BREEZE.
Cutting boards for chopping produce. Bamboo boards are from sustainable resources, naturally antimicrobial, and cost effective.
Solid chef's knife for chopping. Keep it well sharpened but stored separately from your other kitchenware so as not to dull the blade. Tip: A good chef's knife will work for cracking coconuts safely and efficiently.
Sharp paring knife for opening fruits with hard rinds, like pomegranates.
Metal kitchen bowls for catching nut milk and coconut water.
Plastic spatula, or better yet a coconut scraper or "de-meater," for swiftly getting coconut flesh out.
Nut milk bag, or cheesecloth plus a metal sieve, to make homemade nut milks.
Mason jars or clean, recycled glass food jars.
Biodegradable produce wash and biodegradable detergent. (See for homemade produce wash recipes.)
Compost pail
Eric Helms, author and founder, sourcing strawberries at the Union Square Farmers Market in NYC.
## SHOPPING FOR PRODUCE
When it comes to produce, fresh is best, organic is even better, and local and chemical-free is ideal. We can't wait until the day when every person who wants to can easily and affordably adopt a 100 percent organic kitchen. Until that day comes, here are some ways to make the best choices.
* * *
1
If organic produce at your local farmers' market is too costly, look for stalls selling locally grown, pesticide-free produce that may not necessarily be certified organic. Ask the vendors how they farm and what kind of sprays and fertilizers are used. For many small-scale growers, organic certification is prohibitively costly, yet they still refrain from using chemicals either in fertilizing or pest reduction, and their prices are very fair. To find a market in your area, go to localharvest.org.
2
Buy organic for the most pesticide-heavy foods whenever you can. (See Clean Scene). At Juice Generation, we've always been a stickler for organic greens—these foods suck up so much water, we want them to be clean. Fruits with tougher skins like grapefruit, bananas, pineapples, mangoes, watermelons, and avocados will not contain as many pesticides and other chemicals, so these are less of an urgent concern.
3
Be a bargain shopper. If you find a bumper crop of beautiful organic berries, peaches, cherries, or other soft fruits at a market at their seasonally lowest price, stock up, prep if necessary, and freeze in separate baggies for months of off-season smoothie-making. (You'll find easy directions for freezing fruits successfully online.)
4
Get involved with growing your own. A little digging around may produce surprising resources in your area for helping you to plant an edible garden at home, getting involved in farm volunteer programs, or enrolling your kids in a garden initiative at school. This trend is only going to grow and grow.
5
Wax on, wax off: At the supermarket, check if conventionally grown apples and cucumbers are coated with wax (this seals in their water and keeps them looking fresh during long travel times). These waxes can have pesticides and fungicides added, and don't tend to rinse off with water (which is another reason to have a biodegradable produce wash on hand). You can peel these things, of course—but then you're losing valuable nutrients concentrated in the surface layer. Nix the produce that looks suspiciously shiny.
CLEAN SCENE
The following juicing ingredients tend to be the most chemical-laden when grown conventionally, so grab the organic version whenever possible.
Apples
Carrots
Cherries, grapes
Lettuces
Pears
Strawberries
Bell peppers
Celery
Cucumbers
Peaches, nectarines
Spinach, kale, chard
Collard greens
Note: Frozen fruits have been grown in the same way as fresh fruits, so check if your local store carries organic frozen fruit at a price that works for you.
OMG, GMO!
Genetically Modified Organisms are foods that are grown from seeds created in a laboratory. When food is a product of biotechnology instead of nature, its long-term effects on the body become questionable. Soy is one of the top GMO offenders, so that's why you should try to always choose an organic brand of soy milk. (Organic food cannot by law be GMO). There are only four vegetables and fruits grown from GMO seeds at present: some variations of zucchini, yellow crookneck squash, sweet corn, and papaya. The only one that may affect your juicing habit is GMO papaya from Hawaii.
JUICY TIP
Produce stickers on supermarket foods can tell you at a glance if the fruit or vegetable is conventionally grown or organic. A 4-digit code is conventionally grown. A 5-digit code starting with a 9 signifies organic. A number 8 at the start means it's GMO. This labeling is optional however, so it's always better to look for an organic sign on the shelf itself.
## PREPPING THE PRODUCE
Whatever your crunchy friends may tell you, washing all produce is very important. No matter where the fresh food comes from, dirt, germs, soil-born pathogens, human-carried pathogens, and exhaust fumes can all get on it, not to mention chemicals from pesticides, herbicides, and fungicides if it's not organic. Wash all produce well before using, swirling it well in your sink with your hands, and rinsing in fresh water. Scrub root vegetables with a special scrubbing brush under cold water. And wash all citrus fruits before cutting.
To ensure you've done the best job possible, add a tiny squirt of a biodegradable produce wash to ensure contaminants like dirt and any petroleum-based chemicals on conventional produce, as well as applied waxes, are well removed. These tend to be made of food-grade cleansing agents. A little of this goes a long way: You can put some in a spray bottle of water and spritz it onto produce in the sink before rinsing well. Soak fragile berries and herbs in a very diluted solution of produce wash for a few minutes; then soak again in clean water. Of course, produce wash cannot remove the pesticides inside the produce, so it does not make it organic. But it helps. (In case it's not obvious, dish soap is not appropriate for this job!)
* * *
WASH YOUR WAY: THREE PRODUCE WASHES YOU CAN MAKE FROM YOUR PANTRY INGREDIENTS
Combine the following ingredients in a spray bottle: 1 tablespoon lemon juice + 1 tablespoon white vinegar + 1 cup water
OR
1 tablespoon baking soda +1 cup white vinegar + 1 cup water
OR
10 drops grapefruit seed extract + 1 cup white vinegar + 1 cup water
Spray on vegetables and fruit, let sit for 5 minutes, and rinse well under cold water using a scrub brush for hard vegetables and fruits.
Kitchen Wisdom: How to Get the Most from Your Precious Produce
Harder produce like apples, carrots, cucumbers, and pears can be washed in advance, then air dried on a towel and stored. More delicate leafy produce presents a problem: any remaining moisture will quicken the wilt in the fridge. Either salad-spin and leave to air dry extremely well before storing in the fridge, or wash as you need it.
Chopped vegetables will start to oxidize at the surface areas where they're cut. There's no science to show exactly how much this degrades the nutritional value. Keeping them whole until the last minute is preferred, but if chopping in advance helps you fit juicing into a busy day, go for it.
Drying the produce very well after washing and before storing is key. Kick it up a notch by storing your refrigerated produce in produce-saver, BPA-free plastic bags that use a natural mineral to help retain freshness. They are reusable many times over if you take care of them. Look for them in your health-food store. You can also invigorate wilting greens and herbs by storing them in jars of water in the fridge.
These fruits do not need refrigeration until they soften or you slice into them:
Apples
Apricots
Avocados
Melons
Nectarines
Peaches
Pears
Persimmons
Plums
Do not refrigerate the following:
Bananas (they will blacken)
Chiles
Garlic
Mangos
Pineapple
Sweet potatoes
Tomatoes
Root vegetables like carrots and beets do well with refrigeration, but also store pretty well in cool, dark places outside of the fridge if you take the leaves off. Herbs like parsley and cilantro can be kept on the counter with their stems in a glass of water.
Freshly juiced produce will start to oxidize the minute it's made. The best tip for saving juice for later is to put it in a jar that you can fill all the way to the top, so the juice touches the lid. This means it's not exposed to oxygen and won't oxidize further, retaining most nutrients. Put it in the fridge, because exposure to sunlight will also cause oxidization. Some experts think that 90 percent of the juice's value is retained this way if drunk within 12 to 24 hours. We don't recommend freezing your juice; it denatures it too much after all your good efforts. Smoothies typically endure a bit better in the fridge; again, store in an airtight container.
JUICY TIP
Glass jars are better than plastic for storing juice as plastic is permeable to oxygen. You can clean and save different size jars (think: salsa, nut butters, mustard, pickles) to have a range of sizes on hand, or use the American canning classic that's back in fashion with the foodie crowd: Mason jars.
Cold-pressed juicers, like the Norwalk, produce dry, jewel-toned pulp.
## THE PULP PREDICAMENT
Every time you juice you make a lot of pulp. The vast majority of juicers trash this colorful mix in the name of time and convenience. Not so fast! It's full of good things for you and the earth. At Juice Generation, we compost every night and even put free pulp out for neighborhood gardeners, who come and fill baggies to take home to their plants. Consider keeping your juice pulp out of the landfill:
1
Use pulp in snack recipes. Juice pulp can be used to make flax crackers that are dehydrated in the oven on low or in a dehydrator. It's a gluten-free snack that is far cheaper than boxed crackers. A quick search online will reveal recipes for dehydrator crackers, as well as muffins and carrot cakes that use juice pulp. (Some juice blogs even post savory ideas like baked vegetable patties and throwing your pulp into vegetable stocks for soup.)
2
Compost it yourself: If you have a backyard, consider creating a compost pile in a corner for the increased amount of pulp and produce waste you'll be generating, and know your juice waste will go back into the garden. If you have a patio, a tumbler composter should fit easily and somewhat unobtrusively. If you're in an apartment with no outdoor space, an indoor compost contraption—aka a worm tower—is actually doable and delivers you a fertilizing "tea" that your house plants will adore. And if you live in a progressive city like San Francisco, Seattle, Boulder, or Portland, or in a neighborhood that is part of New York City's new green program, you're in business: Compost gets picked up by the city from your curb.
## A GREENER, CLEANER KITCHEN
Juicing and blending require copious amounts of natural ingredients sourced from the earth—so when whipping up your favorite drinks it only seems right to bring some awareness to the environment from which they came. Just a few easy steps make a green drink even greener:
1
Turn the tap off! When washing produce, there's no need to keep water running for five minutes. Fill up your sink once, wash all your produce, then drain and fill a second time to rinse well.
2
When taking your drinks on the road, go for glass. Glass is free from harmful chemicals like BPA, phthalate, PVC, or polycarbonate that can leach into your beverage. Salvaged glass food jars make excellent to-go cups or look for a glass water bottle. If you prefer a less breakable vessel, get an insulated stainless steel thermos.
3
Next time you restock your under-sink supplies, try a natural cleaner for your countertops and reduce the toxic load of chemicals in your home.
4
Before reaching for a new pack of paper towels, stop! Chefs use washable kitchen towels in their kitchens—follow their lead and get a three-pack of cloths for cleanup and drying. (Lay wet vegetables on clean cloths to let them air-dry thoroughly before storing.)
5
Ditch the plastic baggies and shrink wrap: Buying your fruits and vegetables loose by the pound instead of prepacked is instant resource conservation. Take reusable sacks or recycled plastic bags of all sizes to the supermarket and farmers' market.
## SIP TIPS
Believe it or not, the way you drink your juice or smoothie does matter! Drink it at room temperature, not ice cold; this way it's easier to assimilate. Try to resist gulping it down. Sip it slowly and swirl each sip a little in your mouth so it mixes with saliva—this contains digestive enzymes that won't otherwise be activated, as you're not chewing your food when you drink it.
It is good to drink fruit juices on an empty stomach as fruits digest very quickly, and you don't want them to ferment in your stomach on top of slower-digesting solid foods. Then wait 20 minutes or so before eating anything solid. Vegetable juices also tend to give a more energizing effect when consumed on an empty stomach. If drinking them as part of a meal, pay attention to how your belly feels when food and juices combine. For smoothies, it's a similar guideline: consuming them significantly before or after a solid-food meal leads to better digestion
## phase 1
## LIGHT GREEN: BRIGHT AND REFRESHING
Give us five minutes of your morning; or maybe seven. Show up to your kitchen counter with your taste buds just the way they are and nothing but curiosity and a carrot—or ten—in hand. You've just stepped onto the Green Curve.
Nothing in this first phase of making liquid foods requires much preparation or many ingredients—and you're only going to dabble in the color green. This phase is all about small and reasonable steps. You don't even need to invest in a juicer in week one. A blender will do at first if you prefer to ease in conservatively.
Phase 1 is about simplicity and experimentation. You'll meet three key players who are set to become close compatriots on your juicing journey: celery, cucumber, and carrot. These humble vegetables, sometimes overlooked as no more than crudités, prove their preciousness when put through a juicer, because they produce so much liquid with such an array of benefits. They are "base" ingredients that form the foundation of your drink. Cukes and celery are also the two green vegetables that are the easiest to start with on your green journey: Because they're not ultranutrient dense, they don't have strong flavors, which makes them eminently palatable.
This first phase of juicing will also have you liquefying fruits that are positively bursting with goodness, like tart apple and vibrant orange and watermelon. And it offers a gentle introduction to the drinkable versions of two easy-to-find and nourishing leafy greens: kale and spinach. These foods offer a vast range of vitamins, minerals, and antioxidants as well as providing powerful health benefits—from blood sugar regulation to detoxification to improving your cardiovascular and circulatory systems.
Phase 1 also breaks down the smoothie into its simplest components and shows you how to whip one up with a variety of options.
These drinks skew a little on the sweet side. This is a deliberate tactic to lure your palate, not a long-term daily strategy. Be sure to try a range of the combinations in the days and weeks of Phase 1 and don't forget: Make sure a few of them contain spinach or kale.
THE TRADE-OUT: During Phase 1, set yourself a small challenge. Try to replace a midmorning or midafternoon pick-me-up drink with a juice or blended, and see how it makes you feel. After enjoying it, ask yourself: Do I have more energy or alertness? Do I still crave the caffeine top-up or energy drink? Could I do without it today? Don't make huge, hard goals if you don't want to—simply play with this new habit day by day and take a moment to see how it affects you. Use Phase 1 as a time to see how a fruit-and-veg boost can work for you.
Bonus: Phase 1 introduces you to satisfying and energizing drinks made without dairy. Limiting pasteurized dairy products throughout your day—like lattes, yogurt, and cheese—can be one of the most effective things to help you feel clearer, lighter, and brighter.
If this Trade-Out sounds deceptively simple, remember that in a world of rush-rush-rush and no-time-to-think, finding the time to stick something fresh in a juicer or blender is a little, sweet victory. You'll dial it up in the next phase as you learn the ropes.
Hack That Juice! Two-in-one recipes make busy life a little easier. Throughout the book, we'll show you how to "hack" your juice, turning it into a smoothie with one added step.
Carrots, strawberries, Granny Smith apples, and spinach (for a touch of iron): It helps feed my soul and feed my cells and the carrots help me read the fine the print.
—Katie Couric, journalist and broadcaster
## PHASE 1 BUYING GUIDE
Your Green Curve goal in Phase 1 is to make juices or blended drinks with a 30 percent green factor—meaning at least some of them must contain greens. You can have them at any time of day that works for you. Try to incorporate both juices and blended drinks into your routine; the idea is to get familiar with both. Pick different combinations so that you've gotten acquainted with a range of ingredients and flavors and tried a spectrum by the end of this phase.
* * *
## PHASE 1 JUICES: CLASSIC COMBINATIONS
As an athlete, juicing is very important for me because I deplete my body with very intense training every day, and it's impossible to optimize my training without fueling my body with the best foods I can. Juicing makes it a lot easier to eat all the fruits and vegetables I need. The ingredients I use are also good for skin and hair health, inflammation, and coping with stress. I can tell the difference when I'm on a consistent juicing regimen: I am more alert, my recovery is at it's best, and I feel better.
—Sanya Richards-Ross, four-time Olympic gold medalist in track and field
### Sanya's Gold Medal Greens
Race by the market stalls to fill your basket, and you'll have the fixings for a champion drink that delivers vegetables' benefits with a fruity finish.
1 cup spinach
1 cup parsley
1/2 small beet
2 medium apples
1/2 medium pear
4 medium carrots
Juice.
Phase 1 introduces the essential ingredients of juicing. We show you the trios of easy ingredients that fill most juicing fan's fridges—things that harmonize well and that, even more important, deliver satisfying amounts of juice. They follow a flavor-combining pattern: They combine a neutral flavor that isn't too strong, plus a little sweet flavor and a little bold flavor that wouldn't work so well on its own. This achieves a balance in your cup.
The recipes give rough amounts of ingredients to make approximately 12 ounces of juice, but don't worry about being uber-exact. This is in-the-field training; if you get familiar with how much juice you tend to get from your produce, juicing becomes second nature. Unlike baking, which requires exact recipes to produce specific results, we believe that juicing falls under the "Italian grandma" style of food preparation; add a little of this, a little of that. Plus, there's some trial and error involved with discovering the perfect combinations of flavors. When adding ingredients to your juice or blended, think in terms of roughly packed cups, loose handfuls, or small pinches instead of exact measured ounces. Choose experimentation over precision. And have fun!
Not ready to splurge on a juicer yet? Try these combinations as blended drinks if your blender does a great job with hard produce, but add water or ice to make sure they blend. If your blender cannot handle hard produce, stick to the smoothies in this section the first week while you find a juicer that works for you, then start juicing in your second and third weeks.
JUICY TIP
Start by juicing and blending things you already like to eat. You have to enjoy this to stick with it. In most recipes, the order of ingredients juiced is not written in stone. But there is a basic protocol: When juicing several fruits, juice the softest ones first, followed by the harder ones—this helps to push all their pulp through and extract maximum liquid. If using a centrifugal juicer, try rolling up your green leaves into cigar shapes to make them denser before pushing them through; follow with a harder vegetable or fruit.
BEETS
Why We Love Beets
Beets are a welcome addition to any juice, adding palate-pleasing sweetness and equally satisfying health benefits. Beet juice has been found to lower blood pressure, purify the blood, and increase the production of glutathione, which helps the body eliminate environmental toxins. Scrub them well under running water, chop, and juice. (And keep the greens—you can juice them, too.)
CELERY
Why We Love Celery
1. It's one of the most hydrating foods we can put in our bodies.
2. Celery's incredible alkalizing effect helps to equalize the body's pH.
3. These stalks have special essential oils—you can probably smell them right away—that help regulate the nervous system and are very calming.
4. Celery supplies our cells with the soluble, live sodium they need to uptake nutrition and stay hydrated, which is why celery juice is a good rehydration drink for athletes.
CARROTS
Why We Love Carrots
1. Carrot juice is sometimes called the golden juice of healing—it cleanses and restores the liver.
2. As a deep-soil root vegetable, carrots absorb an abundant array of minerals from the earth; they are especially rich in B vitamins and folate.
3. They have a surprising dark side: Early varieties of carrot were mostly purple and black. Our modern orange carrot stems from a mutant source that lacked those pigments.
4. When in a rush or in the mood for simplicity, carrot juice tastes terrific on its own.
### Celery, Carrot, Spinach
2 stalks celery
4 medium carrots
1 cup spinach
Juice.
Hack That Juice! Blend with 1/2 a medium banana to make a smoothie.
### Carrot, Beet, Spinach
4 medium carrots
1/2 small beet
1 cup spinach
Juice.
### Carrot, Orange, Kale
4 medium carrots
1 medium orange, peeled
1 cup kale
Juice.
Hack That Juice! To turn your juice into a smoothie, pour into a blender and add 1/2 medium avocado.
JUICY TIP
Pick out carrots that are firm and smooth; ditch the ones that are cracked or molded. If you scrub the carrots well under water to remove all dirt, there's no need to peel. Chop the tops: Too many carrot greens can trigger your skin to burn in sunlight.
CUCUMBER 101
1. Put cucumbers in the juicer and watch the liquid flow—they are primarily made of water and deliver satisfying amounts of juice.
2. Their outer skin is a superb source of silica, a mineral that helps our connective tissue stay strong—and improves the complexion and skin health.
3. It plays well with others: Cucumber juice on its own doesn't have a whole lot of pep. But its neutral flavor makes it the perfect partner for almost everything else!
ORANGE 101
When juicing oranges, a juicer trumps a hand-held squeezer or citrus press because it puts the important nutrients from the pith into your drink. Wash and roughly peel your oranges, leaving as much white pith as possible on the fruit.
WATERMELON 101
Cooling, sweet, and quite low in sugar, watermelon offers a surprising twist: The rind has a concentration in minerals, antioxidants, and B vitamins as well the fruit's highest concentration of the amino acid citrulline, which supports healthy blood flow, supports detoxification, and refreshes fatigued muscles. If you can get organic watermelon and you wash it very well, juice part of the rind along with the flesh to get all the goodness. If it's not organic, it's safer to nix the rind.
JUICY TIP
If your cucumbers are not organic, wash them very well. If they're waxed, be sure to peel them. Always pick cukes that are medium-to-dark green, not yellowed or aged.
Use blood oranges when available to up the ante on flavor, color, and wow factor.
### Cucumber, Pineapple, Celery
1/2 medium cucumber
1 cup pineapple
3 stalks celery
Juice.
### Cucumber, Watermelon, Lemon
1/2 medium cucumber
2 cups watermelon
1/2 medium lemon, peeled
Juice.
### Orange, Pineapple, Beet
3 medium oranges, peeled
1 cup pineapple
1/2 small beet
Juice.
### Watermelon, Orange, Cucumber
1 cup watermelon
1 medium orange, peeled
1/2 medium cucumber
Juice.
### Celery, Pineapple, Ginger
6 stalks celery
1 cup pineapple
1 inch fresh gingerroot, peeled
Juice.
### Watermelon, Pineapple, Lime
2 cups watermelon
1 cup pineapple
1/2 medium lime, peeled
Juice.
### Orange, Apple, Spinach
2 medium oranges, peeled
1 medium apple
1 cup spinach
Juice.
THE G FACTOR: GINGER
This aromatic spice is one of the easiest ways to add a shot of spicy, warming flavor to your juices. But use a gentle hand—small amounts go a long way. The best way to spike your drink is to toss an inch-long knob into the juicer and judge how strong you like it. Look for firm, almost-hard ginger with unwrinkled skin. The thicker the skin, the stronger the flavor.
Combination Considerations: Some juicers (people, not machines) caution against combining fruits and vegetables in one drink, with the exceptions of green apples and carrots (they almost always get a pass to mix freely). The thinking is that the two food groups break down in the stomach in different ways, and this creates gas, bloating, and discomfort. Other juicers disagree, saying this is more of a philosophical idea than a physiological one, and it's not a hard and fast rule.
The best way is to get to know what works for you is to tune in to your own body's response. If you don't feel any gassy discomfort when mixing fruits and vegetables in your juices and smoothies, you are probably OK to continue. If you notice discomfort in your tummy, scale back to separate fruit-based drinks and vegetable-based drinks, with green apples and carrots available to both, and pay attention to the effect. If separating the two groups works better for your digestion, follow that path moving forward.
### Green Apple, Ginger, Orange
1 medium green apple
1 inch fresh gingerroot, peeled
2 medium oranges, peeled
Juice.
Hack That Juice! Blend with 1/2 a medium avocado to make a smoothie.
## LEMONS AND LIMES
Lemon and lime are a juicer's support crew. When thrown into juices, they add an energizing zing, have an alkalinizing effect—despite being citrus fruits—and mask bitter flavors, which makes them perfect companions for darker and more bitter green vegetables. Always have a stash of limes in your fruit bowl. If you overdo the darker greens like kale and get a too-bitter juice, another lime can help bring it back to balance.
FOR THE LOVE OF LEMONS
Morning juicing goes hand in hand with another easy habit: drinking hot water and lemon on waking. It especially helps if you're pledging to decrease caffeine. As you make your morning juice, sip on the lemon water and enjoy its uplifting effects. It floods your body with alkaline fluid, which is helpful as the body becomes more acidic overnight through digesting and detoxifying. It dissolves mucus and helps to flush the liver, helps you absorb minerals better, and encourages the formation of bile in the gallbladder, which helps to break down fat. It also helps to stimulate the bowels to move in the morning. If you enjoy the taste, drink this simple mix throughout the day—warm or cool.
## APPLES
Don't overlook the humble apple. Taken for granted as an everyday fruit, the humble apple is a shining star in raw juices, which showcase its popping flavor. At Juice Generation, we get our apples from a historic New York State orchard that grows more than 30 different varieties, and we think exploring the spectrum of apple varietals is a journey in itself. Tart, green apples are the primary, low-sugar choice for mixing with vegetables to make green drinks; red varieties like Fujis have an irresistible, pear-like flavor for a sweeter drink. And there are many, many more to try.
It doesn't take much effort to extract the specialness of an apple. A simple combo of one or two ingredients is enough. Try varying red and green apples to learn their flavors and sweet-tart effects.
I am relatively new to juicing and I can honestly say the difference I feel is HUGE. Every morning on set I have my "green" drink, which is spinach, kale, cucumber, lemon, celery, green apple. Sometimes I'll add beets, and if I'm under the weather I'll add ginger. I'm not a big green vegetable eater, so the juice really has filled a huge void in my diet, and I feel stronger for it.
—Debra Messing, actor
### Debra's Green Elixir
The neutral greens of celery and cucumber plus the sweetness of apple and beet make this admirably green juice balanced enough to be completely inviting, not intimidating.
3 leaves kale
1 cup spinach
1 medium apple
5 stalks celery
1/4 medium cucumber
1/2 small beet
1/2 medium lemon, peeled
Juice.
### Tropical Lust
Pineapple is high in bromelain, an enzyme that helps the body digest proteins and reduce inflammation. Eating—or drinking—fresh pineapple is not only a gustatory delight, it can help reduce swelling and pain from injuries.
2 cups watermelon
3/4 cup pineapple
1 medium apple
1 inch fresh gingerroot, peeled
Juice.
### Red Delicious
Orange and carrot add depth and color to red apple juice plus another gift: a good dose of vitamin C and beta-carotene.
11/2 medium red apples
5 medium carrots
1 medium orange, peeled
Juice.
### Apple Zing
Ginger adds a spicy kick while delivering anti-inflammatory benefits and soothing digestive distress like nausea.
3 medium apples
1 inch fresh gingerroot, peeled
1/2 medium lemon, peeled
Juice.
### Apple Mint Smoothie
Proof that fruits, vegetables, and a blender can be best friends. In this drink, that minty multitasker peppermint offers an uplifting hit that is high in potassium, iron, and calcium as well as vitamins A, C, and E.
1 bunch fresh parsley
1/4 medium cucumber
1/2 medium apple
1/2 medium frozen banana
1 sprig fresh mint
1 cup filtered water
Blend.
### Daily Detox
Diversify from the typical carrot juice with the supremely hydrating addition of cucumber and a twist of apple for maximum thirst-quenching refreshment.
5 medium carrots
1/4 medium cucumber
1 medium apple
1 inch fresh gingerroot, peeled
1/2 medium lemon, peeled
Juice.
Juice Smarts: Apples are a rich source of pectin, a gel-forming soluble fiber that helps your intestines draw out toxins and excrete waste, as well as helping to reduce cholesterol.
Apple Picking
Look for apples that are firm and well-colored—more color means the apple was picked when it was more mature, which means it will have more flavor and longer lasting power. An apple that's soft to the touch is overripe. Farmers' markets often have "visually distressed" boxes of organic apples that are a little dinged up but great for juicing.
JUICY TIP
Want to try making an apple "juice" in your high-speed blender? Add some water to help it liquefy, and expect a thicker puree. Just remember to remove the woody stem.
## PINK, WHITE, WHAT'S RIGHT?
Ruby red (also called pink) grapefruit has far more vitamin A than the white-yellow varieties, as well as antioxidants that help lower blood sugar levels and lycopene, which has antitumor properties. The pink fruits also tend to taste considerably sweeter. But both kinds have their fans: Do a taste test and see what you like best. Whichever you choose, pick fruits that are firm, feel heavy for their size, and have no green color showing in the peel.
THINK MINT
Try a touch of mint to add refreshing flavor to sweet and tart fruit juices, coconut blends, and lighter green smoothies. This easy-to-grow herb is soothing on digestion and has some antiviral benefits—but as with many delicate leaves, you may find it juices better in a masticating juicer or high-speed blender than a centrifugal juicer.
* * *
I swear by my Citrus Super C. We do eight shows of Once a week, sometimes nine at the holiday season—it's a taxing schedule. Between shows, juicing is my healthy alternative to cramming down a burger. After beginning to juice, I found that my skin was starting to look better, I was sleeping better, I was waking up in a better place, my days were brighter, and things just felt better. It's almost a spiritual experience; you really start to believe that you can do just anything. I think it shows in the production, it shows in the role, and I think it shows in the way people respond to me.
—Steve Kazee, star of the Broadway show Once
GRAPEFRUIT
Tart 'n' Tangy: Energizing Grapefruit Combos
Grapefruit's bold flavor is complemented by bright additions like mint and ginger. Add more or less as you see fit!
Grapefruit is your energizing wake-up call. Ditch the idea that grapefruit is breakfast for retirees (you know: half a grapefruit with a side of prunes and a cherry on top). This morning glory is better seen as classic. And for good reason: Grapefruit has powerful properties to aid the kidney, liver, and gallbladder and, taken first thing in the morning on an empty stomach, you'll feel its tingle of cleansing, refreshing energy. It's also got a special extra twist: It stimulates the liver to go into fat-burning mode.
Make grapefruit part of your breakfast of champions with a few simple ingredient combos. It's shockingly easy to draw out every sparkling facet of grapefruit—and discover why its Latin name is Citrus paradisi.
It's important to always peel your grapefruit before juicing, because the peel is toxic if ingested. Conventionally grown grapefruit will also have a lot of pesticides on its peel. But leave as much of the white pith on as possible—it's a rich source of phytonutrients.
### Citrus Super C
3/4 cup pineapple
1/2 medium grapefruit, peeled
2 medium oranges, peeled
1 sprig mint
Juice.
### Grapefruit Refreshmint
2 medium grapefruits, peeled
1 sprig mint
Juice.
### Grapefruit Moon
11/2 medium grapefruits, peeled
1/2 medium pear
1 inch fresh gingerroot, peeled
Juice.
### Grapefruit Zinger
2 medium grapefruits, peeled
1 inch fresh gingerroot, peeled
Juice.
### The Grateful Grapefruit Juice
Can you blend your grapefruit? Absolutely: it's a fabulous way to keep the fiber intact, too. The better your blender, the more smooth and silky your drink will be.
2 medium grapefruits, peeled
1/2 cup peach
1/2 medium banana
1 tablespoon raw agave
1/2 cup ice
Blend.
Juice Smarts: Grapefruits contain an enzyme that interacts with some prescription medications, including certain cholesterol-reducing, psychiatric, and impotence drugs—often dangerously enhancing their effects. If you're on medication, check with your doctor for contraindications before getting a serious grapefruit juice habit.
## WHY KALE IS KING
1. It's available year-round because it's hardy in cool weather and a survivor in hot weather.
2. It's durable and lasts for some time in the fridge.
3. There is an array of varieties, from the slightly bitter curly kale, to the dark green, earthy dinosaur (also called lacinto) kale, to the purple-stalked Russian kale, and more. Try whatever looks freshest and most appealing, notice any differences in taste and juice volume, and rotate your choices through several varietals for maximum nutrition.
4. It's a cruciferous vegetable, part of the same family as cabbage, collards, broccoli, and cauliflower (also called the brassica family), which contain unique sulfur-containing compounds that provide a spectrum of anticancer benefits. Kale supercharges the natural protective mechanisms of our cells, and helps prevent deposits of plaque inside blood vessels. It's a health and longevity miracle food!
* * *
KALE
At the Juice Generation stores, we go through crates of kale each day. We're huge fans of this humble vegetable—despite its intimidating, so-green-it's-almost-black appearance—because it scores number one on the vegetable scale of most micronutrients per calorie. Many juice gurus say that kale has such a strong flavor—and bold effect on the body—that it is for expert juicers only. But we beg to differ: If you ease in moderately, it's never too soon to start using the leaf that packs the biggest nutritional punch. Juiced on its own, kale has a way-too-bold taste. But if you combine kale with the right ingredients and in the right balanced amounts, you can enjoy superb nutritional benefits and satisfying flavor. The sweeter combos here help to downplay its naturally bitter (read: good for you) taste. Don't try to drink supersize glasses of kale juice—it's concentrated nutrition and you only need a little to benefit.
Juice Smarts: If you juice or blend a lot of cruciferous vegetables like kale, make sure your diet is well supplied with iodine, which is found in kelp and other seaweeds. Adding 1/2 to 1 teaspoon of powdered kelp to a smoothie every so often is a superb way to do this. You can also use iodized salt, multivitamins, or iodine supplements. You need adequate amounts of iodine because consuming large amounts of raw cruciferous vegetables may interfere with thyroid hormone action in some people by blocking the utilization of iodine. If your dietary iodine levels are adequate, it should all balance out. If you have a known thyroid issue, consult with your health practitioner about the amount of raw kale that is wise for you. In Phase 2, we'll tell you why it's smart for everyone to rotate their greens.
I am obsessed with any and all green juices. Cut spinach, kale, or Swiss chard with a little lemon or apple, and you can't even tell that you are drinking something ridiculously good for you. Making healthy food choices and preparing them takes a great deal of time, often time that I don't have. Juicing takes the work out of the equation and frees me from thinking about food so I can concentrate on other things. I can't think of anything that makes me feel as good and is as easy to do.
—Michelle Williams, actor
JUICY TIP
When juicing kale, the whole leaf can go through the juicer. When blending kale in a smoothie, roughly tear the leaves off the thick stems, then compost or trash the stems.
### Michelle's Leafy Green Goodness
Three kinds of green leaves deliver potent nutrition in an easy-to-drink blend of fresh apple. Use tart green apples to lower the sugar content if you like.
3 leaves kale
1 cup spinach
2 leaves Swiss chard
4 medium apples
1/2 medium lemon, peeled
Juice.
### Emerald + Orange: Kale + Carrot
Sometimes the simplest combos are all you need. 2 powerful ingredients with two vibrant colors.
1 cup kale
5 medium carrots
Juice.
### TropiKale: Kale + Pineapple
Dark, green kale is surprisingly refreshing when combined with clean, sweet pineapple. And the two are nutritional dynamos, creating a juice brimming with calcium, antioxidants, and vitamins K and C.
1 cup kale
2 cups pineapple
Juice.
### Leaves & Roots: Kale + Carrot + Beet
A blend of above-ground and below-ground vegetables treats your body—and your taste buds—well.
1 cup kale
4 medium carrots
1/2 small beet
Juice.
### Hail to Kale
A Juice Generation bestseller, this classic recipe has helped thousands of juicers fall unexpectedly in love with the wonder that is kale.
1 cup kale
1 cup watermelon
1 medium apple
1/2 medium lemon, peeled
Juice.
## PHASE 1 SMOOTHIES: PURE SIMPLICITY
Back in about the late 80s, the smoothie burst on the scene in a riot of sherbet and fruit juice. Thick, goopy, frosty, and oh-so-sugary, these tropical and vivid-hued concoctions weren't exactly paradigms of health. They were jazzy, tangy, exciting fun foods—a new twist on the milkshake!—that were often found alongside the smoothie's best friend, frozen yogurt. We could sort of feel good about them, because of all the fruits. But with that sugar rush-and-crash, and probably a fair dose of colorings and flavorings, they sure left us feeling a little worse for wear.
Today, we're in the middle of a smoothie revolution! Sherbet is out—and vegetables, nut milks, exotic fruits, performance protein powders, superfoods, and medicinal herbs are definitely in. The landscape of blended drinks has totally evolved. We're waking up to the pressing need for more fiber, and much more enzyme action, in our diets and connecting the dots between deficiencies and disease. A new appreciation for green smoothies has millions chucking spinach and parsley into their blenders with crusading zeal, eating pounds more greens than ever before.
It's funny how the passion for upping the ante with new ingredients can sometimes make us forget that a blended drink doesn't have to be complicated to be good. A few ripe and tasty things combined with a good-quality base will deliver a satisfying snack that sneaks lots of vibrant nutrition into our diets with absolutely minimal effort. Just wash, blitz, and go.
The smoothies in this section show you—or remind you—just how easy it can be. Pick a base liquid; select a fruit or two; try sneaking in some greens; and if you feel you need it, add a touch of extra sweet in the form of dates to blend the flavors together. A little sweetness can help downplay the vegetable factor for those taking a first foray into green drinks.
THE VERSATILE SMOOTHIE
Blended drinks come in many tastes and textures and serve many purposes. You can greet the day with a fresh, energizing smoothie made with low-sugar fruits and a handful of greens—an easy introduction for a digestive system that's been resting all night. Or you may whip up a super green smoothie out of a commitment to consume serious amounts of greens. You can spike it with protein and fats to make a meal-in-a-cup, a hearty concoction to take you from the morning meeting to lunch. There are smoothies to support a workout; smoothies that deliver a wallop of superfood goodness; and sweet and creamy smoothies that can stand in for dessert. You'll meet all of these blended drinks and more in Phases 2 and 3.
## THE ESSENTIAL COMPONENTS
It's simple. First, find a base liquid. Next, add fruits and vegetables. Then blend. These juicing prerequisites will make you a seasoned smoothie-maker in no time.
* * *
1
FIND YOUR BASE
The base is the liquid carrier for whatever fruits and vegetables you choose to use. Without it, you'll get a pureed mush—or possibly paralyze your blender. You can play with a spectrum of liquids here to get different kinds of drinks:
Water A totally valid base liquid for many a smoothie, especially those bursting with fruits and greens. It won't add any flavor, so make sure everything else in the drink is popping with taste. Filtered water is ideal. Bottled water, due to its impact on the environment, is less so.
Fruit juice Tangy and tasty, but don't get hooked on big quantities of store-bought juice every day (see Juice Imposters). You only need to use fruit juice in moderation—and a good trick is to add splashes of bold-flavored juices, along with water, into your mix (like pomegranate, acaí, and berry-cherry blends).
Juice your own When possible, we like to juice our own apple, orange, and watermelon and then add to smoothies. It takes a few minutes more, but it's the freshest and most nutritious way to put nature's bounty into your cup, and the taste is incomparable.
Coconut water Boxed coconut water is a big business these days as everyone discovers its refreshing effect, life-supporting electrolytes, and lower-fructose composition. We much prefer drinking from fresh young coconuts—introduced in Phase 2—but packaged varieties are time-saving and can work well in smoothies. There's a huge variety in flavor; the best you'll get (at a higher cost) are the new "100% raw" coconut waters that are pressure-pasteurized (rather than heat-pasteurized). Canned ones may have added sugar or preservatives—but not always. Read the labels.
Nut milk The easy way to add a richer, creamier texture, a decent amount of protein, and a little fat to your drink is with a nut milk. You'll find a great amount of choices on supermarket shelves, from nut, seed, legume, and grain bases. Look for almond, soy, hemp, oat, rice, flax, hazelnut, and coconut milks—and more. Many offer good nutrients and are a fine dairy substitute, but the convenient boxed versions come with a downside: Most contain some added cane juice for sweetening and additives like preservatives, and they are pasteurized, not fresh made. When nut milks are sickly sweet, they overwhelm your fresh fruits and vegetables. It's best to look for unsweetened, unflavored versions (you can use natural sweeteners to adjust the final taste) and with soy milk in particular, make sure it's organic. Stick with us through Phase 3 and we'll show you the absolute best way to get your nut milk on—make it yourself!
Juice Smarts: A seaweed-derived ingredient called carrageenan is often used in boxed soy and nut milks as a thickening agent. Some people find it aggravates gastro-intestinal problems; if these liquids irritate your stomach, seek brands without it.
2
FOCUS ON FLAVOR : SMOOTHIE-CENTRIC FRUITS
Some fruits taste better than others when whirred into a blended drink. Our top smoothie-tastic ingredients include berries (think: blueberries, raspberries, strawberries, blackberries, acaí berries, and even the superfood goji berry). Berries work wonders in a blended drink; they're low in sugar, but high in flavor and color—practically bursting with healing antioxidants. They work well with nut milks and with less dense liquids like coconut water. When they're not in season frozen organic is a good stand-in. Peaches and tropical fruits like mango, pineapple, and papaya are also delectable—and enzyme- and vitamin-packed—additions to any smoothie.
Bananas and avocado—also a fruit—are a smoothie's best friends because their high volume of soluble fiber means they blend brilliantly, integrating all the ingredients into a creamy, even texture. Fruits like pears, papaya, mango, strawberries, and kiwis also have high amounts of soluble fiber. Make a smoothie without these natural thickeners—especially if you are using water or coconut water instead of nut milk—and your smoothie may be chunky or stringy, or separate slightly.
3
GREEN UP YOUR CUP
Almost any kind of smoothie can be easily greened by tossing some leaves into the blender. Spinach is the classic smoothie green as it has a mild flavor that mixes beautifully with other fruits. Kale, the nutritional powerhouse, has a stronger flavor that can be balanced with bright fruits like berries and pineapple. Swiss chard, romaine lettuce, bok choy, and collard greens are also excellent additions and you can even experiment with savory flavors of beet greens and spicy mustard greens in vegetable-only smoothies. Start slowly as you get to know your greens—in Phase 1 the focus is on spinach and kale. Add a small handful to your blender before committing to a deeper green experience.
4
THE FROST FACTOR
Adding ice to your smoothie is a personal choice. On the upside, it can transform a simple smoothie into a decadent, milkshake-like experience, enhancing its flavor and texture. Those watching their weight appreciate how it fills out the drink without adding extra calories. On the downside, ice can make your blended drink too frosty, which can make it harder to drink and—many healers say—be a shock to the digestion, slowing it down. If you're using frozen fruit, you don't need ice. (And if frozen fruit in your smoothie is too teeth-chattering, splash hot water on top to melt it slightly before adding the other ingredients.)
5
SWEETENING THE DEAL
If the ingredients in your smoothie don't quite satisfy your palate and you need it a touch sweeter, use a natural sweetening ingredient that is as unprocessed as possible and experiment with the amounts you need. Aim to decrease the amount of sweet gradually as you get used to enjoying the full flavor spectrum and already-occurring sweetness of your drink.
All very sweet things have lots of calories—there's no getting around that. But some contain higher amounts of fructose—the supersweet kind of sugar molecule that can have the most damaging impact on the body and that gets stored quickly as fat if you eat more than a moderate amount. Choosing what sweetener to use involves balancing your taste preference with an awareness of fructose amounts—and of course, over the long term, adapting your palate so you need only a touch of sweet to be satisfied. Some of our favorite sweeteners include:
Dates These sumptuous dried fruits are not only outrageously delicious, they contain an array of antioxidants, trace minerals, and both soluble and insoluble fiber to add more oomph to your hit of sweet. Two or three medium-size dates in a smoothie or homemade nut milk will more than satisfy your desire (and even one may be enough). You can find fresh dates in most markets; look for plump dates with smooth and unwrinkled skins. They can last for several months when refrigerated in a tightly sealed container. Dried dates can last for up to a year in the fridge (they can be "replumped" with warm water if they dry out). Soaked raisins, figs, and prunes also add sweetness that kids especially will like—an even healthier option is to use the soaking water itself and save the fruits for something else.
Raw honey One of nature's most potent gifts, raw, unfiltered honey is beloved by raw foodies and healers alike because it is so high in healing enzymes, has a great trace mineral content and phenomenal healing compounds like propolis, and is lower in fructose than other natural sweeteners. Unlike conventional honey, raw or unpasteurized honey hasn't been heated and filtered to make perfect-looking golden syrup, and it is free of the questionable things in the cheapest honey products (which may contain high fructose corn syrup, illegal additives from overseas, and zero beneficial pollen).
It's also one of the easiest "wild foods" to acquire—it's now available at stores like Trader Joe's—and when you get your honey from farmers' markets, you help support local beekeepers who are crusading to save our utterly essential bee population—ensuring we can continue to grow food in the future! A dash of raw honey is like putting preventive medicine in your food. Start with 1 tablespoon in your smoothie and adjust downward from there as your palate adjusts.
Raw agave Made from the agave plant—the source of tequila—agave syrup is a low glycemic sweetener that, if processed properly, can have a moderate fructose level, a lower caloric content than table sugar, and inulin, a prebiotic fiber proven to help the absorption of certain nutrients. Look for raw, organic agave that can claim a fructose level of under 50 percent (which is sugar's fructose level). Some agave brands are highly processed and contain a much higher percentage—from 70 to 90 percent, which is as bad as high fructose corn syrup.
Coconut palm sugar The new kid on the block, coconut palm sugar is made from dried and crystallized sap from the coconut tree. It's being embraced for its wonderfully rich, caramel flavor—similar to brown sugar—and its gentler effect on blood sugar than regular sugar. You get a shot of vitamins, minerals, and phytonutrients, and sensitive types might notice they don't get a jittery sugar rush from adding it to their drinks.
What we don't recommend: artificial sweeteners like aspartame and sucralose, which are made of chemicals and connected to a host of health problems from cancer to neurological issues and everyday mind fog and pain.
### Peaches and Greens
Creamy almond milk combined with sweet peaches and dates makes this smoothie a dessert-worthy affair. Peaches are high in the antioxidant chlorogenic acid, which slows the aging process and prevents chronic disease.
1 cup spinach
1/2 cup peaches
1/2 medium frozen banana
1 cup almond milk
3 dates, pitted
Blend.
### Clean Green
This superbly refreshing smoothie spikes dark-green kale with bright-green lime, an ingredient that balances kale's bitterness beautifully
11/2 cups kale
1/4 cup cucumber
1 medium apple
1 medium lime, peeled
1 cup filtered water
Blend.
JUICY TIP
Limes are easy to blend and juice—simply cut off the rind and leave the white pith (it's packed with beneficial plant compounds you don't want to miss).
### Tropical Greens
Don't overlook the furry brown kiwi. This little fruit is jammed with nourishment, offering 16 percent of the RDA for fiber as well as folate, vitamins C and E, and minerals including calcium, magnesium, potassium, and zinc.
1 cup spinach
1/2 cup pineapple
1/2 cup mango
1 medium kiwi, peeled
1 cup almond milk
1/2 cup ice
Blend.
### Nuts for Greens
A handful of raw almonds makes a smoothie into a meal. They add protein, omega-3 and omega-6 fatty acids, plus lots of fiber.
1 cup spinach
1/4 cup raw almonds
1 cup almond milk
1/2 cup strawberries
1/2 cup blueberries
1/2 medium frozen banana
Blend.
Juice Smarts: Soaking raw (not roasted) nuts for a few hours in water before you consume them is a savvy raw-food trick to deactivate the enzyme inhibitors that can make them hard to digest. Some nuts will also germinate and sprout in the hours after soaking if tended correctly, unlocking even more of their good-food power. Simple instructions are easy to find online.
## NOT GOT MILK
Juicing was the beginning of my deeper understanding of nutrition. The great feeling and positive physical results I got from early experiments with "juice fasting" made a big impression on me and made me start paying more serious attention to the connections between what I was eating and my health. The older I get, the more aware I am of how unhealthy most of what passes for food in our culture has become. Personally I'm trying to eat simpler and cleaner and stick to a whole-food, plant-based diet. I'm pushing myself to go as green as I can with juicing and keep the fruits to a more modest percentage. I feel better and it keeps my energy more even.
—Edward Norton, actor
* * *
The smoothies on the Green Curve are free of dairy—there's no yogurt to thicken and enrich them—because on the Green Curve, we want to give you a chance to do a Trade-Out and bring your consumption of dairy products down, to see how it feels for you.
We're not saying dairy in all its forms is terrible for everyone. But there's no denying that dairy is one of the most inflammatory foods in our modern diet, and it's connected to all sorts of gut issues, persistent skin symptoms, mucus formation, and much more, due to both the sugars and the proteins milk contains. And, unless it's organic, dairy can be full of growth hormones and antibiotics; two things you do not want in your—and your children's—bodies.
Our recipes offer you an opportunity to nix some of the milk products in your diet and instead discover the enriching textures of nut milks and coconut meat. Don't worry about getting your calcium. You'll get lots of it from plant foods like almonds, kale, oranges, collard greens, and spinach on the Green Curve, which are also wonderfully alkalinizing.
Juice Smarts: Soy milk has its fans and its detractors: Some worry that its naturally occurring phytonutrients have estrogenic effects on women (promoting, and preventing healing of, breast cancer). Other reputable heath gurus disagree, saying it's a great milk substitute with phytonutrients we need. If you choose to use soy milk, use a product bearing the green USDA Certified Organic seal; soy beans are heavily treated with pesticides and are often GMO; many are often shipped in from overseas where "organic" standards may be questionable. And if you're not sure, drink soy moderately: With so many choices on the shelf, it's easy to rotate your nondairy milks (just like you'll rotate your greens!).
### Cocoverde
Whizz together two fruits, plus greens, plus banana and you've got a classic green smoothie: almost instantaneous, and equally pleasurable to the eyes and the palate. Here, nutrient dense kale and tropical mango—high in vitamins A, C, and D as well as beta-carotene—mingle beautifully in a coconut water base that's tasty and hydrating.
1 cup kale
1/2 cup mango
1/2 medium frozen banana
1 cup fresh coconut water
Blend.
Optional: Add 1 teaspoon cinnamon for a special twist.
### Perfectly Pear
Fusing three shades of green into one pale-hued smoothie, this concoction is irresistible to look at—and drink. Pear adds a delicate, sweet flavor—plus lots of soluble fiber—while romaine lettuce contributes its wonderfully mild-flavored leaves.
1 cup spinach
2 leaves romaine
1 medium pear
1/2 medium frozen banana
1 medium lemon, peeled
1 cup filtered water
Blend.
JUICY TIP
Cinnamon—a spice once considered more valuable than gold—is still revered today for its ability to help lower blood sugar levels.
Hack That Smoothie! Make any smoothie instantly more filling with a generous spoonful or two of fats like avocado, nut butter, or chia seeds. This is especially great for kids, who'll like the tangy flavors of these entry-level blended drinks, but need a little more substance to keep them going. It's wise to let the chia seeds "plump out" in liquid for ten minutes before drinking so they add hydration to the body effectively.
## BANANA 2.0
Shake off the childhood memory of the squished banana at the bottom of your brown bag lunch. This versatile, superbly nutritious fruit elevates an everyday juice into a milkshake-worthy smoothie with just the flip of a blender switch. Bananas add sweetness, body, and a silky smooth feel to blended drinks (they're how healthy beverages masquerade as luscious treats). And they play well with others. Blend bananas with almond milk and cacao nibs for a smoothie that drinks like a dessert; mix banana with coconut water, mango, and greens for a vibrant tropical beverage, and whiz banana with peanut butter and any dairy milk substitute for a creamy, protein-packed delight.
* * *
BANANAS: WHAT DON'T THEY DO?
Bananas are nature's energy shot. Packed with healthy carbohydrates and potassium, they are ideal for a pre- or post-workout boost, helping to restore the body's electrolyte balance. Bananas are famous for their potassium for good reason: The mineral helps to maintain healthy blood pressure and protect against arteriosclerosis. They also contain pectin, a soluble fiber, which helps to ease constipation, while the tryptophan in the fruit is converted to serotonin, which helps us feel happier. Bananas build strong bones by preventing calcium loss and they are a natural antacid, providing relief from acid reflux and heartburn.
### Smooth Strawberry
Juicing your apples before blending this smoothie is one extra step that pays off. Use green apples for a tarter drink and red ones for a sweeter blend.
1 cup fresh apple juice
1/2 cup strawberries
1/2 medium banana
sweetener to taste
1/2 cup ice
Blend.
### PB Split
When you need a little more substance to get you through the day, a smoothie boosted with nut butter, nut milk, and coconut milk will fuel you with fat, the body's favorite source of energy, without a ton of sugar.
2 tablespoons peanut butter
1 medium frozen banana
1 cup almond milk
1/4 cup frozen coconut milk
1 tablespoon raw agave
1/2 cup ice
Blend.
## WHIZ KIDS
For kids, blending tends to work better than juicing initially, because thicker, creamier drinks are more palatable and more entertaining to drink. Transitioning to juices can be just as enjoyable, however. Most kids will shy away from green in their drinks at first, but get sneaky and add a handful of kale or spinach to fruity concoctions when they're not looking, or come clean and let your kids see that sometimes it's easy—and tasty—being green.
Drinking juices is extremely satisfying: I feel like I'm being rewarded with every sip, especially with the green juices, and watching my children drink all those greens is the greatest feeling, knowing they are consuming all the right nutrients. I sleep better at night knowing that all the goodness from the veggies and fruits has gone directly into our systems. There's too much messing with food these days, so the purity of juice makes it the nectar of the gods!
—Naomi Watts, actor
### Kid-Approved Juice Combos
Apple, pear, spinach
Apple, pear, celery, cucumber
Apple, carrot, romaine
Pineapple, kale, apple
Carrot, orange
Beets, tangy citrus
Combos with coconut water
JUICY TIP
Deep red beet pulp makes a colorful mix-in for healthy muffins and treats that kids find especially irresistible.
## AGUA FRESCA
Fruit and herb-infused water is one of the easiest natural beverages to make at home. They're fun for kids to make and create a beautiful-looking drink to serve your friends.
Try using some of the ingredients you already have on hand to make these simple, but restaurant-worthy, drinks. There's lots of room for experimentation here; get creative with ingredients that you feel may go well together and let the inspiration flow.
* * *
METHOD: Place your fruits and vegetables in a pitcher or glass mason jar and lightly mash with the end of a wooden spoon. Amounts can be fairly rough—fill the bottom of your vessel and throw in a small handful of herbs. (You can always add more herbs next time if necessary.)
Gently bruise your herbs or spices like mint and ginger on a cutting board first, so they release their flavor, then add to the mix.
Fill your container with still or sparkling water, sealing it if using sparkling water, and let sit in the fridge for at least two hours. Strain before serving. Use within approximately two days.
### Try These Combos
Watermelon, basil
Cucumber, melon
Grapefruit, mint
Orange, lemon, lime, Cucumber
Berry mixture
Other ingredients to try: cherries, cantaloupe, blood oranges, and pomegranate, and herbs like sage, cilantro, and rosemary.
## phase 2
## MEDIUM GREEN: TAKE YOUR JUICE TO THE NEXT LEVEL
I am ruled by my juicer. Anything green that's not nailed down ends up being juiced. Kale, spinach, a little green apple, and we are good to go. It's also an easy way to get a salad in my six-year-old and one-year-old. If my wife is right and you are what you eat, I'd rather be lean and green than hot and beefy.
—Jason Bateman, actor
On the second part of the Green Curve, you explore a wider array of flavors and colors, including more shades of green. This phase is about expanding your palate and broadening your scope from sweeter tastes to those with a more savory slant, and incorporating many new shades of green in your glass. There are tasty treats galore in store: You'll crack open coconuts, get friendly with hemp (one of nature's humble superstars, a secret weapon of nutrition), blitz an array of unexpected vegetables in your juicer, and discover the joy of flavor-bursting acaí bowls. You'll also discover smoothies with a little more substance that are just the ticket as a heartier snack or perhaps a recovery meal in a cup after a workout.
While it's good to follow your body's wisdom and use ingredients you find appealing, it's also important to stretch a little, and try things you've never even heard of or thought to use—these surprises can often turn out to be the best!
Plan to stay on Phase 2 for three weeks to try a wide range of the recipes and get to know a diversity of new ingredients at a realistic pace. But if you would rather go at your own speed and flip ahead for new recipes sooner, you can do that, too.
THE TRADE-OUT: Phase 2 is an opportunity to drop packaged, sugary, and salty snack foods from your diet and replace them with nourishing drinks. Cookies, muffins, pastries, and pretzels may be an occasional or a frequent fallback habit, but what about switching them out for a fresh juice or smoothie instead? And how about the chips, nachos, bread roll, or French fries that keep showing up with your lunch—what if you had a green drink half an hour before your meal, to cut the craving for those things? If you have a family, how about giving your child a thermos of cool, green smoothie for a brain- and body-fueling school snack?
These switches may require lifestyle adjustments—like taking your juice or smoothie on the road in a cooler bag or stashing a bottle in the fridge at work. But a little thinking ahead lets you reap rewards. Cravings for sugar, baked goods, fake flavors, and candy highs get a chance to fade from focus and you can begin to detect, and desire, new types of fresh, nutrient-rich foods.
Bonus: Goodbye, gluten. We're waking up to the ways that gluten—the protein found in wheat, barley, and rye and used as a hidden filler in many modern foods—can disrupt our physical and mental well-being through intolerances, allergies, and in extreme cases, an auto-immune response. Gluten's ubiquity can make it a challenging thing to remove from your daily diet. Fresh juices and smoothies made filling with fats and protein can take the place of wheat-filled breakfast foods like cereal, toast, and pastries, and they offer great new alternatives to snacks that may have been irritating your system for years, undetected. (This includes oat-based breakfast and snack foods that, unless marked "gluten-free," often contain the gluten protein.)
## PHASE 2 BUYING GUIDE
Your Green Curve goal in Phase 2 is to make five drinks in a week with at least 50 percent containing significant greens. During this phase, aim to make at least five drinks a week—which may be each weekday to get in a rhythm, or three weekdays plus two weekend days, when you have the most time to get creative. Pick and choose the juices and smoothies you want to make as you see fit—you can pull from Phase 1 if you need—but now try to ensure at least half of them contain a good handful of leafy greens. Make them at any time of day that fits in your schedule.
* * *
## DRINK THE RAINBOW
Kick your happy green habit up a notch and get better acquainted with a broader array of nature's bounty. The juices in Phase 2 have a few more ingredients, a greater quantity of greens, and new vegetables you might not have thought to juice before (think: sweet potatoes and bok choy). This rainbow of options gives you the freedom to use what's in season or what looks freshest (you can swap green leaves according to what's available). And these green and vegetable-rich drinks still have a sweet touch. We'll show you how to enhance the juice with good fat for extra nutritional uptake, too.
I juice a wide array of fruits and vegetables according to what I feel my body needs at that time, from spinach to beets to my favorite combination: carrots, green apple, and ginger. This is what I drink when I find I need more energy in my work: It's a great pick-me-up. In summer, I love fresh watermelon juice—it's a sweet treat that's healthy. What I've learned is that our bodies tell us what we need. It's up to us to listen and follow that guidance.
—Hilary Swank, actor
### Very Veggie
Sweet potato as juice? You bet. This pumpkin-colored tuber is not only a surprising—and easily sourced—ingredient with an appealing flavor, it also helps you get your glow on. The carotenoids in orange-colored vegetables like carrot and sweet potato have such beneficial effect on skin, they have a scientifically validated "attraction factor"—meaning that warm glow you naturally acquire makes others rate you as more attractive.
1 cup kale
1 cup spinach
1 cup parsley
1/4 medium sweet potato, peeled
1/4 medium cucumber
4 medium carrots
3 stalks celery
Juice.
### Get Ur Green On
It's never been easier to go green. Here, nutrient-packed kale and spinach are sweetened with apple and pineapple and brightened by mint. Young juicers tend to fall for this tasty green number.
1 cup kale
1 cup spinach
1/2 cup pineapple
2 medium green apples
1 sprig mint
Juice.
Hack That Juice! Blend in 1/2 cup fresh coconut meat to make a smoothie.
### SupaDupa Greens
Juice Generation's Number One Selling Drink
Get ready for graduate level greens. This fortifying brew is big on green veggies and light on fruit, making it satisfyingly savory. Cucumber refreshes and lemon harmonizes, creating an uplifting, energizing drink.
2 cups kale
1 cup spinach
1 cup parsley
2 leaves romaine
3 stalks celery
1 medium green apple
1/4 medium cucumber
1/4 medium lemon, peeled
Juice.
Hack That Juice! Blend in 1/2 medium avocado to make a smoothie.
When it comes to juicing, my favorite color is green. Kale, green apple, and spinach are three musts when I juice. I also add blueberries, and my "secret weapon": daikon radish, it's like a silent giant. Daikon radish is great for your skin, it's packed with vitamin C and digestive enzymes, and it reduces inflammation—it's so powerful! I get really busy, and it's so easy to forgo eating vegetables when I'm in "go" mode, which I really don't like to do. When I'm juicing, I can really feel the difference: I have so much more energy because I'm getting a healthy serving of fruits and vegetables. My nutrition is balanced, and my sugar cravings are satisfied.
—Paula Abdul, entertainer
### Paula's Daikon Blues
Looking like a white icicle and pleasantly mild in flavor, daikon's crisp, cool properties make it tons of fun to juice. A hit of blueberries adds a second surprising twist.
1/2 small daikon radish
1 cup kale
1 cup spinach
2 medium green apples
Juice.
Hack That Juice! Blend in 1/2 cup blueberries.
### Sweet Greens
Explore nature's bounty with the addition of two power greens: watercress and parsley. Peppery watercress contains iron, iodine, vitamins A, C, and E, antioxidants, and folate, while parsley is so much more than a mere garnish. The herb is bursting with vitamins plus iron, calcium, magnesium, potassium, and zinc.
1 cup spinach
1 cup kale
1/2 cup parsley
1/2 cup watercress
3 medium apples
Juice.
Hack That Juice! Blend in 1/2 medium banana to make a smoothie.
JUICY TIP
To extract the most juice out of parsley, remember to follow it with something hard, like apple.
Squeezing spinach out of cans is one way to go about it, but juicing the fresh vibrant green leaves is one of the quickest—and most efficient—ways of accessing its goodness. Spinach is a wonder leaf. One cup delivers more than your RDA of vitamins K and A, and the antioxidants it contains promote cardiovascular health while magnesium helps to lower high blood pressure. Spinach is also a superb source of folate, offering 65 percent of your RDA in just one serving.
### Blake's Intoxicating Detoxification
Sweet, bitter, mild, and fresh—this drink marries many tastes into one beautifully proportioned, and completely addicting, combination.
1 cup kale
2 leaves Swiss chard
1/2 cup parsley
1/2 small beet
1/2 cup pineapple
2 medium green apples
1 sprig fresh mint
1/2 medium lemon, peeled
Juice.
Red apples can also be used; these will add extra sweetness.
I fancy myself as a foodie, because man, oh man, do I love to eat. I come from a Southern family, so my taste leans more toward butter and sugar than veggies; if they're battered in cornmeal and fried, then I'm in! Growing up, I was interested in creative preparations of vegetables that were able to mask their flavor. Then a few years ago, I had a juice that changed it all for me—a mix that's better than any po' boy you'll ever eat. The vegetables in their purest form are refreshing and palate cleansing, while the sweet notes of the fruits and mint make it both quenching and intoxicating. Now I can get my dose of veggies in a delicious way and feel proud doing it. And boy, does is counter the guilt I feel when pulling out the ice cream.
—Blake Lively, actor
## JUICE BOOST: FAT IS YOUR FRIEND
A dash of healthy, unprocessed fat added to a juice can help with the absorption of nutrients from vegetables and fruits, making your drink truly liquid gold. The powerful antioxidant carotenoids found in green foods (like spinach and kale) and red and orange plants (like carrots, bell peppers, watermelon, and grapefruit) are fat soluble, so a dash of seed or nut oil in the drink helps them get into your system. (Or a fatty fruit: Add avocado to a blend of tomatoes, carrots, or bell peppers, and you'll absorb up to five times more of the carotenoids, lycopene, and beta-carotene.)
Fats and oils can also add a host of their own intrinsic nutritional benefits to your supplement-in-a-cup—oils are a great source of energy for your body, trumping sugar in efficiency and impact—and most raw oils come with a host of extra benefits.
* * *
Stirring a spoon of seed oil into your juice or quickly blending your fresh juice with avocado or a spoon of coconut oil to give a thicker texture are two easy ways to add some fat to your glass. Fats slow down absorption of nutrients: This is a bonus when it comes to slowing and stabilizing the impact of juice's sugars on your blood, though some may find the effect of untouched juice more uplifting. As always, the final choice is up to you: Listen to your body and see how you feel in the hour or so after your drink.
FLAXSEED OIL is a rich source of omega-3 fatty acids, essential nutrients that we must get from food and that most of us are deficient in. These fatty acids benefit every cell in the body, helping to improve blood circulation and reduce inflammation, and benefitting hair, nails, and skin. Flaxseed oil is often added to juices in nutritional healing programs because the fatty acids help to carry beta-carotene into the bloodstream to increase the body's immune response. It is fairly delicate: Any heat used in processing damages its structure, so purchase cold-pressed oil from your store's refrigerator case. Keep it in your fridge and, once open, use quickly; within eight weeks is recommended so it does not go rancid. Try: Stirring 1 teaspoon flaxseed oil into your fresh juice.
COCONUT OIL is an extremely healing food with antiviral, antifungal, and antimicrobial properties that actually promote weight loss and help to regulate thyroid function and normalize blood sugar. It contains medium-chain fatty acids (MCFAs), which, unlike the long-chain fatty acids found in other veggie oils, don't accumulate as fat in the body. MCFAs are sent directly to the liver to be converted to energy. This energy boost helps improve sluggish metabolisms and manage weight gain. Lauric acid, a substance also found in human breast milk, makes up most of the MCFAs found in coconut oil. It converts to monolaurin in the body, which has been linked to increased immunity. This multitasking master is also a supreme all-over moisturizer, massage oil, makeup remover, and hair hydrator. Try: Blending 1 teaspoon to 1 tablespoon raw, cold-processed coconut oil into your juice. Blend for under 30 seconds to preserve optimal nutrients in the juice.
AVOCADO'S unsaturated fat contains oleic acid, which research shows activates the brain area that increases the feeling of satiety. Try: Blending a scoop of avocado into a green or vegetable-based juice to give it satisfying, smoothie texture.
JUICY TIP
Coconut oil is quite shelf stable and can be stored in a cupboard. In cool temperatures, coconut oil turns from a liquid to a solid. You can gently heat the oil on a stovetop (a couple of minutes on very low heat) back to liquid form before adding to a cold—or room temperature—beverage to avoid lumps.
All these things can of course be easily added into smoothies, too, plus one more fat-rich addition:
NUT BUTTER. A spoonful of almond butter, peanut butter, cashew butter, as well as seed butters like hemp butter and tahini (sesame seed butter), adds a fabulous range of flavors and fueling fats to a blended drink. Look for minimally processed butters with no added sugar—and seek out a raw variety if possible, to avoid the damaging effects of the highly heated oils. Feeling ambitious? With a masticating juicer, a high-speed blender, or even a food processor, plus a little patience, you can even make your own butter from nothing but raw nuts.
I have been the pickiest eater my entire life. Sadly I hated vegetables growing up. Since cutting meat and dairy entirely from my diet years ago, I was faced with a big dilemma of what to eat in addition to my much loved diet of rice, beans, and avocados. Once I discovered juicing, my whole world changed. I absolutely love vegetable juices and have incorporated them into my daily diet, and I feel fantastic as a result.
—Famke Janssen, actor
JUICY TIP
Fats don't have to be added to the drink itself; many people swear by a handful of raw nuts alongside their juice to maximize the nutritional uptake.
## EXOTIC TASTES AND CREAMY TEXTURES
Next-level smoothies, enhanced with good fats and exciting flavors, are your ticket to a healthier and happier (and yes—less dough-dependent) diet. Lean on these well-balanced blended drinks—brimming with supernutritious greens and tasty, tart-sweet fruits, and filled with the enriching benefits of coconut and avocado, to boot—and they will not only thrill your palate, they will help to achieve some of the Trade-Out goals of the Green Curve's Phase 2. Remember those goals? You want to break away from sugary or salty processed treats and gluten-heavy snacks, along with their quick energy spikes and inevitable crashes. These are smoothies that tantalize and satisfy. You won't look at a cookie the same way again.
## COCO LOVE!
A coconut is one tough nut that we love to crack. Call it guilt-free dessert in a glass, or instant escape to a more tropical state of being. The fragrant, island-evoking flavor of the raw water straight from a fresh, young coconut has a kind of euphoric effect that packaged coconut water, for all its convenience, can never quite achieve. Young coconuts are the white, husk-free variety and have a thin layer of soft, white flesh inside and a reservoir of coconut water.
Raw coconut water is rich in electrolytes, the electrically charged ions that help our cells communicate and that get depleted by hard exercise. It's also high in enzymes that help to detoxify and repair the body, as well as beneficial lauric acid.
Use the refreshing, energizing elixir from young coconuts to make blended drinks and discover how coconuts turn everyday ingredients into a sumptuous treat. Or keep it super simple and eco-aware by sipping the young coconut water straight from the shell: nature's to-go cup.
* * *
## CRACK THAT NUT
THE TOOLS
A large, sharp knife with a heel
A young coconut (This method works best with young or "green" coconuts.)
THE STEPS
1. Lay coconut on its side, keeping any plastic wrapping on the fruit. (Young coconuts that have had their outer green shell removed are often treated with chemicals to keep their inner shell looking white and pretty. Keeping the plastic wrapper in place as long as possible prevents the toxins from seeping into your cutting surface. These chemicals do not harm the inside of the coconut.)
2. Cut away at pointed top of the coconut until the round inner cap is revealed. This will be the "lid" of the coconut.
3. Hit the edge of this lid with your knife at a 45-degree angle so that it pops up.
4. Use the heel of the knife to wedge the lid up.
5. Pour out the water. (If the water has a pink tinge, it has gone bad. Discard the coconut and its water!)
6. Use a flexible spatula to dig out the soft coconut meat, which can then be eaten on its own or blended into smoothies. A coconut scraper or "de-meater" tool makes scooping even easier.
Coconut puts a rich spin on almost any blended drink. Have fun experimenting with this versatile ingredient to make a satisfying and uplifting breakfast smoothie or anytime snack. Here are our favorite four coco-blend drinks
### Kale Kolada
Leafy greens take on a tropical twist when paired with coconut. Add a dash of cinnamon for a sweeter twist.
1 freshly cracked young Thai coconut, water and meat
1 cup spinach
1 cup kale
1/2 medium banana
Blend.
### Carrot Creamsicle
Easy as one-two-three, a touch of sweet carrot brings a surprising and colorful touch to a fresh coco cup.
1 freshly cracked young Thai coconut, water and meat
1 medium carrot
Blend.
### Amazon Acaí
The antioxidant power of the Amazonian berry acaí paired with the decadent creaminess of coconut and banana makes this blend healthy and heavenly.
1 freshly cracked young Thai coconut, water and meat
1 pack frozen acaí
1/2 medium banana
Blend.
See for more on acaí and how to use it.
### Pacific Pineapple
Pineapple and coconut, the classic beachcomber duo, are enhanced with strawberries' fiber, potassium, and vitamin C.
1 freshly cracked young Thai coconut, water and meat
1/4 cup pineapple
1/4 cup strawberries
Blend.
JUICY TIP
When selecting young coconuts, be sure to get the most recent ones to arrive at the store and make sure there is no mold or moisture under the plastic wrap.
I have a big garden and throw in whatever is in season. I love kale, carrot, spinach, apple, and I even get creative throwing in flax oil, aloe juice, and lemons from the tree in my yard. Having fresh juices is mandatory for me—it is a part of my regular diet.
—Kristen Bell, actor
### Sweet 'n' Creamy Greens
1/4 medium avocado
1 cup kale
1 cup almond milk
1/2 medium banana
3 medium dates, pitted
1/2 cup ice
Blend.
### CocoBliss
1 freshly cracked young Thai coconut, water and meat
1/4 medium avocado
Blend.
### Berry Cherry
Tart flavors have a sneaky way of perking up your palate. The acerola cherry, also called the Amazon cherry, has ten times the vitamin C of orange juice—great for immunity—and a refreshing, tart citrus flavor. Here, it mingles with raspberries, which are loaded with antioxidants.
1/2 cup acerola cherries
1/2 cup raspberries
1/2 medium frozen banana
1 cup fresh orange juice
Blend.
### Mango Tango
Like its dark leafy green cousin, kale, Swiss chard is a nutritional winner delivering a jolt of supercharged vitamins and minerals. If you prefer less intense green flavor, stick with the smaller leaves, which are sweeter.
2 leaves Swiss chard
1 cup mango
1/2 medium lime, peeled
1 cup filtered water
1/2 cup ice
Blend.
JUICY TIP
Acerola can be found as a frozen fruit and also as a freeze-dried powder that can be added to all kinds of smoothies for a nutritious enhancement. If acerola is out of reach, use ordinary fresh or frozen cherries; they will have a sweeter taste so adjust the recipe if you like by diluting the orange juice with water.
### Luscious Cup
Sometimes the most unlikely ingredients make the tastiest smoothies or juices. A happy accident led us to this strangely tasty combination of creamy, spicy, tropical, and tart.
1 cup mango
1 cup spinach
1/2 medium orange, peeled
1/2 medium banana
1 cup soy milk
1 inch fresh gingerroot, peeled
Blend.
### Fruity Fiesta
Ginger gives this green smoothie a spicy kick. Keep the potent root on hand to quickly boost the flavor of any juice or blended drink. Hint: Ginger lasts longer if you store it in your crisper drawer in a zip-top bag or vegetable storage bag. If you need to sweeten your smoothie, try adding a date or two.
1 cup spinach
1/2 cup parsley
1/2 medium orange, peeled
1/2 medium apple
1 inch fresh gingerroot, peeled
1/2 medium frozen banana
1/2 medium lemon, peeled
1 cup filtered water
Blend.
### Todo Bueno
This seductive drink contains seven of our favorite things. It gets its beautiful flecks of red by spiking a medley of everyday fruits and vegetables with a sneak preview of a Phase 3 superfood—the tiny goji berry, known to some as wolfberry.
1 cup spinach
2 tablespoons soaked goji berries
1/2 cup strawberries
1/2 medium banana
1/2 medium avocado
1 cup hemp milk
3 dates, pitted
Blend.
See for more on goji berries.
## HEMP SEEDS
THE NATURAL WONDER OF HEMP
Sometimes you want something extra in your cup—a boost of protein after a workout or a balanced dose of protein and fat to make it from breakfast to lunch without crashing. Once, the only easy-to-find option for powering up a smoothie was a massive tub of bodybuilder protein powder. Today, things have changed, as next-gen smoothie makers go back to basics and seek out earthier alternatives: raw, whole-food sources of protein that have not been processed by heat or enhanced with chemical sweeteners or additives.
Our favorite all-natural way to add protein and fat to a smoothie is hemp seed. This mild and nutty-tasting ingredient has one of the most well-rounded nutritional profiles of any plant food and is one of nature's richest sources of plant protein. It's low allergenic—unlike many whey and soy proteins—easily digestible, and blends well into drinks with an appealing taste. (And unlike sweetened powders, it works well in green-based and savory blended drinks.)
Hemp seeds come in many forms, including the raw, hulled seeds, concentrated protein powder, luscious seed butter, cold-pressed oil, and creamy hemp milk, giving you endless options to play with. Not to mention, the complete hemp plant is a natural wonder, providing us with ecofriendly textiles and paper, plastic alternatives and building materials, herbal medicines—and more.
Start with a bag of hulled seeds (also sometimes called hemp hearts) and add 2 tablespoons to your smoothie. Grind them in the blender alone before adding any other ingredients to make the nutrients most absorbable. (A clean coffee grinder can help if your blender fails at the job.) If you like the taste, and need more protein, try a raw hemp protein powder, which is made by concentrating the protein from hemp, giving you 15 grams or more per serving. The more finely ground the powder, the more you'll probably enjoy it.
And, if you love this simple, whole-food addition to your smoothie, you might also try one of the more complex, "sprouted" plant-protein powders on the market that mix raw and unprocessed protein from an array of seeds, peas, and gluten-free grains, often in delicious combinations.
### Hemp Protein Buzz
A satisfying smoothie that will keep you fueled, this can be made extra good with homemade hemp milk, as described in Phase 3.
1 cup hemp milk
1 scoop protein powder
1/4 cup blueberries
1/4 cup strawberries
1/2 medium frozen banana
3 medium dates, pitted
1/2 cup ice
Blend.
HEMP POWER
Raw hemp seeds are about 35 percent protein, with a complete array of amino acids that are easily digested by the body, and about 45 percent fat, with a perfect ratio of omega-3 to omega-6 essential fatty acids, along with the rare "super" polyunsaturated fats, gamma-linolenic acid (GLA) and stearidonic acid (SDA), and the "beautifying" oil of omega 9-fatty acids. Lots of enzymes, low antinutrients, and about 20 trace minerals make it a true super seed.
THE SCOOP ON PROTEIN POWDERS
Navigating the complex world of protein powders is challenging. What's healthy and what's potentially harmful? These foods fall under the category of "supplements" and their claims and ingredients aren't regulated by the FDA. Some muscle-building powders have been found to contain high levels of heavy metals. Look for the most natural and least-processed product you can. Whey, from dairy, is best if cold-processed and from cows free of rBGH (growth hormone) or better yet, fully organic, with no added sugar. If using a powder containing soy protein isolate, just as with soy milk it is wise to seek one that is non-GMO.
I make protein shakes after I work out—it's a really easy way of getting all my protein in as well as chucking in all the other stuff I need. I love eating spinach, but my wife, Thara, manages to find a sneaky way of putting it into my shakes so I don't even know how many extra nutrients I'm getting. And I love berries—I put a lot of them into my shakes.
—Jay Sean, singer-songwriter
JUICY TIP
Store your hemp seeds or powder in the fridge to ensure the fats do not turn rancid; use within three months.
Coconut oil helps you absorb the omega-3 fatty acids in hemp twice as effectively. Try a smoothie featuring both those ingredients.
## ACAÍ
Purple Power: Who doesn't like to consume the color purple? It's not only great for you—dark red, blue, and violet fruits are some of nature's wonder stuffs—it is also, frankly, fun. Acaí grows wild on the banks of the Amazon and has long been a staple food in Brazil, where it's eaten in puree form as part of a savory meal, and where surfers throw the frozen slush into fruit smoothies as a after-surf refueling.
An exotic relative of our blueberry and cranberry, acaí berries are overflowing with antioxidants (of the anthocyanin variety, just like red wine) and healthy fats with not a drop of sugar in sight. When Juice Generation first introduced acaí in 2000, Brazilian expats were the primary takers, scooping up our chilled acaí breakfast bowls: One step beyond a smoothie, an acaí bowl features frozen acaí pulp, granola, banana, and other fruits and veggies. Soon, the pre- and postworkout crowds caught wind and started using acaí bowls to charge up before—or recover from—Spinning and yoga. Today, we sell hundreds of acaí bowls every day to athletes, executives, and anyone looking for a refreshing fuel-up of raw ingredients that won't leave them feeling bogged down and groggy. Replete with protein and good fat, vitamins and antioxidants, these bowls will kick-start the day or carry you from midafternoon to dinner. Skip the bagel and go for the bowl.
* * *
JUICY TIP
You can buy acaí packs in the frozen fruit section of most grocery stores. Use the frozen pulp in acaí bowls or smoothies. Acaí powder is another fun pantry addition; it can be added to all kinds of smoothies and sprinkled on granola.
Our typical day at the Alvin Ailey American Dance Theater is extremely intense. We start with a class in the morning, and from twelve until seven we're in rehearsal. We are basically physical for a full workday, so it's really important that we power our bodies with great food. Almost all the Ailey dancers juice, and I usually have an Amazing Green Acaí Bowl in the morning. It's a great way to get a full breakfast in a really healthy way, and it's quick and easy. If I guarantee that I get my greens in the morning, I feel like the rest of the day is going to go really well.
—Alicia Graf Mack, dancer, Alvin Ailey American Dance Theater
### Amazing Green Acaí Bowl
2 packs frozen acaí
1/2 cup spinach
1/2 cup kale
1/2 medium banana
3/4 cup almond milk
Blend.
Top with 2 teaspoons hemp seeds, 1/3 medium banana, 1/4 cup hemp granola.
### PB Acaí Bowl
The crunch of cacao nibs on a peanut-buttery blend makes this absolutely joy inducing.
2 packs frozen acaí
1 tablespoon peanut butter
1/2 medium banana
3/4 cup almond milk
Blend.
Top with 2 teaspoons peanut butter, 2 teaspoons cacao nibs, 1/3 medium banana, 1/4 cup hemp granola.
### Aloha Acaí Bowl
Bee pollen—a food you'll meet properly in Phase 3—adds a hit of ultrawellness to this island-inspired bowl.
2 packs frozen acaí
1/2 medium banana
3/4 cup almond milk
Blend.
Top with 2 teaspoons bee pollen, 1/2 cup pineapple, 1/3 medium banana, 1/4 cup hemp granola.
### Coco Acaí Bowl
Rich and creamy coconut milk makes any blended treat heavenly. Made fresh at home, it is sumptuous. If using canned coconut milk, look for the variety with no additives and better yet, a can with minimal BPAs in its lining.
2 packs frozen acaí
1/2 medium banana
3/4 cup coconut milk
Blend.
Top with dried shredded coconut, 1/3 medium banana, 1/4 cup hemp granola.
### Hemp Acaí Bowl
Quadruple the hemp and quadruple the goodness. This one will have you dancing, Spinning, and upward-dogging like a pro.
2 packs frozen acaí
1 tablespoon hemp protein
1/2 medium banana
3/4 cup hemp milk
Blend.
Top with 1/4 cup hemp granola, 1/3 medium banana, 2 teaspoons hemp seeds.
JUICY TIP
Hemp granola is available at natural food stores and features hemp seeds mixed into a crunchy, oat, and seed base. It's easy to make your own, and you can use gluten-free oats if you choose.
## phase 3
## ULTRA GREEN: THE FULL FEEL-GOOD EFFECT
This final phase takes you on a journey into the next frontier of juicing and blending, where nature's abundant gifts are used to maximum effect. Juices in this phase feature super-green ingredients that have powerful nourishing and detoxifying qualities. You'll discover how good it feels (and tastes) to make fresh nut milks from scratch; you'll become your own healer, making DIY tonics for the days you feel under the weather and instant wellness shots to keep you boosted year-round. Then, you'll become a master of smoothies using homemade milks, and get adventurous by enhancing these whole-food drinks with superfood ingredients for intriguing flavors and extraprotective benefits. There will be times of coure when you're drawn to making a luscious drink that stands on its own without greens (like an almond-cacao smoothie or a spice-touched nut milk). These drinks also have lots of important nutrients and are fabulous with or without greens. Just try to make a baseline habit of one green-filled drink a day—with some room for treats here and there.
THE TRADE-OUT: In Phase 1 you replaced a caffeinated beverage with a juice or smoothie; Phase 2 was all about ditching a sugary or gluten-heavy snack for a produce-packed drink; now it's about using juices and smoothies strategically, as a tool to see you through each day. Juicing and blending can fit into your unique lifestyle. Perhaps you'll turn to a liquid breakfast—or dinner—if you're feeling puffy and heavy from recent indulgences and want to start or end the day lighter (and sleep better, too). Or maybe you're strapped for time to prepare a healthy meal and want to drink your veggies on the go. This is not about liquefying your diet completely—remember, juicing and blending is about adding, not subtracting. Instead, strategically use juices and smoothies to add balance to your life. Rushing to the airport for an early flight? Drop five supercharged ingredients in the blender and pour the results into a to-go cup; this will serve you better and take you farther (no carb crash later) than a latte and muffin before takeoff. Pushing through a heavy business dinner with nary a lettuce leaf in sight? Find equilibrium again with a green juice for breakfast. Gearing up for a big evening party? Drink a juice or smoothie for lunch to give your digestive system a break before diving into the festivities.
Bonus: Adding detoxifying ingredients will help you cleanse your system more efficiently on a daily basis.
Juice Smarts: When in doubt, go green. A good ratio to aim for most days is 3 parts veggie to 1 part fruit.
## PHASE 3 BUYING GUIDE
Your Green Curve goal in Phase 3 is to make a green-filled drink every day. We'll call this a 90 percent green drink habit—to keep it realistic with a little wiggle room. Whether it's a juice, a smoothie, or a superfood smoothie that you enhance with a handful of greens or perhaps a green superfood powder, and whether you pick your recipes entirely from the ones listed here, or reuse favorites from Phases 1 and 2, we simply want you to get your greens in every day!
* * *
PHASE 3 JUICES: ULTRA GREEN AND DETOXIFYING
Now that any initial resistance to greens-in-a-glass has faded, infuse your juice with some major green players: plants and roots that are a little less commonly used—and that are more intense in flavor than cucumbers or carrots. We've made it easy to drink your dandelion, watercress, wheatgrass, collards, and burdock—something you can feel very good about, because your liver and blood cells will thank you! Then, open the spice cabinet and doctor your juices with turmeric, cayenne, and salt—hits of enhanced flavor with surprising, curative properties.
## COLLARD GREENS
Introducing juicing's up-and-coming superfood: The humble, dark green collard leaf is not especially enticing, but it wins our award for Next Big Thing because it grows abundantly close to home and delivers a ridiculously high quota of nutrition per calorie, including tons of vitamin C and some remarkable anticancer properties. We predict this Southern-food staple will play a leading role in the burgeoning juice revolution, as people fall in love with its affordable price, its ease-of-cultivation for the home gardener, and the large volume of juice it produces. (Not to mention its efficacy in restoring health: Collards have been associated with reduction of inflammation-related diseases like Crohn's disease, irritable bowl syndrome, and rheumatoid arthritis.) On its own, collard juice has a strong flavor, so mix it with the right companions to temper its potency and enjoy its benefits. And as with all deep-green leaves, rotate them over the course of a month rather than relying on them every single day.
### Collard Cooler
Mixed with cucumber, citrus, and apple, as well as the neutral flavors of cucumber and celery, the green goodness goes down easy. Adjust amounts of lemon and lime to taste.
2 leaves collard greens
21/2 medium green apples
1/2 medium cucumber
2 stalks celery
1/2 medium lemon, peeled
1/2 medium lime, peeled
Juice.
### Zesty Green
Collard greens have a similar nutritional profile to that juicing superstar, kale, but they produce significantly more juice, making them not only supremely healthy, but also supremely economical. This mix, enhanced by the detoxifying boost of cilantro, has a delicious sweet-spicy kick.
2 leaves collard greens
1/4 cup cilantro
11/2 medium green apples
3 medium carrots
1/4 medium cucumber
1 inch fresh gingerroot, peeled
Juice.
### Mega Green
Consider this concoction the granddaddy of green—leaves galore with only a kiss of fruit in the form of tart green apple and lemon. For die-hard juicers dedicated to keeping sugars low, this drink is a failsafe staple.
2 leaves collard greens
1 cup spinach
2 leaves romaine
1/4 medium cucumber
3 stalks celery
2 medium green apples
1/2 medium lemon, peeled
Juice.
JUICY TIP
Choose collard leaves that are slightly smaller and avoid yellow or wilted ones. Remember to roll leaves into a cigar-shaped bundle before passing through a centrifugal machine for a better yield.
### Burdock Beauty
1 inch fresh burdock root, peeled
3 leaves dandelion greens
1 cup spinach
1/2 medium cucumber
5 stalks celery
1/2 medium lemon, peeled
Juice.
BURDOCK ROOT
With an earthy sweetness and unexpectedly powerful healing properties, burdock root is prized as a blood purifier and liver detoxifier, treating skin conditions like acne, psoriasis, and eczema and generally helping skin to glow. Burdock root can be wild foraged if you know where to look! More likely, you'll find the fresh root in natural food stores and in Asian grocery stores, where it's sometimes called gobo (in some cuisines it is eaten as a vegetable just like carrot).
### The Detoxifier
2 leaves dandelion greens
1/4 cup watercress
1 cup kale
1 cup spinach
1/2 cup parsley
1/2 medium pear
1/2 medium cucumber
4 stalks celery
1 inch fresh gingerroot, peeled
1/2 medium lemon, peeled
Juice.
DANDELION GREENS
Bitter greens are what juice is made for—the stuff that's hard to eat, but easier to drink. Dandelion leaf deserves the effort. The prolific weed—it's found in the wilds everywhere, but is particularly bountiful in the spring, when the body is due for an after-winter tune-up—boosts the gallbladder's production of bile, which tones the liver. It's fine to pick dandelion greens that are growing wild—if you are sure they are not near lawns or other areas treated with pesticides, or on the shoulders of roads exposed to exhaust fumes.
### Jade Joy
2 stalks bok choy
1 cup spinach
1 cup parsley
1 medium green apple
3 stalks celery
1/4 medium lemon, peeled
Juice.
BOK CHOY
Bok choy is a leafy Chinese cabbage similar to collards in its makeup and boasting all the benefits of cruciferous vegetables, but with a paler color and significantly milder taste. The veggie's gentle flavor, nutritional makeup, and juicing output—each head produces lots of liquid—makes it an ideal base for many juice combinations. When you include bok choy in your juicing recipes, you're infusing your body with anticancer compounds, beta-carotene, folate, plus your daily requirements of vitamins A, C, and K.
### Wild Watercress
1/2 cup watercress
1 cup kale
1 cup spinach
3 medium apples
1 inch fresh gingerroot, peeled
1/2 medium lemon, peeled
Juice.
WATERCRESS
Pungent, peppery watercress is one of juicing's secret weapons. The semiaquatic greens are another deeply purifying plant, packed with vitamin C; calcium; cancer-fighting phytochemicals; and iodine, a much-needed mineral missing from the modern diet. And a little goes a long way! A small shot of this drinkable vitamin added to any juice will deliver its benefits beautifully.
## THE SPICE BAZAAR
Give your juice a new twist in one simple step by exploring the spice bazaar inside your kitchen cabinets and stealing savory ingredients from your favorite cuisines. With a (moderate) dose of spices and salts, you can add surprising boosts of flavor and health-promoting kicks to your drinks.
CAYENNE PEPPER
The slightest pinch of this hotter-than-hot, orange-red pepper will add a touch of fire to your daily juice. Though its heat may tell you otherwise, cayenne contains a plant compound called capsaicin that has anti-inflammatory properties, which helps achy joints and muscles feel better. The warming effects of cayenne are often used in immunity-boosting elixirs to ward off colds—and it's also proven to be good for your heart. Start small—one tiny shake will do it—and dial up the cayenne if you dare!
TURMERIC
The gorgeous, saffron hue of turmeric is a joyful addition in any kind of cooking. The fresh root found at health food stores and Asian markets is even more of a pleasure to use than the powder—slice into the ginger-like root and you'll be dazzled by its vibrant orange interior. Turmeric, which has a slightly earthy, mildly mustardy, and a gingery taste, is considered a "nutritional medicinal"—a food that has high-level health, wellness, and beautifying effects—and has been used for thousands of years in India's cuisine and medicine. Turmeric is now understood in the West to be a powerful anti-inflammatory wonder herb that delivers a full spectrum of benefits, from liver supporting to immune helping and more. A small shake of turmeric powder can be substituted if the root is not available.
JALAPEÑO
Borrow this essential element from Mexican cooking and in a snap you'll add an energizing shot of heat to a green or fruity juice. Pair it with cilantro for an extra Latin-inspired twist. The freshly extracted capsaicin oil contains important minerals and helps with brain aches like migraines and sinus headaches.
Fresh turmeric root is a humble-looking ingredient that is truly a health and wellness powerhouse. Often sourced from Hawaii, and appearing similar to gingerroot from the outside—although sometimes sold as tiny, individual roots—its gorgeous orange flesh can be juiced and added to smoothies. I consider it a powerful anti-inflammatory ingredient that is a modern-life must-have, and predict it will become as familiar in our kitchens as gingerroot is now. Just be careful in handling it—turmeric is famous as a natural clothing dye for good reason!
—Amy Myers, MD, functional medicine clinician and educator
### Cayenne Kick
1 inch fresh gingerroot, peeled
11/2 medium apples
5 medium carrots
1/2 medium lemon, peeled
Juice.
Top with a pinch of cayenne pepper.
### Golden Goddess
1 inch fresh turmeric root, peeled
1 cup kale
4 medium carrots
11/2 medium apples
3 stalks celery
Juice.
### Piña Piquante
1/2 medium jalapeño
1 cup pineapple
2 medium oranges, peeled
1/4 cup cilantro
Juice.
JUICY TIP
Look for firm, ripe jalapeños with shiny skin. If the juice seems too hot, slice the pepper open and scrape out the seeds first. Store unwashed in the fridge, in a paper bag or wrapped in paper towel.
## PINK HIMALAYAN SALT
This pink crystal is a hero product in the raw food world. Sourced from the Himalayan mountains that have formed it over many millions of years, and featuring a precious mix of the 84 trace minerals that our bodies need to function, in extremely absorbable form, Himalayan salt is an ultrapure food source that is sometimes called white gold. Small amounts of salt are necessary for our bodies, but it's the unprocessed kind that our cells crave—not the regular table and cooking salt, which is heat-processed (altering its natural structure) and chemically enhanced to prevent caking and drying. Try a hit of Himalayan salt in these vegetable-rich blends to take your juice in a savory new direction and get the full benefit from this unique commodity.
* * *
### Salsa Samba
Like the most delectable pineapple salsa, this juice is a gustatory joy ride, hitting taste bud hot spots: sweet, salty, and spicy.
2 cups pineapple
1/2 medium jalapeño
1 cup kale
1 cup spinach
1/2 cup parsley
3 stalks celery
Juice.
Top with a pinch of pink Himalayan salt.
Hack That Juice! Each salt-enriched juice can be easily hacked into a savory smoothie by adding a quarter of ripe avocado.
### The Lift-Off
Here, four players from the leafy green wonder team mingle with the satisfying seasonings of lemon, ginger, and pink Himalayan super salt—like a luscious green soup in a glass.
2 leaves Swiss chard
2 leaves collard greens
1 cup kale
1 cup spinach
1/2 medium cucumber
1 inch fresh gingerroot, peeled
1/2 medium lemon, peeled
Juice.
Top with a pinch of pink Himalayan salt.
### Carrot Spice
A twist on a classic combo, carrot and ginger, this juice satisfies on multiple levels. It combines the rooty sweetness of carrot with the zing of ginger, spice of cayenne, and the balance of lime.
7 medium carrots
1 inch fresh gingerroot, peeled
1/4 cup cilantro
1/2 medium lime, peeled
Juice.
Top with a pinch of cayenne pepper and pinch of pink Himalayan salt.
JUICY TIP
A pinch of pink Himalayan salt in a bottle of filtered water is extra hydrating to the body on a hot day. If Himalayan salt is not available in a store near you, it can be easily sourced from online purveyors.
## ULTRA WELLNESS AND SUPERFOODS
By this part of the Green Curve, turning a handful of fresh ingredients into luscious blended drinks has become second nature. In Phase 3, we encourage you to strut your smoothie skills by expanding your ingredient repertoire to include even more diverse raw ingredients as well as delectable, homemade nut milk and supercharged superfoods. The smoothie becomes a true meal-in-a-cup, enhanced with healthy fats and proteins like nut butters, avocado, coconut meat, hemp or chia seeds, or given a green boost with spirulina. You can give your blended drinks a great chocolate flavor by adding nutrient-packed raw cacao and the tonic-herb maca root, or infuse your smoothie with extra antioxidants via a handful of scarlet goji berries. As always, use the following recipes as a starting-off point, a place from which you can freestyle as you get to know new ingredients and experiment in different ways with familiar ones.
* * *
## NUT MILK
A few steps are all it takes to make a liquid food that—quite frankly—completely outshines the store-bought, packaged kind. Light, fresh, mildly sweet, and actually tasting of the real food it's made from.
Making nut milk involves soaking raw nuts to neutralize the enzyme inhibitors that naturally occur in nuts, meaning they become much more digestible. (Allergic to nuts? Try our hemp milk recipe variation.)
High-speed blender. A Vitamix or Blendtec is the most efficient option; a regular blender may also work depending on its strength. A masticating juicer can also be used (with its low RPMs, some say this preserves more nutrients).
Nut milk bag, available at health food stores. Another option is to use a piece of cheesecloth inside a metal strainer, though you may need to double the cloth to ensure that tiny nut pieces don't sneak through.
Medium-size mixing bowl or measuring jug to catch the nut milk.
Glass jar with lid to store the nut milk.
Raw nuts. The easiest and most cost-effective nut milk to make is almond milk. Always look for raw almonds—roasted will not work.
* * *
1
Soak 1 cup of raw almonds in a bowl of water overnight at room temperature, or for 8 to 12 hours. Drain nuts and toss the soaking water.
2
Place nuts in a high-speed blender with 5 cups of water, ideally filtered water. (The exact ratio of nuts to water that you blend is up to you; it depends on the consistency and creaminess you desire. Alter the ratio according to your preference.) Or pour nuts and water slowly through your masticating juicer.
3
Blend the nuts and water until you see the nuts pulverize and the liquid turn creamy white. If using a juicer, you may want to pass the liquid through twice. If the mixture gets caught up in the gear, press "reverse" for a few seconds to dislodge, then continue, adding fewer almonds.
4
Place the nut milk bag in the bowl or jug, with the sides of the bag hanging far over the edge. Pour the liquid slowly in and let it drain through at its own pace.
5
Lift the bag up so more milk drains out and gently pull its drawstrings tight. Now gently twist the bag from the top down and squeeze the contents to extract all the milk possible without letting the pulp through.
6
If you desire plain milk, you're finished. If you want to enhance the flavor, combine the milk with some of the ingredients suggested in the variations. To store, pour the nut milk into a glass jar with an airtight lid and refrigerate for 3 to 4 days. Try to fill it to the very top of the jar to retain the milk's freshness. If you have more than you can use, freeze the extra in freezer-suitable containers. Shake before using as nut milks separate naturally.
### Irresistible Brazil Nut Milk
Follow directions using 1 cup Brazil nuts and 5 cups water (adjust the ratio depending on the thickness desired), but do not soak the Brazil nuts. Blend with dates, pinch of sea salt or pink Himalayan salt, and vanilla bean or vanilla essence to taste.
### Vanilla Almond Milk
Pour almond milk into blender with 1/2 to 1 vanilla beans (or a dash of vanilla essence), filtered water, and dates to taste. Advanced level: Add a pinch of turmeric for a golden-yellow, extrahealing drink!
### Cinnamon Cashew Milk
Follow directions using 1 cup cashews and 5 cups water (adjust the ratio depending on the thickness desired), but soak the cashews only for 2 to 21/2 hours. Blend with dates, pinch of sea salt or pink Himalayan salt, vanilla bean or vanilla essence, cinnamon.
### Chai Hemp Milk
Follow directions using 1 cup hemp seeds and 5 cups water (adjust the ratio depending on the thickness desired), but do not soak the hemp seeds. Blend with a nub of fresh ginger diced small, a dash of cinnamon, seeds from 2 to 3 pods of cardamom, dates to taste.
JUICY TIP
The most commonly available almonds that are labeled "raw" have actually been pasteurized using steam or even chemicals, or possibly irradiated, though they have not been roasted at high heat. It is not easy to find 100 percent unpasteurized nuts, though they may be available at farmers' markets and from online sources. Their price is significantly higher—the same goes for truly "raw" nut butters—though fans say that the taste and benefits are, too. Buying organic almonds labeled "raw" will ensure your nuts didn't undergo a chemical pasteurization process.
## ULTRA WELLNESS AND SUPERFOODS
We have juicers and blenders at our San Francisco offices and we get a fresh supply of organic fruits and vegetables delivered every week, so that everyone who works with us can make what they want. On a crazy-busy, "God I don't have time to have lunch" kind of day, it takes less than four minutes to make a really good smoothie.
— Ido Leffler, cofounder of America's second largest natural beauty brand, Yes To
### Hero's Garden
Go ultragreen in a flash by mixing four kinds of green in a single cup. Two phenomenal green leaves blend with tart, green apple and the lush texture of avocado. (Play with the amount of avocado to alter the creaminess.) Make your own apple juice before blending—an extra step that reaps big flavor rewards.
2 leaves Swiss chard
1 cup kale
1/2 medium green apple
1/2 medium avocado
1 cup fresh apple juice
Blend.
Optional: Use water instead of apple juice.
### Antioxidant All-Star
Dial up the flavor, color, and goodness as a trio of irresistible colors—red, blue, and purple—combine with three super-green leaves in a drink that infuses you with disease-preventing antioxidants. Red pomegranate pops with tart flavor, blueberries balance them with sweetness, and acaí deepens the effect with its purple, cherry-berry taste.
1 pack frozen acaí
1/4 cup pomegranate seeds
1/2 cup blueberries
2 leaves Swiss chard
2 leaves collard greens
1 cup kale
1/2 medium green apple
1 cup filtered water
Blend.
### Emerald Escape
Though tough-textured collards are typically eaten braised with broth, blending breaks down the cell walls effectively too, releasing the prized nutrition. Think: carotenoids, vitamin K, vitamin C, vitamin E, folate, and manganese. Here, collard juice is transformed into an energizing elixir that's sweet and savory when combined with pineapple, lime, cilantro, and an energizing hit of blue-green spirulina—a nourishing plant-food from earth's clean waters.
2 leaves collard greens
1 cup papaya
1 cup pineapple
1/4 cup cilantro
1/2 tablespoon spirulina powder
1 cup fresh coconut water
1/2 medium lime, peeled
Blend.
Optional: Sweeten smoothie with 1 to 2 dates, if needed.
### Island Blue
The aquabotanical called AFA blue-green algae is considered by many to be a wonder food. Sourced from deep, remote lakes, it is the wild-harvested counterpart to spirulina, and considered by many to have superior nutritional quality; it energizes, focuses, and balances the mind and body and delivers resilience to stress. Coconut water works in synergy, helping the body absorb more of the algae's omega-3s.
1 freshly cracked young Thai coconut, water and meat
1 ounce blue green algae
Blend.
SPIRULINA
Spirulina has been on earth since the dawn of time. This blue-green algae grows wild in freshwater lakes and waterways and is cultivated for nutritional use primarily in Hawaii. Its intense color is made up of green chlorophyll and blue phycocyanin, a health-promoting pigment. Spirulina lovers say the algae's highly absorbable, complete protein gives them a boost—vegan athletes often use it in their dietary regimes. In addition, its broad-spectrum nutrients, including essential gamma-linoleic acid, maintains a healthy nervous system. Spirulina's flavor is unusual and a little lakelike, so start very small and let your palate adjust!
JUICY TIP
Notoriously tricky to open without spattering your clothes and counters, a pomegranate can be tamed by first slicing off the top to reveal the seeds, then scoring it lengthwise into six sections with a paring knife. Carefully split the sections apart, peel off the white pith, crack into smaller segments if necessary, and pop the seeds into a bowl. If this is too messy, submerge the fruit in a bowl of water to split and scoop.
In our stores we use E3Live, an organic, wild-gathered blue-green algae from Upper Klamath Lake, Oregon; it's a fresh frozen pulp that is thawed before using. Start slowly due to its detoxifying effect. Always be sure your algae superfoods come from reputable sources.
### The Sage's Smoothie
Go wild for the goji berry, the tiny, flame-red superfruit famed in China and Tibet for its longevity-boosting properties and cherished by foodies for its delicious, cranberry-cherry taste. Add a boost of chia seeds—long used by native Americans of the Southwest for endurance and hydration—to nourishing coconut for a hearty drink that will tide you over for hours.
1 freshly cracked young Thai coconut, meat and water
1/2 cup papaya
2 tablespoons soaked goji berries
1 tablespoon chia seeds
1/2 cup parsley
1/2 medium frozen banana
3 dates, pitted
Blend.
Soak chia seeds in the blender liquid for 10 minutes before blending so they absorb liquid. This helps them to hydrate you more effectively.
### Lynsey's Joyful Almond
This rich and creamy smoothie can satisfy your sweet tooth when you're craving a dessert, or fuel you through a rigorous morning with its slow-burning fats. For a pop of pleasurable texture, use crunchy, raw cacao nibs instead of powder.
1 cup almond milk
2 tablespoons almond butter
1/2 tablespoon raw cacao
1/4 cup frozen coconut milk
1/2 medium banana
2 dates, pitted
Blend.
Juice Smarts: Reputed to have helped Taoist wise men live for centuries, the goji berry is part food, part medicine. Normally purchased in their dried form, good-quality goji berries should be slightly moist, not brittle or very dull in color. Because they're usually imported from overseas, it's wise to research your brands if you want to ensure chemical-free berries. Some farmers' markets now have locally grown fresh berries. Mix a handful of gojis with raw cacao nibs and nuts for a superb on-the-go snack.
