text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
|---|---|---|
module General.InternalMessaging where
import BitcoinCore.Transaction.Transactions (Transaction(..), Value(..))
import BitcoinCore.Keys (Address)
data InternalMessage
= SendTX Transaction
| AddAddress Address
deriving (Show, Eq)
data UIUpdaterMessage
= IncomingFunds Value
| UTXOsUpdated
| NewBlock
deriving (Show, Eq)
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,202 |
Q: making transition effect width 100% to cover page I downloaded this transistion effect from Transistion effect page
source download page
I want to do this transistion effect with image being of 100% width filling the full page
can this transition be modified easily to cover the full page width.
I have modified the divs classes to 100% and set image style 100% css but what happens is it becomes small does the transition and enlarges again. Please advise the best solution to enable this transition to apply with 100% width.
Thanks
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,631 |
<?php
declare(strict_types=1);
namespace ClanWolf\C3\Controller;
use Exception;
use SlaxWeb\Bootstrap\Application;
use ClanWolf\C3\Library\Output\Json\Action as JsonAction;
class API
{
protected $app = null;
protected $config = null;
protected $logger = null;
protected $json = null;
protected $authManager = null;
protected $requiredLogin = true;
public function __construct(Application $app)
{
$this->app = $app;
$this->config = $app["config.service"];
$this->logger = $app["logger.service"]();
$this->json = $this->app["output.service"];
$this->authManager = $app["authManager.service"];
$this->logger->info("API Controller initisialized", ["controller" => get_class($this)]);
$this->setLoginData();
}
protected function checkPrivs(string $priv): bool
{
if ($this->authManager->privileges()->has($priv)) {
return true;
}
$this->logger->info("User attempted to access resource with insufficient permissions");
// set error to JSON response
$this->json->addAction(new JsonAction(
JsonAction::ACT_REDIRECT,
["url" => $this->app["baseUrl"] . "/dashboard"]
))->addError(
"You are not permitted to access this resource.",
401
);
return false;
}
/**
* Set login data to JSON output. The data must at least include if a user is
* validly logged in, and the users username.
*
* @return void
*/
protected function setLoginData()
{
$loggedIn = true;
$username = "";
try {
$user = $this->authManager->getUser();
$username = $user->username;
} catch (Exception $e) {
if ($this->requiredLogin) {
$this->json->addError(
"Not logged in. You will be redirected to login page.",
401
)->addAction(new JsonAction(
JsonAction::ACT_REDIRECT,
["url" => $this->app["request.service"]->getSchemeAndHttpHost()]
));
exit;
}
$loggedIn = false;
}
$this->json->add([
"auth" => ["loggedIn" => $loggedIn, "username" => $username]
]);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,348 |
Q: How to append a unique_id to my express node logs with winston without refactoring everything? I've an Express app. I'd like to trace all the loggings that were made by a single request.
Apache has a module called mod_unique_id which injects in the request headers a special one containing a unique hash. I'd like to use such hash when logging (anything).
For example if an user is assigned by apache the unique_id valued "abcdefg" and somewhere in my code (controller, model, or anything) i generate a debug log i'd like to have "abcdefg" attached to every log entry.
The only idea that pops in my mind is to create a logger instance using app.use() and pass that logger instance to ALL the functions that are needed (models,libs etc) to generate the proper response.
Unfortunately this will cause me to rewrite a lot of the code to let old functions accept this new logger instance.
Does anyone know a better way of having a single "logger" instance per "request" which is accessible somehow without passing this "per-request-created-logger" to anything ?
PS: I'm currently using winston to log
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,407 |
Die Bob-Europameisterschaft 1989 wurde am 21. und 22. Januar im Zweierbob und am 28. und 29. Januar 1989 im Viererbob zum zweiten Mal auf der Bobbahn Winterberg Hochsauerland im sauerländischen Winterberg als vierter von sechs Veranstaltungen des Bobweltcups ausgetragen.
Nach der sportlich eher zweitrangigen Europameisterschaft im Vorjahr, bei der sich die Topathleten bereits in der Vorbereitung für die Olympischen Spiele in Calgary befanden, hatte die Europameisterschaft in der nacholympischen Saison einen wesentlich höheren Stellenwert. Allerdings hatte sich einiges im Boblager getan. Nach dem kaum für möglich gehaltenen Olympiasieg im Viererbob für Ekkehard Fasser war dieser zunächst zurückgetreten. Diesem Rücktritt vom Leistungssport schloss sich auch Hans Hiltebrand an, der im Oktober 1988 ein Angebot als kanadischer Bob-Nationaltrainer annahm. Den Zweien folgte nach einer letztlich enttäuschenden Saison im April 1988 Silvio Giobellina, der französischer Bob-Nationaltrainer wurde. Im August 1988 trat dann schließlich auch noch Ralph Pichler ab, der das Amt des italienischen Bob-Nationaltrainers übernahm. Nach dem Abgang von Erich Schärer ein Jahr zuvor waren nun alle fünf Schweizer Top-Athleten nicht mehr am Start, die für eine glorreiche Phase des Schweizer Bobsports standen. Überdies wurde Schärer, der nach seinem Karriereende das Amt das Schweizer Auswahltrainers übernommen hatte, im Oktober 1988 von Franz Isenegger abgelöst. Der Vorruhestand hielt bei Ekkehard Fasser allerdings nicht lange an, schon im November 1988 trat er zu Qualifikationswettbewerben und später auch im Bob-Weltcup wieder an. Obwohl er immerhin Schweizer Vizemeister im Viererbob wurde, verzichtete er anschließend auf einen Start bei der Europa- und Weltmeisterschaft. Nun waren Gustav Weder und Nico Baracchi die Schweizer Aushängeschilder, vor allem bei Baracchi stand aber der Härtetest gegen die Weltelite noch bevor.
Aber auch im Lager der DDR-Bobsportler hatte es Veränderungen gegeben. Altmeister Bernhard Lehmann war vom Leistungssport verabschiedet worden, ihm folgten Dietmar Schauerhammer, Matthias Trübner, Roland Wetzig, Hans-Joachim Schurack, Ronald Stein und Dietmar Jerke. Zudem schwand mehr und mehr die Oberhofer Dominanz, durch die Altenberger Bobbahn wuchsen vermehrt Zinnwalder Talente heran, allen voran Harald Czudaj. Außerdem konnte die Fachwelt die langsame Wiederauferstehung einer früher sehr erfolgreichen Bobnation beobachten. Ob der EM-Titel von Christian Schebitz dem Bobsport in der Bundesrepublik Deutschland einen Schub gegeben hatte, war nicht zu beurteilen, aber ausgerechnet der bereits 36-jährige Rudi Lochner stieß in der schon laufenden Saison mit Anschieber Markus Zimmermann in die Weltspitze vor.
Regelementsänderungen
Nach den eher unrühmlichen Bobwettbewerben bei Olympia in Calgary, die von nicht wenigen Athleten und Fachleuten als irregulär bezeichnet worden waren, sah sich die FIBTin der Pflicht, durch geeignete Maßnahmen einen sportlich gerechteren Wettkampf zu gewährleisten. Gleichzeitig hatten die Veranstalter mit immer größeren Starterfeldern zu kämpfen, da der Bobsport wohl nicht zuletzt durch die Teilnahme des jamaikanischen Bobs bei Olympia und durch Prinz Albert von Monaco als Bobpilot eine zunehmende mediale Aufmerksamkeit erhalten hatte. Für die EM in Winterberg hatten bei den kleinen Schlitten zum Beispiel sage und schreibe 46 Teams gemeldet. Die FIBT hatte dazu im Sommer 1988 auf ihrem Kongreß in Dresden getagt und beschloss dort die Einteilung der Bob-Teams in Gruppen. Die Startergruppe bestand aus Bobs der 12 bestplatzierten Nationen des Vorjahresweltcups, womit wohl auch dieser in der Wertigkeit angehoben werden sollte. Wen die jeweilige Nation in die Topgruppe entsandte, war allerdings nicht festgelegt, in der Regel war es der interne Qualifikationssieger oder das beste Weltcupteam. Damit war zugleich garantiert, das die Topteams das beste Eis haben würden. Bei der EM wurden die restlichen 34 Bobs in drei weitere Startgruppen eingeteilt. Nach dem ersten Lauf, würden dann die besten zwölf Bobs in umgekehrter Reihenfolge starten, danach folgte der Rest. Dieser Modus war nicht unumstritten und ließ vor allem bei den Athleten aus der Schweiz die Befürchtung aufkommen, dass nunmehr in der Regel nur noch ein Team pro Land Medaillenchancen haben würde.
Zweierbob
Bei Nebel und Regen startete der erwartete Zweikampf Weder - Hoppe, der sich aber zur Freude der Zuschauer in einen Dreikampf ausweitete. Rudi Lochner fuhr im ersten Lauf Bestzeit und ließ so die beiden Favoriten zunächst hinter sich. Allerdings hatte der Mann vom Königssee mit besonderen Schwierigkeiten zu kämpfen, im zweiten und vierten Lauf beschlug sein Helmvisier, was sich sofort in schlechteren Laufzeiten niederschlug. So musste er im zweiten Lauf die Führungsposition an den Schweizer Gustav Weder abgeben, blieb aber noch mit 24 Hundertstel vor dem Hoppe-Bob. Dem Doppelolympiasieger war im zweiten Lauf ein ungewöhnliches Missgeschick passiert. Nach dem Start sprang Hoppe zunächst auf den Sitz seines Anschiebers Bogdan Musiol und musste so nochmals nach vorn rutschen, bis Musiol einsteigen konnte. Dabei ging wertvolle Zeit verloren. Am zweiten Wettkampftag machte Hoppe diesen Ausrutscher vergessen und fuhr in beiden Läufen Bestzeit. Bereits nach dem dritten Lauf lag er mit Fünf Hundertstel Vorsprung auf Lochner auf dem Silberrang. Da Lochner im letzten Lauf durch sein angelaufenes Visier eine deutlich schlechtere Zeit fuhr, war Hoppe nach seiner Fahrt vom Silberrang nicht mehr zu verdrängen. Weder stand durch Hoppes sehr gute Zeit unter Zugzwang, ließ sich den Titel aber nicht mehr nehmen. Am Ende war der zwischenzeitlich auf vier Zehntel angeschwollene Vorsprung auf 13 Hundertstel zusammengeschmolzen. Für den Schweizer bedeutete dies den ersten großen internationalen Titel im Seniorenbereich. Der Zinnwalder Harald Czudaj belegte als bester Bob der zweiten Startgruppe einen guten vierten Platz und etablierte sich immer mehr als zweiter Mann in der DDR-Nationalmannschaft hinter Aushängeschild Wolfgang Hoppe.
Viererbob
Bei den großen Schlitten gingen noch 29 Teams an den Start. Auf der wenig selektiven Kunsteisbahn zeigte sich bereits im Training, dass der Favoritenkreis etwas größer abzustecken war. Neben Weder machten vor allem die Österreicher Appelt und Kienast sowie Weders Teamkollege Baracchi mit guten Traingszeiten auf sich aufmerksam. Letztlich kam der Sieger mit Ingo Appelt nach 11 Jahren erstmals wieder aus Österreich. Dabei hatte es nach einem spannenden Duell bis zum dritten Lauf danach ausgesehen, das der Zinnwalder Harald Czudaj seinen ersten Titel im Seniorenbereich feiern könnte. Im ersten Lauf mit Bestzeit fahrend, hatte die Czudaj-Crew nach drei Läufen nur 5 Hundertstel Rückstand auf Appelt. Der Goldschmied aus Tirol fuhr aber im letzten Lauf Tagesbestzeit und gewann letztlich mit 26 Hundertstel seinen ersten internationalen Titel. Auch der Kampf um Bronze wurde erst im letzten Lauf entschieden, wob vor allem der Schweizer Baracchi nochmal für Spannung sorgte. Zwar hatte der Österreicher Peter Kienast bereits nach dem ersten Wettkampftag auf dem dritten Platz gelegen, doch vier Hundertstel Rückstand auf Hoppe, 8 Hundertstel auf Weder und 22 Hundertstel auf Baracchi waren nicht eben ein Ruhekissen. Während Weder sich durch einen verpatzten dritten Lauf mit der nur neuntbesten Zeit im Kampf um Bronze verabschiedete, wurde dessen Teamkollege Nico Barrachi ärgster Konkurrent von Kienast. Nach dem dritten Lauf war der Vorsprung bereits wieder etwas geschmolzen und mit der gleichen Laufbestzeit wie später Appelt setzte der Schweizer Baracchi den Österreicher Kienast nochmals gehörig unter Druck. Am Ende trennten beide nur noch vier Hundertstel. Für Kienast war es nach WM-Silber 1986 die zweite internationale Medaille.
Medaillenspiegel
Einzelnachweise
1989
Sportveranstaltung 1989
Sportveranstaltung in Winterberg
Wintersport (Deutschland) | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,199 |
Jury deliberations are underway in the trial of a Duluth headshop owner who stands accused of selling banned synthetic drugs.
Jim Carlson, the owner of the Last Place on Earth, his girlfriend and his son are all facing multiple counts of illegally selling banned synthetic drugs by "misbranding" them as incense, bath salts, watch cleaner and other names.
The Star Tribune reports, that the case went to the jury around 4 p.m. Wednesday afternoon, in U.S. District Court in Minneapolis.
Carlson, 56, faces 55 charges, while his girlfriend, Lava Haugen, 33, and son, Joseph Gellerman, 34, face four counts each. Both were employees of the store.
According to the Duluth News Tribune, defense attorney John Markham told jurors that the Last Place on Earth may have been a revolting place, but that didn't make the business illegal.
Assistant U.S. Attorney Surya Saxena argued though that because the defendants business was extremely profitable, they knowingly violated federal laws, or at least avoided knowledge of the laws.
The federal trial is in its third week.
Carlson has been an outspoken critic of the government's crackdown on synthetic drugs, saying the laws used to prosecute sellers have been "unconstitutionally vague." | {
"redpajama_set_name": "RedPajamaC4"
} | 9,195 |
namespace {
// The WebContentsDelegate for the keyboard.
// The delegate deletes itself when the keyboard is destroyed.
class KeyboardContentsDelegate : public content::WebContentsDelegate,
public content::WebContentsObserver {
public:
KeyboardContentsDelegate(keyboard::KeyboardControllerProxy* proxy)
: proxy_(proxy) {}
virtual ~KeyboardContentsDelegate() {}
private:
// Overridden from content::WebContentsDelegate:
virtual content::WebContents* OpenURLFromTab(
content::WebContents* source,
const content::OpenURLParams& params) OVERRIDE {
source->GetController().LoadURL(
params.url, params.referrer, params.transition, params.extra_headers);
Observe(source);
return source;
}
// Overridden from content::WebContentsDelegate:
virtual void RequestMediaAccessPermission(content::WebContents* web_contents,
const content::MediaStreamRequest& request,
const content::MediaResponseCallback& callback) OVERRIDE {
proxy_->RequestAudioInput(web_contents, request, callback);
}
// Overridden from content::WebContentsObserver:
virtual void WebContentsDestroyed(content::WebContents* contents) OVERRIDE {
delete this;
}
keyboard::KeyboardControllerProxy* proxy_;
DISALLOW_COPY_AND_ASSIGN(KeyboardContentsDelegate);
};
} // namespace
namespace keyboard {
KeyboardControllerProxy::KeyboardControllerProxy() {
}
KeyboardControllerProxy::~KeyboardControllerProxy() {
}
aura::Window* KeyboardControllerProxy::GetKeyboardWindow() {
if (!keyboard_contents_) {
content::BrowserContext* context = GetBrowserContext();
GURL url(kKeyboardWebUIURL);
keyboard_contents_.reset(content::WebContents::Create(
content::WebContents::CreateParams(context,
content::SiteInstance::CreateForURL(context, url))));
keyboard_contents_->SetDelegate(new KeyboardContentsDelegate(this));
SetupWebContents(keyboard_contents_.get());
content::OpenURLParams params(url,
content::Referrer(),
SINGLETON_TAB,
content::PAGE_TRANSITION_AUTO_TOPLEVEL,
false);
keyboard_contents_->OpenURL(params);
}
return keyboard_contents_->GetView()->GetNativeView();
}
void KeyboardControllerProxy::ShowKeyboardContainer(aura::Window* container) {
container->Show();
}
void KeyboardControllerProxy::HideKeyboardContainer(aura::Window* container) {
container->Hide();
}
void KeyboardControllerProxy::SetupWebContents(content::WebContents* contents) {
}
} // namespace keyboard
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,518 |
\section{Introduction}\label{sec:introduction}
Many interesting quantum magnets are characterized by significant spatial anisotropy of the exchange interaction pattern and
often can be understood as being built from one-dimensional spin chains. Several recent examples of these include
triangular antiferromagnets Cs$_2$CuCl$_4$ \cite{coldea2003} and Cs$_2$CuBr$_4$ \cite{Ono2005,Ono2005b,takano2009}, actively investigated for their fractionalized spinon continuum
and pronounced 1/3 magnetization plateau, correspondingly, and high-field candidate spin nematic materials such as LiCuVO$_4$ \cite{mourigal2012,svistov2014}
and PbCuSO$_4$(OH)$_2$ \cite{linarite2016,povarov2016}.
Quasi-one-dimensional nature of this class of materials is responsible for the hierarchy of temperature/energy scales when
at high temperature, relative to the weak inter-chain exchange $J'$, the material exhibits mainly one-dimensional physics
with little correlations between spins from different chains. Upon further cooling the inter-chain interactions become
important and determine the ultimate ground state type of order that is realized below the ordering temperature $T_c \sim J'$\cite{schulz1996}.
If the interchain interaction is geometrically frustrated, as for example happens in triangular \cite{olegandbalents} and kagome \cite{Schnyder2008} lattices, the ordering temperature
may be further suppressed below the intuitive mean-field $T_c \sim J'$ estimate.
In the present work we describe novel mechanism of frustrating inter-chain spin exchange. We show that spin chains with strong
uniform Dzyaloshinskii-Moriya (DM) anisotropic exchange interaction, orientation of the DM vector of which is however staggered
between the chains, are too characterized by strongly reduced ordering temperature.
Our work is strongly motivated by two new interesting materials - K$_2$CuSO$_4$Cl$_2$ and K$_2$CuSO$_4$Br$_2$~\cite{Halg2014,smirnov,Halg'sphdthesis} - which are
described by Hamiltonian \eqref{eq:H_0} representing weakly coupled spin chains (chain exchange $J$, inter-chain exchange $J'$, and $J'\ll J$) perturbed by the
uniform within the chain, but staggered between chains, Dzyaloshinskii-Moriya (DM) anisotropic exchange interaction of magnitude $D$,
as shown in Fig.~\ref{fig:lattice}. (Similar DM geometry is also realized in a spin-ladder material (C$_7$H$_{10}$N)$_2$CuBr$_4$.\cite{glazkov2015})
Despite close structural similarity, the two materials are characterized by different $h-T$ phase diagrams in the
situation when magnetic field $\bm h$ is applied along the DM axis $\bm D$ of the material. Our objective here is to provide
theoretical explanation of those phase diagrams, and find reasons for their differences.
We also extend analysis to another special field configuration, when magnetic field is perpendicular to the DM vector.
Individual spin chains with uniform \cite{Gangadharaiah2008,Halg2014,Garate2010,smirnov} and staggered \cite{dender} DM interactions
respond differently to the magnetic field. In the latter case it leads to the opening of significant spin gap \cite{oshikawa1999} while in the former the (much smaller)
gap opens up only in the ${\bm h} \perp {\bm D}$ geometry \cite{Gangadharaiah2008,Garate2010}.
We show below that this difference persists in the presence of the weak inter-chain interaction and is responsible for a very different set
of the ordered states for the uniform DM problem in comparison with the staggered DM one \cite{sato2004}.
The plan of the paper is as follows.
In Sec.~\ref{sec:hamiltonian}, we introduce the pertinent spin chain model. Focusing on the low-energy physics, we attack the problem with the help of bosonization in Sec.~\ref{subsec:bosonization}. We examine the phase diagram of the model for the two special magnetic field orientations,
${\bm h} \parallel {\bm D}$, Sec.~\ref{sec:parallel} and Sec.~\ref{sec:CMF}, and ${\bm h} \perp {\bm D}$, Sec.~\ref{sec:perpendicular}.
Throughout the paper we find competition between transverse cone-like orders and longitudinal spin density wave (SDW) ones. Here by the cone order we mean the order
that develops in the plane perpendicular to the external magnetic field. Combined with finite magnetization, this order can be visualized as the one where spins lie on the surface
of the cone whose axis is oriented along the magnetic field. The longitudinal SDW order is quite different - spins order in the direction of the magnetic field.
Magnitude of the local magnetic moment is position dependent, which makes the resultant modulated pattern quite similar to a charge density wave order often found in itinerant
electron systems.
In Sec.~\ref{sec:parallel}, by means of the renormalization group (RG) analysis, we find a single commensurate cone state
(magnetic order develops in the plane transverse to ${\bm h}$) for weak DM interaction ($D\ll J'$). In the opposite, and novel, case of strong DM interaction
($D\gg J'$ but still $D \ll J$) the inter-chain coupling is strongly frustrated and the cone state is destroyed.
Instead, a collinear longitudinal spin density wave emerges as the ground state of the system of weakly coupled spin chains.
We next show how quantum fluctuations generate a transverse spin exchange between {\em next-nearest} (NN) chains, which competes with the SDW order. The resultant cone-like order, denoted as coneNN, is found to develop above a critical magnetic field $h_c\sim J'$. The coneNN order is a juxtaposition of the two separate cone orders, formed by spins of {\em even} and {\em odd} chains correspondingly.
Owing to the opposite direction of DM axis on even/odd chains, spins making up even/odd cones appear to rotate in {\em opposite} directions. These RG-based findings are supported by the
chain mean-field (CMF) calculations in Sec. \ref{sec:CMF}, where we compute and compare ordering temperature of various two-dimensional instabilities.
Turning to the ${\bm h} \perp {\bm D}$ arrangement in Sec.~\ref{sec:perpendicular}, we carry out chiral rotation of spin currents which reduces the problem
to that in the effective magnetic field the magnitude of which is given by the $\sqrt{h^2 + D^2}$. Subsequent RG analysis leads to detailed $h-D$ phase diagram
which harbors three different orders: two commensurate SDWs along and perpendicular to DM vector, respectively,
and a \textit{distorted-cone} state (elliptic spiral structure). We find that in the experimentally relevant limit $D\ll J$, the phase transition between two different SDWs
happens at $h_c\sim 0.23\pi J$, which is independent of $D$ and is of a spin-flop kind. The distorted-cone phase requires unrealistically large DM interaction $D\sim J$
and is separated from the SDW by a boundary at $h/D\simeq1.5$, which matches well with the classical prediction \cite{Garate2010}.
We conclude the manuscript with a brief summary and a discussion of the relevance of our results to ongoing experimental studies of K$_2$CuSO$_4$Br$_2$
and related materials. Numerous technical details of our analysis are presented in Appendices.
\section{Hamiltonian}
\label{sec:hamiltonian}
We consider weakly coupled antiferromagnetic Heisenberg spin-$1/2$ chains subject to a uniform Dzyaloshinskii-Moriya (DM) interaction and an external magnetic field.
The system is described by the following Hamiltonian,
\begin{equation}
\begin{split}
{\cal H}&=\sum_{x,y}[J{\bm S}_{x,y}\cdot{\bm S} _{x+1,y} + J'{\bm S}_{x,y}\cdot{\bm S} _{x,y+1}]\\
&\quad +{\bm D}\cdot\sum_{x,y}(-1)^{y}{\bm S}_{x,y}\times {\bm S}_{x+1,y}-{\bm h}\cdot \sum_{x,y}{\bm S}_{x,y},\\
\end{split}
\label{eq:H_0}
\end{equation}
where ${\bm S}_{x,y}$ is the spin-$1/2$ operator at position $x$ of $y$-th chain. $J$ and $J'$ denote isotropic intra- and inter-chain antiferromagnetic exchange couplings
as shown in Fig.~\ref{fig:lattice},
and we account for interactions between nearest neighbors only. The inter-chain exchange is weak, of the order of $J'\sim 10^{-2} J$.
DM interaction \cite{Dzyalo,moriya} is parameterized by the DM vector ${\bm D}=D\hat{z}$, direction of which is staggered between adjacent chains -- note the factor $(-1)^y$ in \eqref{eq:H_0}.
Importantly, within a given $y$-th chain vector ${\bm D}$ is uniform. $\bm h$ is an external magnetic field.
\begin{center}
\begin{figure}[!tbp]
\includegraphics[width=0.8\columnwidth]{lattice.eps}
\caption{Geometry of the problem. Intra-chain bonds $J$ (thick lines along $\hat{x}$), inter-chain bonds $J'$ (dashed lines along $\hat{y}$), and $J'\ll J$.
DM vectors on neighboring chain have opposite direction, pointing either into or out of the page.}
\label{fig:lattice}
\end{figure}
\end{center}
\subsection{Lattice rotation of spins}
\label{subsec:lattice-rot}
DM interaction in Eq.~\eqref{eq:H_0} can be gauged away by a position-dependent rotation of spins about $\hat z$ axis \cite{Perk1976,shekhtman1992,oshikawa1999,bocquet2001},
\begin{equation}
S_{x,y}^+\to \tilde S_{x,y}^{+}e^{i\alpha_y x},\quad S_{x,y}^{z}\to \tilde S_{x,y}^{z},
\end{equation}
where the rotation angle $\alpha_y=\arctan[(-1)^y D/J]$ for the $y$-th chain changes sign between even and odd chains.
In our work, we consider $D\ll J$, which is the limit relevant for real materials\cite{Halg2014, smirnov, Dmitrienko2014}, therefore the rotation angle $\alpha_y$ is small.
After the rotation Hamiltonian \eqref{eq:H_0} reads
\begin{equation}
\begin{split}
\tilde{\cal H}&=\sum_{x,y}[\frac{\tilde J}{2} ( \tilde{S}^{+}_{x,y} \tilde{S}^{-}_{x+1,y}+{\rm h.c.})+J \tilde {S}^{z}_{x,y}\tilde{S}_{x+1,y}^{z}]\\
&\quad +\sum_{x,y}[\frac{J'}{2}(\tilde S_{x,y}^{+}\tilde S_{x,y+1}^{-}e^{2i\alpha_y x}+{\rm h.c.})+J' \tilde {S}_{x,y}^{z} \tilde{S}_{x,y+1}^{z}]\\
&\quad -\frac{h_x}{2}\sum_{x,y} (\tilde S_{x,y}^{+}e^{i\alpha_y x}+h.c.)-h_z\sum_{x,y} \tilde S_{x,y}^{z}.
\label{eq:ttH_0}
\end{split}
\end{equation}
where $\tilde J=\sqrt{J^2+D^2}$ describes the transverse component of exchange interaction for the obtained XXZ chain.
Observe that the transverse component of the {\em inter-chain} interaction, $J' e^{2i\alpha_y x}$,
is oscillating function of the chain coordinate $x$.
It is intuitively clear that for sufficiently fast oscillation (that is, for sufficiently large $|\alpha_y|$) this term
must ``average out'' and disappear from the Hamiltonian. Our detailed calculations, reported below, fully confirm this intuition.
\subsection{Determination of the DM vector by ESR experiments}
\label{sec:esr}
The DM vector $\bm D$ can be characterized by the electronic spin resonance (ESR) measurements\cite{Halg2014,p,smirnov}.
In a magnetic field $\bm h\parallel \bm D$, two resonance lines (ESR doublet) are observed at resonance frequencies $\nu_{\pm}$,
\begin{equation}
2\pi\hbar\nu_{\pm}=|g\mu_Bh\pm\frac{\pi}{2}D|.
\label{eq:esr-split}
\end{equation}
This ESR doublet is only observable for magnetic field having a component along $\bm D$, thus this property can be used to determined the direction of $\bm D$.
In another limiting case $\bm h\perp \bm D$, the resonance occurs at the ``gapped" frequency
\begin{equation}
2\pi\hbar\nu=\sqrt{(g\mu_Bh)^2+(\frac{\pi}{2}D)^2}.
\label{eq:esr-gap}
\end{equation}
This gap provides an alternative way to obtain the amplitude $D$. (The lineshape and the temperature dependence of the width of the resonance
were studied in Refs.\onlinecite{karimi2011} and \onlinecite{Furuya2016}, Appendix D, correspondingly.)
In the case of K$_2$CuSO$_4$Br$_2$ several ESR measurements \cite{Halg2014,smirnov}
have consistently predicted $D_{\rm Br} \approx 0.28$ K. In K$_2$CuSO$_4$Cl$_2$ the DM interaction is smaller. Recent experiment \cite{smirnov2016}
estimates it to be $D_{\rm Cl} \approx 0.11$ K.
With regards to other parameters of the microscopic Hamiltonian, the intra-chain exchange $J$ has been estimated\cite{Halg2014} as $J_{\rm Cl} = 3.1$ K and $J_{\rm Br} = 20.5$ K.
Inter-chain interaction $J'$ is most difficult to estimate. Appendix~\ref{app:j'} describes fit of our CMF calculations of the ordering temperatures to experimental
values which allows us to estimate inter-chain exchanges as $J'_{\rm Cl} = 0.08$ K and $J'_{\rm Br} = 0.09$ K.
Thus the ratio $D/J'$ is about $1.3$ for K$_2$CuSO$_4$Cl$_2$ and $3.1$ for K$_2$CuSO$_4$Br$_2$ respectively. This, according to our investigation, places these
two materials into two distinct limits of weak and strong DM interaction, respectively.
\subsection{Bosonization: low-energy field theory}
\label{subsec:bosonization}
In the low-energy continuum limit the spin operator is represented by\cite{Gangadharaiah2008},
\begin{equation}
{\bm S}_{x,y}\to{\bm J}_{yL}(x)+{\bm J}_{yR}(x)+(-1)^{x/a}{\bm N}_y(x),
\label{eq:spin}
\end{equation}
where $a$ is the lattice spacing, and continuous space coordinate is introduced via $x=na$, with $n$ an integer.
${\bm J}_{yL}(x)$ and ${\bm J}_{yR}(x)$, are the uniform left and right spin currents, and ${\bm N}_y(x)$ is the staggered magnetization.
These fields can be conveniently expressed in terms of abelian bosonic fields $(\phi_y(x),\theta_y(x))$,
\begin{equation}
\begin{gathered}
J_{yR}^{+}=\frac{1}{2\pi a}e^{-i\sqrt{2\pi}(\phi_y-\theta_y)},\,
J_{yR}^{z}=\frac{1}{2\sqrt{2\pi}}(\partial_x\phi_y-\partial_x\theta_y),\\
J_{yL}^{+}=\frac{1}{2\pi a}e^{i\sqrt{2\pi}(\phi_y+\theta_y)},\;\,\;
J_{yL}^{z}=\frac{1}{2\sqrt{2\pi}}(\partial_x\phi_y+\partial_x\theta_y).\\
\end{gathered}
\label{eq:J}
\end{equation}
and
\begin{equation}
{\bm N}_y= A(-\sin[\sqrt{2\pi}\theta_y],\; \cos[\sqrt{2\pi}\theta_y],\;-\sin[\sqrt{2\pi}\phi_y]).
\label{eq:N}
\end{equation}
Here, $A\equiv \gamma/(\pi a)$, and $\gamma=\langle \cos(\sqrt{2\pi}\varphi_{\rho})\rangle \sim O(1)$ is
determined by gapped charged modes of the chain.
The above parameterization, applied to the Hamiltonian \eqref{eq:H_0}, produces the following continuum Hamiltonian \cite{Gangadharaiah2008,Schnyder2008,Garate2010}
\begin{equation}
{\cal H}=\sum_y [{\cal H}_0 + {\cal V} + {\cal H}_{\rm bs}+{\cal H}_{\rm inter}],
\label{system_1}
\end{equation}
where
\begin{equation}
\begin{gathered}
{\cal H}_0=\frac{2\pi v}{3}\int \mathrm{d}x ({\bm {J}_{yR} }\cdot{\bm {J}_{yR} }+{\bm {J}_{yL} }\cdot{\bm {J}_{y L} }),\\
{\cal V}=-h_z\int \mathrm{d}x (J_{yR}^{z}+ J_{yL}^{z})-h_x\int \mathrm{d}x(J_{yR}^{x}+J_{yL}^{x})\\
\quad +(-1)^y \tilde{D} \int \mathrm{d}x(J_{yR}^{z}-J_{yL}^{z}),\\
{\cal H}_{\rm bs}=-g_{\rm bs}\int \mathrm{d}x [ J_{yR}^xJ_{yL}^x+J_{yR}^yJ_{yL}^y+(1+\lambda)J_{yR}^zJ_{yL}^z ],\\
{\cal H}_{\rm inter}=J'\int \mathrm{d}x{\bm N}_{y}\cdot{\bm N}_{y+1},\\
\end{gathered}
\label{system_2}
\end{equation}
where $v\simeq J\pi a/2$ is the spin velocity and $\tilde{D}=D(1+2\gamma^2)/\pi \approx D$. $\cal V$ contains the second line of Eq.~\eqref{eq:H_0},
it collects all vector-like perturbations of the bare chain Hamiltonian ${\cal H}_0$.
${\cal H}_{\rm bs}$ describes residual backscattering interaction between right- and left-moving spin modes of the chain,
its coupling is estimated as $g_{\rm bs} \approx 0.23 \times (2\pi v)$, see Ref.~\onlinecite{Garate2010} for details.
An important DM-induced anisotropy parameter $\lambda$ is given, according to Ref.~\onlinecite{Garate2010} (see Eq. (B2) there), by
\begin{equation}
\lambda=c' \frac{D^2}{J^2}, ~\text{where}~ c'=\big(\frac{2\sqrt{2}v}{g_{\rm bs}}\big)^2 \approx 3.83.
\label{eq:lambda}
\end{equation}
The inter-chain interaction is described by ${\cal H}_{\rm inter}$, in which we kept the most relevant, in renormalization group sense, contribution,
${\bm S}_{x,y}\cdot{\bm S}_{x,y+1}\to{\bm N}_{y}(x)\cdot{\bm N}_{y+1}(x)$.
Now we examine phase diagram of the system described by Eq.~\eqref{system_1} and Eq.~\eqref{system_2} under two different field configurations, with
external magnetic field ${\bm h}$ placed parallel, Sec.~\ref{sec:parallel}, and perpendicular, Sec.~\ref{sec:perpendicular}, to the DM vector ${\bm D}$.
\begin{figure}[!tbp]
\includegraphics[width=0.8\columnwidth]{cone-wave-red.pdf}
\caption{(Color online) Staggered magnetization $\bm N$ of the coneNN state from Section~\ref{sec:coneNN}. $\bm h\parallel \bm D$ and spins are ordered in the transverse to $\bm h$ plane.
Red circles with arrows indicates the precession direction of spins, as one moves along each chain.
Note that the arrows' direction alternates between consecutive chains, owing to the staggering of DM vector.
Blue and green curves visualize relative orientation of spin on neighboring chains which oscillates from parallel to anti-parallel as one moves along the chain
leading to the cancellation of exchange interaction between nearest chains.}
\label{fig:cone}
\end{figure}
\section{Key ideas of RG and CMF}
\label{sec:overview}
Our work describes an extended study of a novel mechanism of frustrating inter-chain exchange interaction in a system of weakly coupled spin-1/2 chains.
This section summarizes key ideas of the two main theoretical techniques - renormalization group (RG) and chain mean-field theory (CMF) - that are used in
the paper.
We assume that all interchain couplings are weak. RG proceeds by integrating short-distance modes (small distance $x$ or large momentum $k_x$)
and by progressively reducing the large momentum cutoff from its bare value $\Lambda \sim 1/a$, which is of the order of the inverse lattice spacing $a$ (which we take to be $O(1)$),
to $\Lambda_\ell = \Lambda e^{-\ell}$,
where $\ell \in (0,\infty)$ is the logarithmic RG scale. Correspondingly, the minimal real space scale increases as $a e^\ell$.
Various interaction couplings $\gamma_i$, which enter the Hamiltonian as ${\cal H} = {\cal H}_0 + \sum_i \int dx \gamma_i {\cal O}^i_y(x) {\cal O}^i_{y+1}(x)$, see \eqref{system_2},
where ${\cal O}^i_y$ represent the $y$-th chain operator $J^a_y$ in \eqref{eq:J} or $N^a_y$ in \eqref{eq:N}, get renormalized (flow) during this procedure.
This renormalization is described by the {\em perturbative} RG flow equation of the dimensionless coupling \cite{oleg_cmf} $\tilde{\gamma}_i = \gamma_i/(v \Lambda_\ell^2)$
\begin{equation}
\frac{d \tilde{\gamma}_i}{d \ell} = (2 - 2\Delta_i) \tilde{\gamma}_i
\label{eq:basics}
\end{equation}
Here $\Delta_i$ is the scaling dimension of the operator ${\cal O}^i_y$, which in the case of {\em relevant} operator \eqref{eq:N}, can be represented as $\Delta_i = 1/2 + O(y)$,
where $y$ stands for the dimensionless {\em marginal} coupling. For the marginal operator, say ${\cal O}^k_y$, the scaling dimension is close to 1,
$\Delta_k = 1 + O(y)$, and as a result the flow of the marginal operator obeys $d y/d\ell \sim y^2$.
(See \eqref{eq:rg2} below for the specific example of both of these features.) Dimensionless coupling constants of the relevant operators increase with $\ell$. RG flow
need to be stopped at the RG scale $\ell^*$ at which the {\em first} coupling, say $\tilde{\gamma}_j$, reaches the value $C \sim O(1)$ of order $1$.
According to \eqref{eq:basics} $\ell^*$ can be estimated as $\ell^* = \ln[C/\tilde{\gamma}_j(\ell=0)]/(2-2\Delta_j)$.
The length scale $\xi = a e^{\ell^*}$ defines the correlation length above which the system needs to be treated as two (or three) dimensional.
The type of the developed two-dimensional order is determined by the most relevant operator ${\cal O}^j_y$ the coupling constant of which has reached $C \sim O(1)$ first.
Its expectation value can be estimated as $\langle {\cal O}^j\rangle \sim \xi^{-\Delta_j}$ and therefore, using $\tilde{\gamma}_j(\ell=0) = \gamma_j/(v \Lambda_{\ell=0}^2)$ and $\Lambda_{\ell=0} \sim O(1)$,
we obtain
\begin{equation}
\langle {\cal O}^j\rangle \sim \xi^{-\Delta_j} = \Big(\frac{\gamma_j}{C v}\Big)^{\Delta_j/(2-2\Delta_j)} .
\label{eq:orderparam}
\end{equation}
This discussion makes it clear that perturbative RG procedure is inherently uncertain since both the equation \eqref{eq:basics} and the ``strong-coupling value'' estimate $C$
are based on the perturbation expansion in terms of the coupling constants $\gamma_i$. Moreover, in the case of the competition between the two orders,
associated with operators ${\cal O}^j$ and ${\cal O}^i$ correspondingly, the transition from the one order to another can only be {\em estimated} from the condition
$\ell^*_j = \ell^*_i$.
This approximate treatment becomes more complicated when some of the interactions acquire coordinate-dependent oscillating factor, symbolically
$\int dx \gamma_i {\cal O}^i_y(x) {\cal O}^i_{y+1}(x) e^{i f x}$. Such a dependence is caused by external magnetic field and/or DM interactions,
see for example equations \eqref{shift:J-N} and \eqref{H'} below. Perturbative RG calculation is still possible, see for example Sec.4.2.3 of Giamarchi book \cite{Giamarchi}
for its detailed description, but becomes technically challenging. At the same time the key effect of the oscillating term $e^{i f x}$ can be understood with the help
of much simpler qualitative consideration outlined, for example, in Ref.~\onlinecite{oshikawa1999} and in Sec.18.IV of Gogolin {\em et al} book \cite{Gogolin}.
Oscillation becomes noticeable on the spatial scale $x \sim 1/f$ which has
to be compared with the running RG scale $a e^\ell$. As a result, RG flow can be separated into two stages. During the first stage $0 \leq \ell \leq \ell_{\rm osc} = \ln(1/f)$
oscillating factor $e^{i f x}$ can be approximated by 1, i.e. it does not influence the RG flow. At this stage all RG equations can be well approximated by their
zero-$f$ form. During the second stage $\ell_{\rm osc} \leq \ell \leq \ell^*$ and the product $f x$ is not small anymore. The factor $e^{i f x}$ produces sign-changing
integrand. Provided that the coupling constant of that term remain small (which is the essence of the condition $\ell \leq \ell^*$), the
integration over $x$ removes such an oscillating interaction term from the Hamiltonian altogether.
This is the strategy we assume in this paper. It is clearly far from being exact but it is an exceedingly good approximation in the two important limits:
the small-$f$ limit when $\ell_{\rm osc} \gg \ell^*$ and the external field/DM interaction is not important at all, and in the large-$f$ limit when $\ell_{\rm osc} \ll \ell^*$
and the oscillations are so fast that corresponding interactions average to zero. In-between these two clear limits the proposed {\em two-stage} scheme \cite{oshikawa1999}
provides for a physically sensible interpolation.
Perturbative RG procedure outlined above is great for understanding relative relevance of competing interchain interactions and for approximate
understanding of the role of the field and DM induced oscillations. Its inherent ambiguity makes one to look for a more quantitative description which
matches RG at the scaling level but also allows to account for the numerical factors associated with various interaction terms at the better than
logarithmic accuracy level. Such description is provided by the chain mean-field (CMF) theory proposed in Ref.~\onlinecite{schulz1996} and numerically tested
for the system of weakly coupled chains in Refs.~\onlinecite{Sandvik1999,Yasuda2005}. In CMF, interchain interactions are approximated by a self-consistent Weiss fields
introduction of which reduces the coupled-chains problem to an effective single-chain one of the sine-Gordon kind, which is understood extremely well \cite{schulz1996,Lukyanov1997}.
As described in Section~\ref{sec:CMF} and
Appendix~\ref{app:cmf} below, this approximation allows one to calculate critical temperature $T_i$ of the order associated with operator ${\cal O}^i$.
The order with the highest $T_i$ is assumed to be dominant. As mentioned above, at the scaling level CMF theory matches the RG procedure and
the highest $T_i$ corresponds to the order with the shortest $\ell^*_i$. The benefit of CMF approach consists in the ability to account for the field-dependent
scaling dimensions of various chain operators in a more systematic and uniform way as we detail below.
\section{Parallel configuration, ${\bm h} \parallel{\bm D} $}
\label{sec:parallel}
When the external magnetic field is parallel to DM vector ${\bm D}$ along $\hat{z}$, $h_z=h$ and $h_x=0$. In this configuration it is convenient
to use Abelian bosonization \eqref{eq:J}, by expressing spin currents in $\cal V$ of Eq.~\eqref{system_2} in terms of fields $(\phi_y,\theta_y)$,
\begin{equation}
\begin{gathered}
{\cal H}_0=\frac{v}{2}\int \mathrm{d}x [(\partial_x{\phi_y})^2+(\partial_x{\theta_y})^2], \;{\cal V}={\cal H}_{\rm Z}+{\cal H}_{\rm DM},\\
{\cal H}_{\rm Z}=-\frac{h}{\sqrt{2\pi}}\int \mathrm{d}x \partial_x \phi_y,\\
{\cal H}_{\rm DM}=-(-1)^y\frac{D}{\sqrt{2\pi}}\int \mathrm{d}x \partial_x \theta_y,
\end{gathered}
\label{eq:abelian-H}
\end{equation}
where ${\cal H}_Z$ and ${\cal H}_{\rm DM}$ are the Zeeman and DM interactions, respectively.
Evidently, these linear terms can be {\em absorbed} into ${\cal H}_0$ by shifting fields $\phi_y$ and $\theta_y$ appropriately,
\begin{equation}
\begin{gathered}
\phi_y=\tilde{\phi}_y+\frac{t_{\phi}}{\sqrt{2\pi}}x, \quad t_{\phi} \equiv \frac{h}{v},\\
\theta_y= \tilde{\theta}_y + (-1)^y\frac{t_{\theta}}{\sqrt{2\pi}} x = \tilde{\theta}_y + \frac{t^y_{\theta}}{\sqrt{2\pi}} x ,\\
\quad t^y_{\theta} \equiv (-1)^y t_\theta = (-1)^y\frac{D}{v}.
\end{gathered}
\label{shift1}
\end{equation}
Note that $t_{\theta}^y$ depends on the parity of the chain index $y$, and it is just the continuum version of the angle $\alpha_y$ in Sec.~\ref{subsec:lattice-rot}.
As a result of the shifts, the spin currents and the staggered magnetization are modified as
\begin{equation}
\begin{gathered}
J_{yR}^{+}\to \tilde{J}_{yR}^{+}e^{-i(t_\phi-t_{\theta}^y)x},\quad
J_{yL}^{+}\to \tilde{J}_{yL}^{+}e^{i(t_\phi+t_{\theta}^y)x},\\
J_{yR}^{z}\to \tilde{J}_{yR}^{z}+\frac{(t_\phi-t_{\theta}^y)}{4\pi},\quad
J_{yL}^{z}\to \tilde{J}_{yL}^{z}+\frac{(t_\phi+t_{\theta}^y)}{4\pi},\\
N^{+}_y \to \tilde{N}^{+}_y e^{it_{\theta}^yx},\quad
N^{z}_y \to -A\sin[\sqrt{2\pi}\tilde{\phi}_y+t_\phi x].\\
\end{gathered}
\label{shift:J-N}
\end{equation}
It is important to observe here that {\em tilded} operators in \eqref{shift:J-N} are obtained from the original ones \eqref{eq:J} and \eqref{eq:N} by replacing
original $\phi_y$ and $\theta_y$ with their {\em tilded} versions $\tilde{\phi}_y$ and $\tilde{\theta}_y$.
Note also that the shift introduces oscillating position-dependent factors to transverse components of ${\bm J}_y$ and ${\bm N}_y$.
The Hamiltonian now reads
\begin{equation}
{\cal H}_{\rm chain}=\tilde{\cal H}_0+\tilde{\cal H}_{\rm bs}+\tilde{\cal H}_{\rm inter},
\label{eq:15}
\end{equation}
where $\tilde{\cal H}_0$ retains its quadratic form \eqref{eq:abelian-H} in terms of tilded fields.
It is perturbed by backscattering $\tilde{H}_{\rm bs}$ and inter-chain $\tilde{H}_{\rm inter}$ interactions, which now read
\begin{eqnarray}
\tilde{\cal H}_{\rm bs}&=&\int \mathrm{d}x \big\{\pi vy_B\big(\tilde{J}_{yR}^{+}\tilde{J}_{yL}^{-}e^{-i2t_\phi x}+{\rm h.c.}\big) \nonumber\\
&&+ 2\pi v y_z \tilde{J}_{yR}^{z}\tilde{J}_{y, R}^{z}\big\},
\label{H'1}
\end{eqnarray}
and $\tilde{\cal H}_{\rm inter} = {\cal H}_{\rm cone} + {\cal H}_{\rm sdw}$, where
\begin{equation}
\begin{gathered}
{\cal H}_{\rm cone}=\pi v A^2 g_{\theta} \int \mathrm{d}x \big(e^{i[\sqrt{2\pi}(\tilde{\theta}_y-\tilde{\theta}_{y+1})+2t_{\theta}^{y}x]}+{\rm h.c.}\big),\\
{\cal H}_{\rm sdw}=
\pi v A^2\int \mathrm{d}x \Big\{ {g}_{\phi }\big(e^{i\sqrt{2\pi}(\tilde{\phi}_y-\tilde{\phi}_{y+1})}+{\rm h.c.}\big)\\
\quad\quad-\tilde{g}_{\phi}\big(e^{i[\sqrt{2\pi}(\tilde{\phi}_y+\tilde{\phi}_{y+1})+2t_\phi x]}+{\rm h.c.}\big)\Big\}.\\
\end{gathered}
\label{H'}
\end{equation}
${\cal H}_{\rm cone}$ and ${\cal H}_{\rm sdw}$ are the transverse and longitudinal (with respect to the $z$-axis) components of inter-chain interaction respectively.
Their effect consists in promoting two-dimensional ordered cone and SDW state, correspondingly.
Small terms resulting from the additive shifts in $J_{R/L}^z$ in \eqref{shift:J-N} have been neglected.
Table~\ref{table:term1} describes which inter-chain interactions produce which state.
\begin{table}[!tbp]
\begin{center}
{\renewcommand{\arraystretch}{1.2}%
\begin{tabular}{c| c c c}
\hline\hline
Interaction & $\quad$Coupling$\quad$ & $\quad$Coupling$\quad$ & $\quad$Induced$\quad$\\
term & operator & constant & state\\
\hline
${\cal H}_{\rm cone}$ & $N^+_y N^-_{y+1} $ & $g_{\theta}$ & cone \\[0.6ex]
${\cal H}_{\rm sdw}$ & $N^z_y N^z_{y+1}$ & $g_{z}$ & SDW \\ [0.6ex]
${\cal H}_{\rm NN}$ & $N^+_y N^-_{y+2} $ & $G_{\theta}$ & coneNN \\[0.6ex]
\hline\hline
\end{tabular}}
\end{center}
\caption{Three relevant perturbations from interchain interaction ${\cal H}_{\rm cone}$, ${\cal H}_{\rm sdw}$ in Eq.~\eqref{H'} and ${\cal H}_{\rm NN}$ in Eq.~\eqref{2nd neighbour},
their operator forms, associated coupling constants and types of the ordered states they induce.}
\label{table:term1}
\end{table}
In writing the above we introduced several running coupling constants
\begin{equation}
\begin{gathered}
y_B=\frac{1}{2}(y_x+y_y), \quad y_B(0)=-\frac{g_{\rm bs}}{2\pi v},\\
g_{\theta}=\frac{1}{2}(g_x+g_y), \quad g_\theta(0)=\frac{J'}{2\pi v}, \\
g_{\phi}=\tilde{g}_{\phi}=\frac{1}{2}g_z, \quad g_z(0) = \frac{J'}{2\pi v},\\
\label{eq:ini2}
\end{gathered}
\end{equation}
initial values of which follow from
\begin{equation}
\begin{gathered}
y_x(0)=y_y(0)=-\frac{g_{\rm bs}}{2\pi v},\;\;\;
y_z(0)=-\frac{g_{\rm bs}}{2\pi v}(1+\lambda),\\
g_x(0)=g_y(0)=g_z(0)=\frac{J'}{2\pi v}.
\end{gathered}
\label{eq:ini1}
\end{equation}
Observe that DM interaction produces an effective anisotropy $\lambda=c'(D/J)^2>0$ which leads to $|y_z(0)|>|y_{x,y}(0)|$.
Next we need to identify the most-relevant coupling in perturbation $H'=\tilde{\cal H}_{\rm bs}+\tilde{\cal H}_{\rm inter}$, which is accomplished by the renormalization group (RG) analysis.
\begin{figure}[!tbp]
\centering
\includegraphics[width=0.75\columnwidth]{ktflow.pdf}
\caption{(Color online) Solution of Kosterlitz-Thouless (KT) equations (first line of \eqref{eq:rg2}).
Five sectors of the flow are divided according to the initial conditions. For example, in sector 3: $y_{z/\sigma}(0)<0,y_{B/C}(0)>0$ and $C>0$.}
\label{fig:kt}
\end{figure}
\subsection{Renormalization group (RG) analysis}
\label{subsec:rg_1}
According to standard RG arguments, the low energy properties of the system are determined by the couplings which renormalize to dimensionless values of order one first.
We derived RG equations for various coupling constants with the help of operator product expansion (OPE) technique \cite{fradkin} (see Appendix~\ref{app:ope} for details),
\begin{equation}
\begin{gathered}
\frac{d y_B}{d \ell}=y_By_z,\;\;\;
\frac{d y_z}{d \ell}=y_B^2,\\
\frac{d g_\theta}{d \ell}=g_{\theta}(1-\frac{1}{2}y_z),\;\;\;
\frac{dg_z}{d\ell}=g_z(1+\frac{1}{2}(y_z - 2 y_B)) .\\
\end{gathered}
\label{eq:rg2}
\end{equation}
The first two equations in Eq.~\eqref{eq:rg2} are the well-known Kosterlitz-Thouless (KT) equations for the marginal backscattering couplings $y_{B,z}$ in \eqref{H'1}.
They admit analytic solution which is illustrated in Fig.~\ref{fig:kt}.
Initial conditions \eqref{eq:ini2}, \eqref{eq:ini1} correspond to $y_B<0, y_z<0$ and $C=y_z(\ell)^2-y_B(\ell)^2>0$, which places the KT flow
in sector $4$ in Fig.~\ref{fig:kt}. Physically, this corresponds to DM-induced easy-plane anisotropy ($\lambda >0$) which, if acting alone, would drive
the chain into a critical LL state.
This marginally-irrelevant flow of $y_{B,z}$ is, however, interrupted by the exponentially fast growth of the inter- chain interactions $g_{\theta,\phi}$
which, according to \eqref{eq:rg2}, reach strong coupling limit at $\ell_{\rm inter} \approx \ln(2\pi v/J')$.
This growth describes development of the two-dimensional magnetic order in the system of
weakly coupled chains. As a result, we are allowed to treat chain backscattering $y_{B,z}$, which barely changes on the scale of $\ell_{\rm inter}$,
as a weak correction to the relevant inter-chain interaction.
This is the physical content of the second line of RG equations in \eqref{eq:rg2}.
DM interaction and magnetic field strongly perturb RG flow \eqref{eq:rg2} via coordinate-dependent factors $e^{i 2t_{\theta}^y x}$ and $e^{i 2t_\phi x}$,
rapid oscillations of which become significant once running RG scale $\ell$ becomes greater than $\ell_{\theta} (\ell_\phi)$, where
\begin{equation}
\begin{gathered}
\ell_{\theta}=\ln(\frac{1}{a_0t_\theta}) = \ln(\frac{v}{D a_0}), \: \ell_{\phi}=\ln(\frac{1}{a_0t_\phi}) = \ln(\frac{v}{h a_0}). \\
\end{gathered}
\label{length1}
\end{equation}
These oscillations have the effect of nullifying, or averaging out, corresponding interaction terms in the Hamiltonian, provided that the corresponding
coupling constants remain small at RG scales $\ell_{\theta,\phi}$.
The affected terms are ${\cal H}_{\rm cone}$ and $\tilde{g}_\phi$ term in ${\cal H}_{\rm sdw}$, respectively.
Also affected is backscattering $y_B$ term in \eqref{H'1}.
The short-distance cut-off $a_0$ that appears in \eqref{length1} is determined by the initial value of the backscattering $g_{\rm bs}(0) = 0.23 \times (2\pi v)$,
see Ref.~\onlinecite{Garate2010} for detailed explanation of this point.
In accordance with general discussion in Sec.~\ref{sec:overview}, we define $\ell^*$ as an RG scale
at which the most relevant coupling constant $g$ reaches value of $1$, namely $|g(\ell^*)|=1$. For interchain couplings, we find that
$\ell^*$ is close to $\ell_{\rm inter}\approx \ln(2\pi v/J')$ introduced below Eq.~\eqref{eq:rg2}, and this is noted in the caption of Figures~\ref{fig:flow1},
\ref{fig:nn1} and Figures~\ref{fig:flow01} - \ref{fig:flow03}.
Magnetic field induced oscillations in ${\cal H}_{\rm sdw}$ are well-known and describe magnetization-induced shift of longitudinal spin modes
from the zero wave vector. In addition, magnetic field works to increase scaling dimension of $N^z$ field, from 1/2 at
zero magnetization $M=0$ to 1 at full polarization $M=1/2$, see Table~\ref{table:scaling_d}, making the $N^z$ field less relevant.
Typically, this makes ${\cal H}_{\rm sdw}$ term less important
than ${\cal H}_{\rm cone}$ one, which is build out of transverse spin operators which become more relevant with the field
(the corresponding scaling dimension of which becomes smaller with the field, it changes from 1/2 at $M=0$ to 1/4 at $M=1/2$).
\begin{table}[!tbp]
\begin{center}
{\renewcommand{\arraystretch}{1.2}%
\begin{tabular}{c| c c c}
\hline\hline
Operator &$\quad \Delta\quad$ & $\quad$M=0$\quad$ & $\quad$M=1/2$\quad$ \\ [0.6ex]
\hline
$N^z \quad $ & $\pi/ \beta^2$ & 1/2 & 1 \\ [0.6ex]
$N^+ \quad $ & $\pi R^2$ & 1/2 & 1/4 \\
\hline\hline
\end{tabular}}
\end{center}
\caption{Scaling dimensions $\Delta$ of longitudinal and transverse components for staggered magnetization ${\bm N}$ vs magnetization $M$. }
\label{table:scaling_d}
\end{table}
In our problem, however, the prevalence of the cone state is much less certain due to the presence of the built-in DM-induced
oscillations in ${\cal H}_{\rm cone}$ \eqref{H'}, originating from the staggered geometry of DM interaction. As a result, one needs to distinguish
the cases of weak and strong DM interaction, which in the current case should be compared with the inter-chain exchange interaction $J'$.
\subsection{Weak DM interaction, $D\ll J'$}
\label{sub:weak_DM_para}
First, we consider the case of weak DM interaction, $D\ll J'$. This means $\ell_\theta > \ell_{\rm inter}$, the integrand of ${\cal H}_{\rm cone}$ oscillates slowly
so that the factor $e^{i 2t_{\theta}^y x}$ does not affect the RG flow. As discussed in Appendix~\ref{app:ope}, backscattering terms break the symmetry between $g_\theta$ and $g_z$,
$g_{\theta}(\ell) > g_z(\ell)$. As a result, inter-chain interaction ${\cal H}_{\rm cone}$ reaches strong coupling before ${\cal H}_{\rm sdw}$ and
the ground state realizes the cone phase. Typical RG flow of coupling constants for this case is shown in Fig.~\ref{fig:flow1}.
Minimization of the argument of cosine in ${\cal H}_{\rm cone}$ requires that
$\sqrt{2\pi}(\tilde{\theta}_y-\tilde{\theta}_{y+1})+2t_{\theta}^{y}x = \pi$. This is solved by requiring
$\tilde{\theta}_y(x) = \hat{\theta} - (-1)^y t_\theta x/\sqrt{2\pi} - \sqrt{\pi/2} ~y$, where $\hat{\theta}$ is position-independent constant which describes orientation of the staggered magnetization $N^+_y(x) \sim (-1)^y i e^{i\sqrt{2\pi} \hat{\theta}}$ in the plane perpendicular to the magnetic field.
Observe that the obtained solution describes a {\em commensurate cone} configuration.
The original shift \eqref{shift1} is compensated by the opposite shift needed to minimize the $\tilde{\theta}$ configuration.
As a result the obtained cone state is commensurate along the chain direction: $N^+_y$ is uniform along the chain direction which
means the spin configuration is actually staggered, $S^+_y(x) \sim (-1)^x N^+_y$, see \eqref{eq:spin}. Note also that $N^+_y$ is staggered between chains
(so as to minimize the antiferromagnetic inter-chain exchange $J' >0$), so that in fact $S^+_y(x)$ realizes the standard N\'eel configuration. Thus ground state spin configuration of
the cone phase is described by
\begin{eqnarray}
\langle {\bm S}_y(x) \rangle &&= M {\bf z} + (-1)^{x + y} \Psi_{\rm cone} (-\sin[\sqrt{2\pi}\hat{\theta}] {\bf x} + \nonumber\\
&&+\cos[\sqrt{2\pi}\hat{\theta}] {\bf y}).
\label{eq:cone}
\end{eqnarray}
Here $\Psi_{\rm cone}$ denotes the magnitude of the order parameter at the scale $\ell^*$. According to \eqref{eq:orderparam} and using equations \eqref{eq:N} and \eqref{eq:ini2},
it can be estimated as $\Psi_{\rm cone} = \gamma/(\pi a) \sqrt{g_\theta} \propto (J'/v)^{1/2}$. The square-root dependence of the order parameter on the inter-chain exchange $J'$
is a well-known feature of weakly coupled chain problems \cite{schulz1996}. CMF theory, which we introduce in the next section, can too be used to calculate the
cone order parameter. This is described in Appendix~\ref{app:order_parameter} and its dependence on magnetization $M$, at a fixed $J'/v$ ratio, is illustrated in Fig.~\ref{fig:orderCl}.
Note that its dependence on $M$ occurs via $M$-dependence of scaling dimensions and other parameters in the Hamiltonian which are not easy to capture
with the help of the RG procedure.
\begin{figure}[!tbp]
\includegraphics[width=0.8\columnwidth]{rgflow1.pdf}
\caption{(Color online) Typical RG flow of the coupling constants for weak DM interaction and ${\bm h}\parallel {\bm D}$, $h_x=0$. $D=1\times10^{-4}J$, $g_{\rm bs}/(2\pi v)=0.23$, $J'/(2\pi v)=0.001$,
$h_z/D=1$ and $\lambda=0.2$. Here $\ell_{\rm inter}\simeq 6.9$, $\ell_{\phi}=\ell_{\theta}\simeq 6.6$. The dominant coupling is $g_\theta $ (red solid line), and $g_\theta(\ell^*)=1$ at $\ell^*\simeq6.3$. }
\label{fig:flow1}
\end{figure}
\subsection{Strong DM interaction, $D>J'$}\label{sub:strong_DM_para}
\label{strong_DM_para}
\subsubsection{SDW order}
Now we turn to a less trivial case of strong DM interaction, when $D \gg J'$. Here $\ell_\theta <\ell_{\rm inter}$, which simply eliminates ${\cal H}_{\rm cone}$
from the competition, and from the Hamiltonian. The physical reasoning is that strong DM interaction introduces strong frustration to the transverse
inter-chain interaction, which oscillates rapidly and averages to zero. As a result, the only inter-chain interaction that survives in this situation
is ${\cal H}_{\rm sdw}$, Eq.\eqref{H'}, which establishes two-dimensional longitudinal SDW order.
Two types of SDW ordering are possible. The first - {\em commensurate} SDW order - realizes in low magnetic field $h \leq h_{\rm c-ic} \sim O(J')$
when spatial oscillations due to $t_\phi x$ term in $N^z_y$ operator \eqref{shift:J-N} are not important. This is the regime of $\ell_\phi \gg \ell_{\rm inter}$,
when both $g_\phi$ and $\tilde{g}_\phi$ terms in the SDW inter-chain interaction ${\cal H}_{\rm sdw}$ in \eqref{H'} contribute equally.
In a close similarity to the commensurate cone state discussed above, the $\tilde{\phi}$ configuration here is minimized by
$\tilde{\phi}_y(x) = \hat{\phi} - t_\phi x/\sqrt{2\pi} - \sqrt{\pi/2} ~y$. Here the global constant $\hat{\varphi}$ is determined by the requirement
that $\sin[\sqrt{2\pi} \hat{\phi}] = \pm 1$, corresponding to a maximum possible magnitude of $N^z_y \sim (-1)^y \sin[\sqrt{2\pi} \hat{\phi}]$.
Therefore $\hat{\phi} = \hat{\phi}_k = \sqrt{\pi/2} (k + 1/2)$, where $k=0, 1$. This describes the situation of the commensurate longitudinal SDW order
which is pinned to the lattice, $N^z_y \sim (-1)^y (-1)^k$. Changing $k \to k \pm 1$ corresponds to a discrete translation of the SDW order by one lattice spacing.
In terms of spins this too is a N\'eel-like order, but it is collinear one along the magnetic field axis,
\begin{equation}
\langle {\bm S}_{x,y} \rangle = (M + \Psi_{\rm sdw-c} (-1)^{x+y} (-1)^k){\bf z}.
\label{eq:sdw-comm}
\end{equation}
Increasing the field beyond $h_{\rm c-ic}$ un-pins the SDW ordering from the lattice and transforms spin configuration into collinear {\em incommensurate} SDW.
Technical details of this are described in the Appendix \ref{app:cmf} and here we focus on the physics of this commensurate-incommensurate (C-IC) transition.
Increasing $h$ makes $\ell_\phi$ smaller and at $\ell_\phi \approx \ell_{\rm inter}$ oscillating $e^{i 2 t_\phi x}$ factor in the $\tilde{g}_\phi$ term in \eqref{H'}
becomes very strong and `washes out' that piece of the ${\cal H}_{\rm sdw}$ Hamiltonian. The remaining, $g_\phi$, part of ${\cal H}_{\rm sdw}$
continues to be the only relevant inter-chain interaction and flows to the strong coupling. Therefore now $\sqrt{2\pi}(\tilde{\phi}_y-\tilde{\phi}_{y+1}) = \pi$
which is solved by $\tilde{\phi}_y = \hat{\phi} - \sqrt{\pi/2} ~y$. As a result the shift \eqref{shift1} remains intact and one finds
incommensurate SDW ordering with
\begin{equation}
\langle {\bm S}_y(x)\rangle \sim (M + \Psi_{\rm sdw-ic} (-1)^{x+y} \sin[\sqrt{2\pi} \hat{\phi} + h x/v]) {\bf z}.
\label{eq:sdw-incomm}
\end{equation}
The magnitude of the SDW order parameter $\Psi_{\rm sdw-ic}$ in this equation is calculated in Appendix~\ref{app:order_parameter} and its dependence on magnetization
$M$, at a fixed $J'/v$ ratio, is illustrated in Fig.~\ref{fig:orderBr}. Note that unlike the cone order, the SDW one weakens with increasing $M$.
\begin{figure}[!tbp]
\includegraphics[width=0.8\columnwidth]{nnsmallh.pdf}
\caption{(Color online) RG flow of the coupling constants for strong DM interaction and ${\bm h}\parallel {\bm D}$, $h_x=0$. The case of low magnetic field $h_z/D=0.005$.
$D=0.01J$, $g_{\rm bs}/(2\pi v)=0.23$, $J'/(2\pi v)=0.001$ and $\lambda=0.1$. Here $\ell_{\rm inter}\simeq 6.9$, $\ell_{\phi}\simeq7.4$, $\ell_{\theta}\simeq2$ and $g_{\theta}$ keeps as a constant after $\ell>\ell_\theta$, due to the rapid spatial oscillation. The dominant coupling is $g_z$ (blue solid line), and $g_z(\ell^*)=1$ at $\ell^*\simeq7.5$.}
\label{fig:nn1}
\end{figure}
The global phase $\hat{\phi} \in (0,\sqrt{2\pi})$
is not pinned to any particular value - it describes emergent translational $U(1)$ symmetry of the `high-field' limit of the SDW Hamiltonian [Eq.\eqref{H'} without $\tilde{g}_\phi$ term],
which does not depend on the value of $\hat{\phi}$. Spontaneous selection of some particular $\hat{\phi}$ corresponds to a spontaneous breaking
of the translational symmetry. The resulting incommensurate SDW order is characterized by the emergence of Goldstone-like longitudinal fluctuations,
{\em phasons}. Recent discussion of some aspects of this physics can be found in Ref.~\onlinecite{Starykh2014}.
\subsubsection{Next-nearest chains cone order}
\label{sec:coneNN}
\begin{figure}[!tbp]
\includegraphics[width=0.8\columnwidth]{nnlargeh.pdf}
\caption{(Color online) Typical flow of the coupling constants for strong DM interaction and ${\bm h}\parallel {\bm D}$, $h_x=0$. This is the case of relatively high magnetic field $h_z/D=5$.
$D=0.01J$, $g_{\rm bs}/(2\pi v)=0.23$, $J'/(2\pi v)=0.001$ and $\lambda=0.1$. Here $\ell_{\rm inter}\simeq 6.9$, $\ell_{\varphi}\simeq0.4$, $\ell_{\theta}\simeq2$. The dominant coupling is $G_\theta$ (orange solid line), and $|G_\theta(\ell^*)|=1$ at $\ell^*\simeq7.7$.}
\label{fig:nn2}
\end{figure}
The above SDW-only arguments, however, do not take into account a possibility of a cone-like interaction between more distant chains.
Even though such interactions are absent from the
lattice Hamiltonian \eqref{eq:H_0}, they can (and will) be generated by quantum fluctuations at low energies, as long as they remain consistent with symmetries
of the lattice model \cite{olegandbalents}. The simplest of such interactions is given by the transverse inter-chain interaction between the
{\em next-neighbor} (NN) chains ${\cal H}_{\rm NN}$, see Appendix~\ref{app:nn_chain} for the detailed derivation,
\begin{equation}
{\cal H}_{\rm NN} = 2\pi v G_{\theta} \sum_y \int \mathrm{d}x (\tilde{N}_{y}^{+} \tilde{N}_{y+2}^{-}+{\rm h.c.}).
\label{2nd neighbour}
\end{equation}
This is an indirect exchange, mediated by an intermediate chain ($y+1$), and therefore its exchange coupling
can be estimated as $2\pi v G_{\theta} \sim (J')^2/(2\pi v) \ll J'$.
However the scaling dimension of this term ($\approx 1$ without the magnetic field) is the same as of the original cone interaction ${\cal H}_{\rm cone}$ and thus $G_\theta$ is
expected to grow exponentially fast. Importantly, ${\cal H}_{\rm NN}$ is free of the DM-induced oscillations because DM vectors ${\bm D}$ on chains $y$ and $(y+2)$
point in the {\em same} direction. That is, fields $\tilde{\theta}_y$ and $\tilde{\theta}_{y+2}$ {\em co-rotate}.
This basic physical reason makes ${\cal H}_{\rm NN}$ a legitimate candidate for fluctuation-generated interchain exchange interaction
of the cone kind. Calculation in Appendix~\ref{app:nn_chain} gives the NN coupling constant
\begin{equation}
G_{\theta}=-\frac{\pi A_3^2}{4}f(\Delta_1)\frac{J'}{D}g_{\theta},\; f(\Delta_1)=t_{\theta}^{2\Delta_1-1}\frac{\Gamma(1-\Delta_1)}{\Gamma(\Delta_1)},
\label{eq:gNN}
\end{equation}
which depends on magnetic field via scaling dimension $\Delta_1$. At low fields $\Delta_1\approx 1/2$ and $f(1/2) \approx 1$.
Observe that $G_{\theta}$ describes ferromagnetic interaction and, contrary to naive perturbation theory expectation, has significant
magnitude: $2\pi v G_\theta \propto (J')^2/D \gg (J')^2/J$. RG equation for $G_{\theta}$ coincides with that of $g_\theta$,
\begin{equation}
\frac{d G_\theta}{d \ell}=G_{\theta}(1-\frac{1}{2}y_z).
\label{ini3}
\end{equation}
When $G_{\theta}$ reaches strong coupling first, the $\tilde{\theta}$ configuration is uniform, $\tilde{\theta}_y = \tilde{\theta}_{y+2} = \hat{\theta}_{\rm \nu = e/o}$,
where index $\nu = {\rm e}$ for even $y$ and $\nu = {\rm o}$ for odd $y$ values and in general $\hat{\theta}_{\rm e} \neq \hat{\theta}_{\rm o}$.
At this level of approximation subsystems of {\em even} and {\em odd} chains decouple from each other. The obtained coneNN order is {\em incommensurate},
\begin{eqnarray}
\langle {\bm S}_{x,y} \rangle &&= M {\bf z} + (-1)^{x + y} \Psi_{\rm coneNN} \Big(-\sin[\sqrt{2\pi}\hat{\theta}_\nu + (-1)^y t_\theta x] {\bm x} \nonumber\\
&&+\cos[\sqrt{2\pi}\hat{\theta}_\nu + (-1)^y t_\theta x] {\bm y}\Big), ~\nu = {\rm e}, {\rm o}.
\label{eq:coneNN}
\end{eqnarray}
The described situation is actually very similar to one discussed in Ref.~\onlinecite{oleg_cmf}, see section IV there, where spins in the neighboring layers are found
to counter-rotate, due to oppositely oriented DM vectors, and are not correlated with each other.
By a simple manipulation this spin ordering can also be represented as
\begin{eqnarray}
&&\langle {\bm S}_{x,y} \rangle = M {\bf z} + \nonumber\\
&& + (-1)^{x + y} \Psi_{\rm coneNN} \Big( \cos[t_\theta x] \{-\sin[\sqrt{2\pi}\hat{\theta}_\nu] {\bf x} + \cos[\sqrt{2\pi}\hat{\theta}_\nu] {\bf y}\} \nonumber\\
&& - (-1)^y \sin[t_\theta x] \{\cos[\sqrt{2\pi}\hat{\theta}_\nu] {\bf x} + \sin[\sqrt{2\pi}\hat{\theta}_\nu]{\bf y}\} \Big) .
\label{eq:coneNN2}
\end{eqnarray}
Expressions inside curly brackets represent orthogonal unit vectors which are obtained from the orthogonal pair $({\bf x}, {\bf y})$
by the chain-parity dependent rotation by angle $\pm \sqrt{2\pi} \hat{\theta}_\nu$.
The magnitude of the coneNN order parameter is shown in Appendix~\ref{app:order_parameter}, Figure~\ref{fig:orderBr}, for a particular experimentally
relevant ratio of $J'/J$.
\subsubsection{Competition between SDW and cone/coneNN orders}
Quantitative description of the competition between SDW and cone orders within RG framework represents a very difficult task.
This basically has to do with the fact that RG is not well suited for describing oscillating perturbations such as \eqref{H'} and \eqref{H'1}.
It is quite good at extracting the essential physics of the slow- and fast-oscillation limits, as described in sections \ref{sub:weak_DM_para} and
\ref{sec:coneNN} above, but is not particularly useful in describing the intermediate regime $D \sim J'$ in which the change from one behavior
to the another takes place (see Ref.~\onlinecite{oshikawa1999} for the example of the RG study of the much simpler problem of a single spin-1/2
chain in the magnetic field).
Applied to the cone-SDW competition, one needs to compare effects due to the DM-induced oscillations with those due to the magnetic field induced ones.
Given that magnetic field makes cone terms more relevant and SDW ones less relevant, one can anticipate that even if the DM interaction is strong enough to destroy the cone phase
in small magnetic field, the cone can still prevail over the SDW phase at higher fields. Chain mean field approximation, described in the next section (and also in more
details in Appendix \ref{app:cmf}) indeed shows that the critical $D/J'$ ratio required for suppressing the cone phase increases with magnetization $M$.
Nonetheless, the ratio $D/J'$ is bounded: there exists sufficiently large $D$ (still of the order $J'$) above which the cone order becomes impossible for any $M$.
For $D$ greater than that we need to
examine competition between ${\cal H}_{\rm sdw}$ and ${\cal H}_{\rm NN}$.
Approximating $A$ as $1/2$ here (see Ref.~\onlinecite{Essler2003}, transverse normalization factor $A_3$ is close to $1/2$ at small magnetization),
we observe that $|G_{\theta}|$ is about $J'/(4D)$ times smaller than $g_z$.
However, in the presence of magnetic field $G_{\theta}$ becomes more relevant in RG sense (similar to its frustrated `parent' $g_\theta$), and
grows much faster than SDW interaction $g_z$, which becomes less relevant with magnetic field.
Therefore there should be a range of $J'/D$ such that $G_{\theta}(\ell)$ can compete with $g_z(\ell)$.
Such an example is shown in Fig.~\ref{fig:nn1} and Fig.~\ref{fig:nn2}, $D/J' \sim 1$ there. Fig.~\ref{fig:nn1} shows RG flow in low magnetic field $h_z/D=0.005$,
when $g_z$ grows faster than $|G_{\theta}|$, resulting in the SDW state. However, in higher magnetic field $h_z/D=5$, which is still rather low in comparison with
$J$, $G_{\theta}$ turns to be the most relevant coupling constant. Hence the ground state changes to the coneNN one.
Details of this competition depend strongly on the magnitude of the magnetic field. At low field $h \leq h_{\rm c-ic}$ SDW is commensurate, while at
higher field $h \geq h_{\rm c-ic}$ it turns incommensurate. Calculations reported in Appendix~\ref{app:cmf} find that $h_{\rm c-ic} \approx 1.4 J'$
which is sufficiently small value (the corresponding magnetization is very small as well, $M_{\rm c-ic} = h_{\rm c-ic}/(2\pi v) \approx 1.4 J'/(\pi^2 J) \ll 1$) ,
especially in the most interesting to us regime of strong DM, $D \gg J'$.
Given that the critical temperature of the incommensurate SDW order is lower than that of the commensurate one, see Fig.~\ref{fig:2sdw}, the SDW-coneNN
competition is most pronounced in the $h \geq h_{\rm c-ic}$ limit, on which we mostly focus in the section~\ref{sec:CMF} below.
\begin{figure}[!tbp]
\includegraphics[width=0.8\columnwidth]{cone.pdf}
\caption{(Color online) Ordering temperatures of the cone ($T_{\rm cone}$, green solid line) and incommensurate SDW ($T_{\rm sdw-ic}$, orange dashed line) states, vs. magnetization $M$, for the case
of weak DM interaction. $J=1$ K, $J'=0.01$ K and $D=0.01$ K. Commensurate SDW state ($T_{\rm sdw-c}$) is characterized by $T_{\rm sdw-ic} < T_{\rm sdw-c} < T_{\rm cone}$ but
is present only is the very narrow magnetization interval $0 < M < M_{\rm c-ic} < 0.01$ and is not shown here.
The larger ordering temperature is dominant, thus the ground state is cone in the whole field/magnetization range.}
\label{fig:Tc}
\end{figure}
\section{Chain Mean-field calculation}
\label{sec:CMF}
A more quantitative way to characterize DM-induced competition, described in the previous section with the help of qualitative RG arguments,
is provided by the
chain mean-field (CMF) approximation\cite{oleg_cmf} which allows one to calculate and compare critical temperatures for different
magnetic instabilities. The instability with maximal $T_c$ is assumed to describe the actual magnetic order.
This calculation enables us to directly compare the resulting critical temperature of the dominant instability to the experimental lambda peak in heat capacity measurements \cite{Halg2014}
and therefore to directly compare experimental and theoretical $h-T$ phase diagrams.
It provides one with a reasonable way to estimate the inter-chain exchange $J'$ of the material, as we describe in Appendix~\ref{app:j'}.
It also allows for a straightforward calculation of the microscopic order parameters, see Appendix~\ref{app:order_parameter} .
In applying CMF to our model, there are three inter-chain interactions in Eqns.~\eqref{H'} and ~\eqref{2nd neighbour} that need to be compared,
\begin{equation}
\begin{gathered}
{\cal H}_{\rm cone}=c_1\int \mathrm{d}x \cos[\beta(\tilde{\theta}_{y} - \tilde{\theta}_{y+1})+2(-1)^yt_\theta x],\\
{\cal H}_{\rm sdw-ic}=c_2\int \mathrm{d}x [ \cos\frac{2\pi}{\beta}(\tilde{\phi}_y - \tilde{\phi}_{y+1})],\\
{\cal H}_{\rm NN}=-c_3\int \mathrm{d}x \cos[\beta(\tilde{\theta}_{y} - \tilde{\theta}_{y+2})].\\
\end{gathered}
\label{eq:inter-cmf}
\end{equation}
In accordance with the discussion in the end of the previous section \ref{subsec:rg_1} we focus here on the $h \geq h_{\rm c-ic}$ regime and
neglect oscillating term $\tilde{g}_\phi$ in ${\cal H}_{\rm sdw}$. The amplitudes are
\begin{equation}
\begin{gathered} c_1=J'A_3^2$,\quad $c_2=J'A_1^2/2,\\
c_3=\frac{\pi}{4}\frac{J'^2}{D}A_3^4t_{\theta}^{2\Delta_1-1}\frac{\Gamma(1-\Delta_1)}{\Gamma(\Delta_1)}.
\end{gathered}
\label{eq:cmf_inter}
\end{equation}
\begin{figure}[!tbp]
\includegraphics[width=0.8\columnwidth]{three.pdf}
\caption{(Color online) Ordering temperatures of the cone state (green solid line), commensurate-SDW (purple dashed line) and coneNN (blue solid line) states as a function of $D/J'$ ratio, and
in the limit of zero magnetic field, $M=0$. Here, $J=1$ K, $J'=0.1$ K. Note that solution for coneNN state has physical meaning in the limit $D/J'\gg 1$.
$T_{\rm sdw-c}$ overcomes $T_{\rm cone}$ at $D/J'\simeq1.2$ and solution for $T_{\rm cone}$ disappears at $D/J'\simeq 1.9$. See Section~\ref{sec:CMF} and Appendix \ref{app:cmf}.}
\label{fig:three}
\end{figure}
CMF is designed for the analysis of the relevant perturbations and does not account for the marginal interactions, such as Eq.~\eqref{H'1}, directly.
However much of their effects can still be captured by adopting a more precise expression for the staggered magnetization,
which encodes magnetic field dependence of the scaling dimensions
of transverse and longitudinal components via simple generalization of \eqref{eq:N},
\begin{equation}
{\bm N}_y(x)= (-A_3\sin[\beta\tilde{\theta}_y], A_3\cos[\beta\tilde{\theta}_y], -A_1\sin[\frac{2\pi}{\beta}\tilde{\phi}_y]).
\end{equation}
Here the magnetic field dependence of the scaling dimensions of transverse and longitudinal components of ${\bm N}$ is contained in the
parameter $\beta =2 \pi R$, which in turn is related to the exactly known ``compactification radius" $R$ in the sine-Gordon (SG) model.
At zero magnetization $M=h=0$, the SU(2) invariant
Heisenberg chain has $2\pi R^2=1$. In magnetic field, $\beta$ and $R$ decrease toward the limit $2\pi R^2=1/2$ as the chain approaches full polarization.
The amplitudes $A_1$ and $A_3$ have been determined numerically \cite{hikihara}.
Calculation of $T_c$ is standard and well-documented in Ref.~\onlinecite{oleg_cmf}, additional details are provided in Appendix~\ref{app:cmf}.
For weak DM interaction, we compare the ordering temperatures of ${\cal H}_{\rm cone}$ and ${\cal H}_{\rm sdw}$, and the $T_c$ for each state as a function of magnetization $M$ is
shown in Fig.~\ref{fig:Tc}. For chosen parameters, critical temperature of the cone is always above that of the SDW, therefore the ground state is cone, in agreement with the
RG analysis in Sec.~\ref{sub:weak_DM_para}.
As magnetization increases, the transverse correlations are enhanced, and longitudinal ones are suppressed,
resulting in a greater separation between the two critical temperatures.
At larger magnetization, $T_{\rm cone}$ also decreases, basically due to the Zeeman effect -- spins align more along the direction of the magnetic field,
thereby reducing the magnitude of the transverse spin component.
\begin{figure}[!t]
\includegraphics[width=0.8\columnwidth]{conenn.pdf}
\caption{(Color online) Ordering temperatures of the incommensurate-SDW (orange dashed line) and cone2N (blue solid line) states, as a function of magnetization $M$, in the case of strong DM interaction.
$J=1$ K, $J'=0.01$ K and $D=0.1$ K. Two lines intersect at small magnetization $M\simeq 0.1$, above which the critical temperature of the cone-NN state overcomes that of the SDW one. }
\label{fig:Tc_2}
\end{figure}
Increasing DM interaction frustrates ${\cal H}_{\rm cone}$ until, at some critical $D/J'$ value, its mean-field solution disappears completely, signifying the impossibility
of the standard cone state. This feature is described in much details in Appendices~\ref{app:cmf} and \ref{app:cic}.
Figure~\ref{fig:three} illustrates it.
With the cone state out of the picture, we now need
to consider the transverse NN-chain coupling ${\cal H}_{\rm NN}$ and its competition with the SDW state as magnetization increases from $0$ to the saturation at $M=0.5$.
The result is shown in Fig.~\ref{fig:Tc_2}. In a small magnetic field (when $M\approx h/(2\pi v$)),
$T_{\rm sdw}$ is above $T_{\rm coneNN}$. As magnetization increases, the scaling dimensions get modified, and the two curves intersect, which indicates
a phase transition from the SDW to the cone-NN phase.
This result is fully consistent with our qualitative RG analysis in Sec.~\ref{strong_DM_para}.
%
\section{Orthogonal configuration, ${\bm h}\perp {\bm D}$}
\label{sec:perpendicular}
When ${\bm h} \perp {\bm D}$, the system Hamiltonian is described by Eq.~\eqref{system_2} with $h_x=h$, and $h_z=0$.
In order to treat both vector perturbations, $h$ and $D$, equally, we
perform a chiral rotation of spin currents about the $\hat{y}$ axis,
\begin{equation}
{\bm J}_{y ,R/L}={\cal R}(\theta_{R/L}){\bm M}_{y ,R/L},
\label{chiral rotation}
\end{equation}
where ${\bm M}_{R/L}$ is spin current in the rotated frame, and $\cal R $ is the rotation matrix,
\begin{equation}
\begin{gathered}
{\cal R}(\theta_{R/L})=
\begin{pmatrix}
\cos\theta_{R/L} & 0 & \sin\theta_{R/L} \\
0 & 1 & 0 \\
-\sin\theta_{R/L} & 0 & \cos\theta_{R/L}.
\end{pmatrix},
\end{gathered}
\end{equation}
The general form of chiral rotation angles $\theta_{R/L}$ can be found in references \cite{Garate2010,Gangadharaiah2008}.
Here we apply it to our special ${\bm h}\perp {\bm D}$ case, which gives
\begin{equation}
\begin{gathered}
\theta_R=\frac{\pi}{2}+\theta_0^y,\; \theta_L=\frac{\pi}{2}-\theta_0^y,\; \theta_0^y\equiv(-1)^y \tan^{-1}[\frac{D}{h}].
\label{eq:theta0}
\end{gathered}
\end{equation}
The staggered nature of DM interaction is reflected in the $y$-dependence of the rotation angle $\theta_{R/L}$, via that of $\theta^y_0$, here
(similar to $t^y_\theta$ and $\alpha_y$). The rotation does not affect ${\cal H}_0$ in Eq.\eqref{system_2} but transforms $\cal V$ into
\begin{equation}
\begin{split}
{\cal V}&=-\sqrt{D^2+h^2}\int \mathrm{d}x (M_{y, R}^z+M_{y, L}^z)\\
&=-\frac{\sqrt{D^2+h^2}}{\sqrt{2\pi}}\int \mathrm{d}x ~\partial_x\varphi_y.
\end{split}
\label{eq:effV}
\end{equation}
Here and below abelian fields in the rotated frame are denoted as $(\varphi_y,\vartheta_y)$ and spin current ${\bm M}_{R/L}$ is expressed
in terms of them in the same way as ${\bm J}_{R/L}$ is in terms of original pair $(\phi_y,\theta_y)$ used for the $\bm h\parallel \bm D$ configuration in Sec.~\ref{sec:parallel}.
We see that in the rotated frame the spins are subject to an effective magnetic field $h_{\rm eff} = \sqrt{D^2+h^2}$ along $z$ axis.
The fact that $D$ and $h$ terms are treated equally here represents the major technical advantage of the chiral rotation transformation \eqref{chiral rotation}.
Importantly, $h_{\rm eff}$ is {\em finite} once $D\neq 0$, implying the presence of some oscillating terms in the Hamiltonian even in the absence
of external magnetic field.
Being linear in derivative of $\varphi_y$, the term \eqref{eq:effV} is easily absorbed into ${\cal H}_0$, similar to what was done in \eqref{shift1}.
The parameters of this shift are
\begin{equation}
\begin{gathered}
t_{\varphi}=\frac{\sqrt{D^2+h^2}}{v} = \frac{h_{\rm eff}}{v},\quad t_{\vartheta}=0.
\end{gathered}
\label{s2}
\end{equation}
Observe that no shift of $\vartheta$ is required here.
The chiral rotation also transforms expressions for backscattering and inter-chain interactions, which we analyze next.
\begin{figure}[!tbp]
\includegraphics[width=0.8\columnwidth]{dc-cone-lightblue.pdf}
\caption{(Color online) Staggered magnetization in the \textit{distorted-cone} phase, Eq.\eqref{eq:dist-cone}, in the transverse to $\bm D$ plane.
This distortion is caused by magnetic field, the stronger the field the bigger the distortion. The opposite sense of spin precession in the neighboring chains is due to the staggered DM interaction.}
\label{fig:distorted_cone}
\end{figure}
\subsection{Backscattering ${\cal H}_{\rm bs}$ }
\label{subsec:bs_perp}
Rotation \eqref{chiral rotation} of spin currents transforms backscattering Hamiltonian in \eqref{system_2} into
\begin{eqnarray}
{\cal H}_{\rm bs}&=&2\pi v\int \mathrm{d}x \Big[\sum_a y_a M_{y,R}^{a}M_{y,L}^{a} + \nonumber\\
&&+ y_A (M_{y,R}^z M_{y,L}^x-M_{y,R}^x M_{y,L}^z)\Big],
\end{eqnarray}
where $a=x,y,z$ and,
\begin{equation}
\begin{gathered}
y_x(0)=-\frac{g_{bs}}{2\pi v}\big[(1+\frac{\lambda}{2})\cos[2\theta_0^y] +\frac{\lambda}{2}\big],\\
y_y(0)=-\frac{g_{bs}}{2\pi v},\\
y_z(0)=-\frac{g_{bs}}{2\pi v}\big[(1+\frac{\lambda}{2})\cos[2\theta_0^y] -\frac{\lambda}{2}\big],\\
y_A(0)=\frac{g_{bs}}{2\pi v}(1+\frac{\lambda}{2})\sin[2\theta_0^y].\qquad
\end{gathered}
\label{initial}
\end{equation}
Here $2\theta_0^y = \theta_R-\theta_L$, see \eqref{eq:theta0}.
The subsequent shift of $\varphi$, which eliminates linear term \eqref{eq:effV},
\begin{equation}
{\varphi_y}\to\varphi_y+\frac{t_{\varphi}}{\sqrt{2\pi}}x,
\label{eq:perp-shift}
\end{equation}
produces the end result
\begin{eqnarray}
&&{\cal H}_{\rm bs}\to {\cal H}_A+{\cal H}_B+{\cal H}_C+{\cal H}_{\sigma}, \\
&&{\cal H}_{A}=\pi v y_A\int \mathrm{d}x (M_{y,R}^{z}M_{y,L}^{+}e^{it_{\varphi}x}-M_{y,R}^{+}M_{y,L}^{z}e^{-it_{\varphi}x}+{\rm h.c.}),\nonumber\\
&&{\cal H}_{B}=\pi v y_B\int \mathrm{d}x(M_{y,R}^{+}M_{y,L}^{-}e^{-i2t_{\varphi}x}+{\rm h.c.}), \nonumber\\
&&{\cal H}_{C}=\pi v y_C\int \mathrm{d}x (M_{y,R}^{+}M_{y,L}^{+}+{\rm h.c.}), \nonumber\\
&&{\cal H}_{\sigma}=-2\pi v y_{\sigma}\int \mathrm{d}x M_{y,R}^{z}M_{y,L}^{z}, \nonumber
\label{eq:perp-BS}
\end{eqnarray}
where
\begin{equation}
y_C\equiv\frac{1}{2}(y_x-y_y), \;y_B\equiv\frac{1}{2}(y_x+y_y),\; y_{\sigma}\equiv-y_z.
\end{equation}
\begin{table}[!tbp]
\begin{center}
{\renewcommand{\arraystretch}{1.4}%
\begin{tabular}{c| c c c}
\hline
\hline
Interaction & Coupling & Coupling & Induced\\
term & operator & constant & state\\
\hline
${\cal H}_{x}$ & $\quad$${\cal N}^x_{y} {\cal N}^x_{y+1} $$\quad$ & $\quad$$g_{x}$$\quad$ & SDW(z) \\[0.8ex]
${\cal H}_{y}$ & ${\cal N}^y_y {\cal N}^y_{y+1}$ & $g_{y}$ & SDW (y) \\ [0.8ex]
${\cal H}_{\rm inter,\varphi}$ & $\cos[\sqrt{2\pi}(\varphi_{y}-\varphi_{y+1})]$ & $g_{\varphi_{1}}$ & \text{Distorted-cone} \\[0.8ex]
\hline
\hline
\end{tabular}}
\end{center}
\caption{When $\bm h\perp \bm D $, three relevant interchain interactions are ${\cal H}_{x}\propto {\cal N}^x_y{\cal N}^x_{y+1}$ , ${\cal H}_y\propto {\cal N}^y_y{\cal N}^y_{y+1}$
and ${\cal H}_{\rm inter,\varphi}$ in Hamiltonian~\eqref{eq:perp-inter} and \eqref{eq:perp-varphi}. The Table shows their operator forms
in the {\em rotated} frame, associated coupling constants and the ordered states they induce.}
\label{table:term2}
\end{table}
\subsection{Interchain interaction ${\cal H}_{\rm inter}$}
\label{subsec:inter_perp}
Under the rotation \eqref{chiral rotation} the staggered magnetization ${\bm N}_y$ in the original frame transforms, in terms of that in the rotated frame, ${\bm {\mathcal N}}_y$, as follows
\begin{equation}
{\bm N}_y(x)= ({\cal N}^{z}_y, \cos\theta_0^y{\cal N}^{y}_y +\sin\theta_0^y{\varepsilon}_y, -{\cal N}^{x}_y),
\label{eq:Nrotation}
\end{equation}
where
\begin{equation}
\varepsilon_y=\frac{\gamma}{\pi a}\cos[\sqrt{2\pi}\varphi_y + t_\varphi x],
\end{equation}
is the {\em dimerization} operator in the rotated frame (while $\xi_y=\frac{\gamma}{\pi a}\cos[\sqrt{2\pi}\phi_y]$ is the dimerization in the original frame, see Appendix \ref{app:ope}). Observe that due to \eqref{eq:theta0} $\sin\theta_0^y$ actually oscillates in sign with the chain index $y$.
According to \eqref{eq:N},
\begin{equation}
{\bm {\mathcal N}}_y \propto (- \sin[\sqrt{2\pi}\vartheta_y], \cos[\sqrt{2\pi}\vartheta_y], -\sin[\sqrt{2\pi}\varphi_y + t_\varphi x]),
\label{eq:calN}
\end{equation}
where oscillatory $x$-dependence of ${\cal N}^{z}_y$ follows from the shift \eqref{eq:perp-shift}.
Relation \eqref{eq:Nrotation} can be obtained by connecting chiral rotation \eqref{chiral rotation}
to the spinor rotation of Dirac fermions $\Psi_{R/L, s}$ ($s$ is the spin index) which are related to the spin current via, e.g.,
${\bm J}_R \sim \Psi^\dagger_{R, s} {\bm \sigma}_{s,s'} \Psi_{R, s'}$. The staggered magnetization is expressed in terms of these as
${\bm N} \sim \Psi^\dagger_{R, s} {\bm \sigma}_{s,s'} \Psi_{L, s'} + ({\rm L} \leftrightarrow {\rm R})$.
Rotation of spinors $\Psi_{R/L}$ leads to \eqref{eq:Nrotation}.
Inter-chain interaction in terms of rotated operators reads
\begin{equation}
{\cal H}_{\rm inter}=2\pi v\sum_y \int \mathrm{d}x \Big[\sum_{a}g_a {\cal N}_y^a{\cal N}_{y+1}^a+g_E\varepsilon_{y}\varepsilon_{y+1}\Big].
\label{eq:perp-inter}
\end{equation}
The interchain couplings are
\begin{equation}
\begin{gathered}
g_x(0)=\frac{J'}{2\pi v}, \quad g_y(0)=\frac{J'}{2\pi v}\cos^2\theta_0^y,\\
g_z(0)=\frac{J'}{2\pi v}, \quad
g_E(0)=-\frac{J'}{2\pi v}\sin^2\theta_0^y,\\
\end{gathered}
\label{eq:ini_inter1}
\end{equation}
Two terms in \eqref{eq:perp-inter}, namely $g_z$ and $g_E$ ones, are expressed in terms of $\varphi$ field and therefore
contain oscillating with position $x$ parts. In order to keep the presentation simple, we refrain here from
writing this dependence out explicitly. Beyond the oscillating RG scale $\ell_\varphi = -\ln[a_0 t_\varphi]$, introduced in Section~\ref{subsec:2steprg} below,
these two terms combine into
\begin{equation}
\begin{gathered}
{\cal H}_{\rm inter,\varphi}=2\pi vA^2 \sum_y \int \mathrm{d}x ~g_{\varphi_1}\cos[\sqrt{2\pi}(\varphi_{y}-\varphi_{y+1})],\\
g_{\varphi_1}\equiv\frac{1}{2}(g_E+g_z), \quad g_{\varphi_1}(0)=\frac{J'}{4\pi v}\cos^2\theta_0^y.
\label{eq:perp-varphi}
\end{gathered}
\end{equation}
Interchain interactions \eqref{eq:perp-inter} (terms with $g_{x/y}$) and \eqref{eq:perp-varphi} are the most relevant perturbations.
Three parts of the inter-chain Hamiltonian (namely $g_x$, $g_y$ and $g_{\varphi_1}$ terms) and the ordered states they induce are summarized in Table~\ref{table:term2}.
As discussed previously, Eq.~\eqref{eq:effV}, as well as its consequence, Eq.\eqref{eq:perp-varphi},
implies an effective magnetic field along $z$ in the rotated frame. Recalling the effect of the magnetic field on the scaling
dimensions of various operators, which was discussed in Sec.~\ref{sec:parallel} and ~\ref{sec:CMF},
we must conclude that this magnetic field will suppress the longitudinal ordering
and enhance transverse ones. Therefore we expect $g_{x,y}$ terms in \eqref{eq:perp-inter} to be more relevant than
$g_{\varphi_1}$ one.
\begin{table}
\begin{center}
\centering
{\renewcommand{\arraystretch}{1.2}%
\begin{tabular}{c|c|c|c|c|c}
\hline\hline
Region & I & II & III & IV & V \\
\hline
$y_{C}(0)$ & $\quad+\quad$ & $\;\;+\;\;$ & $\;\;+\;\;$ & $\;\;+\;\;$ & $\quad-\quad$ \\
\hline
$y_{\sigma}(0)$ & $-$ & $-$ & $+$ & $+$ & $+$ \\
\hline
C & $+$ & $-$ & $-$ & $+$ & $+$ \\
\hline
Fastest& \multirow{2}{*}{$g_{\varphi_1}$ }& \multicolumn{3}{c|}{\multirow{2}{*}{$g_x$}}& \multirow{2}{*}{$g_y$} \\
growing& &\multicolumn{3}{c|}{} & \\
\hline\hline
\end{tabular}}
\caption{Signs of $y_C$, $y_{\sigma},C$ in different field regions for intermediate value of $\lambda$ of order $0.1$.
This table summarizes conditions the fastest growing coupling constant in RG system \eqref{eq:RG_tot3}.}
\label{table:c}
\end{center}
\end{table}
\subsection{Two stage RG\cite{Garate2010, Gogolin}}
\label{subsec:2steprg}
RG flow of backscattering Hamiltonian \eqref{eq:perp-BS} is given by
\begin{equation}
\begin{gathered}
\frac{dy_x}{dl}=y_y y_z,\quad
\frac{dy_y}{dl}=y_x y_z+y_A^2,\\
\frac{dy_z}{dl}=y_x y_y,\quad
\frac{dy_A}{dl}=y_y y_A.\\
\end{gathered}
\label{eq:RG_bs}
\end{equation}
The interchain interaction \eqref{eq:perp-inter} changes as
\begin{equation}
\begin{split}
&\frac{dg_x}{dl}=g_x[1+\frac{1}{2}(y_x-y_y-y_z)],\\
&\frac{dg_y}{dl}=g_y[1+\frac{1}{2}(y_y-y_z-y_x)],\\
&\frac{dg_z}{dl}=g_z[1+\frac{1}{2}(y_z-y_x-y_y)],\\
&\frac{dg_E}{dl}=g_E[1+\frac{1}{2}(y_x+y_y+y_z)].\\
\end{split}
\label{eq:RG-inter}
\end{equation}
Similar to discussion around Eq.~\eqref{length1} for the $\bm h\parallel\bm D$ case, here too magnetic field induced oscillations $e^{i t_\varphi x}$ become
prominent beyond the RG scale
\begin{equation}
l_{\varphi}=-\log({a_0t_\varphi}).
\end{equation}
We find that for sufficiently strong DM interaction, approximately $D/J'>0.01$, the oscillating scale is shorter than the interchain one, $l_{\varphi} < l_{\rm inter}$. This means that the RG flow consists of two stages, $0 < l < l_{\varphi}$ and $l_{\varphi} < l <l_{\rm inter}$. During the first stage, $0 < l < l_{\varphi}$, full set of RG equations
\eqref{eq:RG_bs} and \eqref{eq:RG-inter} needs to be analyzed. At this stage all of the couplings remain small.
During the second stage, for $l > l_{\varphi}$, strong oscillations in ${\cal H}_A$, ${\cal H}_B$, see \eqref{eq:perp-BS}, and in the `oscillating part' of \eqref{eq:perp-inter}
lead to the disappearance of these terms.
\begin{figure}[t]
\includegraphics[width=0.8\columnwidth]{C_new.pdf}
\caption{(Color online) $y_C(0)/\eta$, $y_{\sigma}(0)/\eta$ and $C/\eta$ in Eq.\eqref{yyc} as a function of the ratio $h_x/D$. Here we denote $\eta = {\cal G}_{\rm bs}/(2\pi v)$.
$\lambda=1\times10^{-4}$, and $D/J=\sqrt{\lambda/c'}\sim0.005$. Here only region II, III, IV in Table \ref{table:c} are present in low magnetic field.
The inset shows region V appearing when the ratio $h_x/D$ increases to about $50$, which indicates a phase transition from SDW(z) to SDW(y).}
\label{fig:c1}
\end{figure}
Setting $y_A(l)=0$ and $y_B(l)=0$ reduces backscattering RG to the Kosterlitz-Thouless (KT) equations
\begin{equation}
\frac{dy_C}{dl}=y_Cy_\sigma,\;\;\;
\frac{dy_\sigma}{dl}=y_C^2,\\
\label{eq:RG_tot2}
\end{equation}
analytic solution of which is illustrated in Fig.~\ref{fig:kt}.
At the same time, interchain RG reduces to
\begin{equation}
\begin{gathered}
\frac{dg_x}{dl}=g_x(1+y_C+\frac{1}{2}y_{\sigma}),\\
\frac{dg_y}{dl}=g_y(1-y_C+\frac{1}{2}y_{\sigma}),\\
\frac{dg_{\varphi_1}}{dl}=g_{\varphi_1}(1-\frac{1}{2}y_{\sigma}).
\end{gathered}
\label{eq:RG_tot3}
\end{equation}
Initial conditions for $y_C$, $y_{\sigma}$ and $g_{\varphi1}$ at the start of the 2nd RG stage are
\begin{equation}
\begin{gathered}
y_C(l_{\varphi})=\frac{1}{2}[y_x(l_{\varphi})-y_y(l_{\varphi})],\quad
y_\sigma(l_{\varphi})=-y_z(l_{\varphi}),\\
g_{\varphi_1}(l_{\varphi})=\frac{1}{2}[g_E(l_{\varphi})+g_z(l_{\varphi})].\\
\end{gathered}
\end{equation}
\subsection{Types of two-dimensional order}
\label{sec:perp-phases}
In $\bm h\perp\bm D$ configuration, three competing interchain interactions $g_{x,y,\varphi_1}$
lead to three kinds of two-dimensional magnetic orders.
When $g_{x}$ (or $g_y$) is the most relevant coupling, one needs to minimize ${\cal N}^x_y {\cal N}^x_{y+1}$ (or ${\cal N}^y_y {\cal N}^y_{y+1}$), correspondingly.
It is clear that in both cases the appropriate component of $\bm {\mathcal N}$should be staggered as $(-1)^y$ between chains. In terms of $\vartheta_y$, this
order is described by a simple $\vartheta_y = \sqrt{\pi/2} (y+1/2)$ (correspondingly, $\vartheta_y = \sqrt{\pi/2} y$) in the case of $g_x$ (correspondingly, $g_y$) relevance.
The resulting spin ordering is of commensurate SDW kind, which, according to \eqref{eq:Nrotation}, can be more informatively described as SDW(z) (correspondingly, SDW(y)) order
when the coupling $g_x$ (correspondingly, $g_y$) is the most relevant one:
\begin{eqnarray}
\begin{gathered}
\langle {\bm S}_{x,y} \rangle \sim M {\bf x} + (-1)^{x+y} \Psi_{\rm sdw(z)} {\bf z},\\
\langle {\bm S}_{x,y} \rangle \sim M {\bf x} + (-1)^{x+y} \frac{h}{\sqrt{h^2 + D^2}} \Psi_{\rm sdw(y)} {\bf y} .
\end{gathered}
\label{eq:SDWzy}
\end{eqnarray}
Note that uniform magnetization is along the direction of the external magnetic field $h_x$, see \eqref{system_2}, while the antiferromagnetically ordered component
is orthogonal to it. As noted at the end of section~\ref{subsec:inter_perp}, in the rotated frame effective field $h_{\rm eff}$ makes $g_{x,y}$ inter-chain interactions more relevant
by reducing their scaling dimensions.
Therefore, we expect that the critical temperatures of SDW(z) and SDW(y) orders will vary with magnetization $M$ similarly to that of the cone and coneNN phases,
see for example $T_{\rm coneNN}(M)$ in Fig.~\ref{fig:Tc_2}, which is indeed in semi-quantitative agreement with the experiment\cite{Halg'sphdthesis}.
Correspondingly, the magnetization dependence of the orders parameters $\Psi_{\rm sdw(z,y)}$ in \eqref{eq:SDWzy}, for a fixed $J'/J$, should look similar to that of cone and coneNN orders
in Appendix~\ref{app:order_parameter}.
\begin{figure}[!tbp]
\includegraphics[width=0.8\columnwidth]{C2.pdf}
\caption{(Color online) Plot of $y_C(0)/\eta$, $y_{\sigma}(0)/\eta$ and $C/\eta$ in Eq.\eqref{yyc} versus the ratio $h_x/D$. Here
$\eta = {\cal G}_{\rm bs}/(2\pi v)$. $\lambda=0.2$, and $D/J=\sqrt{\lambda /c'}\sim 0.23$. Here all five distinct regions from Table \ref{table:c} are present.}
\label{fig:c2}
\end{figure}
When the most relevant coupling is $g_{\varphi_1}$, minimization of \eqref{eq:perp-varphi} leads to $\varphi_y = \sqrt{\pi/2} y + \hat{\varphi}$
so that the spin order is given by the incommensurate \textit{ distorted-cone} in the ${\bf x}-{\bf y}$ plane
\begin{eqnarray}
\langle {\bm S}_{x,y} \rangle && \sim M {\bf x} + (-1)^{x+y} \Psi_{\rm dist-cone} \Big(\sin[\sqrt{2\pi} \hat{\varphi} + t_\varphi x] {\bf x} \nonumber\\
&& - \frac{(-1)^y D}{\sqrt{h^2 + D^2}} \cos[\sqrt{2\pi} \hat{\varphi} + t_\varphi x] {\bf y}\Big) .
\label{eq:dist-cone}
\end{eqnarray}
$N^{x/y}$ components of the staggered magnetization form an ellipse. We used \eqref{eq:theta0} in deriving this expression.
Notice that the spin pattern \eqref{eq:dist-cone} represents a rotated, by the chain-dependent angle, and then elliptically distorted version of the coneNN state \eqref{eq:coneNN2}.
\begin{figure}[!tbp]
\includegraphics[width=0.8\columnwidth]{C3.pdf}
\caption{(Color online) $y_C(0)/\eta$, $y_{\sigma}(0)/\eta$ and $C/\eta$ in Eq.\eqref{yyc} versus the ratio $h_x/D$, and $\eta = {\cal G}_{\rm bs}/(2\pi v)$.
$\lambda=1$, and $D/J=\sqrt{\lambda/c'}\sim0.5$. Here region I and V from Table \ref{table:c} are present.}
\label{fig:c3}
\end{figure}
\subsection{Distinguishing the most relevant interaction}
The above Eq.~\eqref{eq:RG_tot3} shows that the flow of inter-chain interactions is controlled by the signs of marginal couplings $y_C$ and $y_{\sigma}$, and their relative magnitude,
which are determined by the initial condition in Eq.~\eqref{initial} as well as by their subsequent 1st stage flow.
Given that DM-induced anisotropy $\lambda$ is very small, the effect of the 1st stage RG flow reduces to the overall renormalization
of the value of $g_{\rm bs}$. This really is a direct consequence of the assumed near-SU(2) symmetry of the backscattering Hamiltonian \eqref{eq:perp-BS},
which, in the absence of the field $h_{\rm eff}$ (which is the essence of the 1st stage RG where oscillating factors do not play any role, therefore $e^{i t_\varphi x} \to 1$), is just a rotated version
of the marginally-irrelevant interaction of spin currents $g_{\rm bs} {\bm J}_R \cdot {\bm J}_L$. Therefore the main effect of the 1st stage consists in the renormalization
$g_{\rm bs}(0) \to {\cal G}_{\rm bs} \equiv g_{\rm bs}(0)/(1-g_{\rm bs}(0) l_\varphi/(2\pi v))$, see Ref.~\onlinecite{Schnyder2008} for the discussion of
a similar situation.
Thus, initial values of backscattering couplings for the 2nd stage of the RG are
\begin{equation}
\begin{gathered}
y_C(l_\varphi)=-\frac{{\cal G}_{\rm bs}}{4\pi v}\big[(1+\frac{\lambda}{2})\cos[2\theta_0^y] -1+\frac{\lambda}{2}\big],\\
y_{\sigma}(l_\varphi)=\frac{{\cal G}_{\rm bs}}{2\pi v}\big[(1+\frac{\lambda}{2})\cos[2\theta_0^y] -\frac{\lambda}{2}\big],\\
C=y_{\sigma}(l)^2-y_C(l)^2=y_{\sigma}(l_\varphi)^2-y_C(l_\varphi)^2,\\
\end{gathered}
\label{yyc}
\end{equation}
Finite $h_{\rm eff}$ \eqref{s2} breaks spin-rotational symmetry
and forces couplings $y_{C,\sigma}$ off the marginal diagonal directions in Fig.~\ref{fig:kt}.
Note that situations with significant $\lambda \sim O(1)$, such as shown in generalized phase diagrams in Fig.~\ref{fig:boundaryplot},
requires separate analysis with explicit numerical solution of the 1st stage equations \eqref{eq:RG_bs}.
Noting that $\cos[2\theta_0^y]=(h^2 - D^2)/(h^2 + D^2)$, we have identified 5 distinct regions with different signs of $y_{C,\sigma}$ and
integration constant $C$, which lead to different RG flows. The boundaries of these regions depend on $h/D$ and $\lambda$.
Expression for $C$ is approximated to $O(\lambda)$ accuracy because $\lambda \sim (D/J)^2\ll 1$.
The results are summarized in Table~\ref{table:c} which shows which interchain orders are promoted in different regions.
Several examples of $y_C(0)$, $y_{\sigma}(0)$, and $C$ vs. $h/D$, for three different values of $\lambda$, are shown as Fig.~\ref{fig:c1}, ~\ref{fig:c2}, ~\ref{fig:c3}.
Practically, $\lambda \sim 10^{-4}$ is very small, like in Fig.~\ref{fig:c1}. In low magnetic field one observes regions II, III and IV, all of which result in the two-dimensional
commensurate SDW order along DM vector ($\hat{z}$). At large $h/D$ values ($ >50$, see the inset in the same figure), the region V appears, leading to
a commensurate SDW order along $\hat{y}$-axis, orthogonal to the DM vector. This indicates a spin-flop phase transition where spins change their direction suddenly.
The actual value of the corresponding critical magnetic field $h_{\rm flop}$ does not have to be very high, and is experimentally accessible for most material.
For instance, for $D=0.01J$ we get $h_{\rm flop}\sim50 D=0.5J$.
\begin{figure}[t]
\includegraphics[width=0.8\columnwidth]{phase1.pdf}
\caption{(Color online) Phase diagram for the case of ${\bm h} \perp {\bm D}$, $h_z=0$.
Here $g_{\rm bs}=0.23\times 2\pi v$, $J'=10^{-3}\times 2\pi v$ and $D=0.01J$. We vary $\lambda$ and $h_x$, and treat $\lambda$ as independent from $D$ parameter.
At large $\lambda$ there is a phase transition from the distorted-cone to SDW(y) state. At small $\lambda$ the SDW(z) and SDW(y) phases are separated by the
transition line which approaches $\lambda=0$ as $h_x/D\to \infty$. }
\label{fig:pd2}
\end{figure}
In Fig.~\ref{fig:c2}, all 5 different regions are present, and we expect two phase transitions to be present. As magnetic field increases from zero the system transits from the distorted-cone
to the SDW(z), and then to the SDW(y). However, small initial value of $g_{\varphi_1}\propto\cos^2[\theta^y_0] \sim h^2/D^2$ at low field prevents it from reaching strong coupling limit.
Instead, coupling $g_x$ gets there first. As a result, the distorted-cone phase is not realized at low magnetic field. This feature of the RG flow is evident in the phase
diagrams in Fig.~\ref{fig:pd2} and Fig.~\ref{fig:boundaryplot}, in which the distorted-cone state is present only in the strong DM limit of $D \sim O(1)$.
We therefore conclude that the distorted-cone phase is unlikely to realize in real materials with small $D/J$ ratio.
\subsection{Phase diagram}
\label{subsec:phase_diag_perp}
The ground state of the two-dimensional system is determined by the fastest growing coupling constant of \eqref{eq:RG_tot3}.
For $\lambda$ not vanishingly small (practically, for $\lambda > 0.01$) we numerically solve both the 1st step, Eq.~\eqref{eq:RG_bs},~\eqref{eq:RG-inter},
and the 2nd step, Eq.~\eqref{eq:RG_tot2} and ~\eqref{eq:RG_tot3}, RG equations. The $\lambda-h/D$ phase diagram is shown in Fig.~\ref{fig:pd2}. For small $\lambda$, which for a moment is treated as an independent parameter, there is a phase transition from
SDW(z) to SDW(y) at large ratio of $h_x/D$, and the line separating the two states tends to be horizontal as $h_x/D\to \infty$.
The distorted-cone state appears only at unrealistically large $\lambda$. It transforms to SDW(y) at $h_x/D\simeq 1.5$,
for any $\lambda > 1$. This can be understood from Eq.~\eqref{yyc} and Table~\ref{table:c}: in order to change the sign of $y_C(0)$ and
$y_\sigma(0)$ at the same time, one needs $1+\lambda>2/\lambda$, which implies $\lambda>1$.
The distorted-cone-SDW(y) transition is of incommensurate-commensurate kind in agreement with the classical analysis prediction in Ref.~\onlinecite{Garate2010}.
\begin{figure}[!tbp]
\includegraphics[width=0.8\columnwidth]{boundaryplot_1.pdf}
\caption{(Color online) $h-D$ phase diagram for the case of ${\bm h} \perp {\bm D}$, $h_z=0$.
Here $\lambda\approx 3.8 (D/J)^2$, see Eq.\eqref{eq:lambda}, and $g_{\rm bs}=0.23 \times 2\pi v$ and $J'=10^{-3} \times 2\pi v$.
For small $D/J$, the critical field separating SDW(z) to SDW(y) phases is given by $h_x\simeq0.23\pi$.
The line separating distorted-cone and SDW(y) phases is described by $h_x/D\simeq1.5$. }
\label{fig:boundaryplot}
\end{figure}
It is easy to see that stronger DM interaction leads to a more stable SDW(z).
Indeed, stronger DMI shortens the RG scale $l_{\varphi}$ thereby extending the 2nd stage RG flow which favors $g_x$ process.
Using the relation $\lambda = c' D^2/J^2$, with $c'=(2\sqrt{2} v/g_{\rm bs})^2$,
we are now in position to calculate the physical $h-D$ phase diagram -- the result is presented in Fig.~\ref{fig:boundaryplot}.
The boundary between SDW(y) and distorted-cone is linear with $h_x/D\simeq 1.5$, which corresponds to the vertical boundary in Fig.~\ref{fig:pd2}. The line separating SDW(z) and SDW(y) phases is determined by the condition $g_y(l)=g_x(l)$, which leads to
\begin{equation}
[\cos\theta_0^y]^2\exp[-\int_{0}^{l} dl' 2y_C(l')]=1.
\label{eq:bound2}
\end{equation}
If $D$ is small, $\cos{\theta_0^y}\sim 1$, which implies $y_C(l)<0$. Using \eqref{yyc}, Eq.~\eqref{eq:bound2} reduces to $h^2/D^2=2/\lambda$.
Hence the critical magnetic field $h_c/J=(2\pi v/g_{\rm bs})\pi \sim 0.23\pi$ is independent of the value of $D$.
Being quite large, this value should be considered an order-of-magnitude estimate.
(Here we have used $g_{\rm bs}\simeq 0.23\times (2\pi v)$ from Ref.~\onlinecite{eggert}.)
Typical flows of coupling constants for each of the phases in Fig.~\ref{fig:boundaryplot} are shown in Fig.~\ref{fig:flow01},~\ref{fig:flow02},~\ref{fig:flow03}.
\begin{figure}[!tbp]
\includegraphics[width=0.8\columnwidth]{pf1.pdf}
\caption{(Color online) Typical flow of coupling constants in SDW(z) phase, ${\bm h}\perp {\bm D}$. $g_{\rm bs}/(2\pi v)=0.23$, $J'/(2\pi v)=0.001$,
$D=0.01J$, $h_x/D=0.1$, $h_z=0$ and $\lambda=0.2$. Here $l_{\rm inter}\simeq 6.9$, $l_\varphi\simeq2$. The dominant coupling is $g_x$ shown in red, and $g_x(\ell^*)=1$ at $\ell^*\simeq6.8$.}
\label{fig:flow01}
\end{figure}
\begin{figure}[!tbp]
\includegraphics[width=0.8\columnwidth]{pf2.pdf}
\caption{(Color online) Typical flow of coupling constants in distorted-cone phase, ${\bm h}\perp {\bm D}$. $g_{\rm bs}/(2\pi v)=0.23$, $J'/(2\pi v)=0.001$,
$D=0.01J$, $h_x/D=1$, $h_z=0$ and $\lambda=1.2$. Here $l_{\rm inter}\simeq 6.9$,
$l_\varphi\simeq1.7$. The dominant coupling is $g_{\varphi_1}$ shown in purple, and $g_{\varphi_1}(\ell^*)=1$ at $\ell^*\simeq7.0$.}
\label{fig:flow02}
\end{figure}
\begin{figure}[!tbp]
\includegraphics[width=0.8\columnwidth]{pf3.pdf}
\caption{(Color online) Typical flow of coupling constants in SDW(y) phase, ${\bm h}\perp {\bm D}$. $g_{\rm bs}/(2\pi v)=0.23$, $J'/(2\pi v)=0.001$,
$D=0.01J$, $h_x/D=5$, $h_z=0$ and $\lambda=0.2$. Here $l_{\rm inter}\simeq 6.9$, $l_\varphi\simeq 0.4$. The dominant coupling is $g_y$ shown in blue, $g_y(\ell^*)=1$ at $\ell^*\simeq6.2$.}
\label{fig:flow03}
\end{figure}
\section{Discussion}
\label{sec:conclusion}
Many of recent revolutionary developments in condensed matter physics, ranging from ferroelectrics \cite{Cheong2007} to spintronics \cite{Manchon2015} to
topological quantum phases \cite{annual-review2014,nussinov2015,Savary-Balents}, are associated with strong spin-orbit interactions.
Even when not particularly strong, spin-orbit coupling is seen to control important aspects of low-energy physics of systems such as
$\alpha-$ and $\kappa-$phase BEDT-TTF and BEDT-TSF organic salts, which are made of light C, S, and H atoms \cite{valenti2016}.
Our study adds a new physically-motivated model to this fast growing list: a quasi-2d (or 3d) system of weakly coupled antiferromagnetic Heisenberg
spin-$1/2$ chains subject to the uniform but \textit{staggered between chains} Dzyaloshinskii-Moriya interaction.
\subsection{Experimental implications}
The obtained $T-{\rm vs}-M(h)$ phase diagrams in Fig.~\ref{fig:Tc} and Fig.~\ref{fig:Tc_2} have striking resemblance with the experimentally determined,
via specific heat measurements \cite{Halg2014}, phase diagrams of chain materials
K$_2$CuSO$_4$Cl$_2$ and K$_2$CuSO$_4$Br$_2$, respectively. The first of this is interpreted as a weak-DM material with $(D/J')_{\rm Cl} = 1.3$, see Appendix~\ref{app:j'},
in which the only magnetic order is of the standard cone type.
The Br-based material is more interesting and exhibits a low-field phase transition between
two different orders of experimentally-yet-unknown nature. Interaction parameters for this material have been estimated experimentally \cite{Halg2014} to be $J =20.5$ K, and $D=0.28$ K. Fitting zero-field $T_c$ of this material to that of the commensurate SDW order gives us $J' = 0.09$ K, see Appendix~\ref{app:j'} for more details.
Therefore $(D/J')_{\rm Br}\approx 3.1$, which places K$_2$CuSO$_4$Br$_2$ in the intermediate-DM range.
Fig.~\ref{fig:MDJp} shows that
$D/J' = 3.1$ is strong enough to suppress cone ordering
at small magnetic fields, but nonetheless is not sufficiently strong to prevent the cone phase from emerging at slightly greater magnetic field.
Analysis in Appendix~\ref{app:j'} shows that for this particular value of $D/J'$ one encounters {\em three} quantum phase transitions in the narrow interval
of magnetization $0 \leq M \leq 0.025$: commensurate-incommensurate SDW, incommensurate SDW to coneNN, and finally coneNN to the commensurate cone phase.
The cone gets stabilized above $M=0.025$, see Fig.~\ref{fig:Br0}. This rapid progression of phase transitions is not seen in the experiment \cite{Halg2014}.
There, rather, a single transition at $B_{\rm Br}=0.1$T is observed, although it must be said that the commensurate-incommensurate SDW may be
just too difficult to identify. Converting the observed field magnitude to energy units, via $h_{\rm Br} = g \mu_B B_{\rm Br}/k_B = 0.134$ K,
we estimate the corresponding magnetization value as $M_{\rm Br} = h_{\rm Br}/(2\pi v) = h_{\rm Br}/(\pi^2 J_{\rm Br}) \approx 0.0007$.
This is much smaller than the critical cone magnetization $M=0.025$ estimated above.
However the present discussion, much of which is summarized graphically in Fig.~\ref{fig:MDJp}, shows that the region of $D/J' \approx 3$
is particularly tricky. Small, order of $5\% - 10\%$ changes, in $J'$ and $D$ can significantly affect the ratio $D/J'$ and lead to dramatically
different predictions for the phase composition at small magnetization. Specifically, increasing $D/J'$ to $\simeq 4$ eliminates the cone phase
from the competition completely as now one observes only C-IC SDW and SDW-to-coneNN transitions, in a much closer qualitative agreement
with the experiment. Given significant uncertainties in parameter values of K$_2$CuSO$_4$Br$_2$, a more quantitative description of the full experimental situation
is not possible at the moment.
\begin{figure}[t!]
\includegraphics[width=0.8\columnwidth]{smallphase.pdf}
\caption{\label{fig:MDJp} (Color online) Small magnetization $M-D$ phase diagram for the case of ${\bm h} \parallel {\bm D}$, obtained by the CMF calculation.
Here $J=20.5$ K, $J' = 0.0045 J = 0.09$ K. The cone phase is bounded by $D/J' \approx 4.2$ from above for all $M\in(0,0.5)$.
See Fig.\ref{fig:mdphase} in Appendix \ref{app:j'} for the phase diagram in the
wider range of magnetization $0.02 < M < 0.48$.}
\end{figure}
We hope that our detailed investigation will prompt further experimental studies of these interesting compounds,
in particular in the less studied so far ${\bm h} \perp {\bm D}$ configuration,
and will shed more light on the intricate interplay between the magnetic field, DM and inter-chain interactions present
in this interesting class of quasi-one-dimensional materials.
It is interesting to note that unique geometry of DM interactions makes K$_2$CuSO$_4$Br$_2$ somewhat similar to the honeycomb iridate
material Li$_2$IrO$_3$ an incommensurate magnetic order of
which is characterized by unusual counter-rotating spirals on neighboring sublattices \cite{kimchi2015,kimchi2016}.
\subsection{Summary and future directions}
We have systematically investigated complicated interplay of DM interaction and external magnetic field, applied either along or perpendicular to DM vector ${\bm D}=D\hat{z}$.
Combining techniques of bosonization, renormalizaion group and chain mean-field theory, we are able to identify the phase diagram of the system.
In all considered cases the ground state is determined by the inter-chain interaction, which is however strongly affected by the chain backscattering,
which in turn is very sensitive to the mutual orientation of ${\bm D}$ and ${\bm h}$.
In ${\bm h}\parallel {\bm D}$ configuration the phase diagram is strongly depended on the ratio $D/J'$.
For weak DM interaction, $D < 1.9 J'$, there is only a single cone phase, with spins spiraling in the plane perpendicular to ${\bm D}$.
Strong DM interaction is found to promote the collinear SDW state. The basic reason for this is strong frustration of the inter-chain cone channel,
caused by the opposite sense of rotation of spins in neighboring chains (which, in turn, is caused by the opposite directions
of the DM vectors in the neighboring chains).
As a result, the transverse cone ordering is strongly frustrated and the less-relevant SDW state gets stabilized.
However, the SDW is the ground state only in a very low magnetic field. Increasing the magnetic field upto critical value $h_c\sim J'$,
we find a (most likely, discontinuous) phase transition from the incommensurate SDW state to the coneNN state which is driven by the
fluctuation-generated cone-type interaction between the
next-neighbor (NN) chains. These RG-based arguments are fully supported by the chain mean field calculations.
For ${\bm h}\perp {\bm D}$, we find two distinct SDW states in the plane normal to the magnetic field in the experimentally relevant limit
of not too strong DM interaction, $D\ll J$. Since none of these states is a lower-symmetry version of the other, the
phase transition between the different SDWs is of spin-flop kind, and is expected to be of the first-order. The transition field $h_c \sim 0.23\pi J$ is (almost) independent of $D$.
In the limit of $D\sim J$ (impractical for the experiment), there is also a ``distorted-cone" state in which spins rotate in the plane
normal to vector ${\bm D}$, see Figure~\ref{fig:boundaryplot}. We have carried out two-stage RG calculations and
determined the $\lambda-h/D$ and $h-D$ phase diagrams for this geometry numerically.
All of the obtained results are based on perturbative calculations, framed in either RG or CMF language. The complete consistency between these two techniques
observed in our work provides strong support in favor of its validity. Nonetheless, an independent check of the presented arguments is highly desired. We hope
our work will stimulate numerical studies of this interesting problem along the lines of quantum Monte-Carlo studies in Refs. \onlinecite{Sandvik1999,Yasuda2005}.
In concluding, we would like to mention potential relevance of our model to the currently popular coupled-wire approach to (mostly chiral) spin liquids \cite{kane2002,neupert2014,sela2015}.
The essence of this approach consists in devising interchain interactions in such a way as to suppress all interchain couplings between the relevant, in RG sense, degrees of freedom
(such as staggered magnetization and dimerization). The remaining marginal interactions of current-current kind then conspire to produce gapped chiral phase with gapless
chiral excitations on the edges. Staggered DM interactions of the kind considered here are, as we have shown, actually quite effective in removing
$N^+_y N^{-}_{y+1}$ terms. At the same time, the remaining interchain SDW term grows progressively less relevant as magnetic field is increased towards the
saturation value. Provided that one finds way to suppress fluctuation-generated relevant coneNN like couplings between more distant chains,
described in Section~\ref{sec:coneNN}, one can hope to be able to destabilize weak SDW long-ranged magnetic order with the help of additional
weak interactions (of yet unknown kind) and drive the system into a two-dimensional spin liquid phase.
\section*{Acknowledgement}
We would like to thank M. H\"alg, K. Povarov, A. I. Smirnov and A. Zheludev for detailed discussions of the experiments, and L. Balents for
insightful theoretical remarks. This work is supported by the National Science Foundation grant NSF DMR-1507054.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,541 |
\section{Introduction}
\label{sec:intro}
The texts that are part of French law are modified by amending texts
published in the Official Journal of the French Republic (JORF). The
life cycle of a legislative or regulatory text begins with the
publication of its complete version in the JORF and continues with the
possible publication of texts amending it. The full amended text,
called its \textit{consolidated} version, is never published in the
JORF and has no legal value: only the initial version and the suite of
the ordered modifications of the text are authentic~\cite{SGG2017}.
Since 2008, the French Légifrance~\cite{LEGIFRANCE} website presents
most of the legal texts in their original versions as well as in their
successive versions, consequences of the modifications brought to
these texts over time. The operator of the Légifrance website, the
Direction of Legal and Administrative Information (DILA), manually
reports the modifications described in natural language in the texts
in order to obtain, at each modification date, the complete
consolidated version of the text.
This convenience of access to the texts in an easier-to-read and
easier-to-use version has de facto changed the status of these
consolidated versions: they are seen by most users, including legal
professionals, as the reflection of the applicable
law~\cite{GirardotTX2014}. Moreover, the drafters of new texts, in the
French parliament or in the ministries, start from this consolidated
version to conceive the modifying texts. It is therefore of the utmost
importance that this consolidation work be free of errors and
available as soon as possible.
We present here preliminary work integrated in the Legistix tool that
we are developing, whose objective is to create an automated and
reliable consolidation system for French legal texts. This work is
based both on regular expressions used in several compound grammars,
similar to the successive passes of a compiler, and on a new
specialized language of functional type, allowing to describe the
changes applied to the texts.
For each modifier text, our tool generates fully automatically a
computer program in this new language which, when executed, performs
the changes induced by the modifier text on the target texts. In
previous work on this topic, presented for example
in~\cite{FabriziS2021}, only the problem of classifying types of
modification is addressed. To the best of our knowledge, our work is
the first to present a complete approach to identify target texts and
to transform the natural language instructions of the modifier text
into a computer program formalizing the actual transformation rules.
Unlike other topics of study related to legal texts, such as
extracting automatically reasonings, rules of law or trying to
understand the semantics of the text, we place ourselves in a purely
\textit{legistic}~\cite{SGG2017} perspective, i.e. we do not try to
understand the meaning of the text, but only its structure and its
relations to other texts. Since our problem is clearly defined, it
lends itself well to automation, since the consolidation must be
careful not to interpret the changes but only to apply them to the
letter~\cite{GirardotTX2014}.
\section{Example of consolidation}
\label{sec:exemple}
In order to illustrate the complexity of a tool like Legistix, we will
use in this document an example of consolidation based on the law
2022-1348 of 24 October 2022 published in the JORF of 25 October 2022
and presented fig.~\ref{fig:loi-2022-1348-art-1}. Like all texts
published in the JORF, unless otherwise indicated, this law came into
force the day after its publication, i.e. on October 26, 2022. We can
also note in paragraph III of the law a \textit{delayed entry into
force} of some induced changes on January 1, 2023. The text targeted
by the changes is article L723-4 of the Commercial Code is presented
in fig.~\ref{fig:code:commerce:L723-4:20211013}.\footnote{These
changes, applied manually by the DILA, can be viewed online on the
Légifrance website:
\url{https://www.legifrance.gouv.fr/codes/section_lc/LEGITEXT000005634379/LEGISCTA000006161381/2022-10-26/\#LEGISCTA000006161381}}.
\begin{figure}[ht]
\hrule
\begin{center}
\textbf{Article 1 of law 2022-1348 of october 24, 2022 (partial)}
\end{center}
{\small\begin{itemize}
\item[I.] - Article L723-4 of the Commercial Code is amended as
follows:
\begin{itemize}
\item[1°] At the beginning of the first paragraph, the following
is added: "\textit{I. -}";
\item[2°] In 1°, the second occurrence of the word:
"\textit{and}" is replaced by the word: "\textit{or}";
\item[3°] In 3° and 4°, after the word: "\textit{judicial}",
if inserted the word: "\textit{rescue,}";
\item[4°] In 4° bis, the first occurrence of the word:
"\textit{were}" is suppressed;
\item[5°] In 5°, after the word: "\textit{qualities}", are
inserted the words: "\textit{and duties}";
\item[6°] The last paragraph is replaced by a II redacted as
follows:
\begin{flushleft}
"\textit{II. - Also eligible are, [...]}\\
"\textit{2° [...] establishments registered in the trade
directory or within the jurisdiction of the courts. [...]
}"
\end{flushleft}
\end{itemize}
\item[II.] - In the first sentence of 2° of II of article L723-4
of the French Commercial Code, as amended by I of this article,
the words: "\textit{trade directory}" are replaced by the words:
"\textit{national register of company or establishment in the
trades and crafts sector}".
\item[III.] - II of this article shall apply as of January 1,
2023. This act shall be executed as a law of the of the state.
\end{itemize}}
\hrule
\caption{Partial reproduction of the unique article of the law
2022-1348 of october 24, 2022 published in the official journal
of october 25, 2022~\cite{JORFARTI000046480974}, with the
identifier \texttt{fr/loi/2022-1348/1/20221025}. Non official
translation from the French. Missing text is between [...].}
\label{fig:loi-2022-1348-art-1}
\end{figure}
\begin{figure}[ht]
\hrule
\begin{center}
\textbf{Article L723-4 of the French Commercial Code, in force
since october 13, 2021}
\end{center}
{\small\begin{flushleft}
Persons who are at least thirty years of age shall
be eligible for election as a judge of a commercial court:\\
\begin{itemize}
\item[1°] Registered on the electoral lists of the chambers of
commerce and industry and the chambers of trade and crafts [...]
\item[3°] In respect of which a judicial recovery or liquidation
procedure [...]
\item[4°] [...] a judicial recovery or liquidation procedure is in
progress on the day of the vote;
\item[4° bis] Who were not were subject to the sanctions [...]
\item[5°] And that justify [...] of the qualities listed [...]
\end{itemize}
The following are also eligible for election as members of the
commercial courts, [...].
\end{flushleft}}
\hrule
\caption{Partial reproduction of the article L723-4 of the French
Commercial Code~\cite{LEGIARTI000044191424}, in force since
october 13, 2021, with the identifier
\texttt{fr/code/commerce/L723-4/20211013}. Non official
translation from the French. Missing text is between [...]}
\label{fig:code:commerce:L723-4:20211013}
\end{figure}
The amending text that modifies the target code article contains
instructions for humans to modify the original text and to obtain the
new text. These instructions are insertions, deletions, replacements,
etc. We can also note in the 4° bis paragraph of the article a mistake
made by the legislator of a previous amending law voted in the
Parliament: "\textit{Who were not were...}". The objective of our tool
is to transform these instructions intended for humans into a computer
program allowing to apply them automatically.
\section{Data, identifiers and versions}
\label{sec:data}
The data integrated into Legistix are made up of the whole of the
JORF~\cite{DATAJORF} and LEGI~\cite{DATALEGI} databases provided and
updated daily by the DILA. These databases contain all the texts
published in the JORF since 1990 as well as all the texts that have
been consolidated by the DILA. The data are integrated into the
Legistix database on an ongoing basis, thanks to an integration
process that improves the data, reconstructing in particular the
paragraphs and the versions of the tables of contents not provided in
the original data. For example, the Commercial Code has over 600
versions since 2000.
Each document receives a unique identifier in the form of a URI. The
form of this URI is a continuation of the work carried out with the
DILA in the context of the Légimobile~\cite{LarredeP2011}
project. These identifiers have the particularity of being perennial
and of being able to be systematically derived from the information in
the document itself. Thus, for example, article 1 of the law
2022-1348 of October 24, 2022 presented in
fig.~\ref{fig:loi-2022-1348-art-1} has the unique URI
\url{fr/loi/2022-1348/1}, representing all the versions of this
article over time.
To specify a particular version, the identifiers also support the many
dates governing the life cycle of a law: date of signature, date of
publication in the JORF, dates of modification leading to versions,
date of of abrogation. Thus, the version published in the JORF on
October 25, 2022 of the previous article has as the URI
\url{fr/loi/2022-1348/1/20221025}. Following the same logic, article
L723-4 of the Commercial Code in its version in force since October
13, 2021 presented fig.~\ref{fig:code:commerce:L723-4:20211013} has
the URI \url{fr/code/commerce/L723-4/20211013}.
\section{Detection of modified texts and creation of new versions}
\label{sec:target}
In the example of law 2022-1348, Legistix detects the reference
"\textit{L723-4 of the Commercial Code}" present twice. Thanks to the
identifier mechanism described above, it will be resolved into the
identifier \url{fr/code/commerce/L723-4}, without the need to query an
external resolution mechanism: the character string of the reference
is enough.
Here we can start describing the program obtained automatically by
Legistix: presented here for more clarity in a functional language
with a Python-like syntax, it will allow us to illustrate some of the
mechanisms we are implementing. First of all, the source text
\texttt{s} can be defined as the article 1 of the law 2022-1348 in its
version as of October 25, 2022 as published in the JORF, with
\texttt{db} an object representing the database of the texts and
\texttt{get\_version} a method returning a reference to an existing
version:
\begin{verbatim}
s = db.get_version("fr/loi/2022-1348/1", Date(2022, 10, 25))
# s is fr/loi/2022-1348/1/20221025
\end{verbatim}
Legistix must now find the different versions of the target text that
will be used in the described changes. The first version we need is
the one from which we start, i.e. the version on which the changes are
to be applied. For the first reference found in paragraph I, the date
is the date of publication in the JORF of the source text,
i.e. October 25, 2022. The reference:
\begin{verbatim}
t = db.get_version("fr/code/commerce/L723-4", Date(2022, 10, 25))
# t is fr/code/commerce/L723-4/20211013 (!)
# that is, the version in force on October 25, 2022
\end{verbatim}
\noindent
is positioned in article L723-4 in its version as of October 13,
2021. Indeed, the version in force of this text on October 25, 2022 is
that of October 13, 2021~\cite{LEGIARTI000044191424}, as modified by
Article 1 of Law 2021-1317 which came into force on the same
day~\cite{JORFARTI000044183798}.
As a text in the JORF comes into force by default on the day after its
publication, i.e. here on 26 October 2022, the new version of article
L723-4 described in I of law 2022-1348 must be created on this date
with the function \texttt{new\_version}, from the version represented
by \texttt{t}:
\begin{verbatim}
v1 = t.new_version(Date(2022, 10, 26))
# v1 is fr/code/commerce/L723-4/20221026, created from target t
\end{verbatim}
In II, changes are described with reference to Article L723-4 of the
Commercial Code as revised by I of this article, i.e. \textit{after}
the changes in I have been applied. Combining this information with
the information in III, which indicates that the changes in II are to
apply on January 1, 2023, a new version must be created on that date:
\begin{verbatim}
v2 = v1.new_version(Date(2023, 1, 1))
# v2 is fr/code/commerce/L723-4/20230101, created from version v1
\end{verbatim}
The names \texttt{s}, \texttt{t}, \texttt{v1} and \texttt{v2}
represent abstract references to documents. As we will see in the next
section, these references can be used to abstractly reference portions
of text. For example, the methods \texttt{par} and \texttt{sen} will
allow to generate functions which will respectively return references
to a paragraph or a sentence when they are evaluated. Thus,
\texttt{s.par("I")} generates a function which, when evaluated, will
return a reference to paragraph I of article 1 of law 2022-1348. These
generators can be combined as in:
\begin{verbatim}
v1.par("II").par("2°").sen(1)
\end{verbatim}
\noindent
which generates a function allowing to obtain the first sentence of
the 2° of the II of the article L723-4 of the commercial code in its
version of october 26, 2022.
\section{Detection of changes in the modifying texts}
\label{sec:source}
After identifying the versions of the target texts mentioned in the
modifying texts, Legistix detects the changes and transforms them into
a sequence of functions to apply them. From the text in
fig.~\ref{fig:loi-2022-1348-art-1}, Legistix generates the complete
program shown in fig.~\ref{fig:legistix-loi-2022-1348-art-1}.
\begin{figure}[ht]
\begin{verbatim}
s = db.get_version("fr/loi/2022-1348/1", Date(2022, 10, 25))
t = db.get_version("fr/code/commerce/L723-4", Date(2022, 10, 25))
v1 = t.new_version(Date(2022, 10, 26))
pI = s.par("I")
v1.schedule_changes(s, [
v1.prepend(pI.par("1"), v1.par(1), "I. -"),
v1.replace(pI.par("2"), v1.par("1°"), ("and", 2), "or"),
v1.insert(pI.par("3"), v1.par("3°"), "judicial", "rescue,"),
v1.insert(pI.par("3"), v1.par("4°"), "judicial", "rescue,"),
v1.suppress(pI.par("4"), v1.par("4° bis"), ("were", 1)),
v1.insert(pI.par("5"), v1.par("5°"), "qualities", "and duties"),
v1.replace_par(pI.par("6"), v1.lastpar(), "II. - Also eligible[...]")
])
v1 = db.add_version(v1.apply_changes())
v2 = v1.new_version(Date(2023, 1, 1))
pII = s.par("II")
v2.schedule_changes(s, [
v2.replace(pII, v2.par("II").par("2°").sen(1), "trade directory",
"national register of company[...]")
])
v2 = db.add_version(v2.apply_changes())
\end{verbatim}
\caption{Legistix program derived from article 1 of the law
2022-1348 of October 24, 2022, published in the official journal
of October 25 October 25, 2022~\cite{JORFARTI000046480974}.}
\label{fig:legistix-loi-2022-1348-art-1}
\end{figure}
It creates two new versions of article L723-4 of the Commercial Code,
\texttt{v1} effective October 26, 2022, with the changes described in
paragraph I of article 1 of law 2022-1348 (\texttt{s.par("I")}),
applying to the version of the Commercial Code as of October 13, 2021,
and \texttt{v2} effective January 1, 2023 with the changes described
in paragraph II (\texttt{s.par("II")}). Note that the second version
is created from the first. The methods \texttt{prepend},
\texttt{replace}, \texttt{insert}, \texttt{suppress},
\texttt{replace\_par} are function generators which are not applied
directly by the program, as long as the method
\texttt{apply\_changes()} is not called.
Each method used in the program translates an operation from natural
language. Each function describing a change is of the form
\texttt{action(source, target, what...)}, where \texttt{source} and
\texttt{target} indicate respectively the text fragment at the origin
of the change and the target. The parameters \texttt{what} describe
the changes, with for example \texttt{("and", 2)} which represents the
second occurrence of the word "\texttt{and}" and "\texttt{rescue}" a
replacement word.
\section{Conclusion and perspectives}
We started with a reference database of several decades where the
consolidation was already carried out manually. This historical
consolidation serves as a reference to measure the reliability of our
approach. The Legistix tool is able to automate 93\% of the
consolidation operations that were previously performed manually. Our
efforts will continue in order to reach a rate of 100\%, by analyzing
the undetected cases, some of which are ambiguous even for a human,
thus contradicting the mechanizable aspect desired by the
legislator~\cite{GirardotTX2014}.
The next step will be to extend our work to the EUR-Lex~\cite{EURLEX}
database containing the law of the European Union and where
regulations and directives are published on a publication model
similar to French law.
Third, we will propose an expert system~\cite{DelaetA2022} to assist
legislators for the drafting of modifying texts where the formal rules
of modification (the program) could be generated directly during the
drafting of the text. This would set up a virtuous circle where the
impacts of the modifications could be immediately visualized, thus
improving and making the production of law more reliable.
When the 100\% rate will be reached, there will be no delay anymore
between the publication of the modification texts and the availability
of the consolidated versions. The consolidated text will only be a
by-product of the application of a series of programs starting from
the original text. These programs could be voted on at the same time
as the amending text, making the adage \textit{code is
law}~\cite{LessigL2000} legally real.
\section*{Acknowledgements}
Thanks to Salomé Ouaknine, a student at Mines Paris, for her help
during her two-month research internship on the subject of automatic
consolidation, especially on the clearing of the future hybrid
approach mixing regular expressions and machine learning.
\bibliographystyle{ACM-Reference-Format}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,835 |
<div class="row">
<div class="col-sm-3">
<div class="sidebar-nav">
<div class="navbar navbar-default" role="navigation">
<div class="navbar-header">
<button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".sidebar-navbar-collapse">
<span class="sr-only">Toggle navigation</span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<span class="visible-xs navbar-brand">Sidebar menu</span>
</div>
<div class="navbar-collapse collapse sidebar-navbar-collapse">
<ul class="nav navbar-nav">
<li><a href="#!/analytics">Overview</a></li>
<li><a href="#!/class_stats">Class Statistics</a></li>
<li><a href="#!/individual_stats">Individual Statistics</a></li>
<li class="active"><a href="#">New Reports <span class="badge">6</span></a></li>
</ul>
</div><!--/.nav-collapse -->
</div>
</div>
</div>
<div class="col-sm-9">
<section data-ng-controller="StudentListController">
<!-- Overview header -->
<div class="row" style="padding-left:15px">
<h2 >Daily Aggregated Reports</h2>
</div>
<div class="alert alert-success">
6 new reports aggregated for your class.
</div>
<!-- start showing student list -->
<div class="row" style="padding-left:15px">
<ul class="nav nav-pills">
<li class="active"><a href="#">Overview</a></li>
<li class="dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">
Students with Updated Results <span class="caret"></span>
</a>
<ul class="dropdown-menu">
<li ng-repeat = "student in students">
<a href="#{{student.id}}">{{student.name}}</a>
</li>
<li >
<a href="#Billy">Billy</a>
</li>
</ul>
</li>
</ul>
</section>
</div>
<div class="row" style="padding-left:15px">
<section data-ng-controller="TabsDemoCtrl">
<tabset>
<tab heading="Static title">Static content</tab>
<tab ng-repeat="tab in tabs" heading="{{tab.title}}" active="tab.active" disabled="tab.disabled">
{{tab.content}}
</tab>
</tabset>
</section>
</div>
<!-- end student list -->
<!-- tabbed areas -->
<!-- Tab panes -->
<section data-ng-controller="DropDownController">
<div class="tab-content">
<div ng-repeat = "student in students">
<div class="tab-pane" id="{{student.id}}"></div>
</div>
</div>
</section>
</div>
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,204 |
Obec Dřevěnice se nachází v okrese Jičín, kraj Královéhradecký. Žije zde obyvatel.
Historie
První písemné zprávy pocházejí z roku 1387 o vsi Dolany (nynější část Dolánky) a z roku 1388, kdy se připomíná Jan z Dřevěnice. Ves rozšířil Havel z Dřevěnice v letech 1429-1454, pravděpodobně již majitel tvrze. Výslovně se tvrz se dvorem a vsí připomíná až roku 1511, kdy ji získal nejvyšší zemský sudí Jindřich Berka z Dubé na Dřevěnici. Ten zde zemřel roku 1541 a nápisový kámen s jeho erbem z nadpraží portálu (považovaný za náhrobník) je vsazen do renesanční budovy tvrze, přestavěné později na mlékárnu a sýpku. Jindřichův syn Zdeněk Leopold Berka z Dubé s manželkou Alenou ze Šelmberka přestavěli tvrz a založili zde rodinu, v níž se narodil pozdější pražský arcibiskup Zbyněk Berka z Dubé. Leopold ves Dřevěnici s tvrzí i dvorem roku 1560 prodal svému švagrovi Petrovi ze Šelmberka. Pozdějšími majiteli byli Jan Rudolf Trčka z Lípy, který Dřevěnici připojil k panství Kumburk, po něm Albrecht z Valdštejna a Rudolf z Tiefenbachu, který nechal tvrz zpustnout. Šternberkové vlastnili kumburské panství v letech 1663-1710a a dali do průčelí tvrze vsadit svůj erb.
Pamětihodnosti
Tvrz Dřevěnice – původně gotická tvrz Berků z Dubé byla několikrát přestavěna, počátkem 20. století zcela přestavěna pro hospodářské účely (drůbežárna, pak mlékárna)
Socha Panny Marie a socha svatého Václava - nad vesnicí na kopci
Hospoda Na Špici
Volejbalová Dřevěnice
Obec je proslulá největším volejbalovým turnajem v České republice, který se koná od roku 1954 každoročně počátkem srpna pod záštitou ČOV. Hraje se pod otevřeným nebem na deseti antukových kurtech a účastní se ho i týmy české extraligy nebo hosté ze zahraničí. V roce 1987 byla zaznamenána rekordní účast 589 družstev.
Části obce
Dřevěnice
Dolánky
Rodáci
Zbyněk Berka z Dubé pražský arcibiskup a velmistr Rytířského řádu křižovníků s červenou hvězdou
Odkazy
Reference
Literatura
ŠIMEK, Tomáš (ed.) a kolektiv: Hrady, zámky a tvrze v Čechách, na Moravě a ve Slezsku. VI. Východní Čechy. Svoboda Praha 1989, s. 101
Externí odkazy
Vesnice v okrese Jičín
Obce v okrese Jičín
Zaniklé tvrze v okrese Jičín
Svazek obcí Brada
Sídla v Jičínské pahorkatině | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,480 |
Statehouse Blend Kansas
Here To Listen
StoryCorps One Small Step
StoryCorps In Kansas City
Guns And America
Is Now 'The End of White Christian America'?
By Steve Kraske & Lisa Rodriguez • Aug 5, 2016
Due to technical difficulties, 'Up To Date' lost the connection with Robert Jones at the end of this interview.
White Christians set the tone for this country, dating back to its founding. But that's changing in some profound ways. For one thing, white Christians no longer comprise a majority of the nation. As the cultural and religious ground shifts under them we'll see how their influence is changing.
Robert Jones is the author of The End of White Christian America. He's also the founding CEO of the Public Religion Research Institute.
Black And White Methodist Congregations Discuss Theology, Race And Literature
By Laura Ziegler • Jul 15, 2016
Laura Ziegler / KCUR 89.3
More than 100 members — about half white, half African-American, mostly middle age or younger — of two Methodist churches came together Thursday night to pray, read and discuss their personal experiences of race relations.
In America's Heartland, Building One Home For Three Faiths
By Frank Morris • Dec 18, 2015
Frank Morris / KCUR
A mosque, a church and a synagogue go up on the site of an old Jewish country club ...
It sounds like the setup to a joke — but it's not. It's actually happening in Omaha, Nebraska. The Tri-Faith Initiative may be the first place in history where these three monotheistic faiths have built together — on purpose — with the intention of working together.
The project has inspired some, and angonized others.
In a tiny suburban section of Omaha, kids at Countryside United Church of Christ sing Away in a Manger in preparation for an upcoming Christmas program.
Hamilton and Holland On United Methodist Struggle Over LGBT Issues
By Steve Kraske & Danie Alexander • May 20, 2016
The top policy-making body of the United Methodist Church this week narrowly approved a full review of all church law on sexuality. Up to Date host Steve Kraske speaks with two area ministers about this latest move by the Church.
Rev. Adam Hamilton is the founding pastor of the United Methodist Church of the Resurrection in Leawood, Kansas.
Rev. Mark Holland is also the mayor and CEO of the Unified Government of Wyandotte County.
Missouri's Proposed Religious Freedom Amendment Sets Old Allies At Odds
By Frank Morris • Apr 22, 2016
The battle over religious freedom and LGBT rights has moved from Arizona and Mississippi to Missouri. Conservatives there are backing an amendment to the state Constitution that would protect certain people — clergy, for instance — who refuse to take part in same-sex marriages.
But the measure has run into some unexpected — and unexpectedly stiff — opposition, from a longtime ally of the religious right: the business community. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,119 |
With the housing market well on the way to complete recovery, many licensees making the move to become a real estate broker in Mississippi. After all, one of the benefits of a forming a career in real estate is the control it allows you in shaping your personal success. The step towards becoming a broker is the beginning of an exciting new chapter in the life of a real estate professional. There is no need to wait for a promotion. A real estate licensee is able to simply make the decision to sign up for broker training and the state exam. Once this decision has been made, it may be only a matter of weeks before you are working as a Mississippi broker. Real estate sales associates in Mississippi who are ready to take the next step in their real estate careers can begin the process of becoming a licensed real estate broker by completing the state's requirements for licensure.
Real Estate Broker Licensure Exams are conducted once a month in Mississippi. Before you register for the examination you have to be approved by the Mississippi real estate commision. Then you are given 2 months to take the exam.
The exam has 100 multiple choice questions based on national real estate law and Mississippi state specifications.
4 hours are given to you to complete the Mississippi Real Estate Broker Exam.
If you fail the exam you can retake it at any time in Mississippi and you don't have to pay registration fee one more time.
Arrive 30 minutes before the exam starts and take a calculator with you. You will not be able to open any books during the exam.
You will pay $135 of the registration fee to take the Mississippi Real Estate Broker Exam and $110 to take the salesperson exam. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,807 |
Q: How is the normal ordering on the Natural Numbers defined in Zermelo set theory? A fact that often gets mentioned in the elementary development of arithmetic in ZFC is that there are a bunch of different ways one could have defined the natural numbers. The most common alternative to the modern way of doing things is due to Zermelo, who sets $0=\emptyset$ and $n'=\{n\}$.
My question is how does one define the normal ordering on this collection using only the resources Zermelo allowed himself (i.e. The normal ZFC axioms, minus replacement, foundation, and a modified version of the axiom of infinity which states the existence of the above set rather than the first von Neumann ordinal)?
A: Hint
I think that we have to rely on Frege's definition of the ancestral:
$$a < b =_{\text{def} } \forall w \ [\forall x \ (a \in x \to x \in w) \land \forall x \forall y \ (x \in w \land x \in y \to y \in w) \to b \in w].$$
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,505 |
define([
'jqueryui',
'jsplumb',
'lodash',
'viewcanvas_widget/AbstractNode',
'viewcanvas_widget/SingleSelectionAttribute',
'viewcanvas_widget/SingleValueAttribute',
'viewcanvas_widget/SingleColorValueAttribute',
'viewcanvas_widget/SingleMultiLineValueAttribute',
'viewcanvas_widget/BooleanAttribute',
'text!templates/canvas_widget/edge_shape_node.html'
],/** @lends EdgeShapeNode */function($,jsPlumb,_,AbstractNode,SingleSelectionAttribute,SingleValueAttribute,SingleColorValueAttribute,SingleMultiLineValueAttribute,BooleanAttribute,edgeShapeNodeHtml) {
EdgeShapeNode.TYPE = "Edge Shape";
EdgeShapeNode.DEFAULT_WIDTH = 150;
EdgeShapeNode.DEFAULT_HEIGHT = 150;
EdgeShapeNode.prototype = new AbstractNode();
EdgeShapeNode.prototype.constructor = EdgeShapeNode;
/**
* Abstract Class Node
* @class canvas_widget.EdgeShapeNode
* @extends canvas_widget.AbstractNode
* @memberof canvas_widget
* @constructor
* @param {string} id Entity identifier of node
* @param {number} left x-coordinate of node position
* @param {number} top y-coordinate of node position
* @param {number} width Width of node
* @param {number} height Height of node
* @param {number} zIndex Position of node on z-axis
*/
function EdgeShapeNode(id,left,top,width,height,zIndex){
var that = this;
AbstractNode.call(this,id,EdgeShapeNode.TYPE,left,top,width,height,zIndex);
/**
* jQuery object of node template
* @type {jQuery}
* @private
*/
var _$template = $(_.template(edgeShapeNodeHtml,{type: that.getType()}));
/**
* jQuery object of DOM node representing the node
* @type {jQuery}
* @private
*/
var _$node = AbstractNode.prototype.get$node.call(this).append(_$template).addClass("class");
/**
* jQuery object of DOM node representing the attributes
* @type {jQuery}
* @private
*/
var _$attributeNode = _$node.find(".attributes");
/**
* Attributes of node
* @type {Object}
* @private
*/
var _attributes = this.getAttributes();
/**
* Get JSON representation of the node
* @returns {Object}
*/
this.toJSON = function(){
var json = AbstractNode.prototype.toJSON.call(this);
json.type = EdgeShapeNode.TYPE;
return json;
};
this.addAttribute(new SingleSelectionAttribute(this.getEntityId()+"[arrow]","Arrow",this,{"bidirassociation":"---","unidirassociation":"-->","generalisation":"--▷","diamond":"-◁▷"}));
this.addAttribute(new SingleSelectionAttribute(this.getEntityId()+"[shape]","Shape",this,{"straight":"Straight","curved":"Curved","segmented":"Segmented"}));
this.addAttribute(new SingleColorValueAttribute(this.getEntityId()+"[color]","Color",this));
this.addAttribute(new SingleValueAttribute(this.getEntityId()+"[overlay]","Overlay Text",this));
this.addAttribute(new SingleSelectionAttribute(this.getEntityId()+"[overlayPosition]","Overlay Position",this,{"hidden":"Hide","top":"Top","center":"Center","bottom":"Bottom"}));
this.addAttribute(new BooleanAttribute(this.getEntityId()+"[overlayRotate]","Autoflip Overlay",this));
_$node.find(".label").append(this.getLabel().get$node());
for(var attributeKey in _attributes){
if(_attributes.hasOwnProperty(attributeKey)){
_$attributeNode.append(_attributes[attributeKey].get$node());
}
}
}
return EdgeShapeNode;
}); | {
"redpajama_set_name": "RedPajamaGithub"
} | 4,065 |
Tax increase for St. Louis County to fund the St. Louis Zoo
Posted 5:01 pm, October 31, 2018, by Vic Faust, Updated at 04:03PM, October 31, 2018
ST. LOUIS - Voters in St. Louis County are being asked if they will approve a one-eighth percent sales tax to fund and to help secure the zoo's future.
Both proponents and opponents of Proposition Z want the zoo to do well. But, they differ on how to go about it.
Proposition Z would raise taxes about a penny for every eight dollars spent in St. Louis County and would raise approximately twenty million annually. Zoo CEO Dr. Jeffrey Bonner says the money is a necessity for the zoo.
"To keep this zoo great we need a yes vote on Prop Z. We've got issues with aging infrastructure and sustainability issues with our collections," said Dr. Bonner.
He says the money would also be used on an expansion near the confluence of the Mississippi and Missouri rivers in north county. The new campus would be used for animal conservation and species preservation. County residents would not be charged a fee to enter.
"We've explored a lot of different options for sustaining the zoo and one was to charge admission. But as many people know, it's against the law to do it and the law would be very difficult to change," Dr. Bonner said.
Former Clayton Mayor and opponent of Proposition Z, Ben Uchitelle, says the zoo should go to the state legislature to get the law changed and charge admission. He also says this tax is only for St. Louis County. Nobody else.
"Another minus of sales tax, there will be no outside supervision whatsoever. And another reason, there's no sunset of provision so it could go on forever," said Uchitelle.
Uchitelle also points to a current property tax
"We already have a big property tax which county and city have been paying since 1972. Twenty-one million for the zoo," Uchitelle said.
But, Dr. Jeff Bonner says that the 21-million dollars is split between five organizations and over the past 10 years the property revenue has been flat while expenses are up 36 percent.
Bonner says they will go back to other counties and the city in the next legislative session and see if they can't get the proposition extended to those communities. But for now, it's on St. Louis County voters to decide what they want.
Watch our free movie channel
KPLR's digital channel 11.1 shows hit movies. Find out how you can watch.
County Executive Sam Page seeks $2.7m for police body and in-car cameras
St. Louis County Council decides where Prop P money will go
St. Louis County Council approves police body cameras, subpoenas Northwest Plaza developers
'S' is a 'no.' MSD Proposition proposal fails
St. Louis treasurer touts millions saved from city budget via investments
You Paid For It
County Council approves America's Center funding, get ear full on jail deaths
Outrage after dog recently euthanized by St. Louis County animal shelter
St. Louis Zoo future north campus, Old Jamestown Mall both discussed at North County Town Hall Meeting
St. Louis County Police Department could soon be equipped with 600 body and in car cameras
St. Charles County executive looking to ban sale of kratom
The Pulse of St. Louis
Pulse – Life-changing programs for students
Saint Louis Zoo's 'Primate Canopy Trails' expansion will bring you inside their world | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,505 |
"I would rather die than be paralyzed." This is what Karen Darke thought the night before falling off a cliff at age 21 and becoming paraplegic with no feeling from the chest down. If we are honest, this is the attitude most of us would have, but read on. This story highlights the determination, ambition and downright refusal to live life at anything less than full throttle.
I met Karim Ladki at the end of June at Whistler's Trade Show, where local businesses and organizations were exhibiting their summer adventure products. His t-shirt was the first thing that caught my eye, a distinctive cat emblem with the name "9 Lives Adventures" across the front. Immediately I was intrigued. As he shook my hand he started to explain the logo and his reason for coming to the adventure mecca that is Whistler.
9 Lives Adventures is the brainchild of Ladki and best friend Matt Thola, rooted in an adventure of Ladki's own.
Like most people the travel bug had become an itch they just had to scratch and these boys had their sights set on Africa. The only consideration they had was that Matt is in a wheelchair. Back in May 2006 he was involved in a car accident that resulted in a spinal cord injury that left him unable to walk. Even though they shared the same sense of adventure and ambition, the thought of pushing a wheelchair through villages and on dirt roads depressed them both.
"I will never forget the day I told my friend Matt Thola I was going to Africa. He was genuinely happy for me, but you could tell he was eager to propose that he come. Instead, he replied 'I wish I could go'."
When Karim returned his head was spinning. Although it would have been a tougher journey he believed that the idea of Matt joining him would have been totally realistic. With an enthusiastic partner the cogs started to turn on an idea that would hopefully pave the way for more disabled travellers searching for the same excitement and adrenaline rush that these two were after.
"We are here to open up the world to every able person who has a strong mentality and has a will to fight for more in life. Together we will explore a path of adventure, excitement, and stimulation best fit for different individuals and different disabilities."
After meeting Karim, a quick search on the net revealed similar stories of grit and determination in overcoming disabilities. His statement reminded me of a quote that I had read from Karen Darke's website, which is the perfect example of making what seems an impossible task just another adventurous challenge. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,665 |
Q: Parenthesis vs curly braces #include<iostream>
using namespace std;
class test
{
public:
int a,b;
test()
{
cout<<"default construictor";
}
test(int x,int y):a(x),b(y){
cout<<"parmetrized constructor";
}
};
int main()
{
test t;
cout<<t.a;
//t=(2,3);->gives error
t={2,3}; //calls paramterized constructor
cout<<t.a;
}
Output:- default construictor4196576parmetrized constructor2
why in case of the above example, parameterized constructor(even though default constructor is already called.) is called in case of {} and not in ()
A: I added some additional code to show what is actually happening.
#include<iostream>
using namespace std;
class test
{
public:
int a,b;
test()
{
cout << "default constructor" << endl;
}
~test()
{
cout << "destructor" << endl;
}
test(int x,int y):a(x),b(y)
{
cout << "parameterized constructor" << endl;
}
test& operator=(const test& rhs)
{
a = rhs.a;
b = rhs.b;
cout << "assignment operator" << endl;
return *this;
}
};
int main()
{
test t;
cout << t.a << endl;
//t=(2,3);->gives error
t={2,3}; //calls parameterized constructor
cout << t.a << endl;
}
Output:
default constructor
4197760
parameterized constructor
assignment operator
destructor
2
destructor
So the statement t={2,3}; is actually constructing a new test object using the parameterized constructor, calling the assignment operator to set t to be equal to the new, temporary test object, and then destroying the temporary test object. It's equivalent to the statement t=test(2,3).
A: use
test t(2,3);
instead of
test t;
t=(2,3);
Because parentheses are used after object declaration.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,964 |
@interface MRCTableViewController : MRCViewController <UITableViewDataSource, UITableViewDelegate, DZNEmptyDataSetSource, DZNEmptyDataSetDelegate>
// The table view for tableView controller.
@property (nonatomic, weak, readonly) UITableView *tableView;
@property (nonatomic, assign, readonly) UIEdgeInsets contentInset;
- (UITableViewCell *)tableView:(UITableView *)tableView dequeueReusableCellWithIdentifier:(NSString *)identifier forIndexPath:(NSIndexPath *)indexPath;
- (void)configureCell:(UITableViewCell *)cell atIndexPath:(NSIndexPath *)indexPath withObject:(id)object;
@end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,700 |
Q: How to capture browser activity into a video file I want to capture the activity in a browser for testing purpose. Is it possible using javascript? Is there any other possibilities?
I want to record screen once a record button is pressed and stopped when a stop button is pressed.
A: Have you tried Jing? Our QA often use that app for capturing screencasts of browser bugs. [http://www.techsmith.com/jing-features.html]
A: CrazyEgg: It lets you check your visitor activity across multiple domains and is quite easy to setup. Free account (offers following features
*
*Heatmap Analysis – Visual representation of where people clicked on your site. This tells you what's hot and what's not, so you can make changes that matter.
*Confetti – This will help you dig a little deeper into visitor activity and refine them based on referrers, operating system, browsers etc.
*Overlay – helps you understand how many times a link was clicked? What are the 'hot' links in your site?
*List – Helps you understand activities per element (for instance, how many visitors used the 'search box', clicked on an image.
ClickDensity: offers pretty much similar features as Crazyegg, and there are few features that differentiates it from the rest:
*
*Surprise areas – Are people clicking on areas where they shouldn't? (unlinked logo?). Similarly, what are the unpopular areas/links in your site?
*Precise Heatmaps – Unlike many other services, ClickDensity heatmaps are very precise and it's really easy to compare different sections/components.
-Hover maps – displays usage data for individual items on your pages. All clickable items on the page are highlighted, and can be individually activated to show the number of visitors that clicked on them, and other statistics.
*
*Page stats : You can follow any link on your site and check the stat of that page (even for free accounts).
UserFly: How about watching a video of user activity on the site? Watching where they click, how they scroll? Their mouse movement etc? How do they consume content?
Userfly essentially lets you track visitor activity on the site and stores the videos in your account. We have been using Userfly for quite sometime and really like the service (though there are a lot of features suggestions for the team).
WebVisor: is a module Yandex Metrica which allows you to view your visitors to the activated form of videos.
You can watch actions such as mouse movement, clicks, scrolling de page, form filling and selecting / copying text.
Reference URL:
http://www.pluggd.in/track-website-visitor-activity-services-tools-to-use-297/
http://existenceweb.fr/wordpress/webvisor-enregistrez-lactivite-de-vos-visiteurs-en-video/?lang=en
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,270 |
package lebah.portal;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.Hashtable;
import java.util.Vector;
import javax.portlet.GenericPortlet;
import javax.portlet.PortletConfig;
import javax.portlet.PortletMode;
import javax.portlet.RenderRequest;
import javax.portlet.RenderResponse;
import javax.portlet.WindowState;
import javax.servlet.ServletConfig;
import javax.servlet.ServletContext;
import javax.servlet.ServletException;
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpServletResponse;
import javax.servlet.http.HttpSession;
import org.apache.velocity.VelocityContext;
import org.apache.velocity.app.VelocityEngine;
import lebah.db.DbException;
import lebah.portal.db.AuthenticateUser;
import lebah.portal.db.PrepareUser;
import lebah.portal.db.UserPage;
import lebah.portal.element.Tab;
import lebah.portal.mobile.MFooter;
import lebah.portal.mobile.MHeader;
import lebah.portal.mobile.MTitle;
import lebah.portal.mobile.MobileData;
import lebah.portal.mobile.UserInfo;
import lebah.portal.velocity.VTemplate;
import lebah.util.Util;
/**
*
* @author Shamsul Bahrin Abd Mutalib
* @version 1.01
*/
public class MobileController extends lebah.portal.velocity.VMobileServlet {
private static long icnt = 0;
public void doGet(HttpServletRequest req, HttpServletResponse res) throws ServletException, IOException {
doPost(req, res);
}
public void doPost(HttpServletRequest req, HttpServletResponse res) throws ServletException, IOException {
HttpSession session = req.getSession();
// synchronized(this) {
// context = (org.apache.velocity.VelocityContext) session.getAttribute("_VELOCITY_CONTEXT");
// engine = (org.apache.velocity.app.VelocityEngine) session.getAttribute("_VELOCITY_ENGINE");
// if (context == null) {
// super.initVelocity(getServletConfig());
// session.setAttribute("_VELOCITY_CONTEXT", context);
// session.setAttribute("_VELOCITY_ENGINE", engine);
// session.setAttribute("_VELOCITY_INITIALIZED", "true");
// }
// }
context = (org.apache.velocity.VelocityContext) getServletConfig().getServletContext().getAttribute("VELOCITY_CONTEXT");
engine = (org.apache.velocity.app.VelocityEngine) getServletConfig().getServletContext().getAttribute("VELOCITY_ENGINE");
//STORE VELOCITY ENGINE IN THE SESSION OBJECT
if ( session.getAttribute("_VELOCITY_INITIALIZED") == null ) {
session.setAttribute("_VELOCITY_ENGINE", engine);
session.setAttribute("_VELOCITY_CONTEXT", context);
session.setAttribute("_VELOCITY_INITIALIZED", "true");
}
context.put("util", new Util());
doBody(req, res, session);
}
public void doBody(HttpServletRequest req, HttpServletResponse res, HttpSession session) throws IOException {
PrintWriter out = res.getWriter();
res.setContentType("text/html");
context.put("util", new Util());
String app_path = getServletContext().getRealPath("/");
app_path = app_path != null ? app_path.replace('\\', '/') : "";
session.setAttribute("_portal_app_path", app_path);
String serverName = req.getServerName();
int serverPort = req.getServerPort();
session.setAttribute("_portal_server", serverPort != 80 ? serverName + ":" + serverPort : serverName );
context.put("server", serverPort != 80 ? serverName + ":" + serverPort : serverName);
String reqUrl = req.getRequestURL().toString();
String queryString = req.getQueryString();
String portalReqUrl = reqUrl + "?" + queryString;
session.setAttribute("_portal_reqUrl", portalReqUrl);
String uri = req.getRequestURI();
String s1 = uri.substring(1);
context.put("appname", s1.substring(0, s1.indexOf("/")));
session.setAttribute("_portal_appname", s1.substring(0, s1.indexOf("/")));
//get pathinfo
String pathInfo = req.getPathInfo();
pathInfo = pathInfo.substring(1); //get rid of the first '/'
session.setAttribute("_portal_pathInfo", pathInfo);
//pathInfo only contains action
String action = pathInfo != null ? pathInfo : "";
//Set role to anonymous by default
if ( session.getAttribute("_portal_role") == null || "".equals((String)session.getAttribute("_portal_role"))) {
session.setAttribute("_portal_role", "anon");
session.setAttribute("_portal_username", "Anonymous");
session.setAttribute("_portal_login", "anon");
session.setAttribute("_portal_islogin", "false");
session.setAttribute("_portal_css", null);
//action = "";
}
//module
String module = req.getParameter("_portal_module") != null ?
req.getParameter("_portal_module") : "";
System.out.println("mobile module = " + module);
if ( "".equals(module) && !"login".equals(action)) {
try {
module = MobileData.getCurrentModule(action);
} catch ( Exception e ) {
}
}
if ( "anon".equals((String) session.getAttribute("_portal_role"))
&& "false".equals((String) session.getAttribute("_portal_islogin")) )
{
String visitor = req.getParameter("visitor") != null ?
req.getParameter("visitor") :
session.getAttribute("_portal_visitor") != null ?
(String) session.getAttribute("_portal_visitor") : "anon";
//this visitor user login must be of role anon
if ( !"anon".equals(visitor) && "anon".equals(PrepareUser.getRole(visitor)) ) {
session.setAttribute("_portal_login", visitor);
}
else {
visitor = "anon";
session.setAttribute("_portal_login", "anon");
}
session.setAttribute("_portal_visitor", visitor);
}
//---
session.setAttribute("_portal_action", action);
session.setAttribute("_portal_module", module);
context.put("session", session);
//To store content template
VTemplate content = null;
//**HTML
out.println("<?xml version=\"1.0\"?>");
out.println("<!DOCTYPE html PUBLIC \"-//WAPFORUM//DTD XHTML Mobile 1.0//EN\"");
out.println("\"http://www.wapforum.org/DTD/xhtml-mobile10.dtd\" >");
out.println("<html xmlns=\"http://www.w3.org/1999/xhtml\">");
out.println("<link rel=\"stylesheet\" type=\"text/css\" href=\"../css/mmp.css\" />");
out.println("<title>");
//**HTML
//TITLE
MTitle cTitle = new MTitle(engine, context, req, res);
try {
cTitle.print();
} catch ( Exception ex ) {
out.println(ex.getMessage());
}
//**HTML
out.println("</title>");
out.println("<body>");
//Handle login request
context.put("isLogin", false);
if ( action.equalsIgnoreCase("login") ) {
String usrlogin = req.getParameter("username");
String password = req.getParameter("password");
try {
AuthenticateUser auth = new AuthenticateUser(req);
if ( auth.lookup(usrlogin, password) ) {
session.setAttribute("_portal_role", auth.getRole());
session.setAttribute("_portal_username", auth.getUserName());
session.setAttribute("_portal_login", auth.getUserLogin());
session.setAttribute("_portal_islogin", "true");
String userSessionId = MobileData.createUserSession(auth.getUserLogin());
context.put("userSessionId", userSessionId);
context.put("isLogin", true);
context.put("userName", auth.getUserName());
context.put("user", auth.getUserLogin());
} else {
session.setAttribute("_portal_role", "anon");
session.setAttribute("_portal_username", "Anonymous");
session.setAttribute("_portal_login", "anon");
session.setAttribute("_portal_islogin", "false");
context.put("isLogin", false);
context.put("user", "anon");
context.put("userName", "Guest");
res.sendRedirect("../accessdenied.jsp");
}
} catch ( Exception ex ) {
content = new ErrorMsg(engine, context, req, res);
((ErrorMsg) content).setError(ex.getMessage());
try {
content.print();
} catch ( Exception e) { System.out.println(e); }
}
}
else {
context.put("userSessionId", action);
//get user info from this session
if ( !"anon".equals(action) && !"".equals(action)) {
try {
UserInfo userInfo = MobileData.getUserAction(action, module);
session.setAttribute("_portal_role", userInfo.getRole());
session.setAttribute("_portal_username", userInfo.getName());
session.setAttribute("_portal_login", userInfo.getUserId());
session.setAttribute("_portal_islogin", "true");
context.put("isLogin", true);
context.put("user", userInfo.getUserId());
context.put("userName", userInfo.getName());
} catch ( Exception e ) {
session.setAttribute("_portal_role", "anon");
session.setAttribute("_portal_username", "Anonymous");
session.setAttribute("_portal_login", "anon");
session.setAttribute("_portal_islogin", "false");
context.put("isLogin", false);
context.put("user", "anon");
context.put("userName", "Guest");
}
}
else {
session.setAttribute("_portal_role", "anon");
session.setAttribute("_portal_username", "Anonymous");
session.setAttribute("_portal_login", "anon");
session.setAttribute("_portal_islogin", "false");
context.put("isLogin", false);
context.put("user", "anon");
context.put("userName", "Guest");
}
}
MHeader cHeader = new MHeader(engine, context, req, res);
try {
cHeader.print();
} catch ( Exception ex ) {
out.println(ex.getMessage());
}
out.println("<p>");
boolean isMainMenu = false;
System.out.println("module = " + module);
try {
if ( !"".equals(module) && !"main_menu".equals(module)) {
MDisplayContent.createPageById(engine, context, getServletConfig(), req, res, module, out, session);
}
else {
System.out.println("### MOBILE MAIN MENU ###");
MDisplayContent.createPageByClassName("lebah.portal.mobile.MainMenuModule", getServletContext(), getServletConfig(), engine, context, session, req, res);
isMainMenu = true;
}
} catch ( Exception ex ) {
out.println(ex.getMessage());
}
out.println("</p>");
if ( !isMainMenu ) {
MFooter footer = new MFooter(engine, context, req, res);
try {
footer.print();
} catch ( Exception ex ) {
out.println(ex.getMessage());
}
}
out.println("</body>");
out.println("</html>");
//**HTML
}
private void showError(String err, HttpServletRequest req, HttpServletResponse res) {
ErrorMsg emsg = new ErrorMsg(engine, context, req, res);
emsg.setError(err);
try {
emsg.print();
} catch ( Exception ex ) {
//error while displaying error!!
System.out.println("ERROR WHILE SHOW ERROR");
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 108 |
BCIS has a strong faculty and management team, with teachers and administrators from 21 different countries and regions who have substantial experience in international education.
At BCIS, we feel proud of the quality of learning and teaching in our classrooms, and the collegial and supportive atmosphere that exists throughout the school community. We have an outstanding staff that was recently commended by our accreditation visitors for their enthusiasm and dedication in providing an educational environment in which all students feel valued and supported and where individual success is acknowledged.
BCIS teachers are highly motivated with a strong commitment to the children they teach, and a desire to collaborate closely with like-minded colleagues. Above all, our teachers are dedicated to putting into daily practice our school mission. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,751 |
24H Proto Series
24H/12H Events
FRD LMP3 Series
Historic Racing
Other Series & Events
V de V Series
IMSA Daytona 24 Hours
Nürburgring 24 Hours
Spa 24 Hours
ADAC GT
Britcar
British LMP3 Cup
American Le Mans Series
Blancpain Endurance Cup
GT4 European Series Northern Cup
Le Mans 24 Hours: Hours 19-20, As It Happened, DC Racing Rises To Second In LMP2
Kobayashi holds clear LMP1 lead in #7 Toyota; Ferrari vs Corvette in GTE Pro; Keating still looks strong in GTE Am
Until halfway into the 18th hour, the gaps in LMP1 remained roughly consistent, wth Sebastien Buemi taking over the #8 Toyota, with a gap of around a minute and 50 seconds to leader Mike Conway in #7 Toyota.
There was a further five laps between Buemi and Stoffel Vandoorne in the #11 SMP. However, the #3 Rebellion suffered yet more issues, with Nathanael Berthon going very slowly from halfway down the Mulsanne right around to the pits, where the team got it on the dolly jacks and spun it around, pushing it back into the garage – brakes the problem.
When it went back out 15 minutes later, it had gone 12 laps behind the leading #7 Toyota, and four laps behind Andre Lotterer in #1 Rebellion, which now sat in fourth, three laps behind Vandoorne
However, it wasn't out for that long before pitting again for another unscheduled pitstop, with the car again being pushed back into the garage, with the brakes again the issue as the team attempted to diagnose and resolve the problem. With 80% of the lap around Circuit de la Sarthe on full throttle, brakes are just a little bit important!
The team got the car back out with brand-new brakes, but had slipped to 14 laps back, six behind the #3 Rebellion in fourth, which had Lotterer on board at the time. Berthon had also slipped behind the LMP2 leader, but had clawed back to get the gap just under 25 seconds behind at the four hours left mark.
At around the same time as Berthon pitted for the unscheduled brake change, Vandoorne handed over to Mikhail Aleshin after a three-hour stint at the wheel, with the car in third, six laps behind leader Conway. The Russian had a four-lap gap to Lotterer, with the #11 SMP having a good run with four hours left.
Front-running drama has re-written the story in LMP2, with the #26 G-Drive Oreca and Roman Rusinov falling down the order as we ticked over to the final quarter of the race.
With just over five hours and 45 minutes to run, the complexion of the race changed dramatically in pitlane. A regular pitstop turned into drama for the #26 Oreca; Rusinov came in, but then couldn't get the car fired up again. It was pushed back into the pits, and the #36 Alpine of Thiriet arrived and departed as the G-Drive outfit continued to work on the car.
Ultimately, the G-Drive would lose over 20 minutes, six places and almost five laps in the LMP2 class, dropping to seventh.
Meanwhile, the #30 Duqueine Engineering Oreca moved up to fourth at the expense of the #22 United Autosports Ligier; Pierre Ragues showing superior pace over Phil Hanson, and building a gap of around 20 seconds over the course of the 19th hour. The battle at the lower end of the top five was becoming intriguing, as the #48 IDEC Sport Oreca was within 40 seconds of the #22 Ligier.
Meanwhile, the troubled sister #32 Ligier lost its engine cover on the approach to Indianapolis; Will Owen returned the car to the pits and a full-course yellow was deployed to remove the engine cover from its resting place on-track.
With five hours to go, the #36 Alpine was now a lap clear of the pack, and with Nicolas Lapierre at the wheel.
The battle for second looked much closer with four-and-a-half hours left to run, courtesy of a challenge from the #28 TDS Racing Oreca driven by Loic Duval. The Frenchman was a mere 23 seconds back from the #38 Jackie Chan DC Oreca of Stephane Richelmi. However, Duval pitted at this stage, handing over to bronze-rated Francois Perrodo, who would ultimately struggle to match his predecessor's pace.
Perrodo jumped into the #28 with a near two-lap advantage over Filipe Albuquerque in the #22 Ligier.
Elsewhere, Nigel Moore found himself limping home in the #34 Inter Europol Ligier due to a left-rear puncture; this would do little to change the complexion of the race, with the yellow and green Ligier JSP217 running 16th in class.
As we came towards the end of the twentieth hour, the former leader – the #26 G Drive entry – was running seventh, a lap off the #48 IDEC Sport Oreca ahead. Jean-Eric Vergne is now behind the wheel, but so long as all goes smoothly, even the impressive Frenchman is unlikely to catch the top six.
All is well for Lapierre out front, however; the #36 Signatech Alpine still leads the way by a lap at Le Mans as the clock ticks over to begin the final four hours.
GTE Pro
The fight at the front of the GTE Pro field remained stable, with the #63 Corvette, #51 AF Corse Ferrari and the #91 and #93 Porsches all still in the hunt for the win.
At the 20-hour mark the Corvette held the lead over the AF Corse machine, but the gap was barely 15 seconds with the Corvette owing a pitstop. The keY, though, will be when the safety car periods hit and whether the Corvette can take advantage of its fuel strategy to maximise its result.
The two Porsches are slightly off the pace of the other two, but are within hunting distance if the leading duo have any issues. Gimmi Bruni in the #91 set the car's best lap on lap 272, in an effort to close the gap.
The lap time of 3:50.149 was about 0.5 to a second better than the two cars ahead of it.
Tactics are playing a part for the leaders. The Corvette, driven by Mike Rockenfeller and Antonio Garcia, has slightly better fuel consumption and is running an alternate strategy to the Ferrari.
There's a difference of about five laps between when the cars pit, meaning that the lead swaps between them both, depending on the pitstop cycle.
Both cars are continuing to double-stint drivers and tyres. Daniel Serra and Alessandro Pier Guidi handled the driving duties for the Ferrari over the period.
At the end of the 18th hour, the four cars were covered by less than a minute. Behind the four cars came the four Fords led by the #68 and Sebastien Bourdais. Then the #67 led the #68 and #66, with a little over a lap coving all four cars.
The Risi Competizione Ferrari was in ninth ahead of the leading #82 BMW. Both these cars have had fairly anonymous races, never challenging the front runners.
GTE Am
The #85 Keating Ford continued to lead, with Am driver Ben Keating completing his triple stint, covering 44 laps before handing it to Jeroen Bleekemolen and then Felipe Fraga.
The Ford has spent the vast majority of the race in the lead and has been ensuring its driving trio are getting close to their minimum driving time to ensure there are no panicked situations towards in the final four hours.
Fortunately for the crew, there was no ill effect from the car's earlier spin into the gravel.
Equally, there was a slow brake change for the Ford, with the right front offering issues for the team and losing them 40 seconds to the second-placed car. The gap reduced from more than three minutes to just 50 seconds, though undoubtedly pitstops will play a part, the gap is the smallest it has been for quite some time.
Chasing down the Ford and second in the class was the #56 Project 1 Porsche with Jorg Bergmeister and Egido Perfetti taking the driving duties. They also had a slow brake change, but lost not nearly as much time of the leading car. They also spent much of the period in their own race, they closed the gap to the lead while maintaining more than a minute back to the third placed car – the #84 JMW Ferrari.
Ferraris then take the rest of the top five in class with the Clearwater entry sitting in fourth ahead of the WeatherTech car. Early leader the #77 Dempsey Proton Porsche lies in sixth, two laps off the lead.
Two other Ferraris were handed severe penalties for drive-time infractions during the period. The #54 Spirit of Race Ferrari will have three laps deleted and a three-minute penalty for the infraction. Meanwhile, the #57 CarGuys car received a similar penalty for a similar infraction.
While no doubt bothersome for the teams, they weren't in outright contention with the CarGuys sitting in seventh the Spirit of Race Ferrari in ninth.
Tagged with: Adam Weller, Phil Oakley, Sam Tickell
Previous article Le Mans 24 Hours: Observations After 18 Hours
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Le Mans 24 Hours: Hours 23-24, As It Happened, Win & Title For #8 Toyota Crew
by Stephen Errity 16 June 2019 0 Comments
Le Mans 24 Hours: Hours 21-22, As It Happened, Another Safety-Car Shakeup Hits GTE Pro
Quick Links Schedule
Paddock Notes
Starting Drivers
#LeMans24
Join the conversation across Facebook, Twitter & Instagram
© 2016 Dailysportscar. All Rights Reserved. TJS - Web Design Lincolnshire | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,712 |
Q: Why do I get Index was outside the bounds of the array when moving data to a text field This my code - this section is looking at a message from a NMEA GPS device
Try
degreeString = Words(3).Substring(0, 2)
LatDD = CDec(degreeString)
MinuteString = (Words(3).Substring(2, 8))
LatDM = CDec(CInt(MinuteString) / 60)
LatDecimalDegrees = LatDD + LatDM
If Words(4) = "S" Then
LatDecimalDegrees *= -1
End If
Catch ex As Exception
errorCount = errorCount + 1
ErrorDisplay.Clear()
ErrorDisplay.Text = ToString(errorCount)
GPS_WordOK = False
Exit Function
End Try code here`Try
degreeString = Words(3).Substring(0, 2)
LatDD = CDec(degreeString)
MinuteString = (Words(3).Substring(2, 8))
LatDM = CDec(CInt(MinuteString) / 60)
LatDecimalDegrees = LatDD + LatDM
If Words(4) = "S" Then
LatDecimalDegrees *= -1
End If
Catch ex As Exception
errorCount = errorCount + 1
ErrorDisplay.Clear()
ErrorDisplay.Text = ToString(errorCount)
GPS_WordOK = False
Exit Function
End Try
The error is thrown on this line in the exception processing
ErrorDisplay.Text = ToString(errorCount)
the value of error_count is 49
I don't see where the array is implied in the failing line
The error which caused entry to the exception handler is thrown by the statement
LatDM = CDec(CInt(MinuteString) / 60)
which has the string value 41*68028
I believe some noise on the line caused the decimal to be read as an asterisk and the division failed. This error recovery was successful 48 prior times over a 24 hour period.
A: Use either
ErrorDisplay.Text = errorCount.ToString
or
ErrorDisplay.Text = CStr(errorCount)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,384 |
Biografia
Ha rappresentato il Regno Unito all'Eurovision Song Contest 1969 vincendo con la canzone Boom Bang-a-Bang a pari merito con i Paesi Bassi, la Francia e la Spagna. Tra la fine degli anni 60 ed i primi anni 70 è stata sposata con Maurice Gibb dei Bee Gees.
Nel 1967 il singolo To Sir With Love raggiunge il primo posto nella Billboard Hot 100 per cinque settimane. Il singolo faceva parte della colonna sonora del film La scuola della violenza che vedeva come protagonista Sidney Poitier. Il successo della canzone e del film diede inizio ad una carriera televisiva della cantante che ottenne diverse serie con il suo nome nel titolo.
Nel 1974 ha cantato la canzone del film Agente 007 - L'uomo dalla pistola d'oro interpretato da Roger Moore, nono film con protagonista il noto agente segreto britannico 007 dei romanzi di Ian Fleming. Sempre nel 1974 ha interpretato una versione di The Man Who Sold The World di David Bowie, con lo stesso Bowie ospite alla voce e sax. Nel 1993 Lulu ha duettato con i Take That in Relight My Fire, cover di un successo di Dan Hartman. Nel periodo natalizio 2009 è tornata sulle scene con lo spettacolo Here Come the Girls Tour al quale hanno anche partecipato Anastacia e Chaka Khan.
Discografia
Album in studio
1965 - Something to Shout About
1967 - Love Loves to Love Lulu
1967 - Lulu!
1967 - To Sir with Love
1969 - Lulu's Album
1970 - New Routes
1970 - Melody Fair
1973 - Lulu
1976 - Heaven and Earth and the Stars
1978 - Don't Take Love for Granted
1981 - Lulu
1982 - Take Me To Your Heart Again
1984 - Shape Up and Dance
1993 - Independence
2002 - Togheter
2004 - Back on Track
2005 - Little Soul in Your Heart
2009 - Shout! The Complete Decca Recordings
Raccolte
1971 - The Most of Lulu
2003 - The Greatest Hits
Onorificenze
Note
Altri progetti
Collegamenti esterni
Lulu
Partecipanti all'Eurovision Song Contest 1969
Nati a Glasgow
Commendatori dell'Ordine dell'Impero Britannico | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,523 |
Q: Django Debug Toolbar not displaying SQL I recently installed django-debug-toolbar. The toolbar works and I can see the tabs on the side. However, nothing shows up in the SQL tab even when I have obviously executed an SQL query (such as in the admin):
My settings are as follows:
DATABASES = {
'default': {
'ENGINE': 'django.db.backends.postgresql_psycopg2'
'NAME': 'mydatabase'
....
}
}
# Backwards compatability with apps
DATABASE_ENGINE = DATABASES['default']['ENGINE'].split('.')[-1]
DATABASE_NAME = DATABASES['default']['NAME']
MIDDLEWARE_CLASSES = (
'django.middleware.common.CommonMiddleware',
'django.contrib.sessions.middleware.SessionMiddleware',
'django.middleware.csrf.CsrfViewMiddleware',
'django.contrib.auth.middleware.AuthenticationMiddleware',
'django.contrib.messages.middleware.MessageMiddleware',
'debug_toolbar.middleware.DebugToolbarMiddleware',
)
INSTALLED_APPS = (
...
'debug_toolbar',
...
)
# Settings for the django-debug-toolbar
DEBUG_TOOLBAR_PANELS = (
'debug_toolbar.panels.version.VersionDebugPanel',
'debug_toolbar.panels.cache.CacheDebugPanel',
'debug_toolbar.panels.timer.TimerDebugPanel',
'debug_toolbar.panels.settings_vars.SettingsVarsDebugPanel',
'debug_toolbar.panels.headers.HeaderDebugPanel',
'debug_toolbar.panels.request_vars.RequestVarsDebugPanel',
'debug_toolbar.panels.template.TemplateDebugPanel',
'debug_toolbar.panels.sql.SQLDebugPanel',
'debug_toolbar.panels.signals.SignalDebugPanel',
# 'debug_toolbar.panels.logger.LoggingPanel',
)
def custom_show_toolbar(request):
return request.user.is_staff
DEBUG_TOOLBAR_CONFIG = {
'INTERCEPT_REDIRECTS':False,
'SHOW_TOOLBAR_CALLBACK':custom_show_toolbar,
'SHOW_TEMPLATE_CONTEXT':True,
'HIDE_DJANGO_SQL':False,
}
I'm using Django 1.3 with Toolbar version 0.8.5. Any help with this problem would be awesome...
Edit:
Based on the answer, I have decided to post how I am handling my view functions:
def func1(query, var1):
query = query.filter(var__icontains=var1)
return query
def func2(query, var2):
query = query.filter(var__icontains=var2)
return query
def parse(**kwargs):
# Based on some logic call func1 and func2
return query
def view(request, template="display.html"):
# Do some request processing
query = parse(request.GET.items())
return render(request, template, { 'items':list(query) })
A: Make sure that you are running your SQL in the same thread that handled the request.
The Django debug toolbar only seems to take a look at the SQL statements that are run in the current thread and assumes that these are the only ones that are related to the request that was handled.
A: I have the same problem, and I found the solution in my case.
I am using python 2.5 on Windows Vista. There are 2 problems.
First, the "format" function which is supported from python 2.6 are used in the debug_toolbar.panels.sql module. I fixed this using "%" operator(line 194).
stacktrace.append('<span class="path">%s/</span><span class="file">%s</span> in <span class="func">%s</span>(<span class="lineno">%s</span>)\n <span class="code">%s</span>"' % (params[0], params[1], params[3], params[2], params[4]))
Second, in the same module, '/' character is used as a separation character. Because of this, it does not work on Windows. I changed the separation character and it went well.
A: I just find out a way:
*
*right click on "default"
*click inspect element
*find the nearby table which has style="display:none"
*edit the style attribute to remove it
I don't know why I have to do all that ...
A: This worked for me:
pip install django-debug-toolbar==0.9.4
Also make sure:
*
*DEBUG=True
*Middleware is after encoders and before Flatpage's
I'm late for few years but there's still people with Django 1.3 around :(
A: At the time I'm writing this, it also can happen if you duplicate the debug toolbar middleware. I'm using Django 1.11 with django-debug-toolbar==1.8
.
I had something like this more than once in the code:
if DEBUG and USE_DEBUG_TOOLBAR:
MIDDLEWARE = ('debug_toolbar.middleware.DebugToolbarMiddleware',) + MIDDLEWARE
See: https://github.com/jazzband/django-debug-toolbar/issues/986
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,223 |
\section{Introduction}
Preferences are a key research area in artificial intelligence, and thus a multitude of preference formalisms have been described in the literature \cite{PigozziEtAl2016preferences}. An interesting example is Qualitative Choice Logic (QCL) \cite{BrewkaEtAl2004qcl}, which extends classical propositional logic by the connective $\vv{\times}$ called ordered disjunction. Intuitively, $F \vv{\times} G$ states that $F$ or $G$ should be satisfied, but satisfying $F$ is more preferable than satisfying only $G$.
This allows to express soft-constraints (preferences) and hard-constraints (truth) in a single language.
For example, let us say we want to formalize our choice of pizza toppings, and that we definitely want tomato-sauce~($t$). Moreover, we want either mushrooms~($m$) or artichokes~($a$), but preferably mushrooms. This can easily be expressed in QCL via the formula $t \land (m \vv{\times} a)$.
This formula has three models in QCL, namely
$M_1 = \{t,\allowbreak m,\allowbreak a\}$,
$M_2 = \{t,\allowbreak m\}$, and
$M_3 = \{t,\allowbreak a\}$. QCL-semantics then ranks these models via so-called satisfaction degrees. The lower this degree, the more preferable the model. In this case, $M_1$ and $M_2$ would be assigned a degree of $1$ and $M_3$ would be assigned a degree of $2$, i.e., $M_1$ and $M_2$ are the preferred models of this formula.
\begin{comment}
In the literature, QCL has been studied with regards to possible applications \cite{BrewkaEtAl2004lpods, BenferhatSedki2008qclalert, LietardEtAl2014qcldatabase} and computational properties \cite{BernreiterEtAl2021}.
However, not all aspects of QCL-semantics are uncontroversial. For example, viewing QCL as an extension of classical logic, it is natural to expect a formula $F$ to be logically equivalent to its double negation $\neg \neg F$. But this property does not hold in QCL, as all information about preferences in $F$ is erased in $\neg F$. This issue has been addressed by Prioritized QCL (PQCL) \cite{BenferhatSedki2008pqcl}, which defines ordered disjunction in the same way as QCL but changes the meaning of the classical connectives, including negation. While PQCL solves QCL's problem with double negation, it in turn introduces other controversial behavior, e.g., that both a formula $A$ and its negation $\neg F$ can be satisfied by the same interpretation. No alternative semantics for QCL is known to us that addresses both of these issues at the same time. In this paper, we will make use of game-theoretic semantics (GTS) to define an alternative semantics for QCL that preserves desirable properties while also addressing the aforementioned issues.
Games have a long and varied tradition in logic (see, for example \cite{sep-logic-games,vbenthbook,vbook}). Building on the concepts of rational behavior and strategic thinking, they offer a fruitful viewpoint of logic, complementing the common paradigm of model-theoretic semantics and proof systems by a natural dynamic approach. GTS goes back to Jaakko Hintikka \cite{Hintikka1973-HINLLA}, who designed a win/lose game for two players, called \emph{Me}\xspace (or \emph{I}\xspace) and \emph{You}\xspace\footnote{Hintikka and others call this player \emph{Nature}}, both of which can act in the role of Proponent or Opponent of a formula $F$ of over an interpretation $\mathcal{I}$. The game proceeds by rules for step-wise reducing $F$ to an atomic formula. Most importantly, negation is interpreted in game-theoretic terms as \emph{dual negation}, \cite{tulenheimo}: at formulas $\neg G$, the game continues with $G$ and a role switch. It turns out that \emph{I}\xspace have a winning strategy for this game if and only if $F$ is classically true over $\mathcal{I}$.
In order to capture not only truth but also preferences, we extend this two-valued game with more fine-grained results. We show that our proposed game framework adequately models the degree-semantics of QCL. Game-theoretically speaking, the issues with negation in QCL arise, because the players in the GTS are not fully symmetric. We construct a new game, where this shortcoming does not exist. This yields a new logic that we call Game Choice Logics (GCL), where negation indeed behaves as in classical logic. In the last section, we outline how to lift the GTS to a sequent calculus for GCL for preferred model entailment.
\end{comment}
In the literature, QCL has been studied with regards to possible applications \cite{BrewkaEtAl2004lpods, BenferhatSedki2008qclalert, LietardEtAl2014qcldatabase} and computational properties \cite{BernreiterEtAl2021}.
However, not all aspects of QCL-semantics are uncontroversial. For example, viewing QCL as an extension of classical logic, it is natural to expect a formula $F$ to be logically equivalent to its double negation $\neg \neg F$. But this property does not hold in QCL, as all information about preferences in $F$ is is erased in $\neg F$. This issue has been addressed by Prioritized QCL (PQCL) \cite{BenferhatSedki2008pqcl}, which defines ordered disjunction in the same way as QCL but changes the meaning of the classical connectives, including negation. While PQCL solves QCL's problem with double negation, it in turn introduces other controversial behavior, e.g., that both a formula $F$ and its negation $\neg F$ can be satisfied by the same interpretation. No alternative semantics for QCL is known to us that addresses both of these issues at the same time.
In order to tackle these issues, we develop game-theoretic semantics (GTS) for QCL, embedding choice logics in the rich intersection of the fields of game-theory and logics (\cite{sep-logic-games,vbenthbook,vbook}). Building on the concepts of rational behavior and strategic thinking, GTS offer a natural dynamic viewpoint of dealing with truth and preferences. Originally, GTS go back to Jaakko Hintikka \cite{Hintikka1973-HINLLA}, who designed a win/lose game for two players, called \emph{Me}\xspace (or \emph{I}\xspace) and \emph{You}\xspace\footnote{Hintikka and others call this player \emph{Nature}}, both of which can act in the role of Proponent or Opponent of a formula $F$ of over an interpretation $\mathcal{I}$. The game proceeds by rules for step-wise reducing $F$ to an atomic formula. Most importantly, negation is interpreted in game-theoretic terms as \emph{dual negation}, \cite{tulenheimo}: at formulas $\neg G$, the game continues with $G$ and a role switch. It turns out that \emph{I}\xspace have a winning strategy for this game if and only if $F$ is classically true over $\mathcal{I}$.
To capture not only truth but also preferences, we extend this two-valued game with more fine-grained outcomes. We show that our proposed game framework adequately models the degree-semantics of QCL. Game-theoretically speaking, the aforementioned issues with negation in QCL arise, because the players in the GTS are not fully symmetric. Eliminating this asymmetry leads to a new game and by extension yields a new logic we call Game-induced Choice Logics (GCL), where negation indeed behaves as in classical logic. In the last section, we outline how to lift the GTS to a sequent calculus for preferred model entailment in GCL.
\section{Preliminaries}
In this section, we formally introduce QCL and discuss fundamental notions in GTS.
\subsection{Qualitative Choice Logic (QCL)}
The most prominent choice logic in the literature is QCL \cite{BrewkaEtAl2004qcl}, which adds ordered disjunction ($\vv{\times}$) to classical propositional logic.
\begin{definition}
Let $\mathcal{U}$ denote an infinite set of propositional variables. The set $\mathcal{F}_{\mathit{QCL}}$ of QCL-formulas are built inductively as follows:
(i) $a \in \mathcal{F}_{\mathit{QCL}}$ for all $a \in \mathcal{U}$;
(ii) if $F \in \mathcal{F}_{\mathit{QCL}}$, then $(\neg F) \in \mathcal{F}_{\mathit{QCL}}$;
(iii) if $F, G \in \mathcal{F}_{\mathit{QCL}}$, then $(F \circ G) \in \mathcal{F}_{\mathit{QCL}}$ for $\circ \in \{\land, \lor, \vv{\times}\}$.
\end{definition}
The semantics of QCL is based on two functions, namely optionality and satisfaction degree. The satisfaction degree of a formula can be either a natural number or $\infty$ and is used to rank interpretations: the lower the degree, the better. The optionality of a formula represents the maximum finite satisfaction degree this formula can obtain (as we will see in Lemma~\ref{degopt}) and is used to penalize interpretations that do not satisfy the preferred option $F$ in an ordered disjunct $F \vv{\times} G$.
\begin{definition}\label{def:satisfaction-degree}
The optionality of QCL-formulas is defined inductively as follows:
(i)~$\mathrm{opt}(a) = 1$ for every propositional variable $a \in \mathcal{U}$,
(ii)~$\mathrm{opt}(\neg F) = 1$,
(iii)~$\mathrm{opt}({F \circ G}) = \max(\mathrm{opt}(F),\mathrm{opt}(G))$ for $\circ \in \{\vee,\wedge\}$, and
(iv)~$\mathrm{opt}({F\vv{\times} G}) = \mathrm{opt}(F) + \mathrm{opt}(G)$.
\end{definition}
\begin{definition}
An \emph{interpretation} $\mathcal{I} \subseteq \mathcal{U}$ is a set of propositional variables. The satisfaction degree of QCL-formulas is defined inductively as follows:
\begin{align*}
\mathrm{deg}_\mathcal{I}(a) &=
1 \text{ if } a \in \mathcal{I}, \infty \text{ otherwise } \\
\mathrm{deg}_\mathcal{I}(\neg F) &=
1 \text{ if } \mathrm{deg}_\mathcal{I}(F) = \infty, \infty \text{ otherwise } \\
\mathrm{deg}_\mathcal{I}(F\wedge G) &= \max(\mathrm{deg}_\mathcal{I}(F),\mathrm{deg}_\mathcal{I}(G))\\
\mathrm{deg}_\mathcal{I}(F\vee G) &= \min(\mathrm{deg}_\mathcal{I}(F),\mathrm{deg}_\mathcal{I}(G)) \\
\mathrm{deg}_\mathcal{I}(F\vv{\times} G) &=
\begin{cases}
\mathrm{deg}_\mathcal{I}(F) & \text{if } \mathrm{deg}_\mathcal{I}(F) < \infty \\
\mathrm{opt}(F) + \mathrm{deg}_\mathcal{I}(G) & \text{if } \mathrm{deg}_\mathcal{I}(F) = \infty, \\ & \mathrm{deg}_\mathcal{I}(G) < \infty\\
\infty &\text{otherwise}
\end{cases}
\end{align*}
\end{definition}
If $\mathrm{deg}_\mathcal{I}(F) = k$ we say that $\mathcal{I}$ satisfies $F$ to a degree of~$k$. If $\mathrm{deg}_\mathcal{I}(F) < \infty$ we say that $\mathcal{I}$ classically satisfies $F$, or that $\mathcal{I}$ is a model of $F$. Moreover, if $\mathrm{deg}_\mathcal{I}(F) < \mathrm{deg}_\mathcal{J}(F)$ for two interpretations $\mathcal{I}$ and $\mathcal{J}$ then $\mathcal{I}$ is more preferable than $\mathcal{J}$.
To fully understand QCL-semantics, we must take note that satisfaction degrees are bounded by optionality, as intended:
\begin{lemma}[from \cite{BrewkaEtAl2004qcl}]\label{degopt}
For all QCL-formulas $F$ and all interpretations $\mathcal{I}$, $\mathrm{deg}_\mathcal{I}(F) \leq \mathrm{opt}(F)$ or $\mathrm{deg}_\mathcal{I}(F) = \infty$.
\end{lemma}
Indeed, inspecting Definition~\ref{def:satisfaction-degree} in view of Lemma~\ref{degopt} shows how optionality is used to penalize non-satisfaction: given $F \vv{\times} G$, if some interpretation $\mathcal{I}$ classically satisfies~$F$, i.e., $\mathrm{deg}_\mathcal{I}(F) < \infty$, we get $\mathrm{deg}_\mathcal{I}(F \vv{\times} G) = \mathrm{deg}_\mathcal{I}(F) \leq \mathrm{opt}(F)$; if $\mathcal{I}$ does not classically satisfy~$F$, i.e., $\mathrm{deg}_\mathcal{I}(F) = \infty$, we get $\mathrm{deg}_\mathcal{I}(F \vv{\times} G) = \mathrm{opt}(F) + \mathrm{deg}_\mathcal{I}(G) > \mathrm{opt}(F)$.
We now define the central notion of preferred models, and then give a small example of QCL-semantics in action.
\begin{definition}
Let $F$ be a QCL-formula. $\mathcal{I}$ is a preferred model of $F$ iff $\mathrm{deg}_\mathcal{I}(F) < \infty$ and $\mathrm{deg}_\mathcal{I}(F) \leq \mathrm{deg}_\mathcal{J}(F)$ for all other interpretations $\mathcal{J}$.
\end{definition}
\begin{example}
The QCL-formula $F = (a \land b) \vv{\times} a \vv{\times} b$ expresses that satisfying both $a$ and $b$ is preferable to satisfying only $a$, which in turn is preferable to satisfying only $b$. First, observe that $\mathrm{opt}(F) = 3$. Moreover, $\mathrm{deg}_\emptyset(F) = \infty$, $\mathrm{deg}_{\{b\}}(F) = 3$, $\mathrm{deg}_{\{a\}}(F) = 2$, and $\mathrm{deg}_{\{a,b\}}(F) = 1$. Thus, $\{a,b\}$ is a preferred model of $F$.
Now consider $F' = ((a \land b) \vv{\times} a \vv{\times} b) \land \neg (a \land b)$, which is similar to $F$, but with the additional information that $a$ and $b$ can not be jointly satisfied. Again, $\mathrm{deg}_\emptyset(F') = \infty$, $\mathrm{deg}_{\{b\}}(F') = 3$, and $\mathrm{deg}_{\{a\}}(F') = 2$. However, $\mathrm{deg}_{\{a,b\}}(F') = \infty$, i.e., $\{a,b\}$ does not satisfy $F'$. Since it is not possible to satisfy $F'$ to a degree of $1$, $\{a\}$ is a preferred model of $F'$.
\end{example}
Note that ordered disjunction is associative under QCL-semantics, which means that we can simply write $A_1 \vv{\times} A_2 \vv{\times} \ldots \vv{\times} A_n$ to express that we must satisfy at least one of $A_1,\ldots,A_n$, and that we prefer $A_i$ to $A_j$ for $i < j$.
Formally, this is expressed by the following lemma:
\begin{lemma}[from \cite{BrewkaEtAl2004qcl}]\label{ordered-disjunction-associative}
Let $F$, $G$, and $H$ be QCL-formulas. Then $(F \vv{\times} (G \vv{\times} H))$ and $((F \vv{\times} G) \vv{\times} H)$ have the same optionality and the same satisfaction degree under all interpretations.
\end{lemma}
As mentioned in the introduction, an alternative semantics for QCL has been proposed in the form of PQCL \cite{BenferhatSedki2008pqcl}. Specifically, PQCL changes the semantics for the classical connectives ($\neg,\lor,\land$), but defines ordered disjunction ($\vv{\times}$) in the same way as QCL. For our purposes, it is not necessary to formally define PQCL. Rather, it suffices to note that, in PQCL, negation propagates to the atom level, meaning that $\neg (F \land G)$ is simply assigned the satisfaction degree of $\neg F \lor \neg G$, $\neg (F \lor G)$ is assigned the degree of $\neg F \land \neg G$, and $\neg (F \vv{\times} G)$ is assigned the degree of $\neg F \vv{\times} \neg G$.
\subsection{Game-Theoretic Semantics (GTS)}
We start by recalling Hintikka's game \cite{Hintikka1973-HINLLA} over a formula $F$ in the language restricted to the connectives $\vee, \wedge, \neg$ and over an interpretation $\mathcal{I}$. The game is played between two players, \emph{Me}\xspace and \emph{You}\xspace, both of which can act either in the role of Proponent ($\mathbf{P}$) or Opponent ($\mathbf{O}$). The game starts with \emph{Me}\xspace as $\mathbf{P}$ of the formula $F$ and \emph{You}\xspace as $\mathbf{O}$. At formulas of the form $G_1 \vee G_2$, $\mathbf{P}$ chooses a formula $G_i$ that the game continues with. At formulas of the form $G_1 \wedge G_2$ it is $\mathbf{O}$'s choice. At negations $\neg G$, the game continues with $G$ and a role switch. Every outcome of the game is a propositional variable $a$. The player currently in the role of $\mathbf{P}$ wins the game (and $\mathbf{O}$ loses) iff $a\in \mathcal{I}$. It is known that \emph{I}\xspace have a winning strategy for this game iff $\mathcal{I}\models F$.
How can we extend Hintikka's game from classical logic to choice logic? We propose the following intuitive reading of ordered disjunction ($\vv{\times}$):
at $G_1 \vv{\times} G_2$ it is $\mathbf{P}$'s choice whether to continue with $G_1$ or with $G_2$, \textit{but this player prefers} $G_1$.
\emph{My}\xspace aim in the game is now not only to win the game but to do so with as little compromise to \emph{My}\xspace preferences as possible. Thus, it is natural to express \emph{My}\xspace preference of $G_2$-outcomes $O_2$ over $G_1$-outcomes $O_1$ via the relation $O_1 \ll O_2$. We leave the formal treatment of this game for the next section and conclude with some standard game-theoretic definitions.
\begin{definition}
A \emph{game} is a pair $\mathbf{G} = (T,d)$, where
\begin{enumerate}
\item $T=(V,E,l)$ is a tree with set of nodes $V$ (usually called \emph{(game) states}) and edges $E$. The leafs of $T$ are called \emph{outcomes} and are denoted $\mathcal{O}(\mathbf{G})$. The \emph{labelling function} $l$ maps nodes of $T$ to the set $\{I,Y\}$.
\item $d$ is a payoff-function mapping outcomes to elements of a linear order $(D,\preceq)$.
\end{enumerate}
We write $x\approx y$ if $x\preceq y$ and $y\preceq x$. In the games that we are interested in, $D$ is partitioned into two sets, $W$ and $L$, where $W$ is upward-closed and $L = {D \setminus W}$. Outcomes $O$ are called \emph{winning} if $d(O) \in W$ and \emph{losing} if $d(O)\in L$.
\end{definition}
For example, in Hintikka's game (without negations), the underlying game tree is exactly the tree-representation of the formula $F$. The labels of $\wedge$-formulas are ``Y'', while the label of $\vee$-formulas are ``I''. The payoff functions maps outcomes to $P=\{0,1\}$, where $d(p) = 1$ iff $p \in \mathcal{I}$. $P$ carries the usual ordering $0<1$ and $W = \{1\}$.
A strategy $\sigma$ for \emph{Me}\xspace in a game can be understood as \emph{My}\xspace complete game-plan. For every node of the underlying game-tree labelled ``I'', $\sigma$ tells \emph{Me}\xspace to which node \emph{I}\xspace have to move. Here is a formal definition:
\begin{definition}
A \emph{strategy} $\sigma$ for \emph{Me}\xspace for the game $\mathbf{G}$ is a subset of the nodes of the underlying tree such that (1) the root of $T$ is in $\sigma$ and for all $v\in \sigma$, (2) if $l(v) = I$, then at least one successor of $v$ is in $\sigma$ and (3) if $l(v) = Y$, then all successors of $v$ are in $\sigma$. A strategy for \emph{You}\xspace is defined symmetrically. We denote by $\Sigma_I$ and $\Sigma_{Y}$ the set of all strategies for \emph{Me}\xspace and \emph{You}\xspace, respectively.
\end{definition}
Conditions (1) and (3) make sure that all possible moves by the other player are taken care of by the game-plan.
Note that each pair of strategies $\sigma_I \in \Sigma_{I}$, $\sigma_{Y} \in \Sigma_{Y}$ defines a \emph{unique} outcome of $\mathbf{G}$, which we will denote by $O(\sigma_I,\sigma_{Y})$. We abbreviate $d(O(\sigma_I,\sigma_{Y}))$ by $d(\sigma_I,\sigma_{Y})$. A strategy $\sigma_I^*$ for \emph{Me}\xspace is called \emph{winning} if, playing according to this strategy, \emph{I}\xspace win the game, no matter how \emph{You}\xspace move, i.e. for all $\sigma_{Y} \in \Sigma_{Y}$, $d(\sigma_I^*, \sigma_{Y})\in W$. An outcome $O$ that maximizes \emph{My}\xspace pay-off in light of \emph{Your}\xspace best strategy is called \emph{maxmin-outcome}. Formally, $O$ is a maxmin-outcome iff $d(O) \approx \max^{\preceq}_{\sigma_I} \min^\preceq_{\sigma_{Y}} d(\sigma_I,\sigma_{Y})$ and $d(O)$ is called the \emph{maxmin-value} of the game. A strategy $\sigma_I^*$ for \emph{Me}\xspace is a \emph{maxmin-strategy} for $\mathbf{G}$ if $\sigma_I^* \in \mathrm{arg}\max^{\preceq}_{\sigma_I} \min^\preceq_{\sigma_{Y}} d(\sigma_I,\sigma_{Y})$. Minmax values and strategies for \emph{You}\xspace are defined symmetrically.
The class of games that we have defined falls into the category of \emph{zero-sum games} in game-theory. They are characterized by the fact that the players have strictly opposing interests. In zero-sum games, the minmax and maxmin value always coincide and is referred to as the \emph{value of the game}.
\begin{comment}
the next subsection, we will formally define a preference game $\mathbf{G}^\mathcal{I}(F)$, for an interpretation $\mathcal{I}$ and a QCL-formula $F$. As in Hintikka's game, the underlying game tree is exactly the tree-representation of the formula $F$. The labels of $\wedge$-formulas are ``II'', while the label of $\vee$- and $\vv{\times}$-formulas are ``I''. This coincides with the intuitive turn distribution discussed above. Also, the ordering $\ll$ is defined as above: for leafs $a$ and $b$, we have that $a \ll b$ iff\footnote{We will give a formal definition later.} there is a subformula of $F$ of the form $G_1 \vv{\times} G_2$ and $a$ appears is $G_1$, while $b$ appears in $G_2$. This implies that Player I will always prefer going to $G_1$, if she can reach an atom in $\mathcal{I}$. Consequently, we set $a\in W$ iff $a \in \mathcal{I}$.\\
Naturally, the primary goal of Player I is to reach an acceptable outcome and her secondary goal is to reach such an outcome that is $\ll$-maximal. Player II's primary goal is to reach a (for Player I) unacceptable outcome\footnote{In a later section, we propose a game where the aims of the players are symmetric, unlike in this game for QCL.}. However, the situation is not as clear in the case where only suboptimal outcomes can be achieved. Let us consider the following example: Looking for a hotel, Player I wants to chose one whose restaurant serves pizza, burger, pad thai or burrito, with preference in this order. Additionally, she prefers a soft bed over a hard bed. Her preferences can be expressed via the following QCL-formula:
\[F = (\mathrm{pizza} \vv{\times} \mathrm{burger} \vv{\times} \mathrm{burrito} \vv{\times} \text{pad thai}) \wedge (\text{soft bed}\vv{\times} \text{hard bed})\]
The hotel \emph{La Noche Mexicana} serves burritos and offers hard beds. The corresponding valuation is $\mathcal{I}=\{\text{burrito}, \allowbreak \text{hard bed}\}$. The preference relation in this game is as follows: $\text{pad thai} \ll\text{burrito}\ll\text{burger}\ll\text{pizza}$ and $\text{hard bed}\ll \text{soft bed}$. Therefore, Player I will arrive at a sub-optimal outcome in both subgames of $F$. But what happens in the first round of the game, when Player II chooses between these two subgames? He might be in favor of the second game, because it will end at a $\ll$-minimal outcome. On the other hand, burrito is Player I's third choice, while hard bed is her second. But what if bed preferences weigh more than dinner choices? We decide to leave these questions unanswered and stay as general as possible. To complete our definition of preference games, we will therefore consider any linear order on outcomes extending $\ll$:
\begin{definition}[degree-order]
Let $\preceq$ be a linear order on $\mathcal{O}(\mathbf{G})$. In the case of $O_1 \preceq O_2$ we write $O_1 \approx O_2$, if additionally $O_2 \preceq O_1$ and $O_1 \prec O_2$ otherwise. We say that $\preceq$ is a \emph{degree-order} for $G$ if it satisfies the following two conditions:
\begin{enumerate}
\item If $O_1\in L$ and $O_2 \in W$, then $O_1 \prec O_2$.
\item If $O_1,O_2 \in W$ and $O_1 \ll O_2$, then $O_1 \prec O_2$.
\end{enumerate}
We write $\mathbf{G}^\preceq$ for the game defined by the degree order $\preceq$.
\end{definition}
\end{comment}
\begin{comment}
\begin{example}\label{ex:dfromqcl}
The standard degree-order in the choice-logic literature is defined via the function $d: \mathcal{O}(\mathbf{G}) \rightarrow \mathbb{N}\cup \{\infty\}$:
\[d(O) = \begin{cases}
\text{length of longest } \ll \text{-path starting in } O, &\text{ if } O \in W,\\
\infty, &\text{ if } O \in L.\\
\end{cases}\]
Remember that a single outcome cannot occur twice in a path. Then we set $O_1 \preceq_d O_2$ iff $d(O_1) \geq d(O_2)$. It can be easily checked that $\preceq_d$ is a degree-order. A graphical representation of the winning ranges and preferences in the game $\mathbf{G}^{\preceq_d}$ can be found in Figure~\ref{fig:oldwinningrange}.
\end{example}
\begin{figure*}[t]
\includegraphics[width = 0.9\textwidth]{oldwinningrange.png}
\caption{Preferences and winning ranges of the two players in the game $\mathbf{G}^{\preceq_d}$.}
\label{fig:oldwinningrange}
\end{figure*}
Degree orders like in the example above that do not discriminate between losing outcomes ($O_1 \approx O_2$, whenever $O_1, O_2 \in L$) are called \emph{negation-ignorant}. Game-theoretically, in a game defined by a negation-ignorant degree-order the players do not differentiate between outcomes that are winning for Player II. In the following section, we will see that in games defined by such a degree-order, negation constitutes not only to a role switch, but also to a deletion of preferences, which is in spirit of the degree semantics of QCL.
\subsubsection{Constructions on Preference Games}
In this subsection we give a number of operations on preference games. Let $\mathbf{G}_1 = (T_1, l_1, \ll_1, W_1)$ and $\mathbf{G}_2 = (T_2, l_2, \ll_2, W_2)$ be two preference games. We define the game $\mathbf{G} = (T,l,\ll, U)$ for the following cases:
\begin{enumerate}
\item $\mathbf{G} = \mathbf{G}_1 \wedge \mathbf{G}_2$. Here, $T$ is the tree with root $n$, and its immediate subtrees are $T_1$ and $T_2$. The labelling $l$ is identical to $l_1$ on $T_1$, to $l_2$ on $T_2$ and $l(n) = II$. Finally, $\ll=\ll_1 \cup \ll_2$ and $W = W_1 \cup W_2$.
\item $\mathbf{G} = \mathbf{G}_1 \vee \mathbf{G}_2$ is the same as $\mathbf{G}_1 \wedge \mathbf{G}_2$, except for $l(n) = I$.
\item $\mathbf{G} = \mathbf{G}_1 \vv{\times} \mathbf{G}_2$ is the same as $\mathbf{G}_1 \vee \mathbf{G}_2$, except for the preference relation: $O_1 \ll O_2$ iff $O_1 \ll_1 O_2$, or $O_1 \ll_2 O_2$, or $O_1 \in \mathcal{O}(\mathbf{G}_1)$ and $O_2 \in \mathcal{O}(\mathbf{G}_2)$.
\item $\mathbf{G} = \mathbf{G}_1^*$: Here, $T = T_1$, $l = l_1$, $U = U_1$ and $\ll = \emptyset$, i.e. all preferences are deleted.
\item $\mathbf{G} = \neg \mathbf{G}_1$. Here $T = T_1$, $W = \mathcal{O}(\mathbf{G}_1)\setminus W_1$, $\ll$ is the inverse of $\ll_1$ and $l(n) = I$ iff $l_1(n)= II$.
\end{enumerate}
\end{comment}
\section{A Game for QCL} \label{sec:capturing-qcl}
We now give a formal definition of a Hintikka-style game for QCL. As motivated in the previous section, we seek to capture the intuition that ordered disjunction ($\vv{\times}$) should be interpreted as a preference of a player for all outcomes on the left of $\vv{\times}$ over all outcomes on the right. Game states will be of the form $\mathbf{P}:F$ or $\mathbf{O}:F$, where $F$ is a QCL-formula and the labels ``$\mathbf{P}$'' and ``$\mathbf{O}$'' are to signify that \emph{I}\xspace currently act in the role of proponent and opponent, respectively.
We inductively define the game tree $T(\mathbf{Q}:F)$ of the game $\mathbf{G}(\mathbf{Q}:F,\mathcal{I})$ for $\mathbf{Q}\in \{\mathbf{P},\mathbf{O}\}$, as well as an order $\ll$ on outcomes, which represents preferences in the game from \emph{My}\xspace viewpoint (\emph{Yours}\xspace are the exact opposite). Both definitions will be independent of the given interpretation $\mathcal{I}$. After that we define the payoff-function $d$, which respects $\ll$ on \emph{My}\xspace winning outcomes. The definition of $T(\mathbf{Q}:F)$ depends on the structure of $F$:
\begin{description}
\item[$(R_a)$] ${T}(\mathbf{P}:a)$ consists of the single leaf $r$ and $\ll_{\mathbf{P}:a} = \emptyset$.
\item[$(R_\neg)$] ${T}(\mathbf{P}:\neg G)$, consists of a root $r$ labelled ``I'', and immediate subtree ${T}(\mathbf{O}:G)$ and $\ll_{\mathbf{P}:\neg G} = \emptyset$, i.e. at $\mathbf{P}:\neg G$, the game continues with a role switch and erased preferences for the remainder of the game.
\item[$(R_\wedge)$] ${T}(\mathbf{P}: G_1 \wedge G_2)$ is a tree with root $r$ labelled ``Y'', and immediate subtrees ${T}(\mathbf{P}:G_1)$ and ${T}(\mathbf{P}:G_2) $, i.e. at $\mathbf{P}:G_1 \wedge G_2$, \emph{You}\xspace choose whether to continue with $\mathbf{P}:G_1$ or with $\mathbf{P}:G_2$. The preference is given by $\ll_{\mathbf{P}:G_1 \wedge G_2} = \ll_{\mathbf{P}:G_1 } \cup \ll_{\mathbf{P}:G_2}$.
\item[$(R_\vee)$] ${T}(\mathbf{P}: G_1 \vee G_2)$ is a tree with root $r$ labelled ``I'', and immediate subtrees ${T}(\mathbf{P}:G_1)$ and ${T}(\mathbf{P}:G_2) $, i.e. at $\mathbf{P}:G_1 \vee G_2$, \emph{I}\xspace choose whether to continue with $\mathbf{P}:G_1$ or with $\mathbf{P}:G_2$. The preference is given by $\ll_{\mathbf{P}:G_1 \wedge G_2} = \ll_{\mathbf{P}:G_1 } \cup \ll_{\mathbf{P}:G_2}$.
\item[$(R_{\vv{\times}})$] ${T}(\mathbf{P}: G_1 \vv{\times} G_2)$ is a tree with root $r$ labelled ``I'', and immediate subtrees ${T}(\mathbf{P}:G_1)$ and ${T}(\mathbf{P}:G_2) $, i.e. at $\mathbf{P}:G_1 \vv{\times} G_2$, \emph{I}\xspace choose whether to continue with $\mathbf{P}:G_1$ or with $\mathbf{P}:G_2$. The preference is given by $O_1 \ll_{\mathbf{P}:G_1 \vv{\times} G_2} O_2$ iff $O_1 \in \mathcal{O}(\mathbf{P}:G_2)$\footnote{For simplicity, we write $\mathcal{O}(\mathbf{Q}:F)$ instead of $\mathcal{O}(\mathbf{G}(\mathbf{Q}:F))$} and $O_2 \in \mathcal{O}(\mathbf{P}:G_1)$, or $O_1 \ll_{\mathbf{P}:G_j} O_2$ for $j\in\{1,2\}$. This means that \emph{I}\xspace prefer all winning outcomes of the $G_1$-game over all outcomes of the $G_2$-game.
\end{description}
The tree $T(\mathbf{O}:F)$ is the same as ${T}(\mathbf{P}:F)$, except that labels are swapped and the preference relation is always empty. For example, $T(\mathbf{O}:G_1\vv{\times} G_2)$ consists of the node labelled ``Y'' with immediate subtrees $T(\mathbf{O}:G_1)$ and $T(\mathbf{O}:G_2)$ and $\ll_{\mathbf{O}:G_1\vv{\times} G_2} = \emptyset$. The rule $(R_\neg)$ may sound a bit counter-intuitive, but it precisely captures negation in QCL. For a critical discussion on negation, see Subsetion~\ref{subsect:issues}.
Let us say that an \emph{atomic} game state $\mathbf{P}: a$ is true in $\mathcal{I}$ if $a \in \mathcal{I}$, and false otherwise. Conversely, $\mathbf{O}: a$ is true if $a \not\in \mathcal{I}$, and false otherwise. The payoff-function $d$ is defined as follows: given an outcome $O$, let $\pi_\ll(O) = \{O_1,O_2, ..., O_n\}$ be the longest $\ll$-path starting in $O$, i.e. $O = O_1$, the $O_i$ are pairwise different outcomes and $O_i \ll O_{i+1}$ for all $1 \leq i \leq n-1$. Let us say that is $O$ is true, if $O$ stands for a true atomic game state, and otherwise false. The payoff-function $d_\mathcal{I}$ maps into the set $D = \mathbb{N}\cup \{\infty\}$, linearly ordered by $\preceq$, the inverse natural ordering (1 is best, $\infty$ is worst):
\[d_\mathcal{I}(O) = \begin{cases}
|\pi_\ll(O)|, &\text{ if } O \text{ is true},\\
\infty, &\text{ if } O \text{ is false}.\\
\end{cases}\]If $\mathcal{I}$ is clear from context, we simply write $d$ instead of $d_\mathcal{I}$.
\begin{figure*}[t]
\begin{center}
{\begin{tikzpicture}[level distance = 0.9cm]
\tikzstyle{level 1}=[sibling distance=55mm]
\tikzstyle{level 2}=[sibling distance=40mm]
\tikzstyle{level 2}=[sibling distance=25mm]
\tikzstyle{level 6}=[sibling distance=30mm]
\node {\(\left[\mathbf{P}:((a \vv{\times} b) \vv{\times} c) \land \neg (a \vv{\times} d) \right]^{Y}\)}
child {node {\(\left[\mathbf{P}:(a \vv{\times} b) \vv{\times} c \right]^I\)}
child {node {\(\left[\mathbf{P}:a \vv{\times} b \right]^I\)}
child {node {\(\left[\mathbf{P}:a \right]\)}}
child {node {\(\left[\mathbf{P}:b \right]\)}}
}
child {node {\(\left[\mathbf{P}:c \right]\)}}
}
child {node {\(\left[\mathbf{P}:\neg (a \vv{\times} d) \right]^I\)}
child {node {\(\left[\mathbf{O}:a \vv{\times} d \right]^{Y}\)}
child {node {\(\left[\mathbf{O}:a \right]\)}}
child {node {\(\left[\mathbf{O}:d \right]\)}}
}
};
\end{tikzpicture}}
\end{center}
\caption{A game tree for QCL.}
\label{fig:treeFirstNegation}
\end{figure*}
\begin{comment}
\begin{description}
\item[$(R_a)$] $\mathbf{G}_\preceq^\mathcal{I}(a)$ is a single-node game. The node is contained in $W$ iff $a\in \mathcal{I}$, i.e. Player I wins (and Player II loses) the game iff $a\in \mathcal{I}$.
\item[$(R_\neg)$] $\mathbf{G}_\preceq^\mathcal{I}(\neg G) = \neg (\mathbf{G}_\preceq^\mathcal{I}(G))^*$, i.e. at the game state $\neg G$, the game continues at $G$ with switched roles and deleted preferences.
\item[$(R_\wedge)$] $\mathbf{G}_\preceq^\mathcal{I}(G_1 \wedge G_2) = \mathbf{G}_\preceq^\mathcal{I}(G_1)\wedge \mathbf{G}_\preceq^\mathcal{I}(G_2)$, i.e. at $G_1 \wedge G_2$, Player I chooses whether to move to $G_1$ or to $G_2$.
\item[$(R_\vee)$] $\mathbf{G}_\preceq^\mathcal{I}(G_1 \vee G_2)=\mathbf{G}_\preceq^\mathcal{I}(G_1)\vee \mathbf{G}_\prec^\mathcal{I}(G_2)$, i.e. at $G_1 \vee G_2$, Player I chooses whether to move to $G_1$ or to $G_2$.
\item[$(R_{\vv{\times}})$] $\mathbf{G}_\preceq^\mathcal{I}(G_1 \vv{\times} G_2) = \mathbf{G}_\preceq^\mathcal{I}(G_1) \vv{\times} \mathbf{G}_\preceq^\mathcal{I}(G_2)$, i.e. at $G_1 \vv{\times} G_2$, Player I chooses whether to move to $G_1$ or to $G_2$, but prefers moving to $G_1$: all winning outcomes of the $G_1$-game are preferred to outcomes of the $G_2$-game.
\end{description}
For negation, we would like to consider two possible interpretations:
\begin{description}
\item[$(R_\neg)$] $\mathbf{G}_\preceq^\mathcal{I}(\neg G) = \neg (\mathbf{G}_\preceq^\mathcal{I}(G))^*$, i.e. at the game state $\neg G$, the game continues at $G$ with switched roles and deleted preferences.
\item[$(R_\neg')$] $\mathbf{G}_\preceq^\mathcal{I}(\neg G) = \neg \mathbf{G}_\preceq^\mathcal{I}(G)$, i.e. at the game state $\neg G$, the game continues at $G$ with switched roles. \todo{move to back}
\end{description}
\end{comment}
\begin{example}\label{ex:gameFirstNegation}
Consider the formula $F = ((a \vv{\times} b) \vv{\times} c) \land \neg (a \vv{\times} d)$. Figure~\ref{fig:treeFirstNegation} depicts the corresponding game tree. Observe that the node ${\mathbf{O}: a \vv{\times} d}$ has the label ``Y'' because the roles of the players are switched in the parent node ${\mathbf{P}:\neg (a \vv{\times} d)}$. The order on outcomes is ${\mathbf{P}:c} \ll {\mathbf{P}:b} \ll {\mathbf{P}:a}$. Note that ${\mathbf{O}:d} \centernot\ll {\mathbf{O}:a}$, since preferences are deleted via the negation rule $(R_\neg)$.
Consider the interpretation $\{a\}$. The winning outcomes are ${\mathbf{P}:a}$ and ${\mathbf{O}:d}$ and the degree-order is given by $d({\mathbf{P}:a}) = 1$, $d({\mathbf{P}:b}) = d({\mathbf{P}:c}) = d({\mathbf{O}:a}) = \infty$, $d({\mathbf{O}:d}) = 2$.
In this case, \emph{I}\xspace have no winning strategy: in the root node, it is \emph{Your}\xspace turn, and \emph{You}\xspace can move to the right where the leaf ${\mathbf{O}:a}$ is not a winning outcome because roles were switched.
Now consider $\{b\}$. The winning outcomes are ${\mathbf{P}:b}$, ${\mathbf{O}:a}$ and ${\mathbf{O}:d}$ and the degree-order is given by $d({\mathbf{P}:a}) = d({\mathbf{P}:c}) = \infty$, $d({\mathbf{P}:b}) = 2$, $d({\mathbf{O}:a}) = d({\mathbf{O}:d}) = 1$. If \emph{You}\xspace move to the right this only leads to winning outcomes (with value $1$) for \emph{Me}\xspace (due to switched roles). If \emph{You}\xspace move to the left, it is now always \emph{My}\xspace turn, and \emph{I}\xspace can reach the winning outcome ${\mathbf{P}:b}$ with a value of $2$. Thus, it is better for \emph{You}\xspace to move to the left, and the best outcome for \emph{Me}\xspace is ${\mathbf{P}:b}$.
\end{example}
\begin{lemma}\label{longestpathopt}
The longest $\ll$-path in $\mathcal{O}(\mathbf{P}:F)$ has length $\mathrm{opt}(F)$.
\end{lemma}
The above Lemma can be shown via induction on $F$, using the fact that preferences are erased at negations as well as in all game trees $T(\mathbf{O}:G)$.
This is already quite a nice result as it shows that the notion of optionally arises naturally in our game, whereas in QCL, optionality must be defined a-priori to ensure that the semantics work as intended.
\begin{comment}
\label{subsect:gameqcl}
In this subsection, we consider a preference game that captures the semantics of QCL: the game $\mathbf{G}_{\preceq_d}^\mathcal{I}(F)$, defined via the rule $(R_\neg)$ and the degree order from Example~\ref{ex:dfromqcl}. We prove that this game is adequate for QCL in the sense that the $d$-value of the game $\mathbf{G}_{\preceq_d}^\mathcal{I}(F)$, i.e., the value of $\mathbf{G}_{\preceq_d}^\mathcal{I}(F)$ applied to the $d$-function, and the degree of $F$ coincide.
\end{comment}
We are now ready to show that our game semantics captures QCL:
\begin{theorem}\label{thm:adeqqcl}
The value of $\mathbf{G}(\mathbf{P}:F,\mathcal{I})$ is equal to $\mathrm{deg}_\mathcal{I}(F)$.
\end{theorem}
For the proof of Theorem~\ref{thm:adeqqcl}, we introduce some handy notation: When $\mathcal{I}$ is clear from context, we denote by $O({\mathbf{Q}:F})$ the maxmin-outcome and by $d({\mathbf{Q}:F})$ the maxmin-value of the game $\mathbf{G}({\mathbf{Q}:F},\mathcal{I})$. Where it does not cause confusion, we will identify a formula with the corresponding node in the game tree. Since the payoff-function $d$ differs from one game to another, let us denote by $d_{{\mathbf{Q}:F}}$ the payoff-function for the game $\mathbf{G}({\mathbf{Q}:F},\mathcal{I})$.
\begin{proof}[Proof (of Theorem~\ref{thm:adeqqcl})]
It suffices to show the following two claims by induction on $F$: (1) $d(\mathbf{P}:F)=\mathrm{deg}_\mathcal{I}(F)$ and (2) $d(\mathbf{O}:F) = \infty$, if $\mathrm{deg}_\mathcal{I}(F)<\infty$ and $1$ otherwise. Since in the game $\mathbf{G}(\mathbf{O}:F,\mathcal{I})$ all preferences are deleted, it is essentially Hintikka's game. We will therefore prove only (1). Remember that the ordering $\preceq$ is the inverse of the natural ordering $\leq$ on $\mathbb{N}\cup\{\infty\}$. \emph{I}\xspace therefore seek to $\leq$-\emph{minimize} \emph{My}\xspace payoff in the game.
$F = a$: This game consists of a single node $v$. The longest $\ll$-path starting at $v$ has length 1. Therefore, $d({\mathbf{P}:a}) = 1$ iff $a\in \mathcal{I}$ iff $\mathrm{deg}_\mathcal{I}(a) = 1$ and $d({\mathbf{P}:a}) = \infty$ iff $a\notin \mathcal{I}$ iff $\mathrm{deg}_\mathcal{I}(a) = \infty$.
$F = G_1 \wedge G_2$: In the first round, \emph{You}\xspace choose between $\mathbf{P}:G_1$ and $\mathbf{P}: G_2$. \emph{Your}\xspace best strategy is to go to the subgame with $\preceq$-minimal payoff:
\begin{align*}
d({\mathbf{P}:G_1 \wedge G_2})
&= \min_{\preceq}\{d({\mathbf{P}:G_1}),d({\mathbf{P}:G_2})\}\\
&= \max \{\mathrm{deg}_\mathcal{I}(G_1),\mathrm{deg}_\mathcal{I}(G_2)\} \\
&= \mathrm{deg}_\mathcal{I}(G_1\wedge G_2)
\end{align*}Here, the second step used the fact that $\preceq$ is the inverse of the natural ordering on $\mathbb{N}\cup\{\infty\}$ and
the induction hypothesis.
$F = G_1 \vee G_2$: In the first round, \emph{I}\xspace choose between $\mathbf{P}:G_1$ and $\mathbf{P}:G_2$, Therefore:
\begin{align*}
d(\mathbf{P}:G_1 \vee G_2)
&= \max_{\preceq}\{d(\mathbf{P}:G_1),d({\mathbf{P}:G_2})\}\\
&= \min \{\mathrm{deg}_\mathcal{I}(G_1),\mathrm{deg}_\mathcal{I}(G_2)\} \\
&= \mathrm{deg}_\mathcal{I}(G_1\wedge G_2)
\end{align*}
Again, we used the induction hypothesis in the second step.
$F = G_1 \vv{\times} G_2$: In the first round, \emph{I}\xspace choose between $\mathbf{P}:G_1$ and $\mathbf{P}:G_2$, but all outcomes of the $G_2$-game are in $\ll$-relation to all outcomes of the $G_1$-game, which is respected by the payoff-function for the winning outcomes. Let us write $W(G_i)$ for the winning outcomes of $\mathbf{G}(\mathbf{P}:G_i,\mathcal{I})$, i.e. those outcomes $O$ with $d_{\mathbf{P}:G_i}(O) < \infty$. By Lemma~\ref{longestpathopt}, the longest $\ll$- path in $\mathcal{O}(\mathbf{P}:G_1)$ has length $\mathrm{opt}(G_1)$. Hence, for all $O\in \mathcal{O}(\mathbf{P}:G_1 \vv{\times} G_2)$:
\[d_{\mathbf{P}:F}(O) =
\begin{cases}
d_{\mathbf{P}:G_1}(O), &\text{ if } O\in W(G_1),\\
d_{\mathbf{P}:G_2}(O)+\mathrm{opt}(G_1), &\text{ if } O\in W(G_2),\\
\infty, &\text{ otherwise}.
\end{cases}\]
Therefore, if $O(\mathbf{P}: G_1)$ is winning, i.e., $d({\mathbf{P}:G_1})=\mathrm{deg}_\mathcal{I}(G_1)<\infty$, then \emph{I}\xspace move to $\mathbf{P}:G_1$ and $d({\mathbf{P}:G_1 \vv{\times} G_2}) = d_{\mathbf{P}:F}(O(\mathbf{P}:F)) = d_{\mathbf{P}:G_1}(O(\mathbf{P}: G_1))=\mathrm{deg}_\mathcal{I}(G_1) = \mathrm{deg}_\mathcal{I}(F)$. If $O(\mathbf{P}:G_1)$ is losing, but $O(\mathbf{P}:G_2)$ is winning, i.e., $d({\mathbf{P}:G_1})=\mathrm{deg}_\mathcal{I}(G_1) = \infty$ and $d({\mathbf{P}:G_2}) = \mathrm{deg}_\mathcal{I}(G_2) < \infty$, then \emph{I}\xspace move to $\mathbf{P}:G_2$ and $d({\mathbf{P}:F})=d_{\mathbf{P}:F}(O(\mathbf{P}:F)) = d_{\mathbf{P}: G_2}(O(\mathbf{P}: G_2)) + \mathrm{opt}(G_1) = \mathrm{deg}_\mathcal{I}(G_2) + \mathrm{opt}(G_1) = \mathrm{deg}_\mathcal{I}(F)$. If both $O(\mathbf{P}: G_1)$ and $O(\mathbf{P}: G_2)$ are losing, then $d({\mathbf{P}:F})= \infty = \mathrm{deg}_\mathcal{I}(F)$.
$F = \neg G$: Here the game continues with $\mathbf{O}:G$. By (2), $d({\mathbf{O}:G}) = \infty$, if $\mathrm{deg}_\mathcal{I}(G)<\infty$ and $1$ otherwise. Hence, $d({\mathbf{P}:\neg G}) = d({\mathbf{O}:G}) = \mathrm{deg}_\mathcal{I}(\neg G)$.
\end{proof}
\section{A New Semantics}
In this section, we first identify some contentious behavior in QCL (and PQCL) with regards to negation. We then address these issues by adapting our game semantics from Section~\ref{sec:capturing-qcl} to use GTS negation. Lastly, we specify a degree-semantics for this new game.
\subsection{Negation in QCL (and PQCL)} \label{subsect:issues}
While choice logics are a useful formalism to express both soft constraints (preferences) and hard constraints (truth) in a single language, existing semantics (such as QCL and PQCL) are not without problems. One matter of contention lies in how choice logics deal with negation, as we will now see.
Consider the following statement: \textit{``I want almond or banana ice cream, but preferably almond''}. It is clear how to formalize this sentence in QCL, namely simply as $a \vv{\times} b$, where $a$ and $b$ are abbreviations for almond and banana ice cream respectively. However, it is not obvious, and generally not agreed upon, how the negation of this sentence is to be understood. In QCL, negation erases all information about preferences and only takes classical satisfaction into account. Under this interpretation, $\neg (a \vv{\times} b)$ is to be read as \textit{``I do not want almond or banana ice cream''}, which means that $\neg (a \vv{\times} b)$ is equivalent to $\neg a \land \neg b$ (cf.\ Table~\ref{table:negation-comparison}). This is certainly a pragmatic approach, but, as we believe, potentially problematic because it means that negation does not actually apply to the \emph{entire} sentence, i.e., $\neg(a \vv{\times} b)$ can not be read as \textit{``I do not want almond or banana ice cream, but preferably almond''}. Moreover, this approach means that a QCL-formula $F$ is not logically equivalent to its double negation $\neg \neg F$, which may lead to non-intuitive behavior. Consider the following sentence: \textit{``I do not not want almond or banana icecream, and preferably almond''}. It is certainly reasonable to understand this sentence to be equivalent to
our initial sentence.
However, $\neg \neg (a \vv{\times} b)$ is not logically equivalent to $(a \vv{\times} b)$ in QCL since all information about preferences is lost in $\neg \neg (a \vv{\times} b)$.
PQCL addresses this issue, i.e., $F$ is always equivalent to $\neg\neg F$. However, in our view, PQCL introduces two other problems with negation. In PQCL, $\neg (a \vv{\times} b)$ is interpreted as $\neg a \vv{\times} \neg b$ (cf.\ Table~\ref{table:negation-comparison}).
The first issue is that it is possible for an interpretation to classically satisfy both a formula $F$ and its negation $\neg F$. For example, in Table~\ref{table:negation-comparison} we can see that the interpretations $\{a\}$ and $\{b\}$ classically satisfy both $(a \vv{\times} b)$ and $\neg (a \vv{\times} b)$. However, the ordered disjunct $(a \vv{\times} b)$ not only expresses a preference, but also a hard constraint ($a$ or $b$ must be satisfied). We believe that negation should act on both of these aspects. Moreover, as a result of this behavior, the implication $F \rightarrow G$ can in general not be defined via $\neg F \lor G$. For example, the formula $\neg (a \vv{\times} b) \lor c$ is classically satisfied by the interpretations $\{a\}$ and $\{b\}$, although the antecedent $(a \vv{\times} b)$ is satisfied under these interpretations while the consequent $c$ is not.
Secondly, the satisfaction degree of $\neg F$ does not only depend on the satisfaction degree and optionality of $F$. Looking again at Table ~\ref{table:negation-comparison} we see that the interpretations $\{a\}$ and $\{a,b\}$ satisfy $(a \vv{\times} b)$ to the same degree, i.e., they are equally preferable, but $\{a\}$ satisfies $\neg (a \vv{\times} b)$ to a degree of $2$ while $\{a,b\}$ does not satisfy $\neg (a \vv{\times} b)$ at all.
\begin{table}[t]
\centering
\begin{tabular}{c|ccc}
$\mathcal{I}$ & $a \vv{\times} b$ & $\neg a \land \neg b$ & $\neg a \vv{\times} \neg b$ \\
\hline
$\emptyset$ & $\infty$ & $1$ & $1$ \\
$\{b\}$ & $2$ & $\infty$ & $1$ \\
$\{a\}$ & $1$ & $\infty$ & $2$ \\
$\{a,b\}$ & $1$ & $\infty$ & $\infty$
\end{tabular}
\caption{Truth table showing the satisfaction degrees of $\neg (a \protect\vv{\times} b)$ in QCL (equivalent to $\neg a \land \neg b$) and PQCL (equivalent to $\neg a \protect\vv{\times} \neg b$).}
\label{table:negation-comparison}
\end{table}
When designing our new game semantics, we will keep these issues in mind. Our main goal is to define a negation that acts both on hard-constraints (truth) as in QCL and soft-constraints (preferences) as in PQCL. Moreover, we will ensure that (1) formulas are equivalent to their double negation, (2) formulas and their negation can not be satisfied classically by the same interpretation, and (3) the satisfaction degree of $\neg F$ depends only on the satisfaction degree of $F$.
It must be noted that QCL and PQCL are not the only semantics for propositional logic extended with ordered disjunction. Another example can be found in \cite{MalyWoltran2018hardsoft}, where the concept of satisfaction degrees is abandoned. The semantics induce a partial order among interpretations.
However, negation is handled in the same way as in QCL, i.e., all information about preferences is lost and therefore formulas are not equivalent to their double negation.
\subsection{Using GTS Negation} \label{subsec:new-game}
We now address the issues with negation in previous approaches to choice logics, as outlined in Section~\ref{subsect:issues}. One of the main problems was that all information on preferences is lost in negated formulas. From the game-point of view, this corresponds to the fact that at game states $\neg F$, all preferences are deleted. But in a game-theoretic setting it is natural to consider a game where this deletion does not occur. We therefore propose the following rule for negation:
\begin{description}
\item[$(R_\neg)$] ${T}(\mathbf{P}:\neg G)$, consists of a root $r$ labelled ``I'', the immediate subtree ${T}(\mathbf{O}:G)$, and $\ll_{\mathbf{P}:\neg G}$ equal to $\ll_{\mathbf{O}:G}$, i.e., at $\mathbf{P}:\neg G$, the game continues with a role switch.
\end{description}
All other rules stay the same, except that in $T(\mathbf{O}:F)$ labels are swapped and preferences are switched, i.e. $\ll_{\mathbf{O}:F}$ is the inverse of $\ll_{\mathbf{P}:F}$. For example, if $F = G_1 \vv{\times} G_2$, then $T(\mathbf{O}:F)$ consists of the node labelled ``Y'' with immediate subtrees $T(\mathbf{O}:G_1)$ and $T(\mathbf{O}:G_2)$ and $O_1 \ll_{\mathbf{O:F}} O_2$ iff $O_2 \ll_{\mathbf{P:F}} O_1$.
Additionally, we change our payoff-function to respect preferences not only in Player I's winning outcomes, but in both Player's winning outcomes:
\begin{definition}\label{ex:newdeg}
Let $Z := (\mathbb{Z} \setminus \{0\},\trianglelefteq)$. The ordering $\trianglelefteq$ is the inverse of the natural ordering on $\mathbb{Z}^-$ and on $\mathbb{Z}^+$ and for $a \in \mathbb{Z}^+, b\in \mathbb{Z}^-$ we set $b \triangleleft a$. For an outcome $O$, we set\footnote{Notice the flipped $\ll$-sign in the second case.}
\[\delta_\mathcal{I}(O) = \begin{cases}
|\pi_\ll(O)|, &\text{ if } O \text{ is true},\\
-|\pi_\gg(O)|, &\text{ if } O \text{ is false}.\\
\end{cases}\]
Again, we write $\delta$, instead of $\delta_\mathcal{I}$, if $\mathcal{I}$ is clear from context.
We denote the new game initiated at the game state $\mathbf{Q}:F$ and played over the interpretation $\mathcal{I}$ by $\mathbf{NG}(\mathbf{Q}:F,\mathcal{I})$.
\end{definition}
\begin{figure*}[t]
\includegraphics[width = \textwidth]{Winning_Rangescombined.png}
\caption{Preferences and winning payoffs of the two players in the games $\mathbf{G}$ and $\mathbf{NG}$}
\label{fig:newwinningrange}
\end{figure*}
Observe that with these alterations, the two players become truly symmetric. The goal of \emph{both} players is now to (1)~win the game with (2)~as little compromise as possible, and otherwise (3)~force the opponent in as much compromise as possible. See Figure~\ref{fig:newwinningrange} for an instructive graphical representation, which also shows how this new approach differs from the old approach of QCL and its corresponding game~$\mathbf{G}$.
\begin{example}\label{ex:gameSecondNegation}
Consider again the the formula $((a \vv{\times} b) \vv{\times} c) \land \neg (a \vv{\times} d)$ from Example~\ref{ex:gameFirstNegation}. The game tree is the same as before (see Figure~\ref{fig:treeFirstNegation}). The order on outcomes is now ${\mathbf{P}:c} \ll {\mathbf{P}:b} \ll {\mathbf{P}:a}$ and ${\mathbf{O}:a} \ll {\mathbf{O}:d}$.
Consider the interpretation $\{a\}$. As in Example~\ref{ex:gameFirstNegation}, \emph{I}\xspace have no winning strategy since \emph{You}\xspace can always move to the right side at the root node and to the left side in ${\mathbf{O}:a \vv{\times} d}$ to reach ${\mathbf{O}:a}$ with a value of $-1$.
Now consider $\{d\}$. The only winning outcome is ${\mathbf{O}:a}$ and the payoffs are given by $\delta({\mathbf{P}:c}) = -1$, $\delta({\mathbf{P}:b}) = -2$, $\delta({\mathbf{P}:a}) = -3$, $\delta({\mathbf{O}:a}) = 2$, $\delta({\mathbf{O}:d}) = -2$. If \emph{You}\xspace move to the left at the root node, it is best for \emph{Me}\xspace to reach the outcome ${\mathbf{P}:a}$ with a payoff of $-3$. If \emph{You}\xspace move to the right at the root node, \emph{You}\xspace have to move to the right again in ${\mathbf{O}:a \vv{\times} d}$ to reach a losing outcome, namely ${\mathbf{O}:d}$ with a payoff of $-2$. Thus, it is better for \emph{You}\xspace to move to the right at the root note, giving us the game value $-2$.
\end{example}
\subsection{Extracting a Degree Semantics} \label{subsec:extracting-degree-semantics}
Using our game $\mathbf{NG}$ as a cornerstone, we now define a degree-function for QCL-formulas taking values in the domain $(Z ,\trianglelefteq)$ from Definition~\ref{ex:newdeg} and discuss some of its properties. The resulting logic will be called GCL, for Game-induced Choice Logic. The proof of adequacy of the game $\mathbf{NG}$ with respect to this degree-function is topic of the next subsection.
We denote the optionality function of GCL by $\mathrm{opt}^G$, and define it in the same way as the optionality function $\mathrm{opt}$ of QCL, except for negation:
\[\mathrm{opt}^G(\neg F) = \mathrm{opt}^G(F)\]
With this definition, we can extend Lemma~\ref{longestpathopt} for $\mathbf{NG}$:
\begin{lemma}\label{lem:longestpathng}
Let $\mathbf{Q} \in \{\mathbf{P},\mathbf{Q}\}$. The longest $\ll$-path in $\mathcal{O}({\mathbf{Q}:F})$ has length $\mathrm{opt}^G(F)$.
\end{lemma}
The degree function of GCL is denoted by $\mathrm{deg}_\mathcal{I}^G$. It assigns to each formula a degree relative to an interpretation $\mathcal{I}$ and is defined inductively as follows (for succinctness, we abbreviate $\mathrm{opt}^G(F)$ with $o_F$ and $\mathrm{opt}^G(G)$ with $o_G$):
\begin{align*}
\mathrm{deg}_\mathcal{I}^G(a) &=
1 \text{ if } a \in \mathcal{I}, -1 \text{ otherwise } \\
\mathrm{deg}_\mathcal{I}^G(\neg F) &= - \mathrm{deg}_\mathcal{I}^G(F)\\
\mathrm{deg}_\mathcal{I}^G(F\wedge G) &= \min(\mathrm{deg}_\mathcal{I}^G(F),\mathrm{deg}_\mathcal{I}^G(G))\\
\mathrm{deg}_\mathcal{I}^G(F\vee G) &= \max(\mathrm{deg}_\mathcal{I}^G(F),\mathrm{deg}_\mathcal{I}^G(G)) \\
\mathrm{deg}_\mathcal{I}^G(F\vv{\times} G) &=
\begin{cases}
\mathrm{deg}_\mathcal{I}^G(F) & \text{if } \mathrm{deg}_\mathcal{I}^G(F) \in \mathbb{Z}^+\\
o_F + \mathrm{deg}_\mathcal{I}^G(G) & \text{if } \mathrm{deg}_\mathcal{I}^G(F) \in \mathbb{Z}^-, \\ & \mathrm{deg}_\mathcal{I}^G(G) \in \mathbb{Z}^+\\
\mathrm{deg}_\mathcal{I}^G(F)-o_G & \text{otherwise}
\\\end{cases}
\end{align*}
Here $\min$ and $\max$ are relative to $\trianglelefteq$. If $\mathrm{deg}_\mathcal{I}^G(F) \in \mathbb{Z}^+$ then we say that $\mathcal{I}$ classically satisfies $F$, or that $\mathcal{I}$ is a model of $F$. Note that, in contrast to QCL, those interpretations that result in a higher degree relative to the ordering $\trianglelefteq$ are more preferable, which is also why we take the maximum degree for disjunction and the minimum degree for conjunction. However, since $\trianglelefteq$ inverts the order on $\mathbb{Z}^+$, a degree of $1$ is considered to be higher than a degree of $2$. With this in mind, the notion of preferred models can be defined analogously to QCL:
\begin{definition}
Let $F$ be a QCL-formula. Under our new semantics, $\mathcal{I}$ is a preferred model of $F$ iff $\mathrm{deg}_\mathcal{I}^G(F) \in \mathbb{Z}^+$ and $\mathrm{deg}_\mathcal{J}^G(F) \trianglelefteq \mathrm{deg}_\mathcal{I}^G(F)$ for all other interpretations $\mathcal{J}$.
\end{definition}
First, we show that ordered disjunction is still associative under these new semantics:
\begin{lemma}\label{lemma:new-semantics-associativity}
Let $F_1 = ((A \vv{\times} B) \vv{\times} C)$, $F_2 = (A \vv{\times} (B \vv{\times} C))$ for any QCL-formulas $A,B,C$. Then $\mathrm{opt}^G(F_1) = \mathrm{opt}^G(F_2)$ and $\mathrm{deg}_\mathcal{I}^G(F_1) = \mathrm{deg}_\mathcal{I}^G(F_2)$ for all interpretations~$\mathcal{I}$.
\end{lemma}
\begin{proof}
$\mathrm{opt}^G(F_1) = \mathrm{opt}^G(F_2)$ is immediate. Let $\mathcal{I}$ be an arbitrary interpretation. We can show $\mathrm{deg}_\mathcal{I}^G(F_1) = \mathrm{deg}_\mathcal{I}^G(F_2)$ by distinguishing all cases for $\mathrm{deg}_\mathcal{I}^G(A), \mathrm{deg}_\mathcal{I}^G(B), \mathrm{deg}_\mathcal{I}^G(C) \in \{\mathbb{Z}^-,\mathbb{Z}^+\}$.
We demonstrate the $\mathrm{deg}_\mathcal{I}^G(A) \in \mathbb{Z}^-$, $\mathrm{deg}_\mathcal{I}^G(B) \in \mathbb{Z}^-$, and $\mathrm{deg}_\mathcal{I}^G(C) \in \mathbb{Z}^-$. Then $\mathrm{deg}_\mathcal{I}^G(A \vv{\times} B) = \mathrm{deg}_\mathcal{I}^G(A) - \mathrm{opt}^G(B)$ and $\mathrm{deg}_\mathcal{I}^G(B \vv{\times} C) = \mathrm{deg}_\mathcal{I}^G(B) - \mathrm{opt}^G(C)$. Thus, $\mathrm{deg}_\mathcal{I}^G(F_1) = \mathrm{deg}_\mathcal{I}^G(A \vv{\times} B) - \mathrm{opt}^G(C) = \mathrm{deg}_\mathcal{I}^G(A) - \mathrm{opt}^G(B) - \mathrm{opt}^G(C)$. Moreover, $\mathrm{deg}_\mathcal{I}^G(F_2) = \mathrm{deg}_\mathcal{I}^G(A) - \mathrm{opt}^G(B \vv{\times} C) = \mathrm{deg}_\mathcal{I}^G(A) - (\mathrm{opt}^G(B) + \mathrm{opt}^G(C)) = \mathrm{deg}_\mathcal{I}^G(F_1)$.
\end{proof}
Secondly, it follows directly from the above degree function that negation in our new semantics behaves as desired\footnote{Recall the discussion in Section~\ref{subsect:issues}.}. Crucially, negation acts both on hard- and soft-constraints. Moreover, $F$ and $\neg F$ are never satisfied by the same interpretation, $F$ and $\neg\neg F$ are equivalent, and the degree of $\neg F$ depends only on the degree of $F$.
\begin{lemma}\label{lemma:new-semantics-negation}
Let $F$ be any GCL-formula, and let $\mathcal{I}$ and $\mathcal{J}$ be interpretations. It holds that
\begin{itemize}
\item $\mathrm{deg}_\mathcal{I}^G(F) \in \mathbb{Z}^+$ iff $\mathrm{deg}_\mathcal{I}^G(\neg F) \in \mathbb{Z}^-$,
\item $\mathrm{deg}_\mathcal{I}^G(F) = \mathrm{deg}_\mathcal{I}^G(\neg \neg F)$,
\item if $\mathrm{deg}_\mathcal{I}^G(F) = \mathrm{deg}_\mathcal{J}^G(F)$ then $\mathrm{deg}_\mathcal{I}^G(\neg F) = \mathrm{deg}_\mathcal{J}^G(\neg F)$.
\end{itemize}
\end{lemma}
Intuitively, negation in GCL preserves information on preferences by allowing for \emph{degrees of dissatisfaction}. For example, the formula $\neg(a \vv{\times} b)$ can only be satisfied by the interpretation $\emptyset$. However, we must also inspect the interpretations that do not satisfy the formula: $\{b\}$ will result in a degree of $-2$ while $\{a\}$ and $\{a,b\}$ will result in a degree of $-1$, meaning that $\{b\}$ is more preferable than $\{a\}$ and $\{a,b\}$. This reflects the fact that negation in GCL not only negates truth, as in QCL, but also preferences. Also note that, unlike in PQCL, the implication $F \rightarrow G$ can be defined via $\neg F \lor G$ since the antecedent $F$ is classically satisfied if and only if $\neg F$ is not.
\subsection{Adequacy of $\mathbf{NG}$}
Using the notation of Section~\ref{subsec:new-game} and the degree-function from ~Section~\ref{subsec:extracting-degree-semantics}, we can show the following result:
\begin{theorem}
The value of $\mathbf{NG}(\mathbf{P}:F,\mathcal{I})$ is $\mathrm{deg}_\mathcal{I}^G(F)$.
\end{theorem}
\begin{proof}
We use the same notation as in the proof of Theorem~\ref{thm:adeqqcl} and proceed by induction on the following two claims (1) $\delta(\mathbf{P}:F) = \mathrm{deg}_\mathcal{I}^G(F)$ and (2) $\delta(\mathbf{O}:F) = -\mathrm{deg}_\mathcal{I}^G(F)$. Most of the cases are similar to the proof of Theorem~\ref{thm:adeqqcl}, so we focus on the cases $\mathbf{P}: F$ that require different reasoning:
$F = G_1 \vv{\times} G_2$: From the fact that $\delta$ respects $\ll$ for the winning outcomes of both players and the game rule of $\vv{\times}$, we observe the following facts: First, if the $G_1$-game is winning for \emph{Me}\xspace, \emph{I}\xspace go to $G_1$ in the first round. Secondly, if $G_1$ is losing and $G_2$ is winning, \emph{I}\xspace go to $G_2$. And thirdly, if both games are losing, \emph{I}\xspace go to $G_1$. Since all outcomes of the $G_2$-games are in $\ll$-relation to all outcomes of the $G_1$-game, we have by Lemma~\ref{lem:longestpathng} for all outcomes $O$:
\[\delta_{\mathbf{P}:F}(O) = \begin{cases}
\delta_{\mathbf{P}:G_1}(O), &\text{ if } O\in W(\mathbf{P}:G_1),\\
\delta_{\mathbf{P}:G_2}(O)+\mathrm{opt}(G_1), &\text{ if } O\in W(\mathbf{P}: G_2),\\
\delta_{\mathbf{P}:G_1}(O)-\mathrm{opt}(G_2), &\text{ if } O \in L(\mathbf{P}:G_1).\end{cases}\]
The last case comes from the fact that $O \gg O'$ for all $O' \in \mathcal{O}(\mathbf{P}:G_2)$, Lemma~\ref{lem:longestpathng} and the definition of $\delta$. We now use the inductive hypothesis: in the first case from above, $O({\mathbf{P}:F}) \in W({\mathbf{P}:G_1})$ and therefore $\delta({\mathbf{P}:F}) = \delta({\mathbf{P}:G_1}) = \mathrm{deg}_\mathcal{I}^G(G_1)$. In the second case, $O({\mathbf{P}:F}) \in W({\mathbf{P}:G_2})$ and therefore $\delta({\mathbf{P}:F}) = \delta({\mathbf{P}:G_2})+\mathrm{opt}(G_1) = \mathrm{deg}_\mathcal{I}^G(G_2)+\mathrm{opt}(G_1)$. Finally, in the third case, $O({\mathbf{P}:F}) \in L({\mathbf{P}:G_1})$ and therefore $\delta({\mathbf{P}:F}) = \delta({\mathbf{P}:G_1})-\mathrm{opt}(G_2) = \mathrm{deg}_\mathcal{I}^G(G_2)-\mathrm{opt}(G_2)$.
$F = \neg G$: The game continues at ${\mathbf{O}:G}$. Therefore, using the inductive hypothesis (2), $\delta({\mathbf{P}:F}) = \delta({\mathbf{O}:G}) = -\mathrm{deg}_\mathcal{I}^G(G) = \mathrm{deg}_\mathcal{I}^G(F)$.
Cases where \emph{I}\xspace am in the role of Opponent are similar. For example, let us consider ${\mathbf{O}: G_1 \wedge G_2}$. In the first move \emph{I}\xspace choose between the two subgames ${\mathbf{O}:G_1}$ and ${\mathbf{O}:G_2}$. \emph{I}\xspace seek to maximize \emph{My}\xspace payoff, so \emph{I}\xspace go to the subgame with $\trianglelefteq$-maximal value. Therefore, using the inductive hypothesis, $\delta({\mathbf{O}:G_1 \wedge G_2}) = \max\{\delta({\mathbf{O}: G_1}), \delta({\mathbf{O}: G_2})\} = \max\{-\mathrm{deg}_\mathcal{I}^G(G_1), -\mathrm{deg}_\mathcal{I}^G( G_2)\} \allowbreak = - \min\{\mathrm{deg}_\mathcal{I}^G(G_1),\mathrm{deg}_\mathcal{I}^G(G_2)\} = -\mathrm{deg}_\mathcal{I}^G(G_1\wedge G_2)$.
\end{proof}
\section{Towards Preferred Model Entailment}
In future work we plan to present a lifting of the GTS for GCL to a \emph{provability game} for preferred model entailment\footnote{In preferred model entailment, a set $T$ of QCL-formulas entails a classical formula $F$ if $F$ is true in all preferred models of $T$.}. This lifting is done in two steps. First, the game is extended to a family of \emph{truth-degree comparison games} \cite{FerLanPav20, AlexandraGoedel} parametrized by $r\in Z$. The rules of this game closely follow the rules of $\mathbf{NG}$ to ensure that \emph{I}\xspace have a winning strategy in the new game iff \emph{I}\xspace have a strategy for $\mathbf{NG}$ with payoff $\trianglerighteq r$.
In the second step this game is lifted to a \emph{disjunctive game} \cite{FMGiles,RobHybridLogic}. Intuitively, the two players play all GTS-games over a fixed formula simultaneously over all models. Additionally, \emph{I}\xspace am allowed to make back-up copies of game states, which \emph{I}\xspace can return to later. \emph{I}\xspace win this game iff \emph{I}\xspace win in at least one back-up copy. We will show that the disjunctive game adequalty models preferred model entailment. Furthermore, \emph{My}\xspace winning strategies directly correspond to proofs in a cut-free sequent-calculus.
The technique of disjunctive states has already been demonstrated for a number of GTS for different logics~\cite{FMGiles,RobHybridLogic,FerLanPav20, AlexandraGoedel}. The case of GCL is the first to require a two-step lifting and give rise to a deduction/refutation system~\cite{Goranko2019-GORHDS}.
\section{Conclusion}
This paper proposes game semantics for the language of Qualitative Choice Logic (QCL), and thereby show that game-theoretic semantics (GTS) are well-suited for logics such as QCL in which soft- and hard-constraints are expressed in a single language.
On the one hand, we show that the degree-based semantics of QCL can be captured naturally via GTS.
The notion of optionality, which must be defined a-priori in QCL, arises naturally in our setting as a property of game trees.
On the other hand, we make use of GTS negation to introduce a novel semantics for the language of QCL. We show that this new semantics avoids issues with negation in QCL and Prioritized QCL (PQCL)
while retaining desirable properties such as associativity of ordered disjunction.
Regarding future work, we outlined how our game semantics can be lifted to a provability game by which a cut-free sequent calculus can be obtained. We also plan to examine our new semantics with respect to computational properties, and to investigate how our approach can be adapted to formalisms related to QCL such as other choice logics \cite{BoudjelidaBenferhat2016ccl, BernreiterEtAl2020asp, BernreiterEtAl2021} or the lexicographic logic introduced by Charalambidis, Papadimitriou, Rondogiannis, and Troumpoukis~\cite{CharalambidisEtAl2021}.
\clearpage
\printbibliography
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,856 |
Q: Fetching gitlab repo list : says "401 Unauthorized" I am trying to get repo list from gitlab using OAuth token.
My code looks something like this ... ("github.com/xanzy/go-gitlab")
repositories := []string{}
client, _ := gitlab.NewClient(gitRepoRequest.Token, gitlab.WithBaseURL("https://gitlab.com/api/v4"))
fmt.Println("client...", client.ContainerRegistry)
projects, _, projectListErr := client.Projects.ListProjects(&gitlab.ListProjectsOptions{})
for _, project := range projects {
fmt.Println("ID===", project.ID)
fmt.Println("NAME===", project.Name)
}
if projectListErr != nil {
// return err
}
I am not able to get the project list.. the "projectListErr" says ...
GET https://gitlab.com/api/v4/projects: 401 {message: 401 Unauthorized}
I am confident about the token value because I am getting list of all branches for a repo using the same token, that code looks like ... ("github.com/go-git/go-git/v5")
rem := git.NewRemote(gitMemory.NewStorage(), &gitConfig.RemoteConfig{
Name: "origin",
URLs: []string{gitBranchesRequest.Repository},
})
refs, listErr := rem.List(&git.ListOptions{
Auth: &gitHttp.BasicAuth{Username: gitUserName, Password: gitBranchesRequest.Token},
})
Does that mean there is an issue with the library that I am using ? github.com/xanzy/go-gitlab
A: It depends on the type of token you are using.
For instance, a project access token might very well give you access to the list of all branches for a repository (for that project).
But for using the /projects API, 401 means the authentication information is not valid or is missing.
So make sure to use a PAT (Personal Access Token), linked to a user, not a project.
The OP Keval Bhogayata adds in the comments:
I have found the issue.
The library I am using ("xanzy/go-gitlab"), has different client creation functions for different tokens.
I have been using the function that supports personal access token. Instead I was supposed to use "NewOAuthClient" !
// NewOAuthClient returns a new GitLab API client. To use API methods which
// require authentication, provide a valid oauth token.
func NewOAuthClient(token string, options ...ClientOptionFunc) (*Client, error)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 856 |
{"url":"http:\/\/www.codebymath.com\/index.php\/welcome\/about","text":"This site was created as a place for people to write simple computer programs in the context of exploring mathematics.\n\n# Why this site?\n\nA few reasons drove the development of this site.\n\nThe first is that in today's technologically-based, machine driven society, our youth must learn to use computers for more than a hub of digital media. No matter what their field of study, the computer will play a central role. Be it in research or development, to really make progress, one must invariably program a computer, in one form or another. Further, this programming will be, at least loosely, tied to the principles and logic of mathematics.\n\nIn terms of programming, the second is that the modern operating system is an extremely difficult environment under which to program. We think this is a big turn off for most people, kids in particular. These days, it's simply too hard to get a computer to \"do something.\" Are you really going to sit a beginner in front of Xcode? Visual C++? A Unix prompt? No way. And, is popping up an \"about box\" in JavaScript really going to interest people in programming?\n\nWe grew up programming the first home computers, like the TRS-80s. When you turned these on, you had no choice but to start programming them, because they didn't really do anything else. And the programming made sense. Print would put something on the screen, and input would read keys from the keyboard.\n\nAs we look at computer programming environments today, we wonder what ever happened to the being able to type a single line like circle(0,0,5) and seeing a circle drawn on the screen at (0,0) with a radius of 5?\n\nThe \"instant response\" type programming environments, at least for beginners, are hard to find. We believe such simplicity can draw beginners into programming because once you have the circle (which is a \"head\") you can do a line(0,80,0,-30) for the \"body,\" and you are on you way to programming a stick figure on the screen!\n\nThird, we've noticed that math offers a badly needed context for learning how to code. Likewise, coding offers a badly needed context for learning things about mathematics. You can learn math through coding, or coding through math, and this is our the core theme of our lessons. As A.A. Stepanov said in his book on generic programming, \"The separation of computer science from mathematics greatly impoverishes both.\"\n\n# Codebymath.com\n\nAt Codebymath, you'll find a whole slew of coding lessons set in the context of basic mathematical discovery. Here, we'll show you how to do some creative programming to discover $\\pi$ or calculate a tip. Or, you can also learn some creative math that will verify a trigonometry identity or show the difference between sine and cosine. And remember how boring it was to learn how to convert temperature between the $^\\circ F$ and $^\\circ C$ scales? It's a lot more fun to do it using an Arduino and some simple coding, all with an actual temperature feed coming in.\n\n# Technology\n\nThis site is a big mix of PHP and Javascript. The language used to teach the programming is Lua, chosen because of its minimal punctuation and clean syntax. The code-editor is courtesy of CodeMirror, and of course, how would we do anything without jQuery? The symbolic math is provided by GiNaC, which we integrated into the Lua language.\n\n# Contact\n\nWe'd love to hear from you. Idea? Problem? Suggestion? Let us know. Click the 3 dots to reveal our email address: t...@gmail.com","date":"2017-06-27 20:55:19","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\": 0.20248764753341675, \"perplexity\": 1301.224657424785}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-26\/segments\/1498128321553.70\/warc\/CC-MAIN-20170627203405-20170627223405-00693.warc.gz\"}"} | null | null |
San Roque é uma cidade espanhola da , O município de San Roque tem como lema "la ciudad donde reside la de Gibraltar" ("a cidade onde reside [a cidade] de Gibraltar"). Esta situação ocorre devido à tomada de Gibraltar, por parte dos Britânicos, em 1704, na sequência da Guerra de Sucessão Espanhola. A população espanhola que vivia em Gibraltar é forçada a sair e encontra abrigo nos arredores em lugares que, outrora, tinham sido ocupados por muçulmanos ainda antes da Reconquista Cristã. Um destes lugares era a atual cidade de San Roque cuja fundação data desse tempo. A deslocação dos habitantes de Gibraltar para San Roque implicou o transporte de todo o arquivo oficial e demais documentação, assim como a parte do património histórico que ainda se conseguiu transferir de Gibraltar para San Roque. A fundação da cidade de San Roque passou a ser considerada, realmente, a cidade de Gibraltar no exílio e é por isso que o lema da cidade é "la ciudad donde reside la de Gibraltar", quer dizer, "a cidade onde reside (a cidade) de Gibraltar".
As terras da cidade incluem a área da moderna La Línea de la Concepción.
História
As ruínas de Carteia estão localizadas na cidade de San Roque.
Municípios de Cádis (província)
Municípios por nome da Andaluzia
Municípios da Espanha por nome
Localidades de Cádis (província)
Localidades da Andaluzia
Localidades da Espanha | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,517 |
using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using Cachengue.DesignByContract;
namespace Cachengue.Providers
{
/// <summary>
/// A in memory fast cache provider.
/// </summary>
public class MemoryCacheProvider : CacheProviderBase
{
private readonly Dictionary<string, object> _cache = new Dictionary<string, object>();
private readonly ICacheExpirations _expirations = new InMemoryCacheExpirations();
/// <summary>
/// Gets a value indicating whether the cache provider is available.
/// </summary>
/// <value>
/// <c>true</c> if the cache provider is available; otherwise, <c>false</c>.
/// </value>
public override bool IsAvailable
{
get { return true; }
}
/// <summary>
/// Gets the size.
/// </summary>
/// <value>
/// The size.
/// </value>
public override int Size
{
get { return Cache.Count; }
}
/// <summary>
/// Gets the stored cache keys
/// </summary>
/// <value>
/// The keys.
/// </value>
public override string[] Keys
{
get { return Cache.Keys.Cast<string>().ToArray(); }
}
/// <summary>
/// Gets the cache.
/// </summary>
/// <value>
/// The cache.
/// </value>
protected virtual IDictionary Cache
{
get { return _cache; }
}
/// <summary>
/// Gets the cache expirations.
/// </summary>
/// <value>
/// The cache expirations.
/// </value>
protected virtual ICacheExpirations CacheExpirations
{
get { return _expirations; }
}
/// <summary>
/// Tries to get the value from the cache.
/// </summary>
/// <param name="key">The key.</param>
/// <param name="type">The type.</param>
/// <param name="value">The value.</param>
/// <returns>
/// <c>true</c> if the value exists on the cache, otherwise <c>false</c>.
/// </returns>
public override bool TryGetValue(string key, Type type, out object value)
{
Check.Require<ArgumentNullException>(!string.IsNullOrWhiteSpace(key), "The key is required");
Check.Require<ArgumentNullException>(type != null, "The type is required");
if (Contains(key))
{
value = Cache[key];
return true;
}
value = null;
return false;
}
/// <summary>
/// Stores the object on the cache.
/// </summary>
/// <param name="key">The key.</param>
/// <param name="type">The object type to store.</param>
/// <param name="value">The value.</param>
/// <param name="options">The options.</param>
public override void SetValue(string key, Type type, object value, CacheOptions options)
{
Check.Require<ArgumentNullException>(!string.IsNullOrWhiteSpace(key), "The key is required");
Check.Require<ArgumentNullException>(type != null, "The type is required");
Check.Require<ArgumentNullException>(options != null, "Cache options absolute expiration is required");
Cache[key] = value;
CacheExpirations.SetExpiration(key, options.ExpirationSeconds);
}
/// <summary>
/// Determines whether the specified key exists on the cache.
/// </summary>
/// <param name="key">The key.</param>
/// <returns>
/// <c>true</c> if the specified key exists; otherwise, <c>false</c>.
/// </returns>
public override bool Contains(string key)
{
Check.Require<ArgumentNullException>(!string.IsNullOrWhiteSpace(key), "The key is required");
CheckExpiration(key);
return Cache.Contains(key);
}
/// <summary>
/// Deletes the specified key from the cache.
/// </summary>
/// <param name="key">The key.</param>
/// <returns>
/// <c>true</c> if the key was succesfully removed; otherwise, <c>false</c>.
/// </returns>
public override bool Remove(string key)
{
Check.Require<ArgumentNullException>(!string.IsNullOrWhiteSpace(key), "The key is required");
CheckExpiration(key);
if (!Cache.Contains(key))
{
return false;
}
Cache.Remove(key);
return true;
}
/// <summary>
/// Removes all the keys from the cache.
/// </summary>
public override void FlushAll()
{
Cache.Clear();
CacheExpirations.Clear();
}
private void CheckExpiration(string key)
{
if (CacheExpirations.KeyHasExpired(key))
{
Cache.Remove(key);
}
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,554 |
Q: Entity Framework Set Navigation Property using Reflection I built an Excel importer that is dynamic. Using reflection, its assigning the values to a new instance of an EF object and adding the EF object to the DbSet.
public class Lease
{
public int Id { get; set; }
public int StatusId { get; set; }
public LeaseStatus { get; set; }
}
public class LeaseStatus
{
public int Id { get; set; }
public string Name { get; set; }
public virtual ICollection<Lease> Leases { get; set; }
}
PROBLEM:
When setting Lease.LeaseStatus property via reflection, I get a System.Data.Entity.Infrastructure.DbUpdateExceptionback when saving the DbSet.
INNER EXCEPTION:
System.Data.SqlClient.SqlException: The INSERT statement conflicted with the FOREIGN KEY constraint "FK_Leases_LeaseStatuses". The conflict occurred in database "MyDatabaseName", table "dbo.LeaseStatus", column 'Id'. The statement has been terminated.
QUESTION:
How can I set a navigation property via reflection?
If I'm doing it correctly, what may be causing the Exception?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,237 |
The Cratomorphini are a tribe of fireflies of the large subfamily Lampyrinae. The genera placed here often contain well-sized members of their family. The larvae of many species climb trees to feed on snails. This group contains a few "lightning bugs" (flashing fireflies) from North America, e.g. the genus Pyractomena. Further south in the American tropics, Aspisoma can be found.
Systematics
The group has recently been examined using molecular phylogenetics, using fairly comprehensive sampling.
Genera
Aspisoma Laporte, 1833
Aspisomoides Zaragoza-Caballero, 1995
Cassidomorphus Motschulsky, 1853
Cratomorphus Motschulsky, 1853
Micronaspis Green, 1948
Paracratomorphus Zaragoza-Caballero, 2013
Pyractomena LeConte, 1845
References
Lampyridae | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,338 |
Q: How to query songs list in android (excluding a specific folder) using cursorloader? Following is my code to fetch all the songs from android device:
String[] proj = { MediaStore.Audio.Media._ID,
MediaStore.Audio.Media.DATA,
MediaStore.Audio.Media.DISPLAY_NAME,
MediaStore.Audio.Media.SIZE };
musiccursor = managedQuery(MediaStore.Audio.Media.EXTERNAL_CONTENT_URI,proj, null, null, null);
music_column_index=musiccursor.getColumnIndexOrThrow(MediaStore.Audio.Media.DISPLAY_NAME);
music_column_index = musiccursor.getColumnIndexOrThrow(MediaStore.Audio.Media.SIZE);
The above gives me list of all the songs in any of the folders in the device however i dont want to fetch songs from a specific folder(say music_folder).Can somebody help to modify the query?
A: Try this:
String[] proj = { MediaStore.Audio.Media._ID,
MediaStore.Audio.Media.DATA,
MediaStore.Audio.Media.DISPLAY_NAME,
MediaStore.Audio.Media.SIZE };
String selection = MediaStore.Audio.Media.DATA +" NOT LIKE '%/music_folder/%'";
musiccursor = managedQuery(MediaStore.Audio.Media.EXTERNAL_CONTENT_URI,proj, selection, null, null);
music_column_index=musiccursor.getColumnIndexOrThrow(MediaStore.Audio.Media.DISPLAY_NAME);
music_column_index = musiccursor.getColumnIndexOrThrow(MediaStore.Audio.Media.SIZE);
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,614 |
Each May, Better Hearing & Speech Month (BHSM) provides an opportunity to raise awareness about hearing health and communication disorders.
"Communication Takes Care" is the BHSM 2016 theme chosen by the American Speech-Language-Hearing Association (ASHA).
The ability to speak, hear, and understand language and conversation are central to almost every aspect of daily life. Yet, these skills are often taken for granted until someone loses them. For older Americans, communication disorders are among the most common challenges they may face. Unfortunately, these disorders may go untreated for years—or may never be treated. Often, lack of treatment or treatment delays are due to myths about certain disorders (such as "they are just part of the normal aging process") or outdated perceptions of treatment. During Better Hearing & Speech Month, it's important to prioritize treatment—because the ability to communicate takes care.
Hearing loss is one of the most common chronic health conditions, affecting 50 million Americans. It is highly prevalent among adults, often with serious impact on daily life and functioning. In fact, 8.5% of adults aged 55–64 have disabling hearing loss. Nearly 25% of those aged 65–74 and 50% of those who are age 75 and older have disabling hearing loss. Unfortunately, among adults aged 70 and older who have hearing loss and who could benefit from hearing aids, fewer than one in three (30%) has ever used them. This is in spite of the fact that hearing loss may affect everything from mental health (anxiety, depression, and feelings of social isolation) to vocational success (including premature departure from the workforce) to other health issues (among them, earlier onset of dementia)—and the fact that treatment advances and today's hearing aids are more effective and less noticeable than ever.
Loved ones such as a spouse or adult child are often significantly affected by a family member's communication difficulties. These loved ones are also the people who are in the best position to influence the decision to seek treatment. If you have a concern about a loved one's hearing or speech, encourage them to seek an evaluation from a certified audiologist or speech-language pathologist. If a course of treatment does follow, loved ones play an important role in providing support—from accompanying the person to treatment visits and helping to provide medical information to being compassionate and understanding throughout the process. (For help finding a certified professional, visit http://www.asha.org/profind).
Better Hearing and Speech Month is a time to reflect on the benefits and experiences we gain because of healthy hearing.
The ability to hear is a powerful thing – hearing makes memories of special times shared with loved ones, provides understanding in work and social settings, and connects us to the world around us. In celebration of BHSM, the Hear the World Foundation created an infographic that shows some interesting facts about hearing.
Our ears can distinguish up to 400,000 different sounds and process twice as many impressions as our eyes! Our hearing is used 24 hours a day, is the key to communication, and hence, to social interaction. The ear is man's most efficient but also most sensitive sensory organ. However, its importance in our modern, visually-oriented world is often underestimated.
The Hear the World Foundation created "The Power Beyond Hearing" infographic to raise awareness about the importance and efficiency of our hearing, the influence our hearing has on various aspects of our lives, and how we can protect it.
A noise level of less than 85 dB is considered safe for our ears.
