text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
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Souza se poate referi la următorii autori care au denumit cel puțin o specie:
Jesus R.D. Souza
Moisés B. de Souza | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,444 |
This week's infographic isn't directly related to ebooks but it is fun nonetheless.
It looks back at the many changes to the web over the past 10 years, including browser we don't use anymore and sites which have given up the ghost. We're spending nearly 6 times as many hours online as a decade ago and there's 4 times as many poeple online. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,798 |
Sigle
Roi – Region of interest ("regione di interesse"), in analisi delle immagini o in cartografia e diagnostica per immagini
Roi – Rich only I ("Ricco solo io"), dal vecchio inglese del 1853
Roi – Return on investment, indice di redditività del capitale investito
ROI – Republic of Ireland, ossia l'Irlanda
Altro
Roi – singolo di Bilal Hassani del 2019
Roi – variante galiziana del nome proprio di persona maschile Ruy
Roi – famiglia aristocratica vicentina
Roi – in Benin, titolo onorifico attribuito dallo stato ad alcuni oungan particolarmente prestigiosi, discendenti degli antichi re tribali del Dahomey | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,701 |
\section{Introduction} \label{sec:intro}
Number-magnitude counts have a long tradition of providing a simple,
but effective tool for probing the distribution of stars within the
Milky Way and the large-scale structure of the Universe \citep[such as
visual star-gaging of][]{herschel}. The application of photography
to astronomical research in the late 1800s provided a means of
obtaining permanent records of celestial objects, leading to
systematic surveys such as the Plan of Areas \citep{kapt} and the
star-count analyses \citep{seares,bok}. Additionally, photography
also opened the way for surveys of the distribution of extragalactic
nebulae, notably the Lick survey by \citet{sw54} and the
\citet{abell58} catalog of galaxy clusters, derived from the
wide-field Schmidt plates of the first Palomar Observatory Sky Survey.
Photography captured images of the sky for posterity, but visual
inspection of plates can only yield a qualitative understanding. The
development of scanning densitometers in the 1970s provided the first
means of quantifying photographic data for statistical analyses. When
combined with deep imaging with 4-meter telescopes, photography
yielded the first reliable color-magnitude diagrams for field stars
and galaxies fainter than $\sim\!20$~mag \citep{kron80}, and automated
scans of wide-field Schmidt plate mapped the stellar distribution at
bright magnitudes \citep[e.g.][]{hewett81,gilm85}, but see
\citet{reid93,chin13} for a more extensive discussion of those
developments. In more recent years, these investigations have given
way to direct digital imaging, whether through narrow pencil-beam
surveys, as exemplified by the Hubble Deep Field
\citep[HDF;][]{williams96} and its successors, or through near all-sky
surveys, such as the Sloan Digital Sky Survey \citep[SDSS;][]{york00}.
By and large, stars and galaxies occupy distinct domains in imaging
surveys. At high galactic latitudes, stars are typically bright
($V\!\sim\!20$~mag), while galaxies dominate at fainter magnitudes
($v\!\gtrsim\!25$~mag). However rare objects often challenge
conventional models and highlight short-comings in current theories.
For example, \citet{gilm81} show that rare, faint stars can
significantly contaminate samples of distant objects. In recent years,
the focus has moved to significantly higher redshifts with the deepest
surveys, aided partly by gravitational lensing, reaching beyond
$z\!\sim\!10$ \citep{coe13,ellis13}. At those redshifts, the Lyman
break moves longwards of $\lambda\!\sim\!1~\mu$m and galaxies have
extremely red colors at near-infrared wavelengths. As
\citet{wilkins14} have pointed out, very high-redshift galaxies and
ultracool dwarfs often have similar near-infrared colors. In this
paper, we consider the likely surface density of MLT-dwarfs
\citep{kirk99,cush11} and their potential to bias studies of
high-redshift galaxies.
This paper is organized as follows:~In \S~\ref{sec:background} we give
a brief discussion of stellar populations in the Milky Way, the
relevant properties of ultracool dwarfs, and our choice of {\it
representative} deep fields. In \S~\ref{sec:surveys} we detail the
star-count formalism. In \S~\ref{sec:discuss} we discuss these
results in the context of deep fields with the {\it Hubble Space
Telescope} and the {\it James Webb Space Telescope}. Finally, in
\S~\ref{sec:summary} we conclude with a brief summary, reviewing the
key points. Throughout this paper, we take care to explicitly state
the magnitude system, to avoid confusion between Vega-based (often
used in the Galactic and stellar community) and AB-based (the {\it de
facto} standard in extragalactic work) magnitudes.
\section{Background}\label{sec:background}
\subsection{The Stellar Populations of the Milky Way}\label{sec:pops}
The resolved stellar constituents of nearby galaxies are generally
categorized as members of distinct populations. Following
\citet{baade44} and \citet{oort58}, a {\it stellar population} is
characterized as a collection of stars that have similar dynamical
properties and share a common evolutionary scenario. Within the Milky
Way, the main populations are the thin disk, the thick disk, the
stellar halo, and the Galactic bulge/bar. The last-named population is
generally confined within the central regions of the Galaxy (although
radial migration may lead to some local representation), and we
therefore focus the first two populations as representative of stars
in the outer regions of the Galaxy in general and the Solar
Neighborhood in particular. The main properties of these populations
are well summarized by \citet{freeman12}.
Considering the three local populations, the thin disk is the dominant
baryonic component, with a total mass of $\sim\!5\times10^9~M_\odot$
and encompassing the gas and dust contributing the current star
formation. The density distribution is generally well represented by a
double-exponential, with a radial scale-length of
$\sim\!2.5-2.7$~kpc. Gas, dust, and young stars are closely confined
to the Galactic midplane, with the vertical distribution increasing
rapidly with age as the velocity increases due to scattering by
massive objects such as molecular clouds \citep{spitzer,wielen}. The
oldest stars in the disk have ages $\sim\!8-10$~Gyr and distributed in
a disk of scale-height of $\sim\!250$~pc \citep{juric08}.
The thick disk is a more extended component, again following a
double-exponential distribution with a radial scale-length that is
similar to the thin disk. Originally identified within the Galaxy from
star count analyses by \citet{gr83}, the vertical distribution can be
matched with a scale-height of $\sim\!800-900$~pc. The
color-magnitude diagram clearly indicates that this is an old
population ($\sim\!10-12$~Gyr), with essentially no on-going star
formation. While the exact origin remains unclear, detailed
spectroscopic analyses show that thick-disk stars have enhanced
abundances of $\alpha$-elements \citep{bensby13}, indicating that the
population formed rapidly, before type Ia supernovae could
significantly enhance the iron abundance. The local density of
thick-disk stars is $\sim\!8-10$\% that of the thin disk, with a
likely total mass of $\sim\!(1-2)\times 10^9~M_\odot$.
\subsection{Colors of the Ultracool Dwarf Population}\label{sec:ucds}
Ultracool dwarfs have effective temperatures $T\!\lesssim\!2500$~K and
emergent spectra characterized by absorption from broad molecular and
narrow resonance features (e.g.~H$_2$O, FeH, TiO, CO, CH$_4$,
\ion{Na}{1}, and \ion{K}{1}). Consequently these low-mass stars have
very red optical/near-infrared broad-band colors, which are similar to
galaxies at $z\!\gtrsim\!6$ \citep{yan03,ryan05,cab08,wilkins14}. In
\fig{fig:colors}, we show the \jwst/NIRCam broadband colors
synthesized from the IRTF/SpeX library\footnote{as compiled by
A.~Burgasser and available at
http://pono.ucsd.edu/~adam/browndwarfs/spexprism/} as colored
points. The colored lines show the tracks of powerlaw spectra with
$f_\lambda\!\propto\!\lambda^{-\beta}$ with blue ($\beta\!=\!2$),
green ($\beta\!=\!1$), and red ($\beta\!=\!0$). Additionally, we show
an example selection region for $z\!\gtrsim\!7$ galaxies as a gray
polygon. With a limited number of broad-bands, the ultracool dwarfs
and high-redshift galaxies have similar colors and are easily
misidentified. Medium-bands tailored to sample the molecular features
in the low-mass stars can easily break this {\it identification
degeneracy}, but in their absence it is important to assess the
potential number of stars in the sample.
\begin{figure}
\epsscale{1.2}
\plotone{fig1.ps}
\caption{\jwst/NIRCam broadband colors. Each point represents one
object from the IRTF/SpeX library of A.~Burgasser where the color
encodes spectral type as indicated by the color bar. The colored
tracks show the path of idealized, power-law spectra of the form
$f_\lambda\!\propto\!\lambda^{-\beta}$ with $\beta\!=!-2$ (blue),
$\beta\!=\!-1$ (green), and $\beta\!=\!0$ (red), where each tick
represents $\Delta z\!=\!0.1$. The gray region shows a typical
color-color region for selecting high-redshift galaxies
($z\!\gtrsim\!6.5$), which demonstrates the well-known {\it
identification degeneracy} widely discussed in the literature.
While this degeneracy is readily broken with the suite of
medium-bands designed to sample molecular absorption (from H$_2$O,
CO, and CH$_4$) or additional broadbands at
$\lambda\!\gtrsim\!2~\mu$m, such data are rarely available. The
stars (unlike the high-redshift galaxies) are not homogeneously
distributed on the sky and so we provide simple models to predict
the surface density of Galactic stars in
\S~\ref{sec:surveys}. \label{fig:colors}}
\end{figure}
\subsection{Stellar Luminosities}\label{sec:lums}
We adopt the local $J$-band luminosity function pieced together from
\citet{cruz07,boch10,metchev}, but a general calculation could
transform to an arbitrary near-infrared passband using the IRTF/SpeX
library. However these density estimates have modest uncertainties
($\delta\Phi/\Phi\!\sim\!30\%$), so we take our luminosity function to
be a fourth-order polynomial fit for $8.5\!\leq\!J\!\leq\!16.5$~mag:
\begin{equation}\label{eqn:polylf}
\begin{aligned}
\log\Phi(J)={} & -0.30+0.11\,(J-14)+0.15\,(J-14)^2\\
& +0.015\,(J-14)^3-0.00020\,(J-14)^4
\end{aligned}
\end{equation}
where $\Phi(J)$ has units of $10^{-3}$~pc$^{-3}$~mag$^{-1}$ and $J$ is
Vega-based. In \fig{fig:lf}, we show our polynomial luminosity
function (solid line) and the observations as color symbols, where the
color and shape represent spectral type and reference, respectively.
As our primary goal is to predict the number counts at high-Galactic
latitude, we do not propagate the uncertainty in these data or the
corresponding polynomial model. Finally, we adopt the $M_J({\rm
Vega})$--spectral type relation of \citet{hawl02}.
\begin{figure}
\epsscale{1.2}
\plotone{fig2.ps}
\caption{$J({\rm Vega})$-band luminosity function. The symbols and
colors represent the author from which the data are taken and the
spectral type, respectively. The solid line shows the fourth-order
fit given in \eqn{eqn:polylf}. To map between luminosity and
spectral type, we adopt the \citet{hawl02} relation. As mentioned
in the text, we do not attempt to propagate the uncertainty on these
data (or the uncertainty on the polynomial fit) into uncertainties
on the observed number counts, as our primary goal is provide
estimates for total number of brown dwarfs. \label{fig:lf}}
\end{figure}
\subsection{Representative Deep Fields}\label{sec:fields}
Although the precise details of the forthcoming \jwst\ deep fields are
not yet finalized, a reasonable strawman plan would use the broadband
filters in the standard fields. We consider 11~fields, the five
fields from the Cosmic Assembly Near-infrared Deep Extragalactic
Legacy Survey \citep[CANDELS;][]{amk,nag} and the six Hubble Frontier
Fields\footnote{http://www.stsci.edu/hst/campaigns/frontier-fields/}
\citep[HFF; Lotz et al.~in prep][]{lotz14}. In \tab{tab:fields}, we
list the observational properties of these 11~fields, but regard
COSMOS, Abell S1063, Abell 2744, and MACS~J0717 as {\it
representative} fields, since they cover a range of celestial
coordinates and give the largest spread in the following predictions.
\input{tab1.tex}
\section {Modeling {\it Pencil-Beam} Surveys} \label{sec:surveys}
The majority of recent surveys for high-redshift galaxies are based on
deep, narrow-angle imaging observations. The number of stars $N$
within such fields is given by integrating their density distribution
$p(\bvec{r},M)$ over the sampled volume. Here we make the usual assumption
that the stellar luminosity function $\phi(M)$ is independent of spatial
distribution $n(\bvec{r})$ or position in the Galaxy \citep{bahc86};
hence
\begin{equation}\label{eqn:dens}
p(\bvec{r},M)\,\ensuremath{\mathrm{d}}^3\bvec{r}\,\ensuremath{\mathrm{d}} M = n(\bvec{r})\,\phi(M)\,\ensuremath{\mathrm{d}}^3\bvec{r}\,\ensuremath{\mathrm{d}}{M},
\end{equation}
but we recognize that the cooling of the brown dwarfs may lead to a
vertical dependence on the luminosity function \citep{burg04,ryan11}.
We take $n(\bvec{r})\,\ensuremath{\mathrm{d}}^3\bvec{r}$ and
$\phi(M)\,\ensuremath{\mathrm{d}}{M}$ to be dimensionless, and adopt the local luminosity
function (as discussed in \S~\ref{sec:lums}). Therefore we must
renormalize these distributions as:
\begin{equation}
n(\bvec{r_\odot})=\int \Phi(M')\,\ensuremath{\mathrm{d}}{M'}\equiv n_{\odot},
\end{equation}
where $\Phi(M)$ is the local luminosity function in units of
pc$^{-3}$~mag$^{-1}$. We renormalize the luminosity function as
$\phi(M)\,\ensuremath{\mathrm{d}}{M}\!=\!n_\odot^{-1}\,\Phi(M)\,\ensuremath{\mathrm{d}}{M}$ to have units
of mag$^{-1}$.
For this work, we consider only disk distributions, as the Galactic
halo is at least 11~Gyr old \citep{kali} and any brown dwarfs here
would have cooled below our spectral-type range, but discuss the
contribution in \S~\ref{sec:discuss}. Assuming the standard
double-exponential model, we have
\begin{equation}
\tilde{n}(r,z;r_s,z_s)=n_{\odot}\,\exp\left(\frac{r_\odot-r}{r_s}+\frac{|z_\odot|-|z|}{z_s}\right),
\end{equation}
where $(r_\odot,z_\odot)$ represent the Solar position in the Galaxy.
So, for a thick and thin disk the total density is given by:
\begin{equation}
n(r,z)=\tilde{n}(r,z;r_s,z_s)+f_t\,\tilde{n}(r,z;R_s,Z_s)
\end{equation}
where $f_t$ is the fraction of thick disk stars. The conversion from
these cylindrical coordinates, assuming azimuthal symmetry based on
the Galactic center, to spherical coordinates with to the Sun is given
by \citet{juric08}:
\begin{eqnarray}
r&=&\sqrt{r_0^2+R^2\cos^2 b-2Rr_0\cos b\cos \ell}\\
z&=&R\sin b+z_0,
\end{eqnarray}
\input{tab2.tex}
where $R$ is the heliocentric distance and $(\ell,b)$ are the Galactic
coordinates of the field. In \tab{tab:params} we list the published
estimates for the parameters of these distributions that we will
adopt. With a change of variables from heliocentric distance to
distance modulus $\mu\!=5\log R - 5$, the distance modulus
distribution is given by
\begin{equation}\label{eqn:mu}
n(\mu,\ell,b)\,\ensuremath{\mathrm{d}}\mu=\Delta\Omega\,n(R,\ell,b)\,R^2\,\ensuremath{\mathrm{d}} R
\end{equation}
where $\Delta\Omega$ is the field-of-view. In \fig{fig:pmu} we show
the distance modulus distributions for the four representative,
high-latitude fields. The colors represent the thin disk (blue),
thick disk (red), and total (black). For fields at very high latitude
(such as Abell 2744), the typical distance for a star is $2\,z_{\rm
scl}$, which is {\it independent} of the luminosity of the star and
is generically true for any population confined to the Galactic disk
\citep[e.g.][]{green}. We give the peak and average distance modulus for
all 11~potential \jwst\ deep fields in \tab{tab:pmu}.
\input{tab3.tex}
\begin{figure}
\epsscale{1.2}
\plotone{fig3.ps}
\caption{Distance distributions for representative fields. The blue,
red, and gray distributions show the thin, thick, and total disk
contributions. For fields pointed perpendicular to the Galactic
plane, the distance modulus distribution from the thin disk will
peak at $2\,z_{\rm scl}$, and the peak is only slightly more distant
when including the thick disk. It is important to note, these
distributions only depend on the Galactic model and not the
luminosity of the stars in question. As such, these distributions
are generically true and independent of bandpass, but are derived
under the zero-extinction assumption. Including Galactic extinction
is only necessary for low-latitude fields
($|b|\!\lesssim\!10^\circ$, though there is a longitudinal
dependence on this limit) and will introduce a wavelength
dependence. \label{fig:pmu}}
\end{figure}
The predicted stellar number count is given by integrating
\eqn{eqn:dens}, which is the so-called {\it fundamental equation of
stellar statistics} \citep[equation~1 of][]{bahc86}:
\begin{equation}\label{eqn:fess}
N(m,\ell,b)\,\ensuremath{\mathrm{d}} m=\Delta\Omega\int\limits_0^\infty n(R,\ell,b)\,\phi(M)\,R^2\,\ensuremath{\mathrm{d}}{R}\,\ensuremath{\mathrm{d}}{m},
\end{equation}
where $M$ is constrained to satisfy $M\!=\!m-\mu(R)-A(\ell,b,R)$,
where $A(\cdot)$ is the extinction along a given line-of-sight as a
function of distance. Since the typical \jwst\ deep field is likely
situated far from the Galactic plane, they will have low color
excesses \citep[typically $E_{B-V}\!\lesssim\!0.03$~mag see
\tab{tab:fields};][]{sf11} and infrared extinctions of $A_{\rm
IR}\!\lesssim\!0.02$~mag \citep{sfd}. Moreover, since \jwst\ will
be able to detect L0 to $\sim\!16$~kpc and T8 to $\sim\!$~3 kpc
\citep[assuming $J\!\sim\!29$~mag and absolute magnitudes
of][]{hawl02}, a full, three-dimensional description of $A(\cdot)$
is required for reliable number counts \citep{sale,ryan11,green}.
Therefore we adopt $A(\ell,b,R)\!=\!0$~mag, but stress that fields
near the Galactic plane may require a more sophisticated treatment,
which will modify our predictions. Using the definition from
\eqn{eqn:mu}, we find that \eqn{eqn:fess} is simply a convolution
between the normalized luminosity function and the distance modulus
distribution:
\begin{equation}\label{eqn:conv}
N(m,\ell,b)\,\ensuremath{\mathrm{d}} m=\Delta\Omega\int\limits_{-\infty}^{+\infty} n(\mu,\ell,b)\,\phi(m-\mu)\,\ensuremath{\mathrm{d}}{\mu}\,\ensuremath{\mathrm{d}}{m}.
\end{equation}
We show the differential (\fig{fig:dif}) and integral (\fig{fig:cum})
for our representative fields in units of arcmin$^{-2}$. As in
\fig{fig:pmu}, the colors represent thin (blue), thick (red), and
total (black) disk components. In the Appendix, we tabulate various
statistics of the number counts for the 11~potential \jwst\ deep
fields broken down by spectral type (Tables~4--7). Since stars in the
Milky Way are predominantly confined to an exponential disk, they are
not generally not found at arbitrarily faint brightnesses. Although
the ultracool dwarfs have very low-luminosities, they are expected to
have $J\!\sim\!24$~mag in high-latitude fields
($|b|\!\gtrsim\!20^\circ$).
\begin{figure}
\epsscale{1.2}
\plotone{fig4.ps}
\caption{Differential number counts for representative \jwst\ deep
fields. Here we depict the contribution from the thin disk (blue),
thick disk (red), and total disk populations (grey). The bimodal
behavior comes from the two peaks in the extremal ranges of the luminosity
function (see \fig{fig:lf}). In the Appendix, we show similar plots
for narrower ranges of spectral type.\label{fig:dif}}
\end{figure}
\begin{figure}
\epsscale{1.2}
\plotone{fig5.ps}
\caption{Integral number counts for representative \jwst\ deep fields.
The colors have the same meaning as in \fig{fig:dif}.\label{fig:cum}}
\end{figure}
\section{Discussion}\label{sec:discuss}
We have demonstrated that for an idealized survey (ie.~one with
perfect sample completeness), the ultracool dwarfs are expected to be
reasonably bright --- reaching 50\% of their totals near where their
counts peak of $J\!\sim\!24$~AB mag. However a realistic survey will
not be so complete, and will therefore the expression in
\eqn{eqn:fess} should be modified to include a completeness function.
In most cases, the completeness function does not have an explicit
dependence on sky position, but rather is only modulated by the
non-uniformity of the survey \citep{ryan11,benne}. For most
high-redshift galaxy surveys, the completeness is typically a weak
function of brightness for ${\rm AB}\!\lesssim\!25$~mag
\citep[e.g.][]{bou07}, which leaves many of our results regarding the
surface densities unchanged.
Thus far we have explicitly omitted a halo component, since the
Galactic halo has an age of $\gtrsim\!11$~Gyr \citep{kali} --- but
here we illustrate its potential effect on our results. To have the
colors consistent with a high-redshift galaxy, an ultracool dwarf
would have a spectral type roughly L5--T5 (see \fig{fig:colors}) and
hence a temperature of $2000-1200$~K \citep[Figure 7 of][]{kirk05}.
Based on the expected cooling curves
\citep{burrows97,chabrier00,allard01,baraffe03}, a star with an age of
11.4~Gyr and temperature $1200-2000$~K would have a mass of
$0.075-0.08~M_{\odot}$ and likely sustain hydrogen fusion. Therefore
we include a Galactic halo following the parameterization and values
of \citet{sesar11}, but calculation over this narrow temperature
range. The halo distribution peaks around $J\!\sim\!30$~AB mag and
increases the total surface density of $\sim\!0.1$~arcmin$^{-2}$.
This estimate depends strongly on the cooling models and
star-formation history of brown dwarfs, and so should be regarded as
preliminary. Nevertheless, \jwst\ will have the ability to easily
detect early-T dwarfs in the Galactic halo, indeed the existence of a
sizable population veritably associated with the halo will be a useful
boundary condition on the cooling models.
Throughout this work we have tacitly assumed that none of ultracool
dwarfs are in unresolved binary systems. If we assume that
equal-mass, unresolved binaries would have same colors, luminosities,
and Galactic distribution as single stars, then the stars would be
$2.5\log 2\!=\!0.75$ mag too bright. If all stars were in binary
pairs, then the number counts would shift $\sim\!0.75$~mag to brighter
limits, but the overall number of sources identified would remain
constant (since the binaries are unresolved). Certainly this would
exacerbate the issue of contamination, however this {\it maximum
binarity} assumption is very conservative since the observed binary
fractions are more like $\lesssim\!25$\% \citep[e.g.][]{burg07,abe14}.
Moreover, \citet{ryan11} showed that the model number counts do not
significantly change for binary fractions $\leq\!40$\%.
\section{Summary} \label{sec:summary}
Since brown dwarfs have long been recognized as a potential
contaminating source in high-redshift galaxy surveys
\citep{yan03,ryan05,cab08,wilkins14}, we have provided tangible
predictions for the surface density of these ultracool dwarfs using
the best estimates for their luminosity function and Galactic
distribution. We find that the highest surface densities are (not
surprisingly) near the Galactic plane and with
$\sim\!1$~arcmin$^{-2}$. Therefore in existing datasets with
\hst\ the numbers are typically $\lesssim\!1$ for a single WFC3
field-of-view (such as the HFF or HUDF) or $\sim\!40$ for wide-field
mosaics (such as CANDELS:~UDS, EGS, or COSMOS). With \jwst\ it will be
possible to obtain many shallow fields (${\rm AB}\!\sim\!27$) and
search for dwarfs out to $\sim\!6$~kpc, veritably sampling the
Galactic halo. Although conclusively identifying a given dwarf as a
member of the halo will require kinematic data, which will yield new
constraints on the cooling models of ultracool dwarfs by providing
robust samples of very old, but massive, objects.
\acknowledgments The authors would like to thank Harry Ferguson for
his thoughts regarding future deep fields with \jwst. Support for
this work was provided by NASA through grant number 13266 from the
Space Telescope Science Institute, which is operated by AURA, Inc.,
under NASA contract NAS 5-26555. This research has benefited from the
SpeX Prism Spectral Libraries, maintained by Adam Burgasser at
http://pono.ucsd.edu/~adam/browndwarfs/spexprism.
{\it Facilities:} \facility{JWST (NIRCam)}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,623 |
\section{Introduction}\label{s:1}
The period-luminosity (P-L, also known as Leavitt Law) relation for Cepheid variables is an important astrophysical tool. A calibrated P-L relation can serve as the first rung in the extragalactic distance scale ladder, which can be used to determine the Hubble constant \citep[e.g.,][and reference therein]{fre2001,san2006,rie2011}. In the local Universe, the Cepheid P-L relation can be used to measure the distances to nearby galaxies and investigate the characteristics of our own Galaxy \citep[e.g.,][and reference therein]{maj2009,ped2009}. Research on Cepheid P-L relations includes calibrating the relations \citep[e.g.,][and reference therein]{fou2007}, investigating the metallicity dependence \citep[e.g.,][and reference therein]{rom2008} or universality of the P-L relations \citep[e.g.,][and reference therein]{bon2010}, and the study of non-linearity of these relations \citep[e.g.,][and reference therein]{nge2009}. These works mainly focused on mean light in the optical and near infrared ($JHK$) bands. In this paper, we discuss two aspects of current research in P-L relations: the extension of the P-L relations to mid-infrared (Section \ref{s:2}), and the investigation of P-L relations at various phases of the pulsation -- the multi-phase P-L relations (Section \ref{s:3}).
\section{The Mid-Infrared P-L Relations}\label{s:2}
The Hubble constant is one of the most important cosmological parameters that requires being independently determined to a high degree of accuracy and precision \citep[see, for examples,][]{hu2005,oll2007,fre2010,rie2011}. A convincing example is presented in Figure 23 of \citet{mac2006}, showing the improvement of measuring cosmological parameters when the error in the Hubble constant is reduced from $\sim10$\% to $\sim5$\%. A 2\% determination of the Hubble constant is possible to achieve via mid-infrared (MIR) distance ladder \citep{fre2010}, taking a huge advantage of the fact that extinction is negligible in the MIR. The first step in constructing the MIR distance ladder is the derivation of MIR Cepheid P-L relations.
\subsection{The Empirical Mid-Infrared P-L Relations}\label{ss:2_1}
\begin{table}
\caption{Slopes of the MIR P-L Relations}
\label{tab:1}
\begin{tabular}{c|cc}
\tableline
Band & LMC & SMC \\
\tableline
$3.6\mu \mathrm{m}$ & $-3.25\pm0.01$ & $-3.23\pm0.02$ \\
$4.5\mu \mathrm{m}$ & $-3.21\pm0.01$ & $-3.18\pm0.02$ \\
$5.8\mu \mathrm{m}$ & $-3.18\pm0.02$ & $-3.23\pm0.04$ \\
$8.0\mu \mathrm{m}$ & $-3.20\pm0.04$ & $-3.25\pm0.05$ \\
\tableline
\end{tabular}
\end{table}
The MIR P-L relations can be derived by matching archival data from the {\it Spitzer Space Telescope} to the known Cepheids in the Magellanic Clouds. This has been done in \citet{nge2008} by matching the SAGE catalogs \citep[][single Epoch data]{mei2006} to LMC Cepheids from OGLE-II \citep[$\sim600$ Cepheids,][]{uda1999}, in \citet{nge2009} by matching the updated SAGE catalogs (two Epoch data) to LMC Cepheids from OGLE-III \citep[$\sim1800$ Cepheids,][]{sos2008}, and in \citet{nge2010} by matching the SAGE-SMC catalog \citep[][single Epoch data]{gor2010} to OGLE-III SMC Cepheids from \citet[][$\sim2600$ Cepheids]{sos2010}. Details of deriving these MIR P-L relations are given in the cited papers, and will not be repeated here. The slopes of these MIR P-L relations are summarized in Table \ref{tab:1}. It is worth pointing out that the MIR P-L relations for SMC Cepheids show a break at $\log(P)=0.4$, which is also known to exist in the optical P-L relations \citep{bau1999}, suggesting that this break is due to evolutionary effects \citep{bar1998}\footnote{This is because the evolutionary effects on this P-L break, if exist, should be independent of observed band-passes.}. Independent of the {\it Spitzer} data, the $N3$ band ($\sim 3\mu \mathrm{m}$) P-L relation for LMC Cepheids was also derived based on observations with the {\it AKARI} satellite \citep{nge2010a}. In contrast to the SAGE data, the {\it AKARI} data contains the information on time of observation, which allows for the application of random-phase correction to the single epoch data \citep[for more details, see][]{nge2010a}. The slope of the $N3$ band P-L relation was found to be $-3.25\pm0.05$, in good agreement with the $3.6\mu \mathrm{m}$ P-L slopes listed in Table \ref{tab:1}.
\begin{figure}[h]
\includegraphics[width=\columnwidth]{ngeow_fig1.eps}
\caption{Empirical slopes of the LMC (top panel) and SMC (bottom panel) P-L relations as a function of wavelength. The dashed lines are the expected slopes in the MIR (see text for details). [See on-line edition for a color version.]}
\label{fig:1}
\end{figure}
\begin{figure*}[th]
\includegraphics[width=\columnwidth]{ngeow_fig2a.eps}
\includegraphics[width=\columnwidth]{ngeow_fig2b.eps}
\caption{Fitting of the empirical MIR P-L relations to the Cepheids in IC 1613 \citep[left panel, Cepheids data adopted from][]{fre2009} and NGC 6822 \citep[right panel, Cepheids data adopted from][]{mad2009a}. Distance moduli to LMC and SMC were taken to be $18.50$ and $19.00$, respectively. Note that \citet{tam2008} do not provide uncertainties in their distance moduli.}
\label{fig:2}
\end{figure*}
Following the arguments presented in \citet{nei2010}, the slopes of the MIR P-L relations can be predicted using $L=4\pi R^2B_{\lambda}(T)$, where $B_{\lambda}(T)\propto T$ at MIR due to the Rayleigh-Jean approximation. Then, the MIR P-L relation can be written as $M_{\mathrm{IRAC}}=-5a_R\log(P)+a_T\log(P)+\mathrm{constant}$, where $a_R=0.68$ is the slope of the period-radius relation \citep{gie1999}. For $a_T$, conversion between $(V-I)$ color and temperature ($T$) was adopted from \citet{bea2001}. Using the period-color relations from Sandage et al. (2004, for LMC; 2009, for SMC), the expected slopes for the MIR P-L relations are $-3.22$ and $-3.21$ for the LMC and SMC, respectively. These values are consistent with those listed in Table \ref{tab:1}. Figure \ref{fig:1} shows the empirical P-L slopes, from the $B$ band to the IRAC bands, based on the P-L relations available in literature. The expected MIR P-L slopes are represented as dashed lines in this Figure, and suggest that the P-L slopes approach these asymptotic values around $\sim1.5 \mu \mathrm{m}$. Empirical IRAC band P-L slopes from \citet{mad2009} were included for comparison.
In parallel to the derivation of MIR P-L relations based on Magellanic Cloud Cepheids, \citet{mar2010} have also derived the MIR P-L relations from {\it Spitzer} observations for Galactic Cepheids that possess independent distance measurements in literature.
\subsection{Distance Scale Applications}\label{ss:2_2}
The empirical MIR P-L relations were used to derived the distance to two galaxies, IC 1613 and NGC 6822. The MIR photometry for Cepheids in these two galaxies were adopted from \citet{fre2009} and \citet{mad2009a}, respectively. The fitted P-L relations and the resulted distance moduli using either the LMC or SMC P-L relations were presented in Figure \ref{fig:2} for each of the $3.6\mu \mathrm{m}$ and $4.5\mu \mathrm{m}$ bands. The derived distance moduli were in good agreement when using either the LMC or SMC P-L relations, as well as between the two bands. These distance moduli were also compared to the published distance based on the Tip of the Red Giant Branch (TRGB) method from \citet{sak2004} and RR Lyrae from \citet{tam2008}. Good agreements can be found among these distance moduli as shown in Figure \ref{fig:2}.
\begin{figure}[th]
\includegraphics[width=\columnwidth]{ngeow_fig3.eps}
\caption{Comparison of the empirical P-L slopes from Table \ref{tab:1} to selected synthetic P-L slopes with varying $Z$ (but at constant $Y$). Note that for better visualization, wavelengths for SMC P-L slopes have been shifted slightly.}
\label{fig:3}
\end{figure}
\subsection{The Synthetic Mid-Infrared P-L Relations}\label{ss:2_3}
\begin{figure*}[!bh]
\includegraphics[width=\columnwidth]{ngeow_fig4a.eps}
\includegraphics[width=\columnwidth]{ngeow_fig4b.eps}
\caption{Differences of the empirical and synthetic P-L slopes as a function of wavelength for the LMC (top panels) and SMC (bottom panels). Left and right panels are for the two model sets considered in this work. The symbols are the same as in Figure \ref{fig:1}. Synthetic P-L slopes in the $BVIJK$ bands were adopted from \citet{bon2010}. Error bars include both of the errors in empirical and synthetic P-L slopes. [See on-line edition for a color version.]}
\label{fig:4}
\end{figure*}
A series of pulsation models with different inputs of helium ($Y$) and metal ($Z$) abundances were used to generate the synthetic P-L relations in the {\it Spitzer} IRAC bands. Details of these pulsation models and synthetic P-L relations are given elsewhere \citep{nge2011}. Briefly, non-linear pulsation codes that include time-dependent treatment of pulsation and convection, together with adopted mass-luminosity relations, were used to generate $\sim1000$ pulsators (in the mass range of $\sim5$ to $\sim11$ Solar masses) that populated the instability strip according to a given mass law \citep{ken1998}. Luminosity (and colors) of these pulsators where then converted to the IRAC band magnitudes using stellar atmosphere models.
A comparison of the empirical P-L slopes from Table \ref{tab:1} to the synthetic P-L slopes is presented in Figure \ref{fig:3}, showing that the synthetic P-L slopes from the $(Y=0.25,\ Z=0.008)$ model set agree well to both of the empirical LMC and SMC P-L slopes. The empirical P-L slopes in various bands, as presented in Figure \ref{fig:1}, were also compared to the synthetic P-L slopes from the $(Y=0.25,\ Z=0.008)$ and $(Y=0.25,\ Z=0.004)$ model sets in Figure \ref{fig:4}, as $Z=0.008$ and $Z=0.004$ generally representing the metallicity of the LMC and SMC, respectively. For the LMC, the empirical P-L slopes are in good agreement with the synthetic P-L slopes from the $Z=0.008$ model set \citep[except for the slopes from][]{mad2009}. However, the empirical P-L slopes of the SMC agree better with synthetic P-L slopes from the $Z=0.008$ model set than the $Z=0.004$ model set. Further theoretical and empirical investigations of the SMC P-L relations are needed to solve this discrepancy.
\section{The Multi-Phase P-L Relations}\label{s:3}
Though Cepheid P-L relations are mostly studied at mean light, which is an averaged value over the pulsation cycles, P-L relations at maximum light have also been investigated in the past \citep[for example, see][]{san1968,sim1993,kan1996,kan2003}. Studies of the P-L relations beyond mean light began in a series of papers that investigated the period-color and amplitude-color relations for Cepheids at maximum, mean and minimum light \citep{kan2004,kan2004b,kan2006,kan2007}. The P-L relations at individual phases for a full pulsation cycle -- the multi-phase P-L relation -- have been studied empirically in \citet[][using OGLE-II LMC data]{nge2006}. \citet{kan2010} extended the work of \citet{nge2006} by using OGLE-III LMC data and comparisons that include predictions from theoretical pulsation models. In this Section, we continue our investigation of the multi-phase P-L relations by comparing the results found in the LMC and SMC, as well as investigating the dispersions of the multi-phase P-L relations as a function of pulsational phase.