As a winter athlete, my focus is on warmth, protein that can last all day when I'm in the mountains, good fats, and hydration—it is important in helping to avoid altitude fatigue and to support brain function and circulation. I believe in filling my cup with substance, whether I'm shooting a ski film in Alaska or having a long day of meetings or travel for SheJumps, the girls' empowerment organization I cofounded. Even in the most unusual locations, it is easy to fill a blender, press a button and go—I feel 100 percent more confident when I've been able to take care of my nutrition myself, and not have to depend on what's provided.
—Lynsey Dyer, professional big mountain skier
## THE NEXT FRUIT FRONTIER
Stumbling upon the next hot sensation from the fruit world makes the art of smoothies extra enticing. At Juice Generation we are certifiable flavor hunters—always searching for the next fruity frontier, motivated by the hunger for a new experience of flavor, color, and texture. Meet our three favorite little-known fruits with the power to seduce body, mind, and senses.
ARONIA BERRIES
Watch out acaí, there's a new superberry in town—and it's native to North America. The aronia berry's violet-black flesh is virtually exploding with antioxidant power and antidiabetic and anticancer effects. The tart, slightly sour flavor gives it a menacing alias—black chokeberry—but balance it out with complementary ingredients and you get a delectable dose of ultrawellness that is sourced on U.S. soil. Aronia berries are still new players in the natural-foods market. Frozen packs and powdered fruit are available online or ask your local health-food store to consider supplying them from one of the new crop of North American suppliers. If not available, substitute acaí.
* * *
PITAYA
This diva of fruits—also known as dragonfruit—has a hot-pink outside that conjures a feathered bird of paradise and reveals white, or sometimes vibrant fuchsia, flesh inside that's graphically studded with tiny black seeds. Its delicate flavor, reminiscent of a pear crossed with a kiwi and a melon, has a refreshing and subtle effect that does best when paired with equally mild flavors. Typically sold at Asian food markets, the pitaya is ripe when the leafy scales on the outside are slightly dry and shriveled, not hard and green. Simply slice the fruit in half and scoop the flesh and seeds out with a spoon.
SEA BUCKTHORN BERRIES
Traditionally plucked from shrubs high in the Himalayas, the bright-orange sea buckthorn berry has been used since ancient times in Asian healing and is poised to become the next goji berry. Westerners are discovering why this tangy fruit is nature's ultra multivitamin—in addition to a cocktail of 190 bioactive nutrients, it contains the hard-to-find omega-7, a fatty acid said to support healthy intestines, weight levels, and cardiovascular health as well as keep skin, hair, and nails at their best. Sea buckthorn is currently most easily acquired as a prebottled liquid supplement or as capsule supplements. In the future, it may become possible to find the fruit as a frozen puree.
### All-Star Aronia
1/2 cup aronia berries
1/2 cup strawberries
1 cup spinach
1/2 medium frozen banana
1 cup fresh apple juice
Blend.
### Pink Pitaya
1 freshly cracked young Thai coconut, water and meat
1 cup pitaya
1/2 medium banana
Blend.
### Buckthorn Blast
1 ounce sea buckthorn puree
1 ounce filtered water
Blend.
## MACA & MORE: SUPER BOOSTERS
Treat your body like a temple by integrating a pair of nature's most nourishing plant foods into your daily drinks. These two ingredients have been used—and revered—by people in far-flung locales for millennia for their strengthening, energizing, and balancing properties. But only recently have they entered our modern-day pantries under the tag line of superfood—eatables that have an exceptional amount of wellness-enhancing qualities housed in one turbo-charged package.
RAW CACAO
Solids from the cacao bean that are usually cooked to make chocolate candy bars, but that lose many of their beneficial properties when roasted—can be added to a smoothie as raw cocoa powder or crunchy cacao nibs for a hearty boost of antioxidants, iron, and magnesium.
MACA ROOT
An Andean tuber that has a faintly golden-malted taste—is available as a powder to sprinkle into all kinds of juices and smoothies—delivering a gentle boost in alertness and a handful of significant health benefits.
These pick-me-uppers can replace the lift of morning caffeine for some people, without the edgy side effects and with lots of extra benefits: Cacao has been called the "food of the gods" for its phenomenal combination of compounds that nourish the body, increase alertness and, thanks to the "bliss chemical" anandamide as well as tryptophan and serotonin, noticeably raise the mood. (Plus, science is now showing how these compounds help protect us from a myriad of modern-day problems like cardiovascular disease and type 2 diabetes.) Maca, used as a daily staple food by high-altitude mountain dwellers in Bolivia and Peru, is a famed adaptogen—a tonic herb that strengthens the body against stress and delivers endurance, as well as reproductive health and virility! What's not to enjoy about this superduo of superfoods?
Juice Smarts: A raw-foods chef's secret weapon, Irish moss is a seaweed that delivers a luscious, creamy texture to smoothies and desserts without the caloric boost of nuts and seeds, and with important iodine and iron, as well as antioxidants. (Carrageenan, used in boxed nondairy milks, is its processed and concentrated extract.) The authentic, whole-food ingredient is a cold-water seaweed harvested off the coast of Ireland and that should come fully dried—as always, check the source and quality of your purchase—and it can turn an everyday drink, as well as a thick blended dessert or creamy pie, into an out-of-this-world experience. Soak it for about 20 minutes in water to rehydrate before blending.
JUICY TIP
Cacao taken in large amounts can make some people feel "wired" and overstimulated, so it is still important to tune in to your body's response to evaluate how it works for you and in what quantity. Seek out 100 percent raw, organic cacao products. A Fair Trade stamp on the package helps you know it's ethically sourced from overseas communities.
Maca root powder is easy to find in most natural foods stores. It also goes wonderfully with nut milks spiked with cacao and vanilla.
### Maca Master
History tells us that Incan warriors used maca for fortitude and courage before heading into battle; it's not surprising that this South American root is a go-to superfood helping us stay focused and fearless in the fast-lane of contemporary life. And it won't spark gustatory trepidation: Its slightly malty aroma evokes a malt ball or graham cracker.
1 pack frozen acaí
1 cup strawberries
1 tablespoon maca root powder
1/2 medium banana
1 cup fresh coconut water
3 dates, pitted
Blend.
Hack That Smoothie! Add a tablespoon of soaked chia seeds to give an extra hit of nutrition and hydration to your super drink.
### Queen of Fruits
Blending two of the original superfruits—the dark-red (read: antioxidant-filled) pomegranate with the delicate, white-fleshed mangosteen—this smoothie delivers a medley of surprisingly enchanting, tart-sweet tastes. Mangosteen, the official national fruit of Thailand that is famed for its aromatic flavor, has long been nicknamed the "queen of fruits" by tropical fruit lovers.
2 medium mangosteens, peeled and pitted
1 medium kiwi, pitted
1 cup fresh pomegranate juice
1 inch fresh gingerroot, peeled
3 dates, pitted
Blend.
Hack That Smoothie! Add a handful of mild green leaves like spinach.
### Drink of the Gods
Indulge the senses in the luxuriant experience of chocolate and hemp milk, made creamier with the addition of an unusual natural thickener—a seaweed that secretly adds more minerals to your drink.
1 cup hemp milk
1 tablespoon raw cacao
1/4 cup soaked Irish moss
1 tablespoon coconut oil
1/2 medium banana
3 dates, pitted
Blend.
## CLEANSE AND REVIVE
Juice cleanses are the perfect way to get back on track after you've had a weekend full of consecutive pig-out sessions. They're also just an easy, great way to do something healthy for your body. I'm a big fan of all fruit juices, so I love juice with pear, or watermelon lime, or a spicy lemonade. But I also know that vegetables rule and are the best for you, so when it's time to get hardcore, I drink a green juice with a veggie like kale. But those are the most difficult ones for me, so give me a green juice with something sweet like apple and a little lemon and I can almost pretend it's dessert!
—Gayle King, coanchor of CBS This Morning and editor at large of O, The Oprah Magazine
USING YOUR JUICING TOOLS FOR DETOXING AND HEALING
The three phases of juices and smoothies may have delivered all kinds of results—from enjoying a new awareness of food, to feeling confident in the kitchen with new health-giving ingredients, to noticing a higher energy level, clearer mind, better-functioning body, and more glowing skin. The more your new tools become habitual, the easier it will be to continue to refresh, restore, and energize yourself, on your own terms. Reaching the top of the Green Curve is just the beginning of a new way of being, in which it feels second nature to reach for vital greens and whole-food ingredients to take care of yourself wisely, day in and day out.
Taking good care of yourself may also involve occasionally doing short and easy juice cleanses or using the power of juice to fight colds and other illnesses.
## THE RESET
At Juice Generation we think of cleanses like short resets for your body. They are dietary programs featuring a customized mix of fresh juices, coconut water, and nut or seed milks (if you choose) that you follow for one or a few days to give your digestive system a break and flood your cells with rejuvenating, lifting, and clearing energy. Doing one day of liquid-only foods, or as much as three days in a row, can be a simple and easy-to-succeed way to come back to balance in body, mind, and spirit, without overhauling your entire life to do it.
At Juice Generation, we call these little breaks from regular food programming resets because they are short programs that aren't aiming too high—they're not trying to reverse decades-worth of toxins in 24 or 72 hours. Their goal is not to shed weight or heal chronic health issues. (Those goals can be addressed through a long-term plan of smart nutrition and strategic cleansing programs—but you'll want to accomplish this slowly and over time, and ideally with the guidance of a good practitioner or health coach. For reference, our signature Cooler Cleanse juice deliveries offer six juices that provide approximately 1,200 calories in a day.)
These smaller, shorter programs of one, two, or three days on juice-only diets are about finding your equilibrium and coming back to center; unplugging from ordinary eating and drinking habits; resting your system and boosting immunity; and alkalinizing your blood and feeling a rebound in energy, lightness, and clarity as a result. You are giving your essential detoxification organs a lift by adding lots of natural antioxidants that bind to toxins and convert them to harmless substances and nutrients, such as beta-carotene, that help the liver do its work. This is a key to successful preventive health care.
A cleanse can also reset your relationship to food. It's human nature to fall into food routines that don't support us fully, whether it's consuming foods and drinks that irritate our systems, that fatigue us rather than fuel us, or that don't have enough vital force of live enzymes and micronutrients to help our bodies do their best work. Or, we might already have a balanced, smart diet, but in the busyness of life, that good food gets consumed in unconscious and rushed ways—something that all healers say compromises digestion and overall well-being.
Cleansing programs don't suit everyone, so there's no need to make it a priority if it does not feel right for your body. But for many people, taking a break from regular eating habits can give fresh perspective on what and how we eat daily, helping us to see and feel what works and what does not, and motivating a positive shift toward a cleaner, greener, happier, and healthier way of being for the longer term.
## THE GREEN CURVE CLEANSE
After spending time on the Green Curve, you've probably already experienced some changes in what you crave and what you consume each day. You might have seen some of your existing food habits with fresh, new eyes. Simply implementing daily green drinks into your diet is in itself a mild and steady cleanse: You are slowly and steadily replacing unhealthy foods with healthy ones; you're feeding the liver, the intestines, and the bloodstream with trace nutrients they may previously have lacked; and over time, by replacing sugary foods and foods that may have been irritating you, like gluten and pasteurized dairy, you are allowing the environment of your intestines to rebalance and repair itself. In other words, you've been doing a mild daily cleansing program every day!
* * *
At Juice Generation, we recommend that those new to cleansing programs try a 1-Day or a 3-Day Juice Cleanse, depending on their goals. Some people then go on to try a 5-Day Cleanse at a later date. This longer cleanse is best with a little more preparation and, often, some oversight from a health coach or advisor. All juice cleanse programs have the potential to create uncomfortable detoxification symptoms—though if you have already cleaned up your diet and been using green drinks regularly, you will likely experience much less of this effect. Longer cleansing programs require extra care to ensure your system is getting the best support. Here, we introduce you to the two shorter versions of juice cleansing.
It's so stressful during fashion show preparation time that you end up kind of eating all sorts of crazy things. And you're at the studio until three in the morning. So it's great once the show is done to be able to do a cleanse and get back on track. It's like we've repaired ourselves from all the damage that show week has done to our bodies.
—Peter Som, fashion designer
Juice Smarts: Why no smoothies? Cleansing and detoxification programs use juices, including coconut waters and nut milks, but not smoothies, because the fiber-free juices and drinks are absorbed with minimal work by your digestive system, freeing up the most energy possible for your body to put toward detoxification and healing.
## JUICE FOR A DAY
WHEN TO DO IT
You've overindulged in food and drink and feel the consequences, and want a day to reset your system; you want to take a quiet day oriented toward rest and rejuvenation, to give your digestive system a rest and help support your detoxification system, as part of a greater goal of balance and well-being.
WHAT TO DO
Over your day, consume six fresh-made juices including coconut water and nut or seed milks, if you desire, at regular intervals (approximately every two hours) in lieu of your regular meals and snacks. Include a spectrum of juices with a good selection of green drinks for maximum benefit, as greens have the most nutrients to support the detoxification system. We include juice suggestions here, but you can also customize it yourself. However, do not consume six fruit-based and root-based (i.e., carrot and beet) drinks, as this is an overload of sugar. Mix it up and lean into the green. Most people prefer to have a nut milk as the final drink of the day, as the fats and protein gently nourish through the night and also help bind to toxins that may be have been released, facilitating their excretion. Starting the day with hot water and lemon and ending it with a warm, herbal tea is especially helpful. Have your drinks at room temperature, not ice cold, and sip them slowly.
* * *
If you need more than six juices to get by, add another—make it a nut milk if you want extra calories. Keep all your juices clean and simple without adding in fats (like coconut oil or avocado). Drink plenty of water throughout the day; herbal teas are fine, but try to cut the caffeine. If you must, have lightly steeped green tea.
Try to avoid snacks! If you're struggling with hunger, a small piece of fruit plus raw nuts or nut butter may help.
If possible, rest well on this day. Get to bed early. Take the time for you.
One option for the Juice-for-a-Day program is to begin your cleanse at dinner time the night before, so that your first juice is at night. The next day, continue with your next five juices, and at dinnertime ease out of the cleanse with a light meal such as soup, salad, steamed vegetables.
MAKE YOUR OWN PROGRAM
A wise cleansing menu comprises a spectrum of drinks that focus on low-fruit greens. There is no one way to write a program of six juices in one day, but an ideal day could include a morning green drink; a midmorning drink featuring grapefruit; a vegetable-rich green drink midday or a nut milk for more nourishment; a coconut water or green drink in the midafternoon; a fruit or vegetable juice in the late afternoon, and a nut milk for soothing nourishment in the evening.
For the optimal experience, choose from the following recipes: 2 to 3 dark green juices, 1 to 2 lighter green or fruit-based juices, 1 to 2 nut milks, and 1 coconut water, for a total of six drinks in each 24-hour period (or more if you are very hungry).
WHAT YOU MIGHT EXPERIENCE
This is a simple reset that helps to clear the mental and physical fog or reinvigorate your senses and allow for rest and recharging.
HOW TO USE IT
Use it as an occasional tool; or do it once a week for three or four weeks in a row to experience and integrate gentle self-care into your life in a meaningful way. Some people like to do a Juice-for-a-Day reset once a week, for example on a Sunday, as part of a plan for greater well-being.
## THE 3-DAY CLEANSE
WHEN TO DO IT
You want to do a deeper dive into refreshing and boosting your body, and have some extra time to take care of yourself, rest well, and cut back on busy demands; you are feeling weighed down, sluggish, or off-track, and want to do a significant jump-start toward higher health and wellness.
WHAT TO DO
It is wise to plan the 3-Day Cleanse with some foresight. The two or three days before and after the cleanse are an opportunity to "ease in" and "ease out" of your cleanse by consuming clean, freshly prepared foods free of irritating effects. This means a fairly simple diet based on lightly cooked vegetables, soups, and broths, easily digestible proteins cooked simply, and no common irritants like gluten, dairy, and eggs, as well as processed or heavy foods, excessive sweets, alcohol, and strong caffeine. Do not use these pre- and post-days to cut back on calories; the idea is to take care of yourself kindly.
By easing in and easing out of your cleanse in this way, you'll give your body the maximum nutritional and energetic benefits by taking a load off the digestive system and removing any irritating factors, so that more energy can go toward detoxification and healing. You'll feel, and look, more refreshed and you will sleep better as a result.
* * *
On each day of the cleanse, follow the What to Do directions for the 1-Day Cleanse and pick your drinks according to the What to Drink list.
In addition, you'll want to keep these points in mind:
Try to get to bed early. Light exercise is recommended as movement stimulates the lymphatic system to move waste products out of the body. But hard workouts that use significant calories and require recovery are best left for before and after your cleanse. Turn off your phone and read a book instead.
During the 3-Day Cleanse, it is ideal to support your elimination system to ensure that the body's naturally produced toxins, as well as any not natural toxins that may be released, can leave your system efficiently.
Over these days, you will help yourself get best benefits if you:
Breathe deeply; time on the yoga mat is very well spent.
Ensure that you have good bowel movements every day, which can be helped with a non-stimulating supplement like magnesium powder before bed.
Sweat in a sauna if you can; or do a short, sweaty workout that is not too demanding.
Many people find the first day slightly challenging. Many feel no unsettling side effects, but it's possible to feel some symptoms of withdrawal from caffeine, as well as symptoms of detoxification, which can range from headaches to fatigue to irritation. Try not to see these as wrong, but rather as symptoms of something clearing out. They'll pass.
WHAT YOU MIGHT EXPERIENCE
By the end of the three days, you may feel lighter, brighter, clearer in mind and body. You may feel renewed energy and focus and notice your eyes, skin, and hair looking more vital. You may have a new sensitivity to how the foods you eat either make you feel uplifted—or make you tired. You may have lost a few pounds, but remember, this is not the goal of the cleanse.
HOW TO USE IT
This short reset can be used on a periodic basis, such as every season or every few months. It is important to always remember that juice cleanses are kick starts for healthy, long-term habits and resting periods to recharge and refresh; they are not quick fixes for neglecting your well-being or substitutes for a smart, longer-term strategy.
DARKER GREEN JUICES:
For best results, make sure to include at least two or three of these low-fruit/low-root vegetable green drinks in your daily program.
Michelle's Leafy Green Goodness
Very Veggie
SupaDupa Greens
Collard Cooler
Mega Green
Jade Joy
Burdock Beauty
Wild Watercress
The Detoxifier
The Lift-Off
The Professional
LIGHTER GREEN JUICES:
As these contain slightly more fruits or roots, it's ideal to include these in moderation: just one or two in your daily program.
Debra's Green Elixir
Hail to Kale
Very Veggie
Get Ur Green On
Blake's Intoxicating Detoxification
Golden Goddess
Salsa Samba
Michael's Go-to Greens
Gaia's Garden
Verdant Vista
NUT MILKS:
It's recommended that you have at least one nut milk a day, consumed at the end of the day if you like. Add a second nut milk during the day if you feel a lot of hunger.
Vanilla Almond Milk
Irresistible Brazil Nut Milk
Cinnamon Cashew Milk
Chai Hemp Milk
COCONUT WATER
Have one optional coconut water a day for refreshment.
Plain coconut water from a fresh-cracked nut
Island Blue
FRUIT-BASED JUICES:
Limit to one per day for best results (or exclude if you prefer). Enjoy the juices listed below, or any of the basic recipes listed on pages 80 to 103.
Tropical Lust
Grapefruit Refreshmint
Grapefruit Zinger
Grapefruit Moon
TropiKale
Emerald + Orange
Leaves & Roots
JUICY TIP
Follow the strategies outlined in the Green Curve for making and storing drinks. If you can make each drink of the day fresh—terrific! But if you are making a big batch for later in the day, store juice well in bottles or jars filled right to the brim, and keep them in the fridge.
## JUICE FARMACY
We first developed juice remedies for the Broadway performers who frequent our 9th Avenue store. They requested ginger-spiked elixirs to help counteract a cold or a warm, throat-soothing concoction that wouldn't dehydrate the vocal chords like caffeine does—all so that the show could go on. These actors, singers, and dancers are unusually attuned to what supports and sustains the body. By requesting these healing concoctions, they showed us how a medicine kit of juices, hot drinks, and juice shots can help anyone find their way back to show-stopping form.
Whether aiming to regain strength and energy after six months of chemotherapy, fortify myself during a grueling shooting schedule, or give myself an easy and effective gift of general self-care, juicing is a fundamental tool. My go-to juice is lemon, ginger, green apple, celery, and kale. Nothing does more to provide both instant and sustained vitality.
—Michael C. Hall, actor
### Michael's Go-to Greens
1 cup kale
3 stalks celery
2 medium green apples
1 inch fresh gingerroot, peeled
1/2 medium lemon, peeled
Juice.
## HOT STUFF!
When the weather is chilly or you're fighting off a cold, a warm, vitamin-infused drink can be the ultimate cure. Here, raw ingredients are heated, but many of their benefits are still intact, delivering the nurturing you need.
If I am on Broadway and feel a little under the weather or sluggish, I have a Dr. Bombay before every show. It grounds me, soothes my whole system, and shores me up for eight shows a week. Dr. Bombay has become a staple to my preshow ritual.
—Laura Linney, actor
### Cold Warrior
Zinc and echinacea are prized for their sniffle-fighting capabilities. A few drops of these liquid supplements give a tasty warming brew a healing bonus. Lightly caffeinated green tea gives a gentle lift plus cancer-fighting flavonoids; raw agave sweetens the deal.
1 cup freshly steeped green tea
Juice of 1 medium orange, peeled
1 inch fresh gingerroot, peeled
1 tablespoon raw agave
A few drops of liquid echinacea
A few drops of liquid zinc
Brew a cup of green tea and add the juiced orange and gingerroot. Stir in the agave, echinacea, and liquid zinc.
### Lemon Lozenge
Apple, lemon, and ginger are an immunity boosting power trio, flooding an ailing body with vitamins A, B, and C—plus antioxidants with liver cleansing properties and circulation enhancers. A sprinkle of cayenne helps to relieve congestion and reduce fever.
3 medium apples
1/2 medium lemon, peeled
1 inch fresh gingerroot, peeled
1 tablespoon raw agave
Pinch of cayenne pepper
Juice the apples, lemon, and gingerroot. Stir together and heat on stove top or using an espresso steamer. Sweeten with the agave and sprinkle with the cayenne pepper.
### Ginger Fix
Creamy, spicy, and sweet—this healing tonic is as tasty and restorative as a cup of chai tea. Cinnamon is a powerful antiviral compound also used for its deeply warming properties; practitioners of traditional Chinese medicine often prescribe it to ward off colds. Cardamom is used to treat bronchitis and heal sore throats, and a double dose of ginger works to soothe upper respiratory tract infections and calm nagging coughs.
1 cup almond milk
Juice of 2 inches fresh gingerroot, peeled
1 tablespoon raw agave
Pinch of cinnamon
Pinch of cardamom
Stir together and heat on stove top or use an espresso steamer.
### Dr. Bombay
Like the best holiday cider boosted with additional beneficial support, this hot blend will calm and comfort on cold and windy days.
Juice of 21/2 medium apples
Juice of 1/2 medium pear
Pinch of cinnamon
A few drops of liquid echinacea
A few drops of liquid vitamin C
A few drops of liquid zinc
Stir ingredients together and heat on stove top or use an espresso steamer.
JUICY TIP
Liquid forms of the herb echinacea, as well as vitamin C and zinc, can be sourced at health food stores.
## WHEATGRASS RX
The new grass that germinates from wheatberry seeds is considered one of the ultimate "living foods" for its medicinal properties.
Wheatgrass juice became a buzzword in the 70s through its use in progressive healing programs, but now it's embraced by everyday juicers who add it to their diet to maintain optimal health and wellness. Wheatgrass juice helps give a boost to red blood cells, is a powerful detoxifier and alkalinizer, and is so rich in chlorophyll it's sometimes dubbed a liquid oxygen transfusion. Wheatgrass also helps to neutralize environmental toxins in the body and its devotees say it slows the aging process—like a green elixir of youth!
Its strong, grassy taste makes wheatgrass an "advanced green" drink, but mixed into the right juice combo it will be successfully balanced by other flavors. Wheatgrass oxidizes very quickly after juicing and is meant to be consumed right away. Drink the shots or any juice incorporating wheatgrass fresh, rather than storing it in the fridge.
* * *
JUICING WHEATGRASS
This delicate plant needs some special care; centrifugal juicers are usually too fast and strong to extract its juice. Masticating juicers usually handle it well, and special wheatgrass juicers are even available. The best way to use it is to purchase large flats of wheatgrass from health food stores or farmers' markets and cut the amount you want to juice each day; some careful tending is required to avoid mold growth at the roots. It's also available precut in bags and should last for up to a week in the fridge. If you fall for the wheatgrass habit, it's relatively simple to grow your own, though your indoor garden will require some daily TLC. Supplies and instructions are easily sourced online.
JUICING JARGON
Chlorophyll is the part of the plant that makes it green. When we consume green plants full of chlorophyll, it has an oxygenating, alkalinizing, and purifying effect on our red blood cells and helps to replenish and rebuild them. Chlorophyll also helps to pull out heavy metals from our system, encourages better bowel movements, and promotes good gut flora. It's found in greatest quantity in darker green vegetables like kale, spinach, chard, and arugula; in herbs like parsley and cilantro; in sprouts, and in blue-green algae like chlorella and spirulina, and there's lots of it in wheatgrass. Cooking changes the structure of chlorophyll, which is why juice devotes consider raw juice the most efficient way to get it.
JUICY TIP
A single or double shot of wheatgrass can be tossed back on its own. Consider it the jade-colored opposite of a steaming espresso shot.
### Verdant Vista
The bold green flavor of wheatgrass mingles seamlessly with the fresh sweetness of pineapple and pear—uplifted by a hint of mint—turning this detox drink into a delicious refresher.
2 cups pineapple
1/2 medium pear
1 sprig mint
Juice.
Top with 1 ounce of wheatgrass juice.
### Gaia's Garden
Wheatgrass meets its match with a handful of sweet roots, fortifying leaves, and the refreshing, balancing flavor of cucumber and celery. It's never been so easy to get your grass on.
1 cup spinach
1/2 medium beet
4 medium carrots
1/4 medium cucumber
3 stalks celery
Juice.
Top with 1 ounce of wheatgrass juice.
### The Professional
You leave the fruity green drinks to juicing amateurs. You're serious about your greens—and your grass—and your drink shows it. But at Juice Generation, we know that even hardcore green juicers appreciate the lift of a bit of apple and lemon: They turn a good-for-you drink into a tastes-good drink.
2 leaves Swiss chard
1 cup kale
1/2 cup parsley
3 medium green apples
1/4 medium cucumber
1/2 medium lime, peeled
Juice.
Top with 1 ounce of wheatgrass juice.
## JUICE SHOTS
Lots of good things come in a shot glass, but most of them don't make you feel especially great the next day. Juice shots are designed to boost your body when you need a quick hit of high-octane assistance by delivering small but potent doses of curative natural ingredients. Consider them your secret weapons in staying well and vibrant and toss one back the next time you want to rev up your health. Each shot is approximately 1 ounce of juice.
### The Defender
For added support, dial up your shot with turmeric and a dash of oil of oregano, a potent natural antimicrobial that can help arm the body against germs, and slow the downward slide into persistent coughing and sneezing.
1 inch fresh turmeric root, peeled
1 inch fresh gingerroot, peeled
1/2 medium lemon, peeled
Juice.
Top with a pinch of cayenne pepper and a few drops of oil of oregano.
### Performance +
At the 2012 London Olympics, word got out that endurance runners and cyclists got juiced on a powerful—and all-natural—performance aid: freshly liquefied beets. The high volume of nitrates in the juice is said to help muscles use oxygen more efficiently, with less fatigue. Not a marathoner? A shot of beet juice delivers the vegetable's liver-boosting and detoxifying properties—without the sugar spike and potential stomach upset of an entire glass. No wonder some natural healers say, "A beet a day keeps the doctor away."
1/4 medium beet
1/2 medium lemon, peeled
Juice.
### Fountain of Youth
Legends have been spun around the youth-preserving qualities of bee pollen's tiny golden nuggets. Athletes say the rapidly absorbed, concentrated B vitamins improve strength, endurance, speed, and exercise recovery, while go-go-go urbanites use the "Bs," along with the nuggets' antimicrobial, antibacterial properties, to manage stress and even enhance memory! Bee pollen—the mineral matter gathered by bees as they pollinate plants—is a precious food containing all 22 essential amino acids and the ever-important vitamin B9 (aka folate).
1/4 teaspoon bee pollen
1 ounce fresh coconut water
Soak the bee pollen in the coconut water and strain before drinking.
### Shot of Gold
While India's ayurvedic doctors consider turmeric a mainstay of health and longevity, protecting the immune system against the effects of stress, India's women know the spice to be a beauty booster, promoting radiant, youthful skin from within. (And without: The powder is often used in rejuvenating face masks.) A shot of juice from the freshly cut root is a whole-food version of the (turmeric-derived) curcumin supplements that are now widely used for wellness. Consider it a daily tonic for body and beauty.
1 inch fresh turmeric root, peeled
1/2 medium lemon, peeled
Juice.
### Vital Shot
At the first sign of a cold, try this warming and cleansing blend of spices, lemon, and healing ginger, to help to fire up your immunity to all-systems-go.
1 inch fresh gingerroot, peeled
1/2 medium lemon, peeled
Juice.
Top with a pinch of cayenne pepper.
JUICY TIP
Bee pollen can be purchased dried or fresh—the latter has a fluffier texture. Look for raw and unprocessed pollen sourced from your home country. (If the seller does not say where it is from, nix it—it may come from an industrial source and contain contaminants.) Keep it in the fridge, or freezer, to prolong shelf life. It can also boost a smoothie; start with a small amount, such as 1/4 teaspoon, gradually working up to more over time (up to 1 tablespoon per drink) if you desire.
## LIVING JUICY: MAINTAINING A HAPPY GREEN HABIT FOR LIFE
THE JUICE GENERATION MANIFESTO
Juicing and blending is for everybody. We believe everybody benefits from an amplification of fresh, uncooked vegetables in their diets, whether it's by a factor of five or fifty, and whatever their diet and lifestyle may be.
Juicing is about more, not less. Enrich your well-being with broad-spectrum nutrition containing a riot of colors and flavors and fun. Juicing is not about denial or stripping anything out of your life.
Simplicity trumps luxury. It does not have to be complicated or lavish to be good for you. What counts is that your juice or blended is made fresh, not bought in packaged, processed versions; that it's made from the best ingredients you can find easily; and that it is balanced in its composition.
Juicing can work your way. There's no need to go extreme or change your whole diet. Learn what type of liquid foods work for you, and ease slowly into your habit. This is concentrated nutrition: A little can go a long way.
Juicing and blending can be a refreshing ritual. Getting your bare hands on piles of fresh and vibrant produce is a ritual that balances the mind, calms the senses, and restores the spirit.
Greens are great health insurance. Don't ditch your regular insurance, but incorporate liquid greens into your diet, and you might not have to claim on it.
A happy green habit that lasts for a lifetime means making juicing and blending work for you. We hope this journey through the three stages of the Green Curve has opened the door to the possibilities of a basket of produce and a pantry of whole foods—and piqued your interest in discovering more from here on out.
Moving forward, use any recipe in this book that you like. Keep a commitment to bring greens and other vibrant colored vegetables into your daily diet, and find the rhythm of juicing or blending that works for you. It may mean making something ultrasimple from Phase 1 with only two or three ingredients; or mixing it up like a master and trying something more complex from Phase 3. Perhaps you'll try adding a new healing ingredient that you sense might help you when you need extra support. And occasionally, you'll try a gentle reset of a liquid-only day (or three). The more you juice and blend, the more you will be able to tune into what your body wants in every moment, and the easier the choices of what to make, and when, will become.
As you continue to purchase produce seasonally and from different vendors, inspiration will probably hit as unexpected vegetables and fruits, along with newly discovered seeds, nuts, and superfoods, fall into your bag. Experiment and enjoy—and remember to share what works!
With your newfound passion for squeezing, crushing, and grinding, you are now an official member of the juice generation. May you always see the wonder in a cucumber, a bunch of spinach, and a handful of berries; may your body always feel the uplifting benefits; and may your curiosity never stop leading you in ever-more-juicy new directions.
### ACKNOWLEDGMENTS
Project Manager
Nazli Kfoury
Creative Director
Marc Balet
Still Life Photography
William Brinson
Lifestyle Photography
John Huba
Design
Tyler Mintz
Cristina Vasquez Obando
Touchstone
Matthew Benjamin
Stacy Creamer
Juice Generation
Isain Carino
Luis Garcia
Joel Hernandez
Maria Montanez
Emily Parr
Jamie Pelino
Simone Shepard
Special Thanks To
Jake Benson
Whitney Benson
Elyse Connolly
Denise Fiallo
Andrew Ginsburg
Lynn Helms
Jeff Kleinman
Barry Mandel
Shauna Robertson
Jose Tamez
Neal Tully
* * *
© JOHN HUBA
ERIC HELMS is the founder of Juice Generation, America's premier juicery. Since 1999, his mission has been to create fresh, energizing raw juices and to always be on the lookout for the next super fruit.
MEET THE AUTHORS, WATCH VIDEOS AND MORE AT
SimonandSchuster.com
authors.simonandschuster.com/Eric-Helms
Facebook.com/TouchstoneBooks
@TouchstoneBooks
We hope you enjoyed reading this Touchstone eBook.
* * *
Join our mailing list and get updates on new releases, deals, bonus content and other great books from Touchstone and Simon & Schuster.
CLICK HERE TO SIGN UP
or visit us online to sign up at
eBookNews.SimonandSchuster.com
Who Should Use Caution When Juicing and Blending:
You should consult with your doctor before starting a cleanse program and we advocate caution for some, including:
• Women who are pregnant or breast-feeding should check with their health provider about juicing. It's wiser to wait until after breast-feeding to indulge in the ultra-detox-promoting ingredients mentioned in Phase 3.
• Anyone with a weakened immune system (the elderly, the very young, and those on chemotherapy treatment) should purchase only the freshest produce, and take extra care when washing. Be sure to discuss juicing with their health provider to ensure safe cleansing.
• People with diabetes or hypoglycemia, and those who know they have candida (yeast overgrowth in the intestines) should learn the right way to juice for their bodies and are strongly advised to get guidance from a health provider on a healthy, low-sugar juicing habit.
• Anyone who is using medication should always consult his or her health provider about possible food contraindications.
The Juice Generation
100 Recipes for Fresh Juices and Superfood Smoothies
Eric Helms with Amely Greeven
Touchstone
A Division of Simon & Schuster, Inc.
1230 Avenue of the Americas
New York, NY 10020
www.SimonandSchuster.com
Copyright © 2014 by Eric Helms, LLC.
Design: Tyler Mintz/Cristina Vásquez Obando
Still Life photography: © William Brinson
Lifestyle photography: © John Huba
Cover Photographs © William Brinson
JUICE GENERATION and Design®, HAIL TO KALE®, SUPA DUPA GREENS®, VITAL SHOT®, and PROTEIN BUZZ® are registered service marks, and JUICE GENERATIONSM, PEANUT BUTTER SPLITSM, PB ACAISM, LEMON LOZENGESM, COCO ACAISM, JUICE FARMACYSM, and COLD WARRIORSM are common law service marks, of Juice Generation, Inc.
All rights reserved, including the right to reproduce this book or portions thereof in any form whatsoever. For information address Touchstone Subsidiary Rights Department, 1230 Avenue of the Americas, New York, NY 10020.
This publication contains the opinions and ideas of its author. It is intended to provide helpful and informative material on the subjects addressed in the publication. It is sold with the understanding that the author and publisher are not engaged in rendering medical, health, or any other kind of personal professional services in the book. The reader should consult his or her medical, health or other competent professional before adopting any of the suggestions in this book or drawing inferences from it.
The author and publisher specifically disclaim all responsibility for any liability, loss or risk, personal or otherwise, which is incurred as a consequence, directly or indirectly, of the use and application of any of the contents of this book.
First Touchstone trade paperback edition January 2014
TOUCHSTONE and colophon are registered trademarks of Simon & Schuster, Inc.
The Simon & Schuster Speakers Bureau can bring authors to your live event. For more information or to book an event contact the Simon & Schuster Speakers Bureau at 1-866-248-3049 or visit our website at www.simonspeakers.com.
ISBN 978-1-4767-4568-8
ISBN 978-1-4767-4570-1 (ebook)
### ABOUT THE AUTHOR
Eric Helms is the founder of Juice Generation, New York City's premier juicery. Since 1999, his mission has been to create a friendly, accessible juice bar where New Yorkers of all lifestyles could experience the energizing effects of fresh, raw juices. He cofounded the national juice and raw food delivery service, Cooler Cleanse, with Salma Hayek in 2009. He resides in New York City. To learn more about Juice Generation, visit juicegeneration.com.
Amely Greeven is a bestselling writer whose topics include preventive health care, mind-body balance, and the search for peace in modern life. She lives in Southern California and Jackson Hole, Wyoming.
## WHEN TO JUICE
| {
"redpajama_set_name": "RedPajamaBook"
} | 2,922 |
Posted: Jan 14, 2015
Laser-induced ripples could enhance solar cell efficiency
(Nanowerk News) A*STAR scientists have produced a uniform nanoscale ripple pattern over a wide area on a silicon surface by scanning a femtosecond laser beam across it. Given that a rippled surface is much less reflective than a smooth surface, this simple innovation could enhance the efficiency of solar cells by boosting their ability to harvest more sunlight ("Femtosecond laser fabrication of large-area periodic surface ripple structure on Si substrate").
Scanning electron micrograph showing a ripple pattern formed on a silicon surface using a femtosecond laser beam. This surface absorbs more light than an unprocessed surface and could enhance solar cell efficiency.
The use of lasers to produce periodic surface structures is currently an area of intense research. Laser processing has the important advantage that it heats only the surface of a material, leaving underlying structures unaffected. However, many laser processing methods are limited: they can process only small areas and shallow ripples.
Now, Xincai Wang and co-workers from A*STAR's Singapore Institute of Manufacturing Technology and Nanyang Technological University have successfully addressed these limitations. They demonstrate the potential of their technique by using it to produce a uniform ripple pattern on a silicon substrate (see image) over a large area of 30 millimeters by 30 millimeters, with an average ripple depth of 300 nanometers — about three times greater than that of other techniques.
"This increase in depth can substantially reduce light reflection and improve the light-trapping ability of the ripple structure," Wang notes. "Hence, if the structure is used in photovoltaic devices, more light will be trapped within the structure, thereby enhancing the device efficiency."
Straightforward and inexpensive, the technique simply involves using a cylindrical lens to widen a femtosecond laser beam to a width of 50 micrometers and then scanning the beam across the surface.
As the energy of the laser's photons exceeds the bandgap of silicon, the photons excite electrons from the valence band to the conduction band. Such electrons would usually relax by transferring their energy to the atomic lattice, thereby heating it. However, the extremely short pulse durations mean that instead they generate an electron wave on the surface. This in turn produces a light wave, which interferes with the incoming laser beam. The silicon is removed in locations where the incoming and outgoing light waves constructively interfere with each other, giving rise to the valleys in the ripple pattern.
The researchers found that on rippling the average reflectance of a silicon surface dropped from 39.7 per cent to 12.5 per cent, which meant light absorption was enhanced by 41 per cent as a result of strong scattering by the ripple structure. This effect could be exploited to manage photon behavior in solar cells and light-emitting diodes.
Source: A*STAR
Subscribe to a free copy of one of our daily
Nanowerk Newsletter Email Digests
with a compilation of all of the day's news.
Inspiration for artificial anti-icing surfaces
Quantum physicists make nanoscopic advance of colossal significance
Researchers decipher atomic-scale imperfections in lithium-ion batteries
An open-source stopwatch to time activities between molecules inside living cells
Physicists solve mystery of two-dimensional quasicrystal formation from metal oxides
Nanotechnology researchers discover long-term memory in 2D nanofluidic channels
Scientists generate and measure the shortest electron pulse to date
Nanofiber-hydrogel loaded with stem cells shows success treating severe complication of Crohn's disease
The last mysteries of atomically thin mica
Recyclable mobile phone batteries a step closer with rust-busting invention
New DNA biosensor could unlock powerful, low-cost clinical diagnostics
Spin transport measured through molecular films now long enough to develop spintronic devices
Researchers create a low-cost sensor that detects heavy metals in sweat
Nanotechnology turns to shark skin and dragonfly wings
Physical effect also valid in the quantum world
Incorporation of water molecules into layered materials impacts ion storage capability
In the core of the cell: New insights into the utilization of nanotechnology-based drugs
Nanoscopic tool assesses alternative COVID-19 prevention
New nanoparticles deliver therapy brain-wide, edit Alzheimer's gene in mice
Improving perovskite solar cell resistance to degradation
Correlated rattling atomic chains reduce thermal conductivity of materials
Electronic nose: Sensing odor molecules on graphene surface layered with self-assembled peptides
Approaching the terahertz regime
Novel fluorescent compound could massively boost the efficiency of device screens
...more nanotechnology news | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,001 |
May | 2007 | Spot.
For BT via Sarah Shuter Productions Bronze Winner IVCA A clever, low-fi little film about BT trying to become number one for customer service. We purposefully steered clear of technology to focus on how being human, warm friendly and efficient could help. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,088 |
using namespace arangodb::aql;
DocumentProducingNode::DocumentProducingNode(Variable const* outVariable)
: _outVariable(outVariable),
_count(false),
_useCache(true),
_maxProjections(kMaxProjections) {
TRI_ASSERT(_outVariable != nullptr);
}
DocumentProducingNode::DocumentProducingNode(ExecutionPlan* plan,
arangodb::velocypack::Slice slice)
: _outVariable(
Variable::varFromVPack(plan->getAst(), slice, "outVariable")),
_projections(arangodb::aql::Projections::fromVelocyPack(slice)),
_filterProjections(arangodb::aql::Projections::fromVelocyPack(
slice, "filterProjections")),
_count(false),
_useCache(true),
_maxProjections(kMaxProjections) {
TRI_ASSERT(_outVariable != nullptr);
VPackSlice p = slice.get(StaticStrings::Filter);
if (!p.isNone()) {
Ast* ast = plan->getAst();
// new AstNode is memory-managed by the Ast
setFilter(std::make_unique<Expression>(ast, ast->createNode(p)));
}
_count = arangodb::basics::VelocyPackHelper::getBooleanValue(slice, "count",
false);
_readOwnWrites = arangodb::basics::VelocyPackHelper::getBooleanValue(
slice, StaticStrings::ReadOwnWrites, false)
? ReadOwnWrites::yes
: ReadOwnWrites::no;
_useCache = arangodb::basics::VelocyPackHelper::getBooleanValue(
slice, StaticStrings::UseCache, _useCache);
p = slice.get(StaticStrings::MaxProjections);
if (!p.isNone()) {
setMaxProjections(p.getNumber<size_t>());
}
}
void DocumentProducingNode::cloneInto(ExecutionPlan* plan,
DocumentProducingNode& c) const {
if (_filter != nullptr) {
c.setFilter(
std::unique_ptr<Expression>(_filter->clone(plan->getAst(), true)));
}
c.copyCountFlag(this);
c.setCanReadOwnWrites(canReadOwnWrites());
c.setMaxProjections(maxProjections());
c.setUseCache(useCache());
}
void DocumentProducingNode::replaceVariables(
std::unordered_map<VariableId, Variable const*> const& replacements) {
if (hasFilter()) {
_filter->replaceVariables(replacements);
}
}
void DocumentProducingNode::toVelocyPack(arangodb::velocypack::Builder& builder,
unsigned flags) const {
builder.add(VPackValue("outVariable"));
_outVariable->toVelocyPack(builder);
_projections.toVelocyPack(builder);
if (_filter != nullptr) {
builder.add(VPackValue(StaticStrings::Filter));
_filter->toVelocyPack(builder, flags);
_filterProjections.toVelocyPack(builder, "filterProjections");
} else {
builder.add("filterProjections", VPackValue(VPackValueType::Array));
builder.close();
}
// "producesResult" is read by AQL explainer. don't remove it!
builder.add("count", VPackValue(doCount()));
if (doCount()) {
TRI_ASSERT(_filter == nullptr);
builder.add(StaticStrings::ProducesResult, VPackValue(false));
} else {
builder.add(
StaticStrings::ProducesResult,
VPackValue(_filter != nullptr ||
dynamic_cast<ExecutionNode const*>(this)->isVarUsedLater(
_outVariable)));
}
builder.add(StaticStrings::ReadOwnWrites,
VPackValue(_readOwnWrites == ReadOwnWrites::yes));
builder.add(StaticStrings::UseCache, VPackValue(useCache()));
builder.add(StaticStrings::MaxProjections, VPackValue(maxProjections()));
}
Variable const* DocumentProducingNode::outVariable() const {
return _outVariable;
}
/// @brief remember the condition to execute for early filtering
void DocumentProducingNode::setFilter(std::unique_ptr<Expression> filter) {
_filter = std::move(filter);
}
arangodb::aql::Projections const& DocumentProducingNode::projections()
const noexcept {
return _projections;
}
arangodb::aql::Projections& DocumentProducingNode::projections() noexcept {
return _projections;
}
arangodb::aql::Projections const& DocumentProducingNode::filterProjections()
const noexcept {
return _filterProjections;
}
void DocumentProducingNode::setProjections(
arangodb::aql::Projections projections) {
_projections = std::move(projections);
}
bool DocumentProducingNode::doCount() const {
return _count && (_filter == nullptr);
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,184 |
You may think that small businesses are not vulnerable to cybercrimes just like big corporations. But in fact, about 43 percent of cyber-attacks target small businesses. Micro companies, in general, are not as secure compared to large-scale businesses because of budget issues and because they are "small." Although these businesses are literally less far-reaching compared to large corporations, the security threats they experience are not small, at all. They easily fall victim to hacking, malware, spyware, ransomware, and security breaches because of their low-priced and dated protection.
Cybersecurity should be one of the top priorities for your small business, but how do you keep your business protected from these cyber threats without spending too much? Here are some cybersecurity tips that are simple yet effective for small business owners. These can help reduce the risks of ransomware, malware, and hacking.
If you use passwords that are very easy to figure out such as 1234, 0000, or ABCD, it would be like a walk in the park for hackers to acquire your system's password. Strong passwords are comprised of alphanumeric and special characters that are case-sensitive. The more random the combination, the better it is. If your passwords are secure, it will be difficult for someone to figure it out and hack it. Inform your employees as well to create secure passwords.
Someone who will try to access your system will try all sorts of different passwords randomly until they hit the jackpot and open your account. This can mean that your account is still not safe even with a 6-digit pin that has a million unique possible number combinations. You have to be aware that there are password-cracking software nowadays that can guess your code in a few minutes. So to avoid falling victim to these hackers, you should limit the number of attempts for your authentication process. In most cases, the number of attempts is limited to 3, so after the third attempt, you can no longer try to enter the password.
A password manager tool that creates and stores the password can be helpful for you. But you have to think carefully when choosing one. Remember that this tool stores all passwords in its database; so for a hacker, all he needs is to crack one code. That is why you need to think of its advantages and disadvantages before you use one for your business.
If you are not yet aware, there are hackers that can record your keystrokes using keylogging software. This is common if you're using shared networks. What you can do to avoid this is by using an on-screen or virtual keyboard. The keylogging software will not be able to track keys that you enter on the on-screen keyboard because you're only operating it using mouse clicks. This is commonly used in financial establishments.
Data backups are important. But you have to be careful of any negligence or mishandling of these backups because this can make your data vulnerable to theft. Example, if you choose to keep your data in the cloud, you have to encrypt and keep your documents protected with a password before storing them on the cloud or a remote server, so that no one can access your data easily.
Although you might think that security breach is not so common for small businesses, it is good that you educate your employees about cybersecurity. We do not want to wait for a security breach to happen before we train your employees about it, right? Here are some things you need to remember when teaching your employees about cybersecurity.
Keeping the customer's credit card information with the customer's permission can make transactions in the future more convenient. On the other hand, this can put your customer's confidential information at risk. While it can be a little more convenient to store the CVV number, it would not bother the customer at all to enter the CVV during checkout. This is for their safety, as well.
Never let any outsider or unauthorized person use your system and other devices. If there is a need for someone to use or access it, in the case of a technician from another firm, let them use a general computer or make sure to have someone supervise them during their tasks. Lock or shut down your computer after leaving them and make sure your employees do the same, as well. Also, make sure to monitor your employees' personal devices.
9. Update your security software always.
Make sure your security software is up-to-date. Do not ignore the prompts on your screen that remind you to upgrade and update your software. This will make sure that your computer is protected from malware, ransomware, and hacking.
Software manufacturers provide software updates to address security risks for their products that can be exposed to hackers. These updates usually contain vulnerability fixes and enhancements. What is good about these updates is that they are added onto the existing installation. Make sure you choose a quality and trusted software to protect your system.
Make sure your Wi-Fi network is hidden, or if not hidden, is secured with a password, to avoid any unauthorized access. You can hide your SSID or Wi-Fi name and encrypt and set a password for your access point.
There are simple ways to ensure that you don't fall victim to hackers. All you need to do is keep these tips in mind, so you can avoid any security risks that can harm your business. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,872 |
\section{INTRODUCTION}
\label{sec:introduction}
Most surveys of the cosmic large-scale structure (LSS) rely on galaxies as tracers of the dark matter distribution.
In order to extract the cosmological information from such surveys, it is crucial to understand the difference between the spatial statistics of the detectable galaxies and the underlying density field. At the largest scales, this difference takes the form of a scaling factor, known as linear galaxy bias $b_g$ \citep{1984ApJ...284L...9K}, between the matter and galaxy power spectrum. Prior knowledge of this bias is essential in designing cosmological surveys.
Moreover, the galaxy bias has an important role in the redshift space distortions (RSD) and multi-tracer analyses as a nuisance variable in the former case \citep[e.g.][]{2015clerkin, 2018li} and an integral part of target selection in the latter \citep[e.g.][]{2009mcdonald, 2016raul}. Predicting the galaxy bias from simulations can be used to place priors on galaxy bias in RSD measurements, and compared to lensing and LSS measurements to improve our understanding of galaxy physics. Knowing the galaxy bias can also help to break the classic degeneracy between the linear bias and cosmological parameters such as $\sigma_8$ (the linear rms of the dark matter density perturbations on scales of 8 $h^{-1}$Mpc) and the linear
growth rate $f$ present in 2-point statistics (e.g. \citealt{Ali2018} and references therein); hence priors on the bias might help better determine these parameters.
It is possible to measure the galaxy bias by computing the ratio of the two point correlation function and three point correlation function \citep[see][and references therein]{2002MNRAS.335..432V,2005MNRAS.364..620G} or by exploiting phase-space correlations \citep{Ali2018}. The bias can further be constrained by combining galaxy redshift surveys with gravitational lensing data \citep[e.g.][]{simon2007gabods,jullo2012cosmos}. Existing bias measurements correspond to specific survey selection criteria, such as selecting the galaxies seen in the near infrared (IR) band \citep{2010MNRAS.405.1006O}, the H$\alpha$ emission line \citep{amendola2017constraints}, or 21 cm emission from neutral hydrogen (H{\sc\,i}\xspace) \citep{2017MNRAS.471.1788C}. However, these bias measurements are often uncertain and their extrapolation to different surveys, i.e.\xspace different wavelengths and sensitivities, is challenged by the complex radiative physics of galaxies. For instance, ongoing and upcoming LSS surveys (BOSS\footnote{\url{https://www.sdss3.org/surveys/boss.php}}, eBOSS\footnote{\url{https://www.sdss.org/surveys/eboss}}, DESI\footnote{\url{https://www.desi.lbl.gov}}, LSST\footnote{\url{https://www.lsst.org}}, 4MOST\footnote{\url{https://www.4most.eu/cms}}, EUCLID\footnote{\url{https://www.euclid-ec.org}} for which the references are shown in Section~\ref{sec:results}) are covering a wide range of wavelengths and many of them also use specific emission lines to probe the cosmic LSS. Predictive bias models would help calibrating the analysis of the expected data from these surveys. In addition, it might also be interesting to explore the galaxy bias dependence on some physical properties, such as star formation rate or stellar age, in order to better understand the physical origin of specific bias values. Providing a consensus of the linear bias for various broadband wavelengths, emission lines and physical properties, is therefore a pressing goal.
On the theoretical side, there are two classes of approaches to model the clustering and bias of galaxies \citep{2013PASA...30...30B}. The first class consists of populating simulated or analytically evolved dark matter halos with galaxies drawn from observed luminosity functions, for instance using the so-called halo occupation distribution (HOD) \citep[e.g.][]{berlind2002halo,zheng2005theoretical,wechsler2018connection} method or subhalo abundance matching (SHAM) \citep[e.g.][]{vale2004linking,shankar2006new}. The second class uses hydrodynamics simulations \citep[e.g.][]{schaye2014eagle,vogelsberger2014properties} and semi-analytic models \citep[SAMs, e.g.][]{2016MNRAS.462.3854L, henriques2015galaxy, lagos2018shark, croton2016semi, somerville2015star, xie2017h2} to directly model the bayonic physics involved in galaxy formation. A limitation of the first approach compared to the second is that it is descriptive rather than predictive. Gas dynamics simulations are currently limited to relatively small volumes with large shot noise on linear bias \citep{2007MNRAS.374.1479G}. To address clustering on scales of hundreds of Mpc, semi-analytics models are therefore a sensible choice. The results can in return serve as useful reference points for HOD/SHAM analyses \citep[e.g.][]{2016guo, 2016MNRAS.460.3100C}, as well as for comparisons with hydro simulations such as EAGLE \citep{2017crain} and IllustrisTNG \citep{2018springel}, which would aid in building a better understanding of the broad features of galaxy evolution.
In this paper, we use the semi-analytic model \textsc{GALFORM} \citep{cole2000hierarchical}, specifically an updated variant of \cite{2018MNRAS.474.4024G} to model the linear galaxy bias in the standard $\mathrm{\Lambda CDM}$ cosmology with Planck (2015) parameters \citep{ade2016planck}, for various IR/optical/UV bands, emission lines and intrinsic galaxy properties.
This paper is organised as follows. In Section~\ref{sec:Methods}, we describe our dark matter $N$-body simulation with a semi-analytic galaxy formation model, the techniques used for measuring the large-scale biases and a heuristic 5-parameter model for fitting. In Section~\ref{sec:results}, we show the bias dependence on galaxy properties, emission lines and continuum bands, following up with the large-scale galaxy bias as a function of wavelength. In Section~\ref{sec:discussions}, we discuss the comparison of our model with existing surveys and forecasts, as well as the limitations of this work. In Section~\ref{sec:conclusions}, we conclude with a short synopsis of the paper.
\section{SIMULATIONS AND METHODS}
\label{sec:Methods}
\subsection{Simulations and galaxy formation model}
\label{sec:Simulations}
The \textsc{SURFS} suite consists of N-body simulations of a periodic volume of side lengths from 40 $h^{-1}$Mpc to 900 $h^{-1}$Mpc assuming a Planck (2015) cosmology, where $h$ is the dimensionless Hubble parameter. The simulation used in this work, L210N1536, has a side length of 210 $h^{-1}$Mpc and number of dark matter particles of $1536^3$. This choice of parameters allows us to resolve the host halos of galaxies with stellar masses of $10^8 h^{-1}\rm M_\odot$ at z = 0, with the nominal requirement that the host dark matter halos of such galaxies are resolved with 100 particles, necessary to get accountable halo masses, positions and velocities. This simulation has been run with a memory lean version of the \textsc{GADGET2} code on the Magnus supercomputer at the Pawsey supercomputing centre. For a detailed description of the simulations refer to \cite{2018MNRAS.475.5338E}, and to \cite{poulton2018observing} for a description and performance demonstration of the merger trees used here.
The halo and subhalo catalogs are constructed by \textsc{Velociraptor} \citep{elahi2011peaks}. This code first identifies halos using a 3D Friends-of-Friends(FOF) algorithm in configuration space and then identifies subhalos using a 6D phase-space FOF algorithm on particles that differ dynamically from the dark matter background. We run \textsc{Dhalos} in the SURFS halo catalogs to adapt \textsc{VELOCIraptor} outputs to \textsc{GALFORM} inputs. \textsc{Dhalo} is a tool developed to produce and clean merger trees, which form the basis of \textsc{GALFORM} \citep[see][]{2014MNRAS.440.2115J}. We compare our halo mass function with previous works by using the virial mass defined as $M_\Delta = 4\pi R_\Delta^3 \Delta \rho_{\rm crit}/3$, $\Delta = 200$, where $\rho_{\rm crit}$ is the critical density of the universe and $R_\Delta$ is the radius that encloses this mass. In Fig.~\ref{fig:hmf}, we present the evolving halo mass function compared with \cite{sheth2001ellipsoidal} (hereafter SMT01) and \cite{2010ApJ...724..878T} (hereafter T10) models in the upper panel and the residuals relative to SMT01 in the lower panel. As shown, we find good agreement with T10 model, with an average value of uncertainties less than $10\%$ above the halo mass limit (2.2$\times 10^{10} h^{-1} \rm M_\odot$). The deviation from the SMT01 model is due to the difference of definition of halo mass as explained in \cite{tinker2008toward} and T10.
Galaxy formation is approximated as a two-stage process: structure forms by hierarchical clustering in the dark matter and baryons then fall into the gravitational potential wells to form galaxies by gas cooling, star formation, feedback and stellar evolution \citep{cole2000hierarchical} %
The \textsc{GALFORM} model explicitly accounts for: 1) the shock-heating and radiative cooling of gas inside dark matter halos that drive the formation of gaseous galactic disks; 2) star formation in galaxy disks and in bulges (i.e. starbursts); 3) the growth of super massive black holes and feedback from supernovae, active galactic nucleus (AGN) as well as photo-ionization of the intergalactic medium (IGM); 4) galaxy mergers and bar instabilities which can drive bursts of star formation and lead to the formation of spheroids; 5) calculation of the sizes of disks and spheroids; 6) chemical enrichment of stars and gas; 7) calculation of galaxy stellar luminosities from the predicted star formation and chemical enrichment histories of a stellar population synthesis model; 8) nebular emission line luminosities and equivalent widths; 9) dust attenuation. We use the version of \textsc{GALFORM} based on \citet{2018MNRAS.474.4024G}, hereafter GP18, to investigate the large-scale galaxy biases. This model assumes a single initial mass function (IMF) building upon the previous versions \citep{gonzalez2014sensitive}, which is the major difference from another widely used \textsc{GALFORM} version \citep[][hereafter L16]{2016MNRAS.462.3854L}. The GP18 semi-analytical model has incorporated the merger scheme used in \cite{simha2017modelling} and the gradual stripping of hot gas when satellite galaxies are merging into central galaxies \citep{lagos2014galaxies}.
We specified this model with a set of free parameters which were chosen to provide a reasonable match to the K-band luminosity function from z = 2 to z = 0 and the $b_j$ luminosity function at z = 0. We adopt the photoionisation model (Eq. 5) of \cite{kim2015h} with reionisation parameters of a circular velocity cut-off $v_{\rm cut} = 50$ km/s at a redshift of reionization $z_{\rm cut} = 10$ and the fitting parameter $\alpha_v =-0.82$ in the notation of \citet{2014MNRAS.440.1662S}. We also take the star formation efficiency parameter of the molecular gas $\nu_{\rm sf} = 0.8 Gyr^{-1}$ (Eq. 7 in L16) and the ratio of cooling/free-fall time $\alpha_{\rm cool} = 0.7$ (Eq. 12 in L16) which is an adjustable AGN feedback parameter (more galaxies to be affected by AGN feedback with larger values). The relevant figures used for the adjustment of parameters are shown in Appendix~\ref{appendixobs} and the undiscussed parameters are the same as used in \citet{2018MNRAS.474.4024G}.
The model divides the baryons into five different components: hot gas for cooling in halos, a reservoir of gas ejected by feedback processes, cold gas, stars and central black holes in galaxies.
We assumed that the galaxies have separate disk and spheroid components, which can both contain stars and cold gas. We split the cold gas into atomic hydrogen and molecular hydrogen \citep{lagos2011cosmic}; this distinction is explicitly made throughout the model at every time step. The accreted gas from the halo is added to the disk. The subsequent galaxy mergers and disk instabilities can transfer the gas into a starburst component in the spheroid. Thus we assume two separate modes of star formation: the quiescent mode (in the disk) and the starburst mode (in the spheroid). We calculate the star formation rate in the disk from the molecular gas using the empirical relation in \cite{blitz2006role} , which is based on observations of nearby star-forming disk galaxies as described in \cite{lagos2011impact}. For star formation in bursts, we assume all of the cold gas is molecular. Here we compute the SFR bias including both the quiescent and starburst modes. We also calculate the stellar mass bias by including all the stars in the galaxy.
Broad-band luminosities and absolute magnitudes are calculated from the stellar SEDs of galaxies using a stellar population synthesis model (L16) based on stellar evolution models. This model also includes a simple model for emission lines in star-forming galaxies that uses the number of ionizing photons and the metallicity of the cold, star forming gas to predict emission line luminosities based on the properties of a typical H{\sc\,ii}\xspace region \citep{stasinska1990grid} (see GP18 for an expanded discussion of the modelling of emission lines).
To simulate the effects of dust extinction, \textsc{GALFORM} applies a physical model of absorption and emission of radiation by dust. The dust is assumed to be present in two components: diffuse dust (75\%) and molecular clouds (25\%) based on observations of nearby galaxies \citep{granato2000infrared}. This model includes a self-consistent model for the reprocessing of starlight by dust, in which the UV, optical and near-IR light are absorbed by dusts and reradiated at IR and sub-mm wavelengths. The dust absorption is based on radiative transfer and the temperature of the dust emission can be solved for by energy balance (see L16 for details).
Redshifted magnitudes are needed for predicting the linear bias of future surveys. With the intrinsic properties of galaxies and their cosmological redshifts, we are able to evaluate observer-frame absolute magnitudes by
\begin{equation}
M = -2.5\log\left[\frac{\int L_v(v_e)R(v_o)dv_e}{L_{v_o}\int R(v_o)dv_e}\right],
\label{eq:obsmag}
\end{equation}
where $L_v(v_e)$ is the emitted luminosity per unit frequency and $L_{v_o}$ is the reference luminosity. The emitted (rest-frame) frequency $v_e$ is related to the observed (observer-frame) frequency $v_o$ by $v_e = v_o(1+z)$ and $R(v_o)$ is the filter response of a specified photometric band on the observer frame \citep[Eq. 13 in][]{merson2012lightcone}. Note that we use the symbol $M$ without subscripts as the absolute magnitude to differentiate it from the mass symbol with subscripts. The effect of dust attenuation is included throughout this paper.
For the galaxy samples chosen by continuum filters, we use the observer frame quantities to investigate the bias dependence. The UV/optical/IR filters corresponds to those used in the GALEX/SDSS/UKIRT surveys, except that the Y-band filter is from the UKIDSS survey.
\begin{figure}
\includegraphics[width=\columnwidth]{figures/Vhalo_2_f00}
\caption{Halo mass function at four redshifts.
%
The solid lines are the measurements from the L210N1536 SURFS simulation.
%
The dotted and dashed lines show the SMT10 and T10 prediction respectively, calculated using \textsc{HMFcalc} \citep{2013A&C.....3...23M}.
The gray dashed vertical line shows the halo mass limit $2.2\times 10^{10} h^{-1}\rm M_\odot$.
%
Note that we use the same color caption for redshifts
in all bias plots as this one unless captioned differently.
%
The lower panel shows the residuals relative to SMT01 model.
}
\label{fig:hmf}
\end{figure}
\subsection{Large-scale bias}
\label{sec:Large scale bias}
Based on the current galaxy formation models, galaxies are formed in dark halos, therefore the understanding of halo bias is an essential component of any theory of galaxy bias \citep{smith2007scale}.
\subsubsection{Halo bias}
The halo bias is determined by the relative abundance of
halos in different large-scale density environments. There are two well-known models to describe the halo bias, the peak bias \citep{bardeen1986statistics} and peak-background split model \citep{1984ApJ...284L...9K,cole1989biased,1996MNRAS.282..347M}. The peak bias model is built upon the simplified assumption that collapsed structures form from peaks in the Gaussian initial density field. Given a uniform density background at the early age of the universe, the peak bias model works well till the large-scale structures emerge and act like a local modification of the background density. The more general peak-background split model decomposes the density field into a long-wavelength and short-wavelength part. These models and the numerical calibration in T10 have given us valuable insights into the physics of the halo bias. The most obvious result is the strong dependence of large-scale halo bias on halo mass and redshift. Of course, there are other halo variables that can also produce strong trends even at fixed halo mass, such as the local tidal environment \citep[e.g.][]{2018MNRAS.476.3631P}.
We review some basic theories for the halo bias. The two central quantities are the dark matter overdensity, $\delta$, and halo overdensity, $\delta_h$,
\begin{equation}
\delta=\frac{\rho-\bar{\rho}}{\bar{\rho}},\delta_h=\frac{n_h-\bar{n}_h}{\bar{n}_h},
\label{eq:delta}
\end{equation}
where $\rho$ and $\bar{\rho}$ are the dark matter density and the mean density respectively, and $n_h$ and $\bar{n}_h$ are the halo number density and its mean number density respectively.
The halo bias is essentially a relation between $\delta$ and $\delta_h$, which can be Taylor expanded to \citep{fry1993biasing,mo1997high,pollack2012modelling}
\begin{equation}
\delta_h=b_0+b_1\delta+\frac{b_2}{2}\delta^2+...,
\label{eq:bias}
\end{equation}
where the halo bias is assumed to be local and deterministic. On large scales, it is commonly truncated to first order and the relation simply becomes linear, where $b_0 = 0$ owing to the fact that $\langle\delta_h\rangle \equiv \langle\delta\rangle \equiv 0$ by definition \citep{fry1993biasing}. These assumptions leave $b_1$ as the only relevant parameter and it is commonly regarded as the large-scale halo bias. We note that the halo bias should in principle also contain terms describing non-locality and stochasticity which become important at quasi-linear scales \citep[see Eq. 2.135 in][]{2016arXiv161109787D}, but we are focusing only on measuring the linear bias here.
By looking at equation \eqref{eq:bias} in Fourier space, we can also define a practical measurement of halo bias via the relation between the halo and matter power spectrum
\begin{equation}
b_h(k)=\sqrt{\frac{P_{h}(k)}{P_{m}(k)}},
\label{eq:bh}
\end{equation}
where $P_{m}(k)=\langle|\delta(\bm{k})|^2\rangle$ is the dark matter power spectrum, $\delta(\bm{k})$ is the Fourier representation of dark matter overdensities, and $P_{h}(k)$ accordingly is the halo power spectrum. On large scales, it is easy to see that equation \eqref{eq:bh} can be derived from equation \eqref{eq:bias}, which means $b_h(k) = b_1$ when the wavenumber $k$ (i.e. the magnitude of the wave vector $\bm{k}$) is small in Fourier space. Hereafter we denote the large-scale halo bias as $b_h$ and specify the measurements in Section~\ref{sec:measurement}.
\subsubsection{Galaxy bias}
Galaxies do not trace the mass in the same way as halos do. The difference is that galaxy formation proceeds with an efficiency which depends on halo properties in a non-linear fashion. In the lowest mass halos, feedback from supernovae and UV background ionization prevent efficient star formation while in the high mass halos gas is unable to cool efficiently \citep{2000MNRAS.311..793B} as is heated by AGN \citep{bower2006breaking}. A comprehensive overview of galaxy bias based on perturbation theory can be seen in \cite{2016arXiv161109787D}. Following the definition of halo bias, the galaxy bias can be written as
\begin{equation}
b_g(k)=\sqrt{\frac{P_{g}(k)}{P_{m}(k)}},
\label{eq:bg}
\end{equation}
where $P_{g}(k)$ is the galaxy power spectrum.
Statistically speaking, the galaxy bias can also be expressed via the halo model \citep[see][for a review]{cooray2002halo}. According to this model, the distribution of galaxies depends on how they populated halos. Hence, we can split the galaxy power spectrum into two components, the 1- and 2-halo terms: $P_{g}(k) = P_{g}^{1h}(k) + P_{g}^{2h}(k)$. The 1-halo term $P_{g}^{1h}(k)$ is determined by the density profiles of galaxy-pairs in shared halos and the halo mass function. The 2-halo term $P_{g}^{2h}(k)$ contains the contribution of the galaxies in different halos.
\begin{figure*}
\includegraphics[width=\textwidth]{figures/mag_SDSS-r_o_tot_ext_h08}
\caption{Two-dimensional distribution function of galaxies as a function of r-band luminosity and halo mass.
%
Results are shown at $z = 0, 1, 2, 3$ from left panel to right panel. The color map gives the log of the galaxy number.
}
\label{fig:hvm}
\end{figure*}
On large scales, only the 2-halo term is important and it can be linked with the halo power spectrum if one knows the galaxy distribution at given mass halos. In this case, we can also rewrite the equation~\eqref{eq:bg} by weighting the large-scale halo bias with the number of galaxies contained in the given mass halos \citep[see][for the detailed derivation]{mo2010galaxy}
\begin{equation}
b_g(x)=\frac{\int b_h(M_h)\phi(x|M_h)n(M_h)dM_h}{\int \phi(x|M_h)n(M_h)dM_h},
\label{eq:dif}
\end{equation}
where $n(M_h)$ is the halo mass function and $\phi(x|M_h)$ denotes the conditional galaxy distribution function, such as conditional galaxy mass, star formation rate and luminosity function. The $\phi(x|M_h)$ describes the distribution of galaxies in halos of a given halo of mass $M_h$, which can be computed by the conditional PDF of host halo mass against galaxy property x from Fig.~\ref{fig:hvm}. The looming bimodal distribution from z = 3 to z = 0 is contributed by the central galaxies and satellites due to increased merger events. Here $b_g(x)$ is the large-scale differential galaxy bias, which satisfies the observational selection criteria of galaxy property $x$. Different properties $x$ will be discussed in Section \ref{sec:model}. We note that this equation emphasizes that the galaxy bias only depends on halo mass (i.e. zero galaxy assembly bias), which in practice may not be the case as indicated by many recent studies \citep[e.g.][]{2014MNRAS.443.3044Z, 2019MNRAS.484.1133C}.
Following the same spirit, we note $b_g(\geq x)$ to be the large-scale cumulative galaxy bias above a limited value of $x$, which can be expressed as follows
\begin{equation}
b_g(\geq x)=\frac{\int_{x'=x}^{+\infty} b_g(x')\phi(x')dx'}{\int_{x'=x}^{+\infty}\phi(x')dx'},
\label{eq:cum}
\end{equation}
where $\phi(x')$ is the distribution function for a galaxy property, such as a luminosity.
\subsection{Measurements of bias and uncertainty}
\label{sec:measurement}
To measure the bias from equation \eqref{eq:bh} and \eqref{eq:bg}, one needs to calculate the power spectrum from the halo and galaxy catalogs. We first binned the halos and galaxies into a $256^3$ density mesh by using a top-hat smoothing and computed the Fourier transform to evaluate the power spectrum. All the power spectra are shot-noise subtracted and we divide each Fourier mode by a sinc-function to correct for the top-hat gridding effect. Finally we average the orientation-dependent power spectrum over a spherical shell in k-space in order to take out the orientation dependence and get $P_h(k)$ and $P_g(k)$.
Since we have only one simulation to produce the galaxy samples, we rely on the theory of Gaussian covariance matrices of the power spectrum to measure the uncertainty on the bias. The commonly used expression for the power spectrum variance was derived by \cite{1994ApJ...426...23F,1997PhRvL..79.3806T}:
\begin{equation}
\sigma_{P_g(k)}=\sqrt{\frac{2}{n_{\rm modes}}}\left[P_g(k)+\frac{1}{\bar{n}_g}\right],
\label{eq:error_ps}
\end{equation}
where $\bar{n}_g$ refers to the number density of galaxies which satisfy the given selection criteria and $n_{\rm modes}=V4\pi{k^2}\delta{k}/(2\pi)^3$ is the number of Fourier modes in the spherical shell of width $\delta{k}$ when the volume $V \gg (2\pi/k)^3$. Finally, we provide the uncertainties of large-scale galaxy bias through error propagation as follows
\begin{equation}
\sigma_{b_g(k)} \approx \sqrt[]{\frac{1}{n_{\rm modes}\bar{n}_g P_{m}(k)}}.
\label{eq:berror}
\end{equation}
A derivation and verification with simulations can be found in Appendix~\ref{appendixunc}. We also employ the commonly-used "jackknife" method to estimate the error on the bias in comparison with this derived form as discussed later.
Fig. \ref{fig:halobias} shows the halo bias as a function of wavenumber $k$ for halos of varying mass at $z = 0.33$. The solid and dotted lines are measured from the L210N1536 and L900N2048 SURFS simulations respectively using the equation \eqref{eq:bh} on the left panel. As the linear bias is independent of scale, one can see that the halo bias generally stays constant for $2\times2\pi/L_{\rm box} < k < 0.18 h^{-1}$Mpc and even applicable to larger $k$ in the low mass bins for the L210 simulation, thus we can directly measure the large-scale halo bias by averaging $b_h(k)$ over those modes.
At higher redshifts, these limits on $k$ are more conservative since the nonlinear scale keeps extending towards the smaller $k$ as the universe evolves. Comparing the halo bias of L210 simulation with that of L900 simulation, we are confident that the L210 simulation can be used to study the large-scale bias for a variety of halo mass ranges, except for the most massive samples due to the low number statistics. The shaded error bars for the L210 simulation are estimated by the "jackknife" method. To do so, we calculate the power spectrum for eight subsamples with removing one octant of the box in each subsample, then estimate the errors on the $b_h(k)$ as indicated by the shaded area. The equation~\eqref{eq:berror} are generally consistent with this jackknife method for the less massive halos ($<10^{13} h^{-1} \rm M_\odot$), but tends to overestimate the uncertainties for the massive samples by a factor of two in the considered $k$ scales, which makes the equation~\eqref{eq:berror} more conservative. Therefore we will carry on with the derived form and exclude the points with relative errors larger than 20\% in all the bias plots.
\begin{figure*}
\centering
\begin{subfigure}{\columnwidth}
\centering
\includegraphics[width=\columnwidth]{figures/Vhalo_2_k}
\label{fig:sub1}
\end{subfigure}%
\begin{subfigure}{\columnwidth}
\centering
\includegraphics[width=\columnwidth]{figures/Vhalo_2_xk}
\label{fig:sub2}
\end{subfigure}
\caption{Large-scale halo bias as a function of wavenumber $k$ at z = 0.33.
%
Left: the solid and dotted lines are the measurements from the L210N1536 and L900N2048 SURFS simulations, respectively, using equation \eqref{eq:bh}. The narrower solid errors are estimated by equation \eqref{eq:berror} while the wider shaded errors are calculated by the "jackknife" method.
%
Right: the dashed lines are measured by the cross-power spectrum between halo and dark matter over the dark matter power spectrum from the L210N1536 simulation while the solid lines are the same as on the left panel.
%
The gray dashed vertical lines indicate the lower and upper limits of $2\times2\pi/L_{\rm box}$ and $0.18 h^{-1}$Mpc in $k$ space, where the $L_{\rm box} = 210 h^{-1}$Mpc.
%
Only five mass bins are shown for clarity.
%
The mass bin width is 0.4 in the logarithmic space.}
\label{fig:halobias}
\label{fig:gr}
\end{figure*}
We also check the halo bias as defined by the cross-power spectrum between halo and dark matter over the dark matter power spectrum indicated by the dashed lines on the right panel of Fig. \ref{fig:halobias}. As seen, this measure, whilst immune to shot-noise effects, could be contaminated with higher order bias on larger $k$ scales than the definition of the equation \eqref{eq:bh} for the low mass halos and this is in line with the findings in \citet{smith2007} and \citet{vlah2013}. Considering that the effects of shot-noise are outside the considered $k$ scales (i.e. between the dashed vertical lines) , we therefore chose to use equations \eqref{eq:bh} and \eqref{eq:bg} for the following analyses on the large-scale biases.
We then average the $b_g(k)$ over small $k$ scales weighted by number of modes, which gives the large-scale galaxy bias as
\begin{equation}
b_g = \frac{\sum_k w_k b_g(k)}{\sum_k w_k}.
\label{eq:bga}
\end{equation}
The variance of this weighted average is given by
\begin{equation}
\sigma_{b_g}^2 = \frac{\sum_k w_k (b_g(k) - b_g)^2}{\sum_k w_k},
\label{eq:sbga}
\end{equation}
where $w_k = 1/\sigma_{b_g(k)}^2 $ are the weights given to each measurement.
The galaxy bias depends on the selection of galaxies. Using $x$ as a general placeholder for a scalar galaxy property (e.g. a luminosity, an emission line strength or the stellar mass), the bias $b_g(x)$ and the cumulative bias $b_g(\geq x)$ can only be determined down to a certain value $x_{\rm min}$, below which the mass-resolution of the simulation is insufficient. To determine $x_{\rm min}$ for each property, we first apply a stellar mass cut of $10^8 h^{-1}\rm M_\odot$ to all galaxies. Above this limit, the the model is roughly complete in stellar mass. We then plot the space density function of $x$ (e.g. the luminosity function if $x$ is a luminosity) and determine the point where this function peaks. Finally, we compare the peak positions at the four redshifts (z = 0, 1, 2, 3) and set $x_{\rm min}$ equal to the largest peak value. For instance, Fig.~\ref{fig:glf} shows the galaxy r-band luminosity function compared with observations. The vertical dashed lines indicate the resolution limit for each redshift. The red dashed line represents the magnitude of -17.2, which is the brightest value compared with that of other redshifts, therefore we take it as the lower limit of r-band bias plot. We apply this same principle to all other galaxy bias plots as shown in Section \ref{sec:results}. Note that we use the stellar mass cut only for determining the lower limits of biases, not for excluding the samples at given selection criteria.
\begin{figure}
\includegraphics[width=\columnwidth]{figures/mag_SDSS-r_o_tot_ext_f08}
\caption{The r-band galaxy luminosity function at redshifts z = 0 (black), 1 (blue), 2 (green), 3 (red).
%
The dashed vertical lines show the peaks of these functions, which were used to define the resolution limit of the model.
%
The black dots and open circles indicate the r-band luminosity function measured by \citet{driver2012galaxy} and \citet{blanton2005properties} at z = 0.
}
\label{fig:glf}
\end{figure}
We have thus introduced two methods to compute the large-scale galaxy bias, either through averaging equation \eqref{eq:bg}, i.e. equation \eqref{eq:bga} or through the halo model, i.e. equation \eqref{eq:dif} and \eqref{eq:cum}. For clarification, we refer these two methods as "Measurement" and "Halo model" in the upcoming bias plots.
\subsection{Heuristic 5-parameter model}
\label{sec:model}
\begin{figure}
\includegraphics[width=\columnwidth]{figures/Vhalo_2_db00}
\includegraphics[width=\columnwidth]{figures/Vhalo_2_cb00}
\caption{Large-scale halo bias as a function of halo mass at four redshifts.
%
The upper and lower panels show the differential and
cumulative biases respectively.
%
The filled symbols are directly measured by averaging equation~\eqref{eq:bg} on large scales. Only measurements with a relative uncertainty below than 20\% are shown.
%
The error bars are estimated by linearly propagating the shot noise uncertainties of the power spectrum.
%
Solid lines show the best fits of equation~\eqref{eq:fit} and
%
dashed lines show the T10 results where we utilise the equation~\eqref{eq:cum} to compute the T10 prediction for the cumulative halo bias in the lower panel.
%
The color-coded regions are the 68\% credible intervals in the halo bias estimated from the posterior samples.
%
Note that we use the 3D defined halo mass here to compare with the T10.
}
\label{fig:bh}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{figures/Vhalo_2_db00_corner}
\caption{The posterior distributions for the 5 parameters of equation~\eqref{eq:fit} for the large-scale differential halo bias. The contour levels in the 2-D marginalized posteriors are 1 and 2$\sigma$ while the dashed lines in the 1-D marginalized posteriors span the 2$\sigma$(95\%) credible interval. }
\label{fig:bh_post}
\end{figure}
Previous bias models in the literature usually concentrate on a specific galaxy property, such as the galaxy clustering dependence on galaxy color in a single-band filter \citep{zehavi2011galaxy}, or the redshift dependence \citep{2015MNRAS.448.1389C}. The T10 model uses a universal fitting function which accurately accounts for the mass, redshift and cosmology dependence of halo bias, but cannot easily be linked to observable galaxy properties.
To improve on these models, we now fit different biases using the 5-parameter model.
\begin{equation}
b_g(x,z)=a + b(1+z)^e\left(1 + \exp{[(x-c)d]}\right),
\label{eq:fit}
\end{equation}
where x is a galaxy (or halo) property, z is the redshift and $a$, $b$, $c$, $d$, and $e$ are the five parameters to be fitted. The combination of $a$, $b$, and $e$ acts as a normalization, whereas $c$ and $d$ represent the upturn point and slope on the high ends capturing the major differences of galaxy biases. We use this same formula for fitting the differential bias and the cumulative bias. If $x$ denote a magnitude (defined as negative log of the luminosity), we replace $x-c$ in equation~\eqref{eq:fit} by $c-x$ to cope with the fact the smaller magnitudes correspond to brighter objects.
Assuming that the distribution of errors follows a Gaussian, we can write the likelihood function as:
\begin{equation}
\ln P(b_g(x,z)| a, b, c, d, e) = -\frac{1}{2}\sum \bigg[ \frac{(b_g(x,z)-b_g)^2}{\sigma_{b_g}^2} +\ln(2\pi\sigma_{b_g}^2)\bigg],
\label{eq:maxl}
\end{equation}
where $b_g$ is the large-scale bias measured from the equation~\eqref{eq:bga} and $\sigma_{b_g}$ is the corresponding error measured from equation~\eqref{eq:sbga}. We use {\sc Multinest}\footnote{\url{https://github.com/JohannesBuchner/PyMultiNest}} to fit our model to the "Measurement" and accept the median of posterior samples as the best estimate of each parameter. Multinest is an efficient and robust Bayesian inference tool based on a nested sampling technique \citep{skilling2004nested}, which allows model fitting and produces the posterior samples.
We test our measurements and fitting formula against the well-calibrated large-scale halo bias model by T10. Fig.~\ref{fig:bh} shows the large-scale halo bias as a function of halo mass at four redshifts. Overall, our measurements for the differential halo bias show great agreement with the T10 model. The deviation on the high mass end at high redshifts is due to the low number statistics in the simulation box with a side length of 210 $h^{-1}$Mpc. It is clear that our five-parameter fitting formula can do as fine a job as the six-parameter model does in T10, except for the high mass end at redshift 0. The notable difference between our measurement and T10 prediction on the high mass ends in the lower panel indicates their differences on the halo mass function. The posterior distributions of the five fitted parameters for the large-scale differential halo bias are shown in Fig.~\ref{fig:bh_post}, demonstrating that these parameters are unimodal and well converged.
The best-fitting parameters for all the selected samples can be seen from Table \ref{params_db} and \ref{params_cb} for the differential and cumulative biases respectively, which show the differential and cumulative biases are almost identical with the maximum percentage of difference less than $20\%$ . The similarity between the differential and cumulative measurements is a direct implication of the steepness of the galaxy mass function. This steepness means that at any limit, the cumulative bias is always dominated by the objects near the limit. Thus for brevity, we will focus on the analysis of large-scale differential biases in the next sections.
\section{RESULTS}
\label{sec:results}
\subsection{Large-scale galaxy bias dependence on physical properties}
\begin{figure*}
\includegraphics[width=\textwidth]{figures/physical_db00}
\includegraphics[width=\textwidth]{figures/physical_cb00}
\caption{Large-scale galaxy bias as a function of stellar mass, cold gas mass,
cold atomic gas mass and SFR at redshifts z = 0 (black), 1 (blue), 2 (green), 3(red).
%
The upper and lower panels show the differential and
cumulative biases respectively.
%
The filled symbols are directly measured by averaging equation~\eqref{eq:bg} on large scales.
%
The error bars are estimated by propagating the shot noise of the power spectrum.
%
Solid lines show the best fits of equation~\eqref{eq:fit} and
the dashed lines show the predicted biases from the Halo model.
%
Only measurements with a relative uncertainty below than 20\% are shown.
%
The open circles are not used for the fitting as they lie below the resolution limit of the simulation as defined in Section \ref{sec:measurement}.
}
\label{fig:phys}
\end{figure*}
\begin{figure*}
\includegraphics[width=\textwidth]{figures/emission_db00}
\includegraphics[width=\textwidth]{figures/emission_cb00}
\caption{ Large-scale differential (top) and cumulative (bottom) galaxy bias as a function of
H$\alpha$, H$\beta$, [OII] and Lya line luminosities from z = 0 to z = 3
%
(see caption of Fig.~\ref{fig:phys} for details).}
\label{fig:emib}
\end{figure*}
We show the large-scale galaxy bias as a function of stellar mass, cold gas mass, cold atomic gas (H{\sc\,i}\xspace) mass and SFR in Fig.~\ref{fig:phys}. These properties are amongst the most critical properties in galaxy evolution and their bias will also help us understand the biases of various other observable properties. The H{\sc\,i}\xspace bias can be compared against measurements of the completed H{\sc\,i}\xspace surveys, such as HIPASS and ALFAFA \citep{barnes2001h, haynes2018arecibo}, and forecast for the next generation of extragalactic H{\sc\,i}\xspace surveys, such as MIGHTEE \citep{jarvis2017meerkat}, WALLABY (Koribalski et al., in preparation) and SKA \citep{yahya2015cosmological}.
One can see that the large-scale galaxy biases from the "Measurement" of selected galaxy samples are in good agreement with the "Halo model" prediction, which verifies the "Measurement" in a statistical sense and indicates a lack of assembly bias from this particular simulation in comparison to the findings in \citet{2018MNRAS.476.3631P}. The same upward trend towards the high value ends between the halo mass and galaxy physical property biases demonstrates a close correlation between these galaxy properties and halo mass as the galaxy formation models predict. Compared to the cold gas mass, H{\sc\,i}\xspace mass and SFR biases, the galaxy stellar mass bias shows a steeper slope, which implies that the galaxy stellar mass is fundamentally different from other galaxy properties. The cold gas and H{\sc\,i}\xspace gas trace the SFR, since the SFR is proportional to the mass in the molecular component which correlates with atomic hydrogen. We note the open circles in the middle panels are not used for the fitting due to the mass resolution limits of cold gas at z = 0.
The turn-down feature of the SFR bias at high redshifts on the high star-forming end shows that dense environments have strongly reduced star formation which imposes an anti-bias effect on the distribution of star-forming galaxies at early times ($z \geq 2$). The lack of a turn-down feature in the cold gas bias plots implies the relation between cold gas and SFR is also dependent on density environments during that period of time. However, since this turn-down feature only shows in the high SFR end and the drop in numbers makes it difficult to gather enough samples for robust measurements, we look forward to seeing further verification of this trend from future simulations and observations.
\subsection{Large-scale galaxy bias dependence on emission lines}
\begin{figure}
\includegraphics[width=\columnwidth]{figures/continuum_uf_uv_db00}
\includegraphics[width=\columnwidth]{figures/continuum_uf_uv_cb00}
\caption{Large-scale differential (top) and cumulative (bottom) galaxy bias as a function of absolute magnitude
in u band at $z = 0, 1, 2$ and FUV, NUV bands at $z = 0$ (higher redshifts not shown due to the Lyman limit).
%
The M -5logh on the x-axis stands for all the magnitudes from FUV to u-band.
%
The solid line shows the best-fitting formula estimated using the maximum likelihood method
with only one set of parameters for the FUV, NUV and u bands
%
(see caption of Fig.~\ref{fig:phys} for details).}
\label{fig:uf_uv}
\end{figure}
\begin{figure*}
\includegraphics[width=171mm]{figures/continuum3_db00}
\includegraphics[width=171mm]{figures/continuum7_db00}
\includegraphics[width=171mm]{figures/continuum3_cb00}
\includegraphics[width=171mm]{figures/continuum7_cb00}
\caption{Large-scale galaxy bias as a function of absolute magnitude
from optical g-band to K-band for redshifts spanning the range of $0 \leq z \leq 3$
%
(see caption of Fig.~\ref{fig:phys} for details).
}
\label{fig:continuum}
\end{figure*}
We now move to the galaxy bias as a function of the luminosity for H$\alpha$, H$\beta$, Lya and [OII] lines corresponding to the wavelengths of 6563, 4861, 3727 and 1216 angstroms respectively in Fig.~\ref{fig:emib}. These emission lines are related to the galaxy selection in many current and upcoming surveys, such as UKIDSS, COSMOS, UDS, DESI, 4MOST and EUCLID \citep[e.g.][]{2012MNRAS.426..679G,levi2013desi,de20124most,laureijs2012euclid,duffy2014probing,guzzo2018measuring}.
Narrowband selections allow for a clean selection of star forming galaxies based simply on the strength of an emission line sampled by the corresponding filter. For instance, the PAU Camera survey is a narrow band imaging survey that could be used to extract emission lines over the redshift range covered by GAMA \citep{stothert2018pau}. Most narrowband-selected clustering analyses conducted so-far have targeted the Lyman-$\alpha$ (Lya) emission line. The development of wide-format infrared cameras over the past decade has cleared the way for panoramic near-infrared narrowband surveys which target the H$\alpha$ nebular line.
The H$\alpha$ flux of the Balmer line, created by a hydrogen atom when an electron falls from n = 3 to n = 2, is directly connected to the total hydrogen-ionizing radiation from massive stars, making it a reliable tracer of star formation. The H$\alpha$ emission line has been one of the primary diagnostics used to estimate the SFRs of galaxies in the local universe \citep{1983ApJ...272...54K}, although the measurements are complicated by dust absorption of Lyman-continuum photons within individual H{\sc\,ii}\xspace regions, dust attenuation in the general interstellar medium of galaxy and uncertainties in the shape of the initial mass function \citep{1998ARA&A..36..189K}.
Above z $\sim$ 0.4, H$\alpha$ becomes inaccessible to ground-based optical spectrographs, the higher-order Balmer lines such as H$\beta$ offer a promising alternative. H$\beta$, like all the Balmer lines, inherits the same strength and weaknesses of H$\alpha$: it is equally sensitive to variations in the IMF and the absorption of Lyman-continuum photons within star forming regions. Furthermore, H$\beta$ suffers more interstellar dust attenuation and is more sensitive to underlying stellar absorption. Despite these uncertainties, H$\beta$ may be a superior SFR diagnostic than the more commonly used [OII] nebular emission line \citep{2006ApJ...642..775M}.
The [OII] emission line has also been used widely as a qualitative and quantitative tracer of star formation in galaxies in redshift ranges where the H$\alpha$ emission line moves into the near-infrared \citep{2005MNRAS.362.1143M}. However, SFRs based on [OII] are still subject to considerable systematic uncertainties due to variations in dust reddening, chemical abundance, and ionization among star-forming galaxies \citep{2006ApJ...642..775M}.
One of the most promising ways of detecting very high redshift (z $\gtrsim$ 5) star-forming galaxies is via narrow-band imaging surveys targeting Lya. Lya emission originates from reprocessed ionizing photons of massive stars. The ionizing photons ionize the neutral hydrogen atoms in the interstellar medium (ISM). As a consequence of radiative transfer, H$\alpha$ photons can also be transfered into Lya, which makes the Lya emission line stronger than others as shown in the parameter $c$ for the emission lines.
Fig.~\ref{fig:emib} shows that generally all these emission lines can be treated as fine tracers of the star formation rate of galaxy (in our semi-analytic model). The turn-down of the Lya, H$\beta$ and [OII] bias at the highest luminosities and z = 3 reflects the same feature seen in Fig. 6 for SFR. The H$\alpha$ line does not show an obvious turn-down feature as the others do, which indicates that the H$\alpha$ line could be a better tracer of cold gas than the other lines. However, on the luminous ends, the discrepancy between the "Measurement" and "Halo model" suggests that the systematic uncertainties play a key role in the measurements as explained above. The galaxy assembly bias may also contribute to this discrepancy. However, it would be very difficult to detect without including a third property such as halo formation time in addition to halo mass. This would be an interesting thing to look at in future work. A similar discrepancy also arises for the measurements in the continuum bands as seen in the next section.
\subsection{Large-scale galaxy bias dependence on continuum bands}
\begin{figure*}
\includegraphics[width=171mm]{figures/mag_21_5_o_tot_ext_s00}
\includegraphics[width=171mm]{figures/mag_19_5_o_tot_ext_s00}
\caption{The host halo mass distribution at redshifts 0, 1, 2, 3 from left panel to right panel.
%
The distribution of host halo mass are plotted for two different ranges of
absolute magnitude as indicated in left panels.
%
The lines are color-coded by filters from g-band to K-band.}
\label{fig:halohis}
\end{figure*}
In Fig.~\ref{fig:uf_uv} and~\ref{fig:continuum}, we show the galaxy bias as a function of observer-frame absolute magnitude for UV bands and optical/IR bands. These filters are widely used in the ongoing and upcoming LSS surveys such as BOSS, eBOSS, DES and LSST surveys \citep{dawson2012baryon, dawson2016sdss, dark2005dark, tyson2002large}.
Shorter rest-frame wavelengths than 91nm hardly escape the galaxies and are virtually irrelevant for LSS studies, thus we only show the FUV, NUV bands biases at $z = 0$ and u-band bias at $0 \leq z \leq 2$. From optical g-band to K-band, we are able to cover the redshifts spanning the range $0 \leq z \leq 3$.
In Fig.~\ref{fig:uf_uv}, one can see that the steep slopes are similar to that of emission line biases, which shows a strong correlation between UV continuum and emission lines. In Fig.~\ref{fig:continuum}, all the measured biases from optical g-band to K-band show a self-similar dependence on the magnitude. The physical processes behind UV and IR bands emission on the rest frame are quite different. Like the emission lines, the UV bands are sensitive to the instantaneous and unobscured star formation, as they are driven by massive young stars. Conversely the IR-band is more sensitive to the stellar mass of the galaxy, especially on the luminous end, since the massive red galaxies have already consumed most of their cold gas and live in over dense environments where only few star forming galaxies reside.
In most of the visible bands in the observer frame, contribution from the massive red galaxies and star forming galaxies are mixed, thus bias similarities emerge across those bands. Nevertheless, one can still see that the slopes of biases are decreasing when you look at them from high-energy filter (UV) to low-energy filter (z-band).
\begin{figure*}
\centering
\begin{subfigure}{\columnwidth}
\centering
\includegraphics[width=\columnwidth]{figures/mag_SDSS-r_o_tot_ext_h00_gr}
\label{fig:sub1}
\end{subfigure}%
\begin{subfigure}{\columnwidth}
\centering
\includegraphics[width=\columnwidth]{figures/mag_SDSS-r_o_tot_ext_db00_gr}
\label{fig:sub2}
\end{subfigure}
\caption{Left: (g-r) color magnitude diagram at $z = 0$.
%
The tilted line defined by (g-r) $=-0.058[$M(r)-5$\log$h$]-0.692$ divides the red and blue populations.
%
Right: The galaxy bias as a function of r-band magnitude at $z = 0$
in blue clouds and red sequence shown in corresponding colors.}
\label{fig:gr}
\end{figure*}
We can understand the similar galaxy bias dependence on continuum bands by investigating the host halo distribution. In Fig.~\ref{fig:halohis} we show the host halo mass distribution in magnitude bins for redshifts z = 0, 1, 2, 3. Comparing the colored lines, we see that the effects of filters on the host halo distribution are quite small in this particular SAM, except for the brightest objects at z = 0. We find that many of the brightest objects at z = 0 reside in very massive halos. A plausible cause is the high merger efficiency in the current universe. High merger efficiency generally means high star formation rate; therefore, the luminous galaxies at $z = 0$ with high star formation rate are clustered more than the galaxies with low star formation rate so that the slopes of the biases decrease from UV to z-band. When compared to the turn-down feature at high redshift of the SFR bias, this indicates that the large-scale density environments have changing effects on the large-scale clustering of star-forming galaxies as the universe evolves.
To expand our results, we study the bias dependence on galaxy colors in Fig.~\ref{fig:gr}. We show the color magnitude diagram and differential bias as a function of r-band magnitude at $z = 0$ in the left and right panels. Based on the clear bimodal color distribution, we split the galaxies into red and blue populations using the black line shown in the left panel and produce the biases of the red and blue population respectively. As expected, the distribution of red galaxies is much more clustered against the dark matter background than that of the blue galaxies. This has been well understood within the halo model framework \citep{2009MNRAS.392.1080S}. For the fainter red galaxies, the increasing bias implies that they are mostly the low mass satellites in large host halos (also indicated in Fig.~\ref{fig:hvm}). The trend of bias dependence on galaxy color is consistent with the findings of \citet{zehavi2011galaxy} who investigated the clustering strength with the correlation length. Although there is a significant difference in bias between star forming and passive galaxies caused by the types of halos in which they reside, in a magnitude limited survey the contributions from these two populations is mixed together and hence the bias shows only a dependence on wavelength for the most luminous objects at low redshifts.
\subsection{Large-scale galaxy bias as a function of wavelength}
We now look at how our bias model depends on wavelengths. Fig.~\ref{fig:parameters} shows the five parameters for our fits of equation~\eqref{eq:fit} from g-band to K-band plotted at the effective wavelength of each filter. The decrease of the parameter $d$ (defined in Section \ref{sec:model}) towards higher wavelengths means that the slopes of biases get steeper when we look at them from low-energy filter (z-band) to high-energy filter (UV), as explained via Fig. \ref{fig:halohis} and \ref{fig:gr} in the last section.
\begin{figure}
\includegraphics[width=\columnwidth]{figures/parameters_db00}
\includegraphics[width=\columnwidth]{figures/parameters_cb00}
\caption{The best-fitting parameters for equation~\eqref{eq:fit} as a function of wavelength
from g-band to K-band.
%
The upper and lower panels show the parameters for fitting the differential and
cumulative galaxy biases respectively.
%
The parameter c is represented by adding 25 mag for convenience
%
The dashed lines are color-coded by the observational filters
from g-band to K-band.
}
\label{fig:parameters}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{figures/continuum_uf_db00}
\includegraphics[width=\columnwidth]{figures/continuum_uf_cb00}
\caption{Large-scale galaxy bias as a function of absolute magnitude
from g-band to K-band for redshifts spanning the range $0 \leq z \leq 3$.
%
The M -5logh on the x-axis stands for all the magnitudes from g-band to K-band.
%
The solid line shows the fit of equation~\eqref{eq:fit}
from g-band to K-band with only one set of parameters
%
(see caption of Fig.~\ref{fig:phys} for details).}
\label{fig:uf}
\end{figure}
The other parameters appear to be constant (within their statistical uncertainties) over the considered wavelength range. Thus, we can attempt to model all wavelengths using a single set of parameters (allowing a small systematic error on $d$). To constrain these parameters, we take all the measurements at all wavelengths as the input of equation \eqref{eq:sbga}. The resulting parameters are provided at the bottom of Table \ref{params_db} and \ref{params_cb}. This universal 5-parameter fit for all wavelengths (and redshifts) is shown in Figure 13. The slight discrepancy between the fits (lines) and the simulated data (dots) for the brightest galaxies at z = 0 is due to the assumption of a universal d-parameter, which is not strictly correct in a statistical sense. Of course, better fits can always be obtained by using the wavelength-dependent parameters also given in Table \ref{params_db} and \ref{params_cb}.
\section{DISCUSSIONS}
\label{sec:discussions}
\subsection{Bias forecasts in observer frame quantities}
\label{sec:Survey}
For the convenience of estimating the biases in LSS surveys with fixed redshift ranges, we convert the absolute magnitude and luminosity into the apparent magnitude and flux. We provide the apparent magnitude limited bias as a function of apparent magnitude and redshift for the broad-band filters by
\begin{equation}
b_g(\leq m, z_1,z_2) = \frac{\int_{z_1}^{z_2}\int_{-\infty}^{M(m,z)}
b_g(M',z)\phi(M',z)dM'\frac{dV}{dz}dz}
{\int_{z_1}^{z_2}\int_{-\infty}^{M(m,z)}\phi(M',z)dM'\frac{dV}{dz}dz},
\label{eq:bmz}
\end{equation}
where m is the apparent magnitude and $b_g(M',z)$ is the large-scale differential bias as a function of absolute magnitude and redshift.
Likewise, we provide the flux limited bias as a function of flux and redshift for the emission lines by
\begin{equation}
b_g(\geq F, z_1,z_2) = \frac{\int_{z_1}^{z_2}\int_{L(F,z)}^{\infty}
b_g(L',z)\phi(L',z)dL'\frac{dV}{dz}dz}
{\int_{z_1}^{z_2}\int_{L(F,z)}^{\infty}\phi(L',z)dL'\frac{dV}{dz}dz},
\label{eq:bfz}
\end{equation}
where F is the measured flux and $b_g(L',z)$ is the large-scale differential bias as a function of luminosity and redshift.
The conversions between $m, F$ and $M, L$ are given via
\begin{equation}
M(m,z) = m - 5\log \left(\frac{d_L(z)}{Mpc}\right) - 25 + 2.5\log(1+z),
\end{equation}
\begin{equation}
L(F,z) = F \times 4\pi d_L^2(z),
\end{equation}
where $d_L(z) = \frac{(1+z)}{H_0} \int_0^z \frac{dz^\prime}{\sqrt{\Omega_\Lambda +
\Omega_m(1+z^\prime)^3}}$ is the luminosity distance to the galaxy in unit of Mpc. Note that the conversion between H{\sc\,i}\xspace mass and the flux of H{\sc\,i}\xspace emission line is given via $M_{\rm HI} = 2.356 \times 10^5 d^2_L(z)(1+z)^{-1} S $, where the $M_{\rm HI}$ is in solar mass and the $S$ is an integrated flux in unit of Jy km/s. The $(1+z)$ factor is needed since the integrated flux $S$ is expressed in units of Jy km/s rather than Jy Hz \citep[see Appendix A in][]{obreschkow2009heuristic}.
\subsection{Comparison with existing surveys and forecasts}
In this section, we compare the predictions obtained using the equations of Section \ref{sec:Survey} with existing surveys and forecasts. The results are listed in Table \ref{tab:survey}.
HIPASS was a blind survey of neutral atomic hydrogen (H{\sc\,i}\xspace), which covered 71\% of the sky and identified more than 5000 galaxies below $z \sim 0.02$. \cite{basilakos2007large} measure the overall linear bias of 1619 H{\sc\,i}\xspace galaxies more massive than $1.89 \times 10^9 h^{-1}\rm M_\odot$ (calibrated by the Planck 2015 cosmology) using a correlation function analysis. The ALFALFA survey is a census of galaxies in the local universe, out to $z \sim 0.06$, with much better resolution \citep{haynes2018arecibo}. \cite{martin2012clustering} used the $\alpha$.40 sample of ALFAFA containing the results of the 40\% survey to investigate the bias for H{\sc\,i}\xspace-selected objects. They found the sample became unbiased (i.e. $b_g = 1$) on large scales. The latest forecast of H{\sc\,i}\xspace bias from the \textsc{GALFORM} in \cite{baugh2018galaxy} (hereafter B18) is an intensity mapping prediction that shows the evolution of H{\sc\,i}\xspace bias up to $z = 3$ including all the galaxies within a halo. The B18 forecasts are roughly estimated from the Fig. 11 in that paper. We predict the H{\sc\,i}\xspace bias of galaxies more massive than $M_{\rm HI}=10^7 h^{-1}\rm M_\odot$ for comparison with the B18.