When listening to music on audio devices, keep the level no louder than 60% of the maximum volume.
Listen to music through headphones that fit well and decrease ambient noise.
Wear ear plugs at concerts, in discos, and in other noisy places. (Ear protection can reduce the noise levels by 5 to 45 dB). Maintain an adequate distance from the source of the noise to avoid damage to hearing.
Deliberately take acoustic breaks and turn off all sources of noise (radio, TV, etc.). After going to a concert or disco, or working in a noisy environment, etc. it is especially important that you give your ears a rest of at least 10 hours to enable recovery.
If in spite of precautions, you experience symptoms such as a feeling of pressure in the ear, a dull hearing sensation, or persistent sounds or lingering ringing in the ear, you should rest your hearing as a matter of urgency, drink lots of fluids (which improves the circulation of blood to the hair cells in the cochlea which helps your hearing to function properly), and consult a hearing specialist as soon as possible.
Regardless of noise exposure, be sure to regularly have your hearing checked by a hearing care professional or specialist physician.
© Copyright 2016, Seattle Dizzy Group. All rights reserved. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,482 |
\section{Introduction}
The relativistic heavy ion collisions realized at the Brookhaven RHIC and at the CERN LHC produce a plasma-like system whose properties are similar to the ones expected for the quark-gluon plasma (QGP).
A dense strongly interacting medium is created, with the relevant degrees of freedom not represented by the individual partons, but more appropriately described as a fluid \cite{Heinz:2004pj,Shuryak:2014zxa}.
Simulations aimed at reproducing the experimental observations for, e.g., the elliptic flow which is due to the pressure anisotropy, point to an almost perfect fluid behavior, with a small viscosity to entropy density ratio $\displaystyle{\eta/s}\sim {\cal O}$(0.1) and a short time of ${\cal O}$(1~fm/c) to reach thermal equilibrium.
Perturbative QCD calculations predict larger values of $\displaystyle{\eta/s}$: this leads one to conclude that the created plasma is a realization of a strongly coupled deconfined phase of QCD.
Understanding in detail the features observed in experiment, in particular investigating the system early time dynamics, how the out-of-equilibrium strongly interacting plasma evolves towards a thermalized state, are challenging tasks.
Conventional methods make use of the idea that, soon after the collisions, ensembles of strong, coherent, longitudinal color electric and color magnetic fields are produced, then the evolution of such field configurations is numerically studied (see, e.g., \cite{Ruggieri:2015yea} and references therein).
A completely different theoretical approach exploits the gauge/gravity, in particular the AdS/CFT, duality.
This relates a strongly coupled gauge theory defined in a $d$-dimensional Minkowski space and a classical gravity theory living in a ($d$+1)-dimensional asymptotically AdS space times a compact manifold, with the Minkowski space representing the boundary of the AdS one \cite{Maldacena:1997re,Witten:1998qj,Gubser:1998bc}\footnote{For an introduction to the AdS/CFT principles and applications see the book \cite{Ammon:2015wua}.}.
The holographic approach permits to study how a strongly coupled system, driven out-of-equilibrium through an external quench, reaches a thermalized state, with a determination, e.g., of the time needed for the equilibration process.
In the gauge/gravity duality framework, thermalization in the gauge theory corresponds to the formation of a black brane in the higher dimensional space.
For an expanding strongly coupled plasma displaying a perfect fluid behavior, the boundary stress-energy tensor $T_{\mu\nu}$ components obey the Bjorken's relations \cite{Bjorken:1982qr}.
According to the AdS/CFT correspondence dictionary, each operator in the gauge theory has a dual field in the gravity side, and the stress-energy tensor has the metric as a dual.
The dual of $T_{\mu \nu}$ fulfilling Bjorken's hydrodynamics is identified as a black brane metric with time-dependent horizon \cite{Janik:2005zt}.
Corrections to the perfect fluid behavior can be analyzed through a corresponding gravity dual.\footnote{An overview of the fluid/gravity correspondence can be found in \cite{Hubeny:2011hd}. }
The early-time dynamics and subsequent thermalization have been investigated in recent years, employing holographic techniques within different contexts
\cite{Kovchegov:2007pq,AbajoArrastia:2010yt,Bhattacharyya:2009uu,Albash:2010mv,Aparicio:2011zy,Keranen:2011xs,Galante:2012pv,Baron:2012fv,Caceres:2012em,Basu:2011ft,Auzzi:2013pca,Caceres:2013dma,Liu:2013iza,Basu:2013soa,
Zeng:2013fsa,Caceres:2014pda,Liu:2013qca,Fischler:2013fba,Hubeny:2013dea,Alishahiha:2014cwa,Fonda:2014ula,Zhang:2015dia}.
In particular, a way to study thermalization of a strongly coupled plasma has been proposed in Refs.~\cite{Chesler:2008hg,Chesler:2009cy} (and reviewed in \cite{Chesler:2013lia}): a distortion of the boundary metric is implemented to mimic an effect driving the system out of equilibrium.
The dual metric is computed by solving Einstein's equations in the higher dimensional space, and imposing appropriate boundary conditions.
Using the holographic renormalization procedure \cite{deHaro:2000xn}, the components of the boundary stress-energy tensor are determined in terms of the coefficients of the near-boundary expansion of the gravity metric.
When the boundary distortion, the {\it quench}, is impulsive with finite time duration, one can determine the elapsed time for the stress-energy tensor components to reach the hydrodynamic form after the quench is switched off, accessing the so-called thermalization time.
Hence, the observables are the system energy density and the pressures, which are studied as time proceeds.
Other studies deal with systems put out of equilibrium through initial conditions, while the boundary metric is unperturbed \cite{Heller:2012km,Heller:2013oxa}.
In this case the late-time physics is not described by hydrodynamics, and thermalization is related to holographic isotropization, with the thermalization time defined as the time after which pressure anisotropy is small compared to the energy density.
Another way of introducing a quench is letting the source of some operator vary with time, as in \cite{Ishii:2015gia} and references therein.
In particular, in \cite{Ishii:2015gia} a confining gauge theory is considered, in which a dilaton, with time-dependent UV boundary condition, breaks the conformal invariance.
Thermalization is studied by computing the time evolution of the energy-momentum tensor and of the one-point function of the scalar operator.
These investigations can provide useful hints for the heavy ion collision phenomenology \cite{CasalderreySolana:2011us,Arefeva:2012a}.
Beside local quantities, as the components of $T_{\mu\nu}$, the holographic methods permit one to access nonlocal probes evolving in time as well, such as the two-point correlation function of boundary theory operators, and the expectation values of Wilson loops defined on the boundary \cite{Balasubramanian:2010ce}.
Their calculation requires the length of the geodesics in the bulk connecting the two boundary points in the correlation function, or the area of the extremal surface plugging in the bulk and having the Wilson loop as a contour at the boundary.
Hence, such observables get information from deep regions in the bulk, accessing the IR regime of the boundary field theory.
An example of the use of nonlocal probes has been worked out using a Vaidya metric which describes the collapse of a thin mass shell from the boundary into the bulk \cite{Balasubramanian:2010ce,Balasubramanian:2011ur}.
At late times this metric coincides with a black hole one, dual to the thermalized gauge theory on the boundary. Thermalization has been studied by comparing the nonlocal probes in the Vaidya geometry with those obtained for a black hole metric with a time-independent horizon corresponding to the equilibrium temperature:
it was observed that the time for thermalization depends on the size of the probe in the boundary theory.
The finite chemical potential case has been investigated in a Reissner-Nordstr\"om-AdS black hole Vaidya-type metric \cite{Galante:2012pv}.
Larger thermalization times than those observed in the case of vanishing charge were found for the two-point function and for the expectation value of rectangular Wilson loops.
Different realisations have also been analytically studied \cite{Pedraza:2014moa}.
In \cite{Buchel:2014gta} a quench was introduced in the boundary theory through an operator with time-dependent mass dual to a scalar field in AdS black hole (AdS/BH) geometry.
Given the backreaction of the scalar field on the metric, the perturbed background has been computed using pseudospectral methods while the geometry thermalizes to a static black-hole AdS space, with a temperature higher than the initial one.
Local (e.g. one-point correlation function of the operator dual to the scalar field) and nonlocal (two-point correlation functions and entanglement entropy) observables have been investigated, finding again that the thermalization time can depend on the size of the probe.
The above examples of nonlocal probes do not have a direct connection with the study of thermalization meant as the onset of a hydrodynamic regime, which is instead the main purpose of the present study.
We investigate the thermalization of a system taken out of equilibrium, computing the time needed by nonlocal observables to start behaving hydrodynamically. The comparison between the results obtained by local and nonlocal observables discloses different characteristic times.
We evaluate nonlocal observables in the case of two representative models of quenches scrutinised in \cite{Bellantuono:2015hxa}, using the computed solution of the Einstein equations and hence considering the full dynamical system.
In particular, two-point correlation functions of large dimension boundary operators and the expectation value of an infinite rectangular strip and of a circular Wilson loop are determined, and their time dependence is used to investigate the relaxation towards the hydrodynamic regime.
The distance between the points at which the correlation function is evaluated, and the size of Wilson loops represent the new variables in terms of which thermalization is studied.
The plan of the paper is the following. In Section \ref{sec2} we review the results obtained in \cite{Bellantuono:2015hxa} using local observables, the energy density, entropy density and pressures,
for two models of quenches.
In Section \ref{sec3} we provide the expressions for the two-point correlation functions and the two kinds of Wilson loops used in the calculation. The results for the nonlocal probes are presented in Section \ref{sec4}, and the conclusions are collected in the last Section.
\section{Thermalization by boundary sourcing: results from local probes}\label{sec2}
In \cite{Bellantuono:2015hxa} the thermalization of a boost-invariant non-Abelian plasma has been studied adopting the method of boundary sourcing to drive the system far from equilibrium \cite{Chesler:2008hg,Chesler:2009cy}.
The stress-energy tensor of the boundary theory $ T^\mu_\nu =\frac{N_c^2}{2 \pi^2}\, {diag}(-\epsilon, p_\perp,p_\perp, p_\parallel)$ is written in terms of the system energy density $\epsilon$, of the pressure $p_\perp$ along one of the two transverse directions (with respect, e.g., to the heavy ion collision axis) and of the pressure $p_\parallel$ in the longitudinal direction.\footnote{Throughout the paper, the energy density and pressures are referred to without considering the factor $\frac{N_c^2}{2 \pi^2}$.}
The boundary 4$d$ coordinates are denoted as $x^\mu=(x^0,x^1,x^2,x^3)$, with $x^3=x_\parallel$ direction identified with the collision axis along which the plasma expands. The investigated system has boost invariance along this axis, together with translational and $O(2)$ rotational invariances in the transverse plane $x_\perp=\{x^1,\,x^2 \}$.
The 4$d$ line element: $ds^2_4=-d\tau^2+dx_\perp^2+\tau^2 dy^2$ is expressed in terms of the proper time $\tau$ and of the spacetime rapidity $y$, defined through $x^0=\tau \cosh y$ and $x_\parallel=\tau \sinh y$.
The system is driven out of equilibrium by a quench on the boundary metric.
The quench, described by the profile $\gamma(\tau)$, modifies the line element:
\begin{equation}
ds^2_4=-d\tau^2+e^{\gamma(\tau)} dx_\perp^2+\tau^2 e^{-2\gamma(\tau)} dy^2 \,\, , \label{metric4D}
\end{equation}
leaving the spatial three-volume unchanged and respecting the translational and $O(2)$ symmetries in the transverse plane.
The 5$d$ spacetime on which the gravity dual is defined, having the metric \eqref{metric4D} as a boundary, is described using
Eddington-Finkelstein coordinates, with $r$ the radial coordinate. The 5$d$ metric is written as
\begin{equation}
ds^{2}=-A(r,\tau)d\tau^{2}+\Sigma(r,\tau)^{2}e^{B(r,\tau)}d {x}_{\perp}^{2}+\Sigma(r,\tau)^{2}e^{-2B(r,\tau)}dy^{2}+2d\tau dr \,\,\,.
\label{metric5D}
\end{equation}
The boundary corresponds to $r \to \infty$.
The metric functions $A$, $\Sigma$ and $B$ depend only on $r$ and $\tau$ due to the chosen symmetries.
They have been determined by solving 5$d$ Einstein equations with a negative cosmological constant, that can be cast in the form \cite{Chesler:2009cy}:
\begin{eqnarray}
&&\Sigma ({\dot \Sigma})^\prime +2 \Sigma^\prime {\dot \Sigma}-2 \Sigma^2=0 \nonumber \\
&& \Sigma ({\dot B})^\prime+\frac{3}{2} \left(\Sigma^\prime {\dot B}+B^\prime {\dot \Sigma}\right)=0 \nonumber \\
&& A^{\prime \prime} +3 B^\prime {\dot B} -12 \frac{\Sigma^\prime {\dot \Sigma} }{\Sigma^2}+4=0\label{ein} \\
&& {\ddot \Sigma}+\frac{1}{2} \left( {\dot B} ^2 \Sigma -A^\prime {\dot \Sigma} \right) =0 \nonumber \\
&& \Sigma^{\prime \prime}+\frac{1}{2} B^{\prime 2} \Sigma =0 \,. \nonumber
\end{eqnarray}
In \eqref{ein}, for a generic function $\xi(r,\tau)$, the derivatives $\xi^\prime=\partial_r \xi$ and ${\dot \xi}= \partial_\tau \xi+\frac{1}{2} A \partial_r \xi$ denote directional derivatives along the infalling radial null geodesics and the outgoing radial null geodesics, respectively.
Two boundary conditions are imposed.
The first states that the metric (\ref{metric5D}) produces the 4$d$ metric Eq.~(\ref{metric4D}) for $r \to \infty$.
Moreover, at the initial time slice $\tau=\tau_i$ when the distortion of the boundary metric is switched on, one has to start from the AdS$_5$ bulk metric:
\begin{equation}
ds^2= r^2 \left[ -d \tau^2+ d x_\perp^2 + \left( \tau+\frac{1}{r} \right)^2 dy^2 \right] + 2 dr d\tau \,\,\, . \label{AdS5}
\end{equation}
To investigate whether and how thermalization depends on particular boundary sourcing,
several distortion profiles have been considered in \cite{Bellantuono:2015hxa}. They are characterized by a function $\gamma(\tau)$ representing quenches with different number, structures and intensities, generically written as
\begin{equation}
\gamma(\tau) =w \left[ \tanh \left(\frac{\tau -\tau_0}{\eta} \right) \right]^7 \,+\sum_{j=1}^{N}\gamma_j(\tau,\tau_{0,j}) \label{profile}
\end{equation}
with
\begin{equation}
\gamma_j(\tau,\tau_{0,j}) = c_j f_j(\tau,\tau_{0,j})^6 e^{-1/f_j(\tau,\tau_{0,j})} \Theta\left(1-\frac{(\tau-\tau_{0,j})^2}{\Delta_j^2}\right)\,\, \label{profile1}
\end{equation}
and
\begin{equation}
f_j(\tau,\tau_{0,j})= 1- \frac{(\tau-\tau_{0,j})^2}{\Delta_j^2} \,\,\, . \label{profile2}
\end{equation}
The set of parameters $w, \eta, \tau_0, \tau_{0,j}, c_j$ and $ \Delta_j$ specifies the different quench models: here we focus on the models ${\cal B}$ and ${\cal A}(2)$ studied in Ref.\cite{Bellantuono:2015hxa}.
Model ${\cal A}(2)$ represents two short pulses in the boundary metric: the parameters are set to $w=0$, $N=2$, $c_1 = 1$, $\Delta_{1,2}=1$, $\tau_{0,1}=\frac{5 }{4}\Delta_1$, $c_2 = 2$, $\tau_{0,2}=\frac{9}{4} \Delta_2$. The quench ends at $\tau_f^{\cal A}=3.25$.
Model $\cal B$ represents a slow deformation plus a short pulse, and is obtained using $w=\frac{2}{5}$, $\eta=1.2$, $\tau_0=0.25$, $N=1$, $c_1 = 1$, $\Delta_1=1$, $\tau_{0,1}=4 \Delta_1$.
The pulse ends at $\tau_f^{\cal B}=5$, while the slow distortion continues with $\tau$ and approaches a constant value.
In both cases, the quench is switched on at $\tau_i=0.25$.
The profiles $\gamma(\tau)$ are depicted in Fig.~\ref{fig:lgeo}.
The metric functions $A(r,\tau)$, $\Sigma(r,\tau)$ and $B(r,\tau)$ in \eqref{metric5D} have been computed in \cite{Bellantuono:2015hxa} by solving the Einstein equations \eqref{ein} (considered as three dynamical and two constraint equations), with the conditions provided at the initial time slice and on the boundary.
The solutions have allowed us to determine several quantities of interest, in particular the thermalization time obtained comparing the boundary stress-energy tensor to the viscous hydrodynamics behavior.
It is worth recalling that homogeneity, boost invariance and invariance under rotations in the transverse plane imply that the various components of $T_{\mu}^{\nu}$ depend only on the proper time $\tau$ \cite{Bjorken:1982qr}.
Moreover, for a conserved and traceless $T_{\mu}^{\nu}$ the components depend on a single function $f(\tau)$, so that $T_{\mu}^{\nu}$ can be written as
\begin{equation}
T_{\mu}^{\nu}=diag \left(-f(\tau),\,f(\tau)+\displaystyle{\frac{1}{2}}\tau f^\prime(\tau),\,f(\tau)+\displaystyle{\frac{1}{2}}\tau f^\prime(\tau),\, -f(\tau)-\tau f^\prime(\tau)\right) \,\,\,\ .
\end{equation}
For a perfect fluid, the equation of state $\epsilon=3 p$ and the relation $p=p_\parallel=p_\perp$ fix the $\tau$ dependence: $\epsilon(\tau)=\displaystyle{\frac{const}{\tau^{4/3}}}$, which is modified if viscous effects are included \cite{Janik:2005zt}.
An effective temperature $T_{eff}(\tau)$ can be defined through the relation $\epsilon(\tau)= \displaystyle{\frac{3}{4}} \pi^4 T_{eff}(\tau)^4$, and for $T_{eff}(\tau)$ the subleading terms in the large-$\tau$ expansion can be computed in ${\cal N}=4$ SYM, with the result \cite{Heller:2007qt}:
\begin{eqnarray}
T_{eff}(\tau)&=&\frac{\Lambda}{(\Lambda \tau)^{1/3}} \Bigg[ 1-\frac{1}{6 \pi (\Lambda \tau)^{2/3}}+\frac{-1+\log 2}{36 \pi^2 (\Lambda \tau)^{4/3} }
+\frac{-21+2\pi^2+51 \log 2 -24 (\log 2)^2}{1944 \pi^3 (\Lambda \tau)^2} \nonumber \\ &+& {\cal O}\left( \frac{1}{(\Lambda \tau)^{8/3}} \right )\Bigg] \,\,\, , \label{Teff1}
\end{eqnarray}
and $\Lambda$ a parameter.
This expression corresponds for the energy density $\epsilon$, for the longitudinal $p_\parallel$ and for the transverse $p_\perp$ pressures, to the large $\tau$ dependence given by
\begin{eqnarray}
\epsilon&=& \frac{3 \pi^4 \Lambda^4}{4 (\Lambda \tau)^{4/3} }\left[ 1-\frac{2c_1}{ (\Lambda \tau)^{2/3}}+\frac{c_2}{ (\Lambda \tau)^{4/3}} + {\cal O}\left( \frac{1}{(\Lambda \tau)^2} \right )\right] \,\,\, , \label{hydroeps} \\
p_\parallel (\tau)&=&\frac{ \pi^4 \Lambda^4}{ 4(\Lambda \tau)^{4/3} } \left[ 1-\frac{6c_1}{ (\Lambda \tau)^{2/3}}+\frac{5c_2}{ (\Lambda \tau)^{4/3}} + {\cal O}\left( \frac{1}{(\Lambda \tau)^2} \right )\right] \,\,\, , \label{hydroppar} \\
p_\perp (\tau) &=& \frac{ \pi^4 \Lambda^4}{ 4(\Lambda \tau)^{4/3} } \left[ 1-\frac{c_2}{ (\Lambda \tau)^{4/3}} + {\cal O}\left( \frac{1}{(\Lambda \tau)^2} \right ) \right] \,\,\, ,\label{hydropperp}
\end{eqnarray}
with $c_1=\displaystyle{\frac{1}{3 \pi}}$ and $c_2=\displaystyle{\frac{1+2 \log{2}}{18 \pi^2}}$.
$\Lambda$ depends on the quench model: the values $\Lambda^{\cal B}=1.12$ and $\Lambda^{{\cal A}}=1.73$
have been obtained in \cite{Bellantuono:2015hxa}. The large $\tau$ dependence of the pressure ratio $\displaystyle \frac{p_\parallel}{p_\perp}$ and anisotropy $\displaystyle \frac{\Delta p}{\epsilon}=\frac{p_\perp-p_\parallel}{\epsilon}$ derives from the above expressions.
The results in \cite{Bellantuono:2015hxa} are obtained comparing the energy density and pressures, computed by the holographic renormalization procedure from the explicit metric functions
$A(r,\tau)$, $\Sigma(r,\tau)$ and $B(r,\tau)$ in \eqref{metric5D}, with the asymptotic expressions \eqref{hydroeps}, \eqref{hydroppar} and \eqref{hydropperp}. The results can be summarized as follows.
Regardless of the quench, the energy density evolves according to the viscous hydrodynamic expression (\ref{hydroeps}) as soon as the impulsive quench is switched off, i.e. at $\tau_f^{\cal B}=5$ and $\tau_f^{\cal A}=3.25$ for two models of interest.
For pressures, a thermalization time $\tau_p$ can be defined, considering the system thermalized when the pressure ratio differs from the asymptotic expression obtained from \eqref{hydroppar} and \eqref{hydropperp} by less than 5$\%$.
In model ${\cal B}$ the thermalization time is $\tau_p^{\cal B}=6.74$, with a delay $\tau_p^{\cal B}-\tau_f^{\cal B}=1.74$; in model ${\cal A}(2)$ the values $\tau_p^{\cal A}=6$ and $\tau_p^{\cal A}-\tau_f^{\cal A}=2.75$ have been found. In physical units,
setting the effective temperature at the end of the quench to $T_{eff}=500$ MeV, the delays correspond to $0.42$ fm/c in model ${\cal B}$, and to $1.03$ fm/c in model ${\cal A}(2)$, which are comparable to the values
inferred from phenomenological analyses of heavy ion collisions.
The metric functions $A(r,\tau)$, $\Sigma(r,\tau)$ and $B(r,\tau)$ appearing in \eqref{metric5D} and computed in \cite{Bellantuono:2015hxa} will be used in the analysis of various nonlocal probes.
Also in these cases, to study thermalization using different observables it is necessary to compare the results with those obtained in the hydrodynamic setup.
The 5$d$ metric reproducing, through the holographic renormalization procedure, the results in (\ref{hydroeps}-\ref{hydropperp}) must be known.
In the case of 5$d$ Fefferman-Graham coordinates, the metric was derived in \cite{Janik:2005zt,Janik:2006ft,Heller:2007qt,Heller:2012je}; in the case of Eddington-Finkelstein coordinates this was done in \cite{vanderSchee:2012qj}.
To have a link with the results for the stress-energy tensor components, the 5$d$ metric dual to viscous hydrodynamics can be written as
\begin{equation}
ds^2=-A^H(r,\tau) d\tau^2+ [\Sigma^H(r,\tau)]^2 e^{B^H(r,\tau)} dx_\perp^2+ [\Sigma^H(r,\tau)]^2 e^{-2B^H(r,\tau)}dy^2 + 2 dr d\tau \,\,\, , \label{metric5Dhydro}
\end{equation}
with the metric functions expressed in terms of the energy density and pressures:
\begin{eqnarray}
A^H(r,\tau) &=& r^2 \left(1 - \frac{4}{3 r^4} \epsilon(\tau) \right) \nonumber \\
\Sigma^H(r,\tau) &=&r \left(\tau+\frac{1}{r}\right)^{1/3} \label{AdSBH} \\
B^H(r,\tau) &=&\frac{1}{3 r^4} \left(p_\perp (\tau)-p_\parallel (\tau) \right)-\frac{2}{3}\log\left(\tau +\frac{1}{r}\right) \,\,. \nonumber
\end{eqnarray}
Notice that using \eqref{metric5Dhydro} and \eqref{AdSBH}, the relations \eqref{hydroeps}-\eqref{hydropperp} are reproduced also if a constant is added to the metric function $B^H$: $B^H \to B^H +c$.
In the case of model $\mathcal{B}$ we exploit this freedom and add to $B^H$ the constant $\gamma(\infty)$ in order to take into account the residual effect of the quench that persists in this model at late times.
In the following, the hydrodynamic expressions for the various nonlocal probes are determined using Eqs.~\eqref{metric5Dhydro}, \eqref{AdSBH}, and the expressions \eqref{hydroeps}-\eqref{hydropperp} with $\Lambda$ determined for each model.
\section{Nonlocal probes of thermalization}\label{sec3}
We now consider a set of nonlocal probes of thermalization of the boundary field theory, the equal-time two-point correlation functions and the Wilson loops of different shapes, in particular circular and rectangular.
Their expressions in the holographic framework are given in the following.
Let us first consider equal-time two-point correlation functions and their geodesic approximation.
According to the AdS/CFT dictionary, a boundary scalar operator $\mathcal{O}(t,\bm{x})$ of conformal dimension $\Delta$ in $d$ dimensions is dual to a bulk field $\phi(t,\bm{x},r)$ with mass $m$ in $(d+1)$ dimensions, with $\Delta=\frac{1}{2}(d+\sqrt{d^2+4 m^2})$.
When an expression of the bulk action is available and the wave equation for $\phi(t,\bm{x},r)$ is solved, the equal-time two-point function $\langle \mathcal{O} (t,\bm{x}) \mathcal{O} (t,\bm{x}') \rangle$ can be determined (in the strong-coupling regime of the boundary theory) starting from the on-shell supergravity action.
For involved bulk geometries, the two-point correlation functions can be computed in the geometric optic limit, in terms of the length $\mathcal{L}$ of the space-like geodesics connecting the two points on the boundary \cite{Balasubramanian:1999zv,Louko:2000tp}:
\begin{equation}\label{geo_approximation}
\langle \mathcal{O} (t,\bm{x}) \mathcal{O} (t,\bm{x}') \rangle \simeq \sum_{\mathrm{geodesics}} e^{-\Delta\, \mathcal{L}} \,\,\, .
\end{equation}
The approximation is effective for boundary theory operators with large conformal dimension, $\Delta\gg 1$.
$\mathcal{L}$ is obtained by extremizing the length of the curves connecting the two points, written generically as
\begin{equation}\label{geo_length}
\mathcal{L} = \int_{P}^Q d\lambda\sqrt{\pm g_{MN}\dot{x}^{M} \dot{x}^{N}},
\end{equation}
in terms of the coordinates $x^{M}(\lambda)$ $(M=1,\dots,d+1)$, the parameter $\lambda$, the boundary points ($P$ and $Q$), the metric $g_{MN}$ and the derivative $\dot{x}^{M}\equiv dx^{M}/d\lambda$ (positive and negative signs in the square root for a space-like or time-like curve).
The geodesic, for which $\mathcal{L}$ is extremal, is determined interpreting the integrand in \eqref{geo_length} as a Lagrangian and solving the corresponding Euler-Lagrange equations.
Another nonlocal probe is the expectation value of Wilson loops.
For a closed contour $\mathcal{C}$, the Wilson loop of the boundary theory is defined as
\begin{equation}\label{WL}
W_{\mathcal{C}}[A]=\frac{1}{N_c}Tr\left(P e^{-ig\oint_{\mathcal{C}}dx^{\mu}A_{\mu}^{a}T^{a}}\right).
\end{equation}
In the strong-coupling limit, the expectation value of \eqref{WL} has a holographic expression \cite{Maldacena:1998im}:
\begin{equation}\label{WL_saddle_point}
\langle W_{\mathcal{C}} \rangle \sim e^{-S_{NG}}
\end{equation}
where $S_{NG}$ is the Nambu-Goto action, the area of the string worldsheet bounded by the curve $\mathcal{C}$:
\begin{equation}
S_{NG}=\frac{1}{2\pi\alpha'}\int d^{2}\xi \sqrt{det\left[g_{MN}\partial_{\alpha}X^{M}\partial_{\beta}X^{N}\right]}\,,
\end{equation}
with $\xi^{\alpha}$ $(\alpha,\beta=1,2)$ the worldsheet coordinates, and $X^{M}\left(\xi^{\alpha}\right)$ the embedding of the surface into the target spacetime.
Two-point correlation functions and the vacuum expectation values of Wilson loops of different shapes, in particular circular and rectangular, can be computed in the holographic setup characterized by the Eddington-Finkelstein coordinates $\left(\tau,\bm{x}_{\perp},y,r\right)$ and the metric (\ref{metric5D}).
To exploit the geodesic approximation \eqref{geo_approximation} for a two-point correlation function, we consider the space-like paths connecting the boundary points $P=\left(t_{0},-\ell/2,x_{2},y\right)$ and $Q=\left(t_{0},\ell/2,x_{2},y\right)$, and extending in the bulk at fixed $(x_{2},y)$.
The coordinate $x_{1}\equiv x$ varies along each curve, the profile of which is described by $\tau(x)$ and $r(x)$. In the middle point $x=0$ the values of $\tau$ and $r$ are
\begin{equation}\label{midpoint_conditions0}
\tau(0)=\tau_* , \qquad r(0)=r_* \,\,\, .
\end{equation}
Moreover, we require
\begin{equation}\label{midpoint_conditions}
\tau'(0)=r'(0)=0 \,\,\, ,
\end{equation}
with the prime indicating a derivative with respect to $x$.
The conditions
\begin{equation}\label{boundary_conditions}
\tau(-\ell/2)=\tau(\ell/2)=t_{0} , \qquad r(-\ell/2)=r(\ell/2)=r_{0}
\end{equation}
are fulfilled at the boundary.
Eq.~\eqref{midpoint_conditions} is due to the $x\leftrightarrow -x$ symmetry along the $\tau$ and $r$ axes, while Eqs.~\eqref{boundary_conditions} involve the cutoff $r_{0}$ in the bulk coordinate, which is needed for the numerical computation as discussed below.
The length of the curves is given by
\begin{equation}\label{our_geo_length}
\mathcal{L} =\int_{\lambda_1}^{\lambda_2} d\lambda \left(-A(r,\tau)\dot{\tau}(\lambda)^2+2\dot{\tau}(\lambda)\dot{r}(\lambda)+\tilde{\Sigma}(r,\tau)\dot{x}(\lambda)^2\right)^{1/2},
\end{equation}
with $\tilde{\Sigma}(r,\tau)\equiv\Sigma(r,\tau)^2e^{B(r,\tau)}$ and the dot indicating a derivative with respect to $\lambda$.
$\lambda_1$ and $\lambda_2$ correspond to $x(\lambda_1)=-\ell/2$ and $x(\lambda_2)=\ell/2$.
This expression, obtained parametrizing the curves in terms of $\lambda$, is analogous to \eqref{geo_length} and allows one to interpret
\begin{equation}
L(\dot{x},\tau,\dot{\tau},r,\dot{r})=\left(-A(r,\tau)\dot{\tau}(\lambda)^2+2\dot{\tau}(\lambda)\dot{r}(\lambda)+\tilde{\Sigma}(r,\tau)\dot{x}(\lambda)^2\right)^{1/2}
\end{equation}
as a Lagrangian and $x(\lambda)$ a cyclic variable with conjugate momentum $p_{x}$ conserved along the curve.
The conservation equation, using \eqref{midpoint_conditions0} and \eqref{midpoint_conditions}, can be expressed in terms of the coordinate $x$:
\begin{equation}\label{conservation}
\frac{\tilde{\Sigma}(r,\tau)}{\left(-A(r,\tau)\tau'(x)^2+2\tau'(x)r'(x)+\tilde{\Sigma}(r,\tau)\right)^{1/2}}=\tilde{\Sigma}\left(r_{*},\tau_{*}\right)^{1/2} \,\, .
\end{equation}
The geodesics equations
\begin{eqnarray}\label{eq-geo1}
& & A(r,\tau) \tau''(x) - r''(x) + \left[ - A(r,\tau) \frac{\partial_{\tau} \tilde{\Sigma}(r,\tau)}{\tilde{\Sigma}(r,\tau)} + \frac{1}{2} \partial_{\tau} A(r,\tau) \right] \tau'(x)^2 + \frac{\partial_{r} \tilde{\Sigma}(r,\tau)}{\tilde{\Sigma}(r,\tau)} r'(x)^2 \nonumber \\ & & + \left[ \frac{\partial_{\tau} \tilde{\Sigma}(r,\tau)}{\tilde{\Sigma}(r,\tau)} - A(r,\tau) \frac{\partial_{r} \tilde{\Sigma}(r,\tau)}{\tilde{\Sigma}(r,\tau)} + \partial_r A(r,\tau) \right] r'(x) \tau'(x) + \frac{1}{2} \partial_{\tau} \tilde{\Sigma}(r,\tau) = 0 \nonumber \\
\end{eqnarray}
and
\begin{equation}\label{eq-geo2}
\tau''(x) + \left[ \frac{1}{2} \partial_r A(r,\tau) - \frac{\partial_{\tau} \tilde{\Sigma}(r,\tau)}{\tilde{\Sigma}(r,\tau)} \right] \tau'(x)^2 - \frac{\partial_{r} \tilde{\Sigma}(r,\tau)}{\tilde{\Sigma}(r,\tau)} r'(x) \tau'(x) - \frac{1}{2} \partial_{r} \tilde{\Sigma}(r,\tau) = 0
\end{equation}
are obtained by combining the Euler-Lagrange equations for $\tau$ and $r$ with the conservation equation \eqref{conservation}. The solution $(r(x),\tau(x))$, corresponding to a pair of input values $\left(r_{*},\tau_{*}\right)$, allows one to determine the geodesic length
\begin{equation}\label{geo_length_on_shell}
\mathcal{L}=\int_{-\ell/2}^{\ell/2} dx\frac{\tilde{\Sigma}(r,\tau)}{\sqrt{\tilde{\Sigma}(r_{*},\tau_{*})}} \,\,\, ,
\end{equation}
with the separation $\ell$ deduced from \eqref{boundary_conditions}.
This expression requires a regularization, which we implement
subtracting from the length \eqref{geo_length_on_shell} the same quantity computed in pure $AdS_5$; the subtraction is carried out in the range of $r$ in which the numerical solution of the bulk geometry has been determined, i.e. for $r$ up to a UV scale $r_0$. For model $\cal B$ the asymptotic constant value $\gamma(t_0\to\infty)$ of the quench profile is taken into account in the subtraction.
The determination of the distance $\ell$ is provided by the relation $r\left(\ell/2 \right)=r_0$.
Typical resulting geodesics, obtained from the computed metric functions in (\ref{metric5D}), are depicted in Fig.~\ref{fig:rgeodes}.
The thermalization of the boundary theory is studied by computing their lengths as time proceeds.
The hydrodynamic expression of the geodesic lengths $\mathcal{L}_{H}$ are determined in the geometry \eqref{metric5Dhydro}-\eqref{AdSBH} with the same regularization.
This allows to define an observable by the difference $\Delta\mathcal{L}=\mathcal{L}-\mathcal{L}_{H}$.
\begin{figure}
\begin{center}
\includegraphics[width = .45\textwidth]{plot3df.pdf}
\caption{\baselineskip 10pt Geodesics obtained in the case of the quench model ${\mathcal B}$ for various $(r_*,\tau_*)$. The shaded area represents the event horizon.}\label{fig:rgeodes}
\end{center}
\end{figure}
In the case of Wilson loops as nonlocal probes of the boundary theory thermalization, we consider two shapes, circles and strips.
For a Wilson loop along a circumference of radius $R=\ell/2$ on the plane $\bm{x}_{\perp}\equiv\left(x_{1},x_{2}\right)$ at the boundary, the space-like worldsheet of minimal area based on the circular path and extending in the bulk at fixed $y$ must be computed.
Such a surface has an azimuthal symmetry and a tip at $\left(\tau,\bm{x}_{\perp},r\right)=\left(\tau_{*},\bm{0},r_{*}\right)$ with $\left(r_{*},\tau_{*}\right)$ input values in the calculation.
The transverse section at fixed $\tau$ and $r$ is a circumference. For each section the worldsheet can be parametrized in polar coordinates $\xi^{\alpha}=(\rho,\varphi)$, so that
\begin{equation}
\tau=\tau(\rho), \quad x_{1}=\rho\cos\varphi, \quad x_{2}=\rho\sin\varphi, \quad r=r(\rho) \quad , \,\,\, \text{ $y$ fixed.}
\end{equation}
The area of the worldsheet is obtained from the Nambu-Goto action
\begin{equation}\label{WLcircular_Nambu-Goto}
\mathcal{A}_C=\frac{1}{\alpha'}\int_{0}^{\ell/2}d\rho\,\rho\left(\tilde{\Sigma}(r,\tau)\left[-A(r,\tau)\tau'(\rho)^{2}+\tilde{\Sigma}(r,\tau)+2\tau'(\rho)r'(\rho)\right]\right)^{1/2}\,,
\end{equation}
with the prime in the functions $\tau$ and $r$ denoting a derivative with respect to $\rho$, and the angle $\varphi$ integrated out.
Interpreting the integrand of \eqref{WLcircular_Nambu-Goto} as a Lagrangian, one observes that its explicit $\rho$ dependence implies the absence of a conservation equation.
The resulting Euler-Lagrange equations, although involved, can be worked out in a straightforward way.
The solution $(r(\rho),\tau(\rho))$, together with the conditions \eqref{midpoint_conditions0}-\eqref{midpoint_conditions}, can be used to compute the area of the extremal surface, with the same regularization scheme
adopted for the geodesic lengths.
The corresponding quantity in the hydrodynamic geometry is obtained using the metric functions \eqref{AdSBH}, and the probe of thermalization is given by the difference $\Delta\mathcal{A}_C=\mathcal{A}_C-\mathcal{A}_{C,H}$.
Examples of extremal surfaces of circular Wilson loops, computed using the bulk geometry \eqref{metric5D} for a particular model of quench, are depicted in Fig.~\ref{fig:circWL}.
\begin{figure}
\begin{center}
\includegraphics[width = .25\textwidth]{3D_WLcircular.pdf} \hspace*{3cm}
\includegraphics[width = .22\textwidth]{3D_WL_rectangular_orange.pdf}
\caption{\baselineskip 10pt Extremal surfaces of circular (left) and rectangular (right) Wilson loops, computed for quench model ${\mathcal B}$. The value of $\tau_*$ is set to $\tau_*=3$. }\label{fig:circWL}
\end{center}
\end{figure}
A less symmetric Wilson loop is an infinite rectangular strip, regarded as a limit of an ellipsoidal loop with an elongated axis.
On the boundary, we set a rectangular contour parametrized by the coordinates $\left(x_{1},x_{2}\right)$, with $-\ell/2 \leq x_1 \leq \ell/2$ and $0 \leq x_2 \leq q$.
The side length $q$ is taken to infinity, and the strip is assumed to be translationally invariant along the $x_{2}$ axis.
The profile of the string surface extending in the bulk at fixed $y$, having the rectangular path as its basis, is described by the embedding $\left(\tau\left(x_{1}\right),r\left(x_{1}\right)\right)$, with the conditions \eqref{boundary_conditions}.
In the following, we denote $x \equiv x_{1}$.
The area of the worldsheet, in terms of the side length $q$ and a parameter $\lambda$, is given by
\begin{equation}\label{WLrectangular_Nambu-Goto}
{\mathcal A}_{R}=\frac{q}{2\pi\alpha'}\int_{\lambda_1}^{\lambda_2}d\lambda\left(\tilde{\Sigma}(r,\tau)\left[-A(r,\tau)\dot{\tau}(\lambda)^{2}+2\dot{\tau}(\lambda)\dot{r}(\lambda)+\tilde{\Sigma}(r,\tau)\dot{x}(\lambda)^{2}\right] \right)^{1/2}\, ,
\end{equation}
with $x(\lambda_{1,2})=\mp \ell/2$.
Interpreting the integrand in \eqref{WLrectangular_Nambu-Goto} as a Lagrangian, $x$ is a cyclic variable with conjugate momentum conserved on the worldsheet.
The conservation equation, using \eqref{midpoint_conditions0}-\eqref{midpoint_conditions}, reads
\begin{equation}\label{WLrectangular_conservation}
\frac{\tilde{\Sigma}(r,\tau)^{3/2}}{\left(-A(r,\tau)\tau'(x)^{2}+2\tau'(x)r'(x)+\tilde{\Sigma}(r,\tau)\right)^{1/2}}=\tilde{\Sigma}\left(r_{*},\tau_{*}\right) \,\,\,
\end{equation}
in terms of the coordinate $x$.
Solving the equations
\begin{eqnarray}\label{eq-wl1}
& & A(r,\tau) \tau''(x) - r''(x) + \left[ - \frac{3}{2}A(r,\tau) \frac{\partial_{\tau} \tilde{\Sigma}(r,\tau)}{\tilde{\Sigma}(r,\tau)} + \frac{1}{2} \partial_{\tau} A(r,\tau) \right] \tau'(x)^2 + \frac{\partial_{r} \tilde{\Sigma}(r,\tau)}{\tilde{\Sigma}(r,\tau)} r'(x)^2 \nonumber \\ & & + \left[ 2\frac{\partial_{\tau} \tilde{\Sigma}(r,\tau)}{\tilde{\Sigma}(r,\tau)} - A(r,\tau) \frac{\partial_{r} \tilde{\Sigma}(r,\tau)}{\tilde{\Sigma}(r,\tau)} + \partial_{r} A(r,\tau) \right] r'(x) \tau'(x) + \partial_{\tau} \tilde{\Sigma}(r,\tau) = 0
\end{eqnarray}
and
\begin{eqnarray}\label{eq-wl2}
& &\tau''(x) + \left[ \frac{1}{2} \partial_{r} A(r,\tau) - \frac{\partial_{\tau} \tilde{\Sigma}(r,\tau)}{\tilde{\Sigma}(r,\tau)} + \frac{1}{2}A(r,\tau)\frac{\partial_{r} \tilde{\Sigma}(r,\tau)}{\tilde{\Sigma}(r,\tau)} \right] \tau'(x)^2 \nonumber \\
&&- 2\frac{\partial_{r} \tilde{\Sigma}(r,\tau)}{\tilde{\Sigma}(r,\tau)} r'(x) \tau'(x) - \partial_{r} \tilde{\Sigma}(r,\tau) = 0
\end{eqnarray}
allows one to compute the area
\begin{equation}
\mathcal{A}_R=\frac{q}{2\pi \alpha'}\int_{-\ell/2}^{\ell/2}dx\frac{\tilde{\Sigma}(r,\tau)^{2}}{\tilde{\Sigma}\left(r_{*},\tau_{*}\right)} \,\,\, .
\end{equation}
The mentioned regularization scheme is used also for this observable.
The quantity $\mathcal{A}_{RH}$ is computed in the geometry \eqref{AdSBH}, and the difference $\Delta \mathcal{A}_R=(\mathcal{A}_R-\mathcal{A}_{RH})/q$ at various $\tau_{0}$ and for different $\ell$ defines an observable to study thermalization of the boundary theory.
An example of rectangular Wilson loops computed in the geometry \eqref{metric5D} is shown in Fig.~\ref{fig:circWL}.
\section{Results and discussions}\label{sec4}
We can now compute the nonlocal observables in the geometry \eqref{metric5D}, with the metric functions numerically determined in \cite{Bellantuono:2015hxa} for the different quench models.
In the three cases, two-point correlation functions and Wilson loops, we have solved the systems of differential equations \eqref{eq-geo1}-\eqref{eq-geo2} and \eqref{eq-wl1}-\eqref{eq-wl2}, together with the equations for the circular Wilson loop. The range $r \leqslant r_0$ is considered for the radial coordinate, with $r_0=12$.
\subsection{Quench model $\mathcal{B}$}
In the case of geodesics and the quench model $\mathcal{B}$, a few solutions $r(x)$ and $\tau(x)$ are shown in Fig.~\ref{fig:geort}.
They are obtained by solving Eqs.~\eqref{eq-geo1}-\eqref{eq-geo2} together with the conditions \eqref{midpoint_conditions0}-\eqref{midpoint_conditions}, with parameters specified in the legendae.
Depending on $r_*$ and $\tau_*$, two sets of geodesics $r(x)$ are found: those reaching the AdS boundary, the class we are interested in, and those falling into the bulk.
After the quench, at a fixed $\tau_*$, a critical value $r_{*c}$ separates the two classes of solutions, and corresponds to the position of the black brane event horizon.
The solutions at large $\ell$ approach and follow the horizon, as shown in Fig.~\ref{fig:bh}, and large boundary separations can be obtained with limits only imposed by the accuracy of the numerical algorithm.
The same $r_{*c}(\tau_*)$ is found for the geodesics and the Wilson loops.
During the quench, when large time gradients are present, we have also found solutions starting from the boundary and crossing the apparent horizon. This phenomenon has been remarked for nonlocal observables in rapidly changing time-dependent setups \cite{Hubeny:2002dg,Hubeny:2012ry,Hartman:2013qma,Liu:2013qca}.
\begin{figure}[t!]
\begin{center}
\begin{tabular}{cc}
\includegraphics[width = .45\textwidth]{geodesictts4.pdf} &
\includegraphics[width = .45\textwidth]{geodesicrts4.pdf} \\
(a)&(b)
\end{tabular}
\caption{\baselineskip 10pt Quench model $\mathcal{B}$. Geodesics $r(x)$ (a) and $\tau(x)$ (b), for $\tau_*=4$ and the values of $r_*$ in the legend.}\label{fig:geort}
\end{center}
\end{figure}
\begin{figure}[t!]
\begin{center}
\includegraphics[width = .45\textwidth]{criticalGeov2.pdf}
\caption{\baselineskip 10pt
Geodesics in the $(\tau,r)$ plane for ($\tau_*=6$, $r_*\sim 1.80$) and ($\tau_*=8$, $r_*\sim 1.65$) in quench model $\mathcal{B}$. Increasing $\tau_*$ (after the pulse in the quench) and for large $\ell$, the radial coordinate closely follows the event horizon.}\label{fig:bh}
\end{center}
\end{figure}
Let us discuss in more detail the results for the regularized geodesic length $\mathcal{L}(t_0,\ell)$, the regularized area of extremal surfaces for the rectangular Wilson loop $\mathcal{A_R}(t_0,\ell)$ (divided by $q$) and for the circular Wilson loop $\mathcal{A_C}(t_0,\ell)$ in model $\mathcal{B}$. They are shown in Fig.~\ref{fig:lgeo} for several values of the distance $\ell$ between the points in the correlation function, of the side (again denoted by $\ell$) of the rectangular Wilson loop, and of the diameter $\ell$ of the circular Wilson loop ($\alpha'$ is set to 1).
The curves start at different values of the initial time $t_0$, all corresponding to $\tau_*=0.25$.
In the plots we limit to $\ell \simeq 4$, but it is possible to achieve higher values of $\ell$ by increasing the numerical precision.
Fig.~\ref{fig:lgeo} shows that the observables follow the quench profile, with a delay that increases for increasing sizes of the probes.
Additional structures, namely local minima, are found.
They are due to the different profiles of the geodesics and of the extremal surfaces that enter in the bulk. An example is reported in Fig.~\ref{fig:curves}, in which we collect the
profiles of the extremal surfaces for the rectangular Wilson loop as the time proceeds, at a fixed value of $\ell$, showing that the structures in the regularized area are related to the topologies of the extremal surfaces. Moreover, for such a value of $\ell$ and for values of $t_0$ corresponding to the largest time variations of the geometry (and consequently of the area), extremal surfaces exceeding the event horizon appear, i.e. for some points in branches A (upper part), B, C, D, G.
\begin{figure}[t!]
\begin{center}
\begin{tabular}{ll}
\includegraphics[width = .5\textwidth]{column_full_modB1.pdf} & \hspace*{-1.cm}
\includegraphics[width = .5\textwidth]{column_full_modA.pdf}
\end{tabular}
\caption{\baselineskip 10pt Results for quench models $\mathcal{B}$ (left) and $\mathcal{A}(2)$ (right). From top down: profile of the quench $\gamma$, geodesic regularized lengths, regularized areas of the extremal surfaces for rectangular (divided by $q$) and circular Wilson loops versus $t_0$, for the sizes of the probes specified in the legendae. The regularization scheme consists in subtracting from each observable the corresponding quantity computed in pure $AdS_5$.}\label{fig:lgeo}
\end{center}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{AR_local_minima.pdf}\\
\hspace*{0.85cm} \subfigure[ \, points in A]{\includegraphics[width=0.14\textwidth]{A_blue_curves.pdf}}
\subfigure[ \, in B]{\includegraphics[width=0.14\textwidth]{B_magenta_curves.pdf}}
\subfigure[ \, in C]{\includegraphics[width=0.14\textwidth]{C_red_curves.pdf}}
\subfigure[ \, in D]{\includegraphics[width=0.14\textwidth]{D_green_curves.pdf}}\\
\hspace*{0.85cm} \subfigure[ \, in E]{\includegraphics[width=0.14\textwidth]{E_magenta_curves.pdf}}
\subfigure[ \, in F]{\includegraphics[width=0.14\textwidth]{F_cyan_curves.pdf}}
\subfigure[ \, in G]{\includegraphics[width=0.14\textwidth]{G_red_curves.pdf}}
\subfigure[ \, in H]{\includegraphics[width=0.14\textwidth]{H_blue_curves.pdf}}
\caption{Regularized $\mathcal{A}_{R}$ for model $\mathcal{B}$ and $\ell=1.4$ (top panel). The points with the same color, in various branches in the plot indicated by a capital letter from A to H, correspond to the profiles of the solutions $r(x)$ in the corresponding panels from (a) to (h) in the second and third row.}\label{fig:curves}
\end{figure}
Let us focus on the time region that follows the end of the spike in the quench, when the profile $\gamma(\tau)$ is nearly constant.
We are interested in understanding if the nonlocal observables follow the hydrodynamic behavior and, in that case, how fast such a regime is reached after the end of the quench, in comparison with the thermalization time determined through local observables (in particular the pressures).
In Fig.~\ref{fig:modB} we display the differences of the quantities computed in the metric \eqref{metric5D}, and the same quantities computed in the hydrodynamic geometry \eqref{metric5Dhydro}, i.e. the observables $\Delta\mathcal{L}$, $\Delta\mathcal{A}_{R}$ (divided by $q$) and $\Delta\mathcal{A}_{C}$.
The curves in the left panel start at the different values of $t_0$ corresponding to $\tau_*=\tau_f^\mathcal{B}=5$.
This is due to the fact that, since geodesics are characterised by $\tau_*\leqslant\tau(x)\leqslant t_0$, only the geodesics with $\tau_*\geqslant 5$ are not affected by the quench and can be compared with hydrodynamics.
As shown in Fig.~\ref{fig:modB}, each observable thermalizes at different times where all differences vanish.
The thermalization times are different for different sizes of the probes.
This result, more general than the one found in \cite{Bellantuono:2015hxa}, indicates how nonlocal observables recover the hydrodynamic regime after the end of the quench in comparison with the local observables: $\Delta\mathcal{L}$, $\Delta\mathcal{A}_R$ and $\Delta\mathcal{A}_C$ are smaller for low values of $\ell$, therefore the system is seen to thermalize faster using observables remaining as local as possible.
\begin{figure}[t!]
\begin{center}
\begin{tabular}{ll}
\includegraphics[width = .37\textwidth]{column_delta_modB.pdf} &
\includegraphics[width = .37\textwidth]{column_delta_modA.pdf}
\end{tabular}
\caption{\baselineskip 10pt Results for quench models $\mathcal{B}$ (left) and $\mathcal{A}(2)$ (right). From top down: Difference between the regularized geodesic length $\Delta\mathcal{L}$ (top), the regularized area (divided by $q$) of the extremal surface for the rectangular Wilson loop $\Delta\mathcal{A}_R$ (middle), and the regularized area of the extremal surface for the circular Wilson loop $\Delta\mathcal{A}_C$ (bottom) in the models with quench and using the hydrodynamic metric. The time $t_0$ starts after the end of the pulse in the quench. }\label{fig:modB}
\end{center}
\end{figure}
Other remarks are in order.
An analytic expression for $\mathcal{L}_{Hydro}$ can be obtained in
the small $\ell$ limit and large $t_0$ \cite{Janik:2005zt,Pedraza:2014moa}. The
leading-order correction with respect to $AdS_5$ is
\begin{equation}
\mathcal{L}_{Hydro}-\mathcal{L}_{AdS}=\frac{\ell^3 \pi^4 (10 + \ell^2
r_0^2)}{120 r_0 \sqrt{4 + \ell^2 r_0^2}} t_0^{-4/3} \Lambda^{8/3} \, + \dots ,
\end{equation}
which has a finite limit for $r_0 \to \infty$ that scales as $\ell^4$ and coincides with the one in \cite{Pedraza:2014moa}.
A similar expression holds for the rectangular Wilson loop.
As for the difference of the nonlocal observables with respect to hydrodynamics, the behaviour of the curves in Fig.~\ref{fig:modB} can be described by the form
$\displaystyle \Delta {\cal L}=\frac{C_4(\ell)}{(\Lambda t_0)^{4/3}}+\frac{C_6(\ell)}{(\Lambda t_0)^{6/3}}$, and similarly for Wilson loops. The first term accounts for a residual $t_0^{-4/3}$
dependence of $\Delta\mathcal{L}$, which is negligible
for small values of $\ell$ while it increases with $\ell$ (analogous results hold for $\mathcal{A}_R$ and $\mathcal{A}_C$). The coefficients $C_4(\ell)$ and $C_6(\ell)$ in Fig.~\ref{fig:C4C6} are very close for the two models, showing that after the quench the nonlocal probes share common features.
\begin{figure}[b!]
\begin{center}
\includegraphics[width = .45\textwidth]{C4_e_C6_geoB.pdf}
\caption{\baselineskip 10pt First coefficients of the large $t_0$ expression of the geodesic length $\displaystyle \Delta {\cal L}=\frac{C_4(\ell)}{(\Lambda t_0)^{4/3}}+\frac{C_6(\ell)}{(\Lambda t_0)^{6/3}}$ for model $\mathcal{B}$. }\label{fig:C4C6}
\end{center}
\end{figure}
They can be represented in a rational form $C(\ell)=(a \; \ell^b+c)/(d+\ell^e)$ which seems common to all the observables. For the geodesic length in model $\cal B$ we find
$a=6.58$, $b=-0.03$, $c=-6.59$, $d=0.07$, $e=-2.29$ for $C_4(\ell)$, and
$a=0.19$, $b=1.70$, $c=-0.86$, $d=0.47$, $e=-3.40$ for $C_6(\ell)$.
To provide a quantitative measure of thermalization for the nonlocal probes, we use several criteria to determine the value of the size $\ell$ above which the observables are not thermalized, at a fixed value $t_0=6.74$, corresponding to the restoration of pressure isotropy \cite{Bellantuono:2015hxa}.
\begin{itemize}
\item $\hat{\ell}_{1}$ is the value of $\ell$ corresponding to the inflection point of the curves $\Delta \mathcal{L}/\ell$, $\Delta \mathcal{A}_R/\ell$ and $\Delta \mathcal{A}_C/\ell^2$ versus $\ell$ at fixed $t_0=6.74$. In the quench model $\mathcal{B}$ the two-point correlation function is thermalized for $\ell \lesssim \hat{\ell}_1=1.0$, the rectangular Wilson loop for $\ell\lesssim \hat{\ell}_1=0.5$ and the circular Wilson loop for $\ell\lesssim \hat{\ell}_1=1.0$. Notice that $\hat{\ell}_{1}$ is almost constant at varying $t_0$, since curves with different $t_0$ have close inflection points, Fig.~\ref{fig:flex}. As $t_0$ increases, the curves have smaller asymptotic slopes which vanish at $t_0\to\infty$.
\item
$\hat{\ell}_2$ is the length corresponding to the inflection point of the derivatives of $\Delta \mathcal{L}$, $\Delta \mathcal{A}_R$ (divided by $q$) and $\Delta \mathcal{A}_C/\ell$. The results $\hat{\ell}_2= 0.7$ (for the two-point correlator), $\hat{\ell}_2= 0.3$ (for the rectangular Wilson loop) and $\hat{\ell}_2= 0.7$ (for the circular Wilson loop) are close to the findings obtained using $\hat{\ell}_1$.
\begin{figure}[b!]
\begin{center}
\includegraphics[width = .45\textwidth]{flexLength.pdf}
\caption{\baselineskip 10pt Quench model $\mathcal{B}$: $|\Delta\mathcal{L}|/\ell$ versus $\ell$ at values of $t_0$ specified in the legenda.}\label{fig:flex}
\end{center}
\end{figure}
\item $\ell_{b}$ is the value of $\ell$ where $|\Delta \mathcal{L}|/\ell_{b}= 0.01$, $|\Delta \mathcal{A}_R|/\ell_{b}=0.01$ and $|\Delta \mathcal{A}_C|/\ell_{b}^2= 0.01$. One considers as thermalized the geodesics having $\ell\leqslant \ell_{b}$, where the difference with respect to the hydrodynamic result is less than the chosen bound.
At $t_0=6.74$, we find $\ell_{b}= 1.1$, $\ell_{b}= 0.7$ and $\ell_{b}= 1.6$ for the three observables, respectively.
The values of $\ell_b$ obtained for different $t_0$ are shown in Fig.~\ref{fig:bound}.
\begin{figure}[t!]
\begin{center}
\includegraphics[width = .45\textwidth]{bound1.pdf}\\
\includegraphics[width = .45\textwidth]{bound2.pdf}
\caption{\baselineskip 10pt Quench model $\mathcal{B}$: critical sizes $\ell_b$ (top) and $\ell_{b2}$ (bottom) versus $t_0$ for the three nonlocal observables.}\label{fig:bound}
\end{center}
\end{figure}
\item $\ell_{b2}$ is the value of $\ell$ at which $|\Delta \mathcal{L}|/\mathcal{L}= 0.002$, $|\Delta \mathcal{A}_R|/\mathcal{A}_R=0.002$ and $|\Delta \mathcal{A}_C|/\mathcal{A}_C= 0.002$. In this case, one considers thermalized the geodesics having $\ell\leqslant \ell_{b2}$, considering the chosen bound.
At $t_0=6.74$ we find $\ell_{b2}= 1.1$, $\ell_{b2}= 0.8$ and $\ell_{b2}= 1.5$ for the three observables, respectively.
The values of $\ell_{b2}$ obtained for different $t_0$ are also shown in Fig.~\ref{fig:bound}.
\end{itemize}
The various critical sizes, collected in Table \ref{tab:res}, are consistent with each other, and the criteria produce a coherent quantitative determination of the thermalization size for the three nonlocal observables.
Finally, we define $t_{1/2}(\ell)$ as the value of $t_0$ at which $|\Delta \mathcal{L}|$ is reduced by a half with respect to the end of the quench at fixed $\ell$, and similarly for $|\Delta \mathcal{A}_R|$ and $|\Delta \mathcal{A}_C|$.
The end of the quench is the time $t_0$ corresponding to $\tau_*=5$, a condition ensuring that the whole geodesic $(r(x),\tau(x))$ is not affected by the quench.
The results in Fig.~\ref{fig:thalf} show that $t_{1/2}(\ell)$ exceeds the thermalization time obtained using local observables for size $\ell \simeq 1$, comparable to the critical sizes previously defined.
Regardless of the choice of the criterion, the rectangular Wilson loop takes more time to thermalize.
Another feature emerging for $t_{1/2}$ is the linear increase against the size $\ell$.
This dependence is common to the result obtained in other systems in which the thermalization time for large probes has been scrutinized \cite{Buchel:2014gta}.
The hierarchy found between the thermalization times of the energy density, the pressures and the large-size probes indicates the onset of thermalization starting at short distances.
\begin{figure}[b!]
\begin{center}
\includegraphics[width = .45\textwidth]{thalf.pdf}
\includegraphics[width = .45\textwidth]{t0halfA.pdf}
\caption{\baselineskip 10pt Quench models $\mathcal{B}$ (left) and $\mathcal{A}(2)$ (right): time $t_{1/2}$ versus the size $\ell$ for the three nonlocal observables. The horizontal dashed line indicates the thermalization time obtained from the pressure anisotropy. }\label{fig:thalf}
\end{center}
\end{figure}
\begin{table}
\begin{center}
\begin{tabular}{|c|ccc|| ccc |}
\hline
critical size &GL&RWL&CW & GL& RWL& CWL \\ \hline
$\hat \ell_1$&1&0.5&1 & 0.9&0.4&0.8\\
$\hat \ell_2$&0.7&0.3&0.7&0.6&0.3&0.6\\
$\hat \ell_{b}$&1.1&0.7&1.6&0.9&0.5&1.2\\
$\hat \ell_{b2}$&1.1&0.8&1.5 & 1.0& 0.6&1.1 \\ \hline
\end{tabular}
\caption{\baselineskip 10pt Critical sizes for the regularized geodesic length (GL) and the regularized area of rectangular (RWL) and circular Wilson loop (CWL), for quench model $\mathcal{B}$ with $t_0=6.74$ (left) and quench model $\mathcal{A}(2)$ with $t_0=6$ (right). The definitions are given in the text.}\label{tab:res}
\end{center}
\end{table}
\subsection{Quench model $\mathcal{A}(2)$}
We have computed the regularized geodesic lengths and the regularized areas of the extremal surfaces for rectangular and circular Wilson loops in the quench model $\mathcal{A}(2)$ investigated in \cite{Bellantuono:2015hxa}.
The results in Fig.~\ref{fig:lgeo} show how the nonlocal observables follow the quench in the boundary, and how thermalization is reached with the curves approaching the hydrodynamic behavior, as understood by inspecting Fig.~\ref{fig:modB} (right panel).
The curves in the latter figure start at the different $t_0$ corresponding to $\tau_*=\tau_f^\mathcal{A}=3.25$.
The relaxation to thermalization can be quantified using the same criteria adopted for model $\mathcal{B}$.
The thermalization time found using local observables is $t_0=6$ \cite{Bellantuono:2015hxa}.
From the criterion of the inflection point of $\Delta\mathcal{L}/\ell$, $\Delta\mathcal{A}_R/\ell$ and $\Delta\mathcal{A}_C/\ell^2$ the critical thermalization sizes for the geodesics, the rectangular and the circular Wilson loop are $\hat \ell_1 = 0.9$, $\hat \ell_1 = 0.4$ and $\hat \ell_1 = 0.8$, respectively.
On the other hand, from the inflection point of the derivative of $\Delta\mathcal{L}$, $\Delta\mathcal{A}_R$ and $\Delta\mathcal{A}_C/\ell$, we find $\hat \ell_2 = 0.6$, $\hat \ell_2 = 0.3$ and $\hat \ell_2 = 0.6$, respectively.
The critical sizes $\hat \ell_{b}$ and $\hat \ell_{b2}$, obtained using the same requirements imposed for model $\mathcal B$,
are collected in Table \ref{tab:res} together with $\hat \ell_1$ and $\hat \ell_2$.
The various critical sizes are close to each other, with the different criteria providing a coherent quantitative determination of thermalization for nonlocal observables also in this quench model.
The calculation of the half thermalization time $t_{1/2}(\ell)$ gives the result in Fig.~\ref{fig:thalf}, and the behavior is linear for large sizes. As in model $\mathcal B$, the rectangular Wilson loop thermalizes more slowly than the other two observables.
Let us conclude this section by observing that in both the quench models we have found the emergence of time scaling related to the onset of hydrodynamics and to the size of the probes. The inspection of the coefficients of the time dependence of, e.g., $\Delta \cal L$ in Fig.~\ref{fig:C4C6} does not allow one to identify other time regimes. This is at odds with the results based on the bulk Vaidya geometry \cite{Liu:2013qca} in which various kinds of time dependences
are detected for the geodesic length, related to the so-called pre- and post-equilibrium regimes. As a last remark, the observation of a hierarchy in thermalization among the different sizes and distances is connected to the use of space-like probes. Analyses based on time correlators, or on horizon-to-boundary propagators in the same dynamical framework, would be useful to show a hierarchy in thermalization among different frequencies and modes of the boundary field theory \cite{CaronHuot:2011dr}.
\section{Conclusions}
In a fully dynamical holographic 5$d$ setup with boundary sourcing, we have studied three nonlocal observables, the equal-time two-point correlation function of a large dimension operator in the boundary theory, and the expectation value of a rectangular and circular Wilson loop.
We have computed the observables during the quench, for two different models for the distortion of the boundary metric, and after the end of the last spike in the distortion.
The hydrodynamic behavior of the observables has also been determined using a 5$d$ metric reproducing the viscous hydrodynamic time dependence of the energy density and of the transverse and longitudinal pressures.
Thermalization of the nonlocal observables has been scrutinized using the difference between the observables in the quenched and in the hydrodynamic geometries.
In this time-dependent setup, the energy density follows the viscous behavior immediately after the end of the quench, while there is a time delay for the pressures to reach the viscous dependence and the isotropy condition $p_\perp=p_\parallel$ \cite{Bellantuono:2015hxa}.
For nonlocal observables we have found that the thermalization time changes with the size of the observable. Different criteria defining critical sizes produce coherent results.
For larger sizes, the thermalization time increases with the size of the probe.
In particular, for all the three observables the time $t_{1/2}(\ell)$ increases linearly with $\ell$, a result independent of the quench model.
The hierarchy among the thermalization times of the energy density, pressures and large probes supports the conclusion of a faster thermalization at short distances, a feature of the strongly coupled theories.
\vspace*{1cm} {\bf \noindent Acknowledgments.}
LB is grateful to Prof. I. Arefeva for interesting discussions.
This work has been carried out within the INFN project (Iniziativa Specifica) QFT-HEP.
\bibliographystyle{apsrev4-1}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,149 |
{"url":"https:\/\/cstheory.stackexchange.com\/questions\/47441\/compiling-einstein-sums-optimally","text":"# Compiling einstein sums optimally\n\nEinstein summation is a convenient way to express tensor operations which has found its way in tensor libraries like numpy, torch, tensorflow, etc.\n\nIts flexibility lets us represent the product of three matrices, $$X$$, $$Y$$, $$Z$$ of dimensions $$(a,b)$$, $$(b,c)$$, $$(c,d)$$ as\n\nX.Y.Z = einsum('ab,bc,cd->ad',X,Y,Z)\n\n\nHowever, the above compiles to something like\n\nfor a_ in range(a):\nfor d_ in range(d):\nres[a_,d_] = 0\nfor b_ in range(b):\nfor c_ in range(c):\nres[a_,d_] += X[a_,b_] * Y[b_,c_] * Z[c_, d_]\n\n\nThis native is quadratic in the size of the matrices when simply doing\n\neinsum('ac,cd->ad',einsum('ab,bc'->'ac', X, Y), Z)\n\n\nWould be merely cubic.\n\nThere are roughly three levels of optimization we can imagine a smarter implementation of einsum to perform.\n\n1. Decompose an einsum of tensors $$(x_1, \\ldots, x_n)$$ into an einsum of pairs of tensors $$x_1, x_2$$, $$e(x_1, x_2), x_3$$, etc to optimize computation time.\n\n2. Rely on associativity (where applicable) to pick those pairs judiciously (this is a classic dynamic programming problem) and construct the appropriate intermediary tensors.\n\n3. Discover Strassen-like formulas for the specific tensor computation\n\nWhile 3 seems clearly out of reach, 1 and 2 seem like they could be achievable exactly with a reasonably straightforward algorithm. Are such algorithms known for generic einstein summations? Have they been studied?\n\n\u2022 What does the notation cd->ab mean? \u2013\u00a0Mark Aug 18 at 15:53\n\u2022 The quote inserted was a typo, it's ab,cd->ad \u2013\u00a0Arthur B Aug 18 at 21:36\n\n## 1 Answer\n\nIt seems that the general problem of finding the optimal contraction order is NP-hard [1]. A recent paper on approximately optimizing the contraction order, and containing relevant references, is [2].\n\n[1] Chi-Chung, Lam, P. Sadayappan, and Rephael Wenger. \"On optimizing a class of multi-dimensional loops with reduction for parallel execution.\" Parallel Processing Letters 7.02 (1997): 157-168.\n\n[2] Schindler, Frank, and Adam Jermyn. \"Algorithms for tensor network contraction ordering.\" Machine Learning: Science and Technology (2020).\n\n\u2022 Thank you, \"tensor network contraction\" is the keyword I was missing \u2013\u00a0Arthur B Aug 20 at 10:30\n\u2022 Not all evaluation strategies are contractions though. The naive product of 3 $n \\times n$ matrices in $\\mathcal{O}(n^4)$ time doesn't happen if you follow any one of the two contraction strategy... yet, you'll see numpy's einsum for instance run it in quadratic time anyway. What gives? \u2013\u00a0Arthur B Aug 20 at 10:38\n\u2022 By quadratic, do you actually mean quartic (${\\cal O}(n^4)$)? I guess that any optimal evaluation strategies would consist of contractions. \u2013\u00a0smapers Aug 20 at 10:49\n\u2022 Sorry, yes I meant to write quartic. And the answer to my question is that, yes, this is a thing, but there's a flag... optimized-einsum.readthedocs.io\/en\/stable\/index.html \u2013\u00a0Arthur B Aug 20 at 17:39\n\u2022 Specifically I was thinking: the paper assumes that contractions always dominate naive evaluation, but surely if that were the case, numpy's einsum would implement at least a naive contraction. Turn out it does, but only with a flag. \u2013\u00a0Arthur B Aug 20 at 17:41","date":"2020-10-24 17:55:30","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\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 9, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8469477295875549, \"perplexity\": 3008.555045074509}, \"config\": {\"markdown_headings\": true, \"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-2020-45\/segments\/1603107884322.44\/warc\/CC-MAIN-20201024164841-20201024194841-00478.warc.gz\"}"} | null | null |
aws --profile datafire-web-push s3 sync ./logos/ s3://datafire-logos --acl public-read
aws --profile datafire-web-push s3 sync ./json/ s3://datafire-logos/json --acl public-read
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,077 |
Free FM can refer to:
CFRI-FM, a radio station in Grande Prairie, Alberta, Canada that identifies itself as 104.7 FreeFM
CKLO-FM, a radio station in London, Ontario, Canada that identifies itself as 98.1 Free FM
Free FM, a short-lived, mostly-talk-radio format and brand name for eleven FM CBS Radio stations in the United States
Free-FM (Sydney, Australia), a gay & lesbian radio station formerly operated in Sydney, Australia
Free FM (Hamilton, New Zealand), a community radio station in Hamilton, New Zealand | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,420 |
package org.spongepowered.common.item.recipe.crafting;
import net.minecraft.item.crafting.Ingredient;
import org.spongepowered.api.item.inventory.ItemStack;
import org.spongepowered.common.item.inventory.util.ItemStackUtil;
import java.util.List;
import java.util.function.Predicate;
import javax.annotation.Nullable;
public class CustomIngredient extends Ingredient {
public final List<Predicate<ItemStack>> predicates;
public final List<ItemStack> matchItems;
public CustomIngredient(final List<Predicate<ItemStack>> predicates, final List<ItemStack> matchItems, final List<ItemStack> displayItems) {
super(ItemStackUtil.toNative(displayItems));
this.predicates = predicates;
this.matchItems = matchItems;
}
@Override
public boolean apply(@Nullable final net.minecraft.item.ItemStack item) {
// first check for matching predicates
if (this.predicates.stream().anyMatch(p -> p.test(ItemStackUtil.fromNative(item)))) {
return true;
}
// then apply same logic as super.apply(..) but with this.items
if (item == null) {
return false;
}
for (final ItemStack itemStack : this.matchItems) {
final net.minecraft.item.ItemStack nativeItem = ItemStackUtil.toNative(itemStack);
if (nativeItem.getItem() == item.getItem()) {
final int i = nativeItem.getMetadata();
if (i == 32767 || i == item.getMetadata())
{
return true;
}
}
}
return false;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,279 |
Q: ¿Por qué en algunas computadoras no se ejecutan mis comandos de JAVA? Estoy usando NETBEANS IDE 8.0.1 y para mi proyecto final de preparatoria decidí crear una aplicación (en java) acerca de las herramientas de Windows, algo bastante sencillo, pero tengo un problema, y es que, apesar de que tengo la misma ruta para todas las aplicaciones, en algunas computadoras no abre o simplemente no ejecuta el programa, digamos, tengo 4 herramientas principales (Desfragmentador de disco, liberador de espacio, restaurar sistema y administrador de dispositivo), en mi computadora con Windows 10 se ejecutan TODAS correctamente, pero en la de un amigo para hacer una prueba solo se ejecutan 2 que es liberador de espacio y administrador de dispositivos, en resumen el problema está en que en algunas computadoras ejecuta todas las herramientas y en otras computadoras solo ejecuta algunas mi código es el siguiente:
public static void ADMINDISP(){
try
{
Runtime.getRuntime().exec("powershell.exe Start-Process 'C:\\Windows\\System32\\devmgmt.msc' -verb RunAs");
}
catch (Exception ex)
{
JOptionPane.showMessageDialog(null, ex);
System.out.println(ex);
}
}
En donde está señalada la ruta es lo mismo para todos, sólo cambia obviamente la ruta del archivo que ejecuta esa herramienta, sin embargo no entiendo por qué a algunos no les ejecuta, si hubiera otra manera de que forzara a abrir la aplicación o algo, al final llamo así para que ejecute dentro de mi botón
incluso tengo el JOptionPane donde le mostraría al usuario donde está el error al ejecutar el programa pero aún así no muestra nada, lo he probado personalmente en una pc donde falla y nada...
private void ADMINDISPActionPerformed(java.awt.event.ActionEvent evt) {
ADMINDISP();
}
Dejo el link más actualizado de mi programa por si lo necesitan probar, me haría mucha utilidad saber cuál es mi error, gracias.
https://mega.nz/#!lgpgEACR!uX1n3zPepcQavDj3UXJCeThdKv27FY1PfDhsmZKSXNo
A: buenos dias. Lo mas probable es que tus variables de entorno JAVAPATH o PATH, no estén apuntando correctamente al directorio correcto donde reside tu instalación de java.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,803 |
Depeche Mode – brytyjska grupa muzyczna z kręgu muzyki elektronicznej i alternatywnego rocka, która powstała w 1980 w Basildon w Wielkiej Brytanii. Aktualnie członkami zespołu są Dave Gahan (wokal) i Martin Gore (klawisze, gitara elektryczna i wokal). Obaj należą do składu grupy od początku jej istnienia. Nazwa grupy powstała na podstawie inspiracji , zasugerował ją Gahan. Powstanie Depeche Mode poprzedzała grupa Composition of Sound. W 2006 zespół zdobył statuetkę MTV Europe Music Awards w kategorii "najlepszy zespół". W 1990 grupa otrzymała nagrodę Rockbjörnen w kategorii "najlepszy zespół zagraniczny". W 2020 roku Depeche Mode wprowadzono do Rock and Roll Hall of Fame.
Historia
Wczesne lata (1977–1980)
W 1977 roku Vince Clarke (wokal, gitara) i Andrew Fletcher (bas) założyli zespół No Romance in China, w 1979 Clarke grał na gitarze w Plan razem z Robertem Marlow oraz Paulem Langwith. Martin Gore (gitara), który na początku skłaniał się ku punk rockowi, wraz z Philipem Burdettem (wokal) grał w Norman and the Worms, w 1979 Gore, Clarke, Marlow i Paul Redmond utworzyli grupę The French Look. W marcu 1980 powstał zespół Composition of Sound w składzie Clarke (wokal, gitara), Gore (instrumenty klawiszowe), Fletcher (bas).
Aby zarobić na instrumenty – syntezatory, Gore pracował jako urzędnik bankowy, a Fletcher jako agent ubezpieczeniowy. W 1980 Clarke trafił na występ Dave Gahana, po którym złożył mu propozycję dołączenia do zespołu. Równocześnie została zmieniona jego nazwa na Depeche Mode, zaczerpnięta z francuskiego magazynu. Martin Gore: "Depeche Mode oznacza to, jak szybko zmienia się moda. Lubię brzmienie tych słów". Pierwszy utwór grupy, "Photographic" został umieszczony na kompilacji Some Bizzare Album, następnie został nagrany jeszcze raz, aby trafić na debiutancki album "Speak & Spell".
Speak & Spell (1981)
Zespół zwrócił na siebie uwagę Daniela Millera, założyciela Mute Records, podczas występu w Bridge House w Canning Town. Pierwszym rezultatem był singel "Dreaming of Me" nagrany w grudniu 1980, a wydany w lutym 1981, który zdobył 57. miejsce na brytyjskiej liście przebojów. Następny – "New Life" – zajął miejsce 11. Trzy miesiące później "Just Can't Get Enough" wspiął się na ósmą pozycję. W listopadzie 1981 został wydany Speak & Spell, który zebrał zróżnicowane recenzje w prasie: Melody Maker opisał go jako "wspaniały", natomiast Rolling Stone nie szczędził słów krytyki. Na płycie znalazły się utwory błahe, naiwne, ocierające się o banał, oparte na tanecznych rytmach, na ich tle wyróżniały się kompozycje Gore'a. Depeche Mode zostało zakwalifikowane do nurtu new romantic, mimo że członkowie zespołu mieli przeciwne zdanie na ten temat.
Podczas trasy promującej album, Clarke zaczął wyrażać swoje niezadowolenie z kierunku w jakim podążał zespół: "Nigdy nie było czasu aby móc zrobić cokolwiek", jednak wydaje się, że koledzy byli bardziej zainteresowani kompozycjami Martina i to było prawdziwym powodem odejścia. Clarke pod koniec 1981 ogłosił oficjalnie decyzję o opuszczeniu grupy. Zaproponował jeszcze wspólnie nagranie utworu "Only You", ale oferta została odrzucona. Wraz z Alison Moyet założył Yazoo, a następnie Erasure z Andy Bellem. Po jego odejściu, głównym kompozytorem został Martin Gore, autor "Tora! Tora! Tora!" i "Big Muff" ze Speak & Spell. Martin Gore:
Zespół umieścił anonimowe ogłoszenie w Melody Maker, na które odpowiedział Alan Wilder. Z perspektywy roku 2010 Wilder tak wspominał swoje pierwsze spotkanie z Depeche Mode: Po dwóch przesłuchaniach został przyjęty na początku 1982, najpierw jako muzyk koncertowy, stając się pełnoprawnym członkiem zespołu dopiero pod koniec następnego roku.
A Broken Frame (1982)
W styczniu 1982 ukazał się singel "See You", który wspiął się na szóste miejsce brytyjskiej listy, osiągając tym samym lepszy wynik niż poprzednie nagranie. Zespół udał się na pierwsze światowe tournée, w następnych miesiącach ukazały się dwa następne single "The Meaning of Love" i "Leave in Silence".
W lipcu 1982 rozpoczęły się prace nad kolejnym albumem. Alan Wilder został poinformowany przez Millera, że jego udział w studiu nie jest konieczny, jako że zespół chce udowodnić, że może odnieść sukces bez Clarka. "A Broken Frame" ukazał się we wrześniu, wszystkie utwory były autorstwa Martina Gore'a, charakteryzowały się nastrojowością oraz subtelnym brzmieniem. W "Further Excerpts from my Garden" został użyty riff z "V2 Schneider" Davida Bowie. W październiku odbyła się kolejna światowa trasa koncertowa.
Dave Gahan:
Andrew Fletcher:
Construction Time Again (1983)
W styczniu 1983 ukazał się singel "Get the Balance Right!" i był to pierwszy utwór, w którym udział miał Wilder. Pod wpływem koncertu Einstürzende Neubauten Gore zaczął nagrywać na magnetofonie wszystkie możliwe dźwięki, przetworzone następnie przez Synclavier. W ten sposób powstała baza sampli użyta podczas pracy nad następnym albumem. Przy nagrywaniu "Construction Time Again" zespół pracował z producentem Garethem Jonesem w John Foxx's Garden Studios oraz w Hansa Studios w Berlinie Zachodnim. Płyta charakteryzowała się nowym brzmieniem, głównie dzięki zastosowaniu przez Wildera Synclaviera. Poprzez samplowanie zwykłych, codziennych odgłosów, Depeche Mode stworzyło eklektyczny, industrialny styl, podobny do tego jaki reprezentowały The Art of Noise i Einstürzende Neubauten.
Wraz z muzyką zmieniły się również teksty pisane przez Gore'a, skupiające się na sprawach społecznych i politycznych. Przykładem jest "Everything Counts" opowiadający o chciwości wielkich korporacji, a także napisane przez Wildera: "The Landscape is Changing" – ostrzeżenie przed dewastacją środowiska, "Two Minute Warning" refleksja nad wyścigiem zbrojeń. Także okładka symbolizuje zmiany i zerwanie z nurtem new romantic – przedstawiony robotnik ma "przebudować, a nie niszczyć". "Everything Counts" zajął szóste miejsce w Wielkiej Brytanii, uplasował się w pierwszej trzydziestce list w Irlandii, RPA, Szwajcarii, Szwecji oraz Niemczech. Wilder był autorem piosenek "The Landscape is Changing" oraz "Two Minute Warning".
Andrew Fletcher:
Some Great Reward (1984)
We wczesnych latach Depeche Mode zaistniało tylko w Europie i Australii. To się zmieniło za sprawą następnego singla "People are People" wydanego w marcu 1984, który zajął drugie miejsce w Irlandii, czwarte w Wielkiej Brytanii i pierwsze w Niemczech, a w połowie 1985 roku utwór został zauważony w USA, gdzie zajął trzynastą pozycję.
We wrześniu 1984 ukazała się płyta "Some Great Reward". Pod względem literackim album poruszał takie tematy jak związek oparty na dominacji seksualnej ("Master and Servant"), zdrada ("Lie to Me") czy rozliczenie z Bogiem ("Blasphemous Rumours"). Ten ostatni został potępiony przez brytyjski kler. Natomiast traktujący o równości społecznej "People are People" stał się hymnem środowisk gejów i lesbijek. Some Great Reward zajął po raz pierwszy w historii miejsce na liście w USA.
W lipcu 1985 roku Depeche Mode po raz pierwszy wystąpiło w Polsce. W październiku ukazała się pierwsza składanka największych przebojów zespołu "The Singles 81→85" którą promowały single "Shake the Disease" i "It's Called a Heart".
W tym czasie w niektórych kręgach zespół zaczął być kojarzony z subkulturą gotycką. W USA zespół zdobył takie uznanie za sprawą radia KROQ w Los Angeles czy WLIR z Nowego Jorku. Spostrzeganie w ten sposób Depeche Mode za oceanem pozostaje w dużej mierze w opozycji do Europy i Wielkiej Brytanii gdzie, mimo mrocznego i poważnego tonu w twórczości, grupa była rozpoznawana raczej jako idol nastolatków.
Black Celebration (1986)
Kolejne wydawnictwa to kolejne zmiany. Szesnasty singiel "Stripped" oraz album "Black Celebration" wypełniła muzyka mroczna i ponura. W trakcie jego powstawania, muzycy byli wyczerpani, pojawiła się także groźba rozwiązania formacji. Na płycie znalazła się nowa wersja "Fly on the Windscreen", która pierwotnie ukazała się na drugiej stronie singla "It's Called a Heart". Drugi singiel "A Question of Lust" był pierwszym singlem zespołu wydanym również na kasecie magnetofonowej.
Teledysk do "A Question of Time" był pierwszym zrealizowanym przez reżysera Antona Corbijna, co zapoczątkowało współpracę trwającą po dzień dzisiejszy. Corbijn był odpowiedzialny także za niektóre okładki.
Music for the Masses (1987)
"Music for the Masses" przyniósł kolejne zmiany w sposobie pracy zespołu. Po raz pierwszy do współpracy zaproszono producenta Davida Bascombe'a, który nie był związany z Mute Records. Album nagrywany był w kwietniu i maju w studiu Konk w Londynie oraz Guillame Tell w Paryżu, a w czerwcu i lipcu dopracowywany był w PUK Studio w Danii.
Płyta była bardziej melodyjna i przebojowa w porównaniu do swojej poprzedniczki. Jej światowa sprzedaż wyniosła 2 miliony egzemplarzy. Single "Strangelove", "Never Let Me Down Again" i "Behind the Wheel" znalazły się w pierwszej dziesiątce list przebojów w takich krajach jak: Kanada, Brazylia, Niemcy, RPA, Szwecja i Szwajcaria. "Strangelove" w Wielkiej Brytanii dotarł do miejsca 16. W utworze "I Want You Now" funkcję podkładu rytmicznego spełniają głosy, potraktowane jako instrumenty.
101 (1988)
Lata 1987–1988 zespół spędził na światowym tournée, obejmującym 101 koncertów, którego punktem kulminacyjnym był występ 18 czerwca 1988 na stadionie Rose Bowl w Pasadenie, gdzie publiczność liczyła 75 000 osób. Był to 101 koncert tego tournée. Trasa została udokumentowana filmem w reżyserii D.A. Pennebakera oraz albumem koncertowym 101.
Alan Wilder:
Violator (1990)
W połowie roku 1989 zespół rozpoczął kolejną sesję w Mediolanie z producentem Flood oraz inżynierem dźwięku François Kevorkianem. Pierwszym rezultatem był singel "Personal Jesus". Przed jego wydaniem, w angielskiej prasie ukazało się ogłoszenie "Your own Personal Jesus", a pod wskazanym numerem telefonu można było usłyszeć utwór. W rezultacie piosenka zajęła 13. miejsce w Wielkiej Brytanii, w USA – pierwsze od czasu "People are People", a także wywołała oburzenie wśród organizacji chrześcijańskich. Singel osiągnął najlepszy wynik sprzedaży w historii Warner Bros. Records.
W lutym 1990 "Enjoy the Silence" zajął szóste miejsce w Wielkiej Brytanii oraz ósme w USA. Singel wygrał Best British Single podczas Brit Awards w 1991. Podczas promocji nowego albumu Violator zorganizowano spotkanie z fanami w Wherehouse Entertainment w Los Angeles. Przybyło wówczas około 20 000 osób zainteresowanych otrzymaniem autografu, wiele z nich doznało obrażeń na skutek napierającego tłumu oraz doszło niemalże do zamieszek. W ramach przeprosin ze strony zespołu ukazała się limitowana edycja nagrań dedykowana fanom w Los Angeles, wyemitowana także przez radio KROQ, które było sponsorem spotkania w Wherehouse Entertainment.
"Violator" uplasował się w pierwszej dziesiątce angielskiej listy, w USA pokrył się potrójną platyną za sprzedaż wynoszącą 3,5 miliona egzemplarzy. Ostatni na płycie "Clean" zawiera linię basu "One of These Days" zespołu Pink Floyd. Zespół udał się w trasę World Violation Tour – miarą popularności było 40 000 biletów sprzedanych w przeciągu ośmiu godzin na koncert w Nowym Jorku, 48 000 biletów w ciągu godziny w Los Angeles.
Songs of Faith and Devotion (1993)
W 1991 Gahan rozważał opuszczenie szeregów zespołu, do pozostania przekonały go nowe kompozycje Gore'a oraz wzbogacenie brzmienia o tradycyjne instrumenty. Dave Gahan:
Album "Songs of Faith and Devotion" przyniósł nowe aranżacje oparte na zniekształconym dźwięku gitary elektrycznej, dudach (gościnny udział Steaffana Hannigana) oraz wokalach w stylu gospel (Hilda Campbell, Bazil Meade, Samantha Smith). Kolejna zmiana to Alan Wilder grający na perkusji – w tej roli zadebiutował już w piosence "Clean" z poprzedniego albumu. Płyta dzięki tym zabiegom nabrała bardziej rockowego charakteru. "Songs of Faith and Devotion" zajął pierwsze miejsce na listach w Anglii i USA. Po jego wydaniu odbyła się czternastomiesięczna trasa Devotional, udokumentowana filmem oraz druga płytą koncertową "Songs of Faith and Devotion Live".
W tym czasie Dave Gahan uzależnił się od heroiny, doznał ponadto ataku serca. Andy Fletcher odmówił wzięcia udziału w ostatniej części trasy z powodu załamania nerwowego i został zastąpiony na scenie przez Daryla Bamonte, który był wieloletnim współpracownikiem zespołu.
1 czerwca 1995 Alan Wilder ogłosił odejście z Depeche Mode, w swoim oficjalnym oświadczeniu napisał:
Andrew Fletcher:
Alan Wilder kontynuuje karierę w zespole Recoil.
W tym czasie duże obawy budził stan psychiczny Gahana – w 1995 próbował odebrać sobie życie, a rok później o mało nie przedawkował podczas pobytu w hotelu.
Ultra (1997)
Lata 1995 i 1996 to próby ze strony Martina Gore'a, aby zebrać zespół i rozpocząć pracę nad kolejnym wydawnictwem. Jednakże Gahan jeśli w ogóle zjawiał się na sesje to zajmowało mu tygodnie, aby nagrać cokolwiek. Gore rozważał nawet wydanie napisanych wówczas utworów na swojej solowej płycie, jednak ostatecznie do tego nie doszło. W połowie 1996 roku Gahan z dobrym skutkiem został poddany przymusowej terapii odwykowej. Wraz z producentem Timem Simenonem rozpoczęła się sesja albumu "Ultra", wydanego rok później. Płyta zadebiutowała na miejscu pierwszym w Wielkiej Brytanii oraz piątym w USA. Ukazały się także single "Barrel of a Gun", "It's No Good", "Home" i "Useless".
W 1998 ukazał się singel "Only When I Lose Myself", pochodzący jeszcze z sesji "Ultra", promujący składankę "The Singles (86-98)". Zespół udał się na czteromiesięczną trasę koncertową.
Exciter (2001)
W 2001 roku ukazał się "Exciter", wyprodukowany przez Marka Bella. Albumowi nie udało się osiągnąć wyniku sprzedaży trzech swoich poprzedników, mimo że znalazł się w pierwszej dziesiątce w Wielkiej Brytanii i USA, otrzymał dość zróżnicowane recenzje w prasie. "Exciter" był pierwszą płyta zespołu która uplasowała się wyżej w USA niż w rodzimym kraju zespołu. Jako single zostały wydane "Dream On", "I Feel Loved", "Freelove" oraz "Goodnight Lovers". Na późniejszych koncertach w ramach "Touring The Angel" grupa przedstawiała tylko "Goodnight Lovers" lub w ogóle cały album pomijała. Dave Gahan:
W 2004 ukazało się DVD Devotional, a także kompilacja "Remixes 81–04", zawierająca nową wersję "Enjoy the Silence" autorstwa Mike'a Shinody, zatytułowana "Enjoy the Silence 04".
Playing the Angel (2005)
Jedenasty album "Playing the Angel" ukazał się w październiku 2005, wyprodukowany przez Bena Hilliera. Była to pierwsza płyta Depeche Mode z tekstami Gahana oraz pierwsza od czasu Some Great Reward, zawierająca piosenki które nie zostały napisane przez Gore'a. Dave Gahan:
Album zajął pierwsze miejsce na listach w siedemnastu krajach. Na singlach ukazały się "Precious", "A Pain That I'm Used To", "John the Revelator" oraz "Suffer Well" – pierwszy singel od czasów Clarke'a niebędący kompozycją Gore'a. W latach 2005–2006 zespół udał się w trasę Touring the Angel, obejmującą Amerykę Północną i Europę. Po raz pierwszy grupa odwiedziła Rumunię i Bułgarię. Na koncert w Meksyku 55 000 biletów zostało natychmiast sprzedane, co spowodowało zorganizowanie jeszcze jednego występu w tym mieście. Nagrania z 43 koncertów trasy ukazały się jako limitowane wersje na CD.
W 2006 i 2007 roku sukcesywnie ukazywały się nowe, zremasterowane wersje albumów. 3 kwietnia 2006: Speak & Spell, Music for the Masses i Violator w wersji SACD i DVD; Broken Frame, Some Great Reward, Songs of Faith and Devotion – 2 października 2006; Construction Time Again, Black Celebration: 26 marca 2007; Ultra, Exciter – 1 października 2007. 25 września 2006 ukazało się DVD Touring the Angel: Live in Milan, będący zapisem koncertów z 18 i 19 lutego 2006, w reżyserii Blue Leach. W listopadzie 2006 ukazała się kompilacja "The Best Of, Volume 1", zawierająca nowy utwór "Martyr", pochodzący z sesji Playing the Angel. 2 listopada zespół wygrał MTV Europe Music Awards w kategorii Best Group.
W grudniu 2006 Depeche Mode otrzymało nominację nagrody Grammy w kategorii Best Dance Recording za utwór "Suffer Well". W połowie grudnia iTunes wydał dyskografię The Complete Depeche Mode.
Sounds of the Universe (2009)
W lipcu 2007, podczas promocji drugiego solowego dzieła Gahana "Hourglass", ogłoszono, że w 2008 Depeche Mode planuje nagranie kolejnego albumu. W marcu 2008 pojawiły się pogłoski jakoby Ben Hillier ma być jego producentem. W maju zespół pojawił się w studio, aby pracować nad utworami które przedstawił Gore. W sierpniu zespół pożegnał się z Warner Music, aby podpisać kontrakt z EMI. Podczas konferencji prasowej, która odbyła się 6 października 2008 roku w Berlinie, zespół ogłosił trasę koncertową Tour of the Universe. Na serwisie YouTube ukazała się seria filmów dokumentująca pracę w studiu. 15 stycznia 2009 na oficjalnej stronie zespołu pojawił się tytuł nowej płyty: "Sounds of the Universe". Album ukazał się 20 kwietnia 2009, był promowany singlem "Wrong", do którego teledysk wyreżyserował Patrick Daughters. Wydany został także box set "Sounds of the Universe Deluxe Edition Box Set" zawierający cały materiał z sesji nagraniowej.
Delta Machine (2013)
Premiera "Delta Machine" odbyła się 26 marca 2013 roku. 1 lutego w serwisie Vevo oraz YouTube pojawił się teledysk do najnowszego singla zespołu pt. "Heaven". Miesiące marzec i kwiecień to promocja płyty w kilku stacjach TV w USA oraz Europie [min. 11 marca 2013 New York, Live on Letterman] oraz kameralne występy na żywo [min. 24 marca 2013 roku – Wiedeń, Museums Quartier podczas "Album Launch Event"]. Oficjalnie zespół rozpoczął swoją światową trasę koncertową The Delta Machine Tour 2013/14 występem we francuskim Nice, Palais Nikaia 4 maja 2013 roku, a zakończył 4 marca 2014 w hali Olimpijskij w Moskwie. Koncert Depeche Mode w Polsce miał miejsce 25 lipca na Stadionie Narodowym w Warszawie, sprzedano ponad 53 tys. biletów. 24 lutego 2014 roku odbył się koncert grupy w Atlas Arenie w Łodzi, sprzedano ponad 15 tys. biletów.
Spirit (2017)
Premiera "Spirit" odbyła się 17 marca 2017 roku. 3 lutego w serwisie Vevo oraz YouTube pojawił się teledysk do najnowszego singla zespołu pt. "Where's the Revolution". Zespół rozpoczął swoją światową trasę koncertową The Global Spirit Tour występem w Sztokholmie 5 maja 2017 roku. Koncert Depeche Mode w Polsce miał miejsce 21 lipca 2017 r. na Stadionie Narodowym w Warszawie. Grupa wystąpiła 7, 9 i 11 lutego 2018 r. kolejno w Krakowie, Łodzi i Gdańsku. Kolejny występ odbył się w Polsce 5 lipca 2018 r. na festiwalu Open'er w Gdyni.
W 2020 roku Depeche Mode włączono do Rock and Roll Hall of Fame. Oprócz aktualnego składu, zaszczytu tego dostąpili też byli członkowie grupy, Vince Clarke i Alan Wilder.
Wewnątrz zespołu
Od początku istnienia grupy nad jej karierą czuwał producent, Daniel Miller. Mimo że Miller formalnie nigdy nie należał do zespołu, jego rola w rozwoju Depeche Mode jest jednak bardzo duża. Jego twórczy i organizacyjny wkład w pracę był znaczący zwłaszcza w początkowych latach.
Po odejściu Clarke'a, lidera pierwotnego składu, grupa nie rozwiązała się i kontynuowała działanie. Prawdopodobnie wpłynęło na to niezdecydowanie muzyków i niechęć do podejmowania decyzji oraz właśnie zaangażowanie Daniela Millera, dla którego grupa była wcieleniem młodzieżowego elektronicznego popu, jaką sobie wymyślił, i której sukcesu się spodziewał. Grupa nie doczekała się kolejnego wyraźnego lidera i od tej pory istniała pod życzliwą opieką Millera jako zbitek indywidualności podejmujących wszelkie decyzje w sposób zbiorowy i demokratyczny.
Grupa działa na specyficznych zasadach artystycznych, organizacyjnych i towarzyskich. Trzon Depeche Mode tworzyły trzy osoby: Martin Gore, David Gahan i Andy Fletcher. Kompozytorem repertuaru grupy (i niekiedy wokalistą) jest Gore, jednak jako silny introwertyk nie stara się nią kierować. Z drugiej strony nawet jego solowe projekty i praca z innymi grupami nie odciągnęły go od pracy w zespole. Przeciwieństwem zamkniętego w sobie Gore'a jest wokalista Dave Gahan, ekstrawertyk i urodzony frontman. Tych dwóch członków grupy łączyła osoba Andy'ego Fletchera, który miał wprawdzie najmniejszy wkład w muzyczny dorobek grupy, ale przyjaźnił się ze skrytym Gorem i w naturalny sposób zapewniał jego komunikację z pozostałymi członkami ekipy. Dbał także o sprawy czysto organizacyjne. Andrew Fletcher:
Dave Gahan:
Na płaszczyźnie artystycznej podstawą działalności Depeche Mode jest szczególne porozumienie między Gorem i Gahanem, dwoma twórczymi biegunami grupy, jednak pod względem towarzyskim ci dwaj nie są mocno związani, głównie z powodu zamkniętego usposobienia Gore'a.
Grupa od początku prowadziła bujne życie rozrywkowe, któremu sprzyjała rosnąca popularność i częste trasy koncertowe, a także towarzystwo grup, które supportowały ich występy. Przez wiele lat udawało im się unikać zagrożeń płynących z nieustannego imprezowania, aż w końcu David Gahan popadł z tego powodu w poważne problemy życiowe, zdołał jednak wrócić do formy, a grupa pokonała kryzys wywołany jego uzależnieniami.
Depeche Mode jako grupa elektroniczna często współpracowała z różnymi inżynierami dźwięku. Podobnie jak Miller nie byli oni nigdy członkami grupy, ale na równi z nimi wpływali na kształt i styl kolejnych albumów. To także ważny element tej nietypowej grupy muzycznej.
Muzycy
Obecny skład zespołu
Dave Gahan – wokal prowadzący (od 1980)
Martin Gore – instrumenty klawiszowe, wokal prowadzący, gitara, wokal wspierający (od 1980)
Muzycy koncertowi
Christian Eigner – perkusja, instrumenty klawiszowe (od 1997)
Peter Gordeno – instrumenty klawiszowe, gitara basowa, wokal wspierający (od 1998)
Byli członkowie zespołu
Vince Clarke – instrumenty klawiszowe, wokal prowadzący, wokal wspierający, gitara (1980–1981)
Alan Wilder – instrumenty klawiszowe, wokal wspierający, gitara basowa, sampler, perkusja (1982–1995, 2010)
Andy Fletcher – instrumenty klawiszowe, wokal wspierający, gitara basowa (1980–2022)
Oś czasu
Subkultura
Grupa ma wielu fanów na całym świecie, w tym również w Polsce, gdzie tworzą oni dość charakterystyczną subkulturę. Nazywani są depeszowcami lub depeszami. Fani grupy spotykają się na organizowanych przez siebie zlotach fanów Depeche Mode oraz depotekach. Organizują się także w fanklubach.
Zloty fanów w Polsce
Impreza organizowana przez fanów Depeche Mode dla fanów Depeche Mode. Zloty takie odbywają się w różnych miastach w Polsce i na świecie. Ideą tych spotkań jest wspólna zabawa przy dźwiękach zespołu. Przy okazji tych spotkań spotykają się depesze z różnych zakątków kraju. Na zlotach fanów Depeche Mode często organizowane są wszelakiego rodzaju konkursy jak: Dave dancing (konkurs tańca) czy konkurs śpiewu. Liczba i rodzaj konkursów jest zależna od organizatora. Organizatorami takich zlotów są przeważnie fankluby Depeche Mode. Na zlotach organizowane są także koncerty zespołów grających muzykę pokrewną lub inspirowaną Depeche Mode. Na zlotach o północy zgromadzonym ludziom przygrywa Pimpf – instrumentalny utwór, przy którym fani biorą się za ręce i tworzą okrąg falując ramionami. Organizatorzy zlotów starają się dbać pod każdym względem o uczestnika takiej imprezy przygotowując wystrój lokalu oparty na symbolice zespołu bądź wyświetlając przez telebim materiały związane z Depeche Mode tzw. wizualizacje. Największe zloty w Polsce odbyły i odbywają się w: Warszawie, Bytomiu, Bielsku-Białej, Bydgoszczy, Chorzowie, Inowrocławiu, Katowicach, Łodzi, Pabianicach, Poznaniu, Sopocie, Toruniu, Wrocławiu, Zielonej Górze oraz Nowym Tomyślu. Historycznie pierwszy zlot fanów Depeche Mode w Polsce miał miejsce w Szczecinie i był zorganizowany przez fanklub "Sattelite" (pierwsza połowa lat 80 XX wieku). Drugi zlot i kilka kolejnych było zorganizowanych w Pabianicach przez pabianicki fanklub "Muzyka dla mas". Równie historycznym wydarzeniem był warszawski zlot, który odbył się pod patronatem Radia Wa-wa i Listy Przebojów Pr.3 Polskiego Radia, w 1992 roku w klubie Agon 501. Ci sami organizatorzy, aż do dziś prowadzą cykliczne imprezy z muzyką Depeche Mode w Warszawie pod nazwą My Secret Garden Party.
Dyskografia
Speak & Spell (1981)
A Broken Frame (1982)
Construction Time Again (1983)
Some Great Reward (1984)
Black Celebration (1986)
Music for the Masses (1987)
Violator (1990)
Songs of Faith and Devotion (1993)
Ultra (1997)
Exciter (2001)
Playing the Angel (2005)
Sounds of the Universe (2009)
Delta Machine (2013)
Spirit (2017)
Memento Mori (2023)
Przypisy
Bibliografia
Depeche Mode – Dave Thomas
1990 – Strangers, The Photographs by Anton Corbijn – Anton Corbijn (wydawnictwo CPC – USA)
1991 – Depeche Mode – Marek Sierocki (Polska Oficyna Wydawnicza BGW, Warszawa, )
1994 – Depeche Mode, Some Great Reward – Dave Thompson (wydawnictwo St Martin's Press – USA)
1995 – Depeche Mode, Some Great Reward – Dave Thompson (wydawnictwo Sidwich & Jackson – Wielka Brytania)
1999
Depeche Mode – A Biography – Steve Malins (, Wielka Brytania)
Depeche Mode – Die Biographie – Steve Malins (, Niemcy)
Depeche Mode – CD Books
Depeche Mode – Jürgen Seibold (, Niemcy)
Depeche Mode – "Enjoy the Silence" – Manfred Gillig Degrave, Hans Derer (wydawnictwo Edel Company, Niemcy)
Depeche Mode – Gott, Sex & Liebe – Manfred Gillig Degrave, Hans Derer (, wydawnictwo Edel Company, Niemcy)
2003 – Stripped: Depeche Mode – Jonathan Miller (wydawnictwo Omnibus Press, Wielka Brytania)
2005 – Obnażeni, prawdziwa historia Depeche Mode – Jonathan Miller ()
2010 – Depeche Mode. Black Celebration – Steve Malins (wydanie IV, Wydawnictwo Kagra" )
Linki zewnętrzne
Oficjalna strona internetowa zespołu
Laureaci Europejskich Nagród Muzycznych MTV
Brytyjskie zespoły synthpopowe
Brytyjskie zespoły nowofalowe
Brytyjskie zespoły rocka alternatywnego
Zdobywcy platynowych płyt
Laureaci Rockbjörnen
Członkowie Rock and Roll Hall of Fame | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 335 |
Bergzicht Training has partnered with Tasting Stellenbosch, a social development initiative of Stellenbosch Wine Route, to transfer much-needed skills required in the hospitality industry to the youth. Tasting Stellenbosch and Bergzicht Training will now work together to ensure that unemployed youth obtain essential skills for front of house and the kitchen during a 10-week programme presented by Bergzicht
Lynne2019-07-02T16:57:20+00:00Donors, Employers, Graduates, News, Success Stories|
For the last seven years Bergzicht Training Child Care Programme graduate, Erna Smith from Cloetesville, has played an instrumental role in helping the Serdyn family in Unie Park, Stellenbosch raise their three children – Pierre (7), Petrus (5) and little Rose (3). When mom, Rochelle, and Dad, PW, are at work, Erna fulfills the role
Lynne2019-05-14T15:40:05+00:00Donors, Employers, Graduates, Success Stories|
Gillian Aron (28) has been working as a carer at Andante Retirement Village in Kuils River for the last three years and the thing she enjoys most about her job, says the Eerste River resident, is when she sees a smile on a patient's face as she walks through the door in the morning. "Just
Lynne2019-05-14T15:31:04+00:00Donors, Graduates, Success Stories|
Lynn de Vries has walked a long, winding road to get the job she has always wanted. However, had it not been for that road, she may not have been ready for the position of chef at Ride In Café in Jonkershoek, Stellenbosch, when the opportunity finally presented itself. "I finished matric at Stellenzicht High
Twelve Bergzicht Training beneficiaries recently graduated with Cathsseta accredited certificates in food service assistant and food and beverage service thanks to yet another generous donation by Distell to Bergzicht Training. Distell has sponsored many beneficiaries over the years since it first donated money for the training of individuals in the Cater Care Programme (now called
Teacher uses Bergzicht Training as her stepping stone
In 2015, Devon Valley resident Chrisline Thomas, signed up for an iPOWER Self-Empowering Foundation Programme at Bergzicht Training with the aim of completing the Child Care (previously called Edu Care) Programme of the organisation. She had always dreamt of making a contribution to the education of preschoolers, but had instead followed another dream after school
Providing child care support to working parents
Bergzicht Training, a skills development NGO based in Stellenbosch, has been providing at-home support to working parents in the Stellenbosch area and surrounds for the last 27 years by training child carers and nannies to fulfill a high demand for extra hands at home. However, says Bergzicht Training CEO, Renske Minnaar, not many people are
Lynne2019-02-19T16:04:06+00:00Employers, Graduates, News|
"Whatever you do well, that is your talent"
It may have taken her more than a decade, but Bergzicht Training alumnus, Nadia Andries (34), has finally found her calling and it happens to be a job that has helped her start her own business too. Before Nadia completed Bergzicht Training's Edu Care Programme, she had been employed as a sales assistant at Shoprite,
Lynne2018-12-06T14:58:04+00:00Graduates, Success Stories|
Serving others has always been her purpose
The day that Nathalie Skippers (photo) signed up for a degree in social work, she may have inadvertently found her calling, but she had no idea then that a career spent helping others to empower themselves would fulfill her that much. "I come from Prieska in the Northern Cape. Social work was not even on
A selfless act helped Janet Damane find her calling
In 2015, Bergzicht Training alumnus and then unemployed Janet Damane opened her door to a complete stranger, an elderly, frail man who had been dropped on her doorstep and abandoned by his children. What she didn't know at the time, was that this act of selflessness, while she herself was struggling, would help her find | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,568 |
Cryptotriton is the genus of hidden salamanders in the family Plethodontidae, native to Mexico, Honduras and Guatemala. Most species in this genus are endangered or critically endangered with Cryptotriton sierraminensis being data deficient according to the IUCN.
Species
The following seven species are included in this genus:
External links
. 2008. Amphibian Species of the World: an Online Reference. Version 5.2 (15 July 2008). Cryptotriton. Electronic Database accessible at https://web.archive.org/web/20071024033938/http://research.amnh.org/herpetology/amphibia/index.php. American Museum of Natural History, New York, USA. (Accessed: July 31, 2008).
[web application]. 2008. Berkeley, California: Cryptotriton. AmphibiaWeb, available at http://amphibiaweb.org/. (Accessed: July 31, 2008).
Taxonomy articles created by Polbot | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,946 |
For the love of tea, art and zero waste.
Meet the artist – Ruby Silvious, Philippines-born, US-based artist has found an ingenious way to regenerate used tea bags into stunningly intricate works of art. These are some of our favourites. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,647 |
\section{Numerical modeling}
\label{sect:modeling}
All the data to which the ensuing discussion will refer were obtained
with the versatile MESA code suite, which is comprehensively described
in \citet{Paxton2011}. The computations were performed using release
version 3251. Since we are only interested in the generic behavior of
the model stars, we kept the prescription of the physical ingredients
as simple as possible. Hence, except if mentioned explicitly otherwise
in the text, we computed the stellar-evolution models without
rotation, magnetic fields, and we neglected mass loss. Convection was
treated according to Henyey's MLT prescription and we adopted the
Schwarzschild criterion for convective instability; the mixing-length
was set ad hoc to 1.8 pressure scale-heights.
Even though different microphysics and in particular more appropriate
treatment of dynamical convection will change the results
quantitatively, probably mainly with respect to abundance profiles and
the associated consequences, we are positive that the following
discussion caught the generic nature of low-mass stars' evolution
through the onset of core helium burning and~--~viewed on the HR
diagram~--~their relatively fast transition from the top of the giant
branch onto the horizontal branch or into the clump on the giant branch.
\section{Low-mass stellar evolution to the onset of helium burning}
\label{sect:low-mass-evolution}
\begin{marginfigure}
\includegraphics{figure1} \caption{Conservative evolution
up to central helium burning, traced out in the HR Diagram of a
$1.3 M_\odot$ and a $2.1 M_\odot$ star, respectively, both
initially with the abundances $X=0.70,
Z=0.02$.} \label{fig:HRD}
\end{marginfigure}
In the following, talk of `low-mass stars' shall refer to stars
whose core helium burning starts under degenerate conditions. Since
neutrino cooling usually causes the maximum of temperature to be
reached off-center, helium burning too starts off-center. Eventually,
the \emph{central} helium-burning stage is reached through a series of
thermal pulses of the inwardly propagating helium-burning shell;
during this process, the centers of low-mass stars trace a generic
path on the density~--~temperature plane, the characteristics of which
lies at the center of attention in this exposition.
Figure~\ref{fig:HRD} shows two representative evolutionary tracks of a
$1.3 M_\odot$ (heavy line) and a $2.1 M_\odot$ star (thin line) as
computed with MESA. For the discussion of the off-center onset of
helium burning under degenerate conditions we chose the $1.3 M_\odot$
case because it was historically the first one for which the
off-center He-flash and the ensuing secondary flashes were presented
\citep{Thomas1967}. The star with $2.1 M_\odot$ in Fig.~\ref{fig:HRD}
was chosen because its mass just marginally exceeds the critical
stellar mass above which helium burning ignites in the center and
under only weakly degenerate conditions; the difference of the nuclear
evolution is not visible in the track on the HR plane but it is
evident on the $\log\rho_{\mathrm c} - \log T_{\mathrm c}$ plane
The evolution of the model stars, which are discussed in the
following, was computed in quasi-hydrostatic fashion through core
hydrogen burning, and then into central helium burning until central
helium abundance dropped to $Y_{\mathrm c}=1\cdot 10^{-4}$. The
computations started with chemically homogeneous ZAMS models
assuming $X=0.7, Z=0.02$.
\section{The initial off-center helium flash}
\label{sect:initialflash}
Once a low-mass star reaches the top of the giant branch (e.g. as
shown in Fig.~\ref{fig:HRD}) the maximum temperature is going to
exceed the critical level of about $10^8$~K above which helium starts
to fuse mostly into $^{12}C$ via the $3\alpha$ reaction. The maximum
temperature of the low-mass stars is attained not in the center but at
a mass depth that depends on the total stellar mass and on the
specific microphysics~--~foremost on the efficiency of the neutrino
energy-losses. The particular numbers that will be referred to
throughout this exposition are prone to change depending on the
particular realization of the microphysical processes included in the
evolution computations and on particular choices of the stars. The
qualitative nature of the stellar behavior will, however, remain
unchanged and it is this \emph{qualitative picture} that is the heart
of the present story and that serves us well enough to understand the
stellar behavior.
Table \ref{tab:TP1Selecta} lists a few characteristic stellar
quantities for $1.3 M_\odot$ star models during the initial helium
flash. The first column lists the model numbers to which the text and
the figures refer to occasionally. The second column contains the age
in years of the model stars counted relative to the maximum of the
initial helium flash, which was encountered at $t_0
=$~4\,522\,060\,464.5~yrs \footnote[][-1.5cm]{The at first sight
senseless accuracy of such an epoch statement can be justified in
the context of \emph{relative} timing (i.e. $t^\ast = t-t_0$), which
is helpful to describe the temporal evolution of the onset of core
helium burning. For an absolute timing, it is sufficient to remember
that it takes an $1.3 M_\odot$ star about $4.5$~Gyrs to the top of the
first giant branch.} for the chosen parameters of the evolution
computation. The third column lists the radii of the models, followed
by the total stellar luminosity and the contributions by helium and
hydrogen burning.
\begin{table*}
\caption[][0.5cm]{Selected global quantities of $1.3 M_\odot$ models during the
initial helium flash
cycle, which is discussed in detail in the text.}
\label{tab:TP1Selecta}
\centering
\begin{tabular}{c r r r r r}
\hline
\hline
Model no. & $t^{\ast}/$yrs & $\log R_\ast/R_\odot$ & $\log L_\ast/L_\odot$ &
$\log L_{\mathrm{He}}/L_\odot$ & $\log L_{\mathrm H}/L_\odot$ \\
\hline
12\,850 & -5033.59 & 2.204 & 3.38 & 1.41 & 3.38 \\
12\,950 & -0.45 & 2.204 & 3.38 & 6.45 & 3.28 \\
13\,000 & -0.01 & 2.204 & 3.38 & 8.55 & 2.91 \\
13\,025 & 0 & 2.204 & 3.38 & 9.25 & 2.04 \\
13\,050 & 0.01 & 2.204 & 3.38 & 8.85 & 0.88 \\
13\,100 & 0.08 & 2.204 & 3.38 & 7.75 & -0.96 \\
13\,200 & 6.73 & 2.201 & 3.38 & 5.44 & -3.66 \\
13\,500 & 996.71 & 1.823 & 2.84 & 2.96 & -1.33 \\
13\,700 & 9\,542.92 & 1.406 & 2.23 & -0.09 & 0.30 \\
13\,900 & 105\,296.80 & 1.296 & 2.07 & -0.26 & -2.70 \\
13\,984 & 185\,217.60 & 1.304 & 2.07 & 4.23 & -0.30 \\
\hline
\end{tabular}
\end{table*}
The schematic structure of the stellar model at maximum helium burning
(model no. $13\,025$, at $t^\ast=0$) of the initial helium flash is
sketched and labeled in Fig.~\ref{fig:SchematicM013}. The convective
envelope and the convective shell overlying the helium-burning shell
are hinted at with open circles. Nuclear burning regions, on the other
hand, are hinted at with small black dots. In the graphical
representation, the geometry is not to scale; appropriate physical
quantities at selected locations are listed on the bottom of
the plot, giving the masses, the radii and the corresponding
temperatures, $T_6 \equiv (T/K)/10^6$ at the selected boundaries. A
nuclear burning region was considered as such if the energy generation
rate exceeded $100$~erg/g/s.
\begin{figure}
\includegraphics[width=0.98\textwidth]{figure2}
\caption{Schematic internal structure of a star
model at maximum nuclear energy release during the initial helium
flash. The scales of the radiative, convective, and nuclear burning
regions are not constant through the sketch. Numerical
values of selected physical quantities, adopted from model
number 13\,025, are tabulated on the bottom.}
\label{fig:SchematicM013}
\end{figure}
At model 12\,850, the luminosity generated in the hydrogen-burning
shell is still producing essentially the total stellar luminosity; at
this epoch, i.e. at about $t^\ast\approx$~-5034 yrs, the helium shell
contributes roughly one percent to the total luminosity. Within the
ensuing roughly 5000~yrs, the helium luminosity grows by roughly
eight orders of magnitude. When the temperature exceeds the limit for
the onset of $3\alpha$ burning off-center, the peak of the symmetric
temperature bump lies at about $0.174 M_\odot$ (see model number 12\,850
in Fig.~\ref{fig:M013rhotmulti}). The density at the temperature
maximum does not change significantly during the onset of the initial
flash (see the red line connecting $m=0.174 M_\odot$ in
Fig.~\ref{fig:M013rhotmulti}), all of the generated energy goes into
further rising the temperature.
\sidenote[][0.0cm]{This is exactly the
process associated with the thermal instability of thin
nuclear-burning shells in degenerate matter as encountered in
thermally pulsing AGB stars. The instability is well documented and
explained in standard textbooks on stellar
astrophysics \citep[e.g.][]{kw}}
Applying the energy equation to the steep temperature wall the
develops during the helium flash at the inner edge of this nuclear
burning shell
\begin{equation*}
\partial_m L \approx - c_V \,\partial_t T \,,
\end{equation*}
the inward propagation speed of the wall can be estimated as
\begin{equation*}
\left\vert L \right \vert \tau \approx c_V \left\vert \frac{\Delta T}{\Delta
m} \right \vert
\left\vert \Delta m \right \vert^2 \,.
\end{equation*}
For a given extension in mass, $\Delta m$, and a given generated
luminosity, $L$, the magnitude of the temperature gradient, $\Delta T
/ \Delta m$, determines the timescale of propagation, $\tau$, of the
temperature pulse.
\marginnote[-0.7cm]{The magnitude of $\tau$, to shift the temperature
flank by its own mass thickness, varies between a few hundred
seconds at flash peak (model 13\,025) and many thousand years once
the helium-burning shell stabilizes again.}
Plugging numerical data from the evolutionary models into the above
estimate shows that the temperature wall does essentially not move in
mass during the initial flash. Despite the low values of the opacity
\sidenote[][0.2cm]{Opacity ranges from about 0.1~cm$^2$/g close to the
helium shell to about 0.01~cm$^2$/g in the strongly degenerate stellar center.}
in the inert stellar core, the prevailing temperature gradient is much
too low there to transport energy from the flash region to the
center. Therefore, only through the propagation of the temperature
wall towards the stellar center does energy penetrate the inert core.
\begin{figure}
\includegraphics{figure3}
\caption{Loci on the $\log\rho - \log T$ plane of selected
$1.3 M_\odot$ models during the early initial He flash (model numbers from
$12\,850$ to $13\,500$). The thicker black line marks the model during
the peak of the initial helium flash. The red lines trace the
evolution of a few mass shells (their mass depths are measured in
solar-mass units) on the density~--~temperature plane. The heavier
red line~--~at 0.174~--~traces the locus of maximum
$\varepsilon_{\mathrm{nuc}}$ of the helium burning shell during the
early initial flash.
The green lines with $E_{\mathrm{F}}/kT = 1$ and $20$
illustrate lines of constant degeneracy. Since $E_{\mathrm{F}}\sim
\psi$, with $E_{\mathrm{F}}$ the Fermi energy and $\psi$ the
canonical degeneracy parameter, the low-order approximation of
density in a strongly electron-degenerate environment reads $\rho \sim
\left(\psi k T \right)^{3/2}$ so that $\left.{\mathrm d} \ln T / {\mathrm d} \ln
\rho\right\vert_{\psi={\mathrm{const}}} = 2/3$.
N.B. the black lines trace strati\-fications, i.e. the \emph{spatial
structure} of selected model stars; the red lines delineate
\emph{temporal}, lagrangian state changes along the sequence of
stellar models. }
\label{fig:M013rhotmulti}
\end{figure}
Once helium burning ignites off-center, the energy sink due to
neutrinos is quickly rendered irrelevant by the encountered magnitudes
of nuclear energy generation and the involved thermal energetics (see
also Fig.~\ref{fig:M013Kippi}). Hence, \emph{neutrino losses are essential
to set the mass depth where helium burning ignites, but they do not
influence the energetics of the helium flash itself.}
As the flash gains strength, convection sets in once a critical
temperature gradient, $\nabla T$, is exceeded on the outer flank of
the temperature bump. Since $\nabla T < 0$ on the lower-mass flank,
the stratification there is always stable against convection, hence
the peak becomes asymmetric. The inner edge of the He-shell convection
zone lies close to the maximum of the $3\alpha$ energy generation and
it extends well into the intershell region. At the phase of maximum
extension, at $t^\ast \approx 16$~yrs, the convection zone reaches out
to about $0.455 M_\odot$; this is still sufficiently below the inner
edge of the envelope convection zone (at $0.465 M_\odot$ as noted in
Fig.~\ref{fig:SchematicM013}), and separated by the hydrogen-burning
shell so that under `normal' burning conditions (i.e. PopI or PopII
conditions) no merging of the two respective convection zones and
hence no mixing was ever observed in simulations. The strong entropy
jump at the hydrogen-burning shell efficiently prevents the intershell
convection zone to advance too far out. Under special conditions,
which might not be realized in nature, a merging of convection zones
could be enforced \citep{Despain1976}. Also, modeling the evolution of
very low-metallicity (PopIII) stars revealed that ingestion of
hydrogen into the He-burning shell during the onset of core helium
burning can lead to enhanced convection zones in the core, due to the
additional onset of hydrogen burning, so that eventually the deepening
envelope convection zone can transport nuclearly processed material to
the surface \citep[e.g.][and references
therein]{Hollowell1990,Suda2010}. During even later evolutionary
stages of any population-type star, the envelope convection zone
usually overlaps temporally with regions containing matter that was
previously modified by $3\alpha$ burning and mixes it
($2^{\mathrm{nd}}$ and $3^{\mathrm{rd}}$ dredge-up) into the
superficial layers of red giants along the AGB.
Figure~\ref{fig:M013Kippi} shows Kippenhahn diagrams for nuclear and
gravitational energy generation rates during the initial core helium
flash. To provide a measure of the actual time evolution, epochs
measured in years elapsed since initial flash peak at $t_0$ are given
on top of the upper panel. The epoch of the second helium flash, at
model 13\,984, is denoted as $t_1=t_0 + 185\,218$~yrs. The top panel
depicts the behavior of the hydrogen-burning shell at fractional mass
$q=0.35$ and the helium-burning shell with its basis at $q=0.13$. The
hydrogen shell is, compared with the helium shell, very narrow in mass
and goes essentially extinct shortly after the initial flash but
regains considerable strength after about 2000~yrs. Around minimum
radius of the model star (model 13\,833 at $t^\ast\approx
59\,400$~yrs) the hydrogen energy generation takes another dip because
the radius of the H-shell grows and cools as it partakes in the
expansion of the envelope towards the second thermal flash; shortly
before the second flash, after the H-shell contracted and heated
again, the hydrogen nuclear-energy generation regained its strength.
\begin{marginfigure}
\includegraphics[width=1.08\textwidth]{figure4}
\caption{Color-coded Kippenhahn diagrams showing the energetics in the
deep stellar interior during the initial helium flash, which is
parameterized on abscissa with the model number; this choice
accentuates the fast evolution during the flash peak. Physical times
in years, relative to the epoch of the initial flash, $t_0$, are
overlaid over both panels. The epoch of the second helium flash is
referred to as $t_1$. The ordinates are chosen to be the fractional
stellar mass $q$. The top panel shows the nuclear energy generation
rate $\varepsilon_\mathrm{nuc}/$erg/g/s and the lower panel a
suitably transformed version of the gravitational energy generation
$\varepsilon_\mathrm{grav}/$erg/g/s. }
\label{fig:M013Kippi}
\end{marginfigure}
For a few years around the maximum of the initial flash, the
helium-burning shell achieves a mass depth of about $0.13 M_\odot$. From
$t^\ast=7$~yrs onward, the helium shell burns rather steadily but
with a tendency to get weaker and thinner. The `gravitational energy
generation rate', $\varepsilon_\mathrm{grav}$, shown in the lower
panel is the temporal rate of change of the specific heat-content,
$Q$, of the stellar material: $\partial_t Q =
-\varepsilon_\mathrm{grav}$. The locations of the helium- as well as
hydrogen-burning shell are clearly discernible at about $q=0.13$ and
$q=0.35$, respectively. The stellar core: the sphere interior to the
He-shell does essentially not change its heat content,
i.e. $\partial_t Q = 0$, during the initial flash, which means that
state changes there are adiabatic (cf. red lines connecting e.g. $q=0$
and $q=0.16$ mass layers in Fig.~\ref{fig:M013rhotmulti}).
The envelope above the H-shell shows signs of contraction (red)
shortly after the initial He-flash when the intershell convection zone
reaches its maximum extension and essentially quenches the
H-shell. The intershell region is dominated by the convection zone
induced by the He-burning shell. From the scale on the color bar in
Fig.~\ref{fig:M013rhotmulti} we deduce that, centered around the
initial flash, $\varepsilon_\mathrm{grav}$ can easily compete in
magnitude with the nuclear counterpart from $3 \alpha$ burning; this
is the reason that stars with degenerate He-shell flashes are not
disrupted by the enormous nuclear energy input; it is roughly balanced
by decreasing the internal energy of the region and at the same time
expanding it in the deep gravitational well of the star. The shape of
the blue intershell region in the lower panel coincides with the
extension of intershell convection zone. Since the convective
time-scale is much shorter than the evolutionary time-scale after the
flash peak, the rapid propagation of physical information throughout
the intershell convection zone color along the $q$-axis (in particular
before about model 13\,600) levels out any developing
$\varepsilon_\mathrm{grav}$ gradient. The expansion of the envelope
(above the H-shell) is visible as the blue channel leaving the plot on
the upper right. On the other hand, the red region that establishes
itself on top of the He-shell around model 13\,400 and that continues
to extend outwards, also crossing essentially unimpeded the H-shell
before the second flash is dominated by an increase of the internal
energy but not by volume work, i.e. by contraction.
The intershell convection zone of the $1.3 M_\odot$ model sequence
reaches its maximum extension at about model no. 13\,200, i.e. at
$t^\ast\approx 6.7$~yrs after initial flash peak and it dies out at
$t^\ast \approx 3000$~yrs when $3\alpha$ burning develops a local
minimum after the central sphere below the helium-burning shell
expanded and cooled adiabatically (see Figs.~\ref{fig:M013Kippi} and
\ref{fig:M013Kippenhahn}). The presence of the intershell convection
zone causes the temperature gradient to be smoothed out, i.e. in the
convection zone it is considerably shallower than on the radiative
bottom-side of the He-burning shell (see model numbers $\ge$ 12\,950
in Fig.~\ref{fig:M013rhotmulti}); convection so deep in the stellar
interior is essentially adiabatic so that the stratification is isentropic
there.
\sidenote{Since ${\mathrm d} \ln T / {\mathrm d} \ln P = \nabla_{\mathrm{ad}}$ obtains for the
stratification, an ideal gas with
negligible radiation pressure as well as a non-relativistic
degenerate electron gas both support a slope
\begin{equation*}
\left.\frac{{\mathrm d} \ln T}{{\mathrm d} \ln\rho}
\right\vert_{\mathrm{isentr.}} = \frac{2}{3} \,.
\end{equation*}
}
The steep temperature gradient on the bottom side of the
helium-burning shell persists during the whole flash and is initially
determined by the equation of state because the core cannot absorb any
significant amount of energy during the flash. Since only very little
mass is contained in the region of the sharp temperature drop
(referred to as \emph{temperature flank} in the following), the pressure
gradient remains comparatively flat so that
\begin{equation*}
\left\vert\frac{{\mathrm d} \ln T}{{\mathrm d} m}\right\vert \gg \left\vert\frac{{\mathrm d} \ln
P}{{\mathrm d} m}\right\vert
\end{equation*}
obtains; the slope of the temperature flank on the $\rho - T$ plane
can then be approximated by
\begin{equation*}
\frac{{\mathrm d}\ln T}{{\mathrm d}\ln\rho} \approx \left( \frac{\partial \ln
T}{\partial \ln \rho}\right )_P = -\frac{1}{\delta}\,.
\end{equation*}
\marginnote[-0.8cm]{The notation of physical quantities in this
exposition is essentially that used in \citet{kw}; in particular the
equation of state is assumed to be of the functional form:
$\rho \sim P^\alpha\,T^{-\delta}\,\mu^\varphi$, with the
characteristic exponents $\alpha, \delta, \varphi$.}
Hence, the higher the degeneracy around the temperature maximum, the
steeper the slope of the temperature flank. In the limit of
nonrelativistic full degeneracy, the inner temperature flank is
vertical in the $\log \rho - \log T$ plane.
During the early stage of the helium flash, the density of the core
region of the star does not change noticeably; i.e. the heating due to
the steeply increasing $3\alpha$ energy generation does not inflict
any significant expansion of the stellar material so that all
liberated energy goes into further rising the local temperature at the
nuclear burning shell. With increasing temperature in the flash
region, electron degeneracy diminishes and in conjunction expansion
can set in, i.e. an increasing fraction of the released nuclear energy
goes into volume work and therefore less energy remains for further
temperature rise. As an example: Since $\varepsilon_{3\alpha}\sim
\rho^2 T^{\,41\dots 19 \dots 12}$ at $T = 1\dots 2 \dots 3 \cdot
10^8$~K, the rapid decrease of the temperature dependence of the
energy generation rate with increasing temperature allows for an
increasingly smaller density reaction to compensate the energy
increase inflicted by some temperature rise: With the above numbers,
the energy release produced by a relative temperature increase $\Delta
T / T$ is neutralized by an associated relative density decrease of
$\Delta \rho / \rho = 20.5\dots 9.5\dots 6 \,\cdot\Delta T / T$. Once
such a limit is reached on the way of reducing the material's
degeneracy, the thermal flash has passed its maximum. In the $1.3
M_\odot$ model sequence, this happens when the He-burning shell reaches
the relatively high temperature of about $3\cdot10^8$~K, which lies
already slightly below $E_{\mathrm{F}}/kT=1$ for model number 13\,050
(see Fig.~\ref{fig:M013rhotmulti}).
After the energy generation in the He-shell saturates, the size of the
convection zone stalls too. The radiative regions overlying the
convection zone cannot carry away the surplus energy since the
evolution is still to rapid for diffusion to be effective. State
changes in the layers above the adiabatically stratified intershell
convection zone trace out loci with slopes very close to $2/3$ on the
$\log\rho - \log T$ plane
\sidenote{Introducing the constraint of an adiabatic state change
\begin{equation*}
{\mathrm d} Q = 0 = c_P {\mathrm d} T - \frac{\delta}{\rho}{\mathrm d} P
\end{equation*}
into the equation of state gives:
\begin{equation*}
\left.\frac{{\mathrm d} \ln T}{{\mathrm d} \ln \rho}\right\vert_{{\mathrm d} Q=0} =
\frac{\nabla_{\mathrm{ad}}}{\alpha - \nabla_{\mathrm{ad}}\cdot\delta} \,.
\end{equation*}
Both cases of relevance here, the ideal gas with negligible
radiation pressure with $\alpha=1,\,\delta=1,\,\nabla_{\mathrm{ad}}=2/5$ and the
non-relativistic electron degeneracy with $\alpha=3/5,\,\delta=0,\,
\nabla_{\mathrm{ad}}=2/5$, admit of
\begin{equation*}
\left.\frac{{\mathrm d} \ln T}{{\mathrm d} \ln \rho}\right\vert_{{\mathrm d} Q=0} =
\frac{2}{3} \,.
\end{equation*}
}
(see e.g. the state changes at $q = 0.462$ in
Fig.~\ref{fig:M013rhotmulti}). Only after about model number 13\,400
enough time has elapsed for diffusion of radiation to influence state
changes in the intershell region (see again the state change at mass
shell $q=0.462$ just before model 13\,500 in
Fig.~\ref{fig:M013rhotmulti}) so that their loci on the $\log\rho -
\log T$ deviate from lines with slope 2/3.
The computations show that the expansion speed of the intershell
region above the helium flash proceeds as $\partial_m v \approx
\mathrm{const.}$; using this in the continuity equation together with
the assumption of adiabatic state changes, we find
\begin{equation*}
\frac{\partial_t T}{T} \sim \frac{1}{r}\,.
\end{equation*}
Hence, in the inner parts of the radiative regions of the inter-shell
layers cool stronger than the higher lying ones: This can be observed
in Fig.~\ref{fig:M013rhotmulti} to the left of $E_{\mathrm{F}}/kT =
1$, just outside of the intershell convection zone where a positive
temperature gradient develops during the initial flash cycle.
In the degenerate core, state changes are also adiabatic (see lines of
$q=0$ and $q=0.16$ in Fig.~\ref{fig:M013rhotmulti} or lower panel of
Fig.~\ref{fig:M013Kippi}). The expansion of the He-flash domain lifts
its matter into regions of lower gravitational acceleration; hence,
this expansion reduces the pressure on the inner core so that the
very core expands adiabatically. Expansion is largest where degeneracy
is lowest, i.e. around the He-flash shell. Due to near-adiabaticity of
the state change, temperature change is biggest where expansion is
biggest. Therefore, the originally slightly positive temperature
gradient goes negative at the inner edge of the helium burning zone.
\newthought{The H-shell essentially switches off} temporarily at about
$t^\ast = 7$~yrs when the adiabatic expansion of the intershell
region associated with the He-flash has sufficiently reduced the
temperature at the H-shell. But only at $t^\ast \approx$ 44~yrs has
the surface luminosity dropped by $\vert\Delta L_\ast/L_\ast\vert =
0.1$~--~this being taken as the sign that the star starts to leave the
top of the giant branch at 2417~$L_\odot$ (cf. column 4 in
Table~\ref{tab:TP1Selecta}). At the end of the initial flash, the
star's luminosity reached 113~$L_\odot$, which is roughly twice the
luminosity at which it will finally settle to centrally burn
helium. The core, being here the fractional stellar sphere lying
inside of the H-shell, is hydrostatically insulated from the envelope,
so that the core can change mechanically \emph{without} dragging along
the envelope \citep[e.g.][]{Stein1966, Sugimoto1980}. Therefore, the
delay of the surface luminosity reaction to what happens in the deep
interior can be attributed to the Kelvin-Helmholtz time of the
\emph{radiative} intershell layers which must be overcome by photon
diffusion. Once the envelope adjusts to the new energetic situation,
the bottom of the envelope convection zone retreats. By $t^\ast =$
2412~yrs, i.e. model 13\,600, helium burning eases off sufficiently
for the He-shell convection zone to disappear
(cf. Fig.~\ref{fig:M013Kippi}). Around model number 13\,740 ($t^\ast
\approx 17\,650$~yrs), the first material layers of the contracting
envelope hit and reflect on the steep density gradient at the
H-burning shell. The generated `pulse'
\sidenote{ The trace of the outgoing pulse is seen as the narrow blue
locus close to the upper right corner of the plot on lower panel of
Fig.~\ref{fig:M013Kippi}.
}
propagates back into the envelope and defines, upon its arrival at the
stellar surface, the minimum radius and accordingly the minimum
luminosity reached during the initial pulse ($47 L_\odot$ at model
no. 13\,834, i.e. at $t^\ast \approx 62\,000$~yrs). The epoch of
pulse generation at the H-shell goes along with a re-expansion and
cooling of the H-shell and induces a phase of a nearly extinct
hydrogen-burning shell. The spatial movement of the H-shell is
reminiscent of a suction reaction inflicted by the rapid expansion of
the overlying envelope. Meanwhile, the layers below the H-shell
contract adiabatically (to rise density and temperature along loci of
${\mathrm d} \ln T / {\mathrm d} \ln \rho =2/3$~--~cf.
Fig.~\ref{fig:M013rhotmulti}) to eventually lead to the
next thermal instability of the helium-burning shell.
\section{The thermal pulsing episode of the helium shell}
\label{sect:tps}
The initial helium flash is only the first of a series of flashes that
accompany the inward burning of the He-shell toward the stellar
center. Depending, among other parameters, on the stellar mass, the
number of ensuing flashes can exceed a dozen at low stellar masses;
the number goes down as the stellar mass increases and the initial
flash takes place closer (measured in mass) to the stellar center. The
physics of the thermal stability of thin nuclear-burning
shells is well understood and documented e.g. in \citet{kw}. Most
frequently, shell instability is encountered and studied in the
evolution of stars along the asymptotic giant branch. The physics of
the instability prevailing in the inward-burning He-shell at the onset
of core helium burning of low-mass stars is, however, the same.
In all cases known to us, the first flash of the onset of helium
burning in a low-mass star's core is by a large margin the most
energetic one. In the $1.3\,M_\odot$ sequence exemplified here, the
helium luminosity grows to $10^{9.25} L_\odot$ during the initial flash.
During the second flash, the helium luminosity is already about five
orders of magnitude weaker with the tendency of a continuing weakening
of the later flashes (see Fig.~\ref{fig:M013lums}).
The temporal evolution during the thermal pulsing phase of the nuclear
burning ($\varepsilon_\mathrm{nuc} > 10$~erg/g/s plotted in red) in
the stellar core is displayed in Fig.~\ref{fig:M013Kippenhahn}; the
He-shell convection zone as well as the bottom of the envelope
convection zone~--~both plotted in blue~--~are added for better
orientation. The initial pulse (shown in an appropriately scaled way
in Fig.~\ref{fig:M013Kippi}) lies just off to the left of the diagram.
Pulses two to six can be easily identified by the He-shell convection
zone which they trigger.
The last pulse, which directly leads to sustained central helium
burning is visible on the right of Fig.~\ref{fig:M013Kippenhahn}. The
initial rise of helium burning looks like the previous \emph{shell}
instabilities; however, later during the flash, as the shell burns into
the star's center it can not react as before, the shell morphs into a
central instability and hence into its rising the temperature at
essentially constant density.
\begin{figure}
\centering
\includegraphics[width=1.0\textwidth]{figure5}
\caption{Kippenhahn diagram for the inner $54 \%$ of the $1.3 M_\odot$
model star's mass, covering the end of the first (starting at model
no. 13\,400) and the ensuing five thermal flashes until central helium burning
takes the star into a quasi-static state again. The time
is measured in mega-years (Myrs) relative to $t_0$. Regions with
$\varepsilon_\mathrm{nuc} > 10$~erg/g/s are colored in red. Convective
regions, as prevailing according to Schwarzschild's criterion, are
shaded in light blue. Notice that, according to our models, the bottom
boundary of the envelope convection zone never penetrated deep enough
into the star after the initial helium flash so that \emph{no}
dredge-up of $3\alpha$-processed material takes place.
\smallskip
\noindent
The spotty character of the He-shell convection zone is spurious,
caused by the Delaunay triangulation of strongly unequally spaced
stellar-evolution data onto the regular grid that was computed for the
color-coded plot.}
\label{fig:M013Kippenhahn}
\end{figure}
The innermost part of the envelope convection zone is visible along
the top of the figure as the wavy blue band. The bottom of the
convection zone reacts on the nuclear activity in the stellar
core. Just as during the initial flash, also during the later ones the
inner edge of the convective envelope recedes after each helium flash
to re-penetrate deeper into the star during the later part of the
thermal-pulse cycle. The bottom of the convective envelope never
reached into material that was nuclearly processed during the thermal
pulses so that there is, in our computations, no chance of dredging-up
$3\alpha$ burning products. While the helium shell burns its way into
the stellar center on the timescale of about 2 Myrs, the hydrogen
shell remains essentially at constant mass depth. As can be deduced
from Fig.~\ref{fig:M013Kippenhahn}, the H-burning shell reacts to the
thermal pulsing He-shell by cyclically growing fatter shortly after
each He-flash to later-on thin out again.
Figure~\ref{fig:M013Kippenhahn} illustrates furthermore the regularity
of the thermal flash cycles. As for the stars along the AGB, the time
between two flashes, the interpulse period (IP), $\Delta
t_{\mathrm{IP}}$, appears to correlate with the core mass,
$m_{\mathrm{c}}$. For the $1.3 M_\odot$ model sequence highlighted
here, the core-mass~--~interpulse period relation is shown
by dots in Fig.~\ref{fig:DeltatIP}; they can be fitted by the relation
\begin{equation*}
\log \Delta t_{\mathrm{IP}}/\mathrm{yrs} =
5.83 - 3.23\left(\frac{m_{\mathrm{c}}}{M_\odot}\right)\,.
\end{equation*}
The core mass, $m_{\mathrm{c}}$, was measured at the maximum of
$3\alpha$ burning, the interpulse period, $\Delta t_{\mathrm{IP}}$, be
the time passed between two He-flash peaks. The last point in the
core-mass~--~interpulse-period diagram, i.e. the one belonging to the
last helium flash, which started essentially centrally, was excluded
from the analytical fit. The last flash is no longer pure in the sense
that it is distorted by its proximity to the stellar center. Indeed,
central burning evolves continually out of this distorted last
flash. For comparison, the analytical fit to the interpulse-periods of
the $0.6 M_\odot$ models of \citet{Despain1981} is shown as the
continuous line in Fig.~\ref{fig:DeltatIP}.
\begin{marginfigure}[-1.5cm]
\includegraphics{figure6}
\caption{Interpulse-period~--~core-mass relation as observed in the
evolution computations of the $1.3 M_\odot$ models (red points),
compared with the analytical fit by \citet{Despain1981}:
$
\log \Delta t_{\mathrm{IP}}/\mathrm{yrs} =
5.629 - 4.504\left({m_{\mathrm{c}}}/{M_\odot}\right)\,
$
which is shown as full line in the figure.}
\label{fig:DeltatIP}
\end{marginfigure}
As the last helium flash `hits' the star's center, the
$3\alpha$-burning matter cannot cool anymore by adiabatic expansion
induced by the underlying material as hitherto, but it stays initially
at roughly constant density while the temperature rises so that the
material's degeneracy is being reduced. Once degeneracy is low enough,
the density starts to diminish. All this happens, as illustrated in
\citet{Paxton2011}, at essentially constant total pressure; this is
achieved by the lack of any expansion/contraction of the material
overlying the helium-burning core. Once, the stellar center's
degeneracy is lifted, central helium burning proceeds in complete
equilibrium under essentially ideal-gas conditions.
\begin{figure}
\includegraphics{figure7}
\caption{Evolution on the logarithmic density~--~temperature plane of
the centers of the model stars shown in Fig.\ref{fig:HRD}.
Epochs A, B, and C along the locus traced out by the center of
the 1.3~$M_\odot$ model star define the edges of the `wedge', which is
referred to in the text. In the case of the 2.1~$M_\odot$ star whose
helium burning starts in the center, the corresponding density stays
initially essentially constant but the temperature rises strongly and
maneuvers the star's center out of degeneracy already during
the initial flash.}
\label{fig:M013M021rhoctc}
\end{figure}
\newthought{The major features of the wedge} as traced out on the
$\log\rho_{\mathrm{c}} - \log T_{\mathrm{c}}$ plane by a low-mass star's center during the
onset of core helium burning can eventually be understood
qualitatively: In Fig.~\ref{fig:M013M021rhoctc}, epoch A indicates the
tip of the first giant branch when the initial flash sets in. Epoch B
marks the arrival of helium burning in the star's center. Finally,
state C is reached when the final thermal flash removes electron
degeneracy in the center and quiescent \emph{central} helium burning
takes over. Notice that evolution of the star's center from A to B on
the $\log\rho_{\mathrm{c}} - \log T_{\mathrm{c}}$ does not proceed monotonously. During each
thermal flash the star's center moves back and forth along a locus of
essentially $E_{\mathrm{F}}/kT = \mathrm{const.}$; the magnitude of
$E_{\mathrm{F}}/kT$ which prevails in a star's center remains
essentially constant, determined by the total stellar mass. During
the luminosity decline of each pulse cycle, the central density (and
temperature) decline; during the ascending phases the cycles,
luminosity and central density (and also temperature) rise again
slightly. The magnitudes of the density rises are smaller than the
cyclic declines, so that an effective reduction in central density and
temperature result throughout the flash cycles. The fact that
degeneracy of the stellar center does hardly change during the series
of thermal pulses is attributable to lines of constant degeneracy and
loci traced out by adiabatic state changes, both having the same
slope.
\begin{figure}
\includegraphics{figure8}
\caption{Evolution of the total stellar luminosity ($L_{\ast}$, heavy
line) and its constituent components, luminosity from hydrogen
burning ($L_{\mathrm H}$), luminosity from helium burning
($L_\mathrm {He}$), and the `gravitational luminosity' ($L_{\mathrm
g}$) during the onset of helium burning in the $1.3 M_\odot$ star
model.}
\label{fig:M013lums}
\end{figure}
\newthought{Even though the helium luminosity dominates} early phases
of the initial flash cycle, other components, usually not being in the
limelight of attention, affect the star's luminosity once the thermal
instability of the helium shell fades away.
Figure~\ref{fig:M013lums} shows that it is the gravitational luminosity
\sidenote{ The casually referred to \emph{gravitational luminosity} is
defined as
\begin{equation*}
L_{\mathrm{g}} \doteq \int \varepsilon_{\mathrm{grav}}\, {\mathrm d} m \,;
\end{equation*}
it is a measure of a star's departure from thermal equilibrium.
},
$L_{\mathrm{g}}$, which dominates all other luminosity contributions
(except for $L_\mathrm {He}$ during the short flash peaks) for the
first roughly $1$~Myr after the initial flash; during this phase, the
$1.3 M_\odot$ star evolves from the tip of the giant branch to its clump
position at about $60 L_\odot$. The gravitational luminosity takes over
the r\^ole of the dominant luminosity source at around
$t^\ast=2400$~yrs, after the $L_\mathrm {H}$ minimum passed and the
envelope shrunk from 160 to $43 R_\odot$. During this later phase of the
initial pulse cycle it is the envelope above the H-burning shell
that contributes most to $L_{\mathrm{g}}$. The biggest positive
$L_{\mathrm{g}}$ contribution comes from the very base of the
envelope, the region closest to the H-burning shell, which lies also
in the steepest part of the gravitational potential.
\sidenote[][-2.0cm]{The thermal time-scale ($\intc_V T {\mathrm d}
m/L_\ast$) of the envelope, extending from the photosphere to the
outer edge of the H-burning shell, computed for the conditions at
the tip of the red-giant branch amounts to a few hundred years. Only
when assuming the envelope to encompass also the intershell region
could the corresponding thermal heat content power the star for
about $10^4$~yrs.}
The $L_{\mathrm{g}}$ behavior during the subsequent flashes, with
successively lower amplitude and with accordingly smaller radius and
thermal variation, is qualitatively the same as that during the
initial He-flash cycle.
After the initial flash, the hydrogen shell dims out so that at model
13\,200 (i.e. at $t^\ast=6.7$~yrs) it reaches a minimum at $L_\mathrm
{H}=10^{-3.7}L_\odot$ as also seen in
Fig.~\ref{fig:M013Kippi}. Figure~\ref{fig:M013lums}, on the other
hand, shows the hydrogen shell to regain sufficient strength after the
forth pulse and overtaking $L_{\mathrm{g}}$; the hydrogen-luminosity
continues to grow and finally takes over as the dominant nuclear
energy source of the star during the ensuing inter-flash phases. Even
after central helium burning is established, the H-shell retains the
status as the dominant nuclear energy source. At most, the $3\alpha$
luminosity exceeds the H-luminosity by 35 \% during the initial peak
of central helium burning, but most of the time it is clearly
superseded by the energy output of the H-burning shell.
\sidenote[][-0.2cm]{$L_{\mathrm{H}}/L_{\mathrm{He}}=2.4 - 3.4$ during most of
the central He-burning.}
During the whole thermal-pulse phase, however,
$\varepsilon_{\mathrm{grav}} \approx 0$ obtains in the central sphere
bounded by the He-shell, i.e. it stays inert in every energetic
respect. It is the diffusion time-scale of the He-burning shell into
this inert degenerate central sphere which determines the duration of
the thermal pulsing phase. Analytical guesswork is cumbersome due to
the rather strong variation of the pertinent physical quantities at
the He-burning shell during the flash cycles; depending on the
particular choices, durations between $10^5$ and $10^7$~yrs
result; stellar evolution computations yield $2\times 10^6$~yrs.
\begin{marginfigure}[-0.0cm]
\includegraphics[width=0.95\textwidth]{figure9}
\caption{Spatial variation of the helium abundance in the cores of
$1.3 M_\odot$ models. The epochs of the snapshots, measured in Myrs as
relative times $t^\ast$, are labeled on the respective
profiles. The lowest six epochs were chosen at the local minima of
$L_\mathrm{He}$ between the thermal pulses. At $t^\ast=2.1$~Myrs,
central helium burning was already in progress.}
\label{fig:HeCore}
\end{marginfigure}
\newthought{Off-center helium flashes} burn some of the helium (see
Fig.~\ref{fig:HeCore}) mainly to carbon and oxygen so that heavier
material overlies lighter one in the core~--~a potentially unstable
situation. Since stellar material is not isothermal in the relevant
regions, the stratification is not just Rayleigh-Taylor unstable; the
prevailing temperature profile can stabilize a certain magnitude of
molecular-weight contrast. The non-vanishing diffusivity of heat
requires then the stability condition against double-diffusive mixing
to be
studied.\sidenote[][1.0cm]{This is the same physical phenomenon as the
salinity steps observed in the stratification of sea water
observable at favorable places on the globe. Therefore, even in
highly compressible stellar astrophysics, this double-diffusive
instability is mostly referred to as salt-finger or thermohaline
instability~--~the names used in oceanography.}
Even though the qualitative picture of the onset of core-helium
burning as observed through the results from stellar structure and
evolution
computations\sidenote[][+1.0cm]{Essentially measured heuristically by comparing
the results of different generations of stellar-evolution codes, all
with different micro-physics and many of them with different
numerics.}
seems to be robust, any quantitative study requesting information on
abundances and abundance profiles, either as observed directly on
red-giants' surfaces or possibly deduced via observed oscillation
frequencies of red giants will require detailed multi-dimensional CFD
simulations of the stellar core region. The same applies to the study
of the detailed influence of the dynamical convection and what happens
at the corresponding convective boundaries at the He-burning shell
during the initial flash.
\newthought{Acknowledgment} NASA's Astrophysics Data System was used
extensively for this exposition. Without the open-source project MESA,
none of the illustrations and analyses presented in this paper would
have been possible; the efforts and willingness to communicate, in
particular of the `chief developer', Bill Paxton, are highly
appreciated and equally admired. I am grateful to Hideyuki~Saio who
helped to improve the content of this exposition by critically
commenting on the typescript. H.~Harzenmoser stimulated and followed
closely also this project; he tried to keep up the author's spirits
during numerous culinary late-night sit-ins that reverberated from
exegeses on the virtues of fostering understanding rather than
aggregating yet more information.
\bibliographystyle{aa}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 101 |
package version
import (
"github.com/juju/errgo"
)
var invalidConfigError = errgo.New("invalid config")
// IsInvalidConfig asserts invalidConfigError.
func IsInvalidConfig(err error) bool {
return errgo.Cause(err) == invalidConfigError
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,951 |
\section{Introduction}
To uncover accurately gluon saturation in nucleons and nuclei, precision observables of experimentally-relevant processes are essential. In the last few years, several processes have been investigated, in diffractive DIS, such as exclusive dijet production\cite{Boussarie:2014lxa, Boussarie:2016ogo,Boussarie:2019ero}, exclusive meson production \cite{Boussarie:2016bkq}, as well as, in inclusive DIS, the production of single hadron \cite{Bergabo:2022zhe}, double hadron \cite{PhysRevD.106.054035} and dijet \cite{Caucal:2021ent}.
We propose here the diffractive di-hadron production in $\gamma^{(*)} + p/A$ as another path to saturation. The results are built upon \cite{Boussarie:2016ogo} where the Next-Leading-Order (NLO) impact factors are computed in the shockwave formalism. We will emphasize on the cancellation of infrared (IR) divergences between the virtual, real, and counterterms contributions.
\section{Theoretical framework }
We consider the inclusive production of a pair of hadrons with $\vec{p}_{h_1}^{\, 2} \sim \vec{p}_{h_2}^{\, 2} $
\begin{equation}
\gamma^{(*)}(p_\gamma) + P(p_0) \rightarrow h_1(p_{h1}) + h_2 (p_{h2}) + X + P'(p_0')
\end{equation}
where $X$ stands for the other undetected particles on the projectile side.
A hybrid factorization (shockwave, collinear) is used.
The shockwave framework describes the interaction of the probe with the target, including saturation effects. The space-time dimension is $D = 2 + d = 4 + 2 \epsilon$.
We introduce two light-cone vectors $n_1, n_2$ that define the $+/-$ directions respectively and work in the $n_2 \cdot A = A^+ = 0$ gauge. The gluon field is decomposed into external (internal) field $b^\mu$ ($\mathcal{A}^\mu$), depending on the value of their $+$ momentum being below (above) an arbitrary cut-off $e^\eta p_\gamma^+$. We boost from the target rest frame to our working frame where the photon and target move ultra-relativistically and $p_0^- \sim p_\gamma^+ \sim \sqrt{s}$ with $s$ the center of mass frame of the photon and the target. The $b^\mu$ field then has the form $b^\mu(z) = b^-(\vec{x})\delta(x^+)n_2^\mu $. Wilson lines
\begin{equation}
U_{\vec{z}} = \mathcal{P} \exp \left\{ i g \int_{- \infty}^{+ \infty} d z^+ b^-(z)\right\}
\end{equation}
resum all order eikonal interactions with those fields.
All momenta in the projectile side are decomposed as
\begin{equation}
p_i^\mu = x_i p_\gamma^+ n_1^\mu + \frac{p_i^2 + \vec{p}^{\, 2 }}{2 x_i p_\gamma^+} n_2^\mu + p_{i \perp}^\mu \; .
\end{equation}
The Pomeron exchange between the probe and the target is represented by color-singlet operators built on Wilson lines, e.g. the dipole operator
\begin{equation}
\mathcal{U}_{ij} = \Tr\left(U_{\vec{z}_i}U_{\vec{z}_j}^\dag \right) - N_c\,.
\end{equation}
Those operators evolve according to the B-JIMWLK equation \cite{Balitsky:2001re, BALITSKY199699, Balitsky:1998kc,Balitsky:1998ya, Jalilian-Marian:1997qno,Jalilian-Marian:1997jhx,Jalilian-Marian:1997ubg,Jalilian-Marian:1998tzv,Kovner:2000pt,Weigert:2000gi, Iancu:2000hn, Ferreiro:2001qy, Iancu:2001ad}.
Amplitudes are factorized between the impact factors and the non-perturbative matrix elements of those operators between the target in and out state. Collinear factorization describes the fragmentation part, thanks to the hard scale $\vec{p}_{h}^{\, 2} \gg \Lambda_{QCD}^2$. We also impose $\vec{p}^{\, 2} \gg \vec{p}_{h}^{\, 2}$, $\vec{p}$ being the relative transverse momentum of the two hadrons. This implies that they have a large separation angle, eliminating the possibility of them being produced from one single parton.
From this theorem and the collinearity of the fragmenting parton and the produced hadrons, the LO cross-section is the convolution of Fragmentation Functions (FF) and coefficient functions
\begin{eqnarray}
&&\frac{d \sigma_{0JI}^{h_1 h_2}}{d x_{h_1} d x_{h_2}d^d \vec{p}_{h_1}d^d \vec{p}_{h_2}} = \sum_{q} \int_{x_{h_1}}^1 \frac{d x_q}{x_q} \int_{x_{h_2}}^1 \frac{d x_{\bar{q}}}{x_{\bar{q}}} \left(\frac{x_q}{x_{h_1}}\right)^d \left(\frac{x_{\bar{q}}}{x_{h_2}}\right)^d \nonumber \\
&& \times D_q^{h_1}\left(\frac{x_{h_1}}{x_q}\right) D_{\bar{q}}^{h_2}\left(\frac{x_{h_2}}{x_{\bar{q}}}\right) \frac{d\hat{\sigma}_{JI}}{d x_q d x_{\bar{q}} d^d \vec{p}_q d^d \vec{p}_{\bar{q}}} + (h_1 \leftrightarrow h_2)
\label{LO cross_section}
\end{eqnarray}
expressed in terms of the partonic cross-section, $J,I$ representing the photon polarization for the complex amplitude and the amplitude respectively.
\section{NLO computations in a nutshell}
The NLO density matrix contains all types of contributions depending on the nature of the impact factors, i.e
\vspace{.2cm}
\begin{figure}[h!]
\begin{picture}(430,390)
\put(20,330){\includegraphics[scale=0.2]{images/FF_dihadron_LO_box.eps}}
\put(73,395){ \tiny NLO}
\put(160,350){$=$}
\put(183,330){\includegraphics[scale=0.2]{images/FF_dihadron_LO_box.eps}}
\put(205,395){\tiny 1-loop}
\put(310,352){ \tiny + c.c}
\put(241,320){\small (a)}
\put(20,260){\includegraphics[scale=0.2]{images/FF_dihadron_NLOqqbarg_box.eps}}
\put(8,282){ \tiny +}
\put(78,250){\small (b)}
\put(183,260){\includegraphics[scale=0.2]{images/FF_q_g.eps}}
\put(162,282){\tiny +}
\put(20,190){\includegraphics[scale=0.2]{images/FF_qbar_g.eps}}
\put(241,250){\small (c)}
\put(75,180){ \small(d)}
\put(12, 212){\tiny +}
\put(162, 212){\tiny +}
\put(183,190){\includegraphics[scale=0.2]{images/ct_q_diagram.eps}}
\put(241,180){(e)}
\put(178, 210){\Bigg ( }
\put(308, 212){ \tiny $+ \, q \leftrightarrow \bar{q}$}
\put(333,210){ \Bigg )}
\end{picture}
\vspace{-185pt}
\caption{NLO cross-section dependence on FF, represented by the box.}
\label{fig:NLO_FF}
\end{figure}
\begin{equation}
d \sigma_{JI}^{NLO} = d \sigma_{1 JI} + d \sigma_{2 JI} + d \sigma_{3 JI} + d \sigma_{4 JI} + d \sigma_{5 JI} \; .
\end{equation}
Here $d \sigma_{1 JI}$ and $d\sigma_{2 JI}$ are the dipole $\times$ dipole and dipole $\times$ double dipole virtual contributions while $d\sigma_{3 JI}$, $d\sigma_{4 JI}$ and $d\sigma_{5 JI}$ are the dipole $\times$ dipole, dipole $\times$ double dipole and double dipole $\times$ double dipole real parts. The various contributions depend on the detail of the FF used, as shown by fig~\ref{fig:NLO_FF}.
To deal with divergences, dimensional regularization, and an IR cut-off $\alpha$ are used for the transverse and longitudinal integrations respectively. Soft and collinear are the only divergences present and are contained in $d \sigma_{1 JI}$ and $d\sigma_{3JI}$. The rapidity divergences, proportional to some $\ln \alpha$ terms have been removed at the level of amplitude using the B-JIMWLK equation, as explained in \cite{Boussarie:2016ogo}.
Diagram (e) in fig~\ref{fig:NLO_FF} corresponds to the counterterms produced by putting the FF renormalization and evolution equation taken from \cite{Ivanov:2012iv}
into the LO cross-section eq~\eqref{LO cross_section}.
Collinear divergences can only come from diagrams where the splitting occurs after the shockwave and the same is true for soft divergences, see fig~\ref{fig:div_diagram}.
The collinear divergences appear as denominators of $\left(x_i'\vec{p}_g - x_g \vec{p}_i \right)^2$ with $i \in \{q, \bar{q}\}$ in $d \sigma_{3JI} $.
To extract those divergences, we need to Fourier transform the non-perturbative part to disentangle and integrate over the spectator parton (the non-fragmenting one) transverse momentum easily. We also need to change variables from $(x_i', x_g)$ to $(x_i, \beta)$ where $(x_i', x_g), x_i$ are the longitudinal fractions of the \textit{children} and \textit{parent} partons wrt to the photon momentum and $\beta$ is the longitudinal fraction wrt to the parent parton. This is to be able to compare to the counterterms.
When extracting the divergent part of diagrams (1) and (3) of fig~\ref{fig:div_diagram}, one has to introduce the + prescription and remove the resulting soft contribution to avoid double counting. This issue does not appear for diagrams (5) and (6).
The soft contribution of diagram (b) of fig~\ref{fig:NLO_FF} is computed from diagrams (1-4) of fig~\ref{fig:div_diagram} altogether. We rescale $\vec{p}_g = x_g \vec{u}$ with $|\vec{u}| \sim |\vec{p}_h| $ to isolate the divergences in the form of $\int_{\alpha}^1 \frac{d x_g}{x_g^{3-d}}$. In the rest of the integrand, we put safely $x_g$ to 0 (as $x_q', x_{\bar{q}}'$ cannot be arbitrarily small, being limited by $x_{h}$).
Similar changes of variables as in the collinear case are realized too.
Most of the soft divergences in (1-4) cancel with diagram (a) of fig~\ref{fig:NLO_FF}. The rest cancel with divergences introduced by the $+$ prescription in (1) and (3).
The leftover divergences from diagrams in fig~\ref{fig:div_diagram} cancel with the counterterms.
\begin{figure}[h!]
\begin{picture}(430,385)
\put(20,330){\includegraphics[scale=0.2]{images/FF_dihadron_soft_1.eps}}
\put(37,320){\small (1) : soft + collinear ($qg$) }
\put(183,330){\includegraphics[scale=0.20]{images/FF_dihadron_soft_2.eps}}
\put(230,320){\small (2) : soft }
\put(20,260){\includegraphics[scale=0.20]{images/FF_dihadron_soft_3.eps}}
\put(37,250){\small (3) : soft + collinear ($\bar{q}g$) }
\put(183,260){\includegraphics[scale=0.20]{images/FF_dihadron_soft_4.eps}}
\put(230,250){\small (4) : soft }
\put(20, 190){\includegraphics[scale=0.20]{images/FF_q_g_coll.eps}}
\put(43,180){\small (5) : collinear ($\bar{q}g$) }
\put(183,190){\includegraphics[scale=0.20]{images/FF_qbar_g_coll.eps}}
\put(208,180){\small (6) : collinear ($qg$)}
\end{picture}
\vspace{-185pt}
\caption{Divergent diagrams in the diagram (b), (c), and (d) of fig~ \ref{fig:NLO_FF}. Diagrams (1-4) correspond to the divergent part of diagram (b), diagram (5) is the divergent diagram in diagram (c), and (6) for (d). }
\label{fig:div_diagram}
\end{figure}
\section{Conclusion and Outlook}
We have computed the NLO cross-sections of the diffractive production of a pair of hadrons with large $p_T$ out of $\gamma^{(*)} + p/A $ for all possible sets of photon polarization and in general kinematics $ (Q^2, t, p_T) $. Divergences have been cancelled altogether between the counterterms from the FF renormalization and evolution equation, dipole $\times $ dipole real, and virtual cross-sections. They are applicable to both the LHC with Ultra-Peripheral collisions and to the Electron-Ion Collider.
\bibliographystyle{JHEP}
| {
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Costco reverses course and will keep reduced senior hours as COVID-19 cases increase nationwide
Costco Wholesale will continue to hold special operating hours for members 60 and older and vulnerable shoppers while the coronavirus pandemic continues.
Weeks after announcing it would end the senior hours on July 26, the retailer changed course and is instead reducing them from five days a week to twice-weekly events.
"Instead of discontinuing, we'll maintain hours for seniors Tuesdays and Thursdays, until further notice," Richard Galanti, Costco's chief financial officer, told USA TODAY.
Starting the week of July 26, the reserved shopping time at most clubs for senior shoppers, members with disabilities or those who are immunocompromised will be 9 to 10 a.m. Tuesday and Thursday, the retailer posted on its COVID-19 updates page.
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The update comes as the number of new coronavirus infections is rising in all 50 states and hospitalizations nationwide are increasing at an alarming rate, according to Johns Hopkins University data released last week.
Target extends store hours for holiday shopping through Dec. 23 Holiday shopping: Is it too late to get big-ticket items? 30 gifts for women under $100 Shop Ulta Beauty's Holiday Beauty Blitz and take 50% off your purchase Holiday shopping: Don't forget about online marketplaces
Like most of the nation's major grocery stores, Costco started designating special shopping hours in March 2020 to help those the Centers for Disease Control and Prevention considered most vulnerable and at-risk for COVID-19.
Costco started its senior hours as a twice-weekly event and quickly extended to three times a week. When clubs resumed normal hours in early May 2020, clubs extended the senior hours to weekday mornings at most locations.
Last summer, Costco originally announced plans to reduce the special hours to twice per week in July 2020 but didn't cut the hours as cases spiked. Instead, Costco said at the time the hours would continue indefinitely.
Walmart, Target, BJ's Wholesale Club and Aldi are among retailers still promoting special senior hours on their websites. Hours and criteria vary by location. Trader Joe's has cut senior hours at most of its stores.
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Costco senior hours and exceptions
Costco's designated hour for senior shoppers, members with disabilities or people who are immunocompromised is now being held twice a week from 9 to 10 a.m. Tuesdays and Thursdays at warehouses in the U.S. and Puerto Rico with limited exceptions.
Find all locations' hours at Costco.com/warehouse-locations. Members and guests who don't meet the criteria will not be admitted. The following clubs are the exceptions listed on the COVID-19 updates page:
California Costco clubs with exceptions
Culver City: Special operating hours are 8 to 9 a.m., Tuesday and Thursday.
Temecula: Special operating hours are 8 to 9 a.m., Tuesday and Thursday.
Hawaii Costco club with an exception
Iwilei (Honolulu): Special operating hours are 8 to 9 a.m., Tuesday and Thursday.
New York Costco clubs with exceptions
Brooklyn: Special operating hours are 8 to 9 a.m., Tuesday and Thursday.
Westbury: Special operating hours are 8 to 9 a.m., Tuesday and Thursday.
Contributing: Jordan Culver and John Bacon, USA TODAY
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Follow USA TODAY reporter Kelly Tyko on Twitter: @KellyTyko. For more shopping tips and deals, join us on our Shopping Ninjas Facebook group.
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The 2001–02 North Carolina Tar Heels men's basketball team represented the University of North Carolina at Chapel Hill during the 2001–02 NCAA Division I men's basketball season. Their head coach was Matt Doherty. The team captains for this season were Jason Capel and Kris Lang. The team played its home games in the Dean Smith Center in Chapel Hill, North Carolina as a member of the Atlantic Coast Conference.
Roster
Fingleton only played one game, against Davidson, before announcing he would transfer at the end of 2001. He later transferred to Holy Cross.
Schedule and results
The Tar Heels started their regular season with three losses, the first time they had done so in 73 years. Their first regular season and conference win over Georgia Tech avoided the program's first 0-4 start in its history.
The Tar Heels were ranked number 19 in that season's preseason AP Poll. They fell out of the AP Poll after losing to Hampton. It would be the Tar Heels' only AP Poll ranking that season.
The 2001-02 season was also the first season the Tar Heels did not make it to the championship game of the Tournament of Champions presented by Hardee's in ten years, falling to Charleston in the second game. The Tar Heels did manage to upset Saint Joseph's, then ranked number 15 in the AP Poll, in the consolation game.
Prior to 2002, the largest margin of defeat against the Tar Heels in the Dean Smith Center was set in a 20-point loss against Duke in 1999. Kentucky, with 17 points, and NC State, with 18 points, nearly broke Duke's record, before Wake Forest succeeded with 22 points; Duke then reclaimed the record with a 29-point victory.
At the time, the away game at Cole Field House was the worst defeat in 79 years against Maryland, and the most points an opponent scored over the Tar Heels. The defeat also nearly matched the Tar Heels' worst defeat in their history with the Atlantic Coast Conference.
The home loss against NC State was also the worst home defeat to the Wolfpack since Dean Smith's first year as coach in 1962.
The Tar Heels matched their record for most losses in a season (15 losses in the 1950–51 and 1951-52 seasons) after their loss to Maryland at home. They would end the season with 20 losses, the most losses in the history of the program.
The Tar Heels ended their regular season at home with a 6-9 record, the worst home record in the history of the program.
In the 2002 ACC men's basketball tournament, the seventh-seeded Tar Heels were defeated by second-seeded Duke, who would go on to win that year's tournament.
|-
!colspan=12 style="background:#56A0D3; color:#FFFFFF;"| ACC Tournament
References
North Carolina Tar Heels men's basketball seasons
North Carolina
2001 in sports in North Carolina
2002 in sports in North Carolina | {
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Produced by Carol Ann Brown, Barbara Tozier, Bill Tozier
and the Online Distributed Proofreading Team at
http://www.pgdp.net.
THE GALAXY.
VOL. XXIII.--MARCH, 1877.--No. 3.
Entered, according to Act of Congress, in the year 1877, by SHELDON &
CO., in the office of the Librarian of Congress, at Washington.
THE ENGLISH PEERAGE.
More than one reader must have felt impatient with Milton for spoiling
the fine epitaph on the Marchioness of Winchester with such unfortunate
lines as "A Viscount's daughter, an Earl's heir," and "No Marchioness,
but now a queen." Probably the expressions sounded less absurd to his
contemporaries than they do to us, for titles of nobility, however
unworthily conferred, had more significance in the reign of James I.
than they bear in the reign of Queen Victoria. The memorable despatch in
which Collingwood announced the victory of Trafalgar, and which has been
described by great writers as a masterpiece of simple narration began
with these words: "Sir: The ever to be lamented death of Vice Admiral
Lord Viscount Nelson, in the moment of victory," etc. Now peers of all
ranks, except the highest, are commonly spoken of under the general
designation of "Lord So-and-So," and are rarely accorded in conversation
the honors of "my lord," or "your lordship." Generally speaking, it may
be said that in England titles, like decorations, are still greedily
sought after, but when won are not openly displayed. They are felt by
their bearers to be an anachronism, though no doubt a sufficiently
agreeable one to those most immediately concerned.
Successive governments give as large a share of patronage to the peers
and baronets, and their kinsfolk, as they reasonably can; while the
Premier is only too glad to select men of rank as his colleagues in the
Cabinet, if they are only possessed of decent abilities, and will
work--for a minister must be a hard worker in these days. Thus, Mr.
Gladstone's administration, the first which was ever designated as
"Radical," contained a large proportion of the aristocratic element in
its ranks, though it was even made a charge against Mr. Gladstone by
conservative and pseudo-liberal papers, that he unjustly deprived the
peerage of its due representation in the Cabinet.
As a matter of fact, when the Cabinet resigned it consisted of sixteen
members. Of these, eight were peers or sons of peers. Of the remaining
thirty-six Parliamentary members of the administration, fourteen were
peers or sons of peers. Mr. Disraeli's Cabinet numbers but twelve
ministers. Of these six are peers, another is heir presumptive to a
dukedom; while an eighth is a baronet; and of the remaining members of
the administration, nineteen out of thirty-eight are peers, baronets, or
sons of peers. In the army and navy, in the diplomatic service, the
peerage equally secures its full share of prizes; and even in the legal
profession it is far from being a disadvantage to a young barrister that
his name figures in the pages of Burke. In the Church a large proportion
of the best livings are held by members of the same privileged class,
and even the Stock Exchange lately showed itself eager to confer such
honors as were in its gift on a duke's son, who had been courageous
enough to "go into trade."
The British aristocracy is still, therefore, "a fact," if a favorite
term of Mr. Carlyle's may be permitted in such a connexion, as it
probably may, for the author of "The French Revolution" has himself been
one of the latest eulogists of the governing families of England, and
perhaps a few notes on the origin and history of some of the principal
houses may not be unacceptable to American readers.
The House of Lords, as at present constituted, consists of something
less than five hundred temporal peers. The first in order of hereditary
precedence, after the princes of the blood royal, is the Duke of
Norfolk, a blameless young gentleman of eight-and-twenty years, and a
zealous Catholic, as it is generally supposed that a Howard is compelled
to be by a mysterious law of his nature. As a matter of fact, however,
no family in England has changed its religion so often. Henry Charles,
thirteenth duke, seceded from the Church of Rome on the occasion of the
papal aggression. He declared himself convinced that "ultramontane
opinions were totally incompatible with allegiance to the sovereign and
the Constitution." The Duke's expression of opinion might have had more
weight with his coreligionists had his own reputation for wisdom stood
higher. But it stood very low. His Grace had made himself very
conspicuous during the agitation for the repeal of the corn laws by
recommending a curry powder of his own manufacture as a substitute for
bread, which singular piece of advice to a starving people earned him
the sobriquet of "Curry Norfolk." Charles, eleventh duke, also renounced
the old faith about the year 1780. He had not yet succeeded to his
title, but was known as the Earl of Surrey; was immediately returned to
Parliament for one of his father's boroughs. (The dukes of Norfolk had
eleven boroughs at their disposition before the passing of the reform
bill.) He was a notable personage in his day, and acted in concert with
the party of Fox. For giving the toast of "The people, our Sovereign,"
at a public dinner he was deprived of his lord-lieutenancy and of his
colonelcy of militia. He was remarkable, too, for a dislike of clean
linen, which his friends were grieved to see him carry to excess.[A]
Three other Howards of the same stock are more honorably distinguished
in their country's annals. They are the victor of Flodden and two of his
grandsons; the one the Surrey of history and romance, the other, Charles
Lord Howard of Effingham, the conqueror of the Spanish Armada. The
origin of the family is involved in obscurity, some maintaining that it
sprung from the famous Hereward, the Wake, of whose name they affirm
Howard to be a corruption; while others assert that the word Howard is
neither more nor less than a euphonious form of Hogward, and that the
premier duke and hereditary Earl Marshal of England might ultimately
trace his descent to a swineherd if he were disposed so to do. The first
Howard of whom genealogists can take serious cognizance was a
respectable judge of the court of common pleas in the reigns of Edward
I. and Edward II. (1297-1308). His descendant was ennobled in the reign
of Edward IV.
[Footnote A: "Did your Grace ever try a clean shirt?" Abernethy is said
to have asked the Duke, who had consulted him on some ailment.]
Next on the roll of the Lords to the Duke of Norfolk is Edward St. Maur,
the Duke of Somerset, an extremely clever man, "with a passion for
saying disagreeable things." He recently published a smart attack on the
evidences of Christianity, which occasioned not a little difficulty to
some worthy editors. They were sincere Christians, but it jarred against
their feelings to speak harshly of a duke. The St. Maurs (or Seymours)
are of genuine Norman descent, and began to be heard of in the
thirteenth century. They apparently remained estimable till the time of
Henry VIII., when that uxorious monarch married Jane, the daughter of
Sir John Seymour, by whom he became the father of Edward VI. Strangely
enough, Jane's brother, Lord Seymour of Sudeley, afterward married
Henry's widow, and the knot of family relationships becomes a little
complicated in consequence. More inauspicious unions were never
contracted. Lord Seymour was executed by order of his brother, the
Protector (and first Duke of Somerset), and three years later the
Protector's death-warrant was signed by his own nephew. From the close
of this short chronicle of blood, the Seymours practically disappear
from the pages of English history, though Macaulay has left a graphic
picture of that Sir Edward Seymour who was Speaker of the House of
Commons under Charles II., and who proudly replied to William III., when
asked if he belonged to the Duke of Somerset's family, that "the Duke of
Somerset belonged to his family." Francis, fifth duke, was the occasion
of a few days' gossip and much scandal. During his travels in Italy he
visited the convent of the Augustinians at Lerice, where he was foolish
enough to offer an impertinence to some ladies of the family of Botti,
and was shot by an angry Signor Botti a few hours later. His brother
Charles, who succeeded him, is the hero of a less tragic story. His
second wife, Lady Charlotte Finch, once tapped him with her fan, when he
is said to have rebuked her in these terms: "Madam, my first wife was a
Percy, and she never ventured to take such a liberty." He was known
among his contemporaries as "the proud Duke of Somerset."
The next of the ducal houses in order of precedence traces its descent
from Charles II. and Louisa de Querouaille, "whom our rude ancestors
called Madam Carwell." The Dukes of Richmond have always been known as
honorable gentlemen, but they have left no mark on the political history
of England. The present Duke is perhaps the most distinguished man of
his family, being leader of the Conservative party in the House of
Lords, and, as is generally thought, Mr. Disraeli's destined successor
in the Premiership. The third Duke held high office in the early part of
the reign of George III.; while his nephew, Colonel Lennox, who
afterward succeeded him in the title, had the honor of fighting a duel
with a son of George III. Neither of the combatants suffered any hurt,
and Colonel Lennox was reserved for the most melancholy of deaths;
falling, thirty years after, a victim to hydrophobia, caused by the bite
of a dog. His royal antagonist was Frederic, Duke of York, who
subsequently became Commander-in-Chief of the British army in the most
inglorious period of its annals. Indeed, so disgraceful was his Royal
Highness's conduct of the campaign of 1794, that Pitt demanded one of
two things from the King; viz., either that the Prince should be brought
before a court-martial, or that the Prime Minister should in future have
the right of appointing to great military commands. It must have cost
George III. a bitter pang to accept the latter alternative.
The Duke of Grafton, who holds the fourth place on Garter's Roll, is
equally descended from his Majesty, King Charles II., of happy memory.
Henry Fitzroy, son of Barbara Villiers (created Duchess of Cleveland),
was raised to the highest rank in the peerage, as Duke of Grafton, in
1675. He was one of the first to desert his uncle's cause in 1688, and
two years later he died a soldier's death under the walls of Cork,
fighting for William III. and the liberties of England. His great
grandson was Augustus Henry, third Duke of Grafton, who may still be
seen gibbeted in the pages of Junius. His Grace was a member of
Chatham's second ministry, and succeeded his chief in the Premiership.
Of other Dukes of Grafton history makes no special mention.
The fifth of the dukes in order of precedence quarters the royal arms of
France and England, but without the baton sinister. Henry Charles
Fitzroy Somerset, Duke of Beaufort, is lineally descended from "_old_
John of Gaunt, time-honored Lancaster" (third son of Edward III.) and
Catherine Swinford. John of Gaunt's children by this union were
afterward legitimatized by act of Parliament. Henry, the second son,
took holy orders, and became Bishop of Lincoln, and afterward of
Winchester, as well as Cardinal and Lord Chancellor. He is the Cardinal
Beaufort who figures in the stately Gallery of Shakespeare. He and his
brothers took the name they bore from the Castle of Beaufort, in Anjou,
the place of their nativity. The Cardinal's elder brother was created
Earl and afterward Marquis of Somerset. His descendant, Henry Beaufort,
Duke of Somerset, fell into the hands of the Yorkists, at the battle of
Hexham, and was succeeded in the family honors by his brother Edmund,
who was soon to share the same fate. With him the legitimate male line
of John of Gaunt became extinct. Duke Henry, however, had left a natural
son, who was called Charles Somerset, and who, to use the appropriate
language of chronological dictionaries, "flourished" in the reigns of
Henry VII. and Henry VIII. He was a brave soldier and a skilful
diplomatist; having been chosen a Knight of the Garter; he was also
appointed captain of the King's Guards for his services. Sir Charles
Somerset obtained in marriage Elizabeth, daughter and heiress of William
Herbert, Earl of Huntingdon, and Lord Herbert of Rayland, Chepston, and
Gower; and, in his wife's right, was summoned to Parliament as Lord
Herbert, in the first year of Henry VIII. In 1514 he was advanced to the
Earldom of Worcester, having previously been constituted Lord
Chamberlain for life, as a reward for the distinguished part he had in
the taking of Terouenne and Tournay. He died in 1526, and was succeeded
by his son. Little is heard of the Somersets--Earls of Worcester--during
the sixteenth century, though the marriage of two ladies of that house
called forth the well-known Epithalamium of Spenser. Henry, the fifth
earl, created Marquis of Worcester by Charles I., is celebrated in
English history for his defence of Rayland castle against the forces of
the Parliament, under Sir Thomas Fairfax. On this subject, Mr. George
MacDonald's last novel of "St. George and St. Michael" may be consulted
with advantage.
The brave old cavalier did not long survive the surrender and
destruction of his ancestral home. The same year he died, and was
succeeded in his title by his son Edward, the famous author of the
"Century of Inventions." It is scarcely too much to say that had this
man been divested of rank and fortune, and had he been furnished with
the requisite motive for exertion, he might have anticipated the work of
Watt and Stephenson. As it was, the discoveries he made served but to
amuse his leisure hours. The Marquis of Worcester was well-nigh the last
of his race about whose doings his countrymen would much care to be
informed. His son was created Duke of Beaufort in 1682, and with the
attainment of the highest rank in the peerage came a cessation of mental
activity in the family. One more Somerset, however, deserves honorable
mention--Fitzroy, who was aide-de-camp to Wellington, and lost an arm at
Waterloo. Raised to the peerage in 1852 as Lord Raglan, he was named two
years later to the command of the English army in the Crimea. What he
did, and what he did not, in that post, is still remembered. In truth he
was a gallant soldier, distracted by contradictory instructions, feeling
keenly the criticisms of newspaper writers, who complained that one of
the strongest fortresses in the world was not taken in a few weeks. The
siege had lasted eight months, when Lord Raglan resolved to make one
desperate effort to carry the place by assault on the 18th of June, the
fortieth anniversary of Waterloo. The attack failed, and the allies were
repulsed with severe loss. Ten days later the English general succumbed
to sickness and chagrin.
The Dukes of St. Albans enjoy precedence after the Dukes of Beaufort.
William Amelius Aubrey De Vere Beauclerk, present and tenth duke, is
lineally descended from the Merry Monarch and Nell Gwynn, and through
the marriage of the first duke, from the De Veres, Earls of Oxford. His
Grace is Hereditary Grand Falconer, a pleasant little sinecure of some
$6,000 a year. Of the Dukes of Saint Albans history has nothing to say.
The ninth duke married the widow of Mr. Thomas Coutts, of banking
renown.
Next on Garter's roll comes the Duke of Leeds, lineally descended from
Thomas Osborne, Earl of Danby and Lord High Treasurer under Charles II.,
whom Dutch William afterward made Duke of Leeds. Danby (for he is better
known by this title than by the one which he dishonored) must be
considered to have been an average statesman, and even a patriot, as
public spirit then went. He steadily opposed French influence under
Charles II., and afterward contributed to the success of the Revolution.
He was subsequently impeached by the Commons for taking bribes, but the
principal witness on whom the House relied to substantiate the charge
mysteriously disappeared when most wanted. From that day, however, the
Duke of Leeds was morally extinguished. The subsequent Dukes led worthy
and honorable lives, but were not otherwise notable. The seventh married
(24th of April, 1828) an American lady, Louisa Catharine, third daughter
of Mr. Richard Caton of Maryland, and widow of Sir Felton Bathurst
Hervey.
The two next of the ducal houses, those of Bedford and Devonshire, are
invested by Whig writers with almost a halo of glory, though in truth
they have produced respectable rather than great men. The beginnings of
the house of Russell are somewhat curious. One of the earliest ancestors
of the family of whom anything is accurately known was Speaker of the
House of Commons in the second and tenth years of Henry VI. His
grandson, John Russell, a gentleman of property, resided at Berwick,
about four miles from Bridport, in the county of Dorset. He was a
bookish man, and would probably never have gone to seek out fortune; but
fortune, as is her wont, came to him in the person of the Archduke
Philip of Austria. This Prince, the son of the reckless Maximilian,
having encountered a violent hurricane in his passage from Flanders to
Spain, was driven into Weymouth, where he landed, and was hospitably
received by a Sir Thomas Trenchard, who immediately wrote to court for
instructions. Meanwhile he deputed his first cousin, Mr. Russell, to
wait upon the Prince. His Highness was so fascinated by the conversation
of Mr. Russell, that he begged that gentleman to accompany him to
Windsor, where he spoke of him in such high terms to the King (Henry
VII.), that the monarch at once took him into his favor. He subsequently
accompanied Henry VIII. in his French wars, and afterward becoming a
supple instrument of his master's ecclesiastical policy, was rewarded
with a peerage and a grant of the Abbey of Tavistock, and the extensive
lands thereto belonging. To these possessions the Protector Somerset
added the monastery of Woburn and the Earldom of Bedford. Nor did the
star of John Russell grow dim under the reign of the Catholic Mary, who
named him Lord Privy Seal, and Ambassador to Spain, to conduct Philip
II. to England. He died in 1555. From him were descended various
Russells who enjoyed as many of the good things of this life as they
could decently lay hands upon, and two of whom were famous men in their
day. William, Lord Russell, is best known to posterity as the husband of
the admirable Rachael Wriothesley, daughter of Thomas, Earl of
Southampton, and widow of Francis, Lord Vaughan. With respect to his
execution there has been some difference of opinion; but the probability
is that it was a judicial murder of the worst kind. Immediately after
the Revolution, Lord Russell's attainder was reversed by Parliament. His
widow survived him forty years, and lived to see George I. on the throne
and the Protestant succession firmly established. What is not so
generally known, perhaps, is that the mother of Lord Russell was the
daughter of Carr, Earl of Somerset, by the divorced wife of Essex. She
was herself a virtuous lady, and is said to have fallen down in a fit
when she first learned the horrible details of her family history.
Lord Russell's cousin was the victor of La Hogue, created Earl of Orford
in 1697. He died in 1727 without issue, when the title became
extinct--to be renewed fifteen years later in favor of Sir Robert
Walpole.
Lord Russell's father was created Duke of Bedford by William III., May
11, 1694. He was succeeded by his grandson, Wriothesley, who was married
at the ripe age of fourteen and elevated to a separate peerage the same
year. He had previously been requested to come forward as a candidate
for the county of Middlesex; but the prudent Lady Russell refused to
allow him. In the then state of public opinion he would have been
elected without opposition.
The eighteenth century was the golden age of Whig families, at least
till George III. became king, and the house of Russell continued to
provide the country with a succession of dignified placemen. John IV.,
Duke of Bedford, was Lord Lieutenant of Ireland in 1756. In 1762 his
Grace, as the plenipotentiary of England, signed the preliminaries of
peace at Fontainebleau with France and Spain--a work on which he can
scarcely be congratulated, seeing that by it England was juggled out of
nearly every advantage she had won by seven years of victory. The Duke's
son, Francis, called by courtesy Marquis of Tavistock, married Lady
Elizabeth Keppel, who literally died of grief when her husband was
killed by a fall from his horse. Dr. Johnson's characteristic comment on
this event was that if her ladyship had been a poor washerwoman with
twelve children to mind, she would have had no time to die of grief.
Lord Tavistock left three sons, Francis and John, successively fifth and
sixth Dukes of Bedford, and William (posthumous), the unfortunate
nobleman who, within living memory, was murdered by his French valet
Courvoisier.
John, Earl Russell, the distinguished statesman who "upset the coach,"
is a son of the sixth duke, Lord Odo Russell, one of the ablest of
modern diplomatists, a grandson of the same peer.
On the day after the head of the house of Russell was raised to ducal
rank, the head of the Cavendishes received the same honor, being created
Marquis of Hartington and Duke of Devonshire. This family claims descent
from Sir John Cavendish, Lord Chief Justice of England in 1366, 1373,
and 1377. "In the fourth year of Richard II. his lordship was elected
chancellor of the university of Cambridge, and was next year
commissioned, with Robert de Hales, treasurer of England, to suppress
the insurrection raised in the city of York, in which year the mob,
having risen to the number of fifty thousand, made it a point,
particularly in the county of Suffolk, to plunder and murder the
lawyers; and being incensed in a more than ordinary degree against the
Chief Justice Cavendish, his son John having killed the notorious Wat
Tyler, they seized upon and dragged him, with Sir John of Cambridge,
prior of Bury, into the marketplace of that town, and there caused both
to be beheaded." Thus far Burke, who has small sympathy to bestow on Wat
Tyler, albeit that reformer was murdered in a cowardly way, whether it
were Walworth or Cavendish who struck the blow. "For William Walworth,
mayor of London, having arrested him (Wat Tyler), he furiously struck
the mayor with his dagger, but being armed [_i.e._ the mayor being in
armor], hurt him not; whereupon the mayor, drawing his baselard,
grievously wounded Wat in the neck; in which conflict an esquire of the
King's house, called John Cavendish, drew his sword and wounded him
twice or thrice, even unto death. For which service Cavendish was
knighted in Smithfield, and had a grant of L40 per annum from the King."
The great-great-grandson of this Sir John Cavendish was gentleman usher
to Cardinal Wolsey; after the death of his master King Henry took him
into his own employment, to reward him for the fidelity with which he
had served his former patron. His elder brother William was in 1530
appointed one of the commissioners for visiting and taking the
surrenders of divers religious houses. Needless to add that from that
day Mr. Cavendish had but to do as the King told him and make his
fortune. Before his death he had begun to build the noble seat of
Chatsworth, in Derbyshire, which his descendants still possess. His
second son, and eventual heir, was created Earl of Devonshire by King
James I. in 1618. The first earl's nephew was the renowned cavalier
general created Marquis and subsequently Duke of Newcastle. He was at
one time governor of the Prince of Wales (afterward Charles II.), and
there is a touching epistle extant in which his youthful charge entreats
the Marquis that he may not be compelled to take physic, which he feels
sure would do him no good.
William, fourth earl of Devonshire, although raised to a dukedom by
William III., distinguished himself, as did his son, the Marquis of
Hartington, in the House of Commons, by vehement opposition to the
King's retention of his Dutch guards after the conclusion of peace in
1697; and for this uncourtly conduct the country owes them a deep debt
of gratitude. The Dutch guards were not likely to do much harm, but
foreign troops have no business in a free state.
Henry Cavendish, the eminent chemist and philosopher, was grandson to
the second duke (who married Rachel, daughter of William, Lord Russell).
The present duke was senior wrangler of his year; his eldest son is
leader of the Liberal party in the House of Commons.
Of the dukes of Marlborough, who are next on the list, it is unnecessary
to say much. All the world knows the strange history of John Churchill,
the noblest and the meanest of mankind. The great duke's only son died
of the smallpox while yet a boy; but his honors were made perpetual in
the female as well as the male line. The present duke is lineally
descended on the father's side from a most worthy country gentleman, Sir
Robert Spencer, of Althorp, raised to the peerage as Lord Spencer by
James I. Lord Spencer's name should be dear to every American for the
friendship he showed his neighbors the Washingtons. The Washingtons had
at one time rather a severe struggle to make both ends meet, but they
saw better days. John Washington, the heir of the house, was knighted
and fought for Charles I. in the civil war. Disgusted with the
commonwealth, he emigrated to America, hearing that men were more loyal
on the other side of the Atlantic. He is commonly believed to have been
the ancestor of George Washington. Such is the irony of fate.
The second Duke of Marlborough who, when unwell, would limit himself to
a bottle of brandy a day, proved a real source of danger to his country.
When he succeeded to his grandfather's honors in 1733, the faults of the
victor of Blenheim were forgotten and only his surpassing military
achievements remembered. King and people were alike determined to honor
the man who bore his name, and, it was fondly deemed, inherited his
qualities. He was made lord lieutenant of two counties, a knight of the
garter, and promoted to high military command. Having conducted himself
without discredit at Dettingen, he was thought equal to anything, and in
the year 1758 Pitt, who felt kindly toward the Churchills, and who had
been left L10,000 by Duchess Sarah, was so rash as to name him
commander-in-chief of all the British forces in Germany destined to act
under Prince Ferdinand. After all, the appointment did no harm, for the
Duke died the same year. _Exeunt_ the Dukes of Marlborough into infinite
space. Henceforth they and their doings have no more human interest.
The Dukes of Rutland are another family dating their greatness from a
share in the spoil of the monasteries. Thomas Manners, first Earl of
Rutland, drew one of the best repartees ever made from Sir Thomas More,
then Lord Chancellor. "_Honores mutant mores_," said the Earl to Sir
Thomas in resent for some fancied affront. "Nay, my lord," replied More;
"the pun is better translated into English--Honors change Manners."
Among the descendants of this nobleman two are worthy a passing notice;
viz., John, Marquis of Granby, the most dashing of cavalry officers,
whose bluff features may still be seen on the signboards of many taverns
in England; and Lord John Manners, heir-presumptive to the Dukedom of
Rutland, and a member of the present Cabinet. Lord John is chiefly
famous as the author of a poem in which occur the oft-quoted lines:
Let arts and learning, laws and commerce die,
But keep us still our old nobility--
perhaps the most remarkable sentiment ever uttered even by a young man.
It is fair to Lord John Manners to add that he was a fairly successful
Minister of Public Works under two administrations, showing indeed a
good deal of taste and no contempt at all for the arts. Another Manners
was Archbishop of Canterbury from 1805 to 1828; but beyond having an
income of something like $130,000 punctually during nearly a quarter of
a century, this prelate cannot be considered to have done anything
noteworthy. The Archbishop's son was Speaker of the House of Commons
from 1817 to 1834, and was raised to the peerage in 1835 as Viscount
Canterbury--a peerage being the invariable termination of a modern
Speaker's career. The present Lord Canterbury (his son) has been
Governor of Victoria and two or three other colonies; for men do not
belong to a ducal family for nothing.
There are but eleven Dukes of England properly so called; that is, Dukes
sitting in the House of Lords as such, and deriving their titles from
creations before the union with Scotland. The Duke of Norfolk, as before
stated, is the first of these, and the Duke of Rutland the last in order
of precedence. The patent of the latter as Duke bears date March 29,
1703. There are also Dukes of Great Britain and of the United Kingdom,
as well as of Scotland and Ireland; but those of the two sister kingdoms
sit by inferior titles among their peers, and all the Dukes not of
England take precedence among each other by somewhat intricate rules of
precedence, into which it is not worth while to enter. The dukedoms are
twenty-eight in all, exclusive of those held by princes of the blood
royal. The honor has been very sparingly bestowed in late years. The
last conferred by George III. was that of Northumberland, the King
refusing to make any more creations, except in favor of his own
descendants. The Prince Regent made Lord Wellington a duke, and after
his accession to the throne raised Lord Buckingham to the same dignity.
William IV. made two more, and her present Majesty has added an equal
number to the list.
The history of one ducal family is the history of all. They generally
boast a founder of some abilities, and produce one or two men, seldom
more, who leave their mark on the annals of their country. It would be
strange if it were otherwise, considering the enormous opportunities
which a title, joined to fair means, gives to its possessor in England.
The privileges with which acts of Parliament and courtly lawyers in
bygone ages invested the nobility have long since become nominal. A peer
has now no right as such to tender advice to the Queen. If libelled, he
can no more terrify the offender with the penalties of _scandalum
magnatum_, but must content himself with the same remedies as do other
folk; if he cannot be arrested for debt, he shares that privilege with
all the Queen's subjects; and if he continues to be a hereditary member
of the Legislature, it is because the chamber in which he sits has been
reduced to a moderating committee of the sovereign assembly. But the
nameless privileges of persons of rank are great indeed. The army, the
navy, the Church are filled with them or their dependents. Till within
the last few years, the diplomatic service was regarded as their
peculiar property. In the present House of Commons, the second elected
by household suffrage, fully one-third of the members are sons of peers,
baronets, or closely allied by marriage, or otherwise, to the titled
classes. A fair proportion of these are Liberals; the Queen's
son-in-law, Lord Lorne, member for Argyllshire, being a professor of
"Liberal" opinions, as also Lord Stafford, son of the Duke of
Sutherland, and Lord de Gray, son of the Marquis of Ripon. Such Liberals
serve the useful function of "watering" the creed of their party, which
might otherwise prove too strong for the Constitution. Mr. Gladstone and
Mr. Bright would doubtless have gone much further in the path of reform
if unfettered by ducal retainers.
And yet, though England is still very far from the realization of that
political equality which American citizens enjoy among themselves, and
which is perhaps one of the few ascertainable benefits Frenchmen have
derived from the revolution, there can be no doubt as to the direction
in which England is advancing. Democracy is the goal of the future, and
it is even in sight, though a long way off. For instance, considerable
as is the parliamentary influence of certain noblemen in the present
day, it is influence and no more. Before the Reform act of 1832, the
parliamentary "influence" of a peer, as it was euphemistically termed,
meant that he had the absolute disposal of one or more seats in the
House of Commons. The Duke of Norfolk, as before mentioned, returned
eleven members, the Duke of Richmond three, Lord Buckingham six, the
Duke of Newcastle seven. In the year 1820, out of the twenty-six
prelates sitting in the House of Lords, only six were not directly or
indirectly connected with the peerage; while the value of some of the
sees was enormous. Now public opinion is too formidable to allow of
jobbery that is not very discreetly managed, and a great deal no doubt
is thus managed. But appearances must be kept up.
E. C. GRENVILLE MURRAY.
MISS MISANTHROPE.
BY JUSTIN MCCARTHY.
CHAPTER IV.
"OH, MUCH DESIRED PRIZE, SWEET LIBERTY!"
The summer had gone and much even of the autumn, and Miss Grey and her
companion were settled in London. Minola had had everything planned out
in her mind before they left Dukes-Keeton, and little Miss Blanchet was
positively awed by her leader's energy, knowledge, and fearlessness. The
first night of their arrival in town they went to a quiet, respectable,
old-fashioned hotel, well known of Keeton folk, where Miss Grey's father
used to stay during his visits to London for many years, and where his
name was still well remembered. Then the two strangers from the country
set out to look for lodgings, and Miss Grey was able to test her
knowledge of London, and satisfy her pride of learning, by conducting
her friend straightway to the region in which she had resolved to make a
home for herself. She had been greatly divided in mind for a while
between Kensington and the West Centre; between the neighborhood of the
South Kensington Museum, the glades of the gardens, and all the charms
of the old court suburb, and the temptations of the National Gallery,
the British Museum, and the old-fashioned squares and houses around the
latter. She decided for the British Museum quarter. Miss Blanchet would
have preferred the brightness and air of fashion which belonged to
Kensington, but Miss Grey ruled that to live somewhere near the British
Museum was more like living in London, and she energetically declared
that she would rather live in Seven Dials than out of London.
To find a pleasant and suitable lodging would ordinarily have been a
difficulty; for the regular London lodging-house keeper detests the
sight of women, and only likes the gentleman who disappears in the
morning and returns late at night. But luckily there are Keeton folk
everywhere. As a rule nobody is born in London, "except children," as a
lady once remarked. Come up to London from whatever little Keeton you
will, you can find your compatriots settled everywhere in the
metropolis. Miss Grey obtained from the kindly landlady of the
hotel--who had herself been born in Keeton, and was married to a Glasgow
man--a choice of Keeton folk willing to receive respectable and
well-recommended lodgers--"real ladies" especially. Miss Grey, being
cordially vouched for by the landlady as a real lady, found out a Keeton
woman in the West Centre who had a drawing-room and two bedrooms to let.
Had Miss Grey invented the place it could not have suited her better. It
was an old-fashioned street, running out of a handsome old-fashioned
square. The street was no thoroughfare. Its other end was closed by a
solemn, sombre structure with a portico, and over the portico a plaster
bust of Pallas. This was an institution or foundation of some kind which
had long outlived the uses whereto it had been devoted by its pious
founder. It now had nothing but a library, a lecture hall, an enclosed
garden (into which, happily for her, the windows of Miss Grey's bedroom
looked), an old fountain in the garden, considerable funds, a board of
trustees, and an annual dinner. This place lent an air of severe dignity
to the street, and furthermore kept the street secluded and quiet by
blocking up one of its ends and inviting no traffic. The house in which
our pair of wanderers was lodging was itself old-fashioned, and in a
manner picturesque. It had broad old staircases of stone, and a large
hall and fine rooms. It had once been a noble mansion, and the legend
was that its owner had entertained Dr. Johnson there and Sir Joshua
Reynolds, and that Mrs. Thrale had often been handed up and down that
staircase. Minola loved association with such good company, and it may
be confessed went up and down the stairs several times for no other
purpose whatever than the pleasure of fancying herself following in the
footsteps of bright Mrs. Thrale, with whose wrongs Miss Grey, as a
misanthrope, was especially bound to sympathize.
The drawing-room happily looked at least aslant over the grass and the
trees of the square. Minola's bedroom, as has been said, looked into the
garden of the institution, with its well-kept walks, its shrubs, and its
old-fashioned fountain, whose quiet plash was always heard in the
seclusion of the back of the house. Had the trunks of the trees been
just a little less blackened by smoke our heroine might well have
fancied, as she looked from her bedroom window of nights, that she was
in some quaint old abode in a quiet country town. But in truth she did
not desire to encourage any such delusion. To feel that she was in the
heart of London was her especial delight. This feeling would have
brightened and glorified a far less attractive place. She used to sit
down alone in her bedroom of nights in order to think quietly to
herself, "Now I am at last really in London; not visiting London, but
living in it." There at least was one dream made real. There was one
ambition crowned. "Come what will," she said to herself, "I am living in
London." In London and freedom she grew more and more healthy and happy.
As a wearied Londoner might have sought out say Keeton, and found new
strength and spirits there, so our Keeton girl, who was somewhat pale
and thin when she sat on the steps of the ducal mausoleum, grew stronger
and brighter every day in the West Centre regions of London.
A happier, quieter, freer life could hardly be imagined, at least for
her. She spent hours in the National Gallery and the Museum; she walked
with Mary Blanchet in Regent's Park, and delighted to find out new
vistas and glimpses of beauty among the trees there, and to insist that
it was ever so much better than any place in the country. As autumn came
on and the trees grew barer and the skies became of a heavier silver
gray, Minola found greater charms in their softened half tones than the
brighter lights of summer could give. Even when it rained--and it did
rain sometimes--who could fail to see the beauty, all its own, of the
green of grass, and the darker stems and branches of trees, showing
faintly through the veil of the mist and the soft descending shower? It
was, indeed, a delightful Arcadian life. Its simplicity can hardly be
better illustrated than by the fact that our adventurous pair of women
always dined at one o'clock--when they dined at all--off a chop, except
on Sundays, when they invariably had a cold fowl.
Much as Miss Grey loved London, however, it was still a place made up of
men whom she considered herself bound to dislike, and of women who
depended far too much on these men. Therefore she made studies of scraps
of London life, and amused herself by satirizing them to her friend.
"I have accomplished a chapter of London, Mary," she said one evening
before their reading had set in. "I have completed my social studies of
our neighbors in Gainsborough Place"--a little street of shops near at
hand. "I am prepared to give you a complete court guide as to the grades
of society there, Mary, so that you may know at once how to demean
yourself to each and all."
"Do tell me all about it; I should very much like to know."
"Shall we begin with the highest or the lowest?"
"I think," Miss Blanchet said with a gentle sigh, expressive of no great
delight in the story of the lower classes, "I would rather you begin low
down, dear, and get done with them first."
"Very well; now listen. The lowest of all is the butcher. He is a
wealthy man, I am sure, and his daughter, who sits in the little office
in the shop, is a good-looking girl, I think. But in private life nobody
in Gainsborough Place mixes with them on really cordial terms. Their
friends come from other places; from butchers' shops in other streets.
They do occasionally interchange a few courtesies with the family of the
baker; but the baker's wife, though not nearly so rich, rather
patronizes and looks down upon Mrs. Butcher."
"Dear me!" said the poetess. "What odd people!"
"Well, the pastry-cook's family will have nothing to do, except in the
way of business, with butcher or baker; but they are very friendly with
the grocer, and they have evenings together. Now the two little old
maids, who keep the stationer's shop where the post-office is, are very
genteel, and have explained to me more than once that they don't feel at
home in this quarter, and that their friends are in the West End. But
they are not well off, poor things, I fear, and they like to spend an
evening now and then with the family of the grocer and the pastry-cook,
who are rather proud to receive them, and can give them the best tea and
Madeira cake; and both the little ladies assure me that nothing can be
more respectable than the families of the pastry-cook and the
grocer--for their station in life, they always add."
"Oh, of course," Miss Blanchet said, who was listening with great
interest as to a story, having that order of mind to which anything is
welcome that offers itself in narrative form, but not having any
perception of a satirical purpose in the whole explanation. Minola
appreciated the "of course," and somehow became discouraged.
"Well," she said, "that's nearly all, except for the family of the
chemist, who live next to the little ladies of the post-office, and who
only know even them by sufferance, and would not for all the world have
any social intercourse with any of the others. It's delightful, I think,
to find that London is not one place at all, but only a cluster of
little Keetons. This one street is Keeton to the life, Mary. I want to
pursue my studies deeper though; I want to find out how the gradations
of society go between the mothers of the boy who drives the butcher's
cart, the baker's boy, and pastry-cook's boy."
"Oh, Minola dear!"
"You think all this very unpoetic, Mary, and you are shocked at my
interest in these prosaic and lowly details. But it is a study of life,
my dear poetess, and it amuses and instructs me. Only for chance, you
know, I might have been like _that_, and it is a grand thing to learn
one's own superiority."
"You never could have been like that, Minola; you belong to a different
class."
"Yes, yes, dear, that is quite true. I belong to the higher classes
entirely; my father was a country architect, my stepfather is a
Nonconformist minister--these are of the aristocracy everywhere."
"You are a lady--a woman of education, Minola," the poetess said almost
severely. She could not understand how even Miss Grey herself could
disparage Miss Grey and her parentage in jest.
"I can assure you, dear, that one of the pastry-cook's daughters, whom I
talked with to-day, is a much better educated girl than I am. You should
hear her talk French, Mary. She has been taught in Paris, dear, and
speaks so well that I found it very hard to understand her. She plays
the harp, and knows all about Wagner. I don't. I like her very much, and
she is coming here to take tea with us."
The poetess was not delighted with this kind of society, but she never
ventured to contradict her leader.
"You can talk to every one I do really believe," she said. "I find it so
hard to get on with people--with some people."
"I feel so happy and so free here. I can say all the cynical things that
please me--_you_ don't mind--and I can like or dislike as I choose."
"I am afraid you dislike more than you like, Minola."
"I think I could like any one who had some strong purpose in life; not
the getting of money, or making a way in society. There are such, I
suppose; I don't know."
"When you meet my brother I am sure you will acknowledge that he has a
purpose in life which is not the getting of money," said Miss Blanchet.
"But you don't like men."
Minola made no reply. Poor little Miss Blanchet felt so kindly to all
the race of men that she did not understand how any woman could really
dislike them.
"I am going to do something that will please you to-morrow," Miss Grey
said, feeling that she owed her companion some atonement for not warming
to the mention of her brother. "I am positively going to hunt out Lucy
Money. They must have returned by this time."
This was really very pleasant news for Miss Blanchet. She had been
longing for her friend to renew her acquaintance with Miss Lucy Money,
about whom she had many dreams. It did not occur to Mary Blanchet to
question directly even in her own mind the decrees of Miss Grey, or to
say to herself that the course of life which they were leading was not
the most delightful that could be devised. But, if the little poetess
could have ventured to translate vague yearnings into definite thoughts,
she would, perhaps, have acknowledged to herself a faint desire that the
brilliant passages of the London career she had marked out for herself
in anticipation should come rather more quickly than they just now
seemed likely to do. At present there was not much difference
perceptible to her between London and Duke's-Keeton. Nobody came to see
them. Even her brother had not yet presented himself. Her poem did not
make much progress; there was no great incentive to poetic work. Minola
and she did not know any poets, or artists, or publishers. Mary
Blanchet's poetic tastes were of a somewhat old-fashioned school, and
did not include any particular care for looking at trees, and fields,
and water, and skies, although these objects of natural beauty were made
to figure in the poems a good deal in connection with, and illustrative
of, the emotions of the poetess. Therefore the rambles in the park were
not so delightful to her as to her leader; and when the evening set in,
and Minola and she read to each other, Mary Blanchet was always rather
pleased if an opportunity occurred for interrupting the reading by a
talk. She was particularly anxious that Minola should renew her
acquaintance with her old schoolfellow, Miss Lucy Money, whose father
she understood to be somehow a great sort of person, and through whom
she saw dimly opening up a vista, perhaps the only one for her, into
society and literature. But the Money family were out of town when our
friends came to London, and Miss Blanchet had to wait; and, even when it
was probable that they had returned, Miss Grey did not seem very eager
to renew the acquaintance. Indeed, her resolve to visit Miss Money now
was entirely a good-natured concession to the evident desire of Mary
Blanchet. Minola saw her friend's little ways and weaknesses clearly,
and smiled now and then as she thought of them, and liked her none the
less for them--rather, indeed, felt her breast swell with kindliness and
pity. It pleased her generous heart to gratify her companion in every
way, to find out things that she liked and bring them to her, to study
her little innocent vanities, that she might gratify them. What little
dainties Mary Blanchet liked to have with her tea, what pretty ribbons
she thought it became her to wear--these Miss Grey was always perplexing
herself about. When she found that she liked to be alone sometimes, that
she must have a long walk unaccompanied, that she must have thoughts
which Mary would not care to hear, then she felt a pang of remorse, as
if she were guilty of a breach of true _camaraderie_, and she could not
rest until she had relieved her soul by some special mark of attention
to her friend. On the other hand, Mary Blanchet, for all her dreams and
aspirations, was a sensible and managing little person, who got for Miss
Grey about twice the value that she herself could have obtained out of
her money. This was a fact which Minola always took care to impress upon
her companion, for she dreaded lest Miss Blanchet should feel herself a
dependent. Miss Blanchet, however, in a modest way, knew her value, and
had besides one of the temperaments to which dependence on some really
loved being comes natural, and is inevitable.
So Minola set out next day, about three o'clock, to look up her
schoolfellow, Miss Lucy Money. She went forth on her mission with some
unwillingness, and with a feeling as if she were abandoning some purpose
or giving up a little of a principle in doing so. "I came to London to
live alone and independent," she said to herself sometimes, "and already
I am going out to seek for acquaintances. Why do I do that? I want
strength of purpose. I am just like everybody else"; and she began, as
was her wont, to scrutinize her own weaknesses, and bear heavily on
them. For, absurd as it may seem, this odd young woman really did
propose to live alone--herself and Mary Blanchet--in London until they
died--alone, that is, so far as social life and acquaintanceships in
society were concerned. Vast and vague schemes for doing good to her
neighbors, and for striving in especial to give a helping hand to
troubled women, were in Miss Grey's plans of life; but society, so
called, was to have no part in them. It did not occur to her that she
was far too handsome a girl to be allowed to put herself thus under an
extinguisher or behind a screen. When people looked after her as she
passed through the streets, she assumed that they noticed some rustic
peculiarity in her dress or her hat, and she felt a contempt for them.
Her love of London did not imply a love of Londoners, whom in general
she thought rude and given to staring. But even if she had thought
people were looking at her because of her figure, her face, her eyes,
her superb hair, she would have felt a contempt for them all the same.
She had a proud indifference to personal beauty, and looked down upon
men whose judgment could be affected by the fact that a woman had finer
eyes, or brighter hair, or a more shapely mould than other women.
Once Minola was positively on the point of turning back, and renouncing
all claim on the acquaintanceship of her former school companion. She
suddenly remembered, however, that in condemning her own fancied
weakness she had forgotten that her visit was undertaken to oblige Mary
Blanchet. "Poor Mary! I have only one little acquaintanceship that has
anything to do with society, and am I to deny her that chance if she
likes it?" She went on rapidly and resolutely. Sometimes she felt
inclined to blame herself for bringing Mary Blanchet away from Keeton,
although Mary had for years been complaining of her life and her work
there, and beseeching Miss Grey not to leave her behind when she went to
live in London.
It was a beautiful autumn day. London looks to great advantage on one of
these rare days, and Miss Grey felt her heart swell with mere delight as
she looked from the streets to the sky and from the sky to the streets.
She passed through one or two squares, and stopped to see the sun,
already going down, send its light through the bare branches of the
trees. The western sky was covered with gray, silver-edged clouds, which
brightened into blots of golden fire as they came closer in the track of
the sun. The air was mild, soft, and almost warm. All poets and painters
are full of the autumnal charms of the country; but to certain oddly
constituted minds some street views in London on a fine autumn day have
an unspeakable witchery. Miss Grey walked round and round one of the
squares, and had to remind herself of her purpose on Mary Blanchet's
behalf in order to impel herself on.
The best of the day had gone, and the early evening was looking somewhat
chill and gloomy between the huge ramparts of the Victoria street houses
by the time that Miss Grey stood in that solemn thoroughfare, and her
heart sank a little as she reached the house where her old school friend
lived.
"Perhaps Lucy Money is altogether changed," Miss Grey said to herself as
she came up to the door. "Perhaps she won't care about me; perhaps I
shan't like her any more; and perhaps her mamma will think me a dreadful
person for not honoring my stepfather and stepmother. Perhaps there are
brothers--odious, slangy young men, who think girls fall in love with
them. Oh, yes, here is one of them."
For just as she had rung the bell a hansom cab drove up to the door, and
a tall, dark-complexioned young man leaped out. He raised his hat with
what seemed to Miss Grey something the manner of a foreigner when he saw
her standing at the door, and she felt a momentary thrill of relief,
because, if he was a foreigner, he could not be Lucy Money's brother.
Besides, she knew very well that the great houses in Victoria street
were occupied by several tenants, and there was good hope that the young
man might have business with the upper story, and she with the ground
floor.
The young man was about to ring the bell, when he stopped and said:
"Perhaps you have rung already?"
"Yes, I have rung," Miss Grey coldly replied.
"This is Mr. Money's, I suppose?"
"Mr. Money lives here," she answered, with the manner of one resolute to
close the conversation. The young man did not seem in the least
impressed by her tone.
"Perhaps I have the honor of speaking to Miss Money?" he began, with
delighted eagerness.
"No. I am not Miss Money," she answered, still in her clear monotone.
No words could say more distinctly than the young man's expression did,
"I am sorry to hear it." Indeed, no young man in the world going to
visit Mr. Money could have avoided wishing that the young lady then
standing at the door might prove to be Miss Money.
The door opened, and the young man drew politely back to give Miss Grey
the first chance. She asked for Miss Lucy Money, and the porter rang a
bell for one of Mr. Money's servants. Miss Grey had brought a card with
her, on which she had written over her engraved name, "For Lucy Money,"
and beneath it, "Nola," the short rendering of "Minola," which they used
to adopt at school.
Then the porter looked inquiringly at the other visitor.
"If Mr. Money is at home," said the latter, "I should be glad to see
him. I find I have forgotten my card case, but my name is Heron--Mr.
Victor Heron; and do, please, try to remember it, and to say it
rightly."
CHAPTER V.
MISS GREY'S FIRST CALL.
Mr. Money's home, like Mr. Money himself, conveyed to the intelligent
observer an idea of quiet, self-satisfied strength. Mr. Money had one of
the finest and most expensive suites of rooms to be had in the great
Victoria street buildings, and his rooms were furnished handsomely and
richly. He had servants in sober livery, and a carriage for his wife and
daughters, and a little brougham for himself. He made no pretence at
being fashionable; rather indeed seemed to say deliberately, "I am a
plain man and don't care twopence about fashion, and I despise making a
show of being rich; but I am rich enough for all I want, and whatever
money can buy for me I can buy." He would not allow his wife and
daughters to aim at being persons of fashion had they been so inclined,
but they might spend as much money as ever they pleased. He never made a
boast of his original poverty, or the humbleness of his bringing up, nor
put on any vulgar show of rugged independence. The impression he made
upon everybody was that of a completely self-sufficing--we do not say
self-sufficient--man. It was not very clear how he had made his money.
He had been at the head of one of the working departments under the
Government, had somehow fancied himself ill treated, resigned his place,
and, it was understood, had entered into various contracts to do work
for the governments of foreign States. It was certain that Mr. Money was
not a speculator. His name never appeared in the directors' list of any
new company. He could not be called a city man. But it was certain that
he was rich.
Mr. Money was in Parliament. He was a strong radical in theory, and was
believed to have much stronger opinions than he troubled himself to
express. There was a rough, scornful way about him, as of one who dearly
considered all our existing arrangements merely provisional, and who in
the mean time did not care to occupy himself overmuch with the small
differences between this legislative proposition and that. It was not on
political subjects that he usually spoke. He was a very good speaker,
clear, direct, and expressive in his language, always using plain,
effective words, and always showing a perfect ease in the finishing of
his sentences. There was a savor of literature about him, and it was
evident in many indirect ways that he knew Greek and Latin much better
than most of the university men. The impression he produced was that of
a man who on most subjects knew more than he troubled himself to
display. It seemed as if it would take a very ready speaker indeed to
enter into personal contest with Mr. Money and not get the worst of it.
He was believed to be very shrewd and clever, and was known to be
liberal of his money. People consulted him about many things, and to
some extent admired him; some were a little afraid of him, and, in
homely phrase, fought shy of him. Perhaps he was thought to be
unscrupulous; perhaps his blunt way of going at the very heart of a
scruple in others made them fancy that he rather despised all moral
conventionalities. Whatever the reason was, a certain class of persons
always rather distrusted Mr. Money, and held aloof even while asking his
advice. No one who had come in his way even for a moment forgot him, or
was confused as to his identity, or failed to form some opinion about or
could have put clearly into words an exact statement of the opinion he
had formed.
On this particular day of autumn Mr. Money was in his study reading
letters. He was talking to himself in short, blunt sentences over each
letter as he read it, and put it into a pigeonhole, or tore it and threw
it into the waste-paper basket. His sentences were generally concise
judgments pronounced on each correspondent. "Fool." "Blockhead." "Just
so; I expected that of you!" "Yes, yes, he's all right." "That will do."
Sometimes a comment, begun rather gruffly, ended in a good-natured
smile, and sometimes Mr. Money, having read a letter to the close with a
pleased and satisfied expression, suddenly became thoughtful, and leaned
upon his desk, drumming with the finger tips of one hand upon his teeth.
A servant interrupted his work by bringing him a message and a name. Mr.
Money looked up, said quickly, "Yes, yes; show him in!" and Mr. Victor
Heron was introduced.
Mr. Money advanced to meet his visitor with an air of cordial welcome.
One peculiarity of Mr. Money's strong, homely face was the singular
sweetness of the smile which it sometimes wore. The full lips parted so
pleasantly, the white teeth shone, and the eyes, that usually seemed
heavy, beamed with so kindly an air, that to youth at least the
influence was for the moment irresistible. Victor Heron's emotional face
sparkled with responsive expression.
"Well, well; glad to see you, glad to see you. Knew you would come.
Shove away those blue books and sit down. We haven't long got back; but
I tried to find you, and couldn't get at your address. They didn't know
at the Colonial Institute even. And how are you, and what have you been
doing with yourself?"
"Not much good," Heron replied, thinking as usual of his grievance. "I
couldn't succeed in seeing anybody."
"Of course not, of course not. I could have told you so. People are not
yet coming back to town, except hard working fellows like me. Have you
been cooling your heels in the antechambers of the Colonial office?"
"Yes, I have been there a little; not much. I saw it was no use just
yet, and that isn't a kind of occupation I delight in." The young man's
face reddened with the bare memory of his vexation. "I hate that sort of
thing."
"To go where you know people don't want to see you? Yes, it tries young
and sensitive people a good deal. They've put you off?"
"As I told you, I have seen nobody yet. But I mean to persevere. They
shall find I am not a man to be got rid of in that way."
Mr. Money made no observation on this, but went to a drawer in his desk
and took out a little book with pages alphabetically arranged.
"I have been making inquiries about you," he said, "of various people
who know all about the colonies. Would you like to hear a summary
description of your personal character? Don't be offended--this is a way
I have; the moment a person interests me and seems worth thinking about,
I enter him in my little book here, and sum up his character from my own
observation and from what people tell me. Shall I read it for you? I
wouldn't, you may be sure, if I thought you were anything of a fool."
This compliment, of course, conquered Heron, who was otherwise a good
deal puzzled. But there was something in Mr. Money's manner with those
in whom he took any interest, that prevented their feeling hurt by his
occasional bluntness.
"I don't know myself," Heron said.
"Of course you don't. What busy man, who has to know other people, could
have time to study himself? That work might do for philosophers. I may
teach you something now, and save you the trouble."
"I suppose I ought to make my own acquaintance," said Heron resignedly,
while much preferring to talk of his grievance.
"Very good. Now listen.
"Heron, Victor.--Formerly in administration of St. Xavier's settlements.
Got into difficulty; dropped down. Education good, but literary rather
than businesslike. Plenty of pluck, but wants coolness. Egotistic, but
unselfish. Good deal of talent and go. Very honest, but impracticable. A
good weapon in good hands, but must take care not to be made a
plaything."
Heron laughed. "It's a little like the sort of thing phrenologists give
people," he said, "but I think it's very flattering. I can assure you,
however, no one shall make a plaything of _me_," he added with emphasis.
"So we all think, so we all think," Mr. Money said, putting away his
book. "Well, you are going on with this then?"
"I am going to vindicate my conduct, and compel them to grant me an
inquiry, if you mean that. Nothing on earth shall keep me from that."
"So, so. Very well. We'll talk about that another time--many other
times; and I may give you some advice, which you needn't take if you
don't like, and I shan't be offended. Now, I want to introduce you to my
wife and my girls, and you must have a cup of tea. Odd, isn't it, to
find men drinking tea at five o'clock in the afternoon? Up at the club,
any day about that hour, you might think we were a drawing-room full of
old spinsters, to hear the rattling of teacups that goes on all around."
He took Heron's arm in a friendly, dictatorial way, and conducted him to
the drawing-room on the same floor.
The drawing-room was entered, not by opening a door, but by withdrawing
some folds of a great, heavy, dark-green curtain. Mr. Money drew aside
part of the curtain to make way for his friend; and they both stopped a
moment on the threshold. A peculiar, sweet, half melancholy smile gave a
strange dignity for the moment to Mr. Money's somewhat rough face, and
he gently let the curtain fall.
"Wasn't there some great person, Mr. Heron--Burke, was it?--who used to
say that whatever troubles he had outside all ceased as he stood at his
own door? Well, I always feel like that when I lift this curtain."
It was a pretty sight, as he again raised the curtain and led Heron in.
The drawing-room was very large, and was richly, and, as it seemed to
Heron, somewhat oddly furnished. The light in the lower part was faint
and dim, a sort of yellowish twilight, procured by softened lamps. The
upper extremity was steeped in a far brighter light, and displayed to
Heron, almost as on a stage, a little group of women, among whom his
quick eye at once saw the girl who had come up to the door at the same
time with him. She was, indeed, a very conspicuous figure, for she was
seated on a sofa, and one girl sat at her feet, while another stood at
the arm of the sofa and bent over her. An elderly lady, with voluminous
draperies that floated over the floor, was reclining on a low arm-chair,
with her profile turned to Heron. On a fancy table near, a silver
tea-tray glittered. A daintily dressed waiting-maid was serving tea.
"Take care of the floors as you come along," said Money. "We like to put
rugs, and rolls of carpet, and stools now in all sorts of wrong places,
to trip people up. That shows how artistic we are! Theresa, dear, this
is my friend, Mr. Heron."
"I am glad to see you, Mr. Heron," said a full, deep, melancholy voice,
and a tall, slender lady partly rose from her chair, then sank again
amid her draperies, bowed a head topped by a tiny lace cap, and held out
to Heron a thin hand covered with rings, and having such bracelets and
dependent chainlets that when Heron gave it even the gentlest pressure,
they rattled like the manacles of a captive.
"We saw you in Paris, Mr. Heron," the lady graciously said, "but I think
you hardly saw us."
"These are my daughters, Mr. Heron, Theresa and Lucy. I think them good
girls, though full of nonsense," said Mr. Money.
Lucy, who had been on a footstool at Miss Grey's feet, gathered herself
up, blushing. She was a pretty girl, with brown, frizzy hair, and wore a
dress which fitted her so closely from neck to hip that she might really
have been, to all seeming, melted or moulded into it. The other young
lady, Theresa, slightly and gravely inclined her head to Mr. Heron, who
at once thought the whole group most delightful and beautiful, and found
his breast filled with a new pride in the loved old England that
produced such homes and furnished them with such women.
"Dear, darling papa," exclaimed the enthusiastic little Lucy, swooping
at her father, and throwing both arms round his neck, "we have had such
a joy to-day, such a surprise! Don't you see anybody here? Oh, come now,
do use your eyes."
"I see a young lady whom I have not yet the pleasure of knowing, but
whom I hope you will help me to know, Lucelet."
Mr. Money turned to Miss Grey with his genial smile. She rose from the
sofa and bowed and waited. She did not as yet quite understand the Money
family, and was not sure whether she ought to like them or not. They
impressed her at first as being far too rich for her taste, and odd and
affected, and she hated affectation.
"But this is Nola Grey, papa--my dearest old schoolfellow when I was at
Keeton; you must have heard me talk of Nola Grey a thousand times."
So she dragged her papa up to Nola Grey, whose color grew a little at
this tempestuous kind of welcome.
"Dare say I did, Lucelet, but Miss Grey, I am sure will excuse me if I
have forgotten; I am very glad to see you, Miss Grey--glad to see any
friend of Lucelet's. So you come from Keeton? That's another reason why
I should be glad to see you, for I just now want to ask a question or
two about Keeton. Sit down."
Miss Grey allowed herself to be led to a sofa a little distance from
where she had been sitting. Mr. Money sat beside her.
"Now, Lucelet, I want to ask Miss Grey a sensible question or two, which
I don't think you would care twopence about. Just you go and help our
two Theresas to talk to Mr. Heron."
"But, papa darling, Miss Grey won't care about what you call sensible
subjects any more than I. She won't know anything about them."
"Yes, dear, she will; look at her forehead."
"Oh, I have looked at it! Isn't it beautiful?"
"I didn't mean that," Mr. Money said with a smile; "I meant that it
looked sensible and thoughtful. Now, go away, Lucelet, like a dear
little girl."
Miss Grey sat quietly through all this. She was not in the least
offended. Mr. Money seemed to her to be just what a man ought to
be--uncouth, rough, and domineering. She was amused meanwhile to observe
the kind of devotion and enthusiasm with which Mr. Heron was entering
into conversation with Mrs. Money and her elder daughter. That, too, was
just what a man ought to be--a young man--silly in his devotion to
women, unless, perhaps, where the devotion was to be accounted for
otherwise than by silliness, as in a case like the present, where the
unmarried women might be presumed to have large fortunes. So Miss Grey
liked the whole scene. It was as good as a play to her, especially as
good as a play which confirms all one's own theories of life.
"England, Mr. Heron," said Mrs. Money in her melancholy voice, "is near
her fall."
"Oh, Mrs. Money, pray pardon me--England! you amaze me--I _am_
surprised--do forgive me--to hear an Englishwoman say so; our England
with her glorious destiny!" The young man blushed and grew confused. One
might have thought his mother had been called in question or his
sweetheart.
Mrs. Money shook her head and twirled one of her bracelets.
"She is near her fall, Mr. Heron! You cannot know. You have lived far
away, and do not see what _we_ see. She has proved faithless to her
mission."
"Something--yes--there I agree," Mr. Heron eagerly interposed, thinking
of the St. Xavier's settlements.
"She was the cradle of freedom," Mrs. Money went on. "She ought to have
been always its nursery and home. What have we now, Mr. Heron? A people
absolutely in servitude, the principle of caste everywhere
triumphant--corruption in the aristocracy--corruption in the city. No
man now dares to serve his country except at the penalty of suffering
the blackest ingratitude!"
Mr. Heron was startled. He did not know that Mrs. Money was arguing only
from the assumption that her husband was a very great man, who would
have done wonderful things for England if a perverse and base ruling
class had not thwarted him, and treated him badly.
"England," Theresa Money said, smiling sweetly, but with a suffusion of
melancholy, "can hardly be regenerated until she is once more dipped in
the holy well."
"You see we all think differently, Mr. Heron," said the eager Lucy.
"Mamma thinks we want a republic. Tessy is a saint, and would like to
see roadside shrines."
"And you?" Heron asked, pleased with the girl's bright eyes and winning
ways.
"Oh--I only believe in the regeneration of England through the
renaissance of art. So we all have our different theories, you see, but
we all agree to differ, and we don't quarrel much. Papa laughs at us all
when he has time. But just now I am taken up with Nola Grey. If I were a
man, I should make an idol of her. That lovely, statuesque face, that
figure--like the Diana of the Louvre!"
Mr. Heron looked and admired, but one person's raptures about man or
woman seldom awaken corresponding raptures in impartial breasts. He saw,
however, a handsome, ladylike girl, who conveyed to him a sort of
chilling impression.
"She was my schoolfellow at Keeton," Lucy went on, "and she was so good
and clever that I adored her then, and I do now again. She has come to
London to live alone, and I am sure she must have some strange and
romantic story."
Meanwhile Mr. Money, who prefaced his inquiries by telling Miss Grey
that he was always asking information about something, began to put
several questions to her concerning the local magnates, politics, and
parties of Keeton. Minola was rather pleased to be talked to by a man as
if she were a rational creature. Like most girls brought up in a
Nonconformist household in a country town, she had been surrounded by
political talk from her infancy, but unlike most girls, she had
sometimes listened to it and learned to know what it was all about. So
she gave Mr. Money a good deal of information, which he received with an
approbatory "Yes, yes" or an inquiring "So, so" every now and then.
"You know that there's likely to be a vacancy soon in the
representation-member of Parliament," he added by way of explanation.
"I know what a vacancy in the representation means," Miss Grey answered
demurely, "but I didn't know there was likely to be one just now. I
don't keep up much correspondence with Keeton. I don't love it."
"Why not?"
"Oh, I don't know."
He smiled.
"You are smiling because you think that a woman's answer? So it is, Mr.
Money, and I am afraid it isn't true; but I really didn't think of what
I was saying. I _do_ know why I don't care much about Keeton."
"Yes, yes; well, I dare say you do. But to return, as the books say--do
you know a Mr. Augustus Sheppard?"
She could not help coloring slightly. "Yes, I know him," and a faint
smile broke over her face in spite of herself.
"Is he strong in Keeton?"
"Strong?"
"Well liked, respectable, a likely kind of man to get good Conservative
support if he stood for Keeton? You don't know, perhaps?"
"Yes, I think I do know. I believe he wishes to get into Parliament, and
I am sure he is thought highly of. He is a very good man--a man of very
high character," she added emphatically, anxious to repair the mental
wrong doing of thinking him ridiculous and tiresome.
Just at this moment Mr. Heron rose to take his leave, and Mr. Money left
the room with him, so that the conversation with Miss Grey was broken
off. Then Lucy came to Nola again, and Nola was surrounded by the three
women, who began to lay out various schemes for seeing her often and
making London pleasant to her. Much as our lonely heroine loved her
loneliness, she was greatly touched by their spontaneous kindness, but
she was alarmed by it too.
A card was brought to Mrs. Money, who passed it on to Lucy.
"Oh, how delightful!" Lucy exclaimed. "So glad he has come, mamma. Nola,
dear, a poet--a real poet!"
But Nola would not prolong her visit that day even for a poet. A very
handsome, tall, dark-haired man, who at a distance seemed boyishly
young, and when near looked worn and not very young, was shown in. For
the moment or two that she could see him, Minola thought she had never
seen so self-conceited and affected a creature. She did not hear his
name nor a word he said, but his splendid, dark eyes, deeply set in
hollows, took in every outline of her face and form. She thought him the
poet of a schoolgirl's romance made to order.
Minola tore herself from the clinging embraces of Lucy, with less
difficulty, perhaps, because of the poet's arrival, to whose society
Lucy was clearly anxious to hasten back. It so happened that Mr. Money
had kept Mr. Heron for a few minutes in talk, and the result was that
exactly as Miss Grey reached the door Mr. Heron arrived there too. They
both came out together, and in a moment they were in the gray
atmosphere, dun lines of houses, and twinkling gaslights of Victoria
street. Minola would much rather have been there alone.
Victor Heron, however, was full of the antique ideas of man's chivalrous
duty and woman's sweet dependence, which still lingered in the
out-of-the-way colony where he had spent so much of his time. Also, it
must be owned that he had not yet quite got rid of the sense of
responsibility and universal dictatorship belonging to the chief man in
a petty commonwealth. For some time after his return to London he could
hardly see an omnibus horse fall in the street without thinking it was
an occasion which called for some intervention on his part. Therefore,
when Miss Grey and he stood in the street together Mr. Heron at once
assumed that the young woman must, as a matter of course, require his
escort and protection.
He calmly took his place at her side. Miss Grey was a little surprised,
but said nothing, and they went on.
"Do you live far from this, Miss Money?" he began.
"I am not Miss Money. My name is Grey."
"Of course, yes--I beg your pardon for the mistake. It was only a
mistake of the tongue, for I knew very well that you were not Miss
Money."
"Thank you."
"And your first name is so very pretty and peculiar that I could not
have easily forgotten it."
"I am greatly obliged to my godfathers and godmothers."
"Did you say that you lived in this quarter, Miss Grey?"
"No--I did not make any answer; I had not time."
"I hope you do not live very near," the gallant Heron observed.
"Why do you hope that?" Miss Grey said, turning her eyes upon him with
an air of cold resolution, which would probably have proved very trying
to a less sincere maker of compliments, even though a far more dexterous
person than Mr. Heron.
"Of course, because I should have the less of your company."
"But there is no need of your coming out of your way for me. I don't
require any escort, Mr. Heron."
"I couldn't think of letting a lady walk home by herself. That would
seem very strange to me. Perhaps you think me old-fashioned or
colonial?"
"I have heard that you are from the colonies. In London people have not
time to keep up all these pretty forms and ceremonies. We don't any
longer pretend to think that a girl needs to be defended against giants,
or robbers, or mad bulls, when crossing two or three streets in open
day."
"Well, it is hardly open day now; it is almost quite dark."
"The lamps are lighted," Miss Gray observed.
"Yes, if you call that being lighted! You have such bad gas in London.
Why does not somebody stir up people here, and put things to rights? You
seem to me the most patient people in all the world. I wish they would
give me the ruling of this place for about a twelvemonth."
"I wish they would."
"Do you?" and he looked at her with a glance of genuine gratitude in his
dark eyes, for he thought she meant to express her entire confidence in
his governing power, and her wish to see him at the head of affairs.
Miss Grey, however, only meant that if he were engaged in directing the
municipal government of London he probably would be rather too busy to
walk with her.
"Yes," he went on, "you should soon see a change. For instance"--they
were now at the end of Victoria street, near the Abbey--"I would begin
by having a great broad street, like this, running right up from here to
the British Museum. You know where the British Museum is, of course?"
"Yes; I live near it."
"Do you really? I am so glad to hear that. I have been there lately very
often. How happy you Londoners are to have such glorious places. In that
reading-room I felt inclined to bless England."
Miss Grey was now particularly sorry that she had said anything about
her place of residence. Still it did not seem as if much would have been
gained by any reticence unless she could actually dismiss her companion
peremptorily. Mr. Heron was evidently quite resolved to be her escort
all the way along. He was clearly under the impression that he was
making himself very agreeable. The good-natured youth believed he was
doing quite the right thing, and meant it all for the very best, and
therefore could not suppose that any nice girl could fail to accept his
attendance in a kindly spirit. That Miss Grey must be a nice girl he was
perfectly certain, for he had met her at Mr. Money's, and Money was
evidently a fine fellow--a very fine fellow. Miss Grey was very handsome
too, but that did not count for very much with Heron. At least he would
have made himself just as readily, under the circumstances, the escort
of little Miss Blanchet.
So he talked on about various things--the Moneys, and what charming
people they were! the British Museum, what a noble institution! the
National Gallery, how hideous the building!--why on earth didn't anybody
do something?--the glorious destiny of England--the utter imbecility of
the English Government.
It was not always quite easy to keep up with his talk, for the streets
were crowded and noisy, and Mr. Heron talked right on through every
interruption. When they came to crossings where the perplexed currents
and counter-currents of traffic on wheels would have made a nervous
person shudder, Mr. Heron coolly took Miss Grey's hand and conducted her
in and out, talking all the while as if they were crossing a ball-room
floor. Minola made it a point of honor not to hesitate, or start, or
show that she had nerves. But when he began to run into politics he
always pulled himself up, for he politely remembered that young ladies
did not care about politics, and so he tried to find some prettier
subject to talk about. Miss Grey understood this perfectly well, and was
amused and contemptuous.
"I suppose this man must be a person of some brains and sense," she
thought. "He was in command of something somewhere, and I suppose even
the Government he calls so imbecile would not have put him there if he
were a downright fool. But because he talks to a woman, he feels bound
only to talk of trivial things."
At last the walk came to an end. "Ah, I beg pardon. You live here," Mr.
Heron said. "May I have the honor of calling on your family? I sometimes
come to the Museum, and if I might call, I should be delighted to make
their acquaintance."
"Thank you," Miss Grey said coldly. "I have no family. My father and
mother are dead."
"Oh, I am so sorry! I wish I had not asked such a question." He looked
really distressed, and the expression of his eyes had for the first time
a pleasing, softening effect upon Miss Grey.
"We lodge here all alone--a lady--an old friend of mine--and I. We have
no acquaintances, unless Lucy Money's family may be called so. We read
and study a great deal, and don't go out, and don't see any one."
"I can quite understand," Mr. Heron answered with grave sympathy. "Of
course you don't care to be intruded on by visitors. I thank you for
having allowed me the pleasure of accompanying you so far."
He spoke in tones much more deferential than before, for he assumed that
the young lady was lonely and poor. There was something in his manner,
in his eyes, in his grave, respectful voice, which conveyed to Minola
the idea of genuine sympathy, and brought to her, the object of it, a
new conviction that she really was isolated and friendless, and the
springs of her emotions were touched in a moment, and tears flashed in
her eyes. Perhaps Mr. Heron saw them, and felt that he ought not to see
them, for he raised his hat and instantly left her.
Minola lingered for a moment on the doorstep, in order that she might
recover her expression of cheerfulness before meeting the eyes of Miss
Blanchet. But that little lady had seen her coming to the door, and seen
and marvelled at her escort, and now ran herself and opened the door to
receive her.
"My dear Minola, do tell me who that handsome young man was! What lovely
dark eyes he had! Where did you meet him? Is he young Mr. Money?"
The poetess's susceptible bosom still thrilled and throbbed at the
sight, or even the thought, of a handsome young man. She could not
understand how anybody on earth could avoid liking handsome young men.
But in this case a certain doubt and dissatisfaction suddenly dissolved
away into her instinctive gratification at the sight of Minola's escort.
A handsome and young Mr. Money might prove an inconvenient visitor just
at present.
Minola briefly told her when they were safe in their room. Miss Blanchet
was relieved to find that he was not a young Mr. Money, for a young Mr.
Money, if there were one, would doubtless be rich.
"Isn't he wonderfully handsome! Such a smile!"
"I hardly know," Minola said distressedly; "perhaps he is. I really
didn't notice. He goes to the Museum, and I must exile myself from the
place for evermore, or I shall be always meeting him, and be forced to
listen politely to talk about nothing. Mary Blanchet, our days of
freedom are gone! We are getting to know people. I foresaw it. What
shall we do? We must find some other lodgings ever so far away."
"Do you like Miss Money, dear?" Mary Blanchet asked timidly.
"Lucy? Oh, yes, very much. But there is Mr. Money; and they are going to
be terribly kind to us; and they have all manner of friends; and what is
to become of my independence? Mary Blanchet, I will _not_ bear it! I
_will_ be independent!"
"I have news for you, dear," Miss Blanchet said.
"If it please the destinies, not news of any more friends! Why, we shall
be like the hare in Gay's fable if we go on in this way."
"Not of any more friends, darling, but of one friend. My brother has
been here."
"Oh!"
"Yes; and he is longing to see you."
Minola sincerely wished she could say that she was longing to see him.
But she could not say it, even to please her friend and comrade.
"You don't want to see him," said Mary Blanchet in piteous reproach.
"But you do, dear," Miss Grey said; "and I shall like to see any one, be
sure, who brightens your life."
This was said with full sincerity, although at the very moment the
whimsical thought passed through her, "We only want Mr. Augustus
Sheppard now to complete our social happiness."
CHAPTER VI.
IS THIS ALCESTE?
Minola's mind was a good deal disturbed by the various little events of
the day, the incidents and consequences of her first visit in London.
She began to see with much perplexity and disappointment that her life
of lonely independence was likely to be compromised. She was not sure
that she could much like the Moneys, and yet she felt that they were
disposed and determined to be very kind to her. There was something
ridiculous and painful in the fact that Mr. Augustus Sheppard's name was
thrust upon her almost at the first moment of her crossing for the first
time a strange threshold in London; then there was Mary Blanchet's
brother turning up; and Mary Blanchet herself was evidently falling off
from the high design of lonely independence. Again, there was Mr. Heron,
who now knew where she lived, and who often went to the British Museum,
and who might cross her path at any hour. Sweet, lonely freedom, happy
carelessness of action, farewell!
Mr. Heron was especially a trouble to Minola. The kindly, grave
expression on his face when he heard of her living alone declared, as
nearly as any words could do, that he considered her an object of pity.
Was she an object of pity? Was that the light in which any one could
look at her superb project of playing at a lifelong holiday? And if
people chose to look at it so, what did that matter to her? Are women,
then, the slaves of the opinion of people all around them? "They are,"
Minola said to herself in scorn and melancholy--"they are; we are. I am
shaken to the very soul, because a young man, for whose opinion on any
other subject I should not care anything, chooses to look at me with
pity!"
The night was melancholy. When the outer world was shut out, and the gas
was lighted, and the two women sat down to work and talk, nothing seemed
to Minola quite as it had been. The evident happiness and passing high
spirits of the little poetess oppressed her. Mary Blanchet was so glad
to be making acquaintances, and to have some prospect of seeing the
inside of a London home. Then Minola's kindlier nature returned to her,
and she thought of Mary's delight at seeing her brother, and how unkind
it would be if she, Minola, did not try to enter into her feelings. Her
mind went back to her own brother, to their dear early companionship,
when nothing seemed more natural and more certain than that they two
should walk the world arm-in-arm. Now all that had come to an end--faded
away somehow; and he had gone into the world on his own account, and
made other ties, and forgotten her. But if he were even now to come
back, if she were to hear in the street the sound of the peculiar
whistle with which he always announced his coming to her--oh, how, in
spite of all his forgetfulness and her anger, she would run to him and
throw her arms around his neck! Why should not Mary Blanchet love her
brother, and gladden when he came?
"What is your brother like, Mary, dear?" she said gently, anxious to
propitiate by voluntarily entering on the topic dearest to her friend.
"Oh, very handsome--very, very handsome!"
Miss Grey smiled in spite of herself.
"Now, Minola, I know what you are smiling at; you think it is my
sisterly nonsense, and all that; but wait until you see."
"I'll wait," Minola said.
Miss Grey did not go out the next day as usual, although it was one of
the soft, amber-gray, autumnal days that she loved, and the Regent's
Park would have looked beautiful. She remained nearly all the morning in
her own room, and avoided even Mary Blanchet. Some singular change had
taken place within her, for which she could not account, otherwise than
by assuming that it was begotten of the fear that she would be drawn,
willingly or unwillingly, into uncongenial companionship, and must
renounce her liberty. She was forced into a strange, painful,
self-questioning mood. Was the whole fabric of her self-appointed
happiness and independence only a dream, or, worse than a dream, an
error? So soon to doubt the value and the virtue of the emancipation she
had prayed for and planned for during years? Not often, perhaps, has a
warm-hearted, fanciful, and spirited girl been pressed down by such
peculiar relationship as hers at Keeton lately; a twice removed
stepfather and stepmother, absolutely uncongenial with her, causing her
soul and her youth to congeal amid dull repression. What wonder that to
her all happiness seemed to consist in mere freedom and unrestricted
self-development? And now--so soon--why does she begin to doubt the
reality, the fulfilment of her happiness? Only because an impulsive and
kindly young man, whom she saw for the first time, looked pityingly at
her. This, she said to herself, is what our self-reliance and our
emancipation come to after all.
It was a positive relief to her, after a futile hour or so of such
questioning, when Mary Blanchet ran up stairs, and with beaming eyes
begged that Minola would come and see her brother. "He is longing to see
you--and you will like him--oh, you will like him, Minola dearest?" she
said beseechingly.
Miss Gray went down stairs straightway, without stopping to give one
touch to her hair, or one glance at the glass. The little poetess was
waiting a moment, with an involuntary look toward the dressing table, as
if Miss Grey must needs have some business there before she descended,
but Miss Grey thought nothing of the kind, and they went down stairs
together.
Minola expected, she could not tell why, to see a small and withered man
in Mary Blanchet's brother. When they were entering the drawing-room, he
was looking out of the window, and had his back turned, and she was
surprised to see that he was decidedly tall. When he turned around she
saw not only that he was handsome, but that she had recognized the fact
of his being handsome before. For he was unmistakably the ideal poet of
schoolgirls whom she had met at Mr. Money's house the day before.
The knowledge produced a sort of embarrassment to begin with. Minola was
about to throw her soul into the sacrifice, and greet her friend's
brother with the utmost cordiality. But she had pictured to herself a
sort of Mary Blanchet in trousers, a gentle, old-fashioned, timid
person, whom, perhaps, the outer world was apt to misprize, if not even
to snub, and whom therefore it became her, Minola Grey, as an enemy and
outlaw of the common world, to receive with double consideration. But
this brilliant, self-conceited, affected, oppressively handsome young
man, on whom she had seen Lucy Money and her mother hanging devotedly,
was quite another sort of person. His presence seemed to overcharge the
room; the scene became all compound of tall, bending form and dark eyes.
"I am glad to see you, Mr. Blanchet," Miss Grey began, determined not to
be put out by any self-conceited poet and ideal of schoolgirls. "I must
be glad to see you, because you are Mary's brother."
"You ought rather to be not glad to see me for that reason," he said,
with a deprecating bow and a slight shrug of the shoulders, "for I have
been a very neglectful brother to Mary."
"So I have heard," Miss Grey said, "but not from Mary. She always
defended you. But I have seen you before, Mr. Blanchet, have I not?"
"At Mrs. Money's yesterday? Oh, yes; I only saw you, Miss Grey. I went
there to see you, and only in the most literal way got what I wanted."
"But, Herbert, you never told me that you were going, or that you knew
Mrs. Money," his sister interposed.
"No, dear; that was an innocent deceit on my part. You told me that Miss
Grey had gone there, and as I knew the Moneys I hurried away there
without telling you. I wanted to know what you were like, Miss Grey,
before seeing my sister again. I hope you are not angry? She is so
devoted to you that she painted you in colors the most bewitching; but I
was afraid her friendship was carrying her away, and I wanted to see for
myself when she was not present."
Miss Grey remained resolutely silent. She thought this beginning
particularly disagreeable, and began to fear that she should never be
able to like Mary Blanchet's brother. "Oh, why do women have brothers?"
she asked herself. There seemed something dishonest in Mr. Blanchet's
proceeding despite the frank completeness of his confession.
"Well, Herbert, confess that I didn't do her justice; didn't do her
common justice," the enthusiastic Mary exclaimed.
"If Miss Grey would not be offended," her brother said, "I would say
that I see in her just the woman capable of doing the kind and generous
things I have heard of."
"Yes; but we mustn't talk about it," the poetess said, with tears of
gratefulness blinking in her eyes; "and we'll not say a word more about
it, Minola; not a word, indeed, dear." And she put a deprecating little
hand upon Minola's arm.
Then they all sat down, and Herbert Blanchet began to talk. He talked
very well, and he seemed to have put away most of the airs of
affectation which, even in her very short opportunity of observation,
Minola had seen in him when he was talking to the Money girls.
"You have travelled a great deal," Miss Grey said. "I envy you."
"If you call it travelling. I have drifted about the world a good deal,
and seen the wrong sides of everything. I make it pay in a sort of way.
When any place that I know is brought into public notice by a war or
something of the kind, I write about it. Or if a place is not brought
into any present notice by anything, I write about it, and take a
different view from anybody else. I have done particularly well with
Italy, showing that Naples is the ugliest place in all the world; that
the Roman women have shockingly bad figures, and that the climate is
wretched from the Alps to the Straits of Messina.
"But you don't think that?" Mary Blanchet said wonderingly.
"Don't I? Well, I don't know. I almost think I do for the moment. One
can get into that frame of mind. Besides, I really don't care about
scenery. I don't observe it as I pass along. And I like to say what
other people don't say, and to see what they don't see. Of course I
don't put my name to any of these things; they are only done to make a
living. I live _on_ such stuff as that. I live _for_ Art."
"It is glorious to live for art," his sister exclaimed, pressing her
thin, tiny hands together.
Mr. Blanchet did not seem to care much about his sister's approval.
"My art isn't yours, Mary," he said, with a pitying smile. "Pictures of
flowers and little children saying their prayers, and nice poems about
good young men and women, are your ideas of painting and poetry, I am
sure. You are a lover of the human race, I know."
"I hope I love my neighbors," Mary said earnestly.
"I hope you do, dear. All good little women like you ought to do that.
Do _you_ love your neighbor, Miss Grey?"
"I don't care much for any one," Miss Grey answered decisively, "except
Mary Blanchet. But I have no particular principle or theory about it,
only that I don't care for people."
Although Miss Grey had Alceste for her hero, she did not like sham
misanthropy, which she now fancied her visitor was trying to display.
Perhaps too she began to think that his misanthropy rather caricatured
her own.
Miss Blanchet, on the contrary, was inclined to argue the question, and
to pelt her brother with touching commonplaces.
"The more we know people," she emphatically declared, "the more good we
see in them. In every heart there is a deep spring of goodness. Oh,
yes!"
"There isn't in mine, I know," he said. "I speak for myself."
"For shame, Herbert! How else could you ever feel impelled to try and do
some good for your fellow creatures?"
"But I don't want to do any good to my fellow creatures. I don't care
about my fellow creatures, and I don't even admit that they are my
fellow creatures, those men and those women too that one sees about. Why
should the common possession of two legs make us fellow creatures with
every man, more than with every bird? No, I don't love the human race at
all."
"This is nonsense, Minola; you won't believe a word of it," the little
poetess eagerly said, divided between admiration and alarm.
"You good, little, innocent dear, is it not perfectly true? What did I
ever do for you, let me ask? There, Miss Grey, you see as kind an elder
sister as ever lived. I remember her a perfect mother to me. I dare say
I should have been dead thirty years ago but for her, though whether I
ought to thank her for keeping me alive is another thing. Anyhow, what
was my way of showing my gratitude? As soon as I could shake myself
free, I rambled about the world, a very vagrant, and never took any
thought of her. We are all the same, Miss Grey, believe me--we men."
"I can well believe it," Miss Grey said.
"Of course you can. In all our dealings with you women we are just the
same. Our sisters and mothers take trouble without end for us, and cry
their eyes out for us, and we--what do we care? I am not worse than my
neighbors. But if you ask me, do I admire my fellow man, I answer
frankly, no. Not I. What should I admire him for?"
"One must live for something," the poetess pleaded, much perplexed in
her heart as to what Miss Grey's opinion might be about all this.
"Of course one must live for art; for music and poetry, and colors and
decoration."
"And Nature?" Mary Blanchet gently insinuated.
"Nature--no! Nature is the buxom sweetheart of ploughboy poets. We only
affect to admire Nature because people think we can't be good if we
don't. No one really cares about great cauliflower suns, and startling
contrasts of blazing purple and emerald green. There is nothing really
beautiful in Nature except her decay; her rank weeds, and dank grasses,
and funereal evening glooms."
While he talked this way he was seated on the piano stool, with his face
turned away from the piano, on whose keys he touched every now and then
with a light and seemingly careless hand, bringing out only a faint note
that seemed to help the conversation rather than to interrupt it. He was
very handsome, Minola could not help thinking, and there was something
in his colorless face and deep eyes that seemed congenial with the talk
of glooms and decay. Still, true to her first feeling toward all men,
Minola was disposed to dislike him, the more especially as he spoke with
an air of easy superiority, as one who would imply that he knew how to
maintain his place above women in creation.
"I thought all you poets affected to be in love with Nature," she said.
"I mean you younger poets," and she emphasized the word "younger" with a
certain contemptuous tone, which made it just what it meant to
be--"smaller poets."
"Why younger poets?"
"Well, because the elder ones I think really were in love with Nature,
and didn't affect anything."
He smiled pityingly.
"No," he said decisively, "we don't care about Nature--our school."
"I am from the country; I don't think I know what your school is."
"We don't want to be known in the country; we couldn't endure to be
known in the country."
"But fame?" Minola asked--"does fame not go outside the twelve-mile
radius?"
"Oh, Miss Grey, do pray excuse me, but you really don't understand us;
we don't want fame. What is fame? Vulgarity made immortal."
"Then what do you publish for?"
He rose from his seat and seized his hair with both hands; then
constrained himself to endurance, and sat down again.
"My dear young lady, we don't publish; we don't intend to publish. No
man in his senses would publish for us if we were never so well
inclined. No one could sell six copies. The great, thick-headed public
couldn't understand us. We are satisfied that the true artist never does
have a public--or look for it. The public can have their Tennysons, and
Brownings, and Swinburnes, and Tuppers, and all that lot----"
"That lot!" broke in Miss Blanchet, mildly horrified--"that lot!
Browning and Tupper put together!"
"My dear Mary, I don't know one of these people from another; I never
read any of them now. They are all the same sort of thing to me. These
persons are not artists; they are only men trying to amuse the public.
Some of them, I am told, are positively fond of politics."
"Don't your school care for politics?" Miss Grey asked, now growing
rather amused.
"Oh, no; we never trouble ourselves about such things. What can it
matter whether the Reform bill is carried--is there a Reform bill going
on now?--I believe there always is--or what becomes of the Eastern
Question, or whether New Zealand has a constitution? These are questions
for vestrymen, not artists; we don't love man."
"There I am with you," Miss Grey said; "if that alone were qualification
enough, I should be glad to be one of your fraternity, for I don't love
man; I think he is a poor creature at his best."
"So do I," said the poet, turning toward her with eyes in which for the
moment a deep and genuine feeling seemed to light up; "the poorest
creature, at his best! Why should any one turn aside for a moment from
his path to help such a thing? What does it matter, the welfare of him
and his pitiful race? Let us sing, and play, and paint, and forget him
and the destiny that he makes such a work about. Wisdom only consists in
shutting our ears to his cries of ambition, and jealousy, and pain, and
being happy in our own way and forgetting him."
Their eyes met for a moment, and then Minola lowered hers. In that
instant a gleam of sympathy had passed from her eyes into his, and he
knew it. She felt a little humiliated somehow, like a proud fencer
suddenly disarmed at the first touch of his adversary. For, as he was
speaking scorn of the human race, she was saying to herself, "This man,
I do believe, has suffered deeply. He has found people cold, and mean,
and selfish--as _I_ have--and he feels it, and cannot hide it. I did him
wrong; he is not a fribble or sham cynic, only a disappointed dreamer."
The sympathy which she felt showed itself only too quickly in her very
eloquent eyes.
Herbert Blanchet rose after an instant of silence and took his leave,
asking permission to call again, which Miss Grey would have gladly
refused if she could have stood up against the appealing looks of Mary.
So she had to grant him the permission, thinking as she gave it that
another path of her liberty was closed.
Mary went to the door with her brother, and, much to Minola's
gratification, remained a long time talking with him there.
Miss Grey went to the piano and began to sing; softly to herself, that
she might not be heard outside. The short autumnal day was already
closing in London. Out in the country there would be two hours yet of
light before the round, red sun went down behind the sloping fields,
with the fresh upturned earth, and the clumps of trees, but here, in
West-Central regions of London, the autumn day dies in its youth. The
dusk already gathered around the singer, who sang to please or to soothe
herself. In any troubled mood Miss Grey had long been accustomed to
clear her spirits by singing to herself; and on many a long, dull Sunday
at home--in the place that was called her home--she had committed the
not impious fraud of singing her favorite ballads to slow, slow time,
that they might be mistaken for hymns and pass unreproved. Her voice and
way of singing made the song seem like a sweet, plaintive recitative,
just the singing to hear in the "gloaming," to draw a few people hushed
around it, and hold them in suspense, fearful to lose a single note, and
miss the charm of expression. In truth, the charm of it sprang from the
fact that the singer sang to express her own emotions, and thus every
tone had its reality and its meaning. When women sing for a listening
company, they sing conventionally, and in the way that some teacher has
taught, or in what they believe to be the manner of some great artist;
or they sing to somebody or at somebody, and in any case they are away
from that truthfulness which in art is simply the faithful expression of
real emotion. With Minola Grey singing was an end rather than a means; a
relief in itself, a new mood in itself; a passing away from poor and
personal emotions into ideal regions, where melancholy, if it must be,
was always divine; and pain, if it would intrude, was purifying and
ennobling. So, while the little poetess talked with her brother in the
dusk, at the doorway, with the gas lamps just beginning to light the
monotonous street, Minola was singing herself into the pure blue ether,
above the fogs, and clouds, and discordant, selfish voices.
She came back to earth with something like a heavy fall, as Mary
Blanchet ran in upon her in the dark and exclaimed--
"Now, do tell me--how do you like my brother?"
To say the truth, Miss Grey did not well know. "I wonder is he an
Alceste?" she asked herself. On the whole, his coming had made an
uncomfortable, anxious, uncanny impression upon her, and she looked back
with a kind of hopeless regret on the days when she had London all to
herself, and knew nobody.
WORDSWORTH'S CORRECTIONS.
When an author, in his later editions, departs from his earlier text, he
is apt to reveal some traits of his method and genius that might not
otherwise have been so evident, and a poet's corrections may thus have
more than a merely curious interest. Take Mr. Tennyson's, for instance:
"The Princess," to say nothing of his shorter emended poems, has been,
one might say, rewritten since the first edition, and his corrections
are always interesting. Yet they spring, I think, from a narrower range
of motive than Wordsworth's; they are directed more exclusively toward
the object of artistic finish; they commonly show the poet busied in
casting perfume upon the lily. Take this example from "The Miller's
Daughter." In the first version of that poem, as it appeared in 1842, we
are told that before the heroine's reflection became visible in the
mill-pool--
A water-rat from off the bank
Plunged in the stream.
Later editions give us this more graceful version of what occurred:
Then leapt a trout. In lazy mood
I watch'd the little circles die;
They passed into the level flood,
And there a vision caught my eye.
Unquestionably that is an improvement, and of a sort which Wordsworth
was continually making. But Wordsworth's corrections do not merely
illustrate the effort to reach artistic finish, though very many of them
are made with that intent; they have a relation to his theories, tastes,
creeds, to his temperament and training, to his manner of receiving
friendly or hostile criticism; and in comparing these textual variations
we seem to watch the artist at his work--to enter in some sort into his
very consciousness--as we see him manipulating the form or the thought
of his verses:
Ta de torneuei, ta de kollomelei,
Kai gnomotupei, k'autonomazei.
Nor is this to consider too curiously; Wordsworth himself has invited us
to the task. In his letters as well as in the notes to his poems,
frequent mention is made of these labors of emendation. Writing in 1837
to Edward Quillinan, he asks him to "take the trouble ... of comparing
the corrections in my last edition [that of 1836] with the text in the
preceding one," "in the correction of which I took great pains," as he
had written to Prof. Reed a month before. And there is ample opportunity
of this sort; I do not know an ampler one of the kind in the works of
any other poet. Tasso's _variae lectiones_ are numerous, but they were
mostly made to conciliate his critics; Milton's are of great interest,
but they are comparatively few in number, and Gray's are fewer still:
Pope's are numerous, but not often interesting; while Tennyson's, as I
have intimated, seem to me to spring from a less serious poetic faculty
than Wordsworth's, and are therefore less significant. But I am anxious
not to claim too much significance for Wordsworth's corrections, for I
can do little more here than to point out some of them, leaving for the
most part their interpretation to the reader. To attempt more than this
would be to enter upon an analysis of Wordsworth's genius, for which
this is not the occasion.
And yet we shall see, I think, that his genius might be in some sort
"restored," as naturalists say, were it necessary, from these
fragmentary data, for Wordsworth's corrections cover the whole term of
his literary activity. He preferred, one might say, to correct after
publication rather than before; and, revising his youthful writing
during a second and a third generation following, his final texts had
received the benefit of more than half a century of criticism by himself
and others. From the year 1793, in which his first volumes appeared, the
"Evening Walk" and the "Descriptive Sketches," to the year of his death,
1850, he put forth not fewer than twenty-four separate publications in
verse, each of which contained more or less of poetry previously
unpublished; and in the greater number of these texts may be found
variations from the previous readings. The larger part of them, indeed,
are slight--the change of single words, the alteration of phrases, the
transposition of verses or stanzas. And yet few of them, I think, are
quite without interest for persons in whose reading, as Wordsworth
himself expresses it, "poetry has continued to be comprehended as a
study." I have noted some thousands of his corrections; but a copious
citation of them might weary all but actual students of poetic
_technique_, a class that is hardly as numerous, I suspect, as that of
the actual practitioners of poetry, and I will therefore keep mainly to
such _variae lectiones_ as may be referred to motives of more general
interest.[B]
[Footnote B: After the early poems just mentioned and the "Lyrical
Ballads," 1798 to 1802, the chief editions to be consulted for the
changes of text are the complete editions of 1807, 1815, and 1836, and
the original issues of "The Excursion" (1814), of "The White Doe of
Rylston" (1815), of "Peter Bell," and of "The Waggoner" (1819).
Unfortunately I have not been able to get access to Mr. W. Johnston's
useful collection of Wordsworth's "Earlier Poems" (London, 1857): it
would have lightened the task of collecting the _variantes_, the more
important of which, for the period covered by the collection, are given
in it. But, having gone in nearly every case to the original texts, I
need hardly say that I have been careful to quote them accurately in the
present article.]
The first question which we naturally ask about Wordsworth's corrections
is this: Were they improvements? My readers will decide for themselves;
for my own part, it seems to me that they generally were improvements;
that Wordsworth bettered his text three times out of four when he
changed it. Nor is this surprising; few admirers of Wordsworth's poetry
will deny that there were many passages quite susceptible of amendment
in it; for that task there was ample room. But on the other hand, it
happened not infrequently, as we might expect, that when the poet
returned, in the critical mood, to mend his first form of expression, he
marred it instead. In the poem, for instance, beginning, "Strange fits
of passion have I known," the second stanza as originally published ran
thus:
When she I loved was strong and gay,
And like a rose in June,
I to her cottage bent my way,
Beneath the evening moon.
--_Lyrical Ballads_, 1800.
The passage stood thus for many years, and was finally altered to read:
When she I loved looked every day
Fresh as a rose in June,
I to her cottage bent my way,
Beneath an evening moon.
Is there not some loss of vividness here? The later reading is perhaps
the more graceful, and yet the picture seems to me brighter in the early
version. This, too, seems a doubtful improvement; it occurs in "The
Farmer of Tilsbury Vale." Wordsworth wrote at first:
His staff is a sceptre--his gray hairs a crown:
Erect as a sunflower he stands, and the streak
Of the unfaded rose is expressed on his cheek.
--1815.
In later editions we read:
His bright eyes look brighter, set off by the streak
Of the unfaded rose that still blooms on his cheek.
Here the last line is bettered; but I, for one, am sorry to lose the
sunflower comparison; it is picturesque, and it aptly describes this
hearty child of the earth.
Look now at the poem "We are Seven," as it began in the "Lyrical
Ballads":
A simple child, dear brother Jim,
That lightly draws its breath,
And feels its life in every limb--
What should it know of death?
It is now sixty years since "dear brother Jim" was dismissed from his
place in these lines--dismissed, perhaps, with the less compunction
because the stanza was written by another hand--Coleridge's--as an
introduction to the rest of the poem. But I think the lines were better
as the young poets first sent them forth. "Brother Jim" had, perhaps, no
clearly demonstrable business in the poem; and yet, having been there,
we miss him now that he is gone. That homely apostrophe had in it the
primitive impulses of the Lake school feeling; the phrase refuses to be
forgotten, and seems to have a persistent life of its own. I have seen
the missing words restored, in pencil marks, to their rightful place in
the text of copies belonging to old-fashioned gentlemen who remembered
the original reading. Nor can we easily deny existence to our "dear
brother Jim"; his name still lingers in our memories, haunting about the
page from which it was excluded long ago; he lives, and deserves to
live, as the symbol of immortal fraternity.
But as I have said, Wordsworth mended his text oftener than he marred
it, and first by refining upon his descriptions of outward nature. Among
the cases in point, one occurs in a poem entitled "Influences of Natural
objects in calling forth and strengthening the Imagination in Boyhood
and early Youth"--a cumbrous heading enough. May I digress for a moment
upon the unlucky titles which Wordsworth so often prefixed to his poems,
and the improvements occasionally made in them? Surely a less convenient
caption than the one just quoted is not often met with, or a less
attractive one than this other, prefixed to an inscription not very many
times longer than itself:
"Written at the Request of Sir George Beaumont, Bart., and in his Name,
for an Urn, placed by him at the termination of a newly-planted Avenue
in the same Grounds."
Titles like these are not only fatiguing in the very reading, a
preliminary disenchantment, but they are not properly names at all; they
are headings, rubrics, captions which do not name. Wordsworth seems to
send forth these unlucky children of the muse with a full description of
their eyes, hair, and complexion, but forgets to christen them; and I
believe that this oversight, though it may not appear a very serious
one, has interfered more than a little with the effectiveness of his
minor poetry, and consequently with the fame and influence of the poet.
For it makes reference to them difficult, almost impossible: how is one
to refer to a favorite passage, for instance, in a poem "Written at the
Request of Sir George Beaumont, Bart., and in his Name, for an Urn,
placed by him at the termination of a newly-planted Avenue in the same
Grounds"? These titles are fit to discourage even the admirers of
Wordsworth, and to repel his intending students; nor will they attract
any one, for they are formless; they are the abstracts of essays, the
_precis_ of an argument, rather than fit designations for works of
poetic art. A considerable number, too, of Wordsworth's minor pieces
remain without name, title, or description of any kind whatever. If that
desirable thing, a satisfactory edition of his poems, should ever
appear, it will be given us by some editor who shall be sensitive to
this northern formlessness, and who may venture, perhaps, to improve the
state of Wordsworth's titles.
Let me end this digression by noting another singular title, with its
emendation. In the "Lyrical Ballads" of 1798 appeared a poem with this
extraordinary caption:
"Anecdote for Fathers, shewing how the art of Lying may be taught."
Now, certainly, Wordsworth did not intend to teach the art of lying, yet
nothing can be clearer than his declaration. He failed to see the
ludicrous meaning of these words, and it took him thirty years,
apparently, to find out what he had said; but he saw it at last, and
dropped the explanatory clause of the title, quoting in its place an apt
motto from Eusebius; and we now read:
"Anecdote for Fathers. _Retine vim istam, falsa enim dicam, si coges_;"
and the charming story professes no longer to show how boys may be
taught to lie, but to point out the danger of making them lie when you
press them to give reasons for their sentiments.
And now, returning to the corrections of text in the descriptive
passages, let us note a curious change in the poem already mentioned,
"On the Influence of Natural Objects," etc. Wordsworth is describing the
pleasures of skating; and these are some of them, according to the
passage as originally published in "The Friend":
Not seldom from the uproar I retired
Into a silent bay--or sportively
Glanced sideway, leaving the tumultuous throng
_To cut across the image of a Star
That gleamed upon the ice._
To do this is of course impossible, and the lines which I have
italicized are mere closet description. We cannot skate across the
reflection of a star until we can skate into the end of a rainbow; and
the curious thing is that the so-called "poet of nature" should ever
have fancied, even for a moment at his desk, that he had ever done it.
Clearly, Wordsworth's study was not always out of doors, to use a
favorite phrase of his; on the contrary, this passage is so unreal that
a critic unacquainted with the personal history of the poet might argue
that he had never been on skates--as Coleridge wrote the "Hymn in the
Valley of Chamouni" without ever visiting that valley. But Wordsworth
seems to have found out that his description was false; for he made a
compromise, in the later editions, with the optical law of incidence and
reflection; and we now see him attempting merely, but not achieving, the
impossible thing:
----Leaving the tumultuous throng
To cut across the reflex of a star
That fled, and, flying still before me, gleamed
Upon the glassy plain.
But Wordsworth held stoutly, in the main, to his own experience, his own
impressions; and he did this even to the injury of his descriptions. He
was never, for instance, in sailor's phrase, "off soundings"; he never
saw the mid-ocean; and consequently, when he described Leonard, in the
first edition of "The Brothers," as sailing in mid-ocean, he says that
he gazed upon "the broad green wave and sparkling foam." But he found
out his mistake at last; he was fond of reading voyages and travels, and
he seems to have become convinced finally, perhaps by the testimony of
his sailor brother, that the deep sea was really blue and not green;
that the common epithet was the true one; for he corrected the line to
read "the broad blue wave."
Let us now examine some of those curiously prosaic passages which
Wordsworth strove faithfully to convert into poetry, and strove with
various success. And first, those famous arithmetical passages in "The
Thorn," one of which stands to-day as it stood in the "Lyrical Ballads."
We still read there, indeed, of
A beauteous heap, a hill of moss,
Just half a foot in height,
the precise altitude that Wordsworth gave it in 1798; not an inch to the
critics, he seems to have said. But these other peccant lines in the
preceding stanza he recast, and in a way that is curious to follow:
And to the left, three yards beyond,
You see a little muddy Pond
Of water never dry:
I've measured it from side to side:
'Tis three feet long, and two feet wide.
Of these lines Crabb Robinson said to Wordsworth that "he dared not read
them aloud in company." "They ought to be liked," rejoined the poet.
Well, we may not like them; but they are interesting, for they present a
really instructive specimen of bad art. Clearly enough, here is a poet
in difficulties. The "little muddy pond" was not a pond in nature, but a
pool; and a pool it would have been in verse, but for the particular
exigency--the necessity of rhyming with the word _beyond_. Note now the
honesty of our poet. For rhyme's sake he has temporarily sacrificed
accuracy; he has called a pool a pond; but to show what the piece of
water actually was, that actually it was a pool, though the exigencies
of rhyme had forced him to call it provisionally by another name, he
goes on to give us its accurate measurement, not only from "side to
side," but from end to end as well. "'Tis three feet long and two feet
wide," he tells us; and now his northern conscience is satisfied; he
seems to say, "I was unfortunately compelled to use the wrong word in
this passage, but I make amends at once; these are the precise
dimensions of the object, and you can give it the right name yourself."
This devotion to the topographical truth of the matter was abated,
however, in later editions, perhaps by the derision of the critics.
Wordsworth rewrote the passage, one would say, to please the graces
rather than the mathematical verities; and the lines now read thus:
You see a little muddy pond
Of water, never dry,
Though but of compass small, and bare
To thirsty suns and parching air.
Another considerable improvement was made, a little further on, in the
same poem. These are the lines as they ran in the "Lyrical Ballads":
Poor Martha! on that woful day
A cruel, cruel fire, they say,
Into her bones was sent;
It dried her body like a cinder,
And almost turned her brain to tinder.
--1798.
Certainly there was room for improvement here; and in the edition of
1815 we find the lines recast as follows:
A pang of pitiless dismay
Into her soul was sent;
A Fire was kindled in her breast,
Which might not burn itself to rest.
Or see again this prosaic passage from "The Brothers," as first
published in the "Lyrical Ballads." The lines describe the parting of
James from his companions at a certain rock:
----By our shepherds it is call'd the Pillar.
James, pointing to its summit, over which
They all had purposed to return together,
Inform'd them that he there would wait for them;
They parted, and his comrades pass'd that way
Some two hours after, but they did not find him
At the appointed place, a circumstance
Of which they took no heed.
--1800.
It would occur to few readers to call this poetry were it not visibly
divided into verse; and Wordsworth himself seems to have thought as
much, for after many years he rewrote the passage, condensing and
poetizing it as follows:
----By our shepherds it is called THE PILLAR.
Upon its airy summit crowned with heath
The loiterer, not unnoticed by his comrades,
Lay stretched at ease; but, passing by the place
On their return, they found that he was gone.
No ill was feared.
There are hundreds of corrections in this style; and we naturally ask
what made it necessary for Wordsworth to weed his poetic garden so
often, to amend with care and trouble what some other poets would have
done well at first? We need not hold with some of his critics that
Wordsworth had in any peculiar sense a dual nature, to explain the
amount of prosaic poetry, if I may call it so, that he wrote. No real
poet ever wrote, as I take it, a greater amount of prosaic poetry than
he; and no real poet ever published a greater number of verses that
might fairly be called not only poor poetry, but considered as proof
that their author could not write good poetry at all.
What critic would believe before the proof, that the poet who had
written the lines just quoted from "The Thorn," and others like them,
could have written also the "Lines to H. C." and "She Was a Phantom of
Delight"? But to inquire at length into this contrast is to inquire into
the deepest traits of Wordsworth's genius. One cause of his prosaic
verse, however, may be mentioned here. Wordsworth had injurious habits
of composition; he dictated his prose to an amanuensis, and he composed
his poems in the fields as he walked. He was thus a libertine of
opportunity, and though he strictly economized his subjects, and made
the least yield him up its utmost, yet he was prodigal in the quantity
of his expression. He did not wait for what are called moments of
inspiration; he was always ready to compose, and thus he composed too
much; he made verses whenever he was out of doors, "murmuring them out"
to the astonishment of the rustics. Doubtless the first factor of genius
is this abundance of power. But, on the other hand, the control, the
direction of power is the first essential to the beauty of the work of
art. "Good men may utter whatever comes uppermost; good poets may not,"
says Landor; and the aphorism touches upon a serious fault of
Wordsworth's method. He lacked due power of self-repression; he was too
much interested in his own thoughts to make a sufficiently jealous
choice among them when he came to write them down. Two qualities,
indeed, of his nature he kept in such abeyance, the amative and the
humorous--and he was not without a humorous side--as to express but
little of them in his writings. But he seems to have recorded almost
everything, not humorous or amatory, that came into his mind; and, in
consequence, we feel that his poetry comes perilously near being a
verbatim transcript of his processes of consciousness. But no man's
thought is always sufficiently valuable for a shorthand report; and we
often wish that Wordsworth had reflected, with Herrick, that the poet is
not fitted every day to prophesy:
No; but when the spirit fills
The fantastic pannicles
Full of fire--then I write
As the Godhead doth indite.
Does it seem an invidious task to recall the unhappy readings that I
have mentioned--readings abandoned by Wordsworth long ago, and unknown
to many of his younger students? To do it with slighting intent, or from
mere curiosity, would be unworthy; nor will the routine mind be
persuaded that there is anything more than a merely curious interest in
the comparison of editions. We, thinking that Wordsworth cannot really
be understood in a single edition, must leave the routine mind to its
conviction that one text contains all that there is of value in his
poetry. And to offset the ungraceful verses that we have just
considered, let us look at some changes by which Wordsworth has made
fine passages finer still. Of the sonnets published in 1819 with "The
Waggoner," none is more striking, as I think, than the one beginning,
"Eve's lingering clouds extend in solid bars." In it at first he spoke
as follows of the reflection of the heavens at night in perfectly still
water:
Is it a mirror?--or the nether sphere
Opening its vast abyss, while fancy feeds
On the rich show?--But list! a voice is near;
Great Pan himself low-whispering through the reeds.
In the later editions this passage is enriched by a grand stroke of
imagination:
Is it a mirror?--or the nether sphere
Opening to view the abyss in which she feeds
Her own calm fires?--But list! a voice is near;
Great Pan himself low-whispering through the reeds.
The following change is from the same sonnets; the passage describes a
bright star setting:
Forfeiting his bright attire,
He burns, transmuted to a sullen fire
That droops and dwindles; and, the appointed debt
To the flying moments paid, is seen no more.
So in 1819; in later editions we find the passage as follows:
He burns, transmuted to a dusty fire,
Then pays submissively the appointed debt
To the flying moments, and is seen no more.
That is scarcely an improvement; but the alteration of epithet is
curious: the substitution of fact for fancy in changing the low star's
"sullen fire" into a "dusty fire."
Here, again, is a case where the new reading has a fresher phrase than
the old. It occurs in the last stanza of "Rob Roy's Grave," where
Wordsworth spoke thus of the hero's virtues:
----Far and near, through vale and hill,
Are faces that attest the same;
And kindle, like a fire new-stirred,
At sound of ROB ROY's name.
Later, a new line was substituted as follows:
----Far and near, through vale and hill,
Are faces that attest the same;
The proud heart flashing through the eyes
At sound of ROB ROY's name.
And Wordsworth insisted, quite as strongly as his severest critics, upon
finish, upon literary art as discriminable from the substance. While he
was blaming Byron, Campbell, and other eminent poets for its lack, his
assailants were loud in the same charge against him; they protested that
whatever other merits the new poetry might have, that of artistic finish
was surely not one. Jeffrey wrote in 1807 that Wordsworth "scarcely ever
condescended to give the grace of correctness or melody to his
versification." But Wordsworth, in a letter lately first published,
criticises Campbell's "Hohenlinden" in a way that shows him by no means
unstudious of form. He writes thus to Mr. Hamilton:[C] "I remember
Campbell says, in a composition that is overrun with faulty language,
'And dark as winter was the _flow_ of Iser rolling rapidly'; that is,
'flowing rapidly.' The expression ought to have been 'stream' or
'current.' ... These may appear to you frigid criticisms," he adds; "but
depend upon it, no writings will live in which these rules are
disregarded." This is good doctrine, and we have seen Wordsworth
striving to realize it in his practice. He did realize it to a certain
extent; if his style was not always eloquent, not always poetical, it
was generally better English than that of his popular contemporaries.
And yet a critic in "The Dial," following, as recently as 1843, the lead
of Jeffrey in this blame of Wordsworth, could write of him as
follows:[D] "He has the merit of just moral perception, but not that of
deft poetic execution. How would Milton curl his lip at such slip-shod
newspaper style! Many of his poems, as for example the 'Rylstone Doe,'
might be all improvised.... These are such verses as in a just state of
culture should be _vers de Societe_, such as every gentleman could
write, but none would think of printing." That passage is worth reading
twice; note the condescension of the praise, the flippancy of the blame,
the inaccurate English and French; and what a jaunty misquotation of
Wordsworth's title! It was not very profitable censure; but Wordsworth
received much criticism by which he was glad to profit. Let us look at
some of the cases in which he turned the strictures of friends or of
enemies to account. The changes that he made in deference to criticism
are striking, and so too are some of the cases in which he refused to
profit by criticism. I will speak of both.
[Footnote C: "Prose Works," III., 302.]
[Footnote D: "The Dial," Vol. III., p. 514.]
Of the former kind are the corrections in "Laodamia." That poem appeared
first in 1815, having been suggested during a course of classical
reading which Wordsworth had taken up for the purpose of directing the
studies of his son. Landor criticised this poem in the first volume of
his "Imaginary Conversations," and in the main very favorably; he makes
Porson say that parts of it "might have been heard with shouts of
rapture in the regions he describes"; he calls it "a composition such as
Sophocles might have delighted to own." But he points out blemishes in
two stanzas, the first and the seventeenth; he blames the execution of
one and the thought of the other. Wordsworth rewrote both of them, and I
quote the second passage as affording the more interesting change. In
the first edition Protesilaus, says the poet, returning from the shades
to visit Laodamia,
Spake, as a witness, of a second birth
For all that is most perfect upon earth.
On this Landor remarks, putting the words into Porson's mouth:
How unseasonable is the allusion to _witness_ and _second_
birth, which things, however holy and venerable in
themselves, come stinking and reeking to us from the
conventicle. I desire to see Laodamia in the silent and
gloomy mansion of her beloved Protesilaus; not elbowed by
the godly butchers in Tottenham court road, nor smelling
devoutly of ratafia among the sugar bakers' wives at
Blackfriars.
Wordsworth dropped these lines; and we now read instead, that the hero
Spake of heroic arts in graver mood
Revived, with finer harmony pursued.
In the first volume of his "Imaginary Conversations" Landor said of
Wordsworth: "Those who attack him with virulence or with levity are men
of no morality and no reflection." In a later volume, however, Landor
attacks him thus himself, with both virulence and levity, as I fear we
must say, and Wordsworth declined to profit by these later gibing
criticisms, though some of them, and especially those upon the "Anecdote
for Fathers," were valuable, and suggested real improvements of text. In
this attack, which is contained in the second conversation of Southey
and Porson, Landor had noticed Wordsworth's adoption of his earlier
criticism of Laodamia; and this circumstance was probably a reason why
Wordsworth refused to receive further critical favors at his hands. The
poem "Goody Blake and Harry Gill," for instance, sharply criticised by
Landor, stood almost untouched through the editions of fifty years. And
in a letter of 1843, recently published for the first time,[E]
Wordsworth speaks thus severely of an attack made upon his son-in-law,
Edward Quillinan, by Landor: "I should have disapproved of his
[Quillinan's] condescending to notice anything that a man so deplorably
tormented by ungovernable passion as that unhappy creature might eject.
His character may be given in two or three words: a madman, a bad man;
yet a man of genius, as many a madman is." That criticism seems rather
more than righteously severe; but Wordsworth, while he cared little for
the criticism of the reviews, felt keenly the lash of the violent
Landor. The violent Landor we must call him, for violence was the too
dominant trait of his noble genius; and he exasperated Wordsworth, as we
see. But compare what I have just quoted with his familiar remark about
the small critics: "My ears are stone dead to this idle buzz, and my
flesh as insensible as iron to these petty stings." That Wordsworth said
at thirty-six years of age; and here is a striking reminiscence recorded
during his later years, and published in the "Prose Works." At
seventy-one he said to Lady Richardson:
It would certainly have been a great object to me to have
reaped the profits I should have done from my writings but
for the stupidity of Mr. Gifford and the impertinence of Mr.
Jeffrey. It would have enabled me to purchase many books
which I could not obtain, and I should have gone to Italy
earlier, which I never could afford to do until I was
sixty-five, when Moxon gave me a thousand pounds for my
writings. This was the only kind of injury Mr. Jeffrey did
me, for I immediately perceived that his mind was of that
kind that his individual opinion on poetry was of no
consequence to me whatever; that it was only by the
influence his periodical exercised at the time in preventing
my poems being read and sold that he could injure me.... I
never, therefore, felt his opinion of the slightest value
except in preventing the young of that generation from
receiving impressions which might have been of use to them
through life.
[Footnote E: "Prose Works," III., 381.]
This is grand self-confidence; and it is in the same tone that elsewhere
he says:
Feeling that my writings were founded on what was true and
spiritual in human nature, I knew the time would come when
they must be known.