\subsection{Data and Method}\label{ss:3_1}
Light curves data in the $VI$ bands for fundamental mode Cepheids in LMC and SMC were taken from the OGLE-III catalogs as described in \citet{sos2008,sos2010}, respectively. These catalogs also include the periods ($P$) and time of maximum light ($t_0$) of the Cepheids. Extinction corrections for the data were done by employing the extinction maps from \citet{zar2004,zar2002} for LMC and SMC Cepheids, respectively, using $R_V=3.24$ and $R_I=1.96$. The data for the $V$ and $I$ band light curves were fitted by use of a Fourier expansion in the form of:
\begin{eqnarray}
m(\Phi) & = & m_0 + \sum_{k=1}^{n} A_k \cos[2\pi k \Phi(t) + \phi_k],
\end{eqnarray}
\noindent where $\Phi (t)=(t-t_0)/P - \mathrm{int}[(t-t_0)/P]$ is the phase of the light curves ranging from $0$ to $1$, representing a full cycle of pulsation. Hence, the P-L relation at a given phase can be derived using the magnitudes at this phase from the smooth light curves calculated using equation (1). In addition to $VI$ band multi-phase P-L relations, we also included the multi-phase relations for the extinction free Wesenheit function \citep{mad1991,uda1999a}, $W=I-1.55(V-I)$, by taking the $V$ and $I$ magnitudes at the same phase using equation (1).
\subsection{Comparison of the Multi-Phase P-L Relations for Magellanic Clouds Cepheids}\label{ss:3_2}
Figures \ref{fig:5} and \ref{fig:6} present the slopes and zero-point for the multi-phase P-L relations as a function of pulsational phase for the LMC and SMC Cepheids. In these Figures, Cepheids were separated into short-period ($0.4<\log P <1.0$) and long-period ($\log P>1.0$) groups. The dynamic nature of the P-L relations as a function of pulsational phase can be seen clearly from these Figures. These results also show convincing evidence of non-linearity in the multi-phase relations, though the exact effects on the mean light P-L relations and subsequent estimates of the Hubble constant are still to be determined. Of particular interest are the differences in the long period multi-phase Wesenheit function between the LMC and SMC. This occurrence is important since the extra-galactic distance scale is primarily built with long period Cepheids. The most probable explanation for these differences is that these relations vary with metallicity. Because massive stars usually become variable after leaving the main sequence, understanding the effect that metallicity has on pulsation is important for understanding stellar evolution.
\begin{figure*}
\includegraphics[width=3.1in]{ngeow_fig5a.eps}
\includegraphics[width=3.1in]{ngeow_fig5b.eps} \\
\includegraphics[width=3.1in]{ngeow_fig5c.eps}
\includegraphics[width=3.1in]{ngeow_fig5d.eps} \\
\includegraphics[width=3.1in]{ngeow_fig5e.eps}
\includegraphics[width=3.1in]{ngeow_fig5f.eps}
\caption{Slopes of the P-L relations as a function of pulsational phase for LMC (open circles) and SMC (filled squares) in $V$ (top panels), $I$ (middle panels) and $W$ (bottom panels) bands. Left and right panels are for the short and long period Cepheids, respectively.}
\label{fig:5}
\end{figure*}
\begin{figure*}
\includegraphics[width=3.1in]{ngeow_fig6a.eps}
\includegraphics[width=3.1in]{ngeow_fig6b.eps} \\
\includegraphics[width=3.1in]{ngeow_fig6c.eps}
\includegraphics[width=3.1in]{ngeow_fig6d.eps} \\
\includegraphics[width=3.1in]{ngeow_fig6e.eps}
\includegraphics[width=3.1in]{ngeow_fig6f.eps}
\caption{Same as Figure \ref{fig:5}, but for the zero-points of the multi-phase P-L relations evaluated at $10$ days, i.e. fitting the P-L relations in the form of $m=a\log (P-1.0) + b$.}
\label{fig:6}
\end{figure*}
\subsection{Dispersions of the Multi-Phase P-L Relations}\label{ss:3_3}
\citet{aar1986} listed five criteria for a good distance indicator, one of them being small scatter\footnote{The other four criteria, as quoted from \citet{aar1986}, are: ``sound physical basis, quantitative observables, measurables needing minimal corrections, and applicability over a wide distance range''.}. Even though Cepheid P-L relations at mean light have been widely used in distance scale work, the dynamic nature of the multi-phase P-L relations as seen in the previous sub-section gives reason to postulate the existence of a phase at which the scatter of the respective P-L relation is smallest. If this is indeed the case, then it would be possible to improve the distance measurements, and hence the Hubble constant precision, by applying the P-L relation at this particular phase.
It is straightforward to calculate the dispersion of the multi-phase P-L relations as a function of pulsational phase. We use the LMC multi-phase P-L relations as an demonstration in this sub-section. Short and long period multi-phase P-L relations were used when calculating the overall dispersions. Results for $VIW$ band multi-phase P-L relations are shown in left panel of Figure \ref{fig:7}. In this Figure, dispersions from mean light P-L relations were included for comparison. Right panels of Figure \ref{fig:7} present the percentage change of the dispersions from the multi-phase P-L relations when compared to the mean light P-L dispersions.
\begin{figure*}
\includegraphics[width=\columnwidth]{ngeow_fig7a.eps}
\includegraphics[width=\columnwidth]{ngeow_fig7b.eps} \\
\includegraphics[width=\columnwidth]{ngeow_fig7c.eps}
\includegraphics[width=\columnwidth]{ngeow_fig7d.eps} \\
\includegraphics[width=\columnwidth]{ngeow_fig7e.eps}
\includegraphics[width=\columnwidth]{ngeow_fig7f.eps}
\caption{{\bf (a) Left:} Dispersions of the multi-phase P-L relations as a function of pulsational phase. The dashed lines are the dispersions from the mean light P-L relations. {\bf (b) Right:} Percentage change of the dispersions when compared to the mean light P-L dispersions. Negative percentage means the dispersion is smaller than the mean light P-L dispersion.}
\label{fig:7}
\end{figure*}
From Figure \ref{fig:7} it can be seen that minimum dispersion occurs at phase $\sim0.55$, $\sim0.59$ and $\sim0.14$ in the $VIW$ band, respectively. However, these dispersions are close to the dispersions from mean light P-L relations, with the largest difference being $\sim4$\% in the $W$ band. This result implies that the dispersion at mean light P-L relation is comparable to the minimum dispersion from multi-phase P-L relations. Hence, the applicability of mean light P-L relation in distance scale works is reinforced. Interestingly, the largest dispersion occurs at maximum light for both the $V$ and $I$ band.
\section{Discussion and Conclusion}\label{s:4}
In this paper, we present two new aspects in Cepheid P-L relation research: the study of mid-infrared and multi-phase P-L relations. Both of these studies utilized the LMC and SMC Cepheids catalogs from OGLE-III.
The MIR P-L relations were derived for Cepheids in both Magellanic Clouds using {\it Spitzer} archival data. These MIR P-L relations were also applied to derive the distance moduli to IC 1613 and NGC 6822, showing a good agreement with published distances. When comparing the empirical P-L slopes for LMC and SMC Cepheids, as listed in Table \ref{tab:1}, these P-L slopes suggested that they could be independent of metallicity, at least for metallicities bracketed by these two low-abundance galaxies. This is in contrast with the study of the synthetic P-L relations from \citet{nge2011}, which found that the synthetic MIR P-L slopes could be dependent on metallicity, suggesting a need for future work. Comparisons of the empirical and synthetic P-L slopes show that the LMC P-L slopes agree well with synthetic P-L slopes from the $Z=0.008$ model set. The empirical SMC P-L slopes also show a better agreement to the synthetic P-L slopes from the same model set as in LMC.
The multi-phase P-L relation for Cepheids in the SMC was investigated for the first time and compared to the LMC. These multi-phase P-L relations not only revealed that P-L relations, at least in the $VIW$ bands, are dynamic within the cycles of pulsations, but also behave differently for LMC and SMC Cepheids. This could be due to the metallicity difference of these two galaxies. Minimum dispersions occurs at specific phases for the $VIW$ band multi-phase P-L relations; however, these minimum dispersions do not differ significantly from the dispersions obtained from the mean light P-L relations. Of particular interest is the ``anomalous'' behavior of the multi-phase P-L relations in the phases between $\sim0.7$ and $\sim 0.9$, as evident from Figures \ref{fig:5} to \ref{fig:7}. This may be due to the interaction of the hydrogen ionization front (HIF) and the stellar photosphere, which are not always co-moving during a stellar pulsation cycle and can engage/disengage at various phases and/or period ranges, or the presence of shock in photosphere at these phases.
\acknowledgments
CCN thanks the funding from National Science Council (of Taiwan) under the contract NSC 98-2112-M-008-013-MY3.
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\bibitem[\protect\citeauthoryear{Udalski et al.}{1999b}]{uda1999} Udalski, A., Soszynski, I., Szymanski, M., Kubiak, M., Pietrzynski, G., Wozniak, P., \& Zebrun, K.\ 1999b, \actaa, 49, 223
\bibitem[\protect\citeauthoryear{Zaritsky et al.}{2002}]{zar2002} Zaritsky, D., Harris, J., Thompson, I.~B., Grebel, E.~K., \& Massey, P.\ 2002, \aj, 123, 855
\bibitem[\protect\citeauthoryear{Zaritsky et al.}{2004}]{zar2004} Zaritsky, D., Harris, J., Thompson, I.~B., \& Grebel, E.~K.\ 2004, \aj, 128, 1606
\end{thebibliography}
\end{document}
| {
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} | 1,217 |
\section*{Introduction}
Eisenstein's irreducibility criterion in commutative ring theory states that if $R$ is a commutative ring and $\mathfrak{p}$ is a prime ideal of $R$ and \[f= a_0 + a_1 x + \cdots + a_n x^n \in R[x]\] is a polynomial such that
\begin{enumerate}
\item $a_n \notin \mathfrak{p}$,
\item $a_i \in \mathfrak{p}$, for $i=0,1,\dots,n-1$,
\item $a_0 \notin \mathfrak{p}^2$.
\end{enumerate}
Then $f$ cannot be factored into non-constant polynomials in $R[x]$ (see Proposition 5.17 in \cite{Aluffi2009} and p. 228 in Matsumura's book \cite{Matsumura1989}).
In the current note, we generalize this criterion for semirings. Since the language for semirings is not completely standardized \cite{Glazek2002}, we need to introduce a couple of concepts in semiring theory. First, we need to clarify what we mean by a semiring. In this paper, by a semiring, we understand an algebraic structure, consisting of a nonempty set $S$ with two operations of addition and multiplication such that the following conditions are satisfied:
\begin{enumerate}
\item $(S,+)$ is a commutative monoid with identity element $0$;
\item $(S,\cdot)$ is a commutative monoid with identity element $1 \not= 0$;
\item Multiplication distributes over addition, i.e., $a\cdot (b+c) = a \cdot b + a \cdot c$ for all $a,b,c \in S$;
\item The element $0$ is the absorbing element of the multiplication, i.e., $s \cdot 0=0$ for all $s\in S$.
\end{enumerate}
Let $S$ be a semiring and $I$ a nonempty subset of $S$. The set $I$ is said to be an ideal of $S$, if $a+b \in I$ for all $a,b \in I$ and $sa \in I$ for all $s \in S$ and $a \in I$ \cite{Bourne1951}. The ideal $I$ of $S$ is called proper if $I \neq S$. A proper ideal $P$ of $S$ is called prime, if $ab\in P$ implies either $a\in P$ or $b\in P$. Finally, the ideal $I$ is subtractive if $a+b\in I$ and $a\in I$ imply that $b\in I$ for all $a,b\in S$ \cite{Golan1999(b)}. Now we pass to the next section to prove Eisenstein's irreducibility criterion for polynomials over semirings.
\section*{Eisenstein's Irreducibility Criterion for Polynomials over Semirings}
The German mathematician Ferdinand Gotthold Max Eisenstein (1823--1852) originally stated and proved the irreducibility criterion, we now name after him, in \cite{Eisenstein1850}. A more general form of this criterion is brought in p. 228 in Matsumura's book \cite{Matsumura1989} and Proposition 5.17 in \cite{Aluffi2009}. Now, we prove a semiring version of this famous criterion.
\begin{theorem}[Eisenstein's Irreducibility Criterion] \label{Eisensteincriterion}
Let $S$ be a semiring and $P$ a subtractive prime ideal of $S$. Let \[f= a_n X^n + a_{n-1} X^{n-1} + \cdots +a_0\] be a polynomial in $S[X]$ such that the following statements hold:
\begin{enumerate}
\item \label{E1} $a_n \notin P$,
\item \label{E2} $a_i \in P$, for all $i <n$,
\item \label{E3} $a_0 \notin P^2$.
\end{enumerate}
Then $f$ cannot be factored into non-constant polynomials in $S[X]$.
\begin{proof}
If \[f= (b_r x^r + \cdots + b_0)(c_s x^s + \cdots + c_0)\] is a factorization in $S[X]$ with $r,s<n$, and $b_r$ and $c_s$ are nonzero, then either $b_0$ or $c_0$ is not in $P$. Because if $b_0$ and $c_0$ are both elements of $P$, then $a_0 = b_0 c_0$ is an element of $P^2$, contradicting the Condition (\ref{E3}). Without loss of generality, suppose that $b_0 \notin P$. Since $a_0 \in P$ and $P$ is prime, we have $c_0 \in P$. On the other hand, by Condition (\ref{E1}), since $a_n = b_r c_s$, the elements $b_r$ and $c_s$ cannot be in $P$. Let $m$ be the smallest value of $k$ such that $c_k \notin P$. Then
\begin{displaymath}
a_m = b_0 c_m + b_1 c_{m-1} + \cdots + \left\{ \begin{array}{ll}
b_m c_0 & \textrm{if $r \geq m,$}\\
b_r c_{m-r} & \textrm{if $r<m.$}\\
\end{array} \right.
\end{displaymath}
The fact that neither $b_0$ nor $c_m$ are elements of $P$, while $c_{m-1}, \dots, c_0$ are all elements of $P$ and $P$ is subtractive implies that $a_m \notin P$. Therefore, $m=n$. Consequently, $s = n$, contradicting our assumption that $s<n$. This finishes the proof.
\end{proof}
\end{theorem}
Let us recall that a semiring $S$ is a semidomain if $ab=ac$ with $a\neq 0$ will cause $b=c$, for all $a,b,c\in S$. Similar to the concept of field of fractions in ring theory, one can define the semifield of fractions $F(S)$ of the semidomain $S$ \cite[p. 22]{Golan1999(a)}. An ideal $I$ of a semiring $S$ is called principal if $I = \{sa: s\in S\}$ for some $a\in S$. The ideal $I = \{sa: s\in S\}$ is denoted by $(a)$. Finally, if $S$ is a semiring, for $a,b \in S$, it is written $a \mid b$ and said that ``$a$ divides $b$'', if $b = sa$ for some $s\in S$. This is equivalent to say that $(b) \subseteq (a)$. Also, it is said that $a$ and $b$ are associates if $a=ub$ for some unit and note that if $S$ is a semidomain, then this is equivalent to say that $(a) = (b)$. A nonzero, nonunit element $s$ of a semiring $S$ is said to be irreducible if $s = s_1 s_2$ for some $s_1, s_2 \in S$, then either $s_1$ or $s_2$ is a unit. This is equivalent to say that $(s)$ is maximal among proper principal ideals of $S$. An element $p\in S-\{1\}$ is said to be a prime element, if the principal ideal $(p)$ is a prime ideal of $S$, which is equivalent to say if $p \mid ab$, then either $p \mid a$ or $p \mid b$ \cite{Nasehpour2018}. A semidomain $S$ is called factorial (also unique factorization) if the following conditions are satisfied:
\begin{enumerate}
\item Each irreducible element of $S$ is a prime element of $S$.
\item Any nonzero and nonunit element of $S$ is a product of irreducible elements of $S$.
\end{enumerate}
Let us recall that a semiring $S$ is weak Gaussian if and only if every prime ideal of $S$ is subtractive \cite[Theorem 19]{Nasehpour2016}. The following is a generalization of Eisenstein's criterion for unique factorization domains (see for example p. 147 in \cite{Spindler1994}):
\begin{corollary}
Let $S$ be a weak Gaussian factorial semidomain and $p$ a prime element of $S$. Let \[f= a_n X^n + a_{n-1} X^{n-1} + \cdots +a_0\] be a polynomial in $S[X]$ such that the following statements hold:
\begin{enumerate}
\item $p \nmid a_n$,
\item $p \mid a_i$, for all $i <n$,
\item $p^2 \nmid a_0$.
\end{enumerate}
Then $f$ cannot be factored into non-constant polynomials in $S[X]$.
\end{corollary}
\begin{remark}
Proposition 3.10 in \cite{NasehpourV} gives some examples for weak Gaussian factorial semidomains. Namely, if $D$ is a Dedekind domain, then the semiring $\Id(D)$ of the ideals of $D$ with the standard addition and multiplication of ideals \cite[Proposition 6.29]{Golan1999(b)} is a factorial semidomain such that each ideal of the semiring $\Id(D)$ is subtractive.
\end{remark}
\subsection*{Acknowledgments} It is a pleasure to thank Professor Dara Moazzami for his support and encouragement. The author is supported by the Department of Engineering Science at the Golpayegan University of Technology and his special thanks go to the Department for providing all the necessary facilities available to him for successfully conducting this research.
| {
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} | 6,434 |
Викингур () е исландски футболен отбор от столицата Рейкявик. Основан е на 21 април 1908 година. Клубните цветове са в зелено. Играе домакинските си мачове на стадион "Викингсвьотлюр" с капацитет 1449 зрители. Викингур е пет пъти шампион на Исландия и веднъж носител на националната купа. Клубът често играе в евротурнирите, но нито веднъж не е успявал да премине първия кръг.
Освен футбола спортен клуб "Викингур" развива тенис, тенис на маса, карате, ски и хандбал.
Успехи
Исландска висша лига
Шампион (5): 1920, 1924, 1981, 1982, 1991
Вицешампион (7): 1918, 1921, 1922, 1925, 1938, 1940, 1948
Бронзов медал (8): 1919, 1926, 1927, 1931, 1939, 1941, 1944, 1953
Купа на Исландия:
Носител (4): 1971, 2019, 2021, 2022
Финалист (2): 1967
Купа на Лигата
Финалист (1): 2016
Суперкупа на Исландия:
Носител (2):1982, 1983.
Източници
Външни препратки
Официален уебсайт
Профил на weltfussballarchiv.com
Профил на soccerway.com
Викингур
Спорт в Рейкявик | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 474 |
Rayport proposing another warrant article to restructure NP&EDC
Hillary Hedges Rayport at this year's Town Meeting.
Posted Friday, October 28, 2022 3:36 pm
By Joshua Balling
Email: jballing@inkym.com
Twitter: @JBallingIM
(Oct. 27, 2022) Hillary Hedges Rayport plans to file a new article for the May 2023 Annual Town Meeting, aimed at changing the makeup of the Nantucket Planning & Economic Development Commission.
It will be the second such article she has filed. Voters referred her previous attempt, at this May's Town Meeting, to the NP& EDC for further study by a vote of 188-172.
"There is long-range planning going on, it's just not happening at the regional long-range planning level, at the NP& EDC," Rayport said.
"It's happening at the Coastal Resilience Advisory Committee, in the harbor plan, in housing. We're missing out. The NP& EDC is the connector between our island and state and federal technical expertise and funding."
Like her previous proposal, Rayport said her new article will center around the election of at-large members to the commission. Currently, the NP& EDC appoints its three at-large members. She'd like to see three or more at-large members elected, as well as the inclusion of a representative from the Historical Commission.
"My main intention has always been to give the community a direct voice in electing people to the planning commission," Rayport said.
"The fact is, the NP& EDC is going to appoint people who agree with them. They don't appoint people who they don't agree with, and you get this group-think problem."
Rayport said if approved, she'd like to see the elected members phased in as the appointed at-large members' terms expire.
The commission, an advisory group charged with coordinating long-range planning strategies for the town, took up discussion of its makeup and enabling legislation Monday night.
"The starting point is not the article from Town Meeting, but all the options available to us," NP& EDC chair Mary Longacre said.
Several members appeared amenable to some change, but not necessarily a switch to elected at-large members.
Nat Lowell, who sits on the Planning Board and NP& EDC, said he would support the addition of a representative from the Land Bank, but not elected at-large members.
"If any changes need to be made, I don't think they need to be drastic. There's room for improvement, but we've got to come back to Earth. We don't need to reinvent the wheel," he said.
"There are already seven elected members of the
NP& EDC: The five members of the Planning Board, the Housing Authority member and the Select Board member. It's absolutely ridiculous. It doesn't bring any more diversity or inclusion than the process we have now."
Rayport also saw value in adding a member from the Land Bank.
"The argument can be made that the most impactful planning agency for open space and recreation we have is the Land Bank," she said. "The idea that it would be appropriate for them to be pulled into the larger discussion makes a lot of sense. But it's really their call."
Lowell asked that Rayport not file a new article.
"Based on this meeting, and the meetings we are going to have moving forward, I see no benefit to moving it forward, even if it's simply a place-holder," he said Monday.
"I think you see a commitment to us looking at the commission. For a full sense of calmness this year, maybe we can avoid that process."
Rayport was not deterred. "I have no choice but to file this on Nov. 14 (the deadline for citizen articles) if I feel it is important for the community to have this happen. But I look forward to amendments, and engaging in the study process. I totally object to (the NP& EDC) using their power to go directly to (the legislature). It should come with a mandate from Town Meeting."
Steve Karp's New England Development buys tank-farm property
ZBA denies neighbors' appeal of Monomoy Road STR
Planning Board won't recommend articles on STRs | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,898 |
Q: Getting template spelling without arguments, from a type, in libclang I can't find a way to get a "fully qualified name" for a template type without it's arguments, just plain name.
I.e. for a type which spells NS::NS::TemplatedType<int, char> just NS::NS::TemplatedType.
I know it's possible to do for a cursor in a field declaration; I just use:
plain_type_name = "::".join([c.spelling for c in cursor.get_children()])
Unfortunately in my case I don't have a cursor, because I've obtained type from a TYPEDEF_DECL cursor via typedef_cursor.underlying_typedef_type. So I guess I can just work with a type.
I am trying to process a typedef declaration like typedef NS::NS::TemplatedType<int, char> TTic; and I want to drop template arguments from the source type.
My target is python code but if I get a c++ solution I can work my way and translate it. Obviously I'd like to avoid regexping the spelling.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,742 |
The new iron dome of the US Capitol rising in 1859.
The Secret History of Washington, DC
J. D. Dickey
To my parents
Copyright © 2014 by J. D. Dickey
Distributed by NATIONAL BOOK NETWORK.
ALL RIGHTS RESERVED. No part of this book may be reproduced or transmitted in any form by any means, electronic or mechanical, including photocopying and recording, or by any information storage and retrieval system, except as may be expressly permitted in writing from the publisher.
Lyons Press is an imprint of Rowman & Littlefield.
Frontispiece photo courtesy of the Library of Congress Prints and Photographs Division. Photos on pp. 2, 6, 36, 43, 46, 59, 71, 72 (top and bottom), 76, 83, 93, 114, 122, 125, 142, 153, 174, 187, 189, 216, 235, and 238 courtesy of the Library of Congress Prints and Photographs Division. Photos on pp. 16 and 201 (all) courtesy of the National Archives and Records Administration. Photos on pp. 113, 183, 231, and 244 courtesy of the Historical Society of Washington, DC. Photos on pp. 9, 38, 62, 106, 111, 137, 149, 164, 170, 176, 197, 203, 206, and 211 courtesy of DC Public Library, Washingtoniana Division. Photo on p. 98 from a private collection. Photos on pp. 120 and 156 by the author. All page numbers refer to the printed book.
Maps by Daniel Rosen and Melissa Baker © Rowman & Littlefield
Project editor: Meredith Dias
Layout: Melissa Evarts
Library of Congress Cataloging-in-Publication Data
Dickey, Jeff.
Empire of mud : the secret history of Washington, DC / J. D. Dickey.
pages cm
Includes bibliographical references and index.
ISBN 978-0-7627-8701-2
1. Washington (D.C.)—History. I. Title. II. Title: Secret history of Washington, DC.
F197.D53 2014
975.3—dc23
2014015136
eISBN 978-1-4930-1393-7
Contents
Copyright
A Note on Maps of Washington City
A Note on Geographical Terms
Introduction: Capital Movers
One: The Capital Archipelago
Two: A Plague of Waters
Three: A Mechanic's Guide to Washington City
Four: Driving Souls
Five: The Company They Kept
Six: Coming to the Scratch
Seven: Illicit Congress
Eight: Seeing the Elephant
Nine: Suspicious Characters
Ten: The Fall of Washington City
Eleven: A Gilded Cage
Epilogue: The Sea of Pavement
Acknowledgments
Notes
Bibliography
Index
A Note on Maps of Washington City
Few reliable sources indicate how the District of Columbia appeared when it became the site of the nation's capital. Most of the depictions created by Pierre L'Enfant, Andrew Ellicott, and their imitators present plans for the city rather than descriptive diagrams. Not until Albert Boschke's highly detailed 1857 map of the District did any comprehensive view—as it was, rather than as it should have been—achieve widespread dissemination. After later editions of Boschke's work and that of other cartographers, the District's urban landscape was depicted more accurately.
Yet how the District actually looked in the beginning remained a mystery until recently. Tee Loftin, Joseph Passonneau, Don Hawkins, and the Imaging Research Center have filled in some of the gaps. Daniel Rosen's 1801 map of Washington City (pages 26–27) draws from these sources and period accounts such as reminiscences by Christian Hines and other firsthand witnesses. This book's 1860s map (pages 160–61) draws from the 1861 edition of the Boschke map, providing a clearer view of the downtown area where most of the capital activity occurred. For the years between, especially circa 1830, no accurate, detailed representation of the District exists. Jacksonian-era Washington still awaits its modern cartographer.
A Note on Geographical Terms
Alexandria: Tobacco port and slave-trading city founded in the eighteenth century; included in the District of Columbia from 1801 until its retrocession to the state of Virginia in 1846.
Alexandria County: Largely unincorporated land surrounding Alexandria, west of the Potomac River; included in the District of Columbia from 1801 until its retrocession to the state of Virginia in 1846; since renamed Arlington County.
District of Columbia: The ten-mile square encompassing former parts of Maryland and, until 1846, Virginia; selected by George Washington and designated by Congress as the federal capital of America.
Georgetown: Maryland port city founded in the mid-eighteenth century; included in the District of Columbia from 1801 to the present. In 1871 Congress revoked its charter and designated it as a neighborhood in the District.
Territory of the District of Columbia: Short-lived experiment, from 1871 to 1874, to reorganize the District as a US territory under the control of a federal governor.
Washington City: Independent city founded in 1802; synonymous with the federal capital for much of the nineteenth century and home to most of its key sites. Congress revoked its charter in 1871 and consolidated it into the District.
Washington County: Largely unincorporated land surrounding Washington City east of the Potomac River and a constituent part of the District starting in 1801. Congress consolidated it into the District in 1871.
Washington, DC: Name for the capital in use since the early days of the republic. Since 1871 there has been no official city of Washington—only the District of Columbia—so the term has been both misleading and redundant for nearly 150 years.
Introduction
Capital Movers
Washington is not the official capital of America. Maps include a place called Washington, everyone refers to the seat of federal power as Washington, and the city's homegrown politicians, celebrities, and athletes all claim to hail from Washington. But according to the law—and law is very important in the capital—such a place doesn't exist. There is only the District of Columbia, and it's been that way for nearly a century and a half.
A Washington City did exist once, though, and this older version of the capital, its life span from 1802 to 1871, is the primary subject of this book. But "Washington City" was always a misnomer. When that was its legal name in the nineteenth century, it was hardly a town, let alone a city. By the time it emerged as a city in the Gilded Age, Congress had abolished it and consolidated it into the District of Columbia. Thus, as with so much about the place in its early years, its planners even got the name wrong.
Familiar Origins
The usual story of the origin of the federal capital goes back to two key events: the Residence Act of 1790, by which Congress designated the general site for the future American capital, and Pierre L'Enfant's 1791 presentation of his survey map, which outlined the street plan of that capital. The maneuvers and machinations that led to those events form part of a convoluted tale of nation building that historians have recounted well and often in recent years: political wrangling to choose a suitable site, contentious debates between surveyor and city commissioners, bureaucratic conflicts and inevitable lawsuits.*
* In a nutshell: The founders placed the national capital close to the geographical center of the country but still in the South as a concession to Southern states in exchange for the federal assumption of state debt, most of which the Northern states held.
However, the genesis of the idea of a federal capital began nearly a decade before L'Enfant presented his map. It is a tale that, if not quite the stuff of legend, at least makes for a good yarn with a decent measure of adventure and intrigue. More importantly, it helps explain why Washington City, instead of Philadelphia or New York, became the US capital and why this new capital—far from a citadel of democracy—emerged as a fiefdom ruled by national politicians, and why its citizens were denied the right to vote for those politicians.
The Intrigues of June
In the summer of 1783, all seemed to be going well for the fledgling American states in their fight for independence. The British army still occupied New York City, but a peace treaty looked to be signed in a matter of months, and the nascent republic already had a functional legislature, burgeoning industries from timber harvesting to shipbuilding, and a fateful taste for westward expansion. So it was more than a little surprising that at this moment—when the states finally emerged triumphant from their eight-year struggle against their British overlords—the army of citizens who had done so much to defeat the Royal Army turned against its own leaders and held them captive at the point of bayonets.
Discontent in the soldiers' ranks was nothing new. From 1779 to 1781 Pennsylvania militia members and soldiers engaged in periodic riots and mutinies over inadequate pay and unfair terms of service. In March 1783, Officer John Armstrong Jr., an ally of General Horatio Gates, encouraged veteran soldiers not to disband until their demands for fair treatment were addressed. George Washington himself suppressed this challenge, which became known as the Newburgh Conspiracy—one of the most serious threats to civilian control of the army during the war—by personally stepping in to address the officers' demands.
Three months later a much greater conflict erupted. Congress (aka the Congress of the Confederation) had passed a resolution furloughing the soldiers of the Pennsylvania Line, drawn largely from that state. A group of sergeants wrote to Congress: "We will not accept your furloughs and demand a settlement." When the legislature didn't respond adequately to their demands, on June 17 a group of eighty to a hundred soldiers made for Philadelphia, then the locus of federal as well as state power.
Word of the soldiers' approach stirred the fears of politicians and gave rise to rumors of what the troops would do once they got there—perhaps even joining with other bands of renegades and robbing the mighty Bank of North America to get their money Key power brokers, such as finance chief Robert Morris and Representative Alexander Hamilton, demanded that John Dickinson, president of the Pennsylvania Supreme Executive Council, call out the militia to stop them. But Dickinson balked, doubting the threat of violence from the soldiers as well as the loyalty of the dodgy, homegrown militia. As historian Kenneth Bowling writes, "Pennsylvania, which had exclusive jurisdiction over affairs within its boundaries, had made its decision; Congress, which had no jurisdiction over the capital of the United States at Philadelphia, had to obey Pennsylvania's decision."
Not surprisingly, Hamilton seethed, decrying the state's "weak and disgusting position," and charged Assistant Secretary of War William Jackson with stopping the soldiers' march without resorting to force—a task that predictably failed. The troops arrived at their barracks in Philadelphia on Friday, June 20, ready to bring their case before the Pennsylvania State House. But their audience would consist of state legislators, not federal ones, since the national Congress didn't meet on Saturday, and in any case "Pennsylvania was simply wealthier and more important than the federal government."
The night before they planned to march on the State House, however, the soldiers received a curious group of guests: Jackson, Hamilton, and Gouverneur Morris, the assistant superintendent of finance. History doesn't record the details of who said what at the meeting, but after the national leaders left, the soldiers had grown even angrier than before, no doubt insulted by the trio's patronizing attitude and cheap offer of buying off the men with a month's pay in cash. Thus, enraged by the furloughs and inadequate pay for their lengthy service, mocked by the smug attitudes of national politicians, and nearly given a pass by their state's leaders, the men of the Pennsylvania Line marched on the Pennsylvania legislature—straight into Hamilton's trap.
In 1783 Hamilton hadn't yet achieved most of his fame in the annals of the republic: champion of the Federalist Party, first secretary of the US Treasury, victim of Aaron Burr's bullet. Instead, after his wartime service as a battalion commander, he was serving as a freshman representative from New York . . . albeit one with an unusual amount of pull and a Machiavellian sense of cunning. He could see the strategic opportunity that came with crisis, and he had a great opportunity with the crisis at hand.
The soldiers arrived at the State House on June 21, and their mutiny played out in melodramatic, almost ridiculous fashion. They marched defiantly and flashed their guns. Taverns sold liquor, drunken crowds cheered, politicians cowered. Further entreaties for Dickinson to call out the militia failed, and the Pennsylvania Line surrounded the state legislature. Some feared they might hold the politicians hostage.
However, the troops were after the state politicians, not the federal ones, and the national body, the Congress of the Confederation, didn't even convene on the weekend. But Hamilton knew how insulting it would be if this historic mutiny didn't attack Congress: The underfunded national legislature would look pathetic, not even worthy of a soldiers' march! More importantly, his idea of a strong, central American government would look laughable. So he had Elias Boudinot, president of Congress, call the legislature into session, making it appear the mutineers were assaulting the federal government and by implication the nation itself.
What exactly the members of Congress were supposed to do in a building surrounded by armed troops wasn't clear, and in any case only thirteen members showed up, not even enough for a quorum. The scene that greeted them was more commedia dell'arte than coup d'état. Fired up by cheap booze, the soldiers swore loudly and brandished their bayonets, joined by townsfolk who added to the drinking and shouting. James Madison judged the danger as less "premeditated violence" and more "hasty excess."
By the time congressional leaders rounded up enough members for an official session that evening, the chaos had ebbed. The mutinous troops had returned to their barracks, leaving no violence in their wake. Despite the debauchery, no state or federal legislators sustained attack or were even kept from entering or leaving the building. The Pennsylvania Line had made a show of force more suitable for a village tavern than a national legislature.
For the members of Congress meeting that Saturday night, however, the identity of the villains in the story had shifted from the "grumbling band" of soldiers to the Pennsylvania leaders too scared to do anything about them. Boudinot announced that "this wound to the dignity of the Federal Government will not go unpunished." Congress followed by ordering Washington's own troops to quash the mutiny . . . and by fleeing the state altogether. Its resolutions were kept secret, however, and revealed only when the politicians had safely reached their new home: Princeton, New Jersey.
In the ensuing national debate, Hamilton performed at his best—or worst, depending on your persuasion. He claimed that the soldiers' fury targeted Congress itself, and in the face of danger the national body wrote its steely resolutions with the mutineers laying siege to the building. Dickinson indicated that Congress never faced any real danger, but Hamilton took exception. The impassioned statesman blamed Pennsylvania as much as the soldiers for the debacle, seeing it as an attack not just on the national legislature but on the very notion of legitimate authority. In his view, this "deliberate mutiny of an incensed soldiery carried to the utmost point of outrage" involved an "armed banditti of four to five hundred men" who had the potential to "make the city a scene of plunder and massacre."
As historian William di Giacomantonio writes, "Hamilton converted the appearance of the episode from a demonstration against a state to one against the federal government. Observers came away with an enduring lesson that Congress required immunity from the policing powers of a state government in order to preserve its own dignity and independence." But by that time the mutiny had long ended.
When Dickinson finally called out the militia, a few days after Congress skipped town, the uprising collapsed. The mutineers submitted to government authority without a shot being fired, a person injured, or property damaged. Indeed, for all their supposed threats of plunder and massacre, most of the mutineers received pardons. Congress addressed the soldiers' pay and furlough concerns in July and disbanded the army in October after the Treaty of Paris ended the Revolution.
For all their bluster, the soldiers turned out to be dupes, pawns in the hands of clever political operators who used them to advance their own strategy. Hamilton and his allies, especially, used the spectacle of the splendid little mutiny to advance the cause of increasing the power and privilege of the central government. Although no proof exists that Hamilton himself engineered the revolt, his opponents suspected greater machinations behind his strategy and accused him and his followers of deceit in raising fears that mutineers and armed mobs would subject a weak Congress to attack. Madison saw "profound darkness" behind the affair, and Judge James Mercer placed the blame on unnamed but strongly implied "Capital movers in this nefarious business."
In the end, as with most issues in his political career, Hamilton won. But it wasn't easy relocating the capital or convincing a wary public to support a powerful central government—indeed, it took another four years of struggle. By the time of the 1787 adoption of the Constitution, Hamilton got his way: Congress planned a ten-mile-square federal district, in which the federal government would have exclusive jurisdiction, to prevent "the folly of dependence upon any state for the protection of the national capital." Three years later, the Residence Act of 1790 established the new American capital along the Potomac River between Maryland and Virginia—the exact site chosen by George Washington—and it opened for business within ten years. In 1801, under the District of Columbia Organic Act, Congress gained full control over the capital and organized its constituent cities and counties—and its residents lost their federal voting rights with no recourse to Congress or any other elected body.
At the time of these historic changes, the memory of the Philadelphia mutiny of 1783 had faded only partly, and was still used as an object lesson of how any threat to public order could overwhelm a weak legislature. The story, if anything, grew even more exaggerated: The rogue troops had become "enraged assassins"; John Dickinson, a spineless ninny, dithered while the soldiers and their allied street mobs attacked with ferocity; and Congress did the only sensible thing it could by escaping town before anarchy prevailed. Even today, this view of the mutiny prevails for most historians who mention it.