EUCLID \citep{laureijs2011euclid} is a space-based survey mission designed to understand the origin of the Universe's accelerating expansion using two independent primary cosmological probes: Weak gravitational Lensing (WL) and Baryonic Acoustic Oscillations (BAO). The BAO are determined from a spectroscopic survey predominantly detecting H$\alpha$ emission line galaxies. \cite{amendola2017constraints} forecast the errors on the H$\alpha$ galaxy bias based on a simple power-law model and the polynomial model proposed by \cite{cole20052df}.
The 6dFGS \citep{jones20096df} is a near-infrared selected ($J H K$ ) redshift survey of 125 000 galaxies across four-fifths of the southern sky. \cite{beutler20126df} measured the K-band bias from 6dFGS by exploiting the angular dependence of redshift-space distortions in the 2D correlation function at effective redshift 0.067. Note that we compute the K-band cumulative bias using two sets of best-fitting parameters from K-band in Fig. \ref{fig:continuum} and g$\sim$K band in Fig. \ref{fig:uf} separated by a slash in Table~\ref{tab:survey}.
Comparing the results from our 5-parameter model with existing surveys (HIPASS, ALFAFA, 6dFGS) and forecasts (EUCLID), we find that our model is in good agreement with these references within $1\sigma$ statistical uncertainties especially when accounting for the fact that we all use different background cosmologies and methodologies. However, our model does predict a higher bias beyond the $1\sigma$ uncertainty when compared to the B18 forecast. We elaborate on some limitations in the next section.
\begin{table*}
\centering
\caption{The best-fitting parameters of our 5-parameter model for the large-scale \textit{differential} bias for different observational bands, emission lines, physical properties of galaxies and halo mass as well.}
\begin{tabular}{llccccr}
\hline
\hline
Halo mass & x & a & b & c & d &e\\
\input{tables/Vhalo_2_par_db00.txt}
\hline
\input{tables/physical_par_db00.txt}
\hline
\input{tables/emission_par_db00.txt}
\hline
Bands & x & a & b & c & d & e \\
\input{tables/continuum_uf_uv_par_db00.txt}
\input{tables/continuum3_par_db00.txt}
\input{tables/continuum7_par_db00.txt}
\input{tables/continuum_uf_par_db00.txt}
\end{tabular}
\label{params_db}
\end{table*}
\begin{table*}
\centering
\caption{The best-fitting parameters of our 5-parameter model for the large-scale \textit{cumulative} galaxy bias for different observational bands, emission lines and physical properties of galaxies.}
\begin{tabular}{llccccr}
\hline
\hline
Halo mass & x & a & b & c & d &e\\
\input{tables/Vhalo_2_par_cb00.txt}
\hline
\input{tables/physical_par_cb00.txt}
\hline
\input{tables/emission_par_cb00.txt}
\hline
Bands & x & a & b & c & d & e \\
\input{tables/continuum_uf_uv_par_cb00.txt}
\input{tables/continuum3_par_cb00.txt}
\input{tables/continuum7_par_cb00.txt}
\input{tables/continuum_uf_par_cb00.txt}
\end{tabular}
\label{params_cb}
\end{table*}
\begin{table*}
\centering
\caption{The comparison of our 5-parameter model with existing surveys and forecasts. The uncertainties of our prediction is calculated through error propagation of the five parameters. Note that the B18 is based on an intensity mapping prediction without mass cut on H{\sc\,i}\xspace samples. The $b_g$(Survey/Forecast) and $b_g(x,z)$ stand for the large-scale bias estimated in the existing survey/forecast and predicted from our model respectively.}
\begin{tabular}{llccr}
\hline
\hline
Survey/Forecast & Selection criteria &z & $b_g$(Survey/Forecast) & $b_g(x,z)$\\
\hline
HIPASS & $\rm M_{\rm HI} > 1.89 \times 10^{9} h^{-1}\rm M_\odot$ &0 & 0.94$\pm$0.15 & 0.96$\pm$0.05 \\
B18 & - &[0, 1, 2, 3] & [0.63, 0.8, 1, 1.26] & [0.95$\pm$0.04, 1.19$\pm$0.11, 1.58$\pm$0.26, 2.1$\pm$0.5] \\
EUCLID & $\mathrm{F(H\alpha) > 3 \times 10^{-16} erg \; cm^{-2} s^{-1}}$ &1 & 1.36$\pm$0.03 & 1.49$\pm$0.14 \\
6dFGS & m(K) < 12.75 mag &0.067 & 1.48$\pm$0.27 & 1.34$\pm$0.03/1.36$\pm$0.02 \\
\end{tabular}
\label{tab:survey}
\end{table*}
\subsection{Limitations of our method}
\label{sec:limit}
As seen, our 5-parameter model reproduces the bias reasonably well compared with existing surveys and forecasts, although there are some caveats which one needs to be aware of.
First, we only fit the bias measurements using certain lower limits and extrapolate below this. If we expect the lowest H{\sc\,i}\xspace mass galaxies to have a bias less than unity, then the inclusion of galaxies from $M_{\rm HI}=10^7 h^{-1}\rm M_\odot$ to $M_{\rm HI}=10^9 h^{-1}\rm M_\odot$ (i.e. roughly matching the B18 selection) could reduce the overall galaxy bias for a mass limited survey and bring our predictions closer to those of B18. In general, we do not expect our model to perform well in surveys with fainter limits than the left ends shown in the bias plots.
In addition, our models cannot capture the upturn at low redshifts very well. Including this sharp increase at z = 0 will make our 6dFGS prediction slightly higher (i.e. closer to the 6dFGS survey) and this is an obvious place for improvement in future work. Similarly, our model does not reproduce the turn-down feature at high SFR and high redshifts. We expect more evidence from the upcoming surveys to verify this.
A final caveat is that our model is based on \textsc{GALFORM} galaxies tuned with a Plank cosmology simulation. Therefore those fitting parameters should be dependent on this particular SAM and the cosmology used in there. Although using a SAM has many advantages as mentioned in Section~\ref{sec:introduction}, we note that SAMs are not perfect. For instance, SAMs have a large parameter set such that the degeneracies between these parameters are not clear, therefore there are systematics in the underlying data sets used for fixing the SAM parameters when comparing derived quantities such as the stellar mass function. Thus a comparison of how the fitting values of our 5-parameter model change when the same procedure is applied to a hydro simulation such as the EAGLE would be interesting. Of course, using a range of SAMs and hydro simulations calibrated to fit both the same data sets and different ones should provide a better insight.
\section{CONCLUSIONS}
\label{sec:conclusions}
In conclusion, we use the \textsc{GALFORM} galaxy formation model to predict the large-scale galaxy bias as a function of redshift and magnitude threshold for broadband continuum emission from the far infrared to ultra-violet, as well as for prominent emission lines, such as the H$\alpha$, H{\sc\,i}\xspace lines and and intrinsic physical galaxy properties. We provide the fitting formula $b_g(x,z)=a + b(1+z)^e\left(1 + \exp{[(x-c)d]}\right)$ along with the best-fitting parameters. With this simple model, we can reproduce all of these predictions very efficiently, simply by picking the right set of parameters. We find that the bias for the continuum bands is nearly wavelength-independent due to the mixing of star-forming and quiescent galaxies in a magnitude limited survey.
We also compare our 5-parameter model with existing measurements from large scale structure surveys and forecasts, demonstrating that our model is in reasonable agreement with HIPASS, ALFAFA, EUCLID and 6dFGS within $1\sigma$ statistical uncertainties; the limit of our model on the faint end of the selection criteria arises when compared with B18. Future work could improve on this analysis by: 1) improving the understanding and modelling of the turn-down and upturn features, 2) modelling the bias simultaneously as a function of magnitude/luminosity and color, 3) testing the dependence on cosmology and galaxy formation modelling. Notwithstanding the above improvements, this work provides an overview of the impact of galaxy physics on the bias, and allows for a quick estimation of the bias in a number of current or proposed large scale structure surveys.
\section*{Acknowledgements}
We would like to thank the anonymous referee for a constructive report that has improved this paper. We acknowledge the discussion with Zheng Zheng, Xi Kang, Guoliang Li, Cedric Lacey and the simulations provided by Chris Power.
This work was supported by the UCAS Joint PhD Training Program, China Scholarship Council, and the Science and Technology Facilities Council of the United Kingdom.
This work used the DiRAC@Durham facility managed by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). The equipment was funded by BEIS capital funding via STFC capital grants ST/P002293/1, ST/R002371/1 and ST/S002502/1, Durham University and STFC operations grant ST/R000832/1. DiRAC is part of the National e-Infrastructure.
This work has benefited from the publicly available programming language {\sc python} (\url{https://www.python.org/}) and the package {\sc matplotlib} (\url{https://matplotlib.org/}).
\bibliographystyle{mnras}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,377 |
Jeremiah confirms this, referring to a new covenant God will make with the people of Israel when he would "put my law in their minds and write it on their hearts" (Jer 31.31-33). And he adds that their restoration to Israel – "out of the land of the north and out of all the countries where he had banished them" – will be seen as a greater miracle than the crossing of the Red Sea (Jer 23.7f).
I believe the watching world's involvement (or lack of it) in this great miracle prophesied so prolifically in the Scriptures is a litmus test as to whether they are for or against the purposes of God. This is borne out by Jesus' teaching, in the section of Scriptures addressing the last days, on the sheep and the goats.
Israel is not a peripheral matter for the church, something only for 'Christian Zionists' to get excited about. Tragically, too many preachers see it as a 'political hot potato' and so avoid it like the plague in order not to rock the boat. But this is a dereliction of their duty as servants of Christ. As with the mark of the Beast (see Rev 14.9-11), neutrality is not an option on this issue.
Posted by Phil Bowell on 02 November 2018 . | {
"redpajama_set_name": "RedPajamaC4"
} | 0 |
Newcastle Music Therapy started as a mobile service almost twenty years ago when Susan started to take on private clients in the Newcastle and Lake Macquarie area. Originally as InSync Music Therapy, Susan grew her client base and took on programs such as Sing And Grow (for parents and toddlers) and Snug (a respite camp for the families of children with rare disorders).
As the business grew clients were increasingly asking for a space where they could express themselves freely. Susan also felt the need to bring more music therapists together where their collective skills and gifts could benefit her clients.
Our story really began when a young music student from the Newcastle Conservatorium visited the Mater Hospital Hospice and played for patients in the end stages of their lives. There she met a music therapist who introduced her to the concept of music therapy and how music can be used to help people in many ways.
This young music student already knew about the power of music in her own life and quickly connected with the idea that music could be used in a therapeutic way to change the lives of others. It seemed the perfect combination – using music, which she loved, to work with people and make a difference in their lives, which she also loved.
From there Susan Ashley-Brown embarked on a journey of study and deepening knowledge of music therapy. After graduating from her Bachelor of Music degree at Newcastle University, she completed a Postgraduate Diploma in Music Therapy at the University of Technology, Sydney, and became a Registered Music Therapist with the Australian Music Therapy Association.
This journey has taken her into aged care facilities, children's hospitals, working with people with disabilities and mental health issues, working with families, and into people's homes and lives. Susan was the first Music Therapist employed at the John Hunter Children's Hospital, working in oncology.
In 2018 Susan opened the new practice space in Warners Bay and is excited about offering both individual and group music therapy sessions for many different people. Carlin McLellan joined Susan in 2018 and she is looking to expand the team.
Putting it simply – to change lives through music!
We aim to provide accessible music therapy programs for people of all ages and abilities.
We love to talk about music therapy and share our knowledge. We are advocators for the benefits of music therapy and endeavour to educate the community about music therapy.
To bring joy into people's lives, to create meaningful connections between people and to help people know their worth and reach their potential – through music. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3 |
Q: Fail of markdown parser detected if '_ 's are used in a naked URL In the answer
realloc() for NUMA Systems using HWLOC, the parser breaks my URL link.
The URL was with __word__:
http://www.open-mpi.de/projects/hwloc/doc/v1.2/group__hwlocality__membinding.php#gade5e2c28ea8475a479bf2b1df36c6ccd
After parsing, it becomes (<a href is broken; no clickable link):
hwlocality_membinding.php#gade5e2c28ea8475a479bf2b1df36c6ccd">http://www.open-mpi.de/projects/hwloc/doc/v1.2/group_hwlocality_membinding.php#gade5e2c28ea8475a479bf2b1df36c6ccd
Short test:
http://example.com/_test_ -> test">http://example.com/test
Or if I put in a naked URL with _test_ just here:
http://example.com/test
A: This will work correctly from the next build on: client changeset, server changeset. The underscores will still cause some potentially unwanted styling of the displayed text1, but the link itself works.
1 Not anymore in most cases (including the one here), thanks to point 2. in this change.
A: Too much of an edge condition.
Remember that Markdown does not support "naked" URLs officially, so you have your pick of non-naked URLs to use here:
<http://example.com/foo__bar__baz#hash>
<a href="http://example.com/foo__bar__baz#hash">link</a>
[link](<http://example.com/foo__bar__baz#hash>)
http://example.com/foo__bar__baz#hash
link
link
see https://stackoverflow.com/editing-help
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,020 |
'use strict';
const del = require('del'),
config = require('../config');
module.exports = () => () => del(config.buildPath);
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,878 |
{"url":"https:\/\/steveperkins.com\/understanding-the-new-cross-platform-net-part-4-demo-walkthrough\/","text":"Understanding the New Cross-Platform .NET, part 4 (demo walkthrough)\n\nWe started this four-part series by taking the traditional monolithic .NET Framework, and comparing it to its new modular and cross-platform .NET Core sibling. \u00a0Then we dove into ASP.NET vNext, a family of open-source frameworks and build tools for deploying cross-platform apps. \u00a0In the third part\u00a0we looked at the IDE\u2019s and other tooling under the Visual Studio brand.\n\nNow we will wrap everything up, with a walkthrough demonstrating how to create and deploy a new cross-platform app. \u00a0First, let\u2019s have a quick recap of the main .NET concepts we\u2019ve seen so far, and the Java concepts which they more or less match:\n\n.NET concept Analogous Java concept\nCLR JVM\n.NET implementation (i.e. Framework, Mono, or Core) JRE\n.NET Framework Oracle's proprietary Java binaries\nMono OpenJDK\n.NET Core Upcoming Java 9, with \"Project Jigsaw\" modular redesign\nDNX JDK\nDNVM Java currently has no similar concept. However, this is comparable to RVM for Ruby, or virtualenv for Python.\nASP.NET vNext A mash-up of Spring\/JEE, Hibernate\/JPA, and a Spring Boot-like system for creating and deploying apps.\n\n[1] Install .NET Version Manager (dnvm)\n\nThis tool is basically a PowerShell script on Windows, or a bash script on Linux and OS X. \u00a0For this example I\u2019m working on a Windows machine, so I installed \u201cdnvm\u201d by opening a command-prompt window and running:\n\n@powershell -NoProfile -ExecutionPolicy unrestricted -Command \"&{\\$Branch='dev';iex ((new-object net.webclient).DownloadString('https:\/\/raw.githubusercontent.com\/aspnet\/Home\/dev\/dnvminstall.ps1'))}\"\n\n\nThe process is somewhat different for OS X or Linux, although just as easy. \u00a0Check the main README page in the ASP.NET GitHub repo for current specifics. \u00a0Even on Windows, you should go there to confirm the above command in case it\u2019s out-of-date (things are moving quickly right now!).\n\nIf everything succeeded, then you should be able to type \u201cdnvm\u201d from a command-prompt and see something like this:\n\nC:\\Users\\Steve>dnvm\nYou must specify a command!\n___ _ ___ ____ ___\n\/ _ \\\/ |\/ \/ | \/ \/ |\/ \/\n\/ \/\/ \/ \/| |\/ \/ \/|_\/ \/\n\/____\/_\/|_\/ |___\/_\/ \/_\/\n.NET Version Manager v1.0.0-beta4-10356\nBy Microsoft Open Technologies, Inc.\n\nusage: dnvm <command><\/command> []\n\ncommands:\nalias Lists and manages aliases\nhelp Displays a list of commands, and help for specific commands\ninstall Installs a version of the runtime\nlist Lists available runtimes\nname Gets the full name of a runtime\nsetup Installs the version manager into your User profile directory\nupgrade Installs the latest version of the runtime and reassigns the specified alias to point at it\nuse Adds a runtime to the PATH environment variable for your current shell\n\n\n[2] Update DNX Versions, and Make\u00a0.NET Core Active\n\nGet the latest DNX versions for your platform installed by executing:\n\ndnvm upgrade\n\n\nAt the time of this writing, this currently isn\u2019t working on OS X. \u00a0By default, \u201cdnvm\u201d downloads DNX versions from a \u201cstable\u201d feed. \u00a0\u201cStable\u201d versions do not yet exist for\u00a0non-Windows platforms. \u00a0You can override this, and download cutting-edge \u201cunstable\u201d versions by adding a \u201c-u\u201d argument. \u00a0Hopefully though, this might\u00a0be a moot point by the time you read this.\n\nYou can now run:\n\ndnvm list\n\n\n\u2026 to see which DNX versions are installed on your machine. \u00a0The output should look like this:\n\nC:\\Users\\Steve>dnvm list\n\nActive Version Runtime Architecture Location Alias\n------ ------- ------- ------------ -------- -----\n1.0.0-beta4 clr x64 C:\\Users\\Steve\\.dnx\\runtimes\n1.0.0-beta4 clr x86 C:\\Users\\Steve\\.dnx\\runtimes\n1.0.0-beta4 coreclr x64 C:\\Users\\Steve\\.dnx\\runtimes\n1.0.0-beta4 coreclr x86 C:\\Users\\Steve\\.dnx\\runtimes\n* 1.0.0-beta4-11566 clr x86 C:\\Users\\Steve\\.dnx\\runtimes default\n\n\nThe \u201cactive\u201d DNX version is the one currently loaded into your system PATH. \u00a0When you use \u201cdnu.exe\u201d or \u201cdnx.exe\u201d from the command-line, the executables\u00a0from this installed version will be invoked. \u00a0Initially, the active instance is a\u00a0full-fledged monolithic \u201c.NET Framework\u201d version. \u00a0We want to change this, so that we\u2019re using \u201c.NET Core\u201d instead:\n\nC:\\Users\\Steve\\Desktop>dnvm use 1.0.0-beta4 -arch x64 -r coreclr -p\n\n\n\n[3] Generate an ASP.NET Web Application with Yeoman\n\nIf you haven\u2019t already installed\u00a0Node.js and npm on your workstation, then do so now. \u00a0There are pre-built installers for Windows, OS X, and Linux available on the Node.js website, although OS X and Linux users might prefer to go through a package manager such as\u00a0Homebrew or Apt.\n\nWith Node.js and npm present, install Yeoman and the ASP.NET generator like this:\n\nC:\\Users\\Steve\\Desktop>npm install -g yo grunt-cli generator-aspnet bower\n\nStart the Yeoman ASP.NET generator with \u201cyo aspnet\u201c, and use the arrow keys to select the \u201cWeb Application\u201d project type. \u00a0You can choose whatever name you like, but I\u2019m just sticking with the \u201cWebApplication\u201d default:\n\nC:\\Users\\Steve\\Desktop>yo aspnet\n\n_-----_\n| | .--------------------------.\n|--(o)--| | Welcome to the |\n---------\u00b4 | marvellous ASP.NET 5 |\n( _\u00b4U_ ) | generator! |\n\/___A___\\ '--------------------------'\n| ~ |\n__'.___.'__\n\u00b4 |\u00b0 \u00b4 Y \n\n? What type of application do you want to create?\nEmpty Application\nConsole Application\n> Web Application\nWeb API Application\nNancy ASP.NET Application\nClass Library\n\nYou will see a slew of information about files being created, followed by a success message like this:\n\nYour project is now created, you can use the following commands to get going\ndnu restore\ndnu build\ndnx . run for console projects\ndnx . kestrel or dnx . web for web projects\n\nYou now have a perfectly functional ASP.NET web application! \u00a0I must again note that right now, this process only works on Windows. \u00a0The Yeoman generator on my Macbook Pro produces a broken application\u2026 and the success message talks about the older \u201ckpm\u201d and \u201ck\u201d command names, rather than their current \u201cdnu\u201d and \u201cdnx\u201d counterparts. \u00a0We\u2019re still in very early days here, hopefully\u00a0these issues will be worked out before long.\n\n[4] Run the Web Application\n\nChange into the directory that was just created, and you can run the\u00a0commands suggested above. \u00a0\u201cdnu restore\u201d and \u201cdnu build\u201d work together like Maven, importing the project\u2019s dependencies and building it respectively. \u00a0With the \u201cdnx . kestrel\u201d command, we can now test out the application on port 5001 with the embedded Kestrel web server:\n\n[5] Build a Completely Self-Contained Bundle\n\nLet\u2019s now publish our application into a self-contained deliverable, which can be deployed even on machines without .NET present. \u00a0The documentation is still a bit confusing on how to go about this. \u00a0However, the ASP.NET team is very friendly and active on StackOverflow, and so I was able to work it out through a question posted there:\n\ndnu publish --runtime active\n\n\nThis takes all of the content and dependencies our application needs, and dumps them under the \u201cbin\\output\u201d directory:\n\nIf you look under \u201capproot\\packages\u201c, you\u2019ll see a subdirectory named \u201cdnx-coreclr-win-x64.1.0.0-beta4\u201d (or similar, depending on your DNX version number). \u00a0This contains the entire DNX runtime needed by your application!\n\nThe root directory of this bundle contains a batch file for every command in your project\u2019s \u201cproject.json\u201d file (e.g. \u201ckestrel.cmd\u201c). \u00a0These batch file invoke the DNX runtime that is embedded within your bundle:\n\n...\n@\"%~dp0approot\\packages\\dnx-coreclr-win-x64.1.0.0-beta4\\bin\\dnx.exe\" --appbase \"%~dp0approot\\src\\WebApplication\" Microsoft.Framework.ApplicationHost kestrel %*\n...\n\n\nThis entire \u201coutput\u201d directory compresses to a ZIP file 39 megabytes in size. \u00a0That\u2019s not\u00a0much larger than a Spring Boot executable JAR, and that still requires a 150-500 megabyte Java environment on the target machine!\n\nI should note that while this source code is cross-platform, you are bundling DNX native executables that are specific to a particular platform. \u00a0That\u2019s not such\u00a0a big deal, though. \u00a0Since the source code is cross-platform, we can simply re-publish it for other\u00a0platforms, like compiling Golang or\u00a0Rust applications.\n\nConclusion\n\nThese four articles covered quite a lot of ground, and there are a million different directions you could go from here to learn more. \u00a0There are major open source and cross-platform changes drawing attention and hype to .NET platform right now. \u00a0Hopefully this series provides a helpful overview, for an audience of curious Java developers and other non-Microsoft programmers looking in\u00a0from the outside.","date":"2018-09-20 03:11:35","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\": 0.29250743985176086, \"perplexity\": 13424.272905771717}, \"config\": {\"markdown_headings\": false, \"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-2018-39\/segments\/1537267156376.8\/warc\/CC-MAIN-20180920020606-20180920040606-00102.warc.gz\"}"} | null | null |
Q: How to get the console to "remember" a user input in Python? I am trying to figure out how I can get the console to "remember" what the user has inputted into the console for my hangman game. For example, if the word "tree" is picked from the hangman word string that I created, if a user inputs the letter "r", I want the console to remember that input and keep printing it to the console every time the user inputs a letter until the session ends. I want the console to re-print "- r - -" if the user inputs "r" while the user can find the other letters in the word. I wish for the same thing to happen if a user inputs the letter "t" or "e" as well: "- r e e". Thank you, sorry if I am asking for too much, I can't find the answer to this.
Here is my code:
#hangman mini-project
import random
import string
import time
letters = string.ascii_letters
lettertree = ['a', 'b', 'c', 'd', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 's', 'u', 'v', 'w', 'x', 'y', 'z']
hangmanwords = ['tree','sun']
sunchoices = ['s _ _', '_ u _', '_ _ n']
treechoices = ['t _ _ _', '_ r _ _', ' _ _ e _', '_ _ _ e']
lettercount = [0]
gameWinTree = False
gameWinSun = False
limbCount = 5
hangmanword = random.choice(hangmanwords)
correct = hangmanword
if hangmanword == "sun":
print (random.choice(sunchoices))
if hangmanword == "tree":
print (random.choice(treechoices))
if letters == "r":
print("Nice! You guessed one letter from the word")
if letters == "e":
print("Wow! You guessed two letters from the word, if you wish, you can guess the word")
while True:
letters = input("Please enter a letter to guess the word")
if letters == correct:
input("Correct! The word was " + correct + ". Press enter to play again.")
time.sleep(1)
break
if letters == correct:
gameWinTree == true
if gameWinTree == true:
time.sleep(1)
break
print("The letter that you chose was " + letters)
if letters == "r":
print("Nice! You guessed one letter from the word!\n t r _ _")
if letters == "e":
print("Wow! You guessed two letters from the word!\n t _ e e")
if letters == correct:
print("Correct! The word was tree!")
if letters == lettertree:
print("Sorry, that's not a correct letter, feel free to try again.")
limbCount -=1
if limbCount == 0:
print("Unfortunately, you are out of tries, better luck next time!")
time.sleep(1)
exit()
Sorry if my code seems sloppy, I'm just starting to learn Python after learning other programming languages.
A: Here's how I would construct the string you're looking for. When a player guesses a letter, I'd store it in a set, called guesses. If it's in the set of letters in the word, called correct, then I effectively add it to the intersection of these sets, called correct_guesses. Then, I iterate over the word, and print out each letter into the placeholder string, replaced with an underscore if that letter is not in correct_guesses. This is what it would look like in code:
word = 'tree'
guesses = set()
correct = set(list(word))
correct_guesses = set()
while correct_guesses != correct:
# Get input
guess = input("Guess: ")
guesses.add(guess)
correct_guesses = guesses.intersection(correct)
# Print word status
placeholder = ' '.join(['%s' for _ in word])
print(placeholder % tuple([l if l in correct_guesses else '-' for l in word]))
print("You've guessed: " + ", ".join(guesses))
Let me know if this code doesn't work for you or if it needs more explaining.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,500 |
Finding Aids and Collection GuidesToggle Dropdown
Newspapers and Publications
Postcard Collections
Scrapbook Collections
Small Manuscripts
S.C. Poetry Archives Manuscript Collection
University Archives Finding Aids
Research and Subject GuidesToggle Dropdown
John B. Watson (1878-1958)
Greenville History Resources
World War I Resources
American Civil War Resources
Travel Collections
Queer Zines at Furman: Highlights from the New LGBTQ+ Zine and Small Press Collection
In 2019, the Furman Libraries acquired a core collection of queer zines and LGBTQ+ small press publications from London-based antiquarian bookseller Camp Books. With over 300 examples, this collection was revelatory to us in several ways: the ways in which printed matter and print culture are used by their creators to advocate, share information, and create community within LGBTQ+ circles; the wide array of creative design, content, and expression in the many formats, printing processes, and approaches to creating zines and small press publications; and the important historical moment that this group of printed materials captures, as LGBTQ+ people have become increasingly visible, proud, and vocal within the public sphere in the past 50 years.
This exhibition provides an introduction to the viewpoints and perspectives of several dozen individuals, from five continents, as they record their lives, rant and rave, celebrate their accomplishments, passions and interests, and at a basic level seek to connect with their readerships in personal and intimate ways through the format of zines and small press publications. It also provides glimpses into intimate and highly personal life stories of queer, trans, gay, lesbian, bisexual, asexual, and nonbinary people as they tell their own stories, share their struggles, and creatively celebrate their lives and identities.
LGBTQ+ materials are a collecting interest for the Furman Libraries, from some of the first English-language publications to address same-sex desire in the 19th century, through mid-20th century gay and lesbian periodicals, to 1970s gay and lesbian comix, to this collection, which is mostly contemporary but stretches back to the late 1970s. Furman's queer zine collection has more than doubled since 2019, and is now likely the second largest in the Southeast. As these collections grow, they will provide Furman students and faculty with a rich array of primary sources that allow for unique classroom and research experiences and the creation of new knowledge and creative works as a result. Many thanks are due to Rick Jones for creating the poster for this exhibition.
<< Previous: Travel Collections
Next: Past Exhibitions >>
URL: https://libguides.furman.edu/special-collections/discover | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,226 |
UForage is a plant identification club that emphasizes learning plant families. We don't only focus on edible plants, but all plants found in Utah.
We meet once a week in Salt Lake City, Utah. We meet at a different place each time. We learn to identify the plants and other creatures around our neighborhoods.
The milky sap of this plant is toxic, and may cause blindness if it comes in contact with the eye. Sheep can surprisingly eat this with no problem, but not horses or cattle.
Foraging Arizona meets once a week in Southern Utah North Arizona. Call for more info. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,003 |
package com.dangdang.ddframe.job.lite.console.domain;
import lombok.Getter;
import javax.xml.bind.annotation.XmlAccessType;
import javax.xml.bind.annotation.XmlAccessorType;
import javax.xml.bind.annotation.XmlRootElement;
import java.util.LinkedHashSet;
import java.util.Set;
/**
* 事件追踪数据源配置根对象.
*
* @author zhangxinguo
*/
@Getter
@XmlRootElement
@XmlAccessorType(XmlAccessType.FIELD)
public final class EventTraceDataSourceConfigurations {
private Set<EventTraceDataSourceConfiguration> eventTraceDataSourceConfiguration = new LinkedHashSet<>();
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,902 |
https://www.dustygroove.com/item/870295/Jerry-Butler:Your-Precious-Love-Japanese-pressing
Soul LP Jerry Butler
Jerry Butler
Your Precious Love (Japanese pressing)
LP (Item 870295) Vee Jay/Overseas (Japan), Late 50s/Early 60s — Condition: Near Mint-
Vee Jay
Vee Jay (label)
Overseas (label)
An excellent Japanese collection – featuring sublime early solo work by Jerry Butler, plus a few early tracks with The Impressions too! © 1996-2023, Dusty Groove, Inc.
Near Mint - (minus)
Black vinyl that may show a slight amount of dust or dirt.
Should still be very shiny under a light, even with slight amount of dust on surface.
One or two small marks that would make an otherwise near perfect record slightly less so. These marks cannot be too deep, and should only be surface marks that won't affect play, but might detract from the looks.
May have some flaws and discoloration in the vinyl, but only those that would be intrinsic to the pressing. These should disappear when the record is tilted under the light, and will only show up when looking straight at the record. (Buddah and ABC pressings from the 70's are a good example of this.)
May have some slight marks from aging of the paper sleeve on the vinyl.
Possible minor surface noise when played.
Mercury, 1973. Near Mint-
LP...$11.99 16.99
An easy album to overlook, but not without some nice moments! Johnny Bristol produced the record, and he gives it a nice sweet 70s soul groove, similar to what he was using in his own work from the time. And typical of Jerry's albums from the early 70s, there's lots of nice original material, ... LP, Vinyl record album
Mr Dream Merchant
Mercury, 1967. Very Good+
LP...$4.99 8.99
Sublime soul from Jerry Butler – material recorded during his post-Vee Jay years, when he was really transforming his sound in ways that still made him one of the dominant male voices in sophisticated soul! There's a great balance between poise and emotion in the cuts – served up with ... LP, Vinyl record album
A lost little gem from Jerry – recorded towards the end of his years with Mercury. The record's got Jerry working in a much hipper style than before, drawing off the pool of younger Chicago soul talents that he'd begun to collect on some of his earlier albums for Mercury – and the ... LP, Vinyl record album
Mercury, 1972. Very Good+ 2LP Gatefold
Perhaps the greatest record Jerry Butler made in the 70s, and a very tight bit of baroque Chicago soul with arrangements and production by Samuel F. Brown III. The tracks are a good mix of originals and covers, and they all show Jerry going way past his Gamble & Huff/Mercury years – into ... LP, Vinyl record album
Soul Artistry
Beautiful uptown soul from Jerry – with pre Gamble-Huff arrangements by Jo Renzetti and Jimmy Wisner. The tracks do a great job of maintaining the perfect Iceman sound from Jerry's late Vee Jay years, yet also hint nicely at the direction to come. Titles include "You Walked Into My ... LP, Vinyl record album
More Great Hits Of 1964 And Other Golden Goodies
Vee Jay, 1964. Very Good
(Cover has light surface and edge wear, and a partially split bottom seam.) LP, Vinyl record album
Dee Clark
You're Looking Good
Vee Jay, 1960. Near Mint-
Dee Clark cracked the charts big with a few crossover hits – but he's an excellent soul singer with a raspy tone that almost set the stage for some of the deeper soul acts to come in the 60s! The style here is very much in the mode of some of Jackie Wilson's best for Brunswick from the early ... LP, Vinyl record album
Roy C
Something Nice
Definitely something nice from the great Roy C – one of the overlooked soul singer's great 70s albums for Mercury – all of which are ripe for rediscovery by a younger generation! This one's slightly different than the rest, in that the album was recorded at the Dynamic Studios in ... LP, Vinyl record album
Billy Stewart Teaches Old Standards New Tricks
Chess, 1966. Very Good-
This was the follow-up LP to Billy Stewart's huge single of Gershwin's "Summertime", and it's got a similar approach of "funky soul takes on American pop music standards". "Summertime" isn't on the album, but all the tracks have a sound that falls in the same mode ... LP, Vinyl record album
Young-Holt Unlimited
Brunswick, Late 60s. Very Good
The beat goes on, and just keeps getting better and better too – thanks to the growing sophistication of the Young/Holt duo, once they broke away from Ramsey Lewis! The bass and drums share equal space in the spotlight – and the production has the former really up high in the mix, ... LP, Vinyl record album
There's A Riot Goin' On
Epic, 1971. Very Good Gatefold
LP...$24.99 (LP...$24.99)
A wonderful album from Sly and crew – moving way past the straight funk approach of earlier records, into a complicated crossover soul style that's filled with warmth and righteousness. Despite the political tone implied by the "riot" in the title and the co-option of the American ... LP, Vinyl record album | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,808 |
namespace aura {
class Window;
}
namespace base {
class Timer;
}
namespace views {
class CustomButton;
}
namespace ash {
class FrameMaximizeButton;
// A class which shows a helper UI for the maximize button after a delay.
class ASH_EXPORT MaximizeBubbleController {
public:
class Bubble;
MaximizeBubbleController(FrameMaximizeButton* frame_maximize_button,
MaximizeBubbleFrameState maximize_type,
int appearance_delay_ms);
// Called from the outside to destroy the interface to the UI visuals.
// The visuals will then delete when possible (maybe asynchronously).
virtual ~MaximizeBubbleController();
// Update the UI visuals to reflect the previewed |snap_type| snapping state.
void SetSnapType(SnapType snap_type);
// To achieve proper Z-sorting with the snap animation, this window will be
// presented above the phantom window.
aura::Window* GetBubbleWindow();
// Reset the delay of the menu creation (if it was not created yet).
void DelayCreation();
// Called to tell the owning FrameMaximizeButton that a button was clicked.
void OnButtonClicked(SnapType snap_type);
// Called to tell the the owning FrameMaximizeButton that the hover status
// for a button has changed. |snap_type| can be either SNAP_LEFT, SNAP_RIGHT,
// SNAP_MINIMIZE or SNAP_NONE.
void OnButtonHover(SnapType snap_type);
// Get the owning FrameMaximizeButton.
FrameMaximizeButton* frame_maximize_button() {
return frame_maximize_button_;
}
// The status of the associated window: Maximized or normal.
MaximizeBubbleFrameState maximize_type() const { return maximize_type_; }
// A unit test function to return buttons of the sub menu. |state| can be
// either SNAP_LEFT, SNAP_RIGHT or SNAP_MINIMIZE.
views::CustomButton* GetButtonForUnitTest(SnapType state);
protected:
// Called from the the Bubble class to destroy itself: It tells the owning
// object that it will destroy itself asynchronously. The owner will then
// destroy |this|.
void RequestDestructionThroughOwner();
private:
// The function which creates the bubble once the delay is elapsed.
void CreateBubble();
// The owning button which is also the anchor for the menu.
FrameMaximizeButton* frame_maximize_button_;
// The bubble menu.
Bubble* bubble_;
// The current maximize state of the owning window.
const MaximizeBubbleFrameState maximize_type_;
// The timer for the delayed creation of the menu.
scoped_ptr<base::Timer> timer_;
// The appearance delay in ms (delay and fade in & fade out delay).
const int appearance_delay_ms_;
DISALLOW_COPY_AND_ASSIGN(MaximizeBubbleController);
};
} // namespace ash
#endif // ASH_WM_CAPTION_BUTTONS_MAXIMIZE_BUBBLE_CONTROLLER_H_
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,465 |
Whitmer: Statewide mask requirement remains in effect
By DAVID EGGERT Associated Press
LANSING, Mich. (AP) — Gov. Gretchen Whitmer said Monday that a statewide mask requirement remains in effect despite the Michigan Supreme Court's invalidation of a law that underpins her orders to control the coronavirus pandemic.
She asked the court to declare its Friday ruling not binding until Oct. 30, to give her administration, the Republican-led Legislature and local health departments time to transition. Whitmer warned that people could lose unemployment benefits as a result of the court's decision and called on lawmakers to return to session instead of recessing until after the November election.
She pointed to a separate order issued by the state Department of Health and Human Services in June — under a 1978 public health law — mandating face coverings in enclosed public spaces and crowded outdoor places.
"We know that masks work. It's on all of us to do our part and to have some personal responsibility keeping ourselves, our families and our economy going," Whitmer told reporters following a campaign event for a lawmaker in Davison.
Violators can be fined up to $1,000 under state Health and Human Services Director Robert Gordon's order. They faced a misdemeanor charge under Whitmer's orders but not jail time.
The governor said the "fallout" from the high court's decision was "still being ascertained." The ruling means she needs approval from legislators to extend a state of emergency and cannot act on her own. GOP lawmakers have criticized Whitmer's unilateral approach.
"We're studying it to make sure that where we can act we do, where there are gaps to be filled we work to do that as well," she said. "I am by no means undeterred or finished trying to protect the health of the people of this state."
In asking the Supreme Court to clarify when its opinion should be enforced, the state cited a court rule to argue it should take effect after 21 to 28 days.
Over the weekend, some large counties issued their own COVID-19 restrictions, which included mask requirements. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 349 |
Deze lijst van tallships biedt een overzicht van tallships in verschillende klassen.
Een tallship is een zeegaand zeilschip van organisaties zoals de Sail Training International organisatie (STI), vaak vierkant getuigd, dat wordt gebruikt voor het opleiden van jonge mensen.
De Length Over All (LOA) van een schip is de lengte tussen de voorkant van de boegbalk en het hek. Daarbij horen niet de boegspriet, de preekstoel of andere uitsteeksels aan boeg of hek. De lengte waterlijn (LWL) is de lengte gemeten op de waterlijn.
Class A
Door de STI wordt de class A gedefinieerd als: alle schepen met een LOA >40 m, vierkant getuigd en betrokken bij zeiltraining voor jonge mensen (fulltime of parttime).
De schepen in Class A zijn vermeld bij Tallship.
Class B
Traditioneel-getuigde vaartuigen met een LOA minder dan 40 meter en LWL minstens 9,14 m.
Class C
Modern getuigde vaartuigen met een LOA minder dan 40 m, LWL minstens 9,14 m en bovendien geen spinnaker-achtige zeilen gebruiken.
Class C I
Modern-getuigde vaartuigen met een LOA minder dan 40 m, LWL minstens 9,14 m en bovendien geen spinnaker-achtige zeilen gebruiken.
Class D
Modern-getuigde vaartuigen met een LOA minder dan 40 m, LWL minstens 9,14 m en daarbij spinnaker-achtige zeilen gebruiken.
Tallships | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,666 |
Access video written tutorials, tips, galleries, eBooks more! Click Here to download DriverFinder™.
The days of downloading individual. Lenovo Global Support Home. Aug 05, · Tech support scams are an industry- wide issue where scammers attempt to trick you into paying for unnecessary technical support services. How to update dvd drivers in vista.
Promptly answer your request determine how Tee Support can help via chat Tee Support client. Click Save File ( if your using FireFox).
Driver updates are required for all HP laptops Printers other devices. Universal Offline Automatic Complete Device Driver Install DVD For Windows 7 Vista, XP 8. Known issues with this security update. Drivers includes Graphic Laptop, Bluetooth, Printer, Wireless, Scanner, Desktop etc.
1, Win 10 Supports HP Dell Toshiba Sony Acer Asus Lenovo Compaq IBM. You can help protect yourself from scammers by verifying that the contact is a Microsoft Agent Microsoft Employee that the phone number is an official Microsoft global customer service number. Our website is updated weekly AMD, Dell, you can find newest drivers for different vendors such as HP Realtek etc.
Known issue 1 After you install this security update, fonts that are installed in a location other than the default fonts. DriverFinder identified by scan your PC uniquely identified your PC operating system , motherboard every device drivers using an intelligence algorithm - This ensure your PC & device. More ways to shop: Visit an Apple Store call 1- 800- MY- APPLE find a reseller. For automatically identify fixes missing , keeps your Microsoft device drivers always up- to- date, install the latest official drivers , update Microsoft device drivers you can use DriverFinder. How to update dvd drivers in vista.
Connect securely to your. DUMo ( Drivers Update Monitor) keeps your PC up- to- date & safe by using the most recent version of required hardware drivers. On DriversGuru you can download and update almost all device drivers. Click Start Scan in DriverFinder™.
Your Tee Support expert will: 1. It is recommended you update your HP Drivers regularly in order to avoid conflicts. You may have a problem with your HP Driver. Learn more with Discovery Center. DriverTuner was created to save your time resolving driver problems by providing you with a single, automatic tool.
How To Install DriverFinder and Download New Acer Drivers: 1. Click Run ( if your using Internet Explorer). Double- click DriverFinderSetup. Your home for creative learning.
Missing or corrupt DVD- RW Drivers can cause is recommended you update your DVD & CD Drivers regularly in order to avoid conflicts. You can manually install CD and DVD drivers or you can use a driver e you looking to update VGA Drivers? Now you can easily download VGA Drivers for windows 10, 8, 7, xp & vista with driver whiz. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,067 |
{"url":"https:\/\/coderanch.com\/u\/252321\/Jackson-Curtis","text":"# Jackson Curtis\n\nGreenhorn\nsince Aug 22, 2011\nCows and Likes\nCows\n0\nIn last 30 days\n0\nTotal given\n0\nLikes\n0\n0\nTotal given\n0\nGiven in last 30 days\n0\nScavenger Hunt\nRanch Hand Scavenger Hunt\nGreenhorn Scavenger Hunt\n\n## Recent posts by Jackson Curtis\n\nI just did that and it gave C:\\Program Files\\Java\\jdk1.7.0\nSo yeah. Its in the right place but it doesn't seem to work when I do javac.\n*EDIT*\nNvm. I fixed it.\nThank you so much for your help\n;) see you all around.\n6 years ago\nHi all. I'm just learning java and I was wondering if you could all help me out here.\nI just installed jdk on my computer under C:\\Program Files\\Java\nBut when I try to path it under enviromental variables. It doesn't seem to work.\nMy path is C:\\Program Files\\Java\\jdk1.7.0\\bin and when I type javac at the command line it gives me an error.\nIt works when I go to access it manually with the cd command. But I can't seem to get the path working.\nAny help would be GREATLY appreciated.\nCheers, John\n6 years ago","date":"2018-08-18 03:23:21","metadata":"{\"extraction_info\": {\"found_math\": false, \"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\": 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\": 0.9180522561073303, \"perplexity\": 3382.6112541869275}, \"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-2018-34\/segments\/1534221213264.47\/warc\/CC-MAIN-20180818021014-20180818041014-00661.warc.gz\"}"} | null | null |
Made using recycled timber, this rack is easy to build and gives you a great excuse to stock up on fine wines!
Along centre of recycled timber block, measure and draw marks for 4 holes. Make first hole 110mm from 1 end then space rest of the holes 110mm apart.
Each hole needs to be drilled on an angle to hold a bottle. First, make a drilling guide by marking 1 piece of the scrap timber with 7 degree angle at one end using a protractor and cutting. Place recycled timber block on second scrap piece so spade bit doesn't blow out the back. Sit guide scrap of timber on edge on recycled timber block. Place spade bit on a mark made in Step 1 and tilt drill so bit is in line with angled edge of guide scrap of timber. Drill hole, making sure drill stays on this angle. Repeat for all holes.
To create tabs on racks for hanging, mark out a rebate 35mm wide and 100mm long on both ends of block. Use handsaw to cut out rebates. Drill a 6mm hole through centre of each tab.
Mount rack on wall using pan head screws. If fixing to plasterboard, try to locate timber studs in wall and screw directly to them, otherwise use a plasterboard fixing such as a wall mate. Use masonry wall plugs to go into brick walls.
Also... By chance if you need wine to fill this bad boy, we've got you sorted over on BHG Shop with a great line-up for a steal! | {
"redpajama_set_name": "RedPajamaC4"
} | 7,203 |
I definitely wanted to compose a note so as to appreciate you for those magnificent recommendations you are writing on this site. My time consuming internet research has at the end been paid with excellent suggestions to write about with my family members. I 'd express that many of us visitors actually are unequivocally lucky to be in a decent community with very many special individuals with valuable techniques. I feel very blessed to have seen your entire weblog and look forward to plenty of more amazing minutes reading here. Thank you again for a lot of things. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,175 |
Q: LDAP bind to DC in another forest after bind to its domain results in LDAP error 82 I encountered a strange error when trying to bind to a specific DC using the LdapConnection class. I managed to strip down the code to the following:
static void Main(string[] args)
{
var cred = new NetworkCredential("username", "password", "domainFQDN");
try
{
var ldapConnection = new LdapConnection(new LdapDirectoryIdentifier("domain1.test.local", 389, false, false), cred, AuthType.Kerberos);
ldapConnection.Bind();
Console.WriteLine("Connected 1");
}
catch (Exception e)
{
Console.WriteLine(e);
}
try
{
var ldapConnection2 = new LdapConnection(new LdapDirectoryIdentifier("dc1.domain1.test.local", 389, true, false), cred, AuthType.Kerberos);
ldapConnection2.Bind();
Console.WriteLine("Connected 2");
}
catch (Exception e)
{
Console.WriteLine(e);
}
Console.ReadLine();
}
The output of this program is consistently:
Connected 1
System.DirectoryServices.Protocols.LdapException: A local error occurred.
at System.DirectoryServices.Protocols.LdapConnection.BindHelper(NetworkCredential newCredential, Boolean needSetCredential)
at System.DirectoryServices.Protocols.LdapConnection.Bind()
The only difference between the calls is that in the first connection I use the domain FQDN in the LdapDirectoryIdentifier, while in the second connection I use the exact DC address. Of course, I verified that the first connection goes to the same DC as the second one.
The error only occurs when I specify AuthType.Kerberos for the authentication method. The error occurs always when I try to connect to a domain in a different forest, and only sometimes when I connect to a DC in the local forest.
I can probably work around the error by using the domain name twice, but then I won't ensure stickiness once I get a connection to a specific DC.
How can I make sure that the second connection goes to the same DC without getting this error?
A:
The error only occurs when I specify AuthType.Kerberos for the authentication method.
Your issue is the Kerberos authentication then.
From a command line, try (use the short name of the DC, not the FQDN):
setspn dc1
There should be a bunch in that list, but I think the problem one here would be "ldap/dc1.domain1.test.local/domain1.test.local". Do you see that in the list?
If not, you can add it. As a domain admin, use this from the command line:
setspn -a ldap/dc1.domain1.test.local/domain1.test.local dc1
More details here, although the missing SPN it talks about in that article is one with a GUID. The list at the bottom shows what the list of SPNs should look like: https://support.microsoft.com/en-ca/help/308111/a-missing-service-principal-name-may-prevent-domain-controllers-from-r
If that SPN is already listed, then you can turn on Kerberos logging by following the instructions here: https://support.microsoft.com/en-ca/help/262177/how-to-enable-kerberos-event-logging
Once logging is enabled, Kerberos errors will show up in the System event log. It'll give you a better idea why it's failing.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,747 |
Here's why 2020 has been so wonderful
OK. So, yeah. It's been generally pretty crappy. I can run off a long list of reasons, and your list might be more generous. However, the world spins, the sun rises, and people laugh. Seems to me that's a recipe for hope.
Here then are a few reasons (personally and globally) why 2020 has been, on balance, a positive experience.
1/ We aren't complacent anymore. All those years of warnings from epidemiologists about the dangers of a lethal new virus? Mostly, they went unheard and unheeded. Most of us now know much more about viral contagions and public health issues. (Ignore the conspiracy theorists. All societies have a vocal contingent of village idiots.)
2/ Even in the darkest of times, money can be made. Lots of it, apparently. Just ask all the billionaires who have fattened their wallets.
3/ The written word is more powerful than ever (and I'm not referring to presidential tweets). I'm heartened that important, mainstream media sources (New York Times, Washington Post, and others where quality journalism matters) have seen huge growth in their subscription numbers. Moreover, people are reading books at a fantastic rate. I'm thrilled that I was able to finish The Impossible Series this year and see steady growth in readership. I'm excited about what's next.
4/ Amid all the challenges, this nation rose up and voted like never before (more than 20 million more voters than four years ago). Best yet, they voted for a hopeful future. (Again, ignore the conspiracy theorists. Some people stop growing up after they turn thirteen.)
And for the sake of argument, here are some other nifty developments: "The Mandalorian"; sports without fans (not as bad as I expected); the rise of Sarah Cooper (YouTube her, peeps!); toilet paper hoarding (pathetic but funny); "The Queen's Gambit"; Microsoft Teams and Zoom (how else to do remote school?); Baby Yoda toys (nothing says "awww" like a dose of the baby); and a new sink in Casa Kennedy (no, really - this is a big deal). | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,382 |
{"url":"https:\/\/www.studyadda.com\/sample-papers\/neet-sample-test-paper-21_q82\/210\/277046","text":"\u2022 # question_answer Which of the following has the least bond energy? A) ${{H}_{2}}$\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0B) ${{F}_{2}}$\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0C) \u00a0 ${{O}_{2}}$\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0D) \u00a0 ${{N}_{2}}$\n\nIn ${{F}_{2}},$the bond energy is less due to greater inter- electronic repulsions. Hence, the correct option is (b).","date":"2020-09-23 11:15:05","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\": 0.9194983839988708, \"perplexity\": 8235.598966344063}, \"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-2020-40\/segments\/1600400210616.36\/warc\/CC-MAIN-20200923081833-20200923111833-00513.warc.gz\"}"} | null | null |
The cost of wearing metals on ploughs, cultivators or powered implements can make a serious dent in a farmer's bottom line.
For farmers or contractors working abrasive soils, the cost of wearing metals on ploughs, cultivators or powered implements can make a serious dent in their bottom line.
A new material called Ferobide has recently hit the market from specialist supplier Tenmat which promises to give better wear properties than tungsten carbide and is claimed to be easier to work with than traditional face hardening materials.
Key difference is a composition that sees the material using a hardened steel matrix that bonds particles together. This features allows it to be used easily onfarm where welding skills may be basic, and also gives the product some resistance to chipping, which can be a problem with traditional tungsten carbide facing materials.
The Ferobide tiles are easily cut to size and shape using a standard cutting wheel, or alternatively the cut line can be scored by a cutting wheel, held in a vice along the score line and sheared with a clean hammer blow.
The manufacturer claims that any welded joints are much stronger than brazed items, and will hugely prolong the life of wearing parts. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,402 |
#include "external/seqarrayvector/common/decomposition.h"
namespace pascinference {
namespace algebra {
template<>
Decomposition<SeqArrayVector>::Decomposition(int T, int R, int K, int xdim, int DDT_size){
LOG_FUNC_BEGIN
this->T = T;
this->R = R;
this->K = K;
this->xdim = xdim;
this->DDT_size = 1;
this->DDR_size = 1;
/* no graph provided */
graph = NULL;
LOG_FUNC_END
}
template<>
Decomposition<SeqArrayVector>::Decomposition(int T, BGMGraph<SeqArrayVector> &new_graph, int K, int xdim, int DDR_size){
LOG_FUNC_BEGIN
this->T = T;
this->R = new_graph.get_n();
this->K = K;
this->xdim = xdim;
this->DDT_size = 1;
this->DDR_size = 1;
/* prepare new layout for T */
destroy_DDT_arrays = true;
DDT_ranges = (int *)malloc((this->DDT_size+1)*sizeof(int));
DDT_ranges[0] = 0;
DDT_ranges[1] = T;
compute_rank();
LOG_FUNC_END
}
template<>
Decomposition<SeqArrayVector>::Decomposition(int T, BGMGraph<SeqArrayVector> &new_graph, int K, int xdim, int DDT_size, int DDR_size){
LOG_FUNC_BEGIN
this->T = T;
this->R = new_graph.get_n();
this->K = K;
this->xdim = xdim;
/* prepare new layout for R */
destroy_DDR_arrays = false;
set_graph(new_graph, DDR_size);
this->DDT_size = DDT_size;
this->DDR_size = graph->get_DD_size();
/* prepare new layout for T */
destroy_DDT_arrays = true;
/* unfortunatelly, we have to compute distribution of T manually */
int DDT_optimal_local_size = T/(double)DDT_size;
int DDT_optimal_local_size_residue = T - DDT_optimal_local_size*DDT_size;
DDT_ranges = (int *)malloc((this->DDT_size+1)*sizeof(int));
DDT_ranges[0] = 0;
for(int i=0;i<DDT_size;i++){
DDT_ranges[i+1] = DDT_ranges[i] + DDT_optimal_local_size;
if(i < DDT_optimal_local_size_residue){
DDT_ranges[i+1] += 1;
}
}
compute_rank();
LOG_FUNC_END
}
template<>
Decomposition<SeqArrayVector>::~Decomposition(){
LOG_FUNC_BEGIN
if(destroy_DDT_arrays){
free(DDT_ranges);
}
if(destroy_DDR_arrays){
free(DDR_affiliation);
free(DDR_permutation);
free(DDR_invpermutation);
free(DDR_lengths);
free(DDR_ranges);
}
LOG_FUNC_END
}
template<>
void Decomposition<SeqArrayVector>::compute_rank(){
LOG_FUNC_BEGIN
/* get rank of this processor */
int rank = GlobalManager.get_rank();
this->DDT_rank = rank/(double)this->DDR_size;
this->DDR_rank = rank - (this->DDT_rank)*(this->DDR_size);
/* control the decomposition */
// if(this->DDT_size*this->DDR_size != GlobalManager.get_size()){
// coutMaster << "Sorry, DDT_size*DDR_size != nproc" << std::endl;
// coutMaster << " DDT_size = " << this->DDT_size << std::endl;
// coutMaster << " DDR_size = " << this->DDR_size << std::endl;
// coutMaster << " nproc = " << GlobalManager.get_size() << std::endl;
// TODO: throw error
// }
LOG_FUNC_END
}
template<>
void Decomposition<SeqArrayVector>::set_graph(BGMGraph<SeqArrayVector> &new_graph, int DDR_size) {
if(destroy_DDR_arrays){
free(DDR_affiliation);
free(DDR_permutation);
free(DDR_invpermutation);
free(DDR_lengths);
free(DDR_ranges);
}
/* decompose graph */
this->DDR_size = DDR_size;
new_graph.decompose(DDR_size);
this->graph = &new_graph;
destroy_DDR_arrays = false;
DDR_affiliation = new_graph.get_DD_affiliation();
DDR_permutation = new_graph.get_DD_permutation();
DDR_invpermutation = new_graph.get_DD_invpermutation();
DDR_lengths = new_graph.get_DD_lengths();
DDR_ranges = new_graph.get_DD_ranges();
compute_rank();
}
}
} /* end of namespace */
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,914 |
Your RV adventures start with RV World MI! Here is where you'll find incredibly low prices on high-quality models, such as the 2020 Palomino Backpack Edition SS-1200! This Truck Camper is ready for the road! Visit our massive lot at 7834 S Division Grand Rapids Michigan 49548 to see why we're considered one of the best Michigan dealerships for RVs! Call us at 616-591-3632 to talk to one of our RV experts today!
Your whole family can sleep comfortably at night! This snug and cozy camper sleeps up to 3 people! The master bedroom features an extra comfortable Queen bed, so you won't miss any sleep at night!
You won't miss any sleep while you're camping with the cozy Queen bed in the master bedroom! There's enough sleeping space inside this RV for up to 3 people! | {
"redpajama_set_name": "RedPajamaC4"
} | 4,412 |
Ellen Pompeo and Debra Messing Speak Out in Support of Gabrielle Union After Her Firing From 'AGT': 'White Girls, Stand With Your Sisters'
November 29, 2019 10:53 AM PST
A few of network television's leading actresses are speaking out in support of Gabrielle Union in the wake of her America's Got Talent firing.
via People:
A day after Union, 47, spoke out about her recent and controversial departure from the NBC reality competition series after only one season, Grey's Anatomy star Pompeo came to her fellow actress's defense in a series of tweets.
"It's unfortunate that @nbc the same network that protected disgusting men like Matt Lauer and punished women for speaking out or not putting up with it…has not changed their practices or culture. I support @itsgabrielleu commitment to speaking up to injustice. It takes courage" Pompeo began, noting former Today show anchor Matt Lauer's firing for allegations of sexual misconduct.
In a second tweet, Pompeo, 50, said that she was specifically talking to "white girls" — asking them to "stand with your sisters on the front lines."
"This is a teaching moment..It's important..white girls I'm talking to you..whether you truly understand what racial injustice is or not..that you stand with your sisters on the front lines. Don't cut side deals & don't not get involved because it isn't your issue..because it is," she wrote.
"Workplace cultures will continue to be toxic until there is unity and solidarity among all women. If you go for self in these moments you undermine the work we are out here trying to do. Obviously this network feels like they can operate like this and it's okay," she continued.
Pompeo acknowledged that there have been issues on her own show at rival network ABC.
"Also I feel important to mention our problems on the Greys set and every set has them…some kind of issue …there's lots of people in a workplace.. point is… exec producers and the NETWORK @abc cared enough to help us make change support is crucial," she tweeted.
Not only did Ellen speak out, but 'Will & Grace' star Debra Messing took to Twitter to blast her 'home' network NBC for its 'disgusting' behavior. Take a look at both Ellen and Debra's tweets below.
It's unfortunate that @nbc the same network that protected disgusting men like Matt Lauer and punished women for speaking out or not putting up with it…has not changed their practices or culture. I support @itsgabrielleu commitment to speaking up to injustice. It takes courage
— Ellen Pompeo (@EllenPompeo) November 28, 2019
this is a teaching moment..It's important..white girls I'm talking to you..whether you truly understand what racial injustice is or not..that you stand with your sisters on the front lines. Don't cut side deals & don't not get involved because it isn't your issue..because it is
Workplace cultures will continue to be toxic until there is unity and solidarity among all women. If you go for self in these moments you undermine the work we are out here trying to do. Obviously this network feels like they can operate like this and it's okay.
With that said GIRLS….instead of wack jugglers and messy Simon Cowell watch @ReeseW and Jennifer Anniston in The Morning Show!! Soooo much better. Hard to believe these networks are still getting away with this. Our work continues @itsgabrielleu ??
environment is inconvenient when there is a huge money making machine that is involved. It is cowardice, greed, and protection of the status quo revealed. Being "hands off," is inexcusable and reflects a laissez faire attitude toward systemic racism and sexism. @itsgabrielleu
— Debra Messing (@DebraMessing) November 28, 2019
Tags:Gabrielle Union | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,578 |
I had a reputation for keeping a tidy house. Everyone who knows me understood that, and admired my efforts. I believed fervently in my mother's maxim; 'Everything in its place, and a place for everything,' and so was scrupulous about removing anything that interfered with the spotless ambiance of my dwelling – homosexuals (well, you know what the bible says about them!), prostitutes (need I say more!), divorcees (my marriage is sanctified by God), street people (why on earth don't they get a job!), liberal pastors (wishy washy, like our parish priest) who just don't understand the awesome gravity of God's righteousness and hatred of sin…..and the list goes on.
I have a large box in the cellar into which I consigned all these people. It wasn't a question of 'out of sight, out of mind.' In fact I and my little prayer group prayed for them fervently, that God will convict them, bring them to repentance and turn their lives around. This group met regularly in each other's homes – all spotless like mine. We did have someone in the group for a while whose housekeeping skills left a lot to be desired, so we decided that, while she could come to us, we would rather not go to her. She eventually dropped out (I can't think why), but seeing as she didn't make the grade, I popped her in the box too, to be prayed for like the others.
My relationship with Jesus has always been good – after all, my home was his home, and I made sure it was worthy of his presence. However, there came a time when I could no longer hear his voice, or should I say, it was muffled. I thought I was simply going through a dry spell, and that it would eventually pass. But it didn't. I became thirsty for him, and strained to hear his voice that seemed to come from a distance, and eventually was driven to follow it. I wandered around the house and finally realised that it was coming from the cellar, and, when I went to investigate, from inside the box.
I gingerly lifted the lid, to find the smiling face of Jesus.
I was flabbergasted. Then I realised that he wasn't alone.
Ian, whom I had blithely consigned to the box, was a very familiar face – my wishy washy parish priest. So why was he getting all the accolades?
I fled up the stairs.
Once in the safety of my pristine, familiar surroundings, I paced around the house. I was unsettled. All my concepts of Christian living had been turned upside down, and I didn't like it. Eventually I found myself in the kitchen, staring down at the sink in which I could see my face (yes, I even polished the kitchen sink). But the sight didn't fill me with pride any more. It was some time before I realised that I didn't want to see my reflection in the sink. I wanted to see it in the eyes of Jesus, the way I could see the reflection of all those people – in his eyes.
All sorts of things swirled through my mind. If I went to this party, would my housekeeping deteriorate to the point that I'd be like my lapsed prayer group friend, whom none of my friends would want to visit? If so, would they really be my friends? Would I be condoning the behaviour of Brian and Rosy and Michael, and relaxing my rules of righteousness? Then I wondered if they were only MY rules, and whether God even wanted strict rules and regulations, the sort that (I was discovering) got in the way of his love.
I stewed over the sink for a long time, until I became aware of sounds coming from the cellar. I couldn't help myself. I crept to the top of the cellar stairs and listened. There was indeed a party going on there. I sat down on the top step and stayed there for what seemed to be an eternity, before plucking up courage to go down and join them.
It's been a while since that party. And yes, my 'friends' have distanced themselves from me. But as a result of joining a conga line and dancing out of the box and up the stairs from the cellar and into my home, I now have a group of more interesting friends, who understood my confusion and pain at my loss – even though what I lost needed to go anyway – and loved me through it. My house isn't as perfect as it was, but now it has a cosy lived-in feel about it, and a bit of mess every now and then is a small price to pay for the joy of being closer to Jesus and his friends.
I also went to visit the woman who failed my prayer group's rigid housekeeping rules to apologise and ask her forgiveness. We now have coffee together every week in her lounge room.
And you know, she too has become a really good friend.
And I no longer even notice the mess. | {
"redpajama_set_name": "RedPajamaC4"
} | 50 |
\section*{Abstract}
\section{Introduction}
In contrast to time series for Gaussian responses, where numerous forecasting methods are available, literature on forecasting for count type time series is still very sparse. However, time series data in form of counts is frequently measured in various fields like finance, insurance, biomedical, public health.
As an example, consider a disease surveillance study, where health officials record the number of disease cases over a certain time period to understand the disease trajectory. The main interest in such surveillance studies is to forecast the disease counts in the future, so that public health-care providers are able to respond to disease outbreaks on time, thereby reducing the disease impact and saving economic resources (\cite{myers}). However, forecasting disease counts in these situations is complex, due to the fact that the required forecasts have to be consistent with the non-negative and integer valued sample space of such count time series. The usage of the estimated mean at a future time point which is a non integer, as a suitable point estimate for the future count (\cite{10.2307/30042088}, \cite{doi:10.1080/23737484.2016.1190307}, \cite{jalal}) as practiced in usual ARIMA forecasting techniques gives rise to an incoherent forecast (\cite{FREELAND2004427}).
In this article, we present a forecasting method based on the profile predictive likelihood function for count time series data. The proposed forecast estimates and regions are coherent. The class of models we consider is the observation driven models (\cite{10.2307/2336303}, \cite{Li1994}, \cite{10.2307/30045208}, \cite{Fokianos2004} and \cite{kedembook}), where the conditional distribution of counts given past information belongs to the exponential family. As done in the available statistical literature (\cite{Agresti1990}, \cite{Bishop1975}, \cite{Haberman1974}, \cite{Cameron1998}, \cite{Winkelmann2000}), we model the counts with a Poisson type distribution. These Poisson time series models allow inclusion of both autoregressive and moving average terms along with trend, seasonality and dependence on several covariates. To the best of our knowledge this is the first coherent forecasting method proposed for count time series modeled by such observation driven models.
Mainly two approaches have been used for modelling non Gaussian time series, parameter driven and observation driven models (\cite{cox}). These two types of models differ in the way they account for the autocorrelation in the data. In observation driven models, the
correlation between observations measured at successive time points is modeled through a
function of past responses. However, parameter driven models use an unobserved latent process to
account for the correlation. Conditioning on the
latent process, the observations are assumed to be evolve independently of the past
history of the observation process. Parameter driven models for non-Gaussian time series were first considered by \cite{west}. Later, these models were also investigated by \cite{fahrmeir}, \cite{fahrwagen}, \cite{durbin1997,durbin2000}.
To compute the posterior distributions for the parameters of these models Markov chain Monte Carlo (MCMC) methods are frequently used (some references are \cite{durbin1997}, \cite{sp} and \cite{gamer}). However, often these MCMC algorithms fail to converge resulting in poor inference and predictions. In more recent times, the particle filter algorithm has been used as an alternative to the MCMC method in parameter driven models (\cite{dk}). As compared to parameter driven models, the computational burden for parameter estimation is much less in observation-driven models (\cite{10.2307/2291149},
1995; \cite{durbin2000}, \cite{10.2307/30042088}).
In this article our focus is on observation driven models, the conditional distribution for each observation given past information on responses and past and possibly present covariates is described by a generalized linear model (GLM) distribution. Partial likelihood theory combined with GLMs is used for estimation. This type of a flexible modeling framework include namely, regression models for count time series proposed by \cite{10.2307/2336303}, GLM time series models by \cite{Li1994} and \cite{Fokianos2004}, generalized linear autoregression models (GLMs) of \cite{shephard}, GLARMA models of \cite{10.2307/30042088} and GARMA models of \cite{10.2307/30045208}. However, in all these papers we may note that the main focus is on parameter estimation and in-sample prediction with almost no attention being given to the forecasting component involved. However, out-of-sample prediction based on past behaviour is an important and necessary component of time series studies. Consider a financial data based on number of transactions in stocks, the main interest in such studies is to use the history of stock transactions and information on other external covariates influencing the stocks, to predict the number of future transactions and reap large profits (\cite{GRANGER19923}). In worldwide development of early warning systems for vector borne diseases like dengue, the main aim is to forecast the future disease counts by
considering the effect of past disease outcomes and also different covariates like climate conditions, social ecological conditions
on disease counts (\cite{Shi} and \cite{Lee}). In both count time series mentioned above, number of stock transactions and disease cases, non-negative and integer valued estimates and intervals for future counts are required.
We use the profile predictive likelihood function of \cite{10.2307/4615723} to develop coherent forecasts for count time series. See \cite{bjornstad1990} and the references therein for a detailed review of some of the prediction functions used in the statistical literature. Forecasting using predictive likelihood has been used before for Gaussian models with an autoregressive structure of order one (\cite{10.2307/4616194}). However, to the best of our knowledge, it has not been used for out-of-sample forecasts in any non-Gaussian time series models.
Other forecasting techniques for count time series data modeled using the Poisson auto regressive model (PAR) and the integer auto regressive (INAR) class of models, have been proposed by namely, \cite{FREELAND2004427}, \cite{MCCABE2005315}, \cite{10.2307/41057433} and \cite{doi:10.1111/stan.12083}. However, the PAR and the INAR models are structurally different from the observation driven GLM time series models as discussed above and usually do not accommodate covariates (\cite{mckenzie}).
The original contributions of this article include (i) coherent and consistent point forecasting method for count time series, (ii) coherent forecasting regions based on highest density regions, (iii) use of the the predictive likelihood concept for predicting dependent non Gaussian time series data. The performance of the proposed method is illustrated using several simulated examples and a real data set from a polio surveillance study. The effects of model misspecification on the proposed method and large sample results for the forecasting estimator are also discussed.
The rest of the paper is organized as follows. GLM for time series and particularly Poisson time series models are discussed in Section 2. This is followed by details on predictive likelihood (PL) function and PL for Poisson time series models in Section 3. The steps of the forecasting algorithm, forecasting intervals based on highest density regions and asymptotic properties of the forecast estimator are also discussed in this section. Section 4 gives the details of the simulation results, real data prediction results, and the study of the robustness of the proposed method. Concluding remarks are given in Section 5.
\section{GLMs for time series}
The count at time $t$, $Y_t$ is assumed to depend on the past counts and past and possibly present covariate values.
We assume that the conditional density of each $y_t$ for $t=1,2,\ldots,n$, given the past information, $ H_{t} =\{x_t,\ldots,x_1,y_{t-1},\ldots,$ $y_1,\mu_{t-1},\ldots,\mu_1\}$, is given by,
\begin{equation}\label{A1}
f(y_{t}|H_{t})=exp\Big\{{\frac{y_{t}\gamma_{t}-b(\gamma_{t})}{\psi}+c(y_{t},\psi)}\Big\},
\end{equation}
where $ \gamma_{t} $ is the canonical parameter, $\psi$ is the additional scale or dispersion parameter, while $ b(\cdot) $ and $ c(\cdot) $ are some specific functions corresponding to the type of exponential family considered. The canonical parameter $\gamma_t$ is a function of the conditional mean of $Y_t|H_t$, i.e., $\mu_{t}=b'(\gamma_{t})$. The conditional $Var(Y_t|H_t)$ is of the form $\sigma^{2}_{t}=\psi b''(\gamma_{t}) $.
The mean $\mu_t$ is related to the linear predictor $\eta_t$ by $\mu_t=h(\eta_t)$, where $h$ is a one-to-one sufficiently smooth function. The inverse of $h$, denoted by $g$ is called the link function. To model the dependence of the means at time $t$, $\mu_t$, on $H_t$ the linear predictor is assumed to be,
\begin{equation}\label{A2}
\eta_{t}=\vec{x}'_{t}\svec{\beta}+\sum_{j=1}^{p}\phi_{j}\mathcal{A}(y_{t-j},\vec{x}_{t-j},\svec{\beta})+\sum_{j=1}^{q}\theta_{j}\mathcal{M}(y_{t-j},\mu_{t-j}),
\end{equation}
where $\vec{x}_t$ represents the covariate vector, $ \mathcal{A} $ and $ \mathcal{M} $ represent the autoregressive (AR) and moving average (MA) components, respectively. Some forms for the linear predictor under the general model setup proposed in the statistical literature are:\\
Model form 1: \cite{10.2307/2336303}
\begin{equation}
\eta_t=\vec{x}'_t\svec{\beta}+\sum_{i=1}^{p}\phi_i [g(y_{t-i})-\vec{x}'_{t-i}\svec{\beta}],
\end{equation}
Model form 2: \cite{Li1994} \begin{equation}
\eta_t=\vec{x}'_t\svec{\beta}+\sum_{i=1}^{p}\phi_i y_{t-i}+\sum_{j=1}^{q}\theta_j\mu_{t-j},
\end{equation}
Model form 3: \cite{Fokianos2004} \begin{equation}
\eta_t=\vec{x}'_t\svec{\beta}+\sum_{i=1}^{p}\phi_i g_i(y_{t-i})+\sum_{j=1}^{q}\theta_j d_j(\mu_{t-j}),
\end{equation}
Model form 4: GARMA $(p,q)$ \cite{10.2307/30045208} \begin{equation}
\eta_t=\vec{x}'_{t}\svec{\beta}+\sum_{j=1}^{p}\phi_j \{g(y_{t-j})-\vec{x}'_{t-j}\svec{\beta}\}+\sum_{j=1}^{q}\theta_j \{g(y_{t-j})-\eta_{t-j}\},\label{eta3}
\end{equation}
where $\vec{x}_t$ is the vector of covariates at time $t$, $\svec{\beta}$ are the usual regression parameters, $\svec{\phi}=(\phi_1,\ldots,\phi_p)'$ are the $p$ autoregressive parameters and $\svec{\theta}=(\theta_1,\ldots,\theta_q)'$ correspond to the $q$ moving average components, $g$, $g_i$ and $d_j$ are known functions.
Looking at the above model forms in equations (3-6) we see that they are very similar to each other. We choose the GARMA $(p,q)$ model proposed by \cite{10.2307/30045208} given in equation (\ref{eta3}) for representing the linear predictor. The GARMA models allows both autoregressive and moving average terms to be included in the linear predictor along with covariates.
In this article we model the conditional distribution of the count data using Poisson GARMA models, which we define next.
\subsubsection{Poisson GARMA models}
The conditional density of $y_t$ given the past information is a Poisson distribution with mean parameter $\lambda_t$,
\begin{equation}
f(y_t|H_t)=\frac{\exp({-\lambda_t})\lambda_t^{y_t}}{y_t!},\,\lambda_t>0;\,y_t=0,1,2,\ldots;\,t=1,2,\ldots,n.
\end{equation}
Comparing with equation (\ref{A1}), we get $\gamma_t=\log(\lambda_t)$, $b(\gamma_t)=\lambda_t$, $\psi=1$ and $c(y_t,\psi)=-\log(y_t!)$. The conditional mean and variance of $Y_t$ given $H_t$ is $\lambda_t$. Using the GARMA $(p,q)$ model from equation (\ref{eta3}) and the canonical link function which is log for the Poisson family we write,
\begin{equation}log(\lambda_t)=\eta_t=\vec{x}'_{t}\svec{\beta}+\sum_{j=1}^{p}\phi_j \{g(y_{t-j})-\vec{x}'_{t-j}\svec{\beta}\}+\sum_{j=1}^{q}\theta_j \{g(y_{t-j})-\eta_{t-j}\},\label{3}\end{equation}
if the function $g$ is taken to be the log function, then for zero counts we define $y^{*}_{t-j}=\max(y_{t-j},c)$ where $0<c<1$ and
\begin{equation*}log(\lambda_t)=\eta_t=\vec{x}'_{t}\svec{\beta}+\sum_{j=1}^{p}\phi_j \{\log(y^{*}_{t-j})-\vec{x}'_{t-j}\svec{\beta}\}+\sum_{j=1}^{q}\theta_j \{\log(y^{*}_{t-j}/\lambda_{t-j})\}.\label{3}\end{equation*}
\subsubsection{Estimation of Model Parameters}
As in a standard GLM, the maximum likelihood estimate (MLE) of $\svec{\nu}=({\svec{\beta}},{\phi}_1,\ldots,{\phi}_p,{\theta}_1,\ldots,{\theta}_q)'$, are obtained by using an iterated weighted least squares algorithm. Since here the covariates $\vec{x}_t$ are stochastic in nature, the partial likelihood function ($\prod_{t=1}^{n}f(y_t|H_t)$) instead of the entire likelihood function is maximized.
An estimate of the conditional mean is given by, $\hat{\lambda}_t=\exp(\hat{\eta}_t)$, where \begin{equation*}\label{A2}
\hat{\eta}_{t}=\vec{x}'_{t}\hat{\svec{\beta}}+\sum_{j=1}^{p}\hat{\phi}_j \{\log(y^{*}_{t-j})-\vec{x}'_{t-j}\hat{\svec{\beta}}\}+\sum_{j=1}^{q}\hat{\theta}_j \{\log(y^{*}_{t-j}/\hat{\lambda}_{t-j})\},
\end{equation*}
$\hat{\svec{\nu}}$ is the MLE of $\svec{\nu}$. For the Poisson GARMA model, the conditional information matrix of the parameter estimates is given by $I=\lim_{n\rightarrow\infty}\frac{1}{n}\left[\sum_{t=1}^{n}\lambda_t \left(\frac{\delta\eta_t}{\delta\svec{\nu}}\right)\left(\frac{\delta\eta_t}{\delta\svec{\nu}}\right)'\right]^{-1}$.
\section{Predictive Likelihood}
Prediction of the value of an observation at a future time point is a fundamental problem in statistics, especially in the time series context. To be more precise, suppose we have observations at time points $t_1,\ldots,t_n$, denoted by $\vec{y}=(y_1,\ldots,y_n)'$ and we would like to predict or forecast (out-of-sample) the observation at time point $t_{n+m}, m=1,2,\ldots$. We assume that $(\vec{Y},Y_{n+m})$ has a joint probability density $f_\omega(\vec{y},y_{n+m})$ indexed by the unknown parameter $\omega$. Note in this prediction problem we have two unknown quantities, $y_{n+m}$, the unobserved value of $Y_{n+m}$ and the parameter, $\omega$. However, our primary aim is to find $Y_{n+m}$. So we treat $\omega$ as a nuisance parameter. \cite{10.2307/4615723} proposed several predictive functions for finding the future value $y_{n+m}$ given the observed sample $\vec{y}$.
In this article we choose the prediction function, say $LL_p$, from the likelihood viewpoint,
\begin{equation*}
{LL}_p(y_{n+m}|\vec{y})=\sup_\omega f_\omega(\vec{y},y_{n+m})=f(\vec{y},y_{n+m}|\hat{\omega}_{y_{n+m}}),
\end{equation*}
for inferring about the unknown $y_{n+m}$. In the above equation, the maximum likelihood estimate (MLE) of ${\omega}$ denoted by $\hat{\omega}_{y_{n+m}}$ is computed using the $n$ available observations $\vec{y}$ and the unobserved future count $y_{n+m}$.
Different ways of estimating the nuisance parameters lead to different predictive likelihoods.
For our problem we use the MLE method to estimate and eliminate the dependence on the nuisance parameter $\omega$. This particular form of the prediction function is known as the profile predictive likelihood (PL) function. \cite{10.2307/2335744}, \cite{10.2307/4615564}, \cite{hinkley1979} and \cite{10.2307/2287730}, suggested an alternative method for the elimination of the unknown parameter $\omega$ by using the principle of sufficiency. However, finding closed form sufficient statistic for the parameters is impossible given the complicated framework of the GARMA models and the correlated nature of the responses.
\subsection{PL for the Poisson Time Series}
A sample of size $n$ is observed from the Poisson GARMA $(p,q)$ model and denoted by $\vec{y}=(y_1,\ldots,y_n)'$. We start with the one step at a time prediction (out-of-sample forecasts) of counts. In the context of the Poisson GARMA time series model, the predictive likelihood function is
\begin{equation}
{LL}_p(y_{n+1}|H_{n+1})=\sup_{\svec{\nu}} f_{\svec{\nu}}(y_{n+1},H_{n+1})=\sup_{\svec{\nu}} \prod_{t=1}^{n+1}f_{\svec{\nu}}(y_t|H_t)=\frac{\exp(-\{\sum_{t=1}^{n+1}\hat{\lambda}_t\})\prod_{t=1}^{n+1}\hat{\lambda}_t^{y_t}}{\prod_{t=1}^{n+1}y_t!},
\end{equation}
where \begin{equation*}\hat{\lambda}_t=\exp(\hat{\eta}_t)=\exp(\vec{x}'_{t}\hat{\svec{\beta}}+\sum_{j=1}^{p}\hat{\phi}_j \{\log(y^{*}_{t-j})-\vec{x}'_{t-j}\hat{\svec{\beta}}\}+\sum_{j=1}^{q}\hat{\theta}_j \{\log(y^{*}_{t-j})-\hat{\eta}_{t-j}\}).\label{3}\end{equation*} is the MLE of $\lambda_t$ using the observed sample $\vec{y}$ and the future count $y_{n+1}$. Here, $H_{n+1}=\{x_{n+1},\ldots,x_1,y_{n},\ldots,$ $y_1,\lambda_{n},\ldots,\lambda_1\}$, is the available past information at time $n+1$. The estimated density of $Y_{n+1}$ given the observed time series is then,
\begin{equation}
\hat{p}(y_{n+1})=k(H_{n+1}){LL}_p(y_{n+1}|H_{n+1}),\label{densityest}
\end{equation}
where $k(\cdot)$ is the normalizing constant.
The predictor of $y_{n+1}$ is chosen to be the value of $y_{n+1}$ which maximizes $\hat{p}(y_{n+1})$, and denoted by $\hat{Y}_{n+1(PL)}$. The steps leading to the choice of $\hat{Y}_{n+1(PL)}$ are detailed below and later illustrated with an example:
\begin{enumerate}
\item At the start of the process we have the past information $H_{n+1}$. Our interest is to compute ${p}(y_{n+1})$, the actual density of $Y_{n+1}$ given the past information. However the density depends on the parameters $\lambda_t$ which are unknown. So we first compute the MLEs of the parameters and then use equation (\ref{densityest}) to compute an estimate of ${p}(y_{n+1})$.
\item To compute the MLEs of $\lambda_{t},\,t=1,\ldots,n+1$ we need $H_{n+1}$ and $y_{n+1}$. We have not yet observed $y_{n+1}$. So we start with the first possible value i.e., $ y_{n+1} =0$ and estimate the $\lambda_t$'s and calculate $\hat{p}(y_{n+1}=0)$.
\item We next set $ y_{n+1} = 1$ and re-estimate the parameters and find the corresponding normalized predictive likelihood value $\hat{p}(y_{n+1}=1)$.
\item The above step is repeated for $y_{n+1}=2,3,\ldots$ , each time re-estimating the parameters and computing $\hat{p}(y_{n+1}=i)$. If $\hat{p}(y_{n+1}=i)<1\times 10^{-6}$ for any $i$, then we ignore $y_{n+1}=i$.
\item At the end we have a set of $q$ (say) normalized predictive likelihoods of $y_{n+1}$, denoted by $ \hat{p}(y_{n+1}=0), \hat{p}(y_{n+1}=1), \ldots, \hat{p}(y_{n+1}=q-1)$.
If $\hat{p}(y_{n+1}=d)=\max\{\hat{p}(y_{n+1}=0), \hat{p}(y_{n+1}=1), \ldots, \hat{p}(y_{n+1}=q-1)\}$, we set $ \hat{Y}_{n+1(PL)} = d$.
\end{enumerate}
{\bf Example}: We explain the above steps of the algorithm with a simple example. A sample of size $100$ is drawn from a Poisson GARMA $(0,2)$ model, denoted by $\vec{y}=(y_1,\ldots,y_{100})'$ and the model equation is
\begin{eqnarray*}\label{}
&\log(\lambda_{t})& =0.2+0.01 t+0.4 \cos(2\pi t/12)+0.5 \sin(2\pi t/12)+0.5\cos(2\pi t/6)\\&&+0.5\sin(2\pi t/6)-0.5\log(y^{*}_{t-1}/\lambda_{t-1})+0.6\log(y^{*}_{t-2}/\lambda_{t-2}),
\end{eqnarray*} for $y_{t-j}^{*} = \max(y_{t-j}, 0.1),\,j=1,2$.
We apply the PL procedure as given above for predicting $Y_{101}$. Table \ref{example} shows the $q$ (19) possible values of $y_{101}$ and the corresponding density value. Note $\hat{p}(y_{101})<1\times 10^{-6}$ for $y_{101}>19$.
\begin{table}[h!]
\centering
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
$y_{101}$ & $\hat{p}(y_{101})$ & $y_{101}$ & $\hat{p}(y_{101})$ & $y_{101}$ & $\hat{p}(y_{101})$ & $y_{101}$ & $\hat{p}(y_{101})$ \\ \hline
0 & 0.715$\times 10^{-2}$ & 5 & 0.1754 & 10 & 0.170$\times 10^{-1}$ & 15 & 0.139$\times 10^{-3}$ \\ \hline
1 & 0.353$\times 10^{-1}$ & 6 & 0.1443 & 11 & 0.765$\times 10^{-2}$ & 16 & 0.429$\times 10^{-4}$ \\ \hline
2 & 0.873$\times 10^{-1}$ & 7 & 0.1018 & 12 & 0.315$\times 10^{-2}$ & 17 & 0.124$\times 10^{-4}$ \\ \hline
3 & 0.14378 & 8 & 0.629$\times 10^{-1}$ & 13 & 0.119$\times 10^{-2}$ & 18 & 0.342$\times 10^{-5}$ \\ \hline
4 & 0.1775 & 9 & 0.345$\times 10^{-1}$ & 14 & 0.422$\times 10^{-3}$ & 19 & 0.89$\times 10^{-6}$ \\ \hline
\end{tabular}
\caption{$y_{101}$ and corresponding $\hat{p}(y_{101})$ values}
\label{example}
\end{table}
The maximum value of $\hat{p}(y_{101})$ is 0.1775 corresponding to $y_{101}$ = 4. Thus, predicted value of $y_{101}$ is $ \hat{Y}_{101(PL)} = 4$.
The PL function can also be extended for m-step predictions of Poisson GARMA models.
The predictive likelihood function for $m$ step ahead forecasts is,
\begin{eqnarray}\label{mstep}
\nonumber {LL}_p(y_{n+m}|H_{n+m})&=&\sup_{\svec{\nu}} f_{\svec{\nu}}(H_{n+m},y_{n+m})=\sum_{y_{n+m-1}}\ldots\sum_{y_{n+1}}\sup_{\svec{\nu}} \prod_{t=1}^{n+m}f_{\svec{\nu}}(y_t|H_t)\\&=&\sum_{y_{n+m-1}}\ldots\sum_{y_{n+1}}\frac{\exp(-\sum_{t=1}^{n+m}\hat{\lambda}_t)\prod_{t=1}^{n+m}\hat{\lambda}_t^{y_t}}{\prod_{t=1}^{n+m}y_t!},
\end{eqnarray}
where the MLEs of $\lambda_t$ are found using the observed sample $\vec{y}$ and the past information $H_{n+m}$. The value of $y_{n+m}$ which maximizes the normalized $\hat{p}(y_{n+m})$ is chosen as the predictor of $y_{n+m}$ and denoted by $\hat{Y}_{n+m(PL)}$.
We note from the above forecasting equations that to predict a future count at time $n+m$, we need information on the counts, $y_t$ and also on the covariates $\vec{x}_t$ at time points $n+1,\ldots,n+m-1$. The covariates may be stochastic in nature, say in a disease data set we study the effect of time and also covariates like temperature and humidity on the disease counts. In these situations, separate time series models have to be fitted to the covariates data and used for obtaining forecasts of the covariates. These forecasted values of the covariates can then be used in the PL function to forecast $y_{n+m}$.
\subsection{Forecast Region}
In the last section we used the predictive likelihood to get a point forecast of $Y_{n+m}$ by using the data $Y_1,\ldots, Y_n$. Along with the point forecast it is of our interest also to identify a region in the sample space of $Y_{n+m}|H_{n+m}$ which in some sense will summarize the actual density $p(y_{n+m})$.
Such a forecasting region can be constructed in several ways.
We may suggest that the $(1-\alpha)$ predictive interval of $Y_{n+m}$ given by $[\hat{z}(\alpha/2),\hat{z}(1-\alpha/2)]$, where
$\hat{z}(\alpha)$ is the $\alpha$ th quantile of $p(y)$, is one such region.
However, since we are dealing with an asymmetric distribution here, it would be more prudent to use highest density regions (HDRs) instead of a forecasting region based on quantiles.
These regions are more flexible than those based on quantiles and are able to address the issues of asymmetry, skewness as well as multimodality in the forecast distributions.
The $(1-\alpha)100\%$ HDR denoted by $R(f_\alpha)$ is the region in the sample space of $Y_{n+m}$ such that (\cite{10.2307/2684423})
\begin{equation*}
R(f_\alpha)=p(y_{m+n})\geq f_\alpha,
\end{equation*}
where $f(\alpha)$ is the largest constant such that $Pr(Y_{n+m}\in R(f_\alpha))$ is at least $(1-\alpha)$.
In our computations of HDRs, we used the $\alpha$th sample quantile of $\hat{p}(y_{m+n})$ to estimate
$\hat{f}_\alpha$ and then obtained ${\hat{R}(\hat{f}_\alpha)}$ by choosing the values of $y_{n+m}$ for which $\hat{p}\geq \hat{f}_\alpha$.
{\bf Note}: that the sample space of $y_{n+m}$ is non negative and integer valued. Thus, $y_{n+m}$ can take only the integer values in the computed HDRs giving rise to coherent forecasting regions.
\subsection{Some large sample results}
In this section we discuss the consistent properties and the asymptotic distribution of the forecast estimator.
{\bf Proposition 1}: As $n\rightarrow\infty$, $\hat{p}(y_{n+m})\xrightarrow{P}p(y_{n+m})$.
Proof: We use Theorem 2.3.5 from \cite{sen1994large} which states
If $ T_n \xrightarrow{P} T $ and if $g(t)$ is uniformly continuous, then $g(T_n)\xrightarrow{P}g(T)$.
For our problem, $T=\svec{\nu}$ and $T_n=\hat{\svec{\nu}}$. Also $g(T_n)=\hat{p}(y_{n+m})$ and $g(T)={p}(y_{n+m})$.
The normalized predictive likelihood function $\hat{p}(y_{n+m})=k(H_{n+m}){LL}_p (y_{n+m}|H_{n+m})$ is uniformly continuous since
\begin{equation*}
\frac{d\hat{p}(y)}{d\hat{\svec{\nu}}}=\sum_{y_{n+m-1}}\ldots\sum_{y_{n+1}}\frac{\exp(-\sum_{t=1}^{n+m}\hat{\lambda}_t)\prod_{t=1}^{n+m}\hat{\lambda}_t^{y_t}}{\prod_{t=1}^{n+m}y_t!}\sum_{t=1}^{n+m}\Big(\frac{y_{t}}{\hat{\lambda}_{t}} - 1\Big)\frac{d\hat{\lambda}_{t}}{d\hat{\svec{\nu}}}
\end{equation*}
exists and is bounded.
Thus proved.
{\bf Proposition 2}: As $n\rightarrow\infty$,
\begin{equation*}
\sqrt{n-m}[\hat{p}(y_{m+n})-p(y_{m+n})]\xrightarrow{d}N(0,\nabla p^{T}(y_{n+m})I^{-1}(\svec{\nu})\nabla p(y_{n+m})).
\end{equation*}
Proof: We know that the ML estimator ($ \hat{\svec{\nu}} $) is asymptotically normal (\cite{10.2307/30045208}),
\begin{equation*}
\sqrt{n-m}[ \hat{\svec{\nu}} -\svec{\nu}]\xrightarrow{d}N(0, I^{-1}(\svec{\nu})).
\end{equation*}
Using the the first order approximation of a Taylor series,
\begin{equation*}
\hat{p}(y_{n+m}) \approx p(y_{n+m}) + \nabla p^{T}(y_{n+m}) (\hat{\svec{\nu}} - \svec{\nu}),
\end{equation*}
Rearranging the terms and multiplying both sides by $ \sqrt{n-m} $ we obtain,
\begin{equation*}
\sqrt{n-m}[\hat{p}(y_{n+m}) - p(y_{n+m})] = \nabla p^{T}(y_{n+m})\sqrt{n-m} (\hat{\svec{\nu}} - \svec{\nu}),
\end{equation*}
From Slutsky's theorem it follows,
\begin{equation*}
\sqrt{n-m}[\hat{p}(y_{n+m})-p(y_{n+m})]\xrightarrow{d}N(0,\nabla p^{T}(y_{n+m}) I^{-1}(\svec{\nu})\nabla p(y_{n+m}))
\end{equation*}
This concludes the proof.
{\bf Note}: Though in Propostion 2 we show that the large sample distribution of the forecast estimate is a Gaussian distribution, this fact has not been used anywhere in the computations. We have used the Poisson mass function for all the computations.
\section{Results}
In this section we illustrate the proposed forecasting technique using simulation studies and a real data set based on polio counts. Robustness properties of the PL forecasts are also studied.
\subsection{Simulations}
The performance of the predictive likelihood in forecasting GARMA $(p,q)$ models is evaluated using simulation studies for various values of $p$ and $q$. Along with point prediction, we also compute HDRs for the future counts.
Our simulation results mainly focus on one step at a time forecasts instead of $m$ step ahead forecasts. Note, for computing $m$ step ahead forecasts using equation (\ref{mstep}) complete enumeration of all the sums and products over all the possible projected paths from $n+1$ to $n+m-1$ is necessary which is impossible unless we truncate the sample space. We discuss one simulated example for 2 step ahead forecasting based on a truncated sample space.
Two different GARMA models with the following means were used in the simulations:
\begin{itemize}
\item {\bf Model 1}: GARMA $(5,0)$
\begin{eqnarray*}\label{}
&\log(\lambda_{t})& = \text{x}_{t}^{'}\svec{\beta}+\sum_{j=1}^{5}\phi_{j}\{\log(y^{*}_{t-j})-\text{x}_{t-j}^{'}\svec{\beta}\},
\end{eqnarray*}
where $\text{x}_{t} = [\begin{matrix}1& t& \cos(2\pi t/12)& \sin(2\pi t/12)& \cos(2\pi t/6)& \sin(2\pi t/6) \end{matrix}]^{'}$,\\ $\svec{\beta} = [\begin{matrix} 0.2&0.001 & 0.5& -0.5& 0.6& 0.7 \end{matrix}]^{'}$ and $\phi_{1} = 0.5 ,\phi_{2} = -0.6,\phi_{3} = 0.4,\phi_{4} = -0.6,\phi_{5} = 0.5$.
\item {\bf Model 2}: GARMA $(0,2)$ \begin{eqnarray*}\label{}
&\log(\lambda_{t})& =0.2+0.01 t+0.4 \cos(2\pi t/12)+0.5 \sin(2\pi t/12)+0.5\cos(2\pi t/6)\\&&+0.5\sin(2\pi t/6)-0.5\log(y^{*}_{t-1}/\lambda_{t-1})+0.6\log(y^{*}_{t-2}/\lambda_{t-2}),
\end{eqnarray*}
\end{itemize}
for $y_{t-j}^{*} = \max(y_{t-j}, 0.1),\,j=1,2$.
For both models, we chose three different values of $n=50,100,240$. The different values of $n$ enabled us to study the effect increasing $n$ on the profile likelihood predictions. Ten future counts (time horizon is 10 counts) were predicted one step at a time in each case. It is possible to increase the time horizon to more than 10, however those computations are not shown here.
We explain the simulation steps for a Poisson GARMA $(p,q)$ model in details below for a fixed value of $n$:
\begin{enumerate}
\item Using the chosen GARMA model and the fixed value of $n$ we simulated $N_0$ data sets. For all computations $N_0$ is 1000. Increasing $N_0$ further did not change the results.
\item The PL predictor of $y_{n+m}$ in the $i$th simulation is denoted by $\hat{Y}^{(i)}_{n+m(PL)}$ for $i=1,\ldots,N_0$. We also get $N_0$ HDRs for $y_{n+m}$. The minimum and maximum values of $y_{n+m}$ in the $i$th HDR is denoted as $HDR^{(i)}(min)$ and $HDR^{(i)}(max)$, respectively.
\item The $\text{median}\{\hat{Y}^{(i)}_{n+m(PL)},\,i=1(1)N_0\}$ is selected as the predicted value of $y_{n+m}$.
Selecting the median instead of the mean ensures a integer future count.
\item The median of $\{HDR^{(i)}(min),\,i=1(1)N_0\}$ is selected as the lowest value of $y_{n+m}$ in the HDR and denoted by $Ly_{n+m}$, while
median of $\{HDR^{(i)}(max),\,i=1(1)N_0\}$ is chosen as the highest value and denoted by $Uy_{n+m}$. The HDR is then defined as $\{Ly_{n+m},Uy_{n+m}\}$. Remember $y_{n+m}$ is discrete valued. For clarity, if $Ly_{n+m}=1$ and $Uy_{n+m}=3$, then the HDR is $\{1,2,3\}$.
Note, all the HDRs computed displayed unimodal behavior.
\end{enumerate}
The true and predicted values of the ten future counts and the 50 and 75$\%$ HDRs are reported in Figures 1-2 for simulation models 1 and 2, respectively. Table \ref{RMSE} reports the RMSE values for both simulation models. From the figures and the table it is noted that point prediction using the profile likelihood method improves as $n$ increases. This happens since the MLE, $\hat{\svec{\nu}}$, converges to the true $\svec{\nu}$ as $n$ increases, which in turn causes the normalized ${LL}_p$ to converge to the actual pdf of $Y_{n+m}$ (see Proposition 1). Also we note that the HDRs successfully capture all the true counts in both simulation models for $n=100,240$. For $n=50$, the $50$ and $75\%$ HDRs are unable to capture $y_{55}$, however the $95\%$ HDRs (not shown) are able to capture $y_{55}$.
\begin{figure}
\centering
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{50_true_data.eps}
\caption{Simulated data, $y_1,\ldots,y_{50}$}
\label{}
\end{subfigure}
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{50_hdr_50_75.eps}
\caption{Forecasting results for $y_{51},\ldots,y_{60}$}
\label{}
\end{subfigure}
\quad
\vfill
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{100_true_data.eps}
\caption{Simulated data, $y_1,\ldots,y_{100}$}
\label{}
\end{subfigure}
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{100_hdr_50_75.eps}
\caption{Forecasting results for $y_{101},\ldots,y_{110}$}
\label{}
\end{subfigure}
\quad
\vfill
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{250_true_data.eps}
\caption{Simulated data, $y_1,\ldots,y_{240}$}
\label{}
\end{subfigure}
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{250_hdr_50_75.eps}
\caption{Forecasting results for $y_{241},\ldots,y_{250}$}
\label{}
\end{subfigure}
\caption{Simulation and Forecasting results using the PL function for the GARMA $(5, 0)$ model. Note the HDRs of $y_{n+m}$ though shown as continuous intervals contain only integer values.}
\label{}
\end{figure}
\begin{figure}
\centering
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{sim2_50_true_data.eps}
\caption{Simulated data, $y_1,\ldots,y_{50}$}
\label{}
\end{subfigure}
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{sim2_50_hdr_50_75.eps}
\caption{Forecasting results for $y_{51},\ldots,y_{60}$}
\label{}
\end{subfigure}
\quad
\vfill
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{sim2_100_true_data.eps}
\caption{Simulated data, $y_1,\ldots,y_{100}$}
\label{}
\end{subfigure}
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{sim2_100_hdr_50_75.eps}
\caption{Forecasting results for $y_{101},\ldots,y_{110}$}
\label{}
\end{subfigure}
\quad
\vfill
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{sim2_250_true_data.eps}
\caption{Simulated data, $y_1,\ldots,y_{240}$}
\label{}
\end{subfigure}
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{sim2_250_hdr_50_75.eps}
\caption{Forecasting results for $y_{241},\ldots,y_{250}$}
\label{}
\end{subfigure}
\caption{Simulation and Forecasting results using the PL function for the GARMA $(0, 2)$ model. Note the HDRs of $y_{n+m}$ though shown as continuous intervals contain only integer values.}
\label{}
\end{figure}
\begin{table}[h!]
\centering
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline
Model & \multicolumn{3}{c|}{GARMA(0, 2)} & \multicolumn{3}{c|}{GARMA(5, 0)} \\ \hline
$n$ & 50 & 100 & 240 & 50 & 100 & 240 \\ \hline
RMSE & 3.24037 & 3.04959 & 0.89443 & 2.28035 & 2.19089 & 1.89737 \\ \hline
\end{tabular}
\caption{RMSE values for the two simulation scenarios, GARMA $(0,2)$ and GARMA $(5,0)$ for different values of $n$}
\label{RMSE}
\end{table}
We also assessed the effect of an empirical probability mass function (pmf) instead of the actual pmf on the HDR computations using a GARMA $(0,2)$ model. The comparisons of the empirical and exact pmfs for $n=50,100,240$ are shown in Figure 3. We note from Figure 3, as $n$ increases, $\hat{f}_\alpha\rightarrow f_\alpha$, which in turn causes ($\hat{R}(f_\alpha)\rightarrow {R}(f_\alpha)$), i.e., the estimated HDR ($\hat{R}(f_\alpha)$) to approach the true HDR.
\begin{figure}
\centering
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{50_exact_75.eps}
\caption{75\% HDR: Exact pmf of $Y_{51}$ }
\label{}
\end{subfigure}
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{50_emperical_75.eps}
\caption{75\% HDR: Empirical pmf of $Y_{51}$}
\label{}
\end{subfigure}
\quad
\vfill
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{100_exact_75.eps}
\caption{75\% HDR: Exact pmf of $Y_{101}$}
\label{}
\end{subfigure}
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{100_empirical_75.eps}
\caption{75\% HDR: Empirical pmf of $Y_{101}$}
\label{}
\end{subfigure}
\quad
\vfill
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{250_exact_75.eps}
\caption{75\% HDR: Exact pmf of $Y_{241}$}
\label{}
\end{subfigure}
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.13]{250_empirical_75.eps}
\caption{75\% HDR: Empirical pmf of $Y_{241}$}
\label{}
\end{subfigure}
\caption{Shapes of Exact and Empirical pmfs for different values of $n$ for GARMA $(0,2)$ model}
\label{}
\end{figure}
\subsection{Forecasting of Polio Data}
To illustrate the new forecasting method proposed we use a data set based on monthly cases of poliomyelitis cases reported to the U.S. Centers for Disease
Control for the years 1970 to 1982. This data has been analyzed before by \cite{10.2307/2336303} and \cite{10.2307/30045208}, but no forecasting results have been discussed.
\begin{table}[h!]
\centering
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline
& \multicolumn{3}{c|}{\begin{tabular}[c]{@{}l@{}}Parameter Estimates\\ \end{tabular}} & \multicolumn{3}{c|}{\begin{tabular}[c]{@{}l@{}}Standard Errors\\ \end{tabular}} \\ \hline
Intercept & \multicolumn{3}{c|}{0.409} & \multicolumn{3}{c|}{0.122} \\ \hline
cos(2pt/12) & \multicolumn{3}{c|}{0.143} & \multicolumn{3}{c|}{0.157} \\ \hline
sin(2pt/12) & \multicolumn{3}{c|}{-0.530} & \multicolumn{3}{c|}{0.146} \\ \hline
cos(2pt/6) & \multicolumn{3}{c|}{0.462} & \multicolumn{3}{c|}{0.121} \\ \hline
sin(2pt/6) & \multicolumn{3}{c|}{-0.021} & \multicolumn{3}{c|}{0.123} \\ \hline
MA(1) & \multicolumn{3}{c|}{0.273} & \multicolumn{3}{c|}{0.052} \\ \hline
MA(2) & \multicolumn{3}{c|}{0.242} & \multicolumn{3}{c|}{0.052} \\ \hline
Deviance & \multicolumn{6}{c|}{490.714} \\ \hline
\end{tabular}
\caption{Model estimates for Polio data based on the first 158 observations}
\label{Estimates and stderr}
\end{table}
We used the first 158 polio cases to fit a Poisson GARMA $(0,2)$ model and then forecasted the polio counts for years 1972 to 1982. The model fitting statistics along with the estimates and their standard errors are shown in Table \ref{Estimates and stderr}. Figure 4 shows the true counts, predicted counts using the profile likelihood estimation and the $50$ and $75\%$ HDRs. The RMSE value for the 10 forecasts is 1.1186.
\begin{figure}
\centering
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.135]{polio_true_data}
\caption{Polio data first 158 obervations}
\label{}
\end{subfigure}
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.135]{polio_hdr_new_ext_50_75}
\caption{Forecasting results for $y_{159},\ldots,y_{168}$}
\label{}
\end{subfigure}
\caption{Forecasting results using the PL function for the Polio data. Note the lower bounds of both HDR regions in Figure 4 (b) are zero. Also, the HDRs of $y_{n+m}$ though shown as continuous intervals, contain only integer values.}
\label{}
\end{figure}
\subsection{Two Step Forecasting using the PL function}
The predictive likelihood function for the two step prediction of the Poisson GARMA$(5,0)$ model is
\begin{eqnarray}\label{2step}
\nonumber {LL}_p(y_{n+2}|H_{n+2})&=&\sum_{y_{n+1}}\frac{\exp(-\sum_{t=1}^{n+2}\hat{\lambda}_t)\prod_{t=1}^{n+2}\hat{\lambda}_t^{y_t}}{\prod_{t=1}^{n+2}y_t!}. \end{eqnarray} We chose $n=100$.