In this connexion the English reviews of that time are still interesting
reading, particularly the "Quarterly" and the "Edinburgh." What was
Jeffrey saying in his "organ" during the years of Wordsworth's earlier
fame? In 1807 he described the poem of "The Beggars" as "a very paragon
of silliness and affectation"; and he said of "Alice Fell," "If the
printing of such verses be not felt as an insult on the public taste, we
are afraid it cannot be insulted." Two years later he calls upon the
patrons of the Lake school of poetry to "think with what infinite
contempt the powerful mind of Burns would have perused the story of
Alice Fell and her duffle cloak, of Andrew Jones and the half-crown, or
of little Dan without breeches and his thievish grandfather." Wordsworth
dropped the poem of "Andrew Jones," and never restored it--an omission
almost unique, as we shall see; for he stood by the substance of his
work, if not always by the form, with great pertinacity. He said of
"Alice Fell," in his old age, "It brought upon me a world of ridicule by
the small critics, so that in policy I excluded it from many editions of
my poems, till it was restored at the request of some of my friends."
Wordsworth had no stancher friend, his poetry had no more delicate
critic, than Charles Lamb; and Lamb wrote thus in 1815 to Wordsworth
about "Alice Fell" and the assailants of the poem. He said: "I am glad
that you have not sacrificed a verse to those scoundrels. I would not
have had you offer up the poorest rag that lingered upon the stript
shoulders of little Alice Fell, to have atoned all their malice: I would
not have given 'em a red cloak to save their souls."
Jeffrey decried two other pieces that rank among the most perfect of
Wordsworth's minor poems, as "stuff about dancing daffodils and sister
Emmelines," and spoke of another, which we count for pure poetry to-day,
as "a rapturous, mystical ode to the cuckoo, in which the author,
striving after force and originality, produces nothing but absurdity."
And he attacked these lines in the "Ode to Duty":
Thou dost preserve the stars from wrong:
And the most ancient heavens through thee are fresh and strong.
This, Jeffrey said, is "utterly without meaning: at least we have no
sort of conception in what sense Duty can be said to keep the old skies
_fresh_, and the stars from wrong." We need not be surprised at
Jeffrey's failing to admire these lines: they are transcendentalism, and
it would have troubled Wordsworth himself to render them into the plain
speech which he recommended as the proper diction of poetry. For they
have not a definite translatable content of thought; and we cannot read
them as philosophy or ethics; but as poetry we may feel their power; we
are willing to enjoy them for their own sake, because beauty is enough.
But this Jeffrey did not admit; Jeffrey was not vulnerable by
magnificent phrases, and of course he could not foresee what a power
Wordsworth's transcendentalism was to exert. When the ode "Intimations
of Immortality" first appeared (with the edition of 1807), Jeffrey
called it "the most illegible and unintelligible part of the
publication."[F] The remark need not surprise us. Jeffrey looked for
logical thought in the poem, and logical thought it had not; whatever
else it may contain, it will hardly be said to propound any new
arguments for immortality. But Jeffrey wrote in all sincerity, and later
in his life he read Wordsworth's poetry a second time, with a view to
discover, if he could, the merits which he had failed to see when he
criticised it--the merits which the English public had then found out.
His effort was a failure: for him the primrose remained a primrose to
the last, and nothing more. The acute lawyer was not a poet, nor a judge
of poets; he had an erroneous notion of what the office of poetry is; of
what it has been and will be--to please, to elevate, to suggest, but not
to argue or convince; and to the last he did not get beyond his early
decision, which, in the article just quoted from, runs as follows:
We think there is every reason to hope that the lamentable
consequences which have resulted from Mr. Wordsworth's open
violation of the established laws of poetry, will operate as
a wholesome warning to those who might otherwise have been
seduced by his example, and be the means of restoring to
that ancient and venerable code its honor and authority.
[Footnote F: "Edinburgh Review," October, 1807.]
But the critic cannot always tell what the new "song is destined to, and
what the stars intend to do." It is now evident enough where the early
assailants of Wordsworth were mistaken; and yet which critic of to-day
would be sure of his ground in a similar case? For the faults of genius
are old, familiar, and easily to be discerned; while, on the other hand,
genius itself is always novel, and therefore may be easily mistaken. It
takes genius to recognize genius; and most of Wordsworth's critics were
not men of genius. Landor, who was one, made a wise remark upon this
point. He said, "To compositions of a new kind, like Wordsworth's, we
come without scales and weights, and without the means of making an
assay."
But by pointing out his faults, his critics did him and us a service;
and it was one by which the poet profited, as we have seen, in spite of
his independence.
Let us now look at some of Wordsworth's multiple readings, if we may
call them so--passages, namely, in which he has returned, year after
year, to certain peccant verses, changing them again and again in the
quest of adequate expression. After repeated experiments he sometimes
finds a reading to please himself; sometimes, having allowed a
provisional text to stand throughout many years, he discards it and
returns to the original form; and sometimes, again, he abandons a
passage entirely, after scarring it with a lifetime's emendations. Of
the first sort I will cite three readings of a stanza in "A Poet's
Epitaph." As first published in the "Lyrical Ballads" of 1800, the poem
contained this adjuration to the philosopher "wrapped in his sensual
fleece":
O turn aside, and take, I pray,
That he below may rest in peace,
Thy pin-point of a soul away!
Lamb did not like this; and he wrote to Wordsworth: "The 'Poet's
Epitaph' is disfigured, to my taste, by the coarse epithet of
'pin-point' in the sixth stanza." In the edition of 1815 the "coarse
epithet" disappears, and the passage is modified as follows:
----Take, I pray,
That he below may rest in peace,
That abject thing, thy soul, away!
The years that "bring the philosophic mind" did not, however, reconcile
Wordsworth with the particular "philosopher" here in question. (Sir
Humphrey Davy, as Crabb Robinson, if I am not mistaken, tells us). On
the contrary, the poet devised a still more injurious epithet for that
unhappy physicist; and the passage now reads:
----Take, I pray,...
Thy ever-dwindling soul away!
Another of these multiple corrections has attracted much notice; it
occurs in the successive descriptions of the craft wherein the "Blind
Highland Boy" went sailing. In the first edition of that poem Wordsworth
called it
A Household Tub, like one of those
Which women use to wash their clothes!
It would seem difficult to defend this couplet upon any accepted theory
of aesthetics, rhyme, or syntax; and the "Household Tub" provoked quite
naturally a shout of derision from all the critics; it became the
poetical scandal of the day. Jeffery, mindful of "the established laws"
of poetic art, protested that there was nothing, down to the wiping of
shoes, or the evisceration of chickens, which may not be introduced in
poetry, if this is tolerated. The tub, in short, proved intolerable to
the reviewers; and when next the poem appeared in a new edition, that of
1815, Wordsworth transmuted the craft into a green turtle shell, noting
the change as made "upon the suggestion of a Friend":
The shell of a green Turtle, thin
And hollow: you might sit therein,
It was so wide and deep.
'Twas even the largest of its kind,
Large, thin, and light as birch tree rind;
So light a shell that it would swim,
And gaily lift its fearless brim
Above the tossing waves.
Lamb's comment upon this change was as follows:
I am afraid lest that substitution of a shell (a flat
falsification of the history) for the household implement,
as it stood at first, was a kind of tub thrown out to the
beast, or rather thrown out for him. The tub was a good
honest tub in its place, and nothing could be fairly said
against it. You say you made the alteration for the
"friendly reader," but the "malicious" will take it to
himself. Damn 'em, if you give 'em an inch, etc.
Wordsworth, however, instead of restoring the old text, went on
amending, and with reason; the reading just given is diffuse. But see
now the third and final form which he gave to the passage. The
sublimation of the Household Tub is now completed; it becomes, at last,
A shell of ample size, and light
As the pearly car of Amphitrite,
That sportive dolphins draw.
And as a Coracle that braves
On Vaga's breast the fretful waves,
This shell upon the deep would swim.
Here again are some new readings that Wordsworth discarded after long
trial. A well-known sonnet, one of his earliest, began thus in 1807:
I grieved for Buonaparte, with a vain
And an unthinking grief! The vital blood
Of that Man's mind, what can it be? What food
Fed his first hopes? What knowledge could he gain?
In 1815 we find the passage rewritten as follows:
I grieved for Buonaparte, with a vain
And an unthinking grief! for, who aspires
To genuine greatness but from just desires,
And knowledge such as He could never gain?
But in the later editions the first reading was restored, except the
words "vital blood," and we now read:
The tenderest mood
Of that man's mind, what can it be?
In "The Nightingale" Wordsworth first called that bird "a creature of a
fiery heart"; but in the edition of 1815 it became "a creature of
ebullient heart," a flat disenchantment of the verse. The change was
questioned from the first, as Crabb Robinson tells us, and in later
editions the first reading was restored. A fortunate correction made in
the same edition was retained--the change of "laughing company" to
"jocund company," in "The Daffodils":
A poet could not but be gay
In such a jocund company.
--1815.
The poem "Rural Architecture," in the "Lyrical Ballads" of 1800, was
curtailed of its closing stanza in the edition of 1815:
Some little I've seen of blind boisterous works
In Paris and London, '<DW41> Christians and Turks,
Spirits busy to do and undo, etc., etc.
But in Lamb's correspondence of the same year he complains to Wordsworth
that the omission "leaves it [the poem] in my mind less complete," and
the lines were restored in the later editions. Not to differ hastily
with Lamb, the lines yet seem lines to be spared. In the same sentence
he complains that in the new edition there is another "admirable line
gone (or something come instead of it), 'the stone-chat, and the
glancing sandpiper,' which was a line quite alive. I demand these at
your hand." Wordsworth restored the line, and the three versions of the
passage are worth comparison. It is from the "Lines left upon a Seat in
a Yew Tree," and describes a wanderer in the solitude of the country:
His only visitants a straggling sheep,
The stone-chat, or the glancing sand-piper:
And on these barren rocks, with juniper,
And heath, and thistle, thinly sprinkled o'er,
Fixing his downcast eye, he many an hour
A morbid pleasure nourished.
--"Lyrical Ballads."
In the second reading he corrects a bad assonance thus:
His only visitants a straggling sheep,
The stone-chat, or the sand-lark, restless bird,
Piping along the margin of the lake....
--1815.
Here the "line quite alive" is gone--to be restored in deference,
apparently, to Lamb's request. Another assonance is got rid of in the
later editions, the "thistle thinly sprinkled o'er," and the passage now
reads melodiously as follows:
His only visitants a straggling sheep.
The stone-chat, or the glancing sand-piper:
And on these barren rocks, with fern and heath,
And juniper and thistle, sprinkled o'er,
Fixing his downcast eye, he many an hour
A morbid pleasure nourished.
Wordsworth struck out many lines and stanzas in the course of his
revisions, besides main passages of considerable length, as from the
"Thanksgiving Ode" and the patriotic ode of January, 1816. These
omissions are too long to quote here; but the following lines dropped
from the ode on "Immortality" will have interest; they are not to be
found, I think, in any English edition since that of 1815. Addressing
the child over whom Immortality, in the language of the ode,
Broods like the Day, a Master o'er a Slave,
A Presence which is not to be put by--
this earlier reading continues:
To whom the grave
Is but a lonely bed without the sense or sight
Of day or the warm light:
A place of thought where we in waiting lie.
Another notable omitted passage is the introduction to "Dion," published
in 1816:
Fair is the Swan, whose majesty, prevailing
O'er breezeless water on Locarno's lake....
Here nineteen lines full of beauty are sacrificed by Wordsworth in the
interest of the unity of the poem. He struck out, too, some lines from
"The Daisy," "The Thorn," and "Simon Lee," and eight stanzas have
disappeared from "Peter Bell" since the first edition of that poem.
Among them are these grotesque lines, favorites with Charles Lamb:
Is it a party in a parlour?
Cramm'd just as they on earth were cramm'd--
Some sipping punch, some sipping tea,
All silent and all damn'd!
And here are some verses that have interest from the glimpse they give
of Wordsworth's faculty in a field that he declined to cultivate--the
amatory or "fleshly," as it has been conveniently named for us of late.
I quote from that rare book, the "Descriptive Sketches" of 1793; and as
the lines are not included in any edition of his poems, they are
unfamiliar to most readers. But two copies of this book, so far as I
know, exist in this country. One of them, which belonged to the late
Prof. Henry Reed, Wordsworth's American editor, is full of corrections
in Wordsworth's own handwriting; and it is by the courtesy of its
present owner that I am enabled to give here the early text with these
corrections, never before printed. The young Wordsworth takes leave of
Switzerland, at the conclusion of his pedestrian tour, with this glowing
apostrophe:
ye the
Farewell! those forms that in thy noontide shade
your
Rest near their little plots of oaten glade,
Dark
Those stedfast eyes, that beating breasts inspire,
To throw the "sultry rays" of young Desire;
soft
=Those= lips whose ^ tides of fragrance come and go
Accordant to the cheek's unquiet glow;
Ye warm
Those shadowy breasts In love's soft light array'd
And rising by the moon of passion sway'd.[G]
[Footnote G:
I venture to note, in passing, a small class of corrections in which the
poet has cleared his text from certain innocencies of expression that
were liable to be misread by persons on the alert for double meanings.
The following are among the Wordsworthian simplicities that have been
amended in the later editions; the reference is made to the octavos of
1815, which may be compared with any of the editions since 1836:
Vol. I., page 111, "The Brothers," passage beginning, "James, tired
perhaps."
Vol. I., page 210, "Michael," passage beginning, "Old Michael, while he
was a babe in arms."
Vol. I., page 223, "Laodamia," stanza beginning, "Be taught, O faithful
Consort."]
Wordsworth thus dropped, for one reason or another, many passages from
his poems. But did he abandon entire poems? That did not often happen.
He strove patiently to perfect the form of his thought; but he was
unwilling to let the substance of it go. In the seven volumes of his
poetry, as they now stand, but two poems are lacking, to the best of my
knowledge, of all that he ever published. One of these, an unimportant
piece beginning, "The confidence of youth our only art," was printed
with the "Memorials of a Tour on the Continent" (1822), and no longer
appears in the collected editions. The other missing poem, "Andrew
Jones," was abandoned for reasons, as I think, of considerable critical
interest. In the "Lyrical Ballads" it began thus:
I hate that Andrew Jones: he'll breed
His children up to waste and pillage:
I wish the press-gang or the drum
With its tantara sound would come,
And sweep him from the village!
This poem may be found (with, slight emendations) as late as the edition
of 1815; but after that date I meet with it nowhere but in foreign
reprints. Why was it dropped? It is doubtless a story of unrelieved
though petty suffering; it corresponds, in small, to what Mr. Matthew
Arnold calls the "poetically faulty" situation of Empedocles, a
situation "in which there is everything to be endured, nothing to be
done." But, on the other hand, that fragment of AEschylus, the
"Prometheus Bound," in which everything is endured and nothing done, yet
remains a work of the deepest interest: nor need we think that
Wordsworth abandoned his little poem for a reason so refined as that
which led Mr. Arnold to abandon one of his own. There was, as I take it,
a moral reason which led to Wordsworth's decision; namely, that the
story of "Andrew Jones" is told with bitterness of feeling from
beginning to end; and against bitterness of feeling Wordsworth had
recorded, during his earlier years, a striking protest. We shall read it
presently; but first let us couple with the poem a sentence from his
prose--a sentence full of the same feeling, and which was early dropped
for the same reason. We shall find it in the edition of 1815, in the
essay supplementary to the famous Preface of that date. There Wordsworth
turns upon his critics as follows:
"By what fatality the orb of my genius (for genius none of them seem to
deny me) acts upon these men like the moon upon a certain description of
patients, it would be irksome to enquire: nor would it consist with the
respect which I owe myself to take further notice of opponents whom I
internally despise."
This is not quite in the vein of the serenely meditative poet; and if we
look back to a time twenty years earlier than this, we shall find that
Wordsworth had reproved his heat beforehand. In 1795, when he first
chose definitely the poet's career, he had written these lines:
If thou be one whose heart the holy forms
Of young imagination have kept pure,
Stranger! henceforth be warned; and know that pride,
Howe'er disguised in its own majesty,
Is littleness: that he who feels contempt
For any living thing, hath faculties
Which he has never used: that thought with him
Is in its infancy.
That is the teaching of earlier and serener years, of the time when the
poet was still quietly embayed in youth, when jealous criticism, and
envy, and disappointment were still trials of the future. Youth has its
own passions; but it has also its peculiar serenity; and after
Wordsworth had passed through the stormy years which gave him fame, we
see the maturer man recalling the teaching of his calmer self. It was in
obedience to this, as I believe, that he cancelled the passages that
have just been mentioned; feeling their discord with the pure song of
that early time.
Let us now look at some of the passages which Wordsworth has emended,
not by taking away from the words of his book, but by adding to them. As
he wrote to Mr. Dyce, he diligently revised the "Excursion," in the
edition of 1827, and got the sense "in several instances, ... into less
room"; and minor changes are to be counted by hundreds. But he made some
additions to this poem, and for significant reasons.
Readers of Christopher North's essay, in the "Recreations," on "Sacred
Poetry," will remember the long indictment which he there brings against
the earlier poems of Wordsworth; he complains of them as being
irreligious. It is interesting to find the earthly Christopher
displaying the pious zeal of an inquisitor in the matter, declaring that
in all of Wordsworth's writings, up to the "Excursion," "though we have
much fine poetry, and some high philosophy, it would puzzle the most
ingenious to detect much, if any, Christian religion"; and lamenting its
absence even in the "Excursion," in the story of "Margaret," as told in
the first book. This tale Christopher North calls "perhaps the most
elaborate picture he [Wordsworth] ever painted of any conflict within
any one human heart;" but he adds, with how much sincerity we will not
now ask, that it "is, with all its pathos, repulsive to every religious
mind--_that_ being wanting without which the entire representation is
vitiated.... This utter absence of Revealed Religion ... throws over the
whole poem to which the tale of Margaret belongs an unhappy suspicion of
hollowness and insincerity in that poetical religion which at the best
is a sorry substitute indeed for the light that is from heaven."
That Wordsworth laid to heart this criticism, will appear on comparing
the original passage, as reprobated by Christopher North, with the form
which the poet gave it in the latter editions. Originally the peddler,
finishing the story of "Margaret," moralizes thus:
My Friend! enough to sorrow you have given;
The purposes of wisdom ask no more:
Be wise and cheerful, and no longer read
The forms of things with an unworthy eye;
She sleeps in the calm earth, and peace is here.
I well remember that those very plumes,
Those weeds, and the high spear-grass on that wall,
By mist and silent raindrops silvered o'er,
As once I passed, into my heart convey'd
So still an image of tranquillity,
So calm and still, and look'd so beautiful
Amid the uneasy thoughts which fill'd my mind,
That what we feel of sorrow and despair
From ruin and from change, and all the griefs
The passing shows of Being leave behind,
Appear'd an idle dream, that could not live
Where meditation was. I turn'd away,
And walk'd along my road in happiness.
"What meditation?" cries out Christopher North. "Turn thou, O child of a
day, to the New Testament, and therein thou mayest find comfort." And
Wordsworth in his revision made the following additions to this fine
pagan passage:
----Enough to sorrow you have given;
The purposes of wisdom ask no more:
Nor more would she have craved as due to one
Who in her worst distress, had often felt
The unbounded might of prayer; and learned, with soul
Fixed on the cross, that consolation springs
From sources deeper far than deepest pain
For the meek sufferer. Why then should we read
The forms of things with an unworthy eye?
She sleeps in the calm earth, and peace is here.
Then follow the beautiful lines about the weeds, the spear-grass, the
mist and rain-drops, as quoted above; but the close of the passage is
extended as follows:
----All the griefs
That passing shows of Being leave behind,
Appeared an idle dream, that could maintain
Nowhere dominion o'er the enlightened spirit
Whose meditative sympathies repose
Upon the breast of Faith. I turned away,
And walked along my road in happiness.
It remains to be said that a certain number of Wordsworth's poems--and
these were, as we might expect, among his best--have stood unchanged in
all the editions from the first, running the gauntlet of their author's
critical moods for half a century, and coming out untouched at last. I
will not call them uncorrected poems, but rather poems in which all the
needed corrections were made before their first publication, for they
belong to that exquisite class of creations--too small a class, even in
the works of the greatest masters--in which the poet has fused
completely the refractory element of language before pouring it out into
the mould of poetic form. Among these untouched poems are three from the
"Lyrical Ballads"--"A slumber did my spirit seal," "Three years she grew
in sun and shower," and "She dwelt among the untrodden ways"--all
written at the age of twenty-nine; such are the "Yew Tree," written four
years later, and "She was a phantom of delight." Several of the best
sonnets, too, were unchanged; as that on "Westminster Bridge," and
"Milton! thou shouldst be living at this hour."
And lastly, I may mention one or two changes of text which Wordsworth
did not make, but which belong to the class for which careless editors
or proofreaders are responsible. An edition well known to the American
public is especially peccant in this respect; that beautiful line, for
instance, in "The Pet Lamb"--
And that green corn all day is rustling in thy ears,
becomes,
That green cord all day is rustling in thy ears.
And here is a really interesting _erratum_; it occurs in the poem of
"The Idiot Boy," where it has stood unnoticed for twenty years and more.
Wordsworth's stanzas, describing the boy's night-long ride under the
moon, "from eight o'clock till five," hearing meanwhile "the owls in
tuneful concert strive," originally put these words into his mouth, the
actual words of his hero, as Wordsworth tells us in a note:
The cocks did crow to-whoo, to-whoo,
And the Sun did shine so cold,
Thus answered Johnny in his glory.
But this reading puzzled the proofreader. How could the sun shine at
night? This being clearly impossible, he restored the idiot boy to
partial sanity. He made him say:
The cocks did crow to-whoo, to-whoo,
And the Moon did shine so cold;
and the only wonder is that he did not also read,
The cocks did crow cock-a-doodle-doo.
Some one proposes, I believe, a similar emendation in "As You Like It,"
intending to make the Duke speak better sense than Shakespeare put into
his mouth. He is to say,
Sermons in books.
Stones in the running brooks, and good in everything.
But while in the main the text of Shakespeare is bettering under
criticism, Wordsworth is suffering miscorrection; and for the good that
he has to give us we cannot quite dispense with the original editions.
TITUS MUNSON COAN.
PORTRAIT D'UNE JEUNE FEMME INCONNUE,
GALERIE DE FLORENCE.
I saw a picture in a gallery:
Go where I will, it still abides with me.
The hair rich brown, one lovely golden tress
Strayed from the braid and touched the loveliness
Of the fair neck, so smooth, so white, so young,
It shamed the pearls a prince's hand had strung.
The dress is white, with here and there a gleam
Of amber brilliant, sunlight on a stream!
And hanging on her arm, a scarf; the thing
About that glorious head and neck to fling,
Protecting from the night, scarlet and black and gold,
And gems are woven in each gleaming fold.
The picture has that gracious air which tells
The hand that painted it was Raphael's.
They know she's beautiful, and know no more.
Thus questioned I, as many did before:
"Why art thou sad, thou delicate, proud face?
Thou art a Dame of bright and cheerful race,
Thy fortunes grand, thy home this Florence fair.
Does an unworthy heart thy palace share?
Or with a soft caprice dost turn from joy,
And play with sorrow as a costly toy?
Or has thy page forgotten, or done worse--
Failed he to find the fond expected verse
Thy lover promised thee? I know not why
I linger near thee, beautiful and sad,
Yet with such sorrow, who would have thee glad?"
(Is she not gifted with the anointed eye
That sees the trouble of the passer-by?)
"Is thine that great, that tender sympathy
That calls all heart-aches nearer unto thee?
Or a great soul with aspirations rife,
Feeling the insufficiency of this our life?
Thou hast attraction of a grander tone,
Some charm more subtle e'en than beauty's own!
"Though woman throws no greater lure than this,
The lip regretful which we fain would kiss,
The eye made softer by the unfallen tear,
And sunlight brighter for the shadow near.
Why do I ask? will woman ever tell
The secret of the charm that fits her well?"
She did not answer, sweet, mysterious Dame.
I left her sadly, locked in gilded frame.
M. E. W. S.
MISS TINSEL.
A GOLD-MINER'S LOVE STORY.--IN FIVE CHAPTERS.
CHAPTER I.
A GOLD-DIGGING RECLUSE.
On a knoll, not far from a running stream, was pitched a rough canvas
tent. It was of the "wall" sort, and was pegged to the ground with
strong fastenings. Inside were a hammock, a coarse table, two or three
stools, and some boxes and barrels. There were likewise a gridiron, a
"spider," an iron kettle, some tin dishes and cups, and a pair of
candlesticks of the same material. Outside there was a trench dug, by
way of drainage, so that the floor within was kept hard and dry; but the
floor was of earth merely. There was not a flower, or a picture, or the
least attempt at ornament whatever within the tent. Hence the interior
looked bare, sordid, and forbidding. And yet, grim as it was, the tent
had been the solitary abode of its occupant for many months. In the
midst of gold, in quantity outstripping the wildest dreams of his
boyhood, this man had chosen to be a miser. In the midst of a society
whose reckless joviality and wild profusion were perhaps without
precedent, he had chosen to be a recluse. For this self indulgence he
had to pay a price. But he consoled himself, remembering that a price
has to be paid for everything.
Chester Harding came to Bullion Flat about a year before. He had no
friends and no money. The former he could do without, he thought, but
the latter was indispensable. So he got work on the Flat, turning a
spade and plying a rocker for five dollars a day. Such work was then
better paid as a rule, but Harding, though diligent and strong, was not
used to toil, and hence was awkward and comparatively inefficient. He
improved with practice and strove doggedly on, never losing a day,
saving every penny, spending nothing for drink or good fellowship,
courting no man's smile, and indifferent to all men's frowns. He was
savagely bent on achieving independence, and in no long time, after a
fashion, he got it. Independence, in this sense, consisted in a share of
a paying claim, and in the whole of a "wall" tent. In the former he dug
and washed, morosely enough, with five or six partners; but he made up
for this enforced and distasteful social attrition by living in his tent
alone.
Harding was a man getting toward middle life, strongly built, but not
tall, with a grave, handsome face and speech studiously reserved and
cold. He seemed to fear lest he might be thought educated, and, as if to
disarm such a suspicion, his few words were apt to be abrupt and homely.
When he first came to the Flat he had two leathern trunks, and these in
due time were bestowed in the tent on the knoll. One Sunday Harding
opened them. The first contained some respectable garments, such as
might belong to the ordinary wardrobe of a gentleman. There were white
shirts among the rest, and some pairs of kid gloves. Of all these
articles Harding made a pile in the rear of his tent and then
deliberately set them on fire. "I couldn't afford it before," he
muttered. "They might have bought a meal or two if need were; but
now----" To be rich enough to gratify a caprice was clearly very
agreeable to the man; for presently he brought out a number of
books--old favorites obviously--and treated them in the same incendiary
manner. The Shakespeare and the Milton, the Macaulay and the Buckle
spluttered and crackled reproachfully in the flames; yet their destroyer
never winced, but added to the holocaust heaps of letters, and at last
two or three miniatures saved for the fire as a final tid-bit, and gazed
with grim joy as the whole crumbled in the end to powdery ashes. Chester
Harding reserved nothing but one little volume, bound in velvet with
gilt clasps, and one faded old daguerreotype, which he replaced in his
trunk side by side, and then covered quickly so that they should be out
of sight. It seemed to be his wish to hide and to forget every trace of
his past life.
That life had been a hard and bitter one. From his earliest childhood
Harding had been a victim of the weakness and cruelty of others. A
miserable home, made a hell by drink and contention, was at last broken
up in ruin, and the young man went forth into the world to meet coldness
and injustice at every turn. Suspicion and selfishness are among the
almost certain fruits of an experience like this, and the world is
naturally more ready to condemn such fruits than to find excuses for
them. When Harding found himself unpopular and distrusted he as
naturally shaped his conduct so as to justify its condemnation.
Surrounded from the beginning of his life by bad influences, and by
these almost exclusively, he found little to soften his harsh judgment
of men or to mitigate his resentment for their ill treatment. In time he
fell in with one who with greater strength and higher wisdom might
perhaps have led him up to nobler views and a loftier destiny. For he
loved her deeply and without reservation. But her charms of person found
no counterparts in her mind or heart, and Harding was cheated and
betrayed. To escape old thoughts and associations, and to mend if
possible broken fortunes, he sought the Land of Gold. He had heard that
men were more generous there than elsewhere, less cunning, tricky, and
censorious. Perhaps even he might find average acceptance among new
scenes and among a new people.
But on the day he landed at San Francisco Harding was robbed by a fellow
traveller, whom he had befriended, of the last penny he had in the
world. The man had shared his stateroom on board the steamer, and knew
that he had a draft on the agent of the Rothschilds. When Harding cashed
his draft he took the proceeds, in gold coin, to his hotel. That night
he was visited by his shipmate, who contrived to steal the belt
containing this little fortune, and to escape with it to the mines. Next
morning Harding sought a near relative, an older man of known wealth,
his sole acquaintance on the Pacific coast.
"I've come to you," he said, after receiving a somewhat icy greeting,
"to ask you to help me. A serious misfortune has overtaken me, and----"
"If it's money you want," interrupted the other brusquely, "I've got
none!"
This was not the usual fashion of the pioneers. Happily most of them
were made of sweeter and kindlier stuff. But the fates had woven out
poor Harding's earlier fortune, and it was all destined to be of the
same harsh, pitiless web. He bowed his head when these words were said
to him, and with the kind of smile angels must most hate to see on the
faces of those so near and so little below them, he went forth in
silence. Next morning he pawned his watch and made his way up into the
mines.
* * * * *
"He's cracked; that's what he is," decided Jack Storm. Since the great
find of gold at Bullion Flat there had been a great rush thither from
the immediate neighborhood, and among the rest quite a deputation
arrived from Boone's Bar. Jack was as great a dandy as ever, and still
wore his gaudy Mexican jacket, with its silver bell buttons, his
flapping trousers to match, and his gigantic and carefully nourished
moustache.
"Cracked!" repeated Mr. Copperas suavely. "Not he. He takes too good
care of his money for that. No, boys, that ain't the trouble. He's been
'chasing the eagle' in times past; the bird has been too many for him,
and now he's playing to get even."
"Stuff!" gurgled Judge Carboy, unwilling to part by expectoration with
even the smallest product of his favorite quid. "He's done sutthin' he's
ashamed of. No trifle like that, Cop. He's proberly committed a murder
out East. Bime by we'll hear all about it."
Jack Storm shook his head. "He's worked side by side with me for nigh a
year, and he wouldn't hurt a fly. Besides, it is his turn next week to
go to 'Frisco for stores."
"What's that to do with it?" queried Mr. Copperas.
"A durned sight," returned the other. "Ain't they after these cusses
with a sharp stick who've got in hot water at home? And ain't goin' to
'Frisco for such chaps jes' like walkin' into the lion's mouth? Why,
there's honest miners--and them as ain't honest miners, Cop--who'd a
_leetle_ rather not go down to the Bay jes' now, even among the quiet
folks over at Boone's Bar."
Mr. Copperas coughed uneasily. "So Harding's going down, is he?" he
inquired. "Right off?"
"Sartain. You'd better take a trip and keep him company."
There was a murmur of amusement at this. Everybody at the "Bella Union"
knew that something had been in the air touching chirographic exploits
of Mr. Copperas a few years back at New Orleans, and before he kept the
faro bank at Boone's Bar.
"For my part," put in Jim Blair, who liked to hear injustice done to no
man, "I s'pose there's reasons why a chap might want to live alone, and
yet mightn't a knifed anybody nor robbed 'em either."
"That's so, Jim," affirmed Judge Carboy oracularly. "No doubt on't. But
when it's so we usually hear what them reasons is. Now, who knows air a
word on 'em in the case afore us? Anyhow, I hope he's good--good as
gold--only we've had our sheer of troubles in the county, and it's well
to look sharp."
"When I was a little chap," proceeded Jim Blair with retrospective
deliberation, "I lived in a village on the further side o' the Ohio.
Most folks did their business on t'other bank, and went over generally
by the eight o'clock ferry in the mornin.' Now, there was two or three
that didn't; men whose work lay nigher home, or who went later. But the
crowd went over reg'lar at eight. Arter awhile they got awful sot agin
them who didn't go over at the same time. There weren't no hell's
delights you could think of them fellers didn't lay to the men who
didn't travel by the eight boat; and at last, damn me if they didn't
want to lynch 'em!"
"Lynch 'em for not goin' in the eight boat!" cried the Judge, whose
respect for the majesty of the law always asserted itself, as was meet,
on hearing any tale of its infringement.
Jim Blair nodded. "Not so much, I reckon, for not goin' in the eight
boat as for not doin' what other folks did. However, them who ever try
to trouble Ches Harding'll have a rough time, I guess."
"You think he's sech a game fighter?" inquired Jack Storm with lively
interest.
"That may be too. But what I meant was, there's them on the Flat who
believe in Ches for all his lonesome ways, and won't see him put upon.
For my part I reckon he's more sinned against than sinnin'."
"I guess you're half right, Jim," admitted Judge Carboy with diplomatic
concession; "more'n half right. But mark my words"--and the Judge's
voice rose to the orotund swell which denoted his purpose to be more
than commonly impressive--"thar'll be the devil's own time on the Flat
some day, and that air duck'll be king pin and starter of it. I never
know'd no such silent, sulky cuss as that moonin' round but that he
kicked up pettikiler h-- in the long run."
It will be seen from this that there were differences of opinion
respecting Chester Harding at Bullion Flat, and it cannot be denied that
there was some reason for it.
CHAPTER II.
MISS TINSEL.
It was in a magnificent theatre that Chester Harding first saw her--a
theatre grand in size and tasteful in decoration. It had only lately
been opened, and was one of the lions of the Golden City. Harding went
there to while away an idle hour, and in order, perhaps, that he might
see all there was to be seen before leaving San Francisco. His visit was
one of merest chance, and no trifle had seemed lighter in all his
California life than his straying that night into the Cosmopolitan
Theatre.
And yet perhaps it was the turning-point in his existence. Others who
were there from Bullion Flat said afterward that from that night Harding
was transfigured. A blaze of chandeliers, with golden fretwork skirting
the galleries and rich dark velvet framing the boxes, could hardly
surprise him. Nor was there much to astonish--whatever there might be to
admire--in the rows of handsomely dressed women who gave brilliancy to
the audience. Neither could the drama itself, which the manager was
pleased to style "a grand legendary fairy spectacle," move Harding
seriously from his equilibrium. All these splendors, together with the
resonant orchestra, the dazzling scenery, rich in Dutch metal and gold
foil, the sanguinary and crested Baron, the villain of the play, the
iridescent youth, its hero, the demons, who went through traps, vampire
and other--one Blood-Red Demon with a long nose being especially
conspicuous--the fairies, who brought order out of chaos--of whom the
"Queen of the Fairy Bower" was the large-limbed and voluptuous
principal--the "Amazonian Phalanx," who went through unheard-of
manoeuvres with massive tin battle axes and spears--all these failed, it
must be owned, to startle Mr. Harding from his propriety. He had seen
such things, or things very like them, before. And yet he was taken off
his feet, to use the metaphor, and swept away captive by a very torrent
of emotion excited by Miss Tinsel.
She was only a _coryphee_; that is, she was but one among the minor
subordinates of the ballet. Her advent was accomplished as one of the
"Sprites of the Silver Shower." She had to come chassezing down the
stage, and she never raised her eyelids--before most demurely cast
down--until she was close upon the footlights. But when those eyelids
_did_ go up it was--well, as Judge Carboy afterward used to say, it was
just like sunrise over the mountains at Boone's Bar! A girl with a mass
of bright hair, almost red it looked by daylight, and large gray eyes
that looked as black as soot by the gas, but took on more tender hues by
day--a girl with a figure that was simply perfection, and yet one who
with all her archness seemed to have no vanity. She had many dainty
white skirts, one above another like an artichoke, of fluffy and
diaphanous texture, and although these, it cannot be denied, were
perilously short, somehow Miss Tinsel did not look in the least
immodest.
All the men from Bullion Flat knew it _was_ Miss Tinsel, since the
"Queen of the Fairy Bower" addressed this charming figure more than once
as "Zephyrind," and a reference to the play-bill thereupon at once
established her identity.
What strange magnetism there was about this girl Harding, and indeed all
who looked at her, found it hard to define. Perhaps, apart from her
lovely eyes and hair and her exquisite figure, it was because she always
seemed to be drawing away that she proved so fascinating. Even when she
advanced straight toward you she seemed for ever to retreat. By what
subtle and skilful instinct of coquetry Miss Tinsel was enabled to
convey this impression cannot here be explained. That she did convey it
was universally admitted. It appeared, however, on inquiry, that her
dramatic powers were of the slightest. Her beauty and charm were such
that the manager would gladly have put her forward could he have seen
his way to do so. But her success had been so moderate, when the
experiment was tried, in one or two of the "walking ladies" of farces,
that it was thought wisest to let her be seen as much and heard as
little as possible.
When Harding last saw her that night she was going up to Paradise on one
foot, the other pointing vaguely at nothing behind, the intoxicating
eyes turned up with a charming simulation of pious joy, and the cherry
lips curled into a smile that showed plenty of pearls below. She
vanished from his gaze in a glory of red fire, amid the blare of gongs
and trumpets, while the "Blood-Red Demon" went down to the bad place
under the stage through a trap, and the "Queen of the Fairy Bower," with
felicitous compensation, ascended to the heaven of the flies.
After this tremendous catastrophe Harding went to his hotel and
reflected.
That a Timon like himself--a misogynist indeed of the first
water--should fall in love at first sight with a ballet girl certainly
furnished matter for reflection. But reflection did not prevent Timon
from seeking an interview with his unconscious enslaver the next day.
Even cold and soured natures may become under some incentives
enthusiastic and ingenious.
Harding found out where Miss Tinsel lived, learned that she usually came
from rehearsal at about two, called consequently at three, and coolly
sent in his name, telling the servant that the young lady would know who
he was. As he hoped, the device got him admittance. The girl supposed he
was some one from the theatre whose name she had not caught or had
forgotten.
It was a very plain and humble room, almost us bare and forbidding
perhaps as the inside of Harding's tent on the knoll, and yet how
glorified was the place with the purple atmosphere of romance!
Miss Tinsel was as simply equipped as her room: a gown of dark stuff
with a bit of color at the throat, and that was all. Harding saw that
she was not quite so perfect physically as he had thought, and this,
strange as it may seem, instantly increased his passion for her. Nothing
could make her figure other than beautiful, or impair the lustre of her
eyes; but the fair creature had a little range of freckles across her
delicate nose and cheeks, and her hair by day appeared, as has been said
before, nearly red. Her natural smile, on the other hand, as
distinguished from her stage smile, which was merely intoxicating, was
almost heavenly; and it was not made less so by an occasional look that
was grave almost to sadness.
"Sit down." He was standing stock still and silent in the middle of the
room. "You come from the theatre, don't you?"
It was a sweet voice--sweet and low--too low, in truth, which was one of
the reasons of its failure in the drama--one of those thrilling
contralto voices, most magnetic and charming when heard by one alone, or
close by, but which lost their magnetism and charm if strained to fill
the ears of a crowd.
"No--yes--that is, I was there last night. I saw you there," he replies
stupidly.
"Last night? Oh, yes. But why do you want to see me to-day?"
This is a hard question to answer; so he tries evasion.
"Did you get a bouquet?"
"A perfect love--a beauty--it was thrown at my feet; but I gave it to
her of course."
"Gave it to _her_?"
"Miss De Montague--don't you know--the 'Queen of the Fairy Bower?' She
gets all the bouquets."
"Oh, she does, does she?"
"Certainly. She is the principal, you know. Her engagement calls for all
the bouquets."
"Even when they are plainly intended for somebody else?"
"Ah, but they oughtn't to be intended for somebody else. If any one is
so silly as to think somebody else ought to have a bouquet, any one has
to be punished. Then they forfeit him."
"Forfeit him?"
"Or his flowers. They always forfeit you in theatres--if you're late at
rehearsal, you know, or if you keep the stage waiting. But then you
needn't mind. Miss De Montague is a dear, good soul. She took the
bouquet for the look of the thing, you know; that's business; but she
gave me half the flowers when we got home."
"Does she live here then?"
"Why, to be sure. You know, we always go to the theatre together. Only
for her I should be quite alone."
"And do you like this kind of thing?" he asks clumsily.
She bursts into a merry laugh. "Like it? Why, I get my living by it. We
all have to live, you know, and I've no one to look out for me but
myself, and----"
She pauses suddenly, having caught his eye fixed upon her with a gaze of
passionate admiration. This first calls up the look of gravity we have
spoken of, and then brings the color sharply to her face. It also
reminds her of the somewhat peculiar character of the interview. The
instant after she resumes, as if continuing her sentence, "Did you come
here to ask me that?"
"No," he replies bluntly. "I never thought of the question until the
moment before I asked it."
"Please tell me, then," she proceeds, with gathering surprise, "what
_did_ you come for?"
He hesitates a moment, moved by the superstition or the honest feeling
that he must tell her no word of untruth, and then quietly answers:
"I am not sure that I know."
"Not sure that you know?"
"No."
"Perhaps, then, you'll go away, and when you _are_ sure----"
"Come back again?" hazards he.
"I didn't say that. You look and talk like a gentleman, and if, as I
hope, you are one, you will know that I can't see strangers--people who
have no business with me--and so you must excuse me." She has risen and
moves with some dignity toward the door.
"One moment," he interposes. "Forgive me; you know for your part that it
is impossible I should wish to offend----"
"How should I? You come here to me a stranger, and refuse to say what
for."
"No. I did not refuse. I only said I was not sure that I knew why I
came."
"Then you must be crazy!" she blurts out impulsively.
"Perhaps I am. I begin to think so."
"Then I wish you would go away!" she goes on with apprehension. "I'll
tell you what, Mr. Bellario is here, and he's--oh, terribly strong!"
"Mr. Bellario?" he echoes.
"Yes. The 'Blood-Red Demon,' you know. Didn't you see him go through the
traps?"
Harding laughs, very much amused. "And you mean to threaten me with the
'Blood-Red Demon,' do you?"
"Oh, no," she responds gently, but again edging toward the door--"not
threaten; but"--in a very conciliatory tone--"if you won't say what you
come for and won't go away----"
"But I will," he says gravely.
"Will which?"
"Will both. I will say what I came for and then I will go away."
"I don't mean to be rude, you know," she puts in, softening.
"Nor I. Now I will tell you. I came because I could not possibly stay
away--because you drew me toward you with an irresistible force----"
"I'm sure I didn't!" she protests indignantly.
"Unconsciously, of course. You may think me foolish--wild if you please.
I can't help that. You will know better in time. I come to you saying
not a wrong word, thinking not a wrong thought. There is nothing against
me. At home I was a gentleman. I ask leave to visit you, respectfully as
a friend, nothing more."
"But why?" she asks, bewildered.
"Because I admire you greatly, inexpressibly, and I must tell you so."
She turns scarlet now. "But I shall never tell you this--not again--or
anything else in words you do not choose to hear. All I ask is the leave
now and then to see and to speak with you."
This was very embarrassing. Had he said he loved her, and at first
sight, she would have turned him away. She would have distrusted both
his sincerity and his motives. But he did not say this. On the contrary,
he offered in explicit terms, it would seem, not to say it. She
therefore naturally took refuge in generalities.
"But what you ask won't be possible. What would people say? This is a
very bad, a scandalous country, I mean. What would Miss De Montague
think, or Mr. Bellario?"
"What people will say or think hardly needs to be considered," said
Harding steadily, "since in a week I shall have gone to my home in the
mines. You won't be troubled with me long--twice more perhaps. Only once
if you prefer it. All shall be exactly as you wish it. Is not that
fair?"
Miss Tinsel was saved the present necessity for replying to a question
or coping with a situation both of which she found extremely perplexing,
since at this juncture the door opened and admitted the "Queen of the
Fairy Bower" and the "Blood-Red Demon," who had apparently been out for
a morning walk. To Harding's surprise, the "Queen" was a motherly
looking woman of forty-five and the "Demon" a weak-eyed young man, with
a pasty white face, and some fifteen years younger. Both were much
overdressed, and both stared vigorously at Harding--the "Queen" with an
air intended to represent fashionable raillery, the "Demon" with haughty
surprise. But the visitor avoided explanations that might have been
embarrassing by bowing low to the company and passing from the room.
CHAPTER III.
THE CUP AND THE LIP.
Her real name was Jane Green. But Jane Green would never do for the
play-bill; so the manager, exercising his peculiar and traditional
prerogative, had rechristened the young lady for the histrionic world,
and she appeared as "Aurora Tinsel." A poor, almost friendless girl, she
had left the Atlantic States with an aunt who had been the wife of the
"property man" in the theatre. Soon after the aunt died, and Jane had
gladly accepted the offer of Miss De Montague to live with her, and, by
helping that lady with her dresses, to render an equivalent for her
society and protection.
Harding was a wise man in his generation, foolish as in some respects he
may appear. We offer no explanation of his swift and unreasoning
infatuation, because it is just such men who do just such rash and
impulsive things. But he was sagacious enough to know that a man who
really wants a woman is less likely to get her by being too quick than
even by being too slow. Women who are interested always maintain the
contrary; but this is because they want to bag their game instantly,
whether they mean to throw it away afterward or not. The sex are not
apt, however, to err by over-rating the value of what they get too
easily, and this Harding was philosopher enough to know.
Hence, while he again sought Miss Tinsel twice before his departure, and
while his admiration, although respectful, was not concealed, he did not
go so far as to ask the girl to become his wife. It appeared that after
the run of the current spectacle at the theatre a "great tragedian" was
to play an engagement there, and the opportunity was to be taken for the
ballet and pantomime troupe to make a tour of the mines. Miss De
Montague was to go as a chief attraction, and Miss Tinsel was to go
also, and among the places they were to visit was Bullion Flat.
These plans left open a space of three months, during which Harding
could think of what he was at, and Miss Tinsel could think of what he
meant, and several other persons who were interested could make up their
minds what to do.
The first step taken by Harding on his return was highly confirmatory,
in the judgment of the Flat, of the opinion expressed by Jack Storm some
time before. A contract was made with a builder, and close by the tent
on the knoll there speedily arose a cottage of fair proportions, which
was evidently meant to supersede the humbler structure which for a year
had formed Harding's home. No one doubted his ability prudently to incur
such an outlay. He had been saving to parsimony, and he had been
prosperous. But why, when a tent had so long sufficed to him, and when
he so disliked to part with money, he should go to so needless an
expense, was so obscure that to accept Jack Storm's solution impugning
Harding's sanity was the easiest and consequently the most popular way
of solving the enigma.
The cottage was built notwithstanding, and it was soon the subject of
general remark that Harding was becoming more genial and "sociable" than
before. He astonished Judge Carboy and Jim Blair by asking them to drink
one night at the "Bella Union." He smiled affably and passed the time of
day with Jack Storm and his other companions when they met to begin work
on the claim for the day. He ordered champagne for the crowd on the
evening when a green tree was lashed to the rooftree of his cottage on
the knoll; and at last he raised wonder and surprise to their perihelion
by actually giving a housewarming.
"I know'd it all along," affirmed Judge Carboy that night to his
familiars. They were taking a cocktail at the "Bella Union" by way of
preface to "bucking" against Mr. Copperas's bank--"I know'd it all
along. He's got a wife out East, and she's a comin' out to jine him in
the new house."
"Is that the 'suthin' you talked of that he was ashamed of, Judge?"
laughed Jim Blair. "It looks like it, for sartin he never said nothin'
about her."
"A man may git married," retorted the Judge with judicial acumen, "and
yit do suthin' else to be ashamed of, mayn't he? There's been murderers
and horse thieves stretched afore now who had wives, hain't there? And
the last chap the boys hung to a flume up to Redwood, he had three
wives, didn't he? And they all come to the funeral." And with this
triumphant vindication of his position the Judge sternly deposited half
a paper of fine-cut in his mouth and started for the luxurious apartment
of Mr. Copperas.
Next morning Bullion Flat was in a flurry of excitement and pleasurable
anticipation. The "Grand Cosmopolitan Burlesque, Ballet, and Spectacle
Troupe" had arrived, and were to play in the theatre attached to the
"Bella Union." It was not, however, until the succeeding afternoon that
Chester Harding called upon Miss Tinsel at the same hotel.
It was a good sign that that young lady crimsoned at the first sight of
him; what she first said was another:
"You have not been in a hurry," she pouted, "to come and see me."
"I supposed you would be very busy," said he smiling, and devouring her
with his eyes. "Were you so anxious to have me come?"
"Anxious?" she repeated; and then added, illogically, "I supposed you
would please yourself."
He nodded. "And how do you like Bullion Flat?"
"I think it ever so pretty--only I don't like the earth all torn up, and
such ugly holes and scars."
"We have to get at the gold, you know," he explained, "even at such a
cost. But the hilltops, anyhow, are spared."
She looked through a window and pointed at the most picturesque eminence
in the neighborhood--the knoll. "That is your house?" she observed
shyly.
"Yes. Do you like it?"
"I think it lovely--situation and all."
"And how did you know it was mine?"
"Oh," she said, laughing, "we show-folks see a great many
people--besides being seen by them--and I've heard a lot about you."
Harding's face darkened a little. "Then you've heard that I'm not much
liked?"
"I've heard that some say so. But what of that? Miss De Montague says
she wouldn't give a fig for a man everybody speaks well of--and she
quoted something from a comedy--the 'School for Scandal.'"
"Will you tell me what people say?" he inquired curiously.
"Oh, that you are gloomy, reserved, and live all alone, and that you
are--are not extravagant, and that you haven't had a very happy life."
"That last at least, if true, is a misfortune rather than a fault."
"It's all misfortune, ain't it?" said the girl sagely. "People don't
make themselves. There's Mr. Bellario now. He thinks nature really meant
him for a great warrior--somebody like Napoleon, you know. And instead
of that he's--well, he calls himself a professional gentleman, but the
boys call him a tumbler. I suppose it would be much grander to kill
people than to jump through 'vampire traps'; but you see he didn't get
his choice--any more than I did."
"Then you didn't want to go on the stage?"
"No, indeed. It was just for bread. Aunty was a 'second old woman'--and
they got me in for 'utility,' as they call it. There was no one to care
for me, and I was glad to earn an honest living; but like it! Never!"
"You say there was no one to care for you?" said Harding gently. "Had
you no friends--no parents?"
Jane reddened painfully, and the sad look came quickly into her face.
"My mother is dead, you see," she replied, with hesitancy,
"and--and--I'd rather not speak of this any more, please."
"Surely," he exclaimed hastily, "I've no right to catechize you. Pray
forgive my asking at all. I ought to have been more careful. I know what
trouble is, and how to feel for those who suffer."
She looked at him earnestly. "You have suffered yourself, then--they
were right when they said yours had not been a happy life?"
"I have no right to whine--but happy--no, far from it."
Jane's lovely face took on its softest and tenderest expression.
"They said that lately you have been happier--gayer than ever
before--and that people liked you--oh, ever so much better than they
used to. Why is it that people like those the best who seem to need help
and sympathy the least?"
Jane leaned from the window as she spoke and toyed with some running
vine that clambered to the casement. The grace and beauty of her figure
were made conspicuous by the movement, and Harding paused a moment
before he replied:
"People like to be cheerful, I suppose, and people like others to be
like themselves, I know. It is true that I have been unhappy--that my
life has been morose and solitary. How much this has been my own fault
and how much that of others, need not be said. But it is also true that
of late I have been far happier. Shall I tell you why?"
His voice was deep and earnest, and something in his eyes made the girl
crimson again, and turn her own to the distant hills.
"If you please," she faltered, in her low, musical contralto.
"Shall I tell you too why I have built that cottage you are looking at?"
he went on with increasing earnestness. "It is because it has been my
hope, my prayer, that this sad, lonely life of mine was nearly over. It
is because I have believed that after much pain, and doubt, and
bitterness my trust in men might be brought back through my love for a
woman. The cottage--it is for you, Jane. I love you, Jane. Do you hear
me? From the moment I saw you, I loved you. I resolved to ask you to
marry me. Jane, will you do so?"
While he spoke the color had been fading steadily from her face, and
when he stopped the girl was ashy pale. He looked at her anxiously and
impatiently.
"I--I--am--so sorry," she muttered at last, as if each word were a
separate pain.
"Sorry? God! Why?" Then with swift suspicion, "Jane, do you care
for--are you engaged to some one?"
She shook her head mournfully.
"Do you see that sun going down over the hills?" She turned her
beautiful eyes full upon Harding as she spoke, with a look of ineffable
tenderness and sorrow. "Well, you must let what you have said go down
with that sun, and never think of it--never speak of it again."
It was Harding's turn to blanch now, and the blood retreated from his
swarthy cheeks until they looked almost ghastly.
"Why?" and his voice came involuntarily, almost in a whisper.
"Do not ask me--have pity--do not ask me."
"I must ask you," he cried impetuously, "but yet I need not perhaps. You
care for no one else? Then it must be that you do not, you cannot, care
for me. Is that it, Jane?"
"That is not it."
"Not it!" he cried joyfully. "Then you _do_ care for me a little--just a
little, Jane?--a little which is to grow into a great deal by and by!
Oh, child, child, think how wretched I have been all these years! Think
how I have waited and waited. I lived for twelve long months, Jane,
alone, without a soul, without even a dog, in a tent on that knoll; and
so hungry, Jane--so hungry for sympathy, for love. It comes to me at
last, dear Jane, what I have longed for and begged for so long. Don't,
don't--as you hope for mercy, don't take it away again!"
"You are good," she said softly, "whatever they may say. It is good and
noble of you. Why should I tell you lies? I do like you very much, for
all," looking down with a faint blush, "we have met and known each other
so little. But all the same, it cannot be."
"Cannot again," he cried impatiently. "Once more, I ask you, will you
tell me why not?"
She looked at him half frightened, for there was something of mastery in
his tone; then, standing erect, and with a positiveness as strong as his
own, she answered, "Because I should disgrace you."
"Because you are on the stage!" he exclaimed disdainfully. "Is that it?"
"That is something," returned Jane humbly, "but perhaps not much. I am
hardly important enough to be worth even that sort of reproach. And
besides the people of California are too liberal to apply it. I know I
am only a ballet dancer"--and the poor girl tried to smile here--"and a
pretty bad one at that. But I work hard for an honest living, and no one
can say I have ever disgraced myself."
"Then how can you disgrace me?"
"I have begged you not to ask me."
"I must!" cried Harding passionately; "and I have the right to do so.
Would you have me take your cool 'no' when you care for no one else and
do care for me, and to go my way satisfied? I can't--I won't!"
"You will be sorry," said Jane pitifully.
"Let me be. Anything rather than the doubt. Give me the truth."
"Well then." She turned her back now: and looked from the window with
her grave, sad face, and spoke in a dull, measured way, like the
swinging of a pendulum. "I am a convict's daughter. My father is in the
State prison of New York at Auburn."
"For what crime?"
"Murder. It was in the first degree. The Governor commuted it to
imprisonment for life. There were extenuating circumstances. I went down
on my knees and prayed that he might be saved from the gallows."
"And his victim?"
"Was his wife--my mother."
CHAPTER IV.
A MYSTERY AND A PARTING.
The troupe of which Miss De Montague and Mr. Bellario were prime spirits
made a profound impression at Bullion Flat; so profound, in truth, that
before their three nights were over a fresh engagement was made for
their return a fortnight later. It was agreed that at that time, and on
their return from other points, they should appear for an additional
three nights, and thus afford their admirers opportunities for which the
first essay had been insufficient. This arrangement was highly agreeable
to Miss De Montague and Mr. Bellario for reasons largely connected,
respectively, with the excellent cuisine and bar of the Bella Union.
"Why, my dear," observed the lady, "when I fust come up to do the
'legitimate,' fifteen months ago, love nor money could buy a morsel of
supper after the play. We had to do with a pot of ginger, and dig it out
with the Macbeth daggers, and wash it down with bad beer."
The arrangement was also satisfactory to Miss Tinsel. It seemed well to
her that she should be absent for a time; and yet she could not deny a
feeling of joy over the thought of returning. Her lover had been greatly
shocked by the dismal tale she had recited; but, to the credit of his
manliness, he had refused to accept the facts as conclusive arguments
against his suit. "Was it her fault," argued he, "that her father was a
scoundrel?" Why should stigma or disability of any sort attach to her
for that which she had no hand in, and had been powerless to prevent? On
the contrary, should not the world, or any part of it that might come in
contact with her, treat a helpless and innocent girl with even greater
tenderness and commiseration because of the undeserved and terrible
misfortune that had befallen her?
Jane had resolved that she ought not to be moved by such arguments, and
yet she could not help liking to hear them. It was in the end agreed
between them--by Harding's earnest entreaties--that she should think the
matter over, and that her final decision should be withheld until the
return of the troupe to perform its second engagement. Jane had talked
with Miss De Montague, who, in spite of some foibles, was a kind-hearted
and right-minded woman, and Miss De Montague had strongly urged that
Jane's sensitiveness was overstrained. If Mr. Harding had been told all
the truth without reserve and he still wished to make Jane his wife, and
Jane wished to marry him, that was enough. To stand about and moon over
it, and wonder or care what people would say, was all fiddle-faddle, and
all sensible people would call it so. Besides, California was different
from other places. It was the custom there to give everybody a chance,
and value them for what they did and what they were _now_--and not for
what other people, or even they themselves, had done before. It is right
to admit that the amiable lady's passion for Mr. Bellario--whose similar
feeling for Miss Tinsel was more than suspected--had something to do
with inspiring all these sage suggestions; but the suggestions were not
deprived of good sense by that.
During the fortnight that passed between Jane's departure and her return
the cottage that Harding designed for her future home fast approached
completion. Meanwhile its owner's claim was doing better, and his
coffers were consequently fuller than ever before. He resolved that,
come what might, Jane should become his wife; and it was in this frame
of mind that Harding walked out by the riverside on the night the troupe
returned. As before, he resolved not to hurry in his suit, and therefore
determined to omit calling until the following day.
The night was clear, the stars shining brightly, and the stream ran
gurgling forward with a pleasant sound. Suddenly, as Harding strolled
musing along the bank, some one touched him on the shoulder from behind;
and turning, he beheld the "Blood-Red Demon," Mr. Bellario. That
gentleman wore a long cloak, tossed across his breast and left shoulder,
and a slouched sombrero; and his white, pasty face wore a look of
inscrutable mystery.
"Hist!" he enjoined in a stage whisper; "all is discovered!" Then he
drew back, with finger on lip, as if to watch the effect of his
revelation.
"What's the matter?" said Harding. "What do you mean?"
"Mean! Ha! ha!" and the "Demon" laughed witheringly. "He asks me what I
mean! Mark me," proceeded he, with a sudden transition, "I know your
secret!"
"Oh, you do, do you? Which one do you mean?" questioned Harding
scornfully.
"I have neither time nor heart to trifle," said the "Demon," waving his
arm with an air of ineffable majesty. "I shall be brief and to the
point."
"You'll very much oblige me."
"Enough. What prompts me to this midnight deed, 'twere bootless now to
ask, and idle to reveal. Therefore to my tale. You are in love with
Aurora--with Miss Tinsel?"
"By what right----"
"Spare your reproaches. I am in love with her too!"
"You?"
"Is that so strange? Long ere you crossed our path I knew and loved
her. But this is neither here nor there."
"I should think not."
"Professionally," continued the "Demon," with great dignity, "she is, of
course, my inferior. Socially--well, you know, I think the damning
family secret----"
"Whatever that may be, it is no sin of hers. I think you may wisely
leave it a secret--so far, that is, as to omit crying it on the
housetops."
"Save to yourself and Miss De Montague, no hint of the tragedy has
passed my lips. But to the business between us----"
"My good sir," said Harding, with irritation, "I know of none, so far.
If you have anything to say to me, I'll listen. If not, I'll pass on."
"Ha! ha! ha!" laughed the "Demon" with bitter mockery. "I come to serve
ye, and ye would spurn me from yer path! Poor, poor humanity! Why, why
should I laugh when I should rather weep?"
"I don't know, I'm sure," answered Harding simply, "and I don't want to
be uncivil. But it certainly isn't asking too much to want to know what
you mean."
"No," responded the "Demon," with melodious sadness--"not too much.
Though every word be torture, yet I will e'en go through the ordeal.
Sir, what I have to say--and it cuts me to the heart to say it--is that
this lady--this young girl--this Aurora Tinsel--is worthy of neither of
us."
"What!"
"She is unworthy--lost--and capable of the worst deception!"
"That's false!"
"How, sir?"
"That's false. And you or any one else who says it is a liar!"
The "Demon" drew suddenly back, clapped his hand to an imaginary sword
hung at his left side--and then thought better of it.
"Pshaw!" he exclaimed lightly, but keeping at a wary distance from
Harding's reach. "Why should I yield to rage? My prowess is well
known--and, after all, this worthy gentleman speaks in ignorance. Sir,"
he added, changing his tone with elaborate and chivalrous grace, "I
speak of what I know, and speak only with the best of motives. But it is
due to you that I offer to make good my words. I can absolutely prove
that what I have said is true."
"Prove it, how?"
"By enabling you to witness for yourself that which justifies what I
say."
"And you can do this?"
"Almost to a certainty, and probably this very night."
Harding hesitated. To take the course proposed seemed like doubt, and
doubt was unworthy. To refuse to take that course might subject Jane to
calumny, which he might on the other hand nip in the bud. Presently he
spoke:
"What do you propose?"
"That you go with me at once, and judge for yourself. We may fail
tonight, but if so, our success to-morrow will be all but certainty."
The man's air of conviction was impressive, and Harding, fearful, yet
hoping that he might unearth some strange mistake or deception, agreed
to the plan proposed. It was settled that the two should meet an hour
later at the "Bella Union," and they parted now with that understanding.
Bellario, however, took occasion before leaving his companion to make
his insinuations so far specific as to tell him that Miss Tinsel had
made the acquaintance of a certain handsome, dark-eyed man, who had
followed the troupe ever since it had last been at Bullion Flat; that
this man evidently admired the girl very much, and that she had
encouraged his advances in the most unmistakable manner; that she had
gone so far as to receive her admirer at her room in the hotel, and that
at so late an hour as to excite the censure of the not over-prudish Miss
De Montague; and that, in fine, Miss Tinsel's hitherto spotless name had
been so tarnished by the events of the last fortnight as to make it
certain none would ever again think her the pure girl she had always
hitherto been held to be.
With the blood tingling through every vein, with nerves at extreme
tension, and a heart full of bitterness, Chester Harding passed away.
Something told him that the tale, black and dismal as it was, was
likewise true. When Jane told him the story of her father's crime and
its punishment, Harding felt as if there had fallen between him and his
prospect of happiness a veil that made it look doubtful and unreal. The
girl's firmness in telling him the truth, and the assertion of her
opinion as to the proper bearing and consequence of that truth on her
relations with Harding, had assuredly deeply impressed and comforted
him. It was something to face, after all, and even in California, this
wedding the child of a murderer and felon. Yet her own perfect goodness
was the justification and would be the reward of such an act. But when
Jane's goodness itself was in question it was no wonder that Harding's
heart sank within him. He was no coward, but his experience had taught
him distrust; and he waited for the stipulated hour to pass in an agony
of doubt and pain.
The "Bella Union" had two long wings, perhaps thirty feet apart, running
at right angles with its facade toward the rear. In the second story of
one wing there were sleeping rooms. Both stories of the opposite wing
were occupied by the theatre. The latter was quite dark, and hither
Bellario conducted Harding after they had met in the saloon below.
"Be silent," whispered the "Demon," when they met--"be silent and
follow."
Up two winding staircases, then through a long passage, and they stood
in a gallery over the stage and directly facing the other wing.
"Look!" said the "Demon"; "he's there now!" He still whispered, for the
night was hot and windows were everywhere open. Through one of these
directly opposite Harding distinctly saw Miss Tinsel. She was talking
earnestly with some one not in sight. Harding gazed breathlessly and
listened. Presently a second figure came between the window and the
light within. It was that of a tall, handsome man with dark eyes. He
replied to the girl with earnestness equal to her own, but in tones as
carefully suppressed. As the eyes of the observers got used to the
situation, they descried a bed on the further side of the room. On this
Miss Tinsel, after a time, sat down. The man followed and seated himself
by her side. A moment or two more, and he took both her hands and
clasped them in his own. They still talked, obviously with deep feeling,
and at last Miss Tinsel threw her arms around her companion's neck and
kissed him.
"Enough," hoarsely exclaimed Harding. "Enough--and more than enough!"
"You'll wait no longer?" asked the other.
"Not an instant. Can't you conceive, man--you who profess yourself to
have cared for her--what a hell this is?"
"I've been through it before," muttered the "Demon," "and the wound
isn't quite so fresh."
They descended in silence to the saloon, and there Harding spoke more
freely:
"See here--you've saved me from a great peril--and although I think I
had rather you had shot me outright, you deserve no less gratitude. If
you want help--money--for instance----"
The "Demon" waved his hand in lofty refusal.
"As Claude Melnotte says, sir, I gave you revenge--I did not sell it.
There are better men than I in the world, and lots of them. But I try to
do as I would be done by--at least in a scrape like this. I wish you
good night, and I hope you'll take comfort. After a little it'll seem
easier to you. Certainly the ill news should come easier even now than
it would afterward. As Othello says, ''Tis better as it is.'"
He bowed and passed away. Ascending to the apartment of Miss De
Montague, he made himself so agreeable as to be able to borrow from that
lady a dozen shining eagles; and, thus provided, descended promptly to
Mr. Copperas's bank, where he whiled away the night--assisted by copious
drinks and unlimited cigars--at the enlivening game of faro.
As for Harding, he went to the bar of the saloon and took what was for
him a stiff glass of brandy. Then he turned abruptly on his heel, and
without sending his name before him, marched straight up to Miss
Tinsel's room.
She met him at the door with a glad cry--and then shrank back abashed.
"I see," she murmured, in her low, sweet voice, "you don't care to have
me repulse you again. You have thought it over--and you agree that it is
better not."
He came just inside the door, but did not sit, although she motioned him
to a chair.
"I agree," he repeated mechanically--"I agree--with you that it is
better not." Then he looked suspiciously around the room. There was no
one there--but a door opened into another room beyond. Jane followed his
eyes. "That is Miss De Montague's room," she said; "we are always next
to each other."
"And she is there now?"
"Yes--with Mr. Bellario--he is calling on her."
Harding paused a minute, and then went on in a hard, constrained voice,
like one who repeats a disagreeable lesson.
"I have thought it right to see you--now, for the last time--and say I
think it best--and right--that we should part."
Jane turned very pale, and the old grave look of hopeless pain came over
her face. But she answered with infinite softness and humility:
"It is right--you know I thought so from the first. You should not marry
a--a convict's daughter."
"It is not because you are a convict's daughter."
"The reason is sufficient."
"I repel it," he cried vehemently--"I will have none of it--I told you
so before--I repeat it now. Listen," and he crossed the room swiftly and
closed both doors.
"I loved you for yourself--dearly--dearly. What did it matter to
me--what fault was it of yours--what other people did, or what or where
they were? In this grand, new country, men--some men, at least--have
grown high enough and strong enough to shake off such paltry prejudices
as those. To me they are as nothing."
"You led me to think so," Jane said gently.
"Why should I care for your being a ballet-dancer--or for the other
thing, when you had never disgraced yourself? But now it is different."
"Now it is different!" she echoed in amazement.
"Different in this," pursued he with growing excitement, "that before
you were a pure girl--pure as snow--everybody said that--and now you
are--are--compromised."
The blood rushed in a torrent up to her hair.
"Who says it?" she demanded, now first showing warmth--"who dares say
it?"
"Alas, Jane," he replied, "don't make things worse by deception at
parting. Let us be at least as we have always been, honest and
unreserved to each other."
"What you have said just now," said the girl' proudly, "is an insult.
The time has been when you would not have heard another say such
words--either to me or of me; and yet they are as little deserved now as
they have ever been."
"They are, are they?" he retorted. "Then pray tell me who was that man
you have had here within an hour?"
She turned deadly white, and opened her lips thrice to speak before the
words would shape themselves.
"That--man?"
"Do you deny having a man with you?"
She shook her head piteously. "No--there was a man here--and with me."
"Ah, you confess it then," cried he, as if her admission made what he
knew more heinous. "Who was this man? Confess all!"
"He--he--wanted help--asked for money. He saw me in the play at Boone's
Bar--and thinking me richer than I am, asked me for money."
Harding laughed scornfully. "And do you expect me to believe this?"
"It is true," she hurried on nervously. "He said he was desperate and
must have money to get away."
"Had he any claim upon you?" he asked, scanning her with cold, searching
eyes.
She hesitated and made answer, "No--none."
"Yet he pushed his demand with eloquence?"
"He did."
"And with success?"
"I gave him all I had."
"Even although he had no claim on you?"
"Yes."
"Oh, Jane--Jane!" he cried with a burst of bitter sorrow; "why couldn't
you have been truthful to the end? Why--why must you make me look
back--always and only to despise you!"
She looked at him stonily, but made no reply.
"Jane, it cuts me to the heart to say it--but I saw you--do you
hear?--saw you. He took both your hands in his--you threw your arms
about his neck and kissed him. Do you deny this?"
She still looked him straight in the face, but two tears brimmed into
her eyes and rolled slowly down her cheeks. "No, it is true," she then
answered.
"You own this too," he cried furiously. "Jane, who is this man?"
She remained silent.
"I ask you again, Jane--and for the last time--who is this man?"
"I cannot tell you."
"You refuse?"
"I must."
"Then farewell. We can meet no more." He turned, and stood with his hand
on the door, and with the action the girl's overstrained nerves gave
way.
"Oh, no, no, no! Oh, Chester, I have loved you so! Don't--for mercy's
sake--don't leave me in anger--when I so need comfort--help--and--p--pity!"
She fell on her knees by the bed, and with her face in her hands, sobbed
aloud.
As she did so, a burst of strange, mocking laughter resounded from the
adjoining room, and Harding started as if he had been stung.
"It must be!" he hissed, all that was hardest and worst in his nature
suddenly possessing him. "After this it would only be torture--to both!"
He bent suddenly and kissed--not her lips, no longer pure--but her
forehead, once, twice, thrice, passionately, and then fled away into the
darkness.
CHAPTER V.
GOOD OUT OF EVIL.
Harding went up to his lonely tent. Like a wounded animal, he sought his
lair, and the memory of the many solitary hours he had passed there,
even at this sad moment, refreshed his spirit. There he could be
alone--away from men's eyes--free from their curiosity, from their
comments, or, what would be worse, from their pity.
He had made himself comparatively rich; he had built up a home, as it
were, in the wilderness; he had even tried, and with some success, to
gain men's esteem--and what were all these worth to him now?
Such bitter thoughts as these filled Harding's mind as he arranged his
coarse pallet, and then, throwing himself upon it, sought to forget his
grief during the short space that remained before daylight. He was
awakened, almost instantly, it seemed to him--although, in fact, three
hours had passed--by the sharp crack of a rifle. Harding leaped up and
ran to his door.
It was a dull, gray dawn--the sky overcast, but the air free from wind
or rain. A little below Harding's tent there spread a plain about a mile
wide. This extended along the bank of the river, and terminated in a
clump of redwoods which grew far up the mountain beyond. Here and there
on the plain were scattered a few small trees and copses of manzanita;
but for the most part it was clear from the outskirts of the village up
to the redwoods.
On this plain Harding now saw a remarkable sight. A man was running from
tree to tree, striving always to get nearer the mountain. Perhaps three
hundred yards behind him were five or six armed pursuers trying to close
in on the fugitive, and occasionally firing at him. As Harding gazed,
three shots were discharged in rapid succession. Yet the man still held
on his way, apparently unhurt, and it looked as if he would quickly gain
the cover of the forest. But there was one behind him far swifter than
the rest, who ran like an Indian on the river or further side from
Harding, and who threatened in a few moments to get dangerously near. It
was because this man was so distant from himself that Harding did not at
first recognize his own partner, Jack Storm, although he was in his
usual well known Mexican dress. Now, Storm was the best rifle shot on
Bullion Flat.
It appeared that the fugitive knew this. At all events, as if suddenly
realizing his peril, he turned and ran straight toward Storm, resolved
to draw his fire, apparently, and by confusing his aim to have a better
chance of escape. Storm's ready rifle flew up to his shoulder instantly,
and Harding saw the pale blue ring of smoke and heard the quick report.
Still the fugitive sped on. He was plainly unscathed, or in any case not
disabled; and in his hand there now flashed a bright something which
Harding knew was a bowie-knife. With that, although the combatants were
a mile away, Harding seized a revolver, and dashed at his highest speed
down the hill. Almost at the same moment, there also started in company
from Bullion Flat three figures on horseback. These were Miss Tinsel,
the "Demon," Mr. Bellario, and Judge Carboy. All who were now making for
the scene of the combat heard in sharp repetition five or six shots from
revolvers; but after the last of these, all was still. When they got to
the spot they found Jack Storm fainting from loss of blood, but hurt
only with flesh wounds; and they were told that the other man, his
opponent, was mortally wounded, and had been taken, by his own request,
up on the mountain side, among the redwoods, to die.
With a choking cry, Miss Tinsel galloped on, and in a few moments
Chester Harding and she were again face to face over the dying man's
body. Ghastly white as he was, all dabbled with blood, and the foam
oozing from his lips, her lover at once knew Jane's visitor of the night
before. What had happened had been hurriedly revealed to Harding--in
broken whispers by the bystanders--before Jane came up.
The man had robbed several rooms at the "Bella Union" during the night,
and had succeeded in gathering a large sum. Among the treasures stolen
were all the loose funds belonging to the "Combination Troupe," the
night's winnings of Mr. Copperas's faro bank, and Miss De Montague's
diamonds. But just as the robber, toward daylight, was on the point of
making off in safety, he met a lion in the path in Jack Storm. It
happened that Jack wanted to have a talk with his partner, Harding, and,
as they were then very busy on the claim, made up his mind to compass
this purpose bright and early, before getting to work. Stumbling on the
marauder, the latter was secured after a struggle, and "the boys"
speedily determined to make an example of him. The man begged for a
chance of life, and after some debate, had been given the option of the
halter or running the gauntlet, with three hundred yards' start, in the
way we have described. In the subsequent struggle he had been shot
through the lungs, and terribly cut with his own bowie-knife--wrested
from him by Jack Storm--and his life was now fast ebbing away.
As she came up Jane sprang from her horse, and threw herself on the
ground beside the dying man. They had propped his head on a hillock of
turf, and some charitable soul had brought water from the river. Judge
Carboy quickly put a flask of brandy to the sufferer's lips, and he
opened his eyes:
"Ja--Jane," he gasped, "my pretty Jane--this is the end--the end of
it--a dog's death--and deserved, too-but--I--I--always loved you!"
She burst into tears and began sobbing over him and fondling his head.
"Don't, darling--don't, little Jenny--it won't be long--I am better
away--better for you--there--there! I'm sliding away somewhere--and----"
His voice failed, and his dark face began to grow blue. The doctor, who
had ridden hastily up, forced between the man's teeth some strong
restorative.
"I want you to remember--always--that I was drunk when I did it--drunk
and crazy. I was bad--vile--but not so bad as that. Don't tell who--who
I am. It will only disgrace you--only disgrace you--I'm going, little
Jenny----"
"Oh, _father_! _father!_" and the poor child bowed down her pretty head
on the breast of the wretched thief and murderer, and wept as if her
heart would break.
"No--no," he muttered; "no, little Jenny, I'm not worth it. Only--don't
think worse--worse of me than I deserve. Perhaps mother--in heaven--has
forgiven me! She knows--knows--I was mad when I did it."
"Yes--yes--I shall remember," whispered she, "always. Now don't talk
more--not now."
"No--I shan't talk--much more"--a strange wan smile came over his
face--"not much more, little Jenny." He put up his hand and stroked her
sunny hair.
"Tell them about this last--that I was desperate--I had broke jail--knew
the officers were on my track--and was penniless. Give me--more--brandy.
So. Why, I can't see you any more, little Jenny--and yet it is morning,
isn't it, not night!" He gasped for breath and clutched feebly at the
air. "Kiss me--little Jenny--mer--mercy--_Lord Jesus_--better--better
times--hereafter!"
A shudder, and the man was dead, and Jane was left all alone in the
world. Poor, besotted, frantic Michael Green, all sin-scorched as he
was, had passed from the judgment of men to the more merciful judgment
beyond. Yet the orphan, if alone, lacked neither sympathy nor
protection. Nor did she ever lack from that moment the respect and
confidence of the man of whose heart she had from the first been
mistress. So that the true happiness came in time which is so often the
sweeter for being deferred.
HENRY SEDLEY.
DEFEATED.
Give me your hand--nay, both, as I confront you.
Let me look in your eyes, as once before.
I gaze, and gaze. Oh, how they change and soften!
I stand within the portal: lo! a door--
A door close shut and barred. I knock and listen.
No sound, no answer. Doubtingly I wait.
Oh! for one glance beyond that guarded entrance,
The power that mystic realm to penetrate.
I touch the barrier with hands entreating,
If it would yield to me, and none beside.
What bitter pain, what sense of loss and failure,
To come so near, and come to be denied!
Softly I call, but only silence answers--
Silence, and the quick throbbing of my heart.
Immovable, the frowning bar abideth:
Kneeling, I kiss the threshold and depart.
MARY L. RITTER.
SHALL PUNISHMENT PUNISH?
It is published that in England a man has been undergoing an aggregate
imprisonment of ten years for breaking a shop window, at different
times, and that when recently pardoned he immediately broke the same
window again for the purpose of being again arrested. One who knows
nothing more than this of the facts cannot presume to determine what
punishment should in justice be given to this particular offender; but
the case is interesting as an extreme example of what frequently occurs
in a less striking degree in this country. Police courts become
acquainted with a class of criminals who would rather go to jail for
their dinner, especially in winter, than earn a dinner by hard work.
They are the confirmed vagabonds from whom the army of summer tramps is
chiefly recruited. They never feel truly virtuous and happy in cold
weather except when they have committed a petty offence and are on the
way to "punishment," which consists in accepting from a thoughtful
public a warm shelter and all the food they want. It is their business
to live, at times if not constantly, in this way. Sending them to jail
for their offences is known by the courts that send them to be nothing
but a sorry farce.
There is another equally incorrigible class, who commit greater crimes,
but not chiefly for the sake of "punishment." Detectives keep themselves
advised of the sentences of these offenders, and prepare to shadow them
anew whenever they are released from confinement. It is not expected
that incarceration will have any reformatory effect. The question of
reforming them, as of reforming those who offend to get rid of the
trouble of taking care of themselves, comes to be left out of
consideration, after a little experience, by the officers whose duty it
is to deal with them. Only intimidation remains for a considerable
number. With these, rather than with the English window-breaker, should
probably be classed the subject of this item from a late newspaper:
"Charles Dickens is dead, and died of honest work; but the German
prisoner, Charles Langheimer, whom he saw in the penitentiary at
Philadelphia thirty-three years ago, and over whose punishment by
solitary confinement he lamented in 'American Notes,' describing him as
'a picture of forlorn affliction and distress of mind,' still lives at
the age of seventy-five, and has just been sent back to his old quarters
the sixth time, for his chronic offence of petty theft, which has kept
him in jail full half his long life."
That punishment for crime is necessary, and therefore a public duty, is
admitted, and every community professes to impose it. But what of the
criminals whom punishment as now administered does not punish--who
actually commit crimes for the purpose of receiving it? It would seem
that society has not the power or has not the wisdom to protect itself.
It has the right, of course. It has the power also.
The law does not succeed in what it attempts and professes to do. At
present when we find a criminal who has sufficient good in him to feel
our methods, we punish him in proportion to his--goodness. When we find
one so vile that our methods are like water on a duck's back, we do not
punish him--except as water punishes a duck. He goes unpunished because
he is so bad, while a better man is punished because he is better. What
is this but rewarding insensibility? It is very creditable to the hearts
of the lawmakers--perhaps--but it is fraud on the community. It is
legalized wickedness. It permits incarnate nuisances to wax fat, and
prey upon honest industry, and increase and multiply, until they become
the only prosperous and protected class.
It has been suggested that a criminal on his second conviction be deemed
a professional, and incarcerated for life. It would no doubt be cheaper
for the public to shut him up thus and support him permanently. But
there is the objection that the punishment would generally be out of
proportion to the crime, if it were a punishment at all; and if it were
not a punishment, we would be offering a greater premium on vice than we
now are. To punish petty larceny as if it were as great a crime as
manslaughter or murder would be too unjust to be long possible. The case
seems to demand a new medicine rather than a greater dose of one which
has failed when tried in any practicable quantities.
There is one remedy, so far as the infliction of real punishment is a
remedy, although those who administer justice as above described will
hold up their hands in horror at the mention of it. If it be a fact that
the punishment of criminals is necessary, and if it be a fact that a
class of them is impervious to any punishment except physical pain, then
we are bound to either inflict this pain or else abandon the principle
of punishment. There is no third course if the two facts are
admitted--and to those who will not admit them an unprejudiced reading
of the criminal news of the past three hundred and sixty-five days is
commended. If one man's heart is callous to what will break another's,
all men's backs are of nearly equal tenderness. It is doubtful whether
the whipping-post ever had a fair trial without proving that it might be
made a good thing under such circumstances as we must very soon, if we
do not now, confront.
The fact that it was once used and then abandoned does not settle the
case. It was erected for those who could have been otherwise dealt with,
and for those who deserved no punishment at all. It was not reserved for
only those deserving punishment, on whom our more refined penalties had
been tried and had failed. It is not a fair trial of it to put it into
the hands of a drunken or passionate ship's captain; or the hands of a
religious bigot; or the hands of a slave-driver; or the hands of a
tyrant or autocrat of any kind; or the hands of an incompetent judge; or
the hands of any judge in a ruder age than this. If an ignorant or
brutal use of it in the past condemns an enlightened use of it now, we
should abandon life-taking and imprisonment, for these have been even
more abused. We have no fear that the death penalty will be misused
hereafter because men have been hung for petty larceny heretofore. When
the lash is wielded by a barbarous hand, as it generally has been, of
course we abhor it. But how about it when the hand of Christ wields it
in the temple? Although the incarnation of charity made him a scourge
for those who needed it, yet we cannot follow His example because
Torquemadas have made scourges for those who did not need them. Such is
the logic of those who would cite the past in this matter. The truth is,
the lash was abandoned in the humane belief that criminals could be
punished without it; and the truth also is, some criminals are now
proving that they cannot be punished without it.
Go over the subject as we may, we come back to the question, Is the lash
or something equally unrefined necessary to accomplish all the law now
attempts? It must be looked at in the cold light of certain very sad
facts, as well as in the warm blaze of "chromo" civilization. If we are
not yet compelled to answer it in the affirmative, there is so much
evidence pointing toward such an answer, that it is well to consider
very respectfully indeed whatever can be said on the unpopular side. It
need not frighten those who accept the idea so tersely presented by the
Hare Brothers--of which one is strongly reminded by Mr. Greg in the
"Enigmas of Life," although perhaps he does not expressly state it--that
the tendency of civilization is to barbarism.
Of course flogging is not a panacea; but it is for those who profit by
nothing gentler; and the more enlightened society becomes the more
certainly can these be identified. The generous feeling that has
discontinued it would not cease to be a guarantee against its abuse. Our
courts cannot depart far from public sentiment. We can trust judges and
juries to determine who deserves castigation just as safely as to
determine who deserves imprisonment or death. Most of the censure they
now receive in their treatment of the hopelessly depraved is for their
lenity and not their rigor. There is no offender would not dread and
wish to avoid whipping. Certainly no one would offend for the purpose of
receiving it; and it would probably discourage a man in less than ten
years from breaking the same window. It would be inexpensive, and would
have the merit of being short and sharp, if not decisive. Punishment,
intimidation, is what is here considered, and the point is whether it
shall be administered to all who deserve it, or whether the law society
finds necessary for its protection shall be a falsehood, at war with
itself--a sham. The law cannot shrink from anything that is necessary to
its purpose without impeaching its purpose.
And is it more inhuman to hurt the back of one who cannot be made to
feel anything else than it is to pain the heart and hurt the soul of one
who can? How can Christians so exalt the flesh above the spirit? They
did not do it in the primitive days of the faith. Is it more barbarous
to scourge the body than to gall it with irons, or poison and debilitate
it by confinement, or wear it out by inches at hard labor? We have not
abolished corporeal punishment--only rejected a form of it which is
frequently more merciful, if more dreaded, than some that are retained.
All wrongs right themselves by "inhumanity," if permitted to go far
enough. You are told by good authority, and you know without telling,
that if you find a burglar in your house at night, you perform a public
duty by shooting him dead rather than see him escape. From the
humanitarian point of view, this is certainly more dreadful than it
would have been to stop, by flogging, any minor offences that led him
into your house. Indeed, if the penalty for the burglary itself were a
"barbarous" laceration of his back, it would doubtless have more effect
in keeping him from the burglary and from a bloody death, than does the
risk of imprisonment. We must not whip him in obedience to the law, but
we may safely shoot him dead without regard to it. It is our tenderness
that becomes "inhuman" if it be not wisely bestowed. Would it be quite
in keeping with the pretensions of "advanced" civilization to see the
matrons and maids of the rural neighborhoods going about their dairies
and summer kitchens with revolvers in their belts, and bowie-knives in
their bosoms? That is the spectacle the "tramp" nuisance promises to
produce. Would the whipping-post, set up in the slums of the great
cities, where the miscreants among the tramps breed and form their
characters, look any more like barbarism? The voluntary tramp has but
shown the countryman during the summer what the city suffers during the
winter. He is simply trying to distribute and equalize himself, and
while enjoying his country air, collects the same taxes he collects all
the rest of the year in town. Let the city continue to rear him
tenderly, and not hurt his precious carcass, and feed and warm him, and
punish only his sensitive spirit, until the country people get down
their shot-guns and make a barbarous end of him. And this is being true
to the cause of humanity.
It is noble for the law to withhold its hand when one who has taken a
wrong step can be won back to a good life by other means; and if the
wretches hopelessly saturated with vice can be intimidated by anything
milder than flogging, by all means be mild; but when we find one who
cannot, why not acknowledge the fact and act on it?
The reason why we do not so act is only a sentimental one. A sentimental
reason, however, may be a very good one. Society feels that it is better
to suffer, and to see its laws become a mockery to this degree, than to
shock its own best instincts. This sentiment that obstructs absolute
vindication of the law is respectable so long as it can be respected
with tolerable safety and public satisfaction. But it interferes with
justice by courtesy, and not by right. It is all very well so long as
society does not complain. But if its mouthpieces are to be believed,
society does complain. The public is not satisfied with the present
punishment of certain offenders--indicated with sufficient accuracy by
the tough old Langheimer and the English window-breaker--and is restive
under the pecuniary burden they impose.
Although the history of the whipping-post is nearly worthless to one
seeking to know what its value might be under all the favorable
conditions with which it could be surrounded now and here, yet it is
possible to point readily to one trial that should have been, and
probably was, a fair one. A very few years ago--perhaps four or
five--garroting became a terror to the London pedestrian. For assault
and robbery, without intent to kill, the death penalty was too terrible,
and the other penalties failed to intimidate, as they generally do when
the crime is lucrative, easily accomplished, and not immediately
dangerous. It could not be trifled with, and something had to be done. A
"barbarous" whipping of the bare back was resorted to, and garroting
subsided. The result was what the public wanted. Sentimental eyes may
show their whites, horrified hands may go up, floods of twaddle may come
forth in sympathy with the discouraged garroter, but men of common
sense, especially if they have been garroted themselves, will say the
end was worth what it cost, and believe in the inhumanity that achieved
it.
Nothing has been said of Delaware. No valuable lesson could be drawn
from her without considerable investigation, and perhaps not then. She
may do too much flogging, or she may not do enough. Her ministers of
justice may be models of enlightenment, or they may be models of
debasement. The lash there may be still a class instrument, or it may
not. She has no great city--an exceedingly important consideration--and
two portions of her people are jostling each other as nominal equals in
the race of life, who but the other day held the relation of master and
slave. She is probably not indifferent to a good name, and her retention
of the whip under all the sneers she receives is some evidence that she
at least regards it as still having a defensible use.
CHAUNCEY HICKOX.
RENUNCIATION.
Could I recall thee from that silent shore
Whence never word may reach our longing ears,
To gaze upon thee thro' my happy tears,
And call thee back to life and joy once more,
Could I refrain? If at my touch Death's door
Would open for thee, and thy glad eyes shine
With swift surprise of life, straight into mine,
And we might dwell with love for evermore,
Could I forbear? God knows, who still denies.
Yet being dead, thou art all mine again:
No fear of change can break that perfect rest,
Nor can I be where thou art not; thine eyes
Smile at me out of heaven, and still my pain,
And the whole pitying earth is at thy breast.
KATE HILLARD.
THE EASTERN QUESTION.
"The last word in the Eastern Question," said Lord Derby, "is
Constantinople." If for Constantinople we read not merely the city
itself, but that half of Turkey in Europe bordering upon the Black Sea
and the Sea of Marmora, and understand the real point to be, Shall or
shall not Russia have it? we have the whole Eastern Question in a
nutshell. Russia is bound by every consideration of policy and interest
to get it if she can. Great Britain is bound by every consideration of
interest, and even of self-preservation, to prevent it if she can.
Germany, Austria, and France are bound to prevent it, if possible,
unless they can at the same time gain equivalent advantages which shall
leave them relatively to each other, and especially to Russia, not less
powerful than they now are. The other nations of Europe may be left out
of view in considering the question; for their interest in it is less
vital, and they could do little toward the result, except as allies to
one side or the other, in case of a general European war in which the
great Powers should be quite evenly balanced, when their comparatively
small weight might turn the scale.
A glance at the map will show the paramount importance to Russia of the
acquisition of this territory. Comprising more than half of all Europe,
she is practically cut off from the navigable seas. She has, indeed, a
long coast-line upon the Arctic ocean, but she has there only the
inconsiderable port of Archangel, and this can be reached only by
rounding the North Cape and sailing far within the Arctic Circle, while
the port itself is blocked up by ice seven months of the year. She also
borders for seven hundred miles upon the Baltic and the Gulf of Bothnia;
but here, in the northwestern corner of her territory, she has only two
tolerable ports, Cronstadt and Riga, and these are frozen up for nearly
half the year; but from these ports is carried on three-fourths of her
foreign commerce. She next touches salt water in the Black Sea, almost
1,500 miles from St. Petersburg, on the extreme south of her territory.
This sea, half of whose shores belongs to Russia, is 720 miles long, and
380 miles wide at its broadest point, covering an area, including the
connected Sea of Azof, of nearly 200,000 square miles--more than twice
that of all the great lakes of North America. Russia wishes to be a
great maritime power. The Black Sea has good harbors and abundant
facilities for building ships and exercising fleets. Into it fall all
the great rivers of the southern half of Russia, except the Volga, whose
mouth is in the Caspian; and the Volga may properly be considered a
Black Sea river, for a railway, or perhaps even a canal of a few
leagues, would connect it with the Don and the other rivers of the Black
Sea system. The Black Sea is emphatically a Russian sea; but Russia
enjoys the valuable use of it only by the sufferance of whomsoever holds
Constantinople. By the treaty of Paris, concluded in 1856, after the
reverses of the Crimean war, Russia agreed not to maintain a fleet
there; and it was not till 1870 that taking advantage of the critical
position of the other great Powers, she declared that this article of
the treaty was abrogated. She has now a strong fleet of iron-clads and
other steamers in the sea, but the actual strength of this fleet is
unknown except to herself. It was certainly powerful three years ago,
and is doubtless much more powerful now. A vessel and crew which has
navigated the "Bad Black Sea." as the Turks call it, has nothing to fear
from the broadest ocean. But this sea is liable at any moment to be a
closed one to Russia. No Russian man-of-war has, we believe, ever sailed
into or out of it; no merchantman can enter or leave it except by the
Bosporus and the Dardanelles, which are its gates, and of these gates
Turkey holds the keys.
The Black Sea is joined to the deep, narrow Sea of Marmora by the
straits of the Bosporus, twenty miles long and from three-quarters of a
mile to two and a half miles wide. Just where the straits open out into
the Sea of Marmora stands Constantinople, a spot marked out by nature as
the one on the whole globe best fitted for the site of a great
metropolis. At its western extremity the Sea of Marmora--about one
hundred miles long, with a maximum breadth of forty-three
miles--contracts into the straits usually called the Dardanelles, which
is properly the name of four castles, which, two on each side, command
the passage, here less than a mile wide. Both straits could easily be so
fortified as to be impassable by the combined navies of the world; and
even now we suppose that only the best armored iron-clads could safely
undertake to force the passage, in or out, of the Dardanelles.
Let us now consider the fearful preponderance which Russia would gain by
the possession of these straits, including of course that half of
European Turkey bordering upon them. We have seen that the shores of the
Black Sea furnish every facility for the construction of a navy of any
required strength, and its waters afford ample space for its training.
With these approaches in her grasp, Russia might in ten years construct
and discipline her fleet there, perfectly safe from molestation by the
navies of Europe. Fleets built and equipped at Sebastopol, Kherson, and
Nicolaief, could sweep through the Dardanelles, closed to all except
themselves, enter the Archipelago and the Mediterranean, and dominate
over their shores and over the commerce of every nation which has to use
these waters as a highway. In case of its happening at any time to find
itself overmatched, the Russian fleet could repass the gates of the
Dardanelles, and be as safe from pursuit as an army would be if
sheltered behind the rocks of Gibraltar.
Great Britain would be first and most immediately menaced by this; for a
strong military and naval power established on the Bosporus would hold
in command the shortest way of communication with her possessions in
India. The Czar would hold in control the route by way of the Suez
canal: or at best Great Britain could keep it open only by maintaining a
vastly superior fleet in the Mediterranean; and it would be difficult
for her to maintain there a fleet which would not be practically
overmatched by one which Russia could easily keep up in the Black Sea
and the Sea of Marmora. The days are past when a Hood or a Nelson might
safely risk a battle if the odds against him were much less than two to
one. A British admiral must henceforth make his count upon meeting skill
and seamanship equal to his own, and whatever advantage he gains must be
gained by sheer preponderance of force.
If Great Britain is to retain her Indian empire, a collision there
between her and Russia is a foregone conclusion. An empire which, under
a succession of sovereigns of very different character, has steadily
pressed its march of conquest through the deserts of Turkistan, will not
be likely to look without longing eyes upon the fertile valley of the
Indus; and here Russia would have a fearful advantage in position. The
Suez route practically closed, as it would be in the event of a war,
Britain could only reach India by the long voyage around the Cape of
Good Hope, while Russia would have broad highways for the march of her
troops to the banks of the Indus, whence she could menace the whole
peninsula of Hindostan.
We indeed do not think that the possession of her Indian empire adds
anything to the power of Great Britain. She has never derived any direct
revenue from it. The Indian expenditures to-day exceed, and are likely
in the future to exceed, the revenues. All the vast amounts of plunder
and "loot" which individuals, the East India Company, or the Crown have
gained, have cost to get them more than they were worth. Unlike
Australia and the Dominion of Canada, India offers no field for
colonization for men of British blood, where they or their children may
build up a new Britain under strange stars. It has come to be an
accepted fact that Englishmen cannot long retain health and vigor in
India, and that their offspring, born there, rarely survive childhood
unless sent "home" at an early age. Britain holds India purely and
absolutely as a conquered and subjugated territory. Whether British rule
in India is, upon the whole, a blessing or a curse to the natives, is a
matter of grave doubt; that it is most unwillingly borne, is beyond all
question. It is a despotism pure and unmixed, and a despotism of the
most galling kind--a despotism exercised by a horde alien in race and
religion, alien in habits and modes of thought, in life and manners, in
customs and ideas. Macaulay, when in power in India, forty years ago,
said of it the best that can be said: "India cannot have a free
government; but she may have the next best thing--a firm and impartial
despotism." To maintain this despotism, even against the feeble natives
alone, imposes a heavy strain upon the British government. The British
empire in India is only a thin crust overlying a bottomless quagmire,
into which it is in peril of sinking at any moment by a force from above
or an upheaval from below. How nearly this came to pass during the
accidental Sepoy mutiny of twenty years ago, is known to all men. Had
that mutiny chanced to have broken out three years before, during the
Crimean war, it is safe to say that the course of the world's history
would have taken a different turn. Since then Great Britain has
apparently somewhat consolidated this crust, but it is yet thin, and the
weight of Russia thrown upon it could scarcely fail to break it through.
The commercial value of India to Great Britain is, we think, vastly
exaggerated. India, in proportion to her population, has always been,
and is likely long to be, a very poor country. The trade of Great
Britain with India--exports and imports--is not much greater than that
with France, considerably less than that with Germany, and far less than
that with the United States; and we see no reason to suppose that it is
perceptibly increased by the subjugation of India to the British crown.
India sells to Great Britain what she can, and buys from her what she
wants and can pay for, and would continue to do so in any case. Still,
we do not imagine that the British government or people will ever be
brought to take our view of the value of India to them. It will be held
to the last extremity of the national power, and will only be abandoned
under stress of the direst necessity. And for her secure possession of
India it is absolutely essential, for reasons which have been stated,
that whoever else may have Constantinople in the future, Russia shall
not have it. England's interest in the question is a purely selfish one.
She is content to have the Turks there because for the time being they
keep the Russians out. Whatever worth may formerly have been in the
sentimental averment that it is the duty of the European family of
nations to see to it that no weak member of it is gravely wronged by a
stronger one is past and gone. It is from no love for the Turks that
Great Britain desires that the Sultan should continue to hold at least
nominal sovereignty over Turkey in Europe, and the actual custody of the
keys of the Black Sea. An able English writer says:[H]
The position of the Turk at Constantinople is no choice of
ours, nor any creation of our policy. We do not maintain him
for any love of himself, nor because we rely on his strength
to guard the post--though that is absurdly underrated. His
corruption and weakness are at least as great an
embarrassment to us as an injury to the nations of his
empire. But the whole Eastern question hangs upon the fact
that he is there, and has been there with a long
prescriptive right which he is not likely to yield, or to
have wrested from his grasp till after a frantic struggle of
despair. Nor is any practical mode apparent by which he will
be soon displaced, save that, after a convulsion which would
involve all Europe, the Czar should be enthroned upon the
Bosporus. To prevent that catastrophe, and to avert the
horrors that must precede it, is our real Eastern policy.
[Footnote H: "Quarterly Review;" October, 1876.]
Still more emphatic is the declaration of Lord Derby, the British
Premier, when defending the action of the Government in sending the
Mediterranean fleet, last May, to Besika Bay, at the mouth of the
Dardanelles: "We have in that part of the world great interests which we
must protect.... It is said that we sent the fleet to the Dardanelles to
maintain the Turkish empire. I entirely deny it. _We sent the fleet to
maintain the interests of the British empire._"
Let us now glance rapidly at Turkey in Europe, the coveted prize in this
case. Nominally, and upon the maps, it comprises all except the southern
apex of the great triangular peninsula bounded on the east by the Black
Sea, the Sea of Marmora, and the Archipelago; on the west by the
Adriatic; on the north, the broad base of the peninsula, it is bounded
by Austria; on the south, the narrow apex, by Greece. Russia touches it
only on the northeast corner. Its area is in round numbers 200,000
square miles, not differing materially from that of France or Germany,
or about five-sixths of that of Austria. No other part of Europe, of
anything like equal extent, combines so many natural advantages of
geographical position, soil, and climate. The population is variously
estimated at from 13,000,000 upward; we think that 17,000,000 is a
tolerably close approximation. Of these, in round numbers, only about
2,000,000 are Turks, or, as they style themselves, Osmanlis; 11,500,000
are of various Sclavonic races; 1,500,000 are Albanians; 1,000,000
Greeks; the remainder Armenians, Jews, and Gipsies. In religion there,
there are about 4,800,000 Mohammedans, nearly half of whom are not
Osmanlis, the remainder being of Sclavonic descent, whose ancestors
embraced Islam in order to save their estates; they are, however, quite
as devoted Mussulmans as are the Osmanlis themselves. There are now
about 12,000,000 Christians, of whom some 11,000,000 belong to the Greek
Church, and nearly 1,000,000 are in communion with the Church of Rome.
The name Ottomans is officially given to all the subjects of the empire,
irrespective of race or religion; all except Mussulmans are specifically
designated as _Rayahs_, "the flock." Nominally, at least, by the new
Constitution promulgated in December, 1876, while Islam is the religion
of the State, all subjects are equal before the law, and all, without
distinction of race or creed, are alike eligible for civil and military
positions.
But a very considerable part of this territory is not properly included
in the Ottoman empire. The principality of Roumania, in the northeastern
corner, made up of what was formerly known as Wallachia and Moldavia,
with a population of about 4,500,000, is practically independent, under
a prince of the house of Hohenzollern, elected in 1866. It merely
acknowledges the suzerainty of the Sultan, to whom it pays an annual
tribute of some $200,000. Servia, on the north, bordering upon Austria,
with a population something less than 1,500,000, has for years been
really independent, merely paying a tribute of less than $100,000.
Roumania and Servia are strongly under Russian influence. Besides these
is the little State of Montenegro, on the Adriatic, with a population of
less than 200,000, which disowns the suzerainty of the Sultan, and has
for many months waged a fierce but desultory war against him.
Of what properly constitutes Turkey in Europe, with a population of some
11,000,000, the following are the principal divisions, designating them
by their former names, by which they are still best known: south of
Roumania, and between the Danube and the Balkhan mountains, is Bulgaria;
south of Bulgaria is Roumelia, in which Constantinople is situated; in
the northwest is Herzegovina; between which and Servia is Bosnia; on the
west, along the Adriatic, is Albania. In estimating the defensive
strength of the Ottoman empire we must take main account of Turkey in
Asia, with a population of some 17,000,000, by far the larger portion of
whom are Osmanlis, devoted to Islam, warlike by nature, and fully
capable, as was shown in the Crimean war, of being moulded into
excellent soldiers. But our present concern is with Turkey in Europe.
If the ingenuity of man, working through long centuries of misrule, had
set itself to the task of developing a form of government the most
potent for evil and the least powerful for good, the system could not
have been worse than that which exists in European Turkey; and the worst
of it is that no one but the most hopeful optimist can perceive in it
the slightest hope of reform or practical amendment. In theory the
Sultan is the recognized organ of all executive power in the State. The
dignity is hereditary in the house of Osman; but the brother of a
deceased or deposed Sultan takes precedence of the son, as being nearer
in blood to the great founder of the house. A Sultan, therefore, must
see in his brother a possible rival, who must, in case his life is
spared, be kept immured in the seclusion of the harem. A Sultan who
succeeds his brother naturally comes to the throne at a somewhat mature
age, but as ignorant as a babe of all that belongs to the duties of
government; lucky it is if he is not also physically and mentally worn
out by debauchery and excess. Turkish history is full of instances where
one of the first acts of a Sultan has been to order the execution of his
brothers and nephews. Thus Mahmoud II. put to death his infant nephew,
the son of his predecessor, and caused three pregnant inmates of the
harem to be flung into the Bosporus in order to make sure the
destruction of their unborn offspring. The actual task of government is
in some sort divided between the Sultan and the "Porte," a term which is
used to designate the chief dignitaries of the State. The "Sublime
Porte" is the Council of the Grand Vizier, who presides over the Council
of State, consisting of the ministers for home affairs, for foreign
affairs, and for executive acts, with several secretaries, one of whom
is supposed to be answerable that the acts of the ministry are in
conformity with, the supreme law of the Koran. The Porte of the
Defterdar, or Minister of Finance, whose council is styled the "Divan,"
consists of several ministers and other functionaries. The "Agha"
formerly comprised many civil and military officials whose duties were
in some way immediately connected with the person of the Sultan, not
very unlike what we call a "kitchen cabinet." The foregoing are all
designated as "Dignitaries of the Pen." The "Dignitaries of the Sword"
are the viceregal and provincial governors, styled pachas and beys. They
are at once civil and military commanders; and, most important of all,
tax-gatherers, and not infrequently farmers as well as receivers of
taxes. If they forward to the Porte the required sum of money, little
care is had as to the manner in which their other duties are performed
or neglected. The manifold extortions of the local pachas keep one part
or another of the empire, not only in Europe, but in Asia, in a state of
perpetual insurrection, of which little is ever heard abroad.
The Koran is the acknowledged source of all law, civil and
ecclesiastical. Its interpreter is the _Sheikh-ul-Islam_, "the Chief of
the Faithful," sometimes styled the "Grand Mufti." He is the head of the
_Ulemi_, or "Wise Men," comprising the body of great jurists,
theologians, and _literati_, any or all of whom he may summon to his
council. He is appointed for life by the Sultan, and may be removed by
him. His office is in theory, and sometimes in practice, one of great
importance. To him and his council the Sultan is supposed to refer every
act of importance. He does not declare war or conclude peace until the
Grand Mufti has formally pronounced the act "conformable to the law." It
is only in virtue of his _fetwa_, or decree, that the deposition of a
Sultan is legalized. A _fetwa_ from him would summon around the standard
of the Prophet all the fanatical hordes of Islam to fight to the death
against the infidels, in the firm belief that death on the battlefield
is a sure passport to Paradise. With the Koran as the supreme law, and
the Sheikh-ul-Islam its sole interpreter, nothing can be more futile
than the provision of the new Constitution of December, 1876, that "the
prerogatives of the Sultan are those of the constitutional sovereigns of
the West."
It is necessary here to touch only briefly upon the rise and decline of
the Turkish empire in Europe. The Osmanlis take their name from Osman,
the leader of a Tartar horde driven out from the confines of the Chinese
empire, who overran Asia Minor. His great-grandson, Amurath I., crossed
into Europe, took Adrianople in 1361, and overran Bulgaria and Servia.
Several of his successors pushed far into Hungary and Poland. Mohammed
II. took Constantinople in 1453, and brought the Byzantine empire to a
close. Selim I. (1512-'20) extended his dominion over Mesopotamia,
Syria, and Egypt. Solyman II., "the Magnificent" (1520-1566), raised the
Turkish power to its highest point. He took Buda in 1529; and in 1532
besieged Vienna with a force of 300,000 men, but was routed by the
Polish John Sobieski, with a force hardly a tenth as great. But for
another half century the Turkish power was sufficient to inspire terror
in all Christendom. With the death of Solyman, the power of the Turks
began to wane, slowly but surely, and at the close of the last century
the expulsion of the Turks from Europe seemed close at hand. The great
wars of the French Revolution gave them a new lease of possession, and
at its close Sultan Mahmoud II., who was by blood half French,[I]
endeavored to introduce reforms which some men hoped and others feared
would restore the Ottoman Empire. But the result showed the
impossibility of patching up rotten garments with new cloth. The Greek
revolution broke out, and at its close the Sultan found himself no match
for his vassal, Mehemet Ali, Pacha of Egypt, and it was only the
intervention of Russia, Austria, and Great Britain which prevented the
Pacha from establishing at Constantinople the seat of a new empire,
which, be it what it might, would not have been Turkish. What were the
reasons of Great Britain and France it is not now easy to say. Those of
Russia are patent: she wanted Constantinople to remain in the hands of
the Turks until she herself was in a position to seize it. From that
time the Ottoman Empire became the "sick man of Europe," around whose
bedside all the other powers were watching, each determined that none of
the others should gain the greater share in his estates when he died. In
1844 they formally adopted him into the family of the nations of Europe,
and promised that his safety should be the common care of all.
[Footnote I: His mother was a Creole, a native of Martinique, and cousin
of that other Creole who came to be the Empress Josephine. She had been
sent to France to be educated, and on her voyage homeward was captured
by an Algerine pirate who sold her to the Dey, by whom she was sent as a
present to the Sultan, whose favorite Sultana she became.]
Russia, in the mean while, was busy in endeavoring to make herself the
patron of the Christian subjects of the Sultan, and when the time
appeared ripe, entered upon those overt acts which led to the Crimean
war. Out of this war the Ottoman Empire came with considerable apparent
advantage. The man supposed to be sick unto death showed that there was
unexpected vitality--of a spasmodic sort indeed--in his Asiatic members;
and again there were hopes and fears of his ultimate convalescence, if
not of restoration to robust health. That those hopes and fears were
baseless is now clear enough. Never was the sick man so feeble as within
the last five years.
The existing crisis in the Eastern Question came about in the ordinary
course of things. In the summer of 1875 the pecuniary needs of the
Sublime Porte were more than usually urgent, and the tax-gatherers were
even more than usually exacting. The normal result ensued: there were
local risings in Bosnia and Herzegovina. A secret Bulgarian
revolutionary committee, favored by Russia, has for years existed in
Bucharest, the capital of Roumania. They sent emissaries into Bulgaria
to excite an insurrection in that province. The plan was to set fire to
Adrianople and Philippopolis, each in scores of places, to burn other
towns, mainly inhabited by Mussulmans, and force all the Bulgarian
Rayahs to join the uprising. The insurrection broke out prematurely in
May, 1876, and only a few were actively engaged in it. Two or three
thousand troops would have been sufficient to have quelled the rising;
but there were none in the province, and despite the urgent appeals of
the Pacha none were sent. The Mussulmans, who are in a fearful minority
there, were thrown into a panic; and the Pacha gave orders for calling
an ignorant and fanatical population to arms. Regular troops were at
last sent. The Turks gained an easy victory, and perpetrated those
ineffable atrocities, the recital of which sent a thrill of horror
throughout Christendom. The Bulgarians fled northward toward Servia,
pursued by the Turks, who it is said made predatory incursions. Prince
Milan made some extraordinary demands upon the Sultan, among which were
that the government of Bulgaria should be committed to him and that of
Bosnia to Prince Nicholas of Herzegovina. The Grand Vizier refused to
listen to these demands; whereupon the Prince called the Servians to
arms, declared war against the Sultan, invaded Bulgaria, and soon
assumed the title of King of Servia. His invasion of Bulgaria met with
ill success. Although aided by many Russian soldiers and officers,
absent on special leave from their regiments, the Servians were driven
back over their frontiers; and the war was finally suspended by a truce
for six months. We suppose that there can be no doubt that the rising in
Bulgaria and the action of Servia were favored, if not by the Czar
personally, yet by the Russian government, although it would, if
possible, have withheld Prince Milan from declaring war when he did. The
Servian Bishop Strossmayer expressly affirms that the insurrection in
Herzegovina was prematurely commenced against the advice of Russia, and
that Servia and Montenegro went to war of their own accord, though they
have naturally accepted the Russian aid since accorded to them. He adds
that Prince Gortschakoff, who in the Russian government is all that
Prince Bismarck is in that of Germany, the year before last "informed
Prince Milan that Russia was unprepared; that only within three years
did she count on taking Constantinople; and that only then would she
call on the Sclaves of the South to plant the Greek cross on the dome of
St. Sophia."
Meanwhile, on the news of the Turkish atrocities in Bulgaria, the Czar
put his troops in motion toward the Turkish frontier, and made demands
upon the Sultan which, if acceded to, would have practically made the
Czar the actual sovereign of all Turkey in Europe north of the Balkhan.
Great Britain sent her fleet to the mouth of the Dardanelles to
"maintain the interests of the British empire" in that part of the
world. Diplomatic notes and rejoinders passed between the cabinets of
the great Powers; and early in January an International Conference was
assembled at Constantinople to endeavor to settle, or at least to stave
off the present crisis in the Eastern Question; Great Britain, through
her representative, the Earl of Salisbury, apparently taking the lead.
As we write, in the early days of February, all that is definitely known
is: The Conference has utterly failed; the Sultan absolutely refused to
accede to the propositions made to him; and the ambassadors of the great
Powers have been withdrawn from Constantinople. Surmises and rumors as
to what will next be done are rife; not the least significant or the
least probable being that the Emperors of Germany, Russia, and Austria
are consulting as to taking the matter into their own hands. Whatever
the immediate issue may be--whether a peace of some kind; a partial war
between Russia on the one side, and Turkey, with or without Great
Britain, on the other; or a general European war--of one thing we may be
certain: it will not cause Russia to more than postpone still longer her
long-cherished determination to have Constantinople.
Mr. Carlyle has suggested, as a final settlement of the Eastern
Question, that Turkey in Europe should be divided between Russia,
Austria, and Great Britain. But, as is his wont, he leaves out some
essential factors in the problem. No part of this territory would be of
the slightest use to Great Britain, except perhaps the island of Candia
as a sort of half-way house in the highway to India by the Suez canal.
She has everything to lose and little more than nothing to gain by any
such partition, which, as it necessarily must, would give Constantinople
to Russia. Mr. Carlyle has so thorough a dislike to France--and with him
dislike is nearly equivalent to contempt--that he naturally leaves her
out of the problem. But it is surprising that he leaves out his favorite
Germany, perhaps the most important factor of all.
We can conceive of a partition of Turkey between Russia and Austria
which would be so manifestly and equally advantageous to both that they
might agree to it. And the line of division is clearly indicated by
nature. Austria, like every other great civilized nation, desires to be
a maritime power; but she touches the sea only at one point, the head of
the Adriatic, with the narrow strip known as Dalmatia, running half way
down its eastern coast. There are only two considerable ports, Trieste
and Fiume. Eastward, and back of Dalmatia, are Servia, Bosnia, and
Herzegovina; and below these, on the Adriatic, is the long coast-line of
Albania, with several good harbors. Across the narrowing isthmus is the
Archipelago, with the excellent harbor of Salonika. Now look on any
tolerable map, and one will see on the eastern borders of Servia, where
the Danube breaks through the Carpathians, a range of mountains shooting
southward to and crossing the Balkhan, from which it is continued still
southward to the Archipelago, the whole dividing European Turkey into
two almost equal halves. Let Russia take the eastern half, comprising
Roumania, Bulgaria, and the half of Roumelia, including Constantinople,
the whole shore of the Sea of Marmora and the Dardanelles--all that she
really needs or cares for. Let Austria take the other half, which would
give her the whole eastern coast of the Adriatic, and a large frontage
on the Archipelago, and so a double access to the Mediterranean and
thence to the ocean. She would acquire thereby an access of valuable
territory equal to almost half of her present dominions, which would
render her relatively to Russia fully as strong as she now is.
But such a partition could not be carried into effect without the
concurrence of Germany, for Germany is undoubtedly as a military power
much stronger than Russia. Germany certainly would never assent unless
she could somewhere get something equivalent to that gained by Austria
and Russia, and not an inch of Turkey would be of any use to her. But in
quite another part of Europe is a territory comparatively small in
extent, which would be of priceless value to Germany. This is the little
kingdom of Holland, which is indeed physically a part of Germany, and
essential to the rounding off of the boundaries of the new empire. It
would give her an extended sea-front, which is what she also needs in
order to become a great naval and commercial power. It would give her
also in the Zuyder Zee a naval depot and harbor of refuge inferior only
to that of the Black Sea, and immeasurably superior to any other in
Europe. Furthermore, with Holland would go the possession of Java and as
many other great islands in the Indian Ocean as she might choose to
seize and colonize. To Holland, indeed, we think such an annexation
would be a decided gain. Her people are in race, language, and religion
closely allied to the Germans. It would be better for her to become a
State, inferior only to Prussia, of the great German empire, than a
feeble kingdom, always at the mercy of her powerful neighbors. But
whether it would be for her good or not, would not be likely to be much
taken into account should the great Powers agree upon a reconstruction
of the political map of Europe. The interests of France would suffer no
material damage from this, provided she were left free to extend her
Algerian possessions over the whole Mediterranean coast of Africa, now
almost a desert, but once the granary of the Roman empire, and
abundantly capable of being restored to its ancient fertility; or in
case she should think her dignity required something more, she might
receive in Belgium far more than a counterpoise for her recent loss of
Alsace-Lorraine.
Suppose that in some not remote future the policy of Russia, Germany,
and Austria shall happen to be directed by statesmen as able and
unscrupulous as Gortschakoff, Bismarck, and Von Beust, we think such a
settlement of the Eastern Question by no means an improbable one. And
should these Powers agree to effect it, all the rest of Europe could do
nothing to the contrary.
A. H. GUERNSEY.
THE LASSIE'S COMPLAINT.
Now simmer cleeds the groves in green,
An' decks the flow'ry brae;
An' fain I'd wander out at e'en,
But out I daurna gae.
For there's a laddie down the gate
Wha's like a ghaist to me;
An' gin I meet him air or late,
He winna lat me be.
He glow'rs like ony silly gowk,
He ca's me heavenly fair.
I bid him look like ither fowk,
Nor fash me sae nae mair.
I ca' him coof an' hav'rel too,
An' frown wi' scornfu' ee.
But a' I say, or a' I do,
He winna lat me be.
JAMES KENNEDY.
ASSJA.
BY IVAN TOURGUENEFF.
I was then twenty-five years old, began N. N. As you see, the story is
of days long past. I was absolutely my own master, and was making a
foreign tour, not to "finish my education," as the phrase is nowadays,
but to look about me in the world a little. I was healthy, young,
light-hearted; I had plenty of money and as yet no cares; I lived in the
present and did precisely as I wished; in one word, life was in full
flower with me. It did not occur to me that man is not like a plant, and
that his time of bloom is but once. Youth eats its gilded gingerbread,
and thinks that is to be its daily food; but the time comes when one
longs in vain for a bit of dry bread. But it is not worth while to speak
of that.
I was travelling without aim or plan: made stops wherever it pleased me,
and went on whenever I felt the need of seeing fresh faces--especially
faces. Men interested me above all things. I detested monuments,
collections of curiosities. The mere sight of a guide roused in me
feelings of weariness and fury. In the Dresden "Gruene Gewoelbe" I nearly
lost my wits. Nature made a powerful impression upon me; but I did not
love her so-called beauties--her mighty hills, her crags and torrents. I
did not like to have them take possession of me and disturb my
tranquillity. Faces, on the contrary--living, earthly faces, men's talk,
laughter, movements--I could not do without. In the midst of a crowd I
was always particularly gay and at my ease. It gave me real pleasure
merely to go where others went, to shout when others shouted, and at the
same time to observe how these others shouted. It pleased me to observe
men--yes, I did not observe them merely; I studied them with a delighted
and insatiable curiosity. But I am digressing again.
Twenty years ago, then, I was living in the little German town of S----,
on the left bank of the Rhine. I sought solitude. I had been wounded to
the heart by a young widow whose acquaintance I had made at a
watering-place. She was extremely pretty and vivacious, flirted with
everybody--alas! with me also, poor rustic! At first she had lifted me
to the skies, but soon plunged me in despair when she sacrificed me to a
rosy-cheeked lieutenant from Bavaria. Seriously speaking, the wound in
my heart was not very deep; but I considered it my duty to give myself
for a time to melancholy and retirement--what pleasure youth finds in
these!--and accordingly settled myself in S----.
This little town had attracted me by its position at the foot of high
hills, by its old walls and towers, its hundred-year-old diadems, its
steep bridges over the clear little brook which flowed into the Rhine,
but above all by its good wine. And after sunset--it was in June--the
loveliest of fair-haired Rhineland girls sauntered through the narrow
streets and cried, "Good evening!" in their sweet tones to the stranger
whom they met, some of them even lingering still when the moon rose
behind the peaked roofs of the old houses, and the little stones of the
pavement showed distinctly in her steady light. Then I delighted in
strolling about the old town. The moon seemed to look down benignly from
a cloudless sky, and the town received this glance and lay peacefully
there wrapped in sleep and veiled in moonbeams--the light that at once
soothes and vaguely stirs the soul. The weathercock upon the high, sharp
spire gleamed in dull gold; long gleams of gold quivered on the dark
surface of the stream; some dim lights--O thrifty German folk!--burned
here and there in the small windows under the slated roofs; the vines
stretched out mysterious fingers from the walls; something stirred
perhaps in the shadow of the fountain in the little three-cornered
market-place; suddenly the sleepy cry of the watchman sounded; then a
good-natured dog growled in an undertone; and the air kissed the brow so
softly, and the lindens smelled so sweet, that the breast involuntarily
heaved quicker, and the word "Gretchen" rose to the lips, half a cry,
half question.
This little town of S---- lies about two versts from the Rhine. I went
often to look at the majestic river, and would sit for hours upon a
stone bench under a lonely, large oak, thinking, not without a certain
exertion, of my faithless widow. A little statue of the Virgin, with a
red heart pierced with swords upon her breast, looked sadly out from the
leaves. On the opposite bank lay the town of L----, somewhat larger than
the one in which I had established myself. One evening I was sitting in
my favorite spot, looking in turn at the stream, the sky, and the
vineyards. Before me some white-hooded urchins were climbing over the
sides of a boat that was drawn up on the shore and lay there keel
upward. Little skiffs with sails hardly swollen passed slowly along;
green waves slid by with a gentle, rushing sound. All at once strains of
music greeted my ears. I listened. They were playing a waltz in L----.
The double bass grumbled out its broken tones, the violins rang clear
between, the flutes trilled noisily.
"What is that?" I asked an old man who approached me dressed in a plush
waistcoat, blue stockings, and shoes with buckles.
"That?" he replied, shifting his pipe from one corner of his mouth to
the other. "Those are the students who have come from B---- to the
_Commers_."
"I will see this Commers," I thought. "Besides, I have not yet been in
L----." I found a ferryman and crossed the river.
Perhaps not every one knows what a Commers is. It is a particular kind
of drinking bout, in which the students from one section, or of one
society, unite. Almost every participant of a Commers wears the
conventional costume of the German student: a short jacket, high boots,
and a little cap with vizor. The students generally assemble at
midday and carouse till morning, drinking, singing, smoking, and
occasionally they hire a band.
Such a Commers was at this moment held in L---- at a little inn called
the Sun, in a garden adjoining the street. Flags were flying from the
inn and over the garden itself. The students sat round tables under the
spreading lindens; a huge bulldog under one of the tables. The musicians
were under a trellis at one side, playing with great spirit, and
refreshing themselves from time to time with mugs of beer. A great crowd
had collected in the street before the unpretending little inn. The good
citizens of L---- were not of the stuff to let slip a good opportunity
of seeing strange guests. I mingled with the crowd of lookers-on. It
gave me an immense satisfaction to watch the faces of the students,
their embraces, their exclamations, the innocent affectations of youth,
the eager glances, the unrestrained laughter--the best laughter in the
world. All this generous ferment of young, fresh life, this striving
forward, no matter whither so it be forward, this rollicking,
untrammelled existence excited and infected me. Why not join them, I
thought?
"Assja, have you had enough?" suddenly asked in Russian a man's voice
behind me.
"Let us wait a little longer," answered another voice, a woman's, in the
same tongue.
I turned hastily. My eyes fell on a handsome young fellow in a loose
jacket and cap. On his arm hung a girl of medium height, with a straw
hat which entirely hid the upper part of her face.
"You are Russians?" I said aloud involuntarily.
The young man smiled and answered, "Yes; we are Russians."
"I did not expect, in such an out-of-the-way place----" I began.
"Nor did we," he interrupted me. "But what does that signify? All the
better. Permit me to introduce myself. My name is Gagin, and this
is"--he paused for an instant--"my sister. May we ask your name?"
I told him, and we began a conversation. I learned that Gagin, like
myself, was travelling for pleasure; that he had arrived at L---- the
week previous, and was now staying there. To speak candidly, I was
always unwilling to make the acquaintance of Russians in other
countries. I could recognize them at any distance by their gait, the cut
of their clothes, and more than all by the expression of their faces.
The self-satisfied, scornful, and usually haughty expression would
change suddenly to one timid and suspicious; in a moment the whole man
is on his guard, his glance wanders about unsteadily. "Have I said
anything ridiculous? Are they laughing at me?" this anxious look seems
to say. But a moment more, and the majesty of the physiognomy is
restored, only occasionally replaced by stupidity. Yes, I avoided
Russians, but Gagin pleased me at once. There are such fortunate faces
in the world. To look at them is a pleasure for every one. One feels at
once cheered and caressed by them. Gagin had just such a gentle,
attractive face, with great soft eyes and fine curly hair. When he
spoke, even if you did not see his face, you felt by the mere sound of
his voice that he was smiling.
The young girl whom he had called his sister also seemed to me at the
first glance very lovely. There was something peculiar and remarkable in
the traits of her round, brown face, with its thin, delicate nose, its
round, almost babyish cheeks, and its clear, dark eyes. Her form was
graceful, but apparently not yet fully developed. She did not in the
least resemble her brother.
"Will you come home with us?" Gagin asked me. "I think we have seen
enough of the Germans. Our beloved countrymen would certainly have
broken some window panes or smashed a few chairs, but these fellows are
quite too well behaved. What do you say, Assja, shall we go home?"
The young girl nodded assent.
"We live just beyond the village," Gagin continued, "in a little
solitary house far up the hillside. It is really fine there. You shall
see for yourself. The landlady promised me to have some buttermilk for
us. It will be dark very soon, and then you can cross the Rhine far more
pleasantly by moonlight."
We set out. Through a low gate--for the town was surrounded on all sides
by an old wall, some of whose loop-holes even yet remained
undestroyed--we gained the open country, and after we had walked about a
hundred paces beside a stone wall we came to a steep and narrow path up
the hill, into which Gagin turned. The <DW72> on both sides was planted
with grapes. The sun had but just set, and a soft purple light rested on
the green vines, the long poles, the dusty soil covered with bits of
broken slate and stone, and upon the white walls of a small house with
steep roof and light windows, which stood high above us on the mountain
which we were climbing.
"Here is our place!" exclaimed Gagin as we drew near the house. "And
here is the landlady just bringing us our buttermilk. Good evening,
madam! We will be there in a moment. But first," he added, "look about
you once. What do you say to this outlook?"
The view was indeed charming. The Rhine lay before us, a strip of silver
between green banks. In one place it glowed in the purple and gold of
the sunset. All the houses in the little towns clustering on the shores
stood out distinctly; hills and fields spread far before us. Below us it
was lovely, but above it was lovelier still. The brilliant transparency
of the atmosphere, and the depth and purity of the sky, made a profound
impression on me. The air was fresh and exhilarating. It blew with a
light wave motion, as if it felt itself more free on the hilltop.
"You have chosen a magnificent situation," I said.
"Assja found it out," Gagin answered. "Now, Assja, give your orders. Let
us have everything brought here. We will take tea in the open air. We
can hear the music better here. Haven't you noticed it?" he went on. "A
waltz close at hand may be often good for nothing--mere commonplace
jingle. It becomes exquisite at a distance; sets all the sentimental
strings in one's heart a twanging." Assja (her name was properly Anna;
but Gagin always called her Assja, and I shall allow myself that
privilege)--Assja went into the house and soon returned with the
landlady. Both together they carried a great tea-tray with a jug full of
milk, plates, spoons, sugar, berries, and bread. We seated ourselves and
began to eat. Assja took off her hat. Her black hair, cut rather short,
and curled like a boy's, fell in thick ringlets over neck and shoulders.
At first she was shy; but Gagin said to her:
"Assja, don't be afraid. He won't hurt you!"
She smiled, and immediately addressed a little conversation to me. I
have never seen a more restless creature. She did not sit still a
moment. She stood up, ran into the house, came out again, sang in an
undertone, and laughed often in an odd way. It seemed as if she was not
laughing at what she heard, but at stray thoughts which came into her
head. Her large, clear eyes looked at us frankly and fearlessly. Now and
then, however, the lids fell, and then her glance became suddenly deep
and gentle.
For nearly two hours we chatted together. Daylight was long past, and
the twilight had changed from scarlet and gold to a faint redness, then
to a clear gray, and finally all was lost in night; but our speech
flowed as uninterruptedly, peaceful, and quiet as the air that
surrounded us. Gagin brought a bottle of Rhine wine, and we drank it
leisurely. We could still hear the music. The notes seemed fainter and
sweeter to us. Lights began to appear in the town and on the river.
Assja's head drooped forward so that her hair fell over her eyes. She
was silent and breathed heavily. Then she declared that she was sleepy,
and went into the house; but I saw that she stood for a long time behind
the closed window without lighting her lamp. Then the moon rose, and her
beams quivered on the surface of the water. Everything was bright or in
deep shadow, but certainly took on a different appearance. Even the wine
in our glasses sparkled with a mysterious brilliancy. The wind had
fallen as if it had folded its wings and were resting. Warm, spicy odors
of the night rose from the ground.
"It is time for me to go, or I shall not find a ferryman," I said.
"Yes; it is time," Gagin repeated.
We descended the footpath. Suddenly stones began to rattle down. Assja
was running after us.
"Aren't you asleep then?" her brother asked her. But she ran on before
us without replying. The last dim lights which the students had lighted
in the little inn garden showed through the branches of the trees, and
lent them a gay, fantastic appearance. We found Assja at the shore
talking to the old boatmen. I sprang into the boat and took leave of my
new friends. Gagin promised to visit me on the next day. I shook his
hand and held mine out to Assja, but she merely looked at me and nodded.
The boat was pushed off and was borne down on the swift current. The
ferryman, a hale old fellow, dipped his oars deep into the dark flood.
"You're in the streak of moonshine--you've spoiled it," Assja called
after me.
I looked down. The waves were rippling darkly about the boat.
"Good-by!" rang her voice again.
"Till to-morrow," Gagin added.
The boat touched the bank. I stepped out and looked back, but could see
no one on the shore behind me. The moonshine spanned the stream again
like a golden bridge, and like another good-by I caught the strains of
an old country waltz. Gagin was right. I felt that all the strings of my
heart trembled responsively. I crossed the dusky fields to my house,
drinking great draughts of the balmy air, and giving myself up wholly to
a sweet, vague feeling of expectation. I felt myself happy. But why? I
wished for nothing, I thought of nothing. I was merely happy.
Still smiling from the fulness of delightful and changing sensations, I
sank into bed, and had already closed my eyes when it suddenly occurred
to me that I had not thought of my cruel fair one once in the whole
evening. "What does it mean?" I asked myself. "Am I not hopelessly in
love?" But just as I put this question to myself I fell asleep, as it
seemed, like a baby in its cradle.
* * * * *
The next morning (I was awake, but had not risen) some one knocked with
a stick under my window, and a voice that I immediately recognized as
Gagin's began to sing,
Sleepest thou still?
My lute shall wake thee.
I ran to open the door for him.
"Good morning," said Gagin as he entered. "I disturb you a little early.
But what a morning it is! Fresh, dewy; the larks singing." With his
wavy, shining hair, his bare neck and ruddy checks, he was as fresh as
the morning himself.
I dressed myself, and we went out into the garden, sat down upon a
bench, ordered coffee, and began to talk. Gagin confided to me his plans
for the future. Possessed of a fair property, and entirely independent,
he wished to devote himself to painting; only he regretted that this
decision had been a late one, and that he had already lost much time. I
also detailed my projects, and even took him into the secret of my
unhappy love affair. He listened patiently, but, so far as I could see,
the story of my passion did not awake any very lively sympathy in him.
After he had sighed once or twice out of good manners, he proposed to me
to come and see his studio. I was ready at once.
We did not find Assja. She had gone to the "ruin," the landlady assured
us. Two versts from L---- were the remains of a castle of the middle
ages. Gagin laid all his canvases before me. There was life and truth in
his sketches, a certain breadth and freedom of treatment, but not one
was finished, and the drawing was careless and often faulty. I told him
my opinion frankly.
"Yes, yes," he interrupted me with a sigh. "You are right; it is all
weak and unsatisfactory. But what is to be done? I haven't studied
properly, and the inexcusable carelessness shows everywhere. Before
working it always seems as if I were capable of eagle flights--it seems
as I could hurl the earth out of her course; but when it comes to
execution one loses strength quickly enough, and is tired."
I began to encourage him, but he motioned with his hand that I should be
silent, rolled up his canvases, and threw himself on the sofa. "If my
patience lasts, I shall make something yet," he muttered in his beard;
"if not--then I shall stay a country lout. Come, let us look after
Assja." We started.
* * * * *
The way to the ruin wound round the <DW72> of a wooded valley, at whose
bottom a brook flowed noisily over its pebbles as if it were anxious to
lose itself in the great stream that was shining peacefully behind the
sharply indented mountain side. Gagin called my attention to some
partially lighted spots; in his words the artist certainly spoke, if not
the painter. The river soon appeared. On the summit of the naked rock
rose a square town, black with age but in tolerable preservation, though
it was cleft from top to bottom. Moss-grown walls adjoined this town,
ivy clung here and there, a tangle of briars filled the embrasures and
the shattered arches. A stone foot-walk led to the door that remained
intact. We were already near it when suddenly a girl's figure sped by
us, sprang over the heaps of rubbish, and seated herself on a projection
of the wall directly over the abyss. "There is Assja," cried Gagin. "Is
she mad?"
Through the gate we stepped into a spacious courtyard half filled with
wild apple trees and stinging nettles. It was indeed Assja, who was
sitting on the projection. She looked down at us and laughed, but did
not stir from her place. Gagin threatened her with his finger. I began
to expostulate aloud with her on her recklessness.
"Don't do that," Gagin whispered to me. "Don't exasperate her. You don't
know her. She would be capable of clambering up the town. Look yonder,
rather, and see how ingenious the people hereabouts are."
I looked about me. A thrifty old lady had made herself very comfortable
in a kind of narrow booth made of boards piled up in one corner, and
knitted her stocking, while she occasionally glanced askance at us. She
had beer, cake, and soda-water for tourists. We sat down on a bench and
attacked our heavy tin mugs of cooling beer. Assja still sat motionless;
she had drawn up her feet, and wound her muslin scarf about her head.
Her charming, slender figure showed sharp against the sky, but I could
not look at it without annoyance. Even on the previous day I had seen
something intense, unnatural in her. "Does she want to astonish us?" I
thought. "What for? What a childish freak!" As if she had fathomed my
thought, she cast a quick and piercing glance at me, laughed loudly,
sprang in two bounds from the wall, and going to the old woman, asked
for a glass of water.
"You think that I want to drink it?" she said, turning to her brother.
"No; there are some flowers up there that I must water."
Gagin made no reply, but she scrambled up the ruins glass in hand, and,
stopping from time to time and bending down, with extraordinary
painstaking she let fall some drops of water, which glistened in the
sun. Her movements were full of grace, but I was vexed as before,
although I was forced to admire her lightness and dexterity. In one
perilous spot she uttered a little shriek with design, and then laughed
loudly again. That annoyed me still more.
"The young lady climbs like a goat," mumbled the old woman, and stopped
knitting for a moment.
Meanwhile Assja had emptied her glass and come down, roguishly swaying
to and fro. A strange, imperceptible smile played round her brows, and
nostrils, and lips; half audacious, half merry, the dark eyes were
shining.
"You find my behavior scandalous," her face seemed to say. "Very well. I
know that you admire me."
"Neatly done, Assja; neatly done," said Gagin under his breath.
It seemed as if she felt suddenly ashamed of herself. Her long lashes
fell, and she sat down near us meekly, as if conscious of naughtiness.
Now for the first time I could see her face fairly--the most changeful
that I had ever beheld. For a few moments it was very pale, and took on
a reserved, almost a melancholy expression. Her features seemed larger,
stronger, and more simple. She was perfectly still. We made the tour of
the ruins (Assja followed us), and were very enthusiastic over the view.
Meanwhile dinnertime approached. Gagin paid the old woman, asked for
another glass of beer, and cried, turning to me with a sly look,
"To the health of the lady of your heart!"
"Has he--have you such a lady?" asked Assja suddenly.
"Who hasn't?" replied Gagin.
Assja became thoughtful. Her face assumed yet another expression. The
challenging, almost bold smile returned.
On the way home she laughed more, and her behavior was more whimsical
than ever. She broke for herself a long branch, carried it over her
shoulder like a gun, and bound her scarf about her head. A party of
fair-haired young English dandies met us. As if at a word of command,
they all stood aside to let Assja pass, with a cold glare of
astonishment in their eyes, while she began to sing loudly in mockery.
As soon as we had reached the house she went to her chamber, and
appeared at dinner in a most elaborate dress, with carefully arranged
hair, and wearing gloves. She behaved with great propriety, not to say
stillness, at table, hardly touched her food, and drank water out of a
wineglass. Evidently she wished to appear before me in a new role, that
of a conventional and well brought up young lady. Gagin let her alone.
It was easy to see that it had become a habit with him to let her have
her will in all things. At times he looked at her good-naturedly and
shrugged his shoulders slightly, as much as to say, "Be indulgent; she
is only a child." When the meal was ended Assja rose, made us a
courtesy, and taking up her hat, asked Gagin if she might go to see Frau
Luise.
"Since when have you begun to ask permission?" answered Gagin with his
ready smile, but with a little astonishment. "Is the time long to you
with us?"
"No; but yesterday I promised Frau Luise that I would visit her. And
then I think you two would rather be alone. Mr. N." (she pointed to me)
"may have something to tell you."
She went.
"Frau Luise," Gagin began, taking pains to avoid my glance, "is the
widow of a former burgomaster of this place; a good old soul, but rather
narrow-minded. She has taken a great fancy to Assja. It is Assja's
passion to make the acquaintance of people of the lower classes. I have
found that pride is at the bottom of the matter every time. I have
spoiled her thoroughly, you see," he went on after a pause; "but what
was there for me to do? I never could carry a point by firmness with any
one; most of all not with her. It is my duty to be indulgent with her."
I was silent. Gagin gave another direction to the conversation. The more
I learned of him the more he pleased me. I soon understood him. His was
a real Russian character--truth-loving, faithful, simple, but
unfortunately rather sluggish, lacking firmness, and without the inward
fire. Youth did not flame up in him; it burned with a gentle glow. He
was most amiable and sensible; but I could not imagine what he would
become in manhood. He wished to be an artist. Without constant,
absorbing endeavor, no one is an artist. You exhaust yourself, I
thought, looking at his gentle face and listening to the slow cadence of
his voice. No; you will not strain every nerve; you will never succeed
in mastering yourself. And yet it was impossible not to be attracted by
him. My heart was really drawn to him. It may have been four hours that
we talked together, sometimes sitting on the sofa, sometimes walking
quietly up and down before the house; and in these four hours we became
real friends.
The day was at its close, and it was time to go home. Assja had not
returned.
"She is a wild creature," Gagin said. "If you please, I will go back
with you, and we will go to Frau Luise's on the way, and I will ask if
she is still there. The distance is trifling."
"We descended to the town, turned into a crooked and narrow cross
street, and came to a standstill before a house of four stories with two
windows on a floor. The second story projected into the street beyond
the first; the third and fourth reached still further forward than the
second. The whole house, with its old-fashioned carving, its two thick
pillars below, its steep, tiled roof, and the beak-shaped gutter running
out from the eaves, had the appearance of some monstrous, squatting
bird.
"Assja," called Gagin, "are you there?"
A lighted window in the third story was thrown up, and Assja's little
dark head appeared. Behind her peered forth the face of a toothless and
blear-eyed old woman.
"Here I am," answered Assja, coquettishly leaning over the window-sill
on her elbows. "It is exceedingly pleasant here. Catch," she added,
flinging a bit of geranium down to Gagin. "Imagine that I am the lady of
your heart."
Frau Luise laughed.
"N. is going," responded Gagin. "He would like to take leave of you."
"Indeed?" said Assja. "In that case give him my sprig. I am coming home
directly."
She shut the window, and I fancied that she gave Frau Luise a kiss.
Gagin handed me the sprig without a word. Without a word I put it in my
pocket, went to the ferry, and crossed to the other side.
I remember that I went home thinking of nothing definite, but feeling a
certain dull ache at my heart, when suddenly a strong odor, well known
to me, but not usual in Germany, made me stop puzzled. I stood still and
recognized by the roadside a hemp field of moderate size, whose smell
reminded me at once of my native steppes. A mighty homesickness arose in
me. I had a longing to feel Russian air blowing on my cheeks, to have
Russian ground beneath my feet. "What am I doing here? Why am I
wandering about among strangers in a strange land?" I cried aloud, and
the vague uneasiness that weighed on my spirits changed suddenly to a
bitter burning pain. I reached the house in a mood entirely different
from the one of the preceding day. I was strangely excited. I could not
compose myself. A feeling of vexation which I could not explain to
myself possessed me. At last I sat down to think of my faithless widow
(for I devoted the close of every day to official recollections of this
lady), and I took out one of her letters. But this time I did not even
open it. My thoughts had taken another turn; I thought--of Assja. I
remembered that Gagin, in the course of conversation, had spoken of
certain obstacles which would make his return to Russia very difficult.
"Is she then really his sister?" I cried aloud.
I undressed myself, went to bed, and tried to sleep; but an hour
afterward I was sitting up with my elbow on the pillow, and still
thinking of the "capricious maid with her affected laugh." "She has a
form like the little Galatea of Raphael in the Farnese," I said to
myself. "Yes, and she is not his sister."
Meanwhile the widow's letter lay quietly on the floor, bleached by a
moonbeam.
* * * * *
However, on the following day I went again to L----. I said to myself
that I wished to visit Gagin, but in truth I was curious to watch Assja,
to see if she would pursue the extravagances of the day previous. I
found them both in the parlor, and wonderful!--was it because I had
thought so much of Russia in the night and the morning?--Assja appeared
to me a real Russian girl--yes, even a very ordinary one, almost like a
servant. She wore a shabby gown; her hair was combed back behind her
ears. She sat quietly by the window, busy with some sewing, sedate and
still as if she never in her life had been otherwise. She hardly spoke,
examined her work from time to time; and her features had an expression
so dull and commonplace that I was involuntarily reminded of our own
Kathinkas and Maschinkas. To complete the resemblance, she began to hum
"My darling little mother." I looked at her sallow, languid face,
thought of yesterday's fantasies, and got suddenly out of temper. The
weather was magnificent. Gagin declared that he was going to sketch from
nature. I asked if he would permit me to accompany him, if it would not
disturb him?
"On the contrary," said he, "you will assist me by your suggestions."
He put on his Vandyk hat and his painting blouse, took his canvas under
his arm, and started. I followed him slowly; Assja remained at home. In
going out Gagin begged her to take care that the soup should not be too
watery. Assja promised to oversee it in the kitchen. Gagin reached a
dell which I already knew, sat down upon a stone, and began to sketch an
old, hollow, wide-branched oak. I lay down in the grass and took out a
book, but my reading did not advance beyond the second page, nor did he
blacken much paper. We chatted a great deal, and, if my memory does not
deceive me, we discoursed very subtly and profoundly about work: what
one should avoid, what strive for, and in what consisted the real merit
of the artists of our day. At last Gagin declared that he was not in the
mood for work, threw himself down beside me, and then for the first time
our youthful talk flowed free, now passionate, now dreamy, now almost
inspired, but always vague--a conversation peculiar to Russians. After
we had talked ourselves tired we started for home, filled with
satisfaction that we had accomplished something, had arrived at some
result. I found Assja precisely as I had left her. Whatever pains I
might take with my scrutiny I could discover no trace of coquetry, no
evidence of a part designedly played. This time it was impossible to
accuse her of oddity. "Aha!" Gagin said; "you have imposed penance and
fasting on yourself." In the evening she gaped several times without
pretence at concealment, and retired early. I also took leave of Gagin
betimes, and having reached home, I gave myself up to no more dreams.
This day ended in sober reflections. But I remember that as I settled
myself to sleep I said aloud, "What a chameleon the girl is!" And after
a moment's thought I added, "And she is certainly not his sister."
* * * * *
In this way two whole weeks passed. I visited the Gagins every day.
Assja seemed to shun me. She indulged in no more of those extravagances
which had so astonished me on the first days of our acquaintance. It
seemed to me that she was secretly troubled or perplexed. Neither did
she laugh so much. I observed her with interest.
She spoke French and German indifferently well, but one could see in
everything that she had not been in the hands of women since her
childhood, and the strange, desultory education which she had received
had nothing in common with Gagin's. In spite of the Vandyk hat and the
painter's blouse, the delicate, almost effeminate Russian nobleman was
always apparent in him; but she was not in the least like a noblewoman.
In all her movements there was something unsteady. Here was a graft
lately made, wine not yet fermented. Naturally of a timid and shy
disposition, she yet was annoyed by her own timidity, and in her
vexation she compelled herself to be unconcerned and at her ease, in
which she did not always succeed. Several times I turned the
conversation to her life in Russia, her past. She answered my questions
reluctantly. I learned, however, that she had lived in the country for a
long time before her travels. Once I found her with a book. She was
alone. Her head supported by both hands, the fingers twisted deep in her
hair, she was devouring the words with her eyes.
"Bravo!" I called out to her on entering. "You are very busy."
She raised her head and looked at me with great gravity and earnestness.
"Do you really think that I can do nothing but laugh?" she said, and was
about to withdraw.
I glanced at the title of the book; it was a French novel.
"I can't commend your choice," I said.
"What shall I read then?" she cried. And throwing her book on the table,
she added, "It's better that I fill up my time with nonsense," and with
this she ran out into the garden.
That evening I read "Hermann and Dorothea" aloud to Gagin. At first
Assja occupied herself rather noisily near us, then suddenly ceased and
became attentive, seated herself quietly beside me, and listened to the
reading to the end. On the following day I was again puzzled by her mood
till it occurred to me that she had been seized with a whim to be
womanly and discreet like Dorothea. In a word, she was an enigmatical
creature. Full of conceit and irritable as she was, she attracted me
even while she made me angry. I was more and more convinced that she was
not Gagin's sister. His behavior toward her was not that of a brother;
it was too gentle, too considerate, and at the same time a little
constrained. A singular occurrence seemed, by every token, to confirm my
suspicions.
One evening, when I came to the vineyard where the Gagins lived, I found
the gate locked. Without much thought I went to a broken place which I
had often noticed in the wall, and sprang over. Not far from this place,
and aside from the path, there was a small clump of acacia. I had
reached it, and was on the point of passing it. Suddenly I heard Assja's
voice, the words spoken excitedly and through tears:
"No. I will love no one but you: no, no--you alone and for ever!"
"Listen, Assja. Compose yourself," replied Gagin. "You know that I
believe you." I heard the voices of both in the arbor. I saw both
through the sparse foliage. They were not aware of my presence.
"You--you alone," she repeated, threw herself on his neck, and clinging
to his breast, she kissed him amid violent sobs. "Come, enough," he
said, while he smoothed her hair gently with his hand.
For a moment I stood motionless. Suddenly I recollected myself. Enter
and join them? For nothing in the world! it shot through my brain. With
hasty steps I gained the wall, leaped it, and reached my dwelling almost
on the run. I laughed, rubbed my hands together, and congratulated
myself on the chance which had so unexpectedly confirmed my suspicion
(whose truth I had not doubted for an instant); but my heart was heavy.
"They dissemble well?" I thought. "And for what purpose? Why do they
wish to amuse themselves at my expense? I would not have thought it of
them!" What a disturbing discovery it was!
* * * * *
I slept ill, and on the following day I rose early, buckled on my
knapsack, and after telling my landlady not to expect me at night, I
turned my steps toward the mountains, following the stream on which the
town of S---- is built. These mountains are very interesting from a
geological point of view; they are particularly remarkable for the
regularity and purity of their basaltic formations; but I was not bent
on geological investigation. I could give no account to myself of my own
feelings. One thing, however, was clear: I had not the least desire to
see the Gagins. I insisted to myself that the only ground of my sudden
distaste for their society lay in vexation at their falseness.
What had been the necessity of calling themselves brother and sister? I
resolutely avoided thinking of them, loitered idly among the hills and
valleys, spent much time in village inns in friendly talk with the
landlord and his guests, or lay on a flat or sunny rock in the lovely
weather, and watched the clouds float over. In this way three days
passed not unpleasantly, though from time to time I had a stifled
feeling at my heart. This quiet nature accorded perfectly with my state
of mind. I gave myself up completely to the chance of the moment and the
impressions that it brought to me; following one another without haste,
they flooded my soul, and left finally a single feeling where everything
which I had seen or heard or experienced during these three days was
blended--everything: the faint resinous smell of the woods, cry and
tapping of the woodpeckers, the continual murmur of the clear brooks
with spotted trout in their sandy shallows, the not too bold outlines of
the mountains, gray rock, the friendly villages with venerable churches
and trees, storks in the meadows, snug mills with wheels merrily
turning, the honest faces of the country people with their blue smocks
and gray stockings, the slow creaking wagons and well-fed horses, or
sometimes a yoke of oxen, long-haired lads strolling along the cleanly
kept paths under apple and pear trees. To this day I remember with
pleasure the impressions of that time. I greet you, little nook of
modest ground, with your modest content, with your signs everywhere
visible of busy hands, of labor constant if not severe--greetings to you
and peace.
At the end of the third day I returned to S----. I have forgotten to say
that in my vexation with the Gagins, I had endeavored to reinstate the
image of my hard-hearted widow. But I remember, as I began to think of
her, I saw before me a little peasant girl, about five years old, out of
whose round little face a pair of great innocent eyes were regarding me
curiously. The look was so childlike, so confiding, a kind of shame
swept over me. I could not continue a lie before that gaze, and at once
and for ever I said good-by to my early flame.
I found a note from Gagin waiting for me. My sudden whim astonished him.
He made me some reproaches that I had not taken him with me, and begged
me to come to him as soon as I should return. Distrustfully I read this
note, yet the following day found me at L----.
* * * * *
Gagin's reception was friendly. He overwhelmed me with affectionate
reproaches; but no sooner had Assja caught sight of me than she broke
into loud laughter, designedly, it seemed, and without the least cause,
and ran away precipitately. Gagin lost his temper, grumbled at her for a
crazy girl, and begged me to excuse her. I must confess that I was very
cross with Assja. I was uncomfortable before, and now this unnatural
laughter and ridiculous behavior must be added. However, I acted as if I
had observed nothing, and detailed to Gagin all the incidents of my
little journey. He told me what he had done during my absence. But the
conversation went lame. Assja kept running in and out. Finally I
declared that I had some pressing work, and that it was time for me to
be at home. Gagin tried to detain me at first, then looking keenly at
me, he begged permission to accompany me. In the hall Assja approached
me suddenly, and held out her hand to me. I gave her fingers an almost
imperceptible pressure, and bade her good-by carelessly. We crossed the
Rhine together, strolled to my favorite oak tree near the little shrine
to the Virgin, and sat down on a bench to enjoy the landscape. There a
remarkable conversation took place between us.
At first we only spoke in the briefest words, then fell into silence and
fixed our eyes on the shining river.
"Tell me," Gagin began suddenly, with his accustomed smile, "what is
your opinion of Assja? She must appear a little singular to you. Not
so?"
"Yes," I answered, not without a certain constraint. I had not expected
him to speak of her.
"One must learn to know her well to form a judgment upon her," he
continued. "She has a very good heart, but a wild head. It is hard to
live quietly with her. However, it is not her fault, and if you knew her
history----"
"Her history!" I interrupted him. "Isn't she then your----" Gagin looked
at me.
"Is it possible that you have doubted that she was my sister? No," he
went on, without heeding my confusion. "She is; at least she is my
father's daughter. Listen to me. I have confidence in you, and I will
tell you all about her.
"My father was a very honest, sensible, cultivated, and unfortunate man.
Fate had no harder blows for him than for others, but he could not bear
the first one that he felt from her. He had married early--a love match;
his wife, my mother, soon died, and I was left a six months' old baby.
My father took me to his country estates, and for twelve whole years he
lived there in absolute seclusion. He himself took charge of my
education, and would never have been separated from me if my uncle, his
brother, had not come to visit us in our country house. This uncle lived
in Petersburg, where he held a rather important post. He persuaded my
father, who could not be induced to quit his home under any
consideration, to trust me to his care. He showed his brother what an
injury it was to a boy of my age to live in such complete isolation, and
that, with a companion always melancholy and silent as my father, I
should inevitably remain behind boys of my age--yes, that my character
might easily be endangered by such a life. For a long time my father
resisted his brother's arguments, but at last he yielded. I cried at
parting from my father, whom I loved, though I had never seen a smile on
his face; but Petersburg once reached, our gloomy and silent nest was
soon forgotten. I went to school, and was afterward placed in a regiment
of the Guards. Every year I spent some weeks at our country house, and
with every year I found my father more melancholy, more reserved, and
depressed to an alarming degree. He went to church daily, and had almost
given up speech. On one of my visits--I was then in my twentieth year--I
saw for the first time about the house a little lean, black-eyed girl,
who might have been about ten years old. It was Assja. My father said
she was an orphan whose care he had undertaken: those were his own
words. I gave her no further attention. She was as wild, quick, and shy
as a little animal, and if I entered my father's favorite room, a great
dismal chamber in which my mother had died, and which had to be lighted
even by day, she always slunk out of sight behind my father's
old-fashioned easy chair, or hid behind the bookcase. It happened that
for the three or four years following I was prevented by my service from
visiting our estate. Every month I received a short letter from my
father, in which Assja was spoken of seldom and always incidentally. My
father was already past his fiftieth year, but looked still a young man.
Imagine my distress then when I suddenly received a perfectly unexpected
letter from our steward, announcing the fatal illness of my father, and
begging me urgently to come home as quickly as possible if I wished to
see him alive. I rushed headlong home, and found my father, though in
the last agony. My presence seemed the greatest joy to him; he clasped
me in his wasted arms, turned on me his gaze half doubtful, half
imploring, and after he had obtained from me a promise that I would
carry out his last wishes, he ordered his old servant to fetch Assja.
The old man brought her. She could hardly support herself on her feet,
and was trembling in every limb.
"'Now take her,' said my father to me with earnestness. 'I bequeathe to
you my daughter, your sister. You will hear everything from Jacob,' he
added, while he pointed to his valet.
"Assja burst out sobbing, and threw herself on the bed. Half an hour
afterward my father was dead.
"I learned the following story: Assja was the daughter of my father and
a former waiting maid of my mother's, named Tatiana. She rose distinct
to my remembrance, this Tatiana, with her tall, slender figure, her
serious face, regular features, her dark and earnest eyes. She had the
reputation of a proud, unapproachable girl. As nearly as I could learn
from Jacob's reserved and respectful story, my father had entered into
close relations with her some years after my mother's death. At that
time Tatiana was not in her master's house, but living with a married
sister, the dairywoman, in a separate hut. My father became very much
attached to her, and wished to marry her after my departure, but she
herself refused this in spite of his entreaties.
"'The departed Tatiana Vlassievna'--so Jacob told me, standing against
the door, with his hands crossed behind his back--'was in all things
very thoughtful, and would not lower your father. "A fine wife I should
be for you--a real lady wife!" she said to him--in my presence she has
said it.' Tatiana never would come back to the house, but remained,
together with Assja, living with her sister as before. As a child I had
often seen Tatiana at church on saint days. She stood among the
servants, usually near a window. She wore a dark cloth wound about her
head and a yellow shawl on her shoulders--the strong outline of her face
clear against the transparent pane; and she prayed silently and humbly,
bowing very low after the old fashion. When my uncle took me away Assja
was just two; when she lost her mother, just nine years old.
"Immediately after Tatiana's death my father took Assja home to himself.
He had already expressed a wish to have her with him, but Tatiana had
refused it. You can imagine what Assja must have felt when she was taken
into the master's house. To this day she has not forgotten the hour when
for the first time they dressed her in a silk dress and kissed her
little hand. In her mother's lifetime she had been brought up with great
strictness: my father left her without a single restraint. He was her
instructor; except him, she saw no one. He did not spoil her; at least
he did not follow her about like a nursemaid, but he loved her fondly,
and refused her nothing. He was conscious of guilt toward her. Assja
soon discovered that she was the principal person in the household. She
knew the master was her father, but at the same time she began to
understand her equivocal position. Wilfulness and distrust were
developed to an extreme degree in her. Bad manners were contracted;
simplicity vanished. She wished (she herself told me) to compel the
whole world to forget her origin. She was ashamed of her mother, was
ashamed of being ashamed, and was in turn proud of her. You see that she
knew and knows still many things that should not be known at her age.
But does the blame rest with her? Youth was strong in her: her blood
flowed hot, and no hand near to guide her--the fullest independence in
everything! Is such a fate easily borne? She would not be inferior to
other girls. She rushed headlong into study. But what good could result
from it? The life, lawlessly begun, seemed likely to develop lawlessly.
But the heart remained true and the reason sound.
"And so I found myself, a young fellow of twenty, weighted with the care
of a thirteen-year old girl! In the first days after my father's death
my voice caused her a feeling of feverish horror, my caresses made her
sad, and only by degrees and after a long time did she become accustomed
to me. And later, when she had gained security that I really considered
her my sister, and that I loved her as a sister, she attached herself
passionately to me: with her there is no half feeling.
"I brought her to Petersburg. Hard as it was to leave her--I could not
live with her in any case--I placed her at one of the best
boarding-schools. Assja agreed to the necessity of our separation, but
it cost her a sickness which came near to being a fatal one. Little by
little she reconciled herself, and she staid four years in this
establishment. But contrary to my expectations, she remained almost her
old self. The principal of the school often complained to me. 'I cannot
punish her,' she would say; 'and I can do nothing by kindness.' Assja
comprehended everything with great quickness, learned
wonderfully--better than all; but it was utterly impossible to bring her
under the common rule. She rebelled; was sulky. I could not blame her
much. In her position she must keep herself at the service of every one,
or avoid every one. Only one of all her companions was intimate with
her--an insignificant, silent, and poor girl. The other young girls with
whom she was associated, of good families for the most part, did not
like her, and taunted and jibed her whenever they could find
opportunity. Assja was not behind them by a hair's breadth. Once, in the
hour for religious instruction, the teacher came to speak of the idea of
vice. 'Sycophancy and cowardice,' said Assja aloud, 'are the meanest
vices.' In a word, she continued to walk in her own way, only her
manners improved somewhat; but even in this respect, I fancy, she has
made no wonderful advance.
"She had reached her seventeenth year. It was useless to keep her longer
at school. I found myself in great perplexity. All of a sudden a happy
thought struck me: to quit the service, and to travel with Assja for a
year or two. Done as soon as thought. So here are we both now on the
banks of the Rhine: I occupied in learning to paint, she following out
her whims in her usual way. But now I must hope that you will not pass
too harsh judgment upon her; for however much she may insist that
everything is indifferent to her, she does care very much for the
opinion of others, and especially for your own."
And Gagin smiled again his gentle smile. I wrung his hand.
"That is how it stands now," Gagin continued. "But I have my hands full
with her. A real firebrand, that girl! Up to this time no one has ever
pleased her; but alas if ever she falls in love! At times I do not know
what to do with her. Lately she took it into her head to declare that I
was growing cold to her, but that she loved only me, and would love only
me her life long. And how she sobbed!"
"So that was it," I said to myself, and bit my lip. "But tell me," I
asked Gagin, "now that our hearts are open, has really no one ever
caught her fancy? Surely she must have seen many young men in
Petersburg?"
"And they are all absolutely distasteful to her. No. Assja is seeking a
hero--an entirely extraordinary man, or else an artistic shepherd among
his flock. But enough of this gossip. I am detaining you," he added as
he rose.
"Come," I said, "let us go back. I don't care to go home."
"And your work?"
I made no reply. Gagin laughed good-naturedly, and we returned to L----.
As the well-known vineyard and the little white house on the hillside
came in sight, my heart was warmed in a curious way--yes, that was
it--warmed and soothed as if, unknown to me, some one had poured some
healing drops there. Gagin's story had made me cheerful.
Assja met us at the threshold. I had expected to find her still
laughing, but she stepped forward to us, pale, silent, and with eyes
down cast.
"Here he is again," Gagin said to her, "and be sure of this: it was his
own wish to come back."
Assja looked at me inquiringly. I held out my hand to her, and this time
I grasped tightly her cold and slender fingers. I felt deep pity for
her. Now I understood much that had before disturbed me in her: her
inner restlessness, her offensive manner, her endeavor to show herself
other than she was--all was clear to me. I had had a glimpse into this
soul. A constant weight oppressed it. Fearfully the untrained will
fought and struggled, yet her whole being was striving after truth. Now
I understood why this singular girl had attracted me: it was not only
the charm which invested her whole body; it was her soul which drew me.
Gagin began to fumble among his sketches. I asked Assja to come for a
walk with me through the vineyard. She gave a ready, almost humble
assent. We climbed the hill about half way, and stopped on a broad
plateau.
"And you felt no _ennui_ without us?" Assja began.
"Did you, then, feel any in my absence?" I asked.
Assja looked at me sideways.
"Yes," she replied. "Is it pleasant in the mountains?" she immediately
continued. "Are they high? Higher than the clouds? Tell me what you have
seen. You have told my brother, but I have heard nothing about it."
"Why did you go away?" I interrupted her.
"I went--because---- Now I will not go away," she added in a gentle,
confiding tone. "You were cross today."
"I?"
"You."
"But why? I beg you----"
"I don't know; but you were cross, and went away cross. It was very
unpleasant to me to have you go away in that manner, and I am glad that
you have come back."
"I am equally glad," I replied.
Assja moved her shoulders slightly, one after the other, as children do
when they are in good humor.
"Oh, I am famous at guessing," she went on. "Long ago my father had only
to cough, and I knew instantly whether he was pleased with me or not."
Till this time Assja had never spoken to me of her father. That struck
me.
"You loved your father very much?" I asked, and I felt to my great
annoyance that I was blushing.
She did not answer, but she also blushed. We were both silent. In the
distance a steamboat with its trailing smoke was descending the Rhine:
our looks followed it.
"Why do you not tell me something?" Assja said half aloud.
"Why did you laugh to-day when you saw me coming?" I asked her.
"I do not know myself. Sometimes I want to cry, and yet must laugh. You
must not judge me by what I do. Ah, by the way, what a wonderful story
it is about the Lorelei. Isn't it her rock that we see yonder? They say
that at first she drew every one else beneath the water, but after she
was acquainted with love, she cast herself in. The story pleases me.
Frau Luise tells me all sorts of fairy stories. Frau Luise has a black
cat with yellow eyes----"
Assja raised her head and threw back her hair.
"Ah, how comfortable I feel!" she said.
At this moment broken, monotonous tones fell on our ears. Hundreds of
voices in unison repeated a hymn with measured pauses. A troop of
pilgrims was moving along the way beneath us with flags and crosses.
"I would like to go with them!" cried Assja, while she listened to the
sound of the voices, gradually dying away.
"Are you so devout?"
"I would like to go somewhere far off, to pray, to accomplish something
difficult," she added. "The days hurry by, life will come to an end, and
what have we done?"
"You are ambitious," I said. "You do not wish to live in vain. You would
like to leave behind some trace of your existence."
"Would it be impossible?"
"Impossible," I had nearly repeated. I looked into her clear eyes and
only said:
"Well, try it."
"Tell me," Assja began after a little silence, while flying shadows
followed each other across her face, which had grown pale again--"did
that lady please you very much? You remember, my brother drank to your
health once, in the ruins; it was the day after we had made
acquaintance."
I laughed aloud.
"It was a jest of your brother's; no lady has pleased me, at least no
one now pleases me."
"What is it that pleases you in women?" asked Assja, tossing back her
head in childish curiosity.
"What a singular question!" I exclaimed.
Assja was a little disturbed.
"I should not have asked the question--not so? Forgive me. I am used to
chatter about everything that goes through my head. That is why I am
afraid to talk."
"Only talk, for heaven's sake! Don't be afraid," I broke in. "I am so
glad that at last you cease to be shy." Assja lowered her eyes and
laughed; a still, gentle laughter that I did not recognize as hers.
"Well, tell me something then," she said, while she smoothed her dress
and tucked it about her feet as if disposing herself to sit for a long
while--"tell me something, or read something aloud, as that time when
you read to us out of 'Onegin.'"
She grew suddenly thoughtful.
Where now in green boughs' shadow
The cross rests on my mother's grave--
she said to herself in a low voice.
"In Pushkin the verse is somewhat different," I ventured.[J]
[Footnote J: In Pushkin it reads, "On my nurse's grave."]
"I would have liked to be Pushkin's Tatiana," she continued, still lost
in thought. "Tell me something," she cried suddenly, with vivacity.
But I could find nothing to say. I looked at her as she sat there,
gentle and peaceful, surrounded with the clear sunshine. Everything
about us glowed with happiness; the sky, the earth, the water. It seemed
as if the very air was bathed in a splendor.
"Look, how beautiful!" I said, involuntarily lowering my voice.
"Yes, beautiful," she answered as gently, without looking at me. "If we
were both birds, we would fly high up there--would soar. We would sink
deep into that blue. But we are no birds."
"We may have wings though," I answered.
"How?"
"In time you will discover. There are feelings that swing us off from
the earth. Don't fear; you will have wings."
"Have you had them then?"
"How shall I say? I believe that I have never flown till now."
Assja fell again into thought. I bent toward her a little.
"Can you waltz?" she asked unexpectedly.
"Yes, I can," I answered, somewhat surprised.
"Then come, come--I will ask my brother to play a waltz for us--we will
imagine that we are flying, that our wings have grown."
She ran to the house. I hastened after her, and in a few moments we were
whirling round the narrow room to the music of a charming waltz. Assja
danced exceedingly well, with lightness and skill. Something soft and
feminine came suddenly into her childish, earnest face. For a long time
afterward my hand felt the contact of her delicate form, for a long time
I seemed to feel her close, quickened breathing, and to see before me
the dark, fixed, half-closed eyes, and the animated pale face with its
wreathing hair.
* * * * *
This whole day passed so that one could not have wished it better. We
were merry as children. Assja was very lovable and natural. It was a
pleasure for Gagin to see her. It was late when I went away. In the
middle of the Rhine I told the ferryman to leave the boat to the
current. The old man drew in his oars and the majestic stream bore us
onward. While I looked about me and listened, and called forgotten
things to memory, I felt a sense of unrest in my heart. I turned my eyes
to the heavens, but in the heavens was no rest; with its glittering host
of stars it was in steady motion, revolving, trembling. I bent to the
river, but there also in the dark, cool depths the stars were dancing
and flickering; everywhere the restless spirit of life met me, and the
restlessness in my own heart grew stronger. I leaned over the side of
the boat. The murmuring of the breeze in my ears, the low splash of the
water against the stern of the boat, excited me, and the freshness of
the waves did not cool me. Somewhere on the shore a nightingale began
her song, and this music worked upon me like a sweet poison. Tears
filled my eyes, but not the tears of an indefinite rapture. What I
experienced was not the vague feeling of boundless longing in which it
seems as if the heart could embrace everything: no. In me arose a
burning desire for happiness. Only as yet I did not dare call this
happiness by its real name. But bliss--bliss to overflowing was what I
longed for. The boat drifted further and further, and the old ferryman
sat bowed over his oars and fast asleep.
* * * * *
On my way to the Gagins the following day I did not ask myself if I was
in love with Assja, but I thought of her continually; her destiny
absorbed me, and I rejoiced over our unhoped-for meeting. I felt that I
had known her only since yesterday. Until then she had always avoided
me. And now that she had finally admitted me to her friendship, in what
a bewitching light did her image appear to me; what a mysterious charm
streamed from it to me.
Hastily I sprang up the well-known path, straining my eyes for a glimpse
of the little white house in the distance. I did not think of the
future; I did not think even of the morrow; but my heart was light in
me.
Assja blushed as I entered the room. I observed that she had again
dressed herself with great care, but the expression of her face did not
correspond with her finery; it was melancholy. And I had come so happily
disposed! I believe that she was inclined to run away in her usual
fashion, but forcibly compelled herself to remain. I found Gagin in that
peculiar mood of artistic enthusiasm which catches dilettanti by
surprise whenever they imagine themselves about to take nature by storm,
as they express it. He stood with hair disordered, and bedaubed with
paint, before a fresh canvas, drawing madly. Furiously he nodded to me,
stepped backward, half closed his eyes, and then precipitated himself
again upon his work. I did not like to disturb him, and sat down beside
Assja. Slowly her dark eyes turned on me.
"You are not as you were yesterday," I ventured, after I had made some
vain attempts to bring a smile to her lips.
"No, I am not," she replied, with a slow, suppressed voice. "But that is
nothing. I did not sleep well. I was thinking the whole night."
"About what?"
"Oh, I thought about many things. It has been my habit from childhood,
even when I was living with my mother."
She spoke this with a certain emphasis, and repeated it.
"When I was living with my mother I--I wondered why no one can know
beforehand what is to happen to him. Sometimes one sees a misfortune
coming, and yet cannot turn away from it; and why cannot one always say
boldly the truth? Then I thought that I do not know anything, and that I
must learn. I must be educated over again. I have been very badly
brought up. I do not know how to play the piano, I cannot draw, I sew
dreadfully; I have no capacity; I must be very tiresome."
"You are unjust to yourself," I answered. "You have read much, you are
cultivated, and with your intellect----"
"Have I an intellect?" she asked with such naive curiosity that I could
not help laughing. She did not laugh.
"Brother, have I an intellect?" she asked Gagin.
He made her no answer, but continued his work, busily laying on his
colors, and with one arm flourished in the air.
"Sometimes I hardly know myself what goes through my head," Assja went
on with the same thoughtful expression. "At certain times I am actually
afraid of myself. Ah, I wish---- Is it really true that women ought not
to read much?"
"It is not necessary that they should read much, but----"
"Will you tell me what to read? Will you tell me what to do? I will do
everything that you tell me," she said, turning to me with an innocent
confidence.
I did not readily find any answer to make.
"The time with me will not seem long to you?"
"How can you think so!" I said.
"Well, I thank you," cried Assja, "but I thought you might be _ennuye_."
And her little hot hand grasped
mine tightly.
"N.!" cried Gagin at this moment, "isn't this background too dark?"
I went over to him. Assja rose and left the room.
* * * * *
An hour afterward she returned, stood in the doorway, and beckoned to
me.
"Listen," she said. "Would you be sorry if I died?"
"What ideas you have to-day!" I exclaimed.
"I imagine that I shall die soon. Sometimes it seems to me as if
everything about me was taking leave of me. It is better to die than to
live as---- Ah, don't look at me so. Indeed I am not a hypocrite. I
shall be afraid of you again."
"Have you ever been afraid of me?"
"If I am unlike other people, the fault is not mine," she answered.
"Already, you see, I cannot laugh any more."
She was melancholy and depressed until evening. Something was passing in
her that I could not understand. Her eyes often rested on me, and every
time they did so I felt my heart chilled by their strange expression.
She was quiet--and yet whenever I looked at her it seemed to me that I
must beg her to be calm. Her appearance fascinated me; I found the
greatest charm in her pale features, in her slow, aimless movements; but
she fancied--I do not know why--that I was in ill humor.
"Listen," she said to me a little while before my departure. "The
thought haunts me that you think me frivolous. In future you must
believe everything that I tell you, and you must be frank with me. I
will always tell you the truth, I give you my word of honor."
This "word of honor" made me laugh.
"Oh, do not laugh," she broke in with eagerness, "or else I must say to
you to-day what you said to me yesterday: 'Why do you laugh so much?'"
And after a short silence she continued: "Do you remember, yesterday we
were talking of wings? My wings are grown--but where shall I fly?"
"What are you saying!" I replied. "To you all ways are open."
Assja looked in my eyes long and keenly.
"You have a bad opinion of me today," she said, and drew her eyebrows
together.
"I have a bad opinion? Of you!"
"What is the matter with you two to-day?" Gagin interrupted me. "Shall I
play a waltz for you as I did yesterday?"
"No, no," exclaimed Assja, clasping her hands together--"not for the
world to-day."
"I won't insist--be easy."
"Not for the world," she repeated, and her cheeks grew pale.
* * * * *
Does she love me? I thought, as I came to the Rhine, whose waves rolled
swiftly by.
Does she love me? I asked myself when I awoke the next morning. I did
not wish to look into my own heart. I felt that her image--the image of
the "girl with the bold laugh"--had impressed itself upon my soul, and
that I could not easily get rid of it. I went to L---- and remained there
the whole day; but I had only one glimpse of Assja. She was not well;
her head ached. She came down stairs for a few moments with her head
bound up, her eyes half closed, pale and weak; she smiled feebly, said,
"It will pass; it is nothing; everything passes, does it not?" and went
away. I was depressed and had a painful sense of blankness, but I would
not go home till very late, without, however, seeing her again.
I spent the next day like a man walking in his sleep. I tried to work,
but could not; then I tried to be absolutely idle, and to think of
nothing; but neither did that succeed. I strolled about the town,
returned home, and went out again.
"Are you Mr. N.?" said suddenly the voice of a child behind me. I
turned. A little boy was standing before me. "From Miss Annette," and
handed me a note.
I opened it, and recognized Assja's irregular and scrawling handwriting.
"I must see you," she wrote. "Come to-day at four o'clock to the stone
chapel on the way to the ruins. Something unexpected has happened. For
heaven's sake, come. You shall know everything. Say to the bearer,
'yes.'"
"Any answer?" the boy asked me.
"Say 'yes,'" I replied. The boy ran off.
* * * * *
When I had reached my room I sat down and fell into deep thought. My
heart beat forcibly. I read Assja's note several times over. I looked at
the clock; it was not yet midday.
The door opened: Gagin walked in.
His face was gloomy. He seized my hand and shook it warmly. Apparently
he was very much excited.
"What is the matter?" I asked him.
Gagin took a chair and drew it near mine. "Four days ago," he began with
a forced smile, and stammering a little, "I amazed you with a
confidence; and to-day I shall amaze you even more. With any other I
probably should not--so plainly. But you are a man of honor; you're my
friend, are you not? Well, here then; my sister Assja loves you."
I started up from my chair.
"You say--your sister----"
"Yes, yes," Gagin interrupted me. "I tell you she has lost her senses
and will make me lose mine, moreover. Happily she is not used to lying
and has great trust in me. Oh, what a soul the girl has! But she will
surely do herself a mischief."
"You must be mistaken," I said.
"No, I'm not. Yesterday, you know, she staid in bed nearly all day; she
ate nothing: to be sure she complained of nothing. She never complains.
I was not uneasy, although toward evening she grew feverish. But at two
o'clock this morning our landlady roused me. 'Come to your sister,' said
she. 'There is something wrong with her.' I hastened to Assja, and found
her not yet undressed, very feverish, in tears: her head was burning
hot, her teeth chattered. 'What's the matter?' I asked. 'Are you sick?'
She threw herself upon my neck, and insisted that I should take her away
from there as speedily as possible if I wished her to remain alive. I
could make nothing of it--tried to pacify her. Her sobs increased, and
suddenly among her sobs I heard--well, in one word, I discovered that
she loves you. I assure you, neither of us, being reasonable men, can
have the smallest idea of the impetuosity of her feelings and the
incredible violence with which she expresses them; it is as sudden and
as inevitable as a thunder storm. You are a delightful fellow," Gagin
continued, "But I must confess that I do not see why she has fallen in
love with you. She believes that she has loved you from the first moment
she saw you. She was crying lately on that account, even when she was
declaring that she loved nobody but me. She imagines that you despise
her; she fancies that you know her origin. She asked me if I had told
you the story of her life. I naturally denied it, but it is astonishing
how keen she is. She wishes only one thing: to go away: immediately
away. I staid with her till morning. She wrung a promise from me that we
would leave here to-morrow, and then at last she fell asleep. I thought
it over and over, and decided--to talk with you. Assja is right, in my
opinion. It is best that we should both leave this place. I should have
taken her away to-day if an idea that has got into my head didn't
prevent it. Perhaps--who can tell?--my sister pleases you? If this
should be the case, why should I take her away? So I determined to put
shame aside. Besides, I have myself noticed--so I decided--from your own
mouth to learn----" Poor Gagin became hopelessly confused. "Pray excuse
me," he added. "I am inexperienced in such matters."
I seized his hand.
"You wish to know whether your sister pleases me? Yes, she pleases me,"
I said in a steady voice. Gagin looked at me.
"But," he said with an effort, "you don't want to marry her?"
"How can I answer such a question? Think, yourself, how could I at this
moment----"
"I know, I know," Gagin interrupted me. "I have not the least right to
expect an answer from you, and my question was improper--to the last
degree. But what was I to do? One cannot play with fire. You do not know
Assja. It would be possible for her to drown herself--to run away, to
seek an interview with you. Any other girl would know how to conceal
everything and to wait opportunities--but not she. This is her first
experience. That is the worst of it! If you had seen her as she lay
sobbing at my feet, you would share my anxiety."
I became thoughtful. Gagin's expression, "seek an interview with you,"
sank into my heart. It seemed abominable not to answer his confidence
with confidence as free.
"Yes," I said at last. "You are right. An hour ago I received a note
from your sister. Here it is."
Gagin took the note, read it hurriedly, and let his hands fall on his
knees. The expression of his features was ludicrous enough, but I was in
no mood for laughter.
"You're a man of honor. I repeat it," he said. "But what is to be done
now? What! She wishes to hurry away from here, yet she writes to you and
reproaches herself for her own want of foresight. And when can she have
written this? What does she want of you?"
I succeeded in calming him, and we began to talk, as coolly as we could,
about what we might have to do.
At last we decided as follows: To guard against any desperate step on
her part, I was to meet Assja at the appointed place, and have a fair
explanation with her. Gagin pledged himself to remain at home and to
avoid all appearance of knowing about the note. In the evening we agreed
to meet again. "I have full confidence in you," said Gagin, and pressed
my hand strongly. "Spare Assja and myself. But we shall leave
to-morrow," he added as he rose, "for you will not marry Assja."
"Give me time till evening," I said.
"So be it. But you will not marry her."
He went away. I threw myself on the sofa and shut my eyes. My head spun
round like a top. Too many emotions came crowding upon me. Gagin's
frankness annoyed me, and I was angry with Assja. Her love distressed
and delighted me at once. I could not understand how she could betray
herself to her brother. The necessity of a hasty, an instantaneous
decision tormented me. "Marry a seventeen-year-old girl of such a
disposition! How can I do it?" I said, getting up from my seat.
* * * * *
I crossed the Rhine at the appointed hour, and the first face that met
me on the opposite shore was that of the same boy who had come to me in
the morning. He seemed to be waiting for me.
"From Miss Annette," he said, and gave me another letter. Assja wrote to
appoint another place for our meeting. In half an hour I was to come,
not to the chapel, but to the house of Frau Luise, knock at the door,
and ascend to the third story.
"'Yes' again?" the boy asked me.
"Yes," I answered, and walked along the bank of the river. There was not
time to return to my house, and I had no inclination to stroll about the
streets. Just beyond the limits of the village there was a little garden
with a covered bowling alley and tables for beer drinkers. I entered it.
A few middle-aged men were playing ninepins. The balls rolled noisily,
and from time to time I caught expressions of applause. A pretty girl,
with eyelids reddened by crying, brought me a glass of beer. I looked
her in the face. She turned hastily away and disappeared.
"Yes, yes," said a fat and ruddy-cheeked man who was sitting near me.
"Our little Nancy is in great trouble to-day. Her lover is gone with the
conscripts." I looked after her. She had retired to a corner and buried
her face in her hands. One after another the tears trickled through her
fingers. Some one called for beer. She brought it, and went back to her
place. Her grief reacted upon me. I began to think of the interview
before me; but I thought of it with anxiety, not with joy. I did not go
light-hearted to the rendezvous. No joyful exchange of mutual love was
before me; I had a promise to redeem, a hard duty to perform. "There is
no jesting possible with her"--this expression of Gagin's pierced my
soul like an arrow. And was not this the very happiness for which I had
longed four days ago, in the little boat which the waves bore onward?
Now it seemed to be possible--but I wavered, I thrust it from me; I must
put it away from me. The very unexpectedness of it confused me. Assja
herself, with her impetuosity, her past history, her education--this
charming but singular being--let me confess it--inspired me with fear.
For a long time I gave myself up to these conflicting feelings. The
deferred tryst was at hand. "I cannot marry her," I decided at last,
"and she shall not know that I love her."
I rose, and after I had pressed a thaler in poor Nancy's hand (for which
she did not even thank me) I went straight to Frau Luise's house.
Already the shadow of dusk was in the air, and above the darkening
streets a narrow streak, the reflection of the sunset, reddened in the
sky. I knocked lightly at the door. It was opened instantly. I stepped
across the threshold and found myself suddenly in darkness.
"This way!" whispered an old woman's voice. "Some one is waiting for
you."
I advanced a couple of steps, stumbling. A skinny hand clutched mine.
"Is it you, Frau Luise?" I asked.
"Yes," the same voice answered. "Yes, it is I, my handsome young
gentleman." The old woman led me up one steep staircase and stopped at
the bottom of a second. By the dull light which came in through a little
window I recognized the wrinkled visage of the burgomaster's widow. A
hateful, sly smile distorted her shrunken lips and half closed the
little bleared eyes. She pointed out a small door to me. I opened it
with a hand that trembled, and shut it again behind me.
* * * * *
It was nearly dark in the little room which I entered, and at first I
did not discover Assja. Wrapped in a great cloak, she was sitting in a
chair by the window, with her head averted and almost hidden, like a
frightened bird. Her breath came quickly, and she was trembling in every
limb. I felt an inexpressible pity for her. I approached her; she turned
her head away still more.
"Anna Nicolaevna!" I addressed her.
She started suddenly as if she wished to look at me, but dared not. I
took her hand. It was cold, and lay in mine like a dead thing.
"I wished," Assja began, and tried to smile, but her pallid lips would
not obey her--"I wanted--no, I cannot," she said, and was silent. And in
truth her voice broke at every word.
I sat down beside her.
"Anna Nicolaevna!" I repeated, and again found nothing further to say.
There was a silence. I still held her hand and looked at her. She was in
the same constrained attitude as before: breathed heavily, and bit her
under lip in order to keep back her tears. My eyes were fixed on her.
There was something touchingly helpless in her shy immobility. It seemed
as if she had just been able to reach the chair, and had fallen there.
My heart overflowed.
"Assja!" I whispered, almost inaudibly.
Slowly she raised her eyes to mine. Oh, the glance of a woman who loves!
Who shall describe it? Her eyes expressed entreaty, trust, questioning,
surrender. I could not withstand their magic. A burning fire thrilled me
like the prick of red-hot needles. I bent down and pressed my lips to
her hand.
A little hurried sound as of a broken sob fell on my ear, and I felt on
my hair the tender touch of a hand that trembled like a leaf. I raised
my head, and looked in her face. The expression of fear was gone from
her features. Her glance swept past me into the room. Her lips were a
little apart, her forehead white as marble, and the hair pushed off as
if the wind had blown it back. I forgot everything; I drew her toward
me; willingly her hand obeyed, and her whole body followed; the shawl
slipped from her shoulders, and her head bowed silently to my breast and
laid itself against my burning lips.
"Yours!" she whispered faintly.
Already my arm was about her, when suddenly, like a gleam of lightning,
the thought of Gagin flashed through my brain. "What are we doing?" I
cried, and moved roughly away. "Your brother knows all--he knows that we
are here together."
Assja sank into her chair.
"Yes," I went on, while I rose and went over to the other side of the
room. "Your brother knows everything. I had to tell him everything."
"You had to?" she stammered unintelligibly. She could not come to
herself, and only half comprehended me.
"Yes, yes," I repeated with a certain bitterness, "and you are to blame
for it--you alone. Why did you betray your secret? Who compelled you to
tell your brother? He himself was with me to-day, and told me of your
conversation with him."
I avoided looking at Assja, and went up and down the room with great
strides. "Now everything is lost--everything, everything."
Assja was about to get up from her chair.
"Oh, sit still," I cried; "sit still, I beg you. You have to do with a
man of honor--yes, with a man of honor. But in Heaven's name what
disturbed you so? Have you seen any change in me? But it was impossible
for me to conceal it from your brother when he made me a visit to-day."
"What am I saying?" I thought to myself, and the idea that I should be a
base hypocrite, that Gagin knew of this meeting, that everything had
been talked over, twisted and spoiled, maddened me.
"I did not call my brother," Assja said, in a frightened, harsh voice.
"He came of his own will."
"Only see what you have done," I went on. "Now you want to go away."
"Yes, I must go," she said in a whisper, "and I only asked you to come
here that I might take leave of you."
"And do you think," I retorted, "that it is easy for me to part from
you?"
"Why were you obliged to tell my brother?" repeated Assja with an
expression of amazement.
"I tell you, I could not do otherwise. If you had not betrayed
yourself----"
"I had locked myself into my chamber," she answered simply. "I did not
know that my landlady had another key."
This innocent speech from her mouth at such a moment nearly cost me my
self-control. Even now I cannot think of it without emotion. Poor,
honest, innocent child!
"And so it is all over," I began again. "All. Now indeed we must part."
I threw a stolen glance at Assja, whose face became more and scarlet.
She was, I felt, alarmed and ashamed. I myself was greatly agitated, and
spoke like one in a fever. "You did not leave the budding feeling time
to unfold itself. You yourself have torn the bond between us. You had no
confidence in me; you cherished suspicion against me."
While I was speaking Assja bent forward more and more, then sank
suddenly on her knees, let her head fall into her hands, and broke into
sobs. I rushed to her and tried to raise her, but she resisted me. I
cannot endure women's tears; when I see them I lose my self-possession
at once.
"Anna Nicolaevna, Assja!" I cried repeatedly. "I beg, I implore you!
Stop, for God's sake!" I took her hand again.
But to my extremest astonishment she sprang up suddenly, sped like a
flash through the door, and vanished.
When Frau Luise came in a few moments later, I still stood in the middle
of the chamber as if thunderstruck. I could not believe that the
interview had come to an end so abrupt, so unmeaning, when I myself had
not said the hundredth part of what I meant to say, and was, besides,
quite uncertain how it should finally terminate.
"Is the young lady gone?" Frau Luise asked me, and raised her yellow
eyebrows quite to the parting of her hair.
I stared at her like an idiot, and went away.
* * * * *
I left the village and made my way into the fields. Vexation, the
keenest vexation possessed me. I overwhelmed myself with reproaches. How
had it been possible for me to misunderstand the reason which had
induced Assja to change our place of meeting? How could I have failed to
know what it must have cost her to go to the old woman? Why had I not
detained her! Alone with her in the dim, empty room I had found the
strength, I had had the heart to drive her from me--even to reproach her
for coming. Now her image followed me; I besought her pardon. The memory
of that pale face, those shy, wet eyes, that hair flowing over the bowed
back, the soft nestling of her head against my breast, consumed me like
a fire. "Yours!" Her whisper still rang in my ears. "I have acted
conscientiously," I tried to say to myself. Lies! What was the
conclusion I truly wished? Am I in a condition to part with her? Can I
lose her? "O fool! fool!" I repeated with bitterness.
By this time the night had fallen. With hasty steps I sought the house
where Assja lived.
* * * * *
Gagin came to meet me.
"Have you seen my sister?" he called to me, still at a distance.
"Isn't she at home then?" I returned.
"No."
"She has not come back?"
"No. Excuse me," Gagin went on. "I could not stand it. I went to the
chapel in spite of our agreement; she was not there; she cannot have
gone there."
"She did not go to the chapel."
"And you have not seen her?"
I had to acknowledge that I had seen her.
"Where?"
"At Frau Luise's. We separated an hour ago," I added. "I believed
certainly that she had come home."
"Let us wait," said Gagin.
We entered the house and sat down near each other. We were silent.
Neither of us was without anxiety. We watched the door and listened. At
last Gagin rose.
"This is the end of everything," he cried. "I don't know if my heart is
in my body. She will kill me yet, by God! Come, let us search for her."
We went out. It had grown dark.
"Of what did you talk with her?" asked Gagin as he crushed his hat down
over his eyes.
"I was with her five minutes at longest," I answered. "I spoke to her as
we had decided."
"Well," he said, "we would better go, each for himself; in that way we
shall find her sooner. In any event, come back here in an hour."
* * * * *
Hastily I descended the hill and ran to the town. I made my way rapidly
through all the streets, staring in all directions, took another glance
at the windows of Frau Luise's house, reached the Rhine, and began to
walk quickly along its bank. From time to time I met women, but Assja
was nowhere to be seen. It was no longer vexation that I felt. A secret
fear oppressed me, and not fear alone; no, remorse, the warmest pity.
Love! yes, tenderest love! Wringing my hands, I called on Assja, into
the gathering darkness of the night; softly at first, then louder and
louder; a hundred times I repeated that I loved her. I swore never to
part from her. I would have given everything in the world to hear her
gentle voice again, to hold her cold hand, to see herself standing
before me. So near had she been to me, in perfect trustfulness, in utter
simplicity of heart and feeling had she come to me and laid her
inexperienced youth in my hands; and I had not caught her to my heart; I
had thrown away the bliss of seeing the shy face bloom into a joy, a
rapture of peace--this thought drove me to madness.
"Where can she be gone? What is become of her?" I called out, desperate
with helpless fears. Suddenly something white glimmered near by on the
shore. I knew the spot. An old half sunken cross with quaint inscription
stood there, over the grave of a man drowned seventy years before. My
heart stood still in my body. I ran to the cross. The white figure had
disappeared. "Assja!" I shouted. My wild cry terrified me. No one made
answer.
I determined to see if Gagin had found her.
* * * * *
As I hastened up the footpath I saw a light in Assja's chamber. It
calmed me a little.
I drew near the house. The door was fastened. I knocked. A window in the
darkened first story was carefully raised, and Gagin's head showed
itself.
"Found?" I asked.
"She is come back," he whispered to me. "She is in her chamber, and
undressing. All is as it should be."
"God be thanked!" I cried, in a transport of inexpressible joy. "God be
thanked! Now all will be well. But you know we have something to say to
each other."
"Another time," he answered, softly closing the window--"another time.
For this, good-by."
"Till to-morrow then," I said. "Tomorrow everything will be clear."
"Good-by," Gagin repeated, and the window was shut. I came near to
knocking again. I wished to tell Gagin at once that I sought his
sister's hand. But such a wooing, at such an hour! "Till to-morrow
then," I thought. "To-morrow I shall be happy!"
"To-morrow I shall be happy!" Happiness has no to-morrow; it has no
yesterday; it knows of no past; it thinks of no future. The present
belongs to it, and not even the present day--only the moment.
I do not know how I reached S----. Not my feet brought me; not the boat
carried me; I was borne over as if on broad, mighty wings. My way led me
by a thicket in which a nightingale was singing. It seemed to me it sang
of my love and my joy.
* * * * *
The next morning, as I drew near the familiar little house, one
circumstance seemed strange: all its windows were open, and the door as
well. Scraps of paper lay strewn about the threshold, and behind the
door a maid was visible with her broom.
I stepped up to her.
"They're off!" she volunteered, before I could ask her if the Gagins
were at home.
"Off!" I repeated. "What, gone? Where?"
"They went at six o'clock this morning, and did not say where. But stop.
You are surely Mr. N."
"I am Mr. N."
"There is a letter for you inside." She went in and returned with a
letter. "Here it is, if you please."
"But it isn't possible. How can it be?" I said. The maid stared at me
stupidly, and began to sweep.
I opened the letter. It was Gagin who wrote. From Assja not a line. He
began with a hope that I would not be angry with him on account of his
sudden departure. He felt assured that, after mature thought, I would
agree to his decision. He had found no other way out of a situation
which might easily become difficult, even dangerous. "Yesterday," he
wrote, "as we were both waiting silently for Assja, I convinced myself
fully that a separation was necessary. There are prejudices which I know
how to respect. I understand that you cannot marry Assja. She has told
me everything. For her own sake I am compelled to yield to her repeated,
desperate prayers." In conclusion he expressed his regret that our
acquaintance should be broken off so abruptly; wished me happiness;
shook my hand affectionately; and assured me that it would be useless
for me to try to find them.
"What prejudices?" I cried out, as if he could hear me. "Nonsense! Who
has given him the right to rob me of her?" I clutched my head with my
hands.
The maid began to call loudly for the landlady. Her terror rendered me
my self control. One thought took possession of me--to find them, to
find them at whatever cost. To submit to this stroke, to calmly accept
it, was impossible. I learned from the landlady that they had taken a
steamboat about six o'clock in the morning to go down the Rhine. I went
to the office. There I was told that they had taken tickets for Cologne.
I went home with the intention to pack at once and follow them. My way
led me by Frau Luise's house. All at once I heard some one call me. I
raised my head, and saw the Burgomaster's widow at the window of the
very room where, the day before, I had met Assja. She summoned me with
her disagreeable smile. I turned away, and would have gone on, but she
called after me that something was there for me. This brought me to a
standstill, and I entered the house. How shall I describe my feelings as
I again beheld that little room?
"To tell the truth," the old woman said to me, handing me a little note,
"I was only to give you that if you came here of your own free will. But
you are such a handsome young gentleman. Take it."
I took the letter.
The following words were hastily scrawled in pencil on a scrap of paper:
"Farewell! We shall not see each other any more. It is not from pride
that I go. No; I cannot do anything else. Yesterday, when I was crying
before you, it only needed a word from you--only one single word. I
should have staid. You did not speak it. It must be better so. Farewell,
for always."
* * * * *
One word! Fool that I had been! This word! I had said it with tears over
and over. I had scattered it to the wind. I had repeated it--how
often--to the lonely fields; but to her I had not said it. I had not
told her that I loved her. And now I must never say it. When I met her
in that fatal room, I myself had no clear consciousness of my love.
Perhaps I was not even yet awakened to it while I was sitting with her
brother in helpless and fearful silence. A moment later it broke out
with irresistible force as I shuddered at the possibility of harm to
her, and began to seek her, to call her, but then it was already too
late. "But that is impossible," you say. I do not know whether it is
possible, but I know that it is true. Assja would not have left me if
there had been a trace of coquetry in her, and if her position had not
been a false one. She could not bear that which every other girl could
have borne; but that I had not realized. My evil genius held my
confession back from my lips, as I saw Gagin for the last time, at the
dark window, and the last thread that I might have seized slipped from
my fingers.
On the same day I returned to L---- with my travelling trunk, and took
passage for Cologne. I remember that, as the boat was under way, and I
was taking leave in spirit of the streets and the places I should never
lose from memory, I saw Nancy on the bank. She was sitting on a bench.
Her face was pale, but not sorrowful, and a stalwart young peasant stood
beside her, laughing and talking to her. On the other shore of the river
the little Madonna looked out, sad as ever, from the green shadow of the
old oak tree.
* * * * *
I found myself on the Gagins' track in Cologne. I learned that they had
started for London. Hastily I followed them; but in London all my
inquiries were fruitless. For a long time I would not be discouraged,
for a long time I kept up an obstinate search; but at last I was obliged
to give up hope of finding them.
And I never saw them again; I never saw Assja again. Of her brother I
heard brief news sometimes; but she had for ever vanished from my sight.
I do not know if she is yet living. Once, while travelling, years
afterward, I caught a hasty glimpse of a woman in a railway carriage
whose face reminded me vividly of features never to be forgotten, but I
was deceived by a chance resemblance. Assja remained in my memory as I
had known her in the fairest days of my life, and as I had last seen
her, bowed over the arm of the low wooden chair.
But I will confess that I did not grieve too long for her. Yes, I have
even fancied that Fate had been kind in refusing to unite us. I consoled
myself with the thought that I could not have been happy with such a
wife. I was young, and the future--this short, fleeting life--seemed
endless to me. Why should not that be again which once had been so
sweet, and even better and more beautiful? I have known other women, but
the feeling which Assja awakened in me--that deep and ardent
tenderness--has never repeated itself.
No! No eyes could compensate me for the loss of those that once were
lifted, with such love, to mine. No heart has ever rested on my breast
which could make my own beat with such delicious anguish! Condemned to
the solitary existence of a man without a family tie, I bring my life to
its gloomy end; but I guard still, as a sacred relic, her letters and
the dried geranium sprig which she once tossed me from the window. There
clings a faint fragrance to it even yet; but the hand that gave it, the
hand that it was only once vouchsafed to me to kiss, has mouldered,
perhaps, for many a year in the grave. And I--what has become of me?
What remains to me of myself--of those happy and painful days--of those
winged hopes and desires? So the slight fragrance of a feeble weed
outlasts all the joys and all the sorrows of a man. Nay, it outlasts the
man himself!
TO BEETHOVEN.
Clasped in a too strict calyxing
Lay Music's bud o'er-long unblown,
Till thou, Beethoven, breathed her spring:
Then blushed the perfect rose of tone.
O loving Soul, thy song hath taught
All full-grown passion fast to flee
Where science drives all full-grown thought--
To unity, to unity.
For he whose ear with grave delight
Brings brave revealings from thine art
Oft hears thee calling through the night:
_In Love's large tune all tones have part._
Thy music hushes motherwise,
And motherwise to stillness sings
The slanders told by sickly eyes
On nature's healthy course of things.
It soothes my accusations sour
'Gainst frets that fray the restless soul:
The stain of death; the pain of power;
The lack of love 'twixt part and whole;
The yea-nay of Free-will and Fate,
Whereof both cannot be, yet are;
The praise a poet wins too late
Who starves from earth into a star;
The lies that serve great parties well,
While truths but give their Christs a cross
The loves that send warm souls to hell,
While cold-blood neuters live on loss;
Th' indifferent smile that nature's grace
On Jesus, Judas, pours alike;
Th' indifferent frown on nature's face
When luminous lightnings blindly strike;
The sailor praying on his knees
Along with him that's cursing God--
Whose wives and babes may starve or freeze,
Yet Nature will not stir a clod.
If winds of question blow from out
The large sea-caverns of thy notes,
They do but clear each cloud of doubt
That round a high-path'd purpose floats.
As: why one blind by nature's act
Still feels no law in mercy bend,
No pitfall from his feet retract,
No storm cry out, _Take shelter, friend!_
Or, Can the truth be best for them
That have not stomachs for its strength?
Or, Will the sap in Culture's stem
E'er reach life's furthest fibre-length?
How to know all, save knowingness;
To grasp, yet loosen, feeling's rein;
To sink no manhood in success;
To look with pleasure upon pain;
How, teased by small mixt social claims,
To lose no large simplicity;
How through all clear-seen crimes and shames
To move with manly purity;
How, justly, yet with loving eyes,
Pure art from cleverness to part;
To know the Clever good and wise,
Yet haunt the lonesome heights of Art.
O Psalmist of the weak, the strong,
O Troubadour of love and strife,
Co-Litanist of right and wrong,
Sole Hymner of the whole of life,
I know not how, I care not why,
Thy music brings this broil at ease,
And melts my passion's mortal cry
In satisfying symphonies.
Yea, it forgives me all my sins,
Fits Life to Love like rhyme to rhyme,
And tunes the task each day begins
By the last trumpet-note of Time.
SIDNEY LANIER.
THE DRAMATIC CANONS.
At intervals of varying length, the journals of the Anglo-Saxon races
are given to discussing the question whether the present age be one of
decadence or progress in dramatic art. Most readers of "The Galaxy" have
seen some phases of this discussion, which starts up afresh after the
arrival of every noted foreign actor or the production of a new play. It
is at present confined to the English-speaking nations, and prevails
more in America than England just now.
In France there is no lively interest in the theme. The French dramatic
authors seem to be pretty well satisfied themselves, and to satisfy
their audiences; their best claim to success being found in the fact
that English and American dramatic authors of the present day almost
invariably pilfer from them.
In the course of this perennial discussion we constantly meet with
appeals, on the part of those learned gentlemen, the theatrical critics,
to the "dramatic canons." Such and such a play is said to offend against
these "canons," and they are spoken of as something of which it is
shameful to be ignorant, but at the same time with a vagueness of phrase
betraying a similar vagueness of definition. It has seemed to us that an
inquiry into the nature of these canons may not be out of place at the
present time. This we propose to determine by consulting the practice of
those authors of former times whose productions still hold the stage as
"stock plays," so called, and of those modern authors still living whose
plays are well known and famous, being still successfully acted. By such
an analysis we may possibly settle something, especially if our inquiry
shall call forth the actual experience of those living who have attained
great success, whether as authors or adapters.
The most obvious division of our subject is into tragedy, comedy,
melodrama; but inasmuch as it is plain that the laws of success in all
these walks of dramatic art must contain much in common, we have
preferred a different division for analysis, leaving the kind of drama
as a subdivision common to each part of the inquiry. A less obvious but
equally just division will be as to the canons regulating the subject,
the treatment, and the production of a successful drama, in whatever
walk. We propose to ascertain our canons from the successful plays,
still holding the stage, of Shakespeare, Sheridan, Knowles, Bulwer, Dion
Boucicault, Tom Taylor, Augustin Daly, and Gilbert, together with such
single plays, like "The Honeymoon," "Masks and Faces," and a few others,
as are better known to the public than their authors, whose sole
dramatic successes they were. Ephemeral successes, however great, cannot
be safely taken as guides to a canon; but an established success of long
standing, however repugnant to our tastes, must be examined, even if it
take the form of the "Black Crook."
The influence of the French drama on Anglo-Saxon art has been so decided
that no safe estimates of canons can be made which do not take into
account the works of Sardou, Dumas, and the minor French authors, whose
name is legion. Fortunately for our subject, the French work on simple
principles, and will not confuse us any more than the Greeks, whom they
imitate. Let us try, then, to ascertain our canons in their order,
beginning with the subject of the drama.
What subjects are fit for dramatic treatment, and are there any entirely
unfitted therefor?
We find a pretty wide range in the successful dramas of modern time. In
tragedy we have ancient history, as shown by "Coriolanus," "Julius
Caesar," "Virginius," "Alexander the Great"; medieval history, in
"Macbeth," "Richard III."; legendary stories, in "Lear," "Hamlet,"
"Othello," "Romeo and Juliet." In comedy and melodrama we have an almost
infinite variety, as much so as in novel writing. History, legend, and
pure invention claim equal right in the field. We have "The Tempest,"
"As You Like It," "Much Ado about Nothing," "Twelfth Night," "Henry
IV.," "Henry V.," "Merchant of Venice," "The Wonder," "The Honeymoon,"
"Masks and Faces," "London Assurance," "School for Scandal," "The
Rivals," "The Lady of Lyons," "Richelieu," "Wild Oats," "The Colleen
Bawn," "Arrah-na-Pogue," "The Shaughraun," "The Wife," "The Merry Wives
of Windsor," "Under the Gaslight," "Don Caesar de Bazan," "American
Cousin," "Rip Van Winkle," and the "Black Crook," all well known and
successful plays, many perhaps being acted this very night all over the
Union and England. We are not here examining the question of the
goodness or badness of these plays, their merits or demerits: we are
merely recognizing them as well known plays, constantly being acted, and
always successful when well acted. Of all of these, the most constantly
successful and most frequently acted are those of Shakespeare, Sheridan,
and Bulwer, among the old plays, and those of Boucicault and Daly among
living authors. Almost all playgoers are familiar with these works, and
have seen them once or more; and every new aspirant for histrionic
honors has one or more of the plays of the first three in his list of
test characters. If he be a man and a tragedian, he must play Hamlet,
Othello, Richard, Shylock, Macbeth, Richelieu, Claude Melnotte; if
versatile, he must add Benedick, Charles Surface, Captain Absolute, and
others to the list; if a lady, she must be tested in Portia, Ophelia,
Pauline, Lady Teazle, Juliet--who knows what? Some very versatile ladies
have tried all the light comedy characters, finishing with Lady Macbeth
as an experiment. A short time ago there was quite an epidemic of Lady
Macbeths, but that is over for the present. The stray sheep have
returned to the fold. Let us return to them.
What can we glean about the limitations of the dramatic subject from
these successful plays? There is a limitation somewhere, and the first
and most obvious is--time. A novelist can make the minute description of
a life interesting. The most celebrated novels, such as "Robinson
Crusoe," "Vicar of Wakefield," "David Copperfield," "Pendennis," "The
Three Guardsmen," and others, have been just such books, imitations of
real biographies. But a play is limited in length to five acts, or six
at most, and its time of acting has a practical limit of three hours,
with the inter-acts. Each act is further practically limited to five
scenes, and it is but seldom that it stretches over three, while the
latter average is never exceeded and seldom reached in a five-act play.
No scene can properly contain more than a chapter of a novel, so we find
ourselves practically limited to a story which can be told inside of
fifteen chapters, the further inside the better. The French, who are
much more artificial than the English in their dramatic canons, almost
invariably limit their acts to a single scene, reducing their story
thereby to only five chapters. A careful comparison of successful acting
plays will generally end in bringing us to one obvious canon:
I. The subject of a drama must be capable of being fully
treated in fifteen chapters at most.
The next limitation that we meet is in the nature of the story. A
novelist can describe his hero and heroine and the scenes in which they
move. He can depict them in motion, and describe a long journey in
strange countries, trusting to picturesque scenery and incident to help
him out. He can give us a sketch of their former life, and tell how they
fared after they were happily married. The dramatist cannot do this. He
must put his people down in a given place and leave them there till his
scene is over, opening another scene or another act after a silent
interval. He can, indeed, put a narrative of supposed events into the
mouth of any of his characters, but such narratives are always dull and
prosy, and to be avoided. Shakespeare uses them sometimes, but only when
he cannot help himself, and always makes them short. The nearest
instances that occur to us are, the description by Tressel to Henry VI.
of the murder of Prince Edward, usually put now in the first act of
"Richard III.," and the story of Oliver in "As You Like It." Sometimes a
short story cannot be helped, but if told, it is always found to be of a
collateral circumstance not directly leading to the catastrophe. It
generally is brought in only to explain the presence of a character on
the stage in the successful drama. Sometimes it happens otherwise. For
instance, Coleman makes Mortimer, in the "Iron Chest," tell the whole
mystery of his life in the form of a story instead of acting it. The
result is a poor play, seldom acted, and generally to small audiences,
being only valuable for some special features of which we shall speak
later. It is not too much to ask for acceptance of this second canon
regarding the subject:
II. The subject should be capable of being acted without the
aid of narrative.
Is it still possible to limit the subject, and do novels and dramas
differ still further? A third limitation will reveal itself, if we
compare a typical drama, like "Much Ado About Nothing," or "Hamlet,"
with a typical novel such as "David Copperfield" or "Robinson Crusoe."
These latter depend for their interest on a series of adventures which
befall a hero, sometimes entirely unconnected with each other, just as
they happen to a man in real life, wherein he meets many and various
scenes and persons. Neither possesses any sequence of events, depending
on each other, such as pervades "Hamlet" and all acting plays. It is
true that some few novelists, such as Wilkie Collins, write novels that
depend on plot for their interest, but those typical novels which stand
at the head of the list do not. The masterpieces of Scott, such as
"Ivanhoe," "Talisman," "Old Mortality," are antiquarian studies, with
very slight plots; Dickens and Thackeray's best novels have no plot
worth mentioning; and where perfect plots are found, it is rare to find
a lasting and enduring novel. In a play, on the other hand, a plot seems
to be absolutely necessary to interest the spectator, the more intricate
the better. We have all seen Shakespeare's plays so often, that we are
apt to forget how intricate and involved many of his plots are; and when
we consider that most of his plots were taken from very bad novels which
have utterly perished from sight, while the plays still live, we begin
to realize by the force of contrast another canon relating to the
subject, which is this:
III. The subject must have a connected plot, in which one
event depends on the other.
When we come to restrict the dramatic subject any further, we encounter
more difficulty. Some might hold that the interest of the subject should
depend on either love or death, but we are met at once by instances of
plays in which the real interest is almost wholly political, such as
"Henry V.," "Richard III.," or moral, such as "Lear." Referring once
more to the effect of contrast with the novel for guidance, we find it
very difficult to separate subjects proper for dramatic treatment any
further than we have done, and almost impossible to lay down any
absolute rule to which distinguished exceptions cannot be quoted. It
might be said that the interest should turn on a single action, as it
does in most plays, and especially in tragedies, but here we are met by
"Much Ado About Nothing," "The Honeymoon," and other plays, where two or
three plots progress side by side in perfect harmony. It seems,
therefore, that any further absolute limitation of the abstract dramatic
subject is impracticable, and we must be content with adding a mere
recommendation for our fourth canon, much as follows:
IV. The interest of the plot generally turns on either love
or death, and generally hinges on a single action or
episode.
When we come to speak of the _best_ subjects of dramatic writing, we are
really approaching the domain of treatment, which is much wider and
better defined. There it becomes a question for judgment and discretion,
and much more certainty can be attained. Instead of considering all
dramas, we narrow our search to the best only, judging them by the
simple tests of success and frequency of acting, and finding what sort
of subjects have been taken, and how they have been treated.
Let us then come at once to the question, What is the best method of
treating a given subject? Here we are again confronted by a variety of
decisions, some of which seem to conflict with others, but which all
agree in some common particulars. In the dramas written, down to the
time of Boucicault, it seemed to be assumed as a matter of course that
every first-class play, comedy or tragedy, must be written in five acts.
All of Shakespeare's, Sheridan's, Knowles's, follow this old rule, as
inflexible and artificial as some of the French canons, but with the
same compensating advantage, that author and audience knew what was
expected of each, and troubled themselves little over the structure of
their dramas. Of late years another custom has taken the place of the
five-act play, and many if not most of the modern dramas, while of the
same length as the old ones, are divided into four and even three acts.
Especially is this the case with comedies, and those nondescript plays
that are variously called "melodramas," "dramas," and "domestic dramas."
In the case of three-act plays, the number of scenes in each act is
frequently five, sometimes six or seven, but the common modern practice
restricts the last act, if possible, to a single scene. The number of
scenes must of course depend on how many are absolutely necessary to
develop the story. The French system of a single scene to each act has
one great advantage. It permits of very much finer scenery being
introduced than in a scene which is to be shifted, whether closed in or
drawn aside. For instance, when the curtain comes down between each
scene, the stage may be crowded with furniture, and those temporary
erections called "set pieces." There will always be plenty of time to
remove these between the acts, and noise of hammering is of no
consequence when the curtain is down. If there is more than one scene in
the act, all this is changed. Let us say there are only two scenes. One
of these must be a full-depth scene, but all the furniture and set
pieces are restricted to that part of the stage which lies behind the
two "flats" which make the front scene. In that front scene furniture
is inadmissible, without rudely disturbing the illusion. Let us suppose
the front scene to be the first, and that any furniture is left on the
stage. At the close of the scene the characters leave the stage, but
there stands the furniture. The old way to get rid of it is simple.
Enter a "supe" in livery, who picks up the one table and two chairs.
Exit, amid the howls of the gods in the gallery, who shriek "Soup!
soup!" as if they were suddenly stricken with hunger. Of course this
spoils the illusion; and the better the scenery, the more perfect the
other illusions, the easier they are disturbed by such incongruity.
Sometimes the set pieces in front, if there are any, and the furniture,
disappear through trap doors. In the large city theatres, such as those
where spectacular pieces are constantly produced, this method of
changing a scene is common, but such theatres themselves are not common,
and it costs a great deal to run them on account of the number of
workmen required. Our present inquiry is directed to the ordinary
theatre, with its stock company, simple scenery, and few traps. Of this
kind of theatre every town furnishes at least one sample. In such
theatres at least it will always be best to keep furniture and set
pieces out of the front scenes as much as possible, to preserve the
illusion. If the front scene come after the full-depth one, the wisdom
of this rule becomes still more apparent. A "supe" taking out furniture
is not half as ludicrous as one bringing it in, and without a trap such
a spectacle is unavoidable. The first canon offered by common sense is
obviously sound:
V. Keep furniture and set pieces out of front scenes, if
possible.
This rule being followed, will probably reduce the front scenes of a
drama to the open air, woods, gardens, halls, streets, church porches,
and similar places, where the attention will be concentrated on the
actors, not the picture. The scope of a front scene is further
restricted by the fact that you must bring your characters on and take
them off, being deprived of that valuable ally to illusion, the
"tableau." If the scene be the first of the act, a tableau may indeed be
discovered, but it cannot close the scene. The most common place for a
front scene is between a first and a third full-depth scene, to give
time for the change that goes on behind. This change always makes a
certain amount of noise, and the use of the front scene is to take off
the attention of the audience. This intention must be hidden at any
price, for, if perceived, it is fatal to the illusion. To hide it there
is only one method always reliable, which is to rivet the attention of
the audience on your characters, put in your best writing, and get up an
excitement to cover the scene. If you have any brilliant dialogue, any
passage of great emotion, any mystery to be revealed, put it in your
front scene so that your design may not be suspected, but the scene
appear natural. In brief the canon says:
VI. Put the best writing into the front scenes.
The next question that arises as to the front scene relates to the
character of incident that should be treated therein. It is obvious that
it will not do to put in a crisis or a climax at such a place. At its
best a front scene is only a makeshift, a preparation for the full
scene. Its employment necessitates a loss of nearly three-quarters of
the available space, and the tableau loses all its power, as developed
in the full-depth scene. Its use is therefore a disagreeable necessity,
so disagreeable that the French discard it entirely. Mechanically it is
only an introduction to the full scene, and the more it partakes of the
same character intellectually, the less will it weary the audience. The
best preparation an audience can have for a scene is to make them eager
therefor, and the best way to make them eager is to leave them in
suspense, so that they are impatient for the movement of the flats that
opens the next picture. A familiar instance of this employment of the
front scene is found in the "Shaughraun," by Boucicault, before the
Irish wake. The front scene represents the outside of a cottage with a
door in the right flat; the peasants and other characters come in, talk
about the wake, and enter the house one after another. In this scene it
is also explained that the supposed corpse is not dead, but shamming, so
that there is no tragic interest associated with the coming scene, but
every one is anxious to see it. At last all the characters are off, the
flats are drawn aside, and the celebrated Irish wake makes its
appearance, taking the whole depth of the stage. The audience is
satisfied, and the front scene has answered its end, as expressed in
this canon:
VII. Front scenes ought to terminate in a suspense, which
the following scene will relieve.
From this canon it follows that the front scene should deal only with
explanatory and dependent matters, not the principal action of the
drama. Sheridan, in "The Rivals" and the "School for Scandal," opens his
first acts with front scenes, which introduce little of the matter of
the story. I am inclined to think that he had a reason for this which
still prevails, in the noise made by the audience. The beginning of the
first act of most plays is distinguished in the auditorium by much
shuffling of feet, opening of doors, taking of seats, especially by
those who take the reserved seats in front of the house. All this
disturbs the audience and makes them lose any fine points at the
beginning of a play, unless the actors strain their voices unduly. In a
front scene the flats immediately behind the actors serve as a sounding
board for the voice, and reduce the volume of space to be filled by the
speakers. The advantage gained in this way is balanced by the loss to
the eye in losing the full-depth scene, wherefore this method of opening
a play is not much in favor; but its use in the cases mentioned leads to
a general canon as to the first act of a play, which also recommends
itself to common sense:
VIII. Avoid fine points, and have plenty of action at the
beginning of the first act.
This rule, however safe and sensible, is hampered by the necessities of
the subject, to which everything must be subordinated. Let us see how
the greatest masters of dramatic construction in modern times open their
first acts. Of these Boucicault comes first, _facile princeps_. We will
take the "Shaughraun" and "Flying Scud" for examples. Both open in a
similar manner: in the first a young woman, in the second an old man,
engaged in household work, singing away at nothing particular. A quiet
picture not requiring close attention. To each, enter a disturber,
somewhat disagreeable, arresting attention. A short squabble, then more
characters coming on, one or more at a time, till the stage is pretty
full, and no flagging of interest. The act does not drag. Compare this
with Sardou's "Frou-Frou," "Fernande," and others. Sardou's first acts
almost invariably drag, and the success does not come till afterward.
One great difference is immediately perceptible. Sardou almost always
brings on his people in pairs, and takes them off together, leaving the
first act a succession of dualogues, with very little action. Now take
"The Lady of Lyons," an old success, which nowhere drags. It opens with
a picture, mother and daughter, doing nothing particular. Enter
disagreeable Beauseant, who makes an offer and is rejected. A mild
excitement at once arises, shut in by a front scene, short, lively, and
spirited, where Glavis and Beauseant plot for revenge on Pauline. The
scene ends in suspense, the actors having gone for Claude Melnotte, and
the flats draw aside, revealing Melnotte's cottage and introducing the
hero. By this time the audience is quiet and can take the fine points,
so the third scene of the first act can be made exciting. There is thus
no flagging of interest in either Bulwer or Boucicault. One does the
thing in three scenes, the other in a single scene, but both employ the
same means, which are thus expressed:
IX. Open the first act with a quiet picture, and bring in
the disturbing element at once. Having aroused attention,
bring on all your characters, and end with an excitement.
Avoid bringing on characters in pairs in this act.
The first act of a play is always surrounded with difficulties. The
interest of the audience has to be aroused, and all the characters
brought in. Every part of it must hang together, and the attention must
be excited more and more as the act progresses. This rule applies to the
whole play likewise, but in the first act it is especially necessary,
because there are so many things to divert attention, and the object of
the act is to catch it. After a certain period it must flag, and the
object of the dramatist must be to close his act before that dreadful
period. The office of the first act is to prepare for the second;
therefore it resembles the front scene in one important principle--it
should end in suspense, and make the audience eager for the second act.
Ending as it should in a full scene, it has the advantage over the front
scene that a tableau is possible, and should be used. This tableau must
be natural, and must come, as all tableaux come, out of a climax, but
the climax must not be complete. It must leave the audience in suspense,
and give them something to talk about in the inter-act. It must not be
too long delayed, or the act will drag. These and various other reasons
have led to this further canon, generally observed:
X. The first act should be the shortest, and as soon as a
partial climax is reached the curtain should come down. The
tableau and action should indicate suspense and preparation.
This general rule indicates that the villain should be temporarily
triumphant, if the play is to end in his discomfiture. If his first
scheme fails in the first act, it is difficult to arouse interest in the
nominally imperilled innocence which is left in danger. The structure
becomes too artificial, and the dictum _ars est celare artem_ has been
violated. No rule is so safe in dramatic writing, as also in acting. The
end is--_illusion_.
The rule of putting only suspensory and preparatory action in the first
act is universally followed by Shakespeare and all other successful
writers of plays, and is better settled than any other. The first act
occupies the office of the first volume of a novel, explaining all the
story. Very frequently, in the modern French drama especially, it
assumes the form of a prologue, the action transpiring at an interval of
several years, sometimes a whole generation, before the rest of the
play. Only one instance of this character is found in Shakespeare, in
the "Winter's Tale," where the action of the drama demands a prologue,
but it is quite common in modern times, while another custom of
Shakespeare's--that of dividing a historical play into two "parts"--has
quite gone out of fashion. Its only modern example is that of Wagner's
opera of the "Niebelungen Ring," which takes a week to get through. The
Chinese and Japanese have a strong taste for this kind of play, but the
practice has vanished from Anglo-Saxon civilization. It must be
confessed that the employment of a prologue is rather a clumsy way of
opening a play. It is too apt to be complete in itself, and to join
clumsily to the rest of the drama. Besides this, it is hard to preserve
the illusion that the small child who appears in the prologue has
developed into the good-looking young person who is the heroine of the
rest of the play. The "Sea of Ice" is a familiar instance of this sort
of thing, where the same actress who personates the mother in the first
act, and gets drowned, blossoms into a girl of eighteen in the second
act, supposed to be her own daughter, last seen as a small child. In
"Winter's Tale" there is nothing of this. The supposed Perdita of Act I.
is merely a rag baby, and mother and child reappear together thereafter.
In cases where the interval between prologue and play is limited to a
year or two, this objection does not apply; in fact such prologues are
quite common and useful. The fanciful and magic prologue to the "Marble
Heart" is a very happy instance of conquest of the difficulties inherent
in long separated prologues. The wrench is so sudden from a Greek
sculptor to a French sculptor, from Athenian dresses to Parisian, that
the main interest of the play lies in the identification of the ancient
characters in the new dress, and the very fanciful absurdity of the plot
lends it an air of reality essentially dramatic. The end is illusion,
and illusion it is.
There is little more clear and positive to be said about the first act.
Study of the best models will reveal many points inherent in all, but no
general rules so clear as those of brevity, action, and suspense. The
practical limit of time is from fifteen to thirty minutes, the medium of
twenty being common to mono-scenic acts, but on this no positive canon
can be ascertained. It depends on the interest, and only this general
rule is partially true, that no interest can carry an audience through a
first act of forty-five minutes.
We next come to the middle acts of the play, and here again general
rules are hard to find. The number of acts varies so much that nothing
positive can be said except as regards fixed lengths of drama. Treating
all between the first and last acts as a whole, the first certain rule
that meets us is this truism:
XI. From the second to the last act the interest must be
regularly increased, and each act must end in suspense,
leading to the next.
Without an observance of this rule no play can ever be permanently
successful as a general thing. There have been some poor plays with
little interest, that have been bolstered up for a time by the force of
a single character, portrayed by a peculiar actor, but in that case the
play becomes a mere "star play," not amenable to the common rules, and
useless out of the hands of the peculiar star who owns it. Of such are
those multiform dramas, constantly varying, of which Mr. Sothern makes
Lord Dundreary and Sam the central figures. The actor found he had made
a lucky hit in his character, and he hired out the work of altering the
play to any sort of literary hacks, so that he himself is really the
creator of the plays, and when he dies they will die. In the "American
Cousin," as it was first played, the interest lay entirely in Asa
Trenchard, and the drama was very skilfully constructed, with ascending
interest, to develop the ideal Yankee. In that part Jefferson made his
first public hit. As soon as he found that Dundreary had stolen the play
from its hero, Jefferson was wise enough to drop the contest between
high comedy and broad farce, in which the latter must conquer when they
come together. By taking up the ideal Dutchman (or rather German, as he
makes it) in Rip Van Winkle, he created a part of which no one can
deprive him, but which will probably die with him. No one else has
succeeded with it to the same degree, and "Rip Van Winkle" stands as a
model of a successful star play, wherein all the interest hangs on a
single character.
It is not the intention of this article to enter into the question of
what constitutes the interest of such plays as "Rip Van Winkle." To do
so would be to enter into a field where everything is uncertain, and
where judgment is only an expression of individual liking. The main
elements of the success appear to be humor and pathos, those twin
brethren of genius whose identity and individuality are frequently so
inextricable from each other. Both are drawn in broad, simple lights and
shadows, so that the simplest audience can take the points, while the
most cultivated members of that audience are studying the delicate
touches of the actor. The contrast between--but we must refrain from the
digression, however tempting. We are examining the dramatic canons, and
the only settled canons about which there is little doubt are those
relating to construction, not to sources of interest. In the kingdom of
invention genius is supreme, and amenable to no rules. Each writer must
work out his own salvation.
Constructively it is obvious that the number of acts in a play must be
regulated by the number of natural episodes in the action of its
subject; and the perfection of its construction is tested by the
liberties that can be taken with the acts and scenes. Of late years it
has become the fashion to alter and remodel Shakespeare's and other old
plays, by changing scenes and acts, cutting out and putting in. To an
ardent worshipper of Shakespeare as read, these alterations frequently
appear desecrations, but there is little question that they were and are
improvements. The construction of many of Shakespeare's plays is
decidedly faulty, and the nature of the improvements made by managers
and actors is best illustrated when the original play unaltered is tried
against the adaptation. The acting edition of "Richard III." is a
familiar instance of this. Colley Cibber arranged it, he being a shrewd
old actor and manager. His edition holds the stage today, and always
succeeds, where the original "Richard" fails. In this matter of
construction the chances are all in favor of the improvement of a work
by a shrewd adapter. His attention is directed to only one thing, the
successful presentation of the play. He is not an artist so much as a
workman. He creates nothing, he only alters and improves. He may be
perfectly incapable of creating an ideal character, while yet he can
make its language more compact, can concentrate its action. Such an
adapter is a skilful gardener. He cannot create the fruit tree, but he
can prune it, and stimulate it to the perfection of fruit-bearing.
The French stage has been a prolific nursery for these skilful workmen,
and they have managed to extract splendid successes from their work. It
is by comparing their English adaptations with a simple translation of
the work that one best sees the improvement. For instance, there is the
"Two Orphans," with a plot and incidents so repulsive in the original
that its translation failed in London in spite of its weird power.
Adapted and cleansed by a clever American author, it was the great
success of last year in New York, and is now running a fresh career of
success. Another instance that occurs is Sardou's "Fernande." It was
altered and adapted in New York by Augustin Daly, and succeeded. Another
version by Mr. Schoenberg, then of Wallack's, a straight translation,
failed to secure a hearing in Boston, and ended in a lawsuit. This was
not for want of merit in the translation, which was excellent, but, as
appears from a comparison of the two plays, simply because Daly had
improved on Sardou. The alterations were small, but masterly, and showed
that Daly understood his business. In Sardou's play there appears a
certain character, a young count (I forget his name) who comes in at the
beginning of the first act, the close of the last. In the last he has
some very important business to do, but he appears nowhere else. Of
himself he does not aid the plot, but his last action is indispensable.
In the original play also appears the Spanish Commander, a mere sketch
in the first act. Daly suppressed the Count altogether, gave his best
business to the Commander, and brought the latter in all through the
play. The result was one good character instead of two poor ones, and
indicates a canon which can be confirmed by many other instances. This
canon shapes itself something like this:
XII. Concentrate the interest on few characters, and avoid
numerous unimportant parts.
This canon rests on the necessities of a stock company, as those before
rest on the nature of scenery and audiences. Every company has its
leading man, leading lady, low comedians, old man and old woman, and
those ordinary characters which all playgoers know by heart. If the play
does not fit these, it will not succeed. The appreciation of this fact
is one secret of the great success of Boucicault, Daly, and Lester
Wallack as play writers. They know the exact capacity of their stages
and companies from long experience, and write their plays to fit them.
With even ordinary talents they would have a great advantage to start
with over writers of greater genius, writing with vague ideas of what
the manager wants. As managers they know exactly what they want, and
what their companies can do. To a young writer the difficulties are all
in the start, unless he be an actor, or so closely related to actors or
managers as to be able to get behind the scenes at all times, and become
familiar with scenery, traps, machinery, rehearsals, and all the details
of the _business_ of theatricals. In former times, especially two
centuries ago, the task of writing a good acting play was far easier
than now. Scenery was simple, access behind the scenes easier--there was
not such a wall of separation as now exists between actors and audience
in a first-class city theatre. Even in those days, however, the writing
of plays was confined chiefly to actors, managers, and those men of
fashion who were given to haunting the green room. In the present day no
amount of talent in a writer seems capable of overcoming the
difficulties of technical construction of a drama. It is rare to find an
author of acknowledged talent in other departments, especially in
America, distinguished as a dramatist, and when one of them tries his
hand at playwriting he fails, not from lack of good dialogue and
literary finish, but solely from lack of knowledge of the business of
the drama, the limitations of actors and scenery, and the technique of
dramatic construction.
There is more hope to the American stage in the future in the production
of such undeniably original if mechanically faulty plays as Bret Harte
has given us in the "Two Men of Sandy Bar," than in the rapid carpentry
and skilful patchwork of hosts of French adaptations, whether they run
ten or five hundred nights. Our Hartes and our yet unknown writers daily
coming to the front, with freshness in their hearts and brains in their
heads, lack only technique and the custom of the stage, which no one can
give them but the managers and actors, who shall welcome them as
apprentices to learn the trade. That these latter will find it to their
advantage in the end to encourage a cordial alliance between the men of
the quill and the men of the sock and buskin, follows from a simple
calculation. If men of confessedly small talent and low character, such
as the host of lesser playwrights who furnish pabulum for the outlying
theatres, can write fair acting plays, simply by using mechanical
knowledge and stolen materials, it is probable that men of original
talent, already experienced writers in other branches of literature,
will end by producing much better and fresher work, when they are
offered and have enjoyed the same technical advantages.
FREDERICK WHITTAKER.
AN EVENING PARTY AMONG THE COSSACKS OF THE DON.
Sunset on the Lower Don; a dim waste of gray, unending steppe, looking
vaster and drearier than ever under the fast falling shadows of night; a
red gleam far away to the west, falling luridly across the darkening sky
and the ghostly prairie; a dead, grim silence, broken only by the plash
and welter of our laboring steamer, or the shrill cry of some passing
bird; an immense, crushing loneliness--the solitude not of a region
whence life has died out, but of one where it has never existed. Even my
three comrades, hardened as they are to all such influences, appear
somewhat impressed by the scene.
"Cheerful place, ain't it?" says Sinbad, the traveller; "and the whole
of southern Russia is just the same style--multiply a billiard board by
five million, and subtract the cushions!"
"I wonder what the population of this district can be," muses Allfact,
the statistician, looking disconsolately at his unfilled note-book.
"It's almost impossible to get any reliable information in these parts.
But I should think one man to three square miles must be about the
proportion."
"And not a feather of game in the whole shop!" growls Smoothbore, the
sportsman, with an indignant glance at his pet double barrel. "It's as
bad as that desert where the old sportsman committed suicide, leaving a
letter beside him to the effect that he must be firing at something, and
there being nothing else to shoot, he had shot himself!"
"I'll give you one entry for your note-book, Allfact, my boy,"
interrupted I; "there are _thirty-nine_ sand banks between this and
Rostoff, at the head of the estuary; and the upper stream is all banks
together--no navigation at all!"
"I should think not, by Jove, with that kind of thing going on!" says
Smoothbore, pointing to a solitary horseman who is coolly riding across
our bows with an aggravating grin, his dog following. Our outraged
captain has barely time to hurl at him some pithy suggestions respecting
his portion in a future life, which had better not be quoted, when there
comes a tremendous bump, and we are aground once more!
Just at this moment two wild figures come dashing along the bank at full
gallop, sitting so far forward as to be almost on the horse's
neck--their hair tossing in the wind like a mane, their small black eyes
gleaming savagely under the high sheepskin cap, their dark lean faces
thrust forward like vultures scenting prey--shooting a sharp, hungry
glance at us as they swoop by, in mute protest against the iron age
which compels them to pass a party in distress without robbing it. These
are the famous Cossacks of the Don, the best guerillas and the worst
soldiers in the world; at once the laziest and most active of
men--strangest of all the waifs stranded on the shore of modern
civilization by the ebb of the middle ages--a nation of grown-up
children, with all the virtues and all the vices of barbarism--simple,
good-natured, thievish, pugnacious, hospitable, drunken savages.[K]
[Footnote K: The Cossack is often erroneously classed by untravelled
writers with the native Russian, from whom he is as distinct as the
Circassian or the Tartar.]
It takes us fully ten minutes to "poll off" again, and we have hardly
done so when there comes a sound through the still air, like the moan of
a distant sea; and athwart the last gleam of the sinking sun flits a
cloud of wide-winged living things, shadowy, silent, unearthly, as a
legion of ghosts. The wild fowl of the steppes are upon their annual
migration, and for many minutes the living mass sweeps over us unbroken,
orderly, and even as an army in battle array--a resemblance increased by
the exertions of an active leader, who keeps darting back from his post
at the head of the column, and trimming the ranks like an officer on
parade.
"I wonder how many birds there are in that column," says Allfact,
instinctively feeling for his note-book, as if expecting some leading
bird to volunteer the desired information.
"Just like their mean tricks," mutters Smoothbore savagely. "First the
game won't show at all, and then they come so thick that no fellow would
be such a cad as to fire at 'em."
Night comes on, and the foul-creeping mist begins to steam up from the
low banks of greasy black mud, driving us perforce into the cabin, where
we speedily fall asleep on the benches along the walls--for bed-places
there are none. About midnight I begin to dream that I am a Christian
martyr in the reign of Diocletian, "in the act" (as Paddy would, say) of
being burned alive; and I awake to find it all but true. The fact is,
the steward, with a thoroughly Russian love of overheating, has put wood
enough into the stove to roast an ox; and there is nothing for it but to
bolt on deck again, where we remain for the rest of the night.
The panorama of the deck in the early morning forms an ethnological
study hard to match, except perchance by the Yokohama packet steaming
out of 'Frisco, or a "coolie boat" coming over from Demerara to
Trinidad. Gaunt, aquiline Cossacks, and portly Germans, and bumfaced
Tartars; red-capped, broad-visaged, phlegmatic Turks; slim, graceful
Circassians, beautiful with all the sleek tiger-like beauty of their
gladiator race; sallow, beetle-browed Russians, and black-robed,
dark-eyed, melancholy Jews. We have _one_ Persian on board--a lanky,
hatchet-faced rogue, half buried under a huge black sheepskin cap not
unlike a tarred beehive. He smokes one half the day and sleeps the other
half, and is only once betrayed into any show of emotion. This occurs at
one of our halting places on the second day, when he comes on board
again grinning and whooping like a madman, having succeeded (as I learn
when his excitement subsides) in cheating a Cossack out of a halfpenny.
But the appearance of the Russian _mujiks_ (peasants), and the manner in
which they curl themselves up anywhere and anyhow, and sleep the sleep
of the just with their heads in baskets and their feet in pools of dirty
water, baffles all description. A painter would revel in the third-class
deck about sunrise, when the miscellaneous hash of heads and limbs
begins to animate itself, like a coil of snakes at the approach of
spring--when mothers of families look anxiously about for the little
waddling bundles of clothes that are already thrusting their round faces
and beady black eyes into every place where they ought _not_ to go; and
when brawny peasants, taking their neighbor's elbow out of their mouth,
and their knee out of their neighbor's stomach, make three or four rapid
dips, like a drinking duck, to any village church that may be in sight,
and then fall to with unfailing zest to the huge black loaf which seems
to be their only baggage. The whole thing is like a scene in a fairy
tale:
There was an old captain that lived in a "screw."
He had so many passengers he didn't know what to do;
They'd got nary baggage but one loaf of bread.
They squatted round the funnel, and _that_ was their bed.
As we move southward, our surroundings alter very perceptibly. A genial
warmth and a rich summer blue replace the cold gray sky of the north;
the banks begin to rise higher, and to clothe themselves with thick
patches of bush, and even trees, instead of the coarse prairie grass;
while at every halting place the little wooden jetty is heaped with
perfect mounds of splendid grapes, sold at three cents per pound, by men
in shirtsleeves--phenomena which, to us who are fresh from the furred
wrappings and snow-blocked streets of Moscow, have a rather bewildering
effect. But the most striking sight is (to our friend Allfact at least)
the huge masses of coal which now fuel the steamer instead of the split
logs of the Volga.
"You see Russia's richer than her neighbors think," remark I. "On the
Don alone there are 16,000 square miles of the finest anthracite, which
leaves only two per cent. of ashes in burning."
"Sixteen thousand square miles!" cries the statistician, whipping out
his note-book. "Why on earth doesn't she use it, then, instead of
destroying all that valuable timber?"
"Well, you see, the railways are not completed yet; but when they are I
can promise you that Russia will cut out England altogether in supplying
Constantinople and the Levant."
One by one the little villages slip by us: Alexandrosk, the first sign
of which is the glitter of its gilded church-tower; Nikolaievo, with its
black marble monument to the late Crown Prince; Konstantirovskoe, the
birthplace of Prince Potemkin, brightest and most worthless of Russian
favorites, who "lived like an emperor and died like a dog." They are all
vary much of one pattern: substantial log-cabins, curiously painted,
with little palisaded gardens in front, and red-shirted men sitting
smoking at their doors, alternating with little wickerwork hovels daubed
with mud, which look very much like hampers left behind by a monster
picnic. Gangs of lean dogs (the pest of every Cossack village) are
sniffing hungrily about, while scores of sturdy wenches, with
berry-brown arms and feet, and sunburnt children clothed only in short
pinafores lined with dirt, run to stare at the wonderful fire-breathing
vessel as she comes gliding in.
The sun is just dipping below the horizon as we reach Semi-Karakorskaya,
and anchor for the night as usual; for to navigate the Lower Don in the
dark is beyond the power of any pilot afloat. Here a Cossack
official,[L] whose acquaintance we have made on board, proposes to us to
land and be presented to the "Ataman," or chief of the tribe, with the
certainty of seeing something worth looking at. The offer is joyfully
accepted, and five minutes later we are scrambling up the steep,
crumbling bank--in the course of which feat Allfact slips and rolls
bodily down into the river.
[Footnote L: The "Army of the Don," though now an integral part of
Russia, is still officered to a great extent by its own people.]
"There's something for the notebook at last, old boy!" cries Smoothbore
spitefully. "Write down that you notice _a great falling off_ in this
part of the country!"
To find one's way into a Cossack village at night is almost as hopeless
as the proverbial hunt for a needle in a haystack. The whole country
seems to consist of a series of carefully dug pitfalls, into which we
tumble one over the other, like fish out of a net; and our final
approach to the village is only to be guessed by the yells of the dogs,
which come about us with such zeal as to necessitate some vigorous
cudgelling, and a shower of trenchant Russian oaths, in which our
leader, thanks to his official character, seems to be quite a
proficient. At length a few lights, which appear to start from the very
ground under our feet, announce that we are among houses--underground
ones, it is true, but houses still. Then the first glimmer of the rising
moon lights up a row of log-cabins on either side, and the abyss of
half-dried mud between them; and at last, following our leader, we enter
one of those immeasurable courtyards in which the Cossack heart
delights, pass through a low doorway, ascend a creaking, ladder-like
stair, and, entering a small room at the head of it, find ourselves in
the presence of two men--one old and decrepit, the other in the prime of
life. The younger is the Ataman himself; the elder is his father, an old
soldier of the first campaigns of Nicholas.
Seen by the dim light of the lamp that stands on the rough-hewn table,
the "interior" is sufficiently picturesque: the heavy crossbeams of the
roof, the skins that cover the walls, intermingled with weapons of every
kind, from the long Cossack lance to the light carabine which is fast
superseding it; the fresh complexions and Western costume of the English
party, contrasting strangely enough with the commanding figure and dark,
handsome face of our host, in his picturesque native dress and high
boots; the long white beard and vacant, wondering eyes of the ancient
soldier; the picture of the Ataman's patron saint in the corner, with
its little oil light burning before it, and a pious cockroach making a
laborious pilgrimage around its gilt frame; and, through the narrow,
loophole-like window, a glimpse of the great waste outside, lit by
fitful gleams of moonlight.
Hospitality has been a Cossack virtue since the day that Bogdan
Khmelnitski gave meat from his own dish to the prisoners whom he was
about to slaughter; and we have hardly time to exchange greetings with
our new friends when we are set down to a plentiful meal of rye bread,
the splendid grapes of the Don, and "nardek"--a rich syrup strained from
the rind of the watermelon, not unlike molasses both in appearance and
flavor.
The "bread and salt" (as the Russians technically call it) being
despatched, my three comrades, with the native official as interpreter,
fasten upon the Ataman, while I devote myself to the old soldier, and
begin to question him on the Danubian campaign of 1826. It is a sight to
see how the worn old face lights up, and how the sunken eyes flash at
the sound of the familiar name; and he plunges at once into his story.
Seldom is it given to any man to hear such a tale as that to which I
listen for the next half hour, told by one of its chief actors. Weary
struggles through miles of hideous morass--men dropping from sheer
exhaustion, with the wheels of the heavy artillery ploughing through
their living flesh; vultures haunting the long march of death to tear
the still quivering limbs of the fallen; soldiers, in the rage of
hunger, feeding upon the corpses of their comrades--all the hideous
details of that terrible campaign, told in a quiet, matter-of-course
way, which makes them doubly horrible. My impromptu Xenophon is still in
full swing when high above the clamor of tongues rises a sound from
without, which nothing on earth can match save the war whoop of the
Western Indian--the shrill, long-drawn "Hourra!" of the Cossack, which
made many a veteran grenadier's stout heart grow chill within, as it
came pealing over the endless snows of 1812. We rush headlong to the
outer door, and this is what we see:
In the centre of the courtyard, under the full splendor of the
moonlight, stand some twenty tall, sinewy figures, in the high sheepskin
cap, wide trousers, and huge knee-high boots of the Cossack irregular.
They salute the Ataman as he appears by drawing their long knives and
waving them in the air, again uttering their shrill war cry; and then
begin to move in a kind of measured dance, advancing and retreating by
turns, to the sound of a low, dirge-like chant. Presently the music
grows quicker, the motion faster and fiercer; the dancers dart to and
fro through each other's ranks, brandishing their weapons, turning,
leaping, striking right and left--acting in terribly lifelike pantomime
the fury of a deadly battle. Seen in the heart of this great solitude,
with the cold moon looking silently down upon it, this whirl of wild
figures, and gleaming weapons, and dark, fierce faces, all eyes and
teeth, has a very grim effect; and even Sinbad's seasoned nerves quiver
slightly as the dancers at length join hands, and, whirling round like
madmen, burst forth with the deep, stern chorus with which their
ancestors swept the coasts of the Black Sea five hundred years ago:
Our horses have trodden the steep Kavkaz (Caucasus);
Of the Krim (Crimea) we have taken our share;
And the way that we went is dabbled with blood,
To show that _we_ have been there!
The volume of sound (stern and savage to the last degree, but yet full
of a weird, unearthly melody) fills the whole air like the rush of a
storm; and now, the Cossack blood being thoroughly heated, the play
suddenly turns to earnest. The nearest dancer, a tall, handsome lad with
a heavy black moustache, suddenly fells his next neighbor with a
tremendous blow between the eyes, which Heenan himself might have
applauded. The next moment the conqueror falls in his turn before a
crushing right-hander from his _vis-a-vis_; and in an instant the whole
band are at it hammer and tongs--apparently without "sides," order, or
object of any kind, except the mere pleasure of thrashing and being
thrashed. There is little science among the combatants, who deliver
their blows in a slashing, round-hand style that would agonize a
professional "bruiser"; but every blow dealt by those brawny arms leaves
its mark, and the whole company speedily look as if they had been taking
part in an election.
"By Jove!" says Smoothbore, with considerable feeling; "it does one good
to see a real good fight so far away from home!"
"You'd see plenty such in Central Russia," answer I. "Two villages often
turn out to fight, just as we'd turn out to play cricket.[M] They call
it 'Koolatchni boi.'"
[Footnote M: I remember one such battle near Moscow, in October, 1809,
in which more than a thousand men took part.]
But Sinbad, being a man of humane temper, thinks that the sport has gone
far enough, and appeals to the Ataman to stop it. One word from the
all-powerful chief suffices to part the combatants; and, a messenger
being despatched for some corn-whiskey, they are speedily chinking
glasses as merrily as if nothing had happened. I am standing
unsuspectingly in their midst when suddenly the whole company rush upon
me as one man, and I find myself lifted in their arms and tossed bodily
into the air six times in succession, amid yells of applause, to which
all the previous uproar is as nothing.[N] Next they pounce upon Allfact,
who, in his thirst for new ideas, submits readily enough; but Sinbad and
Smoothbore take to their heels at once, and are with difficulty pacified
by our host and his venerable father, who are looking on from the
doorway.
[Footnote N: This singular compliment (a universal one among the
Cossacks) is probably a relic of the old custom of raising their
"Kosbevoi," or head chief, on a shield when elected.]
This closes the entertainment, for it is now nearly midnight, and we are
to start again at sunrise. We take a cordial leave of our new friends,
and depart, laden with bunches of grapes which are somewhat difficult to
carry conveniently.
"I wonder why they tossed me up like that?" muses Allfact, as we grope
our way down to the shore.
"Why!" answers Smoothbore. "Why, to take a _rise_ out of you, to be
sure."
DAVID KER.
DRIFT-WOOD.
THE WILLS OF THE TRIUMVIRATE.
"Nothing so generally strikes the imagination and engages the affections
of mankind," says Sir William Blackstone, "as the right of property."
Sure it is, that society palpitates whenever a great estate passes to a
new owner, disclosing its vastness in the act of transit. Perhaps for
this fact we may find another reason in Blackstone, where he says:
"There is no foundation in nature why the son should have the right to
exclude his fellow creatures from a determinate spot of ground because
his father had done so before him, or why the occupier of a particular
field or of a jewel, when lying on his death-bed, and no longer able to
maintain possession, should be entitled to tell the rest of the world
which of them should enjoy it after him." But since the law, to reward
thrift and avoid strife, has established this artificial right of
disposal, the disparities of fortune, on these signal occasions of
transfer, always set us to pondering.
Vanderbilt, last of the three monstrously rich men of New York who have
died within three years, furnishes in his will the now tripled evidence
of a new ambition in American Croesuses--an aim to keep their fortunes
rolling and greatening for several generations in the exact paths where
they were started. Supposing that Mr. Stewart's bequest to Judge Hilton
was designed to purchase his entrance into the dry goods firm, we should
have a common aim of the triumvirate, since each has put a chosen man
into his shoes, as if with the hope to live on in this successor, like
Mordecai in "Deronda." The master passion of acquisition is thus
striving to outwit death. Astor and Vanderbilt found their second selves
in favorite sons; childless Stewart could only take his confidential
agent. Each conceivably died in the hope that a successor so carefully
selected and endowed would in turn hand over the bulk of his gigantic
wealth, in its original channel, to some steward chosen with equal care;
so that ages hence the Astor fortune still in houses, the Stewart
fortune still in trade, the Vanderbilt fortune still in railways, might
flourish under successive guardians, faithful to their tradition and
training. The John Jacob, the Cornelius, the Alexander of the past has
been blessed with the vision of his millions multiplying as he would
have them multiply, and haply has dreamed of accomplishing by his own
foresight an entail which he could not create under the laws.
If this be the new tendency that American life is called upon to face,
it is at least not hard to account for. The thirst for posthumous fame
which inflamed old heroes and poets rages still in days when greatness
collects rents, sells dry goods, and corners stocks. And after all, what
is there stranger in struggling to prolong after death one's imperious
railroad sway, his landlord laws, his massive trade monopolies, than in
slaving out one's childless old age in the hard rut of traffic, in order
to turn five surplus millions into ten?
To Dives, after a life of accretion, the prospect of frittering his
wealth into fragments must be painful. Heirs will waste what he toiled
to win. That fortune which grew so great while he rolled it on turns
out, after all, but a snowball, to be broken apart and trampled by
careless spoilers when he is gone. There are, to be sure, hard-headed
philosophers who contemplate coolly the dispersion of their hoard. I
remember from boyhood that when somebody rallied Squire Anthony Briggs,
of Milldale, on his veteran vigilance in money-getting, saying, "Your
children will spend as fast as you have made it," stanch old Tony
answered: "If they get as much pleasure from spending my money as I have
in making it, they are welcome." But with prodigious fortunes like
Astor's and Vanderbilt's, the instinct of accumulation which increases
what is already preposterously great may struggle to keep it
accumulating after death. When Bishop Timothy sonorously declares from
the desk that we brought nothing into this world, neither may we carry
anything out, Croesus in the pew below takes this as a very solemn
warning to him--warning to secure betimes the utmost posthumous control
of his money that the laws allow. Dombey's soul is not wrapt up in the
miser's clutching love of money, but in the money-getting institution of
Dombey & Son; and not only in the Dombey & Son of to-day, but the
Dombeys & Sons of centuries hence. To found a dry-goods dynasty, a line
of railway kings, a house of landed Astors, its owner puts the bulk of
his vast wealth into a single hand--in that _exegi monumentum_ spirit
common to bard and broker, soldier and salesman. _Non omnis moriar,
multaque pars mei vitabit Libitinam_, the millionaire may then
triumphantly say.
On the other hand, the Cornells and Licks of our day, wonderfully
numerous, have made America renowned by their public uses of wealth,
either in lifetime gift or testamentary bequest; and this devotion of
private fortune to the common weal is fostered by the observed
independence of each generation in pursuing its own mode of life without
regard to the customs of ancestors.
But the testamentary aim of the richest trio that ever lived in America
was to escape this national trait of beneficence; to substitute the
perpetuity of one's business monopoly or family trade; to struggle
against any serious division of the enormous fortune, even at the cost
of preferences among equal children; to spare not one dollar out of
fifty millions for the public; to heap the gigantic hoard, save what for
other legatees propriety demands, on some "chip of the old block" or
business "bird of a feather." This purpose also influenced their lives.
"Magnificence is the decency of the rich," but little magnificence
marked the lives of those three rich New Yorkers. Powerful, self-willed,
all-conquering they were, but hardly magnificent. Unprecedented and
incredible thing in America, neither Stewart nor Vanderbilt left one
poor dollar of his fifty or sixty millions to any municipal or
charitable purpose. Filled with his posthumous business plans, neither
cared for New York as Girard cared for Philadelphia and Hopkins for
Baltimore. True, each of the Gotham triumvirate endowed in life an
institution of public beneficence--Astor his library, Vanderbilt his
college away in Tennessee, Stewart his hotel for women. It is further
true that men who, like Vanderbilt and Stewart, give sure pay for many
years to thousands of employees, are benefactors. But to do this, and
then to leave besides some testamentary memorial to the city where one
has heaped up his wealth, has hitherto been the aim of the rich men of
America. Girard not only founded his orphan college, ornament and pride
of Philadelphia, but left great sums to beautify and improve the city by
removing wooden houses and widening thoroughfares. Stewart, scrupulously
just in business dealings, deserves public gratitude as the apostle of
"one price," and as the cash-selling reformer who protected prudent folk
from the higher prices caused in trade by the allowances for bad debts;
but, this apart, in the will of Stewart and the will of Stephen Girard,
what a world-wide difference of public spirit! That one act of grace
that might have tempered his forgetfulness toward New York--the gift of
his picture gallery for public uses--even this act Stewart did not do.
The contrast is startling between the bequests of an Astor, a Stewart, a
Vanderbilt, and those of a Girard, a Peabody, and a Johns Hopkins.
THE DUEL AND THE NEWSPAPERS.
Barring the two services, doctors used, I fancy, to be the great
duellists among professional men. And still, ever and anon, some
irascible Sawbones rushes to the ten-paced turf, where, though he be
spectacled or pot-bellied, those disadvantages rarely calm his
blood-letting rage. But editors are the modern magnates of the code; not
because they thirst for gore, but only because the guild of M. Paul de
Cassagnac is professionally liable to give offence, and hence to be
dragged to the field of glory and to die with boots on. I once saw a
statement that the famous fighting editor of the "Pays" had taken part
in eighteen duels, "besides having a man to kill next month"; and he was
greatly coveted by a Missouri paper that had been losing its writers in
street encounters too rapidly for convenience.
The newspapers have emptied their vials of wrath or ridicule upon Mr.
Bennett for his duel with young May: now in horror over his resort to
the measured ground, and anon in scorn at the bloodless result.
Nevertheless, had Mr. Bennett failed to fight that duel, he and his
newspaper would have been butts during his lifetime for the shafts of
half the editorial archers of the land. A noble refusal to resent the
public insult would have been misrepresented with ingenious malice, in
the hope to disgrace him and ruin his property. In answer to "Herald"
arguments on disputed questions, the unresented cowhiding of its owner
would have been paraded by rival sheets. Rarely in business or political
controversy would they have failed to taunt him with cowardice. Life
would have been a burden to him; and if the consciousness of having
refrained in that instance from breaking the laws of man and of God
could have saved him from desperation, it would not have been for lack
of the sneers of newspapers continually fomenting and reviving public
contempt against him. Sometimes a man is goaded by such stings into a
second duel, after having been able to resist fighting the first; or
else he puts an end to a life which has been made unendurable through
constant imputations. Let those who doubt what would have occurred
recall the instantaneous newspaper sarcasms, after the street assault,
on the question "whether a man is answerable for hereditary tendencies
to receive a public cowhiding without resenting it." The satirist who
eggs on a duel in that fashion feels justified afterward in invoking
public contempt for the man that fights it.
What is the upshot of this comment? That duelling is ever commendable?
Most emphatically no. Duelling, branded by the law, is also now so
branded in public opinion that it would be waste of words to
anathematize it. But what is suggested by the venom of some of the press
writers is that they have never put themselves into the place of a man
who, with the average sensitiveness to personal affront, and with
thorough-going physical courage, had also a clear perception of the
remorselessness of his journalistic rivals. From some of them he could
expect no more mercy than from the red gentry of the plains. Let those
who are sending their arrows into Mr. Bennett ask themselves whether
they are wholly sure that in his position, with his family history
behind them, they would have done otherwise after the street assault. At
any rate, neither duelling nor that cowardly substitute, shooting down
an unprepared man who has done some wrong, will be driven out of fashion
by bringing newspaper taunts of "showing the white feather" against
those who fail to resort to such lawlessness.
THE INDUSTRY OF INTERVIEWERS.
It was a quarrel totally apart from newspaper affairs, as we all know,
that carried the editor of the "Herald" to the field of honor at
Marydell. Indeed, Mr. Bennett's conduct before and after the duel was so
"unjournalistic" that the Philadelphia reporters are said to have sent
him a letter, while he tarried in that city, protesting that a gentleman
so well aware of the "usages of the profession" ought to submit to be
interviewed. But the physician does not always swallow his own drugs.
Mr. Bennett, on receiving the missive, remarked that it was "all right,"
and remained uninterviewed, thus setting an awful example to the
community.
A public attack by a man armed with a cowhide upon another not so armed
is hardly a feat that excites admiration, while the affair at Marydell
was in no sense such reparation for the previous insult as in common
parlance to be thought "satisfaction." But one feature of the
Bennett-May quarrel not unpleasant to read was the outwitting of the
news-gatherers and their resulting desperation. "Had the duel taken
place on the Canada border the parties to it could hardly have evaded
our extensive arrangements to report it," said one journal after the
affair, in a somewhat lugubrious and yet self-vindicating strain. The
promptness of Mr. Bennett's movements, and his skill in throwing the
reporters off the scent, lest the duel might be stopped, were hard blows
to the newspapers. But theirs was no dishonorable defeat--it was one of
the fraternity that beat them. Even the device of giving imaginary
accounts of the battle in order to draw out the true one was
unsuccessful until Mr. Bennett had sailed for Europe.
On the May side there was a trifling gain for the interviewers, but not
much. Dr. May, senior, seems to have been condemned to a copious
acquaintance with journalists; for, though in knowing Mr. Bennett he had
already perhaps known one too many of them, his house appears to have
been overrun, after the Fifth avenue assault, with the fraternity, who,
in the "strict discharge of professional duty," swarmed multitudinously
upon him. At least, one morning the "Tribune" said:
The May mansion in West Nineteenth street was a sealed book
to reporters yesterday, and the door was promptly shut in
the face of those who were recognized as newspaper inquirers
by the <DW64> in charge. Dr. May has made no secret of his
anger at the reports, too accurately drawn, of his
appearance of anxiety and alarm when expecting bad news from
his son, and will have nothing to say to representatives of
the press.
Here, it will be observed, is a claim to something professional in the
very aspect of the "newspaper inquirer" whereby the sable guardian of
the portal may know him well enough to take the responsibility of
slamming the door in his face. Again, we observe here a tribute to the
interviewer's skill; for, prior to the duel, Dr. May, though politely
presenting himself, could give no news; but his lynx-eyed visitors had
gathered from the very attitude, tone, and look of their host the
material for an item as picturesque as any tidings. So the besieged
householder, as we have seen, took refuge in total eclipse, leaving only
a "<DW64> in charge" to determine the status of his callers.
Yet the most discerning <DW64> in charge sometimes proves a weak barrier
against invasion. The trained interviewer can take a protean shape, and
introduce himself under disguise of the most sympathetic friendship or
the most urgent business. Sometimes he is the picture of respectful woe,
or anon it is he who has a favor to confer by bringing news of pressing
importance. Close and private indeed must be that conference whose
secrets he cannot worm out. He gave to the public the "family scene of
astonishment at the opening of the Vanderbilt will" the very morning
after the affair occurred. Should moral borings fail, he can resort to
material ones, as when, a few months since, he cut a hole in a hotel
floor, to apply his ear to, over the room where a Congressional
committee sat in secret session, being detected only by the unlucky
plaster falling among the astonished statesmen below. He is the animal
of the fable, who, having once "got in," cannot be got out until ready
to go. In our war times some commanders looked upon him, coming to camp
in never so fair a guise, with the misgivings of the hapless Trojan
regarding the wooden horse; and it is said of Baron Von Werther that he
"treats as an enemy all newspaper correspondents, even though they have
the best personal introductions to him." Such fears of warriors and
diplomats, who quail before no ordinary foes, are tributes to the
interviewer's prowess.
It must go hard but he gets something from the sullenest and most
refractory customer. We have seen his harvests at the May mansion, when
baffled by real ignorance on the part of his victim; hence we may guess
whether he is to be checked by a mere wilful purpose to conceal, or the
whim to keep a matter private. At very worst, his own description of his
rebuff will be humorous and piquant. Often do we have an entertaining
half column beginning, "Our reporter waited upon," etc., and, after
descriptions of household ornaments, personal dress, and so on, ending
in this way:
_Ques._--You say, then, that you can give me no information
whatever?
_Ans._ (_snappishly_)--As I have already told you a dozen
times, no information whatever.
_Ques._--And that is positive and final?
_Ans._ (_savagely_)--Positive and final.
Here our reporter took his leave, wishing the gentleman a
very good morning, to which politeness of our reporter the
uncommunicative gentleman only distantly bowed.
But these defeats form a rare experience of the interviewer, who even
then continues to pluck victory (that is to say, an item) out of their
jaws. His ordinary career is a round of triumph which has made him a
leading figure in the portrait gallery of modern society. I wonder that
Mr. Daly does not introduce it at length into some of his comedies of
American life. Drawn faithfully, and personated by Mr. James Lewis, the
dramatized interviewer would be a wealth of pleasure.
PHILIP QUILIBET.
SCIENTIFIC MISCELLANY.
THE FORCE OF CRYSTALLIZATION.
The old story of a bombshell filled with water and left to burst by
freezing, upon the plains of Abraham, near Quebec, may now be superseded
as an illustration of the power of frost. The men at a Western dockyard
were surprised to find one morning that the paddle-wheel of a steamer in
the dry dock had fallen from the shaft, and was broken in two pieces.
The hub of the wheel, about fifteen inches long, was slightly hollowed
out at the centre to admit of its being slipped on without difficulty
over any uneven portion of the shaft-end. This recess was full of water
when the boat was placed in the dock, and the keying had been so close
that the liquid--about a pailful--was exposed to the frost. As the water
congealed under the sharp wintry atmosphere of the night it expanded and
burst asunder the five-inch walls of iron, and the broken wheel fell
with a crash.
FROZEN NITRO-GLYCERINE.
Two accidents, both fatal, have lately occurred from the use of
nitro-glycerine for blasting. In one case some frozen cartridges were
recklessly placed in the oven of a stove, while others were held up to
the fire. That an explosion should take place under such circumstances
is not surprising, and comment is unnecessary. The other explosion
partook more clearly of the nature of an accident. A well digger, living
near Sing Sing, had buried a can of nitro-glycerine in his garden for
future use; and while digging it up, January 18, his pick struck the
can, ignition followed, and he was blown to pieces. No doubt the can was
frozen, thus proving anew that frozen nitro-glycerine is more dangerous
to handle, though not so powerful in its effects, as in the liquid form.
This is singular behavior and contrary to theory. In general terms,
explosion may be defined as the result which takes place when a portion
of the nitro-glycerine is raised to a given temperature. Now, to produce
this temperature by the friction resulting from the blow of a pick is
manifestly more difficult with frozen than with tepid liquid. In the
former case some of the heat produced would be absorbed by the
liquefaction of the solid substance, and therefore there would be less
available for producing the temperature of explosion. But, plain as this
proposition is, there must be some unknown condition, for it has been
frequently observed in practical work that nitro-glycerine is never so
dangerous to handle as when frozen. This result, however, is directly
opposed to the experiments of Beckerhinn, of Vienna, who lately
experimented to decide this question. He placed a thin layer of
nitro-glycerine on a Bessemer steel anvil, and a weight of about five
pounds, having a small hardened steel face, was dropped upon it. The
height to which it was necessary to raise this weight in order to
produce explosion determined the comparative delicacy of the explosive.
With tepid nitro-glycerine explosion took place when the weight dropped
about 31 inches (0.78 metres), but with frozen liquid the fall had to be
increased to about 85 inches (2.13 metre). Thus the experimental results
are opposed to the acknowledged experience of practical work in the
hands of common laborers. Mr. Beckerhinn found the density of the solid
nitro-glycerine to be 1.735, that of the liquid 1.599, and the average
melting heat to be 33.54 heat units. Thus the explosive shrinks about
one-twelfth in crystallizing.
ENGLISH GREAT GUNS.
The largest rifled cannon in the world is a 100-ton gun, made for the
Italian government by Sir William Armstrong's firm. But the English
government is preparing to outdo this, and already has the plans ready
for a gun of 164 tons. It hesitates, in fact, between a weapon of this
size and one of 200 tons, a mass of metal which its shops are now
perfectly able to handle. The meaning of the term--200-ton gun--is
simply this: a tube of iron and steel of that weight, fifty feet long,
having a calibre of 20 inches, and firing a shot of 3,500 or 4,000
pounds weight, with a charge of 800 pounds of powder! The human capacity
for astonishment has grown perforce as the successive steps have been
taken from the guns of ten and twenty tons to these weapons, which must
remain huge whatever further advances are made. The character of warfare
with them is best indicated by the fact that the 200-ton gun must be
handled entirely by machinery. The advent of these unmanageable weapons
is signalized by the invention of a hydraulic apparatus for working
them. The vast shock of the recoil from the bursting of thirty-two kegs
of powder--enough to throw down 1,200 tons of rock in mining--is taken
up by a cylinder pierced with small holes. These holes are capped with
valves, held down with a pressure of fifty tons to the square inch. When
the force of the recoil exceeds this the water is forced out of the
holes and the recoil thus taken up in work done. The breech of the piece
is supported on a hydraulic ram, the elevation of which depresses the
muzzle of the gun below the level of the deck, and brings it exactly in
line with an iron tube carrying the sponge. This is run up to the base
of the powder chamber, a deluge of water rushes from apertures in its
head, and the bore is completely cleaned out and every spark of
remaining fire extinguished. The rammer then retires, the sponge is
taken off, and the powder hoisted by tackle to the muzzle, whence the
rammer pushes it home, and then does the same for the shot. The shot and
cartridge, weighing together about 1,350 pounds, are stored on little
iron carriages, every charge in the magazine having its own carriage.
The loading finished, the gun is raised, pointed, the port flies open,
and the discharge immediately follows. What the result of the blow from
such a projectile would be is not to be imagined. It is acknowledged,
however, that in the struggle for mastery the gun has beaten defensive
armor. No ship has been built to stand the shock of a 3,500 pound bolt
moving at the velocity of 1,300 or 1,500 feet a second.
EAR TRUMPETS FOR PILOTS.
Prof. Henry has turned his attention to the discovery of means for
increasing the distinctness of sound signals at sea. It is a very large
hearing trumpet, projecting mouth foremost from the top of the
pilot-house of a steamboat. But he soon found that a single hearing
trumpet would not answer the purpose, for though it greatly augmented
the perceptive power of the ear, it destroyed the capacity of that organ
for distinguishing the direction of sound. For this purpose two ears are
necessary. Prof. Henry then made use of two hearing trumpets, the axes
of which are separated about 30 inches. An india-rubber tube proceeding
from the axis of each is placed so as to terminate in the ear of the
observer--one in each ear. With this instrument the audibility of the
sound was very much increased, but as a means of determining the
direction of the source of sound, it was apparently of little use. For
this purpose the unaided ear is sufficient, provided the head is placed
above all obstructions and away from reflections.
HOT WATER IN DRESSING ORES.
We have before alluded to the investigations made to ascertain the
reason why clay settles more rapidly in solutions of some salts than in
pure water, a fact which appears contrary to reason, since it might be
inferred that the greater the specific gravity the more buoyant the
fluid. But the fact is abundantly confirmed, and it is likely to find
important application some day in the arts. The property which every
substance has of sinking through a fluid of less density than its own
forms the basis upon which nine-tenths of the gold and copper, and
probably six-tenths of the silver produced in this country, is extracted
from its ores. It is the foundation of the art of ore dressing, one of
the most important parts of metallurgy. Anything which increases the
rapidity and thoroughness of the process may have a fortunate
application in this art. Mr. Ramsay, of the Glasgow university
laboratory, thinks the property in question depends upon the varying
absorption of heat by the different solutions. When water containing
suspended clay is heated the rapidity of settling is proportional to the
heat of the water. This mode of accelerating the movement of fine
sediments in water is perhaps more easily applied than the solution of
caustic soda or potash, or of common salt. Rittinger, by a mathematical
discussion of the principles which control the downward movement of
solid particles in an ascending stream of water, showed that the
separation of light from heavy minerals is more complete with solutions
of density greater than that of water than in water alone. He found a
solution of 1.5 sp. gr. extremely favorable. If the addition of heat
will increase the effect of such a solution, it may become possible to
separate, by means of the continuous jig, minerals so near in specific
gravity as barite and galena. This whole subject of ore dressing is one
of the most important questions connected with the future of mineral
industry in America. In the Mississippi valley everything connected with
metallurgy, from the fuels to the finished metal, will one day be
closely dependent on it.
OCEAN ECHOES.
Prof. Henry communicated to the National Academy at Philadelphia his
latest researches into the subject of sound, and among them an
explanation of the echo observed on the water. This echo he had formerly
been inclined to attribute to reflection from the crests of the waves.
Tyndall holds that it is due to reflection from strata of air at
different densities. Prof. Henry's present explanation is that this echo
is produced by the reflection of the sound wave from the uniform surface
of the water. The effect of the echo is produced by the fact that the
original sound wave is interrupted. It has what the learned Professor
calls _shadows_, produced by the intervention of some obstacle in its
path. Sound is not propagated in parallel, but in diverging lines, and
yet there are some cases where what may be called a "sound shadow" is
produced. For instance, let a fog-signal be placed at or near water
level on one side of an island that has a conical elevation. Then the
signal will be heard distinctly by a vessel on the opposite side of the
island at a distance of three miles. But when the vessel sails toward
the island (the signal being on the opposite side), the sound will be
entirely lost when the distance is reduced to a mile, and in any smaller
distance it is not recovered. In this case the station of the vessel at
the shorter distance is in the "sound shadow." The termination of that
shadow is the point at which the diverging beams of sound, passing over
the crest of the island, bend down and reach the surface of the water.
The formation of the sound echo may be explained by this extreme
divergence of the sound waves, for it is rational to suppose that at a
great distance from the source of sound some of the dispersed waves will
reach the water surface at such an angle as to be reflected back to the
hearer. This was well illustrated by an experiment made to test
Tyndall's theory. A steam siren was pointed straight upward to the
zenith, but no echo from the zenith was heard, though the presence of a
cloud from which a few raindrops fell certified the presence of air
strata of different densities. But, strange to say, an echo _was_ heard
from every part of the horizon, half of which was land and half water.
The only explanation of this fact is that the sound waves projected
upward were so dispersed as to reach the earth's surface at a certain
distance, and at that point some of them had curled over and assumed a
direction that caused their reflection back to the siren.
THE DELICACY OF CHEMISTS' BALANCES.
In making chemical balances for fine work the beam is made in the truss
form to prevent the bending which takes place even under such small
loads as an ounce or two. Prof. Mendeleef has a balance that will turn
with one-thousandth of a grain, when each pan is loaded with 15,000
grains. This extreme sensibility is obtained by the use of micrometer
scales and cross threads at the end of the beam, these being observed by
means of a telescope. Of course one weighing with this complicated
apparatus occupies a long time. In most balances the beam rests on steel
knife edges; but a maker who has lately obtained celebrity makes his
supports of pure rock crystal. The steel edges can be seen with the
naked eye; the quartz edges cannot be seen even with a magnifying glass.
One writer on this subject thinks that with these perfect crystal edges,
with an inflexible girder beam, a short beam giving quick vibrations,
and a sensitiveness that can be increased by screwing up the centre of
gravity, there can hardly be a practical limit to the smallness of the
weight that will turn the beam. The amount of motion may be very small,
but if this can be observed, the limit of possible accuracy is very much
extended.
GOVERNMENT CONTROL OF THE DEAD.
What the population of European countries was a hundred years ago it
would be hard to tell with accuracy; but the nations have doubled and
trebled in strength within the century. Sanitary precautions have
increased in importance, and the very noticeable movement in regard to
social hygiene which now possesses English society is perhaps due in
part to the obvious dangers to which thirty million human beings are
subjected when living together on such a small area. The medical officer
for Birkenhead has pointed out that it may be necessary for the
government authorities to take more complete charge of the dead as a
possible source of infection. He says that the intelligence of deaths
from infectious diseases now furnished by local registrary would be much
more useful than it is as a means for limiting the spread of disease if
the medical officer were vested with further powers in respect to the
infected dead body. At present neither the medical officer nor any one
else has any power to order the immediate removal of an infected body,
and those in charge of it might do what they liked with it. He advocated
the necessity of power being given to medical officers to order the
immediate removal of the infected bodies to a public mortuary and their
speedy burial.
MICROSCOPIC LIFE.
Dr. Leidy lately described to the Academy of Sciences in Philadelphia an
encounter for life which he witnessed between two microscopic
animalcules. The two creatures were respectively 1-625th and 1-200th of
an inch in diameter. On the morning of August 27, from some mud adhering
to the roots of sphagnum, obtained the day previously in a nearly
dried-up marsh at Bristol, Pennsylvania, he obtained a drop of material
for examination with the microscope. After a few moments he observed an
amoeba verrucosa, nearly motionless, empty of food, with a large central
vesicle, and measuring 1/25th of a millimetre in diameter. Within a
short distance of it, and moving directly toward it, was another and
more active amoeba, regarding the species of which he was not positive.
It was perhaps the one described by Dujardin as amoeba limax, by which
name it may be called. As first noticed, this amoeba was one-eighth of a
millimetre long, with a number of conical pseudopods projecting from the
front border, which was one-sixteenth of a millimetre wide. The creature
contained a number of spherical food spaces with sienna
contents, a large diatom filled with endochrome, besides several clear
food spaces, a posterior contractile vesicle, and the usual glanular
endosarc. The amoeba limax approached and came into contact with the
motionless amoeba verrucosa. Moving to the right, it left a long
finger-like pseudopod curved around its lower half, and then extended a
similar one around the upper half until it met the first pseudo-pod.
After a few moments the ends of the two projections actually became
continuous, and the verrucosa was enclosed in the embrace of the amoeba
limax. The latter assumed a perfectly circular outline, and after a
while a uniformly smooth surface. It now moved away with its new
capture, and after a short time what had been the head end contracted
and became wrinkled and villous in appearance, while from what had been
the tail end ten conical pseudopods projected. The amoeba verrucosa
assumed an oval form, and the contractile vesicle became indistinct
without collapsing. Moving on, the amoeba limax became more slug-like in
shape. The amoeba verrucosa now appeared enclosed in a large oval, clear
vacuole or space, was constricted so as to be gourd-shaped, and had lost
all trace of its vesicle. Subsequently it was doubled upon itself, and
at this point the amoeba limax discharged from one side of the tail end
the siliceous case of the diatom, which now contained only a shrivelled
cord of endochrome. Later the amoeba verrucosa was broken up into fine
spherical granular balls, and these gradually became obscured and
apparently diffused among the granular contents of the entosarc of the
amoeba limax. The observations from the time of the seizure of the
amoeba verrucosa to its digestion or disappearance among the granular
matter of the entosarc of its captor, occupied seven hours. From naked
amoeba the shell-protected rhizopods were no doubt evolved, and it is a
curious sight to observe them swallowed, home and all, to be digested
out of their house. It was also interesting to observe the cannibal
amoeba swallowing one of its own kind and appropriating its structure to
its own use, just as we might do the contents of an egg. The amoeba
verrucosa he describes as remarkable for its sluggish character, and in
appearance reminds one of a little pile of epithelial scales or a
fragment of dandruff from the head. It is oval or rounded, transparent,
and more or less wrinkled, or marked with delicate, wavy lines.
THE SOURCES OF POTABLE WATER.
In the British Social Science meeting, Mr. Latham, a civil engineer of
London, brought up the question of water supplies and endeavored to find
rules for the guidance of water engineers in those apparently
contradictory facts which the observation of recent years has produced
so abundantly. It has been generally considered that water which has
received the sewage of large populations must be unfit for domestic use;
but careful investigation would show that when such polluting matter has
been passed into a river, and exposed to the influence of light,
vegetation, etc., it becomes innocuous. This is shown by the good health
enjoyed by the inhabitants of London, which place receives its supply
chiefly from the Thames and the Lea, both of which rivers receive a
considerable amount of sewage pollution. The author instanced Wakefield,
Doncaster, and Ely as towns that draw their supplies of water from
sources into which sewage matter enters, and yet whose inhabitants are
healthy. The cholera epidemic at Newcastle-on-Tyne in 1853 was supposed
to have been caused by the use of polluted Tyne water, and yet it was
clearly ascertained that disease was much more rife among those persons
who used local well water. These facts, which have often been quoted,
were not favorably received by the audience, who greeted with laughter
Mr. Latham's assertion that water into which sewage matter has entered
can be purified by a short exposure to the air. That statement may be
too strong; but there is acknowledged truth in the author's main point.
He considered it was clearly proved that water derived from underground
sources, or from which light and air have been excluded, is impure, and
consequently unfit for domestic use. Universal testimony showed that
decaying matter easily found its way into underground sources of supply.
Well water may become seriously contaminated by the slow steeping of
noxious matters, and be less wholesome than the water of a running
stream that receives much larger quantities of impurity.
THEORY OF THE RADIOMETER.
Prof. Crookes has at length announced a theory in explanation of the
movements exhibited by the remarkable "light mill" of his invention. He
says: "The evidence afforded by the experiments is to my mind so strong
as almost to amount to conviction, that the repulsion resulting from
radiation is due to the action of thermometric heat between the surface
of the moving body and the case of the instrument, through the
intervention of the residual gas. This explanation of its action is in
accordance with recent speculations as to the ultimate constitution of
matter, and the dynamical theory of gases." The most refined means for
exhausting the air from the glass bulb which contains the suspended
vanes of the radiometer leave, and if they were to be carried to
absolute mechanical perfection, would still leave a certain amount of
gas in it. But Dr. Crookes has carried this attenuation so far that the
number of gas molecules present can no longer be considered as
practically infinite. Nor is the mean length of their paths between
their collisions any longer very small compared to the size of the bulb.
The latest use to which the radiometer has been put was to test the
viscosity of gases at decreasing pressures. The glass bulb was furnished
with a stopper lubricated with burnt rubber. This was fixed and carried
a fine thread of glass which is almost perfectly elastic. To the end of
this thread hung a thin oblong plate of pith to which a mirror was
attached. The glass stopper being fixed, and the bulb capable of
rotation through a small angle, it is evident that when the bulb is
rotated the pith ball will remain at rest except as it yields to the
friction of the air moved by the bulb. It does move, swinging a certain
distance and then back, like a pendulum. The amount of this movement is
carefully observed by a telescope, and recorded for five successive
beats. As the pith and glass fibre form a torsion pendulum, it is
evident that these beats will gradually die down in consequence of the
resistance of the air. By exhausting the air to various degrees of
rarity, it was proved that Prof. Clerk Maxwell's theory, that the
viscosity of a gas is independent of its density, is correct. The
logarithmic decrement of the first five oscillations (that is, the
decrease, oscillation by oscillation, of the logarithm of the arc
through which the pith vanes swing), was found to be nearly the same
when the air was almost exhausted as when it was at its natural
pressure, proving that its viscosity remained nearly equal for all
pressures. Only in the exceptionally perfect vacuum referred to above
did this logarithmic decrement sink to about one-twentieth of what it
had commenced with. Repulsion of the vane by the action of light
commences when this decrement is one-fourth of what it was before the
exhaustion of air began. As the rarity of the air within the bulb
increases the force of this repulsion begins to diminish, like the
logarithmic decrement, and when the latter has sunk to one-twentieth the
former has fallen off one-half. All these and other facts previously
obtained prove that the action of light is not _direct_, but _indirect_;
and Dr. Crookes has, after repeatedly refusing to consider hasty
judgments, in consequence come to the conclusion stated above, that the
rotation of the light mill is the result of heat. This decision accords
with the opinion of other observers. The radiometer has already entered
the field of industrial science, and is used to measure the duration of
exposure of photographic plates. De Fonvielle has made with it a new
determination of the sun's thermometric power. He made a spectroscope
with a graduated screen, which permitted the amount of light that
entered the apparatus to be graduated at will. In the path of the beam
he placed a radiometer, and by comparing its action in the graduated
light ray, and in the light of a standard oil lamp, burning 42 grammes
(11.3 ounces Troy) per hour, he found that at 4 o'clock, on June 4,
1876, the radiating force of the sun was equal to 14 lamps placed 25
centimetres (10 inches) from the radiometer.
TEMPERED GLASS IN THE HOUSEHOLD.
The "tempered glass," which has made the name of M. de la Bastie, its
discoverer, so well known, does not prove to be always manageable. It
was to have the strength of metal, and not shiver with changes of
temperature. But an English lady has found that it sometimes has
precisely the contrary characteristics. She purchased twelve globes for
gaslights, and they were made in the manufactory of M. de la Bastie
himself. But one night, after the gas had been extinguished for exactly
an hour, one of the globes burst with a report, and fell in pieces on
the floor, leaving the bottom ring still on the burner. These pieces,
which were of course found to be perfectly cold, were some two or three
inches long and an inch or so wide. They continued for an hour or more
splitting up and subdividing themselves into smaller and still smaller
fragments, each split being accompanied by a slight report, until at
length there was not a fragment larger than a hazel nut, and the greater
part of the glass was in pieces of about the size of a pea, and of a
crystalline form. In the morning it was found that the rim had fallen
from the burner to the floor in atoms. In all these phenomena the
behavior was that of unannealed glass, of which so many curious
performances have been related.
THE NEW YORK AQUARIUM.
A marine and fresh-water aquarium has been opened in New York, and both
from its intrinsic merits and as the first attempt to institute in this
country a valuable mode of scientific amusement and instruction, it
deserves mention. It does not equal in size or arrangements any of the
celebrated places of the kind abroad. Still it contains tanks of
considerable size, and in them some very interesting denizens. The
shark, sturgeon, skate, sea-turtle, and other fishes are represented by
large individuals, and their habits can be watched at leisure. A small
white whale was also at one time one of the attractions. Fish breeding
is carried on in the establishment, which receives constant additions to
its occupants by expeditions which are said to be especially planned for
this purpose. In any case New York is an excellent point for an
aquarium, and probably receives every year enough rare living fish at
its great markets to maintain such an institution. The commencement now
made is a worthy one, and it can easily become an important source of
pleasure and usefulness. The system employed is that of constant
circulation, the water being pumped from a reservoir to the several
tanks. Pumps and pipes are made of hard rubber. A library, a
naturalists' laboratory, equipped with tables, microscopes, etc., are
either established or projected in the building.
THE CRUELTY OF HUNTING.
The outcry against the practice of making surgical experiments upon
living dogs, rabbits, and other animals has roused some vivisectionists
to return to the subject of hunting. This is one of the principal themes
of the philosophic philanthropist, whose opposition to the practice
seems to be an outgrowth of the better acquaintance which man has made,
through science, with the lower animals. He accomplishes his task very
effectively by calculating the number of animals which are wounded but
not recovered by English sportsmen every year. The official returns show
that in 1873-'4 there were 132,036 holders of gun licenses, and 65,846
holders of licenses to kill game in the British dominions. In 1874-'5
the numbers were 144,278 and 68,079, showing that the disposition and
ability to hunt are on the increase. As a basis for computation, the
partridge season of 21 weeks is taken, and two days' hunting are allowed
for each week; while three birds are supposed to be wounded and "lost"
daily by each sportsman. This gives 126 birds wounded and left to suffer
unknown torments by each one of the 68,079 holders of game licenses. The
total is no less than 8,296,496 "lost" birds in 1873-'4, and 8,577,954
in 1874-'5. Then the holders of gun licenses have the right to shoot
birds which are destructive to crops, etc., and two lost birds each week
in the year is calculated to be the average. This makes no less than
13,731,744 wounded birds in 1873-'4, and 15,004,912 in 1874-'5. The
total is in round numbers _twenty million_ birds injured each year!
These estimates are made by "Nature," and they correctly represent the
ground on which the modern opposition to the hunt as a cruel and
unnecessary occupation is based. Of course the figures are not exact.
The only effort made was to have them within bounds; and considering all
the varieties of game pursued in England, and the extraordinary keenness
of Englishmen for sport, this estimate is probably correct. Quite lately
they have been confirmed by a noted hunter on the western plains, who
says that in his case a day's sport was usually marked by the "loss" of
two or three animals. As he is an uncommon shot, his experience cannot
be more unfortunate than the average. Such calculations show us how
enormous are the results when the whole human race engages in one
action. At present, English society offers the contradictory spectacle
of a large and increasing body of hunters who oppose vivisection on the
ground of cruelty, and a small and increasing body of vivisectionists
who oppose hunting also on the ground of cruelty.
THE GORILLA IN CONFINEMENT.
Great interest attaches to the career of the young gorilla now in the
Berlin aquarium. Dr. Hermes described some of his peculiarities at a
late meeting of the German Association of Naturalists and Physicians. He
nods and claps his hands to visitors; wakes up like a man, and stretches
himself. His keeper must always be beside him and eat with him. He eats
what his keeper eats; they share dinner and supper. The keeper must
remain by him till he goes to sleep, his sleep lasting eight hours. His
easy life has increased his weight in a few months from thirty-one to
thirty-seven pounds. For some weeks he had inflammation of the lungs,
when his old friend Dr. Falkenstein was fetched, who treated him with
quinine and Ems water, which made him better. When Dr. Hermes left the
gorilla on the previous Sunday the latter showed the doctor his tongue,
clapped his hands, and squeezed the hand of the doctor as an indication,
the latter believed, of his recovery. Apparently he means to support, by
every means in his power, the effort at a hot-house development of the
ape to the man. A large glass house has been built for him in connection
with the palm house.
INSTRUCTION SHOPS IN BOSTON.
The Boston Institute of Technology is somewhat noted for its boldness in
making educational experiments; its efforts so far having been directed
toward the introduction of practical trade instruction into an advanced
school. Some years ago it endeavored to establish a model room for
dressing ores and another for smelting them; but the success of this
trial seems to be more than doubtful. Both of these pursuits are too
extensive to be represented by one shop or by sample work. Nothing
daunted by this failure, President Runkle has lately introduced a
"filing shop" as the first step toward practical instruction in
engineering work. This shop has about thirty work tables, each provided
with a vise and tool drawers. Filing is one of the first things the
young apprentice has to learn; and those who think that anybody can file
who has hands may be surprised to learn that the filing of a hexagon
bolt head is one of the tests for a Whitworth prize scholarship. The
difficulty of making a flat surface is in that task combined with the
necessity of having the faces of equal size and placed at equal angles
to each other. The plan in the Boston institute is to have the student
spend ten weeks in filing, and then the same length of time in each the
forging shop and the turning shop. The two latter are not yet ready.
These three steps form part of a two years' course in mechanical
engineering, the tuition fee to which is $125 yearly. The main objection
to such schools is that engineers and practical men persist in refusing
to accept such instruction as a substitute for actual work. The Boston
institute is making praiseworthy efforts, but it seems to be adopting a
system which has never been in favor just at a time when the smelting
works and machine shops of the country appear willing to unite with the
scientific schools in supplying students with real experience of work as
a requirement for a diploma.
* * * * *
A new mode of compressing arteries is by the use of a hard pad having a
prominent projection, which is pressed against the artery or vein by a
strong elastic ring of rubber passed over the limb.