Many factors ultimately led to the conception of Washington—constitutional, political, sectional—but the mutiny provided the earliest reason for relocating the capital from Philadelphia and the only one that involved fear. The threat was clear: The nation's leaders always stood in jeopardy, and the only way to ensure their safety was to keep the locals on a tight leash.
Despite this foundation, for most of the history of Washington City, residents of the capital could still vote for their local officials because Congress adopted a rather relaxed, even indifferent policy toward the District. After all, it could overrule any municipal policies it didn't like. The appointed commissioners, who had ruled so maladroitly in the 1790s, were replaced in 1802 by popularly elected Washington City councilors and a presidentially appointed mayor, and in 1820 the locals got to vote for mayor too. This partial enfranchisement held until the tumultuous days of Reconstruction, when a new version of the city arose with a Republican-majority Congress and large black voting population. As we'll see, this dramatic shift in the political calculus had an unexpected effect, which eventually resulted in the total abrogation of local voting rights and the disenfranchisement of District residents for a century.
The City of Angles
In the meantime, however, the creation of Washington presented a strange capstone to the struggle for American independence. The logic of the Revolution primarily involved securing individual rights by checking the powers of the state—the right to prevent unfair taxation in the years leading up to the War of Independence; the rights to "life, liberty, and the pursuit of happiness" embodied in the Declaration of Independence; the separation of powers laid out in the Constitution; the enumeration of individual liberties in the Bill of Rights. Yet, at the very time these concepts were codified into law, their antithesis was on the drawing boards just upriver from George Washington's plantation.
Contrary to the blueprints of a nation designed around the popular control of government, the federal Leviathan wielded absolute power over its own turf. Against the idea that all people have self-evident liberties that cannot be taken from them by the state, the residents of Washington couldn't vote for their national leaders. Unlike Jefferson's idea of a rustic capital to guide a nation of sovereign states and "yeoman farmers," Washington would embody a vast, centralized bureaucracy, imagined as a massive neoclassical metropolis with giant radial avenues and boulevards. Some even sketched plans for giant statues like those toppled by the revolutionaries a dozen years before.
Backed by all this federal power, Washington should have emerged as a hub of national power and pride—or at least an object of jealousy for those whose cities had been denied the same prestige and largesse. Instead, Hamilton's Federalists squandered their chance to realize their grand design for the capital, overwhelmed by greedy landowners and incompetent city planners. By the time the city was ready for business at the turn of the nineteenth century, their archrivals in the Democratic-Republican party controlled its levers of power. True to form, Jefferson and his successors had such contempt for Federalist notions of what the District should be like, that whether through neglect or disregard they adopted many policies to ensure the city would fail in embryo.
Even some Federalists later had second thoughts about the whole enterprise. Timothy Pickering, still mulling the lessons of the 1783 mutiny, noted in his journal that if John Dickinson had managed to call up his militia, "Philadelphia would have remained the capital of the United States; America would have saved not only the millions it had wasted by building Washington, DC, but would also have avoided the disastrous measures adopted during the presidencies of Thomas Jefferson and James Madison."
So, instead of a functional municipal government and coherent social planning, what sprang up was a place of near-complete dysfunction. In its early years, real estate bubbles inflated and burst, development was random and scattered, and everything from roads to streetlights either didn't exist or didn't work. By the middle of the nineteenth century, the town only faintly resembled L'Enfant's conception of it, with a great deal of ugliness on view—open sewers doubling as canals, slums doubling as workers' housing, unfinished monuments doubling as city attractions—not to mention an abundance of con men, prostitutes, slave traders, cockfighters, and, of course, politicians. The men and women who lived within the city's sharp angles struggled for decades against its disorder and built it into something worthy of its namesake only near the end of the nineteenth century, by which time the city had experienced many crippling decades of corruption and mismanagement. The capital's emergence as a world icon proved painfully awkward, embarrassing, and slow.
Unearthing Washington City
This book doesn't present the familiar story of Washington so well known to readers of popular history: the horse trading between North and South to create the capital, the Old World stylings of L'Enfant's blueprint, the high-minded rhetoric of politicians, the various doings of presidents and potentates, the grand architectural projects. Such a narrative is warm and comforting, like an old friend spinning a tale by firelight—the heroes of the Revolution engaged in a grand project for the ages, forging a city founded on their ideals. This book takes no interest in roasting these tasty chestnuts of American history.
Instead, this book presents an alternative history of Washington City that shows the actual character of the capital: what it looked like, how it functioned, who controlled its power—and why. In the story, we'll see how the national capital, founded on noble ideals and with a few sparkling public buildings, devolved into an urban dystopia by the time of the Civil War, when British novelist Anthony Trollope memorably described it as "the empire of King Mud," both literally and figuratively, "the Augean stables through which some American Hercules must turn a purifying river before the American people can justly boast either of their capital or of their government."
This book aims to reimagine this forgotten city, a place of dramatic contrasts—landed wealth and desperate poverty, civic liberty and racial oppression, genteel society and shocking squalor. The narrative begins in the 1790s and ends in 1878, describing in between how a visitor might have experienced the town, traversing its miles of unfinished roads that led through swamps and farmland, gambling on cards or cocks in the dusty streets, watching nightly battles between volunteer firefighters, and plunging into the chaotic markets, taverns, and slave depots that held as much importance to the city's social world as its drawing rooms, parlors, and assembly halls.
These days, Washington, DC, scarcely resembles the squalid little town that limped along through the early decades of American history. Bordellos and gambling halls have given way to superblocks. Towering neoclassical monuments dot the landscape. L'Enfant's urban design has taken full shape with magnificent boulevards and avenues. The city has emerged as the urban showpiece, focus of national politics, and center of world power that Hamilton and his cohorts once imagined it could be.
To many Americans, though, the city remains a fearsome metropolis, a place forever to be criticized, satirized, and campaigned against. Such antipathy is nothing new. From the beginning, Americans cast a wary eye on their capital, whether for its concentration of federal power, its suspicious cosmopolitanism, or its pretensions to glory. Indeed, without the original sin of Hamilton's "deliberate distortions" of an obscure mutiny, the place might never have come into existence—no concentration of federal power, no supreme federal district, no citizens stripped of their votes. If we still suspect our capital of dark designs, our fears are embedded in the city's DNA.
One
The Capital Archipelago
The new American capital came with quite a pedigree when it opened for business in the summer of 1800: plotted by and named for a conquering hero and president, designed and surveyed to grand effect by a talented Frenchman, and redesigned by a man who mapped a good part of the early nation. What George Washington, Pierre L'Enfant, and Andrew Ellicott couldn't have imagined, though, was just how dismal the place would turn out to be in its first decades or how much work would have to go into making it a place worth living in, or even visiting.
William Thornton, designer of the US Capitol, had predicted that this proud new citadel of the republic would quickly become home to some 160,000 people and would flourish in accord with the fledgling country's inevitable growth. He was right about the country—but Washington City was another matter. At the turn of the nineteenth century, it barely held three thousand people and could scarcely bear comparison to any other national capital of the era.
Certainly, no other such place had "avenues" consisting of little more than alleys of cleared forest, roads with mud furrows "cavernous enough to hide robbers" and strewn with garbage and the refuse of cows and hogs, swamps that incubated mosquitoes carrying malaria and other diseases, or a landscape littered mostly with "brick kilns and temporary huts for labourers," or a near-complete lack of civic amenities, from a water supply and police force to street lighting and even sidewalks. Disgusted by the whole enterprise, Pierre L'Enfant ultimately called the place a "mere contemptible hamlet," and his contemporaries weren't much kinder. Treasury Secretary Oliver Wolcott observed, "The people are poor, and as far as I can judge they live like fishes by eating each other."
But how could a place with so much promise spend its inaugural decades as a shadow of what it was meant to be, a phantom city fallen to ruin without ever having risen? The roots of this trouble lay within the land itself and the people who came to dominate it.
A Trojan Capital
The Residence Act of 1790 gave President Washington the authority to select the site for the American capital, which he did about sixteen miles upstream from his Mount Vernon estate, offering a variety of reasons for locating it here (as we'll see in the next chapter). Amid this landscape landowners had carved out a few agricultural tracts and plantations with idiosyncratic, often romantic names: The Adventure, Chance, Flint's Discovery, The Hogpen Enlarged, Jamaica, The Nock, Orme's Luck, Port Royal, The Vineyard, and Widow's Mite, among others. Unfortunately, these whimsical labels applied to terrain so overworked by more than a century of tobacco exploitation that much of it lay in ruin, little more than abandoned fields, collapsing barns, and pastures without fences amid plentiful forestland. Hardly a logical place on which to build a national capital from scratch.
The names and property holdings of the original capital proprietors.
The creators of this new city, however, didn't let that stop them. Envisioning a site on which a great capital could rise, L'Enfant admired the tract of Daniel Carroll, pronouncing Jenkins Hill at its center "a pedestal awaiting a monument"—his way of describing an eighty-eight-foot-high mound covered with trees. More warily, Ellicott remarked that the site had "no more proportion to the country about Philadelphia and Germantown, for either wealth or fertility, than a crane does to a stall-fed ox."
The capital mostly rose on ground ceded from Maryland, one of the few bastions of Catholicism in early America. Daniel Carroll's domain had roots in an eighteen-hundred-acre property grant from Lord Baltimore in 1663, and his family was just this side of legendary, producing a US senator, the country's first Roman Catholic bishop, and signers of the Declaration of Independence and Constitution. However, keeping track of all their doings posed a bit of a problem, even for later historians, since, like all good aristocratic families, they desperately lacked originality: No fewer than four of them were named Daniel, and about as many shared the name Charles.
One of these Daniel Carrolls ("of Duddington") was more than happy to relinquish his five hundred acres of what some called New Troy† to the American government in 1791. He'd been trying for more than two decades to attract developer interest to his land, and now the US capital itself would sit on his front porch and the city center would rise around it. Carroll celebrated his victory by becoming a property speculator.
† How this inauspicious moniker ever came to identify the land around what is now Capitol Hill is a bit of a mystery, although its prescience impresses. The British played the role of the Greeks in 1814 by burning it to the ground. It was just one of the classical pretensions in the area. A smaller, neighboring estate was named Rome and a large creek the Tiber.
The Bubble Economy
While today's history books present the early history of Washington City as a careful exercise in political negotiation, high-minded ideals, and daring architectural planning, something much more prosaic—and, to modern eyes, depressing—drove the development of the capital: housing bubbles.
Carroll wasn't alone in thinking his plantation held almost infinite value; his fellow landowners felt the same about theirs. In March 1791, they cut a deal with the commissioners overseeing the development of the capital, letting the government pay them for half their lots and retaining the rest for their own profit. When an auction took place in October of the same year, they appeared to have hit the jackpot. The going rate became $265 per full lot, more than five times its previous value. A speculative frenzy began as the humble planters imagined themselves as lords holding sway over what surely would become the choicest turf in America.
However, despite the auction's promise of raising huge sums for the government and the landowners, only thirty-one lots sold. But Carroll didn't let this stop him, as the appeal of charging exorbitant prices for exhausted agricultural land and forests proved irresistible. Whether he had any buyers at the beginning didn't much matter because it would be only a matter of time before the real boom began. He proudly kept his holdings on Jenkins Hill—i.e., Capitol Hill—among the most expensive in town. His fellow profiteers followed his example by keeping their prices high as well, perhaps fantasizing about all the starry-eyed patriots who would pay top dollar for old tobacco barns and mudflats.
But there weren't enough rubes in America to make the proprietors rich. Real estate sales remained sluggish, and the growth of the future capital site sagged. Instead of recognizing the situation and lowering their prices like proper businessmen, the planters held out and capital development slackened even more. By 1793 the nascent city desperately needed financing, and what little development there was ended up being haphazard and piecemeal. The means of finding new investment capital fell to the city commissioners. One of them was Daniel Carroll of Rock Creek, uncle of Daniel Carroll of Duddington.
Magic Mushrooms
George Washington had selected this Daniel Carroll and his two equally respected fellow commissioners, Thomas Johnson and David Stuart, to manage the surveying of the capital site and to oversee its development and growth. As commission leader, Johnson in particular had a reputation for probity and acumen as a US Supreme Court justice and former Maryland governor. But the capital was desperate for financing, and he knew he had to entertain almost any new idea or source of cash to get the city built.
When twenty-eight-year-old Boston merchant James Greenleaf presented an offer to purchase three thousand lots of real estate from the government—later doubling the offer—Johnson had his opportunity. In exchange for Greenleaf's beneficence, he would give the venture capitalist the bargain rate of $66 per lot with a payback period of seven years, instead of the usual rate of $300 per lot over three years—a 78 percent discount. As a bonus, Greenleaf and his partners, John Nicholson and Robert Morris, would agree to build ten homes a year in the capital and deposit $2,660 a month into the commissioners' coffers. Greenleaf also would purchase $13,300 worth of Maryland land holdings that Johnson was trying to unload. All in all, the commissioner judged it a fair deal for the city and a lucrative deal for himself. It was hard to imagine its failure; Morris himself had helped finance the Revolution!
But Johnson had a surprise waiting for him. Greenleaf hadn't secured the bank loan from Holland to buy the property, nor had he imagined the scale of the chicanery that Greenleaf and his partners had engineered. Instead of improving the capital property, they looked to mortgage their unpaid-for Washington City lots to obtain a further loan to purchase six million acres of Appalachian wilderness, a colossal tract of land that held just as much promise to the Greenleaf syndicate, and yielded roughly the same results, as Florida swampland did to later generations of investors. To achieve this end, the men established a web of financial trickery, sweetheart deals, and bluff and intrigue that historians still have a hard time unraveling two centuries later.
Some knew better. Greenleaf's brother-in-law, famed lexicographer Noah Webster, described his relative's employees as little more than "rogues and whores," and in 1795 George Washington questioned the intelligence of his commissioners in accepting the credit of such speculators in lieu of real bank deposits, especially when they brazenly had resold some of their unpurchased lots at a handsome profit. Increasingly frustrated, the president wrote to Carroll that "the continual disappointments" of the speculators "are really painful."
Financial trickster and Ponzi schemer James Greenleaf.
What Greenleaf lacked in ethics, he made up for in rhetoric. To anyone questioning his motives, he hyperventilated about the rise of the "New Jerusalem," a veritable City of God to tower over the republic. All this hot air didn't convince everyone, but it was enough to fire up Thomas Law, a former officer of the East India Company, to offer as much as $133,000 to purchase property around Capitol Hill, which of course Greenleaf had never legally acquired. The deal went sour, and Law soon found himself deep in litigation with the syndicate, which even held claim to the first mansion where he lived (at 6th and N Streets SW) as it made off with much of his fortune. But Law was a different kind of speculator. Unlike his counterparts' houses, Law had paid for his in pounds sterling instead of credit. He followed all the building requirements and built them solidly (most notably the "10 Buildings" row houses in Southeast DC). By contrast, after Nicholson and Morris held a barbecue for two hundred people to celebrate their own development taking shape on New Jersey Avenue (the "20 Buildings"), they never bothered completing the structures, which remained unfinished and eventually collapsed.
By this point the syndicate was running out of options. The money it received from buyers like Law didn't go to reimburse the federal government but rather to private creditors on whose loans it had defaulted. As Greenleaf's rhetoric became loftier, the pyramid scheme grew larger and more byzantine, until it collapsed in 1797 when his organization finally went bankrupt. The syndicate controlled up to a third of all the available lots in town, though, so countless legal battles remained, and turmoil resulted: Illegitimate owners sold unimproved lots. Rival claimants struggled for control of overlapping or identical properties. Federal officials seized ownership of some lots and re-auctioned them, sometimes to the same people who had defaulted on paying for them in the first place. A litigious nightmare resulted for anyone attempting to venture into Washington City real estate. Court battles continued for decades. Even if land was available with clean title, prices were still outlandish, and, thanks to European wars and financial crises throughout the 1790s, little investment capital was available to pay for it anyway. As a result of the legal quagmire, even into the 1840s, buyers could take hold of the disputed tracts for less than a penny per square foot or forty-seven dollars per lot—for anyone foolhardy enough to take the risk.
Not surprisingly, very little was built. Some isolated tracts did emerge, with bland names like the Six Buildings and the Seven Buildings, but the original plantation owners continued to sit on roughly half the lots available in town, unhappily for most of them, it turned out. Daniel Carroll of Duddington saw his income dwindle and his estate wither, and in 1820 he declared bankruptcy. He spent most of his later years as a recluse in his Duddington estate, dying in 1849. (One of his few successful developments, Carroll Row, lasted much longer, first as a row of fashionable boardinghouses, then as a Union prison in the Civil War.)
The real victim of the speculative frenzy, though, was the capital itself. After all the financial tumult, the city, enormous on paper, contained very few actual buildings, and those that did exist were often half-built, following the "magic appearance of uninhabited structures like mushrooms after a shower." As Secretary Wolcott observed, immense sums "have been squandered in buildings which are but partly finished" and in the end never were. The English writer Charles Janson added that speculation was "the life of the American," and, apart from the buildings set aside for government use:
the remainder of this boasted city is a mere wilderness of wood and stunted shrubs, the occupants of barren land. Strangers, after viewing the offices of state, are apt to enquire for the city, while they are in its very centre . . . some of the few houses which were then building [ten years ago], are now falling to ruin, the unfortunate owner having been ruined before he could get them roofed.
Janson wrote these words in 1806, nearly a decade after the Greenleaf syndicate had collapsed, eight years after its principals had been locked up in a Philadelphia debtors prison, and five years after the federal government officially had moved to the District.
The Wrath of Mr. Burnes
Thanks in part to Daniel Carroll's attempted profiteering on Capitol Hill, the site that the founders intended for the center of town sat mired in lawsuits and speculative chaos. The most reasonable alternative for the builders lay westward, around what L'Enfant had imagined as the "Grand Avenue" between the Capitol and the Executive Mansion. But an angry old farmer stood in their way.
David Burnes and his contingent of slaves grew rye, tobacco, wheat, oats, and corn on 527 hardscrabble acres bundled into tracts with evocative names like The Gleaning, Elinor, Burnes's Discovery, and the less exciting Resurvey on Part of Beall's Levels. Some of it contained arable land, part of it sat on a floodplain, and the rest was swamps or mudflats—not an obvious place to build a city.
The crotchety Burnes had a long list of grievances going back to the birth of the capital. George Washington had tried to induce him to surrender his land on the cheap, often through land agents and subterfuge. Burnes constantly battled with the commissioners over the valuation of his property, and he resisted the creation of a new city in the middle of his homestead. A second lieutenant during the Revolution, Burnes also didn't particularly like Washington, dismissing him as the "Geographer General."
Humble residence of planter David Burnes, who sowed trouble for city founders.
More than anything, though, he fumed about the deal that the land proprietors had cut with the government back in 1791 and which he had signed. While the planters did receive $66.67 for each lot used for public buildings—and half the future proceeds of lots auctioned to the public—they got nothing for any streets, avenues, and alleys that cut through their land. Few expected, then, that the transit corridors would end up as huge as they emerged on the L'Enfant plan, up to 160 feet wide, devouring even more of the proprietors' land but giving them nothing in return. The placement of 17th Street near his ramshackle cottage especially rankled him since it led to Commissioners Wharf, one of the first on the Tiber, a fitting symbol of the type of development and politicians he scorned. The most important one soon would be living just a few blocks north, in what Burnes called the "President's Palace."
Signs of Burnes's wrath arose practically everywhere in the 1790s: open grievances against the commissioners, threats to sue the government, public indignation at the taking down of his fences to clear more land for avenues, and newspaper postings that served as the early American equivalent of "Get off my lawn! ":
I hereby forewarn all persons from hunting with Dog or Gun, within my inclosures or along my shores; likewise, cutting down Timbers, Saplings, Bushes, or Wood of any Kind, carrying off and burning Fence logs, any old wood on the shores, or in the woods. If I should find any person trespassing as above, I will write to my attorney, and suits will be commenced against the trespassers in the general Courts.
Burnes proved so stubborn that Jefferson thought city planners needed an alternative to the L'Enfant plan to deal with the bullheaded planter. In fact, Burnes continued to plant crops on Pennsylvania Avenue long after it was sited as the key road linking the White House and the Capitol, making it difficult to build a town center while corn was growing there. Only after his death in 1799 did the full development of his holdings become possible, when they emerged as a viable site for the urban growth that should have been occurring on Capitol Hill. In an ironic twist, the daughter of this bitter old farmer, Marcia Burnes Van Ness, later became one of the capital's great society hostesses and one of the richest women in the country.
Jerry-Buildings
As if dealing with angry farmers and rampant real estate speculation wasn't enough, builders found themselves confronted by a set of construction rules that assumed acres of wilderness would magically transform into stylish row houses and Georgian manors overnight. The regulations were supposed to make the capital look grand and upstanding, like Georgetown and Alexandria, the other prominent parts of the District of Columbia. But no one could graft the tasteful look of those old port towns onto forest groves and fallow farmland easily, no matter how rigorous the building codes—and in 1791 these rules weren't just rigorous, they were rigid: Only sturdy structures of brick and stone were to be erected, and no vulgar wood-framed houses. Buildings had to stand at least thirty-five feet tall but not taller than forty if on a major road. They had to lie "parallel thereto and . . . advanced to the line of the street." Tasteful row housing was the favored style.
The first test of the regulations came in August 1791, when Daniel Carroll of Rock Creek set about creating a handsome new estate for his nephew, Daniel Carroll of Duddington, helpfully called Duddington. The mansion mistakenly wound up seven feet in the path of New Jersey Avenue, a clear violation of a rule outlawing building walls projecting onto public throughways. To correct this transgression, L'Enfant quickly had those walls razed—and Duddington Daniel Carroll seethed. The error had been his own fault, but the French architect took the blame. L'Enfant first received a reprimand, and then, thanks to the efforts of Uncle Daniel and other city commissioners, who had unsuccessfully tried to make L'Enfant submit to their authority in this and other matters, Washington fired him. The government paid Carroll an indemnity of four thousand dollars, and Duddington soon rose in proud Federal style. It was only the first example of how the rigidity of the rules in Washington varied inversely to the power of those they affected.
Yet imposing such conditions mostly proved a failure because, without incentives or assistance with building codes or costs—such as those provided to real estate speculators—private builders hardly erected any structures. On noticing the capital's glacial growth, and realizing its pace was due in part to their own rules, government administrators decided to act. According to James Sterling Young, they changed the regulations to allow for wooden and single-story dwellings, which had an unexpectedly dreadful effect:
a mushrooming of workers' shantytowns, one such appearing on the very grounds of the executive mansion . . . jerry-built houses which, being too expensive for resident laborers, remained unoccupied and fell victim to vandals and the elements. When the government arrived in 1800 . . . The commissioners then reported 372 dwellings as "habitable," but, as a cabinet officer noted, "most of them are small miserable huts."
By that point nothing the government did helped, and the capital grew uglier. Countless visitors found its ramshackle appearance and its emptiness shocking, one of them reporting in 1796 that "a spectator can scarcely perceive any thing like a town." But financial and regulatory problems weren't the only factors holding the city back. Other difficulties related to the curious beliefs of the Founding Fathers in general, and Thomas Jefferson in particular.
A City of Yeoman Farmers
Planters and their society dominated the Potomac region, like much of the Upper South, emphasizing social caste and proper etiquette while employing draconian methods to turn a profit—foremost among them slavery. Jefferson served as a leading exponent of these beliefs and saw the country as a nation of "yeoman farmers," in which the virtue of American government derived from the strength of its agricultural society as long as there were vacant lands left to exploit. He predictably held a wary view of urban growth.
Ever since serving as secretary of state in the Washington administration, Jefferson thought the capital should be a humble little "federal town" in dramatic contrast to Washington's view of a highly urbanized and muscular "grand capital city" and "Metropolis of America." Moreover, the letters that he wrote to Washington regarding the shape of the capital contained no endorsement of the L'Enfant plan; he preferred a more traditional grid system. While in Europe, Jefferson could do little to prevent the capital plan from taking shape other than arguing against its imperial outlines from the comfort of a Paris salon. But that soon changed.
Pyramid Schemes
The Jeffersonians (i.e., the Democratic-Republican Party) employed more than just pastoral ideology to guide their strategy. Good old-fashioned partisan politics also played a role. Since America was predominantly rural, Jefferson and his followers exploited the straw-man image of the corrupted, European metropolis against their Federalist rivals . . . who just happened to represent the most urbanized parts of the country. It also helped that the adversaries of the Democratic-Republicans kept giving them ripe opportunities to make political mischief.
A prime opportunity came in the late 1790s, when the federal government, seeing construction funds depleted on the hugely expensive Capitol and Executive Mansion, had to chip in and fund its less-than-humble abodes. In the kind of political firestorm that often repeated itself in American history, federal loan guarantees of $300,000 to complete the buildings provoked one of the country's first antigovernment reactions. Jefferson's faction raised hell and organized protest rallies, and indignant newspaper editors wrote scathing editorials laced with doggerel that decried
the ship of state on rocky ground
and fools to pay for Federal Towns.
The situation worsened after George Washington died in 1799 and his Federalist followers proposed a 150-foot-high mausoleum to honor the fallen president.
The Federalist Congress rubber-stamped a weird, giant pyramid with a planned cost of $200,000, and Jefferson's anti-Federalists used the ensuing public controversy to their advantage. The man from Monticello thus swept to power in one of the great electoral victories in American history and swiftly ended the mausoleum project.
The effect of this public reaction was a paradox. The outcry targeted leaders who wanted to enlarge the scope of federal power and spend freely on great public monuments. But despite rhetoric to the contrary, the Jeffersonians arrogated federal power anyway and, other than the mausoleum, built those monuments in full. What suffered was the rest of the city where it all took place. While American voters certainly weren't demanding that Washington City's streets remain unpaved, its garbage go uncollected, or its streets lay enveloped in darkness, that's ultimately what happened. Jefferson's party took power in 1801 and closed the tap for urban improvements for several long, bleak decades.
While he did secure the funding for the Navy Yard on the Eastern Branch, in most other areas the third president cut spending and kept the capital's areas of settlement disconnected from one another, preventing them from forming a coherent urban grid. Behind the scenes, he pushed against congressional bills meant to improve the District's infrastructure and follow the centralized contours of the L'Enfant plan. From the viewpoint of British diplomat Augustus John Foster, Jefferson's attitude toward the city had the effect of forcing members of Congress to rely on visiting the president's house for their "amusement and relief" from public affairs, or else be forced "to live like bears."
Capital Sorrows
Jefferson's successors James Madison and James Monroe continued his policies in the first decades of the nineteenth century. It was a miserable time for the District, rife with incompetent city planning and blatant federal indifference, as the capital engendered little sense of community or civic purpose beyond the creation of government bureaucracy. Outside of the political class, the small, itinerant population struggled with living conditions that were as socially alienated as they were economically strained—and prone to occasional bouts of horrific violence. As a fitting symbol of the era, one of the town's biggest spectacles wasn't a noble ceremony or parade but a public execution gone wrong.
In 1802, James McGirk, an Irish immigrant and bricklayer, came home one evening after a round of heavy drinking and beat his pregnant wife so severely that she died along with their unborn twins. He was tried, found guilty, and sentenced to be hanged at the foot of the Capitol, where an ardent crowd gathered to watch the spectacle. However, after the executioner tied the rope around his neck, but before the hood could be drawn over his head, McGirk suddenly leaped off the platform. With his body swaying and the crowd looking on in horror, the authorities tried to pull him back to the platform to prevent the suicide, but it was too late. After McGirk was cut down, the crowd swooped in and eagerly cut the noose into pieces (said to be helpful in curing headaches, toothaches, and other maladies). They showed rather less respect to his corpse: first buried in a local cemetery, then dug up by living relatives of the dead in nearby plots and dumped into a ravine, retrieved from the ravine by the murderer's friends, reburied in the cemetery, and finally dug up again and deposited in a quagmire under thorn bushes.
This wasn't surprising—topographically, that is—since Washington City's physical landscape could be just as forbidding as its social counterpart, teeming with ravines, quagmires, and other undeveloped land. Magnificent houses stood next to rude shacks, decent housing was hard to find under what some called "pioneer conditions," and the analogy to a patchwork quilt—pockets of random buildings separated by huge stretches of empty land—was so common that it was taken for granted. In an unexpected twist, the one place where a decent number of buildings had sprouted, Greenleaf's Point, took its name from the charlatan who had done so much to impede the city's development. (The area's previous name had been Turkey Buzzard Point, a fitting description of the Washington speculator.)
Without any guidance from the federal government, capital development proceeded on a pell-mell path led, once again, by the greed of the original landowners. Amazingly, even after the first speculative bubble popped and few buyers could be found, these men still possessed the ludicrous idea of selling their land for obscene prices. Each vied with the others to turn his own thinly populated sliver into the focus of development. This competition had the counterintuitive effect of ensuring that much of the region remained countryside and what settlement took place in the capital remained mired in "village conditions." In Benjamin Latrobe's words, "The proprietors of the soil, on which the town is to be spread, are rivals and enemies, and each opposes every project which appears more advantageous to his neighbor than to himself. Speculators, of all degrees of honesty and of desperation, made a game of hazard of the scheme."
Critics saw these problems as an embarrassment not only to the region but to the nation as a whole and called for the relocation of the seat of government to a more sensible spot like New York or Philadelphia. Fearful of being stripped of their would-be urban showpiece, the leaders of Virginia and Maryland stepped in to offer loans for capital improvements. Their unexpected largesse improved prospects for growth in certain pockets, but overall the District remained, according to John Reps, "a kind of archipelago of neighborhoods separated from one another almost as if divided by water instead of expanses of undeveloped land."
But Pierre L'Enfant hadn't designed the city as an island chain.
L'Enfant's Tattered Plan
The French architect had instead imagined the capital as an ideal metropolis, enlivened with triumphal arches, gardens, theaters, museums, a victory column, a national pantheon, a massive central fountain, and a shopping arcade to rival the Palais Royale in Paris. It was a fantastic vision, but though politicians were satisfied with the utopia on paper, they had no effective means of executing it. By its nature, L'Enfant's glorious blueprint couldn't address the boring nuts and bolts of urban planning: adequate investment capital, a broad tax base, reliable funding for infrastructure, and a leadership committed to solving civic problems. Struggles with these issues, along with speculative madness and political haymaking, wrenched the plan away from its charming baroque assumptions and grounded it firmly in the mud of urban reality.
Pierre L'Enfant's idealized plan for the city, before Andrew Ellicott reimagined it.
Quite literally, a lot of real mud lay in the new center of town. Instead of the Capitol and Jenkins Hill acting as the nexus of commerce and housing, a boggy tract of mediocre farmland, once owned by America's angriest farmer, would be the place where the center would rise. As other new pockets of growth emerged, they spread the town's points of interest across even wider distances, making Washington City, for all its pretensions to centralized authority, a strangely decentralized place.
In what's now Foggy Bottom, German immigrant Jacob Funk had created Hamburgh, aka Funkstown, in 1765, subdividing it into lots from 19th to 24th Streets within a few blocks of the Potomac. Even from the beginning, Funk had designed it with speculation in mind. But aside from a brewery and a glassblower, it offered little in the way of business, and few people wanted to live in a place where swamps and mudflats bred mosquitoes that spread malaria and yellow fever and the summertime weather created a tropical sauna of nearly unbearable heat and humidity. Even by the 1840s the area had only sixty households.
Several miles south of the town center, the Navy Yard hosted America's seminal military fleet. In 1799 George Washington had sited the yard two miles up from the confluence of the Potomac on the Eastern Branch, and by 1806 the yard was thriving by building, equipping, and repairing warships. Employees received the unheard-of perk of daily "refreshments" drawn from hundred-barrel lots of whiskey. These refreshments made it a popular place to work, and the yard soon became the chief manufacturing site in the District. Another business thrived there too: whoring. According to Charles Janson, the yard densely featured "Tippling shops and houses of rendezvous for sailors and their doxies, with a number of the lowest order of traders."
To the west, Charles Carroll intended Carrollsburg, near the junction of the Potomac and the Eastern Branch, to be a budding townsite, but it ended up more a potential settlement than an actual one. Nearby, on land at the tip of the rivers' confluence, Greenleaf's Point still had occupants during the early nineteenth century. However, as a fitting tribute to the speculator who gave it his name, the fifty or so houses there were mostly ill-kempt, a handful occupied by squatters, and the warehouse and wharf that offered a few outward signs of industry were disused if not abandoned.
North of the point and south of the Capitol, the neighborhood now known as Southwest was called The Island starting in the 1810s on account of the Washington City Canal acting as a moat between it and the rest of the city. Spec houses clustered here, but mostly The Island offered a ragtag assortment of workers' shanties, industrial facilities, and grand plantations slowly being sold and subdivided, just as their owners were selling their slaves and subdividing their families (about which more is covered in chapter four).
Farther north, and due west of the Capitol, L'Enfant had planned the Mall as a central feature of the city, a "grand and majestic avenue" stretching for a mile and standing four hundred feet wide, bounded by the expansive lawns of ambassadors' residences, peppered with gardens, a pond, groves of trees, a luxury shopping district, arcades, and triumphal arches. Sadly, it looked nothing like that. Other than storage sheds, hardly any buildings rose on it at all, and swamps choked most of the terrain. The rest remained a mishmash of private garden plots, lumber and firewood yards, and dumps for "rubbish of an offensive and unsightly kind." As the cofounder of the National Institute (predecessor to the Smithsonian) put it, the Mall was "a magnificent Sahara of solitude and waste—appropriated as a cow pasture and frog pond, and decorated with a stone-cutter's yard, a slaughter-house and pig-pens."
Practically the only major sites on the L'Enfant map that developed as planned were the Capitol and the Executive Mansion, still the focus of the town's energies and funding. Although the president's house increased in esteem over the years, at the time it provoked divergent views. Some lauded the "pleasing" and "captivating" qualities of the Georgian manor, while others dismissed it as too big and unfurnished, or too "cold and damp in winter." The house of the legislature, by contrast, earned much high praise. Frances Trollope—mother of Anthony, a novelist in her own right and otherwise a bitter critic of America—recalled her "admiration and surprise" at seeing a building of such "beauty and majesty." Other writers, also otherwise hostile, used terms such as "dazzling whiteness," "a creation of fairy-land," and "the eighth wonder of the world" to describe it.
Apart from these well-financed federal structures—which also included the departments of State and Treasury, Post Office, and Patent Office—the rest of the capital continued to languish, its infrastructure and civic amenities either dilapidated or simply nonexistent. As Charles Dickens later wrote in American Notes, to create such a city as this required a perverse sort of inspiration:
plant a great deal of coarse turf in every place where it ought not to be; erect three handsome buildings in stone and marble, anywhere, but the more entirely out of everybody's way the better . . . make it scorching hot in the morning, and freezing cold in the afternoon, with an occasional tornado of wind and dust; leave a brick-field without the bricks, in all central places where a street may naturally be expected; and that's Washington.
Road Rage
Nothing symbolized the sorry state of the capital better than its streets. What looked so elegant on L'Enfant's blueprint—a web of radial baroque avenues overlapping a rectangular street grid—in practice became a confusing network of ragged and rutted strips of mud. Historian Constance Green wrote of the challenges of traversing the roads: "At night the journey was utterly dangerous; pot-holes and tree stumps threatened to overturn carriages; most of the thoroughfares lay in utter darkness." For politicians heading home from the Capitol in the dark, walking presented an occupational hazard: "At times they slipped into the gutter or stumbled against a bank of earth. But even when with care they kept their feet from straying, they fell over barrels or a pile of bricks." In one case, the deplorable condition of the District's roads almost changed the course of history, when the carriage of James A. Bayard Sr. of Delaware nearly overturned in the cratered muck. He survived, though, and cast the key vote in the 1801 House decision that made Thomas Jefferson the president in 1801 after an electoral college tie. Otherwise, Aaron Burr—future killer of Alexander Hamilton and alleged treasonist—might have won.
Pennsylvania Avenue, the most important road in town, was among the worst thoroughfares. Tasteful drawings that promoted the District depicted the avenue as a lovely promenade lined with poplars—which Jefferson ordered planted in neat rows as in Paris—but in reality it was barely more than a quagmire. This "deep morass covered with elder brushes" was, for most of its length, a muddy concourse cutting through the forest. In spring it often flooded, and the rest of the time street children scampered about in search of handouts for sweeping dust from the crossings. It was ridiculously expensive to maintain because, at 160 feet wide, "To pave it was like attempting to pave a field." Not until 1834 did the avenue finally get a decent roadbed to provide for a minimal level of usability.