For predicting $Y_{102}$ we computed MLEs of the model parameters based on the observed data and $q$ possible values of the tuplet $\{y_{101},y_{102}\}$. If $\hat{p}(y_{101},y_{102})<1\times 10^{-6}$, then we did not choose that tuplet. The MLEs were then used to find evaluate the normalized ${LL}_p(y_{102}|H_{102})$ for each $y_{102}$ by summing over all values of $y_{101}$.
The true and forecasted values of ($Y_{102}$) and the 50 and 75$\%$ HDRs are reported in Table \ref{twostep}.
\begin{table}[h!]
\centering
\begin{tabular}{|l|l|l|l|l|l|}
\hline
$Y_{102}$ & $\hat{Y}_{102(PL)}$ & {50$\%$ HDR} &{75$\%$ HDR} \\ \hline
0 & 0 &$\{0,1,2\} $ & $\{0,1,2,3,4,5\}$ \\ \hline
\end{tabular}
\caption{The two step out-of-sample prediction results}
\label{twostep}
\end{table}
\subsection{Robustness Study of the Profile Likelihood Based Prediction}
The PL prediction depends on the model being fitted to the data. In this section, we study the effect of model misspecification on the forecasting. Suppose a data set of size $100$ is drawn from a Poisson GARMA $(0,5)$ model given by,
\begin{eqnarray*}\label{}
&\log(\lambda_{t})& =0.2+0.01 t+0.4 \cos(2\pi t/12)+0.5 \sin(2\pi t/12)+0.5\cos(2\pi t/6)\\&&+0.5\sin(2\pi t/6)-0.5\log(y^{*}_{t-1}/\lambda_{t-1})+0.6\log(y^{*}_{t-2}/\lambda_{t-2})+0.01\log(y^{*}_{t-5}/\lambda_{t-5}).
\end{eqnarray*}
Note the MA coefficients are non zero at lags 1, 2 and 5. However, the coefficient at lag 5 is quite small, so it is easy to misspecify the model as a GARMA (0,2). The estimated GARMA $(0,2)$ model fitted to the data is,
\begin{eqnarray*}\label{}
&\log(\lambda_{t})& =0.2285+0.0102 t+0.3488 \cos(2\pi t/12)+0.4995 \sin(2\pi t/12)+0.5225\cos(2\pi t/6)\\&&+0.4371\sin(2\pi t/6)-0.4095\log(y^{*}_{t-1}/\lambda_{t-1})+0.4951\log(y^{*}_{t-2}/\lambda_{t-2}).
\end{eqnarray*}
We performed forecasting of $10$ future counts on the basis of the actual and the fitted models and recorded the respective RMSEs, $1.26491$ and $3.03315$. From Figure 5 we note that the forecasts based on the estimated model are quite close to the true values and also HDRs successfully captures all the true values except $y_{108}$. Thus, we may conclude on the basis of the example considered that the performance of the PL method in forecasting is not very sensitive to model misspecification.
\begin{figure}
\centering
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.135]{MA5_hdr_50_75.eps}
\caption{Forecasting results for $y_{101},\ldots,y_{110}$ based on the correct model GARMA $(0, 5)$}
\label{}
\end{subfigure}
\begin{subfigure}[b]{0.495\textwidth}
\centering
\includegraphics[scale=0.135]{MA2_hdr_50_75.eps}
\caption{Forecasting results for $y_{101},\ldots,y_{110}$ based on the incorrect model GARMA $(0, 2)$}
\label{}
\end{subfigure}
\caption{Robustness results for the PL forecasting method. Note the HDRs of $y_{n+m}$ shown contain only integer values.}
\label{}
\end{figure}
\subsection{Computations}
All computations have been done in Matlab. The GARMA toolbox of \cite{garma} has been used to estimate the model parameters. The time needed to obtain one simulation result for the one step forecast is 49 seconds while for the two step forecast is 404 seconds. The Matlab program for one step forecast using the PL function GARMA $(5,0)$ model is given in the supplementary material. Other programs are available from the authors on request.
\section{Concluding Remarks}
In this article we look at several Poisson GARMA time series models for different values of $p$ and $q$, and use PL functions to find a point forecast and a forecast region. The large sample properties of the estimators based on PL functions are studied. The new forecasting method proposed gives non negative discrete valued forecasts and forecasting regions coherent with the sample space of the count time series under consideration.
Very often in practical situations we note that the count data collected usually suffer from overdispersion. In such cases the negative binomial distribution instead of the Poisson distribution is used. One possible future extension of our work is to use the PL technique to forecast such overdispersed count time data.
\bibliographystyle{plainnat}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,160 |
Q: GET errors in ruby on rails. Controllers and actions. CRUD I'm working through the "Ruby on rails essential 3 training" on lynda.com. I'm at the point of creating forms and implementing CRUD. So far whenever I try to have rails initiate an action it can never find the definition.
To solve this problem I define the action within the controller and then create a GET within my routes.rb file. My instructor doesn't have to do this and his server starts just fine. I have a feeling I'm doing something wrong because my routes.rb file has far to many GET commands.
Please look at the following folders and let me know if you have an idea of why I have to make a GET every time I try a new action. I heard that when creating a Model there is supposed to be a GET created at the same time but that isn't happening and I'm not sure if I'm understanding that correctly. My subjects controller:
class SubjectsController < ApplicationController
def index
list
render('list')
end
# def index
# show
# render('show')
# end
def list
@subjects = Subject.order("subjects.position ASC")
end
def show
@subject = Subject.find(params[:id])
end
def new
@subject = Subject.new
end
def create
end
end
My new.html.erb file:
<%= link_to("<< Back to List", {:action => 'list'}, :class => 'back- link') %>
<div class="subject new">
<h2>Create Subject</h2>
<%= form_for(:subject, :url => {:action => 'create'}) do |f| %>
<table summary="Subject form fields">
<tr>
<th>Name</th>
<td><%= f.text_field(:name) %></td>
</tr>
<tr>
<th>Position</th>
<td><%= f.text_field(:position) %></td>
</tr>
<tr>
<th>Visible</th>
<td><%= f.text_field(:visible) %></td>
</tr>
</table>
<div class="form-buttons">
<%= submit_tag("Create Subject") %>
</div>
<% end %>
My config/routes.rb
Rails.application.routes.draw do
root :to=>"demo#index"
get 'demo/index'
get 'demo/hello'
get 'demo/other_hello'
get 'subjects/list'
get 'subjects/show'
get 'subjects/new'
get 'subjects/create'
Now having an issue with the Create portion of Crud when trying to create a test subject. Here is my SubjectsController.rb
class SubjectsController < ApplicationController
def index
list
render('list')
end
# def index
# show
# render('show')
# end
def list
@subject = Subject.order("subjects.position ASC")
end
def show
@subject = Subject.find(params[:id])
end
def new
@subject = Subject.new
end
def create
@subject = Subject.new(params[:subject])
if @subject.save
redirect_to(:action => 'list')
else
render('new')
end
end
end
A: Here's what your config/routes.rb should look like:
root 'subjects#index'
resources :subjects
get 'subjects/list' => 'subjects#list'
A: Yes, you do not need to specify GET for CRUD actions. You can use Rails Resource Routing. For example, your subjects controller actions can be called in routes.rb like so:
resources: subjects
This will automatically route all the generic CRUD actions, and look for them in your controller. You can see whether rails "picked up" your routing by typing rake routes in the command line. You can also limit the number of actions you want by passing resources: subjects, only:[:destroy]. This tells Rails to only use the subjects#destroy action. There is more to it. I suggest reading through this RailsGuide for more information
A: Normally, you have to create routes by yourself. They are not created with a model. Also, they are rather related to the controller than to the model.
I recommend to have a look at the official Rails routing guide here. Usually something like subjects/create is not a GET but a POST route. Your instructor might also have used a resources :subjects route instead of multiple GET/POST/etc. routes.
A: Slight variant of @OhHendrie's answer using only the resources dsl
root 'subjects#index'
resources :subjects do
get 'list', on: :collection
end
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,337 |
The Audioblog Presented by Audiobooks.com
Audiobook News
Top Member Downloads
Book Clubbin
Audiobooks.com News
Visit Audiobooks.com
Tag Archives: What You're Really Meant To Do
Great audiobooks for new grads
Posted on June 20, 2017 by Jemma Wolfe
It's that time of year again when a fresh crop of high school and university graduates are stepping out into the world, caps and diplomas in hand, wondering what on earth is next. Whether you're a new grad yourself, know one, or are feeling a little lost at any age, here are our top four picks for getting focused, figuring out adult life, and finding your passion. And if you like what you see, check out more great audiobooks for new grads.
Almost Adulting: All You Need to Know to Get It Together (Sort Of), by Arden Rose
In Almost Adulting—perfect for budding adults, failing adults, and eaters of microwave mug brownies—social media influencer and lifestyle vlogger Arden Rose tells you how to survive your future adulthood. Topics include:
– Making internet friends who are cool and not murderers
– Eating enough protein
– Assembling a somewhat acceptable adult wardrobe when you have zero dollars
– How sex is supposed to feel, but, like, actually though
By the end of the book—a mash-up of essays, lists, and artwork—you'll have learned not only how to dress yourself, how to travel alone, how to talk to strangers online, and how to date strangers (in PERSON!), but also how to pass as a real, functioning, appropriately socialized adult.
What You're Really Meant To Do: A Road Map for Reaching Your Unique Potential, by Robert Steven Kaplan
Harvard Business School's Robert Steven Kaplan, leadership expert and author of the highly successful book What to Ask the Person in the Mirror, regularly advises executives and students on how to tackle these questions. In this indispensable new audiobook, Kaplan shares a specific and actionable approach to defining your own success and reaching your potential. Drawing on his years of experience, Kaplan proposes an integrated plan for identifying and achieving your goals. He outlines specific steps and exercises to help you understand yourself more deeply, take control of your career, and build your capabilities in a way that fits your passions and aspirations.
The Opposite of Loneliness: Essays and Stories, by Marina Keegan
Marina Keegan's star was on the rise when she graduated magna cum laude from Yale in May 2012. She had a play that was to be produced at the New York International Fringe Festival and a job waiting for her at the New Yorker. Tragically, five days after graduation, Marina died in a car crash.
Even though she was just twenty-two when she died, Marina left behind a rich, expansive trove of prose that, like her title essay, captures the hope, uncertainty, and possibility of her generation. The Opposite of Loneliness is an assemblage of Marina's essays and stories that, like The Last Lecture, articulates the universal struggle that all of us face as we figure out what we aspire to be and how we can harness our talents to make an impact on the world.
Lean In: For Graduates
Expanded and updated exclusively for graduates just entering the workforce, this extraordinary edition of Lean In includes a letter to graduates from Sheryl Sandberg and six additional chapters from experts offering advice on finding and getting the most out of a first job; résumé writing; best interviewing practices; negotiating your salary; listening to your inner voice; owning who you are; and leaning in for millennial men.
This enhanced edition provides the entire text of the original book updated with more recent statistics and features a passionate letter from Sandberg encouraging graduates to find and commit to work they love. A combination of inspiration and practical advice, this new edition will speak directly to graduates and, like the original, will change lives.
Posted in We Recommend | Tagged adulting, Almost Adulting, Arden Rose, audiobooks, graduation, Lean In, marina keegan, Robert Steven Kaplan, Sheryl Sandberg, The Opposite of Loneliness, What You're Really Meant To Do
© 2022 Audiobooks.com. All rights reserved. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,465 |
ClassifiedsPhotosAboutContactAdvertise
The Wahkiakum County Eagle - Established as The Skamokawa Eagle in 1891
Open Public Meetings
Wahkiakum People
By Diana Zimmerman
On the refuge: White-tail numbers are expanding
Though a scenic through way along the Columbia River may never be recovered, what seemed to be a setback at the Julia Butler Hansen Refuge for Columbian White-tailed Deer a few years ago has led to positive outcomes for salmon and waterfowl habitat, all without an adverse affect on deer population.
"I think it was 2011 when we first noticed that Steamboat Slough (dike) was washing out," Paul Meyers, a wildlife biologist for the U.S. Fish and Wildlife Service, who has been at JBH for 10 years, said recently. "It took a long time to sort of get to a solution for it, because it was during the sequester and money was tight. Bonneville Power Administration came in and said we can build a setback levee to get the salmon restoration credits that they are trying to get throughout the lower Columbia."
The U.S. Army Corps of Engineers built a setback levee and created channels for fish habitat before breaching the dike along Steamboat Slough Road in 2014. The breech severed a public through-road along the river and sloughs, and the refuge lost 70 acres of deer habitat to the project, but the good news is that it isn't hurting their numbers.
"That has been a real successful project," Meyers said of the new salmon habitat. "BPA has been doing some monitoring of fish in that area, and there is a lot of salmon coming in. In addition it's created a lot of waterfowl habitat and it's created a lot of swallow habitat.
"It's a really productive area, actually. If you go down there, there is tons of wildlife in that area. Deer can use it when the tide goes out. They obviously don't use it as much as they used to, because it used to be dry. But they do go in there. We've seen deer in there foraging when the tide goes out."
"About 80 percent of what we do here is deer and that is sort of the primary purpose of the refuge, but we also manage for other species," Meyers said. "Waterfowl is always a big one. This is always a big winter waterfowl place. Other species that we see may be of concern. There is a nesting colony of white pelicans nesting on Miller Sands now which showed up about five years ago. That is a species of interest that we spend some time on, trying to monitor and doing what we can to manage those."
Prior to the breach, USFWS was unsure of the outcome or how to move forward, so they decided to move as many deer as they could to another location.
"When you remove deer from an area where there are deer, they tend to rebound rather quickly," Meyers said. "I think there were 90 deer on the refuge when we did this, and we removed almost half that number, so we were down to about 50 deer and within about three years it was back to 100 deer."
"That's resulted in a very nice population of deer at Ridgefield," Meyers said. "That's been an additional secure sub-population which counts toward recovery of the population. So that was super successful as well. We don't have the final count, but I think it's safe to say there are over 200-250 deer down in Ridgefield right now, which is pretty good. It's about 5,000 acres. So it is a lot bigger than this area. It can support more deer just because of its size."
The fish and wildlife service manages the refuge for about 125 deer, according to Meyers, so 100 deer is pretty good.
"It puts us at about 25 deer per square mile, which turns out to be similar to the density of deer at Ridgefield.
Curiously, there are more than 200 white-tailed deer on Tenasillahe Island, formerly the site of a dairy.
"The density on Tenasillahe is incredible," Meyers said. "It's probably some of the highest density of white-tailed deer in the nation. It's probably 50-60 deer per square mile."
Numbers have been increasing throughout the Columbian White-tailed deer habitat, and according to Meyers, the endangered species was down-listed to threatened three years ago.
Each of the areas that comprise white tailed deer habitat have different management prescriptions, Meyers said. Recovery is a slow process.
Still he sees progress.
"The population is about three times as big as it was when the deer were listed," he said. "The distribution is about three times as big as what it was in 1972."
At one time, the deer were concentrated in the valleys along the Columbia and Willamette Rivers.
"The Willamette Valley used to be a mixed prairie, an oak savanna: a really good deer habitat," Meyers said, "200 years ago there were deer everywhere."
After the area was cleared for agriculture, they disappeared. Except for Douglas County in Oregon, where white-tailed deer population climbed enough for them to be de-listed, the deer have not returned to the valley.
Along the lower Columbia in 1972, when the refuge was formed, the population was limited to Puget Island, Tenasillahe Island, Westport and the what was formerly known as Skamokawa Island, where the refuge is today.
"Now they are all the way down to Ridgefield, Vancouver Lake, Sauvie Island, and Shillapoo," Meyers said. "That's all the result of translocations, or physically picking up deer and putting them into these areas."
"Even though it looks like we've really increased the population from an overall big picture sense, it's still a pretty small area that they've recovered in," Meyers said. "But there are about 1,200 deer now. We started out in the 300-400 range. It's been a long haul.
"You wouldn't think a deer would be so hard to de-list, but it's not so much biology as it is social, political issues, It's hard to convince people that moving an endangered species around is a good idea."
They have a lot to tackle from a biological perspective, in order to increase the population. As stated earlier, each section has its own management prescription. At JBH, one of their prescriptions is to plant trees.
JBH had been forested at one time, but like the Willamette Valley, it was cleared for agriculture.
"There a lot of big wide open areas," Meyers said. "Deer are fairly risk averse. They don't like to be out in the open. They don't usually like to get more than a hundred meters from some area of cover that they can dash back to. So when you reduce the amount of cover there is, you're really reducing the likelihood that they are going to be comfortable in that area. There is a lot of exceptions, but in general that's true."
Fish and wildlife have set about planting trees. But there are always obstacles of one kind or another. One such obstacle is universal. The budget.
"The only areas where there are legacy forests are down by Skamokawa and in the center section," Meyers said. "All these trees have been planted in the last 20 to 30 years. We continue that. We try to get in as many as we can afford every year, but it is a long, slow process. The original thought, I think, when fish and wildlife service took over management of this area was to remove all the agriculture and let this area come back naturally."
Unfortunately, an invasive species ruined that plan.
"Reed canary grass is about the worst," Meyers said. "It's a grass that thrives really well in wet soils. It was brought purposely to the U.S. for cattle grazing in wet areas. Cattle can do pretty well on it, but they have a different digestive system than deer do. They can eat it when deer can't. Deer can only eat it when it's really young."
"Reed canary grass forms these huge dense mats and nothing can grow in there," Meyers said. "It takes a lot of work to grow trees here, but once they shade out the reed canary grass you have the opposite situation. We plant a lot of trees and a lot of them don't make it because the reed canary grass gets so high they just get shaded out."
"It's a slow process," Meyers said. "We plant trees and sometimes we have to go back to those lots and plant some more."
"It's very hard to get rid of," Meyers said.
That's one reason they graze at the refuge. The cattle knock down the grass, but as soon as they stop grazing the grass takes over again. It's got them considering other options.
There is another invasive species that affects the deer population in a more direct manner. Coyotes.
"I've heard different stories about when coyotes first came here," Meyers said. "They never made it past the Cascades until the wolves were gone. Then coyotes started showing up. Coyotes can do a lot of damage. They can create a lot of fawn mortality. That's one of the issues we deal with here."
"Back in the 80s there was a spike in the population of deer after this became a refuge; you no longer had agriculture on here and you just had a ton of stuff growing here. You also had a parvovirus outbreak in coyotes and so there was really low predation and a tremendous food supply. We peaked out at 500 animals. Which was unsustainable and crazy dense. As expected that started to crash and it crashed pretty hard, and now we're back up at a more sustainable level."
They've been seeing a lot of coyotes this year, according to Meyers, and they will be watching fawn survival.
"It goes in cycles," Meyers said. "All populations do this. The deer population has been on an upcycle. We've been really good for the past five six years or so. So I don't know. We'll see how that goes."
Most of the growth in population is mostly from the fact that we are getting more fawns surviving than adults dying, he noted.
"In general, this population, and I mean the whole thing, has fairly high mortality rates," Meyers said. "We're looking at 20 percent a year for does, and 40 percent for bucks. So you're looking on average 25-30 percent mortality per year for adults. That's a lot of deer dying."
"They don't have a real long life span," he added. "There are some deer that will live to be 12 or even up to 20 years old. But most of them die after five or six years. It's various things. Some of them are preyed upon, some are not healthy to begin with. There are some diseases out there that will get them as well. Vehicle strikes are a big one."
"The point is, with that high of an adult mortality, you have to have a pretty high fawn survival rate to offset that. So when you have a lot of fawn predation, that is what can set you back," Meyers said.
Management isn't just about biology or about how humans affect deer population, it's about how the deer affect the human population, socially and politically.
"When you look at the places where we have moved deer to," Meyers said, "we have had to work with all of the landowners and state agencies. We can't just pick deer up and move them anywhere we want. If we did, I'd move them to Vancouver, because they do great in the cities. But we can't do that, because there are effects on the social environment.
"Around the country, there are really good examples of urban deer populations," Meyers explained. "There are little greenways where they can survive and probably do quite well. But once you do that, they probably aren't going to stay there. They'll go into these areas and find gardens, so you can't in good conscience create a situation like that."
"So every time we want to create a new sub-population it takes years because we have to figure out how to do that without affecting the social environment," Meyers said.
After explaining the mission at JBH, Meyers' thoughts returned to the changes resulting from the setback levee and subsequent breach of the dike.
"The take home message is that the BPA project was a win-win situation," Meyers said. "BPA got some really good salmon habitat. That area is pretty darn productive even though it's no longer deer habitat. And we were able to establish a new and very successful sub-population at Ridgefield."
Sea lion follows high water to Grays River
Local teen, her family deal with cancer
High water closes SR 4 west of Grays River
Local woman recounts experience with covid
Flooding in the Grays River Valley
Sea lion follows high...Diana Zimmerman
Time to get the hip wa...Kay Chamberlain
Restaurants work to se...Andrew Weiler
Sheriff's Report, Janu...
Corporations say we're...
The Wahkiakum County Eagle
Cathlamet, WA 98612
© 2021 The Wahkiakum County Eagle Inc. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,880 |
\section{Gaussian states and Gaussian maps}\label{secdef}
\paragraph*{Gaussian states and Gaussian maps.}
Given an $n$-mode CV system, Gaussian states $\rho$ are defined as those having a Gaussian characteristic function in phase space \cite{adesso2007,ournewreview,paris2005}. These states are fully characterized by the first and second statistical moments of their quadrature vector $\hat{O}=\{\hat{q}_1,\hat{p}_1,\dots,\hat{q}_n,\hat{p}_n\}$, where $\hat{q}_j$ and $\hat{p}_k$ are canonically conjugate coordinates satisfying $[\hat{q}_j,\hat{p}_k]=\mbox{$\frac{i}{2}$}\delta_{jk}$ (in natural units, $\hslash=1$). The first moment vector $D=\langle\hat{O}\rangle$ is also called the displacement vector, while the second moments ${(\sigma_n)}_{jk}=\frac12\langle\{\hat O_j, \hat O_k\}_+\rangle$ form the covariance matrix $\sigma_n$. All physical states must satisfy the Robertson-Schr\"{o}dinger uncertainty relation, $\sigma_n\geq\mbox{$\frac{i}{2}$}\Omega_n$, where $\Omega_n = {{\ 0 \ \ 1} \choose {-1 \ 0}}^{\oplus n}$ is the $n$-mode symplectic matrix \cite{Simon94}.
Quantum channels that preserve Gaussianity of their inputs are known as Gaussian maps. A Gaussian map acting on $n$-mode Gaussian states is represented by a pair of $2n \times 2n$ matrices $(X,Y)$, with $Y$ symmetric, acting on the displacement vector $D$ and the covariance matrix $\sigma_n$ as follows \cite{nogo1,nogo2,nogo3,torre2015,Lindblad2002,heinosaari2010},
\begin{equation}
D \ \ \rightarrow \ \ D'=XD\,, \qquad \sigma_n \ \ \rightarrow \ \ \sigma'_n=X\sigma_n X^T+Y\,. \label{xsigy}
\end{equation}
A Gaussian map described by the pair $(X,Y)$ is CP if and only if the following well-known inequality is fulfilled \cite{torre2015,Lindblad2002,heinosaari2010,DePalma2015}
\begin{equation}\label{eq:cp}
Y-\mbox{$\frac{i}{2}$}\Omega_n+\mbox{$\frac{i}{2}$}X\Omega_nX^T\geq0~.
\end{equation}
This inequality can be obtained from the Stinespring dilation theorem \cite{Stinespring1955}, i.e.~considering the Gaussian map as the result of a Gaussian unitary evolution acting on system and environment, initialized in an uncorrelated $(n+m)$-mode Gaussian state, followed by partial trace over the $m$ environment modes, $\sigma_n \rightarrow \sigma'_n = {\rm Tr}_E \left[S ( \sigma_n \oplus \sigma_m^E ) S^T\right]$; here one uses the fact that a Gaussian unitary is represented by a symplectic transformation $S \in \text{Sp}(2(n+m),\mathbb{R})$ (i.e., one that preserves the symplectic matrix $\Omega$) acting by congruence on covariance matrices~\cite{ournewreview}.
\paragraph*{$k$-positivity of Gaussian maps.}
We now introduce a notion of $k$-positivity for Gaussian maps with Gaussian inputs, inspired by the hierarchy of $k$-positivity for finite-dimensional channels arising from Choi's theorem \cite{Choi1975}. We define a Gaussian map acting on $n$-mode Gaussian inputs as $k$-positive ($k$P) if its extension on $k$ additional modes is positive, i.e.~if, for all $(n+k)$-mode Gaussian states described by covariance matrices $\sigma_{n+k}\geq \frac{i}{2}\Omega_{n+k}$, it holds
\begin{equation}\label{eq:kpos}
(X\oplus\mathds{1}_k)\sigma_{n+k}(X\oplus\mathds{1}_k)^T+Y\oplus\mathbb{0}_k\geq \mbox{$\frac{i}{2}$}\Omega_{n+k}~.
\end{equation}
Interestingly, we prove in the Appendix \cite{epaps} that a Gaussian map with Gaussian inputs is CP if and only if it is $k$P with any $k \geq 1$. Precisely, we establish the following result.
\begin{theorem}\label{thm1}
For any $n$, the CP condition (\ref{eq:cp}) is equivalent to the $k$P condition (\ref{eq:kpos}) with $k=1$.
\end{theorem}
This means that, in the Gaussian scenario (unlike the general finite-dimensional case \cite{notefoot}), one has a very simple hierarchy of $k$-positivity, consisting of only three classes: completely positive (CP, $k=1$), positive (P, $k=0$) and not positive (NP) Gaussian maps.
We can derive a simple (and, to our knowledge, original) condition to distinguish between the latter two classes, in terms of the pair $(X,Y)$. Noting that for (\ref{eq:kpos}) to hold it suffices to check its validity on pure Gaussian states, whose covariance matrix can always be written as $\sigma=\frac12 SS^T$ with $S$ a symplectic transformation, we find that a Gaussian map with Gaussian inputs is positive ($k=0$) if and only if
\begin{equation}\label{eq:p}
\quad \mbox{$\frac{1}{2}$}XSS^TX^T+Y-\mbox{$\frac{i}{2}$}\Omega_n\geq0\,, \quad \forall~S\in \text{Sp}(2n,\mathbb{R})~.
\end{equation}
Conditions (\ref{eq:cp}) and (\ref{eq:p}) allow one to fully classify the positivity properties of any $(n \rightarrow n)$-mode Gaussian map described by the pair $(X,Y)$ acting on Gaussian inputs. The conditions can be easily generalized to $(n \rightarrow m)$-mode Gaussian maps.
\paragraph*{Hierarchy of Gaussian non-Markovianity.}
Gaussian processes which are continuous in time are represented by a pair of time-dependent matrices $(X_t,Y_t)$ acting as in (\ref{xsigy}). Since we are interested in the divisibility properties of these maps, we can follow the approach of \cite{torre2015} and study the positivity of
the intermediate map $(X_\tau(t),Y_\tau(t))$ acting on the evolving system between times $t$ and $t+\tau$ and affecting the covariance matrix as usual, $\sigma(t)\rightarrow\sigma(t+\tau)=X_\tau(t)\sigma(t) X_\tau^T(t)+Y_\tau(t)$, with \cite{torre2015}
\begin{equation}
X_\tau(t)=X_{t+\tau}X^{-1}_t~,\label{eq:intermediateXY} \quad
Y_\tau(t)=Y_{t+\tau}-X_\tau(t)Y_tX_\tau^T(t)~.
\end{equation}
Our aim is now to provide a complete (non-)\!\!~Markovianity hierarchy of Gaussian maps.
We first recall that imposing complete positivity of the intermediate map for all $t,\tau>0$, one obtains the condition for a Markovian evolution as in \cite{torre2015},
\begin{equation}
\mbox{$\frac{i}{2}$}X_\tau(t)\Omega X_\tau^T(t)+Y_\tau(t)-\mbox{$\frac{i}{2}$}\Omega\geq 0~.\label{cpco}
\end{equation}
Any Gaussian map not complying with condition (\ref{cpco}) at some intermediate times is non-Markovian \cite{torre2015}.
We can now add an extra layer to such a dichotomic characterization. Namely, if not all intermediate maps are CP, i.e.~if for some times condition (\ref{cpco}) is violated, but the positivity condition
\begin{equation}
\mbox{$\frac{1}{2}$}X_\tau(t)SS^TX_\tau^T(t)+Y_\tau(t)- \mbox{$\frac{i}{2}$}\Omega\geq 0\,, \quad \forall~S\in \text{Sp}(2n,\mathbb{R})~.\label{pco}
\end{equation}
holds for all the maps, then the evolution is said to be \emph{weakly} non-Markovian. Finally, if there is at least one intermediate map violating (\ref{pco}), the process is \emph{strongly} non-Markovian.
It is worth noting that, to check CP- (respectively~P-) divisibility of the map $(X_t,Y_t)$, it suffices to verify that inequality (\ref{cpco}) [resp.~(\ref{pco})] holds in the limit of small $\tau$, since the composition of an arbitrary number of intermediate CP (P) maps is CP (P).
\paragraph*{Complete classification of one-mode Gaussian maps.}
In what follows, we focus on one-mode quantum Gaussian processes. From the global map $(X_t,Y_t)$, we can construct, thanks to (\ref{eq:intermediateXY}), the intermediate maps given by the pairs of $2\times2$ matrices $(X_\tau(t),Y_\tau(t))$. In the limit of small $\tau$, $X_\tau(t)$ and $Y_\tau(t)$ are close to the identity and to the null matrix respectively. Expanding these matrices up to first order in $\tau$ we get
\begin{equation}
X_\tau(t)=\left(1+\epsilon_t\tau\right)~\mathds{1}+\tau~{\cal X}(t)+o(\tau^2), \quad Y_\tau(t) = \tau~{\cal Y}(t)+o(\tau^2),\label{Xseries}
\end{equation}
where ${\cal X}(t)$ and ${\cal Y}(t)$ are arbitrary real matrices, with ${\cal Y}(t)$ being symmetric.
The following two Theorems (proofs in the Appendix \cite{epaps}) then completely characterize the degree of Gaussian (non-)\!\!~Markovianity of any one-mode Gaussian map given by $(X_t,Y_t)$, in terms of the three real parameters
\begin{eqnarray}
\epsilon_t&\equiv& \mbox{$\frac{{d}~}{{d}t}$}\ln\left(\sqrt{|\det X_t|}\right)~,\label{eq:eps}\\
\delta_t&\equiv&\left(\det X_t\right)^2\det \left( \mbox{$\frac{{d}~}{{d}t}$}\left(X^{-1}_tY_tX^{-T}_t\right)\right)~,\label{eq:del}\\
\kappa_t&\equiv&\mbox{$\frac{{d}~}{{d}t}$}\mbox{tr}~Y_t- 2~\mbox{tr}\left(Y_t\mbox{$\frac{{d}~}{{d}t}$}\ln|X_t|\right)~.\label{eq:trace}
\end{eqnarray}
\begin{theorem}\label{propom}
A one-mode Gaussian process given by $(X_t,Y_t)$ is CP-divisible if, for all $t>0$, it holds:
$\delta_t \geq \epsilon_t^2$ and $\kappa_t\geq 0$.
\end{theorem}
\begin{theorem}\label{propok}
A one-mode Gaussian process given by $(X_t,Y_t)$ is divisible into positive intermediate maps (P-divisible) if, for all $t>0$, it holds:
$ \delta_t \geq \mbox{$\frac14$} {(|\epsilon_t|-\epsilon_t)^2}$ and $\kappa_t \geq 0$.
\end{theorem}
The Gaussian processes for which Theorem~\ref{propom} is satisfied are Markovian. Those for which Theorem~\ref{propok} is satisfied while Theorem~\ref{propom} is not are weakly non-Markovian. Those for which Theorem~\ref{propok} is not satisfied are strongly non-Markovian.
Let us now define
\begin{equation}\label{eq:mudef}
\mu_t \equiv \left\{ \begin{array}{r@{\quad}cr}
\mathrm{sgn}(\kappa_t)\sqrt{\delta_t}~,\quad\mbox{for}~~\delta_t\geq0\\
-\sqrt{|\delta_t|}~,\quad\mbox{for}~~\delta_t<0
\end{array}\right.~.
\end{equation}
Due to Theorems \ref{propom} and \ref{propok}, for a one-mode Gaussian process we can then distinguish three regions in the space of parameters $\epsilon$ and $\mu$ as shown in Fig.~\ref{fi2}, which correspond to the intermediate map being respectively CP, P, and NP:
\begin{equation}\label{eq:regions}\left.
\begin{array}{llll}
\Upsilon_{\mbox{\scriptsize CP}}&\equiv&\{(\epsilon,\mu)~|~\mu\geq|\epsilon|\}, & \hbox{} \\
\Upsilon_{\mbox{\scriptsize P}}&\equiv&\{(\epsilon,\mu)~|~2\mu\geq|\epsilon|-\epsilon\}, & \hbox{} \\
\Upsilon_{\mbox{\scriptsize NP}}&\equiv&\mathbb{R}^2\backslash\Upsilon_P. & \hbox{}
\end{array}
\right.
\end{equation}
A similar diagram can be found e.g.~in \cite{Schaefer2013,Giovannetti2014,DePalma2015}. However, the parameters there characterize global quantum channels, so regions analogous to $\Upsilon_{\mbox{\scriptsize P}\backslash \mbox{\scriptsize CP}}\equiv\Upsilon_{\mbox{\scriptsize P}}\backslash\Upsilon_{\mbox{\scriptsize CP}}$ and $\Upsilon_{\mbox{\scriptsize NP}}$ are denoted as non-physical. Here, since the diagram is built for intermediate maps of a globally CP process, which by themselves do not need to be CP, these regions are permitted.
We can in fact fully classify the Gaussian (non-)\!\!~Markovianity degree of any one-mode Gaussian process by studying the paths $\Gamma_t\equiv\{(\epsilon_s,\mu_s)\}_{s=0}^t$ defined by its intermediate maps on the $(\epsilon,\mu)$ diagram of Fig.~\ref{fi2}. If an evolution is Markovian then the trajectory will be confined at all times in the $\Upsilon_{\mbox{\scriptsize CP}}$ region, $\Gamma_t~\in~\Upsilon_{\mbox{\scriptsize CP}}\quad\forall~t>0$. If at some times the trajectory trespasses in the $\Upsilon_{\mbox{\scriptsize P}\backslash\mbox{\scriptsize CP}}$ region but never trespasses in the $\Upsilon_{\mbox{\scriptsize NP}}$ one, i.e.~if $\Gamma_t~\in~\Upsilon_{\mbox{\scriptsize P}}\quad\forall~t>0$ and $\exists~s : (\epsilon_s, \mu_s) \not\in \Upsilon_{\mbox{\scriptsize CP}}$, then the evolution is weakly non-Markovian. If at some times the trajectory crosses into the $\Upsilon_{\mbox{\scriptsize NP}}$ region, i.e.~$\exists~s : (\epsilon_s, \mu_s) \not\in \Upsilon_{\mbox{\scriptsize P}}$, then the evolution is strongly non-Markovian.
\paragraph*{Phase-insensitive maps: Allowed trajectories and examples.}
We now analyze in more detail the physical constraints imposed on processes described by CP maps $(X_t,Y_t)$, transforming Gaussian states from an initial $t=0$ to a later time $t$.
For ease of illustration, we will focus on the special case of phase-insensitive maps, which encompass the most physically relevant bosonic processes, such as quantum Brownian motion and amplitude damping \cite{Petruccione,schlosshauer,Vasile2011,Eisert2015,guarni2016,Souza2015,torre2015}. These have intermediate maps of the form $X_\tau(t) = \left(1+\epsilon_t\tau\right)~\mathds{1}$, $Y_\tau(t)=\mu_t~\tau~\mathds{1}$, with $\mu_t\equiv\mbox{sgn}(\kappa_t)\sqrt{\delta_t}$, obtained by setting ${\cal X}(t)=\mathbb{0}$ and ${\cal Y}(t) = \mu_t \mathds{1}$ in (\ref{Xseries}).
Applying the composition law for Gaussian maps,
it is easy to show that the global map from $t=0$ to $t=N\tau$, such that $\lim_{N\to\infty}\lim_{\tau\to0}N\tau=t>0$, is:
\begin{equation}
X_t = e^{\int_0^t\epsilon_s ds}~\mathds{1}, \quad Y_t=\mbox{$\Big(e^{2\int_0^t\epsilon_s ds}\int_0^t\mu_r e^{-2\int_0^r\epsilon_s ds}dr\Big) \mathds{1}$}\,.\label{XYt}
\end{equation}
\begin{figure}
\center
\vspace*{-.3cm}
\includegraphics[width=7.5cm]{qbmtrajnodamp.pdf}
\caption{Pictorial diagram of parameters $(\epsilon,\mu)$ characterizing one-mode Gaussian intermediate maps. The diagonal striped pattern corresponds to the P- but not CP-divisible region $\Upsilon_{\mbox{\scriptsize P}\backslash\mbox{\scriptsize CP}}$. The crosshatch pattern identifies the CP-divisible region $\Upsilon_{\mbox{\scriptsize CP}}$. The white region corresponds to $\Upsilon_{\mbox{\scriptsize NP}}$. A path on the diagram denotes a process with parameters changed continuously in time. The solid black path represents a quantum Brownian motion process as described in the text.
}
\label{fi2}
\end{figure}
A paradigmatic and widely studied example (see e.g.~\cite{Petruccione,schlosshauer} and references therein) is quantum Brownian motion. With a secular and weak-coupling approximation, the master equation is given by: $
\dot{\rho}_t=\frac{\Delta_t+\gamma_t}{2}[2\hat a\rho_t \hat a^\dagger-\{\hat a^\dagger \hat a,\rho_t\}_+]+\frac{\Delta_t-\gamma_t}{2}[2\hat a^\dagger\rho_t \hat a-\{\hat a \hat a^\dagger,\rho_t\}_+]$, where $\hat{a}, \hat{a}^\dagger$ are the ladder operators satisfying $[\hat{a},\hat{a}^\dagger]=1$, while
$\Delta_t$ and $\gamma_t$ are respectively the diffusion and damping coefficients, which depend on the spectral density of the bath.
The evolved covariance matrix of a one-mode Gaussian state undergoing this dynamics is:
$ \sigma(t) = \mbox{$\big(e^{-\int_0^t\gamma_s ds}\mathds{1}\big)\,\sigma(0)\,\big(e^{-\int_0^t\gamma_s ds}\mathds{1}\big)$}
+ \mbox{$e^{-2\int_0^t\gamma_s ds}\int_0^te^{2\int_0^s\gamma_r dr}\Delta_s ds~\mathds{1}$}$,
which corresponds to the map $(X_t,Y_t)$ given by (\ref{XYt}) with the substitutions $\epsilon_t\rightarrow-\gamma_t$, $\mu_t\rightarrow\Delta_t$. A trajectory on the $(\epsilon,\mu)$ plane, for a system with characteristic frequency $\omega_0$ and a zero-temperature bath with Ohmic spectral density $J(\omega)=\omega e^{-\omega/\omega_c}$ and cut-off frequency $\omega_c=\omega_0/2$, is depicted in Fig.~\ref{fi2}.
More generally, to have a physical evolution from a composition of infinitesimal phase-insensitive maps, we must impose the CP condition (\ref{eq:cp}) on the global map $(X_t,Y_t)$ given by (\ref{XYt}). The eigenvalues of the lhs of (\ref{eq:cp}) are in this case:
$\Lambda_\pm=\mbox{$\pm\mbox{$\frac{1}{2}$}+e^{2\int_0^t\epsilon_s ds}\left(\mp\mbox{$\frac{1}{2}$}+\int_0^te^{-2\int_0^r\epsilon_s ds}\mu_r dr\right)$}$.
The conditions $\Lambda_\pm\geq0$ can be rewritten as (see Appendix \cite{epaps})
\begin{equation}
\mbox{$ \int_0^te^{-2\int_0^s\epsilon_s ds}\left(\mu_r\pm\epsilon_r\right)dr\geq0,~\quad\forall~t>0$}~.\label{Lambda222}
\end{equation}
As expected, these conditions are weaker than the condition for CP-divisibility, allowing the trajectories in the diagram of Fig.~\ref{fi2} to go beyond the region $\Upsilon_{\mbox{\scriptsize CP}}$. However, the following constraint on the physical paths can be derived.
By expanding the lhs of inequalities (\ref{Lambda222}) at first order in $t$ we get $ \mu_0\geq|\epsilon_0|$,
that is, the trajectory must begin in the CP region $\Upsilon_{\mbox{\scriptsize CP}}$. Moreover, if it starts on the boundaries of $\Upsilon_{CP}$, i.e.,~$\mu_0=|\epsilon_0|$, then $\dot{\mu}_0\geq|\dot{\epsilon}_0|$. This tells us that not only the trajectory must start in the CP-divisibility region, but it has to have an initial ``speed'' such that it will remain in there for the immediate subsequent time. A path which starts in the origin, then moves along the boundary of the crosshatched region up to a time $t_i$ and then trespasses in either region $\Upsilon_{\mbox{\scriptsize NP}}$ or $\Upsilon_{\mbox{\scriptsize P}\backslash\mbox{\scriptsize CP}}$, is not allowed.
\paragraph*{Operational significance of Gaussian non-Markovianity degrees.
The significance of the last no-go rule is related to fundamental physical properties.
Suppose indeed that at time $t=0$ an initial state is described by a thermal covariance matrix $\sigma=\mbox{diag}\{\nu,\nu\}$, with $\nu \geq \frac12$. Under the action of the map (\ref{XYt})
at time $\tilde{t}>0$, the product of the canonical variances is
$ \mbox{$\langle\hat{q}^2\rangle\langle\hat{p}^2\rangle=e^{4 \int_0^{\tilde{t}} \epsilon_s \, ds} \Big(\nu+ \int_0^{\tilde{t}} \mu_r e^{-2 \int_0^r \epsilon_s \,
ds} \, dr\Big)^2$}$.
If $\Lambda_-< 0$, we obtain $\langle\hat{q}^2\rangle\langle\hat{p}^2\rangle <
e^{2 \int_0^{\tilde{t}} \epsilon_s \, ds} \Big(e^{ \int_0^{\tilde{t}} \epsilon_s \, ds}\nu-\sinh\big(\int_0^{\tilde{t}} \epsilon_s \,
ds\big) \Big)^2$, which for a pure initial state (i.e.~the vacuum or a Glauber coherent state, with $\nu=\frac12)$ reduces to
$ \langle\hat{q}^2\rangle\langle\hat{p}^2\rangle<\mbox{$\frac{1}{4}$}$,
i.e.~to a violation of the uncertainty principle, which is not physically admitted. Indeed, a trajectory lying along the border between $\Upsilon_{CP}$ and $\Upsilon_{NP}$ (representing, e.g., a damping master equation with generally time-dependent damping constant) preserves the purity of such a state. To better understand this, let us consider the limiting case of having a map such that $-\epsilon_t=\mu_t>0$ for $0<t<t_i$ and $-\epsilon_t>\mu_t$ for $t_i<t<\tilde{t}$. Up to $t_i$, the $X_t$ part of the map decreases both variances of the pure input state, while the noise added by the $Y_t$ part compensates the loss and the state remains pure. Then, for $t>t_i$, the noise introduced by $Y_t$ is not enough and the uncertainty relation is violated.
However, crossing the border during the evolution would be possible if the preceding dynamics shrank the state domain of the intermediate map such that its subsequent action, corresponding to a temporary dilation of this domain, would not violate the uncertainty relation. The non-Markovian effect, manifested in the dilation of the volume of the physical states accessible during the dynamics, can then be seen as a backflow of information from the environment into the system \cite{lorenzo2013}.
Let us now comment on the other border of the CP region, between $\Upsilon_{\mbox{\scriptsize CP}}$ and $\Upsilon_{\mbox{\scriptsize P}\backslash\mbox{\scriptsize CP}}$. For any dynamics with added noise ($\mu_t > 0$), a trajectory along this border is such that $\epsilon_t=\mu_t>0$, which is responsible for an {\em amplification}, that is, the multiplication of the displacement vector $D$ by a factor greater than $1$ and a corresponding increase of the variances. Along such a path, the noise added is the minimum allowed for quantum linear amplifiers \cite{Clerk2010}. Crossing this border into the $\Upsilon_{\mbox{\scriptsize P}\backslash\mbox{\scriptsize CP}}$ region at a time $t_i>0$ is allowed only if the noise added up to that time is sufficient to permit a subsequent amplification beyond the quantum limit. This is possible thanks to correlations established between system and environment during the preceding evolution. We can conclude therefore that a Gaussian phase-insensitive process (with added noise) is weakly non-Markovian if at any moment in time one observes that, although the covariances increase, a Gaussian state evolving under such a process is amplified beating the quantum limit. This provides an {\it operational interpretation} for the elusive phenomenon of weak non-Markovianity in the context of quantum amplification.
\paragraph*{Conclusions.} This Letter introduced a meaningful hierarchy of non-Markovianity for CV Gaussian processes and established its physical significance. We provided a necessary and sufficient condition for positivity of a Gaussian map acting on Gaussian inputs. Applying this to intermediate maps, we then distinguished three main types of Gaussian processes: Markovian, weakly and strongly non-Markovian ones.
In the one-mode case, we gave a simple prescription to identify to which class a Gaussian map belongs, based on its representation as a path $(\epsilon_t,\mu_t)$ in a two-dimensional diagram, where $\epsilon_t$ and $\mu_t$ can be computed explicitly from the pair of matrices $(X_t,Y_t)$ describing the action of the map. We also studied, in the physically relevant case of phase-insensitive channels, the constraints on these paths due to the requirement of having a global CP map. This allowed us to give a physical interpretation to weakly and strongly non-Markovian processes in terms of amplification beyond the quantum limit and of information backflow from the environment, respectively.
These findings can be of importance for quantum cryptography \cite{Vasile2011}. An eavesdropper with access to knowledge whether a given communication channel is weakly or strongly non-Markovian can amplify a state in such a way that the legitimate parties may find it too noisy to be useful, discarding it. Moreover, if the legitimate parties do not fully control the way the shared state is prepared, unexpected behaviour can be observed if possible non-Markovian effects are ignored.
We finally note that in all the Gaussian processes we considered explicitly (e.g.~quantum Brownian model and damping model), we found either instances of Markovian or strongly non-Markovian evolutions, but no weakly non-Markovian ones. This may be due to the fact that all these processes admit a final state at thermal equilibrium with the environment. Some purely weak non-Markovian processes might be retrieved in case an evolution in an active environment that pumps energy into the system is analyzed. Investigating memory effects in such processes deserves further investigation.
\begin{acknowledgments}
\paragraph*{Acknowledgments.} We thank Sabrina Maniscalco, Dariusz Chru\'{s}ci\'{n}ski, John Jeffers, Marco Piani, Gianpaolo Torre, and Fabrizio Illuminati for discussions. This work was supported by the UK EPSRC Quantum Imaging Hub (Grant No.~EP/M01326X/1), the European Research Council (ERC) Starting Grant GQCOP (Grant No.~637352), the Foundational Questions Institute (fqxi.org) Physics of the Observer Programme (Grant No.~FQXi-RFP-1601), the Brazilian Agencies CAPES (Grant No.~6842/2014-03) and CNPq (Grant No.~470131/2013-6), and the University of Nottingham (Graduate School Travel Prize 2015).
\end{acknowledgments}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 799 |
{"url":"https:\/\/plainmath.net\/7810\/demoivres-theorem-indicated-power-complex-number-answer-rectangular","text":"# Use DeMoivre\u2019s Theorem to find the indicated power of the complex number .Write answer in rectangular form. (sqrt3-i)^6\n\nUse DeMoivre\u2019s Theorem to find the indicated power of the complex number .Write answer in rectangular form.\n${\\left(\\sqrt{3}-i\\right)}^{6}$\nYou can still ask an expert for help\n\n\u2022 Questions are typically answered in as fast as 30 minutes\n\nSolve your problem for the price of one coffee\n\n\u2022 Math expert for every subject\n\u2022 Pay only if we can solve it\n\ncomentezq\nThe complex number can be written as,\n$\\left(\\sqrt{3}-i\\right)=2\\left(\\frac{\\sqrt{3}}{2}-i\\frac{1}{2}\\right)$\n$\\left(\\sqrt{3}-i\\right)=2\\left(\\mathrm{cos}\\left(-\\frac{\\pi }{6}\\right)+i\\mathrm{sin}\\left(-\\frac{\\pi }{6}\\right)\\right)$\ntherefore, it can be represented as,\n$2\\left(\\mathrm{cos}\\left(-\\frac{\\pi }{6}\\right)+i\\mathrm{sin}\\left(-\\frac{\\pi }{6}\\right)\\right)=2{e}^{-i\\left(\\frac{\\pi }{6}\\right)}$\ntherefore,\n${\\left(\\sqrt{3}-i\\right)}^{6}={\\left[2{e}^{-i\\left(\\frac{\\pi }{6}\\right)}\\right]}^{6}={2}^{6}{e}^{-i\\pi }=64{e}^{-\\pi }$\nTherefore ,the given complex number can be simplified further as,\n${\\left(\\sqrt{3}-i\\right)}^{6}=64\\left(\\mathrm{cos}\\left(-\\pi \\right)+i\\mathrm{sin}\\left(-\\pi \\right)\\right)=64\\cdot \\left(-1\\right)+i0\\right)=64\\cdot \\left(-1\\right)=-64$\nHence, the given complex number becomes \u221264.","date":"2022-06-27 08:59:34","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 17, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"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\": 0.773250937461853, \"perplexity\": 1393.8142449748264}, \"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\/1656103329963.19\/warc\/CC-MAIN-20220627073417-20220627103417-00717.warc.gz\"}"} | null | null |
# The Fetterman Massacre
### Dee Brown
_For L. L. B._
# Contents
[_I. April:_
MOON WHEN THE GEESE LAY EGGS](6-page2.xhtml#chap1)
[_II. May:_
PLANTING MOON](7-chap2.xhtml#chap2)
[_III. June:_
MOON WHEN THE GREEN GRASS IS UP](8-chap3.xhtml#chap3)
[_IV. July:_
MOON WHEN THE CHOKECHERRIES ARE RIPE](9-chap6.xhtml#chap6)
[_V. August:_
MOON WHEN THE GEESE SHED THEIR FEATHERS](10-chap7.xhtml#chap7)
[_VI. September:_
DRYING GRASS MOON](11-chap8.xhtml#chap8)
[_VII. October:_
HARVEST MOON](12-chap9.xhtml#chap9)
[_VIII. November:_
DEER RUTTING MOON](13-chap10.xhtml#chap10)
[_IX. December:_
MOON WHEN THE DEER SHED THEIR HORNS](14-chap11.xhtml#chap11)
[_X. January_
MOON OF STRONG COLD](15-chap20.xhtml#chap20)
_XI. Aftermath_
_1_
_2_
_3_
_4_
_5_
Bibliography
Notes
Index
A Biography of Dee Brown
# _I. April:_
MOON WHEN THE GEESE LAY EGGS
> _My name is Henry B. Carrington: forty-three years of age, colonel Eighteenth U.S. Infantry, and now commanding post Fort McPherson, Nebraska, late commanding post Philip Kearny, Dakota Territory, and previously thereto commanding Mountain District, Department of the Platte, which command embraced the route from Fort Reno westward to Virginia City via the Big Horn and Yellowstone Rivers, and being the new route I occupied during the summer of 1866._
SO BEGAN, ON A spring day in 1867, Colonel Carrington's testimony before a commission convened at Fort McPherson to investigate the Fetterman Massacre of December 21, 1866. For several days Carrington defended his past actions, offering letters, records and reports relating to his command at Fort Phil Kearny, narrating a relentless procession of events which led to the violent deaths of three officers, seventy-six enlisted men and two civilians.
The Fetterman Massacre was the second battle in American history from which came no survivors, and was a nationally debated incident for ten years—until overshadowed by the Custer Massacre of 1876. Acting under orders from Colonel Carrington, Brevet-Colonel William Judd Fetterman led eighty men out of the gates of Fort Phil Kearny at 11:15 A.M. of that dark December day. Carrington's orders were explicit: relieve the wood train from Indian attack, but do not pursue the enemy beyond Lodge Trail Ridge.
At 11:45 A.M. Fetterman's command of forty-nine infantrymen and twenty-seven cavalrymen halted on the crest of Lodge Trail Ridge, with skirmishers out. The sky was bitter gray, thickening for snow, temperature dropping rapidly. A few minutes later Fetterman's rear guard disappeared from view of the fort, passing over the ridge, moving north. At 12 noon, almost as the bugler was sounding dinner call in the fort, sentinels at the gate heard firing from beyond Lodge Trail Ridge. Colonel Carrington was notified immediately. By the time the colonel had mounted the lookout tower above his headquarters, firing was continuous and rapid. Without further delay, Carrington ordered Captain Tenodor Ten Eyck to move out to Fetterman's relief. At 12:45 P.M., Ten Eyck and seventy-six men reached the summit of a ridge overlooking Peno Creek. The valley was swarming with Indians, at least two thousand of them, probably more. One or two scattered shots rang out from the hill beyond; then there was no more firing, only the jubilant cries of Indians racing their ponies, some shouting derisively at Ten Eyck's troops, beckoning them to come down into the valley.
For several minutes Captain Ten Eyck could see no sign of Fetterman's command, neither the mounted nor dismounted men. Then as the Indians began withdrawing from the valley, an enlisted man cried: "There're the men down there, all dead!"
Maintaining his position on high ground until the Indian forces had vanished northward, Ten Eyck then cautiously advanced toward the battlefield. Near the Bozeman Road, dead men lay naked and mutilated, blood frozen in their wounds, in a circle about forty feet in diameter. They were mostly infantrymen. After loading the dead into his two ammunition wagons, Ten Eyck began a slow withdrawal to the fort, not reaching the gates until darkness was falling. The following morning, against the advice of his staff, Carrington led a second party out to the scene of battle and recovered the remaining bodies, mostly cavalrymen.
The full story of what happened in that brief hour of bloody carnage at high noon under the wintry sky of December 21, 1866, will never be known. During the years which followed, various Indian participants—Sioux, Cheyenne and Arapaho—told conflicting accounts of the battle. Yet the mystery is not so much what happened as why it happened. Why did Fetterman disobey Carrington's orders? Why did the cavalrymen leave the infantrymen to meet the full force of attack, and retire to high ground only to die a few minutes later as they had watched the infantrymen die? Why did the Indians retire from the field instead of attempting to annihilate Captain Ten Eyck's seventy-six men, a move which if successful would have left the fort vulnerable to immediate capture?
In the first place, why were Fetterman and his men there in that lonely, uncharted wilderness, 236 miles north of Fort Laramie, in a country which only one year earlier had been ceded by treaty to the tribes as inviolable Indian territory?
The commission investigating the Fetterman Massacre examined some of these questions directly, dwelling upon the necessity for three forts along the Bozeman Trail, debating whether or not the strength of Carrington's military force was sufficient, yet never more than hinting at reasons for opening this road through the Plains Indians' last unspoiled hunting ground.
The motivating factor of course was gold, which had been discovered in Montana in 1862, creating a rush to Virginia City through 1863 and 1864. During the Civil War, thousands of miners traveled to the diggings by two routes—either up the Missouri River by way of Fort Benton, or overland along the Platte Trail to Fort Hall and then doubling back into Montana Territory. These were roundabout routes, requiring weeks for passage. Public demand for a more direct route led two explorers in 1864 to mark out trails northward from Fort Laramie. Jim Bridger, aware of the Indians' determination to keep the white man out of their sacred Powder River country, avoided that area and led his party of trail blazers west of the Big Horn Mountains. John Bozeman, seeking an even more direct route, ran his wagons east of the Big Horns, straight through the heart of the hunting grounds.
Except for Indian resistance, Bozeman's route was by far the easier to travel, and by 1865 several parties of brave or foolhardy gold seekers risked their lives to make the crossing of what soon became known as the Montana Road.
In 1865, the Federal Government also became vitally interested in a direct route to the gold fields. After four years of Civil War, the United States Treasury was virtually bankrupt; gold was urgently needed to liquidate the accruing interest of the national debt. In hopes of encouraging more prospectors to make the journey to Montana, the government financed a survey for a direct route from Sioux City by way of the Niobrara River. Leader of this expedition of about one hundred men and 250 wagons was Colonel James A. Sawyer. The party included engineers and gold prospectors, and was escorted by two companies of former Confederate soldiers, who had sworn oaths of allegiance in exchange for release from military prisons.
Although Sawyer met with such strong Indian resistance that he was forced to abandon his original course, he finally reached Virginia City by following Bozeman's route much of the way. His official report, ordered printed by Congress in March 1866, received wide publicity and increased pressure from civilians to make the Montana Road safe for travel. Recently discharged Civil War veterans were especially eager to journey west and seek their fortunes in the gold fields, but after surviving four years of war they were reluctant to fight their way there through tribes of hostile Indians.
In an effort to halt attacks upon travelers through the Powder River country, General Patrick E. Connor in the summer of 1865 led a three-pronged expedition northward into the Sioux country. Connor's orders to his officers were short and to the point: "You will not receive overtures of peace or submission from Indians, but will attack and kill every male Indian over twelve years of age." Two of Connor's three columns suffered severely from Indian attacks; they lost many of their horses in night raids, and ran out of rations. The commander's own column managed to destroy one Arapaho village, and established a fort on the Powder that was first known as Fort Connor, later as Fort Reno.
But soon after Connor withdrew from the field, reports from Montana indicated that Indian resistance was more determined than ever along the overland route. "We thought it an impossibility to get through, and had to fight our way through," one correspondent wrote. "There is no place between Fort Reno and Virginia City where news can be sent. There will be no more travel on that road until the government takes care of the Indians. There is plenty of firewood, water and game, but the Indians won't let you use them."
During the autumn of 1865, treaties were signed with several bands of Sioux, Cheyenne and Arapaho. Government representatives guaranteed tribal rights to territory lying between the Black Hills, the Big Horns and the Yellowstone—in exchange for the Indians' conceding white travelers safe passage through this Powder River country. The commissioners, however, overlooked the fact that almost all the treaty signers were peaceable Indians, chiefs who had already abandoned the warpath and were content to camp around the white man's forts and live off his handouts. White soldiers and warrior Indians alike referred to them contemptuously as "Laramie Loafers."
Under leadership of belligerent warriors such as Red Cloud, raids against white invaders of the Powder River country continued as before, and in the spring of 1866 the government sent a second treaty commission to Fort Laramie to offer new terms.
At the same time, in its slow, ponderous way the War Department was responding to pressures to police the Montana Road. The commander of the Department of the Missouri—which included the Powder River country—was Major-General John Pope, one of President Lincoln's unsuccessful commanders in the East. After disastrous defeat in the second battle of Bull Run, Pope had been sent west, and for three years had been battling Indians with little more success than he had had against Confederates. On March 10, 1866, Pope issued the following order:
> The 2nd Battalion, 18th U.S. Infantry, will constitute the garrison of Fort Reno on Powder River, and the two new posts on the route between that place and Virginia City in Montana.... At these posts the battalion will be distributed as follows: Four companies at Fort Reno and two companies at each of the other posts. The Colonel of the Regiment will take post at Fort Reno.
The "colonel of the regiment" was Henry Beebe Carrington, and this order sealed the doom of the eighty-one men who died nine months later on Peno Creek. No more unlikely commander could have been selected for so dangerous a mission at that time or place than Colonel Carrington. In the spring of 1866, the United States Army was overstaffed to the point of absurdity with both permanent and breveted colonels and generals (literally hundreds of senior officers with three and four years of battle experience), many of them young men with West Point training. Yet Carrington had never heard a shot fired in combat; he had never commanded upon the field of action.
An ardent antislavery man practicing law in Ohio, he had organized the 18th Regiment with smooth efficiency during the first days after Fort Sumter, and was appointed colonel on May 14, 1861. His ability as a recruiter and organizer kept him in Ohio while his regiment moved south, and as the war wore on he was called to Indiana to establish prisoner-of-war camps, to deal with Copperheads and prosecute the leaders of the Northwest Conspiracy. Meanwhile the 18th Regiment, with other men acting in command, was winning an enviable record as a fighting unit. The 2nd Battalion came out of the Battle of Stone's River with half its officers and men dead or wounded. The junior officers who would serve later under Colonel Carrington at Fort Phil Kearny may have understood the reasons for his absence from the Civil War battlefields, but they never forgot that fact during the Wyoming ordeal of 1866.
Not until late in 1865, after all the battles were ended, did Colonel Carrington at last join his command. Determined to remain in military service, he shrewdly foresaw that future opportunities lay on the Indian frontier beyond the Mississippi. It was no mere chance that the 18th Infantry was the first regular regiment to reach the frontier; Carrington had been in a position during the war to make friends with men of considerable political influence in Washington. During the winter of 1865–66, eight companies of the 18th moved across the plains to occupy Fort Kearney,* Nebraska Territory, on the old Oregon Trail. Henry Carrington had finally achieved his dearest ambition, a military command in the field.
He was a small man physically (the Indians called him Little White Chief) with a dark beard and hair worn long, sensitive eyes set deep under a high forehead. Sickly as a youth, he had been unable to enter West Point. He went to Yale instead, where he was in ill health much of the time. Graduating in 1845, he took a position as teacher at Irving Institute, Tarrytown, New York.
The next year Carrington would have liked more than anything else to become a soldier in the war with Mexico, but instead he stayed in Tarrytown, meeting Washington Irving and serving for a time as that author's secretary. His brief acquaintanceship with Irving no doubt influenced his later ambition to become a writer. In 1847 he was back at Yale, teaching part-time and studying for a law degree.
A year later he made his big move—to Columbus, Ohio, where he began a successful legal career. He was fortunate in the choice of a law partner, William Dennison, who became Ohio's governor at the time of the Civil War. It was in Columbus that Carrington also met and married Margaret Irvin Sullivant, who would share with him the ordeal of Fort Phil Kearny.
This was the man, then, who largely through his own calculated actions had placed himself in position in the spring of 1866 to be chosen to lead the 2nd Battalion of the 18th Infantry into the heart of the most hostile Indian country of North America. Unfortunately neither he nor scarcely any other man of authority in the United States Government knew the real temper of the Plains Indians at that time.
In the years before 1850 the tribes had permitted settlers and gold seekers to move across their lands with only an occasional raid. But when the invaders from the east built forts and chains of stations for overland stage routes, the Indians began to raid in earnest. To protect its westward-moving citizens, the government in 1851 invited leaders of the Sioux, Cheyenne, Arapaho, Crow, and other tribes to Fort Laramie for a peace conference. Treaties were signed giving the United States rights to maintain roads and forts across the plains, and reserving vast hunting areas for exclusive use of the various tribes.
Pressures upon these Indian lands continued, however, from white buffalo hunters and trappers, from gold seekers and settlers. In 1862 the Sioux in western Minnesota went to war with the settlers; in 1864 conflict in Colorado resulted in the massacre of the Cheyennes at Sand Creek. General Connor's invasion of the Powder River country followed in 1865. For fifteen years treaties had been made and broken; from south and east the Indians were being pressed continually toward the Rockies. Their hunting grounds grew smaller after every treaty, and now the last and best of these reserved areas was being invaded by miners and soldiers. In 1866 many of the Plains Indians' leaders had finally reached the conclusion that the white man's treaties were worthless; they were convinced that their way of life could endure only if they made a stand and fought for their lands.
On March 28, in complete disregard of the belligerent temper of the Indians, the Army ordered Carrington "to move immediately" to occupy Fort Reno and open two new forts along the Bozeman Trail. He was promised a year's supply of tools, rations, quartermaster stores, "the best horses and equipments and transportation in the district," and a water-power sawmill. In late March, however, the 2nd Battalion at Fort Kearney carried only 220 men on its muster rolls, about one-fourth normal strength, and they were armed with obsolete muzzle-loading Springfields in poor condition. Carrington immediately queried his superiors concerning the whereabouts of promised recruits and arms, and asked for a departure delay until their arrival.
On April 13, he received orders establishing the Mountain District, with himself in command. The Mountain District encompassed the Powder River country; he would report directly to General Philip St. George Cooke, commanding the Department of the Platte, a crusty fifty-seven-year-old campaigner with almost forty years of frontier dragoon service behind him.
General Cooke's mood in 1866 certainly could not have inclined him toward friendship for ambitious "civilian" colonels. After graduating high in his class from West Point in 1827, Cooke had seen service in the Black Hawk War, the Mexican War, won distinction in operations against the Apache and Sioux, commanded cavalry in the Utah expedition of 1857–58, and had moved up to the rank of colonel when the Civil War began. Although a Virginian, Cooke announced immediately that he would keep his "solemn oath to bear true allegiance to the United States of America." His son, his nephew, and his famed son-in-law, J. E. B. Stuart, all went with the Confederacy.
Because of his long cavalry experience, Cooke's first Civil War assignment was command of that arm of the service under General George McClellan, even though certain high officials in the War Department seemed to consider his loyalty suspect. During McClellan's Peninsular Campaign of 1862, Cooke's cavalry was made to look foolish by his own dashing son-in-law, "Jeb" Stuart, and soon afterward he was relieved of command. He spent the remainder of the war out of combat action, serving on various boards, on recruiting duty, and as a functionary in occupied territory. He came out of the war with only the rank of brigadier-general; consequently when he took over command of the Department of the Platte in 1866 he was an embittered man.
At this time Carrington knew very little about Cooke; he would learn a great deal about him as events unfolded. For the moment he wasted no time in carrying out Cooke's order. "Immediately on receipt of the order establishing the Mountain District," Carrington recorded, "I issued General Order No. 1, assuming command, and made requisition for commissary and quartermaster supplies for one year, upon the full basis of eight hundred men, and fifty per cent additional for wastage and contingencies."
Carrington's zeal for his new assignment as well as his cautious stubbornness are revealed in this first general order. He was determined to hold out for full battalion strength, eight hundred men, before marching into the Indian stronghold.
High command decision, and communications transmitting them, moved slowly on the frontier. Carrington waited almost a month at Fort Kearney before he received official sanction on April 26 from General Cooke for delaying action on his "move immediately" order of March 28.
Carrington acknowledged Cooke's telegram with a long letter in which he proudly recorded all the steps he had taken to ready the battalion for marching. He had obtained two hundred excellent horses, almost enough to mount his entire present force; he had assembled fifty wagon teams, sets of tools for erecting forts, instruments for measuring distances and surveying routes. He had armed his regimental band "with Spencer carbines to make their services valuable every way." (Carrington must have sensed that he would be criticized for taking a 25-piece band into hostile Indian country, but he loved martial music, the pomp and ceremony of parade reviews, and considered his musicians among the least expendable units.) With his gift for never overlooking the most minute details, Carrington also reported purchase of a quantity of "potatoes and onions for seed and use," adding that he also had "other seeds, if practicable to use them this season."
He closed his letter with a suggestion that it would be "of value to my future operations if I reach Laramie in time for the meeting with the Indian tribes in council and thereby form acquaintance of many with whom I will have subsequent relations." Those were the words of a lawyer preparing to meet his opposition; soon enough Carrington would learn to think like a soldier.
* Fort Kearney should not be confused with Fort Phil Kearny. Fort Kearney, Nebraska, established in 1849, was named for General Stephen W. Kearny. The second "e" in the name was used erroneously in so many official records that it became recognized as the standard spelling. Fort Phil Kearny, Dakota Territory (now Wyoming), was named for General Philip Kearny, Civil War hero, and was not established until the time of this narrative, 1866.
# _II. May:_
PLANTING MOON
> _On the 16th of May Major-General Sherman reached Fort Kearney, Nebraska, and upon full consultation with him I matured my plans for the establishment of the new posts and the occupation of the proposed new line to Montana. Two days later, May 19, 1866, recruits having arrived, I marched, reaching the vicinity of Fort Laramie June 14, in nineteen marching days._
SPRING WAS BACKWARD ON the Great Plains that year, ice lingering in the swales and fringing the running streams. At Fort Kearney in early May the men arose to curse the monotonous frosty mornings. After a winter spent in barracks of rotting cottonwood logs through which biting prairie winds whistled and made them shiver in their bunks, the men were ready for spring, ready for a change.
Quarters were only half large enough for the eight skeleton companies of the 2nd Battalion. Officers' families shared cabins designed for bachelors. Lieutenant William H. Bisbee, battalion adjutant, recorded that he, his wife and young son were assigned one room and a small space under a hall stairway. "We cooked, ate, and slept in this one room."
Bisbee's fellow tenant, who would play a tragic role in the Fetterman Massacre, was the regimental quartermaster, Lieutenant Frederick H. Brown, a reckless, happy-go-lucky bachelor. Brown's room, according to Bisbee, "was separated by a thin partition from mine. His chief joy was to pack the room full of Pawnee Indians, fill them with 'chow,' in return for which they gave gruesome and noisy exhibitions of scalping, war dances, and buffalo hunts."
While the officers waited impatiently for the promised recruits and finals orders to march, they pored over new maps recently arrived from Washington and were surprised at how sparse was official knowledge of the Mountain District which they had been ordered to occupy. The maps told them almost nothings and there were no guidebooks. They passed around tattered copies of Lewis and Clark's reports, and exchanged newspaper clippings, but they still could not learn whether the region was frigid or temperate, barren or covered with vegetation. All they knew was that it was precious to the Indians, and was the most direct route for emigration to Montana.
Occasionally the monotony of daily duties was relieved by arrival of Volunteer troops reporting from lonely western outposts to receive delayed discharges from Civil War service. Colonel Carrington wasted no time in mustering out these troops, especially if they were cavalrymen. He had been given authority to take over their horses, and every additional company passing through meant an increase in mounts, sorely needed for the march to Powder River.
Meanwhile the entire battalion was engaged in gathering and packing additional supplies. Mowing machines, shingle and brick machines, doors/ window sash, locks, and nails began arriving from Fort Leavenworth. The officers' wives saw to it that rocking chairs and sewing chairs, churns and washing machines, and good supplies of canned fruit were posted on requisition lists. "Turkeys and chickens and one brace of swine," Mrs. Carrington recorded, "added a domestic cast to some of the establishments preparing for the journey."
The colonel searched through his ranks for blacksmiths, wheelwrights, painters, harness makers and carpenters, and ordered these men to collect from the Fort Kearney storehouses all tools needed for their specialties. He tried to impress on every member of the expedition that no contingency should be overlooked; as soon as the column moved north of Fort Laramie it would be cut off from the States for several months.
By mid-May the weather had turned fine, and the regimental band under Bandmaster Samuel Curry was out drilling every day with new Spencer carbines, the envy of the regular infantrymen, who were still armed with old muzzle-loading Spring-fields. The Spencer was a breechloader with a seven-shot magazine, and each musician was supplied with an accompanying cartridge box containing tubes of seven cartridges which could be inserted into the carbine in one operation. The men were warned to guard these weapons carefully; any soldier who lost one would be charged thirty dollars, about two months' pay for a private.
At the same time, the infantrymen were learning how to ride the horses acquired from discharged Volunteer cavalrymen. "The men got upon the horses," Margaret Carrington noted, "and the majority actually made the first trip to water without being dismounted. Some men were embarrassed when the long Springfield rifle was put on the horse with them, but both man and horse soon learned how it was to be done."
At last, on Sunday May 13, the 3rd Battalion of the 18th came marching in from Fort Leavenworth, with several hundred recruits for the regiment. Two days later, Captain J. L. Proctor arrived with another company of recruits, one of them being Private William Murphy who recalled later that upon arrival he was issued "two days rations, consisting chiefly of hardtack. Each hardtack was about four inches square and three-eighths of an inch thick.... A hungry man could have eaten the entire two rations at one meal and asked for more." The half-famished arrivals were told simply that the quartermaster had run short.
What had happened was not unusual on the army frontier of 1866. The 3rd Battalion had expected the 2nd Battalion to be well stocked with rations in their cozy quarters at Fort Kearney, and had carried only enough supplies for the march from Leavenworth. At the same time the 2nd Battalion had hopefully expected the 3rd Battalion to bring in fresh rations along with the recruits. The result, of course, was a temporary famine, with several hundred men camped around Fort Kearney waiting for an overdue supply train.
Supplies arrived on the 16th, and accompanying the train was an old hero to the men of the 18th Infantry, Lieutenant-General William T. Sherman, then in command of all western departments.
In contrast to the grim seriousness of his Civil War character, Sherman seemed quite relaxed during his brief visit. Margaret Carrington reported that he entered into the spirit and plans for the expedition with his "usual energy and skill." Perhaps because he was conscious of having made so much recent history, he suggested to her and the other officers' wives that they keep daily journals of experiences in the new country so that records might be available for posterity.
At that time Sherman had had little experience with Plains Indians; he foresaw no dangers for the women and children of the party, but advised Carrington that he should avoid a contest of arms with the tribes if possible. He spent much of his visit relaxing in the spring sunshine around Fort Kearney. Carrington's son, James, told afterward of a contest sponsored by Sherman between him and some of the Pawnee boys. Sherman wanted to see which of the youngsters could shoot an arrow the highest. "My bow was boy's size," Jimmy Carrington recalled, "but I won by lying on my back and putting both feet against the bow to pull it."
Jimmy Carrington also remembered an exciting event which occurred soon after Sherman departed. "Our house burned down early in the morning, and I recall the terror of the scene, the mad scramble to save a few things, but especially the rapid popping of several big army revolvers that the fire set off." His mother mourned the loss of her best chairs and mattresses, all packed and ready for the overland journey, but the Carringtons accepted the losses philosophically—"an incident very possible in army life"—and moved their few salvaged goods into an army ambulance which would be their home during the long march west.
On May 18 recruits were assigned to the respective companies of the 2nd Battalion. The Fort Kearney magazine was opened, and ammunition which could be spared was drawn out and loaded into wagons. It was a meager supply, but Carrington had been assured that the deficit would be made up at Fort Laramie. With high spirits he announced that the regiment would march out for Laramie early on the following morning.
Saturday May 19 was a sunny spring day, the wide sky blue from horizon to horizon. More than a thousand men and 226 mule-drawn wagons moved out to stirring music from the regimental band, and by noon the column was beyond the adobe huts of Kearney City and strung along the Platte, a cloud of dust floating in its wake.
For the first time since the war the 2nd Battalion was at full strength, about seven hundred men, the majority being recruits in new blue uniforms which were darkened with sweat under the warm sun. The dismounted men of both battalions marched in advance, the wagon trains next, most of them driven by civilian teamsters employed by the quartermaster. Following the wagons was the cattle herd of about a thousand animals, with the mounted men serving as a rear guard.
Women and children rode in ambulances, and by midafternoon a few recruits, sore-footed from unaccustomed marching, were permitted to join these passengers. Each officer was responsible for the movement of his family and household goods. "My personal allowance," said Adjutant Bisbee, "embraced two six-mule teams, an ambulance, three saddle horses, cow, and chickens." Before the end of the day the expedition moved fourteen miles up the Platte, and someone had dubbed the long train "Carrington's Overland Circus."
In addition to Adjutant Bisbee and Quartermaster Fred Brown, the 2nd Battalion's officers at that time included Captain Henry Haymond, battalion commander, Captains Nathaniel C. Kinney, Tenodor Ten Eyck, Joshua L. Proctor, and Thomas B. Burrowes, Lieutenants John I. Adair, Isaac D'Isay, Frederick Phisterer and Thaddeus Kirtland, the last being a cousin of Colonel Carrington. The battalion was well staffed with medical officers—Captain Samuel M. Horton, chief surgeon, and contract surgeons Mathews, McCleary and Buelon.
The second day out of Fort Kearney was a Sunday, and after a brief religious service, they marched twenty miles to Plum Creek. At dawn Monday the "Overland Circus" was moving west again, the weather still good, recruits marching more briskly now that soreness was gone from their muscles. "My brother and I," James Carrington wrote afterward, "had been given a small Indian pony that we called 'Calico' and during the day we would take turns riding him, to get relief from the monotony and cramped quarters of the ambulance.* I can still remember passing prairie-dog villages where there were thousands of funny little rodents running around, or sitting up to bark at us and then ducking down into their holes. Never a day without a sight of leaping antelopes, an occasional sneaking coyote, big jack-rabbits, often herds of buffalo in the distance, and ever the monotonous expanse of sage-covered plain, blinding dust, the big skies stretching to the blue horizon, distant mountains, gorgeous sunsets, and in the heat of some days a shimmering mirage that looked like a great sea."
While his young sons, Jimmy and Harry, were racing their calico pony alongside the wagon train, Colonel Carrington was rapidly becoming acquainted with three important civilian members of his party. They were Jack Stead, Henry Williams, and James Bridger. Stead was employed as official interpreter for the expedition; he had lived many years with the Pawnees, participating in their wars with the Sioux, who hated Stead and reputedly had placed a high price on his scalp. Henry Williams and Jim Bridger had served as scouts with General Patrick Connor during the Powder River expedition the previous year.
No white man knew more of the geography of the Big Horn and Powder River country than did "Old Gabe" Bridger. For forty years he had trapped, explored, and scouted in the area which was soon to become Wyoming Territory. He was a member of the party which opened the Oregon Trail; in 1843 he had defied the Indians by building a trading post known as Fort Bridger. In 1866 Bridger was approaching the end of his career—he was sixty-two—but Carrington would have been the first to admit that the grizzled frontiersman was the least expendable member of his expedition. Bridger's pay was ten dollars a day, more than Carrington received, and more than twice the income of a junior officer, but he was a walking encyclopedia of Indian lore readily available to any man who needed him.
Carrington probably met Bridger early in 1866 at Fort Kearney. According to the _Kearney Herald,_ he was there during the winter, en route to Washington "to tell the authorities how to manage the Indians." The _Herald_ described him as being "fully six feet high, raw boned, blue eyes, auburn hair (now somewhat gray) is very active and communicative." Lieutenant William Bisbee said he was "a plain farmer-like looking man dressed in the customary store clothes garments, low crowned soft felt hat, never affecting long hair or showy fringed buckskin suits, though he may on occasion have donned them as a convenience. His name of scout belied his calling in our expedition for we had no occasion to scout for Indians, they were always nearby."
As the Overland Circus moved into hostile Indian country, Bridger and his assistant, Henry Williams, became more active, rising every morning before the bugler, preparing their own coffee, eating a few bites of pemmican, saddling their mounts. At reveille call, they would ride over to Carrington's tent, engage in brief conversation with the colonel, then canter out in advance of the column. Around sunset they would come riding back and report to Carrington. They always bedded down a short distance from the military camp, and except for Carrington and one or two other officers, few members of the battalion spoke with them or even saw them during the march. Bridger had little respect for what he called "paper-collared soldiers," inexperienced on the frontier.
On May 24 the column marched into Fort McPherson—where less than a year later Carrington would be commanding under the shadow of an official inquiry. The fort was a dismal collection of shabby log-and-adobe quarters. Carrington had hoped to find additional rifle ammunition here, but there was none to spare. He ordered a detail to dismantle an idle steam sawmill which had been transferred to the expedition. The men loaded boiler and frame into spare wagons, and the train moved on, to camp for two days near O'Fallon's Bluffs.
On the 29th they reached Beauvais Ranche near the Old California Crossing. Westward travelers usually crossed the Platte at this point, but Carrington had been advised to proceed to Fort Sedgwick before attempting to ford his heavy wagon train. Late in the afternoon he received a visitor, a Cheyenne named Old Little Dog, who complained that some soldiers had entered his lodge nearby and stolen his rifle.
Carrington assured the Cheyenne that his rifle would be returned, and then to please his guest, ordered the regimental band to present a concert. Old Little Dog obviously enjoyed the music, especially admiring the bell chimes, and when the performance was ended and his rifle was returned to him, he thanked his host, leaped upon the bare back of his pony and galloped away. Carrington watched the Cheyenne until he vanished in the dusk, wondering if he had made a proper beginning in his first meeting with a representative of one of the tribes with which he must deal in the Powder River country.
Next day the train rumbled on westward, reaching Fort Sedgwick outside Julesburg, Colorado Territory, near sundown. After eleven days of marching they had put only two hundred miles between them and Fort Kearney. Laramie still lay more than a week's travel away, and the Powder River country was almost two hundred miles farther.
Carrington had allowed one day of his march schedule for fording the Platte at Julesburg. He was four days making the crossing. Melting snows upstream had flooded the river, and after conferring with his officers, he decided to float the wagons across on a large flatboat. He assigned the task of fitting out and caulking the boat to Captain Tenodor Ten Eyck, who had been a surveyor and lumberman before the war.
During the stay at Sedgwick, officers and men not on duty inspected the post. Few of them had ever before seen a fort constructed for defense against frontal Indian attack. A parapet and ditch guarded a rectangle of two-story adobes, each situated so that if one was attacked, the besiegers would be caught in a cross fire from the others. Another feature which impressed the visitors was a system of window barricades, pierced with loopholes and ready to be put into position at a moment's warning. All this was very sobering to recruits who had heard and read about Indian warfare, but as yet had not even seen a hostile Indian.
Meanwhile Ten Eyck and a detail of two hundred men made quick work of the flatboat, dragged it to the bank of the Platte, and laboriously set about stringing a cable across the currents and shoals of that treacherous stream. A twenty-mule team was then hitched to the cable, but the animals could not move the boat out of the sandy riverbank. Ten Eyck ordered the mules replaced by oxen, and the flatboat reluctantly became buoyant. Planking was laid out and wagons and teams moved aboard. Adjutant Bisbee, his wife and young son made the first crossing in the ambulance assigned to them.
But the capricious Platte was already falling again. By morning of the second day, sand bars were shining where currents had run a few hours earlier. "On trying the scow," Private William Murphy recorded, "we found it would not work owing to the quicksands and shallows. In places the water would be only two or three inches deep, while a few feet away there would be seven or eight feet of water."
Captain Charles Norris, commanding a 2nd Cavalry company stationed at Fort Sedgwick, came down to the riverbank to commiserate with Carrington and his officers. "You'll have to push, cuss, and drive your train team by team across that mile of flat river," Norris advised. Carrington ordered Ten Eyck to change his tactics, unload the wagons, replace them with false beds, and reload lightly. On Captain Norris' suggestion, a sizable collection of light and heavy timbers for prying and shoving was also assembled.
Realizing that the actual crossing would be delayed another day, Carrington decided to lighten the tension of waiting by arranging an evening entertainment. Soldiers not assigned to river-crossing operations erected several hospital tents into a single pavilion, and set up rows of campstools and chairs from the unloaded baggage wagons. Major James Van Voast, en route to Laramie to assume command of the post and the 18th Regiment's 1st Battalion, organized a program of music and comedy which he called the "Ironclad Minstrels." Amateur soldier actors blacked their faces, poked fun at their frontier environment, and sang to the accompaniment of the band's rollicking music which was complete with banjos and bones.
In a way, the evening's jollity was also a farewell party for officers of the 3rd Battalion, whose companies would take different routes west from Julesburg to forts in Colorado Territory and beyond on the old Oregon Trail. As he shook hands with these officers in front of his tent after the performance, Carrington must have wondered how he was going to accomplish his administrative duties as colonel of a regiment strung out across half the West—from headquarters in an isolated fort far north in the Powder River country.
One of the minor incidents occurring during the regiment's stay at Fort Sedgwick concerned a member of the band, Frank M. Fessenden. Although not yet twenty, Fessenden had brought his teen-age bride west with him, and all along the trail from Fort Kearney it had been obvious that young Mrs. Fessenden would soon become a mother. The Fessendens had been hopeful of reaching Fort Laramie, where the column would halt for a time, but the birth appeared so imminent at Fort Sedgwick that Surgeon Horton advised the expectant mother to travel no farther. "I was left behind the command with my wife," Fessenden wrote later. "A daughter was born to us here at Fort Sedgwick. She was a great favorite with Captain Fetterman who wanted to name her Sedgwick."
Because of his youth and size—he stood only five feet, five inches high—Fessenden was a favorite of the regiment, a gray-eyed, brown-haired youngster from Twinsburg, Ohio, who upon enlistment noted his occupation as painter but soon ended up as a musician in the Army. When Carrington learned of the reason for Fessenden's temporary detachment from the regiment, he ordered a promotion in rank, dated back to the first of the month.
On June 2 and 3, Carrington's Overland Circus completed the formidable task of fording the Platte. "We finally crossed by having a long rope stretched from man to man," said Private Murphy, "strapping our guns and equipment to our backs and holding to the rope. Some of the men were up to their arm pits in water and some traveled nearly dry shod. We were ordered not to stop for anything, for if we did we would get stuck in the quicksand." A few mules drowned, and in spite of all precautions some stores were damaged. Water melted the sugar, caked the flour, and swept away an occasional stray knapsack. But the Platte was crossed.
* Calico was to become a casualty of the Fetterman Massacre.
# _III June:_
MOON WHEN THE GREEN GRASS IS UP
> _On June 16, while encamped four miles east of Laramie, I was visited by Standing Elk, chief of the Brûlés (a band of the Sioux). He was thoroughly friendly—was entertained in my tent, and asked "Where I was going;" I told him; he answered me as follows: "There is a treaty being made at Laramie with the Sioux that are in the country where you are going. The fighting men in that country have not come to Laramie, and you will have to fight them. They will not give you the road unless you whip them."_
## 1.
EARLY ON THE MORNING of June 4, the last of Carrington's wagons was across the Platte, and the train camped that night on Lodgepole Creek. Next day they made eighteen miles, halting at Louis Ranche.
Along the trails of the West, crude stage stops had sprung up during the years between the California gold rush and the Civil War, most of them known as road _ranches._ Like many other wagon trains, Carrington's Traveling Circus took advantage of such amenities as were available at these stops, and often camped in the vicinity of a ranche. Margaret Carrington described Louis Ranche as "quite a fort, and the out-houses and stables are advanced like bastions, so that enfilading fire can be had in all directions... a large yard surrounded by a stockade paling, with stabling, feed troughs, and hayricks, with here and there loopholes for the rifle... the wall of the upper stories and every angle of house or stable has its outlets for firing upon an approaching foe." She noted a wide selection of merchandise offered for sale: nutmegs, peppermint, navy tobacco, clay pipes, salaratus, baking powder, bologna, ready-made clothing, rows of canned fruits, black snake whips, tin cups, camp kettles, frying pans, wine, gin and whiskey.
Next morning, Colonel Carrington and his officers said their farewells to the last companies of the 3rd Battalion, who were taking a route through Lodgepole Canyon on the first leg of a long journey to Camp Douglas, Utah. With their departure the train was shortened considerably; only the 2nd Battalion and recruits for the 1st Battalion remained. Carrington ordered a faster marching pace, over a smooth, hard-packed trail, but by noon the sun was scorching, and hourly rest stops had to be lengthened. The only trailside well marked on the map proved to be dry, and orders were passed to the men to conserve water in their canteens.
By midafternoon the thermometer in Mrs. Carrington's open ambulance indicated 101°, and a steadily rising wind tore at wagon covers. Clouds of gritty dust swirled across the treeless plain, driving into eyes, ears and noses. To add to the discomfort, swarms of buffalo gnats appeared out of nowhere, annoying the teams, stinging every exposed part of the human body. For protection, the men donned gloves and tied handkerchiefs over faces and necks. By late afternoon all vacant spaces in ambulances and wagons were filled with men suffering from lameness and heat exhaustion. Surgeon Horton and his assistants were kept busy trying to restore as many as possible to duty.
Yet in spite of everything the train traveled twenty-eight miles that day, rolling in to camp at Mud Springs where they found a group of log huts occupied by relief drivers for the Overland Mail. Off in the southwest the sky had turned a greenish gray, marked by jagged lightning flashes. No wood was available at Mud Springs, and details were ordered out to gather buffalo chips. By the time coffee fires were started, a thunderstorm was upon them. Mules and horses jerked at their fastenings; tents ballooned, ripped up stakes, and flattened upon their occupants. The storm carried more wind than water and soon blew over, leaving little damage in its wake.
"Each day was much like another," Lieutenant Bisbee remembered. "The march at earliest dawn, the same adventures with rattlesnakes, the inopportune thunderstorms, routine of evening guard-mount and sound slumber."
On the 7th an early halt was made near Court House Rock to take advantage of the plentiful supply of water in Pumpkin Creek. Several of the younger officers and wives, led by the adventurous regimental adjutant, Lieutenant Frederick Phisterer,* spent the last hours of the day climbing that curiously shaped bluff with its vast domed top and cupola which always reminded eastern travelers of their courthouses back home.
Most of the next day as they rolled westward through shimmering heat, they could see another famous landmark far ahead. When first sighted across the treeless plain it resembled the dead trunk of a gigantic tree, but as the train drew nearer, it took on the appearance of a chimney, tapering slightly to the top. That night they camped near this stratified clay mound known as Chimney Rock, and at dawn of the 9th were marching again, passing through Scotts Bluff down a gorge floored by drifting sands. The trail through Mitchell Pass narrowed in several places to the width of a single wagon.
Scotts Bluff, the Gibraltar of the Plains, was the most magnificent piece of scenery yet encountered by the travelers, the highest point in Nebraska Territory, embellished with terraced formations, fanciful towers and castles carved by water and wind. Here the expedition met with its first serious accident, involving the precious steam sawmill brought from Fort McPherson. "An eight-yoke bull-team," said William Murphy, "stampeded with two wagons loaded with parts and equipment for a sawmill, and ran down a steep hill to the North Platte. I do not believe any of the steers were alive when they got to the bottom of the hill. This sawmill was intended for Fort Phil Kearny and arrived a month or six weeks later. This of course delayed us some in building the fort."
At Camp Mitchell, west of the bluff, Carrington detached a company of the 1st Battalion under Captain Robert P. Hughes, assigned to replace Volunteer troops from Ohio and Missouri who had been there for many months. That night the train camped along the river west of the small fort.
Next day was a Sunday, and after holding morning religious services, the command rested. Mrs. Carrington recorded that Lieutenants Adair, Kirtland, D'Isay and the ebullient German, Frederick Phisterer, "helped to make something like true melody from the sweet Sabbath bell sent us by the Sabbath school of Rev. Mr. Dimock of Omaha before our departure from Kearney."
Although Fort Laramie was only two days' march from Camp Mitchell, so many wagons were showing signs of wear from the long journey and the added rough jolting through Mitchell Pass, that Carrington decided to devote Monday, June 11, to emergency repairs, axle greasing, and reshoeing of some horses and mules. He also conferred with Jim Bridger. The trail between Scotts Bluff and Laramie was subject to occasional raids from hostile bands, but Bridger was confident that Indians would not attack so formidable a train. He expected, however, that they might attempt to raid livestock herds after dark.
Consequently, Carrington summoned his quartermaster, Lieutenant Fred Brown, and issued that day a special order:
> The troops and trains of this command will hereafter be camped and parked closely together, and in the following manner whenever the camping ground permits: All the trains will be parked, forming one closely locked square. If the wagons do not close together, the interval will be closed by means of ropes stretched from wagon to wagon, so that no animal may be able to escape. Headquarters will camp on one front of the square, the second battalion on the second, the mounted portion of the command on the third, and the quartermaster employees on the fourth front, and all outside of the square. In the fourth front a sufficiently large opening will be left to permit the public animals to be driven in in the evening, to stay there during the night. After sunset all animals must be within that square, and the quartermaster will be held responsible for the strict observance of this order. The second battalion will furnish the guard for its own and the fourth front; the mounted command will furnish the guard for its own and the front occupied by headquarters.
Early Tuesday morning the column moved out, and by day's end was halfway to Fort Laramie. They camped on Cold Creek, a clear-water stream flowing into the North Platte. Sergeant John Barnes, a musician from Cincinnati, dropped a hook and line into the junction of creek and river and hooked a mountain pike. In a few minutes other soldiers joined him, making a seine from gunny sacks sewn together and weighted with mule shoes. Before sunset they had caught over a hundred fish. "Their hard white meat," Margaret Carrington recorded, "was excellent."
It is not on record what her husband thought of the fishing party or the flavor of the catch, but for the past few days the colonel had noted with disapproval the casual attitude of his troops on the march and in camp, their habits of straggling, of riding out to shoot at wild game along the way, of carelessness after nightfall. Although Bridger had assured him that an Indian attack on the whole column was most unlikely, the scout had warned that any roving war party would strike without hesitation at small groups of men isolated by only a few hundred yards from the train.
With these thoughts in mind, Carrington decided to tighten security still further by issuing another special order. It was read that evening to all companies.
I. Straggling for hunting or other purposes will at once be discontinued.
II. Soldiers requiring rest or relief must avail themselves of the regular intervals of rest on the march, as established by battalion or detachment commanders.
III. Orderlies will remain with the officers for whom they are detailed, except when sent with orders.
IV. The mounted men attached to headquarters will march in front of headquarters train when not otherwise ordered, and all mounted men will carry their rifles by a uniform method and in readiness for use.
V. The regimental band will accompany the headquarters train, and will not stray from it unless by special permission of the regimental adjutant.
VI. No soldier will be permitted to visit ranches, or posts, or other sutlers than the one accompanying the command, or to leave the guard limits, except for wood and water, without permission of his battalion or detachment commander. Except in cases of trivial import, or such as only concern regimental headquarters or the mounted men of such, the permission above referred to must have the approval of the commanding officer of the Second Battalion Eighteenth U.S. Infantry.
VII. Wagon-masters, their assistants, teamsters, and all employees or attachés, connected with or accompanying this command will conform to these instructions, and such as they receive, pursuant thereto, from Captain F. Phisterer, acting assistant adjutant-general, and Lieut. F. H. Brown, chief quartermaster.
VIII. Order and silence after 9 o'clock P.M. will be observed by all within the command, whether soldiers or otherwise, and the chief quartermaster will so instruct wagon-masters and their assistants. The officer of the day, of the second battalion, will cause the arrest of all offenders against this paragraph.
The column moved out early on the 13th for the last day's march to Fort Laramie, halting early in the afternoon by pre-arrangement about four miles east of the fort. Carrington wanted his camp close enough to Laramie to transact necessary military business, but far enough away to prevent any mingling of troops with the two thousand Indians who were there for the treaty ceremonies.
In accordance with his security orders, the train formed in a hollow square along the South Platte, and additional orders were read to the men:
> The pending treaty between the United States and the Sioux Indians at Fort Laramie renders it the duty of every soldier to treat all Indians with kindness. Every Indian who is wronged will visit his vengeance upon _any_ white man he may meet. As soldiers are sent to preserve the peace of the border and prevent warfare, as much as to fight well if warfare becomes indispensable, it will be considered a very gross offense for a soldier to wrong or insult an Indian.... Soldiers will attend to their own duties as soldiers and all intercourse with Indian lodges or individuals while at Laramie, or on the march from Laramie westward, will be through headquarters. Indian visitors will be kindly and patiently received, their chiefs only being admitted within the line, and such chiefs will be courteously conducted to headquarters for the transaction of their business.
The ink was scarcely dry on this special order when Carrington received his first Indian visitor, a Brûlé chief. He was Standing Elk, a tall broad-faced man, with a single feather in his thick shoulder-length hair. The Brûlé was camped nearby, and his curiosity had been aroused by the arrival of the long military train.
With Jack Stead as interpreter, Carrington went through the necessary formalities of greeting, first presenting Standing Elk with tobacco, then smoking a pipe with him. The chief's first inquiry was blunt: "Where are you going?" Carrington replied frankly that he was taking his troops to the Powder River country to guard the Montana Road.
"There is a treaty being made in Laramie with the Sioux that are in the country where you are going," Standing Elk said. "The fighting men in that country have not come to Laramie and you will have to fight them."
Carrington replied that he hoped the presence of his troops would prevent a war rather than cause one. He said he was not going to the Powder River country to make war on the Sioux, but only to guard the road.
"They will not sell their hunting grounds to the white man for a road," Standing Elk declared. "They will not give you the road unless you whip them." The chief was quick to add that he expected to sign the treaty and that Pegaleshka, who was called Spotted Tail by the white men, also would sign the treaty. The Brûlés wanted no war, he said. Those who talked of fighting were of the Miniconjou and Oglala bands, some of the Bad Faces led by Red Cloud.
With this sober warning of Standing Elk on his mind, Colonel Carrington rode into Fort Laramie early the next morning. He was accompanied by Major Van Voast and recruits for the 1st Battalion, assigned to replace Volunteers at the post.
The fort lay between the Laramie and Platte rivers, a rectangle of thirty or forty log-and-adobe structures surrounding a parade ground bare of sod. A flag flapped from a staff near a corner of the rectangle, a spot of color against the somber landscape. Extending to right and left of the post along the riverbanks was a mile-long ribbon of Indian tepees, white cones topped by blackened lodgepoles, smoke of cooking fires drifting from smoke holes. Several hundred varicolored ponies were corralled here and there, finding scanty pasture in the sandy valley. Small groups of Indians, a few mounted, moved aimlessly in the open spaces.
As Carrington's party splashed over the Laramie River crossing, they could see strips of bright cloth flying from an Indian burial platform a few hundred yards off to the north. They rode on between horse corrals, passed a row of warehouses, and were on the edge of the parade. Carrington noted then that there was no stockade around Fort Laramie. No sentries challenged. Indians and civilians wandered about as freely as if they were on the streets of a frontier town rather than in a military post.
At the southwest end of the parade a temporary platform with wooden benches had been erected for treaty negotiations. In the headquarters building beyond, Carrington and Van Voast met with the post commander, Colonel Henry E. Maynadier. The commandant was particularly pleased to greet Major Van Voast; three companies of the 1st Battalion had arrived some days earlier from Colorado Territory, and now that the major was there Maynadier would soon be free to relinquish command and arrange for the long-delayed discharges of his Civil War Volunteer troops.
Along with other duties, Maynadier was serving as a member of the Peace Commission, and within the hour he was introducing Carrington to his associates, Thomas Wistar, E. B. Taylor, and Colonel Robert N. McLaren. A number of Brûlé and Oglala chiefs were also arriving for the day's harangues, most of them tall, well-formed men wearing buffalo-skin or red blanket robes, fringed leggings and beaded moccasins. They stood with arms folded over their broad chests, the vermilion paint on their stolid faces glistening in the sunlight.
"I was introduced to several chiefs," Carrington recalled later. "Without exception, every chief to whom I was then introduced as the 'White Chief going up to occupy Powder River, the Big Horn county, and the Yellowstone' treated me coldly."
Commissioner Taylor, acting as chairman, was an ambitious Indian Bureau superintendent, dedicated to making a success of the treaty negotiations. He assured Carrington that everything was going well, that at least seven-eighths of the Brûlés and Oglalas were represented by leaders who would sign. Pegaleshka, or Spotted Tail, the influential leader of the Brûlés, had capitulated completely. It was his daughter, Fleet Foot, who lay on the platform in the post cemetery; on her deathbed she had asked to be baptized as a Christian and laid to rest there. Spotted Tail bowed to her wishes. After her death he slew her four favorite ponies and tied their tails to the four posts of the platform. He said that since his daughter had been adopted by the white man's Great Spirit he had no heart to fight the white man any more.
Carrington was encouraged by Taylor's remarks. He felt that if he could meet all the chiefs and some of the young warriors and talk with them face to face, he could convince them of his friendship. But such negotiations would require time, several days. Aware that Fort Laramie was in direct telegraphic communication with his headquarters at Omaha, he decided to request authority to remain at Fort Laramie until treaty negotiations were complete.
On the following morning, still confident of contributing personally to a treaty that would guarantee peace in the Powder River country, Carrington rode to the fort in company with his quartermaster, Lieutenant Brown, and several others of his regimental and headquarters staff. Mrs. Carrington and some of the other officers' wives, being eager to see the fort and visit the sutler's store, followed in an ambulance. A few wagons filled with infantrymen rolled in the rear. Carrington hoped to load these wagons with ammunition from the fort's magazine, and to mount the infantrymen on horses from the quartermaster's corrals. But this was to be a day of disappointments, even of personal danger, for Henry Beebe Carrington.
His first duty of the morning was to arrange for transfer of the ammunition. He had drawn up a requisition for 100,000 rounds which Omaha headquarters had assured him would be available. To his dismay, the post quartermaster informed him that Laramie would be placed in jeopardy if even a thousand rounds were removed. Carrington insisted on the thousand rounds.
The promised horses also were nonexistent. "I could not even find horses to make an exchange of twelve at that post," he testified later.
The only significant acquisitions for his expedition were twenty-six wagons loaded with provisions. Mules were available, but the drivers would have to be furnished from his command, removing half a company of men from combat readiness in case of sudden attack en route. A hasty inspection of the boxes and barrels also revealed that much of the food was inedible. The pilot bread, or hardtack, was so stale it had turned dark, and was so hard it could not be bitten, could scarcely be broken with a metal tool. "The flour drawn at Laramie," said Carrington, "was musty, caked, and very poor." And nowhere on the post could be found utensils for baking it.
Meanwhile, Margaret Carrington and her "little coterie of ladies" were enjoying the sights in and around Bullock &Ward's sutler's store. They saw cups of rice, sugar and coffee emptied into the looped-up skirts or blankets of the squaws, they stared at a tall warrior grimacing delightedly as he sucked a long stick of peppermint candy. "Bright shawls, red squaw cloth, brilliant calicoes, and flashy ribbons passed over the same counter with knives and tobacco, brass nails and glass beads... the debris of munched crackers lying loose under foot furnished both nutriment and employment for little bits of Indians too big to ride on mama's back, and too little to reach the good things on counter or shelves."
The wives were received courteously by the traders, W. G. Bullock and Seth Ward, both of whom had lived in the Platte country for years. They assured their visitors that they had nothing to fear from Indians around the fort. Ward had been a trapper, but now wore fine clothes and a soft hat of the latest eastern fashion. A huge diamond glittered in his shirt front, and a large gold watch chain hung over his vest.
According to John Hunton, one of the clerks who "could talk Sioux, Cheyenne or English just as the case comes to hand," the Laramie sutler's store averaged one hundred dollars per day in cash trade, with additional credit sales. Because paper money was used to pay soldiers, greenbacks were standard medium of exchange, the wartime shinplasters—five, ten, twenty-five and fifty cent notes—being heavily discounted in that inflationary period.
While his wife was absorbed in all the sights, sounds, and smells of the sutler's store, Colonel Carrington was meeting for the first time with some of the chiefs who had expressed opposition to opening the Montana Road. The chiefs, the commission members, and Carrington were seated around rough tables on the platform before post headquarters. On the parade in front of them, hundreds of warriors and squaws had gathered to watch and listen, some standing, some squatting, some sitting on extemporized benches under a blazing June sun.
Commissioner Taylor introduced Carrington and began a brief discourse upon the destination of the military train, and the purpose of the expedition. It was obvious from the beginning that the hostile chiefs already knew everything they wanted to know about the "Little White Chief." No doubt they had heard from Standing Elk full details of his conversation with Carrington the first evening the soldiers had camped outside Fort Laramie. As Carrington now rose to speak, the muttering grew in intensity, the Indians moving restlessly in their seats. Carrington's interpreter quietly suggested that it might be wise to allow the chiefs to speak first.