* * * * *
The Harvard summer schools were so far successful that the last
catalogue reports forty students in geology, twenty-five in chemistry,
twenty-five in phenogamic botany, and six in cryptogamic botany.
* * * * *
A case in which the heart was severely wounded without causing immediate
death lately occurred in England. The wound was made by a knife which
passed between the third and fourth ribs, through the wall of the heart
into the cavity of the left ventricle. The man lived sixty-four hours.
* * * * *
M. Peligot warns housekeepers against the advice so often given, to use
borax for the preserving of meat. He finds that borax and the borates
affect plants very seriously, and doubts whether it can be innocuous to
animals. French beans watered once with a solution of borax quickly
withered and died.
* * * * *
A young American, Dr. James by name, was killed with his partner (a
Swede) at Yule Island in September last, by the natives of New Guinea.
They were hunting birds of paradise at the time. Dr. James left some
valuable collections which have been described before the Linnaean
Society of London.
* * * * *
In extending the underground railway of London, the excavations
disclosed Roman and other remains of considerable interest. Among the
former there were found fragments of urns, specimens of pottery, and
bronze coins. The most remarkable discovery was that of a thick stratum
of bullock's horns, commencing about twenty feet below the surface, and
extending to an unascertained distance beneath. Although the deposit was
doubtless made many centuries ago, the horns had suffered so little by
decay that they found a ready sale in the market. This road has carried
in thirteen years 408,500,000 passengers. In 1863, the first year, the
number was 9,500,000, which increased to 48,500,000 last year.
* * * * *
Foreign papers say that Mr. Floyd, the President of the board of
trustees for the Lick donation, has come to an arrangement with M.
Leverrier, the celebrated French astronomer, for the better execution of
the instruments to be made for the Lick Observatory. The masses of glass
required are to be made in Paris, at Feil's glass works, and the
object-glasses very likely by an English optician.
* * * * *
Two distinguished men were officially superannuated last year: Profs.
Milne-Edwards and Delafosse of the Paris Museum. The son of the former
takes his place, and Descloiseaux succeeds to the chair of mineralogy.
Professors Dove of Berlin and Woehler of Goettingen have had their
_jubilaeum_ or fiftieth anniversary of their doctorates. All these facts
illustrate the conservative influence of student life.
* * * * *
The Western mines of gold and silver have lately yielded some new and
interesting minerals. Roscoelite is a vanadium mica from a gold mine at
Granite creek, California. The vanadic acid varies from 20 to 23 per
cent. Psittacinite is a vanadate of lead and copper, which occurs
associated with gold, lead, and copper minerals at several mines in
Silver Star district, Montana. It is considered to be a favorable
indication, for when that is found the vein is said to become rich in
gold. Coloradoite is a telluride of mercury, also a new mineral and
quite rare.
* * * * *
Dr. Piggott proposes to replace the spider's web of telescopes by a star
illuminated transit eye-piece. A sheet of glass, on which a thin film of
silver is deposited, is placed in the focus of the eye lens; transparent
lines are drawn on the film, instead of wires, and as the star passes
across the lines it is seen to flash out brightly. The film of silver is
made sufficiently thin to permit of the star being seen when it is
between the lines, but it appears that the lines themselves are only
visible, except in the case of very large stars, when the star disc is
in transit across a line.
* * * * *
Singular results of strains existing in the granite rocks through which
the St. Gothard tunnel is passing are recorded. When the shots are fired
at the end of the gallery they are sometimes succeeded at unequal
intervals by other explosions at points where there is no drill hole and
no powder. Workmen have been injured by these spontaneous explosions,
which are to be explained only on the theory that there are strains in
the rock; and when this tension is increased by the shock of a heavy
explosion, the rock flies in pieces with noise. Similar effects have
been noticed in other granites.
* * * * *
It is said that aniline colors are now used to color wines, and that
enough of them is taken into the Bordeaux district of France to color
one-third of its whole product. Husson gives the following method for
detecting it: Take a small quantity of the wine and add a little
ammonia, when the mixture turns a dirty green. Steep a thread of white
woollen yarn in the liquor and allow a drop of vinegar to flow along it.
If the color of the wine is natural, as the drop advances the original
whiteness of the wool is restored; but if the wine has been
sophisticated with magenta, the wool will take a rose color. This test
is simple, easily tried, and effective.
* * * * *
An inquiry into the results of systematic gymnastic exercises in a
French military school shows that the strength is increased on the
average 15 to 17 per cent., and is also equalized on both sides of the
body. The capacity of the chest is increased at least 16 per cent. and
the weight 6 to 7 per cent. Coincident with this increase is a decrease
in the bulk of the body, showing that fat is changed to muscle. The
improvement is confined to the first three months of the course unless
the exercise is then moderated. If continued at too high a rate,
weakness succeeds the increase of strength. It would be a good plan to
place a dynamometer in every gymnasium as a measure of the changes which
take place in the gymnast.
MOON MADNESS.
The popular belief that the moon's rays will cause madness in any person
who sleeps exposed to them has long been felt to be absurd, and yet it
has appeared to have its source in undoubted facts. Some deleterious
influence is experienced by those who rashly court slumber in full
moonshine, and probably there is no superstition to which the well-to-do
pay more attention. Windows are often carefully covered to keep the
moonbeams from entering sleeping rooms. A gentleman living in India
furnishes "Nature" with an explanation of this phenomenon which is at
least plausible. He says: "It has often been observed that when the moon
is full, or near its full time, there are rarely any clouds about; and
if there be clouds before the full moon rises, they are soon dissipated;
and therefore a perfectly clear sky, with a bright full moon, is
frequently observed. A clear sky admits of rapid radiation of heat from
the surface of the earth, and any person exposed to such radiation is
sure to be chilled by rapid loss of heat. There is reason to believe
that, under the circumstances, paralysis of one side of the face is
sometimes likely to occur from chill, as one side of the face is more
likely to be exposed to rapid radiation, and consequent loss of its
heat. This chill is more likely to occur when the sky is perfectly
clear. I have often slept in the open in India on a clear summer night,
when there was no moon; and although the first part of the night may
have been hot, yet toward two or three o'clock in the morning, the chill
has been so great that I have often been awakened by an ache in my
forehead, which I as often have counteracted by wrapping a handkerchief
round my head, and drawing the blanket over my face. As the chill is
likely to be greatest on a very clear night, and the clearest nights are
likely to be those on which there is a bright moonshine, it is very
possible that neuralgia, paralysis, or other similar injury, caused by
sleeping in the open, has been attributed to the moon, when the
proximate cause may really have been the _chill_, and the moon only a
remote cause acting by dissipating the clouds and haze (if it do so),
and leaving a perfectly clear sky for the play of radiation into space."
THE ARGUMENT AGAINST VACCINATION.
An English physician opposes compulsory vaccination on the ground that
it prevents further discovery, and compels medical science to halt at
just that point, because it forbids experiment upon methods of
prevention that may prove to be better. He says: "It stereotypes a
particular stage of scientific knowledge, and bars further progress. If
I remind you of the great improvement thought to have been made by the
introduction of inoculation by Lady Mary Wortley Montagu at the end of
the last century, and ask you to suppose that Parliament might then have
passed an act to compel every one to be inoculated, you will, I think,
see what is meant. This method was tried for some years with great
_eclat_, but afterward it was found to spread the smallpox so much that
an act of Parliament was passed to forbid its use. Vaccination,
introduced by Dr. Jenner, has followed, and this was another step in
advance. I was the first child in my father's family vaccinated
seventy-one years ago, several elder brothers and sisters having been
inoculated. Both methods answered in our cases. But for many years I
have been satisfied that other diseases besides the modified small-pox
(called cow-pox) are now introduced by the old vaccine, and have
steadily refused to use it, seeking rather, at increased trouble and
expense, new vaccine. And the question which comes forcibly to the front
is this: May not some other preservative be discovered which shall be a
further improvement? This question cannot be answered so long as
vaccination is compelled by law. There are no persons upon whom
experiments can be tried." So far as it goes, this is valid ground for
criticising vaccination laws. But the proof that small-pox is more
disastrous to the human race than the evils that vaccination brings with
it is so strong that there is little likelihood society will subject
itself to the attacks of the greater enemy in order to avoid the lesser.
The evils of the old system of using vaccine taken from human beings for
new inoculations are now no longer inevitable. Fresh vaccine direct from
the calf, and called "Bovine," can be had everywhere. A large
establishment for obtaining it is situated near New York.
CURRENT LITERATURE.
Colonel Dodge's "Plains of the Great West"[O] is one of the most
entertaining and important books of the kind we have met with. Whether
he treats of the chase, the natural history of the wild animals found on
our continent, or the Indians, he draws upon abundant resources of
observation and experience. His description of the much talked of
"plains" is new. He distinguishes three of these, the first lying next
the mountains, the next known as the "High Plains," being to the
eastward, and finally the broad surface of the lower plains. As the high
plains are more fertile than either of the others (owing to diversities
of soil), we have the singular effect of a country suddenly becoming
more fertile as the interior of the continent is more deeply penetrated.
Of other peculiarities exhibited in this region our author gives a vivid
account, and it requires all our faith in his accuracy to have
confidence in the following description of the famous Bad Lands, the
scene of so much Scientific search:
The ground is covered with fragments of the bones of animals
and reptiles, and the man must indeed be insensible who can
pass unmoved through these most magnificent burying-grounds
of animals extinct before the advent of his race.
Almost everywhere throughout the whole length and breadth of
the plains are found, in greater or less profusion, animal
remains, fossils, shells, and petrifactions. Bones are very
numerous and in great variety, from the saurian and mastodon
to the minutest reptile, ranging in point of time from the
remotest ages to the present day.
[Footnote O: "_The Plains of the Great West and their Inhabitants._" By
(Lieutenant-Colonel) RICHARD IRVING DODGE. With an Introduction by
William Blackmore. Illustrated. New York: G. P. Putnam's Sons.]
His description of other features of this vast region is full of
interest. The two remarkable belts of forest, called the cross timbers,
stretching for a hundred miles through a trackless country, but not
increasing their width beyond their normal eight to twelve miles; the
extraordinary rivers, half sand, half water, the mazes of which confound
the Indian, usually so acute in the field; the sand streams, which
repeat in that material the puzzle of the cross timbers, and are even
more inexplicable. While the desert does not narrow the cross timber
belts, nor water widen them, the wind seems to have no effect on these
sand streams, though the material that composes them is so light as to
rise on every puff of air. Like the cross timbers, the sand streams
pursue their way across the country, regarding neither wet nor dry, hill
nor stream. Their origin lies in forces not yet known, and though they
may seem to be the sport of existing conditions, they really maintain
themselves indifferent to their surroundings. Things like these prove
that Americans need not go to the Sahara for novel aspects of nature.
Our author has a quick perception of what is striking in these scenes,
and describes them in vigorous and pictorial language.
Colonel Dodge is one of the most noted hunters in our army, and his
descriptions of the chase deserve to rank with those of Cummings, Baker,
and other great African sportsmen. It is true our country does not
afford the hunter such a slaughter field as South Africa has been. A few
animals have increased on our soil to such an extent as to afford at
certain seasons opportunities for unlimited slaughter. But the past five
years have seen such destruction of the last of these--the buffalo--that
wholesale killing is no longer possible on any ground the white man is
suffered to visit. Three years more will carry us to the end of the
decade, and probably of the buffalo hunt as it has been in the past.
About five years ago a change came over the pursuit of this animal. He
began to be killed for his hide alone, and the results are almost
incredible. Colonel Dodge shows that in three years no less than
4,373,730 buffalo were killed by whites and Indians. It is evidently
impossible for any animal, bringing forth but one at a birth, to
maintain its increase against such heedless destruction. The present
winter has witnessed what is probably the last grand attack upon these
animals, as they took refuge in the sheltering mountains of northwestern
Texas from the cold and snow-covered plains. Very soon the noblest prey
of the sportsman on this continent will be one of his rarest prizes.
Colonel Dodge does not lack the usual hunter's fund of anecdote. His own
adventures are modestly told, and when "seven antelope and a fine dog"
are bagged with one shot, the story is credited (with the Colonel's
guarantee) to an anonymous "old hunter"! We have said that the plains do
not rival the African field in quantity of game, but the dimensions of
two separate "bags," shot in successive years, shows how great even in
this country the rewards of the chase may be. In 1872 five gentlemen, of
whom Colonel Dodge was one, bagged 1,262 head, and next year four shot
1,141 head on the same ground, and the author thinks "the whole world
can be safely challenged to offer a greater variety of game."
But interesting as the chase is in our author's hands, the most
important part of the book is that in which the Indians are described
and discussed. To one who knows the unanimity of army opinion concerning
the much debated Indian question in the West, it is almost unnecessary
to say that Colonel Dodge wishes to see the tribes transferred to the
sole control of the War Department, treaty-making stopped at once,
discipline introduced, the vagabond whites eliminated from the tribes,
and the never-ceasing stream of outrages stopped. These opinions, which
the author shares with the Western community at large, are founded on a
very intimate knowledge of the Indians, and while they are invaluable as
the testimony of so competent an authority, they must yield in immediate
interest to the very vivid picture which the author gives of Indian life
and his estimate of Indian character. While what he says is not novel,
and could hardly be novel after the many thousands of works on the same
subject, his views are based on his own observation, and the facts are
presented with so much force that we gain a new idea of the American
savage. His essential moral characteristic is his love of cruelty. What
the savage thinks about in the frequent and long continued seasons of
idle solitude, it has long puzzled the ethnologist to discover. Colonel
Dodge says that a large part of the Indian's brooding thoughts are given
to the invention of modes of inflicting pain when he has the opportunity
to do so, and many of the camp fire discussions are upon suggestions for
cruelty. When the captive is brought in his tortures are not inflicted
in mere accordance with the momentary promptings of a brutal nature.
They may have been invented years before in some far distant camp, in
the profoundest peace, or may be copied from some noted example of
successful cruelty. They may have grown by one suggestion added to
another, among men whose knowledge of natural history includes a
marvellous perception of what parts of the frame are most sensitive to
pain. The Indian's cruelty is his pride. He gains credit by it among his
people, and he who invents a new torture is a leader. Cruelty is a merit
among these savages. It has rewards which make this passion one of the
most noticeable elements in their system of morality. No other author
has presented this aspect of Indian character with the clearness of
Colonel Dodge. His frequent illustrations show that it is no temporary
impulse, but a race characteristic carefully fostered by tradition and
perhaps by religion. But what position does all this give the Indian
among other races of men? Clearly he stands apart. The cannibal may
dance around the living victims who are soon to appear upon his table,
and the prisoner may be made to grace his conqueror's triumph, or the
altar of his conqueror's god, at any cost of suffering to himself, but
no other race, savage or civilized, has ever been shown to cultivate
cruelty for its own sake as the American Indian does. It is not from
fear, revenge, hate, or any other extraneous cause that he studies so
fondly and long over the means of giving pain. Cruelty is a thing to be
enjoyed for itself. The author has spoken with such plainness upon the
position of captive women in the hands of Indians, that we fear his book
will be objected to in just those quarters where its revelations are
most likely to do good. There is one thing which we wish he had made
clear--whether the brutality shown toward captive women is a practice
which has grown among the Cheyennes since they were driven from their
old home, or whether that has always been their mode of procedure. In
some quarters this particular brutality has been spoken of as the
outgrowth of their sufferings at the hands of the whites.
Colonel Dodge's book shows a rare combination of acute observation, long
experience, and the spirit of good fellowship. It is one of the best
books of hunting we know of, the best book ever written about the
plains, and its pictures and anecdotes of hunting life and Indian
fighting are a faithful reproduction of the peculiar conditions to be
found only on our great plains, with the anomalous relations of the
civilized and barbarous races that haunt them. The publishers have
illustrated it liberally. The Indian portraits are worthy of especial
mention for the minute accuracy which makes them ethnological examples
of unusual value.
* * * * *
The zoological collections described in the fifth volume of Reports,
Survey west of the Hundredth Meridian,[P] were all obtained in that
zoological province known as the "Campestrian region," from the great
plains which it includes. There the animal colors are pale and tend
toward uniformity, corresponding to the low rainfall of from three to
twenty inches per year. In this peculiarity, and also in comparison with
the surrounding more humid regions, the district of country in which the
Government surveys are now carried on sustains the general theory that
coloration in animals is closely dependent on rainfall, a humid
atmosphere serving to cloak the sun's rays and preserve the natural dyes
(mostly organic) from bleaching out. Dr. Yarrow thinks that the entirely
rainless parts of this vast Campestrian region may ultimately deserve
recognition as a separate zoological province. The observations made as
to the mimicry of color which some animals, especially reptiles, exert
or suffer lead him to believe that "a law may yet be formulated in this
respect which will equally apply to all classes of animals." This
mimicry was especially noticed in serpents and lizards found near red
sandstone deposits, the well-known little _Phrynosoma_, or horned toad,
being greenish gray, nearly white, or deep red, as it was found on the
plain, the alkali flat, or the sandstone soil. But however profound the
change, the skin returned to its normal color within a day or two after
removal from the determining locality. In regard to the rattlesnake, we
have the welcome information that it is apparently decreasing in
numbers, and the less agreeable fact that with other serpents, it
principally frequents the neighborhood of settlements. The collections
of all kinds made by the explorers prove to be unexpectedly perfect in
spite of the rapidity with which they are forced to move, and losses by
fire and railroad accident. The report upon these collections is drawn
up with the care and thoroughness that are such creditable features of
recent American official work. A copious bibliography and synonomy is
attached to the descriptions of species. The allotment of reports is as
follows: Geographical Distribution, Dr. H. C. Yarrow; Mammals, Dr.
Elliott Coues and Dr. Yarrow; Birds, H. W. Henshaw; Batrachians and
Reptiles, Dr. Yarrow; Fishes, Prof. E. D. Cope and Dr. Yarrow; Insects,
E. T. Cresson, E. Norton, T. L. Mead, R. H. Stretch, C. R. Osten-Sacken,
H. Ulke, R. P. Uhler, Cyrus Thomas, H. A. Hagen; Mollusca, Dr. Yarrow.
These names show how carefully the head of the survey, Lieutenant
Wheeler, has sought assistance in the important work of classification.
But these are by no means all from whom he and his assistants
acknowledge service. The list given in the preface numbers more than
forty persons, and includes the best known specialists in this country.
Forty-five plates, when necessary, accompany the text. In every
respect the report is worthy the important survey from which it
emanates.
[Footnote P: "_Report upon Geographical and Geological Explorations and
Surveys West of the Hundredth Meridian_," in charge of First Lieutenant
GEORGE M. WHEELER. Vol. V., Zoology.]
* * * * *
Though it is now quite common to find the life of two or even three
continents mingled in one web of fiction, few writers make so close a
subjective study of the immigrant's experiences as Mr. Boyesen has done
in his "Tales from Two Hemispheres."[Q] In fact he stands almost alone
in this field, and for a good reason; he is a participant where others
are onlookers. We are often told of the impression American ladies make
on foreign gentlemen, but rarely receive an analysis of it or are
offered even an attempt to analyze it. And yet this appears to be one of
the most promising exhibitions of human feeling ever studied. The
intercourse of the sexes, necessarily the subject of all romance, may
obviously have its situations heightened in every way by the
juxtaposition of two races, two diverse educations, and two opposite
moral systems, conjointly with the customary incidents of love-making.
Our author is fully alive to his opportunity, and, short as his tales
are, they bristle with dramatic scenes, and have an element of the
mythical and legendary in them, even when they are removed from such
professedly mystical subjects as he has treated in "Asathor's
Vengeance." Even in drawing-room scenes in New York the love-making is
ideal and romantic instead of calculating or passionate, as the current
novel commonly paints it. This mode of treatment implies that the tales
are either pathetic or fanciful, and in Mr. Boyesen's hands they are all
pathetic. He shows unusual power in this style of writing, and has the
natural and quiet humor which it demands. But there is a rudeness in the
construction and language of all of these stories which sometimes blinds
the reader to the really delicate insight into human feeling displayed
in them. The author writes like one who has the conception of what he
wants to do, but not yet the full command of the means. But this is a
fault that practice cures, and we trust Mr. Boyesen will continue his
studies in this essentially novel and peculiarly promising field of
literature.
[Footnote Q: "_Tales from Two Hemispheres._" By HJALMAR HJORTH BOYESEN.
Boston: James R. Osgood & Co.]
--In "Captain Mago"[R] we have a kind of book which with proper
attention may be made extremely interesting and valuable. It is an
attempt to reconstruct the life of three thousand years ago, not merely
among the Phoenicians, but in many other countries. Under the guise of
an expedition sent by the King of Tyre to Tarshish for the purpose of
collecting materials for the Jewish temple which King David was then
planning, we are taken to Judaea, Egypt, Crete, Italy, Spain, France,
England, and Africa. Such an expedition of course gives the author an
opportunity to present a panoramic view of the civilization in those
countries thirty centuries ago. We cannot say that he has performed the
task well. He dwells too much upon what he imagines to be the language
and conversation of the ancients and too little on those material facts
in their life which can be proved or plausibly imagined from the remains
of it which we have gathered. Ancient habits are but very obscurely
exhibited in the rude tools, the fragments of village houses, the
necklace of the Man of Mentone, the whistles and other toys of the
caves, the funereal fireplaces, and similar objects, but they are much
more plainly discernible than are the peculiarities of speech which must
have made up the bulk of daily conversation among our ancestors. A
reconstruction of ancient life based on a good knowledge of these
objects is likely to be more instructive and real than one that depends
for its force on a fanciful conception of their _thouing_ and _theeing_,
their love-making, and what oaths they swore. In fact, real service
could be done to "popular" science by a book that should exhibit our
remote forefathers as we really know them, and not attempting to go
beyond that point. Difficult as it will necessarily be to make such an
undertaking successful, we have no doubt that it will one day be
accomplished. "Captain Mago," though falling far short even of
excellence in this field, is nevertheless an interesting and peculiar
book.
[Footnote R: "_The Adventures of Captain Mago_; or, A Phoenician
Expedition B.C. 1000." By LEON CAHUN. Translated by Ellen E. Frewer.
Illustrated. New York: Scribner, Armstrong & Co.]
--The defect of "Captain Mago" is that its author has endeavored to
reconstruct from remains of a purely literary kind the life of a time
which was antecedent to the most of our oldest literature. Another
author, Mr. Mahaffy, has had great success in a similar field because he
chose for reconstruction a society which has left literary monuments of
a very varied character and great abundance. His "Social Life in Greece"
and other works about the ancient Greeks were written before he ever saw
that historic country, and yet he tells us in his last work,[S] written
after a personal visit and stay of some time, that his former writings
were sufficiently true to the Greece of to-day to deceive living Greeks
into the belief that he had been intimately acquainted with their
landscapes and familiar customs. Mr. Mahaffy's "Rambles" among modern
Greeks are a very interesting finish to his idealizations of their
ancestors. It is comforting to know that after all her spoliations the
country is still so rich in remains of ancient art as to retain more
fine and pure specimens of the best work than are to be found in all the
rest of the world. Very little is done toward uncovering and nothing
toward restoring these sculptures, for the Greeks are jealous of
foreigners and unable or not sufficiently interested to do this
themselves. They are willing to allow others to do the work, but Greece
must have all the profit. Still, there the works lie, and may be
recovered at some future day. We may even be comforted to think they are
well covered with soil, for the present inhabitants of the country, with
exquisite barbarity that their ancestors could not have practised, use
the standing monuments of art as a mark for pistol practice! Another
point in which they show a constitutional divergence from their
forefathers is in the singular barrenness that has fallen upon their
women. Once their land teemed with a native-born population. Now the
household remains so long childless that it is very common to find the
wife's mother a permanent member of the household, being retained for
companionship! Even the mature family contains but few children, and
this in the best agricultural parts of the country. While these
differences exist the author is not at a loss to find strange
resemblances. The yellow hair and fair complexion, the forms which are
even now types of the same race that stood for the old statues, the
language, and a multitude of other things prove that the old race
continues in purity and that Greece is not now filled with a mere
mixture of Turks, Albanians, and Sclaves. Our author has a poor opinion
of the Greek's capacity for government, and likens them to the Irish. He
thinks that both these races are constitutionally incapable of
government, and need subjugation by a foreigner. In this characteristic
he finds a strong resemblance between the modern and the ancient Greek,
for both have suffered personal jealousy to outweigh the strongest
promptings of patriotism. Mr. Mahaffy shows himself to be as able as an
observer as he is as an historian.
[Footnote S: "_Rambles and Studies in Greece._" By J. P. MAHAFFY.
Macmillan & Co.]
--The peculiar character of De Quincey's work gives unusual opportunity
for such a volume of selections as this, published under the untasteful
name of "Beauties."[T] He had all the mental power required for
sustained efforts in composition, though his plans for such works were
always defeated by physical weakness. His productions, therefore, though
incomplete, are not those of a literary trifler. His genius and methods
seem to be especially suited to the tastes of the present day, for he
excelled in the qualities that make the professional magazinist: great
learning, research, and acuteness, combined with a humor that sports
most waywardly through everything he wrote, a vivid fancy, a wonderful
use of words, and a style which even in its faults exhibits the needs of
periodical literature. He was, perhaps, more exactly fitted to serve the
world in its chosen field of current publications than any other man who
has written for it. Were he living now he would be acknowledged the
prince of the nebulous gentlemen who occupy easy chairs, gather in
contributors' clubs, and fill up "editors' baskets" with their
effusions. We have additional respect for the somewhat chopped up
productions of these gentlemen, after reading the numerous volumes that
bear his name, for there we find how much of every sort of literary good
they can contain. The editor of these selections is a lucky man, for his
work has the merit, rare among such books, of being thoroughly good in
itself. He has with excellent judgment given us somewhat of
autobiography, somewhat of the rare and indescribable dream life of De
Quincey, and somewhat of his tales, essays, and critiques. The character
of his author's writings relieves these morsels from the air of
incompleteness and decapitation which so often attaches to selections.
What he has given us is not all of De Quincey, but each chapter is
complete in itself. Selections usually repel us. We cannot join in the
argument so often found in prefaces to such works, that the reading of
them may lead to the reading of the author's whole works. On the
contrary, we are of that class to whom the cutting up of a good author
is apt to seem like vivisection--necessary, perhaps, but revolting. This
book, however, does not leave such an impression. On laying it down we
wonder why we are not constantly reading the great essayist, the
precursor of the literary spirit of our own times, probably a better
example than any now living of the many virtues demanded from the
popular writer.
[Footnote T: "_Beauties Selected from the Writings of Thomas De
Quincey._" New York: Hurd & Houghton.]
* * * * *
Under the editorship of Mr. John Austin Stevens we may look for a
valuable and permanent publication in the "Magazine of American History,
with Notes and Queries," of which A. S. Barnes & Co. are the publishers.
The position of the editor as librarian of the New York Historical
Society will, or at all events should, be an additional source of
strength to the publication. Experience shows that literary undertakings
which possess more merit than popularity can derive great advantages
from the official countenance of societies pursuing allied subjects of
investigation. Properly managed, the two modes of obtaining union in
action can be made to help each other materially. This hint will perhaps
be considered not amiss since the pamphlet, printed with the neatness
characteristic of such works, which lies before us, is but a specimen
and preliminary number, which is to be followed by monthly issues in
quarto form, at $5 yearly, if sufficient support is obtained. The editor
says: "Each number will contain: I. An original article on some point of
American history from a recognized and authoritative pen. II. A
biographical sketch of some character of historic interest. III.
Original documents, diaries, and letters. IV. Reprints of rare
documents. V. Notes and queries in the well-known English form. VI.
Reports of the proceedings of the New York Historical Society. VII.
Notices of historical publications." He also promises to keep it free
from sectional prejudices and "from personality and controversy in any
form." He has ready for publication a large number of interesting old
manuscripts contributed by historians and collectors, and it is to be
hoped his attempt to establish a periodical for historical literature
will be sustained.
BOOKS RECEIVED.
"_Materialism and Theology._" JAMES MARTINEAU, LL.D. G. P. Putnam's
Sons.
"_Waverley Novels_," Riverside Edition, "Heart of Midlothian." Hurd &
Houghton.
_The Same._ "Bride of Lammermoor."
_The Same._ "The Monastery."
"_Footsteps of the Master._" HARRIET B. STOWE. J. B. Ford & Co.
"_Functions of the Brain._" Illustrated. D. FERRIER, M.D. G. P. Putnam's
Sons.
"_The Plains of the Great West._" Illustrated. Lieutenant Colonel
RICHARD I. DODGE. G. P. Putnam's Sons.
"_The Sons of Godwin._" A Tragedy. WILLIAM LEIGHTON, Jr. J. B.
Lippincott & Co.
"_Personal Relations Between Librarian and Readers._" SAM. S. GREEN.
Chas. Hamilton, Worcester, Mass.
"_Special Report on Worcester Free Library._" The same.
"_Tales from Two Hemispheres._" H. H. BOYESEN. Jas. R. Osgood & Co.
"_The Problems of Problems._" CLARK BRADEN. Chase & Hall, Cincinnati.
"_Archology_; or, The Science of Government." V. BLAKESLEE. A. Roman &
Co.
"_Woman as a Musician._" FANNY RAYMOND RITTER. Ed. Schuberth & Co.
"_Vivisection._" Copp Clark & Co., Toronto.
"_Cholera Facts of the Last Year._" E. MCCLELLAN, M.D. Richmond &
Louisville Medical Journal office.
"_Art Journal._" Photo-Engraving Co., New York.
"_History of the City of New York._" Parts 5 to 10. Mrs. M. J. LAMB. A.
S. Barnes & Co.
"_The Magazine of American History._" JNO. AUSTIN STEVENS, editor. A. S.
Barnes & Co.
"_National Quarterly Review._" D. A. GORTON, editor.
"_National Survey West of 100th Meridian._" Vol. 5, Zoology. Dr. H. C.
YARROW and others. Government Printing Office.
"_Catalogue Siamese Exhibit International Exhibition._" J. B. Lippincott
& Co.
"_Planetary Meteorology, Mansill's Almanac of._" R. MANSILL. R.
Crampton, Rock Island.
"_Notes on Assaying._" R. DE P. RICKETTS. Art Printing Establishment.
"_Mental Powers of Insects._" A. S. PACKARD, Jr. Estes & Lauriat.
"_Beauties of De Quincey._" Hurd & Houghton.
"_The Convicts._" B. AUERBACH. H. Holt & Co.
"_Philosophical Discussions._" C. WRIGHT. H. Holt & Co.
"_The Sons of Goodwin._" W. LEIGHTON. J. B. Lippincott & Co.
"_Rambles and Studies in Greece._" J. P. MAHAFFY. Macmillan & Co.
"_Mother and Daughter._" F. S. VERDI, M. D. J. B. Ford & Co.
"_Marie._ A Story of Russian Lore." MARIE H. DE ZIELINSKI. Jansen,
McClurg & Co.
"_The Barton Experiment._" By the author of "Helen's Babies." G. P.
Putnam's Sons.
NEBULAE.
--It would seem that we must return to the old fashion of strong boxes,
old stockings, and cracked pipkins as the receptacles of our savings. As
to savings banks and trust companies, and life insurance companies, the
revelations of the last few months go to show that they do anything but
save; that they are no longer to be trusted, and that they ensure
nothing but total loss to those who put their money into them. Ere long
it will be said of a young man that he was poor but honest, although he
had the misfortune to have a father who was a director in several
important financial institutions. The state of affairs in this respect
is frightful; and it frightens. The financial panic has been followed by
a moral panic which is really as much more deplorable than its
predecessor as moral causes are more radical in their operation and more
enduring than those which are merely material. Confidence is gone. How
it is to be restored is a problem far more perplexing than how to revive
drooping trade. For that the real wealth of the country, never greater
than it is now and constantly increasing, must bring about sooner or
later. But if men of wealth and of fair reputation are no longer to be
trusted, what is the use of saving, to put money into a box where it
gains nothing and where thieves break through and steal? Robbery seems
to be the fashion; on the one hand masked burglars with pistols at your
heads and gags in the mouths of your wife and children, and on the other
hypocritical, lying, false-swearing, thieving scoundrels who get your
money under fair pretences, and because of your trust in their
characters and good faith, and then waste it in speculations and in
luxurious living. Of the two, the burglars seem to be rather the more
respectable. It is said, on good authority, that the West India slaves
of a past generation could be trusted to carry bags of gold from one
part of the Spanish Main to another, and that they were constantly so
trusted with entire impunity. They would kidnap, and on occasion stab or
cut a throat; but if they were trusted, they would not break their
faith. The honesty of the Turkish porters is so well known that it has
become almost proverbial. Does not the honesty of these pirates and
pagans put to shame the Christians who with the professions and the
faces of Pharisees "devour widows' houses"?
--For as to the business of life insurance, savings banks, and trust
companies, it is somewhat more, or surely somewhat other, than mere
business. And so those who practise it and profit by it profess that it
is. A life insurance company is a grand combination
philanthropico-financial corporation whose motto is, "Cast thy bread
upon the waters, and after many days thou shalt receive it again." But
the truth of the matter turns out to be that if you cast your bread upon
the waters, the chances are that you will see it devoured before your
eyes by financial sharks. One case in point has come directly to our
knowledge. A gentleman, a Government officer, who has a moderate salary,
with little or no hope of acquiring property, insured his life twenty
years or more ago in what was thought a good company. His premium was
always promptly paid even in the flush times of the war and afterward,
when the fixed salaries of public officers lost more than half their
purchasing power. Within the last few months he has suddenly found that
his policy is not worth the paper on which it is magnificently printed.
But worse than this: within the last few years, as age has crept upon
him, there has come with it a disease which is incurable although he may
live for some time longer. Now, however, he cannot get his life insured
at all; no company will take his life; (it is a rueful jest to say that
the company in question _did_ take his life); and he has the prospect
before him of a widow left entirely without provision, although for
nearly a quarter of a century he and she stinted themselves to provide
against such a contingency. Meantime the officers of the company lived
luxuriously, and used the money in their hands for speculation, and in
living which if not riotous, was at least shameless and dishonest. And
they were all men of reputation, were selected for their positions
because it was thought that men of their position and habits of life and
outward bearing were incorruptible. Have they not devoured that
prospective widow's house? If He who condemned the hypocritical
Pharisees of old were on the earth now, would he not pronounce Woe upon
them? And much would they care about His condemnation if they could get
their commissions, and their pickings and stealings, and live in
splendid houses, and be known as the managers of an institution that
handled millions of dollars yearly, and whose offices were gorgeous with
many- marbles, and gilding, and inlaid wood, and rich carpets!
And like their predecessors in the devouring of widows' houses for a
pretence, they make long prayers. They, we say; but of course we do not
mean all; for there are honest officers of life insurance companies, and
even sound companies; but the number of both is shown day after day to
be less and less; and when we think that those that we hear about are
only they which have reached the end of their tether in fraud, perjury,
and swindling, the prospect before us is one of the most disheartening
that could be presented to a reflecting people. For remember, these
defaulting, false-swearing life insurance and savings bank officers are
picked men, and that their dishonest practices are from their very
nature deliberate, slow of execution, and that in fact they have gone on
for years. It is no clutch of drowning men at financial straws that we
have here; it is the regular "confidence game" played on an enormous
scale by men who are regarded as the most respectable that can be found
in the whole community. They are vestrymen, and deacons, and elders, and
grave and reverend signors, and these men have deliberately used and
abused the confidence not only of the community in general, but of their
friends and acquaintance, to "convey" in Nym's phrase, to steal in plain
English, money which was brought within their reach because of their
pretended high principle and their philanthropic motives. For, we
repeat, it must constantly be kept in mind as an aggravation of these
wrongs, that life insurance companies and savings banks are essentially
and professedly benevolent institutions. They are, and they openly
profess to be, chiefly for the benefit of widows and children. The man
who takes to himself the money of a life insurance company or of a
savings bank is not a mere thief and swindler; he robs the widow and the
fatherless; he takes his place among those who are accursed of all men;
and moreover, in all these cases he is a hypocrite of the deepest dye.
--In any case, however, there is reason for fearing that the business of
life insurance has in the main long been rotten, even when it has not
been deliberately corrupt. Professedly and originally a benevolent
contrivance by which men of moderate incomes could year by year make
provision for wives and children who might otherwise be left destitute,
it was reasonable and right to expect that the business of life
insurance would be conducted upon the most economical principles and in
the simplest and most unpretending fashion; that there would have been
only as much expenditure as was absolutely necessary for the proper
conduct of the business; and that safety for the insured would have been
the first if not the only ruling motive with the insurers. And such
indeed was life insurance in the beginning. But by and by it was found
that there was "money in it," and the sleek, snug hypocrites that prey
upon society under the guise of philanthropy and religion began to swarm
around it. Life insurance companies began to have a host of officers;
they had "actuaries," whatever they may be, who, by whatever motives
they were actuated, contrived and put forth statements which to the
common mind were equally plausible and bewildering; they entered into
bitter rivalry with each other in their philanthropic careers; they had
agents who went abroad over the land in swarms, smooth-speaking,
shameless creatures who would say anything, promise anything so long as
they got their commissions; they published gorgeous pamphlets, tumid and
splendid with self-praise, and filled with tabular statements that
justified and illustrated the denying that there is nothing so
untrustworthy as facts, except figures; they contrived the "mutual"
plan, by which they made it appear to some men that they could insure
their own lives--which is much like a man's trying to hoist himself over
a fence by the straps of his boots--and yet these mutual officers,
benevolent creatures, were as eager to get business and as ready to pay
large commissions as if, poor, simple-minded souls, they had expected to
get rich by life insuring; and then they put up huge and enormously
expensive buildings, more like palaces than any others known to our
country. And all this came out of the pockets of those who are, with
cruel mockery, called the insured. It is the old story: ten cents to the
beneficiary and ninety cents to the agent through whose hands the money
passes. Is it not plain, merely from the grand scale and the large
pretence on which this life insurance business has been carried on of
late years, that it is rotten? It is a scheme for making money. Now,
making money is right enough; but when it is carried on under
philanthropic and benevolent pretences its tendency must naturally be,
as we have seen that it has been, to gross corruption and the most
heartless fraud.
* * * * *
The point of honor has been deemed of use
To teach good manners and to curb abuse.
So wrote Cowper in his "Conversation," nearly a century ago, when
duelling was beginning to go out of fashion, even among men who did not
look upon it from a religious point of view. There is no doubt that the
passage which these lines introduce did much to bring the custom of
settling personal quarrels by single combat into disrepute. Cowper, the
moral poet _par excellence_ of the English language, attained this
eminence chiefly because he wrote, not like a fanatic, or a canting
pietist, but like a Christian gentleman and a man of sense. A man of
family, he thought and felt as a gentleman, and addressed himself to
gentlemen; and indeed, in his day poetry, at least of the quality that
he produced, had very few readers outside the pale of gentry. His view
of duelling is the one which now prevails in most communities of English
blood in all parts of the world. Germans and Frenchmen and the Latin
races generally still fight upon personal provocation, and in our late
slave States and among the rude and fierce men who guard and extend our
western borders, "misunderstandings" are settled by the bullet or the
knife, and if not on the spot, with the weapon at hand, then in a
regularly arranged duel in which the forms are entirely subordinate to
the essentials of a bloody and vindictive contest. With these
exceptions, however, duelling among the English-speaking people has come
to be regarded as both folly and crime. Nothing could evince more
strongly the change that has taken place in the moral sense of the
world; for to resent an insult by a challenge to fight, and to accept
such a challenge without a moment's hesitation, were once the highest
duties of a gentleman. There was a reason for this; and without
advocating or defending the practice of duelling, it may be questioned
whether that reason has entirely disappeared.
* * * * *
--Our readers need not fear that we are about to defend or to palliate
the conduct of either of the parties to the recent affair which began in
Fifth Avenue in New York and ended on the Maryland border; but the fact
that that occurrence or series of occurrences has attracted the
attention of the whole country, makes it a proper occasion of remark
upon the questions involved in such encounters. And first we must set
aside the Cowper view of the subject, not in its conclusion, but in its
reasoning. For however Christian in sentiment and sound in its final
judgment the passage in the "Conversation" may be, its author's position
is not logically impregnable. For it rests upon the assumption embodied
in the couplet--
Amoral, sensible, and well-bred man
Will not affront me, and no other can.
But if this be true, it follows that a man cannot be insulted, which is
an absurdity; for men are insulted, as we all know--and we are happy if
we do not know it by experience. Moreover, men are insulted more
frequently where the "code of honor" does not prevail than where it
does; for that code is of use; and if it does not teach good manners, it
certainly does curb abuse. The question to be decided is whether in the
teaching of manners and the curbing of abuse by the alternative and
arbitrament of bloody combat we are not paying too high a price for what
we gain. To consider the example which is the occasion of our remark. A
man is met in the street by another with whom he has been upon terms of
social intercourse, and is there publicly whipped. He faces his
assailant, resists, but is overcome because the assailant is the
stronger and the more dexterous. What shall he do? Submit quietly? That
may be Christian conduct; but whether it is good public policy, to say
nothing more, may at least be questioned; for it would place the greater
part of the community at the mercy of the strong brawling bullies. Two
courses are open to a person so assailed--either to place the matter in
the hands of the law, in a civil or a criminal suit, or to challenge the
assailant. In most cases it may be admitted that the former course is
the wiser and the better course. Where mere protection against personal
injury is sought a police justice and a police officer are the effective
as well as the lawful means. But there is something else to be
considered. The mere personal injury may be slight, and there may be no
fear of its repetition, and yet there is a wrong done that may rankle
deeper than a wound. Personal indignity is something that most men of
character and spirit feel more than bodily pain or than loss of money or
of property. It is a sentimental grievance, and therefore one which the
law cannot provide against or punish. It cannot be estimated in damages;
none the less, therefore, but rather the more, does the man who suffers
it take it to heart; none the less, therefore, but rather the more, do
gentlemen set up barriers against it which, although invisible, and not
even expressed, if indeed they are expressible in words, are more
forbidding in their frown, more difficult of assault than the regular
bulwarks of the law. It must be repeated that this wrong is not to be
measured by the bodily injury or the bodily pain that is inflicted. Two
men may be boxing or fencing, and one may severely injure the other; but
no sense of wrong accompanies the injury, and that not because no injury
was intended, but because no offence was meant; whereas the flirt of a
kid glove across the face, or a word, may inflict a wrong that if not
atoned for or expiated, may rankle through a man's whole life. To
attempt to set aside or to do away with this feeling is quite useless:
as well attempt to set aside or to do away with human nature. It is this
feeling that has been at the bottom of most duels since duels passed out
of use as a mode of determining guilt or innocence, or of deciding
questions as to property, or position, or title. In the sixteenth,
seventeenth, and eighteenth centuries duels were chiefly the remedy for
wounded honor, as they are when they are rarely fought nowadays. True
there was the duel fought between two gentlemen "to prevent the
inconvenience of their both addressing the same lady"; but the duel for
that reason pure and simple was always comparatively rare, as, owing to
the infirmity of human nature, the agreement in opinion of the lady and
the disagreement as to the disposition to be made of her were almost
sure to take the form of a more reasonable if not more deadly cause of
quarrel.
--But society--that is, society in which Anglo-Saxon modes of thought
and feeling prevail--says that no matter what the provocation, or how
great the sense of wrong, the duel shall not be; it has been made a
crime in some if not in most of such communities even to send a
challenge. This is done on grounds of public policy and of morality, and
not, as some persons seem to think, because killing in a duel is murder.
Murder is more than a mere killing, and is in its essence entirely
inconsistent with the fact that the person killed voluntarily placed
himself, and generally with much trouble and at great inconvenience, in
the way of his death. The duel is in fact a sort of _hari-kari_, or
happy release, as our Japanese friends have well phrased it, but it is
with the cooperation of a second party who voluntarily places himself in
similar peril, the happy release being in both cases from the stigma of
dishonor. This is shown very clearly by the distinction which is drawn
in general estimation between the man who challenges because he has
suffered an insult or an injury to his family honor, and one who does so
from a feeling of revenge and with the intent to rid himself of a hated
opponent, as for example in the case of Aaron Burr in his duel with
Alexander Hamilton. That was more than half a century ago, when there
were no such laws against duelling as now exist; but Burr, although he
rid himself of his hated rival on what was called the field of honor,
was from that day a degraded, detested, ruined man. If Hamilton had
offered him a personal indignity, or had injured him in his family
relations, the result of the duel would have added nothing to the weight
of disrepute under which Burr was already suffering. The whole world
recognizes this distinction, and there is hardly a man whose breeding
and habits make him what is rightly called a gentleman in the full sense
of the term, who, however his judgment may condemn the duellist who
fights because of an insult or an injury to family honor, does not feel
a certain sympathy with him. Notwithstanding the teachings of
Christianity, and the example of its founder as to the patient suffering
of indignity, notwithstanding the law, we all, or most of us, have the
feeling that Barclay of Wry's battle-tried comrade had when he saw his
old friend and heroic commander openly insulted by a throng of
swashbucklers in the streets of Aberdeen, because he had become a
Quaker, and which Whittier has expressed with such spirit in his poem on
the subject, which is one of the few truly admirable ballads of modern
days (although its author does not so class it), and which is, we are
inclined to think, the most admirable of them all:
Woe's the day, he sadly said,
With a slowly shaking head,
And a look of pity:
Wry's honest lord reviled,
Mock of knave and sport of child,
In his own good city.
Speak the word, and master mine,
As we charged on Tilly's line
And his Walloon lancers,
Smiting through their midst, we'll teach
Civil look and decent speech
To these boyish prancers.
--What then is to be done? for the question is a serious one. We all
feel that personal indignity is of all wrongs the hardest one to bear;
we know that it is a wrong of a kind that cannot be redressed by law;
and yet we restrain men from the only redress, "satisfaction," as it is
called, that human ingenuity has bean able to devise, and with which
human nature, of the unregenerate sort, is satisfied. We cannot expect
all men to behave like members of the Society of Friends. All men have
not proved their courage and high spirit like Barclay of Wry, who
----stood
Ankle deep in Lutzen's blood
With the great Gustavus.
We cannot compel all men to be Christians; and yet we would compel them
by law to bear insult as if they were Christians and great captains
turned Quakers. We can do this, which thus far society has neglected to
do: we can put a social ban upon the man who deliberately offers a
personal indignity to another. This should be a social duty. Let it be
understood, according to one of those silent social laws which are the
most binding of all laws because the sheriff cannot enforce them, that
the man who flourishes a horsewhip over another's head, or who uses his
tongue as a scourge with like purpose, or who offers personal indignity
of any kind, insults society as well as his victim, and is not to be
pardoned until he has made the amend to the injured party, and there
would soon be an end of provocation to duelling, except that which
touches the family, and that cannot be done away with until men have so
developed morally and intellectually that they see that a man's honor is
not in the keeping of a woman, not in that of any other person than
himself, not even his wife. Her conduct may indeed involve his dishonor,
if he is what used to be called a wittol, but even then _his_ dishonor
is because of his own disgrace. Only then can we reconcile the making of
a challenge a felony with the feeling that a man who has had a personal
indignity put upon him has suffered the deepest wrong he could be called
upon to bear, yet a wrong which society fails to right while it forbids
him to seek the only reparation.
--That reparation is defined, if not prescribed, by the code of honor,
as to which code there seems to be a very general misapprehension. The
purpose of the code is this, that no gentleman shall offer a personal
indignity to another except with the certainty of its being at the risk
of his life. If society would provide a remedy or preventive that would
operate like this risk, the code would soon pass absolutely out of
practice and into oblivion. It is generally supposed that the code is a
very bloodthirsty law, and that those who acknowledge it and act upon it
are "sudden and quick in quarrel," lovers of fighting, revengeful and
implacable, and that the code gives them the means of gratifying their
murderous or combative propensities. No notion of it could be more
erroneous; the misconception is like that which supposes military men to
be desirous of using arms on slight provocation; whereas the contrary is
the case. No men are so reluctant to begin fighting as thoroughbred
soldiers; for they know what it means and to what end it must be carried
if it is once begun. The code has been reduced to writing, and by a
"fire-eating" South Carolinian, so that we can see just how bloodthirsty
it is. It provides first that if an insult be received in public it
should not be resented or noticed there, out of respect to those
present, except in case of a blow or the like, because this is insult to
the company which did not originate with the person receiving it; that a
challenge should never be sent in the first instance because "that
precludes all negotiation," and that in the note asking explanation and
reparation the writer should "cautiously avoid attributing to the
adverse party any improper motive"; that the aggrieved party's second
should manage the whole affair even before a challenge is sent, because
he "is supposed to be cool and collected, and his friends' feelings are
more or less irritated" ["more or less" here is excellent good as
expressive of the state of mind of a man so aggrieved that he is ready
to risk his life]; the second is to "use every effort to soothe and
tranquillize his principal," not to "see things in the aggravated light
in which he views them, but to extenuate the conduct of his adversary
whenever he sees clearly an opportunity to do so"; to "endeavor to
persuade him that there has been some misunderstanding in the matter,"
and to "check him if he uses opprobrious epithets toward his adversary";
"when an accommodation is tendered," the code says in a paragraph worthy
of the most respectful consideration, "never require too much; and if
the party offering the _amende honorable_ wishes to give a reason for
his conduct in the matter, do not, unless it is offensive to your
friend, refuse to receive it. By doing so you heal the breach more
effectively." Strangers may call upon you for your offices as second,
"for strangers are entitled to redress for wrongs as well as others, and
the rules of honor and of hospitality should protect them." The second
of the party challenged is also told, "Use your utmost efforts to allay
the excitement which your principal may labor under," to search
diligently into the origin of the misunderstanding, "for gentlemen
seldom insult each other unless they labor under some misapprehension or
mistake," and if the matter be investigated in the right spirit, it is
probable that "harmony will be restored." The other parts of the code
refer to the arrangements for and the etiquette of the hostile meeting,
of which we shall only notice the censure passed upon the seconds if
after either party is hit the fight is allowed to go on. The last
section implies, although it does not positively assert, that "every
insult may be compromised" without a hostile meeting, and it is directly
said that "the old opinion that a blow must require blood is of no
force; blows may be compromised in many cases." We do by no means
advocate the fighting of duels; but we must say that we cannot see in
this code the blood-thirstiness and the quarrel-seeking generally
attributed to it. On the contrary, all its instructions seem to tend
toward peacemaking, the restoration of harmony, the restraining of even
expressions of ill feeling. It does recognize as indisputable that an
insult must be atoned for, and if necessary, at the risk of life. That
necessity society can do away with by placing its ban upon the man who
insults another.
* * * * *
--It is generally supposed that the "average American" beats the world
in his love of big titles, and in his use of them; but the freed
southern <DW64> beats his white fellow citizen all hollow. We hear from
Texas of one who is Head Centre of a Lodge--exactly of what sort we
don't know, but we suppose that it must be a lodge in the wilderness or
perhaps, in Solomon's phrase, a lodge in a garden of cucumbers. This
cullud pusson will spend two months' wages to "report" at a grand
junction "jamboree" of his "lodge." The titles of the officers of these
associations are something wonderful. A <DW64> office boy down there
asked leave of absence for a day to attend a meeting. "Why," said his
master, "Scip, I didn't know you belonged to a lodge." "Oh, yes, boss,"
replied Africanus, "Ise Supreme Grand King, an' Ise nowhar near de top
nuther." Who shall say that the abolition of slavery was not worth all
that it cost?
Transcriber's Notes:
Obvious punctuation errors corrected.
Text changes:
English Peerage: replaced "e.i." with "i.e."
..._i.e._ the mayor being...
Misanthrope: replaced "acquintance" with "acquaintance"
...to renew her acquaintance with Miss Lucy...
Wordsworth: Corrected "ta de, kollomelei" to "ta de kollomelei"
The Greek word "k'autonomazei" appears in other editions as
"k'antonomazei."
Replaced "Jeffry" with "Jeffrey" ...Jeffrey looked for logical...
Used =[text]= to indicate word typed with strike-out
=Those= lips...
Replaced "chearful" with "cheerful" ...Be wise and cheerful...
Portrait: Open quote without close quote in poem retained;
"Is thine that great,...
Tinsel: Removed extra period: ...before I asked it.".
Eastern: Corrected "Mediterannean" to "Mediterranean"
...superior fleet in the Mediterranean;...
Added comma between "there there" ...In religion there, there are...
Assja: Consolidated 'The young man smiled and answered, "Yes; we are
Russians."' into one paragraph.
Removed hyphen from "hemp-field" ...a hemp field of moderate size...
Scientific: Added thought breaks between paragraphs at change of topic.
Nebulae: Added thought breaks between paragraphs at change of topic.
End of the Project Gutenberg EBook of The Galaxy, by Various
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{"url":"https:\/\/math.stackexchange.com\/questions\/2660585\/laurent-series-expansion-about-z-0","text":"# Laurent series expansion about z=0\n\nI am to obtain the first 3 terms of the Laurent series about $z = 0$ for:\n\n$$f(z)=1\/(e^z-1-z)$$\n\nI know that there is 1 singularity at $z=0$. My denominator is not in a polynomial form so I can convert it into such by taking a Taylor series of the function around z=0 which yields the denominator as:\n\n$$(e^z-1-z) = x^2\/2 + x^3\/6 + x^4\/24 + ...$$\n\nThis is the part where I get stuck. I'm supposed to bring that back in and perhaps factor something out of the denominator so the left side is analytic at z=0 and the singularities are shifted to the term on the right side. Any tips on what my next step should be? Many thanks!\n\nSince $$e^{z}-1-z=z^2\\sum_{n=0}^\\infty\\frac{z^n}{(n+2)!}\\tag1$$ let $$\\frac{z^2}{e^{z}-1-z}=\\sum_{k=0}^\\infty a_kz^k\\tag2$$ Then using the Cauchy Product Formula \\begin{align} 1 &=\\sum_{n=0}^\\infty\\frac{z^n}{(n+2)!}\\sum_{k=0}^\\infty a_kz^k\\\\ &=\\sum_{n=0}^\\infty\\sum_{k=0}^n\\frac{a_{n-k}}{(k+2)!}z^n\\tag3 \\end{align} That is, equating the coefficients of the powers of $z$, $$\\sum_{k=0}^n\\frac{a_{n-k}}{(k+2)!}=[n=0]\\tag4$$ where $[\\cdots]$ are Iverson Brackets.\n\nPlugging $n=0$ into $(4)$, we get $a_0=2$.\n\nSolving for $a_n$, for $n\\ge1$, in terms of previous terms, we get $$a_n=-2\\sum_{k=1}^n\\frac{a_{n-k}}{(k+2)!}\\tag5$$ So we can compute all the $a_n$ iteratively using $(5)$.\n\nThen we get the Laurent series: \\begin{align} \\frac1{e^z-1-z} &=\\sum_{k=0}^\\infty a_kz^{k-2}\\\\ &=\\frac2{z^2}-\\frac2{3z}+\\frac1{18}+\\frac{z}{270}-\\frac{z^2}{3240}-\\frac{z^3}{13608}-\\cdots\\tag6 \\end{align}\n\nSince the Taylor series of $e^z-1-z$ begins with the term of degree $2$, the Laurent series that you're after is something like$$\\frac{a_{-2}}{z^2}+\\frac{a_{-1}}z+a_0+a_1z+\\cdots$$So, you have\\begin{align}1&=\\left(\\frac{z^2}2+\\frac{z^3}6+\\frac{z^4}{24}+\\cdots\\right)\\left(\\frac{a_{-2}}{z^2}+\\frac{a_{-1}}z+a_0+a_1z+\\cdots\\right)\\\\&=\\left(\\frac12+\\frac z6+\\frac{z^2}{24}+\\cdots\\right)\\left(a_{-2}+a_{-1}z+a_0z^2+a_1z^3+\\cdots\\right)\\\\&=\\frac{a_{-2}}2+\\left(\\frac{a_{-1}}2+\\frac{a_{-2}}6\\right)z+\\left(\\frac{a_0}2+\\frac{a_{-1}}6+\\frac{a_{-2}}{24}\\right)z^2+\\cdots\\end{align}and so all you need is to solve the system$$\\left\\{\\begin{array}{l}\\frac{a_{-1}}2=1\\\\\\frac{a_{-1}}2+\\frac{a_{-2}}6=0\\\\\\frac{a_0}2+\\frac{a_{-1}}6+\\frac{a_{-2}}{24}=0.\\end{array}\\right.$$\n\nAnother approach:\n\nUsing the power series of $\\;e^z\\;$ , we get:\n\n$$e^z-1-z=\\sum_{n=0}^\\infty\\frac{z^n}{n!}-1-z=\\frac{z^2}{2}+\\frac{z^3}{6}+\\ldots$$\n\nSince we're interested in $\\;z\\;$ \"close\" to zero (meaning $\\;|z|<1\\;$) , we get:\n\n$$\\frac1{e^z-1-z}=\\frac1{\\frac{z^2}2\\left(1+\\frac z3+\\frac{z^2}{12} +\\ldots\\right)}=\\frac2{z^2}\\left(1-\\frac z3-\\frac{z^2}{12}+\\left(\\frac z3+\\frac{z^2}{12}\\right)^2-\\ldots\\right)=$$\n\n$$=\\frac2{z^2}-\\frac{2}{3z}-\\frac16+\\frac29-\\ldots=\\frac2{z^2}-\\frac2{3z}+\\frac1{18}+\\ldots$$\n\nHow to know how many summands to take in the development of $\\;\\frac1{1+\\frac z3+\\frac{z^2}{12}+\\ldots}\\;$ ? As many as required, and since we need only the first three elements and zero is a double pole, we only need to evaluate the coefficients of $\\;z^{-2},\\,z^{-1}\\,,\\,z^0\\;$ ...\n\nBorrowing from that answer I commented, we have \\begin{align} \\frac{1}{e^z - 1 - z} &= \\frac{1}{(1 + z + z^2\/2! + \\dots) - 1 - z}\\\\ &= \\frac{1}{z^2\/2! + z^3\/3! + z^4\/4! + \\dots}\\\\ &= \\frac{2}{z^2} \\cdot \\frac{1}{1 + 2z\/3! + 2z^2\/4! + \\dots} \\end{align} Now letting $P(z) = 2z\/3! + 2z^2\/4! + \\dots$, we have \\begin{align} \\frac{1}{e^z - 1 - z} &= \\frac{2}{z^2} \\cdot (1 - P(z) + P(z)^2 - P(z)^3 + \\dots)\\\\ &= \\frac{2}{z^2} \\cdot (1 - 2z\/3! + z^2(-2\/4! + (2\/3!)^2) + \\dots)\\\\ &= 2z^{-2} - \\frac{2z^{-1}}{3} + \\frac{1}{18} - \\dots \\end{align} Getting higher order terms starts to get a bit complicated, so I'd suggest using Wolfram Alpha to fill in the rest: http:\/\/www.wolframalpha.com\/input\/?i=laurent+series+of+1%2F(e%5Ez+-+1+-+z)","date":"2020-01-28 13:32:54","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\": 5, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9998080134391785, \"perplexity\": 384.9196183632798}, \"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-2020-05\/segments\/1579251778272.69\/warc\/CC-MAIN-20200128122813-20200128152813-00273.warc.gz\"}"} | null | null |
DEDICATION
Of the Abyss is dedicated to Ria and Zim, whose challenge to try NaNoWriMo sparked this entire crazy trilogy; to Mason, who tolerated (or perhaps encouraged) my obsession; and to my mother, who introduced me to Freudian theory and has been one of my best beta-readers this round.
I also tip my hat to UMass Boston's QSC and Classics Club, two organizations that provided invaluable resources, inspiration, and encouragement as I first created this world, and to Remy and the rest of my writing group, who have helped me bring it together in final form.
CONTENTS
Dedication
Prologue
Part 1
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
Chapter 19
Chapter 20
Chapter 21
Chapter 22
Part 2
["This is not what you . . ."]
Chapter 23
Chapter 24
Chapter 25
Chapter 26
Chapter 27
Chapter 28
Chapter 29
Chapter 30
Chapter 31
Chapter 32
Chapter 33
Chapter 34
Chapter 35
Chapter 36
Chapter 37
Chapter 38
Chapter 39
Chapter 40
Chapter 41
Epilogue
About the Author
Young Adult Novels by Amelia Atwater-Rhodes
Copyright
About the Publisher
PROLOGUE
The surface of the Abyss was covered with an immense desert that had once been a fathomless ocean. It was a place of glistening black sand, venomous beasts, creeping vermin, and of course the Abyssi—those perfect, beautiful predators who ruled the infernal realm by fang and claw.
One such creature looked past the gray, smoky sky above him to a realm where the ocean was cold and tasted of salt, where verdant green cascaded across rich earth, and where the mortal creatures lived.
Soon, thought the Abyssi.
It was a powerful thought, for one of his kind. Most Abyssi had no concept of soon; they could only consider now, and whether what stood before them could be devoured or enjoyed in other ways. They certainly did not have the patience to create a mancer, an effort that took many careful years siphoning power into one of the frail creatures of the mortal realm. A mancer who would—soon—be able to break the barrier that separated this world from the one before it.
In the mortal world, the creatures who considered themselves strongest had nearly no fur. Their teeth were dull as if for grinding grass, and their nails were short and rounded, useless for shredding flesh. In the mortal world, the Abyssi would play.
Part 1
AUTUMN
YEAR 3988 IN THE AGE OF THE REALMS
CHAPTER 1
The mingled smells of brine, fish, and sweat from the docks failed to bury the cloying, meaty odor that greeted Lieutenant Hansa Viridian as he shouldered open the back door of a small warehouse that had seen better days. As the stench rose, he swallowed repeatedly in an effort to keep the bile from fleeing his stomach, along with everything he had eaten that day.
When Captain Feldgrau had given him and his second lieutenant, Jenkins Upsdell, the assignment less than an hour before Hansa was supposed to be off duty, he had assured them it was probably a false alarm. The landlord was fed up with a tenant who refused to respond to complaints about vermin, and instead of filing a complaint with the harbormaster or the minister of health, he had cried sorcery and summoned soldiers.
A brief survey of the warehouse made Hansa doubt this was a quick job. He drew his sword and visually swept the room, looking for threats.
The interior was dimly lit; the windows had been boarded up long ago, so the only light left came from candles burning on every raised surface. Most had melted completely but a few still flickered feebly, illuminating the carnage of small animals—mostly rats, though some were bigger. Some had simply been cut apart. Others had been disemboweled, skinned, and set around the room in ritualistic form, primarily on top of a leather altar Hansa hoped was made from a cow.
Something moved in the shadows of the back wall and Hansa raised his weapon, stepping out of the way so Jenkins could join him. They made their way across the room, trying to ignore things that squished and popped under their boots, increasing the rank odor that already rose from the decaying sludge that slicked the floor.
Movement caught Hansa's eye—pale fingers twitching in the far corner. Splashes of blood and darker fluids had camouflaged the man who lay sprawled in the back of the room.
"Jenkins?" Hansa asked before moving closer. Jenkins had the sight, which meant he could see the magic sorcerers used, though he couldn't control it himself. He might be able to tell if the man was a threat.
"I can't tell," Jenkins replied. "There's too much power all over this place."
That left finding out the hard way. "Watch my back," Hansa said as he sheathed his sword and knelt to establish if this man was a victim or a villain. In any other situation, it would be difficult to imagine a naked, unarmed man could be a threat, but a mancer wasn't only dangerous if he was dressed and armed. Abyssumancers were more powerful in the presence of blood, and they had an unsettling ability to hide weapons in plain sight.
"Sir?" he said. "If you can hear my voice, please let me know."
The body didn't move again. The man's skin was so ashen Hansa began to wonder if he had really seen him move in the first place. He reached forward to check for a pulse and Jenkins whispered, "Left hand, Hansa."
His eyes flickered down, and he saw the small dagger within inches of the injured man's left hand. Hansa knocked it aside with a boot, then once again leaned over and this time set two fingers to the man's throat, looking for any evidence of life.
He jumped back when the man's chest rose in a hitching, pained breath that soon became a rattling, wet cough.
"Help me," the man whispered. He lifted one languid arm.
"Do you need a doctor?"
"Need . . . to get out of this place," the man answered. "The . . . Abyssumancer . . . could come back. Please."
"Can you walk?" Hansa asked the injured man.
"Not . . . on my own."
"How did you get here?" Jenkins asked. Meanwhile, Hansa tried to ascertain the extent of the injuries and whether it would be safe to lift the man—for him, and for them, if he turned out to be dangerous.
"Don't know. I—" He coughed again.
A slash across the man's rib cage revealed the white glint of bone, and three parallel slices like claw marks savaged his thigh. Many of the injuries should have caused death within moments, but this man wasn't dead. Though blood was smeared across much of his skin, it wasn't concentrated around the wounds, which meant it wasn't his. That meant he wasn't as helpless and innocent as he pretended.
Hansa tried to suppress his instinctive frown, but the man must have seen something that said his ploy of being pathetic wasn't working. He struck; Hansa cried out as a blade swiped across his withdrawing hand, drawing blood and sending pain like fire up his arm.
The pain wasn't just the wound—it was magic. When it reached Hansa's heart, it wrapped around that vulnerable organ, and suddenly the air was smothering, dark, and hot as ash. Hansa's knees hit the ground, and then his palms, and then—
The air cleared and he coughed as he drew desperate, cool breaths. He struggled to draw his sword before he realized it wasn't necessary.
Jenkins had buried a small dagger in the Abyssumancer's back, just under his shoulder blade. It wasn't enough to kill, but it had been treated with a fast-acting poison that would put the sorcerer into a deep, powerless delirium for several hours. While he was out, they could search him more thoroughly and get him back to the cells beneath the Quinacridone Compound.
"Are you all right?" Jenkins asked as he helped Hansa to his feet.
Hansa nodded, sheathed his sword again, and instinctively checked his left pocket, which held a gold ring wrapped in white silk. The ring was set with a star ruby and two small diamonds.
"Do you ever plan to actually propose?" Jenkins asked as he trussed their prisoner's wrists. In addition to being second lieutenant of Hansa's company, Jenkins had been his best friend since before they could walk. Despite how long they had known each other, Hansa was still a little unsettled by Jenkins's ability to tease him about something like proposal nerves while they were surrounded by the gory remnants of magical malfeasance.
"I meant to tonight, but then this came up."
"Rubbish. You've 'meant' to every night for weeks now. A girl like Ruby isn't going to wait forever." His tone mellowed some as he hauled the mancer to his feet, and removed his own travel cloak to wrap around the naked man. "And in the meantime, do me a favor and don't make my sister a widow before you make her a wife. How's the hand?"
"It's not deep," Hansa said. Now that there was no magic backing it up, the wound itself was barely a scratch. "Let's get this gentleman back to the cells and see if he can tell us anything useful."
He spoke optimistically, but they both knew interrogating a mancer was normally futile. Men who made deals with demons were not easily caught in petty verbal traps, and anyone who would willingly walk the Abyss wasn't intimidated by a human soldier.
They left the warehouse with their prisoner slung over Jenkins's shoulder and entered the raucous bustle of the Mars docks.
The capital city of Kavet changed from one world to another the moment they crossed Harbor Road. The neat lanes and well-maintained stone and brick buildings of the upper city gave way to a haphazard, ramshackle wooden maze of flophouses, warehouses, shops, taverns, and inns that only those who lived there knew how to navigate. The jangle of merchants hawking their wares blended with a half-dozen languages spoken in drunken volumes, the ringing of instruments played by street performers, and the screaming of sea birds.
Immediately around Hansa and Jenkins, those noises quieted. Sailors out of Silmat and Tamar wouldn't know what a mancer was—they had their own forms of magic, but nothing as dangerous as sorcery—but they still responded to two men in official uniform carrying a bound, bloody man. They drew back, taking their games and drinking back to their own ships, or otherwise further away from authority.
The whores and thieves—or, as they called themselves, disciples of A'hknet, a religious order that, as far as Hansa could tell, believed in nothing—followed their clients or disappeared into the night, few wanting to be noticed by members of the 126.
"We're always so popular here," Jenkins murmured, the words just loud enough to reach Hansa's ears. Raising his voice, he shouted at two men half-hidden in the shadows, "You two, break it up."
The taller man was wearing the uniform of a Tamari sailor; he turned to Jenkins with a glare before the other half of his illicit embrace realized what was going on and jerked back. The sailor tried to catch his arm, but got an elbow in the ribs in return. Whatever the prostitute had hoped to earn by engaging this particular fare, it must not balance out with a charge of perversion and public display.
"Like we have time to chase after them tonight," Jenkins said, keeping an eye on the sailor long enough to establish he wasn't going to pick a fight after losing his intended roll in the hay. "As it is, we can't carry this fellow all the way back to the city square."
The Quinacridone Compound at the heart of the upper city had been a palace before the revolution, and was now the center of Kavet's government. Most citizens just knew it for the great hall where debate and voting took place, but underneath the pale, honey-colored stone was a dungeon where mancer powers were suppressed by centuries-old magics built into the foundations. That was where they needed to bring their prisoner, preferably before he woke up and attacked them again.
"Ma'am," Hansa said to an older merchant woman who was watching them without fear, "may we borrow your cart?"
The elderly woman swept him with an expression that should have been as deadly as the mancer's power, and asked, "Can I stop you?"
"Not really," Jenkins admitted, "but you'll be compensated, and we will make sure it is returned—"
The woman took a step back and spat at their feet. "Quinacridone brats. Just so you know, I voted against Initiative One-Twenty-Six."
Hansa sighed, as Jenkins shifted the mancer's weight. "I'm sure you did," he said.
Citizen's Initiative 126 had created the small, elite band of soldiers to which Hansa and Jenkins both belonged. Occasionally they were called in when lesser authorities could not deal with a civil problem, but mostly they had the dubious glory of walking into dens where sorcerers wielded power enough to breach the veil to the realm beyond. Some mancers could manipulate the thoughts of those around them, or even outright possess them. Some caused sickness. Some just killed, bloody and violent, in ever-escalating patterns. This one started with rats, but he would have moved on to his neighbors soon enough, if he hadn't already.
Yet women like this protested the authority that gave Hansa and Jenkins the power to walk into such places and risk their lives to protect the citizens of Kavet.
Jenkins nodded to Hansa, who pulled the cart forward. The woman wore the symbol of A'hknet on a pin at her throat. If she had any trouble with her belongings because of the missing cart, other members of that order would assist her. They had scattered at the appearance of soldiers, but would return quickly to get all the gossip once Hansa, Jenkins, and the mancer were gone.
"Numen-crossed Quin. You call us thieves, and here you are in the night taking what's mine."
Hansa winced. Was she trying to get arrested, giving them a hard time when their nostrils were still filled with the odor of rotting rat viscera and Hansa's head pounded from whatever the mancer had done to him?
"Ma'am," Hansa said tiredly, struggling to be polite, "if you give us your name, we will have the cart returned. If you prefer to remain anonymous, you may come to the compound to pick it up tomorrow. Your only other choice is causing a scene right now and spending the night in lockup for interfering."
He had no interest in arresting this old woman. He just wanted to get this over with and get home.
"Let's go," Jenkins said, lifting the cart and ignoring its owner, who continued to glare but stopped arguing. "It's going to be a long night."
Hansa suspected "long night" was a gross understatement.
CHAPTER 2
You won't hurt her, will you? Xaz thought. She tried not to let the distrustful words form clearly enough in her mind for the Numini to hear them, but knew she had failed when she sensed the chill of their disapproval and saw the rime of frost appear on her nails.
Speaking with the Others of the divine realm was always a delicate, apologetic dance. She had been learning the steps since her power first manifested when she was a little girl, but still hadn't mastered it.
Why would we harm a child?
Their voices were musical, but if the beauty of them had ever moved her, she didn't remember it. The Numini claimed mortals craved the divine instinctively, the way plants bowed toward sunlight, but Xaz never had. The only reason she knew for why people wanted to go to the Numen when they died was that the alternative—the Abyss—was so much worse.
Why would they harm a child? She didn't know. She also didn't know why they wanted a child. The Numini didn't explain their demands, and a smart mortal didn't question them. There was a young girl named Pearl who lived in the city. The Numini wanted Xaz to bring her to them, and they wouldn't tolerate reservations, excuses, or hesitation.
"As you will," she whispered. She ran her hands once more over the embroidered white silk altar-cloth, then pushed to her feet.
The altar had once been a hand-carved cherry footstool, purchased from a tree-farmer near her childhood home. It was one of the few things she had brought with her when she cut ties with her family, leaving her parents with the memory of their youngest daughter's swift death falling from an apple tree instead of the true memory of catching her conversing with the Numini. She had only been fifteen, but it wouldn't have mattered to the soldiers who would have come next.
Her parents, hours away in Kavet's highlands, had five other children. Losing one was probably a blessing.
She took a small, silver disc from the altar and tucked the rest under a spindly nightstand draped with a decorative woven blanket to hide the damning evidence. Most likely, no one would have seen it even if she had left it out. The bed blocked the view from the hall and no one but her had reason to come into this room. The few friends she had made in the city were almost all married now, but it didn't seem likely for her.
By Kavet's standards she was almost eminently marriageable. She was educated, unafraid of hard work, healthy, and at least passably attractive. Twenty-six was older than many women married out in the country, but in the city, it wasn't unusual. The only thing getting in the way of a long and happy life of domestic bliss was the automatic death sentence on her head, should her husband discover a Numenmancer's tools in her possession.
She liked her privacy, anyway.
She ran a brush indifferently through her cinnamon-auburn hair before tying it back with a faded blue ribbon, then pulled a heavy wool outdoor dress over her shift. Thick stockings under scuffed boots, tan leather gloves, and a gray hooded cloak completed her outfit. The disc went in a small pocket concealed in the cloak's lining, hidden from sight or pickpockets but available if she needed it during her mission. She wished she could curl up in front of the hearth fire until the chill left from talking to the Numini had dissipated a little, but that wasn't an option. Worse, she could sense shards of ice in the brewing storm clouds; there would be snow soon.
When she paused on the front step, gathering her nerve, the door of the home across the street from hers opened. Xaz groaned inwardly, but outwardly smiled, because people smile when a neighborhood friend appears. Normal people, who aren't dreading running an errand for the divine.
Had Ruby's beau finally found the courage to give her the ring everyone knew he had been carrying around in his pocket for the last week?
"Oh!" Ruby said, her face brightening in an answering smile as she crossed the street. "I was on my way to see if you were up for dinner. I was expecting Hansa, but they just sent word he won't make it, so I have more food than I need." A frown tried to overshadow the smile when Ruby mentioned Hansa's delay; Xaz saw her struggle a moment, then hide it. Disappointment that the expected proposal had been delayed another night, or fear for her soldier boyfriend?
Xaz could have pried further, but she had enough of her own worries without trying to divine Ruby's. She kept her expression carefully neutral as she wondered whom the 126 had caught that night, and whether it was someone she knew—or who knew her. There were many reasons most mancers didn't keep ties to others. Quin interrogation was the first.
"I'm sorry, I'm on my way out," Xaz said. "I have some errands to run before the markets close."
Pearl, the child Xaz was supposed to fetch, liked to come out in the evenings to bring cider to the guards coming off duty at the Quin compound. Since she otherwise lived in the Cobalt Hall, which might as well have been a fortress against Xaz's kind, that would be the best time to grab her.
"Are you still not feeling well?" Ruby asked. "Did the tisane help at all?"
It took Xaz a second to connect Ruby's words to the way she was looking at Xaz's cloak with concern. Ruby was wearing a lemon-yellow bodice over a simple, ankle-length day dress—prettier than the smocks and pants she normally wore at the herbaria where she worked, and far lighter than what Xaz had on.
Ruby didn't wait for Xaz to answer. She put a hand on Xaz's cheek and said, "You're still chilled. You should lie down. I can run to the market for you if you need."
How much of Xaz's life was dedicated to avoiding suspicion? She had declined an invitation to have dinner with Ruby and her boyfriend the previous night by claiming to be under the weather. Feigning illness to a senior journeyman at the herbaria had resulted in Ruby solicitously preparing and delivering a mixture of herbs designed to clear up the symptoms Xaz had made up on the spot.
Xaz hadn't been sick; she just hadn't been in the mood to feign friendship with Hansa Viridian. Ruby's boyfriend wasn't as paranoid or power-hungry as many of his cohorts in the 126, but he was still a soldier and a devout Follower of the Quinacridone. His only ambitions in life were to marry his childhood sweetheart, raise a perfect Quin family, and protect them all from those dastardly mancers. It didn't help that Ruby occasionally invited her brother Jenkins along with the hope of setting him up with Xaz. Keeping her power hidden from a man with the sight all evening was exhausting.
Ruby wasn't easy to keep at arm's length, and Xaz couldn't afford to alienate her. Her best protection at the moment was the fact that Ruby and her high-ranked soldier boyfriend liked Xaz. They trusted her, so no one else gave her much mind.
It was an adequate situation.
A sensation like the trill of harp strings, vibrating across her skin and not quite resonating in her ears, reminded her that she had work to do.
"I'm going," she whispered.
"Excuse me?" Ruby asked, taken aback by the irritated tone.
Xaz hated using magic on someone she lived so close to, but she didn't have time for this social dance. She put a hand on Ruby's shoulder and said, "I'm sure Hansa will be home soon. You should go wait for him."
Her power drove the words into Ruby's mind. A brief objection rose in Ruby's thoughts—she wasn't the kind of woman who waited passively at home—but Xaz's magic squashed it.
Without saying goodbye, Ruby walked away with languid, dazed steps. She would snap out of her trance in a few minutes and think going home had been her idea. Hopefully she wouldn't run into anyone else before then.
Before any other well-meaning neighbors could appear, Xaz returned to the house long enough to drop off the cloak and transfer the silver disc to the inner pocket in her dress along with her spending money. It was late autumn, but the last few days had been unseasonably warm. For most people, it was not yet cold enough for winter-wear, even if the chill in her bones seemed to justify it.
Dressed less warmly than she wished to be, she started out on foot toward the market square at the center of the city, a little under two miles away. It was one of the last places she ever went willingly, but defying the Numini was a worse idea.
Those who dared to speak of such things said the Numen was where good souls went in the afterlife, but anyone who thought its denizens the Numini were all peace and joy and love had never met one. They were not as bloodthirsty as the Abyssi, but they were still Others. They didn't think like humans, and their displeasure was distinctly unpleasant.
Few people did speak of the Others. The Followers of the Quinacridone believed focusing on the realms beyond drew value away from the current day and world, and the Order of the Napthol warned over-fascination with them could begin one on the road toward sorcery. Of course, what they taught was irrelevant, since it was illegal for anyone to write or speak about them anyway, with the exception of a select few highly placed individuals in the Cobalt Hall.
Those laws were enforced by the soldiers of the 126. The black-and-tan livery of that group had always reminded Xaz of rattlesnakes, even back when she had been an innocent little girl with nothing to fear from them.
Like Pearl.
Xaz spotted the girl talking with a spice merchant selling nutmeg, cinnamon, and other goods imported from Kavet's trading partners. Business was apparently slow enough the man tending the stall didn't mind Pearl's chatter.
According to Xaz's father, the city square had once been packed with foreign traders selling every luxury imaginable. She could almost see it. The ground was cobbled in blocks of irregularly-sized stone from around the world; she recognized marble in a dozen colors, sandstone, limestone, granite, and slate among others she couldn't name. Like the ornate well in the center and the towering buildings to the north and south, it suggested a time when Kavet was a prosperous trading power, not a large but unimpressive backwater.
The grand marble and limestone four-story building that towered over the north side of the square had once been the palace. Now it was the Quinacridone Compound. The old ballroom had been filled with benches and turned into a meeting hall, and the long halls of bedrooms that had once belonged to the royal family and visiting dignitaries now housed President Winsor Indathrone in one wing—along with offices for government use—and Quin monks in training in the other.
She had only gone there once, when shortly after moving to the city she had gathered the nerve to attend a debate about a trade ordinance she wanted to vote on. She had lasted less than an hour before the effort of hiding her power from sighted guards and her general anxiety at being in the belly of the beast had chased her out.
Stop stalling.
Forcing her steps to be calm and casual, she approached the spice merchant. All she needed to do was put a hand on the girl's arm and whisper a few words and she would be able to sneak off with her. It had to be done now, before Pearl went back into the Cobalt Hall.
Pearl lived with the novices and initiates of the Napthol Order, who had taken her in when the girl's mother had abandoned her on their front step. Once she returned home to the Cobalt Hall, she would be out of Xaz's reach. Supposedly many areas of the Hall were public, since the Napthol Order offered spiritual counseling and the best medical care in Kavet, but mancers weren't able to enter the building.
Xaz suspected the only reason Kavet hadn't passed a law ordering every citizen to prove their innocence by crossing that threshold was that no one understood why it worked.
I don't want to do this, Xaz thought, as much a prayer and a plea as a private contemplation.
A cool, shimmering sensation responded; the Numini reminding her of their presence without bothering to answer in words.
Xaz had almost reached the spice merchant when soldiers approached from the west, the direction of the docks. She recognized Hansa and Jenkins. Out of the corner of her eye, she could see a miasma of lingering dark power on Hansa, but it looked like he had won the fight in the end. Jenkins was pushing a cart that held a bound, unconscious man.
If it had been Numen power that marked Hansa, Xaz could have read it clearly, but this came from a hotter, darker plane, which meant the unconscious man was an Abyssumancer, not one of her own kind.
Xaz wasn't the only one who stared, but she was certainly the only one who felt her stomach drop as she saw one of the soldiers on the door whisper to the other, who went inside, probably to fetch more guards. A man in the violet robes of the Napthol Order saw the commotion and started striding protectively toward Pearl.
The Numini had to understand, Xaz couldn't afford to act now. She would end up in the cart next to the Abyssumancer, and then in a cell, and then in the next world. She started backing away, careful to avoid drawing attention.
She couldn't decide if she believed the Numini might accept such an excuse before the Abyssumancer stirred with a groan—then moved with impossible speed, rolling out of the cart and cutting the bonds on his wrists and ankles with a black blade as long as his forearm, which Hansa and Jenkins surely would have taken from him if the mancer hadn't hidden it magically.
The soldiers of the 126 surrounded him, and he met them with a bared blade . . . and then his eyes went past them, to Xaz, and she could see on his face the same expression she must have worn earlier when the Numini had asked her to get Pearl: utter terror, and resignation.
He threw the knife with a smooth, fluid motion.
She didn't see how the Quin responded, because the knife had not been aimed at any of them.
She looked down, and discovered two things:
She was numb.
She had a hilt jutting out of her stomach, marking the spot where several inches of blade had pierced her body.
The Quin started to turn toward her.
If they saw her, they would try to bring her into the Cobalt Hall so their healers could tend to her. The Hall would reject her, and they would know what she was.
She stumbled back as the pain hit her. Leaning against a building, she slid to the ground with one hand on her stomach bracing the hilt of the knife, and the other fumbling in her pocket for something she needed.
Desperately, she tried to conceal herself and to use her power to control the bleeding as she started to pull the knife out of her guts.
The blade moved maybe an inch before the pain became intolerable, and her stomach heaved, wanting to throw up and in the process shredding itself more.
Help, she prayed, as her hand closed around an etched silver tablet. The Numini did not like bloodshed, but this wasn't her fault. They had to help her.
I did what I can, was the only message she received, as her mind drifted at the edge of unconsciousness. You do the rest.
CHAPTER 3
Cadmia jumped as the door to the temple squeaked behind her. Her first thought was a guilty one—she had been failing to meditate, and had a feeling she had actually dozed off—followed by, I need to have someone wax those hinges, and only then by the question, What is a soldier doing in the Cobalt Hall? The Cobalt Hall was part hospital and part holy sanctuary, and was the home and workplace for initiates in the Napthol Order.
The man who entered the room, escorted by one of the Order's youngest initiates, was dressed in the black-and-tan livery of a soldier of the 126, including a sword at his belt. He was probably in his midtwenties, tall and broad-shouldered like most professional soldiers, with dark hair worn short and brown eyes set in a face that seemed undecided as to whether it should be pretty or rugged. He was pale and looked exhausted, adding to the latter impression, but he lacked the agonized twist of doubt and despair that marked many people who entered this place. Instead, his expression was tired but gentle.
The softness was probably directed at Pearl, his guide. The seven-year-old had been taken in by the Order of the Napthol after her mother abandoned her on their front step four years ago. She had few official duties at her age, but delighted in taking snacks and warm drinks to the soldiers assigned to guard the marketplace and the doors of the Quin Compound.
Pearl's face was set in a determinedly solemn expression, as if she wanted to smile at the man with her but knew her responsibilities were serious.
"Sister Paynes," Pearl said formally, "Lieutenant Hansa Viridian of the One-Twenty-Six has come to request your counsel."
Cadmia rose, smoothing down the violet robes of her office and schooling her face to patience. Anyone had a right to come to the hall for healing or spiritual guidance, but if Hansa had come for that reason, he should have come as himself, not as a soldier.
"I would be happy to meet with Hansa Viridian," she said firmly, "if he returns in civilian clothes, unarmed." Cadmia didn't normally work with soldiers, but knew Sister Marigold, who specialized in granting them counsel, refused to let them into her office while they were in uniform.
"I haven't come for myself," Hansa explained. "A prisoner has asked to see you."
She raised a brow, intrigued. Normally a courier from the justice department brought news her services were needed.
Cadmia's cohorts generally thought it odd that, out of all the more illustrious opportunities her years of study and hard work could have earned her, she had decided to specialize in offering guidance to the dredges of Kavet society. Even the older ones, who knew what a checkered history had preceded her vows, didn't really understand. Thankfully, she now had a high enough rank that she didn't need them to understand or approve.
She almost asked why a man in such an elite position was in charge of delivering this news before the obvious answer came to her.
"Is this the mancer who was arrested last night?" She had not witnessed the scene in the marketplace, but she had heard about it from Pearl and the other novices who had been minding her.
"It is," Hansa answered. She couldn't think of him as Lieutenant Viridian. They might have been the same age, and he must have been good in his field to have achieved the rank he had, but guards in the 126 always seemed young to her. It was the idealism, she supposed. "If you wish to refuse, I understand."
She shook her head. "If he has asked for counsel, he has the right to it." She meant the words, even though the concept of trying to provide guidance and solace to a sorcerer chilled her.
"Hansa will keep you safe," Pearl chimed in, her tone nervous and her mismatched blue and green eyes trained on Hansa as she added firmly, "Right?"
Hansa ruffled the girl's hair and gave her a tired smile, saying, "That's my job." To Cadmia, he added, "He has been disarmed and branded. I cannot guarantee he is harmless, but he is powerless."
Without his magic, he should be no more dangerous than many men she had counseled. Drunkards, abusers, murderers, thieves; Kavet's laws gave them the right to be heard.
"Lead the way, Lieutenant," she said. "Pearl, thank you for bringing Lieutenant Viridian to me." The novices and other initiates all knew to funnel requests from criminals and other disreputable sorts to her, but Cadmia was impressed that Pearl had been astute enough to bring Hansa to her and not to Marigold.
Pearl nodded, ducking her head shyly.
Without delay, Cadmia followed Hansa across the street and into the Quinacridone Compound, wondering why a mancer had asked for a representative from the Napthol. Maybe he was just trying to stall his execution by a few minutes, but maybe he genuinely wanted forgiveness. Maybe he wanted to tell them something.
Though she had been to the sections of the Compound that served as Kavet's main government building many times, she had never taken the rough stone staircase that led downward to a row of cells, evidence of the building's darker past.
"Why keep such a dangerous prisoner so close to the President?" she asked. Winsor Indathrone's living quarters were upstairs in this building.
"The cells are warded," Hansa explained. His voice dropped, as if he knew from experience that the stone walls would make his words echo unpleasantly. "They dampen a mancer's power. The forge we use to create the brands is built into the wall down here, too. It can't be moved."
"How does the warding work?"
Hansa glanced back and gave her a puzzled look, as if wondering why she asked. "We don't know," he said. "We think the royal house must have had some connection to sorcery before the revolution—some say they were in charge of controlling it, but others say they were overthrown partly because they were enabling it. Either way, the tools they left behind are the only ones we have."
Cadmia shook her head, making a mental note to see if she could find more information. She was highly enough ranked in the Order that it seemed like she should have heard of these indispensable tools before now; that she hadn't might just mean the information wasn't widely shared, but she feared it could mean there was no more knowledge to be had.
Quin in general weren't encouraged to ask questions, and soldiers in the 126 were given only the information they needed to do their jobs and warned that too much curiosity into the nature of magic could put them in danger of becoming the sorcerers they hunted. If they ever had trouble with the indispensable tools they needed for that hunt—these cells, the brands, and the poison used to apprehend mancers—they would come to the Order of the Napthol for help. If at that time no one had the answers, it could spell disaster.
At the base of the stairs, the hall was lined in dark stone, and bone dry despite its proximity to the coast and elevation below sea level. The air, which was neither hot nor cold but seemed flatly odorless, left a chalky sensation on Cadmia's skin and a bitter taste in her mouth.
As they neared the first cell, she caught a brief whiff of . . . something, like frying meat.
Hansa must have smelled it at the same time. He paused and drew his sword, and approached the cell cautiously.
Cadmia followed closely. The mancer had been left a candle for light, and he was sitting at the table with one of his palms just above the flame. He held his hand in place, not flinching, despite his own skin cooking, charring.
"Stop that!" Hansa barked, obviously unnerved.
The mancer looked up, but his pain-darkened eyes did not focus on Hansa. He moved his hand away from the candle flame with dreamlike slowness. As he did so he shivered, and Cadmia noticed every bare inch of skin was covered in goose bumps.
"Let me in," she ordered. Mancer or not, the man before her was in agony—not from the burn, but worse, so bad the burn itself had been nothing but a way to pass the time.
"Are you sure—"
"Open it."
Technically, she was speaking to one of the few individuals in the entire country of Kavet who could unilaterally overrule her. Citizen's Initiative 126 gave these guards the authority to make any decisions they deemed necessary to protect the populace from mancers, but they were trained to defer to the expertise of the Cobalt Hall, so Cadmia didn't expect Hansa to argue.
Hansa asked, "Do you want me to bind his hands first?"
She shook her head, and he unlocked the cell.
"I'll stay near," he said, and in those words she heard a firmness that said he would object if she tried to insist the meeting be private. In truth, she was relieved.
The mancer did not look threatening as she approached, but then again, they didn't have to be physically menacing. Their magic did the damage.
"Cadmia," he said. "I hoped it would be you." His voice was dry, hoarse, but the water pitcher he had been left was still full and the mug next to it unused, so if he felt thirst he had not chosen to alleviate it. "Do you remember me?"
She did not allow the familiar greeting to unsettle her, but tried to search his face. "I'm sorry," she said. "Have we met?"
"Fifteen . . . twenty years ago?" he said. "My—" A compulsive shiver took him, severe enough that Cadmia feared he was having a seizure, but when she moved forward he waved her back. "My father used to visit with your mother."
The list of men who used to visit Scarlet Paynes, initiate of A'hknet, was very, very long. The list of boys who had come with those men was much shorter.
"Baryte?" she asked. Did she recognize somewhere deep in this sorcerer's eyes a child she had played with while her mother worked?
The mancer sighed, and nodded. He reached toward the candle flame again, then jerked back, clenching his hand into a fist.
"Does that hurt?" she asked.
Baryte frowned, as if he had no idea what she was asking. When he followed her gaze to his hand, he opened his fist and turned upward a blackened, blistered palm. Cadmia swallowed to keep from gagging.
"No," he said, "it doesn't hurt."
He reached up with fingers that trembled a little, and began to undo buttons on his shirt. Cadmia waited quietly, ready to protest if he went further than his shirt. If there was something he needed to show her, it was her job to see.
Beneath the shirt were bandages covering most of his ribs and much of his arms. The brand was visible on his left forearm, a coin-sized burn from which black lines like blood poisoning seeped.
"What are you doing?" she asked, concerned, as he started unwrapping one of the bandages on his arms.
"Worried I'll bleed to death, or get an infection?" he asked, his voice now sharply derisive. "Thank you for the concern, but it's rather irrelevant. I'm a convicted mancer, with sorcery and murder to my credit. They will execute me as soon as you have been dismissed."
"Murder?" she asked, almost hoping he would deny it.
He looked up at her with a gaze gone flat and ugly, with no hint inside it of the boy she had once known. "The power gets hungry," he said, utterly unapologetic, as he removed the last of the bandage he had been unwinding.
The wounds beneath were a set of parallel cuts that could have been made by a blade—but Cadmia suspected not, given who and what the victim was. They were claw marks.
The cuts had been stitched closed, though blood still crusted the surface.
"I wouldn't be here, but it got in my head and wouldn't let me defend myself," he said.
"Who?" she asked.
"The black Abyssi," he said. "Talking to him did this to me. Cut me open. I had to . . . the things I had to do to crawl back up from that . . ." He shuddered, and closed his eyes.
"Are you saying you were forced to do what you did?" Cadmia asked.
The condemned often tried to explain why they were not at fault, but even if this man had once been an innocent child, he had admitted he was a murderer.
"I'm saying," he snapped, "that he wanted me to get caught. Even in the market, once he woke me up, I could have escaped. I was armed. I could have slit the throats of the two guards next to me and disappeared before anyone else could touch me. But he made me throw the knife away."
I could have . . . Again, his voice and face held no guilt about having contemplated two additional murders. Mostly, he sounded angry.
"You asked for my counsel," Cadmia said, somewhat sharply, as she began to wonder whether the mancer might have had no goal but to unsettle her. "Most people who call for me want the Napthol's blessing, but you—"
Unsurprisingly, the Abyssumancer started to laugh. "Don't waste your blessings on me, Sister," he said. "We all know the Numini will never let me into their realm. I asked for you because the Quin will ignore me, but it is your duty to listen, and to meditate on a man's last words.
"Abyssi are creatures of heat, lust, impulse, and hunger. As a rule, they do not plan. But the black Abyssi is planning something important enough that he was willing to—"
He stopped abruptly, and his burned hand went to his throat. He coughed wetly, and droplets of blood and blackish bile spattered from his lips.
"Hansa!" Cadmia called. She didn't know what to do as the mancer continued to cough, falling out of his chair, shaking and desperately trying to draw air.
Soldiers streamed into the room, with Hansa at the forefront, but what could they do? The fit might be a trick or might be magically induced. Either way, none of them dared touch him as it ran its course. A few minutes later the mancer lay on the stone floor, still and silent.
Baryte, she told herself. She had distanced herself mentally from a man who had chosen a life of sorcery and violence, but now she forced herself to think of him by name because the man had once been a boy and perhaps that boy had been innocent. Cadmia had been taught that mancers started on their path to sorcery through an unhealthy fascination with the Other planes combined with a selfish obsession with power . . . but she had never been able to find a definitive source to prove it. No one seemed to know for certain how a child grew up to be a monster.
One of the soldiers nudged Baryte onto his back, and his head lolled to the side, eyes staring sightlessly at the ceiling. Cadmia tried not to imagine what his spirit gazed upon as his mortal eyes clouded. Even for a Sister of the Napthol, that was a contemplation best avoided.
CHAPTER 4
When Xaz woke, she was certain it was not for the first time.
She was bathed in sweat, and felt flushed and feverish. Turning her head to the side to try to see where she was made the world swirl, so it was difficult to make out any details of the rough room in which she found herself. All she knew for sure was that she was not in a cell. Curtains covered most of the nearby window, but they weren't thick enough to completely block what seemed to be midmorning sunshine.
She was wearing a man's shirt, a sleeveless, shapeless piece with eyelets at the throat empty of lacing. It fit her loosely, but she was more concerned with who had stripped her than she was with her modesty.
As she tried to recall anything of how she had come to this place, her hand went instinctively to her stomach. Tugging up the hem of the shirt, she discovered bandages wrapped around her torso.
She was alive—how? And where? And almost as important, why?
Xaz struggled to her feet, conscious of the twinge of pain in her guts but not knowing what to do about it. She couldn't stay here, no matter where here was.
She barely managed to stand before blackness encroached on her vision and she needed to catch herself on the bedside table, sending several items that had been on it to the floor with a tremendous clatter. A small hand-mirror shattered as it hit the ground.
The door opened from the outside before Xaz tested whether or not she could take a step.
An ancient-looking woman wearing a loose nightdress stepped inside. Her gaze fell to the mess on the floor, and she shook her head. "Sit down before you hurt yourself."
Xaz had little choice but to agree, since she did not have the energy necessary to remain standing. The old woman wasn't overtly threatening, except that Xaz was so exhausted it was an effort to sense her own power, making her feel helpless and jumpy.
The woman put a hand on Xaz's forehead. "You're still feverish," she said.
"How did I get here?"
The woman shrugged. "I found you hurt."
Animamancer? Xaz wondered. There were four kinds of mancer—five, if you were willing to believe myths and whispers. Abyssumancers and Numenmancers gained their power from the Other realms. Necromancers were rumored to disturb the dead for power to extend their own lives and achieve control over other mortals. Animamancers were healers.
According to the Quin, the seemingly benign ability had a dark price. They claimed animamancers healed by siphoning healthy energy from the living into their patients.
It might even be true; to her knowledge, Xaz had never met one of the healers before. If they were anything like Numenmancers, the power still needed, demanded to be used. Maybe one of them had stumbled across Xaz, and nature—if there was anything natural about a mancer's power—had taken over.
"You should eat while you're awake. Is there anything particular I can get you?"
Again, though the woman said nothing specifically indicating she was a sorcerer, or asking if Xaz was, the question was telling. The different kinds of mancer each had their own tools, their own sources of power, and their own needs. In her discreet way, the old woman was trying to ask what Xaz was.
"I don't think I could eat anything right now," Xaz answered. Her stomach was churning, perhaps from the wound or the fever, but perhaps from pure terror. She had never been identified before, much less captured. The fact that this woman did not seem to be about to turn Xaz over to the Quin did not mean her intentions were benign.
"I'll let you rest, then," the woman said. "If you need anything, you can ring, or if you're strong enough to walk, you can come out to the parlor." She leaned down, bracing herself on the bed, to retrieve the bell that had previously been on the table. No wonder it had all made so much noise, falling.
"I'm sorry," Xaz said.
The words covered much. I am sorry I broke your mirror, and made you bend down to care for me. I am sorry I cannot trust you enough to answer the questions I see in your eyes. I am sorry I need to do this. . .
She reached up, and with what little power she could muster, she pushed at the woman's mind.
"Thank you for helping me while I was ill." She sent an image of sickness, but not injury. There was nothing suspicious about a fever in the fall. In return, she felt the edge of a secret; this woman had told someone else the same lie. Hopefully she'd also had the sense to hide Xaz's bloody clothing. "I will repay you in any way I can."
The old woman's eyes unfocused for a moment, then she nodded. A chill swept over Xaz briefly, a break in the fever accompanied by new droplets of sweat that appeared on her brow, before the sensation of heat returned.
"It's my way," the old woman said. "You sleep now. Ring if you need anything, and Cinnabar or I will be right in."
As she turned away, Xaz saw the shoulder of the woman's nightgown had slipped a little, revealing a scar that could only be one thing—the brand. How had she escaped execution? Had there been a time in this woman's long life when a branded sorcerer had been allowed to leave the detention cells alive?
Xaz's eyes were not sharp enough, but her power could see where the edge was marred. This branding had been done in haste, and it had been imperfect.
It wasn't much of a crack, but it might have been enough to allow the Numini to whisper in her ear and send her after one of their mancers. Their ability to manipulate her, however, did not mean she would be sympathetic to Xaz's plight; having escaped execution once did not mean she would be willing to risk herself now for a stranger. Thankfully, she would now give no more thought to odd injuries, or to how swiftly her guest healed.
The moment Xaz was alone, she put both hands over the wound, shut her eyes, and went into deep trance. She was no animamancer, but she could encourage her own flesh to return to its proper form.
Her power responded sluggishly, alarmingly so, and as she tried to work around the wound pain shot through her.
Poisoned. The knife the Abyssumancer had hit her with had been steeped in power that was the antitheses of hers. Unfortunately, the ritual needed to purify her magic would be more complicated than she could afford to do here. She forced the healing enough to function, but then she stopped, obeying her body's warning signs.
Using so much power while she was already weakened left her starving.
Still a little unsteady, she managed to walk to the door. She had intended to keep walking and find something more solid to wear along the way home, but the rush of warmth, the aroma of cooking food, and the sight of a handsome man with a violin locked her in place. The man plucked at each violin string in turn, eyes half-closed as he listened to the note brought forth and occasionally adjusted a tuning pin.
The man was lounging against several of the mass of pillows that filled almost the entire floor save for a sensible distance around a large, cast iron wood-burning stove. He was wearing loose-fitting slacks and nothing else, comfortable in his own home. His skin still held onto summer's tan and his muscles remembered a season of hard labor, possibly aboard a ship. Yet those chapped, hard-worn fingers started to pull a haunting tune from the violin. He was still picking at the strings instead of using the bow, but it was clear he had finished tuning the instrument and was now testing it with a deliberate melody.
Watching his hands, Xaz noticed the ring on his smallest finger, which boasted the symbol of A'hknet. That might explain why he hadn't asked too many questions when the woman had brought Xaz home. Members of the Order of A'hknet followed a philosophy of, "Do what you wish, and accept the consequences." They were as likely to help a stranger as rob her . . . which reminded Xaz she had no idea where her clothes or possessions were.
The musician looked up with an amused half smile, and remarked, "Normally, when a woman stares that long, her next question is 'how much do you cost?' "
Xaz jumped and felt her face flush as she realized how long she had been standing there, watching him. "I'm sorry," she said, hoping the blush would be mistaken for a product of the fever. Yes, he was an attractive man, but it wasn't like her to be captivated by a pretty form. "I didn't mean . . ." She wasn't sure how to finish the sentence.
The man unfolded gracefully, leaving the instrument propped against the wall as he said, "Sit down. You're shaking like a leaf. Mother made me prepare some tonic for you, and leave some hot and put some out to cool. Given how flushed you are, I imagine you would rather have something cold."
She nodded, grateful he had forgiven her rudeness and decided to change the subject.
"My name is Cinnabar," he said, when he returned. "I think I've seen you working near the main docks' marketplace. Am I right?"
"That's right." The work she did there—whatever needed doing, really—should be inoffensive to the Order of A'hknet, unless this particular member objected purely because it was legal.
She sipped the tonic he had provided, welcoming the cold the way she normally did heat when she had worked too much magic.
"Mother brought you in during the middle of last night," Cinnabar said. "What were you doing out alone in this kind of condition?"
"I didn't realize how sick I was," Xaz lied, effortlessly. She had been providing excuses for her behavior for as long as she could remember. "I went to the market to buy tea." Halfway through the explanation, she remembered she hadn't had any money on her, a fact most followers of A'hknet were unlikely to miss. "I must have been delirious. I don't think I even brought my purse. Did I faint? Where did your mother find me?"
"Not my mother; that's just what we all call her," Cinnabar replied. "She takes long walks sometimes, when nightmares trouble her. She found you near the upper market."
Nightmares. Probably the Numini whispering to her. They must also have hidden Xaz from searching Quin guards, since otherwise they would have discovered her when they tried to find the knife the Abyssumancer threw.
"She gave you her bed, which means she's in mine," Cinnabar added, with a raised brow, "so I can't invite you back there even if you are feeling well enough."
Apparently he hadn't decided to ignore her earlier stare. The only safe answer seemed to be, "Pity," before she took another large sip of the tonic. He and Mother had taken her in, saving her life in the process, so there was no need to tell him she would sooner swim in the frozen Mars harbor than engage the services of a prostitute.
That the Numini objected to such practices was only part of her hesitation. The other part was pure resentment: despite Quin disapproval, prostitution remained legal.
The Order of A'hknet was a small, foreign sect that stood in the face of almost everything the Quin believed, but it was a powerful force in Tamar, one of Kavet's major trade partners. Without Tamar, there was no rice, tea, or coffee, not to mention a variety of luxury goods. There were no mancers in Tamar, or Silmat, or even the Wild Islands or anywhere Xaz had heard of.
Therefore, the freedom of the Order of A'hknet had been carefully safeguarded, while the laws that made a mancer's life ever more difficult—such as restrictions on the use, possession, or trade of key spell components—were constantly refined and expanded. Occasionally Xaz daydreamed about hopping on a Tamari or Silmari ship and traveling to one of those other countries, but passenger rooms were exorbitantly expensive and few hired foreigners.
"I need to get ready to head out," Cinnabar said, glancing to the clock ticking on the mantel. "You are welcome to stay a while longer, if you need the rest."
"I think I can make it home now."
Cinnabar looked skeptical, but it wasn't the Order's way to interfere if someone wanted to be stupid. He was right that Xaz would not be able to walk far in her condition, but she needed to get out of this house and away from these strange, prying eyes, and thought she could manage as long as she took it slow.
"You'll want your belongings, then. Let me go see where Mother put them."
He disappeared into the next room, and emerged again several minutes later with a clean set of clothes in about Xaz's size. There was no sign of the knife. She fervently hoped it had slipped from sight, as Abyssumancers' tools tended to do until called back by their owners.
CHAPTER 5
Captain Feldgrau of the 126 listened diligently as Cadmia reported word-for-word what the mancer had said to her before his black magic caught up to him.
"What is your opinion?" he asked, before voicing any thoughts of his own.
She took a deep breath, passing the mancer's statement through her mind again. As Baryte had said, it was her duty to remember and meditate upon a man's last words, which meant her training had prepared her to recall and reproduce those words exactly.
"Baryte was angry," she said. "He felt the Abyssi he was working with had betrayed him, and he wanted to thwart whatever plan he believed it was trying to enact. The fact that they silenced him implies they did not want him speaking." With a mental shudder, she added, "That they could silence him, even though he was branded and in a warded area, is a little frightening. They shouldn't have been able to do that."
Feldgrau nodded, slowly.
"He mentioned having a knife, which the Abyssi made him throw away. Has anyone found it?"
"The guards who arrested him say the mancer produced another knife when he woke," Feldgrau confirmed, "but they did not see what happened to it, and we have been unable to locate the item." Unsettling. Anyone could have picked the knife up, in which case what might it be doing to them? "Do you believe the Abyssi could be planning something?"
Cadmia shook her head. "I was taught Abyssi can't plan. My guess is that Baryte assigned human motivations to creatures incapable of such forethought, but I'm not comfortable dismissing his words entirely."
Feldgrau nodded again. "I'll confer with the other captains about what precautions they think we should take. Thank you for your counsel."
"Of course."
She wished she had not been the one called. All her study supported what she had told the captain; Abyssi were not creatures of rational thought. They were powerful, bloodthirsty monsters, but they lacked the ability to scheme. So why were her instincts still telling her something was deeply awry?
She had barely stepped out of the Quinacridone Compound when she was confronted by another individual from the Order of A'hknet. This one was not a run-down mancer but an exhausted monger, as that order called its members who engaged in the trade of questionable goods and services. He was dressed in the loose, casual pants, shirt, and vividly colored vest he favored. His fashionably-long hair, which Cadmia knew was naturally a weathered straw color before an application of henna turned it rich, chocolate brown, looked like it had been hastily tied back without the benefit of a mirror. For Cinnabar of A'hknet, who took pains with his appearance as a professional asset, that was positively unkempt.
Cadmia smiled in greeting while instinctively putting a hand on her small purse. "Were you looking for me?" she asked. There was no other reason for Cinnabar to loiter outside the Quinacridone Compound, within sight of four members of the 126.
Noticing her distrustful gesture, Cinnabar said, "I wouldn't steal from family."
"We are not family," she pointed out.
"Not by blood, thank Numen," he replied with a flirtatious smile that was as engrained a habit for him as breathing—and which still made her blush. "You look good, Caddy."
Cadmia stifled the impulse to check her own hair and clothes self-consciously, even though she was confident the wavy, strawberry-blond hair Cinnabar had once admitted to envying was held primly back with wooden hair combs and the plum-violet robes of her order were neat and modest.
If he had been a stranger or a distant acquaintance it would have been easier to meet his eye and respond as a Sister of the Napthol should, but she was keenly aware the nearby guards were watching her. It didn't matter that they didn't know her history with him. She knew.
"What do you need with the Order of the Napthol, Cinnabar?" If he teases, I'll just turn my back and walk away. That's all.
"I need to show you something," he said, all flirtation leaving his face and tone. "Can we go inside?"
She led the way into the Cobalt Hall. Only once over its threshold did Cinnabar begin to relax.
"I lifted this from a guest we had recently," he said. "I took it because it looked like silver. I didn't examine it until she was gone." He flipped the disk onto the table between them, using the end of his sleeve to keep his hands from touching it directly.
The round disc was about the size of Cadmia's palm around, but thin as a coin. The upward-facing surface was marked with elaborate geometric designs that shifted and made Cadmia's eyes water as she tried to make sense of them.
When she picked it up, cold flashed up her arm as far as her shoulder. It spun twice before falling to the floor with a bell-like ring.
That kind of cold could only come from the Numen. The divine realm was supposed to be the destination for good souls when they died, but Numenmancers were not content to wait. They manipulated the Numen and disturbed the peaceful dead to command the Numini and achieve more power in mortal life. Though not as physically brutal as Abyssumancers, Numenmancers were in some ways more dangerous, as they altered the nature of divinity and so could endanger not just this life, but the next.
"I came to you because I know you'll trust me it isn't mine," Cinnabar said, his voice soft and desperate. "Mother got up last night after one of her nightmares, and brought back a woman who looked half-dead. I figured it was ship-fever, something like that, until I saw this. She was in my house, Caddy. She was alone with Mother."
Mother Avignon was one of the oldest and most respected members of the Order of A'hknet. She had lived through the revolution, or so people said, though she never spoke on those days. Cadmia had left that order and joined the Napthol when she was seventeen, but she still shared Cinnabar's instinctive outrage that a mancer had come so close to Mother.
"I know Mother probably will not wish to, but both you and she are welcome to stay here until the mancer is identified and captured," Cadmia said. No one knew why mancers could not enter the Hall, but Cadmia had seen one faint trying. She did not question the blessing, but appreciated that there was one safe place in the city. "Can you give me a description of the woman?"
"Description, name, workplace," Cinnabar answered. "I've seen her around before—not professionally," he was quick to add. "She's moderately attractive, a bit on the thin side, average height, brownish-auburn hair, brown eyes. Well-spoken when called to be, but she keeps her head down. She calls herself Dioxazine—Xaz—and she works down at the docks market almost every morning. I don't know where she lives, but I'm sure someone there can tell you. I can't believe I—" He broke off. "Just find her, please."
"Would you be willing to come with me to make this report directly to the One-Twenty-Six?" Cadmia asked, because she was expected to, though she was certain the fear that had driven Cinnabar here would never get him across the threshold of the Quinacridone Compound. She didn't bother to ask if he wanted guards posted near Mother's home.
Cinnabar shook his head and said, "I trust you to do what needs to be done."
So it was that Cadmia crossed to the compound for the second time in one day, and found Captain Feldgrau conferring with one of the guards that Cadmia recognized as one of Pearl's favorites. Bole had a daughter near Pearl's age, and so had a soft spot for the orphan girl who lived at the Cobalt Hall.
Tiredly, she said to Captain Feldgrau, "I think I have another one for you." She handed over the disc, now carefully wrapped, and said, "A monger just brought this to me. He stole it from a houseguest, then realized that it is obviously a Numenmancer's tool. He said the woman's name is Dioxazine, and that she works down at the docks."
"Did he say what she looks like?" The soldier who interrupted them appeared alarmed. "Pardon me, Captain."
Captain Feldgrau indicated for Cadmia to continue, so she repeated Cinnabar's description, and watched the soldier go pale.
"Do you know her, Bole?"
The soldier nodded. "I know her. She moved in to the river way in the south district about a year ago."
"Near Lieutenant Viridian?" the captain asked.
"Right next door to his childhood sweetheart." Bole grimaced. "With your leave, I'd like to go warn him immediately."
Feldgrau shook his head. "We don't know if she might be watching him. Sister Paynes, thank you for the information. We will handle this from here."
Cadmia returned to the market square feeling unsettled. It seemed like mancer activity had been steadily increasing in the last few years, despite every effort to control the threat. Of course, the 126's efforts were sabotaged by the fact that every paranoid farmer and fishwife cried sorcery whenever anything went wrong, so the few soldiers with the sight were constantly running around trying to determine if slaughtered chickens were the result of mancers or foxes.
That wasn't to say mancers weren't far more dangerous than foxes. They had the ability to stop a person's breath with a touch. The power was addictive, and just like a man who had fallen to Tamari crystal elation or even something as mundane as alcohol, those who meddled with sorcery seemed to need more and to become more irrational about how they supported that magic.
The power gets hungry, Baryte had said, to explain why he had committed murder.
The soldiers will deal with it, she told herself. That is what they are for.
She spotted Cinnabar again in the market, this time with one hand on an empty wooden pull-cart as he spoke with a honey merchant, his famous smile no doubt getting him a deep discount. If he was still worried about the mancer, it didn't show—but then again, a man in his profession had to be good at hiding his thoughts while appearing to be an open book.
He glanced up and noticed Cadmia watching him, and raised a hand in a half wave, half salute.
This time she managed to school her face. As a Sister of the Napthol, especially with her specialty counseling individuals who had fallen on the wrong side of the law, it was expected that she knew all types of people—even an Order of A'hknet prostitute. Others who observed them had no way to know Cinnabar was also the man to whom she had lost her virginity long before Kavet's legal age of consent.
"The Quin stole Mother's cart," he explained as she approached, patting the worn wooden handle. "It took a while to get them to give it back to me. Did you . . . get everything sorted out?"
She appreciated that he kept the question intentionally vague to avoid being overheard and causing a disturbance. She nodded, and told him the only part he would care about. "It will be dealt with. I didn't need to use your name."
"Thanks." He smiled again, and this time she thought it was genuine. "Do you want to walk down with me? You haven't come to visit us in ages."
"I used to come to visit Mother—my mother," Cadmia reminded him. Scarlet Paynes had died two years prior, caught in the middle of a fight for her affection between two men who would have forgotten her within the day. Cadmia had never known her father, so Scarlet's death had meant the last of her blood family was gone, and with it the last of her responsibility to visit with those who followed A'hknet.
"She isn't the only one who looked forward to your visits," Cinnabar said, softly.
"Have a good day, Cinnabar," Cadmia said, trying to disengage from the conversation.
"If I asked for your counsel—"
"If you put in a request for counsel, I will be sure to send one of the Brothers." It was more common for men interested in religious study to dedicate themselves to the Quinacridone and become monks, but there were a few among the Napthol as well.
Cinnabar quirked a brow, reminding her wordlessly that his flirting wasn't limited to women. Despite Kavet laws and Quin norms that made same-sex relations strictly illegal, Cinnabar willingly worked both sides—he was just a little more careful not to get caught when his clients were male.
Her scowl made him say, "You used to be fun."
He turned away, and Cadmia found herself relieved and disappointed to see him go—and fighting the urge to watch him go. Cinnabar had been awkwardly cute when they were younger. Now that he had grown into his broad shoulders and sharp, dramatic features it was clear how he was so successful in his chosen line of work.
It might have been easier to stoically toe the "no sex outside marriage" line both the Quin and the Order of Napthol held so dear if Cadmia had been as naïve as most initiates were when they took vows, but Scarlet Paynes's daughter had needed to start fighting off amorous intentions, often from sailors twice her age, when she was twelve or thirteen. Though only a couple years older, Cinnabar had taken it upon himself to become her protector, which included sleeping beside her with a dagger in his boot. They had become lovers when she was fourteen.
When she was seventeen, Tamari slavers had beaten Cinnabar senseless while attempting to claim him and Cadmia. She had put Cinnabar's dagger in the slaver's back, carried Cinnabar to the Cobalt Hall for healing, and dedicated herself to the Order of Napthol on the spot.
She only occasionally regretted the decision.
CHAPTER 6
Hansa had faced down murderers, sorcerers, would-be-slavers, and all manner of violent, dissolute men and women, but this was probably the most frightened he had ever been—at least since the last time he had tried to propose to Ruby, back when he was twenty-three and she was twenty.
She hadn't said "no" last time, but "later." She wanted to establish herself in her career before settling down. She was three years younger than he was; he had understood why she wanted to wait. Four years later, he prayed the answer would be different.
At least his nerves were keeping him awake. Between returning home late after overseeing the mancer's branding and getting up early to honor his request for counsel before his scheduled execution, Hansa had managed only a few hours' sleep. After the horror of the mancer's grisly death, he had almost put this off one more time—going home to sleep sounded very nice—but told himself no. Dealing with horrors was the nature of his work. It was time to stop using that as an excuse to put off the good parts of his life. As soon as Sister Paynes had finished her report, Hansa had reminded his commander that he had asked for the day off, then gone back home.
Now he tried to focus on cooking. Smell suggested the sweet bread was nearly ready, as it should be. He had fresh cider warming on the stove, and homemade maple butter ready on the table, which covered almost all of Ruby's favorite breakfast foods with the exception of fresh strawberries, which were unavailable this time of year. Trying to replace fresh strawberries with preserves was likely to end with the jar dumped over his head. At least the warm bread and hot cider would be appreciated, in the face of the cold wind that had started last night and brought winter in like a thief in the night.
Ruby started work very early in the morning, but was often able to come home for a few hours while an apprentice minded the distillery, so they frequently met at her home on days when Hansa was not scheduled. Hansa tended to breakfast more heavily when left to his own devices, but Ruby preferred to eat like a butterfly and snack all day, so they normally compromised when they met for brunch. But today was all about her.
When she walked in, her cheeks were pink from the cold outside and her gray eyes were bright. She pulled off her heavy overcloak and hung it on the peg next to the door before she greeted him with a kiss on the cheek and the words, "Do I smell sweet bread?"
She moved in a wreath of her own spicy-sweet scent, which lingered from her work at the herbarium. She spent much of the day distilling essential oils, which judging from the orange stains on her fingertips, today meant wild carrots. The seeds left behind after the lacy white flowers were gone had a variety of medicinal properties.
Hansa was just glad today hadn't been devoted to garlic, or skunk cabbage. It was hard to be romantic on skunk cabbage days, which had been all too frequent during Ruby's apprenticeship as an herbalist. She was now a senior journeyman and spent much of her spare time working toward her master work piece, an illustrated account of Tamari herbs and their cultural and medicinal uses.
"Oo, and maple butter, you darling!" Her delight abruptly shifted and she focused her gray eyes on him with suspicion as she asked, "What's wrong?"
"Wrong?" he repeated. Did she know about the mancer who had taken a swipe at him? She always berated him for choosing such a dangerous position . . . no, she was responding to the meal, which had her favorites and nothing he would have prepared for himself. "Nothing's wrong."
"Just tell me it's not another woman," she said, wide-eyed, with one hand to her breast, and her gray eyes sparkling in a way that unbalanced Hansa, unsure if he was supposed to be comforting her, defending himself, or laughing.
How had she always been able to do that? Even when she was just "Jenkins's kid sister" tagging along on their boyish adventures, her friendly teasing and sharp wit had been able to cut circles around his.
"You know there's never been anyone else," he replied, hoping to recover some of the nerve he had spent most of the last two weeks gathering.
"Oh, good." Moving to the oven, she peeked in and took the bread out, knowing he would have had it just ready. "You put in such an effort, I'm sorry to say I need to eat and run. I left the boy alone with a whole crop of bitterwort, and you know the Cobalt Hall will be on me if we let it scald. You'll forgive me, won't you?"
Forgive her? He might strangle her!
"Oh, darling," she said, moving close and putting a hand on his cheek. "Don't look at me so. I suppose I could stay a few minutes . . . but only if it is a very shiny ring."
"You evil woman!" Hansa declared as she danced back, the gleam in her eye now decidedly mischievous. She knew exactly why he had put this all together.
"I'm evil?" she asked. "Your mother has been asking me every day for the last week where this is." She held up her hand, and in it was the small silk bag that had been in his pocket a moment ago, before she had snuggled up close to him. Like many young ladies born to conservative Quin families, Ruby had spent some time fascinated with the Order of A'hknet when she was younger; in her case, the interest had caused a fallout with her parents that persisted to this day despite Ruby's return to a more decorous lifestyle. Her nimble, sticky fingers still held the skills she had learned in her eight months with the mongers, though these days she mostly employed them to perform sleight-of-hand tricks for children.
Before Hansa could even begin to sputter a reply, much less a proposal, a knock on the door made them both frown and turn from their playful teasing. Hansa debated ignoring it, but the pounding was too insistent.
"Sorry," he said.
Ruby followed after him as he went to open the door.
"Jenkins!" she scolded upon seeing her older brother on the front step. "Hansa was just about to propose. Do you mind coming back in a few minutes?" She swatted Hansa on the arm to add, "For your information, I took the afternoon off for this."
So did I, Hansa thought. Jenkins knew that, and knew why.
"Keep smiling, Hansa," Jenkins said, his voice soft. "The captain only gave me permission to give you the heads-up because I swore up and down that none of your neighbors would question my coming here for a social visit while I'm off duty."
"But this isn't a social visit," Ruby said, voice flat.
"Unfortunately, no, and I'm very sorry it had to happen today of all days. Let's go inside."
"What's this about?" Hansa asked as Jenkins let himself in despite Ruby's glare.
In response, Jenkins handed him one of the small stilettos carried specifically for use on sorcerers. The poison on it was difficult to craft and broke down quickly, so only on-duty officers carried it.
"We just got a report from a reputable source naming Dioxazine of 16 River Street as a mancer. I know you're supposed to be off today, but I thought you might want to be involved in this one. Also, I understand that you're neighborly enough that she might not panic if you knock on the door."
"Xaz?" Ruby asked incredulously. "But she's so . . . so . . . and I . . ."
She trailed off, probably considering the exact same things Hansa was: She's so quiet and reserved, shy, always polite. Like someone who had something to hide? It was hard to imagine the woman Ruby had occasionally coerced into joining them for social calls as a mancer, but that seemed to be what people always said when someone was named.
"You're sure?" Hansa asked.
"If she isn't a mancer, she's at least a sympathizer," Jenkins said. "The report came from a Sister of the Napthol."
"No," Ruby said, wide-eyed. "Hansa, you are off duty. I'm not letting you—"
"You know I need to go. I need to know what she has been doing here."
Xaz had been living next to Ruby for months. Even if a mancer did nothing directly nefarious, the power itself was dangerous and unpredictable. Ruby could have been hurt—and that was assuming Xaz had the best of intentions, and had not put herself near someone so important to a lieutenant of the 126 for her own purposes.
Ruby crossed her arms silently.
"Go or stay, Hansa," Jenkins said. "I told them I wasn't sure what you would choose to do. If the rest of the company doesn't see us soon, they'll break in."
"You've re-treated this since last night, I assume?" he asked Jenkins, as he took the stiletto and palmed it. The Abyssumancer should not have been able to wake as quickly as he had.
Jenkins nodded. "The paraphernalia found on her was clearly a Numenmancer's, so I was able to mix this pure for one of them. It should put her out fast and keep her down for a long time."
Hansa nodded. Like the brands, the poison was a remnant of an earlier age; it could only be distilled using equipment no one fully understood in the basement of the Quinacridone Compound, and it needed to be matched to the specific type of power the mancer wielded. If they knew going into an arrest what kind of sorcerer they were dealing with, they could use more effective poisons.
"You could both let them go without you," Ruby whispered, but the slump in her shoulders made it clear she knew they couldn't. "Why couldn't one of you have become a . . . a florist or something?"
"Sorry, sis," Jenkins said. "I wasn't cut out to be a monk." Jenkins had been born with the sight. There weren't a lot of options for him outside the Order of the Napthol and the monks who followed the Quinacridone. "Hansa, we have to go."
"We'll talk later," Hansa said to Ruby, knowing time was short. The last thing he wanted was for the others to move while both their lieutenant and second lieutenant were here. That would leave only Captain Feldgrau with the poison needed to bring the mancer down.
Ruby nodded sharply. He resisted the urge to keep arguing with her. She was afraid now; later, when they had all returned safely, she would understand why they had gone.
Trying to school his face to a friendly, open expression, Hansa stepped through the door. He couldn't see the other men from the street, but he trusted that they were nearby and would move quickly if Xaz tried to resist and Hansa could not subdue her immediately.
The shades on the Numenmancer's house were drawn tightly closed as Hansa approached.
He knocked politely, resisting the urge to pound on the door. If Xaz didn't answer, they would need to break in, which was risky. If she was out entirely, they could set an ambush, but that was still more dangerous than having her willingly come to the door.
Abyssumancers had the unsettling ability to be armed even after being searched and stripped naked, but Numenmancers could summon lightning or make the air turn so cold it could freeze a man's blood. Dangerous sorcery like that normally required a ritual, which gave men like Hansa an advantage if they moved quickly, but that potential delay was dwindling quickly if Xaz had realized what was going on and was at her altar preparing her defense.
Hansa reached for the doorknob, and then jumped as it turned and the door opened from the other side.
Xaz was normally a pretty enough woman, with auburn highlights in her brown hair and wide, expressive eyes, even though she constantly seemed on the side of too thin and too tired. At that moment, she looked feverish and exhausted, and she hung back from the door just enough that she would have room to jump back if he reached for her.
Hansa wasn't much of a natural liar, so he let neighborly instincts speak for him. "I'm sorry to bother you. I didn't realize you were sick. Did I wake you?"
She shook her head, and asked, "How did the proposal go?" Then she frowned and her eyes focused before she asked, "What are you doing here?"
Xaz had handed him an excuse, so he was about to say that Ruby had asked people to come over to celebrate—he would feel a little guilt later for using her that way, but it was better than tipping the mancer off—but before he could speak or even hesitate and fumble a lie, the Numenmancer must have guessed the truth.
She darted back and slammed the door behind her, but didn't have time to lock it before Hansa shouldered it back open and went after her, trusting the rest of his men to follow.
He found her in the living room, trapped and wide-eyed like a deer. Jenkins had taken some of the men around back; they had probably slipped in through the windows as soon as Dioxazine had come to the door, and now they had blocked her escape.
"Quin bastards," Xaz hissed, looking from Hansa to Jenkins with an expression of betrayal that eerily mirrored how Hansa felt. He had thought, before now, that Xaz was a friend.
She twisted to face Jenkins when he started to step forward, which left Hansa with a clear enough shot that he was able to bury the blade in the meat of her shoulder.
She hissed in pain and stumbled to her hands and knees—but stopped there.
The temperature in the room rose abruptly as she shoved herself back up and turned toward Hansa again, reaching out and seeming to realize only as she did so that there was a knife in her hand: a black-bladed bone knife that Hansa recognized instantly from the Abyssumancer Baryte. How did she have it?
This wasn't the time to ask; the poison seemed to disorient her, but it hadn't taken her down entirely because it was designed for a Numenmancer's power, and that clearly wasn't what she was using. Someone had made a disastrous mistake. They hadn't come here prepared to fight an Abyssumancer.
Bole must not have seen the knife before he attacked. His sword took a slice out of the mancer's arm before she dodged, but then she struck back and her blade found him between the ribs. It wasn't a heart-wound, but it was close enough, and with that kind of magic . . .
The air seemed to darken, becoming thick and hard to breathe.
Xaz shouted, "Just help me, damn you!" and then the world became red ruin as Bole's skin steamed and split.
Hansa couldn't see it, but he knew it was there by the bloody claw marks it left across the skin of the next soldier to reach it. Abyssi. It would only be put back by killing its master. Jenkins was closest . . . so it was Jenkins who, a moment later, was nothing but a crimson splash, a few shards of bone, and a slowly falling residue of ash. Meanwhile, Xaz fled through the back room.
Hansa couldn't see anything, beyond a fourth soldier flying across the room and hitting the wall near the door hard enough that he fell, dazed, and another kneeling on the floor with an upraised arm suddenly becoming a mass of clawed meat. Hansa swung at where the creature had to be, but hit nothing; his sword moved as if through air, even as whatever it was continued to claw at the other guard.
It wasn't possible for a man to fight a creature from the Abyss, but thankfully it was also impossible for a mancer to control one for long. This one would eventually turn on the Abyssumancer who had summoned it, and in the process it would send itself back to the Abyss.
Hansa just needed to survive that long.
While the Abyssi was focused on one of the others, taking its time now that no one was directly threatening the escaped mancer, Hansa slung an arm under the unconscious guard it had thrown across the room, lifted him, and then ran.
He had barely reached the street when he felt claws down his back. He fell hard, twisting to try to avoid slamming the head of the guard he had tried to rescue into the stone path.
And then he could see. Nothing solid, just a general shape, but that was enough because that shape was made of nothing from this world. It was darkness and pain incarnate, and as it went for the fallen guard, Hansa's nerve broke.
Hansa had always considered himself brave, or at the very least loyal, but in that moment he abandoned those illusions. He stood, and he ran. He fell because of the wounds down his back and crawled instead, dragging himself away from the horror of a mancer's wrath.
CHAPTER 7
Xaz collapsed, her limbs too heavy for her to even crawl any more. Her vision was blurred, her head was pounding, and the contents of her stomach seemed to have turned to lead. She didn't know where she was, or where the guards were, or exactly what had just happened.
She had barely made it home before collapsing into a deep, trancelike daze. When she finally recovered enough energy to try to speak to the Numini, she had discovered that the disc was missing, which made calling on the Numini for help nearly impossible unless they initiated the communication—which they didn't. She would need to get to the mancers' temple, a magical rift between the planes, in order to communicate with them.
Aching in every muscle of her body, she had tried to sleep, only to find herself unable to tune out the damn Quin's obsessive anxiety about his intended proposal. She was normally able to keep others' thoughts from intruding on hers, but her power was so muddled she couldn't seem to form the mental walls that she had habitually maintained since childhood.
The inability had probably saved her life. When Hansa had knocked on the door, Xaz had assumed that he had come to deliver the good news in a jovial, neighborly way, but that hadn't been the focus of his thoughts when he looked at her.
Like every mancer, she craved the touch of her power's realm, but knew the dangers of succumbing to that desire. She had never dared try to summon the Numini into the mortal realm. However, the alternative at that moment seemed to be branding and execution, so she responded instantly when one of the Others reached to her and whispered, I can help you. Pull me over.
Then she had felt the poison. It had disoriented and weakened her even more than she already had been, turning fear into panic. The Abyssumancer's bone blade had appeared in her hand without her in any way intending to summon it, and then the blood of one of the guards had been on her skin and she had shouted for help and fled as soon as the circle broke.
"Come back," she said, trying to speak with power in addition to her voice. It was difficult. "Please. I need your help." The creature appeared before her in an instant, but looking at it just made her head hurt even more, so she shut her eyes as she pleaded, "I need to be somewhere safe. I need to rest until the poison wears off, where they can't find me. Help."
As you wish. Its voice reverberated through her muscle and bone. She felt herself lifted before she fainted.
She had dreams of a little girl. Pearl, from the Cobalt Hall. The girl was shy, had always been shy. She had a long, dusky-gray feather in her hand, and was deep in prayer. But there was a wolf at the door, and it was hungry.
The black Abyssi watched, knowing. Once the girl was at the temple, he would be able to reach her.
Xaz woke, gasping, from a nightmare she couldn't quite recall. The last thing she clearly remembered was the command from the Numini to capture Pearl and bring her to the temple . . . what happened after that? She had been injured. She had woken up in the home of one of the members of the Order of A'hknet.
At that thought, she realized that she was curled up against what felt like a man's chest. It was too dark to see anything, so her sense of touch was all she had. Her first thought was, Cinnabar? She wouldn't have bedded him—
She tried to pull away, but there was a wall against her back and the ceiling was only inches above. Where was she?
Not with Cinnabar, she realized. She had left there. Gone home.
The soldiers.
She realized suddenly that the "man" lying in front of her had to be the creature she had pulled through the veil. She shouldn't have had enough power to do that without days of elaborate ritual, but she had been so scared . . . and the Other had helped, more than she would have expected. As a rule, Others did not like to tie themselves too tightly to mancers. It made them vulnerable.
She relaxed and curled closer, grateful for its warmth. Despite knowing what it was, knowing intellectually how much trouble she could be in, the Other's presence was comforting. The tie between them, the lie of power's voice, was what made this creature feel so safe; Xaz was aware of that. But in that moment, she was tired, and the creature was warm, and they were both wrapped in what felt like fur and silk.
The Other opened its eyes, which were deep indigo and shone like a cat's—except a cat's eyes just reflected present light. This creature's glowed from within, with an electric black luminescence.
Only once she noticed that did Xaz realize that part of the fur she was feeling was the creature itself. With her arm around its waist like a lover, it was hard to miss the feel of hard muscle beneath the fine, silky-soft pelt.
"You're Abyssi," she said in shock. Her voice seemed very loud.
"Yes?" It sounded amused.
"That's impossible." She tried to pull away, and remembered that she couldn't.
"You're mistaken." Despite its infernal origins, the creature had a beautiful voice, like water flowing over stone, or the warm crackle of fire. "It must be possible, for I am here, and I am Abyssi. You may call me Alizarin. And you are a Numenmancer."
"That's the problem," she said, fully aware of the amused lilt in the Abyss's tone. Now she remembered the blade, and the blood, and the screaming of soldiers after the Other appeared, but none of it made any sense. "I cannot have summoned you, much less pulled you through a rift into this plane. The human plane. Are we still there? Where have you brought us?"
"We're still on the human plane. We were both too weak to survive a passage through the rift, or to travel far. I found somewhere close."
"How far are we from the city?" she asked, trying to ignore metaphysic impossibilities for the moment and focus on what obviously had and was going on.
"We are in the city," Alizarin answered.
"What? They'll be searching for us. They'll find us. We need to go—"
"Hush, Mancer," he bid her, pressing a fingertip to her lips. She felt the barest hint of a claw tip against the sensitive skin above her upper lip. "They will not find us here. And you need to rest longer before we travel again."
Struck by a horrifying notion, Xaz pressed her hands to the "ceiling" again, feeling padded silk. Then the walls. A fourth wall on the other side of the Abyssi. A wall just above their heads, and a last one below their feet.
"Dear Numen, we're in a coffin." Since the passage of Citizen's Initiative 126, all bodies had been burned to keep them safe from necromancers and Abyssumancers, but there were still some old graveyards left.
"A royal coffin," Alizarin said. "A standard one would be far too small to fit us both. About a century ago, a prince was lost at sea. His body was never found, but the king and queen nevertheless buried a coffin, filled with furs and silks and jewels, in the family crypt. The jewels were looted from the coffin before it was even sealed, but the box remains. We are behind walls of stone, and then soil. The Quinacridone itself ordered the crypt filled in, after the royal family was disposed of."
"But, the air," Xaz protested. "There can't be enough air in here."
"While I am with you, I can sustain such a slight need," Alizarin explained. "The power it takes for me to do so is even less than that which it takes for you to fill and empty your lungs."
"Still, we should move on. We . . ." She trailed off. What could she possibly do next?
"You need to rest, Mancer. As do I," Alizarin insisted. "You are too weak. Without your own power to assist, I would probably lose my grip on you if I tried to bring you back to the surface now. Sleep a while. Sleep deeply, and I can leave enough power to keep you alive long enough for me to go to the surface and feed."
"Feed," Xaz repeated, concerned. "Feed on what?"
"No one you would care about." He licked her cheek, making her flinch. "You still taste like their poison."
"I don't care," she snapped. "I want to get out of this grave. Bring us to the surface."
"Right now?" he asked, tone too innocent. "Right this instant? Into the freezing rain that is currently falling? And, around in which the Quin guards are wandering as they search for you? Give it time, Dioxazine, until some of this settles."
She sighed. What choice did she have? "Okay. We'll wait, just a little while longer."
Except that, waiting in the darkness, she couldn't help but think. Very softly, not wanting the answer but unable to resist the words, she asked, "How many of them did you kill?"
"Don't trouble yourself, Mancer," Alizarin replied.
"How many?" she repeated.
"I killed no one who would not have killed us first," he said this time. "And I will feed upon no blood that would not be willing to spill ours. Would you have me do differently?"
Her chest was tight, maybe from tears for those whose lives had been lost . . . and maybe from her own knowledge that no, she would not have had him do differently. She had fought for her survival.
She had done exactly what the Quin most feared, what they had passed CI–126 to try to prevent.
"I'm a Numenmancer," she asserted, feeling at the edge of outright hysteria.
"The Numini rejected you because you were bloodied trying to do their bidding. When you tried to call for help, they fled, fearful of being enslaved by a mancer who could control them. I alone chose to answer you, Mancer." He added, very significantly, "And it was a choice. It was a choice for me to come to your side when you called, as well, and it was a choice for me to bring you here. So do not trouble yourself over the bodies behind us. Not until we both know how much 'choice' I have left."
Dear Numen.
He was right. She had no innate power over the Abyss; she had successfully summoned a creature over whom she might have absolutely no control. He needed for her to survive, since without her he would be forced back into the Abyss, but if she could not find a way to rule him, it was possible that he could just lock her away somewhere secure and think about her only enough to allow her to sustain his tie to this plane.
"You and I, Mancer, are going to have an . . . interesting partnership," Alizarin speculated. "Now close your eyes."
CHAPTER 8
There was blood in Hansa's left eye. He blinked, and it seemed to take an impossible effort to open his eyes again after that.
He was on the street, in a residential area. Someone was kneeling next to him and weeping. Everyone else had run.
Almost everyone.
His vision was going dim, but nevertheless, he couldn't help but see that one person had stayed, and was kneeling next to the body of the soldier Hansa had carried out with him. He was a man, and then, for an instant . . . not a man. He looked up at Hansa, and his detached expression quickly changed to concern.
"Help me?" Hansa whispered.
The man flinched as if Hansa had struck him.
"I'm trying." He recognized Ruby's hitching, fiercely-controlled voice. Had she seen the man? Was he even there? "You're—you're going to be okay. I've sent for a healer, and I'll do everything I can until someone arrives." She shifted, and he realized she had all her weight on the wounds on his back. Shouldn't that hurt more?
"Please," Hansa whispered.
The man snarled, his lip drawing back for an instant, and then he shook his head and walked toward Hansa, his movements a delicate glide, catlike. He put a hand on Ruby's shoulder and said, "Go."
She stood up, then paused, frowning down at Hansa as if confused. "I should—"
"Go," the stranger said again, his blue eyes seeming to flash.
"Okay," she mumbled, still frowning. She took several steps back, as if trying to remember what she had been doing, then turned to leave. Hansa almost called after her, but his voice broke.
Still standing above Hansa, the man said, "I can heal you, if you ask me."
Not human, Hansa thought. A mancer? Why would a mancer be offering to help him?
What else could he be?
"I could leave you to die if you prefer," the man said.
Hansa wasn't brave enough to accept that offer, no matter what the man might be. "Help. Please."
"One boon," the man said, the words sounding very formal.
He knelt, and pressed a hand directly to the wound on Hansa's back, making Hansa whimper. He was too weak to scream any more.
The world went black. For a while, Hansa was sure he was dead, but then he opened his eyes. The pain was still present, though lessened, but the growing pool of blood was . . . gone. He managed to reach a hand back, and found his armored vest tattered, but his flesh whole.
The man stood and started walking away.
"Wait!" Hansa called, through a throat that was raw from trying to scream. The man hesitated, his frame going rigid. "What . . . who are you?"
He twisted, just far enough for electric blue eyes to meet Hansa's. "My name is Umber," he said. "And I only assisted you because, if you lived, the taint from the Abyssi might have made you dangerous. Do not call to me again."
With that, he stalked from the plaza.
Everything was blurry. The pain had gone away and the blood had disappeared, but Hansa still felt too tired to lift himself from the cobblestone plaza.
But he had to get up. The Abyssi could still be around. The others might need him.
He pushed himself to his knees, but was shaking by the time he got there, and his breath was coming so hard the muscles in his chest felt strained. He tried to go further, to stand, but ended up collapsing all the way back to the cold ground. Maybe he could just rest a little while . . .
"Hansa!"
"Uuh?" Couldn't he sleep a bit longer?
"Hansa, I can't carry you. You have to get up! Can you hear me?"
Ruby. That was Ruby's voice.
In what he considered to be a remarkable act of willpower and valor, he opened his eyes.
"That's it, baby," Ruby said. "Wake up. You hear me. You can't stay here."
"Ruby," he mumbled. "You . . . you have to run. It could come back."
"I had to see what happened," she said. "Thank the divine you're all right. But you have to get up. I don't think you're badly hurt, but you'll freeze if you stay here. Oh, here's the healer. Sister, here he is! Please help me."
One of the violet-robed Sisters of the Napthol ran to his side, and knelt down, telling Ruby, "Don't move him. If he's as hurt as . . ." She trailed off, and said, "Let me get some guards to help me carry the stretcher. Miss Upsdell, you should go back inside."
"I'm not leaving him," Ruby protested.
"Then at least go fetch some warmer clothes. You'll both freeze this way. Then you can come with us to the Cobalt Hall." She raised her voice as she continued, "Guards! Could you please help me?"
He was pretty sure he could sit up. He struggled to do so, while the healer from the Cobalt Hall conferred with the guards. He recognized them from his own company, which meant some had survived.
That was good.
But how many were dead?
He was half-upright when one of them said, "Here, let me help you," and offered a hand.
"Thanks."
He reached out for the hand. Took it. Was barely aware of the needle-like blade in the man's other hand, which caught him by surprise an instant before the darkness did.
Hansa woke cold, damp, and half-naked, and unfortunately he knew exactly where he was. The perpetual gloom of the Quinacridone cells was distinctive.
He was somewhat relieved to discover that he was in one of the first-floor cells, instead of the deeper ones, which were reserved only for irredeemably evil and violent offenders . . . but that was only slight relief, since it still left him in a cell in a prison only used for sorcerers and their sympathizers.
Also, he had a roommate, a middle-aged woman who was staring at him with curiosity and suspicion. Given this cell was generally only occupied by mancers, that normally would have terrified him, but he knew this woman; Rose had been a member of the Order of Napthol before joining the Order of A'hknet. He couldn't count the number of times she had been picked up due to her outspoken ways, only to be released as a favor to the Cobalt Hall.
"A mancer in the One-Twenty-Six," Rose said, each word bitten off sharply. "I'm not sure who I would accuse you of betraying worst."
"I'm not a mancer," Hansa protested. Across his mind's eye, the images of all his fellows' bodies flashed. The memory of their screams. Could anyone really think he had something to do with that?
"That's what they say," his roommate said. "I heard them arguing after they tossed you in. Some of the guards don't want to believe it, but there are dozens of witnesses who say the demon killed the man with you, but let you live."
"I couldn't . . ." He had spoken to someone. Asked for help. He didn't understand exactly what had happened or how he was alive, but he knew he wasn't a mancer. "The mancer summoned it. Maybe she—"
"A Numenmancer couldn't summon an Abyssi," she scoffed, "and a Numini wouldn't have bloodied the soldiers that way."
Hansa had seen just enough of the Others—both divine and infernal—to know Rose was right. Numini could kill, but they did so softly and silently, without ever spilling a drop of blood.
"They identified her wrong," he whispered. "We were told she was a Numenmancer, but she must not have been. I . . ."
Ran away. His friends had been attacked, and he had run.
"I ran," he whispered. "They were dying. I couldn't see what was doing it, and I couldn't fight it, and they . . . everyone was dying. And I ran. And it came after me. I don't know why I'm not dead."
The woman clucked her tongue. "Well, neither do I. You're sure you're not a mancer?"
"I think I'd know," Hansa said sharply. "And even if I didn't, my second lieutenant has the sight. We've known each other since we were kids. He would—" He broke off as his throat closed up. Jenkins had been Hansa's second. Before . . .
Hansa raised a hand, wanting to rub blood from his face even though he knew it was already gone. If they even suspected he was involved in sorcery, they would have searched him and washed away the blood. Blood could be a tool for them.
Apparently deciding he was either honest or harmless, Rose said, "For your sake, I wish you would clear your name and get out of here, but you and I both know that is impossible. One-Twenty-Six gives them the right to hold you here as long as they like. With evidence against you from members of the Order of the Napthol, and multiple dead bodies to account for, they won't need to give you a trial."
"I know," Hansa said. "Damn it all, I know. Is this why it helped me? So it could then watch me rot?" he wondered aloud.
" 'It?' " Rose asked. "So that part's true, about you being helped by one of them?"
He nodded, miserably. "I was dying, I think. There was someone—something, I guess—there, watching. I asked for help. He said . . ." He tried to remember exactly what the creature had said. "He said it was a boon, and he was only doing it because the taint from the Abyssi could make me dangerous if I lived."
Rose sat forward, her voice going soft and excited. "A boon, really?" she asked.
What did it matter? Hansa nodded, looking around the gray cell and wondering if this was to be the place where he would die.
He understood how damning the evidence against him was. He had come to much the same conclusion when he had realized that the man they found in the warehouse in the wharf was covered in claw marks that gaped without blood. He was grateful to be alive, but short of sorcery, it was hard to explain how he was.
"Did you ask its name?" Rose asked.
"Umber." He was amazed he even remembered.
"Hansa, you may have a way out of this yet," she whispered, keeping her voice pitched low. "That wasn't an Abyssi who helped you. I don't know what made the Abyssi leave you alone, but the person who helped you wasn't a demon, and he wasn't a mancer."
"Thank you; I now have the faith of a fellow prisoner. What are you in here for this time, anyway?" Hansa asked. "Must be terrible, for you to get stuck in a cell with a man who is accused of slaughtering his friends."
"Just be quiet and listen to me."
"Like you said, I don't get a trial," he said. "Even if he was just some foreign witch—not that that would be appreciated, but at least it's better than a mancer—it won't matter, because he'll never speak to—"
"Shut your self-indulgent mouth, you idiot!" Rose interrupted. "For your information, I'm in here for collecting and studying every text I've ever been able to find on mancers and Others—and on the spawn."
Was she making any kind of sense? It was hard to tell, past the spinning sensation left by the crumbling of Hansa's entire world. "The what?"
"It takes a fool of a sorcerer to tear the veil and invite one of the Others into this realm," Rose explained. "It takes an incredible amount of power to control them, and Abyssi especially can be vicious if the summoner loses control. But as difficult and dangerous as it is, some mancers do it anyway. And some of them go further. Very, very rarely, the Others breed on this plane with mancers or other humans who run afoul of them. And that is how you get spawn."
She certainly sounded like a mancer. No wonder she was lucky enough to get thrown in a cell with someone accused of consorting with creatures of the Abyss. "Lucky me," he said, sarcastically. "I have a champion crossbreed."
"Shut up," Rose snapped. "The spawn walk in human form, but they are incredibly powerful. Whereas an Abyssi or Numini needs to bond to a mancer in order to remain on the mortal plane, the spawn have their own mortal blood to tie them here. However, the Other power continues to seek a bond, so they are susceptible to—"
Hansa waved a hand, cutting her off. "I believe that you're trying to be helpful, but keep in mind that, despite the accusation, I am the one of us who has never studied sorcery. I don't understand a word you're saying."
Rose drew a deep breath. "The spawn granted you a boon. The first boon has to be willingly given, but after that, a link is formed. If he gave you his name—and you're lucky you asked him, since otherwise he most certainly wouldn't have—then you can summon him, and he will be forced to grant another boon you demand. Spawn are incredibly powerful. Call him now, and he could make these charges disappear."
"You're actually suggesting that I should summon a half-demon creature in order to clear myself of practicing sorcery?" Hansa asked, incredulous. "That's insane. No. I just need to think clearly. Stop panicking. Mancers don't get trials, but they can have counsel. That's all I need."
They hadn't branded him while he was unconscious, or bound him physically, which meant someone out there believed he was innocent. He had been a soldier since he was eighteen; he had joined the 126 when he was twenty-three, had been promoted to lieutenant when he was twenty-five, and had spent a year in that position.
In the entirety of his life, the only time he had been in trouble was when Jenkins's poor timing and often off-color sense of humor had convinced some new soldier that they had some kind of disturbing sexual relationship. Officially, both Hansa and Jenkins had been suspected of illicit behavior and perversion, but in reality, their superiors had gone through the required motions without any belief that an investigation was warranted. Jenkins was chastised and warned to watch his words in the future, and it had ended there.
No one who knew Hansa could believe this nonsense about sorcery. He could ask to speak to one of the Sisters of Napthol, and tell them what the spawn had said about healing him only to keep him from becoming dangerous. The Sisters studied the Others; they probably knew about the spawn, and would be able to understand and explain why one of them would have helped him without his delving into black magic.
He had joined the 126 because he believed in the laws and the system that enforced them. He had to trust them now.
CHAPTER 9
Maybe I should move in, Cadmia thought, as she entered the Quinacridone Compound for the third time in two days.
She remembered the young guard who had come to fetch her to speak to Baryte, which meant she was simultaneously one of the strongest witnesses in his defense, and against him.
Hansa had arrested Baryte, and therefore had been closest when the bone knife that later showed up in the Numenmancer's home had disappeared. He had also been closest when Baryte had died, obviously destroyed by Abyssi even with the brand on his skin that should have blocked the Other's power.
Hansa had for some reason been on point when they made the Numenmancer's arrest, though witnesses who stayed behind said that before they left the compound, Captain Feldgrau had said Hansa should not be spoken to in case the mancer was watching him.
No one could ask Captain Feldgrau, because Hansa Viridian was the only survivor of the group that had gone to arrest Dioxazine.
On the other hand, Hansa had crossed the threshold of the Cobalt Hall, which supposedly no mancer could do. That was a strong point in his favor, but not a definitive one; no one understood how the Cobalt Hall protected itself, so it wasn't impossible that a mancer could find a way to bypass the magical defense, just as many of them learned to hide from guards with the sight. It was also possible that Hansa was a sympathizer, working with the mancers somehow but not one himself.
Finally, he might have been framed. Cadmia had spoken to several of his surviving peers; they loved him, and were horrified by his supposed betrayal, and terrified by the idea that a man in line for captainship in the 126 could have been a sorcerer all this time. What better way to unbalance that illustrious group, than turning them against each other?
"The black Abyssi," as Baryte had called it, had injured him enough that he was caught, had instructed him to throw away the knife, and had probably killed him.
If one of the Abyssi had gained the ability to plot directly against the 126, Kavet had far more frightening problems than one turncoat soldier.
She heard the shouting as she approached the cells—a woman's voice, raised high. "You bastard!" she shrieked. "How long have you known? How long have you and Xaz been playing with me? With Jenkins?"
"Ruby!"
Cadmia hurried her steps toward the sound of a scuffle, and found two guards watching a petite woman rail at the occupant of the visitation cell in front of her. One of the guards had a bloody lip, but had obviously decided he would rather stand back than manhandle the distressed woman.
"I saw it with my own eyes!" she shouted. "I saw wounds down your back that should have killed you. I was still covered in your blood when the healer arrived, but you weren't any more. I forgot at first what I had seen, but I couldn't understand where the blood came from so I asked one of the guards with the sight to tell me and—it killed eleven people, Hansa! It killed Jenkins! How could you—"
"Ma'am!" Another guard had rushed into the room, and shot a cold look at the two who seemed reluctant to touch her as he stepped forward, cutting between her and the bars.
Hansa's voice came from within. "Ruby, I swear to you, I—"
"I don't want to hear it," she whispered. "Take me out of here," she pleaded, of the last guard who had come in.
She leaned on him, and seemed oblivious to Cadmia's presence as they exited together.
"I'm sorry," one of the guards said, to Hansa. "When she asked to come in, she didn't seem . . . I didn't think she—"
"Soldiers are not permitted to speak with prisoners suspected of sorcery," Hansa interrupted, his voice cold and bitter. "Such prisoners are also not allowed personal visitors. Maybe for all our sakes you should consider enforcing those rules."
"Yes, sir," the soldier replied. As he saw Cadmia, he added, "Do you still want counsel from the Napthol?"
"Is she here?" He came forward to the bars, and then backed away and sat at the table at the far end of the room without being told. "Please, send her in."
Still an officer, even in here, Cadmia thought. Even with such a pile of evidence against him, the other soldiers were unwilling to completely turn against him. If he was a mancer, they were all in trouble.
"The prisoner has a right to privacy," she told the two guards after they locked her into the cell with Hansa. They obligingly moved down the hall, far enough that they would hear her only if she shouted.
She sat across from Hansa, who looked as pale and drawn as any man she had ever faced in such a position. Was he responsible for the deaths of nearly a dozen men, or was he an innocent victim? How many times had Cadmia sat at a table like this one and wondered that?
"You asked for me?" she asked.
He nodded. "I'm innocent," he said. "I might be a coward for running away, but I'm not a mancer."
"What happened?"
"I took point because we knew she would come to the door for me," Hansa explained, his voice calm and even, as if he had given these words much thought and knew perfectly well that this was the one chance he had to defend himself. "I think they must have been wrong about what kind of mancer she was. Jenkins had mixed the poison for a Numenmancer, but it didn't work. She stabbed Bole with that damn bone knife, and summoned what had to be an Abyssi."
"What did it look like?" Cadmia asked. Hansa Viridian did not have the sight, and the Other powers were invisible to anyone without it.
He paled, his skin going ashen gray at the memory. "I couldn't see it until it took a swipe at me, and then . . ." He trailed off, his gaze distant, lost in traumatic memory. "There was so much blood, and I didn't know what to do but run away. I tried to help one of the others, but I think the creature got him, too. Then it hit me."
"And you survived."
"The mancer must have called it back."
He must not have known that the evidence at Dioxazine's house made it very clear that she worked with the Numen powers. An altar hidden in the closet had been covered with white silk embroidered with gold and silver thread. Small silver vessels holding honey and what was probably rainwater had also been found. Those were not the tools of an Abyssumancer.
"You say the Abyssi hurt you before it disappeared?" she asked, returning to that point.
"Yes," Hansa said, tightly. "I know that's why I look so guilty." That's the least of it, Cadmia thought, but she let him continue. "I thought I was dying. There was someone there, and I think maybe whatever let me see the Abyssi let me realize he was different, too. He was looking at the bodies, and then he came up to me and told Ruby to leave. She just walked away. The man said that, if I survived, the taint from the Abyssi might make me dangerous, so he healed me. I guess he expected exactly what happened, that I would be arrested, and so assumed I would never be able to track him down later." He drew a deep breath, and added, "Rose, the woman who was in the cell with me when I woke up, says he was probably one of the . . . the spawn?" He said the last word as if he was not entirely certain of its meaning, but repeating something he had heard. "She says they are powerful enough to do that."
The spawn had been vaguely referenced in Cadmia's study, but never in detail. Most members of the Order of the Napthol believed they were a myth, something of a cautionary tale for mancers.
"Can you describe this man?"
"He had blue eyes," Hansa answered. "That's all I really remember. They seemed to glow. Have you ever heard of the spawn? Do you believe me?"
"Hansa . . ." She sighed. "Guards have searched Dioxazine's home, and the tools they found make it clear she is a Numenmancer. How could she get an Abyssumancer's blade, or for that matter, summon an Abyssi?"
"You are more qualified to answer that than I am." Hansa's expression closed off, becoming more withdrawn. "Surely there is some possible explanation?" She shook her head. "Sister, please. I'm not a sorcerer!"
He seemed so sincere, so desperate, but there was no rational explanation for events that did not involve his having power. He said the spawn healed him to keep him from becoming dangerous, but if that were the case, why hadn't it let Hansa die, or helped him along, to eliminate the threat in the simplest way?
"I will meditate on your words," she said, rising to go.
"Sister . . ." He trailed off, looking defeated. "This is impossible."
All she could offer was one last assurance. "They will brand you before they execute you. If you are innocent as you say, you can at least have the comfort of knowing your name will be cleared at that time."
"Small comfort," he replied. "Have you seen what the brand does to a man without power? I have."
She had never seen it, but she had heard of the case a few years before where a sorcerer woke and managed to turn the brand around on the guard who held it. One of the other guards who had been there had come to the Cobalt Hall afterward for counseling. His description of the event had been graphic.
"I'm sorry."
She was, really. Hansa seemed like a good man. Then again, so many of them did, once it was too late for it to make any difference.
After she made her report to the remaining captains and left the Quinacridone Compound, though, she stared at the Cobalt Hall and couldn't stomach returning to it. She went in only long enough to exchange her official violet robes for simpler dress, and walked down to the docks.
Unsurprisingly, she found Cinnabar first, leaning back against the outside wall of the King's Ransom. He had his arms crossed and was shaking his head to a sailor who was obviously trying to buy his time.
Normally, Cadmia would have walked by without bothering him, but Cinnabar noticed her and waved, extracting himself from his would-be-client with a smile.
Cadmia kept her face as politely blank as she could as Cinnabar hurried toward her, but he must have read something in her expression, because he took a look at her and laughed. "What have they done to you up there, Caddy?" he asked dramatically. "Such a scowl over a perfectly legitimate business transaction."
"Odd," she remarked, "it looked like an utterly illegal business transaction to me."
"Not if we go back to his ship," Cinnabar answered. "Tamari ships adhere to Tamari laws."
"You wouldn't—"
"I didn't, obviously," he pointed out, his tone softening in response to her alarm. "I'm not stupid enough to put myself on a Tamari ship. They turn slaver as often as the sun sets, and they know Kavet officials would never object to one less child of A'hknet. Speaking of, Rose is in jail again."
"I know," Cadmia sighed. Rose had traveled the opposite path as Cadmia had, becoming a full Sister of the Napthol before giving up that life and turning to A'hknet. She had refused to cease her studies, but she was well enough respected from her time in the Cobalt Hall that the Quin tended to arrest her, keep her a few days, fine her, and then release her. Hansa had mentioned her, but Cadmia's focus had been on Hansa himself. "I'll check on her the next time I am up there." And talk to her about giving ideas for excuses to suspected mancers.
"In the meantime, what brings you down here disguised as a lowly monger?" Cinnabar asked, with a gesture toward her casual clothes.
Maybe the same thing that drives Rose to the Quin jails time and again, Cadmia thought. "I decided you were right—it's been too long since I visited."
Followers of the Quinacridone and the Napthol were not supposed to question much. They certainly were not supposed to hear enough evidence to convince anyone of guilt, and then look at a condemned prisoner and be gut-certain that he was innocent.
She couldn't start doubting her mind and logic and everything she knew now.
CHAPTER 10
After the guards took him back to his own cell from the meeting room where he had spoken to Cadmia, Hansa found himself for a long time unable to form words or do anything but stare at the cell door. The soldiers outside had moved a greater distance away, and had not tried to talk to him since his return.
Rose spoke his name at least twice before he turned toward her.
"She doesn't believe me." That much had been clear before Cadmia left. "They say the mancer we went to arrest was a Numenmancer. She couldn't have summoned an Abyssi, so they think I must have done it." Rose did not say, I told you so, but the words were visible on her face. "You know about these things!" he pleaded. "There must be some kind of explanation. I'm not a sorcerer."
"Then you'll die an innocent man," Rose said. "At least you'll have the comfort of knowing that the Numen takes those who died righteously."
He shook his head, remembering the look Ruby had given him before she left. She also thought he was guilty. How would she feel when they told her he had died screaming, innocent, under the brand?
He tried to squash the instant of satisfaction he felt as he pictured those who had condemned him when they realized they had been wrong, so wrong.
"I don't think I'm a righteous man," he admitted. His parents, his friends, and Ruby would all be devastated when they realized what had happened. How could he even for a moment have felt . . .
"There may still be time to ask the spawn for help," Rose said, softly, with a glance toward the guards who were standing well away down the hall. They didn't want to be near him.
"Why would he be mad enough to come here so I could ask him anything?" Hansa asked. Was he really contemplating dealing with a demon, practicing black magic, in order to convince everyone he was innocent of dealing with demons and practicing black magic?
Could two wrongs make a right?
"You can summon him," she explained. "His power will force him to come to your call, as quickly as he can."
"How?"
His only other choice was to sit here and rot until his friends conquered their squeamishness and took him to the branding chamber. Until his friends, unaware until it was too late, murdered him.
"When Umber helped you, did you get any sense of feathers, or fur? A tail, scales, horns, wings, anything?"
Hansa closed his eyes, trying to remember. "All I can recall is how blue his eyes were. They seemed to glow."
"Half-Abyssi, then," Rose said, nodding sagely. "That's good."
"Good?" Hansa whispered. "Aren't the Abyssi the nasty vicious ones that tear people to pieces? Isn't an Abyssi what—"
"Yes, yes, what nearly killed you. But this is a crossbreed, and bonded to you now from the first boon. He can't hurt you."
He had no choice. He had decided to go for this mad plan, so he had to trust her now. "Okay, half-Abyssi. What does that mean?"
"It means, you shed blood, and you say his name, and he will appear."
Blood. Why did it have to be blood? He wiped at his face, unable to forget the sensation of Jenkins's blood raining down on him.
They would never have left a suspected Abyssumancer with any kind of cutting tool, but Hansa had gone in and out of this cell often enough to know there was a sharp burr on one of the metal bars. He had nicked himself on it accidentally more than once. Trying not to think too much, he slid his hand down the bar now, quickly, feeling the bite of the metal as it sliced across the meat of his thumb, deeply enough that the cut bled freely.
"Umber . . ." As the crimson drops fell to the ground, Hansa wondered what the guards outside would do, if one glanced in now and saw him. No, he didn't need to wonder; they would kill him on sight. "Umber, come to me now."
As soon as he uttered the words, Hansa had a sensation of force, pressure, pushing against him from all sides, as if he were deep under the ocean where only strange, eyeless fish dwelled. He struggled to draw breath, and felt Rose trying to help him back to his feet. He managed to make it back to his cot to sit, but the sensation did not abate.
"He feels it, too," Rose said. "He will come."
Hansa shut his eyes and focused on breathing, not thinking, not feeling, just breathing. Not passing out. Not wondering if the first person to come would be the half-demon, or the executioner.
He heard a conversation down the hall, but was unable to focus on it enough to know who it was. The impossible thickness in the air did not clear until the moment someone dragged him to his feet.
"I'm quite certain I told you never to call to me again," the spawn snarled. The cell door was open, and there was no sign of the guards down the hall, who otherwise would have come running in response to the ringing impact of Hansa's shoulders hitting the metal bars as Umber shoved him into them. "And yet suddenly I hear my name, and I feel the pull of blood. Do you have a death wish, Quin?"
"No," Hansa squeaked out. Healed of the Abyssi's wounds, he could no longer see the demon inside this man, but he knew it was there—and even if Umber had been just a man, the fury in those eyes would have frightened him.
"He called you to demand a second boon," Rose said.
Umber hissed at her, a feral expression that no pure human could accurately mimic, and then looked back at Hansa. His face only inches away, he asked, "So the witch has been giving you ideas. Has she warned you of the consequences?"
"There are no consequences to a second boon," Rose insisted.
"Every time power is used, there is a price," Umber returned.
"For you," Rose said. "The first two boons only bind you." To Hansa, she added, "The second boon will force him to protect you, since harm to you will be harm to him."
"And vice versa, of course," Umber added. "It goes both ways."
"Not much can hurt one of the spawn," Rose pointed out.
As they argued, Hansa tried to pull away, only to have Umber shove him back against the wall and then take another step forward, so his body was flush against Hansa's, pinning him against the bars. The spawn's lips hovered just above Hansa's as he whispered his warnings.
"I granted the first boon because you had been so infected by the Abyss that your survival would have made you a mancer, and the last thing Kavet needs is for one of those bastards to have an elite position in the One-Twenty-Six. The first boon leaves a connection, but it dissolves quickly. The second boon binds two souls tighter, and longer." Umber continued, his breath warm, and his voice a gentle whisper. "And in case you find this to be a convenient way to correct your problems, you should know that the third boon creates a permanent bond, one that can take many shapes." He ran a hand up Hansa's chest, slowly sliding skin against skin. "The submissive party—and that would be you, pretty man, since you have no power of your own with which to make it otherwise—may find himself losing all he is, his every thought, every breath, devoted only to his master. It's called a soul-bond. Sometimes the bond takes a less intense form, a gentle ache when the master is away, one that can be ignored and lived with, but often it is an all-consuming passion.
"Know this, boy: I do not want you as my slave. But if you force me, I assure you, I will enjoy you."
At that, he kissed him.
A punch to the jaw might have been expected. He would have known how to respond to that. Strong fingers twining in his disheveled hair, holding his head in place, were not. Umber's body was almost fever-hot, hard against his, and his mouth was unapologetic, demanding, challenging.
Hansa hesitated, off-balance, unable at first to process the bewildering move so he could respond appropriately. For a wild moment, he could only think, If Ruby kissed this way—He managed to jerk his head to the side only when Umber bit him, drawing blood from his lip, and then licking it away.
"Guh!" He shoved at Umber with all his strength. The move only pushed the spawn back a couple feet, but at least it was something. "Don't you ever do that again!" he shouted. "Ever!"
"He's trying to scare you," Rose said.
"It's working," Hansa grumbled. He scrubbed at his tingling lips with the back of his hand.
You're the one who called me here, pretty little soldier, Umber replied, his voice an invasive ripple in Hansa's mind. He stepped forward again, placing one hand on the bars to each side of Hansa's head. Tell me to go, and I will leave you alone. Insist on this boon, on the other hand, and you will not be rid of me for years, until the bond fades. Harm to you will mean harm to me, and since your status in the guard makes you less than popular with Abyssi and mancers, you can be assured that I will be nearby. All the time.
"You aren't asking for a third boon, Hansa," Rose said. "Just a second. And as far as I can tell, you don't have much of a choice, so whatever he is telling you . . . it can't mean much."
She was right, but having decided that this was the only way to save his own life did not mean he was willing to inflict this creature on his friends and family. He asked Rose, "If I do this, how do I keep him away from me after?"
Rose answered carefully. "When you speak your demands for the second boon, you can and should be very specific."
Hansa drew a deep breath.
"Okay."
His voice cracked. He cleared his throat, trying to get his pounding heart out of it, and started again.
"Okay. This is what I want:
"First, I want to be cleared of all charges. Make a new, reliable witness, do whatever you have to do—don't hurt anyone," he added quickly, "but I want to walk out of here with a personal apology from Winsor Indathrone and an agreement that I can return to my job if I want, but that when I choose to leave it I will receive a continuing salary, for life, in order to make up for the false charges."
"That's easy enough," Umber sighed. "What else?"
Easy. Any release from this cell would have been sufficient; Hansa had aimed high because he had expected to be told it was impossible, and he wanted to know the limits of the creature's power. Now he realized he had no idea what an Abyss-spawn might be capable of. He asked, "Can you bring Jenkins back? My friend, who was killed by the Abyssi. Can you—"
Umber started shaking his head before Hansa finished. "I know how Abyssi kill. There probably wasn't enough left of that body for even a necromancer to revive, and that's before the Quin burned the remains."
He had to swallow twice to rid his throat of the lump that had suddenly developed there. So far, Jenkins's death seemed like an abstract thing, but he could feel the reality of that loss waiting for the moment when he was past his panic of this moment and stopped to breathe the first sigh of relief.
"Then . . . what I said before. I go free. And I want you to stay away after that. You aren't to go near Ruby, or anyone in my family. You don't talk to them, you don't make eye contact, you don't even stay in the same room with them."
This time, Umber did not just accede to the terms. "Two exceptions. You have enemies, and I have enemies that could use you to get to me. Therefore, I go where I must, to protect you, should I need to, regardless who else is there. And, should one of your kin approach me, walk into the market where I am shopping or into the hall where I am dancing, I'll avoid speaking to them but I won't get up and run away just because you wish it."
Hansa turned those words over in his mind, but they seemed reasonable. "All right." He glanced to Rose.
"Your freedom," she said.
"What?"
"A clause anyone who deals with the Others needs to know," she said simply. "You want to add the condition that he must do nothing to impinge upon your freedom, beyond what is absolutely necessary in order to ensure your reasonable safety. Otherwise, he could lock you in a room somewhere without violating the agreement or endangering himself."
Again, the thought, What am I getting myself into? flashed across Hansa's thoughts.
It isn't too late to change your mind, Umber suggested.
Yes, it was.
"Finally, you are to do nothing . . ." He tried to re-create Rose's exact wording. "Nothing that impinges upon my freedom, beyond what is absolutely necessary to ensure my reasonable safety." He glanced to Rose again, but this time she just nodded.
"You're sure of this?" Umber asked, though by now he no longer sounded as if he expected the answer to be anything but "Yes."
"I am."
"The boon must be sealed in blood."
Blood . . . of course it was blood. If this was a taste of what a mancer lived with, Hansa could understand why the Quin wanted so strongly to wipe them from the city.
"Okay," he said, nervously. "How—"
Umber lashed out with a small dagger, which Hansa hadn't even noticed sheathed at the creature's waist. Hansa recoiled, unsure at first if he had been cut. Then he noticed the beads of crimson, along a cut low on his stomach. It wasn't deep, but the blood welled immediately.
Umber hooked one hand over Hansa's belt, and then knelt, holding Hansa in place as he licked the blood away with leisurely laps of his tongue. Hansa looked desperately to Rose for guidance, but saw that she had blushed and averted her gaze.
Umber rose, and pulled Hansa close again, to whisper in his ear. "A taste for me—and a taste for you. Call to me again, demand of me anything else, and it will be more than a taste."
"I thought you couldn't hurt me," Hansa managed to choke out.
" 'Hurt' is a relative term." Umber pulled away with a grin whose joviality was disturbing in context. "I'm off to meddle with the legal system. Hansa, I'm sure your fiancée will come running up, eyes swimming with her apologies. Give her a kiss for me."
At that, he walked away, pausing only to close the cell door behind himself again with the words, "We wouldn't want anyone to be suspicious." How he had opened it in the first place was a mystery.
Hansa collapsed to the ground, cutting the back of his shoulder on the same burr he had used to slice open his thumb earlier. "Damn it," he cursed, pressing a hand to the new wound. The others, he realized only then, had both closed. The one on his thumb was gone completely, and the hand-long slice across his stomach had faded to a shiny scar.
CHAPTER 11
"Mancer?"
Xaz grumbled, and tried to turn about in her sleep.
"Wake up, Mancer."
"Five more minutes." Pulling the edge of her cloak more tightly around her, she rolled onto her stomach, burying her face in the fluffy silk and fur beneath.
Someone crawled onto her back. She was almost awake enough to protest when he nipped her on the fleshy bend between her neck and shoulder, hard enough that she yelped and jerked up—slamming Alizarin into the ceiling of the coffin. He hung on, so when she fell back to the coffin's floor, he collapsed on top of her.
"Awake now?" he asked.
"Yes, I—stop that." That last, as he started to lick the side of her neck, lapping away blood. The bite hadn't been hard, but an Abyssi's teeth were sharp like daggers, and cut through flesh easily. "Get off me."
Instead, he started to purr, the deep rumbling making Xaz's whole rib cage and spine vibrate.
"You taste uncomfortable, and a little angry," Alizarin pronounced. "But you also taste of power. A little dusty, cold like the Numini, but still power."
"Okay. I'm awake," she snapped. "What did you want?"
"I don't remember," he said.
She drew a deep breath, resisting the urge to cuss, before she asked, "Did it have to do, just maybe, with our leaving this Abyss-spawned coffin?"
"Maybe it did."
She waited patiently, but no more information was forthcoming. "Get off my back," she said, trying to sound more confident than she felt. "You're making me nervous."
"Am I?" He nuzzled at the back of her neck, and then leaned his cheek against hers. "You and I are going to have to deal with each other, Numenmancer. It would be best if we learned to get along. Or something like that."
"It would help if you would get off me," she answered, "and then promise not to bite me again."
He did roll to the side enough to let her shift onto hers, but he chuckled as he did so. "Mancer, Mancer, you forget who you're talking to. Letting a little blood occasionally shouldn't upset you."
"Well, it does." She raised a hand to where he had bitten her, now that she could. The wound was gone, though there was a warm wetness, almost like her own sweat, from his saliva. "And I have no desire to do it again."
"Pity." He wrapped his tail around her waist, holding her close. "Because I do. And you're going to have to deal with the fact that you are not dealing with one of the Numini. Hold on now."
"Hold—what?"
She clung tightly to his shoulders as she felt the world dissolve and spin. Suddenly she was upright, aboveground, standing—clinging to him—and freezing, wondering why she had wanted to come back up to the surface.
She pulled back, which made her immediately realize that she was still wearing nothing but her nightgown; she had lost her robe in her struggle with the guards, and the following flight. The cotton was thick and warm for its intended purpose, but it did not provide nearly enough protection for what seemed to be midafternoon in the city of Mars.
"Where are we?" she asked, through chattering teeth, though a moment later she recognized the salt tang in the air. "Are we at the waterfront?"
"Not far from it," Alizarin said, "but people do not go to this section much since the Abyssumancer was discovered here. They do not like to walk where demons have been called."
"I c-can't imagine," she drawled, through chattering teeth. "I need to g-get ins-side, and warm up. Need cl-clo-clothes," she added. She couldn't walk into any human establishment looking like this.
"This way," he said.
He put an arm around her waist, and despite her intellectual desire to pull away, she could feel his heat radiating through her nightgown and into her, and she was glad for it. As he had said, the Numini were cold creatures. They didn't produce warmth. Abyssi were creatures of fire.
"We can't let people see us," she protested, as he led them into an alleyway that would cut into one of the busier streets.
"It will be fine," he assured her. "No one in there has the sight, and I can hide us from anyone else."
Nevertheless, she cringed as he guided them both past a pair of men speaking in furtive tones at the alley's mouth. Xaz brushed against one of them accidentally, but he did nothing more than scratch at his arm after she passed.
Alizarin pushed open the door of one of the most popular taverns on the wharf, and she tentatively followed. If any of the sailors here did notice a scantily-clad woman walking into this kind of place, she was going to be in trouble. Or, they were going to be in trouble, since Alizarin was likely to kill them all.
No one even glanced their way.
The demon walked past the innkeeper, who didn't blink as Alizarin put a hand to the door to the back room and pulled it open. Neither did the matron tending the kitchen, as Alizarin and Xaz stepped inside, the Abyssi guiding his mancer to the fire.
"If you wait here, I can find you more suitable clothes," Alizarin said.
"Don't kill anyone?" she asked, knowing she was powerless to keep him from doing so, if he wanted.
"Then you'll have to wait a little longer. Warm up. Take food if you want it. No one will notice you. I will be back."
He turned and disappeared into the main tavern hall.
Xaz's willpower lasted perhaps a heartbeat, and that was only because she was still unconvinced that no one would notice her, especially now that Alizarin was gone. Her shivering body and empty stomach swiftly vanquished her fear of being caught, as well as any vestigial desire to obey the law, and she edged past the kitchen matron in order to serve herself a bowl full of the stew being kept warm on the back of the stove.
There was something fundamentally unnerving about being in a room with someone who was absolutely oblivious to her presence. On the other hand, it was far preferable to being in a room with Quin guards who were aware.
She snatched a piece of bread before retreating to the fire. She wondered what the matron did see. Surely she would have noticed floating food, or if the things Xaz took just disappeared.
Those thoughts didn't last long, as Xaz began to scarf down the food, burning her tongue on the thick venison stew, nearly choking on a piece of bread as she inhaled the nourishment she so desperately needed—as well as the blessed, blessed heat.
She had finished the bread, and was down to only an inch left of soup, when a pile of clothing fell with a fump to her right. "I had to seduce a barmaid out of it," Alizarin drawled.
Xaz turned, prepared to say something witty in response, but her mind went blank as for the first time she actually looked at the Abyssi she had pulled through a rift and onto this plane. She hadn't been able to see him when they had been in the coffin, and she hadn't been aware of much of anything besides how cold she was when they first got to the surface.
She knew Abyssi had fur, fangs, claws, and tails. That was an intellectual kind of knowledge. What she had not known was that they looked like this.
He stood just over six feet, and was mostly shaped like a man. His chest had muscles as well-defined as a lifelong sailor's, which could be seen despite the soft pelt of fur that covered him everywhere she could see. The fur itself was shiny, mottled blue and green, like the plumage of exotic birds. It was thick and luxurious like a short-haired cat's fur along most of his body, but shortened until it was the texture of moleskin on his palms. She had actually stood and reached out a hand, drawn to touch it and learn if it was really as soft as it looked, before she realized what she was doing.
His face looked almost like a man's, though it was androgynous, slender, with high cheekbones and full lips. His almond-shaped eyes were surrounded by lashes that were actually white, making the iridescent orbs stand out that much more. Atop his head, the fur changed to hair, which was inky black with highlights the same colors as his fur; it tumbled to his shoulders in a waved mass.
His tail twitched, wrapping his body, drawing her attention downward, at which point she found herself grateful that he, too, had found at least some clothes. He was wearing oiled black suede breeches, of the style that was common among men who worked down on the docks, though he had slit the back a bit in order to accommodate his lashing tail. He had not chosen to add shoes to the outfit; his feet were also covered in only short, fine fur, and he stood balanced on the balls, catlike, apparently comfortable that way.
"Like what you see?" he asked.
It wasn't until then that she realized she had been standing, staring, one hand half lifted. She shook herself and took a step back, trying to resist the continued instinct to touch him, to lean against him and rub herself along that so-soft looking fur.
No, she chastised herself. This attraction was a lie crafted by Abyssal power. She didn't have to give in to it. Instead she turned away, picking up the clothing he had brought.
"You weren't joking about seducing a barmaid, were you?" she asked, looking at the clothes. They were not badly made, but they were rough, and Xaz was certain the bodice had been designed for a woman with more curves than she had, and more of a desire to show them off. On the other hand, they were clean, and included an outdoor underskirt, and a heavy gray woolen cloak with a border of black fur. Last in the bundle were a pair of soft leather boots, also lined in fur. "Thank you," she added. The dress was more risqué than she normally chose, but overall the clothing was practical, and fit better than she would have imagined. He must have made an effort to find someone the right size.
He seemed unconcerned about her gratitude. It was also quickly evident that he did not intend to look away to give her privacy to dress. She suspected that asking him to do so would only invite one of his dismissive remarks, so she turned her back on him instead and tried to pretend he wasn't present. After she dressed, she looked back to see that he had wandered over to the counter of food, and was looking at it skeptically. He picked up a cheese pastry, sniffed it, and then threw it at the cook. He hit her on the top of her head, making her start, and wave at the air beside her head as if to discourage an annoying fly.
Xaz couldn't help snickering, which made Alizarin smile. "There may be hope for you yet, Mancer." He brushed flaky bits of pastry from the tips of his fingers. "So. What now? Do you run and hide? Smite those who have wronged you? Clear your name? Or just stretch your metaphysical legs, and see what you can do with them? Because, in case you are not aware, you currently have access to more power than you have ever had in your life. There's no knowing yet exactly what you're capable of—a Numenmancer tied to the Abyss. But I, at least, look forward to finding out."
Having for the moment nowhere else to go, Xaz sat in front of the fire, enjoying its warmth but not her own thoughts. Alizarin lounged next to her, his body bending in a way that suggested bones and joints not quite identical to a human's.
"I don't know," Xaz admitted. "I'm being hunted. I cannot return to my own home." For the moment, the demon was keeping her from being noticed, but his kind was not known for consistency. As soon as something distracted him, she would need to fend for herself. "We killed—I don't know how many guards we killed. They will not stop searching for me. I will have to find a way to change my appearance. Flee to the countryside. I—" She brushed his tail away as it wrapped around her, and tickled her nose. "Stop that."
"You're being dull," he remarked.
"I'm answering you."
"The soldiers have already found their prey," he reported. "The spawn saw to that. He fed them an Abyssumancer to appease their bloodlust."
"What?" Xaz had heard of spawn before, but had never met one, and certainly never earned one's friendship or loyalty. "Why would one of them help me?"
"Not you," the Abyssi answered, rolling onto his back and stretching like a dog who wants its belly rubbed. "The guard who led the hunt for you. The one who poisoned you. He summoned the spawn and had a second boon of him. The spawn's reply did not clear your name completely, but many believe the words against you and the Numenmancer's tools found in your home were an Abyssumancer's trick, to lure the guards close and make sure they prepared to face the wrong power."
"They believe that?" she asked, incredulous. How would an Abyssumancer have acquired such belongings as they would have found in her home?
"It is easier to believe in an Abyssumancer's plot," Alizarin replied, his grin revealing sharp teeth, "than to believe a Numenmancer breached the Abyss, and a loyal guard meddled with blood-magic. That would be unthinkable."
He sprang to his feet in a fluid movement that seemed to reveal shadow and flame beneath his otherwise beautiful, almost disarming, form. Xaz flinched back instinctively, and in the next moment he was gone. As she pushed herself up and looked around, it seemed that the cook turned at the sound; Xaz hurriedly sought the door, and as she pushed through it, she heard the cook call, "Hello?"
Likewise, back in the main room, she was once again visible. One man swatted her on the backside and called for a meal, mistaking her for a woman working in the tavern, but she kept moving until she was back outside.
Where did you go, you foul little blue beast? she wondered.
No matter what assurances he had given her, she knew she needed to get away from the docks. She was too well-known there, and if Cinnabar was the one who had reported her, then the gossip that she was a mancer had surely made it through the entire Order of A'hknet by now.
Her heart nearly stopped when she saw Cinnabar and Cadmia Paynes walking together; she ducked back into the shadows of an alley as they passed, and only remembered to breathe once they were well away. She kept her head down as if against the cold-blowing wind, and tried not to give anyone reason to look twice at her as she cut through the outskirts of the city. There was no firm plan in her mind except to flee those who would gladly turn her over to the soldiers again.
CHAPTER 12
It had been too long, Cadmia realized as she walked through the market with Cinnabar.
Unlike the central market, the one by the docks was loud, crowded, and rank. The brine of the ocean mingled with the smells of fresh and rotting fish, and the inescapable odor of sailors who had been too long without a proper bath.
A sealing ship was loading casks of salt in preparation for its journey north. The captain of a Tamari vessel heavy with rice, coffee, and assorted luxury goods was arguing loudly with a customs officer, while the mate of a Silmari vessel was soliciting crewmen for its next trip out.
The noise, smell, and general commotion was overwhelming now, though Cadmia knew that there had been a time in her life when this had been commonplace. Certainly Cinnabar had no problem with it.
They stopped at Mother's cart-based shop. Though she carried some useful items like herbal remedies—the ones for hangover were always the best sellers there—most of Mother's trade was in trinkets and gifts suitable for a sailor returning home to a sweetheart he hoped to find waiting.
She smiled warmly when she saw Cadmia.
"If it isn't Scarlet's girl," Mother greeted her. "It's been too long. Is life in the violet order not treating you well?"
"It treats me fine," Cadmia answered. "I had an impulse to come down here. I have missed you. I'm sorry I haven't visited more often."
"They say an impulse you can't explain is caused by the Others whispering in your ears," Mother remarked.
"Hm." There was no good way to reply to that. Cadmia's education with the Order of the Napthol had covered concepts like that, but she was not supposed to discuss them with anyone outside the order. "How has business been?" she asked instead, deliberately changing the subject.
"Better when the Quin aren't down here stealing from me," Mother griped. "Those boys think they own the city."
Not any more, they don't. The thought struck Cadmia like a kick in the guts, but again, her knowledge of the attack, the arrest, and Hansa's protestations of innocence weren't things she could talk about.
She was searching mentally for another subject when Mother nodded to someone in the crowd, and said to Cinnabar, "Looks like someone's looking for you."
Cadmia and Cinnabar both looked up and caught sight of the man Mother had noticed. Handsome, well-groomed, and immaculately attired, the dark-haired gentleman stood out in the crowd of sailors and mongers. He was working his way deliberately through the crowd, his eyes on Cinnabar.
"Do you know him?" Cadmia asked, under her breath.
"Never seen him in my life," Cinnabar murmured. But he didn't look down. Instead, he boldly met the other man's gaze, and smiled.
Cadmia took a step back, uncomfortably recalling why she generally didn't come here, even for a brief visit. Even though it was barely a twenty-minute walk between the docks and the city proper, location of both the Quinacridone Compound and the Cobalt Hall, this place fostered a disregard for the laws of the land. Too many foreign sailors, unfamiliar with or flat-out disdainful of Kavet customs, turned the port into a morally gray place.
For example, Cadmia had no doubt that Cinnabar had already balanced his desire to be friendly with Cadmia and the risk of getting arrested against the likelihood that this stranger had as much coin in his pockets as his attire suggested. He hadn't exactly put his back to Cadmia, but he had shifted position so they didn't appear to be together.
"Are you Cinnabar of A'hknet?" the man asked, once he was close enough not to need to shout over the crowd.
"That's me," Cinnabar answered. "What can I do for you?"
"So very many things," the man said, bright blue eyes raking down Cinnabar's body before returning to his face. "But right now, it's more about what I intend to do for you."
"I'm flexible."
"I've heard that." Time to leave, Cadmia thought, knowing her face was bright red at the verbal byplay. When she started to try to slide unobtrusively back into the crowd, however, the man unerringly caught her gaze and said, "You may wish to stay, Cadmia. Our conversation might interest a Sister of the Napthol."
Cinnabar tensed, obviously reevaluating his impression of this man, and his assumptions about what he wanted.
Mother broke in, asking, "Are you here to buy something, or to be a pest?"
The man quirked a brow, then reached into his pocket, and dropped a pair of silver coins on top of the shelf she had set up across the wagon handles. "The red silk shawl there."
Mother looked at the coins, then the shawl. She took the former while wrapping the latter in white paper, then handed the merchandise over without bickering about the price, which meant that her customer had just offered so much money that she didn't want to risk having him realize his mistake.
"A gift for a special lady?" Cinnabar asked.
"An engagement present for a friend's fiancée."
"Men who buy red silk for their friends' future brides usually aren't terribly interested in preserving the friendship," Cinnabar observed.
"That all depends on how you define friendship," the man said. "You and I, for example, could probably have a lovely one, assuming you don't rot in a Quinacridone jail, or have your guts torn out by an Abyssi."
"Excuse me?" All Cinnabar's practiced flirting disappeared in the face of the stranger's blunt words.
"Your testimony against Dioxazine led to the deaths of nearly a dozen Quin guards. They think you misled them deliberately, sent them into a trap against an Abyssumancer. The mancers, of course, just think you report to the Quin."
"Who are you?" Cadmia demanded.
"Someone who's willing to help out your friend . . . and yourself."
"They captured the mancer," Cadmia asserted, a little less certainly than she would have liked.
"They captured an innocent man and you know it. The Quin know it now, too, which puts the two of you in an awkward position. They wouldn't dare cause trouble for a Sister of the Napthol, but they wouldn't think much about using a monger as a scapegoat."
Cinnabar had gone pale, but that wasn't where Cadmia's gaze was locked. Instead, she was looking at blue eyes. Electric blue.
"I thought you deserved a warning," the man said to Cinnabar, who nodded without a word. "I also happen to know of a Silmari trading vessel shipping out soon that's still looking for an extra hand or two."
"Why are you helping me?" Cinnabar asked, pulling himself together. "I don't even know you."
"I would hate to see a man punished for daring to do what he thought was the right thing," the blue-eyed man answered.
Or he's trying to remove a witness, Cadmia thought. Instinct, or paranoia? She remembered what Hansa had said about the creature who had helped him. All he saw was blue eyes. They seemed to glow. This man's eyes weren't exactly glowing, but they were brighter than she had ever seen.
"Can you tell me what exactly has happened?" she asked, trying to keep her tone calm and nonjudgmental. "I think I've missed something."
"Well . . ." The man paused, as if he needed to think about it. "Hansa Viridian has been released, but I suppose that's no surprise to you, as the Sister who interviewed him." Did he see her shock and ignore it? Or was he so certain of the truth of his statement that he was oblivious to her response? "The Quin discovered the real Abyssumancer, and in interrogation he admitted to planting a Numenmancer's tools on Dioxazine so the guards would walk into his trap unprepared."
"What about Viridian's wounds?" She wasn't thinking about Cinnabar any more. She was thinking about what she had seen, and heard . . . and said. Could she have spoken against an innocent man?
"What wounds?" the blue-eyed man responded, innocently. "The only person who claims to have seen them was Hansa's hysterical fiancée."
It was at that moment that Cadmia became stone-sure that there was more going on than this man was reporting.
Cinnabar, like any good child of A'hknet, shook his head and said, "Doesn't matter to me if he is or isn't guilty. What's the name of that ship?"
"The Tally-ho. I've already spoken to the captain on your behalf, but the sooner you report, the more he'll probably like you."
"I . . . thank you."
The blue-eyed man smiled once again, and said, "Maybe I'll look you up onboard later."
"Any time." Cinnabar's smile was a ghost of its usual stuff. "Caddy . . . I'll see you around." He kissed her cheek, barely a peck, said goodbye to Mother, and then hurried off as if Abyssi were chasing his heels.
Maybe they were.
The stranger started away from Mother's cart, and Cadmia followed.
Softly, she said, "I saw the tools they took from Dioxazine. No one but a Numenmancer would have had them. An Abyssumancer wouldn't even have been able to acquire them."
"Sister, you may be allowed to discuss the Others with impunity, but as a simple citizen of Kavet I do believe it would be illegal for me to speculate on the subject."
But his eyes were dancing with amusement.
She bit her tongue, because he was right . . . damn it . . . even if she was certain he was playing with her.
She was still trying to form another question for him when she saw Novice Sienna waving at her through the crowd, trying to get her attention. When she ran forward, Cadmia thought she would mention Hansa's release, but that wasn't the subject on her mind.
"Cadmia, do you have Pearl with you?" Sienna asked, breathless.
"Pearl? Why would she be with me?" Cadmia responded.
"I have no idea why, but I was hoping anyway. She's been missing for . . . I'm not sure for how long, actually, but no one remembers seeing her for hours, probably since she last went outside."
"Would she have run away?" the stranger asked.
Cadmia wanted to snap at him to stay out of this, but Sienna answered, wringing her hands. "She's always been happy at the Hall. And she never goes anywhere without permission. I think she's afraid if she wanders off, no one will be there when she comes back."
"That girl should not be alone in this city." In contrast to his cavalier or frankly manipulating tone earlier, the man now seemed genuinely concerned. To Sienna, he said, "You should go back to the Hall."
"No, we should alert the guards," Cadmia argued, trying to think of the best way to respond . . . only to realize that Sienna had already turned away, and was ignoring her as she followed the stranger's "suggestion."
"You don't want sighted guards looking for her," he said.
"You're not implying . . . Pearl is the sweetest little girl I've ever met!" Cadmia hissed. "Every guard in the One-Twenty-Six already knows and adores her. She likes to bring them cookies and cider and talk to them while they're on duty. And how would you know anything, unless—"
As her mind caught up to her mouth, Cadmia realized her suspicions had not only crystallized into certainty, but that the stranger knew it. Cadmia took a step back, eyes searching for the nearest guard as she drew breath to call out.
"I have no intention of harming you," the man said, his tone still casual, as if he were discussing the weather, "and in fact, I may be able to help you find Pearl, but if you raise your voice at this moment I can kill you, without anyone in this plaza noticing, much less raising a hand to help you."
"Do you know where she is?" Cadmia asked, in a soft, trembling voice.
"I may be able to make some inquiries," he responded, "if you agree not to cause trouble for Mars's newest Quin hero."
"You monster," Cadmia hissed. "You would really hold the safety of a nine-year-old child hostage, just for my silence?"
"Your voice is getting loud," he warned, prompting her to snap her mouth shut again. "And yes, I would. I don't do favors, but I will make deals. You stay out of our way, and I will do my best to return Pearl to you, or, if she is already safe and wishes to stay where she is, to let you know as much."
For all she knew, he was the one who had taken Pearl—just as she was now quite sure that he had healed Hansa, and probably manipulated events to secure that guard's freedom.
The Others cannot lie, she thought, and if he is spawn, like Hansa believed, they also cannot back out of an agreement once they have given their word. If she was right about what he was, then he would need to help Pearl, as long as she kept her mouth shut about Hansa.
She had felt Hansa's innocence when she went to him. If this creature had healed him for its own reasons, then every word Hansa had spoken in his own defense had probably been true. He wasn't a mancer; he had been caught in a trap involving magic and creatures beyond his training or understanding. In that case, did she even want to cause more trouble for him?
Or was she just justifying her own actions, when she said, "If you will do everything in your power to ensure Pearl's safe return to the Cobalt Hall, then I will refrain from mentioning my . . . concerns . . . to anyone."
"If I discover Pearl had a good reason to leave the Hall of her own free will, I will not force her to return. But I will see to her safety."
Cadmia nodded. "Do I say thank you?" she asked.
"We shake hands," he said, "and then you don't see me again until I intend for you to."
They did, and then he was gone in the crowd, as if he had never been there.
CHAPTER 13
After a meeting with Winsor Indathrone, in which Hansa was informed that he had acted valiantly when he had confronted the demon and slain the responsible Abyssumancer, Hansa returned to his apartment with the intention of curling up in bed and not thinking about the fact that he had obviously done no such thing.
In the morning, he would visit Ruby and beg her forgiveness.
How would he approach her? Should he apologize outright? Should he wait for her to apologize?
Would he ever be able to tell her what really happened?
Self-consciously, he touched fingertips to the front of his new shirt—compliments of the Quinacridone—over his new scar.
Insist on this boon, on the other hand, and you will not be rid of me. . .
He shuddered as he pushed open the front door of his apartment. Exhausted and heartsick, he pulled off his winter outerwear and kicked off his boots. He would have liked a hot bath, to help take away the chill of the Quin dungeons, but didn't have the energy required to haul and heat water.
He was halfway across the living room when the assault came. All he could do was brace himself. The door slammed as he fell back against it, his wits slow to catch up to the fact that the slender shape that had launched itself at him was Ruby.
"I was waiting for you . . . I had to talk to you . . . I'm sorry," she whispered, her arms still wrapped around his neck, and her soft body leaning against his tense one. "I'm so sorry. I don't know how I believed that horrible story. I'm sorry!"
I saw the blood with my own eyes, she had said. Had Umber come up with an alternate explanation for how Hansa had been injured one minute and healed the next, or had he erased the memory of the brutal wounds from Ruby's mind? "Ruby, there's something I have to tell you—"
"Not tonight," she said. She raised onto her toes and kissed him with trembling lips. "I can't talk tonight. I need you to just hold me and tell me you're okay and that you forgive me."
"Of course I forgive you." How could he not? He was the one who should have been begging her to forgive him.
"Jenkins is dead, Hansa," Ruby whispered. "Did they tell you that?"
"I saw it. I'm so sorry. It was too fast. There was nothing I could do."
She let out a whimpering cry and buried her face in his shoulder. Her body trembled against his, soft and rounded but alarmingly chilled.
I do believe my little sister has a crush on you, Hansa. Be nice. Jenkins's teasing warning from years before, when Hansa had been eighteen and Ruby fifteen, floated through Hansa's mind. Four years later, it had changed to, You might as well give in. Ruby gets what she wants. Finally, when Hansa had told him about buying the ring, Jenkins's only response had been, It's about time. Be good to her.
Jenkins wouldn't be beside Hansa at the wedding. He wouldn't be there to tease Hansa about his anxiety or to congratulate him on finally finding the nerve to tie the knot.
There was nothing I could do! Hansa told himself.
You saved yourself by letting a monster meddle with my sister's mind. Twice.
The words weren't from Jenkins's ghost—normal people couldn't see or hear the dead that way—but they might as well have been.
"Ruby—"
In response to his saying her name, Ruby lifted her face and pressed her lips to his again. He could taste the salt of her tears.
Give her a kiss for me.
The memory of Umber's combination of threats and promises, combined with his imagination's rendering of Jenkins's horror, made him stiffen and instinctively recoil.
"I'm sorry," Ruby whispered. "I said such horrible things to you, and now here I am throwing myself at you like all should instantly be forgiven." She stood up, backing away. "I'm sorry. I'll . . . I'll go."
She turned to flee, and he caught her arm. "Don't. It isn't like that. I just . . ." She turned back to him, tears in her beautiful eyes. "I have too many awful things in my head right now."
She nodded, biting her lower lip. "Of course. And you must be exhausted. I am, too. We should both get some rest. Do you need anything before I go?"
I need you, he could have said. Should have said, for her benefit. "You shouldn't be alone," he managed.
"Olive said she would stay over tonight." It took Hansa a moment to place the name. Ruby had friends at the herbarium, but Hansa hadn't met many of them. "She's making a tisane to make sure I sleep. I'll see you tomorrow?"
"Breakfast?" he suggested. Somewhere with air and sunlight, and no blood or screaming or iron doors. That's all I ask.
Ruby nodded again. "I think the Green Jewel still serves breakfast?" she suggested. "I doubt either of us wants to cook."
He forced a smile, and saw her relax a little. "I'll see you tomorrow."
He wanted to add something sweet, or suave, or romantic, but nothing came. They said awkward goodbyes, and then Hansa was alone. He climbed into bed, but it was a long time before he fell asleep.
When he did, he tumbled into dreams of the Abyss.
The world was full of black fire. He was trying to walk between the flames, but every time he brushed against one, they seared, and drew blood, until it ran down his skin from dozens of lacerations. Still he stumbled onward, trying to flee.
He had to get out. He couldn't stay here. This wasn't his world.
"Let me help you," a voice said, as someone took his hand and pulled him through the flames, onto an endless plain, surrounded by needle-like mountains on all sides.
He turned to thank his savior, and found himself facing a creature out of nightmare, darkness made solid. Pain shot up his arm from the hand it still gripped as if with a vise of needles. He tried to scream, but the breath he drew was full of smoke, so he choked instead.
He woke coughing, shaking and sweating as if in the grip of the worst winter flu. His entire arm ached, the pain radiating upward from his tightly-clenched fist.
He had to fight to relax, to tell his body it was just a dream. Nightmares were understandable, after what he had been through.
It was just a dream, wasn't it?
He looked at his hand, remembering how the Abyssumancer's blade had felt when it had cut him. Could it have done something to him? Would it be stupider to ask someone, or to risk someone with the sight noticing something off about him that he hadn't reported?
This was the kind of quandary he would have gone to Jenkins about.
The thought hit him hard, taking his legs out from under him.
He couldn't stand to speak to other guards yet, and after his disastrous interview with Cadmia Paynes he didn't dare seek guidance from the Napthol.
He cleaned up, dressed, and then walked to the Green Jewel Inn as if in a trance.
His already dark mood was not helped when his gaze swept over the crowd in the breakfast room and he beheld a familiar figure at another table, one long leg hooked over the bottom rung of his stool as he nursed a drink and chatted with the young woman sitting next to him.
Hansa stood, prepared to challenge the half-breed before Ruby arrived, and immediately heard Umber's voice quite clearly in his mind:
Sit down. We'll talk about this in a minute.
Hansa took a step forward, with the thought, Oh, no, we'll talk about this right now.
Umber chuckled at something the woman next to him said, but his silent voice was cold. This pretty girl next to me happens to be a Numenmancer. She is confident that she is well-hidden, but if the hero of Kavet approaches us right now, she is going to panic, and you and your beloved are all going to be in the middle of her undoubtedly violent response. So sit. Back. Down.
Hansa sat, resisting the instinct to take a second look at the woman Umber had identified as a mancer. He had seen enough to know it wasn't Dioxazine, and he didn't want to put all innocent bystanders at risk by trying to see more.
He jumped as a hand touched his shoulder.
"Sorry," Ruby said. As he stood to greet her properly, her eyes widened. "Oh, darling, you look exhausted. Did you sleep at all?"
His shoulder blades itched as he tried to ignore the mancer and spawn on the other side of the room. "A little. Not well. How are you?"
"I . . . don't know," she admitted. "I feel numb. I tell myself Jenkins is dead and I just feel blank. I can't make myself believe it. I know it will hit me eventually, but until then I'm just going through the motions."
"I know how you feel." At least you didn't wear his blood and then get arrested for his murder. Hansa shoved the nasty thought away, and dropped his gaze to the menu so she wouldn't see it in his eyes. He was too tense, too tired, too overwhelmed, but he didn't want to take it out on her. He struggled to think of something he could stand to say to her. It's my fault for not realizing what Dioxazine was years ago, and for somehow tipping her off at the door so she had time to summon that creature. I'm a coward for running. I've never felt so helpless in my life. And now I'm only sitting here because I broke the laws I swore I would fight and die if necessary to uphold.
The silence had stretched too long while he considered and discarded ideas. She asked, "Will you have to visit his parents?"
She asked as if Jenkins's parents weren't hers, too. Hansa almost said, That's the captain's job, then remembered Captain Feldgrau was dead, too. "Someone from the Napthol will," he said. "They wouldn't want to see me." Ruby hadn't spoken to her parents in years, but Jenkins had kept in touch a little.
He was about to say that they should probably visit his parents—Jenkins had been like a second son to them, and they deserved to hear what had happened from Hansa instead of a messenger from the 126 or the Napthol—but a chuckle from the mancer behind him made the hairs down the back of his neck lift. With relief he realized she was standing up and saying farewell to Umber. She strolled out of the Green Jewel without a single glance at Hansa, and some of the tightness left his chest.
We should talk now, Umber suggested, at the same time that Ruby sighed and said, "Do you want to talk about . . . it? About . . . how it happened, I mean?"
Her wide expression and trembling lip said she didn't want to, but was trying to give him what he needed. Wasn't that supposed to be his job—to take care of her?
He couldn't speak aloud to Umber, but knew the spawn had previously read his thoughts, so he tried responding by clearly thinking, Later. For now, you aren't supposed to be here.
I was here first, Umber replied. I'll meet you out back.
Umber stood, and smiled at the waitress as he paid his tab. Judging by the woman's expression, the tip he left was generous.
"Hansa?" Ruby prompted.
"I'm sorry, I . . . I don't even know how to—" Now, Quin! "—put what happened in words. I don't think I want to," he admitted.
"Well then," Ruby said in a voice full of forced lightness and cheer. "You don't have to. But you do have to take care of yourself. I'm going to make sure you eat, then put you back to bed."
If you make me come over there, you're going to have to introduce me, Umber threatened.
"I'm sorry," Hansa said, "I need to deal with something. I'll be right back." Umber wasn't supposed to be able to come near Ruby, but Hansa didn't have much faith in the rules he had set out when demanding the second boon.
Ruby frowned, but said, "Okay. I'll order for you?"
"It won't take long," he assured her. He tried to kiss her goodbye, but she nodded and turned her face away with the excuse of looking at a menu Hansa knew she had to have memorized by now.
Trying to hide his sudden desire to strangle someone, Hansa made his way to the back door of the inn. Outside, leaning against the wall, stood Umber. Despite the frigid autumn air, he didn't even have the decency to wear a proper cloak or gloves or otherwise make any attempt to appear normal.
"What do you want?" Hansa demanded. "In case you hadn't noticed, my almost-fiancée is waiting for me."
"Oh, you're engaged again, are you?" Umber asked, without the least bit of interest in his voice. "I'm sure that's very important to you, but I couldn't care less. I need you to do something for me."
Hansa couldn't help a snicker. "No."
He turned to go back inside, and Umber stepped in the way. "I've made you into a hero, Hansa. The least you can do is play the part."
"Not for you," Hansa pointed out. "We made our deal. As far as I understand, that means it's over. I don't have to—"
"Fine," Umber said. "You made your demon-deal. You won the woman, and became everyone's favorite man. You are under no obligation to live up to your legend."
"Damn right."
"After all, the city was perfectly willing to lock you up and throw away the key before you were guilty."
"Do you have a point?" Hansa grumbled. "Or are you going to get out of the way?"
"My point is," Umber said, "maybe the girl won't blame you, when she faces the next century in slavery. But I certainly will."
Hansa sighed heavily. "What girl?"
"Oh, now you're listening?" Umber asked, quirking one eyebrow.
"Not for long, unless you get around to telling me before I decide I would rather be inside, with my fiancée and a nice breakfast, than outside, freezing, with a half-demon pervert."
Umber looked skyward for a moment, before saying, "I'll ignore the end of that sentence, and the many responses it deserves, because I don't want to see Pearl hurt."
Hansa's attention suddenly focused, all awareness of the cold fading away. "What's wrong with Pearl?"
"She ran off," Umber explained. "She has been perfectly safe inside the Cobalt Hall, but now she has ended up among very unsavory people. I need you to take her back. And to be clear, this is in no way related to our boon," Umber added. "I am asking you because you possess the traits necessary, no other reason. If you do what I say, you should be perfectly safe, but in the case that there are any repercussions, I will deal with them, as part of this simple arrangement."
"The fact that you feel the need to say that makes me nervous," Hansa said. But it was Pearl. "What do you need me to do?"
CHAPTER 14
Xaz had spent the night curled up in the back of an unheated shed. She couldn't freeze to death, but her body alternated between shivering and actually sweating, the result of the Abyssal power still in her body. The Abyssi—Alizarin, he called himself—came and went, a less-than-soothing warmth when he was present.
She had decided that the Abyssumancer had targeted her intentionally. She had seen the expression on his face. He hadn't been trying to get rid of evidence, and he certainly hadn't thrown that blade randomly. He had been ordered to attack her and then give himself up.
Why?
Why would an Abyssumancer—or more likely, an Abyssi—intentionally infect a Numenmancer with Abyssal power? The Others gained power through their mancers. They wouldn't casually sacrifice one.
On the other hand, if he hadn't infected her, then she wouldn't have had a bond to the Abyss. She wouldn't have been able to pull Alizarin into the human plane. Had that been the goal all along? If so, then he might have arranged for the attempted arrest, as well. Without it, she never would have been desperate enough to summon anything. She hadn't thought Abyssi were able to plan that well, but all she knew of the Abyssal realm came from the Numini, who disdained the Abyssi as mindless animals and therefore might underestimate them.
She had to go back to the temple. That was the only place she could get the information or assistance she needed.
The temple wasn't part of the Numen or Abyss, but it didn't exist fully on the mortal plane either. Well-rested, with proper tools and a prepared ritual space, she would have opened a rift to it on her own, but that wasn't an option at the moment. Thankfully, there were other ways. She wasn't sure if the doorways were intentionally created by the Others, or sprang up with no more deliberation than flowers after rain, but they were the only way sick or otherwise weakened mancers could get to the temple. The doorways themselves were regularly found and destroyed by Quin guards, but the temple remained safely out of reach. Even sighted guards would be destroyed by a passage through rift.
"Do you know where the nearest temple rift is?" she asked Alizarin. If she needed to scry to find it, she would need to gather tools. She didn't need anything elaborate, but given her current circumstance, she preferred to avoid any extra risks.
"Of course," he answered. "But why would you want to go there?"
"I still—" His tail wrapped around her, and she batted it away. "I still need supplies, and since you—" This time his tail chucked under her chin. "Stop that. Since you aren't Numini, I can't get them through you."
"Why do you need them?" he asked, propping himself up on one elbow to look up at her, so he was effectively spooning around her back.
"For one, so I don't get in trouble with any more of your kind," she pointed out.
Alizarin hmphed, his tail twitching again. He hooked it around her waist, and she decided maybe it was best to just leave it there. "I can protect you from other Abyssi."
"Until you see something shiny, and run off," she said. "Your kind isn't known for long attention spans or impulse control. I also need to be able to hide us from any of the Quin guards who have the sight. That requires tools."
"Not for an Abyssumancer."
"Which would be helpful, if I were—stop it!" This last as he started tickling her nose. "You're the one who asked me why! Stop distracting me so I can tell you."
"You weren't saying anything interesting," Alizarin complained. "You should pet me."
"I—what? No. Alizarin, can you focus for just a moment? We need—"
"You want to," he interrupted, utterly unmoved by her pleas.
"No, I don't. I want to find the temple, get supplies, and then—"
"Pet the Abyssi."
"You're not a cat," she bit out. "I do not. Want. To pet. The Abyssi. I want to find the temple."
"You don't know what you want," Alizarin said. "Too much time among the Numini. You want to pet me."
She patted him twice on the head. "There. Okay?" His hair was incredibly soft, and seemed to reach toward her hand.
He sighed, and for a moment thought he had grown bored of the game and was ready to give up, but instead he moved in front of her. She yelped as he put a hand on her shoulder and leaned forward, overbalancing her so she toppled onto her back, and put a hand up to push him away.
He leaned down, and nuzzled at her chin, then rubbed his cheek against hers, just like an overgrown cat. Only, he wasn't a cat. He was a demon. A demon who, aside from the fur and the tail, was shaped like a man. The combination was unnerving in this position, no matter how pretty his fur was.
"Get off me," she said.
"Pet the Abyssi," he insisted.
"Get off me, and then I'll pet the Abyssi," she offered, as a compromise.
He paused to consider for a moment, and then rolled off her, propping his head on his hands as he stretched out on his back. If he had been a cat, the image would have been amusing, innocent, even adorable. Though his words had been every bit as childlike and naïve as a kitten, given his form, the posture was sensual, beautiful, and threatening.
She sat up, now regretting the deal she had just proposed, and he wrapped his tail around her waist and tugged her forward so she fell onto his chest.
"This is absurd," she mumbled. She lay against Alizarin's side—she didn't have much choice about that, what with his tail locked tightly around her waist—and tentatively put a hand on his shoulder, then ran her palm down his upper arm. The fur there was less than an inch long, and heartbreakingly soft. Looking closely, she could see that each individual hair was variegated, ranging from black to cobalt to emerald to aquamarine, iridescent.
Maybe a minute had passed before she realized she had snuggled against the Abyssi, and with her cheek resting on his shoulder, she was petting his chest in slow, loverlike motions. There was something hypnotic about the shine and the impossible softness of that blue-green pelt, and so even after she noticed what she was doing, at first she didn't really care.
Alizarin's tail twitched, tickling her spine at her lower back, and making her shudder. Of course he noticed the reaction, and did it again, with the same result.
"You have a ticklish spot," he said.
"Thanks for pointing it out," she grumbled. "For a moment I was in danger of feeling peaceful."
"You're happier now," he said.
She almost argued with him, and then she realized that she was feeling better . . . and she hadn't realized she was feeling badly beforehand. Her head felt clearer, and the dull ache behind her eyes was gone. It was more than just being more relaxed; touching him had settled her magic.
Power lies, she thought, remembering the warning she had been taught when she was first learning a mancer's trade. It will woo you, and it will try to comfort you, but it lies.
She wanted to snuggle up against the Abyssi and rub her whole body on that incredible fur, but she could resist that impulse, at least for the moment.
"You're right," she admitted. "I did want to pet the Abyssi. And I still do. But we need to find the temple first. We can't stay here forever."
"Why not?" he asked, with a stretch.
"Because . . ." She struggled to find reasoning that would make sense to him. Finally, she decided on, "It would be boring."
"Hm." He nodded and rolled to his feet, in a liquid motion she envied. There was strength and grace in that catlike frame—more than she could imagine, or for that matter wanted to imagine. His current form looked disarmingly beautiful, but she remembered what it had done to human flesh when she was almost arrested.
"How far away is the nearest temple doorway?" she asked.
"The nearest one, no one uses. They don't remember it's there," he said.
Xaz frowned. "Where is it?"
"In the palace," Alizarin answered.
It took her a moment to realize what he had just said. "The Quinacridone? There is a temple doorway inside the Quin central compound?"
Alizarin nodded. "Power ran in the royal line for many generations."
"Oh." She had heard rumors of sorcery in the overthrown royal house, but had assumed they were just attempts to discredit the family during the revolution.
"The next nearest doorway rift is maybe two days walking from here," Alizarin said, "but you don't need one. I can carry you there."
"Will you?" The Abyssi's reactions were so unpredictable to her that it hadn't occurred to her to ask him.
In response, he did just that, sweeping them out of the mortal realm and into the sphere of Other power that was the temple.
For her, entering the temple was usually like stepping into a swiftly-flowing river. The power tried to pull her away, and she needed to struggle to keep her feet. This time, it was like she had dived headfirst into the pounding surf that pounded Kavet during a storm. Normally, Abyssi and Abyssal power existed as shadows at the edge of her awareness, but the taint in her magic made her overwhelmingly aware of everything.
The temple, which she normally perceived as an icy cave filled with the scents of honey and lilac, now reeked of blood and smoke. The translucent, crystalline walls were stained and streaked with velvety-dark patches.
Worse were the Abyssi themselves. She could see them, not as solid forms but like glowing afterimages left from staring too long at the sun. They pulsed and writhed and they could see her, too.
"What's this?" one hissed, slithering closer to her. Its voice rang in her mind, making her head ache.
"Cold meat," another answered disdainfully. "Reeks of Numini."
"I've heard Numini are good to eat," the first said, "if you can catch one."
Xaz looked around desperately, but if Alizarin was here she couldn't find him, and the others were hanging back.
These Abyssi might just be grandstanding. The temple should be a safe place; the Others made it impossible for mancers to hurt each other there, which was the only way Numenmancers and Abyssumancers could be in the same place at the same time. But normally Abyssi couldn't see Numenmancers, or the reverse.
The few Numini she saw ducked away, ignoring her plight.
Instead, she caught the gaze of another Numenmancer, who was wrestling with a small figure who lacked the glimmer of a mancer's power.
"I thought you must be dead," the mancer said. Compared to the Others, her voice was like a whisper, barely audible. "The stir you made." The softness didn't hide the disdain and irritation in her tone. Xaz understood the emotion; every time one of them was caught, life became harder for the rest of them. "And I was left to finish your task."
Pearl. With no magic or training, the girl had to be utterly overwhelmed by the temple's power.
Bitterly, Xaz thought, The Numini didn't waste time, did they? As soon as I was injured they cast me aside and found another for their task.
She spun, world swimming, as one of the Abyssi touched her. She shouldn't have turned her back on it. She gathered her power to cast it aside, but the creature just laughed. The little Abyssal magic that flowed through her was just enough to get her in trouble, not enough to help her fight.
"Not yours."
The words were spoken in a deep, rumbling purr that made Xaz's bones vibrate. The power that accompanied them made the Abyssi who had harassed her seem like kittens in comparison—and, thank Numen, it was familiar.
"Alizarin," she breathed, turning with wary relief as the other Abyssi scattered.
In this place, the Abyssi's veneer of near-humanity was gone, leaving only a hair-raising sense of fangs and claws in the dark. Could she sense his power better than the others because she was bonded to him, or was he actually this much more fearsome?
"I told you, I can protect you from other Abyssi," Alizarin said. "My sire was the last lord of the Abyss. Nothing this close to the human plane is a threat to us."
That was both comforting and terrifying.
She shook off her unease. She had things to do.
"You won't find your Numini here," the other Numenmancer informed her. "I've heard them whispering. Your Numini is in disgrace because his mancer caused such bloodshed and violence. He—"
She broke off as one of the Numini stepped forward. Given the way it loomed protectively over the other mancer, Xaz suspected it was bound to her.
"We cannot help you," it said flatly. "You breached the boundary. You violated agreements made to us, and made agreements with the creatures of blood. You have tangled your power in the Abyssal realm, and until it is cleansed, we can make no further associations."
"I just want to send the Abyssi back!" Xaz argued. "How do I do that?"
"I doubt you have that ability," the Numini said. "Even if you did, you would probably still be unable to remove the infernal taint from your power. You must find a stronger conduit."
How was Xaz supposed to fix anything if the Numini wouldn't help her? Break into the Quin dungeons to retrieve the supplies they confiscated from her home? Kill the Abyssi bound to her with her bare hands—oh, and in a way that didn't spill any blood? Neither seemed likely.
"You could ask the guard to help you," one of the weaker Abyssi who had shied away from Alizarin suggested with a syrupy tone of mock sympathy. When Alizarin turned to him, he took a step back and murmured, "I'm just trying to help your . . . what is she to you?"
Alizarin growled. It was an elemental sound, and even the other Numenmancer seemed to hear it. She took a minute to create a bubble of protective power and tuck the unconscious Pearl inside to hold her and keep her safe, and then disappeared as she willed herself out of the temple.
"The one who calls himself Hansa. If you stay, you will see him," the other Abyssi said. "He is working up the nerve to step through the rift at the well."
Xaz's first response was relief—if the rift didn't destroy Hansa, the Others in the temple would. These Abyssi were held from harming mancers in this place, but would delight in the flesh of a poor Quin guard who stumbled into their sanctuary.
Unless . . .
She remembered the way Abyssal power had flowed around Hansa after he had arrested Baryte. He had been bloodied again when Xaz had summoned Alizarin, further tainted with infernal power. Could that have been enough for Baryte's Abyssi to make a connection to him once its previous mancer was dead?
Xaz didn't know for sure, but it seemed likely enough that Mars's newest hero had just become its newest mancer as well.
Either way, she didn't want to see him. She focused her thoughts and fled the temple.
She emerged from between two large boulders on the southern coast, a spot she knew well, though she hadn't used this rift in many years. Her parents' house was less than an hour's walk to the north, if one was desperate enough to cut through brackish marshland.
It was high tide, and salt spray stung her as it slapped against the rocky shore, soaking her skin and clothes. Further out to sea, she could see the islands occupied by the Osei; their wheeling winged shapes were visible in silhouette against the cobalt sky as they gyred in search of prey in the water. Their favorite prey this time of year was the blue sharks that schooled in the area, much to the ire of local fishermen.
Move! she ordered herself. She had been hypnotized by the play of light and shadow off the water, and the giant predators that hunted it. Some said the Osei were part Abyssi, a legacy of the royal house's meddling with infernal magic before the revolution and rise of the current democracy. Their tendency to eat people was one reason this isolated rift was rarely used, which meant she should get under cover.
There was a fire pit nearby, but it clearly hadn't been used in a long time. She cleared it out with rapidly-numbing fingers, then lethargically gathered driftwood and dried seaweed to burn. She wished she had an Abyssumancer's power to start a fire with her power, but had to settle for the flint and steel her younger self had hidden in a jelly jar under the rocks.
As she sat by the fire, she tested her power. Could she draw strength from the flame, like an Abyssumancer could? Could she cool it, the way she used to? She needed to know what she could still do so she could come up with a plan for what to do next.
CHAPTER 15
This is madness, Hansa thought as he stared at the well in front of him. Located at the back of a mostly-abandoned, rocky acre of scrub that had once been farmland, the well's wooden cover was rotten and half-collapsed. There was plenty of room to allow a crazy person to jump inside.
That was exactly what he had been told to do.
His breath made a white fog in front of his face as he stared into the blackness below. His fingertips trembled, but not from the cold.
No, he didn't feel cold at all. His heart was pounding much too fast for him to be affected by temperature.
He had told Ruby as much truth as he dared, but even though she adored Pearl as much as anyone, she hadn't understood why one of the other guards couldn't go. He couldn't tell her the assignment had come from a half-Abyssi creature instead of his captain. No matter how much Hansa wanted to cut all ties to Umber, he couldn't abandon Pearl. Not darling Pearl, who used to sit on the front steps of the Cobalt Hall for hours, and who sneaked out to deliver hot cider when he was serving that long, cold night's watch. He couldn't stand the thought of her being hurt.
He was still insane, and he knew it, to have agreed to Umber's plan.
He hadn't asked why Pearl meant so much to a half-Abyssi because he hadn't trusted him not to lie. Once Hansa got the girl, he was taking her straight back to the Cobalt Hall. He wouldn't have agreed to this plan if Umber had even implied he expected Hansa to turn Pearl over to him.
Now he was at the well.
Hansa wondered which of the many unpleasant ways he would die, if Umber was wrong, or had lied to him. Depending on how deep the well was, and whether or not it still had water, he might just break a leg, and die of infection or starvation. Or he could drown. Or freeze to death. Those options might, however, all be better than the possible ways to die if Umber was right, and telling the truth.
Trying to resist the instinct to hold his breath, Hansa stepped up onto the side of the well. He could not refrain from squeezing his eyes shut, as he took another step forward, his hands clenched into fists at his sides as he tried to keep himself from flailing out to try to stop his fall.
Instead of rock bottom, or cold water, he felt like he hit a lake full of blood. Suddenly he was enveloped in warmth. His senses screamed we'll drown! as his eyes shot open.
Someone near him purred, "Oh, look, fresh blood."
"New?" someone else whistled.
"He isn't new," yet another voice replied. "I've tasted that one before."
Hansa struggled to keep from screaming. The voices that rippled around him had a physical quality, like hot breath on the back of his neck.
Or, suddenly, silky fur against his cheek.
"I know you," the one who had just brushed against him observed. "You're the one Xaz stopped me from eating."
Hansa struggled to remember all the things Umber had told him. Umber had not anticipated this exact situation, but he had explained to Hansa why it made perfect sense that a man who had just recently been a Quin guard would now be standing in a mancer's temple.
Then it's you who did this to me, Hansa told the Abyssi who had challenged him. The Abyssi who had slaughtered nearly a dozen Quin guards.
The world around Hansa turned green, rolling, as he realized that.
Stop that, the Abyssi snapped.
And, from somewhere else, a small whimper.
Umber had told him that technically, there was no "space" in the temple, no moving, but that everything was controlled by one's own mind. Even so, Hansa thought of himself as walking toward the small sound.
What he found, huddled at the back of the temple, was . . . almost a shadow. He couldn't quite see her, or feel her, or hear her. Umber had told him that would be the case, too.
"She isn't yours," a voice like icicles said. It was hard to hear, faint like a distant puff of wind.
"She shouldn't be here."
"That isn't your concern," the creature said. "She was brought here. You have no claim to her. You cannot take from the temple that which you have no claim to."
Umber had given several suggestions for dealing with the challenges Hansa was likely to face in the temple, but one had been at the top of the list, and it was the one Hansa went with now:
Run.
"I'll take you home," he said to the little girl, as he tried to wrap his thoughts around her. "Pearl?"
"Hansa?" Her voice sounded very far away, but at last, he felt her clinging back.
The hardest part is going to be getting out of the temple, Umber had said. There is no physical door to open or pass through; you have to will yourself through it.
With a demon quite possibly on his heels, one that had already nearly killed him once, Hansa found himself strangely motivated.
DOOR!
Abruptly, he was stumbling on a dew-covered mat of fallen leaves and pine needles near the defunct well, his arms wrapped around a crying child.
A moment later, the Abyssi was in front of him, its fur glistening in the moonlight, and its tail lashing back and forth. "Quin, you and I should talk about your charade, before you go."
Hansa put his back to a tree, holding Pearl protectively as he searched for the mancer.
"Xaz is elsewhere," the Abyssi said. "As for the girl . . . I only want to talk to you. If she runs, I won't chase her."
Hansa set Pearl on her feet.
"Pearl, see the lights, way up there?" he asked, pointing the girl toward the inn that stood sentinel at the start of the path to the well. "You run toward them. Hide in the stables. There's a sweet horse there, and a kitten. Run! As fast as you can."
The girl took off, nearly flying, without needing another word. Umber would look for her in the stables if Hansa didn't make it out of this.
The Abyssi watched Pearl go for a moment, but then turned back to Hansa.
"So," the demon purred. "Let's start with, I recognize your taste. I've had your blood. The only thing I would recognize more easily is my own power, which is not the magic infecting you. A mancer wouldn't be able to tell the difference. Your story would have worked around most Abyssi. But not me. So explain yourself, before I remember I'm hungry, and decide that Xaz would probably not object to my killing a Quin guard who infiltrated the temple and stole someone from it."
Where was Umber? He had assured Hansa that he would deal with any "consequences" of his taking Pearl from the temple. This was a pretty serious consequence!
"I'm not after the temple," Hansa said. He tried to edge away, and the Abyssi leaned forward, trapping Hansa between itself and a large oak trunk. "I don't care about the temple. I'm not going to report the temple. I learned that lesson."
The Abyssi smiled, baring twin rows of sharp teeth. "Oh, did you?" it asked. "That 'lesson' ended up making you the hero of Mars. I was worried you might have become arrogant."
"I want nothing more to do with mancers, demons, or half-breeds," Hansa avowed.
"Of course, the spawn," the Abyssi said. "The power is his. That must have been exciting for you."
Umber had lent Hansa enough power to make it through the rift and impersonate a mancer. The process had been uncomfortable to the extreme, and had involved knives and blood—and why had Hansa been surprised?
Hansa flinched as the Abyssi leaned forward, its cheek brushing against his.
"It doesn't have to involve blood," it whispered. "And, with all his magic pumping through you, he won't be able to take it back without your cooperation, so if you wish you can demand an alternative ritual."
"Why do I not feel like you're trying to help me?" Hansa asked, the words a little choked because he was straining away from the demon. Even through his cloak, vest, and shirt, his back was probably going to have a perfect map of the bark of the tree behind him later.
"Do you think I want you to keep that power?" the Abyssi asked.
"Mind if I cut in?"
Hansa had never been so grateful to see Umber in his life. The crossbreed stepped forward with no hesitation at all and wedged himself between Hansa and the Abyssi, facing the demon straight on. They were nearly the same height, both a couple inches taller than Hansa, and Umber didn't flinch as he looked into the glowing blue eyes.
Instead, he said, "Oh, how lovely. Blue." Leaning back against Hansa, who was frozen like a rabbit trying to evade notice by a predator, Umber reached up and caressed the demon's cheek, and then trailed his fingers through its hair. "And so soft. Dioxazine is a lucky, lucky girl."
Was Hansa going mad—a distinct possibility—or had the Abyssi just started to purr?
The Abyssi gave ground as Umber stepped forward a bit, now running a hand up its chest. "If the mancer ever bores you—and Numenmancers can be so dull—and you're looking for some fun—" He wrapped a hand around the back of the Abyssi's neck. "You are welcome to look me up."
Umber had by that point backed the Abyssi up until it was now leaning against the edge of the well; another nudge from Umber, and it obligingly leaned backward, balanced over the door to the rift. At first Hansa thought Umber planned to push the Abyssi in, and he wondered what was going to stop it from coming back out, furious with them.
Instead, Umber kissed it.
Hansa backed away, but couldn't quite force his eyes from the two creatures, who strained toward each other, both apparently oblivious to Hansa.
Apparently oblivious . . . so what in the name of the Abyss was he still doing there?
After too long watching the two creatures twine tongues, he turned, and dashed toward where he had told Pearl to hide.
"Pearl?" he called, a strained whisper, as he stepped into the stables.
"Hansa!" The little girl appeared from behind a stack of barrels, and threw herself at the guard. "I got lost," she whimpered. "I got lost in there, and they wouldn't let me out . . ."
"Ssh. It's okay," he whispered. "But you've got to be a big girl now, Pearl. We can't stay here. Can you be a big girl, and hop up onto this horse with me, and I'll take you back to the Cobalt Hall?"
She nodded.
He lifted Pearl onto the horse Umber had lent him, which he had left saddled, anticipating he might need to make a quick escape. As he did so, he noted that there was now a second one, a roan stallion, in the stable. The beasts were rare enough in Kavet that he suspected the horse had to belong to Umber as well. Well, hopefully it would be there a long time, as the Abyssi and the Abyssi-spawn entertained each other.
Hansa's gorge tried to rise as that thought crossed his mind, and he failed to get a leg fully across the beast on the first try. At least his crazy, arm-waving attempt to get his balance without smacking Pearl, made Pearl giggle.
"Hold on," he warned her. "Off we go!"
As a member of the Quin guard, he was one of the few citizens of Mars who knew how to ride. Pearl on the other hand had obviously never been on a horse. She let out an exhilarated "Whee!" that made him laugh despite all else.
The second set of hoofbeats didn't register in Hansa's mind until Pearl let out a whimper, and Umber, on the roan stallion, drew up beside Hansa.
You can let the girl know I'm not going to hurt her.
Despite his better judgment, Hansa relayed the message. "It's okay, Pearl. This man helped me get you out of there."
Pearl nodded that she heard, but she didn't look up, and didn't seem to be enjoying the ride any more.
That was one of the most disgusting things I've ever seen, Hansa observed.
You've never seen some of the other creatures of the Abyss, Umber replied. Where exactly do you think spawn come from?
Another thought Hansa hadn't wanted to have.
The trick to kissing an Abyssi, Umber continued, apparently enjoying Hansa's discomfort about the subject, is to always let him lead. Stick your tongue past all those sharp little teeth, and you will almost inevitably lose it. Hansa squirmed; Umber chuckled. Really, what else was I supposed to do? Abyssi are pleasure-centered. They don't have "logic," just wants. They feed, they fuck, they play. The only good way to distract them from one is to offer another. Since I wasn't about to let it eat you, I had to offer better bait.
Dear Numen, would the visual images never cease? And Hansa had thought that seeing that creature rip through all his fellows had been the worst thing a man could ever see in his life. No, now he had this new, harrowing image in his mind.
And despite all that, he still felt obliged to say, Thank you. For not letting it eat me.
It would have made things complicated. Umber sighed. Unfortunately, Dioxazine pulled her pet away before we could have too much fun. Very frustrating. Though, if you have a few hours, we could take care of your gratitude. . .
If I join the Napthol Order, will I be able to hide from you? Hansa hadn't meant to send that thought as a question, but apparently it got across. Umber started laughing so hard, he actually had to slow his horse in order to avoid being unseated, allowing Hansa to pull ahead.
It was several minutes later when Umber caught up again. By that time, Pearl seemed to be half asleep in Hansa's arms.
She probably hasn't slept since she was taken, Umber remarked, regarding the girl fondly. And the temple would have been exhausting.
Why did you do this? Hansa asked, as Umber again moved alongside. What's in it for you?
The silence of the prime witness against you.
Liar, Hansa accused, thinking of all the other strings Umber had pulled. Unless the Napthol Sisterhood really is that much of a problem for your magic?
Umber snickered. The Cobalt Hall is a problem. It is vested with magic. The Sisters themselves have no special powers . . . in general. He glanced to Pearl as he said the last bit. That one is special, in a way that means the mancers will want her. I may be half-Abyssi, but I'm also half-human. More human than Abyssi, really, since I've been raised on this plane. I know you don't think highly of me, but you should at least consider the possibility that the idea of a child being enslaved and abused might upset me.
Hansa couldn't figure out how to respond.
After a while, Umber added, I saved your life. I won you back your fiancée. I didn't let the Abyssi have you. You might want, at some point, to consider acknowledging that I am not, in fact, evil.
You also pretty much assaulted me while I was in that jail cell.
Umber shrugged. I wanted to make sure you fully considered your actions.
So, you're saying those threats were . . . idle? Hansa asked, hopefully.
Umber chuckled. Oh, darling, idle threats are useless. I never make them. You're a beautiful man. I meant every word I said about that matter.
And that's where you lose me, Hansa said.
Oh, so saving your life—
You said yourself, you only did that to avoid my possibly becoming a mancer.
—and your reputation—
Because I forced you to.
—and saving Pearl's life . . . what, no witty comeback to that one? All of that doesn't balance out more heavily than the fact that I happen to find you lovely?
You apparently find a lot of things lovely.
Again, that damned image of Umber and the Abyssi together.
Umber shook his head. "Spoken like a Quin," he said, softly. It wasn't a jest, or a warning, or even an insult. Just a disappointed statement of fact. "We should drop the horses off at the edge of town and try to get to the Cobalt Hall before dawn. We need to pull that extra magic out of you before you get spotted by someone with the sight."
CHAPTER 16
She lay on her stomach on a mound of pillows and blankets, her knees bent and her feet swinging, as she watched the sparkle of the performer's billions of tiny bells and coins. At least, it seemed like billions, to Cadmia. They shone in the firelight, and let off a kind of music that made Cadmia tap her feet in the air.
The dancer's body rippled, swayed, undulated, in a way that Cadmia wondered if hers ever would. So far, her body was scrawny, and flat like a boy's.
But maybe, someday, she would grow up to look like her mother.
Scarlet Paynes had tried to teach her daughter some of her dance steps, but Cadmia had yet to grow into her long, awkward limbs, and she just couldn't make her body move the way she wanted to. Maybe with more time she would learn, but there never seemed to be enough time. Mother had her performances, and then hours spent with her fans and her beaus, and then a meal and then sleep so she could do it again the next day.
"It's what keeps the food on the table," Scarlet told her daughter once.
But mostly, the A'hknet dancer did not reference such hard facts of life. After all, she loved to dance. She loved the power of sensuality, and she loved the adoration she received, so why should she complain about long hours and few days off?
Cadmia fell asleep in front of the fire.
When she woke, it was just a few hours after dawn. A few others were sleeping near her, but no one she knew. She stood up and went into the kitchen, where she found some milk and an apple for breakfast.
She stepped out the door—
And into the public garden behind the Quinacridone. A woman was weeping, on her knees, with her hands pressed to the stone wall between the gardens and the inner hall.
"Are you all right?"
"I'm lost," the woman said. "I'm so lost."
"Where are you trying to find?"
The woman looked up, revealing eyes that were empty sockets. "I don't remember."
Cadmia flung herself back and tripped over something behind her. She pushed herself up, turning to see what she had tripped on.
Pearl was locked in the Quin dungeon.
"She's a monster," one of the guards said.
"Let's keep this between us, all right?" the monster in the market said. He flipped something in the air, something that glimmered in the light: a key, which Cadmia knew went to Pearl's shackles.
"Let her go," Cadmia begged.
"She's safer here." He flipped the key at her, hard, and she flinched.
Cadmia woke with a gasp from jumbled dreams, some of her childhood, and some of her fears. She shook herself as she walked to the window, trying to make sense of the images. Her trip to the docks had probably inspired the dream of her childhood, and her anxiety about Pearl explained much of the rest, but what of the blind woman?
The Order taught its initiates to consider their dreams carefully because the Others sometimes spoke through them, but if this one had a message, it was lost to her.
Maybe it was just meant to horrify me awake, she thought, as she saw the two figures picking their way through the darkened street. One was carrying a large bundle.
Heart pounding as she imagined the worst, Cadmia drew on her robe and then dashed down the stairs, not even bothering to light a lamp. She reached the foyer, which was open to the public at all hours, just as Hansa crossed the threshold. His arms trembled and his face was flushed with the effort of carrying Pearl, but if he had difficulty entering this place he hid it well.
"She's all right," he said in response to Cadmia's panicked expression. "Just exhausted. If I can figure out how to catch the mancer who kidnapped her I will, but in the meantime you should keep her here. I don't know why they want her or if this will make them give up."
"Thank you," Cadmia breathed. She started to reach to take Pearl, and caught sight of the other man lingering outside the doorway. Unlike Hansa, he clearly had no intention of crossing the threshold. Pitching her voice low, she asked, "Are you all right? I know I'm probably the last person you're inclined to trust right now, but if you're in trouble—"
Hansa shook his head. "Everything I told you before was true. I'm with him now only because he needed my help to rescue Pearl. After this, I'm going back to my normal life, and he's getting out of it."
Cadmia nodded, but the chill that ran down her back as she took Pearl from Hansa warned her it might not be that easy.
Cadmia wasn't strong enough to carry Pearl all the way to her bed, but the girl roused only enough to sleepily walk there and say good-night before closing her eyes as Cadmia tucked her in.
Cadmia, unfortunately, was now wide awake. A cool bath and a hot cup of coffee rubbed the grogginess from her mind, and she went to the temple, where a young woman was kneeling in the meditation area reserved for those waiting for an audience.
"Are you seeking guidance?" she asked.
When the woman looked up, Cadmia recognized her tearstained face as that of Hansa's fiancée. They must have barely missed each other on the street.
"Yes," she said. "Please. Can we go somewhere private?"
Cadmia led them into her office. The shivering woman accepted tea, but seemed more interested in holding it in her hands than actually drinking it. Cadmia waited patiently, trying not to make assumptions about the woman's reason for being here.
"I'm such a fool," Ruby sighed.
"Why do you say that?" Cadmia had enough practice to keep her face neutral and attentive as she considered how she would react to questions about Hansa. She was almost certain now that he had been set up and had told her the truth, but she still didn't understand exactly what had happened or who was responsible. All her education said this puzzle couldn't fit together the way it seemed to.
If Abyssi had suddenly learned to plan, they were all in trouble.
"Hansa was a family friend almost since birth," Ruby said, staring down at the ring on her finger. Cadmia's upbringing in the Order A'hknet made her instinctively calculate its value, and decide it was either a family heirloom or evidence of months of saved wages at a guard's salary. "Our fathers work together and he and Jenkins were close to the same age. I don't even know when we started dating. At some point, Jenkins just didn't come along as often so it was just me and Hansa and everything . . ."
She trailed off. The eyes she lifted to Cadmia were sparkling with tears.
"I love him. He loves me. We're the perfect little—" She broke off, blushing.
Cadmia said it for her. She had heard the phrase a million times, usually by her mother's people. "Perfect little Quin couple?" she suggested. The phrase implied so many things. Some of the more devout used it as a compliment when they saw a couple they felt were well-matched, living well, and prepared to raise the next generation of Followers of the Quinacridone. More often, it was a jab at a couple who seemed too pure, too honest, too naïve to be true.
Ruby looked back at her tea. "I can't believe I . . ." Her voice was barely a whisper. "I'm hotheaded. I know that. My parents disowned me when I was sixteen after I tried to join the Order of A'hknet. Jenkins had an apprenticeship lined up to a ship carpenter who was willing to take him on despite his having the sight, but it would have left him financially dependent on our parents and they would have told him to cut ties to me, so he applied to join the One-Twenty-Six. And I can't help thinking . . ." When she looked back up, the tears were streaming down her face. "It's my fault he's dead. I killed him by being stupid and impulsive. Nearly killed Hansa, too. And Xaz! She was my friend. She never let me be a close friend, but I liked her."
Ruby's tears started in earnest then.
"None of this is your fault," Cadmia said, reaching out to take the tea from Ruby's trembling hand before the other woman burned herself. "You aren't responsible for the decisions other people—"
"Do you think Xaz used magic to make me like her?" Ruby interrupted. "People say mancers can do that. How can anyone trust anything if—" She broke off with a strangled sound, half curse and half sob. "Any other day, I would have gone to Jenkins if I felt this way. He would have made some stupid joke and cheered me up."
Cadmia normally had conversations like this with people crippled by guilt because they actually had murdered someone, which made her perhaps not the best confidant for someone struggling with Ruby's concerns. She knew the answer to Ruby's question about Dioxazine—yes, Numenmancers were capable of manipulating people that way—but Ruby was looking for comfort, not a lecture on mancers' powers.
Cadmia suggested gently, "I can stay if you prefer, but you should know that there are Brothers and Sisters here who specialize in guiding people through loss and grief. It isn't my area of expertise. Would you rather—"
"I want to talk to you," Ruby interrupted. She flinched from her own raised voice, then added more quietly, "If that's all right, I mean. They say you advise the One-Twenty-Six, and work with soldiers and even sorcerers. I know you're the one Hansa spoke to when he was arrested. They're talking about making him a captain now . . . now that it's been cleared up." She frowned as she said it.
Did Ruby doubt her beau's innocence? Had she noticed how the pieces of his arrest and exoneration didn't quite fit together? Not wanting her own bias to lead Ruby away from what she wanted to discuss, Cadmia kept her response simple. "Oh?"
"I felt so ashamed of how I acted when he was arrested, when I realized he was innocent I put on his ring. I decided on the spot, yes, this is the man I want to marry. I was going to tell him so as soon as he noticed . . ." She trailed off. Cadmia suspected that Hansa either hadn't seen or hadn't acknowledged the ring on Ruby's finger. "I went to the compound to ask what happened, after he—well, he wanted to be alone for a while," Ruby admitted. "I received dozens of condolences about Jenkins and as many congratulations about Hansa's expected promotion, just like I was him instead of me. He hadn't gone back yet, but I was Hansa's girl so . . ."
This time when Ruby paused, Cadmia thought she understood. "How do you feel about being Hansa's girl?"
Ruby sniffed. Instead of directly answering the question, she asked, "Did you know in Tamar it's considered perfectly normal for a woman to own and captain a ship? She might choose to marry and have a family, but she isn't expected to settle down to do it. And if she doesn't want the man around anymore, she just kicks him off the ship. They don't think of marriage the way we do."
Cadmia tried to make sense of the shift from Ruby's grief about her brother to these seemingly less-important pre-marriage jitters. "It must have been hard to be offered condolences for Hansa's sake instead of your own."
"Hard," Ruby echoed. "But not new. And if I marry him, it's something I'm going to have to face the rest of my life. Dear Numen, Jenkins would be horrified to hear me talking this way. He thinks—he thought we should have married years ago." Cadmia could tell there was more to come, so she waited, and slowly Ruby gathered her nerve. "Hansa will be a captain in the most elite position in the country," she said. "I should be honored, but all I see is a future where I'm nothing but an extension of him. Hansa Viridian's wife. The only thing that scares me more is knowing it probably won't be long before I'm . . . before I'm Hansa Viridian's widow. I've been going through the motions because I do love him and I am proud of him, but I don't know if I can stand to give up everything and settle down in a proper Quin life as his sweetly supportive wife just to lose him. It was easier to accept he was a mancer—I could be furious and end it fast and not wait for the day someone comes to my door again to say . . . and it will be soon, because Hansa never backs down or lets someone else take a risk he feels is his responsibility."
Cadmia couldn't argue. She didn't know exactly what Pearl's rescue had entailed, but she suspected it was something few other men would have done.
"I think you need to talk to Hansa," she said. This kind of issue wasn't her specialty, but "talk to him" was usually good advice for relationship questions. "You've both just lost someone dear to you, and faced a hard truth about someone you considered a friend. Give yourselves time to heal and support each other before you do anything drastic either way. Don't let fear drive you to any decision you're not ready for."
"You're right." Ruby sighed. "I'll talk to him. I will." She drained her tea like a shot of whiskey. "He's been so busy since he was promoted to lieutenant, and I've been so focused on finishing my master work at the herbaria, we haven't really had a serious conversation in a long time. That's all we need. To talk." She stood, gathering herself visibly. "Thank you, Sister. I'm sorry if I wasted your time."
"Time in counsel is never wasted." At least this was a break from murderers and mancers, Cadmia thought as she kissed Ruby on the forehead and whispered the traditional blessing, "May the Numen hold you and light your path."
She escorted Ruby out, and immediately turned her thoughts to a harder and less pleasant task: preparing for that evening's mourning service for the eleven guards who had been killed by the Abyssi. Quin monks would perform the moving-on ceremony. Her job would be comforting the living and turning thoughts and conversations away from how they had died. Lore said that souls slain by the denizens of the Abyss would dwell in the Abyss after, so it was a good thing that she was not expected to share comforting words about the next world those near-dozen would find after death.
CHAPTER 17
Hansa found the chattering of birds, mixed only with the sound of the horses' hooves, a remarkably peaceful experience, especially when compared to the events of recent days. It also felt good to see Pearl safely home.
It wasn't until they were nearly back at his apartment that it occurred to him to ask Umber, Why did you need me for this? Though the silent communication was not his favorite form of speech, he didn't want to risk words that could be overheard by passersby. As the sun rose, so did the people of Kavet. You certainly didn't have any trouble handling that Abyssi.
The denizens of the Abyss are simple-minded and easily dealt with, Umber demurred. Even Numini are not much of a threat, since they have no interest in one of my kind. Mancers, on the other hand, are dangerous. You were safe in the temple, because it was made by mancers for people with power; they can't be held or hurt within that sphere of magic. My kind on the other hand . . . if I run afoul of an Abyssumancer, especially somewhere like the temple where my powers to defend myself are limited, I'm little more than meat.
And Pearl? Hansa asked. Why would the mancers want her? I didn't . . . see . . . any power on her.
It felt strange to say that, but that was the best he could put it. With the borrowed magic from Umber, Hansa could once again see the glow to the half-Abyssi's eyes, and the veil of power wrapped around him. The Abyssi by the temple had seeped energy, which crackled like heat lightning. Pearl was just a girl. She had barely been visible amidst the magic of the temple.
You wouldn't, Umber answered as they reached Hansa's front door. Aloud, he added, "Ready?"
"Never," Hansa replied, letting them both in. He would have preferred a brief "goodbye" and maybe a firm handshake—though he could do without even that—but Umber had made it clear the power Hansa had borrowed would be visible to sighted guards and wouldn't naturally fade fast enough for him to just ignore it.
The process by which Umber had infused Hansa with enough power for him to impersonate a mancer had been terrifying and disgusting, but short and simple. Umber had greeted Hansa at Hansa's home. He had confirmed that there was no one else in the house, and then had grabbed Hansa's hand, and slit his forearm open from his wrist to his elbow.
While Hansa had been shouting obscenities, convinced the crossbreed had gone mad and was trying to kill him, Umber had matter-of-factly drawn his knife across his own palm, and then grabbed Hansa's hand again in order to let his own Abyssal blood drip into Hansa's.
Hansa couldn't remember passing out—did one ever?—but when he woke, he had been shocked again to find himself alive, not covered with blood, and unmarked where Umber had cut him. Once he had finished cursing at Umber, the half-Abyssi had said only, "There's a horse waiting for you at the stables at the edge of the city."
Hansa hoped returning the power would be less . . .
Titillating? Umber suggested.
"Have I mentioned how much I despise the fact that you can read my mind?" Hansa groused.
"You would hardly need to mention it, now would you?" Umber said. "Your fiancée would be pleased to realize how constantly you think of her. You don't even notice it most of the time; you're thinking about something completely different, and then suddenly it's—"
—Ruby. . .
"It's kind of nauseating. Oh," he added, as if in afterthought, "and, returning the power? Not nearly so easy, unless I'm willing to kill you, since just ripping the power out of you would certainly make you combust."
"You couldn't have mentioned this sooner?" Hansa sighed as he unlocked his front door.
"I could have," he said, "but then you would have wanted details, and once I gave them to you, you would have chickened out. Take off your shirt, will you?"
"Excuse me?"
"No use getting blood on it needlessly." Umber's words made Hansa freeze just inside the front door. Umber, ignoring his hesitation, slipped past Hansa and added, "Oh, and lock the door. We don't want unexpected company."
Though he followed the suggestion about the door, Hansa was still fully dressed when he followed the half-breed into the kitchen to find Umber prodding at the coals at the bottom of the hearth.
Much as Hansa didn't like the idea of listening to an Abyssi, he trusted it no less than he trusted Umber. "The Abyssi said something about other options, which didn't involve, well, bleeding. To do this."
"Nice to hear you two had a fun little chat," Umber said dryly. "Yes, there are options, if that's your preference."
"My preference is not to have to see the sharp end of that knife you wear ever again, if that's all right with you," Hansa sighed, relieved. "What is it with you people and blood?"
"Coin of the Abyss," Umber said vaguely. "Blood, pain, fire—"
As he imagined all the other ways this could go, Hansa added hastily, "My preference for 'no blood' does not extend into a preference for pain and fire instead."
"We'll work something out." Umber chuckled. "Fire's no good for this kind of work anyway. Fire's for destruction. Yes, I could burn away your flesh and the power would come back to me, but given our current bond, that wouldn't end well for me either. I'm building up the fire because it's cold in here," he continued. "Nothing likes the cold but the Numini and the righteous dead. Since we are neither divine nor deceased . . ." He snapped his fingers, and suddenly the coals caught, as did the new log he had added. They burned merrily, as if perfectly kindled.
Only then did Umber address the actual concern. "No blood, no fire, no pain. Do you actually expect a solution here that suits you?"
Hansa collapsed into one of the chairs in front of the fire as his hopes fell—though not too far. The demon's word had never been enough to lift them high.
"So, the Abyssi was lying. Probably just trying to make trouble," he said.
"Oh, no," Umber answered, as he moved from the fire to lounge against the counter. "Abyssi and Numini have a few things in common, one of those being that they can't lie. Not outright at least. Occasionally they will present their own misconceptions as the truth, but they cannot deliberately lie."
"So it was wrong then," Hansa said. He didn't care much about the semantics, beyond the fact that the Abyssi had not spoken any information that happened to be helpful in this circumstance.
"No," Umber replied, infuriatingly, "it was right. There are ways to transfer power that don't involve blood. They would actually be safer for you. They do, however, take longer, and would require more effort on your part."
"I'm willing to put forth a little effort to avoid having you slice me open. What would I need to do?"
He realized a moment later that, with a little thought, he probably could have predicted the half-breed's response. Umber responded by leaning down over Hansa's chair, putting his hands over Hansa's to hold them in place, and kissing him.
Unlike the angry warning Umber had delivered through a kiss in the jail cell, this was soft and fluttering, as if Umber was trying to ask with his body, Isn't this less frightening than blood and blade? It spoke to how long and terrifying the last few days had been that, even momentarily, Hansa considered it.
As if he hadn't already betrayed Ruby—and Jenkins, and all his coworkers, and his family, and anyone else who trusted him to stay honest and on the right side of the law—enough. He didn't like the idea of letting Umber cut him again, but there was one line Hansa could still refuse to cross.
He turned his head to the side and drew a breath to say something intelligible. Instead of desisting, Umber nibbled his way down Hansa's neck with light nips, each of which made Hansa gasp. When he reached the edge of Hansa's shirt, he lifted his head again.
"As I was saying," he murmured at Hansa's ear, "the four coins of the Abyss are blood, pain, fire—and flesh. If you prefer this way, I am happy to oblige."
Speaking broke the spell. Hansa wrenched his hands out from under Umber's and pushed the other man back. "You've made your point! We'll do it the other way."
Umber pulled away with a chuckle. "I'm not quite sure which point I've made, but I'll leave you to tackle those thoughts on your own." He turned, and as Hansa tried to shake off the fatalistic madness that had briefly snared him, Umber began to rummage through the kitchen cabinets.
He had to clear his throat twice before he managed to ask, "What are you looking for?"
"Something stronger than cider to drink," Umber said.
"It worries me when you go searching for a drink."
"Almost anything I say or do worries you," Umber observed. "If it makes you feel better, it's for you, not me."
"Not better." Hansa pushed Umber out of the way, and quickly retrieved a bottle of the same kind of full-bodied red wine that could be found in almost every home in Mars. Heated with honey and spices, it was what kept most of the population from freezing during those frigid Kavet winter nights.
Umber sniffed. "That's it?"
"I don't drink much." Hansa shrugged. He resisted an impulse to try to hustle Umber along; his previous attempts to assert any control over the situation had only made matters worse.
Umber considered the bottle of wine, then filled a coffee mug. After a little more thought, he poured a second cup, which he set in front of Hansa.
"Is this necessary?" Hansa asked. The wine was meant for mulling. It was pretty foul on its own.
Even more foul when cold, was Umber's response, as he opened a window and set the mug out on the sill before carefully closing the window again. But you'll need it. You don't realize how hot the power you're carrying burns when you're saturated in it, but once it's gone, you'll need something to slow you down and cool you down.
"I'll try to stop asking stupid questions if you'll get on with it," Hansa offered.
"Excellent," Umber said. "Now take off your shirt."
Hansa started to undo buttons, but despite his resolve to stop asking questions, he asked, "Would you at least warn me this time before you slit my throat or any other major arteries?"
"I need to cut your chest, right over your heart," Umber explained. "It won't be a deep cut."
Hansa wasn't naïve enough to hope that was the worst part. "And then?"
"Then I drink, to help me form a link back to my own power, so I can control how fast it flows out of you. Too fast, and you'll burn out. It may be a . . . strange . . . sensation, but it shouldn't hurt. If you relax and don't fight me, it will be over in moments."
Hansa stared at the mug of wine, considering it now.
Shaking his head, he folded his shirt and set it next to the full mug of wine. "Okay then. Let's do this before I lose my nerve. Should I stand up or something?" He focused on the practical details, since that was less disturbing than actually concentrating on what he was doing.
"You should probably sit or lie on the sofa," Umber suggested, with a nod toward the sitting room.
Hansa sat, reminding himself there was no point to stupid questions because they not only made this take longer, there was nothing he needed to know. He didn't need to understand this because he never wanted to think of it again. Umber waited a few seconds, as if to see if Hansa was going to protest again, and then drew his dagger.
"You might prefer to close your eyes," Umber suggested.
Hansa did so. In his head, he started to recite an old Tamari nursery rhyme his mother used to say to him when he was a child. It was better than focusing on the knife and the half-demon leaning over him.
The sails are white, the deck is brown, the sky above is—
Ouch. There was the slice. Umber leaned across Hansa's lap, one hand on the arm of the couch to stabilize himself as he caressed Hansa's cheek then eased his head to the side.
Where was he? Tamari sailors often raised their children on ships. His grandfather had been raised that way before meeting his grandmother and settling in Kavet. If Hansa could just keep his mind in inanities like family songs and stories, he could get through this.
The sky above is blue. And there's a word we use to name the ocean's hundred hues. Then the chorus, which always confused him as a young boy because it had words in some old Tamari language. What was it? The ocean's colors had a name, but he couldn't remember it.
When Umber started laughing, Hansa opened his eyes. "What?"
"Ayalee," Umber provided. Once again, he was far too close for comfort. "Tamari sailors call the ocean Ayalee. I don't know the song, though."
"Az Ayalee," Hansa returned, with a near-hysterical giggle, before squeezing his eyes shut again as Umber leaned down. Keep you safe az Ayalee.
Sailing ships. Think of ships on the water, not of the demon who was leaning against him, whose warm mouth had just touched the new cut on Hansa's chest.
Where was he? The summer sun is hot and gold, the storm clouds cool and gray . . . red hat, gray mountains. . .
The words of the poem scrambled in his memory as his head swam. He pushed against Umber, worried he was going to be ill. "What—"
Don't fight it, Umber said. Relax. Remember you don't want this power.
He could do that. Even if he was getting a little seasick.
CHAPTER 18
He lost the words of the poem and all other awareness of where he was and what he had been doing until Umber said, "Okay. Take a moment to come back to Kavet."
"Mm." Hansa opened his eyes and sat up, shaking his head to clear it. He didn't know when they had separated, but Umber was now sitting back, probably waiting for him to reorient himself for the next step. Hansa wished he could believe they were done, but the cut on his chest was still bleeding, and he had learned enough recently to know that meant the magic wasn't finished. "What next?"
There was still a residue of laughter in Umber's voice when he said, "Your turn, Hansa."
"No." He spoke without even processing the entire implications of the statement, and pushed to his feet. Gray fog encroached on the edge of his vision and the ground under his feet seemed to take a sharp tilt to the side. He ended up kneeling on the wool carpet with his head down. "How much blood did you take?"
"Not much. What's wrong with you is that you're leaking power." Umber stood, passed Hansa on his way to the kitchen, and returned with the mug of wine from the table. "Drink, then we'll finish this."
With the mug on the carpet in front of him, Hansa started to translate just what Umber meant when he said, "Your turn."
"You don't mean . . . I mean, you can't expect me to . . ."
Umber hefted Hansa with one hand on his arm, lifted his wine with the other, and deposited Hansa on the couch before putting the wine in his hand. Then he sat and began to unbutton his own shirt. "Drink your wine if you need it, and then we have to do this before you pass out."
"You couldn't have warned me?"
"Not unless I wanted to argue with you all night."
Given the circumstances, Hansa thought that was an unfair accusation—he had argued very little, and even tried to stop asking questions—but Umber was right that he probably would have objected more if he had been told the entire process up front.
Hansa stared at the wine for only an instant this time, then lifted it to his lips and chugged the foul stuff. Umber was out of his mind. Out of his Abyss-spawned mind. When Hansa put down the mug and looked back at the spawn, Umber's expression was tight; Hansa suspected he was trying for the sake of his Quin partner-in-madness to suppress a grin or a chortle.
"This part might take a little longer," Umber said, "but once it starts, you'll probably find yourself drifting again. I doubt you'll be aware of much."
"Thank Numen for small favors," Hansa whispered, only barely aware that the words would have earned him a censure at work.
"These particular favors come from a lower plane," Umber pointed out, before leaning back against the sofa's arm again, and lifting the knife. He cut the same spot on his chest that he had on Hansa's.
"What did I ever do to deserve this?" Hansa grumbled as he leaned forward, trying to find a way to do this disgusting thing without actually touching the half-Abyssi.
"As I recall," Umber answered, "you summoned me by blood and demanded a second boon. You meddled in the affairs of the Abyss." He locked an arm around Hansa's back, pulling him forward. Hansa recoiled, trying to stop himself from falling against the other man. "Now quit being such a Quin."
Ayalee, Hansa thought, as he stared at the wound on Umber's chest. The blood wasn't flowing like normal blood should; it seemed thicker. It was also darker, with an incandescent sheen.
What do you suppose the Tamari would call that color? Umber supplied helpfully.
Well, that ruined that song forever.
Shut up, Hansa snarled back. Umber put a hand on the back of his head, encouraging him. You're enjoying this far too much.
There are other things I'd enjoy more.
Just . . . quit talking.
Then quit stalling.
Okay. Just get it over with, Hansa told himself. Umber, thankfully, did not reply. He touched his lips to the blood, then had to pull back, suppressing a gag. He licked his lips instinctively and discovered that the half-demon's blood tasted like something you would expect from the Abyss: smoky, dark, and spiced. He still knew what it was, but maybe he could go through with this if he could pretend it was something—anything—else.
No choice, he told himself. Just do it to get it done.
He closed his eyes and leaned forward again, and this time closed his lips over the wound. Umber offered no encouragement this time, which was helpful, since it meant Hansa could think about anything but what he was doing. He could do this. Had to, really, unless he wanted to walk around looking like a mancer to anyone with the sight for the rest of his life.
He made the mistake of taking a breath, which brought with it the smell of flesh, reminding him that he was not at a tavern with a hot mug of some spicy mulled beverage, but rather pressed against another man.
Get over it, Quin, Umber snarled.
Get over it, indeed. This would have been easier if Hansa didn't suspect, given Umber's many previous flirtatious comments, that the spawn was enjoying it.
To the Abyss with it all. Hansa put a hand on Umber's shoulder in order to brace himself, and then leaned down to the blood one more time. Lips to flesh, he deliberately licked along the length of the cut, drawing fresh blood to the surface. Umber shuddered, and his fingers twined in Hansa's hair, but he didn't speak, thank Numen . . . or Abyss, whoever there was to thank.
The blood filled his mouth, and his throat swallowed, reflex he couldn't have avoided kicking in. He tried to clear his mind of exactly where he was or what he was doing, but couldn't, since he was very awkwardly bent over Umber. His neck hurt.
He could fix that.
Never lifting his lips away from the wound, he reached around Umber's back, lifting him enough to turn him. Umber let out a surprised yelp, but didn't struggle. He let Hansa move him so he was lying full-length on the couch, shoulders propped up by the sofa's end-pillow and arm-rest, with Hansa more comfortably sprawled atop him. That done, Hansa could close his eyes, and go back to what he was doing.
Vaguely, he was aware of a struggle, a pulling sensation, not physical but rather somewhere else.
Don't fight it, Umber said, as he had before, though this time his mental voice sounded a little dazed.
Okay. He didn't want to pay attention to that, anyway.
It was easier now. Thinking, he decided, was overrated. Unnecessary, unhelpful.
Hansa? Umber's mental voice was wobbly.
Mm?
Why hadn't he noticed before how soft Umber's skin was? It was like fine silk.
That's enough, Hansa, Umber said.
No, it wasn't.
Yes, it is. Hansa felt a strong hand, still twined in his hair, pulling his head back. He hissed in protest. You're blood-drunk, Quin. Intoxicated, though damned if I know how.
Hansa stopped struggling against the hands pulling him away from the wound when he saw the flesh close, sealing the blood away. It didn't matter. There were other coins of this realm, ones he had been offered earlier and refused for some silly reason he couldn't remember now.
He reached a hand under the half-Abyssi's head, and lifted him just far enough to kiss him. Lips met lips, tongues twined, but one long, deep kiss later, Umber snarled, "Back off!"
The blow came not physically, but in the form of raw power. It hit Hansa hard enough to knock him back, at which point Umber shoved him from the couch and sprang to his feet.
Hansa lay on the floor, dazed, suddenly aware that his heart was pounding like the hooves of a racehorse. He gasped for breath, body inexplicably heavy. He couldn't even summon the energy to lift his arm to wipe away the sweat he could feel gathering on his brow.
He wasn't sure how long he lay there before Umber crept back, helped him sit up and lean against the couch, and placed a cold cloth across the back of his neck. He offered the mug of chilled wine, which Hansa cradled in trembling hands, sipping carefully, still steadied by Umber's arm.
"That last bit shouldn't have happened," Umber said as Hansa drank. "Abyssi, spawn and mancers can get intoxicated off blood if they aren't careful, but it shouldn't have happened to someone who has no natural tie to the Abyss."
The words reached Hansa, but they were next to meaningless. What mattered in that moment was the cold ceramic mug in his hands, and the warm arm across his back.
"I know these words mean nothing to you now," Umber continued, "but later, I hope you remember that I chose to stop you. I didn't have to."
Hansa was starting to come back to himself then, enough that his eyes finally focused. He turned to look at Umber, whose deep blue eyes swam with concern. Full lips, slightly reddened with blood, moved as the man continued to speak, but Hansa didn't hear whatever he was saying.
"Get away from me," he managed to choke out.
Umber frowned. "Well, I guess that's the gratitude I should have expected from you." He stood, lithe body uncoiling in one smooth moment, and started toward the door.
"Not what I meant." Hansa coughed. "You just—" He was not going to say that. Umber paused, twisting back, expression still cross. "You still look . . . feel . . . really good." He closed his eyes after he said it, squeezing them shut as if doing so could block out the truth.
"It'll wear off," Umber said sadly. "Let me help you to bed. Sleep a few hours, and when you wake, you should be back to normal."
Hansa let Umber help him to his feet mostly because he couldn't have stood on his own. One arm looped across Umber's shoulders, he couldn't quite resist smoothing his free hand down Umber's chest. After he realized what he had done, he curled that hand into a fist, trying to control himself.
They stumbled at the doorway to the bedroom. Hansa wrapped his arms around Umber's waist and tried very hard to remind himself that he did not want to kiss the half-naked spawn again. Even if he smelled and felt as good as he looked.
Umber chuckled. "I guarantee, as soon as you're back to yourself, you will be cursing my name and blaming me for all of this. A good little Quin like you couldn't possibly be interested in anything so untoward."
The sound of the front door opening caused them both to turn.
"Didn't you lock that?" Umber asked.
Hansa nodded. "Ruby has a key."
"Ruby . . . your fiancée?"
Umber's expression of concern pierced Hansa's mental fog a moment too late. He heard Ruby saying, "Hansa? Are you here? I need to—"
She broke off as she stepped into the sitting room and saw them.
"Hansa? You should probably step back," Umber suggested quietly.
Ruby moved further into the room, and her eyes went to the two mugs they had used for wine, then Umber's shirt crumpled on the floor, and then back to Hansa and Umber.
"Back up," Umber said again.
Hansa took a step backward, and bumped into the opposite side of the doorway.
"Well. This explains a lot," Ruby said.
"This really isn't what it looks like," Hansa managed to say. It was perhaps the stupidest defense he could have come up with, but it was so hard to think.
"You know? It . . . just . . . I don't . . ." Ruby shook her head. "Never mind." She turned away.
"Ruby, wait!" He managed to step away from Umber and put a hand on Ruby's arm to try to slow her down. "Please, will you listen to my explanation?" He would probably tell her the truth if she was willing to hear it, but if she walked away again without even considering there might be an explanation . . .
She shook off his hand and pulled off her ring. "I think you should just keep this. It's clear neither one of us is ready to marry."
When he refused to take the ring from her, she handed it to Umber instead.
"I won't say anything to the Quinacridone," she said as she moved away.
She closed the door quietly behind herself.
Umber sighed. Hansa snapped, "Could you have helped less?" Surely the spawn could have said something useful while Hansa was trying to find his tongue!
"If you recall, you forbid me from even speaking to her," Umber reminded him. "I can't arbitrarily violate the terms you set on the second boon just because it's convenient. Besides, there are other ways to fix this."
As soon as Umber made the offer, Hansa's irritation snuffed out. He still felt dazed, but there was one thing he felt sure about. "No."
"I agreed to help clean up any problems you got into on account of helping me rescue Pearl," Umber reminded him. "This falls in that category."
"No," Hansa said again. "This . . ." It hurt to admit it, but he couldn't avoid the truth any more. "This isn't really a new problem."
She hadn't been willing to listen to him last time either. Yes, Umber would be able to clean up this mess, manipulate Ruby once again . . . but what did it mean, if his relationship needed that?
"You're sure?" Umber asked.
"Yeah." He took the ring from Umber, and then stumbled into the bedroom. "I'm going to sleep. Then maybe I'll try to talk to her . . . explain . . . accept whatever comes of it . . ." He collapsed onto the bed. "Sleep first. Thanks," he added. "But I need to deal with this myself."
Deal with the mess he had made of his own life.
"As you wish," Umber said. "Sleep well, Quin. Good luck."
Hansa was already asleep, the star ruby ring curled in his palm.
CHAPTER 19
Xaz had been exhausted enough to drift into a deep and dreamless sleep by the fire. The rest would have been more satisfying if she hadn't woken once again snuggled against a furry blue body. Her cheek lay against his chest, and his tail was hooked securely around her waist.
They had established with their "pet the Abyssi" conversation that she did like being near him, and his warmth was probably the only reason she had been able to rest as well as she had, but she knew just enough about his kind to know snuggling wasn't all he was likely to be interested in.
The instant she tried to ease out of his arms, his tail and arm tightened around her and his eyes flew open. She froze, afraid to even breathe with his claws noticeably pricking the soft skin of her side.
His tail twitched, fur tickling her spine at her lower back, just in that spot that always made her jump. Enclosed within Alizarin's arms the way she was, she couldn't go far, but ended up sneezing as fur tickled her nose. His claws probably would have shredded her skin if he hadn't retracted them just in time.
His tail moved again, eliciting the same reaction.
"Stop that," she said.
"You say that a lot," he replied.
"Because dealing with you is a lot like dealing with a three-year-old child," she snapped.
She started to pull back, but though his grip loosened a little, he didn't let her go. Instead, he asked, "Really? Just like that?" He stretched to emphasize his point, making her blush. She remembered the way she had stared at Cinnabar after she had been injured, and only now realized that embarrassing fixation had been a result of the Abyssal power seeping into her. Love was of the Numen, but lust came from the Abyss.
"No," she said, meaning two things: No, he wasn't like a child, and no, she didn't want to continue this line of conversation.
"No, what?" he purred.
Her instinct was to be subtle, to use euphemisms or avoid the conversation entirely, but she had to keep in mind what she was dealing with. She gathered her nerve and said bluntly, "I will never have sex with you. Is that clear?"
The words didn't seem to surprise or insult him. He asked almost innocently, "Why not?"
"Why . . ." She sputtered. "Because I know what you are. And you know what I am. I'm a Numenmancer. I'm not going to have sex with a creature of the Abyss. If you were anywhere near capable of rational thought, you would have figured that out by now. Now, please let me up."
He didn't reply at all to the last words. Instead, he twitched his tail—she jumped—and said with a huff, "I'm perfectly capable of rational thought. Far better than you."
"You haven't demonstrated it," she grumbled.
Apparently he took the words as a challenge. "Point one." Xaz did her best to relax, since he obviously wasn't going to let her up until he was bored with this conversation, as he had bored of the last one. Hopefully, trying to apply logic, a trait traditionally associated with the divine realm, would bore him very quickly. "You like to touch me. You like to be near me. You like the way I feel. You like the way I look. Point two: Your magic is also attracted to me because we have a bond, and mine is attracted to you. You are my tie to this plane. I am your tie to the power of the Abyss. Point three: You need as much power as you can get, especially now that the Numini have disowned you."
"They haven't—"
He hushed her with a finger to her lips.
"Point four: Sex is fun. That's just a generally accepted fact. It would make the Abyssi happy, and it would make you happy.
"Final point: The four coins of the Abyss are blood, pain, fire, and flesh. Sex raises power. You don't like blood, pain, or fire, and you do like the look and feel of the Abyssi, and you do need power, and you would enjoy this form of raising power. Taking all these points into your oh-so-logical Numenmancer brain, tell me how you can possibly come to a different conclusion."
"You're a demon!" she shouted. "You have fur. And a tail. Oh, and you eat people!"
"You eat ducks," he said, as if that were a logical argument.
"Yes, I eat duck." Was she really having this argument? "That's because I'm not a duck. Also, I wouldn't have sex with a duck. Your argument sounds logical on the surface, but—"
"Until you apply human irrationality and Numini interference," he interrupted, tone haughty. "The divine realm is the only one responsible when you say no to something you obviously both want and need."
"And the Abyssal realm is the one responsible when fifty-year-old men have affairs with sixteen-year-old girls. Let me up. This argument is over."
Just when she began to fear he might refuse to accept "no," his arms loosened and he released her. "Can I have a kitten?"
"No—what?" Scrambling to her feet, it took her a moment to realize he had changed the subject. At least, she hoped he had changed the subject.
"I want a pet," he said.
"Why?" she asked, warily.
"To play with," he replied, brightening the instant her answer wasn't just, "No." "And I'm hungry."
"I'm not getting you a kitten to eat."
He deflated again. "Puppy?"
"You are a foul creature," she mumbled.
"I saved your life," he reminded her. "And I haven't eaten in days."
That made her stop. She had thought of the Abyssi she had summoned as a fiend and an annoyance, but the truth was, she had summoned him. If she had called one of the Numini into this plane, she would have fed it, but Numini couldn't eat flesh. It hadn't even occurred to her until then that one of the Abyssi might not be able to eat anything else.
So far, Alizarin had done exactly what she had asked of him. He had protected her and brought her somewhere safe so she could rest and recover her strength. He had helped her get warm clothing, and sustenance. He had brought her to the temple, and when the Quin guard had shown up, Alizarin had followed him in order to assess the threat he might pose. In return, Xaz had refused almost every request he had made, not just for entertainment but for food.
She was a Numenmancer. She didn't know how to treat a denizen of the Abyss. What she did know was that, even if she didn't feel guilty for abusing a creature that thus far had treated her very well—which she did—it was not a good idea to make a demon she had no magical control over unhappy.
"I'm sorry," she said. "I never expected to spend so much time with one of your kind. I know the Numini are very particular with what they can and cannot eat. Can you tell me what works for you—beyond kittens, I mean?"
"Numini are difficult," Alizarin agreed. "Milk, honey, clear water, new fruit." He listed with a swish of his tail some of the Numini's simplest food choices when on the human plane. "Abyssi are easy. Dirt isn't food. What comes from dirt isn't food. Everything hot is food. Once it's cold it's dirt again."
"Does 'hot' include things that are warmed by fire?" she asked.
Alizarin frowned. "Fire is good, but it doesn't turn dirt into food."
"So hot means alive, or just-dead. Nothing you could buy at a butcher's or order at a restaurant."
He nodded. His expression looked pleased, but his tail was twitching in a way she had come to associate with his impatience.
"Without eating any people, and doing your best not to eat anyone's beloved new pet, would you be able to find yourself enough to eat?"
He nodded again, the swish of his tail now more lively.
"Okay then. Why don't you go . . . do that." And she would try not to think too much about it. "I'm going to go back to our room and try to get a little sleep. I'll meet you later."
"Hunt well," he bid her, before bounding off into the near-dawn without waiting for her reply.
"You, too," she sighed.
Once he was gone, the chill of the damp sea air and winter wind settled into her bones. She built up the fire, shivering all the while and wishing fiercely that she had a way to make the flame brighter. Most of her magic responded to will and words, but her invocations did nothing here. It occurred to her that a real Abyssumancer might use blood, but her nerve failed her despite the cold.
It wasn't just Alizarin who made the idea of turning into an Abyssumancer terrifying. Though she had personal experience to know the Quins' thoughts about most mancers were more scary stories and exaggeration than truth, she suspected much of what they said about Abyssumancers was true. The Abyss was a realm of impulse and need. Dark hungers drove its denizens and infected the mancers bound to them.
That all meant she couldn't trust an Abyssumancer to help her break her bond with Alizarin. Then who? Another Numenmancer couldn't help; they wouldn't be able to see the Abyssal magic even if their Numini would let them try. Xaz needed someone with more diverse talents. Outside myths, where impossibly-powerful mancers could manipulate all four realms of existence—the Abyss, the Numen, life and death—she knew of only one creature who might have the skills she needed.
The spawn.
Spawn didn't rely on the Numini's or Abyssi's approval in order to work magic. Though they were most closely tied to the realm from which they had been born, they weren't blind to the opposite realm the way a mortal mancer was. Finally, since they were born with their power instead of having it unnaturally thrust upon them like a mancer, they learned to use it instinctively. They were supposed to be capable of incredible feats.
Xaz had never met one—or hoped to do so—because they usually utilized those incredible abilities to hide from her kind. Spawn seeped Other energy, which meant an unscrupulous mancer who could catch one could use it as an unending fount of power. She had heard of one, though, from Alizarin—he said a spawn had helped Hansa escape Quin clutches a free man. If the spawn had really granted Hansa a second boon, he would have to keep him in sight no matter what Hansa was now. If Hansa was in danger—say if a mancer with a grudge approached him—the spawn would come running.
Now that she'd had time to consider his change in status, Xaz had a word or two she wanted to exchange with the hero of Mars anyway.
CHAPTER 20
Cadmia wiped snow from her eyes, then checked her notes again. Other Sisters and Brothers of Napthol had gone by horseback to try to make the next-of-kin calls in the countryside for the deceased soldiers, but she had agreed to do the local ones. The house listed as the home address of Soldier Rosso's sister was one she remembered from her childhood as a flophouse frequented by the poorer members of the Order of A'hknet.
White flurries had started to fall a little after dawn and grown steadily heavier since, and the snow had caused an instant change in the temperament of the docks. Children bundled up in heavy winter cloaks passed through the crowd, running back and forth to deliver mugs of hot drinks and still-warm pastries from the taverns to anyone with a penny to spare. The wharf market had mostly closed down, as the women who usually sat out with their nets, ropes, and weaving moved inside so they could work without their fingers going numb. Fishermen shook their heads, packing new snow around the morning's catch even though they knew few people would come shop.
"Looks like an early winter," observed a man loitering in front of the house. She chose to ignore the bag he carried, which she had seen him hurriedly slip something into the moment he saw her violet robes.
"This might just be an early freeze," she said practically, letting him know she intended to keep the conversation casual and not harass him about whatever contraband he had just hidden. "I'm looking for Fawn Rosso. Is she around?"
The man shook his head. "Not a freeze, real winter. This snow will be here until spring. I'll bet you a week's earning."
"I never bet with a man who sounds that sure," Cadmia said. In fact, she never bet; the Napthol Order discouraged it. "Fawn isn't in any trouble. Her brother was one of the victims of—"
"Shame," the man interrupted, continuing to ignore her request. It was hard to tell if he was stalling for time, probably while someone inside cleared away evidence of illegal activity, or just giving her a hard time because she was from the Napthol Order. "I was hoping I could use that extra pay to take my daughter somewhere special."
"Sorry to disappoint her. I'm going inside."
He waited until her hand touched the doorknob to ask, "Aren't you Scarlet's girl?"
"I'm—"
"Sister!" She spun toward the frantic voice to find a young Tamari girl in sailor's garb, probably a cabin girl, slipping and sliding across the street toward her. "Sister, can you come?"
The man by the door tensed. No matter how much he wanted to harass Cadmia, he was clearly torn on whether he wanted to warn her about getting onto a Tamari ship.
"Captain saw your—" She gestured to her clothes breathlessly. "Told me to get you. It's an emergency."
Cadmia reminded herself that she wasn't a child in the Order of A'hknet anymore. Even a would-be slaver had to know that trying to kidnap a Sister of the Napthol would be more trouble than it was worth.
"Where's your ship?"
The cabin girl turned and dashed to lead the way. Cadmia followed as quickly as she could without falling, barely breaking her stride when she hit a slick patch of ice on the boarding ramp and had to grab the rail to keep from falling into the icy waters.
"She said she wanted passage wherever we were going," the captain said quickly, guiding Cadmia toward the bow of the ship. "I told her we don't carry passengers. That's when she climbed up. My first mate's been trying to talk her into coming back down, but then I saw you—that's what you people do, right?"
By the time Cadmia reached the bow of the boat, the first mate had just grabbed the woman's arm to pull her back away from the rail and stand her safely on the deck, but it didn't look like the crisis was over. The woman shoved the mate away, and though she didn't climb the rail again, she pressed her back against it.
Cadmia bit back a curse as she recognized Ruby's tear-streaked face and remembered their last conversation. She must have confronted Hansa. What had he said to her?
"Ruby, Ruby, can you hear me?" Cadmia asked, trying to get the woman to look at her.
Ruby nodded, slowly, though her eyes never quite came into focus. Her gloveless hands continued to grip the railing, her slender fingers nearly blue from the cold.
She wasn't wearing her ring.
"Did something happen?" Cadmia asked. "Did you and Hansa argue?"
Ruby shook her head. "Winsor Indathrone pardoned him," she said in a dazed voice.
"Yes, he did."
Again, Ruby shook her head. "But he—" She sniffed. "But he's guilty."
Cadmia felt a new chill, unrelated to the weather. "Can we talk somewhere private, Ruby?" she asked. She was less worried about privacy than she was about wanting to get the woman out of the freezing weather and away from the rail.
Ruby just glared. "Indathrone pardoned him. A Sister of Napthol condemned him. I saw the blood . . . and then . . . he wouldn't even make love to me," she finished in a very small voice.
Cadmia blinked, confused by the change of subject. "Excuse me?"
"He wouldn't make love to me," she said. "All the times I threw myself at him and he said no, that we needed to wait, it was so frustrating. He was so damn Quin. And I know why now. Why does it hurt more knowing that? He might be a sorcerer, but I can barely even think of that. But I find him with . . ." She trailed off.
"He's not sleeping with Umber," Cadmia blurted out before she could think better of it. Why hadn't she thought? Her only excuse was that Hansa had said he didn't intend to have anything to do with Umber after rescuing Pearl. It never occurred to her the spawn might be there when she encouraged Ruby to talk to her fiancée.
"Even you know about it?" Ruby gasped.
"I think this is a conversation for just you girls," the first mate murmured, distancing himself a little.
"I know he isn't," Cadmia asserted. "I . . . Umber and Hansa were helping me find someone. If you saw something—"
"I saw something," Ruby spat. "I saw them together. Saw even the knife."
The second change of subject made Cadmia wince. It would probably be better for everyone if Ruby just thought Hansa was attracted to men—what the Quin considered "sexually deviant." That charge could result in his losing his position in the 126, but it wouldn't get him executed. "Excuse me . . . knife?"
"Sister, tell me he's innocent," Ruby challenged. "Tell me I did not see my fiancé in the arms of another man, both wine and blood on his lips. Tell me I didn't see him nearly dead one moment, and then find him perfectly healed only hours later. Tell me Winsor Indathrone himself wasn't fooled by some mancer trick. Tell me . . . tell me that everything I believe isn't a lie."
"I—" Cadmia knew she should lie, but Ruby's words highlighted all her own doubts and fears. She saw the cost of her hesitation as Ruby's desperation hardened to peaceful resolve. "Ruby, come away from the rail."
"Sister?" Ruby said, her voice sweetly inquiring.
"Yes?"
"You . . . you and all the holy orders . . ." Ruby leaned close and continued in a whisper. "You're all full of shit."
Without warning, she shoved Cadmia, sending her sprawling. The first mate cried out, but his first instinct was to try to catch Cadmia, so he wasn't fast enough to stop Ruby as she turned, boosting herself onto the ship's rail—and over. The quiet splash was barely audible over the general bustle of the docks.
Shouts rang out and several sailors ran toward the railing.
"Merciful Khet," the first mate whispered. Despite the frigid weather, he and two others started to pull off their boots and drop heavy jackets to the deck in a frantic rush. Cadmia stared down at the dark water, but didn't see Ruby resurface.
"Lydie, get off the ship, bring back blankets, hot rum," the captain ordered his cabin girl, who jumped to obey. "Grent, Taylor, help her."
Everyone moved as if there was a chance, but as precious seconds ticked by, Cadmia knew it was going to take more than hot rum and blankets to fix this. They would be for the valiant rescuers who were only now easing themselves into the water—carefully, because diving headfirst into the mess of lines, chains, nets, and weeds that filled the harbor was a recipe for . . .
Well, for suicide.
My fault. I knew she was hotheaded and impulsive. I knew she had just lost a lifelong best friend. I sent her to Hansa—
No! She couldn't think that way. Yes, Ruby had been upset. Cadmia had sent her to talk to the man she still loved, with whom she should have been able to share her grief and express her fears. Instead, Ruby believed she had found proof not only that her intended was disloyal, not only that he was involved with a man in conflict with all Quin dictates, and not only that he was involved with sorcery, but that somehow he had fooled everyone, including the most powerful man in Kavet.
If you thought you had been wrong about all of that, how could you possibly trust anything you believed to be true?
Cadmia stepped back from the rail, so the deck blocked the rescue efforts from her view. No one was paying any attention to her when she turned and ran back toward the city—toward Hansa Viridian's house.
She didn't know what Hansa had gotten involved in, but if he had power, maybe it would be enough to save the woman who had loved him. After, Cadmia would make him talk to her and she would decide if he needed to be reported to the Quin.
If you really thought he was guilty, you wouldn't risk talking to him. What are you hoping to learn?
First she needed to see if Hansa could save Ruby. Then she could decide what to do about her own faith.
CHAPTER 21
"Hansa, wake up, or I swear to the Abyss I'll—"
The combination of the shouting and a slap brought Hansa out of his nearly comatose state.
" 'Kay, okay," he grumbled, struggling to open his eyes. "Okay. Stop hitting me."
"Hansa, you need to—"
He finally focused his gaze and discovered that the woman who had been abusing him was none other than Cadmia Paynes. "How'd you get in here?"
"The door was unlocked. Hansa, you have to get up now. Ruby's been hurt."
Hansa sat up so fast his head spun and he gagged. He hadn't felt this hung-over since a poorly conceived overnight trip with Jenkins, Ruby, and a bottle of cheap rum when they had been teenagers. "What's wrong with Ruby?"
As soon as he asked, he remembered. "Ooh . . . oh, no." He pressed a hand to his temple as he climbed to his feet.
"I don't care if you're sleeping with the spawn or making deals with the Abyss," Cadmia said, her voice frigidly controlled, "but if this is your fault, then it's your responsibility to make it right." She threw a shirt at him, which he fumbled at, trying to remember how to put it on.
"I'm not—"
"I just said, I don't care," she snapped. "Hurry up!"
"Ruby left me," he said. "I didn't . . . I mean, there's nothing to make right. We're over."
"I figured that when she said she—oh, never mind!" Cadmia snarled. "Didn't you hear me say she's hurt?"
He had, but he hadn't been awake enough to think about it. This time the words reached him. "Hurt how? Is she okay?" He managed to get the shirt on. He misaligned one pair of buttons, but Cadmia didn't wait for him to fix it before she threw more clothes at him, followed by socks and boots.
"If she were okay, I wouldn't have come here!" Cadmia shouted, as he hustled to finish dressing. "Come on."
Heart pounding again now, he raced after her, pulling on his boots as he stumbled with her out the door. "Where are we going?"
"Docks," Cadmia answered. She was already nearly sprinting; he loped after her, his long legs keeping up easily despite his care not to slip on the still-falling snow.
"What happened?" he managed to gasp.
Cadmia shook her head.