However, just about the time that macadam covered Pennsylvania Avenue, the few dozen whale-oil lamps lighting it went dark due to high fuel prices, and they wouldn't be turned back on until the next decade. Thus, as the District's two glittering monuments, the White House and Capitol, rose proudly at either end, the main drag connecting them was a pothole-choked mire littered with bricks and tree stumps, unwise to cross during the day and unsafe to cross at night.
The Tap Runs Dry
As with its battered system of thoroughfares, the basic services and amenities that other cities took for granted either came late to the District or didn't come at all. Buildings were designed poorly and then left to stand empty until they fell apart. Farmers still were seeding crops near major roads and impeding traffic. Most roads didn't have sidewalks. Livestock wandered freely. No sewer system served the city. Flu and other diseases broke out with disturbing regularity. The minimal population had settled largely around the old Burnes tract and a few far-flung locations, but most travel took place across wide distances on foot or by horseback.
Like many cities of the era, the District couldn't afford a modern waterworks, so a "pump mender" got the water out of the ground in lieu of an actual engineer or water department. This arrangement proved searingly inadequate when fires erupted and consumed the mostly wood-framed structures with ease . . . usually while volunteer firefighters—in the absence of a commissioned department—watched helplessly.
Major crimes were uncommon, but petty crimes ran rampant. Along with fending off low-rent thieves and burglars, the few law enforcement officers (basically a marshal and a sheriff) checked volunteer fire companies' fire buckets and issued health regulations to prevent the spread of infectious diseases, all the more challenging in a place littered with swampland and pools of stagnant water.
All in all, Washington's "grand capital city" resembled a dysfunctional village. The president's and the legislature's houses loomed formidably, to be sure, along with a few other stately federal buildings, but everything else was crumbling or absent. According to Charles Hurd, two things existed in abundance: "ample space to disperse the slops and garbage thrown into the streets, and plenty of mud to absorb the droppings of horses, cattle and hogs that had the run of the streets."
For most cities, then or now, such decrepit conditions would have led to a mayoral recall, voter revolt, political conflict, or at least a few protest marches. But the dismal state of civic amenities didn't lead to any of these outcomes. Without being able to vote for their national leaders, hold their government accountable, or challenge it in any way, the voters of Washington City had no choice but to take what scraps the members of Congress deigned to give them, which most of the time was very little.
Politics in Extremis
Visitors could tell the town was in bad shape even before they arrived, because it was so hard to get there. A network of turnpikes—wide, graded roads allowing for the interstate transport of goods and material such as crops, livestock, alcohol, and fuel—was interlacing much of the Northeast and the mid-Atlantic region. But Washington City remained virtually stranded, again like an island chain. The District had faced problems with constructing turnpikes to tie the region to the western frontier since its founding. Functional roads went only to Maryland and the South, and the "western route proved impossible to develop in the face of undisguised hostility from Baltimore," which had little interest in a new economic competitor springing up practically in its backyard.
Maryland's biggest city served as the source of other painful contrasts too. Baltimore streets glowed with gas lighting around 1820, while Washington City's denizens still were fumbling around in the dark, lurching from one distant corner lit by whale oil to another. The District didn't see gas light until 1848, long after the new technology had become widespread in other cities. Earlier attempts to establish a municipal gas company also failed because local government "had no desire to encourage an innovation so dangerous, so offensive and one likely to injure the business of candle makers and oil dealers."
In the same parochial fashion, Washington's hackmen fought against the development of sidewalks for fear that, if it were easier to walk down the road, fewer people would pay for horse-drawn transit. On account of their lobbying efforts, along with the usual mix of political cowardice and civic apathy, no omnibus line or other regular public transport existed in the District's first three decades.
The town also offered limited or no means of education to its residents. Although the inglorious rise of the capital took place before the large-scale development of government-run schools, the District largely ignored the expansion of public schooling in other major cities of the time. Even as late as 1839, one study showed that, of the 5,200 children in the capital, around a thousand went either to private or "pauper" schools, but the rest—80 percent—had no means of education beyond what they could learn on their own. Higher education didn't fare much better. The creation of a national university, which some had proposed at the same time as the formation of the District itself, foundered when Congress couldn't find the funds to build one but stubbornly refused offers of private assistance. The desperate solution of a lottery to raise funds also flopped when the lottery operator ended up in jail.
Financial Mud Pit
The fiscal problems were manifold: Local government revenue came mostly from property taxes and license fees, but federal property—the only kind worth anything—was off-limits. A justice of the peace appointed by the president, not a local official, assessed real estate values. Redundant city and county taxes exposed residents to double taxation, and half of the entire budget went to road and bridge maintenance.
That last point was the core problem. With a few exceptions, Congress left the full cost of grading and leveling roads to the local government, which couldn't afford it. In the first twenty years of the capital's life, Congress provided a pittance of $15,000 for work on Pennsylvania Avenue and the roads around the White House. Road maintenance in 1821 alone ran to $43,000. Local leaders had no choice but to take the town further into debt to pay for it.
Fiscal challenges led to fiscal emergencies, and these, combined with national recessions and the "panics" of bank runs, left the District starving for cash. Money shortages prompted banks to offer paper not backed by specie and prompted local officials to issue the equivalent of IOUs, sometimes down to a penny.
Throughout these decades the attitude that congressmen took was curious. They represented their own, often distant constituencies, but they had to live and work in Washington City for part of the year. Only a deep-seated and rabid antigovernment hostility or a serious case of masochism could explain how they could tolerate a place so often on the verge of fiscal collapse or why they kept funding to a minimum even as they "floundered through oceans of mud to reach the Capitol from lodgings jammed to the eaves." In 1822, Senator John Eaton of Tennessee called for the federal government to take a larger share of maintaining Pennsylvania Avenue since it was unusable by humans or horses. The burden had been falling on taxpayers already being taxed at wartime levels, and the critical roadway was still a wreck. Congress responded by dribbling some money into the District's common fund, but the meager show of support had little effect.
Requiem for a Dreamer
Meanwhile, L'Enfant was faring even worse than the city he had planned. Instead of leaving the place that had done so much to make his reputation, then forever broke him, he hung around, increasingly miserable, living off friends and sometimes lodging at Rhodes Tavern. Latrobe described the "picture of famine, L'Enfant and his dog . . . He is too proud to receive any assistance, and it is very doubtful in what manner he subsists." L'Enfant claimed that the federal government owed him up to $100,000, and, while occasional offers would have provided a fraction of that amount, he refused all recompense until he was paid in full. That never happened, of course, and he cut a bleak figure in Washington City, where people might recognize this "quiet, harmless, and unoffending . . . Old Major," then in his sixties, whose "broken shoes [and] rent pantaloons" made him more suitable for a Greek tragedy than a revolutionary epic.
By the time he died in 1825, the capital L'Enfant had designed also looked moribund. Along with a crumbling infrastructure, few civic amenities, and a feeble transit network, the town lacked any significant mercantile house or means of profitable commerce except for the keeping of boardinghouses, many of which ended up as brothels (about which more later). The only commodity it had in abundance was politicians.
The aggregation of numerous factors—economic, fiscal, political, psychological—meant that, however much its creators, promoters, and residents wished otherwise, Washington City still hadn't become a real city. Not only did it lag far behind other nearby urban areas such as Baltimore and Philadelphia, it even trailed the other towns in the District, Georgetown and Alexandria, which its founders expected it to eclipse quickly. Every year of decline brought louder calls to move the national capital elsewhere.
The numbers told the tale. Even as the rest of America was exploding with dynamic growth, the capital remained its own little island chain, and could barely hold back the tide or keep from drowning in a sea of apathy and red ink. Its population rarely grew by more than a thousand people a year from 1800 until the Civil War, and from 1800 to 1830 the country's four most urbanized counties outpaced it by 115 to 300 percent. Even the mostly rural nation as a whole grew 12 percent more.
Visiting Washington City in 1804, Irish poet Thomas Moore gazed upon the condition of the town and, like so many critics, summed it up mordantly:
This embryo capital, where Fancy sees
Squares in morasses, obelisks in trees;
Where second-sighted seers e'en now adorn
With shrines unbuilt and heroes yet unborn
Though now but woods—and Jefferson—they see
Where streets should run and sages ought to be.
Two
A Plague of Waters
If Washington had formed a metaphorical island chain spread across vast distances, it was becoming in some places a literal one too. The unexpected focus of downtown development on the Burnes tract meant that Washington City was rising on one of the marshiest and swampiest tracts in the region—and the lowest point of a huge drainage basin stretching miles north of the city—with much of downtown having a high water table that made it damp and prone to flooding. Even the president's house sat in an unhealthy location prone to pollution and disease. It comes as no surprise, then, that the lowest-lying tracts ultimately came to be occupied by the poor and transient while more well-to-do Washingtonians fled northward to drier land.
Of course, one person's failed city is another person's arcadia. Thanks to city leaders' maladroit attempts at development, much of this sodden land remained rustic and unexploited—or to some, sylvan and idyllic. Just after the Civil War, eighty-five-year-old Christian Hines wrote a series of reminiscences of his youth, published as the book Early Recollections of Washington City. In these evocative anecdotes from the early 1800s, in stories "we had treasured up in memory from our youthful days," he describes a place barely cut from the wilderness, hardly a village let alone a city.
The City of Hines
At the time, the western half of what we know today as the Mall didn't yet exist. Instead, submerging the area was the sizable Tiber Creek, "a large sheet of water clear from Burnes' old farm-house to the Seventh-street bridge above the market-house" where "a great many sycamore and other trees" grew and Hines often walked "in search of turtle nests." Near the bridge "was a considerable swamp, overgrown with bushes, briars, thorns, &c. . . . At times, when the tides were high, the fish would come up the little stream as high as E street, especially the smaller kind, such as perch, smelts, eels &c." The land was rich and verdant, thick with thorn bushes and grape vines, as well as hickory, oak and chestnut trees, making for "a complete little wilderness."
Not surprising for a place littered with swamps and marshes, the region was one of the most well-watered landscapes on the East Coast, featuring no fewer than thirty-eight individual springs, a convenient and accessible source of drinking water in the first half of the nineteenth century, much of it drawn by pumps and wells from the groundwater just below the surface. Some of the springs fed creeks of varying size. These included Rock Creek, cascading in from the north and forming the border between Georgetown and Washington City; its tributary, Slash Run, just east of it; and James Creek, leading from the Capitol south to the Eastern Branch near Greenleaf's Point.
The largest and most important creek, the Tiber, didn't quite live up to the grandeur of its namesake, but at least it was a lot cleaner than its Roman counterpart. It began three and a half miles north of the Capitol, its main branch taking a westward turn near what became downtown—past the complete wilderness from Hines's youth—then widening around 17th Street before dumping into the Potomac. Together, the Tiber and the tidal marshes near its mouth gave the appearance of a lake, stretching a thousand feet across, thronged with swans, ducks, and geese. (Tiber Creek was better and perhaps more accurately known as Goose Creek.) The creek and its marshlands formed the center of the city, which sat in a broad natural amphitheater surrounded by a series of river terraces with bluffs up to thirty feet high and peppered with countless bogs, ponds, and swamps. Farther north lay an even steeper escarpment, where Boundary Avenue marked the curving northern edge of Washington City.
Where the Tiber met the Potomac, along its northern bank, stood the so-called Key of All Keys, a huge rocky outcrop where British general Edward Braddock reputedly landed in 1755 during the French and Indian War, before enemy forces ambushed him at Fort Duquesne. A landmark of sorts, also known as Braddock's Rock, it later became a quarry, and its stone helped form the foundations of the White House and Capitol until what remained of it was blasted away in the 1830s. (A fragment of it remains, hidden deep in a rocky shaft just off an approach ramp to Highway 50 and covered by several feet of groundwater.) Among General Braddock's men was a lieutenant colonel named George Washington, whose subsequent acquaintance with this part of the Potomac in no small measure encouraged him to site the new American capital here thirty-five years later.
Washington's Potomac Logic
Well before he became president, Washington had developed a theory on why the inland Potomac region would make an ideal spot for settlement. For one, the site lay at the nexus of future commerce, near the primary north-south coastal road along the eastern seaboard, yet it also could capture its share of maritime trade on Chesapeake Bay. It lay inland enough to have access to the American heartland, in the mountains and valleys of which lay deposits for mining, forests for lumber, and wheat and cattle for farming. The area had a great historical pedigree: Captain John Smith had explored this part of the bay in 1608, his party dining on venison and bear while trading with the Natives for beaver and otter skins. Smith remarked that the fish were "lying so thicke with their heads aboue the water, as for want of nets . . . we attempted to catch them with a frying pan."
Georgetown already had shown what opportunities the area offered, its deepwater port accommodating vessels for overseas trade, carrying a variety of goods from tobacco, leather, and candles to soap, flour, and beer, as well as river craft hauling shad and herring to neighboring colonies. Just down the river sat Alexandria, which dominated the Virginia trade in wheat, flour, and tobacco and boasted plantation manors owned by some of the biggest names in the Tidewater. However, above all this stood the most important geographic reason for the new capital to be sited here: the Fall Line.
At the Fall Line, the harder, erosion-resistant rocks of the Piedmont plateau meet the softer sediments of the Atlantic coastal plain. In the topography of the region, a series of waterfalls or rapids typically marks this boundary, of which Great Falls, with its "wild and romantic scenery," is the most prominent near Washington. Most major East Coast cities sprang up along this line to give them access to the river-borne trade of the interior, as well as saltwater commerce overseas, and to use the water power to operate mills and other industrial enterprises. Washington City was no different. But navigating past the Fall Line presented challenges: Strong currents capsized boats and dumped commercial loads overboard, especially during floods, and in low water rocks and snags transformed rivers into obstacle courses. For practical purposes, the Fall Line marked the "head of navigation," the farthest point upriver where boats could travel without locks or portage as well as the most inland reach of the tidewater. On the Potomac, the head of navigation lay at Little Falls, and the modest whitewater of these falls spilled out over the northwest border of the District. For these reasons, Washington was sold on the river, thanking "the goodness of that Providence which has dealt its favors to us with so profuse a hand. Would to God we had the wisdom enough to improve them."
Improving on nature in this case meant building canals, which would breach the Fall Line and open the western interior as far as Cumberland, Maryland, and beyond—perhaps even to the Great Lakes. Washington saw it as a great opportunity for anyone "who wants land to cultivate [and] may repair thither and abound, as in the Land of Promise, with milk and honey: the ways are preparing, and the road will be made easy thro' the channels of the Potomac."
To that end, in 1785 he became the first president of the Pawtomack Company, also known as the Potomack Canal Company, its stated goal to link the Tidewater region to the interior West. The plan first called for removing obstructions in the river and then constructing five canals to skirt the various falls that made upstream travel so difficult. With this auspicious beginning, the people of the nation would come together in common purpose as they developed the resources of the heartland, thereby building the country into a peerless commercial and industrial juggernaut.
That was the theory, anyway.
The Trouble with Canals, Part One
George Washington was many things: skillful surveyor, stalwart general, supreme president. But a successful entrepreneur he wasn't. His political skills and those of his fellow directors helped the company receive charters from the state legislatures of Maryland and Virginia in 1784 and 1785, respectively, and the initial capital seemed sufficient to start constructing the canals. But stockholders funded the Pawtomack Company on a pay-as-you-go basis, and this financing method proved disastrous when construction costs doubled and the original investors could pay no more. Faced with the prospect of their operation going under, the directors resorted to the desperate solution of lotteries to raise capital. When that didn't raise enough money, the company went into debt to pay its bills and kept borrowing. In the end, the Pawtomack Company devolved into a financial disaster. By the time the tidewater states finally revoked its charter, it had lost half a million dollars.
From an engineering standpoint, however, the company's bypass canals were an amazing feat. Untrained builders with almost no formal technical knowledge constructed them, and they succeeded in allowing passage for rafts and keelboats through 218 upstream miles of the Potomac. Unfortunately, the canals took a long time to build—the last one, at Great Falls, was completed in 1802 after Washington's death—and low water levels meant that they operated only for about six weeks of the year. Instead of shaping the Potomac into an essential commercial artery through the heart of America, the canals offered little more than a scenic curiosity. Their failure hardly dampened the desire of Washingtonians to develop the region's resources, however, and that desire would only increase in coming decades.
Diamond on the Potomac
Washington's insistence on squeezing Alexandria, Georgetown, and sites like Little Falls into the diamond-shaped boundary of the new federal district ensured that the enclave would be huge: one hundred square miles that needed roads, buildings, canals, wharves, and all manner of improvements. Encouraging citizens to relocate to the capital and building adequate housing and infrastructure for them posed an obvious challenge. But an even bigger question was the water—and what to do with all of it.
As with all of its early problems, the District had to look to its own sopping backyard for a solution. As historian Frederick Gutheim says, "the city was literally built out of the natural resources" of the region, from the timber and stone for its buildings and streets, to the marble for its monuments, to the canals cut from its creek beds. Those who worked the rivers had a head start on exploiting their potential. Shippers in Georgetown and Alexandria offered prices comparable to or even lower than the costs for transporting goods overland; the Navy Yard manufactured vessels and ordnance to defend the nation (albeit increasingly underfunded by the Jeffersonians); and an array of maritime facilities lined the Eastern Branch. The region's fishermen made a good catch in shad, gar, eels, pike, sturgeon, perch, and smelt, with herring being especially abundant in the waters of the mid-Atlantic.
Elsewhere, shipping facilities operated at Lear's Wharf, Barry's Wharf, and Commissioners Wharf, and riverside links connected Virginia to the Georgetown and Alexandria and Bridgepoint ferry landings (soon the site of the Long Bridge) and to the small settlements in Anacostia at the Upper and Lower Ferry sites. All that needed to happen was for the leaders of Washington, like those of Baltimore and other ports, to develop their city's docks, yards, and other maritime infrastructure, thus giving the District a real commercial vigor and making it a valid threat to its Atlantic competitors.
But the city's planners didn't just envision an economically viable city. They wanted a place with grand aesthetic appeal and visual harmony, a majestic landscape to serve as a testament to republican strength and virtue and to rival any of the creaky old cities of Europe. So why not start the District's rise to greatness with a bold stroke by channeling its waterways into beautiful fountains and canals, both functional and attractive?
Artful Designs
Pierre L'Enfant envisioned a magnificent canal in the French style flowing through the center of the capital. At Versailles, the Grand Canal and copious fountains not only offered visual delight but also drained the area's lowlands. So too would those of the federal city, according to his plan. Tiber Creek would become a grand canal in the American style, and fountains would cascade forth from Jenkins Hill below the Capitol, in a colossal show of engineering skill and invention. The new canal would link the Potomac near old Funkstown (now Foggy Bottom), run between downtown and the Mall, take a great turn southward at the Capitol, and finally split into two branches terminating respectively near the mouth of James Creek and New Jersey Avenue SE.‡
‡ Many early maps of the District depict both canal branches. However, the James Creek canal never existed at the same time as the New Jersey Avenue canal. It took seventy-five years for the former to be built, and then only after the latter had been converted into a sewer, making maps from the era more aspirational than factual.
The canal also would open nautical traffic, and thus trade and industry, between the Potomac and the Eastern Branch, conveniently passing the capital's major civil and commercial centers along the way. George Washington quickly saw the benefits of L'Enfant's vision, endorsing it in a letter to Jefferson in August 1791 as essential to the prosperity of the city. But the following February, Washington fired the prickly city surveyor, and in a huff L'Enfant took his capital plans with him.
The setback was serious but not insurmountable. Into L'Enfant's place stepped Andrew Ellicott, and the map he created bore many of the hallmarks of L'Enfant's baroque design, including the much-vaunted canal. A few twists and turns had changed, but in many respects it was the same waterway that the peevish Frenchman had designed. All the capital's canal needed was capital.
At the time, private companies funded most urban improvement ventures, whether through pay-as-you-go investments or devices like lotteries. Usually with the blessing of a municipal or federal charter, such companies constructed bridges, turnpikes, and canals, their work overseen by a board of directors that included a host of prominent citizens. In the case of the Washington City Canal, one of them was a certain Mr. Law.
Tom Law, Canal Builder
When we last encountered him, Tom Law was wading neck deep into property speculation, letting James Greenleaf take him for a ride through the turbulent waters of Washington real estate. But along with property development, Tom Law had another great interest: public works projects. In 1796 the Maryland legislature authorized Law and Daniel Carroll to raise $52,000 for the creation of the Washington City Canal. In the District's logrolling environment, it made sense: The two men obviously wanted to enhance the value of their property, and a lovely watercourse nearby wouldn't hurt. They were banking on it, literally and figuratively, to provide a profitable link between their waterside lots in Southeast Washington and the riches of the Georgetown market.
Progress on raising capital for the canal had come slowly ever since it had appeared so tantalizingly on the maps of L'Enfant and Ellicott half a decade earlier. So Law and Carroll, along with a few other directors of the enterprise, opted for lotteries to provide investment capital. But they soon found it rough going, as the lotteries failed to provide significant funds. So they shelved the idea for several more years.
But Law didn't give up. His speculative energies may have fizzled and his fortune may have vanished into the black hole of the Greenleaf syndicate, but he entered the nineteenth century more committed than ever to see his projects through. In 1802 Congress granted him and his partners—including two different Daniel Carrolls—a charter to dig the Washington City Canal as long as they could raise the money. Ever industrious, Law already had a plan to run packet boats between Tiber Creek and the Navy Yard as a means of transport to compete with hackney cabs. Two years later, he anonymously wrote a pamphlet claiming "the salubrity of the city will be benefited by the canal," while adding the caveat that "few will be induced to become subscribers, unless it can be demonstrated by calculation, that it will yield an immediate and constantly increasing profit." He should have listened to his own advice.
The Washington Canal Company failed to raise the funds by 1809, when the company's charter ran out. Congress reauthorized the company the same year to seek out $100,000 for construction, and it held a groundbreaking ceremony the following year, digging a few trenches before running out of money again in 1812. Congress once more came to the company's aid and declared that the old Maryland lotteries remained intact to raise capital, but these too failed. Two years later, during the War of 1812, the British invaded and burned down the capital.
By this point it should have become clear that it wasn't easy or simple to fund a canal by private means in the early nineteenth century. The construction required too much labor and capital for the tastes of fickle pay-as-you-go investors or lottery-ticket buyers, and not enough well-heeled investors wanted to risk their fortunes on speculative building schemes—enough of those already existed on dry land. Civic leaders didn't help matters either since they took more interest in envisioning grand plans than finding the practical means of executing them. But in the end it didn't matter—the canal got built anyway.
With its reauthorization from Congress, the canal company was supposed to raise $100,000 in capital stock. However, according to Frederick May, the president of the company, it actually began "with permission to go into operation when 40,000 Dollars should be subscribed. Stock in the amount of 47,000 Dollars was taken and the work commenced." It was a clever tactic, and it got work on the canal started. (It's worth noting, however, that, in the letter from May to the secretary of the treasury, the original script says "without permission." Someone later went back and struck through "out," raising the question of whether initial work had ever actually—and legally—been authorized.)
The Trouble with Canals, Part Two
Thanks largely to the labor of Irish immigrants (about which more in chapter three) the canal had opened for business by the end of 1815. The November celebration commenced with proud Tom Law and the other company directors, along with prominent citizens and city council members, floating through it on a barge followed by the Marine Band in another boat. It was all very lively and inspiring, just as it had been five years earlier when work had begun, but the company's financial state didn't stand in much better shape than it had then, and the canal itself left much to be desired.
With a few wharves and bridges already in place, the canal accommodated some barges and rafts carrying firewood, food, stone, and, of course, whiskey. But most larger boats couldn't travel on it because of a lack of drawbridges at critical downtown crossings at 12th and 14th Streets. Any boat that drew more than a foot or two of water wouldn't make it either because the canal had been cut to a depth of just three feet. In a slightly ridiculous touch, builders even lined the canal with stone to accommodate the wash of steamboats somehow expected to crowd the waterway. It all added up to a sorry sight: "Business was lacking, but even if that had come, the canal was useless."
What made the canal worse than useless, though, were the tides. At high tide, water rushed in and inundated the canal, sending some boats out of control and grounding others along its banks. At low tide, hardly any water filled the middle section of the canal, which resembled little more than a muddy trench. No one had accounted for these fluctuations, and the situation worsened. By 1818 the channel was usable only at high tide because of the buildup of silt deposited by the river, and cargo had to be scowed in to the wharves downtown. (The silt resulted from the felling of area trees, which promoted erosion as the Potomac and Eastern Branch sent unrooted earth downriver, plugging up river channels as well as the outlets of the city canal.) The canal's center section soon turned stagnant, and garbage began to collect there.
Nevertheless, canal promoters, Tom Law among them, refused to consider their project a failure. If the canal could be deepened and improved, they argued, the District would have its economic lifeline in working order. That may have been true, but there wasn't enough money in the canal company's coffers to do anything about it. Maintenance and repair work were lacking, and the company had barely enough money to exist: as little as $5,402 in 1822 to cover its annual costs. Even though the federal government stood to gain from the success of the canal, it refused to help until the company effectively foundered and the canal had become a financial disaster.
That didn't happen until 1831, but in the meantime came another, much more serious bout of canal fever.
The stagnant city canal created a moat around Southwest Washington City, which became known as The Island.
Canal Fever
To most in the country, public works glory reached its pinnacle with the Erie Canal, "the greatest water resource project of the nineteenth century." That legendary concourse of commerce connected New York City with the Great Lakes and gave it access to all the riches of America's heartland and the Midwest. Completed in 1825, the Erie Canal helped New York usurp what should have been the glory of New Orleans and secure its place as the country's greatest port, commercial entrepôt, financial capital, and population nexus. With good reason historians use the phrase "canal fever" to refer to the heady promise of the Erie Canal for many American cities, which then built other channels in its wake, a phenomenon that "almost reached the proportions of a mania." Washington's leaders gave into the fever as well—even as their earlier attempt at creating a municipal canal sat pungent and moldering under ever-deeper layers of mud and silt, a dirty open scar of civic failure that couldn't be wished or washed away.
Perhaps not surprisingly, one of the promoters of the brand-new canal was Tom Law. While still a director of the failed city canal, Law put his remaining energy, at seventy years old, into the freshly devised Chesapeake and Ohio Canal. A member of the promotions committee for the canal, he had been working since 1823 to help create a new watercourse to unite the mid-Atlantic with the Midwest politically and commercially. Four years later, Law testified before Congress about the glories of the proposed channel, and a year after that, on the Fourth of July, toasted the alliance of "the River of Swans with la belle Riviere"—a fancy French way of saying that the Potomac would link up to the Ohio Valley and the growing city of Pittsburgh. It was the District's last, best chance to develop a canal that worked.
The Next Wonder of the World
The Chesapeake and Ohio Canal still exists. You can visit this national historical park on a tour of Georgetown, enjoy a boat ride through some of its locks, hike along its banks, take pictures of its industrial technology, and try to imagine the picaresque days of canal men piloting their barges in view of the Potomac while mules did most of the work on the towpath. In fact, if you didn't know better, you might never suspect that this 184.5-mile watercourse nearly ruined the city of Washington, plunged the region into a fiscal crisis, and caused the nineteenth-century federal government to take that rarest of actions—bailing out a failed corporation—all to prevent foreign creditors from calling in their debts and forcing the nation's capital into bankruptcy and liquidation. Such are the ironies of the C&O Canal.
But at least the C&O wasn't as ill-considered as its Washington City counterpart. The C&O did have a useful aim in paralleling the Potomac and getting around its obstructions, and the old Pawtomack Company's assets and infrastructure transferred into the new enterprise too. Reaching the Monongahela River would give the region a lifeline into the agricultural and industrial riches of the Ohio Valley, and Washington City surely would make a reasonable outlet for that commerce (which, after all, couldn't all go to New York City). Even better, the brilliant Benjamin Wright would serve as head engineer for the new canal, as he had for the Erie Canal. With business and public enthusiasm to spare and countless newspaper editorials hailing the inevitable greatness of the canal, the groundbreaking ceremony took place on Independence Day in 1828, with President John Quincy Adams himself holding the shovel. He proclaimed the C&O would be a "conquest over physical nature such as never yet been achieved by man. . . . The wonders of the ancient world, the Pyramids of Egypt, the Colossus of Rhodes, the Temple of Ephesus, the Mausoleum of Artemisia, the Wall of China, sink into significance before it."
A leisurely boat ride along the Chesapeake and Ohio Canal in later years.
Inspired by his own hyperbole at the groundbreaking, President Adams plunged in his shovel—and immediately hit the root of a hickory tree (an ominous portent, since Old Hickory himself, Andrew Jackson, beat him in the November election). Taking off his jacket, President Adams hacked at it for a while until it gave way and the first chunk of soil could be cut from the earth. It was an obvious warning sign, but the problems had begun well before the president struck that pesky root.
The earliest red flag had been an 1826 report by the Army Board of Engineers that estimated the project to cost more than twenty-two million dollars, four times its original budget. After an outcry, another report deftly reduced the required sum to four million dollars, with the capital to be raised from corporate subscription. Lower Potomac cities would borrow money and raise taxes to pay the interest on their new public debt, which of course would be retired when the canal began paying dividends. The new report made another change: It halved the canal's path, which now would run only to Cumberland, Maryland, stopping well short of the Monongahela River and making its name a misnomer. The C&O Canal had lost its "O" and arguably its reason for being. As you might expect, however, this twist didn't halt work on the canal. Instead, canal fever raged.
In 1828 Congress passed a bill allowing municipalities in the District to triple their public debt to help fund the canal. Instead of public alarm or even debate ensuing, Washington's mayor hoisted the flag, and a cannon sounded a peal of fiery joy. Business owners in Georgetown took note of the frenzy and dramatically raised the sale prices of their land and easements to allow the canal to pass through. Among them, Charles Carroll, like his relative Daniel, couldn't resist a bit of speculation when he had the chance. Everyone wanted to cash in.
Potomac Valley Blues
The area's desperation for a link to the C&O stemmed from more than just canal fever, though. The District's commercial and industrial development was languishing, banks were closing, and the mood was growing dire. Washington City's mayor rued his town's "almost total absence" of commerce, and even those in Georgetown took a bleak outlook: "Our town, notwithstanding its local and natural advantages for trade, has been gradually declining, our population is deminished; our houses untenanted; and the people earnestly pleading that the avenues of commerce may be opened."
Residents and leaders of the cities saw the waterway almost as a magical talisman, hoping and expecting it to bring them relief from their doldrums. Alexandria created an aqueduct that carried C&O barges across the Potomac from Georgetown and fed into a branch of the canal that traveled seven miles south before reaching the city. The cost ran to $1.25 million, an amount difficult to raise by private subscription, which meant that the Virginia channel took until 1843 to complete. Washington City, however, as the seat of federal power, had more clout than Alexandria. It just blackmailed Georgetown to get what it wanted.
Georgetown had the gall to propose terminating the C&O at Little Falls, well north of the capital city's border. But Washington City's trump card was simple: It too was an investor in the C&O, but it hadn't yet paid its million-dollar subscription. Nor would it unless the canal's directors approved a linkage to the Washington City Canal. Already short of funds, the C&O directors had no choice but to pay for an extension and locks to connect it to the city canal. But by then, in 1833, the bill for canal fever was coming due.
The Trouble with Canals, Part Three
The problems this time had started in 1831 when Washington City bought out the Washington City Canal Company for fifty thousand dollars and then contributed more money to widening the dysfunctional waterway, with the notion that such improvements would be needed for the linkup to the C&O. In reality, the buyout did little to stimulate commerce and only pulled the city further into debt, made worse by its capital contributions to getting the C&O finished and losses from lotteries to pay for the city canal. The debt level reached $1.7 million, which Washington City tried to offset by raising its municipal tax rate to the highest in the nation.
It's worth remembering that at this time most of Washington's roads were unlit, unpaved, rutted, and dangerous. Garbage lined the streets, and feral hogs scavenged the filth. Pockets of unfinished, derelict houses gave the place the look of a village instead of a city. In short, the place was commercially and industrially stunted. Yet despite such a clear need for major civic improvements, the city's leaders funneled money foolishly and profligately into the canal business and made the town suffer for it. As Senator Samuel Southard, chairman of a committee overseeing the District, put it: The city had such colossal debt that "it is utterly impossible that it can be relieved by any means within its own control" and "it will very probably in a short time be driven to the surrender of its charter"—meaning an abrupt end to Washington City itself.
In their zeal to find funding, the District's cities had borrowed lustily from bankers overseas, in this case from Holland, long a favored source of foreign investment. Now that the debt was maturing and the cities scarcely could pay the interest, let alone the principal, panic bloomed. Southard saw, at a minimum, that bankers would "become the owners of a great proportion of the property within the capital of the Union" and other politicians worried that "the agents of the foreign creditors are here ready to purchase the property of these citizens of Washington [the canal shareholders] under the hammer, so that there is danger emphatically that this city may be sold to the Dutch." It wasn't an empty threat, either. As one observer wrote, "it may be safely affirmed, that unless Congress pays the debt . . . the whole city of Washington must soon be for sale, and be the property of the Dutch bankers." Indeed, the foreign investors had already arrived in the District and stood at the ready to get their money back by laying claim to the collateral.
Facing the absurd possibility of the capital of American democracy legally falling into the hands of Europeans, Congress finally stepped in and paid $1.5 million to settle the cities' debts in exchange for control of their canal stock. In 1836 the nation thereby took ownership of the watery white elephants created by the cities of the District of Columbia. It wasn't much of a bargain for the federal government.
The Alexandria and Washington City Canals never lived up to their promise, and the C&O Canal took another fourteen years to complete. While that canal did prove useful during the Civil War for ferrying troops into Maryland and for hauling great loads of coal downstream from Cumberland, this $11 million watercourse for the most part failed to deliver on its promise and became increasingly antiquated as the years passed.
As a telling coincidence, ground broke on the C&O Canal and the Baltimore and Ohio (B&O) Railroad on the same day, July 4, 1828. But the rail line struck much more successfully into the heart of the Midwest, often paralleling the canal itself and reaching Cumberland in 1842, eight full years before the canal did. The railroad even extended a branch to Washington City in 1835 (though Congress perversely forbade steam engines from entering the capital itself for another seventeen years), ending the stagecoach monopoly over land transit and halving the travel time between Baltimore and Washington City. Even more than the railroad, the Panic of 1837 delivered the ultimate cure for canal fever, thrusting America into a six-year economic tailspin and scuttling most of the major waterway projects not already under way.
The battle for American transportation supremacy had ended, and canals had lost.
The Pride of Waters
Natural waterways continued to fare better than their man-made counterparts. Lined with facilities for making or storing beer, guns, rope, sugar, and tobacco, the Eastern Branch hummed with activity. On that river, the Navy Yard wasn't just the local military powerhouse, it also offered one of the few bright spots in the District for manufacturing, its forges and furnaces churning out everything from anchors and anvils to copper nails and lead pumps. Around the Navy Yard, a thriving working-class neighborhood developed. To the west, the Potomac River continued its profitable commerce in bar iron, flour, grain, sugar, timber, and whiskey, providing an economic pulse to the struggling cities of the District and showing how much more valuable the workaday river trade was to the capital than the chimera of canal trade. Area rivers boasted some 150 fisheries that hauled in so much fish—including 400,000 barrels of herring, according to one report—that the surplus catch was used for fertilizer.
In the end, the rivers greatly advantaged the District, and the tidewater served as an essential economic outlet. But civic planners continued to look the wrong way with their ill-fated schemes to reach the interior of the country by channeling upriver and forcibly imposing an urban waterscape on a region that naturally resisted it.
In the shadow of a domeless Capitol, the dismal Washington City Canal flows through the Mall in 1860.
Arcadia Lost
In his reminiscences, Christian Hines focused on the years of his youth, around 1800, with good reason. Shortly after that, the city slowly emerged, and his little wilderness began to disappear. The old streams that once funneled freshwater through the terraces vanished first, replaced by drains and culverts starting in 1810. Some thirty years later, spring and well water began to flow into private residences, and sewage was pumped out and into those same drains and culverts. By the eve of the Civil War, most waterborne waste poured directly into the rivers. Washington City accordingly became as dirty as any other city, its freshwater springs and wells increasingly polluted or drying up. Even the grounds south of the White House transformed into a filthy marsh choked with sewage and wastewater from urban runoff.
But worst of all, the "Great Tiber Freshet" became the Washington City Canal. While its northern reach fed into a system of drains and culverts, the part running along downtown was channeled, graded, walled, and streamlined to become the city's most notorious public works disaster. Unlike the C&O Canal—which functioned to some extent—the city canal posed an active and worsening public health threat. Even in the mid-nineteenth century, it served as an ongoing and unavoidable reminder of the poor decisions and political ineptitude that had marked the District from the moment it became the capital.