Out of the long harangues which followed, it became clear that some of the chiefs considered the presence of Carrington and his soldiers proof that the United States Government was determined to occupy their hunting grounds even without consent by treaty. Two Oglala chiefs made no secret of their bitter opposition to construction of forts in the Powder River country—Red Cloud and Young-Man-Afraid-of-His-Horses.*
Young-Man-Afraid-of-His-Horses declared that if the soldiers went any farther into Sioux country, his people would fight. "In two moons the command would not have a hoof left," he boasted.
In spite of the efforts of Commissioner Taylor and his associates, the covert hostility had now become open. Toward the end of that day's council, Red Cloud arose and made a dramatic speech. "Great Father sends us presents and wants new road," he shouted. "But White Chief goes with soldiers, to steal road before Indian says yes or no."
Most of the Brûlés remained silent, but an approving chorus of _hun-huns_ indicated that Red Cloud had followers on the platform. When the meeting began to grow disorderly, Commissioner Taylor ended it abruptly.
Margaret Carrington witnessed part of the affair while waiting in her ambulance beside post headquarters. "I could not hear what was said," she recorded, "but there was evidently some trouble which caused a sudden adjournment of the conference for the afternoon. Henry soon left the platform, walking rapidly towards his horse, which an orderly was lightly holding by the rein near the ambulance, and at his left were two Indians, one of them Red Cloud, who had his right hand upon a large knife at his side, and looking at Grey Eagle [Carrington's horse]. I thought the Indian was going to stab Henry in the back, and perhaps jump on Grey Eagle and ride off."
In her fright, Mrs. Carrington called her husband's name. He caught her warning and her indicative gesture, and slacking his step so the Indians would come within range, he drew his revolver belt to the front, keeping his hand upon it, then slowed his step, looking sidewise at the Indians and allowing them to pass. Whatever Red Cloud's original intention, he passed as stolidly as if Carrington were not even there, and walked with his companion across the parade and out of the fort.
Carrington was depressed by this show of cold hostility; he felt that his presence at the council had made matters worse instead of better. And before he left the fort for camp, another disappointment was added to his day of frustrations. He received a telegram from Omaha in reply to his request for permission to remain at Fort Laramie until the peace treaty was signed. Headquarters not only denied his request but ordered him to resume march for Fort Reno no later than June 17. This was the crowning blow. Now he would have only one day in which to make his peace with Red Cloud and the other hostile leaders.
As Carrington prepared to start back to his camp, Colonel Maynadier attempted to reassure him concerning Red Cloud's actions. "Indians always have those tantrums," Maynadier said. "Red Cloud was no chief when he first came here, but as the old warriors said that he was at the head of the young men whom they call Bad Faces... the commission [appointed] him a chief as they did Spotted Tail... to make him our friend."
After learning this, perhaps Carrington felt there was still a glimmer of hope that Red Cloud might yet be won over from war to peace. In the evening he talked with Jim Bridger about this and other matters, but Old Gabe was not sanguine about prospects. Instead the scout added one more burden to Carrington's bad day. He had seen kegs of gunpowder on Indian ponies around the river camps, and some of them were going north away from the fort. Carrington thought of the miserly thousand rounds of ammunition so grudgingly issued him that day, and was puzzled that even Bridger could not tell him who was responsible for the kegs of powder in the Indians' possession. After four years of Civil War experience, he was accustomed to military muddling, but now he was beginning to wonder if he was not taking his 2nd Battalion into a muddle more dangerous than he had bargained for.
If he had hoped for a better day on June 16, he was quickly disillusioned. The first tidings of morning concerned Red Cloud and his followers. During the night they had dismantled their tepees, loaded their travois, and vanished. Their trail led north toward the Powder River country.
When Carrington reached the fort, he found the peace commissioners arranging for a hasty conclusion to the council. Perhaps Commissioner Taylor feared that any further delay might be disastrous; other bands might follow Red Cloud's example and depart without signing a treaty.
As usual, the treaty signing was an elaborate ceremony. The chiefs were seated in a circle with the commissioners, and after long palavering, a fancifully carved redstone pipe was passed around, each Indian taking two or three slow puffs of smoke. They were all old men—Spotted Tail, Standing Elk, and the others—and it must have been clear to the knowledgeable white men present that these chiefs did not represent any of the belligerent young warriors in the north.
After signatures were duly affixed and witnessed, the commissioners distributed presents, and in a few hours "the friendly camps were ablaze with mounted Indians decked in yellow, red, and other brilliantly colored cheap fabrics flying in the winds."
Private William Murphy of Company A, who had come into Laramie with a duty detail, said the Indians were also given beef steers to kill. "They ate them all but the hides, hoofs, and horns without washing.... We were shown samples of marksmanship with the bow and arrow. The young boys could hit a button, pencil or any small article at about thirty yards."
All afternoon the fort was a festive whirlpool of colors, sounds, and smells. "Indians filled every available space, dressed, half dressed and undressed," said Lieutenant Bisbee, "all mingling with soldiers, teamsters, emigrants, speculators, half-breeds, squaw men, and interpreters... under the eaves of buildings, by doorsteps and porches were groups of Indians in assorted sizes, sexes and conditions, with the element of cleanliness just as critically wanting as usual among the aborigines."
In his listing of human types frequenting the fort that day, Bisbee overlooked one bizarre newcomer who was engaged in an occupation then extremely novel to the frontier. He was Ridgway Glover, a photographer from Philadelphia, a well-to-do Quaker, with vague ambitions of recording the entire frontier in photographs. "I hope to make my talents for making negatives available to science," Glover wrote the editor of the _Philadelphia Photographer_ from Fort Laramie. "I had much difficulty in making pictures of the Indians at first.... Some of the Indians think they will die in three days, if they get their pictures taken. At the ferry today I pointed the instrument at one of that opinion. The poor fellow fell on the sand, and rolled himself in his blanket. The most of them know better though, and some I have made understand the light comes from the sun, strikes them, and then goes into the machine. I explained it to one yesterday, by means of his looking-glass, and showed him an image on the ground glass. When he caught the idea, he brightened up, and was willing to stand for me. I make them Ferrotypes, and put brass around them, and they think they are _wash-ta-le-poka_ (their superlative for good)."
Like all frontier photographers, Glover had his problems with wind, sand, and lack of clean water for washing negatives. "The water is muddy, and out of fifty negatives I have taken, I shall only publish prints from twenty-two.... The wind was blowing, and the sand flying. The negative is therefore not quite clean." In spite of difficulties he obtained stereoscopic views of Indian camps around Fort Laramie, and single and group photographs of Indians.
A blond-haired, energetic young man, Glover quickly became acquainted with Jim Bridger and Colonel Carrington, and when he learned of the proposed new forts on the Montana Road, immediately decided to visit the Powder River country. "I expect to travel, and trap this fall, and spend the winter in Virginia City, Montana, and to secure some winter Rocky Mountain scenery." Carrington's main column, however, was leaving too early to suit Glover's plans. The photographer decided to wait and travel north later with another wagon train.
## 2.
Among last-minute duties at Fort Laramie, Colonel Carrington dispatched two reports to Omaha, stating in the first that he was still short of ammunition, and that the supply of hard bread obtainable at Laramie would last only four days. "I find myself greatly in need of officers, but must await the arrival of new appointments, or until others are relieved from recruiting service. I move tomorrow."
After he had sent this off, he decided he should be more explicit concerning his need for ammunition:
> I respectfully urge that the supplies of ammunition en route from Leavenworth, per order, be forwarded forthwith. The entire supply of .58 caliber at Laramie being only 1,000 rounds renders many troops almost powerless in case of delay of supplies and remoteness from base. All the commissioners agree that I go to occupy a region which the Indians will only surrender for a great equivalent; even my arrival has started among them many absurd rumors, but I apprehend no serious difficulty. Patience, forbearance, and common sense in dealing with the Sioux and Cheyennes will do much with all who really desire peace, but it is indispensable that ample supplies of ammunition come promptly.
Carrington was still overconfident. But he had learned much during his three days at Fort Laramie.
When E. B. Taylor came out that evening to bid the colonel and his wife farewell, the commissioner was frank enough to say that Carrington should not place too much confidence in the treaty signing insofar as it would affect the expedition. Neither Carrington nor his wife were surprised or dismayed at this confirmation of their own feelings. As Margaret Carrington put it, "the ladies kept up a good heart, and as they could not well go back, concluded to go on, but agreed to limit their riding on horseback to the vicinity of the train."
Being a religious man, Henry Carrington disliked marching on Sunday, but at dawn of June 17, he put his column in motion, crossed Laramie River and headed northwest past the fort. Many of the Indians were also preparing to depart, leaving barren circles where their tepees had stood on the greening grass.
As the wagons creaked past the cemetery, all could plainly see the scaffold where Spotted Tail's daughter lay, the white tails of her ponies swaying in the morning breeze. Dwarf sunflowers, cactus and thistle blossoms brightened the slope, but off in the distance the hills were bare and bleak.
After leaving the fort, the Montana Road followed the North Platte. On the left was a perpendicular bluff, and in places the trail was so narrow that wagon hubs scraped against yellow clay walls upon which earlier travelers had carved their initials.
Carrington's command now consisted only of the 2nd Battalion. His eight companies, with regimental headquarters staff and band, totaled about seven hundred men, "splendidly furnished with everything except arms, ammunition, and horses." Almost five hundred of these soldiers were new recruits, and to train and lead them Carrington had only twelve officers, including himself.
Whenever he gazed at the barren landscape across the Platte, Carrington was looking at the southern border of the Mountain District, a vast region of mountains and plains—unmapped, mysterious, ominous. Once they were across the river at Bridger's Ferry, he would be responsible for the peace and security of this domain. He believed that his force was sufficient to erect new forts, to build barracks, warehouses and stables, to make preparations for winter, to protect emigrants from small parties of thieving Indians. Yet he knew, inexperienced though he was in Indian fighting, that his seven hundred men could never sustain an aggressive campaign against the powerful Sioux and Cheyennes if the Indians chose war instead of peace. With the help of God, and by trusting in human forbearance and reason, he hoped to avoid such a war.
A few miles out of Laramie, Jim Bridger sighted the dust of a mounted party approaching from the west. The scout dropped back to notify Carrington; the train was halted and security precautions taken immediately. A few minutes later the horsemen came in peacefully, at a walk. They were Indians, Winnebagos, a thousand miles from their Wisconsin homeland.
For the past year this company of Winnebagos had been serving as soldiers at Fort Reno; the commandant there had discharged them a few days previously. When they learned that Carrington was marching to occupy the Powder River country, several begged to be allowed to return with him. At first, Carrington was inclined to add these Indians to his command, but Bridger was shaking his head. The Winnebagos, Bridger said, were the best of scouts, but they had been deadly enemies of the Sioux for many years, and some of the chiefs at Laramie had expressly demanded as a condition of the treaty that the Winnebagos must leave the country. To keep any one of them on, Old Gabe explained, would be construed by the Sioux as a hostile act.
Carrington admitted he had not known of this. He thanked Bridger for his counsel and informed the Winnebagos diplomatically that he had no authority to employ them.
The column moved on, passed Nine-Mile Ranche, and halted a mile and a half beyond at a campsite along the North Platte. Dissatisfied because the train had covered only thirteen miles the first day, Carrington had the men bugled out at 3 A.M. and kept the wagons moving briskly until noon. On Bridger's advice, however, after a sixteen-mile march, he made an early halt on Little Bitter Cottonwood. A dangerous defile lay just ahead, the scout said, with no campsites in reach before sundown.
On the 19th they pushed forward eighteen more miles, passing the last telegraph station, Horseshoe Creek. None could have imagined on this bright June day that only six months later the operator there would flash to the world the first news of the Fetterman Massacre.
All afternoon the wagons rolled through a crooking gorge, with rock walls on either side rising to conical summits. Jim Bridger and his guides kept an alert watch for Indians, but there was no sign-of hostiles anywhere. During one rest stop Adjutant Phisterer and Surgeon Horton led a party of wives into a side canyon in search of colorful stones and to try the echo effect of pistol shots. Bridger rode up and quietly warned them: "There's Indians enough lyin' under wolfskins or skulkin' on them cliffs, I warrant. They follow ye always. They've seen ye, every day, and when ye don't see any of 'em about, is just the time to look for their devilment."
The camp that evening would be the last before they reached the Platte and entered the Mountain District. Lieutenant Phisterer rode ahead with Bridger, selecting a velvety sward beside the river, with a backdrop of cedars. When Carrington saw the location, he was so pleased that he named it Camp Phisterer. The dashing German was one of his and Mrs. Carrington's favorites. "He was most conspicuous in all that contributed to the pleasure or progress of the march," she wrote in her journal.
Before noon of the 20th, the train reached Bridger's Ferry. This was familiar ground to Jim Bridger, who had bought and improved the crossing ten years earlier. After collecting a small fortune in tolls, the scout had grown reckless, sold out, and moved on to less confining activities. A squaw man named Mills was the current proprietor, and he was much excited over an Indian raid upon his livestock which had occurred only twenty-four hours earlier.
Because his wife was a Sioux, Mills previously had been immune from Indian depredations. After the raid he had sent some of his employees, also Indians, in pursuit; they had returned after recovering part of the stock. The raiders, they said, were Bad Faces of Red Cloud's band.
Jim Bridger advised Carrington that this was not a good sign. If Red Cloud's followers had worked themselves up to raiding stock from a squaw man, they could be expected to stampede animals from the train at the first evidence of carelessness.
As two days were required to ferry his wagons across the Platte, Carrington had considerable time to consult further with his guides. In addition to Bridger and Williams, he had acquired two others at Laramie: James J. Brannan and James P. Beckwourth. Brannan had served as scout with one of General Connor's columns the previous year, and knew the Tongue River country above the Powder. Beckwourth, a mulatto, had several Crow wives, and was considered a minor chief in the tribe. He had been recommended to Carrington as a useful negotiator. From his Crow friends, Beckwourth could obtain intelligence concerning the activities of hostile Sioux, Cheyenne and Arapaho bands in the north.
After discussions with his staff and guides, Carrington on June 21 drew up a new series of orders which he hoped would enhance security when march was resumed across the Mountain District to Fort Reno:
> The instructions heretofore given respecting the encampment of the command belonging to the Mountain District, Department Platte, derive special importance from the doubtful attitude of certain Indian tribes which lie in advance of the command and along and near its route. A careful and prompt conformity to orders will save the reorganization of a camp after it is once established. The following additional instructions are given:
1. No mules will be unharnessed or turned loose until the wagon-masters shall be so instructed by the chief quartermaster [Lieutenant Brown].
2. When the trains are parked the chief quartermaster will report at headquarters for orders or any additional instructions before the wagon-masters receive their instructions.
3. All wagon-masters will, accordingly, report to the chief quartermaster after trains are parked, and will, with all their assistants and subordinates, be held to strict obedience to orders received from or through this office.
4. Commanding officers of battalion or detachments will report daily, at 8 o'clock P.M., at the office of the acting assistant adjutant-general [Lieutenant Phisterer] for marching orders for the day following and during the march. Immediate report will be made of Indian signs or the appearance of Indians, indicative of doubtful or hostile intentions; also of any serious difficulties of the road, impeding or interrupting the march, or of any other substantial cause of delay, which will throw any portion of the command behind or break up the close order of march.
5. Assignments of commands to their respective locations in camp will be made from headquarters, and will be carried into effect under the direction of the chief quartermaster, and those assignments will be daily made on survey of the ground selected, with view of the greatest compactness and efficiency in case of alarm, access to grass, water, etc.
6. As the only probable risk to be entertained on the march will be that of attempt to stampede or steal stock, the wagons will be corralled closely, so as to prevent any possible outbreak of animals, if alarmed, and no regard will be paid to night-feeding of animals, inconsistent with their perfect security; and wagon-masters, herdsmen, and drivers must observe the same regard to order, the same silence after tattoo, and the same rules as to leaving camp without due authority which govern the officers and soldiers of this command.
7. No discharge of firearms within or near the camp, or during the march, except the discharge of pieces by the guard, will be permitted, unless by due authority, and no firing will be permitted on the march, even upon Indians showing hostile intent, except under immediate orders of a commissioned officer; and not then without reference to headquarters, unless an attack be so sudden as to require instant repulse.
8. Bands of Indians met on the march desiring parley or conference will be referred to headquarters, or passed with simple recognition and common courtesy, and previous orders respecting intercourse or dealings between soldiers and Indians will be rigidly enforced.
9. Headquarters, with pioneer party, will as a general rule move in advance, then will follow the infantry command, then headquarters train, the train of the second battalion, and the present mounted rearguard thereof, then the supply trains, and in rear of all wagons and mounted command.
10. Unless otherwise at any time ordered, when the command halts for rest, trains will also halt, so as to preserve the entirety of the command and prevent inconvenience to the troops by the passing or sudden stopping of trains.
11. The camp of the infantry and the mounted detachment will conform in front to the line of wagons they cover, and in depth will as at general headquarters be restricted to the space actually necessary to give a reasonable distinctness of position to quarters for officers and companies.
12. The trains must be kept compactly closed up, and the chief quartermaster is charged with the direct enforcement of this instruction.
13. Immediately after coming in camp, the commanding officer of the mounted detachment [Lieutenant Adair] will report to the field officer of the day six noncommissioned officers and 42 privates for picket duty. These men are to form a cordon or line of pickets beyond the grazing ground, and will be returned to their camp by the senior noncommissioned officer with them after all the animals have been driven in and corralled. On the approach of Indians, they will give the herders timely notice to collect and drive in the stock and make report thereof to headquarters.
14. Every evening at 5 o'clock the commanding officer of the second battalion [Captain Haymond] will cause one company officer and one company to report to the assistant adjutant-general for outpost duty; the officer with this company will perform the duties of a field officer of the day and report to the colonel commanding for orders. The company thus detailed will, previous to reporting, be inspected by the adjutant of the second battalion [Lieutenant Bisbee] and every man thereof should be supplied with 10 rounds of ammunition.
While Carrington was composing this comprehensive set of orders, his men were ferrying wagons and mules across the Platte. Thanks to the ingenious system of cables and pulleys devised by Jim Bridger, round trips averaged only eleven minutes. During the afternoon a detail of about one hundred lusty-lunged men, armed with poles, forced the beef herd into the swift current and compelled the animals to swim across.
In early daylight of the 22nd, the last wagons were ferried over, and the train rolled smoothly for sixteen miles along the north bank of the river, camping opposite the mouth of La Vinta Creek, where water, grass, and wood were in abundance. "We had a picket line outside of the guards," Private Murphy noted, in reference to Carrington's new orders.
On the morning of the 23rd the column swung northward from the Platte, mules straining against traces to pull the heavily loaded wagons across several miles of red buttes, sand hills and rocky ridges. Once they were out of the valley the scenery was spectacular; the windings of the river could be seen far below, the level plain beyond extending into the horizon.
Near the Sage Creek crossing of the old Mormon Trail, they halted for nooning, and here discovered a sort of portable "ranche," an extemporized plank shed, offering merchandise to expected summer travelers over the Montana Road. The proprietors were Louis Gazzous and Henry Arrison, the former known to Jim Bridger and his fellow guides as "French Pete." Gazzous was married to a Sioux, and several of his half-breed children were playing happily over displays of canned fruit, liquor, tobacco, cutlery, and cheese.
Gazzous was a friendly sort, eager to gain the good will of the military, and when Surgeon Horton's wife expressed admiration for a young antelope the Frenchman was raising as a pet, he presented it to her as a gift.
Although the 24th was a Sunday, Carrington decided the urgency of his mission was too compelling to spare a day for rest. That night the train camped at the head of Sage Creek, and on Monday marched to the South Fork of the Cheyenne, where buffalo grass and timber were plentiful, and water was obtainable by digging into a sandy stream bed.
On the 26th, acting upon Jim Bridger's advice, the train cut away from the old Bozeman Trail and covered twenty miles in rapid time to Antelope Creek. Early the following morning, they had their first view of the Big Horns, bright under the blaze of the eastern sun. Margaret Carrington excitedly borrowed her husband's field glass for a closer look. Somewhere in the vicinity of that magnificent snow-crested range, still eighty miles away, the 2nd Battalion would build the first fort.
With their destination now in view, the infantrymen marched with lighter steps. "In half an hour," Mrs. Carrington wrote, "the air itself was invigorated by the currents from the snow banks; and even at that distance shawls became necessary, the ambulance side curtains were closed, and it seemed as if a November day was to succeed the summer's morning."
Off to the right, the travelers soon sighted the four columns of Pumpkin Buttes, and by nightfall they were at the Dry Branch of Powder River. Fort Reno was now only a long day's march away. Thus far their enemies had been summer heat, dust, shortage of rations, and plain weariness of bone and muscle. The Indians as yet had made no demonstrations of hostility.
If the mood among the men was relaxation of tensions, there was certainly no relaxation of security precautions on this last camp before Reno. Bridger had assured Carrington that bands of Sioux were watching their every move; the scout had picked up Indian signs every day; at the first slacking of vigilance they would strike. On this last night, Carrington cautioned his officers to follow security orders to the letter. And because he was eager to reach Fort Reno early the next day, he also announced that march would be resumed as soon after midnight as the sky lightened.
By sunup the wagons were rolling again. For twelve miles the road followed the Dry Fork's bed, wagon wheels sometimes running in damp sand, sometimes in three or four inches of milky water. During the early morning they were confined to a narrow butte-locked basin, and Bridger and his fellow guides were doubly vigilant, riding far up on the powder-colored, cactus-studded ridges.
At last they swung northwest out of the Dry Fork, facing across a dusty gray plain broken by red-shaled hills. Even at midmorning the sun burned at their backs, but Carrington kept the column moving steadily. Shortly before noon the advance party topped a rise, and there was Powder River. Just beyond on a level bench above the stream lay Fort Reno.
With his headquarters party, Carrington led the way down through a mile of cottonwood bottomland, and at almost exactly 12 o'clock they were splashing across the shallow reddish stream. While Carrington rode on to report to the Reno commander, the first wagons were turning to form a corral just south of the fort.
Fort Reno was an open post, the building constructed of Cottonwood logs with earthen roofs, a high staked fence protecting warehouses and stables. The first view of its bareness was depressing, but Margaret Carrington recorded cheerfully that "so far, we are all right, and fast seeing the country." Every member of the expedition knew that this fort, however unadorned it might be, was their last link with civilization, the jumping-off place before they entered the _terra incognita_ which lay between them and the Montana gold settlements.
General Patrick Connor had ordered its construction during his unsuccessful campaign of the previous summer, and since the withdrawal of his columns, the post had been manned by Companies C and D of the 5th U.S. Volunteers and the company of Winnebago scouts met by the expedition on the first day out of Laramie. The 5th U.S. Volunteers was one of those odd by-products of the late Civil War, the enlisted men being "galvanized Yankees," or former Confederate prisoners who had taken the oath of allegiance with a proviso that they would not be required to fight against the South but only against the Indians.*
The officer in command was Captain George M. Bailey, and he greeted Colonel Carrington almost as a deliverer. Bailey's men were in low spirits, irritable, some of them almost mutinous. The Civil War had been ended for a year, and they wanted to return home.
Carrington explained that he carried no orders for the discharge of the 5th U.S. Volunteers, but he did possess authority to appropriate all ordnance stores, rations, supplies and government livestock. In other words, Fort Reno was to be moved some miles to the northwest, probably near Tongue River where wood, water and grass were more abundant.
The dilemma of what was to be done with the galvanized Yankees was resolved that afternoon by arrival of a mail courier from Fort Laramie. Among other messages for Carrington was a telegram from General Pope authorizing relief of the U.S. Volunteers and directing them to proceed to Fort McPherson for eventual discharge from service. John Ryan, a private in the 2nd Battalion, was present in the fort when the news was announced to the Volunteers. "They were certainly glad to be relieved," he said. "They had had no trouble with the Indians but had found the place far from being desirable as a permanent place of residence."
Meanwhile, the 2nd Battalion proceeded to take over operation of the fort. Lieutenant Adair's mounted command camped at the base of the hill for ready access to the alkaline waters of the Powder, the wagon train and infantry companies formed their usual tight corral south of the fort, and regimental headquarters tents were erected near the fort's flagstaff. To establish proper military chain of command, Carrington ordered that Fort Reno would be garrisoned by Companies A, B, C, and H, under Captain Tenodor Ten Eyck, this command to be responsible for dismantling the old fort and establishing the new one.
As the busy day drew to a close, a sudden summer hailstorm swept down from the Big Horns. Private William Murphy, on herding detail, said the hailstones were as large as pullets' eggs. "We had had some trouble about an hour before in getting the stock to ford the Powder River, but they went back over it as though it were dry land. The animals that were picketed pulled their pins; the hobbled ones and even the stock the herders were riding all stampeded. The herders finally stopped their horses two or three miles from where they started."
Not long after his arrival at Fort Reno, Colonel Carrington was surprised to discover the presence of three emigrant trains camped a few hundred yards beyond the post. These Montana-bound caravans had halted a few days earlier on the advice of Captain Bailey and were awaiting arrival of the soldiers before proceeding farther.
On the morning of the 29th, Carrington rode down to confer with the leaders. He was shocked by their lack of security precautions, by the slovenliness of their camps. "They were waiting for the protection it was understood would be furnished by the troops... these emigrants were impatient to proceed, but so mixed with mule and ox trains that they had no concert of purpose. They were naturally restless under the circumstances, and could not agree among themselves."
Carrington realized at once that the movement of civilians through his Mountain District was going to be a greater problem than he had believed. He informed the emigrants that within twenty-four hours he would draw up a set of regulations for civilian travelers to ensure their safety through the Indian country. One of the train captains made light of the Indian danger. "We'll never see an Indian," he said, "unless they come to beg for sugar, flour, or tobacco."
Carrington hoped the man was right, but warned all the travelers to stay in camp until they received further orders from him. On his way back to the fort, he noted a herd of horses and mules grazing unguarded in a ravine. These animals, he learned, were the property of Sutler A. C. Leighton, who seemed confident the Indians would not disturb them.
That afternoon Carrington visited Leighton in his trailside store just north of the fort. Perhaps the colonel wished to become better acquainted with the sutler, who had been authorized to supply stores for the three new forts. Carrington had just entered Leighton's quarters when a soldier rushed in shouting "Indians!" and excitedly informed the sutler that his livestock was being raided. The men rushed to the door, and off across the Powder they could see the herd stampeding up a hill, followed by a party of Indians. Leighton was both astonished and angry; he had never had any trouble with the Indians before, he declared.
As soon as Carrington could reach his headquarters, he ordered his bugler to sound the alarm, and a few minutes later the mounted infantrymen were saddling up. In less than half an hour after the Indian raid, Captain Haymond and Lieutenant Adair with ninety men were in pursuit. But the time lapse, Carrington knew, had been too great. His men must learn to react more quickly in future.
The afternoon wore on, watchers in the fort keeping an eye out for Haymond's pursuit party. There had been no sound of rifle fire, no trace of riders on the hills across the Powder.
Meanwhile, in preparation for moving the fort, Captain Ten Eyck's details were busily loading wagons with provisions from the warehouses. "The ware-rooms," said Private Murphy, "were built of cottonwood logs, chinked and daubed with mud. Some of the daubing had dropped out and snow had drifted in [during the previous winter]. The dirt roofs also leaked and added to the dirty mess. We loaded up some sacks of bacon. I do not know how old it was, but the fat had commenced to sluff off from the lean and it was from three to five inches thick. There was a lot of flour in the storerooms and the mice had tunneled through it and the bacon, evidently for some time."
The day ended with the usual routines of retreat, roll call, mess, and guard mounting, but Haymond and Adair and their pursuit party were still missing. Carrington spent a bad night, was immensely relieved the next morning to see the column come riding in across the Powder, with no empty saddles. Captain Haymond reported that he had followed the raiders' trail into the Pumpkin Buttes, probably thirty miles, but had captured only one Indian pony abandoned so hastily that it still bore a pack. Haymond exhibited the contents—bags of brown sugar, coffee, navy tobacco, an army blanket, a stable frock, a folded length of bright calico. All Laramie treaty presents! The raiders no doubt had followed the train all the way north, waiting for an opportunity to take livestock. Sutler Leighton's herd had offered too tempting a target, too easy a reward for their patience. For Carrington, the incident was proof that his strict security precautions were necessary; the well-guarded military livestock had not even been threatened.
On the last day of June a decision was made, either by Carrington alone, or in council with his staff and civilian guides, not to abandon Fort Reno entirely. Possibly the presence of civilian wagon trains influenced the judgment; at any rate it was decided that at least one secure stopping place was needed on the long route between Bridger's Ferry and the future site of New Fort Reno—a place where travelers could halt to rest lame stock and repair wagons. Carrington assigned one of his companies to garrison the station. Details from this company were to be used for escorting mail, aiding travelers in distress, and other emergency duties. For want of a better name, the place would be called Reno Station.
It was also decided that the 2nd Battalion could not possibly provide military escorts for the many emigrant trains expected to be moving over the road during the summer. Yet the safe passage of civilians was Carrington's immediate responsibility, and recognizing this, he issued on June 30 a series of regulations governing the movement of civilian trains to Montana:
1. All trains, whether large or small, must stop at Reno Station, formerly Fort Reno, on Powder River, and report to the post commander.
2. Thirty armed men constitute a party which, upon selection of its commander or conductor, will be allowed to proceed. The reduction of this number will depend upon the general conduct of trains and the conditions and safety of the route, of which due notice will be given.
3. When a train shall have organized, the conductor will present to the post commander a list of the men accompanying the said train, upon which list, if satisfactory, he will endorse, "Permission given to pass to Fort Reno [soon to be named Fort Phil Kearny]." Upon arrival of a train at Fort Reno [Fort Phil Kearny], the conductor will report with his list, indorsed as above mentioned, to the post commander to receive the same indorsed approval as in the first instance to pass to the next post. This examination and approval must be had at each post, so that the last post commander on the Upper Yellowstone will have the evidence that the train has passed all posts.
4. The constant separation and scattering of trains pretending to act in concert must be stopped; and for the information of emigrants and well-disposed citizens the following reasons are given: viz:
> First, nearly all danger from Indians lies in the recklessness of travelers. A small party when separated, either sell whisky to or fire upon scattering Indians, or get in dispute with them, and somebody is hurt. An insult to an Indian is resented by the Indians against the first white men they meet, and innocent travelers suffer. Again, the new route is short and will be made perfectly secure. The cooperation of citizens is therefore essential for their own personal comfort as well as for the interests of the public at large; and if citizens ask, as they will of course rightly expect, the protection and aid from Government troops, they must themselves be equally diligent in avoiding difficulties with Indians, or among themselves, and the consideration paid to any complaint will be measured by the apparent good faith with which citizens regard the regulations for the management of the route.
5. When trains scatter and upon reporting at any post there shall be found a substantial variation from the list furnished, all of the remaining teams will be stopped until the residue of the train arrives, or is accounted for; and until this is done they will not be permitted to unite with other trains to complete numbers, which their insubordination or haste has lost or scattered.
6. The main object being perfect security to travel, all citizens are cautioned against any unnecessary dealings with Indians, against giving or selling ardent spirits, against personal quarrels with them, or any acts having a tendency to irritate them, or develop hostile acts or plans. A faithful and wise regard for these instructions will, with the aid of the Government troops, insure peace, which is all important and can be made certain.
7. A copy of these instructions will be properly and publicly posted at the office of each post or station commandant, and all conductors of trains will have their attention called thereto, with instructions to notify all who travel in their charge.
* Phisterer is best known today as the compiler of _Statistical Record of the Armies of the United States,_ a standard source book for Civil War historians.
* A more exact translation of the latter: The-Mere-Sight-of-His-Horses-Inspires-Fear.
* A unique member of these galvanized Yankees at Fort Reno was Private Milo B. Tanner who was actually a Union soldier originally of the 121st New York Volunteers. Captured by the Confederates at Cold Harbor, he was sent to Andersonville prison. Tanner escaped from there in a stolen Confederate uniform and fell in with a Confederate patrol, only to be captured by Colonel Benjamin Grierson's Federal cavalry raiders. Unable to convince Grierson that he was truly a Union soldier, Tanner was sent to prison at Alton, Illinois, where the authorities also refused to believe his story. In desperation, he finally took the oath of allegiance and eventually found himself in a blue uniform again at Fort Reno.
# _IV. July:_
MOON WHEN THE CHOKECHERRIES ARE RIPE
> _Whatever my own force I can not settle down and say I have not the men; I must do all this, however arduous. The work is my mission here and I must meet it._
A MOST WELCOME VISITOR to Fort Reno on July 3was Major Henry Almstedt, paymaster for the Department of the Platte. Although the men had received no pay for four months, almost any experienced frontier commander would have delayed payment until after the July 4 holiday. But perhaps Carrington did not realize how much contraband whiskey a flood of greenbacks combined with a holiday could attract even at so remote a post as Reno.
Independence Day was started in proper patriotic fashion by the firing of the fort's 12-pounder field howitzer. Paymaster Almstedt, being the only artillery officer present, supervised the loading and placed the portfire. A review and a few patriotic orations followed, and the men were free for the day.
According to Private Murphy there was some bootlegging but not much drunkenness. He described the punishment of one man who imbibed too freely that day: "At the guard tent four stakes were driven into the ground and the drunken soldier was stretched out full length and tied to them. This was called the 'Spread Eagle.' The sun was beating down on him when I saw him, and I thought he was dead. Flies were eating him up and were running in and out of his mouth, ears and nose. It was reported that he died, but in the army one can hear all kinds of reports."
After reveille next morning all celebrants—regardless of the condition of their heads—resumed duties. Special details were assigned to remove wheels from wagons, grease axles, secure all nuts. Others inspected harness for flaws. The fort's six pieces of artillery were cleaned and prepared for movement; in addition to the 12-pounder field howitzer, there were five 12-pounder mountain howitzers.
Quartermaster Fred Brown kept the headquarters clerks busy invoicing supplies being transferred from warehouses to wagons, and it was already evident that available empty wagon beds could haul only about half the stocks.
As Carrington had definitely decided to keep Reno active, the depot stores which must be left behind presented no problem. Lieutenant Kirtland's Company B was ordered to remain at Reno, the post commander to be Captain Joshua Proctor, an aging officer with a full gray beard and a harassed though kindly face. Twenty-two horses were assigned so that Kirtland could mount about one-third of his men for necessary messenger and escort duties.
At four o'clock the morning of July 9, the seven remaining companies of the 2nd Battalion marched northward out of Fort Reno, exact destination unknown. The day before, a mail courier from Laramie had arrived, and the news from Omaha was not good; the Mountain District could expect no reinforcements before autumn at the earliest.
Carrington passed the word to his officers and established tentative assignments. Ten Eyck with three companies would command the new Fort Reno; regimental headquarters and the band would also occupy that post. Kinney with two companies would establish a post somewhere on the Big Horn River. Haymond with two companies would proceed to the Upper Yellowstone. It would be a long line, thinly held, but Carrington was determined to carry out his orders.
The day chosen for the march was the hottest of the summer of 1866. The sun was blinding, the mercury reaching 113 in the shade by afternoon. Even the sagebrush seemed to shrivel under the baking heat. "Many of the soldiers had bad feet," said Private Murphy. "Add to this the fact that there was only one ambulance available for sick soldiers, as the women and children had all the others in use, and you have a picture of what it meant for a soldier to be sick."
Except for water carried in canteens and barrels, there was none anywhere between Reno and Crazy Woman's Fork. Drivers were forbidden to use any for wetting wagon wheels which began to shrink, loosening the metal tires. Spares were used up rapidly.
And for the first time, they saw parties of Indians riding on the flanks, or watching from rises far ahead. Bridger and his guides parleyed with one small party of Sioux. These Indians said they were going across the Big Horns to fight the Shoshoni, but when Bridger reported to Carrington the scout expressed skepticism. He suggested the Sioux were counting soldiers, wagons and livestock—sizing up the strength of the train.
After twenty-six miles of heat, aching weariness, and wagon wheels falling apart, they reached Crazy Woman's Fork at dusk, finding sparse grass burned to a crisp and only a trickle of alkali water in the creek. From the guides, the soldiers heard two stories as to how the place received its name. One was that a squaw living alone there in a tepee had become demented and died; the other told of a party of whites attacked there, one man being killed and mutilated before the eyes of his wife, who became insane, wandered away, and disappeared forever. After what they had seen of Crazy Woman's Fork, the men could easily believe either story. It was not a good place to be.
Next morning the first order of business was a wagon inspection by Carrington and Brown. Almost half the wagons were unfit for another day's journey, and it was soon apparent that temporary repairs would not suffice. So much damage had been done to axles, spokes, and tires that smithies must be improvised. Details went to work immediately, cutting timber and digging charcoal pits. Every available wheelwright and blacksmith was drafted from both soldier and civilian contingents. One ingenious workman devised a method of cutting gunny sacks in strips, soaking them in water, and tacking them to repaired wooden rims; when a heated tire was placed over one of these strips, it made a perfect seal.
After forty-eight hours of waiting for sufficient charcoal to be burned, Carrington grew restless. The best days of summer were passing, and he had three forts to build before winter. On the 12th, he ordered Captain Haymond to take command of the temporary camp at Crazy Woman's Fork. With Captain Ten Eyck and Companies A, C, and H, he would move on toward Tongue River.
Marching early to avoid the heat, the three companies by sunrise found themselves in a new and different country. "One narrow divide only is crossed, and the transition is like the quick turn of a kaleidoscope," wrote Margaret Carrington. The air was suddenly delightfully cool. Sagebrush and cactus disappeared, to be gradually replaced by green grass. Forests of evergreens showed dark against the slopes. By noon the first horses were plunging into Clear Fork, a swift mountain-fed stream "so clear that every pebble and fish is well defined."
As they had been traveling steadily for nine hours, Carrington ordered his abbreviated train into camp. Tents were pitched along the banks of the rushing creek, and Mrs. Carrington told of how she, Mrs. Bisbee, and Mrs. Horton—the only women in the advance party—were sitting in camp chairs admiring the scenery when to their horror they discovered rattlesnakes coiled under their chairs. An orderly, hearing their screams, rushed to the rescue.
During late afternoon a small band of Indians visited the camp, cautiously escorted in by guides Bridger, Williams and Brannan. "We were peacefully inclined," Lieutenant Bisbee commented, "having nothing as yet to fight for, but suspicions grew strong that they were treacherous and we tied Gene (my son) by a trunk strap to the tent pole to prevent his straying away."
Another of the small boys in camp, six-year-old Jimmy Carrington, afterward recalled these last nights of the long journey to the site of Fort Phil Kearny. "Nightly, we heard the weird and mournful howling of wolves, sometimes the deep rumble of a stampeded herd of buffalo, that fairly shook the earth. And all through the dark, at regular intervals, the reassuring calls of the sentinels on watch."
Somewhat reluctantly next morning tents were struck and march resumed, the snow-covered Big Horns towering in the west, the land growing richer in timber and grass. Mounted Indians appeared suddenly on a high hill to the left, then vanished. After passing Rock Creek, Bridger's forward scouts came upon two small pieces of wooden cracker box posted by the roadside. Dismounting, they found messages scrawled on the boards, dated one week earlier. Indians had attacked two civilian trains there, driving off oxen and horses.
Bridger reported his discovery to Carrington. Soldiers were ordered to ready rifles, and flankers were sent farther out on the ridges. Hourly halts were suspended until they were clear of a long ravine. If the Indians had planned an attack, the bristling array of rifles must have discouraged them.
Before noon they were in more open country, with the glistening blue waters of Lake De Smet off to the east. With every passing mile, the luxuriance of plant growth increased. Stands of tall pines stretched for miles along the mountainsides, and grass was so heavy and thick in the bottomlands that a horse could not be trotted through it. For the first time they began to understand the fierce possessiveness of the Indians for this rich and beautiful country.
After a halt for nooning, they marched five or six miles and crossed Little Piney Creek. Carrington noted that on the left the ground rose gradually to a flat-topped grassy plateau. From where he sat his horse, the length and width of the rise seemed to be just about right for the dimensions of the headquarters fort he had planned back at Kearney. He pointed the location out to Bridger, indicating the expanse of timber a few miles beyond, and asked the scout's opinion. Old Gabe insisted that the colonel go on to Goose Creek or Tongue River before selecting a site.
The column moved on a short distance to Big Piney Creek, and Carrington ordered a halt. It was still early in the afternoon but he wanted to examine this location more closely. "The camp," according to Mrs. Carrington, "was organized with especial care. Greatly to the annoyance of the teamsters, the colonel had the corral formed three times until it was sufficiently compact and trim to suit." Not until then did the meticulous commander select an escort for a seven-mile reconnaissance up Piney Fork toward the mountains "to determine whether the position was a judicious one for establishment of a post."
"At last we had the prospect of finding a home," wrote his wife, "and Cloud Peak seemed to look down upon us with a cheerful face as the sunlight made his features glow and glisten." During the next six months, that shining mountain would be her source of strength through hours of minor trials and fierce ordeals.
Carrington was up before dawn on the 14th, and at five o'clock rode off for a day's reconnaissance of the Goose Creek and Tongue River country. Captain Ten Eyck, Lieutenants Brown and Phisterer, Jim Brannan, Jack Stead, and twenty enlisted men accompanied him. Jim Bridger—the man who had been so insistent upon the superiority of the upper country—was conspicuous by his absence from the party. Just why Carrington left him behind is not clear; perhaps the colonel wanted to be free of Old Gabe's persuasive advice for a day, wanted to make the important decision of locating the new post entirely on his own responsibility.
The explorers rode for thirteen hours in a circuit of nearly seventy miles, sighting bear, buffalo, elk, deer, antelope, rabbits and sage hens. Wild raspberries, strawberries, gooseberries, currants, plums and cherries grew in profusion. Along Tongue River they found two brush tepees with signs of recent occupation, but did not see a single Indian all day. "I found less cottonwood on the streams, and that the pine region would be eighteen miles distant," Carrington later informed Omaha. "Neither in respect of grass, timber, water, or fuel, nor in any military sense, could I find any position even approximately equal to this [the ground between the Big and Little Pineys]."
About six P.M., the reconnaissance party returned, to find the camp in a state of great excitement.
Everything had run smoothly in camp that morning until nine o'clock, at which time it was reported to Lieutenant Adair, officer-of-the-day, that nine men had deserted sometime during the night to head for the gold mines of Montana. Adair immediately sent a mounted detail in pursuit up the Bozeman Trail, but the party returned before noon, reporting they had been stopped about seven miles north by a band of Cheyennes who refused to permit them to go any farther. At the point where the Indians halted the detail, Louis (French Pete) Gazzous and Henry Arrison were camped with their traveling ranche, and were busily trading trinkets, and probably whiskey, for furs and buffalo robes.
Gazzous and Arrison had passed Fort Reno while the 2nd Battalion was there, and had added four civilians to their group, one a teamster who had left quartermaster employment to try his luck in Montana. The teamster's name was Joe Donaldson, and when the Cheyennes observed that he was well known to the soldiers, they ordered Donaldson to return to the military camp and deliver a message to Little White Chief, Carrington.
The message given to Donaldson by Chief Black Horse, through Gazzous as interpreter, was: "We wish to know does the White Chief want peace or war? Tell him to come to me with a black white man." Donaldson and the soldiers finally understood through questions and sign language that the "black white man" was the colonel's interpreter, swarthy Jack Stead.
When the pursuit party returned to camp with Donaldson, Lieutenant Adair was at a loss as to what reply he should make to Black Horse. He feared the Cheyenne might take it as a hostile gesture if Donaldson was allowed to return without an answer. Donaldson indicated, however, that he had no intention of waiting around camp all day for the colonel to return, and Adair was forced to order him held in a guard tent.
During the afternoon a lone Cheyenne appeared outside Adair's picket lines, and in a few words of English made it known that he was a second messenger from Black Horse, sent to inquire about Donaldson. He asked that Donaldson be sent out, but Adair refused. The Cheyenne vanished, leaving a worried young officer-of-the-day and an excited camp behind him.
As soon as Carrington returned and learned of the situation, he lost no time in interviewing Donaldson and preparing a reply to Black Horse's message. The influence of Stead or Bridger is apparent in the style and wording of Carrington's letter, which ignored Black Horse's request for the colonel to come to him. Carrington also insisted on a delay of two days before the meeting, so that a show of military strength could be prepared for the visitors, if they came.
> HEADQUARTERS MOUNTAIN DISTRICT
>
> Piney Fork, July14, 1866
The Great Chief of the Cheyennes:
> Friend: A young white man tells me that you wish to come and have a talk with me. I shall be happy to have you come and tell me what you wish. The Great Father at Washington wishes to be your friend, and so do I and all my soldiers.
>
> I tell all the white men that go on the road that if they hurt Indians or steal their ponies I will follow and catch them and punish them. I will not let white men do hurt to the Indians who wish peace.
>
> I wish the Indians would also find who stole mules and horses on Powder River and who stole mules and horses at Rock Creek two nights past.
>
> You may come and see me with two other chiefs and two of your big fighting men, when the sun is over head, after two sleeps.
>
> You may come and talk and no one shall hurt you, and when you wish to go you may go in peace and no one shall hurt you.
>
> I will tell all my chiefs and soldiers that you are my friends and they will obey.
>
> Your white friend
>
> HENRY B. CARRINGTON
At twilight, Joe Donaldson and Jack Stead rode out of camp, bearing this first, and last, written communication from Carrington to the Indians.
Next day was Sunday, but it was not to be a day of rest. After brief religious services in the open, Carrington gave the order to lay out the new fort. During the night he had definitely decided to build the post on high ground between the two Pineys. Tongue River was not only too remote from pine timber, there was less grass and water, less advantage as to position. By running the stockade lengthwise of the site, water from Little Piney could easily be diverted and carried within the fort. Along both streams Carrington had noted an abundance of clay which would make a fine plaster for chinking and coating the buildings. And from the fort's interior the 12-pounder howitzers could command all nearby slopes and hills.
For years afterward—even into the twentieth century—Carrington was criticized for this choice of a fort site. It was said that soldiers within the fort could see nothing, but that their enemies could look down upon them and see everything. Actually the only restricted view was to the northeast, and this deficiency was overcome by placing a mounted picket on Pilot Hill, directly to the north across Big Piney. Private Murphy complained that "for some reason they picked out a location about seven miles from the timber and from five to eight miles from any hay bottom." But Murphy, like the enlisted man of all armies, was a chronic grumbler, and if the fort had been in either a hay bottom or a forest, he would have continued to find fault. It is not on record that any of Carrington's officers objected to the site, nor did Jim Bridger, who had wanted to go on to Tongue River—probably because the hunting was better there.
During that Sunday morning, Carrington and Captain Ten Eyck staked out the future post's dimensions, following plans which they had drawn at Fort Kearney in the early spring. (They borrowed liberally from treatises on fortifications by Dennis Hart Mahan, professor of engineering at West Point.) The fort proper was to be a 400-foot square, with sixteen hundred feet of stockade enclosing barracks, officers' quarters, warehouses, administration buildings, sutler's store, hospital, magazine, battery, bandstand, and parade. To the southeast a quartermaster's yard 200 x 600 feet would extend to the waters of Little Piney. Here would be the stables, civilian teamsters' quarters, mechanics' sheds, woodyard and hay yard. The fort was planned to house one thousand men.
Its log stockade would be eight feet high with a continuous banquette about three feet above the ground. A flaring loophole was provided for every fourth log, and at diagonal corners of the square, enfilading blockhouses were designed with portholes for cannon. Carrington and Ten Eyck also worked out a detailed scheme for hewing the stockade logs to two smooth touching surfaces so that spikes would not be needed, the only tools required for construction being broadaxes, augers and chisels.*
They laid out the fort so that it fronted on the Bozeman Trail, with Big Piney and Pilot Hill just beyond. Little Piney was on the south, and to the west was an unnamed ridge which Carrington promptly called Sullivant Hills in honor of his wife's maiden name. To the northwest was Lodge Trail Ridge and beyond that Peno Creek. Carrington eyed this landscape with the delight of a discoverer, and proudly wrote to General Cooke in Omaha that he had occupied the very heart of the Indians' hunting grounds. "The mountains, five miles distant, are precipitous, but the gorges are full of pine, hemlock, balsam, fir, and spruce. This ridge is about 800 feet above the Piney bottoms, but behind, and stretching to the foot of the next or 'snow-capped' range is a sweep of prairie as rich in game as it is in grass and flowers.... In thirty days this post can be held by a small force against any force...."
After stakes were driven on that busy Sunday morning, the colonel assembled a train of wagons and ordered them driven repeatedly around the 400-foot square of the fort proper, until streets were beaten out of the high grass. When this was done, he brought up hay mowers to trim the inner parade into a lawn. Tents were pitched in exact mathematical lines along streets where buildings would rise; the 12-pounder howitzers were placed on the parade; signs were posted forbidding pedestrians to cross the freshly mown grass. Headquarters, adjutant, and guard tents were erected, sentinels and pickets posted. By noon, the camp looked as permanent as a tent camp can look, with a military precision about it that would have pleased the strictest of professional drillmasters.
The only diversion of the day was a grasshopper attack. The Carrington's Negro servant, George, rushed to inform Mrs. Carrington that it was snowing for sure, right out of the bright July sky. Instead, she found her tent was being eaten by giant grasshoppers. "They came in clouds like the drifting smoke of a prairie fire.... In vain were turkeys and chickens let loose against the destroyers; the whole camp hummed with the rustle of their wings as they filed themselves on the blades of grass and became familiar generally. A kind wind from the mountains came along in the afternoon, and they left as suddenly as they arrived."
During the afternoon every soldier not on guard duty was assigned to a work detail—ditching, chopping, hewing or hauling. J. B. Gregory, a civilian engineer attached to the quartermaster, took a group of men down to the Little Piney and started assembling the horse-powered sawmill. The steam mill which had crashed into the Platte back at Scotts Bluff still had not caught up with the expedition, but was expected to arrive soon with one of the supply trains from Nebraska.
When sundown finally ended that first day of work on the new fort, three companies of weary men formed for hasty roll calls, fell out for supper, and rolled gratefully into blankets. The hard marches from Fort Kearney had toughened their muscles; now it seemed as if they would have to grow some new ones to build this fort fast enough to suit Colonel Carrington.
If the Indians had been forgotten in all the day's activities, the return of Jack Stead late that night was a reminder that they were still watching and waiting. Stead and the messenger, Joe Donaldson, had found Black Horse's camp thirty miles away on Tongue River. The Cheyennes had moved away from French Pete's camp, fearful of an attack from the soldiers. Stead informed Carrington that Black Horse accepted the colonel's invitation to visit the soldiers' camp. The Cheyennes would arrive "after two sleeps," which now would be sometime the following day.
During guard mount on the morning of July 16, the men were warned to be on the lookout for expected friendly Cheyennes. It was almost noon when the first few Indians appeared on the hills, waving white flags. Carrington sent Jack Stead out to assure them of a welcome, and about forty Cheyennes came riding in—eleven chiefs and subchiefs, several warriors, and a few squaws.
Preparations had already been made for an elaborate reception on the parade. Carrington and his officers donned shoulder scales, epaulets, and dress hats, hastily unpacked from trunks, and as soon as the Indians crossed Big Piney, Bandmaster Samuel Curry led the regimental band out on the parade where the musicians began performing a series of evolutions to the accompaniment of their brassiest martial tunes.
The Cheyennes also were dressed in their best—richly embroidered and beaded moccasins, fancy breechclouts, gay-feathered headdresses. Some wore large silver medallions, stamped with the heads of Presidents Jefferson, Madison or Jackson, over their naked chests. These trophies were highly prized, perhaps handed down from fathers who had visited Washington, or perhaps obtained in battle or trade. One tall chieftain carried a bright-colored umbrella over his head as his pony galloped briskly along.
To impress his guests, Carrington exhibited one of the howitzers, then ordered it fired at a distant hill. The Indians were startled by the loud noise of this "shooting wagon," were even more surprised when the spherical case shot exploded in the distance. "It shoots twice," said Chief Black Horse solemnly. "White Chief shoot once. Then White Chief's Great Spirit fires it once more, for his white children."
A large hospital tent had been erected in front of Carrington's headquarters, and here the guests were assembled for a parley. Jim Bridger was present of course, sitting cross-legged facing the Cheyennes, listening attentively, saying nothing, leaving the business of conversation to Jack Stead, Carrington, and the chiefs. Black Horse was the Cheyenne leader, and with him was Two Moons, who in the next decade would make his name that of a mighty warrior, and another who was destined to become the greatest of all Cheyenne chiefs—Dull Knife. Ten years later Dull Knife would lead his people against Custer, and later still would lead them in an exodus from Indian Territory, a heroic flight which excited the admiration of even the men who hunted him down.
As the day was warm, the flies of both the hospital and headquarters tents were raised, and Mrs. Carrington, Mrs. Bisbee, and Mrs. Horton gathered in the latter to enjoy "a dress-circle view of the whole performance." After pipes were passed, Jack Stead arose and moved to the center of the tent. Although of English blood, Stead's hair and eyes were as dark as any of the Indians', his skin tanned to swarthiness. As a youth he had run away to sea, and after surviving a shipwreck near the mouth of the Columbia, he crossed the Rockies, took an Indian wife, learned the languages of the Plains tribes, and became skilled in hunting and fighting. "He was fond of big stories and much whiskey," said Margaret Carrington, "but a fair interpreter when mastered and held to duty."
Now he was the first to break silence after the pipe smoking. "Black Horse wants talk," he said.
The old chief rose and began the formalities of greeting. He and the other leaders present, he said, represented 176 Cheyenne lodges. They had recently quarreled with and broken away from another band of Cheyennes who wanted war. The other Cheyennes were willing to join the Sioux as allies to drive the white soldiers back to Powder River. But his own people wanted to make a strong treaty with the white men so that they might live out their lives in peace. "White man wants all," Black Horse said. "He will have it all."
After Black Horse finished his first harangue, the other chiefs spoke, and it soon became dramatically clear to Carrington that every move he had made since leaving Fort Reno had been observed and reported to Indian encampments throughout the area. He also realized for the first time that Red Cloud was his implacable enemy.
"They represented that on the day of my arrival," he said later, "Sioux Indians were encamped near them, and told them, 'I would be there that noon; that I had left half my white soldiers on the road at Crazy Woman's Fork; that I had sent men out from Fort Reno to chase Indians who had stolen mules, but the white soldiers did not catch them; that they (the Sioux) had a sun dance which was not over, and were insisting that they (the Cheyennes) must unite with them and not let the white soldiers go farther west; that if I would go back to Powder River (Fort Reno), a fort of last year, the white soldiers might stay there, but should build no more forts.' Responsive to my questions, they further stated 'that the band of Sioux referred to was led by Red Cloud, and numbered five hundred warriors; that they (the Cheyennes) were weak and could not fight the Sioux, and that if I would give them provisions they would make a lasting peace, to go wherever I told them, away from the Sioux and away from this road."
In all the speeches the name of Makhpia-sha, or Red Cloud, was repeated again and again; there seemed no doubt in the minds of the Cheyennes that this tall, handsome Oglala—then in his middle forties—was the real leader of the hostiles. To the soldiers of the Mountain District he would soon become the symbol, the personification, of the enemy.
One piece of information concerning Red Cloud's activities was especially disturbing to Carrington. Red Cloud's warriors, said the Cheyennes, had gone toward Powder River to cut off further approach of travel. Being a theoretical military tactician, Carrington could understand the Sioux leader's reasoning: cut off the main body, isolate it, attack. The colonel was grateful for the warning. He must be prepared to meet a force led by a chief who knew how to fight a war.
The endless talk, slowed by translation, dragged on into late afternoon. But Carrington was patient. He knew that this was an opportunity to show his sincerity for peace; at the same time he was learning much which could be useful should hostilities become unavoidable. At one point he asked about the Crows. "This country is called Absaraka," he said, "the home of the Crows. Why do the Sioux and Cheyennes claim land which belongs to the Crows?"
"We stole the hunting grounds of the Crows because they were the best," was the reply. "The white man is along the great waters, and we wanted more room. We fight the Crows because they will not take half and give us peace with the other half."
Late in the day the arrival of Captain Haymond and his four companies from Crazy Woman's Fork provided a welcome interruption to the parley. Carrington excused himself and went to meet Haymond, who reported that repairs had been adequate to bring all wagons through. The four companies, Carrington decided, would camp between the forks of the Pineys. He informed Haymond to prepare for ten days' or two weeks' delay, at least until more junior officers reported for duty with the 2nd Battalion. In the meantime, Haymond's men could help with the building of this fort before moving north to erect others.
When Carrington returned to the council tent, he found the Cheyennes had become restless, perhaps suspicious because of the arrival of so many more soldiers in camp. Black Horse motioned toward the sun. It was going over, he said, and the Cheyenne chiefs must return to their camp. If they stayed too long in white soldiers' camp, the Sioux might attack in their absence. Then he made an unexpected offer: As soon as his young men returned from hunting he would give the Little White Chief one hundred warriors to go against the Sioux.
Carrington concealed his surprise. "I have men enough to fight the Sioux," he replied, "but if the Cheyennes keep good faith with the white men and have trouble with the Sioux, I will help them." As a gesture of his own good faith, Carrington then asked Lieutenant Phisterer to write a special "paper" for Black Horse:
> TO MILITARY OFFICERS, SOLDIERS, AND EMIGRANTS:
>
> Black Horse, a Cheyenne chief, having come in and shaken hands and agreed to a lasting peace with the whites and all travelers on the road, it is my direction that he be treated kindly, and in no way molested in hunting while he remains at peace.
>
> When any Indian is seen who holds up this paper he must be treated kindly.
>
> HENRY B. CARRINGTON
>
> Colonel, 18th U.S. Infantry,
>
> Commanding Mountain District
Jack Stead translated, the Cheyenne leader expressed his thanks, and the other chiefs pressed forward immediately, requesting similar papers. While Phisterer wrote out copies, presents were distributed—twenty pounds of tobacco for the party, and one day's army rations for each visitor, including flour, bacon, sugar and coffee.
By the time the Cheyennes rode away, the sun was down, and the evening's guard mount was taking posts.
At five o'clock next morning, July 17, Red Cloud's war began. As reconstructed afterward, it was evident that several Indians had infiltrated Captain Haymond's picket lines. One brave leaped upon the bare back of Wagon Master Hill's bell mare and took off at a gallop, knowing from previous observation that the other animals would follow. "When the herd stampeded," said Private Murphy, "they ran across the Piney and we could scarcely see them for the cloud of dust they raised."
At the first alarm, Haymond and his orderly flung saddles on their horses. After ordering his mounted detachment to follow as quickly as possible, Haymond took off in pursuit, accompanied only by his orderly. The trail of the Indians was easy to follow at first, with 175 stampeded animals, mostly mules, stirring up dust. Haymond held to high ground so that he could keep the course of the raiders in view until his men came up. But because of the suddenness of the raid, and the excited condition of the corralled riding horses, his mounted unit was slow in getting away, the men riding out in little groups of twos and fours instead of in proper formation. Consequently the pursuing force was strung out between the Pineys and Peno Creek.
This was exactly the opportunity the Sioux had been waiting for; small bands dropped back and began attacking the scattered pursuers. Haymond finally managed to rally his men, but when the Indians continued to press the attacks, he sent messengers galloping back to camp for reinforcements.
Colonel Carrington meanwhile had been waiting with angry impatience for some word from Haymond. On receiving Haymond's call for reinforcements, he dispatched fifty mounted men under Lieutenant Bisbee, and two companies of infantry. He also ordered work details in the fort to exchange tools for arms. Tarpaulins were removed from the howitzers, and the camp put in readiness for attack.
Back in the field, Captain Haymond was beginning to disengage his forces when the first elements of the relief party arrived. With Lieutenant Bisbee's fresh-mounted company, he resumed pursuit, later described by Bisbee as "a running fight for fifteen miles but the odds were against us and we lost the mules as Red Cloud had promised."
They recovered only four animals, a poor exchange for their first casualties from Indian attack. Two men were dead, three wounded. "One man—John Donovan of my company," reported Private Murphy, "was wounded twice, once with a poisoned arrow and another a bullet wound."
Falling back on the Bozeman Road, Haymond and Bisbee reluctantly turned about for camp. As the advance party rode down toward Peno Creek, they sighted the wagons of French Pete Gazzous's temporary trading post. It was obvious that something was wrong. Covers had been ripped from wagons, and plunder strewn all around. They found six dead white men, all mutilated.
"It was a terrible sight," said Private John Ryan. "The poor victims had been mutilated in the most horrible manner and it gave us all a most convincing lesson on what our fate would be should we fall into the hands of the Indians."
Louis Gazzous had been killed by his wife's own tribesmen, and with him died his partner, Henry Arrison; the young teamster, Joe Donaldson; and three adventurers who had joined on for safe passage to Montana.
Bisbee reported briefly that signs indicated French Pete's "unlawful load of whiskey had led to his destruction, despite his squaw wife who was spared." The men found her with the five Gazzous children hidden in some bushes nearby.
A few scattered beef cattle also were recovered; goods and stores not destroyed by the Indians were reloaded into wagons; the mutilated bodies were buried. Haymond's party then returned to camp, the captain reporting to Carrington and presenting the Frenchman's squaw for interrogation.
The Gazzous woman talked freely. She told Carrington that the Cheyenne chiefs had stopped at her husband's camp the previous evening after leaving the soldier camp, and they had talked and traded for some hours. During this time, Red Cloud and a party of Sioux came up from Peno Valley. Red Cloud asked Black Horse what the white soldiers had said to him. Was the Little White Chief, Carrington, going to return to Powder River? Black Horse replied that the Little White Chief was not going back, but was going on north to build more forts. Red Cloud then asked: What did the Little White Chief give them for presents? "All we wanted to eat," Black Horse replied, and added that Carrington had promised presents for all the Indians in Tongue River valley whenever they went to Laramie and signed the treaty. "Let us take the white man's hand and what he gives us, rather than fight him longer and lose all," Black Horse had said.
Red Cloud retorted angrily: "White man lies and steals. My lodges were many, but now they are few. The white man wants all. The white man must fight, and the Indian will die where his fathers died."
At this point, the Sioux unslung their bows and whipped Black Horse, Dull Knife, and the other Cheyennes over their backs and faces. After the Sioux left, Black Horse told French Pete that he was going with his people up to the mountains, and he advised the trader to go back to the white soldiers' camp or the Sioux would kill him.
Carrington of course was disturbed by the Gazzous woman's story. He thanked her for her co-operation, assured her that she and her children would be welcome to the protection of his camp, and then, as a lawyer might have been expected to do, he assigned an administrator, John Hugas—one of the civilian contractors in camp—to settle her husband's estate. Her ultimate fate is obscure. According to the laconic Private Murphy, "she was at the fort about two months and left one night."
As soon as Carrington finished his interrogation, he sent Haymond an order to move his four companies closer to the fort site. He also gave the captain a mild dressing down for not reporting to headquarters before going in pursuit of Indians that morning. Privately he excused Haymond for his hasty action; after all, the captain had commanded the 2nd Battalion through its hardest fighting in the Civil War and had been cited for gallantry. Indian warfare was new and strange; none of them had really believed the Sioux would dare attack so large a force. But now they knew. Two soldiers were dead; three wounded. So ended the first day of Red Cloud's war.
The following week was deceptively peaceful around the Pineys. Work on the stockade continued without interruption except for daily military routines of reveille, roll call, guard mount, retreat, tattoo, and lights out. Wagons were unloaded, goods stored under canvas. A mail courier arrived from Laramie, bringing official communications relieving Captain Haymond and Lieutenant Phisterer from field duty and reassigning them to recruiting service in the States. Although commissioned replacements were en route to the Mountain District, Carrington was dismayed over the prospect of losing any officers, especially when they were as experienced as Haymond and Phisterer.
Food was also becoming a problem. Long hard hours in the open air gave the men voracious appetites which could not be satisfied by hardtack and half-spoiled meat. A few beef cattle from the herd brought overland were slain, but Carrington was determined to reserve most of this supply until winter. An occasional deer or antelope shot by men working in the timber also provided fresh meat, but there was never enough to fill demand. A few boxes of desiccated vegetables had been brought from Reno, and these were carefully rationed.
One of the enlisted men, Alson Ostrander, recorded his sergeant's description of the desiccated vegetables: "Somewhere back east there is a factory where they put 'em up. They take a heap of each kind of vegetable and slice 'em just as thin as possible and then they are thoroughly dried out. Then they mix them all together and put them under a tremendous hydraulic pressure until they are squeezed just like plug tobacco. They come in cakes about nine inches long, three inches wide, and nearly an inch thick. Then they are packed in air-tight caddies and when opened they look just like a big plug of tobacco, but when placed in boiling water, how they do swell! One of these plugs will make several gallons of good rich soup."
At first the enlisted men used the same mess system as they had in the Civil War, four to eight men in each mess rotating duties of cooking, collecting fuel, and hauling water. To free more men for work details, however, informal company kitchens were encouraged, with regular cooks assigned. Private Murphy noted that "about July 20, Orderly-Sergeant Lang and I bought two fresh cows from an immigrant train. No one wanted to work in the kitchen, so I volunteered in order to be able to take care of the cows morning and evening. It was not known that I had any interest in the cows or it might have caused some trouble. We had a first class baker in the company who volunteered to do the baking. At that time the Government did not furnish cooks or bakers. They simply furnished the rations and the soldier could cook them himself or eat them raw if he saw fit.... We cooked soup, bacon and coffee and dished it out to the men in their cups and plates—we had no dining room. We boiled everything. I believe the bacon would have killed the men if it had not been thoroughly boiled... the bacon and flour I had seen at Reno was given to us. The flour had been hauled sixty-five miles and handled several times. The result was that the refuse left by the mice was well mixed with the flour and we found a number of dead mice in it also. As we could not get a sieve, we manufactured one out of burlap sack by pulling out some of the strings and nailed it on a wooden frame. We got most of the larger refuse out. The bacon where the fat had commenced to sluff off from the lean was yellow with age and bitter as quinine. Some of the worst we shaved off, but we could not spare too much. One reason why our rations were so scanty was that flour was worth $100 per sack and bacon, coffee and beans proportionately. The companies of those times had no quartermaster or commissary agents and two or three men would be detailed to go and get the rations. They were piled out in a heap and you could take them or leave them."
By the weekend of the 22nd, a sufficient number of wagons had been unloaded and reconditioned to make up a return train to Reno to pick up stores left behind for lack of wagon space. Carrington gave the assignment to Captain Thomas Burrowes' G Company, with an added detachment of mounted men, and Jim Bridger as scout.
Sunday, the day of the wagon train's departure, was marked by a return of Indian raiding, not in force but in small parties. The Sioux were unable to break through Carrington's alert defenses, but succeeded in capturing four horses and four mules from a civilian train camped nearby.
At one o'clock in the morning of July 24, Carrington was awakened by his orderly. A courier had just arrived with an urgent message from Captain Burrowes. By the light of his tent lamp, the colonel read the penciled scrawl:
> COL. CARRINGTON:
>
> There is a train engaged 3 mi. from here. I can not send them any help. The Sioux are very numerous. Send a force at once.
>
> CLEAR FORK, 7:15 P.M. [JULY 23] T. B. BURROWES
On the reverse of this paper was the appeal for help Burrowes had received the previous evening:
> COMMANDING OFFICER:
>
> SIR: We have received the papers from you through Black Horse, and we would inform you that about 3 miles from this watering place, Mr. Kirkendall's train has been engaged all this afternoon. Troops should be sent immediately, as we are not in position to leave this bull outfit and they can not come in by no means.
>
> Yours,
>
> THOS. DILLON
It was clear at once to Carrington that Red Cloud had not been merely boasting when he told Black Horse he would cut off further travel from Fort Reno. Three trains were under simultaneous attack—Burrowes', Dillon's and Kirkendall's. And Black Horse and his Cheyennes were in the same area, complicating matters by presenting their letters of conduct signed by Carrington. The colonel wondered how many civilian wagon drivers, surrounded by Sioux, would stop to distinguish one tribesman from another.
Without delay, Carrington aroused Captain Nathaniel Kinney and ordered him to march Company D with one of the mountain howitzers to Clear Fork and relieve Burrowes.
What Carrington did not know on this dark night was that the main force of Sioux was engaged still farther south against a party of thirty-four, which included five long-overdue officer replacements for the 2nd Battalion. For twenty-four hours they had been the victims of an Indian surround, typical in most of its features of the classic surrounds which would become a part of the folklore of the West.
Their story began at Fort Sedgwick, where Musician Frank Fessenden had been left with his wife back in May. After Carrington's Traveling Circus moved on, the Fessendens became parents of the baby girl whom Captain Fetterman jestingly suggested should be named Sedgwick. Late in June they journeyed by army ambulance to Fort Laramie, and on July 13 left there with a small detachment under Lieutenant George Templeton en route to Fort Reno. In addition to Mrs. Fessenden, two other women were in the party, the wife of Lieutenant Alexander H. Wands, and her colored maid, Laura. The Wands also had a small child, a son named Bobby. In addition, three civilians accompanied the detachment, including the Philadelphia photographer, Ridgway Glover, and a former officer of Missouri Volunteers, Captain Marr.
"Our first camp after leaving Fort Laramie," Fessenden recorded, "a number of Indians came to our command. They appeared very friendly—so much so that it excited our curiosity. We soon discovered the reason. The squaws wanted to buy our baby, offering beads, furs and trinkets of all kinds in exchange. When we refused they acted very sullen, and told us plainly they would steal her if they got the chance." For the remainder of the journey the Fessendens and the Wands guarded their children with special care.
After the detachment crossed the Platte at Bridger's Ferry, Ridgway Glover set up his camera and made a stereoscopic view of the river, but he was disappointed to find "very little scenery worth photographing."
At Fort Reno they were joined by Chaplain David White and Assistant Surgeon C. M. Hines, who were under orders to report to Carrington. Captain Joshua Proctor, commanding at Reno, was reluctant to grant Templeton's party permission to proceed to the Pineys. Templeton had ten enlisted men, four lieutenants (Alexander Wands, James H. Bradley, Napoleon H. Daniels, Prescott M. Skinner), Chaplain White, Surgeon Hines, nine wagon drivers, and three civilians—or only twenty-nine armed men, including himself.
Proctor, however, recognized that all the officers and several of the men had long Civil War records, and he finally issued a permit to pass. Early in the morning of July 20, their five wagons and two ambulances rolled northward on the Bozeman Trail. As they had only four saddle horses, the officers took turns at riding.
One of the enlisted men, S. S. Peters, afterward wrote an account of the latter part of the journey. The first night camp, he said, was excessively warm, and coyotes howled unceasingly so that sleep was almost impossible. "Lieutenant Daniels, an Indianan, was especially restless and came over to where I was on guard and walked the beat with me. He said that he had a presentiment that something was going to happen to him very soon and he did not know how to account for it. All efforts to discourage him from entertaining the gloomy phantasy were unavailing, and he seemed determined to dwell upon it, and remained with me until the signal for calling in the guard was given and preparations were ordered made for the start before daylight."
They marched to Dry Creek without incident, hoping to find water there. They found not water, but in the dry basin of a pool they discovered the dead body of a white man, filled with arrows, scalped, and mutilated. "The fragment of a gray shirt still hanging about the shoulders of the dead man indicated that he was in all probability a soldier. He was evidently a courier."
After a hasty burial, they resumed march. "The finding of the dead body... had a very depressing effect on the entire command, and with the ascending sun the heat became intense. Our water supply, which was meagre at the best, had now given completely out and the animals began showing signs of severe suffering."
As they approached Crazy Woman Creek around nine o'clock in the morning they could see the first thin fringe of cottonwoods five miles away, and beyond on a slope several dark moving objects. Lieutenant Daniels put his field glass on the objects and pronounced them to be buffalo. He persuaded Lieutenant Templeton that it would be a good idea for them to ride ahead, cross the creek somewhere above the buffalo and turn the herd in toward the road. By the time the wagons reached the valley, the buffalo should be within shooting distance of the entire party. Daniels took the lead, galloping away with Templeton close behind.
A few minutes later the train dropped down a hill toward the creek, and a belt of timber screened the two officers from view. Everyone was alert, readying rifles for the expected chase, forgetting thirst and heat in the excitement. For a hundred yards the trail ran through deep sand that slowed the pace of the mules; the drivers shouted, slapping their reins, eager to reach the creek.
"The entire detachment was in this dry bed urging the teams through the sand, when to our complete astonishment a volley of arrows and rifle-shots were poured into us. The shots were accompanied with a chorus of savage yells, and the timber land and brush above and about us was fairly alive with Indians."
Miraculously no one was hurt in this first violent attack, and because rifles were held ready for the expected buffalo, fire was returned almost instantly. Led by Lieutenant Bradley, a dozen men jumped from the wagons and charged up a slope ahead of the lead team, driving the Sioux back toward the creek. Wagons and ambulances were brought up out of the sandy bed to higher ground. The first wagon was swung crossways, the second and fourth moving to the left, the third and fifth to the right, and then the two ambulances were swung crosswise to close the square, with leader and swing mules being turned inside for protection.
Even before this hasty corral was formed, the Sioux came whooping back, but another volley sent them scurrying. A moment later a riderless horse dashed out of the brush, its saddle twisted under, arrows sticking from neck and flanks. It was Lieutenant Daniels' mount. The premonition of doom he had revealed to Private Peters had come true. "A second later, Lieutenant Templeton appeared, riding up out of the dry bed of the creek, hatless, two or three arrows in his horse's withers and flanks, and an arrow in his own back. Templeton was bleeding profusely from a wound in the face, and his whole visage was one of extreme terror, and as soon as he reached the corral he reeled and partly fell from his horse. He was lifted from the saddle in a state of complete collapse." Before he lost consciousness, Templeton uttered four words: "Daniels! My God, Indians!"
The wounded lieutenant was laid in one of the wagons for protection. Surgeon Hines removed the arrow as quickly as possible, but he could not remain to dress the wound. He was needed back on the line with a rifle. The Sioux were closing in, and two mules were already so badly wounded they had to be cut loose.
With Templeton out of action, Lieutenant Wands assumed command, and from his Civil War experience he realized that he was in an untenable position. The Sioux were sheltered by trees and brush and could pick off animals and soldiers one by one.
A half mile to the south was a high treeless knoll. Once corralled and dug in there, they could hold out at least until dark. But a withdrawal to a new position would be extremely dangerous. After a quick conference it was decided to bunch the wagons, two in front, the ambulances with the women and children next, and the other three wagons following as cover. Bradley, with seven men, established a rear guard, and Wands and Skinner with twelve men covered the flanks and advance.
As soon as the movement was begun, the Sioux guessed its purpose, and a party swarmed out of the creek bottom, attempting to reach the hill first.
"The advance guard held their ground like heroes," Private Peters recorded, "and fought every foot of the way. The teams were kept on the run and then came the charge of twelve men under Lieutenant Wands and Lieutenant Skinner up the hill for its possession. The Indians were poor shooters, and wounded only two men in the charge... then broke and ran from the hill. Captain Marr, who had a Henry rifle, a sixteen shooter, used it with wholesome effect on the running Indians, and stopped two of them permanently. They were gathered up, however, by a bunch of Indian horsemen and carried away.... In the meanwhile the rear guard was holding the Indians in check from the creek side, and the wagons and ambulances were safely brought to the hill. A corral was immediately made, with mules inside the corral. The ambulances were protected by the wagons...."
They dug a ring of rifle pits just outside the corral, and for the first time felt some sense of security. The scorching sun and lack of water seemed more unbearable than the constantly yelling Sioux, who now kept beyond rifle range.
The photographer, Ridgway Glover, meanwhile had been awaiting a good time and place to set up his Roettger camera. The Indians, he said, "looked very wild and savage-like while galloping around us; and I desired to make some instantaneous views." Lieutenant Wands, however, forbade Glover to do so. Under the circumstances, Wands doubtless felt that if Glover meant to shoot Indians he should do so with a rifle rather than a camera. Thus was lost one of the rarest opportunities to photograph an Indian attack, although the slow-speed camera shutter of that period probably would have caught only a series of blurs as the Indians swept past on their ponies.
Not long after the establishment of the defensive position, a shower of arrows zipped in from the left without warning, wounding three men. One of the wounded was Chaplain White, more angered than injured. The arrows came again, seeming to fly out of the ground, but closer observation revealed their source as a narrow ravine, cutting its way down toward the creek. The Sioux had crept up this ditch unobserved until they were in arrow range.
White and an enlisted man named Fuller volunteered to clear out the ravine. Running crouched forward, the two men charged the position. White was armed with an old-fashioned pepperbox seven-shooter pistol, Fuller with a rifle. They dropped out of sight, and a moment later the watchers on the hill heard what sounded like a volley of rapid fire. Several Sioux leaped from the ravine, the men in the rifle pits opening fire upon them. Shortly afterward White and Fuller reappeared. "Got two of the devils!" the chaplain shouted. "Ravine clear down as far as the creek." All seven charges in his pepperbox had gone off at once, killing one Indian and frightening the others into flight.
The afternoon wore on, the men in the pits suffering acutely from thirst. Every few minutes a party of mounted Sioux would circle the hill, yelling their eerie wolflike war cries. Occasionally two or three warriors would swing to the off sides of their ponies and make quick dashes close to the corral, firing with remarkable accuracy from under their ponies' necks. By midafternoon, over half the men in the detachment were wounded, some seriously.
In Frank Fessenden's account of this ordeal he told of seeing a Sioux "stationed on a little hill directing the fight by signals with a flag." The most disturbing sight of the afternoon, however, was the sudden appearance down by the creek of a man dressed in army blues. When the figure began a savage dance, they realized it was a Sioux warrior dressed in Lieutenant Daniels' uniform.
Near sundown the piteous moaning of the wounded men for water led Lieutenant Wands to risk a dash for the creek. A small detail collected empty canteens and water buckets, and crawled one by one over into the ravine held by Chaplain White and Private Fuller. Then a diversionary party moved out of the rifle pits to cover the water detail concealed in the ditch.
Either the Sioux misunderstood the purpose of the action, or they could not resist the opportunity of rushing the weakened defenses of the corral. They ignored the diversionary party, and swarmed up to the rifle pits. With coolly spaced firing, however, the remaining riflemen—many of whom were already minor casualties—drove the chargers back. Before the Sioux could reform, the water detail was back, the first canteens being passed in to Mrs. Wands and Mrs. Fessenden, who were attending the severely wounded cases. "The two ladies," said Private Peters, "were angels of mercy and tenderness and looked after the wounded most heroically and bravely."
Refreshed by water, some of the wounded returned to the pits just in time to help beat off two direct mounted charges. The Sioux—about 160 of them according to Fessenden—attacked fiercely, killing one sergeant and seriously wounding three more men. "Our condition was now becoming so desperate that a council of war was held. It was solemnly decided, that in case it came to the worst that we would mercifully kill all the wounded... and then ourselves." Chaplain White, who had returned from the ravine for the conference, was reluctant to agree to this. He volunteered to try to cut his way out of the surround and ride back to Fort Reno for reinforcements. Private William Wallace immediately offered to join the chaplain in the attempt, and Wands and Marr offered their saddle horses.
"They were properly mounted and furnished with a revolver each, and heroically rode out from the corral amid the prayers and God speeds of the little band. They succeeded in reaching the dry creek bed before they were apparently discovered by the Indians. As they rode out of the creek bed up toward the hill, a body of Indians were seen to hurriedly ride out from the forks of the two creeks up the hill toward the two couriers. The ride was a magnificent one. White and Wallace saw the Indians coming and put spurs to their horses and soon reached the crest of the hill far in advance of their pursuers. A moment or two later, pursued and pursuers were lost to view in the gathering twilight, for the sun was already going down beyond the Big Horn Mountains to the west of us."
As the long summer twilight deepened, the air turned cooler. The Sioux made no more attacks, but seemed to be gathering along the creek for a council of war of their own. Just before dark the men in the pits saw a dust cloud off to the northwest, and with dejected spirits watched its rapid approach. They were certain it marked the trail of reinforcements for the Sioux.
A few seconds later the Indians along the creek began dispersing, small groups moving away in different directions. Daylight was almost gone now, the mounted Indians vanishing into the dark smudge of cottonwoods.
One of the riflemen cried out, pointing to a low ridge beyond the leftward ravine. A silhouette of an approaching horseman was black against the paling sky. Before the lone rider reached the ravine, Lieutenant Wands called an order to halt.
The horseman reined up, shouting that he was a friend.
"What's your name?"
"Jim Bridger."
And so it was. The men cheered Old Gabe as he let his horse pick its way around the ravine and up to the corral. He told them that Captain Burrowes and two companies of the 2nd Battalion were coming down the road a mile or so back. The action at Crazy Woman's Fork was ended.
Next morning they found Lieutenant Daniels' body near the road. Frank Fessenden, a member of the search party, said it had been pierced by three bullets and "there were twenty-two arrows sticking in it." Daniels' scalp and fingers were gone, and he had been "barbarously tortured with a stake inserted from below." The men also found a dead Sioux in a ditch nearby; in the Indian's possessions were the lieutenant's shirt and scalp.
On the advice of Bridger and Captain Burrowes, Lieutenant Wands decided to turn back to Fort Reno with the wagon train. The return march had scarcely begun when they met a detachment of mounted infantry led by Lieutenant Kirtland from Reno. With the horsemen were Chaplain White and Private Wallace, safe but weary from their long night ride.
In the last week of July, the Wands party returned with Burrowes' wagon train to the Pineys, where the young officers at last reported for duty with the 2nd Battalion. Carrington welcomed them warmly, assigned them to companies, and they were soon engaged in the major work at hand—the building of the fort.
Ridgway Glover was delighted with the fort and the scenery around it, although he was disappointed over a failure to obtain photographs of some visiting Cheyennes. "My collodion was too hot, and my bath too full of alcohol," he wrote the editor of the _Philadelphia Photographer,_ "to get any pictures of them, though I tried hard." He added that the military camp was "hemmed in by yelling savages who are surprising and killing some one every day. I expect to get some good pictures here, and hope that before Christmas you will see how these mountains look in July."
Frank Fessenden reported to Bandmaster Samuel Curry and was assigned a double tent for his wife and child. In addition to morning and evening band duties, Fessenden assisted with construction work. The stockade around the 400-foot square of the main fort was almost completed now, and foundations were being laid for quartermaster storehouses. "Colonel Carrington," wrote Fessenden, "was a very busy man, and took great interest in the building of the fort. He was always out early in the morning and saw that everyone was in charge of their special departments, doing their duty."
During the first ten days of construction, Carrington had been pondering over a name for his new fort. Officially it was Fort Reno, but he had already notified Omaha that he was retaining the original Fort Reno. Some of his junior officers suggested that it be called Fort Carrington, but he knew that recent Army policy disapproved use of names of living officers for forts. The problem was solved when Adjutant Phisterer opened the mail-bag brought back from Reno by Captain Burrowes. Among the dispatches was an order from the Department of the Platte:
> The 2nd Battalion, 18th U.S. Infantry, will take post as follows:
>
> Two companies at Fort Reno, on Powder River; four companies about 80 miles nearly north of Reno, on the new route to Virginia City, Montana.... This post will be known as Fort Philip Kearny.
And so on July 27, Carrington issued a general order proclaiming the new post as Fort Philip Kearny, in honor of the heroic one-armed general killed in action at Chantilly in 1862. To veterans of the Grand Army of the Republic, however, General Kearny was _Phil_ Kearny, and in popular usage the post would be Fort Phil Kearny.
On July 29 a contract wagon train arrived with the long-overdue steam sawmill which had been badly damaged at Scotts Bluff when the eight-yoke bull team hauling it had stampeded down a steep hill into the North Platte. Carrington ordered Engineer Gregory to put the steam mill into operation immediately. He also notified Quartermaster Fred Brown to establish a timber cutters' camp on Piney Island and to make preparations for daily log train movements from the cuttings to the fort.
The steam sawmill was a Lane & Bodley, manufactured at Cincinnati, and was set up to slab large logs on two sides so that each would have a touching surface of at least four inches. It was equipped with a steam whistle which soon proved useful for sounding Indian alarms. (When the mill was renovated in 1940, the cast flange was found to have been mended in several places with strips of wrought iron; one of the bearings from the saw shaft had been crudely babbitted, and several holes had been cut through the frame with cold chisels. Some of these repairs may have been made after the accident at Scotts Bluff; others probably by J. B. Gregory. But in spite of its condition, the mill sawed thousands of feet of timber for construction of Fort Phil Kearny.)
Piney Island, the source of timber six miles west of the fort, was not a real island but was a thick stand of tall pines surrounded by North and South Piney and Spring creeks.* Frank Fessenden, who was occasionally assigned to timber-cutting duties, said there were two separate loggers' camps. "We built two blockhouses, one at each cutting, we having what was known as the 'upper' and 'lower' cuttings. Detachments of men went out and cut timber each day. Every morning twenty wagons were sent out for this purpose. About half a mile before reaching the timber, the road forked at an angle of about 45 degrees, one road running to each cutting. Here we found trees that were 90 feet to first limb and straight as an arrow."
Operation of logging and hauling work was Quartermaster Brown's responsibility, and he used both military and civilian personnel. He must have been at constant odds with company, battalion and regimental adjutants in efforts to secure adequate details of men. To add to his burdens, wild grass in the nearby bottomlands was ripening for mowing, and he had to find additional men to operate mowing machines and rakes.
During this busy period the weather was fine, the air dry and winy, temperatures sometimes reaching ninety during the afternoons but dropping to sixty after dark. Only six men reported on sick call during the month of July, and these were minor surgical cases, results of accidents.
The clear nights were beautiful with a sky full of huge glittering stars, and sometimes a moon bathed the snow-clad Big Horns in a magical silver. By moonlight the limitless expanse of hills and mountains seemed empty, the silence broken by the deep roar of Big Piney. Late in the month, wolves began gathering after dark around the slaughter yard near Little Piney, howling and snarling over the offal there, ending the peaceful nights. For a time sentries were permitted to fire at the wolves, but the firing broke more sleep than the animals' howls, and Carrington forbade the practice, ordering poison put out to kill them. The unseen but watchful Indians noted this change, and one night a Sioux warrior donned a wolfskin, crept near the stockade, and shot a sentry from the banquette. A man was dead; another lesson in frontier warfare had been learned.
By the 29th of July, Carrington had completed interviewing leaders (Dillon and Kirkendall) of civilian trains which had been attacked by the Sioux at the same time Lieutenant Wands' party was under siege at Crazy Woman's Fork. The colonel was much disturbed by reported treacherous actions of the Sioux. In two instances the Indians had approached trains, expressing friendship, and then after shaking hands and accepting presents of tobacco, had shot their benefactors in the backs.
There was no longer any doubt in Carrington's mind that Red Cloud had opened aggressive operations in his rear, threatening communications with the outside world. At the same time, General Cooke in Omaha had already made clear that no reinforcements could be expected before autumn. The arrival of Alex Wands and the other three lieutenants had been a timely gain, but the post was still so short of officers that two lieutenants were alternating as officer-of-the-day.
On the 29th, Carrington decided his situation was grave enough to warrant a direct appeal to The Adjutant General in Washington. After protesting the transfers of Captain Haymond and Lieutenant Phisterer to recruiting duties, he added: "I have to give sergeants important duties, having for a line of one hundred miles active Indian hostilities. Lieutenant Daniels, en route to join me with escort of fifteen men, was scalped and horribly mutilated. I have lost three men, killed and wounded, besides Lieutenant Daniels. I need officers and either Indian auxiliaries or men of my regiment to build my posts, prepare for winter, and clear out the Indians. I can resist all attacks and do much active fighting, but I have a long line to watch and cover. The Indians are aggressive to stop the new route."
The next day he also composed a long report for General Cooke:
> Character of Indian affairs hostile. The treaty does not yet benefit this route.... My ammunition has not arrived; neither has my Leavenworth supply train. Working parties keep arms in constant readiness for use: and with this dispatch I send an escort to look for advices and guard emigrants and supplies.
>
> My infantry make poor riders, and, as I can only fight Indians successfully on foot, my horses suffer in pursuit and in fight.
>
> I am equal to any attack they may make, but have to build quarters and prepare for winter, escort trains, and guaranty the whole road from the Platte to Virginia City with eight companies of infantry. I have to economize ammunition, and yet, from Kearney out, I picked up all I could get. I send two officers on recruiting service, under peremptory orders from Washington, leaving me crippled and obliged to trust too much to non-commissioned officers... there is at Laramie and elsewhere a false security, which results in emigrant trains scattering between posts, and involving danger to themselves and others.
>
>... It is a critical period with the road, and many more outrages will injure it. Still, if emigrants will properly arm and keep together, having due warning, I have confidence in the route.
>
>... My eight companies of eighty effective men each, with quarters to build, and 560 of them new recruits... do not give me a fixed adequate command for the present emergency. My own supply trains are to be guarded, trains are to be escorted, a courier line is to be maintained. Whatever my own force I can not settle down and say I have not the men; I must do all this, however arduous. The work is my mission here and I must meet it. But... when I am my own engineer, draughtsman, and visit my pickets and guards nightly, with scarcely a day or night without attempts to steal stock or surprise pickets, you will see that much is being done, while I ought to have all my officers and some cavalry or Indian auxiliaries at each post.
On the 31st, the harassed colonel wound up his paper work for the month of July by ordering F Company to join B Company at Reno—in compliance with Cooke's order to retain that fort as a two-company post. At the same time he brought Fort Phil Kearny's strength to four companies by transferring E and H to the permanent garrison. As Companies A and C were already assigned to Phil Kearny, this left D and G to make the march north to the Big Horn River to build the third post on the Montana Road.
* This system was later adopted by the British for construction of log defenses in South Africa and India.
* It is the present site of Story, Wyoming.
# _V. August:_
MOON WHEN THE GEESE SHED THEIR FEATHERS
> _From the middle or latter part of August, Indians appeared more frequently about Fort Philip Kearny, and from that time I assumed the condition of affairs to be decided, unequivocal hostility on the part of the Indian tribes about me. On the 29th August I made reports to the department commander of the condition of affairs._
AUGUST WAS TO BE a month of accelerated activities as Fort Phil Kearny's stockade was completed and warehouses and quarters began to take form around the green close-clipped parade. From sunrise to sundown, every day including Sundays, there was a continuous humming of sawmills, pounding of hammers and ripping of handsaws, as the post grew log by log. Military routines were cut to a minimum; the men were transformed into blacksmiths, painters, harness makers, teamsters, wheelwrights, carpenters. In Quartermaster Brown's storage tents, details began unpacking quantities of nails, doors, sash, glass, and stoves.
On the first day of the month Captain Ten Eyck, commanding post, also assumed command of the 2nd Battalion, replacing Captain Haymond. In his official record of events for August, Ten Eyck wrote: "Stockade around garrison completed early in this month and the entire force of the garrison was employed, officers and men laboring incessantly on the public buildings necessary for the preservation of the stores, and our company quarters. Our steam sawmill was put in operation during the month."
The shortage of officers led to a combination of duties for all. Lieutenant Bisbee commanded E Company and also served as post adjutant and 2nd Battalion adjutant. Lieutenant John Adair commanded C Company and also performed the duties of regimental adjutant and acting adjutant general for the Mountain District.
As Phil Kearny was simultaneously headquarters for a district, regiment, battalion, and post, the paper work even in that day was immense. Before the month was scarcely begun, Colonel Carrington transferred four enlisted men into the combined headquarters tent for various duties—Private Dominic St. Geiger, Archibald Sample, Horace Van Kirk, and Thomas Maddeon. Sample eventually became the colonel's orderly, and played an important role in the Fetterman Massacre. Maddeon was an excellent gunsmith, but he preferred action in the field rather than the duties of regimental armorer. He would die in the Massacre.
The first day of August saw the departure of two of Carrington's most experienced officers, Captain Haymond and Lieutenant Phisterer. The entire staff turned out to bid them farewell as they departed for Laramie with the mail escort.
Very early on the third day, Captains Nathaniel C. Kinney and Thomas Burrowes had their respective companies, D and G, ready for the march north to open a new post on the Big Horn River. Carrington spared them a few horses for scouting and dispatch duties, and also one of the mountain howitzers. As ranking captain, Kinney would be in command. The new post by orders from Washington was to be called Fort C. F. Smith, in honor of the Mexican War hero, and was to be located some ninety miles northwest of Fort Phil Kearny.
Carrington ordered Jim Bridger to act as chief guide, but insisted that Old Gabe return to Phil Kearny as soon as the new fort was located. The colonel also sent Jim Beckwourth along to assist Bridger in gathering information from Crow tribes in the north. As Beckwourth was married to several Crow squaws and claimed to be a tribal chief, Carrington hoped to learn through him the Crows' "disposition toward the whites and the occupation of the route, and to induce them, if possible to communicate with Red Cloud quietly, and learn the disposition of himself and the Sioux of the Tongue River valley." Military intelligence work against an Indian enemy, the colonel had discovered, was exceedingly difficult. He did not know what his enemy was doing, and it troubled him.
The two companies moved out with a line of wagons belonging to civilian trains which had been camped for several days along the Pineys, awaiting this well-armed escort. "Jim Bridger was our pilot," one of the wagon drivers recalled afterward. "He was a quiet familiar figure about the camp.... He would ride ahead across the untraveled country and return to the train at noon, or sometimes not until nightfall, when we had made camp. He rode a quiet, old flea-bitten, gray mare, with a musket across his saddle in front of him and wore an old-fashioned blue army overcoat and an ordinary slouch hat. He was very quiet in camp and I never saw him ride as fast as a slow trot."
August saw the high tide of 1866 emigration over the Montana Road, with wagons trains rolling past Phil Kearny almost every day. Several drivers had tragic stories to tell of surprise Indian attacks along the route. In terse military language the post records reveal what was happening: "Train under H. Merriam as captain left Phil Kearny for Montana. Lost two men killed by Indians between Forts Laramie and Phil Kearny, viz. Geo. M. Moore of Georgetown, III. and P. G. Carr of Charlestown, III." On the same day, August 6, another train was listed as having lost fifteen men killed and five wounded between Laramie and Phil Kearny.
The sturdy stockade of Phil Kearny was always a welcome sight for these harassed travelers. "Stopped below the fort," George W. Fox recorded in his diary for August 8. "I was up to the parade ground. They were mounting guard. They have a good band, 30 members. The music sounded well; something like civilization.... A captain [Ten Eyck probably] went down and saw the men and guns and we were permitted to go on. Had to have 60 armed men. The fort is just building; the garrison is in tents.... We left the fort at 11, crossed 2nd Piney fork, 50 ft. wide, 2 ft. deep, swift and rocky."
As George Fox indicated, the post band which "sounded something like civilization" never failed to surprise and delight travelers passing through this wild country. The band was also highly prized by the fort's occupants. "We had the fine music of our splendid band... which played at guard-mounting in the morning and at dress-parade at sunset, while their afternoon drills and evening entertainments were in strange contrast with the solemn conditions that were constantly suggestive of war and sacrifice of life."
Rumors had been flying about all year that as an economy move the Army would abolish regimental bands, and reports from The Adjutant General's office now began to confirm this drastic action. No direct orders had been received from Washington, but in fearful anticipation of losing the 18th Regimental Band, an anonymous correspondent signing himself "Dacotah" addressed an urgent letter about this time to the _Army and Navy Journal:_
> Concerning the subject of Army bands, we can but consider it small economy to deprive the regiments of their bands.... What soldier is there who does not take the greatest pains with his musket, put an extra polish to his plates and bootees, knowing he will march to "Dress parade" to the sound of music... it adds to the pleasures of the soldiers, it gives them amusement and enjoyment, when otherwise they might look to the card-table or whisky-bottle for excitement, and it gives them an _esprit de corps_ and a life to the command that it never felt without it.
If put to a choice, the men and women of Fort Phil Kearny undoubtedly would have voted for a cut in rations over elimination of their beloved band. The noncombatants, confined as they were to the stockade, regulated their lives around its performances.
As there was yet no floored building for holding party dances, recreation was at a premium, and when the band was not making music on the parade, the post's single croquet set was in constant use by women and children on the smooth green turf.
At least eleven married couples lived within the stockade: the Carringtons, Bisbees, Hortons, Wands, and Currys on officers' row, and six others among the enlisted men and civilian employees. Frank Fessenden afterward recalled that there were eleven children, six girls and five boys. Adding a domestic cast to this assemblage were two colored servants: the Carringtons' faithful George, and Mrs. Wands' maid, Laura.
The post's only pets were Mrs. Horton's spotted fawn, given her by the ill-fated Louis Gazzous, and Jimmy Carrington's pony, Calico. Both were destined for violent ends, the fawn from drinking paint, Calico from Indian arrows in the Fetterman Massacre.
Early in August—before the first attacks were made on the timber trains—Colonel Carrington granted permission for a picnic to be held at Piney Island. This would be the last opportunity for women and children to leave the eight-foot walls of their stockade. The food was a delightful treat, dainties being furnished by Judge Jefferson T. Kinney, who had recently arrived at the fort and purchased the sutlership. (Kinney was a former Utah territorial judge, dismissed by President Lincoln during the war. Because of clashing temperaments and differing political viewpoints, he and Carrington soon grew to dislike each other. After the Fetterman Massacre, Kinney's criticism of Carrington did much to undermine the colonel's reputation.)
"Choice elk steaks, furnished by the timber choppers, and suitable accessories, supplied a delightful meal, and no Indian disturbed the pleasure," wrote Margaret Carrington. "The bill of fare was not printed, but canned lobster, cove oysters, and salmon were a very fair first course; and associated with the game, were jellies, pineapples, tomatoes, sweet corn, peas, pickles, and such creature comforts, while puddings, pies, and domestic cake, from doughnuts and gingerbread up to plum cake and jelly cake, with coffee, and Madame Cliquot for those who wished it, and pipes and cigars for the gentlemen, enabled everybody to satisfy desires." After the simple rations of the fort, Judge Kinney's catering seemed more like a banquet than a picnic.
Only a day or so following this outing, the Sioux made their first strike at a timber train. Along the road about four miles southwest of the fort, a war party sent a shower of arrows into a loaded train. One of the civilian drivers panicked, cut his mules loose, mounted one and headed for the fort. Rifle fire from the train's guard meanwhile had alerted Captain Ten Eyck, and he sent out a mounted platoon from Company H under Corporal George Phillips. The corporal proved to be a good Indian fighter; he recovered the mules, killed one Indian, wounded another. Ten Eyck recorded the incident in his usual terse style: "A party of troops had an engagement with Indians four miles from post. Indians attempted to stampede mules from teams coming from timber. One Indian killed and one mortally wounded." Corporal Phillips had got his first Indian. Four months later the score would be evened when the Indians killed George Phillips in the Fetterman Massacre.
Although Carrington was pleased with the work of Corporal Phillips, he was determined to secure his wood trains against further attacks. Uninterrupted movement of timber from Piney Island was vital to construction of the fort. Wagons and mules must be protected, drivers taught to defend themselves with a minimum of guard forces.
"The system adopted in the management of my wood train," he explained afterward, "guaranteed protection whenever there was due conformity to orders. The train, varying from twenty-four to forty wagons, went in two parallel lines, about three hundred feet apart, after leaving the mill-gate until they reached the pinery, with mounted pickets on either flank, especially on the crest of Sullivant Hills with orders, upon an Indian alarm, for the front wagons to turn in, left and right, and halt; and all other wagons to move on the trot or run; the mules to pass within each wagon in advance, thus making an instant corral."
As an added security measure, a permanent lookout was established on Pilot Hill, just across Little Piney east of the fort. From this point observers could obtain unobstructed views of the country for several miles in all directions. A simple system of flag signals was devised for communicating with a watch within the fort:
> Flag out of sight: "All quiet."
>
> Flag raised and still: "Attention."
>
> Flag waved, three times from vertical to right: "Small party on Reno road."
>
> Flag waved three times from vertical to left: "Small party on Big Horn road."
>
> Flag waved five times from vertical to right: "Large party on Reno road."
>
> Flag waved five times from vertical to left: "Large party on Big Horn road."
>
> Flag waved three times from right to left: "Indians."
>
> Flag waved around the head: "Train attacked."
>
> Flag raised and carried in a vertical position around the picket defense: "The attack."
The Sioux, however, refused to relax their pressure. As if in amused defiance, they began using flags themselves, and on sunny days from every hill there seemed to be a continuous flashing of their mirror signals. On the 13th they made a quick dash at another wood train, which happened to be guarded by Corporal Phillips' platoon, and this time Phillips' first sergeant, Alexander Smith, had to rush to the corporal's rescue. Alex Smith claimed two dead Indians that day, but his life also was destined for forfeit in the Massacre.
This constant vigilance kept timber moving from Piney Island into the fort in a steady stream, the tall trees furnishing 30-inch boards without knots or blemishes. Many of the planks coming off Engineer Gregory's saws would fit into a wall so neatly that no chinking was necessary. By mid-August, shingles were needed for roofing buildings, and these were rived from bolts sawed by hand. Determined to beat the cold autumn weather which would soon be upon them, Quartermaster Brown organized a series of all-night shingle bees, but even these efforts could not supply demand, and earthen roofs had to be used on several structures.
Meanwhile the hostile Indians seemed to have shifted their main efforts back to the Reno road. On the 12th they raided a civilian train camped for a Sunday rest near Powder River, driving off cattle and horses. Lieutenant Kirtland led his mounted detachment in pursuit, recapturing some of the cattle but none of the horses. On the 14th two civilians were killed within four miles of Reno, and three days later the Indians boldly entered that fort's corral, driving off seventeen mules and seven of Kirtland's precious cavalry mounts. None was recovered.
During this breathing spell at Fort Phil Kearny, three civilians who were to play important parts in the Fetterman Massacre arrived at the post. They were James Wheatley, Isaac Fisher, and John "Portugee" Phillips. When they were offered quartermaster employment by Lieutenant Brown, they decided that as the season was growing late they would defer their mining ventures until the next year and remain at the fort for the winter. Wheatley had brought his beautiful nineteen-year-old wife and two young sons from Nebraska, and post records for August show that he asked for permission to erect a building just outside the stockade for keeping a civilian mess. The building was constructed shortly afterward alongside the Bozeman Trail, with ready access to the main gate of the stockade, and no doubt young Mrs. Wheatley served as cook in this family business venture.
On August 22, the first mail in three weeks came through from Laramie, and there was welcome news indeed in a telegram which had been dispatched August 11 by General Cooke: "Two companies of 2nd Cavalry have been ordered to assist in the protection of the road. You are authorized to enlist not to exceed fifty Indian scouts. Pay and allowance of cavalry soldiers. Let them use their ponies if you can't do better. Be very cautious. Don't undertake unnecessary risky detachments." A second telegram dated August 9 stated briefly that "reinforcements have left St. Louis. Colonel Carrington must use his judgment about establishing Fort C. F. Smith at present."
Also in the mailbag was a surprise letter from Fort Reno:
> August 20, 1866
>
> Col. H. B. Carrington,
>
> Commanding Mountain District:
>
> DEAR COLONEL: I am on my way through the district as assistant inspector-general of the department, and will be at your post as soon as cavalry escort ordered to join me reaches here in about one week.
>
> The mail going up will carry from General Cooke authority for you to suspend establishing the extreme west post (C. F. Smith) if you think from the condition of Indian affairs it is expedient. He telegraphed me at Laramie to consult with you about it, and since coming within the theater of Indian troubles I am of the opinion that there is no sufficient reason for longer delaying the establishment of that post, but, on the contrary, it should be established without further delay.
>
> I think there is no danger on the route to parties well organized and that do not straggle, but that the greatest caution will be necessary both on the route and at the posts till the Indians are thrashed.