When they reached the docks, a man in the garb of a sailor grabbed Cadmia's arm. "Sister, where have you—"
"Where did they bring her?"
The man dropped his gaze. "They brought healers from the Napthol, but . . ."
Hansa listened to the exchange, and felt all the warmth drain out of his body. "What happened?" he said, his voice little more than a whisper.
"Who are you?" the sailor asked.
"This is Hansa. Ruby's fiancé," Cadmia said.
The man's eyes widened. "I'm sorry," he said, words broken. "They . . . she's at the King's Ransom. We had to send for the Quinacridone to . . . to pick her up. I'm sorry," he said again.
Hansa leapt ahead. Both of them hurried after him, but he was barely aware. They couldn't mean what he knew they meant. She couldn't be dead. She was alive just a few hours ago. She was fine.
He fell into the door of the King's Ransom, and was instantly cussed at by a man who had been on the other side.
"Where's Ruby?" he demanded.
The man looked at him as if he were mad—which was probably how he looked. "Who?"
Cadmia had caught up. She guided him inside. "This way," she said softly. Behind them, the sailor was giving their apologies to the person Hansa had nearly knocked over.
"You can't—"
Hansa glared at the maid who tried to keep him out of the room where Ruby lay. A single candle by the bedside provided the only light. Even in the flickering, rosy glow, reflected by an absurd glass vase full of silk flowers, Ruby's skin was icy pale, her lips white, her fingertips blue.
The sailor was speaking to Cadmia in the doorway. He probably thought his voice was soft enough that Hansa wouldn't hear, but Hansa had discovered that the world seemed to have gone very quiet. He could hear his own pulse. He could certainly hear this man's voice. "It took too long to find her in the water. The doctor is still worried about the first mate, he was so frozen by the time he brought her out. She never even woke."
Hansa gripped Ruby's hand. "What was she doing at the docks?" he managed to choke out.
"Trying to find a ship from Kavet," the sailor said.
He dropped his head. Ruby's hand was cold. Cold. Her normally bright eyes were closed, but it wasn't like people said. She didn't look like she was sleeping.
"I'm sorry," he whispered. "Ruby, I'm sorry . . ."
She was trying to get a ship, yes, but not away from Kavet: away from him. He had been willing to lose her, but not this way.
"I'm sorry," Cadmia said, her soft words like barbs. "I should have told you more gently, but I thought if I got you here in time, maybe you could . . ." She trailed off, clearly deciding she had been wrong.
She wasn't wrong. There was one thing he could do.
When he had asked Umber if he could bring Jenkins back, the spawn hadn't said, No, it's impossible to revive the dead. He had said that, given how Abyssi kill, there probably wasn't enough of the body. He was looking at Ruby's body, which was whole and unmarred as long as he ignored the blue cast of her skin.
He reached over to the absurd vase of decorative flowers: silk lilies, in what looked like hand-blown glass. It didn't matter much; it shattered as he brought it down on the corner of the nightstand.
The sound seemed to go on and on. It took him a few seconds to realize he wasn't just hearing breaking glass, but shouting, from Cadmia and the sailor.
It didn't matter what happened to him after this. It was about time he accepted responsibility for the choices he had made. It wasn't his fault the Abyssi had injured him or that Umber had saved him the first time; if they had executed him then, it would have been unjust. That didn't absolve him of meddling with powers he knew were treacherous. He had been furious that Xaz was so close to Ruby because it was well known that, even when a mancer did nothing intentionally malevolent, the powers they worked with were dangerous to anyone around them.
He knew all that. He meddled anyway. Ruby paid the price.
He picked up one of the shards of glass. Cadmia grabbed his wrist, trying to stop him.
"Hansa, calm down," she said. "Calm down. You don't want to hurt yourself."
"I'm pretty sure he's not trying to hurt himself," came the sailor's voice.
"I'm doing what you wanted," Hansa said. "I'll be fine." Fine wasn't exactly true. He would be arrested and executed. All that was okay, though, if Ruby was alive.
Cadmia was holding both of his wrists, but that didn't matter. He heard the other man say, "Sister, maybe you should leave him alone," as he closed his hand around the glass. He just needed blood.
The glass sliced across the inside of his fingers and his palm. He whispered, "Umber, get your ass in here."
Cadmia's eyes widened.
"This was a bad idea," she whispered. The sailor clearly agreed, since he had already run out, probably on his way to get guards. It didn't matter; Umber hadn't had any trouble getting past guards in the Quin compound.
"You should probably go," Hansa told Cadmia. "You don't want to appear involved." Once again, that tight feeling in his chest made breathing and speaking difficult. Or was that panic? Or the lingering residue of last night's adventures?
"Hansa, I was wrong," Cadmia said. "I wasn't thinking clearly. You're not thinking clearly. A terrible thing has happened, but . . ." She shook her head, and murmured as if to herself, "They say an impulse you can't explain is caused by the Others whispering in your ears."
"I feel like I'm thinking more clearly than I have been in days," Hansa said. He had started this. He would finish it.
"I don't think you—"
Umber interrupted her, storming into the room with the words, "Hansa, what in the three planes do you think you are—" He broke off as he took in the scene. "Hansa, don't do this."
"Hansa—" Cadmia tried again, but Umber held up a hand, silencing her.
"Sister, go get a drink or something," Umber said. "Make sure we aren't bothered."
A moment later, Umber, Hansa, and Ruby were alone.
"You can bring her back," Hansa said.
Umber winced. "You absolved me of this, Hansa."
"But you can."
"Alone? No," Umber replied. He kept his tone even, trying to sound reasonable, but Hansa was past being reasonable. "I can heal, but she's dead, Hansa. Look at her. She's frozen."
"Could a necromancer bring her back?" Umber had implied that in the jail cell, too.
"Probably, but—"
"Then find one!"
"Hansa—"
"Don't argue with me! She died because of me, because of us. Because I wanted—"
"To live?" Umber suggested. "To save a young girl? Hansa, you haven't done anything wrong. You aren't responsible for her choices."
"She doesn't really have any choices left, does she?" Hansa demanded. "If I had had any sense at all, I would have let go of her when she first tried to leave me. Instead, I committed the crime she had broken the marriage off over in order to manipulate her into forgiving me. Into begging my forgiveness. I could have just asked you to save me from rotting in that jail, but did I stop with that? No. I let you make me into some kind of hero. Maybe that's why the Quinacridone says pride is so dangerous."
"Self-pity is dangerous, too, Quin," Umber warned. "It can make you do stupid things. Take a deep breath and remind yourself that sometimes bad things happen. We can't control everything."
"What happens to suicides?"
"What—what?" Umber asked.
"Suicides. Napthol and A'hknet both mostly say suicides . . ." His voice choked off.
"I don't know where they go," Umber said. "And even in the Order of the Napthol, individuals disagree about exactly what happens in the afterlife."
"She was good," Hansa insisted. "I've known her since we were little kids. She doesn't deserve to end up in the Abyss because of what I did."
"Hansa, why don't we go get something to eat and put you back to bed?" Umber said gently. "There's nothing you can do."
"You said a necromancer could help her."
"Neither of us is a necromancer," Umber pointed out.
"You could get one."
"Let's not go down that road, Hansa," Umber said. "The last thing you want is to get more mancers involved in your life."
"I've messed up my life already. I'll deal with that when I come to it. Ruby shouldn't pay for what I've done. I know you say it's not my fault, but if I'd been the person I pretended to be, then we wouldn't be in this mess because she never would have had reason to doubt me. Bring her back."
"Hansa, I can't—"
"Find a necromancer," Hansa demanded, "and make him bring her back. Convince her they saved her, convince everyone they pulled her out of the water in time. I know you can do it."
"Hansa, you don't want to do this," Umber said. Pleaded, really. "Let her go."
"I don't care what happens to me—"
"I rather care what happens to you, since my doing this would mean cementing the bond between us. Do you understand that? There are ways to work around the bond, usually. All spawn know how to do it. You make deals, tit for tat as it goes, like I agreed to help Pearl for Cadmia in exchange for her silence. I could have silenced her myself, and I would have helped Pearl in for nothing, but sometimes power does things we don't expect. Making a 'fair' deal keeps the scales even and keeps a bond from forming."
"So what do you want?" Hansa asked. "Make me a deal. I'll do it."
"You don't understand what you're saying," Umber said, speaking very clearly and slowly. "Spawn do not associate with mancers. There is nothing you could possibly offer me that would convince me to make any deal that forced me to not only seek one out, but do whatever was necessary to get one's help."
"I don't need to convince you."
"Which is why I am trying to convince you that you do not want to do this."
Hansa picked up another shard of the vase. It glistened in the candlelight.
"Blood to seal the boon, right?" he asked.
"Hansa, listen to me," Umber argued. "The third boon creates a permanent bond. Permanent. There is no way to break it. The symptoms of that bond vary drastically, but it is possible that you will lose all you are and become so obsessive that I'll have to lock you away."
"That's the risk I'll take, then. You know what I want."
"You don't want this," Umber sighed.
"Not really," Hansa said. "But I don't see a choice." He held up the shard of glass, examining the edge. "Do you have a preference of location?"
"Don't do this."
"I imagine the longer we wait, the more difficult it is going to be to bring her back," Hansa said. "We should get on with it."
Speaking very quietly, his gaze not leaving the shard of glass Hansa held, Umber explained, "I don't even know if I can do what you're asking of me. Even if I can find a necromancer, there is no guarantee he will agree to help, or that this will be within his power." He reached out slowly, attempting to remove the glass from Hansa's hand. When Hansa resisted, Umber held up his own knife instead. "It's my blood we need for the third boon, anyway. So listen to me: I will try to find someone who can help. I will do everything within my power to bring him back here, and you and I can attempt to find a way to convince him to do what you want." He pulled the knife blade across the flesh of his forearm, but instead of offering the wound to Hansa, he tore a strip from his shirt and awkwardly bandaged the wound. "You can still choose not to seal this boon. I ask that you wait to decide until I've done my best to discover if I'm even capable of fulfilling this demand. And in the meantime, I beg you to consider carefully whether, when I return, you really want to do this."
Hansa nodded, gripping Ruby's cold hand in his uninjured one.
Umber turned to go, but paused one more time in the doorway to say, "You know there's a chance that, if I go out searching for a mancer, I may stumble across the wrong kind and not make it back?" When Hansa just nodded again, Umber shook his head and hissed, "Bastard," under his breath before he stormed out.
CHAPTER 22
The falling snow meant Xaz had an excuse to keep her head down and her hood up as she walked through the thinning harbor crowds. She thought she had managed to put a veil over her power, but wasn't confident about it. Thankfully, the sight was rare and sighted guards were rarer, so she thought she would be safe as long as no one recognized her face.
When Alizarin returned from hunting and she told him her plan to find the spawn, the Abyssi didn't ask why. He was too thrilled by the idea of seeking out the spawn—who he called Umber, and who he felt would be more amicable to his advances than a Numenmancer—to ask why.
She had planned to go up to the city to start her search for Hansa, but the bustle at the waterfront caused her to detour. She heard Hansa's name whispered by more than one person—Hansa's fiancée, she thought—but that wasn't what drew her attention. The docks hummed with cold power, as if another Numenmancer had been there. Who? Even if Hansa had become a mancer, his power would come from the Abyss. How was he involved with anything involving the Numen?
You're a Numenmancer. How were you able to summon an Abyssi?
They stumbled across Umber before they found the guard. He greeted her with a dry, "Mancer. I can't say it's a pleasure to see you. Excuse me."
Xaz shivered as the spawn she had come here to find moved past her. "Wait, please," she called after him.
He turned slightly, waiting for her to continue.
Alizarin pranced toward Umber, unconcerned about the snow around his bare feet or falling on his fur, beyond a slight twitch of his ear when a snowflake dropped onto it. "Xaz has been feeling a little sexually frustrated," he announced blithely. "Think you could help?"
Xaz fought a blush as Umber lifted one sardonic brow, amused. "Sorry . . . Xaz, you're not my type."
This time as he tried to push past her, she caught his arm. Her grip wasn't strong, but he winced. Xaz noticed the blush of blood on the fabric of his shirt.
"You and your mancer having some difficulties?" she asked. The only time Abyssi or spawn actually bled was when they meant to spill power. A wound that stayed open meant something was unfinished—a dangerous state which left the creature vulnerable. Even Xaz, who had no natural tie to the Abyss, could feel the weakness.
Umber pulled his arm out of her grip. "I would believe that the lovely Abyssi sought me out entirely for sex—and I'm flattered, Alizarin, I really am, and I would love to take you up on the offer if I weren't in the middle of something already." Alizarin purred at the praise. "But you, Mancer, want something or you wouldn't be here. Spit it out so I can say no and we can move on."
Alizarin rested his chin on Umber's shoulder, looking bored. As Xaz had suspected, he was far too interested in Umber as entertainment to consider that his knowledge might be a threat. Umber leaned back against the Abyssi, and Alizarin wrapped his arms around his waist.
Xaz said, "I need your help. Can we maybe talk somewhere more private?" This wasn't the kind of conversation she wanted to risk having overheard.
The spawn actually laughed out loud. As if struck by a sudden idea, he twisted to speak to Alizarin. "Darling, you don't happen to know where I might find a necromancer around here, do you? Ideally one powerful enough to raise the recently dead, but easily bribed."
This time it was Xaz's turn to snicker. "You are looking for a mancer? You really are in trouble, aren't you?"
"If you could help me," Umber continued, now completely ignoring Xaz as he addressed Alizarin, "I'll have plenty of time for more enjoyable activities when I'm done."
"If you help me first," Xaz offered, "I can cast a finding spell. I think I should be able to locate a necromancer for you."
Umber's focus returned to her. "What do you need? I don't have much time."
"Can't we go somewhere—"
Umber interrupted her with a half grunt, half snicker. He looked from her to Alizarin—who was watching the crowds hustle past them with apparent fascination—and then back to her. "You want me to strip the Abyssal taint from your magic." Alizarin either hadn't heard or didn't care, so Xaz nodded. "If the Abyssi cooperated, I might be able to, but not in this state." He held up his wounded arm. The small bloodstain had spread slightly. Whatever he had begun, he would be leaking power until it was done, or risk the magical equivalent of bleeding to death. "If you can find a necromancer—"
This time it was her turn to interrupt with a humorless laugh. "I would need tools I can't get until the Numini will talk to me again." The spawn might be powerful enough to break in to wherever the Quin kept such things, but again, it was clear he couldn't do much at that moment.
Alizarin apparently had been listening. He turned to ask, "You need a body resurrected?"
Umber nodded. "If it can be."
Alizarin brightened. "I could eat it," he suggested. "Then it can't be raised."
It was obviously, for the Abyssi, a reasonable idea. Umber even responded to it as such, though he regretfully explained, "It's long cold."
Alizarin frowned. "Necromancer," he said. "They don't even go to the temples."
"I know," Umber replied. He didn't seem to mind that Alizarin's hands had drifted, so one wrapped around his waist but the other rested on top of the open wound. "How do we find one?"
"Kill something?" Xaz suggested sarcastically.
The two men looked to each other thoughtfully, apparently taking the suggestion seriously.
Seeing the contemplative looks, Xaz had to point out, "If a necromancer came running every time someone died, your corpse would already have one."
"Good point," Umber conceded.
"Abyssi are drawn to Abyssumancers. Numini are drawn to Numenmancers. The living are drawn to animamancers. Could the dead find a necromancer?" Umber asked Xaz.
"Not being a necromancer myself," she said, "I neither know the answer to that question, nor how we would expect to make a request of one of the dead even if it were true."
"Is it true," a soft voice asked from the doorway behind them, "that those devoured by the Abyss dwell in the Abyss?"
The three of them turned to see a slender woman with a strawberry-blond braid and tawny hazel eyes. Xaz's heart leapt into her throat as she recognized the violet robes of a Sister of the Napthol and she cringed in anticipation of the bloodbath that might follow.
Alizarin answered, "Yes. For a while."
The woman frowned, her eyes narrowing as she searched the area. She shouldn't be able to see the Abyssi without a mancer's power, but a Sister of the Napthol was likely observant enough to notice the way the rest of them looked toward the apparently empty air.
The Sister spoke to Umber directly. "Is it true?"
"I've heard that," he answered. He didn't seem to feel that this woman was a threat. "Do they teach you to eavesdrop at the Cobalt Hall?"
"They teach us to attend to important conversations around us," the woman said. "The Order of A'hknet taught me to eavesdrop. Am I right this is the Numenmancer they tried to arrest the day Hansa was nearly killed?"
Umber nodded. Xaz was ready to flee, but so far, this Sister didn't seem inclined to raise an alarm.
"Is the Abyssi here, too?"
Alizarin smiled proudly as Umber said, "That would be true."
"Then you have eleven souls in the Abyss. Eleven dead, to whom your demon has a blood-connection. Have them find your necromancer."
"Pardon me," Xaz said tightly, "but who in the name of Numen are you, and why are you helping us?"
Umber performed the introductions. "Xaz, this is Cadmia Paynes of the Napthol Order, and I believe she is trying to help me, not us, because I did a favor for her recently."
"Okay . . ." Xaz said, still nervous about the stranger in their midst. The Napthol Order wasn't a large step away from the Quinacridone. "So, you're saying we send Alizarin into the Abyss." If she could do it right, that might be a good way to lose him—though she decided not to say that bit aloud. "And have him . . . what? Tell them to find us a mancer? Why would they want to help us?"
"Tell them if they find you a necromancer, you'll guide them to the Numen. That is your realm, isn't it?"
Was that possible? Xaz had never spoken to the dead and gave little thought to the afterlife. If encouraging the Abyssi to go back to his native plane willingly didn't sever his bond to her, perhaps the Numini would be pleased by her attempt to guide the souls she had bloodied back to them.
"Let's move this conversation somewhere more private," Umber suggested. "We'll go back to the King's Ransom. If we're lucky, Hansa has changed his mind."
Hansa hadn't changed his mind. He had allowed the fire to go out and opened a window to keep the body fresher, and there was snow drifting in the corners of the room. Even though Hansa had bits of ice caught in his hair and eyelashes, he looked flushed and feverish.
"Hansa, please tell me you've reconsidered," Umber said.
Hansa just shook his head. He didn't even look at Cadmia and Xaz, just stared at Ruby as if hypnotized. Grief? The effect of the open boon? Xaz didn't know enough about spawn and the Abyss to know.
"I—" Umber broke off, swaying; Alizarin caught him with a hand on each of Umber's arms, but the Abyssi's attention no longer looked solicitous. It looked hungry. Umber jerked back without a flirtatious word. "If we're going to do this, we had best do it fast. Hansa, Cadmia has an idea that we can talk to your friends in the Abyss and ask them to help us find a necromancer in exchange for Xaz helping them move on to the Numen."
A little life returned to Hansa's face. He looked around as if just noticing everyone else for the first time. "Can you do that?" he asked Xaz.
Xaz had been braced for him to react to Alizarin's presence, though she wasn't sure if she expected panic due to his near-death or fascination due to his new mancer power. Instead, Hansa's gaze skipped over the Abyssi as if he were invisible. She didn't question the fortuitous turn; they didn't have time to waste. "I think I should be able to," she said. "I've never tried anything like it." Despite her resolve not to spend time on unnecessary confrontations, recriminations, or questions, she couldn't help adding, "I never meant to hurt them, or you. I thought I was summoning a Numini. I thought . . ."
She trailed off when Hansa looked away, the grief briefly so plain on his face that she couldn't stand it. He asked Cadmia, "Why are you here?"
The question seemed to take the Sister of the Napthol aback. "I . . ." She frowned, clearly puzzled.
Once again, Xaz glimpsed the swirl of the Numen power she had seen at the docks. Ruby's body was painted with its residue, and it actively clenched around Cadmia as the Sister of the Napthol tried to consider her actions logically.
Before Xaz could examine the trace, Alizarin distracted her by reaching to Umber again. This time, the hand that brushed Umber's arm had claws that drew fine lines of blood from the spawn's skin. Umber jumped, pulled back with a hiss, and snapped, "No." He turned to Hansa. "Hansa, call this off or don't, but do it now, before I'm too weak to do anything to help and the Abyssi decides I'm nothing but meat."
Hansa's eyes had momentarily cleared as Xaz spoke to him and he questioned Cadmia's presence, but now they fogged again as he returned to his contemplation of the dead woman. "I'm not calling it off," he said.
Umber unwrapped the bandage on his arm. "Then seal this boon, and I will quite gladly drag you into the Abyss with me."
Xaz tried not to look, but her gaze was morbidly drawn back. A burst of hot power like the breath of some immense animal wafted through the room as Umber revealed a wound that was not only slowly bleeding, but had also blackened around the edges. As Hansa pulled Umber close and set his lips to the wound, that breath drew back in until the power coiled tightly around the two men and the room went cold again.
The next seconds that passed seemed unnaturally peaceful, almost romantically gentle. Xaz's gaze traveled out the open window, to the driving snow turning the world to white.
Is it warm in the Abyss? she wondered.
Part 2
"This is not what you promised me!" The Abyssi snarled and whined, his voice replete with the offensive blend of arrogant and juvenile that seemed the province of the creatures of the infernal realm.
The Numini drew back, disgusted. "Promise," it echoed. "I would never make a promise to one of your kind. All I have done is try to clean up the mess you have created."
The Abyssi growled. If it could have reached across the realms with its body in addition to its awareness, it would have pounced on the Numini, heedless of the death that would have immediately followed. "The blue prince," it said petulantly. "He killed my mancer. I want his."
The Numini did not need to reply in words. The blue Abyssi, Alizarin, had bonded himself to a Numenmancer. Even this low creature surely knew better than to threaten one of them while speaking to a lord of the divine realm. The bridge of power that allowed them to speak became rimed with frost and sparked with arcs of blue electricity.
"Then I want something else of his," the Abyssi said, compromising in the face of the Numini's wordless threat.
"I agree that Alizarin has been a . . . complication." The Numini sighed. "I understand that he often meddles with others' property. Deal with him as you see fit. I will see to the rest."
CHAPTER 23
Cadmia hadn't felt this right about her life in a long time. She had been feeling extraordinarily anxious for a while there, but now she couldn't remember why. The plan to help Hansa, help Ruby, and help the guards who had died was a good one, and she was glad she had been able to suggest it.
She was blind to the Abyssi itself, but she could see all too clearly when the air tore, leaving a jagged scar in reality that could only be the rift to the Abyss. Snow swirling in through the open window became steam as it struck the rapidly growing rip, which quickly became a doorway-sized hole leading to tarry darkness. A twinge of unease tried to pierce her meditative calm when she saw the portal the Abyssi had opened so they could step into its native realm in search of the slain guards.
Calm, calm, the snow around her seemed to whisper.
How much power must it take to cut a portal like that? "It probably won't stay open long," she said, when none of the others seemed inclined to step forward. "We should go."
Umber caught her arm when she moved to lead the way. "You can't really intend to go with us," the spawn said.
What a funny moment to question her. "Yes, I do," she asserted, and then put action to her claim and walked into the rift.
Like the nursery-rhyme child whose cradle tumbles when the wind blows, she plummeted into a harsh reality. She had been wrapped in a warm blanket of peace and contentment, and completely unaware how unnatural that calm was until it was ripped brutally away. There had been something . . . someone . . . with her, but they were gone now. She was achingly alone.
Not alone.
Her skin crawled as the last few minutes caught up to her, and she remembered who had come here with her. The half-Abyssi spawn. The Numenmancer. The Abyssi.
What have I done?
She turned, hoping futilely that the rift would still be open and she could go right back through it. Instead, her eyes found the creature she had been blind to on the mortal plane, and the sight of it made her blood run cold.
Its shape shifted, never holding a single, identifiable form, but there was no mistaking what it was: Feral. Hungry. Vicious. Cadmia couldn't make out teeth or claws, but she knew in her gut that it had those things. And in the primitive, furthest-back portion of her brain, she knew that if she didn't get away . . . if she didn't run . . .
"Hold it together, Hansa," she heard Umber say. She looked past the Abyssi to find Umber with a hand on Hansa's arm, clearly trying to stop him from bolting. Both men were wreathed in a hazy indigo glow, Umber's brighter than Hansa's. "Breathe. He's on our side."
"Thank Numen he is," Xaz whispered. She was furthest back, as if she had come through the rift last before it disappeared. The light she emitted was gray-yellow, like the first breath of sunrise on a foggy spring morning, but so faint it seemed to disappear when Cadmia looked at her directly.
Hansa's panic gave Cadmia the strength to quash her own. She forced herself to turn away from the Abyssi. Ancient instincts screamed that doing so was deadly, but she was more than her instincts and refused to be ruled by them. Instead, she looked around, to confirm they really were in the realm whose name was synonymous with all that was cruel, avaricious, and venal.
The ground was rolling black sand littered with bones—or maybe they were shells, though unlike any found off the shores of Kavet. Many had sharp barbs. Most were deep, rusty colors instead of the bleached white or dull black that most often washed up on Kavet's shores. All hinted at creatures more fierce than a clam or a snail, like an ash-colored claw as long as Cadmia's forearm that lay, empty, inches from her feet. What kind of creature left a shell like that?
What kind of creature killed something with a shell like that?
The answer to that question came in the form of a chorus of low, bone-quivering growls. She looked up to see a trio of beasts that looked a little like wolves, though their low-slung front shoulders bristled with spines, their heads were flat and wedge-shaped like snakes, and their fur was the color of slick blood. Cadmia froze, her breath turning to lead in her lungs.
The Abyssi flowed in front of the mortals and advanced toward the three scarlet beasts. When it struck them, the wolflike creatures scattered and tumbled, letting out pained, yipping cries as the personified darkness wrapped around them. A whiff of scalded fur reached Cadmia's nose, and then the Abyssi moved on, leaving only a few fragments of red fur and gray bone behind.
She swallowed thickly.
Don't you dare run, she told herself as the Abyssi approached again. If it wanted to kill her, she wouldn't be able to stop it. If it was an ally, she needed to be able to look it in the . . . face? Cadmia locked her knees and forced herself to stand.
"Thank you," she managed to say. Her voice came out a tight squeak, but she was proud of herself for making it work at all.
The longer she stared into the darkness, the easier it became. The visceral terror that had nearly overwhelmed her edged aside and she noted the colors—sparks like firefly lights, but in a thousand unnamable hues—that danced inside the shadow. They swirled and blinked, hypnotic, like the will-o-wisps whose beauty drew unwary storybook travelers to their doom.
Her voice under control at last, she asked, "Are we . . . safe now?" She hesitated on the word, because if they really were in the Abyss, they certainly were not "safe."
The creature shrugged. How something made of pure amorphous terror could shrug, or how it could be perfectly clear that was exactly what it had done, Cadmia wasn't sure. However, the gesture was very human, almost comical, and made her relax further.
"From the red dogs, for now," the Abyssi said. "They can't best an Abyssi."
Cadmia would have expected its voice to be a growl or a hiss, as much animal as human. Instead it bordered on musical, like something you would expect crooned to you by a would-be lover.
Xaz asked, "Can you go back to your normal form?"
"The lovely form with the blue fur, she means," Umber clarified before the Abyssi could respond. "It's easier on mortal minds."
Cadmia braced herself, every description of Abyssi she had ever read running through her mind. She knew fur, scales, tails, and claws were normal, as were poisonous barbs and razor-sharp spines and—and what do you really know? she chastised her thoughts. What Order scholars have actually seen what you are now seeing now?
The thump her heart gave as smoke and shadow condensed was not entirely anxiety.
Where a moment before there had been a creature from nightmare, now there was a creature who stood like a man—or, almost like a man. The Abyssi balanced on the balls of his feet. Iridescent cobalt and turquoise fur, a lashing tail, and soft, tufted ears made it impossible to mistake him for a human.
"Is this better?" he asked, tilting his head.
"Much," Xaz breathed.
The Abyssi had long, silky black hair in addition to its fur, and the quizzical gesture caused several strands to fall forward and caress one cheek. Utterly inappropriate, the part of Cadmia that had grown up in the Order of A'hknet and had been trained to put a value to everything piped up to say, If it weren't for the fur, that face could earn a lot of money down at the wharf. Dramatic cheekbones, full lips, heavy white lashes around wide blue eyes.
Alizarin smiled, and Cadmia felt a brief panic that he had heard her thought. Could Abyssi do that? But the expression was open, engaging, not the sly, knowing look of a man who had caught a woman staring.
"Stronger Abyssi only take on solid forms to communicate with mortals, or for play," Umber told Xaz, oblivious to Cadmia's uncomfortable moment. "His normal form is the one we saw a few minutes ago."
"Oh," Xaz said.
It was time to get back on task.
As soon as Cadmia could remember what that task was.
She remembered the plan she had proposed, but not why she had suggested it.
"We're . . . looking for the shades of the slain guards," she said hesitantly, speaking aloud to try to make sense of her own jumbled memories.
"Tell me again," Umber drawled, "why you felt the need to come with us?"
Cadmia opened her mouth to reply, then closed it without speaking. Why had she done this? She had run to Hansa thinking he and Umber might be able to heal Ruby, or possibly revive her with magic. How had that goal morphed into necromancy, resurrection, and an intended trek through the Abyss?
Hansa was also frowning. Tentatively, he admitted, "I don't entirely understand why we're here."
"Because you're a brat willing to use power you don't understand to get your way," Xaz snapped. She rolled her shoulders like someone who has slept in an uncomfortable position. "Or have you forgotten hysterically demanding that Umber save Ruby?"
Hansa paled, and stared around as if the answers might be found on this desolate stretch of shell and bone-littered beach—if you could call it that, since where the water should be there was only an endless stretch of porous rock, which undulated like frozen waves. The sand, like the stone, was black and sparkled like raven feathers. Its beauty was only marred by Cadmia's imagination telling her what creatures might come out of the dozen dark caves she could see among the stone sea.
"I . . . did," Hansa said, sounding as if he would like to deny it. "And then you came. And you." He looked first at Xaz, and then at Cadmia. In his eyes she could see the desperate need for reassurance that was ever in the eyes of a man who has done something unforgivable.
"We'll talk about it later," Umber murmured. "We have more company on the way. Alizarin, am I right that the upper-level Abyssi respect my kind's right to claim property?"
"That is correct."
"Upper-level?" Cadmia asked, before immediately adding, "Never mind. It's not a good time for questions."
Hansa let out a startled protest as Umber reached out, wrapped an arm around his waist, and pulled the guard tightly to his side. Cadmia had an instant to wonder if he would further object to being considered "property," and then Alizarin stepped up and casually looped his tail around her waist.
The Abyssi's current form was beautiful, but Cadmia had seen what Umber called its "natural" form, and she had seen what it did to the red dogs that threatened them. The only thing that kept her from screaming when she found herself suddenly clamped to Alizarin's side was long years of rigid self-control. Her chosen vocation required her to listen to the worst horrors the human race could manage, confessions from men and women who had committed atrocities most people assumed were confined to the Abyss, without flinching.
He was protecting her, so it would be stupid to argue and fight to get away.
She thought he was protecting her.
She hoped so, anyway.
Meanwhile, the creature coming toward them seemed to be Abyssi, though it wasn't like Alizarin. Its body was slender and serpentine, its skin slick, and its eyes cold and slitted. Its six limbs were thick like a lizard's, though it seemed to disregard them as it moved in long undulations of its snakelike body.
The new Abyssi paused before them and bowed to Alizarin, bending armored front legs and dropping a diamond-shaped head with long, glistening fangs in a deferential bob. Then it rose up like a snake about to strike, front legs—arms?—folded across its scaled gray torso. When it spoke, the sound was like claws on stone, a fierce etching noise that made all the hair on Cadmia's body rise.
"You bring gifts for the royal court?" it asked optimistically, its head sliding side to side as it looked at their assembled group.
Alizarin grinned, but Cadmia didn't think it was a happy expression. It showed too many sharp white teeth. "You were rude about my last gift."
The lizard-Abyssi seemed puzzled for a moment, as if he wasn't sure what Alizarin meant by "rude." Then he took a half-wriggle back, maybe a flinch. "He was my protector," the Abyssi wheedled. "You killed him while I was sleeping, and I didn't even get to eat him."
The silly notion that Abyssi were very like human beings, an idea that had been formed from Alizarin's shrugs and grins, disappeared from Cadmia's mind as she tried to parse what the lizard-Abyssi had just said. He was my protector . . . I didn't get to eat him.
The lizard-Abyssi took another step back and said, "Antioch has been in a rage. He says you got his mancer killed. If you give us gifts, maybe we can help you with him?"
Alizarin's grin faded and his tail lashed, releasing Cadmia. She desperately hoped he was irritated by the other Abyssi pushing the idea of gifts, and wasn't concerned enough to be considering it. Umber's question suggested that Hansa was considered his property, and she doubted Alizarin wanted to get rid of his mancer. That left Cadmia.
"He is a prince of the fourth level," the lizard-Abyssi said, Alizarin's reaction making him bolder. "You are only of the third. You will need help."
Some of the older texts in the Order of the Napthol's most restricted libraries spoke of the "levels of the Abyss." Cadmia had always thought it was euphemistic until now. If this Antioch was of a deeper level than Alizarin, he was stronger.
"He is fourth-level chattel," Alizarin answered in a grumbling voice that bordered on a growl, "and you are a lord of the high court only because I slew all the Abyssi there stronger than you. These four are mine." His tail wrapped snugly around Cadmia again, emphasizing his point. "If you touch them, I will eat you. Now go away."
The lizard-Abyssi didn't stay to argue with the threat in Alizarin's voice, but turned and fled across the black dunes of sand in the direction from which it had come.
"I think I probably speak for the group," Hansa said, his throat so tight with tension that his voice came out a soft rasp, "when I say we should finish what we came here to do and then leave as quickly as possible."
"Is this Antioch likely to be a problem for you?" Umber asked.
"Did you kill his mancer?" Xaz sounded like she was taking that more personally than the threat to the rest of their safety.
"I didn't kill him," Alizarin huffed, responding only to Xaz. "Hansa did."
"Excuse me?" Hansa chirped.
"I'm not the one who made him throw the knife away when you arrested him," Alizarin told Hansa, sounding irritated that his role in Antioch's mancer's death was being questioned, and obviously missing the fact that the Quin guard looked terrified as he suddenly realized how many enemies he might have in this place.
The scene came clear to Cadmia.
"Baryte," she said, recalling the name of the Abyssumancer who had asked for her counsel, as well as the stink of burning flesh as he held his hand over the candle, and the abrupt horror of his death. "Antioch was his Abyssi? Is he the black Abyssi Baryte mentioned?" All the puzzle pieces tumbled over and over in her mind, trying to find a pattern that made sense. "Did he somehow call us here?"
"I think we should leave here quickly," Hansa said. Then he winced, as if struck by a sudden pain. "As soon as we've done what we need to do."
He started to lean against Umber, flinched away, and then immediately repeated the action. Umber gave him an opaque look and shook his head, not acknowledging the touch or the comment.
Was he trying to be discreet? Cadmia hadn't thought that Hansa and Umber were lovers, but Hansa's motions had the look of a man trying to resist old habits.
Cadmia drew a deep breath, trying to find the best way to articulate the certainty that had been growing in her since they had stepped into the Abyss.
"We're looking for a shade," she said haltingly, "to help us find a necromancer back in Kavet so you can resurrect a woman whose life is so dear to you, Hansa . . . that we all left her unguarded in a public inn." Since the others didn't seem inclined to clarify why this made sense or argue with her, she continued. "We all seem to have taken extreme measures to accomplish something I'm not sure any of us would ever desire. Unless you really think Ruby would want you to do this, Hansa?"
The guard shook his head fractionally, horror and bewilderment warring in his eyes as he considered his own irrational actions.
Cadmia remembered the old warnings: An impulse you can't explain is the Others whispering in your ears. This time, the Others had done more than whisper, and the result was more than an impulsive walk down to the docks to visit old faces.
But were they done yet? Or were they just now starting to speak?
CHAPTER 24
The last thing Xaz wanted was to focus the others' suspicions on her, but she didn't seem to have a choice. Cadmia was too obviously right; they hadn't done this of their own free will.
"I saw Numen power all around the docks and Ruby's body," she admitted. When the others just looked at her, waiting for further explanation, she shut her eyes to block out their stares and continued. "Ruby was impulsive," she said, remembering the woman who—in another world—might have been her friend. "She had a temper. She wasn't the kind of person who would normally have run off and hurt herself, but a Numenmancer could have convinced her to jump, and then nudged Hansa and Cadmia into reacting the way they did."
"That's crazy," Cadmia objected. "Why would a Numenmancer go to that kind of trouble?"
Xaz snickered. "You two can't imagine why a mancer would think it's funny to trick you into crawling into the Abyss? It wasn't me," she added sharply. "If it were, I wouldn't be with you."
Cadmia's face suddenly went stone serious. She turned to Umber. "What about you? Could a Numenmancer have manipulated you? Or Alizarin?"
Umber shook his head. "Abyssi—though beautiful and powerful, Alizarin, so do not take my words badly—are not known for their forethought or careful analysis when unbridled impulse is an option. As for me, I owed Hansa a boon. That bond isn't something that can be argued with."
"How much power would it take to influence you?" Cadmia pushed.
Umber tensed, and Xaz sensed a defensive reply on the way. He clearly changed his mind at the last moment and said instead, "An Abyssumancer could have forced me to act, but not subtly. Even the most powerful Abyssumancer in Kavet couldn't have tricked me into stepping into the Abyss without my sensing it."
Xaz saw where Cadmia was going with her logic, but hoped there was another explanation. She would far prefer a garden-variety mancer had put them into this position.
"Why did you save Hansa's life?" Cadmia asked the spawn.
Umber ignored Hansa's squawked protest. "He had been tainted by the Abyssi who injured him. If he survived, that taint could have turned him into a mancer. I didn't want to risk it. I told him—"
"Yes, yes, you told him that," Cadmia said brusquely. "I didn't believe it then and I don't believe it now. You could have killed him. Instead you granted him a boon. Why?"
Umber tensed his jaw, and didn't answer.
"Could an Abyssi have done it?" Cadmia asked, looking at Alizarin. "Baryte talked about a black Abyssi. Is that Antioch?"
Alizarin considered, and said, "Abyssi come in many colors. Antioch is ashy."
"Might Baryte have described him as black?" she pressed. Alizarin gave a half shrug, half nod, as if it wasn't the description he would use but he could see why someone might. "Could he have done this? Baryte said he had a plan."
"This is a very intricate plan for an Abyssi," Umber suggested.
"Is it?" Cadmia asked Alizarin.
"For most of us," he answered. Xaz couldn't tell if he was intentionally being evasive, or was just too distracted to give the matter much thought. He was pacing a slow circle around their group, face lifted as if scenting the wind.
"I think we're looking at the wrong plane for our explanation," Xaz admitted. "Abyssi might not be able to plot, but Numini can."
The Sister of the Napthol frowned, an expression of scholarly analysis rather than confusion or concern. "I was always told the Others can manipulate humans in little ways, but can't push them into anything that violates their basic natures and values. Forgive me, Hansa, but traversing the Abyss and practicing necromancy and raising the dead is not something I would ever . . ." She trailed off, gulping a little, as she considered that she had, if ever so briefly. "And you say Ruby wouldn't have killed herself. Can the Numini force a person to do something so opposite all reason?"
Xaz wished she could just say yes, because honesty meant admitting how much of this blame probably fell on her shoulders. Unfortunately, whether or not her reason for coming to the Abyss made any more sense than anyone else's, she couldn't afford to sabotage her only allies here. That meant telling the truth.
"As for you, Cadmia, perhaps it's true that you allow the Numini in when you study them and pray for their guidance. They could have reached Hansa when he went to the mancers' temple to rescue Pearl." She was not about to tell anyone that she, too, had attempted to take the girl.
"And Ruby?" Cadmia prompted.
She had hoped she could avoid answering that one. "A few days ago, I was in a hurry and Ruby insisted on stopping me to talk. I used my power on her. It could have given the Numini a way in if they wanted to manipulate her."
She kept her eyes on Hansa as she spoke, and saw the way he gritted his teeth and his hand flexed into a fist, like he might take a swing at her. He had every right to be furious, not just for Ruby's death but for the other guards'. She hoped he could control himself long enough for them to work this out.
"But why?" Cadmia asked, either oblivious to the tense moment or deliberately trying to move past it. "What possible use are we to the Numini in the Abyss?"
Umber squeezed Hansa's shoulder, a simple move that made Hansa's whole body relax. His attention left Xaz completely, all hints of his justifiable rage snuffing like a candle flame.
Umber declared, "I don't personally care what the Numini want with us. I plan to accomplish our task, asinine as it is, and then get back to the human realm as soon as—" He broke off, then settled his gaze on Alizarin. "You brought us here, but you can't bring us back, can you?"
The Abyssi looked back at the spawn with amusement. After a moment he said, in tones that suggested the fact was blatantly obvious, "If Abyssi could open rifts to the human plane at will, there would be more of us there."
"Xaz?" Cadmia prompted. "You're a mancer."
"I'm a Numenmancer," Xaz spat, only realizing the full scope of their predicament now that Umber had pointed it out. "I have no control over the Abyss."
"We're after shades first anyway," Hansa said hollowly.
Xaz almost snapped at him, pointing out that they had bigger concerns and he needed to catch up, and then she remembered Hansa leaning forward to take blood from Umber. It didn't matter what had manipulated the two men into coming here. Hansa had sealed the third boon. The magic would drive him and Umber to fulfill the task for which it had been raised, regardless of their wishes.
"Can we talk to the Numini?" Cadmia asked, looking at Xaz expectantly. "Ask what they want with us? If the Numini manipulated us once, they're likely to do it again," she added, when it looked like Hansa and Umber might argue. "You two are more likely to succeed if you don't unexpectedly encounter divine interference."
She had a good point—and damn her for it. Did Cadmia realize what she was asking? Yes, Cadmia had come up with the plan that sent them here, and Hansa had taken three boons of an Abyss-spawn, but every instinct Xaz possessed still told her it was nigh suicidal to allow a Sister of the Napthol and a soldier of the 126 to see her speak to the Numini.
"I'll try," she sighed, "but I can't promise they'll speak to me. They've refused recently."
"What do you need us to do to help?" Cadmia asked.
Go away. "Give me space. As much as you can."
As the others backed away, following Alizarin's directions, Xaz sat cross-legged on the debris-strewn ground and cast out her awareness.
Before her questing power reached anywhere near the Numini, it brushed across scores of Abyssi. She could feel them, including the dense gathering that must be the court. As her awareness brushed each one, she had a momentary sense of what it was doing—hunting, stalking, grooming, sleeping, playing, coupling. Abyssi "play" was brutal.
Focus, Xaz, she chided herself.
"Beings of the Numen," she whispered. In the Numen, names and words had power. Unlike Alizarin, the Numini who had given Xaz her mancer's power had never shared his name with her. "I, Dioxazine, your chosen child, call to you. I petition you. I implore you." A proper invocation was always threefold. Xaz had spent much of her childhood looking for synonyms for "beg" and "grovel." "Please grant me your attention, speak to me, advise me."
She sent up the call, supporting it with as much power as she could muster.
She waited, unmoving, trying not to listen to the distant sounds of scraping, screaming, and howling. The Numini would expect her to be a vessel ready for their regard.
An interminable time seemed to pass before the first awareness of another being trickled into her mind, along with a seeping cold that made the Abyssal wind seem balmy.
I am here.
She sighed in relief at the familiar voice. Her patron. "I am grateful for your attention." How those words grated on her! If one of the Numini had sent them here, it was probably him. She spoke the courtesy by rote, though, because he would disappear again if he felt she had been rude. "May I assume you know our situation?"
I am aware, he said. I have a task for you.
She had to swallow back her fury like bile rising from her gut. A task. "You did send us here, then?"
I was involved, he admitted. I regret my methods had to be so crude and convoluted. The Numini spoke about regret, but Xaz didn't think he actually felt it. There were complications that held me from acting more directly.
Those complications had sent her to the Abyss, and had apparently killed at least one person—more if the guards Alizarin had killed were included. She gritted her teeth, and struggled to keep her mental voice calm. "Is it your wish that we find the guards' shades?"
There was a long hesitation, as if the Numini wrestled with how much she needed to know. The shades are inconsequential. If the Abyssi who slew them is willing to give them up, and you are strong enough to transport them across the veil, we will take them. They died righteously even though they died in violence. Your task is to return someone far more precious to us.
"Who?"
Again that pause, during which she had to struggle to contain her impatience. The Abyssi hold a sorcerer named Terre Verte imprisoned in their royal court. We need him retrieved.
"Why?"
The chill filling her deepened. That is most certainly not your concern.
She didn't know much about the Abyss, but she had no desire to go closer to the gathering of Abyssi her power had allowed her to glimpse. "Are the Abyssi the ones who caused your 'complications'?" she asked. "If they were able to interfere with you, how do you expect me to do better? And how will I convince the others to help me? Hansa and Umber need to fulfill the terms of the boon."
They will help you, he informed her, because you will tell them that Terre Verte is their only hope of fulfilling the boon. The woman's body will be cremated within the hour. A necromancer cannot revive her, but Terre Verte can. As long as they have an option that will allow them to fulfill the boon, they must take it.
"That's cruel," she accused, unthinking.
I have given you your task, he declared, with a spike of chastising power that made her flinch. It is up to you to obey, not to judge. Now return to your Abyssi master, and tell your companions what must be done.
The Numini's tone was bitter and disappointed as he referred to Alizarin.
Then he was gone. She gasped and opened her eyes, shivering convulsively.
Stupid, demanding, arrogant bastard!
How she wished she could say those words to his face.
The others had withdrawn several yards, but came toward her expectantly when they saw her move.
"Anything?" Hansa asked.
Xaz cleared her throat of the fury that had tightened it. "What happens," she asked, "if you cannot fulfill the boon? The Quin will cremate the body the instant sighted guards see Numen and Abyssal power in that room. Can a necromancer still resurrect her then?"
Umber looked at her speculatively. He answered, "If it cannot be done, then once we are absolutely certain of that, the boon will be fulfilled. Speaking for myself, I have never met a necromancer, and cannot say for sure the limits of one's power without asking."
I won't tell them, Xaz decided, with a giddy blend of terror and exultation.
If the Numini could have spoken directly to the spawn and the guard, they wouldn't have bothered to go through Xaz. As long as Xaz didn't tell them about Terre Verte, they wouldn't have to go after him. They could complete their original mission—speak to the shades and try to find a necromancer—and then find a way back to the mortal realm.
"The Numini told me only that they would accept the souls of the dead guards if we have the power to bring them across," she said, hoping that even if Umber or the others realized she was lying, they would have the sense not to question her further. "If they have other plans for us, they do not deign to tell them to a mere mortal like myself." To explain her obvious irritation and how long the conversation had been, she added, "They do not like having their Numenmancer question them."
She wasn't lying to protect Hansa and Umber, but herself. She couldn't trust Alizarin to always have the presence of mind or the motivation to protect them, and without him, Umber was the only one of them with a chance of being able to navigate the Abyss and find a way back to the mortal realm successfully. If Xaz had any choice in the matter, she would do everything in her power to avoid trekking into the bowels of the Abyssal court, but if Umber went, she would need to go with him.
CHAPTER 25
What is wrong with me?
Hansa's training had been focused on how to identify and fight mancers, the mortals who served the Abyssi and Numini, not on the capabilities of the Others themselves—that last was knowledge reserved for the Order of the Napthol. Without Cadmia's education, Umber's Abyssi parentage, or Xaz's experience as a mancer, it was hard for him to follow the theories the others bandied about regarding what the Others could or couldn't do.
It was even harder than it might have been, because every now and then his attention would be caught by the shape of Umber's jaw or the warmth of his body and long moments would go by. Hansa would realize he had moved close to the spawn, or pressed his hand into the deep indigo glow that surrounded him and shimmered in response to his touch.
Blood-drunk, he reminded himself, remembering what Umber had called his reaction after they had rescued Pearl. He had tasted Umber's blood again just before stepping into the Abyssi, hadn't he?
Each time he noticed what he had done, he moved back, though something inside him wept to pull away from that shivering glow. It had passed last time; it would pass this time.
"There is a camp of shades outside the court, or was when I was here before," Alizarin said, sounding impatient. "We should go there."
He started walking, leaving the rest of them to scramble after him.
"Why there?" Xaz asked.
"They have walls," Alizarin answered. "And weapons. I should hunt before Antioch finds us, and you want to be somewhere safer before I leave you."
The logic seemed sound, but as Hansa tried to follow Alizarin, a feeling like ants skittering across his skin overwhelmed him. It made his muscles twitch. Before he could identify the sensation, Umber asked, "Is it possible that the shades we're seeking have found this camp?"
The Abyssi glanced over his shoulder just long enough to shrug, then said, "Shades normally appear near where they died."
Was that an answer?
Alizarin kept walking. Cadmia trotted after him, catching up and speaking excitedly. "So the Abyss really is analogous to the mortal plane?" she asked. "And there are really levels," she added. "How many?"
That was a yes, Umber supplied, for Hansa's benefit. His warmth against Hansa's side and arm across his shoulders was as much a comfort as the words, though Hansa wasn't sure which of them had initiated the contact. They might be nearby. We can get to safety and still pursue our goal.
As soon as the assurance had been uttered, the jittery discomfort faded.
When Hansa tried to gather his will to shrug off the spawn's touch, though, he found he lacked the motivation. This had already happened too many times for him to hope the others wouldn't notice, so what was the point?
Meanwhile, Alizarin sidled closer to Cadmia, his feet barely seeming to disturb the black sand beneath them. Hansa would have stepped back; Cadmia almost leaned toward him, as if he were a fascinating butterfly she wanted to observe. "Five," he said. "I have never been deeper than the third, but my sire was of the fifth."
"You are exceptionally excited to be in the land of the damned," Xaz remarked, speaking Hansa's thoughts in what sounded like a forcedly level tone.
Cadmia tensed, her face taking on the placid, thoughtful expression Hansa was beginning to realize was a mask. "I know I should be horrified by this entire situation, but this is a chance to learn more about the field I have spent my adult life studying. Don't you understand?"
"I understand you're the one of us who should have been arrested," Xaz grumbled.
As they moved away from the beach, skeletal structures rose from the sand to surround them. Like ancient trees fossilized in black marble, they were slick in appearance and rippled with glints of copper and rusted iron like dried blood. Luminescent pods the size of chicken eggs hung from their branches, glowing in nursery shades of pale pink, sea-foam green, and powder blue.
As they passed near one of the trees, Cadmia lifted a hand as if to touch a candy-pink orb.
Alizarin moved like smoke; faster than Hansa could blink, the Abyssi was on Cadmia's other side, his tail around her wrist yanking her back. The Sister choked out a cry, and asked, "What—"
"Watch," the Abyssi commanded. He moved Cadmia several feet further back, then reached up to bat at one of the delicate-looking pink orbs.
Hansa cringed from the shriek that followed, so he barely saw when the pod burst, spattering the surrounding area with silver ichor that steamed where it hit Alizarin's fur and ate through the back of a large conch-shaped shell resting at the base of the stone tree.
After a moment, the mercury-like substance drew together and climbed back up the stone column, higher this time, and reformed into its harmless-looking pod.
"Don't touch anything that glows," Alizarin advised. He shook himself, fluffing his fur then smoothing it back down. Hansa saw singed areas on the Abyssi's arms, face, and chest, and didn't want to imagine what would have happened to human flesh. "Except me," he added as he loped back toward Cadmia.
"Thank you," Cadmia said, her voice breathy. She lifted a hand, hesitated, then responded to the Abyssi's implied invitation by smoothing a hand down the now-patchy fur on his forearm. "Are you all right? Your poor fur."
Was Alizarin purring?
"It'll grow back," Xaz muttered.
"Is that from the shades' camp?" Umber asked, lifting a hand to point to a thread of lighter gray rising into the dark sky. "It looks like smoke."
Alizarin nodded, tail lashing. Hansa might not have recognized the frustrated expression if it hadn't echoed exactly how he felt every time he stepped away from Umber. If he could find a moment when the Abyssi wasn't around, Hansa would warn Cadmia that while Alizarin was being remarkably well behaved so far, it wasn't a good idea to draw an Abyssi's attention physically.
"This is as close as I should go," Alizarin said. "If they see me they will not accept you."
"Are you well enough to do this?" Umber asked Hansa. He spoke slowly, as if choosing his words with care.
Hansa pulled reluctantly away from Umber's warmth. It seemed overly optimistic to assume they would find the other guards in the first place they looked, but if they did, it would go better if they didn't see him snuggling against the Abyss-spawn man.
What am I going to say to them, anyway? he wondered. How will I explain being here with the Abyssi and mancer responsible for their deaths?
What if I see Ruby?
How had it not occurred to him until that moment that she, too, should be here? If shades appeared near where they died, shouldn't she have been at the beach?
Ruby, at least, wouldn't be surprised to see Umber. Hansa remembered her expression when she found them together, as if it confirmed something she had suspected for a long time.
He cleared his throat and said, "Let's go."
They walked toward the smoke, leaving the Abyssi behind.
When Alizarin said wall, Hansa had pictured stones. Instead, an assortment of junk—large, cracked shells, stones, and thorn-covered vines—made a neck-high barrier that spanned the empty space between the stony trees, enclosing a lopsided circle maybe a quarter acre in total. A man and a woman armed with rough, crooked spears watched them approach with serious expressions.
"Come around this way," the woman said. "There's a gate."
Hansa fought to keep his expression neutral. The shades looked like any other humans . . . if he discounted the disquieting tone of their skin and eyes. The woman who had greeted them at the gate looked like she was at the peak of a bout of flu; her skin was clammy and blotchy as if with unbroken fever, gray tinged in a way that made it impossible to tell if she had once been fair or tanned, and her brown eyes had a strange haze to them.
"I'm Yarrow, of Tamar," the woman said. "Do you know your names?"
They hadn't considered what they were going to tell any shades they met. Supposedly, the dead were sent here for a reason. Could they be trusted? Out of habit, Hansa looked at Cadmia.
"Is it normal not to?" the Sister of the Napthol asked. She sounded composed and neutral as she implied that maybe they didn't know who they were.
Yarrow nodded. "Many people don't at first. They don't know who they are, where they're from . . . how they got here. It can take weeks to sort it out, and most don't have weeks before they—well, you're lucky to have found us quickly." With the same compassionate bluntness, she asked, "Do you know where you are?"
"Yes," Cadmia answered this time.
"Weeks?" Hansa asked. He hoped Yarrow thought the panic in his voice was due to his own lost memory, because he couldn't help it. Would they have to be here that long before they had any hope of finding Jenkins and the others? Could they wait? Just thinking about it made something in his chest constrict. He didn't think they had that kind of time before the boon would demand they do something else, but the thought of abandoning the others was equally horrific.
Yarrow nodded and said comfortingly, "Don't worry. We'll guide you through it. In the meantime, we have a fire to keep you from the cold, and a little food we can share."
There were a half-dozen other shades in the enclosed area, most looking worse than Yarrow. A few stood near the walls, clearly acting as sentries. The others hung back, watching the new group with suspicion.
"I'm guessing you haven't been here long?" Yarrow asked. As she led them to the fire, which was flickering against the wind and belching tarry smoke, one of the other shades stood and walked away without comment.
"Not long," Umber replied. "It shows?"
Yarrow just smiled sadly. If she was an example of what a shade looked like after a time in the Abyss, it was obvious that Hansa and the others were new. "You must be hungry then. After a while the body starts to forget things like that . . ." She trailed off as if the thought had inspired another, more disturbing one. After a moment she shook herself and continued. "Early on, you still feel things like cold, hunger, and thirst, though they can't kill you."
She ducked into a patchwork, lean-to shelter and returned with a bone bowl full of what looked like some strange kind of fruit. Each was about the size of an egg, slate-gray, and protected by sharp spines. Yarrow demonstrated how to scrape the spines off on the sharp edge of the bowl before cracking the shell to eat the pulpy seeds inside.
"These quench the thirst," Yarrow said. She put the bowl down next to the fire and said, "I should check on Vim. He's one of our hunters, but was hurt today. It will give the three of you time to talk if you want."
"You hunt the Abyssi?" Umber asked.
Yarrow's eyes widened. "We hunt the mindless beasts who roam this level of the Abyss," she clarified. "It's dangerous but necessary. None of us could fight one of the true Abyssi."
She turned away without further word and disappeared into another of the ramshackle shelters. The other shades had drawn back, giving them privacy either from kindness or lack of interest.
"Damn," Umber whispered. "I knew finding them might be difficult, but it never occurred to me they might not be here to be found yet."
Wryly, Cadmia said, "We don't have much information from people who recall dying. The things I could teach the others, if only—"
She broke off, perhaps noticing that everyone was staring at her. Yes, it was her order's task to study these things, but this level of interest was as disconcerting as Hansa's incessant pull toward Umber.
Who he was too close to again.
Who cares? he thought. Your friends aren't here to judge you.
" 'Ware!" The shout came from the far wall, and made them all jump. After years as a guard, Hansa responded to the sentry's warning instinctively. Even thoughts of Umber disappeared from his mind as he shot to his feet and put the others behind him, wishing he had a weapon.
He looked around at the shades, assuming they had plans for these situations, but instead of running to fight, those who had been armed were dropping their weapons and backing away. Hansa caught the whispered warning: "Abyssi."
The creature who approached the wall had a sleek, furred body, though its shape was closer to the jungle cats Hansa had seen in some Silmari art than Alizarin's mostly humanoid form. Its shaggy fur was mottled gray and black, but the eyes it lifted to them still burned a familiar, brilliant blue.
As it reached the wall its form flickered, shifting to an Abyssi's less-substantial and more terrifying natural shape as briefly as an eye-blink; a moment later it was inside the camp, solid again, and clearly focused on their group.
Umber stepped forward, pushing Hansa aside to do so. His body was rigid with tension.
"Greetings," he said, "from myself and from Alizarin. Are you seeking us?"
Supposedly, Umber had the ability to claim Hansa, and he was clearly invoking Alizarin's ownership to protect the others. Hansa noted the Abyssi's color, though, which one might easily describe as "ashy." He suspected Antioch might have no interest in respecting Abyssi rules.
"You have something of mine." Whereas Alizarin's voice had been musical, Antioch's was gravelly, scree cascading down a hillside.
"The Numenmancer belongs to Alizarin," Umber answered, his poise impressive given what he was facing. "This human belongs to me," he said, putting a warm hand on Hansa's shoulder before removing it to wave dismissively at Cadmia and add, "And this one is also Alizarin's. I'm sure you can taste his power on her."
The new Abyssi snarled, a noise that struck Hansa like a blow, driving a sharp pain between his temples. Its fur rose, as well as a crest of inky spines around its jaw and above its eyes, tipped in the brilliant green and orange stripes Hansa associated with poisonous frogs. "Alizarin owes me."
Stall, Hansa thought. Alizarin said he would be nearby hunting. He had to have anticipated a challenge like this coming. If he could sense another Abyssi so close, he would come back.
Right?
It was hard to hold to that fragile hope as Antioch stalked closer and looked past Umber's shoulder to directly meet Hansa's eyes. The light of the Abyss glowed in them like the blue heart of a pyre. "You stole my mancer," he accused.
Help came from the last place Hansa ever would have expected. Xaz said, "From what I heard, you had nearly destroyed your mancer already. Hansa wouldn't have been there if you hadn't used him so carelessly."
Another of those horrifying blinks, and the Abyssi was suddenly in front of Xaz. He lifted a hand and touched her face.
Xaz flinched, and Hansa saw beads of blood run down her cheek.
"Alizarin asked permission to give my chosen one a gift. Do you know what that gift was?"
Xaz paused an instant to think, then guessed, "The knife." Her voice was tight and strangled. "That's how he formed a bond with me."
"He said it would make a powerful tool," Antioch growled. "But as soon as it was time to fight, he forced my mancer to discard it."
"Alizarin didn't make Baryte throw the knife away," Cadmia said. She sounded breathy, as if it was hard to get the words out. Was she mad enough to think arguing with Antioch was a good idea, or had she, like Hansa, decided playing for time was their only way to survive this?
As Antioch flickered in front of Cadmia, he remarked, "I only need to keep one of you." The words sounded contemplative, though they were clearly a threat. He looked from her to Hansa as if trying to decide which one he wanted.
Hansa looked around, desperately hoping the shades had some kind of secret weapon they could use against the Abyssi, but they had scattered like leaves before a storm. No help from that quarter.
"Hansa belongs to me," Umber said, drawing the Abyssi's attention back to him, "and I did nothing to you. Perhaps we could discuss an arrangement?"
He's not serious, Hansa thought. I really hope he's not serious. He didn't think Umber was the type to sell one of them to an Abyssi if he had a choice, but he might not feel there was another option. Maybe there wasn't.
"Your human took my mancer," the Abyssi spat, "so I was going to take him. Baryte marked him for me. You tried to remove the mark, but you can't own prey I already claimed."
This time, when the Abyssi looked back at Hansa, he felt the old, healed injury in his left hand flare to life again. Compared to the suffocating heat he had felt when Baryte had first cut him, this was like holding a winter-chilled hand up before a slightly-too-hot fire to warm, but understanding made him shudder.
If it hadn't been for Umber, he really could have become a mancer—not from the deep rents down his back from Alizarin, but from a tiny scratch made by an Abyssumancer's blade.
"That's why he was able to get blood-drunk," Umber said, clearly trying to pull Antioch's attention away from Hansa again. "I was able to remove Alizarin's power from him, but didn't notice your mark among the larger contamination."
Whatever Antioch might have said in return was lost. The Abyssi bounded past Umber, brushing against Hansa before shouldering Cadmia out of the way, sending her sprawling. Hansa spun, relieved to see that Antioch was heading toward another form now slipping over the gate—this one a familiar, luminescent blue.
Alizarin's humanity had faded away. As he crossed the sands, he was once again the formless terror they had seen when they first appeared in the Abyss, something Hansa flinched instinctively away from even as he breathed relief at his appearance. Knees weak, he leaned against Umber for support, listening to the rapid pounding of the spawn's anxious heart. Xaz scrambled to help Cadmia.
Antioch leapt. Alizarin met him, and they clashed as a void of darkness, claws, fangs, and hunger.
A deep rumbling came from the combatants. Hansa felt it as a grating sensation, as if his bones were moving tectonically past each other. A hiss from one of the Abyssi reached him like a sharp wind.
Come on, Umber urged, his voice in Hansa's head momentarily loud enough to get his attention. He was trying to make them all move.
Hansa's limbs felt leaden, and the others looked the same. With Xaz's help, Cadmia was pushing to her feet haltingly, her mouth set in a grim line. The Numenmancer was gray-pale except for the blood seeping down her face.
Hansa spared a look back to the two Abyssi. They were lost in a swirling miasma of indefinable violence.
"Get out!" Hansa jumped as the shade who had greeted them so graciously earlier hissed at them to leave. "Don't come back here."
"But—"
He hadn't really intended to argue, just hadn't been able to think quickly enough to process Yarrow's words. The shade snapped, "We survive here because the Abyssi have no interest in us. Get out!"
Stumbling, gasping, they fled the encampment.
CHAPTER 26
Xaz's only injuries were the small cuts on her face, but she felt battered. When a dog growled, it raised its hackles and tried to look big to avoid a fight. When an Abyssi growled, it wasn't posturing; it was a first attack. Power flared like a mantle, striking those within range. Just being near the two battling creatures was enough to do damage to a mortal.
They limped along, following Umber with no thought beyond get away, until Cadmia collapsed and gasped, "Can't."
A plume of fine black sand rose around her, looking too inviting to resist. Xaz fell next to her with little more grace.
The others didn't argue either, but sprawled nearby, alternately coughing and panting as if they had all inhaled something caustic.
Cadmia clutched a hand to her ribs, grimacing.
"How badly are you hurt?" Xaz asked, remembering Antioch striking Cadmia on his way by.
"I don't know."
"You're bleeding," Umber told her. "Your arm, your side."
The light that had grayed the sky when they first arrived had been dying since some time at the shades' camp, and even the glowing creatures on the trees seemed less numerous now. In the dim light, any blood on Cadmia's dark clothes was invisible to Xaz. Was Umber's vision better, or could he sense the blood another way?
"Let me see," Umber said.
Cadmia set her jaw as if the movement hurt, and gingerly raised her shirt. Jagged scratches ran up and down her chest and arm on the side where Antioch had brushed against her. Several were still bleeding, and the skin around them was inflamed.
Umber pulled off his own shirt and started tearing it into strips, using the pieces to apply pressure to the deepest cuts. Cadmia let out a small, pained sound at the back of her throat.
"How bad is it?" Xaz asked. She didn't like the look of the swollen flesh that surrounded the wounds. They reminded her of the brightly colored spines Antioch had lifted when angered, which in a natural creature would have warned of poison.
"The blood might attract predators," Hansa said. His words were carefully measured, as if forming them was a struggle. "We should . . ." He looked around, eyes scanning the ground, then made a waving gesture as if trying to recall the word. No, not as if searching for a word; as if swinging a sword.
"Weapons," Cadmia agreed.
Her voice choked on the end of the word and she started coughing, a fit that racked her body so severely Umber had to grip her tightly to keep her from falling face-first in the sand. By the time she had recovered, her face was flushed and covered with a sheen of sweat, but her lips were gray-blue.
Umber lifted the cloth he was using to staunch the blood, and Xaz clamped her teeth on her horror as she saw the way the skin around the wounds had started to blister and blacken.
"Can you do anything?" she asked the spawn. "You healed Hansa."
"With effort, I could close the wounds and stop the bleeding," Umber said hesitantly. "I can't remove the poison from her blood, though." Cadmia bit her lip, suppressing her first response to the obvious death sentence Umber had just declared, and the spawn added hastily, "It's an Abyssal poison. Divine power might be able to cleanse it."
They both looked at Xaz expectantly, Umber calmly and Cadmia with a desperate plea.
"Xaz?" Umber prompted. His voice was too calm, carefully managed to avoid panicking Cadmia, as if she couldn't see and undoubtedly feel the poison's rapid spread.
"I don't know if I can do anything." She was unable to make her voice any stronger than a whisper. "I haven't had much control over my power since Alizarin bonded to me."
"Try?" Cadmia urged.
Xaz nodded sharply, and forced herself to step forward. She knelt next to the Sister of the Napthol, and touched her fingertips to a spot of unmarked skin. Cadmia jumped, reminding Xaz that her hands were usually icy. Ruby used to remark on it when Xaz accidentally touched her while passing a dish at dinner or something similar.
"Sorry," she said to Cadmia, closing her eyes and resisting the impulse to look at Hansa. "My power is cold."
It wasn't the first time Ruby had come to mind unexpectedly and it wouldn't be the last. Despite all Xaz's attempts to keep her distance, Ruby had been a friend, and Xaz was almost certainly at least partially responsible for her death. Now that the strange madness that had gripped them all had receded, Xaz didn't like the idea of trying to resurrect the woman, but if she could save Ruby's soul from the Abyss along with the dead guards, she would do it.
Finger-walking along Cadmia's skin, she found the edges of Antioch's poison and tugged at it. She envisioned her own, cool power flowing through the wounds to cleanse them like a river flooding a stagnant pool.
Instead of her magic rising in her body, an icy voice slipped into her mind. Now you seek our aid? it asked. After defying us, you dare seek our assistance?
Xaz felt a new kind of coldness wash over her, one that had nothing to do with her magic and everything to do with fury.
"Napthol is a Numini, isn't it? That means she is sworn to one of you," she murmured, her voice sub-audible, only intended for her disapproving Numini patron. "You won't let her die."
She has already been given to us as a tool for our plans, the Numini replied indifferently. If those plans are not to find success, she is of no more use to us.
Oh, those bastards. Those arrogant, manipulative—
Watch your thoughts, Mancer, the Numini hissed warningly. Your tie to the Abyssi is making you irrational and disrespectful. We have given you a task. If you are not our servant, we have no responsibility to give you aid.
"Is this the first time you've manipulated Antioch into helping you get your way?" she asked, this time not worrying about keeping her voice quiet enough to keep the others from overhearing. "Or were you the one who made his mancer throw the knife at me, too?"
If you hope to save her, you had best decide swiftly, the Numini advised.
Xaz opened her eyes, and blinked them twice to clear the rim of frost that tried to stick the lashes together. The world around her had the silver halo she knew meant the Numini were still riding her.
She said the words swiftly, bluntly. "A necromancer cannot raise Ruby unless she has a body to raise, and the Quin will have destroyed that by now." She saw Hansa and Umber both tense, their faces showing wary relief that disappeared swiftly when she continued. "There is a sorcerer who can raise her, though, a man named Terre Verte. The Numini want us to retrieve him from the Abyssi court."
Hansa's breath hissed in as if he, too, had been stung by the Abyssi. Umber raised his eyes skyward, took a breath, and said flatly, "You've relayed your message. Can you help Cadmia now?"
Before Xaz could turn her attention to the effort, she felt the Numini's power rush through her, not a river but a torrent. Cadmia called out wordlessly, her body spasming once as the magic struck her.
When it was done, Xaz collapsed, panting, on the black sand, which was rimed with ice in a spreading circle. She wasn't sure when Umber had moved away, but he and Hansa had judiciously stepped back from the needle-like icicles and frost heaves that grew like strange plants ringing her and Cadmia.
Umber called, "Are you two all right?"
Before Xaz could catch her breath to answer, Cadmia's dazed voice said, "I think so." As Xaz struggled to sit up, Cadmia prodded at the remnants of the wounds on her side and arm. The bleeding had stopped, though not in the neat way an Abyssumancer's wounds healed; it looked more like the injuries had been seared shut with frostbite. More importantly, though, the swelling had gone down, and Cadmia's skin had returned to a healthier shade.
As she remembered the price she had paid for that healing, Xaz looked up at Umber and said, "I'm sorry."
He gave a half shrug, his other arm around Hansa, who looked as dazed and exhausted as Xaz felt.
Briefly, Xaz indulged a fantasy in which the hero of Mars had discovered himself to be a mancer following Baryte's death. Would Antioch have been able to twist him fast enough to secure his loyalty even as he served Kavet from such a lofty role? Or would Hansa have found an excuse to resign when he realized what he was? Would he have killed himself?
"We need to rest before we can accomplish anything else," Umber said, surveying their bedraggled group. "That will give Alizarin time to come back. Or not," he admitted with a wince. "I do not think we can plan a trip into the royal court until we know if we have him on our side."
Xaz had been so focused on Cadmia, it hadn't occurred to her until that moment that Alizarin hadn't come after them. The fight had to be over by now. She looked out over the Abyss, which had now grown so dark it was hard to even see Hansa and Umber a few feet off. A breeze had sprung up as the light faded, and though it couldn't compete with a Kavet winter or come anywhere near to divine cold, Hansa and Cadmia both hunched against it.
Hansa stepped away from Umber as he asked, "Can we make a fire?"
"Do you see anything that might burn?" Umber asked in reply. "I don't know what the shades made their fire from, but all I see here is stone and sand. If we all stay close, we should be all right."
Cadmia nodded, warily looking between the two men, as if recognizing the logic in the suggestion but not entirely comfortable with it. Hansa, who Xaz would have expected to jump at the invitation to lie down with the Abyss-spawn he had been intermittently cuddling against all day, continued to make excuses.
"One of us should stand guard. I'll take first shift," Hansa volunteered. "I know I can't kill an Abyssi if one comes, but those shades talked about hunting. That means there are some creatures here a mortal is strong enough to fight."
Umber sighed, shook his head, and said, "Do whatever you want, Quin. Just don't wander off."
"Are we really helpless against the Abyssi?" Cadmia asked. "Aren't Numenmancers supposed to be able to summon lightning?"
Supposed to was the operative word. Cadmia clearly hadn't been coherent enough to realize how close she had come to dying through the Numini's stupid pride and refusal to help unless Xaz heeded their will.
She said, "Don't count on the Numini's help. They aren't that generous."
It was the closest to a direct criticism of her divine masters as she had ever dared speak aloud, but she was too tired to worry about whether they heard her and would make her pay for the words later. She led the way to a hollow where black stones and sand dunes would block the worst of the wind and reached out to smooth the sand—
Umber pulled her back an instant before a glistening, transparent tentacle no thicker than her little finger flailed upward, seized nothing, and disappeared again beneath the sand.
"What was that?" Cadmia asked hoarsely.
"I think . . ." Umber trailed off and frowned, looking around. After a moment he found a shell a little longer than his forearm, which he used to gingerly prod the black sand.
Again the tentacle came up, this time joined by several others. They slapped the shell with a meaty sound and wrapped around it, questing both directions. Just before they reached Umber's hand, he yanked on the shell, pulling the creature attached to the tentacles up like a carrot.
The little beast had a fat, bulbous body that looked like a jellyfish's, eight thick legs segmented like an insect's, and a mass of slender tentacles that groped toward Umber's hand before he threw the shell and dangling thing away. Every part of it looked watery and translucent, like something that should have been crushed by the sand in which it had hidden.
It started moving toward Umber, who pulled Xaz with him as he backed away.
Hansa stepped forward with another long, sharp-edged shell, which he used to decisively cut the creature in half.
"Be careful of sheltered places where the sand is soft and deep," Umber said. "There are small creatures in the Abyss that can devour a man or woman as surely as the larger beasts can. They just do it more slowly."
Xaz was reconsidering whether she ever again needed to sleep when she felt the approach of familiar power.
Alizarin's normal bounding stride was more subdued than usual, and as he drew close, Xaz could see scalds and tufts where his fur pulled irregularly over new injuries. It was hard to tell in the dim light, but even his colors seemed subdued, blue tinged gray instead of his normal brilliant turquoise and sapphire.
"Are you all right?" she asked, reaching toward him instinctively.
Somehow Cadmia got there first. Alizarin leaned toward her hand.
Through their magical bond, Xaz could feel the Abyssi's overwhelming fatigue, but he tossed his head dismissively as Cadmia crooned sympathetic words.
"I won," Alizarin announced. "I needed to hunt after. You did, too?" he asked, looking at the still-twitching creature. "I don't think you can eat those."
"I wasn't going to try," Hansa said.
"They taste bad," Alizarin said idly, "and their poison rots flesh, though it takes a few days to get all the way in to the heart and brain. They didn't touch you, did they?" he asked Hansa, seeming reluctant to spend time on the question.
Eyes wide, Hansa paused to look at his hands, then shook his head.
"Good," Alizarin said. "Umber wouldn't want to cut pieces off you." With no further concern, he stretched, fluffed his fur, yawned widely and announced, "It's time to sleep. You picked a good spot."
He didn't wait for Xaz to reply, but went to the hollow Xaz had considered before realizing how dangerous it was. As Alizarin paced the spot, kicking at the sand, a half-dozen creatures rose and scampered away, including a second jellyfish-beast and a strange mass Xaz might have mistaken for a brightly-colored dust bunny if it hadn't moved with deliberate speed away from the Abyssi.
We would never have made it through the night without him, she realized abruptly.
The Abyssi sprawled out on the sand, and Xaz thought for a moment he was going to leave the rest of them to find their own beds. Then he stretched, and looked up at them. Specifically, he frowned at Cadmia. "Why are you glowing like a Numini?"
"Antioch hurt me," she answered. Xaz wasn't sure if the Sister of Napthol kept the words simple in deference to the Abyssi's simple nature, or if she didn't want to dwell on her near death. "Xaz healed me."
Alizarin began to growl, then swallowed it. "Sleep here," he said, tapping the sand near him with his tail. "Nothing will try to eat you beside me."
There were two ways to interpret those words, but Cadmia clearly took them to be reassuring, because she accepted the offer. Xaz squelched an instinctive, irrational moment of jealousy as the Abyssi invited someone else to snuggle close. Yes, her power drew her to him, but she wasn't a slave to her power.
Besides, the cold wouldn't bother her as much as it would Cadmia.
With the magic gone and the fear of Alizarin's absence abated, the anxiety and lack of food or water during the previous day caught up to Xaz. All her muscles felt so weak she could barely stand. Cadmia lay down inches from the Abyssi, and Xaz took the spot next to her.
That left Hansa and Umber. As if on cue, the guard's sharp protest reached Xaz's ears.
"Don't touch me." All day long, Hansa had gone back and forth between moving close to Umber and pulling away. Xaz had resisted the urge to needle him about it only because she remembered her own reaction to Alizarin, the physical draw of Abyssal power that craved the slide of skin on skin—or fur, in that case.
"Come on, Hansa," Umber sighed.
"It's not cold enough to freeze to death," Hansa said, "and I doubt anything really dangerous will come close with Alizarin here."
Umber's reply was too soft to hear, as was Hansa's, but it must not have been flattering because Umber didn't bother to lower his voice as he grumbled, "Have I done anything to suggest I might be interested in assaulting you in your sleep?"
More muttering from Hansa, but this time Umber laughed. A brief, quiet conversation later, and Xaz heard the two men's quiet footsteps on the sand moving toward them. She judiciously kept her eyes closed, pretending not to notice and sparing Hansa's . . . whatever it was that was stopping him from being practical. Pride? Shame?
"Sleep, Hansa," Umber whispered, when Hansa again hesitated to lie down. The words were quiet, but they reached Xaz on a wave of power; Hansa's knees buckled and Umber caught him and lowered him gently to the ground.
"Is everything all right?" she asked. It shouldn't have taken so much energy to knock out a human unless something equally strong was fighting to keep him awake.
"Is anything?" Umber replied, before giving a long, drawn-out sigh and pointedly turning his back.
In the darkness, Xaz listened to the sounds of the Abyss at night: rattling, hissing noises from the stones around them as smaller creatures marked their passing; distant, baying howls too deep and undulating for dogs; and the occasional, piercing shriek as some distant creature . . . died? Was that what it was here?
Would they find out firsthand?
CHAPTER 27
It was nice to be warm. That was the thought Hansa woke up with. It was nice to be warm, and it was nice to be safe, to be in someone's arms and held gently—
The sense of peace shattered as he remembered where he was, how he got there, and who he was with. His head was on Umber's tanned arm; his own arm was around the other man's waist. And the worst part was, that was where he had wanted to be all the day before. Umber thought Hansa was worried the spawn would assault him if they slept next to each other. Hansa's real fear was that he would pounce on the spawn with less inhibition than an A'hknet monger.
For now, Umber was still asleep, black lashes making soft crescents on his honey skin. In sleep, his full lips were relaxed instead of quirked up in the half smile, half sneer to which Hansa had become accustomed. His lithe body was finely muscled, his chest lightly dusted with black hair, his—
"Fuck," Hansa breathed, squeezing his eyes shut. This was supposed to wear off.
Eyes open again, he tried to gather the willpower to sneak out of Umber's arms. He didn't want to be this close when the Abyssi-spawn woke. If Umber said anything snide—and how often did he say anything else?—Hansa was going to have to hit him.
He lifted his arm from around Umber's waist, but that was as far as he got.
The hair on Umber's chest was softer than it looked. Lower down on his stomach, it was almost fine enough to be fur, like the Abyssi's. The skin beneath was smooth and hot.
Umber's eyes shot open. They seemed to hold a thousand different colors of blue, even in the fine band left by dilated pupils. "Hansa?"
Hansa shoved at the other man, tried to push himself to his feet, and then fell, breathing as if he had just run an uphill race and lost. "Why hasn't this worn off?"
Umber rose to his knees and helped Hansa do the same, hands on his wrists the only thing that kept Hansa from reaching out again. " 'This'?" Umber echoed.
Showing was easier than forming words. Umber released Hansa's wrists as Hansa pushed forward to wrap one hand around the back of the Abyssi-spawn's neck and pull him forward to kiss him. Dear Numen; he tasted even better than he looked, and felt even better than that. Umber didn't object. He twined a hand in Hansa's hair and pressed his other hand to his lower back.
Hansa barely noticed when Umber shoved him back and his shoulders impacted the black sand beneath them. He also barely noticed the swift kick someone delivered to his shoulder, despite the fact that it was hard enough to make his fingers tingle.
Umber did react, slowly lifting his head and turning from Hansa to snarl at Xaz.
"Glare all you like," Xaz said. "I thought I'd warn you before Alizarin decided to make this a threesome."
The possibility of suddenly being joined by a full Abyssi was just enough to jolt Hansa back to reality and make him realize what he had been doing. He pushed Umber away, but didn't get much further than that. Umber stood. Hansa stayed on the ground, knees up with his head resting on them while he relearned how to breathe.
Cadmia asked Umber, "Is he all right?"
Umber paused, thinking too long for Hansa's taste, before he answered, "He could be much worse."
If he let go of his knees, Hansa was sure he was going to throw himself at Umber again. "What in the name of the Abyss have you done to me?" he gasped.
"Me?" Umber asked. "Done to you? This, dear Quin, is your own fault. And I find it beautifully ironic."
"If you two are . . . awake," Cadmia said, with a judicious pause that made it clear she had to consider whether or not to comment on what she had just seen, "Alizarin brought food."
Hansa pushed to his feet, shaking himself. He felt like he had taken a beating, and he was still exhausted despite having slept deeply and dreamlessly. He vaguely recalled Umber convincing him that sleeping next to each other wasn't a fate worse than death, and then . . . nothing.
Xaz had gone back to dissecting some kind of purplish fruit, and Cadmia was examining a broad, shallow shell serving as a platter for what Hansa could only assume was meat. Looking at either option made Hansa's stomach roll.
That wasn't what he wanted.
He crossed his arms, fingers bruising his own skin with the effort it took not to close the distance between himself and Umber, who had joined the others at their meal. This wasn't as bad as yesterday—it was worse.
I did warn you, Umber said silently.
Hansa tried to think of a way to change the subject, to focus his mind on the task at hand, but he couldn't.
Don't think about Umber. Think about why you're here.
He tried. He remembered what Xaz had told them about Ruby's body being burned, and the Numini's desire for some sorcerer, but he couldn't even begin to process what that meant for their next steps. All he knew was that thinking about Jenkins and Ruby and all the others should make him sick with grief, but when he tried to let that emotion in, it was shoved aside by the longing for Umber's skin against his.
As if desperate to start a conversation that didn't involve Hansa's relationship with Umber, Cadmia asked Alizarin, "Why are you wearing pants?"
The question was so bizarre it momentarily drew Hansa's attention. Xaz snickered.
"No one else finds this odd?" Cadmia asked defensively.
"A little, only now that you mention it," Umber said.
Hansa thought he would have noticed immediately if the Abyssi hadn't been wearing pants . . . maybe. He thought back to the other Abyssi they had seen in this place. He had been far too distracted by his terror and focused on details like teeth, claws, and poisonous spines to take note of Abyssal wardrobe choices.
Alizarin tilted his head in the teasing way he had. "Humans find nakedness distracting."
"I didn't realize one of your kind would worry about that," she remarked.
Hansa had already given up all his preconceptions on Abyssi. It had never been his job to know more about them than he needed to fight their Abyssumancers, so he dealt with being wrong with relative equanimity, but Cadmia was clearly more intent on understanding.
He wished he had learned more about the spawn, though. Maybe he would have known . . .
Trains crashed in his head as he considered what he did know about Umber's kind—specifically, as he recalled Umber's warnings when Hansa had summoned him to the jail cell.
Hansa had demanded a third boon. He had sealed it. Just before they stepped into the Abyss.
Mm-hmm, Umber said. He excused himself from the others and returned to Hansa's side.
"This . . . isn't going to go away." Hansa resisted the urge to look at Umber because he didn't trust himself if he did, but he desperately hoped the other man was about to snicker and call him an idiot. Just as long as he told him he was wrong.
The third boon creates a bond, Umber reminded him. It's permanent—or at least, as permanent as your life. I've yet to find anyone who checked to see if it carried over to the afterlife.
Much as Hansa hated having the spawn talk in his head, he preferred not to have Cadmia and Xaz overhear this particular conversation, so he responded the same way. So what does that mean, really?
It means . . . it means, in many ways you are lucky. Hansa snickered at the absurdity, but Umber continued undaunted. I wasn't making idle threats before. I've seen bonds that destroy both parties. I've seen soulbonds where the submissive party weeps whenever his master's attention turns elsewhere and would starve if his master didn't force him to eat. I've seen bonds go so mad they had to be locked away. You're obviously still capable of thinking, and just as obviously not terrified of my displeasure, so all things considered, you're lucky.
Lucky.
"Bastard," Hansa mumbled. "Lucky?"
"Yes, lucky," Umber insisted, replying aloud in response to Hansa doing the same. "In addition to everything else I just said, you could have been flesh-bound to someone who didn't find you attractive, or wasn't attracted to men at all."
He couldn't help but notice Cadmia's startled glance his way. She immediately looked forward again, but this time Hansa was too focused on his own concerns to follow her conversation with Alizarin. Umber hooked an arm around his waist, guiding them both further away for privacy.
"I'm not attracted to men," Hansa snarled. "Doesn't that matter at all?"
Umber lifted a brow, as if he might have the nerve to point out that there had been moments that brought that assertion into question. Hansa remembered once more the factious teasing with Jenkins that had once caused them both to be censured, and Ruby's resigned—but unsurprised—expression as she walked out on him for the last time, saying only, I won't tell.
Instead, the spawn said, "Power easily and often overrides preference. You should know that from all the mancers you've arrested."
"You're thrilled about this, aren't you?"
"I'm not exactly weeping," Umber admitted.
"I'm not an animal," Hansa said. "I have self-control. I don't care what power says. I'm not—" At that point, he remembered Umber's arm around his waist. He removed it and took a step away. "I despise you. I will never sleep with you. Do you understand that?"
"Whatever you say."
"Son of a bitch," Hansa spat, though even the epithet lacked the strength of anger. Talking wasn't what he wanted in that moment, and since Umber tended to read his mind, he had to know that.
"I'm not lucky," Hansa said. "I can't think. I can be useful—I should be able to be useful. I'm a trained soldier. But I can't focus long enough to contribute to any kind of plan or even to . . . to . . ." He lost the thought. This would be easier if Umber had a shirt on. He had taken it off to use as bandaging for Cadmia's wounds the day before.
Hansa remembered that moment, when he knew he should have offered help, should have been standing guard, should have at least cared that Cadmia was clearly dying—but could only stare at the skin Umber revealed.
"You sealed the bond over twelve hours ago," Umber said, his tone conversational despite Hansa's turmoil. "The fact that you're still rational enough to notice you're impaired is remarkable. I suspect you're one of those people who has a natural potential for power. That would explain your success in the One-Twenty-Six and why Antioch found you an attractive replacement for his mancer."
Hansa hadn't thought to ask Umber about that confrontation, though he'd had plenty of questions at the time.
"Rational enough," he echoed. "I can't live like this. If we make it back to Kavet, how can I possibly function?"
"That's an 'if' I'm not certain of at all," Umber said, sounding concerned for the first time in the conversation. His gaze and tone sharpened and he said, "The four coins of the Abyss are blood, fire, pain, and flesh. Some of the bonds form in emotion or thought, which is what makes them so devastating, but a fleshbond is simple. It wants power. It will steal your reason if it needs to, but if you keep it satiated, it will leave you alone. Right now it's starving, so it's directing all your attention to the source of its desired meal."
Hansa blinked at him, trying to decipher the long string of words, half of which had been lost in a vivid, unwanted image of what Umber had looked like sprawled on Hansa's couch. He wanted to be angry, to yell and blame the spawn, but unfortunately he wasn't yet stupid enough to believe this was anyone's fault but his own. He thought he had understood the others saying his hysteria and demand for the third boon had been coerced by the Numini. Given the way their lives seemed to be going, he wouldn't be surprised if someone said the Numini had even put Rose into that jail cell to give him information about how to demand a second boon. But he had to accept responsibility for what he could, and that many of the decisions he made were his own. He had started on this path willingly, despite every Quin teaching and Kavet law warning him that any step toward sorcery was a slippery slope to the bottom.
He was at the bottom now.
Umber gave up waiting for a response, and rephrased in simpler terms. "The bond wants its flesh. The more you try to ignore it, the more insistent it grows. Like this."
He leaned forward; Hansa saw the movement, but had no will to pull away. Umber kissed him, almost chastely, but the brief contact was enough to derail any futile attempt at logic and make his knees weak. Umber had to catch him around the waist.
"Ruby," he protested, though he knew it was stupid even as he said it. Even if they were able to bring her back, even if their relationship hadn't been over before she killed herself, and even if she forgave him for practicing black magic to save her—doubtful—she would never accept his allying with the mancer and Abyssi responsible for her brother's death.
"I know I've screwed up," he whispered, "but I want . . . I do hope I can recover . . . something. I had accepted that Ruby and I weren't going to work out before she—hurt herself, but that doesn't mean I've given up on the kind of life I wanted. It isn't just the Quinacridone talking, saying that this, with you—" He broke off, and tried again. "Quin, Napthol, Order, mancer. It isn't a matter of 'religion' or 'morality' at this point. I want a life. I want to be able to have a family. I want . . ." Numen, he wanted to wrap his arms around the Abyssi-spawn and kiss the line that had formed between his brows as Hansa spoke.
"Hansa . . ." Umber looked away. "I'm not a jealous lover. I feel no possessiveness over you, beyond the need to keep you safe because you are my bond. I am going, to the best of my ability, to try not to interfere with your life."
"So, what?" Hansa asked. "You propose that I just roll over and leave your bed in the morning to go back to my wife?"
Again, that look. "No, I propose that, whatever I do, you are not going to have the perfect Quin life. Whether or not you were manipulated into it, the bond remains. At the very least you will need to take precautions to avoid sighted guards noticing Abyssal power on you. And as I said before, power will have its way no matter what you prefer. If you try to ignore the bond and the power gets desperate, in addition to me, you might find yourself drawn to subgroups like the spawn, maybe Abyssumancers or Abyssi outright. You can't afford to respond to a call for the One-Twenty-Six and find yourself dazzled like a schoolboy by your target."
Abyssumancers had given that as their excuse more than once when Hansa arrested them: the power needs this. It needs blood. It needs pain. Some of the younger ones still seemed horrified by the appalling things they had done in the name of their magic. Hansa had never understood.
He understood now.
"You're right," Umber said. "Part of what makes Abyssumancers so dangerous is that even the best-intentioned of their lot lose any moral compass when their power makes a demand. The boon has more specific needs, so it has no reason to push you to the kind of abuse a mancer may commit, but if you deny its demands, it can strip you down until you lose all reason. Maybe you would rather let yourself get to that state so you can absolve yourself of all responsibility. Personally, I hope you'll make a decision early enough that you're still capable of giving consent. As I've assured you before, I am not interested in rape."
Hansa flinched from the coarse word, the last of a series of truths he wished he could refute.
"Do you want to go back to the others now?" Umber asked, leaving the other option gently unspoken.
Hansa fought to organize his thoughts, to exercise some form of logic.
I despise you. I will never sleep with you. Those words, spoken in anger and fear and defensiveness, now gave him a barb of guilt. How many men, half-Abyssi or not, would have disregarded Hansa's countless jabs and insults and still attempted to be decent in this situation?
He couldn't find the words he needed. He believed Umber, but didn't know how to say yes. Especially here. Now. "I can't," he said, not answering the question Umber had asked aloud, but the other one, the implied one. "Not with Cadmia and Xaz only a few paces away and an Abyssi who might be inclined to jump in. I . . . just can't." There were so many other things wrapped up in that can't, but Umber nodded, accepting either the reasons he had stated aloud or the dozens of others swirling scattered in his thoughts. "If we were alone . . ." If Xaz and the others hadn't been around, the question would already have been decided.
"I can't promise privacy anytime soon." Umber didn't sound like he was pushing Hansa to change his mind, just reminding him of one of the many complications they faced.
Hansa swallowed his squeamishness. "I'm not saying no to you." The words heated his face, but he continued, because he hated that ugly word Umber had used and it was important to get this out in case he couldn't say it later. "I'm saying no to the situation. If we ever get somewhere where we're alone, or if I get to the point where I'm not able to make a decision on my own any more, you have a yes."
Umber's smile was wistful, with none of his usual cavalier derision. That was good; if he had made a smart quip in response to Hansa's struggling to give him the consent he claimed to care about, Hansa would probably have punched him.
"We should get back to the others," Umber said. Hansa tensed as the spawn reached for him, but Umber said, "Some touch is better than none. Little bits of power may tide you over until the situation changes. Being here in the Abyss helps, too; the power in the air isn't quite what your body needs, but it's close, like bread for a man who needs meat. It will fill your stomach a while."
How long was a while? Long enough for them to get this ridiculous boon out of the way and get back to the mortal realm? Unless his luck drastically changed course, it seemed more likely a descent into madness would find him first.
CHAPTER 28
Cadmia sighed, momentarily luxuriating in the feeling of a full belly and a comfortable spot to sit.
Once she overcame her initial hesitation, the strange food Alizarin had provided proved satisfying. The odd, spiked fruit was a deep purple, segmented inside a little like an orange, but with a flavor more akin to whiskey. She expected it to leave her parched, but the juice soothed her dry throat. The meat—which they ate raw because even Alizarin could not make a fire from bare sand and the scattered shells let off a greasy, smoky flame that made them all cough—had the soft-grained texture of high-grade tuna, and was delicious as long as she could put the image of the slimy, sharp-toothed orange-and-yellow snake it came from out of her mind.
She ate lounging against Alizarin's side the way she had once sprawled on the large throw pillows that filled her mother's parlor—except this "pillow" was warm, vibrated with energy, and was firm underneath a layer of the softest fur she had ever touched.
"You would make a good Abyssi," Alizarin declared, tapping her knee with his tail to punctuate his point.
When Cadmia had first woken tucked against the Abyssi's chest, she had frozen, caught by too many dissonant sensations: the long-missed familiarity of having a man's body next to her after a decade spent sleeping alone, the exotic feel of soft fur over hard muscle, and the trepidation that filled her as she remembered where she was and who—what—she lay against.
Before she could decide what to do, her stomach had rumbled. The sound woke Alizarin, who stretched unselfconsciously, seeming not to notice the way doing so made Cadmia's breath hitch, and asked, "Do you need food?"
That brought them to here and now.
"Thank you," she said, because the words seemed intended as praise. "Why do you say so?"
"You take pleasure in things when you have them," he said.
"She thinks too much to be an Abyssi," Xaz remarked.
Alizarin paused to consider the comment, which made Cadmia say, "Alizarin thinks a great deal, too." It was not her first attempt to get Alizarin to confirm if all Abyssi were so different than she had been taught, or if he was atypical for his kind. Of everyone she had come to the Abyss with, he was most open to her curiosity, but he tended to deflect direct questions about himself.
Hansa and Umber returned at that moment, though. Hansa walked with an arm around Umber's waist, but seemed unable to make eye contact with the rest of them.
Growing up with Cinnabar and other men in the Order of A'hknet who were open to male bed partners had left Cadmia jaded to such relations, but Quin were unequivocal in their opinion. Hansa would have been raised believing men were only attracted to other men out of some perverse, selfish obsession that focused their lust on others like themselves instead of "proper" partners. It wasn't easy to set a lifetime of indoctrination aside.
But sometimes it's worth it, she thought, considering the way she had once walked away from the Order of A'hknet, where education and study were generally considered a waste of time, and embraced a path of learning.
Umber joined their circle and helped himself to food enthusiastically, seeming undisturbed by its form. Hansa leaned against Umber, picking mechanically at what he was offered as if he didn't see or taste any of it.
Now that everyone was accounted for, it was time to turn their minds to what they needed to do next.
"We obviously need a new plan," Cadmia said once the men were settled.
She hated the thought of abandoning the lost guards in the Abyss, but it would be foolish to stay longer than necessary to try to save them. Assuming Antioch was the only dangerous foe they might face, or that he wouldn't return, were gambles they couldn't take. It also seemed clear that Umber and Hansa couldn't afford to pursue any path that didn't fulfill the boon.
"What exactly do we need to accomplish?" she asked. She thought she understood the gist of their need, but it seemed so silly that one way to accomplish the task was to decide it couldn't be done.
Hansa and Umber exchanged a heavy look, the guard looking lost and overwhelmed, and Umber contemplative. "We need to either find someone who can resurrect Ruby, or find someone with the authority to say for sure that it can't be done," Umber summarized. "According to the Numini, that means finding this Terre Verte fellow."
Cadmia's skin crawled as she imagined another mancer, a stranger, walking in and restoring Ruby to life. Despite her current alliance with Alizarin, Xaz, and Umber, it was hard to picture raising the dead without horror. She couldn't remember how she had justified it to herself during that surreal hour when she had gone to Hansa to get him to help his once-fiancée.
"And Numini can't lie?" she asked. The others nodded, and Cadmia mentally checked off another bit of information she had learned via speculation and rumor.
"Could they have misled you about this man's powers?" she asked Xaz. "I know Others can't lie, but did they say outright he can do this, or did they just hint at it or tell you to tell us that?"
Xaz paused, seeming to run the conversation through her mind. "They said it outright," she decided after a minute.
"Do we have any leeway?" She needed to understand this situation with the bond and the boon better in order to address the problem rationally. "How is this boon enforced?"
"Fighting against the boon is . . . unpleasant." Umber's words were dry and vague, but Hansa's grimace suggested the magic's reaction was fairly immediate. "I've tried to fight a sealed boon before. It's a little like slitting a wrist then trying to row a boat."
Dramatic image.
"You have another bond?" Hansa asked.
"Priorities, Quin." Xaz's cue wasn't as sharp as usual. Cadmia could still see the tension of guilt in her face, probably as she considered her role in bringing them to this point.
"Can we rescue Terre Verte?" Cadmia asked, twisting to look at Alizarin as the obvious solution came to her. Surely the word of a third-level prince of the Abyss would be enough to convince Umber or Hansa this boon couldn't be fulfilled. "Without you, we have no chance of surviving the court, much less stealing someone from it. And you don't need to help. If you make it impossible for them, Umber and Hansa don't have to do this."
Alizarin's fur flattened and his body sagged. "Even if I refuse, the Numini will force Xaz to try."
His obvious frustration and disappointment struck her. She hadn't realized she meant to pet him until she felt his soft black hair trickling through her fingers and saw his head tilt toward the caress.
"If we're going through with this madness," Xaz said, her voice a bit too high as she considered it, "how do we go about it? Even if Alizarin is powerful enough to help us get this sorcerer away from the court, that won't help us if we're trapped in the Abyss."
Alizarin looked at Umber apologetically before he said, "An Abyssumancer would be able to open a rift."
It seemed a simpler solution in words than the others' expressions made it out to be. Umber in particular looked pained, as if he recognized the logic of Alizarin's suggestion, but still wished he hadn't made it.
"Clearly much of what I've been taught is misconception and propaganda," Cadmia said, considering the Numenmancer, Abyss-spawn, and Abyssi who were her current companions. "Are Abyssumancers as dangerous as we're told?"
"Yes," the others answered, almost in unison, voices ranging from shocked to horrified. Even Hansa joined the chorus.
Umber was the one who explained. "Mancers spend their lives fighting to balance their humanity with the demands of their power, which ultimately only wants one thing: to feed."
Cadmia looked doubtfully to Xaz, who tensed and said, "Numini don't use their mancers the way Abyssi do, so we don't lose control the same way."
The huffy reply seemed to prod Hansa out of his distracted state. He protested, "Tell that to the twenty-eight people killed in Fuscio last year when the summer temperature dropped so abruptly in the market square that they froze where they stood, or the three guards struck by lightning when we tried to apprehend the Numenmancer responsible."
Cadmia wasn't familiar with the event, but Xaz's livid expression made it clear she was. "Of course, blame the mancer," she spat. "Did you even look at the scene when you arrived? Did you see the noose those twenty-eight people had thrown over the chapel's balcony rail? It was a lynch mob!"
"Enough!" Cadmia shouted, interrupting the argument before the two could come to blows. Given Hansa and Xaz had effectively tried to kill each other only a few days ago, it was amazing they had made it this long without conflict, but the topic under discussion was Abyssumancers. "We don't have time for this." The conversation had made it clear that even Xaz was biased on the subject, so Cadmia asked Umber bluntly, "If a tie to the Abyss makes one so irredeemable, why aren't you a monster?"
"I'm not a human bound magically to an Abyssi," he answered, apparently unoffended. "I am part Abyssi. I don't have one using me as a valuable—but ultimately disposable—source of food. Unless," he continued, frustration leaking into his tone, "we find an Abyssumancer who sees me as just that."
That explained why he so clearly wished there was another way.
"Can we do this without an Abyssumancer?" Cadmia asked Alizarin.
"I do not believe so," he answered.
"Then how do we find one?"
"I normally follow the trail of corpses." Hansa set aside his half-eaten food. "Even if an Abyssumancer can help us, do we have a reason to expect one will?"
"There is an Abyssumancer named Naples attached to the high court," Alizarin said. "He will help as a favor to me."
"If we need to go to such a person," Xaz said grudgingly, "I advise that we don't mention the Numini. Even if he wants to help you, Alizarin, an Abyssumancer might be contrary enough to refuse any request that might please the Numini."
Alizarin shrugged, as if he hadn't considered that point but didn't intend to dispute it.
"No offense, Alizarin," Umber said, "but you've been accused of getting the last mancer who helped you killed. Will this Naples trust you?"
Alizarin shifted uneasily behind Cadmia. "He will help."
"Won't his Abyssi object?" Hansa asked.
"He never has before."
"Do we have any other ideas?" Cadmia asked one last time. No one responded, or seemed inclined to meet her eye, so she said, "Then this is our plan. Alizarin, how far are we from this Abyssumancer?"
She imagined trekking through this dangerous wilderness for days, eating the kills Alizarin brought back and engaging in battle with whatever enemies challenged them.
Alizarin rolled onto his back, thought, and said, "At your speed, not far. Less than an hour."
Cadmia did some mental geography, considered their earlier conversation about the analogous nature of the Abyss to the mortal realm, and asked incredulously, "The Abyssal high court is directly under the city of Mars?"
"That's . . . mighty convenient." Umber spoke with his customary suspicion.
Xaz rolled her eyes to the sky, or what would be the sky if there were anything but a sooty darkness above, and said in long-suffering tones, "The palace of the Numini is the same, or so I have been told. It isn't surprising, really. Kavet is the only country in the world with mancers. Perhaps that's because it is so close to the strongest Abyssi and Numini."
"That might explain the country," Cadmia agreed, "but what explains the capital city being exactly above—and below, I suppose—the Other courts?"
"The royal house." Hansa sounded uncharacteristically impatient. "They were accused of sorcery in the revolution, and they're the ones who first established the city of Mars. What's to say they didn't build it there intentionally?" All record of the royal house had been destroyed during the revolution, but it seemed as sound a theory as any. He moved as if to stand, then hesitated. "Are we going?"
"We're going," Umber answered, abandoning his half-eaten food and pushing to his feet.
As if noticing that the rest of them were hastily using black sand to clean their hands, Hansa said, "I don't think it's a good plan, but it's what we need to do."
Cadmia understood the need for haste, or thought she did, until she saw the way Hansa kept shifting his weight like a man whose muscles have gone to pins and needles. He was trying, and failing, to conceal the signs of his physical discomfort.
Umber was doing a better job. Cadmia might not have interpreted his stone-faced expression as anything but laconic disinterest if she didn't know the situation.
Like slitting a wrist then trying to row a boat.
She'd had enough to eat. When she stood, Xaz and Alizarin followed.
A flickering glow out of the corner of her eye drew Cadmia's attention to the butchered snake Alizarin had left a few yards off. The shining creatures that normally hung from the trees flowed over the carcass like phosphorescent slugs. Another scavenger, a trundling creature the size of Cadmia's palm with a dense shell like a turtle's, had buried its muzzle in the snake's eye. Occasionally one of the wisps slapped at it with a gleaming tendril, but though the blow let off a hiss of steam, it didn't seem able to penetrate the beast's shell.
"Not worth eating," Alizarin proclaimed, seeing the direction of her gaze. "Too much bone and shell, and the meat is dry."
The circle of life in the Abyss, Cadmia thought, and then they started uphill to the high court.
As they walked, the stone dunes on their left rose higher and became sharper. Dagger-sharp stones pierced the soft black sand with increasing frequency, making the footing treacherous for all but Alizarin, who avoided them with ease.
Stepping on a sharp rock wasn't the only hazard. Tiny crabs with bodies the color of fresh blood scuttled forward aggressively, snapping hooked claws if one stepped too close, and long-legged white spiders with sharp mandibles that glistened with venom perched in flat, sticky nests. Occasionally they passed old, dry bones, or newer carcasses, these latter wrapped in spider's silk or covered in the Abyss's other scavengers.
The trip should have taken Alizarin's promised "less than an hour," but at their careful pace it seemed to last for days. Even Cadmia didn't have the energy or attention to hold a conversation, and no one else seemed to want to try.
Alizarin often bounded ahead, impatient, and circled back. Xaz minced in the front of their group, with Cadmia next and Hansa and Umber lagging behind. They walked close to each other, touching whenever they could.
Alizarin was on one of his jaunts when they topped a rise and saw a man kneeling on the ground to butcher a . . . Cadmia had no idea what it had once been, except that it seemed to have far too many legs, each tipped with a nasty-looking barbed claw. The man was using an irregular gray blade to deftly remove each claw without touching it. He looked up without surprise as they approached, used a handful of black sand to wipe the knife clean, then sheathed the knife in a boot and stood.
Unlike the shades at the camp, whose clothes had been cobbled together from frequently-mended scraps, this man was dressed in well-fitted soft leather and fine fabric with the pulled look of raw silk. His ashy-black boots stopped just below his knees, and his forearms were protected by gauntlets of speckled gray leather. Under a tough vest of the same material, reinforced by glistening, plum-violet scales, he wore a burgundy shirt that laced at the throat. His skin was fair but had none of the ghastly pallor of the shades, and instead of being fogged and colorless his eyes were bright, coppery brown.
In case any doubt remained, the knives—the one he had just tucked in his boot and another she could see on his right thigh—made it clear what he was.
Instinctively, Cadmia looked for Alizarin, who was frustratingly out of sight. Based on her understanding of the Abyss's rules, it should have been up to Umber to speak for their group when Alizarin was absent, but the spawn had halted and seemed to have no intention of moving any closer to the stranger.
Cadmia cleared her throat. "Are you Naples, the Abyssumancer?" She sounded more confident than she felt.
"Yes?" His gaze flicked dispassionately down her body as if to assess—and dismiss—her worth before turning to the others. Umber had taken another step backward, but Naples didn't attempt to close the awkward distance. Instead, his brows lifted as he saw Xaz. "I cannot begin to imagine the circumstances that bring a Numenmancer into the Abyss."
Xaz took a deep breath. Her voice was steady as she answered, "Alizarin, of the third-level court. He—"
Xaz didn't have a chance to finish before the Abyssumancer twisted to look behind him a heartbeat before Cadmia's eyes caught the distant, distinctive sheen of blue approaching rapidly from the direction of the court.
She tensed, wondering how Naples would respond. Alizarin had known of Naples, but she didn't know how well informed an Abyssumancer would be. Did he know about Baryte's death and Antioch's grudge? Would he be concerned about the tension between Alizarin and the high court?
Naples' expression brightened and he shouted, "Alizarin!"
Alizarin vaulted up to the mancer, who reached out confidently as if to embrace the blue Abyssi. Alizarin had implied earlier that he had a relationship with this mancer, but Cadmia hadn't imagined it to be this friendly.
When the mancer tried to lean against the Abyssi, however, Alizarin pushed him back, saying, "You're hungry. You haven't been hunting?"
It seemed an odd question, since that was exactly what Cadmia assumed Naples had been doing before their approach. The Abyssumancer shrugged and changed the subject. "You know I always look forward to your visits, and your companions are of course welcome as well. Let's get inside where it's more comfortable. I'll send someone back for this." He gestured dismissively to the half-butchered carcass beside him. He led the way to the crest of the dune over which Alizarin had bounded with ease, then paused at the top. With a sweeping gesture before him, he said, "Welcome, all, to the high court of the Abyss."
For the first time in what felt like months, Cadmia lifted her gaze instead of cautiously watching her step.
"Oh," she whispered, as she beheld the edge of the court.
Slices of stone, like those along the beach but hundreds of times taller, formed walls with razor-edges that glistened, transparent, where they caught the light. Cadmia couldn't see over them except for the irregular obelisk-like structures that towered on the other side, some so tall they seemed to merge with the smoke-gray sky. The towers' positions appeared haphazard and they leaned crookedly, a few seeming in danger of collapse at any moment. Had they been built? Did Abyssi build? Or had they grown on their own, like crystals?
Outside the wall, the dark sand clumped and solidified into glass, as if the buildings had been formed through magnificent heat.
Naples led them around the wall until they found a fissure where the vertical stone had cracked, leaving a gap wide enough to allow them all to enter side by side with room to spare. There were no gates or guards, and the opening in the wall appeared to be a natural formation instead of an intentional doorway, but beyond it were signs of cultivation. An amber-colored, mosslike plant with tiny, trumpet-shaped flowers defended by fine black needles bordered the path.
The building Naples led them to—if it was a building—was blocky, with no apparent doors or windows. A sphere of cinnamon-colored light floated near the blank wall. Cadmia gave it a wide berth, remembering the wisps, but Naples seemed unconcerned as he approached. He reached up and a section of the wall dissolved like smoke caught by the wind, revealing an open doorway.
Xaz had used her power in front of Cadmia more than once, but it had been subtle and quiet. This was the first obvious magic Cadmia had observed since Alizarin opened the rift from Kavet. Was the shiver that passed over her skin fear, an instinctive reaction caused by a lifetime of being told mancers were dangerous, or excitement?
Alizarin took the lead, passing through the doorway and into an interior that was either as dark as the caves in which they had first appeared or hidden by magic. Cadmia started to follow, then hesitated, because the others looked like they might balk.
Naples shook his head at their wary looks. "From the outside, the doorways only respond to me, Azo, or the other true Abyssi. From the inside, they respond to anyone. If you honestly feel safer outside, you will be able to get out at any time."
Without waiting for them to respond, he walked inside.
Cadmia understood their reasonable fear of putting themselves at an Abyssumancer's mercy, but did they really feel safer out here? She followed Alizarin.
Inside, what had been a cavelike chamber had been turned into a welcoming parlor. Woven wall hangings softened the black walls and the floor was warmed by furs and leathers that had been dyed and set out as area rugs. The light was provided by orbs of flickering, ghostly flames hovering near the ceiling.
"Pardon me a moment," Naples said, as he started unlacing his bracers. "I'm a bit overdressed for company at home. Alizarin, I assume you'll want to greet Azo, then utilize the baths?"
Alizarin didn't hesitate—he loped off through one of the two doors in the opposite wall. Cadmia hoped that meant he trusted the Abyssumancer, and not that he didn't care about the rest of them.
For the first time, Naples' gaze focused on Cadmia. "The third level of the Abyss is hot, and steaming seas cover much of it. Rin hates the constant grime of this level."
"You know him well," Cadmia observed, noticing the affectionate nickname Naples used for the Abyssi.
Despite where they were, it was hard to remember he was supposedly an Abyssumancer. He appeared younger than she was, probably by almost a decade, though the poise and manners with which he presented himself made him seem older.
His wistful smile also seemed to hold too many years for his face. "It isn't hard to know an Abyssi well," he said, "as long as you don't mind blood."
CHAPTER 29
"Our other option is staying outside at the edge of the Abyssal high court," Hansa said. He couldn't help remembering the shack where he and Jenkins had found Baryte. Gore and chaos were standard for Abyssumancers' lairs. He didn't want to imagine how much worse one here, where the mancer had no reason to fear discovery, might be.
For a moment, he thought Umber might say staying outside was better. If he did, Hansa might agree. Then the spawn released Hansa's hand and was gone from sight, leaving Hansa hurrying after.
He emerged in a warm, brightly lit parlor. It would never be mistaken for a home in Kavet, but compared to what Hansa was expecting it was dizzying in its normalcy.
Alizarin was nowhere to be seen, and Naples was in the process of removing his armor. As Umber, Hansa, and Xaz entered, he was hanging his vest on a peg by the door. The burgundy shirt beneath clung to his skin, revealing a body muscled like a wolf's, long and lean without a hint of extra softness. When he leaned down to take the knife out of his boot, Hansa heard Umber's voice clearly in his mind: Close your mouth, Hansa.
Hansa jerked his gaze away just as the Abyssumancer dropped both knives onto a table next to the entryway, then turned to greet a middle-aged woman who had just entered the room. Based on her pallor and the strange, clouded color of her eyes, Hansa assumed she must be a shade.
Naples conferred with her briefly, then said, "I assume you will all want to clean up before you meet Azo, the mistress of this household. Ladies, Aurelian here will see to your needs. She is better equipped than I am to identify clothes that might fit you. You two gentlemen . . ." He paused. Uncertain?
No, politely questioning. Umber caught on first. "Umber," the spawn said. "My bond is Hansa."
"Pleasure to meet you both," Naples said. He didn't offer to shake hands. Maybe he knew neither of them would want to accept. Lightly teasing, he said, "If you're willing to follow the scary Abyssumancer upstairs, I'll show you to a guest room and find you clean clothes as well."
Once again he didn't wait for them to make up their minds, but turned and led the way.
He was young, Hansa realized, or at least appeared to be—twenty at most. The realization made Hansa's stomach turn as he considered the way he had been staring a moment ago.
As they followed Naples up a steep, winding staircase, Hansa made a point to keep his gaze anywhere but on the most obvious view. Umber had warned him that the bond might cause him to be attracted to others with Abyssal power, but he refused to let that be an excuse to be vulgar.
He kept his focus on the places where the wall was recessed to accommodate orbs like the one that had illuminated the front door. These were smaller, each about the size of an egg, and varied in brightness and hue.
"Who makes the foxfire?" Umber asked.
"I do," Naples replied. "Azo likes the colors." When the Abyssumancer mentioned the woman who apparently owned this household, his voice lifted and his expression softened. The obvious fondness he held for her, whoever she was, made Hansa strengthen his resolve to keep Naples from noticing his irrepressible fascination.
"That takes quite a bit of talent," Umber said.
Naples shrugged, then pushed open a doorway. Like the others, Hansa hadn't seen the door before it opened; he wasn't entirely convinced it had been there. It reminded him eerily of the way Abyssumancers were able to produce weapons from apparently nowhere, though of the two, he far preferred a door.
They stepped into another parlor, this one comfortable, but holding an anonymous quality.
"You may use these rooms as long as you're here," Naples said. "We chose this spot for the hot spring beneath it, so all the bathing rooms have hot running water. I'll find you some fresh clothes and have one of the servants drop them off before I go wash up."
Water; clean clothes. That promise was sufficient to overcome Hansa's hesitation to accept the Abyssumancer's hospitality.
It wasn't enough to make him forget what he had told Umber. If we ever get somewhere where we're alone—
At the time, that "if" had seemed impossibly far off. Now it was too close.
Past the parlor was a bedroom, and then a washroom more luxurious than any Hansa had ever seen. After some fiddling, Umber located the lever that let in a stream of hot water that started to fill the deep marble tub. While the water was running, one of Naples' servants dropped off cakes of soap, lavishly soft towels, and a pile of clothes.
Then it was just Hansa and Umber again. Umber kept his back to Hansa as he stripped and bent to check the water. Hansa suspected the spawn was specifically not looking at him, the way one would try to avoid spooking a timid animal. Watching that golden body move, Hansa felt his mouth go dry, but he couldn't make himself close the distance between them.
He had accepted his bond to Umber as a reality, but that didn't mean he was emotionally ready to embrace it—or him—fully. Knowing he was being an idiot and a coward, he backed away.
When he reached the far wall, the stone faded away, turning into an open archway. He stepped into the hall, telling himself he wouldn't go far. He just needed to be somewhere he couldn't hear water splashing, couldn't see Umber's body—so lithe and relaxed and confident—couldn't feel the bond between them pulsing, drawing him closer . . .
He squeezed his eyes closed and drew a deep breath, berating himself mentally. Umber didn't understand . . . Hansa couldn't find the words to tell him . . . this wasn't—
"Hansa? Do you need something?" He jumped, lifting his head to see Naples descending the stairs toward him.
Naples had replaced the sweat-slicked burgundy shirt with an indigo-blue one. The neck was loosely laced, revealing a chain with an amethyst pendant beneath, and the bottom had been tucked into snug black pants. His waist was cinched in a wide belt that accented his narrow hips and flat stomach.
Stop it, Hansa!
"No, I'm—" He lost track of what he was saying in the effort of not staring.
This time, Naples noticed. Their eyes met for the first time, leaving Hansa momentarily disoriented by irises too bright to be called brown. Was that a natural color, or did his power lend the flame-touched brightness to his gaze?
"Exactly how long have you and Umber been bonded?" Naples asked.
Hansa thought back, couldn't come up with an exact span of time in his apparently addled mind, and said, "A couple days."
Naples nodded thoughtfully. "It's overwhelming at first," he said. "You'll learn to manage it better over time."
Naples' position in the household and the way he spoke of the woman who owned it came abruptly clear. "You and Azo?" Hansa asked.
"For a very long time now." Naples looked up and down the stairs with a grimace. "There are more comfortable places to have this conversation. Let's step out on the balcony for a few minutes?"
This time, when he pressed a hand to the wall, it didn't mist away; there was a shimmer and shiver in the stone, perhaps as the Abyssumancer summoned the doorway he wanted instead of using one already in place.
The casual example of power made Hansa hesitate, but given he was already alone with the man, moving to a different room didn't seem any more stupid. The temptation to talk to someone who had been through what Hansa was now experiencing was overpowering.
A moment later they were on a balcony overlooking the dried ocean. Night had fallen, so the balcony was lit only by two subtle orbs of lavender foxfire. The bleak sky was heavy like earth, while the luminescent creatures in the dried sea made it look like a vast, starry sky. Hansa fought a sudden sense of vertigo, brought on by the seeming inversion.
Naples leaned against the railing. Hansa did the same, if only for the excuse to hold onto something—one, to fight the disorientation, and two, to fight the urge to reach out and see if Naples' hair was as soft as it looked. "Tell me about Umber?"
"I don't know him well," Hansa admitted.
"He's mortal-born?" At Hansa's confused expression, Naples rephrased the question. "He was born on the mortal plane?"
"I . . . don't know. I don't think he has been to the Abyss before," Hansa answered. Then he remembered some of the things Umber had said since they arrived. "Maybe he has. He knows a lot about it."
"Spawn inherit memories from their parents," Naples explained. "A mortal-born spawn wouldn't be able to make sense of all his Abyssi sire's memories, but they're there. He probably has some from his mother, too." He suddenly frowned, and said with a more cautious tone, "I should have asked if he's possessive before I asked you here alone."
Hansa shook his head, recalling the assurances Umber had given him. "He isn't the jealous type."
"Good. Azo will be furious if I offend a guest, especially one brought to us by Alizarin. His patronage is one of the reasons Azo and I are able to have as fine a lifestyle as we do." Hansa jumped as the Abyssumancer put a hand over his on the rail, slender fingers tapping along the back of Hansa's knuckles, which were white from gripping so tightly. "Do you realize you're leaking power?"
"I don't even know what that means." His voice shook. With the Abyssumancer this close it was hard to draw a steady breath, but Hansa couldn't make himself step away either.
"I'm guessing an unfulfilled boon," Naples said. "Is that what brings you to the Abyss?"
Hansa nodded. "You can tell?"
"The moment I saw you. The boon . . . whispers? No, that isn't the right word. It's constantly reaching out and seeking fulfillment. No one who can feel Abyssal power could miss it."
"I'm sorry." Did that response make any sense?
"It's okay," Naples crooned, moving closer. He gently lifted Hansa's hand from the balcony rail. "You're bonded to the Abyss without any idea how to control it. You can't help sweating magic, and you can't help craving it. Luckily for you, I can help us both."
Freed of its death-grip on the rail, Hansa's hand inexorably sought the Abyssumancer. His palm on Naples' chest, he could feel the other man's heart pounding rapidly.
"Azo," Hansa said, invoking the other spawn's name in an effort to make sense of a situation that had rapidly moved beyond his control.
Naples flinched at the spawn's name, but didn't pull back. "She understands," he said.
Abyssumancer, the last of Hansa's beleaguered common sense reminded him. He recalled Umber's lesson on the four coins of the Abyss, flesh among them, and Alizarin's first words to Naples: You're hungry. You haven't been hunting?
Naples grabbed Hansa's belt with his free hand and pulled him forward, clearly done talking. Hansa groaned, couldn't help it, and couldn't seem to turn his head away from a kiss that made Umber's seem chaste and gentle. It was as if the last of his willpower had been exhausted when he ran away from Umber, and now his body had no intention of responding to the frantic yapping of his better judgement.
"What—" he managed to gasp as Naples pulled back, not going far but rather dragging Hansa with him away from the rail.
"I don't believe anyone is that naïve," Naples answered. He leaned back, taking them both through another doorway and into a room lit only by a single, candle-bright globe of flickering red foxfire. Bedroom, Hansa realized, as Naples shoved him against a post that seemed grown from the black stone floor, one of four delineating the massive, fur, and blanket-piled bed that dominated the room. "You've been staring at me since we met."
"I didn't mean—"
Once again Naples cut him off, this time with a finger across his lips that turned into a caress over his cheek, down his neck and to his chest. "Trust me," the Abyssumancer said, "I don't mind." Deft hands untied the laces holding the neck of Hansa's shirt closed, then dropped to slide under the bottom of it.
"I mind," Hansa managed to say.
"You can't mind much." Naples' voice was almost lost in cloth and skin as he pulled the shirt over Hansa's head and tossed it away, then started licking and nibbling his way down Hansa's chest. "You haven't asked me to stop."
There was a flaw in that logic somewhere, but Hansa couldn't put it into words as pale fingers slid down his skin and the world dissolved except for the feel of flesh on flesh.
Then it was gone. Naples reeled back; in the absence of his heat, Hansa's flesh raised in gooseflesh. He blinked eyes that didn't seem to want to work correctly in the dim light and identified Umber, who had slammed the Abyssumancer against the wall.
"Damn it," Naples growled. "He told me you weren't the jealous type."
"He probably also told you 'no,'" Umber spat. "Not that I'd expect an Abyssumancer to give a damn about anyone's preference but his own."
Hansa leaned against the bedpost, trying to get his spinning mind back under his control. This was worse than the constant, gnawing craving for Umber. Getting words out was difficult, but he managed to say, "My fault. I should have . . ." He lost the thought as his eyes finally focused on the two men, both dark-haired and shirtless, Umber's broader-shouldered form pinning Naples' leaner one against the wall.
Umber glanced back when Hansa spoke, and Naples took that opportunity to shove him away.
"Hear that? He didn't—"
"Didn't fight and protest?" Umber looked like he wanted to shake the Abyssumancer again but didn't quite dare. "You know he's a fleshbond. I'm sure you can read how new the bond is, and since you're in one yourself, you know how overwhelming those first days can be. You can't even make the excuse that you're an adolescent mancer who's helpless to resist the whims of the Abyss. You're powerful enough that—"
"I'm powerful enough that, if I didn't respect your complaint, I could have stopped your heart already. Consider that," Naples growled. "I tried to confirm with him that you would not be upset. I apologize that I was mistaken."
"You don't have the faintest idea why I'm upset, do you?"
Naples looked Umber up and down as if the answer might be written somewhere on his body. Apparently he thought it was. He put a hand on Umber's chest and said, "Oh, I see." Umber growled and flinched away from the touch, but Naples' expression was strangely gentle as he said, "You hide your power better than he does. I had no idea how dangerously starved you are. Have you been funneling raw power into him to sustain him? Why? You two are flesh-bound. You should be—"
"That's a rather personal question," a soft, alto voice interrupted.
Naples broke off, face going pale as he turned toward the new speaker. All the arrogance, fury, and even attempted kindness melted from his expression, replaced by despair so clear it broke through the druglike lust that had overwhelmed Hansa's reason.
It wasn't Umber who had stolen Naples' confidence, but a woman standing silently in the shadows at the far doorway.
Umber shook his head, muttering a curse as he pulled away from Naples. "Don't touch him. Or me. Ever again. Do I make myself clear?"
"I would never knowingly trespass on a guest's property," Naples said, the words sounding wooden as he kept his eyes locked on the other figure.
"Well," the woman said. At the single word, reverberating with irritation, Naples flinched.
"I'm sorry," Naples whispered.
"Umber, go take care of yourself and your bond," the woman said. "Take your time. When you're ready, we'll meet you downstairs to talk about your situation. I'm sure Naples will be anxious to help." Her tone was one of command, not suggestion.
"Thank you for your assistance locating my bond, Azo," Umber answered formally. Without another look to the Abyssumancer, he said, "Hansa, let's go."
On legs that felt like they might betray him any moment, Hansa followed Umber into the hall.
"I should have listened to you," he said as soon as they were alone in the stairwell. Umber had warned him that the bond might leave him especially vulnerable to Abyssumancers, but all he had heard was how his life was falling apart.
"I knew what would happen if I let you walk out of the room on your own," Umber said. "I could have stopped you. I felt it was important for you to . . . learn. I know it sounds cruel, but I preferred to have it happen here, in relative safety, than back in Kavet."
Hansa sighed. Just the way he hadn't been able to look away from Naples would have gotten him in trouble if it had been someone in Kavet. So he also repeated himself: "I should have listened to you. I can't even blame Naples. I practically threw myself at him."
Umber grimaced. "Would you blame yourself if you had been drugged, too? You might as well have been. Naples sensed the bond's hunger and fed it. You were more vulnerable than you might have been if we'd had more privacy the last few days, but an Abyssumancer of Naples' power . . ." He reached up to stroke the wall next to the sphere of teal foxfire Hansa remembered from in front of their rooms, and the door appeared. "There was nothing you could do. When we get back to Kavet, I'll teach you how to shield yourself and hide from his kind."
"And for now?" Hansa asked. Umber had told him before that Abyssumancers were dangerous even to spawn, but Hansa hadn't believed it—or at least, hadn't believed they could be more dangerous to someone like Umber than they were to a soldier in the 126. Now he did.
"As long as we're here, Naples is on a short leash." He growled, rumpling still-damp hair with his fingers. "Most of the Abyssumancers you've met in the One-Twenty-Six are newly tied to the Abyss. Their Abyssi don't understand the danger or don't have the self-control to protect their mancers, so they make stupid mistakes and get caught long before they master their power. They're like kittens who can't help swatting at pretty bouncing lights. Naples . . ." He shook his head. "Mortals don't age in the Abyss, so I don't know how old he really is, but he is long past the stage of being a helpless slave to his power. Azo and the Abyssi of the court won't tolerate him unless he follows their rules."
"Don't those rules include not stealing others', um, property?" He chose and discarded a half-dozen other words before deciding on the last one, none he liked better when referring to himself and several that were worse.
"He could only abuse you because he could claim to believe—or really did believe—that I wouldn't mind. He probably told himself I wouldn't have let you go off on your own unless I was willing to share you." He flashed a feral grin Hansa was certain had nothing to do with joy. "Though you'll notice he was careful not to actually ask me."
"And he didn't need to ask me," Hansa grumbled. Both because the laws of the Abyss apparently said a human's opinions didn't count, and because Hansa lacked the ability to say no. That reminded him of something else important. "He said I was leaking power because of the unfulfilled boon. And you. He described you as starved."
Umber nodded. "I've been giving you as much power as I can risk losing to keep you coherent. Between that and the open boon, the two of us might as well put out a sign for Abyssumancers saying, Free Meal." This time, his slow smile, coupled with a meaningful glance around the opulent room, looked more genuine. "Thankfully, we now have the opportunity to address one of those failings, and a plan for how to address the other. If nothing else, Azo will force Naples to help us to make up for his gaffe."
Umber reached out, and his fingers slid against Hansa's bare shoulder. Hansa tensed instinctively, fighting the flesh-craving that touch renewed, and Umber took his hand away.
"I don't want to push you," Umber said. "I know the Quin have rather unpleasant precepts about men with male lovers. As long as we're in the Abyss, I can keep doing what I've been doing, but once we're back in Kavet that won't be an option."
Hansa didn't think it was an option here, either. Naples hadn't used the word starved to be poetic. Now that he was paying attention, Hansa could see the way Umber's jaw and cheekbones seemed more pronounced and his tanned skin a shade paler. He hadn't seen it before because he had been trying so hard not to notice anything about how Umber looked. Giving away so much power had to be dangerous for him.
Either guessing or reading Hansa's thoughts, Umber admitted, "There are other sources of power here. Once you're settled, I can seek them out."
Umber was trying to give him an easy answer. The only thing easier would have been if Umber had taken Naples' approach and deftly removed all opportunity to refuse. If only Xaz hadn't stopped them that morning, when waking in Umber's arms had made it so easy to let the bond take over without thinking about it . . .
"It's not just that you're a man," Hansa managed to say, trying to express the jangling thoughts that made it so hard to step forward and take Umber in his arms when the magic wasn't overwhelming him. "I mean, yes, that's . . . awkward . . . for me, but . . . I mean . . . you know I was raised Quin. Ruby and I, we both were."
"I'm aware of that." Umber sounded puzzled. "I—" He stopped. "Quin believe in waiting for marriage. You're telling me you've never . . ." He trailed off as if the possibility was too absurd. "You're twenty-seven years old!"
"Maybe Abyss-spawn can't survive without sex, but humans can."
"They can," Umber conceded. "But why would you want to? Are you sure you ever were attracted to women?" He bit his lip before Hansa had to dignify the question with an answer. "Sorry. Dear Numen, Hansa, I nearly fed you to the Abyssumancer!" Hansa felt the ghost of a smile on his own face as he watched Umber try to come to grips with a fact he clearly didn't know how to handle. It was nice to see him off-balance for once, instead of Umber always being confident while Hansa fumbled.
"I don't want to pressure you," Hansa said, struggling to keep a straight face as he repeated the words Umber had recently spoken more seriously. "If you need some time to—"
"Come here, Quin." Umber grabbed his wrists and tugged him toward the bed. The grip was light enough that Hansa could have pulled away, but he followed despite his pounding heart. "I'm glad you put me off before. You deserve better than a quick tumble on the beach of the dry sea for your first time."
"Careful," Hansa said, trying to maintain a façade of humor to keep from revealing just how nervous Umber's intense gaze made him. "You're starting to sound like a Numini."
He had moved closer to Umber without even noticing. It would have been impossible not to. Now, Umber wrapped his arms around Hansa's waist.
"How can I introduce you to new and obscene acts if you've never even made love?" he purred, his tone once again sardonic, expression sultry. "Come to bed. Let me show you how it's done."
CHAPTER 30
The Abyssumancer had separated them the moment they entered the building. Xaz could only hope the hospitality was genuine, and Alizarin and Azo were enough to keep Naples in check.
Aurelian had mouthed apologies about the simple accommodations she offered Cadmia and Xaz, explaining that there was only one real guest room. She didn't say it outright, but it was clear that the guest room had been given to either the Abyssi or the Abyss-spawn, and the rest of them were lucky to have a place to stay.
Xaz didn't care if it was a space normally reserved for servants. The room was simple, but it was clean and warm. The floor was almost entirely covered by a startlingly crimson fur throw, the bed was topped by mounds of blankets, and most importantly, it wasn't likely to be invaded by the predatory beasts of the Abyss. Did anything else matter?
Well, there were the baths down the hall, which she made full use of.
The water was hot to the edge of scalding, and felt marvelous after walking through the Abyss. The heat soothed her aching muscles, and water and caked soap made quick work of sweat and grime. The fresh clothes Aurelian brought were nothing intricate—loose slacks and a shirt in the same style as everyone else in the household wore—but they were made of deliciously soft material that felt lovely against Xaz's chapped and sand-scuffed skin.
She meant only to put her sore feet up for a minute, but realized she had drifted into a doze when Aurelian announced, "Lady Azo will see you now." No matter how exhausted she had been, or how lulling the comfortable accommodations had been, she couldn't believe she had fallen asleep!
Back in the front parlor, a tray had been set out with a variety of fruit and bite-sized pieces of roasted meat. Xaz wondered if any of it had previously belonged to the multilegged creature they had seen Naples butchering, then decided that was a contemplation best avoided.
"Should we wait?" Cadmia asked, looking at the food and then around the empty room.
"I'm a Numenmancer," Xaz said. "You're human. I don't think we need to worry about falling further in their esteem."
She understood where she fell in the Abyss's hierarchy of importance. She wasn't sure if being a Numenmancer made her more valuable than Cadmia or less, but either way she suspected she ranked about as high as the jellyfish creatures Hansa had killed.
Besides, she was hungry. Alizarin had brought a little bit of fruit, but mostly meat, which Xaz had only eaten enough to keep from feeling like she was starving. After that, she couldn't stand it. Even this offering, which was spiced and roasted instead of raw, didn't sit well on her palate.
"I didn't expect there to be a place like this in the Abyss," Cadmia remarked as she helped herself to a small plate of food. "How would something like this be built?"
"It may have been a natural cave system Naples and Azo modified," Xaz speculated, "or the Abyssumancer may have carved it out entirely. The doorways and foxfire are clearly his work." With effort, sacrifice and ritual, Xaz thought she could create a hidden door like the ones that peppered this warren, but she would never be able to maintain one, much less the dozens she had seen here so far.
Focused on her contemplation of the magic she had seen so far, and what it implied about Naples' power, Xaz was startled when Cadmia asked, "How did you become a Numenmancer?"
Xaz bristled. She knew what the Quinacridone and the Napthol said about how her kind came into being. She stared into Cadmia's face, but saw no judgement there, only genuine curiosity.
"The Numini started speaking to me when I was a child," she said at last. "Five or six, maybe? I don't remember when it started. They told me to keep them secret, and it was years before I connected my dreams and invisible playmates with the creatures my parents warned me about, and the tricks they taught me to do with sorcery." There was no way to describe the depth of her horror when she had finally made the connection between the wicked things they warned about at her school and the beautiful power the Numini had given her, or the extent of her hurt at the Numini's cold dismissal of her terrified, guilty questions. "When I finally understood and tried to question the Numini, they told me they had chosen me and I should be honored and grateful. Refusing them has never been an option."
Now there was disapproval in Cadmia's face—at least for a moment, before she hid it behind her professional mask—but she didn't have a chance to ask a follow-up question before a doorway opened in the far wall and Naples entered. The Abyssumancer had changed his clothes, and his dark hair was loosely tied back. He walked close to a woman who could only be Azo, the mistress of the household.
Umber was a handsome man, but unless one could see Abyssal power, there was nothing remarkable about him beyond his striking blue eyes. Azo, on the other hand, could never be mistaken for fully human. Her skin was the deep burgundy color of well-aged wine, and the hair that cascaded across her shoulders and down her back in frothy waves was plum-violet. Dressed in the same kind of loose slacks and blouse as Xaz and Cadmia, she nevertheless carried an air of lethality with her.
"The others may be delayed," she informed them, without bothering with courtesies like introductions. They already knew who she was, and clearly she already knew who they were, so what was the point? "Alizarin is hunting, and Hansa and Umber have their own needs to take care of. Perhaps you two can explain your troubles to us?"
Azo and Naples settled into one of the couches, their bodies touching at the hand, knee, hip, and shoulder. Xaz shook her head, disgusted by how slow she had been, as she realized the obvious: Azo and Naples were bonded. No wonder one of the spawn was able to keep an Abyssumancer under control.
Xaz and Cadmia exchanged a look, perhaps both wondering who would sound less stupid if they explained the idiotic logic that had brought them here. Without the explanation that the Numini had manipulated them, they had no excuse for their foolishness, but they had all agreed that the Abyssumancer was more likely to balk and refuse to help them if he knew this quest was divinely mandated.
Xaz, no stranger to blows to her pride, launched into the tale. Naples' eyes widened when he heard about Alizarin's confrontation with Antioch, and he went very still when she said Cadmia had heard about a sorcerer called Terre Verte in her studies at the Order of the Napthol, but otherwise they both listened impassively until the end.
"Alizarin said you might be able to help us," Xaz concluded, looking at the Abyssumancer, "though I'll admit, you have far more to lose by crossing the Abyssi court than we do. We hope to return to the mortal realm. I imagine that isn't an option for you."
She meant the words kindly, as an acknowledgement of his bond to Azo and the risk he would run if he chose to help them, but could see instantly that she had misjudged. Azo's face went stony. Naples froze. For a moment they both hesitated, as if in between heartbeats they existed as statues instead of living flesh.
Then Azo shoved to her feet and announced, "I need to go to the court and explain to them why we are harboring a Numenmancer in our walls. Naples, deal with them." She hesitated, met his gaze, and added flatly, "However you see fit."
She walked out without further apology.
A chill passed over Xaz that had nothing to do with divine power, and everything to do with that last, ominous command.
But Naples only sighed heavily. He closed his eyes and sank against the couch like a man whose body has been much abused and exhausted. "Alizarin has been a good friend to me," he said, his voice sounding hollow. "I would be honored to help him. And I—"
He broke off as Hansa and Umber entered, along with a breath of Abyssal power so strong Xaz instinctively looked past them for Alizarin. Naples' breath hissed in and his body tensed in reaction to the magic.
When he at last looked up again, his expression was like porcelain, crafted and emotionless.
"Naples was just about to say if he could help us," Xaz prompted, when too many seconds passed without anyone speaking again.
"We would be very grateful," Umber replied, settling on to the love seat across from Naples with Hansa beside him. Naples' controlled veneer cracked for a moment, revealing raw hunger visible in his copper eyes. Too late, Xaz reconsidered her assumption about his relationship with Azo.
He caught her looking, and as his gaze flicked to her, the spark of famine became fury—and then nothing. Cadmia couldn't help but recall the way Umber had described how hard it was for an Abyssumancer to retain his humanity in the face of his power's demands. How much effort did it take Naples to push the Abyss aside?
This time it was Cadmia who reacted to the unfocused moment, as Naples apparently lost the thread of the conversation. "Is everything all right?" she asked softly.
"Yes," Naples said, firmly, the word and tone both seeming to suggest, No. He shook himself like an animal exiting cold water. "I was just considering, and deciding how to begin," he explained. "I owe Umber a favor, so I would make this simple if I could, but a necromancer can't help you fulfill this bond. A necromancer could summon and control your spirit on the human plane, but you need someone with power over the Abyss in order to find her soul here and drag it back across the veil, and power over life as well in order to recreate the body."
"You're talking about a Gressumancer." Xaz had heard of mancers who could control all four planes of existence, but she gave the rumors no credence. Even when the Numini had first mentioned Terre Verte, she had assumed they referred to an especially powerful necromancer, not a mythical creature.
"What's a Gressumancer?" Cadmia asked.
"They're also known as planes-walkers," Xaz said. "They're a legend among mancers."
"Legends are based on truth," Naples said. "And based on the stories I've heard, if there's a man in the three realms who might have inspired this one, it's Terre Verte. He lived before the mancers began to be born in Kavet. The Abyssi talk about him, say he was so powerful the king of the Abyss offered him a chance to become one of them, but he refused so they imprisoned him instead."
"In the royal court," Cadmia said nervously. "Alizarin seems comfortable with his ability to manage the Abyssi of this level, but I don't know if that's an honest assessment of his abilities or an unwillingness to reveal weakness. Do you know?"
"Oh, Rin is capable of laying waste to the high court," Naples said, too casually. "He's done it before. That's how the current lord of the high court came to power." He grinned, a feral expression that showed some pride in the blue Abyssi, but more savagery than joy. "I'm powerful enough on my own to walk through the high court in relative safety, even without Azo's claim. And I have, which is how I know for certain Terre Verte is not there."
"Were the Numini wrong?" Hansa asked optimistically. "Maybe he's just a story."
Umber's voice was far, far too calm as he said, "The Abyss has five royal courts, one on each level of the Abyss." It was clear he wished he didn't need to ask Naples, "Where do the stories say Terre Verte is?"
"The fifth-level court, called the low court."
"You're mad," Hansa said. "Alizarin had to fight one fourth-level Abyssi on our way here, and it was a close call. We can't take on the entire Abyss. Xaz, I'm sorry, I know your Numini are trying to shove us into this, but as far as I'm concerned, this is impossible."
Naples yawned, seeming more relaxed instead of less now that he had revealed just how hopeless their situation was. "You didn't have an Abyssumancer with you before," he said.
"Why would you help us?" Xaz demanded. She had stumbled with her earlier question, she knew that, but she raised it again because this situation didn't make sense without the answer. "Why would you risk the wrath of the entire Abyss to drag this man out of the depths? If you just want to help Umber and Hansa, you can best do that by refusing to help."
Naples gave a sunny smile. "Because all things serve the divine, sweetheart," he said. "Haven't you heard?"
He knew. They hadn't mentioned the Numini, but somehow Naples knew. Or did he know something about Terre Verte? Or was he just quoting the old adage because rescuing an innocent man from the Abyss would be considered a divine act?
She prepared to press the question with Naples further, but Umber answered for him. "He'll help because he wants this man, too. If he's as powerful as the stories say, he can break the bond. That's it, isn't it?"
As he had when Xaz had brought it up, Naples reacted to the reference to the bond as if it were a physical assault. He nodded sharply.
"If anyone can, he can," Naples said. "If you two have decided you don't want the boon Hansa foolishly demanded, maybe he can break your bond as well. I figure a man who has been imprisoned in the deepest cell in the Abyss is probably willing to make a hefty deal."
"If this man can solve all your problems, why haven't you gone after him before now?" Umber pressed.
"I didn't have a Numenmancer before," Naples explained. "The palace is an interesting vortex. Power is in flux. I can hold back the more damaging magics of the Abyss so we can survive the journey down to the low court, but that will take all my attention. I can't do it while fighting Abyssi."
The laugh that broke from Xaz's throat was startled and dry. "And you expect me to?" Even her Numini couldn't be arrogant enough to think she could battle the entire Abyssal court . . . right?
"A properly-trained and motivated Numenmancer could destroy an Abyssi," Naples said, "but I'm aware you're not that well versed. I don't expect you to fight. The deeper Abyssi don't see with eyes; they see with power. A Numenmancer's power can blind them."
"And the higher Abyssi?" Umber asked. He leaned forward, one arm on the table, now listening intently. "They'll still be able to see us, won't they?"
"Through the second level, the spawn are respected and allowed to own property," Naples said. "So you could claim Hansa, Cadmia, and Dioxazine. Below that . . . on the third level, it may be assumed that we are there due to our connection to Alizarin, at least long enough for us to get through. Beyond that, Dioxazine can keep us clear."
"Even if it's remotely possible, it's still insane," Hansa said. "You can't really expect us to—" He broke off, breath hitching with a grunt. Umber set his teeth. Trying to refuse must have caused the magic of the boon to show its teeth.
"Maybe you should have thought of that before you demanded the third boon," Naples purred. "As it is, I don't see that you have any choice."
"You say the Abyssi offered to make Terre Verte one of them?" Xaz asked. What kind of man was this, that the Abyssi wanted to enthrone and the Numini wanted to liberate?
"Well, I wasn't there personally," Naples said sardonically, "but the stories say the king of the Abyss offered to make him a prince."
"Do you know anything for certain?" She was desperate to have some say in her own fate, and that meant she at least wanted to know why they were being sent on this impossible mission.
"I know for certain that there is a cell at the lowest level of the Abyss," Naples said. "I can scry that deep. I cannot see into the cell because it is designed to keep something or someone of great power contained, and my magic isn't strong enough to penetrate its walls. But based on everything I've heard over the years, I believe there is a man inside who can help us all."
Give up, she told herself. The Numini would get what they wanted. They always did. Her task, as it ever had been, was only to nod her head and obey.
"I'll need to consult with the Numini," Xaz said. This was what they wanted, but perhaps they didn't realize exactly where Terre Verte was, and what rescuing him would require. Naples spoke confidently, but Xaz knew her power had never been particularly strong.
"We'll take a break, then," Naples suggested. "We all need . . ." His gaze rested on Hansa and Umber for a moment with enough heat that Xaz took a deep breath, fighting not to blush. "Rest," he concluded, the word clearly standing in for what he assumed they would actually be doing. "I'll speak to Azo when she returns, and we will make further plans in the morning."
CHAPTER 31
Naples had the pretty face and earnest eyes of the best mongers in Kavet, which meant Cadmia didn't plan to trust anything he said. Thankfully, she had another expert on the Abyss to consult. If Naples knew of Terre Verte through Abyssal rumors, Alizarin probably did as well. Why hadn't he said anything?
After they separated to rest for their intended adventure, Cadmia asked the household servants if they would let Alizarin know she was looking for him when he returned. Obligingly, Alizarin came to her less than an hour later. His disquieting pallor had gone, and his aquamarine fur once again gleamed impeccably and felt like the finest silk when he brushed against her side in a catlike greeting.
Seeing him happy and well released the knot of tension that had appeared between her shoulder blades the moment Naples separated them upon arrival. Seeing the others unharmed had helped a little, but she felt much better with the blue Abyssi near. For a minute she just leaned against him, letting his warmth soak into her before she jumped into the topic of Terre Verte.
"Naples knows about Terre Verte, and thinks he can help us get to him," she explained eventually, only reluctantly pulling away to have the conversation. "He says he's heard Abyssi talk about him?"
The words were half statement, and half question, intended not to be accusatory.
Alizarin nodded.
"You didn't say anything."
His ears and tail drooped, signs she had learned meant hurt and disappointment. "You didn't ask."
Of course. She thought about the conversation when the rest of them had discussed Terre Verte and their plans, when Alizarin had eventually suggested they come to Naples. She had asked Alizarin questions about strength and whether they could get to the court, and he had answered the questions she had posed aloud. It had never occurred to ask about Terre Verte because she had associated the sorcerer with the Numini.
Cadmia didn't have as much experience with Abyssi as Xaz or Umber did. Why hadn't one of them realized Alizarin probably had useful information?
Because they do have experience with them, she realized. They don't expect Alizarin to be thoughtful.
"Do you like it when I ask you questions?" Except for personal questions about his nature, he had responded cheerfully to all her inquiries, though they ranged from the nature of the five levels of the Abyss to the way he had cleverly adapted human-made pants to fit over his tail.
He smiled—a radiant, utterly honest expression that made her heart give an inappropriate lurch in her chest. "It's fun to know answers," he said.
Their conversation was interrupted by Naples stepping through the bedroom door.
He paused in the doorway, as if hesitant about his welcome. "I wanted to make sure you know I don't expect you to go with us tomorrow," he said to Alizarin, making no indication he had even noticed Cadmia's presence. "You've talked about wanting a Numenmancer for a long time, and I know the risk you've taken by bringing her to me now that you finally have one. I would never ask you to directly cross the low court."
Cadmia tensed at the implication that Alizarin was the one who had brought them here, but the Abyssi tilted his head, appearing confused. "You never told me you wanted Terre Verte," he replied. "Why would I bring you a Numenmancer I didn't know you needed?"
"You . . ." Naples frowned. "I assumed . . . You worked so hard to get a tie to the mortal realm. Why else would you bring her to the Abyss?"
Abyssi can't lie, Cadmia thought. How would Naples react when he learned the Numini had manipulated them all into coming here?
But Alizarin didn't answer that question. Instead, he said, "I'll go with you after Terre Verte."
"You—" Naples broke off, as if startled Alizarin had returned to the earlier part of the conversation. "Do you know what happened to the last Abyssi who meddled with this man?"
"The previous king of the low court wanted to make him one of us. Terre Verte said no, and the other Abyssi slew the king."
"That . . . seems extreme," Cadmia interjected. "Just because he said no?"
"The king murdered many Abyssi to work the magic," Alizarin answered. "Others were angry. They brought him to the crystal caves and sacrificed him where his blood would seed the crystals and make more Abyssi. It's how I was born."
"Hm. Well, if you're willing to risk it, we can talk about it—" Naples broke off. He shifted his eyes to look at Cadmia, and the warm, open expression on his face, so different from the desperate awe he wore when looking at Azo or the desperate hunger when he saw Umber and Hansa, abruptly disappeared. He finished his sentence "—later. Are you sleeping here?"
Alizarin nodded. He added, "You need to speak to Azo about your plans. She should return soon."
Naples let out a long, slow breath and nodded. "You're right." He looked around the small room apologetically and said, "If I had realized, I would have set you up in the good guest room. Alizarin, you know where to find me if you need me. Good night."
Why hadn't Alizarin been given the good guest room? Had Naples expected Alizarin to sleep with the court, or somewhere out in the Abyss?
She had barely finished the thought before she realized how stupid it was. Everything Naples had said so far implied he had expected Alizarin to stay with him. Clearly they had a close relationship—which had involved many long conversations about Numenmancers.
"Did you bond to Xaz intentionally?" she asked.
She had assumed—and thought the others did as well—that Alizarin's bond to Xaz had been accidental, another consequence of the strange circumstances of Baryte's arrest and the Numini manipulating them. Naples apparently thought differently.
"Not Xaz specifically," Alizarin answered. "Baryte was supposed to talk to a Numenmancer for me. Antioch pushed him too hard and the Quin found him. Then he died."
"And he just happened to throw the knife at a Numenmancer? That didn't seem odd to you?"
Alizarin had the grace to look puzzled. He sat on the bed and leaned his head on his hand, tapping his tail on his knee as he thought. "I don't know why he did that."
"Could the Numini have made him do it?" She was willing to believe the Numini could manipulate her and Hansa that easily, but wouldn't an Abyssi or an Abyssumancer be protected from their whisperings?
Alizarin shrugged. "Maybe."
"Could Naples?"
"Probably."
"If he knew you wanted a bond to a Numenmancer and he needed a Numenmancer for his own plan, would Naples have been willing to sacrifice another Abyssumancer to achieve that end?"
"He thought I did it," Alizarin pointed out.
"He said so. Humans can lie." Antioch had targeted Alizarin because he considered him responsible for his mancer's death. She could understand why Naples would want to hide his own involvement.
Alizarin just shrugged.
Cadmia resolved to bring the question up again when the others were around to help her consider it, but accepted that the mystery wouldn't be solved that night. It was time for sleep.
The bed in the guest room was warmer than the Abyss and softer than stone and sand, removing all the excuses for why she had slept curled against Alizarin the night before, but he had clearly assumed she would want him to stay. She couldn't find it in her to be affronted by that; she wanted him to stay, too.
Years ago, she had turned her back on the Order of A'hknet and become a Sister of the Napthol. She had needed to reevaluate every bias and instinct she had, relearn everything from table manners to social norms, and give up vices she had never considered as such. As she climbed into bed, she realized she was on the cusp of doing something similar now.
Except this change was madness. The Order of the Napthol was respected. Valued. If she started to sympathize with people like Dioxazine and Umber . . . and Alizarin . . . but she didn't even have power. People in this place treated her like what she was: a foolish human woman who had jumped in deep water without knowing how to swim.
Alizarin stretched out next to her and used his tail to tuck her snugly against his chest just as he had the previous night, but this time she found it difficult to relax. Closing her eyes to try to sleep only made it worse. Without the coarse sand and biting wind to distract her, she was hyperaware of him, of how good it felt to have his arm across her waist and feel the firm planes of muscle under the impossibly soft fur that covered his chest. Her outdoor dress and cloak had also been a thicker barrier between them than the comfortable but lightweight shirt and pants she now wore.
"Alizarin?" she asked, opening her eyes.
"Yes?" His face was startlingly close to hers.
"Please don't take this as an insult, but . . . are you a man, or an animal?"
He blinked, not offended, but confused. "I'm Abyssi."
She should have expected that patiently obvious response, because Alizarin clearly wasn't either.
"I just mean . . ." She struggled for a way to ask the question, trying not to blush, and embarrassed to consider how she had unthinkingly leaned against him the night and day before. He had never indicated that he thought anything more of it than a housecat thought of sprawling across a person's lap.
"Which one gets petted, man or animal?" Alizarin asked in his practical way.
"Animal, usually." It had been a stupid question.
"So that's fine?" he suggested, running a hand down her side. His hands felt warm, and very human, through the thin fabric.
"Animals don't usually pet back," she pointed out.
"Abyssi do."
"Do Abyssi—" That was an even stupider question, with an equally obvious answer.
She was having trouble asking the question because she didn't know what she wanted him to say. Drawing a deep breath, she asked herself, Are you about to proposition an Abyssi?
Was she?
If he said no, that he had snuggled against her for the same reason an animal might—for comfort, company, and warmth—then she would have to ask him to leave, because that was clearly not how her body was responding to his presence. It would be like lusting over a pet dog. Disgusting.
And if he said yes . . .
Alizarin had his flighty moments, but he was a thinking, rational being. He was also beautiful.
And an Abyssi.
Her last lover had been a prostitute. Some people who would consider this a step up.
Alizarin started purring again, and at this distance—none—and with so little between them, the sensation made her shiver.
"That tickles," she said, suddenly breathless.
He nuzzled at the crook of her neck, and nipped her there. She held her breath, too aware of how sharp those teeth were, but he released her without drawing a drop of blood. Then he paused, waiting.
She had the sense that he knew exactly what was going through her mind, but was giving her the authority to decide what happened next. Realizing that the Abyssi in bed with her was more considerate and patient than most of the human beasts that had frequented Scarlet's bed, that despite all she knew about the denizens of the infernal realm he cared enough about her comfort and consent that he hadn't even indicated interest until she had, made her decision easy.
She closed the scant distance between them, giving in to the desire to press her lips to the Abyssi's and tangle her fingers in his silken black hair. She was already in the Abyss. What was the worst that could happen at the end of this particular fall from grace?
No one bothered them, though Cadmia certainly felt like they slept late, satiated and wrapped in fur and blankets. They made love again after waking, and then Alizarin said, "I need to hunt and make sure the high court is clear before we go. Azo will provide breakfast for you."
"Mmm." She hadn't quite recovered her voice yet. It had been a very long time since she'd had any lover, and she had to admit that teenage Cinnabar couldn't compare. "Happy hunting."
She found her feet several minutes after he had left, bathed, dressed, and went in search of the promised breakfast before she needed to face a trip into the bowels of the Abyss. She ran into Umber along the way. For the first time since they came to the Abyss, Hansa wasn't with him.
"Is Hansa all right?"
"He offered to help prepare breakfast," Umber said. "I wanted to talk to you alone. Are you okay?"
The sincerity in his tone and expression was worrying compared to his normally cavalier, ironic attitude.
"Yes?" she answered, the word turned into a question by her confusion.
He paused, as if there was more he wanted to say, and then nodded sharply and started to go.
She caught his arm. "You can't ask a question like that and not explain yourself."
He turned reluctantly back to her. Not mincing words, he explained, "Abyssi aren't known to be kind and gentle lovers. In general, they won't heed a refusal, and mortal partners often don't survive the encounter. Given how you clearly spent your night, I wanted to make sure you were all right."
Until that moment, Cadmia hadn't thought a person could feel chills while blushing. "How did yo—"
"One of the servants mentioned that he stayed in your room," Umber explained, "and I can see his power on you now. Naples, Azo, and Dioxazine will all be able to tell."
"Oh." She wasn't ashamed of sex, but she'd never had someone confront her so bluntly about it afterward either. "Well, I'm fine," she said. "Alizarin is . . ."
When she struggled to find the word she wanted, Umber supplied, "He's impossible. If he were as sweet and affectionate as he seems, he never would have become a prince of the third level. Either something changed him recently, or he's terrifyingly good at concealing his true nature."
Cadmia took in the words. She couldn't imagine any creature as irredeemably vicious as the Abyssi she had learned about feigning Alizarin's level of consideration. "Something changed him." She even had a good idea what. "Or someone. Could being bonded to a Numenmancer have done it? According to Naples, Alizarin has wanted one for a long time."
"I don't know," Umber said. "When the other Abyssi talk about him, I almost remember him. I think my sire knew him, or knew of him. Abyssi memories aren't very coherent." Cadmia had heard that spawn, like Abyssi, inherited their parents' memories, but it was unsettling to see Umber casually consult another's recollections. "One way or another, the pretty blue Abyssi we know is not the same creature he used to be. But if being bonded to a Numenmancer is what changed him, what made him want that?"
"Could Naples have manipulated him?" Cadmia suggested. "I gather they have a close history, and Naples is desperate to break his bond to Azo."
"No," Umber said, this time unequivocal. "Naples has been putting everything he has into this plan since he brought it up last night. He has to fight the bond to do it. When we showed up he saw his opportunity, and he's powerful enough it just might work, but I don't think he could have premeditated anything this complex." He sighed, shaking his head. "Given all the mysteries we're facing, I suppose the question of how Alizarin changed is almost moot. I'm glad for all our sakes—and especially yours—that he has. I was concerned."
"Why do you care?" she asked, curious. Before now, Umber's interest in her had been entirely as a means to an end.
As if the question made him realize he had betrayed too much genuine emotion, Umber lifted a sardonic brow. "Because, like most people born on the mortal realm, I had a mother and was rather fond of her. You do know what this kind of behavior causes, don't you?"
If the question had been asked with the same sympathetic concern as his first one, she would have tolerated it. As it was, she bristled. "My mother was the most sought-after paid companion in Kavet. I know how to count my cycle."
"Is there much call for that in the Order of the Napthol?" Umber asked, with the same casually mocking tone. "And was your mother sleeping with Abyssi?"
The habit of watching her cycle to avoid sex during her fertile period had been drilled into her from the day of her first menstruation, when her mother had sat her down to explain the possible consequences of intimacy—Scarlet being what she was, she had included "unwanted emotional entanglements" right before pregnancy—and how to avoid them. She had also taught Cadmia the herbs women could employ to further protect themselves, but those probably weren't available in the Abyss.
Cadmia was about to say something biting in return when Umber's previous words caught up to her: I had a mother. She knew what Umber was but had never stopped to consider where he had come from.
"Was your mother an Abyssumancer?" she asked. If so, had he seen her arrested by the Quin? Had he tried, and failed, to save her? Or had he lost her to the ever-hungry power and needed to flee his own parent?
"No." At first she didn't think he intended to say more. His gaze traveled the ceiling as if an answer was written in the slick stone. Not looking at her, he said, "Her name was Bonnie Holland."
He said the name as if she should recognize it, but it meant nothing to her. "I'm sorry. Should I know who that is?"
"Hansa would know," he said. "Speaking of my favorite Quin, let's see what he's made for our breakfast." Umber changed the subject without subtlety or apology, but Cadmia made a mental note to ask Hansa as soon as they had a private moment.
If they ever did. First they needed to travel with an incomprehensible Abyssi and a desperate Abyssumancer into the heart of the Abyss to rescue a sorcerer who had once been offered a throne in the infernal realm.
CHAPTER 32
We will be with you.
"Can't you tell me anything more?" Xaz pleaded with her Numini. "I am your willing servant." If having no other choices counted as willing. "I am preparing to walk into the deepest level of the Abyss for you, with allies I'm not sure I can trust. I fear only failure to achieve your desires." Also death, devouring and enslavement to Abyssi.
She thought the Numini would dismiss her again, but instead she felt his resignation like a drift of snow across her skin. The Abyssumancer is right that our brilliance can conceal you from the creatures of the lower Abyss. We used to use it to shelter those we protected, in the world before the realms were rift. Wait to cast it until you are past the glow of fires and luminescence that light the higher levels of the Abyss. It will not help against creatures who use their eyes to hunt, and you need to save your limited strength.
"Thank you," she breathed, grateful for the assurance.
Your bond to us will protect you, and the Abyssumancer's bond to his master will protect him, but your other human companions must not look on the lower Abyssi in their natural forms, he warned. Cover their eyes or they will suffer madness from which even our grace cannot save them.
Xaz shuddered, thinking of the sight of Antioch's and Alizarin's battle, and recalling that they were only from the third and fourth level. "I am grateful for your protection."
His power wrapped her, and for once she thought she felt a hint of fondness from the creature who was sending her on this likely suicide mission. I will be with you, he said. Know that. The comfort in those words was somewhat lessened when he added, You are my chosen servant, and you are dear to me. If you fall along the way, I will bring you home.
She emerged from her trance disoriented, coughing and sputtering, as if the Numini had exhausted any gentleness he possessed with that last statement and then needed to rid himself of her presence like a prickling burr.
The others, gathered around the table packing supplies, looked up at her expectantly.
"He says Naples is right that I should be able to hide us from the lower Abyssi," she reported. Her voice was hoarse, and there was a rime of ice gathered around her splayed fingers on the table. She cleared her throat and continued. "He also says we need to make sure to blindfold Hansa and Cadmia so they don't see the lower Abyssi and lose their minds."
Hansa froze in the middle of testing the weight of his bag, let out a breath, shook his head, and set it down with a klunk. "What happens if you die in the Abyss?" he asked, his voice a bit too jolly, bordering on hysterical.
"Supposedly, you stay in the Abyss," Umber said. "Some say you fall to a deeper level. Not even the Abyssi really understand."
"Well then, it's a good thing we're going to find a guy who can raise the dead out of ash."
"I'll ask Aurelian for some fabric we can use for blindfolds," Cadmia said more practically.
As she left the room, Naples came in and dropped a heavy bundle on one of the chairs—the armor he had been wearing when they first met, plus additional protection and weaponry. Xaz watched with increasing alarm as he put on the vest, high boots, bracers, and five knives—one on the outer edge of each boot, two at his waist and one strapped to his upper arm—to his outfit.
"I thought you said we wouldn't be fighting?" she asked, eyeing the daggers.
Naples pulled out the dagger sheathed at his upper arm, holding it up so they could all admire the fine, sinuous blade, which was glistening black and let off a reddish glow of damped power. He flipped it around deftly, showing off the fact that the weapon was all one piece, the handle made of the same material but less polished, so it was ashy, matte black. It looked as if it had been made to fit his hand.
"Anyone know what this is?" he asked.
Umber nodded. "It's made with a bone from an Abyssi," he said. "Who did you kill for it?"
"This is a souvenir from one of Alizarin's visits to the first-level court," Naples replied. "He wanted me to make a special one for him, but I needed to practice the technique before using more precious materials." Naples sheathed the blade again in one slick movement. "Did you know an Abyssi can regrow an arm in less than a week?"
He shot Xaz a look as he asked the seemingly idle question.
"You!" she gasped, grasping the meaning instantly. "You made the knife Alizarin gave to Baryte of Alizarin's own bone. That's how he was able to bond with me. Did you convince Baryte you were his Abyssi when you had him throw it at me?"
"No," Naples replied, "I have no idea how Rin managed that part. Has it occurred to you that your Numini doesn't seem to like you very much?"
Xaz's retort cut off and her jaw snapped shut. She couldn't make the retort she wanted because, damn it, Naples was being intentionally insulting but he was also right. She wouldn't put it past her Numini to prompt Baryte to throw the knife at her, then give her grief about it. Numini couldn't lie, but they had never said, We didn't cause this. They had only whined at her about the Abyssal taint in her power and told her she needed to fix it, which sent her to Umber, which sent her to the Abyss.
"Can we get back to Xaz's question of why you're fully armed?" Hansa asked. "And why if you need to be, we aren't? I can handle a weapon."
Naples shot him a condescending look. "I'm an Abyssumancer."
"So you require weaponry?"
"I require my tools."
"Blood, pain, fire, flesh," Umber murmured to Hansa, just loudly enough for Xaz to make out the words.
Hansa cringed closer to Umber and grumbled, "As long as he keeps them far, far away from me."
"If I end up needing your power," Naples replied, as he checked each of his daggers to make sure they were settled correctly in their sheaths, "it will be because I'm having trouble keeping the Abyss from crashing down on our heads. So I suggest you don't in that instant decide to be squeamish."
"Just how likely is that?" Xaz asked.
Naples glanced up just long enough to cast her an amused look. "I've never been lower than the third level of the Abyss, and I've never traveled with so many people I needed to protect. So I'm not prepared to give you odds at this time." In the middle of speaking, he turned toward the doorway, where a heartbeat later Azo appeared.
Watching the way those two responded to each other made Xaz's skin crawl. They predicted each other's movements, moved toward each other like flowers bending toward the sun, but it was all a sham. Magic. How could two people be deeply in love yet so achingly miserable?
"You're still doing this?" Azo asked Naples. Their hushed conversation carried across the quiet room.
Naples nodded, not meeting Azo's gaze. "I'm doing it for you."
Azo winced. "You don't have to . . ." She touched his cheek.
He shut his eyes, and drew a deep breath. "You know it's the bond talking. Once this is over . . . you'll be glad. You will be."
"Will you?" she asked.
"Don't you think I—" He clamped his mouth around his first response, then chose another. "We'll both be." The words sounded as if they hurt him to say. They clearly hurt her to hear.
She pulled him close, and while he didn't pull away, there was an exacting care in the way he wrapped an arm around her and kissed her oh so gently.
Low enough that the words shouldn't carry to the couple across the room, Hansa asked Umber, "What kind of bond do they have?"
Xaz eavesdropped on Umber's equally quiet response, both from curiosity and self-defense. They needed Naples for this plan to work.
"Heartbond. Naples' power is what makes it affect them both, instead of just him."
Hansa didn't ask for clarification. Xaz didn't either. No one could look at the spawn and mancer in the doorway and fail to see the anguished love when they looked at each other. Given the careful dance they both performed as they kissed, it was also clear that, unlike a fleshbond, a heartbond didn't control physical attraction. That had to be awkward, given Naples' obvious preference for men and the blurred line in the Abyss between sex and power.
"Be safe," Azo whispered. "Maybe you're right about the bond, and when it is gone I will be pleased." She swallowed, an audible sound. "If magic is all this is, has been, then when it is gone I imagine I'll want to kill you if you ever cross my path again. So if it works, don't come back here." She choked out the words. "And . . . take care of your damned self on the way."
She spun away and walked out again.
Naples didn't look at anyone else, but devoted his attention to pulling on a cloak, tying it at the front to hide the arsenal he was wearing from any casual observer.
Umber was the one who spoke, voice gentle. "Are you going to be able to do this?"
Naples nodded sharply.
"The first thing we need to do is find our way into the court," he said. "With Alizarin, that will be easier. Xaz is bonded to him, Hansa is yours, and everyone there knows I'm—" He cut off, shaking his head. "Anyway. We move fast, following Alizarin and keeping our heads down, just long enough to get to the well. Don't speak to any of the Abyssi there. Hansa, Dioxazine, if you value your lives and your skins, do not say a word. They'll defer to Alizarin, and they are supposed to respect the claim of the spawn, but the royals will mess with you given any excuse. Having a mortal speak to them is an insult and thus a valid excuse."
Hansa nodded. Xaz did the same, though she was looking forward to returning to the human realm someday so she could go back to being considered a person instead of property.
Umber said, "That wasn't my concern."
Naples glared at him, eyes flashing. "Don't you think I see the way it kills her, when I—" He let out an inarticulate sound of frustration. "I would be loyal to her bed, if I could. I would make love to her, if I could. I know it's magic talking, but knowledge doesn't change the fact that I would do anything to take that look of pain from her face."
"Ever consider chastity?" Hansa suggested, before biting his tongue. "Sorry. None of my business. I mean, except for my being on the other side of . . . never mind."
Xaz had only recently come to understand the connection between sex and sustenance in the Abyss. She didn't think she would ever personally be comfortable with it, but she could predict Umber's answer.
"A chaste Abyssumancer cuts himself off from one of the four coins of power," the spawn explained. "It would be like a human trying to live on bread and water. You can do it for a while, until you get the sailors' disease and your muscles wither away from lack of meat. Azo wouldn't let him, even if he tried."
"I can do this," Naples said, concluding his answer to Umber's question, "because I do it for her." One of the servants came in and handed Naples another bag, this one smaller and made of what looked like felted fabric instead of leather. Naples held it as if it might bite, glanced inside briefly, then passed it to Dioxazine. "That's all I can offer you."
Xaz looked inside, and her breath caught. "Where did you get these?"
A sparkle of silver inside hummed with Numen power, but it was nothing compared to the long, soft plume of what had to be a Numini feather and a small vial she knew to contain Numini tears. Such powerful tools normally took weeks of ritual and pleading to acquire. It felt odd to hold them now and have no one else in the room evince any interest, but Hansa and Umber had turned back to their own tasks now and even Naples appeared only vaguely solicitous and uncomfortable.
Naples said, "One of the Numini passed through here several years ago, seeking—well, I suppose there's no harm in admitting it now. He was trying to get to Terre Verte, the witch we're after. He left those with me."
Xaz couldn't help but notice what Naples hadn't said. "What happened to him?"
She could almost see Naples considering a lie, then realizing there was nothing he could say that wouldn't raise more questions. "I don't know. I never saw him again. All I know is that the cell is still intact, and was never opened."
Xaz exclaimed, "The Numini want me to do something they couldn't?" The only reason she was considering this possible was that the Numini were willing to help her, but if they had already failed once, what hope did she have? She only remembered after she had spoken that they had agreed not to tell Naples about their divine orders.
"Nice of you to get around to admitting it," Naples said. "I was starting to worry you hadn't noticed the divine dancing you all around like puppets." Before Xaz could form an apology and explain why they had tried to deceive him, Naples continued. "The Numini who came here was shocked by how weak he became the moment he crossed into the Abyss, and he didn't understand Abyssi. He planned to ask one for help, because like all Numini he was idiotic enough to believe 'all things serve the divine.' After the Abyssi ate him, as I'm sure they did, the other Numini must have come up with a new plan."
"And that's when they decided to send me," Xaz said, her voice unsettlingly close to a growl.
"You, and me, and Hansa and Umber and Cadmia. If we survive this and Terre Verte can do what they say he can, we should all sit down and figure out the details," Naples said. "Because you have realized even a Numini couldn't arrange all this alone, haven't you?"
His coppery gaze settled on hers heavily, waiting.
"I . . ." She trailed off. She hadn't realized that. "Are you sure they couldn't?"
"Quite sure. There's no point quibbling and speculating until we've fulfilled the boon and broken the bond, but I suggest we take a hard look at all the facts before anyone returns to the mortal realm." He nodded to the bag, and the divine tools within. "In the meantime, will that help?"
Head spinning with the implications, she closed the bag. "Yes. Thank you."
Finally they were ready to go. As soon as Alizarin returned and reported the way was as clear as it was ever likely to be, Naples reiterated his instructions.
"Alizarin will lead us through the palace. Umber, you'll be a little behind him, but still at the front of our party. The rest of us walk behind, mouths shut. Except for Alizarin and Umber, we speak to no one, even if they speak to us. Try not to look at the other Abyssi, or even think about them, no matter what is said or what you see. Alizarin, are you ready?"
In response, Alizarin pushed his way through the door and back into the Abyss.
Xaz hadn't missed the slick black paths or the eerie perpetual twilight of the sky, but they seemed comfortable and homey compared to the hulking, irregular stone structure Naples identified as the palace, with its arching, cavelike maw. As they approached, she saw Naples' shoulders draw together, tensing, and couldn't help but react to his nervousness, her heart speeding.
It took less than four minutes to walk into the high, vaulted entryway of the High Palace of the Abyss, which sparkled inside like a strange geode; to pass through that first room and into an even larger hall, with doors in the walls and strange arches and pedestals of varying heights set into the floor seemingly randomly; and finally to follow Alizarin through another, smaller doorway at the far end of the room.
Four minutes, but perhaps the longest four minutes of her life.
There were creatures in the room. Abyssi, certainly, but most of them were more similar to the lizardlike lord of the high court who had first challenged them than like Alizarin. Some had several pairs of arms and legs, thick like lizards or slender and sharp like insects or spiders. They lounged on the structures about the room, occasionally seeming to sleep, but mostly looking directly at the visitors passing through.
From a distance, Xaz saw the dense-bodied lord of this court acknowledge Alizarin with a bow, never removing one front, clawed foot from the back of another of its kind it held pinned. Then, realizing she had let her attention wander, she snapped her eyes back to Alizarin. Her whole body went cold as she felt other Abyssi circling behind them, pressing close without quite touching.
Alizarin kept them moving until they once more encountered the gray-black Abyssi, Antioch.
Unlike Alizarin, Antioch had not fully recovered from the fight. His fur was shaggy, matted in places with blood that glowed indigo in the dim palace light. He had been lying against the back wall, but now he pushed himself up to growl.
Alizarin stepped forward to meet the challenge, his growl making the air rumble. Xaz had to look away as living darkness flowed around him, though doing so made her more aware of the other Abyssi, many of whom were inching closer as if drawn to the conflict. How many of them could Alizarin fight at once?
Abruptly it was over. The sudden, dead silence made Xaz return her attention to the near-fight in time to see Antioch drop back to the floor, roll onto his back and lift his chin to bare his throat. The expression in his half-closed eyes was resigned. Did he expect Alizarin to kill him?
Would Alizarin kill him? The blue Abyssi paused, his own hackles still raised, though he had returned to his solid form.
He said something to Antioch in the hissing, incomprehensible language he had spoken before, then guided their group past the other Abyssi and to the doorway at the back of the hall. There Alizarin pushed both hands against heavy double doors of shocking crimson. When Xaz glanced back, unable to stop herself, she saw that the defeated Abyssi had rolled onto his stomach to watch them go, his eyes wide with surprise.
She watched just long enough to see one of the other Abyssi pounce on him, and then Alizarin's hand was gently urging her to turn her head and look away. Behind her, she could hear a chorus of snarls and yips.
CHAPTER 33
As they passed through the doorway and Alizarin pulled it shut behind them, Cadmia realized she was shaking. She couldn't help it. Those creatures . . . They were Abyssi, like Alizarin, but they weren't like Alizarin. Their eyes were cold and hungry. When they watched her, she knew they stared with nothing but a predator's fascination.
Alizarin picked her up and she laid her cheek against his shoulder and waited for her heart to slow. Umber reached back and pulled Hansa to himself. Xaz and Naples looked at each other, and Naples chuckled, the sound sharp with near hysteria.
"I thought we were in trouble for a minute there," Hansa said.
"Me, too," Cadmia admitted.
"Apparently the Numini can bring even an Abyssi low," Xaz observed.
"We should keep moving, before the others tire of Antioch and consider following us," Alizarin suggested.
The room they were in was empty except for themselves. Its walls seemed to go straight up without end, without a ceiling, impossibly high; this had to be one of the towers Cadmia had seen from outside. In the center of the room was the mouth to a spiral staircase. The visible stairs were long but shallow, and made of what looked like black volcanic stone, pitted in places and in others worn so smooth she knew it would be slick and treacherous to descend.
"Are there any more Abyssal grudges we should know about before we go in there?" Hansa asked Alizarin, as they all regarded the well before them.
Alizarin shrugged, said, "I will clear the way ahead," and started down the stairs with a bounding stride.
"Alizarin is a prince of the third level," Umber said. "He wouldn't be unless he had killed or maimed enough of his kind to intimidate every Abyssi from here to there. That leaves three levels of Abyssi who may consider him an enemy."
"Don't forget he also bested Antioch," Naples remarked, as if commenting on a bit of market gossip instead of all their potential enemies. "Some will consider that a first assault against the fourth level." With a pointed look at Cadmia, he added, "It wasn't only concern for his well-being that made me hope he would stay behind. I can't even risk drawing power from him, because the other Abyssi will pounce if he betrays weakness. Can we go now?"
Hansa cleared his throat, a gesture of unease. "Just walk?" he asked.
"More or less," Naples said. "The distance and the path varies, but yes, we 'just' walk."
"Alizarin opened a rift from the mortal plane to this one," Cadmia said. "If he opens a rift from here to the low court, we wouldn't need to risk passing the second, third or fourth courts, right?"
"And the trip would end with our eyes boiling out of our skulls," Naples replied. "I need the gradual change in order to raise the power I'll need to. Even just jumping down to the third level suddenly, I don't think I could protect us quickly enough to keep us alive once we stepped through."
"But . . ." Cadmia trailed off, realizing that she wasn't raising useful objections, but simply stalling. She did not want to walk into that great maw of a staircase.
"After you, Abyssumancer," Xaz said, but this time it was obvious that her sharp tone was a cover to nervousness.
Naples shrugged. "Keep up. And watch your step. The stairs aren't made for humans. They aren't even; there are flat areas, and then there are areas where a single stair might drop six or eight feet. I don't know what happens if you fall off the edge, but my educated guess is that you won't come back."
Naples led the way, taking the stairs carefully but not slowly. Cadmia followed, happy to take all the time in the world.
At first, the descent was awkward, uncomfortable, and nerve-wracking. At times the stairs became too small to comfortably support a foot. They all crept along sideways, and Cadmia longed for railings. At other points, the steps were unevenly wide, and of varying depths, so there was no comfortable stride.
Alizarin ran ahead most of the time, then loped back to check on them before disappearing down the stairwell again. Occasionally when he returned his fur was wet with the viscous, glowing fluid Cadmia recognized as the blood of other Abyssi. What would happen if someone below raised a challenge he could not best?
Awkward and uncomfortable became painful as the hours progressed. They reached an area where the "stairs" were so narrow and steep they couldn't truly be called stairs. They had to use the narrow ridges as foot and handholds while they scaled the way like a cliff face.
"How long is this staircase?" Cadmia gasped, past lungs and throat that ached from heavy breaths of the increasingly hot, dry air. She longed for a drink of water, but couldn't reach into her bag without falling.
"We can rest and eat as soon as we're back on more level ground," Naples promised. "I—gah."
Scratching. Scrambling. A whispered curse.
Thump.
"Naples?" Her voice was shrill.
"I'm okay," he said shakily. "When you reach the last handhold, get as far down as you can using your hands, then drop."
Just her hands? She was barely holding herself up using hands and legs both.
"Let go," Alizarin said. "I'll catch."
Squeezing her eyes shut, she released her grip on the stairs and let herself fall back. She swore when the fall was longer than she expected, but the sound was only half-complete before she landed safely in the Abyssi's arms.
"Thanks," she said, looking up. They were now on a flat area, but right in front of her was a vertical face of maybe ten feet, before the steep clifflike stairs they had been navigating. "I'm glad I didn't see that before I jumped," she mumbled.
Umber glanced down, scrambled a little further toward the sheer face, and then let go and landed like a cat, neatly and apparently painlessly. Hansa looked down when Umber jumped, but he seemed less enthused about the drop. He did as Naples had advised, lowering himself until he was supporting himself with his hands and there was a reasonable drop between the ground and his feet.
He landed with an "umph."
Cadmia pulled open her water bag and took a sip, swishing the water around her mouth before swallowing. The others were doing the same.
"Catch your breath," Naples advised, "and then we'll eat something before moving on. We're almost at the second level, and we don't want to stop too near any of the—"
"We're only almost at the second level?" Xaz gasped. "How many stairs can there possibly be?"
"How many stairs can there be, between the five levels of the Abyss?" Naples replied. "How many stairs did you expect to be in a well that passes between planes of existence?"
After hours of walking, Cadmia didn't have the energy to engage in the argument. Alizarin rejoined them as they pulled out rations, mostly tightly wrapped cakes of dried meat and fruit, and she sat against his side. His warmth was less soothing than usual because she could feel the way his body thrummed with pent-up energy and agitation. He put on a confident face, but he was anxious about this trip as well.
All too soon, Naples was urging them to stand again. Cadmia winced, discovering newly pulled muscles, especially in her shoulders and down her back.
"We won't stop at the second-level court, but I don't think we'll get far past it before we need to rest and cast the protection spell. I can make it almost to the third-level court on my own, but I doubt anyone without an Abyssumancer's power or Abyssi blood can stand to go that deep."
Cadmia remembered Naples describing Alizarin's home on the third level as full of steaming seas. Why had he ever wanted to come all the way up to dry, snowy Kavet?
"I'm going ahead again," Alizarin announced the moment they prepared to move again, before disappearing into the dim well ahead of them. He had no trouble hurrying down the stairs, like a kitten bounding across hills. Was he constantly fighting other Abyssi or mindless monsters to clear their path before they arrived? Sometimes negotiating for safe passage? Or was he just unable to stand their slow, mortal's pace?
"I wish I had his energy," Xaz said.
"What are you complaining about?" Hansa asked, hefting his pack with a significant glance to the very light-looking bag Xaz was carrying, its strap angled across her chest. They had all agreed the mancers would have a difficult enough task with their magic and shouldn't be additionally burdened by supplies, but in that moment, Cadmia shared Hansa's envy.
Talk disappeared as they continued to walk, the way becoming darker and less even. When the stairs turned, twisting into the walls of a tunnel, no one bothered to complain. Naples held up a hand, summoning a pale green orb of foxfire, and in its sickly luminescence they continued into the Abyss.
CHAPTER 34
Stairs. Stairs. Cliff. Stairs. Tunnel. Stairs in a tunnel. Hansa's feet made their way across slick, half-worn stairs, many of which held pools of water that shone silvery-pink and which stuck to his boots when he stepped in them.
The only sign of their progress was the change in the air. It was thicker here, hot and oppressive. There had been a heavy scent in the caves, but Hansa had assumed it was just the dankness in there; as they exited the tunnel, the odor became foul, like marsh-water. It seemed to coat the back of his tongue and taint the taste of the water he drank to console his parched throat.
How could the air smell so damp yet still feel like sandpaper when he drew it in?
"And we have company," Umber whispered, nodding discreetly across the way before asking Naples in low tones, "Do we greet them or wait?"
"Wait and hope they won't challenge us before Alizarin comes back," Naples advised.
On the other side of the well was a hole in the wall, large but too irregular to be rightly called a doorway. Slithering out of it was a creature with the wet look of something found under a log. Its long body was lizardlike, and the color of rusty mud except for a mane of orange and black tentacles. It opened its mouth to taste the air with a flickering black tongue, in the process revealing rows of sharp teeth, including four longer ones that were curved like a viper's fangs.
With that coloring, it's probably poisonous, Hansa thought, an inane observation, since the beast wasn't the size of a rattlesnake. Given that each fang was the size of a hip dagger, a single bite from that creature would kill too quickly for poison to be a factor.
Its eyes were black pools, without visible pupils, streaked with flecks of red and orange like splattered paint. In them, Hansa could see intelligence. Abyssi.
"Hansa," Umber hissed.
Hansa jerked his gaze away, too late it seemed, since the Abyssi started slinking toward them.
"Vanadium of the second-level court greets you." The Abyssi's voice was startlingly musical in combination with its owner's slimy form, almost sweetly feminine. "You've brought me presents?" She spoke to Umber, then looked past him to the rest of them.
"They aren't for you," Umber answered.
"Surely you didn't mean to pass by my court without offering tribute?" Vanadium asked, sounding affronted. "There must be one you can spare."
"I'm afraid not."
"A loan? The pretty one, perhaps."
Hansa didn't want to know which of them she meant. Umber didn't ask. "Perhaps you should ask Alizarin when he returns. He would better understand proper, um, niceties."
Vanadium's brilliant crest collapsed when Umber invoked Alizarin's name, the color leaching from it as she drooped. "Him," she said flatly. "I knew him when he was nothing but a plaything to the previous lord of this level."
Naples spoke up. "Then you knew him when he devoured the previous lord of this level, too. We'll wait here if you want to talk to him about tribute."
Vanadium opened her mouth to hiss at Naples, then turned and slithered back through the gap in the wall.
"Move. Quickly," Naples advised.
They tried, but it wasn't easy. As they started down the next set of stairs, Hansa realized he was sweating, though the moisture disappeared from his skin almost as soon as it appeared. His chest ached, and his dry throat hurt so badly it was hard to swallow. Even though the stairs were reasonable for the moment, his heart pounded as if he were climbing a mountain.
Fighting just to keep moving, he couldn't judge how much time passed before Naples paused, raising a hand. He glanced back at Hansa, and then at Cadmia, who was lagging even further behind. "There's a plateau just around the bend," the Abyssumancer said. "We'll stop there to sleep."
"Thank Numen and Abyss," Cadmia gasped. "I feel like I have a blood-fever."
"Close enough to the truth," Naples said. "Much lower than this, your blood would start burning. All the liquid in your body would evaporate."
"Well, now I really look forward to tomorrow," Hansa griped as they reached the plateau and collapsed. He drank in greedy gulps, now understanding why Azo had insisted they would need so much water.
Naples took a sip and ate a couple bites of food distractedly, then sat cross-legged at the center of the plateau. He drew the knife from his upper arm in his right hand, and the one from his left boot in his left hand. Hansa recognized the black-red, wavering blade of the former. The other was simpler, made of dark metal, with a fine, slender blade and a handle made of ebony or mahogany wood.
Matter-of-factly, Naples undid the buttons down the front of his shirt, then opened his shirt-cuffs and rolled back the sleeves to just below his elbows. "Cadmia, you first."
Cadmia jumped, eyes widening. "Me first what?"
"I need to tie the spell to the people I'm trying to protect." He added, "It shouldn't hurt, and it will only take a moment."
She inched forward, apparently not comforted by his words. Hansa understood how she felt. He had responded much the same way whenever Umber pulled out a knife. "Do I have to be first?"
"You're the most human, and therefore you're in the most distress," Naples said. "You don't need to go first, but I thought you might prefer to."
Again, she looked at him skeptically.
"I'll go." Hansa didn't want the Abyssumancer touching him or cutting him, but at least he had some experience. He was starting to feel a bit jaded, in that his mind did not come up with a single scenario as he crossed the small plateau to Naples.
"Thanks," Cadmia whispered as he passed.
He shrugged, then he knelt in front of Naples. "What do you need me to do?"
"Roll up your left sleeve," Naples instructed. "To the elbow is fine."
Hansa obeyed, hoping Naples' ritual would be less dramatic than Umber's had been when he gave a similar instruction before slicing Hansa's arm open to give him the power to pretend to be a mancer.
Naples shut his eyes. Gracefully, without any hesitation or sign of discomfort, he used the Abyssi-bone knife to cut a rough triangle over his own heart.
Blood welled to the surface, but it only beaded there, seeming to thicken like tar instead of running down his skin. Power began to pool around the symbol, spreading like a thick mist which let off light the color of a particularly nasty bruise, deep cranberry-black.
"Your hand," Naples said, holding out his own as he opened his eyes, which now glowed like the Abyssi's.
Seeing that eerie light made it harder to calmly reach out, but Hansa forced himself to do so without hesitating. Using the metal blade, Naples made three rapid, shallow cuts in the meaty part of Hansa's arm, marking a coin-sized piece of flesh. Then he touched the flat of the Abyssi-bone knife to the blood.
A wave of heat slapped Hansa, as if he had leaned toward an open flame. It passed and he shivered as both the sudden warmth and the insidious, dry heat of the Abyss abated. The sense of constant weight that had grown with each step deeper in the well lifted.
When Naples took the blade away, the wound seemed to smolder, the scar-slick surface glowing amber like hot coals.
Naples returned the knife to his own skin, this time to make a single stroke beneath the symbol he had previously carved, mingling Hansa's blood with his own.
He waved Hansa off. "Cadmia, you next."
"You'll be fine," Hansa said, squeezing Cadmia's shoulder as he passed.
Umber inspected the mark on Hansa's arm suspiciously, but seemed satisfied that it would do what it was supposed to, or at least that it wouldn't do anything else. He went after Cadmia, though he and the Abyssumancer watched each other with open hostility as Naples repeated the process with the spawn.
Finally it was Xaz's turn. When Naples first touched the blade to her arm, she cried out and jerked back, clapping a hand over the wound as a curse hissed between her teeth. Umber arched one brow, and Cadmia rolled her eyes, but Hansa moved closer. "Is something wrong?"
Xaz reluctantly lifted the hand she had held over the first cut Naples had made. The blood beading on her skin hissed and bubbled, letting off faint steam as white as Xaz's face had gone. Though she hadn't made a sound beyond the single cry, her jaw was set with pain.
"What happened?" Cadmia asked.
"Xaz, you're going to have to work with me here," Naples said, his tone bland and unsympathetic. "Your magic might not like mine, but my magic will keep you alive. You're going to have to deal with it."
She knelt in front of him again and offered her arm. Her fingers trembled, so she drew them into a tight fist.
Naples made the remaining cuts quickly. Xaz's body went rigid, but she didn't scream or pull away again. When he slicked the Abyssi-bone knife with her blood, she let out a single whimper; even Naples winced at the hissing sound made when the bone touched the Numenmancer's blood.
When Naples released her arm, the mark left behind on Xaz's skin was black like a cinder, with faint blue ripples.
Naples set his own teeth as he cut the last mark in his chest, as if joining Xaz's blood with his hurt him as much as it had her. Finally, he licked the remnants of blood from both blades before wiping them on his cloak and returning them to their sheaths. He buttoned his shirt over the symbol on his skin, which was no longer bleeding, but pulsed with dark magic.
"The further you go from me, the harder it will be to keep you within the sphere of power," Naples said, as he undid his cloak and spread it on the plateau to sleep on. "Especially while we sleep, I want to be in contact, so I'm not spending more power holding on to you all than I can actually recover resting. Hansa, you're next to me."
"Not likely," Umber replied, draping a protective—possibly possessive—arm across Hansa's shoulders.
"What do you think I might do with you an arm's reach away?" Naples snapped. "He's human, and unlike you, he won't have the instinct to defend his energies while he sleeps. That means I can draw power off him, both to help maintain the link and to strengthen it and myself while we sleep. It won't hurt either of you, and it's the only way I might have the strength to make it to the fifth level." He added the last bit when Hansa frowned, not happy about the idea of being used as living fuel.
Come to think of it, he still wasn't happy about it, but he realized he should have expected as much. What other use had he expected to have in this group?
They ended up in a cuddling-line like hostile kittens, with Naples in the middle, Hansa and Umber on one side of him, and Cadmia and Xaz on the other. Snuggled between Naples and Umber, Hansa found himself uncomfortable on about fifteen different levels, so he was remarkably glad when the Abyssumancer and the Abyss-spawn looked at him at the same moment and both said, "Just go to sleep."
There were good uses for magic. Falling asleep and not having to be aware of the others . . . that was a good use.
CHAPTER 35
Xaz woke sore and sweating, with a large furry body sprawled across her. Instead of waking Xaz so he could take the place next to Cadmia, Alizarin had draped himself over them. Xaz mostly had his legs, his torso crossed Cadmia, and his head rested on Naples' shoulder. The Abyssumancer had turned so his cheek rested against Alizarin's hair. On his other side, Hansa had turned his back on Naples and was nestled against Umber.
"Get off me," Xaz said, shifting to wriggle free of the Abyssi's weight. Her muscles ached from hours of walking the day before, and her shoulder and hip were needles of pain where they had been pressed against the stone.
"You're comfortable," Alizarin yawned.
Cadmia opened her eyes, shifted, and said with a wince, "Stone is not a good bed. Let me up."
Alizarin rolled off everyone, stretched to his feet, and offered a hand to help Cadmia up.
"We still on the stairs?" Hansa asked.
"Seems like," Umber answered.
He pushed himself halfway up then paused on his knees, waiting for Hansa, who said, "Still in the Abyss?"
"Unless Kavet had a sudden change of weather," Naples replied, rolling to his feet with a smoothness that made Xaz want to slap him. How did he manage to feel so fresh?
He slept against an Abyssi, a spawn, and a mortal. That's powerful fuel, even after the amount he must have burned protecting us.
"Sleep well?" Umber asked, as they both pushed themselves up.
"Like I took a magical hammer to the head," Hansa answered, rolling his shoulders.
They ate a brief meal, but too soon it was time to move again, this time into a place where only Naples' power would keep the deadly force of the Abyss at bay.
On second thought, maybe Xaz wouldn't begrudge Naples his rich meal.
Alizarin went ahead again; he clearly couldn't stand traveling at their slow, careful pace. The rest of them walked, climbed, jumped, skulked, even at one point crawled, in mind-numbing repetition. The rank odor of the second-level swamps fell behind them, replaced by whiffs of musk and smoke.
"Almost at the third level," Naples announced, as they descended a section of stairway that looked like a chunk of it had fallen away.
With Naples' magic suppressing the Abyss's scalding power, the air felt dead; voices and footsteps didn't carry any distance, but faded to nothing. The stairs were worn and ashy, black and white, coated in a fine dust that puffed lazily into the air with each footstep and not quite wide enough to feel entirely comfortable walking without angling one's body toward the wall. Hansa, whose shoulders were broadest, seemed most off-balance.
Looking at the wall was easier than looking out, anyway. The edge of Naples' spell was easy to recognize, because beyond it the air thickened and wavered like a heat-mirage in the fading light. It was impossible to see across the well.
Alizarin skidded up the stairs. He was still wearing his natural form when he came to a stop inches from Xaz, and she jerked back in reflex, slamming her shoulder into Cadmia. In the ensuing scuffle, Hansa let out a yelp and Umber cursed, probably as he kept his bond from tumbling off the side.
Xaz didn't spare a moment to look. Her eyes were on the Abyssi, whose monstrous form was coalescing into the more familiar furred body she knew.
He looked as if someone had splattered him with paint—if anyone had ever created a paint that shimmered in the light like the inside of an oyster shell.
Naples, who had been traveling in the middle of their pack, pushed past Cadmia and Xaz along the open edge of the stairs as if unafraid to tumble into the well. "You're hurt," he exclaimed. "How much of that is yours?"
Blood. Xaz wouldn't have realized what the sparkly, lovely but viscous goo that covered Alizarin was, but Naples better knew what it looked like when an Abyssi bled.
"Only some," Alizarin replied vaguely. "It would be best if Dioxazine casts her spell before passing the third level."
"Here?" Xaz squeaked. "Now?"
They had talked about waiting until after they passed the third-level court, not to mention the fact that she had expected to be on level ground, where half her concentration wasn't focused on not falling off the side.
Naples turned to her with a look she had come to know well: a mixture of irritation, contempt, and impatience.
"I just mean—" She cleared her throat, which was dry from ash. "The third-level Abyssi can see us, can't they? The spell is only designed to hide power, not make us invisible. If I cast it, then they see us, they will know what we're doing."
"I was unable to convince them that I have a right to claim all of you exclusively," Alizarin answered patiently. "The lord of the third level insists you join him for a feast if you want to pass his court. He did promise me I could have you all back after?" The last sentence was questioning, accompanied by a tilt of his head that betrayed a jagged tear down the side of his face, only partly concealed by his fur.
Xaz didn't want to imagine what an Abyssi feast might include, but Naples, the crazy bastard, had the gall to look intrigued.
"Feast?" Cadmia chirped tightly from the end of the line, as if her endless curiosity was warring with the knowledge that this probably wasn't information she wanted in her head.
"Cast the damn spell, girl," Umber growled.
Was Xaz misreading his face in the dim light, or was Naples trying not to laugh?
Naples caught her gaze and must have seen the judgement in her expression. In explanation, he wondered aloud, "What do you think they could get Hansa and Umber to do by saying it was the only way to pass?"
"Xaz?" Hansa prompted, the panic in his voice suggesting the answer to Naples' question was, More than any of us want to imagine.
"I'll do the spell," she said. "How do we stop them from then seeing us?"
"As long as they cannot sense you, I can distract the court while you pass," Alizarin answered. His color brightened and his ears lifted again with relief.
"Will you be all right?" Cadmia asked.
Alizarin grinned, as if he were not already covered with his own and others' blood. "Abyssi do not kill each other casually," he answered, as if "all right" and "dead" were the only two possibilities. "I will find you again before you reach the fourth-level court."
He scurried back down the stairs, leaving Xaz with anxiety coating her tongue like sour milk. Could she do this?
The Numini had sent her on this mission. They had to think she could succeed. But one of them had already failed once, hadn't he? Did their influence really reach this deep into the Abyss?
She looked up and down the stairwell, wishing there were somewhere more comfortable to work, then slipped past Naples and moved as far beyond him as she could without passing into the deadly heat of the Abyss.
Their water was scarce and precious, but she knew better than to risk smearing grime on the tools she intended to use to reach for the Numini, so she used as much as she needed to wash her hands before kneeling on the narrow staircase and opening the leather pouch Naples had given her.
Inside was a tiny glass vial filled with a clear, iridescent liquid that cast a pure silver glow, and a feather as long as her forearm the color of rose gold. The objects pulsed with power. Just holding them made her heart leap into her throat, skipping merrily, as if she had just seen an old friend in a crowd.
Xaz rested the Numini's feather across her palms, and reached mentally into and through it.
I am here of your will, she said, casting the words to the Numen. An Abyssumancer could shed blood to invoke magic, but the Numen's power was best directed through words. If that is the case, then I believe you must be listening for me.
She pictured a sphere of soft white power around their group, acting as a veil between them and the eyes of the lower Abyssi.
"I invoke the Numen realm for protection," she said aloud. "I invoke you twice, to hide us from those who would harm us." She couldn't remember how young she had been when the Numini had taught her the power of a threefold invocation to cast and bind the magic. "I invoke you thrice, to—"
She didn't get through the final words. Power rushed through her, striking like lightning and filling the sphere she had pictured with brilliance. The shock wave began at the edges of the circle and slammed inward, so she felt it flow first over and through Cadmia, recognizing her as kindred. Umber braced against the power, but even so it sent him to his knees, hands gripping the staircase as if to battle a hurricane's wind. When it slapped Hansa, he stumbled and fell against the wall, then sprawled on the stairs with a painful thump.
Then it hit Naples and the Abyssumancer cried out, shuddering as the Numini's power raked over him and the carefully formed bubble of power he had cast to hold back the Abyss.
Ears ringing and vision rippling, Xaz struggled to draw breath in a world that had suddenly become all smoke and ash. Her eyes, lungs, and skin burned as Naples' magic contracted, hiding itself from the Numini like a turtle in its shell.
"Naples!" she choked out.
"Shit," Naples hissed, unsteadily lifting himself onto his hands and knees.
Naples didn't give any warning; he crawled up the stairs until he reached Hansa and set a hand to the prone guard's arm. "Sorry for the lack of foreplay," he whispered, giving Hansa a very brief kiss before pushing him back against the stairs and opening his shirt.
"What—aack!"
Naples straddled him and made a slash on Hansa's chest, just above his heart. Not shyly, he locked his lips over the wound. At any other moment, Xaz might have been disgusted, but she could feel Naples desperately rebuilding the power protecting them. She struggled to keep her own magic from shying away from his.
For an agonizing moment, she feared the two couldn't coexist, but at last the heat and pressure slipped away and both protective spells solidified. Xaz was able to draw a full breath again, a sensation so wonderful it was hard to imagine it hadn't dazzled her every other moment of her life.
"Breathe, you damn girl," Umber growled. Xaz looked past Hansa and Naples to find the spawn braced over Cadmia's limp form. Xaz's power had been gentler to the Sister of Napthol than it had been to anyone else, but the Abyss had not been as kind.
Umber leaned down and set his lips to Cadmia's, his breath making her chest rise and fall.
Another breath, and finally Cadmia began to cough. "What . . ." Her voice was barely a squeak, and she cut off after one word with a grimace.
"Don't try to talk yet," Umber advised. His voice was also hoarse, though not as bad. "You got a lungful of the Abyss. Naples lost the shield for a moment when Xaz's spell took effect." He glanced back to Naples to confirm; the Abyssumancer was still lying on the ground, but he let out an affirmative-sounding grunt. "You were closest to the edge, and you're most human."
Cadmia nodded, rubbing her throat.
"Get the lady some water," Naples advised.
Umber nodded, and Hansa fished out the water. Cadmia drank a few, painful sips.
"Did the spell—" Hansa broke off halfway through the question when his voice broke. He helped himself to some of the water, then went back to Naples.
"You okay?" he asked.
Naples nodded, his hair shifting in the ash. "Check on Xaz."
"I'm fine," Xaz said, as soon as the others had confirmed they were all right. Her brush with the Abyss hadn't been pleasant, but the Numini's power rushing through her had protected her from the worst of it. She was more nervous about what the Abyssi in the third-level court might have felt when her spell took effect and Naples' snapped closed and back open. "I think we should move past the court and out of the light as quickly as possible. Alizarin might not be able to distract the other Abyssi long."
"Can you stand?" Umber asked Naples, who was still stretched out on the stairs.
The Abyssumancer drew a deep breath, rolled onto his stomach, and pushed himself to hands and knees. "I think so." All evidence of the energetic grace Xaz had envied was gone as he rose agonizingly to his feet.
"Can you walk?" Hansa asked Cadmia, helping her up.
"Can you?" she replied, when her tug on his hand made him wobble and need to catch his balance with a hand on the wall.
"We can move slowly," Xaz allowed, seeing the way the two humans stumbled, "but we need to move."
"We're moving," Umber said. He draped his arm around Hansa's waist.
This time Xaz led the way, and the others followed. Coated in ash, throats and lungs scorched, they limped onward.
As they passed the maw of the third-level court, they walked with soft, hurried footsteps, wincing at each crunch of loose scree, and the tiny splashes they made as they waded a shallow, hot stream that meandered through the open arch and cascaded over the edge. By tacit agreement, no one commented on the sounds they could hear from the court: snarls, growls, and howls mixed with noises that could not be named with mortal vocabulary.
The well had never been bright, but now the limited light cast by luminescent creatures faded until they were groping their way down the stairs, feeling for the step-edges with their shuffling feet. Naples summoned an orb of foxfire, but it was a faint, yellow creation that barely revealed the way even when it hovered only inches above the ground. He had it follow the edge of the stairs, so they could at least tell when there were sudden dips, and know where the stairs ended and the endless fall of the well began.
"Fourth level ahead," Naples breathed. "I need a rest. Short."
Xaz nodded silently, but didn't dare speak aloud. The euphoria that had filled her when she had first cast the magic had faded. Keeping her spell active was like holding sand in her cupped hands. It took all her concentration to keep the grains from spilling between her fingers, and the hands that held that sand had started to ache and tremble with the effort.
"It's hard to judge time here," Cadmia said, "but it feels like it's been hours, and we have another level to go. Should we try to get some sleep while we're on a relatively flat stretch?"
"No," Naples said. Xaz thought she had shaken her head, but her physical body felt far away and not entirely in her control. "Can't sleep. And do this," Naples managed to add, his voice a ragged gasp.
He stumbled, as if speaking had taken too much of his energy. Hansa caught him, and helped him steady himself until he seemed solidly on his feet again.
"Are you going to make it?" Hansa spoke quietly to Naples, but the words carried in the strange, dead air that remained inside their two protective bubbles of magic.
"Sure hope so," Naples answered.
"I . . . can I help?" Hansa asked, haltingly.
Xaz expected Umber to object on principle. When he didn't, a shiver ran down her spine. If he was willing to share his bond, he was truly worried about the limits of the Abyssumancer's power.
Naples pulled Hansa against himself and slid a hand under his shirt so he could wrap an arm around his waist, skin to skin.
The foxfire sphere brightened a little, a candle-flame briefly touched by purer air.
Onward.
They were just past the fourth-level court when Xaz felt something press against the boundary of her spell. She fought it instinctively, but a heartbeat later she recognized the power and invited it in, wrapping it carefully in her magic.
"Ksh." The sharp exhalation was a reaction to the spark of recognition she felt from her Numini. With his power riding her, she couldn't help feeling his wrath and revulsion when he regarded this Abyssi.
She didn't have the mental energy to contemplate whether that was how a Numini would react to being asked to protect any Abyssal creature, or if it might be personal. All she could think clearly was, Please! We need him, and he cannot walk safely in the lower courts any more than we can.
The magic relaxed grudgingly, and veiled Alizarin's distinctive blue glow in its own shimmering silver, which would make him—like the rest of them—invisible to the other beasts of this low plane who saw only with power.
"Alizarin," Cadmia breathed, as she saw the blue Abyssi. "You're all right."
"Xaz's spell works," he reported. "I could not sense you until I was here. You have no scent or heartbeat from outside either."
"That's good to hear," Umber said. "Can you help Naples at all?"
Alizarin moved closer to Naples, then hesitated, twitched his tail and shook his head. Once he was standing closer to the foxfire, Xaz could see how much worse for wear the Abyssi appeared. One of his legs sported a deep enough rent that he was visibly limping.
"I won't be able to hunt until we return to the higher levels," he said. "There is not much further to go."
Not much further, he said, but it was slow going. Alizarin, who had previously seemed chaffed if asked to slow to their pace for more than a minute, walked sedately next to Cadmia. She reached up to touch him.
Hot blood, soft skin. Alizarin's thoughts, which were more sense than words, reached Xaz through their bond at the same time she saw him jerk away from Cadmia. She could feel the depth of his hunger. Abyssi were not creatures of great self-control. It was taking all his concentration to ignore the instinct to hunt the ready, nearly helpless prey that so trustingly walked beside him.
She tried to block the dark awareness from her own mind, but not before she heard an answering thought from the Numini: She is bound to one of us, and swaddled in your power. She will not be lost if the Abyssi kills her.
The words had the ring of a well thought-out plan rather than a just-considered declaration. Xaz had assumed Cadmia was with them for her knowledge about the Abyss and as an additional bond between their group and the Numen, but feared she had stumbled across the woman's real purpose: a sacrifice, which the Numini could justify to themselves because they had the ability to claim her after death no matter how she died.
There was nothing she could do about it, except hope she would be able to sense if Alizarin's self-control started to fray, and intercede somehow.
Meanwhile, the way grew darker, and despite Naples' spell, the air grew thick. Sounds were muffled. They had to shout in order to speak to each other, and doing so was so unnerving in this place that for most of the final descent, they did not say anything at all.
When Naples stumbled, Umber moved beside him. The movement simultaneously matter-of-fact and resentful, the Abyssi-spawn used his knife to slice across Naples' palm, and then his own. The two twined their hands together, and Naples let out a sharp gasp.
Xaz tried to sense how strong—or weak—Naples' spell had become, but as soon as she turned her attention from her own work she felt her connection to the Numen start to fray. She had to stop, close her eyes and reestablish it.
They kept walking.
Finally the stairs widened, until Naples' faint globe of foxfire could not illuminate any visible walls or ceiling. Umber was all but carrying the Abyssumancer, who had entirely stopped responding to questions. Xaz wondered exactly how they expected to carry him up the stairs later, or whether at any moment the Abyss would come rushing in on their little fishbowl of existence.
CHAPTER 36
There were noises in the darkness. A deep scratching, hissing ring made goose bumps rise on Hansa's skin.
Instead of shapes, he could see power. Unlike Alizarin's soft, alluring blue-violet glow, these creatures let off ripples the slick red of fresh blood, and the dark rusty color of that same blood once dried. These dark lights made visible creatures the mind could not comprehend, not and stay sane.
Close your eyes, Umber ordered. Hansa did as commanded, and Umber passed him a strip of fabric to tie across his eyes, then turned to help Cadmia. Naples is holding back most of their power, or that glimpse would have been devastating.
Hansa tied the blindfold into place, and then felt the pressure of Naples' arm around his waist guiding him forward while Umber led the Abyssumancer by the hand.
Blindfolding Hansa may have protected him from the ruinous sight of Abyssal power, but it made him more aware of his other senses: the heat on his skin, distant sounds of Abyssi at their gruesome play, the tangy odor of charring flesh, and an unnamable, spicy taste that settled on his tongue from the air.
They walked toward the gathered Abyssi. The noises of the court grew closer with each step, and their path started to weave irregularly as Alizarin sought the safest route. Safest. What an absurd word. Safest would mean turning around and leaving, if only that were possible.
A furred hand on his chest stopped him short, just before he felt movement in the air and heard something pass by. It never hesitated, and left the scent of brine and ash in its wake.
They really can't see us, he thought.
Naples' magic blocks the scent of our blood and the melody of our footsteps and beating hearts from them. Hansa bit his tongue to keep from shouting as Alizarin's mental voice slipped into his head. Dioxazine's blocks the sight of our power and the sound of our thoughts. With no true light, I would be blind to you here as well, if I had not been allowed inside the spell.
What would happen if they caught us? He didn't mean to ask the question, but couldn't help thinking it.
They would eat most of us, Alizarin answered. Either he was mentally more focused than he tended to be verbally, or this was a subject that had finally sobered him, because his mental voice was low and wary. Dioxazine would be prey for Modigliani, lord of the Abyss, but he might share you or Cadmia with his favorites. I don't know Naples' patron, but there are not many Abyssi whose anger Modigliani would worry about, so he would probably also be taken.
Umber?
If he were alone, they might keep him for sport, Alizarin answered, but he wouldn't survive your death.
Hansa, Umber said, his voice cutting like a cool breeze into their conversation, please stop asking stupid questions. Some of us don't want to know the answers. His mental voice, Hansa thought, sounded very tired.
They were all tired. Hansa had tried, for the last half hour or so, to ignore the way the air had begun to heat as Naples' strength faded. He tried not to wonder how much of the fatigue in his legs was from descending stairs for so long without rest, and how much of it was due to Naples steadily draining power from him.
How much power could one human have, after all? With Xaz's magic hiding their magic, would Umber notice if Naples was taking too much? Hansa was pretty sure Naples wouldn't notice at all.
"We're almost there," Alizarin said aloud, his voice a low grumble that just barely reached their ears. Even if the mancers' magic was supposedly hiding the sounds of their passage, Alizarin clearly didn't want to test the protection by speaking up. "There are stairs here, with some debris. Climb carefully."
Hansa jumped at a low groan not far from his left ear, then realized it was a sound of protest from Cadmia. She had been quiet since the blindfolds went on, as wary as the rest of them of drawing attention.
"Not too far," Alizarin added.
Will there be guards by the cell? Umber asked.
Unlikely. Abyssi do not make good guards, Alizarin assured them, with a touch of the old amusement in his tone. Even Modigliani cannot convince them to attend to a closed box for long, and Terre Verte doesn't offer much amusement any more.
Hansa consciously worked to blank his thoughts so Alizarin wouldn't answer the next question that logically crossed his mind: What normally amuses an Abyssi? He knew just enough not to want Alizarin to say more.
Instead, he focused all his attention on scrambling up a pile of stone and . . . other clutter. He tried to tell himself it was shells, like those littering the first level's dry sea, but when he stumbled and his groping hand closed on the curve of what could only be a skull he jerked back so abruptly he nearly brought himself, Naples, and Umber all down.
"We're here," Alizarin announced at last.
"Keep your eyes forward," Umber cautioned as he removed the blindfold.
Hansa looked around, blinking at the faint, white light cast by Dioxazine. He and Naples were standing in the open doorway to a small, not-quite-square room, short enough that Hansa could have reached up and touched the ceiling—if he had wanted to, which he really didn't, since it seemed to be writhing.
Where Xaz stood near enough to illuminate one wall in detail, Hansa could make out sharp, needle-thin spines that rippled across the surface of the wall, pulsing, retracting and then growing again, as if they were all inside a giant, inverted sea-urchin. Umber had gone ahead into the room, though he stayed far from the walls. Cadmia lingered hesitantly behind Alizarin, who had crossed the room to a box against the far wall.
About two feet high, two feet deep, and a little longer than a man, it would have been difficult to call it anything but a coffin. The exterior sparkled, reflecting Xaz's glow from thousands of tiny crystals. What could possibly be inside but the man they had come to rescue?
Careful, Naples gasped when Hansa tried to move into the room. The Abyssumancer's eyes fluttered, half opening, and then closing again. Doorway . . . close. Can't.
"What?"
Umber touched Naples' face gently before saying aloud, "He opened a doorway from the stairwell to this room. Considering who's imprisoned here, opening a doorway from the inside is probably impossible, so it would be best if we didn't all cross the threshold and have this one close behind us."
Yes, Naples said.
The show of life, at least, was promising.
While they were speaking, Alizarin had crossed to the coffin. He knelt in front of it and placed his hands on the sparkling surface.
"Will the other Abyssi know when we open it?" Cadmia asked.
Alizarin shook his head. "The box is designed to hold power captive. The room is, too, in case the box is ever opened."
"It seems too easy," Cadmia said.
Easy? Naples echoed.
"Speak for yourself, Cadmia," Umber concurred.
Alizarin was still kneeling in front of the coffin, now frowning, his tail twitching.
"How do we open it?" Umber asked as time went by.
Alizarin growled in response.
Naples drew a breath, something Hansa hadn't been convinced he had done in a while. "Umber, let me down. You and Hansa stay in the doorway."
"You seem stronger," Umber observed as he set the Abyssumancer on his feet.
Naples shook his head. "This room is doing some of my work from me. Xaz's, too. It's designed to be its own bubble, to keep in what's in, and out what's out." He held up a hand and a new globe of foxfire appeared, this one deep crimson. It hung in the doorway between him and Hansa. "Come inside. That will hold for a while."
He walked toward Alizarin and the coffin, his steps heavy with fatigue, but still more than he had done independently for hours. As the Abyssi had done, he knelt in front of the box and set a hand on it.
Unlike Alizarin, Naples drew in a sharp breath, his body sparkling with power for a moment. Xaz groaned, and Cadmia caught her arm to steady her.
Hansa and Umber had a chance to exchange one worried look before Xaz got her spell back under control.
"How do we open it?" Umber asked again as Naples examined the coffin.
"Power," Naples answered vaguely. "It's like anything in the Abyss. It wants sacrifice."
"In my experience the last few days, that usually means blood," Hansa said. "So one of us opens a vein. Again."
"Or a little more than that," Umber said ominously.
One hand still on the coffin, Naples turned, his gaze going from one person to the next in a way that made Hansa distinctly nervous, and made Alizarin start to growl again.
"Don't look at me that way, Hansa," Naples said when his attention turned that direction. "The only reason we're all standing at the moment is that the denizens of this level of the Abyss have built their own little sphere of the human realm. Once we go back out that doorway, I'll need you and Umber again."
"You're needed to hold back the Abyss." Cadmia's voice pierced the air clearly. "You need Hansa and Umber to help you do it. You need Dioxazine to keep you hidden." The pitch of her voice steadily increased as she continued to speak.
"Correct," Naples replied.
"How large a sacrifice are we talking about?" Umber asked.
Judging by Alizarin's low growl, and the protective tail he kept wrapped around Cadmia's waist, Hansa suspected the answer was more than a few drops.
"I am not killing someone in order to get into that box," Hansa said, though even as he said it, he felt the squeeze of the boon trying to argue with him. The magic can threaten all it wants, he thought desperately. I won't do it. I'll let it kill me first.
Naples didn't bother to argue with Hansa. He spoke to Alizarin instead. "I don't know why you came with us, but I know you wouldn't have done so unless you wanted this witch as much as I do. Are you going to protect her to the point of turning around now and admitting defeat?"
"I will," Hansa insisted, striding forward to try to get between Naples and Cadmia. That was his intention, anyway. When he tried, the muscles in his legs seemed to lock, the warning heat of the boon's power becoming a buzzing, piercing burn.
"You can't," Naples spat. "Don't pretend you can. If there's a way, you'll have to find it. And even if you had it in you to turn around and leave, you can't leave without me, and I am not going to leave without him."
"We're talking about murder!" Hansa shouted, flinching at the way his voice rang off the cell's walls.
"To be precise, it seems we're talking about my murder," Cadmia added, voice remarkably level. "And I think I'm going to have to decline."
"No, we're talking about survival," Naples retorted. "Nothing personal, Cadmia, but I did not come this far to stop here, and you're the one person in this group who is expendable. Why do you think the Numini sent you here? They must have known."
"I doubt the Numini are in favor of human sacrifice," Umber argued.
"No one's expendable, since we won't cooperate with you if you do this, and you need us, too," Hansa reasoned.
Naples drew a deep breath, and walked back toward the doorway to try to reason with the man standing there. "Look . . ." He glanced to the foxfire in the doorway, which was starting to waver, then reached up and pressed his hand to the top of the opening. He winced as the sharp spines at the top cut open his palm, but didn't pull back. As the blood dripped, it formed a lattice of strands as fine as a spider's web. "Step inside," he said, as Hansa nervously watched the growing web. "If we're going to take the time to fight, I need to make this more solid."
With all of them inside the cell, and a web of bloodred power keeping the doorway open, Naples stood in the middle of the room and looked at each of them in turn. "You were saying?"
Hansa took up the reply. "We were saying, you need us, too. You can't get to the surface without us, and we won't cooperate if you hurt her."
"You won't cooperate . . . meaning, you'll stay down here in the Abyss until your lungs burn out?" Naples asked. "Even if the boon would let you leave without doing everything within your power to fulfill it, I won't let you leave, and your threat not to help me leave is a thin bluff. Especially since, of everyone here, I am the one person who would rather die than return without this witch. So what about you? Are you willing to kill us all, including Cadmia, in your noble stand?"
"It doesn't matter what we say, since Alizarin doesn't look like he is willing to make that sacrifice," Umber pointed out. "I consider the refusal of a fully grown third-level prince of the Abyss to be suitable cause for me to declare this as something that is impossible. Which—"
"Which means very, very little," Naples said softly. "I didn't want to do this."
In a flash, he had drawn the blade from his right boot. Umber and Alizarin each made a move toward him, but neither was fast enough to stop him from dragging the blade across his palm. He flicked his hand in Umber's direction, and a wave of power threw the Abyssi-spawn backward until he slammed into the spines writhing on the wall. Hansa felt every muscle in his own body spasm, felt the pain as if the daggerlike blades had pierced his own back.
As he collapsed, unable to control his own muscles, he saw Alizarin finish closing the distance between himself and Naples, just in time to meet Naples' still-bleeding palm as the Abyssumancer pressed it to the Abyssi's chest.
"Step aside."
Naples' voice rang through Hansa's head, even though he was obviously speaking to Alizarin. The demon's growl deepened, becoming a vibration so low and powerful it made Hansa's bones ache as he struggled to remember how to move his arms and legs.
"Xaz . . ." Cadmia tried to appeal to the Numenmancer, but unlike Naples, Dioxazine was still blind to this world as she kept her own magic working. "Alizarin?"
"Step. ASIDE."
Slowly, tightly, tail lashing, Alizarin eased back.
"Don't make me chase you, dear," Naples said, as Cadmia inched away as far as she could without running into the walls. "Think of the man you're saving. Is one human death such a sacrifice, when the divine realm itself wants him freed? And of course, your death will save the rest of us here. Without it, we go nowhere until my power runs out, that doorway closes, and we starve to death." As if with sudden inspiration, he added, "If Terre Verte really can raise the dead, maybe he'll even take it upon himself to bring you back."
Hansa doubted Cadmia was swayed by Naples' reasoning, but there wasn't anywhere to run. Hansa had barely even managed to get an arm under himself to try to push himself up before Naples grabbed Cadmia's arms and dragged her over to the coffin.
She struggled, but Naples was stronger. The knife he had used moments ago clattered to the ground, but Hansa couldn't help but remember how many he was wearing. When Naples released Cadmia's wrists to pin her against the coffin, she hit him. Her nails drew blood from his cheek, but he barely flinched—what were pain and blood to an Abyssumancer, beyond another source of power?
CHAPTER 37
Cadmia would not calmly accept death. She didn't care what Naples said about lofty goals, possible resurrection, or the futility of resistance. As Naples levered her toward the coffin, she fought.
Hansa, Umber, and Alizarin had been neutralized with a few drops of the Abyssumancer's blood and Xaz was still lost in her trance, so it was just her, and she hadn't needed to physically fight to defend herself since leaving the Order of A'hknet. She threw everything she had into her struggle—every possible low blow, elbows and feet and fists—but Naples was stronger than his slender stature suggested. Once he had a grip on her, she couldn't break it.
The coffin's surface was scalding hot against her back, and the crystals pressed into her skin, bruising and cutting.
Yes. She could feel the power singing as it tasted her blood and cried for more. It overwhelmed her, making even Naples' grinding grip on her wrist and throat seem distant.
Deep in that song was another melody, this one cool and soothing. She closed her eyes, trying to hear it better.
Daughter of the Napthol, it called to her. We see your plight.
Underneath the music was the sound of gently lapping waves. Against her closed eyelids she saw not the twitching, pulsing walls of this cell or even the black beach of the Abyss, but silver-white sands endlessly washed by crystalline waters.
She didn't question the offer, but reached mentally toward that beautiful sea and the winged form who stood beside it, offering its hand.
"Help me. Please," she whispered.
The figure who had been reaching for her turned toward another, whose voice was rimed with frost and sharp like crackling ice as it said, How dare you risk our child in your scheme?
I have hold of her. She will not be lost.
She felt the edge of Naples' knife at her throat, and realized the Numini's idea of "help" was different than hers. It didn't care if her blood was spilled.
I will not have her tormented this way, the second voice protested.
An icy winter draft howled through the cell. Naples hesitated, the knife moving fractionally away from Cadmia's skin.
Cadmia opened her eyes just in time to see Dioxazine turn her head toward them—and then Alizarin, freed of whatever spell the Abyssumancer had put on him, crossed the room in a flash of claws and fangs. He pounced on Naples, knocking him away. Cadmia scrambled back, but she didn't get far before the cool wind became ashen heat.
She threw her arms in front of her face and felt blood splash like a hot wave. She frantically wiped at it, only to have it almost immediately evaporate into the Abyssal air, soaked up by the cell walls and by the fine filaments of power Naples had left holding open the gate.
It had only taken a second. If Cadmia had blinked, she never would have seen it, and how she wished she had blinked, that she hadn't seen Alizarin's handsome form dissolve into the black-and-indigo blur of claws and fangs, the monster, that had rushed over Naples and left nothing behind.
Nothing but the box, which Alizarin pulled open. Dioxazine was giving off enough light now that Cadmia could make out every crystal on the coffin's lid. She could tell that the fabric wrapped around the bundle Alizarin lifted out was charcoal-gray velvet, tied by cords so black they seemed to absorb Xaz's glow and darken everything a hand's-span around themselves.
"I guess it got its blood," Umber whispered as Alizarin lifted the limp bundle into his arms.
The Abyssi glanced at Cadmia. She flinched as those hot blue eyes settled on her. Before she could make any conscious movement, Alizarin had looked away again.
He had saved her life. She knew that. But the image locked in her mind at that moment wasn't one of a hero rescuing her, but of the creature inside, the creature that had sent a rain of hot blood down on all of them.
And a white beach somewhere oh so far away . . . had she really seen that? The image was fading, dreamlike. Had the Numini been arguing?
"I hate to be the one to ask," Umber said, "but do we have another way out of here?"
Alizarin looked at the doorway, where the magic Naples had left behind was starting to tremble. He reached toward it, and the web of power clung to his skin. When he pulled his hand back, the air tore, leaving behind not a door into the next room but another rift, like the one that had taken them to the Abyss.
"Does that go back to the human plane?" Cadmia asked, heart rising with hope.
"Surface of the Abyss," Alizarin replied.
"Still so much better than here," Hansa said practically before stepping into the tear in the world. Umber followed immediately behind.
"Bring Dioxazine," Alizarin added when Cadmia started to move toward the portal. Cadmia turned back to the Numenmancer, who had returned to her trance but allowed Cadmia to guide her into the rift.
She hadn't taken the time to wonder where they would end up—in the well, in the middle of the palace, out by the dead sea, or somewhere else—and was pleasantly surprised to find herself in a familiar parlor. Nothing had changed since they had left. Even the extra supplies they hadn't been able to carry—some bundles of food, a jug of water, and extra knives Naples had considered and set aside—were still on the table.
Cadmia's relief lasted one heartbeat before Xaz let out a small sigh and collapsed. She struggled to catch the limp woman, whose body was radiating cold like a winter draft, and guided her onto one of the couches. She searched for and found a heartbeat, but didn't know anything else to do.
Meanwhile, Alizarin knelt to unwrap yards of velvet from around the man they had brought out of the lowest level of the Abyss. He was still working when Aurelian ran into the room.
"Naples," she gasped. "Where is he? Azo's fainted. I don't know what to do."
Cadmia hadn't had a chance to consider how Naples' death would affect Azo. Maybe this wasn't the refuge she had thought when they arrived.
Alizarin looked up from his prize, who hadn't moved, and asked evenly, "She's alive?"
"Yes," Aurelian breathed, barely able to form the word around her anxiety. "What—"
"Aurelian, thank you." The heavy voice from the doorway made Cadmia's stomach jerk, as if it couldn't handle another swing from anxiety to relief and back to concern. "You—you're dismissed. Prepare a meal."
"Yes, my lady." Aurelian cast one last look around the room for Naples before hurrying to obey her mistress's command.
The silence stretched. Azo hung in the doorway, leaning on the frame as if she lacked the strength to do more. Her burgundy skin had turned a fungal gray-black with blotches of paler mauve, and her blue eyes seemed flat and lifeless as one of the shades'.
After a long, guilty moment, Hansa pushed away from Umber to offer assistance. He made it halfway across the room before he staggered, catching the arm of a couch and dropping his head and shoulders as if to fight dizziness. Umber, body trembling slightly with fatigue, caught up to his bond and urged him to sit.
Still no one had spoken. Cadmia opened her mouth to say something, but all her training—glib words and easy lies learned from the Order of A'hknet and comfort and honesty from the Order of the Napthol—abandoned her.
Azo spoke one word: "How?"
Alizarin unwound the last length of fabric, revealing a man who appeared in his early twenties. His warm brown hair wrapped him like another layer of cloth; if he were standing, it would probably fall nearly to his waist. His arms were crossed neatly across his dawn-gray leather doublet, which itself rested on top of a pristine white shirt with onyx buttons.
He looked as if he had been dressed and poised for the grave.
This task done, Alizarin finally looked at Azo to say, "It couldn't be avoided."
Azo tried to step forward but fell, one knee striking the ground as she hissed in frustration.
"Can I help you?" Cadmia managed to ask, kneeling beside her to offer a hand. Azo's response was frank, a heated look that Cadmia had seen plenty of times before—but usually from men. She didn't have a chance to limit her offer before Azo started to cough, body shuddering with the barking spasms that brought blood to her lips.
"She's too weak to feed through flesh," Umber said. "Hansa and I are too drained to give blood. Alizarin?"
"No," Azo spat when the Abyssi approached. She pulled in a pained breath, and pushed the next words out one at a time. "I'm not . . . a fool. I can smell him. His power. On you. From here. I won't—" Again her body spasmed, though whether with a suppressed gag, cough or sob, Cadmia couldn't tell.
"Can I?" Cadmia asked, this time knowing what she was offering, only unsure about whether her mortal blood was powerful enough to matter.
Umber shrugged. "If she'll accept. Heart blood's best." He made a sketching motion over his own chest, then half stood and half fell to go to Terre Verte's still form, as if unconcerned about Azo and Cadmia now. The boon, she reminded herself. He and Hansa had lost a lot of power in the bowels of the Abyss. They couldn't afford to neglect the boon now.
That left her alone tending to Azo, whose eyes were fixed on Cadmia in a predatory way that would have made Scarlet Paynes turn a customer away no matter how much coin he held. A look like that meant violence.
Steeling herself, Cadmia reached for one of the knives on the table, which looked like it had been made of one of the massive shells they had seen on the beach. She unlaced the neck of her shirt and shrugged the fabric off her left shoulder to expose the place below her collarbone that Umber had indicated. When it came time to set the knife to her flesh, however, she hesitated.
Azo's hand closed over hers. Her face was suddenly close enough Cadmia thought maybe she had gone back to her first response, but then the spawn's gaze dropped, the blade moved swiftly, and Azo tossed the knife aside as her lips closed over the wound.
Cadmia bit back a scream at the first sensation, blade and teeth at her flesh; she would have jerked away if Azo's arm hadn't become an iron shackle around her back. When she opened her eyes again—when had she closed them?—she saw Alizarin on his feet, tail lashing with anxiety as he watched them.
"She'll be all right," Umber said, a hand on the Abyssi's arm.
Within seconds, the pain had faded to a faint, bruised ache. "I'm okay," she said, catching her breath.
Alizarin hates the constant grime of this level.
You know him well.
The brief exchange with Naples passed through her mind unbidden, along with the memory of his blood splashing hot across her skin. Naples had been Alizarin's friend, hadn't he? Yet Alizarin had ripped through him the instant the Abyssumancer's power had been disrupted.
A deep, rumbling growl from Azo warned her to police her thoughts. She nodded to Terre Verte and asked, "Is he alive?"
"Nearly," Alizarin said.
"Nearly?" Hansa repeated. "What does that mean? Please tell me this wasn't all for nothing."
"Not dead," Alizarin clarified, unhelpfully. "But not quite alive."
"Will he wake?" Umber asked.
"I hope so." He looked at Cadmia and Azo again. "It's not magic I'm capable of making on my own, but it was supposed to be a life given to restore his life."
Cadmia didn't let herself contemplate that further yet either. "What about . . . Xaz?" she asked, hesitating in the middle as Azo's arm around her back released its death grip and moved so the spawn could pet her hair.
"She isn't injured," Alizarin said, sounding even less sure this time. "I would know if she were. I don't think it would be wise to pull her back from her trance before she is ready."
"So we just—" She grabbed Azo's free hand, which had drifted up her side and come a bit closer to a breast than Cadmia was comfortable with. Azo let out a distracted, frustrated half growl and her head lifted. Her eyes were dilated as they met Cadmia's, but the slim blue rings had regained some of their glow.
Her gaze traveled down Cadmia's face, paused at her lips, then returned to Cadmia's eyes. "Let me know if you change your mind."
"Are you all right now?"
Azo shook her head, but said, "I can hunt now. I—" She winced, shut her eyes, took a breath. "There was no choice?"
I was the choice. Cadmia tried to come up with a better response, but could see in Azo's eyes that she had heard the thought.
"I see." Azo nodded, then stood, the move slow and unsteady. "He was willing to die to accomplish his goal." She looked at Terre Verte's still form impassively. "I hope he's worth it. I'm going to go kill something. You all should eat and rest. Your rooms are still available." She limped from the room, only pausing in the doorway to add, "Cadmia, thank you. We will speak later about how I can repay you."
"I don't know much about magic, mancers or the somewhat-dead," Hansa announced once Azo was gone, "but if there's nothing we can do about Terre Verte or Xaz right now, I second the suggestion about food and sleep."
"Naples pulled a dangerous amount of power from both of us," Umber said, wrapping an arm around Hansa's waist to walk with him toward the kitchen. "Food is a good start to getting it back. After that, I have other plans for you."
They disappeared through the door, leaving Cadmia and Alizarin alone with the two unconscious sorcerers.
"Did you want me to let him kill you?" Alizarin asked.
"No." Cadmia shook her head. "I . . . did you have to kill him?"
"Yes."
"To get the box open."
"Partially for that reason," Alizarin answered.
"And partially to protect me?"
He nodded. "Also because of that."
"Is there a third part?" She sounded so ungrateful. She started again, trying to explain. "I'm glad you saved me. I'm very glad not to have died down there. But I had thought that you and Naples were friends?"
Alizarin shrugged. "He said so."
"You don't agree?"
He paused, tail flicking around his body, then back out again, as if he were struggling to find the words for what he wanted to say. "Abyssi are strong or weak," he said. "We have prey or playthings or chattel, or we are those things for someone stronger."
He looked at her, as if searching for understanding. She hazarded a guess. "Abyssi don't have friends?"
He nodded.
"Because most Abyssi wouldn't understand what that means?" she asked, recalling how unlike the others of his kind Alizarin was. He nodded again. "So you killed Naples because . . . friendship isn't important to you?"
She tried to say the words without judgement, but there was a tremor in her voice she couldn't help. This was a man she had taken to bed. Had she misjudged him so critically? Did he save her and sacrifice Naples because sex was more important to an Abyssi than friendship?
Alizarin hissed in frustration, but when she flinched, his ears and tail drooped. "He touched me," he said, tail lashing swiftly now as he tried to make his point. "He used his power against me. I am a prince of the third level of the Abyss, but I couldn't have escaped on my own."
Cadmia rubbed her temple, trying to see the world through an Abyssi's point of view. In Alizarin's world of strong versus weak, nothing mattered but power. Alizarin was the spawn of the previous king of the Abyss. He had proudly bested Antioch, an Abyssi of the fourth level. According to Vanadium, Alizarin had been a plaything of the previous lord of the second level, before he gained the strength to best him. Devour him was the phrase Vanadium had used. Was that all his relationship with Naples was? When Naples showed himself to be too strong, too much of a threat, Alizarin disposed of him?
She looked at Alizarin's brilliant indigo eyes. Was she imagining the sorrow there?
She was looking at this wrong. Alizarin wasn't a typical Abyssi.
"You considered him a friend," she said, trying to make sense of the blood, "but he treated you like . . . like . . ." She struggled to find the right word from Alizarin's explanation. "Like prey, not like a friend."
Ears and tail lifted halfway, indicating she had understood him, but he wasn't sure what she thought of it. "Yes." Hesitantly. "Did I do the wrong thing?"
By Abyssi standards, he had done the only thing he could do.
By human standards . . . "You did the right thing." She remembered the moment of Naples' death with horrific detail, but something had happened just before, something her memory couldn't seem to wrap around. "If he was so strong, how did you escape Naples' spell?"
"Something interrupted Naples' power," he said. "Xaz's Numini, I think."
"I . . . oh." She frowned, trying to recall the distant conversation she had overheard. The words had already slipped from her mind, but she thought someone had been arguing?
Alizarin turned away from her to kneel next to Terre Verte again. "You should eat, too," he suggested. "And sleep."
"What will you do with him?"
"I'll bring him to a guest room. I hope he just needs some time. I will stay with him a while."
"Will you—" She broke off. Did she want him to come to her room later?
Alizarin tilted his head. "I'll be with our guest. Sleep well."
"I'll . . . try."
She enjoyed their conversations. Could she forget the part of him that was darkness incarnate—or, more difficult still, embrace it? Had she accepted Alizarin as her lover despite what he was, and if so, was that so wrong? Alizarin had sought a tie to the Numen. He clearly wanted to be more than just an Abyssi.
He had saved her life.
He had torn Naples apart, sent his blood splashing across the room, without a moment of hesitation.
And he had done so, in part, to protect her. How much of her sudden unease was because of what the Abyssi had done, and how much was because she felt uncomfortable with the fact that, given the choice, she would have chosen Naples' death instead of her own?
No matter in what form the end came.
CHAPTER 38
Umber's heartbeat was slow and even. Even when it raced, it never matched the pace of Hansa's own. The pace—Hansa knew, intellectually—of a human heart. Like the rest of him, Umber's heart was stronger, strong enough to survive levels of the Abyss that would burn a human's soul out.
After the days in the darkness, they had satisfied all their appetites in aggressive and determined fashion. Now, sprawled across Umber's chest, tangled in the last vestiges of blankets, Hansa found himself listening to the Abyssi-spawn's heartbeat and wondering what was going to happen next.
"What happens if that witch wakes and really can do what Naples thought he could?" he asked. "He breaks the bond, we return to Kavet, and . . . then what?"
"Shouldn't you be asking what happens if he doesn't wake?" Umber rolled onto his side so Hansa fit comfortably, tucked against his body. "If Azo regains her strength and decides she is furious about Naples' death? Spawn on the human plane rarely survive the death of a bond. I don't know if the emotional attachment will have dissipated with his death, or if she is still in love with her now-dead Abyssumancer. And of course, without Naples, unless this Terre Verte can form a rift, we have no way back to the human plane at all."
"That worries me, too." Hansa had pictured it a few times, as Azo's and Naples' flustered servant had brought them all dinner. "But would I sound crazy if I said it worries me less?"
"Because you wouldn't be the one making choices," Umber guessed, correctly. "If the witch can break our bond, you return to normal. You get another chance at that life you wanted."
"I don't think you're evil." He blurted out the words without thinking them through. Umber chuckled. "Neither are Azo or Xaz. I have a hard time even thinking Alizarin is, and that's supposed to be the definition of Abyssi."
"Mmhmm." Umber trailed a hand down Hansa's back. "If—" He broke off. "Hansa, are you engaging in pillow talk?"
"Of course not," he replied instinctively.
Umber laughed again. "Fine, we'll call it deep and important conversation. That happens to occur on the bed. You were saying?"
Hansa briefly debated the merits of arguing the term "pillow talk," but he didn't have much ground to argue. There hadn't been any discussion as he and Umber had limped up to this room, muscles protesting going up stairs now after so many days of the opposite. They had passed through the door, into the bedroom, and Hansa had moved into Umber's arms like water seeking level ground.
Part of him had wondered whether it would be for the last time, whether when he woke the witch would also be awake, and would wave his hand and turn all this into an impossibly elaborate dream.
"I was saying . . ." He valiantly struggled to remember his train of thought with Umber tickling his chest. "I was saying, mancers aren't evil, spawn aren't evil, maybe the Abyssi aren't evil and certainly the Numini aren't evil. So why is keeping all of them out of human society the central goal of the Quinacridone, and of the entire government of Kavet?"
"Oooh." Umber flopped back onto his back. "Pillow talk just turned to politics. Hansa, I don't know. I can give you theories. Humans get nervous when other people have power over them. Or, given the way Kavet's government works, one man wrote a good speech and others voted for it."
"The Quinacridone made mancers illegal. What happened before that? I mean, yes, Naples was terrifying and I'm not really sorry he's dead, but since murder and . . . other things . . . are already illegal, what happened to make them pass a law making even animamancers, healers, punishable by death? If we had never tried to arrest Xaz, I don't think she ever would have hurt anyone. So . . . yeah. What happened, before One-Twenty-Six?"
Several seconds passed as Umber drew a deep breath, and then released it in a sigh. "I don't know. I wasn't alive in those days, obviously, and given the way they're marginalized, the mancers don't keep much of an historical record. The Quinacridone probably do, since they keep accounts of just about everything, but I don't know how accurate their portrayal of that time frame would be."
Hansa frowned. It had been a little over sixty years since 126 had passed. He remembered the ancient woman of the Order of A'hknet berating him about it in the marketplace. Maybe she could answer his questions.
Then what?
"I just feel like we should . . . I don't know, change things."
" 'Show up at the next election and speak to your fellow citizens,' " Umber said, tiredly quoting the Quinacridone mantra.
"Since sympathizing with a mancer is a crime, I don't think I would get far."
"True." Umber pulled him close again. "Maybe the deep thoughts should be saved until after our new witch wakes. He may not. If he does, he may not be able to bring us to the human plane, much less break the bond. And if he can break the bond, all these thoughts you're having might fade away."
"You're saying the fact that I now believe you're more than an Abyss-spawn pervert might just be the bond talking," Hansa said with a frown.
"For the record, I concur that I'm more than an Abyss-spawn pervert, but yes, it's possible the bond is affecting you, and when it is gone your opinions will change."
The possibility unsettled Hansa enough that he sat up, eliciting a groan from Umber.
"This doesn't feel like magic talking," Hansa asserted.
"When magic is involved, free will is a slippery concept. How exactly we make our decisions often isn't clear, and within that ambiguity there is a lot of room for magic to give a gentle nudge."
"I went with you to rescue Pearl," Hansa argued. "I know you put yourself at unnecessary risk to help her. You defended me against Naples, even though it made him more likely to be a problem later. You didn't let him kill Cadmia—or more importantly, Alizarin, who is a pure Abyssi, didn't let him kill Cadmia. That isn't evil, at least, it's not what I was taught evil was."
"Maybe. But just a week ago, when I tried to point that out to you, you threw it back in my face."
Hansa remembered the argument. Spoken like a Quin, Umber had said, after Hansa had ignored all his arguments that he might, in fact, not be evil incarnate.
"I was scared," he admitted, "and I was ignorant, and I was an asshole." He remembered a lot of the things he had said and done, not just around Umber but to others. At the very least, he had been a hypocrite; he had condemned Umber as evil while taking hold of that power with both hands and using it to try to make the world what he wanted. "A week ago, I hadn't seen a Sister of Napthol pray to the divine and have a prince of the third level of the Abyss come to her aid. I hadn't spent days walking into the deepest level of the infernal realm. I feel like I've finally started thinking for myself," he finished lamely. "Instead of believing what the Quinacridone says, just because it's easier than making my own decisions."
"Maybe," was all that Umber said in reply.
"Losing the bond could make me forget all that?" he asked.
"It probably won't make you forget," Umber said, "but you may reevaluate what has occurred and come to a different conclusion."
Hansa shook his head, even though one thing he knew from these last several days was that what he wanted often seemed not to come into play. "I don't like who I was," he said. "There are things I want, which the bond might deny me, but that doesn't mean I want to go back to being one of the Quinacridone's drones."
Umber's lips quirked, a wry smile, as he attempted to change the subject. "You just don't want to go back to abstinence. Face it, Quin. Your opinion of me would have been different if you hadn't done most of your deep thinking in bed." More seriously, he added, "I hope it isn't all the bond talking. That's a selfish wish, by the way. If it is all the bond, once that is broken, you'll be much happier returning to Kavet than you will be returning as you are now. But yes, I also prefer you as you are now."
"So you say," Hansa said, taking a page from Umber's book. "And how much of that is because of a bed?"
"Eh, you're all right," Umber returned. "You just need some practice."
"Then by all means, let's practice."
They put away unanswerable questions and stayed in bed until other needs drove them out. They bathed, ate another meal, and then looked at each other, wordlessly debating the merits of going straight back to bed.
"We should check on the others," Hansa admitted. Maybe the bond had changed him or maybe it hadn't, but one thing was definitely the same: he had been a guard, and he still had the instinct to keep track of his companions. As he thought about the group that had gone down into that cell, he found himself asking, "Is Naples really dead? I mean, I saw him killed, but what does that mean? An Abyssumancer, killed in a cell designed to hold in power, at the lowest level of the Abyss?"
"I don't know." Umber opened the doorway to the guest room where Xaz and Terre Verte had been moved. "I don't know how strong Naples was. I know it took an incredible amount of power to do what he did. I have no idea what he might be capable of, or what death in this place means to him."
They were speaking in hushed tones now, not because of the subject, but because of the atmosphere of the room they had just entered.
They stood in an elegantly decorated parlor. To their left, an open doorway revealed the bedroom, where the sorcerer they had brought here lay in the same funeral pose he had been in when they had first seen him. Closer, Xaz was stretched out on one of the sitting room's couches, her posture more natural but her countenance deathly still. Alizarin was kneeling next to her, his cheek resting on her wrist.
They crossed to stand beside Alizarin, and Umber asked, "How is she?"
"Cold," Alizarin replied.
Hansa touched the Numenmancer's brow, fearing the worst, and then snatched his hand back with surprise. "Not just cold—frozen," he said.
Umber reached for Xaz, as if needing to confirm. He brushed frost from her eyelids. "Should we try to warm her?"
"I don't know." Alizarin sounded strangely childlike, and the glow in his blue eyes seemed faded and lost.
"What about Terre Verte?" Hansa asked.
Alizarin shook his head again.
"How soon should we expect retaliation from the other Abyssi?" Hansa's thoughts hadn't yet moved past relief for their immediate survival and concern for the two unconscious sorcerers when Umber brought up the larger threat that still loomed over all of them. "The high court was already angry at you for keeping a Numenmancer here. We hoped to be gone before they decided to cause trouble. Now we have no idea when we will be able to leave, and likely more enemies."
Alizarin growled, or started to but then swallowed the sound. "We have as much time as we have," he answered.
"Was the magic shielding Terre Verte's cell sufficient to keep the lower Abyssi from noticing his absence right away?" Umber pressed. "Or do they know already?"
"They might not know," Alizarin said, though Hansa didn't like the lack of confidence in his tone.
"I hate to ask," Hansa interjected, "but should we be worried about Naples' Abyssi?" Naples had been significantly more powerful than Baryte. If he understood right, that additional strength was mostly due to age, but some of it had to come from his Abyssal patron, didn't it?
Alizarin tilted his head thoughtfully. "I do not know Naples' patron. He never came to investigate my being near his mancer. He may know he is not strong enough to challenge me, so did not dare interfere."
Or he was strong enough he didn't think you were a threat, so didn't bother to object. His gaze met Umber's worried one, as the spawn clearly heard Hansa's thought and agreed.
"We have no choice but to wait, and hope Terre Verte wakes and is able to open a rift before consequences catch up to us," Umber said.
They all stood awkwardly for a few moments, staring at the corpse-still man who remained their only hope for survival like strangers gathered together by the funeral of a mutual acquaintance, unable to even share comfort.
At last Umber spoke again. "We should probably check on Azo. We may be able to do more good there."
It was a sign of how uncomfortable the quiet vigil over the two unconscious sorcerers had been that Hansa felt relieved to leave and seek the . . . would she be called a widow? Azo and Naples hadn't been married, but the bond was a stronger tie than any human ceremony declaring partnership could ever be. It seemed like there should be a word for the survivor.
Azo called them into the room when they knocked. Hansa swiftly averted his eyes when he realized she was entirely nude, combing her damp hair in front of an aggressively lit fireplace as if she had just finished a bath.
"I see you two have been enjoying yourselves," she purred. Out of the corner of his eye, Hansa saw her stretch, unabashed. "Feeling better?"
"Quite," Umber replied, sounding amused, probably by Hansa's furious blushes. Did you expect her to be ashamed? he asked silently.
Even if neither Hansa nor Umber was likely to react lustfully, there was still such a thing as modesty—or at least, there always had been in Hansa's previous experience. If an acquaintance from work had dropped by unexpectedly, Hansa would have at least put on pants before casually inviting him in the way Azo had done when they knocked.
Apparently undisturbed by the naked woman, Umber said, "We came to see if we can help you in any way."
Hansa was so focused on not looking at Azo—the wall hangings in this room were particularly complex and fascinating—that he let out a high-pitched yip when she touched his chin, tilting his head down to force him to look her in the eye.
"S-sorry," he stammered.
Since his own attention remained on her remarkable blue-violet eyes, he couldn't help but notice that she looked him up and down frankly before meeting his gaze again, as if inviting him to do the same. A moment later she sighed in clear disappointment.
She released him, and replied to Umber's offer. "Clearly not."
As she sauntered back to the fire, Hansa belatedly realized that her disappointment hadn't been based on what she had seen when checking him out, but that he hadn't returned the gesture. She stared into the roaring fire as she said with obviously feigned idleness, "I spent a long time with a beautiful man who would give me anything but flesh. I have no taste for that offer now." She reached out her hand as if to pet the flames before her.
"Then we will leave you to your recovery," Umber said formally. Hansa needed no urging to follow him out.
CHAPTER 39
The Numini were displeased. Xaz could feel their disappointment in the needles of ice like frozen rain falling on her skin, and taste it in the salt of the air.
We did not wish for anyone to be killed.
Dioxazine had not wished to descend to the lowest level of the Abyss and witness a brutal sacrifice of blood. She had not wished to feel the Numini reach through her in order to act, as if she were nothing more than a tool, with no will of her own.
She certainly did not wish to be here now, in this world-between-worlds, facing their condemnation.
"I'm sorry," she said by rote and habit, though frankly, she couldn't care less. It was their magic holding her here, not hers. She was so tired she would have collapsed if only they would let her.
We are not pleased.
"Then maybe you should have done something," Dioxazine suggested, the arrogant words escaping her.
We disrupted the Abyssumancer's power.
"Long enough for Alizarin to eat him," Xaz pointed out, too frustrated to be polite and obsequious. "What did you expect the Abyssi to do?' "
Do you mean to chastise us?
The world around her, a barely real plane much like a mancer's temple but built by the Numini alone, shuddered with their anger.
"No, I do not chastise you," Xaz said, trying to regain her respectful tone. "I just want to know why you are chastising me. I did what you wanted, didn't I? I helped bring Terre Verte out of his prison."
At the cost of a life.
"The Abyssumancer was killed when he threatened a woman sworn to the Napthol, to one of you," Xaz tried to reason.
We had plans for him.
Again, her temper ran away with her. "If you love him so much, get your witch to resurrect him. Terre Verte is supposed to be able to do things like that, isn't he?"
The Numen did not answer the question. Instead, they said, We do not care for your tone.
Xaz drew a deep breath, which burned her lungs with cold. "I apologize if I gave offense. I am very tired, and my words are poorly chosen."
Mortal excuses are not within our purview.
"Perhaps, but they are my limitation," Xaz sighed. "If you allowed me to rest, maybe I would be better able to understand what you want of me."
She was so cold, the way only working with the Numini could make her. She had barely even been aware of the events that had transpired after she had cast her spell; it had taken all her concentration to maintain her tenuous connection to the Numen as she descended into the Abyss. She had been pulled partially from her trance when the Numini took note of Cadmia's predicament, but even then she had not had power to act. The divine had acted through her, using her as a conduit.
What we wish, the Numini said now, is your genuine repentance.
"For what?"
You have vows to us, Numenmancer, they reminded her. You have made agreements with our realm. And yet you scorn our will—
This time she snapped, she knew she snapped, and she made no attempt to reign herself in. "I have lived my entire life by your will!" she spat. "I never asked you for favors. You chose me. You made the decision before I was even old enough to walk, though I never in my life wanted—"
Your tone, Numenmancer.
For a heartbeat she hesitated, but it was all too much. "To the Abyss with my tone! I have lived my entire life fearful of all three planes. I have been afraid to disappoint you, afraid to be harmed by the Abyssi, and terrified of coming to the attention of the Quinacridone. I have crawled into the deepest crevice of the infernal realm to do your will, and now you chastise me over something over which I had no control?"
The world around her twisted with the Numini's scandalized shock, and Xaz found herself savagely glad.
Dioxazine, you should—
"Go away and let me sleep!"
As she shouted the last, she pushed with all the power she could find. She made the words into a command, and threw it at the Numini who had held her here.
The rift the divine creatures had formed shattered.
Xaz knew she was awake and back in her body, but she couldn't feel, much less move, her limbs. She struggled to open her eyes; the lids stuck together, the eyelashes fused by ice.
She let out a moan and became aware of a warm, lightly-furred hand touching her arm, and a tongue, hot and raspy like a cat's, licking her cheek.
Finally she managed to open her eyes and croak, "Alizarin."
"I was worried," the Abyssi leaning over her said softly. "You were cold."
"Still cold," she said, on a difficult breath.
Alizarin responded by crawling on top of her and licking her cheek again. He lay down and rested his head on her shoulder.
At first he was painfully hot, and Xaz had to clamp her jaws shut to keep from telling him to go away. Then her body started to warm and remember that it was alive. The feeling returned to her fingers and toes in the form of hot pins and needles, and her chest ached as her heart drew in the icy cold blood that rushed in from her extremities when the veins opened to accept the new warmth.
At last she started shivering as violently as a woman in the midst of a seizure. Alizarin held her tightly, warming her and keeping her safe until her body lay limp, spent. Then he helped her sit up and handed her a cup of hot broth. She had no idea what was in it, only that it had obviously been sitting on the bedside in hopes of this occasion, heated only by its own power. It burned her tongue, but it thawed the knot of cold left in her belly.
"How did we get back here?" she asked when she was finally able to look around. They were obviously in one of Naples' and Azo's guest suites, though she could remember nothing of the return trip.
"I opened a rift," Alizarin replied.
"From the lowest dungeon of the lowest level of the Abyss?" she asked, skeptically. Then she remembered what had happened just before. "You absorbed Naples' power." Alizarin nodded. "How is Azo dealing with his loss?"
"She is injured, but alive," Alizarin said. "She refuses to see me."
"She won't be a problem for you, will she?" Xaz asked.
"Not in handling her, if I must," Alizarin assured her. "But I do not wish to need to."
Xaz rocked herself to her feet and leaned heavily on Alizarin as she walked toward the four-poster bed she could see through the nearby open doorway. There lay Terre Verte, the sorcerer they had saved—perhaps.
"The Numini say he may be weak for a long time, from his captivity," she said, trying to remember everything the divine others had whispered to her while she was connected to them. "They had wanted Naples to open the rift back to Kavet so Terre Verte wouldn't need to." She added, "They wanted a lot of things they didn't get. I told them off. You did what you did. It was the only thing you could do, and I think it was the right thing. Hopefully our guest will recover fast enough to get us home this century."
Home. She realized after she said it that technically, the human plane wasn't home to Alizarin.
"He's stirring." The man looked completely unconscious to Xaz, but she lacked an Abyssi's senses. Alizarin put a hand on Terre Verte's chest, as if to draw attention to the very slight rise and fall of his breathing. "Maybe he is responding to the power you used to send the Numini away. He didn't respond to Abyssal power, but yours is different."
Terre Verte's skin was fair and his features were delicate, masculine but finely wrought. His nails were a bit long, but there was evidence that at some point they had been well manicured. Xaz reached out to touch his hand, wondering if she would be able to sense anything about his supposed power. Before she could focus to use her magic, Hansa and Umber walked in.
"You're awake." Hansa sounded surprised but genuinely glad. "How are you feeling?"
"Fine, now," she said. She would tell them the details of her conversation with the Numini later. Right then, she wanted to know what else she had missed. "Is Cadmia all right?"
"Cadmia is fine," Umber said. "You saved her life, or the Numini did. She is with Azo at the moment."
"And how is the lady of the house?"
"Azo is . . ." He gave a wry smile. "Her full strength will not quickly return, but she is recovered enough to wish we were willing to share more than blood."
"How does she feel about our helping her after we murdered her lover?" That word "we" just slipped out. No one protested. Alizarin had shed Naples' blood, but they had all been there, and none of them would have stopped him even if they could.
"It is hard to say."
"You two lost a lot of power down there, too," Xaz said, remembering that Naples had started feeding on them when his own magic wasn't enough. "Are you all right?"
Umber raised one brow. "We have ways of raising power." Hansa blushed. "We'll be fine. Are you—"
"Is he waking up?" Hansa interrupted Umber unapologetically, drawing their attention back to Terre Verte. "I thought I saw his eyelids move."
Umber edged forward and put the back of his hand on Terre Verte's brow. "There is more color in his cheeks, and he's warmer."
Xaz hadn't seen Terre Verte's eyes, but she felt his fingers twitch under hers. Remembering what Alizarin said about Terre Verte possibly responding to Numen power, she reached out with a tendril of magic.
Magical shields slammed up around the rousing sorcerer, knocking Xaz's breath from her lungs. Umber wrenched his hand back with a start and Alizarin drew away with an instinctive snarl.
His eyes opened, focused first on Alizarin, then half shut in a momentary flinch. Given where he had been for the past however-many years, Xaz could only imagine what Terre Verte expected when he opened his eyes and saw an Abyssi hovering over him.
He controlled himself quickly. As his expression smoothed into one Xaz could best describe as calm arrogance, a soft silver glow returned to his eyes.
"You're a Numenmancer?" Xaz asked. Naples had called Terre Verte a Gressumancer, but in that moment the only Abyssal power she sensed on the strange sorcerer was sloughing away from him, remnants of his time spent imprisoned.
"A what?" He pushed himself to his feet, leaning for a moment on the edge of the bed before he seemed capable of standing on his own.
"Do you need help?" Hansa reached forward to offer a hand. "You've been—" The cool look Terre Verte gave the guard made it perfectly clear that he knew perfectly well where and how he had been, that he didn't want to talk about it, and that he equally did not want to accept any help Hansa might give him.
Then, once again, the expression cleared. He drew a deep breath. "We're in the Abyss?" he asked.
"On the surface, in the home of one of the spawn connected to the court," Umber said.
Terre Verte looked around, then moved toward the invisible doorway as if he could see or sense it. Though obviously weak, he moved with an authoritative stride, his gaze never lingering on the elegance of the room but rather focused on some goal. When he touched the wall and it opened, he did not seem surprised.
"How did we get here?"
"We rescued you," Xaz said.
Terre Verte turned around, his gaze searching, penetrating in a way that made Xaz feel as if she were wearing far less than she was.
At last, he said, "Thank you." Another moment went by, and he asked, "And who are 'we'?"
"Myself," she answered, "and these are Alizarin, Umber, and Hansa. An Abyssumancer named Naples was with us, and Cadmia, who's a Sister of the Napthol."
She watched him as she spoke the names, wondering if he would recognize any of them, or show surprise that an Abyssi, Abyssumancer or Abyss-spawn had helped him, or . . . anything. He only looked contemplative again. "And your name?" he asked.
"Dioxazine." It was nice to be regarded as a person by someone, instead of "a Numenmancer" who was therefore less important than anyone else in the room, but she wished she knew what was going on behind that carefully controlled expression.
Despite her unease, his response was the epitome of courtesy. "Dioxazine, I am honored to make your acquaintance. I am Terre Verte. You may address me as Verte, if you like."
He said the last bit as if she should be flattered by it.
"Are you the mistress of this household?"
A snorting laugh made it out of her before she could try for something more dignified. "Sorry, no."
He looked at the others, clearly dismissing Alizarin as someone—or something—that could run a household and considering Umber. Before he could ask, Umber said, "I believe Azo and Cadmia have just gone hunting."
Xaz's brows lifted. Cadmia? Hunting? With Azo?
Hansa of all people saw the expression and gave a half smile, half shrug.
Alizarin started toward the door as if to join Azo and Cadmia, then hesitated in front of Terre Verte, just the tip of his tail twitching with what Xaz recognized as indecision.
Terre Verte cleared his throat. "I apologize for not greeting you sooner, or thanking you for your role in my release. When I first saw you, I assumed—it doesn't matter what I assumed, suffice to say it was based on the experiences I've had with Abyssi before now. I am in your debt."
Alizarin seemed mollified by the words, but still apparently decided he would stay with the newly risen sorcerer rather than go to his lover.
"Do you think we could catch up to the ladies before their hunt?" Terre Verte asked. "I would like to introduce myself to the mistress of the household, and express my gratitude that she has opened her home to me during my convalescence."
"I would let her hunt, then choose if she wants to introduce herself," Umber advised. "She may not want to speak with you at all. She was bonded to the Abyssumancer who planned your rescue, and who was killed in the process."
If Xaz had expected to see guilt on Terre Verte's expression, she would have been disappointed. Instead, he paused thoughtfully, then asked, "Since you've used the term twice, pray tell, what is an Abyssumancer?"
He had seemed confused when Xaz asked if he was a Numenmancer, too. "How can you not know what a mancer is?" she asked.
Terre Verte simply regarded her with polite curiosity, clearly waiting for an explanation.
"A mancer is—" She stopped. How to summarize everything she was?
"I think the term mancer is only used in Kavet." Hansa spoke carefully. Xaz could hear him mentally editing what he was going to say, which was probably based on what he had been taught. "When we've had to speak to foreigners as part of an investigation, most of them know the word sorcerer. I'm not sure if they're completely interchangeable, but it's a close enough match they normally know what I'm talking about."
It hadn't occurred to Xaz that Terre Verte might not be from Kavet because his power felt so much like hers. "Are you not from Kavet?" she asked. "Did you come from somewhere sorcery isn't condemned?" It was hard to imagine such a place.
"These . . . mancers . . . aren't respected in Kavet?" It was the first time he had allowed them to see his surprise. "Why not?"
"Respected." Xaz wished it was that simple. Her gaze slid unwittingly to Hansa. "A mancer faces automatic execution if identified and caught."
Terre Verte's lips twisted with disgust. "I think I need to know a bit more about the world into which I'm being rescued." His hand played idly over the back of the couch, drumming thoughtfully. "And, if sorcery is so reviled, I believe I need to know what desperation drove you all to risk so much to bring me out. Suddenly I doubt it was done out of the kindness of all your hearts."
They each glanced to the others, clearly trying to decide where to begin.
"The Numini arranged it," Xaz said, trying not to let Terre Verte hear her anger in case he thought it was directed at him. "They—" She hesitated, not from fear of her masters, but shame as she considered what they had done. "Between multiple Abyssi and Numini fighting to do different things, it didn't work out exactly the way they wanted." The Numini had wanted her to appreciate the lengths they had gone to "for her," so they had shared some of the challenges and setbacks they had faced. Xaz grinned at Alizarin, remembering their irritation, as she added, "You were apparently not part of the plan." So, after Baryte threw the knife at me, they sulked a while that their plans weren't perfectly followed before they decided to help again. "But they did admit to arranging Ruby's death and to manipulating Hansa into taking the third boon and Naples into going after Terre Verte—um, you."
Hansa, Umber, and Alizarin were frowning and nodding, their theories confirmed, but Terre Verte rubbed at a knot at his brow and said, "Can you begin earlier?"
So they did. They described what life was like for a mancer in Kavet, and then Hansa told about his time in the 126. Umber, who had been least involved, picked up the story from Baryte's arrest to Hansa's, and then Hansa haltingly described why and how he had demanded the two boons. Xaz filled in the blanks whenever a mancer's power needed to be explained, so she was the one who described their first steps into the Abyss, and how they had made their way to the prison where Terre Verte had lain, "not quite alive," for so many years.
CHAPTER 40
Dawn in the Abyss came in the form of light creeping in from the distant hills, changing the vast, featureless sky from flat black to the paler, rusty gray that marked an Abyssal day.
"Is there a sun?" Cadmia's words masked the fact that Azo had paused again to catch her breath. The Abyss-spawn woman was clearly exhausted, but had insisted on going out. She had taken a bow with her, but Cadmia wondered if she had the strength to pull it. Cadmia hoped she hadn't been overestimating her abilities when she claimed that, aside from the Abyssi themselves, few truly dangerous beasts ventured so near the court.
Azo gestured toward the source of the light. "If you travel that way for several hours, you will reach fields of parched land that burn with forest-high flames each day. They protect the mouth of the crystal caves."
"Where Abyssi are born."
Azo nodded, and sank down to sit on a rocky outcropping with a hiss of frustration and pain.
"Are you all right?"
Azo growled. "I refuse to be this weak."
"My understanding is that you must be very strong to have survived what happened." Cadmia was careful to keep her words frank and avoid any hint of a patronizing tone, but she also avoided referring directly to Naples. "No one thinks less of you for—"
"I think less of me," Azo snapped, "and the Abyssi of the high court will think less of me. I stink like prey. I—" She broke off, and this time Cadmia wasn't sure if it was physical pain that had taken Azo's breath. Her voice was a low growl when she continued. "I survived many years without Naples." She said the word rapidly, like spitting out a mouthful of glass. "He would have been devoured by the beasts of the Abyss when he first fell into this realm if I hadn't—"
She broke off, coughing spasmodically. Cadmia wrapped an arm around her to keep her from tumbling off her stone perch before she recovered.
When she had, she said abruptly, "Terre Verte is awake." Cadmia looked around for the sorcerer. "Not here," Azo said. "I can sense him, his power."
"Do you want to go back?" Cadmia asked optimistically.
Azo gave a feral smile. "I suppose we should."
They started back across the black sand toward the royal court. They didn't have far to go, but Azo's pace was slow. On the way out, Azo had made idle conversation about the beasts of the Abyss, including which ones it took no extraordinary power to kill. This time, she said nothing, until at last Cadmia asked, "Do you want to talk about . . . anything?"
For some reason, the question made Azo laugh. "You're so tactful. Why don't you just ask: do I want to talk about the man who was not quite my lover, the man whose affection I always knew was nothing but magic's lie but couldn't help returning? Or do you think I should talk about the Abyssi who killed him, the one who is normally in your bed—though he wasn't last night. Did the blood frighten you away?"
"He was watching Terre Verte." She only realized how defensive the words sounded after they came to her lips.
She had slept alone for so many years, an empty bed shouldn't feel alien to her, but she had missed Alizarin the night before. She couldn't help but feel he had stayed away because he wanted to give her space to decide how she felt. She had flinched at his touch when she was overwhelmed by exhaustion and the lingering memory of Naples' blood, but the long, dark hours had made her regret the instinctive recoil.
"Even if you had no interest in the blue prince last night, there was no need for you to sleep alone."
Cadmia understood now the irritation she had seen Hansa express when Umber casually responded to his thoughts. Instead of debating whether or not Alizarin would have been jealous, Cadmia said, "If I were attracted to women, I'm sure we could have had a lovely time."
This time, Azo's laugh was full and rich, devoid of the bitterness Cadmia had heard before. "Lovely," she repeated, chuckling. "If you're ever in the mood to play, Sister, I promise to show you a time that will require better adjectives than lovely."
At last, Azo succeeded in making Cadmia blush. She groped mentally for a topic change, grateful now that Umber seemed to be only interested in men.
That was odd, now that Cadmia thought to compare him to Alizarin and Azo, both of whom clearly didn't care about their partner's sex.
Azo's mirth dissipated. "Umber has a lover, or had one," she said. "The Abyssi say that spawn imprint on their first lovers. How strong the imprint depends on how serious the relationship was. To be as exclusive as he is, Umber must have had someone quite special in his past. Or his present, I suppose."
Neither of them said aloud that, despite the heartbond, apparently Azo's relationship with Naples didn't count. Given how Abyssal power worked, Cadmia wasn't surprised to learn that flesh mattered more than heart in a relationship.
If Azo heard the thought, she chose not to comment before they reached the house. Azo was hungry, so they went first to the dining room, where they found the others already gathered—including Xaz, who looked battle-worn but proud, and Terre Verte, who had taken a seat at the far end of the table.
"Oh," the spawn said, gripping the back of a chair as if a moment's surprise had been enough to nearly knock her off her feet. "I didn't know your name, but I know your face."
"I'm sorry," Terre Verte said, standing to greet their hostess. "Have we met?"
Azo drew a steadying breath and shook her head. "You have your father's eyes and jaw, quite clearly. I recognize them from my mother's memories of her husband."
Cadmia remembered Umber's explanation that spawn retained memories from their parents, but it still took her less time to understand what Azo had said than it apparently did Terre Verte. His brows lifted and eyes widened as he exclaimed, "Your mother—my mother?"
Xaz was the first of them to recover enough to ask, "Your mother had a child in the Abyss?"
Terre Verte cleared his throat. "I knew my parents were estranged, but I never realized quite—" Azo winced, and Terre Verte broke off, nodding as if she were saying something silently to him. More subdued, he said, "I suppose that makes sense. Please, I'm being terribly rude. You're exhausted and made to stand at your own table. Aurelian?"
The man had already taken charge of Azo's servants. As Terre Verte helped Azo into a chair at the head of the table, Aurelian jumped to pour wine and serve her a plate. Cadmia slipped into an empty chair further down, not far from Alizarin.
The space he held between them seemed cold and unnatural.
"I'm sorry," she blurted out.
"For?" Alizarin asked.
"For being a fool," she said. She needed to get these words out, and she didn't care if the others overheard. "For being overwhelmed by everything that happened and blaming it on you, even for an instant. You saved my life. I blamed you for killing your friend instead of saying thank you for choosing me and I'm sorry you had to choose me."
He hushed her with a finger over her lips, and his tail wrapped around her waist. "Time for breakfast now," he said. "Time for talk later."
That was fine. She leaned against him, wishing all their problems could be solved so easily.
"And this is Cadmia." Cadmia gave a guilty start as Azo said her name and she belatedly realized how rude she had been to ignore Terre Verte the way she had, but the spawn and the new sorcerer both had indulgent expressions on their faces. "She's as human as they come but might have a bit of Abyssi soul in her."
Cadmia stood, though the attempt at courtesy was marred by Alizarin's tail lingering around her waist. "Cadmia Paynes, Sister of Napthol." The title slipped out by habit, an attempt to cover her earlier informality.
"That explains it." Cadmia wasn't sure what was explained how, but Terre Verte didn't give her a chance to question him. "Pleasure to meet you, Sister Paynes. The others have been filling me in on the rather remarkable series of events that led to this point."
"Including, apparently, the birth of your sister," Xaz said, still shaking her head incredulously. "Is that how you have your connection to the Abyss, even though you otherwise work with the Numen? Your mother?"
Terre Verte paused to consider the question. "Both my parents dabbled, my mother with the Abyss and my father with the Numen. It was common enough where I grew up."
"Dabbled," Umber muttered, apparently thinking the same thing as Cadmia. What kind of dabbling led one to have a child in the Abyss?
"Where exactly was that, if I may ask?" Cadmia could hear the longing in Xaz's tone.
"A very different land than yours, certainly. One without your Quinacridone strangling the populace." Terre Verte shook his head, making a sound of disgust. "All of you are welcome to accompany me when I return to it."
"I would like that very much," Xaz said instantly.
Cadmia looked away from the sorcerers as she considered, and her gaze met Hansa's. He had been quiet since they came in, and she saw on his expression the same thoughts she harbored. Kavet was her home. She had a life there. She didn't want to flee.
She wanted to fix it.
"It will take me some time to regain enough strength to bring any of us back to the mortal realm," Terre Verte said. He continued, speaking to Hansa and Umber as if picking up the conversation Azo and Cadmia had interrupted. "In the meantime, I will study the bond between you two and search for this Ruby you speak of, and see if I can do anything to solve either of your problems. It is the least I can do to repay your efforts to procure my release."
"We would appreciate that," Umber replied.
"Speaking of repayment," Azo said. "I, too, feel I am in your debt."
Xaz spoke first. "You have given us a safe place to stay and supported our quest to get Terre Verte even when it was clear you did not wish it yourself. You have given us enough."
Xaz didn't have the benefit of Cadmia's recent conversations with Azo. She couldn't predict the spawn's sharp, swift retort.
"Intentionally or not, you freed me from a magical entanglement I could not escape on my own. I survived the immediate sundering of the bond, but I might not have survived the days after if one of your companions had not been willing to share power, since in my madness immediately after Naples' death I would have willingly starved rather than accept Alizarin's help. Finally, almost incidentally, you have apparently freed my brother from a prison in the Abyss. I do not like unresolved debts," she concluded. "I'm sure you understand. Cadmia, what would you have of me?"
Cadmia didn't care for such things herself, but Azo's tone made it clear she was talking about more than a sense of guilt. No one had fully explained how boons and bonds worked, but Cadmia had heard enough to understand the implication.
She looked at Hansa, considering a favor she had almost asked earlier, but had held back because like Xaz she had not realized the level of obligation Azo felt.
They had come to the Abyss for many reasons. "Eleven guards from the One-Twenty-Six were killed when Dioxazine first summoned Alizarin." She kept her words as neutral as she could. None of them were the same people they had been then. "We hoped to find them here in the Abyss and help them to the Numen, but have been told it can take weeks for shades to regain their memories of who they were." She paused, remembering the pathetic encampment they had found their first day here. "Would you be willing to take them into your household? They won't be useless. They were soldiers in life. They can probably help hunt."
"Do you think Quin guards killed by an Abyssi will accept help from an Abyss-spawn?" Xaz spoke with incredulity, but also hope. The soldier's deaths had not been her intention, but that blood was still on her soul. Knowing there was still a way to help them could be a comfort.
"Some of them might not," Hansa acknowledged, "but some probably will. I think Jenkins would, and some of the others, if you tell them you know me. Then, if there's ever a way and we can help them move to the Numen, we'll bring them over."
"I believe I can do as you ask," Azo said. "I should be able to cast a beacon to draw them here, anyway, and I will offer them a place."
"The Numini have given permission for them to be escorted to the Numen," Xaz said, "if we can determine how to do so."
"Once they are gathered in the same place, Xaz and I should be able to create a ritual to bring them over," Terre Verte said. "Having a safe haven here will give them time to recover their memories and self-awareness so they are strong enough for the crossing."
"Thank you," Hansa breathed, relief painfully clear on his every feature. He couldn't save his friends' mortal lives, but he could keep them from wandering, lost and starving, for the next life. Cadmia smiled; she didn't have Hansa's personal attachment to these shades, but she was relieved to know they could be taken care of.
Terre Verte rubbed at his temple. It was the first sign of weakness he had given during their conversation, but it reminded Cadmia that the man had been locked in a prison until recently. "If you'll excuse me," he said, "I think I need to rest." With a wry smile, he added, "And I imagine you all have things you would like to discuss without a stranger in your midst, such as the stranger himself. Lady Azo, by your leave?"
Azo nodded, then rose. She hadn't done more than pick at her food in the few minutes they had been at the table. "I will walk up with you," she said. "My appetite is still scarce."
Terre Verte offered his arm with the casual ease of a man used to formal gestures. Azo leaned on it lightly as they exited together.
"A man used to having power," Xaz observed, the moment the doorway had closed behind the pair. "Used to having it, and having others recognize it. You would think that however long he spent down imprisoned in the Abyss would have changed that."
"Anyone have thoughts on why the Numini went to such lengths to rescue him?" Hansa asked, looking at Xaz.
"As if they would explain their intentions to me," Xaz scoffed.
Cadmia leaned forward, trying to improve her focus by moving away from Alizarin's warmth. "Does he seem familiar to anyone else?"
Hansa frowned, considering, then shook his head. "You meet more people in Kavet than most of us do."
"Particularly of the unsavory sort," Xaz added, "but he says he isn't from Kavet. Do you think he's lying?"
Cadmia shook her head. "I don't know . . . I don't think so. His face just looks familiar. I can't—you're not helping me think," she added, batting at Alizarin's tail, which kept tickling her cheek.
"We could always ask Azo," Umber suggested.
"Was anyone else surprised by that connection?" Hansa asked.
Cadmia nodded, and saw the others doing the same. "I'll try to ask her next time we're alone."
Umber lifted his brows suggestively. "Have fun."
Xaz stood with a stretch. "I'm better off than Azo and Terre Verte it seems, but I could use a nap as well. Possibly six months of hibernation."
Umber chuckled. "Alizarin, Azo's stores of meat are low. I gather Naples did much of the hunting. Would you be willing to help me replenish them? I'll be more effective with your assistance."
Alizarin turned to Cadmia as if to invite her to join them, but then his ears and tail drooped before he even spoke. Apologetically, he said, "I would like to help Azo, and we'll hunt better without mortals."
Hansa shrugged, standing and pulling away from Umber reluctantly. "I guess that means Cadmia and I are on cleanup duty. I can't say I'm disappointed to miss the hunt."
Cadmia was a little disappointed, but once the others were gone, she remembered the question she had wanted to ask Hansa ever since her earlier conversation with Umber about his mother.
The servants took the dishes from their hands as soon as they tried to gather them. While they were doing so, Cadmia asked, "Do you know who Bonnie Holland is?"
Hansa's hand clutched spasmodically on the dish he had just lifted, nearly overturning a platter of fruit before Aurelian swooped in to take it from him.
"Was," he said. "Not is. Anyone in the One-Twenty-Six does. I gather President Indathrone had objected for years to women serving as soldiers, but after Holland . . . well, he used her as an excuse to push for official limitations, though I've always felt what happened to her could just as easily have happened to a man."
"She was a guard?" Cadmia asked. That put a new and interesting spin on Umber's relationship with Hansa, especially given what she knew of spawn's inherited memories.
"A lieutenant," Hansa said. "Her company ran afoul of an Abyssumancer and his Abyssi. It's one of the stories used in training." His frown became something deeper, darker. "I guess soon they'll be telling about Company Four going to arrest a Numenmancer and facing an Abyssi. The loss of life when Lieutenant Holland went after Blakemore—that was the mancer's name—was similar. Holland was one of only two who survived. She managed to kill the mancer and send the Abyssi back, but was badly hurt in the process."
"Hurt," Cadmia echoed, trying not to let the horror she felt tell Hansa more than Umber wanted him to know, but suddenly understanding all too well the concern that had led Umber to check on her after her first night with Alizarin.
Hansa looked puzzled. "I know the doctors didn't think she would live at first," he said. "She never walked again. She chose to leave the city, and the guard paid for a home in . . . mm, I don't remember the name of the town. She died not long after. Does that answer your question?"
"I suppose," Cadmia said. "Do you know how she died?" And how many months later?
"She never fully recovered from her injuries," Hansa said. The topic disturbed him, but it was also clearly history, a dark lesson he had been taught and was now reciting. "It was always implied that her death was from long-term complications of those wounds, but I heard rumors she killed herself. It was before my time."
"Shortly before you were born, I'd guess." Unless spawn aged differently than humans, a fact she had never previously considered, Umber seemed to be about Hansa's age.
Hansa nodded, confirming the timing.
"Why ask about an old soldier?"
If Umber wanted Hansa to know, he would tell him. Cadmia settled her expression into her professional mask. "The conversation where her name came up was private. I shouldn't disclose details."
"All right." He knew better than to press a Sister of the Napthol to break a confidence, no matter how curious he was.
Damn Umber. Cadmia wished she hadn't asked for more information. It had been easier to momentarily assume that, like Hansa, or like Azo's mother, Umber's mother had had an illicit, sorcery-enabled affair. The chill that settled into her bones as she considered the violent reality refused to dissipate.
When Alizarin returned, she put herself into his arms, soaking in his heat. His comforting purr and confused queries about why she was upset reminded her how different he was from the rest of his kind. How unique. And how beautiful, like all the dangerous, predatory lights in the Abyss.
CHAPTER 41
"No. No." Terre Verte recoiled from Hansa's touch, startling Hansa from a near-doze. Terre Verte said he would use Hansa's connection to Ruby to find her shade, but he hadn't felt a thing beyond the sorcerer's cool hands on his as they sat facing each other in Azo's dining room chairs.
His eyes opened to reveal gray irises filled with sparkling snow.
"Are you all right?" Cadmia asked. Though uninvolved in the simple ritual, she had asked to observe.
It had taken Terre Verte almost two weeks of rest and ritual before he felt strong enough to attempt this task. Had he overestimated his abilities now? Hansa said, "If you're still too weak—"
He broke off as Terre Verte closed his eyes and raked his fingers down his cheeks, leaving white trails that swiftly turned pink, then faded.
"Are you with us?" Umber asked, when Terre Verte didn't respond to Cadmia's or Hansa's words.
In one of their many late-night conversations, Umber had admitted to Hansa that he was unable to read any thoughts from Terre Verte. The man was a mystery—even more so since he evaded most questions about his past, and Azo had respected his wishes by refusing to share anything she might know.
Cadmia, unsurprisingly, had been able to get the most from the strange sorcerer, but when she pressed him about the specifics of where he had come from or how he had ended up in the Abyss, he had bluntly told her, "I am grateful to you all for bringing me out of that cell, but I am under no obligation to detail events I have every wish to put from my mind and memory. Please pass on to your companions my sincerest wish that they stop interrogating me about a life and circumstance that is saturated with blood and despair."
Cadmia had indeed passed on those words, almost two weeks ago now. After that, they had all stopped asking questions.
"I'm here," Terre Verte said hoarsely. He opened his eyes again. They had returned to their previous slate-gray. "I found your shade. I should have known where I would find her. Idiot." The last word was snarled, as if to himself.
Hansa looked around instinctively, as if Ruby might materialize in their midst.
"Where?" Umber asked.
"When an Abyssi slays a mortal, the shade falls to the Abyss." Terre Verte's voice was barely a whisper. "The Numini slew Ruby. Of course they brought her to their realm after."
Of course. Because she had killed herself, Hansa had assumed Ruby would fall to the Abyss. Even with everything he had learned in the last few weeks about the nature of both the Numen and the Abyss, he had never paused to reconsider that assumption. Surely they couldn't be expected to drag her soul back from the Numen to—
The thought made Hansa's chest tight, his horror mingling with the magic's insistence that, yes, they would do anything they needed to or else face the consequences.
"The walls around the Numen are crystal and silver." Terre Verte continued as if in a daze, as if arguing with unspoken words. "They are too high to scale and too strong to breach."
"You can't do it?" Hansa breathed.
"It is irrelevant if I can." Finally Terre Verte's gaze focused. "I will not. I have seen it done. It was a horror. To pull a soul from that place—" He stood so abruptly his chair wobbled and Umber had to grab it to keep it from crashing to the floor. "Never. I am sorry. I cannot help you. No one can help you."
Hansa had started to stand, but gripped the back of his own chair for balance as his head spun. Their last option had just clearly declared itself impossible. A vise relaxed around his body, letting air pass in and out of his lungs and the blood rush about more freely than it had in weeks.
"I'm sorry the search was so painful for you," Umber said, his voice sounding steadier than Hansa felt, but just barely.
Terre Verte shook his head sharply, as if offended by the suggestion of weakness. "I apologize for my discomposure. It was . . . unexpected, to reach for a soul I assumed would be in the Abyss or the mortal realm, and suddenly find myself standing magically before the Numen's shining gate." He shivered, and ran his hands over his arms to settle himself. "Have I given you the information you need to resolve the boon?"
"Yes," Umber sighed.
"I could sense the bond as well while we were connected," Terre Verte reported. "I did not dare try to manipulate it, though. I am not strong enough to control the severing, and having seen how Azo was affected by the sudden loss of her Abyssumancer, I do not think it is wise to act rashly."
Light-headed from the boon's release, Hansa struggled to process what he felt at Terre Verte's words. A sense of reprieve, he decided.
Questions, decisions, put off until another day.
Part of the feeling was cowardice, not wanting to face the truth of who he might be, once the bond was removed. Even so, he was grateful for the delay.
"Not strong enough, ever," Cadmia asked, breaking in when neither Umber nor Hansa asked the obvious question, "or not strong enough for now?"
"For now." Terre Verte shuddered and rubbed his palms over his arms. "I was in that cell for—I don't know how long, actually. I'm weak, and being here in the Abyss makes the bond stronger."
"What about after we return to the human plane?"
He nodded. "I need some time to recover my strength first—a few weeks breathing mortal air—but after that I will be able to help you. I am certain of it."
Umber's breath let out in a long, slow exhalation that seemed to let a world of tension out of his body.
Hansa asked, "And when do you think we can return to the human plane?"
"Tomorrow," Terre Verte answered. "I've been working on the ritual to open a rift. It is nearly complete. I wanted to search for your shade before crossing because you all assumed she was in the Abyss, but that was the last task I needed to accomplish here."
"What about Xaz and Rin?" Cadmia asked, uncharacteristically hesitantly. She didn't quite cross her arms as she spoke, but her posture closed, as if she had started to flinch for a knife at her waist but then stopped.
Xaz hadn't discussed her desire to break her bond to the Abyssi much since their trek into the prison at the heart of the Abyss, but Hansa doubted she had forgotten it.
"That may be more difficult," Terre Verte answered. "The bond between you and Umber is solid. Concrete. The connection between Dioxazine and Alizarin is harder to understand. His power has seeped into her, and hers has seeped into him. With time and study I'm sure I can unravel it, but it may be more a slow process instead of a clean cut."
"How will it affect Alizarin?" Cadmia's voice was carefully even, as it had been when she spoke to Baryte and later Hansa in the cells under the Quin Compound. "I know Xaz has a right to her freedom, but Alizarin fought for this tie to the Numen. In my understanding, it's what allows him to reason and empathize, and makes him so different from the rest of his kind. What will happen if you break his tie to Xaz?"
"That's part of why I need to be careful." Terre Verte glanced down, looking Cadmia over assessingly. "I'm not particularly fond of the Numini, but it's not a good idea to cross them until I understand their plans, and I don't want to anger a third-level prince of the Abyss in the process. If I can free Dioxazine while allowing Alizarin to maintain a tie to the Numen, I will."
Cadmia tensed in response to the frank gaze, and didn't continue her questions, so Hansa responded instead. "The Numini put a lot of effort into freeing you from the Abyss. Why aren't you fond of them?" Beyond Terre Verte's words just now, his reaction at glimpsing the Numen had seemed one of revulsion, not awe or gratitude.
The words had been spoken before Hansa realized they probably fell in the realm of things they had all agreed not to ask.
Terre Verte's gray eyes went cold. "I did a favor for the Numini once. As Xaz may have told you, their gratitude leaves much to be desired. Freeing me from that box was the least they could do to put things right." He shook his head, and some of the life returned to his expression. "I am sorry the Numini dragged you all into their mess, but at least I can help free you from it and allow you to return to your own realm." He settled another heavy glance on Cadmia before adding, "Unless you would rather remain here. I'm sure Azo would let you stay with her for a few months, if you want."
Hansa felt like he had walked into a play while missing a page of the script. He glanced to Umber, wondering if he had been privy to a conversation Hansa had missed.