Three
A Mechanic's Guide to Washington City
Aside from gaining access to inland rivers, George Washington had another key reason for locating the capital so far upstream: wartime defense. In his view, the city would be much safer nestled upstream between the dicey shoals and bars of its rivers. Only a foolhardy attacker would risk sailing into the treacherous waters in sight of the guns of the Navy Yard and the eighty-nine-acre US Arsenal at Greenleaf's Point. The theory was reasonably sound; to date, no foreign power has made a successful attack on Washington, DC, by sea. But in the end it didn't matter. The British burned it to the ground anyway.
In August 1814, in one of the last acts of the futile and misnamed War of 1812, British forces dropped anchor at Benedict, Maryland, some forty-five miles southeast of the District. Avenging the American army's devastation of the Canadian city of York, the British marched to Bladensburg, where they routed a force of capital militia. From there they attacked Washington City from the north, only to find it abandoned by its defenders. The British torched the Capitol, the Library of Congress, and other public buildings before finding a fully prepared meal laid out for guests at the Executive Mansion, which they gobbled down before burning that building too.
As an act of political vengeance, it was a bold stroke; as a strategic maneuver, it was pointless. The British lost a much more important battle at Baltimore the next month, denting the reputation of the king's navy and leading Francis Scott Key to write a dramatic poem that became a stirring though nearly unsingable anthem for the American cause.
The burning of Washington City had important repercussions. As author Margaret Bayard Smith wrote at the time, "The district certainly was not in a state of preparation . . . [but] The city was capable of defence and ought to have been defended." Some blamed the disorderly militia retreat from the initial battle, which soon became known as the Bladensburg Races. Others saw treason in the behavior of those who chose to stay and bargain with the enemy. (In one case, instead of receiving praise for talking the British out of burning the Patent Office, Dr. William Thornton faced questions about his patriotism from the mayor.) Still others criticized the executive branch and the president, who chose to scuttle away rather than stand and fight. Whatever the case, nature itself did more to save Washington City than any human defender, sending down a timely rainstorm just as flames threatened to immolate the entire town.
The Capitol stood in wartime ruin in 1814.
Phantom Rome
Following the war, the city was a carbonized shell of its former self. Some critics—mostly representing rival claimants to the capital site—demanded that the seat of government should be moved away from the lowly, marshy village and all its problems. In response to the threat, Congress authorized funds to rebuild key public structures, and private companies raised fresh capital for construction projects. A heroic legend even emerged to give the capital the luster of preordained, classical glory. Author D. B. Warden wrote in 1816 that one mythical farmer, in naming his creek the Tiber and his place of residence Rome, was "endowed with prophetical powers [and] foresaw the destinies of the Columbia territory." As Ms. Smith put it, "May a Roman spirit animate our people, and the Roman example be followed by the Americans." Similarly, later writers couldn't resist describing the capital as such a shining city, "an emporium that should vie with the noblest cities of the ancient world," among other hosannas.
Needless to say, Washington City had little in common with ancient Rome—other than that most of its citizens couldn't vote. The gilded rhetoric of politicians and promoters didn't fool everyone, of course. Visiting British authors were the most obvious critics, but their critiques often met with hostility, the inevitable insults of monarch-worshipping foreigners.
But one American writer had a more potent effect, seeing the capital as it was, without illusion:
Washington city is repeated with a sort of holy enthusiasm; nothing evil or low mingles with the sound; it conveys sentiments at once the most pleasing, the most elevated. But how are we disappointed upon coming to this Idol of America! . . . I will venture to say that no city of the same age has kept pace with it in vice and dissolute manners.
Anne Royall—a trenchant, thought-provoking, frequently infuriating critic of the town and its denizens—has contributed much to our knowledge of how Washington City actually looked, who lived there, what they did, and why the place had so many problems. Moreover, unlike many writers and critics at the time, she looked past the grand public buildings and the political rhetoric to take stock of the lives of the common residents of Washington City, the "mechanics" who made up much of its working class and the poor who composed the class below them.
Royall Style
Anne developed an interest in writing during her marriage to Captain William Royall, who had raised a Virginia company and served under Lafayette during the revolution. He introduced her to several entities that would prove influential, including Masonry, Shakespeare, and Voltaire, and it was the writing of that groundbreaking French iconoclast that most shaped the style and invective of her later work. Although writing represented an uncommon career for women of the era, some like Royall pursued it vigorously, describing more than just the doings of politicians and the elite (as later stereotypes had it). Indeed, her voice had no limits, no matter how unseemly or contrary to the national mood. In five years she wrote ten volumes of Travels in the United States and "tramped around all day, in all weathers, taking notes, holding interviews and acting as her own soliciting and delivery agent." In the capital, she took a keen interest in dissecting the class structure:
The population of Washington may be said to consist of four classes of people, whose pursuits, interests, and manners differ as widely as though they lived on opposite sides of the globe, viz. those who keep congress boarders and their mutual friends, the subordinate officers of government . . . secondly, the labouring class; thirdly, what may be called the better sort; and fourthly, the free negroes.
To her, the ruling caste of politicians was "proud, ignorant, and many of them insolent," while the workers were "mostly very dissipated," all too ready to spend their wages as quickly as they earned them. It was a punchy counterargument to the notion that America had no class system, an idea that made plain the barriers to social advancement that existed and highlighted the struggles of those without wealth or status.
Scavengers and Sweepmasters
Workers didn't make much money: only half or three-quarters of a dollar per day, with female servants and seamstresses making as little as two to four dollars a month. This was at a time when the average national wage was around a dollar per day. Competition with slave labor no doubt depressed the average wage in the District, but so too did the lack of jobs stemming from the moribund commercial and industrial state of Washington City. What jobs there were, outside the government, tended to involve small-scale merchandising, skilled and unskilled labor, and perilous grunt work. Judah Delano's comprehensive 1822 Washington Directory lists each head of household in Washington City along with his or her occupation and address. Some of the names and jobs include:
John L. Brightwell, sexton of eastern burial ground
Mary Cook, widow
Mrs. Corbett, school mistress
Hugh Dawson, ornamental plasterer
Mrs. E. Fonde, ladies' fancy wareroom
Thomas Green, huckster
Henry Guegan, foreign bookseller and teacher of French language
Alice Hepburn, midwife
Jacob Hilbus, organ builder
Mary Hughes, milliner
Henry Kurtz, foreman anchor smith at navy yard
Vincent Massi, dancing master
Joshua Millard, keeper of the tollhouse at the Washington Bridge
Elizabeth Queen, boarding house
John Smith, sweepmaster
John Tucker, whitesmith and bell hanger
Alexander Ward, tinman
Thomas Wheat, teacher Hamiltonian school
Thomas White, ship carpenter
John Wilson, scavenger
Samuel Wimsatt, wood corder and coal measurer
A talented historian could write a book about the information contained in Delano's directory, but a few key points stand out: It includes few women other than widows. Free blacks are identified as "col'd," while other residents are assumed to be white. Most of the jobs belong to tradesmen and laborers, and some of the job titles provide only a hint of the challenges involved with low-paying, sometimes dangerous work.
A scavenger had to "remove nuisances and all offensive substances" from privies, receiving half a dollar per every seven cubic feet emptied. A sweepmaster shimmied down chimneys and cleaned them for a fee of ten cents per building story. A huckster sold cheap, sometimes shoddy wares from a street wagon. A tinman worked tin, of course, while a whitesmith finished iron, and a burial-ground sexton and his deputies were the only people allowed by law to dig and fill graves. Along with these jobs came the full range of familiar antebellum occupations: bricklayer, carpenter, carter, cooper, hatter, miller, saddler, shoemaker, stone cutter, and tailor. The directory also lists a few prominent names and occupations, such as Charles Bulfinch, "architect of capitol, e side 6w btw D and En near Unitarian church," and James Monroe, "president of the United States, at the president's house."
In the Trenches
Although the directory doesn't specifically mention canal workers, plenty lived and worked in the District too—many of them Irish immigrants. As early as the 1780s, a notable Irish presence had formed there. An initial group of two hundred built the ill-fated Pawtomack Canal, with later waves of Irish immigrants contributing labor for the building trades and various public works projects. D. B. Warden even claimed, with some embellishment: "Nearly one half of the population of Washington is of Irish origin. The labouring class is chiefly Irish, and many of them have no acquaintance with the English language. They have cut the canal, made, and repaired the streets, and executed most of the manual labour of the city."
It's no exaggeration, however, to say that aside from slave labor the Irish did some of the toughest, dirtiest, riskiest jobs in the District. On the Washington City Canal, regardless of weather or temperature, they used picks, shovels, and wheelbarrows to carve a ditch into the sodden earth, suffering a reduced chance of survival in "the hot and humid District with its canals . . . swamps, and mosquitos." Margaret Bayard Smith took pause from detailing the lifestyles of the elite to remark that the Irish had to board with the poorest citizens in town, crowded into rude shacks, and worked "in the midst of disease," much of it fatal.
Not all immigrants had to do trench work. Some skilled artisans, such as bricklayers and stone cutters, did well enough to have other men working for them, establishing their own companies and contracting for work with the federal or city government or private businesses. Young men could apprentice for several years with well-established master artisans and learn a trade in exchange for room and board, and when the contract was fulfilled, receive a set amount of money and a "freedom suit" of new clothing. It could be a useful system to someone committed to starting a career, but it came with a lot of strings. All of the following could be forbidden: revealing the master's secrets; wasting the master's goods; leaving work without permission; playing cards, dice, or other games of chance; visiting alehouses, taverns, or theaters; or getting married.
Regardless of their skill level, mechanics had to contend with an uncertain economic environment, unexpected layoffs, a high cost of living, and stagnating wages. For the Irish and other Roman Catholics, their practicing of a religion contrary to that of the majority in town didn't help matters, either. As Anne Royall wrote, "I have heard them stigmatized by every harsh name, and accounted little better than heretics."
However, some political groups, such as Andrew Jackson's Democrats, had better ideas. Instead of insulting the mechanics, they made them the bulwark of their electoral power.
Laborers' Levees
This newfound embrace of the white working classes, no matter their heritage, made for some rousing scenes. President Jackson threw a lively "levee" at the White House that included a large contingent of Irish. For visiting English critics such as Thomas Hamilton, these "great unwashed" represented "the very lowest sort of people." Despite his prejudice, though, Hamilton detailed a growing, albeit chaotic, democratic spirit that came to animate the politics of the District, along with the rest of the country:
There were present at this levee, men begrimed with all the sweat and filth accumulated in their day's—perhaps their week's—labours . . . There were majors in broad cloth and corduroys, redolent of gin and tobacco, and majors' ladies in chintz or russet, with huge Paris ear-rings, and tawny necks, profusely decorated with beads of colored glass. There were tailors from the board, and judges from the bench; lawyers who opened their mouths at one bar, and the tapster who closed them at another;—in short, every trade, craft, calling, and profession, appeared to have sent its delegates to this extraordinary convention.
Nor was this the first time that common folk had enjoyed a party at the seat of the government. In 1802 Thomas Jefferson had welcomed the public to the White House to feast their eyes on a 1,200-pound block of Massachusetts cheese and take a hearty bite of it. (Two years later, Jefferson was still snacking on the once-colossal, now pungent remnants of the cheese.) Also during Jefferson's administration, a crowd of laborers burst into the Capitol bearing a loaf of bread, some beef sirloin, and casks of wine, cider, and whiskey, throwing an impromptu barbecue for all: rich and poor, black and white, free and enslaved. Never one to miss a public display of food, the president strolled in and cut off a chunk of meat with his pocketknife before irate senators shut down the drunken proceedings.
Indeed, no matter how much power they wielded, presidents couldn't overlook the interests of the mechanics, especially as property requirements for voting were disappearing and the franchise was opening to more people than ever before. As Thomas Hamilton wrote, the president's only hope of staying in power was by "conciliating the favour of the lowest—and, therefore, most numerous—order of his constituents," despite having to "shake hands with men whose very appearance suggested the precaution of a glove." Even in a town where the locals couldn't vote for their federal leaders, mingling with the commoners made for good practice.
Uncertain Arrivals
The Irish weren't the only new arrivals to change the social and cultural makeup of the capital. The Germans had a presence that started small, hampered no doubt by the failure of Jacob Funk's Funkstown to draw property buyers. But their number slowly increased in size and influence in the first half of the nineteenth century, topping three thousand by the Civil War. They found employment as brewers, butchers, jewelers, machinists, printers, tailors, and woodworkers. The English and Scottish continued to arrive, along with Swiss and French immigrants and a broad range of other Europeans, including a handful of Italians who worked as music teachers and dancing masters and played in ensembles like the Marine Band. All of them came to town with high hopes of finding suitable jobs. Some did, but many found a scarcity of steady work and were soon cast adrift in an inhospitable place that offered few social bonds for help when times got tough.
The lack of work made for a lot of poverty in town. Yet most of the tracts and pamphlets about the District—so vivid in their descriptions of the public buildings, so eager to promote the capital to audiences domestic and foreign—said very little about its economic failures or the growing numbers of the destitute. Anne Royall stood out as the exception.
Asylum Records
Royall carefully observed the poor because she herself had once been penniless. Her husband, William Royall, died in 1813 a wealthy man and dictated that the bulk of his estate go to Anne. But his relatives had other ideas, contesting the will and beginning one of those legal sagas that seems more at home in the pages of Dickens than in early nineteenth-century America. It took ten years for the case to be decided, and she lost. Now impoverished, dodging debt collectors, her health failing, and "without a cent in my pocket or change of raiment, badly dressed," she petitioned Congress in 1824 to receive her husband's pension as the widow of a Revolutionary War officer. So began an even longer legal saga. In the meantime, she still needed money, so she devoted herself to writing, beginning her work in earnest at the age of fifty-four.
Her own struggles gave her considerably more insight into the lives of the underprivileged than other writers at a time when poverty was considered more a moral nuisance than a public outrage: "In every other country, in every other town or city, some semblance is maintained in that attention which is due to the poor and the rich. But if you are poor, you have no business in Washington, and unless you are well dressed, you will have good luck if you be not kicked out of doors by the servants, should you attempt to enter a house."
On Pennsylvania Avenue, orphaned and homeless children begged for money, sometimes picking up spare change by sweeping the giant road or by shining the shoes of passersby. Other of the town's destitute received penance at the local poorhouse, the Washington Asylum. Founded in the early days of the District, the Washington Asylum was becoming increasingly overcrowded, disease-ridden, and dangerous. It wasn't just an almshouse but a workhouse that confined vagrants and minor lawbreakers. It also took in the overflow from the Washington County Jail, which had too little space and too many criminals. The Washington Infirmary, the town's first hospital, functioned as a de facto poorhouse as well, though with little means to fight poverty and the illnesses that accompanied it. Public money available for the relief of the poor was paltry and also balkanized by city ward. The central districts got the lion's share, while the outlying areas northeast of the center and along the riverfront received much less, setting a geographic pattern for poverty that persists to this day.
For Anne Royall, the Washington Asylum was abysmal. "This wretched establishment only exists to disgrace Washington. I found several wretched children in this dreary and comfortless asylum, without one cheering voice, or hand of kindness to comfort or cherish them." It was a "place replete with human wo[e]" run by a man "wholly unfit for the place, and his wife a perfect she dragon. . . . Death would be mercy compared to the situation of the unfortunate inmates." By contrast, she voiced her support of the orphan asylum and the women who ran it—"the glory of Washington" that "reflects the highest honor upon its promoters"—noting the vigorous spirit of charity for children that elsewhere proved all too absent for adults.
The era she described was a transitional one for poor relief. In 1802 Washington City had allocated 42 percent of its fiscal budget for purchasing housing and clothing for the underprivileged, but that figure plunged to just 6 percent by the Civil War. Like other Southern cities, the District of Columbia relied on a mix of middle-class philanthropists and charitable groups to provide assistance. They did what they could to fight destitution but still had a limited effect on it. Anne Royall saw how poverty washed over the District: "Daily and hourly . . . you see some woman or child begging a mouthful of victuals at our doors," as the local government stood largely indifferent, merely offering to "throw a few cents to the poor wretches."
Churches of course had their own charitable entities, such as the Roman Catholic Orphan Asylum, run by the Sisters of Charity of St. Joseph, which included a day school that cared for up to two hundred indigent girls. It was a noble effort—if something of a bandage over a bullet wound. Nonetheless, many religious organizations saw helping the poor as an opportunity to fulfill the gospel mission, establish a greater social presence in town, and perhaps make a few converts along the way. Their efforts took place during the Second Great Awakening, a time when new forms of worship were sprouting almost overnight and the clergy were assuming a greater public and political role than before.
Black Book versus Black Book
The denominations in the District were mostly Protestant, consisting of thirty-eight churches by midcentury: around one-third Methodist, half other mainline Protestant groups, and most of the rest Roman Catholic, with one synagogue and one Quaker meetinghouse. But Anne Royall wasn't comfortable with any of them. The bulk of her ire fell on the rapidly growing evangelical sects, which she saw not only as a threat to rationality and humanist endeavor but to the republic itself. She made it her mission "with a full determination to keep my eye on priests and missionaries, determined to strip the mask from hypocrisy, expose evil, patronize virtue, and side with no sect or party."
But America in the throes of the Second Great Awakening was no place for a Voltaire in training. Though she was far from an atheist and if anything believed strongly in the ecumenical tenets of her beloved Masonry, the charges that Anne Royall levied against clergymen sound caustic even today: "Their visage is long, their complexion a dirty wan; they are generally tall, gaunt and supple! Distant and vulgar in their manners, the gloom of their countenance is never interrupted with a smile. They usually have a train of women after them with the same lowering looks." She counted their worst offense eroding the separation between church and state and advocating for laws that tried to ban public and private activity on Sunday. In her Black Book of travel writing and commentary, she laid out her view of evangelical churchmen and missionaries in bracing style, positing her view of the Bible against theirs:
A Christian is one thing, they another. A Christian honors his country and respects its rulers. They disgrace their country, and call their rulers a lawless set of men, that must be put down. A Christian is meek and merciful. They are turbulent and cruel. . . . A Christian loves his neighbor and honors God. They hate their neighbor; call him a heretic, an infidel; and make God no better than a usurer.
In one chapter alone, she rails for more than eighty pages against the evils of missionaries, going into hair-splitting detail about their severe and inhuman philosophy, their insidious methods of conversion, and their subversive methods of undermining the body politic. Needless to say, the churchmen took notice.
Sacred versus Profane
For her strong opinions, the clergymen made Anne Royall a pariah and inveighed against her brand of anticlericalism. They cast her as a godless harpy and a threat to moral order. A man she called a "missionary" even attacked her in Vermont in 1827, dislocating her ankle and keeping her off her feet for six months. But her foremost nemesis was the Reverend Ezra Stiles Ely of Philadelphia, a champion of melding church and state through the election of avowedly Christian candidates for office.
A skillful polemicist—through his American Tract Society, which widely distributed his pamphlets in the 1820s—Ely and his associate in the District, John Coyle, hatched a plan to bait Royall into trouble. First, a group of children on their way to Sunday school threw rocks at her house and broke her windows. She told their parents, but they took no action to stop the little miscreants. Instead, groups of churchgoers prayed and chanted below her broken windows around the clock. After several days of religious racket, she had had enough and called one prayer leader, Coyle himself, a "damned old bald headed son of a bitch." This rare example of her using profanity lit the fuse, and soon a group of young boys and church leaders came "to shower the house with stones, yell and blow horns." A grand jury convened—but instead of going after the rock-throwers, it indicted Anne Royall herself.
The clergymen got what they wanted. The local district attorney accused her of being "a public nuisance, a common brawler, and a common scold." Those were the official charges, but the unofficial charge was just as damning: Anne Royall was a menace to the natural ideal of womanhood. Instead of being demure, unthreatening, and docile, she was proud, acerbic, and fierce. Had she been a man, she never would have faced the same legal complaint, particularly in the vigorous culture of dispute that prevailed then in which pro- and anticlerical activists used all manner of rhetoric and sometimes violence against one another. A frail sixty-year-old widow couldn't use physical force to her advantage, but her words got her into more than enough trouble.
The idea of the "common scold" had a long and dubious history, going all the way back to the medieval era. Originally it amounted to little more than a woman disturbing the peace, but it evolved into an all-purpose charge to contain the behavior of "disorderly" women. With a growing number of such women in the frenzied, increasingly democratic culture of the 1820s and 1830s, the list of charges expanded for female offenders, including such "crimes" as "lewd and lascivious carriage, stubbornness and disorderly conduct, to adultery and fornication." To those in charge, Anne Royall seemed as good a test case as any.
Virago on Trial
The trial that followed owed less to tragedy and more to farce. Instead of sober testimony, Royall offered up an impressive display of wit and sarcasm that had the galleries laughing. She labeled her accusers "Satan's walking-stick" and "a good natured simpleton." She described one of them this way: "His hair is macaroni, his arms over five feet extended, his face pale, his nose hooked, with a gray goggle eye, and Shakespeare's smile." She facetiously suggested the trial was a great event to be "painted and put in the rotunda of the Capitol with our national paintings, reserving a conspicuous place for myself." The opposing side offered up the usual ponderous arguments, depicting her as a vulgar harridan, a threat to public order, and a "virago"—that is, a woman who broke established gender boundaries and behaved like a man. (More ambivalently, John Quincy Adams had once pronounced her "a virago errant in enchanted armor.") In the end, the US Circuit Court found her guilty. Then the real absurdity began.
The traditional punishment for a common scold was "ducking," in which the offender was lowered by chair into a body of cold water. The time spent underwater could last a few seconds or, as one wag put it, "in Mrs. Royall's case, perhaps from two to four hours." Marines at the Navy Yard duly constructed the ducking stool in short order and showed it off to interested crowds. Its rope coil turned a lever that could deposit a chair into, say, the Eastern Branch of the Potomac, with the common scold buckled in for her chilly plunge and public shaming. It was one of the most ingenious and ridiculous disciplinary devices ever created in America, and luckily it never got to "duck" anyone. Anne Royall got off with a ten-dollar fine, the equivalent of a modern speeding ticket.
Although embarrassed by the episode, Royall had become a public figure. People were now seeking out and buying her writing, and she made some surprising friends in influential places, namely at such newspapers as the National Intelligencer—whose reporters paid the fine in her honor—and in the Andrew Jackson wing of the Democratic Party, which she generally supported. (In one famous legend, upon arriving in town, Ms. Royall encountered Jackson's nemesis, John Quincy Adams, skinny-dipping in the river. Finding a captive audience, she sat down on his clothes while lecturing the naked president on various issues of the day.)
Understandably the whole episode only fired her up more to write about corruption and injustice where she saw it, to root out malefactors where she found them, and to add to her growing ranks of friends and enemies—all of which made her a fitting symbol of an adversarial age.
Unsteady State
These events occurred at a time when Jackson's policies were sending his admirers into a lather of excitement and his detractors into a stew of contempt, whether he set his targets on opposition senators, New York bankers, or Native tribes. Regardless of their effect, Jackson's policies did help secure the votes and loyalty of much of the white working class, turning the party into an electoral force that dominated American politics until the Civil War.
Still, while they had attained a newfound political importance, the mechanics remained economically vulnerable. No matter how many hands Jackson shook at his levees, his political ethos didn't do much for laborers struggling to make ends meet. Skilled tradesmen still eked out a meager existence, sometimes sufficient for survival but more often hampered by the lack of commerce and industry in the District. Unskilled laborers had to make do with seasonal work that depended on whether congressional funds, private capital, or lotteries could get a construction project started or keep one going for more than a few months. Everyone lived under the constant threat of the next economic bubble or "panic" that could put workers out of work and into the poorhouse. This unsteady state was most apparent in how and where people lived.
Capital Enclaves
The houses of Washington City were scattered widely over the terrain, making for a crazy quilt of farmland, log cabins, simple frame houses, and planter estates more akin to a rural landscape than anything urban. In 1800 the city had only 372 houses, most wooden but a good number brick, and this number increased to 2,346 by 1823. Many workers lodged at taverns or boardinghouses, with multiple men and sometimes entire families jammed into spaces meant for far fewer people. The lack of affordable housing caused the construction grounds around the Capitol and President's House to mushroom with dumpy wooden huts, giving a dismal cast to even the finest landscapes of the District. Even "permanent" structures looked ramshackle and temporary, including an array of one- and two-story frame houses and tiny wooden hovels that resembled booths at English country fairs, stuffed with up to eight people inside.
The Patent Office looming over the chockablock buildings of downtown Washington City in 1846.
As the years progressed, the larger houses were subdivided and their yards filled in with smaller, often dark and cramped back-buildings that lined the interior streets and alleys. This created a neo-medieval but characteristically Washingtonian housing pattern that bred disease and claustrophobia during the next century. In more established cities like Georgetown, housing conditions for workers and the poor didn't rate much better. Some single-story wooden houses contained as little as two hundred square feet lit by two small windows. Some of the crudest structures had walls of planks or logs, the smallest no more than ten feet square.
Amid this landscape of scattershot development, a few pockets of dwellings made for what some called neighborhoods, but they were really more like tiny enclaves where ethnic groups crowded together, rudimentary gangs established hangouts, and feral children roamed in packs. Samuel Busey's nostalgic Pictures of the City of Washington in the Past and Constance Green's urban history provide a glimpse into some of the more colorful redoubts:
* • Camp Hill, near the US Observatory, the local lovers' lane
* • Chicken Cock Hill, part of the former Carroll estate that became contested turf for rival groups of stone-throwing children
* • Chronic Row, north of Foggy Bottom, home to "chronic drinkers and fighters"
* • English Hill, northeast of downtown, small weedy area with its own street gang
* • Frogtown, south of the Capitol, known less for amphibians than for its street gangs
* • The Island, mostly downtrodden area southwest of the city canal, which acted as a moat between it and the rest of town
* • Night Hawk Hill, northeast of the White House, a favorite place for hunters to shoot the eponymous birds
* • Northern Liberties, north of downtown, known for its market, firehouse company, and street gang
* • Paddy Mageetown, north of Foggy Bottom, named for a mythical Irish tavern keeper and home to "good drinkers and a jolly set"
* • School House Hill, between Georgetown and Washington City, where children battled and "the weapons were stones, and cut heads were the usual casualties"
* • Shinar's Lake, southeast of Capitol Hill, one of many disease-breeding swamps
* • Swampoodle, half a mile north of the Capitol, notorious Irish slum built over the Tiber Creek marsh
Traveling from one of these areas to another—to go to work, visit a favorite tavern, or hunt down a rival group of schoolchildren—was no easy task in Washington City. The distances were ridiculously long, the streets uniformly terrible, and the landscape littered with swamps, gullies, and rocky outcrops. You could get around, though, if you had a few cents.
Taking the Low Roads
Coming in to Washington City from the Potomac shoreline, Anne Royall rode in a "carry-all," a sort of stagecoach that could hold up to twenty people and conveyed its passengers under the power of a pair of draft horses. Several irregularly scheduled omnibus lines operated around town, and on a typical trip, for twelve and a half cents, a rider could expect to be jostled to the point of nausea in a cramped wooden box at the mercy of a driver going much too fast for the capital's miserable, mire-choked roads. Smaller hackney cabs cost a little more, between twelve and twenty-five cents, and, though the city established exact rates, unscrupulous drivers often hid the official rate sheet and charged up to four times as much.
If you wanted to get out of town and away from the heat and dust of the capital, taking a stagecoach was a more expensive proposition. During the early nineteenth century, it cost three dollars (almost a week's wages) to take a trip from, say, Georgetown to Annapolis. But riding in a stagecoach over any distance amounted to slow-moving torture, as Thomas Twining recounts in his Travels in America 100 Years Ago. Not only was the road itself "in a very rude state," full of stumps and mud, but the passengers were mashed together in the wagon to prevent it from overturning, and the "obscurity and suffocation" of the vehicle's interior was "very dark and oppressively hot, there being no aperture for light and air excepting the front."
Mechanic Gastronomy
If a coach ride lay beyond the means of the mechanics of the District, so too did a good meal. Taverns commonly offered sustenance for all classes, as we'll see, but workers had fewer options at home. They could put soup and vegetables on the table, but hardly any of them had more than spoons with which to eat; knives and forks were uncommon. Most people had plenty of chairs on which to seat their guests around mahogany tables, but the majority didn't have tablecloths to cover them. The food served on those tables was bland and monotonous—bread, bacon, sweet potatoes, and cabbage—but diners did have the option of nineteenth-century takeout: One Alexandria business sold hot mutton, beef, veal, and chicken pies for those who didn't feel like cooking.
Of course, dining out anywhere was a luxury, and gourmands typically had to make do at one of the markets in town. By the 1840s the District had four of them, one on Capitol Hill, one at the Navy Yard, and two downtown. At the better markets and certain groceries you could find a variety of meat and fish, fruits and vegetables, nuts and spices, wine and pastries, and even oysters and wild mushrooms. Despite the variety of options on site, buyers often griped about prices, which could exceed the budgets of many laborers. In the summer of 1820, for example, a bushel of potatoes cost between fifty and seventy-five cents, as much as a daily wage for some.
The largest emporium, the legendary Centre Market, bordered the city canal on 7th Street and began at the turn of the nineteenth century. Known as the "Marsh Market," it was built on Tiber Creek swampland at one of the lowest points in the District, and as it grew it expanded over the reclaimed mire. Charged an annual fee of just ten dollars for renting a market stall, sellers flocked to the popular market and brought a bounty of goods. Librarian of Congress George Watterston claimed "the quality and abundance of the commodities brought there for sale, is not excelled by any market in the United States"—an exaggeration, but it was one of the biggest in the Chesapeake region. Jefferson even maintained a seasonality chart that showed which of the market's thirty-seven different vegetables were available when. It directed him to buy sprouts from February to May, asparagus from April to June, and radishes from September to December. Less appealingly, in a live-fish market at the back of the complex, fishmongers kept their selection "fresh" in baskets lowered into the fetid waters of the city canal.
Centre Market, the famed meat and produce emporium, stood for nearly 130 years in various forms.
The market sat at one of the liveliest corners in town, adjacent to an energetic street scene where Washingtonians gambled, ate and drank, caroused, and sometimes fought. Theaters, saloons, and restaurants lined Pennsylvania Avenue here, along with messier butcheries, tanneries, and woolen mills. Area undertakers announced their services with wooden coffins propped up on the sidewalk. The market's popularity made it the center of chaos: An array of tumbledown huts and shacks littered the street; sellers hawked their wares from rickety frame sheds; and produce wagons backed up traffic to 11th Street. But the market offered chaos with a purpose: By paying rent to the town, the vendors provided one of the few reliable sources of municipal income. After the Civil War, the site grew into the largest and most modern food market in the country.
Popular Distractions
Also along this busy stretch of avenue, a goodly number of amusements gave the mechanics a break from their toil and bland diets. Although violent forms of "entertainment" like fistfights and blood sport were well established by the mid-nineteenth century (as we'll see later), less aggressive pursuits were also on offer.
In the 1790s, for between twenty-five and seventy-five cents, a Georgetowner or Alexandrian could drop by a local tavern like Suter's or Ward's and catch an itinerant theater troupe performing a recent play, with musical interludes for those who wanted to stretch their legs and dance. On view might be a stirring drama such as The Roman Father; or, He Saved All Who Saved the State, a farce such as The Devil to Pay, or a rousing selection of "Republican Songs of Mount Vernon and the Land of Freedom." The shows often included material from British authors, with various Shakespearean plays, comedies of manners, tear-jerking melodramas, and a "historical pantomime" of Robinson Crusoe making appearances.
A more permanent theater came into being just after the capital did. On its opening night in 1804, the Washington Theatre, a major draw, promised to delight crowds with a "Grand Medley Entertainment" of assorted "songs, magic, dancing and acting automatons, mechanical pictures, and spectacular effects." That theater lasted until 1836, when the National Theatre, founded the year before, put it out of business and became a theatrical institution. The National Theatre offered a similar repertoire and a shifting seating design. At first the lower classes occupied the parterre (floor seating), with the elites in boxes above, as in Elizabethan England. But once the theater owners realized that some of the best seats were down below, they redesigned it, moving working-class folk to the upper balcony—where there was a convenient saloon—and putting black theatergoers even farther back on the most distant, third level, a segregation policy that lasted until 1952.
The theater business was a rough trade. Actors were paid minimal sums and had to travel by crude wagons or on foot between venues. Newspapers largely ignored theatrical performances, except for displaying their ads. Most of the venues, though well attended, left a lot to be desired. When the National opened, Frances Trollope complained it was "astonishingly dirty and void of decoration, considering that it is the only place of amusement the city affords." Audiences were rowdy at best, disdainful at worst, prone to "loud talking, whooping, hee-hawing, swearing" and yelling "Hats off in front!" As Trollope reports:
One man in the pit was seized with a violent fit of vomiting, which appeared not in the least to annoy or surprise his neighbours. . . . The spitting was incessant; and not one in ten of the male part of the illustrious legislative audiences sat according to the usual custom of human beings; the legs were thrown sometimes over the front of the box, sometimes over the side of it. . . . In many instances the front rail was preferred as a seat.
The crowd knew what it liked, and it particularly liked theater legend Edwin Forrest, who made triumphant appearances in Washington City in the 1830s in an assortment of Shakespearean roles, delighting theatergoers with his punchy, emphatic style. He wasn't what you'd call naturalistic, but he did send the crowd into a frenzy with his "explosions of physical action" as he showcased "the vital, burly, aggressive Americanism of his age" —which of course reflected the behavior of much of the audience.
Related Diversions
Theater wasn't the only amusement in town for mechanics with a little spare cash. One of the first circuses appeared in the 1790s, featuring rope dancing and "comic feats on horseback" by a husband-and-wife team with a "Polander Dwarf too and a trained horse known as Cornplanter." George Washington even made an honorary appearance in the audience. Traveling circuses also came to town, with names such as "The Grand Caravan of Most Rare and Interesting Animals," which advertised their exotic beasts and charged visitors a quarter to see leopards, monkeys, tigers, and zebras. The National Theatre itself briefly became a circus in 1844, "the pit becoming an amphitheatre for clowns, trained horses, and educated dogs."
Just a few years later, panoramas—huge sheets of painted canvas—provided the first "moving pictures" long before the invention of cinema. For fifty cents, viewers could watch exotic foreign scenes or heroic continental landscapes unwind across giant cylinders in dramatically lit rooms. On tour in Washington City in April 1850, Henry Lewis's panorama depicted Mississippi River scenes on a colossal scroll a mile long, among the largest in America or Europe. In the crowd sat President Zachary Taylor, who gazed at evocative scenes that included his own Cypress Grove estate, one of the last times he "saw" his plantation before dying two months later.
For less enlightened pursuits, the District had a number of racecourses that drew a wide mix of gamblers. Christian Hines recalls several popular tracks where bettors could watch stock horses compete in the heat and dust of graded farmland near cornfields and apple orchards. As one reverend who attended a race in 1803 recalled, the spectators were "three and four thousand, black, white and yellow; of all conditions from the President of the United States to the beggar in his rags, of all ages and of both sexes, for I should judge one-third were females."
Wagering offered a great amusement for all corners of society, whether that meant senators playing whist, merchants betting on cards in a tavern, or laborers speculating on which rooster would hack the other to pieces. In most American cities in the early nineteenth century, the most popular games included Hazard, which involved slamming boxes of dice on a well-worn tavern table; Brag, a card game like poker; and Faro, a table game with intricate rules. The District had harsh laws against gambling, but the authorities usually ignored them unless someone needed to go to court to get his money back from a swindler. The pastime was so visible throughout the District that the most prominent stretch of Pennsylvania Avenue was "lined with faro banks, where good suppers were served and well-supplied sideboards were free to all comers." As Anne Royall wrote, "Gambling, and play of almost every description, is almost wholly exploded in Washington at present, and (I am sorry to add) I wish I could say the same of other vices.
Crank for the Ages
With her trenchant commentary, Anne Royall continued to play a notable role in the District in the 1830s, tormenting her enemies with her gadfly prose and acting as a keen, sardonic observer of the changes taking place. She soured on the Jacksonians by the later part of the decade, using her publications Paul Pry and The Huntress—arguably the first muckraking papers in the country—to inveigh against corruption and fight against atrocities like "Post Office frauds," "Indian land frauds," and "the abandonment of Reform by General Jackson." For her uniquely abrasive style and scabrous opinions, her rivals called her a "public nuisance," an "old hag," and a "crank." Insults escalated to violence when a crazed bookstore clerk in Pittsburgh whipped her bloody with a cowskin, and she barely escaped an angry mob in Charlottesville, Virginia.
Undaunted, this small, elderly woman continued to stir the pot, exploring and writing about the various regions of the expanding nation. She provided detailed descriptions of the best and worst of the American character, including the myriad run-ins she had with any number of people. Although not the most even-tempered witness to her times, she gives a clear picture of the violent, ragged world of Washington City in the antebellum years, imparting details of the social and cultural life of the capital that might otherwise have been lost to history or obscured by more reverent writers. That's one reason, among many, that her work seems so engaging and lively today, while the writing of her contemporaries often feels so dry, musty, and dead. Not surprisingly, thanks to her vitality, she outlasted many of her adversaries and the obstacles they put in her path, and finally received her husband's pension in 1848—at the age of seventy-nine.