>
> W. B. HAZEN
>
> Bvt. Brig. General,
>
> Asst. Inspector,
>
> Dept. of the Platte
Carrington no doubt was pleased that the general agreed with his plan to open Fort C. F. Smith, but he must have reflected on the slowness of communications which inhibited co-ordinated planning, and the fact that during the forthcoming week construction must be delayed somewhat in order to put Fort Phil Kearny into spit-and-polish condition for the visit of the veteran Indian fighter and West Pointer, General William Babcock Hazen.
In the mail also were the first personal letters any of the men had received since leaving Fort Kearney, Nebraska, in May. Many letters had gone through error to the 1st Battalion in Utah and had been forwarded from there. A few scattered newspapers from New York were ten weeks old, but were welcomed nonetheless. The frontier soldier's forum for complaints, the letters column of the _Army and Navy Journal,_ not long afterward contained this significant contribution from an anonymous correspondent of the 2nd Battalion: "The common report is that Ben Holladay* throws out all papers as worthless. However true this may be, I know that _very_ few papers reach these outposts. I think there should be some remedy, as without a regular mail, and deprived of our newspapers, we will be unable to keep posted in the affairs of the outside world."
General Hazen arrived on the 27th, escorted by a mounted detachment of Lieutenant Kirtland's Reno company rather than by the expected 2nd Cavalry company from Laramie. The general could not explain the cavalry's delay, but he was an optimistic man and assured Carrington that the two companies of cavalry should be reporting any day, and that a regiment of infantry could be expected from St. Louis in a matter of weeks. (No cavalry reached Fort Phil Kearny to join the permanent garrison until November, and then only one company. The infantry regiment never arrived.)
Hazen spent three days inspecting the fort and pinery, expressed his satisfaction over Carrington's progress, and was most complimentary about the solid eight-foot stockade. "The best stockade I have seen," he said, "excepting one in British America built by Hudson Bay Company."
On the 29th Hazen announced that he would be departing the following day to inspect Fort C. F. Smith, and would require an escort troop. Had Carrington been able to foresee the future he might not have been so generous, but as he had been assured of the arrival of two companies of cavalry, he ordered the best horseman among his lieutenants, James Bradley,† to collect twenty-six picked men of the mounted infantry. The colonel also assigned one of his two remaining scouts, James J. Brannan, to act as guide for the general's escort. (Carrington of course could not foresee that the promised cavalry would be delayed until November and that Hazen would retain Bradley's escort for almost two months at a time when Fort Phil Kearny was critically short of officers and mounted men.)
On this same day, photographer Ridgway Glover wrote the editor of the _Philadelphia Photographer_ that he was "waiting for the medical supply train to come up, to get some chemicals, being at present in a 'stick'; but though unable to make negatives, I have been enjoying the climate and scenery, both being delightful." Glover had made several views, the nature of which he did not disclose. He was not destined to live until the medical supplies arrived in October.
As soon as General Hazen departed, work on the fort returned to normal. The weather had been good all month, the clear nights growing perceptibly cooler as August drew to a close. The Sioux held off attacks on the heavily guarded wood trains, but from the middle or latter part of August, as Carrington reported afterward, "Indians appeared more frequently about Fort Philip Kearny, and from that time I assumed the condition of affairs to be decided, unequivocal hostility on the part of Indian tribes about me.... I had at first little drill on parade, except at roll call, but I had willing, obedient soldiers. Drunkenness was rare; the post was orderly and quiet at all times. My men went from guard duty to hard work, and from hard work to guard duty without a murmur. Often they could not have two consecutive nights in bed, and were always subject to instant call."
Muster rolls of the fort for August 31 showed 345 officers and men present for duty, 43 absent.
* Holladay operated the Overland Mail system through the West.
†Tenyears later in 1876, Lieutenant Bradley was in command of the company of mounted scouts which discovered Custer's dead at Little Big Horn. He was killed in action during the Nez Percé War of 1877.
# _VI. September:_
DRYING GRASS MOON
> _The foregoing furnishes an outline of the main hostile demonstrations in September resulting in loss of stock or life; but, as will appear from my official correspondence, there were other and almost constant hostile demonstrations of some kind requiring of the garrison that every detail sent out for whatever purpose should exercise constant watchfulness and be kept well in hand_.
ON THE FIRST DAY of September snow fell on the Big Horns only four miles from Fort Phil Kearny. In the hayfields along Goose Creek and out toward Lake De Smet, the high grass had turned a golden yellow. Reacting to these signs of approaching autumn, Lieutenant Fred Brown kept his quartermaster crews working long hours. Great mounds of hay for stock were heaped in the quartermaster yard; billets and bark slabs for winter fuel were stacked high in an improvised woodyard.
On the 4th a long-overdue freight train escorted by a detachment of the 2nd Cavalry arrived at the fort in four sections, fifty-three wagons in all, loaded with commissary and military stores brought overland from Nebraska by contractor A. Caldwell. The sacks and barrels of hams, beef, bacon, flour, coffee, sugar, hardtack and soap ensured adequate rations for weeks ahead, but Quartermaster Brown was deeply disappointed that not one bag of corn or oats was in the shipment. Horses and mules under his care were losing weight daily from their monotonous diet of hay.
For lack of ready tents and storehouse space, unloading was delayed four days, and on the morning of the 8th, during a blinding storm of wind and rain, a corralled herd broke loose from contractor Caldwell's train. The wagoners pursued, but a band of Sioux in the vicinity made off with twenty of the stampeded horses and mules. Later in the day—as if this easy booty had aroused their zeal for raiding—the Indians made a daring strike at one of the fort's herds. Carrington's alert pickets headed them off, however, and Lieutenants Brown and Adair gave the raiders a fast chase into the hills.
On that same day the industrious Lieutenant Brown sat on a board of survey with Lieutenant Wands, "to examine and report upon the quality and condition of certain military stores and supplies arrived at this post." As was usual in long overland shipments, there were shortages in Caldwell's bills of lading. The hams and bacon had shrunk; soap and coffee were short; 210 sacks of flour and 238 boxes of P. Bread (pilot bread or hardtack) were missing.
After hours of questioning drivers and members of the train's cavalry escort, Brown and Wands finally adjusted matters satisfactorily. They were inclined to be lenient because Caldwell had been delayed four days for unloading and then had lost livestock to the Sioux. Meat shrinkages were blamed on "drying out in a dry season" and "oil and grease absorbed into sacks." Sergeant William H. Brooks, in charge of the 2nd Cavalry detachment, presented a written receipt explaining shortages of soap and coffee: "On the road between Laramie and Fort Reno, the Sgt. in charge of the escort run short of provisions and got an order from Captain Shanks commanding a post on the road [Bridger's Ferry] and on this order took from this train 17½ lbs. roasted coffee and 10 lbs. of soap." The missing flour and P. Bread had been erroneously unloaded at Fort Reno "owing to changes in names of military posts in this District since this [Fort Phil Kearny] has been started."
Two days later, the 10th, the Sioux returned with a band of Arapaho allies, eager for more horses. In the deceptive faint light of early dawn, they swept down the hills and cut out forty-two mules from a grazing herd belonging to A. C. Leighton, who had just brought up several wagons of supplies for the sutler's store. Lieutenant Adair pursued for twenty miles, but caught no Indians, recovered no stock.* His horses, starving for grain, were no match for the fleet Indian ponies.
While Adair was still out, the Indians, in a gesture almost of contempt for the soldiers' ability to pursue, raided again—this time one of the fort's herds only a mile from the stockade—and swept away thirty-three horses and seventy-eight mules. "They were pursued promptly," Carrington reported, "but night and broken-down horses rendered pursuit hopeless."
This was a most serious loss of riding and draft stock, and no doubt led the colonel to make an immediate decision concerning recruitment of a company of Indian scouts which had been authorized by General Cooke on August 11. Carrington would have liked Jim Bridger's counsel on this matter. Back in June the scout had warned against re-enlisting Winnebagos for fear it would antagonize the Sioux. But the Sioux had already demonstrated their inflexible hostility, and Carrington decided he must act before Bridger returned from Fort C. F. Smith.
"I have the honor," he wrote General Cooke that evening, "to send by bearer, Mr. W. B. C. Smith, who desires to organize a band of Winnebago scouts, the following report, as he goes by stage and may anticipate a mail. He is a good man for the work, if it has not been earlier attempted.... I sent twenty-five of my best mounted men with Gen. Hazen—have no corn, and with all pains to keep up my stock can not pursue successfully until I have more cavalry... if the single company of Indians, which were sent down for muster out on my way here, had been with me I could have punished the Indians and regained much stock...."
The day ended sadly for the garrison of Fort Phil Kearny. Bandmaster Samuel Curry, who had been ill only a few days, died of an ailment diagnosed by Surgeon Horton as typhoid pneumonia. "The night he died," Frank Fessenden recalled, "I well remember how the wolves howled and made the night hideous, and we could hear them scratch at the stockade posts." Next morning the band under a new leader, Peter Damme, marched with muffled drums to the cemetery at the base of Pilot Hill. "When we buried the body we had to dig very deep, place heavy planks over the box, and then haul heavy stones and fill the grave to prevent the wolves from digging the body out." Bandmaster Curry was the first occupant of the post's rapidly growing graveyard to die of natural causes.
After a three-day respite, the Sioux and Arapaho unleashed a well-co-ordinated double thrust at the fort's beef herd and upon a camp of about eighty civilian hay cutters along Goose Creek. The attacks came late in the day, and it was after midnight before a messenger brought the alarm to Fort Phil Kearny.
John Bratt, a bullwhacker who arrived at the fort early in September, had hired out to the hay contractor, Leviticus Carter, for sixty dollars per month, and was present during the fighting at the hay camp. He reported:
> One afternoon the Indians had made several attacks on us. They killed three of our men and wounded some others, captured nearly all our mowing and rake teams and had us all corralled on a high hill where we spent the evening and greater part of the night in digging rifle pits and defending ourselves and the stock we had left.
>
> Mr. Carter was with us and paid our old stuttering blacksmith, Jose, five hundred dollars to go to the fort to get relief.... Mr. Carter knew Jose and he knew he would execute the order or die in the attempt.... We estimated that more than one thousand Indians had us surrounded, and judging from the many signal fires being built around us other Indians were being told to come and help finish us.... It must have been about nine o'clock in the evening when Jose mounted the best horse we had in camp and started for the fort. A few stars were out but the night was rather dark. Thin clouds of smoke from the prairie fire the Indians had started in the afternoon hung over our camp.... Jose, armed with two revolvers and a sharp butcher knife on his belt, had been gone some ten minutes... when to our surprise he came at breakneck speed into camp followed by a bunch of Indians, some of whom we tumbled off their horses before they escaped. Mr. Carter and others were soon at Jose's side asking him what he proposed to do next when Jose answered, "I most believe I will try it another way," and in less than ten minutes he disappeared in the darkness in an opposite direction....
>
> Just about the peep of day we saw the Indians scattering to right and left of a large body of mounted men... with old Jose in the lead."
It was Jose, the blacksmith, who taking a circuitous route had finally reached Fort Phil Kearny about one o'clock in the morning of the 13th and awakened Colonel Carrington. "Six mowing machines had been broken with hatchets, hay heaped upon them and fired," Carrington reported later. " I sent Lieutenant Adair with forty men to relieve them, in wagons. Six miles out, a small body of Indians rode toward the train; prompt deployment of the men sent them galloping to the hills. Lieutenant Adair reports from two hundred to three hundred Indians on the hills following his course."
A most damaging blow in this double action was suffered by the fort's beef herd which had been grazing nearby under a guard of a sergeant and ten men. The Indians shrewdly maneuvered a buffalo herd into the area, drove them among the cattle, and stampeded the combined animals. At least two hundred beef cattle, sorely needed for the post's meat supply, were irrecoverably lost.
That morning Carrington scarcely had time to promise contractor Carter a stronger military guard for his hay cutters and to offer assistance in the prompt repair of mowing machines, before the Indians struck again. They stampeded a convalescent herd of horses and mules just outside the stockade, wounding two privates on picket duty, one taking an arrow in his hip, the other a bullet in his side. Captain Ten Eyck and Lieutenants Brown, Bisbee and Wands led mounted parties out in various directions, but all returned without success, blaming failure to overtake the scattering raiders on the poor condition of their horses. After this night and day of staggering losses, Carrington decided he must tighten defensive measures against the hostiles, and issued a new special order:
1. Owing to recent depredation of Indians near Fort Philip Kearny, Dak., the post commander [Ten Eyck] will issue such regulation and at once provide such additional escorts for wood trains, guard for stock and hay and the steam saw-mills as the chief quartermaster [Brown] may deem essential. He will also give
2. Instructions, so that upon Indian alarm no troops leave the post without an officer or under the antecedent direction of an officer, and the garrison will be so organized that it may at all times be available and disposable for exterior duty or interior defense.
3. One relief of the guard will promptly support any picket threatened at night, and the detail on posts should be visited hourly by a non-commissioned officer of the guard between the hours of posting successive reliefs.
4. Stringent regulations are enjoined to prevent camp rumors and false reports, and any picket or soldier bringing reports of Indian sign or hostilities must be required to report to the post commander or officer of the day or to the nearest commissioned officer in cases of urgent import.
5. Owing to the non-arrival of corn for the post and the present reduced condition of the public stock, the quartermaster is authorized, upon the approval of the post commander, to purchase sufficient corn for moderate issues, to last until a supply already due, shall arrive, but the issue will be governed by the condition of the stock, and will only be issued to horses unless the same in half ration shall be necessary for such mules as are daily in use and can not graze or be furnished with hay.
6. Reports will be made of all Indian depredations, with the results, in order that a proper summary may be sent to department headquarters.
7. Soldiers while on duty in the timber or elsewhere are forbidden to waste ammunition in hunting, every hour of their time being indispensable in preparing for their own comfort and the well-being of the garrison during the approaching winter.
The next day another casualty was added to the morning report. Private Allando Gilchrist, unreported for four days, was listed as "missing, presumed killed by Indians" when "a portion of his clothes were found bloody, without his body."
Two days later, Sunday the 16th, a train of twelve wagons was sent out to the hay flats near Lake De Smet. A rifleman sat beside each driver, and six mounted infantrymen covered flanks, rear, and forward positions. After the wagons were loaded, Private Peter Johnson moved out on point position and carelessly allowed his horse to take him three or four hundred yards ahead of the slow-moving train. As Johnson approached a ravine, an Indian dashed suddenly between him and the wagons. "Johnson would have been all right had he returned to the hay detail," said Private John Ryan, one of the guards, "but he must have become confused, as he started toward the fort with the evident intention of trying to outride the Indian. The savage, however, mounted on a fast pony, rapidly gained on him, when Johnson apparently lost his head completely, jumped off his horse, threw his gun away, and made for a washout east of the road. Being still armed with a six-shooter, he could have defended himself, but he did not, and the Indian had no trouble capturing him."
According to Ryan there was nothing the others could do to help Johnson. The hills surrounding them had suddenly become alive with Indians, and any attempt to leave the protection of the wagons might have sacrificed the entire party. Another problem was shortage of ammunition (Carrington still had received none since leaving Laramie). "The guards had but three rounds of ammunition to the man and the teamsters were practically unarmed." After the hay train reached the fort and reported the incident, Lieutenant Brown led a large detachment out to the scene, but no trace was ever found of Peter Johnson's body.
On this same Sunday one of the fort's civilians, Ridgway Glover, was also spending his last day on earth. "He had a camera outfit," said Frank Fessenden, "and was taking views for his paper. While taking pictures he would go around alone on the mountains, and sometimes would not be seen for five or six days at a time. He made his headquarters with the woodchoppers. He had long yellow hair, and I had often told him that the Indians would delight to clip that hair for him some day. He said he was safe, as the Indians would take him for a Mormon."
For some reason on this Sunday, Glover decided to leave the timber camps and go to the fort. When the photographer was told that the wood train detail had been given a Sunday holiday, he announced that he intended to walk in alone. "The woodchoppers tried to get him to remain and wait for the wood train Monday. He left one cutting and said he would go to the other, which he did. The men at this cutting also warned him of the danger, and almost certain death, if he attempted to go on to the fort alone. He told these choppers that he would return to the other cutting—which he did not do, as he was on his way to the fort alone, when he met the certain fate which overtook every man caught alone away from the garrison. Glover had escaped so many times that he apparently thought he was Indian proof."
They found his naked body next morning less than two miles from the stockade. He had been scalped, his back cleft with a hatchet. Lieutenant Bisbee, commanding the detail which discovered Glover, said he was "lying face down across the roadway, a sign that he had not been brave." An ambulance was attached to Bisbee's detail, the driver being the same Private Ryan who had witnessed the capture of Peter Johnson the previous day.
"We were something over a mile from the fort," Ryan recalled, "and I could look across the Big Piney to the north and the Little Piney to the south and see Indians who were watching our every movement, and I did not relish the idea of going back unsupported by the soldiers, and I asked the officer [Bisbee] if he did not think the body would be all right where it was for a while, and we could get it on our return. He was obdurate, however, and said, 'Young man, if you don't obey my orders it will go hard with you.' I told him it would go hard with me also if the Indians caught me, but I had to go back just the same."*
The reason for Lieutenant Bisbee's impatience was that he was in command of a follow-up party to a large mounted detachment under Lieutenant Brown, who as usual was pursuing Indians. Early that morning a large force of hostiles had appeared out of the valley at the junction of the Pineys, galloping upon what was left of the fort's beef herd. The pickets being short of ammunition withheld fire until the raiders surprised them by using revolvers for the first time in an attack. Forty-eight head of cattle were cut loose, but this time Fred Brown was ready for immediate pursuit and was successful in recapturing all the stock. In his report of this action, Colonel Carrington said that he witnessed the swift attack and was fearful that all the pickets would be killed before a rescue party could reach them. "I loaded and fired a 12-pound field howitzer, having no one else experienced, bursting the first shell in the Indians' midst. This drove them back to the creek. A second shell dismounted one Indian, and all crossed to the hills."
This day, the 17th of September, was to be a busy Monday at Fort Phil Kearny. Lieutenant Brown had scarcely returned with the recaptured beef cattle when a contract commissary train arrived with sixty thousand rounds of Springfield rifle ammunition. The contractor was also willing to sell a few bushels of corn, badly needed for reconditioning mounts. At about the same time a mail escort arrived, with a baggage wagon and an ambulance, aboard which were two contract surgeons, a young lieutenant, and his wife.
The lieutenant was George Washington Grummond, and he and his wife, Frances, who was pregnant, were the post's most romantic couple. Grummond had served through the Civil War as officer of a Michigan Volunteer Infantry regiment. He met Frances in Tennessee and married her after the war's end. Determined to pursue a military career, he applied for a regular commission, and as his war record was brilliant (he held a brevet rank of lieutenant-colonel) he was assigned to the 2nd Battalion as a second lieutenant.
In recording her arrival at Fort Phil Kearny, Frances Grummond told of seeing the picket on Pilot Hill signaling the approach of the mail party on the east road. "We moved toward the stockade," she wrote, "but just before entering a halt was made, and I looked eagerly for the occasion of the delay. It almost took my breath away for a strange feeling of apprehension came over me. We had halted to give passage to a wagon, escorted by a guard from the wood train.... In the wagon was the scalped and naked body of one of their comrades.... My whole being seemed to be absorbed in the one desire—an agonized but unuttered cry, 'Let me get within the gate!'... That strange feeling of apprehension never left me, enhanced as it was by my delicate condition...."
Frances Grummond's fears were not without prescience. Her husband was one of the three officers who would die in the Fetterman Massacre.
In the mail for Carrington was a letter from General Sherman, written at Fort Laramie where the general had visited near the end of August on a tour of western defense posts. "I shall instruct General Cooke to reinforce his force at this post," Sherman wrote, "so that expeditions in sufficient strength can go out to punish the Indians. We want to avoid a general Indian war, as long as possible, until we get the new army further advanced in recruiting. The Indians seem to oppose the opening of the new road, but that must stimulate us to its prosecution, and you may rest assured that you will be supported all that is possible.... We must try and distinguish friendly from hostile and kill the latter, but if you or any other commanding officer strike a blow I will approve, for it seems impossible to tell the true from the false."
Carrington did not share Sherman's philosophy of ruthless extermination, but agreed with his hope of avoiding a general war as long as possible, and was grateful for any support from a general who was second in command to Ulysses Grant.
The mail also contained a petulant message from General Cooke complaining about women and children being captured on the Montana Road, reports of which he had read in newspapers. As Carrington had seen no recent newspapers and had heard of no such incidents, he was puzzled as to what Cooke meant. An even more annoying letter, dated August 15, had been sent directly from The Adjutant General's office in Washington. The A. G. complained that no returns of the post for June 1866 had been received—the reason for which should have been obvious had the Washington officials checked the date of the fort's establishment, July 14.
Toward the close of this busy day a party of about forty miners arrived from the north. They had been unsuccessful in finding gold in Montana, and had decided to prospect the Big Horn country, but on the trail down from Virginia City hostile Indians had given them a bad time. Two men had been killed only the previous day near Tongue River.
Their leader, William Bailey, reported to Carrington, requesting permission to camp near the fort for protection for themselves and their horses. When the colonel learned that Bailey had been a scout and prospector in the West for seventeen years and that his followers were all of the same rugged mold—crack shots, well armed and well mounted—he suggested that the miners would be more than welcome to spend the winter, and would be given quartermaster employment if they wished it. The miners put the offer to a vote and accepted. By nightfall they had pitched their tents in front of the fort, just across Big Piney under a slope rising to the north, and Carrington had gained for the post the equal of a company of trained cavalrymen.
Accompanying Bailey's party was a messenger from Fort C. F. Smith, with news of Jim Bridger. Old Gabe reported that he had talked with several Crows, who had informed him that at least five hundred lodges of Sioux were along the Tongue, all hostile, some armed with rifles. Bridger also had heard from the Crows of renegade white men among the Arapaho, squaw men and miners probably, who had allied themselves with the hostiles to drive other white men out of the gold country.
Carrington worked late that night over his lantern-lit writing table, while the season's first snow whirled across the fort's parade. The mail escort for Laramie was scheduled to leave at dawn, and the colonel had much to report to General Cooke:
> Mail has arrived. I send directly back. Lt.-Gen. Sherman wrote me from Laramie to endeavor to keep you more frequently advised. I am doing all I can with my broken down and famished horses, not having received a pound of corn yet.... No women or children have been captured or injured by Indians in this district since I entered it.... While more troops are needed I can say (and I am in the very heart of the hostile district) that most of the newspaper reports are gross exaggerations. I gather and furnish you, as requested, all the bad news, neither coloring nor disguising facts.
He went on to tell of Bridger's report, of the purchase of a few bushels of corn from a contractor, of the welcome arrival of sixty thousand rounds of Springfield ammunition. "I ought to have, if possible, a hundred thousand more, and from Laramie more ammunition for my 12-pounder field howitzer and mountain howitzers.... Red Cloud is known to command the parties now immediately engaged... they are determined to burn the country, cut off supplies, and hamper every movement."
Next morning when Frances Grummond awoke after her first night of unsound sleep in Fort Phil Kearny, she found that snow had drifted into her tent, "covered my face, and there melting trickled down my cheeks until if I had shed tears they would have been indistinguishable... pillows, bedding, and even the stove and the ground within the tent were also covered."
Almost a foot of feathery snow had fallen on the fort, but the sun was out bright and warm, and by afternoon most of it had melted. The Indians kept to their lodges this day, and Captain Ten Eyck chose the peaceful interlude for a post arms inspection. His report to Carrington was blunt: "Many Springfield rifles unserviceable. Some men not armed at all, because of thefts by deserters and others. Want pistols and carbines, as rifles no good for mounted men."
With most of the snow gone by Wednesday (the 19th) the hostiles came back just after breakfast, as Peter Damme was marching the regimental band out on parade. Their objective was the open camp of Bailey's miners across the Piney. Frances Grummond watched the incident from inside the stockade; it was her first experience of hostile Indian attack and she described it vividly.
"Quite a large body of Indians suddenly appeared at the summit of the hill in full warpaint, brandishing their spears, giving loud yells and lifting their blankets high in the air as they moved down slowly in an attempted charge upon the miners' camp. Between one and two hundred Indians were scattered along the crest of that hill, but hardly three minutes had elapsed after they first came in view before the smoke and crack of the miners' rifles, out from the cottonwood brush that lined the bank of the creek, had emptied half a dozen warriors' seats and brought down three times as many ponies, while the cheers of the miners and their perfect confidence in defending their camp were enlivened by the music of the 18th Band which Colonel Carrington had play on the parade ground, while the whole garrison was under arms ready for a fight, and three howitzers were ready to open their fire in case of need. A small detachment had been sent to support the miners..."
Colonel Carrington, having grown accustomed to these monotonous raids, reported the same incident much more succinctly. "A large force attacked the miners encamped across Big Piney.... A shell from the fort scattered them; no stock was lost; miners pursued several hours in view."
The next day's report was equally brief: "Indians attacked citizen train lying in angle of two Pineys, repulsed by aid from fort, losing one red man killed and another wounded."
But on the 21st he was sufficiently concerned by another heavy attack upon Levi Carter's hay mowers to order the party to cease operations. Melting snow and rain showers had almost halted cutting already, and the colonel sent one of his new officers, Lieutenant Winfield Scott Matson, out with forty men to assist in bringing in all hay and equipment.
That Carrington was more alarmed over continuous Indian raids than his sparse reports indicate is revealed in a special order issued that same day:
> The fastenings of all gates must be finished this day; the locks for large gates will be similar, and the district commander, post commander, officer of the day, and quartermaster will alone have keys. Keys for the wicket gates will be with the same officers.
>
> Upon a general alarm or appearance of Indians in force or near the gates, the same will be closed, and no soldier or civilian will leave the fort without orders.
>
> No large gate will be opened, except the quartermaster gate, unless it shall be necessary for wagons. Stock must invariably pass in and out of that gate.
>
> The west or officers' gate will not be opened without permission, even for wagons, unless for timber wagons or ambulances, or mounted men.
>
> Upon a general alarm the employees in the sutlers' department will form at the store and wait for orders and assignment to some part of the interior defense, but will not be expected to act without the fort unless voluntarily, and then after sanction is given, and under strict military control.
>
> All soldiers, however detailed or attached, or in whatever capacity serving, will, upon a general alarm, take arms and be subject to immediate disposal with their companies or at the headquarters or department with which serving.
>
> All horses of mounted men will be saddled at reveille.
>
> It is also expressly enjoined that in no case shall there be needless running in haste upon an alarm. Shouting, tale-bearing, and gross perversion of facts by excited men does more mischief than Indians. And the duty of guards being to advise of danger, soldiers who have information must report to the proper officer, and not to comrades.
>
> At the sounding of assembly the troops of the garrison not on daily duty will form in front of their respective quarters.
>
> The general alarm referred to in foregoing paragraph will be indicated by the sounding of the assembly, followed by three quick shots from the guard-house, which latter will be the distinction between the general alarm and the simple alarm for turning out the troops of the garrison.
>
> This order will be placed upon a bulletin-board for early and general information.
>
> Officers and non-commissioned officers are charged with its execution, and the soldiers of the 18th Infantry are especially called upon to vindicate and maintain, as they ever have, the record of their regiment.
>
> This will require much hard work, much guard duty, and much patience, but they will have an honorable field to occupy in this country, and both Indian outrages and approaching winter stimulate them to work, and work with zeal and tireless industry.
>
> Their colonel will with his officers share all, and no idling or indifference can, under these circumstances, have any quarters in the breast of a true soldier.
Since early August the women of the fort had been virtual prisoners within the 400-foot-square stockade. From now on the same situation would apply to soldiers and civilian employees. In reference to these regulations Frank Fessenden said that "orders were given that none of our men should ever go out of the fort alone.... The chaplain bought a cow for which he paid $75. He told me if I would milk her I could have all the milk that was left after he was served. I remember how I used to arm myself and go out hunting after that cow. I presume the Indians also wanted her for they eventually got her anyhow. Orders finally became so strict that I did not dare go outside the stockade."
Meanwhile, Lieutenant Matson's detachment and the hay-field workers were having a difficult time withdrawing machinery and wagons from the Goose Creek flats. A force of three hundred Sioux and Arapaho forced them to corral five miles from the fort, pinning them down until Carrington sent out a mounted relief Saturday morning. During the fluid action of the Indians' withdrawal, Matson was suddenly confronted by a horseman on the road, a white man dressed like an Indian, the fingers missing from one of his hands. He identified himself as Captain Bob North, but Matson, remembering rumors of white men fighting with the Arapahos, was suspicious. A few minutes later Matson's advance scouts reported that a contractor's train returning from Fort C. F. Smith had also been attacked on the road. The contractor, Grull, and two of his drivers had been killed. During the ensuing excitement, the mysterious "Captain North" disappeared.
The mystery of Captain North may or may not have been solved the next day. In the gray dawn of Sunday, under cover of a rainstorm, a raiding party struck at a civilian cattle herd. They dashed among the grazing animals, yelling and waving blankets and buffalo hides, stampeding almost a hundred. This time there was no delay in pursuing. In accordance with Carrington's order of the 21st, horses had been saddled at reveille, and before the raiders could head away, a small detachment under Lieutenant Brown dashed out the east gate of the quartermaster's corral. Fifteen miners joined Brown's galloping pursuit force, and after a ten-mile chase they overtook the Indians. For a few minutes the Indians tried hard to keep their stolen cattle, but Brown dismounted his men and went into quick skirmish formation.
The hostiles grouped for a charge, and as they thundered down upon the soldiers, the men were startled to recognize the leader as a white man. Two or three times the Indians charged, each time led by the white man swearing in English, but in each attack they were driven back, several warriors dropping from their ponies. In the last charge, the white leader went down; an Indian swept him up and carried him off the field, apparently dead.
Was he the same man Lieutenant Matson had met Saturday on the road, the mysterious Captain Bob North, the renegade mountain man with four missing fingers?
In his official report Colonel Carrington assumed he was. "Lieutenant Brown and a few men charged the Indians with revolvers, killing five Indians and one white man, I think Bob North, who led them in every case, and wounding sixteen." (If the renegade was North, he survived only to die three years later in Kansas by hanging.)
Carrington also considered this fight his first real victory over the hostiles:
> One of our party was wounded slightly with an arrow, which grazed the temple, and six of our horses were wounded by revolvers and rifle shots. All were brought from the field. One chief carried from the field by his men wore an elaborate feather head-dress and proper ornament of the same kind upon his person. They retired to a high hill silently, and without their usual bravado. They felt the blow. Every head of stock was rescued and brought back to the fort. It has inspired my men with new courage.... One week's feeding on corn has given new life also to my horses....
Carrington's claim that the hostiles "felt the blow" in the wounding or death of at least two leaders is supported by the fact that they made no demonstrations around the fort during the next three days.
This breathing spell gave Carrington an opportunity to collect his thoughts and compose two leisurely letters to General Cooke, discussing the flora and fauna, the climate and minerals, of the surrounding country.
> Coal abounds in exhaustless supply. I have recently opened a vein of cannel-coal, that will weld iron within fifty feet of the quartermaster's corral, east of the fort.... Late in the season as it is now, while the cottonwood is yellow from frost, the hills and slopes bear innumerable patches of green shrubs, marking the work of the last lingering snows of spring and the abounding springs which are everywhere found... . The pine timber has furnished novel results: the trees of one mountain have been girdled by fire apparently two years since. The boards from these take the plane and polish equal to No. 1 merchantable seasoned pine lumber. The pitch has dried out, the grain is close, and the material is sound. Shingles that are rived from it furnish bolts three feet in diameter and of the best quality....
>
> Altitude of the post I find to be 5,790 feet by barometer.... The mountain range nearest rises abruptly from 850 to 900 feet more.... It has rained at the post when snow was falling within two miles... and again we have had snow when on the creek, 160 feet below, there was rain.
He also discussed the progress of the fort's construction and the morale of his men:
> I have changed company buildings to 84 feet in length, kitchen in rear. This will allow four buildings each side, and these four will be roofed this week. A large commissary building with plank floor and good roof will be equally advanced.
>
> Everything moves well; the men cheerfully come off guard and go to work and respond to alarm instantly and eagerly by night and day. Sickness is almost unknown. Sometimes one, and often none, at sick-call. Antiscorbutics arrived in good time, as scurvy began to appear. I trust fresh potatoes will be sent us on my April requisition. I shall have a cellar ready.
By that last week of September, Carrington had perfected the defenses of his fort to a point where the Indians respected its immediate power of retaliation, and no longer dared approach the stockade. Wagon trains, strongly guarded by escorts of seventy-five to one hundred men, were also seldom attacked. Two vulnerable points remained, however—Pilot Hill where mounted pickets rotated duty in fours, and the timber cuttings where the men, because of the nature of their work, were sometimes separated individually by several yards from their comrades.
On the 27th, Red Cloud's hostiles moved against both these weak positions. It was a sunny morning, with snow still lingering under the tall trees on Piney Island. The crack of axes and shouts of the cutters rang clear in the crisp air. Private Patrick Smith and two companions had worked their way upslope about half a mile from the nearest pine-log blockhouse; a dozen or more men were less than a hundred yards below them trimming fallen trunks in a partial clearing. Without warning nearly a hundred Indians dashed between the three men and the main party, and the latter immediately exchanged axes for rifles. Within a few minutes the cutters withdrew to the safety of their blockhouse. Shortly afterward two of the isolated men came in safely, after eluding the Indians by dashing into a thick part of the forest. They assumed that Private Smith was dead.
Private Smith had been shot down by arrows and hastily scalped, the Indians leaving him to die. Recovering consciousness, he began crawling the half mile toward the blockhouse. He was too weak to withdraw the arrows deeply imbedded in his body, but managed to break off the shafts so that he could crawl unimpeded through the thickets.
When he appeared, scalped and bleeding, before the blockhouse, his comrades lifted him into a bunk and sent an emergency detail hurrying to the fort for a surgeon.
In the meantime the same band of Indians which scalped Private Smith had moved east from the cuttings, crossed Little Piney, and was making a dash toward Pilot Hill where four pickets were on duty.
Margaret Carrington, who witnessed this incident, said "the sudden repeated shriek of the steamwhistle at the farther mill, and the equally hasty signal of the pickets, gave the alarm that Indians were again close by. We could all see fifteen Indians between the fort and the mountain, galloping... directly for Pilot Hill, with the plain purpose of capturing and scalping the picket under the very eyes of the garrison."
Lieutenants Brown and Adair by this time were out the gate and in hot pursuit with a party of twenty mounted men. "Private Rover (who is of a good Chicago family, and enlisted under the false name of Rover) was in charge of the picket.* He had been signally brave in several tight places before. On this occasion he dismounted his three men, turned his horses loose toward the fort with a good urgency, and slowly fell off the northern slope, with arms at a 'ready' to join the supporting party. The horses came down the steep grade toward the fort on a run, passing through the Indians, who dared not stop them and could only give them a few arrows as they passed."
Lieutenant Brown, who seemed to consider Indian chasing a part of his regular quartermaster duties, pursued this band until almost dark. As he was on the point of breaking off pursuit, Brown saw the hostiles suddenly stop and parley with another party of Indians coming from the east. Brown ordered his men forward at a gallop; the hostiles scattered into the dusk, the other Indians remaining where they were. As Brown approached, he recognized the new arrivals as Cheyennes. Some were holding up the good-conduct passes signed by Carrington back in July.
There were only nine of them, three chiefs, five warriors and a squaw. Two Moons was the spokesman. He said Black Horse was sick, that the old chief and the rest of the band were in the mountains. Two Moons' party was en route to Fort Phil Kearny to ask the Little White Chief, Carrington, for permission to hunt in Tongue River valley.
They were brought back to the fort, and after Carrington questioned them closely he granted permission to pass on to Tongue River. He also ordered the quartermaster to issue them rations of bacon and coffee, and told them they might camp for the night across Little Piney opposite the sawmills.
By this time wagons from the pineries had come in, and the story of Private Smith spread rapidly through the fort. Nothing the Indians had done before had so aroused the anger of the men as the scalping of one of their comrades and leaving him to die. Stories of Smith's blood-smeared face, the skin hanging in strips from his forehead, the broken arrows in his body, were recounted around all the mess fires that evening. The contract surgeon, Edwin Reid, marveled that the man was still alive; Reid had found it almost impossible to remove one arrow deep in Smith's chest.
From inside the fort the men could see the near campfires of the Cheyennes down by Little Piney. Those who had ridden with Brown and Adair that day were skeptical of the Cheyennes' genuine friendliness. For all they knew, these Cheyennes might have been the ones who scalped Pat Smith and left him to die. If the Cheyennes were real friends of the soldiers, why had the hostile Sioux passed them by without harm?
In the close confines of the 400-foot stockade, the men were restive, their bitterness deepening with the spreading rumors. Like General Sherman in his recent letter to Carrington, they were eager to "strike a blow" against any Indians; as the general had written, it seemed "impossible to tell the true from the false."
Chaplain David White, closer to the enlisted men than any of the officers, heard enough threats to worry him. Soon after tattoo was sounded, White called on Carrington and warned him that some of the men were talking openly of surrounding and killing the Cheyennes in their camp.
Carrington summoned Captain Ten Eyck immediately, and suggested that the post commander throw a guard around the Cheyenne camp. The colonel as usual went along to see that everything was done properly, and when the two officers and the guard detail marched down toward the Indian campfire, they surprised a mob of some ninety soldiers spread out along the creek. "The troops," Carrington said afterward, "armed themselves and climbed the stockade, or went through the wicket of the quartermaster's gate." Some of them had "cocked their pieces, and were ready to deliver fire, when their muskets were thrown up by two reliefs of the guard sent to quell the disturbance."
The mob broke in the darkness; some started running for the water gate. Ten Eyck cried an order to halt, but this only caused others to turn and run for fear of being recognized and punished. "I ordered them to halt twice," Carrington said, "was disobeyed, but two shots from my revolver halted the men..." In the dim light of the Cheyenne camphres he recognized a few familiar faces. Among them were some of the best men in the garrison. He gave them a brief tongue-lashing, warned against any such demonstrations in the future, and ordered them back to their quarters.
Next morning the colonel interviewed the Cheyennes again, hoping to learn something of the movements of the Sioux and Arapaho. They told him they had heard Red Cloud and Man-Afraid-of-His-Horses were operating from Tongue River valley and that Buffalo Tongue was directing harassment of trains around Reno and Powder River. They also had heard that Bob North, a white man with one thumb, a big medicine man to the Arapaho, had made an alliance with the Sioux in August. Their information tallied with what Jim Bridger had heard from the Crows, and although Carrington could not take the field for punitive action with the small force at his command, he at least was satisfied that he knew where his enemies were.
Entries in post records indicate that the month of September ended routinely. Daniel Bradford, an unlucky Third Class Musician from Pittsburgh, reported his carbine and cartridge box missing, and was listed as owing the "U.S. for one Spencer carbine $30, and one cartridge box, $1.05. Total $31.05."
By the month's end Indian raids had caused serious losses in the beef herd. Six hundred of the seven hundred head brought overland from Fort Kearney were gone, most of them to raiding Indians, and the post's prospects for fresh meat during the winter were poor indeed.
Three enlisted men and five civilians in government employ had been killed; one enlisted man had deserted. Officers and men present for duty totaled 341. One building 50 x 24 feet for commissary stores, one building 44 x 52 feet for officers' quarters, and four buildings 84 x 24 feet for company quarters were approaching completion.
And on the last day of the month, Train No. 33 crossed the ford of Little Piney, ending its long slow journey from Nebraska, loaded with tons of corn and oats for the starving horses and mules of the mounted infantry and wood trains.
* Leighton put in a bill for his lost mules to the War Department, valuing them at $250 each. Twenty-four years later, 1890, he received a check for the loss.
* One of the unsolved mysteries of Fort Phil Kearny is what happened to the photographs made there by Ridgway Glover. Twenty-two of his Laramie negatives were sent to Wenderoth, Taylor & Brown in Philadelphia. His Fort Phil Kearny negatives or prints, if ever discovered, would furnish the only photographic record ever made of scenes and personnel in and around that vanished Wyoming post.
* Rover's real name was Ephraim C. Bissell. Mrs. Carrington said that "a hasty indiscretion impelled him to the army." He was killed three months later in the Fetterman Massacre.
# _VII. October:_
HARVEST MOON
> _On the 7th of October I issued an order assuming command of Fort Philip Kearny, to have more immediate personal command of the post, at which were my district headquarters... I took charge of the system of police and discipline of the post, entertaining the idea that the future policy might involve more formidable Indian aggression and require a more exact and careful watchfulness and defense._
AS OCTOBER CAME IN, frosty mornings and crusted ice on the edges of the Pineys warned of winter's approach. Wagon trains were hurrying north to be clear of the road before the heavy snows fell. Inside the fort's stockade the parade was being closed in by rows of buildings nearing completion.
Two more freighting trains ended their sixty-day runs from Lone Tree, Nebraska, bringing in enough corn and oats to supply the post's livestock' into midwinter. As usual there were shortages in bills of lading, and Lieutenants Bisbee and Wands spent three days as a board of survey determining whether Train No. 33's deficiencies of 4,195 pounds of corn from a shipment of 179,882 pounds, and 397 pounds of oats from a shipment of 20,199 pounds, were allowable. After taking testimony from three civilians, the young lieutenants reported that "Leviticus Carter, James Hill, and James Henning, who have for many years freighted grain over the plains for the Government and private parties, find that the deficiency is only a fair allowance arising from shrinkage and spilling from old and worn sacks and other causes incident to freighting, being only 2¼% of the total delivered."
The survey board consequently exonerated contractor Herman Kountz from all blame and responsibility. After studying the deficiencies of subcontractor W. H. Berger's Train No. 41 and F. M. Square's Train No. 43, Bisbee and Wands reached the same conclusion. Perhaps they felt that any freighters who had the raw courage to risk lives, stock, and wagons hauling grain over the dangerous Montana Road to remote Fort Phil Kearny deserved approbation rather than penalties.
Meanwhile disturbing news had come from Fort Reno. The aging commander, Captain Proctor, had placed Lieutenant Kirtland under arrest, blaming him for losses of the post's mounts to raiding Sioux. On the 4th, Carrington dispatched an urgent communication to Omaha concerning this: "I wish to visit the other posts and inspect them, as soon as I can get a few mounted men... I fear Captain Proctor is too ill and nervous to command, but have no one to succeed him. He has lost nearly all his stock; has arrested his adjutant, Lieutenant Kirtland, without notifying me or furnishing me or the lieutenant with a copy of charges. He may have sent them up direct to you, as he follows no regulations in correspondence with these headquarters. If so, please return them for my action. Gen. Hazen told me that he found the same inefficiency. I hope to go there in a few days and judge for myself."
The colonel also felt that he should make some explanation of the recent uprising of his men against the visiting Cheyennes. "I had trouble to keep my men from killing the Cheyennes, they are so bitter against all Indians; I do not put full confidence in them yet, but those that came seemed faithful to their agreement of July. They are great beggars, and I give them very little, as they can find plenty of game, but they seem to fear the Sioux... I gave the three chiefs one day's ration of flour, but refused any luxuries, and told them they must hunt for their living, and if they kept away from the road and trains I would keep peace with them."
Next day he was confronted by an angry trio of freighters, the contractors who had delivered the grain from Nebraska. They complained that several of their teamsters had deserted and moved in with the fort's civilian employees. Some had even been given employment by Captain Ten Eyck and Lieutenant Brown.
Sympathizing with the plight of the contractors, whose wagons must be manned on the return journey, Carrington assured them the Army would co-operate. He issued an immediate order establishing the Mountain District's policy, and notified Ten Eyck and Brown to discharge the deserting teamsters without delay.
> The attention of post commander is directed to the constant difficulties arising between owners of trains, or Government contractors, and their teamsters and employés.
>
> Men hire at the Missouri River ostensibly as teamsters, but really to obtain hereby the means of transportation to this new country. Hence it is frequently the case trains are partially deserted and much property exposed to loss by Indians, if the train returns short of men, or the owner is put to great expense by delay in supplying himself with teamsters.
>
> Whenever teamsters desert at any post and a fair examination that they so desert without fault of their employer, and in breach of their contract for the purpose of higher wages, such teamsters will not be hired by any quartermaster or other officer of this command, neither will they be harbored or permitted to remain within the limits of any post.
On the 6th, after more than a week of uneasy peace around the fort, a war party estimated at one hundred Indians ambushed a detachment of twenty enlisted men working at the pinery. In the initial attack one man was wounded and Privates John Wasser and Christian Oberly of A Company were killed. After the survivors fought their way to the nearest blockhouse, some of the Indians boldly rushed the loopholes, firing inside. The Indians finally were driven off, but when the timber cutters attempted to return to work, they were constantly harassed by bullets and arrows fired from woods concealment.
As soon as Carrington learned of the situation, he took a mountain howitzer and a thirty-man detachment out to the pinery and shelled the woods and ravines. After clearing the area, he left the weapon and a gunnery detail on permanent duty, and from that day until late in December the Indians gave the timber cutters very little trouble.
For some time Carrington had realized that his relations with post commander Ten Eyck were becoming awkward and strained. With daily emergencies arising, the colonel often acted without consulting Ten Eyck. It was not always easy to differentiate between matters which concerned the Mountain District alone or the post alone. Under the new security precautions, the District was virtually confined to the stockade and the pinery. The distant posts of Reno and C. F. Smith might as well have been on different continents insofar as Carrington's immediate authority affected them, and as soon as winter halted timber cutting and further isolated the other posts, the Mountain District and Fort Phil Kearny would share the same boundaries.
Aware that such a situation could cause serious command friction, Carrington issued an order on the 7th, assuming command of Fort Phil Kearny, "to have more immediate personal command of the post, at which were my district headquarters." His first action was to reorganize the post's defenses. "Every officer and soldier, every citizen, employé, and teamster, and every clerk in the sutler's store had his loophole, or place at which to report at a general alarm by night or day." He also reshuffled his officers. Ten Eyck was now free to devote all his time to commanding the 2nd Battalion and to reassume command of his old company, H, which had been under temporary command of Lieutenant Wands.
Wands in turn was assigned to duty with the regimental quartermaster, Fred Brown, who had received his captain's commission and was awaiting transfer orders to Laramie. Lieutenant Bisbee became regimental adjutant, replacing John Adair who had announced he would resign his commission as soon as Lieutenant Bradley returned from escort duty with General Hazen. Carrington also acquired a new orderly, one of the bright young clerks in his office, Private Archibald Sample.
The worst deficiency was serviceable horses. After a personal inspection of all mounts, he pronounced only forty in condition for Indian pursuit. Several were absent, of course, with mail escorts to Laramie and C. F. Smith.
Any hopes he may have had of obtaining replacements from the Department of the Platte were dashed by the next communication he received from General Cooke: "Having one company of cavalry you can probably dispense with your ninety-four horses, after mounting all the cavalry. They could be used for cavalry at Laramie. The same as to any useless horses at C. F. Smith and Reno." If Carrington ever used profanity he must have indulged himself freely at the moment of reading this telegram. In the first place he had no cavalry as yet; secondly, there were no longer ninety-four serviceable horses at Phil Kearny; thirdly, horses were so short at Reno and C. F. Smith that even three-legged ones would not have been considered expendable.
It may seem incredible that Cooke, author of the classic _Cavalry Tactics_ and a cavalryman of many years' service, showed so little interest in or understanding of Carrington's need for mounted men. In 1866, however, the general was still suffering bitter disappointment and emotional strain from the Civil War. He felt that his career had been blighted; he was grieving because his son, John Rogers Cooke of the defeated Confederate Army, had broken all relations with him, and because his daughter, Jeb Stuart's widow, was also estranged from him and living in poverty in the ruins of Richmond.
Whatever the reasons for Cooke's appalling indifference to conditions at Phil Kearny, this new evidence of it shook Carrington much more than a second message from the general, a curt order abolishing the Mountain District. In a way this was only a paper adjustment; Carrington still commanded the 18th Infantry Regiment; he would still report directly to Omaha. If he considered the order a reprimand, he never said so. He announced the district's dissolution on October 13, and those of his officers who had been carrying Mountain District assignments as extra duties were happy to be relieved of the paper work.
Reporting compliance of the order to Cooke, Carrington added that "the change to fine weather fills the valleys with Indians who are getting winter provisions, and I expect some trouble with them, but can meet it."
In the midst of these organizational changes, a remarkable cavalcade arrived at the fort—twenty-five cowboys driving more than six hundred head of Texas longhorns. This was Nelson Story's legendary trail drive of 1866, probably the longest continuous overland drive ever made north from Texas.
An enterprising young man in his late twenties, Nelson Story had washed thirty thousand dollars in gold out of a placer claim in Alder Gulch, Montana. By the time the ore was exhausted, Story had had enough of gold mining. But instead of returning to his home in Ohio, he decided to parlay his strike into a larger fortune by venturing into the cattle business. He heard that longhorns could be bought for low prices in Texas, driven north to a railhead, and sold for enormous profits.
With ten thousand dollars sewed in the lining of his clothes, he went to Texas early in 1866. Establishing headquarters at Fort Worth, he collected a herd of about a thousand longhorns, hired a crew of cowboys, and started trailing north. Near Baxter Springs, Kansas, he met opposition from bands of vigilant Jayhawkers who refused to permit any Texas cattle to cross their small farms. Some of the Kansans feared Texas fever, a fatal cattle disease; others were willing to fight to keep the herds from wrecking fences and trampling crops. Instead of battling the Jayhawkers as many of the Texas drovers did, Story detoured. He remembered how hungry he had been for beef when he was digging gold in Montana, and he was certain he could obtain premium prices for every steer he could deliver to the northwestern mining camps. He also must have known what a foolhardy chance he was taking, but he went boldly ahead with his plans.
At Fort Leavenworth he made thorough preparations for the long drive, buying an ox-drawn wagon and loading it with groceries. His little army of cowboys and bullwhackers moved leisurely along the old Oregon Trail across Nebraska to Fort Laramie. Army officers there tried to persuade him to abandon his plans for going on to Montana. They told him that Sioux and Arapahos were swarming all over the north country, attacking everything that moved along the Bozeman Trail, and warned that if he drove north Red Cloud would stampede all his cattle and probably take several scalps to boot.
Story calmly purchased new Remington rapid-fire breechloaders from the Laramie sutler for each of his twenty-seven men, and started north. Below Fort Reno, they met their first Sioux, a war party that boiled up suddenly over a hill. The Indians' hit-and-run punch left two trail drivers badly hurt with arrows. They also cut away a good slice of the herd, leaving the remainder in a state of stampede.
As soon as Story and his men had quieted the cattle and taken care of their wounded, they organized a war party of their own to pursue the Indians. Dusk was falling, but just before darkness ended the chase, Story and his seasoned trail herders tracked the Sioux into camp. The Indians had the longhorns bedded down in the center of an arc of tepees.
One of the drivers present on this occasion later said: "We surprised them in their camp and they weren't in shape to protest much against our taking back the cattle." Story also told his son some years afterward that he had never killed an Indian before that night attack. "We had to wipe out the entire group to recover our Longhorns," he said.
When the herd was reassembled, the drivers pushed them north to Reno, left their two wounded comrades there, and moved on to Fort Phil Kearny. Carrington, in his new role as post commander, politely informed Story that military regulations forbade movement of trains between Phil Kearny and C. F. Smith unless there were forty armed men in the party. Story had only twenty-five.
The young cattleman replied angrily that he had no intention of halting at Fort Phil Kearny until another Montana-bound train arrived to strengthen his own. As late as the season was, another train might never arrive. He pointed out that his men had Remington breechloaders, giving them firepower equal to a hundred men with old-fashioned Springfields. But Carrington was firm; forty men was the minimum. The colonel advised Story to corral his stock three miles from the fort and await further orders.
When Story demanded to know why he must camp three miles from the safety of the stockade, Carrington informed him coldly that the post's herd needed the grass near the fort.
During these negotiations it is possible that Carrington offered Story the Army's maximum price for his beef cattle; the post was in sore need of the entire herd to replace animals driven off by Indians. If he did make such an offer, Story surely declined it. Story knew he could obtain four or five times the Army's price anywhere in the gold fields. Whether Carrington made the offer or not, Story no doubt suspected the colonel wanted the cattle and was purposely holding the herd at the fort in hopes of obtaining them. A prolonged delay, followed by a series of snowstorms, would jeopardize Story's entire venture, possibly force a sale to Carrington's quartermaster at low prices. Nelson Story knew this, and relations were strained between him and Colonel Carrington. Nevertheless, the young cattleman decided to gamble one week of time before tangling with military authority. He ordered his herd into corral and set up a vigilant guard against Indians.
Shortly after the arrival of Story's cattle herd, a small supply train came up from Laramie with the mail escort. It carried a long-needed shipment of medical and hospital supplies. As usual there were deficiencies in the bill of lading, the largest shortage occurring in a consignment of porter, meant for use as a tonic for invalids: 205 of 258 bottles failed to arrive. The mystery was never cleared up, even thought testimony was taken from a number of men who had access to the mildly alcoholic brew. The official assumption was that the bottles had broken en route, but few believed that. Everyone who had crossed the dry plain below Reno knew how tempting was a bottle of porter in an easily accessible covered wagon.
Among the medicines received by Surgeon Horton for administering to his ailing or wounded patients was ammonial liquor, used as a liniment and for loss of consciousness; asafetida, used as a carminative; ceratum adipsis for dressing wounds, licorice root extract for coughs, ferrous iodide syrup for colds and consumption; castor oil and epsom salts for cathartic use; tincture of peppermint oil for nausea and flatulence; scillae syrupus for use as an expectorant and emetic; chlorinated soda and zinc chloride solution for antiseptics; barley for making malt extract to be used in digestive troubles; beef extract, tapioca, and what was left of the porter, for restoring invalids.
To supply his hospital the surgeon received forty-five yards of adhesive plaster, twenty pounds of lint, eighty pounds of oakum, three hundred dozen roller bandages, seventy-two hair mattresses, one hundred hair pillows, seventy-three dressing gowns, twenty-seven delft bed chambers, and sixty-six meteorological report blanks. One of the extra duties of surgeons at that time on the frontier was recording temperatures, precipitation, and other weather phenomena.
Arrival of these medical and hospital supplies—with the previously received corn and oats, rations and ammunition-brought Phil Kearny's stores to a point where the post could operate well into the winter. The problem of replenishing stores before spring was a formidable one, but Carrington was confident he could solve it.
On the morning of the 22nd, the colonel was notified that Nelson Story's cow camp had vanished during the night. Unknown to anyone in the fort, Story had called his men together the previous evening and asked them to vote on whether they should continue to abide by Carrington's orders or slip away toward Montana. "All in favor of moving out tonight say 'Aye.' Opposed say 'No.'"
One driver named George Dow said "No!"
As soon as the word was out of Dow's mouth, Story had the man covered with his six-gun. "We'll have to tie you up, George, until we're one day gone." In the darkness, Story and his men hitched oxen to wagons, moved the cattle out of corral, and headed for Montana. Next day, Dow was released and informed that he could return to Fort Phil Kearny. He decided to stay with the drive.
Meanwhile Carrington was furious over Story's willful violation of orders. At the same time the colonel remembered his responsibility for civilians' safety, and ordered a fifteen-man detail under a sergeant to move out north, join Story, and bring the party up to regulation strength of forty men. The fifteen soldiers, armed only with muzzle-loading Springfields, were supernumeraries, of course. Story's cowboys pushed the herd through to Montana without a hitch, trailing by night, grazing by day. They beat off two Indian attacks with ease, and lost only one man, a careless cowboy who rode too far ahead and was killed and scalped. On December 9, Story's historic drive reached its goal, the mining country near Virginia City.
During the day following Nelson Story's unauthorized departure from Phil Kearny, Colonel Carrington brooded over this act of insubordination and decided he could not permit its repetition. Such actions would surely weaken his authority over other civilian travelers, possibly over his own men. He decided that personnel of all civilian trains awaiting permits to proceed over the Montana Road would in future be quartered within the stockade. And to ensure that none of them might emulate Nelson Story and depart after nightfall against orders, he issued a new four-point regulation:
I. No citizen will be permitted to enter or leave the gates after retreat, unless connected with the sutler or quartermaster's department, and then to be properly passed by the officer of the day or sergeant of the guard.
II. All gates and wickets will be locked at retreat, except that at the quartermaster's gate, which will be closed at tattoo, and then only will be opened by the officer of the day or sergeant of the guard in their line of duty or for good cause.
III. All soldiers absent from quarters after tattoo will be promptly arrested, and unless sent on messages by officers, or otherwise duly authorized to be absent, will be confined and held to answer to charges before a garrison or general court-martial.
IV. This order is to be read at the first parade after its issue, and posted upon the bulletin board for three days from said issue.
From this time it is evident that Carrington's desire for absolute security became an obsession; he was reaching the point where he could trust no one but himself. A year later, during the inquiry which followed the Fetterman Massacre, he virtually admitted this. "I took charge of the system of police and discipline of the post, entertaining the idea that the future policy might involve more formidable Indian aggression and require a more exact and careful watchfulness and defense." His wife, recalling this period of tension, wrote that he "slept for weeks in succession without removal of garments, and nightly made his rounds to secure personal knowledge of deportment of guards and condition of post."
Meanwhile the weather continued bright, the air cold and crisp, the sky incredibly blue. Most of the post's essential buildings were nearing completion.
On the 27th, after a two-months absence on escort duty with General Hazen, Lieutenant Bradley returned with his detachment of mounted infantry. Four men failed to return. Jim Brannan, scouting ahead, had been killed, between Fort Benton and Fort C. F. Smith in a surprise Indian attack. Surgeon McCleary had his horse shot from under him, but was unharmed. Only one soldier, Private Brooks of Company H, was wounded in the brief engagement. Three others had deserted previously while the detachment was marching through the gold country of Montana.
Carrington was immensely cheered by the return of his best mounted group, and in this temporary mood of elation announced that he was declaring a holiday on the last day of the month to celebrate completion of the fort's construction.
Actually many of the men enjoyed two holidays in succession, the 30th being given over to preparations for ceremonies of the 31st. One small detail spent the morning carrying out a special assignment. They placed dozens of slender poles tipped with strips of white cloth at various distances from the stockade. The poles represented different ranges of the positioned howitzers, including the maximum range, so that gunners could determine instantly whether an enemy was within accurate firing distance and thus not waste time and ammunition finding the range.
Out in the center of the parade, two men were putting finishing touches to a towering 124-foot flagpole. They were Principal Musician John H. Barnes, who had been a ship's carpenter before his army enlistment, and Private William Daley, an expert woodworker and mechanic. They tested and retested the halyards to make certain the new garrison flag would rise smoothly to the masthead.
Most of the men, however, lined up by companies in front of the new quartermaster storehouse, and filed in to receive brand-new uniforms carefully hoarded for the celebration. Returning to their new pine-smelling barracks, they smoothed wrinkles out of trousers and blouses, burnished their boots, polished buttons and belt plates.
Officers also were refurbishing uniforms, those with wives calling upon them to assist in brightening swords and shoulder scales, and seeing that plumes were properly fixed on dress hats. Several had already moved into officers' row, and others were busily transferring from tents into still-unfinished buildings. Frances Grummond was especially proud of her large double bedstead fashioned by the carpenters, "a luxury indeed, with mattress stuffed with dried grass, army blanket and a large gay-colored shawl for counterpane."
The children naturally were caught up in the holiday spirit, and Judge Kinney, the sutler, handed out so many free ginger-snaps and sugar balls to the youngsters that Mrs. Wands and Mrs. Carrington had to interrupt preparations for the big day in order to empty their sons' pockets of this oversupply of unaccustomed sweets.
October 31 was ideal for a celebration day, the sun rising out of a clean azure sky, turning the air soft and balmy and brightening the golden leaves of aspens on the Big Horn slopes.
First order of the day was an inspection and review held in the morning on the level plain between the stockade and Big Piney. Every man, every animal, every weapon, was rigidly inspected by company commanders, and the findings were mixed. In their new uniforms, hard-muscled and ruddy with health from weeks of rough outdoor life, the soldiers met all tests. Horses and mules, however, were suffering from unavoidable overstrain, and serious deficiencies were found among the arms. The few Spencer carbines were in good condition, but many Springfields showed effects of constant wear and tear. Regimental armorers had worked hard to recondition all rifles for this inspection, but more than a hundred were found unserviceable. Lieutenant Grummond, for instance, reported twenty of twenty-seven unfit for use in Company C.
With this bad but not unexpected news out of the way, companies marched back into the fort to prepare for the grand ceremonies. Early in the afternoon the bugler sounded adjutant's call. Companies formed before their respective quarters and moved out to the center of the parade, forming three sides of a square around the octagonal band platform at the base of Barnes and Daley's towering flagstaff. The fourth side of the square was occupied by a temporary platform upon which were seated officers' wives, civilian employees, and children.
On the speakers' platform with Colonel Carrington and his aides were Chaplain White and Judge Kinney. Private William Murphy, recalling afterward the presence of the obsequious sutler, noted: "There was a man who was surely 'on to his job.' He was a good diplomat. He made love to men, women, and children." Mrs. Carrington was less trenchant in her brief comment: "Judge Kinney read an appropriate poem of Miss Carmichael's * chaste and spirited collection." She added: "Chaplain White offered the prayer, and principal musician Barnes presented to be read an original poem of his own, which at least did justice to his patriotic spirit."
Following these preliminaries, the colonel delivered the main address. He began with a salute to those men of the command who had lost their lives since the first stakes were driven at Fort Phil Kearny.
"Fifteen weeks have passed, varied by many skirmishes and both day and night alarms.... In every work done your arms have been at hand. In the pine tracts or hay fields, on picket or general guard duty, no one has failed to find a constant exposure to some hostile shaft, and to feel that a cunning adversary was watching every chance to harass and kill....
"The steam whistle and the rattle of the mower have followed your steps in this westward march of empire. You have built a central post that will bear comparison with any for security, completeness, and adaptation to the ends in view, wherever the other may be located, or however long in erection.
"Surrounded by temptation to hunt the choicest game, and allured by tales of golden treasure just beyond you, you have spared your powder for your foes, and have given the labor of your hands to your proper work. Passing from guard-watching to fatigue-work, and, after one night in bed, often disturbed, returning to your post as sentry; attempting with success all trades and callings, and handling the broad-axe and hammer, the saw and the chisel, with the same success as that with which you have sped the bullet, your work has proven how well deserved was the confidence I reposed in all of you....
"And now this day, laying aside the worn and tattered garments, which have done their part during weeks of toil and struggle, the veteran battalion of the 18th Infantry... puts on its fresh full-dress attire for muster and review.
"The crowning office, without which you would regard your work as scarcely begun, is now to be performed, and to its fulfillment I assign _soldiers;_ neither discharging the duty myself, nor delegating it to some brother officer; but some veteran soldier of good desert shall share with a sergeant from each of their companies, and the worthy man whose work rises high above us, the honor of raising our new and beautiful garrison flag to the top of the handsomest flag-staff in America.
"It is the first full garrison flag that has floated between the Platte and Montana....
"With music and the roar of cannon we shall greet its unfoldings.
"This day shall be a holiday, and a fresh starting point for future endeavor.
"And yet all is not said that I wish to say! While we exalt the national standard, and rejoice in its glory and its power, let us not forget the true source of that glory and power....
"Let me, then, ask all, with uncovered heads and grateful hearts, to pause in our act of consecration, while the chaplain shall invoke God's own blessing upon that act; so that while this banner rises heavenward, and so shall rise with each recurring sun, all hearts shall rise to the throne of the Infinite, and for this day, its duties and its pleasures, we shall become better men and better soldiers of the great Republic."
At a signal from Adjutant Adair, Private William Daley and a group of sergeants and enlisted men assembled around the flagstaff. While Daley carefully gathered the halyards, Chaplain White offered a brief prayer. Immediately following his loud "Amen!" a succession of commands rang clear in the autumn air: "Attention!" "Present, arms!" "Play!" "Hoist!" "Fire!"
Frances Grummond recorded that emotion-filled scene. "With the simultaneous _snap_ of presented arms in salute, the 'long roll' of the combined drum-corps was followed by the full band playing 'The Star Spangled Banner,' the guns opened fire, and the magnificent flag with its 'thirty-six-foot fly' and its 'twenty-foot _hoist'_ slowly rose to masthead and was broken out in one glorious flame of red, white, and blue!
"The very shadow of the immense flag, as it floated at full length in the breeze, seemed to answer back our waving handkerchiefs; and while cheers were not permitted to break the dignified exultation of the occasion, we _did_ involuntarily clap our hands, and our beating hearts did respond to the vibrations of the guns, whose echoes among the hills seemed to magnify their number as if a battle were raging all about us. Then, every officer on the alert, at the order, 'pass in review'... column was formed, the review received, and with the order 'parade dismissed' each company marched to its quarters, the band playing 'Hail Columbia' until the troops disappeared."
It was a great day for Fort Phil Kearny, all officers and men not on guard duty free to loaf away the afternoon under a warm October sun, to view for the first time with casual ease the fruits of their fifteen weeks of labor.
Around the browning turf of the parade a score of buildings cast their shadows—two 84 x 24-foot quartermaster warehouses, four company quarters, 60 x 25 feet; a sutler's store; adjutant's quarters; laundry; a bachelor officers quarters, 44 x 52 feet; a row of completed and partially completed cabins for married officers. Most of the buildings were faced with half logs, bark sides to the weather. Some were roofed with shingles, others with four-inch poles set close together and covered with corn sacks, grass, and six inches of earth.
Colonel Carrington's headquarters, topped by a lookout tower, faced north along a twelve-foot-wide graveled walk which curved around the flagpole and bandstand and crossed a similar walk running east and west. Under construction in the southeast quadrant of the parade was a 16 x 16-foot magazine of 14-inch timbers, sunk eight feet below ground, waterproofed and ventilated. Bordering the entire parade was a twenty-foot-wide graded street, and at diagonal corners of the stockade were two massive blockhouses of 18-inch logs. Gates were twelve feet wide of heavy planking, with small wickets in the right halves just large enough for one man to pass in a stooping position.
To the east of the parade cluster, and separated by a solid strip of stockade, lay the quartermaster's yard, six hundred feet long, two hundred feet wide, its ten-foot cottonwood palisade enclosing quarters for civilian employees, a blacksmith and wagon shop, carpenters', saddlers', and armorers' shops, stabling for mules and horses, a woodyard and a hay yard.
According to quartermaster records, more than twelve thousand logs had been cut, hauled and sawed to bring this fort into being, and considering the difficulties under which the work had been accomplished, the men had a right to take pride in the results.
For Henry B. Carrington this fort was the realization of a life's dream, and in summing up the official record of events for his first month as post commander, he noted with gratification that "work at the fort has progressed satisfactorily during the month, the weather being exceedingly favorable. Storehouses, officers quarters and substantial and commodious quarters for the troops, stabling for the public animals are all in a manner completed."
He was also pleased by the number of civilians who had passed safely over the Montana Road since it had come under his responsibility—979 men, 32 women, and 26 children. Yet it was some relief to know that the emigration season was ending and that there would probably be only a few more trains to worry over before another spring and summer rolled around.
On that last day of October the garrison's strength was 360 officers and men, a gain of nineteen during the month. Two enlisted men of the 2nd Cavalry were listed on the muster rolls, casuals from escort duties, but neither of the two full companies promised in August had yet reported.
At three o'clock in the afternoon of the holiday, Indians made their first close appearance in three weeks. They had come up from camps along Tongue River, their curiosity aroused by the massed firing of howitzers during the flag-raising ceremony. They splashed across Big Piney and galloped around the bend of Sullivant Hills so quickly they almost passed the west gate before pickets sounded an alarm. "Others appeared upon the hills, and flashing mirrors were constantly passing signals for nearly an hour," said Margaret Carrington. "They had at least the satisfaction of seeing the stars and stripes, and thus getting new hints as to the proposed length of our visit." As a precautionary measure, extra ammunition was dispatched to each company quarters, howitzer details were called to stations, and a few men were added to the guard. By sundown, however, the inquisitive visitors from Tongue River had vanished back into their hills.
In the evening the Carringtons entertained officers and wives with a levee in their new quarters. It was a full-dress affair, with music, dancing, and party games. In proper military fashion, the merrymaking ended promptly at midnight, the guests strolling to their neighboring quarters under a star-filled autumn sky. Frances Grummond, who had temporarily forgotten her almost constant forebodings, was cheered by the calls of the sentries on the banquette: "Twelve o'clock and all's well." It was the first hour of November, the Deer Rutting Moon.
* Sarah E. Carmichael, who published her own works "for private circulation."
# _VIII. November:_
DEER RUTTING MOON
> _Because the country was broken, because most of the officers had not been with me in reconnaissances and had recently arrived at post entirely unused to Indian warfare, because I knew the Indians to be in large numbers, I would not authorize them to make hazardous adventures.... I did (as I believed) fail to have the confidence of some officers. Few came from Omaha or Laramie without prejudice, believing I was not doing enough fighting._
LATE ON NOVEMBER 1, THE last Montana-bound civilian train of the season was camped outside the fort. This party had met with little Indian resistance on the journey up from Laramie, and some of the men had grown careless enough to sit around campfires after dark, playing cards by the light of the flames. About nine o'clock on this evening a band of Indians crept close upon them in the surrounding darkness, and without warning fired upon the card players. Three men were wounded, one fatally, in the first fusillade. A few moments later signal fires appeared on hills around the fort, and Indians could be seen dancing around them.
"Colonel Carrington concluded to try his mountain howitzer on the Indian dancers," teamster John Bratt later recorded. "After a few shots, the gunners got range on some of the Indian fires, and many fires were extinguished and some dancers' lives went out with them." The colonel also dispatched a skirmish party, but no trace of the night attackers was found.
Two days later one of the two cavalry companies assigned to Phil Kearny in August finally arrived from Laramie—sixty-three men of Company C under command of Lieutenant Horatio S. Bingham, a young Minnesotan with Civil War experience. For Bingham and twenty-seven of his men, this would be their last post assignment. The lieutenant had less than a month to live, and Company C would suffer the heaviest loss of any of the five companies represented in the detachment which marched out with Fetterman on December 21. They were armed with obsolete Enfield rifles and Starr carbines.
Accompanying Bingham's cavalrymen from Fort Laramie was the man who would lead so many of them to their deaths—Captain William J. Fetterman. While Carrington as nominal commander of the 18th Regiment had remained in Ohio and Indiana through most of the Civil War, Fetterman had been winning honors in combat. In the spring of 1862, Fetterman commanded Company A of the 2nd Battalion during the siege of Corinth; later that year he was cited for gallantry at Stone's River after thirty-six hours of continuous fighting. As commander of the 2nd Battalion he fought throughout most of Sherman's Georgia campaign of 1864—Resaca, Kennesaw Mountain, Peach Tree Creek, Jonesboro, the siege of Atlanta. Official dispatches were filled with numerous commendatory references: "Captain Fetterman's command marched to my assistance with great promptness... conspicuous for gallantry and bravery... displayed great gallantry and spirit... the conduct of Captain Fetterman in throwing up a salient and maintaining his positions against repeated attempts to dislodge him by the enemy, is worthy of particular notice...." By the end of the campaign he was breveted lieutenant-colonel and assigned to brigade staff.
Brilliant as his record was, Fetterman knew nothing of Indian warfare, and was boastfully contemptuous of the savages' ability to withstand attacks from trained soldiers of the United States Army. Because he had held rank longer than Ten Eyck, Fetterman superseded him as commander of the 2nd Battalion—his old outfit which he had led in the bitterest fighting in Georgia. Ten Eyck thus was dropped another notch in authority; the former post and battalion commander was left with only Company H.
Captain James W. Powell and Major Henry Almstedt, the paymaster, also arrived with this party. Powell was assigned to C Company, which Lieutenant Adair had been commanding in addition to his duties as regimental adjutant.
In the mailbag from Laramie was a scolding telegram from General Cooke, complaining about delays in receiving communications from Fort Phil Kearny, and suggesting that Carrington send mails more frequently. There was also a formal query from The Adjutant General in Washington wanting to know the location of the fort. To this Adjutant Adair replied politely that Phil Kearny was in Dakota Territory, sixty-five miles northwest of Fort Reno.
With restrained impatience, Carrington answered Cooke's complaint by pointing out that he had sent three mails in October, as required by orders. "My mail just received," he added, "was twelve days, on account of snow, bad roads, and weather, and this on return trip alone. It must not be overlooked that our snows, which leave the hills bare, fill the intermediate ravines, valleys, and gulches so that no one can travel. While we had no snow at this post, owing to its position, there were four feet within a mile of it... I believe that the general commanding would prefer to lose a mail occasionally, with the assurance that in an emergency I will advise him at all risk, rather than embarrass me in any skirmish or temporary encounter which calls for use of my present force."
Jim Bridger returned during that first week in November, reporting on his talks with the Crows around Fort C. F. Smith and along Clark's Fork. Old Gabe was confident the Crows would not join the Sioux and Arapaho as allies, but he had heard many disturbing rumors of war plans and of the great strength the hostiles were amassing along Tongue River. The Crow chiefs reported that it took half a day to ride through all villages of war parties there. Sissetons, Bad Faces, Oglalas, Hunkpapas, Arapaho, and some Gros Ventres and Cheyennes were together, and there was big talk of destroying the two new forts in their hunting grounds. Yellow-Face, a Crow warrior, declared that he had passed hostile camps in close array along a forty-mile stretch of the Tongue Valley.
Some of the Crows told Bridger of an interview with Red Cloud. "We want you to aid us in destroying the whites," Red Cloud had said, and then boasted that he would cut off the soldiers' supplies when bad weather came, and would starve them out of the forts during the winter and kill them all.
Bridger also had conferred some weeks earlier with Jim Beckwourth, who had been living in one of the Crow villages.* Beckwourth told Bridger he had enlisted 250 young Crows who were willing to join the soldiers and go on the warpath against the hostiles. When Bridger mentioned this, Carrington informed the scout that he had authority to enlist only fifty Indian auxiliaries, and had already sent a man (W. B. C. Smith) to Omaha to arrange for enlistment of Winnebagos or Pawnees. After pondering the matter, Bridger allowed that if Pawnees or Winnebagos could be brought from Omaha with rifles, it would be better than enlisting Crows nearer at hand but who possessed only bows and arrows.
When he reported to Omaha on Bridger's findings, Carrington expressed no alarm over Red Cloud's threat to starve the soldiers out of the forts. "He does not comprehend the idea of a year's supplies, nor that we are now prepared to not only pass the winter, but next spring and summer, even if he takes the offensive." This was careless boasting on the colonel's part; supplies on hand were adequate for full rations only into midwinter.
In this same letter, Carrington repeated his deep disillusionment with the Laramie treaty. "I had not the slightest confidence in the result of the proposed treaty, and so wrote you. And in fact the whole result of the negotiations there [Laramie] was a mere temporary suspension of hostile acts, if it even amounted to that... I look for this month to determine their purpose, and hope yet to be able to strike a blow which they will feel more than the last, and not risk a single post on the line in the attempt."
His comment, _I hope yet to be able to strike a blow,_ may have been a subconscious reply to pressures which had been exerted upon him during the past two days by his ambitious new captain, William J. Fetterman. Since the hour of his arrival at Fort Phil Kearny, Fetterman had given Carrington no peace.
The two men were almost exact opposites in temperament, Fetterman being a man of action, a fighter pure and simple, descended from generations of professional soldiers. Before leaving his eastern assignment to journey to Phil Kearny, he had been informed that in an impending reorganization of the Army he probably would supersede Carrington as commander of the post. (In a move to increase the size of the frontier army, the War Department was planning to use the 18th Infantry's 2nd Battalion as nucleus for a new 27th Infantry Regiment. The 1st Battalion was to be enlarged to regiment strength, retaining the original 18th regimental number.)
Fetterman was eager to further his advancement, and from the first day of his arrival was openly critical of Carrington's cautious policy toward the hostiles. His old comrades of Civil War days, Fred Brown and William Bisbee, quickly sided with Fetterman. Young George Grummond was another supporter of his proposal to attack instead of defend, and a few days after Fetterman's arrival, officers and men were quoting some of the captain's reckless boasts: "A single company of regulars could whip a thousand Indians." "A full regiment could whip the entire array of hostile tribes." "With eighty men I could ride through the Sioux nation."
This was the beginning of a schism between Carrington and his officers which would grow deeper and more dangerous with each passing week until the tragedy of late December.
On the second day after reporting for duty, Fetterman came to Carrington with a plan for tricking the Indians into a night ambush. He had talked it over previously with Brown and Grummond, and both had approved. The plan was to conceal a heavily armed detachment in a cottonwood thicket along Big Piney opposite the fort, hobble some mules between the thicket and the fort as live bait, and thus decoy the Indians into position for a cross-fire attack.
Carrington considered it a risky business, but granted permission after advising Fetterman to exercise the greatest caution in exposing men needlessly in any such action as a massed charge out of concealment. The Sioux, he warned, did not fight in the same manner as Fetterman's recent opponents, the soldiers of the Confederacy.
Fetterman laid his trap after dark, setting out the hobbled mules and placing his detachment carefully in the thicket. "The entire garrison," Frances Grummond wrote, "was keenfully watchful of this experiment." She was worrying about her husband, George, who was out in the cottonwood thicket waiting for Indians while she waited for his safe return. Unable to sleep, she wandered about their three-room pine-log cabin. She had hung pieces of sheeting over the living room windows for shades, covered the unglazed kitchen windows with old newspapers, and carpeted her living room with gunny sacks sewn together. Crude as the cabin was, it seemed like a palace after six weeks of housekeeping in a tent, a warm dry haven in which to give birth to her expected child.
Elsewhere in the fort others also stayed up late, waiting for the Indians to dart into Fetterman's trap. Some played cards (Authors was a favorite with the women and older children) and some brought out their musical instruments or sang; others read books or reread old newspapers from the last Laramie mail. Most of the women sewed, using patterns swapped back and forth, fashioning dresses and coats from calico, flannel and linsey-woolsey procured from the sutler's store.
In the sutler's store, the usual evening crowd stayed late, talking, drinking, nibbling at cheese and crackers, half listening for a fusillade from the thicket along Big Piney. Jim Bridger was in the store, tilted back in a chair with one arm on the trading counter, his dingy, smoke-stained hat pulled down so that it half hid his weathered stubbly-bearded face. Squatting in a corner near Old Gabe was a Crow Indian who had come down with him from Fort C. F. Smith to serve as an interpreter. Almost every evening for hours at a time the Crow took this same position, speaking to no one, no one speaking to him. Bridger had neither offered nor been invited to participate in Fetterman's ambush scheme. His rheumatism was bothering him, and since his return from the north he had been in a somber mood. "Bridger would walk about, constantly scanning the opposite hills that commanded a good view of the fort," Frances Grummond wrote of him at this time, "as if he suspected Indians of having scouts behind every sage clump or fallen Cottonwood."
After midnight the unofficial post watch diminished in numbers as most of them gave up and went to bed. Bright moonlight exposed the hobbled mules grazing quietly between the fort and the shadowed ambush. A few meteors streaked across the sky, wolves howled back in the hills, but not one Indian appeared on the Big Piney side of the fort.
They struck instead on the opposite side, stampeding a small herd of cattle belonging to James Wheatley, by daylight soon after Fetterman quit in disgust and led his sleepy-eyed men back into the fort. That should have been Lesson Number One for Fetterman (the Indians would give him the benefit of only two more lessons). But at this time in the short life of William J. Fetterman his cocksureness would not admit that anything could be learned from a savage Indian.
For several days after the unsuccessful decoy attempt, life in the fort fell into an even pattern of military routine. Fifty of the sixty-three recently arrived cavalrymen departed on escort duties, ten accompanying a mail carrier to Fort Casper, and forty forming a heavy guard for Paymaster Almstedt en route to Fort C. F. Smith.
On the 11th an incident involving two men of Company A further deepened the rift between Carrington and Fetterman. For reasons not clear, Sergeant Garrett attacked Private Thomas Burke, verbally and physically, in full view of several officers and their wives. When a guard was summoned to put the combatants under arrest, the commanding officer of Company A interceded, resorting to violent profanity himself as he endorsed the actions of his sergeant. The commanding officer of Company A was Captain Fetterman.
Carrington, who witnessed part of the incident, was horrified, especially because the fighting and profanity occurred on a Sunday morning and in sight and hearing of women who were on their way to church services. The colonel walked on with his wife to the building which was then being used for Sunday services, listened to Chaplain David White's sermon and the music of a string band, and joined in the spirited singing of such familiar hymns as "Old Hundred," "Gloria in Excelsis," and "There Is a Light in the Window."
After services he returned to his headquarters, summoned Adjutant Bisbee, and issued a sternly worded general order (No. 38) condemning "profane swearing, verbal abuse, kicks, and blows," and declaring that such "perversion of authority... will be dealt with in the most decided manner." While most of his order was directed toward noncommissioned officers, one paragraph was surely aimed at Fetterman:
> Officers at this post will communicate and carefully enforce this order, seeking to inspire among non-commissioned officers, by precept and example, that calm and steady habit of command which will surely secure implicit obedience, and no less augment respect for authority requiring obedience.
Although Lieutenant Bisbee's name was signed to the order as post adjutant, Bisbee recognized the implied reprimand to his old friend, Fetterman, and lost no time in informing the latter that he thoroughly disapproved of it. In a few hours, the pro-Fetterman group was referring to General Order No. 38 as "Bully 38," and not a few profane jokes about it were being privately passed around officers' row. Those who now sided openly with Fetterman against Carrington included Captains Brown and Powell, Lieutenants Bisbee and Grummond, and one of the contract surgeons, C. M. Hines.
Ironically, the officer who had twice been demoted in authority, Captain Ten Eyck, was perhaps most loyal to Carrington. Ten Eyck's nature was introspective as was Carrington's. Although he had served in the field with the 18th Regiment during the war, Ten Eyck had been wounded and captured at Chickamauga, and was not bound to Fetterman by shared hardships in the long Georgia campaigns as were Brown, Powell and Bisbee.
For various reasons there was a great deal of discontent at this time among officers of the frontier army. Most of them had held brevet ranks in the Civil War much higher than their permanent ranks. It was not easy for a brevet lieutenant-colonel to resume the duties and pay of a mere lieutenant without expectations of immediate promotion, and by late 1866 it was evident that promotions would be very hard to come by in this vastly shrunken army. A letter from one of Carrington's junior officers who signed himself "Dacotah" appeared in the _Army and Navy Journal_ in November, decrying inadequate army pay. "There is not an officer in the Army but will testify that it is next to an impossibility to live like an officer and a gentleman on his pay. Pay of a second lieutenant amounts to $110.80 for a 31-day month, tax off. On this one must live, clothe ourselves and appear like gentlemen. When uniform suits cost $100, overcoats from $125 to $150, boots $17... what is left to pay board bills and mess bills and where and how are we to obtain a cigar if we desire to smoke after our scanty meals?"
At Fort Phil Kearny there was also a sharp differential in civilian pay and officers' pay, which led to added dissatisfaction among the latter. Civilian guides received three times as much money as lieutenants, civilian clerks more than captains. Blacksmiths, carpenters and wagon masters were almost as well paid as second lieutenants and they had no problems of dress uniforms or burdens of extra military duties. As for teamsters and laborers, they were far better off economically than noncommissioned officers.
The blame for slow promotions, for inequitable pay, had to be placed somewhere, and naturally it fell upon the symbol of army authority nearest at hand, the colonel of the regiment, Henry B. Carrington.
As if to compound the dissociated position in which Carrington now found himself, a telegram arrived on November 12 from General Cooke, casually threatening him with a general court-martial. The message and one other were brought by a special express from Laramie, the lone courier risking his life to cross 236 miles of snowdrifts, with hostile war parties all along the route. The first telegram demanded copies of the post's monthly and trimonthly returns since July. "If not immediately sent, with explanation, this matter must be brought before a general court-martial." The second telegram was less ominous. It acknowledged previous receipt of the missing returns, and according to the courier, had been received at Fort Laramie after his departure, then had been rushed up to Bridger's Ferry by another messenger who there overtook the first rider. Such was the state of communications between Fort Phil Kearny and Omaha headquarters in November.
During the week of the 12th, Carrington lost two of his best junior officers, Lieutenant John Adair resigning his commission to return to civilian life, and Lieutenant James Bradley transferring to the 3rd Battalion in Utah. Five enlisted men deserted that week to seek their fortunes in the Montana gold fields. The civilian master of transportation also left without notice. "In his pockets went the money for our supply of wood and hay," Private Murphy noted. "It was reported that he went to Canada." Another indication of a slackening of discipline within the garrison was a report on the 18th of pilfered stores and forage. An extra guard had to be placed over the quartermaster buildings and corn piles.
To add to these mounting internal troubles, the Indians began showing themselves in strength again, and on the 21st attacked a beef contractor's train coming up from Reno. Company C under Captain Powell beat off the attack and no cattle were lost, but the men were unable to overtake and punish the raiders.
Next afternoon Captain Fetterman made his first visit to the pinery, accompanying the regular escort which was to return with the wagons. With Fetterman was his close friend, Lieutenant Bisbee, and as the two officers approached the timber of Piney Island ahead of the escort, they halted to water their horses. "Suddenly from behind a huge log fifty yards away," Bisbee wrote later, "came yells and shots from ambushed redskins. Taking immediate shelter under the bank of the creek for better observation and to await reinforcements from the train guard in rear, we plainly discovered larger parties of Indians in the timber waiting our further approach. One lone 'buck' only came into the open, plainly a decoy tempting us to a trap. It was not accepted, but in temptation to see what the young brave was really made of I charged him. Zip, zip, came several shots from concealed Indians in the woods to which he escaped in great haste."
From this account it is clear that Bisbee had learned something of Indian fighting; he recognized a decoy trap when he saw one. Perhaps he passed a warning to Fetterman on that day, and restrained the overconfident captain from dashing on into the woods. But whether he did so or not, Fetterman must have received the lesson with skepticism, or soon forgot it.
Soon after the sounds of firing rang through the woods, a false alarm was somehow carried to the fort, spreading by word of mouth until the post bugler dashed up to Carrington's headquarters with the startling news that Indians had attacked the wood train and "all were killed." Frances Grummond and Mrs. Bisbee were both nearby and heard the announcement. "I recall as if yesterday, the blanched face of Mrs. Bisbee, knowing as she did that her husband was with the wood party."
Within a few minutes Carrington himself formed a relief party and dashed out the gate at a gallop. A mile or so from the fort he met Fetterman and Bisbee, both completely unaware of the false report of their deaths. They passed it off as a joke, and as they approached the fort and saw the flag at half-mast, began swapping banter as to which of their brother officers would receive promotions now that they were no longer among the living. To Carrington such talk was in extremely bad taste, and he called the officers up sharply. Carrington was not a humorless man, but he had seen too much of death since July to joke about it in November.
A mail arrived from Laramie on Sunday the 25th with another of those oddly unrealistic messages which were coming with increased frequency from General Cooke:
> COLONEL: You are hereby instructed that so soon as the troops and stores are covered from the weather, to turn your earnest attention to the possibility of striking the hostile band of Indians by surprise in their winter camps, as intimated in telegram of September 27 ultimo from these headquarters.
>
> An extraordinary effort in winter, when the Indian horses are unserviceable, it is believed, should be followed by more success than can be accomplished by very large expeditions in the summer, when the Indians can so easily scatter into deserts and mountain hiding places almost beyond pursuit.
>
> Four companies of infantry will be available, besides some cavalry. You have a large arrear of murderous and insulting attacks by the savages upon emigrant trains and troops to settle, and you are ordered, if there prove to be any promise of success, to conduct or to send under another officer, such an expedition.
By this late date Carrington had almost despaired of ever making General Cooke understand the realities of the situation at Fort Phil Kearny. But once again he wrote of arms shortages, of the demands upon his single cavalry company for almost constant escort service. He pointed out that the cavalry's promised new carbines had not arrived; they were armed only with obsolete rifles and antiquated Starr carbines. The infantry companies required at least one hundred Springfields to replace broken and worn-out pieces. "I shall look for another company of cavalry soon," he added, "as mentioned in previous telegram." And then because there was nothing else he could do in the face of a direct order, he concluded: "I will, in person, command expeditions, when severe weather confines them [the Indians] to their villages, and make the winter one of active operations in different directions, as best affords chance of punishment."
Before that Sunday ended, the Indians gave Carrington a chance to strike a blow. They made a daring raid upon the beef herd, cutting out sixteen head of cattle. In a mood of extreme anger, the colonel took charge of the pursuit, ordering out every available mounted man. Lieutenant Bingham led off with his cavalry company, and Fetterman, Brown and Grummond commanded separate mounted detachments. None of them overtook a single Indian, but they recovered eight steers, and found five others slaughtered and partially butchered.
On the 27th, Lieutenant Bingham and a detachment of twenty-four cavalrymen departed for Fort C. F. Smith with dispatches and mail, and on the 29th a sergeant and ten men left for Fort Reno on a similar assignment. With these men and others absent, post returns for the last day of the month showed 427 officers and men, a gain of sixty-seven over October.
Another routine item which Carrington entered in his post records for November concerned the transfer of Lieutenant-Colonel Henry Walton Wessells, Brevet Brigadier-General of Volunteers, from Omaha to Fort Reno to replace the ailing Captain Proctor. In a time when brigadier-generals of Volunteers were as numerous as regular army lieutenants, Carrington probably gave little thought to the rank of his new Reno commander. He could not anticipate that dark twenty-first day of December, in the Moon When the Deer Shed Their Horns, nor could he have believed that in another month Wessells would replace him as commander of Fort Phil Kearny.
* Beckwourth never returned from the Crow village, dying there during the autumn under mysterious circumstances; by poison, it was rumored.
# _IX. December:_
MOON WHEN THE DEER SHED THEIR HORNS
> _Fort Phil Kearny was established amid hostilities. Fifty-one skirmishes have occurred. No disaster other than the usual incidents to border warfare occurred, until gross disobedience of orders sacrificed nearly eighty of the choice men of my command... Life was the forfeit. In the grave I bury disobedience._
## 1.
ON DECEMBER 3, LIEUTENANT HORATIO Bingham set a new record for a round-trip escort to Fort C. F. Smith by returning to Phil Kearny seven days after departure. Later that same day, Lieutenant Wilbur F. Arnold arrived from Laramie with forty-three infantry recruits; most of these men were formed into a new unit designated as Company K. Although these infantrymen were "perfectly new recruits from the general depot," they were given a warm welcome as well as immediate assistance in completing a new barracks for their use.
On the same day in Washington, President Andrew Johnson was delivering a message to Congress. "The Army has been promptly paid," he declared, "carefully provided with medical treatment, well sheltered and subsisted, and is to be furnished with breech-loading small arms... Treaties have been concluded with the Indians who... have unconditionally submitted to our authority and manifested an earnest desire for a renewal of friendly relations."
The President was many hundreds of miles from Fort Phil Kearny, of course, but had he been there on December 6, he might have been surprised at the "friendly relations" manifested by a large band of Sioux which attacked a wood train that day.
Around one o'clock in the afternoon, pickets on Pilot Hill began waving signal flags around their heads, repeating the warning five times in succession to indicate large parties were engaged in the attack. As soon as he was apprised of the action, Carrington climbed to his lookout tower and swept the horizon with his field glass. The wood train was four miles west of the fort, just south of Sullivant Hills. Off to the north along Lodge Trail Ridge, other Indians were flashing mirror signals. Several mounted warriors were within two miles of Big Piney, moving down the ridge toward the fort.
In keeping with his new policy of striking a blow at every opportunity, Carrington immediately ordered all serviceable horses saddled. To Captain Fetterman he assigned Bingham's cavalry company and one squad of mounted infantry, and ordered the captain to gallop straight west, relieve the wood train, and drive the Indians back across the Piney. At the same time Carrington with Lieutenant Grummond's mounted squad would sweep around to the north between Sullivant Hills and Lodge Trail Ridge and endeavor to cut off the Indians' retreat.
After five months of directing pursuit of the hostiles, Carrington could assume that "there was no outlet for the attacking force, except across Lodge Trail Ridge or between that ridge and Peno Head, about nine miles distant from the fort." With Lieutenant Grummond at his side, the colonel led his twenty-four mounted men rapidly up the valley of the Piney, keeping to the south bank. The temperature was below freezing, with a cold wind off the Big Horns. As soon as the column came opposite the slope of Lodge Trail Ridge, he signaled for a crossing of the Piney. The mounted Indians previously sighted along the creek had disappeared, and only three were visible on the upper ridge.
Big Piney was sheeted with ice, but Carrington turned his horse into the creek, hoping its hoofs would break the crust. Instead the animal floundered, and Carrington slid from his saddle. He kicked disgustedly at the ice with his boots, breaking a passage for the others as he waded the nervous mount across in three feet of freezing water.
When all were across, he ordered march resumed up the eastern slope of Lodge Trail Ridge. They were now four miles from the post, and in a few minutes the Bozeman Road came into view off to the right. Four Indians, widely spaced, held their horses on the road while a war party attempted hurried concealment in a nearby ravine. Carrington saw all of them clearly, quickly counting thirty-two. "At the same time I saw on the hills across the creek over one hundred Indians descending to the creek, followed by... Fetterman's command, which had properly carried out the original order on the left. Delivering a sharp fire at a small party in my way, who instantly fled, I pushed on at a gallop westward along the ridge."
Reaching the end of Lodge Trail Ridge, the colonel saw that he must bring his men down at full speed if he hoped to intercept the Indians being driven by Fetterman. At the same time he warned his men not to scatter as they guided their horses down the rough terrain. During the descent, Lieutenant Grummond's eagerness overcame his caution. He galloped so far ahead that Carrington sent an orderly after him, with an order to "keep with me and obey orders or return to the post." The orderly, Private D. Harman, failed to overtake the lieutenant.
"Upon descending the ridge," Carrington later reported, "I found to my surprise fifteen cavalry, dismounted and without an officer. I passed through them, ordering them to mount and follow upon the gallop." Before the colonel could slow his horse to a walk, the trail jogged sharply, and he found himself suddenly blocked by a band of yelling Indians spread along a low hill. He swung in his saddle. Only six men were still with him, one of them being Bugler Adolf Metzger of Bingham's cavalry.
"Where's Lieutenant Bingham?" Carrington demanded.
Metzger replied that Bingham had gone down the road around a hill to the left, and Carrington realized then that the cavalry leader must have dashed ahead, the Indians deliberately allowing him to pass through into a trap. He ordered Metzger to sound recall, the bugle notes echoing back from the hills in the cold air.
Meanwhile several mounted infantrymen strung out behind Carrington had come up, and he was ordering them to spread out in skirmish formation just as the first wave of Indians swarmed from the base of the hill and began attacking. Private James McGuire, one of Bingham's troopers, was thrown from his wounded mount. A warrior dashed forward, intent upon counting coup with a raised war club. Carrington swung over toward McGuire, dismounted, and drove the Indian away. At least one hundred warriors were circling and yelling, but the soldiers had dismounted and formed a defensive front. Firing was steady, the carbines crackling, the rifle fire slower spaced, ramrods glistening in the pale sunlight. Along the ridges to right and left, Indian lookouts were flashing mirror signals and waving white flags. There was still no sign of Bingham or Grummond.
For twenty minutes Carrington was engaged in what would be the only real military action of his entire career. "One saddle," he reported afterward, "was emptied by a single shot fired by myself." At the end of the twenty minutes, Captain Fetterman's slow-moving squad arrived, and the attackers immediately vanished over the hill.
Conferring briefly with Fetterman, Carrington informed him that Bingham and Grummond and probably several men were missing somewhere off to the right, and he ordered an immediate movement in that direction. A few minutes later a drumming of hoofs sounded on their front, and Lieutenant Grummond and three men dashed suddenly into view, closely pursued by seven Indians, who veered away, shaking their lances, as they sighted the oncoming relief force.
Exactly what words Carrington and Grummond exchanged as they brought their sweated horses together are unrecorded, but if one may believe hearsay accounts, the young lieutenant was more angry than frightened, and "very hotly asked the colonel if he was a fool or a coward to allow his men to be cut to pieces without offering help." If Grummond did say this, Carrington never made public record of it, possibly out of deference to the lieutenant's widow, who in after years became the colonel's second wife. At that moment on the field of action, Carrington was more interested in finding Lieutenant Bingham who undoubtedly was in trouble. Grummond told Carrington that as he was descending Lodge Trail Ridge he had sighted Bingham and hurried forward to join him, assuming that Bingham's cavalry company was close behind.
Bingham's cavalrymen, however, had fallen back "in the most unaccountable manner," as Fetterman put it in his report. "I, assisted by Captain Brown and Lieutenant Wands," the captain added, "used every exertion to check [the retreat]. The Indians, corralling and closing around us, it was plain the retreat, if continued, would be a rout and massacre." Instead of staying with his men, Bingham chose to dash forward. "I cannot account for this movement on the part of an officer of such unquestionable gallantry," Fetterman declared, somewhat with the same puzzlement that his surviving fellow officers would ponder his own fatal actions two weeks later.
Of this same incident, Lieutenant Wands said that he and Captain Brown, "leveling their guns" at the cavalrymen, warned them they would shoot if the retreat was not halted. At the same time, according to Wands, Bingham called back, "Come on," beckoned, and went ahead with some of his men in the direction of Carrington's squad which could be seen a half mile away descending Lodge Trail Ridge.
While it was never possible to determine why Bingham acted as he did, the reason could be blamed upon his lack of experience in Indian warfare. The same excuse could be given for the actions of his men, most of whom were green recruits, some untrained even in horsemanship. They had made several escort journeys with the mail, but this was their first close encounter with armed hostiles. Like most newcomers to the frontier, they attributed almost superhuman powers to the Indians and dreaded close fighting with them.
When Grummond overtook Bingham on that narrow twisting trail beyond Lodge Trail Ridge, the cavalry officer and the few men still with him were pursuing a single dismounted Indian. This Indian was performing the oldest trick of frontier warfare, the decoy trap, and as the soldiers galloped down Peno Valley, dozens of warriors began springing from concealment in their rear. One of the men in the trap who lived to tell the tale was Private John Guthrie of Bingham's C Company. Bingham, said Guthrie, was the first to be hit. "He fell off his horse, shot in the head. This was a bad place to be, as we could not use our arms very well on the Indians. The red skins tried to save our horses for their own use. This move is what saved our lives, they tried to lasso us from the horses."
In the confusion of hand-to-hand fighting, Grummond and three men broke out of the surround, the lieutenant using his saber, the men swinging their rifles as clubs. They were in pell-mell flight from seven Indians armed with lances when they met Carrington's search party.
The search for Bingham now continued, and within an hour they found his body "in the brush... shot with over fifty arrows, lying over an old stump." Nearby was Sergeant G. R. Bowers, E Company, an experienced Civil War veteran. He had slain three Indians with his revolver, but his skull was split with a hatchet, and he died before an ambulance could arrive from the fort.
It was midafternoon, only two hours having passed since the two mounted forces left the fort, but the cold was intensifying, the low December sun hidden by hills, a gray cloud scud covering the sky. Not an Indian was in view anywhere. Carrington called off the pursuit, asking for a casualty count. Bingham and Bowers were dead, one sergeant and four privates wounded. Eight horses were out of action, three so badly wounded they had to be destroyed.
As for the hostiles, no one could be sure of their losses, as all casualties had been carried from the field. Carrington estimated ten enemy killed, several wounded. But not an officer or man in the field that day could take any pride in his accomplishments. Blunders, disobedience of orders, misunderstandings, recklessness, cowardice, had almost brought disaster to the fort's defenders. Bingham had left his confused company of green recruits to ride to his death; Grummond had disobeyed Carrington and almost met the same fate as Bingham. Lieutenant Wands, who had been ordered to ride with Carrington's party, had instead joined Fetterman. (He claimed afterward he misunderstood Carrington's order.) When Carrington dispatched a written order to Fort Phil Kearny for reinforcements and an ambulance, he specifically asked for Captain Powell to head the relief. But Powell remained in his quarters, ordering Lieutenant Wilbur Arnold to go in his place. Carrington himself was not blameless. When he came off Lodge Trail Ridge, he outrode his own men, galloped through Bingham's disorganized cavalry, and almost ran headlong without support into an Indian ambush. Not every one of this succession of military discords could be laid to the wide cleavage between Carrington and his officers, but most of them could be. The pattern for disaster on December 21was laid on that afternoon of December 6.
After returning with their casualties to the warmth and security of post quarters, the participants in the day's blunders spent the remaining hours before taps in recounting and reassessing their experiences. One of the cavalrymen, offering a reason why Bingham left his disorganized command, said that the lieutenant's horse "ran away with him and he could not restrain him." Another declared that "Bingham lost one pistol, and after firing the other, so excited did he become that he threw it away." Private John Donovan, who had been riding in the front of the action, said that Lieutenant Bingham was armed only with a saber, and that both the lieutenant and Sergeant Bowers had been pulled from their horses by Indians. Frank Fessenden's later account corroborates Donovan's: "The savages attempted to catch several of our boys by trying to put their strong bows over their necks and drag them off their horses." Fessenden also reported that Lieutenant Grummond told him "that he shut his eyes and literally slashed his way out, as did many of the others. Grummond said he could hear his saber 'click' every time he cleaved an Indian's skull."
In recording the reunion with her husband after the fight, Frances Grummond wrote: "We both sat for a long time in silence, then mingled our tears in gratitude for the wonderful deliverance... he said that he abandoned the use of spurs and jammed his sword into the weary beast to urge him to greater effort, followed by the chief, in full war-dress, with spear at his back so near that but for his good horse he would then and there have met a terrible fate.... A sense of apprehension that I seemed to have been conscious of ever since my arrival at the post, deepened from that hour. No sleep came to my weary eyes, except fitfully, for many nights, and even then in my dreams I could see him riding madly from me with the Indians in pursuit."
Even the cocky Captain Fetterman seemed to be sobered by the day's events. When he handed his official report to Carrington he professed to have learned a lesson. "This Indian war," he said, "has become a hand-to-hand fight, requiring the utmost caution."
Unfortunately, Fetterman forgot this lesson, the last he would learn from the Indians. Jim Bridger, growing more melancholy every day, must have sensed that he would. "Your men who fought down south are crazy," he told Carrington. "They don't know anything about fighting Indians."
But if Fetterman forgot what he learned, the Indians remembered everything which happened that day. From the high ridges, Red Cloud and other leading chiefs had observed the foolish actions of the soldiers, and later that week in the Sioux lodges along Tongue River, they heard many details of the fighting from a subchief, Yellow Eagle, who had led the main attacks. Years afterward, white men would learn from the Indians that the fight of December 6 convinced the hostiles that they could overpower and destroy any force sent out from the fort to fight them. They decided that on the first auspicious day after the coming of the next full moon they would lay a great trap of more than a thousand warriors, make another feint at the wood train, work the decoy trick, lure as many men out as possible, kill them all, and then burn the fort.
As the gloomy hours of December 6 dragged toward midnight, voices of sentries on the stockade echoed "All's well!" But the fate of eighty-one men in Fort Phil Kearny was already cast. Doom waited for them only a fortnight away, along the frozen flats of Peno Creek.
## 2.
They buried Lieutenant Bingham and Sergeant Bowers on Sunday the 9th. As Bingham had been a Mason, he was accorded the honors of that society, Lieutenant Grummond conducting the rites with the assistance of six other members. Chaplain White led the religious services, and when the chaplain came to speak of Sergeant Bowers, Captain Fred Brown stepped forward and placed his long-treasured Army of the Cumberland badge upon the breast of the dead sergeant. Brown, Bisbee, Powell and other veterans of the regiment had soldiered with Sergeant Bowers from Stone's River to Atlanta and held him in high regard.