"Do you want to stay here?" Umber asked Cadmia. "If not, I am happy to offer any assistance you need when you return to Kavet."
Cadmia tensed, bristling like an angry cat in the face of the two solicitous gazes. It was not the look of a woman who had idly considered staying in the Abyss to, what?
Be with Alizarin? Get to know Azo? Practice her hunting?
"Thank you for your offer of support." Her words contained more grit than gratitude. "If they cast me out of the Cobalt Hall, I can go to the Order of A'hknet. I might go anyway. I'm feeling a little disenchanted with Kavet right now."
"You would be better off in the Cobalt Hall," Umber argued. "Every Abyssumancer in Kavet will want that child. Alizarin can offer some protection, as long as severing his bond to Dioxazine doesn't make him forget he cares about it, but a strong enough Abyssumancer will be a threat to him, too."
That child. The Cobalt Hall, the one place in Kavet where mancers could not go. And Alizarin could be protection if he doesn't forget he cares about . . . it.
"You're pregnant?" The words tumbled out, astonished, before he could contain them.
"I suspected, but didn't know for sure yet," Cadmia growled back. "Incidentally, boys, that's the kind of thing a woman prefers to learn for herself and share when she chooses to, not be told." Umber looked chastened, but if Terre Verte felt any guilt, it didn't show. Neither argued with her. "Fine. I'll stay at the Cobalt Hall—for now. I'll accept your help, Umber, anyone's help, to teach me what I need to know to protect myself and my child."
The Cobalt Hall would keep Cadmia and her child safer from mancers, but it was across the street from the Quin Compound and the barracks for the 126, the most likely place in Kavet to find trained men and women with the sight.
"It isn't just Abyssumancers you need to worry about," Hansa said. "You can excuse a lot of study as a Sister of the Napthol, but if someone notices an Abyssal taint on you—"
"Then I will change Kavet," Cadmia declared.
Was it Hansa's imagination, or did he see a flash of blue light in the depths of her eyes? She stared at Hansa as if waiting for him to argue. He didn't dare.
He didn't want to.
"I'll help you," he said instead.
Umber sighed heavily, an expression Hansa knew usually came before something worldly and at least borderline patronizing.
"Both of you should wait to risk your lives to change the world until after your link to the Abyss is gone. Power—"
"Easily and often overrides preference," Hansa interrupted. The words had been indelibly etched in his brain during his first serious conversation with Umber about the boon. "I know. You think I'll change my mind. I refuse to live under the assumption that the person I am right now will die once Terre Verte is strong enough to break our bond."
In the meantime, he had come to realize how ignorant and marred the laws of Kavet and her people were. How could he serve as a guard whose one duty was to enforce those errant regulations? At the same time, how could he, who had chosen to join the 126 from a genuine desire to protect the people of Kavet, and who had been raised to believe that the democratic system was a vehicle for right, walk away from what was so obviously wrong?
Just don't get us killed, Umber whispered in his mind.
"I've heard of women whose personalities changed while they were pregnant," Cadmia conceded, "but I made the decision to have this child. I'm not a victim of the Abyss. I'm a scholar, a lover, and now soon to be a mother, and if I have to remake the world in an image of my choosing, I will."
That was the end of the discussion.
The next day, they returned to the well at the back of the high court.
"There is already a rift to the human plane there," Terre Verte explained when he told them his plan. "It has been mostly closed through disuse, but it will be easier to push through there than somewhere new."
Hansa found himself strangely unaffected by the prospect of having to cross the court again. Compared to the fifth-level Abyssi court, walking across the high court proved almost dull. Alizarin led the way again, with his tail around Cadmia's waist as usual.
No other Abyssi challenged them, though many cast speculative or wary glances their way. Was it Hansa's imagination, or did many of them seem to stare with more anxiety at Terre Verte than they did at Alizarin?
Once they reached the well, Terre Verte put his hands to the smooth wall, his brow tensing with concentration.
"Do you need anything?" Xaz asked. She was wearing the pack Naples had provided her with a Numenmancer's tools inside; she patted it gently as if to confirm it was secure.
The rest of them had small bags containing a few foodstuffs and extra clothing, since they didn't know exactly where they would end up or what their first steps would be once they arrived. Umber had claimed the bone blade Naples had previously wielded, saying it was too valuable a tool to be lost in the Abyss. Having seen that blade up close and personal twice already, Hansa wasn't looking forward to the next time Umber wielded it.
Cadmia wore a weapon now, as well. She had blanched when Alizarin had first presented the dagger to her—the one forged of his own bone—but he had insisted that she keep it, saying it would act as a warning to others who might try to harm her, as well as a weapon she could wield in her own defense.
"I'm fine," Terre Verte replied, his eyes closed. "It's . . ." He stopped speaking for a few seconds, and then breathed, "Here."
The portal he opened was not black like those Alizarin made, but glistening silver. It came into existence with a whiff of sweet, smoky aroma, like incense.
Terre Verte stepped back from the portal and gestured for them to go ahead.
Umber moved forward first, and Hansa followed. He emerged with a shiver, brushing flakes of frost from his skin as the others stepped through behind him.
"Where are we?" he asked, looking around pointlessly. The light from the portal was just enough to give the impression of clutter and perhaps walls, but no other details of the room around them.
"Somewhere dark." Cadmia sneezed, and added, "And dusty."
Terre Verte emerged from the portal last. As it closed behind him, he lifted a hand and summoned an orb of silver-white foxfire, which illuminated a vast, windowless room which had once been elegant but now showed years of disuse.
A long couch hugged one wall, which looked like it had been softly elegant long ago; now it was impossible to even tell what fabric upholstered it. Bookcases laden with texts made unreadable by time and grime filled another wall, and a round table at knee height that appeared to have been an altar dominated the center of the floor. It was draped with cloth and set with odds and ends that were hard to identify under the dust of ages, which coated every surface in the room and billowed when they moved.
Xaz started to move forward as if to examine the altar, then seemed to think better of it. She put a hand in front of her nose to keep from inhaling the musty particles that grew thicker in the air each time one of them took a step. "Is there a door?" she asked.
It was a reasonable question. The foxfire Terre Verte had summoned was bright enough to illuminate the entirety of the small room, but Hansa couldn't see any exit.
"Of course," Terre Verte said before crossing and pressing a hand to an apparently blank wall.
Hansa blinked. If he hadn't seen so many doors appear and disappear at Naples' and Azo's estate, he might have thought he hadn't seen this one previously due to the tears in his irritated eyes. Instead of an empty arch, a sturdy-looking door of slick, polished wood appeared.
"We are back in the human plane, right?" he asked.
"Yes," Terre Verte answered. "But this was a hidden room, not meant for the eyes of anyone who might stumble across it."
They all moved toward the doorway, anxious to get away from the stagnant air and now nearly blinding, billowing dust.
The moment they crossed the threshold, though, Hansa's breath hissed in with unwanted familiarity. Carved cherry wainscoting rose waist-high on the walls, below horse-hair lime plaster smoothed over old stone and painted soft, barely-blue gray. Like most soldiers in Kavet, Hansa had spent his share of hours repointing and painting those damned walls, one of the many mind-numbing tasks that could be assigned to young grunts without the authority to object or older soldiers being disciplined. Even the smell was familiar: spices of winter stews and familiar tea, ever available this time of year in the guards' mess.
All that meant they were in the last place they wanted to be.
"Shit," he hissed, anxiously looking up and down the hallway. It was a miracle no one had seen them emerge from what should have been a blank wall. "We have to get out of here."
"Where is here?" Cadmia asked, rubbing at her nose, probably to clear away the dust.
"We're in the Quinacridone," Hansa said. "I don't know exactly where, which means probably one of the private halls, maybe where the monks live. I recognize the—"
A figure turned the corner, one he wouldn't need to introduce.
President Winsor Indathrone was fifty-three years old, dark-haired and shrewd-eyed. At that moment, he was wearing slacks and a shirt without vest or jacket; he was comfortably at home, which meant this hall was probably part of his personal residence. He frowned at them all, then focused his gaze on Hansa.
"Viridian? What is the meaning of this?"
Think! "We . . ." Was there any excuse for this? Would President Indathrone recognize Xaz? Even if he didn't, how could Hansa explain even his own presence in the president's private wing of the Quin compound?
Instead of coming up with something clever to say, he couldn't help calculating how many guards would come running the instant His Eminence opened his mouth to summon them. How many guards would, based on what Hansa had seen when they had gone to arrest Xaz, be slaughtered as Alizarin moved to protect their group.
Or, if it was true that the Quinacridone Compound was protected from the Abyss and the Numen by its own human spells, how many guards would appear to execute everyone in their party on sight.
"Hansa?" Indathrone prompted, voice colder this time, warning that it wouldn't be long before he lost patience.
He skimmed their party, his eyes never fixing on Alizarin, reminding Hansa that on the mortal plane most humans couldn't see the Abyssi at all.
Terre Verte took charge, stepping past Hansa. "Winsor Indathrone, you are the very image of your grandmother."
"My . . ." Indathrone frowned with confusion. "Who are you?"
Terre Verte extended a hand. "How rude of me not to introduce myself." Indathrone offered his own hand, as one tends to do out of habit when offered such an engrained sign of courtesy. "I am Terre Verte. And I believe you have overstayed your welcome."
The next movement was swift. Terre Verte accepted the hand Indathrone had lifted, but used it only to tug him forward before he reached up, bracing his Eminence's body with his own, and matter-of-factly broke the neck of the most powerful man in Kavet with a single, undramatic crunch.
"We invited that family to supper. Not to move in."
Terre Verte released him, and Indathrone's body collapsed unremarkably to the ground. Hansa stared at it, waiting for it to . . . what? Echo? The death of such a man should resonate. It should shriek in a way that made bones quiver, like when Abyssi fought. His fallen form should flicker with escaping force.
But he was only a man, and his body was only meat, so he lay there unmoving.
Terre Verte turned around, brushing dust from his elegant clothing. "Now I think I'd like to walk about my city. It has been a long time."
EPILOGUE
"I thought you said you could control your children," the black Abyssi accused, his voice an angry purr. " 'All things serve the divine,' or so you say."
"Mortals are . . . limited," the Numini conceded. "They have unanticipated qualms, and choose to rebel at unpredictable moments."
"Thousands of years of life," the black Abyssi spat, "and that is your belief? Mortals are unpredictable? A newborn Abyssi could tell you that a mortal will choose survival first. Faced with death, they always run."
"Not always," the Numini minced. "Though I suppose that is a newborn Abyssi's perspective, given it is your own. Your kind sees a few centuries at most before you are destroyed by your own folly. I have seen millennia."
"You and your endless years got my mancer killed."
"You were supposed to deal with the blue Abyssi before he reached the pit."
"Antioch wasn't equal to the task."
"And the king of the Abyss couldn't send another?" the Numini scoffed. "Don't you have any power over your subjects?"
The black Abyssi did not rise to the challenge. "Abyssi do not jump to follow commands the way Numini do, especially when those commands may make an Abyssi dead. I have no wish to be sacrificed in the crystal caves just yet."
"They have all returned to the mortal realm now," the Numini said. "Let us wait and see what they do next. They may yet serve. If not, we both have other tools. If the worst comes to pass, these can be . . . discarded."
ABOUT THE AUTHOR
AMELIA ATWATER-RHODES started writing when she was thirteen, and has since then published seventeen young adult novels in the Den of Shadows, Kiesha'ra and Maeve'ra series. Several of her novels have been ALA Quick Picks for Young Adults, and Hawksong was The School Library Journal Best Book of the Year, and Voice of Youth Advocates Best Science Fiction, Fantasy, and Horror Selection. In 2006, Amelia decided to take a break from YA and started writing the Mancer trilogy as part of National Novel Writing Month. Of the Abyss is her first adult novel.
Discover great authors, exclusive offers, and more at hc.com.
Young Adult Novels by Amelia Atwater-Rhodes
Den of Shadows
In the Forests of the Night
Demon in My View
Shattered Mirror
Midnight Predator
Persistence of Memory
Token of Darkness
All Just Glass
Poison Tree
Promises to Keep
The Kiesha'ra
Hawksong
Snakecharm
Falcondance
Wolfcry
Wyvernhail
The Maeve'ra
Bloodwitch
Bloodkin
Bloodtraitor
COPYRIGHT
This is a work of fiction. Names, characters, places, and incidents are products of the author's imagination or are used fictitiously and are not to be construed as real. Any resemblance to actual events, locales, organizations, or persons, living or dead, is entirely coincidental.
OF THE ABYSS. Copyright © 2016 by Amelia Atwater-Rhodes. All rights reserved under International and Pan-American Copyright Conventions. By payment of the required fees, you have been granted the nonexclusive, nontransferable right to access and read the text of this e-book on screen. 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 hereafter invented, without the express written permission of HarperCollins e-books. For information, address HarperCollins Publishers, 195 Broadway, New York, NY 10007.
EPub Edition SEPTEMBER 2016 ISBN: 9780062562135
Print Edition ISBN: 9780062562142
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About the Publisher
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1. Dedication
2. Contents
3. Prologue
4. Part 1
5. Chapter 1
6. Chapter 2
7. Chapter 3
8. Chapter 4
9. Chapter 5
10. Chapter 6
11. Chapter 7
12. Chapter 8
13. Chapter 9
14. Chapter 10
15. Chapter 11
16. Chapter 12
17. Chapter 13
18. Chapter 14
19. Chapter 15
20. Chapter 16
21. Chapter 17
22. Chapter 18
23. Chapter 19
24. Chapter 20
25. Chapter 21
26. Chapter 22
27. Part 2
28. ["This is not what you . . ."]
29. Chapter 23
30. Chapter 24
31. Chapter 25
32. Chapter 26
33. Chapter 27
34. Chapter 28
35. Chapter 29
36. Chapter 30
37. Chapter 31
38. Chapter 32
39. Chapter 33
40. Chapter 34
41. Chapter 35
42. Chapter 36
43. Chapter 37
44. Chapter 38
45. Chapter 39
46. Chapter 40
47. Chapter 41
48. Epilogue
49. About the Author
50. Young Adult Novels by Amelia Atwater-Rhodes
51. Copyright
52. About the Publisher
1. Cover
2. Contents
3. Startup Page
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Hollis Thompson (Pasadena, 3 de abril de 1991) é um jogador norte-americano de basquete profissional que atualmente joga pelo Olympiacos BC, disputando a Euroliga.
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{"url":"https:\/\/encyclopediaofmath.org\/wiki\/L%C3%A9vy_metric","text":"# L\u00e9vy metric\n\n2010 Mathematics Subject Classification: Primary: 60E05 [MSN][ZBL]\n\nA metric $L$ in the space ${\\mathcal F}$ of distribution functions (cf. Distribution function) of one-dimensional random variables such that:\n\n$$L \\equiv L ( F , G ) =$$\n\n$$= \\ \\inf \\{ \\epsilon : {F ( x - \\epsilon ) - \\epsilon \\leq G ( x) \\leq F ( x + \\epsilon ) + \\epsilon \\textrm{ for all } x } \\}$$\n\nfor any $F , G \\in {\\mathcal F}$. It was introduced by P. L\u00e9vy (see [Le]). If between the graphs of $F$ and $G$ one inscribes squares with sides parallel to the coordinate axes (at points of discontinuity of a graph vertical segments are added), then a side of the largest of them is equal to $L$.\n\nThe L\u00e9vy metric can be regarded as a special case of the L\u00e9vy\u2013Prokhorov metric. The definition of the L\u00e9vy metric carries over to the set $M$ of all non-decreasing functions on $\\mathbf R ^ {1}$( infinite values of the metric being allowed).\n\n## Most important properties of the L\u00e9vy metric.\n\n1) The L\u00e9vy metric induces a weak topology in ${\\mathcal F}$( cf. Distributions, convergence of). The metric space ( ${\\mathcal F} , L$) is separable and complete. Convergence of a sequence of functions from $M$ in the metric $L$ is equivalent to complete convergence.\n\n2) If $F \\in M$ and if\n\n$$F _ {-} 1 ( x) = \\inf \\{ {t } : {F ( t) < x } \\} ,$$\n\nthen for any $F , G \\in M$,\n\n$$L ( F , G ) = L ( F _ {-} 1 , G _ {-} 1 ) .$$\n\n3) Regularity of the L\u00e9vy metric: For any $F , G , H \\in {\\mathcal F}$,\n\n$$L ( F \\star H , G \\star H ) \\leq L ( F , G )$$\n\n(here $\\star$ denotes convolution, cf. Convolution of functions). A consequence of this property is the property of semi-additivity:\n\n$$L ( F _ {1} \\star F _ {2} , G _ {1} \\star G _ {2} ) \\leq L ( F _ {1} ,\\ G _ {1} ) + L ( F _ {2} , G _ {2} )$$\n\nand the \"smoothing inequality\"\u00a0:\n\n$$L ( F , G ) \\leq L ( F \\star H , G \\times H ) + 2L ( E , H )$$\n\n( $E$ being a distribution that is degenerate at zero).\n\n4) If $\\alpha _ {k} \\geq 0$, $F _ {k} , G _ {k} \\in {\\mathcal F}$, then\n\n$$L \\left ( \\sum \\alpha _ {k} F _ {k} , \\sum \\alpha _ {k} G _ {k} \\right ) \\leq \\ \\max \\left ( 1 , \\sum \\alpha _ {k} \\right ) \\max L ( F _ {k} , G _ {k} ) .$$\n\n5) If $\\beta _ {r} ( F )$, $r > 0$, is an absolute moment of the distribution $F$, then\n\n$$L ( F , E ) \\leq \\{ \\beta _ {r} ( F ) \\} ^ {r \/ ( r+ 1 ) } .$$\n\n6) The L\u00e9vy metric on $M$ is related to the integral mean metric\n\n$$\\rho _ {1} = \\rho _ {1} ( F , G ) = \\int\\limits | F ( x) - G ( x) | dx$$\n\nby the inequality\n\n$$L ^ {2} \\leq \\rho _ {1} .$$\n\n7) The L\u00e9vy metric on $M$ is related to the uniform metric\n\n$$\\rho = \\rho ( F , G ) = \\sup _ { x } | F ( x) - G ( x) |$$\n\nby the relations\n\n$$\\tag{* } L \\leq \\rho \\leq L + \\min \\{ Q _ {F} ( L) , Q _ {G} ( L) \\} ,$$\n\nwhere\n\n$$Q _ {F} ( x) = \\sup _ { t } | F ( t+ x ) - F ( t) |$$\n\n( $Q _ {F} ( x)$ is the concentration function for $F \\in {\\mathcal F}$). In particular, if one of the functions, for example $G$, has a uniformly bounded derivative, then\n\n$$\\rho \\leq \\left ( 1 + \\sup _ { x } G ^ \\prime ( x) \\right ) L .$$\n\nA consequence of (*) is the P\u00f3lya\u2013Glivenko theorem on the equivalence of weak and uniform convergence in the case when the limit distribution is continuous.\n\n8) If $F _ {a , \\sigma } ( x) = F ( \\sigma x + a )$, where $a$ and $\\sigma > 0$ are constants, then for any $F , G \\in {\\mathcal F}$,\n\n$$L ( \\sigma F , \\sigma G ) \\leq \\sigma L ( F _ {a , \\sigma } , G _ {a , \\sigma } )$$\n\n(in particular, the L\u00e9vy metric is invariant with respect to a shift of the distributions) and\n\n$$\\lim\\limits _ {\\sigma \\rightarrow 0 } L ( F _ {a , \\sigma } , G _ {a , \\sigma } ) = \\rho ( F , G ) .$$\n\n9) If $f$ and $g$ are the characteristic functions (cf. Characteristic function) corresponding to the distributions $F$ and $G$, then for any $T > e$,\n\n$$L ( F , G ) \\leq \\frac{1} \\pi \\int\\limits _ { 0 } ^ { T } | f ( t) - g ( t) | \\frac{dt}{t} + 2e \\frac{ \\mathop{\\rm ln} T }{T} .$$\n\nThe concept of the L\u00e9vy metric can be extended to the case of distributions in $\\mathbf R ^ {n}$.\n\n#### References\n\n [Le] P. L\u00e9vy, \"Th\u00e9orie de l'addition des variables al\u00e9atoires\" , Gauthier-Villars (1937) [Z] V.M. Zolotarev, \"Estimates of the difference between distributions in the L\u00e9vy metric\" Proc. Steklov Inst. Math. , 112 (1973) pp. 232\u2013240 Trudy Mat. Inst. Steklov. , 112 (1971) pp. 224\u2013231 [ZS] V.M. Zolotarev, V.V. Senatov, \"Two-sided estimates of L\u00e9vy's metric\" Theor. Probab. Appl. , 20 (1975) pp. 234\u2013245 Teor. Veroyatnost. i Primenen. , 20\u00a0: 2 (1975) pp. 239\u2013250 [LO] Yu.V. Linnik, I.V. Ostrovskii, \"Decomposition of random variables and vectors\" , Amer. Math. Soc. (1977) (Translated from Russian) MR0428382 Zbl 0358.60020\n\nLet $F$ be a distribution function or, more generally, a non-decreasing left-continuous function. Then $F$ has a countable set of discontinuity points. The complement of this set is called the continuity set $C ( F )$ of $F$. A series of distribution functions $F _ {n}$ is said to converge weakly to a distribution $F$ if this is the case on the continuity set $C ( F )$ of $F$. The series converges completely if moreover $F _ {n} ( + \\infty ) \\rightarrow F ( \\infty )$ and $F _ {n} ( - \\infty ) \\rightarrow F ( - \\infty )$. Cf. also Convergence of distributions and Convergence, types of.","date":"2020-11-24 03:40:18","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\": 0.9471120834350586, \"perplexity\": 401.1620631209997}, \"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\/1606141171077.4\/warc\/CC-MAIN-20201124025131-20201124055131-00365.warc.gz\"}"} | null | null |
Deposition Author(s): Adolph, R.S., Kleinboelting, S., Weyand, M., Steegborn, C.
Banerjee, A., Adolph, R.S., Gopalakrishnapai, J., Kleinboelting, S., Emmerich, C., Steegborn, C., Visweswariah, S.S.
Mycobacteria are endowed with rich and diverse machinery for the synthesis, utilization, and degradation of cAMP. The actions of cyclic nucleotides are generally mediated by binding of cAMP to conserved and well characterized cyclic nucleotide binding domains or structurally distinct cGMP-specific and -regulated cyclic nucleotide phosphodiesterase, adenylyl cyclase, and E. coli transcription factor FhlA (GAF) domain-containing proteins. Proteins with cyclic nucleotide binding and GAF domains can be identified in the genome of mycobacterial species, and some of them have been characterized. Here, we show that a significant fraction of intracellular cAMP is bound to protein in mycobacterial species, and by using affinity chromatography techniques, we identify specific universal stress proteins (USP) as abundantly expressed cAMP-binding proteins in slow growing as well as fast growing mycobacteria. We have characterized the biochemical and thermodynamic parameters for binding of cAMP, and we show that these USPs bind cAMP with a higher affinity than ATP, an established ligand for other USPs. We determined the structure of the USP MSMEG_3811 bound to cAMP, and we confirmed through structure-guided mutagenesis, the residues important for cAMP binding. This family of USPs is conserved in all mycobacteria, and we suggest that they serve as "sinks" for cAMP, making this second messenger available for downstream effectors as and when ATP levels are altered in the cell.
From the Department of Molecular Reproduction, Development and Genetics, Indian Institute of Science, Bangalore 560012, India and. | {
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Q: Editor for FormatJS messages We are using FormatJS and React Intl for a web application of ours, to translate the UI. What we are currently missing is an editor for the messages files.
Does anybody know of a any decent editor for message files? Editing the bare JSON resources is not really an ideal option when dealing with large files.
Thanks,
Gerald
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{"url":"https:\/\/math.stackexchange.com\/questions\/1559467\/g-cyclic-group-of-order-24-and-h-langle-x6-rangle-find-the-order-of-ea","text":"# $G$ cyclic group of order $24$, and $H=\\langle x^6\\rangle$, find the order of each element of $G\/H$\n\nAs the title says I have: $G$ cyclic group of order 24, and $H= \\langle x^6 \\rangle$ , we also know that $x$ is a generator of $G$ so, $\\langle x \\rangle = G$\n\ni have to find the order of each element of the quotient group $G\/H$\n\nand say how many generators have $G\/H$\n\n\u2022 I'm the \\langle \\rangle fairy, here to let you know that $\\langle, \\rangle$ plays nicer with TeX than <, > does :) \u2013\u00a0Patrick Stevens Dec 4 '15 at 8:12\n\u2022 Is $H$ generated by $x^6$ for some particular $x$ you forgot to define or $H$ is generated by all elements of $G$ that are of the form $x^6$? \u2013\u00a0Cl\u00e9ment Gu\u00e9rin Dec 4 '15 at 8:13\n\u2022 I think she forgot to mention that $x$ is a generator of $G.$ \u2013\u00a0Justpassingby Dec 4 '15 at 8:13\n\u2022 i think that $G=\\{e,x,x^2,x^3,...,x^6,...,x^(23) \\}$ since $G$ is a cyclic group. \u2013\u00a0Zigisfredo Dec 4 '15 at 8:15\n\u2022 @Zigisfredo it's not automatic, you need to mention that. If $x$ is an arbitrary element of $G$ then its order could be less than $24.$ \u2013\u00a0Justpassingby Dec 4 '15 at 8:17\n\nThe order of $H$ is the order of its generator $x^6,$ i.e., 4. Therefore the order of $G\/H$ is 6: there are 6 different cosets of the form $x^iH.$\n\nWe can choose the first powers of $x$ as representatives of these cosets:\n\n$$G\/H=\\left\\{H,xH,x^2H,x^3H,x^4H,x^5H\\right\\}$$\n\nThe order of an individual coset $x^iH$ is the smallest nonzero natural number $n$ such that $i.n$ is a multiple of 6.\n\nNow at least one of the elements of $G\/H$ turns out to have its order equal to the order of $G\/H$ itself, implying that $G\/H$ is cyclic.\n\nA cyclic group is generated by an individual element $g$ iff the order of that element is the order of the group.\n\n\u2022 i think that i found the order of $H$, since $H=\\langle x^6 \\rangle=\\{e,x^6,x^12,x^18\\}$ so the order of $H=4$ therefore the order of $G\/H$ is 4. But after that i'm confused about how to get for each element the order. \u2013\u00a0Zigisfredo Dec 4 '15 at 8:24\n\u2022 No, the order of $G\/H$ is determined by Lagrange's theorem and it's different from 4. \u2013\u00a0Justpassingby Dec 4 '15 at 8:25\n\u2022 oh, so i have, $o(G\/H)=o(G)\/o(H)=24\/4=6$. \u2013\u00a0Zigisfredo Dec 4 '15 at 8:28\n\u2022 Yep, you're on your way! Now propose representatives of the 6 cosets of $H.$ \u2013\u00a0Justpassingby Dec 4 '15 at 8:29\n\u2022 Should i take $x^p$ with $p$ a prime number so i could get the order easier? \u2013\u00a0Zigisfredo Dec 4 '15 at 8:41","date":"2021-01-24 13:55:11","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\": 0.8946313261985779, \"perplexity\": 183.48589016380342}, \"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-2021-04\/segments\/1610703548716.53\/warc\/CC-MAIN-20210124111006-20210124141006-00132.warc.gz\"}"} | null | null |
{"url":"https:\/\/questions.examside.com\/past-years\/jee\/question\/what-will-be-the-average-value-of-energy-for-a-monoatomic-ga-jee-main-physics-units-and-measurements-vfg9s3racyvcqrxm","text":"1\nJEE Main 2021 (Online) 22th July Evening Shift\n+4\n-1\nWhat will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T?\nA\n$${3 \\over 2}{k_B}T$$\nB\n$${k_B}T$$\nC\n$${2 \\over 3}{k_B}T$$\nD\n$${1 \\over 2}{k_B}T$$\n2\nJEE Main 2021 (Online) 20th July Evening Shift\n+4\n-1\nWhich of the following graphs represent the behavior of an ideal gas? Symbols have their usual meaning.\nA\nB\nC\nD\n3\nJEE Main 2021 (Online) 20th July Evening Shift\n+4\n-1\nThe correct relation between the degrees of freedom f and the ratio of specific heat $$\\gamma$$ is :\nA\n$$f = {2 \\over {\\gamma - 1}}$$\nB\n$$f = {2 \\over {\\gamma + 1}}$$\nC\n$$f = {{\\gamma + 1} \\over 2}$$\nD\n$$f = {1 \\over {\\gamma + 1}}$$\n4\nJEE Main 2021 (Online) 20th July Morning Shift\n+4\n-1\nConsider a mixture of gas molecule of types A, B and C having masses mA < mB < mC. The ratio of their root mean square speeds at normal temperature and pressure is :\nA\n$${v_A} = {v_B} \\ne {v_C}$$\nB\n$${1 \\over {{v_A}}} > {1 \\over {{v_B}}} > {1 \\over {{v_C}}}$$\nC\n$${1 \\over {{v_A}}} < {1 \\over {{v_B}}} < {1 \\over {{v_C}}}$$\nD\n$${v_A} = {v_B} = {v_C} = 0$$\nJEE Main Subjects\nPhysics\nMechanics\nElectricity\nOptics\nModern Physics\nChemistry\nPhysical Chemistry\nInorganic Chemistry\nOrganic Chemistry\nMathematics\nAlgebra\nTrigonometry\nCoordinate Geometry\nCalculus\nEXAM MAP\nJoint Entrance Examination","date":"2023-03-29 01:11:22","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7865833044052124, \"perplexity\": 3167.1372493086665}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-14\/segments\/1679296948900.50\/warc\/CC-MAIN-20230328232645-20230329022645-00675.warc.gz\"}"} | null | null |
Властимир Годић (Каменаре, код Крушевца, 1917 - Београд, 1976) био је лекар, учесник Народноослободилачке борбе, професор Медицинског факултета у Београду и носилац Партизанске споменице 1941.
Биографија
Рођен је 1917. године у селу Каменаре, код Крушевца. у осредње богатој сеоској породици која је одлучила да га школује. Уписао је гимназију у Крушевцу и по завршетку одлучује да, у предвечерје Другог светског рата, студира медицину у Београду. Средства која је добијао од своје породице за студирање нису му омогућавала нормалан живот, па је радио као радник у једној од београдских пиљарница, истовремено студирајући и радећи. Као радник и студент приближио се идејама левице и Комунистичкој партији Југославије где му је главни ментор био Мирко Томић. По почетку Другог светског рата прекинуо је студије и вратио се у свој родни крај.
На почетку устанка 1941. године одмах се укључио у партизански покрет где је био предводник десетина које су отпочеле борбе против окупатора и њихових помагача у Парцану и Залоговцу. Више пута током рата био је хапшен и ослобађан. У присуству делегације ПК КПЈ за Србију предвођене Недељком Караичићем Брком, у периоду од 14. до 18.08.1943.године код Шавранских колиба на Јастребцу реорганизован је штаб Расинског партизанског одреда, Властимир Годић - Миша изабран је за заменика команданта Драгослава Петровића Горског.
Властимир Годић је био први партизан који је 14. октобра 1944. године ушао у Крушевац и објавио ослобођење овог града од окупатора и домаћих издајника.
После рата постаје специјалиста физикалне медицине и рехабилитације, балнеолог, професор на Медицинском факултету у Београду. Дипломирао на Медицинском факултету у Београду, докторирао на истом Факултету 1963. године са дисертацијом "Промет минералних материјала код улкусних болесника лечења у Врњачкој Бањи". Прошао је сва академска звања до редовног професора Медицинског факултета у Београду. Био је управник Завода за рехабилитацију интерних болесника, који је по њему касније добио име - Завод за интерне болести "Др Властимир Годић". Такође, Дом здравља у Варварину носи његово име, Дом здравља "Др Властимир Годић". Аутор је више књига и уџбеника, великог броја радова, нарочито из балнеоклиматологије. Живео је у Београду. Сахрањен је у Алеји заслужних грађана на Новом гробљу у Београду.
Извори
Победа 1944
Дом здравља "Др Властимир Годић", Варварин
Крушевљани
Рођени 1917.
Умрли 1976.
Комунисти Србије
Југословенски партизани
Србија у Народноослободилачкој борби
Сахрањени у Алеји заслужних грађана на Новом гробљу у Београду
Српски лекари | {
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Home › Events Calendar › Virtual Event - Women's Speaker Series: Renée Rosen, author of The Social Graces
Virtual Event - Women's Speaker Series: Renée Rosen, author of The Social Graces
June 21, 2021 - 7:00pm
Margy Stratton, founder and executive producer of Milwaukee Reads produces this series of events featuring writers of particular interest to women.
Lynden Sculpture Garden's Women's Speaker Series and Boswell Books welcome Renée Rosen, author of The Social Graces, back to Milwaukee for a virtual, BYOS (bring-your-own-snack) event on Monday, June 21, 2021 at 7 pm.
Fee: Tickets are $5 plus sales tax and ticket fee or you can upgrade to admission-with book for $17. Books can be picked up at Boswell or for an additional fee, shipped out be USPS media mail. $5 from each ticket will be donated back to the Lynden Sculpture Garden.
Registration: Purchase tickets for the virtual event here.
For more information on upcoming Women's Speaker Series Events, click here.
About The Social Graces
The bestselling author of Park Avenue Summer throws back the curtain on one of the most remarkable feuds in history: Mrs. Vanderbilt and Mrs. Astor's notorious battle for control of New York society during the Gilded Age.
In the glittering world of Manhattan's upper crust, where wives turn a blind eye to husbands' infidelities, and women have few rights and even less independence, society is everything. The more celebrated the hostess, the more powerful the woman. And none is more powerful than Caroline Astor – the Mrs. Astor.
But times are changing. Alva Vanderbilt has recently married into one of America's richest families. But what good is money when society refuses to acknowledge you? Alva, who knows what it is to have nothing, will do whatever it takes to have everything. Sweeping three decades and based on true events, this is a gripping novel about two fascinating, complicated women going head to head, behaving badly, and discovering what's truly at stake.
Renée Rosen is the bestselling author of historical fiction. Her novels include Park Avenue Summer, Windy City Blues, White Collar Girl, What the Lady Wants and Dollface, as well as the young adult novel, Every Crooked Pot. Her new novel, The Social Graces, a story about Mrs. Astor and Mrs. Vanderbilt vying for control of New York society during the Gilded Age, will be out April 20, 2021 from Penguin Random House/Berkley. Renee is a native of Akron, Ohio and a graduate of The American University in Washington DC. She now lives in Chicago where she is at work on a new novel. | {
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Q: IDEA PHP type annotation I am using IntelliJ IDEA to develop a PHP project. However, in some functions I get dynamically typed variables, i. e. I do not know beforehand what type they are, for instance when I loop through an array of objects, IDEA does not know what type the objects within have.
My question is: how can I, using comment annotations, tell IDEA which suggestions to show me for that object? That would be pretty handy, thanks in advance! I think it would be something like this:
/* @type: $object:MyClassName */
A: See PHPDoc support and phpdoc suggesting type for $this->someField.
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Hello, I'm from Germany a fan of Digimon since watching the German dub of Digimon Adventure for the first time in August 2000. I have mainly known Digimon through (the German dubs of) the anime before I learned about the other things (games, virtual pets, cards etc.) over the Internet, including Wikimon.
I made my first edit on Wikimon in November 2010 and was promoted to an admin in January 2012. I mainly edit the pages of Digimon species, adding images, headings, profiles and so on, and occasionally I also work on templates (at least I try to do so).
Another franchise I enjoy is the Kirby series. I'd be glad if you visit my Kirby fansite, Kirbytraum, mostly in German as of now.
This page was last modified on 20 September 2015, at 09:42. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,021 |
\section{Introduction}\label{S:I}
Let $G$ be a universal Chevalley-Demazure group scheme associated to a reduced irreducible root system $\Phi$ of rank $> 1$. Given a commutative ring $R$, we let $G(R)$ denote the group of $R$-points of $G$, and let $E(R) \subset G(R)$ be the corresponding elementary subgroup. (We recall that $E(R)$ is defined as the subgroup generated by the images $e_{\alpha} (R) =: U_{\alpha} (R)$ for all $\alpha \in \Phi$, where $e_{\alpha} \colon \mathbb{G}_a \to G$ is the canonical 1-parameter subgroup corresponding to a root $\alpha \in \Phi$ --- see \cite{Bo1} for details.) The goal of this note is to make a contribution to the analysis of the congruence subgroup problem for $E(R)$ over a general commutative noetherian ring $R$ (with some minor restrictions if $\Phi$ is of type $C_n$ $(n \geq 2)$ or $G_2$).
While the congruence subgroup problem for $S$-arithmetic groups is a well-established subject (see \cite{PR} for a recent survey), its analysis over general rings, at least from the point of view we adopt in this note, has been rather limited, despite a large number of results dealing with arbitrary normal subgroups of Chevalley groups over commutative rings. For this reason, we begin with a careful description of our set-up.
Let $R$ be a commutative ring and $n \geq 1.$ Then to every ideal $\mathfrak{a} \subset R$, one associates the congruence subgroup $GL_n (R, \mathfrak{a}) = \ker (GL_n (R) \to GL_n (R/ \mathfrak{a}))$, where the map is the one induced by the canonical homomorphism $R \to R/ \mathfrak{a}$. Clearly, if $\mathfrak{a}$ is of {\it finite index} (i.e. the quotient $R/ \mathfrak{a}$ is a finite ring), then $GL_n (R, \mathfrak{a})$ is a normal subgroup of $GL_n (R)$ of {\it finite index}. Given a subgroup $\Gamma \subset GL_n (R),$ we set $\Gamma (\mathfrak{a}) = \Gamma \cap GL_n (R, \mathfrak{a}).$ Then, by the congruence subgroup problem for $\Gamma$, we understand the following question:
\vskip3mm
(CSP) \hskip2mm \parbox{14.9cm}{Does every normal subgroup $\Delta \subset \Gamma$ of {\it finite index} contain the congruence subgroup $\Gamma (\mathfrak{a})$ for some ideal $\mathfrak{a} \subset R$ of {\it finite index}?}
\vskip3mm
\noindent The affirmative answer would give us information about the profinite completion $\widehat{\Gamma}$, which is precisely what is needed for the analysis of representations of $\Gamma$, as well as other issues (cf. \cite{BMS}, \cite{KN}, \cite{Sh}). However, even when $\Gamma$ is $S$-arithmetic, the answer to (CSP) is often negative. So one is instead interested in the computation of the congruence kernel, which measures the deviation from a~positive solution. For this, just as in the arithmetic case, we introduce two topologies on $\Gamma$: the profinite topology $\tau_p^{\Gamma}$ and the congruence topology $\tau_c^{\Gamma}.$ The fundamental system of neighborhoods of the identity for the former consists of all normal subgroups $N \subset \Gamma$ of finite index, and for the latter of the congruence subgroups $\Gamma (\mathfrak{a}),$ where $\mathfrak{a}$ runs through all ideals of $R$ of finite index. The corresponding completions are then given by
$$
\widehat{\Gamma} = \lim_{\longleftarrow} \Gamma / N, \ \ \ \text{where} \ N \lhd \Gamma \ \text{and} \ [\Gamma :N ] < \infty
$$
and
$$
\overline{\Gamma} = \lim_{\longleftarrow} \Gamma / \Gamma (\mathfrak{a}), \ \ \ \text{where} \ \vert R/ \mathfrak{a} \vert < \infty.
$$
As $\tau_p^{\Gamma}$ is stronger than $\tau_c^{\Gamma}$, there exists a continuous surjective homomorphism $\pi^{\Gamma} \colon \widehat{\Gamma} \to \overline{\Gamma},$ whose kernel is called the {\it congruence kernel} and denoted $C(\Gamma).$ Clearly, $C(\Gamma)$ is trivial if and only if the answer to (CSP) is affirmative; in general, its size measures the extent of deviation from the affirmative answer. Unfortunately, as remarked above, in many situations, $C(\Gamma)$ is nontrivial, and the focus of this note is on a different property, viz. the {\it centrality} of $C(\Gamma)$ (which means that $C(\Gamma)$ is contained in the center of $\widehat{\Gamma}$). We note that in some cases, centrality is almost as good as triviality (cf. \cite{KN}, \cite{Sh}), and in arithmetic cases actually implies the finiteness of $C (\Gamma).$
Returning to Chevalley groups, we observe that congruence subgroups $G(R, \mathfrak{a}) \subset G(R)$ can be defined either as pullbacks of the congruence subgroups $GL_n (R, \mathfrak{a})$ under a faithful representation of group schemes $G \hookrightarrow GL_n$ over $\Z$, or, intrinsically, as the kernel of the natural homomorphism $G(R) \to G(R/\mathfrak{a}).$
Our main result concerns the congruence kernel of the elementary group $\Gamma = E(R).$ We note that the congruence topology on $\Gamma$ is induced by that on $G(R)$, i.e. is defined by the intersections $\Gamma \cap G(R, \mathfrak{a})$, where $\mathfrak{a}$ runs over all ideals $\mathfrak{a} \subset R$ of finite index. On the other hand, the profinite topology on $\Gamma$ may {\it a priori} be different from the topology induced by the profinite topology of $G(R)$ (cf. the remarks at the end of \S 4).
\vskip2mm
\noindent {\bf Main Theorem.} {\it Let $G$ be a universal Chevalley-Demazure group scheme corresponding to a reduced irreducible root system $\Phi$ of rank $>1.$ Furthermore, let $R$ be a noetherian commutative ring such that $2 \in R^{\times}$ if $\Phi$ is of type $C_n$ ($n \geq 2$) or $G_2$, and let $\Gamma = E(R)$ be the corresponding elementary subgroup. Then the congruence kernel $C(\Gamma)$ is central.}
\vskip2mm
The centrality of the congruence kernel for $SL_n$ ($n \geq 3$) and $Sp_{2n}$ ($n \geq 2$) over rings of algebraic integers was proved by Bass, Milnor, and Serre \cite{BMS}. Their result was generalized to arbitrary Chevalley groups of rank $> 1$ over rings of algebraic integers by Matsumoto \cite{M1}. The only known result for general rings is due to Kassabov and Nikolov \cite{KN}, where centrality was established for $SL_n (\Z [x_1, \dots, x_k])$, with $n \geq 3$, and hence for the elementary group $E_n (R)$ over any finitely generated ring $R$, using $K$-theoretic methods. Although our proof shares some elements with the argument in \cite{KN}, it is purely group-theoretic and is inspired by the proof of centrality for $SL_n$ ($n \geq 3$) over arithmetic rings given in \cite{AR}; in addition, we do not use any results of Matsumoto \cite{M1}.
\vskip2mm
\noindent {\bf Conventions and notations.} All of our rings will be assumed to be commutative and unital. Unless explicitly stated otherwise, $G$ will always denote a universal Chevalley-Demazure group scheme corresponding to a reduced irreducible root system $\Phi$ of rank $> 1$. Furthermore, if $R$ is a commutative ring, then for a subgroup $\Gamma \subset G(R)$, we let $\widehat{\Gamma}$ and $\overline{\Gamma}$ denote the profinite and congruence completions of $\Gamma$, respectively.
\section{Structure of $\overline{G(R)}$}
Let $\mathcal{I}$ be the set of all ideals $\mathfrak{a} \subset R$ of finite index, and let $\mathcal{M} \subset \mathcal{I}$ be the subset of maximal ideals. It is not difficult to see (cf. the proof of Proposition \ref{P-2}) that $\overline{G(R)}$ can be identified with the closure of the image of $G(R)$ in $G(\widehat{R})$, where
$$
\widehat{R} = {\lim_{\longleftarrow}}_{\mathfrak{a} \in \I} R/ \mathfrak{a}
$$
is the profinite completion of $R$. The proof of the Main Theorem relies on the fact that $G(\widehat{R})$ has the bounded generation property with respect to the set $\widehat{S} = \{ e_{\alpha} (t) \mid t \in \widehat{R}, \ \alpha \in \Phi \}$ of elementaries, which we will establish at the end of this section (cf. Corollary \ref{C-1}). We begin, however, by describing the structure of $\widehat{R}$ itself. For each $\mathfrak{m} \in \M$, we let $$R_{\mathfrak{m}} = \lim_{\longleftarrow} R/ \mathfrak{m}^n$$ denote the $\m$-adic completion of $R$ (cf. \cite{At}, Chapter 10).
\begin{lemma}\label{L-1}
Let $R$ be a noetherian ring.
\vskip1mm
\noindent {\rm (1)} \parbox[t]{15cm}{There exists a natural isomorphism of topological rings
$$
\widehat{R} = \prod_{\m \in \M} R_{\m}.
$$}
\vskip1mm
\noindent {\rm (2)} \parbox[t]{15cm}{Each $R_{\m}$ is a complete local ring.}
\end{lemma}
\begin{proof}
(1) Since $R$ is noetherian, for any $\mathfrak{a} \in \I$ and any $n \geq 2$, the quotient $\mathfrak{a}^{n-1}/ \mathfrak{a}^n$ is a finitely generated $R/ \mathfrak{a}$-module, hence finite. It follows that $R/ \mathfrak{a}^n$ is finite for any $n \geq 1.$ In particular, for any $\m \in \M$ and $n \geq 1,$ there exists a natural continuous surjective projection
$$
\rho_{\m, n} \colon \widehat{R} \to R/ \m^n.
$$
For a fixed $\m$, the inverse limit of the $\rho_{\m, n}$ over all $n \geq 1$ yields a continuous ring homomorphism $\rho_{\m} \colon \widehat{R} \to R_{\m}.$ Taking the direct product of the $\rho_{\m}$ over all $\m \in \M,$ we obtain a continuous ring homomorphism
$$
\rho \colon \widehat{R} \to \prod_{\m \in \M} R_{\m} =: \overline{R}.
$$
We claim that $\rho$ is the required isomorphism.
Note that ideals of the form
$$
\overline{\ba} = \m_1^{\alpha_1} R_{\m_1} \times \cdots \times \m_n^{\alpha_n} R_{\m_n} \times \prod_{\m \neq \m_i} R_{\m},
$$
where $\{ \m_1, \dots, \m_n \} \subset \M$ is a finite subset and $\alpha_i \geq 1,$ form a base of neighborhoods of zero in $\overline{R}$, with
$$
\overline{R}/ \overline{\ba} = R / \m_1^{\alpha_1} \times \cdots \times R/ \m_{n}^{\alpha_n}
$$
(cf. \cite{At}, Proposition 10.15). Set $\ba = \m_1^{\alpha_1} \cdots \m_n^{\alpha_n}.$ By the Chinese Remainder Theorem,
$$
R / \ba \simeq R/ \m_1^{\alpha_1} \times \cdots \times R/ \m_n^{\alpha_n},
$$
which implies that the composite map
$$
\widehat{R} \to \overline{R} \to \overline{R}/ \overline{\ba}
$$
is surjective. Since this is true for all $\overline{\ba},$ we conclude that the image of $\rho$ is dense. On the other hand, $\widehat{R}$ is compact, so the image is closed, and we obtain that $\rho$ is in fact surjective.
To prove the injectivity of $\rho$, we observe that for any $\ba \in \I$, the quotient $R/ \ba$, being a finite, hence artinian ring, is a product of finite local ring $R_1, \dots, R_r$ (\cite{At}, Theorem 8.7). Furthermore, for each maximal ideal $\n_i \subset R_i$, there exists $\beta_i \geq 1$ such that $\n_i^{\beta_i} = 0$ (cf. \cite{At}, Proposition 8.4). Letting $\m_i$ denote the pullback of $\n_i$ in $R$, we obtain that $\ba$ contains $\mathfrak{b} := \m_1^{\beta_1} \cdots \m_r^{\beta_r} \in \I.$ It follows that any nonzero $x \in \widehat{R}$ will have a nonzero projection to some $R/ \mathfrak{b} = R/ \m_1^{\beta_1} \times \cdots \times R/ \m_r^{\beta_r}$, and hence to some $R_{\m_i}$, as required.
\vskip1mm
\noindent (2) It is well-known that $R_{\m}$ is both complete and local (cf. \cite{At}, Propositions 10.5 and 10.16).
\end{proof}
As a first step towards establishing bounded generation of $G(\widehat{R})$ with respect to the set of elementaries, we prove
\begin{prop}\label{P-1}
There exists an integer $N = N(\Phi)$, depending only on the root system $\Phi$, such that for any commutative local ring $\cR$, any element of $G(\cR)$ is a product of $\leq N$ elements of $S = \{ e_{\alpha} (r) \mid r \in \cR, \ \alpha \in \Phi \}.$
\end{prop}
\begin{proof}
Fix a system of simple roots $\Pi \subset \Phi,$ and let $\Phi^+$ and $\Phi^-$ be the corresponding sets of positive and negative roots. Let $T \subset G$ be the canonical maximal torus, and $U^+$ and $U^-$ be the canonical unipotent $\Z$-subschemes corresponding to $\Phi^+$ and $\Phi^-.$ It is well-known (see, for example, \cite{Bo1}, Lemma 4.5) that the product map $\mu \colon U^- \times T \times U^+ \to G$ is an isomorphism onto a principal open subscheme $\Omega \subset G$ defined by some $d \in \Z[G].$ We have decompositions
$$
U^{\pm} = \prod_{\alpha \in \Phi^{\pm}} U_{\alpha} \ \ \ \text{and} \ \ \ T = \prod_{\alpha \in \Pi} T_{\alpha},
$$
where $T_{\alpha}$ is the maximal diagonal torus in $G_{\alpha} = <U_{\alpha}, U_{-\alpha}> = SL_2.$ So, the identity
$$
\left( \begin{array}{cl} a & 0 \\ 0 & a^{-1} \end{array} \right) = \left( \begin{array}{lr} 1 & -1 \\ 0 & 1 \end{array} \right) \left( \begin{array}{cc} 1 & 0 \\ 1-a & 1 \end{array} \right) \left( \begin{array}{ll} 1 & a^{-1} \\ 0 & 1 \end{array} \right) \left( \begin{array}{cc} 1 & 0 \\ a(a-1) & 1 \end{array} \right)
$$
shows that there exists $N_1 = N_1 (\Phi)$ such that any element of $\Omega (R)$ is a product of $\leq N_1$ elementaries, for {\it any} ring $\cR.$
On the other hand, it follows from the existence of the Bruhat decomposition in Chevalley groups over fields that there exists $N_2 = N_2 (\Phi)$ such that any element of $G(k)$ is a product of $\leq N_2$ elementaries, for any field $k.$ We will now show that $N:= N_1 + N_2$ has the required property for any local ring $\cR.$ Indeed, let $\m \subset \cR$ be the maximal ideal, and $k = \cR/ \m$ be the residue field. As $G(k)$ is generated by elementaries, the canonical homomorphism $\omega \colon G(\cR) \to G(k)$ is surjective. Given $g \in G(\cR)$, there exists $h \in G(\cR)$ that is a product of $\leq N_2$ elementaries and for which we have $\omega (g) = \omega (h).$ Then, for $t = gh^{-1}$, we have $\omega (t) = 1$ (in particular, $\omega (t) \in \Omega (k)$), and therefore $d(t) \not\equiv 0 (\text{mod} \ \m)$. Since $\cR$ is local, this means that $d(t) \in \cR^{\times}$, and therefore $t \in \Omega (\cR)$. Thus, $t$ is a product of $\leq N_1$ elementaries, and the required fact follows.
\end{proof}
Next, we have the following
\begin{lemma}\label{L-2}
Let $\cR_i$ ($i \in I$) be a family of commutative rings such that there exists an integer $N$ with the property that for any $i \in I,$ any $x_i \in G(\cR_i)$ is a product of $\leq N$ elementaries. Set $\cR = \prod_{i \in I} \cR_i.$ Then any $x \in G(\cR)$ is a product of $\leq N \cdot \vert \Phi \vert$ elementaries.
\end{lemma}
\begin{proof}
It is enough to observe that any element of the form
$$
(e_{\alpha_i} (r_i)) \in G(\cR) = \prod_{i \in I} G(\cR_i),
$$
with $\alpha_i \in \Phi,$ $r_i \in \cR_i$, can be written as
$$
\prod_{\alpha \in \Phi} e_{\alpha} (t_{\alpha})
$$
for some $t_{\alpha} \in \cR.$
\end{proof}
Using this result, together with Lemma \ref{L-1} and Proposition \ref{P-1}, we obtain
\begin{cor}\label{C-1}
Let $R$ be a noetherian ring. Then there exists an integer $M > 0$ such that any element of $G(\widehat{R})$ is a product of $\leq M$ elementaries from the set $\widehat{S} = \{e_{\alpha} (t) \mid t \in \widehat{R}, \alpha \in \Phi \}.$
\end{cor}
As we noted earlier, one can identify the congruence completion $\overline{G(R)}$ with the closure of the image of $G(R)$ in $G(\widehat{R})$. The following proposition gives more precise information.
\begin{prop}\label{P-2}
Let $R$ be a noetherian ring. Then $\overline{E(R)} = \overline{G(R)}$ can be naturally identified with $G(\widehat{R})$. Furthermore, there exists an integer $M > 0$ such that any element of $\overline{E(R)} = \overline{G(R)}$ is a product of $\leq M$ elements of the set $\overline{S} := \overline{ \{ e_{\alpha} (r) \mid \alpha \in \Phi, r \in R \} } $ (closure in the congruence topology).
\end{prop}
\begin{proof}
For any $\mathfrak{a} \in \I$, there exists a natural injective homomorphism $\omega_{\mathfrak{a}} \colon G(R) / G(R, \mathfrak{a}) \to G(R/ \mathfrak{a}),$ where as before, $G(R, \mathfrak{a})$ is the principal congruence subgroup of level $\mathfrak{a}.$ Taking the inverse limit over all $\mathfrak{a} \in \I,$ we obtain a continuous injective homomorphism
$$
\omega \colon \overline{G(R)} \to G(\widehat{R}).
$$
Clearly, the image of $\omega$ coincides with the closure of the image of the natural homomorphism $G(R) \to G(\widehat{R})$.
From the definitions, one easily sees that if $\overline{e_{\alpha} (r)}$ is the image of $e_{\alpha} (r)$ ($\alpha \in \Phi, r \in R$) in $\overline{G(R)}$, then
$$
\omega (\overline{e_{\alpha} (r)}) = e_{\alpha} (\hat{r}),
$$
where $\hat{r}$ is the image of $r$ in $\widehat{R}.$ It follows that $\omega$ maps $\overline{S}$ onto $\widehat{S} = \{ e_{\alpha} (t) \mid \alpha \in \Phi, \ t \in \widehat{R} \}.$ Since by Corollary \ref{C-1}, $\widehat{S}$ generates $G(\widehat{R}),$ we obtain that $\omega (\overline{E(R)}) = G(\widehat{R})$, and consequently $\omega$ identifies $\overline{E(R)} = \overline{G(R)}$ with $G(\widehat{R})$. Furthermore, if $M$ is the same integer as in Corollary \ref{C-1}, then since every element of $G(\widehat{R})$ is a product of $\leq M$ elements of $\widehat{S}$, our second claim follows.
\end{proof}
\vskip1mm
\noindent {\bf Remark.} Recall that a group $\G$ is said to have {\it bounded generation} with respect to a generating set $X \subset \G$ if there exists an integer $N > 0$ such that every $g \in \G$ can be written as $g = x_1^{\varepsilon_1} \cdots x_d^{\varepsilon_d}$ with $x_i \in X$, $d \leq N$, and $\varepsilon_i = \pm 1.$ It follows from the Baire category theorem (cf. \cite{Mun}, Theorem 48.2) that if a compact topological group $\G$ is (algebraically) generated by a compact subset $X$, then in fact, $\G$ is automatically {\it boundedly} generated by $X$. Indeed, replacing $X$ by $X \cup X^{-1} \cup \{1 \},$ we may assume that $X = X^{-1}$ and $1 \in X.$ Set $X^{(n)} = X \cdots X$ ($n$-fold product). Then the fact that $\G = < X>$ means that
$$
\G = \bigcup_{n \geq 1} X^{(n)}.
$$
Since each $X^{(n)}$ is compact, hence closed, we conclude from Baire's theorem that for some $n \geq 1,$ $X^{(n)}$ contains an open set. Then $\G$ can be covered by finitely many translates of $X^{(n)}$, and therefore there exists $M > 0$ such that $X^{(M)} = \G$, as required. This remark shows, in particular, that (algebraic) generation of $\overline{G (R)}$ by $\overline{S}$, or that of $G(\widehat{R})$ by $\widehat{S},$ automatically yields bounded generation.
\vskip2mm
We would like to point out that the fact that $\overline{G(R)} = \overline{E(R)}$ is not used in the proof of the Main Theorem; all we need is that $\overline{E(R)}$ is boundedly generated by $\overline{S}.$ So, we will indicate another way to prove this based on some ideas of Tavgen (cf. \cite{Tav}, Lemma 1), which also gives an explicit bound on the constant $M$ in Proposition \ref{P-2}. First we observe that it is enough to establish the bounded generation of $E(\widehat{R})$ by $\widehat{S} = \{ e_{\alpha} (t) \mid \alpha \in \Phi, \ t \in \widehat{R} \}$ (indeed, this will show that $E(\widehat{R})$ is a continuous image of $\widehat{R}^N$ for some $N > 0$, hence compact, implying that the map $\omega$ from the proof of Proposition \ref{P-2} identifies $\overline{E(R)}$ with $E(\widehat{R})$, and also $\overline{S}$ with $\widehat{S}$). In turn, by the same argument as above, we see that to prove bounded generation of $E(\widehat{R})$, it suffices to show that there exists an integer $N >0$ depending only on $\Phi$ such that for any local ring $R$, any element of $E(R)$ is a product of $\leq N$ elementaries. We will show that in fact
\begin{equation}\label{E-BG}
E(R) = (U^+ (R) U^- (R))^4,
\end{equation}
so one can take $N = 4 \cdot \vert \Phi \vert.$ Let us now prove (\ref{E-BG}) by induction on the rank $\ell$ of $\Phi$. If $\ell = 1,$ then $G = SL_2$, and one easily checks that $$G(R) = E(R) = (U^+ (R) U^- (R))^4.$$ Now, we assume that (\ref{E-BG}) is valid for every reduced irreducible root system of rank $\leq \ell-1$, with $\ell \geq 2$, and prove it for a root system $\Phi$ of rank $\ell.$ Set $X = (U^+(R) U^-(R))^4$, and let $\Delta \subset \Phi$ be a system of simple roots. Since the group $E(R)$ is generated by $e_{\pm \beta} (t)$ for $\beta \in \Delta$ and $t \in R$ (cf. the proof of (\ref{E:St-1}) in \S 4), to prove (\ref{E-BG}), it suffices to show that
$$
e_{\pm \beta} (t) X \subset X.
$$
Pick $\alpha \in \Delta,$ $\alpha \neq \beta$, that corresponds to an extremal node in the Dynkin diagram of $\Phi.$ Let $\Phi_0$ (resp., $\Phi_1$) be the set of roots in $\Phi$ that do not contain (resp., contain) $\alpha$, and let $\Phi_i^{\pm} = \Phi_i \cap \Phi^{\pm}.$ Then $\Phi_0$ is an irreducible root system having $\Delta_0 = \Delta \setminus \{ \alpha \}$ as a system of simple roots; in particular, $\Phi_0$ has rank $\ell - 1.$ If we let $G_0$ denote the corresponding universal Chevalley-Demazure group scheme, then by the induction hypothesis
$$
E_0 (R) = (U_0^+ (R) U_0^- (R))^4,
$$
with the obvious notations. Let $U_1^{\pm} (R)$ be the subgroup generated by $e_{\alpha} (r)$ for $\alpha \in \Phi_1^+$ (resp., $\alpha \in \Phi_1^-$) and $r \in R.$ Then
$U^{\pm} (R) = U_0^{\pm} (R) U_1^{\pm} (R)$, and according to (\cite{Stb}, Lemma 17),
$$
U_0^{\pm} (R) U_1^{\mp} (R) = U_1^{\mp} (R) U_0^{\pm} (R).
$$
So,
$$
X = (U_0^+ (R) U_1^+ (R) U_0^- (R) U_1^- (R))^4 = (U_0^+ (R) U_0^- (R))^4 (U_1^+ (R) U_1^- (R))^4 = E_0 (R) (U_1^+ (R) U_1^- (R))^4.
$$
Since $e_{\pm \beta} (t) \in E_0 (R),$ we obtain that
$$
e_{\pm \beta} (t) X = e_{\pm \beta} (t) E_0 (R) (U_1^+ (R) U_1^- (R))^4 = X,
$$
as required.
\section{Profinite and congruence topologies coincide on 1-parameter root subgroups}
\begin{prop}\label{P-3}
Let $\Phi$ be a reduced irreducible root system of rank $\geq 2$, $G$ be the corresponding universal Chevalley-Demazure group scheme, and $E(R)$ be the elementary subgroup of the group $G(R)$ over a commutative ring $R$. Furthermore, suppose $N \subset E(R)$ is a normal subgroup of finite index. If $\Phi$ is not of type $C_n$ $(n \geq 2)$ or $G_2$, then there exists an ideal $\ba \subset R$ of finite index such that \begin{equation}\label{E-Ideal}
e_{\alpha} (\ba) \subset N \cap U_{\alpha} (R)
\end{equation}
for all $\alpha \in \Phi$, where $e_{\alpha} (\ba) = \{ e_{\alpha} (t) \mid t \in \ba \}.$ The same conclusion holds for $\Phi$ of type $C_n$ $(n \geq 2)$ and $G_2$ if $2 \in R^{\times}$. Thus, in these cases, the profinite and the congruence topologies of $E(R)$ induce the same topology on $U_{\alpha} (R)$, for all $\alpha \in \Phi.$
\end{prop}
\begin{proof}
We begin with two preliminary remarks. First, for any root $\alpha \in \Phi$,
$$
\ba (\alpha) := \{ t \in R \mid e_{\alpha} (t) \in N \}
$$
is obviously a finite index subgroup of the additive group of $R$. What one needs to show is that either $\ba(\alpha)$ itself is an ideal of $R$, or that it at least contains an ideal of finite index. Second, if $\alpha_1, \alpha_2 \in \Phi$ are roots of the same length, then by (\cite{H1}, 10.4, Lemma C), there exists an element $\tilde{w}$ of the Weyl group $W(\Phi)$ such that $\alpha_2 = \tilde{w} \cdot \alpha_1$. Consequently, it follows from (\cite{St1}, 3.8, relation (R4)) that we can find $w \in E(R)$ such that
$$
w e_{\alpha_1}(t) w^{-1} = e_{\alpha_2} (\varepsilon(w) t)
$$
for all $t \in R$, where $\varepsilon(w) \in \{ \pm 1 \}$ is independent of $t.$ Since $N$ is a normal subgroup of $E(R)$, we conclude that
\begin{equation}\label{E-Ideal1}
\ba (\alpha_1) = \ba (\alpha_2).
\end{equation}
Thus, it is enough to find a finite index ideal $\ba \subset R$ such that (\ref{E-Ideal}) holds for a {\it single} root of each length.
Let us now prove our claim for $\Phi$ of type $A_2$ using explicit computations with commutator relations. We will use the standard realization of $\Phi$, described in \cite{Bour}, where the roots are of the form $\varepsilon_i - \varepsilon_j$,
with $i,j \in \{1, 2, 3 \}, i \neq j.$ To simplify notation, we will write $e_{ij} (t)$ to denote $e_{\alpha} (t)$ for $\alpha = \varepsilon_i - \varepsilon_j.$ Set $\alpha_1 = \varepsilon_1 - \varepsilon_2.$ We will now show that $\ba (\alpha_1)$ is an ideal of $R$, and then it will follow from our previous remarks that $\ba := \ba(\alpha_1)$ is as required. Let $r \in \ba (\alpha_1)$ and $s \in R.$ Since $N \lhd E(R)$, the (well-known) relation
$$
[e_{12} (r), e_{23} (s)] = e_{13} (rs),
$$
where $[g,h] = gh g^{-1} h^{-1}$, shows that $rs \in \ba (\alpha_2)$ for $\alpha_2 = \varepsilon_1 - \varepsilon_2.$ But then (\ref{E-Ideal1}) yields $rs \in \ba(\alpha_1),$ completing the argument.
Now let $\Phi$ be any root system of rank $\geq 2$ in which all roots have the same length. Then clearly $\Phi$ contains a subsystem $\Phi_0$ of type $A_2$, so our previous considerations show that there exists a~finite index ideal $\ba \subset R$ with the property that $\ba \subset \ba(\alpha)$ for all $\alpha \in \Phi_0.$ But then, by (\ref{E-Ideal1}), the same inclusion holds for all $\alpha \in \Phi.$
Next, we consider the case of $\Phi$ of type $B_n$ with $n \geq 3$. Note that since the system of type $F_4$ contains a subsystem of type $B_3$, this will automatically take care of the case when $\Phi$ is of type $F_4$ as well.
We will use the standard realization of $\Phi$ of type $B_n$, where the roots are of the form $\pm \varepsilon_i$, $\pm \varepsilon_i \pm \varepsilon_j$ with $i, j \in \{ 1, \dots, n \}, i \neq j.$ The system $\Phi$ contains a subsystem $\Phi_0$ of type $A_{n-1}$, all of whose roots are long roots in $\Phi.$ Arguing as above, we see that there exists an ideal $\ba \subset R$ of finite index such that (\ref{E-Ideal}) holds for all $\alpha \in \Phi_0,$ and hence for all long roots $\alpha \in \Phi.$ To show that the same ideal also works for short roots, we will use the following relation, which is verified by direct computation:
\begin{equation}\label{E-3}
[e_{\varepsilon_1 + \varepsilon_2} (r), e_{-\varepsilon_2}(s)] = e_{\varepsilon_1} (rs) e_{-\varepsilon_1 - \varepsilon_2} (-rs^2).
\end{equation}
for any $r, s \in R$. Now, if $r \in \ba,$ then $e_{\varepsilon_1 + \varepsilon_2} (r), e_{- \varepsilon_1 - \varepsilon_2} (-r) \in N.$ So, setting $s = 1$ in (\ref{E-3}) and noting that $[e_{\varepsilon_1 + \varepsilon_2} (r), e_{- \varepsilon_2} (1)] \in N$ as $N \lhd E(R),$ we obtain that $e_{\varepsilon_1} (r) \in N.$ Thus, (\ref{E-Ideal}) holds for $\alpha = \varepsilon_1$, and therefore for all short roots.
Next, we proceed to the case of $\Phi$ of type $B_2 = C_2$, where we assume that $2 \in R^{\times}.$
We will use the same realization of $\Phi$ as in the previous paragraph (for $n = 2$). Set $\ba = \ba (\varepsilon_1).$ Then for $r \in \ba$, $s \in R$, one can check by direct computation that
\begin{equation}\label{E-2}
[e_{\varepsilon_1} (r), e_{\varepsilon_2} (s/4)] = e_{\varepsilon_1 + \varepsilon_2} (rs/2) \in N.
\end{equation}
Next, using (\ref{E-3}), in conjunction with the fact that $e_{\varepsilon_1} (u)$ and $e_{\varepsilon_1 - \varepsilon_2} (v)$ commute for all $u, v \in R$, we obtain
$$
[e_{\varepsilon_1 + \varepsilon_2} (rs/2), e_{- \varepsilon_2} (1)][e_{\varepsilon_1 + \varepsilon_2} (rs/2), e_{- \varepsilon_2} (-1)]^{-1} = e_{\varepsilon_1} (rs) \in N,
$$
i.e. $rs \in \ba$, which shows that $\ba$ is an ideal. Furthermore, from (\ref{E-2}), we see that for any $r \in \ba,$ we have
$$
[e_{\varepsilon_1} (r), e_{\varepsilon_2} (1/2)] = e_{\varepsilon_1 + \varepsilon_2} (r) \in N.
$$
Thus, $e_{\varepsilon_1 + \varepsilon_2} (\ba) \subset N,$ and therefore (\ref{E-Ideal}) holds for all $\alpha \in \Phi.$
Finally, suppose that $\Phi$ is of type $G_2$ and assume again that $2 \in R^{\times}.$
We will use the realization of $\Phi$ described in \cite{CK}: one picks a system of simple roots $\{k, c \}$ in $\Phi$, where $k$ is long and $c$ is short, and then the long roots of $\Phi$ are
$$\pm k, \pm (3c + k), \pm (3c + 2k),$$ and the short roots are $$\pm c, \pm (c+k), \pm (2c + k).$$ Set $\ba = \ba (k).$
Since the long roots of $\Phi$ form a subsystem of type $A_2$, for which our claim has already been established, we conclude that
$\ba$ is a finite index ideal in $R$ and that (\ref{E-Ideal}) holds for all long roots. To show that (\ref{E-Ideal}) is true for the short roots as well, we need to recall the following explicit forms of the Steinberg commutator relations that were established in (\cite{CK}, Theorem 1.1):
\begin{equation}\label{E-4}
[e_{k}(s), e_{c} (t)] = e_{c+k} (\varepsilon_1 st) e_{2c + k} (\varepsilon_2 st^2) e_{3c + k} (\varepsilon_3 st^3) e_{3c + 2k} (\varepsilon_4 s^2 t^3),
\end{equation}
\begin{equation}\label{E-5}
[e_{c+k} (s), e_{2c+k}(t)] = e_{3c+2k} (3 \varepsilon_5 st),
\end{equation}
where $\varepsilon_i = \pm 1.$
Using (\ref{E-4}), we obtain
$$
[e_k(s), e_c(1)] [e_k (s), e_c(-1)] =
$$
$$
=e_{c+k} (\varepsilon_1 s) e_{2c+k} (\varepsilon_2 s) e_{3c + k} (\varepsilon_3 s) e_{3c+2k} (\varepsilon_4 s^2) e_{c+k} (-\varepsilon_1 s) e_{2c+k} (\varepsilon_2 s) e_{3c + k} (-\varepsilon_3 s) e_{3c+2k} (-\varepsilon_4 s^2).
$$
Since the terms $e_{3c+k} (-\varepsilon_3 s)$ and $e_{3c + 2k} (-\varepsilon_4 s^2)$ commute with all other terms, the last expression reduces to
$$
e_{c+k} (\varepsilon_1 s) e_{2c +k} (\varepsilon_2 s) e_{c+k}(-\varepsilon_1 s) e_{2c + k} (\varepsilon_2 s),
$$
which, using (\ref{E-5}), can be written in the form
$$
e_{3c + 2k} (3 \varepsilon_5 \varepsilon_1 \varepsilon_2 s^2) e_{2c + k} (2 \varepsilon_2 s).
$$
Hence if $s \in \ba$, we obtain that
$$
[e_k(s/2), e_c(1)] [e_k (s/2), e_c(-1)] = e_{3c + 2k} (3 \varepsilon_5 \varepsilon_1 \varepsilon_2 s^2/4) e_{2c + k} (\varepsilon_2 s) \in N.
$$
But $e_{3c + 2k} (3 \varepsilon_5 \varepsilon_1 \varepsilon_2 s^2/4) \in N,$ from which it follows that $e_{2c + k} (\mathfrak{a}) \subset N.$ This completes the proof.
\end{proof}
\vskip1mm
\noindent {\bf Remark.} If $R$ is the ring of algebraic $S$-integers, then any subgroup of finite index of the additive group of $R$ contains an ideal of finite index, so the conclusion of Proposition \ref{P-3} holds for root systems of rank $>1$ of all types without any additional restrictions on $R$. On the other hand, if $R$ is the ring of $S$-integers in a global field of positive characteristic $>2$, then $2 \in R^{\times}$, and Proposition \ref{P-3} again applies to all root systems without any extra assumptions.
\section{Proof of the main theorem}
We return to the notations introduced in \S \ref{S:I}. In particular, we set $\Gamma = E(R)$, where $R$ is a commutative noetherian ring such that $2 \in R^{\times}$ if our root system $\Phi$ is of type $C_n$ ($n \geq 2$) or $G_2$, and let $\widehat{\Gamma}$ and $\overline{\Gamma}$ denote the profinite and congruence completions of $\Gamma$, respectively. Furthermore, we let $\pi \colon \widehat{\Gamma} \to \overline{\Gamma}$ denote the canonical continuous homomorphism, so that $C(\Gamma) := \ker \pi$ is the congruence kernel. For each root $\alpha \in \Phi$, we let $\widehat{U}_{\alpha}$ and $\overline{U}_{\alpha}$ denote the closures of the images of the natural homomorphisms $U_{\alpha} (R) \to \widehat{\Gamma}$ and $U_{\alpha} (R) \to \overline{\Gamma}.$ By Proposition \ref{P-3}, the profinite and congruence topologies of $\Gamma$ induce the same topology on each $U_{\alpha} (R)$, which implies that $\pi \vert_{\widehat{U}_{\alpha}} \colon \widehat{U}_{\alpha} \to \overline{U}_{\alpha}$ is a group isomorphism. From the definitions, it is clear that $\overline{U}_{\alpha}$ coincides with $\overline{e}_{\alpha} (\widehat{R})$, where $\overline{e}_{\alpha} \colon \widehat{R} \to G(\widehat{R}) = \overline{G(R)}$ is the 1-parameter subgroup associated with $\alpha$ over the ring $\widehat{R}.$ Set
$$
\widehat{e}_{\alpha} = (\pi \vert_{\widehat{U}_{\alpha}})^{-1} \circ \overline{e}_{\alpha}.
$$
Then $\widehat{e}_{\alpha} \colon \widehat{R} \to \widehat{U}_{\alpha}$ is an isomorphism of topological groups, and in particular, we have
$$
\widehat{e}_{\alpha} (r+s) = \widehat{e}_{\alpha} (r) \widehat{e}_{\alpha} (s)
$$
for all $r, s \in \widehat{R}$ and any $\alpha \in \Phi.$
Before establishing some further properties of the $\widehat{e}_{\alpha}$, let us recall that for any commutative ring $S$ and any $\alpha, \beta \in \Phi$, $\beta \neq -\alpha$, there is a relation in $G(S)$ of the form
\begin{equation}\label{E-Steinberg}
[e_{\alpha} (s), e_{\beta} (t)] = \prod e_{i \alpha + j \beta} (N_{\alpha, \beta}^{i,j} s^i t^j)
\end{equation}
for all $s,t \in S$,
where the product is taken over all roots of the form $i \alpha + j \beta$ with $i, j \in \Z^+$, listed in an arbitrary (but {\it fixed}) order, and the $N^{i,j}_{\alpha, \beta}$ are integers depending only on $\alpha, \beta \in \Phi$ and the order of the factors in (\ref{E-Steinberg}), but not on $s, t \in S$. Furthermore, recall that the abstract group $\tilde{G}(S)$ with generators $x_{\alpha} (s)$ for all $s \in S$ and $\alpha \in \Phi$ subject to the relations
\vskip1mm
(R1) $\tilde{x}_{\alpha}(s) \tilde{x}_{\alpha}(t) = \tilde{x}_{\alpha} (s+t)$,
\vskip1mm
(R2) \parbox[t]{15cm}{$[\tilde{x}_{\alpha} (s), \tilde{x}_{\beta} (t)] = \prod \tilde{x}_{i \alpha + j \beta} (N^{i,j}_{\alpha, \beta} s^i t^j)$, where $N_{\alpha, \beta}^{i,j}$ are the same integers, and the roots are listed in the same order, as in (\ref{E-Steinberg}),}
\vskip1mm
\noindent is called the {\it Steinberg group}. It follows from (\ref{E-Steinberg}) that there exists a canonical homomorphism $\tilde{G}(S) \to G(S)$, defined by $x_{\alpha} (s) \mapsto e_{\alpha} (s)$, whose kernel is denoted by $K_2 (\Phi, S).$
\begin{lemma}\label{L-3}
{\rm (1)} \parbox[t]{15cm}{For any $\alpha, \beta \in \Phi$, $\beta \neq -\alpha$, and $s, t \in \widehat{R}$, we have $[\widehat{e}_{\alpha} (s), \widehat{e}_{\beta} (t)] = \prod \widehat{e}_{i \alpha + j \beta} (N_{\alpha, \beta}^{i,j} s^i t^j).$}
\vskip2mm
\noindent Let $\widehat{R} = \prod_{\m \in \M} R_{\m}$ be the decomposition from Lemma \ref{L-1}(1), and for $\m \in \M$, let $\widehat{\Gamma}_{\m}$ (resp. $\widehat{\Gamma}_{\m}'$) be the subgroup of $\widehat{\Gamma}$ (algebraically) generated by $\widehat{e}_{\alpha} (r)$ for all $r \in R_{\m}$ (resp., $r \in R_{\m}' := \prod_{\n \neq \m} R_{\n}$) and all $\alpha \in \Phi$. Then
\noindent {\rm (2)} \parbox[t]{16cm}{There exists a surjective group homomorphism $\theta_{\m} \colon \tilde{G}(R_{\m}) \to \widehat{\Gamma}_{\m}$ such that $x_{\alpha} (r) \mapsto \widehat{e}_{\alpha} (r)$ for all $r \in R_{\m}$ and $\alpha \in \Phi.$}
\vskip1mm
\noindent {\rm (3)} \parbox[t]{16cm}{$\widehat{\Gamma}_{\m}$ and $\widehat{\Gamma}_{\m}'$ commute elementwise inside $\widehat{\Gamma}.$}
\end{lemma}
\begin{proof}
(1) Define two continuous maps
$$
\varphi \colon \widehat{R} \times \widehat{R} \to \widehat{\Gamma}, \ \ \ (s,t) \mapsto [\widehat{e}_{\alpha} (s), \widehat{e}_{\beta} (t)]
$$
and
$$
\psi \colon \widehat{R} \times \widehat{R} \to \widehat{\Gamma}, \ \ \ (s,t) \mapsto \prod \widehat{e}_{i \alpha + j \beta} (N_{\alpha, \beta}^{i,j} s^i t^j).
$$
It follows from (\ref{E-Steinberg}) that these maps coincide on $R \times R.$ Since $R \times R$ is dense in $\widehat{R} \times \widehat{R},$ we have $\varphi \equiv \psi,$ yielding our claim.
(2) Since we have shown that the $\widehat{e}_{\alpha}(r)$, $r \in R_{\m}$, $\alpha \in \Phi,$ satisfy the relations (R1) and (R2), the existence of the homomorphism $\theta_{\m}$ follows.
(3) It suffices to show that for any $\alpha, \beta \in \Phi$ and any $r \in R_{\m}, \ s \in R_{\m}',$ the elements $\widehat{e}_{\alpha} (r), \widehat{e}_{\beta} (s) \in \widehat{\Gamma}$ commute. Since $r s= 0$ in $\widehat{R},$ this fact immediately follows from (1) if $\beta \neq -\alpha.$ To handle the remaining case $\beta = - \alpha,$ we observe that for any ring $S$ and the corresponding Steinberg group $\tilde{G}(S)$, we have
\begin{equation}\label{E:St-1}
\tilde{G}(S) = <x_{\gamma} (r) \mid \gamma \in \Phi \setminus \{ \alpha \}, r \in S>.
\end{equation}
Indeed, it is well-known that $\tilde{G}(S)$ is generated by the elements $x_{\gamma} (r)$ for all $r \in R$ and all $\gamma$ in an arbitrarily chosen system $\Pi \subset \Phi$ of simple roots (this follows, for example, from the fact that the Weyl group of $\Phi$ is generated by the reflections corresponding to simple roots, and moreover, every root lies in the orbit of a simple root under the action of the Weyl group).
On the other hand, since $\Phi$ is of rank $\geq 2$, for any $\alpha \in \Phi,$ one can find a system of simple roots $\Pi \subset \Phi$ that does not contain $\alpha$, and (\ref{E:St-1}) follows. Using the homomorphism $\theta_{\m}$ constructed in part (2), we conclude from (\ref{E:St-1}) that $\widehat{\Gamma}_{\m} = \theta_{\m} (\tilde{G}(R_{\m}))$ is generated by $\widehat{e}_{\gamma}(r)$ for $r \in R_{\m}$, $\gamma \in \Phi \setminus \{ \alpha \}$. So, since we already know that $\widehat{e}_{-\alpha} (s)$, with $s \in R_{\m}'$, commutes with all of these elements, it also commutes with $\widehat{e}_{\alpha} (r),$ yielding our claim.
\end{proof}
The following lemma, which uses results of Stein \cite{St2} on the computation of $K_2$ over semi-local rings, is a key ingredient in the proof of the Main Theorem.
\begin{lemma}\label{L-4}
The kernel $\ker (\pi \vert_{\widehat{\Gamma}_{\m}})$ of the restriction $\pi \vert_{\widehat{\Gamma}_{\m}}$ lies in the center of $\widehat{\Gamma}_{\m}$, for any $\m \in \M.$
\end{lemma}
\begin{proof}
Stein has shown that if $\Phi$ has rank $\geq 2$ and $S$ is a semi-local ring which is generated by its units, then $K_2 (\Phi, S)$ lies in the center of $\tilde{G}(S)$ (cf. \cite{St2}, Theorem 2.13). Since $S = R_{\m}$ is local, it is automatically generated by its units, hence $K_2 (\Phi, R_{\m}) = \ker (\tilde{G}(R_{\m}) \stackrel{\mu}{\longrightarrow} E(R_{\m}))$ is central. On the other hand, $\mu$ admits the following factorization:
$$
\tilde{G}(R_{\m}) \stackrel{\theta_{\m}}{\longrightarrow} \widehat{\Gamma}_{\m} \stackrel{\pi \vert_{\widehat{\Gamma}_{\m}}}{\longrightarrow} E(R_{\m}).
$$
Since $\theta_{\m}$ is surjective, we conclude that
$$
\ker (\pi \vert_{\widehat{\Gamma}_{\m}}) = \theta_{\m} (K_2 (\Phi, R_{\m}))
$$
is central in $\widehat{\Gamma}_{\m}.$
\end{proof}
Now fix $\m \in \M$ and let $\Delta_{\m} = \widehat{\Gamma}_{\m} \widehat{\Gamma}_{\m}'$ be the subgroup of $\widehat{\Gamma}$ (algebraically) generated by $\widehat{\Gamma}_{\m}$ and $\widehat{\Gamma}_{\m}'.$ Let $c \in C(\Gamma) \cap \Delta_{\m},$ and write $c = c_1 c_2,$ with $c_1 \in \widehat{\Gamma}_{\m}, c_2 \in \widehat{\Gamma}_{\m}'.$
We have $\overline{\Gamma} = \overline{\Gamma}_{\m} \times \overline{\Gamma}_{\m}'$, where $\overline{\Gamma}_{\m} = E(R_{\m})$ and $\overline{\Gamma}_{\m}' = E(R_{\m}').$
Since $\pi (c_1) \in \overline{\Gamma}_{\m}$, $\pi(c_2) \in \overline{\Gamma}_{\m}',$ we conclude from $$\pi(c) = e = \pi(c_1) \pi(c_2)$$ that $\pi(c_1) = e,$ i.e. $c_1 \in \ker (\pi \vert_{\widehat{\Gamma}_{\m}}).$ Then by Lemma \ref{L-4}, $\widehat{\Gamma}_{\m}$ centralizes $c_1.$ On the other hand, $\widehat{\Gamma}_{\m}$ centralizes $c_2 \in \widehat{\Gamma}_{\m}'$ by Lemma \ref{L-3}(3). So, $\widehat{\Gamma}_{\m}$ centralizes $c.$ Thus, we have shown that $C \cap \Delta_{\m}$ is centralized by $\widehat{\Gamma}_{\m}.$ To prove that $\widehat{\Gamma}_{\m}$ actually centralizes all of $C$, we need the following
\begin{lemma}\label{L-5}
Let $\varphi \colon \mathcal{G}_1 \to \mathcal{G}_2$ be a continuous homomorphism of topological groups, and let $\mathcal{F} = \ker \varphi.$ Suppose $\Theta \subset \mathcal{G}_1$ is a dense subgroup such that there exists a compact set $\Omega \subset \Theta$ whose image $\varphi(\Omega)$ is a neighborhood of the identity in $\mathcal{G}_2.$ Then $\mathcal{F} \cap \Theta$ is dense in $\mathcal{F}.$
\end{lemma}
\begin{proof}
Since $\varphi(\Omega)$ is a neighborhood of the identity in $\mathcal{G}_2$, we can find an open set $U \subset \mathcal{G}_1$ such that
$$
\mathcal{F} \subset U \subset \varphi^{-1}(\varphi(\Omega)) = \Omega \mathcal{F}.
$$
Now since $\Theta$ is dense in $\mathcal{G}_1$, we have $U \subset \overline{\Theta \cap U},$ where the bar denotes the closure in $\mathcal{G}_1.$ Thus,
$$
\mathcal{F} \subset \overline{\Theta \cap U} \subset \overline{\Theta \cap \Omega \mathcal{F}}.
$$
But $\Theta \cap \Omega \mathcal{F} = \Omega (\Theta \cap \mathcal{F}),$ and since $\Omega$ is compact, the product $\Omega \overline{(\Theta \cap \mathcal{F})}$ is closed. So
$$
\mathcal{F} \subset \overline{\Theta \cap \Omega \mathcal{F}} \subset \Omega \overline{(\Theta \cap \mathcal{F})}.
$$
Since $\mathcal{F}$ is closed, we have $\overline{\Theta \cap \mathcal{F}} \subset \mathcal{F},$ so
$$
\mathcal{F} = (\Omega \cap \mathcal{F}) \overline{(\Theta \cap \mathcal{F})} \subset (\Theta \cap \mathcal{F}) \overline{(\Theta \cap \mathcal{F})} = \overline{\Theta \cap \mathcal{F}},
$$
as required.
\end{proof}
In order to apply Lemma \ref{L-5} in our situation, we noted the following simple fact
\begin{lemma}\label{L-6}
The subgroup $\Delta \subset \widehat{\Gamma}$ (algebraically) generated by the $\widehat{\Gamma}_{\m}$ for all $\m \in \M$ is dense. Consequently, for any $\m \in \M,$ the subgroup $\Delta_{\m} = \widehat{\Gamma}_{\m} \widehat{\Gamma}_{\m}' \subset \widehat{\Gamma}$ is dense.
\end{lemma}
\begin{proof}
Let
$$
R_0 := \sum_{\m \in \M} R_{\m} \subset \widehat{R} = \prod_{\m \in \M} R_{\m}.
$$
Clearly $R_0$ is a dense subring of $\widehat{R}.$ On the other hand, $\Delta$ obviously contains $\widehat{e}_{\alpha} (R_0)$ for any $\alpha \in \Phi.$ So, the closure $\overline{\Delta}$ contains $\widehat{e}_{\alpha} (R)$ for all $\alpha \in \Phi$, and therefore coincides with $\widehat{\Gamma},$ yielding our first assertion. Furthermore, for any $\m \in \M,$ the subgroup $\Delta_{\m}$ contains $\Gamma_{\n}$ for all $\n \in \M,$ so our second assertion follows.
\end{proof}
\vskip1mm
\noindent {\it Conclusion of the proof of the Main Theorem}: Fix $\m \in \M.$ We have already seen that $\widehat{\Gamma}_{\m}$ centralizes $C \cap \Delta_{\m}.$ We claim that $C \cap \Delta_{\m}$ is dense in $C$, and hence $\widehat{\Gamma}_{\m}$ centralizes $C$. Indeed, by Lemma~\ref{L-6}, $\Delta_{\m}$ is dense in $\widehat{\Gamma}.$ On the other hand, it follows from Corollary \ref{C-1} that there exists a string of roots $(\alpha_1, \dots, \alpha_L)$ such that the map
$$
\widehat{R}^L \to \overline{\Gamma}, \ \ \ \ \ (r_1, \dots, r_L) \mapsto \prod_{i=1}^L \overline{e}_{\alpha_i} (r_i)
$$
is surjective. Then
$$
\Omega := \widehat{e}_{\alpha_1} (\widehat{R}) \cdots \widehat{e}_{\alpha_L} (\widehat{R}) = \left( \widehat{e}_{\alpha_1} (R_{\m}) \cdots \widehat{e}_{\alpha_L} (R_{\m}) \right) \left( \widehat{e}_{\alpha_1} (R_{\m}') \cdots \widehat{e}_{\alpha_L} (R_{\m}') \right)
$$
is a compact subset of $\widehat{\Gamma}$ that is contained in $\Delta_{\m}$ and has the property that $\pi(\Omega) = \overline{\Gamma}.$ Invoking Lemma \ref{L-5}, we obtain that $C \cap \Delta_{\m}$ is dense in $C$, as required.
We now see that $\widehat{\Gamma}_{\m}$ centralizes $C$ for all $\m \in \M.$ Since the subgroup $\Delta \subset \widehat{\Gamma}$ generated by the $\widehat{\Gamma}_{\m}$ is dense in $\widehat{\Gamma}$ by Lemma \ref{L-6}, we obtain that $\widehat{\Gamma}$ centralizes $C$, completing the proof.
\hfill $\Box$
\vskip2mm
To put our proof of the Main Theorem into perspective, we recall the following criterion for the centrality of the congruence kernel in the context of the congruence subgroup problem for algebraic groups over global fields (see \cite{PR}, Theorem 4). Let $G$ be an absolutely almost simple simply connected algebraic group over a global field $K$, and $S$ be a set of places of $K$, which we assume to contain all archimedean places if $K$ is a number field, such that the corresponding $S$-arithmetic group $G(\mathcal{O}_S)$ is infinite (where $\mathcal{O}_S$ is the ring of $S$-integers in $K$). Then by the Strong Approximation Theorem, the $S$-congruence completion $\overline{G(K)}$ of the group $G(K)$ of $K$-rational points can be identified with the group of $S$-adeles $G(\mathbb{A}_S)$, and in particular the group $G(K_v)$, for $v \notin S$, can be viewed as a subgroup of $\overline{G(K)}.$ Assume furthermore that $S$ contains no nonarchimedean anisotropic places for $G$ and that $G/K$ satisfies the Margulis-Platonov conjecture. If for each $v \in S$, there exists a subgroup $H_v$ of the $S$-arithmetic completion $\widehat{G(K)}$ such that
\vskip1mm
(1) \parbox[t]{16cm}{$\pi (H_v) = G(K_v)$ for all $v \notin S$, where $\pi \colon \widehat{G(K)} \to \overline{G(K)}$ is the canonical projection;}
\vskip1mm
(2) \parbox[t]{16cm}{$H_{v_1}$ and $H_{v_2}$ commute elementwise for $v_1 \neq v_2$;}
\vskip1mm
(3) \parbox[t]{16cm}{the $H_v$, for $v \notin S$, (algebraically) generate a dense subgroup of $\widehat{G(K)}$,}
\vskip1mm
\noindent then the congruence kernel $C^S(G) := \ker \pi$ is central. So, this criterion basically states that in the arithmetic situation, the mere existence of elementwise commuting lifts of ``local groups" implies the centrality of the congruence kernel. In our situation, the existence of elementwise commuting lifts (which we denoted $\widehat{\Gamma}_{\m}$ above) also plays a part in the proof of centrality (cf. Lemma \ref{L-4}(3)), but some additional considerations (such as the result of Stein and the bounded generation property for $E(\widehat{R}) = G(\widehat{R})$) are needed; the facilitating factor in the arithmetic situation is the action of the group $G(K)$ on the congruence kernel, which is not available over more general rings.
Finally, we will relate our result on the centrality of the congruence kernel $C(\Gamma)$ for $\Gamma = E(R)$ to the congruence subgroup problem for $G(R).$ We have the following commutative diagram induced by the natural embedding $\Gamma \hookrightarrow G(R)$:
$$
\xymatrix{1 \ar[r] & C(\Gamma) \ar[r] \ar[d]_{\alpha} & \widehat{\Gamma} \ar[d]_{\beta} \ar[r]^{\pi^{\Gamma}} & \overline{\Gamma} \ar[d]_{\gamma} \ar[r] & 1 \\ 1 \ar[r] & C(G(R)) \ar[r] & \widehat{G(R)} \ar[r]^{\pi^{G(R)}} & \overline{G(R)} \ar[r] & 1}
$$
We note that by Proposition \ref{P-2}, $\gamma$ is an isomorphism. So, $\alpha(C(\Gamma)) = C(G(R)) \cap \beta (\widehat{\Gamma})$, and $\beta (\widehat{\Gamma})$ coincides with the closure $\check{\Gamma}$ of $\Gamma$ in $\widehat{G(R)}$. Thus, our Main Theorem yields the following
\begin{cor}
$C(G(R)) \cap \check{\Gamma}$ is centralized by $\check{\Gamma}.$
\end{cor}
The exact relationship between $C(G(R))$ and $C(G(R)) \cap \check{\Gamma}$ (or $C(\Gamma)$) remains unclear except in a few cases. Matsumoto \cite{M1} showed that $G(R) = E(R)$ for any ring $R$ of algebraic $S$-integers, which combined with our Main Theorem and the remark at the end of \S 3, yields the centrality of $C(E(R)) = C(G(R))$, established by Matsumoto himself. Furthermore,
for $G = SL_n$ $(n \geq 3)$ and $R = \Z[x_1, \dots, x_k]$, by a result of Suslin \cite{Su}, we again have $G(R) = E(R),$ so $C(G(R)) = C(E(R))$ is central in $\widehat{E(R)} = \widehat{G(R)},$
which was established in \cite{KN}. On the other hand, there exist principal ideal domains $R$ for which $SL_n (R) \neq E(R)$ (cf. \cite{G}, \cite{I}), and then the analysis of $C(G(R))$ requires more effort. We only note that if $\Gamma = E(R)$ has finite index in $G(R)$, then the profinite topology on $\Gamma$ is induced by the profinite topology of $G(R)$, which implies that $\beta$ is injective, and therefore $C(\Gamma)$ is identified with a finite index subgroup of $C(G(R)).$
\vskip2mm
\noindent {\bf Acknowledgements.} The first-named author was partially supported by NSF grant DMS-0965758 and the Humboldt Foundation. The paper was finalized when both authors were visiting SFB 701 (Bielefeld), whose hospitality is gratefully acknowledged.
\bibliographystyle{amsplain}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,078 |
\section{Introduction}
\label{sec:intro}
The decays $B \to \ell^-\bar\nu$ and $B \to D^{(\ast)} \ell^- \bar\nu$
($\ell=e,\mu,\tau$) play a prominent role in testing the Standard Model (SM)
and looking for hints of New Physics (NP) in charged-current interactions.
In the SM scenario a measurement of these decays provides a direct route
to determine values of the $B$ meson decay constant $f_B$ and the semileptonic
form factors. They also help to determine the Cabibbo-Kobayashi-Maskawa (CKM)
matrix elements $|V_{ub}|$ and $|V_{cb}|$ to a better precision. A puzzling
feature of these decays is that there have been some recent hints that lepton
universality is broken in the tauonic modes of these decays.
The leptonic and semileptonic modes are difficult to measure experimentally
due to
the presence of a neutrino in the final state. Ideal in this regard
are B-factories where a $B$ meson pair is generated from
the process $e^+e^- \to \Upsilon(4S) \to B\bar{B}$. One of the $B$ mesons
($B_{\rm tag}$) is then reconstructed in hadronic or semileptonic modes,
while signal decays of the other $B$ meson ($B_{\rm sig}$) are identified.
A new player has entered the game in that the LHCb collaboration has been
able to identify the semileptonic decays
$\bar{B}^0 \to D^{\ast} \tau^- \bar{\nu}_{\tau}$ and
$\bar{B}^0 \to D^{\ast} \mu^- \bar{\nu}_{\mu}$
in hadronic collisions~\cite{Aaij:2015yra}.
Since the first evidence reported by Belle collaboration in
2006~\cite{Ikado:2006un}, many measurements of the branching fraction
$ \mathcal{B}(B^- \to \tau^- \bar{\nu}_{\tau})$ have been reported by both Belle and BABAR collaborations. There had been a consistent excess compared
to the SM prediction until Belle published their result of
$ \mathcal{B}(B^- \to \tau^- \bar{\nu}_{\tau})
=[(7.2^{+2.7}_{-2.5} ({\rm stat}) \pm 1.1 ({\rm syst}))] \times 10^{-5}$
with a significance of $3.0 \sigma$ \cite{Hara:2012mm}. This result reduced
the tension between theory and experiment and decreased the world average of
the measured branching fraction to the recent value of
$ \mathcal{B}(B^- \to \tau^- \bar{\nu}_{\tau})
=(11.4 \pm 2.2) \times 10^{-5}$~\cite{Bona:2009cj},
which is slightly larger than the SM expectation $(8.1 \pm 0.7) \times 10^{-5}$
obtained from a global fit to CKM matrix elements~\cite{Bona:2009cj}.
Note that the most recent result of
$ \mathcal{B}(B^- \to \tau^- \bar{\nu}_{\tau})
=[12.5 \pm 2.8 ({\rm stat}) \pm 2.7 ({\rm syst})]
\times 10^{-5}$~\cite{Abdesselam:2014hkd}
reported by Belle in September 2014 is in good agreement with its previous
result.
The SM calculation of the leptonic decays suffers from uncertainties in the
input values of $f_B$ and $V_{ub}$. One can eliminate the $V_{ub}$ dependence by
calculating the ratio of branching fractions
\begin{equation}
R^{\tau}_{\pi} = \frac{\tau_{\bar{B}^0}}{\tau_{B^-}}
\frac{\mathcal{B}(B^- \to \tau^- \bar{\nu}_{\tau})}
{ \mathcal{B}(\bar{B}^0 \to \pi^+ \ell^- \bar{\nu}_{\ell})},
\end{equation}
where $\ell = \mu, e$. The ratio is measured to be
$(0.73 \pm 0.15)$~\cite{Fajfer:2012jt}, which exceeds the SM prediction of
$R^{\tau}_{\pi} =0.31 \pm 0.06$~\cite{Fajfer:2012jt}
by more than a factor of 2, while the measured value of
$\mathcal{B}(\bar B^0 \to \pi^+ \ell^- \bar{\nu}_{\ell})
=(14.6\pm 0.7)\times 10^{-5}$
~\cite{delAmoSanchez:2010af,Ha:2010rf,Asner:2010qj}
is consistent with the SM expectation.
The semileptonic decays $B \to D^{(\ast)} \ell \nu$ have a much richer
structure than the leptonic decays. There is a large number of observables
in these decays, e.g., the forward-backward asymmetry of the charged
lepton. Recently there has been much interest in the ratios
of branching fractions
\begin{equation}
R(D^{(\ast)}) \equiv
\frac{\mathcal{B}(\bar{B}^0 \to D^{(\ast)} \tau^- \bar{\nu}_{\tau})}
{\mathcal{B}(\bar{B}^0 \to D^{(*)} \ell^- \bar{\nu}_{\ell})}.
\end{equation}
In taking these ratios some of the uncertainties in the form factors
are reduced. Furthermore, the dependence on the poorly known CKM matrix
element $|V_{cb}|$ drops out in the ratio.
Recently, three groups have reported measurements of these ratios
\[
\begin{array}{ll}
R(D)|_{\rm BABAR} = 0.440 \pm 0.072 \qquad & \qquad
R(D^\ast)|_{\rm BABAR} = 0.332 \pm 0.030 \quad \text{\cite{Lees:2012xj}}
\\
R(D)|_{\rm BELLE}\,\, = 0.375 \pm 0.069 \qquad & \qquad
R(D^\ast)|_{\rm BELLE} \,\,= 0.293 \pm 0.041 \quad
\text{\cite{Huschle:2015rga} }
\\
& \qquad R(D^\ast)|_{\rm LHCb} \;\;\; = 0.336 \pm 0.040 \quad
\text{\cite{Aaij:2015yra}}
\\
\end{array}
\]
where the statistical and systematic uncertainties have been combined
in quadrature. These measurements were combined in \cite{Rotondo:2015FPCP}
\begin{equation}
R(D)|_{\rm expt} = 0.388 \pm 0.047 ,
\qquad
R(D^\ast)|_{\rm expt} = 0.321 \pm 0.021 ,
\label{eq:RD-expt}
\end{equation}
and compared with the SM expectations given in
\cite{Lees:2012xj,Tanaka:2010se,Fajfer:2012vx,Kamenik:2008tj}
\begin{equation}
R(D)|_{\rm SM} = 0.297 \pm 0.017 ,
\qquad
R(D^\ast)|_{\rm SM} = 0.252 \pm 0.003 .
\label{eq:RD-SM}
\end{equation}
It is seen that there is a discrepancy of 1.8~$\sigma$
for $R(D)$ and 3.3~$\sigma$ for $R(D^\ast)$.
The deviation of leptonic and semileptonic
tauonic $B$ meson decays from SM expectations has been the motivation of
many theoretical studies in search for NP effects, including
the two-Higgs-doublet models (2HDMs)~\cite{Hou:1992sy,Baek:1999ch,Crivellin:2015hha,Crivellin:2012ye},
the minimal supersymmetric standard model (MSSM)~\cite{Martin:1997ns}, and
leptoquark models~\cite{Buchmuller:1986zs,Calibbi:2015kma}. In many studies, a general
effective Lagrangian for the $b \to u \ell \nu$ and the $b \to c \ell \nu$
transitions in the presence of NP is imposed to investigate various NP
operators and their coupling, together with their correlations
~\cite{Datta:2012qk,Tanaka:2012nw,Biancofiore:2013ki,Fajfer:2012vx}.
In this paper we focus on these decays within the SM framework using
results from our covariant constituent quark model for the dynamics of the
transitions.
Most of the theoretical studies on the semileptonic decays have been relying
on elements of the Heavy Quark Effective Theory
(HQET)~\cite{Neubert:1993mb,grozin2004heavy}, based on
a systematic $1/m_Q$-expansion of the QCD Lagrangian. The leading order
of the HQET-expansion corresponds to the Heavy Quark Symmetry when the heavy
quark mass tends to infinity, simplifying the structure of the weak current
transitions.
The form factors of these transitions are then expressed through only
a few universal functions. Unfortunately, HQET can give predictions
only for the normalization of the form factors at zero recoil. As one moves
away from the zero-recoil point one has to take recourse to full
nonperturbative calculations. In this paper, we present a description of
these decays that does not rely on HQET. We employ the covariant constituent
quark model (CQM) with built-in infrared confinement which has
been developed in several previous papers by our group
(see~\cite{Branz:2009cd,Ivanov:2011aa} and references therein).
In the CQM approach, the entire physical range of momentum transfer
is accessible. This is one of those features that make the CQM different from other model approaches
for the calculation of hadronic quantities. We mention that a similar study was done by authors of~\cite{Ebert:2006hj,Ebert:2006nz,Faustov:2012nk} in the framework of a relativistic quark model based on the quasipotential approach, in which the full range of momentum transfer is also achievable. Our aim is to give an independent
calculation of these decays including the $q^{2}$ behavior of the
transition form factors, the leptonic
decay constants of the $B$ and $D$ mesons, the forward-backward asymmetry of
the lepton and other polarization observables as well as ratios of branching
fractions.
\section{Model}
\label{sec:model}
The CQM is based on an effective Lagrangian describing the coupling of a
hadron $H$ to its constituent quarks, the coupling strength of which is
determined by the compositeness condition
$Z_H = 0$~\cite{Salam:1962ap,Weinberg:1962hj}, where $Z_H$
is the wave function renormalization constant of the hadron $H$.
Here $Z^{1/2}_H$ is the matrix element between a physical particle state and
the corresponding bare state. For $Z_H=0$ it then follows that
the physical state does not contain the bare one and is therefore described
as a bound state. This does not mean that we can solve the QCD bound state
equations but we are able to show that the compositeness condition
provides an effective and self-consistent way to describe the coupling
of a particle to its constituents.
One starts with an effective Lagrangian written down in terms of quark and
hadron variables \cite{Efimov:1988yd,Efimov:zg}. Then, by using
Feynman rules, the $S$-matrix elements describing hadronic interactions
are derived from a set of quark diagrams. In particular, the compositeness
condition enables one to avoid a double counting of hadronic degrees of
freedom. This approach is self-consistent and all calculations of physical
observables are straightforward. There is a small set of model parameters:
the constituent quark masses, the scale parameters
that define the size of the constituent quarks distribution inside
a given hadron, and the infrared cutoff parameter $\lambda$.
The coupling of a meson $M$ to its constituent quarks $q_1$ and $\bar q_2$
is given by the Lagrangian
\begin{equation}
\label{eq:lag}
{\cal L}_{\rm int}(x)=g_M\,M(x)\cdot J_M (x) + {\rm H.c.},
\end{equation}
where $g_M$ denotes the coupling strength of the meson with its constituent
quarks. The interpolating quark current in~(\ref{eq:lag}) is taken to be
\begin{equation}\label{eq:current}
J_M (x)=\int\!\! dx_1\!\! \int\!\! dx_2\, F_M (x;x_1,x_2)\,
\bar{q}_2 (x_2)\,\Gamma_M\, q_1(x_1),
\end{equation}
where the Dirac matrix $\Gamma_M$ projects onto the relevant meson state,
i.e., $\Gamma_M=I$ for a scalar meson, $\Gamma_M=\gamma^5$ for a
pseudo-scalar meson, and
$\Gamma_M=\gamma^{\mu}$ for a vector meson. The vertex function $F_M$ is
related to the scalar part of the Bethe-Salpeter amplitude and characterizes
the finite size of the meson. We adopt the following form for the vertex
function
\begin{equation}
F_M (x;x_1,x_2)=\delta(x - w_1 x_1 - w_2 x_2) \Phi_M((x_1-x_2)^2),
\label{eq:vertex}
\end{equation}
where $w_i = m_{q_i}/(m_{q_1}+m_{q_2})$ so that $w_1+w_2=1$.
This form of $F_M$ is invariant under
the translation $F_M(x+a;x_1+a,x_2+a)=F_M(x;x_1,x_2)$, which is a necessary
condition to provide the Lorentz invariance of the Lagrangian~(\ref{eq:lag}).
In order to simplify the calculations we adopt a Gaussian form for the vertex
function as follows:
\begin{equation}
\widetilde\Phi_M(-p^2) = \int\! dx\, e^{ipx} \Phi_M(x^2)
= e^{p^2/\Lambda^2_M},
\label{eq:Gauss}
\end{equation}
where the parameter $\Lambda_M$ characterizes the meson size.
Calculations of Feynman diagrams proceed
in the Euclidean region where $p^2=-p^2_E$, in which
the vertex function has the appropriate falloff
behavior to provide for the ultraviolet convergence of the loop integral.
In the evaluation of the quark-loop diagrams we use
the free local fermion propagator of the constituent quark
\begin{equation}
\label{eq:prop}
S_q(k) = \frac{1}{ m_q-\not\! k -i\epsilon } =
\frac{m_q + \not\! k}{m^2_q - k^2 -i\epsilon }
\end{equation}
with an effective constituent quark mass $m_q$.
\begin{figure}[htbp]
\includegraphics[scale=0.6]{fig_mass}
\caption{One-loop self-energy diagram for a meson.}
\label{fig:mass}
\end{figure}
For the evaluation of the compositeness condition, we consider the meson mass
function defined by the diagram in Fig.~\ref{fig:mass}.
One has
\begin{eqnarray}
\widetilde\Pi_P(p^2) &=& N_c g_{P}^{2}
\int\frac{d^4k}{(2\pi)^4i} \widetilde\Phi^2_P(-k^2)
\mbox{\rm{tr}}\Big(\gamma^5 S_1(k+w_1 p)\gamma^5 S_2(k-w_2 p)\Big),
\label{eq:massP}\\[2ex]
\widetilde\Pi^{\mu\nu}_V(p^2) &=&N_c g_{V}^{2}
\int\frac{d^4k}{(2\pi)^4i} \widetilde\Phi^2_V(-k^2)
\mbox{\rm{tr}}\Big(\gamma^\mu S_1(k+w_1 p)\gamma^\nu S_2(k-w_2 p)\Big),
\label{eq:massV}
\end{eqnarray}
where $N_c=3$ is the number of colors. Since the vector meson is
on its mass-shell one has $\epsilon_V\cdot p=0$ and
one needs only the part of the vector meson function proportional
to $g_{\mu\nu}$. It is given by
\begin{equation}
\widetilde\Pi_V(p^2) = \frac13 \bigl(g_{\mu\nu}-\frac{p_\mu p_\nu}{p^2} \bigr)
\widetilde\Pi^{\mu\nu}_V(p).
\end{equation}
The coupling constant $g_M$ in Eq.~(\ref{eq:lag}) is determined
by the compositeness condition which is written in the form
\begin{equation}
Z_M = 1 - \widetilde\Pi'_M(m^2_M) = 0,
\label{eq:Z=0}
\end{equation}
where $ \widetilde\Pi'_M(p^2)$ is the derivative of the mass operator
taken on the mass-shell $p^2=m^2_M$.
It is convenient to calculate the derivatives of the meson mass functions
by using the following identities
\begin{eqnarray}
\frac{d}{dp^2} \widetilde\Pi_M(p^2) &=&
\frac{1}{2p^2} p^\mu\frac{d}{dp^\mu} \widetilde\Pi_M(p^2),
\nonumber\\
p^\mu\frac{d}{dp^\mu} S(k + w p)&=& w\, S(k + w p)\not\! p\, S(k + w p).
\label{eq:identity}
\end{eqnarray}
Accordingly the derivatives of the meson mass functions
can be written as
\begin{eqnarray}
\widetilde\Pi'_P(p^2)&=&
\frac{1}{2p^2}\,\frac{3g^2_P}{4\pi^2}\int\!\! \frac{dk}{4\pi^2i}
\widetilde\Phi^2_P \left(-k^2\right)
\nonumber\\
&\times&
\Big\{ w_1\,\mbox{\rm{tr}}\left[ S_1(k+w_1p)\not\!p \,S_1(k+w_1p)\gamma^5
S_2(k-w_2p)\gamma^5\right]
\nonumber\\
&& - w_2\, \mbox{\rm{tr}}\left[ S_1(k+w_1p)\gamma^5 S_2(k-w_2p)\not\!p \,
S_2(k-w_2p)\gamma^5\right]
\Big\},
\label{eq:primeP}\\[1.5ex]
\widetilde\Pi'_V(p^2)&=&
\frac{1}{2p^2}\,\frac13\left(g^{\mu\nu} - \frac{p^\mu p^\nu}{p^2}\right)
\frac{3g^2_V}{4\pi^2}
\int\!\! \frac{dk}{4\pi^2i}\widetilde\Phi^2_V \left(-k^2\right)
\nonumber\\
&\times&
\Big\{ w_1\,\mbox{\rm{tr}}\left[ S_1(k+w_1p)\not\!p \,S_1(k+w_1p)\gamma_\mu
S_2(k-w_2p)\gamma_\nu\right]
\nonumber\\
&& -w_2\,\mbox{\rm{tr}}\left[ S_1(k+w_1p)\gamma_\mu S_2(k-w_2p)\not\!p \,
S_2(k-w_2p)\gamma_\nu\right]\Big\}.
\label{eq:primeV}
\end{eqnarray}
The loop integrations in Eqs.~(\ref{eq:primeP}) and ~(\ref{eq:primeV})
are done with the help of the Fock-Schwinger representation of quark
propagators
\begin{eqnarray}
S_q (k+w p) &=& \frac{1}{ m_q-\not\! k- w \not\! p }
= \frac{m_q + \not\! k + w \not\! p}{m^2_q - (k+w p)^2}
\nonumber\\
&=& (m_q + \not\! k + w \not\! p)\int\limits_0^\infty \!\!d\alpha\,
e^{-\alpha [m_q^2-(k+w p)^2]}.
\label{eq:Fock}
\end{eqnarray}
As will be described later, the use of the Fock-Schwinger representation allows
one to do tensor loop integrals in a very efficient way since one can
convert loop momenta into derivatives of the exponent function
(see, e.g.,~\cite{Faessler:2001mr,Anastasiou:1999bn,Fiorentin:2015vha}).
As mentioned above, all loop integrations are carried out in Euclidean space.
The transition from Minkowski space to Euclidean space is performed
by using the Wick rotation
\begin{equation}
k_0=e^{i\frac{\pi}{2}}k_4=ik_4
\label{eq:Wick}
\end{equation}
so that $k^2=k_0^2-\vec{k}^2=-k_4^2-\vec{k}^2=-k_E^2 \leq 0.$
Simultaneously one has to rotate all external momenta, i.e.
$p_0 \to ip_4$ so that $p^2=-p_E^2 \leq 0$.
Then the quadratic form in Eq.~(\ref{eq:Fock}) becomes positive-definite,
\[
m^2_q-(k+w p)^2=m^2_q + (k_E+w p_E)^2>0,
\]
and the integral over $\alpha$ is absolutely convergent.
We will keep the Minkowski notation to avoid
excessive relabeling. We simply imply that
$k^2 \leq 0$ and $p^2 \leq 0$.
Collecting the representations of the vertex functions
and quark propagators given by Eqs.~(\ref{eq:Gauss})
and (\ref{eq:Fock}), respectively, one can perform the Gaussian
integration in the derivatives of the mass functions
in Eqs.~(\ref{eq:massP}) and (\ref{eq:massV}).
The exponent has the form $ak^2+2kr+z_0$, where $r=b\,p$.
Using the following properties ($k$ is the loop momentum)
\begin{equation}
\left.
\begin{aligned}
k^\mu\, \exp(ak^2+2kr+z_0) &=\frac{1}{2}\frac{\partial }
{\partial r_\mu }\exp(ak^2+2kr+z_0)\\
k^\mu k^\nu\, \exp(ak^2+2kr+z_0) &=
\frac{1}{2}\frac{\partial }{\partial r_\mu }
\frac{1}{2} \frac{\partial }{\partial r_\nu } \exp(ak^2+2kr+z_0)
\\
\text{etc.}&
\end{aligned}
\right\},
\label{eq:change-to-r}
\end{equation}
one can replace
$\not\! k $ by $ {\not\! \partial}_r
= \gamma^\mu\frac{\partial}{\partial r_\mu}$
which allows one to exchange the tensor integrations
for a differentiation of the Gaussian exponent. For example,
Eq.~(\ref{eq:massP}) now has the form
\begin{equation}
\widetilde\Pi_P(p^2) = \frac{3g^2_P}{16\pi^2}
\int\limits_0^\infty\!\! \int\limits_0^\infty\!
\frac{d\alpha_1 d\alpha_2}{a^2}
\,
\mbox{\rm{tr}}\left[\gamma^5 (m_1+{\not\! \partial}_r+w_1\not\!p)\gamma^5
(m_2+{\not\! \partial}_r-w_2\not\!p)\right]
e^{-\frac{r^2}{a}+z_0}.
\label{eq:Pmass2}\,
\end{equation}
The $r$-dependent Gaussian exponent $e^{-r^2/a}$ can be moved to the left
through the differential operator $\not\! \partial_r$ by using the following
properties
\begin{eqnarray}
\frac{\partial}{\partial r_\mu}\,e^{-r^2/a} &=& e^{-r^2/a}
\left[-\frac{2r^\mu}{a}+\frac{\partial}{\partial r_\mu}\right],
\nonumber\\[1.2ex]
\frac{\partial}{\partial r_\mu}\,
\frac{\partial}{\partial r_\nu}\,e^{-r^2/a} &=& e^{-r^2/a}
\left[-\frac{2r^\mu}{a}+\frac{\partial}{\partial r_\mu}\right]\cdot
\left[-\frac{2r^\nu}{a}+\frac{\partial}{\partial r_\nu}\right],
\nonumber\\[1.2ex]
\text{etc.}&&
\label{eq:dif}
\end{eqnarray}
Finally, one has to move the derivatives to the right by using
the commutation relation
\begin{equation}
\left[\frac{\partial}{\partial r_\mu},r^\nu \right]
=g^{\mu\nu}.
\label{eq:comrel}
\end{equation}
The last step has been done by using a \textsc{form} code which
works for any numbers of loops and propagators.
In the remaining integrals over the Fock-Schwinger parameters
$0\le \alpha_i<\infty$
we introduce an additional integration which converts the set of
Fock-Schwinger parameters into a simplex. Using the transformation
\begin{equation}
\prod\limits_{i=1}^n\int\limits_0^{\infty}
\!\! d\alpha_i f(\alpha_1,\ldots,\alpha_n)
=\int\limits_0^{\infty} \!\! dtt^{n-1}
\prod\limits_{i=1}^n \int\!\!d\alpha_i
\delta\left(1-\sum\limits_{i=1}^n\alpha_i\right)
f(t\alpha_1,\ldots,t\alpha_n)
\label{eq:simplex}
\end{equation}
one finds
\begin{eqnarray}
\widetilde\Pi'_M(p^2) &=& \frac{3g^2_M}{4\pi^2}\int\limits_0^{\infty} \!\!
\frac{dt\,t}{a_M^2} \int\limits_0^1\!\!d\alpha\,
e^{-t\,z_0 + z_M}\,f_M(t,\alpha),
\label{eq:prime_fin}\\[2ex]
z_0 &=& \alpha m^2_{q_1} +(1-\alpha)m^2_{q_2} - \alpha(1-\alpha) p^2,
\nonumber\\
z_M &=& \frac{2s_Mt}{2s_M+t} (\alpha-w_2)^2 p^2,
\nonumber\\[2ex]
a_M &=& 2s_M+t , \qquad b = (\alpha-w_2)t.
\nonumber
\end{eqnarray}
The function $f_M(t,\alpha)$ arises from the trace evaluation.
Further, we have introduced the parameter $s_M=1/\Lambda^2_M$.
It is readily seen that the integral over $t$ in Eq.~(\ref{eq:prime_fin})
is well defined and convergent if $z_0>0$, i.e.
below the threshold $p^2< (m_{q_1} + m_{q_2})^2$.
The convergence of the integral in the case of negative
values of $z_0\le 0$, i.e. above threshold
$p^2\ge (m_{q_1} + m_{q_2})^2$,
is guaranteed by the addition of a small imaginary to the quark
mass, i.e. $m_q\to m_q - i\epsilon, \quad \epsilon>0$
in the quark propagator Eq.~(\ref{eq:prop}). It allows one to rotate
the integration variable $t$ to the imaginary axis $t\to i t$.
As a result the integral Eq.~(\ref{eq:prime_fin})
becomes convergent but obtains an imaginary part corresponding to
quark pair production.
However, by cutting the scale integration at the upper limit
corresponding to the introduction of an infrared cutoff
\begin{equation}
\int\limits_0^\infty dt (\ldots) \to \int\limits_0^{1/\lambda^2} dt (\ldots),
\label{eq:conf}
\end{equation}
one can remove all possible thresholds present in the initial quark
diagram \cite{Branz:2009cd}. Thus the infrared cutoff parameter
$\lambda$ effectively guarantees the confinement of quarks within hadrons.
This method is quite general and can be used for diagrams with an arbitrary
number of loops and propagators.
In the CQM the infrared cutoff parameter $\lambda$ is taken to be universal
for all physical processes.
\section{Leptonic B-meson decays}
\label{sec:lepdecays}
The model parameters are determined by fitting calculated quantities
of basic processes to available experimental data or
lattice simulations (for details, see Ref.~\cite{Branz:2009cd},
where a different set of weak and electromagnetic decays has been used).
In this paper we will use the updated least-squares fit
performed in Refs.~\cite{Gutsche:2015mxa,Ganbold:2014pua,Issadykov:2015iba}.
In this fit we have also updated some of the theoretical/experimental
input values. The infrared cutoff parameter $\lambda$ of the model has
been kept fixed. The numerical values of the constituent quark masses
and the parameter $\lambda$ are given by (all in GeV)
\begin{equation}
\def1.1{1.2}
\begin{array}{cccccc}
m_u & m_s & m_c & m_b & \lambda
\\\hline
\ \ 0.241\ \ & \ \ 0.428\ \ & \ \ 1.67\ \ & \ \ 5.04\ \ &
\ \ 0.181\ \
\end{array}
.
\label{eq: fitmas}
\end{equation}
Our prime goal is to study the pure leptonic B meson decays as well as
the semileptonic $B\to D^{(\ast)} \ell\bar\nu_\ell$ decays.
The most recent results of the fit for those parameters
involved in this paper are taken from
our papers \cite{Gutsche:2015mxa,Ganbold:2014pua,Issadykov:2015iba} (all in GeV):
\begin{equation}
\def1.1{1.2}
\begin{tabular}{c c c c c c c c c }
\ \ $\Lambda_{D^*}$ \ \ & \ \ $\Lambda_{D^*_s}$ \ \ &
\ \ $\Lambda_D$ \ \ & \ \ $\Lambda_{D_s}$ \ \ & \ \ $\Lambda_{B^*_s}$ \ \
& \ \ $\Lambda_{B^*}$ \ \ & \ \ $\Lambda_B$ \ \ &
\ \ $\Lambda_{B_s}$ \ \ & \ \ $\Lambda_{B_c}$ \ \
\\\hline
1.53 & 1.56 & 1.60 & 1.75 & 1.79 & 1.81 & 1.96 & 2.05 & 2.73 \\
\end{tabular}
.
\label{eq:sizeparam}
\end{equation}
The matrix elements of the leptonic decays are described by
the Feynman diagram shown in Fig.~\ref{fig:leptonic}.
\begin{figure}[htbp]
\includegraphics[scale=0.6]{fig_leptonic}
\caption{Quark model diagram for the B meson leptonic decay.}
\label{fig:leptonic}
\end{figure}
The leptonic decay constants of the pseudoscalar and vector mesons are
defined~by
\begin{eqnarray}
N_c\, g_P\! \int\!\! \frac{d^4k}{ (2\pi)^4 i}\, \widetilde\Phi_P(-k^2)\,
{\rm tr} \biggl[O^{\,\mu} S_1(k+w_1 p) \gamma^5 S_2(k-w_2 p) \biggr]
&=&f_P p^\mu ,
\nonumber\\
N_c\, g_V\! \int\!\! \frac{d^4k}{ (2\pi)^4 i}\, \widetilde\Phi_V(-k^2)\,
{\rm tr} \biggl[O^{\,\mu} S_1(k+w_1 p)\not\!\epsilon_V S_2(k-w_2 p) \biggr]
&=& m_V f_V \epsilon_V^\mu,
\label{eq:lept}
\end{eqnarray}
where $N_c=3$ is the number of colors, and $O^\mu=\gamma^\mu(1-\gamma_5)$ is
the weak Dirac matrix with left chirality. The mesons are taken on
their mass-shells. The calculation of the matrix elements (\ref{eq:lept})
proceeds in a way similar to the case of the mass functions.
Our results for the leptonic decay constants of $B^{(*)}_{(s)}$ and
$D^{(*)}_{(s)}$
mesons are given in Table~\ref{tab:decayconst}. For comparison, we also list
the values of these constants obtained from experiments, Lattice and QCD sum
rules. Our results show good agreement (within $10\%$) with results of
the other studies. We mention that early attempts to account for flavor symmetry
breaking in pseudoscalar meson decay constants were done
in~\cite{Gershtein:1976aq,Khlopov:1978id}.
\begin{table}[htbp]
\begin{tabular}{c c c c}
\hline\hline
{} & This work & Other & Ref.\\
\hline
$f_B$ & 193.1 & 190.6$\pm$4.7 & PDG~\cite{Agashe:2014kda}\\
$f_{B_s}$ & 238.7 & 242.0(9.5) & LAT~\cite{Bazavov:2011aa}\\
{} & {} & 259(32) & HPQCD LAT~\cite{Gray:2005ad}\\
{} & {} & 193(7) & LAT~\cite{DellaMorte:2007ij}\\
$f_{B_c}$ & 489.0 & $489\pm4\pm3$ & LAT~\cite{Chiu:2007km}\\
$f_{B^*}$ & 196.0 & $196(24)^{+39}_{-2}$ & LAT~\cite{Becirevic:1998ua}\\
{} & {} & $186.4\pm3.2$ & QCDSR~\cite{Lucha:2014nba}\\
$f_{B^*_s}$ & 229.0 & $229(20)^{+41}_{-16}$ & LAT~\cite{Becirevic:1998ua} \\
{} & {} & $215.2\pm3.0$ & QCD SR~\cite{Lucha:2014nba}\\
$f_{B_s}/f_B$ & 1.236 & 1.20(3)(1) & HPQCD LAT~\cite{Gray:2005ad} \\
{} & {} & 1.229(26) & LAT~\cite{Bazavov:2011aa}\\
$f_D$ & 206.1 & 204.6$\pm$5.0 & PDG~\cite{Agashe:2014kda} \\
$f_{D^*}$ & 244.3 & $278\pm13\pm10$ & LAT~\cite{Becirevic:2012ti}\\
{} & {} & $245(20)^{+3}_{-2}$ & LAT~\cite{Becirevic:1998ua} \\
{} & {} & $252.2\pm22.3\pm4$ & QCD SR~\cite{Lucha:2014xla}\\
$f_{D_s}$ & 257.5 & 257.5$\pm$4.6 & PDG~\cite{Agashe:2014kda}\\
$f_{D^*_s}$ & 272.0 & 311$\pm$9 & LAT~\cite{Becirevic:2012ti}\\
{} & {} & $272(16)^{+3}_{-20}$ & LAT~\cite{Becirevic:1998ua}\\
{} & {} & $305.5\pm26.8\pm5$ & QCD SR~\cite{Lucha:2014xla}\\
$f_{D_s}/f_D$ & 1.249 & 1.258$\pm$0.038 & PDG~\cite{Agashe:2014kda}\\
\hline\hline
\end{tabular}
\caption{Results for the leptonic decay constants $f_H$ (in MeV).}
\label{tab:decayconst}
\end{table}
In the SM, the purely leptonic decays $B^- \to \ell^- \bar{\nu}_{\ell}$
proceed via the annihilation of the quark-pair into an off-shell $W$ boson.
The branching fraction for the leptonic decays is given by
\begin{equation}
\mathcal{B}(B^- \to \ell^- \bar{\nu}_{\ell})=
\frac{G_F^2}{8\pi}m_Bm_{\ell}^2\left(1-\frac{m_{\ell}^2}{m_B^2}\right)^2
f_B^2|V_{ub}|^2\tau_B,
\end{equation}
where $G_F$ is the Fermi coupling constant, $m_B$ and $m_{\ell}$ are the $B$
meson and lepton masses, respectively, and $\tau_B$ is the $B$ meson life time.
The expected branching fractions are $O(10^{-4})$, $O(10^{-7})$, and
$O(10^{-11})$ for $\ell = \tau, \mu,$ and $e$, respectively.
The different lepton masses affect the values of the
branching fractions through the helicity flip factor
$\left(1-m_\ell^2/m_B^2\right)^2$.
\begin{table}
\begin{center}
\def1.1{1.1}
\begin{tabular}{lccr}
\hline\hline
& This work & Data & Ref.\\
\hline
\quad $B^- \to e^- \bar{\nu}_e $ \quad
& \quad $ 1.16\cdot 10^{-11} $ \quad
& \quad $< 9.8 \cdot 10^{-7} $ \quad
& \quad PGD~\cite{Agashe:2014kda} \quad
\\
\quad\quad & \quad \quad
&\quad $ (0.88 \pm 0.12)\cdot 10^{-11} $ \quad
& \quad UTfit~\cite{Bona:2009cj}\quad
\\
\quad \quad & \quad\quad
& \quad $ (0.85\pm 0.27 )\cdot 10^{-11} $\quad
&\quad CKMfitter~\cite{Charles:2004jd} \quad
\\[1.2ex]
\quad $B^- \to {\mu}^- \bar{\nu}_{\mu}$ \quad
& \quad $ 0.49\cdot 10^{-6} $ \quad
& \quad $< 1.0$ $\cdot 10^{-6}$ \quad
& \quad PGD~\cite{Agashe:2014kda} \quad
\\
\quad\quad &\quad \quad
&\quad $ (0.38 \pm 0.05)\cdot 10^{-6} $\quad
& \quad UTfit~\cite{Bona:2009cj}\quad
\\
\quad\quad & \quad \quad
&\quad $ (0.37 \pm 0.02)\cdot 10^{-6} $ \quad
& \quad CKMfitter~\cite{Charles:2004jd}\quad
\\[1.2ex]
\quad $B^- \to {\tau}^- \bar{\nu}_{\tau}$ \quad
& \quad $ 1.10 \cdot 10^{-4} $ \quad
& \quad $ (1.14 \pm 0.27)\cdot 10^{-4}$ \quad
& \quad PGD~\cite{Agashe:2014kda} \quad \\
\hline\hline
\end{tabular}
\end{center}
\caption{Leptonic B-decay branching fractions.}
\label{tab:leptBr}
\end{table}
\section{Form factors of semileptonic B-meson decays}
The invariant matrix element of the semileptonic decays
$B\to D^{(\ast)} \ell^- \bar\nu_\ell$ can be written as
\begin{equation}
M(B\to D^{(\ast)} \ell^- \bar\nu_\ell ) =
\frac{G_F}{\sqrt{2}} V_{cb}
<D^{(\ast)}\,|\,\bar{c}\,O^\mu\, b\,|\,B>\,
\bar\ell O_\mu \nu_\ell ,
\end{equation}
where the matrix elements of the semileptonic $B \to D^{(\ast)}$ transitions
in the covariant quark model are defined by the diagram
in Fig.~\ref{fig:semilept}
\begin{figure}[htbp]
\includegraphics[scale=0.5]{fig_diag}
\caption{Quark model diagram for B meson semileptonic decay.}
\label{fig:semilept}
\end{figure}
and are written as
\begin{eqnarray}
&&
T^\mu \equiv
\langle D(p_2)\,
|\,\bar c\, O^{\,\mu}\, b\,
| B(p_1) \rangle
\,=\,
\nonumber\\[1.2ex]
&=&
N_c\, g_B\,g_D\!\! \int\!\! \frac{d^4k}{ (2\pi)^4 i}\,
\widetilde\Phi_B\Big(-(k+w_{13} p_1)^2\Big)\,
\widetilde\Phi_{D}\Big(-(k+w_{23} p_2)^2\Big)
\nonumber\\
&\times&
\mbox{\rm{tr}} \biggl[
O^{\,\mu}\, S_1(k+p_1)\, \gamma^5\, S_3(k)\, \gamma^5\, S_2(k+p_2)
\biggr]
\nonumber\\[1.2ex]
& = & F_+(q^2)\, P^{\,\mu} + F_-(q^2)\, q^{\,\mu},\quad \text{and}
\label{eq:PP'}\\[1.5ex]
&&
\epsilon^\dagger_{2\,\alpha} T^{\mu\alpha} \equiv
\langle D^\ast(p_2,\epsilon_2)\,
|\,\bar c\, O^{\,\mu}\,b\, |\,B(p_1)
\rangle
\,=\,
\nonumber\\[1.2ex]
&=&
N_c\, g_B\,g_{D^\ast} \!\! \int\!\! \frac{d^4k}{ (2\pi)^4 i}\,
\widetilde\Phi_B\Big(-(k+w_{13} p_1)^2\Big)\,
\widetilde\Phi_{D^\ast}\Big(-(k+w_{23}p_2)^2\Big)
\nonumber\\
&\times&
\mbox{\rm{tr}} \biggl[
O^{\,\mu} \,S_1(k+p_1)\,\gamma^5\, S_3(k) \not\!\epsilon_2^{\,\,\dagger} \,
S_2(k+p_2)\, \biggr]
\nonumber\\[1.2ex]
& = &
\frac{\epsilon^{\,\dagger}_{2\,\alpha}}{m_1+m_2}\,
\left( - g^{\mu\alpha}\,Pq\,A_0(q^2) + P^{\,\mu}\,P^{\,\alpha}\,A_+(q^2)
+ q^{\,\mu}\,P^{\,\alpha}\,A_-(q^2)
+ i\,\varepsilon^{\mu\alpha P q}\,V(q^2)\right).
\label{eq:PV}
\end{eqnarray}
Here, $P=p_1+p_2$, \,$q=p_1-p_2$, and $\epsilon_2$ is the polarization vector
of the $D^\ast$ meson so that $\epsilon_2^\dagger\cdot p_2=0$.
The particles are on their mass-shells: $p_1^2=m_1^2=m_B^2$ and
$p_2^2=m_2^2=m_{D^{(\ast)}}^2$.
Altogether there are three flavors of quarks involved in these
processes. We therefore introduce a notation with two subscripts
$w_{ij}=m_{q_j}/(m_{q_i}+m_{q_j})$ $(i,j=1,2,3)$ such that $w_{ij}+w_{ji}=1$.
In our case one has $q_1=b$, $q_2=c$, and $q_3=d$.
Our numerical results for the form factors are well represented
by a double--pole parametrization
\begin{equation}
F(q^2)=\frac{F(0)}{1 - a s + b s^2}, \quad s=\frac{q^2}{m_1^2}.
\label{eq:DPP}
\end{equation}
The double--pole approximation is quite accurate. The error
relative to the exact results is less than $1\%$ over the entire $q^{2}$
range.
For the $B \to D^{(\ast)}$ transition the parameters of the dipole
approximation are given by
\begin{equation}
\begin{array}{c|rr|rrrr}
& \quad F_+ \quad & \quad F_- \quad & \quad A_0 \quad & \quad A_+ \quad &
\quad A_- \quad & \quad V \quad \\[1.1ex]
\hline
F(0) & 0.78 & -0.36 & 1.62 & 0.67 & -0.77 & 0.77
\\[1ex]
a & 0.74 & 0.76 & 0.34 & 0.87 & 0.89 & 0.90
\\[1ex]
b & 0.038 & 0.046 & -0.16 & 0.057 & 0.070 & 0.075.
\\[1.1ex]
\hline
\end{array}
\label{eq:ff_param}
\end{equation}
\vspace{1.2ex}
Since $b/a$ is quite small for the form factors $F_{+},\,F_{-},\,A_+,\,A_-$,
and $V$, these form factors show a monopole-like falloff behavior
whereas $A_{0}$ has a substantial $(q^{2})^{-2}$ contribution.
In Fig.~\ref{fig:formfactors} we present our results for the semileptonic
form factors within the full range of momentum transfer
$0\le q^2 \le q^2_{\rm max}$, where $q^2_{\rm max}=(m_B-m_{D^{(*)}})^2$.
The results of the exact calculations are shown by solid lines
whereas the results obtained in the heavy quark limit are
shown by dashed lines. We will discuss the heavy quark limit in
the next section.
\begin{figure}[htbp]
\begin{tabular}{lr}
\includegraphics[scale=0.6]{Fp} &
\includegraphics[scale=0.6]{Fm}\\
\includegraphics[scale=0.6]{A0}&
\includegraphics[scale=0.6]{Ap}\\
\includegraphics[scale=0.6]{Am}&
\includegraphics[scale=0.6]{V}\\
\end{tabular}
\caption{Form factors of the decays $B \to D^{(*)} \ell \nu$.
The solid lines are the results of exact calculations in our approach,
the dashed lines are the form factors obtained in the heavy quark limit. }
\label{fig:formfactors}
\end{figure}
It is interesting to note that the QCD counting rules prescribe a
$(q^{2})^{-1}$ and a $(q^{2})^{-2}$ falloff behavior for the form factors
$F_{+},\,F_{-},\,A_{0}$ and $A_+,\,A_-,V$, respectively.
As recently noticed in~\cite{Becirevic:2012jf}, the ratio
$F_0(q^2)/F_+(q^2)$ exhibits a linear $q^2$ behavior
\begin{equation}
F_0(q^2) = F_+(q^2) + \frac{q^2}{Pq}\,F_-(q^2),
\qquad
\frac{F_0(q^2)}{F_+(q^2)} = 1-\alpha q^2,
\label{FFlinear}
\end{equation}
where the slope $\alpha=0.020(1)~\text{GeV}^{-2}$ was determined precisely
based on lattice values of the two form factors.
We also plot the $q^2$ dependence of the ratio
$F_0(q^2)/F_+(q^2)$ in Fig.~\ref{fig:formfactorRate},
which shows a linear behavior as mentioned. Our value for the slope
is $\alpha=0.019~\text{GeV}^{-2}$ which very well agrees with
the lattice result.
\clearpage
\begin{figure}[htbp]
\includegraphics[scale=0.6]{F0Fp-ratio}
\caption{Ratio $F_0(q^2)/F_+(q^2)$.}
\label{fig:formfactorRate}
\end{figure}
\section{Heavy quark limit}
It is instructive to explore the heavy quark limit (HQL) in the heavy-to-heavy
transition $B\to D(D^\ast)$. In the HQL one takes
the limit $m_B=m_b + E,\,\,\,m_b\to\infty $ and
$m_D=m_{D^\ast}=m_c + E,\,\,\,m_c\to\infty $
in the expressions for the coupling constants and form factors.
In this limit the heavy quark propagators are reduced to the static form
\begin{eqnarray}
S_b(k+p_1)&=&\frac{1}{m_b-\!\not\! k - \!\not\! p_1 }\to
\frac{1+\not\! v_1}{-2kv_1-2 E} + O\left(\frac{1}{m_b}\right),
\nonumber\\
S_c(k+p_2)&=&\frac{1}{m_c-\!\not\! k - \!\not\! p_2 }\to
\frac{1+\not\! v_2}{-2kv_2-2 E} + O\left(\frac{1}{m_c}\right),
\label{eq:prop_HQL}
\end{eqnarray}
where $p_i$ and $v_i=p_i/m_i$ ($i=1,2$) are the momenta and
the four-velocities of the initial and final states.
Moreover, we have to keep the size parameters of heavy hadrons equal to
each other in order to provide the correct normalization
of the Isgur-Wise function at zero recoil.
By using technique developed in our previous papers, see, for instance,
\cite{Ivanov:1992wx,Ivanov:1998ms}, one can arrive at the following
expressions for the semileptonic heavy-to-heavy transitions
defined by Eqs.~(\ref{eq:PP'}) and ~(\ref{eq:PV})
\begin{eqnarray}
T^\mu_{\rm HQL} &=&
\xi(w)\cdot
\tfrac14\mbox{\rm{tr}}\Big[O^\mu(1+\not\! v_1)\gamma^5\cdot\gamma^5(1+\not\! v_2)\Big]
=\xi(w)\cdot(v_1^\mu + v_2^\mu),
\label{eq:PP'-HQL}\\[1.5ex]
\epsilon^\dagger_{2\,\nu} T^{\mu\nu}_{\rm HQL} &=&
\xi(w)\cdot
\tfrac14\mbox{\rm{tr}}\Big[O^\mu(1+\not\! v_1)\gamma^5\cdot
\not\!\epsilon_2^{\,\dagger}(1+\not\! v_2)\Big]
\nonumber\\
&=&\xi(w)\cdot\epsilon^\dagger_{2\,\nu}
( -g^{\mu\nu}(1+w) + v_1^\mu v_2^\nu + v_1^\nu v_2^\mu
- i\,\varepsilon^{\mu\nu v_1 v_2} ).
\label{eq:PV-HQL}
\end{eqnarray}
Here, $w=v_1v_2$, and the Isgur-Wise function is equal to
\begin{equation}
\xi(w) = \frac{J_3(E,w)}{J_3(E,1)}, \qquad
J_3(E,w) = \int\limits_0^1 \frac{d\tau}{W}
\int\limits_0^\infty\!\! du\, \widetilde\Phi^2(z)
\left( \sigma_S(z) + \sqrt{\frac{u}{W}} \sigma_V(z) \right),
\label{eq:IW}
\end{equation}
where $W=1+2\tau(1-\tau)(w-1)$, $z=u - 2 E \sqrt{u/W}$, and
\[
\widetilde\Phi(z) = \exp(-z/\Lambda^2), \qquad
\sigma_S(z) = \frac{m_u}{m_u^2 +z}, \qquad
\sigma_V(z) = \frac{1}{m_u^2 +z}.
\]
By using the definition of the form factors given by
Eqs.~(\ref{eq:PP'}) and ~(\ref{eq:PV}) one can easily obtain
the expressions of the form factors in the HQL. One finds
\begin{eqnarray}
F_\pm(q^2) &=& \pm\frac{m_1 \pm m_2}{2\sqrt{m_1m_2}}\,\xi(w),
\nonumber\\
A_0(q^2) &=& \frac{\sqrt{m_1 m_2}}{m_1 - m_2} (1+w)\xi(w),
\quad
A_+(q^2) = - A_-(q^2) = V(q^2) = \frac{m_1 + m_2}{2\sqrt{m_1m_2}}\,\xi(w),
\end{eqnarray}
where $w=(m_1^2+m_2^2-q^2)/(2m_1m_2)$. We use the physical masses
of the heavy hadrons in the numerical calculations. For the size
parameter we adopt the average value
$\Lambda=(\Lambda_B+\Lambda_D+\Lambda_{D^\ast})/3= 1.70$~GeV.
The parameter $E$ characterizes the difference in mass between the heavy hadron and
the corresponding heavy quark. We use its minimal value $E=m_D-m_c=0.20$~GeV
in order to avoid the complication with confinement.
In Fig.~\ref{fig:formfactors} we display the heavy-to-heavy transition
form factors calculated in the HQL and compare them with the results
of exact calculations. One can see that the two results obtained with and without use of the HQL behave very similar to each other which demonstrates the fidelity of HQET.
One can also consider the near zero-recoil behavior of the form factors
in a similar way as we did in our paper on the semileptonic decay
$\Lambda_b\to \Lambda_c + \tau\bar\nu_\tau$~\cite{Gutsche:2015mxa}.
The standard parametrization of the $(w-1)$ expansion takes the form
\[
F(q^2(w)) = F(q^2_{\rm max})\,\Big[1 - \rho^2 (w-1)+c\,(w-1)^2 + \ldots
\Big],
\]
where $\rho^2$ is called the slope parameter and $c$ the convexity parameter.
The numerical results are given below
\begin{equation}
\begin{array}{c|rr|rrrr}
& \quad F_+ \quad & \quad F_- \quad & \quad A_0 \quad & \quad A_+ \quad &
\quad A_- \quad & \quad V \quad \\[1.1ex]
\hline
F(q^{2}_{\rm max}) & 1.12 & -0.52 & 1.91 & 0.99 & -1.15 & 1.16
\\[1ex]
\rho^2 & 0.72 & 0.74 & 0.42 & 0.93 & 0.95 & 0.96
\\[1ex]
c & 0.49 & 0.51 & 0.28 & 0.82 & 0.85 & 0.86
\\[1.1ex]
\hline
\end{array}
\label{eq:zerorecoil}
\end{equation}
\vspace{1.2ex}
which may be compared with the results obtained
for the monopole form factor of a $B_c$-resonance contribution:
$\rho^2$=0.71 and $c=0.51$.
It is interesting to compare the zero-recoil values of our exact form factors
with the predictions of leading order HQET at $w=1$ where $\xi(1)=1$.
One has
\begin{eqnarray}
F_{+}&=&\frac{m_{1}+m_{2}}{2\sqrt{m_{1}m_{2}}}=1.138, \qquad
F_{-}=-\frac{m_{1}-m_{2}}{2\sqrt{m_{1}m_{2}}}=-0.543,
\nonumber\\[1.2ex]
A_+ &=& -A_{-} = V =\frac{m_{1}+m_{2}}{2\sqrt{m_{1}m_{2}}}=1.119, \qquad
A_0 = \frac{2\sqrt{m_{1}m_{2}}}{m_{1}-m_{2}}=1.993.
\end{eqnarray}
The zero-recoil values of our model form factors can be seen to be quite
close to the corresponding HQET values except for the form factor $A_{+}$
where our form factor value exceeds the HQET result by $\sim 13\, \%$.
\section{Helicity amplitudes and two-fold distributions}
Let us first consider the polar angle differential decay distribution
in the momentum transfer squared $q^2$. The polar angle is defined
by the angle between $\vec q=\vec p_1-\vec p_2$ and the three-momentum of
the charged lepton $\vec k_1$ in the ($\ell^-\bar\nu_\ell$) rest frame as
shown in Fig.~\ref{fig:bkangl}. One has
\begin{equation}
\frac{d^2\Gamma}{dq^2 d\cos\theta} =
\frac{|{\bf p_2}| \, v}{(2\pi)^3\,32\,m_1^2}
\cdot\sum\limits_{\rm pol}|M|^2
=\frac{G^2_F}{(2\pi)^3}\,|V_{cb}|^2
\frac{|{\bf p_2}|\,v }{64 m_1^2}
H^{\mu\nu} L_{\mu\nu}\,,
\label{eq:2-fold-dis}
\end{equation}
where $|{\bf p_2}|=\lambda^{1/2}(m_1^2,m_2^2,q^2)/2m_1 $
is the momentum of the daughter meson and where we have introduced the
velocity-type parameter $v=1-m_\ell^2/q^2$ as well as the contraction
of hadron and lepton tensors $H^{\mu\nu}L_{\mu\nu}$.
\begin{figure}[htbp]
\begin{center}
\epsfig{figure=bkangl,scale=.6}
\caption{Definition of angles $\theta$, $\theta^\ast$, and $\chi$ in
the cascade decay $\bar B^0\to D^{\ast\,+}(\to D^0\pi^+)\ell^-\bar\nu_\ell$.}
\label{fig:bkangl}
\end{center}
\end{figure}
As discussed in some detail in~\cite{Gutsche:2015mxa}
the covariant contraction $H^{\mu\nu} L_{\mu\nu}$ can be converted to a sum
of bilinear products of hadronic and leptonic helicity amplitudes using the
completeness relation for the polarization four-vectors of the process.
A synopsis of the necessary steps in this transformation is provided in
the Appendix.
One needs to relate the mesonic helicity amplitudes to the
invariant form factors defined in Eqs.~(\ref{eq:PP'}) and (\ref{eq:PV}).
To do so one requires explicit representations of the polarization
four-vectors $\epsilon^{\mu}(\lambda_{W})$. They read
\begin{equation}
\epsilon^\mu(t) =
\frac{1}{\sqrt{q^2}}(q_0,0,0,|{\bf p_2}|\,),\quad
\epsilon^\mu(\pm) =
\frac{1}{\sqrt{2}}(0,\mp 1,-i,0), \quad
\epsilon^\mu(0) =
\frac{1}{\sqrt{q^2}}(\,|{\bf p_2}|,0,0,q_0).
\end{equation}
The linear relations between the two sets of form factors can then
be calculated in the following way. \\[1.2ex]
\noindent
{\boldmath{$B\to D$} \,\,\,\bf transition:}\\
The helicity amplitudes are defined by
$H_{\lambda_{W}} = \epsilon^{\dagger \mu}(\lambda_{W})T_\mu$.
One obtains
\begin{equation}
H_t = \frac{1}{\sqrt{q^2}}(Pq\, F_+ + q^2\, F_-),
\qquad
H_\pm = 0,
\qquad
H_0 = \frac{2\,m_1\,|{\bf p_2}|}{\sqrt{q^2}} \,F_+.
\label{eq:hel_pp}
\end{equation}
Note the zero-recoil relation $H_{0}=0$. At the other end of the spectrum
at maximal recoil $q^{2}=0$ one has $H_{t}=H_{0}$.
In the Appendix we describe how to obtain the differential
$(q^2,\cos\theta)$ distribution. One has
\begin{eqnarray}
\lefteqn{\frac{d\Gamma(B\to D \ell^-\bar\nu_\ell)}{dq^2d\cos\theta}
\ =\ \,\frac{G_F^2 |V_{cb}|^2 |{\bf p_2}| q^2 v^2}{32 (2\pi)^3 m_1^2}}\nonumber\\
&& \hspace{2cm} \times \Big\{
2\,\sin^2\theta\,{\cal H}_L
+ 2\,\delta_\ell \left(
2\,\cos^2\theta\,{\cal H}_L
+ 2\,{\cal H}_S - 4\,\cos\theta\,{\cal H}_{SL} \right)
\Big\},
\label{eq:distr2}
\end{eqnarray}
where we have introduced the helicity flip penalty factor
$\delta_\ell = m^2_\ell/2q^2$ and the helicity
structure functions ${\cal H}_L = |H_{ 0}|^2 $,
${\cal H}_S = |H_{ t}|^2$,
and ${\cal H}_{SL} = {\rm Re}( H_{0} H_{t}^\dagger ) $. \\
\noindent
{\boldmath$B\to D^\ast$ \,\,\bf transition:}\\
The helicity amplitudes are defined by
$H_{\lambda_{W}\,\lambda_{D^{\ast}}} = \epsilon^{\dagger \mu}(\lambda_{W})
\epsilon_2^{\dagger\alpha}(\lambda_{D^{\ast}})T_{\mu \alpha}$.
In addition to the $W_{\rm off-shell}$ polarization four-vectors
$\epsilon^{\mu}(\lambda_{W})$
one needs the polarization four-vectors
$\epsilon^\alpha_2(\lambda_{D^{\ast}})$ of the $D^{\ast}$. They
read ($E_{2}=m_{1}-q_{0}$)
\begin{equation}
\epsilon^\alpha_2(\pm) =
\frac{1}{\sqrt{2}}(0\,,\,\,\pm 1\,,\,\,-i\,,\,\,0\,)\,,
\qquad
\epsilon^\alpha_2(0) =
\frac{1}{m_2}(|{\bf p_2}|\,,\,\,0\,,\,\,0\,,\,\,-E_2\,).
\label{eq:vect_pol}
\end{equation}
One obtains
\begin{eqnarray}
H_{t0} &=&
\epsilon^{\dagger \mu}(t)\epsilon_2^{\dagger \alpha}(0)T_{\mu\alpha}
\,=\,
\frac{1}{m_1+m_2}\frac{m_1\,|{\bf p_2}|}{m_2\sqrt{q^2}}
\left(Pq\,(-A_0+A_+)+q^2 A_-\right),
\nonumber\\[1.2ex]
H_{\pm1\pm1} &=&
\epsilon^{\dagger \mu}(\pm)\epsilon_2^{\dagger \alpha}(\pm)T_{\mu\alpha}
\,=\,
\frac{1}{m_1+m_2}\left(-Pq\, A_0\pm 2\,m_1\,|{\bf p_2}|\, V \right),
\nonumber\\[1.2ex]
H_{00} &=&
\epsilon^{\dagger \mu}(0)\epsilon_2^{\dagger \alpha}(0)T_{\mu\alpha}
\nonumber\\
&=&
\frac{1}{m_1+m_2}\frac{1}{2\,m_2\sqrt{q^2}}
\left(-Pq\,(m_1^2 - m_2^2 - q^2)\, A_0 + 4\,m_1^2\,|{\bf p_2}|^2\, A_+\right).
\label{eq:hel_vv}
\end{eqnarray}
Note the zero-recoil relations $H_{t0}=0$ and $H_{\pm1\pm1}=H_{00}$.
At maximal recoil $q^{2}=0$ the dominating helicity amplitudes are
$H_{t0}$ and $H_{00}$ with $H_{t0}=H_{00}$.
The differential $(q^2,\cos\theta)$ distribution finally reads (see the
Appendix)
\begin{eqnarray}
\frac{d\Gamma(B\to D^{\ast} \ell^-\bar\nu_\ell)}{dq^2d(\cos\theta)} &=&\,
\frac{G_F^2 |V_{cb}|^2 |{\bf p_2}| q^2 v^2}{32 (2\pi)^3 m_1^2}
{\rm Br}(D^\ast\to D\pi)
\nonumber\\
&\times& \Big\{
(1+\cos^2\theta)\,{\cal H}_U + 2\,\sin^2\theta\,{\cal H}_L
-2\,\cos\theta\,{\cal H}_P
\nonumber\\
&+& 2\,\delta_\ell \left( \sin^2\theta\,{\cal H}_U
+ 2\,\cos^2\theta\,{\cal H}_L
+ 2\,{\cal H}_S - 4\,\cos\theta\,{\cal H}_{SL} \right)
\Big\}.
\label{eq:distrII}
\end{eqnarray}
We have used the zero width approximation for the $D^\ast$ intermediate state
which brings in the branching fraction ${\rm Br}(D^\ast\to D\pi)$.
The relevant bilinear combinations of the helicity amplitudes
are defined in Table~\ref{tab:bilinears}. We have dropped
a factor of ``3'' in the definition of ${\cal H}_S$ and ${\cal H}_{IS}$
compared to our paper \cite{Faessler:2002ut}. Note that the
helicity structure functions satisfy the zero-recoil relations
$2{\cal H}_U={\cal H}_L={\cal H}_T={\cal H}_I$ and
${\cal H}_P={\cal H}_A={\cal H}_S={\cal H}_{SA}={\cal H}_{ST}={\cal H}_{S}=0$.
Similar relations hold for the imaginary parts. At maximal recoil one has
${\cal H}_L={\cal H}_S={\cal H}_{SL}$ for the dominating helicity structure
functions.
\begin{table}[htbp]
\begin{center}
\caption{ Definition of helicity structure functions and their parity
properties for the case \newline
$B\to D^{\ast} \ell^-\bar\nu_\ell$.}
\def1.1{1}
\begin{tabular}{ll}
\hline
parity-conserving (p.c.) \qquad & \qquad parity-violating (p.v.) \\
\hline
${\cal H}_U = |H_{+1 +1}|^2 + |H_{-1 -1}|^2$ \qquad & \qquad
${\cal H}_P = |H_{+1 +1}|^2 - |H_{-1 -1}|^2$ \\
${\cal H}_L = |H_{0 0}|^2 $ \qquad & \qquad
${\cal H}_{A} = \tfrac 12 {\rm Re}\left( H_{+1 +1} H_{0\, 0}^\dagger
- H_{-1 -1} H_{0\,0}^\dagger \right)$
\\
${\cal H}_{T} ={\rm Re}\left( H_{+1+1}H_{-1-1}^{\dagger}\right)$
\qquad & \qquad
${\cal H}_{IA} = \tfrac 12 {\rm Im}\left( H_{+1 +1} H_{0\, 0}^\dagger
- H_{-1 -1} H_{0\,0}^\dagger \right)$
\\
${\cal H}_{IT} ={\rm Im}\left( H_{+1+1}H_{-1-1}^{\dagger}\right)$
\qquad & \qquad
${\cal H}_{SA} = \tfrac 12 \, {\rm Re}\left( H_{+1 +1} H_{0\, t}^\dagger
- H_{-1 -1} H_{0\,t}^\dagger \right)$
\\
${\cal H}_{I} = \tfrac 12 \, {\rm Re}\left( H_{+1 +1} H_{0\, 0}^\dagger
+ H_{-1 -1} H_{0\,0}^\dagger \right)$
\qquad & \qquad
${\cal H}_{ISA} = \tfrac 12 \, {\rm Im}\left( H_{+1 +1} H_{0\, t}^\dagger
- H_{-1 -1} H_{0\,t}^\dagger \right)$
\\
${\cal H}_{II} = \tfrac 12 \, {\rm Im}\left( H_{+1 +1} H_{0\, 0}^\dagger
+ H_{-1 -1} H_{0\,0}^\dagger \right)$
\qquad & \qquad
\\
${\cal H}_S = |H_{0 t}|^2$ \qquad & \qquad
\\
${\cal H}_{ST} = \tfrac 12 \,{\rm Re}\left( H_{+1 +1} H_{0\, t}^\dagger
+ H_{-1 -1} H_{0\,t}^\dagger \right)$
\qquad & \qquad
\\
${\cal H}_{IST} = \tfrac 12 \,{\rm Im}\left( H_{+1 +1} H_{0\, t}^\dagger
+ H_{-1 -1} H_{0\,t}^\dagger \right)$
\qquad & \qquad
\\
${\cal H}_{SL} = {\rm Re}\left( H_{0\,0} H_{0\,t}^\dagger \right) $
\qquad & \qquad
\\
${\cal H}_{ISL} = {\rm Im}\left( H_{0\,0} H_{0\,t}^\dagger \right) $
\qquad & \qquad
\\
${\cal H}_{\rm tot} = {\cal H}_U+{\cal H}_L+\delta_{\ell}\Big(
{\cal H}_U+{\cal H}_L+3{\cal H}_S \Big) $
\qquad & \qquad
\\[2ex]
\hline
\end{tabular}
\label{tab:bilinears}
\end{center}
\end{table}
Let us begin discussing the $\cos\theta$ distribution for the
$B \to D^{\ast}\ell^{-}\bar \nu_{\ell}$ case.
The distribution~(\ref{eq:distr2}) is described by a
tilted parabola whose normalized form reads
\begin{equation}
\widetilde W(\theta)=\frac{a+b\cos\theta+c\cos^{2}\theta}{2(a+c/3)}.
\end{equation}
The linear
coefficient $b/2(a+c/3)$ can be projected out by defining a
forward-backward asymmetry given by \footnote{We take this opportunity to
correct a typo in~\cite{Gutsche:2015mxa}. The factor $-3/2$ in~Eq.~(38) of
\cite{Gutsche:2015mxa} should read $-3/4$. }
\begin{eqnarray}
\mathcal{A}_{FB}(q^2) =
\frac{d\Gamma(F)-d\Gamma(B)}{d\Gamma(F)+d\Gamma(B)}
&=&
\frac{ \int_{0}^{1} d\!\cos\theta\, d\Gamma/d\!\cos\theta
-\int_{-1}^{0} d\!\cos\theta\, d\Gamma/d\!\cos\theta }
{ \int_{0}^{1} d\!\cos\theta\, d\Gamma/d\!\cos\theta
+\int_{-1}^{0} d\!\cos\theta\, d\Gamma/d\!\cos\theta}
\nonumber\\[1.2ex]
&=& \frac{b}{2(a+c/3)}=-\frac34 \frac{{\cal H}_P\,
+4\,\delta_\ell\,{\cal H}_{SL}}{{\cal H}_{\rm tot}}.
\label{fbAsym}
\end{eqnarray}
In the $\tau$ mode there are two sources of the parity-odd forward-backward
asymmetry, namely, a purely parity-violating source from the VA interaction
leading to the ${\cal H}_P$ contribution, and a parity-conserving source from
the VV and AA interactions leading to the ${\cal H}_{SL}$ contribution.
The parity-conserving parity-odd contribution ${\cal H}_{SL}$ arises from the
interference of the $(0^{+};1^{-})$ and $(0^{-};1^{+})$ components of the
$VV$ and
$AA$ product of currents, respectively. In the case of the
$B \to D$ transition the forward-backward asymmetry arises solely from the
$(0^{+};1^{-})$ interference term of the $VV$ product of currents.
The coefficient $c/2(a+c/3)$ of the quadratic contribution is obtained
by taken the second derivative of $\widetilde W(\theta)$. Accordingly we
define a convexity parameter by writing
\begin{equation}
C_F^\ell(q^2) = \frac{d^{2}\widetilde W(\theta)}{d(\cos\theta)^{2}}
= \frac{c}{a+c/3}
= \frac34 (1-2\delta_\ell)
\frac{ {\cal H}_U - 2 {\cal H}_L }{ {\cal H}_{\rm tot} }.
\label{eq:convex_lep}
\end{equation}
When calculating the $q^{2}$ averages of the forward-backward asymmetry
and the convexity parameter one
has to multiply the numerator and denominator of (\ref{fbAsym}) and
(\ref{eq:convex_lep}) by the
$q^{2}$-dependent piece of the phase space factor in~(\ref{eq:distr2})
given by
$
C(q^2) = |\mathbf{p_2}| q^2 v^2.
$
For example, the mean forward-backward asymmetry can then be calculated
according to
\begin{equation}
\langle \mathcal{A}_{FB}\rangle = -\frac34 \,\,
\frac{\int dq^{2} C(q^{2})\big({\cal H}_P\,+4\,\delta_\ell\,{\cal H}_{SL}\big)}
{\int dq^{2} C(q^{2}){\cal H}_{\rm tot}}.
\label{eq:FBint}
\end{equation}
Finally, integrating Eq.~(\ref{eq:distr2}) over $\cos\theta$ one obtains
\begin{equation}
\frac{d\Gamma(B\to D^{(\ast)} \ell^-\bar\nu_\ell)}{dq^2} =\,
\frac{G_F^2 |V_{cb}|^2 |{\bf p_2}| q^2 v^2}{12 (2\pi)^3 m_1^2}
\,\,{\rm Br}(D^\ast\to D\pi)\,\,\cdot{\cal H}_{\rm tot},
\label{eq:distr1}
\end{equation}
where ${\cal H}_{\rm tot} = {\cal H}_U+{\cal H}_L+\delta_{\ell}\Big(
{\cal H}_U+{\cal H}_L+3{\cal H}_S \Big) $.
The discussion of the $\cos\theta$ distribution for the
$B \to D\ell^{-}\bar \nu_{\ell}$ case proceeds in a similar way except that
one has to drop the contributions of the helicity structure functions
${\cal H}_U$ and ${\cal H}_P$.
\section{Four-fold angular decay distribution}
The lepton-hadron correlation function $L_{\mu\nu}H^{\mu\nu}$ reveals
even more structures when one uses the cascade decay
$\bar{B}^0\to D^{\ast\,+}(\to D^0\pi^+) \ell^-\bar\nu_\ell$ to analyze the
polarization of the $D^\ast$ meson. The derivation of the four-fold angular
decay distribution is detailed in Appendix A. One has
\begin{equation}
\frac{d\Gamma(\bar{B}^0\to D^{\ast\,+}(\to D^0\pi^+) \ell^-\bar\nu_\ell)}
{dq^2\,d\cos\theta\,d(\chi/2\pi)\,d\cos\theta^\ast}
=
\frac{G_F^2}{(2\pi)^3}\frac{ |V_{cb}|^2 |{\bf p_2}| q^2 v^2}{12 m_1^2}\,
{\rm Br}(D^\ast\to D\pi)\,W(\theta^\ast,\theta,\chi),
\label{eq:four-width}
\end{equation}
where
\begin{eqnarray}
W(\theta^\ast,\theta,\chi) &=&
\,\, \frac{9}{32}\,(1+\cos^2\theta)\,\sin^2\theta^\ast\,{\cal H}_U
+ \frac{9}{8}\,\sin^2\theta\,\cos^2\theta^\ast\,{\cal H}_L
- \frac{9}{16}\,\cos\theta\,\sin^2\theta^\ast\,{\cal H}_P
\nonumber\\[1.2ex]
&&\,-\,\frac{9}{16}\,\sin^2\theta\,\sin^2\theta^\ast\,\cos 2\chi\, {\cal H}_T
-\,\frac{9}{8}\, \sin\theta\,\sin 2\theta^\ast\,\cos\chi\, {\cal H}_A
\nonumber\\[1.2ex]
&&
+\,\frac{9}{16}\,\sin 2\theta\,\sin 2\theta^\ast\,\cos\chi\, {\cal H}_I
+\,\frac{9}{8}\,\sin\theta\,\sin 2\theta^\ast\,\sin\chi\, {\cal H}_{II}
\nonumber\\[1.2ex]
&&
-\,\frac{9}{16}\,\sin 2\theta\,\sin 2\theta^\ast\,\sin\chi\, {\cal H}_{IA}
+\,\frac{9}{16}\,\sin^2\theta\,\sin^2\theta^\ast\,\sin 2\chi\,
{\cal H}_{IT}
\nonumber\\[1.2ex]
&+&\,\delta_\ell\,\Big[
\,\,\, \frac{9}{4}\,\cos^2\theta^\ast\,{\cal H}_S
-\,\frac{9}{2}\,\cos\theta\,\cos^2\theta^\ast\,{\cal H}_{SL}
+\,\frac{9}{4}\,\cos^2\theta\,\cos^2\theta^\ast\,{\cal H}_{L}
\nonumber\\[1.2ex]
&&
\qquad +\,\frac{9}{16}\,\sin^2\theta\,\sin^2\theta^\ast\,{\cal H}_{U}
+\,\frac{9}{8}\,\sin^2\theta\,\sin^2\theta^\ast\,\cos 2\chi\, {\cal H}_{T}
\nonumber\\[1.2ex]
&&\qquad
+\,\frac{9}{4}\,\sin\theta\,\sin 2\theta^\ast\,\cos\chi\, {\cal H}_{ST}
-\,\frac{9}{8}\,\sin 2\theta\,\sin 2\theta^\ast\,\cos\chi\, {\cal H}_{I}
\nonumber\\[1.2ex]
&&\qquad
-\,\frac{9}{4}\,\sin\theta\,\sin 2\theta^\ast\,\sin\chi\, {\cal H}_{ISA}
+\,\frac{9}{8}\,\sin 2\theta\,\sin 2\theta^\ast\,\sin\chi\, {\cal H}_{IA}
\nonumber\\[1.2ex]
&&\qquad
-\,\frac{9}{8}\,\sin^2\theta\,\sin^2\theta^\ast\,\sin 2\chi\, {\cal H}_{IT}
\Big].
\label{eq:distr4}
\end{eqnarray}
In our quark model all helicity amplitudes are real, which implies the
vanishing of all terms proportional to $\sin\chi$ and $\sin2\chi$.
The angular decay distribution for the remaining terms agrees with the results
of~\cite{Korner:1987kd,Korner:1989qb,Korner:1989ve} when one takes into
account the different definition of the polar angle $\theta$ used
in~\cite{Korner:1987kd,Korner:1989ve,Korner:1989qb} such that
$\theta \to 180^{\circ}-\theta$.
The four-fold distribution allows one to define a number of physical
observables which can be measured experimentally.
Integrating Eq.~(\ref{eq:distr4}) over $\cos\theta^\ast$ and
$\chi$ one recovers the two-fold ($q^2,\cos\theta$) distribution of
Eq.~(\ref{eq:distr2}) that gives rise to the lepton side forward-backward
asymmetry parameter $A_{FB}$ and the convexity parameter $C_F^\ell(q^2)$.
Integrating
Eq.~(\ref{eq:distr4}) over $\cos\theta$ and
$\chi$ one obtains the hadron side $\cos\theta^\ast$ distribution described
by a untilted parabola (without a linear term). The normalized form of the
$\cos\theta^\ast$ distribution
reads $\widetilde {W} (\theta^\ast)=(a'+c'\cos^{2}\theta^\ast)/2(a'+c'/3)$,
which can again be characterized by its convexity
parameter given by
\begin{equation}
C_F^h(q^2) = \frac{d^{2}\widetilde W(\theta)}{d(\cos\theta^{\ast})^{2}}
=\frac{c'}{a'+c'/3}=-\,\frac32
\frac{ {\cal H}_U - 2 {\cal H}_L
+\delta_\ell( {\cal H}_U - 2 {\cal H}_L -6{\cal H}_S )}{
{\cal H}_{\rm tot} }.
\label{eq:convex_had}
\end{equation}
We define a normalized angular decay distribution
$\widetilde W(\theta^\ast,\theta,\chi)$ through
\begin{equation}
\widetilde W(\theta^\ast,\theta,\chi)=\frac{W(\theta^\ast,\theta,\chi)}
{ {\cal H}_{\rm tot}}.
\label{eq:normdis}
\end{equation}
\noindent
The normalized angular decay distribution
$\widetilde W(\theta^\ast,\theta,\chi)$ obviously integrates to $1$ after
$\cos\theta^\ast,\,\cos\theta$, and $\chi/2\pi$ integration.
The remaining coefficient functions ${\cal H}_{T}(1 - 2\delta_\ell)$,
${\cal H}_{T}(1 - 2\delta_\ell)$, and
$ ({\cal H}_{A} - 2 \delta_\ell{\cal H}_{ST})$ in Eq.(\ref{eq:distr4}) can be
projected from the
three-fold angular decay distribution Eq.(\ref{eq:distr4}) by taking the
appropriate trigonometric moments of the normalized decay distribution
$\widetilde W(\theta^\ast,\theta,\chi)$. The trigonometric moments are
defined by
\begin{equation}
W_{i} = \int d\cos\theta\,d\cos\theta^\ast\,d(\chi/2\pi)\,
M_{i}(\theta^\ast,\theta,\chi)\widetilde W(\theta^\ast,\theta,\chi)
\equiv <\, M_{i}(\theta^\ast,\theta,\chi) \,> ,
\end{equation}
where $M_{i}(\theta^\ast,\theta,\chi)$ defines the trigonometric moment that
is being taken.
One finds
\begin{eqnarray}
W_T(q^2) &\equiv& <\, \cos 2\chi \,>
= -\,\tfrac 12\,(1 - 2\delta_\ell) \,\frac{{\cal H}_{T}}{{\cal H}_{\rm tot}},
\nonumber\\
W_I(q^2) &\equiv& <\,
\cos\theta\cos\theta^{\ast}\cos \chi \,>
= \frac{9\pi^2\,(1 - 2\delta_\ell)}{512}
\, \frac{{\cal H}_{I}}{{\cal H}_{\rm tot}},
\nonumber\\
W_A(q^2) &\equiv&<\,\sin\theta\cos\theta^{\ast}\cos \chi \,>
= \,- \frac{3\pi}{16}\,
\frac{ {\cal H}_{A} - 2 \delta_\ell{\cal H}_{ST} }{ {\cal H}_{\rm tot} }.
\label{eq:W}
\end{eqnarray}
The coefficient functions ${\cal H}_{T}(1 - 2\delta_\ell)$,
${\cal H}_{T}(1 - 2\delta_\ell)$, and
$ ({\cal H}_{A} - 2 \delta_\ell{\cal H}_{ST})$ can also be projected out by
taking piecewise sums and differences of different sectors of the angular
phase space \cite{Korner:1989qb}.
Finally, we consider the longitudinal and transverse polarizations of the
lepton where we consider only the angular average of the two polarization
states. For the longitudinal polarization one obtains
\begin{equation}
P^\ell_z(q^2) =\frac{\delta_{\ell}{\cal H}_{hf}-{\cal H}_{nf}}
{\delta_{\ell}{\cal H}_{hf}+{\cal H}_{nf}}= -\,
\frac{ {\cal H}_U + {\cal H}_L
- \delta_\ell( {\cal H}_U + {\cal H}_L + 3 {\cal H}_S )}
{ {\cal H}_{\rm tot} }.
\label{eq:lpolarization}
\end{equation}
The transverse polarization can be calculated using the representation of the
polarized lepton tensor written down in the Appendix
of~\cite{Gutsche:2015mxa}. One obtains
\begin{equation}
P^\ell_x(q^2) = -\, \frac{3\pi\sqrt{\delta_\ell}}{4\sqrt{2}}
\frac{ {\cal H}_P - 2 {\cal H}_{SL}} { {\cal H}_{\rm tot} }.
\label{eq:tpolarization}
\end{equation}
For the decay $B \to D\ell^{-}\bar \nu_{\ell}$ one has to drop the
transverse contributions ${\cal H}_U $ and ${\cal H}_P $ in
Eqs~(\ref{eq:lpolarization}) and (\ref{eq:tpolarization}).
It is interesting to note that for this decay
there exists a very simple relation connecting $P^\ell_x(q^2)$ and
$A_{FB}(q^{2})$ which reads
\begin{equation}
P^{\ell}_x(q^2) = -\frac{\pi\sqrt{q^2}}{2m_\tau} A_{FB}(q^2).
\end{equation}
The polarization of the lepton depends on the frame in which it is defined.
The polarization components $P^{\ell}_{z}$ and $P^{\ell}_{x}$ in
(\ref{eq:lpolarization}) and (\ref{eq:tpolarization}) are calculated in the
$(\ell^{-}\bar \nu_{\tau})$ rest frame. The corresponding polarization
components in the $B$ rest frame have been calculated
in~\cite{Hagiwara:1989cu}.
\section{Results and discussion}
\label{sec:result}
The values of the lepton and meson masses and their lifetimes are taken from
Ref.~\cite{Agashe:2014kda}. We also adopt the following values for the
CKM matrix elements $|V_{ub}|=0.00413$ and $|V_{bc}|=0.0411$.
In Fig.~\ref{fig:difwidths} we represent our results for the differential
branching fractions of the decays $B \to D^{(*)} \ell \nu$ within the full
range of the momentum transfer squared. For comparison, we also display
the form factors calculated in heavy quark limit. It is readily seen that
both forms are very close to each other. It confirms that HQET
works very well in the leading order for $b-c$~transitions. In what follows
we will not display the curves for observables obtained in the HQL.
\begin{figure}[htbp]
\begin{tabular}{lr}
\includegraphics[scale=0.6]{difBD_el} &
\includegraphics[scale=0.6]{difBDv_el}\\
\includegraphics[scale=0.6]{difBD_mu}&
\includegraphics[scale=0.6]{difBDv_mu}\\
\includegraphics[scale=0.6]{difBD_tau}&
\includegraphics[scale=0.6]{difBDv_tau}\\
\end{tabular}
\caption{Differential branching fractions of the decays
$B \to D^{(*)} \ell \nu$.
The solid lines are the results of exact calculations in our approach,
the dashed lines are the form factors obtained in the heavy quark limit.}
\label{fig:difwidths}
\end{figure}
In Fig.~\ref{fig:asym} we represent our results for
the forward-backward asymmetries of the decays
$B \to D^{(*)} \ell \nu$ within the full range of the momentum
transfer squared. The forward-backward asymmetry
for the decay $B \to D\tau^{-}\bar \nu_{\tau}$ is quite large in the lower
half of the $q^{2}$ spectrum which can be understood from the fact that
$A_{FB}=-3\delta_{\ell}{\cal H}_{SL}$ and that $3\delta(q^{2})$ is large
in the threshold region. It is quite interesting that the forward-backward
asymmetry for the decay $B \to D^{\ast}\tau^{-}\bar \nu_{\tau}$ goes through
zero at $q^{2}=6.25$ GeV$^{2}$.
\begin{figure}[htbp]
\begin{tabular}{lr}
\includegraphics[scale=0.6]{AsymBD_el} &
\includegraphics[scale=0.6]{AsymBDv_el}\\
\includegraphics[scale=0.6]{AsymBD_mu}&
\includegraphics[scale=0.6]{AsymBDv_mu}\\
\includegraphics[scale=0.6]{AsymBD_tau}&
\includegraphics[scale=0.6]{AsymBDv_tau}\\
\end{tabular}
\caption{Forward-backward asymmetries of the decays $B \to D^{(*)} \ell \nu$.}
\label{fig:asym}
\end{figure}
The branching fractions of the decays $B \to \ell^-\bar\nu$,
$B \to D^{(*)} \ell^-\bar\nu$, and
$B \to \pi\ell^-\bar\nu$, as well as the ratios of branching fractions
$R(D^{(*)})$ are presented in Tables~\ref{tab:leptBr},
\ref{tab:semileptbran} and \ref{tab:ratebran}. The branching fractions
$\mathcal{B}(B \to \ell^-\bar\nu)$, ($\ell = e,\mu$), satisfy the experimental
constraints and show good agreement with the CKMfitter results, while
the branching fraction $\mathcal{B}(B \to\tau^-\bar\nu_\tau)$ is consistent
with experimental data, giving more constraints on NP effects that may
contribute to the transitions. The situation is different for the semileptonic
decays.
The results for $\mathcal{B}(B \to D^{(*)} \ell^-\bar\nu)$ are slightly larger,
while the results for $\mathcal{B}(B \to D^{(*)} \tau^-\bar\nu_\tau)$ are
slightly smaller in comparison with experimental data. As a result,
the calculated ratios $R(D^{(*)})$ are slightly smaller than the SM
expectation,
which means they deviate from the experimental values even more.
This may imply the appearance of NP.
\begin{table}
\begin{tabular}{l c c c l}
\hline\hline
& \qquad Unit \qquad & \qquad This work\qquad &\qquad Data\qquad &
\qquad Ref.\qquad \\
\hline
$\bar{B}^0 \to D^+ \ell^- \bar\nu$
& \qquad $10^{-2}$\qquad &\qquad $2.74\,(2.65)$ \qquad &
\qquad $2.17\pm0.12$ \qquad &
\qquad HFAG~\cite{Asner:2010qj}
\\
& & &\qquad $2.21\pm0.16$ &
\qquad BABAR~\cite{Aubert:2007qw}
\\[1.2ex]
$\bar{B}^0 \to D^+ {\tau}^- \bar\nu_\tau$
& \qquad $10^{-2}$ \qquad & \qquad $0.73\,(0.71)$\qquad &
\qquad $1.02\pm0.17$ \qquad &
\qquad BABAR~\cite{Lees:2012xj}
\\[1.2ex]
$\bar{B}^0 \to D^{\ast\,+} \ell^- \bar\nu$
& \qquad $10^{-2}$ \qquad & \qquad $6.64\,(7.21)$ \qquad &
\qquad $5.05 \pm 0.12$ \qquad & \qquad HFAG~\cite{Asner:2010qj}
\\
& & & \qquad $5.49 \pm 0.30$ \qquad &
\qquad BABAR~\cite{Aubert:2007qw}
\\[1.2ex]
$\bar{B}^0 \to D^{\ast\,+} \tau^- \bar\nu_\tau$
& \qquad $10^{-2}$ \qquad & \qquad $1.57\,(1.70)$ \qquad &
\qquad $1.76\pm0.18$ \qquad & \qquad BABAR~\cite{Lees:2012xj}
\\[1.2ex]
\hline
$\bar{B}^0 \to \pi^+ \ell^- \bar\nu$
& \qquad $10^{-4}$ \qquad & \qquad 1.69 \qquad &
\qquad $1.41 \pm 0.09$ \qquad &
\qquad BABAR~\cite{delAmoSanchez:2010af}
\\
& & & \qquad $1.49 \pm 0.08 $ \qquad & \qquad Belle~\cite{Ha:2010rf}
\\
$\bar{B}^0 \to \pi^+ \tau^- \bar\nu_\tau$
& \qquad $10^{-4} $ \qquad & \qquad 1.01 \qquad & \qquad $\ldots$ \qquad &
\qquad $\ldots$ \\[1.2ex]
\hline\hline
\end{tabular}
\caption{Semileptonic decay branching fractions of $B$ meson.
The values obtained in the HQL are given in brackets.
The experimental errors are combined in quadrature.}
\label{tab:semileptbran}
\end{table}
\begin{table}[htbp]
\begin{tabular}{cccc}
\hline\hline
\qquad\qquad & \qquad This work \qquad & \qquad SM \qquad
& \qquad Data \qquad
\\
\hline
\qquad $R(D)$ \qquad & \qquad $ 0.265\,(0.268) $ \qquad &
\qquad $ 0.297 \pm 0.017 $ \qquad & \qquad $ 0.388 \pm 0.047 $ \qquad
\\[1.2ex]
\qquad $R(D^\ast)$ \qquad &\qquad $ 0.237\,(0.235) $ \qquad &
\qquad $ 0.252 \pm 0.003 $ \qquad & \qquad $ 0.321 \pm 0.021 $\qquad
\\[1.2ex]
\hline\hline
\end{tabular}
\caption{Ratios of branching fractions $R(D)$ and $R(D^\ast)$ calculated
in our model (the values obtained in the HQL are given in brackets)
and compared with the SM expectations and experimental data.
}
\label{tab:ratebran}
\end{table}
Next we define the partial helicity rates by
\begin{equation}
\frac{d\Gamma_X}{dq^2} =
\frac{G_F^2}{(2\pi)^3}\frac{ |V_{cb}|^2 |{\bf p_2}| q^2 v^2}{12 m_1^2}\,
{\cal H}_X, \qquad
\frac{d\widetilde\Gamma_X}{dq^2}=\delta_\ell\,\frac{d\Gamma_X}{dq^2},
\label{eq:hel_rates}
\end{equation}
where $X=U,L,P,\ldots$
In Figs.~\ref{fig:dL.BD} and \ref{fig:dUL.BDv} we display
the $q^{2}$ dependence of the partial differential rates
$d\Gamma_{U}/dq^{2}$, $d\Gamma_{L}/dq^{2}$, and
the total differential rate $d\Gamma_{U+L}/dq^{2}$ for the $e$ mode.
The transverse rate dominates in the low recoil region while the longitudinal
rate dominates in the large recoil region. The longitudinal and thereby the
total rate show a step-like behavior near the threshold $q^{2}=m^{2}_{e}$.
Figs.~\ref{fig:dLtot.BD} and \ref{fig:dULS.BDv} show the corresponding plots
for the $\tau$ mode including the partial flip rates
$d\,\widetilde\Gamma_{U,L}/d\,q^{2}$ and $3\,d\,\widetilde\Gamma_{S}/d\,q^{2}$.
We also show the total differential rate
$d\Gamma_{U+L}/dq^{2} + d\,\widetilde\Gamma_{U+L+3S}/d\,q^{2}$.
The helicity flip rates are smaller than the helicity nonflip rates but
contribute significantly to the total rate.
In Figs.~\ref{fig:dCFL.BD}, \ref{fig:dCFL.BDv},
and \ref{fig:dCFH.BDv} we display the $q^{2}$ dependence
of the convexity parameters $C^{\ell}_{F}$ and $C^{h}_{F}$ for the lepton
and hadron sides defined in Eqs.~(\ref{eq:convex_lep}) and
(\ref{eq:convex_had}). In the $B \to D$ case the $\cos\theta$ distribution
is described by a downward open parabola which becomes much flatter for
the $\tau$ mode.
We do not plot the hadron-side convexity parameter $C_F^h(q^{2})$ for the
$B\to D$~transition since it trivially reads $C_F^h=3$ following from the definition~(\ref{eq:convex_had}). For the $B\to D^{\ast}$
transition the lepton-side $\cos\theta$ distribution is again described by
a downward open parabola which becomes almost flat for the $\tau$ mode.
The hadron-side $\cos\theta^{\ast}$ distribution is described by an upward
open parabola which does not become flat at the zero-recoil point.
Lepton mass effects are not very pronounced.
In Figs.~\ref{fig:dPz_Lept.BD}, \ref{fig:dPx_Lept.BD}, and \ref{fig:dPLtot.BD}
we show plots of the $q^{2}$ dependence of the longitudinal, transverse
and total polarization of the lepton for the
$B \to D \ell^{-}\bar \nu_{\ell}$ transition. In the case of
the electron the curves reflect the chiral limit of a massless lepton
in which the lepton is purely left-handed, i.e. one has $P^{\ell}_{z}=-1$,
$P^{\ell}_{x}=0$, and $|\vec P^{\ell}|=1$. For $\ell=\tau$ the transverse
polarization is large and positive and dominates the total polarization.
The transverse polarization of the $\tau$ drops out after
the appropiate azimuthal averaging, as has been done in~\cite{Tanaka:2010se}.
Note that the transverse polarization in the $\tau$ mode results solely
from the scalar-longitudinal interference contribution ${\cal H}_{SL}$.
The longitudinal polarization has switched its sign relative to the
$m_{\ell}=0$ case.
The corresponding curves for the
$B \to D^{\ast}\ell^{-}\bar \nu_{\ell}$ transition are shown in
Figs.~\ref{fig:dPz_Lept.BDv}, \ref{fig:dPx_Lept.BDv},
and \ref{fig:dPLtot.BDv}. The longitudinal and transverse polarization
components are distinctly different from their $m_{\ell}=0$ values
$P^{\ell}_{z}=-1$ and $P^{\ell}_{x}=0$. The
longitudinal component becomes larger in magnitude when $q^{2}$
increases while the transverse polarization becomes smaller as $q^{2}$
increases. At zero recoil
the transverse polarization of the charged lepton $P^{\tau}_{x}$ tends to
zero in agreement with the vanishing of ${\cal H}_{P}$ and ${\cal H}_{SL}$
at zero recoil. The total polarization of the $\tau$ shown
in Fig.~\ref{fig:dPLtot.BDv} has an almost flat behavior with
$|\vec P^{\ell}|\sim 0.7$. The overall picture is that the polarization is
mostly transverse at threshold and turns to longitudinal as $q^{2}$ reaches
the zero-recoil point.
In Figs.~\ref{fig:W1}, \ref{fig:W2},
and \ref{fig:W3} we display
the $q^{2}$ dependence of the three trigonometric moments $W_i\,(i=T,I,A)$
of the normalized three-fold angular function $\widetilde W(\theta^{\ast},
\theta,\chi)$ defined in Eq.~(\ref{eq:W}). Lepton mass effects can be seen
to be quite large for all three moments.
Finally, in Figs.~\ref{fig:RD} and \ref{fig:RDv} we present the
$q^{2}$ dependence
of the rate ratios ($\ell=e,\mu$)
\begin{equation}
R_{D^{(\ast)}}(q^{2})=\frac{d\Gamma(B\to D^{(\ast)}\tau^{-}\bar \nu_{\tau})}
{dq^{2}}
\bigg/\,\frac{d\Gamma(B\to D^{(\ast)}\ell^{-}\bar \nu_{\ell})}{dq^{2}}.
\end{equation}
Hopefully there will be enough data in the future to explore the apparent
flavor violation in the tauonic semileptonic $B \to D^{(\ast)}$ transitions in
more detail by measuring the rate ratios in different $q^{2}$ bins.
Next we present our model results for the average values of the polarization
observables:
the forward-backward asymmetry $<A_{FB}>$,
the convexity parameter $<C_F>$,
the leptonic $<P^\ell_{x,z}>$ polarization components,
and the three trigonometric moments $<W_i\,\,(i=T,I,A)$. Lepton mass effects
can be seen to be quite large for the average values
of the polarization observables.
\clearpage
\begin{figure}[htbp]
\begin{center}
\vspace*{.25cm}
\epsfig{figure=dL_BD,scale=.8}
\caption{ {\boldmath\bf $B\to D$~transition:}
the $q^{2}$ dependence of the partial rate
$d\Gamma_{L}/dq^{2}$
for the $e^-$ mode (in units of $10^{-15}$~GeV$^{-1}$).
\label{fig:dL.BD}
}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\begin{tabular}{lr}
\epsfig{figure=dLtot_BD,scale=0.55}
\qquad & \qquad
\epsfig{figure=dtildeLS_BD,scale=0.55}
\end{tabular}
\caption{ {\boldmath\bf $B\to D$~transition:}
the $q^{2}$ dependence of the partial nonflip rates
$d\Gamma_{L}/dq^{2}$, and the flip rates
$ d\,\widetilde\Gamma_{U,L}/d\,q^{2}$ and
$3\,d\,\widetilde \Gamma_{S}/d\,q^{2}$ for the $\tau^-$ mode
(in units of $10^{-15}$~GeV$^{-1}$). Also shown is the total rate
$d\,\Gamma_{L}/d\,q^{2}
+ d\,\widetilde\Gamma_{L}/d\,q^{2} + 3\,d\,\widetilde\Gamma_{S}/d\,q^{2}$.
\label{fig:dLtot.BD}
}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\vspace*{.25cm}
\epsfig{figure=dUL_BDv,scale=.8}
\caption{ {\boldmath\bf $B\to D^\ast$~transition:}
the $q^{2}$ dependence of the partial rates
$d\Gamma_{U}/dq^{2}$ (dashed), $d\Gamma_{L}/dq^{2}$ (dot-dashed) and their
sum $d\Gamma_{U+L}/dq^{2}$ (solid)
for the $e^-$ mode (in units of $10^{-15}$~GeV$^{-1}$).
\label{fig:dUL.BDv}
}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\begin{tabular}{lr}
\epsfig{figure=dULtot_BDv,scale=0.5}
\qquad & \qquad
\epsfig{figure=dtildeULS_BDv,scale=0.5}
\end{tabular}
\caption{ {\boldmath\bf $B\to D^\ast$~transition:}
the $q^{2}$ dependence of the partial nonflip rates
$d\Gamma_{U,L}/dq^{2}$, and the flip rates
$d\,\widetilde\Gamma_{U,L}/d\,q^{2}$ and
$3\,d\,\widetilde \Gamma_{S}/d\,q^{2}$ for the $\tau^-$ mode
(in units of $10^{-15}$~GeV$^{-1}$). Also shown is the total rate
$d\,\Gamma_{U+L}/d\,q^{2}+ d\,\widetilde\Gamma_{U+L}/d\,q^{2}+
3\,d\, \widetilde\Gamma_{S}/d\,q^{2}$.
\label{fig:dULS.BDv}
}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\vspace*{.25cm}
\epsfig{figure=dCFL_BD,scale=.9}
\caption{ {\boldmath\bf $B\to D$~transition:}
the $q^{2}$ dependence of the lepton convexity parameter
$C^\ell_{F}(q^{2})$ for the $e^-$- (solid) and $\tau^-$-mode (dashed).
\label{fig:dCFL.BD}
}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\vspace*{.25cm}
\epsfig{figure=dCFL_BDv,scale=.9}
\caption{ {\boldmath\bf $B\to D^\ast$~transition:}
the $q^{2}$ dependence of the lepton convexity parameter
$C^\ell_{F}(q^{2})$ for the $e^-$- (solid) and $\tau^-$-mode (dashed).
\label{fig:dCFL.BDv}
}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\vspace*{.25cm}
\epsfig{figure=dCFH_BDv,scale=.9}
\caption{ {\boldmath\bf $B\to D^\ast$~transition:}
the $q^{2}$ dependence of the hadron convexity parameter
$C^h_{F}(q^{2})$ for the $e^-$- (solid) and $\tau^-$-mode (dashed).
\label{fig:dCFH.BDv}
}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\vspace*{.25cm}
\epsfig{figure=dPLz_BD,scale=.9}
\caption{{\boldmath\bf $B\to D$~transition:}
The $q^{2}$ dependence of the longitudinal polarization component
$P^\ell_z(q^{2})$ for the charged leptons $e^-$- (solid) and $\tau^-$-mode
(dashed).
\label{fig:dPz_Lept.BD}
}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\vspace*{.25cm}
\epsfig{figure=dPLx_BD,scale=.9}
\caption{{\boldmath\bf $B\to D$~transition:}
the $q^{2}$ dependence of the transverse polarization component
$P^\ell_x(q^{2})$ for the charged leptons $e^-$- (solid) and $\tau^-$-mode
(dashed).
\label{fig:dPx_Lept.BD}
}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\vspace*{.25cm}
\epsfig{figure=dPLtot_BD,scale=.9}
\caption{{\boldmath\bf $B\to D$~transition:}
the $q^{2}$ dependence of the total lepton polarization
$|\vec{P}\,^\ell|(q^{2})=\sqrt{(P^\ell_x)^2+(P^\ell_z)^2}$
for the $e^-$- (solid) and $\tau^-$-mode (dashed).
\label{fig:dPLtot.BD}
}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\vspace*{.25cm}
\epsfig{figure=dPLz_BDv,scale=.9}
\caption{{\boldmath\bf $B\to D^\ast$~transition:}
the $q^{2}$ dependence of the longitudinal polarization component
$P^\ell_z(q^{2})$ for the charged leptons $e^-$- (solid) and $\tau^-$-mode
(dashed).
\label{fig:dPz_Lept.BDv}
}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\vspace*{.25cm}
\epsfig{figure=dPLx_BDv,scale=.9}
\caption{{\boldmath\bf $B\to D^\ast$~transition:}
the $q^{2}$ dependence of the transverse polarization component
$P^\ell_x(q^{2})$ for the charged leptons $e^-$- (solid) and $\tau^-$-mode
(dashed).
\label{fig:dPx_Lept.BDv}
}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\vspace*{.25cm}
\epsfig{figure=dPLtot_BDv,scale=.9}
\caption{ {\boldmath\bf $B\to D^\ast$~transition:}
the $q^{2}$ dependence of the total lepton polarization
$|\vec{P}\,^\ell|(q^{2})=\sqrt{(P^\ell_x)^2+(P^\ell_z)^2}$
for the $e^-$- (solid) and $\tau^-$-mode (dashed).
\label{fig:dPLtot.BDv}
}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\vspace*{.25cm}
\epsfig{figure=WT_BDv,scale=.9}
\caption{ {\boldmath\bf $B\to D^\ast$~transition:} the $q^{2}$ dependence
of the trigonometric moment
$W_T$ defined in Eq.~(\ref{eq:W}) for the
$e^-$- (solid) and $\tau^-$-mode (dashed).
\label{fig:W1}
}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\vspace*{.25cm}
\epsfig{figure=WI_BDv,scale=.9}
\caption{ {\boldmath\bf $B\to D^\ast$~transition:} the $q^{2}$ dependence
of the trigonometric moment $W_I$ defined in Eq.~(\ref{eq:W})
for the $e^-$- (solid) and $\tau^-$-mode (dashed).
\label{fig:W2}
}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\vspace*{.25cm}
\epsfig{figure=WA_BDv,scale=.9}
\caption{ {\boldmath\bf $B\to D^\ast$~transition:} the $q^{2}$ dependence
of the trigonometric moment $W_A$ defined in Eq.~(\ref{eq:W})
for the $e^-$- (solid) and $\tau^-$-mode (dashed).
\label{fig:W3}
}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\vspace*{.25cm}
\epsfig{figure=RD,scale=.9}
\caption{The $q^{2}$ dependence of the ratio $R(D)$.
\label{fig:RD}
}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\vspace*{.25cm}
\epsfig{figure=RDv,scale=.9}
\caption{The $q^{2}$ dependence of the ratio $R(D^\ast)$.
\label{fig:RDv}
}
\end{center}
\end{figure}
\begin{table}[htbp]
\begin{center}
\vspace*{0.5cm}
\begin{tabular}{c|ccccccc}
\hline
\multicolumn{8}{c}{ $B\to D$ }\\
\hline
\qquad \qquad
&\quad $\Gamma_{L}$ \qquad
&\quad \qquad
&\quad \qquad
&\quad \qquad
&\quad \qquad
&\quad \qquad
&\quad \qquad
\\
\hline
\qquad $e$\qquad \quad
&\quad $ 11.9 $ \qquad
&\quad \qquad
&\quad \qquad
&\quad \qquad
&\quad \qquad
&\quad \qquad
&\quad \qquad
\\
\qquad $\tau$ \qquad \quad
&\quad $ 1.05 $ \qquad
&\quad \qquad
&\quad \qquad
&\quad \qquad
&\quad \qquad
&\quad \qquad
&\quad \qquad
\\
\hline
\qquad\qquad
&\quad $\widetilde{\Gamma}_{L}$ \qquad
&\quad $\widetilde{\Gamma}_{S}$ \qquad
&\quad $\widetilde{\Gamma}_{SL}$ \qquad
&\quad \qquad
&\quad \qquad
&\quad \qquad
&\quad \qquad
\\
\hline
\qquad $\tau$ \qquad \quad
&\quad $ 0.25 $ \qquad
&\quad $ 0.62 $ \qquad
&\quad $ 0.38 $ \qquad
&\quad \qquad
&\quad \qquad
&\quad \qquad
&\quad \qquad
\\
\hline\hline
\multicolumn{8}{c}{ $B\to D^\ast$ }\\
\hline
\qquad \qquad
&\quad $\Gamma_{U}$ \qquad
&\quad $\Gamma_{L}$ \qquad
&\quad $\Gamma_{T}$ \qquad
&\quad $\Gamma_{I}$ \qquad
&\quad $\Gamma_{P}$ \qquad
&\quad $\Gamma_{A}$ \qquad
& \qquad \qquad
\\
\hline
\qquad $e$\qquad \quad
&\quad $ 13.2 $ \qquad
&\quad $ 15.6 $ \qquad
&\quad $ 5.35 $ \qquad
&\quad $ 8.94 $ \qquad
&\quad $ -7.42$ \qquad
&\quad $ -3.01 $ \qquad
&\quad $ $ \qquad
\\
\qquad $\tau$ \qquad \quad
&\quad $ 3.02 $ \qquad
&\quad $ 2.08 $ \qquad
&\quad $ 1.32 $ \qquad
&\quad $ 1.70 $ \qquad
&\quad $-1.42 $ \qquad
&\quad $ -0.44 $ \qquad
&\quad $ $ \qquad
\\
\hline
\qquad\qquad
&\quad $\widetilde{\Gamma}_{U}$ \qquad
&\quad $\widetilde{\Gamma}_{L}$ \qquad
&\quad $\widetilde{\Gamma}_{T}$ \qquad
&\quad $\widetilde{\Gamma}_{I}$ \qquad
&\quad $\widetilde{\Gamma}_{S}$ \qquad
&\quad $\widetilde{\Gamma}_{SL}$ \qquad
&\quad $\widetilde{\Gamma}_{ST}$ \qquad
\\
\hline
\qquad $\tau$ \qquad \quad
&\quad $ 0.64 $ \qquad
&\quad $ 0.46 $ \qquad
&\quad $ 0.27 $ \qquad
&\quad $ 0.37 $ \qquad
&\quad $ 0.20 $ \qquad
&\quad $ 0.29 $ \qquad
&\quad $ 0.22 $ \qquad
\\
\hline
\end{tabular}
\caption{$q^{2}$ averages of the rate functions in units of
$10^{-15}$~GeV. We do not display the helicity flip results for the $e$ mode
because they are of the order of $10^{-6}-10^{-7}$ in the above units.}
\label{tab:bilinears-numerics}
\end{center}
\end{table}
\begin{table}[htbp]
\begin{center}
\vspace*{0.5cm}
\begin{tabular}{c|ccc}
\hline\hline
\multicolumn{4}{c}{ $B\to D$ }\\
\hline
\qquad \qquad
&\quad $<A_{FB}^\ell>$ \qquad
&\quad $<C_{F}^\ell>$\qquad
&\quad $<C_{F}^h>$ \qquad
\\
\hline
\qquad $e$\qquad \quad
&\quad $ -1.17\,(-1.16)\cdot 10^{-6} $ \qquad
&\quad $ -1.5\,(-1.5) $ \qquad
&\quad $ 3\,(3) $ \qquad
\\
\qquad $\tau$ \qquad \quad
&\quad $ -0.36\,(-0.36) $ \qquad
&\quad $ -0.26\,(-0.26) $\qquad
&\quad $ 3\,(3) $ \qquad
\\
\hline
&\quad $<P_{z}^\ell>$\qquad
&\quad $<P_{x}^\ell>$ \qquad
&\quad $<|\vec P^\ell |>$ \qquad
\\
\hline
\qquad $e$\qquad \quad
&\quad $ -1\,(-1) $ \qquad
&\quad $ 0\,(0) $ \qquad
&\quad $ 1\,(1) $ \qquad
\\
\qquad $\tau$ \qquad \quad
&\quad $ 0.33\,(0.33) $ \qquad
&\quad $ 0.84\,(0.84) $ \qquad
&\quad $ 0.91\,(0.91) $ \qquad
\\
\hline
\multicolumn{4}{c}{ $B\to D^\ast$ }\\
\hline
\qquad \qquad
&\quad $<A_{FB}^\ell>$ \qquad
&\quad $<C_{F}^\ell>$\qquad
&\quad $<C_{F}^h>$ \qquad
\\
\hline
\qquad $e$\qquad \quad
&\quad $ 0.19\,(0.18) $ \qquad
&\quad $ -0.47\,(-0.44) $ \qquad
&\quad $ 0.93\,(0.88) $ \qquad
\\
\qquad $\tau$ \qquad \quad
&\quad $ 0.027\,(0.021) $ \qquad
&\quad $ -0.062\,(-0.057) $ \qquad
&\quad $ 0.58\,(0.52) $ \qquad
\\
\hline
&\quad $<P_{z}^\ell>$\qquad
&\quad $<P_{x}^\ell>$ \qquad
&\quad $<|\vec P^\ell |>$ \qquad
\\
\hline
\qquad $e$\qquad \quad
&\quad $ -1\,(-1) $\qquad
&\quad $ 0\,(0) $ \qquad
&\quad $ 1\,(1) $ \qquad
\\
\qquad $\tau$ \qquad \quad
&\quad $ -0.50\,(-0.51) $ \qquad
&\quad $ 0.46\,(0.43) $ \qquad
&\quad $ 0.71\,(0.71) $ \qquad
\\
\hline
\qquad \qquad
&\quad $<W_T>$ \qquad
&\quad $<W_I>$\qquad
&\quad $<W_A>$\qquad
\\
\hline
\qquad $e$\qquad \quad
&\quad $ -0.093\,(-0.098) $ \qquad
&\quad $ 0.054\,(0.055) $ \qquad
&\quad $ 0.062\,(0.059) $ \qquad
\\
\qquad $\tau$ \qquad \quad
&\quad $ -0.057\,(-0.059) $ \qquad
&\quad $ 0.025\,(0.025) $\qquad
&\quad $ 0.077\,(0.074) $ \qquad
\\
\hline\hline
\end{tabular}
\caption{$q^{2}$ averages of polarization observables. For comparison with
results from the HQL, we add in brackets the corresponding HQL values.
}
\label{tab:obs-numerics}
\end{center}
\end{table}
\clearpage
\section{Summary and conclusions}
\label{sec:summary}
We have provided a detailed analysis of the pure leptonic and semileptonic decays
$B \to \ell^{-}\bar \nu_{\ell}$ and
$B \to D^{(\ast)} \ell^{-}\bar \nu_{\ell}$ $(\ell=e,\mu,\tau)$ within the
SM in the framework of our covariant quark model with built-in quark
confinement. We have described in some detail how to compute the
one-loop quark contributions needed for the calculation of the transition form factors including a discussion of how the confinement of the
constituent quarks is achieved in the covariant quark model.
In the light of the recent experimental indications for a possible breaking of
lepton universality in the $\tau$ sector we have put
particular emphasis on how to isolate heavy lepton mass effects in the semileptonic
decays.
We have described how to obtain the full angular decay
distributions for $B \to D\ell^{-}\bar \nu_{\ell}$ and the cascade decay
process $B \to D^{\ast}(\to D\pi) \ell^{-}\bar \nu_{\ell}$ as well as the
corresponding
angular decay distributions for their charge-conjugate processes.
The coefficients multiplying the angular factors in the angular decay
distributions have been given in terms of
helicity structure functions for which we have provided simple expressions
for the maximal recoil $q^{2}=0$ and the minimal (zero) recoil
$q^{2}=(m_{1}-m_{2})^{2}$.
Starting from the angular decay distributions we have defined a multitude of
polarization observables for which we have provided numerical results on their
$q^{2}$ spectra and their $q^{2}$ averages for zero and nonzero lepton masses.
The polarization observables include the transverse and
longitudinal polarizations of the charged $\tau^{-}$ which considerably deviate
from their simple $m_{\ell}=0$ left-chiral structure.
We are looking forward to a wealth of data on these
decays expected in the near future which will allow one to
deeply probe into their decay structure, in particular for the tauonic mode.
Such an analysis will reveal possible deviations
from the SM predictions not only in the branching fractions of the
processes but also in the
multitude of polarization observables and their $q^{2}$ spectra.
\begin{acknowledgments}
M.A.I.\ acknowledges the support from Mainz Institute for Theoretical
Physics (MITP). M.A.I. and J.G.K. thank the Heisenberg-Landau Grant for providing support for their collaboration.
\end{acknowledgments}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,480 |
{"url":"https:\/\/www.greencarcongress.com\/2020\/07\/20200715-esgc.html","text":"## DOE releases draft energy storage grand challenge roadmap and requests stakeholder input\n\n##### 15 July 2020\n\nThe US Department of Energy (DOE) released the Energy Storage Grand Challenge Draft Roadmap and a Request for Information (RFI) seeking stakeholder input on the Draft Roadmap.\n\nAnnounced in January 2020 by US Secretary of Energy Dan Brouillette, the Energy Storage Grand Challenge (ESGC) is a comprehensive program to accelerate the development, commercialization, and utilization of next-generation energy storage. The Draft Roadmap outlines a Department-wide strategy to accelerate innovation across a range of storage technologies based on three concepts: Innovate Here, Make Here, Deploy Everywhere.\n\nCategories of storage included in the Energy Storage Grand Challenge\n\nOver the Fiscal Years 2017-2019, DOE has invested more than $1.2 billion into energy storage research and development (R&D)\u2014$400 million per year\u2014on average establishing an agency-wide, long-term strategy to address energy storage. The vision for the ESGC is, by 2030, to create and sustain US global leadership in energy storage utilization and exports, with a secure domestic manufacturing base and supply chain that is independent of foreign sources of critical materials. The Draft Roadmap provides planned activities for each of the ESGC five tracks:\n\n\u2022 The Technology Development Track will focus DOE\u2019s ongoing and future energy storage R&D around user-centric goals and long-term leadership. This R&D strategy consists of three components: use cases; technology portfolios; and development pathways.\n\n\u2022 The Manufacturing and Supply Chain Track will work to strengthen the domestic production of energy storage technologies by accelerating the scale-up of innovations produced by the successes of the Technology Development Track, lowering the cost of manufacturing energy storage technologies, and decreasing reliance on foreign sources of critical materials. To accomplish these goals, the Manufacturing and Supply Chain Track will pursue five types of activities, in coordination with industry and other ESGC tracks.\n\n\u2022 The Technology Transition Track will strengthen US leadership in energy storage through the commercialization of energy storage innovations. This will be accomplished through the development of proactive field validation, public-private partnerships, bankable business models, financing, technology and interconnection standards, contract standards, and the dissemination of high-quality market data. These mechanisms will enable the commercialization, private sector financing, and deployment of energy storage technologies. Such work gives market participants confidence that an energy storage asset will perform to expectations and have market demand, thus reducing production or project risk, lowering project costs, increasing investment, and accelerating scalable deployment.\n\n\u2022 The Policy and Valuation Track will provide tools, analysis, and recommendations that maximize the value of energy storage to the electric and transportation systems, driving US leadership in the innovation, manufacturing, and deployment of energy storage technologies. While other ESGC tracks support energy storage technologies, projects, and companies, the Policy and Valuation Track focuses on providing support to decision-makers, who are looking to optimize the power or energy system as a whole.\n\nThe track will leverage DOE\u2019s unique analytical capabilities, data, and computing resources to enhance the technical characterization of energy storage technologies, develop more sophisticated tools, and deliver a program of systematic, coordinated institutional support targeting key stakeholder needs. The track will be continuously updated and informed by the evolving challenges and concerns of the policy, regulatory, and planning bodies who need them most.\n\n\u2022 The Workforce Development Track will focus DOE\u2019s technical education and workforce development programs to leverage existing resources to train and educate the workforce, who can then research, develop, design, manufacture and operate energy storage systems widely within US industry. To ensure a proper focus, DOE will continue to solicit feedback from relevant stakeholders on workforce development issues through ongoing stakeholder engagement across a broad spectrum of energy-storage related industries. DOE will assess existing education and workforce development programs in areas of energy storage and the related technologies to see where gaps exist and where DOE can initiate, grow, or focus these programs. These opportunities will span a wide range of educational and focus levels from scientists to engineers to trades.\n\nAdditionally, the Draft Roadmap identifies six use cases derived from high-level energy or infrastructure goals of communities, businesses, and regions, which will be translated into a set of technology-neutral functional requirements.\n\nThe ESGC use case topics include facilitating an evolving grid, serving remote communities, electrified mobility, interdependent network infrastructure, critical services, and facility flexibility, efficiency and value enhancement. These broad specifications will help identify new and augmented research and development paths for a portfolio of energy storage and flexibility technologies that meet emerging needs.\n\nThis Draft Roadmap focuses on three key challenges, applied to each of the five tracks, to ensure that the US sustains global leadership in energy storage:\n\n\u2022 Innovate Here \u2013 How can DOE enable the United States to lead in energy storage R&D and retain IP developed through DOE investment in the United States?\n\n\u2022 Make Here \u2013 How can DOE work to lower the cost and energy impact of manufacturing existing technologies, and strengthen domestic supply chains by reducing dependence on foreign sources of materials and components?\n\n\u2022 Deploy Everywhere \u2013 How can DOE work with relevant stakeholders to develop technologies that meet our domestic usage needs and enable the United States to not only successfully deploy technologies in domestic markets but also export technologies?\n\nDOE is requesting information from stakeholders to inform the suite of activities proposed in the Draft Roadmap through a formal RFI. 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\section{Introduction} \label{sec:introduction}
Since the era of high-resolution interferometry, many circumstellar disks are known to show ring-like substructures in the millimeter continuum emission of
the dust, e.g., HL~Tauri \citep{2015ApJ...808L...3A}, TW~Hydrae \citep{2016ApJ...820L..40A, 2016ApJ...829L..35T}, and HD~163296 \citep{2016PhRvL.117y1101I}.
Recently, the DSHARP survey \citep{2018ApJ...869L..41A} observed 20 protoplanetary disks at a wavelength of 1.25\,mm with an angular resolution of $\sim$0\farcs035. Most of the observed disks show substructures such as rings, spirals, and vortices \citep{2018ApJ...869L..42H, 2018ApJ...869L..43H}.
One of the most promising explanations for substructures in protoplanetary disks is the existence of planets carving gaps in the gas surface density. The outer edge of the planet induced gap acts as a pressure bump and halts the inward drift of dust particles \citep{2006MNRAS.373.1619R, 2012A&A...545A..81P}.
\citet{2018ApJ...869L..46D} analyzed a subset of eight rings in five disks of the DSHARP sample in greater detail and found evidence for dust trapping in pressure bumps. Furthermore, their observations of the azimuthally averaged intensity profiles hint to the existence of a particle size distribution, as apposed to a single grain size. Additionally, a background pressure gradient is needed to account for the deviations from Gaussian profiles in the intensity.
Another remarkable result of the DSHARP survey is that the derived peak optical depths in the analyzed rings are all very similar: not completely optically thick, but marginally thick with values between about 0.2 and 0.5 (see figure \ref{fig:figure1}). The reason for these seemingly fine-tuned optically thicknesses is unclear. Since \citet{2018ApJ...869L..46D} analyzed only the brightest rings within the DSHARP survey, it makes sense that none of the rings is fully optically thin. It cannot, however, explain why none of the rings is fully optically thick. Since the sample of eight rings is rather small, even coincidence cannot be completely ruled out. Nevertheless, with only a few exceptions the other disks in the DSHARP sample show a similar behavior at the location of substructures \citep{2018ApJ...869L..42H}. Similar results have been obtained by \citet{2018A&A...619A.161C} in the case of HD~135344B and by \citet{2019arXiv190707277M} in HD~169142.
\begin{figure}[tbp!]
\includegraphics[width=\linewidth]{figure1}
\caption{Peak optical depths in the eight rings of the DSHARP sample \citep{2018ApJ...869L..46D} and in the rings of HD~169142 \citep{2019arXiv190707277M}.}
\label{fig:figure1}
\end{figure}
One possible explanation is dust removal by planetesimal formation. Streaming instability is a hydrodynamical mechanism driven by the relative flow of dust and gas that concentrates dust particles until they collapse under their own gravity, forming 100-kilometer-sized planetesimals \citep{2005ApJ...620..459Y, 2007Natur.448.1022J}. \citet{2009ApJ...704L..75J} found that the planetesimal formation via the streaming instability is conditioned by the vertically integrated dust-to-gas ratio, with a threshold of 0.02 in the case of grains with Stokes numbers between 0.1 and 0.4. \citet{2010ApJ...722.1437B} confirmed this threshold and noticed that only the pebbles of $\mathrm{St} \geq 10^{-2}$ actively clump and thus only the large grains should be taken into account when calculating metallicity to compare with the threshold. \citet{2015A&A...579A..43C} and \citet{2017A&A...606A..80Y} performed systematic studies for the conditions necessary for planetesimal formation and proposed a threshold metallicity criterion as a function of the grain's Stokes number. However, these studies adapted initially laminar disks, where there is only self-driven turbulence. Global disk turbulence can potentially undermine the efficiency of the streaming instability \citep{2018MNRAS.473..796A, 2018ApJ...868...27Y}, however in disks which are turbulent due to a magneto-hydrodynamic instability, zonal flows have been shown to form, which create pressure bumps that concentrate pebbles sufficiently to allow for a spontaneous gravitational collapse \citep{2013ApJ...763..117D}. Also, lower pressure gradients present in pressure bumps have been shown to favour planetesimal formation and the planetesimal formation criterion should depend on the pressure gradient \citep{2010ApJ...722L.220B, 2018arXiv181010018A, 2018ApJ...860..140S}.
While the detailed criteria of conditions allowing for planetesimal formation in the streaming instability in turbulent disks are subject to ongoing studies, in this paper we follow \citet{2016A&A...594A.105D} and \citet{2017A&A...602A..21S} and adopt a simple criterion based on the midplane dust-to-gas ratio exceeding unity, as this seems to be a general criterion for fast growth in the linear phase and development of strong clumping in the non-linear phase of the streaming instability \citep{2007ApJ...662..613Y, 2007ApJ...662..627J}.
The transformation of dust particles into planetesimals could naturally explain the limitation in optical thickness that is observed in dust rings. The self-regulating nature of this process -- a high concentration of dust particles is required and streaming instability might be stalled as soon as enough dust is converted into planetesimals -- could explain why the optical depths in these rings seem to be all within a narrow range.
To investigate this hypothesis, we reproduced the model presented in \citet{2018ApJ...869L..46D} by imposing a Gaussian gap onto the gas which is imitating the gap caused by a planet, but including the full grain size distribution regulated by particle growth and fragmentation. What is more, we implemented a simple recipe for the formation of planetesimals in dust concentrations and analyzed the evolution of the peak optical depth in the dust ring that forms at the outer edge of the gap. Furthermore, we compare this model to a model without planetesimal formation.
In section \ref{sec:analytic}, we derive a simple analytical formula for the optical depth resulting from a monodisperse particle size distribution that is just at the threshold, where streaming instability can act. Section \ref{sec:model} describes the numerical model with which we simulate the growth and transport of dust in protoplanetary disks. In section \ref{sec:results}, we present the results, which are discussed in section \ref{sec:discussion}. In section \ref{sec:alternatives}, we briefly discuss alternative explanations for the observed peak optical depths. We summarize our findings in Section~\ref{sec:last}.
\section{Analytic derivation} \label{sec:analytic}
For a monodisperse dust size distribution, the maximum optical depth can be calculated analytically. The optical depth is the product of the opacity $\kappa_\nu$ and the dust surface density~$\Sigma_\mathrm{d}$
\begin{equation}
\tau_\nu = \kappa_\nu \Sigma_\mathrm{d}.
\label{eqn:taunu}
\end{equation}
The opacity $\kappa_\nu$ can be expressed in terms of the dimensionless absorption coefficient $Q_\nu$
\begin{equation}
\kappa_\nu = \frac{\pi a^2}{m} Q_\nu = \frac{3}{4} \frac{Q_\nu}{a\rho_\mathrm{s}},
\end{equation}
with the particle bulk density $\rho_\mathrm{s}$. The particle size $a$ can be expressed via the dimensionless Stokes number
\begin{equation}
\mathrm{St} = \frac{\pi}{2} \frac{a\rho_\mathrm{s}}{\Sigma_\mathrm{g}},
\end{equation}
with the gas surface density $\Sigma_\mathrm{g}$.
An important criterion for the streaming instability is the midplane dust-to-gas ratio $\rho_\mathrm{d}/\rho_\mathrm{g}$ \citep{2005ApJ...620..459Y}. We therefore convert the surface
densities to midplane volume densities via
\begin{eqnarray}
\Sigma_\mathrm{g} &= \sqrt{2\pi} H \rho_\mathrm{g}, \\
\Sigma_\mathrm{d} &= \sqrt{2\pi} h \rho_\mathrm{d},
\end{eqnarray}
with the pressure scale height of the gas $H$ and the dust scale height $h$, which is given by \citet{1995Icar..114..237D} as
\begin{equation}
h = \sqrt{\frac{\alpha}{\alpha + \mathrm{St}}} H
\simeq \sqrt{\frac{\alpha}{\mathrm{St}}} H,
\end{equation}
where $\alpha$ is the viscosity parameter \citep{1973A&A....24..337S}. The last step is an approximation for $\alpha \ll \mathrm{St}$.
Putting everything into equation (\ref{eqn:taunu}) results in
\begin{equation}
\tau_\nu = \frac{3\pi}{8} \sqrt{\frac{\alpha}{\mathrm{St}^3}} Q_\nu \frac{\rho_\mathrm{d}}{\rho_\mathrm{g}}.
\end{equation}
For the threshold midplane dust-to-gas ratio of unity and reasonable values of the needed quantities, the resulting equation reads
\begin{equation}
\tau_\nu = 0.5\ \frac{Q_\nu}{0.4}\ \left( \frac{\alpha}{0.001} \right)^\frac{1}{2}\ \left( \frac{\mathrm{St}}{0.1} \right)^{-\frac{3}{2}}.
\label{eqn:peakTauAnalyic}
\end{equation}
The value of $Q_\nu$ was calculated by using the DSHARP opacities \citep{2018ApJ...869L..45B} and the local conditions in the dust ring in the simulation presented in section \ref{sec:results}. While equation (\ref{eqn:peakTauAnalyic}) has a rather steep dependence on the Stokes number, we would like to point out, that $Q_\nu$ itself depends on the particle size and therefore the Stokes number. To first order approximation $Q_\nu \propto a \propto \mathrm{St}$ in a regime where $\lambda > 2 \pi a$ \citep{1997MNRAS.291..121I}. This lowers the effective dependence on the Stokes number.
When planetesimal formation is able to keep the midplane dust-to-gas ratio at unity, this could be a natural explanation for the marginally optically thick dust rings in the DSHARP survey. The idea is that, as soon as the dust surface density (and thereby the optical depth) exceeds this threshold, particle concentration sets in \citep{2018ApJ...861...47S}. Clumps of dust form, which gravitationally collapse to form planetesimals. This takes mass away from the dust population, lowering the dust surface density, and shutting down the streaming instability again. This self-regulated process will thus keep the dust surface density right at the border of stability, and thus keep the optical depth close to the value given by equation~(\ref{eqn:peakTauAnalyic}).
However, this simple expression is only valid for a single particle size. For a more detailed analysis with a particle size distribution, we performed full numerical models.
\section{Numerical Model} \label{sec:model}
We modeled the second dust ring of HD~163296 in a similar way as \citet{2018ApJ...869L..46D}. The one-dimensional simulations have been performed with \texttt{DustPy}, a \texttt{Python}-based software package for dust growth and evolution in protoplanetary disks, which is based on the model of \citet{2010A&A...513A..79B}. We imposed a Gaussian-shaped gap onto the gas by increasing the viscosity in this region respectively. Gas and dust dynamics have been implemented by solving their continuity equations. We followed grain growth and fragmentation by solving the Smoluchowski equation with a simple sticking-fragmentation collision model. To account for planetesimal formation by streaming instability, we removed mass from the dust distribution with a simple recipe.
All input parameters of our model are listed in table~\ref{tab:inputs}. Note that the radial mixing parameter $\delta$ is a factor of two larger than the viscosity parameter $\alpha_0$ to reproduce the observed width of the dust ring.
\begin{deluxetable}{llrl}[tbp!]
\tablecaption{Input parameters of the model. \label{tab:inputs}}
\tablecolumns{4}
\tablehead{
\colhead{Symbol} &
\colhead{Description} &
\colhead{Value} &
\colhead{Unit}
}
\startdata
$\alpha_0$ & viscosity parameter & $0.001$ & -- \\
$\delta$ & radial mixing parameter & $0.002$ & -- \\
$\epsilon$ & efficiency of planetesimal formation & $0.1$ & -- \\
$f$ & gap depth & 2.0 & -- \\
$\gamma$ & slope of surface density & 1.0 & -- \\
$L_*$ & stellar luminosity & 17.0 & $L_\sun$ \\
$M_*$ & stellar mass & 2.04 & $M_\sun$ \\
$M_\mathrm{disk}$ & initial disk mass & 0.4 & $M_\sun$ \\
$\varphi$ & irradiation angle & 0.02 & rad \\
$r_\mathrm{c}$ & critical cut-off radius & 200 & AU \\
$r_\mathrm{p}$ & gap position & 83.5 & AU \\
$\rho_\mathrm{s}$ & particle bulk density & 1.6 & g/cm$^3$ \\
$\Sigma_\mathrm{d}/\Sigma_\mathrm{g}$ & dust-to-gas ratio & 0.01 & -- \\
$v_\mathrm{f}$ & fragmentation velocity & 10.0 & m/s \\
$w_\mathrm{gap}$ & gap width & 6 & AU
\enddata
\end{deluxetable}
\subsection{Gas and dust dynamics}
We initially set the gas disk according the self-similar solution of \citet{1974MNRAS.168..603L}:
\begin{equation}
\Sigma_\mathrm{g} \left( r \right) = \Sigma_0 \left( \frac{r}{r_\mathrm{c}} \right)^{-\gamma} \exp \left[ \left( -\frac{r}{r_\mathrm{c}} \right)^{2-\gamma} \right].
\end{equation}
The parameter $\Sigma_0 = \left( 2 - \gamma \right) M_\mathrm{disk} / \left( 2 \pi r_\mathrm{c}^2 \right)$ is set by the initial disk mass.
The initial dust distribution follows the gas distribution with a constant dust-to-gas ratio. The initial particles sizes follow the distribution of the interstellar medium \citep{1977ApJ...217..425M} with a maximum particle size of 1\,$\mu$m.
We follow the gas evolution by solving the continuity equation
\begin{equation}
\frac{\partial}{\partial t} \Sigma_\mathrm{g} + \frac{1}{r} \frac{\partial}{\partial r} \left( r \Sigma_\mathrm{g} v_{\mathrm{g},r} \right) = 0,
\end{equation}
where the radial gas velocity is given by
\begin{equation}
v_{\mathrm{g},r} = - \frac{3}{\Sigma_\mathrm{g}\sqrt{r}} \frac{\partial}{\partial r} \left( \Sigma_\mathrm{g}\sqrt{r} \nu \right),
\end{equation}
with $\nu = \alpha c_\mathrm{s}^2 / \Omega_\mathrm{K}$ being the turbulent viscosity, $\alpha$ the viscosity parameter, $c_\mathrm{s}$ the sound speed, and $\Omega_\mathrm{K}$ the Keplerian frequency.
Every dust particle size $i$ follows its own advection-diffusion equation:
\begin{equation}
\frac{\partial}{\partial t} \Sigma_\mathrm{d}^i + \frac{1}{r} \frac{\partial}{\partial r} \left( r \Sigma_\mathrm{d}^i v_{\mathrm{d},r}^i \right)
= \frac{1}{r}\frac{\partial}{\partial r} \left[ rD^i\Sigma_\mathrm{g} \frac{\partial}{\partial r} \left( \frac{\Sigma_\mathrm{d}^i}{\Sigma_\mathrm{g}} \right) \right],
\end{equation}
where the dust diffusivity is given by \citet{2007Icar..192..588Y} as
\begin{equation}
D^i = \frac{\delta c_\mathrm{s}^2 / \Omega_\mathrm{K}}{1+{\mathrm{St}^i}^2}.
\end{equation}
$\delta$ is the radial mixing parameter, similar to $\alpha$ for the gas evolution. The radial dust velocity is
\begin{equation}
v_{\mathrm{d},r}^i = \frac{1}{1+{\mathrm{St}^i}^2} v_{\mathrm{g},r} + \frac{1}{{\mathrm{St}^i}+1/{\mathrm{St}^i}} \frac{c_\mathrm{s}^2}{\Omega_\mathrm{K}r}
\frac{\mathrm{d}\ln p}{\mathrm{d}\ln r},
\end{equation}
where $p$ is the gas pressure. The Stokes number is defined as
\begin{equation}
\label{eq:stokesNumber}
\mathrm{St}^i = \frac{\pi}{2} \frac{a^i\rho_\mathrm{s}}{\Sigma_\mathrm{g}},
\end{equation}
with the particle radii $a^i$ and the particle bulk density $\rho_\mathrm{s}$.
\subsection{Dust growth}
We simulate dust growth by following the particle mass distribution $f\left( m \right)$. This is done by solving the Smoluchowski equation
\begin{equation}
\frac{\partial}{\partial t} f \left( m \right)
= \iint f \left( m^\prime \right) f \left( m^{\prime\prime} \right) M \left(m, m^\prime, m^{\prime\prime} \right) \mathrm{d}m^{\prime\prime} \mathrm{d}m^\prime,
\end{equation}
with the coagulation Kernel $M \left(m, m^\prime, m^{\prime\prime} \right)$. Particles grow by hit-and-stick collisions until their relative collision velocities exceed the fragmentation velocity $v_\mathrm{f}$, where they start to fragment. The exact collisional physics are hidden in the coagulation Kernel. For a detailed description of the coagulation/fragmentation method used here we refer to \citet{2010A&A...513A..79B}.
\subsection{Temperature profile}
For the temperature profile, we assume a simple irradiated disk model with the midplane temperature given by
\begin{equation}
T \left( r \right) = \left( \frac{\frac{1}{2} \varphi L_*}{4 \pi r^2 \sigma_\mathrm{SB}} \right)^{1/4},
\end{equation}
with the stellar luminosity $L_*$, the Stefan-Boltzmann constant $\sigma_\mathrm{SB}$, and the irradiation angle $\varphi$. We assume that gas and dust are always well-coupled and share the same temperature. Further, we assume that the temperature does not change with height above the midplane. The stellar luminosity does not change during our simulation.
\subsection{Streaming instability}
Since we cannot self-consistently solve for the hydrodynamical interactions between dust and gas leading to the streaming instability in our one-dimensional model, we implemented a simple recipe for forming planetesimals in dust concentrations \citep[see, e.g.,][]{2016A&A...594A.105D, 2018A&A...620A.134S}. As soon as the midplane dust-to-gas ratio exceeds unity, we remove a fraction $\epsilon=0.1$ of the dust surface density per settling timescale and shift this mass into the surface density of planetesimals. The rate of change $R^i$ per species is then given by
\begin{equation}
R^i = \frac{\partial}{\partial t} \Sigma_\mathrm{d}^i = - \epsilon \frac{\Sigma_\mathrm{d}^i}{t_\mathrm{sett}^i}
= - \epsilon \Sigma_\mathrm{d}^i \mathrm{St}^i \Omega_\mathrm{K}.
\end{equation}
The mass that gets added to the planetesimals is then simply the sum over all dust sizes
\begin{equation}
\frac{\partial}{\partial t} \Sigma_\mathrm{pl} = -\sum_i R^i.
\end{equation}
We do not further evolve the surface density of planetesimals.
\subsection{Gas gap}
To model a gap carved by a planet we follow the approach of \citet{2018ApJ...869L..46D}. Since in the steady state $\alpha\cdot\Sigma_{g}$ is constant, a method for inducing a gap in the gas density is to have a bump in the $\alpha$ viscosity parameter
\begin{equation}
\alpha \left( r \right) = \frac{\alpha_0}{F\left( r \right)},
\end{equation}
where the function $F\left( r \right)$ is given by
\begin{equation}
F \left( r \right) = \exp \left[ -f \exp \left( -\frac{\left( r - r_\mathrm{p} \right)^2}{2w_\mathrm{gap}^2} \right) \right].
\end{equation}
This only changes the turbulent viscosity of the gas. The radial mixing of the dust or the calculation of the turbulent collision velocity of the dust particles is not affected by this modification.
\subsection{Optical properties}
To calculate the optical depth, the intensity profiles, and the spectral index we use the DSHARP opacity model \citep{2018ApJ...869L..45B}, which uses optical constants of water ice from \citet{2008JGRD..11314220W}, of astronomical silicates from \citet{2003ApJ...598.1026D}, and of troilite and organics from \citet{1996A&A...311..291H}.
\section{Results} \label{sec:results}
\begin{figure}[tbp!]
\includegraphics[width=\linewidth]{figure2}
\caption{{\it Top panel}: Snapshot of the dust distribution after 13\,Myrs in the simulation with planetesimal formation. The white line shows particles sizes with St=1. The dashed blue and green lines correspond to the fragmentation and drift limits, respectively \citep{2012A&A...539A.148B}. {\it Middle panel}: Solid lines show the modeled intensity profiles at 1.25\,mm convolved with the beam size at different snapshots. The dotted lines show the corresponding unconvolved intensity profiles. The dashed black line shows the observed intensity profile \citep{2018ApJ...869L..41A}. {\it Bottom panel}: Optical depth profiles calculated from the convolved (solid) and unconvolved (dotted) intensity profiles using the DSHARP opacity model \citep{2018ApJ...869L..45B}. The data point corresponds to the derived optical depth in the second dust ring of HD~163296 \citep{2018ApJ...869L..46D}.}
\label{fig:figure2}
\end{figure}
We performed two simulations evolving dust for several million years each. The first simulation included planetesimal formation through the streaming instability, and the second one is a control case without planetesimal formation. The top panel of figure~\ref{fig:figure2} shows the dust surface density distribution of the simulation with planetesimal formation after 13\,Myrs. The plotted quantity $\sigma_\mathrm{d}$ corresponds to the dust surface density of each logarithmic size bin:
\begin{equation}
\Sigma_\mathrm{d} \left( r \right) = \int\limits_0^\infty \sigma_\mathrm{d} \left( r, a \right) \mathrm{d} \ln a.
\end{equation}
The white solid line representing $\mathrm{St}=1$ particles is proportional to the gas surface density (cf. equation (\ref{eq:stokesNumber})) and shows the gap carved in the gas by a hypothetical planet at 83.5\,AU. At this stage of the simulation, the particles sizes are limited by radial drift everywhere in the disk except for the dust trap at the outer edge of the gas gap at about 100\,AU, where the particles are limited by fragmentation. Particles in the pressure trap reach maximum sizes of about 3\,cm, which corresponds to a Stokes number of about 0.5. Outside the dust ring the particles are limited to a few millimeters or less in size. The vertically integrated dust-to-gas ratio in the pressure bump is about 6\,\%.
We calculated the intensity profile by solving the radiative transfer equation
\begin{equation}
I_\nu \left( r \right) = \left( 1 - e^{-\tau_\nu\left( r \right)} \right) B_\nu \left( T\left( r \right) \right),
\end{equation}
with the Planck function $B_\nu$ and the optical depth $\tau_\nu$, which is computed using the DSHARP opacity model \citep{2018ApJ...869L..45B}. The middle panel of figure \ref{fig:figure2} shows the intensity profiles at a wavelength of 1.25\,mm at different snapshots in the region of the dust ring. The intensity profile has been convolved with a Gaussian filter with the size of the beam $\sigma_\mathrm{b} = 3.3375\,\mathrm{AU}$ used in the observations of \citet{2018ApJ...869L..41A}. The unconvolved intensity profiles are plotted with dotted lines. The black dashed line is the observed intensity profile, which should be compared to the convolved profiles. The snapshot at 13\,Myrs fits the observed intensity profile best, while it still lacks emission in the outer wings of the bump.
The bottom panel of figure \ref{fig:figure2} shows the corresponding optical depth profiles at 1.25\,mm at the same snapshots. The optical depths has been calculated from the convolved (solid) and unconvolved (dotted) intensity profiles. The data point corresponds to the peak optical depth in the second ring of HD~163296 and its error derived in \citet{2018ApJ...869L..46D}. Again, the peak optical depth at 13\,Myrs in the simulation fits best to the observation. However, the model lies within the error bars for almost the entire lifetime of the protoplanetary disk, between 2\, Myr up to 20\,Myrs.
\begin{figure}[tbp!]
\includegraphics[width=\linewidth]{figure3}
\caption{{\it Top panel:} Time evolution of the peak optical depth in the dust ring calculated from the convolved intensity profiles. The data point corresponds to the second dust ring in HD~163296 \citep{2018ApJ...869L..41A, 2018ApJ...869L..46D}. {\it Bottom panel:} Time evolution of the peak midplane dust-to-gas ratio in the dust ring. The solid lines correspond to the model with and the dotted line to the model without planetesimal formation in each panel.}
\label{fig:peakOpticalDepth}
\end{figure}
Figure \ref{fig:peakOpticalDepth} shows the time evolution of the peak optical depth in the dust ring calculated from the convolved intensity profile and the maximum midplane dust-to-gas ratio. The control simulation without streaming instability is plotted for comparison. In the dust ring, streaming instability sets in after about 300\,000\,yrs, when the dust-to-gas ratio in the midplane reaches the threshold value of unity. At this point the optical depth levels off and stays within the error bars derived from the observations for almost the whole lifetime of the disk. The optical depth in the control case without streaming instability, on the other hand, continues to rise up to values of 1.75. Also the midplane dust-to-gas ratio is stabilized after the streaming instability sets in thanks to its self-regulating nature. In the control case without streaming instability the midplane dust-to-gas ratio reaches values as high as 10.
The peak that is seen in the optical depth in figure \ref{fig:peakOpticalDepth} shortly after 100\,000\,years marks the point in time when the particles hit the fragmentation barrier. Fragmentation limited particles roughly resemble a power law size distribution from the maximum particles size down to monomers. The size distribution of particles that have not yet hit the fragmentation limit is rather comparable to a Gaussian \citep[see e.g.][]{2012A&A...540A..73W}. This influences the resulting opacity of the particle distribution, with the fragmentation limited distribution being slightly less opaque, causing the drop in figure \ref{fig:peakOpticalDepth}. after 150\,000\,years.
\begin{figure}[tbp!]
\includegraphics[width=\linewidth]{figure4}
\caption{Mass budget of gas, total dust, dust in the ring, and planetesimals. The data point corresponds to the observed dust mass in the ring derived by the DSHARP survey \citep{2018ApJ...869L..41A, 2018ApJ...869L..46D}.}
\label{fig:massBudget}
\end{figure}
Figure \ref{fig:massBudget} shows the mass budget of gas, dust, and planetesimals during the simulation. The dashed red line represents the dust mass in the ring, where the ring size is defined by the full width at half maximum of the dust surface density. This value should be compared to the data point which corresponds to the dust mass in the ring as estimated by \citet{2018ApJ...869L..46D}.
Planetesimal formation starts after about 300\,000\,yrs and about 600 Earth masses of planetesimals are produced until the end of the simulation. After about 6\,Myrs, 95\,\% of the planetesimals have been formed. The planetesimal were not evolved any further, but simply stayed at the location of their formation.
\begin{figure}[tbp!]
\includegraphics[width=\linewidth]{figure5}
\caption{Spectral index profile in the dust ring region at different snapshots calculated from the convolved intensity profiles.}
\label{fig:spectralIndexProfile}
\end{figure}
Figure \ref{fig:spectralIndexProfile} shows the spectral index in the ring at different snapshots. The spectral index has been calculated using the intensity profiles at the two wavelengths 1.25\,mm and 3.00\,mm convolved with the beamsize at 3\,mm. As soon as fragmentation sets in and the particle size distribution roughly resembles a power law, the spectral index in the dust ring reaches its minimum values between 3.0 and 3.5, while it is significantly higher outside the dust ring later in the simulation.
\section{Discussion} \label{sec:discussion}
\citet{2018ApJ...869L..46D} analyzed eight bright rings observed in the DSHARP survey \citep{2018ApJ...869L..41A}. They found that the rings seen in the continuum emission can be explained by dust particles trapped in pressure bumps. The deviation from a Gaussian intensity profile can be explained by particle size distribution, the asymmetry by a background pressure gradient.
We see the same behavior in our numerical model concerning the outer ring of HD~163296 and including the full size distribution regulated by dust growth and fragmentation. But even in the snapshot at 13\,Myrs, which fits the observations best, the wings of the intensity bump are significantly lower than the observation. However, we only simulated one gap carved by a planet at 83.5\,AU. HD~163296 may have at least three more planets at 50\,AU \citep{2016PhRvL.117y1101I}, at 137\,AU \citep{2018ApJ...860L..12T}, and at 260\,AU \citep{2018ApJ...860L..13P}. If there are additional dust traps inside and outside of the pressure bump simulated in this work, the excess in emission that is observed may be explained by this. Modeling of multiple gaps and a deeper study of disk parameters will be part of future studies.
In our simulation, gravitational collapse of locally concentrated pebbles regulated by streaming instability leads to the formation of more than a Jupiter mass in planetesimals in a narrow ring. We did not further simulate the evolution of these planetesimals, but just let them stay at the location of their formation. Merging, scattering or pebble accretion onto planetesimals was not taken into account and will be a part of future works. Since we did not model any other planet farther outside in the disk, the dust initially located in the outer disk could drift to the dust ring thus increasing the formation rate of planetesimals. A pressure bump in the outer disk could trap some of the dust and lower the drift rate thereby reducing the final mass of planetesimals in the modeled ring.
Following the steps outlined in \citet{2017ASSL..445..197O}, we can estimate the pebble accretion rate onto the planetesimals in the dust ring. Assuming a typical planetesimal size of 100\,km, a single planetesimal would accrete $\sim 10^{-9}\,\mathrm{M}_\oplus/\mathrm{yr}$ using the particle size distribution and densities in the dust ring at 13\,Myrs. At this time we have about $10^{8}$ planetesimals in the simulation, leading to a total pebble accretion rate of $\sim 0.1\,\mathrm{M}_\oplus/\mathrm{yr}$. This is significant compared to the peak planetesimal formation rate of $\sim 10^{-3}\,\mathrm{M}_\oplus/\mathrm{yr}$ in the early simulation and should be taken into account in future works.
\subsection{Alternative explanations}
\label{sec:alternatives}
The formation of planetesimals from small dust particles is not the only possible explanation for the seemingly fine-tuned optical depths in the DSHARP rings. The back reaction of dust particles onto the gas can also smear out concentrations (\citealt{2016A&A...591A..86T, 2019arXiv190607708G}). This effect was not taken into account in this work. Back reaction can usually be neglected, if the dust-to-gas ratio is much lower than unity. But as seen in figure \ref{fig:peakOpticalDepth}, the midplane dust-to-gas ratio in the simulation without planetesimal formation reaches values of about 10. The influence of the back reaction of dust onto the gas on the appearance of the dust rings and the optical depth will be part of future works.
Recent publications have indicated that not only the absorption, but also the scattering opacity plays a significant role in the interpretation of (sub-)millimeter observations \citep{2015ApJ...809...78K, 2019arXiv190400333L, 2019arXiv190402127Z}. Whether the inclusion of scattering effects in the radiative transfer formalism can have a significant influence on the perceived optical depths will be part of future investigations. Observations with longer wavelengths (e.g. with facilities like the ngVLA, \citealp{2018arXiv180304467R}) could help to distinguish the scattering from the planetesimal formation scenario, since scattering effects are highly wavelength-dependent and suppressed at long wavelengths.
\section{Summary}
\label{sec:last}
In this publication, we show that a natural explanation for the peculiar optical depths observed in dust rings in protoplanetary disks is the formation of planetesimals converting small dust into large bodies. A simple analytical derivation assuming a single particle size (see equation~\ref{eqn:peakTauAnalyic}) shows that the optical depth of $\sim0.5$ is naturally obtained if the dust density is regulated by planetesimal formation. This would mean that the observed narrow distribution of optical depths in dust rings can be evidence of ongoing planetesimal formation.
As long as the streaming instability is acting, the midplane dust-to-gas ratio is limited to unity by formation of planetesimals from pebbles. This naturally limits the peak optical depth in the dust ring to values reported by the DSHARP survey for almost the whole lifetime of the protoplanetary disk. Additionally, the dust mass in the ring compares well to the value derived by \citet{2018ApJ...869L..46D}, which is a consequence of using the same opacities with a model that also reproduces the emission.
In a future works we aim to explore a larger parameter space to confirm if planetesimal formation can explain the other rings in the DSHARP survey.
\acknowledgments
We thank the anonymous referee for the helpful comments. S.M.S, J.D., and T.B. have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program under grant agreement No 714769.
S.M.S, J.D., T.B., and C.P.D. acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) ref. no. FOR 2634/1.
S.M.A. acknowledges funding from the National Aeronautics and Space Administration under grant No.~17-XRP17 2-0012 issued through the Exoplanets Research Program.
Part of this work was performed by S.M.S., J.D., and T.B. at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611.
The authors gratefully acknowledge the compute and data resources provided by the Leibniz Supercomputing Centre (\href{http://www.lrz.de/}{www.lrz.de}).
H.K. received funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) as part of the Schwerpunktprogramm (SPP, Priority Program) SPP 1833 "Building a Habitable Earth", Priority Programme "Exploring the Diversity of Extrasolar Planets" (SPP 1992) and in part at KITP Santa Barbara by the National Science Foundation under Grant No. NSF PHY17-48958. Part of this work was performed at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607761. This research was supported by the Munich Institute for Astro- and Particle Physics (MIAPP) of the DFG cluster of excellence "Origin and Structure of the Universe".
\bibliographystyle{aasjournal}
| {
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} | 291 |
Walter van Marvis (Doornik, omstreeks 1175 - aldaar, 1252) was bisschop van Doornik van 1219 tot 1252. Toen omvatte het bisdom onder meer de huidige bisdommen Gent en Brugge.
Sorbonne
Hij kreeg zijn eerste opleiding aan de kapittelschool van de kathedraal te Doornik om daarna verder theologie te gaan studeren aan de pas opgerichte Sorbonne in Parijs. Terug in Doornik gaf hij vanaf 1205 tot 1220 les aan diezelfde kapittelschool. Vervolgens nam hij deel aan de Vijfde Kruistocht waarbij hij - de later heilig verklaarde - Franciscus van Assisi ontmoette.
Bisschop geworden in 1219 bond Walter van Marvis in de periode 1226-1229 de strijd aan tegen de katharen daarbij gesteund door paus Gregorius IX.
Parochies
De volgende jaren was Walter van Marvis volop actief in zijn eigen bisdom waarbij hij zich telkens ten dienste stelde van de paus. Hij stelde orde op zaken in de kloosters, stichtte begijnhoven en richtte hospitalen op.
In Vlaanderen is hij vooral bekend omwille van de oprichting van talrijke parochies o.a. in de streek tussen Aalter en Brugge (Bulskampveld), het Land van Waas en het Meetjesland. In 1242 ondernam hij in deze contreien een rondreis om de verschillende parochies af te bakenen door het merken van kruisen op bomen of het laten plaatsen van (grens)kruisen. Talrijke plaats- en straatnamen verwijzen nog steeds naar deze gebeurtenis.
Marvis, W
Marvis, W
Bisschop in de Nederlanden in de 13e eeuw | {
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Gentag announces low-cost NFC/RFID phone
By Sarah Clark • 10 February 2011 19 May 2011 • nfcworld.com
The US$119 GT-601 NFC handset is designed for "people who are concerned only with basic voice communication, mobile payments, social networks, and diagnostics using a low-cost mobile wireless device," says Gentag.
GT-601: NFC for less than US$120
RFID medical sensor specialist Gentag has announced availability of a low cost mobile phone able to handle both NFC and RFID applications. The phone incorporates an NXP PN544 NFC chip and was co-developed in Asia by Gentag in collaboration with NXP and other partners.
The GT-601 is a quad band phone featuring a 2.2-inch screen, 1.3 megapixel camera, Bluetooth, MP3/MP4 player and an FM radio. It is directly compatible with the disposable NFC sensors and devices produced by Gentag and can be bundled with specific diagnostic kits or sensors for medical applications.
"This low-cost cell phone will be about one fourth the cost of a current 'smart' NFC cell phone and is specifically targeted to the needs of people who are concerned only with basic voice communication, mobile payments, social networks, and diagnostics using a low-cost mobile wireless device," says Gentag.
"We believe this combination of wireless technologies creates immediate global market opportunities for us in Asia, Europe, South and North America and India," explains Dr John P Peeters, founder of Gentag. "We plan to rapidly follow the release of this first phone with an NFC tablet and new types of Android-based cell phones, and we look forward to an expanded collaboration with NXP."
"Gentag's work to bring the technology to low-cost cell phone markets offers great potential to the telemedicine applications," adds NXP's Charles Dachs. "NFC will allow healthcare professionals to monitor their patients' health remotely, introducing over-the-counter technologies directly to consumer cell phones."
"We believe this phone is the first fully integrated cell phone that opens all the NFC and HF RFID market opportunities at the same time for consumers," Peeters told NFC World. "We are not aware of any NFC phone out today where the ISO15693 read- and write capabilities (that are part of the complete NFC specification) are available in combination with the other NFC capabilities. GT-601 supports all NFC functions including ISO15693 (e.g. NXP iCode SLI, Texas Instruments HF, and comparable industry standard tags)."
"The phone is also fully compatible with our disposable proprietary RFID IC platform that we can customize to work with any sensor, device or application," he added. "Therefore we are now in a unique market position to create custom consumer cell phone wireless 'bundles' for consumer diagnostics, industry applications or even homeland security. The technology is covered under our issued and pending US and international patents."
"In terms of pricing: It really depends on volumes, software configuration and what types of NFC sensor 'bundles' are included in the cell phone package as options, as well as the scope of the license under the Gentag/Altivera and Motorola patents," Peeters explained.
"We expect that some carriers and some of our business partners will want to give this phone away for free with a one- or two-year wireless plan," he added. "If the unlocked (SIM-lock free) GT-601 phone is sold without any monthly plan commitment, thus leaving the consumer free to insert any carrier's prepaid SIM, the suggested retail/street price to the individual end-user in the USA is $119 exclusive of sales taxes. This is the equivalent of 89 euros. Such price includes one full year warranty and appropriate margins for all involved stakeholders including the retailers."
"If bundled with one or more of Gentag's sensors or devices for diagnostics or industrial uses, the price depends on the actual bundle configuration and the actual business deal," Peeters told NFC World. We believe that some medical partners of Gentag will create their own data/patient monitoring plans and therefore will also provide the GT-601 cell phone at no cost."
Volume production of the GT-601 is due to begin in March 2011. The phones are available direct from Gentag, subject to a minimum order quantity of 5,000 units.
Explore: Altivera, Gentag, Motorola, NXP, Texas Instruments
Learn more: Android, GT-601, Healthcare, HF RFID, iCode, ID, ISO 15693, mHealth, New products, PN544, RFID, Wireless healthcare
Inside Secure bids for share of Android NFC chip market
Uncovered: The hidden NFC potential of the Google Nexus S and the Nokia C7
One thought on "Gentag announces low-cost NFC/RFID phone"
Stanton Kaye says:
13 February 2011 at 21:16 UTC
Is this a two chip, two memory configuration????:
Where the diagnostics are done in one chip and communicated through the RFID interface memory of the same chip or the rfid chip serial interace? | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,771 |
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Carrara Restaurant at the St James Theatre
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{"url":"https:\/\/math.stackexchange.com\/questions\/1264977\/how-can-i-finish-integrating-int-sqrtx2-49-over-x-using-trig-substitu","text":"# How can I finish integrating $\\int {\\sqrt{x^2-49} \\over x}$ using trig substitution?\n\n$$\\int {\\sqrt{x^2-49} \\over x}\\,dx$$ $$x = 7\\sec\\theta$$ $$dx = 7\\tan\\theta \\sec\\theta \\,d\\theta$$ $$\\int {\\sqrt{7^2\\sec^2\\theta - 7^2} \\over 7\\sec\\theta}\\left(7\\tan\\theta \\sec\\theta \\,d\\theta\\right) = \\int \\sqrt{7^2\\sec^2\\theta - 49} \\left(\\tan\\theta d\\theta\\right)$$ $$\\int\\sqrt{7^2(\\sec^2\\theta - 1)} (\\tan\\theta \\,d\\theta) = 7\\int\\sqrt{\\sec^2\\theta - 1} (\\tan\\theta \\,d\\theta)$$ $$7\\int \\tan^2\\theta \\,d\\theta = 7\\int \\sec^2\\theta - 1 \\,d\\theta$$ $$7\\int \\sec^2\\theta - 7\\int d\\theta$$ $$7\\tan\\theta - 7\\theta + C = 7(\\tan\\theta - \\theta) + C$$\n\nThis makes: $$\\theta = \\sec^{-1}\\left(x \\over 7\\right)$$\n\nAnd plugging back in to the indefinite integral:\n\n$$7\\left(\\left(\\sqrt{x^2-49} \\over 7 \\right) - \\sec^{-1}\\left(x \\over 7 \\right)\\right) + C$$\n\nMy question really is, how can I evaluate $\\sec^{-1}\\left(x \\over 7 \\right)$ ?\n\n\u2022 What do you mean by \"evaluating\" it? This is the correct answer. \u2013\u00a0KittyL May 3 '15 at 18:00\n\u2022 I think that's about as good as you can get, honestly. \u2013\u00a0Cameron Williams May 3 '15 at 18:00\n\u2022 Ok, my professor is really anal about simplification so I wasn't sure if it could be simplified more, or maybe look better in a way so it's not an inverse trig \u2013\u00a0Jay May 3 '15 at 18:05\n\u2022 The only thing you can simplify more is to distribute the $7$ and cancel them in the first term. An inverse trig is fine. You cannot simplify them to make them disappear. \u2013\u00a0KittyL May 3 '15 at 18:17\n\u2022 An alternative start is to first multiply top and bottom by $x$, and let $u^2=x^2-49$. Quickly we end up with $\\int \\frac{u^2}{u^2+49}\\,du$. So we want to integrate $1-\\frac{49}{u^2+49}$.. \u2013\u00a0Andr\u00e9 Nicolas May 3 '15 at 18:56\n\nLooks to me like you nailed it, and kudos as well for providing your work with such nice formatting! The quantity $\\sec^{-1}\\left(\\frac{x}{7}\\right)$ is as reduced as it's going to get. You cannot \"evaluate\" it anymore than you could further evaluate $\\sin(x)$. $\\sin(x)$ is simply $\\sin(x)$ for whatever value of $x$ you choose, just as $\\sec^{-1}\\left(\\frac{x}{7}\\right)$ is $\\sec^{-1}\\left(\\frac{x}{7}\\right)$. As a personal preference I would probably distribute that $7$ you have factored outside of everything, since it'll cancel the $7$ in the denominator of the term with the radical. Up to you though.\nIf it matters, $\\sec^{-1}(x) = \\cos^{-1}\\left(\\frac 1x\\right)$. No getting away from inverse trig, though.","date":"2019-08-21 01:13:15","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\": 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\": 0.7857432961463928, \"perplexity\": 414.0353047343223}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-35\/segments\/1566027315695.36\/warc\/CC-MAIN-20190821001802-20190821023802-00099.warc.gz\"}"} | null | null |
Say Somethin' to piosenka w stylu pop / R&B z elementami hip-hopu skomponowana przez Mariah Carey, Snoop Dogga, Chada Hugo oraz Pharella Williamsa na dziesiąty studyjny album Carey, The Emancipation of Mimi. Za produkcję odpowiedzialni są The Neptunes. Utwór został wybrany jako szósty singiel promujący album The Emancipation of Mimi i został wydany tego samego dnia co piosenka "Fly Like a Bird".
Lista i format singla
Europa CD singel
"Say Somethin'" (Wersja albumowa)
"Say Somethin'" (Morales Radio Edit)
Australia / Europa CD maxi singel
"Say Somethin'" (Wersja albumowa)
"Say Somethin'" (Stereo Anthem Mix)
"Say Somethin'" (Stereo Dub)
"Say Somethin'" (Teledysk)
Listy przebojów
Sprzedaż i certyfikaty
Przypisy
Linki zewnętrzne
Okładka
Oficjalna strona internetowa artystki
Single Mariah Carey
Single wydane w roku 2006 | {
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\section{Introduction}
\vskip 4mm
The analysis reported here was done in the years 2001--3 in
collaboration with three senior members of the BES collaboration.
The work was funded by the Royal Society and Queen Mary College
via a contractual agreement with the Chinese Academy of Sciences
and the BES collaboration.
This contract guaranteed access to BES 2 data for the purpose of
publications.
Since then, the BES management has refused to appoint internal
referees, hence blocking a collaboration publication.
The data illuminate the spectroscopy of $J^P=0^-$ mesons
and should be in the public domain.
There is a responsibility to publish work which has
been supported from public funds with approximately $\pounds 60,000$.
The wording of the present article is close to a document submitted
late in 2008 to the BES management, but some further
detail is added in Section 8.
There have been several earlier studies of
$J/\Psi \to \gamma (\pi ^+ \pi ^-\pi ^+\pi ^-)$.
The Mark III \cite {MarkIII} and DM2 collaborations \cite {DM2}
observed a large $0^-$ signal and peaks at 1500, 1760 and 2100 MeV.
Later, Expt. E760 at Fermilab found three peaks in $\eta \eta$
\cite {E760} with masses and widths very similar to those in
$J/\Psi \to \gamma 4\pi$.
In the $\eta \eta$ channel, quantum numbers $J^P = 0^-$ are
forbidden by Bose statistics.
A re-analysis of the Mark III data \cite {Scott} led to the conclusion
that the peaks have quantum numbers $J^{PC} = 0^{++}$, but sit on a
large $0^{-+}$ signal extending over the whole mass range up to
2400 MeV.
BES I data led to similar conclusions \cite {BESI}, but added the
identification of a broad $2^{++}$ signal at $\sim 2$ GeV, decaying
to $f_2(1270)\sigma$ and $\rho \rho$.
Here statistics a factor 7 higher are presented from BES II, using
58M $J/\Psi$ hadronic interactions.
The new data reveal further detail in the $0^-$ sector.
There is clear evidence for a $0^-$ resonance at 1970 MeV.
This new feature alters details of what may be fitted in this
mass range to $f_0(2100)$ and the $J^P = 2^+$ amplitude.
There is also a strong $\rho \rho$ peak at $\sim 1600$ MeV.
Two alternative ways of fitting this peak are presented.
The first alternative is that it may simply be a threshold $\rho \rho$
cusp.
The second investigates evidence that the peak is actually resonant.
The distinction between the two alternatives depends rather delicately
on the phase of the $0^-$ amplitude.
In the $J^P = 0^+$ sector, there is clear evidence for
the existence of an $f_0(1790)$ which is definitely distinct from
$f_0(1710)$.
The layout of the paper is as follows.
Section 2 concerns technicalities of data selection and reduction of
experimental backgrounds.
There is a troublesome background at high $4\pi$ mass from
$\pi ^0\pi^+\pi^-\pi^+\pi^-$, mostly $a_2(1320)\rho$ and
$a_1(1260)\rho$.
This background has little consequence below 2 GeV, but does obstruct
separation of $J^P = 2^+$ and $0^+$ from 2 to 2.3 GeV.
Sections 3 and 4 present a fit to the $4\pi$ mass spectrum in slices
of mass.
The key point is that $J/\Psi$ radiative decays are pointlike,
because of the large $c\bar c$ mass and because photons interact at a
point.
The consequence is that only the lowest angular momentum states
contribute, making the selection of partial waves clean, see Fig. 3.
The dominant $J^P = 0^-$ channel, produced by an M1 transition,
varies in intensity as $P^3_\gamma$, where $P_\gamma$ is photon
momentum.
Superimposed on this broad signal is a narrow structure requiring
the phase variation of a resonance at $\sim 1970$ MeV.
For $J^P = 0^+$, there is a strong clear $f_0(1790)$ peak, definitely
distinct from $f_0(1710)$, see Figs. 3(b) and (c).
The $2^+$ channel is fairly weak.
There is a definite signal in the mass range 2--2.3 GeV, but it is
difficult to say whether it is a single broad component or may be
due to more than one resonance.
The experimental background is the limiting feature in this mass
range.
Section 5 shows detailed fits to $4\pi$ mass projections.
Section 6 concerns the question of how to fit the dominant very broad
$0^-$ component.
From other data, it is known that there are threshold peaks, see
Fig. 10, in $\omega \omega$, $\bar KK^*$, $\bar K^*K^*$ and
$\phi \phi$, as well as in the strong $\rho \rho$ signal observed here.
One or more of these peaks could be resonant, but it seems unlikely
there is one resonance per channel.
The alternative is that they are threshold cusps.
The formula fitting the broad $0^-$ component is based on this
conservative approach.
Section 7 concerns fitted branching fractions.
The fit to the $4\pi$ mass spectrum from 1500 to 1650 MeV is not
perfect in this approach.
This mass range can be fitted significantly better if the strong peak
observed in $\rho \rho$ (and elsewhere in $\eta \pi \pi$) is
resonant.
However, in the absence of strong interferences with other partial
waves, this evidence for a resonance is tentative, and is discussed
in Section 8.
There is one feature of the present data which is in strong
disagreement to an earlier publication claiming an $\eta (1760)$
resonance which completely dominates data on
$J/\Psi \to \gamma \omega \omega$.
It is suggested in Section 9 that an alternative way of fitting those
data is in terms of a simple cusp due to the $\omega \omega$
P-wave threshold.
Section 10 summarises conclusions and the Appendix outlines the SU2
relation concerning Section 9.
\section {Event Selection and Backgrounds}
The data presented here were taken with the BES\,II detector.
Full details of the detector and its upgrade are reported by
Bai et al. \cite {DetectA}, \cite {DetectB}.
It has cylindrical symmetry around the intersecting $e^+e^-$ beams.
Its essential features are
(i) a Main Drift Chamber (MDC) for the measurement of charged particles,
(ii) time of flight detectors with a $\sigma$ of 180 ps, and
(iii) a 12 radiation length Barrel Shower Counter comprised of
gas proportional tubes interleaved with lead sheets.
The MDC measures $dE/dx$.
Together with the time of flight detectors, it separates $\pi$ and $K$
up to $\sim 700$ MeV/c.
Outside the $\gamma$ detectors is a magnet providing a field of
0.4T.
This magnet is instrumented with muon detectors, but for present
work they serve simply to reject $\mu ^+\mu ^-$ pairs.
The Main Drift Chamber provides full coverage of charged particles for
lab angles $\theta$ with $|\cos \theta | < 0.84$.
Events are selected initially by demanding four charged tracks in
the Main Drift Chamber with balancing charges, plus at least one photon
in the lead-scintillator detectors.
Any charged track with either time-of-flight or $dE/dx$ favouring kaon
identification is rejected.
Charged tracks are required to have a transverse momentum $>60$ MeV/c;
this reduces background from $J/\Psi \to \pi ^0\pi ^+\pi ^-\pi ^+\pi
^-$.
A geometrical cut is applied to ensure that all particles lie
inside a region well inside the known detector geometry, so as
to eliminate edge effects in detector performance and acceptance.
The vertex is required to lie within a cylindrical region of radius
2 cm and $\pm 20$ cm in length, with
respect to the known intersection point of the $e^+e^-$ beams.
Events have then been fitted kinematically to
$\gamma (\pi ^+\pi ^-\pi ^+ \pi ^- )$, using all photon showers in turn;
some photons may originate from interactions of charged particles in the
detector, but any photons within a cone of $6^\circ$ around a charged
particle are rejected.
Events with a $\chi ^2$ probability $>5\%$ are selected.
It is also required that $\chi ^2$ is better than that for likely
background channels:
(a) $4\pi$ ignoring photons,
(b) $2\gamma 4\pi$ if there is more than one photon and
$M(2\gamma)$ is within 50 MeV of the $\pi ^0$ mass.
A small detail is that background from $J/\Psi \to \omega \pi ^+\pi ^-$
has been rejected by a cut $|M_{\pi ^+\pi ^-\pi ^0} - M_\omega| > 25$
MeV, where the $\pi ^0$ is associated with missing momentum.
Also, to remove a small background from $J/\Psi \to \gamma K^0_S K^0_S$,
a double cut is made on the two $\pi ^+\pi ^-$ masses:
$|M_{\pi ^+\pi ^-}| > 25$ MeV.
The Monte Carlo generates 300K events to simulate the BES detector
and its acceptance; it uses the standard SIMBES package released in
February 2002, in its version as of March 2003.
During discussions with the BES management,
they have claimed that alterations to the calibration of the
time-of-flight system after March 2003 could affect the selection of
events.
I have investigated this claim thoroughly and it has no
foundation.
Firstly, there is excellent agreement between $dE/dx$ and
time-of-flight measurements.
Secondly, a search has been made for contamination of data due to
misidentified $\gamma K^+K^-\pi ^+\pi ^-$ events.
These are rather well separated from $\gamma 4\pi$ events by
kinematics as well as $dE/dx$ and time-of-flight.
For $60\%$ of events, the kinematic fit alone fails to fit
$\gamma K^+K^-\pi ^+ \pi ^-$ by a difference of $\chi ^2 >50$.
This is because production angles are sensitive to the different
masses of kaons and pions.
\begin{figure}
\begin{center}
\vskip -1cm
\epsfig{file=kkpp.eps,width=12cm}
\vskip -6mm
\caption[]{Mass projections for (a) $\pi \pi$ pairs from
events fitted to $\gamma \pi ^+\pi ^-\pi ^+\pi ^-$, taking $P(\pi ^+_1)
> P(\pi ^+_3)$ and $P(\pi ^- _2) > P(\pi_4^+)$; other panels refer to
events fitted to all combinations of $\gamma K^+K^-\pi ^+\pi ^-$: (b)
both $K\pi$ pairs, (c) $\pi ^+\pi^-$ pairs, (d) $K\bar K$ pairs.}
\end{center}
\end{figure}
Fig. 1(a) shows the mass distribution for $\pi _1^+\pi _2^-$ pairs
fitted to $\gamma 4\pi $ with momenta $P_1 > P_3$ and $P_2 >P_4$.
(Results for other $\pi ^+\pi ^-$ combinations are similar).
There is an obvious $\rho (770)$ signal; a small dip at 500 MeV
arises from the cut against $K^0_S$.
Next, these events have been fitted to all four combinations of
$\gamma K^+K^-\pi ^+\pi ^-$ after $dE/dx$ and time-of-flight cuts.
Events fitting with a $\chi ^2 < 50$ have the $K\pi$ mass
distribution shown in Fig. 1(b).
It is known from BES 1 data \cite {KKpp} that the
$\gamma K^+K^-\pi ^+ \pi ^-$ channel contains a very strong $K^*(890)$
signal.
There is no evidence for this in Fig. 1(b),
demonstrating that any contamination from $\gamma K^+K^-\pi ^+\pi ^-$
is $<1\%$ of good $\gamma 4\pi$ events.
Likewise there is no structure in the $K\bar K$ mass spectrum of
Fig. 1(d).
Fig. 1(c) shows the $\pi \pi$ mass spectrum from events surviving the
$dE/dx$ and time-of-flight cuts but fitted as
$\gamma K^+K^-\pi ^+ \pi ^-$.
One sees that the effect of the kinematic fit to the wrong
$\gamma K^+K^-\pi ^+\pi ^-$
hypothesis is to shift the $\rho (770)$ peak down in mass.
Other background processes and the acceptance for data are studied
using the standard SIMBES Monte Carlo simulation of the detector.
The main background arises from the $\pi ^0 \pi ^+\pi ^-\pi ^+\pi ^-$
channel after the loss of one photon.
This is well known from all earlier publications.
The $\pi ^0\pi ^+\pi ^-\pi ^+ \pi ^-$ channel has been studied by DM2
\cite {Augustin}.
It contains a strong $a_2(1320)\rho$ signal, a less
prominent $a_1(1260)\rho$ signal and thirdly a diffuse signal over all
of phase space.
The Monte Carlo has been used to generate $a_2(1320)\rho$ and
$a_1(1260)\rho$ events with the acceptance of the BES 2 detector.
Background from these channels in $\gamma 4\pi$ data peak strongly at
high $4\pi$ mass, because of the loss of low energy photons
associated with low energy $\pi ^0$.
This background dominates the $4\pi$ mass range $> 2400$ MeV/c$^2$,
allowing a firm determination of its magnitude.
\begin{figure}
\begin{center}
\vskip -1.5cm
\epsfig{file=fig1.eps,width=12cm}
\vskip -5mm
\caption[]{Mass projections: (a)--(c) refer to events where charged
particles alone are
consistent with the $\pi ^0 \pi ^+\pi ^-\pi ^+\pi ^-$ hypothesis.
(a) $M(\pi ^0 \pi ^{\pm })$,
(b) $M(3\pi )$ after selecting $M(\pi ^0 \pi ^{\pm})$
from 670 to 870 MeV, (c) $M(\pi ^0 \pi ^+\pi ^-)$, all events;
(d) $M(\pi ^+\pi ^- \pi ^+\pi ^-)$ after the full selection of
$\gamma \pi ^+\pi ^-\pi ^+\pi ^-$ events.}
\end{center}
\end{figure}
Both backgrounds produce clear $\rho (770) \to \pi ^0\pi ^{\pm}$,
see Fig. 2(a).
In these events, the background due to $a_2(1320)\rho$ leads to an
$a_2(1320)$ peak in the $\rho \pi$ mass distribution, shown in
Fig.~2(b).
Its magnitude is fitted freely and is consistent within errors with the
branching fraction quoted by the Particle Data Group (PDG) \cite {PDG}.
The $a_1$ is sufficiently broad that the $a_1(1260)\rho$ background
after cuts is consistent within errors with $5\pi$ phase space and
is fitted like that.
This background contribution is somewhat larger
than DM2 quote, suggesting that further diffuse background close to
$5\pi$ phase space is also present.
The combination of $a_1(1260)\rho$ and diffuse background is
again fitted freely to the $4\pi$ mass range above 2.4 GeV.
The sum of experimental backgrounds from $a_2(1320)\rho$ and
$a_1(1260)\rho$ is shown below by the dotted curve in Fig. 5(d).
Fig. 2(c) shows the observed $\pi ^0\pi ^+\pi ^-$ mass spectrum
in events fitted to $\pi ^0\pi ^+\pi ^-\pi ^+\pi ^-$.
The $\omega $ peak disappears after cuts used to select
$\gamma 4\pi$.
Fig.~2(d) shows the whole mass distribution for
$\pi ^+\pi ^- \pi ^+\pi ^-$ after the full event selection.
Peaks are visible below a mass of 2.4 GeV.
Above that, background dominates, so the analysis reported here is
confined to the mass range below 2400 MeV.
The total background up to 2.4 GeV is 27.3$\%$ of the whole
$\gamma 4\pi$ sample.
From Monte Carlo studies, estimated backgrounds from
$K^+K^-\pi ^+ \pi ^-$ and $\pi ^0K^+ K^-\pi ^+\pi ^-$ are $<2\%$;
the latter background is peaked at high $K^+K^-\pi ^+\pi ^-$
masses, like the $\pi ^0\pi ^+\pi ^-\pi ^+\pi ^-$ background,
and is mostly removed by selecting events with $4\pi$ mass
$< 2400 $ MeV.
\section {Introduction to formulae for partial waves}
Required channels are $\rho \rho$, $\sigma \sigma$ and
$f_2(1270)\sigma$.
There are several parametrisations of the $\sigma$
amplitude with increasing complexity as its couplings to $K\bar K$,
$\eta \eta $ and $4\pi$ have been unravelled \cite {Zou},
\cite {sigpole}, \cite {f01370}.
Only the coupling to $\pi \pi$ is important here.
All have been tried in the analysis, but there is little to choose
between them.
The first formula parametrises $\pi \pi$ data adequately and gives
slightly the best fit; it is the simplest and is used here.
There might be contributions from resonances decaying
to $a_2(1320)\pi$ and/or $a_1(1260)\pi$.
There is no evidence for $a_2\pi$ from this source in mass projections
of $\rho \pi$ after background subtraction.
Decays of $0^-$ to $a_1\pi$ are forbidden by parity conservation.
Adding decays of $f_0$ and $f_2$ to $a_1\pi$ from each resonance
one by one gives negligible improvements in log likelihood $(< 3)$.
The angular momentum in decays of resonances will be denoted by
$L$ and the angular momentum in the production process $J/\Psi \to
\gamma X$ will be denoted by $L'$.
The dominant process for production of $X$ with $J^P = 0^-$
requires $L'=1$.
The coupling of the photon to $c\bar c$ is a point interaction.
Because the charmed quarks are massive, the interaction of gluons with
$c\bar c$ is expected to be of very short range, with a
radius parameter of order $1/m_c \sim 0.1$ fm.
The intensity for $J/\Psi \to \gamma 0^-$ is then proportional to
$P^3$, (where $P$ is the momentum of the photon and hence the $4\pi$
system), multiplied by a very slowly varying form factor discussed
below.
The data are indeed close to the predicted $P^3$ dependence.
This has an important consequence: production with $L' > 1$ should be
strongly inhibited.
Higher $L'$ values were tried in the fit, and in all cases
are negligible.
This leads to a major simplification in the analysis.
For production of $J^P = 0^-$, the $L' = 1$ operator is represented
by the total momentum $K_X$ of $X$ in the $J/\Psi$ rest frame.
When it decays to $\rho _A \rho _B$, followed by
$\rho _A \to \pi _1 ^+\pi _2^-$ and $\rho _B \to \pi _3^+\pi _4^-$ the
vectors describing $\rho _A$ and $\rho _B$ are $K_A = k_1 - k_2$
and $K_B = k_3 - k_4$, where $k$ are momenta of pions in the rest
frame of each $\rho$.
[The 14 and 23 combinations also need to be added coherently
in the program].
The full formalism for Lorentz invariant tensors is presented in
Ref. \cite {formulae}.
It involves a Lorentz transformation of $K_A$ and $K_B$ to the
centre of mass of X.
Apart from this complication, the formula for production and
decay of $0^-$ is given by $K_A\wedge K_B.K_X$.
This form is highly distinctive, particularly the vital dependence
on $K_X$.
The states with $J^P=0^+$ and $2^+$ are produced with $L' = 0$.
The $0^+$ amplitude for $\sigma \sigma$ decays is isotropic;
for decays to $\rho \rho$ it is proportional to $K_A.K_B$.
The $2^+$ amplitude is given by the well-known spin 2 tensor:
$K^\alpha _A K^\beta _B - (1/3)(K_A.K_B)$.
All three $J^P$ components are cleanly and simply identified.
There is no evidence for components with other $J^P$, e.g. $1^+$
and $2^-$.
A check on all amplitudes in the program is that they are orthogonal
when integrated over $4\pi$ solid angle.
\begin{figure}
\begin{center}
\vskip -16mm
\epsfig{file=slice.eps,width=11cm}
\vskip -6mm
\caption[]{$J^P = 0^-$, $0^+$ and $2^+$ components from a fit in 50
MeV slices of $4\pi$ mass from 1350 to 2350 MeV. (b) shows
the sum of $\sigma \sigma$ and $\rho \rho$ signals;
the former dominates strongly.}
\end{center}
\end{figure}
\section {The Slice Analysis}
The data are fitted in 50 MeV bins of $4\pi$ mass and results
are shown in Fig. 3.
The $0^+$ amplitude peaks near 1790 MeV and has a shoulder near 1500
MeV.
For $J^P = 2^+$, decays to both $\rho \rho$ and $f_2(1270)\sigma$
are observed.
There is some cross-talk between these two final states, but both are
consistent with a broad peak at $\sim 2150$ MeV, plus a small
$f_2(1270) \to \rho \rho$ at masses 1270--1400 MeV.
The latter is weak and not well defined by present data.
Its magnitude is known from the analysis of $J/\Psi \to \gamma \pi ^+
\pi ^-$ and the $3.3\%$ branching fraction of
$f_2(1270) $ to $\rho ^0 \rho ^0$, and is fixed to this value in the
full fit described below; its phase is fitted freely.
From Fig. 3(a), the $J^P = 0^-$ amplitude appears to be made of two
components: peaks at 1600 and 2100 MeV.
However, the data cannot be fitted successfully like that.
The reason is that there is clear evidence for phase variation
consistent with a resonance near 1970 MeV interfering with the
broad $0^-$ component.
A good fit is obtained with a peak at $\sim 1600$ MeV in the broad
component, dropping smoothly to 2400 MeV, plus an interfering component
over the mass range 1850 to 2200 MeV, as shown below in Fig. 5(a).
The smooth drop in the broad component from 1600 to 2400 MeV is close
to the $P^3$ dependence expected for point-like production.
\begin{figure}
\begin{center}
\vskip -20mm
\epsfig{file=g4phase.eps,width=9cm}
\vskip -6mm
\caption[]{Differences in the slice fit between phases of
(a) $2^+ (\rho \rho )$ and $0^+$, (b)$ 2^+
[f_2(1270)\sigma ]$ and $2^+ (\rho \rho )$. }
\end{center}
\end{figure}
Although the magnitudes of the dominant components are well determined
in Fig. 3, their relative phases are poorly determined.
The final state with $J^P = 0^-$ is produced by an M1 transition
and that with $J^P = 0^+$ is produced by an E1 transition.
The program takes the trace over the two photon polarisations
allowed by Gauge Invariance and there is then no interference
between $0^-$ and $0^+$.
There is interference between $0^+$ and $2^+$ and between
$0^-$ and $2^+$, but it is fairly small in practice.
However, when the program takes the trace using all three
spins $0^-$, $0^+$ and $2^+$, there does remain some significant
information from details of angular correlations on the phase of the
$0^-$ amplitude and this will be discussed in detail in Section 8.
Fig. 4 displays information on phases from the slice fit after
integrating over all angles.
Errors for $0^-$, $0^+$ and $2^+$ are determined from the change in log
likelihood as the phase of each individual partial wave is moved in
steps.
Errors for the phase difference between $0^-$ and $0^+$ span most of the
range 0 to $360^\circ$, so these results are inconclusive and are not
shown.
The relative phase between $2^+$ and $0^+$ is shown in Fig.
4(a).
The two $2^+$ amplitudes are compatible within errors with a
constant or with a slowly rising phase difference in Fig. 4(b).
However, Fig. 4 is not able to display the delicate correlations
between all three spins if the angular information is used in addition.
This point will be discussed in Section 8.
\section {Full fit to data}
The dominant feature in the $4\pi$ mass spectrum is the broad
$J^{PC} = 0^{-+}$ signal in $\rho \rho$, extending
over the whole mass range from 1500 to 2400 MeV.
It will be described here as `the broad $0^-$'.
The rapid rise of the $0^-$ cross section at low mass is due
to the threshold for $\rho \rho$.
In Fig. 5(a), the upper histogram in each panel shows the overall fit
to the $4\pi$ mass projection.
The fit to the mass region 1500-1750 MeV is not perfect.
There appears to be one low point at 1610 MeV.
No available ingredient is narrow enough to fit a single bin.
The closest is $f_2(1565)$, but it has a full-width at half-maximum of
150 MeV.
Section 8 will present improvements if the 1600 MeV
$\rho \rho$ peak is fitted as a resonance rather than a threshold
cusp.
\begin{figure}
\begin{center}
\vskip -2cm
\epsfig{file=projns.eps,width=12.5cm}
\vskip -6mm
\caption[]{In each panel, the data points and upper histogram show
the full $4\pi$ signal for reference.
There is a cut from 1245 to 1325 MeV to remove $f_1(1285) \to 4\pi$.
Lower histograms show
individual components: (a) Full $0^-$ intensity (full histogram) and
from the broad $0^-$ alone (dotted); (b) $\eta (1970)$;
(c) coherent sum of all $0^+$; (d) coherent sum of all $2^+$ components
(full histogram) and background (dotted). }
\end{center}
\end{figure}
Fig. 5(a) shows as the lower full histogram the whole fitted $0^-$
component.
The dotted histogram shows the slowly varying $0^-$
component, which falls smoothly from 1560 to 2400 MeV.
Fig. 5(b) shows the component fitted as a $0^-$ resonance at
$1970 \pm 25(stat) \pm 60(syst)$ MeV
with $\Gamma = 210 \pm 25(stat) \pm 60(syst)$ MeV.
Systematic errors cover the whole range of fits and variations in the
form factors describing the broad $0^-$ component.
The $\eta (1970)$ contribution is close to $90^\circ$ out of phase
with the broad $0^-$, producing a dispersive shaped curve
in Fig. 5(a) due to destructive interference
between the real part of the $\eta(1970)$ and the imaginary part of
the broad $0^-$ amplitude.
Fig. 5(c) shows the full $0^+$ component, with
clear peaks at 1500 and 1800 MeV.
In Fig. 5(d), the full histogram shows the $2^+$ component, which may
be fitted by a broad resonance at 2150 MeV, plus a small contribution
from $f_2(1270) \to \rho \rho$.
This panel also displays as the dashed histogram the total incoherent
background, which is included in the fit to data.
In more detail, the $f_2(2150)$ requires almost equal contributions
from decays to $\rho \rho$ and $f_2(1270)\sigma$.
The fitted mass is $2150 \pm 29(stat) \pm 60(syst)$ MeV and the width
$506 \pm 30(stat) \pm 100(syst)$ MeV.
The largest uncertainty in fitting parameters arises from the
large and rapidly varying background of Fig. 5(d).
The mass of the broad $2^+$ component is significantly higher than
the $f_2(1940)$ found in BES I data \cite {BESI} and also higher than
the $f_2(1950)$ of the PDG, which quotes $M = 1944 \pm 12$ MeV,
$\Gamma = 472 \pm 18$ MeV.
This raises the possibility that the $2^+$ component observed
here consists of two or more unresolved states.
In the production process, the short-range interaction between the
photon and gluons limits the process to production of
$^3P_2$ $\bar qq$ states and excludes $^3F_2$.
Crystal Barrel analysis identifies two $^3P_2$ states, namely
$f_2(1910)$ of the Particle Data Group and $f_2(2240)$ \cite {CBAR},
well identified by polarisation data for $\bar pp \to \pi ^+\pi ^-$,
but incorrectly listed by the Particle Group under the $\bar ss$ state
$f_2(2300)$.
An alternative fit to the $2^+$ signal is made using $f_2(1910)$ and
$f_2(2240)$.
This gives an almost identical fit with log likelihood
better than the first alternative by only 0.8; this is not
statistically significant.
The fit to the $4\pi$ mass projection shows no significant difference
either.
So this is a feature of the data which cannot be resolved
conclusively at the moment.
The Table of results will use the single broad $f_2(2150)$.
\begin{figure}
\begin{center}
\vskip -12mm
\epsfig{file=0plus.eps,width=7.5cm}
\vskip -6mm
\caption[]{$0^+$ contributions from (i) the coherent sum of
$f_0(1370) + f_0(1500)$, (ii) $f_0(1790)$ and (iii) $f_0(1370)$.
There is a cut from 1245 to 1325 MeV to remove $f_1(1285) \to 4\pi$.
}
\end{center}
\end{figure}
The fit to $0^+$ definitely requires contributions from all of
$f_0(1370)$, $f_0(1500)$ and $f_0(1790)$.
The mass and width of $f_0(1370)$ are fixed at values 1309 and
325 MeV from the recent re-analysis of Ref. \cite {f01370}.
If $f_0(1370)$ is omitted from the fit, log likelihood is worse by
100.3, a highly significant amount.
Because of the rapid increase in $4\pi$ phase space,
its peak in $4\pi$ is at 1390 MeV but it has a long tail in $4\pi$ at
high mass and interferes with all other $0^+$ components.
Consequently, it is not well determined in magnitude.
The possible process $\sigma \to 4\pi$ is inconsistent with the slice
fit of Fig. 3(b) since it would give a broad contribution rising
continuously with mass according to $4\pi$ phase space.
Fig. 6 shows contributions from the coherent sum of $f_0(1370)$ and
$f_0(1500)$.
The effect of $f_0(1370)$ is needed to
broaden the contribution from $f_0(1500)$.
But the resulting tail interferes with $f_0(1790)$.
If the parametrisation of the $f_0(1370)$ component is varied within
its known errors, the observed mass of the 1790 MeV peak and its full
width at half-maximum remain very steady at $M = 1800 \pm 25$ MeV,
$\Gamma = 230 \pm 30$ MeV.
The observed peak is visually incompatible with
$f_0(1710)$, to which the PDG assigns a width of 137 MeV.
So the observed peak provides independent evidence for the existence of
$f_0(1790)$.
If the mass and width of $f_0(1790)$ are changed to PDG
values for $f_0(1710)$ MeV and the fit is re-optimised, the $4\pi$ mass
projection is very badly fitted, see Fig. 7.
\begin{figure}
\begin{center}
\vskip -10mm
\epsfig{file=allX.eps,width=6cm}
\vskip -7.5mm
\caption[]{The poor fit to the $4\pi$ mass spectrum if the mass and
width of $f_0(1790)$ are changed to those of $f_0(1710)$. }
\end{center}
\end{figure}
An important result is that previous evidence for $f_0(2100)$ in
these data has decreased substantially; it is now almost invisible in
the mass projection of Fig. 5(c).
The reason for the change is the new evidence for the
$\eta (1970)$.
The $f_0(2100)$ does appear clearly in E785 data on $\bar pp \to
(\eta \eta )\pi ^0$, and there is independent evidence for it in
Crystal Barrel data \cite {CBAR}.
\begin{figure}
\begin{center}
\vskip -6mm
\epsfig{file=fitall.eps,width=7.5cm}\
\vskip -6mm
\caption[]{Fit to mass projection for (a) $2\pi$,
(b) all $3\pi$, (c) $\rho \pi$, with a cut on the $\rho$ from 670 to
870 MeV; (d) the azimuthal angle $\chi$ between the planes of $\rho $
pairs.}
\end{center}
\end{figure}
Fig. 8 shows further details of the fit to data.
Fig. 8(a) shows the fit to the $\rho(770)$ peak.
The $3\pi$ mass projection of Fig. 8(b) and the $\rho \pi$ mass
projection of Fig. 8(c) exhibit the peak at 1320 MeV due
to the $a_2(1320)\rho$ background.
Fig. 8(d) shows the azimuthal angular distribution between
$K_A$ and $K_B$, requiring a large $0^-$ component, which
varies as $\sin ^2 \chi$.
Fig. 8(d) also reveals a substantial flat component.
Unfortunately, the dependence on $\sin ^2 \chi$ alone does not
separate $0^-$, $0^+$ and $2^+$ components cleanly.
Note also that there are two $\rho ^0\rho ^0$ combinations which
interfere coherently; this further hampers a separation of the three
available $J^P$ from $\sin ^2 \chi$ alone.
This is a well known problem in analysis of multi-body final states.
However, the full multi-dimensional correlations between production
angles, decay angles of intermediate isobars and the azimuthal angle
between pairs such as $\rho \rho$ do separate $J^P$ cleanly, as
displayed in Fig. 3.
There is no simple way of displaying the 3-dimensional angular
correlations (or 5-dimensional when two $\rho \rho$ combinations are
included); it is necessary to rely on the detailed amplitude analysis
and the variation of log likelihood with parametrisations of individual
resonances.
\section {More detail on formulae}
The final state $X$ has a radius of interaction between final
$\rho \rho$ or $\sigma \sigma$ configuations of order $R = 0.7$ fm.
It is necessary to include a form factor describing this
radius of interaction.
The conventional form factor for decays is
\begin {equation}
F_d = \exp (-k^2 R^2/6) = \exp (-\alpha _d k^2),
\end {equation}
where $\alpha _d= (1/6)(R/\hbar c)^2 = (1/6)(R (fm)/0.197321)^2$
with $\alpha _d$ in (GeV/c)$^{-2}$.
For decays with $L=1$, the standard Blatt-Weisskopf centrigual
barrier factor in the amplitude is
\begin {equation}
B = K/[(\hbar c/R')^2 + K^2]^{1/2}.
\end {equation}
Note that the derivation of this formula replaces the centrifugal
barrier by an equivalent square barrier, so $R'$ may be slighly
different from $R$ in the form factor.
However, the Gaussian form factor is only an approximation to unknown
wave functions, so it is convenient to fit data using a single radius
parameter, setting $R = R'$.
There is also a centrifugal barrier and form factor for
the production process, except that $R$ takes a much smaller
value; the parameter $\alpha _d$ of Eq. (1) is replaced by a much
smaller parameter $\alpha _p$.
The intensity of the $J^P = 0^-$ signal as a function of mass is
given by the square of the form factor and centrifugual barrier
factor, multiplied by a factor $P$ for phase space in the production.