Four
Driving Souls
Perceptive as she was, Anne Royall couldn't overcome the great moral blind spot of her age: slavery. She firmly opposed the institution in print, but she held slaves at various points in her life along with a wary view of abolition. Like her, many intellectuals of the era ought to have known better, but they instead chose to rationalize a practice that even casual visitors to America knew caused limitless human suffering and terror. Washington City served as one of the nation's most prominent depots of slave trading, but the town's guidebook writers barely mentioned it. In this respect, Anne Royall fell squarely in line with the shameless civic boosters she despised.
Slavery came to the English colonies in 1619 when a Dutch trading ship brought twenty slaves to Jamestown, Virginia. Tobacco planters favored forced human labor to cultivate their cash crop, but by the end of the eighteenth century, tobacco cultivation had largely become a dead letter along the Potomac. Farmers had exhausted the soil on many of the old plantations, and the agricultural infrastructure was collapsing. Slavery, however, persisted.
In 1800 African Americans made up 29 percent of the District's roughly 14,000 people, with 80 percent of their number enslaved. Few free blacks owned property in the capital or held prominent occupations. (Benjamin Banneker, Andrew Ellicott's surveyor assistant in 1791, had been a rare exception.) The laws of Maryland and Virginia, which held sway in DC until the 1830s, severely limited them with a broad range of codes and restrictions. In Virginia, freed slaves couldn't even remain in the state, which gave them six months to leave after their manumission or risk being sold back into slavery.
Forced labor was common enough in Washington City that contractors used slaves to build the Capitol. This fact went unremarked in histories of the District throughout the nineteenth century, but in more recent decades the weight of evidence has made the conclusion unavoidable. Even Congress itself had to recognize the truth when in 2009 it produced a formal resolution that included the following introductory clauses:
Whereas enslaved African-Americans provided labor essential to the construction of the United States Capitol;
Whereas enslaved African-Americans performed the back-breaking work of quarrying the stone which comprised many of the floors, walls, and columns of the Capitol;
Whereas enslaved African-Americans also participated in other facets of the construction of the Capitol, including carpentry, masonry, carting, rafting, roofing, plastering, glazing, painting, and sawing;
Whereas the marble columns in the Old Senate Chamber and the sandstone walls of the East Front corridor remain as the lasting legacies of the enslaved African-Americans who worked the quarries. . .
. . . therefore a plaque would be placed in the visitor center.
As admissions of guilt go, it wasn't much. But at least it put an official imprimatur on our understanding of just how fundamental slavery was to the District. Indeed, the very presence of the "peculiar institution" in the capital served as a symbol for all the contradictions of a place where the defenders of human bondage and the champions of personal liberty not only coexisted but bizarrely were often one in the same.
Slavery Calculus
American slavery didn't belong exclusively to the province of white-suit-wearing, mint-julep-swilling plantation masters in Greek Revival mansions on the banks of the Mississippi. Instead, it was an endemic transnational phenomenon that connected the "slave supply in Virginia, credit availability from New York, cotton prices on the Liverpool market, and the prices and demand for slaves at New Orleans and Natchez."
Numerous corporations took part in this complex financial web of buying and selling human beings. Modern descendants of those companies include investment banks such as Lehman Brothers; railroads Norfolk Southern and CSX (which took over the B&O Railroad); publishers Knight Ridder, Gannett, and Tribune Company; and insurance carriers Aetna and AIG—and that doesn't take into account the many institutions, including the nation's oldest and most prestigious universities, that invested in and therefore profited from the companies doing the dirty work.
With the mortality rate for humans used as chattel as high as it was, a range of insurance companies issued policies to slaveholders to protect their "property," including one in 1856 that cost $2.00 to insure a ten-year-old domestic worker and another that cost $5.50 for a middle-aged adult slave. Carrying the calculus of human bondage further, D. B. Warden notes in his 1816 Washington City guide that the daily expense of a slave, which took into account food, drink, clothing, and insurance, totaled "nearly twenty-seven cents." Washington City taxed the owners of male slaves aged fifteen to forty-five $1.50 each and comparable females a dollar.
Once established, slavery inevitably required a fully integrated network to support it: Owners had title to fellow humans; traders trafficked in such "commodities"; companies created infrastructure to support that economy; local governments regulated the trade with laws and taxes; and the national government tied domestic slavery to foreign trade, principally with Britain. All these aspects of the slave trade united in one place: the American capital itself.
The Architecture of Confinement
In 1800 slaves were visible on area plantations and at occasional slave auctions, but not to the degree that came after Congress banned the transatlantic slave trade in 1808. That ban wasn't as high-minded as it sounded: It had less to do with abolishing the barbaric practice than with increasing the value of slaves already present in North America and fostering an increasingly lucrative domestic trade.
By the middle of the next decade, a boom in cotton sales and production in the Deep South created a yawning demand for slaves nationwide, with Alexandria and Washington City quickly taking advantage. Within two decades the region had transformed itself from a sleepy backwater with a scattering of slaves on shambling farmsteads into a fearsome juggernaut of slave trading, the "great Man-market of the nation," according to a famous broadside.
Abolitionist broadsides decried the sale of human beings in "the land of the free." See next page for detail images.
The port of Alexandria in particular became a hub for the delivery of slaves from Philadelphia, Baltimore, and other American locations. The Virginia port also shipped out men, women, and children born and raised in the capital area as captives to plantations and other sites around the country. Ship manifests from the late eighteenth and early nineteenth centuries provide physical descriptions of their human cargo with elliptical yet revealing notes. Along with age, height, and skin tone—"dark," "brown," "light," "fair"—slaves are identified by the scars on their bodies. In one case, sixteen-year-old Alexandria native Jonathan Horne had a lump on his lower lip, a smallpox mark on his chin, a mark of unknown origin on his left arm, and a "crossmark by the bite of a dog on his left cheek." Other slaves exhibited telltale burns, cuts, pricks, scars and "red marks" across their bodies.
One of the largest landowners was Notley Young, his acreage occupying almost all of Southwest Washington City in a sprawling estate worked by sixty bondsmen housed in eleven buildings marked "Negro quarters." A typical slave quarter might contain "pens" made of rough logs, with walls, fireplace, a roof, and little else. Only fourteen by sixteen feet in size, such a cramped wooden box may have held up to ten people. Bondsmen planted and harvested crops of various kinds and brought them to market. They assisted in the operation of the estate houses by cooking, sewing, cleaning, and undertaking other household chores. They built new outbuildings and fixed old ones and generally performed the labors necessary to make the farm profitable.
Even free blacks could be sold into slavery.
The Alexandria prison where slaves were held until being sold to plantations in the Deep South.
More numerous than the planters, though, were common slaveholders, who usually had only a few slaves they used as domestic workers. Some stayed in their masters' attics, stables, or carriage houses, but in other cases the middle-class house itself served as a sort of prison. Back yards essentially became slave spaces, often with a two-story outbuilding with kitchens, laundries, and other service rooms on the ground floor and sleeping quarters above. Confined by high brick walls up to a foot thick, forced laborers found themselves trapped away from public view, in isolated rooms without windows, and corridors without exits. Inside this harsh, inhuman space, "the bondsman could see only a maze of brick and stone, the forbidding reminders of his servile confinement."
Newer urban houses for the elite replaced the old plantations with stylish architecture in front and hidden slave quarters in back. One of the most prominent examples, John Tayloe's Octagon—which had six sides instead of eight—was among the most famous private houses in Washington City. Designed by Capitol architect William Thornton in the Federal style, it hosted ambassadors and treaty signings and served as the residence of the president after the British burned the White House. Its high walls enclosed a two-story structure for slaves and outbuildings, which included a stable, smokehouse, and cowshed. It also had a basement with a kitchen and a warren of narrow little rooms and work spaces. While slaves labored in the hot, choking confines belowground, "men in their picturesque costumes [and] ladies in their Empire dresses of soft silk" danced "graceful minuets" on the floors above.
Rise of the Slavemongers
But slaves who had the misfortune to pass through the District, instead of living there, had it worse. Everyone knew what awaited bondsmen sold to the Deep South, say, to a mosquito-infested Louisiana sugar cane plantation or, more likely, an industrial cotton operation in the wilds of Alabama and Mississippi: isolation on a remote farmstead, the violence of the lash, years of crushing labor, and often an early death. Masters in the capital used their slaves' knowledge of the terror of being sold to the Deep South as leverage beyond the whip, or shipped them away without a second thought if there wasn't enough work available.
Isaac Franklin, one of the District's upstarts, founded his slaving operation in the capital with his nephew John Armfield (along with partner Rice Ballard outside DC) in 1828. It was the first and most notorious of five successive slave-trading firms to operate from the same headquarters in Alexandria, the last operating until the Civil War. The Franklin and Armfield business initially acquired capital from a range of national banks to buy slaves from the decaying plantations of Maryland and Virginia. From there, they sent their human cargo to New Orleans and Natchez, then routed their profits back through banks in New York and Philadelphia. They fiendishly converted human beings into commodities, whether "packed onto slavers' brigs like cordwood, imprisoned in cholera-infested Natchez pens like cattle, or displayed on the market like wool and ivory." They used that last phrase, "wool and ivory," as shorthand for blacks in general and developed a range of euphemisms to describe both their business operations and those whom they shipped into bondage. One such term was "fancy maid," which, despite its winsome connotations, referred to a woman sold for carnal exploitation, to be kept as a sex slave for planters or otherwise raped by the traders themselves. To this end, the slavers impudently called themselves "one-eyed men," in crude reference to their genitals.
The traders didn't open their prison to the general public, but they weren't exactly discreet, either. One of their advertisements in an Alexandria newspaper promised CASH FOR 500 NEGROES:
Including both sexes, from 12 to 25 years of age. Persons having likely servants to dispose of, will find it to their interest to give us a call, as we will give higher prices, in cash, than any other purchaser who is now, or may hereafter come into this market.
Professor E. A. Andrews, a fervent critic of slavery, received a rare private tour of Franklin and Armfield's slave pen. It was the early American equivalent of a publicity tour for a prison, with inmates lined up for inspection, "the most studied attention paid to cleanliness" of the facility, and the slave traders acting as witty, gracious hosts. But Andrews saw the great lie for what it was, a testament to the "countless evils occasioned in this world of sin and misery."
The slavemongers couldn't fully conceal their horrors from the general public, and more than a few residents found it contradictory at the very least that those operations should spring up in a town that billed itself as a paragon of liberty. One man, Solomon Northup, whose story of being kidnapped into Southern slavery, Twelve Years a Slave, has become quite well known recently, recalls looking out from the windows of a holding cell to see a familiar building: "Strange as it may seem, within plain sight of this same house, looking down from its commanding height upon it, was the Capitol. The voices of patriotic representatives boasting of freedom and equality, and the rattling of the poor slave's chains, almost commingled. A slave pen within the very shadow of the Capitol!"
Even more conspicuous was the sight of slave drivers forcing their gangs through the street with "the whip of the slave-driver and the clanking of chains" providing the soundtrack as "the gangs were kept together and driven like sheep under the watchful eyes of their brutal guards." In regular public human auctions, slavers broke up families and parceled them out to different parts of the country, stripped and revealed the naked bodies of their captives before the eyes of eager buyers, and even forced them to dance to showcase their "liveliness." Such inhumanity composed a typical day's work for the men known as "soul-drivers."
Slaves in leg irons being marched off to auction were a common sight in prewar DC.
Private Prisons
The drivers held their captives in notorious slave warrens in cellars and basements of houses, hotels, and taverns, carefully confined away from the public view. The Williams Slave Pen sat across from the Smithsonian grounds, a three-story, "pleasant looking" brick house in which slaves were tightly shackled in a holding room next to the kitchen. The pen at Robey's Tavern was a "wretched hovel" near the Capitol with no air circulation, oppressively hot in summer and frigid in winter, its conditions worse than regular jail cells. The St. Charles Hotel contained subterranean rooms with six thirty-foot-long barrel-vaulted cells with iron rings attached to the walls to secure the captives. It even advertised its services: "The Proprietor of this hotel has roomy underground cells for confining slaves for safe keeping, and patrons are notified that their slaves will be well cared for. In case of escape, full value of the Negro will be paid for by the Proprietor."
"Well cared for" is an audacious euphemism—most accounts of these prisons describe people forced to sleep on cold floors, chained to walls, whipped and beaten by overseers, stuffed into gloomy cells, and unprotected from vermin or disease. During an 1832 cholera epidemic, the number of deaths at one slave pen reached such a number "that both coffins and undertakers were insufficient to fill the demand, and they were obliged to send to other cities for help."
The Picture of Cruelty
As the slave trade became more visible, some began calling for change. One event in particular crystallized many opinions against the practice. In 1815 a black woman, name unknown, jumped from the third-story window of a downtown tavern where she was being held and broke her back and both arms in the fall. She was desperately trying to escape the men who had confined her and to keep from being separated from her husband and children—to no avail. The story spread widely thanks to Jesse Torrey's seminal book A Portraiture of Domestic Slavery, in the United States, which not only brought attention to the cruelties meted out to slaves but also to the kidnapping of free black citizens.
Torrey had spoken to two such individuals, Delaware residents, whom the slavers had kidnapped and held in the same tavern from which the woman had leapt. He then went a step further and raised funds for their legal defense, and a few months later a court freed them. This episode wasn't isolated. Critics of slavery claimed the traders' primary goal was to "kidnap every colored stranger they could lay their hands on," and the burden of proof lay on black citizens to prove they were free. If they didn't have the right papers, they could be arrested and sold at auction. Even if they did have proof but were arrested mistakenly, they could still be sold as slaves if they couldn't pay for their room and board while wrongly imprisoned.
The sight of captives manacled and dragged through the streets, the horrific conditions of the slave pens, the division of families at auction, the kidnapping of free blacks—these atrocities led many to call for the end of slave trafficking in the capital. One of the most vocal was John Randolph, House member from Virginia, an active slaveholder and ardent states' rights champion, who nevertheless saw slave trading as "a crying shame before God and man, not surpassed in abomination in any part of the earth; for in no part of it, not even excepting the rivers on the coast of Africa, is there so great, so infamous a slave market as in the metropolis, in the seat of government of this nation which prides itself on freedom."
Judge James Morsell of the Circuit Court conducted a judicial investigation on the legality of "manacled captives" being driven through the streets, seeing it as "repugnant" to the spirit of the republic and the rights of humanity. Jesse Torrey called for Congress, as "guardians of the public liberty," to ensure that free blacks were not kidnapped or otherwise abused by the traffickers. Washington City citizens, including a number of slaveholders, presented a petition to Congress in 1819 demanding an end to the transport of slaves through the city and their shipment from it. To these carefully worded calls, petitions, and entreaties, members of the national legislature considered this great moral question, took stock of the weighty issues—and did nothing.
The Colonial Gambit
In the absence of congressional action, it appeared that the nation's leading politicians might find a different way to end slave trafficking. Just before Torrey's polemic against the trade appeared, figures such as John Randolph, Henry Clay, and Daniel Webster staged the first meeting of the American Colonization Society. With Torrey himself claiming credit for the idea behind the group, the society stated its goal as bringing about the demise of slave trading and similar practices by founding an African colony that would take in blacks from America and develop a sort of model society of freedmen. In 1820 the first waves of expatriated blacks began arriving on the western coast of Africa, and two years after that they founded the new country of Liberia. They named their capital Monrovia in honor of then-president James Monroe, author of the political doctrine that forbade European colonization of or interference in the Western Hemisphere but helpfully said nothing about American colonization of or interference in the Eastern Hemisphere.
Leading opponents of slavery supported the society, as did leading slaveholders, but the group favored getting rid of the public eyesore of slave trading rather than eradicating the institution itself. It never wanted to free slaves but to ship free blacks to Africa. Thus the group's dual purpose, according to critics, was salving the conscience of whites troubled by signs of the slave economy and reducing the number of free blacks in America who might threaten that economy. Which explains why major slaveholders such as Randolph, who owned hundreds of people, supported and belonged to the group.
Fighting the Plague
By contrast, the District's first real abolition movement took as much of a stance against colonization as it did slavery. Activists in the movement suspected the society of trying to ship the most ardent black opponents of slavery out of the country in order to strengthen the business of human bondage. Educator John Prout denounced moves to remove blacks from the only country most had ever known—the native country of many—and leading black figures from Baltimore, including teacher Jacob Greener and minister William Watkins, attacked the society in print and in public forums. They advocated a branch of abolition called "immediatism" to counter the gradualism that wasn't making much progress against the moral scourge.
Among the most famous abolitionists in the Chesapeake region were Benjamin Lundy and William Lloyd Garrison. Lundy, a white Quaker, published his weekly Genius of Universal Emancipation in the Midwest before moving to Baltimore in 1824. There he worked with Greener and Watkins to print the newspaper and got into all manner of altercations with local slaveholders. He denounced one who brutally beat him in return; in court the judge called the beating a "merited chastisement" and let the slaver off with a dollar fine. Lundy left Baltimore soon after, finding Maryland's "spirit of tyranny . . . too strong and malignant for me."
Garrison wrote for Lundy's paper before he famously began his own antislavery newspaper, The Liberator, on January 1, 1831. In it he denounced both African colonization and gradual abolition as wrong-headed and counterproductive ideas. In that first issue, he didn't mince words about the capital:
That District is rotten with the plague, and stinks in the nostrils of the world . . . a fouler spot scarcely exists on earth. In it the worst features of slavery are exhibited; and as a mart for slave-traders, it is unequalled. These facts are well known to our two or three hundred representatives, but no remedy is proposed; they are known, if not minutely at least generally, to our whole population,—but who calls for redress?
The answer of course was Garrison himself. However, while the columnist activist had a huge impact on the nation, he did most of his pioneering work from New England, and many of his opinions—which favored women's rights and nonviolent protest and condemned American politics and organized religion—lay so far ahead of their time that many abolitionists, both black and white, kept their distance, seeing him as a distraction from their primary goal.
These abolitionists had more important matters to worry about than Garrison, though. They operated in a place hostile to their goals at best, at worst malicious and violent. Their protests often met with fists, bricks, knives, or guns. One of their prime enemies was slave trader Hope Slatter, notorious for separating black families at the auction block, abusing slaves and their rescuers, and inciting mobs to attack abolitionists and blacks in general. The threat that Slatter and many like him presented had the paradoxical effect of binding black and white activists together, whether "as victors over slaveholders or victims of their wrath."
Mob Mentality
By the 1830s racial violence spread beyond those with a direct economic interest in slavery to larger sections of the white public, who took alarm at the competition that black emancipation might introduce to the white working classes. Throughout the North, mobs attacked abolitionists and free blacks in churches and their homes, with conflicts in 1834 in New York City and Philadelphia turning especially fierce.
The next summer in Washington City, the simmering climate of racial hostility increased as rumors flew of a slave attacking his master after being caught stealing. It worsened when officers arrested Reuben Crandall, a botanist and physician, for possession of abolitionist literature. District Attorney Francis Scott Key—composer of "The Star Spangled Banner," promoter of African colonization, and enemy of abolitionists—charged him with sedition and threw him in jail. In response, a mob of four hundred mechanics, including many striking laborers from the Navy Yard, converged on the jail to "take the damned rascal and hang him up on one of the trees."
Finding him well guarded and inaccessible, the mob moved on to Beverly Snow, a black restaurateur, who allegedly had insulted the wives of white mechanics. Again not finding their intended victim, they settled for ransacking Snow's restaurant and destroying several black homes, schools, and churches. Before the mob could march on the city's public buildings and destroy them too, soldiers were called out to be "posted at their doors, and their windows barricaded, to defend them against the citizens of Washington." When the tumult subsided, the city council took quick action, not by enforcing laws against mob violence but by cracking down on business licenses issued to free blacks and by imposing other sanctions on them.
Gag Reflex
Amid the chaos, some abolitionists continued to hold out hope that Congress would see the damage wrought by this social crisis and end slavery in the capital for good. In the mid-1830s they sent the government 100,000 petitions arguing for the abolition of slavery in DC, and by the end of the decade another half-million signatures arrived. Again, the gridlocked legislature failed to take action. Southern members vowed to defend slavery at all costs and even threatened the dissolution of the Union if they didn't get their way. One measure that did break the gridlock and pass the House was the infamous gag rule, which prevented any petition related to slavery in the District to be read or discussed.
Around the same time, William Lloyd Garrison's American Anti-Slavery Society mailed one million pamphlets to Southern editors, businessmen, and others to illuminate them on the topic of slavery. The pamphlets had their intended effect: The Southerners held great public bonfires with the mailers as fuel. The South saw the elimination of slave trading in terms of domino theory: Abolishing that institution would cause other established social traditions to tumble in an unbroken path that would lead invariably to the demise of the plantation system and of white supremacy.
Antislavery politicians of the North countered with a more immediate issue: They wanted to get rid of DC slavery because Northern tax dollars were financing the capital prisons where slave traffickers kept their captives, a business of which they obviously wanted no part. But the most powerful Northerner, President Martin Van Buren, had a different view. In 1837 he promised to be "the inflexible and uncompromising opponent of every attempt on the part of Congress to abolish slavery in the District of Columbia against the wishes of the slaveholding states." (This exercise in political cowardice didn't win him any friends in the North. In his failed reelection attempt, he lost 158 of the region's 170 electoral votes.)
The federal government was proving to be feckless. No matter the legal violation, the violent event, the moral outrage, Congress and the president chose inertia over action, and when they did act it usually made matters worse for the capital's black residents. In turn, many abolitionists gave up on legal paths to achieve an end to slavery, seeing the law as an impediment—instead of an avenue—to their goals.
Tales from the Underground
The Underground Railroad—a vast, awe-inspiring institution—had a formidable reach into the South. To white Southerners, it represented a conspiracy to deprive them of their property; for Northerners, it gave proof positive of the nightmarish conditions that slaves endured and their determination to escape it. The District of Columbia had one of the earliest and most well-established lines, which years later Frederick Douglass recalled as stretching from the capital to Philadelphia, New York, Albany, Rochester, and finally Canada, the true land of freedom. Before escaped slaves reached any of those destinations, though, they traveled through a shadowy network of safe houses, many of them in destitute areas of Southern cities where they could find shelter and seclusion but police rarely ventured.
The South fought back by limiting slaves' knowledge of local geography, levying steep and violent penalties on escapees, and fostering a counternetwork of professional slave catchers. The Washington Auxiliary Guard, which employed eighteen such men in the District, arrested free blacks for curfew violations and hunted down runaway slaves. As the official history of the police department explains it: "The ringing of the [signal] bell at 10 p.m. was of special importance to the colored people, as after that hour if out without a pass they were subject to arrest, fine, and flogging. The last was administered sometimes at the guard-house and sometimes at the whipping-post of the jail, on the northeast corner of Judiciary Square."
For violating the Black Code, countless blacks faced grim conditions at the city jail.
The Railroad needed daring and clever figures to counteract these measures, and two of the most adept were Thomas Smallwood, a middle-class shoemaker and former slave, and the Reverend Charles Torrey, whom some called "the regular Rob Roy MacGregor of dare-devil philanthropy." Together the two worked to free Southern captives, establishing a wide network that included black and white abolitionists, among them a dentist, a minister, a boardinghouse owner, and an Ohio congressman. In 1842 alone they freed between 150 and 400 slaves in groups of ten to fifteen at a time. Individuals escaped singly or in pairs from bondage and converged at prearranged "places of deposit" around the Washington region, from where teamsters in wagons conveyed them northward. The journey wasn't cheap to arrange; Smallwood and Torrey initially paid teamsters between eight and twenty-five dollars per escapee, later deciding to purchase their own wagon and horses instead.
Slaveholders offered handsome rewards for the return of their "property," so those running the Underground Railroad took care not to trust people unknown to them. Skirting the law and avoiding capture proved hard and dangerous work, yet it didn't stop Smallwood from taunting slaveholders in the pages of abolitionist newspapers that Torrey edited. Using the pen name Samivel Weller Jr. (after a character in The Pickwick Papers by Charles Dickens), Smallwood baited his enemies and mocked them as "poor puppies," among other jabs. Taking care not to be identified, he successfully eluded capture over the years. If people did discover his name, authorities had difficulty finding him amid all the other Smallwoods in Washington City.
Eventually his luck and Torrey's ran out, though. In November 1843 the police came upon their wagon, horses, and fourteen runaways and took possession of all of them. (Torrey brazenly filed suit to recover the wagon and horses seized from their illegal mission.) The police raid ended Smallwood's activities in the capital, after which he relocated to Canada. Later in a memoir he condemned his former country as "hypocritical, guileful, and arrogant" and worse than any other nation in its treatment of black people.
In his own writings Torrey offered an open threat to those holding slaves, saying "God judgeth the heart of each man. I do not. I only affirm the guilt of the sin, and its inconsistency with piety, and warn men to leave it off." He continued his clandestine if increasingly daring liberation of slaves until late 1844, when Hope Slatter arranged for his arrest by Baltimore authorities. From a jail cell Torrey wrote: "The question of my prudence, I must adjourn to Judgement Day. I have done, many things in the South, that prudent men dared not do . . . I am bold & decided. God made me so. He did not make me cautious."
Torrey may have been a zealot, but his zealotry did more to weaken the bonds of slavery in the Chesapeake than all the well-meaning words of politicians or the impassioned editorials of newspaper writers. It came at a cost, though. The reward for Torrey's lack of caution was death from tuberculosis in a Maryland prison in 1846.
The Freedmen's Progress
The Underground Railroad offered the most prominent local means of undermining slavery, but another force had just as great an impact. Its effects were subtle and took many years to accumulate, but in the end they proved unstoppable in undermining human bondage in the District. It was a small but fatal flaw in the mechanism of slavery itself.
From the beginning of the capital's history, Washington City constantly needed laborers to construct public buildings as well as its mansions and other structures. Contractors routinely ran short of workers, and the easiest, most expedient way of finding them was to hire slaves from their masters. In the most visible example, from 1795 to 1801 contractors constructing the Capitol paid slaveholders sixty dollars per month per slave for all manner of manual labor, from carting and carpentry to plastering and painting. Most of the money went to the master of course, but slaves received allowances for working nights, Sundays, and holidays. (This was notably the case for black sawyers on the project; for other trades and unskilled labor, the recompense may have been less.) Around the same time, city commissioners developed a plan for building projects that would pay slaves thirteen cents a day beyond what was owed the master. The commissioners offered this small sum not out of any sense of charity, but because they believed the amount would provide an incentive for bondsmen to work even harder at their backbreaking labors.
From this arrangement, the system broadened beyond the construction trades and increased dramatically in the capital in decades to come, reaching the point at which most waiters, private servants, and many artisans were hired-out slaves. Other Southern cities employed this system as well, if to a lesser degree, and Washington was much more open to it than neighboring Baltimore, which had the least slave hiring of any urban area in the South.
From a purely financial angle, this form of hiring reallocated the labor supply to jobs where demand was highest, and parties to the contracts specified price, length of service, working conditions, and work to be performed. Hired-out slaves often lived on the premises of their temporary employer, whether a ropewalk, tavern, mill, or bakery. But in some cases, to lessen the financial cost of the employer, they found independent housing of their own, often in neighborhoods with many free black residents. It made economic sense to all parties: The slave owner made money hiring out the bondsman, the temporary employer didn't have to pay for housing, and the slave caught a break from the employer's constant watch. While out on their own, slaves could sell homegrown vegetables in the market for small amounts of money, and in certain cases could make a bit more money by hiring their own time—namely, finding their own work, paying their master a certain percentage, and keeping the rest. Richard Wade, in his pioneering study Slavery in the Cities, explains it this way:
Under this arrangement, masters told their Negroes to locate a job, make their own agreement on wages, and simply bring back a certain sum every week or month. The slave, moreover, could pocket any profit he made. . . . Often the owner did not know where his blacks worked; no contract bound master and employer; and no special public supervision governed the arrangement.
Frederick Douglass took part in this system, writing in his autobiography that as a slave he learned to caulk, and then "I sought my own employment . . . made my own contracts, and collected my own earnings." If a slave salted away enough earnings, he might purchase his own freedom and, in less common cases, that of family members. Althea Tanner remains one of the most notable examples of this phenomenon. She sold enough of her garden produce to such customers as Thomas Jefferson that she eventually raised $1,400 for her own freedom and that of twenty-two friends and relatives.
Jonathan Martin, in his key recent study of slave hiring in antebellum America, posits that the will of enslaved peoples was fundamental to this economic system. Specifically, slaves did what they could to control their hiring and used their capacity for work as a means of leverage with their employer. Of course, they took a real risk in standing up for their labor, and they were still subject to physical violence and punishment if they came into conflict with their masters. Nonetheless, in Washington City at least, the economic incentive for slave hiring became too great for slaveholders and employers to resist, and a chain reaction began—well beyond anyone's expectations.
As slaves were hired out, they earned small sums of money above the wages paid to masters; as they gained extra money from that and side jobs like gardening, they could live on their own; as they lived on their own, they developed a sense of autonomy; and when they developed enough autonomy, they bought their freedom. Slave hiring—combined with bondsmen's escapes from captivity and the ongoing sale of slaves from cities to plantations—dramatically reduced the presence of urban slavery as a percentage of the labor force. The census for Washington City told the story:
Year | 1800 | 1820 | 1840 | 1860
---|---|---|---|---
Free blacks | 123 | 1,796 | 4,808 | 9,209
Slaves | 623 | 1,945 | 1,713 | 1,774
Even as the capital's population grew, the number of slaves remained static after 1820, while the number of free blacks increased dramatically. To put it another way: In 1800, one of every five residents of Washington City was enslaved, and by 1860 that ratio had dropped to one in thirty-five.
That said, the long-term effect of slave hiring in reducing the number of bondsmen had nothing to do with the development of a conscience among slaveholders, who still benefited greatly from the arrangement. Masters who freed their slaves had benefited from years of unpaid labor that never was reimbursed. Masters who manumitted slaves in their wills still received the full benefit of slaves' forced labor and merely prevented their heirs from receiving that same benefit. Masters who hired out their slaves received the benefit of years of (mostly) unpaid labor and received a substantial capital gain when slaves paid for their freedom.
But the experience of slavery gave newly freed blacks a commitment to abolishing the system entirely. Many of them lived among current slaves and heard their stories and struggles. In many cases, slaves and free blacks didn't exist as separate, distinct classes but instead overlapped in countless ways in their jobs, families, churches, and neighborhoods. Marriage between free and enslaved blacks was common, making up half the black marriages in the District by midcentury, and churches supported and extended community ties by helping to provide assistance to children if a parent was sold at auction or died.
The Chesapeake had the nation's largest concentration of free blacks even before the capital was built, and as they became a greater percentage of the population they became more active in the abolition movement and the Underground Railroad, which included many important figures who had once been enslaved, such as Jacob Greener, Thomas Smallwood, and of course Frederick Douglass. Slaves hiring out their time not only opened the door to more autonomy, they also helped marshal the forces fighting their oppression nationwide.
Internal Immigrants
Whether formerly enslaved or not, free blacks in the District increased in number as they abandoned the tobacco farmsteads of Maryland and Virginia, where work was hard to find, and came to Washington City in search of jobs. Often these rural areas imposed such harsh limitations on free blacks that relocation was their only choice. Maryland slaveholders even considered them "a standing incitement to servile disorder" and made it a priority to drive them out of the state.
The capital, by contrast, even though it had its own stringent racial codes, as we'll see, became one of the Southern cities most open to black immigration. This distinction alone elevated Washington City above other Southern towns and drew more blacks to the District, which cemented an even stronger community. Most of the work they found when they arrived fell into a few occupations: carter, coach driver, cook, domestic servant, manual laborer, seamstress, waiter, or washwoman. The income from such jobs didn't amount to much—less than 2 percent of total income in the District, though they were 16 percent of the population—but at least it was theirs and not going into the pocket of someone who claimed to own them. Some even became entrepreneurs, selling perfume, baked goods, or seafood, or opening their own oyster houses or restaurants, like Beverly Snow's.
If an antebellum African American saved up enough money, he or she might purchase property in one of the neighborhoods of the District. Particular concentrations of black homeowners cropped up in the southeast District from Capitol Hill to the Navy Yard, the more down-at-heel "Island" southwest of the Capitol, and the slowly expanding reaches of northwest and northeast DC. But poorer blacks lived in alleys with such names as Willow Tree, Goat Alley, and Tin Cup Alley, within tiny rooms in "flimsy frame shacks or converted carriage houses and horse stables behind the more respectable homes of the whites." In this way, the geography of poverty still followed the contours established by the slave quarters behind the old mansions.
The Rock of Abolition
As more blacks gained their freedom and the community expanded, churches played an enormous role in the bonding and cohesion of that community. The first, Mount Zion Negro Church, established in 1814, was integrated, but later churches separated from their white counterparts due to parishioner disgust at segregated seating or at ministers owning slaves. Many of the breakaway institutions and their preachers took overtly antislavery stances, including Daniel Alexander Payne and John F. Cook, both enslaved once and happy to work with Northern and local abolitionists to eradicate the institution for good. Cook's aunt Althea—the same vegetable seller who paid for her freedom and that of nearly two dozen others—freed him as a child, and he became a shoemaker and messenger as well as a minister at Fifteenth Street Presbyterian Church.
Perhaps the most important denomination in the District was Methodism. Wesley Zion Church and African Methodist Episcopal, like the Fifteenth Street church, went well beyond spiritual centers and took part in all aspects of the lives of freedmen as well as slaves. Wesley Zion in particular provided a broad range of help: information on jobs and social services to established free blacks; food, housing, and work for newly freed slaves; Sunday schools and community forums; plus shelter for runaway slaves, training for active abolitionist ministers, and fund-raising for the Underground Railroad.
Education proved especially critical for blacks in Washington City. Slaveholders had tried to deny their captives any sort of enlightenment and prevented them from joining together to transmit information, communicate with the outside world, find ways to escape, or otherwise rebel. But any sort of education for the lower classes, white or black, was inadequate in the District. Numerous private schools existed in the early capital, as did underfunded "pauper schools" for indigent children, but both excluded black children. It took until nearly the middle of the century for the city to fund a few taxpayer-supported public schools, but only about four hundred students enrolled, and unfortunately, again, black children were mostly kept out.
Instead, an array of privately funded schools for blacks arose, and they started even before Washington City itself existed. In the 1790s, Quaker abolitionists funded both childhood and adult education, and the undertaking increased in the 1820s and 1830s as abolitionists fostered a range of schools with biracial instructors. By the Civil War, African Americans funded fifty-two schools in the District, and some of them, such as the Columbian Institute, were quite well regarded. School benefactors put a strong focus on antislavery teaching, and students soon learned from opponents of slavery the importance and methods of eliminating that system.
A frail white New Yorker, Myrtilla Miner ran the most prominent school and received funding from such notable abolitionists as Henry Ward Beecher, Wendell Phillips, and Lucretia Mott. She referred to her institution as "a genteel school for missus of color," but the lessons proved anything but quiet and conventional. She provided her pupils with a potent mix of abolitionism and feminism, tying together the fate of all women and blacks and charging that women were "left to the same degraded position in regard to liberty as the degraded African." She strove to train a new class of black women to become effective, well-trained opponents of slavery south of the Mason-Dixon Line, and to that end the quality of instruction at her school often exceeded the education offered by schools for white students.
Her plan was daring, direct, determined, and doomed. As progressive as he was, Frederick Douglass considered her strategy "reckless, almost to the point of madness," considering the growing hostility from whites in Washington of the 1850s. Sure enough, she and her students soon faced threats and intimidation from racists, legal disputes from landlords, and the deterioration of Miner's health, which she described as "that stage of nervousness and irritability which ends in insanity." Hostility from official Washington and an arson attack forced the school to close in 1860.
The Black Code
The struggles that free blacks faced in education formed a microcosm of their challenges in the District as a whole. Those started with the law itself. In 1808 the capital passed its first "Black Code," which it updated and tightened periodically in later decades, usually after a race riot or major slave escape or rebellion. Many of these criminal regulations derived from archaic Maryland and Virginia laws, while Congress passed additional overlapping laws that only confused the issue. By midcentury the District had such a tangle of racial regulations that it was hard to keep track of them all. Some of the major provisions held as follows:
* • Masters were prohibited from allowing slaves to be hired by contract, and employers from entering into such contracts.
* • Persons undertaking any economic transaction with a slave, but without a license from the slave's owner, were fined two thousand pounds of tobacco.
* • Slaves found away from their homes could be punished with up to thirty-nine lashes.
* • No black person could testify in court against a white person, but he or she could against a fellow black person.
* • Free blacks had to post a bond with the city with testimony from five white witnesses who could vouch for their good behavior.
* • A white woman bearing a black man's child became enslaved for seven years.
* • A white man siring a black woman's child became enslaved for seven years.