In wooden boxes lined with tin, the dead were buried in the little cemetery at the foot of Pilot Hill; their graves were mounded with frozen earth and then covered with stones against the wolves.
Letters had to be written to relatives, and the duty of informing Miss Stella Bingham, St. Charles, Minnesota, of the death of her brother, Horatio, was assigned to Captain Fetterman.
> I send you herewith an Inventory of his Effects taken by me by virtue of my position as his Military Administrator. The money has been forwarded to the Adjutant General, U.S. Army, Washington, D. C, by applying to him it can easily be obtained by his heirs... the sword, sash and epaulettes, with private correspondence etc. have been sent to you. His other effects were sold at auction & the proceeds as before stated sent to the Adjt. Gen.... This is the customary manner of disposing of the effects of deceased officers, which it is supposed his heirs will not want, and which cannot be easily sent to them. Your brother was much esteemed by all who knew him, and his death is severely felt by all. He was buried with military and Masonic honors and the whole garrison attended his remains to the grave, all being desirous to pay their last tribute of respect to one whom all esteemed so highly.
I am madam,
Very Respectfully
Your Obt. Svt.
WILLIAM J. FETTERMAN
Ironically, only a few days later another appointed military administrator would be writing a similar letter concerning the composer of this one.
As soon as funeral services were ended, a mail escort of one corporal and eight troopers from the cavalry gathered in front of headquarters. Joining this escort were Lieutenant Bisbee and his wife and son, who boarded a canvas-topped army wagon which had been especially prepared for winter travel to Laramie. Floor and sides were double-boarded, and a stove had been placed inside. "My outfit," wrote Bisbee, "consisted of buffalo skin cap, two woolen shirts under a heavy blanket suit, buffalo-lined hip boots over two pairs of woolen socks, two pairs of gloves...." All of Bisbee's fellow officers were on hand to wish him luck in his new assignment at department headquarters in Omaha, and Bisbee in turn gave his blessing to the lieutenant succeeding him as post adjutant, Lieutenant Wilbur F. Arnold.
In the mailbag for Omaha were Carrington's full reports of the "skirmish with a body of Indians, numbering in the aggregate not less than three hundred warriors," with accounts of the deaths of Bingham and Bowers. "I need mittens for the men," he added, "and especially do I need every officer I can get. The cavalry has none. There are but six for six companies, including staff.... This is all wrong. There is much at stake; I will take my full share, but two officers to a company is small allowance enough, with mercury at zero and active operations on hand."
Beginning the second week of December, Carrington tightened the duties of his "six officers for six companies." Captain Powell was assigned to drill C Company, 2nd Cavalry, in such basic elements as mounting and dismounting, forming columns of twos and fours, and firing carbines and pistols by command. Daily at retreat, Captain Fetterman drilled the infantry in loading and firing by file and by numbers. Lieutenant Grummond was given full command of the mounted infantry, with orders to keep all serviceable horses—about fifty—saddled and ready for pursuit from dawn to dusk.
During the fortnight following the fight of the 6th, the Indians did not approach the fort or the pinery, yet scarcely a day passed without their scouting parties appearing on distant hills, signaling with mirrors or flags. Carrington doubled the guards assigned to wood trains, and maintained a state of watchful waiting. The weather continued bitter cold, and Surgeon Horton's hospital records showed a sharp increase in rheumatic complaints and frostbitten ears.
The Indians made their long-planned decoy attack on the 19th, and as soon as the vigilant Carrington saw the picket on Pilot Hill signaling "wood train under attack," he ordered his most cautious officer, Captain Powell, to command the relief party. Orders were explicit: "Heed the lessons of the 6th. Do not pursue Indians across Lodge Trail Ridge." Powell performed his task to the letter, keeping his well-drilled cavalry company and Grummond's mounted infantry in check and permitting no individual dashes or pursuits. Neither he nor Carrington knew, of course, that the Indians wanted no fight near the pinery; their objective was the same as that of the 6th—to draw the soldiers off, scatter them with decoys, and attack the small parties in force. But Powell did not pursue, and the hostiles withdrew without inflicting or suffering any casualties.
A fight had been avoided, yet as if anticipating criticism from those of his officers who believed in taking the offensive at every opportunity, Carrington explained to his staff that he intended to continue his policy of caution until more reinforcements arrived. The immediate objective, he added, was to continue movement of timber supplies from the pinery to the fort so as to complete winter quarters for such troops as the Department of the Platte might later send him. He also covered his policy of restraint by dispatching a special courier to Laramie with a telegram for transmittal to Omaha: "Indians appeared today and fired on wood train, but were repulsed. They are accomplishing nothing, while I am perfecting all details of the post and preparing for active movements." (At the time of his appearance before a court of inquiry in the spring of 1867, Carrington told of sending Captain Powell to relieve the train. "He did his work—pressed the Indians toward Lodge Trail Ridge, but having peremptory orders not to cross it, he returned with the train, reporting the Indians in large force, and that if he had crossed the ridge he never would have come back with his command.")
Snow fell that night, light and powdery, the sun rising in a clear sky at dawn upon a glittering-white world. The air was bracing, and Carrington decided to ride out to the pinery with the wood train. "On the morning of the 20th, very early," he later told the court of inquiry, "I had both saw-mills at work upon 3-inch plank, and at 9 o'clock, with sixty infantry and twenty cavalry, and the ordinary train guard, I went myself to the woods to test the animus and force of the Indians, and to build a bridge across Piney Creek, to facilitate the passage of the wagons off Pine Island.... Trees were felled for stringers; the bridge, forty-five feet long and sixteen feet wide, was built; the wagons were loaded, and the train reached the fort at 6 P.M. without casualty. I saw no Indians, and no fresh trail upon the snow which had fallen the night before."
That evening Captains Fetterman and Brown called unexpectedly upon the colonel in his headquarters. Brown was in a genial mood. He had slung his spurs carelessly in the buttonholes of his greatcoat, and wore a pair of revolvers at his waist. Acting as spokesman, he told Carrington that he and Fetterman had secured the promises of fifty civilian employees to join an equal number of mounted soldiers in an expedition to Tongue River to clear out the Indians. Both men were convinced that if the hostile villages were destroyed, the fort could settle down to a peaceful winter.
Carrington listened politely, then picked up his morning report for that day and handed it to Brown. If he let fifty seasoned men go to the Tongue, the colonel pointed out, he could not keep the mails moving, or maintain adequate picket and guard assignments. Fifty veterans were the core of his strength; most of those left behind to defend the fort would be untried recruits. Also, he added soberly, only forty-two horses had been reported serviceable that morning, and if he let them go, he would have none left at the fort.
Fred Brown was disappointed. He had almost completed his quartermaster records, and expected to be leaving for Laramie after Christmas to report for his new assignment. He wanted one more good fight, a smashing victory such as the one he had led against the Arapaho back in September.
Fetterman had little to say during this interview, and when it was clear that Carrington had no intention of authorizing a Tongue River expedition, he rose to go. As he and Brown left, the latter admitted that "he knew it was impossible, but that he just felt he could kill a dozen himself." Scarcely twelve hours later, Captain Brown would know—too late—just how impossible it was.
On the eve of the massacre which would bear Fetterman's name, the weather was remarkably fine, almost temperate, the sky faintly hazed but casting enough light to outline the sturdy stockade and buildings. All warehouses were completed; the last barracks was habitable; one more load of logs from the pinery should finish up the hospital. Military strength was slightly above four hundred, but many men carried faulty arms, and ammunition was in short supply.
In the rarefied atmosphere of that high country, sounds carried for long distances, and when there was no sound the stillness was almost overpowering. The Pineys were frozen across, their waters moving quietly below the ice. Except for the occasional howl of a wolf, the night was broken only by monotonous calls from the sentry posts: "All's well!"
## 3.
From early autumn into December, Red Cloud and other hostile chiefs had been assembling recruits along the headwaters of the Tongue, not more than fifty miles north of Fort Phil Kearny. Visiting Crows, who had been welcomed in the lodges and invited to join the hostiles, reported tepees spread out over a stretch of forty miles, and the number of warriors gathered there in mid-December probably totaled almost four thousand.
Although his military opponents considered Red Cloud the commanding general of all hostile operations in the Powder River country, certainly by December such was not the case. Opposition inspired during the summer by this relentless Oglala leader had grown to such proportions by late autumn that it was beyond control of one tribal chief. Roman Nose and Medicine Man of the Cheyennes, and Little Chief and Sorrel Horse of the Arapaho had joined Red Cloud's camp along the Tongue as allies, not as subordinates. Nor did the six hereditary chiefs of the Miniconjous, including Black Shield, yield any authority to Red Cloud.
In the days following the fight of December 6, however, the chiefs came to a general agreement; they would combine to lay a great ambush of many warriors, then send out a few young men on fast ponies to lure the soldiers from the hated fort on the Pineys into their trap.
When the moon was at the full in the third week of December, detachments of Oglalas, Miniconjous and Cheyennes began moving south out of the lodges along the Tongue. How many warriors made this journey is not certain, estimates ranging from fifteen hundred to two thousand, the latter figure being more often mentioned by the few white men who saw them and survived.
Black Shield led the Miniconjous, Crazy Horse the first war party of young Oglalas. The weather was very cold and the warriors wore buffalo robes with the hair turned in, leggings of dark woolen cloth, high-topped buffalo-fur moccasins, and carried red Hudson's Bay blankets strapped to their saddles. Most of them rode pack horses, leading their fast-footed war ponies by lariats. Some had rifles, but most were armed with bows and arrows, knives and lances. They carried enough pemmican to last several days, and when an opportunity offered, small groups would turn off the trail, kill buffalo or deer, and take as much meat as could be carried on their saddles.
When they were about ten miles northwest of Fort Phil Kearny, the first detachments made camp and waited for the others to come down and join them. As more warriors arrived, the camp spread out in three circles of Sioux, Cheyennes and Arapaho. While the chiefs held council, scouts moved out along the high ridges to watch the soldiers in the fort. It was decided that the best place to lay an ambush was in the forks of Peno Creek, about halfway between camp and the fort.*
On the morning of the 19th, they made their first decoy attack, but that was the day Captain Powell obeyed Carrington's strict orders and refused to follow the warriors. Snow fell during the night, and the Indians stayed in their camp on the 20th, warming themselves by fires inside saddle-blanket windbreaks. Much of the powdery snow melted except along shadowed slopes, and by the morning of the 21st, the chiefs again decided to send decoys out against the soldiers' wood train.
This time the most daring of the young braves were chosen to tantalize the soldiers into pursuit. The medicine men were certain that this time the soldiers would come running into the trap, and while the decoys rode off toward the fort a great ambush was laid on each side of the Bozeman Road where it ran along a narrow ridge and descended to Peno Creek. The Cheyennes and Arapaho took the west side. Some of the Sioux hid in a grassy flat on the opposite side; others remained mounted and concealed themselves behind two rocky ridges. By midmorning almost two thousand warriors were waiting there for Captain Fetterman and his eighty men.
## 4.
When Colonel Carrington stepped out of his quarters early on the morning of the 21st, he found the day bright and clear, the air cold and dry. Most of the snow was gone from the ground around the fort, but it lay on the ridges, ice-sheeted in places where the previous day's sun had partially melted it. Big Piney was still frozen from bank to bank. The snow, he knew, would still be deep in the pine woods, and he notified Lieutenant Wands to delay departure of the wood train until there was some indication the good weather would hold through the day.
About ten o'clock Carrington ordered the train to move out. As though he had some premonition of danger, he attached an extra guard from E Company under Corporal Legrow so that soldiers and civilian teamsters together formed an armed force of almost ninety men. Less than an hour later, as the post guard was changing, pickets on Pilot Hill began wigwagging the signal for many Indians attacking the train. Companies were bugled out immediately, and as the men hurried to assigned positions, two Indians appeared on the slope across Big Piney. They dismounted beyond rifle range, wrapped themselves in red blankets, and sat down near a tree to watch the action inside the fort. The time was now almost eleven o'clock.
At the first alarm, Carrington ordered Captain Powell to take command of the relief party. The colonel had been satisfied with the efficient yet cautious manner in which Powell had handled the Indians on the 19th, and saw no reason to use another officer now. When Captain Fetterman reported in front of headquarters with Company A, however, he reminded Carrington that he outranked Powell and demanded firmly that he be given the relief command.
With some misgivings Carrington acquiesced, and told Fetterman to move out with his own company, A, and a detachment of C Company. Lieutenant Grummond would follow with the cavalry in time to overtake the infantry before they reached the besieged wood train. "Support the wood train," Carrington ordered. "Relieve it and report to me. Do not engage or pursue Indians at its expense. Under no circumstances pursue over the ridge, that is, Lodge Trail Ridge."
Fetterman saluted and turned back to the assembled infantrymen. Sergeants began barking orders, and Companies A and C moved out on the double for the south gate. Carrington turned to his acting adjutant, Lieutenant Wands, and asked him to hurry after Fetterman's troops, halt them at the gate, and repeat the orders. The time was now 11:15.
Meanwhile Lieutenant Grummond had formed his horsemen for a hurried inspection. Carrington himself walked down the line of dismounted men, inspecting rifles and carbines. A number of the mounted infantry were dismissed from formation because of ammunition shortages or faulty weapons, but all of the twenty-seven cavalrymen reporting for duty passed inspection. Only a few days earlier Carrington had transferred the regimental band's Spencer carbines to the troopers.
During the inspection Private Thomas Maddeon, the regimental armorer, stepped forward and asked permission to join the relief party. Maddeon, a favorite of the colonel, had often expressed a desire for action. Carrington glanced at his rifle and told him to join a small detail from H Company. Captain Brown also appeared, eager for "one more chance," as he expressed it, "to bring in the scalp of Red Cloud myself." He added with a smile that he had arranged to borrow a mount from Jimmy Carrington—the mottled pony, Calico. Two other eager volunteers were James Wheatley and Isaac Fisher, civilian employees, both of whom had been officers during the Civil War. They were armed with new 16-shot Henry rifles, and were the envy of the infantrymen with their obsolete single-shot muzzle-loading Springfields.
"I was standing in front of my door next to the commanding officer's headquarters," Frances Grummond recorded, "and both saw and heard all that transpired. I was filled with dread and horror at the thought that after my husband's hairbreadth escape scarcely three weeks before he could be so eager to fight the Indians again....
"To my husband was given the order, 'Report to Captain Fetterman, implicitly obey orders, and never leave him.' Solicitude on my behalf prompted Lieutenant Wands to urge my husband 'for his family's sake to be prudent and avoid rash movements, or any pursuit,' and with these orders ringing in their ears they left the gate. Before they were out of hearing Colonel Carrington sprang upon the _banquet_ inside the stockade (the sentry walk), halted the column, and in clear tones heard by everybody, repeated his orders more minutely, 'Under no circumstances must you cross Lodge Trail Ridge;' and the column moved quickly from sight." As Grummond's mounted men left the gate, the time was nearing 11:30.
Carrington, watching from the sentry platform, saw that Fetterman was not following the wagon road which led south of Sullivant Hills but had turned into the north trail which ran between the hills and Lodge Trail Ridge. This was the same route which Carrington himself had followed on the 6th when the objective had been to take the Indians in reverse, and the colonel assumed now that Fetterman had a similar plan in mind. Within a minute or so, Grummond was swinging his mounted column into the trail; he overtook Fetterman's foot soldiers at the crossing of Big Piney just south of Lodge Trail Ridge.
"I remarked the fact," Carrington reported later, "that he [Fetterman] had deployed his men as skirmishers, and was evidently moving wisely up the creek and along the southern slope of Lodge Trail Ridge, with good promise of cutting off the Indians as they should withdraw, repulsed at the train, and his position giving him perfect vantage ground to save the train if the Indians pressed the attack. It is true that the usual course was to follow the road directly to the train, but the course adopted was not an error, unless there was then a purpose to disobey orders."
At about this same time Carrington suddenly remembered that no surgeon had been assigned to Fetterman's command, and he immediately ordered Assistant Surgeon C. M. Hines and two orderlies to mount up and ride directly for the wood train. If a surgeon was not needed there, Hines was to swing around Sullivant Hills and join Fetterman. The surgeon and his escort had scarcely galloped out of the gate when the pickets on Pilot Hill signaled that the wood train was no longer under attack, that the wagons had broken corral, and were proceeding unmolested toward the pinery.
During the next few minutes, Carrington's attention was distracted by a party of about twenty Indians which appeared across Big Piney near the Bozeman Road ford. Noting that they were within howitzer range, he ordered the gunners to drop a few case shot among them. At the first explosion, thirty more Indians were flushed out of the brush, one falling from his pony. The party scattered, fleeing toward the valley north of Lodge Trail Ridge.
For the first time since the alarm, Carrington relaxed. He stepped down from his position on the banquette and walked across the graveled street before officers' row and entered the rear of his headquarters. He did not know, of course, that the Indians at that moment were engaged in decoying Fetterman's men over Lodge Trail Ridge.
## 5.
A few minutes before twelve o'clock, Fetterman's command was moving up Lodge Trail Ridge, with Grummond's cavalry out on the flanks and advancing ahead of the infantry. Along the slope, little bands of decoys raced ponies back and forth, the young warriors yipping their wolflike barks, taunting the soldiers, waving blankets to frighten the soldiers' horses. When Fetterman gave orders to the infantry to fire, the decoys danced their ponies away, but as soon as the firing stopped, the Indians darted back into range, daring the soldiers to follow and shoot again.
Fetterman had seen no fighting such as this when he soldiered with Sherman in Georgia. He was accustomed to orthodox lines of battle. He knew how to form salients for defense, to storm rifle pits, to handle men under heavy artillery fire. But these Indian warriors, unlike his former Confederate adversaries, refused to follow the rules laid down in military manuals.
As he urged his infantrymen forward to overtake the cavalrymen on the crest of the ridge, the small party of Indians which had been fired upon by Carrington's howitzers came galloping along the Bozeman Road just below. These Indians slowed and joined the decoys. For a short while Fetterman held his position, the fort yet in view, his infantrymen still firing by command at an occasional daring Indian who rode within easy rifle range. When the decoys saw that the soldiers were reluctant to pursue, they became more reckless than ever, zigzagging their ponies and screaming insults.
By this time the warriors who had made the original attack upon the wagon train appeared to the south, some following Peno Creek valley, while many were beginning to ascend the slope of Lodge Trail Ridge in Fetterman's rear. It is possible that at this moment Fetterman made a hasty decision to drop north off Lodge Trail Ridge, kill as many of the outnumbered decoys as possible, and then swing back east along the Bozeman Road to the fort.
But if he intended to turn east when he struck the Bozeman Road, he changed his mind and turned west. Perhaps the tantalizing decoys offered too many easy targets to disregard. At high noon Fetterman gave the command to move, the cavalry at a walk so the infantry could keep closed up. They entered the Bozeman Trail where it ran along a narrow ridge sloping to the northwest, and followed this descent past a few large boulders toward the flats of Peno Creek. There were eighty-one men, about half of them mounted, the cavalrymen so eager to overtake the decoys that the gap began widening between horsemen and infantry. The firing was fairly regular now and several decoys were wounded, some fatally. Every hoofbeat, every footfall, however, brought these eighty-one men closer to the great ambush—two thousand Sioux, Cheyennes and Arapaho, waiting in concealment in the high grass of the flats and behind the rocky ridges on either side of the trail.
Among the individual Sioux and Cheyenne warriors who risked their lives to lure the soldiers into the trap were several who during the next decade would become famous chiefs—Crazy Horse, Dull Knife, Black Shield, Big Nose, White Bull. Crazy Horse won a great name for himself that day with his acts of defiance, sometimes dismounting within rifle range and pretending to ignore the presence of the soldiers and the screams of their bullets.
Years later in his old age Red Cloud claimed to have directed the fighting, but the testimony of several Indian participants indicates that the Oglala leader was not present. On that day, they said, he was either on his way down from Tongue River, or on a recruiting mission to the north. But whether he was there or not, the ambush was the fruition of Red Cloud's long summer campaign of harassment, put into execution by such leaders as High Back Bone, Red Leaf and Little Wolf.
A few minutes past noon, the decoys were beginning to ford the broken ice of Peno Creek, with Grummond's cavalry pressing pursuit. The infantrymen, now well within the silent ambush, were marching rapidly. As soon as all the decoys were across the creek they separated into two parties, riding away from each other, and then turning, came back and crossed files. This crossing of files was the prearranged signal for attack.
A moment later it seemed that every clump of yellow grass on the Peno flats had been transformed into a hostile Indian, the mass swarming up on foot like a gale-blown prairie fire toward the road. Beyond them other warriors on horseback also sprang from concealment, their hoofbeats like sudden thunder. And from the left came the Cheyennes, most of them mounted. The Indians' concentrated yelling drowned out commands from Fetterman and the other officers.
At the first assault Grummond managed to halt the cavalry, Fetterman quickly closing the gap with his foot soldiers. The civilians, Wheatley and Fisher, and four or five mounted infantrymen, all seasoned Civil War veterans who were riding the point, dismounted quickly. These men formed a defensive ring and delivered such concentrated fire that the first wave of attack was blunted. In that first minute of confusion a lone mounted Miniconjou, impelled by some mystical dream of glory, charged down the Bozeman Road from the rear, racing right into the infantrymen until he was slain. A moment later another Sioux on foot performed a similar act of reckless courage, and also died.
The air was now filled with arrows, warriors on foot closing in, pony riders circling, their war whoops reverberating in the cold damp wind. Yet Fetterman somehow managed to start his infantrymen back upslope to the nearest cover, a collection of flat boulders.
Whether Lieutenant Grummond ordered the cavalry to cover the infantry is not certain; the horsemen may have broken formations in terror. They swung up the hill to the left, all except Wheatley, Fisher, and the handful of men who had dismounted and formed a circle of defense. Nor can anyone be certain when or how Grummond died, but it is probable that he was killed early in the fighting, either in a vain effort to keep the cavalry with the infantry, or in a gallant rear-guard covering action. Long afterward some of the Indians who were there said a pony-soldier chief was killed on the road and that his men then gave way and fled up the ridge. Others told of a soldier chief on a white horse who fought a brave delaying action, cutting off an Indian's head with a single stroke of his saber. All that is known for certain is that Grummond's body was found on the road beside that of Sergeant Augustus Lang of Company A, somewhere between the infantry's position and the defensive ring of Wheatley and Fisher.
In any case, cavalry and infantry were separated in the first fury of attack, the men on foot facing a thousand warriors so close it was possible to see the color of their war paint and the metal ornaments and brass studs of their shields. Feathered arrows streamed like flights of bright speeding birds, and the trapped soldiers felt the pains of sharp heads wrapped in sinew, driving deep into flesh, drawing warm blood to trickle along the grooves of shafts until it froze in the bitter air. Neither Sioux nor Cheyennes carried many rifles that day, but their quivers were filled with arrows which they had learned from boyhood to drive with accuracy into the thickest buffalo hides.
How the eighty-one trapped men died, the order of their dying, can only be reconstructed from the positions of the dead, the record of cartridge shells, the bloodstains of the enemy, and later accounts of Indian survivors. As soon as the retreating infantry reached the rock formation, they flung themselves down and began firing. Fetterman then formed a thin skirmish line facing the Oglalas and Cheyennes to north and east, the Miniconjous to south and west, and ordered his men to fire at will. For several minutes fighting was intense, the infantry firing volleys from their muzzle-loaders while the cavalry floundered about without an officer, a hundred yards above on the hillside, their Spencer carbines scarcely used.
Farther down the road, Wheatley and Fisher, supported by the Springfields of five or six soldiers who had joined them, kept up a rattling fire with their Henrys. They knocked down several Indian ponies whose riders tried to rush them, and then used the animals' bodies as cover. Dead and wounded Indians were ringed around them.
For fifteen or twenty minutes, the rock-sheltered infantrymen were able to hold the attackers off. Then their ammunition began to run short. Men bunched together, and the Indians sensing their growing panic moved in closer, Miniconjous on one side, Oglalas on the other—so close that Miniconjous were killing Oglalas, and Oglalas were killing Miniconjous, with their own arrows. The Sioux leaped over the rocks, using lances and war clubs, and some of the infantrymen broke away and started running up the hill toward the cavalry position. Indians pursued them. One warrior running with a raised bow to count coup came within two steps of a soldier before one of the man's comrades shot the Indian down.
Some time during the fighting, Captain Fred Brown released his borrowed pony, Calico, and joined Fetterman among the boulders. The two officers were together at the last, their ammunition exhausted, capture and torture almost inevitable. As they had sworn to do, each man saved one unexpended cartridge. At the end they faced each other—the ambitious, good-natured, balding quartermaster, and the determined and overconfident infantry veteran who had boasted that eighty men could ride through the Sioux nation. With revolvers held against each other's temple, they counted quickly in unison to three, and squeezed triggers.
About this time, the position held by Wheatley and Fisher and the six infantrymen was overrun. The defenders fought with gunstocks, bayonets and knives until the last man was slain.
The cavalry, knowing that they would be next, had already dismounted and started climbing farther up the ridge, leading their horses. A handful of infantrymen joined them, and two or three surviving noncommissioned officers tried to keep some sort of military order. On the high slope, snow had formed ice sheets which made walking difficult, and when they reached the rocky summit they abandoned any hopes they may have had of descending the south side and racing for the fort. The south slope was alive with Indians coming up from the other fork of the Peno.
There was nothing the survivors could do now but seek cover among the rocks and try to keep alive until help could come from the fort. They turned their horses loose (there was no place for horse holders to go) and moved along the ridge toward a cluster of large boulders. For a few minutes the showers of arrows lessened as the Indians devoted their attention to capturing abandoned cavalry horses. Then the fight was resumed with renewed fury along the ridgetop, a narrow forty-foot shelf swept by icy winds that froze blood in wounds.
As they took cover among the massive boulders, these inexperienced cavalrymen must have felt a momentary revival of hope. They formed into compact units, firing carbine volleys downslope into their besiegers, the rear guard kneeling for accuracy, sometimes half hidden in powder smoke. One of the men fighting this delaying action was running backward, yelling, swinging his carbine in an arc as he fired, reloaded, and fired again. It was told later among the Miniconjous of how White Bull rushed this brave pony-soldier, shooting him through the heart with an arrow, and when he fell on his back White Bull struck him across the head with his lance, knocking his cap off, counting coup.
By this time, Indian scouts watching from hills near Phil Kearny had signaled that reinforcements were coming from the fort, and chiefs passed the word that the pony-soldiers must all be killed as quickly as possible. The leaders knew it would not be easy; the cavalrymen were in a much better position than the infantrymen had been. But enough warriors crawled and darted forward among the rocks until they were in sufficient numbers to charge. Heedless of screaming bullets, they rushed in among the dismounted pony-soldiers, fighting and scuffling hand to hand in the carbine smoke, swinging bludgeons and hatchets, scalping men alive. Years afterward the Sioux showed a knotted war club of bur oak, driven full of nails and spikes, still clotted with dried blood and hair of cavalrymen who died that day on Massacre Hill. But the Indians paid dearly for this quick victory, many more dying among the boulders on the ridge than had lost lives against the infantrymen on the road below.
One of the last soldiers to die was Adolph Metzger, the little German-born bugler, an army veteran since 1855. Metzger beat off his assailants with his bugle until the instrument was a battered, shapeless mass of metal, until his body was bleeding from a dozen wounds. He fell on the ridge near where a monument now stands to mark the Fetterman Massacre, his dead comrades all about him, their ammunition boxes still half-filled. The fighting was all over. Forty minutes had passed since the Sioux first sprang their trap and surged up out of the grass flats at the forks of Peno Creek.
As the last carbines were fired, a relief party from the fort was reaching high ground east of the scene of fighting. Along the road and down in the valley, hundreds of Indians circled their war ponies and jeered at the cautious bluecoats. Others of the victors stripped uniforms off the dead and began mutilating the bodies according to tribal rituals. Trouser legs were cut off to use for leggings; paper money and coins were shaken from pockets. The coins were kept, the paper money discarded. Soldier overcoats were fastened to saddles or donned as replacements for buffalo robes.
When a dog belonging to one of the dead soldiers came running and barking out of the rocks, one of the warriors cried: "All are dead but the dog. Let him carry the news to the fort." But another warrior shot the animal through with an arrow. "No," he said. "Do not let even a dog get away."
The last task of all was recovering arrows from the field of battle. Almost forty thousand had been fired, a thousand for each minute of the fighting, and those which had not found a human target or were not blunted or broken were quickly collected and replaced in quivers.
Among the Indians were many wounded and dead, although exactly how many will be never be known. Estimates of the participants varied from ten to a hundred dead, and from sixty to three hundred wounded. The more reliable informants believed at least sixty were killed on the field, and of about three hundred wounded probably a hundred more died. Many years later, Red Cloud would recall the names of eleven Oglalas killed in the fighting and several others of the tribe who died later of wounds. White Elk, a Cheyenne, often said that more Indians were killed in the Fetterman fight than in the Custer fight ten years later. But whatever the casualties, the victory was not a cheap one for the combined tribes of Tongue River.
## 6.
After Assistant Surgeon Hines left the fort some minutes before noon, he proceeded rapidly with his escort along the road toward the pinery. Hines' orders were to join the wood train, and if not needed there to find Fetterman and return with him. The surgeon, of course, discovered that the attack on the train had already ceased; the wagons were moving unmolested toward Piney Island. Requesting two additional escorts from the train guard, Hines hurried on west, expecting to meet Fetterman coming around the end of Sullivant Hills. Instead, as soon as Lodge Trail Ridge came into his view, Hines saw hundreds of Indians swarming in the valley and up the slopes of the ridge. He saw no trace of Fetterman's detachment, and as there were too many Indians between him and the ridge to move in that direction, he turned back at a fast gallop toward the fort.
A few minutes later Hines was back in the fort reporting to Carrington. Neither the surgeon nor the colonel was especially concerned as yet over the whereabouts of Fetterman, each probably assuming the soldiers were returning along the Bozeman Road or by one of the trails north of Big Piney.
Hines had scarcely left post headquarters, however, when sounds of heavy rifle fire came from the northwest. "Just about dinner call," Carrington recorded later, "or near twelve noon... my office orderly told me that the sentry at the door reported firing. I went to the top of the house, on which was a lookout, and heard a few shots, apparently in the direction of Peno Creek. With my glass I could see neither Indian nor soldier. I think I counted six scattering shots at first, succeeded by more rapid firing.* I directed the orderly, then in front of the house, to notify the officer of the day; had sentry call the corporal of the guard, and the guard formed immediately. Sent one man who was bringing boards into the unfinished part of the house, to the quartermaster's office, to have wagons and ambulances hitched, and to immediately go and notify every unarmed man in the quartermaster's employ to report at once to the magazine for arms.
"Lieutenant Wands, Captain Ten Eyck, and another officer whose name I do not recollect, were in sight from the top of the house.
"I directed Captain Ten Eyck to be prepared to move at once. I called Lieutenant Wands to the top of the house to watch the firing and went in person to hasten and organize the detail that was to move. It moved in a very few minutes. I rejected some men from the detail after it was formed, taking those only who had most ammunition and had reported promptly, not wanting to have any boxes re-supplied."
Less than a quarter hour after the first alarm, Ten Eyck marched with seventy-five officers and men, including Lieutenant Winfield Scott Matson and Surgeons Hines and Ould, "being all the men for duty in the fort." Most of these men were on foot, but among those mounted was Carrington's orderly, Private Archibald Sample, who was to act as messenger. They were under orders to join Fetterman's troops and return with them to the fort. According to Private Murphy, "they went at a double-quick or as fast as they could, until they came to the crossing of the Piney." Big Piney was never easy to cross on foot, and with the added hindrance of broken ice, "the men had to remove their shoes and stockings to get across."
After fording the creek, Ten Eyck followed the Bozeman Road for a short distance, then turned right, seeking high ground on the north. For taking this less direct route to the scene of the fighting, Ten Eyck would suffer bitter condemnation in years to come. Accused of cowardice, shunned by fellow officers, he turned to alcohol and quit the Army. Yet it is very probable that any responsible officer operating under the same conditions would have made a similar move to higher ground, and it is most likely that had Ten Eyck not done so, his detachment would have met the same fate as Fetterman's.
By the time Ten Eyck was across the Piney, sounds of firing were lessening, and he must have assumed that Fetterman either had beaten off the foe or was beyond retrieval. When he reached the summit of the ridge, about 12:45 P.M., all firing had ceased. According to Surgeon Hines, they were "just in time to see the last man killed."Peno Valley was swarming with more Indians than any man in the detachment had ever seen gathered in one place.
As soon as the victorious hostiles sighted this relief force, scores of mounted warriors galloped up the Bozeman Trail to the base of the ridge, daring the soldiers to come down, slapping their buttocks, calling obscenities. Ten Eyck held his position, dispatched a messenger to the fort, and waited.
In the meantime Carrington had already started more reinforcements and ammunition. "I sent immediately after Ten Eyck moved, the remainder of Company C, 2nd U.S. Cavalry, dismounted (nearly thirty men in all), having the new carbine, requiring them to fill their pockets with all the surplus ammunition they could carry." Convinced that Fetterman's men had suffered casualties and were in need of ammunition, he also ordered an ambulance and two wagons to join this detachment. "In the first wagon that reported I placed three thousand rounds Springfield and two cases of Spencer, to give this command, and also Fetterman's, additional ammunition. I sent Williams, master of transportation, in charge of the wagons and ammunition, with forty-two men, they quickly following the details that had already left." Most of the men in this latter group were civilian teamsters from the quartermaster department, some mounted on their own horses, others on broken-down cavalry horses.
By now an hour had passed since the first alarm, and there were no longer any sounds of firing. In the words of Frances Grummond who was anxiously awaiting news of the fate of her husband, "the silence was dreadful." She and other wives in the fort had gathered near the headquarters building, watching the hills to the northwest.
A few minutes past one o'clock, they sighted a lone horseman galloping furiously down the slope beyond Big Piney. As the rider crossed the stream, they recognized him as the colonel's orderly, Private Sample. Without checking the speed of his horse, Sample swept through the gate and crossed the parade. Carrington was waiting for him in front of headquarters as he dismounted.
"Captain Ten Eyck says he can see or hear nothing of Captain Fetterman," Sample reported. "The Indians are on the road challenging him to come down."
Carrington asked how many Indians there were. Sample replied that the valleys for miles around were filled with them, and added quickly that Captain Ten Eyck requested reinforcements and one of the mountain howitzers. Carrington began scrawling a message on a sheet of paper, and as he wrote, Sample said quietly: "The Captain is afraid Fetterman's party is all gone up, sir." The colonel continued writing:
> CAPTAIN: Forty well-armed men, with 3,000 rounds, ambulance, etc., left before your courier came in.
>
> You must unite with Fetterman, fire slowly, and keep men in hand; you could have saved two miles toward the scene of action if you had taken Lodge Trail Ridge.
>
> I order the wood train in, which will give 50 more men to spare.
>
> H. B. CARRINGTON
>
> Colonel Commanding
Afterward Carrington explained that he made no mention of the howitzer because the gun could not be sent. No fit horses were left in the fort, he said, nor did Ten Eyck have any men with him who knew how to cut a fuse or handle the piece. "If he were compelled to fall back I was prepared to support him to better advantage, and I deemed the gun useless to him."
Sample started back immediately on a fresh horse—riding Carrington's favorite mount, Grey Eagle—and reached Ten Eyck's position about the time the Indians began leaving Peno Valley. While the victors were still streaming westward, an enlisted man called out suddenly, pointing to the Bozeman Road: "There're the men down there, all dead!"
Private Murphy afterward described the scene: "There was at that time a large stone that had the appearance of having dropped from a great height and thereby split open, leaving a space between the pieces men could pass through, which made a good protection for a small body of men, I should say for about twenty-five or thirty. Around this rock was where the main body of the men lay. There were just a few down on the side of the ridge north of the rock, not more than fifty feet from the main body."
As soon as the last of the Indians had forded Peno crossing and vanished beyond the ridges, Ten Eyck ordered his men to march, foot soldiers advancing cautiously toward the road, mounted soldiers and civilians riding flanks. The boulders where the infantrymen had died were surrounded by dead Indian ponies and army horses, the latter with their heads pointing toward the fort. Many broken arrows, some with points deep in the earth, littered the ground. All Indian casualties had been removed, numerous bloodstains marking the grass where they had lain. The dead soldiers lay in a space no more than forty feet in diameter, most of the bodies stripped naked and mutilated, and beginning to freeze in the bitter air. "The greater number," Surgeon Hines noted, "were in one heap." Most of them had been killed by arrows. Several unexpended cartridge shells were scattered near the rocks.
Private Murphy told of finding a man of his company "scalped, stripped and mutilated.... It looked as though they had first stripped him and then filled his body with arrows, as they were sticking out of him all over like porcupine quills... all of the bodies were stripped, scalped and mutilated with the exception of two who were not scalped, but the Indians had drawn a buffalo bag over their heads."
In Colonel Carrington's official report, suppressed and unpublished until twenty years after the event, no details were spared in describing the mutilations: "Eyes torn out and laid on rocks; noses cut off; ears cut off; chins hewn off; teeth chopped out; joints of fingers, brains taken out and placed on rocks with other members of the body; entrails taken out and exposed; hands cut off; feet cut off; arms taken out from sockets; private parts severed and indecently placed on the person; eyes, ears, mouth, and arms penetrated with spear-heads, sticks, and arrows; ribs slashed to separation with knives; skulls severed in every form, from chin to crown, muscles of calves, thighs, stomach, breast, back, arms, and cheek taken out. Punctures upon every sensitive part of the body, even to the soles of the feet and palms of the hand."
Captains Fetterman and Brown had suffered similar treatment, the latter's body, according to Private John Guthrie, "hacked up and a lot of arrows in him (he had a little tuft of hair back of the ears and was nicknamed by the Indians 'Bald Head Eagle') and scalped." The two officers were found together, each shot through the left temple, with powder burned into the skin and flesh about the wounds. They had carried out their often expressed declaration that they would never be taken alive by Indians.
Only one living being was found on that field of death—a gray mount named Dapple Dave, belonging to the 2nd Cavalry. The horse lay near the boulders, blood oozing from a dozen arrow wounds. Ten Eyck ordered a soldier to put the animal out of its misery, and then signaled the ambulance and wagons down from the ridge. The December afternoon was waning and the sun would be gone before other vehicles could be brought from the fort. The dead would have to be packed aboard like butchered animals. "We brought in about fifty in wagons," wrote Surgeon Hines, "like you see hogs brought to market."
## 7.
In the fort, after Ten Eyck's relief forces departed, the anxieties of those left inside soon deepened to an awful apprehension of what must have happened beyond Lodge Trail Ridge. Carrington was acutely aware of how small his remaining force was; almost three-fourths of his combatant strength was in the field, divided between the pinery, Fetterman's detachment, and Ten Eyck's relief column.
He placed the entire garrison under arms, including all civilians and several prisoners released from the guardhouse. He suspended all activities of a nonmilitary nature, and ordered arms stacked before quarters.
"This occupied not a very few minutes," he later reported, "and I joined Lieutenant Wands upon the house to watch indications of the position of the parties out. There had been a short lull in the firing (namely, only scattered shots here and there), succeeded by a very brisk firing, apparently by file at first, and quite regular, and an occasional volley, followed by indiscriminate firing, gradually dying out in a few scattered shots. Being satisfied that the affair was occurring beyond the range of Brevet Lieutenant-Colonel Fetterman's instructions, I became apprehensive of disaster, and directed Brevet Captain Arnold, post adjutant, to determine and report to me at once the number of men remaining at the post—soldiers and civilians—who were armed, to determine whether I had any force to spare for further operations outside. He reported the number at 119, including guard...."
An observer of these grave developments was Frances Grummond, whose earlier concern for her husband had turned to bitter anguish. "I shall never forget the face of Colonel Carrington as he descended from the lookout when the firing ceased. The howitzers were put in position and loaded with grape, or case-shot, and all things were in readiness for whatever might betide. He seemed to try to impress us with the assurance that no apprehension could be entertained for the safety of the fort itself, but encouraged all to wait patiently and be ready for the return of the troops. How different was the reality, soon to be realized!"
To increase his defensive force, Carrington next sent couriers to the pinery, ordering all men there to return immediately to the fort. The woods detail had been completely unaware of the Fetterman fight, being too far away to hear the rifle fire. They came in well before twilight, with most of their wagons empty, and took up positions around the banquette.
As darkness was falling guards sighted the first horsemen of Ten Eyck's forward scouts on the Bozeman Trail, and in a few minutes they could hear the rumble of wheels on axles. Ten Eyck had recovered forty-nine bodies, filling his wagons, and had started back for the fort in the biting cold of the early December dusk. A few Indians appeared on the ridges, but no fight was offered, and the relief force returned without firing a shot.
Musician Frank Fessenden was among those at the gate when the wagons came in with their gruesome cargo of naked mutilated bodies, "arms and legs in all shapes, divulging the horrible manner in which our brave comrades had died. It was a horrible and a sickening sight, and brought tears to every eye, to see those men, many of whom had served four years in the War of the Rebellion, meeting such an awful death on the western plains. Some of these men had but ten days more to serve, when their enlistment would have expired, and they could have returned to their homes."
Young Jimmy Carrington also witnessed the arrival of the wagons. "How many times later," he wrote as an adult, "I awoke in the dark in terror, to see again the tortured bodies and bloody arrows of that night."
For all in the fort the night of that Black Friday was long and terrible—filled with bitter gloom, anxieties and alarms. Indian signal fires ringed the hills, and every enlisted man was assigned to guard watches. Few slept even when off duty, shocked by the loss of their comrades, aware that there was not a single full cartridge box left in the garrison. Carrington and his officers were so certain of an impending direct attack upon the stockade that none of them slept at all.
"We had orders to bar up our windows and doors," said Frank Fessenden, "but to leave port-holes in the windows to fire through. There was a magazine in one corner of the parade ground, which was a large hole in the ground, well supported with heavy timbers and covered with earth and sodded over. This magazine was well supplied with ammunition of all kinds. Wagons were hauled in; the beds taken off their gears and placed on their sides and surrounded this magazine. Then more wagons were placed in a circle, until we had three circles surrounding the magazine. The soldiers were then placed three in number at every port-hole around the inside of the stockade.
"We had ten women and several children with us. The colonel gave orders that as soon as the Indians made the expected attack, the women and children should enter the magazine, and the men should hold the fort as long as possible. When they could hold it no longer, they were to get behind the wagons that surrounded the magazine, and when the colonel saw that all was lost, he would himself blow up the magazine and take the lives of all, rather than allow the Indians to capture any of the inmates alive."
For Frances Grummond the events of the day were only a confirmation of the forebodings which had filled her thoughts since the September day when she and her husband had arrived at Phil Kearny. All through the late afternoon, the officers' wives had waited in the Wands' quarters, and soon after the arrival of the wagons, Margaret Carrington came to inform Frances that Lieutenant Grummond had not been found alive. Nor was he among the recovered dead. Certain there was little hope that Frances would ever see her husband alive again, Margaret insisted that she move into the Carringtons' quarters so that she would not be alone.
Early in the evening Frances received an unexpected caller, a swarthy man in his middle thirties, tough and wiry of frame, with a pointed black beard and bright piercing eyes. He was John (Portugee) Phillips, a mining partner of James Wheatley and Isaac Fisher, all of whom had come to Phil Kearny in August and accepted jobs with the quartermaster. Had he not been engaged in hauling water to fill the post's water barrels at the time of the Indian alarm, Phillips no doubt would have volunteered and met the same fate as his partners.
Although he was an admirer of Lieutenant Grummond, Phillips had never before so much as spoken to Frances. Perhaps he felt it his duty now to reassure her that she and her unborn child would be protected. He began speaking in his strange soft accent (Phillips was born in the Azores of Portuguese parents), explaining that he had offered his services as a messenger to Laramie for reinforcements. "I will go if it costs me my life. I am going for your sake."
Writing of this moment in later life, Frances Grummond recalled that Portugee Phillips had tears in his eyes as he handed her a wolf robe in a sort of symbolic gesture. "Here is my wolf robe. I brought it for you to keep and remember me by it if you never see me again."
While this interview was in progress, Colonel Carrington was in his adjoining lamplit office, penning dispatches to General Cooke in Omaha and to General Grant in Washington. These messages were almost incoherent, hastily written attempts to report the disaster, combined with desperate pleas for help. "Do send me reinforcements forthwith," he begged General Cooke. "Expedition now with my force is impossible. I risk everything but the post and its stores. I venture as much as any one can, but I have had today a fight unexampled in Indian warfare." As yet, he knew only that forty-nine bodies had been recovered, but company roll calls had not yet been taken, and he estimated thirty-five dead still to be brought in, three more than the actual number. He listed Fetterman, Brown, and Grummond among the dead, although the latter's body had not yet been found. "No such mutilation as that today is on record. Depend upon it that the post will be held so long as a round or a man is left. Promptness is the vital thing. Give me officers and men. Only the new Spencer arms should be sent; the Indians are desperate; I spare none, and they spare none."
To a copy of this plea, he attached a covering message direct to General Grant:
> I send copy of dispatch to General Cooke simply as a case when in uncertain communication, I think you should know the facts at once. I want all my officers. I want men. Depend upon it, as I wrote in July, not treaty but hard fighting is to assure this line. I have had no reason to think otherwise. I will operate all winter, whatever the season, if supported; but to redeem my pledge to open and guarantee this line, I must have re-enforcements and the best of arms up to my full estimate.
In the folklore of the western frontier, the ride of Portugee Phillips from Phil Kearny to Laramie has achieved a status equal to that of Paul Revere's ride. And as in the case of the New Englander's exploit, there also seems to have been more than one rider. A sergeant writing from Phil Kearny on December 28 said that "Colonel Carrington sent citizen couriers to Laramie with dispatches to department headquarters for re-enforcements." John Hunton, a Fort Laramie sutler's store clerk who knew Phillips well, listed four riders, including a sergeant "and a man named Gregory." John Friend, the telegraph operator at Horseshoe Station, said that when Phillips arrived there on Christmas Day he was accompanied by William Bailey and George Dillon. Colonel Carrington in his testimony before a commission of inquiry in the spring of 1867 stated that he "hired two citizens to take dispatches to Laramie."
It appears likely that Carrington selected both Phillips and Bailey for the ride, and it is logical that he would have ordered them to leave the fort separately on the theory that if one did not make it through to Laramie, the other might. Also it is probable that other riders joined one or both of them en route—at Fort Reno or Bridger's Ferry—which explains the presence of the veteran wagon train captain, George Dillon, when Phillips and Bailey rode into Horseshoe Station.
That Phillips left Phil Kearny alone, that he traveled most of the 236-mile journey alone through raging blizzards, that he rode alone the last forty miles from Horseshoe Station to Laramie—all appear to be facts. It was an almost incredible feat of horsemanship, a heroic four-day ride.
On that cold dark evening of December 21, Phillips stuffed his saddlebag with hardtack, took a quarter of a sack of oats for his mount, and went with Colonel Carrington to the stables. There by lantern light he saddled one of Carrington's horses, variously described as a "thoroughbred charger," "a Kentucky saddle horse," "a white horse." The two men then walked together, Phillips leading the horse, to the water gate at the southeast end of the quartermaster yard.
Since sundown Private John C. Brough had been posted at the water gate, and as the two men approached, Brough challenged them. A moment later the sergeant of the guard called out: "Attention! It's the commanding officer." Carrington spoke up then: "Never mind, sergeant, open the gate." The sergeant unlocked the padlocks and Carrington and Phillips stepped forward, pulling out the bars and pushing the gate open.
"I recovered arms," Private Brough recalled afterward, "stepped back and stood at present arms while the two men walked to the gate opening....They conversed for a minute or two, and finally one of them mounted the horse, which was restive and prancing around. The other man... he was Colonel Carrington... reached up, took the man's hand, and spoke a few words. I could not hear all he said, but did hear him say, 'May God help you!'
"The horseman wheeled and started off on a trot. For about thirty seconds we could hear the hoof-beats, and then they ceased. The colonel stood with his head bent on one side, as if listening intently, and then straightening up and speaking to no one in particular, said, 'Good, he has taken softer ground at the side of the trail!'"
Wind gusts swirled bits of sleet and snow around Carrington's lantern as he and the sergeant closed the gate and replaced the bars. The colonel turned back toward his headquarters, the sergeant accompanying him. Private Brough slapped at his tingling ears, and continued walking his post in the below-zero temperature.
## 8.
Carrington waited impatiently for daylight on the morning of the 22nd. He had not slept, indeed had scarcely rested at all during the night, and having learned the ways of the Indians he expected a dawn attack, perhaps a massive assault against the stockade at the earliest show of light.
In occasional interludes of self-examination during that long night, he had attempted to adopt the viewpoint of the hostiles, tried to reason what he would do if he were an Indian. "I could not but feel that if I had been a red man," he admitted later, "I would have fought as bitterly, if not as cruelly, for my rights and my home as the red man fought."
But when daylight came, pale gray and bitter cold, not an Indian was visible anywhere, in the valley or on the ridges. The sky was heavy with snow, warning white man and red man to seek shelter from a threatening blizzard. The morning gun echoed back from the hills; bugles and drums sounded reveille.
Soon after breakfast, Carrington summoned his four surviving officers for a council. Company roll calls had shown thirty-one enlisted men and Lieutenant Grummond still missing, and as none had come in during the night, they were all assumed to be dead. The first order of business, as Carrington saw it, was to recover the bodies of these dead comrades. Ten Eyck, Powell, Wands, and Matson listened respectfully, then each in turn offered his opinion. It would be hazardous for any small party to return to the battlefield while the Indians were still celebrating their victory. If a large party left the stockade, the lives of all left behind would be in peril.
In the room adjoining this meeting, Frances Grummond and Margaret Carrington could hear every word spoken. "I will not let the Indians entertain the conviction that the dead cannot and will not be rescued," the colonel declared. "If we cannot rescue our dead, as the Indians always do at whatever risk, how can you send details out for any purpose, and that single fact would give them an idea of weakness here, and would only stimulate them to risk an assault." Carrington concluded by announcing that he would lead the expedition himself. He wanted eighty picked men, soldiers and civilians. Ten Eyck, Matson, and Surgeon Ould would accompany him. He dismissed the group and turned immediately to the door of the adjoining room, knocking on the panel.
"Mrs. Carrington was sitting near the window," Frances Grummond recorded, "deep in thought... I was lying down, equally absorbed by the momentous question at stake.... When the door opened, we sprang trembling to our feet. The Colonel advanced to his wife and quietly announced his decision....
"Turning to me, he said, 'Mrs. Grummond, I shall go in person, and will bring back to you the remains of your husband.'"
While his eighty men were assembling and awaiting inspection, Carrington penciled two separate orders, delivering them in person to Captain Powell, who was officer of the day. The first order concerned communications arrangements between the fort and the expedition while it was in the field. "Fire the usual sunset gun, running a white lamp to mast head on the flag-staff. If the Indians appear, fire three guns from the twelve pounder at minute intervals and later substitute a red lantern for the white."
The second order was to be a secret between Carrington and the officer of the day. "If in my absence, Indians in overwhelming numbers attack, put the women and children in the magazine with supplies of water, bread, crackers and other supplies that seem best, and, in the event of a last desperate struggle, destroy all together, rather than have any captured alive."
To make certain that Powell could carry out this last order, Carrington opened the magazine (which was surrounded by a circular defense of upturned wagon beds), cut the Boorman fuses of spherical case shot, and laid a train of powder which would blow up everything at the touch of a match.
Under a darkening winter sky, the eighty men marched out to the Bozeman Road and turned west. The cavalrymen moved briskly to the flanks. A few of the infantrymen rode in the mule-drawn wagons. As soon as the last man was through the gate, Carrington signaled for it to be closed and bolted, and then galloped forward to the head of the column.
Jim Bridger, although suffering from arthritis, had volunteered as a scout, and he assisted in placing pickets along the ridges so that a surprise attack might be avoided. On every high point two men were posted, each pair in sight of two other guard positions so as to form a continuous signal link to the fort. The temperature held around zero; there was still no sign of hostiles.
Among the boulders on high ground to the left of the road they found most of the remaining dead. "It was terrible work to load the frozen corpses into the wagons," said Finn Burnett, one of the volunteer civilians in the party. "The ground was fairly sodden with blood, the smell of which frightened the mules until they were well-nigh unmanageable. A man was obliged to hold the head of every animal while other teamsters loaded the naked, mutilated remains like cordwood into the wagon-boxes.
"When the first wagon had been half loaded, the mules began to lurch and kick, until they succeeded in throwing the men aside. Turning the wagon around they overturned it in their frenzy, and the bodies were dumped out before the animals could be recaptured and subdued. It was a terrible sight and a horrible job."
John Guthrie, hard-bitten little cavalryman of the 2nd, described the same scene in his crude but vivid vernacular: "Some had crosses cut on their breasts, faces to the sky, some crosses on the back, faces to the ground, a mark cut that we could not find out. We walked on top of their internals and did not know it in the high grass. Picked them up, that is their internals, did not know the soldier they belonged to, so you see the cavalry man got an infantry man's gutts and an infantry man got a cavalry man's gutts."
Carrington was shocked by what he saw, yet in his introspective way sought a reason for such evidences of savagery as the methodical removal of dorsal, thigh and calf muscles, of arms and limbs torn from sockets. Not until many years afterward, when he talked with a survivor of Red Cloud's Oglalas, did he learn the answer—a variation of the white man's myth of Tantalus. "The key to the mutilations were startling and impressive. Their idea of the spirit land is that it is a physical paradise; but we enter upon its mysteries just as in the condition we hold when we die. In the Indian paradise every physical taste or longing is promptly met. If he wants food, it is at hand; water springs up for ready use; ponies and game abound, blossoms, leaves, and fruit never fail; all is perennial and perpetual. But what is the Indian hell? It is the same in place and profusion of mercies, but the bad cannot partake.... With the muscles of the arms cut out, the victim could not pull a bowstring or trigger, with other muscles gone, he could not put foot in a stirrup or stoop to drink; so that, while every sense was in agony for relief from hunger or thirst, there could be no relief at all."
According to Finn Burnett, only the body of the bugler, Adolph Metzger, was left untouched. "His heroism had aroused the admiration of the savages, they covered his corpse with a buffalo robe as a symbol of extreme respect." John Guthrie, however, said that Metzger's body was never found, and a few weeks after the fight the Helena (Montana) _Herald_ reported an interview between fur trappers and a band of Crows who had heard from the Sioux a story of the last survivor, who may have been Metzger. "He stood up and fought hand to hand till overwhelmed by their closing upon him, and carrying him off a prisoner to their camp where he was finally tortured to death."
After loading all bodies found on the high ground, Carrington ordered the wagons moved cautiously along the road toward Peno Creek. Over a distance of three-quarters of a mile they recovered six more dead, including Lieutenant Grummond and Sergeant Augustus Lang. The lieutenant's head was almost severed from his body; his fingers had been chopped off, his naked body filled with arrows. Along this same stretch of road, they also found Jimmy Carrington's calico pony, which had been hastily borrowed by Captain Brown. The pony was dead, its head badly cut up, and someone remarked that the Indians must have scalped it out of hatred for Captain Brown.
A few hundred yards farther on, they found Wheatley, Fisher and "four or five of the old long-tried and experienced soldiers. A great number of empty cartridge shells were on the ground at this point." In front of the bodies, the last to be recovered, was a ring of dead Indian ponies, and "sixty-five pools of dark and clotted blood" on the ground and grass. Wheatley had 105 arrows in his body and had been scalped.
The cautious march out, and the tedious and painful search for the dead, which was made even more difficult by bitter cold, occupied most of the day. As they were turning back from Peno Creek they heard the fort's sunset gun, and a black wintry darkness settled over the land before they sighted the gleam of a lantern on the flagstaff. It was a white light, signaling the reassuring news that Indians had not attacked the fort in their absence.
"We hauled them all into the fort," said John Guthrie, "and made the guard house at the fort a dead house."
The first act of the colonel when he returned was a sentimental gesture. He visited Frances Grummond, handed her a sealed envelope, then left her to a moment of private grief. "I opened the envelope," she wrote afterward, "with eager but trembling hands. It contained a lock of my husband's hair." She suddenly remembered, then, another memento, an encased miniature portrait of herself which George Grummond had worn since their wedding, and she wondered sadly if some Indian warrior carried it in his possession as a trophy of the battle.
Another who had to be consoled was the nineteen-year-old widow of James Wheatley.* Wagoner Finn Burnett described her as "a beautiful girl, a fine woman... a brave splendid little soldier."
On the night of the 22nd, the blizzard which had been threatening for two days began in earnest, its fierce winds sweeping a blinding snow across the land and dropping temperatures to twenty below zero. Arm-length mittens, thigh-length leggings, buffalo boots, and a variety of fur hats were issued to the guards, and shifts were cut to one-half hour. At daylight of the 23rd the storm still raged, and snowdrifts crested the west flank of the stockade, packed so tightly that guards could walk from the parade directly over the upright posts. As a security measure, Carrington ordered a ten-foot trench cleared outside, but the biting winds refilled it almost as fast as men could dig.
That day and Christmas Eve were devoted to the melancholy task of preparing the dead for burial. Bodies were cleaned, mutilated fragments put together, arrows drawn out or cut off. Because most of the dead were left naked by the Indians, their comrades volunteered uniforms to clothe them. While this work went on in the hospital, carpenters constructed coffins. And in spite of the weather, a grave-digging detail cleared snow from the burial ground and started digging a trench for interment.
"One-half of the headquarters building, which was my temporary home," wrote Frances Grummond, "was utilized by carpenters for making pine cases for the dead. I knew that my husband's coffin was being made, and the sound of hammers and the grating of saws was torture to my sensitive nerves.... During the nights I would dream of Indians, of being captured and carried away by Red Cloud himself while frantically screaming for help, and then awaken in terror only to spring from my bed involuntarily to listen if the nearby sentry would still voice the welcome cry, 'All's well.' Sleeping draughts and the kind ministrations of Dr. Horton seemed rather to aggravate than reduce the nervous tension..."
On Christmas Day, the burial detail placed lines of pine cases by companies along officers' row. Two enlisted men were sealed in each box; the three officers rated separate coffins. Cases were carefully numbered to identify the occupants.
Carrington had hoped to bury the dead in solemn Christmas Day services, but the gravediggers, even though working in continuous half-hour shifts, were unable to complete excavation of the trench. Not until Wednesday, the 26th, five days after the battle, was burial completed, in a pit fifty feet long, seven feet deep, seven feet wide. "The severity of the weather," a sergeant wrote two days later, "and probability of immediate attack upon the fort compelled us to bury our dead in trenches, without ceremony or military honors."*
On that same day—December 26—the War Department in Washington received the first telegraphic dispatches of the Fort Phil Kearny disaster. From General Cooke in Omaha: "On the 21st instant three officers and ninety men, cavalry and infantry, were massacred by Indians very near Fort Phil Kearny." At 3:15 that afternoon direct from Fort Laramie, General Grant received Carrington's dispatch pleading for reinforcements.
To give this news to the outside world, John (Portugee) Phillips had forced his way through almost continuous blizzards, riding only at nights, rationing oats carefully to his horse, sometimes digging tufts of grass for it from under the snow. Late on Christmas morning he rode into Horseshoe Station, accompanied by William Bailey and George Dillon, and handed his dispatches to the telegraph operator, John Friend. Phillips had crossed 190 miles of snow that was in some places four or five feet deep.
After Friend had tapped out a condensation of the messages, Phillips rebound his legs with sacks, wrapped himself in a buffalo coat, saddled up, and prepared to ride the forty remaining miles to Fort Laramie. He had promised Colonel Carrington he would deliver the dispatches to the commander at Laramie, and neither his companions nor the telegraph operator could dissuade him from completing his mission.
After riding all afternoon across a dazzling-white land that blinded him, he welcomed the relief of nightfall even though more snow began falling and the temperature dropped far below zero. Between eleven o'clock and midnight he arrived at Fort Laramie. Icicles were hanging from his clothing; snow and ice matted his beard. From lighted windows of the main officers' quarters, he could hear gay dance music.
Phillips slid out of his saddle, staggering from exhaustion, and a minute later the officer of the guard, Lieutenant Herman Haas, was at his side, asking his name and what he wanted. Phillips was so weak he could barely reply that he wanted to see the commanding officer.
Lieutenant David Gordon (who later became a brigadier-general) was stationed at Laramie with a company of the 2nd Cavalry. "It was on Christmas night, 11 P.M.," Gordon later recorded, "when a full-dress garrison ball was progressing and everybody appeared superlatively happy, enjoying the dance, notwithstanding the snow was from ten to fifteen inches deep on the level and the thermometer indicated twenty-five degrees below zero, when a huge form dressed in buffalo overcoat, pants, gauntlets and cap, accompanied by an orderly, desired to see the commanding officer. The dress of the man, and at this hour looking for the commanding officer, made a deep impression upon the officers and others that happened to get a glimpse of him, and consequently, and naturally, too, excited their curiosity as to his mission in this strange garb, dropping into our full-dress garrison ball at this unseasonable hour.
"As we were about to select partners for another dance word was passed into our ball-room that General Palmer desired to see me..." A few moments later, Lieutenant Gordon met Portugee Phillips face to face.
During the preceding forty-eight hours, Laramie officers had been hearing rumors from Indians around the fort of a great battle which had supposedly taken place near Phil Kearny. At two o'clock that afternoon, General Innis N. Palmer, the new commanding officer, had received a garbled telegram from Horseshoe Station, reporting a massacre. Palmer had immediately forwarded the message to Omaha, but evidently he still considered the massacre a rumor until Phillips arrived with Carrington's dispatches. Not until early in the morning of the 26th did Carrington's full report go to Omaha, and Lieutenant Gordon afterward stated that Fort Laramie received "nothing authentic until the dispatch was handed the commanding officer by one Portuguese Phillips, who was employed by Colonel Carrington at Fort Phil Kearny." *
Thus the world outside Dakota Territory learned of the incident which would be known thereafter as the Fetterman Massacre.
* Peno Creek, named for a French trapper, was later changed to Prairie Dog Creek.
* Others in the fort reported hearing four volleys in succession, each time the sound seeming farther away—then a continuous and rapid fire with a fierceness indicating a pitched battle. "At the noon hour we could hear volleys plainly," said Private William Murphy, "and they continued for a long period of time."
* Burnett said that Mrs. Wheatley remained at the fort until the following spring when her brother came for her and took her back to the family home in Ohio. William Murphy, however, stated that she later married a man by the name of Breckinridge and lived on a ranch about five miles from Fort Laramie.
* These bodies with those of thirty-seven other soldiers buried at Fort Phil Kearny were exhumed in October 1888 and reburied in the National Cemetery at Custer Battlefield.
* The horse used by John Phillips on his four-day, 236-mile ride died soon after arriving at Fort Laramie. Phillips himself collapsed from exhaustion and exposure, suffering for weeks from severe frostbite. Lieutenant Gordon said that Phillips was paid one thousand dollars for the ride, but official records indicate that the amount he received for quartermaster services at Fort Phil Kearny and for the ride totaled only about three hundred dollars. Thirty-three years later, in 1899, his widow received five thousand dollars in partial recognition of Phillips' ride from Phil Kearny to Laramie.
# _X. January:_
MOON OF STRONG COLD
> _Upon being relieved I moved to Fort Casper with regimental headquarters, staff, and officers' families, with mercury at 38° below zero (the second day), and having more than halt my escort of sixty men frosted the first sixty-five miles, requiring two amputations at Reno._
ON DECEMBER 27, THE DAY following the mass burials at Fort Phil Kearny, a small party of soldiers appeared unexpectedly on the snow-drifted road east of Little Piney. They were three officers and twenty-two enlisted men who upon reaching Fort Reno had learned of the Fetterman disaster, and instead of waiting at Reno for the weather to improve had pushed on through blizzards to Phil Kearny. Senior officer of the group was Captain George B. Dandy, who some weeks earlier had been assigned to replace Captain Brown. Accompanying him were Lieutenant Thomas J. Gregg, 2nd Cavalry, replacement for the late Lieutenant Bingham, and Lieutenant Alphonse Borsman.
Borsman's orders were for service with the 27th Infantry Regiment, which after weeks of rumors was now a fact—created from the 18th's 2nd Battalion. The mail from Omaha informed Carrington that new headquarters for the 18th Infantry would be Fort Casper, where companies of the 1st Battalion would become cadres for new battalions of the 18th.
This news was not unexpected. Following the arrival of Captain Fetterman in November, Carrington had assumed there would be a change eventually. But after Fetterman's death, Carrington probably clung to a hope that he might be permitted to remain in command of the fort he had so painstakingly designed and constructed, and which had become so vital a part of his existence.
He welcomed the arrival of Captain Dandy and the reinforcements, but he knew he needed ten times their number as well as replenishment of his arms and ammunition if he hoped to equal the power demonstrated by the Indians on December 21. His enlisted men also knew this, and some indication of their morale at this time is revealed in a letter written by a sergeant on the night of December 28:
> It is now past tattoo; the night is cold; the men are sleeping in their clothes, and accouterments on. Indian signals have been seen, and we don't know what hour the post may be attacked. Self and two soldiers are keeping watch so as to awake the men in case of alarm. At midnight I shall have Sgt. Clark and three others to relieve us. So you can imagine the state of affairs here.
>
> We are fighting a foe that is the devil. In your last you spoke about some newspapers which you had sent me. I did not get them. Please write soon, and pray God to hasten the day when I shall get out of this horrible place. Goodbye; this may be my last letter; should it reach you, don't forget your friend...
By New Year's Day, however, fears of an Indian attack had diminished. Valleys and trails were deep with snow, and Jim Bridger assured Carrington that even the most hostile of Indian bands would hesitate to go on the warpath under such conditions. It was Bridger's opinion that most of the warriors were holed up in their villages on Tongue River.
(Bridger's surmise was good, as far as it went. Actually there had been no danger of attack upon the fort since the day of the Fetterman fight. As soon as the fight ended, the main body of warriors departed for Tongue River, leaving a few scouts behind to watch movements around the fort. Red Cloud and other chiefs expected retaliatory measures from the soldiers before winter ended, and in spite of bitter weather, the leaders decided to abandon their Tongue River stronghold. The Arapaho went to the Yellowstone, the Cheyennes into the Big Horns, the Sioux scattering down the valleys of the Powder and Tongue.)
On New Year's Day Carrington issued his first general order of 1867, offering a solemn memorial to the men who fell in the Fetterman fight. "As a feeble tribute to their memory, their names are published in this order, so that the records of the post shall bear them in remembrance so long as the post shall remain... a copy of this order shall be read before each company and at the first garrison parade..."
In addition to the three officers and seventy-six enlisted men killed in Peno Valley, Carrington included the names of Lieutenant Bingham and Sergeant Bowers, killed on December 6. Had he summed up losses from the day of Fort Phil Kearny's establishment, he would have listed five officers, ninety-one enlisted men, and fifty-eight civilians killed, with many additional wounded. Indians had attacked almost every wagon train and traveler attempting to pass over the Montana Road.
By January 4 the weather had moderated sufficiently for a mail party to start for Laramie, and Carrington composed a long report for General Cooke in which he claimed the Fetterman disaster confirmed his previous judgment as to the hostility of the Indians. "It vindicates every report from my pen," he wrote. "It vindicates my administration of the Mountain District.... It vindicates my application so often made for reinforcements... it proves correct my report of 1,500 lodges of hostile Indians on Tongue River."
Having thus attempted to justify his position in the disaster of December 21, Carrington added significantly: "My duty will be done when I leave, as ordered to my new regimental headquarters, Fort Casper."
This transfer order, which he must have dreaded, came with the arrival of his replacement, Lieutenant-Colonel Henry W. Wessells, on January 16. First to sight this long-awaited relief column from Laramie and Reno was the picket on Pilot Hill, who immediately signaled the lookout on Carrington's headquarters tower. "The bugle call and the long roll were never more gladly echoed in hearts," wrote Frances Grummond. "Our spontaneous cry was 'Open wide the gates, and admit our deliverers!' We hardly had patience to don protective outer-garments because of the flow of our quickened blood, and our common outbreak of joy was simply, 'At last! At last! We are saved! We are saved! Phillips was saved, saved for us!'... The band was on hand with its preparations for a share in that welcome and an escort was hastened from the gates to facilitate their arrival. As for myself, I felt that I could have hugged every half-frozen man as he entered, and I still feel that their story as it unfolded would have justified the impulse, if not the action."
The relief column's story had begun unfolding on December 26 a few minutes after General Cooke in Omaha received the first authentic telegraph report of the Fetterman disaster. Without waiting for Carrington's full report, Cooke dispatched a curt order to Laramie:
> Brevet Brigadier General I. N. Palmer, commanding Fort Laramie will send from the garrison of that post two companies of the second cavalry and four companies of the eighteenth infantry, to report to Brevet Brigadier General Wessells at Fort Reno.
>
> Brevet Brigadier General Wessells will proceed with the re-enforcements and assume command of Fort Philip Kearny, and will also have authority to order such movements of the troops at Forts Reno and C. F. Smith as he may find necessary. The commanding officers at Forts Reno and C. F. Smith will obey all orders they may receive from Brevet Brigadier General Wessells.
>
> Colonel H. B. Carrington, 18th United States Infantry, will be relieved from the command of Fort Philip Kearny by Brevet Brigadier General Wessells, and will proceed immediately to Fort Casper, to which post the headquarters of the new 18th Regiment have been heretofore ordered, and assume command of the post and that regiment.
When General Palmer received this message, Laramie was experiencing its worst weather of the winter. He waited hopefully for the blizzard to pass, then replied on the 27th: "The most violent blinding storm now raging; there would be nothing gained by moving in such a snow storm; meantime all preparations which can be made in-doors are going on."
Cooke meanwhile continued to counter any possible criticism of his own responsibility in the Fetterman affair by directing blame toward Carrington. "Colonel Carrington is very plausible," he wrote General Grant on the 27th, "an energetic, industrious man in garrison; but it is too evident that he has not maintained discipline, and that his officers have no confidence in him."
Not until New Year's Day were the first relief units able to leave Fort Laramie—four companies of the 18th Infantry's 1st Battalion under Major James Van Voast. Forty-eight hours later, two companies of the 2nd Cavalry under Lieutenant Gordon moved out, and overtook the infantry January 5.
"On account of the severity of the weather and deep snow," said Gordon, "there was no grazing for the animals, a scarcity of wood, and the water in the streams that we crossed was partly frozen to the bottom, except in the deep holes, where we were compelled to chop holes in the ice and water the animals out of buckets.... Our long forage gave out after being on the road ten days and the mules were cold and hungry for hay... they broke their halters, eat at wagon tongues, manes and tails of each other. Had to replace some tongues and ridge poles on wagons."
At Fort Reno, Wessells was informed of Cooke's order naming him as Carrington's replacement. He took command of the expedition, which reached Fort Phil Kearny on the 16th, "with but one casualty, a man being frozen to death."
Carrington reacted mildly to the news that one of his subordinates, Lieutenant-Colonel and Brevet Brigadier-General Wessells, was replacing him. He had suffered so many frustrations from department headquarters that one more scarcely mattered, although he was bitter over the way Cooke had deliberately worded the replacement orders to make it appear "that the purpose of changing my post occurred simultaneously with report of the massacre, before receipt of my telegram." He may have taken some satisfaction from the War Department's abrupt removal of General Cooke himself from command of the Department of the Platte shortly afterward, but thirty years would pass before Carrington could forgive Cooke for the manner in which he handled his transfer from Fort Phil Kearny.
On the day that General Christopher C. Augur reported as Cooke's replacement in Omaha, January 23, Carrington was making an emotional departure from the fort he had dreamed all his life of building and commanding. The dream had come to fruition, flourished, and died all within six short months. He later summed up the midwinter change of stations in a single trenchant paragraph: "Upon being relieved I moved to Fort Casper with regimental headquarters, staff and officers' families, with mercury at 38° below zero (the second day), and having more than half my escort of sixty men frosted the first sixty-five miles, requiring two amputations at Reno."
Margaret Carrington and Frances Grummond both recorded much more detailed accounts of this harrowing march. Frances was in an advanced state of pregnancy by this time, sensitive to every movement of the jolting wagon in which she rode. She had insisted on taking her husband's body with her to Tennessee, and Carrington had arranged for George Grummond's pine box to be disinterred and placed in one of the wagons.
In preparation for the journey, wagon covers were doubled, and carpenters boarded up sides and ends of wagon beds, leaving only a tiny window at each end. They placed a hinged door at the back of each vehicle for entry, and near the door a small sheet-iron stove made from a stovepipe, with a smoke vent through the wagon cover. Pine knots and short blocks of wood for fuel were packed in one corner. Women and children huddled themselves into cloaks, shawls, beaver hoods, buffalo boots, and all the furs they owned or could borrow.
Snow was falling at 1:30 P.M. on the 23rd when Carrington gave the order to march. The first afternoon and on into the dark night, the column struggled against the storm and the snow-packed road. A pioneer corps was formed and sent in advance to shovel out the deepest drifts. By ten o'clock that night, they had made only six miles. Carrington ordered a corral on a summit for defensive reasons, leaving the party open to fierce gusts of wind which almost swept the sentries off their feet.
At one o'clock in the morning the moon rose, casting a cold blue light across the frozen land. Carrington ordered the bugle sounded, and by three o'clock they were moving again. The sky was clear, the stars brilliant, the aurora borealis dancing weirdly behind them in the north sky. The thermometer in Margaret Carrington's wagon dropped to thirteen below zero.
On through the moonlit night the column crawled, wheels creaking, the cold intense. When Frances Grummond looked out her peephole window at dawn, she saw hundreds of buffalo wallowing in the snow. All that day the column was surrounded by buffalo, twenty-five miles of buffalo—a cheering sight, for it indicated lack of Indians in the vicinity.
At duskfall they halted on Crazy Woman's Fork and formed a corral in a grove beside the stream. Pickets were stationed on an adjoining bluff. The men dug wood out of the snow for night fires; as the wood burned the snow melted, then turned to ice, forming a crystal ring around each fire. They had to use axes to break their bread; coffee taken from the fires turned to frozen slush before it could be swallowed. From each wagon vent, smoke poured in plumes, but Margaret Carrington's children were crying from the cold. The turkey she had cooked before leaving the fort was frozen so hard she had to chop pieces from it with a hatchet, then soften them over her little stove before they could be eaten.
Reveille again was at one o'clock in the morning. As the moon rose, the half-frozen men began shoveling snow off the stream, broke through the ice for water to refill the kegs. A cavalryman had to be lifted from the saddle, his legs frozen from toes to knees. To keep other mounted men from suffering a similar fate, Carrington ordered their legs lashed with whips to start the circulation going.
Inside the wagons, the women wrapped themselves in buffalo skins and beaver hoods and sat with their feet to the tiny red-hot stoves. Margaret Carrington's thermometer dropped to forty below; then the mercury congealed in the bulb.
As soon as teams were hitched, the column crossed the creek, moved forward to a sixty-foot bluff and began a slow ascent. Only one wagon could go up at a time, details of men tugging at the wheels, others pulling with ropes.
"When my turn came," Frances Grummond said, "I rolled over on my bed, clung for dear life to the sides of the wagon, with eyes shut and jaws clamped, to assist or ignore the situation, both being equally ineffective, for it all depended upon those mules.... Of all rides I ever had taken in army life or out of it, this one in an army wagon without springs, with mules on a gallop over such a road, or no road, exceeded all in utter misery. One learns something from such an experience and I had learned to seize the sideboards of the wagon firmly, half reclining on the mattress with pillows compactly adjusted, and holding my breath abide the result."
Dawn was breaking when the last wagon reached the crest of the bluff. Fort Reno and temporary security still lay twenty miles to the south. By midmorning the sun's glare was blinding and those who had goggles put them on. All day buffalo herds moved alongside, occasionally coming close as if seeking company, the bulls tearing at the snow to uncover grass. Carrington passed along an order forbidding drivers to crack their whips lest the buffalo become frightened and stampede the train. There was one false alarm of Indians attacking the rear wagons, and an hour was lost in preparing defenses.
At dusk the first wagon rolled into Fort Reno, ending a sixty-five-mile journey that had required almost three days' time. They were all thankful to be alive, even the men who must lose fingers, toes and legs by amputation in the post's hospital.
After three days' rest in the warm quarters of Reno, they took the trail again, this time to Fort Casper, a march that was without perilous incident until the final day. As they neared the fort, Frances Grummond noted that her wagon was moving with increasing speed, and looking out her window she discovered the whole train at a trot, in column of six wagons front, moving all in mass. Indians had approached the train, stealing some of the led horses, but they dashed away without a fight.
At Casper, Carrington learned that the unpredictable higher command back in the States had changed its bureaucratic mind and transferred the 18th Regiment's headquarters to Fort McPherson. With the weather still formidable, he had to lead his little column back over a long stretch of rough trail already traveled. Near Sage Creek, while he was galloping his horse, his revolver was accidentally discharged, wounding him seriously in the thigh. Luck seemed to have run out for the Little White Chief. The surgeons prepared a sling for him in his wife's wagon, and thus he was carried on to Fort Laramie. After a two-weeks convalescence, he traveled by ambulance to Fort McPherson, where he reassumed command of the 18th Infantry. And there at McPherson during the early weeks of spring, he faced the ordeal of a special commission formed to fix responsibility for the Fetterman disaster.
# _XI:_
AFTERMATH
## 1.
WHILE COLONEL CARRINGTON WAS marching his headquarters complement through the blizzards of Wyoming, recovering from his wound at Fort Laramie, and proceeding to his new headquarters at Fort McPherson, he was also becoming a national figure. In newspapers and illustrated weeklies he was in most cases the target of uninformed journalists who held him solely responsible for the "Fetterman Massacre." In the War Department he was rapidly assuming the role of scapegoat. The Department of Interior's Office of Indian Affairs issued statements absolving the "friendly Indians" and placing all blame on Carrington. He was the victim of a public trial of which he was unaware for some weeks, and in which he was given no opportunity to present his side of the affair.
One correspondent for a New York newspaper described the fight as taking place at the gates of the fort. "When the last band of survivors were driven to the gates of the fort, knocking and screaming in vain for admission; when the last cartridge for revolver, carbine, and rifle was expended; when the sabers and butts of muskets were broken; and when, leaning against the gates, weary and bleeding and all resistance fruitless, all fell in one heap of mangled humanity, unsupported and uncared for." While all this was occurring, the writer continued, Carrington and two full companies were looking on, afraid to fire or open the gates lest the garrison within be massacred by the attacking Indians. An illustrated weekly carried a report from "the only eye witness of the massacre" who supposedly was cut off by Indians, and watched the fight from a nearby thicket. This survivor vividly described repeated cavalry charges and saw "the last shot discharged by the last survivor through his own brain." Newspapers in New York and Washington also accused Carrington of giving gunpowder to his enemies, and said he permitted officers' wives to toss packages of sugar and coffee over the stockade to passing squaws.
Not to be outdone by these lurid stories in the press, the Commissioner of Indian Affairs, Lewis V. Bogy, issued a statement claiming that the Indians around Fort Phil Kearny had been provoked into attacking Carrington's forces. "These Indians being in absolute want of guns and ammunition to make their winter hunt," he said, "were on a friendly visit to the fort, desiring to communicate with the commanding officer... so that they might be enabled to procure their winter supply of buffalo." In a later statement Bogy declared "the whole affair seems incredible... and I find it difficult to account for the tragedy upon any other theory than that heretofore advanced by this office, to wit: that the Indians, almost in a state of starvation, having made repeated attempts at a conference, that they might make peace and obtain supplies for their families... were rendered desperate, and resorted to the stratagem which proved too successful. It seems as if the officer commanding could have avoided the catastrophe; and it seems also that men thus armed could have repelled an attack by all the Indians in Western Dakota."
Commissioner Bogy ridiculed Carrington's estimate that three thousand Indians could have assembled in one place to attack Fetterman's detachment. "An enormous exaggeration," he charged, and then also expressed disbelief that three hundred Indians would have attacked the wood train and withdrawn without inflicting casualties. Clearly the Commissioner knew nothing of Indian decoy fighting or very little else about affairs in Dakota Territory.
His statements, however, precipitated Carrington into the midst of the perennial political struggle between the War Department and the Office of Indian Affairs. This struggle had been raging off and on since 1849 when control of Indian affairs was transferred from the War Department to the Interior Department. It was the viewpoint of the military that the bureau had been corrupted by politicians who were dishonest, inefficient, and working at cross purposes with national policy. It was the viewpoint of the Interior Department that Indian affairs could be better administered by civilians with humanitarian objectives. Each frequently accused the other of endangering lives, and neither overlooked an opportunity to make the other appear blameworthy.
General Sherman, who had recently completed several months' inspection of western frontier posts, advised General Grant that "if our troops are to keep open a highway of travel they must be allowed to take their own precautions and make their regulations for the guardianship of the Indians. The Indian Bureau should be transferred to the War Department." On February 1, Grant himself expressed this same view in a letter to Secretary of War Stanton, claiming that events at Fort Phil Kearny "show urgent necessity for an immediate transfer of the Indian Bureau to the War Department." The _Army and Navy Journal_ leaped into the fight with bitter editorials denouncing the Indian Bureau's practice of issuing arms to Indians, "thus supplying the Indians with the means of repeating indefinitely the scenes of Fort Phil Kearny."
Reacting to pressures from the civilian population which had been aroused by shocking accounts of the Fetterman disaster, the United States Senate on January 30 passed a resolution requesting the Secretaries of War and Interior "to furnish the Senate all official reports, papers, and other facts in possession of their respective departments which may tend to explain the origin, causes and extent of the late massacre of United States troops by Indians at or near Fort Phil Kearny, in Dakota Territory."
While Colonel Carrington still lay recuperating from his thigh wound at Fort Laramie, Washington bureaucracy became more deeply involved over what he had or had not done at Fort Phil Kearny. A few days after the Senate's demand for an explanation of the causes of the Fetterman disaster, the President appointed a special commission "to visit the Indian country in the neighborhood of Fort Phil Kearny, for the purpose of ascertaining all the facts." The commission, ordered to meet at Omaha on February 23, was composed of four army officers, Generals Alfred Sully, J. B. Sanborn, N. B. Buford and Colonel E. S. Parker; and two civilians, G. P. Beauvais and J. T. Kinney. Beauvais was a St. Louis trader who had lived among the Sioux for many years; Kinney had held the sutlership at Phil Kearny (and was no friend of Carrington).
By late March the commission was at Fort McPherson taking testimony from Colonel Carrington. For the first time he had an opportunity to present his side of the controversial incident, offering in evidence official messages and letters which he had sent and received, and patiently explaining all his actions from the time he received orders at Fort Kearney to the last day of his command at Fort Phil Kearny. "I close by stating," he said, "that if further testimony should be deemed necessary there are at this post the following witnesses." And he listed the names of his orderly, Archibald Sample, three other enlisted men who had been present at moments of crucial decision, and William Bailey, the civilian guide who had come with him to Fort McPherson. The commission, however, called none of these witnesses, and as soon as hearings were declared closed, departed for Laramie and Fort Phil Kearny to continue its investigations.
While Carrington waited anxiously through the spring for the commission's verdict of responsibility—a verdict which might exonerate him or be "fatal to his reputation," he received support from an unexpected source—Jim Bridger. Bridger had disagreed with Carrington on some actions at Phil Kearny, but when the scout learned of the colonel's difficulties, he prepared a statement for the _Army and Navy Journal:_
> Now as to the Philip Kearny massacre, it has been said that the Indians did not approach with hostile intent, but that the commanding officer, mistaking their intentions, fired on them, and thus brought on a fight. This is preposterous. Up to that time the Indians had been hanging around the fort every day, stealing stock on every opportunity, attacking the trains going to the woods, and even stealing up at night and shooting men connected with passing trains, while they were sitting around their camp fires, within one hundred yards of the fort. But a few days before the massacre a train going to the wood was attacked, and in defending it, Lieutenant Bingham, a promising young officer of the 2nd Cavalry, and one Sergeant, lost their lives. This may be a sign of friendship, but I don't think so. Every person that knows anything of affairs in this country knows very well that the massacre at Fort Philip Kearny was planned weeks before, and that the Sioux, Cheyennes and Arapahos had been collecting together, in preparation for it, on Tongue River, until they numbered 2,200 lodges. The intention was to attack Fort Philip Kearny first, and if they were successful to then attack Fort C. F. Smith. At the present time the entire tribe of the Northern Sioux are collecting on Powder River below the mouth of Little Powder River, and their vowed intention is to make a vigorous and determined attack on each of the three posts, and on all trains that may come along the road. Friendly Indians report that they are being supplied with ammunition by half-breed traders connected with the Hudson's Bay Company. There is no use sending out commissioners to treat with them, as it will be only acting over again last Summer's scenes. They would be willing to enter into any temporary treaty to enable themselves to get fully supplied with powder with which to carry on the war. The only way to settle the question is to send out a sufficient number of troops to completely whip the hostile Sioux, Cheyennes and Arapahos and make them sue for peace. Unless this is done the road had better be abandoned and the country given up to the Indians.
>
> I have been in this country among these Indians nearly forty-four years, and I am familiar with their past history, and my experience and knowledge of them is greater than can be gained by commissioners during the sittings of any council that may be held. I know that these Indians will not respect any treaty until they have been whipped into it.
>
> May 4, 1867 JAMES BRIDGER
At last on July 8, General Sanborn as spokesman for the investigating commission issued a report on the causes and circumstances which led "to the horrible massacre of Brevet Lieutenant-Colonel Fetterman's party, December 21, 1866." Sanborn reported the facts as he saw them, and instead of censuring Carrington, gently absolved him from blame. "The difficulty 'in a nutshell,'" said Sanborn, "was that the commanding officer of the district was furnished no more troops or supplies for this state of war than had been provided and furnished him in a state of profound peace. In regions where all was peace, as at Laramie in November, twelve companies were stationed, while in regions where all was war, as at Phil Kearny, there were only five companies allowed."
Unfortunately for Carrington, Sanborn's favorable report was buried among derogatory statements from the Commissioner of Indian Affairs, comments of biased Indian agents, letters from personal enemies such as Surgeon C. M. Hines and an unidentified sergeant, excerpts from unfriendly newspapers, and the damning comments of General Cooke. All these were published a few months later by the Senate's Committee on Indian Affairs.
As for Carrington's own testimony with its supporting documents, these papers were conveniently stored away by someone in authority in the Department of the Interior. For twenty years they would remain hidden in the files, and for twenty years Henry B. Carrington would fight a continuing battle to clear his tarnished reputation as a soldier.
## 2.
At Fort Phil Kearny, after Carrington departed in January 1867, bitter winter weather sealed the Montana Road to north and south, and for weeks at a time until spring Lieutenant-Colonel Wessells was without communication with the outside world. Old-timers afterward remembered that winter as being unusually severe in the Wyoming country—"cold, and a great deal of snow." One of the men at the fort noted that "the thermometer most of the time was from 25 to 40 degrees below zero."
Wessells had come up from Reno determined to conduct a punitive winter campaign against the hostiles, but the terrible weather combined with shortages of supplies forced him to abandon his plans. From the day of his arrival the supply shortage grew rapidly more acute. Private William Murphy said the additional reinforcements from Laramie "made our condition, if anything, worse, for they had no provisions, and no feed for stock." Reluctantly Wessells ordered Captain James Peale to take the two companies of the 2nd Cavalry back to Laramie in an attempt to save the horses from starvation. Peale and his men reached Laramie, but "without the animals, 150 in number; as evidence of that march, their carcasses could be seen many years afterward strewn along the road."
In February, ration allowances of hardtack, coffee, salt pork and flour were cut drastically. Supplies in the commissary were dwindling, and no one could foresee how many weeks would pass before supply trains could move again from the south. Corn supplies for the mules were still relatively abundant in February, and Finn Burnett told of burning ashes for lye, and then soaking corn in it to loosen the hulls. After removing the lye, he fried the softened corn in bacon grease. "Others learned the trick," he said. "Many in garrison that winter lived on mules' corn."
Another narrator who endured the winter at Phil Kearny complained of the lack of fresh meat and vegetables. "One small loaf of bread was issued to us daily—just enough for one meal. After we had eaten that, we had to fall back on the musty hardtack and frowsy bacon or salt pork with black coffee. Sometimes we had bean soup."
By late winter all corn and forage for the livestock was exhausted, and Private Murphy said the mules began eating holes through the logs in their stables. "It was pitiful to witness the suffering of these poor patient animals," wrote Frank Fessenden, who had remained at Phil Kearny with the regimental band. "At night, especially, we could hear them fairly moan and groan like a human being in their agony of hunger." As soon as weather permitted, Quartermaster Dandy sent teams up Big Piney to cut green cottonwood limbs which the animals consumed avidly, and he risked one small expedition to Fort Reno for corn. "The snow was very deep," said Private Murphy, "and it took several days to make the trip."
Other discomforts came from lack of warm clothing and firewood. "Our shoes were made of cheap split leather," Murphy recorded, "and the shoddy clothes that were furnished at that time were not any protection. One thing in our favor was that after the first few days' storm we had very little wind. Burlap sacks were at a premium and saved our lives. We wrapped them about our shoes to keep from freezing, for there were no overshoes or rubbers to be had at the fort." Because of the continuous below-zero temperatures the huge pile of billets and slabs in the woodyard vanished long before winter's end, and the wagons going up Big Piney for cottonwood branches for the mules began bringing back logs for fuel. "We often had to saw wood," one enlisted man recalled, "for our heating stoves in the barracks until after tattoo at 9 P.M."
After weeks of poor diet, lack of proper exercise, and exposure to cold, the physical condition of officers and men began declining. "There was no place in the barracks to wash, and after the creeks were frozen over we could not take a bath until they thawed out the following spring." __ Scurvy cases began showing up at the hospital, and according to Frank Fessenden few men escaped the disease. "For lack of vegetables," Lieutenant Gordon noted, "the hospital was crowded to its limits by men down on their backs with scurvy and no special remedy other than drugs to prevent the entire garrison being afflicted. It was indeed a pitiable sight to see some of these poor soldiers so emaciated and weak and afflicted to that extent that their teeth were ready to drop out of their mouth."
Lieutenant-Colonel Wessells reported in his official record of events at the end of February: "Health of garrison not good, scurvy prevailing complaint." On March 17 he recorded: "Train with antiscorbutants arrived from Laramie, weather extremely cold, snow storms frequent, forage exhausted, wood, fuel, exhausted. Outdoor drill impossible." In April, cases of sickness were the highest for any month since establishment of the fort.
Morale collapsed of course, and with the coming of spring several men deserted. Some disappeared at night, over the stockade; others were more ingenious, Wessells recording in his May report that two men deserted with a party of Crow Indians, "painted and dressed in Indian costumes."
As bad as conditions were at Phil Kearny during that agonizing winter, the garrison was convinced that Fort C. F. Smith was worse off. From November 1866 until late March 1867, the fort on the Big Horn River was completely isolated, and a soldier writing from Laramie in midwinter reported pessimistically: "We have heard nothing from Fort C. F. Smith since the massacre, and we fear it has 'gone up.'"
However, when Wessells dispatched a small mail party to C. F. Smith in March "to see what had become of the men there," his messengers returned with the news that C. F. Smith had survived the winter far better than Phil Kearny. The soldiers there had lived for weeks on a basic diet of corn, but their provident quartermaster had stocked a supply of potatoes and cabbages-secured from Bozeman in the autumn—and these vegetables were sufficient to keep down scurvy. More than anything else, the men had missed their mail and tobacco.
Perhaps the single individual who suffered most acutely during the winter at Phil Kearny was not a victim of disease, malnutrition, exposure, or physical wounds. His was an ordeal of the spirit, a mental desolation. In January when Carrington was preparing to leave, Lieutenant-Colonel Wessells had requested that Captain Ten Eyck be temporarily detached from the 18th Infantry so that he might remain at the fort as commander of Company H, recently transferred to the newly formed 27th Infantry.
Exactly what happened to Ten Eyck after Carrington departed probably will never be known. Undoubtedly some of the new officers up from Laramie believed certain whispered allegations that Ten Eyck had acted in a cowardly manner when he was sent in relief of Fetterman. Some may have avoided his society from the time of their arrival; others may have shunned him because he had begun to drink heavily. Ten Eyck seemed to lose the confidence of the men under him; Wessells shifted him from H Company to F, then to A in February, and to C in March.
Late in the summer Ten Eyck transferred to Fort McPherson, rejoining the 18th Infantry, but the change brought no halt to his drinking. He reported for duty one day in a state of drunkenness so advanced that his commanding officer, Colonel William Dye, preferred charges against him. After Ten Eyck became sober, he promised to abstain thereafter from similar conduct, and the charges were withdrawn. A few days later he became drunk again, was charged with "conduct unbecoming an officer and a gentleman" and ordered to a general court-martial, which found him guilty.
When General Grant reviewed the court-martial proceedings he directed that the finding be set aside. "Captain Ten Eyck," Grant wrote, "will resume his sword and report for duty."
For Tenodor Ten Eyck this was but a temporary reprieve. He was plagued by chronic diarrhea, hemorrhoids, and rheumatism. And the whispers—real or imagined—followed him wherever he went. Five years after the Fetterman fight he quit the Army. Like Carrington he was a victim of rumors to which he had no opportunity of replying, but unlike Carrington he engaged in no campaign to clear his record, preferring a straitened civilian life to continuous abuse in the military.
## 3.
As Jim Bridger predicted in his May letter to the _Army and Navy Journal,_ Fort Phil Kearny was destined for more Indian troubles. In June, Red Cloud's hostiles began a steady harassment of the fort, with occasional darting raids against wood trains. In July they became so dangerous in the pinery that Wessells assigned full companies to guard the woodcutters.
For defense, fourteen wagon boxes were formed into an oval-shaped corral on an open plain near the pinery. Tents were pitched just outside the ring of boxes so that the soldiers and civilian wood choppers could remain overnight outside the protection of the fort.
Early on the morning of August 2, several hundred Indians appeared suddenly on the foothills north of this wagon-box corral. As the Indians approached, wood choppers and soldiers rushed to the corral to take up positions. In command was Captain James Powell, who had remained at Phil Kearny as an officer of the 27th Infantry Regiment, and as he watched the waves of hostiles riding swiftly up from the creek he must have recalled the recent fate of Fetterman's command.
Unlike Fetterman, however, Powell had the advantage of cover, and he also had a second advantage—each man of his command was armed with a new breech-loading Springfield rifle. Inside the corral were several carefully arranged boxes filled with several thousand rounds of ammunition. "Instead of drawing ramrods and thus losing precious time," said Sergeant Samuel Gibson, "we simply threw open the breech-blocks of our new rifles to eject the empty shell and slapped in fresh ones."
In their first assault the Indians were mounted, circling the soldiers' position, then charging in, expecting to overrun the wagon boxes when the defenders paused to reload. To the vast surprise of the attackers, the soldiers' fire was continuous. Many ponies went down, screaming in agony, and many braves died within a few yards of the wagon boxes.
Driven back, the hostiles dismounted, sent their surviving horses to the rear, stripped themselves, and returned to resume the fighting. "It chilled my blood," Sam Gibson said, on recalling his first sight of the naked Indians attacking on foot. "Hundreds and hundreds of Indians swarming up a ravine about ninety yards to the west of the corral... formed in the shape of a letter V... immediately we opened a terrific fire upon them.... Our fire was accurate, coolly delivered and given with most telling effect, but nevertheless it looked for a minute as though our last moment on earth had come. Just when it seemed as if all hope was gone, the Indians suddenly broke and fled."
According to Sergeant Gibson, Red Cloud was in the field that day directing the fighting from a ridge just out of rifle range. Years afterward Red Cloud said he lost the flower of his fighting warriors in the Wagon Box Fight.
That hostile forces of the Powder River country were operating in concert is indicated by the fact that on the day preceding the Wagon Box Fight, a similar attack was made against soldiers and civilians working in a hayfield near Fort C. F. Smith. As at Phil Kearny the men were prepared, having constructed a barricade of willow matting, and they were armed with the new repeating rifles. Three soldiers were killed, four wounded, in the Hayfield Fight; Indian losses were much heavier.
These two crushing defeats of the Indians came too late, however, to save the Montana Road. Fetterman's disaster had shaken the nation; its military and political effects ran so deep that once the machinery of appeasement was set in motion, the midsummer victories could not reverse the course of events. Fort Phil Kearny's days were numbered, and so were C. F. Smith's and Reno's.
In October, Captain Dandy, quartermaster at Fort Phil Kearny, met with a group of Sioux, Cheyenne and Arapaho leaders on Big Piney, five hundred yards from the fort. Here were held the first preliminary talks toward an agreement for eventual abandonment of the three forts and closing of the Montana Road. The Indians agreed to cease all hostilities if the soldiers would leave the country north of the Platte and west of the Black Hills.
Red Cloud, however, was not a participant in this first council, and when the recalcitrant Sioux leader was sent a second invitation to come to Laramie in the spring for further talks, he replied disdainfully that he would sign no treaty until the garrisons at all three forts were withdrawn.
In April 1868, a full-fledged peace commission gathered at Laramie, and after lengthy parleys, representatives from the Brûlés, Oglalas, Miniconjous, Yanktonais, and Arapaho signed the new treaty. Again Red Cloud stayed away, and again he sent down word that he would not sign a peace treaty until the forts were abandoned and the road closed through the Powder River country.
On May 19, Major-General Augur issued an order to abandon "the military posts of C. F. Smith, Phil Kearny and Reno, on what is known as the Powder River route.... The public property at Fort C. F. Smith will be sold at public auction, and that at Fort Phil Kearny and Reno—commencing and finishing first with the former—will be transferred to such of the lower posts as the chief quartermaster of the department shall direct." At last after two years of unyielding resistance, the enduring Sioux leader, Red Cloud, had won his war.
Dismantlement of the three forts began in early summer, and in August the last wagon train rolled out of Fort Phil Kearny. Records vary as to the exact date of abandonment—probably August 18 or 20—and there is also disagreement as to whether the soldiers or the Indians burned the fort. Some accounts say the soldiers put torches to the buildings; others say that Little Wolf led a party of warriors down from the hills and burned the fort before the departing wagons were out of sight on the Reno road. It must have been a cruel shock to Colonel Carrington when he learned that his beloved fort was gone. Under his exacting and proprietary eye, every post, board and shingle had been fashioned with mathematical exactness and placed in assigned positions to form his dream of an architecturally perfect fort. Now it was ashes.
By the end of August, the last soldiers had left Fort Reno, and the Montana Road was closed. On November 6, Red Cloud arrived at Fort Laramie, surrounded by a coterie of warriors. He had won everything he had fought for. Now, a conquering hero, he would sign the treaty.
For the first time in its history the United States Government had negotiated a peace which conceded everything demanded by the enemy and which exacted nothing in return. Through another stormy decade the Powder River country would belong to the Indians.
## 4.
In 1868, the year of the peace, Margaret Carrington published her story of Fort Phil Kearny, _Absaraka; Home of the Crows,_ basing it largely upon the daily journal of experiences which she had kept at the suggestion of General Sherman. Two years later, Colonel Carrington retired from active military service and became a professor of military science at Wabash College, Crawfordsville, Indiana. That same year, 1870, Margaret Carrington died.
One of the interested readers of _Absaraka_ was Frances Grummond, who after bidding the Carringtons farewell at Fort Laramie had continued her sad journey home to Franklin, Tennessee, to bury her husband and rejoin her family. In 1868, Frances traveled to Cincinnati to visit her sister, and there obtained a copy of the book, learning for the first time that the Carringtons were living in Indiana. When she later heard of the death of Margaret Carrington, she wrote a letter of condolence to the colonel. Ensuing correspondence between the two led to their marriage in 1871.
During the decade that Carrington spent at Wabash College, he continued his campaign to clear his reputation of all blame for the Fetterman Massacre. Even after Custer's disaster, which replaced the Fetterman affair in the public's memory, he persisted in bringing out new editions of his first wife's book (there were seven in all), revising and adding to the text so as to present his side of the story in minute detail.
In 1887, twenty years after the event, he at last persuaded the United States Senate to make public his official report and the transcript of his remarks before the commission of inquiry at Fort McPherson. After three strong demands from the Senate, these papers were finally dredged out of the cellar files of the Department of the Interior. With their publication, Carrington felt that he had secured at least a belated vindication.
By this late date many of the actors in the tragedy were dead or forgotten. Old military feuds, however, die hard. William Bisbee, for one, never forgave Carrington. Bisbee and Fetterman had been close friends during the Civil War, and Bisbee preferred to believe that Fetterman was blameless, and that Carrington had tried to shift the blame on Fetterman who was dead and could not reply. After leaving Phil Kearny in December 1866, Bisbee moved up in rank rapidly, becoming a brigadier-general in 1901. In later life he devoted considerable effort to defending Fetterman's reputation, even going so far as to gather statements from witnesses who contradicted Carrington's charge of disobedience, and placing these papers in the files of the Indian fighters' organization in Washington, the Order of Indian Wars.
The man who had done most to impugn Carrington's command abilities, General Philip St. George Cooke, waited until 1890 before admitting that he might have been wrong. "The country was greatly excited, and the government very urgent, so I endorsed the papers for transmission by one of my staff," Cooke explained to Carrington when the latter visited the general in Detroit. "I can do nothing more now than to express my deep pain at what transpired. My memory recalls nothing of the details, except that it was hurried off to General Sherman, and you must take my regrets as sincere, and my congratulations, that in the end you were fully vindicated."
## 5.
In 1908 all survivors of the Fort Phil Kearny garrison of 1866 were invited to attend a special Independence Day celebration in the town of Sheridan, Wyoming. The Carringtons, well along in years by then, responded with enthusiasm, and at Sheridan they were joined by a small group of former enlisted men, scarcely enough to form a corporal's guard. Among those present were S. S. Peters, Sam Gibson, William Murphy, and William Daley.
On July 3 these honored guests were taken to the scene of the Fetterman disaster, to a monument which was to be dedicated on the slope where the last troopers of the 2nd Cavalry had died on December 21, 1866. A large crowd assembled there, most of them young men and women from the new towns which had been founded in the area during the four decades since Fort Phil Kearny had blazed into oblivion. They came in the rackety open touring cars of the period, on horseback, and in buggies gaily bedecked with holiday bunting.
The former enlisted men wore plain civilian suits, but Carrington was dressed in his old blue uniform, every brass button of his frock coat freshly burnished. His wide-brimmed campaign hat was set squarely on his head; his white beard was trimmed to a neat military cut. Standing straight as a parade-ground soldier, he launched into a dedicatory address, an hour-long speech which was essentially a spirited defense of his actions at Fort Phil Kearny, embroidered with a few mild attacks upon his ancient critics.
Those few in the audience who had been with him in 1866 listened patiently, but the thoughts of most of them must have gone rushing back to that other time. Surely it all seemed like a strange dream to Frances Grummond Carrington. She sat in the seat of a buggy drawn up near the small stone monument, a sturdy little old lady in a starched white shirtwaist and a dark ruffled skirt. Her hat—a sort of toque with a magnificent plume—was set at a jaunty angle. She listened to the words of the man who was her husband, but he spoke of a time when the love of her life had been George Grummond, long dead, George Grummond who had died bravely on the rocky slope where the crowd—so lighthearted, so free of danger—listened now in the glaring summer sunlight.