The result is the factor $P^3$ quoted above, multiplied by a weak
form factor $F_p = \exp (-\alpha _p P^2)$.
A general remark concerns the mass of the $\rho \rho$ peak.
If the width of the $\rho$ were zero, the P-wave intensity
for $\rho \rho$ would rise from threshold as $k^3$ where $k$ is the
momentum of each particle in the $\rho \rho$ system.
A centrifugal barrier and decay form factor of conventional radius
$\sim 0.7$ fm would make the $\rho \rho$ and $\omega \omega$
intensities both peak in the range 1700-1800 MeV.
The width of the $\rho$ spreads this peak out further than that
for $\omega \omega$.
It is the factor $P^3$ for the production cross section from a
point-like source which reduces the mass of the peak to $\sim 1600$ MeV.
It is necessary to fold the width of the two $\rho$ into the evaluation
of $4\pi$ phase space. This is given by
\begin {equation} \rho _{4\pi}(s) =
\int ^{(\sqrt {s} - 2m_\pi )^2} _{4m^2_\pi}
\frac {ds_1}{\pi} \int ^{(\sqrt {s} - \sqrt {s_1})^2}_{4m^2_\pi}
\frac {ds_2}{\pi}
\frac {8|k|\,|k_1| \, |k_2|} {\sqrt {s \, s_1 \, s_2}}
|T_1(s_1)|^2 |T_2(s_2)|^2 \exp (-2\alpha _d k^2),
\end {equation}
where $k_1$ and $k_2$ are momenta of pions from the decay of each
$\rho$ in its rest frame, and $k$ stands for the momenta of the $\rho$
in the rest frame of the resonance $X$.
The amplitude $T(s)$ is the usual Breit-Wigner amplitude for the
$\rho$.
These integrals are done numerically and then parametrised by smooth
functions of $s$.
\subsection {The effect of thresholds on resonances}
It is common practice to fit resonances with Breit-Wigner amplitudes
with constant width.
However, the Flatt\' e formula shows this to be only an approximation.
That formula describes the amplitude by
\begin {equation}
T=F(s)/[M^2 - s - i \sum _i g^2_i \rho _i(s)],
\end {equation}
where $F(s)=F_pF_d$, $g_i$ is the coupling constant and $\rho _i$ the
Lorentz invariant phase space for each channel $i$.
Eqn. (4) however requires a further term if the amplitude is to be
described correctly by an analytic function of $s$.
It has been known since the 1950's that the full form for $T$ is
\begin {eqnarray}
T &=& F(s)/[M^2 - s -m(s) - i\sum g^2_i\rho _i(s) ]
\\ m(s) &=& \frac {(s - M^2)}{\pi}P \int \frac {\sum _i g^2_i \rho
_i(s')\, ds'}{(s' - s)(s' - M^2)}.
\end {eqnarray}
The additional term $m(s)$ describes the $s$-dependence of the real part
of the amplitude going with the $s$-dependence of the imaginary part.
It is essential in fitting the present data near the $\rho \rho$
threshold; without it, the fit is very bad, see Fig. 11(b) below.
The mass dependence of $m(s)$ is shown in Fig. 9.
The new parametrisation of the broad $0^-$ amplitude supercedes
primitive alternatives used in Refs. [4] and [5].
\begin{figure}
\begin{center}
\vskip -1.5cm
\epsfig{file=dispbrn.eps,width=6cm}\
\vskip -0.6cm
\caption[]{The dispersive term $m(s)$ for the broad $0^-$ contribution.}
\end{center}
\end{figure}
A general comment is needed on the role of $M^2$ in Eqs. (4)--(6).
There may be further decay channels, presently unknown.
Also the exponential form factor of Eq. (1) is a conventional educated
guess; it is needed to make the dispersion integral of Eq. (6)
converge.
Realistically there are uncertainties in the high energy behaviour of
this integral, well known as a renormalisation effect.
The value of $M^2$ may be viewed as a way of applying an empirical
correction to $m(s)$ for such effects.
A single broad resonance has been used in the earlier work by Bugg,
Dong and Zou \cite {Broad0M}.
In the earlier work $M$ was 2.19 GeV; now it moves to 2.04 GeV.
Fig. 10 shows that similar threshold behaviour is observed in $\eta
\pi\pi$ , $K\bar K^*$, $\omega \omega$ (from Mark III) \cite
{Wermes}, $K^*\bar K^*$ and $\phi \phi$.
Fig. 10(a) shows the broad $0^-$ component fitted to
$\gamma (\eta \pi \pi)$ data, the sum of $\eta \sigma$ and $a_0\pi$.
Fig. 10(b) shows the coherent sum of $\eta
(1440)$ and the broad $0^-$ fitted to the $K\bar K^*$ channel in an
accompanying paper on $J/\Psi \to \gamma (\eta \pi ^+\pi ^-)$ and
$\gamma (K^\pm K^0_S \pi ^\mp )$ \cite {iota}.
Fig. 10(c) shows what is observed with $J^P = 0^-$ in $\gamma \rho
\rho$.
A further threshold peak (not shown) is observed in BES II data
for $J^P = 0^+$ on $J/\Psi \to \gamma \omega \phi$ \cite {omphi}.
The natural explanation of all these processes is that
$J/\Psi \to \gamma GG$, where $G$ are gluons.
These produce pairs of vector mesons via colour
neutralisation.
In turn, these may de-excite to lower mass
configurations, e.g. $[\rho \rho]_{L=1} \to [\eta \sigma ]_{L=1}$.
This can explain why the $\eta \sigma$ intensity peaks strongly at the
same mass as $\rho \rho$.
The inference is that all these peaks may be threshold cusps.
Such cusps are well known in other processes.
Examples are threshold peaks in $\pi d \to NN$ and
$\bar pp \to \bar \Lambda \Lambda$ \cite {cusps}.
The other possibility is that one or more of these peaks is resonant.
\begin{figure}
\begin{center}
\vskip -1.5cm
\epsfig{file=iofit.ps,width=9cm}\
\vskip -6mm
\caption[]{Fit to mass projections for $0^-$ signals in 6 channels.}
\end{center}
\end{figure}
The data have been fitted using Eqs. (5) and (6) including the effects
of cusps in all coupled channels.
The coupling constants $g^2_i$ are adjusted iteratively to reproduce
branching fractions of every channel in Fig. 10.
As a result, the form of the broad $0^-$ is tightly constrained.
The dispersive term associated with the opening of the $\rho \rho$
threshold plays a crucial role.
Without it, the fit to data, shown on Fig. 11(b), is hopelessly bad.
Fig. 11(a) shows the Argand diagram for Eq. (5).
Note that what is plotted is the amplitude without the
form factor $F(s)$ of the numerator.
The reason for this is that the factors $P$ for production and $k$
for decay are built into the tensor expressions for amplitudes,
as well as the associated form factors.
The intensity observed in data at low momentum in Fig. 10(b) is
inflated by the factor $P^3$ for production.
Note too that there are two interfering $\rho \rho$ combinations in
Fig. 11(b).
Approaching 1900 MeV, the magnitude of the amplitude on Fig. 11(a)
is decreased by the opening of the strong $K^*\bar K^*$ threshold.
As this channel decreases above 2200 MeV, the amplitude recovers.
Note that this threshold does {\it not} account for the structure
near 1900 MeV which has been fitted by the additional $\eta (1970)$.
On the Argand diagram of Fig. 11(a), there is not a complete loop
corresponding to a resonance in the mass range near 1600 MeV.
It is being fitted as a simple threshold cusp.
Below the threshold, the real part of the amplitude moves positive.
Over the threshold, the imaginary part of the amplitude increases
rapidly.
Above the threshold, the real part of the amplitude decreases
slowly.
The result is a half loop, characteristic of a cusp.
\begin{figure}
\begin{center}
\vskip -2cm
\epsfig{file=badfitn.ps,width=12cm}\
\vskip -6mm
\caption{(a) Argand diagram for the broad $0^-$; masses are shown in
GeV;
(b) the bad fit to the $0^-$ mass projection with the dispersive term
$m(s)$ omitted.}
\end{center}
\end{figure}
However, from Eqs. (5) and (6) and fitted parameters, it turns out
that there is a broad pole at $M=M_0 -i\Gamma /2 = 1.564 \pm
0.012 - i(0.139 -i 0.035)$ GeV; errors are systematic and are
estimated from the parametrisation of the $\rho \rho$ channel and its
extrapolation into the complex $s$-plane.
There is no discernable pole due to the weaker P-wave $\omega \omega$
threshold which peaks at 1750 MeV.
There are more distant poles, including one at $1.862 - i0.210$ GeV
associated with the opening of the $K^*\bar K^*$ channel.
For present data, the parameter $\alpha _d$ controlling the form factor
in Eq. (1) optimises at $2.25 \pm 0.25$ GeV$^{-2}$, corresponding to
a reasonable radius of interaction for decays, $0.73 \pm 0.04$ fm.
The value of $\alpha _p$ for the production process optimises at
0.06 GeV$^{-2}$, corresponding to a radius of interaction 0.12 fm.
As an aid to future work where the broad $0^-$ is relevant,
the fully annotated Fortran code used for it is available directly
from the author.
This code includes numerical parametrisations of $\rho _i(s)$ for
$\alpha _d$ in steps of 0.25 GeV$^{-2}$.
For values of $\alpha _d$ or $\alpha_p$ different to those used here, it
will be necessary to re-optimise $g^2_i$ fitted to all relevant sets of
data.
\section {Branching fractions}
Table 1 summarises the significance levels for each component,
measured by changes $\Delta S$ in log likelihood when the
component is removed from the fit and all other components are
re-optimised.
Statistically, $\chi ^2$ is approximarely twice $\Delta S$.
However, experience shows that signals less than 20 in log likelihood
are of questionable significance because of the possibility of
systematic errors.
Contributions in this category are the weak decays of $f_0(1790)$ and
$f_0(2100)$ to $\rho \rho$ and also $f_2(1565)$, which produces
a change of log likelihood of just 11.9.
\begin{table}[htb]
\begin {center}
\begin{tabular}{ccc}
\hline
channel & $\delta (ln L)$ & Branching fraction $\times 10^4$ \\\hline
$\eta (2190) \to \rho \rho$ & $> 1000$ & \\
$\eta (1970) \to \rho \rho$ & $233.5$ & $2.0 \pm 0.3$ \\
Both $0^-$ & &$13.7 \pm 1.4$ \\
$f_0(1370) \to \sigma \sigma$ & $100.3$ & $1.1 \pm 0.4$ \\
$f_0(1500) \to \sigma \sigma$ & $163.8$ & $1.5 \pm 0.4$ \\
$f_0(1790) \to \sigma \sigma$ & $140.0$ & $5.8 \pm 1.2$ \\
$f_0(1790) \to \rho \rho $ & $3.0$ & \\
$f_0(2105) \to \sigma \sigma$ & $25.2$ & \\
$f_0(2105) \to \rho \rho$ & $6.0$ & \\
$f_2(1565) \to \rho \rho$ & $11.9$ & $0.7 \pm 0.3$ \\
$f_2(2150) \to \rho \rho$ & $70.2$ & \\
$f_2(2150) \to f_2(1270)\sigma $ & $178.5$ & \\
$f_2(2150) \to \rho \rho + f_2(1270)\sigma $ & $190.5$ & $3.1 \pm 0.5$
\\\hline
\end{tabular}
\caption{Changes in log likelihood when each
channel is dropped from the fit and remaining contributions are
re-optimised.
Column 3 shows branching fractions for $J/\Psi \to \gamma X$, $X \to
\pi ^+\pi ^-\pi ^+\pi ^-$.
Missing elements are not quoted because of large uncertainties due to
interferences.
Errors include systematic errors on the overall normalisation.}
\end {center}
\end{table}
The total number of selected events is 23591.
The total background fitted up to a mass of 2.4 GeV is 27.3\% of all
events, leaving a total signal of 72.7\%.
The corresponding branching fraction for all events is
\begin {equation}
J/\Psi \to \gamma (\pi ^+\pi ^-\pi ^+\pi ^-) = (25.5 \pm 2.6(syst))
\times 10^{-4}, ~M(4\pi) < 2.4~ {\rm GeV}.
\end {equation}
The error is systematic and arises mostly from uncertainty in the
experimental background.
In determining branching fractions given in Table 1,
interferences within one channel between the two possible $\pi ^+\pi
^-$ combinations are included, but interferences between different
channels are dropped.
This is because interferences within one resonance should be universal,
but interferences with other channels vary from process to process.
Note that the PDG quotes branching fractions for all $\rho \rho$ and
$\sigma \sigma$ charge states.
These are conventionally obtained by multiplying the branching
fractions of Table 1 by a factor 3 for $\rho \rho$ and a factor $9/4$
for $\sigma \sigma$.
However, it is likely that interferences between different
charge configurations of a single resonance will be different between
$\rho ^0\rho ^0$ and $\rho ^+\rho ^-$.
Chen et al. \cite {Chen} have estimated the magnitudes of such effects.
The fitting program itemises the magnitudes of all individual resonances
and all interferences between them.
A warning is that interferences are quite large within
one $J^P$.
There is destructive interference between the two decay modes
of $f_2(2150)$, so the branching fraction is quoted only for their
coherent sum.
There is also destructive interference between the broad $0^-$
amplitude and $\eta (1970)$, so the table quotes the total $0^-$
branching ratio.
Within the $0^+$ sector, the branching fractions of $f_0(1500)$
and $f_0(1770)$ are quite well determined, but there is a poorly
determined interference with the tail of $f_0(1370)$.
The magnitude of any possible $f_0(2100)$ contribution is difficult
to determine because of interferences with the high mass tails of
all of $f_0(1370)$, $f_0(1500)$ and $f_0(1790)$, and is therefore
not quoted.
There is no direct interference between $J^P = 0^-$ and $0^+$.
Interferences between $0^+$ and $2^+$ are also quite small.
The summed events for $0^-$, $0^+$ and $2^+$ add up to 17166
events, to be compared with the total of 17146 events after
background subtraction.
\begin{figure} [htb]
\begin{center}
\vskip -1cm
\epsfig{file=projnsx.eps,width=12cm}\
\vskip -6mm
\caption{The fit, including an $\eta (1560)$, to the $4\pi$ mass
projection and magnitudes of fitted components in the same format as
Fig. 5.}
\end{center}
\end{figure}
\section {Subtle evidence for a $0^{-+}$ resonance near
1560 MeV}
The $4\pi$ mass projection shown on Fig. 5 is not fitted perfectly
from 1500 to 1650 MeV.
There is one low point at 1610 MeV.
Moving the edges of bins or changing the bin width does not
alter this point significantly.
There is also some evidence for a similar dip in DM2 data
\cite {DM2} and a dip in Mark III data at 1650 MeV \cite {Scott}.
It is unreasonable to invent a new narrow resonance to fit the
single low point at 1610 MeV.
However, the observed pole in the broad $0^-$ component is already
a hint that the $\rho \rho$ threshold peak is resonant.
This is what would be called in today's terminology a dynamically
driven $\rho \rho$ resonance.
It is quite likely to mix with the $n\bar n$ radial excitation
expected in this general mass range, for example the radial excitation
of $\eta (1295)$ if it exists.
Suppose there is such a $0^-$ resonance in the range
1550--1700 MeV.
Experience with other sets of data, for example Crystal
Barrel data, Refs. \cite {f01370} and \cite {wrho}, is
that a resonance at or close to a broad threshold is in practice
described well by a simple pole with a high mass dispersive tail
given by the term $m(s)$ of Eq. (6).
That is, a good approximation can be obtained by adding a simple
Breit-Wigner pole to the dispersive amplitude used so far.
It is instructive to fit the data this way, scanning the mass and
width of the additional pole.
It turns out that this gives a distinct improvement in the fit to
the $4\pi$ mass projection and the dip at 1610 MeV.
It gives an improvement in $2 \times$ log likelihood (which
follows a distribution very close to $\chi ^2$) of 194 for four extra
fitting parameters, statistically a 10.6 standard deviation effect.
Systematic errors quoted for mass and width cover all variations
as masses and widths of $f_0(1500)$ and $f_0(1790)$ are varied over
their allowed ranges from earlier data; systematic errors
also cover uncertainty in the dispersive contribution of the $\eta
\pi\pi$ channel.
The improvement in the fit comes partially from the fit to the $4\pi$
mass spectrum.
However, it also comes from systematic improvements amongst decays to
$0^+$, $2^+$ and $0^-$ partial waves.
The fitting program takes the trace over both allowed spin states
of the photon.
There are interferences between $0^-$ and $2^+$
and between $0^+$ and $2^+$, dependent in subtle ways on
three-dimensional angular correlations, hence giving information
on relative phases.
The new fit is shown in Fig. 12 in precisely the same format as
Fig. 5.
There is an obvious improvement in the fit to the $4\pi$ mass
spectrum from 1500 to 1650 MeV, particularly near the dip.
The signal due to $f_0(1500)$ in Fig. 12(c) decreases slightly
and the dip before $f_0(1790)$ is also slightly lower.
No change is required to the parameters of $f_0(1790)$.
The mass of $\eta (1970)$ does not change, but its width
decreases from $210 \pm 25(stat) \pm 60(syst)$ to
$165 \pm 25(stat) \pm 60(syst)$ MeV.
A knock-on effect of this reduction is that the width of
the broad $2^+$ component at 2150 MeV decreases from 506 MeV to
$300 \pm 75$ MeV.
The evidence for $f_0(2100)$ increases slightly on Fig. 12(c).
A definite $f_2(1565)$ appears in Fig. 12(d).
Except for this state, branching fractions remain within the errors
shown in Table 1.
The branching fraction for $f_2(1565)$ rises to $(1.3 \pm 0.3) \times
10^{-4}$, nearly double that of Table 1.
\begin{figure} [htb]
\begin{center}
\vskip -1.5cm
\epsfig{file=arganx.ps,width=7cm}\
\vskip -6mm
\caption{The Argand diagram for the coherent sum of the 1560 MeV
$0^-$ pole and the dispersive cusp; masses are shown in GeV}
\end{center}
\end{figure}
The Argand diagram for the coherent sum of the 1560 MeV pole and
the dispersive cusp is instructive and is shown in Fig.
13.
The pole term is $\sim 35^\circ$ out of phase with the
dispersive term, and the result is to increase the speed
with which the amplitude describes the Argand loop of
Fig. 13.
As one sees from Fig. 12(a), the direct effect on the whole $0^-$
amplitude is to produce half the required dip at 1610 MeV.
The remaining dip is created by a decrease in the $0^+$
amplitude between $f_0(1500)$ and $f_0(1790)$.
The increased $f_2(1565)$ intensity in Fig. 12(d) and its
interference with the $0^+$ amplitude contributes to the fit to the
$4\pi$ mass spectrum near 1560 MeV.
The coherent sum of the additional pole and the broad $0^-$
has been parametrised as a function of $s$ and extrapolated into the
complex plane.
A pole is observed at $M = 1560 \pm 12 - i(143\pm 35) $ MeV,
close to that of the broad $0^-$ alone.
The improvement in log likelihood when the $0^-$ pole at 1560 MeV
is included is larger than for most of the other contributions in
Table 1, so the evidence for this resonance must be taken seriously.
In summary, there is no doubt about the existence of a strong
$\rho \rho$ peak at $\sim 1600$ MeV.
However, evidence for resonant behaviour is hidden in the angular
correlations.
It would be valuable to have further $4\pi$ data in which the $0^-$
component interferes with another well defined component;
central production in the Compass experiment is one such possibility.
\section {A conflict with $\gamma \omega \omega$ analysis}
A BES II paper on $J/\Psi \to \gamma \omega \omega$ claims a large and
almost pure $\eta (1760)$ signal in $\omega \omega$ \cite {gww}.
No such resonance is observed in the present data.
This raises a problem.
There is a well known relation, coming from SU(2) symmetry,
that an $I=0$ resonance should have equal couplings to
$\omega \omega$ and $\rho ^0\rho ^0$.
Physically, light quarks do not discriminate between charges and
therefore couple equally strongly to $\omega \omega$ and
$\rho ^0\rho ^0$.
Because there are three charge states for $\rho \rho$, the
relation is normally written $g^2(\rho \rho ) = 3g^2(\omega\omega)$.
This relation applies equally to $q\bar q$ states, hybrids and
glueballs, since it springs from SU(2) symmetry, which is obeyed by all
these configurations.
The Appendix gives an elementary derivation of
this result for a $q\bar q$ state.
Similar algebra generalises the result to all three types of state.
The branching fraction quoted for production of $\eta (1760)$ in
the $\gamma \omega \omega$ data is
$(1.98 \pm 0.08(stat) \pm 0.32 (syst)) \times 10^{-3}$.
This is larger than the branching fraction in present data for
production of $\rho ^0\rho^0$ with $J^P = 0^-$ over the
{\it entire} mass range: $(1.37 \pm 0.14) \times 10^{-3}$.
It should lead to a huge peak with resonant phase variation
interfering with the broad $0^-$ component.
The present data are in complete disagreement with that
possibility.
Furthermore, such a large resonance is also in conflict with all
earlier data from BES 1 \cite {BESI}, Mark III \cite {MarkIII} and
DM2 \cite {DM2}.
The DM2 group did claim a small $\eta (1760)$ signal originating from
the peak near this mass in the total $4\pi$ mass projection; however,
this had a branching fraction an order of magnitude smaller than
BES II claim.
Furthermore, DM2 did not try a $0^+ \to \sigma \sigma$ contribution
which fits the peak in present work.
The likely explanation of the conflicts is that the $0^-$ signal in
$\omega \omega$ is not a resonance, but a threshold cusp.
Note that there is no phase information identifying resonant
behaviour of $\eta (1760)$ in BES data.
It was simply assumed that the peak is resonant.
A threshold cusp arises because the $\omega \omega$ intensity
rises initially from threshold as $k^3$, but peaks near 1700 MeV due to
the form factor $\exp -(\alpha _d p^2)$; here $k$ is the momentum of
each $\omega$ in the $\omega \omega$ rest frame.
The precise position of the peak depends rather strongly on
$\alpha _d$.
The BES publication does not give details of the form factor assumed
for the P-wave.
This explanation may be tested by refitting the
$\omega \omega$ mass projection of BES II data using the $\omega \omega$
decay of the broad $0^-$ fitted to present data.
The $\eta (1970)$ component should also obey the SU(2) relation between
$g^2_{\omega \omega }$ and $g^2_{\rho ^0 \rho ^0}$.
This constraint is applied by fixing relative magnitudes of $\eta
(1970)$ and the broad $0^-$ to the value fitted to present
data.
However, the phase of $\eta (1970)$ relative to the broad $0^-$
is fitted freely, since it is determined by multiple
scattering amongst all components, which are different in $\omega
\omega$ and $4\pi$ final states.
Decays of $f_0(1790)$ to $\omega \omega$ are also included. but are
limited in intensity to $20\%$ of the broad $0^-$.
This is the maximum which can be fitted to $f_0(1790) \to \rho ^0 \rho
^0$ in present data.
Decays of the $0^+$ state produce a $\cos ^2 \chi$ decay distribution
(where $\chi$ is the angle between $\omega $ decay planes)
which combines with an equal amount of $0^-$ to produce a flat
component in the $\chi$ distribution.
This allows the $0^-$ component of BES II data to rise to $\sim 46\%$
of those data.
There may be small $2^+$ contributions from $f_2(1565)$ and
$f_2(1910)$/$f_2(2150)$.
Figs. 5(d) and 12(d) show that these are almost zero at 1750 MeV.
They can only be determined from the $\gamma \omega \omega$ data
using the full angular correlations.
They are therefore omitted from the test made here.
\begin{figure}
\begin{center}
\vskip -2cm
\epsfig{file=beswwg.eps,width=12cm}\
\vskip -6mm
\caption{The fit to BES II $\gamma \omega \omega $ data as a threshold
cusp.
In (b), the upper full curve shows the total contribution;
the dotted curve shows the broad $0^-$ alone, and the
dashed curve its coherent sum with $\eta (1970)$.
The chain curve shows the $f_0(1790)$ intensity and the lower
full curve the experimental background scaled from the BES II
publication.}
\end{center}
\end{figure}
Fig. 14(a) shows the resulting fit to the $\omega \omega$ mass
spectrum.
The optimum fit requires some reduction of the parameter $\alpha _d$
of the form factor for decays to 2.0 GeV$^{-2}$.
The fit is close to the data, showing that they may indeed be fitted
by a non-resonant threshold cusp.
The optimum fit would require $\alpha _d < 2.0$ GeV$^{-2}$, but that
would create an inconsistency with the $\rho \rho$ data.
Details of the components are shown on Fig. 14(b).
The full curve is the same as in Fig. 14(a) as a reference.
The dotted curve shows the contribution from the broad $0^-$,
and the dashed curve shows its coherent sum with the $\eta (1970)$.
The overall effect of $\eta (1970)$ is quite small.
The chain curve shows the $f_0(1790)$ contribution, fitted with the
required phase space for S-wave decays.
The broad $0^-$ makes a small but significant
contribution above 2 GeV; BES II fitted that mass range purely as
background.
To allow for this, the $s$-dependence of the background is taken from
the BES publication, but its absolute magnitude is fitted freely and
is shown by the lower full curve on Fig. 14(b).
The fit in Fig. 14 is made without considering the absolute magnitude
of the branching fraction for $J/\Psi \to \gamma \omega \omega$.
The BES II publication quotes branching fractions in their
Table 2 adding to $(2.77 \pm 0.12) \times 10^{-3}$ of all $J/\Psi$
decays.
It is a matter of conern that this is considerably larger than
quoted by DM2 \cite {DM2}, $1.42 \pm 0.2 \pm 0.42$ and Mark III, $1.76
\pm 0.09 \pm 0.45$ \cite {MarkIII}.
Also, one would expect the branching fraction for $\rho \rho$
after integration over all masses to be roughly the same as for
$\omega \omega$; the $\rho \rho$ peak is simply spread out compared
with $\omega \omega$ by the width of the $\rho$.
The disagreements over branching fractions raises the question of
backgrounds in the BES data.
Those used in the BES publication were estimated by Monte Carlo
simulations, which really need checking against the standard sideband
subtraction procedure.
Also the BES II analysis chose the best of 15 combinations of photons
fitting $\gamma \omega \omega$; wrong combinations will make a
significant background, but this background is not discussed in the
BES publication.
\section {Summary and Conclusions}
In summary, the new data confirm earlier detection of $0^+$ states at
1500 and 1790 MeV in this channel.
There is a broad $2^+$ signal at $\sim 2150$ MeV decaying to both $\rho
\rho$ and $f_2(1270)\sigma$, but this may be an unresolved combination
of more than one state.
For $J^P= 0^-$, the new data give a distinctly
improved definition of the broad $0^-$ component.
The exponential form factor for decays is well determined, with
$\alpha _d = 2.25 \pm 0.25$ (GeV/c)$^2$, corresponding to a radius of
interaction of $0.73 \pm 0.04$ fm for decays.
The exponential form factor for production is also well determined,
with very small $\alpha _p = 0.06$, corresponding to a radius of
interaction of $0.12$ fm for the production process; this
is consistent with the expected point-like interaction.
There is also a definite dispersive shaped effect with a
resonant phase variation with respect to the broad $0^-$
component, requiring the presence of a $0^-$ resonance with mass $1970
\pm 25(stat) \pm 60(syst)$ MeV and width $210 \pm 25(stat) \pm
60(syst)$ MeV, in fair agreement with a less definitive Crystal Barrel
observation \cite {CBAR}.
There is subtle but persuasive evidence that the observed
$\rho \rho$ threshold peak with $J^P = 0^-$ resonates at
$\sim 1560$ MeV.
Because there is only limited phase information from interference with
$f_2(1565)$ (which in turn interferes with $f_0(1500)$ and
$f_0(1790)$), confirmation of a resonance is needed in other data
where some well defined component plays the role of an interferometer.
In both Crystal Barrel data on (a) $\bar pp \to \eta \pi ^0 \pi ^0$
\cite {zeromA} and (b) $\bar pp \to 3\eta$ \cite {zeromB}, there is
evidence for a $J^{PC} = 0^{-+}$ resonance in $f_0(1500)\eta$ at
$2285 \pm 20$ MeV in (a) and at $2320 \pm 15$ MeV in (b).
The latter is a particularly simple channel exhibiting a clear peak.
One can now identify a Regge trajectory of conventional slope for
$\eta (550)$, $\eta (1295)$, $\eta (1970)$ and $\eta (2320)$.
The possible $\eta (1560)$ falls 100 MeV below this trajectory.
However, its mass is subject to a systematic error of $\pm 60$ MeV at
present.
\vspace{0.5cm} I wish to acknowledge financial support from the Royal
Society and Queen Mary College. I am also grateful for help from
members of the BES collaboration in processing data and running the
Monte Carlo simulation of acceptance and backgrounds.
\section {Appendix}
The $I=0$ $\bar nn$ combination is
$(u\bar u + d\bar d)/\sqrt {2}$.
Its decay is via the production of a $^3P_0$ pair
$(u\bar u + d\bar d)/\sqrt {2}$.
The final states is $(u\bar u + d\bar d)(u\bar u + d\bar d)/2$.
An $\omega \omega $ pair has this compositon by inspection.
What about $\rho \rho$ decays?
The isospin Clebsch-Gordan coefficients for an $I=0$ resonance
coupling to two $I=1$ particles is
$(\rho ^+\rho ^- + \rho ^- \rho ^+ - \rho ^0 \rho ^0)/\sqrt {3}$,
where $\rho ^+ = u\bar d$, $\rho ^0 = (u\bar u - d\bar d)/\sqrt {2}$
and $\rho^- = -\bar u d$. So
\begin {eqnarray}
(\rho ^+\rho ^- - \rho ^0 \rho ^0 +\rho ^-\rho ^+)/\sqrt {3} &=&
-u\bar d \bar u d - (u\bar u - d\bar d)(u\bar u - d\bar d)/2
- \bar ud u\bar d \\
&=&(-2u\bar d\bar u d - u\bar u u\bar u - d\bar d d\bar d +
u\bar d \bar u d + \bar u d u\bar d - 2\bar u d u \bar d)/2 \\
&=&-(u\bar u u\bar u + d\bar d d\bar d + u\bar d \bar u d
+ \bar u d u \bar d)/2 \\
&=& -(u\bar u + d\bar d)(d\bar u + d\bar d)/2.
\end {eqnarray}
So the decay of $I=0$ $\bar nn$ produces the combination
$(\rho ^- \rho ^0 -\rho ^+\rho ^- - \rho ^-\rho ^+)$,
i.e. the same $\rho \rho ^0$ intensity as $\omega \omega$
and also $\rho ^-\rho ^+$.
\par
{\hskip 0.4cm}
\begin {thebibliography}{99}
\bibitem{MarkIII} R.M. Baltrusaitis {\it et al.} (Mark III
Collaboration), Phys. Rev. {\bf D33} 1222 (1986)
\bibitem{DM2} D. Bisello {\it et al.} (DM2
Collaboration), Phys. Rev. {\bf D39} 701 (1989)
\bibitem{E760} T.A. Armstrong {\it et al.} (E760 Collaboration),
Phys. Lett. {\bf 307} 394 (1993)
\bibitem{Scott} D.V. Bugg {\it et al.}, Phys. Lett. {\bf B353} 378
(1995)
\bibitem{BESI} J.Z. Bai {\it et al.} (BES 1 Collaboration)),
Phys. Lett. {\bf B472} 207 (2000)
\bibitem {DetectA} J.Z. Bai {\it et al.} (BES
Collaboration), Nucl. Instr. Methods {\bf A344} 319 (1994)
\bibitem {DetectB} J.Z. Bai {\it et al.} (BES Collaboration),
Nucl. Instr. Methods {\bf A458} 627 (2001)
\bibitem{KKpp} J.Z. Bai {\it et al.} (BES 1 Collaboration),
Phys. Lett. {\bf B472} 200 (2000)
\bibitem{Augustin} J.E. Augustin {\it et al.} (DM2 Collaboration), Nucl.
Phys. {\bf B320} (1989) 1
\bibitem{PDG} Particle Data Group (PDG), Phys. Lett. G:
{\bf B667} 1 (2008)
\bibitem{Zou} B.S. Zou and D.V. Bugg, Phys. Rev. {\bf D48}
3948 (1993)
\bibitem{sigpole} D.V. Bugg, J. Phys. {\bf G 34} 151 (2007)
\bibitem{f01370} D.V. Bugg, Eur. Phys. J {\bf C 52} 55 (2007)
\bibitem {formulae} B.S. Zou and D.V. Bugg, Eur. Phys. J
{\bf A 16} 537 (2003)
\bibitem{CBAR} A.V. Anisovich {\it et al.} (Crystal Barrel
Collaboration), Phys. Lett. {\bf B491} 47 (2000)
\bibitem{Wermes} L. K\" opke and N. Wermes, Phys. Rep. {\bf 174} 67
(1989), Fig. 92
\bibitem{iota} D.V. Bugg, accompanying paper arXiv:0907.3015
\bibitem{omphi} M. Ablikim {\it et al.} (BES 2 Collaboration),
Phys. Rev. Lett. {\bf 96} 162002 (2006)
\bibitem{cusps} D.V. Bugg, Phys. Lett. {\bf B598} 8 (2004)
\bibitem {Broad0M} D.V. Bugg, L.Y. Dong and B.S. Zou 1991 Phys.
Lett. {\bf B458} 511 (1999)
\bibitem {Chen} J. Chen, X.Q. Li and B.S. Zou, Phys. Rev. {\bf D62}
034011 (2000)
\bibitem {wrho} C.A. Baker {\it et al.} (Crystal Barrel Collaboration),
Phys. Lett. {\bf B563} 140 (2003)
\bibitem {gww} M. Ablikim {\it et al.} (BES 2 Collaboration),
Phys. Rev. {\bf D 73} 112007 (2006)
\bibitem {zeromA} A.V. Anisovich {\it et al.} Phys. Lett. B {\bf 491}
47 (2000)
\bibitem {zeromB} A.V. Anisovich {\it et al.} Phys. Lett. B {\bf 496}
145 (2000)
\end{thebibliography}
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,834 |
Time Stands Still...RIP Neil Peart.
I was going to post a video from last night, but I just heard some very depressing news. Neil Peart, drummer for the band Rush, passed away at age 67, of apparent brain caner (I am tired of hearing that damned word).
My wife Beth and several close friends are Rush fanatics. I liked their music, but it wasn't until Beth and I attended a concert a few years back that I saw just how incredible this band is. And I learned how Neil, besides being one of the greatest drummers of all time, was a survivor of the worse a man could take. In 1997, he lost his only child, Selena, and in 1998, his wife Jackie. This happened in the course of ten months. He recounts the 18 month motorcycle ride he took to heal himself, riding from Canada to Brazil, in his book Ghost Rider.
Rest In Peace Neil. You're with Jackie and Selena now. And thank you for the joy you brought to millions with your music, and you.
Labels: Canada, Life in General, Motorcycles, Music
An interesting loook at the killing of Suleimani
In the initial aftermath of our killing of the sack of excrement, I heard General Petraeus was not in favor of the operation. But it looks like his view is a bit more nuanced.
Petraeus Says Trump May Have Helped 'Reestablish Deterrence' by Killing Suleimani
The former U.S. commander and CIA director says Iran's "very fragile" situation may limit its response.
As a former commander of U.S. forces in Iraq and Afghanistan and a former CIA director, retired Gen. David Petraeus is keenly familiar with Qassem Suleimani, the powerful chief of Iran's Quds Force, who was killed in a U.S. airstrike in Baghdad Friday morning.
After months of a muted U.S. response to Tehran's repeated lashing out—the downing of a U.S. military drone, a devastating attack on Saudi oil infrastructure, and more—Suleimani's killing was designed to send a pointed message to the regime that the United States will not tolerate continued provocation, he said.
Petraeus spoke to Foreign Policy on Friday about the implications of an action he called "more significant than the killing of Osama bin Laden." This interview has been edited for clarity and length.
Foreign Policy: What impact will the killing of Gen. Suleimani have on regional tensions?
David Petraeus: It is impossible to overstate the importance of this particular action. It is more significant than the killing of Osama bin Laden or even the death of [Islamic State leader Abu Bakr] al-Baghdadi. Suleimani was the architect and operational commander of the Iranian effort to solidify control of the so-called Shia crescent, stretching from Iran to Iraq through Syria into southern Lebanon. He is responsible for providing explosives, projectiles, and arms and other munitions that killed well over 600 American soldiers and many more of our coalition and Iraqi partners just in Iraq, as well as in many other countries such as Syria. So his death is of enormous significance.
The question of course is how does Iran respond in terms of direct action by its military and Revolutionary Guard Corps forces? And how does it direct its proxies—the Iranian-supported Shia militia in Iraq and Syria and southern Lebanon, and throughout the world?
FP: Two previous administrations have reportedly considered this course of action and dismissed it. Why did Trump act now?
DP: The reasoning seems to be to show in the most significant way possible that the U.S. is just not going to allow the continued violence—the rocketing of our bases, the killing of an American contractor, the attacks on shipping, on unarmed drones—without a very significant response...
FP: Do you think this response was proportionate?
DP: It was a defensive response and this is, again, of enormous consequence and significance. But now the question is: How does Iran respond with its own forces and its proxies, and then what does that lead the U.S. to do?
Iran is in a very precarious economic situation, it is very fragile domestically—they've killed many, many hundreds if not thousands of Iranian citizens who were demonstrating on the streets of Iran in response to the dismal economic situation and the mismanagement and corruption. I just don't see the Iranians as anywhere near as supportive of the regime at this point as they were decades ago during the Iran-Iraq War. Clearly the supreme leader has to consider that as Iran considers the potential responses to what the U.S. has done...
FP: ...Do you think the decision to conduct this attack on Iraqi soil was overly provocative?
DP: Again what was the alternative? Do it in Iran? Think of the implications of that. This is the most formidable adversary that we have faced for decades. He is a combination of CIA director, JSOC [Joint Special Operations Command] commander, and special presidential envoy for the region. This is a very significant effort to reestablish deterrence, which obviously had not been shored up by the relatively insignificant responses up until now.
FP: What is the likelihood that there will be an all-out war?
DP: Obviously all sides will suffer if this becomes a wider war, but Iran has to be very worried that—in the state of its economy, the significant popular unrest and demonstrations against the regime—that this is a real threat to the regime in a way that we have not seen prior to this.
FP: Given the maximum pressure campaign that has crippled its economy, the designation of the Islamic Revolutionary Guard Corps as a terrorist organization, and now this assassination, what incentive does Iran have to negotiate now?
DP: The incentive would be to get out from under the sanctions, which are crippling. Could we get back to the Iran nuclear deal plus some additional actions that could address the shortcomings of the agreement?
This is a very significant escalation, and they don't know where this goes any more than anyone else does. Yes, they can respond and they can retaliate, and that can lead to further retaliation—and that it is clear now that the administration is willing to take very substantial action. This is a pretty clarifying moment in that regard...
Interesting look at the killing of Suleimani.
Labels: Donald Trump, Iran
A good look at the integration of women into the combat arms.
I have worked with great women in the service, and the police. However, there is no question in my mind that women have no business in the direct combat arms, i.e. infantry, armor, and tube artillery. One of the (many) cluster f^&*s of the Obama years was putting women into subs. Once a submarine submerges for a 90 plus day tour, it has one main purpose: To not be scene. I'm just waiting for the first case of a woman walking up to the captain, 60s days into the cruise, "Sir, I'm pregnant..." At that moment, the ship must surface, the sailor put on the largest surface ship they can find (assumption it has the best medical facilities), and evacuated to land.
Sorry Obama, Ash, Mrs Bill Clinton, you cannot change the facts of life, put women and men close together, they will do what comes naturally. That is one of the reasons we don't put women into the close combat arms. Now, my close friend COL Mike Ford has reviewed another book on my "to read" bookcase (Goal for the year is 36 books...one can only hope!), and I will read this soon enough (Just breezed through it so far). I hope you find this interesting.
Book Review: Women in Combat; Feminism Goes to War
Book Review: Women in Combat; Feminism Goes to WarSome time ago, I had been asked to look over the final, pre-publication draft of a book, written by a friend of one of my West Point classmates whose father just happens to be a Medal of Honor recipient. More on that later. I made note of some things and informed the author. Below is my review of the final, published book.
The book, Women in Combat; Feminism Goes to War, is written by Mark C. Atkins, a self-described, "failed Marine" (I checked; He has an Honorable Discharge) does what few folks today have courage to do, call out the current feminization of our military for what it is. This book is a natural extension to the feminist effort described by Bruce Deitrick Price; "K-12: The War on Boys and Men," now being used to weaken our military.
Mr Atkins gets out of the blocks quickly and right in your face—with his choice of a title: Women in Combat: Feminism goes to War. With this title alone, he is sure to become a target of the feminist left.
In Part One of his book, Atkins sets the stage, starting with the feminist agenda, differences between men and women, finishing the first part of his book by stating that the concepts of freedom and equality, are "false justification for women in combat."
In Part Two of the book, He introduces what he clearly considers the crux of the issue, namely human nature and its most important product, the natural-rational-family. In his words:
We humans possess a healthy-nature, and this nature inclines us to produce instinctively and forever the natural-rational-family. Inasmuch as any ideal can be reduced to a formula, I posit as sovereign truth and offer no evidence beyond what common sense observation can provide, that the ideal family, born of our healthy-nature, consists of: A masculine man and a feminine woman united for life, in mutual respect, in a sexually exclusive union, the man leading, the woman following, the woman providing them and their offspring a home, the man protecting and providing for them and their home, both committed to the well-being and development of their children, both emotionally and physically affectionate towards each other and their children.
This family is most likely to produce the well being and survival of children and by extension the people. This family is the greenhouse that is most likely to produce the young man or woman that will withstand the vagaries of life, and make, support, and protect what is good, passing on the strengths of the people to the next generation. It is least likely to produce the young man or woman that is laden with baggage or dysfunctions.
That this ideal is rarely achieved does not justify our chucking it out the window. It is in fact broadly achieved by many, and many more over the course of a lifetime will make progress towards it. Indeed, the strength of any given people is a product of the degree to which its constituent families are able to embrace the ideal of the natural-rational-family. The further removed a people's families are from this ideal, the weaker the people.
Atkins then goes on to blast feminism for the damage it has done to the American family and offers a dire warning. He writes…
Feminism has pounded the square peg into the round hole, damaged both, and declared victory. Not satisfied with having wrecked the American family and thus American culture with its bad ideas, Feminism is now wrecking the United States military.
Later, Mr Atkins goes on to describes feminism's objectives and methodologies—those culminating in a horrible end:
In order to sustain Sexual Liberation as a practical reality, Feminism has encouraged women to do that which is most contrary to their nature, i.e., to destroy their own offspring.
In Chapters 11-20, Mr. Atkins walks us through the physical and psychological differences between men and women while comparing them to the attributes desirable for a Soldier in close combat. He elaborates on just how the attributes of men are far superior to women for close combat, even in today's technological era. He further expands this by detailing how having women in close combat formations, can actually be a significant detriment.
I enjoyed this book, likely because Mr. Atkins is saying what I, and the vast majority of Americans, believed not all that long ago. He writes well, and throws in just enough humor to keep the book from being a finger-wagging lecture. The greatest strength of this book is that it is organized well and leads the reader through a logical progression to the author's conclusion.
Now for the other shoe. Lack of citations for the fundamental assertions in the book detract from its credibility. Yes. "Everybody knows" that, on average, female upper body strength is less than that of males. "Everybody knows" that males are more aggressive than females. "Everybody knows" that strength and aggressiveness are critical attributes in close combat. However, unless it's an opinion piece, the author needs some citations for these basic assertions. Fortunately, there is easily found and credible research out there to support all of the fundamental assertions upon which Mr. Atkins bases his argument.
What might have helped (Monday morning quarterback here) is to have brought one or two distinguished senior officers with combat experience along as co-authors. I had mentioned this to Atkins earlier, but it was too late to do so. It also would have been unethical to ask a senior military personage to "rubber stamp" an already written manuscript as his own.
To his great credit, Mr. Atkins did the next best thing by sending copies of his book to a number of senior officers with extensive combat experience who agree with his positions and who have given glowing reviews inside the cover. Best of all, the forward to this great book was written by Major General (Retired) Patrick Henry Brady, Medivac Pilot in Vietnam and recipient of the Medal of Honor.
This is a book worth reading for those who wish to get to the root of the problem which, according to Atkins, is a mass rejection of a common sense understanding of basic human nature. It lays out a logical path that can only end up in one place. As Atkins states…
Just as home is what it is because it is an extension of woman's nature, combat is what it is because it is an extension of man's nature. He does not need to alter his nature to enter this arena. She must.
You can find "Women in Combat," on Amazon
Mike Ford, a retired Infantry Officer, writes on Military, Foreign Affairs and occasionally dabbles in Political and Economic matters...
I'll probably start this after this coming weekend. Take care.
Labels: B Hussein Obama, Books, Feminism, Military
The year ends...
Before you had an iPhone that call any song up instantly, it took an effort to listen to specific music. And this was a song that always comes along as the year ends, and we look back at the previous year. In the case of this song, to a memory of "the one that you let get away," if you will. The lyrics are perfect, the story of two former lovers meeting by complete coincidence, and the years are irrelevant, and the memories fresh as today.
As the year ends, 2020 arrives, and we get ready for the resolutions, sit back and enjoy the end of year classic. Dan Fogelberg, Same Old Lang Syne.
Labels: Holidays, Life in General, Music
The false god of diversity über alles...
In November, 2009, Major Nidal Hasan murdered 13 Americans at Fort Hood, Texas, screaming "'Allahu Akba!" In the immediate aftermath, as it was discovered how his problematic behavior was known and swept under the rug, the then Army Chief of Staff made a disgusting statement. As the bodies had not even been removed (only slight exaggeration), he showed what he was concerned about:
"You know, there's been a lot of speculation going on and probably the curiosity is a good thing," said Casey of accused killer Nidal Malik Hasan. "But we have to be careful because we can't jump to conclusions now based on little snippets of information that come out. And frankly, I am worried — not worried, not worried, but I'm concerned — that this increased speculation could cause a backlash against some of our Muslim soldiers and I've asked our army leaders to be on the look out for that. it would be a shame — as great a tragedy as this was — it would be a shame if our diversity became a casualty as well."
Well, move on, we find one criminal act after another of un-assimilated foreigners, the thought that "diversity" is not all that it's cracked up to be. In the last two months, we've had multiple attacks on Jews in New York, and it's a "diverse" group of attackers. Well, found this article earlier today, and it's interesting:
Diversity Obsession Partly to Blame for Rise in Anti-Semitism
The horrible attack on a Jewish shul in Monsey, New York on the seventh night of Hanukkah is not directly connected to the atmosphere on American campuses and, sadly, in certain quarters of the U.S. Congress. But they are of a piece spiritually and psychologically.
Something is drastically wrong. The canary in the coal mine (Jews first, others later) is back. It's permissible to slur Jews and to beat or stab them (five different violent incidents during this Hanukkah alone in the New York City area). Jewish students on college campuses are hiding their religious affiliation as they cross the green to class.
Why now? What has caused all this?
It's not the sole reason, but I am going to say something outrageous to some. It is the worship of diversity. Note that word—worship.
Diversity is by itself a good thing. We are a diverse society. As many have said, that's part of our strength...
Disagreement, "diversity" of skin color, religion, etc, is not a strength. Diversity of thought is a strength. Also, tolerance and acceptance of different peoples, religions, etc, is a strength. Knowing a black man can work well with a white woman, etc, is good and helpful. More on this later.
"...What has developed in recent decades, however, is the elevation of diversity above all. The slogan "E pluribus unum" (out of many one) has virtually disappeared from our country, the "unum" pushed to irrelevance.
Everywhere we go these days, diversity is counted and measured ad nauseum. How many of this group? How many of that group? It's an obsession.
Where you worship diversity, there will always be winners and losers in that diversity. Like it or not, it creates a pecking order. And these pecking orders are reinforced, consciously and unconsciously, by our media, entertainment, and the academy.
And, naturally enough, out of pecking orders, hatreds (or old hatreds, as in the case of anti-Semitism) emerge.
Today's Democratic Party with its devotion to and reliance on identity politics fans these hatreds, deliberately or not....
Deliberately so. They cannot appeal to the broad population as a whole, so it must divide into groups and play them against each other. See Rules for Radicals.
...How absurd and morally and psychologically damaging this is when we are all humans with nearly identical DNA. It's a reactionary and proto-fascist idea masquerading as progressive. It is, in essence, a new form of segregationism.
Yet it has spread and been transmogrified to many aspects of our society. Identity is everywhere. Even the recent killings at the New Jersey kosher market were motivated by some people thinking they were the real Jews and the other people weren't. How crazy is that!...
Excellent look at how the idol worship of the outer self is destroying our nation. A point Mr. Simon made is "E pluribus unum" (out of many one)" has largely disappeared. The American melting pot has been replaced with a salad bowl. Instead of assimilating into America as a whole, we keep the groups separate and against each other. And it's a result of deliberate action of the federal government.
In reference to my comment on diversity, tolerance, etc, I recall the wisdom of my last professor of military science (PMS) at Tulane University. He was a Special Forces officer, a Vietnam veteran, and he grew up in the Army of the 60s and 70s. The one that was broken by, among other things, racism. Now the ROTC detachment he headed covered six universities around New Orleans, including 3 traditionally black colleges. When we did operations, field problems, etc, the PMS instructed his staff, "Mix every university, insure we have blacks from one college working with whites from another, women with men, etc. They will be leading a mixed army, they need to know how to be comfortable and competent with people not like them." That was intelligence guided by experience and wisdom. Unlike the race baiting poverty industry we have now.
Labels: Crime, Diversity/multiculturalism, Jewish issues, Military
A Hail Mary that didn't work.....
The Battle of the Bulge (officially called the Ardennes Counteroffensive) started in early December 1944. Hitler hoped to catch the Allies napping. He did.
In the beginning of the operations, the US 106th Infantry Division was overrun, and the 101st Airborne Division went to secure the critical city of Bastone. And it's arguable, this was the Finest Hour, for the American Army. This week marks the 75th Anniversary of this epic battle. I think I gotta watch Pattonthis weekend.
'Nuts!' US troops thwarted Hitler's last gamble 75 years ago
BASTOGNE, Belgium (AP) — Pvt. Arthur Jacobson was seeking cover in the snow behind a tank moving slowly through the wooded hills of Belgium's Ardennes, German bullets whizzing by.
That was when he lost his best friend and Bazooka team partner to sniper fire. "They couldn't hit him, he shouted," Jacobson said wistfully. "Those were his last words."
The recollection of his worst day in the Battle of the Bulge still haunts him, three quarters of a century later during the first return of the 95-year-old to the battlefield....
The fighting in the bitterly cold winter of 1944 was unforgiving to the extreme...
...What Jacobson didn't know then was that he was part of the battle to contain Nazi Germany's desperate last offensive that Adolf Hitler hoped would become his version of the Allies' D-Day: A momentous thrust that would change the course of World War II by forcing U.S. and British troops to sue for peace, thus freeing Germany to focus on rapidly advancing Soviet armies in the east.
"WE WERE THERE TO DO SOMETHING ABOUT IT"
The Battle of the Bulge "is arguably the greatest battle in American military history," according to the U.S. army historical center. Such perspective came only later to Jacobson, who was barely 20 at the time.
"They really didn't tell us anything," he said . "The Germans had attacked through Belgium, and we were there to do something about it."
Out of the blue at dawn on Dec. 16, 1944, over 200,000 German troops counter-attacked across the front line in Belgium and Luxembourg, smashing into battle-weary US soldiers positioned in terrain as foreign to them as it was familiar to the Germans.
Yet somehow, the Americans blunted the advance and started turning back the enemy for good, setting allied troops on a roll that would end the war in Europe less than five months later.
This battle gained fame not so much for the commanders' tactics as for the resilience of small units hampered by poor communications that stood shoulder to shoulder to deny Hitler the quick breakthrough he desperately needed. Even though the Americans were often pushed back, they were able to delay the German advance in its crucial initial stages. The tipping point was to come later...
..."The thought was that Germany was on its knees and could no longer raise a big army,"said Mathieu Billa, director of the Bastogne War Museum.
Still, Hitler believed Germany could turn the tide, and centered on regaining the northern Belgian port of Antwerp with a push through the sparsely populated Ardennes.
The 120-mile (170 kilometer) dash seemed so fanciful that few of Hitler's own generals believed in it, let alone the allied command. Allied intelligence heard something might be afoot, but even on the eve of the attack the U.S. VIII Corps daily note said that "There is nothing to report."
For days to follow, the only reports would be bad for U.S. troops retreating amid word that SS troops were executing their prisoners — like at Malmedy, where 80 surrendered soldiers were murdered in a frozen field...
...Nowhere was that tipping point more visible than in the southern Ardennes town of Bastogne, where surrounded U.S. troops were cut off for days with little ammunition or food.
When Brig. Gen. Anthony C. McAuliffe of the 101st Airborne received a Dec. 22 ultimatum to surrender or face total destruction, he offered one of the most famous — and brief — replies in military history: ""Nuts.""
Four days later, Patton's troops broke the encirclement. And so it went with the Battle of the Bulge too, with the U.S. troops gaining momentum after Christmas...
The German's had the initial advantage of surprise, and poor weather that kept Allies air grounded. However, the German's never got to their first objective of Antwerp, and the Allies quickly recovered:
...firm resistance by various isolated units provided time for the U.S. First and Ninth Armies to shift against the northern flank of the penetration, for the British to send reserves to secure the line to the Meuse, and for Patton's Third Army to hit the salient from the south. Denied vital roads and hampered by air attack when the weather cleared, the German attack resulted only in a large bulge in the Allied lines which did not even extend to the Meuse River, the Germans' first objective. The Americans suffered some 75,000 casualties in the Battle of the Bulge, but the Germans lost 80,000 to l00,000. German strength had been irredeemably impaired. By the end of January 1945, American units had retaken all ground they had lost, and the defeat of Germany was clearly only a matter of time. In the east the Red Army had opened a winter offensive that was to carry, eventually, to and beyond Berlin.
The father of a close friend was in one of Patton's "three divisions" that broke though to Bastone, relieving the 101st. The youngest veterans of that fight are now in their 90s. Damn, has time flown. But to borrow the phrase from Lincoln's Gettysburg address, "...The world will little note, nor long remember what we say here, but it can never forget what they did here...."
To the men who have passed, Rest In Peace. To those who are still here, thank you is all we can say. God knows, we can never repay our dept to you.
Labels: History, Military, World War II
An incredible version of While My Guitar Gently Weeps
Sometimes when you don't look, you find.
I was watching YouTube last week and found this performance of the George Harrison classic by pure accident. From the 2003 Concert for George, the list of performers is like a who's who of multiple musical halls of fame. Both living Beetles (Paul McCartney on piano, Ringo Starr on drums), George Harrison's son Dhani and ELO founder Jeff Lynne on guitar, and on lead vocals and guitar, the only three time inductee into the Rock and Roll Hall of Fame, Slow Hand himself, Eric Clapton.
Towards the end (5:45), I love the look on Clapton's face, after he's been on a two minute tear on his guitar, "TOP THIS MOTHER F&*(ER!"
Enjoy, and have a great weekend!
OK. a Christian church is lying about the birth of Christ...
Again, the People's Democratic Republic of Kalifornia comes through. Whenever you think they have hit rock bottom, someone takes out a pick ax, or a jackhammer (coal powered, of course) and goes deeper.
At the Claremont United Methodist Church, a "nativity" scene. I amazes me that anyone with a basic knowledge of the Bible knows Mary and Joseph did not invade another nation, they were in Bethlehem to participate in a census and pay their taxes. But never let realty get in the way of political correctness. And where is Americans United for Separation of Church and State on this? Isn't a "church" getting involved in a political issue here?
BTY libtards, it was B Hussein Obama who put the illegal aliens into cages.
Labels: B Hussein Obama, Immigration, Religion
Tell me Chicago is not a war zone...
I recall the experience of Brigadier General James Dozier, who was kidnapped in 1981 by the Red Brigade in Italy. In the 42 days he was held hostage, he found out how easy he was to track. He left his apartment almost every day at the same time (plus or minus 10 minutes), took the same route, left the office at almost the same time every day, etc. Helps the bad guys to know where the target is.
CBS Chicago, Friday, December 6, 2019:
Off-duty Chicago police officer followed from station, shot at The officer was not injured in the attack Yesterday at 11:20 AM
PoliceOne Staff
CHICAGO — An off-duty Chicago police officer was followed and shot at after he left his station Tuesday night.
According to CBS 2, police say the shooting happened after a man jumped out of a gray Dodge Caravan and began firing at the officer's vehicle. A former police officer who lived nearby and heard the shooting, but didn't want to identify himself to media, said he heard "at least twelve" gunshots.
"It sounded like an automatic," the former officer told CBS 2. "The first thing I did was duck away from the window. I did hit the floor."
Officials told CBS 2 the shooter got back into the Caravan and drove away. The off-duty officer was uninjured and did not fire his weapon during the attack. Police have yet to make an arrest in the case.
Ever now and then I remind my officers to vary where they take a break, where they sit in the restaurant, where they do their reports, as this may make you more vulnerable. Thankfully I'm in Houston where the population is supportive of my officers. Unfortunately, our Blue family in the Windy City has more issues. It's bad we have to practice antiterrorism techniques in our third largest city.
Labels: Domestic Terrorists, Police, Terrorism
I know I love my niece. I am missing this bucket list item for her wedding...
Almost a quarter century ago, my brothers, their wives, a friend of mine, and I attended the Hell Freezes Over Tour of the Eagles, the reunion Don Henley swore would never happen. But when I heard they had reunited, I called my brother Bobby and said, "As broke as I am, if I have to rob an old woman for her Social Security check, I'll do it to make this concert!" And one my of life's objectives was achieved.
Fast forward a 24 years, and I was hoping to see Kansas. Alas, they will be here the weekend of Jessica's wedding. You know I must love you if I'm missing this!
Real rock and roll, from a legendary band. Enjoy their signature song, Carry on Wayward Son.
I'm hoping they extend the tour in 2020! Have a great weekend!
Labels: Family/Friends, Life in General, Music
Detective Christopher Cranston
New York City Police Department, New York
End of Watch Saturday, July 20, 2019
Detective Christopher Cranston died as the result of cancer that he developed following his assignment to the search and recovery efforts at the World Trade Center site following the 9/11 Terrorist Attacks.
Detective Cranston is survived by his wife.
On the morning of September 11th, 2001, seventy-two officers from a total of eight local, state, and federal agencies were killed when terrorist hijackers working for the al Qaeda terrorist network, headed by Osama bin Laden, crashed four hijacked planes into the World Trade Center towers in New York City, the Pentagon in Arlington, Virginia, and a field near Shanksville, Pennsylvania.
After the impact of the first plane into the World Trade Center's North Tower, putting the safety of others before their own, law enforcement officers along with fire and EMS personnel, rushed to the burning Twin Towers of the World Trade Center to aid the victims and lead them to safety. Due to their quick actions, it is estimated that over 25,000 people were saved.
As the evacuation continued, the South Tower unexpectedly collapsed as a result of the intense fire caused by the impact. The North Tower collapsed a short time later. Seventy-one law enforcement officers, 343 members of the New York City Fire Department and over 2,800 civilians were killed at the World Trade Center site.
A third hijacked plane crashed into a field in rural Pennsylvania when the passengers attempted to re-take control of the plane. One law enforcement officer, who was a passenger on the plane, was killed in that crash.
The fourth hijacked plane was crashed into the Pentagon in Arlington, Virginia, killing almost 200 military and civilian personnel. No law enforcement officers were killed at the Pentagon on 9/11.
The terrorist attacks resulted in the declaration of war against the Taliban regime, the illegal rulers of Afghanistan, and the al Qaeda terrorist network which also was based in Afghanistan.
On September 9th, 2005, all of the public safety officers killed on September 11th, 2001, were posthumously awarded the 9/11 Heroes Medal of Valor by President George W. Bush.
The contamination in the air at the World Trade Center site caused many rescue personnel to become extremely ill and eventually led to the death of several rescue workers.
On May 1st, 2011 members of the United States military conducted a raid on a compound in Abbottabad, Pakistan, and killed Osama bin Laden.
Sergeant Michael Stephen
Stone County Sheriff's Office, Arkansas
End of Watch Thursday, July 18, 2019
Sergeant Mike Stephen was shot and killed while responding to a domestic incident at a home in the area of 2020 Flag Road at about 9:00 am.
He was speaking to a female in the front yard when another subject opened fire, striking Sergeant Stephen and the woman. The subject who shot Sergeant Stephen was found dead by responding deputies.
Sergeant Stephen was a U.S. Army veteran and had served with the Stone County Sheriff's Office for 20 years. He also served as chief of the Pineville Fire Department and had previously served with the Arkansas Department of Correction. He is survived by his wife.
Even for the ultra PC crowd, this is ridiculus.
Mispronounced names are the latest form of racism. Another case of you can't believe they are this ridiculous. It's something so preposterous it has to be federally funded. Oh, yea, it comes from an NPR podcast
The racist practice of mispronouncing names
When Zuheera Ali walks into a coffee shop, she stands outside the door, opens her wallet, takes out her card, figures out exactly what she wants to order, and she reminds herself: 'You're Billy. You're Billy.'
The barista doesn't believe her, of course. But they can't do anything about it.
As her co-host Keya Roy says, "You can be whoever you want because you will never see this barista again..."
...Kumar remembers a time in second grade when she had to give a PowerPoint presentation in front of her class: "I was standing in front of my classmates and my teacher had turned on autocorrect. The first slide was just supposed to be my name, but was corrected to read 'Media K-Mart.' It was so embarrassing."
Keya Roy says she has stopped correcting her teachers when they mispronounce her name. "At some point, it's just futile," Roy says.
Zuheera Ali says she was never one to let someone say her name wrong.
"My name is my identity, and allowing someone else to say it wrong is stripping me of that," she says. "I feel like as a woman of color, I'm expected to make these changes, especially when I'm at school. But asking me to make my name easier to pronounce is a very unfair way that I have to change."
Says co-host Keya Roy: "I always felt like by giving into that pressure to conform and allowing my name to be butchered, I was somehow making life easier for others...
"My name is a way to push me aside, and most of the time, the people who are doing this don't realize the damage they could be doing to my self-worth and sense of confidence."
"People will try to — as a blatant sign of disrespect — mispronounce my name or mock my name," Oluo says. "I get that on social media all the time."
Oluo says people on social media will "deliberately, wildly misspell my name to show to other people how serious must I be taken if I don't even have what they would consider to be a serious name. It's racist at its core to think that other cultures names are invalid. It's othering and purposefully disrespectful, and it's often used as a weapon against me."
She continues: "It's my name and I won't let anyone take that from me..."
"The changing of peoples names has a racialized history," said Kohli. "It's grounded in slavery — the renaming during slavery — renaming Americanization schools for Latinx communities and indigenous communities, and so there is a lot of history that's tied to this practice that is directly tied to racism."
This history is painful even though it seems so far in the past, Zuheera Ali says. But history is not removed for many African-Americans, many of whom don't know their ancestors' names and carry the names of slave owners...
When I was in Kuwait (2005/06) I met a Navy lieutenant commander with a Polish last name, about 15 letters long. I asked how it was pronounced, and he said it. I lost lost track after the third syllable, and I said, "Ski, yea, got it!" He laughed and said that was what most people called him. We shook hands, introduced ourselves, talked about having unusual names for a few minutes, and went on with our day.
My last name has been mispronounced (FYI, it's Parisian French) for my entire life. I once had it butchered by the announcer at the Superdome in New Orleans when I commanded the Army ROTC Color Guard at a Saints game. And my vagina was never in pain (I'm rephrasing it to be decent) over that. Grow up children, if someone mispronounces your name, politely correct them. If you accidentally mispronounce theirs, don't take offense when they correct you. Otherwise, go back to your safe space and leave the world to the adults.
Labels: Media, Political Correctness
Real country music for the end of the week...
A man contemplating his escape from his loneliness, the whiskey. Not the first man to use booze to cover other things, won't be the last.
Country recently has become, in far too many cases, pop music with pickup trucks and cowboy boots. This ain't that crap.
Hope your Thanksgiving was great, have a great weekend.
Conservation Officer Shannon Lee "Opie" Barron
Red Lake Nation Conservation Department, Tribal Police
End of Watch Sunday, July 7, 2019
Badge 32
Conservation Officer Opie Barron suffered a fatal heart attack while investigating an illegal harvesting call off of Highway 89 north of Red Lake.
He and other officers had just cleared from the call when he radioed dispatch requesting EMS for himself. The other officers returned and immediately began performing life-saving measures. He was transported to Red Lake Indian Health Service Hospital where he was pronounced dead.
Officer Barron had served with the Red Lake Nation Conservation Department for 19 years. He is survived by his wife, two children, and aunt who raised him.
Deputy Sheriff Nicolas Blane Dixon
Hall County Sheriff's Office, Georgia
Tour 3 years
Badge P90
Deputy Sheriff Nicolas Dixon was shot and killed following a vehicle pursuit of a stolen vehicle at approximately 11:15 pm.
The vehicle was believed to have been connected to several burglaries and car break-ins over the previous days. A vehicle pursuit started when deputies attempted to stop it. Multiple suspects then fled on foot after the car crashed. Deputy Dixon pursued one of the suspects and exchanged shots with him in the 600 block of Highland Avenue.
Deputy Dixon was fatally shot during the exchange and the suspect was seriously wounded. A second suspect was apprehended approximately eight hours later and the two remaining suspects were apprehended the following day. One of the men who was taken into custody was charged with murder.
Deputy Dixon had served with the Hall County Sheriff's Office for three years. He is survived by his wife, two sons, parents, two brothers, and grandparents.
Deputy Sheriff Omar Diaz
Harris County Sheriff's Office, Texas
End of Watch Saturday, July 6, 2019
Deputy Sheriff Omar Diaz died after collapsing at the scene of a stabbing call in the 7500 block of Stone Pine Lane.
He and other deputies had responded to the scene where a woman had been stabbed several times. Deputy Diaz was securing the crime scene with police line tape when he collapsed. He was transported to a local hospital where he passed away a short time later.
Deputy Diaz had served with the Harris County Sheriff's Office for 10 years. He is survived by his wife and young daughter.
"We win. They loose."
To borrow Ronald Reagan's great plan for detente.
One of the many disasters of the Obama years was the Iran Nuke, aka the Joint Comprehensive Plan of Action (JCPOA). When you give them 150 billion first, then implement restrictions on their WMD programs, that alone is a debacle. But to give the Iranians 24 days notice of inspection, that is beyond ludicrous.
Thank God Mrs. Bill Clinton did not make it into the White House, and our current president took us out of this unconstitutional abomination, and imposed sanctions that are doing what is necessary. And when Foreign Policy magazine is saying it is hurting the Iranians, you know it's bad.
Iran Protests Suggest Trump Sanctions Are Inflicting Serious Pain
The regime has survived uprisings in the past. But now it is starting to kill demonstrators in great numbers.
View of Tehran shops that were destroyed after nationwide demonstrations broke out in protest of fuel price hikes and led to widespread destruction of property, on Nov. 20. ATTA KENARE/AFP/GETTY IMAGES
The deadly drama playing out in Iran since last Friday, leaving more than 100 protesters dead, shows three things. Tehran is increasingly in desperate economic straits, in part because of intense U.S. sanctions; Iranian popular discontent with the regime's economic mismanagement seems to have reached a breaking point; and the regime is more frightened of popular unrest than at any time in recent years.
The latest explosion of popular protest in Iran began on Friday after the government rescinded fuel subsidies, which essentially tripled the price of gasoline—a painful blow to millions of ordinary Iranians already struggling to survive a debased currency, high unemployment, and a shrinking economy. But the demonstrations that began over fuel subsidies quickly became a sweeping, nationwide protest against the Iranian regime itself, with outbreaks in dozens of cities in every Iranian province, targeting especially government buildings such as police stations and state-owned banks.
The government's response has been much more brutal than in previous outbreaks of protest, such as in 2017-2018, including a near-total shutdown of the internet and unrestrained use of violence by security forces. Groups including Amnesty International have documented at least 106 deaths during the protests, as regime security forces have used live ammunition to target demonstrators. The brutal crackdown is both evidence of the regime's desperation at its own inability to sway popular opinion and a result of watching weeks of similar deadly protests (also directed against Iran) in Iraq and Lebanon.
"Fundamentally, it is an economic protest. But clearly, among some protesters, there is the opportunity to make broader complaints about the government," said Henry Rome, an Iran analyst at the Eurasia Group.
The fuel price reform, which effectively raised the price of gasoline and diesel for most drivers from about 8 cents a liter to about 25 cents a liter, is meant to save the government a few hundred million dollars over the course of a year, as well as husbanding increasingly scarce supplies of motor fuel, which can be exported for greater earnings than essentially giving it away domestically. The government hoped that its plan to redistribute most of the revenue from the price hike back to low-income families would blunt the pain of the measure, but delays in getting cash back into people's hands left the protests still simmering through Tuesday.
The fact that Iran would risk sparking such widespread anger for minimal economic gain underscores the dire condition of the Iranian economy, hammered by U.S. sanctions in its inability to export practically any oil, one of the main sources of revenue for the government.
"They did the reform because they are broke," said Alireza Nader, a senior fellow at the Foundation for Defense of Democracies (FDD). "People can't afford a 300 percent increase in gas prices, but the regime didn't have any other choice...."
...Another problem is that many people simply didn't believe the government would follow through on the cash transfers. Yet another is that they worried that higher gas prices would just trickle down to higher prices for all sorts of other consumer goods, at a time when annual inflation in Iran is officially at least 40 percent and perhaps as much as five times higher.
Though Iranian officials, including President Hassan Rouhani, have blamed foreign countries and especially the United States for organizing the uprising, the U.S. role is—as far as is publicly known—mostly indirect, rather than actively supporting opposition groups. Since U.S. President Donald Trump reimposed sweeping sanctions on Iran's economy, including the ban on oil sales, Iran's economy has been in a free fall. Because of the increased pinch from sanctions, the International Monetary Fund recently revised downward its expectations for Iran's economy: It now expects it to shrink by almost 10 percent this year.
But the protests, like those that also swept the country in 2017-2018, are about more than just U.S.-inflicted pain. Many Iranians are irate at rampant corruption and economic mismanagement, constants in the 40 years since Iran's revolution.
"The underlying grievances were there without the maximum pressure campaign, but it's the fiscal strain that the government is under which has forced it to take these steps, which has brought those grievances to the fore," Rome said. And once people are in the street, narrow protests can snowball.
"Once there is an avenue open for protest, the dam is burst," he said...
It's somewhat amusing to me that "progressives" (better called "regressives," what they want has never worked, will never work) will "Boycott, Divest, and Sanction" (BCS) the only democracy in the Middle East, but they are very supportive (relatively) of the Iranian regime. The left was overjoyed when Obama gave his greatest asset in dealing with the Iranians away for only their word. A solemn vow that's worth less than, "If you like your doctor, you can keep your doctor..." Then again, they are not liberal (in the classical sense), but militant fascists, and anti-Semites to boot.
One of the many opportunities Obama missed was the Green Revolution in Iran, back in 2009. The population, a majority of which does not have memory of the Shah, is tired of living in a 3rd world hell hole, especially when then can see how much better the rest of the world (Hell, the Middle East) is living now. That din't stop him for sticking his nose and ears into Egypt, Libya or Syria, stilling up multiple disasters and leaving a major mess for his successor to handle. Hopefully the Iranian people will handle the mullahs and we can replaced the Islamic "republic" with a more stable regime.
Labels: B Hussein Obama, Donald Trump, Iran, Mrs. Bill Clinton, Ronald Reagan
It was actually Ann Street....
But it will always be Main Street to me.
A few months back I posted on how Bob Seger has Turned the Page, he visited Houston as part of his final tour. One of his classics, Main Street, was about watching a dancer in a club, just waiting for her to watch here come on past. Young and fantasizing, hoping against hope to meet a woman you are, or think you are, in love with.
One fact I've learned in over fifty years on the Earth, no man loves but one woman in his lifetime. And Seger writes a great look at how a young man attempts to capture love, or at the very least, engage in it. Well put in one of my favorite episodes of Star Trek-TOS, Requiem For Methuselah .. As Spock and McCoy discuss two men fighting over a woman they are in love with, McCoy puts it well to his non-feeling Vulcan friend:
...You wouldn't understand that, would you, Spock? You see, I feel sorrier for you than I do for him because you'll never know the things that love can drive a man to. The ecstasies, the miseries, the broken rules, the desperate chances, the glorious failures, the glorious victories. All of these things you'll never know simply because the word love isn't written into your book. Goodnight, Spock..
I'm getting too philosphical as the week ends. Heading to New Orleans for the wedding of a friend. Have a great weekend!
From the final tour of Bob Seger and the Silver Bullet Band, Main Street, performed January 21, 2019, in Columbus Ohio.
Labels: Life in General, Music
Police Officer John Ralph Anderson, IV
Metro Nashville Police Department, Tennessee
End of Watch Thursday, July 4, 2019
Police Officer John Anderson was killed in a vehicle crash at the intersection of Woodland Street and Interstate Drive.
The vehicle that struck him had just fled from other officers who attempted to make a traffic stop on it. The officer terminated the stop when the vehicle fled and did not pursue it. Officer Anderson was en route to assist on an unrelated call involving a pedestrian on the interstate when the fleeing vehicle ran a red light and struck his patrol car.
Officer Anderson's patrol car became engulfed in flames. The passenger in the fleeing vehicle suffered life-threatening injuries. The juvenile driver of the vehicle suffered minor injuries and was charged with vehicular homicide.
Officer Anderson was a U.S Marine Corps Reserve veteran and had served with the Metro Nashville Police Department for four years and was assigned to the Central Precinct.
Deputy Jailer Michaela Elizabeth Smith
Murray County Sheriff's Office, Georgia
End of Watch Wednesday, July 3, 2019
Tour 6 months
Deputy Jailer Michaela Smith succumbed to injuries sustained during defensive tactics training in Whitfield County.
Deputy Jailer Smith was completing her jailer certification requirements which involved defensive tactics and being pepper sprayed. She suffered a strike to the head during the defensive tactics training. She returned home following the pepper-spraying practical and then went to the hospital when she began to show symptoms of a head injury. She was treated and released but readmitted to the hospital in the morning when her condition worsened.
She became unresponsive after returning to the hospital and she passed away on July 3rd, 2019.
Deputy Jailer Smith had served with the Murray County Sheriff's Office for only six months. She is survived by her parents.
Rest in Peace Sis…We Got The Watch
K9 Assuan
Marion Police Department, Indiana
End of Watch Thursday, June 27, 2019
Breed Belgian Malinois
K9 Assuan died as the result of injuries sustained during a criminal apprehension training exercise at the Marion Police Athletic Club facility at 555 East Morton Street.
He failed to negotiate a fence jump at high speed and struck his head on the fence's top rail. He immediately became unresponsive as a result of the injury. His handler transported him to a local veterinary hospital where he died without regaining consciousness.
K9 Assuan had served with the Marion Police Department for five years.
Rest in Peace Assuan…till our next roll call at the Rainbow Bridge!
In Memory of all Police Dogs
They handled themselves with beauty & grace
And who could ever forget that beautiful face
Whether at work; or at home; whatever the test
They always worked hard; and did their best
They were real champions; at work or at play
But their lives were cut short; suddenly one day
While working on the job with their partner one day
They put themselves out on a limb; out into harms way
They gave the ultimate sacrifice; any dog can give
They gave up their life; so someone could live
The best of their breed; as his partner and anyone would say
Many hearts are now broken; that he had to prove it this way
Now as the trees are blowing in the gentle breeze
The sun is shining; thru the leaves on the trees
The meadows are green; and the grass grows tall
Off in the distance they can see a waterfall
As they look over the falls; down through the creek
The water flows gently; as a rabbit sneaks a peek
Far up above; in the deep blue sky
They see the birds soar high; as they fly by
They see animals playing; at the bridge by a waterfall
Chasing each other; and just having a ball
They play all day; from morning to night
There's no more rain; just warm sunlight
Off in the distance; they hear trumpets blow
Then all the animals look up; and notice a bright glow
The harps would play and the angels would sing
As they know they've come home; they've earned their wings
We remember that they died; in the line of duty
And are now with the Lord; sharing in heaven's beauty
Off to the meadows now; where they can play and roam free
With an occasional rest stop; under a tall oak tree
No more bad guys to chase; or bullets to take
Just a run through the meadow; down to the lake
A quick splash in the water; then back to the shore
Then it's off to the forest; to go play some more
These special dogs are back home; up in heaven above
They're cradled in God's arm's; and covered with His love
We'll light a candle for all of them; in the dark of night
In loving memory of all; these very special knights
By John Quealy
Labels: K9, K9 Down, Officer Safety, Police, Police Training
I must be an intellectual masochist..I read the New York Times.
Sunday I was reading the Houston Chronicle and on the front page, below the fold, was a propaganda piece from Pravda on the Hudson on how Federal Express, a multi-billion dollar corporation, had not paid any taxes in 2018, after the Trump tax cuts in 2017.
By Jim Tankersley, Peter Eavis and Ben CasselmanPublished Nov. 17, 2019
WASHINGTON — In the 2017 fiscal year, FedEx owed more than $1.5 billion in taxes. The next year, it owed nothing. What changed was the Trump administration's tax cut — for which the company had lobbied hard.
The public face of its lobbying effort, which included a tax proposal of its own, was FedEx's founder and chief executive, Frederick Smith, who repeatedly took to the airwaves to champion the power of tax cuts. "If you make the United States a better place to invest, there is no question in my mind that we would see a renaissance of capital investment," he said on an August 2017 radio show hosted by Larry Kudlow, who is now chairman of the National Economic Council.
Four months later, President Trump signed into law the $1.5 trillion tax cut that became his signature legislative achievement. FedEx reaped big savings, bringing its effective tax rate from 34 percent in fiscal year 2017 to less than zero in fiscal year 2018, meaning that, overall, the government technically owed it money. But it did not increase investment in new equipment and other assets in the fiscal year that followed, as Mr. Smith said businesses like his would.
Nearly two years after the tax law passed, the windfall to corporations like FedEx is becoming clear. A New York Times analysis of data compiled by Capital IQ shows no statistically meaningful relationship between the size of the tax cut that companies and industries received and the investments they made. If anything, the companies that received the biggest tax cuts increased their capital investment by less, on average, than companies that got smaller cuts...
Now, they are challenging a company founded by a legendary businessman, Fred Smith. It says enough of the man that both Bill Clinton and George W Bush wanted him as Secretary of Defense. And a Yale professor did not agree with the concept of flying time sensitive packages overnight would be a good business model (As an aside, people wonder why I despise confusing education and intelligence). But Mr. Smith, not a man to back down from being lied about, responded to this slander:
The New York Times published a distorted and factually incorrect story on the front page of the Sunday, November 17 edition concerning FedEx and our billions of dollars of tax payments and billions of dollars of investments in the U.S. economy. Pertinent to this outrageous distortion of the truth is the fact that unlike FedEx, the New York Times paid zero federal income tax in 2017 on earnings of $111 million, and only $30 million in 2018 – 18% of their pretax book income. Also in 2018 the New York Times cut their capital investments nearly in half to $57 million, which equates to a rounding error when compared to the $6 billion of capital that FedEx invested in the U.S. economy during that same year.
I hereby challenge A.G. Sulzberger, publisher of the New York Times and the business section editor to a public debate in Washington, DC with me and the FedEx corporate vice president of tax. The focus of the debate should be federal tax policy and the relative societal benefits of business investments and the enormous intended benefits to the United States economy, especially lower and middle class wage earners.
I look forward to promptly hearing from Mr. Sulzberger and scheduling this open event to bring further public awareness of the facts related to these important issues.
Something to remember about the New York Times, they say something, especially on political issues, the planning assumption is it is a bold faced lie. Hyperbold? This is the rag that pushed "Russian collusion," Ukrianin quid pro quo, etc for years. But for some reason the multiple scandals of the Obama years are not covered (IRS, Fast and Furious, etc) It's a leftist propaganda source, but unlike the Nation or MSNBC, they won't admit what they are. Every time I read it (full disclosure, I do subscribe to the digital edition, and get it often from the other sources I read) I recall the wisdom of a cartoon from the 1980s. First block shows a Moscow factory worker reading this morning's edition of Pravda. The second block shows a Harvard professor reading the same edition of the paper. "The difference? The guy in Moscow knows he getting lied to."
But another point, and I don't know if Mr. Smith is a registered Democrat or Republican, it shows what you must do in today's propaganda filled media. You get hit, you strike back, three times as hard. Too many Republicans (especially the Never Trumpers/RINOs) would just stand their and take it. Mr. Smith is not, thank God. Rags like the New York Times need to be called out, challenged, and held to account.
Mr. Smith, I really doubt you will get your debate, Pinch is a coward. But thank you for showing people how it's done.
Labels: Business, Media, Newspapers, Taxation, Trump
The only question of the Iran nuke deal, was this cluster f%^& on purpose or because of the incompetence of the Obama foreign policy?
In 2009, the Iranian regime was dealing with a very angry population, protest and other issues. And the nation was primed for assistance from us to the people. And Barrack Obama, with his Secretary of State Mrs. Bill Clinton, sent their call for help to voice mail. He wanted a "deal," not regime change.
Fast forward six years, he got the "deal," and the mullahs got 150 billion dollars in cash. I've often argued with Obamaites who scream "This money belongs to the Iranians!" Yes, you are right, it belongs to the Iranian people. That is not who that incompetent moron gave it to, but the mullahs who seized the nation in 1979. And they did not use it to upgrade the lives of the Iranians, but to fund insurgency throughout the Middle East, and work on their WMD program (You really didn't think the Iran nuke deal would slow that down).
Well, the mullahs are showing how well they can handle the economy. Hopefully this again revs up the insurgency, and unlike 2009, we have a president that actually is interested in ending the terrorist Iranian regime.
Uprisings Against the Mullahs
Short on cash, the regime faces protests at home and in Iraq.
The latest anti-regime protests in Iran look like a major political event, and judging by its vigorous and violent response the regime agrees. Now is a moment for the political left and right in the U.S. and Europe to unite in support of the Iranian people.
The protests erupted in several cities across the country in response to government increases of 50% in fuel prices. The increase raises the price of a liter of gasoline to only about 35 cents, or 50 cents a gallon. But the reaction to the increase reveals the desperation and anger of Iranians as the economy falters under the pressure of U.S. sanctions.
With parliamentary elections scheduled for February, the regime would only have reduced its fuel subsidies if it felt it had no choice. The mullahs must be short on cash as their oil sales abroad have been sharply reduced by Trump Administration sanctions. Oil sales are the regime's main source of revenue.
Supreme Leader Ayatollah Ali Khameini publicly supported the price increases on Sunday and called protesters "thugs." The government shut down internet access across most of the country, which makes it difficult to assess the extent of the protests. But the reports and videos that have emerged show clashes that sometimes turned violent. Mr. Khameini also blamed loyalists of the former Shah, who was deposed 40 years ago.
The truth is that this turmoil is made in Tehran by the mullahs themselves. They could have used the financial windfall they received from the 2015 nuclear deal to invest in their own country. Instead they used those resources to spread revolution throughout the Middle East. They've continued to plow cash into developing ballistic missiles and arming Houthis in Yemen, Hezbollah in Syria, and Shiite militias in nearby Iraq.
Iran's heavy-handed meddling has also inspired a backlash in Iraq. Protesters have chanted anti-Persian slogans and demonstrated against Shiite sites in Karbala and other holy cities. Most Iraqis are Shiites but they are also nationalists and resent Iran's political interference that includes direction to militias by Qasem Soleimani, head of the Quds Force that is Iran's vanguard abroad.
...Above all, the world should speak up in support of Iranian aspirations to become a normal country, instead of a theocracy that spreads revolution and terror. Barack Obama made an historic blunder when he stayed mute amid the Iranian regime's bloody crackdown on democratic protests in 2009. President Trump should not make the same mistake.
I have no doubt President Trump is directing his national security staff to help this Green Revolution. He can remember the wisdom of Ronald Reagan and his view of handing the Cold War, "We win, they lose."
Labels: B Hussein Obama, Foreign Policy/Relations, Iran, Mrs. Bill Clinton, Ronald Reagan, WMD
Deputy Sheriff Carlos A. Ramirez
Kendall County Sheriff's Office, Texas
End of Watch Tuesday, July 2, 2019
Deputy Sheriff Carlos Ramirez was struck and killed by a vehicle while he and another deputy were conducting a traffic stop on I-10 near mile marker 533 at 7:30 am.
Another vehicle struck Deputy Ramirez and the other deputy before striking the vehicle that had been stopped. Deputy Ramirez succumbed to his injuries while the other deputy was seriously injured.
Deputy Ramirez was a U.S. Army Reserve veteran and had served with the Kendall County Sheriff's Office for three years. He is survived by his wife and two young children.
A good look at the integration of women into the c... | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,749 |
Die Hole-Halbinsel ist eine markante, niedrige und größtenteils vereiste Halbinsel, die den südöstlichen Teil der westantarktischen Rothschild-Insel bildet. Auf der Halbinsel befindet sich der östliche Teil der Desko Mountains einschließlich des Schenck Peak.
Das UK Antarctic Place-Names Committee benannte die Halbinsel 2021 nach dem Geologen Malcom J. Hole (* 1960) von der University of Aberdeen, der in drei Kampagnen für den British Antarctic Survey zwischen 1983 und 1987 in Antarktika einschließlich dieses Gebiets tätig war.
Weblinks
Hole Peninsula im Composite Gazetteer of Antarctica (englisch)
Antarctic peninsula named in recognition of Aberdeen geologist's work. In: The Guardian, 28. April 2021 (englisch)
Halbinsel (Antarktika)
Halbinsel (Südlicher Ozean)
Rothschild-Insel | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,686 |
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Home / Space Themed Stickers / Sputnik Sticker from the Historic Robotic Spacecraft Series
Sputnik Sticker from the Historic Robotic Spacecraft Series
By Chop Shop in Space
Free Shipping in the US!
Sputnik was the first artificial Earth satellite. It was a 58 cm (23 in) diameter polished metal sphere, with four external radio antennas to broadcast radio pulses. Launched by the Soviet Union in 1957. Stickers are 3" circular and vinyl. Ideal for both indoor and outdoor use.
Set Single Set of 3 Set of 6
Single Set of 3 Set of 6 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,181 |
Hello from South West London, England!
My passion for all things health started when I was just five years old, pushing my dollies around in their pram! And now having grown a family (including me) with multiple allergy and autoimmune issues, the ancestral way and the science behind it was simply irresistible.
Since becoming a Primal Health Coach, as a family we've reversed diabetes, managed little ones with complex health needs, are moving towards zero medication for familial hypertension and enjoy a mad, mad life together.
We're far from perfect – I'm still campaigning for no fizzy drink arriving at my house and have my own love affair with wine (working on it) and understand all too well the challenges that come everyday in making the right choices.
People who know me, also know I'm not a gym bunny! But I am into MovNat and just love the ethos of moving to get fit - a perfect match to the Primal lifestyle and my ambition is to get certified. Why not join me and let's get you fit and well too? | {
"redpajama_set_name": "RedPajamaC4"
} | 7,719 |
\section{Introduction}
The Galactic bulge (GB), an important dynamical and morphological component of
our Galaxy, offers an environment distinct from the Galactic disk for study of
stellar populations, stellar evolution, and the mass-loss processes that
accompany and, in the end, control the last. Understanding and calibrating the
physical processes whereby mass ejected by evolved stars into the bulge
environment is recycled back into new generations of stars requires a
statistical knowledge of mass loss as a function of fundamental stellar
parameters in this region. Because of the limited sensitivity of previous
surveys of the bulge, fundamental questions for late stellar evolution, such as
the stage at which substantial mass-loss begins on the red giant branch (RGB),
and its dependence on fundamental stellar properties, remain unanswered. The GB
is an ideal laboratory for addressing these issues, providing a very large
sample of stars at an almost identical distance.
We therefore observed seven $15\times15$\,arcmin$^2$ fields that sample a
range of distances from the Galactic centre with unprecedented sensitivity
using the Infrared Array Camera \citep[IRAC;][]{Faz04} and the Multiband Imaging
Photometer for {\em Spitzer} \citep[MIPS;][]{Rie04}, the imaging instruments
on-board the {\em Spitzer} Space Telescope \citep{Wer04}, in order to determine
mass-loss rates and luminosities of a statistically large sample of stars at
several galactocentric radii. These data enable us to detect stars with very
low mass-loss rates through their infrared excess, determine the dependence of
the mass-loss rate on luminosity and effective temperature along the giant
branches, and conduct a census of mass-losing stars at different rates. The
observations, together with existing studies that probe higher mass-loss rate
stars, will enable us to infer the total rate of mass loss in the bulge, a key
input to evolutionary models of the bulge. The data have already led to the
discovery of mid-IR $\log P$ vs.\ magnitude relations \citep{Gla09}. In this
paper we present the observations, the data reduction, and the source
catalogue. We also compare the data to previous mid-IR surveys of the bulge and
to theoretical isochrones.
The outline of this paper is as follows. In \S\ref{sec_obs}, we describe the
observations, the data reduction, the different steps of point source
extraction, and how the catalogues were created. We then proceed in
\S\ref{sec_surveys} with checking our photometric data against other mid-IR
surveys of the Galactic bulge. Further checks are presented in \S\ref{sec_cmds},
where colour-magnitude diagrams (CMDs) are compared to theoretical isochrones.
Finally, \S\ref{sec_conclu} draws conclusions on the catalogues and the data
quality.
\section{Observations and Data Reduction} \label{sec_obs}
\subsection{Field selection and observations}
The locations of the observed fields were chosen to sample the bulge on a
variety of scales, to measure how the mix of stellar populations varies with
Galactic latitude. They were also chosen to avoid the relative intense,
saturating emission from near the Galactic plane. Our innermost fields are
within the central stellar cusp, which presumably contains stars of various
ages \citep[c.f.][]{Blu03,Fig04}. Because the stars within this domain are
believed to have formed within the central molecular zone and then to have
diffused into an increasingly thicker distribution as a result of scattering
off molecular clouds \citep{Kim01}, we expect a vertical segregation of stellar
ages. Thus, inasmuch as the luminosities and mass-loss rates of red giants and
asymptotic giant branch (AGB) stars depend on their masses, hence their ages,
the radial distributions of the different kinds of evolved stellar objects can
be used to model the star formation and dynamical history of this region.
Two fields were selected to sample the nuclear bulge at
$(l,b)=(0\fdg00,-1\fdg00)$ and $(l,b)=(0\fdg63,-0\fdg36)$, namely N\,1 and
N\,2, both of which were observed by ISOGAL \citep[project for imaging part of
the Galaxy using ISO, the Infrared Space Observatory;][]{Omo03} at 7 and
15\,$\mu$m. Five fields were selected beyond the nuclear bulge in areas where
they overlap the Optical Gravitational Lensing Experiment III
\citep[OGLE-III;][]{Uda00} micro-lensing survey. Four of these are located below
the Galactic plane along a radial vector that subtends the minor axis of the
Galaxy at an angle of about 13\fdg5, and terminates at the well-studied field in
Baade's window at $(l,b)=(1\fdg03,-3\fdg83)$, containing the globular cluster
\object{NGC\,6522} \citep[e.g.][]{Gla99}. The three fields inside this are
located at $(l,b)=(0\fdg30,-1\fdg42)$, $(0\fdg56,-2\fdg23)$, and
$(0\fdg76,-3\fdg07)$. The fifth field is positioned above the plane at
$(l,b)=(2\fdg87,0\fdg35)$. All fields are approximately rectangular in right
ascension (RA) and declination (Dec) coordinates. Figure~\ref{fields} shows the
location of the seven observed fields with respect to the Galactic centre, and
Table~\ref{tbl_fields} summarises some of their main characteristics. The range
in RA and Dec (J2000) given in Table~\ref{tbl_fields} refers to where there is
full overlap between MIPS and all four IRAC bands. Particularly in IRAC we do
have some coverage outside the given range.
\begin{figure}
\includegraphics[width=\columnwidth]{fig1.jpg}
\caption{Map of the seven fields observed in this campaign with the labels
used throughout this paper.}
\label{fields}
\end{figure}
\begin{table*}
\caption{Main characteristics of the seven fields towards the GB observed with
{\em Spitzer} as part of programme 2345.}
\label{tbl_fields}
\centering
\begin{tabular}{lcccrcc}
\hline\hline
Field name & RA range (h m s) & Dec range ($\hbox{$^\circ$}\ \hbox{$^\prime$}\ \hbox{$^{\prime\prime}$}$) & l centre & b centre & Date IRAC obs & Date MIPS obs \\
\hline
Bulge 1 & 17 51 14.2 \dots 17 52 36.7 & $-$29 15 22 \dots $-$29 34 15 & 0.30 & $-$1.42 & 2005 03 30 & 2005 04 09 \\
Bulge 2 & 17 55 02.1 \dots 17 56 24.2 & $-$29 26 25 \dots $-$29 45 13 & 0.56 & $-$2.23 & 2005 03 31 & 2005 04 10 \\
Bulge 3 & 17 58 50.7 \dots 18 00 13.3 & $-$29 41 08 \dots $-$29 59 59 & 0.76 & $-$3.07 & 2005 03 30 & 2005 04 10 \\
Bulge 4 & 17 50 16.1 \dots 17 51 36.4 & $-$26 08 56 \dots $-$26 27 51 & 2.87 & 0.35 & 2005 03 30 & 2005 04 09 \\
Bulge N\,1 & 17 48 51.9 \dots 17 50 14.8 & $-$29 17 42 \dots $-$29 36 42 & 0.00 & $-$1.00 & 2005 03 30 & 2005 04 08 \\
Bulge N\,2 & 17 47 55.8 \dots 17 49 16.3 & $-$28 28 41 \dots $-$28 46 19 & 0.63 & $-$0.36 & $-$ & 2005 04 13 \\
NGC\,6522 & 18 02 30.4 \dots 18 03 53.5 & $-$29 49 26 \dots $-$30 08 24 & 1.03 & $-$3.83 & 2005 03 30 & 2005 04 10 \\
\hline
\end{tabular}
\end{table*}
Observations of the GB fields were performed using the IRAC instrument in all
four channels at 3.6, 4.5, 5.8, and 8.0\,$\mu$m, and the MIPS instrument in the
24\,$\mu$m channel on board the {\em Spitzer} Space Telescope within the
programme 2345. Bulge field N\,2 was observed only with MIPS in our programme,
because this field was covered by IRAC observations within the general observer
(GO) programme 3677 \citep[principal investigator: S.\ Stolovy;][]{Ram08}. The
IRAC observations were carried out on 2005 March 30 and 31, and the MIPS
observations between 2005 April 08 and 13.
With IRAC, observations were done in the full-array read out-mode, one frame
per pointing with 2\,s integration time per frame -- the shortest full-array
integration time was used to minimise the effects of saturation and resulting
latency problems. The mapping was done in a $6\times6$ rectangular grid with
step size 260\hbox{$^{\prime\prime}$}, with five dither positions, and a medium scale factor,
giving a total exposure time of 10\,s per pixel. The MIPS observations
were obtained using the photometry/raster mode with 10\,s integration time and
full-array read-out mode, $3\times3$ rectangular grid and two cycles,
giving a total integration time of 331\,s per pixel.
The fields of view of IRAC channels 1 and 3, 2 and 4, as well as MIPS did not
fully overlap. Nevertheless, the MIPS field of view is fully contained in all
four IRAC fields of view.
\subsection{Data reduction}
We corrected the IRAC basic calibrated data (bcd) files to mitigate artifacts
such as muxbleed or column pulldown with the tools provided by S.\ Carey at the
{\em Spitzer} Science Center (SSC). Post-bcd processing was then conducted on
the corrected bcd files using the MOsaicker and Point source EXtractor (MOPEX)
software and its subsystem APEX \citep[version 18.2.0,][]{MaM05}.
\subsubsection{Step 1: Point source detection and extraction}
Before further processing, mosaics were created by MOPEX for each field and
channel from the corrected bcd frames. In this step, the pipeline interpolates
the input images onto the output grid, taking geometric distortion into account.
An outlier detection scheme flags bad pixels and any pixels affected by cosmic
ray hits or moving objects, and these pixels are re-computed before co-addition.
Finally, the interpolated images are co-added to one mosaic image. After
mosaicking, APEX determines the background by calculating the median in a
$45\times45$ pixel box around each pixel, and subtracts it from the image.
These background-subtracted images were used in the detection step. Then,
background fluctuations in the images were estimated and noise images derived,
which were used for signal-to-noise ratio (SNR) estimation and the generation
of point source probability images. With those, the detection table was
compiled. We chose a detection threshold of $2.3 \sigma$ above the background.
We used both the point response function (PRF) fitting capability and the
aperture photometry functionality with circular apertures with radii of 2, 3,
and 4 pixels. Larger apertures were not applicable owing to the crowding in the
fields. The tiles used for PRF fitting also had to be chosen to be very small
($3\times3$ pixels). We used the most up-to-date mean PRFs as provided by the
SSC, and set the PRF normalisation radius accordingly.
The measured $\chi^2$ values in our data seem to be very high, even for
successfully fitted sources, e.g.\ in the least-crowded field NGC\,6522, they
are between 2.5 and 3.3 in the IRAC channels 1 and 2, between 1.4 and 1.8 in
IRAC\,3, and only in IRAC\,4 at the perfect value of 1. This may stem from
confusion noise, which is not included in the provided uncertainty images
and/or from the high source density. Confusion noise is created by the
amplitude variations from PRFs of closely spaced sources
\citep{Hac87,Rie95}. Modelling the confusion noise has not improved the
resulting $\chi^2$ values. This has consequences for the reliability of
automatic de-blending procedures, which were not working properly in this
field. We thus had to disable the active and passive de-blending capabilities
of APEX (see Appendix~\ref{sec_blending}).
In all MIPS fields, we first detected bright sources, removed the Airy rings of
these sources to do the source detection on the residual images, and performed
the point source extraction on the original images. The southern half of the
field N\,2 has strong diffuse emission. In that area, the detection threshold
is certainly higher than in areas with low diffuse background emission, as is
also evident from the histograms of magnitudes in Appendix~\ref{sec_histo}.
\subsubsection{Step 2: Assigning quality grades to the sources}
\label{sec_qualgr}
Three different effects can be seen when plotting the flux obtained by PRF
fitting versus that found with aperture photometry for all the extracted
sources (Fig.~\ref{errors}). The first effect is present when we use a large
aperture with a radius of 3 or 4 pixels. At very low PRF fluxes, there are
several sources that show disproportionately large aperture fluxes, i.e.\ are
above the dashed line. These sources are faint sources close to a bright
source. In case of the larger aperture, we therefore already get a
significant contribution in the aperture from the bright source. The second
effect is relevant for some bright sources, whose PRF fluxes are smaller than
the aperture fluxes. These sources are super-saturated; i.e., the radial
intensity profile has a dip in the centre and so it shows a double peak
structure. In a few cases, depending on the depth of the central valley, these
two peaks are identified as two individual sources that are each fitted with a
fainter PRF; i.e., both sources lie above the dashed line. In other cases, the
fitted PRF ends up with a central flux between that of the central valley and
that of the wings, meaning PRF fitting underestimates the total flux, so these
sources are also shifted to the left in Fig.~\ref{errors}.
The SSC homepage provides values of the maximum flux of unsaturated point
sources as a function of {\em integration} time. Table~\ref{tbl_limits}
presents the flux values interpolated to a frame {\em exposure} time of 1.2\,s,
along with a lower flux limit. This lower flux limit was adopted on subjective
grounds for the quality grade labelling (see below). We thus have to be
cautious with sources brighter than about 320\,mJy in IRAC\,1. Consistent with
this warning is a third slight effect that seems to set in at fluxes close to
this value and affects all brighter sources: the PRF fluxes increase
disproportionately compared to the aperture fluxes, leading to a bending to the
right, away from the dashed line in Fig.~\ref{errors} (top). Aperture
photometry thus measures the saturated plateau of the PRF, while PRF fitting
seems to ignore the missing flux that would be present beyond the plateau and
fits the wings. The individual source then lies below the dashed line, with a
larger PRF flux than the aperture flux.
\begin{table}
\caption{Flux limits applied for assigning quality grades.}
\label{tbl_limits}
\centering
\begin{tabular}{ccc}
\hline\hline
Band & Lower limit (mJy) & Saturation limit (mJy) \\
\hline
IRAC 3.6\,$\mu$m & 40 & 320 \\
IRAC 4.5\,$\mu$m & 30 & 330 \\
IRAC 5.8\,$\mu$m & 20 & 2300 \\
IRAC 8.0\,$\mu$m & 20 & 1200 \\
MIPS 24\,$\mu$m & 40 & 220 \\
\hline
\end{tabular}
\end{table}
If dividing the aperture flux by the linear least squares fit to sources with
$\chi^{2} < 5$, the fluxes measured with both ways are almost identical for
many of the sources with $\chi^{2} < 5$. The slope of this fit is not
the aperture correction factor, to be derived in Sect.~\ref{sec_apt_corr}.
Except for the sources affected by the three aforementioned effects, the
relative difference calculated as
\begin{equation}
{\rm rel.\ difference} = \frac{{\rm f}_{\rm PRF} - {\rm f}_{\rm aperture}^{\rm
corrected}}{{\rm f}_{\rm PRF}}
\label{equ_relerr}
\end{equation}
scatters around 7\% (Fig.~\ref{errors}, bottom). The superscript ``corrected''
in Eq.~\ref{equ_relerr} indicates that the aperture flux has been divided by
the linear fit to sources with $\chi^{2} < 5$. Sources that are within this
range are considered as quality grade~A. This test is performed first,
therefore grade~A sources span the whole range of fluxes, from faint to almost
saturated sources.
\begin{figure}[!ht]
\includegraphics[width=8.7cm]{figure2_1.png}\\
\includegraphics[width=8.7cm]{figure2_2.png}\\
\includegraphics[width=8.7cm]{figure2_3.png}\\
\caption{Comparison of the fluxes resulting from PRF fitting and aperture
photometry for the IRAC\,1 observations of the NGC\,6522 field. Top:
PRF fitting fluxes and aperture photometry for the aperture with a radius of
2 pixels; middle: the same as top panel, but for the aperture with a radius
of 3 pixels; bottom: relative difference between the measured fluxes (3
pixels aperture radius) versus the PRF flux for all sources. The dotted lines
in the bottom panel mark relative differences of $\pm7$\%. In the upper and
middle panels, the dashed line is a linear least squares fit to the sources
with $\chi^{2} < 5$, and the solid horizontal and vertical lines mark the
lower and saturation limits of Table~\ref{tbl_limits} used for quality grade
labelling.}
\label{errors}
\end{figure}
Faint sources with fluxes smaller than a certain lower limit
(Table~\ref{tbl_limits}) and outside the 7\% range are classified as quality
grade~B. Sources whose fluxes are above the saturation limit are classified as
quality grade~C. They would have to be treated differently with dedicated tools.
However, since these sources are probably mostly foreground stars, they are not
of prime interest to the science goals, thus we decided not to invest more time
in their flux determination. The interested reader is invited to download and
analyse the mosaics, which will be made available as on-line material at Centre
de Donn\'{e}es astronomiques de Strasbourg (CDS).
Sources that failed all of the above criteria are classified as quality
grade~D. These are blended sources for which the PRFs overlap such that even
the aperture with the smallest radius includes both peaks; i.e., no reliable
flux measurement is available for these sources. This effect is the same as
the first one mentioned above related to the larger aperture with a radius of 3
pixels or larger.
The statistics of grades for all seven fields and all five bands are given in
Table~\ref{tbl_stats_grades}. The percentage given for grades A and B is
relative to the total number of sources in the catalogue for the respective
field that is given in the last column. The seventh column gives the
number of sources not detected in the respective channel, but detected in at
least one of the other bands plus in the reference catalogues (see
Sect.~\ref{sect_catalogue}).
\begin{table*}
\caption{Statistics of sources with their grades for all seven fields and
five bands.}
\label{tbl_stats_grades}
\centering
\begin{tabular}{ccrrrrrr}
\hline\hline
Field & Band & Grade A & Grade B & Grade C & Grade D & Not detected & total \\
\hline
Bulge 1 & 3.6\,$\mu$m & 12446 (18\%) & 39177 (57\%) & 183 & 626 & 16661 & 69093 \\
& 4.5\,$\mu$m & 16173 (23\%) & 35598 (52\%) & 85 & 216 & 17021 & \\
& 5.8\,$\mu$m & 13839 (20\%) & 21757 (31\%) & 1 & 169 & 33327 & \\
& 8.0\,$\mu$m & 12669 (18\%) & 17044 (25\%) & 7 & 96 & 39277 & \\
& 24\,$\mu$m & 577 ( 1\%) & 1197 ( 2\%) & 1 & 2 & 67316 & \\
Bulge 2 & 3.6\,$\mu$m & 14889 (25\%) & 30525 (51\%) & 197 & 748 & 13963 & 60322 \\
& 4.5\,$\mu$m & 17495 (29\%) & 28190 (47\%) & 72 & 492 & 14073 & \\
& 5.8\,$\mu$m & 13712 (23\%) & 17900 (30\%) & 0 & 214 & 28496 & \\
& 8.0\,$\mu$m & 11960 (20\%) & 15752 (26\%) & 1 & 152 & 32457 & \\
& 24\,$\mu$m & 503 ( 1\%) & 1119 ( 2\%) & 4 & 4 & 58692 & \\
Bulge 3 & 3.6\,$\mu$m & 13476 (26\%) & 27927 (53\%) & 131 & 101 & 11031 & 52666 \\
& 4.5\,$\mu$m & 16329 (31\%) & 25159 (48\%) & 62 & 64 & 11052 & \\
& 5.8\,$\mu$m & 12085 (23\%) & 15880 (30\%) & 0 & 35 & 24666 & \\
& 8.0\,$\mu$m & 10712 (20\%) & 13220 (25\%) & 4 & 24 & 28706 & \\
& 24\,$\mu$m & 383 ( 1\%) & 976 ( 2\%) & 1 & 2 & 51304 & \\
Bulge 4 & 3.6\,$\mu$m & 12938 (22\%) & 33046 (57\%) & 136 & 197 & 12091 & 58408 \\
& 4.5\,$\mu$m & 15689 (27\%) & 29961 (51\%) & 75 & 95 & 12588 & \\
& 5.8\,$\mu$m & 11311 (19\%) & 18283 (31\%) & 3 & 177 & 28634 & \\
& 8.0\,$\mu$m & 9239 (16\%) & 13588 (23\%) & 19 & 98 & 35464 & \\
& 24\,$\mu$m & 267 ( 0\%) & 817 ( 1\%) & 3 & 4 & 57317 & \\
Bulge N\,1 & 3.6\,$\mu$m & 12553 (19\%) & 35826 (55\%) & 198 & 724 & 15534 & 64835 \\
& 4.5\,$\mu$m & 15402 (24\%) & 34527 (53\%) & 85 & 296 & 14525 & \\
& 5.8\,$\mu$m & 11819 (18\%) & 21845 (34\%) & 5 & 520 & 30646 & \\
& 8.0\,$\mu$m & 12035 (19\%) & 16565 (26\%) & 11 & 144 & 36080 & \\
& 24\,$\mu$m & 467 ( 1\%) & 1126 ( 2\%) & 3 & 23 & 63216 & \\
Bulge N\,2 & 24\,$\mu$m & 21 ( 5\%) & 316 (74\%) & 17 & 74 & 0 & 428 \\
NGC\,6522 & 3.6\,$\mu$m & 12430 (26\%) & 24924 (53\%) & 79 & 55 & 9796 & 47284 \\
& 4.5\,$\mu$m & 15637 (33\%) & 21263 (45\%) & 32 & 21 & 10331 & \\
& 5.8\,$\mu$m & 12011 (25\%) & 11907 (25\%) & 0 & 30 & 23336 & \\
& 8.0\,$\mu$m & 10263 (22\%) & 10432 (22\%) & 0 & 12 & 26577 & \\
& 24\,$\mu$m & 431 ( 1\%) & 1152 ( 2\%) & 0 & 0 & 45701 & \\
\hline
\end{tabular}
\end{table*}
\subsubsection{Step 3: Determination of the aperture corrections}
\label{sec_apt_corr}
Since we do not use a larger aperture to estimate the background, which would
give unreliable photometry in the crowded fields, but do aperture photometry on
the background-subtracted images instead, the aperture corrections are expected
to be different from the standard values given in the instrument handbooks.
To derive aperture corrections, we created point spread functions with
stinytim2.0 \citep{Kri06} for all five bands.
We then inserted artificial sources with known flux in our mosaicked,
background-subtracted images and compared the resulting fluxes given by APEX
with the initial fluxes with which we had created the sources. The slope of a
linear least squares fit to the initial vs.\ measured flux gives the aperture
correction factors. The derived aperture corrections for the aperture with two
pixels radius
are given in Table~\ref{tbl_aper_corr}, along with their statistical error as
derived from the linear fit. Also given in the table are the values as
recommended by the SSC, for a 2 pixel radius on source and a 10 -- 20 pixel
radius background annulus in the case of IRAC, and a 3\farcs5 on source
aperture without any background annulus in the case of MIPS. The SSC
recommended values are not directly comparable to our aperture correction
factors, so they are only given for illustrative purposes. Despite the high
value of the aperture correction factor for MIPS\,24, we adopted the small
aperture with 2 pixels radius because i) our observations are not photon noise
limited, thus a larger aperture would not reduce the error estimate; ii) there
is a ``population'' of blended sources whose flux increases disproportionally
with growing aperture because more of the neighbouring source's flux is
measured with larger aperture; iii) the SSC lists aperture corrections for an
even smaller aperture, so our value is not an extreme. We also corrected
the PRF fluxes with the photometric correction factors as recommended by the
SSC.
\begin{table}
\caption{Aperture correction factors}
\label{tbl_aper_corr}
\centering
\begin{tabular}{ccc}
\hline\hline
Band & Aperture correction & SSC recommended \\
\hline
IRAC 3.6\,$\mu$m & 1.2129$\pm$0.0008 & 1.205 \\
IRAC 4.5\,$\mu$m & 1.2730$\pm$0.0005 & 1.221 \\
IRAC 5.8\,$\mu$m & 1.4693$\pm$0.0007 & 1.363 \\
IRAC 8.0\,$\mu$m & 1.6556$\pm$0.0006 & 1.571 \\
MIPS 24\,$\mu$m & 1.5742$\pm$0.0007 & 2.560 \\
\hline
\end{tabular}
\end{table}
Besides the aperture correction and the photometric correction for the PRF
fluxes, we did not apply any other correction factors such as the colour
correction. According to the IRAC data handbook, the colour correction factor
for blackbody spectra with temperatures between 2\,000 and 5\,000\,K is around
1\%, except for IRAC\,4, where it can reach as much as 2.7\% for the hotter
stars. Since the colour correction is small and we do not know a priori the
nature and spectrum of our objects, we did not apply these corrections.
\subsubsection{Step 4: Creating the point source catalogue}
\label{sect_catalogue}
We finally decided to adopt only the PRF fluxes for the final catalogue
on the basis of comparison with other catalogues and with isochrones in CMDs.
With this choice, we find, on the one hand, slightly better agreement with
other catalogues, and on the other, somewhat reduced scatter at the faint end
of CMDs. See Sect.~\ref{sec_surveys} and \ref{sec_cmds} for a comparison
with other catalogues and isochrones.
The last step is the cross-identification, for each field, of the extraction
tables of all five bands among each other and with other reference catalogues.
As reference catalogues we adopt the Deep Near Infrared Survey
\citep[DENIS;][]{Epc97}, the 2~Micron All Sky Survey \citep[2MASS;][]{Skr06},
the Midcourse Space Experiment (MSX) catalogue, and the Infra-Red Astronomical
Satellite (IRAS) point source catalogue. We applied the following criteria to
include a source in the final catalogue. We identified individual sources by
their RA and Dec position and allowed for an error margin of 1\farcs6, i.e.\
slightly more than one pixel size, for the cross-identification among our five
bands. Sources that are detected in at least two of our five bands are included
in any case in the final catalogue. A cross-identification is made for these
sources with a search radius of 3\farcs0 with DENIS and 2MASS, and 30\farcs0 for
identification with an MSX or IRAS counterpart. The information about these
counterparts is included in the catalogue. Sources that are detected in only one
of our five bands are only included in the final catalogue if they also have a
counterpart in at least one of the reference catalogues, with the same search
radii applied as for the sources with two or more {\em Spitzer} detections.
This procedure was followed to include as many of the sources in the final
catalogue that were only detected in MIPS\,24. These might very well be real
objects, albeit extremely red (i.e.\ not detected with IRAC). Additionally, by
following this procedure, more of the sources that are located in the areas that
are not sampled by all five bands will be included in the catalogue. These areas
are also included in the final catalogue. The least reliable sources in our
catalogue are those with detection in only one IRAC band and no MIPS detection,
and with (i) either no 2MASS and DENIS counterpart (depending on the field,
between 3.1\% and 6.7\% of the sources), or (ii) a DENIS and 2MASS counterpart
at a distance between 1.6 and 3 arcseconds (depending on the field, between
0.4\% and 1.0\% of the sources).
Table~\ref{cattable_1} gives ten lines of the band-merged catalogue of the Bulge
N\,1 field as an example. The entire table will be made available for download
from CDS. A portion is shown here for guidance regarding its form and content.
The columns of our point source catalogue are explained as follows.
\begin{description}
\item[Column 1:] Source identification, IAU-conform identifier.
\item[Column 2:] Right ascension in degrees (J2000).
\item[Column 3:] Declination in degrees (J2000).
\item[Column 4:] PRF flux in IRAC\,1 (in $\mu$Jy), set to ``$-$9.99999e+99'' if
not detected.
\item[Column 5:] PRF flux in IRAC\,2 (in $\mu$Jy), set to ``$-$9.99999e+99'' if
not detected.
\item[Column 6:] PRF flux in IRAC\,3 (in $\mu$Jy), set to ``$-$9.99999e+99'' if
not detected.
\item[Column 7:] PRF flux in IRAC\,4 (in $\mu$Jy), set to ``$-$9.99999e+99'' if
not detected.
\item[Column 8:] PRF flux in MIPS\,24 (in $\mu$Jy), set to ``$-$9.99999e+99''
if not detected.
\item[Column 9:] Quality flags of the IRAC\,1, 2, 3, 4, and MIPS\,24
channels (see Section~\ref{sec_qualgr}), set to ``$-$'' if not detected.
\item[Column 10:] Uncertainty of the PRF flux in IRAC\,1 (in $\mu$Jy), set to
``$-$9.99999e+99'' if not detected.
\item[Column 11:] Uncertainty of the PRF flux in IRAC\,2 (in $\mu$Jy), set to
``$-$9.99999e+99'' if not detected.
\item[Column 12:] Uncertainty of the PRF flux in IRAC\,3 (in $\mu$Jy), set to
``$-$9.99999e+99'' if not detected.
\item[Column 13:] Uncertainty of the PRF flux in IRAC\,4 (in $\mu$Jy), set to
``$-$9.99999e+99'' if not detected.
\item[Column 14:] Uncertainty of the PRF flux in MIPS\,24 (in $\mu$Jy), set to
``$-$9.99999e+99'' if not detected.
\item[Column 15:] Observation flag. The first four bits state if the position
of the source was in the field of view of the IRAC bands (``1'') or not
(``0''), the fifth bit is for MIPS\,24.
\item[--]
\item[Column 16:] Distance to closest DENIS source (arcsec; only
\mbox{$<3\farcs0$}), set to ``$-$'' if no counterpart.
\item[Column 17:] DENIS $I$-band magnitude, set to ``$-$'' if no counterpart
or the counterpart has no $I$-band measurement.
\item[Column 18:] DENIS $J$-band magnitude, set to ``$-$'' if no counterpart
or the counterpart has no $J$-band measurement.
\item[Column 19:] DENIS $K$-band magnitude, set to ``$-$'' if no counterpart
or the counterpart has no $K$-band measurement.
\item[--]
\item[Column 20:] Distance to closest 2MASS source (arcsec; only
\mbox{$<3\farcs0$}), set to ``$-$'' if no counterpart. Only sources with
quality flags A, B, C, or D in at least one 2MASS filter have been considered.
\item[Column 21:] 2MASS $J$-band magnitude, set to ``$-$'' if no counterpart
within \mbox{$3\farcs0$} was found, or ``$-9.999$'' if the counterpart has no
measured $J$-band magnitude available or too low quality flag.
\item[Column 22:] 2MASS $H$-band magnitude, set to ``$-$'' if no counterpart
within \mbox{$3\farcs0$} was found, or ``$-9.999$'' if the counterpart has no
measured $H$-band magnitude available or too low quality flag.
\item[Column 23:] 2MASS $K$-band magnitude, set to ``$-$'' if no counterpart
within \mbox{$3\farcs0$} was found, or ``$-9.999$'' if the counterpart has no
measured $K$-band magnitude available or too low quality flag.
\item[Column 24:] 2MASS quality flags, set to ``$-$'' if no counterpart or too
low quality flag.
\item[--]
\item[Column 25:] Distance to closest IRAS source (arcsec; only
\mbox{$<30\hbox{$^{\prime\prime}$}$}), set to ``$-$'' if no counterpart. Only sources with
quality flags 2 or 3 in at least one IRAS band have been considered.
\item[Column 26:] IRAS 12\,$\mu$m flux (Jy), set to ``$-$'' if no counterpart,
and to ``$-$9.9e+99'' if the counterpart has no measured flux in the
12\,$\mu$m band or too low quality flag.
\item[Column 27:] IRAS 12\,$\mu$m quality flag, set to ``$-$'' if no
counterpart or too low quality flag.
\item[Column 28:] IRAS 25\,$\mu$m flux (Jy), set to ``$-$'' if no counterpart,
and to ``$-$9.9e+99'' if the counterpart has no measured flux in the
25\,$\mu$m band or too low quality flag.
\item[Column 29:] IRAS 25\,$\mu$m quality flag, set to ``$-$'' if no
counterpart or too low quality flag.
\item[Column 30:] IRAS 60\,$\mu$m flux (Jy), set to ``$-$'' if no counterpart,
and to ``$-$9.9e+99'' if the counterpart has no measured flux in the
60\,$\mu$m band or too low quality flag.
\item[Column 31:] IRAS 60\,$\mu$m quality flag, set to ``$-$'' if no
counterpart or too low quality flag.
\item[Column 32:] IRAS 100\,$\mu$m flux (Jy), set to ``$-$'' if no counterpart,
and to ``$-$9.9e+99'' if the counterpart has no measured flux in the
100\,$\mu$m band or too low quality flag.
\item[Column 33:] IRAS 100\,$\mu$m quality flag, set to ``$-$'' if no
counterpart or too low quality flag.
\item[--]
\item[Column 34:] Distance to closest MSX source (arcsec; only
\mbox{$<30\hbox{$^{\prime\prime}$}$}), set to ``$-$'' if no counterpart. Only sources with
quality flags 2, 3, or 4 in at least one MSX band have been considered.
\item[Column 35:] MSX B1 band flux (Jy), set to ``$-$'' if no counterpart,
and to ``$-$9.999e+99'' if the counterpart has no measured flux in the
B1 band or too low B1 band quality flag.
\item[Column 36:] MSX B1 band quality flag, set to ``$-$'' if no counterpart or
too low quality flag.
\item[Column 37:] MSX B2 band flux (Jy), set to ``$-$'' if no counterpart,
and to ``$-$9.999e+99'' if the counterpart has no measured flux in the
B2 band or too low B2 band quality flag.
\item[Column 38:] MSX B2 band quality flag, set to ``$-$'' if no counterpart or
too low quality flag.
\item[Column 39:] MSX A band flux (Jy), set to ``$-$'' if no counterpart,
and to ``$-$9.999e+99'' if the counterpart has no measured flux in the
A band or too low A band quality flag.
\item[Column 40:] MSX A band quality flag, set to ``$-$'' if no counterpart or
too low quality flag.
\item[Column 41:] MSX C band flux (Jy), set to ``$-$'' if no counterpart,
and to ``$-$9.999e+99'' if the counterpart has no measured flux in the
C band or too low C band quality flag.
\item[Column 42:] MSX C band quality flag, set to ``$-$'' if no counterpart or
too low quality flag.
\item[Column 43:] MSX D band flux (Jy), set to ``$-$'' if no counterpart,
and to ``$-$9.999e+99'' if the counterpart has no measured flux in the
D band or too low D band quality flag.
\item[Column 44:] MSX D band quality flag, set to ``$-$'' if no counterpart or
too low quality flag.
\item[Column 45:] MSX E band flux (Jy), set to ``$-$'' if no counterpart,
and to ``$-$9.999e+99'' if the counterpart has no measured flux in the
E band or too low E band quality flag.
\item[Column 46:] MSX E band quality flag, set to ``$-$'' if no counterpart or
too low quality flag.
\end{description}
\begin{landscape}
\centering
\begin{table}
\setcounter{table}{4}
\caption{Sample table of the band-merged catalogue of the N\,1 field.
}
\label{cattable_1}
\begin{tabular}{cccccccccc}
\hline\hline
Source id.\ & RA & Dec & IRAC\,1 & IRAC\,2 & IRAC\,3 & IRAC\,4 & MIPS\,24 & Quality flags & $\Delta$\,IRAC\,1 \\
(1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10) \\
\hline
USB267.50681$-$29.54985 & 267.506807 & $-$29.549854 & 2.707150e+05 & 1.996047e+05 & 2.018591e+05 & $-$9.99999e+99 & 1.293678e+05 & A A A $-$ D & 6.895201e+02 \\
USB267.50882$-$29.54757 & 267.508822 & $-$29.547572 & 2.885406e+03 & 2.078063e+03 & $-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & B B $-$ $-$ $-$ & 5.886386e+01 \\
USB267.50743$-$29.55153 & 267.507432 & $-$29.551530 & 4.349657e+03 & $-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & B $-$ $-$ $-$ $-$ & 5.367287e+01 \\
USB267.50761$-$29.55523 & 267.507612 & $-$29.555234 & 8.086190e+04 & $-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & 2.392784e+06 & D $-$ $-$ $-$ C & 2.820764e+02 \\
USB267.50862$-$29.55417 & 267.508623 & $-$29.554167 & 1.133203e+05 & 7.665020e+04 & 8.380626e+04 & $-$9.99999e+99 & $-$9.99999e+99 & D D D $-$ $-$ & 3.408423e+02 \\
USB267.50730$-$29.55596 & 267.507301 & $-$29.555959 & 2.159647e+05 & 1.786561e+05 & $-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & C C $-$ $-$ $-$ & 9.627816e+02 \\
USB267.50860$-$29.55727 & 267.508600 & $-$29.557267 & 3.002938e+05 & $-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & C $-$ $-$ $-$ $-$ & 1.635651e+03 \\
USB267.50811$-$29.55797 & 267.508113 & $-$29.557972 & 1.587659e+05 & $-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & C $-$ $-$ $-$ $-$ & 9.000979e+02 \\
USB267.50573$-$29.55593 & 267.505733 & $-$29.555935 & 8.429971e+04 & 6.759881e+04 & 1.763209e+05 & $-$9.99999e+99 & $-$9.99999e+99 & D D D $-$ $-$ & 4.045054e+02 \\
USB267.50479$-$29.55561 & 267.504790 & $-$29.555611 & 4.142997e+04 & $-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & D $-$ $-$ $-$ $-$ & 1.880509e+02 \\
\hline
\end{tabular}
\end{table}
\centering
\begin{table}
\setcounter{table}{4}
\caption{Sample table of the band-merged catalogue of the N\,1 field
(continued).}
\label{cattable_2}
\begin{tabular}{ccccccccccccccccc}
\hline\hline
$\Delta$\,IRAC\,2 & $\Delta$\,IRAC\,3 & $\Delta$\,IRAC\,4 & $\Delta$\,MIPS\,24 & obs.\ flag & & & & & & & & & & & & \\
(11) & (12) & (13) & (14) & (15) & & (16) & (17) & (18) & (19) & & (20) & (21) & (22) & (23) & (24) & \\
\hline
5.543478e+02 & 5.596869e+02 & $-$9.99999e+99 & 5.804075e+01 & 11111 & $|$ & 0.431 & 14.684 & 10.946 & 8.699 & $|$ & 0.316 & 10.799 & 9.300 & 8.452 & AAA & $|$ \\
4.209486e+01 & $-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & 11111 & $|$ & $-$ & $-$ & $-$ & $-$ & $|$ & 0.152 & $-$9.999 & 12.902 & 12.604 & UAA & $|$ \\
$-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & 11111 & $|$ & 2.682 & 14.974 & $-$ & $-$ & $|$ & 0.370 & $-$9.999 & 13.389 & $-$9.999 & UBU & $|$ \\
$-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & 3.545098e+02 & 11111 & $|$ & $-$ & $-$ & $-$ & $-$ & $|$ & $-$ & $-$ & $-$ & $-$ & $-$ & $|$ \\
2.687747e+02 & 3.786693e+02 & $-$9.99999e+99 & $-$9.99999e+99 & 11111 & $|$ & 0.288 & 14.974 & 11.759 & 9.230 & $|$ & 0.281 & 11.225 & 9.678 & 9.084 & AAA & $|$ \\
6.126482e+02 & $-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & 11111 & $|$ & 0.700 & 14.535 & $-$ & $-$ & $|$ & $-$ & $-$ & $-$ & $-$ & $-$ & $|$ \\
$-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & 11111 & $|$ & 2.840 & $-$ & 9.955 & 5.166 & $|$ & 2.781 & $-$9.999 & 13.012 & $-$9.999 & UAU & $|$ \\
$-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & 11111 & $|$ & $-$ & $-$ & $-$ & $-$ & $|$ & $-$ & $-$ & $-$ & $-$ & $-$ & $|$ \\
2.687747e+02 & 6.536204e+02 & $-$9.99999e+99 & $-$9.99999e+99 & 11111 & $|$ & 2.717 & $-$ & 14.089 & 12.045 & $|$ & 2.779 & 13.725 & 12.248 & 11.631 & AAB & $|$ \\
$-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & $-$9.99999e+99 & 11111 & $|$ & 0.900 & $-$ & 14.089 & 12.045 & $|$ & 0.708 & 13.725 & 12.248 & 11.631 & AAB & $|$ \\
\hline
\end{tabular}
\end{table}
\centering
\begin{table}
\setcounter{table}{4}
\caption{Sample table of the band-merged catalogue of the N\,1 field
(continued).}
\label{cattable_3}
\begin{tabular}{cccccccccccccccccc}
\hline\hline
& & & & & & & & & & & & & & & & & \\
(25) & (26) & (27) & (28) & (29) & (30) & (31) & (32) & (33) & & (34) & (35) & (36) & (37) & (38) & (39) & (40) & (41) \\
\hline
23.1 & 1.89e+01 & 3 & 1.59e+01 & 3 & $-$9.9e+99 & 1 & $-$9.9e+99 & 1 & $|$ & 26.5 & 9.063e+00 & 3 & $-$9.999e+99 & 0 & 1.678e+01 & 4 & 2.109e+01 \\
$-$ & $-$ & $-$ & $-$ & $-$ & $-$ & $-$ & $-$ & $-$ & $|$ & $-$ & $-$ & $-$ & $-$ & $-$ & $-$ & $-$ & $-$ \\
17.2 & 1.89e+01 & 3 & 1.59e+01 & 3 & $-$9.9e+99 & 1 & $-$9.9e+99 & 1 & $|$ & 20.4 & 9.063e+00 & 3 & $-$9.999e+99 & 0 & 1.678e+01 & 4 & 2.109e+01 \\
4.6 & 1.89e+01 & 3 & 1.59e+01 & 3 & $-$9.9e+99 & 1 & $-$9.9e+99 & 1 & $|$ & 7.1 & 9.063e+00 & 3 & $-$9.999e+99 & 0 & 1.678e+01 & 4 & 2.109e+01 \\
9.6 & 1.89e+01 & 3 & 1.59e+01 & 3 & $-$9.9e+99 & 1 & $-$9.9e+99 & 1 & $|$ & 11.6 & 9.063e+00 & 3 & $-$9.999e+99 & 0 & 1.678e+01 & 4 & 2.109e+01 \\
2.1 & 1.89e+01 & 3 & 1.59e+01 & 3 & $-$9.9e+99 & 1 & $-$9.9e+99 & 1 & $|$ & 4.5 & 9.063e+00 & 3 & $-$9.999e+99 & 0 & 1.678e+01 & 4 & 2.109e+01 \\
6.9 & 1.89e+01 & 3 & 1.59e+01 & 3 & $-$9.9e+99 & 1 & $-$9.9e+99 & 1 & $|$ & 3.8 & 9.063e+00 & 3 & $-$9.999e+99 & 0 & 1.678e+01 & 4 & 2.109e+01 \\
7.5 & 1.89e+01 & 3 & 1.59e+01 & 3 & $-$9.9e+99 & 1 & $-$9.9e+99 & 1 & $|$ & 3.6 & 9.063e+00 & 3 & $-$9.999e+99 & 0 & 1.678e+01 & 4 & 2.109e+01 \\
3.4 & 1.89e+01 & 3 & 1.59e+01 & 3 & $-$9.9e+99 & 1 & $-$9.9e+99 & 1 & $|$ & 6.9 & 9.063e+00 & 3 & $-$9.999e+99 & 0 & 1.678e+01 & 4 & 2.109e+01 \\
6.5 & 1.89e+01 & 3 & 1.59e+01 & 3 & $-$9.9e+99 & 1 & $-$9.9e+99 & 1 & $|$ & 10.0 & 9.063e+00 & 3 & $-$9.999e+99 & 0 & 1.678e+01 & 4 & 2.109e+01 \\
\hline
\end{tabular}
\end{table}
\clearpage
\centering
\begin{table}
\setcounter{table}{4}
\caption{Sample table of the band-merged catalogue of the N\,1 field
(continued).}
\label{cattable_4}
\begin{tabular}{ccccc}
\hline\hline
& & & & \\
(42) & (43) & (44) & (45) & (46) \\
\hline
4 & 1.698e+01 & 4 & 1.593e+01 & 4 \\
$-$ & $-$ & $-$ & $-$ & $-$ \\
4 & 1.698e+01 & 4 & 1.593e+01 & 4 \\
4 & 1.698e+01 & 4 & 1.593e+01 & 4 \\
4 & 1.698e+01 & 4 & 1.593e+01 & 4 \\
4 & 1.698e+01 & 4 & 1.593e+01 & 4 \\
4 & 1.698e+01 & 4 & 1.593e+01 & 4 \\
4 & 1.698e+01 & 4 & 1.593e+01 & 4 \\
4 & 1.698e+01 & 4 & 1.593e+01 & 4 \\
4 & 1.698e+01 & 4 & 1.593e+01 & 4 \\
\hline
\end{tabular}
\end{table}
\end{landscape}
\clearpage
\section{Comparison with other missions and catalogues}\label{sec_surveys}
Our observations overlap with a number of other mid-IR surveys. These are
\begin{enumerate}
\item ISOGAL: Survey with the ISO Camera (ISOCAM) on-board the ISO satellite,
combined with DENIS $IJK_S$ photometry.
\item Galactic Legacy Infrared Mid-Plane Survey Extraordinaire II (GLIMPSE-II),
a {\em Spitzer}/IRAC survey of the area $\pm 1\hbox{$^\circ$}$ around the Galactic
plane and the Galactic centre \citep{GLIMPSE}.
\item GALactic CENtre (GALCEN), a {\em Spitzer}/IRAC survey of the inner
$\sim 1\fdg4 \times 2\fdg0$ of the Galaxy \citep{Ram08}.
\item A {\em Spitzer}/MIPS survey of the inner $\sim 1\fdg5 \times 8\fdg0$ of
the Galaxy \citep{Hin08}.
\end{enumerate}
\subsection{Comparison with ISOGAL}\label{comp_isogal}
ISOGAL \citep{Omo03} is a survey with the ISOCAM instrument on-board the ISO
satellite in two bands at 7 and 15\,$\mu$m, combined with $IJK_{\rm{S}}$
photometry from the DENIS project \citep{Epc97}. The 7\,$\mu$m LW2 band of
ISOCAM ($\sim 5.0 - 8.5$\,$\mu$m, central wavelength 6.75\,$\mu$m) overlaps in
wavelength with the IRAC\,4 channel \citep[$\sim 6.4 - 9.4$\,$\mu$m, nominal
wavelength 7.844\,$\mu$m;][]{Hor08}. For IRAC\,4, we have overlap with ISOGAL
in the fields Bulge\,2, Bulge\,4, N\,1, and NGC\,6522. The number of sources in
common (with less than $2\farcs0$ positional offset) is 163 for Bulge\,2, 335
for Bulge\,4, 288 for N\,1, and 264 in NGC\,6522. We present here a brief
comparison for the NGC\,6522 field, because the ISO 7\,$\mu$m photometry goes
deepest in that field (least crowding and diffuse background emission). The
results for the other fields are very similar.
Figure~\ref{ISOGAL_NGC6522} shows the magnitude difference between the
{\em Spitzer} IRAC\,4 band and the ISO LW2 band for the NGC\,6522 field. The
data points do not scatter randomly around zero. Rather, faint sources tend to
be brighter in the ISO 7\,$\mu$m band, whereas bright sources tend to be
brighter in the IRAC\,4 band. The relation found to convert between the
two bands is
\begin{equation}
mag_{\rm{ISO}\,7} = 0.866 \times mag_{\rm{IRAC}\,4} + 1.024.
\label{equ_iso}
\end{equation}
The slopes and zero points of this linear fit are similar for all fields, with a
cross-over ({\em Spitzer} IRAC\,4 equal to ISO 7\,$\mu$m magnitude) between
$6\fm0$ and $7\fm7$. The trend might be a reflection of a dependence of the
strength of the SiO fundamental band at $\sim 7.5$\,$\mu$m and/or a water band
at $\sim 5.5$\,$\mu$m on the brightness of the star. At least the SiO first
overtone band at $\sim 4.0$\,$\mu$m has been found to decrease in strength from
semi-regular variables to Mira-like variables \citep{Ari99}.
On top of that, instrumental effects in one or both missions cannot be
excluded.
\begin{figure}
\includegraphics[width=\columnwidth,bb=70 368 540 556]{ISO7_vs_IRAC4_NGC6522.pdf}
\caption{Magnitude difference between the {\em Spitzer} IRAC\,4 band and the
ISO 7\,$\mu$m LW2 band for 264 sources in common in the NGC\,6522 field. The
dotted line marks the identity relation, the dashed line is a linear least
squares fit through the data points, excluding those sources fainter than
9\fm3 in either of the data sets to avoid Malmquist bias.}
\label{ISOGAL_NGC6522}
\end{figure}
\subsection{Comparison with GLIMPSE-II}\label{comp_GLIMPSE}
The Galactic Legacy Infrared Mid-Plane Survey Extraordinaire
\citep[GLIMPSE-II;][]{GLIMPSE}, is a {\em Spitzer} Legacy Science Programme of
most of the inner Galactic disk using the IRAC instrument. Our programme has
overlaps the GLIMPSE-II survey in the fields Bulge\,1, Bulge\,2, Bulge\,4, and
Bulge N\,1. A comparison with this large data set is especially interesting
because the same instrument and the same filter bands have been used, though
the observing strategies and data reduction techniques are different.
In Fig.~\ref{GLIMPSE_N1} we show the magnitude differences between our and
the GLIMPSE-II catalogue for all four IRAC channels for the Bulge N\,1 field,
since there is a large number of sources in common in this field (31\,191).
These plots look very similar for the other fields with overlap.
In general, the agreement between our and the GLIMPSE-II catalogue is good in
the bright to medium brightness range.
However, at the faint end, starting at around $10^{\rm{m}} - 11^{\rm{m}}$, we
notice a strong trend such that the magnitudes become increasingly fainter in
our catalogue than in the GLIMPSE-II catalogue. This is not only true for the
flag~B sources (most of the red dots at faint magnitudes in
Fig.~\ref{GLIMPSE_N1}), but also for flag~A sources fainter than this
magnitude limit, and for all filters. The same trend is revealed in a
comparison\footnote{http://www.astro.wisc.edu/sirtf/glm2\_galcen\_comparison.pdf}
between the GLIMPSE-II catalogue and the one of
\citet[][see next section]{Ram08}. According to B.\ Babler of the GLIMPSE-II
team (private communication, 2008), this trend at the faint magnitude limit
arises because of GLIMPSE-II's limitation to ``single frame'' photometry.
GLIMPSE-II does photometry only on single bcd frames instead of mosaics, because
each patch of the sky is observed only twice. This strategy may cause a
Malmquist bias, such that GLIMPSE-II magnitudes will be increasingly too bright
the closer a source is to the faint limit. Thus, for sources at the faint
limit, our magnitudes are likely more accurate than GLIMPSE-II magnitudes.
Finally, we also notice some saturation effects above $\sim6\fm5$ in IRAC\,1,
and a few sources that are significantly fainter in the GLIMPSE-II catalogue
than in our catalogue that can be found at all magnitudes.
\begin{figure*}
\includegraphics{comp_GLIMPSE_N1.png}
\caption{Magnitude differences between our and the GLIMPSE-II catalogue for the
sources in common in the N\,1 field. Sources with quality flag~A in our
catalogue are represented by black dots, all other quality flags by red dots.}
\label{GLIMPSE_N1}
\end{figure*}
Due to the large number of sources in common with the GLIMPSE-II survey, we are
able to check whether or not the combined errors are of realistic magnitude. To
do so, we inspect the sigma-factor, which is also discussed in the
aforementioned comparison between the GLIMPSE-II and \citet{Ram08} catalogues:
\begin{equation}
\sigma = \frac{\rm{our~mag} - \rm{GLIMPSE~mag}}{\sqrt{(\rm{our~error})^2 + (\rm{GLIMPSE~error})^2}}.
\label{sigma}
\end{equation}
If the combined errors are close to the magnitude differences, the
sigma-factor will have a Gaussian distribution of width 1. If the errors are
underestimated, the distribution will be broader than that and narrower if the
error estimates are too large. Figure~\ref{GLIMPSEerr_fig} displays the sigma
distribution for all four IRAC channels for the field Bulge N\,1, along with a
Gaussian fit to the data. Also plotted is a Gaussian for a ``perfect''
distribution with the same area under the graph, i.e.\ when magnitude
differences and combined error are on average of the same size ($\sigma = 1$).
The source selection was restricted to the magnitude range $7\fm0 - 10\fm0$ to
avoid the tail of faint sources with a Malmquist bias (see above). We see that
the distributions are centred on zero, but there is a surplus of negative sigma
values, because of the sources with negative magnitude difference, as noted
above. The actual distributions for IRAC\,1 and 2 are only slightly broader
than what would be expected if the errors were correctly estimated. This means
that the combined errors for these channels are only slightly underestimated.
For IRAC\,3 and 4, the distributions are definitely broader than in the ideal
case. For these channels we have to assume that the combined errors are
underestimated by factor of 1.8 to 2.2. Indeed, our error estimates are on
average smaller than the ones estimated by GLIMPSE-II, but this is mostly due
to the longer exposure time per pixel in our survey, and we are doing the
photometry on the mosaicked images. If we used two times the error as given by
GLIMPSE-II in Eq.~\ref{sigma}, the sigma distribution would have the perfect
width of 1.0 for IRAC\,1, would be slightly too narrow for IRAC\,2 (too large
errors), and would still be too broad for IRAC\,3 and 4 (too small errors). We
therefore conclude that our error estimates for IRAC\,1 and 2 are probably only
slightly too small, and too small by a somewhat larger amount for IRAC\,3 and
4. The GLIMPSE-II errors, on the other hand, are probably correctly estimated
for IRAC\,1, slightly too large for IRAC\,2, and slightly underestimated for
IRAC\,3 and 4. Table~\ref{GLIMPSEerr_tab} summarises the width, centre, and
peak values of the Gaussian fits to the sigma distributions of
Fig.~\ref{GLIMPSEerr_fig}.
\begin{table}
\caption{Width, centre, and peak values of the sigma distributions.}
\label{GLIMPSEerr_tab}
\centering
\begin{tabular}{crrr}
\hline\hline
Band & $\sigma$ & Centre & Peak \\
\hline
IRAC\,1 & 1.42 & $-0.22$ & 241.5 \\
IRAC\,2 & 1.27 & 0.17 & 159.0 \\
IRAC\,3 & 1.80 & $-0.24$ & 202.7 \\
IRAC\,4 & 2.15 & $-0.17$ & 98.6 \\
\hline
\end{tabular}
\end{table}
\begin{figure*}[!ht]
\includegraphics[bb=66 364 549 720]{err_GLIMPSE_N1.pdf}
\caption{Distribution of sigma-factors (Eq.~\ref{sigma}) for all IRAC channels
in the field N\,1 in the magnitude range $7\fm0 - 10\fm0$. The solid line is a
Gaussian fit to the distribution. The dotted line indicates a Gaussian of width
1 and the same area under the graph, the ideal case of correctly estimated
errors.}
\label{GLIMPSEerr_fig}
\end{figure*}
\subsection{Comparison with \citet{Ram08}}
The overlap with the GALCEN survey of \citet{Ram08} is limited to the Bulge
N\,1 field. The reason for this is that the {\em Spitzer} time allocation
committee tried to avoid redundant observations of the same fields of sky
within GO programmes (GLIMPSE-II, on the other hand, is a legacy survey). A
comparison between our own and the GALCEN observations is useful, because for
our N\,2 field we will have to use the IRAC observations of GALCEN.
Nevertheless, because IRAC channels~1 and 3 are seeing a patch of the sky
neighbouring that of channels~2 and 4, we got a small overlap with
\citet{Ram08} in our Bulge N\,1 field in order to fully sample that field in
all bands. Adopting a stringent 1\farcs0 search radius, there are 5172 sources
in common in any one of the four IRAC bands. In the Bulge N\,2 field, 337
sources detected with MIPS\,24 have a counterpart in \citet{Ram08}, adopting a
less stringent 3\farcs0 search radius because of the less precise MIPS
coordinates.
Figure~\ref{ramirez_fig} shows the magnitude differences found for the sources
in common with \citet{Ram08} in the Bulge N\,1 field. The agreement in the
IRAC\,1 and 2 bands is very good. In the IRAC\,3 band, the GALCEN magnitudes
(of flag~A sources in the medium brightness range $7\fm0 - 10\fm0$) are on
average $\sim0\fm05$ fainter than our magnitudes. In the IRAC\,4 band, a
``knee'' appears for sources brighter than $8\fm2$. Since the same effect is
found in the aforementioned comparison between GLIMPSE-II and GALCEN data, the
origin of this ``knee'' most probably comes from an underestimation of fluxes
for sources brighter than $\sim8\fm2$ in IRAC\,4 by GALCEN. We will have to
consider these differences between our IRAC photometry and that of
\citet{Ram08} when comparing the results for Bulge N\,2 to those of other
fields.
The differences between our reduction and that of GALCEN, on the one hand, and
GLIMPSE-II, on the other, should be noted. While in our reduction the
background is determined for each pixel in a $45\times45$ pixel box centred on
that pixel and subtracted prior to the photometric measurements, GALCEN uses
the local background determined by PRF fitting and subtracts it from the
corresponding aperture flux of each detected source. For the fitting, PRFs
pre-defined by the SSC are used. GALCEN uses the aperture corrections as
recommended by the SSC, but adopts the PRF fluxes for their final catalogue
(except for sources where the ratio between PRF flux and aperture flux exceeds
1.5; for those sources the aperture flux is adopted). We adopted the PRF flux
in our catalogue, derived from the most recent mean PRFs provided by the SSC.
GLIMPSE-II, on the other hand, performs photometry on individual bcd frames,
not on mosaics. A combination of PRF fitting and aperture photometry called
``tweaking''\footnote{http://www.astro.wisc.edu/sirtf/glimpse\_photometry\_v1.0.pdf}
is used to measure the flux of a source. PRFs dynamically determined from each
individual frame are fitted to the sources and subtracted from the image. On
the residual image, aperture photometry was performed around the positions where
PRFs had been subtracted in the previous step. If the resultant aperture flux
is substantially positive or negative, the source has been under- or
over-subtracted. This residual aperture flux is then subtracted from or added
to the PRF flux to compensate for the under- or over-subtraction. However,
tweaking was applied rather sparingly and only in the IRAC\,1 and IRAC\,2 bands
of the GLIMPSE-II observations. These differences in reduction have to be kept
in mind, just as for the comparison between GALCEN and GLIMPSE-II.
\begin{figure*}[!th]
\includegraphics{comp_Ramirez.png}
\caption{Magnitude differences between our photometry and that of \citet{Ram08}
for the small overlap in field N\,1. Symbols as in Fig.~\ref{GLIMPSE_N1}.}
\label{ramirez_fig}
\end{figure*}
\subsection{Comparison of MIPS\,24 measurements with \citet{Hin08}}
A catalogue of {\em Spitzer}/MIPS 24\,$\mu$m sources towards the region of
$\sim 1\fdg5 \times 8\fdg0$ around the Galactic centre has recently been
presented by \citet{Hin08}. With this survey, we have 371 sources in common
(i.e.\ unique counterparts within a one physical pixel = 2\farcs55 search
radius) in our Bulge\,4 field, 280 in the Bulge N\,1 field, and 129 in the
Bulge N\,2 field. Thanks to the longer exposure time of our observations
(331\,s per pixel compared to 15\,s per pixel in the fast scan mode used by
Hinz et al.), our catalogue reaches much fainter flux levels.
For the N\,1 field, we only have a small overlap with the survey of
\citet{Hin08}. In the N\,2 field there is strong diffuse galactic emission,
and a small fraction of the sources might actually be false detections. We thus
concentrate on the Bulge\,4 field for a comparison with the \citet{Hin08}
catalogue. This is also the field with the most sources in common. In
Fig.~\ref{comp_MIPS_fig} we show the magnitude differences between our
measurements and that of \citet{Hin08} as a function of the source magnitude in
our catalogue. There might be a general offset of $\sim0\fm15$ in the sense
that our magnitudes are on average fainter, but the scatter is considerable. At
least there seems to be no trend at the faint magnitude end.
As for the comparison with GLIMPSE-II, we also checked the error estimates of
the MIPS\,24 data by investigating the distribution of sigma-factors
(Eq.~\ref{sigma}). The result of this exercise is that the combined errors are
too small by a factor of six or more. Even adopting twice the error estimate of
\citet{Hin08}, which is somewhat larger than ours, instead of a combination of
the errors, gives a sigma distribution that is wider by a factor of four than
what is expected from a correct estimate. We thus conclude that the errors are
still largely underestimated in both catalogues, and that the uncertainty due
to crowding and strong background radiations renders a precise flux
determination in the vicinity of the Galactic centre impossible. Some part of
the found differences, however, may be explained by a real variability, since
many of the bright sources are expected to be AGB variables in the bulge
\citep{Gla09}. At a wavelength of 20\,$\mu$m, a full amplitude of up to 0\fm7
is found for C-rich pulsating AGB variables in the solar neighbourhood
\citep[see e.g.\ Fig.~7 of][]{LeB92}.
\begin{figure}
\includegraphics[width=\columnwidth,bb=69 368 546 703]{compare_MIPS24.pdf}
\caption{Magnitude differences between our MIPS\,24 magnitudes and
\citet{Hin08}, for our Bulge\,4 field.}
\label{comp_MIPS_fig}
\end{figure}
\section{Colour-magnitude diagrams and comparison with theoretical isochrones}
\label{sec_cmds}
A final check on the quality of our data reduction are colour-magnitude diagrams
(CMDs) in combination with theoretical isochrones. If the flux measurement has
no systematic error (and also the isochrones are producing realistic colours),
the observed giant branch will be described well by the isochrone. This check is
restricted to the IRAC bands, since for many sources the MIPS\,24 band will be
affected by dust emission, which is very difficult to model accurately in
isochrones. We chose to use the most recent isochrones from \citet{Mar08}. A
web-form can be used for computing these isochrones with different
parameters\footnote{http://stev.oapd.inaf.it/cgi-bin/cmd\_2.1}. We computed an
isochrone with an age of 10\,Gyrs, me\-tal\-li\-ci\-ty $Z = 0.019$ (solar
me\-tal\-li\-ci\-ty), and no dust formation. In the mid-IR, the isochrones are
not very sensitive to the precise choice of the parameters such as age,
me\-tal\-li\-ci\-ty, and dust formation.
To disentangle possible systematic errors in the IRAC channels, we want to
include a flux measurement that is independent of our reduction method in the
comparison with the isochrone. Since all our fields are covered by 2MASS, which
can be regarded as a reliable source of $K_{\rm{S}}$ magnitudes, we decided
to construct dereddened $K_{\rm{S,0}}$ vs.\ $(K_{\rm{S}} - \rm{IRAC})_0$ CMDs.
Most of the fields towards the Galactic bulge suffer from strong extinction.
Thus, it is necessary to correct the photometric measurements for this
extinction before comparing them to the theoretical isochrone. Several
extinction maps for the Galactic centre region have been published.
\citet{Sch99} derived the extinction from the shift of the giant branch in the
$K_{\rm{S}}$ vs.\ $(J - K_{\rm{S}})$ CMD based on DENIS data. The extinction
values published in that work are given in the $V$ band. Another map of $A_{V}$
values towards fields in the Galactic bulge is presented by \citet{Sum04}.
These are based on the extinction measured on red clump giants in fields of the
OGLE-II survey \citep{Uda00}. Finally, the map of \citet{Dut03} uses the same
technique as \citet{Sch99} and applies it to 2MASS data. That map gives the
reddening value in the $K_{\rm{S}}$ band. Its spatial resolution is lower than
that of the other maps, but it is the only one that fully covers all of our
{\em Spitzer} fields.
\begin{table}
\caption{Coverage of our fields by different extinction maps of the Galactic
centre region.}
\label{tbl_maps}\centering
\begin{tabular}{lrr}
\hline\hline
Field & Ref.\ & median $A_{V}$\\
\hline
Bulge 1 & (1), 3 & 4.38 \\
Bulge 2 & 2, 3 & 2.45 \\
Bulge 3 & (1), 3 & 2.00 \\
Bulge 4 & 1, 3 & 15.75 \\
Bulge N\,1 & 1, 3 & 7.25 \\
Bulge N\,2 & 1, 3 & 20.06 \\
NGC\,6522 & 1, 2, 3 & 1.13 \\
\hline
\end{tabular}\\
\flushleft
References: 1: \citet{Sch99}; 2: \citet{Sum04}; 3: \citet{Dut03}.
Numbers in brackets mean that the field is not entirely covered by the
respective map, but to a significant fraction.
\end{table}
Table~\ref{tbl_maps} summarises the coverage of our seven fields by these
extinction maps, and the median extinction in the $V$ band is given. The
NGC\,6522 field is the only one that is covered by all three extinction maps.
Since this field also has the lowest extinction of all our {\em Spitzer} fields
so that uncertainties in the extinction determination should play a minor
role, it serves here as a ``fiducial'' field for the comparison with
theoretical isochrones in CMDs. We used the average values for the diffuse
inter-stellar medium determined by \citet{Ind05} for the extinction in the IRAC
bands:
$A_{K,\rm{S}} : A_{3.6} : A_{4.5} : A_{5.8} : A_{8.0} = 1 : 0.56 : 0.43 : 0.43 : 0.43$,
as well as $A_V : A_{K,\rm{S}} = 1 : 0.089$. Using the somewhat different
values found by other studies \citep[e.g.][]{Fla07,Nis09} has only a negligible
impact on the results. Figure~\ref{NGC6522_CMD} shows CMDs of the NGC\,6522
field involving the 2MASS $K_{\rm{S}}$ magnitude and the magnitudes of the four
IRAC bands.
The following observations can be made from these CMDs. At the faint end, the
distribution in colour is quite broad since the errors become quite large for
these faint sources, and some of the objects probably are background galaxies.
There are also a small number of objects with extremely red or extremely blue
colours. Possibly, false identifications are involved in some cases (we include
only sources with a 2MASS counterpart within 2\farcs0 search radius for the
comparison with CMDs). At intermediate brightnesses, the distribution in colour
is much narrower, and only very few outliers can be found. At the bright end,
the number of sources far from the isochrone locus increases again. This is
partly due to saturated sources, e.g.\ in IRAC\,1 (blue ``sequence'' at the
bright end), and to dust emission that already shows up at IRAC\,4 wavelengths.
In general we find good agreement between the observed and the predicted
location of the giant branch in the CMDs. In the
$(K_{\rm{S}} - \rm{IRAC\,1})_0$ CMD (upper left panel of
Fig.~\ref{NGC6522_CMD}), the tip of the giant branch in the isochrone is
somewhat bluer than the observed tip. In the $(K_{\rm{S}} - \rm{IRAC\,3})_0$
CMD (lower left panel), the theoretical isochrone is bluer than the observed
giant branch by about 0\fm1 over the whole brightness range. In this filter,
the agreement with the GLIMPSE-II survey is very good, but the GALCEN
magnitudes are fainter than our magnitudes. Thus, by adopting the GALCEN
magnitude scale, the shift of the isochrone would be somewhat alleviated, but
not all catalogues and the isochrone can be made agree. We do not find any
trends in magnitude in the IRAC\,1 filter in the comparison with any of the
other surveys, thus we assume that the difference is related to a small problem
with the isochrone in the $(K_{\rm{S}} - \rm{IRAC\,1})_0$ colour. The same
might be suspected for the $(K_{\rm{S}} - \rm{IRAC\,3})_0$ colour.
The comparison with the isochrones also allows for a check on how deep our
{\em Spitzer} photometry goes. We find that in all IRAC bands, we reach sources
down to the beginning of the He-core burning (horizontal branch), although
probably with a reduced detection probability and less accurate photometry. The
He-core burning phase is covered until its end, hence also the whole AGB
evolution. However, the sensitivity of the present observations is still far
too low to reach the beginning of the RGB phase, and our investigations will be
limited to the brighter half of the RGB. The MIPS photometry does not reach
down to the horizontal arm. The faintest sources that are detected with MIPS in
the NGC\,6522 field are roughly $3\fm5$ fainter than the RGB tip of the
isochrones.
As for the colour dependence on the used extinction map, we find that for
individual sources the de-reddened $K_{\rm{S}} - \rm{IRAC}$ colour may vary
by a few 0\fm01. However, no general trend is observed when different extinction
maps are applied. Thus, though the fine structure of the extinction varies
somewhat from map to map, the average magnitude of the extinction is very
similar among the maps.
\begin{figure*}[!ht]
\includegraphics{NGC6522_CMD.png}
\caption{Colour-magnitude diagrams of the field NGC\,6522 involving the 2MASS
$K_{\rm{S}}$ and different IRAC magnitudes. For this version, the extinction
map of \citet{Sch99} has been used. A theoretical isochrone from
\citet{Mar08} is included as a blue line (see text for details). Symbols are
as in Fig.~\ref{GLIMPSE_N1}.}
\label{NGC6522_CMD}
\end{figure*}
\section{Summary and conclusions}\label{sec_conclu}
We present a catalogue of {\em Spitzer} IRAC/MIPS observations of seven fields
towards the Galactic bulge, sampling a range of galactocentric radii. These
observations allow us, amongst other things, to study the mass loss of a large
and homogeneous sample of RGB and AGB stars down to lower luminosities and
mass-loss rates than previously achieved.
In this first paper, we present the observations, the data reduction procedure,
and comparisons to other mid-IR surveys of the Galactic bulge. In general, we
find good agreement with other surveys. The comparison between the
{\em Spitzer} IRAC\,4 band and the ISOGAL LW2 band shows good agreement, but
reveals a slight trend with magnitude. GLIMPSE-II magnitudes are in good
agreement with our magnitudes in the bright-to-medium brightness range, but a
strong trend is present at the faint end. This trend is probably related to a
Malmquist bias in the GLIMPSE-II data set. The error estimates of GLIMPSE-II
and our IRAC photometry are reasonable in the IRAC\,1 and 2 bands, but somewhat
too small in the IRAC\,3 and 4 bands. In the comparison with GALCEN, we find on
average $\sim0\fm05$ brighter magnitudes in the IRAC\,3 band. The source of the
discrepancy at the bright end of the IRAC\,4 band is probably not related to
our catalogue. A comparison with the MIPS\,24 catalogue of \cite{{Hin08}}
reveals that our magnitudes are probably brighter at the level of $\sim0\fm15$,
although with larger scatter. We also find good agreement between our data
and recent isochrones in colour-magnitude diagrams for at least three of the
four IRAC bands. The $\sim0\fm1$ offset from isochrones involving IRAC\,3
deserves some more attention. We thus may assume that the observations and
data reduction are accurate on the level of $\sim0\fm1$ or better, as well as
precise on the level of $\lesssim0\fm1$, except for faint sources with quality
grade~B. The science exploitation of the data will follow in subsequent papers.
\begin{acknowledgements}
We thank Sean Carey for providing the artifact correction tools used for this
work.
This research made use of Tiny Tim/{\em Spitzer}, developed by John Krist for
the {\em Spitzer} Science Center. The Center is managed by the California
Institute of Technology under a contract with NASA.
The research described in this publication was partly carried out at the Jet
Propulsion Laboratory, California Institute of Technology, under a contract
with the National Aeronautics and Space Administration.
This work is based on observations made with the {\em Spitzer} Space Telescope,
which is operated by the Jet Propulsion Laboratory, California Institute of
Technology under a contract with NASA. Support for this work was provided by
NASA through an award issued by the JPL/Caltech.
This publication makes use of data products from the Two Micron All Sky Survey,
which is a joint project of the University of Massachusetts and the Infrared
Processing and Analysis Center/California Institute of Technology, funded by
NASA and the National Science Foundation.
SU acknowledges support from the Fund for Scientific Research of Flanders (FWO)
under grant number G.0470.07.
MSt has been supported by the European Community's Marie Curie Actions - Human
Resource and Mobility within the JETSET (Jet Simulations, Experiments and
Theory) network under contract MRTN-CT-2004 005592.
\end{acknowledgements}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,593 |
SMITH
The Story of a Pickpocket
Leon Garfield
THE NEW YORK REVIEW CHILDREN'S COLLECTION
New York
THIS IS A NEW YORK REVIEW BOOK
PUBLISHED BY THE NEW YORK REVIEW OF BOOKS
435 Hudson Street, New York, NY 10014
www.nyrb.com
Copyright © 1967 by Leon Garfield; copyright renewed © 1995 by Leon Garfield
All rights reserved.
The Library of Congress has cataloged the earlier printing as follows: Garfield, Leon.
Smith : the story of a pickpocket / by Leon Garfield. pages cm. — (New York Review books children's collection) First published in New York by Pantheon Books in 1967. Summary: Moments after he steals a document from a man's pocket, an illiterate young pickpocket in eighteenth-century London witnesses the man's murder by two men who want the document.
ISBN 978-1-59017-675-7 (hardback)
[1. Robbers and outlaws—Fiction.
2. London (England)—History—18th century—Fiction.
3. Great Britain—History—18th century—Fiction.] I. Title.
PZ7.G17943Sm 2013
[Fic]—dc23
2013018766
eISBN 978-1-59017-710-5
v1.0
Cover design by Louise Fili Ltd.
Cover art by Francis Mosley
For a complete list of books in the New York Review Children's Collection, visit www.nyrb.com or write to:
Catalog Requests, NYRB, 435 Hudson Street, New York, NY 10014
_To my Brother_
# Contents
Title Page
Copyright and More Information
Dedication
, , , , , , , , , , , , , , , , , , ,
About the Author
## 1
HE WAS CALLED SMITH and was twelve years old. Which, in itself, was a marvel; for it seemed as if the smallpox, the consumption, brain-fever, jail-fever and even the hangman's rope had given him a wide berth for fear of catching something. Or else they weren't quick enough.
Smith had a turn of speed that was remarkable, and a neatness in nipping down an alley or vanishing in a court that had to be seen to be believed. Not that it was often seen, for Smith was rather a sooty spirit of the violent and ramshackle Town, and inhabited the tumbledown mazes about fat St. Paul's like the subtle air itself. A rat was like a snail beside Smith, and the most his thousand victims ever got of him was the powerful whiff of his passing and a cold draft in their dexterously emptied pockets.
Only the sanctimonious birds that perched on the church's dome ever saw Smith's progress entire, and as their beady eyes followed him, they chattered savagely, " _Pick_ -pocket! _Pick_ -pocket! Jug him! Jug-jug-jug him!" as if they'd been appointed by the Town to save it from such as Smith.
His favorite spot was Ludgate Hill, where the world's coaches, chairs and curricles were met and locked, from morning to night, in a horrible, blasphemous confusion. And here, in one or other of the ancient doorways, he leaned and grinned while the shouting and cursing and scraping and raging went endlessly, hopelessly on—till, sooner or later, something prosperous would come his way.
At about half past ten of a cold December morning an old gentleman got furiously out of his carriage, in which he'd been trapped for an hour, shook his red fist at his helpless coachman and the roaring but motionless world, and began to stump up Ludgate Hill.
" _Pick_ -pocket! _Pick_ -pocket!" shrieked the cathedral birds in a fury.
A country gentleman—judging by his complexion, his clean old-fashioned coat and his broad-legged, lumbering walk which bumped out his pockets in a manner most provoking.
Smith twitched his nose and nipped neatly along like a shadow . . .
The old man's pace was variable: sometimes it was brisk for his years, then he'd slow down, hesitate, look about him—as if the Town had changed much since last he'd visited and he was now no longer confident of his way. He took one turning, then another; stopped, scratched the crisp edge of his wig, then eyed the sallow, seedy city gentry as if to ask the way, till he spied another turn, nodded, briskly took it—and came straight back into Ludgate Hill . . .
A dingy fellow creaked out of a doorway, like he was hinged on it, and made to accost the old man: but did not. He'd glimpsed Smith. Looks had been exchanged, shoulders shrugged—and the old villain gave way to the young one.
On went the old gentleman, confident now in his bearings, deeper and deeper into the musty, tottering forest of the Town where Smith hunted fastest and best.
Now a sharpish wind sprang up, and the cathedral birds eyed the leaden sky (which looked too thick and heavy to admit them), screeched, and flew to the lower eminence of Old Bailey. Here, they set up a terrific commotion with their legal brethren, till both Church and Law became absorbed in watching the progress of Smith.
" _Pick_ -pocket! _Pick_ -pocket! Jug-jug-jug him!"
The old gentleman was very deep in Smith's country now, and paused many a time to peer down the shambling lanes and alleys. Then he'd shake his head vaguely and touch at his coat pocket—as if a queer, deep sense had warned him of a pair of sharp eyes fairly cutting into the cloth like scissors. At last he saw something familiar—some landmark he'd remembered—Godliman Street. Yes: he was in Godliman Street . . .
As suddenly as it had sprung up, the wind died—and the cathedral birds flew back to their dome.
" _Pick_ -pocket! _Pick_ -pocket!"
The old gentleman began to stump very particularly down Godliman Street, eyeing the old, crumbly houses that were lived in by God knew how many quiet, mysterious souls. And, as he went, he seemed to have two shadows—his own and another, a thin cautious shadow that was not so much seen as sensed . . .
This was the deepest heart of Smith's forest, hidden even from the cathedral birds. Here, the houses reared and clustered as if to shut out the sky, and so promoted the growth of the flat, pale and unhealthy moon-faces of the clerks and scriveners, glimpsed in their dark caves through dusty windows, silent and intent.
Now came a slit between two such properties, a quiet way roofed over at first-floor level: Curtis Alley, leading to Curtis Court.
Framed by the darkness of its alley, Curtis Court presented a gray and peaceful brightness—a neglected clearing in the forest of the Town, where nothing grew, and all save one of the enclosed houses had had their eyes put out with bricks (on account of the tax).
As the old gentleman's steps echoed in the alley, a solitary, dusty raven flew up out of the court with a bitter croak.
Suddenly, the old gentleman gave an involuntary shudder, as if someone—something—had swiftly passed him by and made a draft.
"Someone's walked over me grave!" he muttered, shook his head and entered Curtis Court.
"Beg pardon, sir! Beg pardon—"
Out of a doorway on the left of the court came Smith. Which was the first time the old man had ever laid eyes on him; though all the way from Ludgate Hill there'd never been more than two yards between them.
He stopped, flustered, about six paces from the end of the alley. Which way was the damned urchin going? This way? That way? Angrily he shifted, and Smith, with a quaint clumsiness, brushed against him, and—it was done! In an instant! Smith had emptied the old gentleman's pocket of—
He halted. His eyes glittered sharply. Footsteps in the alley! It would be blocked! He changed direction as briefly as a speck in the wind—and vanished back into his doorway. But so quickly that, seconds after he'd disappeared, the old gentleman was still staggering and bewildered.
Out of the alley came two men in brown. Curious fellows of a very particular aspect—which Smith knew well. Uneasily, he scowled—and wished he might vanish through the crumbling bricks.
The old gentleman had recovered himself. He stared round angrily—till courtesy got the better of him.
"Good day to ye, gentlemen!" he said, with an apologetic smile.
The newcomers glanced quickly across the court towards the house that had kept one window, and grinned.
"And good day to _you_!"
They moved very neat, and with no commotion. They were proficient in their trade. The taller came at the old man from the front; the other took on his back—and slid a knife into it.
The old gentleman's face was fatefully towards a certain dark doorway. He seemed to peer very anxiously round the heavy shoulder of the man who was holding him—as if for a better view. His eyes flickered with pain at the knife's quick prick. Then he looked surprised—amazed, even—as he felt the cold blade slip into his warm heart.
"Oh! Oh! Oh my—" he murmured, gave a long sigh—and died.
His last sight on this earth had been of a small, wild and despairing face whose flooded eyes shone out of the shadows with all the dread and pity they were capable of.
(Smith was only twelve and, hangings apart, had seen no more than three men murdered in all his life.)
They say that murdered men's eyes keep the image of their last sight for—for how long? Do they take it, hereafter, up to the Seat of Judgment? Smith shivered. He'd no wish for his face to be shown in any place of judgment—in this world or the next!
In a terror as violent as his dislike, he watched the two men in brown. They were dragging the luckless old gentleman towards the darkness of the alley. (Why hadn't he stayed in the country where he'd belonged? What business had he to come stumping—so stupid and defenseless—into Smith's secret forest?)
Now Smith could hear the quick, fumbling sounds of searching; methodical gentry. Still no commotion. Oh, they knew what they were at! But the sounds grew harsh and hasty. Even irritable. Muttered one, "God rot the old fool! He ain't got it!"
Came a new sound. A very queer one. A tapping, limping, scraping sound—as of a lame man's footsteps on the cobbles. Then a soft, gentlemanly voice.
"Well?"
"Nothing—nothing, yer honor!"
"Liars! Fools! Look again!"
Again the sounds of searching—accompanied by strained, indrawn breath.
"Told you so. Nothing."
A groan: a very dreadful affair.
"Again! Again! It _must_ be there!"
"Well it ain't, yer honor! And if we stays much longer, we'll be on our way to join 'im . . . on the end of a rope! Come—let's be off."
"Again! Search once more!"
"With respect—do it yerself, sir."
"No!"
"Then we're off! Quick! Quick! There's someone coming—"
There was a scuffling and scraping, then the alley and court were momentarily quiet. A shadow crossed the broken, moss-piped paving. It was the raven, making ready to return.
But Smith did not move yet. Voices and clustering footsteps could be heard coming from the far side of the alley. The pale-faced clerks and scriveners and thin-necked attorneys had caught the scent of spilt blood. They'd come out of their rooms and chambers to congregate solemnly and stare.
(But no one came out from the houses within the court; not even from the house with the single window.)
Now the crowd had grown and oozed into the court itself. The raven flapped sourly up to a gable and croaked with a sardonic air; Smith had invisibly joined the outskirts of the crowd, muttering away with the best of them; then he was through, like a needle through shoddy, to Godliman Street and beyond.
As he went, a door opened in the court, and someone came quietly out . . .
A quarter mile off, on the other side of St. Paul's, Smith stopped running. He sat on some steps and fumbled in his ragged, ancient coat. What had he got this time? Something valuable. Something that had been worth the old gentleman's life.
He fished it out. A document. _A document?_ Smith stood up, swore, spat and cursed. For, though he was quicker than a rat, sharper than a stoat, foxier than a fox, though he knew the Town's corners and alleys and courts and by-ways better than he knew his own heart, and though he could vanish into the thick air in the twinkling of an eye, he lacked one necessary quality for the circumstance in hand. He could not read. Not so much as a word!
## 2
DARKNESS CAME PREMATURELY to the Town, owing to the sun's habit of vanishing into the tall chimney pots of Hanover Square—where, for all Smith knew, it blazed away in the rich parlors till the time came for it to be trundled off to Wapping and begin its course anew.
By four o'clock, the dome of St. Paul's stood black and surly against the darkening sky, and its huge shadow was flung eastward over the narrow streets and lanes of that part of the Town.
At last Smith gave up his efforts to force the cramped and awkward ink-lines to yield up their secret. For the light was gone and his eyes, wits and soul were aching with strain. A hundred stratagems had presented themselves to him—and a hundred stratagems he'd rejected. He'd thought of applying to the various scholars of his acquaintance . . . but which one could he trust? He'd thought of cutting the document into its various lines—or even words—and giving each of them to a different reader. But what if he muddled the order, or lost something that proved to be vital?
He walked; he sat; he tramped as far as the churchyard in Old Street, where he leaned up against a headstone, puffed at his short clay pipe, and fished out the document yet again. He stared; he screwed up his eyes and face till he looked like an old walnut, but the dim air and his own dark ignorance made the document seem like the last will and testament of a very old, very lame, very inky spider—on its weary way home.
So Smith likewise, with a deep sigh, packed up his thoughts and went home.
Between Saffron Hill and Turnmill Street stood—or, rather slouched—the Red Lion Tavern. A very evil-looking, tumbledown structure, weatherboarded on three sides and bounded on the fourth by the great Fleet Ditch, which stank and gurgled and gurgled and stank by day and night, like the parlor of the Tavern itself.
This parlor was an ill-lit, noxious place, full of hoarse secrets and red-eyed morsels—not so much from all walks as from all falls of life. Thieves, pick-pockets, footpads, unlucky swindlers and ruined gamblers boozed and snoozed here, and were presided over by a greasy landlord who never sold a customer to the gallows for less than a guinea.
Here was Smith's home. Not in the dignity of the parlor itself, but in the cellar below it where he lodged with his sisters, Miss Bridget and Miss Fanny.
"Not nubbed yet?" remarked the landlord humorously, as Smith humped broodily in.
Smith, his head full of darker things than even the Red Lion Tavern, made no answer.
"I spoke to you, Smith."
"Did you now! I thought it was a belch from the old Ditch!"
Two or three customers grinned, and Smith dodged deftly past the landlord to the cellar steps, but was not quite quick enough to miss a fist on his ear. He howled and vanished . . . and the landlord laughed fit to burst.
"Got him that time!"
"You asked for it! You brought it on yourself!" remarked Miss Bridget, looking up from stitching a brown velveteen coat.
"Poor little Smut!" murmured Miss Fanny, over a pair of gray breeches. "One day he'll come down them steps stone dead!"
" _I'm_ not complaining," said Smith, rubbing his ear which, had it been clean, would have been red as a strawberry, but instead was now a warm black. "Saw an old gent done in today."
"Indeed? And what's that to do with abusing the landlord?"
"Me mind was on other things."
" 'Tis no excuse! We brung you up to be genteel. Fanny and me feels the disgrace."
"Put a dab of vinegar on your little lug, Smut," said Miss Fanny. " 'Twill take out the sting."
She mentioned vinegar as there was a quantity of it in the cellar; for the sisters engaged in scouring and cleaning besides making genteel alterations to cast-off clothing from unfortunates who were hanged and so never had a chance to wear their last garments out. The velveteen coat and the gray breeches were bespoken by the hangman himself, for they'd come off a very high-stepping rogue indeed—and one everybody was sorry to see nubbed.
"But the law must take its course," had said Miss Bridget, and, " 'Tis an ill wind," had said Miss Fanny, when Smith brought the garments in.
"Look what I got this time!" said Smith, after he'd wiped his ear with vinegar. He fished out the document and spread it on the table, full in the light of the tallows. "Just before he was done in. Not a quarter of a minute!"
The Smith family stared at the document. None of them could read.
"What is it?" asked Miss Fanny.
" 'Twas what he was killed for," said Smith, and went on to relate all the circumstances of the crime, not forgetting the unseen man with the limp, the thought of whom terrified him more than anything else.
"It's a deed to property," declared Miss Bridget. "For that queer thing"—she jabbed her needle at a piece of writing—"that looks so like a horse and cart, is the word 'property'. Indeed it is. I'd know it anywhere!"
Smith was not convinced.
"Then why was he done in for it? And why was they so frantic when they couldn't find it? Poor old fool!"
"Reasons," said Miss Bridget darkly and returned to the velveteen coat. "Reasons."
" _I_ think," said Miss Fanny, "that it's a confession, or an accusation. For that's the sort of thing a murder's done for—excepting money; and it ain't money. Now—though I don't quarrel with Brid's 'property,' for I believe her to be right, there's a 'whereas,' most distinct; and that piece like a nest of maggots, there"—she pricked with her needle—"I _know_ to be 'felonious.' Oh yes indeed, Smut dear: you got a confession which will be very valuable if we can only find out what's been done. For, if they was willing and able to kill for it—well, they'll be equal willing to _pay_ for it! Clever Smut!"
Smith frowned, still not convinced, but inclined more to a confession than a property deed. In his heart of hearts he thought the document might be something else altogether, but said nothing, having nothing to go on, nor any piece of knowledge to contradict his sisters with.
"So we must get it read out to us," continued Miss Fanny, neglecting the breeches, "so we can know where to apply."
"And who, miss, would you ask?" queried Miss Bridget irritably.
"Lord Tom can read," said Smith, thinking of his highwayman idol and friend.
"Lord Tom?" repeated Miss Fanny, blushing and smiling. "The very scholar!"
Miss Bridget sneered. "That high toby is so much in his cups, his mouth's grown like a spout! Mark my words, miss, I'd as soon trust him with anything worth money as I'd trust the landlord! Not that I think the paper's worth money at all: for it's neither more nor less than a deed to property."
They went on arguing thus till the tallows burned low: with Miss Bridget inclining more and more to property, and Miss Fanny, who was softer and younger, being scarce nineteen, keeping to the romantic notion of a confession on whose value as blackmail they might all live happily ever after. But on one thing they were all agreed: the difficulty of finding anyone they could trust enough to read it to them.
At length, when the room was full of tallow smoke and shifting shadows, Miss Bridget and Miss Fanny retired to their curtained-off bedroom, and Smith to his corner in the workroom itself.
For some minutes one tallow remained alight, and afforded Smith a somber view of the brown velveteen coat and the gray breeches bespoken by the hangman. They were upon a hook in a corner and presented a disagreeable resemblance to their aspect when their last owner had last worn them. Smith wondered if he was likely to come back for them, fearfully white and moaning about the cold. Well—they'd not fit him now!
He screwed up his face scornfully at the thought of ghosts; but continued to stare into dark corners till he fell asleep, and, when he awoke, did so with a startled air and looked about him with some relief to see the old brick and plaster walls and the dim gray daylight falling down the cellar steps . . . as if his dreams had given him cause to doubt his firm belief in no ghosts.
The document was still on the table. He folded it up and began to tiptoe towards the stairs.
"Where are you off to, Smut dear?"
Miss Fanny, much tousled and creased, had poked her head through the curtain.
"Newgate," said Smith, briefly. "Got business."
"What are you going to do with our dockiment, Smut?"
"Don't know—yet."
"Wouldn't it be safer here?"
"Why?"
"Well, dear—if them that wanted it did in an old man for it, they won't think twice about doing in a boy."
"Don't know I got it! Never saw me! There's only you and Miss Bridget what knows."
"Oh yes . . . that's true. But you never can tell, Smut. _Someone_ may have seen you. Won't you leave it behind?"
"No."
"Are you going to show it to Lord Tom?"
"Don't know. Maybe."
"If he's going to Newgate," came Miss Bridget's voice, still croaked with sleep, "tell him to screw some money out of that Mister Jones—for there'll not be another stitch done till there's something on account! Hangmen is horrible customers! So degrading!"
Miss Fanny's head, which had vanished for the moment, reappeared.
"Mister Jones, Smut. Brid says, see Mister Jones." Then she sighed. "For the last time, dear—leave the dockiment behind. 'Twill be safe as houses. Oh, Smut! I've an 'orrible feeling you was seen and are in danger! Oh, Smut! I fear you'll be coming down them steps tonight stone dead!"
## 3
A TREMENDOUS IDEA HAD lodged in Smith's mind and, like all truly great things, answered its purpose so exactly that one exclaimed, "Why hadn't it been thought of before?" He would learn to read!
The morning was dull and windy. The cathedral birds were huddled upon Old Bailey, which stood to the leeward side of the stench from Newgate Jail. Such merchants and clerks and attorneys who walked the whipping streets kept their heads down and their hands to their wigs and hats—as if to hold their aspiring thoughts from flying out to become common property. A general frown and scowl creased their faces: another day was bad enough, without the insolent wind aggravating it!
Smith had spread the document inside his coat and across his chest, where it kept him from the worst of the weather.
"Be still, old fellow," he muttered from time to time as the stiff paper pricked and tickled. "You and me's got business. You and me's going up in the world . . . just as soon as I gets you to talk!"
He was crossing Ludgate Hill when suddenly he fancied he saw the murdered old gentleman, stumping along ahead of him. He stopped, much frightened. Then he looked again and saw that the old gentleman was someone else altogether. But thereafter the murdered man stayed pretty firmly in his thoughts—as if keeping a watch on his document and where Smith was taking it.
Which, in the first place, was to the blackened and gloomy felonry of Newgate Jail. Smith turned in at the lodge, greeted the jailer there, and lit up his battered pipe against the dreadful smells to come.
First, he found out Mr. Jones, the hangman: a short, stout, horny-handed gent who shone with pomatum. He got three shillings out of him on account—together with a surly prophecy that if he, Smith, didn't mind his _P_ 's and _Q_ 's he'd become Mr. Jones's customer in a transaction with a yardage of hemp.
" _P_ 's and _Q_ 's?" said Smith, earnestly. "Them's letters, ain't they?"
Mr. Jones agreed.
"Then show us a _P_ , Mister Jones, and then show us a _Q_ , and I'll try to mind 'em!"
For the thought had occurred to Smith that two letters would be a fair start to the day's work of learning to read. Unluckily, Mr. Jones took him for a humorist and aimed a thump that would not have been pleasurable if it had struck.
Bleeding scholars! thought Smith, as he scuttled out of the hangman's office. Want to keep everything to themselves!
From Mr. Jones's, it was but a brief, though dark and sullen, way down a ragged stairway, along a passage, a turn to the right, then up two steps, to the Stone Hall, where Smith's present hopes were most likely to be passing the time of what was neither night nor day. The Stone Hall was a long, low, arched room with its own stone sky and its own six lanterns for a sun. When these were lit, it was day, when they were out, it was night—no matter what the outside heavens were declaring.
Smith's present hopes shuffled somewhere among the lost multitude of the Town's rubbish and dregs. Grumbling ragbags and tattered felons, debtors who always looked surprised and, here and there, like a fallen moon, a pale white face of unbroken pride—most likely of a man due to be hanged.
Here was Smith's place of daily business; for he ran errands for the debtors—twopence a mile dry, and fourpence when it rained.
Very educated gentlemen, the debtors. A man needs to be educated to get into debt. Scholars all. The first Smith tried was a tall, fine-looking gentleman who, though still in leg-irons, walked like he owned the jail—as well he might, for his debts could have bought it entire.
He smiled; he was never at a loss for a smile . . . which was, perhaps, why he was there; when a man can't pay what he owes, a smile is a deal worse than nothing!
"Learn us to read, mister!" said Smith, humbly.
The fine debtor stopped, looked—and sighed.
"Not in ten thousand years, my boy!" and, before Smith could ask him why, he told him.
"Be happy that you can't! For what will you get by it? You'll read and fret over disasters that might never touch you. You'll read hurtful letters that might have passed you by. You'll read warrants and summonses where you might have pleaded ignorance. You'll read of bills overdue and creditors' anger—where you might have ignored it all for another month! Don't learn to read, Smith! Oh! I implore you!"
Then the gentleman drifted, smiling, away, with his back straight, his head held high—and his ankles jingling.
Next, Smith applied to a learned felon, a ferret-faced man with small, starry eyes.
"What d'yer want to read for, Smith? No need. And if it weren't for me skill as a reader, I'd not be here today. I was on the run—and saw a new goldsmith's sign. Stopped to read it—and 'ere I am! No, stay ignorant, me boy—and keep out of 'arm's way."
Smith pleaded—but the felon was determined, so Smith left him and would have gone from the Stone Hall had he not seen Mr. Palmer.
This Mr. Palmer was a debtor of a different sort: a gentle, sad man who could not bring himself to believe that the world had been so spiteful as to jail him. (Even though it had been these past five years.) For Mr. Palmer—did the world but know it—nourished a very high opinion of himself, which he was careful to hide for fear of its being damaged.
"Learn us to read, Mister Palmer!"
Mr. Palmer stopped in mid-shuffle.
"Learn us to read, Mister Palmer!"
Mr. Palmer turned on Smith a look of amazement that hid a powerful contempt and dislike—even loathing—for this debtor loathed, hated and despised every mortal thing that was better off than himself by being free.
"A pleasure to _'learn'_ you, Smith," he said. "Here, boy." He bent down and beckoned. Smith approached. "This is how we begin!"
He seized Smith's nose as hard as he could and pulled and twisted and wrenched it till Smith's squeals filled the Stone Hall and his eyes fairly gushed with tears. Then his own voice was raised even louder, in a fearful bellow of pain. He'd forgotten Smith wore no leg-irons and could use his feet to advantage.
In an instant Smith was fled, leaving Mr. Palmer with an empty finger and thumb, and a pair of shins that were splintered with booting. He lay on the ground and continued to roar, only breaking off to pray that the ungrateful brat who'd crippled him might come to a bad end on Mr. Jones's rope; while Smith, full of anger and humiliation and a burning pain in his nose, left Newgate Jail swearing a solemn oath that, not till he was took, would he ever set foot in that foul place again!
With his hands pressed to his chest and his eyes still streaming with forced tears, he ran towards the nestling of lanes about the great cathedral. Softhearted ladies stared as he passed, moved by the sight of the weeping urchin. Then his eyes dried up, his nose recovered—and his grand determination flared anew. He _would_ learn to read! For he and the document were going up in the world—though the Devil himself stood against them!
Surely the Town had more scholars than those in Newgate Jail? The streets must be full of them! He'd only to ask. No harm in asking . . . He crossed the windy street to meet with a round-faced old gentleman with an absentminded air.
"Mister—mister! Learn me to read!"
The gentleman paused—momentarily taking his hand from his hat. In an instant the wind whipped it off, together with his wig, leaving him as bald as the dome of St. Paul's. Smith, meaning no offense, began to grin. The gentleman raised his stick—and Smith fled for his life!
He asked a lawyer, a clerk, a country schoolmaster—but they'd have none of him. He poked his head through the window of a carriage waiting outside an apothecary's to ask of the elderly lady who sat within. But she shrieked and shouted for her footman to frighten him off. At last, he found himself in Holborn Hill, passing by gray, high-shouldered St. Andrew's Church. The Church: Mother of the Town—and all creatures in it!
With renewed hope he shuffled up to the porch and peered into the richly stained gloom of the church's insides. Blood of glass martyrs fell across the aisle and drenched the altar . . . and there was a smell of damp stone in the quiet air. A very peaceful, genteel sort of place.
At first, it seemed empty—and Smith had some brief thoughts concerning the candlesticks.
"What d'you want, my child?"
A priest was in the pulpit, still as a carven saint.
"Oh, it's beautiful!" said Smith, ingratiatingly. "Just like me sisters' stories of heaven!"
The priest nodded and smiled kindly.
"What are you looking for, my child?"
"Guidance, Your Reverence," said Smith, who'd decided, this time, to ask roundabout.
"Are you lost?"
"Oh no, Your Worship! This is 'olborn 'ill!"
The priest compressed his lips and eyed Smith shrewdly. Hurriedly, Smith went on, "Learn me to read, Your 'oliness. That's what I come for. Learn me to read so's I can read the 'oly Scripture."
The priest stared in amazement at the filthy, strong-smelling little creature who stood in the aisle with his black hands pressed to his grubby heart.
"If you come and stand by the door during Service, then you'll hear me reading from the Holy Scripture, child. Won't that be a comfort and help?"
"Oh yes, Your Grace. And I'm humbly obliged. But what of when I'm 'ome—all in dirt and disorder? Who'll read to me then? And me two poor sisters—a-panting, a-groaning, a-supplicating for salvation? Who'll read to them? Oh no, Your Reverence—I got to learn to read so's I can comfort meself in the dark o' the night . . . and light a little lamp in me sisters' souls with perusings aloud from the Good Book!"
But this was too much.
"You're a little liar!" exclaimed the priest, abruptly. Smith gazed thoughtfully up at him, proud in his white surplice and bands.
"And you're a fat bag of rotting flour!" he snarled suddenly. "I 'ope the weevils gets you!"
Was there no one in all the Town who'd teach Smith to read?
He passed the top of Godliman Street. A man came out from somewhere, stopped . . . and stared at him palely. But Smith, still disheartened by the church's rejection, did not see him and went wearily on.
Smith came to the booksellers in St. Paul's Churchyard. A last hope for the day. And where better to learn to read than in a bookshop?
Several times he idled up and down, judging his chances in each shop. Here, a proprietor scowled at him; there, a clerk shook his fist . . . and there an entrance was blocked by a fat man who seemed to have died in the act of reading, but came to life to turn a page and acknowledge the helpless bookseller with a corpse-like nod.
But there was one shop that attracted Smith by the mad profusion and tottery architecture of its wares. Books stood in walls and towers and battlements, as if the owner had been in a state of siege for a hundred years—which was partly borne out by his appearance. He was an amazingly thin, wary little man with a nervous affliction which made his head dart from side to side as if wondering from where the attack might come. Nor was he put at ease when he saw Smith. For he'd seen Smith before—even knew him . . .
He sat in a curious kind of cave of books where he could jerk and twitch in privacy and quiet.
"Learn us to read, mister!"
"Be off with you!" he said curtly, jerking his head to the right.
"Ain't you got no feelings for yore trade?" asked Smith earnestly. "Don't you want it to prosper with more readers—"
"—You're a wicked little thief!" said the bookseller, now jerking to the left.
"—Only because I'm ignorant!"
"Get out of here!"
" _Why_ won't you learn me?"
"Keep your thieving hands to yourself!"
"Why won't anybody learn me?"
"Because they've too much sense—"
"—All this goodness and wisdom and learning—" Smith was grandly pointing to the dusty cliffs that reared on either side.
"Touch a book and I'll finish you!"
The bookseller was now jerking and twitching pretty vigorously and, as his head flew from side to side, Smith considerately tried to keep pace with it—which made him appear as if he was performing a wild dance.
"Keep still!" shouted the bookseller of a sudden—and jerked worse than ever.
Too late. Smith, capering wider and wider, struck first against one and then against the other of the two tottering shelves.
The calamity that followed, though of brief duration, was terrific in its scope. It was as if the long siege was at last over and the enemy had breached all the walls at once!
The two walls of shelves had collapsed and with them, brought down in a mighty and thunderous torrent, every last item in the whole of the ramshackle shop!
Books in their fluttering and dusty thousands poured and thumped down as if the very skies had been loaded with them. Histories, Memoirs, Diaries, Lexicons, Grammars, Atlases, Journals, Biographies, Poems, Plays . . . books about heaven, books about hell, huge books about pygmies, tiny books about giants—even books about books—all, all slid and tumbled into a desperate ruin overhung by a bitter cloud of dust. And somewhere underneath it all, still jerking and twitching, though feebly now, lay the unlucky bookseller himself!
Gawd! thought Smith, halfway round the Cathedral and going like the wind, 'e must be squashed flatter than an old sixpence!
But the bookseller was alive, and, while Smith was still running and wondering hopelessly whom next he could ask to teach him to read, his last victim was being exhumed by neighbors and passersby. Strangely enough he seemed almost the better for the disaster, as though, all his life, he'd expected and dreaded it and now that it had happened a load was fallen from his soul. He jerked and twitched hardly at all as he told how it had come about and who'd been chiefly to blame.
"They call him Smith," he said.
"And where does he come from?"
"Somewhere near the Ditch. I fancy it's the Red Lion Tavern . . ."
The questioner had been a passerby: the man who'd earlier come out of Godliman Street.
## 4
AT ABOUT FIVE O'CLOCK Smith went home, having spent every penny he had (except the three shillings he'd screwed out of Mr. Jones) on meat pie, ale and tobacco. And, though there'd been pockets in plenty for the picking, he'd kept his hands to himself. For the first time he could remember he was frightened of being caught; for then he'd lose whatever might be the benefits of the document, which was still pressed against his chest, where it was growing strong with sweat.
"Hullo, Smith! Not nubbed yet?"
Deep in thought, he ignored the landlord's pleasantry and made for the cellar steps. From below the tallows gleamed yellowly and cast strange shadows on the wall. He began to descend, when—
"Stand and deliver!"
A voice like twelve o'clock of St. Paul's roared from the heart of the cellar! Smith started, missed a step, and came down the rest any way but on his feet!
A dangerous, glittering, murdering adventurer of a gentleman in green stood before him, aiming a pistol the scope of a cannon directly at his head! It was his friend, Lord Tom, the high toby, come on a sociable visit.
"Do watch how you go, Smut," cried Miss Fanny, "or you'll be coming down them steps stone dead! And _then_ where will our dockiment be?"
"Did you see that degrading Mister Jones?" asked Miss Bridget. "For if you didn't you can go straight out again, broken pate or nothing!"
"Pleased to see you, Lord Tom," said Smith, picking himself up and rubbing his head. "They told me you was nubbed—but I never believed 'em."
"Ah!" said the highwayman, putting up his pistol and smiling sadly through his brackenish beard. "It happens to all of us, sooner or later, Smut. With some, it's sooner; but with Lord Tom, let's hope it'll be vastly the later!"
"And so say all of us," murmured Miss Fanny, as she might have said, Amen!
"Trade been good these past ten days, Lord Tom?" asked Smith, giving over the three shillings to Miss Bridget who hid them somewhere behind the curtain, away from the highwayman's quick green eyes.
"Been on the Finchley Common, Smut, me young friend. Wild and free on the snaffling lay!"
"Don't use them coarse expressions!" came Miss Bridget's voice. "If you mean pilfering from unarmed travelers, then say so. Or are you ashamed?"
Lord Tom grinned at Smith (who grinned back) and then at Miss Fanny who sighed and blushed.
"Many coaches, Lord Tom? And was there danger?"
"Fine smart equipages, little Smut! Windows fair sparkling with satin and brilliants. Like traveling stars, I tell you. Gleaming in the foggy nights. It's a life, my boy! Stand and deliver! Stern with the gentry: courteous with the ladies. 'Madam, your necklace—if you please! Sir, your purse—or I'll blow your head off!' "
"And did you, Lord Tom?" asked Smith, smiling wistfully at the thought of riding out with his friend—which had always been one of his dearest dreams. "Did you blow any heads off this time?"
"Only a pair of coachmen's, Smut! And then unwillingly—for they went for their weapons."
"How many coaches did you take?"
"Six, me friend! Six gay glitterers—"
"Then where's your profit, you ugly murderer!" came Miss Bridget's voice—for she'd refused to come out and join the company. "Where's the necklaces and purses, sir?"
Lord Tom sighed. "Spent, Miss Bridget—as well you know. That's the way of our lives. Risk all for the chase—then spend the profit in high contempt. The chase and the danger's all!" (Here, Smith nodded vigorously.) "There was a diamond brooch I parted with for an evening's ale in Highgate, ma'am. And, by God, but it was a good exchange! Eat, drink and be merry, as they say—for tomorrow we'll all be nubbed!"
"A pity it wasn't yesterday!" snapped Miss Bridget and, for the first time, the highwayman looked angry. But it passed and he went on with his adventures, to Miss Fanny's admiration and Smith's envy and delight.
"But what's this I hear," he said at length and, with his hands on his hips, his high-booted legs apart, surveyed Smith with an amiable smile. "For the news I hear"—he nodded affectionately to Miss Fanny—"is that _you've_ come upon a rare treasure, me lad! Already me rival in accomplishment? Well, indeed—I'm proud of you! A document, I hear tell. And curiously valuable—from all accounts."
"I told Lord Tom," put in Miss Fanny, stopping her sewing with her needle at full stretch. "And we're of an opinion that—"
" 'Tis nothing of value!" said Miss Bridget, coming at last through the curtain, her handsome face much flushed. "A property deed, most likely. Of no use to anyone at all!"
"And I say it's a confession, Brid! Reely, Lord Tom dear—I'm convinced! Indeed, the more I think on it, it had such—such a _guilty_ look!"
"Well, then," exclaimed Lord Tom cheerfully, "let's put an end to conjecture and see it. Here, Smut, old comrade-in-arms, let's see the document. Lord Tom'll read it for you."
Smith, suddenly uneasy, stared at his two sisters, one frowning and the other softly open-mouthed. Then he looked up at his friend, the glittering, dangerous highwayman. He hesitated . . . and began to back towards the stairs. Now that his secret was about to be revealed he felt unsure, even unwilling . . . For a whole day the document had been next to his heart. He felt strangely that he'd be betraying it if he gave it up now. He continued to look suspiciously from one to another of the company.
"Well, Smut, friend—where's the treasure?"
"I—I ain't got it, Lord Tom . . . I—I left it with a friend!"
"Not that creeping Mister Palmer?" exclaimed Miss Bridget. "How I hate debtors! They're worse'n thieves!"
Smith shook his head and rubbed his nose ruefully.
"Then who's got it, Smut, dear? Who's got our valuable dockiment?"
"The parson in Saint Andrew's."
"And who's he, when he's at home? You little liar!" said Miss Bridget coldly.
"A friend o' mine."
"You made him up!"
"No, Miss Bridget! True as I live an' breathe. Big fat man all in white. Friend of mine. Cross my heart and hope to be nubbed!"
"And where did you meet him?"
"In church—"
"Now I _know_ you're lying! For you never was in a church in all your born days! Liar and blasphemer! Oh, how I hate a liar! Nothing's more degrading! You come here—you young person—and I'll wash your mouth out with vinegar for you. Don't think you'll escape this time!"
Miss Bridget—who had indeed a jar of vinegar in her hand—began to advance on Smith with her eyes glinting venomously. Smith dodged briefly behind Lord Tom and hung on to the tops of his boots.
"Never come 'tween a family," chuckled the highwayman—and stepped aside so's Smith stumbled and fell. Miss Bridget came on. Smith howled and fled behind Miss Fanny. Who obliged by crying, "Poor Smut!" and flouncing aside to the stairs.
Smith began to dart round the cellar at so great a rate that the tallow flames tore after him as if to rip loose from their seatings.
"I'll teach you to lie to me!" shouted Miss Bridget, making strong dives at her brother who, between howling and roaring his innocence, kept dragging table and stools and every movable article into her path.
On the stair—cutting off all retreat—sat Miss Fanny and Lord Tom, laughing fit to burst.
"Let me through!" panted Smith, each time he passed.
"Not till you give up the document!" laughed Lord Tom.
"Oh, do as Lord Tom says, dear Smut," cried Miss Fanny, "before Brid mashes you stone dead! For she's that vexed."
Smith shook his head and rushed on more fiercely than ever, for Miss Bridget, having the longer legs, was gaining . . . Round and round he scuttled and darted—now like a sooty moth—now like a quick black rat. And each time he passed the stair he begged and implored Miss Fanny and Lord Tom to make way for his desperate, panting self.
"Not till we see the document! Ha-ha! Not till you give up your treasure!"
While from behind, Miss Bridget panted grimly, "Nothing'll save you this time! You degrading little liar, you!"
She made a last tremendous lunge—both to save herself (for she'd tripped on a stool) and to seize her brother's hair. Smith shrieked. Lord Tom laughed. Miss Fanny cried, "Poor Smut!" When there was a fateful interruption: the landlord. His greasy head hung over the stair like a dirty street lamp.
"Smith! Smith! Forgot to tell you something!"
Hastily, Miss Bridget let go of his hair and genteelly wiped her fingers.
"What?"
"You 'ad callers. Two."
"Who? Me?"
"Yes, indeed. Had you off to a _T_. Dirty, weaselish, villainous-looking remnant. Eyes like chips of coal. Teeth like the same. About twelve year old.—'That's him!' I says directly.—'Good!' says they. 'And where is he?'—'Nubbed, most likely,' says I.—'Oh-ho!' says they, 'we'll be back then—to inspect the remains.' Then they was off. No message. Just that."
"W-what was they like?"
"One tall, t'other short. Wearing brown. And, though I says it myself (and I ought to know), as unsavory and throat-slittish a pair as ever I've clapped eyes on! Ha-ha!"
The landlord's head was hoisted out of view and there was a deep silence in the cellar. Smith shivered uncontrollably. He was desperately frightened. God knew how the two men in brown had tracked him down; but they had done so. He could not stop his teeth chattering. Even Miss Bridget looked at him compassionately.
"It—it's them!" he whispered. "They've come to slit me throat!"
"Don't you worry, me lad!" exclaimed Lord Tom, grimly. "There's no high toby, thief or rascal who'd dare come here when he knows Lord Tom's on your side! By God, Smut! If they so much as sets foot on them stairs, I'll blow blue daylight through the both of them! You've a man to protect you now. And I can't say fairer than that."
"No," muttered Smith. "You don't know 'em. They're not your sort, Lord Tom—"
"Why, Smut! You'll be safe with Lord Tom! There, dear—you just give him our dockiment and all will be well."
"You don't understand! They'll do for me anyways. They're that sort."
"Then what will you do, child?" asked Miss Bridget, much troubled.
"I don't know . . . But I can't stay 'ere. Not now. Not at night! I'll go off somewhere. Maybe to—"
"To the parson at Saint Andrew's?" smiled Lord Tom.
"Maybe . . ."
"Don't lie now, child. It may be for the last time . . . and you'd go to Hell."
Smith looked round the cellar which was his home, very mournfully and wretchedly. "I got to go! For Gawd's sake, let me past!"
Lord Tom shrugged his shoulders, but stood aside. "I'd protect you, Smut. Honest, I would."
"The dockiment, Smut. Won't you leave it, dear? It'll bring you no good—"
"No!" said Smith, fiercely. "Never! Never! Never!" He paused, as if shocked by his own determination, then added, "Besides, it's with the parson at Saint Andrew's."
"Oh, Smut," sighed Miss Fanny. "Brid's right—and you're a liar. For you got it inside of your coat. I can see it, dear."
"Out o' my way!" shouted Smith—and, with a desperate rush, flew up the stairs and was gone.
## 5
TWO MEN—one short, the other tall—who might have been dressed in brown (the street was too dark to be sure), saw Smith hurry out of the Red Lion Tavern. They'd been in a doorway nearby. Deep in shadows. They did not think they'd been observed. After a few seconds they set off together in the wake of the hurrying boy. They followed him for about five minutes along the nearly empty Saffron Hill. Then they lost him. He seemed to have vanished into the gloomy air. Half a minute later he was seen— unexpectedly—on their left, at the corner of Cross Street, hurrying like a mad thing. They nodded and set off again.
This time they kept him in sight for nearly ten minutes; then he vanished near Cony Court. They waited awhile, listening, for the narrow streets and alleys hereabouts were very quiet, and even a rat's scuttle would have been heard. Now they entered the shadowy confines of the court—were about three yards within it— when the boy was seen again, darting desperately back towards Cross Street, his alarmed eyes glittering in the light of some late merchant's window.
Back went the two followers, their shoulders hunched—for the night was growing bitterer by the minute—and their feet kissing the cobbles with a grim, urgent passion. They did not let him out of their sight for more than an instant. Portpool Lane—Hatton Garden—Chart Street—back into Saffron Hill, then Holborn Hill—Union Court—Hatton Garden again—and so to Cross Street—Saffron Hill—Cox's Court . . .
An intricate necklace of flight was being threaded as the three hurrying figures shifted through and round the lanes, courts and alleys that lay, ragged and near deserted, under a gnawed rind of the moon.
Sometimes there was not above five yards between them; and then they'd lose him for a few seconds—oddly, unaccountably— like he'd gone up in a puff of black smoke . . . Till there he'd be again, come suddenly from some dark passageway of which nothing had been seen till then.
There seemed to be many dozens of these crevices in the black, lumpy substance of the frowning houses—but, sooner or later, there'd be one whose end would be sewn up tight as a sock: a fatal passage from which there'd be no panting scuttle of escape.
The boy had left the Red Lion Tavern at half after six by St. Paul's. At a quarter to nine o'clock, the followers leaned up against a wall in Hatton Garden.
Breathed one: "Fer God's sake! I can't go another step! Me heart'll burst—I swear it!"
Came a low reply, much charged with pain and phlegm: "All right! We'll go back—some'ow—to the Red Lion. We'll wait there . . . God rot the crafty little perisher!"
With painful steps they limped away, so wind-broken by two and a quarter hours of unceasing pursuit that they seemed scarce able to drag their own meager shadows down the cold street.
Ten minutes later, in a narrow abutment no more than a yard from where they'd been leaning, a shadow moved. Then a face edged out: a small, pointed, wary face. It surveyed the empty street. It grinned—not with pleasure, but with a savage and desperate triumph. Smith had done what he'd set out to do when he'd seen the men waiting for him as he'd left the Red Lion. He'd run his pursuers into the ground.
He began to walk—somewhat slowly, for his own sides were aching villainously. Presently, he stopped and drew the sweat-drenched document from under his coat. He studied it by the thin, cold light of the moon. It did not seem much the worse for its wetting. Miss Bridget's "property" and Miss Fanny's "felonious" looked as much like a horse and cart and a nest of maggots as ever. None the less, at the first opportunity, he picked a passing pocket of a handkerchief and wrapped the document up. Then he sighed with relief and set off for another part of the Town.
Though no one followed him now, he moved with extraordinary circumspection; for the dark houses and the dimly silvered streets held another, more formidable menace. Time and again he fancied he heard other footsteps—steps that limped awkwardly—and he thought of the unseen lame man with the soft voice.
But these alarms were in his mind alone and, if they ever came to anything, they never turned into more than the totterings of some drunken home-goer, or the limping of a chairman, weary unto death and cursing under his breath.
Now he was in High Holborn, and the tall buildings on either side scowled blackly down with, here and there through an ill-drawn drape, a yellow sneer of light; while ceaselessly down the wide street, like the Devil's own crossings' sweeper, came a bitter wind, whipping up the Town's rubbish into spiteful ghosts of dust and paper that plucked and nipped and stung the living boy.
His nose, chin and fingers were beginning to burn with the cold. Not a night to be out in: black and windy, with the moon now doused in a creeping sea of cloud. He passed by a gloomy alehouse with a bunch of iron grapes groaning from its sign. He stopped—fingered a guinea he'd got with the handkerchief—and thought of a bed for the night.
But the house was full, so he took a half a pint of gin to keep out the cold, the loneliness and the shifting fear—to no purpose. The gin sickened him and inflamed his brain so's he heard everywhere the soft voice he dreaded and the awkward scrape of a leg, quaintly lame. He began to search for the door—and was helped by a pair of potboys who came at him, slantwise, from somewhere in the smoky room.
Out again into the bitter street. Above his head the iron grapes creaked menacingly, back and forth—back and forth . . . He moved away, fearful that they'd drop and crack him like an egg.
But it was not the grapes alone; the very houses seemed to be shuddering against the blotched sky. He shifted out into the middle of the street, for he'd a sudden horror that all the buildings were tottering in upon him. The sky seemed to grow smaller and smaller and the jagged roofs, fanged with chimneys, seemed to snarl and snap as if to gobble him up.
He began to run, wildly: now from side to side of the street, banging into posts, stumbling across the gutter, turning down lanes and alleys that were new even to him . . . And all this with a curious, hopeless urgency: his feet running like a hanged man's feet—seeming to reach for a purchase on a world that was slipping away.
Where was he going? God knew! Maybe even in search of the two men in brown to give up the document. For suddenly it seemed to him that the document was a fearful disease that was burning and poisoning him—after tempting him madly from the shelter of his home.
At last he found himself in a long, wide street, where the moon had widowed all the houses, with black hatchments under their porches . . . Vaguely, he thought he knew where he was. There was a narrow turning any minute now . . . an alleyway that would lead him, deviously, back to the Red Lion. He fancied he saw it. He turned—
"Watch out! Watch out! Oh! Oh! Ah!"
At the very moment Smith had turned into the alley a gentleman had come out of it. They met and, though the gentleman was tall and stout and huge beside Smith, he was struck with such speed and force that he fell with an angry frightened cry.
Smith struggled to his feet, was about to rush on, when a hand grasped at his ankle.
"Let go!" he shouted.
"Damn you, no! Help me, first—"
Smith glared wildly down. He saw the gentleman's face, gray as a puddle. His eyes were sunken and dark: no spark of light in them.
"Help me up! Help me, I say! For pity's sake, sir! Can't you see I'm blind?"
"A blind man!" gasped Smith. "Oh Gawd! A mole-in-the-hole!"
The gin's tempest dropped abruptly away and left a glum wreckage behind, bleak and forlorn in the freezing night.
A boy—a child, thought the blind man, uneasily. Most likely a young thief. Most likely he'll rob me and run off—frightened out of his miserable wits. Oh God! How am I to get home?
"If you let go me ankle," muttered Smith, "I'll help you up; that's if you're really blind. Can you see me?"
The gentleman shook his head.
"What am I doing now?" asked Smith, pulling a hideous face.
"I don't know—I don't know! I swear I'm blind! Look at my eyes! Any light in 'em? Look for my smoked spectacles. They're somewhere about. Look for—"
"What am I doing now?" demanded Smith, pulling another, even more monstrous face; for he'd help no one who didn't need it.
The blind man loosed his hold on Smith's ankle and heaved himself up on one elbow. He'd lost his hat and his wig was awry, but otherwise he'd suffered no harm. He began to feel the adjacent cobbles for his possessions. Smith watched him and his face returned to normal, but as a last measure he fished inside his coat and pulled out the document.
"What have I got in me hand?" he asked gruffly.
The blind man sighed. "My life, my boy . . . my life's in your hand."
Smith scowled and put away the document. "Here you are, Mister Mole-in-the-hole! Here's me 'and, then! Up with you! Up on yer pins! And 'ere's your 'at and stick and black spectacles . . . though why you wears 'em foxes me! My, but you're a real giant of a gent! Did you know it?"
This last as the blind man stood up and fairly towered over the helpful Smith.
"Thank you, boy. Now—tell me if I'm in the street or the alley and I'll give you a guinea for your pains."
"You're on the corner."
"Facing which way?"
"The Lord knows! I've been sick meself."
"Fever?"
"Half a pint o' gin."
Suddenly, Smith felt a strong desire to confide in the blind man. After all—it could do no harm.
"Smith," he said, and held out one hand to be shook while with the other he guided the blind man's hand to meet it. "Smith. 'Unted, 'ounded, 'omeless and part gin-sodden. Smith. Twelve years old. That's me. Very small, but wiry, as they say. Dark 'aired and lately residing in the Red Lion Tavern off Saffron 'ill. Smith."
Helplessly, the blind man smiled . . . and his questing hand grasped Smith's firmly.
"Mansfield," he said. "Blind as a wall for these past twelve years. Well-to-do—but not much enjoying it. Mansfield. Residing at Number Seven Vine Street under the care of a daughter. Mansfield. Believe it or not—a magistrate!"
"Gawd!" gasped Smith. "Oo'd 'ave thought I'd ever be shaking 'ands with a bleeding Justice?"
If Mr. Mansfield heard he was too gentlemanly to remark on it. Instead, he fumbled in his coat for the promised guinea.
"And now, just point me toward the church that should stand at one end of the street and the guinea's yours, Smith, with my deepest thanks."
Smith obliged—and took the guinea.
"Seems a lot for a little," he said.
"Good night, Smith."
"Same to you, Mister Mansfield, J.P."
He watched the blind man tap his way down the street, bumping, here and there, into the posts—and sometimes raising his hat to them and mumbling, "Sorry, good sir . . . couldn't see you . . . so sorry."
Smith smiled indulgently and was about to make off, when a strangely familiar feeling of pity stirred in him. He had been reminded of the murdered old gentleman. He scowled at his own indecision, stuck his ancient pipe defiantly in his mouth, and hastened in the blind man's wake.
"That you, Smith?"
Smith grunted.
"Didn't expect you—"
"Going the same way meself."
"To Vine Street?"
"Thereabouts."
"Glad to hear it, Smith."
Smith grunted again. "Oh well—'ere's me 'and, then . . . you old blind Justice, you! Just tell me where to turn and where to cross and I'll see you 'ome safe an' sound. After all—I ain't done much for that guinea."
Mr. Mansfield found the offered hand and, once more, grasped it. He sighed and reflected in his heart (which was far from being as blind as his eyes) that it was an uncanny thing to be the cause of kindness in others.
Vine Street lay about twenty minutes away. Mr. Mansfield had strolled far that night, having a troublesome problem that gnawed him. But now, holding Smith's thin hand, the problem sank somewhat.
"Were it a sickness?" asked Smith after a while.
"My blindness, d'you mean? No. Lost my sight when a house burned down. Lost my wife as well. A costly fire, that!"
"Oh."
"Take the next turning on the left, Smith."
"What's it like—being blind?"
"Dark, Smith. Very dark. What's it like having eyes?"
"The moon's gone in again—so we're two of a kind, Mister Mansfield, you an' me."
The blind magistrate felt somewhat taken down—but was cautious not to show it. Twelve years of his misfortune had taught him that a bland face was the best security for one in his situation and that, for a blind man to frown, scowl or laugh, even, was like a fool discharging his pistol wildly in the night. The Lord knew who'd be hit by it.
"If you can see a new-built church with a round tower, cross in front of it and walk with it to your right."
Smith obliged. Hand in hand they passed by the church—a very curious pair indeed: small Smith, half a pace ahead, and huge, stout Mr. Mansfield walking somewhat sideways and behind—for Smith tended to pull, rather.
"Vine Street is the next street that crosses this one. My house is to the right. I'll be safe enough now, Smith."
"No trouble. I'm going the same way. To the door, Mister Mansfield."
They came to Vine Street. Said Mr. Mansfield: "If you've nought better to do, will you come in and take a bite of late supper with me, Smith?"
"Don't mind if I do, Mister Mansfield."
"Care to stay the night, Smith?"
"Don't mind if I do, Mister Mansfield."
"Any family, Smith?"
"Sisters. Two of 'em."
"Likely to worry?"
"Not much."
"Then it's settled?"
"Just as you say, Mister Mansfield."
"Anything else I can do for you, Smith?"
Smith sighed ruefully. The only thing he really wanted, Mr. Mansfield was unable to provide.
"No, thank you, Mister Mansfield. You done all you can."
They came towards the door of Number Seven. In spite of himself Smith grinned at the irony of his situation. Of all the men in the Town to bump into and befriend, he'd lit on the one who was blind and so could never teach him to read!
## 6
THOUGH SHE WAS AMIABLE, charitable and kind to a degree, no one with a pair of eyes in his head would have mistaken her for a saint. She was made of a commoner humanity than that, and took full advantage of her father's blindness to scowl and grimace—and sometimes shake her small, fierce fist—when the blind man's disability caused her irritation or annoyance: which it often did. Thus, when Mr. Mansfield blundered and broke some precious piece of porcelain, she'd cast her eyes to the ceiling with a look of phenomenal rage, but declare: " 'Twas only a chipped cup, sir! I promise you, I'm glad it's gone! Come, sir, let me help you." And her voice was always gentle and kind.
For all of twelve years this outward show of her human feelings, unseen by her father, had somehow created within a disposition of rare excellence, so that, at one and twenty she stood—not very tall but of great consequence—the most kindly but peevish and altogether remarkable young woman in the length and breadth of Vine Street.
Miss Mansfield stood on the topmost step, full in the light of the porch lamp. Below her waited a footman, ready to help his master.
"Papa!" she cried warmly. "I was so worried! You've been gone so long, sir! I thought you was—"
Here she paused as Smith came into the light and she saw— what the blind man could not—that Smith was the filthiest, wretchedest and nearly the most sinister-looking object in the Town. "—Lost," she finished up, and her face expressed wonderfully her opinion of Smith.
Smith tugged at Mr. Mansfield's hand, for he feared Miss Mansfield would set the footman on to do him a mischief.
"Daughter," said the blind man. "Here's Smith. As good-hearted a child as the Town can boast of."
Miss Mansfield did not look as though she believed it. Her face said very clearly: So. You've deceived him! Very well, then. You won't deceive me! _I've_ a pair of eyes in my head! But aloud, she said: "Pleased to make your acquaintance, Smith. Any friend of my father's is more than welcome."
"Daughter," said Mr. Mansfield, mounting the steps and pulling Smith after him, "my young friend's taking supper with us, and then he'll stay the night. For it's very bitter in the air and he's far from home."
At this, Miss Mansfield looked so little pleased that Smith was amazed that even the blind man couldn't see it.
"Any friend of yours, sir—" she repeated, and bustled back into the house to attend to her father's wish.
They took supper in a back parlor—as clean, spacious and handsome a room as Smith had ever dreamed of, furnished with mahogany and with much neat silver on display. There were pictures on the walls and a fire in the grate, and it was a shame the blind man could see none of it, for a deal of trouble seemed to have been taken.
While they ate Miss Mansfield came and went some dozen times, with amiable inquiries or amusing observations (she was very talkative and spoke rather quick), but always with a look of the sharpest suspicion at Smith followed by a glance round the room to see what had been stolen. (I know what you're up to, her angry face said. But you'll not succeed. Not while _I've_ a pair of eyes in my head!)
"A saint," remarked Mr. Mansfield once, when he was assured his daughter was gone from the room.
"Oh," said Smith.
"You don't meet with a saint every day, Smith!" said Mr. Mansfield, sounding somewhat offended by the cool response.
"No. You don't."
Just then the saint came in to say Smith's bed was ready in a small room at the top of the house—and to shoot him as venomous and disgusted a look as ever he'd received in his life. He shivered, for he found his haven for the night uncanny . . . what with the blind Justice and the daughter at odds with herself.
None the less, he was, at bottom, an affable soul, and continued to talk with Mr. Mansfield a while longer. He talked about life in the streets of the Town, life in the Red Lion's cellar, life in Newgate Jail, death at Tyburn, and—death in Curtis Court. Yes, indeed, Smith mentioned—almost in passing—the happening that had turned him upside down and inside out.
"Indeed, I heard of it," said the magistrate gravely. "For the gentleman was known and wealthy."
"Poor old so-and-so!" said Smith.
"Did you see him, then?"
"No!" said Smith, quickly; for how could he have known which was the old gentleman unless he'd seen him murdered? And if he'd seen that unlawful act, why hadn't he come forward?
Yes, indeed, Smith knew the law. And he suspected that the magistrate knew it even better.
"No, I never saw 'im. But I 'eard about it. Poor old so-and-so!"
Even as he spoke, some movement in the air—most likely due to their voices—caused the sideboard candle to flicker and jump and glint ironically in the blind man's dark spectacles . . . and a shadow was cast upon the opposing wall, strangely like the shape of the murdered old gentleman come quietly into the room to reproach Smith for denying him and to see what was becoming of his document.
"A Mister Field of Prickler's Hill in Hertfordshire. I knew him, Smith. A good but sad old gentleman. I'd like to have his murderer before me."
"And so would I, Mister Mansfield!" muttered Smith somberly, for he remembered well the old gentleman's look as the knife had gone in. "Why was 'e done in?"
"I don't know, Smith; I don't know. But it's a vile, dark business . . ."
Mr. Mansfield's ordinarily bland face grew hard and grim.
"It troubles me," he murmured, more to himself than to Smith.
"What troubles you, Mister Mansfield?"
"My blindness. Because I shall never clap eyes on that murderer. Because, till the day I die, I'll never know what such a monster looks like. D'you understand me, Smith? D'you understand that, to me, devils and angels are all one?"
Smith did not entirely understand the blind man's strange sorrow; maybe because his mind was filled with the news that Mr. Field had been wealthy. Hopes of the document were now very high.
"D'you understand me, Smith?"
Smith nodded, then recollected Mr. Mansfield couldn't see him and said, "Yes, indeed!" and went on thinking of his prospects.
Soon after this Miss Mansfield came into the room and declared that it was growing too late to be talking.
"Not so much for you, Papa, but for your young friend. Truly, he looks tired, sir! His bed is ready—and he ought to be in it."
Which remark, delivered most affably, was accompanied by a casting of eyes to the ceiling which said very plain: And the sheets he sleeps in will have to be burned! Oh Papa! This is outrageous!
Smith's room was small and oddly shaped, owing to its situation under the roof. It was as though the builder, arriving nearly at the summit of his labor, had come upon this extra space by surprise and, on the spur of the moment, had popped a door and a window to it so's not to embarrass the stairs with leading to nowhere. A bed, a chest and a chair were the sole furnishings—and a pot of strong sweet herbs. For, though Miss Mansfield could burn the sheets after Smith had slept in them, she could not burn the room, so the herbs were the next best thing.
Now Smith, though he'd slept on straw all his life, wasn't so ignorant as not to know a bed when he saw one. He prodded it; he sat on it; he lay on it; he lay in it. He grinned—and directly went to sleep. This had not been his intention. He'd meant to have a great brood on his curious situation and enriched hopes. But the day had been too long for him, and the night too fierce. He was tired almost unto death. He slept without dreaming, without moving . . . He slept so long and so deep that Miss Mansfield, poking her head round the door in the morning, thought for the instant that he'd perished in the night and left behind him a small, black corpse.
"Smith!" she cried. "Boy! Wake up! Directly!" And she poked at him with a walking stick she seemed to have brought especially for the purpose.
Smith woke up, saw Miss Mansfield's ferocious concern—and rolled deftly away. But he forgot he was sleeping two feet off the floor. He fell, and swore.
"Language!" shrieked Miss Mansfield and poked at Smith furiously with the stick. He howled.
"What's wrong?" Mr. Mansfield cried from below.
"Nothing, Papa! Your young friend fell out of bed. Ha-ha! No harm done!"
Smith, unable to reach the door, had bolted under the bed. And there he crouched, very like a mouse, staring at Miss Mansfield's neat ankles and brisk, black shoes.
"Come out!" she muttered, and down flew her head, with her braided hair falling bolt downward to the floor like a pair of handsomely turned table-legs. "No one's going to harm you!" And she prodded him with her stick to prove it.
"Are you here, daughter?"
Came a second pair of feet, large and slippered. Miss Mansfield's head—with a last furious scowl—vanished.
"Papa! You shouldn't have come without help! You might have fallen, sir!"
Mr. Mansfield laughed. Miss Mansfield's feet shifted impatiently. The point of her stick kept prodding her toes—as if in default of another target.
"Morning, Smith. Sleep well? My daughter has a fine breakfast for you. She's a saint, child! As I told you—a real saint!"
Down came the saint's head. Come out! said her angry eyes. Come out, you disgusting object! Up went her head and vanished from view.
"Mornin', Mister Mansfield." Smith had no quarrel with the blind man.
"What? Back in bed?" The slippered feet moved towards him. "The voice betrays you! Give me your hand . . ."
Miss Mansfield's head was back again, peering round her father's ankles. Her lips moved. " _Please_ come out!" Sourly triumphant, Smith shook his head.
"Where's your hand, Smith?" Mr. Mansfield's voice—puzzled.
Miss Mansfield's eyes were filled with tears! (I beg you—for pity's sake, boy! Don't shame me in his blind eyes.)
Bewildered, Smith stared back. The mouse had made a discovery. The cat was as frightened and lost and lonely as he. Which was no comfort at all. Gloomily, he came out.
"Here's me hand, then . . . you old blind Justice, you!"
Over breakfast, which was taken in the back parlor, Mr. Mansfield said: "And will you go back to your cellar, Smith?"
Smith shrugged his thin shoulders. Miss Mansfield looked at him—and then to her father in weary aggravation. Did the blind man live but to spite her? What was he thinking of? So why didn't he come out with it, then? Must _everything_ be left to her?
"Smith," she said, affecting a careless, everyday tone not reflected in her face, "Mister Mansfield means, will you stay here? And work for your board and keep, of course! Mister Mansfield is very concerned about you. He thinks you deserve better of the world than you've got, and would give it to you. My father is quite a saint, you know—"
"Come, daughter! 'Tis your own idea."
"Never! Never in ten thousand years! I read it all in your face, sir."
"My face?"
" 'Tis like an open book to me."
Smith, his mouth full, looked from one to the other of the Mansfields, each accusing the other of a kindness. He shrugged his shoulders. They might quarrel about it till the end of time. It would make no difference. He wasn't going to stay in that uncanny house. No, sir! Nothing on earth would have kept him with the Mansfields—blind father and mad daughter.
"Then it's settled," said Miss Mansfield, with another irritated look at her father. "Mister Mansfield will employ you in the stables, Smith . . . and I—" (Here, she looked: God help me!) "—will attend to your improvement. For a beginning, Smith, I shall teach you to read!"
Smith stared. He gaped. He poked his finger in his ear and scraped it about. What was it she'd said? Teach him to read? _To read!_ He beamed . . . and beamed! He couldn't stop himself. He wondered if his face would ever go back again.
"I think he's pleased, Papa," murmured Miss Mansfield in a low voice. "I suppose he's fond of horses."
Mr. Mansfield offered to send a servant to the Red Lion to acquaint Miss Fanny and Miss Bridget with their brother's situation. But Smith said he'd rather go himself. The last thing he wanted was his improvement boasted of in the Red Lion's cellar! For, though he loved and trusted his sisters, he feared that, under such tortures as the two men in brown might inflict (such as the sight of five shillings—or even four), they'd wag their tongues like a pair of windy flags. "Smut's in Vine Street! Poor little Smut!"
"I'll tell 'em tomorrow," he said, and left it at that.
Now all was settled indeed, and Smith—on Miss Mansfield's orders—returned to his mad-shaped room. In high good humor he fell upon the bed and took out the precious document—the last remains of Mr. Field of Prickler's Hill in Hertfordshire. Excitedly, he waved it aloft like a banner.
"Won't be long now, old fellow! Very soon you and me will be better acquainted! And then—up we'll go in the world!"
He folded it and wrapped it once more in the pilfered handkerchief. And not a moment too soon! Footsteps. Quickly, he pushed it into the tumbled bed linen. The door opened. Two footmen with real hangmen's faces. Alarm seized Smith. Why had they come? And why so grim?
"Up with you!" said one.
"And then down with you!" said the other.
"W-what d'you mean?"
They grinned. "Miss's instructions. She says, afore you commence on scrubbing the yard, that selfsame necessary thing must be done to you! So down to the scullery, young Smith!"
Smith's eyes glittered in alarm. Most likely he paled, too . . . but that wasn't so easy to see. He looked about him. But there was no escape. He looked up to the footmen. No mercy, nor even pity, there.
"To the scullery, young Smith."
Now Smith had never been washed since, most likely, the midwife had obliged, twelve darkening years ago. Consequently, he suspected the task would be long, hard and painful. He was not mistaken.
Two more footmen, aproned over their livery, stood ready and waiting by a steaming iron tub.
"Take off them wretched rags, Smith."
"Rags? What rags?" (The scullery was gray and stony and full of strong vapors.)
"Your clothes, Smith. Take off your clothes."
The window was barred and the door was shut. He began to undress. Disdainfully, the footmen watched him; and indignantly, he stared back.
"Ain't you never seen a person take off his clothes before?"
Disdain gave way to amusement . . . and then to surprise. Several times the footmen reached forward to seize him, for they thought he'd finished, but each time he waved them back.
" 'Ave the goodness to wait till I'm done, gen'lemen! 'Ave the goodness!"
For Smith wore a great many clothes. Indeed, to the best of anyone's knowledge, he'd never thrown a single item away. Coats and waistcoats worn to nothing but armlets and thread now came off him, and shirts down to wisps of mournful lace: one by one, removed carefully and with dignity, then dropped, gossamer-like, to the floor.
Then there were breeches consisting in nothing more than the ghosts of button-holes, and breeches that came off in greasy strips—like over-cured slices of ham; and breeches underneath that were no more than a memory of worsted, printed on his lean, sharp bottom.
These memories of perished clothes were everywhere, and plainest of all on his chest, where there was so exact an imprint of ancient linen that Smith himself was deceived—and made to take off his skin!
At last he crouched, naked as a charred twig, quivering and twitching as if the air was full of tickling feathers.
"Ready," he said, in a low, uneasy voice, and the four footmen set to work.
Two held him in the tub; one scrubbed, and one acted as ladleman. This last task was on account of the water having been dosed with sulphur, and it consisted in spooning off Smith's livestock as it rushed to the surface in a speckled throng.
From beginning to end, the washing of Smith took close upon three hours, with the scullery so filled with sulphurous steam that the footmen's misted faces grew red as the copper saucepans that hung like midnight suns on the scullery's streaming walls.
At last it was done. He was taken out, rinsed, and wrapped in a sheet—the ghost of his former self. For he was now a stark white replica of the previous Smith and, had his sisters seen him they'd have shrieked and sworn it was his spectral image!
His clothes were burned before his oddly saddened eyes . . . which eyes were now seen to be somewhat larger and rounder than might have been supposed. But his hair, in spite of shock and scrubbing, remained as black as the river at night.
"Me clothes," he said. "Me belongings. I can't go about like this."
Then he was told a livery was being cut down for him, and he was to go back to his room and wait. He mounted the stairs, much hampered by the sheet he was wrapped in. But there was great determination in him. Each fresh disaster he endured seemed to strengthen his bond with the document . . . and whatever it might contain. In a way, it seemed to be payment in advance.
He opened the door to his room. He stared. His eyes filled with tears of horror and dismay. The bed was stripped. The bedding was gone. And with it—the document!
## 7
WHEN THEY BROUGHT him his fine new livery (blue, with brass buttons), they wondered why he was sat, crouched on his bare bed, with his knees drawn up like battlements before his face. And they remarked, when they left him, on the look in his eyes as he watched them come and go: dismay and despair. They laughed on the way downstairs—but not unkindly—and decided his system was still shocked from his washing.
"Give him another half an hour and he'll be trying on his new clothes and strutting like the king of the weasels!"
But after half an hour there was no change, save that, maybe, Smith's head was sunk a little lower and his eyes stared with a deeper despair. His livery was untouched and the sheet that covered him had slipped an inch or two off his shoulders, leaving those thin objects to fend for themselves against the cold air.
"Maybe he's taken a chill?" suggested the housekeeper, and rummaged in her wits for a remedy.
"But he ain't flushed or feverish. He looks more froze than inly heated."
Miss Mansfield came to see him. She scowled angrily at his sick, despairing air.
"Are you ill, Smith? What's wrong with you? Answer me!"
"Nothing, miss. Nothing."
She went away, much troubled, and ordered blankets to be taken up—and Smith to be wrapped inside them.
Several times during the afternoon she returned, hoping against hope to find him restored. But each time he seemed more sunk within himself—as if something necessary had perished inside, and all was sinking inwards for lack of support. She questioned the four footmen and consulted with the housekeeper who gave it as her opinion that the child had been poisoned by too much sulphur and offered to prepare a draft. Gladly Miss Mansfield agreed. The draft was mixed and carried upstairs.
"Come, Smith. This will make you well again!"
But it was no use. He'd take neither draft nor anything else to sustain him.
"It's as if," said the housekeeper quietly, "that poor mite has made up his mind to die."
"What an idea!"
"Scowl and frown as you please, miss, but I've seen it happen. These little souls of the Town perish like you and I go to sleep."
And so it began to seem to all the Vine Street household save Mr. Mansfield himself, from whom it was desperately kept—as was the late visit of a physician, brought in against all dignity through the tradesman's door with much secrecy and quiet.
He studied Smith. Felt his head, his wrist, his chest. Bade Smith look this way, that way, and to a point above his head. Wearily, Smith obliged, and everywhere his eyes turned they seemed to see even more misery—as if there was no end, no bottom to it. The physician shook his head. In all justice he could find nothing wrong; but in all compassion and pity there was something grievously amiss. But it was out of his scope to find it. He spread his hands, pocketed his fee, and left.
More and more Miss Mansfield blamed herself; had not the child been bright and well before his violent washing? But to her father's repeated inquiries she answered cheerfully: "He's quite worn out from the footmen's labor, sir. I fancy he'll sleep the clock round. Best not disturb him yet."
During the evening, Mr. Billing called. Mr. Billing was a youngish attorney and was both Mr. Mansfield's friend and also deeply in love with his daughter. Mr. Mansfield had high hopes of a marriage but he feared his daughter would never leave Vine Street as long as he lived. She always laughed when he brought the matter up and declared that Mr. Billing was so agreeable a suitor that it would be a shame to bury him in a husband! Mr. Mansfield would have dearly liked to have seen his daughter's face when she spoke so lightly . . . if only to see if her eyes were filled with regretful tears.
But on this evening Miss Mansfield found the attorney tiresome and overstaying his welcome; she longed to creep up to the top of the house and see the strange, sad child. She had a terrible feeling he'd die in the night.
Mr. Billing stayed and stayed, affable and talkative as ever . . . and all the while she longed to cry out: "Begone! Begone! There's a dying boy upstairs, and I must go to him."
Instead, she helped him to port and brandy (as her father directed), and never left the room for an instant, being afraid of arousing her father's suspicions that all was not well with Smith. She chattered as amiably as she was able—and hoped her suitor would read the anxious impatience in her eyes. But, unluckily, Mr. Billing was used to Miss Mansfield's varied and odd expressions and, though he loved each and all of them, he took no particular note of any.
Below stairs, all but two of the servants had gone to bed: a dozing footman and a certain scullery maid called Meg—a softhearted person with large arms the color of boiled lobsters.
All the evening her muddled, motherly mind had been fixed on the sick child at the top of the house and a certain notion had come to her. Knowing that the boy had been brought up in an ale cellar she supposed he was homesick for all familiar things. She brooded on this till there was no one about to question her, then she crept up to Smith with a pint of ale.
Not that she supposed he'd drink it, but she firmly believed that the sight and smell of it would do his aching heart a power of good.
Smith stared up at her mournfully. Her heart was fairly wrung. She moved about the tiny room to spread the ale's odors. Smith watched her. She smiled and held out the tankard.
"Come along, little one. It'll do you a power of good. Drink it up—for not the Red Lion itself has a better ale!"
Smith gazed at her somberly.
"Nothing but kindness is meant. All's for your own good! They'll feed an' clothe you an' treat you like a yewmanbeen. You'll want for nought, here!"
Smith looked as though all he ever wanted was to pass, unhindered, away. Meg's eyes grew great with tears.
"They 'ad to wash you! You was that black! You should have seen the sheets—"
"The sheets? Did you see 'em?"
For the first time Smith showed signs of interest in the world. His nose twitched and his eyes began to kindle.
The ale, thought Meg triumphantly. It's the smell o' the ale what's doing it!
"Why, bless you, yes! And they was that horrible Miss wanted 'em burned!"
"And—did you?"
"Lor' no! Burn good sheets? I biled 'em!"
At this, Smith stared at her so strangely that she began to fidget.
"W-was there anything—anything else w-with the sheets?"
Obligingly, Meg shut her eyes to recall the scene.
"There was a handkerchief . . . but 'twas so far gone, I burned it—"
" _Burned it?_ "
Here Smith gave such a shriek and a groan that Meg thought his last moment was come.
"I 'ad to, little one! 'Twas in a shameful state. It smelled, dear, like . . . well, I don't know what it smelled like, for I've nought to compare it with! Powerful. Clinging. I only 'ope it'll wear off the master's paper—"
"Paper?" whispered Smith, not daring to hope—and yet not able to prevent it. "What—paper?" His eyes glittered so brilliantly, and he began to shiver so violently, that Meg edged away, fearing a contagious, mortal fever.
"Why—one of the master's documents that had somehow got itself muddled up in that dreadful 'andkerchief. Sometimes he drops 'is papers in the queerest places . . . what with his disability—"
"What was in it?"
"Lor' child! _I_ don't know! 'Twas a lawyer's document of sorts— and no one must read _them_ save the mistress or the master's clerk. And then only when the master asks!"
"Then how do you know it was a lawyer's document?" Smith said this with desperate sharpness, for he was coming back to life with a vengeance.
Meg, seeing nothing but the boy's improvement and wanting to humor him, smiled confidentially. " 'Twas marked for the attorneys, Billing and Lennard . . . with 'oom we 'ave dealings." She sighed sentimentally. "Billing and Cooing I call 'em—on account of Mister Billing being sweet on Miss Mansfield. He's in the parlor now. Such a handsome pair!" Her smile grew soft and misty—then she remembered Smith's question. "So what else _could_ it have been but one of the master's documents? Answer me that!"
Dazedly, Smith nodded. What else could it have been but one of the magistrate's documents? For what would a light-fingered alley-scuttler like Smith be doing with a document marked for a lawyer?
"Did—did you give it to 'im?"
"To our Mister Billing? Lor' no! That's for the master to do! Besides, it were for the other one, for Mister Lennard."
"So you g-gave it to Mister Mansfield?"
"Questions, questions! Was you a cat, you'd be stone dead! No: I never gave it to him. There. Why, it smelled so bad it would 'ave knocked him flat—what with 'is disability an' all! I put it in his study along with 'is other papers. Only I put it at the bottom so's the smell might wear off afore he comes to it! That's what makes a good servant," she added proudly. "Consideration for 'er master's feelings. Oho! There's a good lad! Drunk up your ale! Just 'omesick, weren't you. Knew it all the time. Trust Meg!"
She repeated this several times with some triumph, then beamed encouragingly at Smith and left the room. On the way downstairs she sniffed and tossed her head in high contempt and muttered: "Chills and fevers and sulphury poisonings? 'Omesick! Ha! And it took a motherly soul like Meg to see it. Brains? Give you a farthing for 'em!"
She prodded the snoozing footman and boasted of Smith's improvement.
"A touch of 'eart," she said. "That's all this big busy Town 'as need of! Take that boy, f'rinstance . . ."
It was now midnight and, to Miss Mansfield's aggravation and distress, Mr. Billing stayed for another hour. Then at last he went, and, when her father was safely in bed, she flew upstairs with an anguished heart—expecting she knew not what.
She opened the door; she looked inside, and she all but dropped her candle. The room was empty! The boy was gone! Her face grew pale with dread. A terrible fear assailed her. The boy, feeling himself to be dying, had struggled from his bed and crept from the house. The housekeeper's grim words echoed in her mind. "These little souls of the Town perish easily . . ."
In blackest despair she began to go downstairs. Suddenly, she stopped. She'd heard a noise: very gentle, very subtle, very secretive. A papery rustle. From her father's study.
She approached the door. She was much frightened and would have aroused the house—but an odd instinct prevented her. She opened the door. She held up the candle—
" _Smith!_ "
"Oh my Gawd! I'm done for!"
The floor about Mr. Mansfield's desk looked as though it had been snowed on by documents! Depositions, Confessions, Summonses and Judgments lay in a guilty profusion, and in the midst of them crouched Smith, wearing only his shirt and looking like an outsize document himself with his face turned up like a gray seal of terror!
All Miss Mansfield's dread and anguish turned now into a violent fury and bitterness.
" _Smith!_ Is this how you repay Mister Mansfield? By robbing him? Stealing from a blind man? Is _this_ the kindness of heart that so moved him? Nothing but the cunning skill of a cruel rogue?"
She spoke in a trembling whisper—for she dared not awake her father.
Smith, still among the documents, stared up at her with a mixture of misery and fear. He'd not yet found his precious document, which he knew he'd have recognized even among the hundreds he'd strewn about. Now he was done for. Flight was impossible. Miss Mansfield stood in the doorway, and the builder had provided no other way out. He wondered what would be done with him. The worst he could count on was being taken and hanged for a thief. The best—to be sent furiously out into the night. Either way, the document was lost forever.
"I—I ain't cruel," he mumbled unhappily. "Reely, I ain't . . ."
Miss Mansfield bit on her lip. She scowled—and her face in the candlelight looked like a small thundercloud. Fiercely, she continued to stare at the unlucky Smith. Really! What could one expect of such a child? All his life a thief! She began to grow angry with her father again. He ought to have expected something like this. But he was so foolishly sentimental! Just because the boy showed him a kindness when any other wretch would have robbed him and left him for dead . . . why should he think Smith was exceptional? And reformed? A stupid idea. As if such a boy would change in an evening! It takes time. And her father, of all people, should have known!
Miss Mansfield's breast began to heave with aggravation, and Smith watched her piteously.
Her father was outrageous! Always he expected her to have the patience of a saint. Well—she hadn't! She was peevish. And now he'd left her to deal with the wretched boy while he slept on in happy ignorance. Oh!
"Smith," she said at length, scowling worse than ever under the strain of her long inner quarrel. "I—I'm disappointed, it's true. But—you're fortunate that Mister Mansfield is more understanding than his daughter. _She_ , I promise you, would have had you clapped straight into Newgate! But Mister Mansfield never expected an angel out of you all at once. Mister Mansfield's a saint, Smith, and on that account you may thank your stars! Go back to bed this instant—and we'll say no more of tonight. But—if I catch you doing any such thing again—then it's Newgate for you, my lad, on the instant. Now—to bed! Don't gape. Don't cry! Tears won't move me. Or don't you understand, Smith? You've been given another chance."
## 8
THE HOUSE IN VINE STREET was both joined to and separated from its neighbor by a brick built arch that led to the stable and yard. This arch was so clumsy in its brickwork that, skillful as was the coachman, he was forever scraping the paintwork of Miss Mansfield's curricle and her father's coach. But nothing was ever done to remedy this; Mr. Mansfield had grown used to the sound of it and Miss Mansfield would allow no change to anything that helped her father to see with his ears or hands. So the carriages continued to be scraped and the stable boy was forever being sent to the paint shop for pigment or varnish to make good the damage. Which task fell naturally to Smith. It was on one of these journeys that he fell in with a certain muffin-man with whom he had an old street acquaintance.
"Ain't I seed you before?" asked the muffin-man, thrown out by Smith's cleanliness and livery.
"Maybe," said Smith cautiously, and then decided to make use of the acquaintance.
"D'you know the Red Lion Tavern in Saffron Hill?"
The muffin-man grinned. He knew it all right.
"And d'you know the two ladies what reside in its nether regions?" (Smith's education had begun and he'd acquired a fanciful taste in words.)
"The darlings in the cellar? Miss Bridget and Miss Fanny? Everyone knows them!"
"The very same! I'd be obleeged if you'd carry 'em a message."
The muffin-man thrust out his lower lip till it looked like the last quarter of a muffin.
"Tell 'em a—a _certain person's_ well and prospering. Tell 'em 'e's on 'is way up in the world . . . and will communicate further when a suitable occasion has arose."
Much impressed, the muffin-man nodded. "I'll tell 'em."
"Don't forget now. A certain person's on his way up in the world."
Then, watched all the way by the admiring muffin-man, Smith strolled back to the house in Vine Street, whistling cheerfully—for he'd just discharged a duty that had been weighing on him these three weeks past; he'd set his sisters' minds at rest (always supposing they'd ever been otherwise), and so had kept his word with Mr. Mansfield. He smiled somewhat wistfully as he pictured Miss Bridget's and Miss Fanny's faces when they got his news. And he sighed when he thought of his friend, Lord Tom. Well—well . . . they weren't gone forever. Someday, soon, they'd all meet again, when he'd got what he wanted from the document . . .
His face darkened. The document was still in Mr. Mansfield's study and not all of his wit and deftness had brought him any nearer to recovering it. When he was in the house Miss Mansfield watched him like a brisk and suspicious hawk; and when he was in the yard the coachman watched him even sharper . . . while the three ugly, lumbering horses, Smith felt, kept more than an ordinary eye on him.
At night, he dared not try again, for Miss Mansfield slept light as a feather . . . and she'd give him no second chance. His credit on her kindness was stretched to its limit and he shivered as he thought of its breaking. For he'd come, little by little, to think as well of the Mansfields as anyone else (Lord Tom and his sisters excepted) in the world.
Though both of them, on occasion, frightened him half to death, there were times when they did no such thing. There were times, even, when they made him grin: viz, when they quarreled over which of them was to be blamed for a kindness. There were times when they made him shrug his shoulders in bewilderment: viz, when Miss Mansfield lit candles for her blind father and did everything to persuade the house he could see it . . . and yet she'd have nothing moved—be it ever so awkward and ill-placed—lest her father stumble against it and so betray what the whole world knew: viz, that he was blind as a mole. There were times when nothing pleased Smith more than Miss Mansfield's praise of his progress in reading, so that, for the moment, her good opinion seemed the chief purpose in his studying and not the document at all! Of which studying Meg the scullery maid took a vexatious view.
"Learning?" she'd say contemptuously, while Smith sat in the kitchen of a late afternoon or evening, his small white face cupped in his thin white hands, staring up at Meg's big red face pillowed in her big red arms. "Learning? Give you a farthing for it! Mark my words, little one—a yewmanbeen's better off without it! What good's it ever done a soul? Brains? Wouldn't have 'em if you paid me! A penn'orth of heart's worth all your skinny clever heads!" She stared thoughtfully at Smith's own skinny face and pushed over a piece of pie as if to fill him out as quickly as possible. "I saw some clever heads—once. When I was a little girl. Me mother—God rest her—showed me. Three of 'em: a Lord, a Sir and a Mister. On the Traitors' Gate. Cut off at the neck! Very clever heads, they was. And much good it did 'em! 'Meg!' said she—and I'll always remember her words—'Meg! Take note. Heads without hearts is nought but bleeding pom-poms! Of no use to man, woman or child.'"
"But at least you can read, Meg," said Smith, munching at the pie. "For you read the name on that old paper you found when I was washed."
Meg stared at him crossly, as if she felt all her warning were wasted. "I can read what's proper and needful, young man! But no more than that. F'rinstance, I'd never read a _book_!"
"But what about Miss Mansfield?"
Meg shut her eyes in vexation.
"Yes! You look at the mistress. All trouble and worry and storms in the heart! And then you look at the master who can neither read nor write on account of his disability—which is, maybe, a blessing in disguise. All smiles and even-faced. All contentment, _I'd_ say. There, now!" Surprised by her own powers of observation, she opened her eyes triumphantly. "So who's the better off? Brains? Give you a farthing for 'em!"
But in spite of Meg's warnings Smith continued to study as hard as he was able. He mastered the alphabet—that sinister collection of twists and curls and crosses and gibbet-shaped signs that resembled nothing so much as the irons that hung on Newgate's most dreadful walls and, by the time of his meeting with the muffin-man, he could pronounce aloud such words as Miss Mansfield wrote on his slate.
"M-y n-a-m-e i-s S-m-i-t-h . . . th," he spluttered out with great difficulty, only understanding the sentiment as he heard the sounds he made.
"Well done!" cried Miss Mansfield, and Smith, though pleased to have pleased her, was mildly aggrieved to discover that so much effort had gone into saying aloud what was perfectly well known to both of them all the time. None the less, he was much encouraged and Miss Mansfield promised him that, in but a short while more, he'd be able to read whatever his heart desired. On which Smith's eyes would stray towards Mr. Mansfield's study with an expression of great yearning and hope.
Sometimes, Mr. Mansfield himself would stay to listen to Smith's lesson, now and then explaining something of which his poor blind eyes still held the memory. But mostly he kept silent, save when he, too, had occasion to praise the boy's quickness and progress. And this, when it happened, moved Smith oddly, for he sensed a deep generosity behind it, and if anything could bring tears to Smith's eyes (apart from a thump on the nose), it was the sudden warmth of a generous heart.
Nor were the Mansfields the only ones who were pleased by Smith's redemption from black ignorance—which was following so pat on his redemption from his other blackness. Mr. Billing had come to hear of Miss Mansfield's pupil, and the lad's arrival and subsequent improvement at Miss Mansfield's hands formed a fresh subject for his lively chatter.
This Mr. Billing was a handsome fellow of thirty or thereabouts. He had rosy cheeks, a prosperous, dark moustache and eyes that, when they weren't shining with devotion to Miss Mansfield, were shining with all of an attorney's shrewdness and wit. He walked with quick springy steps and put off his cloak with an air. These facts Smith had learned from observing him from the dark top of the stairs, for, as Miss Mansfield had never yet seen fit to introduce the stable boy to her suitor, Mr. Billing and Smith had not yet met; even though he called often and unexpectedly, knowing that, in courtship, the sudden is worth its weight in gold.
Sometimes he'd come mid-morning with a, "I was passing and couldn't resist," and sometimes mid-afternoon with a, "I found myself at your door as if by magic!" Then there'd be much cheerful laughter and in he'd come and settle for an hour, dispensing pleasure to Miss Mansfield and irritation to Smith who would be banished to the kitchen. For Miss Mansfield preferred to break off the lesson rather than have her suitor and the stable boy—whose tongue she couldn't answer for—meet face to face.
This uneasiness of hers persisted and even grew, and what at first had been a fleeting and foolish embarrassment became a deep and odd fear, so that a meeting she'd begun preventing almost lightly, became an affair of strange importance that must be avoided at all costs.
She'd grown deeply fond of Smith, who'd darted into her heart as neatly as she supposed he'd once darted from doorway to doorway in the freezing, friendless streets. An extraordinary child: a fascinating, quick-witted, dear-faced, obliging and determined child . . . but a child whose sometimes violent tongue she couldn't answer for, and whose resentment at Mr. Billing's interruptions alarmed her. More and more, she came to dread the meeting she'd so far put off, but which she knew she could not put off forever.
There's no doubt that, by keeping all this to herself, she'd helped it grow to formidable dimensions in her mind; but Smith's resentment seemed to be growing likewise—as if his patience was running out. As if there was some goal he'd set his heart on, and the nearer he came to it the more enraged he was at being delayed.
Which was nothing less than the truth; for Smith was now very close to being able to read. His long battle was nearly won. Letters were making words for him; words were making sentences. Great pages of print that, scarce four weeks ago had seemed no more than a mad patterning of the paper, now spoke haltingly to him—even told stories—as if long-dead gentlemen woke up under his struggling eyes, buttonholed his mind and breathed their thoughts and dreams into it. Gentlemen who were dead and dust a thousand years stirred and shifted and began to live their lives again.
But still there were gaps and lapses and conjunctions of letters that seemed to have no business together. He thought often of the document but he knew it was useless to him till he could fill those gaps and lapses. So he waited for the day when Miss Mansfield should declare, "Smith: now you can read whatever your heart desires."
But with the over-attentive attorney's interruptions, that day did not come till a certain Tuesday morning when the event Miss Mansfield had tried so hard to prevent also came to pass, as sooner or later it had to.
"Well, Smith," she said with a proud and affectionate smile, "now all the wisdom of the world is yours for the taking. For you can read, my dear—"
On which Smith's heart leaped almost to the skies; and when there came at almost the selfsame moment the familiar double knock on the front door, he felt, in place of his customary resentment, a grand relief that he could escape and caper and dance in a private triumph.
"It's Mister Billing, miss!" he said with a cheerfulness that amazed Miss Mansfield. "Come a-cooing! So I'll be off and 'ide meself now. The best of luck to you, miss! I'm sure you'll be very 'appy!"
With that, he fled from the library in high delight, and with the best will in the world (for Smith, when he wished anyone happiness, really meant it—happiness being a word he didn't use lightly), stopped in the hall to wish Mr. Billing the same.
"Best of 'appiness in your cooing, Mister Billing!" he cried— then faltered on his way down the stairs.
The rosy-cheeked attorney had gone a deathly white. A look of wild amazement had come upon his face. His eyes had widened; his mouth had dropped open. A shudder had gone through him. Then, as abruptly as his color had gone, so did he—without so much as a word for the lady of his heart. The door slammed violently and Smith, sensing he was the cause, went hastily to the kitchen, puzzled and vaguely alarmed.
About half an hour after he'd left, Mr. Billing returned—and in a state of such high excitement, said the footman who'd admitted him, that he felt sure the gentleman had at last plucked up his courage to ask for the mistress's hand. He'd been shown into the library where the mistress and master were wondering on his unaccountable departure. The footman had listened for long enough to hear Mr. Billing declare that Miss Mansfield was looking handsomer than ever he could remember.
"So she is," nodded Meg wisely. "For love paints our faces something beautiful."
Here, the housekeeper—a single lady with a complexion midway between a lemon and a turnip—muttered, "Stuff and nonsense!" but looked very wistful; and Smith, whose uneasiness had taken a sharp turn for the worse on the attorney's return, said, "Thank Gawd!"
The housekeeper looked at him curiously, and Smith, feeling the vague danger past, said, "It was only that I thought 'e'd been took ill before," and went on to relate the brief meeting which he'd previously kept to himself.
The coachman, who'd come into the kitchen for his morning mug of ale, shook his head with all the pessimism of a man whose days are spent reasoning with horses.
"Mark my words—he's most likely got a wife and child in Clapham or somewheres an' the sight of our young Smith reminded him. Small wonder he went white. Any man would.
"Stuff and nonsense!" declared the housekeeper looking even more wistful. "Nothing but biliousness. There's a deal of it about. Just popped out to clear his head. Very sensible."
But Meg was of the opinion that Mr. Billing's sudden pallor and departure were due to nothing other than a brief loss of courage in his heart's intentions which he'd forthwith gone out to strengthen at the nearest tavern.
"I'll wager he'd a smell of brandy about him!" she said.
These three opinions now provoked the Vine Street household into a lively dispute for some minutes, during which the coachman's was rejected with contempt, and the housekeeper's thought the most likely—though it was Meg's that won the day. For the Vine Street household was of a sentimental and hopeful turn of mind and always looked forward to the time when Miss Mansfield's tempestuous person should be removed, happily, to another establishment.
The footman who'd answered the door now agreed that there _had_ been a brandy-ish air about the attorney, and a parlormaid who'd been listening at the library door came down with the news that the attorney seemed tongue-tied—a sure sign, for someone in his calling, of being in the last extreme of love.
On this, there was a general burst of smiling and pleasure and the unfortunate coachman had his elbow jogged as he sought to hide his pessimistic face in his mug of ale. Then Meg, in a mood of powerful tenderness, laid her large arm about Smith's shoulders and declared:
"And this little mite's the one who's brought it all on. The mistress has grown that tender since he's been with us. He's warmed her heart and opened it up to Mister Billing's cooing. It would never have come about without our little Smith. So give honor and kindness where the same are due!"
With that, she imprinted a large, moist kiss on Smith's surprised face. He blushed—and everyone laughed . . . including the coachman who laughed loudest of all. So in a matter of moments, Smith was become quite a hero, and when the parlormaid (who'd gone back to her post at the library door), came down with the news that Smith was wanted, everyone—even Smith himself—was convinced it was because Miss Mansfield wanted to show off the wonders she'd worked in him. He got off his chair and straightened his coat. The housekeeper found a comb and brought order to his hair. A footman wiped a smut off his face; another suggested a quick bath—and chuckled.
"Go on up, Smith!"—"Do us all proud, Smith!"—"God bless you, Smith!"—"Don't forget, Smith—we're all behind you, lad!"
And so they were, for, as Smith went proudly up the stairs, the Vine Street household followed closely after to give him a last pat on the back as he knocked on the library door and went inside.
It was just on midday. A brisk fire was burning in the library, for the weather was turned very bitter and the sky bulged with unshed snow. For a second time Smith and Mr. Billing stared at one another; and for a second time the attorney shuddered—to the depths of his soul, it seemed.
"It is him. This is the boy I saw. In the Court. This boy stabbed Field. I saw him! He is the murderer! My poor friends—how monstrously you've been deceived!"
Mr. Billing was the man from Godliman Street: the same man who'd questioned the unlucky bookseller.
## 9
GREAT HOPES, GREAT JOY, great trust, when they fall, do so swiftly—in a bleak and evil instant. They do not diminish, little by little so that a man you trusted yesterday, today you trust a little less. He is lost, damned; nothing of him remains but is false as quicksand—
"Snake! Venomous little snake!"
From outside of the library door, where the Vine Street household was gathered, eager and close, to hear its prodigy's triumph, came this single, bitter, trembling voice.
"Snake!"
Whether it was the housekeeper's, a footman's, the coachman's—no one knew. It was of no consequence. It was the voice of the household, shaken and shocked out of its pleasant dream by the dreadful words of the attorney.
Within the library the brisk fire still danced and gleamed on the polished wood, the calm brown walls and the gilded backs of the books.
Miss Mansfield—elegant, handsome and gay in a yellow brocaded dress—had lost every scrap of her complexion. She'd put her hand to her face as if to hide from the world her horror and dismay. She cried: "No! No! It's not so! You're mistook, sir! Not this boy! Never, I tell you!" But in her heart of hearts she could not but believe the attorney, not because she wanted to, but because she dreaded it was so.
"It is the boy I saw from my window in Curtis Court. I saw him struggle. I saw him stab. I saw him escape. There is no doubt. I wish to God there was. Forgive me . . ."
The attorney spoke low and shakingly, but his eyes were cold as stone. If anything gleamed or flickered in them, the terrified Smith never saw it. If anything pricked in that subtle, black and dreadful place that he suddenly divined was the attorney's heart, there was nothing to show for it. Save once. When Miss Mansfield cried out for a second time, there was in her voice such a world of misery that Mr. Billing's white hands clenched and he seemed to flinch— as if his real love for Miss Mansfield had moaned: You're murdering me, Thomas Billing!
Miss Mansfield moved—and the rustling of her dress was as a dragging sigh. She crossed the room to her father—that motionless man in his high-backed chair. She made to lay her hand on his (which was fixed upon his stick), but he sensed her intention and waved her off. The customary blandness of his face seemed carved out of granite.
While Smith—Smith, who'd done nothing— _could_ do nothing but moan in a dreadful amazement several times over, "You're mad! You're mad! I never laid a finger on the old man! I never touched the old man! I never—never—never . . ." He retreated from them and began to glare very hopelessly about the room . . . to Miss Mansfield, to the window (against which stood the sorrowful, terrible attorney), to the door behind which was the Vine Street household.
No way out. Thoughts—such as they were—whirled in his head and made him feel sick. The blow that had fallen was inexplicable, frightful, crushing. He crept to Mr. Billing. Stared up at him very piteously.
"You—you was wrong, Mister Billing! For Gawd's sake, tell 'em! For you're a-killing me!"
But the attorney shook his handsome head.
"Not wrong, Smith. I saw. I know."
"Then damn you!" shouted Smith and flew to the Mansfields— blind father and tragic daughter.
"Miss! You knows me! I never done it! Swear on the Scriptures! Swear! Swear! You believe me, Miss Mansfield? _Please_ —"
In an inward agony Miss Mansfield stared down at Smith . . . and then to the sad but certain attorney—who seemed to have no reason in the world to lie. Maybe she remembered the Smith who'd first come to her—and tried to rob her blind father's study? Maybe she thought the boy's fall was a punishment for her own pride in imagining she'd redeemed him? Who can tell what went on in her unhappy soul!
"Oh, Smith!" she whispered, and turned away.
"Then damn you, too! You Bedlam-mad saint!" wept Smith helplessly, and bent down, crouching, at the magistrate's feet: his old blind justice . . . his mole-in-the-hole.
"Mister Mansfield! You believe me. I know it. I can see it in your—your . . . You know me—and I know you. You know I never done him in!"
But the magistrate—to whom justice was the only fixed thing in a dark, uncertain world—said nothing. He was casting out of his heart and mind everything save the attorney's measured words and the urchin's frantic denials. Word against word.
"Mister Mansfield!" whispered Smith, staring up and seeing his own face distortedly reflected in the blind man's black spectacles. "You _must_ believe! It wasn't me! It was them two men in brown and—"
"—Two men in brown?"
"Yes! Yes! And—"
"—You saw them kill him?"
"I—I—"
"Yet you told me once you'd never seen Mister Field!"
Too late! Smith realized he'd ruined himself! Now he was done for.
The blind man sighed like the winter wind.
"So . . . so . . . it was you who killed him."
The world fell away, and Smith, still crouching on the floor and watching the blind man's lips, felt as lonely, bitter and forlorn as if he were already on the gallows. Softly, the blind man went on:
"Which hand did you use, Smith? Was it the one you gave me that night we met? Was it that same, small, helping hand? Tell me, Smith! Don't be ashamed—for didn't I say to you that devils and angels are all one to me?"
"Voices in the night!" muttered Smith, despairingly. "We're all voices in the night to you—you poor old blind fool!"
"You will be committed to prison to await your trial."
"Trial? What d'you want to try me for? Might as well do me in now. What's one voice less in your noisy night, Mister Magistrate Mansfield? You'll never see me face when I'm nubbed. Nothing'll haunt you! You done right, you have! All I 'ope is—fer your sake and mine—that if you goes to heaven, then I goes to hell! For I wouldn't want you to clap even dead eyes on me!"
"Smith—"
"I never done it, Mister Mansfield."
"You'll be tried—"
"—And nubbed!"
"God have mercy on your soul!"
"Not if He's a blind old gent like you!"
"Smith—"
But Smith did not say another word. He shook his head with an air of grimness and despair. He had retired a great way within himself and whatever he found there seemed to absorb him entirely.
He was much mishandled as he was bundled into the coach, for the Vine Street household were very bitter and outraged by the monstrousness of Smith. Even those who, but an hour before, had decided once and for all that there was much goodness in him and had vowed never again to judge by appearances—even they thrust bleak and savage faces close to his, to let him know what the world now thought.
There was a good deal of treading on his feet and jerking of his clothes. Two of his bright buttons were torn off and the side of his face was bruised. But all he did was to shake his head endlessly . . . even to the one kindly face that managed to push its way in among all the anger and contempt to look at him through the coach window. It was Meg, the scullery maid. Her eyes were as large and round and wet as Margate oysters.
"I'll come and see you, dear. I'll bring you something nourishing. Don't fret, little Smith. Meg won't forget you, dear!"
In the general commotion something had been forgotten, or would have been but for the scrupulous attorney.
"Wait! Wait!" he shouted from the window. "The warrant!"
The warrant was sworn and witnessed.
"I'll take it down, sir."
The magistrate nodded, wearily.
"And I'll go with him to the jail."
"There's no need, Billing. There's no need for you to endure any more."
"I'll go, sir. It—it's the least I can do. Let the wretched child have some company on his journey. I'll see him decently lodged."
Miss Mansfield raised her eyes to Mr. Billing. Their look much moved him.
"We thank you, sir, for this—kindness." She sighed. "I blame myself for this. It was I who encouraged the boy. My father was not a party to it. But he was too kind to urge his better judgment. And now—and now—" She spread out her hands and shook her head. Then she seemed to recover herself somewhat and frowned in a semblance of her old manner. "Papa! You have a donkey for a daughter! A sentimental Mister foolish donkey! So we must be thankful for Mister Billing who's proved himself the best and truest of friends!" She curtsied. "Your servant, sir. Your very humble servant!"
The coach was waiting, much scraped from a more than ordinary collision with the uneven arch. Within crouched Smith, wiping from his face what the coachman had spat in it.
"To Newgate!" ordered the attorney, and joined his victim.
The coach moved off and, for a little way, the two occupants stared at each other: the one, incredulously—the other, calmly. Then, when the wheels had settled down to a steady, loud rattle, Mr. Billing leaned forward.
The skin round his eyes puckered somewhat—as if to suggest a smile. But his eyes were still like stone.
"Give it to me, boy."
Dully, Smith began to comprehend. He stared back at the attorney with violent hatred.
"For God's sake, boy! There's not much time! Give it to me— the paper you stole from the old man. Let me have it—and you can go."
"I ain't got it."
"And I know you have!"
"Search me—or are you afraid of being bit? For I'm a venomous little snake, I am!"
The attorney looked at the boy sharply; then withdrew the hand he'd held out. He shook his head with a curious air of gentleness.
"All right, lad—I believe you. What was in it?"
"Don't know."
"Then—where is it?"
"Don't know."
"Don't your life mean a fig to you?"
"Don't know."
Mr. Billing compressed his lips, then shook his head again with the same strange gentleness as before. He sighed.
"You're foolish, young man. I promise I'll help you, but you must tell me. It's your only chance. All right—all right! Keep silent now, if you must. I'll understand. But believe me, young Smith, I'm your truest friend! And soon you'll come to see it. Not today, nor even tonight—but tomorrow, maybe. I'll visit you, boy—and we'll talk again. Lay our cards on the table, eh? And then—and then, who knows, but we may be friends? You and me, Smith. Don't look so despairing, son. I'm not a villain. It's this vile world we live in, boy!"
But Smith continued to look despairing; the blow that had befallen him was more terrible, even, than the attorney guessed at. The document was lost and, though at last he could have read it, it was further away from him now than ever it had been since he'd picked Mr. Field's pocket. It had brought him nothing but disaster, but it seemed his life depended on it. He hated it; he dreaded it; yet it was as though he'd sold his soul for it.
"Newgate Jail, sir!" shouted the coachman, grimly.
Mr. Billing sighed—and Smith groaned . . . while the birds on Old Bailey and St. Paul's screeched out in high triumph:
"Jug him! Jug—jug—jug him!"
At last, they were about to be obliged.
## 10
THERE LAY IN NEWGATE a very famous felon whose days were drawing to a close. Indeed, on this Wednesday, there was less than a fortnight's life left in him; on Tuesday, January twenty-third, Dick Mulrone was to be taken out and hanged. A great many petitions had been got up to save him, but none had succeeded, and no one in his heart of hearts was truly sorry, for the death of a hero (even though he was a murderous ruffian) was a vastly romantic thing.
From morning to night there was a press of carriages outside the jail—for Mr. Mulrone had more friends and admirers than he knew what to do with. They came to see him, to talk with him, even to drink with him, and then go away and brood on the frailty of human life (Mr. Mulrone's, not their own).
Even great ladies came and went—their huge skirts swinging and pealing down the doleful passages like so many brocaded bells, tolling:
_What a pity. What a shame. Dick's to die on Tuesday week. What a pity. What a shame. Poor Mr. Mulrone_.
So it was that Smith, and his bitterness and bewilderment with all the world, dropped into Newgate with no more stir than a driblet of spittle into the Fleet Ditch. True, the jailer at the lodge had been surprised when he'd discovered that the undersized object in livery was Smith.
"Not old Smith?" he'd said, with a shrug and a grin. "Not grubby little Smith? Thieving Smith, Smith o' the doorways and corners? Smith o' the stinking Red Lion?"
Then he'd thrust his reeking, bristly face close and remarked on Smith's cleanliness and said he'd never suspected his features were so human.
"But washing ain't exackly been profitable, eh? For yore dirt, Smith, hid a multitude o' sins and now them sins is exposed to the view, so here you are, me lad! Jailed, jugged and bottled—as we say in the trade!"
But when he learned the charge was murder, he withdrew somewhat and said reproachfully: "Ah now, Smith—that's bad! Poor Miss Fanny and Miss Bridget. When they comes to alter them clothes—why, they'll wash 'em with their tears!"
Smith was lodged in the Stone Hall, but was spared fetters on account of Mr. Billing's having paid the jailer the necessary dues; which charitable act had been accompanied by a whispered, "Don't take it too hard, lad!" and a look as deep as the ocean. Then the Stone Hall was locked and Smith was, for the first time, a resident in it and not a visitor. Which was a dark and lonely time for him . . .
Though he'd been shut in the Stone Hall as a kindness—there being worse places in the jail where he might fairly have been lodged—he dreaded meeting with old acquaintances now his circumstances were so come down. He shrank from Mr. Palmer and his friends, for he remembered, burningly, that he'd last departed from them with some defiance, being on his way up in the world. Mercifully, he was spared Mr. Palmer's sneers and scorn. The gentleman was otherwise engaged. Indeed, all the superior debtors were, at that time, too full of Dick Mulrone's grand visitors to spare a glance for the dismal, fearful, pallid child who crept from corner to corner like a persecuted ghost.
The only soul to pay him any heed had been an old man who'd not seen daylight for fifteen years. This queer old fettered bird slept in the fireplace all the year round, save on Christmas Day when the fire was lit (when with much good-natured laughter they shoveled him out), and had come to resemble a dusty ember.
He beckoned Smith over with four or five sharp gestures and offered to share his strange nest. Salubrious, he said it was, owing to a good down draft from the chimney. With a clank of his fetters, he pointed upward to the ragged black hole and declared that sometimes a star might be seen, twinkling away like it was sat on Newgate's roof.
"It ain't so bad, little sparrow. You gets used to it. Though we never sees the sun, we never gets doused by the rain, neither! And it's a comfort to know you're in the worst place in the world . . . so you've nought more to fret and slave about to keep yourself from falling lower. For you've arrived!"
Then he settled back on his haunches and appeared to doze off, leaving Smith to stare up into the darkness. From time to time the old man—now sunk into a nesting coil—would twitch and jerk in a curious fashion, bringing his chained wrists together and thumping them down as if on a hated head. This done, he'd sigh and settle down once more into a contented sleep . . . till the next time.
Smith shivered and wondered if the old man, too, had his Billing and Mansfields to plague his very sleep. Smith had come to hate the Mansfields more, even, than he hated Mr. Billing. Once he'd admired and even loved them. He'd respected them and trusted them. He had, so to speak, made great exports from his heart towards them and had reasonably expected some sort of return. But at the first squall, they'd defaulted—bankrupted Smith—and left him in a state of blind rebellion. If ever Mr. Billing was able to get him out of the jail, Smith would make it his business to take a good revenge on the saints of Vine Street.
This resolution, in part, calmed him, though the mystery that clung about Mr. Billing, the document and—worst of all—about the unseen man with the limp, remained as dark and menacing as ever.
Next day, at about ten o'clock in the morning, Smith had visitors: Miss Bridget and Miss Fanny. He was both pleased and surprised. How had they learned so soon! Miss Bridget sighed bitterly, and remarked that bad news travels quick; while it took three weeks to learn that Smith was going up in the world, it took but the same number of hours to discover he was come down.
"And a common jailer had to tell us! Oh! The shame of it! The degradation!"
Dismally, Smith picked at his brass buttons and neat coat.
"Fine clothes and a clean face are but the trappings of shame," went on Miss Bridget, with furious sorrow, "when the child what has them is so degradingly jugged. Oh!"
"I never done it!" said Smith. "You know I never done it."
"You're here, ain't you?" said Miss Bridget unhappily. "That speaks volumes, don't it? You done something!"
"I was wrongly accused! Victimized!"
Said Miss Fanny: "Innocence is no excuse in the eyes of the Law, Smut dear. _That_ much your sisters know!"
They stared at him angrily and tragically, while he looked back with as much of defiance as he could manage; then Miss Fanny, as was her nature, thought of a brighter side. She sighed and poked at her remarkable hat (for whenever the sisters came out of their cellar, they dressed very grandly indeed—as an advertisement of their taste and skill).
"Leastways, 'tis lucky you picked on such a time to get nabbed, sweet. For with dear Dick Mulrone in residence the tone goes up, don't it! My, but there's fashion and elegance coming and going. Don't you think, Brid, 'twill do our Smut good to be mixing with such gentility? As I always said, 'tis an ill wind that don't blow the silver lining out of the dreariest cloud!"
She sipped genteelly at her gin—they were in the taproom— and made a face. Miss Bridget, who was drinking ale, put down her pot and looked at her sister scornfully.
"Much good his gentility will do him when that disgusting Mister Jones has done with him! It's his clothes that'll be coming down our steps with no boy inside of them, Fanny. And have you thought, sister, what it'll cost to have possession of him for to bury him proper and decent? Or would you have him be took off to Surgeons' Hall to be bottled for all the world to jeer at?"
Miss Fanny shivered and shook her head; then she murmured: "Oh, Smut, dear—if only you'd given up the dockiment when Lord Tom asked, then there'd be no Surgeons' Hall, nor Mister Jones—nor even them two fierce gents in brown—"
"Did they come back, then?" muttered Smith, coming out of his pint pot of ale, where he'd been hiding his face while his sisters disposed of his remains.
Yes, they'd come back . . . and back again. They'd haunted the Red Lion for several days. A terrible pair with eyes like burning coals . . . though the taller of them (said Miss Fanny) might have been more presentable if he'd been on the snaffling lay instead of on the sneaking, throat-slitting budge . . .
Here, Miss Bridget remarked that Miss Fanny's language was as bad as her low-class friend's. To which Miss Fanny said gently that she liked to find good in everyone and that, had it not been for dear Lord Tom, the villains in brown might still have been there.
"He took them on one side, Smut, and spoke to them so fierce, that they've never been back since that moment!"
Then Miss Fanny went off into a melancholy memory of how cheered they'd been to get the good news. Which had the effect of disheartening Smith into miserable tears.
Round about them the dregs of the Town ebbed and shuffled and flowed in ever-changing groups and pairs, sometimes eyeing Smith and his visitors with sneering curiosity, but more often discussing the latest news of doomed Mulrone.
Smith's fireplace companion alone seemed to keep his interest; he crouched but two yards off, with his head on one side and his old, bleared eyes quite sharp—like an ancient parrot. Contrary to her usual habit, Miss Fanny saw no good in him at all, but shuddered to the depths of her soul whenever his old, old eyes caught hers.
At length, to Smith's great pleasure and pride, Lord Tom joined them. He'd come from paying his respects to his old comrade-in-arms, Dick Mulrone. He wore a melancholy, romantic air like a new green cloak and seemed to swirl it from the tips of his ragged eyelashes to the ends of his powder-stained fingers.
"Well, Smut, me lad! Alas, it seems you've forestalled me! Not lost, but gone before, eh?" He sighed, "Oh, me boy! You go in good company: the best i' the world. For, though I'm a Finchley Common man and poor Dick's a Hounslow Heath boy, I give him best! The grandest of the roisterers! The gayest, dashingest, noblest of us all! He's in good spirits, lad. Ha-ha! The best! For he's drunk as a lord!"
"Disgusting!" muttered Miss Bridget and drew her discreet finery as close to her person as her hoops allowed. Lord Tom sat back with a toby-sized sigh and his glittering eyes roamed the stinking, shadowy, shuffling room with a touch of compassion—or was it only dread?
Smith looked very piteously from his sisters to his grand friend, and the world seemed—even in the Stone Hall—too fair a place to be leaving after so few years in it. Suddenly, Lord Tom's eyes flickered—as if some distant shade had provoked a thought. He bent forward to his small friend.
"But we'll see, me fine lad! Yes, we'll see! While there's life, there's hope—as we say on the lay. Maybe Mister Jones won't have you yet awhile? Maybe Lord Tom can help?"
Smith, though not convinced, was sensible of Lord Tom's aim to be cheerful. He looked up with a mournful smile.
"How, Lord Tom?"
"That document, young fellow! D'you have it still?"
"N-not with me, Lord Tom."
The highwayman looked doubtful—then brightened again.
"But d'you know where it lies?"
"That I do, Lord Tom!"
"And, given certain circumstances—such as you might know best—could you lay your hands on the aforementioned property?"
"That I could, Lord Tom!"
"And would you, me boy?"
"That I would, Lord Tom! With all me heart!"
"Then we'll see, me bright young heart. Dark though these matters be, while Lord Tom's about there's yet a ray of light."
Lord Tom spread out his strong arms to escort Miss Fanny and Miss Bridget away. One arm was took but the other was left like an empty bracket: Miss Bridget had no need of support. She fidgeted with her hands and then, with a strange timidity, stretched out and fleetingly touched Smith's sunken head.
"Be back tomorrow, you—you felonious child! Just remember . . . though you be . . . not so good as you ought . . . you ain't forgot, dear. Fan and me'll be back!"
When Smith raised his head they were gone, but on the table beside his empty pot was a guinea. Which one had left it? Smith scratched his head—and looked to the old man who seemed to have gone off into a dozy brood. The old man yawned and his eyes flickered.
"Ah! Me sparrow. That would be telling, wouldn't it? Which one cares a guinea's worth? The pigeon? The starling? Or that seedy hawk? He-he! It's worse than not knowing who's done you an injury—not knowing who's done you a kindness. It's horrible not knowing who to thank!"
But before Smith could abuse the old man, another visitor came quickly towards him. He and Smith's earlier visitors must have crossed paths without knowing it. It was Mr. Billing.
He wore black, which gave his complexion an oddly high, artificial air. The old man looked at him uneasily and then clanked farther off—as if anticipating the attorney's wish. He turned his bony head and seemed to absorb himself in a corner.
"Well, lad," murmured Mr. Billing, sitting down and fingering the guinea idly. "As you see, I've not forgot you."
"No, Mister Billing," muttered Smith, watching his money being scratched at by a neatly polished claw, "I don't suppose you 'ave. And I've not forgot you, Mister lying Billing—Mister murdering Billing. Not till Mister Jones turns me off up the road will I forget you! And if there's sich a thing as ghosts, Mister conniving Billing, there'll be a screaming, shrieking ghost awaiting you for every night of your life when you goes to bed!"
The attorney looked momentarily taken aback by the force of Smith's gloomy hate. Was it possible he hadn't expected it?
"I—I'm not a bad lot, y'know. I live in the world, so to speak . . . and can't help being of it. Take me all in all, I'm no worse than anyone else. Believe me, young man, you'll come to see that! Life's a race for rats . . . and it's Devil take the hindmost, the foremost— _and_ the one in the middle. We're all rats, Smith—and it's eat or be eaten. Blame nature, if you like—but don't blame me!"
Having delivered himself of this, Mr. Billing contrived to look oddly wistful—as if he wished the world were constituted otherwise and he might then be as honorable a man as could be met with in a month of Sundays.
Smith looked up at him dubiously—but couldn't help observing that, no matter what melancholy sincerity there was in the attorney's face, his fingers continued to play with the guinea like a cat with a fledgling bird.
"All right, then," sighed Mr. Billing at length, administering a final tap to the coin and blinking his stony eyes. "Don't trust me. I don't blame you. No! If I was in your situation, I suppose I'd be just as suspicious. Good God! It's human nature! But I'll tell you here and now, my friend (and I _do_ think of you as my friend, Smith . . . I like you, you know), I'll have you know I've saved your life!"
"By having me nubbed?" asked Smith, much bewildered by the talkative attorney. Mr. Billing smiled playfully and shook his head.
"They knew you were in Vine Street, Smith."
"Who did?"
"The two men in brown. And they'd have come to murder you if I'd done nothing and left you there."
"Ain't they your friends, then, Mister Billing?"
The attorney looked about him quickly—then bent forward so's his red lips were close to Smith's dusty ear and his sharp moustache pricked and scraped almost painfully.
"Listen, friend," he whispered. "I'll lay my cards on the table. Open and aboveboard. I'll not lie to you—for I like you. We're two of a kind, Smith, you and me. Men who know what's what in the world. Eyes open, chins up—and outface the Devil!"
Despite himself, Smith felt flattered, for he was but twelve and small, while Mr. Billing was a grown man . . . He began to think less harshly of Mr. Billing. A rogue he might be, but at least he was being an open one. He did indeed lay his cards on the table— and a very grubby pack they were! Though, as Mr. Billing himself pointed out with a wry laugh, all cards get soiled when you play with 'em!
Yes, indeed, Mr. Billing and the two men in brown had once been concerned with each other . . .
"Did they ' _ave_ to kill the old man?" muttered Smith dismally. "Were it necessary?"
The attorney shrugged his shoulders.
"Ask Mister Black, my friend."
Smith shivered, and once more his blood was uncannily chilled.
"W-was he the _other_ one? The one I heard? The one with the limp?"
"More than a limp, Smith. A wooden leg. Very soft-spoken man. Very devilish. I don't think I'd like to meet with Mister Black on a dark night!"
The attorney paused and looked uneasily about him, as if he expected soft-spoken Mr. Black to limp out of a shadow and knife him where he sat.
"Right, my lad! I'll lay my cards on the table . . ." (Here, Smith wondered, bemusedly, whether this was the same pack or a second one.)
"That document's worth money. A vast deal of money. Enough for you and me and the chimney-sweep down the road! I mean our friend, Mister Black. For I tell you, young man, I see no way of keeping him out of it. None! He's got the pair of us, Smith! We're the little running rats—and he's the gobbling Devil! If only, Smith—ah, if only—"
"If only what, Mister Billing?"
"You and me . . . just you and me . . . Where did you leave the document?"
"In—" began Smith; then something distracted him. The fettered old man. Was he having a fit? He was banging his chained wrists down on the floor.
"Where, Smith? Where?"
But Smith had suddenly thought more deeply.
"Lorst me memory, Mister Billing."
"What d'you mean?"
"Strain of waiting to be nubbed, Mister Billing. Can't remember a thing. Leastways, not while I'm 'ere."
"Don't you trust me, friend?"
Smith stared into the attorney's reproachful face and slowly shook his head.
"No, Mister Billing. I've had enough of trust to last the rest of me life."
A dreadful bitterness had come back into Smith's small pointed face, making it seem as old as the hills. Mr. Billing's smooth cheeks seemed to pale somewhat. He murmured something about Smith "sleeping on it" and that he'd see him tomorrow. Then he stood up and began to move away, trying to hold Smith's eyes till the shuffling ragbag of Newgate inhabitants got between him and his prey.
For long minutes Smith stared after him, not moving till he was taken up with the sounds of a commotion that seemed to be flowing through the prison's veins. A rumor: Dick Mulrone had been pardoned! But, even before that rumor had gone its rounds, its contradiction was already at its heels. No pardon. Poor Dick Mulrone's prospects were like a wave in the sea—forever followed by its trough. Twelve more days remained to him and Mr. Jones, being Welsh and tuneful and fanciful, had already begun his Tyburn Carol:
" _On the first day of counting_
_My true love sent to me_ ,
_A felon in an elm tree_."
"That's my boy!" wheezed the old man, recovered from his fit. "Voice like a blooming nightingale!"
## 11
THEY SAY THE DEVIL is a bald man with spectacles, but Smith thought of him as being rosy-cheeked, with a prosperous moustache and a shrewd sense of a bargain when he saw one.
In his first nights in Newgate Smith dreamed many times of the Devil and what terms he might get for his soul. He had long conversations with him in which the Devil offered him escape, vengeance on the Mansfields, and enough money for himself, Mr. Billing _and_ the chimney-sweep down the road—and all for a little future frying.
"I like you, Smith," the Devil murmured. "We're both men of the world, and I'm partial to you. Particularly fried."
Which prospect didn't seem as horrible as it might have done, for nights in the Stone Hall were that dismal and cold that the thought of any fire—even Hell's—was agreeable. Also, these nights were unnaturally long and hard to sleep in. There were continual mutterings and mumblings and sudden cryings out. There was the clinking of leg-irons which sounded—when it was regular—like an endless chain being winched into some deep pit. While from far off—from that part of the jail that was called The Castle, where wealthy felons and prisoners of State paid high money for their lodging—came the faint sounds of singing and good cheer as Dick Mulrone was swigged and swilled on his way to his end.
" _On the fourth day of counting_
_My true love sent to me_ —
_Four sextons digging_ ,
_Three parsons praying_ ,
_Two horses drawing_ ,
_And a felon in an elm tree_."
On which, Smith's ancient fireplace companion would moan and wheeze and finally wake up with a "That's my boy!" and jingle into a sitting position from which he'd watch Smith with deceiving bright eyes.
"Looking for the Newgate star?" he'd begin, for Smith usually lay with his eyes wide open and fixed on the ragged black hole above.
Then the old man would mumble and mutter about Smith's visitors and what they'd had to say. He missed nothing and it seemed, at times, as if pecking up scraps of other folks' business was the only thing that kept him alive.
Of all Smith's visitors he was most inquisitive about Mr. Billing, whom he regarded as a "real caution of a gent," and "one to be handled with the tongs."
Mr. Billing had come to see Smith each day, sometimes only for minutes, but at other times for an hour or more. Once he met Miss Bridget and Miss Fanny and exchanged the briefest of courtesies with them, then left almost directly, saying he'd be out of place in family discussions. Miss Fanny was much impressed by him and even Miss Bridget had to admit he was "quite gentlemanly to the look." All of which gave Smith a certain gloomy pride—though he never admitted to more than "legal business" between himself and the visiting attorney and so left his sisters most respectfully puzzled. But no matter whether Mr. Billing stayed long or short, he contrived to strengthen his acquaintance with Smith by unexpected touches of humor and warmth.
He scarce ever referred to the document again for it was as plain as a pikestaff there'd be no escape without it. Once or twice he spoke of Mr. Black, but it was only to say that, thank God, that evil man had not shown himself. Also, he begged Smith to be on his guard against such a visitor, though he doubted if Mr. Black would dare to show his face in Newgate. He hinted also of "a departure from this place to pastures new . . . which was being thought of, never fear! Was the other matter, likewise in hand?" To which Smith had nodded very gloomily indeed.
This sadness of his had been carefully observed by the ancient eavesdropper who taxed Smith with it that night.
"You ain't got it, have you!" he said triumphantly.
"Got what?"
"What he wants. So you'll have to stay!" He looked pleased as Punch at the thought of Smith being his companion forever.
"You mind yer own business!" muttered Smith savagely, and glared the old man's beam off his face.
"Ain't got none to mind," said the old man forlornly, and Smith relented somewhat and explained dismally: "If I stays, they'll nub me!"
But the old man seemed not to have heard him for he stared vacantly into the air for several minutes, then slowly closed up his eyes and went to sleep still sitting, and leaving Smith to worry himself into a state of sick desperation.
His trial was already fixed: January twenty-third, the very day they were nubbing Dick Mulrone. "Swing out the old, swing in the new," so to speak.
Smith came to thinking his fate and Mr. Mulrone's were somehow linked and if the highwayman perished, then he'd not be long after. Eight more days had Dick Mulrone. How many had Smith?
The document! The cursed document! Furiously, he shut his eyes and tried to picture it, hoping his new skill in reading would reveal—from his mind's eye—what Mr. Billing wanted to know. But, alas, he could make no more of it now than when he'd looked at it in his darkest ignorance. His mind's eye showed him nothing but a spidery jumble. Not having understood what he'd seen, he'd not known what to remember.