* • Slaves, and in some cases all blacks, couldn't bathe in the river, be drunk in public, beg, break the Sabbath, carry weapons, gamble, go out in public after 10:00 p.m., go to church after 10:00 p.m., hold private meetings after 10:00 p.m., hold dances without a license, join "disorderly or tumultuous assemblages," keep barnyard animals, kill game, "ramble," ride horses, run horses in the street, sell "old metals," sell liquor, set off firecrackers, or travel without a pass.
Arbitrary, mean-spirited, and draconian, the District's Black Code represented the accumulated pathology of Washington's fear and paranoia about what a quarter of its residents might be doing at any given time. At fifty-seven single-spaced pages by the middle of the century, it covered just about every possibility.
In the end, such laws proved futile. The same financial logic that created a fully functioning network to support slavery also crippled it. Despite all the restrictions on it, slave hiring prevailed in the District of Columbia as an economic necessity. Even the behavior code for free blacks was only "periodically enforced, usually when whites were anxious over the threat of a slave riot or the protests of abolitionists." Likewise, a prohibition on black-owned and black-run businesses was never effective, put to use only in a climate of fear or retribution. Indeed, no matter how many rigid, punitive clauses the city and Congress added after a riot or revolt, the needs of business owners combined with black determination trumped each edition of the code before it took effect.
Interior of the slave prison in Alexandria, one of several throughout the capital area.
Decline of Slave Power
By the mid-1840s slavery was collapsing in Washington City. Virginia planters and others with an economic interest in slavery took the first step, pushing a bill through Congress in 1846 to return to their state its share of the District of Columbia: one-third of the capital's total square miles. Although disgruntled at the capital's weak economy, they really wanted to add more pro-slavery members to the Virginia legislature against antislavery adversaries on the western side of the state (a clever strategy for sixteen years, at which point those westerners, tired of being pushed around, created their own state: West Virginia). Virginia law mandated forcing out freed slaves after their manumission, which of course only encouraged them to migrate to Washington City, dramatically increasing its free black population, which jumped almost 70 percent from 1840 to 1850. The District developed an even stronger black community, while Virginia slithered further into the slavery camp. The Potomac River had become as much a racial and social divide as a geographic one.
Two years later, in 1848, the schooner Pearl ran adrift outside the capital on a Potomac shoal. A ship owned by a Georgetown tobacco merchant intercepted it, and authorities discovered seventy-seven slaves aboard, who were trying to escape. One of the men who had arranged their failed journey, Paul Jennings, was a free black servant of US Senator Daniel Webster. Riots ensued, in which white mobs attacked the Centre Market, where many blacks worked; destroyed the offices of an abolitionist newspaper; and assaulted Congressman Joshua Giddings, who had defended members of the Pearl 's crew publicly. The recaptured slaves were put into slave pens in Alexandria and then sold into the Deep South, and the terrible public spectacle played out in the capital and on the pages of national newspapers. Northerners reacted in horror; Southerners called for increased legislation and vigilance against all blacks. In Washington City, abolitionists may have lost the Pearl fight, but they helped cement antislavery feeling in the North and, through changing public opinion, won "a strategic victory that further weakened slavery in the nation's capital."
In 1850, perhaps sensing the shifting tide of opinion, Congress finally passed a measure to control slavery in the District—or at least that's what some of its members claimed. Technically the bill prohibited the importation of slaves and their transportation elsewhere. But in practice, those movements could continue in Alexandria, no longer a part of DC, and nothing in the bill stopped people from owning slaves in Washington City, slave pens from operating in its jails and taverns, or chain gangs of slaves from traveling through its streets. It was a paper victory, a feel-good attempt to remove some of the ugliness of human trafficking in the capital while doing little to affect the practice itself. More than anything else, the congressional rear-guard action showed how much the debate over slavery had reshaped public opinion.
The policies of the federal and local government clearly inhibited blacks instead of helping them, but despite such baleful efforts, Washington City was becoming more hospitable, or at least less intolerable, to blacks than almost anywhere else in the South. As with so many endeavors the authorities undertook—from selling houses at auction to creating canals, from providing for the poor to building a functional economy—they demonstrated once again their ineptitude in running a capital. But in this case, their heavy-handed attempts at racial and social control positively, mercifully failed.
The rising class of free blacks stood as the rare positive result from official neglect, inertia, and incompetence, and it proved critical in years to come. For when a new administration came to town in 1861, it found not just planters and slave traders as sworn enemies but also abolitionists and free blacks as potential allies, providing a firm if fragile base for the prosecution of the Civil War, the fight to protect the Union, and the ultimate demise of slavery.
Five
The Company They Kept
In the hardscrabble landscape of Washington City, as slaves, free blacks, and white mechanics toiled at their respective labors, the capital elite were busy enjoying the fruits of their leisure. At one memorable party in 1820, miles from town at a hillside villa, the views evoked "a Tivoli grandeur of atmosphere and Roman landscape . . . like the sybil's rhapsodies to the eye and the soul." A splendid array of the highest echelons of society held court: Maryland planters, country gentlemen, and the District gentry. The guests drank punch by a woodside spring then feasted and sang songs. President Monroe himself laughed with delight, "beating time with his fork" to the lively tunes. Amid the revels, the lord of the house arrived by carriage, his white horse charging through the clover like a thunderbolt. Out stepped the master of ceremonies—Tom Law.
But appearances deceived. The man throwing the resplendent party was anything but rich. Nearly broke, he couldn't even pay his wife alimony. Luckily, the spectacle so delighted and mesmerized his guests that they couldn't help but offer "ready money" to the star-crossed Mr. Law to help him stay afloat—as a gift, of course, not charity.
Law's troubles began with the Greenleaf syndicate and the city canal project, and he remained financially unstable for the rest of his life. But he seemed as though he should be wealthy, and that's what counted. In that respect, he had plenty of company, for most upper-class Washingtonians were well practiced in the arts of guile and deception, developing elaborate codes, etiquette, and manners to create a rigid social pecking order that hid behind a veil of grace and whimsy. Seemingly inconsequential details—from the kind of forks on the dinner table to the method of inviting someone to a party—teemed with meaning and purpose, showing how the elite sorted and ranked themselves. The company they kept, from their elegant soirees to their secret societies, said a lot about how Washington City really operated inside its grand public buildings and palatial mansions. Here, a flair for wit and charm could wield more power than a flush bank account, and a well-deployed smile could conceal the most baleful thoughts or ruthless ambition.
Edge of the Vortex
The guests at Tom Law's party provided a good microcosm of Washington City's upper caste. Its nucleus was the rich planters who owned land and slaves in the District, along with established countryside families who held property dating from the days of Lord Baltimore (and who intermarried like European royalty to preserve their dynasties) and old-time Georgetown landowners and merchants who formed the core of the local elite before the capital was built. But there were other, less expected figures too, including British critics and authors, smartly dressed foreign diplomats, and journalists in favor with the ruling class.
The town's biggest names included Robert Brent, who served as the town's first mayor; Thomas Peter, who built the elegant Tudor Place mansion; William Seaton, who ran the National Intelligencer and served as mayor in the 1820s; John Tayloe, whose slaves tarried underground in his Octagon house; and Elisha Riggs, who set up the eponymous Georgetown bank. But the women of Washington City's elite society were arguably its most important operators, planning its functions, arranging its liaisons, enforcing its codes, and recording its history. Indeed, Mary Bagot, Margaret Bayard Smith, Mary Boardman Crowninshield, and Harriet Martineau stood as some of the District's most incisive writers, chronicling social life in their often voluminous journals and letters.
Martineau in particular—an English intellectual who wrote books on politics, economics, and sociology—proved herself a fine and thoughtful critic of America and a bold supporter of women's rights, secularism, and abolition. (She even traveled south to inform the locals their support for slavery was "inconsistent with the law of God." The Southerners offered a quick response: "They would hang me: they would cut my tongue out, and cast it on a dunghill.") What attracted her to the provincial aristocracy of the District of Columbia is anyone's guess, but the considerable time she spent in Washington City gave her work perspective and insight lacking in the more superficial dismissals of the capital from the likes of Charles Dickens and Anthony Trollope. Her overview of DC society was especially acute. It was
singularly compounded from the largest variety of elements—foreign ambassadors, the American government, members of Congress . . . flippant young belles, "pious" wives . . . grave judges, saucy travellers, pert newspaper reporters, melancholy Indian chiefs, and timid New England ladies, trembling on the edge of the vortex,—all this was wholly unlike any thing that is to be seen in any other city in the world; for all these are mixed up together in daily intercourse, like the higher circle of a little village, and there is nothing else. You have this or nothing; you pass your days among these people, or you spend them alone.
Not overly fond of the capital, Martineau saw it as a place for those "who love dissipation . . . It is dreary to those whose pursuits and affections are domestic." Despite this view, a lot of the high-society action took place in salons and drawing rooms—the few spaces in the early republic that provided women with domains in which they could exercise social power and influence. By contrast, in the public eye, young ladies of distinction couldn't walk through town without a male escort, and precise codes of gender segregation held sway at prominent events like balls and banquets. An independent figure such as Anne Royall obviously broke the mold, but she never belonged to the social set—especially when she revealed secrets like purebred ladies' affection for drinking wine every day, often to excess. Gender conventions began to change in the 1830s, as women became more involved in American politics, especially with the Whig Party, but most elite women still focused much of their attention on private affairs.
The queen of her class was undoubtedly Marcia Burnes, who reigned over her own segment of blue-blooded society . . . despite her embarrassing origin as the daughter of the District's angriest farmer, Davy Burnes. Many in the elite conveniently forgot this fact when she became the wife of John Peter Van Ness, a House representative, general of the city militia, and mayor of Washington City in the 1830s. As Marcia Van Ness, she combined her husband's ties to the District's political brass with her own substantial real estate holdings to become the socialite par excellence. At her parties, ladies and gentlemen commingled with a sense of "freedom and equality," and the Van Ness mansion became the focal point for top-shelf amusements. Its social functions attracted presidents, politicians, and diplomats; its rose gardens featured secluded "lovers' walks" for venturesome paramours; and its elaborate Spanish tile decor, Turkish carpets, and woodwork and tapestries "were the wonder and gossip of their day." Even Anne Royall, a severe critic as any, compared Mrs. Van Ness favorably to John Milton's Eve.
Gilbert Stuart's portrait of David Burnes's daughter at age twenty-three, the future socialite and philanthropist Marcia Van Ness.
Visual Discord
The Van Nesses' peers also built great mansions throughout town, many of them next to the modest dwellings of the poor and working class, regardless of the visual or moral contradictions. Such structures included anything from modest Federal-style houses to such grand estates as Commodore David Porter's Meridian Hill, which was "set in a hundred and ten acres of grounds and required the employment of enough servants, grooms and gardeners to people a small village." (Despite its grandeur, Porter didn't long enjoy it: He was court-martialed seven years after he built the estate and fled to become the commander of the Mexican Navy.)
Plantation tracts and colossal estates like Porter's obviously wouldn't last long in a modern city, but Washington City wasn't anything like a real city in its early days. The rural landholders of Virginia and Maryland stamped their provincial character all over the capital, from the large houses built with stables, gardens, carriage houses, kitchens, and slave quarters, to the style of their hospitality and the fashion of their parties, to their rigid emphasis on class order and place-holding in society. These phenomena only added to the visual mishmash of Washington City: plantations suitable for Chesapeake tobacco farming, public buildings echoing ancient Rome, a street layout in the style of Baroque France, shambling log cabins like those on the western frontier, and wretched shacks and hovels as bad as any urban slum in America.
Reign of the Gourmands
Other contrasts emerged as well. Common folk had to content themselves with diets consisting mostly of bread, cabbage, and sweet potatoes, but upper-crusters had a cornucopia of delights with which to stuff themselves. Attorney General William Wirt mentions in one letter to his wife how he gorged on a range of delights: a small ham, a goose, two chickens, various vegetables, beans, sweetmeats, cheeses, peaches, and pears, crowning the feast with a fine glass of claret. Society banquets featured all kinds of game, side dishes, and desserts, with particular attention to one local delicacy: the canvasback duck. English diplomat Sir Augustus John Foster gushed wildly over this waterfowl in his book on America, hailing them as "the most delicious eating, and I have frequently seen four dishes of them served up at the same time on the same table." Mary Bagot described another favorite, turtle, as being served "in the shell steamed with a little pepper & butter"—which might sound appetizing until you consider that her companion sourced the creature from a roadside ditch.
To eat the likes of turtle (roadkill or otherwise), guests were provided with glittering silver forks, which were as much a status symbol as a fine wardrobe or handsome carriage. Although presidents such as John Adams and Thomas Jefferson dined with these refined "French forks," other bluebloods such as Charles Carroll saw them as an improper indulgence and Mary Crowninshield complained about how heavy and clumsy they were. More humble Americans had a darker view, as some feared the new republic would be "stuck to death with four-prong'd forks" and others vowed never to cast a ballot for a presidential candidate who ate with such fancy utensils.
The Jam and Squeeze
Thomas Jefferson, master of the fork and other things French, ironically proved much more democratic when it came to entertaining. He invited small groups of no more than fourteen to the White House and seated them without regard to rank or custom, breaking up cliques to force people to mingle with one another in lively conversations. But Jefferson was an anomaly, and in later years presidents and their congressional counterparts refined and tightened social codes to the point where rank became paramount and White House dinners became dreary rituals, thick with rigid etiquette.
Private affairs were a bit more animated but still required a lengthy, formal process of invitation, acceptance, and scheduling as precise as it was inflexible. Librarian of Congress George Watterston provides this overview to the rather elaborate procedure:
The cards of invitation to those parties are sent out about nine days before they are to be given, and if the invitation be to dinner, the person invited must return a written acceptance of the invitation, or an apology for declining. . . . The guest appears at the hour designated, generally about six o'clock, P.M.; for it is deemed uncivil to attend too early or too late on such an occasion. At soirees, or evening parties, the company usually assemble at from nine to eleven o'clock, and retire at from twelve to two o'clock.
At these large nighttime parties, known as "jams" or "squeezes," plenty of elegant gentlemen and ladies knew how to make a fine impression—even as others just wanted to make a splash with personal style bordering on the ridiculous. Men might wear ballooning "Cossack" trousers with "Hessian" boots adorned with gold tassels, or dress coats with "enormous collars and short waists" or "tight-fitting pantaloons, silk stockings and pumps." Women with a flair for "scantiness" might wear dresses that stopped at the ankle and sport silk stockings with slippers ornamented with rosettes and tiny buckles.
At the fashionable balls, they all stepped lively to country dances, quadrilles, minuets, and the basket dance, a forerunner to the modern square dance. The musicians were usually black, both free and enslaved, as were most of the servants. They doled out ice cream, lemonade, port wine, and desserts to the ravenous gourmands, who in their gluttony might appear "with one hand bearing well-filled glasses, and in the other sustaining a plate heaped up with cake."
The cream of society's crop made an even greater effort to entertain their cronies. George Custis—son of Martha Washington by her first husband and adopted by George Washington—built a dancing pavilion at his estate at Arlington and held elaborate picnics on the grounds. At one event he presented a full-dress performance of a play he wrote, Pocahontas; or, the First Settlers of Virginia, with dresses, props, and scenery provided by the federal Indian Bureau, "to aid the aboriginal effect." With its elaborate manor house, gardens, and hundreds of slaves, the massive estate also hosted the 1831 wedding of his daughter, Mary. It was a grand social affair in which she wed a lieutenant in the US Army who happened to be one of her third cousins: Robert E. Lee.
"The Natural Best"
The capital elite didn't just eat canvasback ducks and dress up for fancy balls and weddings. Some joined secret societies, establishing fraternal, business, and sometimes political connections with those deemed worthy. The most famous group were the Freemasons. They claimed their secret heritage dated back millennia to Biblical times, but Masonry really took off in America only during and after the revolutionary era, when such figures as Benjamin Franklin and George Washington associated themselves with it. The group stated its aim as spreading republican ideals and serving as "priests, teachers, and missionaries of liberty, virtue, and true religion." They claimed to be meritocratic, elevating the so-called "natural aristoi" to positions of prominence without regard to birth and wealth. In practice, though, membership amounted to an effective way to establish credentials within the tight circle of the wealthy and powerful. Some well-heeled artisans joined, but the lower orders were excluded because admitting them would "inevitably bring the Craft into the greatest Disgrace imaginable."
Masons favored public spectacle and acknowledgment in splashy parades and honorary processions through town, but they also favored privacy and countless arcane codes, systems, and rituals—including, for the higher levels, forcing initiates to crawl over a pile of garbage or drink wine from a skull. Nonetheless, for the first few American decades, they did well, providing education, charity, and funerals for their members—and for their proponents, such as Anne Royall, who would have had a tough time surviving the lean years without such charity. At the same time they dampened potentially noxious strains of religious conflict and tribalism that had weakened many failed republics. Their proudest public display came in 1793, when President Washington laid the cornerstone of the US Capitol in a ceremony thick with Masonic ritual, followed by chanting, prayers, and an artillery volley.
In theory, Freemasonry tried to limit partisan strife and bridge political, ethnic, and religious divides between gentlemen. That it failed and itself became a political issue represented just one of the bitter little ironies that animated the tumultuous 1820s and 1830s. During that time, with the rise of Jacksonian democracy, the Masons' secretive rituals and bizarre symbolism invited a backlash, even though Jackson himself belonged to the order. The group already had a dangerous reputation for being cosmopolitan, elitist, and potentially irreligious, but when a handful of its members decided to kidnap New Yorker William Morgan, who had threatened to expose their secrets, and he was later found dead, the masses revolted. Freemasonry became a "hydra-headed monster," an enemy of Christians and republicans everywhere, and the Anti-Masonic Party formed. The party attacked social privilege and decried the secret order as evil, murderous, monarchical, antirepublican, elitist, and barbaric; and "We aim, therefore, at its annihilation."
Such a potentially revolutionary (or reactionary) group should have made the Washington City elites quake in their Hessian boots, and no doubt many of the town's top citizens did—but not all. The first and only presidential candidate of the Anti-Masons was William Wirt, the insatiable attorney general who had stuffed himself with that lengthy grocery list of dishes among elite company. But his candidacy made for dish of a different sort: Wirt, once a Mason, now had to justify all those inconvenient social bonds in accepting the party's nomination. He tried to ride the democratic wave as best he could, calling Freemasonry a "noxious institution" that would "sacrifice its victims with pleasure and with impunity" by silencing the opposition with "mysterious terrors"—which of course he knew only too well but wasn't at liberty to reveal since, of course, he had taken the Masonic oath.
Wirt told the Anti-Masonic convention what it wanted to hear, but really he was maneuvering to become the anti-Jackson candidate. When Henry Clay got the nod instead, Wirt had doubts about remaining with the Anti-Masons and tried to reject the nomination several times, but his new radical friends wouldn't hear of it. "I cannot think of a rational or patriotic motive they can have for continuing me in the field," he complained in a private letter. But he was stuck . . . and running for president, like it or not. In the 1832 election, he won a single state: Vermont.§
§ He made a more ghoulish appearance in 2005 when his skull turned up in the office of a District councilman. Apparently, in the 1970s a grave robber had rifled through the coffins of the family vault, stolen Wirt's cranium, and then presumably sold it to a dealer in macabre relics. It has since returned to the Wirt vault at Congressional Cemetery. (Mark W. Grabowski, et al., "Cemetery Vandalism: The Strange Case of William Wirt," Washington History 22 (2010): 57–68)
Society Improvements
If we take Wirt as an example, the District elite had a hard time navigating the new political landscape of the 1830s. Nothing about their lifestyle—acres of land, great mansions, legions of slaves, indulgent dining, Cossack trousers, silk stockings—related even remotely to the common man or woman. Their secret societies, incantations, and mysticism only proved how they had removed themselves from the day-to-day existence of those who labored in the trenches, scraped by in the poorhouse, or stood on the auction block. But the top shelf had to display some sympathy to those below them in rank. The French Revolution, inspired by the American one, had long before showed them that. Many remained indifferent to the plight of less wealthy citizens, but some participated in charitable societies that counterbalanced private societies like the Masons that were causing so much trouble. The more notable organizations included:
* • American Historical Society (old papers and artifacts)
* • Columbia Horticultural Society (flowers and gardens)
* • Columbian Institute (art and science)
* • Female Union Benevolent Society (poor women)
* • Howard Society (job training for the poor)
* • Navy Yard Beneficial Society (sailors' families)
* • Temperance societies (alcohol prohibition)
* • Union Literary Debating Society (public speaking)
* • Washington City Benevolent Society (poverty relief)
* • Washington Relief Society (aiding poor immigrants)
Perhaps the most well-regarded philanthropist was Marcia Van Ness, who was as devoted to public service as she was to her private social world, if not more so. She cofounded and directed the Washington Female Orphan Asylum after the 1814 British invasion to care for the town's many destitute children, offering the land for the asylum's building and donating food, clothing, furniture, and other supplies. She continued her good works until 1832, when cholera hit Washington City and killed many of its citizens. One of them was Van Ness herself, who died from the plague while nursing its victims.
Phoenix in Brick
The most community-minded figure among the elite, however, had the least claim to be there. Cash-poor from the real estate bubble and facing constant struggles with the city canal, Tom Law remained only a nominal member of the upper class in the early nineteenth century. But he persevered and found himself in the right place at the right time when the capital needed help.
It never needed more help than after it burned in 1814. With many of the federal buildings in ruin, politicians from Pennsylvania and other states tried to use the District's sorry condition as an excuse to move the national capital elsewhere. "The appearance of our public buildings is enough to make one cut his throat," said one Virginian. While Congress was debating what to do, Law took the lead in raising $500,000 in loans for the construction of a temporary building to house the legislature, which had been laying down the law in Blodgett's Hotel while its chambers were in ruins. Some later claimed Law's efforts for this new "Brick Capitol" kept the seat of government in Washington City, but in practice Congress had already decided to rebuild the Capitol when the brick version opened for business. Still, a rosy halo formed over him as one of the saviors of the capital, and he imagined the future growth and glory of the rebuilt city:
At this methought a peal of victory rung
And a new edifice in splendor sprung,
Like phoenix from its ashes, and a sound
Of triumph and rejoicing rose around.
It wasn't the first time he waxed poetic, nor was it the last time he tried to help his adopted city. But who was this failed real estate baron, struggling canal builder, legendary partier, and would-be poet, and why did he care so much about Washington City?
The Poetical Ludubrian
Law came to America with an impeccable English pedigree and legacy. His father, Edmund Law, bishop of Carlisle, had written the trailblazing Theory of Religion, which excited many ecclesiastical debates in the old country. His most famous brother was Edmund Law, later attorney general and speaker of the House of Lords. Unlike his relatives, Law found his calling overseas, alighting for India at age seventeen and remaining in the employ of the East India Company for nearly two decades. As revenue collector for the state of Bihar, he transformed an onerous system of taxation and introduced the concept of private property rights independent of lands owned by the crown. As newspaper editor William Duane said of him, "Mr. Law's revolution without bloodshed eventually changed the whole moral and social condition of Hindostan." Law returned to England in 1791, fighting the East India Company over a claim against a paymaster in his employ and for whom he had vouched. In the first of many financial twists of fate, Law was held responsible for the £10,000 claim, a fifth of his total fortune. He filed suit against the company and left for America in 1794 to start over.
Arriving in the new republic, he immediately discovered the potential riches on offer. Oddly, for someone who already had plenty of money and never showed a weakness for greed during the rest of his life, Law swooned at the prospect of speculation, with the capital itself his drug: "I shall certainly go to Washington City & my heart & my mind are full of it—You may say that I had rather sell my horses or books or any thing rather than part with a foot at present of Washington City."
In town only a year, the socially adept thirty-seven-year-old wed the first lady's nineteen-year-old granddaughter, Eliza Parke Custis. A few years later, a young Thomas Twining visited from Britain and observed Law hard at work building spec houses: "The clearing of ground and building of small houses, amongst the woods of the Potomac, seemed an uncongenial occupation for a man of so accomplished a mind. . . . America, of all countries, seemed the least suited to the activity or leisure of such a person." Twining had a foreboding about his friend, thinking that "his inexperience in commercial affairs, amidst rivals so experienced and intelligent, might expose him to litigation and disappointment, and involve a considerable diminution of his fortune." The young man's prophecy proved true.
The ever-optimistic, often financially troubled Thomas Law.
Even as Law was busy losing money on real estate, he was investing even more of it elsewhere. In 1797, near the Eastern Branch, he helped create the first and largest manufacturing operation in Washington City, a sugar refinery. Law planned to import sugar from India using non-slave labor to establish a thriving business in America while encouraging India to free the bondsmen who worked the sugar plantations there. Sadly, that noble idea resulted four years later in "a very large but perfectly empty warehouse, and a wharf graced by not a single vessel."
But Law kept trying. In 1798 he became a director of the District's first bank, then designed and advocated a plan for a national currency, which fell on deaf congressional ears. For decades after, he wrote a column in the National Intelligencer, under the pseudonym "Homo," pushing for a national banking system, publicly financed debt, and an agricultural society, among other points. In 1814 he wrote to President Madison recommending the establishment of a university and military college, since Congress was treating the District with an "opprobrium of neglect."
Three years later, Law helped found the Columbian Institute, which Congress chartered in 1818 to promote math, science, literature, and art. He summoned all the top names in town, including Benjamin Latrobe, William Seaton, and William Thornton to help him run the institution, a forerunner to the modern museums in the District today, which collected an array of books, minerals, shrubs, and trees. The institute also built at the foot of the Capitol a fine botanical garden, which collected specimens of plants, fossils, and minerals from around the world—perhaps its greatest endeavor. The Columbian Institute closed its doors in 1838, but its collection formed the core of the National Institute, which later became part of the Smithsonian.
Any good philanthropist might have pursued the founding of institutions or the funding of civic improvements, but Law, despite his tenuous status as a "rich man," followed all manner of whims and curiosities too. He had a flair for what he called "poetical ludubria" and indulged it when the short-lived United States Theatre opened in Washington City in 1800 by writing a prologue to the main play with a gentle poke at his audience:
Those ruddy cheeks evince the air is fine,
And those fat sides show on the best you dine.
Well faith, we've form'd a tolerable stage;
Here's room for comic glee or tragic rage;
But there [pointing at the crowd] the city populates so quick,
I fear you've stowed yourselves away too thick
Wordsworth it wasn't, but Law cut a charming figure as a patron of the theater, both in verse and purse, and helped fund other arty endeavors, such as the Washington Dancing Assembly. Law's charisma was substantial enough that even his respected biographer Allen Clark abandoned objectivity and wildly praised him as "the scion of Britsh aristocracy, a lord of India, bright in speech, elegant in manner, and handsome . . . Tom Law, paragon of manly perfection"
More unusual, considering the circles in which he moved, was his association with freethinkers and the Unitarian Church. He generously funded the latter and commented that people should "seek salvation according to the dictates of their own conscience," thereby denying the authority of established churches.Defying the racist attitudes of the era, this associate of wealthy planters called presciently in his newspaper column for the abolition of slavery as a way to prevent civil war. He publicly acknowledged and supported his three mixed-race sons from a previous marriage in India, who became prominent figures in the District and, like their father, were "generous, kind-hearted, and most intelligent . . . free from all aristocratic pride."
Needless to say, many of Law's peers didn't know what to make of him. Margaret Bayard Smith saw him as generous to a fault, "connected with the most respectable people," always raising money for some good cause or other, but still—"it is impossible to describe this man; he is one of the strangest I ever met with." She was right: He was a true oddball. Not only did he declaim in verse whatever random subject crossed his mind, but he impulsively went skinny-dipping and strutted around in the nude afterward. He had a curious knack for kneading bread in his hands while lost in deep thought on a walk and had such a terrible memory that when a random notion hit, he would "wildly rush about, exclaiming, 'Pen and ink, pen and ink, an idea, I have an idea, quick!' " He read and spoke Persian and encouraged his guests to smoke a hookah with him by the riverside. Yet despite all his eccentricities, his top-shelf friends, perhaps amused by him, helped him fund his lifestyle and his civic projects—if only because at his grand picnics he made sure to indulge them in "cold meat, bread & cheese & oceans of wine, punch & brandy."
Whether using his own cash or his friends', Law funded or helped start a great many projects that otherwise would have died in Congress. His own returns from those projects were usually quite meager, and he managed to lose money on many of them. Ultimately, apart from the District's major public buildings, Law invested more in the capital than the federal government did throughout the course of thirty years, a fact both remarkable and depressing.
The Great Castle
Holding a core collection derived from the institutions that Law and his peers helped fund, the greatest emblem of private philanthropy in the capital was and still is the Smithsonian Institution. In 1826 English scientist James Smithson left a bequest for an institution to be founded in America for "the increase and diffusion of knowledge among men." Smithson never visited the United States, yet to the new country he left his fortune (though it took a dozen years for the will to be settled). The $500,000 bequest arrived in the United States in 1838 in the form of 105 bags of gold bullion coins sent by packet boat. Leading politicians had all kinds of ideas about what the money should fund, so Congress dithered for eight years trying to figure out what to do with it. In 1846 the legislature accepted the money to fund a facility that would include a museum with art and science displays, a library, lecture halls, and research labs. Six years later a great icon of red sandstone emerged, rich with turrets and battlements, known appropriately as The Castle.
A visual anomaly as much as the Capitol and White House, the Smithsonian stood out as a lone Gothic sentry along the barren landscape of the Mall. Citizens starved for scenic beauty even used the Institution's grounds as an ad hoc resort. But the building's magnificence made the rest of the Mall look shabby and decrepit by comparison. This was especially apparent when anyone compared The Castle's lovely neo-medieval form with the architectural attempt, just west, to honor George Washington with a great public monument. Indeed, no other building represented so colossally the failure of federal politicians to aid a worthy cause than the Washington Monument.
Monumental Struggles
Congress had been searching for a way to honor the nation's first president since the failure of the giant pyramid project at the end of the eighteenth century. The obvious solution to some was to preserve his house at Mount Vernon, which certainly needed the help, as Harriet Martineau observed in the mid-1830s:
The land appears to be quite impoverished; the fences and gates are in bad order; much of the road was swampy, and the poor young lambs, shivering in the biting wind, seemed to look round for shelter and care. The conservatories were almost in ruins, scarcely a single pane of glass being unbroken; and the house looked as if it had not been painted on the outside for years.
Members of the legislature, however, cared less about the fate of the general's estate than of his body, which was buried there.
Congress had wanted to entomb Washington in the Capitol almost as soon as he died, and they even built a crypt on the lower level to house the remains. On the centenary of Washington's birth, in 1832, Congress formed a Centennial Committee to devise a way to commandeer the body from Mount Vernon and spirit it to the Capitol. But certain Virginians would have none of it, vowing to "contend to the last for the body," and one Georgia congressman even warned of "the severance of this union" should Washington's cadaver be swiped from its vault at Mount Vernon.
In the end, John A. Washington, the president's great-nephew, helped stop the congressional action. But just in case, Virginia passed legislation preventing the removal of the body, and leading politicians, North Carolina senator Willie Mangum among them, demanded the governor dispatch the state militia to stop the federal grave robbers at gunpoint.
The attempt at "honoring" Washington didn't end there. Just after the jockeying for his body ended, Congress decided to commission a sculpture of the president, giving Horatio Greenough the task of creating a huge marble statue. The giant, twenty-ton carving arrived by boat in 1841 but shocked Washingtonians with its vulgarity. Greenough depicted the president as Zeus, enthroned and clad in a toga. Naked from the waist up, the great general looked angry, pointing at the sky for no particular reason. Congress didn't know what to do with the monstrosity, placing it first in the Rotunda and then exiling it to the east Capitol grounds, a wooden barn, the Capitol basement, and the Naval Academy. (It now sits in the Smithsonian's American History Museum.)
Horatio Greenough's unloved statue of George Washington, depicting him as Zeus in a toga.
Congress had racked up three failures in trying to honor a national hero. Still, the attempts continued—and in even more colossal form. In 1833 a group of civic-minded citizens created the Washington National Monument Society, Chief Justice John Marshall its president. The society held a design competition, which in 1836 Robert Mills won with a proposal for a five-hundred-foot neoclassical obelisk rising from a colonnaded base. The society didn't care for the base but accepted the obelisk and began raising funds for the monument, to be located near the spot where L'Enfant once imagined a statue of Washington on horseback.
But raising funds for the monument proved slow going, and it took more than a decade for construction to begin. On July 4, 1848, the Masonic lodge of Washington City laid the cornerstone for the monument. But instead of sitting at the intersection of the axes aligned to the Capitol and the White House, the obelisk rose off-center, one hundred yards south, where the ground was higher, the soil not so marshy. Construction continued apace for six years but then ground to a halt when the society ran out of money in 1854. The nativist Know-Nothing Party took over the society through violence and intimidation (about which more in the next chapter), and, though Congress rescinded its $200,000 donation, it did nothing to stop the interloping agitators from destroying the society's reputation. The result: a drab stump of granite that over the course of nearly three decades symbolized the repeated failures of Congress, and by implication the struggles of the capital itself.
The granite stump of the Washington Monument, which stood unfinished for nearly three decades.
Capitol Captives
In contrast to the bumbling of the national legislature, the philanthropy of wealthy Washingtonians helped keep the capital from collapsing or sliding into total poverty and structural decay. The rich dealt with such problems because of the total lack of charity and good works from the town's other elite society—the politicians from around the country who congregated in Washington City but didn't consider it their home. These out-of-towners held power in the capital, but, despite being "public" figures, they lived lives even more removed from the average Washingtonian than did the planters and grande dames. It began with how they lived and with whom they chose to associate.
The seeds of the politicians' isolation germinated when the capital moved to Washington City in 1800. Few legislators wanted to live in the barren, undeveloped village year-round, so they looked for only temporary accommodation. Some entrepreneurs opened hotels, but most of these met with failure. Taverns made a poor choice because boarders had to share beds with random bunkmates—not an option for congressmen who needed privacy and workspace. The answer came in the Washington boardinghouse.
William Thornton described the early US Capitol, before it was remodeled, as a "large sugar dish between two tea canisters."
This form of collective housing represented the only viable option for most legislators, almost all of them initially living in eight boardinghouses on Capitol Hill. Around these three-story brick structures sprang up businesses and facilities that catered to every whim and need of their guests: barbers, bathhouses, bookstores, churches, clothiers, groceries, libraries, liquor stores, post offices, restaurants, schools, stables, and tailors. Most of the time, though, the politicians just hung out in the House and Senate chambers where they aired their windy speeches.
A legislator might live in a boardinghouse with anywhere from two to seventeen or more boarders, often from his region or state. Proprietors advertised in newspapers their houses' spacious kitchens, fine gardens, and proximity to the Capitol. Lodging didn't come cheap, though, and they jacked up their prices whenever their customers came to town. Their residents didn't have much choice but to accept the steep rates, so keeping a boardinghouse became one of the few profitable businesses in the District. In his 1822 Washington Directory, Judah Delano fills the first eight pages of his guide with nothing but the names of Senate and House members, their states of origin, and the names of the boardinghouses where they lodged.
Fortresses of Solitude
More than a few writers referred to the cloistered congressional life as monk-like, since the members lived, ate, socialized, killed time, and talked politics only among their kind. Each house "had an invisible drawbridge and portcullis. One was a fortress for New Yorkers or the same party, another for Pennsylvanians, another for Ohioans." They ignored non-politicians in the same house and often broke into smaller cliques based on state, party, or sectional interests, voting that way in Congress too. Their herd mentality held so strong that if a member defied his "fraternity" he was more or less excommunicated. Margaret Bayard Smith recalls one such apostate, who, after casting his vote against the wishes of his messmates, "looked wretchedly, tears running down his cheeks," and begged forgiveness; another who did the same was shunned by his fellows: "we let him continue with us, sit at the same table with us, but we do not speak to him. He is beneath anything but contempt, and he is an old man."
This incestuous climate fed upon itself, until even the leisure and social life of congressmen became politicized with gossip and innuendo. As James Sterling Young writes in his pioneering study of the life of politicians in the early District, "Who was and was not invited to a tea, a dinner, or a reception, who accepted and who declined, who was and was not calling upon whom, became matters pregnant with social significance." But there was nothing genteel about the ways of those politicians in their private boys' club. On the floors of Congress they brought their hunting dogs (particularly John Randolph); they drank, whittled, yelled at friends in the gallery, took snuff, chewed tobacco, and spat anywhere they wanted. Their boardinghouses sometimes looked even rougher around the edges. Anne Royall recalls a few houses known for their bullies and thugs: "It is out of the question even to have a card delivered to any member in the house without endangering life."
These raw, aggressive attitudes came at a cost, though. The local elite weren't exactly rushing to welcome low-mannered congressmen to their balls and salons. As Constance McLaughlin Green writes, "cultivated Washingtonians felt no obligation to open their drawing rooms to congressmen of very modest political, and still less social, savoir-faire."