Former Private William Murphy remembered the hard days of toil, the hot summer, the cold bitter winter, scanty rations, the constant dread of Indian attack. For Sam Gibson, the scene deepest seared into his memory was the day of the Wagon Box Fight, when he had watched the Indians charge and charge again, and each time they came on with their war cries he had said what he thought was his last prayer on earth. S. S. Peters remembered Crazy Woman's Fork, every detail of every minute of that long day-and-night surround which began with the ambush of Lieutenants Daniels and Templeton and ended with Chaplain White's dash for help. The high moment in William Daley's memory was the bright October day when he had raised the first flag above Fort Phil Kearny.
They waited respectfully until Carrington closed his speech, his voice showing weariness at the end, his shoulders stooping a little. When a bugler sounded taps and Carrington uncovered, someone stepped forward with a parasol to shield the old man's head from the sun.
As soon as the dedication formalities ended, the crowd moved to the site of the fort where a staff had been erected on the former parade ground for a flag-raising ceremony. The tall pole stood in the midst of a field of alfalfa growing lush and green from the waters of irrigation ditches. Few traces remained of the stockade, quartermaster yard, officers' quarters and barracks. It was as if the fort had never existed, had been only a dream common to those who remembered it.
Standing knee-deep in alfalfa, the survivors gathered at the base of the flagstaff, and William Daley—who had raised the first flag—was given the honor of raising this one. Afterward the colonel politely pointed out landmarks for the young spectators; the former enlisted men recalled a few incidents long forgotten. The guests of honor seemed to enjoy their day of glory.
But they knew it was all gone, the old harsh leathery life, the sweet zest of danger, the toil and uncertainty. It was all gone and soon they would be gone, too, with the vanished fort. Only a myth remained, a few dreamlike memories of the saga they had helped to create.
# _Bibliography_
_Army and Navy Journal,_ Volumes 4-5, 1866-68.
Birge, Julius C, _The Awakening of the Desert._ Boston, Richard G. Badger, 1912.
Bisbee, William H., "Items of Indian Service." Order of Indian Wars of the United States, _Proceedings,_ 1928.
Bisbee, William H., _Through Four American Wars._ Boston, 1931.
Boehmer, George A., Unpublished notebook. Bureau of American Ethnology, Smithsonian Institution. "Bradley Manuscript." _Contributions to the Historical Society of Montana,_ Vol. 8, 1917, 223-24.
Brady, Cyrus T., "Indian Fights and Fighters; the Tragedy of Fort Phil Kearny," _Pearson's Magazine,_ Vol. 11, 1904, 211-24.
Bratt, John, _Trails of Yesterday._ Lincoln, Nebraska, University Publishing Co., 1921.
Brown, Dee, and Martin F. Schmitt, _Trail Driving Days._ New York, Scribner's, 1952. Brown, Jesse, "The Freighter in Early Days." _Annals of Wyoming,_ Vol. 17, 1947, 112.
Bryant, Thomas J., "Harry S. Yount." _Annals of Wyoming,_ Vol. 3, 1925,164-75.
Burt, Struthers, _Powder River._ New York, Farrar and Rinehart, 1938.
Carrington, Frances C, _My Army Life._ Philadelphia, Lippincott, 1911.
Carrington, Henry B., _The Indian Question._ Boston, De Wolfe and Fiske, 1909.
Carrington, James B., "Across the Plains with Bridger as Guide." _Scribner's Magazine,_ Vol. 85, 1929, 66-71.
Carrington, Margaret Irvin, _Absaraka, Home of the Crows._ Philadelphia, Lippincott, 1878.
Cook, James H., _Fifty Years on the Old Frontier._ New Haven, Yale, 1923.
David, Robert B., _Finn Burnett, Frontiersman._ Glendale, Calif., A. H. Clark, 1937.
De Land, Charles E., "The Sioux Wars." _South Dakota Historical Collections,_ Vol. 15, 1930.
Dunn, J. P., _Massacres of the Mountains; a History of the Indian Wars of the Far West._ New York, Harper, 1886.
Ellison, R. S., "John 'Portugee' Phillips and His Famous Ride." _Old Travois Trails,_ Vol. 2, No. 1, 1941.
Evans, Major W. H., Letter to Major Roger Jones, May 21, 1866. _Annals of Wyoming,_ Vol. 9, 1932, 752-54.
Fox, George W., "Diary." _Annals of Wyoming,_ Vol. 8, 1932, 580-601.
Frackelton, William, "Prelude to Fred Newcomer." _Old Travois Trails,_ Vol. 2, No. 2, 1941.
Gatchell, T. J., "Events of the Year 1865." _Annals of Wyoming,_ Vol. 27, 1955, 142-58.
Gatchell, T. J., "Life of John Ryan." _Annals of Wyoming,_ Vol. 31, 1959, 48-52.
Glover, Ridgway, Letters to Editor of _Philadelphia Photographer,_ Vol. 3, 1866.
Gordon, David S., "The Relief of Fort Phil Kearny." _Journal of the Military Service Institutions of the U.S.,_ Vol. 49, 1911, 281-84.
Grinnell, George B., _The Fighting Cheyennes._ Norman, University of Oklahoma Press, 1956.
Guthrie, John, "The Fetterman Massacre." _Annals of Wyoming,_ Vol. 9, 1932, 714-18.
Hafen, LeRoy R., and F. M. Young, _Fort Laramie and the Pageant of the West._ Glendale, Calif., A. H. Clark, 1938.
Hebard, Grace R., "James Bridger." _The Frontier,_ Vol. 9, 1929, 145-48.
Hebard, Grace R., and E. A. Brininstool, _The Bozeman Trail._ Cleveland, A. H. Clark, 1922. 2 vols.
Hunton, John, "History of the Old Sutler Store Coins." _Fort Laramie Scout,_ Dec. 12, 1928.
Hunton, John, Letter to Grace Raymond Hebard, Fort Laramie, Wyoming, February 20, 1919. _The Frontier,_ Vol. 11, 1931, 176.
Jones, Hoyle, "Seth E. Ward." _Annals of Wyoming,_ Vol. 5, 1927, 5-12.
Murphy, William, "The Forgotten Battalion." _Annals of Wyoming,_ Vol. 7. 1930, 383-401.
Ostrander, Alson B., _An Army Boy of the Sixties._ Yonkers, N. Y., World Book Co., 1924.
Palmer, H. E., "History of the Powder River Indian Expedition of 1865." Nebraska State Historical Society, _Transactions,_ Vol. 2, 1887, 197-229.
Parry, Henry C, "Letters from the Frontier." _Annals of Wyoming,_ Vol. 30, 1958, 127-48.
"Peno Creek." _Annals of Wyoming,_ Vol. 4, 1926, 317.
Richardson, Warren, "Tribute to John Phillips." _Annals of Wyoming,_ Vol. 27. 955, 183-86.
Robinson, Doane, "A History of the Dakota or Sioux Indians." South Dakota Department of History, _Collections,_ Vol. 2, 1904.
Schreibeis, Charles D., "The Old Saw Mill." _Old Travois Trails,_ Vol. 1, No. 3, 1940.
Schreibeis, Charles D., "The Tragedy of Fort Philip Kearny." _Old Travois Trails,_ Vol. 1, No. 6, 1941.
Schreibeis, Charles D., "The Tragedy of Fort Philip Kearny." _Westerners' Brand Book,_ Denver Posse, Vol. 7, 1951, 337-62.
Shockley, Lieutenant P. M., "A Forgotten Hero; a Tale of Old Phil Kearny." _Quartermaster Review,_ Vol.12, July-August, 1932, 17-20.
Shockley, Lieutenant P. M., "Fort Phil Kearny, the Fetterman Massacre." _Quartermaster Review,_ Vol.11, May-June 1932, 27-32.
Story, Byron, "The First Cattle up from Texas." _American Cattle Producer,_ Vol. 20, No. 6, November 1938, 6-7.
U.S. Congress. 39th. 1st sess. House. _Wagon Road from Niobrara to Virginia City._ (Executive Document 58)Washington, D. C, 1866.
U.S. Congress. 39th. 2nd sess. House. _Message of the President._ (Executive Document l)Washington, D. C, 1867.
U.S. Congress. 40th. 1st sess. Senate. _Indian Hostilities._ (Executive Document 13)Washington, D. C, 1868.
U.S. Congress. 50th. 1st sess. Senate. _Indian Operations on the Plains._ (Executive Document 33) Washington, D. C, 1888.
U.S. Interior Department. _Annual Report on Indian Affairs, 1867._ Washington, D. C, 1868.
U.S. War Department, Department of the Platte. Letter Book No. 1, 1866. National Archives.
U.S. War Department, 18th Infantry Regiment. Muster Rolls and Record of Events, April 1866-July 1867. National Archives.
U.S. War Department, Fort Philip Kearny, Dakota Territory. Board of Survey Orders, September 1866-July 1867.National Archives.
U.S. War Department, Fort Philip Kearny, Dakota Territory. Post Returns, July 1866-July 1867. National Archives.
U.S. War Department. _The War of the Rebellion: A Compilation of the Official Records,_ Series I, Vol. 38, Pt. 1; Vol. 48, Pt. 2.
Vestal, Stanley, _Jim Bridger._ New York, Morrow, 1946.
Vestal, Stanley, _Warpath, the True Story of the Fighting Sioux._ Boston, Houghton Mifflin, 1934.
Watson, Elmo Scott, "The Bravery of Our Bugler Is Much Spoken Of." _Old Travois Trails,_ Vol. I, No. 6, 1941.
Wellman, Paul, _The Trampling Herd._ New York, Carrick and Evans, 1939.
Young, Otis E., _The West of Philip St. George Cooke, 1809-1895._ Glendale, Calif., A. H. Clark, 1955.
# _Notes_
_CHAPTER I: APRIL_
1. U S. Congress. 50th. 1st sess. Senate executive document 33, 1.
2. Murphy, 390.
3. U.S. Congress. 39th. 1st sess. House executive document 58.
4. U.S. War Dept. _The War of the Rebellion... Official Records,_ Ser. I, Vol. 48, Pt. 2, 356.
5. _Army and Navy Journal,_ October 13, 1866, Vol. 4, 125.
6. U.S. Congress. 50th. 1st sess. Senate executive document 33, 51.
7. _Ibid.,_ 53.
8. Young, 323-25.
9. U.S. Congress. 50th. 1stsess. Senate executive document 33, 2.
10. _Ibid.,_ 2-3.
Other sources used for background material: Birge, 188; Bisbee, "Items,"23; Brady, 213; M. Carrington, 263; Dunn, 479, 483; Grinnell, 208, 230; Hafen and Young, 351; Hebard and Brininstool, Vol. I, 342; Ostrander, 266-67; Palmer, 219, 221.
_CHAPTER II: MAY_
1. U.S. Congress. 50th. 1st sess. Senate executive document 33, 3.
2. Bisbee, _Through Four American Wars,_ 161.
3. M. Carrington, 42.
4. _Ibid.,_ 41.
5. Murphy, 383.
6. M. Carrington, 38.
7. J. Carrington, 70.
8. M. Carrington, 43.
9. Bisbee, 162-63.
10. J. Carrington, 71.
11. _Kearney Herald,_ January 6, 1866.
12. Bisbee, 162.
13. Palmer, 213.
14. Murphy, 383.
15. Bisbee, "Items of Indian Service," 26.
16. Hebard and Brininstool, II, 89-90.
17. Murphy, 383.
Other sources used for background material: Brady, 224; Parry, 131; U.S. War Dept., 18th Infantry Regiment, Muster Rolls and Record of Events, April-May1866;Vestal, _Jim Bridger,_ 224, 246.
_CHAPTER III: JUNE_
1. U.S. Congress. 50th. 1st sess. Senate executive document 33, 5.
2. M. Carrington, 59.
3. Bisbee, _Through Four American Wars,_ 163.
4. Murphy, 383.
5. M. Carrington, 46.
6. U.S. Congress. 50th. 1st sess. Senate executive document 33, 3.
7. M. Carrington, 70.
8. U.S. Congress. 50th. 1st sess. Senate executive document 33, 3-4.
9. _Ibid.,_ 4.
10. _Ibid.,_ 5.
11. _Ibid.,_ 6.
12. _Ibid.,_ 8.
13. M. Carrington, 76.
14. Hunton, John, "History of the Old Sutler Store Coins," _Fort Laramie Scout,_ Dec. 12, 1918.
15. U.S. Congress. 50th. 1st sess. Senate executive document 33, 18; M. Carrington, 79.
16. H. B. Carrington, 3; M. Carrington, 79-80.
17. F. Carrington, 124-25.
18. _Ibid.,_ 125.
19. Birge, 181.
20. Murphy, 384.
21. Bisbee, "Items of Indian Service," 26.
22. Glover, 239-40.
23. U.S. Congress. 50th. 1st sess. Senate executive document 33, 6.
24. M. Carrington, 80.
25. Dunn, 485.
26. M. Carrington, 94.
27. _Ibid.,_ 83.
28. _Ibid.,_ 84.
29. U.S. Congress. 50th. 1st sess. Senate executive document 33, 4-5.
30. Murphy, 384.
31. M. Carrington, 90.
32. _Ibid.,_ 91-92.
33. Gatchell, "Events of the Year 1865," _Annals of Wyoming,_ Vol. 27, 1955, 156.
34. Gatchell, "Life of John Ryan," _Annals of Wyoming,_ Vol. 31, 1959, 48-52.
35. Murphy, 384.
36. U.S. Congress. 50th. 1st sess. Senate executive document 33, 7; M. Carrington, 95.
37. Murphy.
38. U.S. Congress. 50th. 1stsess. Senate executive document 33.
Other sources used for background material: Brady, 211-213; David, 120; Evans, 752; Fox, 589; Hafen and Young, 341-50; Jones, 6; Ostrander, 101-114, 134-141; Schreibeis, "The Old Saw Mill," 21; U.S. Congress, 40th, 1stsess., Senate executive document 13, 61-63, 106-108, 134; U.S. War Dept., 18th Infantry Regt., Muster Rolls and Record of Events, June 1866; Vestal, _Jim Bridger,_ 249, 318.
_CHAPTER IV: JULY_
1. U.S. Congress. 50th. 1st sess. Senate executive document 33, 16.
2. Murphy, 385.
3. _Ibid._
4. M. Carrington, 25-26.
5. Bisbee, _Through Four American Wars,_ 168.
6. J. B. Carrington, 70.
7. M. Carrington, 101.
8. U.S. Congress. 50th. 1st sess. Senate executive document 33, 9.
9. M. Carrington, 101.
10. U.S. Congress. 50th. 1st sess. Senate executive document 33, 13.
11. _Ibid.,_ 9.
12. _Ibid._
13. Murphy, 386.
14. U.S. Congress. 50th. 1st sess. Senate executive document 33, 14.
15. M. Carrington 29, 107.
16. H. B. Carrington, 9.
17. M. Carrington, 112-15.
18. _Ibid.,_ 115.
19. U.S. Congress. 50th. 1st sess. Senate executive document 33, 10.
20. Hebard and Brininstool, I, 264.
21. U.S. Congress. 50th. 1st sess. Senate executive document 33, 12.
22. Murphy, 386.
23. Bisbee, "Items of Indian Service," 27.
24. Murphy, 386.
25. Gatchell, "Life of John Ryan," 49.
26. Bisbee, 27.
27. M. Carrington, 184-85.
28. Murphy, 386.
29. Ostrander, 149.
30. Murphy, 387.
31. U.S. Congress. 50th. 1st sess. Senate executive document 33, 11.
32. Hebard and Brininstool, II, 90.
33. Glover, 339.
34. F. Carrington, 74-75.
35. _Ibid.,_ 76.
36. _Ibid._
37. _Ibid.,_ 77-78.
38. Glover, 339.
39. F. Carrington, 78.
40. Hebard and Brininstool, II, 91.
41. F. Carrington, 79-80.
42. _Ibid.,_ 80.
43. Hebard and Brininstool, II, 92.
44. U.S. Congress. 50th. 1st sess. Senate executive document 33, 13.
45. Glover, 339.
46. Hebard and Brininstool, II, 94.
47. U.S. Congress. 50th. 1st sess. Senate executive document 33, 55.
48. Hebard and Brininstool, II, 93.
49. U.S. Congress. 50th. 1st sess. Senate executive document 33, 12-13.
50. _Ibid.,_ 13, 16.
Other sources used for background material: _Army and Navy Journal,_ Vol. 4, 215, 642; Brady, 215; Brown, 112-16; Bryant, 166, 173; Burt, 120, 123; David, 121; De Land, 65, 77; Dunn, 480, 486; Fox, 589; Palmer, 209; Schreibeis, "The Old Saw Mill," 10-11, 20; U.S. War Dept., 18th Infantry Regiment, Muster Rolls and Record of Events, July 1866; U.S. War Dept., Fort Philip Kearny, Dakota Territory, Post Returns, July 1866; U.S. War Dept., Dept. of the Platte, Letter Book No. 1, 1866; Vestal, _Jim Bridger,_ 252, 259, 261-68.
_CHAPTER V: AUGUST_
1. U.S. Congress. 50th. 1st sess. Senate executive document 33, 18.
2. U.S. War Dept., 18th Infantry Regiment. Muster Rolls and Record of Events, August 1866.
3. U.S. Congress. 50th. 1st sess. Senate executive document 33, 20.
4. Hebard, "James Bridger," 145-48.
5. _Army and Navy Journal,_ December 29, 1866, Vol. 4, 294.
6. Fox, 594.
7. F. Carrington, 97.
8. _Army and Navy Journal,_ November 3, 1866, Vol. 4, 169.
9. M. Carrington, 141-42.
10. U.S. War Dept., 18th Infantry Regiment. Muster Rolls and Record of Events, August 1866.
11. U.S. Congress. 50th. 1st sess. Senate executive document 33, 44.
12. Boehmer, George A., Unpublished notebook. Bureau of American Ethnology, Smithsonian Institution.
13. U.S. Congress. 40th. 1st sess. Senate executive document 13, 36.
14. U.S. Congress. 50th. 1st sess. Senate executive document 33, 17.
15. _Ibid.,_ 17-18.
16. _Army and Navy Journal,_ November 17, 1866, Vol. 4, 198.
17. Hebard and Brininstool, I, 286.
18. Glover, 367-69.
19. U.S. Congress. 50th. 1stsess. Senate executive document 33, 18, 48.
Other sources used for background material: Dunn, 487, 503; Shockley, "Fort Phil Kearny,"28; U.S. War Dept., Fort Philip Kearny, Post Returns, August 1866.
_CHAPTER VI: SEPTEMBER_
1. U.S. Congress. 50th. 1st sess. Senate executive document 33, 23.
2. U.S. War Dept., Fort Phil Kearny, Dakota Territory. Board of Survey Orders, September 1866.
3. U.S. Congress. 50th. 1st sess. Senate executive document 33, 22.
4. _Ibid.,_ 23.
5. U.S. War Dept., Fort Phil Kearny, Dakota Territory. Post Returns, December 1866; Hebard and Brininstool, II, 98.
6. Bratt, 87-94.
7. U.S. Congress. 50th. 1st sess. Senate executive document 33, 24.
8. _Ibid.,_ 28.
9. _Ibid.,_ 22.
10. Gatchell, "Life of John Ryan," 50.
11. Hebard and Brininstool, II, 96-97.
12. Bisbee, _Through Four American Wars,_ 170.
13. Gatchell, 50.
14. U.S. Congress. 50th. 1st sess. Senate executive document 33, 24.
15. F. Carrington, 85-86.
16. U.S. Congress. 50th. 1st sess. Senate executive document 33, 30.
17. _Ibid.,_ 23-25.
18. F. Carrington, 90.
19. U.S. War Dept., Dept. of the Platte. Letter Book No. 1, 1866.
20. F. Carrington, 121.
21. U.S. Congress. 50th. 1st sess. Senate executive document 33, 25.
22. U.S. War Dept., 18th Infantry Regiment. Muster Rolls and Record of Events, September 1866.
23. U.S. Congress. 50th. 1st sess. Senate executive document 33, 28-29.
24. Hebard and Brininstool, I, 99.
25. U.S. Congress. 50th. 1st sess. Senate executive document 33, 25.
26. _Ibid.,_ 25-27.
27. M. Carrington, 159-60.
28. U.S. Congress. 50th. 1st sess. Senate executive document 33, 29.
Other sources used for background material: Bisbee, "Items," 28; David, 123-124; Dunn, 487; Ostrander, 255; Schreibeis, "Tragedy of Fort Phil Kearny," _Old Travois Trails,_ 6; Shockley, "Fort Phil Kearny," 28; Vestal, _Jim Bridger,_ 266-67.
_CHAPTER VII. OCTOBER_
1. U.S. Congress. 50th. 1st sess. Senate executive document 33, 32.
2. U.S. War Dept., Fort Philip Kearny, Dakota Territory. Board of Survey Orders, October 1866.
3. U.S. Congress. 50th. 1st sess. Senate executive document 33, 32.
4. _Ibid.,_ 31.
5. _Ibid.,_ 46.
6. U.S. Congress. 40th. 1st sess. Senate executive document 13, 31.
7. U.S. Congress. 50th.1st sess. Senate executive document 33, 32.
8. Story, 6-7.
9. Wellman, 95-100; Brown and Schmitt, 179-181.
10. U.S. Congress. 50th. 1st sess. Senate executive document 33, 32-33.
11. _Ibid.,_ 32.
12. M. Carrington, 172.
13. Murphy, 386.
14. M. Carrington, 151.
15. _Ibid.,_ 152-56.
16. F. Carrington, 116-17.
17. U.S. War Dept., 18th Infantry Regiment. Muster Rolls and Record of Events, October 1866.
18. M. Carrington, 156.
Other sources used for background material: _Army and Navy Journal,_ Vol. 4, 214, 236; Brady, 217; Burt, 120; Hebard and Brininstool, I, 289, 293; II, 94; Ostrander, 255; Shockley, "Fort Phil Kearny,"27-32; U.S. War Dept., Fort Philip Kearny, Dakota Territory, Post Returns, October 1866; Young, 345-49.
_CHAPTER VIII: NOVEMBER_
1. U.S. Congress. 50th. 1st sess. Senate executive document 33, 47.
2. Bratt, 96-98.
3. U.S. War Dept. _The War of the Rebellion... Official Records,_ Ser. I, Vol. 38, Pt. I, 94, 527, 558, 560, 577-78. 586-88.
4. U.S. Congress. 50th. 1st sess. Senate executive document 33, 34.
5. _Ibid.,_ 20-21.
6. _Ibid.,_ 21.
7. M. Carrington, 171; Hebard and Brininstool, I, 305.
8. F. Carrington, 120.
9. _Ibid.,_ 96.
10. U.S. Congress. 50th. 1st sess. Senate executive document 33, 33; F. Carrington, 111.
11. _Army and Navy Journal,_ November 3, 1866, Vol. 4, 169.
12. U.S. Congress. 50th. 1st sess. Senate executive document, 33, 34.
13. Murphy, 391.
14. Bisbee, _Through Four American Wars,_ 172-73.
15. F. Carrington, 122.
16. U.S. Congress. 50th. 1st sess. Senate executive document 33, 34-35.
17. _Ibid.,_ 36.
Other sources used for background material: Bisbee, "Items," 29-30; "Bradley Manuscript," 223-24; Burt, 127; Gatchell, "Life of John Ryan," 51; Ostrander, 137, 191-95, 260; U.S. Congress, 40th, 1st sess., Senate executive document 13, 41-42, 63; U.S. War Dept., Dept. of the Platte, Letter Book No. 1, 1866; U.S. War Dept., 18th Infantry Regiment, Muster Rolls and Record of Events, November 1866; U.S. War Dept., Fort Philip Kearny, Dakota Territory, Post Returns, November 1866; Vestal, _Jim Bridger,_ 273.
_CHAPTER IX: DECEMBER_
1. U.S. Congress. 50th. 1st sess. Senate executive document33, 49.
2. _Ibid.,_ 47.
3. U.S. Congress. 39th. 2nd sess. House. _Message of the President_ (Executive document 1) Washington, D. C, 1867.
4. U.S. Congress. 50th. 1st sess. Senate executive document 33, 37.
5. _Ibid._
6. _Ibid.,_ 38.
7. Bisbee, "Items," 29.
8. U.S. Congress. 40th. 1st sess. Senate executive document 13, 37-38.
9. _Ibid.,_ 14.
10. Guthrie, 718.
11. _Ibid._
12. Murphy, 389; Hebard and Brininstool, II, 99.
13. F. Carrington, 134.
14. M. Carrington, 194.
15. Vestal, _Jim Bridger,_ 270.
16. _Old Travois Trails,_ Vol. 3, No. 3, 1942, 65.
17. Bisbee, _Through Four American Wars,_ 176.
18. U.S. Congress. 50th. 1st sess. Senate executive document 33, 36-38.
19. _Ibid.,_ 39; F. Carrington, 135.
20. U.S. Congress. 40th.1st sess. Senate executive document13, 38; U.S. Congress.50th. 1st sess. Senate executive document 33, 39.
21. U.S. Congress. 50th. 1st sess. Senate executive document 33, 39.
22. Vestal, _Jim Bridger,_ 273; M. Carrington, 202.
23. U.S. Congress. 50th. 1st sess. Senate executive document 33, 40.
24. F. Carrington, 143.
25. _Ibid.,_ 143-44.
26. U.S. Congress. 50th. 1st sess. Senate executive document 33, 44.
27. Grinnell, 243-44.
28. U.S. Congress. 50th.1st sess. Senate executive document 33, 45.
29. U.S. Congress. 40th. 1st sess. Senate executive document 13, 64.
30. Murphy, 389-90.
31. U.S. Congress. 40th. 1st sess. Senate executive document 13, 15.
32. U.S. Congress. 50th. 1st sess. Senate executive document 33, 45.
33. F. Carrington, 146.
34. U.S. Congress. 50th. 1st sess. Senate executive document 33, 46.
35. _Ibid._
36. Murphy, 390.
37. U.S. Congress. 40th. 1st sess. Senate executive document 13, 15.
38. Murphy, 390-91.
39. U.S. Congress. 50th. 1st sess. Senate executive document 33, 41.
40. Guthrie, 717.
41. U.S. Congress. 40th.1st sess. Senate executive document 13,15.
42. U.S. Congress. 50th. 1st sess. Senate executive document 33, 45.
43. F. Carrington, 146-47.
44. Hebard and Brininstool, II, 101-102.
45. J. Carrington, 71.
46. Hebard and Brininstool, II, 101-102.
47. F. Carrington, 149.
48. U.S. Congress. 50th. 1st sess. Senate executive document 33, 49-50.
49. U.S. Congress. 40th. 1st sess. Senate executive document 13, 35.
50. Hunton, John, Letter to Grace R. Hebard. _The Frontier,_ Vol. II, 1931, 376.
51. U.S. Congress. 50th. 1st sess. Senate executive document 33, 44.
52. Shockley, "A Forgotten Hero," 17-20; Burt, 128-30; Ostrander, 168.
53. Ostrander, 169.
54. H. B. Carrington, 8.
55. F. Carrington, 151.
56. _Ibid.,_ 152.
57. _Ibid.,_ 153-54.
58. David, 129.
59. Guthrie, 717.
60. H. B. Carrington, 16.
61. David, 127.
62. _Army and Navy Journal,_ April 13, 1867, Vol. 4, 546.
63. U.S. Congress. 40th. 1st sess. Senate executive document 13, 65.
64. Guthrie, 717.
65. F. Carrington, 155.
66. David, 129.
67. F. Carrington, 155, 158.
68. U.S. Congress. 40th. 1st sess. Senate executive document 13, 35.
69. _Ibid.,_ 24-25.
70. Gordon, 281.
Other sources used for background material: "Bradley Manuscript," 223; Brady, 219-22; Cook, 229; Dunn, 492-99; Ellison, 5-15; "Peno Creek," 317-18; Richardson, 185-86; Robinson, 360, 363; U.S. War Dept., 18th Infantry Regiment, Muster Rolls and Record of Events, December 1866; U.S. War Dept., Fort Philip Kearny, Dakota Territory, Post Returns, December 1866; Vestal, _Warpath, the True Story of the Fighting Sioux,_ 51-68.
_CHAPTER X: JANUARY_
1. U.S. Congress. 50th. 1st sess. Senate executive document 33, 49.
2. U.S. Congress. 40th. 1st sess. Senate executive document 13, 36.
3. U.S. Congress. 50th. 1st sess. Senate executive document 33, 42-43.
4. _Ibid.,_ 39-41.
5. F. Carrington, 164.
6. U.S. Congress. 40th. 1st sess. Senate executive document 13, 28.
7. _Ibid.,_ 29.
8. _Ibid._
9. Gordon, 281-84.
10. _Ibid._
11. U.S. Congress. 50th. 1st sess. Senate executive document 33, 44.
12. _Ibid.,_ 49.
13. F. Carrington,187-89.
Other sources used for background material: _Army and Navy Journal,_ Vol. 4, 411, 413; "Bradley Manuscript,"223-24; Brady, 217; M. Carrington, 211-43; Hafen and Young, 353; Hebard and Brininstool, I, 330; Robinson, 371; Shockley, "Fort Phil Kearny,"28; U.S. War Dept., 18th Infantry Regiment, Muster Rolls and Record of Events, December 1866-January 1867.
_CHAPTER XI: AFTERMATH_
1. M. Carrington, 220-21.
2. U.S. Congress. 40th. 1st sess. Senate executive document 13, 8-9.
3. _Ibid.,_ 16.
4. _Army and Navy Journal,_ January 5, 1867, Vol. 4, 317.
5. U.S. Congress. 40th. 1st sess. Senate executive document 13, 40.
6. _Army and Navy Journal,_ February 9, 1867, Vol. 4, 397.
7. U.S. Congress. 40th. 1st sess. Senate executive document 13, 7.
8. _Ibid.,_ 55.
9. U.S. Congress. 50th. 1st sess. Senate executive document 33, 50.
10. _Ibid.,_ 50.
11. _Army and Navy Journal,_ June 29,1867, Vol. 4, 714-15.
12. U.S. Congress. 40th. 1st sess. Senate executive document 13, 61-66.
13. _Army and Navy Journal,_ February 16, 1867, Vol. 4, 406.
14. Shockley, "Fort Phil Kearny," 32.
15. Murphy, 392.
16. Gordon, 283.
17. David, 135.
18. Shockley, 32.
19. Hebard and Brininstool, II, 105.
20. Murphy, 392.
21. _Ibid._
22. Shockley, 32.
23. _Ibid._
24. Gordon, 283.
25. U.S. War Dept., Fort Philip Kearny, Dakota Territory. Post Returns, March 1867.
26. _Ibid.,_ May 1867.
27. _Army and Navy Journal,_ February 16, 1867, Vol. 4, 406.
28. Murphy, 392.
29. _Army and Navy Journal,_ May 2, 1868, Vol. 5, 582.
30. Hebard and Brininstool, II, 54.
31. _Ibid.,_ 66-67.
32. _Army and Navy Journal,_ May 30, 1868, Vol. 5, 646.
33. Carrington, H. B., Letter to George Coutant, June 6, 1902. (Hebard and Brininstool, I, 340-41.)
Other sources used for background material: Bisbee, "Items," 31-32; Bisbee, _Through Four American Wars,_ 175; Brady, 382; Burt, 139; F. Carrington, 217; De Land **,** 203; Dunn **,** 500-04; Frackelton, 24; Grinnell, 244; Guthrie, 718; U.S. Interior Department, _Annual Report on Indian Affairs,_ 1867, 231; Ù. S. War Dept., 18th Infantry Regiment, Muster Rolls and Record of Events, February-July 1867; Vestal, _Jim Bridger,_ 292-94.
# _Index_
A | B | C | D | E
F | G | H | I | J
K | L | M | N | O
P | R | S | T
U | V | W | Y
Absaraka,
_Absaraka; Home of the Crows_ , 225-226
Adair, John, , , , 57-59, 68-69, , 108-109, , , , , ,
Alder Gulch, Mont.,
Almstedt, Henry, , ,
Amusements, 99-100, ,
Arapaho Indians, 13-15, , , 109-110, , 121-122, , , 148-149, 170-173, , , ,
Arms and ammunition, , , , , 62-63, , 87-88, , , 118-119, , 135-136, , , , , 174-175, , 186-187, , , 223-224
_Army and Navy Journal_ , , , , 215-217,
Arnold, Wilbur F., , , ,
Arrison, Henry, , ,
Augur, Christopher C, ,
Bailey, George M., 56-57
Bailey, William, , , , ,
Band, Regimental, _see_ Eighteenth Infantry Regiment, Regimental band
Barnes, John H., , 140-141
Baxter Springs, Kans.,
Beauvais, G. P.,
Beauvais Ranche, Nebr.,
Beckwourth, James P., , 97-98,
Berger, W. H.,
Big Horn Mts., , , , , , , , , , , , , , , ,
Big Horn River, , , ,
Big Nose,
Big Piney, 66-67, 69-71, , 76-77, , , 114-115, , , , , , 151-152, , 170-171, , , , 184-186, 219-220,
Bingham, Horatio S., , 157-165, 167-168, ,
Bingham, Stella,
Bisbee, Eugene, ,
Bisbee, William H., 20-21, , , , , 45-53, 65-78, , , , 114-115, 129-130, , , 153-156, 167-168,
Bisbee, Mrs., , , , ,
Bissell, Ephraim C.,
Black Hills, ,
Black Horse, 68-69, 72-77, , 82-83,
Black Shield, ,
Bogy, Lewis V.,
Borsman, Alphonse,
Bowers, G. R., 164-165, 167-168, ,
Bozeman, John,
Bozeman, Mont.,
Bozeman Road, _see_ Montana Road
Bradford, Daniel,
Bradley, James H., 84-86, , , ,
Brannan, James J., , , , ,
Bratt, John, , 146-147
Bridger, James, , 26-27, 35-36, , , 48-50, 53-55, 64-67, 69-70, , , , 97-98, , 117-118, , 148-149, 151-152, , , , 216-217,
Bridger's Ferry, , , , , ,
Brooks, William H.,
Brough, John C, 194-195
Brown, Frederick H., , , , , , 63-64, , 92-93, , 102-103, 107-108, 111-113, , , 125-126, 131-132, , 153-154, , , , 170-171, , , , , ,
Brulé Indians, 38-40, ,
Buelon, Surgeon,
Buffalo Tongue,
Buffaloes, , , , 210-211
Buford, N. B.,
Bullock, W. G., 41-42
Burke, Thomas,
Burnett, Finn, 197-198, ,
Burrowes, Thomas B., , 82-83, 90-91,
Caldwell, A., 107-108
California Crossing,
Camp Douglas, Utah,
Camp Mitchell, Nebr.,
Carmichael, Sarah F.,
Carrington, Frances Grummond, 115-116, 118-119, , , , 151-152, , 165-166, , , , , , 199-201, , 209-211, 225-226,
Carrington, Harry, ,
Carrington, Henry Beebe, early life, 16-17; at Ft. Kearney, 17-20, , , ; en route to Ft. Phil Kearny, 26-28; 32-33, , , 48-50, 53-54, 64-66; at Ft. Sedgwick, 29-30; at Ft. Laramie, 38-48, 212-213; at Ft. Reno, 55-64; selects fort site, 67-69; builds Ft. Phil Kearny, 70-83, 90-139; assumes command of post, ; at Ft. Phil Kearny, , , 146-157, 166-206; celebrates completion of fort, 139-145; pursues Indians, 157-158, 160-166; relieved of command, 206-209; march to Ft. Casper, 209-211; transferred to Ft. McPherson, 212-213; blamed for disaster, 213-214; absolved from blame, ; at Ft. McPherson, , , , ; retires to Wabash College, 225-226; weds Frances Grummond, ; returns for celebration, 227-229
Carrington, James, , , , , , , ,
Carrington, Margaret I., , 22-24, 32-33, 35-36, , 43-44, , , 54-56, , , , , , , 140-141, , , , 209-210, 225-226
Carter, Leviticus, 110-111, ,
Cavalry, _see_ Second Cavalry Regt.
Cheyenne Indians, , , , , 47-48, , 68-69, 72-77, , , , 126-127, , , 171-173, 178-189, , ,
Chimney Rock,
Civil War, , , , , , , , 80-81, , , , , , , 150-151, , , 166-167, , , ,
Clark, Sgt.,
Clear Fork, , 82-83
Cloud Peak,
Colorado Terr., , ,
Connor, Patrick E., 14-15, , , ,
Cooke, Philip St. George, 19-20, , 94-95-103-104, , 116-118, , , , , , 156-157, 192-193, , 206-209, , 226-227
Court House Rock,
Crazy Horse, ,
Crazy Woman's Creek, 64-65, 75-76, 210-211; fight at, 85-90, ,
Crow Indians, , 50-51, 75-76, , , , 148-149, 151-152, , , ,
Curry, Samuel, , , , ,
Custer, George A., ,
Custer Battlefield,
Custer Massacre, , ,
Daley, William, 140-141, , 227-228
Damme, Peter, ,
Dandy, George B., 204-205, ,
Daniels, Napoleon H., 84-86, , , ,
Dennison, William,
Dillon, George, ,
Dillon, Thomas, ,
D'Isay, Isaac, ,
Donaldson, Joe, 68-69, ,
Donovan, John, ,
Dow, George,
Dull Knife, , ,
Dye, William,
Eighteenth Infantry Regiment, 16-17, , , , , , , , ,
1st battalion, , , , , , , , ,
2nd battalion, , , , , , , , , , , , , , , , , 90-91, , , , , , ,
3rd battalion, , , ,
Regimental band, , , , , , , 98-99, , , , ,
Fessenden, Frank, , , 88-92, , , 112-113, , , 190-191, 219-220
Fessenden, Mrs., , ,
Fetterman, William J., 11-13, , , 147-148, 150-153, 155-157, 160-163, 165-168, 170-181, 184-190, , , 217-218, , 223-224,
Fetterman Massacre, , , , , 100-102, , , 178-203, 205-207, 212-213, 215-218, , , 226-227
Fisher, Isaac, , , 179-181, ,
Fleet Foot, ,
Food supplies, , , , 80-82, 100-101, 107-108, 218-221
Fort Benton, ,
Fort Bridger,
Fort C. F. Smith, , 103-105, , , , 132-133, , , , , , , , , 223-224
Fort Casper, , , 206-207, ,
Fort Connor, _see_ Fort Reno
Fort Hall,
Fort Kearney, , 20-25, , , , , , , , ,
Fort Laramie, , , , , , , , 35-48, , 79-80, , , 97-98, 103-104, , 115-116, , 132-133, 135-136, 146-149, , 155-156, , 169-170, 192-194, 200-203, 206-208, 212-213, 215-216, 218-221, 224-225
Fort Leavenworth, 22-23,
Fort McPherson, , , , , 212-213, , ,
Fort Reno, 14-16, , , , 51-64, , 74-75, 80-84, 89-91, , , , , , , 132-133, 135-136, , , , , 206-209, , 217-219, 224-225
Fort Sedgwick, 28-30,
Fort Worth, Tex.,
Fox, George W., 98-99
Friend, John, ,
Fuller, Pvt.,
"Galvanized Yankees," , 56-57
Garrett, Sgt.,
Gazzous, Louis, , , , 78-79,
Gazzous, Mrs., 78-79
Gibson, Samuel, , 227-228
Gilchrist, Allando,
Glover, Ridgway, , , , , ,
Goose Creek, 66-67, , ,
Gordon, David, 202-203, ,
Grant, Ulysses S., , 192-193, , , ,
Grasshoppers,
Gregg, Thomas J.,
Gregory, J. B., , , ,
Gros Ventres,
Grummond, Frances, _see_ Carrington, Frances Grummond
Grummond,George W., 115-116, , 150-151, , , 160-169, 174-180, 192-193, , 199-200, ,
Guthrie, John, , , 197-199
Haas, Herman,
Harman, D.,
Hayfield Fight, 223-224
Haymond, Henry, , , 58-59, 63-64, 76-80, , 96-97
Hazen, William B., 104-106, log, , ,
Helena, Mont.,
Henning, James,
High Back Bone,
Hill, James, ,
Hines, C. M., , , , , 183-185, 188-189,
Holladay, Ben,
Horseshoe Station, , 193-194, ,
Horton, Samuel M., , , , , , , , ,
Horton, Mrs., , , ,
Hudson's Bay Co., ,
Hugas, John,
Hughes, Robert P.,
Hunkpapas, 148-149
Hunton, John, ,
Indian Bureau, _see_ U.S. Indian Affairs, Office of
Indians, Plains, 17-18, , , , 38-39, 41-46, , , , , , , , 186-188, 195-196, ; _see also_ by tribes
Infantry, _see_ Eighteenth Infantry; Twenty-seventh Infantry
Irving, Washington,
Johnson, Andrew,
Johnson, Peter, 113-114
Julesburg, Colo., ,
Kansas,
Kearney City, Nebr.,
_Kearney Herald_ ,
Kearny, Philip, ,
Kearny, Stephen W.,
Kinney, Jefferson T., 100-101, 140-141,
Kinney, Nathaniel C, , , ,
Kirkendall, Hugh, ,
Kirtland, Thaddeus, , , , , , ,
Kountz, Herman,
Lake De Smet, , ,
Lang, Augustus, , ,
Laramie River, ,
Legrow, Corp.,
Leighton, A. C, 58-59,
Lincoln, Abraham, ,
Little Chief,
Little Piney, 66-67, 69-72, 76-77, , , , 114-115, , 125-126, 128-129, ,
Little Wolf, ,
Lodge Trail Ridge, , , 160-161, , , , 174-177, , ,
Lodgepole Canyon,
Lodgepole Creek, Nebr.,
Lone Tree, Nebr.,
Louis Ranche, Nebr., 32-33
McCleary, Surgeon, ,
McClellan, George B.,
McGuire, James,
McLaren, Robert N.,
Maddeon, Thomas, , 174-175
Mahan, Dennis H.,
Makhpia-sha, _see_ Red Cloud
Marr, Capt., , ,
Massacre Hill,
Mathews, Surgeon,
Matson, Winfield Scott, 120-122, ,
Maynadier, Henry E., 39-40,
Medical supplies, 136-137
Medicine Man,
Merriam, H.,
Metzger, Adolf, , , 198-199
Miniconjous, , , 179-180, ,
Minnesota, ,
Missouri River,
Mitchell Pass, 34-35
Montana Road, 12-15, , , , , , , , , , , , , 102-103, , 130-131, , , , , , 176-179, 183-187, , , , , 224-225
Montana Terr., 13-16, , , , , , , , 134-135, 137-139, , , , , ,
Mountain District, Dept. of the Platte, 18-19, , , , , , , 75-76, , , , , 131-132, ; abolition of, 133-134
Mud Springs, Nebr., 33-34
Murphy, William, , 29-30, , , , , , , , , 77-79, , , , 184-185, 187-188, , 219-220, 227-228
Mutilations by Indians, , , , 188-191, , 198-199
Nebraska Terr., 32-34, , , 128-129, ,
Nine-Mile Ranche,
Niobrara River,
Norris, Charles,
North, Bob, 121-122,
Oberly, Christian,
O'Fallon's Bluffs, Nebr.,
Oglalas, 39-40, , , , 171-172, , , , ,
Old Little Dog,
Omaha, Nebr., , , , , , , , , , , , , , 168-169, , , , ,
Order of Indian Wars,
Oregon Trail, , ,
Ostrander, Alson,
Ould, Surgeon, ,
Overland Mail, ,
Palmer, Innis N., 202-203, 207-208
Parker, E. S.,
Pawnee Indians, , , ,
Peale, James,
Pegaleshka, _see_ Spotted Tail
Peno Creek, , , , 77-79, , , 172-173, 177-179, , 183-185, 187-188, ,
Peno Head,
Peters, S. S., , 86-87, , ,
_Philadelphia Photographer_ , , ,
Phillips, George, 101-102
Phillips, John (Portugee), , ; his ride, 193-194, 201-203,
Phisterer, Frederick, , 34-35, , , 50-51, , 76-77, , , ,
Photography on the frontier, 46-47, , , , , 113-115
Pilot Hill, 70-71, , , , 124-125, , , , , ,
Piney Island, , 100-102, , 131-133, , ,
Platte, Dept. of the, , , , , , , ; _see also_ Mountain District, Dept. of the Platte
Platte River, , 28-32, 35-37, , , 48-50, 53-54, , 84-92, , ,
Plum Creek, Nebr.,
Pope, John, ,
Powder River, , , , , , , , , 45-46, , , 57-60, , 74-75, , , , , , , 223-225
Powell, James W., , 153-155, , 167-169, 172-174, 196-197, 222-223
Prairie Dog Creek, _see_ Peno Creek
Proctor, J. L., , , , , ,
Pumpkin Buttes, ,
Ranches, Road, , 32-33,
Red Cloud, , , 43-45, , 74-75, 77-80, , , , , , , , , 171-172, , , , , , 222-225
Red Leaf,
Reid, Edwin,
Roman Nose,
Rover, Pvt., _see_ Bissell, Ephraim C.
Ryan, John, , , 113-115
Sage Creek,
St. Geiger, Dominic,
Sample, Archibald, , , 185-187,
Sanborn, J. B., 216-218
Sand Creek Massacre,
Sawmills, , 34-35, , , , ,
Sawyer, James A.,
Scotts Bluff, Nebr., 34-35, ,
Scurvy, , 220-221
Second Cavalry Regt., , , , 107-108, , , , ,
Co. C, , , , 160-165, , , 177-182, , , , ,
Shanks, John T.,
Sheridan, Wyo.,
Sherman, William T., , , , , , , ,
Shoshoni Indians,
Sioux City, Iowa,
Sioux Indians, 13-15, 18-19, , , , 47-49, , 54-55, , 74-77, 79-80, 82-83, 85-90, , , 101-102, , 108-110, , , 126-127, , , , , 160-166, 172-173, 178-189, , 222-224
Sissetons,
Skinner, Prescott M., , 86-87
Smith, Alexander,
Smith, Patrick, 124-126
Smith, W. B. C, ,
Sorrel Horse, 171-172
Spotted Tail, 39-40, 44-45,
Square, F. M.,
Standing Elk, 38-39, ,
Stanton, Edwin M.,
Stead, Jack, , , 67-69, 72-74,
Stone's River, Battle of,
Story, Nelson, 134-138
Story, Wyo.,
Stuart, J. E. B.,
Sullivant, Margaret I., _see_ Carrington, Margaret I.
Sullivant Hills, , , , , 175-176,
Sally, Alfred,
Sutlers' stores, 41-42, , ,
Tanner, Milo B.,
Taylor, E. B., , 42-43, ,
Templeton, George M., 83-86,
Ten Eyck, Tenodor, 12-13, 28-29, , , , , , 70-71, , , , 111-112, , , 131-132, 147-148, , 184-190, 195-196, 221-222
Texas,
Tongue River, , 65-67, , , , , , 126-127, , 148-149, , 170-172, , , 205-206,
Trails, 13-14, , , ,
Treaties, , , , , , , , , , 224-225
Twenty-seventh Infantry Regt., , , 221-222
Two Moons, ,
U.S. Indian Affairs, Office of, , , 213-215
U.S. Interior Department, , , ,
U.S. Volunteers, _see_ "Galvanized Yankees"
U.S. War Department, , , , , , 213-215
Van Kirk, Horace,
Van Voast, James, , ,
Virginia City, Mont., 13-15, , , , ,
Wabash College, 225-226
Wagon Box Fight, 222-223,
Wallace, William, 89-90
Wands, Alexander H., 83-84, 86-90, 93-94, , , , 129-130, , , , 173-175, 184-185, , ,
Wands, Mrs., , , , ,
Wands, Robert, ,
Ward, Seth, 41-42
Wasser, John,
Wessells, Henry W., , 206-208, 218-222
Wheatley, James, , , , 179-181, , 199-200
Wheatley, Mrs., ,
White, David, , 87-90, , , , , , ,
White Bull, ,
White Elk,
Williams, Henry, 26-27, , ,
Winnebago scouts, , , ,
Wistar, Thomas,
Yanktonai,
Yellow Eagle,
Yellow-Face,
Yellowstone River, , , , ,
Young-Man-Afraid-of-His-Horses, ,
Colonel Henry B. Carrington
ARCHIVES AND WESTERN HISTORY DEPT., UNIVERSITY OF WYOMING LIBRARY
Margaret Carrington, wife of Col. Carrington
ARCHIVES AND WESTERN HISTORY DEPT., UNIVERSITY OF WYOMING LIBRARY
Frances (Grummond) Carrington
ARCHIVES AND WESTERN HISTORY DEPT., UNIVERSITY OF WYOMING LIBRARY
Captain William J. Fetterman
NATIONAL ARCHIVES
Red Cloud
BUREAU OF AMERICAN ETHNOLOGY, THE SMITHSONIAN INSTITUTION
Captain Frederick Brown
Lieutenant George W. Grummond
UNIVERSITY OF ILLINOIS LIBRARY
Captain Tenodor Ten Eyck
NATIONAL ARCHIVES
Lieutenant. Grummond's hand-to-hand running fight
From a drawing by Charles Schreyyogel, _Pearson's Magazine_ , 1904
General Philip St. George Cooke
U.S. SIGNAI.CORPS PHOTO, NATIONAL ARCHIVES
Jim Bridger
KANSAS STATE HISTORICAL SOCIETY
Lieutenant George Templeton
LIBRARY OF CONGRESS
John (Portugee) Phillips _(seated)_ Captain James Powell _(standing)_
EASTERWOOD COLLECTION, UNIVERSITY OF OREGON
Sitting Bull's drawing of a horse he captured on the Montana Trail in 1866 BUREAU OF AMERICAN ETHNOLOGY, THE SMITHSONIAN INSTITUTION
Fort Phil Kearny, as drawn by Antonio Nicoli, 2nd Cavalry Bugler
U.S. SIGNAL CORPS, NATIONAL ARCHIVES
Two Moons, Cheyenne leader
EASTERWOOD COLLECTION, UNIVERSITY OF OREGON
# A Biography of Dee Brown
Dorris Alexander "Dee" Brown (1908–2002) was the author of many fiction and nonfiction books about the American West and the Civil War. He is best remembered for his celebrated chronicle _Bury My Heart at Wounded Knee_ , which is widely credited with exposing the systematic destruction of American Indian tribes to a world audience.
Born in Alberta, Louisiana, Brown grew up in the small town of Stephens in Ouachita County, Arkansas. His father died when he was five years old, and he was raised by his mother and maternal grandmother, who proved instrumental in igniting his interest in reading at an early age. His grandmother told him stories from the Civil War, as well as tales of Davy Crockett, the frontier hero who had been an acquaintance of her father's. A regard for Pawnee baseball pitcher Moses Yellowhorse, as well as Brown's friendship with an Indian peer, helped fuel his lifelong interest in the plight and history of American Indians.
As an adolescent, Brown was drawn to literature, particularly the works of John Dos Passos, William Faulkner, Jack London, and Robert Louis Stevenson. His interest in history was reinforced when a teacher introduced him to the expedition of Lewis and Clark. He was also drawn to journalism, and published his first story at the age of fifteen in a neighborhood tabloid he started with friends. Brown worked as both a reporter and a printer before enrolling at Arkansas State Teachers College (now the University of Central Arkansas), where he met his future wife, Sally Stroud. Brown later earned bachelor's and master's degrees in library science from George Washington University and the University of Illinois at Urbana-Champaign, respectively. In the years between these studies, during World War II, he was drafted to into the U.S. Army and served as a librarian in the Department of Agriculture, a position that gave him frequent access to the National Archives.
Brown began publishing magazine articles in the 1930s, followed by a novel in 1942. His writing career took off in 1948, with the publication of the first of three books of frontier history he had co-authored with Martin Schmitt, titled _Fighting Indians of the West_. Legendary Scribner's editor Maxwell Perkins oversaw the series.
Brown went on to publish more than thirty books during his lifetime. His novels, which unite a love of storytelling and high adventure with rigorous historical accuracy, include _Action at Beecher Island_ , _Cavalry Scout_ , _Conspiracy of Knaves_ , _Killdeer Mountain_ , _The Girl from Fort Wicked_ , and _Creek Mary's Blood_ , a notable saga about five generations of one American Indian family. Among his extensively researched works of nonfiction are _The Gentle Tamers_ , about the role of women in the Old West; _Hear That Lonesome Whistle Blow_ , a history of the beginnings of the railroads; and _The Year of the Century: 1876_ , a look at America at the time of its first centennial. Brown's most famous title is _Bury My Heart at Wounded Knee_ (1970). During years of research, Brown compiled eyewitness accounts, tribal histories, and other archived documents, synthesizing them into a record of the deadly frontier conflicts in the late nineteenth century from an American Indian perspective. The book has been translated into more than thirty languages over the years, and continues to be translated for new audiences today. It remains one of the definitive works on American history, as it revealed a devastating side to western expansion.
Brown died in 2002 in Little Rock, Arkansas. He was ninety-four and at work on a new novel that was to be a sequel to _The Way to Bright Star,_ which he published at the age of 90.
Infant Dee Brown with his half-siblings, Mildred and Daniel Brown, around 1908.
A young Brown in Arkansas, before 1920. (Photo courtesy of the Dee Brown LLC.)
Brown in the early 1920s. (Photo courtesy of the Dee Brown LLC.)
Brown's college photo, taken in the 1920s.
Brown in the late 1920s in Wilson, Arkansas.
Brown with his mother, Lula Brown (left), and wife, Sally Stroud (right), in Washington, DC. in the 1930s.
A portrait of Brown taken during World War II.
Brown in the 1940s with his dog, Ivan, most likely taken in Maryland.
A studio shot of Brown from around 1950.
Brown with his grandson, Nicolas Wolfe, in 1972. He dedicated _Bury My Heart at Wounded Knee_ to Nicolas. (Photo courtesy of Linda Luise Brown.)
Brown in the 1970s, in a photo taken by friend Rueben Thomas.
Brown in 1981, after the publication of _Bury My Heart at Wounded Knee_. (Photo courtesy of Linda Luise Brown.)
All rights reserved under International and Pan-American Copyright Conventions. By payment of the required fees, you have been granted the non-exclusive, non-transferable right to access and read the text of this ebook onscreen. No part of this text may be reproduced, transmitted, downloaded, decompiled, reverse engineered, or stored in or introduced into any information storage and retrieval system, in any form or by any means, whether electronic or mechanical, now known or hereinafter invented, without the express written permission of the publisher.
Formerly entitled _Fort Phil Kearny: An American Saga_. First published in 1962 by G. P. Putnam's Sons.
copyright © 1962 by Dee Brown
cover design by Angela Goddard
978-1-4532-7416-3
This edition published in 2012 by Open Road Integrated Media
180 Varick Street
New York, NY 10014
www.openroadmedia.com
# **EBOOKS BY DEE BROWN**
**FROM OPEN ROAD MEDIA**
**Available wherever ebooks are sold**
**Open Road Integrated Media** **is a digital publisher and multimedia content company. Open Road creates connections between authors and their audiences by marketing its ebooks through a new proprietary online platform, which uses premium video content and social media.**
**Videos, Archival Documents, and New Releases**
**Sign up for the Open Road Media newsletter and get news delivered straight to your inbox.**
**Sign up now at**
**www.openroadmedia.com/newsletters**
**FIND OUT MORE AT**
**WWW.OPENROADMEDIA.COM**
**FOLLOW US:**
**@openroadmedia** **and**
**Facebook.com/OpenRoadMedia**
| {
"redpajama_set_name": "RedPajamaBook"
} | 2,818 |
Q: Method (x) is undefined for the type String So I have two Strings: type and color. For some reason I can't use "getType" or "getColor". The error comes at the bottom in the second method (public boolean equals(String aClothing)). How can I fix this?
public class Clothing {
// Attributes
private String type;
private String color;
// Constructors
public Clothing() {
this.type = "no type yet";
this.color = "no color yet";
}
public Clothing(String aType, String aColor) {
this.setType(aType);
this.setColor(aColor);
}
// Accessors (getters)
public String getType() {
return this.type;
}
public String getColor() {
return this.color;
}
// Mutators (setters)
public void setType(String aType) {
this.type = aType; // TODO check invalid values
}
public void setColor(String aColor) {
this.color = aColor; // TODO check invalid values
}
// Methods
public String toString() {
return this.type + " " + this.color;
}
public boolean equals(String aClothing) {
return aClothing != null && this.type.equals(aClothing.getType()) && this.color.equals(aClothing.getColor());
}
}
A: You should implement equals as an override of java.lang.Object's equals method, which means that your method needs to take Object as a parameter:
@Override
public boolean equals(object aClothingObj) {
if (aClothingObj == this) return true; // reference check for this
if (!(aClosingObj instanceof Clothing)) return false;
Clothing aClothing = (Clothing)aClothingObj;
return this.type.equals(aClothing.getType()) &&
this.color.equals(aClothing.getColor());
}
When you override equals, you must also override hashCode:
@Override
public int hashCode() {
return 31*type.hashCode()+color.hashCode();
}
A: aClothing is of type String not Clothing.
String has no getType/getColor method.
A: The problem is that you pass in a String for your comparison method:
public boolean equals(String aClothing) <--- here your input type is a string
{
return aClothing != null &&
this.type.equals(aClothing.getType())&&
this.color.equals(aClothing.getColor());
}
Instead, your method for equals should take in a generic object and override the equals method that all objects have:
@Override
public boolean equals(Object aClothing)
{
return aClothing instanceof Clothing && aClothing != null &&
this.type.equals(aClothing.getType())&&
this.color.equals(aClothing.getColor());
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,715 |
{"url":"https:\/\/ncatlab.org\/nlab\/show\/clone","text":"Clones\n\nClones\n\nIdea\n\nAn abstract clone is a structure that describes a single-sorted algebraic theory in a presentation-invariant way.\n\nAn abstract clone is equivalent to a cartesian operad, that is, a cartesian multicategory with one object. However, clones are presented differently, and quite economically, with projections rather than with symmetries, contraction and weakening.\n\nAbstract clones are equivalent to Lawvere theories, and also to finitary monads. These are all different ways of giving presentation-invariant descriptions of single-sorted algebraic theories.\n\nDefinition\n\nA set of algebraic operations on a fixed set $S$ is a concrete clone on $S$ if it contains all (component) projections $S^{n}\\to S$ and is closed under composition (\u201csuperposition\u201d).\n\nAn abstract clone consists of an abstract set of \u201c$n$-ary operations\u201d for every $n$ together with projection and composition operations. This is the notion that\u2019s equivalent to a cartesian operad or a Lawvere theory.\n\nMore precisely, the usual presentation of abstract clone comprises\n\n\u2022 a set $T(n)$ for each natural number $n$;\n\n\u2022 functions $\\eta_n : n \\to T(n)$;\n\n\u2022 functions $c_{m,n} : T(m) \\times T(n)^m\\to T(n)$\n\nsuch that\n\n\u2022 $\\eta(i) \\rhd j. t=t$;\n\n\u2022 $t \\rhd i.\\eta(i) =t$;\n\n\u2022 $t \\rhd i.(u(i) \\rhd j.v(j)) = (t \\rhd i.u(i)) \\rhd j. v(j)$\n\nwhere we omit subscripts and write $(t \\rhd i.u(i))$ for $c(t,(u_i)_i)$.\n\nThis resembles the Kleisli triple presentation of a monad, except that $n$ is a natural number rather than an arbitrary set; in this sense it is the Kleisli triple form of a relative monad for the embedding $\\mathbf{FinSet}\\to\\mathbf{Set}$.\n\nExamples\n\nConcrete clones as abstract clones\n\nSuppose a concrete clone is given on a set $S$, i.e. a set of operations $S^n\\to S$ of different arities, closed under composition and containing all the projections. We regard this as an abstract clone by putting $T(n)$ as the set of admitted operations $S^n\\to S$. The functions $\\eta_n$ pick out the projections, and $c_{m,n}$ is multi-ary function composition.\n\nAbstract clones from algebraic signatures\n\nAn algebraic signature comprises, for each number $n$, a set $\\Sigma_n$ of formal $n$-ary operations. For example, the theory of groups has $\\Sigma_0=\\{1\\}$; $\\Sigma_1=\\{(-)^{-1}\\}$; $\\Sigma_2=\\{\\cdot\\}$.\n\nWe then build for all $n$ the terms in $n$ variables, written $x_1\\dots x_n\\vdash x_i$, by the following inductive definition:\n\n\u2022 $x_1\\dots x_n\\vdash x_i$ is a term if $1\\leq i\\leq n$;\n\n\u2022 if $n\\vdash t_1\\ \\ \\dots\\ \\ n\\vdash t_m$ are terms and $\\sigma\\in \\Sigma_m$ then $n\\vdash \\sigma(t_1,\\dots, t_m)$ is a term. Here we write $n =(x_1\\dots x_n)$.\n\nNow we form an abstract clone by putting $T_\\Sigma(n)=\\{t\\ \\ |\\ \\ (n\\vdash t\\ \\ \\text{ is a term})\\}$. The functions $\\eta_n$ picks out the variables, and the function $c_{m,n}$ amount to substitutions of terms for variables, which produces well-formed terms.\n\nThe inhabitants of $T_\\Sigma$ are sometimes called \u201cderived operations\u201d, since although they are not in the signature they have an interpretation in any model.\n\nAbstract clones from presentations of algebraic theories\n\nAn algebraic theory over a signature is given by a collection of axioms of the form $\\Gamma\\vdash t=u$, where $\\Gamma \\vdash t$ and $\\Gamma \\vdash u$. We then form equivalence relations $\\sim_n$ of terms by closing under substitution instances, congruence, and reflexivity, symmetry and transitivity. These are the equations that are true in all models of the theory.\n\nWe can now form an abstract clone for the theory, derived from the abstract clone for the signature. Put $T(n)=T_\\Sigma(n)\/_{\\sim_n}$. The $\\eta$ and $c$ respect equivalence relations because we closed under substitution instances and congruence.\n\nFor example, starting from the theory of groups, $T(n)$ will be the free group on $n$ generators.\n\nAlgebraic theories from abstract clones\n\nConversely, any abstract clone can be regarded as a presentation of an algebraic theory. The signature has $\\Sigma_n=T(n)$, and we include the axioms\n\n\u2022 $\\eta_n(i) = x_i$\n\n\u2022 $s(t_1\\dots t_n) = (s \\rhd i. t(i))$.\n\nAn abstract clone is a presentation of a \u201csaturated\u201d algebraic theory: all derived operations are equivalent to basic operations that are already in the signature.\n\nLawvere theories and abstract clones\n\nIf $T$ is an abstract clone, we can form a category whose objects are natural numbers and where a morphism $m\\to n$ is a tuple $T(m)^n$. The identity morphisms are $\\eta_n$. Composition is $(g\\circ f)(i)=(g(i)\\rhd j.f(j))$. This category is a Lawvere theory.\n\n(This is the opposite category of the Kleisli category of $T$ regarded as a relative monad.)\n\nConversely, if $L$ is a Lawvere theory then we can build a clone $T(n)=L(n,1)$. This gives an equivalence between abstract clones and Lawvere theories.\n\nAlgebras of abstract clones and connection with finitary monads\n\nWe can define an algebra of an abstract clone $T$ to be a set $X$ together with $n$-ary function $t \\rhd : X^n\\to X$ for each $t\\in T(n)$, such that\n\n\u2022 $\\eta_i \\rhd i.x(i)= x(i)$;\n\n\u2022 $(t\\rhd i.u(i))\\rhd j.x(j)= t\\rhd i.(u(i)\\rhd j.x(j))$.\n\nHere we are writing $\\rhd$ for both the clone composition and the algebra structure, and again writing $t \\rhd i.x(i)$ for $t\\rhd(x_i)_i$.\n\nFor example, an algebra for the abstract clone of groups is a group.\n\nNow the category of $T$-algebras has a forgetful functor\n\n$T\\mathbf{-Alg} \\to \\mathbf{Set}$\n\nOne can show that this functor is monadic by showing it preserves limits, satisfies the solution set condition, reflects isomorphisms, and has reflexive coequalizers. Thus every abstract clone gives rise to a monad.\n\nAnother way to define this monad is to note that $T$ can be regarded as a functor $\\mathbf{FinSet}\\to \\mathbf{Set}$, with $T(f):T(m)\\to T(n)$ given by $T(f)(t)=(t\\rhd i.\\eta(f(i)))$. Then we extend this to a functor $M:\\mathbf{Set}\\to\\mathbf{Set}$ by a coend or by Kan extension:\n\n$M(X) = \\int^n T(n)\\times X^n = (\\mathrm{Lan}\\,T)(X)$\n\nIn other words, an inhabitant of $M(X)$ is a derived operation $t\\in T(n)$ formally applied to an $n$-tuple in $X^n$, modulo change of variables. This functor $M$ can be given the structure of a monad on $\\mathbf{Set}$, and its Eilenberg-Moore algebras are the $T$-algebras.\n\nConversely, suppose that $M$ is a monad on the category of sets. We can define an abstract clone by regarding a natural number $n$ as a finite set and putting $T(n)=M(n)$. Then $\\eta$ is the unit of the monad and $c$ is the Kleisli composition (called \u201cmonadic bind\u201d).\n\nThis gives an equivalence between finitary monads and abstract clones. They are also the monads with arities in $\\mathbf{FinSet}$.\n\nMonadicity of the category of abstract clones\n\nThe definition of abstract clones given here is itself a presentation of algebraic structure. Indeed we can consider an obvious notion of homomorphism of clones, and then the forgetful functor\n\n$\\mathbf{AbstractClones} \\to [\\mathbf{FinSet},\\mathbf{Set}]$\n\nIn fact this adjunction is enriched in $[\\mathbf{FinSet},\\mathbf{Set}]$. Moreover, we can consider a more general notion of abstract clone enriched in a locally presentable category, where the arities $n$ are replaced by finitely presentable objects. Then the plain abstract clones themselves are algebras for an abstract clone enriched in $[\\mathbf{FinSet},\\mathbf{Set}]$. One way to present this formally is in terms of the substitution algebras of Fiore, Plotkin and Turi.\n\nAnother view of this adjunction starts from viewing $[\\mathbf{FinSet},\\mathbf{Set}]$ as a monoidal category. To get this, we can understand functors $\\mathbf{FinSet}\\to \\mathbf{Set}$ as filtered colimit preserving endofunctors $\\mathbf{Set}\\to\\mathbf{Set}$, and then composition forms a monoidal structure on a category of endofunctors. In detail, the unit is $\\mathbf{FinSet}(1,-)$ and tensor product is\n\n$(F \\otimes G) (n) = \\int^m F(m) \\times G(n)^m = ((\\mathrm{Lan}\\,F)\\circ G)(n)$\n\nThen the category of abstract clones is (equivalent to) the category of monoids for this monoidal structure. Since a finitary monad is a filtered-colimit-preserving \u201cmonoid in the category of endofunctors\u201d, this also gives an abstract view of the connection between abstract clones and finitary monads on $\\mathbf{Set}$.\n\nReferences\n\n\u2022 \u00c1gnes Szendrei, Clones in universal algebra, S\u00e9minaire de math\u00e9matiques sup\u00e9rieures 99, Les presses de l\u2019universit\u00e9 de Montreal, 1986. \u2014 166 p.\n\nA rather general framework is discussed in\n\n\u2022 Zhaohua Luo, Clone theory, its syntax and semantics, applications to universal algebra, lambda calculus and algebraic logic, arxiv\/0810.3162\n\u2022 Dietlinde Lau, Function algebras on finite sets: Basic course on many-valued logic and clone theory, Springer Monographs in Mathematics\n\nA common generalization of a clone and of an operad is proposed, using a new notion of a verbal category, in\n\n\u2022 S. Tronin, Abstract clones and operads, Siberian Mathematical Journal 43, No.4, 746\u2013755, 2002 link\n\nAnother unification of clones and operads is via the formalism in\n\n\u2022 Pierre-Louis Curien, Operads, clones, and distributive laws, arxiv\/1205.3050\n\nSubstitution algebras as a theory over $[\\mathbf{FinSet},\\mathbf{Set}]$ are presented in:","date":"2023-03-29 09:56:52","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 103, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"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\": 0.8574804067611694, \"perplexity\": 510.69791769334614}, \"config\": {\"markdown_headings\": false, \"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\/1679296948965.80\/warc\/CC-MAIN-20230329085436-20230329115436-00631.warc.gz\"}"} | null | null |
Q: How to populate quantities between 2 transaction dates I have a table with dates, Products, Quantity (Purchase is positive and Sales are negative) and Price, like the following
Date Prod_Name Qty Price
1/3/2017 ProductA 8 150
1/9/2017 ProductB 2 170
1/11/2017 ProductA -8 160
1/12/2017 ProductB -2 180
I would like to have a query that generates the total quantity by product for every business day like the following:
date A B
1/3/2017 8 0
1/4/2017 8 0
1/5/2017 8 0
1/6/2017 8 0
1/9/2017 8 2
1/10/2017 8 2
1/11/2017 8 2
1/12/2017 0 2
1/13/2017 0 0
A: You require to generate dates and need to do sum over windowing function as below:
Declare @startdate date = '2017-01-03'
Declare @enddate date = '2017-01-13'
;with Datescte as (
Select top (datediff(day, @startdate, @enddate) +1) Dt = Dateadd(day, Row_Number() over (order by (Select null))-1, @startdate)
from master..spt_values s1, master..spt_values s2
), cte2 as (
Select * from
( Select [Date], Prod_name, Qty from #Dates ) a
pivot (max(Qty) for prod_name in ([ProductA],[ProductB])) p
)
Select Dt as [Date], sum(ProductA) over(order by Dt) as [A], Coalesce(sum(ProductB) over(order by dt),0) as [B]
from Datescte d
left join cte2 d2
on d.dt = d2.Date
First CTE generates dates between two dates.
Second CTE does pivot for two products and query returns sum based on date column
A: WITH C AS
(
SELECT Date, Prod_Name,qty,price
FROM YourTable
)
SELECT *
FROM C
PIVOT(SUM([qty])
FOR Prod_Name IN ([ProductA],[ProductB])) AS P;
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 106 |
Danae e Giove è un dipinto realizzato nel 1736 da Giambattista Tiepolo, basato sul celebre episodio descritto nel poema latino Le Metamorfosi di Ovidio.
L'artista ha preso spunto dalle due più celebri rappresentazioni di questo mito, entrambe eseguite da Tiziano due secoli prima: sono presenti infatti sia la figura di Cupido sia quella della vecchia nutrice-guardiana, desunte rispettivamente dalla Danae di Napoli e da quella di Madrid. Nell'opera settecentesca però Giove appare anche nel suo vero aspetto.
Altri progetti
Dipinti a soggetto mitologico di Giambattista Tiepolo
Opere basate su Le metamorfosi (Ovidio)
Dipinti su Danae
Dipinti su Giove
Dipinti su Cupido
Dipinti a Stoccolma | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,888 |
def run
op = FileOperation.new
op.move_autorename_new
end
def verify_source
assert_source_nonexist('file1.txt')
assert_source_nonexist('file1__new1.txt')
assert_source_nonexist('file1__new2.txt')
assert_source_nonexist('file1__new3.txt')
end
def verify_target
assert_target_file('file1.txt', /target0/)
assert_target_file('file1__new1.txt', /target1/)
assert_target_file('file1__new2.txt', /target2/)
assert_target_file('file1__new3.txt', /source/)
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,881 |
{"url":"https:\/\/www.rocketryforum.com\/threads\/next-generation-tilt-sensor-attitude-monitor.140061\/page-2","text":"# Next Generation Tilt Sensor\/ Attitude Monitor\n\n### Help Support The Rocketry Forum:\n\n#### UhClem\n\n##### Well-Known Member\nThe MPU9250 board DOES have a magnetometer, but if you think about it you don't really need it. You aren't trying to figure out which direction your rocket is pointing, just what the tilt is. Using the accelerometer to give you the tilt on the pad and the gyros to correct it in flight is the easiest way to do this, and it's not dependent on the velocity or acceleration of your rocket. For that matter, you don't need to worry about the z-axis gyro either, it doesn't affect the tilt.\nYou only need the accels for launch detect.\n\nYou don't want the rocket to fly straight up but to stay pointed in the same direction that it was on the pad. This way you can adjust its trajectory based on winds so that it has a better chance of landing where you want it to. Plus going straight up messes with the best practices of angling the rocket away from the flight line.\n\nAll the gyro axes are required because any rotation around the longitudinal axis changes the orientation of the other two.What was providing tilt in the north-south plane a moment ago could now be east-west.\n\nI have a little project on the bench at the moment to record MPU-9250 data at high speed. Once I get that code working I will dust off what I remember about quaternions.\n\n#### cerving\n\n##### Owner, Eggtimer Rocketry\nTRF Supporter\nAll the gyro axes are required because any rotation around the longitudinal axis changes the orientation of the other two.What was providing tilt in the north-south plane a moment ago could now be east-west.\nI will submit that if you only care about the amount of tilt and not the orientation, then you don't need the Z axis rotation. Yes, the Z axis rotation will change the ORIENTATION as the X and Y values change (think of a 3D spiral), but it won't change the TILT (the angle of Z to vertical). If you were lucky enough to have no X\/Y rotation at all, the Z rotation will simply cause the rocket to spin around the Z axis.\n\n#### mikec\n\n##### Well-Known Member\nAs I continue to dig into the MPU-6050 documentation, I find that it should be possible to put the DMP in a mode where it is internally integrating the gyros at 200 Hz but not trying to do anything with the accelerometer, which should be the best of both worlds for how to operate post-launch. I don't think this mode is supported in the Rowberg library as yet, but it should be possible to add. BTW, there's a more complete library for the MPU-9250 ( https:\/\/github.com\/sparkfun\/MPU-9250_Breakout ).\n\nLast edited:\n\n#### VernK\n\n##### Member\/Vendor\nTRF Supporter\nI will submit that if you only care about the amount of tilt and not the orientation, then you don't need the Z axis rotation. Yes, the Z axis rotation will change the ORIENTATION as the X and Y values change (think of a 3D spiral), but it won't change the TILT (the angle of Z to vertical). If you were lucky enough to have no X\/Y rotation at all, the Z rotation will simply cause the rocket to spin around the Z axis.\nI think you do need all three axis because the tilt you care about is the orientation with respect to the earth. For example, imagine a rocket that pitches +5 degrees on its pitch axis. Then it rolls 180 degrees on its longitudinal axis. Then it pitches another +5 degrees on its pitch axis. (Which is now oriented in the opposite direction from before.). The pitch gyro by itself would indicate a total of 10 degrees of pitch where as the total tilt with respect to the earth is zero degrees.\n\nLast edited:\n\n#### ekchess\n\n##### Member\nThe MPU9250 board DOES have a magnetometer, but if you think about it you don't really need it. You aren't trying to figure out which direction your rocket is pointing, just what the tilt is. Using the accelerometer to give you the tilt on the pad and the gyros to correct it in flight is the easiest way to do this, and it's not dependent on the velocity or acceleration of your rocket. For that matter, you don't need to worry about the z-axis gyro either, it doesn't affect the tilt.\nThanks Cris. I downloaded the open-sourced code from Altus Metrum, in which they tackle this problem as you described for use with their Telemega, but they are using a full quaternion. The code is very complex, and has so many interacting functions in their .c files that it is difficult for me to follow. I'll keep at this, though, as the problem is worth solving. The most interesting functions are in the altos\/src\/kernel\/ao_sample.c files, but you also need the functions in the ao_quaternion.c file and some others.\n\n#### ekchess\n\n##### Member\nAs I continue to dig into the MPU-6050 documentation, I find that it should be possible to put the DMP in a mode where it is internally integrating the gyros at 200 Hz but not trying to do anything with the accelerometer, which should be the best of both worlds for how to operate post-launch. I don't think this mode is supported in the Rowberg library as yet, but it should be possible to add. BTW, there's a more complete library for the MPU-9250 ( https:\/\/github.com\/sparkfun\/MPU-9250_Breakout ).\nFabulous! Good luck. I agree that the Rowberg library is limited with respect to gyro use--he really pushed using the accel functions, and that makes sense for folks who are not concerned about high accelerations (like folks whos applications mirror the the teapot\/rabbit AHRS demo). Please keep us informed of your progress.\n\nTRF Supporter\n\n#### jderimig\n\nThat's my concern, that the DMP is using the accelerometer inputs under thrust to \"correct\" gyro drift as though thrust was gravity -- if true that would defeat the whole purpose. I can't tell from the fairly minimal DMP docs I've been able to find online so far exactly how it works.\nThe DMP has an option to not use the accelerometers to compute the quaternions, just the gyros. (As MikeC has mentioned in an earlier post).\n\n#### mikec\n\n##### Well-Known Member\nI downloaded the open-sourced code from Altus Metrum, in which they tackle this problem as you described for use with their Telemega, but they are using a full quaternion. The code is very complex, and has so many interacting functions in their .c files that it is difficult for me to follow.\nThere's lots of open-source software from the drone community that works with gyros, and I might recommend some of that over the Altus Metrum code, which I find pretty complex and hard to follow. http:\/\/wiki.paparazziuav.org\/w\/images\/e\/e5\/DCMDraft2.pdf is some early work in this area, though it uses direction cosine matrices instead of quaternions (basically equivalent.) But keep in mind that it works on aircraft, where the sensed gravity vector means something when the plane is in level flight, whereas rockets are never in level flight.\n\nBut I think your code is fundamentally OK, it's just that we want to reference everything to the pre-launch gravity direction and not use the accelerometers post-launch.\n\n#### JimJarvis50\n\n##### Well-Known Member\nThere's lots of open-source software from the drone community that works with gyros, and I might recommend some of that over the Altus Metrum code, which I find pretty complex and hard to follow. http:\/\/wiki.paparazziuav.org\/w\/images\/e\/e5\/DCMDraft2.pdf is some early work in this area, though it uses direction cosine matrices instead of quaternions (basically equivalent.) But keep in mind that it works on aircraft, where the sensed gravity vector means something when the plane is in level flight, whereas rockets are never in level flight.\n\nBut I think your code is fundamentally OK, it's just that we want to reference everything to the pre-launch gravity direction and not use the accelerometers post-launch.\nI wish I knew a bit more about the math and programming associated with these systems. It would really help me in my development of a vertical stabilization system, which depends entirely on the accurate measurement of tilt. Fortunately for me, my Guru, William Premerlani, knows a lot about those things. He developed the cosine matrix theory you referenced in the link and worked with Frank Hermes to develop the Tiltometer, which unfortunately is no longer being made. Bill has also developed flight software and hardware primarily for autopilot systems for drones and helicopters, and now rockets.\n\nFor the last couple of years, I've been working with Bill, Frank and others to adapt the flight hardware he has developed to produce a vertical stabilization system for rockets. I think Bill has produced a number of innovations and we have had many lessons learned. Just as an example, Bill has developed a way to reduce the gyro offsets on all three axes to essentially zero right up to the moment the button is pushed. This is combined with a launch detect algorithm that then decouples the gyros and the accelerometers during the flight. The trick to this is to optimize the offset correction rate so that there is enough time to reduce the offset, but not enough time to change the offsets in the time it takes to detect launch. One of several examples.\n\nWith respect to lessons learned, I think we have conceded that for the type of gyros we are using (MPU-6000), it is simply not possible to obtain accurate tilt measurements if the rocket is rotating. I don't understand the technical basis for this, but what I do know is that rotation in the vertical axis imparts a \"reading\" in the two horizontal axis gyros. Rotating back to the starting point undoes this, but not exactly. As a result, after perhaps 10 rotations, the tilt reading becomes meaningless. Consequently, my focus on the application of the technology is to try to eliminate as much roll as possible.\n\nI'm not exactly sure why I am posting this except to perhaps encourage a little more cross talk in the development of these systems. The capability and available hardware is something the hobby really needs.\n\nJim\n\n#### mikec\n\n##### Well-Known Member\nWith respect to lessons learned, I think we have conceded that for the type of gyros we are using (MPU-6000), it is simply not possible to obtain accurate tilt measurements if the rocket is rotating. I don't understand the technical basis for this, but what I do know is that rotation in the vertical axis imparts a \"reading\" in the two horizontal axis gyros.\nInteresting. There could be two reasons for this. One is that the hardware just has some gyro or accelerometer\/gyro crosstalk. That wouldn't be too surprising since these things are really designed for applications like device orientation for gaming, fitness trackers, 3D mice, etc, where the gravity vector is usually available in some form to correct gyro drift. Rockets are obviously a very stressing case of high acceleration and no gravity vector.\n\nThe other possibility is that the devices would work but we're just not using them right. This is entirely possible, because the math is really pretty complicated and the device documentation is IMHO appallingly poor. I have a fair amount of flight data using an older generation Sparkfun Razor IMU with separate gyro (ITG-3200) and accelerometer (ADXL345) chips and I thought it was getting the tilt right with rocket rotation, but I'll go back and look at that in more detail. I have some flights where I have both tilt data and onboard video and that provides a good rotation cross-check.\n\nBack to this thread a bit: I spent some time looking at the Rowland library, but since it's based on an old version of the DMP for which I can't find any documentation, I think modifying it in any way is basically hopeless, at least for me. There is a good library from Sparkfun for the newer version of the DMP that is based on the MPU-9150 but it could probably be backported to the MPU-6050 so I think that will be what I will look at next. One possible thing that would help these applications is magnetometer data fusion, since the Earth's magnetic field should be a stable reference frame.\n\n#### JimJarvis50\n\n##### Well-Known Member\nInteresting. There could be two reasons for this. One is that the hardware just has some gyro or accelerometer\/gyro crosstalk. That wouldn't be too surprising since these things are really designed for applications like device orientation for gaming, fitness trackers, 3D mice, etc, where the gravity vector is usually available in some form to correct gyro drift. Rockets are obviously a very stressing case of high acceleration and no gravity vector.\n\nThe other possibility is that the devices would work but we're just not using them right. This is entirely possible, because the math is really pretty complicated and the device documentation is IMHO appallingly poor. I have a fair amount of flight data using an older generation Sparkfun Razor IMU with separate gyro (ITG-3200) and accelerometer (ADXL345) chips and I thought it was getting the tilt right with rocket rotation, but I'll go back and look at that in more detail. I have some flights where I have both tilt data and onboard video and that provides a good rotation cross-check.\n\nBack to this thread a bit: I spent some time looking at the Rowland library, but since it's based on an old version of the DMP for which I can't find any documentation, I think modifying it in any way is basically hopeless, at least for me. There is a good library from Sparkfun for the newer version of the DMP that is based on the MPU-9150 but it could probably be backported to the MPU-6050 so I think that will be what I will look at next. One possible thing that would help these applications is magnetometer data fusion, since the Earth's magnetic field should be a stable reference frame.\nI should clarify that the testing I mentioned was done with the accelerometers off. Obviously, if they are on and correcting, there is no problem (except that you can't fly that way in a rocket). I think cross talk is the issue with perhaps thousands of degrees of rotation in the vertical axis against only a few degrees in the horizontal. Any rotation accumulates an error.\n\nJim\n\n#### UhClem\n\n##### Well-Known Member\nInteresting. There could be two reasons for this. One is that the hardware just has some gyro or accelerometer\/gyro crosstalk.\nThe reason isn't a mystery as it is right there in the data sheet: cross axis sensitivity: 2% typical, no maximum given.\n\nYou could compensate for this if the sensitivity is stable or at least predictable and you can measure it. I nice rate table would be nice but you should be able to find a 200 d\/s table pretty easily.\n\n#### jderimig\n\nThe reason isn't a mystery as it is right there in the data sheet: cross axis sensitivity: 2% typical, no maximum given.\n\nYou could compensate for this if the sensitivity is stable or at least predictable and you can measure it. I nice rate table would be nice but you should be able to find a 200 d\/s table pretty easily.\n^ Yup. I have several 198 d\/s tables (I had to blow the dust off them) that I used to create a correction lookup table for the ST gyro chip I am playing with.\n\n#### mikec\n\n##### Well-Known Member\nI nice rate table would be nice but you should be able to find a 200 d\/s table pretty easily.\nPardon my ignorance, but I can't parse this. What's a d\/s table?\n\n#### UhClem\n\n##### Well-Known Member\nPardon my ignorance, but I can't parse this. What's a d\/s table?\n200 degrees\/second = 33 1\/3 RPM\n\nphono cartridge optional\n\n#### JimJarvis50\n\n##### Well-Known Member\nThanks Cris. I downloaded the open-sourced code from Altus Metrum, in which they tackle this problem as you described for use with their Telemega, but they are using a full quaternion.\nCan you direct me to where this is located?\n\nThanks.\n\nJim\n\n#### keithp\n\n##### Well-Known Member\nAs noted upstream, IMHO this code is not very comprehensible.\nThe rotation tracking is a tiny portion of the overall flight state tracking code in src\/kernel\/ao_sample.c. There are two pieces, the first uses the accelerometer in the MPU to compute the rotation on the ground. The quaternion tracking the current total rotation in all three axes is stored in 'ao_rotation':\n\nCode:\n\tao_quaternion_init_vector(&orient,\n(ao_ground_accel_across - ao_config.accel_zero_across),\n(ao_ground_accel_through - ao_config.accel_zero_through),\n(ao_ground_accel_along - ao_config.accel_zero_along));\n\nao_quaternion_normalize(&orient,\n&orient);\n\n\/* Here's up *\/\n\nstruct ao_quaternion\tup = { .r = 0, .x = 0, .y = 0, .z = 1 };\n\nup.z = -1;\n\n\/* Compute rotation to get from up to our current orientation, set\n* that as the current rotation vector\n*\/\nao_quaternion_vectors_to_rotation(&ao_rotation, &up, &orient);\nThe other bit of code takes the gyro data and stirs that into ao_rotation. The first bit takes the raw sensor values, subtracts out the calibration data recorded on the ground (which assumes that the rocket is stationary on the pad). Those values are just the sum of 512 samples of the sensor, hence the weird shifting and dividing. Finally, the result is multiplied by the time step so we get rotation amount from rotation speed:\n\nCode:\n\tfloat\tx = ao_mpu6000_gyro((float) ((ao_sample_pitch << 9) - ao_ground_pitch) \/ 512.0f) * dt;\nfloat\ty = ao_mpu6000_gyro((float) ((ao_sample_yaw << 9) - ao_ground_yaw) \/ 512.0f) * dt;\nfloat\tz = ao_mpu6000_gyro((float) ((ao_sample_roll << 9) - ao_ground_roll) \/ 512.0f) * dt;\nNext, we convert the rotation amount into a quaternion and apply that to the current rotation:\n\nCode:\n\tao_quaternion_init_half_euler(&rot, x, y, z);\nao_quaternion_multiply(&ao_rotation, &rot, &ao_rotation);\n\n\/* And normalize to make sure it remains a unit vector *\/\nao_quaternion_normalize(&ao_rotation, &ao_rotation);\nThe last bit has a huge comment, because it's the 'tricky' part (at least for me). This extracts just the tilt angle from the overall ao_rotation quaternion by measuring the angle from a quaternion pointing vertically. Oddly, that doesn't take a full quaternion multiply as we only want one of the four values. So, the comment describes how that shortcut works. Of course, the result is actually the cosine of the tilt angle, because quaternions store ratios, not angles, so we run that back through acosf to get the angle. Finally, that's converted from radians to degrees.\n\nCode:\n\t\/* Compute pitch angle from vertical by taking the pad\n* orientation vector and rotating it by the current total\n* rotation value. That will be a unit vector pointing along\n* the airframe axis. The Z value will be the cosine of the\n* change in the angle from vertical since boost.\n*\n* rot = ao_rotation * vertical * ao_rotation\u00b0\n* rot = ao_rotation * (0,0,0,1) * ao_rotation\u00b0\n* = ((a.z, a.y, -a.x, a.r) * (a.r, -a.x, -a.y, -a.z)) .z\n*\n* = (-a.z * -a.z) + (a.y * -a.y) - (-a.x * -a.x) + (a.r * a.r)\n* = a.z\u00b2 - a.y\u00b2 - a.x\u00b2 + a.r\u00b2\n*\n* rot = ao_rotation * (0, 0, 0, -1) * ao_rotation\u00b0\n* = ((-a.z, -a.y, a.x, -a.r) * (a.r, -a.x, -a.y, -a.z)) .z\n*\n* = (a.z * -a.z) + (-a.y * -a.y) - (a.x * -a.x) + (-a.r * a.r)\n* = -a.z\u00b2 + a.y\u00b2 + a.x\u00b2 - a.r\u00b2\n*\/\n\nfloat rotz;\nrotz = ao_rotation.z * ao_rotation.z - ao_rotation.y * ao_rotation.y - ao_rotation.x * ao_rotation.x + ao_rotation.r * ao_rotation.r;\n\nao_sample_orient = acosf(rotz) * (float) (180.0\/M_PI);\nThat's the whole algorithm. Just like the Kalman filter, it took a few weeks to understand the math well enough to write it all down, but it's only a few lines of code in the final implementation.\n\nWhat I want to eventually do is take this value and the magnetic sensor data and fuse those in another Kalman filter so I can get long-term stable rotation data, instead of having it slowly lose accuracy during the flight.\n\n#### UhClem\n\n##### Well-Known Member\nThere's lots of open-source software from the drone community that works with gyros, and I might recommend some of that over the Altus Metrum code, which I find pretty complex and hard to follow.\nA quick summary of what is going on. But I am by no means an expert on quaternions. Every time I think about them my brain hurts.\n\nQuaternions describe rotations of 3D vectors and you can combine two rotations into one simply by multiplying the quaternions together. So the integration step is easy. Just multiply the current rotation by the small rotation given by the gyro measurement.\n\nNASA Technical Memorandum 4775 goes through a lot of math to get to the same point. It is interesting reading though. It describes a project where they lift a UAV by balloon. When released at altitude it uses a small rocket motor to bring it from its initial nose down attitude to level flight.\n\nThis is where you can make an optimization. Converting those gyro measurements into a quaternion requires both a sine and cosine. Depending on the platform that can be expensive in terms of code space and\/or time. If the rotation is small enough, you can use the small angle approximation where cos(x) = 1 and sin(x) = x. That is what I do since my data is collected at 32KSPS. Altos is running at 100SPS and a 2000d\/s range so it tries another approximation. I wouldn't worry about it.\n\nThe maximum possible rotation in Altos is 20 degrees per sample. I suspect that if you have rotation anywhere near the 2000 degrees\/sec sensor maximum you are going to quickly blow past your tilt threshold. Errors from the small angle approximation aren't likely to matter much.\n\nOne nice feature of this is that it is norm preserving. (Vector length = 1) Errors will creep in that denormalize the quaternion over time so you will want to normalize it occasionally but there is no need to waste time doing it for every sample. Once a second seemed to do just as well with my 32KSPS data.\n\nSo keep your starting quaternion set to zero rotation until you detect launch and then start integrating. Launch detect criteria should be such that the rocket is still on the rod\/rail!\n\nMeasuring the angle is pretty simple as well. Use the quaternion to rotate a vector from your starting orientation to the current orientation and then calculate the angle between those two vectors.\n\nThis can be simplified a lot if the starting vector is something simple like [1 0 0]. Then you can skip the full strength quaternion multiply and dot products.\n\nNote that you don't even need an arccos function here unless you absolutely require angles in degrees. If you store your threshold for disabling outputs as cosines of the angles, you can skip that. So you don't need anything more complicated than: add, multiply, and square root. Fixed or floating point is your choice. Speed is important as the quaternion multiply requires 16 multiplications.\n\nIf this is integrated within an altimeter, you only need to check the angle when you are about to fire an output conditioned on it. No need to waste time doing it every stinkin' sample.\n\nI dug up the code I wrote when trying this on Glen Overby's data and whipped up a quick plot using some 32KSPS data. I tried to do three 90 degree rotations isolated to a single axis. The failure to return to zero could be because of a flaw in my code or non-linearity\/cross axis sensitivity in the sensor.\n\n#### UhClem\n\n##### Well-Known Member\nI captured a little data using my rate table (Denon DP-45F) and the cross axis sensitivity was interesting. Because I expected that the sensitivity might vary depending on the direction of rotation, I flipped the logger over so as to rotate it in both directions around the Y axis.\n\nThe results showed that it did indeed vary quite a lot. See the attached plots.\n\nThe data was run through a 1000 point moving average filter in order to tamp down the sensor noise a bit.\n\nWith rotation of -200 degrees\/second both the X and Z gyros showed not much sensitivity with a shift of less than 1\/2 degree\/second in output.\n\nBut with a positive 200 degree\/second rotation things were different. The X gyro shifted by more than 3 degrees\/second and the shift was negative just like it was in the first case. You would kind of expect the sign to change.\n\nThe Z axis did exhibit the expected sign change but the magnitude was unexpected as it was around 10 degrees\/second. (5%) I would say that was out of specification except that the data sheet just gives a typical value of 2% with no indication of a maximum.\n\nI also expect that this might vary with temperature but I do not have a temperature controlled chamber to set over my rate table. The best I will be able to do is toss the logger into the freezer for a while. So it will be warming up throughout the test.\n\nStaff member\nGlobal Mod\nsubscribed.\n\n#### UhClem\n\n##### Well-Known Member\nIt turns out that the cross axis sensitivity is not as horrible as I thought.\n\nI used the mount I had built for early flight testing and while that is adequate for that purpose, it has flaws for rate table testing. It is just a simple ply sled with centering rings at either end to hold it in place in a payload bay. But I noticed that one of the rings isn't as well aligned as the other. The result being that when standing on end, such as when I did the rate test, it has a noticeable tilt one way and not the other.\n\nI unmounted the board and flipped it over. If the problem really was cross axis sensitivity then it would continue being bad for positive rates.\n\nIt wasn't. The results were about the opposite from the first test.\n\nI am not sure how I am going to compensate for the misalignment with the rotation. Maybe the accels will help by measuring tilt...\n\n#### soopirV\n\n##### Well-Known Member\nSubscribed, better late than never! op:\n\n#### SparkyVTFlyer\n\n##### Senior Member\nTRF Supporter\nI've also been working on something similar. At NARAM last summer I built and demo'd an ATMega328 (Arduino Uno) based logging altimeter capable of dual deploy and 2-stage functions (separation & ignition). I developed my own simple algorithm to estimate the angle off vertical. The unit is capable of recording the following at 400 samples\/sec to an external SD card:\n\n3-axis 16G accelerometer (LSM303)\n3-axis 2000dps gyro (L3GD20)\nbaro pressure sensor (BMP180) (20 samples\/sec)\nIntegrated velocity, altitude, and off-vertical\nStatus of all flight events\nMach immune staging and deployment\n\nThe algorithm to integrate angle off vertical was the hardest part. I attempted quaternions but couldn't get them to work. I tried traditional quaternions and differential quaternions to no avail. Mostly through luck, I came up with a simple algorithm that only required 10 floating point operations per cycle. I sped it up by using small-angle approximations in combination with the angle-addition trig identity and fixed-point math. It won't work for complex rotations, but for simple rocket trajectories it works well. I have about a two dozen flights with the algorithm now and its fairly accurate. Onboard video shows it to be typically within 2-5 degrees of the actual off-vertical value at apogee.\n\nI might give quaternions another try using Keith's code from his post. It took me a while to understand quaternions but couldn't get them to work in practice. I used my code to build a test unit for a friend. Here is a youtube video of it working. Yes, I know its not a difficult test of the functionality.\n\nhttps:\/\/youtu.be\/mih46qINaT4\n\nI've found that the cross-axis sensitivity is definitely a problem. I ran some bench tests to collect data and used a simple linear regression model to back-out the cross-axis \"spillover.\" It works pretty well and tamped-down the cycling that was present for the flights with significant roll rates.\n\nI attached a graphic of the algorithm output. This was an EX M-powered flight to about 9,000 ft and just shy of supersonic. The algorithm estimate matches the onboard video very well. In fact, its no more than 2 degrees off at apogee.\n\nHere's the bit of code (but doesn't have the linear regression model, that will probably be hardware dependent):\n\nlong gdt = 0L;\nlong ang_x = 0L;\nlong ang_y = 0L;\nlong ang_z = 0L;\nfloat ang_y0;\nfloat ang_z0;\nint angX = 0;\nint angY;\nint angZ;\nfloat cosX = 1.0;\nfloat sinX = 0.0;\nfloat PrevCosX = 1.0;\nfloat PrevSinX = 0.0;\nint gyroBiasX = 14;\nint gyroBiasY = 35;\nint gyroBiasZ = 3;\nconst long oneDeg = 14285714L;\/\/oneDeg = mln\/0.070\nconst long oneTenthDeg = 1428571L;\/\/oneTenthDeg = oneDeg\/10\nint counterSign = 1;\nboolean calcOffVert = false;\nint offVert = 0;\n\n\/\/Eliminate gyro bias\ngyro_event.gyro.x -= gyroBiasX;\ngyro_event.gyro.y -= gyroBiasY;\ngyro_event.gyro.z -= gyroBiasZ;\n\n\/\/Calculate new X angle from gyro data\nang_x += gyro_event.gyro.x * gdt;\n\/\/Overflow X data and recompute as needed\nwhile (abs(ang_x) > oneDeg) {\nif (ang_x > 0) {counterSign = 1;}\nelse {counterSign = -1;}\nang_x -= counterSign * oneDeg;\nangX += counterSign;\n\/\/cos(A+B) = cosAcosB - sinAsinB A=big B=small cos(1deg)=0.999847695\ncosX = PrevCosX * 0.999847695 - PrevSinX * (counterSign * 0.017452406);\n\/\/sin(A+B) = sinAcosB + cosAsinB A=big B=small\nsinX = PrevSinX * 0.999847695 + PrevCosX * (counterSign * 0.017452406);\nPrevCosX = cosX;\nPrevSinX = sinX;}\n\n\/\/Compute the new y and z angles\nang_z += cosX * gyro_event.gyro.z * gdt;\nang_z += sinX * gyro_event.gyro.y * gdt;\nang_y += cosX * gyro_event.gyro.y * gdt;\nang_y -= sinX * gyro_event.gyro.z * gdt;\n\/\/Overflow Y data and recompute as needed\nwhile (abs(ang_y) > oneTenthDeg) {\nif (ang_y > 0) {counterSign = 1;}\nelse {counterSign = -1;}\nang_y -= counterSign * oneTenthDeg;\nangY += counterSign;\ncalcOffVert = true;}\n\/\/Overflow Z data and recompute as needed\nwhile (abs(ang_z) > oneTenthDeg) {\nif (ang_z > 0) {counterSign = 1;}\nelse {counterSign = -1;}\nang_z -= counterSign * oneTenthDeg;\nangZ += counterSign;\ncalcOffVert = true;}\n\n#### cerving\n\n##### Owner, Eggtimer Rocketry\nTRF Supporter\nVery nice. BTW, the BMP180 is discontinued and basically unavailable, you're going to want to try another baro soon. I went with the TE\/Meas-Spec MS5637 to replace the BMP180's in the Eggtimer altimeters. Unfortunately the code isn't compatible, but I'll send you the code snippet if you're interested. (Don't use MS5607\/5611 code, it \"looks\" the same but it's not.) It's a bit faster than the BMP180, but the temperature sensor takes longer to stabilize.\n\n#### plugger\n\n##### Well-Known Member\nI am adding 2 clustomatics from Whooshtronics (great product:smile:, also discontinued:cry. Since plans call for starting up to 6 motors, and I have some concerns about the amperage limitations of the solid state relays, this will move the high amperage ignition circuit from the companion board to the Clustomatic, as well as meter out proper current to each individual igniter and not allow one short from stealing all the electrons.\nAgreed. PK's uMAD was another product from Wooshtronics that is incredibly useful. It's crazy to think that his Clustomatics were \\$25AUD less than 5 years ago. Talk about VALUE!\n\n#### SparkyVTFlyer\n\n##### Senior Member\nTRF Supporter\nHere are some visuals highlighting the cross-axis sensitivity problem. This might be part of the reason I can't get quaternions to work correctly. Now that I know how to correct for it, I'll give them another shot.\n\nThe first graph shows my algorithm without the cross-axis correction. You can see the cycling when the roll rate gets high. The second graph corrects this effect with a simple linear regression model. Notice the big difference between the two. This matches really well with the onboard video. In particular, at apogee the video show the rocket pointed directly at the horizon (90 degrees), which is exactly what the algorithm is estimating. This was a 2-stage I-to-I flight that topped out around 6,000 ft.\n\n#### ekchess\n\n##### Member\nSparky, With respect to your code, you have define gdt = 0L. Since that doesn't get updated anywhere in code, the computed angles zero out. Can you let us know what value gdt should take (I'm assuming it has to do with frequency of gyro readout and will be dependent on the gyro settings and hardware used in the circuit)? I implemented the code as written with an MPU6050 and printed out the values of angX, angY, and andZ, and found them to be consistently 0. With my current hardware\/firmware settings, the gyro is being sampled at 8000Hz (obviously not using all the data when printing is occurring). I can slow that down to 1000Hz by increasing the filtering. Thanks for following the thread! I haven't been able to implement Keith's quaternion-based method as yet, but I'm still working on it. Your method seems much simpler.\n\n#### SparkyVTFlyer\n\n##### Senior Member\nTRF Supporter\nSorry, I forgot that part. The full flight computer code is around 800 lines. gdt is the between samples time in microseconds.\n\ngdt = currentClockTime - previousClockTime\n\nSorry my code isn't exactly clear as to what's going on. Its a little tricky because I did the math to make it run on integers and not floats. I also sacrificed resolution to make it run faster. You will need to update the values for oneTenthDeg and oneDeg to be your gain value x 1,000,000. For mine, the gain is set to 2000 dps, which is 0.07 degree per lsb (least significant bit). Yours will be different depending on your gyro.\n\nI just looked up the MPU6050. Your settings should be:\n\noneDeg = 16400000L;\noneTenthDeg = 1640000L;\n\nThe angX, angY, and angZ values are the current orientation of the rocket which you want to output. angX is in degrees and angY, angZ are in tenths of a degree. Divide these by 10 in the output to get the estimate. These values only get updated when the rocket's rotation exceed the oneDeg and oneTenthDeg thresholds. ang_x, ang_y, and ang_z keep the pieces of the angle between the thresholds. Precision is maintained, but resolution is sacrificed.\n\nThe algorithm requires the cosine and sine of the angX rotation. Again, to make it go faster, I update these only when the thresholds oneDeg is exceeded. Since I only update these values when it has moved by exactly one degree of rotation, then I can employ the trig angle-addition identity very efficiently.\n\nThe heart of the algorithm is here:\nang_z += cosX * gyro_event.gyro.z * gdt;\nang_z += sinX * gyro_event.gyro.y * gdt;\nang_y += cosX * gyro_event.gyro.y * gdt;\nang_y -= sinX * gyro_event.gyro.z * gdt;\n\nDon't be fooled by its simplicity. It took me months to stumble upon it. It then took me twice as long to understand the math behind it. It looks like Euler's formula for 2-D rotations, but its not. Its actually employing a hidden series of arctan and tangent calculations. As long as the update rate is fast enough, I eliminate the tangent calculations with the small-angle approximation tan(x) ~= x.\n\nIf you are a NAR member, you can login and download my report from NARAM-58. Its not very well written, so if you don't understand it, it's just my crappy writing.\n\nLike I said before, this ONLY works with relatively simple rotations restricted to roughly one plane in 3D. If you swing the unit all over the place in many directions, then it will be wildly inaccurate. However, if you spin it around the vertical axis (like a rocket spinning in flight) and tilt it in any ONE direction (like a rocket tilting over at apogee), then it will be accurate. You can omit any cross-axis correction and it will still be relatively accurate, but you will see some cycling when the unit is spinning fast.\n\nLast edited:","date":"2020-11-28 16:39:07","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\": 0.5594319701194763, \"perplexity\": 1505.0937238111733}, \"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-2020-50\/segments\/1606141195687.51\/warc\/CC-MAIN-20201128155305-20201128185305-00671.warc.gz\"}"} | null | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.