He wondered if Miss Mansfield had come upon the document yet—and if it had meant anything to her. He sweated with terror at the thought of her giving it to the attorney for nothing.
"Oh Gawd!" whispered Smith, staring up into the blackness of the chimney as if for an answer. "Why did the old gent have to stuff his pockets with sich deadly papers? What right 'ad 'e to go stumping through the streets, 'eavy with the Devil's literature for to tempt the likes of me with?"
He shook his head and groaned and groaned at the misery of his lot—and wondered if he'd be hanged without ever discovering what he was being hanged for.
Smith's hopes were low. Only one held out any promise: Meg, the scullery maid from Vine Street. And then, at last, she came.
She'd kept her word even though a heavy fall of snow had begun during the night and was not yet done with. Her shawl and bonnet were grandly dappled with it and her nose had been whipped by the wind to a strawberry . . . but she'd brought Smith some veal pie, sausage and white bread. Also two shirts he'd left behind. She'd have come earlier—but she'd been that afraid of having her heart broke, she'd not dared leave the kitchen.
"You pore thing," she said, giving him the bundle. "Oh, you pore thing!" She gazed at him sadly. "You've grown smaller and wizeneder. You needs feeding up, and—not meaning to be personal, dear—you needs another good wash!"
Smith shuddered at the memory and began to unwrap his bundle while Meg looked about her at the skinny, blotched and sadly cunning faces that haunted the Stone Hall.
"Cleverness?" she sniffed. "Look where it gets you! I'll wager there's enough cleverness here to sink London Bridge! Brains? Give you a farthing for 'em!"
Then she settled down with a great commotion of her bonnet and shawl and began to talk of the changes for the worse in Vine Street since Smith had gone. Mr. Mansfield, it seemed, hardly had a civil word for anybody and the mistress was a regular demon, finding fault where there was none . . . which Meg considered was a demon's chief office. Even handsome Mr. Billing wasn't particularly welcome for, try as he might to be cheerful of an evening, the talk always came back to Smith; and there was an end of all cheerfulness. Meg said this with some satisfaction, as if it ought to've been a real comfort to Smith to learn he was the cause of misery. But Smith nodded and smiled and bided his time. Then, at last, through all the byways of her conversation, Meg came back to "You pore thing!" with the sigh of someone who's been the long way round.
Smith said: "They're a-going to hang me, Meg."
"Oh, you pore thing!"
"There's but one soul who can save me, Meg."
"Ah! The master!"
"No, Meg. You!"
Meg looked astonished, fidgeted with the fringe of her shawl, then slowly shook her head with an air of great sadness.
"If heart can save you, child—then it's done. But this is a wicked world of cleverness . . ."
"It's heart I need, Meg—for it's cleverness what put me 'ere!"
Meg nodded deeply. That was no less than the truth.
"Say on, little one."
So Smith bent close and began to mutter urgently and pleadingly in Meg's large, gentle ear.
Did she recall the paper she'd found when he'd been washed? She nodded.
Was it still where she'd put it?
Most likely . . . most likely, for it had been deep in a drawer.
Could she get at it?
Most likely—
_Would_ she get at it—for Smith?
She opened her eyes in alarm. "Why, child, it's the master's!"
"No! It was mine! And it's the only thing that'll save me."
"I—I couldn't steal from the master."
"But it was mine—"
"It's all a nasty piece of cleverness, child! You'd be best off without it! Believe Meg!"
"Meg—Meg! You're a-hanging me! True as we're 'ere! If I don't get it, I'll be buried afore the spring! Meg—"
"Oh little one . . . Oh . . ."
The frightened Meg had begun to cry with the sudden misery of her dilemma. Her heart and conscience were much at odds. More than ever, she hated cleverness and all it brought in its sly train.
"I—I don't know what to do. Oh Lord! What would me mother have said?"
As she rocked herself to and fro, the old man began to rock himself likewise—and then croaked, amazingly like the parrot he so closely resembled: "Meg! Meg! Follow your 'eart, Meg!"
She looked startled—then stared with wet eyes at the disreputable old man. She nodded.
"That's her voice, child, and them's her words. She often talks to me now she's dead and gone. Sometimes out of old men, sometimes out of mischievous urchins—and sometimes out of heaps of potato peelings! And it's always, 'Follow your heart, Meg.' So I'll fetch you the paper, little Smith, and may it save yore poor neck from the shameful noose!"
Smith considered himself as good as out of the jail, and the change in him was as astonishing as it was abrupt. His spirits rose and he put on a confident, almost patronizing air. He strutted importantly about the dismal Stone Hall, even finding opportunities to practice his reading upon the scratched messages, prayers and rages that scarred the damp walls. God have mercy on me, he read out; and shrugged his shoulders. Next, he read, Jo loves Bess. He scratched his head and wondered why anybody should want to write such a thing on a prison wall. Then, God rot all lawyers. Hm! That was more like it!
His high spirits were bewildering to his sisters—who'd last seen him in the depths of gloom.
"Oh, Smut!" said Miss Fanny. "To see you in such spirits is better than a pint of gin, dear. Now, no matter what befalls, we'll know you went happy!"
"Oh, I'll be 'appy going!" said Smith, enigmatically; and Miss Bridget stared at him sadly, as if he was a lost soul.
But Mr. Billing understood. Maybe at first he wondered if Smith had the document already . . . for he'd arrived shortly after Meg had left. Not that it was really likely he'd seen her—there being such a stew in Newgate at that time, what with Mulrone's visitors and the bad weather—but he saw the bundle and smiled knowingly. Smith, seeing this look, divined its meaning. He shook his head and grinned.
"Not yet, Mister Billing. But it won't be long before the chimney-sweep down the road'll be situated to buy himself new brooms and a whole new chimney for his very own! If you take my meaning, Mister Billing."
Mr. Billing took his meaning.
"And it won't be long before a certain little bird flies out of its stone cage, eh lad?" He beamed and laid his hand on Smith's thin shoulder.
"How much better it is to put our cards on the table—play fair—and be friends. Oh, the world's not such a bad place after all—for the likes of you and me!"
This was on Sunday, January fifteen: a day remembered, if for no other reason than for the extraordinary violence and passion of its snowstorm. It was as if the Devil's cat had got among the angels and was scattering their feathers everywhere. There seemed no end to the snow . . .
## 12
THE SNOW CONTINUED to fall . . . sometimes in great whirling quantities, and sometimes—for half a day at a stretch—in idle, drifting flakes that wafted wearily down as if the air was filled with invisible obstructions, then added themselves imperceptibly to the general whiteness below.
The worn old streets were gone; the blackened roof-tiles were gone; the mournful chimneys and the dirty posts wore high white hats—and the houses themselves seemed to float, muffled, in a sea of white. Never, in all its life, had the Town looked so clean; it shamed the very sky, which was of a dirty, yellowish gray.
The business of the Town was slow and tedious: carriages and chairs crawled along where they supposed the streets to be like huge, tottery snails, bearing snow houses on their backs and leaving wet black trails to mark their passing. Even the nimble piemen capered silently, sometimes slipped and lost their smoking trays so that half a hundred hot pies burned into the snow and pitted it like a black pox.
Visitors to Newgate Jail were few and far between. Only the loving and hardy called. Dick Mulrone's friends were much diminished and it was said he grew scornful and sour and melancholy. Smith, waiting on Meg, grew uneasy; there was no snow inside of Newgate, so the traveling troubles of the world seemed as remote as the stars. Only his sisters and the ever-faithful Mr. Billing came to see him and, once in a while, Lord Tom. In these days Lord Tom spent a deal of time with his doomed colleague, whose room, being less crowded, offered more space for Lord Tom to be noticed and welcomed. After which, smelling strongly of wine and with a kind of swaggering stagger, the green-cloaked high toby would look in briefly on Smith and give him the news of "glorious Dick."
"He's hopes," said Lord Tom, with a mournful grin, "of the snow piling so high under the Tree that, when the cart drives off, he'll be left standing instead of the horrible swing!"
Smith nodded, and was not above being grateful for his friend's efforts to be companionable. Then his abstracted air returned as he tried hard to imagine what was preventing Meg.
There was now little time left; Thursday came and went without a sniff of her. Smith feared Mr. Billing would wax suspicious and impatient. But he never did and always contrived to remain amiable. Sometimes, though, Smith fancied he detected a curiously calculating air behind the attorney's good-will: as if he was not going to commit himself, heart and soul, till he knew the outcome of some other event. And it was on the Thursday that this abstraction of Mr. Billing's became most plain. He was almost agitated . . . but still cautious not to offend. When he went, he left a more than ordinarily puzzled Smith.
But on the Friday Mr. Billing came to Smith with a rueful and disarming smile which Smith returned with a look of such deep and earnest hope that stonier hearts than Mr. Billing's (if any there were) would have been melted by it. He shook his head and laughed and murmured something about "Smith's winning," and "friendship coming before all." Then he sat down and, to Smith's amazement, relief and delight, confided the plan for the escape.
Not long before, there'd been set up on Newgate's roof a great windmill with vanes a full twenty feet across. Its purpose was to purify the air. As it turned, it drew (by natural suction and skillful design), through tubes and tunnels joining into a middle shaft, much of the foul and pestilential vapors of the jail. So? The ventilators! The grated apertures in the walls. The narrow tunnels that led, through dark and angled ways, to the great shaft that rose up to the windmill on the roof. From which grimy eminence, it was but a hop, a jump and a scramble to the nestage of adjoining roofs.
With beating heart and glittering eyes, Smith listened as the attorney muttered rapidly on. Dipping his finger fastidiously in Smith's ale he drew on the tabletop a plan of the wards and halls of the jail alongside which the ventages ran. Very narrow were the lower tunnels—wide enough only to admit a thin child. But on the next floor they were somewhat more spacious and roughly bricked so's to afford finger- and toe-holds for "little birds to reach the sky."
Wider and wider grew these tunnels, till at last they came into the main shaft that rose to the windmill and the heavens. Upward, always upward, must the little bird go, else he'd find himself in another cage!
Mr. Billing carefully wiped his finger on his handkerchief and Smith stared at the shining lines and squares that were beginning to dry and lose their powerful meaning. But they were already well fixed in his mind. He nodded and looked up for the last question. When was he to go? Not yet. Why? The grating was not yet unlocked. The good offices of a certain gentleman (here, Mr. Billing looked about him quickly) were not yet bespoke. But, never fear, they would be. When? On the Tuesday. Why so long? Not so long, only four more days. But why not Monday? Ah! Tuesday would be a day of great commotion. Dick Mulrone would be setting forth. Jailers and turnkeys would be busied in keeping order—and too busy to notice a little bird fly out of its cage! Tuesday, at six o'clock, before Smith would have been moved to the sessions house for his trial. Tuesday: freedom day! Mr. Billing grinned: document day!
Smith's wavering spirits lifted and he stared long and hard at the ventilator grating that was let into the wall beside the fireplace. But even now it was impossible to rid himself of a thousand uncanny fears of disasters pouncing before the Tuesday. Yet Mr. Billing had been confident—and Mr. Billing was nobody's fool. All that remained, then, was the visit from Meg with the document. Surely she'd not fail him! Not Meg with her monstrous great heart!
She didn't fail him. Or, at least, not entirely. She came on the following day. Her shawl, bonnet, skirts and shoes were loaded with snow. She'd walked the whole way and the effort had made her stream, so that there was a general melting-ness about her. Her hair, eyebrows, nose and chin all seemed to be discharging water, which gave her red face a curiously dismayed air.
"A glass of gin, Meg?" said Smith anxiously, as she dripped into the tap-room.
She shivered and shook her head . . . and seemed unwilling to sit down. Suddenly, Smith—with a dreadful fear—saw that her dismay was more than snow deep. Her customarily round face was oval and her eyes were unnaturally red.
"Have you—have you got it, Meg?"
She stared at him in terrified sorrow—as if imploring him to hold his peace.
"Meg! Where is it?"
"Oh, child! Oh, little one! They'll hang you now for sure, and bury you afore the spring! Oh, you pore thing!"
"Meg! Where is it?"
"Heart weren't enough, little one. Horrible cleverness is all. Brains? Lord! I wish I had 'em!"
" _Where is it?_ "
She dabbed at her nose with her sleeve and her whole face grew veiled with fearful memories.
"On Thursday . . . yes, the Thursday, the master and mistress went out together; so I took me chance, little one, and crept like a mouse to the study . . ."
Smith, the first shock of dread spent, listened in a sick dismay. What had gone so grievously awry?
"I was in the very room, child—the very room—" She repeated herself, as if to prove her heart had ever been twice as strong as any circumstance. "—When I heard a noise, child, from upstairs. From upstairs where you used to sleep. Oh Lord, dear! I thought—I feared you'd lost patience and gone from the jail and come back on your own desperate account. I was worried half out of my mind! I thought of calling out to you . . . then I thought it'd frighten you off. So, quiet as a mouse, I crept out and went up them dreadful stairs. Sure enough, there was noise coming from your own dear room. But queer noise: scraping—dragging— pulling—panting . . . like it was being torn apart by dumb beasts. Lord! Lord! I was that frightened! I thought maybe a bear had got in!"
" _What was it, Meg?_ " whispered Smith—though maybe he had already guessed . . .
"I screamed, child! That I did! Screamed and shrieked till Vine Street echoed. I got a good pair of lungs, child—a good pair of lungs."
"And—then?"
"It must have scared 'em!"
"Who?"
"Two horrible men in brown! They burst out of the room in a terrible rage! I thought they'd kill me—but they rushed past me and down the stairs, then out through the front door like the wind o' Hell!"
"The Thursday? This was on—on the Thursday, Meg?"
Meg stared at him vaguely, wondering why the day should have mattered so much. But among all the wild and panic-stricken thoughts that had whirled through Smith's head, one had stuck fast. On the day following that Thursday (when the attorney had been so agitated), Mr. Billing had come to him with a rueful smile—a smile that Smith knew now was of disappointment. And he'd said Smith had won. Indeed, he'd won! The men in brown had failed.
"So there's no more hope, little one," said Meg at last, with the grandmother of all sighs.
"No more hope?"
Smith looked at her, bewildered—having missed the chief part of her bad news. With a groan she repeated it. The burglary had so alarmed Mr. Mansfield that he'd locked all his papers securely away. There was now no hope in the world of getting at them.
"Oh, child! They'll hang you now, and Meg, heart and all, won't be able to stop 'em! Why, child—you're a-smiling! Why, Smith, dear—you ain't down-hearted! Oh, God bless you, dear, for not breaking Meg's heart with your despairing. You'll go straight to heaven, Smith—no matter _what_ you done!"
Smith, in spite of the evil news, was smiling in the most strangely excited way; and when at last she went, promising that she'd try to do something, no matter what, to save him, he called loudly after her: "Thank you, Meg! Truly, thank you! You've saved me life!" Which was like Sunday bells in her ears!
Even the old man had been surprised, and he'd thought himself long past such sensations. But Smith, saying nothing, grinned most knowingly. Aggravated, the old man shuffled close beside him.
"You've not got it yet, have you?"
"No. I ain't. But nor has he!"
"So what are you grinning for? And why did you thank that sloppy baggage?"
"Because that lawyer's got ears as long as Watling Street—and I'd like him to think I'm pleased!"
The old man chuckled. No matter what the cause, he enjoyed folk being misled.
"He thought he'd have me for 'is dinner," went on Smith, his face darkening with contempt. "He thought I was that easy. Oh! That crafty lawyer, him!"
The old man grinned. He liked to hear of scoundrelly behavior. Very satisfying he found it.
"And his friends in brown! Wish I'd seen their faces! Wish I'd seen _his_ face when they told him what luck they'd had!"
The old man agreed. _He'd_ liked to have seen such a multiplication of dismay. He enjoyed dismay.
"And picture his oily face now—when 'e hears simple little Smith has just thanked Meg 'eartily! 'Tom Billing,' he'll say to himself, 'you got to help that lad. It stands to reason he's got the document already. Else why did he thank that sloppy baggage?' Oh yes! Picture 'is face!"
The old man pictured it and seemed to enjoy that most of all. The two of them—the old man not much bigger than Smith—sat grinning at each other across the mournful fireplace like a pair of goblin fire-dogs.
"Won't be long now," said the old man, jerking his head towards the ventilator; and Smith felt an odd pang of regret—even shame—that he'd be escaping and the old man would not. But the old man didn't seem to mind. Indeed, he seemed quite gay at the thought for, though there were many things he liked much better, he was quite partial to the idea of the occasional little bird flying off.
Not that there was any remarkable sympathy between these two strongly differing prisoners, or even any mysterious bond of friendship. There was nothing in common between them save the fireplace, and even there each maintained his own side and scowled pretty formidably if there was any encroachment by the other.
"What d'you want? A whole bleeding park?" the offended one would mutter; and the trespasser would sniff and move back again. Then there'd be silence between them for several minutes while they watched the fierce and dingy residents of the Stone Hall going about their endless, purposeless business.
God knows what the old man thought as he gazed at his eternal neighbors to whom each day was as a year (with but a single season) and yesterday was a thousand years gone and of no more account. He must have had some thoughts—for every man has thoughts, be they never so dark—but maybe they were too awkward for words, like the prints left by a bird in the sky.
Even Smith's thoughts were vague and shifting. The anticipation of escaping gave him both a superior feeling towards those who could not—and a queer affection. His time among them, he was firmly convinced, could now be counted in hours.
Then something happened on the Monday evening that frightened the wits out of him and filled those last hours with commotion and dread.
"Visitor!" croaked the old man, sharpishly. "Look lively! Visitor!"
Smith looked up—and was at once struck with astonishment and apprehension. The visitor was Miss Mansfield!
A terrible feeling that Mr. Billing had confided the plan to Miss Mansfield and she, in a righteous rage, had come to wreck it, chilled his heart. He could conceive of no other reason. His eyes glittered desperately.
"Smith!" cried Miss Mansfield, throwing back her hood and staring about her in horror and shame. "You've grown vastly dirty again!"
"Mister Jones won't mind—"
"Who's he?"
"The 'angman!"
Impulsively, Miss Mansfield knelt down and stretched out her arms (careless of her cloak, whose yellow lining flashed out, abrupt as a flower), and took Smith's shoulders.
"Keep off! Keep off!" he cried fearfully—with black memories of his last day in Vine Street and a feeling that Miss Mansfield was come on a worse errand than to tell him he was dirty. This feeling was exceedingly strong and set up a shivering through all his thin body.
Miss Mansfield scowled ferociously, and tried to blink away her tears. She turned to the old man who was watching with abiding interest.
"I—I would help him—"
"He don't need your help, ma'am."
"What d'you want with me? Keep off! Leave me alone! I hate you!" almost screeched Smith in his fright.
The pain that he was inflicting was out of all proportion to his small size. His revenge on the Saint of Vine Street—did he but know it—was complete indeed. The lady's face had so distraught and tormented an aspect that even the sneering watchers were struck by it. Though she'd come to the jail to tell Smith something, she could not overcome her own distress sufficiently to say more than: "Smith . . . child . . . I—I would help . . . Don't hate us, I beg of you! Smith—Smith—"
But Smith glared and glared, morbidly convinced that the mad daughter of the mad father was come as harbinger of doom.
Which, in a way, she was. Suddenly there was a disturbance at the other end of the hall. Turnkeys were shouting; the seething, irritable crowd was being pushed and chivied. It moved this way and that, till at last it parted and fell away somewhat savagely from a tremendous figure who'd been caught in its midst, despite the turnkeys who'd been beating at the felons and debtors and shouting:
"Blind man! Blind man! Make way—"
It was Mr. Mansfield, blind as night, helplessly upright, his black spectacles in the great gloom looking more than ever like deep holes in his head. The turnkeys pushed obstructions from his path and led him, with many an important scowl at the resentful crowd, towards the fireplace.
Miss Mansfield looked alarmed and angry. She'd left her father in the carriage; bade him not come in, said she'd accomplish all without interference or help . . . So why _had_ he come, with that strange, desperate look about his mouth that disturbed her violently?
"Daughter—"
"Yes, sir—"
The blind man nodded and seemed to stare at the wall, as if, even to his useless eyes, the horror, darkness, degradation and shame of the Stone Hall was a sight not to be endured.
"Is—he—here?"
"Yes, sir."
"Smith," said Mr. Mansfield, quietly. "Do you know what this is?"
He thrust his hand into his coat and drew out— _the document_!
A sound between a scream and a groan told Mr. Mansfield that Smith knew.
"Meg told us," murmured Miss Mansfield. "In tears, she came—poor soul! She was at her wits' end, and said it was the only thing that would save you . . ."
"Do you know what it is, Smith?"
" _No! No! Never seen it before!"_
"Look again. Look closely. Look hard."
Helplessly, Smith looked. Yellower and more stained than he remembered—smaller, even—but it was the document. Now he could read on the outside: _To Mr. Lennard. Billing and Lennard of Curtis Court, Godliman Street_.
Frantically his eyes strove to pierce the fold in the paper and read what was within, but in vain. He had a mad idea of snatching it. But where could he fly? Up the chimney?
"Never—seen—it—before!" he repeated, but his voice was harsh and unequal.
Mr. Mansfield put the paper away and Smith's eyes followed it, into the vital pocket where all was black as night.
"Mister Lennard is at Prickler's Hill. I'm taking this document to him, Smith."
"W-what's in it, then?"
"I—I do not know. It is for Mister Lennard. A dead man's wish, Smith. Binding. No arguing with it. It shall be delivered. Tomorrow."
"And let's hope and pray, Smith," said Miss Mansfield, still kneeling, "that it will indeed save you—"
"Tomorrow," went on Mr. Mansfield, "Mister Billing will apply for an adjournment of your trial. I have asked him—"
"Then _he_ knows?" This was meant for a whisper, but it came out very near a scream.
"He knows no more than I've told him. Why should he? This is Mister Lennard's affair—"
"He knows—he knows!" moaned Smith, now in blackest despair, for it seemed to him that the evil document was coming full circle. He knew for certain that blind Mr. Mansfield was as marked and doomed a soul as had been Mr. Field.
All Smith's hatred and feelings of revenge sank abruptly in a sea of pity. The two men in brown would waylay the magistrate and murder him. And so at last they'd have what they'd been paid to get; and maybe Mr. Black would thank them in his soft voice . . . In his mind's eye Smith could already see the look on Mr. Mansfield's face as his soul left his body; and it was the selfsame look he'd seen in Curtis Court.
"You blind old fool!" he wept furiously. "They'll kill you! You old madman! Blind, blind, blind right through you are!"
But Mr. Mansfield and his daughter were already moving, and the turnkeys were clearing their path. Men stared at the blind Justice hostilely, shook their fists at him, made threatening faces—and sometimes jeered. Someone managed to push his foot out so that the blind man staggered and nearly fell; but his daughter gripped hold on his arm and steadied him—in body, if not in spirit.
When they were gone, Smith looked dismally about for a certain fish-eyed jailer who, he had reason to believe, was the one who retailed everything to Mr. Billing and had most likely been paid to unlock the grating. His heart quickened. The man was nowhere to be seen. He had not been present. Was it still possible, then, that the escape would go forward? That the jailer would do what he'd been paid for without further reference to his employer? Or had Mr. Billing, knowing what he knew, already summoned him and grimly shaken his head? Scarce eighteen hours remained . . .
## 13
IT WAS A STRANGE NIGHT, much given over to restlessness and rumors about Dick Mulrone. Rumors that he'd nubbed himself to cheat Mr. Jones; rumors that he'd been reprieved and was dead drunk on that score; rumors that he'd changed clothes with a visitor and gone out as the Duchess of Newcastle; rumors that twenty of his roistering friends had broke in, armed with pistols, muskets and poniards, to whisk him back to the freedom of Hounslow Heath where coaches lumbered in their dozens, overripe for the plucking . . .
Then, between midnight and dawn, the easy voice of Mr. Jones, the hangman, put a stop to it all:
" _On the last day of counting_
_My true love sent to me:_
_Twelve jurors juggling_ ,
_Eleven clerks a-counting_
_Ten friends a-failing_ ,
_Nine dead men_ . . .
_Eight widows weeping_ ,
_Seven judges judging_ ,
_Six drummers drumming_ ,
_Five yards of rope_ . . .
_Four sextons digging_ ,
_Three parsons praying_ ,
_Two horses drawing_ —
_And a felon in an elm tree_."
"That's my boy!" mumbled the old man—and leaned over to dig his companion in the ribs. But Smith had at last gone to sleep, so the old man desisted and rocked himself to and fro, humming the tune of the Tyburn Carol as softly as a lullaby, and gently clinking his fetters in time, so that the tune and the jingling might have sounded like Christmas harness in a dreaming ear.
At a quarter to six—or thereabouts—the old man shook Smith and bade him be gone.
The Stone Hall was dark and quiet, still—as a consequence of the disturbed night. Probably no one was awake save the old man and the furtive boy.
"Up on me back!" breathed the old man and knelt so's Smith might mount on that bony eminence to reach the grating.
"What if it ain't unlocked?" whispered Smith, full of last minute dreads and alarms.
"It's been done?"
"When?"
"While you slept. I heard. I saw. Come, now—up! Up! Up!"
Smith paused. "D'you think you could come too?"
"Don't want to. This is me home. Got company."
Smith nodded. He shook the old man's hand.
"I'll not be seeing you more—"
"I hopes not! Up you go!"
Smith hoisted himself onto the old man's back, which was as hard and steady as a rock.
"Hope you gets a gentleman for the fireplace what suits—"
"That's my affair!"
"No offense—"
"None took. In you go, you scabby little sparrow!"
Smith had opened the grating. The air within was thick and damp and laden with evil smells. For a moment he thought the vent was too narrow even for him. Then he pushed with his feet against the old man's back and felt, first his shoulders, then his arms, elbows and hips scrape the rough stone walls.
"You're in!" he heard the old man whisper. "Best of luck—and watch out for—"
Smith never heard what he was to watch out for, as all sound behind him was lost in the eerie sighing of the prison's secret lungs.
This sighing was as regular as breathing itself—and a thousand times more foul for, high up on the roof, the windmill was motionless, under a muffling blockage of snow.
A hundred and fifty feet of rough, uncanny darkness, divided into three steep channels, lay between Smith and the last great shaft. At the juncture of each of these channels, once jagged but now smooth and somewhat slippery apertures were let in; these led to other parts of the jail and furnished Smith with foot- and fingerholds to heave himself round each sharp bend and continue his upward burrowing. That he _was_ moving upward, he knew chiefly by the direction of his own sweat which ran continually into his eyes . . . not that those organs were of much use, for the darkness was formidable and absolute.
"So what was I to watch out for?" he muttered, ironically. "Black rats? Black cats?"
The sound of his own voice cheered him . . . and henceforward he mocked his trembling spirits aloud: with a curious effect of which he had no knowledge. His mumbling, muttering tones traveled weirdly through devious passages and stony veins till they were wafted into the deepest and most dreadful parts of the jail.
A man in the Press-Room—on whom were weights past bearing—heard faintly:
"Come on, now, me boy! Give in? Not you, me sweeting! What's a bruised belly between friends? On with you! Up with you—to the waiting heavens!"
But other jailbirds in their remote cages heard, maybe, nothing so apt and heartening. Curses and abuse of the prison's scope and architecture came out of the various gratings—as if Newgate were alive to its own wretchedness and was at last complaining aloud. Then (in the King's Bench Ward), "Be off with you! You fat, wicked 'orror! What are you waiting for? Dinner? Be off or I'll bite your 'orrible 'ead off!"
Smith and a rat. He'd met it by a nest of vents, its eyes gleaming in some vague, wandering light. It had come from a deeper channel and now stopped, amazed to watch what it took to be a grand relation, passing bulkily by.
"Upways, downways, in me lady's chamber! Which way now? Lost! 'Up,' he said. But which way's up? Where's the sky? Which of these dismal ways is the one to 'eaven? Come, me old friend! Try this fair stinker! Feet first—as they says in the trade!"
This, heard in My Lady's Hold, caused much terror and consternation; but farther on the wandering voice (believed by some to be that of a stoned-up ghost) was not so gay. It complained horribly of bruises and swellings got from scrapes and pressures against the ragged, bulging walls. It complained of having taken a wrong turn and finding itself, baffled and helpless, staring through bars into a cage more desolate than the one that had been left. It seemed to be losing heart under the strain of an intolerable journey. So miserable did the voice become at this point, that those who heard it were moved almost to tears by a plight they had no notion of, and whispered: "Whatever you are—wherever you are—for God's sake cheer up—and the best of luck!"
Maybe this had reached its mark? At all events, nothing more was heard of the traveling voice, and the iron-barred vents were as silent as the grave.
What had happened? Smith had come into the last great shaft: the broad-ribbed, secret gullet that led to the windmill and the sky.
Bruised and much fouled from his journeying, he crouched in the last bend and stared triumphantly up. Fifteen feet above him hung the motionless vanes of the windmill, folded in snow. Beyond was the sky: gray and weighty and still dispensing its flakes which flickered down and down and down—even kissing Smith's upturned face.
A tremendous moment. Not even the Dean of St. Paul's had as fine a view to heaven, nor a more heartfelt gaze at the sky. Smith began to climb . . .
He stopped. There was an oddness about the lip of the shaft. A ragged irregularity, which seemed to be growing subtly. Two swellings . . .
A sudden gust of wind whipped a veil of snow across his vision; then it was gone and the two swellings were most marked.
What were they? Heads. Two men. A pair of hands reached down. Fingers twitched and beckoned . . .
In the sudden and terrible agony of his betrayal, Smith screamed aloud! Looking down upon him, waiting for him, grinning at him, were the two men in brown!
There came a second gust of wind, which performed a curious office. Or it might have been the effect of the amazed and horrified child's scream . . . for sudden noises of a certain pitch sometimes have the power of a giant's hand.
A quantity of snow shook and fell from the mechanism of the windmill, which now began to turn and draw up the air into the shaft, thus setting into motion all the stagnant, thick and heavy vapors that lay in the deep, stone veins of the jail. Up they came, blundering into the churning mill.
But this was not all. A second, more fearful circumstance attended. An uproar—as if the lid of Hell itself had been lifted—filled the shaft and shrieked and jabbered to the sky!
Together with the air, there had been sucked up from the gratings—through every portage and vent—the furious and savage voices of the jail's inhabitants. Groans from the Press-Room, curses from the Stone Hall, hard, high laughter from the Master Debtors, and shrieks and wild whisperings from holds and wards and cells unknown—all mingled together in a chorus of truly monstrous scope and dimensions.
Fearfully, the men in brown stared at one another. Then they recalled their purpose. They looked down and added their own curses to the dreadful torrent. The boy was gone!
Smith, choked, deafened and despairing, had let go his hold. Eight feet he'd thumped to the bottom of the shaft. Then, his force not spent, he'd slipped, squealing, down a hole of formidable steepness—a vent that led, God knew where!
Had Smith been brought up to the Church, he'd have had a prayer off pat—for he traveled at speed on what he was sure was his last journey. (But, if he'd been brought up to the Church, he'd most likely not have been falling down a ventilator in Newgate Jail!)
"Gawd!" he panted. "Watch out—for 'ere comes Smith!"
Then—from some seven feet above the floor, between the pulpit and the open pews of the prison chapel—shot out a dusty, dirty bundle of commotion that howled as it fell, picked itself up—and bolted directly for the door.
Smith was back in jail.
The chapel was empty; but outside its door was a regular hubbub. The last sermon had just been preached over Dick Mulrone. He was on his way to the hangman's cart. All of his friends, all of his admirers, all of his well-wishers had come to watch him—and now crowded the passages for a last pat on the back and a last sad wave.
The crowd was tremendous—more than enough to engulf the scurrying Smith. On all fours, he went among skirts and legs that were like a trampling forest.
"Got to get out! Got to get out!" he muttered—and butted and bit his way along. He came to a corner at the head of some stairs and was momentarily free—
"Smut!" shrieked a voice. "It's Smut!"
His sisters! Come to attend his trial; but had been first dragged by Lord Tom to see the last of the hero of Hounslow Heath. ("Give him a good send-off, m'dears. He'd have done as much for me.")
"Got to get out!" panted Smith, still on his hands and knees and glaring up at his family as though he was their faithful mongrel hound.
"Oh, Smut!" cried Miss Fanny. "You'll be took and ironed for this!"
"Quick!" whispered Miss Bridget, handsome in her Tuesday best. "Under my skirt, child! Pop underneath—and not a sound!"
Miss Bridget tipped her great hoop so's her skirt rose like a monstrous black bell about to chime against the strongly pantalooned clappers which were her legs. Smith looked briefly at his elder sister—and grinned. He darted forward and Miss Bridget dropped her skirts.
So began Smith's escape from Newgate Jail, not at all as he'd dreamed—nor certainly as had been planned for him—but rather a quiet, muffled exit through the great gate itself.
True, there were alarms on the way, and some discomforts. Smith found it hard to keep out of the way of Miss Bridget's feet—else _she_ found it hard to prevent herself booting her felonious brother as if for his sins.
Miss Fanny also gave cause for alarm by asking aloud if "little Smut was all right in his flannel nest?" till Miss Bridget was heard to declare aloud: "You are a foolish cow, Fan! Hold your tongue, for pity's sake!"
Then Lord Tom joined them (Smith would have known those sturdy feet anywhere) and Miss Fanny couldn't resist whispering: "We've got him safe and sound! You'll never guess where, Lord Tom! Not in a thousand years!"
But it seemed Miss Fanny ogled and stared and giggled so much at her sister's heaving skirt that Lord Tom guessed directly, but had the good sense to hold his peace and bid Miss Fanny to do likewise.
Then, at last, they were outside and beginning to walk away.
"Look! Look!" shrieked Miss Fanny, suddenly. "Oh, Brid! Look!"
She pointed. Miss Bridget paled. Lord Tom looked alarmed.
In the thick snow behind Miss Bridget were not only her own footprints, but the unmistakable hop and scamper marks of an extra pair of feet!
"We'll walk behind you, Brid," said Miss Fanny; and for the rest of that extraordinary journey, Miss Bridget had two of the most particular and devoted followers a lady could have wished for. They followed in all of her four footprints with a caution and respect most exemplary!
By the time they got to Turnmill Street it was hard on ten o'clock.
"Home, child!" whispered Miss Bridget—and raised her skirt a trifle to step across the familiar door of the Red Lion Tavern.
As she did so, there was a faint shouting and roaring that seemed to be coming from a long way off.
"What was that, Lord Tom?"
The highwayman sighed. "From Tyburn, m'dear. They've just nubbed grand Dick Mulrone! I'm the only one left, Fanny. When will it be my turn?"
## 14
IF EVER A MAN COULD TELL, to the nearest five minutes, how long it would take a particular coach, leaving a particular part of the Town and going north, to come to the edge of the Finchley Common, that man was Lord Tom. Not your fat rumbling trundler nor your light-slung gig, passing northward through the Town, was capable of keeping Lord Tom waiting upon his wild and lonely hunting ground. He knew their paces as well as his own and boasted famously that his prizes came, so to speak, by prompt appointment.
Indeed, it was said in the trade that Lord Tom might have made a better living by employing his genius in Town and auctioning his judgment for others to ride out for the "stand and deliver."
Not that he didn't ride well and shoot well, but it was sometimes said, by those who'd accompanied him, that his nature was too bold for so secret an undertaking and he was inclined to show courage when there was no call for it.
"Given the size of the coach—as you've described it—given this weather, given the crowds for Dick Mulrone this day, given the starting from Vine Street—your Mister Mansfield will take luncheon at the Queen's Head in Lamb's Conduit Fields and come upon the Common at half after four o'clock. 'Tis certain, Smut. Sure as we're in this cellar. Sure as my name's Lord Tom. At half after four. And at five—" He paused, his finger raised, like he was hailing a chair.
"At five, Lord Tom?"
"We'll have him!"
Miss Fanny looked at her friend admiringly, but Smith was yet doubtful.
"Ye-es, Lord Tom . . . if _someone else_ don't have him first!" Lord Tom sighed and scratched his cheek—then examined the hand he'd employed.
"D'you mean our two friends in brown?"
Smith shivered—and nodded.
Said Miss Fanny: "Lord Tom'll see them off, Smut. You'll see!"
And Lord Tom, with a mighty scowl, agreed.
"I'll blow blue daylight through 'em, Smut! There's never a man yet who's dared come 'tween Lord Tom and his lawful prize. You'll see 'em scamper, my lad!"
"And then—our dockiment, at last!"
"The document!" suddenly exclaimed Miss Bridget, bitterly. All this while, during the making and testing of the plan, she'd kept a resentful quiet; but now she could no more hold her peace.
"How I hate and despise it! For it's brought an old man to his death and made murderers of nought but common thieves. And now—and now it's turned our own poor mite, what has never sinned deeper than a passing pocket, into a dwarfish toby! To take such a child on to the murdering Common for to rob a blind man! Oh, for shame—shame—shame!"
Lord Tom chewed his lip and shook his head. He stood up with a clatter of ironware and began to pace the cellar.
"What would you have me do, Miss Bridget? In your own very hearing—not an hour ago—in this very residence I've a-pleaded with him; I've a-begged him; I've a-warned him and I've a-supplicated with him not to come. But that lad's determined. Nothing anyone can say will shake him. He's iron, Miss Bridget. He's steel. He's rock. He's a fixture, ma'am!"
Smith—who felt as far from any of these things as was imaginable—nodded vigorously.
Since he'd left the dreadful jail in the vinegary, rustling blackness of his sister's skirt, with her legs coming and going like engines of destruction, he'd thought of nothing but Mr. Mansfield with the fatal document on his way to Prickler's Hill. To say that nothing would have stopped Smith wasn't quite true. A knife in the ribs would have stopped him; likewise, a ball in the chest. But Lord Tom's warnings and Miss Bridget's respectable anger stood but a small chance against the furious urgings of his own heart and head.
Miss Fanny—to do her justice—must have seen this right from the start, for she never opposed her "sweet Smut," but agreed "our dockiment must come first." Miss Bridget upbraided her, sneered at her, called her an "avaricious slut." But Miss Fanny only looked forgiving as her sister railed and put her arm round Smith's shoulders and declared: "If his heart's in it, Brid dear, 'tis wicked to thwart him!"
So Miss Bridget turned the full force of her tongue upon Lord Tom, who was somewhat shaken by it; for he had, maybe, more prideful feelings than Miss Fanny. So the highwayman was driven to defend himself, and feel that he had to restore himself in the eyes of Miss Fanny and Smith.
Not that Miss Bridget's tempest could ever have sunk Lord Tom in Smith's bright eyes, for the boy held the green-cloaked robber in the deepest admiration and respect. Which respect, agreeably enough, was treasured up by Lord Tom as a bright warm day to remember in the winter of his life. With energy and dignity, he painted such a picture of his trade that only the coldest of hearts could have scorned.
"Gallantry, ma'am—there's gallantry on the Common! And fierce beauty and soaring adventure!"
The highwayman's eyes sparkled and he brushed the back of his hand across his cheek, as if he could feel the wild night upon it. Then he went on to relate exploits that he'd told of many times before—but never so handsomely. And he spoke of other famous gentlemen who'd once waited, hid and pounced where _he_ now waited, hid and pounced: Duval ("Hanged!" snapped Miss Bridget), Turpin ("Hanged!"), Captain Robinson ("Hanged!").
"Yes, ma'am, they paid for their joys. They're dead and gone . . . and so've a great many other folk. 'Tis the common penalty for living. But it's not the quiet, mewing, moaning bed-perishings that haunt the Common of a moony night. No, ma'am! When we ride out, we ride with the great ghostly company of the nubbed! Many a time I've heard, 'Lord Tom, Lord Tom—I'm a-watching you, friend,' in Turpin's own voice!"
Then Lord Tom, with dreamy grandeur, told of these dead men's doings in the days of their lives—and then back to his own (to draw a parallel)—then back again . . . till it was hard to tell who'd done what: Duval, Robinson, Turpin—or Lord Tom.
In spite of herself, Miss Bridget's heart beat a little faster . . . for she was but three and twenty and Miss Fanny's and Smith's sister, when all was said and done.
Smith's heart, also, was beating faster—but from a strong anxiety that Lord Tom's eloquence was dangerously delaying them, and that they'd be too late upon the Common. For the first time in his life, he wished Lord Tom had had fewer adventures—and hadn't remembered them so well!
"By tonight, we'll have our dockiment safe and sound," he heard Miss Fanny murmur. "And Smut'll read it to us . . . with new tallows and we three sat at the table . . . for all the world, Brid, like reading a psalm from the Scriptures."
The document: with a start, Smith remembered it. Not that he'd ever forgotten it, but its importance now seemed changed. If, by destroying the document, he could have destroyed Mr. Black and his friends, he'd have done so. The document was now not so much a means of his going up in the world, but a way of preventing his going down.
"Well, Smut, me comrade-in-arms of this day! Are we fit and ready?" exclaimed Lord Tom at last, staring at a fine French watch that had been the subject of his last told adventure. "Five minutes to make your adieus, Smut—then it's the Common for the pair of us!"
Thankfully, and with mounting excitement, Smith left his seat and stationed himself beside the tremendous highwayman, when Miss Bridget, somewhat desperately, protested: "But he'll freeze to death! He cannot go so ill-dressed!"
There was a further delay, while an ancient cloak was found to cover Smith's bedraggled finery and a queer hat, that Miss Fanny had once toyed with, to cover his tangled and matted head.
He had a certain shabby splendor—and even Miss Bridget gazed at him with surprise and a reluctant admiration as he began to mount the stairs. Smith, caught up in the romantic spirit, felt himself full of the gallantest dreams. He turned, waved and cried: "Adieu, dear ladies! Wish me—"
He stopped. There was a loud knock on the door.
"Gawd!" muttered Smith. "It's for me!"
He bolted back into the cellar, his cloak flapping like ruined wings, and hid behind the curtain. Lord Tom stood, grandly guarding his small friend's sanctuary, and the two sisters rose together.
"Come in!"
There entered a small, wizened man with eager eyes, carrying a bundle. He peered down into the body of the cellar and grinned and nodded to the company. It was Mr. Jones's assistant come, not for Smith, but with Dick Mulrone's fine suit. To be altered for Mr. Jones's father. "There's a good son for you!"
He threw the bundle on the table and said Mr. Jones himself would be calling to describe his father's figure and shape: tomorrow. Today he was tired out. The crowds! The shouting! Fairly frayed him!
Then he went—and left behind a gloomy silence. If ever four souls and a cellar were haunted by the lack of a ghost, they were gathered now. A coat, a waistcoat and a pair of breeches: that was all there was of Dick Mulrone. No breath nor whisper of a ghost came into the Red Lion's cellar to quicken the four sad hearts, or stir the pitiful heap of clothing. The gallantest robber of the Hounslow Heath was as dead as mutton; not able, even, to haunt his own breeches.
Lord Tom bowed his head. Miss Fanny wept. Said Miss Bridget: "Take care of him, Lord Tom. For my heart chills. Watch over little Smut."
"I'll guard him, ma'am. With me very life I do assure you—while he's with Lord Tom, no danger will offer. I—I promise you, ma'am. Come, lad—away!"
With the best will in the world Lord Tom tried to be in good spirits on the way to Finchley Common; but the sadness lingered, and he kept falling into a silence as heavy as the glum sky. And Smith, whose dearest dream and brightest hope had come to pass—to be riding out on the snaffling lay with his hero, Lord Tom—was as melancholy as sin.
Sitting on the front of the highwayman's saddle he turned round, from time to time, and saw Lord Tom's great, bristling face, dark under his hat, much troubled . . .
So they rode on, this weirdly romantic, fantastic pair—the infant jailbird and the glowering highwayman—through the thick snow towards the famous place where Lord Tom and all of his hanged ghosts waited, hid—and pounced.
## 15
THE SNOW, which had held off for some three hours, began again in earnest at about four o'clock as the light was perishing from the sky and there came up to Bob's Inn on the steep of Highgate Hill, a most weary horse bearing a full-sized man and an undersized boy.
"Is this the place, Lord Tom?"
"The very same."
Bob's Inn, a pleasant, newly built structure with three parlors and rooms for seven gentlemen (three double and one single), sat about fifty yards northward from the top of Highgate Hill and commanded a spacious view of the southern fingers of Finchley Common, from which it was distant by about half a steep mile. Thus from the snug windows, not a curricle, gig or coach could venture on to the Common without being interestedly viewed. For the further entertainment of his customers, Mr. Bob had provided a strong spy-glass (at sixpence a half-hour) and certain information that might be of service. Mr. Bob's customers were high tobies to a man.
"Knew 'em all!" was Mr. Bob's proud boast as he stood by the cheerful fire of an evening. "Duval—Turpin—Robinson . . . many's the time they've sat about this very snug, drinking and laughing—and popping to the windows for a nifty look!" (This, notwithstanding the glum fact that Duval had been hanged eighty years before and Bob looked no more than forty.) "Yes, indeed! Knew 'em all!"
He welcomed Lord Tom and grinned affectionately at Smith, whom he recognized as a "brisk, bright and prosperous apprentice to the Trade." He made a place for the highwayman and his apprentice by the fire and dispatched an evil-eyed potboy for "jars of the best."
"Nothing coming, nothing going," he murmured, jerking his head to the windows that commanded the best view of the Common. "Not our sort of weather, eh, Lord Tom? Many's the time—ah, many's the time—great Duval himself would curse the snow for muffling his pickings! Aye, and a-warming his backside where you're a-warming yours, friend!"
Lord Tom was handsomely thawing himself out—and fizzing and drizzling into the hearth. His caped coat, whited like a sepulchre, was now beginning to patch through the covering of snow into a wet green—like a lawn after winter. Likewise, Smith, buffeted and stung by the whirling snow, bruised beyond belief by the dreadful horse, began to come to himself and crack and thaw and ease himself into a furtive smile.
"There's a coach due, Bob, within—" (Lord Tom drew out his French watch which the landlord eyed merrily and murmured, "Ah! we remember that one, eh?") "—within this half-hour. From Town toward Barnet."
"You know best, friend. You got a reputation. But it surprises me: yes, indeed. Must be powerful business to draw an equipage across this murderous white nothingness!"
"It is, Bob. It surely is."
He winked at Smith—then raised his fingers warningly to his lips as the potboy returned with the ale.
Not fifty yards to the west of Bob's stood another inn—an ancient, tottery, smoky building, the speaking likeness of Smith's Red Lion. This was The Wrestlers. It seemed that Lord Tom had a little brief business there. He charged Smith to wait for him and not to stir from Mr. Bob's parlor: under no circumstances.
Mr. Bob nodded. Lord Tom wasn't to worry. His own stout person would go bail for the apprentice's not shifting till Lord Tom returned.
The highwayman thanked him—then turned to his apprentice: "Watch out for the coach, Smut. Mr. Bob'll show you where. Here's a sixpence, Bob. Let the lad watch through the spyglass. Let him be a real high toby while I'm gone! Just for ten minutes, eh?"
He tossed a coin on the table, but Bob shook his greasy, good-natured head.
"Keep your money, friend. On a night like this I'm all for the warmth of kindness. The lad can watch for free. Duval would have liked that. Yes, sir, I can hear him say, 'Bob! Let the lad watch for free!'"
"There, Smut," said Lord Tom, with sudden pride. "There's a small taste of our companionage. You're among friends!"
Then, with a quick wave, he opened the door and his place was took by a flurry of snow, as he strode across the invisible road to The Wrestlers.
"A grand fellow!" remarked Bob. "One of the best!"
He eased himself into a seat close by Smith and prepared to unburden himself of all his superior memories for the amazement of a new pair of ears. But Smith was staring so fiercely and anxiously at the window that overlooked the approaches to the Common, that Bob, seeing his best tales might pass unheeded, took pity on the boy and pointed to where the spyglass stood on the mantelshelf.
"Take it, lad. Go watch for the coach. And remember, through that selfsame glass the proudest, sharpest, gallantest eyes these parts have ever known, once stared. May their brilliancy lighten your viewing. Go stand by the window . . . elbows on the sill . . . left knee cocked on the seat. The very attitude of Turpin! Duval was a taller man. He always used to sit . . ."
The capacious-memoried landlord rambled on, following Smith from the fire to the window, obliging him by pulling out the spyglass into all of its gilt sections—then standing to one side with the warming remark that Smith was "the very image of Claude Duval as a lad!"
Smith, pleased in spite of his urgency, stared out into the gathering night . . . past the ghostly reflection of his own thin, fierce face, through the snow-filled air, on to the deep white world that sank and humped and valleyed and hillocked for many a quiet, mysterious mile. This was northward. Southward lay the Town, speckled and spotted with lights.
"D'you see that long, shadowy finger?" breathed Mr. Bob. "That's the road the coach'll come by . . . _if_ it comes."
Smith saw, and raised the spyglass so's the landscape jumped amazingly close at hand. He saw bushes and trees creaking under their white fruit which, every once in a while, the wind would shift and cause to thump and shower down, adding more whiteness to the overburdened ground.
Then, distant even in the spyglass, he saw a square black creature, with a pair of gleaming yellow eyes, tipping and lumbering in the wake of two horses.
"It's coming!" muttered Smith, triumphantly. "Lord Tom had best be quick!"
He turned to the side window and swung the spyglass towards The Wrestlers, to see if the romantic figure of the highwayman was yet come out and was leaning through the whirling weather.
It was amazing! So strong was the glass that Smith felt he could have touched the door and walls and poked his head through the parlor window to say: "Make haste, Lord Tom! The coach is sighted! Hurry, good friend of mine. Get up off your chair and leave those—"
Those what? For there sat Lord Tom, large and near as life—leaning across a table, in deep discussion with . . .
Smith lowered the spyglass abruptly and wiped the lens. Then he looked again. He grew pale. His skin began to prickle as if the air was full of thorns and arrows. His belly turned unquiet and he began to feel sick.
Lord Tom was in deep discussion with the two men in brown. Lord Tom. His strong friend, his champion, even his hero . . . Very fearful of face, was he: very cringing, very humble. (Yes, sirs! No, sirs! The blind man's as good as dead, sirs! And ain't I betrayed the lad neatly? Hope you're pleased with me, sirs!)
Smith put down the glass.
"What's amiss, lad?"
"Nothing! You mind your own damned business, Mister Bob —and I'll mind mine!"
Smith spoke through his hands—which were before his face to hide his rushing tears.
A very black, bitter and tragic place was the world to Smith as he understood the scope of his friend's treachery. It was not Miss Fanny's prattling that had betrayed his whereabouts, but the whispers of gallant Lord Tom! The blind man's turning against him was as nothing to the wretchedness he now endured. Smith had been struck deep indeed.
"I'll fetch you a tot of brandy, lad!" murmured Bob, much concerned and believing the apprentice to be, so to speak, the victim of "stagecoach fright." "That'll put fire into you for the 'stand and deliver'!"
He was gone only a second, but when he returned the door was banging open and the parlor was empty, save for a whirl of snow. The highwayman's apprentice was gone.
"Come back! Come back!" he bellowed—but the small, rumbling, hurtling figure that plunged down the hillside was fast vanishing—and heeded him not.
In places the snow lay two feet deep and Smith, to rise out of it, had to bound in a mighty, springing fashion—like a tremendous flea. Every now and then he'd strike on an unexpectedly shallow patch, so his feet, meeting resistance, would shoot him more powerfully than ever into the air—from which he'd fall and roll over and over in a whirl of white. Then up he'd scramble, wet and panting, to bound onward—till he fell again . . .
Such tracks as he made were almost instantly filled in after him, so that the effect of his progress was oddly supernatural. And all the while, in a harsh, sobbing voice, he'd plead and cajole and curse and beg his own despairing person to hurry, hurry, hurry!
Three devils were after him: two in brown—and one in green. But the snow kept flinging coldly suffocating arms about him—as if to hold him forever in its freezing bosom—and, as he rose, the very heavens seemed to beat him down again with their fluffy torrents. The whole huge universe was turned against him: the earth, the sky, the wind—even his own failing limbs which ached for nothing more than a bed in the dreadful, loving snow.
But each time, there came up out of the hole he'd made in the ground, a small rebellious voice:
"Come on with you, Smith! You dozy weasel! Up! Up! What for did you come out of the 'ouse of bondage? To sink and perish in this great Fleet Ditch of common 'opelessness? Not bleeding likely!" And then, in tones which shook with bitterness, grief and contempt: "So to Hell with you, Lord Tom! For that's where you belongs!"
On which the indomitable figure of Smith would rise up out of the white, and fumble on.
Where to? The road the coach would take: the shadowy finger that Mr. Bob had pointed to. But where was it? He stared about him. Whiteness everywhere. No landmark, no post—nothing!
Once more, a feeling of hopelessness gripped him. He looked back up the hill. Three small black figures were on their way . . . In a sudden rage, Smith stamped his foot and glared about him.
Not seventy yards off, lumbered the coach! Towards him! The road—he was on it!
The horses panted and dragged and steamed. The coachman, high up on his snow-capped black mountain, leaned forward, eyes fairly glued to the vague shadow which was all he could see of firm ground. He dared not look elsewhere; one false move might end in a drift and finish the vital journey then and there.
Smith scrambled aside; sank up to his knees in snow; crouched down. He wished to God he'd waited for Mr. Bob's tot of brandy; for what parts of him the weather neglected to chill, fright did for wonderfully.
On came the coach, its yellow lamps leaping like alarmed eyes as it rocked perilously, all haste and commotion—yet soundless. The snow and the wind muffled all. It might have been a spectral equipage, already lost some way back and only its spirit persisting.
Now it was close enough for Smith to pick out the coachman's features—his one-time master in the Vine Street yard. He heard the horses thumping in the snow and the harness groan and creak in the angry singing of the air. Still he waited. The coach drew level . . .
A friendly gust of wind whipped and whirled and sent stinging flakes into the coachman's face and eyes. Smith moved quickly; he seized hold on the door; dragged it open—
"Who's there? Who is it?" Mr. Mansfield's voice, angry and alarmed, was swallowed up in the wind.
Smith reached within. He clutched at a coat sleeve—a wrist—a hand—and pulled with all his might.
"My God! My God!"
Out heaved the blind man, falling with the tilt of the coach into the muffling snow.
"For God's sake, who is it? What d'you want with me?"
Smith, still holding tight, did not answer. Instead, he dragged him down into the drifts by the side of the road while the untenanted coach—its door swinging helpless, like a one-armed soldier's sleeve—quaked and jolted on.
Again the blind man cried out and Smith fixed his hand over the betraying mouth and, in a whisper no man could have recognized, breathed: "Quiet—if you values yore life!"
Twenty yards on the coach rocked to a halt. It had been accosted and pistols pointed the way to the coachman's brains.
The wind whipped familiar voices back to where the snow was fast hiding Smith and his prisoner.
"The lousy coach is empty!"
"Thank the Lord!" (The coachman.)
"That boy of your'n—Lord piddling Tom!—he's beat us to it."
"Friends!" (Lord piddling Tom.) "I swear I did what I could—"
"Not enough—not enough! You should have slit his mean throat—you green windbag!"
"Friends—friends! How was I to know—"
"You swore you'd fix him!"
"And so I meant to! I swear it!"
"Swear it to Mister Black! If he gives you leave! You'll bleed for this!"
"No! No! They must be near at hand! Let's search!"
"In this great 'owling blizzard?"
"Yes—yes!"
"We've had experience afore! Your little rat near killed us once with chasing him!"
(Smith, in concealment, couldn't restrain a beam of pride.)
"Then what's to be done?"
"On to Mister Black in the morning. That's what."
"But—but—"
" 'But' to yore heart's content, fat man. Yore day's done. You blotted yore book. Maybe with blood, eh?"
"The coach! The coach!"
While they'd been thus engaged, the coachman had taken advantage. He'd whipped his horses and yelled them into a frenzy. Already, the coach heaved and plunged on its way!
"Stop, you fool! Stop—or you're dead!" Lord Tom raised his pistol—aimed—and fired. A cry from ahead. The coachman, high up, clutched at his side and began to slip . . . then he seemed to recover himself partly . . . and was lost from sight behind a clump of trees. When the coach reappeared, still lumbering fast, there was nothing on the box but a heavy, jerking shape that, any moment, would fail by the wayside, unheeded.
Smith, in his excitement, had withdrawn his hand from the magistrate's mouth.
"Is he—is he—killed?" whispered Mr. Mansfield.
Smith did not answer. Instead, with bitter, lonely eyes, he watched the three figures turn and begin their climb up the hill. Then he stood up, brushed the accumulated snow from the magistrate's shoulders and head, and pulled him to his feet.
Four miles to the north lay Prickler's Hill. Smith set his face in that direction and, with his hand firmly about the blind man's wrist, began to walk. And the snow came down like a disaster . . .
## 16
THEY MADE POOR PROGRESS: in two hours something less than three-quarters of a mile. Every once in a while the boy would turn his back to the weather and face the blind man, drawing him on and, at the same time, seeming to retreat under the impassive stare of the snow-stained face. For there was no doubt the blind man sensed the scrutiny of unseen eyes (or did he feel warm breath softening the bitter wind?) and, as was his old habit, emptied his face of all telltale expression . . . Then the boy would grunt and turn about—to plod on into the scourging snow.
Sometimes, when they passed among the heavily bandaged trees, the wind would dislodge snow from the lower branches so that it thumped down, knocking the breath out of the two travelers and forcing them to halt for recovery. Then the blind man would once more ask his guide who he was and why he'd saved him and was leading him through this huge and bitter night. Perhaps he knew? It was hard to say.
"Very well, then—speak . . . anything . . . anything at all. Or are you dumb? A fine pair—we two! One with no tongue to tell what he sees—and the other with no eyes to see what's worth the telling. A humorous pair! Well, then—if you won't speak, sing!"
But Smith uttered never a word. He was deeply frightened of the magistrate's mania for justice. He dreaded that the blind man would give him up at the first opportunity. So let him think it's a perishing angel what's leading 'im, thought Smith and held his tongue.
At seven o'clock the snow began to abate—though the wind did not—and a great clearness and brilliancy settled upon the landscape, across which the boy and the blind man seemed to be the only moving things.
The magistrate, having worn out his conversation, turned to singing and chanting (maybe in the hope that his silent guide would join in and betray himself).
" 'The Lord is my shepherd, I shall not want.' "
You said it! thought Smith, plodding on.
" 'He maketh me to lie down in green pastures—' "
You should see 'em! mouthed Smith with fierce irony. He blinked about him; the hills were white and the valleys were white, likewise the slopes between . . . The sky alone offered relief, being of a velvety blackness, pricked out with some fifteen or twenty frosty stars.
" 'Thou preparest a table before me in the presence of mine enemies—' " Smith scowled through his windy tears for he'd not eaten that day.
The thought struck him that Mr. Mansfield knew who he was all the time and was subtly mocking him—till the chance should offer of giving him up. Certainly, everything the blind man said seemed now to be cruelly humorous—and he said a great deal! Songs and poems and lumps of the Scriptures came puffing out of his mouth with much issue of smoking breath. This was Mr. Mansfield's stock-in-trade—his vision of the world, seen through other men's eyes who'd digested their vision into words, and it made him a supper to last all of his life.
His own memories of what the world looked like, he no longer trusted. He was a sensible man and knew full well the changes that must have been wrought since last he'd looked. His beloved daughter could no longer have been the fearful child caught in the fire he'd remembered for so long. Even the Town itself he knew to be much changed for everywhere he heard sounds of building and of tumbling and of men losing their way. Even Nature herself he suspected of aging—and the wind and the cold seemed crueler than he recalled.
Maybe, even, they were breeding a new style of boy, now? He smiled—or tried to, but his cheeks were partly frozen. The child, Smith, for instance . . . He frowned as he recalled the powerful evidence against him. No. Whatever else might alter, justice remained fixed—like God Himself. Justice: the last refuge of a blind man.
Suddenly, he felt the grip on his wrist disappear. Frightened, he stopped, turning his face this way and that in the lonely wind. Had he been left? Oh God! Why?
Smith, beaten breathless by the weather—with a lock of his black hair (his hat was in Mr. Bob's) frozen solid so's it banged against his forehead like a door-knocker, was suddenly attacked by common sense. The old mole-in-the-hole was not changed. Stern and cold was his face—colder even than the snow that spotted it. Smith was not leading him; he was leading Smith—back into the horrible house of bondage! A thousand windy voices shouted in his ears, bidding him leave the old Justice and begone. The world was a freezing, lonely place. No one would give Smith quarter in it. Not his sisters, not his treacherous friend—and, least of all, the stern-faced magistrate. Not even the howling weather!
Further and further off backed Smith, amazed by his own madness in coming thus far. He stared at the stark, menacing form of the blind man with his stony heart.
Take, take, take! And never give nought in return! I'm done with you!
And then, as Smith watched, the blind man raised his hands. He turned about, tried to take a step, stumbled, recovered himself and cried out: "Am I alone? Am I alone?"
His face, though much limited in expression by his shrouded eyes, was suddenly, and deeply, wretched. A desolate face, bespeaking a starved soul. That soul of his had been nourished on thin fare, these past twelve years, and it had grown weak without his knowing it, so that, when the wind blew, it bowed as if to break. And the wind blew as hard for the blind man as it did for the boy.
"You old blind Justice, you!" mumbled Smith, lurching back to Mr. Mansfield. "Give us your hand, then!"
The magistrate stretched out his hands, and nature made strange amends for a certain disability of his. Snow, dislodged from his spectacles and fallen against his eyes, had begun to melt so that water trickled down his cheeks as if he was doing what he could not: weeping.
Bewildered, Smith gazed on Mr. Mansfield's melting face. He took both the outstretched hands.
"Here—here, then. Both me hands. You ain't alone, Mister Mansfield—nor never was. I—I was only resting—"
"Smith—Smith—Smith!" cried the blind man, grasping in return the hands he'd never forgotten. "Your voice at last! How I longed to hear it!"
"You knew it was me, then?"
"Yes—yes!"
"Then—why didn't you say?"
"You didn't want me to know, did you?"
"No. I was thinking you'd 'and me over to the Law."
"And even so you came back?"
"I'm only a yewmanbeen."
" _Only!_ "
Smith freed one of Mr. Mansfield's hands and turned once more into the weather.
"We'd best be moving—or we'll freeze in situation!"
They stumbled on awhile longer—but no more in silence. A curious warmth seemed to have sprung up between them and rendered the wind less savage. Mr. Mansfield told Smith that his daughter had stayed behind to attend his trial and to keep Mr. Billing to his promise of the adjournment. It seemed it was she, the Saint of Vine Street, who'd kept her faith in Smith.
"Not you, Mister Mansfield?" asked Smith shrewdly.
"No, alas, not me. I'm no saint, Smith. Like you, I'm only a human being."
"Queer, then, being an old mole-in-the-hole and helpless, you should come out in sich weather for . . . for what, Mister Mansfield? For the 'ealthy cold air?"
Mr. Mansfield grinned awkwardly.
"That's it, Smith! For my health!"
Smith grinned back—then remembered his companion's disability and said: "I'm a-smiling, Mister Mansfield!"
"Pleased to hear it, Smith."
"You, too, Mister Mansfield. And a very cheering thing to see. You got a friendly smile, you know."
"I didn't know, Smith. But now you've mentioned it, I'll take a special pride in it!"
And Mr. Mansfield continued to smile into the icy wind in the firm hope that Smith would sometimes turn and get the benefit; which Smith did, always remembering to return the compliment aloud. Then he'd turn back again and chatter about what he could see and what he'd seen . . . describing his life and the doings of his sisters . . . and even his escape from the jail. But he never mentioned Lord Tom nor any of the darkness that hemmed him in. Likewise, Mr. Mansfield, though he confided in Smith much of his warmer past, said nothing of what must have lain deepest in both their thoughts—the murder of Mr. Field.
Presently, they reached the top of a gentle slope.
"Cottage, Mister Mansfield . . . quarter mile off . . . light in the window . . . nice, snug little place. Looks warm. What say we knock on the door?"
"Don't mind if we do."
Smith tucked his head as far as it would go into his collar and began the descent toward the cottage which lay in a snow-filled hollow.
A neat, well-built cottage, with good windows and a stout fence marking off its garden from the Common—though with the snow lying so heavy on garden and Common alike, the fence looked more peevish than necessary. There was a strong blossoming of smoke from the chimney that bespoke a warmer nature within than without . . . and the cottage's windows gleamed most cheerfully.
All this Smith described to Mr. Mansfield, who nodded as they approached the door and said he was reminded of old fairy tales.
"A wood-chopper's cottage . . . an old wood-chopper and his brown-eyed wife—"
"Then there's money in chopping wood," said Smith shrewdly. "For there's a stable at the back and space for a carriage."
He knocked on the door and Mr. Mansfield sighed as if he was almost sorry that their winter's journey—murderous as it had been—was ending in so ordinary and genteel a place.
The door opened an inch.
"Who's there? What d'you want?" The voice was harsh and irritable.
"Shelter!" cried Smith and Mr. Mansfield together.
"Who for?"
"A blind man and a frozen child!"
"What was that?" came a woman's voice from within.
"Blind man and frozen child," answered the first voice.
"Stuff and nonsense, Charlie!"
"That's what they said."
"Have a look!"
The door opened farther to the full extent of its chain. A stout, waistcoated man, bald and frowning, peered out.
"Man and child, right enough, Mrs. P.," he called out.
"How big, Charlie?"
"Child's about—um—high as your chair and the man's taller than me."
"Don't like it, Charlie."
"No more do I. Shall I shut 'em out, Mrs. P.?"
"Good God, sir!" exclaimed Mr. Mansfield. "In humanity's name! On such a night?"
"Did you hear that, Mrs. P.? The weather, y'know!"
"Mrs. P.!" shouted Smith. "We're frozen near to death—and me friend's as blind as a post."
"Charlie! See if he's blind!" came Mrs. P.'s complaining voice. Obligingly, Mr. Mansfield took off his spectacles and presented his face.
"Nasty," said Charlie. "Blind all right."
"Then let 'em in, Charlie!" cried Mrs. P. "Keeping a blind man and a frozen child on your doorstep; ain't you got no humanity, sir? Oh, you're a weak vessel, Charlie Parkin!"
Thereupon, the chain was unfastened, the door opened wide and Smith and Mr. Mansfield welcomed directly into the parlor.
"Hats! Coats! Boots!" shouted Mrs. P. "Quick, Charlie! Into the kitchen with 'em before we're drowned out again!"
"Least said, soonest mended," said Charlie, collecting up those snowy articles, which were already dripping fast in the great heat of the parlor.
He bustled out and Mrs. P.—a very small woman with sharp features and a blue cap—fixed Smith and Mr. Mansfield on either side of the neat fire. Indeed, everything about the parlor was neat: the cloth upon the table was neatly embroidered with neat little flowers, the plates upon that cloth were neat, and even the crumbs remaining on those plates had been neatly arranged, like soldiers drawn up for review.
"A very neat home," said Smith to Mr. Mansfield.
"You poor things!" said Mrs. P., busy by the sideboard with glasses and some warming spirits. "Lost your ways on the Common, I suppose?"
"Our coach was held up, ma'am," said Mr. Mansfield. "Highwaymen."
"Charlie!" shouted Mrs. P. "They was held up! Highwaymen!"
Instantly, Charlie reappeared, with a pistol in his hand. His eyes were fiery. "Highwaymen? Where?"
"No, no! They"—she nodded to Smith and Mr. Mansfield—"was held up by highwaymen. Victims, Charlie. And come to us for succor."
"Oh!" said Charlie, putting up his weapon. "Them damned high tobies!"
"Fetch the book, Charlie."
Charlie nodded, vanished back into the kitchen and reappeared with spectacles and a large ledger.
"Ink and a fresh pen, Charlie."
They were got from the sideboard.
"Brown paper, Charlie."
This was to spread on the tablecloth to protect it from the consequences of Charlie's writings.
"Now, Charlie—off you go!"
Wonderingly, Smith watched and Mr. Mansfield listened to these preparations.
"Blind man and boy," said Mrs. P.—and Charlie repeated it and slowly, with much help from his fumbling tongue, wrote it in the book.
"Held up—where was you held up?"
"On the Common, ma'am."
"On the Common, Charlie."
"On the Common, Mrs. P. Two _M_ 's and one _N_."
"Robbed?"
"No, ma'am."
"Not robbed, Charlie."
Charlie wrote and Mrs. P. sighed at her husband's slowness. ("A slow vessel, Mister Parkin.")
"Injured?"
"Our coachman was—murdered, I believe," said Mr. Mansfield, bleakly.
"Coachman murdered, Charlie."
Charlie looked up and exchanged a long, deep stare with Mrs. P. Then he shook his head. "Them damned high tobies!"
Now Mrs. P. came over with two glasses of spirits.
"Two measures of brandy, Charlie!" she called out as she offered them.
"Two measures of brandy," wrote Charlie. "And two suppers to follow, Mrs. P.?"
"Two suppers, Charlie—and two seats by the fire for the night." She turned to her guests.
"Nothing but chairs remaining."
Charlie finished his writing and looked up.
"Names? What names, please?"
"Mansfield," said the magistrate somewhat coolly—for he was more than surprised by the above formalities. "Mister Mansfield. Justice of the Peace, sir."
"A magistrate! Fancy that, Mrs. P. Well, well, sir, it seems we're in the same line of business. For I'm a constable—among other things. Yes, sir! Here to keep law and order! And let me tell you, sir, there's not a vagabond, rogue or footpad who dares to set foot across the fence."
"That's right!" agreed Mrs. P. "This cottage and all the ground enclosed by the fence belongs to the parish—and we keep it clean and aboveboard. The law's respected here, sir."
"And everything's recorded," went on Charlie, patting the ledger. "Accounts square and trim. Two measures of brandy offered; two measures of brandy writ down; two measures of brandy back from the parish. Not a drop more—not a drop less."
"A name for honesty," said Mrs. P.
"And for neatness," added Charlie.
Smith looked at Mr. Mansfield and observed his face had grown redder than the fire could have made it. For the magistrate felt that this demonstration of upholding the law struck too shrewdly to be smiled at. And he wondered if the Parkins' neat cottage and clean garden over which they watched so exactly—and let the rest of the Common go hang—was not an image of what his own heart had been and, indeed, of the whole tidy business of the law itself.
Charlie had been about to put the ledger away, when a thought struck him.
"Lad's name, sir? Servant of your'n?"
"Friend!" said Mr. Mansfield, vigorously. "A friend!"
"Name?" said Charlie, his pen poised like a sword.
"Jones," lied Mr. Mansfield blandly.
Smith, the escaped and no doubt hunted jailbird, regarded the perjured magistrate with the warmest affection—and surprise.
"Jones," wrote down Charlie, sanded the ink and shut the ledger. He looked to Mrs. P.
"Shall we show why we got no bed to spare, Mrs. P.?"
"Parish business, Charlie. You ain't got the right."
"But he's a Justice, Mrs. P., and concerned, I fancy."
"You're a sentimental vessel, Charlie Parkin. Dangerous for one with your responsibilities."
"Just this once, Mrs. P. And he's blind."
"Very well, Charlie—as he's blind, then."
Whereupon the sentimental constable chuckled and reopened the ledger which he carried to Mr. Mansfield's side.
"There was someone before you, sir."
"Indeed?"
"We took him in."
"Generous, sir. Generous!"
"He was bleeding."
"Who was he?"
"Your coachman, sir. Yes, indeed—we've succored him and nourished him and put him to bed."
"Thank God! Thank God!" cried Mr. Mansfield, deeply moved.
"Here it is," went on Charlie, proud to have been of service to humanity, the parish _and_ a Justice of the Peace. And, forthwith, he read out the coachman's name, wound, where sustained, quantity of bandage applied, sustenance consumed and quality of lodging, together with the care of horses and use of coach-house. All of which was chargeable to the parish . . . as was the meager warmth from Charlie Parkin's respectable heart.
Then the ledger was put away and Mrs. P. busied herself with fetching hot suppers for her guests while her husband talked and talked of how he kept his garden clear and expressed the hope that Mr. Mansfield would bring his vigilance to the ears of all his legal friends in Town.
At about ten o'clock the Parkins went to bed (after assuring Mr. Mansfield that his coachman was not badly hurt and was sleeping peacefully) and left their guests to doze and brood in their chairs beside the banked-up fire.
"It's been a long day," murmured Mr. Mansfield.
"A long day," agreed Smith.
"A lifetime long."
Smith said nothing, but fancied he understood. Slowly, Mr. Mansfield's head sank down on his chest and his fine, strong face glowed in the firelight. Smith stared at him profoundly. Dreamily, he wondered what sort of man the magistrate had been before he'd lost his sight.
"Smith!"
Mr. Mansfield was still awake. He'd taken off his spectacles and was staring to where he supposed Smith to be. His eyes were in a tragically ruinous state. But he was smiling. He fumbled inside his waistcoat.
"Here, Smith. Isn't this something you wanted? Take it then. Read it. Aloud, I beg of you!"
He was offering Smith the document.
## 17
THE DOCUMENT! All the time in the snow, when he and Mr. Mansfield had been alone, the precious item had been within his grasp—and he'd forgotten it! Forgotten it so entirely, that its sudden appearance before the cottage fire was almost terrifying.
"Take it, Smith—and tell me what old Mister Field had to say."
Fearfully, Smith reached out his hand and took the document. Ten thousand thoughts, fears and questions filled his head. Why had he been given it now? Why the enormous trust? Didn't the magistrate still believe him to be a murderer? But what other choice had he—in his condition? Trust was obligatory: a necessary quality of life.
"Read, Smith. Don't be afraid. Read!"
So Smith crouched down at the blind man's feet, close by the fire where the light was sufficient. And, as he sat, Mr. Mansfield's hand dropped by chance on his shoulder, then moved lightly upward and rested on his head.
Smith read: slowly, shakily—for he was not over proficient and the writing was crabbed and there were words he could not pronounce.
Neither confession, nor deed to property was the document. It was a letter to Mr. Lennard. A strange letter of an uncanny power in the firelit room. For, as Smith read on, murdered old Mr. Field seemed to creep into the parlor and cast his cold shadow between the blind man and the boy . . . so that Mr. Mansfield shivered and withdrew his hand from Smith's head—and Smith shrank back towards his own side of the fire.
The old man had written in deep agitation. Something had disturbed and shaken him profoundly. Also, there was fear . . . of a distressing kind. He knew his life to be threatened. Several times, he mentioned it. "I lie awake of nights, Lennard—and hear such sounds, and have such thoughts . . . at my age!" Then, later, he wrote of a discovery he'd made—but did not say what . . . only that he meant to carry it to his grave. A terrible discovery. This, also, was repeated and underlined . . . "A _terrible, terrible_ discovery."
But now came an oddity. An instruction quite plain and without any of the confused fears that invaded the rest of the document. "The _trifle_ " (trifle was underlined) "I wrote you of previously is buried in a shrewd place. Andrews knows where. Ask him where Jack used to play as a boy. When you have it, dispose of it as pleases you. I shall care no longer . . ." There followed here some bitter and pathetic words of the world in general, all once more in a very agitated manner, together with a last reference to his discovery, reaffirming his intention of carrying it to the grave, "where it would be hidden and forgot forever."
Smith stopped reading. There was a restless silence in which the fire leaped and cast strange lightnings across the blind man's face.
"Go on," Mr. Mansfield said.
"There's nothing more."
"Nothing?"
"Nothing!" muttered Smith. "Or d'you think I'm hiding the rest from you?"
He scowled furiously into the fire; his heart felt grievously empty. The document, the precious item that was to have raised him up in the world: nothing but an old man's misery and dread and the whereabouts of a trifle—a locket, most likely, or a brooch with a twist of his grandma's hair.
For this he'd endured so much. He stared at the paper, through which the fire shone redly, and noted the stains made by his own sweat when first he'd fled from the men in brown. Then he remembered his grief when he'd thought the document had been destroyed; and then his joy when he'd discovered it was safe. He remembered Miss Fanny's hopes in it—not much less than his own . . . And now? Not even a "whereas" or a "felonious" or a "property" to justify a family's dreams. Good God! And the old man had been killed for it!
"The discovery . . . the discovery," whispered Mr. Mansfield. "What was it?"
"Took it with him to the grave," said Smith dully. "Dead man's wish. To be respected. Remember?"
Mr. Mansfield shook his head. "We must know it, Smith. There'll be no peace otherwise."
"You find out on your own, Mister Mansfield. I'm done with it. I'm off."
"But I'm blind, Smith. I—I need your eyes—"
"Your daughter's eyes are just as sharp."
"Not so. They're partial. They're dimmed by affection. Yours, Smith, are clear."
Smith, whose eyes were, at that time, anything but clear, being misted with tears of disappointment and general dissatisfaction with the world, nodded.
"True enough."
Mr. Mansfield frowned and his projecting brows hid his empty eyes in pools of darkness so that, to an ignorant glance, he was no more blind than the boy.
"What did you hope for from the document? Great riches? Power? What was it, Smith, that you struggled so hugely for?"
Smith did not answer, partly on account of an obscure anger against the magistrate, and partly because he'd never had a clear notion of what he'd hoped for . . . save to make his way up in the world.
Mr. Mansfield waited, seeming to stare into the fire. Little by little, his head sank once more onto his chest. Smith watched him. Surely he was asleep? Maybe half an hour passed . . .
"Smith!"
"I'm here."
"I thought you'd gone. You said you were going. Have you changed your mind?"
"I'll go in the morning."
Once more there was silence: a long silence, broken only by the crackling of the fire and the blind man's regular breathing. Desolately, Smith stared at the unlucky document. The words jiggled and danced before his tired eyes—but never again to shape themselves into the mystery of hope.
Why had the old man been killed? As if it mattered! He was dead as mutton! Smith frowned. In the morning he'd be off, and the document, the dead man and the blind man would be left behind. Tomorrow, it would be the Town again—with all its subtle alleys and dozy pockets. Back to the beginning.
As if that was possible! Most miserably, Smith knew there could be no returning. Wherever he went, whatever he did, Curtis Court and its long consequences would haunt him. What had the old man discovered—and why had he been so coldly done in?
The blind man had been right. There'd be no peace for Smith till he knew. And, little by little, as he sat by the small fire, the desire to uncover the mystery of Mr. Field's dread became as strong as his first desire to read the document itself.
No more snow had fallen in the night and now a bloodless, bewildered-looking sun stood poised on the eastern hills—as if one nudge of a cloud would topple it into snowy oblivion. Everywhere, there was an air of universal crystallization; for a frost had overlaid the snow and set tiny needles on the fatted twigs of bushes, trees and thickets, that glinted sharply, blue, green and orange.
Sometimes, these bushes took on the shapes of men, unhorsed and frozen as they'd stumbled on; here was a fellow with a slouched hat; there, one with a great nose and a pipe; and there was another, brandishing a huge pistol, fixed for the winter in a murderous aggression.
Somberly, Smith wondered if such a fate had befallen Lord Tom and the two men in brown, for he and Mr. Mansfield were on the last stage of their singular journey to Prickler's Hill, and Smith was as watchful as a hawk.
He sat atop the coach beside the wounded coachman, who was now recovered enough—he swore—to hold the reins in his right hand; though he looked to Smith for help and support whenever the coach tipped. He'd been greatly surprised to see the "weasel" in his master's company—and had inadvertently said so, much confusing Charlie Parkin.
"Weasel? But I understood his name was Jones. I've writ down Jones."
"Jones? He's Smith!" declared the coachman.
" _Jones!_ " said Mr. Mansfield.
"Smith—Jones—Weasel . . ." muttered Charlie. "There's more to this than meets the eye."
"There is indeed!" agreed Mr. Mansfield; and the constable never knew why the blind man laughed.
But now they were nearing the end of their journey. They skirted the village of Whetstone—and still no sign of pursuers.
"The house!" said the coachman, jerking his head towards the eminence of Prickler's Hill.
The house, built in the Palladian style, stood a third of the way up the hill, sheltered from the north by rising ground and separated from Whetstone by an old stone church whose yard, shrouded in snow, was the very image of white and peaceful sleep.
The coach could go no further. The road was steep and vilely slippery. The horses steamed and labored in vain.
"On foot, then," said Mr. Mansfield and he bade the coachman return into Whetstone while he and Smith went forward on foot.
"Pistols, Mister Mansfield? Shall I take 'em?"
The magistrate shook his head. "The gentlemen from Highgate Hill seem to've given up. No need for weapons now."
Smith shrugged his shoulders, took Mr. Mansfield's hand and began the last ascent. Though he could see nothing uneasy anywhere in the white landscape, he could not rid himself of the feeling that they were being watched closely. Where from? The house? The village? Or from the quiet churchyard?
He said nothing of this to Mr. Mansfield, there being no sense in alarming the blind man without just cause. Instead, he listened and commented as Mr. Mansfield talked of Mr. Field and his unlucky life.
He learned, with but half a mind, about the disappearance and most likely death of Mr. Field's only son some years before—which had been followed by so relentless a siege of the old man and his property by his brothers, their wives and children that—
"—That what, Mister Mansfield?"
"That there were suspicions—grim suspicions—that the eager family knew more than they said about the son's death."
Smith sighed. "D'you think that could have been the old man's discovery, Mister Mansfield? That he found out for certain what they'd done?"
Mr. Mansfield had been about to answer when he felt a sudden, strong pressure from Smith's hand.
"What is it, Smith?"
"Nothing. Just the cold."
Smith stared towards the churchyard. He was tolerably certain he'd seen something shift, slightly and secretly . . .
## 18
THOUGH Mr. Field was now many weeks dead, there was still a bereaved air about his house. Dogs barked as the blind man and the boy trudged along the short, curved drive, but no one bade them be quiet—or came to see why they barked. Five yards from the door, Smith faltered.
"What is it? The cold again?"
"Freezing!" said Smith. He had fancied that he'd again seen a movement in the churchyard, which now lay below them.
The barking of the unseen dogs grew louder and to Smith it seemed they were warning, not the house, but the blind man and him to keep away—to abandon whatever it was that had brought them across the snow.
Go back! Back! Wickedness is here! The Devil is here!
But it was too late. They'd been seen approaching. The tall door opened and a footman received them. At the sound of the door the dogs fell silent and the footman nodded.
"The master's beasts, sir. There's no hushing them till they hear the door. The ignorant creatures still believe he will come back and only when they hear the door do they understand he's not come yet. For he always went to them first. Poor, ignorant beasts, God help them!"
Yet Smith felt that the footman was oddly proud of the "ignorant beasts," and maybe thought them not so ignorant after all.
He was old, but still upright—though the worn shine of his livery across his back betrayed a straining—even a longing—to bow at last. He took Mr. Mansfield's card, lowered his eyes to read it—as if to avoid the blind man's stare.
"Yes—yes, of course, sir. I should have known you. You have been before."
"Long ago."
"Long ago, sir."
Now they were in the hall of Mr. Field's house and Smith stared about him as if the discovery the unlucky old man had made might be written somewhere on the walls . . . or was being whispered from the faintly jingling chandelier. But the walls betrayed nothing, only some ghostly pale patches where pictures had once hung.
"Grand paintings used to be there!" said the servant with ancient pride, seeing Smith's looks.
"I remember them," said Mr. Mansfield softly. "I remember a King Saul and David—"
"Aye, sir. That was the first to go."
"To go?"
"Sold, sold, sir . . . to pay the butcher, the baker and—"
"—And the chimney-sweep down the road?" put in Smith quickly.
The servant looked at him curiously: then shrugged his shoulders. "If you will, lad. The chimney-sweep down the road—whoever he may be!"
"A gent with a wooden leg."
At this, the old servant seemed to stiffen and lose what little color the years had left him. Then he recovered. An angry look came into his eyes, and Smith knew he'd made an enemy of the old man. But for the life of him he couldn't imagine why.
Mr. Mansfield inquired for Mr. Lennard but it seemed the attorney was in Barnet and would not be at the house till midday. Indeed, there was no one in the house but Miss Field (the dead master's sister) and two of the nephews.
The footman said "no one" with a strong inflection, so that Miss Field and the nephews coming after, did indeed seem part and parcel of "no one." Not that the old man had been contemptuous—but there was in his voice a weariness of something too well known for contempt.
"The others are with Mister Lennard, sir. They are always with Mister Lennard. They give him no peace, sir—not even to conduct the business. He stayed here, sir, for two nights. But he had to leave. They were at him all the while. Poor souls! For they're in need even of the necessary penny to bless themselves with . . . and so will go to Hell. For who will bless them now? Not I! Not I!"
They were now come into the chief drawing room: a long, handsome apartment with tall windows giving out onto the church and Whetstone beyond it. There was a fire in the grate, but it burned cheerlessly, with uneasy flames and little heat. Here, too, there were ghosts on the walls . . . and a small writing table by one of the windows.
Was it here he'd written of the discovery that had sent him hurrying to the Town?
Smith stared somberly out of the window towards the churchyard. Once more, he had the feeling of being secretly watched.
"Not I," said the servant for a third time; and his grim sentiment was not to be answered.
"You are a hard fellow," said Mr. Mansfield sternly; for hardness begets hardness.
"I am an old man, sir, and in the course of nature, I'll soon be with my master. _Then_ I'll make my reckoning with the Almighty; but before that I must finish my account with Mister Field. Though he is dead, sir, my duty to him is not."
He assisted Mr. Mansfield to a chair which the blind man, being unused to the hands that were guiding him, felt carefully and exactly. He frowned. The upholstery was much torn—a strange state of affairs in so short a time since the master's death.
But it was not that chair alone; everywhere in the room, cushions and seats were in a grievous state—with their white insides peeping forth for all the world as though the wild, pervasive snow had crept into the house and hid itself everywhere.
"Aye," said the servant. " 'Tis the same elsewhere. You'll not find a cushion, chair-covering nor bolster unslit, nor a floorboard unopened. The family have been hard at it. For they've a heathenish belief the master hid a great fortune somewhere against the chance of—of poor dead Jack's returning! But Jack will come back when his father does—and that will be at the Judgment of us all! Not a day before! Aye! And _then_ the beasts will bark and bark!"
(But where did Jack play as a boy? suddenly wondered Smith—with an excitement that had been steadily mounting within him as he remembered the document's injunction.)
Now the servant—after brushing some ash from the hearth, on which the fire looked more wretched than ever—left the room to announce Mr. Mansfield to Miss Field. Smith and the blind man were alone.
"Andrews!" muttered Smith urgently. "We'd best ask Andrews where Jack played as a boy!"
"Why? D'you still have your hopes? If so—forget them, Smith. We'll wait for Mister Lennard. This is his affair alone."
The blind man spoke sharpishly—as if Smith had suddenly lost ground with him. He breathed deeply—and provoked a silence, in which he regretted profoundly what he'd said. But there was no other way. He was much tormented. Though he trusted Smith with his very life, he could not trust him with the dead man's secret. He dreaded the boy would be off, never to be found again in the dark world—save to be hanged.
He said, more gently, "Where are you now?"
"By the fire."
"Oh yes—yes . . ."
"Why did you ask?"
"I—I thought you were over there." He pointed to the windows. "I thought you were staring at me."
But before Smith could answer Miss Field came hurriedly into the room. She was a gaunt-boned, elderly lady—large, though frail and anxious-looking. She rustled tremendously as she moved—like great sweepings of autumn leaves.
"Mister Mansfield! Kate Field at your service, sir!" She held out a hand—looked puzzled when it wasn't taken—then flushed at her mistake and glanced apologetically at Smith, as if she'd wounded _him_.
"Sad times, Mister Mansfield! A brother dead . . . the family penniless! Sell, sell, sell! But we must! To live, you know! I expect you've noticed great change— Oh!" Once more she flushed and bit her lip. "But how's dear little Rose? It—it _is_ Rose, isn't it, sir?"
She seemed particularly anxious to get _something_ right, and was much relieved when the blind man nodded. So she went breathlessly on, shifting about the room—even picking at the ruined furnishings, like a large black moth in search of a meal.
She faintly resembled her murdered brother—and this touched Smith curiously, so that, when she returned—as she often did—to the family's distress and disappointed hopes and desperation for money, he could not share the blind man's indifference. Why shouldn't the silly old woman long for money? And be open about it? Steeped as he was in the darknesses of the Town, Smith understood too well Miss Field's painful distraction—that had pushed out even seemly grief at her brother's death.
Then abruptly, Miss Field realized she was not recommending herself to anyone but the curious urchin the magistrate had brought with him; she cast a rapid, melancholy smile at Smith and began to talk hurriedly and sadly about the dead man.
"Yes—yes . . . a sad life, my brother's! A tragedy, Mister Mansfield! Never, never for a day did he get over the loss of Jack, never accepted it. The shock, I suppose. Always expected him to come riding up the drive. Tragic! Even turned on the rest of us when we tried to tell him. Tragic for _us_! _We_ only meant to help. And—and believe me, it was for the best!" (Here, she glanced uneasily at the servant—as if she suspected him of something worse than contempt.) "Not a worthy son! Not likable. Though I was his aunt, I say it—and God forgive me—he's better off dead! But—but we mustn't speak ill of them—the dead, I mean—for there they lie—" (She was by the window, momentarily looking out.) "—in the churchyard: my brother and his dear wife . . . Well, well! Maybe he's with his precious Jack in heaven now." (She glanced almost defiantly at the servant, who turned away.) "And maybe he repents of having hid his fortune away from us! Cruel, cruel thing to do! Unnatural, don't you think, Mister Mansfield?"
Mr. Mansfield's lips were tight—and Smith was sorry for it. He was, at that time, sorry for a great many things: not least that the long search and deep pursuit should end in this cheerless, ransacked house with the pitiful old lady somehow driving a deeper wedge than ever between him and the implacable blind man.
" _Our_ tragedy, Mister Mansfield! It's all _our_ tragedy! Everyone turns against us! Even Attorney Lennard. Oh, I can tell! He turns away—he frowns—he would not stay here. _God knows_ what he thinks of us all! You come at a sad time, sir! And all on account of the money! Oh, where can it be? _God knows_ we've done our part! _God knows_ we've searched!" (She stared at the torn furnishings.) "Oh, it's cruel! And yet it _must_ be somewhere—Ah!"
She stopped as a far-off tumbling was heard. "My nephews in the attic, sir. I must go! Pray to God they've found something! Pray to _God_!"
She was already half through the door—when she remembered her responsibilities. "Do forgive me, sir. Mind on other things. Our tragedy, you know. Serve wine, Andrews!"
With that, she was gone, leaving Smith to stare, dismayed, at the old servant of whom he'd made an enemy. At Andrews, who held the key to one secret at least.
"Ask him!" breathed Smith desperately into the blind man's ear as Andrews was at a side table. But the magistrate grimly shook his head.
Back came Andrews with a glass of wine for Mr. Mansfield—and for Smith, a deeply hostile look. So Smith returned to staring restlessly and unhappily through the windows. An obscure feeling of haste was gripping him . . . as if he'd been infected by the general unquiet of the house itself. Outside, the churchyard was hid by snow-hatted yews. But up stood the bell tower on tiptoe—with an air of stony peeping.
Andrews was talking with Mr. Mansfield about Jack. Defending the dead son against the unjust attack. Andrews was very jealous of the dead's good name: both father and son. For the living, he'd not so much to say. And the blind man was nodding gravely as he heard how well and handsomely Jack had grown to manhood—instead of asking Andrews where Jack had played as a boy. "Dead man's wishes!" Smith longed to cry out. "To be respected! Ask of Andrews where Jack used to play as a boy!"
"It's twelve years, now," went on Andrews. "And still they've not forgiven him for being loved! Still they dislike him—abuse him—hate and envy him—as if he will indeed come riding up the drive and snatch some trifle out of their greedy hands!"
"Is it twelve years already, Andrews?"
Twelve years it was, and Jack had been just twenty—with the world before him. And then—he'd vanished. Gone into London it was supposed, and been swallowed up. There was a tale he'd been pressed aboard a ship that had gone down with all hands off the Lizard. But did it matter now? After twelve years the dead lie deep and it's only their good name that can be distressed.
"So why can't they let him rest in peace with his father?" Andrews nodded to the windows and beyond, and the peering belfry seemed to nod back. Yet the yews had a secret air . . . These yews were not so close together as Smith had at first supposed. Here and there there were thin gaps. Was it from these gaps that came the sense of watching?
"I'll leave you now, sir," Andrews was saying, and Smith's desperation grew extreme. He sensed that Mr. Mansfield was lost to him. All that remained was "the trifle." Such hopes as he had, had dwindled to that, and he clung to them as if for his life. It was eleven o'clock. The attorney was to come at midday. Smith believed he'd an hour remaining. (But the time was shorter than he dreamed.)
"Mister Andrews!" he cried out.
The servant's hand was on the door. He paused.
"Tell us—what was Jack like as—as a boy?"
"Smith!" muttered the magistrate unhappily.
But Andrews—for some reason—turned to answer.
"Why—he was well-built . . . very well-built. Handsome. Oh yes! And thoughtful. He was of a thoughtful disposition."
"Were he like me, then?"
"He was—country bred." (With a sneer.)
"D'you mean he didn't run an' climb an' play like—like other lads?" went on Smith—who'd done none of these things, save run. "Didn't he 'ave no favorite places to nip into when the going was 'ot? Didn't he 'ave no little alley or court he could call his own, Mister Andrews?"
"Smith!" whispered the blind man fiercely.
"For if he didn't, Mister Andrews, he weren't a very natural boy!"
Andrews—touched on a raw place—answered almost contemptuously: "Where you, boy, might make a nest in a dirty corner of the wicked Town, Jack, when the secret mood was on him (such as comes to all boys who love to dream), would go—"
"—Where? Where would he go?"
Smith's excitement was intense. So near—so near!
" _Smith_ —"
But Andrews had already crossed the room. Not even the furious magistrate could prevent him defending the dead Jack's quality against the urchin.
With wide eyes Smith watched him. He halted by the window. He pointed—and Smith's blood chilled!
" _There_ was Jack's nest! In yonder churchyard—by the statue of a carved black angel. _There_ he'd sit and dream his dreams—and, maybe, even watch us all—"
Andrews was gone from the room. Mr. Mansfield had heard him take his leave.
"Smith!" he whispered, urgently. No answer. "Smith! Smith! Where are you?"
Silence and darkness . . . deeper than the blind man had ever known it. The boy was gone!
He rose to his feet and began, with desperate haste, to feel his way towards the last sound he'd heard: the door closing. The empty air mocked at him—offering the feeling of obstacles, then declaring: Nothing here, blind man—as he jerked and staggered until, thankfully, he struck against the wall.
"Smith! Smith! Come back! You're mad, child! You'll damn yourself. No one will help you now, Smith!"
He found the door, opened it, and felt cold air blowing in his face. This he knew he must follow. He prayed to God no one would see him as he tottered foolishly, ridiculously after the urchin to whom he seemed uncannily chained.
"Smith . . . Smith!" he kept whispering into what he imagined were corners, in the hope the child was hiding from him—was playing a cruel game—was only pretending to be gone to the damnable churchyard to dig up "the trifle," to be gone forever into the implacable silence and dark. "Voices in the night" he'd said on a certain terrible day. Did he know the truth of it? And did he know what the dark was like when the voices were gone? Did he know the _other_ voices that plague a blind man?
"Smith—Smith—"
He was now very near the source of the cold air. He heard a chandelier jingling as a draft stirred it. He was in the hall. The front door was open.
"Smith!" he called helplessly and fell out into the snow. Much shaken, he struggled upright.
"Smith!" he cried out, as loudly as he dared, for he was committed too deeply with the invisible, infant criminal to court any other's knowledge of it. He'd perjured himself for him; he'd given up a dead man's trust to him; he'd broken the law and compromised his own honor for him; he'd wracked himself for him—and because of what? Wretchedly, he shook his head—and the snow fell away from his hair. "Child! Come back to me! Smith—I'm frightened . . . for you . . . for me! Smith—"
There was no answer—nothing but the restless motion of cold air through unseen shrubs. And then a dog began to bark, then another, and another! A shrill, dreadful sound in the blind man's ears. For the creatures now sounded ferocious, as if warning of a new crisis in the house's affairs which they—if they were loosed—could avert. Was it him they would tear and snap at? Or was there someone else on his way?
Suddenly, a hand clutched at his wrist and dragged him furiously to one side. Smith had come back.
"Smith—"
"Quiet! Someone's on his way! The ignorant beasts have gone mad again!"
Smith's voice was low and trembling. He sounded frightened half to death. Had he already been to the churchyard?
"Child—"
"Quiet, I tell you!" His grip on the blind man's wrist was almost vicious in its strength—as if the boy were exacting such small vengeance as he could for having been drawn back. But Smith had conceived with dread that the dogs were barking the approach of the two men in brown!
He'd seen the blind man swaying in the drive. He'd heard him calling. But he had not moved till the dogs barked. So where had he been, so still and quiet and unbreathing, even? By the lych-gate of the churchyard . . . staring into the snow. Certain footprints had appalled him, frozen him body and soul—till he'd heard the warning dogs; which sound had awoken him.
"Where are you dragging me, child?"
"To the churchyard."
"Why?"
"You'll see."
"Have you forgotten—I'm blind?"
"Not that blind, Mister Mansfield."
The dogs were still barking. Whoever was coming was not yet near enough to disappoint them. Smith fancied he heard a carriage door . . . but still he dragged Mr. Mansfield through the concealing bushes, enjoining him to absolute quiet; there was yet more to fear than whatever the dogs barked at and yet more to discover than ever those creatures would learn.
Down, down to the churchyard—with the snow flurrying secretly about them—hurried the boy and the blind man, till they were at the lych-gate. The blind man felt the boy halt a moment: he felt his fingers tremble and grip tighter than ever before; he heard him draw in his breath. Then they went inside . . .
Still and silent was the little garden where the dead were planted and bloomed in stone. Very prettily did the headstones wear their widows' caps of snow and stand respectfully in groups and rows.
But even in death there's ambition, and a carved black angel knelt upon one tomb as if to say: What a special one lies here.
Now this angel knelt upon a flat stone to which mounted three steps. Upon these steps was a second figure, still enough to be likewise carved. A figure with an easy, familiar air—as if he was come back at last to a place much loved in childhood—the figure of a man with a wooden leg . . .
## 19
STILL KNOWING NOTHING for certain but the need for extreme secrecy, the blind man suffered himself to be pulled and dragged down till he felt the stone of the church at his back and heard Smith's voice breathe close in his ear: "He's there, by the statue! Peg-top! Old Hop-an'-Scrape! Whispering Jack! Jack o' the alley! Little Jackie Field—and the spitting image of his done-for Pa! It's my _Mister Black_!"
"The son! Alive?"
"Yes. More's the pity! It was him what done the old man in. Little, limping, whispering Jack!"
"Horrible, horrible!"
"He's not of your opinion! For he's a-smiling, there. He's of a thoughtful disposition, he is. Country bred. Who'd have thought the Devil was born among the green fields out Barnet way? Yes—he's a-smiling very thoughtful. You got no eyes, friend, and you should be thankful. For you ain't missing much!"
So now they knew—beyond all doubt—what discovery the old man had made and sought to take with him to the grave. He had discovered his son was still alive—and would have been better dead. That the hope, the dream, the golden place in his life was as wicked and monstrous a morsel of man and wood as stalked and whispered and hid anywhere in the world.
To this dreadful thing, the document had at last led Smith and Mr. Mansfield . . . to this one-legged gentleman, squatting in the shadow of a carved angel's wing, smiling broodily, with the air of having come by appointment . . . Fearfully, Smith's mind went back to his one-time hopes that the document would raise him up in the world. Instead, it had given him a sight of depths past even his darkest dreams.
But the one-legged gentleman was looking up. Someone was coming—keeping the appointment. Who'd arranged to meet with the Devil?
"Here he comes!" breathed Smith, with bitter triumph. "Yore friend and mine."
For into the churchyard, skipping across the snow with his black coattails flapping—like a prosperous bird of prey—came the neat Mr. Billing!
"Jack!" he called gently.
"Billing!"
Mr. Mansfield stiffened as if to rise. Grimly, Smith held him back. He would have the magistrate hear all there was to be heard.
"The document. Have you got it?" This, from Mr. Billing who was come to "Mr. Black's" side.
"No. Our brown friends are not yet come."
"Ah well, it won't be long now, dear Jack!" Mr. Billing laid his hand round the other's shoulder. The one-legged man seemed to shiver slightly—as if submitting with an ill-grace.
"As you say—not long, dear Billing . . . and we'll be rid of each other!"
"Why, Jack! We're friends! Have been so for years. Why the bitterness—now?"
"You made me kill him, Billing."
" _I_ made you? Jack, Jack, it's not so."
" _You_ planned! _You_ urged! _You_ tempted!"
"Ah, but _you_ acted, Jack! Never forget that!"
"How can I? Not till I die! And, maybe, not even then." He looked up at the black angel—then back to the attorney with a harsh groan. "And d'you remember, you even swore it would be Andrews coming—"
"A murder's a murder, Jack—no matter who perishes. But don't blame yourself, dear. It's not you—or me. It's this world we live in, Jack! What can we do? We've got to live. Take the rough with the smooth, Jack. It'll all come out in the wash! If there's a God in heaven—He knows the difficulties we're up against down here. He'll understand. He'll forgive us. And—if there's no such Judge—well, Jack, what have we got to lose? It's all in the mind, my dear! Well, well—we'd all like to be saints through and through. Nothing nicer. But we can't. It's the world, Jack, not us. And we can't change that. No, sir!"
In the quiet, cold air, the voices carried intimately, so's no inflection, even, was lost on the listeners. It was not Mr. Black, then, but Mr. Billing who was the Devil! Mr. Black was but the outward image of evil—its eyes, teeth, hands, skin and hair—but Mr. Billing was its inward, horrible, cajoling, obliging soul!
They continued murmuring, in a like vein, for a while longer, and it became plain it was not for the first time. There was a weariness in Mr. Black's bitterness and a boredom in the attorney's evasions that bespoke much repetition. Over and above them, the black angel brooded thoughtfully . . . and somewhere beneath them lay whatever it was they'd murdered for: the buried trifle.
But now, a slight breeze sprang up, lifting little tufts of snow from the stones, as if there were a restlessness below—a stirring . . .
"Oh God for Judgment!" groaned Mr. Mansfield. "But what sort of Judgment can there be?"
"At last!" exclaimed the terrible Mr. Black. "They've come!"
And the yet more terrible Mr. Billing smiled and waved.
From the far end of the churchyard, through the quiet yews, came the two men in brown. Very dark-faced and frozen they were, as they approached their employers. But the breeze quickened, and their exchanges were partly lost.
". . . the document?"
". . . not got it!"
". . . not? Why not? Not killed the blind man, then?"
They shook their wicked heads. Mr. Black—gray with terror and rage—raised his hand to strike at them. But Mr. Billing—everyone's friend—stayed his hand, and did not free it. Instead, he forced it down . . . and made it point—(Would Mr. Billing have used even his own finger? Not if another was to hand!)—to the snow. What was so remarkable about the snow? Footmarks. There were his own. There—so curious that they'd chilled Smith's blood when he'd first spied them—were the one-legged man's. And . . . two sets more—not to be accounted for—leading through the gate.
Through the gate, close by the church wall, to a certain old tree.
"They've found us!" whispered Smith. "We ain't got a chance, Mister Mansfield. Judgment's come all right—but it's come for us!"
Slowly, the two men in brown turned to peer at the tree. Then a single grin spread over their faces. They began to walk.
The breeze grew into a wind and the snow about their feet shuddered and shifted as if there was a creeping turmoil below.
"Kill them!" screamed Mr. Billing abruptly. "No help for it! You've got to do it!"
Could Smith have escaped? In all certainty, yes! He'd the agility, the quickness, the wit and the terror to vanish from the abominable churchyard before the men had covered half the distance. But not so Mr. Mansfield. The old "mole-in-the-hole" could never have got further than the gate without a sharp knife in his broad back. So Smith, with all his quickness, wit and terror, lacked the last ingredient for flight: the will. He was not capable of leaving the blind man behind.
"They're a-coming, Mister Mansfield."
"Then for God's sake, go!"
"For God's sake? That's a queer thing!"
The men were now very close. They carried short, glittering knives. Already they could see Smith and were grinning widely—even encouragingly—at him.
Now Smith, in spite of all his knowledge of the worst of the Town—its rogues and vagrants, its thieves and slinking byways—was really no more than a child . . . and he turned to childish weapons for his last defense. With small, trembling fingers he made a snowball, stood up and, with a loud, defiant shriek, flung it at the nearer of the advancing pair.
The man swore—but stopped. His companion—instead of dispatching the boy—laughed. A very costly laugh, that. The seconds thus spent were important.
Momentarily, the wind puffed up a little storm of snow and out of it—as if resurrected from under the white ground itself—staggered a formidable figure.
"Stop! Hold! Stand, there!"
Cloaked, large, pistoled, stood Lord Tom!
"You dirty great bag of wind! Be off with you!" snarled the man with snow in his face.
"Spare the boy! I'll—I'll not have him harmed!"
" _You'll_ not? And who's _you_ , Lord piddling Tom? Be off—or we'll slit you in tiny pieces, friend!"
Lord Tom's frostily bristling face grew pitifully angry.
"Smut!" he called, waving vaguely. "Never fear! Lord Tom's beside you! I'll save you, lad! I'll blow blue daylight through 'em!"
"Be off, Lord Tom!" answered Smith bitterly. "You'd best save your own lousy skin. I'm done with you now! I know you, Lord Tom. And I don't like what I know!"
The huge highwayman flinched. He screwed up his little eyes. Whether or not he really loved the boy was hard to say. Maybe he did, maybe the sharp wound he'd just received was all but mortal. And so, maybe from this moment on, he was fighting for more than his life; he was fighting for his soul.
"Back! Back!" shouted Lord Tom, with the utmost valor and rage.
"And if we don't?" sneered the two men.
"Then you're dead as mutton!"
For a second time, the smaller of the two men in brown laughed. He steadied his knife. Took a pace forward—
"Blue daylight!" roared Lord Tom and fired.
A terrible, double roar; a terrible, double shout and the man who laughed—laughed no more. He was dead. And Lord Tom—Lord Tom, much astonished—was capering foolishly in the snow, opening and shutting his mouth in defiant shouts that emerged as silent puffs of scarlet air.
There was a ball inside of him. Mr. Black had shot him even as he'd discharged his own pistol. Lord Tom was as good as dead, but he seemed not to know it yet. Instead, with the meager remains of his life, he threatened the second of the two men with a pistol that was suddenly grown marvelously heavy. And this second fellow, seeing his companion dead, waited no longer. Wildly, he rushed away.
Lord Tom's dance grew slower and most comically clumsy as he strove to lift his great boots out of the clinging snow. Even as the amazed and suddenly heartbroken Smith watched, all the fire and fury and daring rage drained out of his old hero's face. He halted, tottering, then sank upon his knees, curiously crossing his pistols upon his chest, where there was a warm, gushing pain.
"Ha—ha! Blue daylight, eh, lad?"
They were alone in the graveyard now. Mr. Black had hopped crazily in the wake of his adviser and friend Mr. Billing. They'd heard sounds from the house and escaped. The shots had set up an alarm. The dogs were howling wretchedly.
Lord Tom lay with his head on the lowest of the steps where Mr. Black had sat and waited. Above him brooded the stone angel. If he knew he was done for, the sight must have frightened him. Yet he showed none of it. Sadly, Smith approached him, leading blind Mr. Mansfield.
"Glad to make your—acquaintance, sir! Never—never thought to! Ha-ha! Shake hands? Really, an honor—"
"And for me, Lord Tom. And for me!"
Solemnly, their hands, guided by Smith, met and grasped: the dying highwayman's and the blind magistrate's. And both were glad of it, for both had reached the end of a journey: for Lord Tom it was the last, but for Mr. Mansfield it was, maybe, his first. A very strange journey—from justice to compassion.
Now Lord Tom closed his eyes and from out of his side a red patch blossomed in the snow, spread and gently melted into tiny scarlet needles and caves . . . then filled up.
"Nights on the Common, Smut!" he whispered. "Duval . . . Turpin . . . Robinson . . . and—and—"
"—And Lord Tom!" wept Smith, for his friend was dead.
And so was Mr. Black. Andrews had followed him, as he leapt and hopped away. He'd taken a fowling-piece, caught him this side of Whetstone, and shot him dead.
Mr. Black lay like a malformed dark star in the snow—a giant child's star, with a wooden stick to hold it by—that shadowy, formidable ruin of a good man's son.
What had been his history? As dark and shadowy as the rest of him. Where had he lived, how lost his leg, how met with his corrupt adviser? These were questions to which there were no answers. All that was known for certain was that he'd fled his home twelve years before and never dared return on account of some hanging offense. This, Andrews knew of, and preferred that the world and Mr. Field should think Jack dead rather than damned. A heavy secret—and the granity old fellow's shoulders were bending under it.
But to hide an evil is not to destroy it. The old man had made his discovery and had been hurried into his grave.
Andrews must have stood a great while upon a hillock above the fallen figure for, when Mr. Lennard's coach came towards Prickler's Hill, he was still there, looking to the sky, as if the spread shape below had fallen a great way to this cold, white ruin.
But of Mr. Billing there was no sign, and it seemed for a while as though the earth itself had swallowed him up. No one saw him—neither anyone in the house, nor Mr. Lennard coming from Barnet, nor Miss Mansfield coming afoot from Whetstone, where Mr. Billing, whom she'd insisted on accompanying, had begged her to remain, as if to spare her from the tragic news he was confident was awaiting—that her father had been murdered on Finchley Common. There was no doubt that this vile and hateful man still loved Miss Mansfield; for the sake of which spark of humanity in him, maybe his sentence in the courts of Heaven will be to burn in Hell for one day less than if he'd never loved at all.
## 20
MOURNFUL Smith, Smith of disasters, Smith who'd led the blind so fatefully—storm-tossed, heartbroken Smith. He stared through the windows of the house to the widowy yew trees behind which lay his idol, Lord Tom.
His snow-stained, tear-stained face came but rarely out of its faraway look to survey the busy drawing room and only the most serious commotion could hold him for long. The coming of Mr. Lennard, together with as many of the old man's family as could get into his coach, interested him but little; and even Mr. Mansfield's proud introduction of him to the old-fashioned lawyer with his old-fashioned face—"My guardian angel, sir! A little singed and tattered about the wings—but then he's flown through the caves of hell! Meet Smith."—even this grand introduction provoked but a melancholy smile.
"Pleased to meet you," he muttered, "I'm sure," and turned back to the viewing of his private grief.
Lord Tom—Lord Tom! You blew blue daylight through 'em just like you said! Oh, Lord Tom—you went like the grandest toby of them all!
Cowardice, boastfulness and double-dealing had bled out of Lord Tom into the snow and what remained in Smith's heart was "the grandest toby of them all."
Then Miss Mansfield came and Smith turned and smiled compassionately across the room at her. She'd learned of Mr. Billing's monstrousness and the pain and bitterness in her heart was written in her eyes. Quickly, she crossed to the window, put her arm about Smith's shoulder and pressed her cold face to his, so that her dark hair curtained them off in a private night.
"Sorry you lost a friend, miss," he said. Then he turned away even from her, to the dark yew trees and the strangely moving whiteness beyond.
"Smith," murmured Mr. Mansfield, who had not left his side. "What did he—look like?"
Smith sniffed and swallowed hard. " 'E was a big man, Mister Mansfield, and always wore green. Green 'at, green cloak, green breeches—and 'e'd bright green eyes as well. 'E bristled a bit about the chops, but 'ad such a smile on 'im when he talked of the Common, that 'e fair shone. 'E was a real gallant 'igh toby, Mister Mansfield. One of the best!"
"He—went well, Smith."
"None better, Mister Mansfield."
"He's in Heaven, Smith."
"If there's Commons up there, that's where 'e is, Mister Mansfield. Right up 'igh on the snaffling lay!"
Then Mr. Lennard came over, followed by the inquisitive eyes of Mr. Field's family—the beneficiaries of nothing in particular. He began to talk in low tones to Mr. Mansfield and Smith's mournful attention drifted away; till a piece of sardonic humor struck him—a wry, Smith-like humor.
Mr. Mansfield was mentioning his name and handing over the document to Mr. Lennard. With an awful smile Smith watched the stained and tattered paper change hands. In a moment, it was done.
"Bleeding mail-boy, that's what I been!" he brooded. "Documents took and delivered. No charge. And you may 'ave confidence. I'll rent me an office in the shadow of Saint Paul's. Come wind, come snow, come Newgate Jail and the deaths of friends—Smith gets through with the documents! From Curtis Court to Prickler's Hill in less than three months! Well done, Smith!"
But Mr. Lennard had come now to "the trifle." Mild interest tickled Smith—in spite of his aching heart. It was proposed to go at once to the burying place. Smith sighed. He'd no wish to visit that spot so soon, but the beneficiaries were eager.
"Come, Smith," murmured Mr. Mansfield, hearing sounds of movement to the door. "Let's see it out."
So Smith, still heavy of heart, but none the less inquisitive enough not to be left behind, followed the respectfully hopeful beneficiaries to the sheeted churchyard. Strange occasion: strange procession; to go to a churchyard in hope.
Through the well-remembered little gate they wound, past the rents in the snow to show where the dead man in brown and the mortality of Lord Tom had been decently dragged away.
"He's gone," whispered Smith, and Mr. Mansfield took off his hat.
Black and peaceful was the angel, undisturbed at its mysterious devotions though the world had rocked and tumbled about it.
"Is this the place?"
Andrews nodded. This was the place.
The sexton was fetched from the church and, under a host of desperate eyes, he began to dig.
Strangely like the old man himself were the crowding beneficiaries, thought Smith, as he watched them moving their lips in silent prayer. Like echoes of him: there was his nose, there his chin and there, in his frail, gaunt sister, were his very eyes. Indeed, it was as though Mr. Field was come back to see his wishes at last fulfilled.
Smith turned to watch the toiling sexton who'd pierced the snow and was a foot into the frozen earth. He paused to wipe his brow. Hard on the beneficiaries—to wait while he drew breath. He grunted and continued.
"Ah! What 'ave we 'ere?"
A straining forward: an excitement.
"No. Nothing. A slab of stone. Sorry, good people."
A general perishing of excitement. A gloom, almost. Old Miss Field had begun to weep. Smith bowed his small, storm-tossed head. Was everyone to be disappointed?
"Ah! What 'ave we 'ere?"
The sexton was looking up, frowning. What had been buried and not by him? A trifle. A wooden box . . . a traveling box . . .
"It was _his_!" whispered Miss Field. "I know it! He always used to take it with him to—"
"But 'e's left it behind now, ma'am!" grunted the sexton and struck off the strap with his spade.
It may be that it's unseemly for beneficiaries to beam and twinkle in a churchyard—even to caper gently in the snow and crowd and shake a lawyer's hand. But in God's name, what else were they to do? Crocodiles might have wept, but the beneficiaries were needy human souls.
Mr. Field's wooden box was filled, stuffed and glutted with a prosperous lifetime's guineas! Guineas that lay upon guineas in sunny shoals, gleaming and winking in the cold light. The old man must have carried them there in bags which had long since split and sunk under the spreading weight of coinage for, here and there, tufts of canvas poked up, like threads of cloud in a golden sky.
A hundred thousand! thought Smith dreamily. Must be a hundred thousand golden flatties down there! God save the King! For Smith, whenever he saw a sight too grand for any of his words, always said, "God save the King!"
And sometime later that morning, when the company—in radiant spirits—were back in the house, he had occasion to say once more, "God save the King!"
It is night in the Red Lion Tavern between Turnmill Street and Saffron Hill. In the cellar, Miss Fanny and Miss Bridget—reduced to four or five smoking tallows—are sewing mournfully. Miss Fanny has heard of the death of her admirer and is red-eyed and sniffy. Miss Bridget does not speak but sighs and shrugs her shoulders from time to time. Their shadows hugely comment on them upon the wall.
Miss Bridget looks up as if she will speak—but thinks better of it and returns to her work. Miss Fanny loudly sniffs again.
Suddenly, there are certain sounds from above. Miss Bridget frowns and shakes her head. (Her great shadow does likewise, as if in agreement.) But Miss Fanny puts down her work with an air of presentiment.
"It's him!"
"Never!"
"It's him, Brid! It's him!"
The door opens. There's a clatter and scuffle. Once more, Smith has missed his footing and fallen down the stairs!
"It's him! It's Smut!" cries Miss Fanny, dropping her work entirely and bustling to her feet.
"And about time, too!" says Miss Bridget, looking as stern as she might. "Oh, you felonious child! We thought you was shamefully dead!"
Now Smith picks himself up, rubs his elbows, the side of his head and a shin. He squints disparagingly round the cellar, then grandly at his sisters.
"Dead?" he says. "What business would I 'ave being dead with ten thousand guineas to me name? Answer me that!"
And he stares at them with such an air of offended dignity and unnatural honesty, that they're half inclined to believe him. The half so inclined is Miss Fanny. The half which is not, is Miss Bridget—who's worked hard all of her young life and never dreamed of being related to more than twenty pound in cash.
Resolutely, she's ever set her handsome but toil-sterned face against her softer sister's imaginings, saying over and over again that such gaudy thoughts are as tinsel thread—fit enough to decorate a bodice, but never to hold up a hem. Tears start to her eyes as she sees her sister dote and smile foolishly upon the small Smith whose heart she thought she knew as being closer to her own.
Of a sudden, Miss Bridget feels tired and lonely in the seedy world of the Red Lion's cellar. Why must it always be me, she thinks, who's got to spoil the dreaming? Do they suppose I like this shameful place? But someone must face it out—for we can't live off dreams alone!
"What would you say," says Smith, adding insult to injury by disengaging himself from Miss Fanny and coming to outface the stern Miss Bridget herself, "to a carriage an' pair, and a 'ouse in Golden Square?"
Miss Bridget looks at her silly sister and the thin child whose sharp face is fairly shining with pleasure. She sighs. Why not? she thinks. What harm in a few hours of cheerful dreaming? Soon enough the gray, gray dawn. So Miss Bridget nods and smiles and reaches out to ruffle Smith's head.
"I'd say, child, I'd like it very much. When do we move?"
"Tomorrow," says Smith. "And what would you say to a footman, a maid and a coachie?"
"I'd say, very elegant, child. When do we engage them?" Is it possible Miss Bridget is beginning to enjoy the dreaming—or are her eyes shining only because she's warmed by Smith's generosity even in his dreams?
"Tomorrow," says Smith.
"Oh, Smut!" cries Miss Fanny. "You are good! Might we have a tall coachman, in green livery?"
Smith nods in an offhand fashion. "And what would you say to offering me old friend Mister Magistrate Mansfield of Vine Street a tot of what might warm him against the cold night air?"
Miss Bridget smiles. "I'd say it would be an honor and we'd be very pleased to oblige. When do we invite him?"
"Now!" says Smith and shouts: "Come in, Mister Mansfield! I prepared 'em! Mind the steps. There's thirteen!"
Upon which Miss Fanny shrieks and Miss Bridget goes white as her stockings, for the door has opened and the great blind magistrate himself stands incredibly at the head of the stairs.
"Good evening, ladies. I've heard much about you—"
Very pitiable to behold is now Miss Bridget, for she's gone quite distracted and begins to fly about the cellar in a terrible frenzy of tidying and making seemly. Her thoughts are in a whirl and she knows not if she's on her head or her heels. She keeps crying out very breathlessly: "Oh, Smut! You should have said—you should have warned—Oh, Smut!"
Till Smith puts an end to her cellar-proud misery by saying: "Don't fret, Miss Bridget. He's as blind as a mole. If it wasn't for the whiff, he might as well be in Saint James's Palace! Ain't that so, Mister Mansfield?"
And the great man smiles and nods and Miss Bridget is no longer in any doubt of which way up she is: she _knows_ she is on her head!
And that was how Smith came home: Smith of the courts and alleys: Smith of the corners and byways and many a passing pocket: Smith the ten thousand guinea man! For he'd spoke not a halfpenny less than the truth.
On the morning at Prickler's Hill—to the beneficiaries' approval and his own speechless (save for "God save the King!") delight, Attorney Lennard had awarded him one tenth of the churchyard treasure as a mark of gratitude and esteem: ten thousand guineas!
"A good, round sum," had said Mr. Mansfield, with satisfaction. "And what are you going to do with it, Smith?" But Smith had answered never a word, for he'd fainted away on "King!"
Small wonder, then, that Miss Bridget was distracted and, even after an hour with the magistrate sitting beside her talking gently and wisely of all their futures, still believed she'd fallen a victim to her sister's foolish dreaming and was no more awake than a bed-post!
But at last, when morning brought no gloomy fact to dispel the night's fancy, she permitted herself to believe that the future was a rosy and splendid affair . . . and even to tolerate, with a gracious smile, her sister's favorite remark that, "I always said, Brid, that there was _some_ good in our dockiment, didn't I?"
Though there was no more snow, the weather continued very cold until the beginning of March, when an unlooked-for warmth set in, and the sun came out in spring-like glory. Everywhere, the snow—which had grown as flat, tired and grubby as an old sheet—went into little green holes. Then, swiftly, these holes spread into islands which put out fingers, like children in a round dance, eager to touch their neighbors. So the green islands joined up and the whiteness shrank away till it vanished entirely, and nothing more was left of the snow but a crusty puddle or two in the vicinity of Godliman Street and Curtis Court, where Mr. Lennard, the attorney, has his office and sometimes works late . . . for he's short of a partner. Even though, one night, Mr. Billing came quietly and furtively back!
Much shocked, amazed and a trifle uneasy, Mr. Lennard let him in after warning him that he must and would have him arrested for his monstrous villainy.
"Don't be too harsh on me, sir!" Mr. Billing had muttered, with an apologetic smile. "It's this world we live in that's to blame! But believe me, sir, I've come to make amends!"
Mr. Lennard stared at him—and Mr. Billing promptly declared his intention of turning King's Evidence! He knew where was the second murderer in brown and, for the usual consideration, was prepared to give him up. The "usual consideration" was the sparing of his wretched life. Which, indeed, came to pass; for, though Mr. Billing's heart was black as pitch, his plump lawyer's hands were still as clean as snow.
There was nothing the justice of the law could do with him but sentence him to three years in Newgate Jail. Of which he served a month—and then fell an odd victim . . .
The old man who dwelt in the fireplace took a strong fancy to him and offered him Smith's old snoozing place. Which Mr. Billing, being temporarily without friends, was very glad of, and slept there comfortably till, in one of the old man's dreadful twitchy nightmares, his head was stove in by the old man's chained wrists.
Naturally a great fuss was made, and it was strongly urged that the old man be sent to Bedlam as being a danger to himself and other prisoners. But he never went, for (and not for the first time) his son—to whom the State was much obliged—pleaded powerfully and successfully for his father to remain in the Stone Hall. His son was Mr. Jones, the hangman . . . so the State could scarce refuse _him_ . . .
For a while Smith and Mr. Mansfield wondered uneasily if this strange and violent incident would affect Miss Mansfield—considering her one-time regard for the lying attorney. But Miss Mansfield was well out of that wood and, indeed, out of the wood that had shadowed most of her life.
Smith, staying as he did in Vine Street, had become so much Mr. Mansfield's companion and friend that the tempestuous young lady found herself—as often as not—quite unnecessary. She was able to go out and about in the Town, where, by an extraordinary coincidence, she found a likable young gentleman from Sussex who had been waiting for her all his life (though neither of them suspected it at first).
So Smith, despite his independence of pocket and spirit, has stayed on in Vine Street as firmly and cheerfully and contentedly as only a truly free spirit could have done. Nothing holds him but affection, and nothing feeds this affection so much as the deep understanding of his own fair situation in his blind friend's dark world.
Sometimes, of a late afternoon, the pair of them go out together, and stroll as far as Golden Square, where Smith tells Mr. Mansfield how fine and prosperous a certain Establishment is looking these days. Then they go inside it, and Miss Bridget and Miss Fanny are pleased and charmed to serve them with chocolate. (Gin? The very idea! We are dealing now with ladies!) Then they go out again, and Smith looks up at the shop sign with a grin.
_Miss Bridget and Miss Fanny. Court Dressmakers_.
He nudges Mr. Mansfield in the ribs.
"Oo's to know the Court they was makers for was the Criminal one at Old Bailey?"
And, from their fine bay window, the sisters smile and wave and watch their neat, small brother and his grand and gentle friend walk side by side along the square, till at last they take the corner and are lost from sight.
But now the sun goes down and the air darkens. A wind sets in and clouds swing across the sky. Miss Fanny looks out somewhat sadly and dabs at her eyes with a piece of fine lace. She is thinking of Lord Tom and his glittering ways. But then she looks northward and sighs and smiles. For Lord Tom sleeps in a neat grave at the top of Highgate Hill, overlooking the Finchley Common. Nothing would have pleased him better . . . for from there 'tis but a ghost's step to visit Bob's Inn and go a-riding the night wind with Turpin, Robinson and Duval. A splendid and gallant company!
LEON GARFIELD (1921–1996) was born and raised in the seaside town of Brighton, England. His father owned a series of businesses, and the family's fortunes fluctuated wildly. Garfield enrolled in art school, left to work in an office, and in 1940 was drafted into the army, serving in the medical corps. After the war, he returned to London and worked as a biochemical technician. In 1948 he married Vivian Alcock, an artist who would later become a successful writer of children's books, and it was she who encouraged him to write his first novel, _Jack Holborn_ , which was published in 1964. In all, Garfield would write some fifty books, including a continuation of Charles Dickens's _Mystery of Edwin Drood_ and retellings of biblical and Shakespearean stories. Among his best-known books are _Devil-in-the-Fog_ (1966, winner of _The Guardian_ Children's Fiction Prize), _The God Beneath the Sea_ (1970, winner of the Carnegie Medal), _Bostock and Harris; or, The Night of the Comet_ (1979; forthcoming from The New York Review Children's Collection), and _John Diamond_ (1980, winner of the Whitbread Award).
| {
"redpajama_set_name": "RedPajamaBook"
} | 6,009 |
<h1>{{world.locations[env.location].name}}</h1>
<p class="lead">{{world.locations[env.location].description}}</p>
<p class="lead">
<ul>
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<a href="#/" ng-click="locGoTo(link)">Go to {{world.locations[link].name}}</a>
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| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,568 |
Das Liceo classico Cavour ist das älteste Gymnasium in Turin und eine der traditionsreichsten Oberschulen Italiens. Das nach Camillo Benso von Cavour benannte humanistische Gymnasium befindet sich in der Via Alessandro Tassoni 15, nahe der Metrostation Bernini. Darüber hinaus unterhält es im Stadtteil Santa Rita, unweit des Olympiastadions, eine Außenstelle.
Geschichte
Die Geschichte des heutigen Liceo Cavour geht zurück auf das 1568 von Emanuel Philibert von Savoyen gegründete Collegio dei Nobili. An dieser von Jesuiten geleiteten Ritterakademie wurde rund drei Jahrhunderte lang die adelige und später auch großbürgerliche Elite des Herzogtums Savoyen und dann des Königreiches Sardinien-Piemont ausgebildet. 1787 zog in das ursprüngliche Schulgebäude die Turiner Akademie der Wissenschaften ein. Die Schule kam bis 1931 in einem Karmeliten-Konvent unter.
Nach der Besetzung Piemonts durch Napoleon Bonaparte wurde die Schule nach französischem Vorbild als Liceo bezeichnet. Viktor Emanuel I. stellte sie 1818 als Reale Collegio Maggiore in ihrer früheren Form wieder her und vertraute sie vorübergehend nochmals den Jesuiten an, bis sie 1848 unter staatliche Kontrolle kam. Mit dem Schulgesetz von 1859 wurde im Königreich Sardinien, aus dem 1861 das Königreich Italien hervorging, unter anderem ein achtjähriges Gymnasium eingeführt. Die fünfjährige Unter- und Mittelstufe erhielt den Namen ginnasio, die dreijährige Oberstufe bezeichnete man als liceo. 1865 wurde das ehemalige Collegio Maggiore nach dem verstorbenen piemontesischen und italienischen Premierminister Cavour benannt, 1874 alle Schulstufen unter der Bezeichnung Liceo Ginnasio zusammengefasst. Auch im vereinten Italien blieb das Liceo Ginnasio Cavour eine der besten und prestigeträchtigsten Schulen. Bis zur Jahrhundertwende hatte sie selten mehr als 350 Schüler.
Bei den 1859 eingeführten (oder umbenannten) Gymnasien handelte es sich ausschließlich um humanistische oder altsprachliche Oberschulen. 1911 wurde in Italien das eher naturwissenschaftlich orientierte Liceo Moderno eingeführt, aus dem 1923 das heutige Liceo Scientifico entstand. Beim Liceo Ginnasio Cavour in Turin richtete man 1911 ein Liceo Moderno als Schulzweig ein. Zur Abgrenzung dazu nannte man die bisherige Oberstufe dann Liceo Classico. 1931 zog die Schule in ein neues Gebäude in der Via Tassoni, wo sie sich noch heute befindet. Ab dem Jahr 1940 wurde aus den ersten drei Klassen der Unterstufen von Gymnasien und Fachschulen die neue Mittelschule (scuola media) gegründet, weswegen auch das Liceo Ginnasio Cavour drei Jahrgangsstufen verlor. Wie bei allen humanistischen Gymnasien Italiens behielten jedoch in der Mittelstufe die Jahrgangsstufen 9 und 10 ihre alte Nummerierung IV und V. 1986 wurde im Stadtteil Santa Rita eine Außenstelle eingerichtet.
Bibliothek
Das Liceo Cavour hat eine Bibliothek mit rund 30.000 Bänden und eine Sammlung alter wissenschaftlicher Instrumente.
Alumni
Zu den vielen prominenten Absolventen des Liceo Cavour gehörten der ehemalige Staatspräsident Luigi Einaudi und der ehemalige Erzbischof von Turin Agostino Richelmy.
Siehe auch
Bildungssystem in Italien
Liste altsprachlicher Gymnasien
Weblinks
Website des Liceo classico Cavour
Einzelnachweise
Gymnasium in Italien
Organisation (Turin)
Gegründet 1568
Bildung und Forschung in Turin | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,273 |
Q: How to release a handle through C#? I have an application that IMPLICITLY opens a handle on a dll/file. At some point in the application, I want to release this handle. How can I do it? My application is in C#.
A: What exactly you are trying to do? If you want to load an assembly to do some stuff with that, and then unload it completely, you need to rely on creating a new app domain.
public static void Main(string[] args)
{
AppDomain appDomain = AppDomain.CreateDomain("NewAppDomain");
appDomain.DoCallBack(new CrossAppDomainDelegate(AsmLoad));
// At this point, your assembly is locked, you can't delete
AppDomain.Unload(appDomain);
Console.WriteLine("AppDomain unloaded");
//You've completely unloaded your assembly. Now if you want, you can delete the same
}
public static void AsmLoad()
{
Assembly assembly = Assembly.LoadFrom(@"c:\Yourassembly.dll");
//Loaded to the new app domain. You can do some stuff here
Console.WriteLine("Assembly loaded in {0}",AppDomain.CurrentDomain.FriendlyName);
}
Have a look at this post for more, http://blogs.msdn.com/suzcook/archive/2003/07/08/57211.aspx
Or, if you're only worried about
keeping the file locked, you could use
shadow copying. That will make a copy
of the file on disk and load it from
the new location. The original file
will not be locked by that load. To
do that, set
AppDomainSetup.ShadowCopyFiles to
"true" when creating the AppDomain or
set AppDomain.ShadowCopyFiles to true
after it's already been created.
A: use PInvoke if you have an handler that you want to close
[System.Runtime.InteropServices.DllImport("Kernel32")]
private extern static Boolean CloseHandle(IntPtr handle);
A: Just use the Dispose or Close method of the class that opened the handle.
A: I don't know an easy way. Excessive implicit file locking is something I've always disliked about Windows.
If you need to replace the file, MoveFileEx can do it at next boot. You'd use it to rename or delete the original, and then rename something else into its place.
http://msdn.microsoft.com/en-us/library/aa365240(VS.85).aspx
http://www.pinvoke.net/default.aspx/kernel32/MoveFileEx.html
If you don't want to mess with the API directly there's MoveFile in the SysInternals suite which does the same: http://technet.microsoft.com/en-us/sysinternals/bb897556.aspx
Or you can have another program access the file when your program isn't running.
There's ways to get a list of handles per process, if you really want to try to close the handle, which would most likely just crash your program if .NET tries to access it again. It's not pretty, and the example is C++:
http://www.codeguru.com/forum/showthread.php?t=176997
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 50 |
Als Autotomie () bezeichnet man bei Tieren die Fähigkeit mancher Arten, bei Gefahr einen Körperteil abzuwerfen.
Je nach Tiergruppe wächst der abgeworfene Körperteil danach vollständig, unvollständig oder gar nicht nach (Regeneration).
Beispiele
Eidechsen können bei Gefahr ihren Schwanz abwerfen. Dieser bewegt sich noch mehrere Minuten nach dem Abwerfen und zieht so die Aufmerksamkeit des Fressfeinds auf sich, während die Eidechse flüchten kann. Meistens wächst der Schwanz nur in verkürzter Form nach. Gleiches können auch die Nattern der Unterfamilie Sibynophiinae. Bei ihnen wächst der Schwanz aber nicht nach.
Zwei afrikanische Stachelmausarten, Acomys kempi und Acomys percivali, können einem Zugriff durch Räuber durch ihre ohne großen Widerstand abstreifbare Haut entgegenwirken. Sie sind die ersten Säugetiere, bei welchen die Autotomie der Haut nachgewiesen wurde. Alle Schichten der verlorenen Haut können mit kaum bis keiner Narbenbildung inklusive Haarfollikeln, Schweißdrüsen und anderem vollständig regeneriert werden. Diese Eigenschaften werden derzeit auf Anwendung in der menschlichen Wundheilung hin untersucht.
Einige Schlafmäuse können ihre Schwanzhaut abstreifen, wenn sie daran gepackt werden, und so entkommen.
Regenwürmer und auch Schlammröhrenwürmer können einige Segmente ihres Körpers am Hinterende abtrennen, die später regeneriert werden.
Nur bei einigen Arten der Weberknechte wachsen abgeworfene Beine wieder nach; deshalb sieht man oft Weberknechte mit weniger als acht Beinen.
Viele Arten der Gespenstschrecken besitzen die Fähigkeit, Extremitäten an vorgesehenen Bruchstellen zwischen Schenkel und Schenkelring abzuwerfen und diese bei den nächsten Häutungen Stück für Stück wieder zu ersetzen.
Werden Harfenschnecken angegriffen, so werfen sie einen Teil des Fußes ab, der sich weiterhin bewegt und den Fressfeind ablenkt.
Seesterne können einzelne Körperteile abschnüren. Sie sind auf diese Weise auch in der Lage, sich ungeschlechtlich fortzupflanzen, da aus abgeworfenen Teilen bei manchen Arten neue Individuen entstehen können (Fissiparie).
Seegurken können Teile ihrer inneren Organe abschnüren und sie regenerieren.
Larven der Gemeinen Binsenjungfer können ihre Kiemenblättchen bei Gefahr abwerfen. Sie regenerieren sich mit den folgenden Häutungen wieder.
2021 wurde eine besonders weitgehende Autotomie bei Schlundsackschnecken entdeckt. Zwei Arten können an einer Sollbruchstelle den Großteil des Körpers samt Herz und Organen vom Kopf, der kriechfähig bleibt, abtrennen. Während der Regeneration über etwa 2 Wochen überlebt die Schnecke dank Photosynthese.
Einzelnachweise
Anatomie
Verhaltensbiologie | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,576 |
\section{Introduction}
One of the fundamental problems in studies of low-mass ($M <$ few \msun )
star formation is to track the flow of material from the dense molecular
cloud core through the disk and onto the protostar. Several theoretical
models exist that describe the hydrodynamic collapse of protostellar
envelopes (e.g., Larson 1969; Penston 1969; Hunter 1977; Shu 1977; Tereby, Shu,
\& Cassen 1984; Whitworth \& Summers 1985; Foster \& Chevalier 1993;
Galli et al. 1993; Li \& Shu 1996; McLaughlin \& Pudritz 1997;
Fatuzzo et al. 2004; Adams \& Shu 2007). Observations of the density, temperature,
and kinematic structure of the dense cores and disk can distinguish
between these theoretical models.
Since the timescale
for formation of a solar mass star is typically longer than a million years,
we must track the evolution of material by observing protostellar objects
in different evolutionary states and piece together
an evolutionary theory for the collapse of dense cores and the
subsequent growth and dissipation of a protostellar disk
(e.g, Shu, Adams, \& Lizano 1987; Andr\'e et al. 1993, 2000).
The Class 0 phase is of particular interest because it represents the earliest phase
of star formation after the formation of a first hydrostatic core.
Class 0 objects are defined as protostars that have yet to accrete the
majority of their final mass (Andr\'e et al. 2000) although in practice this
definition is difficult to confirm for individual objects.
Observationally, Class 0 protostars are defined
as protostars which emit more than $0.5$\% of their luminosity at wavlengths
longer than $350$ $\mu$m\ (see Andr\'e et al. 1993).
They are deeply-embedded in a
dense gas and dust envelope (Shirley et al. 2000), they typically drive strong
molecular outflows (Bontemps et al. 1996),
and their luminosities are dominated by a variable accretion luminosity (Evans et al. 2009).
Over the past decade, deep mid-infrared surveys have cataloged the population
of Class 0 protostars in nearby molecular clouds (Dunham et al. 2008,
Evans et al. 2009).
Observations at submillimeter and millimeter wavelengths of Class 0
protostars are useful for constraining the density and
temperature structure of envelopes and disks. The emission is
dominated by optically thin dust continuum emission (Adams 1991, Shirley et al. 2003).
Radiative transfer modeling of the submillimeter continuum has determined
the envelope density structure for several Class 0 protostars
(e.g., Shirley et al. 2002, J\o rgensen et al. 2002) which
is a particularly good discriminant between theoretical
models of inflow and collapse in the protostellar envelope
(see Myers et al. 2000; Andr\'e et al. 2000). The majority of the modeling
has been focused on single-dish (sub)millimeter observations with modest ($10$\mbox{\arcsec} )
resolution; but, in order to study
the connection between the envelope and the disk and in order to study
the properties of Class 0 disks themselves, (sub)millimeter interferometric
observations are needed; however, the interferometric observations must be
modeled in combination with single-dish observations (which provide the
zero spacing data)
to constrain the amplitude of model visibilities. Furthermore, combined
interferometric plus single-dish observations are needed at multiple
wavelengths to constrain the properties of the dust emission
(i.e. $\beta$, the dust opacity index) which is a large source
of uncertainty in the state-of-the-art radiative transfer models.
The spectral energy distribution (SED) of several famous Class 0 sources
have been observed from mid-infrared through centimeter wavelengths; however,
there is a gap in the observations of an order of magnitude in wavelength
in the millimeter spectrum. Traditionally, the longest wavelength
bolometer arrays utilized for star formation studies
operate in the 1 mm band (e.g. MAMBO 1.25 mm,
SIMBA 1.2 mm, BOLOCAM 1.1mm, AzTEC 1.1 mm).
Recently, a new bolometer camera, MUSTANG, that operates at 3.3 mm (90 GHz) was
built for the 100-m Green Bank Telescope\footnote{The Green Bank Telescope
is operated by the National Radio Astronomy Observatory. The National Radio Astronomy
Observatory is a facility of the National Science Foundation operated under cooperative
agreement by Associated Universities, Inc.}
This region of the spectrum is of
interest because observations at longer wavelengths provide a larger lever-arm
for calculating dust opacity properties. At these long wavelengths, the
emission from a protostellar disk may become an
important component to the total flux. MUSTANG observations can provide
the zero spacing data for future interferometric observations (e.g. with ALMA)
of these sources to study the envelope and disk emission at a longer millimeter
wavelength than previously possible.
In this study, we have observed six Class 0 protostars with MUSTANG at 3.3 mm.
We describe the reduction techniques and present calibrated photometry
for the sources (\S2).
We present an analysis
of the spectral indices between the observed bands and published fluxes short-ward
of our 3.3 mm observations. We constrain the properties
of the dust emission (\S3), accounting for emission from both the
envelope (\S3.1) and disk (\S3.2).
\section{MUSTANG Observations and Image Reduction}
We observed six Class 0 protostars (see Table 1) with the MUSTANG 3.3 mm camera
(Dicker et al. 2006, 2008) using the 100-m Green Bank
Telescope (GBT, Jewell \& Prestage 2004). MUSTANG is a 64-pixel bolometer camera with
an 18 GHz wide continuum filter centered at 90 GHz (3.3 m).
The pixels are transition edge-sensors spaced at
$\theta_{FWHM}/2\sim 4''$ with an instantaneous field-of-view of
$40$\mbox{\arcsec} . The theoretical beamsize is $8.5$\mbox{\arcsec}\ on the GBT , however,
the illumination pattern plus surface inaccuracies result in slightly
larger beamsizes of $\sim 11''$ which we characterize with frequent
measurements of bright secondary calibrator sources in each observing
run. Observations were made over three days (February 6, April 24,
and May 8) in 2009. At the start of each run, observations of a bright
compact source (e.g. quasars) are used to solve for primary aperture wavefront phase
errors using the ``Out of Focus'' (OOF) holography technique
(Nikolic et al. 2007; Schwab \& Hunter, in preparation).
The solutions were applied to the active GBT surface.
After the surface is calibrated, we observed the protostars using a
centrally-weighted daisy scanning pattern. This scan pattern strikes a
balance between modulating the sky quickly to beat-down detector noise
drifts, and accumulating integration time on a single, small region of
interest ($\sim 1'$ in diameter). Typical scan speeds on the sky are
$\sim 30$~-~$45''/s$.
Images are reduced by IDL routines through a custom pipeline.
Detector gains are determined by pulsing an internal calibration
lamp periodically. A ``common mode'' template is computed as a function of time by
taking the median of the set consisting of each good detector sample
for a given integration. This common mode template can optionally be low-pass filtered.
The common mode template is fit to and subtracted from each
detector timestream. Most systematic effects, such as atmospheric
emission fluctuations, make almost identical contributions to each
detectors' data. The common mode is highly effective at removing
these systematics. It also, however, filters out astronomical
information on spatial scales larger than the instantaneous camera
field-of-view ($40'' \times 40''$). The optional low-pass filtering mitigates
this effect.
A low-order polynomial is fit to and subtracted from each detector timestream
individually. The order of the polynomial is chosen based on the
duration of the scan in question to have 1 degree of freedom per $\sim 10$
seconds of data, depending on the stability of the data in question.
Individual detector weights are assigned based on the variance
of the fully cleaned detector timestream. A preliminary SNR map is
made before this calculation using the detector white noise level as
an initial weight estimate; segments of the timestream corresponding
to regions of the map with SNR higher than 5 are excluded from the
detector weight calculation, to avoid biasing the weights by the
presence of bright signal.
The data are corrected for atmospheric opacity with the opacity values for each observing
session calculated from
publicly available National Weather Service data\footnote{{\tt
http://www.gb.nrao.edu/$\sim$rmaddale/Weather/index.html}}.
Finally, the data are gridded into a map.
This procedure is iterated once to back out the effect of sky domain
signal on the common mode and polynomial solutions. At the signal
levels in our maps, further iteration does not have a significant
effect on the results. Further details on the data analysis procedures
can be found in Dicker et al. (2009) and Mason et al. (2010).
The MUSTANG 3.3 mm images are shown in Figure 1.
The common mode subtraction used to remove atmospheric emission
also has the effect of removing some large angular-scale source signals.
We have characterized this effect with Monte Carlo simulations using the calculated
model envelope surface brightness profile of B335 from Shirley et al. (2010),
with the range of data reduction parameters used in our actual image production scripts.
These simulations are passed through our full data reduction pipeline so their results
incorporate the effects of all stages of the data reduction process. Of particular significance
is the cutoff frequency of the low-pass filter applied to the common mode template
(typically 0.1 Hz - 0.2 Hz for the data we present). We find that for B335, the peak surface
brightness of the filtered envelope is 80\% to 87\% of the envelope as it would be seen by the GBT+MUSTANG
in the absence of common mode subtraction. By way of comparison, the map obtained with a pure common
mode subtraction ({\it i.e.}, no low-pass filtering of the common mode template) retrieves only
71\% of the peak central surface brightness. Note that this analysis includes the effects of the
error beam of the telescope (discussed in Mason et al. 2010).
The maximum effect, at the center of the envelope, causes $\sim 11$\% more power to be coupled
in from the extended emission than would be seen in the absence of the error beam.
Since we do not know, a priori, the disk contribution at 3.3 mm (\S3.2), we have only
characterized the surface brightness recovery of the envelope.
Observations were made of standard calibrators Ceres (February 6),
Neptune (April 24), and CRL2688 (May 8). The final maps were calibrated in
mJy/beam and in mJy in a $20$\mbox{\arcsec}\ aperture by comparing the peak flux
and flux in a $20$\mbox{\arcsec}\ aperture respectively for the observed calibrators. We limit the
aperture photometry to apertures $\leq 1/2$ the field-of-view of the
MUSTANG array. The total predicted flux at 3.3 mm from Ceres was 465 mJy on
February 6 (Thomas Mueller, private communication). A brightness
temperature of $142 \pm 12$ K was assumed for Neptune observations
(Weiland et al. 2010) in April. The total flux from CRL2688 was
bootstrapped from previous MUSTANG observations over the 2009 season
and was calculated to be 141 mJy. Aperture photometry on the Class 0
sources were performed to determine the peak voltage and the total
voltage in a $20$\mbox{\arcsec}\ aperture which was then multiplied by the
appropriate calibration factor (mJy/Volts) for each day (Table 1). We note that
the weather was dry with low winds on February 6, but that the weather
was much wetter on April 24 and May 8. Calculated zenith opacities
varied from $\tau_{3.3} = 0.074$ to $0.25$. Taking into account the fact that
errors in the assumed zenith opacity also affect the celestial
calibrator sources, we estimate that even in the most extreme case the
overall uncertainty in our results due to the uncertainty in the
zenith opacity is $< 5\%$. This is substantially less than the $8\%$ -
$10\%$ uncertainty in Neptune and Ceres absolute temperature scale.
We therefore assume a $10$\% systematic flux calibration uncertainty at 3.3 mm.
\section{Results}
In this section we constrain the dust opacity index ($\beta$; defined such that
$\kappa_{\nu} \propto \nu^{\beta}$) at millimeter wavelengths using estimates
for the dust temperature calculated from dust continuum radiative
transfer models. We first
calculate the spectral index at (sub)millimeter wavelengths, then develop
a method for calculating the appropriate single dust temperature to characterize
emission within a central aperture. We use the calculated dust
temperatures to determine the range in $\beta$. Finally, in \S3.2 we estimate
the relative contributions to the observed $\beta$ from the envelope and disk
for each of the Class 0 source in our sample.
\subsection{Analyzing Spectral Indices}
We characterize the emission between two wavelengths by assuming that
the SED follows a power-law ($S_{\nu} \propto \nu^{\alpha}$) and calculating
the spectral index
\begin{equation}
\alpha_{\lambda_1/\lambda_2} = \frac{\log(S_{\lambda_1}/S_{\lambda_2})}{\log(\lambda_2/\lambda_1)} \;\; .
\end{equation}
The spectral index is an empirical property of the observed SED that
can be related to the underlying properties of the emission.
We have tabulated the observed spectral indices from 0.86 mm to 3.3 mm
in Table 1. The spectral index between 1.25 mm and 3.3 mm is calculated
from the peak flux density (mJy/beam) in both the MAMBO 1.25 mm observations
of M\"otte \& Andr\'e (2001) and our MUSTANG observations. A direct comparison
is feasible since the solid angles of the IRAM 30-m at 1.25 mm and the GBT 100-m
at 3.3 mm are both approximately equivalent to the solid angle of a
Gaussian beam with FWHM of $11$\mbox{\arcsec} . Unfortunately, we were
not able to make the same peak
flux density comparison with SCUBA observations at 0.862 mm since
the effective beamsize of the JCMT is $16$\mbox{\arcsec} . Therefore, we calculate the
spectral index between 0.86 mm and 3.3 mm using matched $20$\mbox{\arcsec}\ diameter aperture
photometry. The typical millimeter spectral index varies between $\alpha_{1.25/3.3}
= 2.6$ to $3.8$ with an average of $\mean{\alpha_{1.25/3.3}} = 3.2$ for this sample.
Due to L1448NW being at the edge of the map, we were unable to calculate
the flux in a $20$\mbox{\arcsec}\ aperture at 3.3 mm for this source. Excluding L1448NW, the average
$\mean{\alpha_{0.86/3.3}} = 3.0$ is very similar to the spectral index calculated
at 1.25 mm for the same sources.
If we assume the dust opacity ($\kappa_{\nu}$ cm$^2$ gram$^{-1}$)
follows a single-power law at
(sub)millimeter wavelengths ($\kappa_{\nu} \propto \nu^{\beta}$),
then the dust opacity index, $\beta$, may be found from the ratio of fluxes
at the two wavelengths
\begin{equation}
\frac{S_{\lambda_1}}{S_{\lambda_2}} = \left( \frac{\lambda_2}{\lambda_1} \right)^{(3+\beta)}
\frac{exp(h\nu_2/kT_{d}) - 1}{exp(h\nu_1/kT_{d}) - 1} \;\;\;.
\end{equation}
Equation 2 assumes that a single dust temperature, $T_d$, characterizes the emission at
both wavelengths
The derived $\beta$ can
be sensitive to the choice of the dust temperature. For instance, at submillimeter
wavelengths of $442$ and $862$ $\mu$m , $\beta$ varies by a factor of 0.5 for
assumed dust temperatures that range from $10$ to $20$ K (Shirley et al. 2000).
The variation is less severe when two wavelengths longer than $1$ mm are compared;
nevertheless, a suitable single dust temperature must be found.
In reality there are strong gradients
in the density and temperature increasing toward the center of the core.
Since the dust continuum emission
of the envelopes of four of the sources in this survey have been modeled using
radiative transfer, we may use the calculated temperature profiles
$T(s)$ and constrained density profiles $n(s)$ along each line-of-sight distance, $s$,
to estimate the appropriate
characteristic dust temperature within an aperture.
We define the isothermal envelope temperature, $T_{iso}^{env}$,
as the single dust temperature that characterizes the observed emission from
density and temperature gradients within a central aperture.
For a telescope with normalized beam pattern, $P_n(\theta, \phi)$,
the isothermal envelope temperature in a central aperture is derived from the
equation for specific intensity of optically thin dust emission convolved
with the telescope beam pattern,
\begin{equation}
B_{\nu}(T_{iso}^{env}) \int_{\Omega} \int_{s} P_n(\theta,\phi) n(s) ds d\Omega =
\int_{\Omega} \int_{s} P_n(\theta,\phi) B_{\nu}[T(s)] n(s) ds d\Omega \;\;,
\end{equation}
where $B_{\nu}$ is the Planck function. Solving for $T_{iso}^{env}$ gives,
\begin{equation}
T_{iso}^{env} = (h\nu/k) \left[ \ln \left(1 + \frac{\int_{\Omega} P_n(\theta,\phi) N(\theta,\phi) d\Omega}{\int_{\Omega} P_n(\theta,\phi) \int_{s} \frac{n(s) ds}{exp(h\nu/kT(s)) - 1} d\Omega }\right) \right]^{-1} \;\;,
\end{equation}
where $N(\theta,\phi)$ is the column density at an impact parameter $\theta$ away from
the protostar.
The line-of-sight distance is related to the
impact parameter $\theta$ geometrically by $s^2 + \theta^2 = r^2$ where $r$ is the
radial distance from the protostar (see Adams 1991, Shirley et al. 2003).
The isothermal envelope temperatures for the best-fit one-dimensional dust
continuum models of Class 0 sources in this survey are shown in Figure 2.
\mbox{$T^{env}_{iso}$}\ depends on the frequency of the observations. The \mbox{$T^{env}_{iso}$}\ curves
in Figure 2 flatten at millimeter wavelengths. As a result, it is a good
assumption to assume a single characteristic dust temperature at
both wavelengths in Equation 2 as long as both of those wavelengths are
greater than $0.6$ mm ($\Delta T_{iso}^{env} < 0.5$ K).
The single temperature assumption starts to break down
at submillimeter wavelengths, although the variation in \mbox{$T^{env}_{iso}$}\ is not strong.
For instance, the typical difference in \mbox{$T^{env}_{iso}$}\ between \textit{Herschel Space
Observatory} SPIRE wavelengths ($250 - 500$ $\mu$m ) is slightly less than 2 K.
If the emission within the central aperture is dominated by envelope emission,
then the curves in Figure 2 constrain the appropriate dust temperature to use
in calculating $\beta$. In \S3.2, we explore the effects of the contribution
of the disk.
We constrain the dust opacity index using Equation 2 from a plot of $\beta$ versus
the characteristic dust temperature (Figure 3). The $\beta$ curves for
the 0.86 to 3.3 mm flux ratio (blue curves) and 1.25 to 3.3 mm flux ratio (red curves)
are shown as solid lines in Figure 3. The dashed lines represent the $\pm 1 \sigma$
statistical uncertainty in the flux at each wavelength. At the characteristic
\mbox{$T^{env}_{iso}$}\ $\sim 16$ K for this sample
of Class 0 protostars, $\beta$ does not have a strong dependence on the
dust temperature. In general, the derived opacity index agrees within the statistical
calibration uncertainty between $\beta_{0.86/3.3}$ and $\beta_{1.25/3.3}$. Typical
values range from $\beta_{mm} = 0.8$ to $2.2$ with an average value of
$\mean{\beta_{mm}} = 1.5 \pm 0.4$. In the next section, we
interpret the derived $\beta_{mm}$ by accounting for the contribution from disk and envelope
emission.
In all cases except for L1527, the $\beta_{0.86/3.3}$
curve agrees within the statistical errorbars with
the $\beta_{1.25/3.3}$ curve. For L1527, the offset may be accounted
for by a systematic
calibration error of $20$\%
at one or more of the three wavelengths (e.g., with SCUBA, MAMBO, and
or MUSTANG calibration).
The dominant source of uncertainty in determining $\beta_{mm}$
is the uncertainty in the flux ratio at two wavelengths. The uncertainty is lower
if the two wavelengths are more widely spaced (e.g. lower for the
ratio $0.86/3.3$ vs. $1.25/3.3$). An
uncertainty in the fluxes of $20$\% results in a typical uncertainty of $\pm 0.4$ in
$\beta_{1.25/3.3}$ and $\pm 0.3$ in $\beta_{0.86/3.3}$. An accurate flux calibration
at both wavelengths and deep photometry is required to minimize this uncertainty.
A second possibility for this discrepancy is that the emission between 0.86 mm
and 3.3 mm is mixing different fractions of grain populations from the envelope
and disk. This possibility is explored in the next section.
\subsection{Estimating the Disk Contribution}
The total flux observed at 3.3 mm is the sum
of emission from the protostellar envelope, disk, and wind (or jet)
\begin{equation}
S_{\nu}^{dust} = S_{\nu}^{env} + S_{\nu}^{disk} + S_{\nu}^{ff} \;\;\;.
\end{equation}
At submillimeter wavelengths, the dust continuum emission from
Class 0 sources are expected to be dominated by their massive envelopes.
At millimeter wavelengths, this assumption may no longer be valid and the
disk emission may be a significant fraction of the total emission in the
central beam. At centimeter wavelengths, thermal
radio continuum emission (free-free emission) from the protostellar
jet or wind becomes the dominant emission mechanism (Anglada 1995).
The centimeter wavelength free-free emission can be variable from Class 0
protostars (see Shirley et al. 2007). Unfortunately, we do not
have simultaneous centimeter continuum observations at the same epoch as
the MUSTANG observations; however, extrapolation from published VLA
fluxes and spectral indices indicate that the expected contribution from
free-free emission at 3.3 mm is expected to be small ($< 10$\%).
Therefore, we ignore the free-free contribution to the 3.3mm fluxes
in the following analysis.
While it may be advantageous to study dust properties at
millimeter wavelengths close to the Rayleigh-Jeans limit,
the interpretation of single-dish observations
becomes more difficult since
derived $\beta_{mm}$ are an amalgamation of disk plus envelope opacities.
This is a particular issue for calculating $\beta$ since dust grains
may undergo coagulation in the dense enviornments of Class 0 disks,
and therefore the resulting $\beta_{mm}$ is expected to be lower
than for dust in the protostellar envelope (e.g., Henning \& Stognienko 1996,
Dominik \& Tielens 1997,
Poppe et al. 2000, Draine 2006, Birnstiel et al. 2010). We can identify the disk
contribution at (sub)millimeter wavlengths from the visibility amplitudes
of interferometric observations. Since disks are typically small
($R < 100$ AU corresponding to $\theta < 1$\mbox{\arcsec} ), they appear as
unresolved structures on baselines shorter than the characteristic
size. The disk flux may be determined from the flux level of
a flattening in the visibility amplitudes, and a spectral index from
interferometric observations at two wavelengths. In this section,
we estimate the fraction of disk emission at $3.3$ mm
and the
impact on our interpretation of $\beta_{mm}$
for four of
the sources (L483, L1527, B335, and L1448C)
with published multi-wavelength interferometric observations.
L483 is perhaps the easiest example to analyze as the emission from
a disk is thought to be very weak for this source,
even at wavelengths as long as 3 mm (J\o rgensen et al. 2004, 2007, 2009).
This source has been observed with the SMA and OVRO at wavelengths
ranging from 0.8 mm to 3.0 mm and no evidence for a compact component
is seen in the visibility amplitudes. J\o rgensen et al. (2009) estimates a negligible
disk mass compared to the envelope mass.
The measured spectral index for L483 observed in this
paper is consistent
with the spectral index observed by J\o rgensen et al. (2007) with the SMA
between 0.8 and 1.25 mm ($\alpha_{0.8/1.25} = 3.7$ on baselines $> 40$ k$\lambda$).
Therefore, our observations at 3.3 mm are probing the envelope structure
and are not significantly contaminated by emission from a disk.
The observed range of $\beta_{mm} = 1.57 - 2.00$ is consistent with the
opacities typically assumed
for radiative transfer models of Class 0 envelopes. For instance,
the widely used OH5 opacities have a $\beta_{OH5} = 1.85$ for
coagulated dust grains at a density
of $10^6$ cm$^{-3}$ for $10^5$ years with thin ice mantles (Table 2,
column 5 of Ossenkopf \& Henning 1994; also see Table 2 of Shirley et al. 2005
for a summary of $\beta$ for various dust models).
In contrast, the emission from L1527 at 3.3 mm within a central MUSTANG
aperture appears to be dominated by the
disk emission. L1527 has also been observed by J\o rgensen et al (2007)
with the SMA at 0.8 and 1.3 mm where a very flat spectral index of
$\alpha_{0.8/1.3} = 1.9$ is observed on baselines $> 40$ k$\lambda$.
Observations of this source have also been made using BIMA with the combination
of four array
configurations at 2.7 mm where a distinct flattening in visibility amplitudes
is observed on baselines $> 10$ k$\lambda$ with a flux of $42$ mJy
(Y. Shirley, unpublished observations).
The observed spectral index between 1.3 and 2.7 mm is consistent with
SMA results ($\alpha_{1.3/2.7} = 1.8$). All of the observed emission in the MUSTANG
central beam may be accounted for by extrapolating this disk flux and
interferometric spectral indices to 3.3 mm. The spectral indicies reported in Table 1
are larger than the interferometric spectral indices because a significant fraction
($\geq 50$\%) of the flux in the single dish apertures at 0.86 and 1.25 mm is still
coming from the envelope. If the envelope dust has a steeper opacity index
than the disk dust opacity index, the resulting $\beta_{mm} = 0.82 - 1.42$ is then an
overestimate of the true $\beta$ in the disk. Despite this uncertainty in the true disk $\beta$,
the low value is consistent with evidence of evolution of the dust properties
in the L1527 disk and indicates that different dust opacities than are used to model
the envelope are needed (cf. Shirley et al. 2002).
B335 is a popular target with extensive interferometric observations;
however, not all of these observations agree on the disk contribution.
B335 was studied extensively at 1.2 and 3.0 mm
with the Plateau de Bure Interferometer (PdBI)
by Harvey et al. (2003). They found a slight flattening in the visibility
amplitudes for baselines greater than $60$ k$\lambda$. The observed flux on these
long baselines was $21 \pm 3$ mJy at 1.2 mm and $\approx 2$ mJy at 3.0 mm. The
resulting spectral index is $2.6$, slightly less than the spectral index of $3.1$
observed in this paper. Extrapolation of the 3.0 mm disk flux to 3.3 mm results in a
small contribution to the MUSTANG flux ($1.7$ mJy or $10$\% of the 3.3 mm flux).
The PdBI observations do not
agree with the flux estimates from extrapolation of the J\o rgensen et al. (2007) SMA
observations on baselines greater than $40$ k$\lambda$ which predict
a $3.3$ mm disk flux of $7$ mJy or approximately $50$\% of the MUSTANG flux.
The real contribution of the disk flux for B335 is probably somewhere in between
these estimates. It is likely that the J\o rgensen et al. (2007) fluxes
include a contribution from the envelope since emission has been seen on
baselines longer than $40$ k$\lambda$ from the envelope toward B335 (Harvey
et al. 2003).
With the caveat that our estimates of $\beta_{mm}$ toward B335 may have some contribution ($10 - 50$\%)
from a disk component, the derived opacity index $\beta_{mm} = 1.18 - 1.45$
is significantly lower than has been
observed in the outer envelope (Shirley et al. 2010). A comparison
of the opacity ratios at $442/2.2$ $\mu$m\ and $862/2.2$ $\mu$m\
from near-infrared extinction observations and submillimeter continuum images
yields a $\beta_{submm} = 2.1 - 2.5$ for lines-of-sight greater than $15$\mbox{\arcsec}\
from the protostar (lines-of-sight where background stars were detected in NICMOS observations
by Harvey et al. 2001).
This may be direct evidence of a change in the opacity
in the inner envelope and disk of B335. Our derived $\beta_{mm}$ is
consistent with the slope of OH2 dust ($\beta_{OH2} = 1.35$; Ossenkopf \& Henning 1994; Shirley
et al. 2005)
for coagulated dust grains with no ice mantles as might be expected in the warm
inner envelope of a Class 0 protostar. However, contribution from disk emission may be
responsible, in part, for this percieved lowering of $\beta_{mm}$. If we subtract the maximal
disk flux from $1.25$ mm and $3.3$ mm photometry, then $\beta_{mm} = 1.6 - 2.4$
which is consistent with the Shirley et al. 2010 outer envelope determination.
Unfortunately, until observations are performed with an interferometer
at two wavelengths that match the wavelengths of single dish continuum
observations (e.g., 0.86 mm and 3.3 mm with ALMA), then this
level of uncertainty in determining the envelope $\beta_{mm}$ in the
central aperture toward B335 will persist.
Observations of L1448C were also made by J\o rgensen et al. (2007) with the
SMA. \textit{Spitzer Space Telescope} imaging of this region (J\o rgensen et al. 2006)
have discovered that this source is actually two
Class 0 sources in $8$\mbox{\arcsec}\ proximity (L1448C(N) and L1448C(S)).
Because the southern source is
significantly weaker than the northern source (only $7$\% of the flux of the northern
source in the 1.25 mm SMA observations; J\o rgensen et al. 2007), it is likely that
the MUSTANG fluxes are predominantly from the northern source.
The observed spectral index between 0.8 and 1.25 mm on baselines greater
than $40$ k$\lambda$ is significantly shallower than the spectral indices
observed with single dish telescopes. Extrapolating the SMA results to
$3.3$ mm indicates that as much as $50$\% of the MUSTANG flux may be
due to the emission from the disk.
Again, without multi-wavelength interferometric observations that
match the wavelength of single-dish observations, we cannot accurately
determine
the envelope $\beta_{mm}$. The range of $\beta_{mm} = 1.10 - 1.52$
observed toward L1448C is very similar to the range observed toward B335.
Accounting for the maximal disk contribution can also increase the
range of $\beta_{mm}$ in the envelope by $0.5$.
Unfortunately, there are no published u,v amplitude curves
for L1448N and L1448NW; therefore, we are unable
to assess the disk contribution to the MUSTANG fluxes in these two cases.
Interferometric observations have been made at 1.3 and 2.7mm toward
the L1448 IRS3 region which includes these two sources (Looney et al. 2000,
Kwon et al. 2006). L1448N is comprised of two bright sources
separated by 10\mbox{\arcsec}\ (labeled L1448 IRS3 A
and B in Looney et al. 2000) which makes separating their visibility
amplitudes very difficult.
We note that L1448NW has the highest range in $\beta_{mm} = 1.94 - 2.23$.
Given such high values and the expectation that the opacity index is lower
in disks, it seems unlikely that L1448NW has a significant disk contribution.
However, the only way to confidently constrain the envelope and disk
opacities is to analyze the visibility amplitudes at multiple wavelengths with an
interferometer.
\section{Summary}
We have observed 6 Class 0 protostars with the MUSTANG camera at 3.3 mm.
We report fluxes and calculate the spectral indicies
at millimeter wavelengths. Systematic flux uncertainties of up to $20$\%
at (sub)millimeter wavelengths limit determinations of $\beta_{mm}$ to
$\pm 0.4$ if an appropriate characteristic dust temperature is used.
We have estimated the characteristic isothermal temperature
in a central beam ($11$\mbox{\arcsec} ) from previously published dust continuum
radiaitve transfer models ($\mean{\mbox{$T^{env}_{iso}$} } = 16$ K).
The disk emission fraction at $3.3$ mm was estimated
from published interferometric observations. We found emission
at $3.3$ mm is dominated by the envelope for L483 and by the disk
for L1527. The envelope $\beta_{mm}$
for L483 is between $1.6$ to $2.0$, consistent with the opacity index
for the widely used OH5 dust opacities for Class 0 envelopes
($\beta_{OH5} = 1.85$).
The disk $\beta_{mm} \leq 0.8$ to $1.4$
for L1527 is flatter than typical envelope opacity indicies likely
indicating that grain growth is occuring in the disk of L1527.
B335 and L1448C may have comparable disk and envelope
emission although interferometric observations are needed to
better constrain the emission fraction. Taking the maximal disk
contribution at 3.3 mm into account for B335 leads to an estimate
of the envelope $\beta_{mm} = 1.6 - 2.4$ that is consistent with the
recent $\beta_{submm}$
determination in the outer envelope by Shirley et al. (2010).
The 3.3mm obsevations in this paper should be used in conjunction with future
interferometric observations to constrain the properties of the dust emission
in the envelope and disk of Class 0 sources. The next step required
in understanding the physical structure of these sources is muti-dimensional
dust continuum radiative transfer which includes the envelope, disk, and
outflow cavity with dust properties constrained from multi-wavelength
interferometric and single-dish observations. With the incredible sensitivity
of ALMA over a wide range of baselines, it will be possible to obtain
the necessary observations at wavelengths that are well matched to
current single-dish bolometer cameras. The MUSTANG observations presented
in this paper have extended this wavelength
coverage well into the millimeter.
\acknowledgements{Acknowledgements}
We graciously thank the UA/NASA Space Grant Undergraduate
Research Internship Program for funding
David E. Bolin. The authors would like to thank the MUSTANG instrument team from
the University of Pennsylvania, Cardiff University, NASA-GSFC, NRAO and NIST for
their efforts on the instrument and software that have made this work possible.
We thank the operators of the Green Bank Telescope for their assistance
during the observations. We are especially grateful to Todd Hunter whom was present
during the February 2009 observations to test the OOF holography and greatly increase the
GBT aperture efficiency for our MUSTANG observing. We also thank the referee for
a speedy response and many useful comments that benefited this paper.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,353 |
class MakeupBagsController < ApplicationController
get '/bags' do
redirect_if_not_logged_in
@bags = MakeupBag.all
@lipsticks = Lipstick.all
@user = current_user
erb :'makeup_bags/index'
end
get '/bags/new' do
redirect_if_not_logged_in
@error_message = params[:error]
erb :'makeup_bags/new'
end
get '/bags/:id/edit' do
redirect_if_not_logged_in
@error_message = params[:error]
@bag = MakeupBag.find_by_id(params[:id])
erb :'makeup_bags/edit'
end
post '/bags/:id' do
redirect_if_not_logged_in
@bag = MakeupBag.find_by_id(params[:id])
unless MakeupBag.valid_params?(params)
redirect "/bags/#{@bag.id}/edit?error=invalid bag"
end
@bag.update(params.select{|k|k=="name"})
redirect "/bags/#{@bag.id}"
end
get '/bags/:id' do
redirect_if_not_logged_in
@bag = MakeupBag.find_by_id(params[:id])
erb :'makeup_bags/show'
end
post '/bags' do
redirect_if_not_logged_in
unless MakeupBag.valid_params?(params)
redirect "/bags/new?error=invalid bag"
end
MakeupBag.create(:name => params[:name])
redirect "/bags"
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,492 |
04/25/2019 17:36:55 96961091 1 0 0 3730 1 1 Retail Retail - General Store Manager Trainee Store Manager Trainee Full Time circle k | Alexandria, LA NEW I bet you want to know more about the Store Manager position! Leadership skills are essential: You must have the ability to supervise and train the store s... NEW Do you match?
04/22/2019 16:33:12 96299620 2 3 0 3553 1 1 Retail Retail - General $16-$35+/Hour Cashier Jobs Hiring: (Positions Open) $16-$35+/Hour Cashier Jobs Hiring: (Positions Open) Full Time cashier.FindDreamJobs.com | Ball, LA 4 DAYS AGO Easy Apply, Immediate Hire Cashier Jobs Listings $16-$35+/Hour (Positions Open) 4 DAYS AGO Do you match?
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04/20/2019 11:58:46 95789284 5 5 0 3553 1 1 Retail Retail - General $16-$35+/Hour Cashier Jobs Hiring: (Positions Open) $16-$35+/Hour Cashier Jobs Hiring: (Positions Open) Full Time cashier.FindDreamJobs.com | Pollock, LA 6 DAYS AGO Easy Apply, Immediate Hire Cashier Jobs Listings $16-$35+/Hour (Positions Open) 6 DAYS AGO Do you match? | {
"redpajama_set_name": "RedPajamaC4"
} | 1,112 |
Q: "Must be defined" Parametro no definido en consulta Mysql Voy a realizar un update en un formulario con Vb.Net y Mysql, pero me tira el error siguiente "Parameter ?nombre_lugar WHERE must be defined" y bueno no permite editar
Esta es mi consulta;
Dim connstr As String = ConfigurationManager.ConnectionStrings("db").ConnectionString
Dim txt_id_lugar = CType(editableItem.FindControl("txt_id_lugar"), TextBox)
Dim txt_nombre_lugar = CType(editableItem.FindControl("txt_nombre_lugar"), TextBox)
Dim lbl_error = CType(editableItem.FindControl("lblErr1"), Label)
sqlQuery = "UPDATE t_salas set nombre_lugar = ?nombre_lugar"
sqlQuery = sqlQuery & "WHERE id_lugar=?id_lugar"
myconn = New MySqlConnection(connstr)
myconn.Open()
mycommand = New MySqlCommand(sqlQuery, myconn)
mycommand.Parameters.AddWithValue("?id_lugar", txt_id_lugar.Text)
mycommand.Parameters.AddWithValue("?nombre_lugar", txt_nombre_lugar.Text)
A: El error era que ocurria lo siguiente, se pegaba el parametro y el WHERE forMando una sola palabra y bueno le di espacio tal cual y funciono :/
`?nombre_lugarWHERE` ------> `?nombre_lugar WHERE`
//El espacio entre lugar y WHERE
sqlQuery = "UPDATE t_salas set nombre_lugar =?nombre_lugar WHERE id_lugar=?id_lugar"
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,691 |
{"url":"http:\/\/tex.stackexchange.com\/questions\/96862\/what-are-the-effects-of-an-empty-group\/97471","text":"# What are the effects of an empty group, {}?\n\nIn order to have a syntactic space after a no-argument command, one is taught to delimit the command token with an empty group ({}), like this: \\somecommand{} more LaTeX material.\n\nHowever an empty group isn't without meaning: in math mode, $${} + a$$ is typeset differently from $$+ a$$.\n\nAlso, $$\\somecommand{} + a$$ and $$\\somecommand + a$$ are interestingly different. (Insert for example \\empty or \\allowbreak for \\somecommand here.) (An explanatory note: Spaces don't matter in math mode, so since in $$\\somecommand + a$$ the \\somecommand eats up the following space, I would have expected the two to yield identical results. An explanation for why these two are different is given here.)\n\nThis makes me wonder about what else one might need to pay attention to when using empty groups. What are the effects of an empty group and where might one use one?\n\n-\nMay be this is somehow related: What is the difference between \\relax and {} \u2013\u00a0 Manuel Feb 5 '13 at 13:27\n\nMy understanding is that {} has no effect in printing (so long as it doesn't follow a macro with arguments). As { isn't a letter, the collecting of command name stops (a quirk of TeX is that if the collecting stops at whitespace, said whitespace is gobbled up). In math mode, if you write $+ a$, it is a plus sign, while in $a + b$ it is a binary addition symbol (written the same, different meaning, different spacing). Writing ${} + a$ means nothing (an empty group) added to $a$, i.e., an addition.\n\nSummary:\n\n\u2022 In text, use \\somecommand{} to stop (La)TeX from eating the following space, or \\somecommand{}moretext to stop the command name timely (but perhaps {\\somecommand} (if this is safe, meaning \\somecommand does not perform an assignment) in both cases is clearer)\n\u2022 In math, use it as a \"nothing here, but pretend there was\" term\/factor in expressions to force interpretation\/spacing as a binary operator.\n-\n\"Expansion\" in TeX has a technical meaning that doesn't apply here. More precisely, {} in text mode does (almost) nothing (if it's not the argument to a command). It might prevent automatic kerning if placed in the middle of a word, though. \u2013\u00a0 egreg Feb 5 '13 at 17:13\n@egreg, please edit my ramblings to fix any misunderstandings of wrong wording. \u2013\u00a0 vonbrand Feb 5 '13 at 18:12\nI think egreg's comment about kerning is important. In such a case, one should use \\somecommand moretext with nothing in between. \u2013\u00a0 Bruno Le Floch Feb 5 '13 at 18:49\n@egreg Can one really use {\\somecommand} instead of \\somecommand in all cases where \\somecommand does not take arguments? Doesn't the grouping localize (i.e., locally limit) the scope of certain changes? \u2013\u00a0 Lover of Structure Feb 8 '13 at 14:03\n@LoverofStructure If \\somecommand performs some assignment, it of course shouldn't be in braces. In most cases parameterless macros don't. \u2013\u00a0 egreg Feb 8 '13 at 14:12\n\nThis is in reply to the OP's question in the @vonbrand answer thread.\n\nIn fact, an empty group in the middle of a word (but not just a command by itself) prevents kerning (special spacing between pairs of letters) and ligatures. The effect on ligatures is the most visible.\n\n\\def\\f{f}\nffi % => ligature of ffi\nf\\f i % => ligature of ffi\nf\\f{}i % => ligature of ff, then i.\n\\bye\n\nHere, it is typographically better to simply leave a single space after the parameterless macro \\f. Admittedly, this is not a practical example, since no one in their right mind would define such a macro.\n\nA more practical example, perhaps is for someone who defines macros for shorthands of words (don't do this), for instance \\c for constrain, and then adds s, or t, or whatever missing letters for plural, verb, etc. The computer modern font (default of TeX) has a little bit of kerning (space) between n and t. In the first two cases, TeX's stomach sees constraints and \\c ts as a word, and applies kerning as appropriate. In the last case, the empty group in \\c{}ts makes TeX's stomach see two words: constrain and ts, thus no kerning is applied between n and t.\n\n\\def\\c{constrain}\n\\def\\test#1#2{\\setbox0\\hbox{#2}\\immediate\\write16{#1: \\the\\wd0}}\n\\test{No shorthand}{This constrains $a$ to obey some constraints.}\n\\test{No braces}{This \\c s $a$ to obey some \\c ts.}\n\\test{Braces}{This \\c{}s $a$ to obey some \\c{}ts.}\n\\bye\n\nThis might not apply to LuaTeX.\n\n-\nI don't think it applies to XeLaTex either. I read somewhere that an empty group is not enough to stop OpenType ligatures in XeLaTeX. \u2013\u00a0 Johan_E Feb 10 '13 at 0:34\n\nTo add to the existing information: In math mode, {} is also used to affect horizontal subscript\/superscript positioning and to subtly affect vertical subscript\/superscript positioning.\n\n-","date":"2015-07-30 04:22:15","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\": 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\": 0.922342836856842, \"perplexity\": 3018.0486555038387}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"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-2015-32\/segments\/1438042987127.36\/warc\/CC-MAIN-20150728002307-00301-ip-10-236-191-2.ec2.internal.warc.gz\"}"} | null | null |
\section{Introduction}
Systematic monitoring of marine ecosystems is a key objective to promote sustainability and guarantee natural preservation. Developing and testing innovative monitoring systems is thus rapidly becoming a priority in research agendas, and modern technologies have already shown great potential to advance our understanding of marine communities and their habitat \citep{danovaro2016implementing}.
Acoustic approaches are widely used to investigate underwater activity thanks to their ability to detect and classify sensitive targets even in low visibility conditions; moreover, passive acoustic technologies (e.g., hydrophones) allow to perform non-invasive continuous monitoring without interfering with biological processes \citep{sousa2013review}. Notably, most species of marine mammals are acoustic specialists that rely on sounds for communication, reproduction, foraging and navigational purposes. Here we focus on the task of detecting whistles generated by bottlenose dolphins (\textit{Tursiops truncatus}), which can produce a remarkable variety of sound calls for communication purposes (for a review, see \cite{janik2013communication}).
Traditional bioacoustic tools to detect odontocete vocalizations typically rely on template matching or algorithmic analysis of audio spectrograms. For example, in the reference approach pursued by \cite{gillespie2013automatic} three noise removal algorithms are first applied to the spectrogram of sound data, and then a connected region search is conducted to link together sections of the spectrogram which are above a pre-determined threshold and close in time and frequency. A similar technique exploits a probabilistic Hough transform algorithm to detect ridges similar to thick line segments, which are then adjusted to the geometry of the potential whistles in the image via an active contour algorithm \citep{serra2020active}. Other algorithmic methods aim at quantifying the variation in complexity (randomness) occurring in the acoustic time series containing the vocalization, for example by measuring signal entropy \citep{siddagangaiah2020automatic}.
Nevertheless, automatic environmental monitoring can nowadays be made much more efficient thanks to the deployment of surveying techniques based on Artificial Intelligence. Indeed, recent work has shown that machine learning has the potential to identify signals in large data sets with greater consistency than human analysts, leading to significant advantages in terms of accuracy, efficiency and cost \citep{ditria2022artificial}.
In particular, deep learning approaches based on Convolutional Neural Networks (CNN) \citep{lecun1995convolutional} have been applied to detection of whales vocalizations, producing false-positive rates that are orders of magnitude lower than traditional algorithms, while substantially increasing the ability to detect calls \citep{jiang2019whistle,shiu2020deep}. Deep learning has also been used to automatically classify dolphin whistles into specific categories \citep{li2021automated} and to extract whistle contours by exploiting peak tracking algorithms \citep{li2020learning} or by training CNN-based semantic segmentation models \citep{jin2022semantic}.
Here we further demonstrate the advantage of deep learning models over alternative algorithmic approaches by testing the detection capability of convolutional neural networks on a large-scale dataset of recordings, collected in a series of sea experiments and carefully tagged by human experts. We show that the performance of deep learning models dramatically exceeds that of traditional algorithms, and we further show that transfer learning \citep{pan2009survey} from pre-trained models is a promising way to further improve detection accuracy. The complete dataset of dolphin recordings collected for this study is stored on a cloud server and made publicly available to download \citep{DataRepo}.
\section{Method}
\subsection{Dataset}
We created a large-scale database of sound recordings by exploiting a self-made acoustic recorder that comprised a Raspberry Pi-Nano, a sound card sampling at 96~kHz@3B, a pre-amplifier, a battery set, two Geospectrum M18 hydrophones, and a custom made housing. The recorder was anchored by scuba divers at depth of 50~m roughly 200~m from the dolphin's reef in Eilat, Israel. Using floats, the hydrophones were set to hang 1.5~m above the seabed. A picture from the deployment is shown in Fig.~\ref{fig:recorder}. The recorder was made to continuously log \textit{flac} files for 27 days during the Summer period of year 2021: once recovered, the data passed a quality assurance (QA) procedure to remove sporadic cut-offs and extensive noise periods. The QA involved canceling of noise transients by wavelet denoising, and identifying and discarding cut-off events by thresholding and bias removal.
\begin{figure}[]
\centering
\includegraphics[width=0.7\textwidth]{figures/Recorder.png}
\caption{The deployed acoustic recorder with dolphins inspecting the operation. Picture taken from the Eilat deployment site at depth of 50~m.}
\label{fig:recorder}
\end{figure}
\subsection{Data pre-processing and data tagging}
The data passed through a bandpass filter of range 5~kHz-20~kHz to fit most dolphins' whistle vocalizations, and through a whitening filter designed to correct for ripples in the hydrophone's open circuit voltage response and the sound card's sensitivity. Recorded audio files consisted of 2 channels, which were averaged before creating the spectrograms in order to reduce noise (see example in Fig.~\ref{fig:signal_channelling}).
Our pre-processing pipeline also removed signal outliers based on their length, using the quartiles-based Tukey method \cite{tukey1949comparing}. This resulted in discarding signals longer than 0.78 seconds and shorter than 0.14 seconds.
\begin{figure}[]
\centering
\includegraphics[width=1\textwidth]{figures/signal_channelling.png}
\caption{Visualization of the spectrogram (top panels) and raw audio data (bottom panels) of a representative sample containing a dolphin whistle (curved line in the time-frequency plots). Our detection system receives as input the average of the two recording channels.}
\captionsetup{justification=centering}
\label{fig:signal_channelling}
\end{figure}
Spectrograms of dolphin whistles were then created by calculating the short-time fast Fourier transform of the signal using MATLAB's \textit{spectrogram} function from the digital signal processing toolbox, using a Blackman function window with 2048 points, periodic sampling and a hop size obtained by multiplying the window length by 0.8. Subsequent spectrograms were calculated by shifting the signal window by 0.4 seconds. Spectrogram images were finally produced by applying a gray-scale colormap, converting the frequency to kHz and the power spectrum density to dB and limiting the y-axis between 3 and 20 kHz to focus on the most relevant frequency range.
Spectrograms were then manually tagged by one human expert in two phases: 1) marking tagging and 2) validation tagging. The former involved accurate annotation of 5~seconds spectrograms over 10 days of data collection, in order to train a preliminary version of a deep learning classifier that was then used to select new portions of recordings containing putative dolphin sounds. This allowed to more efficiently tag the remaining data during the validation tagging phase, which only involved the verification of positive samples detected by the preliminary deep learning classifier. Although the accuracy of the preliminary classifier was not as high as that reported here for the final classifiers, it nevertheless allowed to significantly speed-up the labeling process by automatically selecting the portions or recordings that most likely contained dolphin whistles.
The human expert was instructed to identify dolphin's whistles as curving lines in the time-frequency domain and to ignore contour lines produced by shipping radiated noise. When discrimination was challenging, the expert directly listened to the recorded audio track to identify whistle-like sounds. The tagging resulted in a binary classification (whistle \textit{vs.} noise) and a contour line marking the time-frequency characteristic of the identified whistle. The latter was used to explore the quality of the manual tagging by checking that the bandwidth of the identified whistle met expected thresholds for a dolphin's whistle, namely between 3~kHz to 20~kHz. A second quality assessment was made by measuring the variance of the acoustic intensity of the identified whistle along the time-frequency contour, where we expect the acoustic intensity of a valid whistle to be stable.
\subsection{Baseline detection method}
As a benchmark detection method we used PamGuard \citep{gillespie2013automatic}, which is a popular software specifically developed to automatically identify vocalizations of marine mammals. The working parameters of PamGuard were set as follows:
\begin{itemize}
\item the ``Sound Acquisition" module from the ``Sound Processing" section was added to handle a data acquisition device and transmit its data to other modules;
\item the ``FFT (spectrogram) Engine" module from the ``Sound Processing" section was added to compute spectrograms;
\item the ``Whistle and Moan Detector" module from the ``Detectors" section was added to capture dolphin whistles;
\item the ``Binary Storage" module from the ``Utilities" section was added to store information from various modules.
\item the ``User Display" module from the ``Displays" section was added to create a new spectrogram display.
\end{itemize}
Input spectrograms were created using the FFT analysis described above, using the same parameters: FFT window length was set to 2048 points, and the hop size was set to the length multiplied by 0.8 using the Blackman window from the ``FFT (spectrogram) Engine" module in the software settings. The frequency range was set between 3 and 20 kHz, and ``FFT (spectrogram) Engine Noise free FTT data" was selected as source of FFT data from the ``Whistle and Moan Detector" module in settings. While creating a new spectrogram display, the number of panels was set to 2 to visualize both channels. The PamGuard output was considered as a true positive detection if the signal window identified by the software overlapped with at least 5\% of the ground truth signal interval. Although this might seem a permissive criterion, it allowed to consider many PamGuard detections that otherwise would have been discarded.
\subsection{Deep learning detection methods}
We explored two different deep neural network architectures: a vanilla CNN and a pre-trained CNN based on the VGG16 architecture used in object recognition \citep{simonyan2014very}. Note that the spectrogram images were resized to 224x224 and converted into 3D tensors in order to match the number of input channels required by VGG. This was simply achieved by replicating the same image array across the 3 dimensions. Image pixels were normalized by dividing each RGB value by 255.
The vanilla CNN model included two convolutional layers interleaved with max pooling layers (pool size = 2) and dropout layers (dropout factor = 0.2). The convolutional layers used 16 and 32 kernels, respectively, with kernel sizes of (7,7) and (5,5), and a stride value of 2. The last convolutional layer was then flattened and fed to 2 fully connected layers containing 32 and 16 nodes, respectively. All layers used a ReLU activation function; only the output layer used a softmax activation. The model was trained using the Adam optimizer with an initial learning rate of 0.0001.
To implement the transfer learning architecture, the top layers of a pre-trained VGG16 were replaced by 2 new fully connected layers with size 50 and 20, respectively, and the \textit{trainable parameter} was set to ``True''. This allowed the optimizer to jointly train all layers of the VGG model, in order to also adjust low-level features to the new data domain. A ReLU activation function was used in both fully connected layers, while the output layer used a softmax activation. The model was trained using the Adam optimizer with an initial learning rate of 0.00001.
In both cases, binary cross-entropy was used as a loss function and overfitting was monitored by using an early stop criteria (with patience parameter of 15 epochs) applied to a separate validation set. Deep learning models were implemented using Tensorflow \citep{abadi2016tensorflow}. All model hyperparameters were automatically optimized using the Optuna framework (\url{https://optuna.org/}).
\subsection{Evaluation procedure}
To guarantee a robust assessment of our detection method, the dataset was split into separate training and test sets. The training set only contained spectrograms obtained from audio files recorded between July 24th and July 30th, while the test set only contained spectrograms of audio files recorded between July 13th and July 15th. This allowed to test the generalization performance of our models using a completely different set of recordings, thus evaluating the detection accuracy with variable sea conditions.
Overall, the training set contained 108317 spectrograms, of which 49807 were tagged as noise and 58510 as dolphin whistles. The test set contained 6869 spectrograms, of which 4212 were tagged as noise and 2657 were tagged as dolphin whistles. The training set was then randomly shuffled and further split into training and validation sets, using 5-fold cross-validation. Cross-validation was implemented using the ``StratifiedKFold'' function from the scikit-learn library in order to make sure that each validation set contained a balanced amount of data from both classes.
Model performance was assessed by computing mean detection accuracy and by visualizing confusion matrices. True Positive rate and False Positive rate were also computed in order to produce Receiver Operating Characteristic (ROC) curves and measure the corresponding Area Under the Curve (AUC) \citep{davis2006relationship}:
\begin{equation}
\label{eq:PrecRec}
\begin{array}{l}
Precision=
\frac{TP}{TP+FP};\\
\vspace{3pt}
Recall=
\frac{TP}{TP+FN};\\
\vspace{3pt}
True \: Positive \: Rate=
\frac{TP}{TP+FN};\\
\vspace{3pt}
False \: Positive \: Rate=
\frac{FP}{FP+TN}
\end{array}
\end{equation}
where $TP$ indicates True Positives, $TN$ True Negatives, $FP$ False Positives and $FN$ False Negatives.
\section{Results}
The vanilla CNN model achieved a remarkable mean detection accuracy of 80.6\%, significantly outperforming the PamGuard baseline, which achieved 66.4\%. Most notably, the performance of the VGG model implementing the transfer learning approach was even more impressive, achieving a mean detection accuracy of 92.3\%.
The advantage of deep learning models is even more striking when considering the confusion matrices: as shown in Fig.~\ref{fig:CM}, although the amount of True Negatives (Label = 0) was comparable across different methods, the number of True Positives was remarkably higher for deep learning models, especially for the VGG architecture. The low sensitivity of PamGuard was highlighted by the very high number of False Negatives ($n$ = 2139), suggesting that this method is not very effective in identifying dolphin whistles when the level of signal to noise ratio makes detection particularly challenging.
\begin{figure}[]
\centering
\includegraphics[width=0.9\textwidth]{figures/confusion_matrices.png}
\caption{Confusion matrices for the deep learning models (vanilla CNN and VGG with transfer learning) and for the PamGuard baseline.}
\captionsetup{justification=centering}
\label{fig:CM}
\end{figure}
The ROC curves and AUC scores reported in Fig.~\ref{fig:ROC} allow to further compare the performance of deep learning models. The superior accuracy of the VGG architecture is evident also in this case, approaching the performance of the ideal classifier.
\begin{figure}[]
\centering
\includegraphics[width=0.8\textwidth]{figures/roc_curves.png}
\caption{Receiver Operating Characteristic (ROC) curves and corresponding Area Under the Curve (AUC) values for both deep learning models.}
\captionsetup{justification=centering}
\label{fig:ROC}
\end{figure}
\section{Discussion}
With the large increase in human marine activity, our seas have become populated with boats and ships projecting acoustic emissions of extremely high power that often affect areas of more than 20 $\mathrm{km}^2$. The underwater radiated noise level from large ships can exceed 100 PSI with a clear disturbance impact on the hearing, self-navigation and foraging capabilities of marine mammals and especially coastal dolphins \citep{ketten2008underwater, erbe2019effects}. Monitoring the marine ecosystem and the sea life is thus a crucial task to promote environment preservation.
Nevertheless, traditional monitoring technologies rely on sub-optimal detection methods, which limit the possibility of conducting long-term and large-scale surveys. Automatic detection methods can greatly improve our surveying capability, however algorithmic solutions do not achieve satisfactory performance in the presence of high levels of background noise. In this paper we demonstrated that modern deep learning approaches can detect dolphin whistles with an impressive accuracy, and are thus well-suited to become the new standard for the automatic processing of underwater acoustic signals. Although further research is needed to validate these methods in different marine environments and with different animal species, we believe that deep learning will finally enable the creation and deployment of cost-effective monitoring platforms.
\section*{Conflict of Interest Statement}
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
\section*{Author Contributions}
RD and AT contributed to conception and design of the study. RD performed the sea experiments and provided the recordings database. BKN and AT designed the deep learning models. BKN implemented the models and performed the analyses. GD performed data tagging. All authors contributed to manuscript writing, revision, read, and approved the submitted version.
\section*{Funding}
The research was funded in part by a grant from the University of Haifa's Data Science Research Center.
\section*{Data Availability Statement}
The datasets created and analyzed for this study can be found here: https://csms-acoustic.haifa.ac.il/index.php/s/2UmUoK80Izt0Roe
| {
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{"url":"https:\/\/crypto.stackexchange.com\/questions\/98088\/is-it-necessary-for-a-round-function-f-in-a-feistel-cipher-to-be-pseudorandom","text":"# Is it necessary for a round function $F$ in a Feistel cipher to be pseudorandom?\n\nI stumbled across this question where the questioner asked for specific requirements for the round function $$F$$ in a Feistel network so that the construction is secure. The answer explained that a pseudorandom function in a four round Feistel cipher is sufficient for it to achieve security.\n\nIs that also necessarily the case? In other words, can a Feistel cipher be constructed with a round function that is not a PRF?\n\n\u2022 The Feistel circuit converts a PRF into a PRP. If not a PRF, what are you planning to have as F? Jan 13 at 16:15\n\u2022 @user93353 This is exactly the question, is there an F that is not a PRF but the Feistel network still gives a PRP? Jan 13 at 16:26\n\u2022 Could you explain what is not a PRF for you? See Tiny Encryption Algorithm (TEA) that uses simple round operations and it is secure with sufficient rounds. Jan 13 at 19:49\n\u2022 @kelalaka I used PRF as defined by the rigorous mathematical definition. But if I understand TEA correctly, I think this is already a counter example. Thank you! Jan 16 at 10:17","date":"2022-01-26 08:44:26","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\": 1, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.4884309768676758, \"perplexity\": 834.841190953535}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-05\/segments\/1642320304928.27\/warc\/CC-MAIN-20220126071320-20220126101320-00590.warc.gz\"}"} | null | null |
Battle for the Boat 75 — 'The Anniversary Show' on Jan. 9th
by Press Releases on Jan.06, 2010, under Boxing News
George 'Monk' Foreman III, David Torres vs. Raymundo Beltran, and the return of Walter Wright featured
TACOMA, Wash. – Brian Halquist Productions and the Emerald Queen Casino will start their 14th year of pro-boxing Saturday, January 9, 2010, with Battle at the Boat 75 – The Anniversary Show. Doors open at 6:00 pm, first fight is scheduled for 7 pm. Battle at the Boat 75 will feature fighters well known to the Northwest boxing fan along with some new faces that will become familiar to the Northwest boxing scene.
The Main Event will feature Othello, Washington's David "El' Torrito" Torres (21-1, 13 KO's) vs. Raymundo Beltran (22-4, 14 KO's) in a 10 round contest. Torres who last fought in October of 2008, will look to gain ground in the light welterweight division. "It's great to have David back at the Emerald Queen. He's had lots of success fighting in Tacoma and we look forward to a great fight with Beltran," said Promoter Brian Halquist.
Also on the card will be George "Monk" Foreman III (4-0, 4 KO's), son of former three time heavyweight champion George Foreman. "George III just started his pro-career this past June and has been extremely active. When we saw that another Foreman was fighting, we set our sights on featuring him on one of our shows," Halquist stated. Foreman III will fight a four rounder. This isn't the first time that a Foreman has fought locally. George Foreman fought an exhibition fight at Fort Lewis at the beginning of his comeback some 20 years ago.
Making his return to the Emerald Queen Casino will be local fan favorite Walter "2 Guns" Wright (13-3, 7 KO's). Wright, who was featured on ESPN's "The Contender" reality television show, will be fighting 6 rounds in the semi-main. "Walter has the skills to be a champion. We built him at the Emerald Queen Casino and the crowd loves him. We want to get Walter back in the ring and feature him in 2010," said Halquist. Wright is a Seattle native who signed with BHP after turning professional.
Making his pro debut will be 2008 Olympic alternate David "Thunder" Clark who is trained by Freddie Roach. "We'll be working with Freddie to develop David in the years to come. Clark was one of the best amateurs in the world and we are very excited about working with him, Freddie and the crew at Wild Card Gym," Halquist said. Roach will be making the trek from the famed Hollywood, California gym to Tacoma with Clark. .
Also making his pro debut is Tacoma's Mike "Imagine" Gavronski. Gavronski is a 3 time Tacoma Golden Gloves champion and was named the "Golden Boy" at the 60th annual Tacoma Golden Gloves tournament in 2008. "Gavronski is ready to turn a pro. He is coming in with an impressive amateur career and the Emerald Queen Casino fight fans have been excited to see his pro-debut," said Halquist. "It's great to turn another local kid pro. Northwest fight fans are so supportive of our local fighters. Mike already has a big local following and there is a big buzz about him."
The Battle at the Boat started on July 9, 1997 in a big circus tent when the Emerald Queen Casino was on a riverboat located on the Tacoma tide flats. On that night Tacoma's Emmett "Laser" Linton faced Jose "Shibata" Flores for the IBA light middleweight world title. A sold out crowed watched the fight and the series was launched.
Showtime, HBO, ESPN, ESPN 2, Telemundo, Fox Sports Network, Univision, Direct TV, and Azteca have all broadcast Battle at the Boat shows from the Emerald Queen Casino. Fights from the series have been shown nationally and internationally.
In July of 2007, The Battle at the Boat saw Vernon Forrest face Carlos Baldomir for the WBC Super Welterweight Title which aired on HBO. It was dubbed one of the biggest fights in Washington State history and definitely lived up to its hype, as Vernon Forrest defeated Carlos Baldomir by Unanimous Decision to lay claim to the vacant world title.
Shortly after that, ShoBox celebrated their 100th telecast on November 2nd 2007 at the Emerald Queen Casino. On that night, heavyweights Eddie Chambers and Calvin Brock fought to a 12 round Split Decision victory for Chambers.
On August 2nd, 2008 Showtime came back to the Emerald Queen Casino to present the Dmitry Kirillov-Vic Darchinyan IBF Super Flyweight Title fight. Vic Darchinyan dominated from the very start and was able to score a 5th round KO to take the title from Kirillov.
The fight series will continue into 2010. Five fights have been scheduled for the year. "We were only planning on doing one show back in 1997," Halquist said. "Thirteen years later we are still going strong. It's been an incredible run and we are looking forward to many more shows in the future. This series has taken on a life of its own. I feel so fortunate to have been a part of this." Halquist said, with a smile on his face.
The Fight card
Main Event – 10 Rounds
David Torres (21-1, 13 KO's) vs. Raymundo Beltran (22-4, 14 KO's)
Semi-Main – 6 Rounds
Walter Wright (13-3, 7 KO's) vs. TBA
Also Featuring:
George Foreman III (4-0, 4 KO's) vs. TBA
Francisco Reyes (3-0, 2 KO's) vs. Darren Darby (5-7-2)
David Clark (Pro Debut) vs. Rob Diezel (Pro Debut)
Mike Gavronski (Pro Debut) vs. Darren Azeie (Pro Debut)
Available at the Emerald Queen Casino box office 1-888-831-7655 and at all Ticketmaster outlets. Or online at www.ticketmaster.com
Ticket Prices: **VIP Ringside $100 – Reserved $60 – General Adm. $30
**All VIP ticket buyers will be invited to a pre-party function at the EQC Bridge Nightclub starting at 5:00 pm.
Quickie Facts
What: Battle at the Boat 75 – The Anniversary Show
Where: Emerald Queen Casino's I-5 Showroom
When: January 9th, 2010
Time: Event starts at 7:00 P.M. Doors open at 6:00 P.M.
2010 Battle at the Boat Schedule
January 9th, 2010: Battle at the Boat 75
April 3rd, 2010: Battle at the Boat 76
June 19th, 2010: Battle at the Boat 77
August 28th, 2010: Battle at the Boat 78
November 13th, 2010: Battle at the Boat 79
Get up to date information at: www.Halquistproductions.com
For more information or fighter interviews contact event coordinator Kelly Thompson at (509) 607-0497
:David Torres, George "Monk" Foreman III, Raymundo Beltran, Walter Wright | {
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coming to New York City to audition for the big 2017 fashion show. While I wish I was actually able to watch the auditions, it was exciting to watch the models show up for their chance to be picked.
Each potential Victoria's Secret model has shown up in a cute outfit while strutting her confidence as she walked into her audition. I knew when a model was coming since the paparazzi would snap into action and start taking pictures.
Some of the models would have some fun and would show us their practice runway walks. They would also do a quick photo shoot for some of the photographers.
Last Monday, the auditions took place during the solar eclipse! So there I was watching the breathtaking moment with both friends and some of the models. It was really nice because it brought everyone together where we were all sharing our eclipse glasses or homemade eclipse viewers. It was definitely a once in a lifetime kind of moment.
Victoria's Secret model Liela Nda borrowed my friend's solar eclipse glasses and the paparazzi took a photo. I really wish I had also taken a picture of it! I checked to see if the photo was released online but I haven't found it yet. But I did find different pictures of the Victoria's Secret models arriving at the office. Another one of my friends had snuck into the background of one of the photos! I couldn't stop laughing! It was fun to Google pictures & videos of the past few weeks and see how many of the models I actually saw.
Good luck to all the models!
Honestly, I have made my own career path by fumbling through the modeling world and just learning along the way. The most important thing I would say is you don't need to wait for a top agency to accept you in order to become a model. When I was 16, I was really excited about modeling. When I first got rejected from the top New York agencies, I assumed that path was permanently closed to me. It wasn't until I was 24, when I was living in Jordan and started freelancing as a model there for local designers, that I realized there are 100 different pathways into this industry.
You should never feel that your fate rests with a few individuals who might have the power to tell you if you have "the look" or not. Obviously, working with a top agency is ideal if that is an option for you. If not, that should not stop you from modeling. I started modeling for local designers until I built up my portfolio. I would also go to castings for runway shows which even allowed me to walk during New York Fashion Week. Finally, after a year of working on my own, I was offered representation.
For models interested specifically in walking during the Cannes Film Festival, I would advise them to attend a casting held by Andres Aquino for New York Fashion Week. He holds castings for his New York shows but not for his Cannes ones. But if you can slip into New York, you can ask about attending Cannes.
I would also advise keeping an eye out for information about castings or fashion shows in Cannes starting in April or the beginning of May. Even if you don't see a notice that is specifically about a casting, there is nothing wrong with contacting the organizer of a fashion show and asking if models are still needed. I have ended up on the runway more than once by simply reaching out and asking. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,779 |
Q: Referring to the caption of current item in a For Next loop Self-taught VBA newbie here. I'm working on a userform where the user will be able to select checkboxes, and the captions of those checkboxes need to be compiled into a single cell (see here). Previously, I just had an If statement for every check box on the form (all 13 of them), but it's getting pretty unwieldy and I'm trying to clean it up.
So far, I've got a For Next loop that runs through all form controls to look for checkboxes and see if they're checked. Next I want to refer to the caption of the current ctrl in the loop, but there is no ctrl.Caption property. I tried to get around this by populating the variable currentcb with the current ctrl's name, but the phrase currentcb.Caption is also returning an Invalid Qualifier error.
UPDATE: I changed around the code a little - @YowE3K was right that ctrl.Caption is a valid property, but now I get Run Time Error 1004: Application-defined or Object-defined error. The debugger highlights the line that starts with ws.Cells(lrow, 7).Value. Any ideas? New code updated below.
For Each ctrl In Me.Controls
If TypeName(ctrl) = "CheckBox" Then
If ctrl.Value = True Then
ws.Cells(lrow, 7).Value = ws.Cells(lrow, 7) & vbCrLf & "|" & ctrl.Caption 'error thrown here
End If
End If
Next ctrl
Is there any workaround for this scenario?
A: @YowE3K was right - ctrl.Caption does exist. Error 1004 was just from some of the hoop-jumping I did in the debugging process. Final, cleaned-up code below:
For Each ctrl In Me.Controls
If TypeName(ctrl) = "CheckBox" Then
If ctrl.Value = True Then
ws.Cells(lrow, 7).Value = ws.Cells(lrow, 7) & vbCrLf & "|" & ctrl.Caption
End If
End If
Next ctrl
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,286 |
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Valuable Insights: Recent CMS Updates Affecting ACOs
Erin DeLoreto – Assistant Vice President, Value-based Programs
Recently, the Centers for Medicare & Medicaid Services announced several updates that affect accountable care organizations (ACOs). Watch this webcast, or read a summary below, to get an overview of the following updates:
Performance Year 2019 Quality Payment Program Deadline Extension and Impacts
Shared Savings Program "Extreme and Uncontrollable Circumstances" Policy
Key Waivers for ACO Participants
Quality Payment Program ("QPP") Extends PY2019 Reporting Deadline
The Centers for Medicare and Medicaid Services ("CMS") Quality Payment Program ("QPP") has extended the performance year ("PY") 2019 reporting deadline from March 31st to April 30th. Eligible clinicians participating in the Merit Based Payment Incentive Program ("MIPS") or the Shared Savings Program ("SSP") now have additional time to meet the minimum reporting requirement for PY2019. This extension applies to MIPS Quality, Promoting Interoperability ("PI"), Clinical Practice Improvement Activities, and Cost categories; as well as Web Interface quality reporting for the SSP Accountable Care Organizations ("ACOs").
Eligible clinicians that do not meet the new deadline will automatically be granted an "extreme and uncontrollable circumstance" exemption: resulting in a neutral payment adjustment for payment year 2021. Providers participating in SSP ACOs that are granted this exemption will be removed from the ACO's MIPS APM scoring for Promoting Interoperability.
Since MIPS payment adjustments are largely budget neutral – meaning that negative payment adjustments offset positive payment adjustments – CMS' broad-based exemption in response to COVID-19 may result in lower-than-projected adjustments for payment year 2021.
For more information about the QPP extension, please visit https://www.cms.gov/newsroom/press-releases/cms-announces-relief-clinicians-providers-hospitals-and-facilities-participating-quality-reporting.
Impact of "Extreme and Uncontrollable Circumstance" Policy for ACOs
In 2017, after a harrowing hurricane season for many parts of the country, CMS refined the "Extreme and Uncontrollable Circumstances" policy for ACOs participating in the SSP. This policy is intended to insulate ACOs from adverse quality and financial penalties due to disasters.
On quality, CMS determines an ACO to be considered impacted by an "extreme and uncontrollable circumstance" if 20% or more of the ACO's attributed beneficiaries reside in an impacted area or if the ACO's legal entity address is located in an impacted area. If an ACO meets either of these criteria, CMS will set the ACO's quality performance score to the mean quality performance score for all ACOs in that performance year. In the event that the ACO completely and accurately reported quality data, CMS will set the ACO's quality score as the higher of the ACO's quality performance score or the mean quality performance score for all ACOs (42 CFR 425.502(f)).
On finance, CMS mitigates shared losses incurred in a performance year in which the ACO was impacted by an "extreme and uncontrollable circumstance" by reducing the ACO's repayment amount. The amount by which shared losses are reduced is calculated as follows: [ACO's shared losses] x [% of months impacted by "extreme and uncontrollable circumstance" during performance year] x [% of ACO's beneficiaries who reside in an area affected by the "extreme and uncontrollable circumstance"] (42 CFR 425.610(i)).
It is important to note that CMS has sole discretion to determine the time period during which an extreme and uncontrollable circumstance occurred, the percentage of the ACO's assigned beneficiaries residing in the affected areas, and the location of the ACO legal entity. Per the interim final rule issued by CMS on March 30th, 100% of counties in the country are impacted by the COVID-19 public health emergency; the timing of this impact commenced in March 2020 and will conclude at the end of the public health emergency.
Centers for Medicare and Medicaid Services ("CMS") Waiver Authority during Public Health Emergency
The declaration of disaster or emergency under the Stafford Act or National Emergencies Act by the President and a subsequent statement of public health emergency under Section 319 of the Public Health Service Act by the Secretary of Health and Human Services ("HHS") authorizes the Secretary to issue "waivers" or modifications to federal program guidelines.
In the wake of the COVID-19 pandemic, a cascade of such waivers have been issued by the Trump Administration to help ensure that sufficient health care items and services are available to meet the needs of persons enrolled in federal health care programs – namely, Medicare, Medicaid, and CHIP. It is important to note that these waivers apply to the federally governed aspects of those program, although, following a federal waiver, state agencies will often waive regulations under their authority.
1135 waivers – named for the pertinent section of the Social Security Act – authorize providers and facilities to be reimbursed for services provided in good faith during a public health emergency. Examples of 1135 waivers include temporary suspension of prior authorization requirements, extending exiting authorizations through the end of the public health emergency, and relax provider enrollment requirements. An up-to-date list of states with 1135 Medicaid waivers as a result of COVID-19 can be found at https://www.medicaid.gov/state-resource-center/disaster-response-toolkit/federal-disaster-resources/index.html.
In addition to the 1135 waiver, the Secretary will frequently authorize an 1812(f) waiver to provide for skilled nursing facility ("SNF") coverage in the absence of a qualifying hospital stay under structure circumstances.
If you are unsure if you are covered by a waiver issued in response to the COVID-19 public health emergency, we encourage you to contact your local Medicare Administrative Coordinator ("MAC"). A list of MACs by region can be found at https://www.cms.gov/Medicare/Medicare-Contracting/Medicare-Administrative-Contractors/Who-are-the-MACs.
If your MAC determines that you are not covered under the provision of the 1135 waiver in your state, you can request a waiver through your local CMS regional office. Instructions for requesting coverage under an 1135 waiver can be found at https://www.cms.gov/Medicare/Provider-Enrollment-and-Certification/SurveyCertEmergPrep/Downloads/Requesting-an-1135-Waiver-101.pdf.
CMS Expands Use of Telehealth
In an effort to minimize the community spread of COVID-19, the Trump Administration has expanded access to telehealth for Medicare beneficiaries. Typically reserved for use in rural areas only, the waiver directs Medicare to reimburse providers for office, hospital, and other visits furnished via telehealth anywhere in the United States.
Providers and patients with access to more robust telehealth platforms can bill a fuller list of services which can be found at https://www.cms.gov/Medicare/Medicare-General-Information/Telehealth/Telehealth-Codes. Additional E&M codes interimly approved by CMS for use during the public health emergency can be accessed at https://www.cms.gov/files/document/covid-19-physicians-and-practitioners.pdf.
Per the interim final rule issued by CMS on March 30th, CMS established an exemption to the definition of telecommunication system as follows, "Interactive telecommunications system means multimedia communications equipment that includes, at a minimum, audio and video equipment permitting two-way, real-time interactive communication between the patient and distant site physician or practitioner" (410.78(a)(3)(i)). CMS further clarified that, for the duration of the COVID-19 public health emergency, the Department of Health and Human Services will be exercising enforcement discretion and waiving penalties for HIPAA violations against health care providers that serve patients in good faith through everyday communications technologies, such as FaceTime or Skype.
The CMS Office of Inspector General ("OIG") has also issued guidance in response to the COVID-19 public health emergency to notify physicians and other practitioners that they will not be subject to administrative sanctions for reducing or waiving any cost-sharing obligations Federal health care program beneficiaries may owe for telehealth services furnished consistent with the applicable coverage and payment rules. The specific terms of the OIG's policy statement can be found at https://oig.hhs.gov/fraud/docs/alertsandbulletins/2020/policy-telehealth-2020.pdf.
As many provider offices and facilities have seen their routine census drop during the COVID-19 outbreak, the use of expanded telehealth services can help stabilize reimbursements for wellness activities, including Annual Wellness Visits, as well as ensure continuity of care for patients during the COVID-19 pandemic. For more information about CMS' telehealth expansion, visit https://www.cms.gov/newsroom/fact-sheets/medicare-telemedicine-health-care-provider-fact-sheet.
Health care professionals: the Medical Necessity Guidelines from the original site are available here.
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\section{Introduction}
Biological cells exhibit a myriad of complex nonlinear responses to stress or strain, exhibiting stress stiffening and softening, viscous flow, elastic recovery, creep and plastic deformation depending on the nature of the applied stress. This wide range of response behaviors results in part from semiflexible actin networks that pervade the cytoskeleton, providing the cell with tensile strength while allowing for morphological changes during cell motion, replication, division, aptosis \cite{stricker2010mechanics, wen2011polymer, gardel2008mechanical}. A host of actin-binding proteins (ABP) present in the cell result in crosslinked actin networks that range from isotropically connected to heterogeneous and highly bundled depending on the length and concentration of actin filaments and ABPs \cite{gardel2010mechanical, schwarz2012united, parsons2010cell}. Crosslinked actin networks also play a principal role in the mechanics and morphology of the extracellular matrix~\cite{machesky1997role}, cortex ~\cite{haase2013role}, and mitotic spindles~\cite{theesfeld1999role, thery2007experimental}. Motivated by such physiological significance and spatiotemporal complexity, the mechanical response of in vitro crosslinked actin networks have been extensively studied and remain a topic of debate~\cite{jensen2015mechanics, tharmann2007viscoelasticity, broedersz2010measurement,wachsstock1994cross,stricker2010mechanics,janmey1994mechanical,enrique2015actin,mason1995optical,gardel2003microrheology}.
Crosslinked actin networks display wide-ranging mechanical responses resulting in part from varying sizes and densities of both ABPs and actin filaments, as well as the compliance and binding affinity of the ABPs and actin filaments~\cite{broedersz2010measurement, wachsstock1994cross}. Further, the mechanical response has been shown to be highly dependent on the length and time scale of the applied strain and measurement~\cite{stricker2010mechanics, janmey1994mechanical, kas1996f, koenderink2006high, liu2007visualizing, gurmessa2016entanglement, broedersz2010measurement}. While extensive rheological measurements at both the microscopic and macroscopic scales have been carried out on crosslinked actin networks~\cite{lee2010passive,luan2008micro, kim2011dynamic}, previous experimental and theoretical work probing the microscale response has been restricted to the linear response limit of small forces and perturbations~\cite{koenderink2006high, kas1996f, semmrich2008nonlinear, gardel2004elastic}. Thus, the nonlinear response of semiflexible networks and gels at the microscale remains largely unexplored. While several studies have investigated the nonlinear response of crosslinked networks at the macroscale, it has been well established that the microscale response of semiflexible networks is distinct from that at the macroscale, and that the deformations and mobility of single or several filaments does not reflect the macroscopic network response~\cite{falzone2015entangled,falzone2015active,uhde2005viscoelasticity,uhde2005osmotic,mason1995optical}. Thus understanding the nonlinear mechanical response of actin networks at the microscale, the filament motions and deformations that give rise to this response, and how such response propagates to the mesoscopic and macroscopic scales remains an important unanswered question.
While crosslinked networks display predominantly elastic response, nearly all networks exhibit some degree of relaxation and fluidity~\cite{enrique2015actin, broedersz2010measurement, lieleg2008transient, wang2010confining}. Networks of sterically entangled actin can relax via several mechanisms unique to semiflexible polymers such as bending, stretching, retraction of filament ends, and chain disentanglement ~\cite{doi1988theory, de1979scaling, isambert1996dynamics}.
However, many of these relaxation mechanisms, most notably disentanglement, are limited in crosslinked networks as many of the molecular crossings in these networks are permanent chemical actin-ABP bonds rather than purely steric interactions. Therefore, the source of relaxation in crosslinked networks remains a topic of debate, with studies suggesting the source to be ABP unbinding, crosslink slippage, or filament buckling, rupture or turnover due to treadmilling~\cite{enrique2015actin,kim2011dynamic, lieleg2011slow, torres2009reversible}. Previous experimental and theoretical studies have shown that the mechanical response of networks crosslinked with ABPs such as heavy meromyosin (HMM) and $\alpha$-actinin are controlled principally by dynamic ABP unbinding/rebinding, in contrast to crosslinking with scruin, fascin and epsin in which the response is dominated by filament buckling and rupture~\cite{huber2013emergent,ferrer2008measuring}. Further, larger, more compliant crosslinkers such as filamin lead to a mechanical response that is dominated by the flexibility of the ABP rather than actin~\cite{kasza2010actin, ferrer2008measuring}. While concentrated crosslinked networks will indeed be influenced by both entanglements and crosslinks, at high enough crosslinker ratio (short enough crosslinker length $l_c$), the dynamics will be governed by the crosslinker length rather than the length between entanglements $l_e$. Previous experiments on actin crosslinked with HMM, reported that the transition between crosslink-dominated to entangled dynamics in the linear regime occurred at $l_c <$ 15 $\mu $m (comparable to the persistence length of actin $l_p \sim 17 \mu $m)~\cite{lieleg2008transient, luan2008micro}. However the extension of this crossover lengthscale to more permanent crosslinkers and to the nonlinear regime, in which filaments are deformed far from equilibrium, remains unknown.
Related topics of debate are how applied stresses propagate or distribute throughout crosslinked networks, and the nature of filament and network deformations that give rise to this distribution. While several studies have suggested that stress is distributed evenly throughout the network due to unbinding and re-binding events and reorganization~\cite{yang2013microrheology, kim2014determinants, head2003deformation, head2003distinct, ferrer2008measuring}; recent studies have also suggested that the stress distribution is highly nonuniform, with the stress being maintained by only a small fraction of highly strained connected filaments that span the network, with the remainder of the network able to relax~\cite{kim2014determinants, vzagar2015two, aastrom2008strain}. Further, induced strains in crosslinked networks are presumed to be affine (uniform) collective deformations at the macroscopic scale, which result in stress hardening/stiffening behavior. However, it has been shown that below a critical strain, $\gamma_c \sim (l_c/l_p)/6$, and lengthscale $\lambda\sim$ ($l_cl_p)^{1/2}$ ($\sim10^{-3}$ and $\sim$1 $\mu$m for the systems under consideration) ~\cite{onck2005alternative}, deformations become nonaffine and heterogeneous, and stress curves exhibit softening rather than stiffening~\cite{broedersz2014modeling, head2003deformation, head2003distinct, das2007effective, liu2007visualizing}. While it is well established that most crosslinked actin filaments display nonlinear stress stiffening/hardening followed by softening; the molecular mechanisms that lead to this signature nonlinear elasticity remain debated. Stiffening has been suggested to arise from suppressing bending modes as the filaments extend to align with the strain, as well as from increasing tension as the filaments are stretched by the strain, with the relative contributions from each depending on the ratio of the polymer bending lengthscale $l_b$ ($\sim$2.3 nm for actin~\cite{onck2005alternative}) and $l_c$~\cite{head2003deformation, onck2005alternative}. For $l_b/l_c << 1 $ bending modes are predicted to dominate and deformations can lead to percolating stress paths, while for $l_b/l_c \sim ~ 0.1$ filament stretching and more uniform stress distribution is predicted as bending between crosslinks becomes more energetically costly~\cite{vzagar2015two, licup2016elastic}. As $l_b/l_c$ approaches 1 stiffening is delayed and suppressed due to the transition of the deformation mode from a bending dominated to stretching dominated regime~\cite{vzagar2015two}. While stiffening has typically been coupled with collective affine network deformations~\cite{head2003deformation, head2003distinct,das2007effective}, recent simulations have shown that stiffening can arise from discrete highly-strained stress paths (i.e. percolating paths of stressed filaments) that are not reflective of the rest of the network that relaxes its induced stress~\cite{kim2014determinants, vzagar2015two, aastrom2008strain}. Further, stiffening has been reported to increase, decrease or stay the same as $l_c$ is increased depending on the system and the scale of the strain~\cite{vzagar2015two, chaudhuri2007reversible}.
On the other hand, entangled and weakly crosslinked actin networks have typically only exhibited softening and nonaffine deformation due to allowed bending modes and retraction of free filament ends dominating stress response~\cite{gardel2004elastic}. Softening, and ultimately yielding, can also arise from stress-alleviating network reorganization on the timescale of the strain, due to intrinsic relaxation mechanisms or strain induced network breakup~\cite{doi1988theory, wang2003relaxation, wang2007new,sussman2012microscopic,lu2014origin}. However, our previous nonlinear microrheology measurements have shown that the response of entangled actin at high enough concentrations ($c>0.4$ mg/ml) is similar to crosslinked networks at the microscopic scale when subject to fast enough strain rates ($\dot\gamma > 3 s^{-1}$) over large enough distances (10 $\mu$m). Namely, entangled actin exhibited stress stiffening coupled with filament deformation that was principally affine (in the direction of the strain). However, these key nonlinear features that arise from spatially-varying filament deformations were only apparent for filaments within $\sim l_p$ of the strain path, decaying to collective linear behavior at larger lengthscales~\cite{falzone2015active, gurmessa2016entanglement}.
These findings motivate the question as to how chemically crosslinked networks respond to nonlinear microscale strains. Are entangled networks able to mimic all features of crosslinked networks at small enough lengthscales for large enough strains? Or are there signature features that emerge that separate entangled and crosslinked networks, and if so what is the degree of crosslinking necessary to invoke these changes? This work also aims to address the important questions outlined above. Specifically, what is the source of nonlinear stress relaxation of crosslinked actin networks at the microscale, what filament deformations and motions lead to this signature relaxation, and how is stress propagated in this nonlinear regime?
We use optical tweezers to drag a microsphere 10 $\mu$m at constant speed through entangled actin networks of varying ABP:actin ratios $R = 0 - 0.07$ and measure the force the network exerts to resist the strain. We subsequently hold the trapped bead fixed following the strain and measure how the built-up force evolves or relaxes over time. Simultaneously we track fluorescent-labeled segments of actin filaments in the network to determine the underlying filament and network deformations that give rise to the stress response and how this stress build-up propagates from segment to segment through the network from the site of the microscale strain. To focus on the response of isotropic networks and the mechanics arising exclusively from actin properties and dynamics, we use biotin-NeutrAvidin as our ABP, which is a small, rigid, and nearly permanent crosslinker; and we solely probe $R$ values high enough to measure an appreciable difference from $R = 0$ but low enough to not induce bundling.
Despite the previously revealed similarities between entangled and crosslinked networks in this regime, we report here a marked shift in mechanics from entangled to highly crosslinked networks. We find that the elasticity of the network is exponentially dependent on the average length between crosslinkers, $l_c$, and the critical crosslinking length where crosslinking dominates entanglement effects occurs when $l_c$ becomes smaller than the entanglement length $l_e$. While all networks exhibit initial stress stiffening followed by subsequent softening, the degree of stiffening exponentially increases with $R$. This initial stiffening is coupled with acceleration of actin segments near the strain, due to entropic stretching along the strain path, while softening is a result of deceleration and even recoil for modestly crosslinked networks, due to network breakup from forced crosslinker unbinding. The filament velocity during strain further exhibits a surprising nonmonotonic dependence on crosslinking, with both $R=0$ and $R = 0.07$ exhibiting the fastest filament speeds while the intermediate $R$ values show less pronounced deformation. By analyzing the relaxation phase, we show that the extreme $R = 0$ strain response is a result of viscous flow and ample network reorganization and yielding while the $R = 0.07$ response is due to the pulling of the highly elastic network with minimal ability to reorient or relax to relieve the strain. The systems in which reorganization and elasticity are comparable result in smaller filament deformations. Further, high levels of elastic stress for $l_c < l_e$ are maintained with minimal relaxation, while the corresponding tracked segments exhibit highly elastic retraction or recoil following deformation with the retraction increasing with increased crosslinking. These contradictory results indicate that the stress is maintained by only a small fraction of connected highly-strained filaments while the majority of the network can elastically retract.
\section*{Materials and Methods}
Lyophilized unlabeled (A), biotinylated (BA) and Alexa-568-labeled (FA) rabbit skeletal muscle globular actin (G-actin) purchased from Cytoskeleton (AKL99, AB07) and Invitrogen (A12374), respectively, were resuspended to concentrations of 2 mg/mL (A), 1 mg/mL (BA) and 1.5 mg/mL (FA) respectively in Ca Buffer G [2 mM Tris pH 8.0, 0.2 mM ATP, 0.5 mM DTT, 0.1 mM $\mathrm{CaCl_2]}$ and stored at $-80^{\circ}C$. Labeled actin segments for tracking were assembled as described in Ref.~\cite{falzone2015active}. Briefly, an equimolar mixture of A and FA were polymerized at 5 $\mu$M for 1 h in F-buffer [10 mM Imidazole pH 7.0, 50 mM KCl, 1 mM $\mathrm{MgCl_2}$, 1 mM EGTA, 0.2 mM ATP]. Filaments were then sheared through a 26 s gauge Hamilton syringe and then immediately mixed with 100\% unlabeled actin of the same concentration (5 $\mu$M) to form actin filaments with interspersed labeled and unlabeled segments (Fig.~\ref{ffig1}). Crosslinked actin networks were formed by polymerizing actin to 0.5 mg/mL with variable concentrations of pre-assembled BA-NeutrAvidin complexes in a twofold molar excess of BA:NeutrAvidin (i.e BA:NA = 2:1). The molar ratio of NA to actin spans a range of $R = 0 - 0.07$ to create networks with average filament lengths between crosslinkers of $l_c = 0.1-0.7~\mu$m. 4.5 $\mu$m carboxylated polystyrene microspheres for measurements (probes, Polysciences Inc.) were labeled with Alexa-488 BSA (Invitrogen) to inhibit interaction with the actin network~\cite{valentine2004colloid} and visualize the probes during measurement. Actin networks for experiments were generated by mixing pre-assembled discretely labeled actin filaments, unlabeled G-actin, BA:NA crosslinker complexes and probes in F-buffer for a final actin concentration of 0.5 mg/ml. The mixture was quickly pipetted into a sample chamber made from a glass slide and cover slip separated $\sim$100 $\mu$m by double sided tape, sealed with epoxy, and allowed to polymerize and crosslink for 1 hr prior to measurement.
The optical trap used in measurements was formed by outfitting an Olympus IX71 fluorescence microscope with a 1064 nm Nd:YAG fiber laser (Manlight) focused with a 60x 1.4 NA objective (Olympus). A position-sensing detector (Pacific Silicon Sensors) measured the deflection of the trapping laser, which is proportional to the force acting on the trapped probe over our entire force range. The trap stiffness was calibrated via Stokes drag in water~\cite{williams2002optical} and passive equipartition methods~\cite{brau2007passive}. During measurements, a probe embedded in the network is trapped and moved 10 $\mu$m at a constant speed of 8 $\mu$m/s relative to the sample chamber via steering of a nanopositioning piezoelectric mirror (Physik Instrumente) while measuring both the laser deflection and stage position at a rate of 20 $kHz$ during the three phases of experiment: equilibration ($5 ~s$), strain ($2 ~s$) and relaxation ($15 ~s$) (Fig.~\ref{ffig1}). The actin concentration and strain rate were both chosen to be higher than our previously determined concentration and strain rate necessary for the onset of nonlinear mechanics. Displayed force curves are averages of $50$ trials using $50$ different probes each at different locations in the sample chamber.
\begin{figure}[ht!]
\centering
\includegraphics[width=8cm,height=16cm,keepaspectratio]{fig1}
\caption{Schematic of coupled microrheology and particle-tracking experiments. (A) Cartoon of actin network crosslinked by NeutrAvidin (red dots) and doped with filaments with interspersed labeled segments (yellow) for tracking. Three phases of experiments shown: equilibration (no trap movement), strain (middle: trapped probe (white) moves 10 $\mu$m through the network at 8$\mu$m/s) and relaxation (no trap movement, probe remains trapped). The white arrows indicate the unbinding/binding of NeutrAvidin during the strain/relaxation phases. (B) Measured force traces for networks with $R = 0.01$ and $R = 0.07$ during three experimental phases. Dashed lines during strain phase indicate the times at which images of labeled filaments are captured. Highlighted region corresponds to time depicted in (D). (C) Sample $122~\mu$m x $140~\mu$m image displaying all filament tracks (rainbow colors) measured for 85 individual measurements. Data for $R = 0.07$ is shown. Image is sectioned into co-centric annuli, each $4.5~\mu$m wide, with increasing radii $d$ centered on the center of the strain path. (D) Probability distributions of tracked particle velocities parallel to the strain $P(v_x)$ at a single window of time (highlighted in (B)) for $R =0.01$ and $R = 0.07$ networks. Distributions for annuli near ($d = 9~\mu$m, top) and far ($d = 40~\mu$m, bottom) from strain path are shown.}\label{ffig1}
\end{figure}
To track labeled filament segments during and following the strain, $122~\mu$m x $140~\mu$m images were recorded at 2.5 fps with a Hamamatsu ORCA flash 2.8 CMOS camera. Each image contained $\sim1.5*10^4$ labeled segments and all tracking data shown is a result of $\sim$85 videos for each condition (Fig.~\ref{ffig1}). The custom particle-tracking code we used to track segment velocities was based on the Matlab implementation of Crocker and Weeks' particle tracking algorithms that obtains the position of each labeled segment and links those positions into tracks in time~\cite{crocker1996methods}. To determine the dependence of particle velocities on distance from the applied strain $d$ we constructed co-centric annuli, each 4.5 $\mu$m wide, with increasing radii centered on the center of the strain path (Fig.~\ref{ffig1}C). For each annulus we calculated the velocity distribution and ensemble-averaged velocity of tracked segments in the $x$ and $y$ directions ($<v_{x}>$ and $<v_{y}>$). All presented data is for $<v_{x}>$ as all $<v_{y}>$ measurements were within the Brownian noise of $\sim$ 63 $nm$, quantified by the average track length per frame during the equilibrium phase. Force and image data was acquired using LabVIEW while custom-written MATLAB programs were used for post-measurement data analysis.
Confocal imaging of networks was also carried out to confirm network structure and morphology. As shown in Figure~\ref{ffig7} all networks are largely homogeneous with minimal bundling. Images also show that as $R$ increases network mobility decreases and connectivity increases.
\begin{figure}[ht!]
\centering
\includegraphics[width=8cm,height=10cm,keepaspectratio]{fig2}
\caption{Steady-state network morphology and structure show decreased mobility and increased connectivity of actin networks with increasing $R$. Images shown are collapsed time-series of networks taken on a Nikon A1R confocal microscope with 60x objective. Each image is a sum of 2700 frames captured over 3 minutes (15 fps). 1\% of actin filaments in the network are labeled with Alexa-568 to resolve network and filament structure and dynamics. As shown, as $R$ increases the time-averaged images have more contrast and less Brownian noise demonstrating that filament mobility is suppressed as $R$ increased. Images also demonstrate that all networks are largely homogeneous. }\label{ffig7}
\end{figure}
\section*{Results}
We first characterize the force exerted on the probe and the corresponding filament motions that result from varying actin networks resisting the constant speed strain. As shown in Figure~\ref{ffig2}, both the magnitude and slope of the induced force increases substantially with increasing $R$ over the entire strain path, indicating that as $R$ increases the available relaxations and reorganizations to alleviate stress are suppressed. To quantify this increased elasticity we evaluate how the differential modulus ($K = dF/dx$) evolves during strain. We find that all networks exhibit stress stiffening ($dK/dt>0$), followed by softening ($dK/dt<0$) and yielding to a steady-state regime, with the maximum stiffness achieved ($K_{max}$) displaying an exponential dependence on $R$ ($K_{max} \sim \exp{(R/R^*)}$) with $R^* = 0.015$. The terminal steady-state $K$ value ($K_t$), as well as the timescale over which the network yields to the terminal regime (yield time, $t_y$), also both exhibit a similar exponential dependence on $R$ (Fig.~\ref{ffig2}). The average $R^*$ value for all three quantities is $R^* \simeq 0.014$, which corresponds to a crosslinking length of $l_c \simeq $0.50 $\mu$m which is smaller than but quite close to the predicted entanglement length $l_e \simeq $0.80 $\mu$m of the network~\cite{falzone2015entangled}. This result suggests that crosslinking dominates the network response once the number of crosslinks exceeds the number of entanglements in the system. In this regime ($l_c < l_e$), relaxation mechanisms of single entanglement segments and filaments are highly suppressed.
While $K$ softens to a principally viscous terminal regime ($K \simeq 0$) for the network with no crosslinks, the terminal force response becomes exponentially more elastic as $R$ increases. For $R = 0$ this largely viscous steady-state regime arises from an equal density of deformed filaments being maintained in front of the bead as it is dragged through the network, with the induced strain on each filament neither increasing or decreasing~\cite{uhde2005osmotic, falzone2015active}. The population of filaments that is deformed is constantly turning over with old filaments sweeping off the probe while new ones are picked up; however the total filament density and the amount that single filaments are stretched remains the same.~\cite{uhde2005osmotic,falzone2015active}. This terminal state is possible because it is achieved at times longer than the fastest relaxation time of the network, $t_{fast} \simeq 0.73~s$ (Fig.~\ref{ffig5}), so filaments are able to evade the constraining entanglements that increase deformation and strain at shorter timescales. Conversely, for highly crosslinked filaments ($R = 0.07$) this terminal regime is principally elastic ($K_t \simeq$ 10 pN/$\mu$m) suggesting that filaments are being stretched throughout the entire strain with few available mechanisms with which they can rearrange or conformationally relax. As $R$ is reduced, substantially less elasticity is sustained, indicating more relaxation mechanisms are introduced into the network as permanent bonds (from crosslinkers) are replaced with transient entanglements. We note that the modest stress softening and yielding exhibited by all networks, which occurs on the order of $t_{fast}$ (see Fig.~\ref{ffig5}) suggests some degree of available relaxation for all networks~\cite{wang2013new}. We previously attributed this fast relaxation in entangled actin solutions to a recently predicted lateral hopping mechanism that can arise in the nonlinear regime, whereby fluctuating filament segments can momentarily evade entanglement confinement due to a reduction in entanglement density induced by nonlinear straining~\cite{gurmessa2016entanglement, sussman2013entangled, wang2013new}. By analogy, similar yielding phenomena in crosslinked networks would imply momentary evasion of crosslinking confinement, which can arise from forced crosslinker unbinding and subsequent rebinding~\cite{kim2014determinants, vzagar2015two, aastrom2008strain}. As $l_c$ decreases and the number of crosslinks per filament increases, each forced crosslinker turnover event would lead to less relaxation per filament and thus less network reorganization and more sustained elasticity (as shown in Fig.~\ref{ffig2}D). While we cannot rule out filament rupturing events, we would expect rupture events to increase for higher forces and more constrained networks, so we would expect to see more dramatic yielding and flow for higher $R$ values yet we see the opposite~\cite{tharmann2007viscoelasticity, ferrer2008measuring}.
\begin{figure}[ht!]
\centering
\includegraphics[width=8cm,height=10cm,keepaspectratio]{fig3}
\caption{Viscoelastic response of actin networks with varying degrees of crosslinking ($R = 0 - 0.07$). (A) Average force exerted by actin networks to resist probe motion. (B) Elastic differential modulus as a function of time as obtained from the derivative of the force in (A) with respect to stage position. Dashed line indicates the maximum $K$ value reached ($K_{max}$) before yielding. (C) Maximum differential modulus ($K_{max}$) follows an exponential function $K_{max} \sim \exp{(R/R^*)}$ with a critical crosslinking ratio of $R^* = 0.015$. (D) Terminal modulus $K_t$ versus $R$, indicating steady-state sustained elasticity, increases exponentially with $R$ with $R^* = 0.018$. (E) Yield time, $t_y$, defined as the time at which $K(t) = K(0)/2e$, displays a similar exponential dependence on $R$ with $R^*=0.009$.}\label{ffig2}
\end{figure}
To better understand the filament and network deformations responsible for the observed stress stiffening and yielding we evaluate the corresponding time-dependent velocities of filament segments surrounding the strain. Specifically, we examine the ensemble-averaged velocities of filament segments in the direction of the strain $<v_x>$ at four different time points during the $1.6$ s strain ($0.4, 0.8, 1.2, 1.6$ s) and for varying distances from the strain path ($d = 9 - 40~\mu$m). As shown in Figure~\ref{ffig3}, despite the constant rate applied strain, the filament strain is highly nonlinear and thus can inform the nonlinear stress response. For all networks, filaments accelerate in the direction of the strain up to t $\simeq$ 0.5 s $\simeq t_y$, after which all filaments exhibit deceleration and eventual halting, with crosslinked networks even displaying varying degrees of recoil. The acceleration phase, which coincides with stress stiffening, can be explained by filaments being conformationally extended (entropically stretched) in the direction of the strain, as predicted for networks with $l_b/l_c<<$1~\cite{vzagar2015two, licup2016elastic}. Halting and recoil, which coincides with yielding to steady-state stress response, suggests entanglement release and/or crosslinker unbinding which both allow the segments to momentarily disengage from the rest of the strained network. The recoil becomes less pronounced for increasing $R$ because as $R$ increases the fraction of the network that remains pinned or strained by the moving probe increases due to more permanent connections (crosslinks), prohibiting filament segments from elastically retracting towards their starting configuration. The fact that we see any deceleration and recoil for high $R$, despite the large elastic stress response sustained, suggests that the stress is only maintained by a small fraction of filaments in the network, while the majority of the network is able to alleviate its stress. This result is in line with recent simulations that show that crosslinked actin networks can distribute stress nonuniformly along percolated paths of connected filaments that make up only a small fraction of the filaments in the network~\cite{kim2014determinants}.
\begin{figure}[ht!]
\centering
\includegraphics[width=8cm,height=10cm,keepaspectratio]{fig4}
\caption{Ensemble-averaged velocities $<v_x>$ of actin filaments during strain for networks with varying crosslinking ratios $R$. (A-C) Ensemble-averaged velocities $<v_x>$ at four different time points during the $1.6~s$ strain ($0.4, 0.8, 1.2, 1.6~s$) and for varying distances $d$ from the strain path: (A) $d = 9~\mu$m, (B) $d = 21~\mu$m and (C) $d = 40~\mu$m. Time-evolution of velocities show filament acceleration followed by deceleration, halting and recoil dependent on $R$ and $d$. (D-F) Time-average of $<v_x>$ values depicted in (A-C) versus crosslinker ratio $R$ for varying distances $d$ from the strain path. Note the non-monotonic dependence of filament mobility on $R$.}\label{ffig3}
\end{figure}
Figure~\ref{ffig3} also reveals a surprising non-monotonic dependence of filament velocity on $R$ at each time point during the strain. Close to the strain path $R = 0$ and $R = 0.07$ filaments display the fastest forward velocities at each time point, followed by $R = 0.05$ then $R = 0.01$. To understand this unexpected trend, we can imagine how particles in a purely viscous and purely elastic material would respond to such a strain. For a purely viscous solution one would expect particles near the strain to easily flow in the direction of the strain as there is no network connectivity or entanglements to resist this motion. Because there is no memory in the system, following strain, the particles would come to halt, but could not recoil or attempt to return to their initial state, and any stress would be instantly released (Stoke's flow). Conversely, for a purely elastic network we would expect, once again, particles near the strain to move along with the strain because the probe is pulling and stretching the network as it moves and the network has no means of relaxation. However, following this strain the particles will all attempt to elastically retract to their starting configurations (Hookean response). Only those particles that are held stretched by the probe will be unable to retract and will retain elastic stress indefinitely. For systems that exhibit features of both of these systems, the particles will not move as much as either the purely elastic or purely viscous networks during strain. Because particles will be restricted by entanglements and crosslinks, they cannot flow as freely as in the viscous case, and because there is some reorganization and relaxation available to the system not all of the particles will be forced to be stretched by probe. Thus, segments not being dragged and stretched by the probe will pull back on segments moving along with the probe, leading to less pronounced motion along the strain direction. Forward moving particles will then attempt to recoil to their starting configurations and because less of the network will be forced (by crosslinked connections) to be held in a stretched state by the probe, ensemble-averaged recoil will be more apparent for networks with fewer permanent crosslinks. This picture is exactly what we see in Figures~\ref{ffig3} and ~\ref{ffig4}. $R = 0$ segments exhibit high initial velocities and no recoil, $R = 0.07$ segments also display large initial velocities but with some recoil, and $R = 0.05$ and $R = 0.01$ networks display reduced forward velocities that increase with $R$ and increased recoil velocities that decrease with $R$. Finally, as shown in Figure~\ref{ffig4}A the measured velocities at each time point decay exponentially with distance from the strain path, out to $\sim$40 $\mu$m, with a critical decay distance of $\sim$10 $\mu$m, suggesting substantial connectivity and stress propagation along segments even at low $R$. We do note, however, that the spatial decay is stronger for a purely entangled solution as we would expect given the transient nature of the entanglements~\cite{falzone2015active}.
\begin{figure}[ht!]
\centering
\includegraphics[width=8cm,height=10cm,keepaspectratio]{fig5}
\caption{Ensemble-averaged filament velocities as a function of distance from the strain path $d$ displays the propagation of induced strain throughout the network at the beginning (A) and end (B) of the applied strain (times displayed in plots). Dashed lines in (A) show exponentially decaying functions of $d$ with critical decay distances of $9.4~\mu$m and $10.7~\mu$m. (B) Velocities at the end of the strain show that particle deceleration and recoil during strain, responsible for stress softening, exhibits a non-monotonic dependence on the degree of crosslinking.}\label{ffig4}
\end{figure}
Much of the interpretation of the data presented in Figures~\ref{ffig2}-\ref{ffig4} is based on stress relaxation mechanisms available to networks with varying degrees of crosslinking. Thus, we also characterize the evolution of the induced stress and filament deformations following the strain. After we pull the probe through the network at constant speed we hold the trapped probe fixed and measure the time-dependent relaxation of the force exerted by the network and corresponding filament motion. The timescale over which we measure relaxation was chosen as the necessary timescale for induced force to relax to zero in our previous measurements on entangled actin networks for concentrations up to 1.4 mg/ml and strain speeds up to 10 $\mu$m/s. In these previous measurements, entangled networks relaxed via 2 relaxation mechanisms, that occurred at timescales of $\sim 1~s$ ($t_{fast}$) and $\sim 10~s$ ($t_{slow}$) and were attributed to disengagement of actin polymers from dilated entanglements tubes ($t_{slow}$) and lateral hopping of entanglement segments between entanglements ($t_{fast}$)~\cite{gurmessa2016entanglement}. Similar to these previous measurements, the force decay of all actin networks are well described by a sum of two exponentials with well-separated timescales (Fig.~\ref{ffig5}).
\begin{figure}[ht!]
\centering
\includegraphics[width=8cm,height=10cm,keepaspectratio]{fig6}
\caption{Relaxation of induced force is strongly suppressed as crosslinker ratio $R$ increases. (A) Time evolution of induced force following the strain. Dashed lines are fits of the data to a sum of two exponential decay functions with well-separated decay times $t_{fast}$ and $t_{slow}$. Inset shows zoomed in data for $R < 0.07$. (B) Measured force decay times, $t_{slow}$ and $t_{fast}$ (inset), as a function of $R$, determined from the corresponding fits in (A). Black lines show fits to exponential functions of crosslinker ratio $R$ ($t \sim \exp{(R/R^*)}$) with critical crosslinker ratios $R^*$ listed in corresponding plots. C) Terminal sustained force $F_t$, defined as the force reached at the end of the relaxation phase, as a function of $R$, with an exponential fit (black line) that gives $R^* = 0.007$.}\label{ffig5}
\end{figure}
While the timescales for $R = 0$ correspond with our previous measurements, both $t_{fast}$ and $t_{slow}$ exponentially increase with $R$ with $R^* \simeq 0.008$ comparable to the exponential dependence of the strain dynamics (Fig.~\ref{ffig2}). As described above, we can understand $t_{fast}$ as crosslink ``hopping'' or unbinding/rebinding in analogy to lateral hopping in entangled solutions. Likewise $t_{slow}$ can be understood as the time necessary for filaments to completely disengage from constraints, which becomes exponentially more difficult as more permanent crosslinks are incorporated into the system. Specifically, when $l_c < l_e$, entanglement relaxation mechanisms are no longer sufficient to alleviate stress, resulting in long-lived sustained stress in crosslinked systems, as shown in Figure \ref{ffig5}A. To intuitively understand the results displayed in Figure~\ref{ffig5} we can once again depict the expected behavior for the limiting cases of purely viscous and elastic materials. A purely viscous fluid would yield a nearly instant relaxation to zero force when the probe motion stops, while a completely elastic material would exhibit a sustained constant force proportional to the distance the material was strained. Intermediate materials would be able to release or relax some of the induced force, however on a longer timescale than the viscous case, and could also potentially maintain some fraction of the force indefinitely or over an extremely long timescale. In accord with this description we see that only the $R = 0$ network relaxes to negligible force over the measurement timescale while all $R>0$ networks sustain some force, with the sustained terminal force ($F_t$) exhibiting the signature exponential dependence on $R$, with $R^* \simeq 0.007$, that suggests that crosslinking suppresses entanglement-dominated network relaxations when the crosslink lengthscale becomes shorter than the length between entanglements. Further, the fact that there is measurable relaxation for $R = 0.07$ despite the largely elastic response again supports the concept that the force is sustained in the network by only a fraction of the filaments connected along a stress path while the rest of the network can relax. Thus, while the initial force build-up is from straining a large fraction of the network, a substantial fraction of the strained network is able to ``disconnect'' from the stressed percolation path via crosslinker turnover and subsequent reorganization on the timescale of $t_{fast}$ and $t_{slow}$ respectively.
To further elucidate the mechanisms whereby stress at the strain site can be alleviated and how this stress is distributed to the rest of the network we once again turn to the filament motion. Figure~\ref{ffig6} shows the ensemble-average velocities for 15 different time points following the strain. While all networks exhibit some recoil back to starting configurations the fastest recoil is exhibited by $R = 0.07$ as it has the most elasticity and most built-up stress. Recoil speeds decrease with decreasing $R$ as expected for decreasing elasticity and more rearrangement possible between frames (Fig.~\ref{ffig6}B). Further, the velocities for all $R > 0$ networks smoothly decrease monotonically to zero as $t$ approaches $\sim 10~s$, suggesting a collective relaxation of a well-connected network over time. In contrast, the time-evolution of filament velocities following the strain for networks without crosslinks ($R = 0$) is much noisier indicating that the network is only loosely connected resulting in filament motion that is much less ordered.
\begin{figure}[ht!]
\centering
\includegraphics[width=8cm,height=10cm,keepaspectratio]{fig7}
\caption{Ensemble-averaged recoil velocities $<v_x>$ during the relaxation phase for filaments closest to the strain path ($d = 9~\mu$m). (A) $<v_x>$ as a function of time for networks of varying $R$. (B) Recoil velocities immediately following the strain as a function of crosslinker ratio $R$. Velocities correspond to the data in the first time point of (A). While all networks exhibit some recoil to starting configurations recoil speeds decrease with decreasing $R$, as expected for networks with decreasing elasticity.}\label{ffig6}
\end{figure}
\section*{Conclusion}
We have combined force measuring optical tweezers and fluorescence microscopy, along with novel discrete labeling of actin segments and particle-velocity-tracking analysis to directly couple the nonlinear stress response of crosslinked and entangled actin with the underlying molecular and network deformation and rearrangements. Despite the previously revealed microscale similarities between entangled and crosslinked networks in the nonlinear regime, we find that the elasticity of the network is exponentially dependent on the length between crosslinkers, $l_c$, with the critical crosslinking length in which crosslinking dominates entanglement effects occurring when $l_c$ becomes smaller than the entanglement length $l_e$. We have demonstrated that the initial stiffening, present for both entangled and crosslinked networks in this regime, arises from the acceleration of actin segments near the strain, due to entropic stretching along the strain path. Subsequent filament deceleration and recoil, due to force-induced disentanglement and crosslinker unbinding/rebinding, leads to stress softening and yielding to a steady-state regime. This terminal regime occurs at timescales longer the fastest relaxation timescale of the network, and exhibits constant elastic resistance that exponentially increases with crosslinker density. The filament velocity during strain further exhibits a surprising nonmonotonic dependence on crosslinker density, with both $R=0$ and $R = 0.07$ exhibiting the fastest filament speeds while the intermediate $R$ values show less pronounced deformation. By analyzing the relaxation phase, we show that the extreme $R = 0$ strain response is a result of viscous flow and ample network reorganization and yielding, while the $R = 0.07$ response arises from pulling of the highly elastic network with minimal ability to reorient or relax to relieve the strain. The systems in which reorganization and elasticity are comparable ($R = 0.1$, $0.5$) result in smaller filament deformations and increased recoil. Further, high levels of elastic stress for $l_c < l_e$ are maintained with minimal relaxation, while the corresponding tracked segments exhibit highly elastic retraction following deformation. In agreement with recent simulations~\cite{kim2014determinants}, these contradictory results indicate the stress is maintained by only a small fraction of highly-strained connected filaments while the majority of the network can elastically retract.
\section*{Author Contributions}
B.G. conducted experiments, analyzed data, wrote manuscript; S.R. prepared reagents, conducted confocal microscopy experiments; R.M.R.A. designed experiments, interpreted data, wrote manuscript.
\section*{Acknowledgements}
This research was funded by an NSF CAREER Award (DMR-1255446) and a Scialog Collaborative Innovation Award funded by Research Corporation for Scientific Advancement (grant no. 24192).
\bibliographystyle{achemso}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,791 |
\section{Introduction} \label{S:intro}
In this article, rings are associative with unity. The Jacobson radical, set of units, set of idempotents, set of nilpotent elements and centre of a ring $R$ are denoted by $J(R)$, $U(R)$, $Idem(R)$, $Nil(R)$ and $C(R)$ respectively. Nicholson \cite{nicholson1977lifting} defined an element $x$ of a ring $R$ to be a clean element, if $x=e+u$ for some $e\in Idem(R)$, $u\in U(R)$ and called the ring $R$ as clean ring if all its elements are clean. Diesl \cite{Diesl} defined a ring $R$ to be nil clean ring if every element of $R$ can be written as a sum of an idempotent and a nilpotent element of $R$. Weakening the condition of clean ring, Ahn and Anderson \cite{ahn2006weakly} defined a ring $R$ to be weakly clean, if every $x\in R$ can be expressed as $x=u+e$ or $x=u-e$, where $u\in U(R)$, $e\in Idem(R)$. Also Basnet and Bhattacharyya \cite{WNCR} defined a ring $R$ to be weak nil clean, if every element $x\in R$ can be written as $x=n+e$ or $x=n-e$, where $n\in Nil(R)$ and $e\in Idem(R)$. H. Chen and M. Chen \cite{chen2003clean} defined an ideal $I$ of a ring $R$ to be clean ideal, if for any $x\in I$, $x=u+e$, for some $u\in U(R)$ and $e\in Idem(R)$. They proved that every ideal having stable range one of a regular ring is clean. Following the idea of clean ideal, Sharma and Basnet \cite{Ajay1} defined an ideal $I$ of a ring $R$ to be nil clean ideal, if for any $x\in I$, $x=n+e$, where $n\in Nil(R)$ and $e\in Idem(R)$. They proved that for a nil clean expression of an element of a nil clean ideal of a ring $R$, the nilpotent and idempotent elements are actually elements of the ideal. Also they characterized a nil clean ring with its nil clean ideals. As a generalization of clean ideal, Sharma and Basnet \cite{Ajay2} also introduced weakly clean ideal of a ring. An ideal $I$ of a ring $R$ is said to be weakly clean ideal, if for any $x\in I$, $x=u+e$ or $x=u-e$, where $u\in U(R)$ and $e\in Idem(R)$.
In this article we introduce the notion of weak nil clean ideal as a generalization of nil clean ideal. An ideal $I$ of a ring $R$ is called weak nil clean ideal if for each $a\in I$, either $a=e+n$ or $a=-e+n$, where $e\in Idem(R)$ and $n\in Nil(R)$. Here also we proved that for a weak nil clean expression of an element of a weak nil clean ideal of a ring $R$, the nilpotent and idempotent elements are actually elements of the ideal. Further we characterized a weak nil clean ring with its weak nil clean ideal and nil clean ideal of $R$. Also we discuss some interesting properties of weak nil clean ideals.
\section{Weak nil clean ideal}
\begin{Def}
An ideal $I$ of a ring $R$ is called weak nil clean ideal of $R$ if for any $x\in I$, there exist $e\in Idem(R)$ and $n\in Nil(R)$ such that $x=e+n$ or $x=-e+n$. Also $I$ is called uniquely weak nil clean ideal of $R$ if for any $x\in I$ there exists a unique $e\in Idem(R)$ such that $x-e\in Nil(R)$ or $x+e\in Nil(R)$.
\end{Def}
Clear from the definition that every ideal of a weak nil clean ring is weak nil clean ideal. But there are non weak nil clean rings which contains some weak nil clean ideals, for example the ring $\mathbb{Z}_{p^n}$, where $n>1$ and $p>5$, a prime number, is not weak nil clean ring but every proper ideal of $\mathbb{Z}_{p^n}$ is weak nil clean ideal. Another such example is given below.
\begin{example}
Let $R_1$ be weak nil clean ring and $R_2$ be non weak nil clean ring. Then $R=R_1\oplus R_2$ is not a weak nil clean ring. But clearly $I=R_1\oplus 0$ is weak nil clean ideal of $R$.
\end{example}
Observe that every nil clean ideal is weak nil clean ideal but the converse is not true as $\{0,2,4\}$ is weak nil clean ideal of $\mathbb{Z}_6$ but not nil clean ideal of $\mathbb{Z}_6$.
\begin{Lem}\label{L1}
Every weak nil clean ideal of a ring $R$ is weakly clean ideal of $R$.
\end{Lem}
\begin{proof}
Let $I$ be a weak nil clean ideal of $R$. For $x\in I$, either $x=e+n$ or $x=-e+n$, where $e\in Idem(R)$ and $n\in Nil(R)$. If $x=e+n$ then $x=(1-e)+(2e-1+n)$ and if $x=-e+n$ then $x=(1-e)+(-1+n)$, where $1-e \in Idem(R)$ and $-1+n$, $2e-1+n\in U(R)$.
\end{proof}
The converse of Lemma \ref{L1} is not true as ideal $\{0,3,6,9,12\}$ of $\mathbb{Z}_{15}$ is weakly clean ideal but not weak nil clean ideal of $\mathbb{Z}_{15}$.
\begin{Prop}\label{PPP1}
If $I$ is a weak nil clean ideal of a ring $R$ then $I\cap J(R)$ is a nil ideal of $R$.
\end{Prop}
\begin{proof}
Let $x\in I\cap J(R)$, so either $x=e+n$ or $x=-e+n$, where $e\in Idem(R)$ and $n\in Nil(R)$. If $x=e+n$, then by Proposition $2.4$ \cite{Ajay1}, $x=n$. If $x=-e+n$ then there exists $k\in \mathbb{N}$ such that $n^k=0$. Now $n^k=(x+e)^k=\sum_{t,r\in R}^{finite}txr +e^k=0\Rightarrow e=-\sum_{t,r\in R}^{finite}txr\in J(R)$ as $x\in J(R)$. So $1-e\in Idem(R)\cap U(R)=\{1\}$, hence $1-e=1\Rightarrow e=0\Rightarrow x=n$. Thus the result follows.
\end{proof}
\begin{Cor}
If $R$ is a weak nil clean ring then $J(R)\subseteq N(R)$. In particular for is a commutative ring $R$, $J(R)=N(R)$.
\end{Cor}
Let $R$ be a ring. An element $a\in R$ is called weakly clean element of type-I if $a=e+u$ and called weakly clean element of type-II if $a=-e+u$, where $e\in Idem(R)$ and $u\in U(R)$.
\begin{Def}
An ideal $I$ of a ring $R$ is said to be strongly weak nil clean ideal if for any $x\in I$, there exist $e\in Idem(R)$ and $n\in Nil(R)$ such that $x=e+n$ or $x=-e+n$ and $en=ne$. Also $I$ is called strongly weakly clean ideal if for any $x\in I$, there exist $e\in Idem(R)$ and $u\in U(R)$ such that $x=e+u$ or $x=-e+u$ and $eu=ue$.
\end{Def}
\begin{Thm}
Let $I$ be an ideal of $R$ then
\begin{enumerate}
\item If $I$ is strongly weak nil clean ideal then it is strongly weakly clean ideal and $a-a^2$ or $a+a^2$ is nilpotent.
\item If $I$ is strongly weakly clean ideal and $a-a^2$ or $a+a^2$ is nilpotent provided $a$ is of type-I or type-II weakly clean element of $R$ respectively, then $I$ is strongly weak nil clean ideal.
\end{enumerate}
\end{Thm}
\begin{proof}
\begin{enumerate}
\item Let $I$ be a strongly weak nil clean ideal and $a\in R$. Then either $a=e+n$ or $a=-e+n$, where $e\in Idem(R)$, $n\in Nil(R)$ and $en=ne$. If $a=e+n$ then $a=(1-e)+(2e-1+n)$ is strongly weakly clean decomposition of $a$ and also $a-a^2=(1-2e-n)n$ is nilpotent. If $a=-e+n$, then $a=-(1-e)+(1-2e+n)$ is strongly weakly clean decomposition of $a$ and also $a+a^2=(1-2e+n)n$ is nilpotent.
\item Let $a\in I$, so either $a=e+u$ or $a=-e+u$, where $e\in Idem(R)$ and $u\in U(R)$. If $a=e+u$, then $a-a^2$ is nilpotent, which implies $1-2e-u$ is nilpotent and $a=(1-e)+(-1+2e+u)$, a strongly weak nil clean expression of $a$. If $a=-e+u$, then $a+a^2$ is nilpotent, which implies $1-2e+u$ is nilpotent and $a=-(1-e)+(1-2e+u)$, a strongly weak nil clean expression of $a$.
\end{enumerate}
\end{proof}
\begin{Lem}
Every idempotent in a uniquely weak nil clean ideal is a central idempotent.
\end{Lem}
\begin{proof}
Let $I$ be a uniquely weak nil clean ideal of a ring $R$ and $e$ be any idempotent in $I$. For any $x\in R$, since $e=(e+ex(1-e))+(-ex(1-e))=e+0$, so $e+ex(1-e)=e\Rightarrow ex=exe$, as $e+ex(1-e)\in Idem(R)$. Similarly we can show that $xe=exe$. Hence $xe=ex$.
\end{proof}
The following theorem shows that, for a weak nil clean expression of an element of a weak nil clean ideal of a ring $R$, the nilpotent and idempotent elements are actually elements of the ideal.
\begin{Thm}\label{111}
An ideal $I$ of a ring $R$ is weak nil clean ideal \textit{if and only if} for any $x\in I$, either $x=e+n$ or $x=-e+n$, where $e\in Idem(I)$ and $n\in Nil(I)$.
\end{Thm}
\begin{proof}
Let $I$ be a weak nil clean ideal of $R$ and $x\in I$. There exist $n\in Nil(R)$ and $e\in Idem(R)$ such that either $x=e+n$ or $x=-e+n$. So $n^k=0$, for some $k\in \mathbb{N}$. If $x=e+n$, then $(x-n)^k=(-1)^kn^k+\sum_{i=1}^{s} q_ixp_i$, for some $p_i, q_i\in R$, $(x-n)^k=\sum_{i=1}^{s} q_ixp_i\in I$, so $e^k=e\in I$. Similarly if $x=-e+n$, then also we get $e\in I$. Hence $n\in I$, as required.
\end{proof}
The following corollary is immediate.
\begin{Cor}
If $R$ is a local ring, then every proper weak nil clean ideal of $R$ is nil ideal. In fact if $R$ has no non trivial idempotents, then every proper weak nil clean ideal of $R$ is nil ideal.
\end{Cor}
In the following Theorem, we characterize weak nil clean ring $R$ by weak nil clean ideal and nil clean ideal of $R$.
\begin{Thm}\label{main}
$R$ is a weak nil clean ring \textit{if and only if} there exists a central idempotent $e$ in $R$ such that ideals generated by $e$ and $1-e$ are both weak nil clean ideals of $R$ and one of them is nil clean ideal of $R$.
\end{Thm}
\begin{proof}
If $R$ is weak nil clean ring, then $e=1$ works. Conversely, without loss of generality assume that $<e>$ is weak nil clean ideal and $<1-e>$ is nil clean ideal of $R$. For $x\in R$, since $R=<e>+<1-e>$, so $x=a+b$, where $a\in <e>$ and $b\in <1-e>$. There exist $f_1\in Idem(<e>)$ and $n_1\in Nil(<e>)$, such that either $a=f_1+n_1$ or $a=-f_1+n_1$. If $a=f_1+n_1$, then we set $b=f_2+n_2$, where $f_2\in Idem(<1-e>)$ and $n_2\in Nil(<1-e>)$, then $x=(f_1+f_2)+(n_1+n_2)$ is a nil clean expression of $x$ in $R$. Also if $a=-f_1+n_1$ then we set $b=-f_2+n_2$, where $f_2\in Idem(<1-e>)$ and $n_2\in Nil(<1-e>)$, so $x=-(f_1+f_2)+(n_1+n_2)$ is a weak nil clean expression of $x$ in $R$. Hence $R$ is a weak nil clean ring.
\end{proof}
A finite orthogonal set of idempotents $e_1, \cdot\cdot\cdot , e_n$ in a ring $R$, is said to be complete set if $e_1+ \cdot\cdot\cdot +e_n=1$. Now we generalize the above result in terms of complete set of idempotents.
\begin{Thm}
Ring $R$ is weak nil clean \textit{if and only if} there exists a complete set of central idempotents $e_1, \cdot\cdot\cdot , e_n$ in $R$, such that ideal generated by $e_i$ is weak nil clean ideal of $R$ for all $i$ and at most one $<e_i>$ is not nil clean ideal.
\end{Thm}
\begin{proof}
$(\Rightarrow)$ Taking $e=1$.\\
$(\Leftarrow)$ Clearly $<e_1>+<e_2>+\cdot\cdot\cdot+<e_n>=R$, so similar to the proof of Theorem \ref{main}, we can show that $R$ is weak nil clean ring.
\end{proof}
\begin{Prop}
Let $I$ be an ideal of a ring $R$. Then the following are equivalent:
\begin{enumerate}
\item $I$ is weak nil clean ideal of $R$.
\item There exists a complete set of central idempotents $e_1, \cdot\cdot\cdot , e_n$ such that $e_iI$ is a weak nil clean ideal of $e_iR$, for all $i$ and at most one $e_iI$ is not nil clean ideal of $e_iR$.
\end{enumerate}
\end{Prop}
\begin{proof}
(1)$ \Rightarrow $ (2) Taking $e=1$.\\
(2)$\Rightarrow $(1) Let $e_1, \cdot\cdot\cdot , e_n$ be a complete set of idempotents in $R$ such that $e_iI$ is a weak nil clean ideal of $e_iR$, for all $i$ and at most one $e_iI$ is not nil clean ideal of $e_iR$. It is enough to show the result for $n=2$. Clearly $I=e_1I\oplus e_2I$. Without loss of generality assume $e_1I$ is a nil clean ideal of $e_1R$. Let $x\in I$, then $x=a+b$, where $a\in e_1I$ and $b\in e_2I$, so there exist $f_2\in Idem(e_2I)$ and $m_2\in Nil(e_2I)$ such that either $b=f_2+m_2$ or $b=-f_2+m_2$. If $b=f_2+m_2$, then we set $a=f_1+m_1$, where $f_1\in Idem(e_1I)$ and $m_1\in Nil(e_1I)$ and we get $x=(f_1+f_2)+(m_1+m_2)$ is a weak nil clean expression of $x$. If $b=-f_2+m_2$, then we set $a=-f_1+m_1$, where $f_1\in Idem(e_1I)$ and $m_1\in Nil(e_1I)$ and we get $x=-(f_1+f_2)+(m_1+m_2)$ is a weak nil clean expression of $x$.
\end{proof}
\begin{Thm}
Let $R$ be a ring and $I_1$ be an ideal containing the nil ideal $I$. Then $I_1$ is weak nil clean ideal of $R$ \textit{if and only if} $I_1/I$ is weak nil clean ideal of $R/I$.
\end{Thm}
\begin{proof}
If $I_1$ is weak nil clean ideal of $R$, then clearly $I_1/I$ is weak nil clean ideal of $R/I$. Conversely, let $I_1/I$ be weak nil clean ideal of $R/I$ and $x\in I_1$. Then either $\overline{x}=\overline{e}+\overline{n}$ or $\overline{x}=-\overline{e}+\overline{n}$, where $\overline{e}\in Idem(I_1/I)$ and $\overline{n}\in Nil(I_1/I)$. Since idempotents can be lifted modulo nil ideal, so lift $\overline{e}$ to $e\in I_1$. Then $x-e$ or $x+e$ is nilpotent in $I_1$, modulo $I$ and hence $x-e$ or $x+e$ is nilpotent in $I_1$.
\end{proof}
\begin{Thm}\label{HOMIMAGE}
Every homomorphic image of weak nil clean ideal of a ring is also weak nil clean ideal.
\end{Thm}
\begin{Thm}\label{Th1}
Let $\{R_i\}_{i=1}^m$ be a family of rings and $I_i's$ are ideals of $R_i$, then the ideal $I=\prod_{i=1}^{m} I_i$ of $R=\prod_{i=1}^{m} R_i$ is weak nil clean ideal \textit{if and only if} each $I_i$ is weak nil clean ideal of $R_i$ and at most one $I_i$ is not nil clean ideal.
\end{Thm}
\begin{proof}
$(\Rightarrow)$ Let $I$ be weak nil clean ideal of $R$. Then being homomorphic image of $I$ each $I_{\alpha}$ is weak nil clean ideal of $R_{\alpha}$. Suppose $I_{\alpha_1}$ and $I_{\alpha_2}$ are not nil clean ideals, where ${\alpha}_1\neq {\alpha}_2$. Since $I_{\alpha_1}$ is not nil clean ideal, so not all elements $x\in I_{\alpha_1}$ are of the form $x=n-e$, where $n\in Nil(R_{\alpha_1})$ and $e\in Idem(R_{\alpha_1})$. As $I_{\alpha_1}$ is weak nil clean ideal of $R_{\alpha_1}$, so there exists $x_{\alpha_1}\in I_{\alpha_1}$ with $x_{\alpha_1}=n_{\alpha_1}+e_{\alpha_1}$, where $n_{\alpha_1}\in Nil(R_{\alpha_1})$ and $e_{\alpha_1}\in Idem(R_{\alpha_1})$, but $x_{\alpha_1}\neq n-e$, for any $n\in Nil(R_{\alpha_1})$ and $e\in Idem(R_{\alpha_1})$. Similarly there exists $x_{\alpha_2}\in I_{\alpha_2}$ with $x_{\alpha_2}=n_{\alpha_2}-e_{\alpha_2}$, where $n_{\alpha_2}\in Nil(R_{\alpha_2})$ and $e_{\alpha_2}\in Idem(R_{\alpha_2})$, but $x_{\alpha_2}\neq n+e$, for any $n\in Nil(R_{\alpha_2})$ and $e\in Idem(R_{\alpha_2})$. Define $x=(x_\alpha)\in I$ by \begin{align*}
x_\alpha &=x_{\alpha}\,\, \,\,\,\,\,\,\,if\,\, \alpha \in \{\alpha_1,\alpha_2\} \\
&=0 \,\,\,\,\,\,\,\,\,\,\,\,\,if \,\,\alpha \notin \{\alpha_1,\alpha_2\}
\end{align*}
Then clearly $x\neq n\pm e$, for any $n\in Nil(R)$ and $e\in Idem(R)$. Hence at most one $I_\alpha$ is not nil clean ideal.\par
$(\Leftarrow)$ If each $I_\alpha$ is nil clean ideal of $R_{\alpha}$ then $I=\prod I_\alpha$ is nil clean ideal of $R$ by Theorem $2.20$ \cite{Ajay1} and hence weak nil clean ideal of $R$. Assume $I_{\alpha_0}$ is weak nil clean ideal but not nil clean ideal of $R_{\alpha_0}$ and that all other $I_{\alpha}$'s are nil clean ideals of $R_{\alpha}$. If $x=(x_\alpha) \in I$, then in $I_{\alpha_0}$, we can write $x_{\alpha_0}=n_{\alpha_0}+e_{\alpha_0}$ or $x_{\alpha_0}=n_{\alpha_0}-e_{\alpha_0}$, where $n_{\alpha_0}\in Nil(R_{\alpha_0})$ and $e_{\alpha_0}\in Idem(R_{\alpha_0})$. If $x_{\alpha_0}=n_{\alpha_0}+e_{\alpha_0}$, then for $\alpha \neq \alpha_0$ we set, $x_{\alpha}=n_{\alpha}+e_{\alpha}$, where $n_{\alpha}\in Nil(I_\alpha)$ and $e_{\alpha}\in Idem(I_\alpha)$. If $x_{\alpha_0}=n_{\alpha_0}-e_{\alpha_0}$, then for $\alpha \neq \alpha_0$ we set, $x_{\alpha}=n_{\alpha}-e_{\alpha}$, where $n_{\alpha}\in Nil(I_\alpha)$ and $e_{\alpha}\in Idem(I_\alpha)$; then $n=(n_\alpha)\in Nil(R)$ and $e=(e_\alpha)\in Idem(R)$, such that $x=n+e$ or $x=n-e$ and hence $I$ is weak nil clean ideal of $R$.
\end{proof}
If the collection of rings is infinite then Theorem \ref{Th1} is not true as shown by the following example.
\begin{example}
Consider the ring $R=\mathbb{Z}_3\times \mathbb{Z}_{2^2}\times \mathbb{Z}_{2^3}\times \cdot\cdot\cdot $, clearly for any $n\in \mathbb{N}$, $\mathbb{Z}_{2^n}$ is weak nil clean ring and hence ideal generated by $2$ in $\mathbb{Z}_{2^n}$ say $<2>_n$ is also weak nil clean ideal of $\mathbb{Z}_{2^n}$. But the ideal $I=<3>\times <2>_2\times <2>_3\times \cdot\cdot\cdot$ is not weak nil clean ideal of $R$ as $(3,2,2,\cdot\cdot\cdot)\in I$ can not be written as a sum of an idempotent and a nilpotent element of $R$.
\end{example}
Next we study the relationship between weak nil clean ideal of a given ring $R$ and weak nil clean ideal of upper triangular matrix ring $\mathbb{T}_n(R)$. Here given a matrix $X$, $X_{ij}$ denotes the $(i,j)^{th}$ entry of $X$.
\begin{Lem}\label{D211}
For $E, N\in \mathbb{T}_n(R)$ the following hold:
\begin{enumerate}
\item If $E^2=E$, then $(E_{ii})^2=E_{ii}$ for $1\leq i\leq n$.
\item $N$ is nilpotent if and only if $N_{ii}$ is nilpotent for $1\leq i\leq n$.
\end{enumerate}
\end{Lem}
\begin{proof}
See Lemma $2.1.1$ \cite{Diesl1}.
\end{proof}
\begin{Thm}
Let $T$ be a $2\times2$ upper triangular matrix ring over $R$. Then an ideal $S=\left(
\begin{array}{cc}
I & R \\
0 & J \\
\end{array}
\right)$ of $T$ is weak nil clean ideal \textit{if and only if} $I$ and $J$ are weak nil clean ideals of $R$ and one of them is nil clean ideal.
\end{Thm}
\begin{proof}
Without loss of generality, assume that $I$ and $J$ are respectively nil clean and weak nil clean ideals of $R$. Let $x=\left(
\begin{array}{cc}
a & r \\
0 & b \\
\end{array}
\right)\in \left(
\begin{array}{cc}
I & R \\
0 & J \\
\end{array}
\right)
$. So either $b=f+n_1$ or $b=-f+n_1$, where $f\in Idem(J)$ and $n_1\in Nil(J)$. If $b=f+n_1$, set $a=e+n$, where $e\in Idem(I)$ and $n\in Nil(I)$. Then $x=\left(
\begin{array}{cc}
e & 0 \\
0 & f \\
\end{array}
\right)+\left(
\begin{array}{cc}
n & r \\
0 & n_1 \\
\end{array}
\right)
$, where $\left(
\begin{array}{cc}
e & 0 \\
0 & f \\
\end{array}
\right)\in Idem(T)$
and $\left(
\begin{array}{cc}
n & r \\
0 & n_1 \\
\end{array}
\right)\in Nil(T)
$. If $b=-f+n_1$, set $a=-e+n$, where $e\in Idem(I)$ and $n\in Nil(I)$. Then $x=-\left(
\begin{array}{cc}
e & 0 \\
0 & f \\
\end{array}
\right)+\left(
\begin{array}{cc}
n & r \\
0 & n_1 \\
\end{array}
\right)
$, where $\left(
\begin{array}{cc}
n & r \\
0 & n_1 \\
\end{array}
\right)\in Nil(T)$
and $\left(
\begin{array}{cc}
e & 0 \\
0 & f \\
\end{array}
\right)\in Idem(T)$ by
Lemma \ref{D211}. \\
For the converse, clearly $I$ and $J$ are weak nil clean ideals of $R$. Suppose both are not nil clean ideals of $R$. As $I$ is not weak nil clean ideal of $R$, so there exists $x\in I$ such that $x=e_1+n_1$, where $e_1\in Idem(I)$ and $n_1\in Nil(I)$ but $x\neq n-e$, for all $n\in Nil(I)$ and $e\in Idem(I)$. Similarly there exists $y\in J$ such that $y=-e_2+n_2$, where $e_2\in Idem(J)$ and $n_2\in Nil(J)$ but $y\neq n+e$, for all $n\in Nil(J)$ and $e\in Idem(J)$. Then it is easy to see that $\left(
\begin{array}{cc}
x & 0 \\
0 & y \\
\end{array}
\right)
$ is not weak nil clean element of $T$.
\end{proof}
Let $R$ be a commutative ring and $M$ be a $R$-module. Then the idealization of $R$ and $M$ is the ring $R(M)$ with underlying set $R\times M$ under coordinatewise addition and multiplication given by $(r,m)(r',m')=(rr', rm'+r'm)$, for all $r, r'\in R$ and $m, m' \in M$. It is obvious that if $I$ is an ideal of $R$ then for any submodule $N$ of $M$, $I(N)=\{(r,n)\, : \,r\in I \,\, ,\, \,n\in N \}$ is an ideal of $R(M)$. First we mention basic existing results about idempotents and nilpotent elements in $R(M)$ and study the nil clean ideals of the idealization $R(M)$ of $R$ and $R$-module $M$.
\begin{Lem}\label{RM}
Let $R$ be a commutative ring and $R(M)$ be the idealization of $R$ and $R$-module $M$. Then the following hold:
\begin{enumerate}
\item $(r,m) \in Idem(R(M))$ if and only if $r \in Idem(R)$ and $m =0$.
\item $(r,m) \in Nil(R(M))$ if and only if $r \in Nil(R)$.
\end{enumerate}
\end{Lem}
\begin{proof}
(1) is obvious and (2) follows from the fact that $(r,m)^n=(r^n, nr^{n-1}m)$, for any $r\in R$ and $m\in M$.
\end{proof}
\begin{Prop}\label{RM1}
Let $R$ be a commutative ring and $R(M)$, the idealization of $R$ and $R$-module $M$. Then an ideal $I$ of $R$ is weak nil clean ideal of $R$ \textit{if and only if} $I(N)$ is weak nil clean ideal of $R(M)$, for any submodule $N$ of $M$.
\end{Prop}
\begin{proof}
$(\Rightarrow)$ Let $I$ be weak nil clean ideal of $R$. Consider an Ideal $I(N)$ of $R(M)$, for some submodule $N$ of $M$. Let $(x,m)\in I(N)$. Then either $x=n+e$ or $x=-e+n$, for some $e\in Idem(R)$ and $n\in Nil(R)$. So either $(x,m)=(e,0)+(n,m)$ or $(x,m)=-(e,0)+(n,m)$, where $(e,0)\in Idem(R(M))$ and $(n,m)\in Nil(R(M))$ by Lemma \ref{RM}.\\
$(\Leftarrow)$ Let $I(N)$ be a weak nil clean ideal of $R(M)$ and $r\in I$. For $(r,0)\in I(N)$, either $(r,0)=(e,0)+(n,0)$ or $(r,0)=-(e,0)+(n,0)$, for some $(e,0)\in Idem(R(M))$ and $(n,0)\in Nil(R(M))$. By Lemma \ref{RM}, we conclude that either $r=e+n$ or $r=-e+n$, where $e\in Idem(R)$ and $n\in Nil(R)$.
\end{proof}
In the following proposition we study about weak nil clean element of a corner ring.
\begin{Prop}
Let $R$ be a ring and $f\in Idem(R)$. An element $a\in fRf$ is strongly weak nil clean element of $R$ \textit{if and only if} $a\in fRf$ is strongly weak nil clean element of $fRf$.
\end{Prop}
\begin{proof}
As $fRf$ is a left ideal of $fR$ and $fR$ is a right ideal of $R$. Hence the result follows from Theorem \ref{111}.
\end{proof}
\begin{Cor}\label{cor1}
If $R$ is strongly weak nil clean ring and $f\in R$ is any idempotent, then the corner ring $fRf$ is strongly weak nil clean.
\end{Cor}
A Morita context denoted by $(R,S,M,N,\psi,\phi)$ consists of two rings $R$ and $S$, two bimodules $_RN_S$ and $_SM_R$ and a pair of bimodule homomorphisms (called pairings) $\psi:N\otimes _SM\rightarrow R$ and $\phi:M\otimes _RN\rightarrow S$, which satisfy the following associativity: $\psi(n\otimes m)n'=n\phi(m\otimes n')$ and $\phi (m\otimes n)m'=m\psi(n\otimes m')$, for any $m,\,m'\in M$ and $n,\,n'\in N$. These conditions ensure that the set of matrices $\left(
\begin{array}{cc}
r & n \\
m & s \\
\end{array}
\right)$, where $r\in R$, $s\in S$, $m\in M$ and $n\in N$ forms a ring denoted by $T$, called the ring of the context. For any subset $I$ of $T$, define $p_R(I)=\{a\in R\,:\,\left(
\begin{array}{cc}
a & x\\
y & b \\
\end{array}
\right)\in I \}$, $p_M(I)=\{y\in M\,:\,\left(
\begin{array}{cc}
a & x\\
y & b \\
\end{array}
\right)\in I \}$, $p_S(I)=\{b\in S\,:\,\left(
\begin{array}{cc}
a & x\\
y & b \\
\end{array}
\right)\in I \}$ and $p_N(I)=\{x\in N\,:\,\left(
\begin{array}{cc}
a & x\\
y & b \\
\end{array}
\right)\in I \}$\par
A morita context $R= \left(
\begin{array}{cc}
A & M \\
N & B \\
\end{array}
\right)$ is called morita context of zero pairing if context products $MN=0$ and $NM=0$.
\begin{Lem}
Let $T= \left(
\begin{array}{cc}
A & M \\
N & B \\
\end{array}
\right)$ be a morita context. Then $I$ is an ideal of $T$ \textit{if and only if} $I=\left(
\begin{array}{cc}
A_1 & M_1 \\
N_1 & B_1 \\
\end{array}
\right)$,
where $A_1$ and $B_1$ are ideals of $A$ and $B$ respectively, $M_1$ and $N_1$ are submodules of $ _AM_B$ and $ _BN_A$ respectively, with $M_1N\subseteq A_1$, $N_1M\subseteq B_1$, $A_1M\subseteq M_1$, $B_1N\subseteq N_1$, $MN_1\subseteq A_1$, $NM_1\subseteq B_1$, $MB_1\subseteq M_1$ and $NA_1\subseteq N_1$. In this case $A_1=p_{A}(I)$, $B_1=p_B(I)$, $M_1=p_M(I)$ and $N_1=p_N(I)$.
\end{Lem}
\begin{proof}
See Lemma $2.1$ \cite{Tang}.
\end{proof}
\begin{Thm}
Let $R= \left(
\begin{array}{cc}
A & M \\
N & B \\
\end{array}
\right)$ be a morita context and $I= \left(
\begin{array}{cc}
A_1 & M_1 \\
N_1 & B_1 \\
\end{array}
\right)$ be a strongly weak nil clean ideal of $R$. Then $A_1$ and $B_1$ are strongly weak nil clean ideals of $A$ and $B$ respectively.
\end{Thm}
\begin{proof}
The proof follows from Corollary \ref{cor1} and Theorem \ref{111}.
\end{proof}
\begin{Thm}
Let $R= \left(
\begin{array}{cc}
A & M \\
N & B \\
\end{array}
\right)$ be a morita context of zero pairing. If $A_1$ and $B_1$ are weak nil clean ideals of $A$ and $B$ respectively, where at least one of them is strongly nil clean ideal then $I= \left(
\begin{array}{cc}
A_1 & M_1 \\
N_1 & B_1 \\
\end{array}
\right)$ is a weak nil clean ideal of $R$.
\end{Thm}
\begin{proof}
Let $A_1$ be strongly nil clean ideal of $A$ and $B_1$ be strongly weak nil clean ideal of $B$ respectively. Let $x= \left(
\begin{array}{cc}
a & m \\
n & b \\
\end{array}
\right)\in I$.
Then there exist $e\in Idem(B_1)$ and $q\in Nil(B_1)$ such that either $b=e+q$ or $b=-e+q$. If $b=e+q$, then set $a=f+p$, where $f\in Idem(A_1)$ and $p\in Nil(A_1)$ and we get, $x= \left(
\begin{array}{cc}
f & 0 \\
0 & e \\
\end{array}
\right)+ \left(
\begin{array}{cc}
p & m \\
n & q \\
\end{array}
\right)$
and $p^k=0$ and $q^k=0$, for some $k\in \mathbb{N}$, where $\left(
\begin{array}{cc}
f & 0 \\
0 & e \\
\end{array}
\right)\in Idem(R)$.
Now from Theorem $2.28$ \cite{Ajay1}, we conclude that $\left(
\begin{array}{cc}
p & m \\
n & q \\
\end{array}
\right)\in Nil(R)$.
Also if $b=-e+q$ then set $a=-f+p$ and similar as above we can show that $x$ is weak nil clean element of $R$.
\end{proof}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,271 |
Q: Finding an appropriate data structure I have N keys.
I need to find a data structure which i can do with the following operations :
*
*building it in O(N)
*finding min in O(1)
*deleting the median in O(logn)
*finding the n/2+7-th biggest number
I thought about using a minimum heap (building is O(n),minimum is O(1) - root).
however, I'm having hard time finding a way to do 3 and 4.
I think the median suppose to be on of the leaves, but that's as far as i reached.
A: When you say building in O(n), do you mean that addition has to be O(n), or that you have to build a collection of elements in O(n) such that addition has to be O(1)?
You could augment pretty much any data structure with an extra reference to retrieve the minimal element in constant time.
For #3, it sounds like you need to be able to find the median in O(lg n) and delete in O(1), or vice versa.
For #4, you didn't specify the time complexity.
To other posters - this is marked as homework. Please give hints rather than posting the answer.
A: A popular question asked in Data Structures 1 exams/hws/tutorials.
I'll try to give you some hints, if they don't suffice, comment, and I'll give you more hints.
*
*Remember that you don't have to use just one data structure, you can use several data structures.
*Recall the definition of a median: n/2 of the numbers are larger, and n/2 of the numbers are smaller
*What data structures do you know that are built in O(n), and complex operations on them are O(logn) or less? - Reread the tutorials slides on these data structures.
*It might be easier for you to solve 1+3 seperately from 1+2, and then think about merging them.
A: Simple sorted Array would solve the problem for #2 #3 and #4. But the construction of it would take O(nn). However, there are no restrictions put on space complexity. I am thinking hard to use Hashing concept during the construction of the data structure which would bring down the order to O(n).
Hope this helps. Will get back if I find a better solution
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,080 |
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