Vortex of Ruin
Members of the executive branch, from cabinet secretaries to clerks, also clustered in houses and boardinghouses around the White House and the departments of State, War, Treasury, and Navy. They kept to themselves and had their own schools, churches, library, banks, and theater. With the president as the nucleus of their orbit, they had their own salons too, at which conversation, games, music, and poetry readings took place as well as celebrity visits by the likes of James Fenimore Cooper and Washington Irving. Throughout the executive branch, in the so-called "Court end of the city," the need to be stylish and fashionable affected every rank and class." Even midlevel bureaucrats had to participate:
although their salaries are small and their means limited, they fancy it would be unpardonable not to ape those above them and be what is called fashionable, and thus they plunge into the vortex of ruin. They give evening parties, pay morning visits with cards in their own carriages, or any they can procure, give routs [nighttime parties], go to assemblies, and, in short, exhibit every folly their superiors think proper to practice because it is said to be haut ton, and they cannot think of being unfashionable, whatever may be the result.
But they avoided social commerce with their counterparts on Capitol Hill, from whom they kept a wary distance. James Madison's secretary of the Treasury, like those who worked for him, wasn't unusual in steering clear of congressmen: "Mr. Gallatin leaves no cards, makes no visits, scarcely ever invites a member to dine, or even has a tea party." The high-minded pursuit of separating the branches of government wasn't the only factor that encouraged such distance: Many members of the executive branch considered themselves superior to the rubes in Congress and to people in general. As visiting critic William Faux saw it, "no men in the world are more aristocratical than the heads of departments; they spurn, and cannot even speak to, common men, unless it be to purchase popularity cheaply."
Thus Washington City's political elite comprised separate, warring tribes, each with its own redoubts and its own enclaves, its own tightly knit society and social codes, its own suspicions and hostility to outsiders. The same insularity applied to justices on the Supreme Court, who worked in the basement courtroom in the Capitol and all lived and dined at the same boardinghouse on Capitol Hill, an arrangement that lasted until 1845. Each political clan kept to itself, its members trusting only those who slept, dined, worked, and relaxed in the same company. Some commingled with the elite in town, but many didn't, and far fewer of them socialized in any meaningful way with the slaves, free blacks, and white mechanics who made up the bulk of the District's population. As for the small middle class in town, it was more of a merchant class and consisted of shopkeepers, clerks, artisans, and the like, but it never cohered as a unified group. Its upper order sought out the company of the elite, while its lower order were considered mechanics who had made a bit of money. The old social divisions remained.
Nobody's Constituents
Ultimately, national politicians considered themselves outsiders, not responsible for correcting the problems that their policies obviously had caused. The capital "was not 'our' community in the eyes of the governing politicians; it was 'theirs'—the townspeople's." As a result, Congress regularly refused to upkeep the town's roads, streetlamps, sidewalks, sanitation, schools, and city canal, telling Washington City to tax itself—which it did heavily. But such efforts couldn't come to much when the prized real estate lay off-limits to taxation: the public buildings and the houses of the Congress and the president.
The capital remained a shambling mess throughout the first half of the nineteenth century, but the politicians, ironically, had the audacity to complain about it, calling the town "a hateful place . . . splendid misery . . . [producing] nothing but absolute loathing and disgust." When local business leaders tried to jump-start the capital's anemic economy with a new railroad link in the middle of the century, Congress balked. Said one senator, "Washington was not intended to be a great business mart." Instead, it was run by leaders indifferent to its plight and beholden to voters of other, increasingly distant states. As one irate letter-writer put it in the National Intelligencer: "Every member takes care of the needs of his constituents, but we are the constituents of no one."
The situation reached such a crisis point that by 1835, with the legislature still withholding essential funds needed to modernize the town, Senator Samuel Southard admitted in a report to Congress that Washington City had exhausted its resources. In response, he reasoned that the legislature should assume some of the city's debts and help pay for elementary services like road paving and lighting, sidewalks, poverty relief, and other functions. The stingy legislators needed to debate these urgent topics for a few more years, but at least they relieved the District's canal debt and kept the American capital from going broke and being sold to the Dutch.
Walled off in its own fortress, Congress had crippled the growth and development of the capital, ensuring its abysmal physical condition and that it had few successful enterprises beyond slave trading and boardinghouses. Indeed, if it weren't for local elite society—with its elaborate social codes, gluttonous dining habits, fancy soirees, and extravagant outfits—Washington City couldn't have taken care of orphans, helped the poor, trained people for jobs, promoted art and science, or established museums and gardens. Thus the capital consisted of two distinct high societies: the elected one that completely dismissed the interests of the people it lorded over and the unelected one that didn't.
Twilight of an Englishman
Tom Law had a hard time of it in his final years, though you'd never know it from his cheerful demeanor and irrepressible charm. He and his young wife, Eliza, separated in 1804 and divorced seven years later, leaving great recriminations between the two and alimony payments for him for several decades afterward. These, as we've seen, he couldn't afford, and he had to seek the assistance of friends and relatives to pay them. In the early 1820s, English critics Charles Janson and William Faux separately published salacious gossip that his wife had cuckolded him while she was "attached to the military, at the marine barracks in Washington . . . dressed à la militiaire in company with the officers." Law skillfully fought the charge in print, but it only added to a reputation that he was as maladroit with women as he was with money.
But the worst was yet to come. In August 1822 his daughter, Eliza Rogers, died unexpectedly at the age of twenty-six, and less than two months later his son John, an attorney and city councilmember, followed her. Another son, Edmund, also a city councilmember, died at the end of the decade, and even his young ex-wife preceded him to the grave. That shocking number of deaths in fewer than ten years, more than his financial failures or any other challenges, finally seemed to break his spirit. One Washingtonian saw him at a restaurant near the end of his life, recalling him "as a grave, sweet old man . . . who read a poem of his own composing, which served as a dessert after the oysters."
Look not in public places for a wife;
Be not deluded by the charms of sight.
Retirement only gives the friend for life
Who shares your grief and doubles your delight.
Law died in 1834, at age seventy-seven, and was buried in an unmarked grave in Rock Creek Cemetery. Like his gravesite, most of his endeavors have long since disappeared, including his spec developments, canal, theater, sugar refinery, scientific institute, country estate, and temporary capitol. Almost all that remains is the house that he and Eliza shared after their marriage. Located in the southwest quadrant of town, the Thomas Law House stands out among the sea of drab condos built in the frenzy of 1950s and 1960s urban renewal, which leveled so many other old estates but left this smart, elegant, unpretentious home as a fitting if lonely tribute to its long-forgotten owner.
Thomas Law House, one of the last remnants of Law's life in Washington City.
Six
Coming to the Scratch
The gentlemen of Washington City did more than just attend balls, feast with abandon, raise funds for charity, and live in their elite cocoons. They had other concerns too—such as trying to kill each other. The code duello, an elaborate honor code, enabled a gentleman whose pride or dignity was impugned to murder his adversary freely, as long as he did so with the proper etiquette and ceremony.
Dueling was only the tip of the sword of the varieties of violence in the Chesapeake, which spanned a broad range of socially tolerated mayhem in an era dominated by male bravado and almost cartoonish virility. Mobs rampaged, street gangs battled, and blood sport entertained, usually in combination with alcohol and social pressure, to create a heady climate of brutality that held sway from the colonial era all the way to the Civil War. Thomas Twining noticed how the region reveled in fighting, dueling, and "cruel sports," with eye-gouging and "other barbarities" among the specialties. Not just criminals out for blood took part. All creeds and classes participated in the bloodletting, using violence as a tool of dominance to keep pariahs in line and to enforce racial, social, and cultural codes. They often did so with a wink and a nod from the proper legal authorities, who had neither the inclination nor the means to fund an effective system of law and order. Disorder resulted and verged on anarchy during times of open conflict, when citizens could maim and mangle each other at will.
The Rules of Honor
Dueling represented the most acceptable form of social violence because this kind of attempted homicide "did not lower the would-be murderer in the respect and esteem of the elite of Washington society." Treasury Secretary Alexander Hamilton and Vice President Aaron Burr fought the country's most famous duel in 1804 in New Jersey, but countless other contests in the years after drew considerable attention as well, provided the adversaries had sufficient social standing to merit it. Indeed, some of the most esteemed gentlemen in the nation, and particularly in the South, became its most visible champions.
By the early nineteenth century, refined dueling etiquette in the Chesapeake went something like this: One gentleman offended another by an insult real or imagined. The aggrieved party posted a note in a newspaper or other public place declaring his nemesis, say, "an unprincipaled villain and a coward." The other party responded in kind, and the technical legwork began as the gentlemen and their allies, or "seconds," proposed a date and time, weapons (usually pistols), and choice of venue. All very formal and precise, it adhered to the code duello as the parties understood it. With the appropriate rules and ceremony, honor would be satisfied, regardless of whether it resulted in death or grievous injury.
The parties usually picked the dueling ground outside Bladensburg as their venue. Enclosed by hills with a little brook running through it, the site made a stirring and romantic spot for mortal combat. More importantly, while Maryland had laws against its own citizens dueling, it said nothing about Washingtonians doing the same on the state's turf. In reality, the combatants were unlikely to be caught and arrested anyway: The District had no effective law against dueling, and tradition kept them going back to the Maryland border to uphold the demands of honor, year after year.
The dueling ground at Bladensburg, Maryland, where gentlemen cordially met to kill each other.
The Power of Custom
Perhaps the most famous battle between American naval commodores took place not at sea but in a Bladensburg forest clearing. The challenger of the duel, James Barron, had commanded the USS Chesapeake, which in 1807 the British HMS Leopard had attacked and boarded in order to seize four deserters from the Royal Navy. The shameful encounter led to Barron's court-martial, after which the US Navy barred him from command for five years and resisted his appeals for reinstatement thereafter. Barron never forgot the humiliation and nursed a grudge against Stephen Decatur, the naval officer who had served on the court-martial and worked to keep him from commanding a ship afterward.
Commodore Decatur, one of the most accomplished and legendary officers the US Navy ever produced, commanded a squadron against the Barbary states, fought in the War of 1812, and had a mansion near the president's. Decatur and his wife were planning a wedding reception in their elegant home for President Monroe's daughter even as Barron and Decatur were quietly exchanging notes in preparation for their duel. Barron felt Decatur had ruined his career and good name and demanded satisfaction; Decatur argued that his motives were strictly professional, not personal, but recognized the necessity of the contest. He had fought five duels before, killing an Englishman in one of them. Even though he philosophically opposed duels, he had no choice but to participate in them, due to the social demands of the dueling code, backed by "the omnipotence of public opinion." The president had the power to stop the actions of such men in the military, but as William Faux saw it, "such is the power of custom, that he cannot and dare not do it."
Separated by only eight yards, the commodores each shot the other in the hip, but Barron's bullet hit one of Decatur's major arteries. Decatur died on the evening of March 22, 1820, in excruciating pain. Barron lived for another thirty years. Thus, thanks to the near-random result of a socially sanctioned gunfight, a mediocre seaman who had embarrassed his country lived to a ripe old age, while "one of the first officers of our navy, the pride of his country, the noble-hearted gentleman" expired early at age forty-one.
Blacklegs and Dressing Gowns
Not all duels took place at Bladensburg, nor did honor always have anything to do with dignity. One such counterexample occurred in April 1826 between Secretary of State Henry Clay and Virginia senator John Randolph. In one of Randolph's signature tirades in the Senate, he had quoted a foreign minister's denunciation of the John Quincy Adams administration, of which Clay was a key part, as a "puritanic, diplomatic, black-legged coalition" and dared anyone to take issue with that opinion. According to the code, Clay had no choice but to challenge the senator to a gunfight. After some hemming and hawing on Randolph's part, the men met in a forest basin on the Virginia side of the Potomac, their loyal seconds acting as intermediaries and weapons loaders.
But instead of wearing a garment appropriate to the solemnity of the occasion, Randolph arrived in his flannel dressing gown, a billowy robe that fit him like a tent. The seconds were outraged by this flagrant disregard for the decorum of the contest, but Clay let it go. Then Randolph's hair-triggered gun fired into the ground by mistake, and one of Clay's allies threatened to call off the duel and leave. But again, Clay wasn't bothered. The contest finally began: Randolph took the first shot and fired gallantly into the air. But Clay, ironically known as "The Great Pacificator," took time to respond with his own, potentially fatal shot. He slowly counted down and took careful aim at the "vast circumference" of the senator in his "unseemly garment." He pulled the trigger and shot a hole in it.
As Clay said later, "I might as well have tried to shoot at a pair of tongs as at Randolph." The senator had spread his legs under his gown to keep the bullet from striking him. He had played a sneaky trick, unbecoming of a gentleman, but it was technically okay since the dueling code said nothing about housecoats and wide stances. Dignity suffered, but honor was satisfied. With that unpleasant business out of the way, the men met cheerfully and later exchanged calling cards, and "social relations were thus formally and courteously restored."
Hero of Anarchy
Events took a rather less genteel turn two years later when Andrew Jackson became president in 1828. "Old Hickory," an accomplished gunfighter and military man, carried lead in his chest from a prior shooting and served as a living symbol of the duelist triumphant. Under his reign, dueling drew in a wider class of people than just the elite, becoming "democratized" while also becoming cruder and bloodier as social climbers used one-on-one warfare to draw out and murder their rivals and make quick names for themselves. Social critics such as Philip Hone took alarm at dueling's rapid rise and expansion. "Sanguinary semi-barbarous conflicts" appeared constantly in the news, as the combatants tried desperately to "write their title to fame in blood." No longer were single-shot pistols the preferred weapons; instead, combatants used revolvers, shotguns, and even bowie knives to enforce their own idea of the duel, which increasingly resembled the bloody brawl that it was instead of the dignified contest it pretended to be.
Andrew Jackson's 1829 inaugural party at the White House, at which drunken revelers incited a riot.
Jackson perfectly embodied this increasingly democratic, increasingly malicious era. Exceeding any other figure of his time, his personality and actions—more than his politics—made him greatly popular, and he became a sort of "anarchic hero" to a wide swath of Americans. Nowhere did this become more evident than at his inauguration celebration. It began as a friendly levee at the White House, its doors thrown open to the people. However, executive staff made the mistake of providing the crowd with buckets and tubs of punch and other liquor, potentially serving up to twenty thousand people. Soon, according to Margaret Bayard Smith, a "rabble mob" began smashing glass and china and almost killed their hero by accident. He was "literally nearly pressed to death and almost suffocated and torn to pieces by the people in their eagerness to shake hands." The madness of the crowd reminded Smith of the worst aspects of the French Revolution. As Supreme Court Justice Joseph Story observed: "The reign of 'King Mob' seemed triumphant."
Happy Animalism
The inauguration riot was hardly unusual. Civil disturbances around the nation in the Jacksonian age were common. Historian Paul Gilje, in his study Rioting in America, saw the violence growing out of the democratic, egalitarian impulses of the era. The voting franchise expanded to wider classes of white men (though still not blacks and women) who used guns and fisticuffs to express their anger, fear, and resentment.
The chaos increased throughout Jackson's presidency until 1834, the "great riot year," with scores of battles involving anyone from gamblers and bankers to immigrants and anti-abolitionists. These included Irish labor riots in New England, antibank riots in Baltimore and Portsmouth, anti-Mormon riots in Missouri, anti-Catholic and antiblack riots in the Northeast, and even an antiballoonist riot in Philadelphia. The next year descended into even greater chaos with 147 riots fueled by similar grievances and loathing, including mobs lynching gamblers, abolitionists rioting in order to free slaves, Catholics attacking anti-Catholics (and vice versa), and, strangest of all, an anti–free love riot in New Hampshire.
As electoral battles between Jackson's Democrats and rival Whigs turned nasty across the nation, strongmen at the polls told citizens for whom to vote, using verbal intimidation and outright attack to keep people from choosing the wrong side. In some cities, according to one historian, during Election Day's "genial mayhem [of] swearing, swilling and fighting, the black eyes and bloody noses and torn coats made this a time that tried men's bodies by smart raps and sound kicks" as the political process devolved into a "hell of happy animalism." Jackson himself nearly fell victim to the chaos of the era when an attacker tried to kill him outside the White House in early 1835—the first assassination attempt in American history. After the would-be murderer failed twice to shoot him, Jackson subdued the man by beating him with his walking cane.
By 1837 the conflict so disturbed a young Abraham Lincoln that he saw an "ill omen" in the "increasing disregard for law which pervades the country" as "Accounts of outrages committed by mobs form the every-day news of the times." Hezekiah Niles, the important but little-remembered journalist who published the Niles Weekly Register in Baltimore, took a more direct view:
Society seems everywhere unhinged, and the demon of "blood and slaughter" has been let loose upon us! . . . mobs growing out of local matters—and a great collection of acts of violence of a private, or personal nature, ending in death . . . We have executions, and murders, and riots to the utmost limits of the union. The character of our countrymen seems suddenly changed, and thousands interpret the law in their own way.
Riots Almighty
A black witness to the Chesapeake violence, Michael Shiner, kept a journal from his time as a slave and then as a free man, now preserved in the Library of Congress (and transcribed here from his colloquial shorthand). Born in Maryland in 1805, he spent the next thirty-five years as the property of the chief clerk of the Washington Navy Yard, Thomas Howard Sr. Howard hired out Shiner to the Navy, where Shiner worked in the paint shop while also recording the details of what he saw around him, from ship construction and working conditions to mob attacks and racial hostility. In one 1828 instance of the latter, twenty young thugs surrounded and attacked him, during which "I had Christmas in me [as they] lit me up torch-like fashion with the firecrackers." A justice of the peace arrived in the middle of the mayhem, but instead of stopping the violence, he said "You scamp, what are you doing here?" and punched Shiner, who managed to escape into an alley. Later that year, Shiner had to flee from a vicious gang of sailors who took him for a runaway slave.
Even when not being physically attacked, Shiner revealed just how threatening life could be for a common laborer in Washington City and for a slave in particular. Dangers that he faced or witnessed included falling overboard and nearly drowning in ice-cold river water, watching a fellow worker accidentally decapitated, and desperately trying and succeeding to free his wife and children from the confines of a Franklin & Armfield slave pen.
In 1835 Shiner witnessed the Snow Riot. His fellow Navy Yard mechanics, on a break from their labor strike, attacked Beverly Snow's restaurant and destroyed it "Root and Branch." Later, they also nearly destroyed a jailhouse where a slave was being held under suspicion of trying to kill his master. Thanks to feeble law enforcement, the mob "raged with great vigor" until the secretary of the Navy detached a column of Marines to protect the jail. After the disturbance, instead of punishing the rioters, President Jackson inquired about their concerns and wondered if there was "anything he could do for them in an honorable way to promote their happiness." As a first step, he promised the thugs that "by the eternal God in this City" he would crack down on any "negroes [who] had violated any law whatever" and punish them severely for it.
The eternal god of the city, however, had nothing on Andrew Jackson. The belligerent-in-chief cast himself as the stalwart tribune of democracy, someone who didn't need to follow the tired old rules of legal procedure when guided by his own sense of purpose, a man above the law who stood as the fulfillment of a righteous society rather than as a threat to it. Not surprisingly, a lot of his followers felt the same way. They rioted not against but in favor of the status quo in order to enforce their own sense of justice without worrying what the law had to say about it.
Liquid Aggression
Shiner wasn't always a victim of his time. Sometimes he perpetrated the kind of violence he observed—before inevitably falling victim to it again. Alcohol often provided the fuel for conflict. After a heavy bout of drinking mysterious liquors called "Tom Cat" and "Run from the Gun," Shiner and another black worker got into a "tussle," during which Shiner threw him in a mud hole. Another time, he flung a man into a basement, "going crazy" with drink, before Marines wrestled him down and stuck a bayonet in his shoulder. Yet another drunken escapade resulted in Shiner getting mauled with stones and brickbats, arrested, and sent to navy lockup. Ultimately he escaped from lockup and went back at work as usual.
None of Shiner's alcoholic tumults would have surprised Frederick Douglass, who saw liquor and slavery as inseparable. Slaveholders routinely used alcohol as a means to suppress rebellion and numb potential escapees into compliance. "In order to make a man a slave . . . it is necessary to silence or drown his mind," said Douglass. Other abolitionists and temperance supporters saw "Rum and Negro hate" as two sides of the same coin and worked to eradicate drinking altogether to dampen the spark that seemed to ignite so much racial violence.
For their reward, the temperance advocates became a new target for the rioters, who saw any steps toward black self-improvement as a threat and made a special effort to destroy assembly halls that hosted temperance meetings, just as they did black businesses, schools, and churches—of course leaving brothels and dance halls alone. A danger to the old order, black temperance found many supporters across the region, Michael Shiner among them. In 1836 he quit drinking, and "I never have had a drop of liquor in my mouth since that time."
A Frenzy of Spirits
It wasn't so easy for others to stave off the power of liquor, however. Taverns offered a wide array of spirits, gambling, and other amusements, and they also featured dances, balls, and assemblies, with anything from a "wonderful mathematical dog [to] a collection of the works of some distinguished artist." They housed the Orphans Court and circuit courts in the early days, hosted political protests and rallies and nominating conventions for municipal politics, and offered an ideal place to celebrate George Washington's birthday in high style. John Adams stepped into the City Tavern in 1800 to offer no fewer than seventeen toasts to the health of the country, and later politicos stumped for votes over glasses of rum and whiskey. Drinking hard liquor and politicking went hand in hand, and election-day drunkenness was common. William Henry Harrison won the presidency in 1840 with a campaign that boasted of his supposed log-cabin origins and taste for hard cider.
Non-political figures also drew crowds. Georgetown's Union Tavern hosted Talleyrand, Napoleon's brother Jerome Bonaparte, King Louis Philippe, inventor Robert Fulton, and Washington Irving. Such figures lodged at taverns when few other accommodations were available in the District, and some continued to do so after proper hotels were built. The most prominent taverns provided little reason for visitors to go anywhere else. The Columbian Tavern, for example, advertised "good Beds and Boarding, with a variety of Liquors [and] Dinners dressed at the shortest notice," while others like Tunnicliff's and Rhodes acted as hubs for social activity and even a dancing assembly.
But alcohol was still their prime draw. Americans drank more alcohol in the first third of the 1800s than at any other time in the history of the country. In 1830 the average American drank some five gallons of hard alcohol per year, more than one shot of high-proof liquor a day. It's no accident, then, that the country's most brutal decade outside of wartime followed. "Violence often came in bottles," and countless conflicts occurred in and around taverns, occasionally punctuated by murder. At the time, heavy drinking counted as a pursuit of proper manhood, and booze became the elixir of brotherhood and camaraderie, especially for the working class. But this potent mix of drinking, violence, and social communion had grave consequences. It deformed everything from the way people interacted and communicated to how they solved problems and had fun.
Killing Games
"Fun" often meant watching animals tear one another apart. Blood sport was a prime source of antebellum entertainment. Taverns featured fights between men, dogs, and even rats for the amusement and wagering of spectators. Providing such battles was technically illegal, but again the laws were rarely enforced and countless creatures became carcasses to satisfy drinkers' gambling lust. Baltimore even featured spectacles like bull and bear baiting, in which a large beast in chains had to fight off a team of hunting dogs while bettors wagered on which creatures would survive. As early as the 1780s, English critic J. F. D. Smyth noticed how locals in the Chesapeake devoured all manner of "sport, gaming, and dissipation" as well as "that most barbarous of all diversions, that peculiar species of cruelty, cock-fighting."
Indeed, if the capital was known for one blood sport, it was cockfighting. In this contest, owners of gamecocks would place their prized roosters into rings known as cockpits. The birds were fitted with little weapons around their legs, such as knives or gaffs—"sharp blades of finely tempered steel"—with which they could hack their rivals to death. Aficionados of the sport obsessed over the various breeds and types of birds, their proper fighting weights, and their various colors and plumages. Not surprisingly, arch duelist Andrew Jackson was a fan of cockfighting and even attended one public event in Bladensburg, which for once hosted a bloody contest between chickens instead of humans. The birds came from Jackson's own stock in Tennessee, and the president put great faith in them. But they never fought that day: The contest was canceled due to the sorry condition of their rival cocks, which were in no state to battle after a lengthy ride cooped up in a stagecoach.
Many fowl fights occurred in taverns, though not all did. In Virginia, when local courts were in session, courthouse squares became popular sites for cockfighting, along with gambling, slave auctions, debt collection, and religious ceremonies. Across the Potomac in Georgetown, cockfighting had been banned since 1796, so its practitioners relocated to the Washington City circle at 23rd Street north of Funkstown. Christian Hines, in his recollections, reports that the site became the preferred place for blood sport of the human and animal varieties. During one match, a group of local cockfight fanatics tried to drive away interlopers from Georgetown using cudgels. Many suffered injuries, but one man made it all the way back home with a creative bit of self-protection: using a fence rail to deflect the blows of his attackers and beat them to the ground.
The Rise of Fistiana
Although common, human fighting didn't become widely popular as a sport per se until the 1840s. One of its earliest guides, Patrick Timony's American Fistiana, lays out the rules for bare-knuckled combat and presents letters between famous boxers as a prelude to their battle. They read curiously like overtures to a duel. In one case, the challenger, James Sullivan, contends that reigning champ Tom Hyer "assailed [him] in a most cowardly manner" inside a saloon. Hyer disputes the charge by claiming Sullivan attacked him first, and he pledges to show no mercy to anyone who improperly assails him. The fight was on.
Hyer's father, Jacob, was the first widely recognized American champion of the sport, but it didn't really take off until his son got into the ring with Sullivan. The match occurred in 1849 in a no-man's-land on the Eastern Shore of Maryland—a day trip from the capital—where federal and state jurisdiction was disputed, making it something like boxing's own Bladensburg. That didn't prevent authorities from trying to shut down the affair, but the boxers, along with a rowdy crowd of two hundred, escaped their clutches with an elaborate caper involving oyster boats.
The match began with the two parties "coming to the scratch," that is, getting into the ring or field of combat. Soon they pummeled each other with rawboned vigor in a contest that a modern pugilist might consider unorthodox: Sullivan demonstrated "superior wrestling" moves in the first round. The men pounded each other mercilessly "with the rapidity of two cocks" in the second. Both were "clotted with gore" and barely able to stand in the ninth. Hyer tried to wrench Sullivan's arm from its socket in the fifteenth, and Hyer smashed his rival with both fists in the sixteenth, which finally did the trick. Hyer prevailed when Sullivan couldn't make it back to the scratch, which in the setting sun had become a gory crimson mess. The triumph was total: Hyer had won a stunning ten thousand dollars in a mere seventeen minutes, and the "hurricane fight" became greatly influential in making sportsmen in the Chesapeake and across the nation take notice of a new kind of blood sport, one that by comparison made cockfighting look almost humane.
Serving Not to Protect
Boxing was one of several violent, technically illegal activities that occurred in the District due to the lack of an effective police force to stop them. In the early days of Washington City, the constables—a group of four, one per city ward—worked mainly during the day, keeping an eye out for disorderly persons; inspecting taverns, markets, and other public facilities; and rounding up wandering pigs and livestock. As the town grew, however, this force became inadequate. By the mid-1830s, only a dozen officers patrolled an area that by the previous census had become home to nearly forty thousand people. After a group of hooligans caused a minor riot on the grounds of the White House—and with robberies, burglaries, and arson on the uptick—Congress established the Auxiliary Guard as a nighttime force in 1842. Along with chasing thieves and firebugs, the guard was supposed to suppress riots and monitor the firehouse gangs that plagued the town. But with only fifteen men on duty, the guard never became an effective force of law and order, concentrating instead on harassing slaves and free blacks.
Unfortunately there was precedent for this brutal activity. Washington City originally paid its first constables fifty cents for each time they whipped a slave accused of violating the law. Not surprisingly, one of the chief duties of the Auxiliary Guard was to hunt down any blacks out after curfew or presumably violating city ordinances. The guard could arrest or fine them or flog them at the city jail, which had a whipping post for that very purpose. The pattern was then set wherein the skeleton police force had a limited effect on controlling urban crime but a major effect on keeping blacks living in terror of being arrested, jailed, and put to the lash.
Officers of the Auxiliary Guard developed a lasting reputation, however, for sleeping at their posts, smoking cigars, and drinking heavily rather than walking their beats. When they did feel like enforcing the law, most used noisy rattles instead of whistles and carried clubs with iron spearheads instead of guns. By contrast, urban murderers were resorting to lethal force: From 1846 to 1860 their use of guns doubled throughout America to become the weapon of choice in a third of all killings. Criminals shot and maimed a number of District officers and ran riot throughout town, committing what newspapers called "outrages of a most audacious and alarming character." In response, members of Congress and the city council passed new laws, reorganized the police, and made fiery speeches decrying the free rein of miscreants, but nothing they did had much effect. The police were too few, their budgets too small, and they were fighting a mania of antebellum mayhem that afflicted both criminals and law abiders alike. In 1849 this was evident even during Christmas:
Long before daylight began the fusillade by gun, pistol and cracker, the blowing of whistles and small horns, the beating of small drums and tin pans . . . At the same time there were bonfires blazing in different parts of the city . . . Primitive were the instruments used. The old-fashioned horse pistol, some with flint lock, the half-dollar brass pistol and Colt's revolver, then known as the pepper box, were for shooting purposes.
One rotund fellow had the misfortune of resembling Santa Claus. After spotting him on a street corner, a crowd of a hundred hooligans surrounded him, mocked him with vulgar rhymes, and then chased him back to his house while pelting him with firecrackers.
Ragged Parades
The local militia system wasn't much better than the guard. A law from 1803 provided for an armed citizenry to protect the town, but in later years this militia often operated without arms and equipment. Any effort to make the town folk perform their civic duty met with griping over "oppression and tyranny." In one case, a group of local businessmen became so annoyed with militia drills that they organized a counterparade, with brooms for guns, a "general" who wielded a horse's shinbone as a sword, and old smokestacks dragged along like cannons.
The real militia degenerated to the point where, in 1835, their attempt to present a proper parade resembled the ridiculous pantomime of those who had mocked them, prompting Michael Shiner's derision:
They were the raggediest white people that ever I saw in my life, and their uniforms were of old rags . . . and they had drums and fifes and they had clarinets. Their drums were composed of old tin pans and old pots and all kinds of old sheet iron, and their flutes, clarinets and fifes and bugles were composed of ram's horn and oyster horns.
A month later, the Snow rioters went on a rampage. The poorly trained and equipped militia could do nothing to stop them, which proved only how defenseless the capital was in the face of mob rule.¶ If not for the last-ditch efforts of the US military, the rioters would have completed the work started by the British in 1814 and incinerated the capital. The old militia system soon died, and the town had no effective means of civic order throughout 1836. A few companies were organized the next year, but they did little to provide for the basic security and safety of residents. Even Georgetown and Alexandria had basic police services, as did countless other towns in the Chesapeake, but Washington City stood almost alone in its unguarded, helpless condition in the face of riot and disorder.
¶ The federal response to mobs also depended on whom they were rioting against. The test case came in winter 1834, when rival groups of Irish mechanics digging the C&O Canal in Maryland violently went on strike. Unlike the gentle treatment he would show the Snow rioters, Andrew Jackson dealt with the workers by calling out federal troops. The US forces teamed with the state militia to arrest thirty rioters and throw them in jail, and a military presence remained on the canal the rest of the winter. The aggressive federal reaction was revealing—attacking the lives and property of citizens was one thing; attacking the property of the government was quite another. (Richard B. Morris, "Andrew Jackson, Strikebreaker," American Historical Review 55:1 (1949): 63–64)
The Right to Riot
Members of Congress didn't help matters. The legislature hadn't even passed a law against rioting in the District and often watched feebly as violent events occurred on its watch. (By contrast, neighboring Maryland and other states not only had laws against riot and civil disorder but also an effective state militia with which to enforce them.) In 1848, when a simple law against DC rioting was suggested, some Southern congressmen argued residents had a "right to riot" in certain cases—against, say, abolitionists and other such threats. The bill died. But at least the politicians deserved credit for a rare lack of hypocrisy, since they ranked among the most belligerent figures in town.
It was probably inevitable that the political boys' club—which encouraged chewing tobacco, whittling, yelling, and spitting—also embraced more violent behavior. Marked by aggressive bravado and occasional threats of bodily harm, the atmosphere was already threatening and no doubt worsened with members' drinking. In the 1830s, politicians attacked each other physically no fewer than eight times. These conflicts ranged from a policy debate that turned into a fistfight—when one member called another "the tool of tools"—to actual murder threats on the House floor, which resulted in most congressmen carrying concealed daggers, bowie knives, and guns for protection.
Even out-of-towners got into altercations with the local politicians. On visiting the District in 1832, former Tennessee (and future Texas) governor Sam Houston spotted his nemesis, Congressman William Stanbery, on Pennsylvania Avenue and severely beat him with a hickory cane. Stanbery pulled out a pistol and tried to shoot him, but the gun failed to fire, so Houston beat him some more until he was unable to speak. For this assault, a DC court fined the governor five hundred dollars.
Others still resorted to the increasingly antiquated practice of dueling. In 1838 one of the last major contests pitted Maine's Jonathan Cilley against Kentucky's William Graves, the latter an exceptional shot. The event took place at Bladensburg as usual, but this time the duelists used rifles instead of pistols. After each man twice missed his mark, the parties took a third shot, and Graves hit Cilley in the groin and killed him.
However, instead of the usual hosannas in praise of satisfied honor, the event sparked outrage. Northerners lionized Cilley, condemned Graves, and flooded Congress with petitions demanding an end to what they called "Murder Most Foul." Many Southerners resisted the change, but few in Congress wanted to go on record in favor of dueling, especially as the practice was falling into disrepute thanks to the worsening climate of violence in general. After much debate, the legislators finally passed a measure in 1839 that not only made issuing or accepting a challenge to a duel illegal in the District but also wisely provided criminal penalties for doing so. The law had plenty of holes in it, and it wasn't fully enforced, but it did provide a good legal justification for politicians to avoid mortal combat and gave an official stamp of disapproval to socially sanctioned murder. It did not, however, prevent politicians from fighting each other without guns.
Incendiarism
For some residents of Washington City, dueling and mob riots didn't happen often enough, and they required a more regular schedule of violent action. Firehouse gangs fit the bill by providing their members a chance to engage in fisticuffs and skirmishes with their enemies—as well as an opportunity to extinguish fires or even set them occasionally.
One of the early hook-and-ladder companies in DC.
In the early days of the capital, fighting the town's fires was a responsible, respected, unpaid occupation. Households had leather buckets to help put out fires, and each ward had its own volunteer fire company. Their members came from the working and middle classes and had stirring names like Union, Franklin, Alert, Star, Eagle, Vigilance, Perseverance, and Columbia. Although the companies served ably for several decades, the older, more experienced men began dropping out in the 1830s because they had to do double duty with the town militia and found it a challenge to battle blazes across the vast distances of the capital. Into that void stepped rowdy gangs of teenage boys, who within a decade transformed the venerable companies into veritable gangs.
Gang rivalries that had existed from the earliest days of the capital were initially petty, mostly limited to neighborhood fights and rock throwing in Frogtown, English Hill, or The Island. Some of the more notable groups included the Gumballs, Round Tops, Never Sweats, Razors, Blood-tubs, Chunkers, and Rams. (The last of these had its headquarters on Capitol Hill, though history doesn't reveal whether any of its members also served in Congress.) When the gangs took over the fire companies, though, they suddenly had access to fancy equipment and engines, and suddenly commanded a great deal more attention. The capital soon divided into warring fiefdoms, each based around a firehouse.
The gangs naturally proved better at fighting one another than fighting fires. If one engine house arrived on the scene of a blaze in their ward first, they might put it out. But just as often, buildings burned down if two or more companies arrived at a fire at the same time, as each group tried to prevent its rivals from extinguishing it—by hoisting a barrel over a over a street hydrant and sitting on it—while the structure blazed. Sometimes the battles became violent, and a street fight that began with rocks and other small missiles grew into a full-fledged riot. In 1844, exactly that happened right in front of the White House as various thugs battled one another with "stones, fence rails, and other dangerous weapons." If authorities caught and tried the rioters, they usually received small fines (five dollars in one case) and often served no jail time. Even worse, some gangsters even started fires in order to create chaos and enjoy a run with the fire engine—and then had the nerve to take credit for putting the blazes out.
Newspapers carried all-too-frequent reports of "incendiarism," which told of the latest antics of the gangs in their efforts to start or extinguish local fires: "the fire-bells ring out, and the gangs of boys who have taken charge of the respective engines of the city are all on the qui vive [lookout] to run roaring and swearing through the streets . . . Who is to be burnt up next Saturday night no one knows, only some one must furnish the required food for excitement of undisciplined boys."
Amid the turmoil, authorities had few means to stop the gangs. Although professional departments were rare in the antebellum South, Washington City lagged behind even Alexandria and other area cities in the organization and control of its firefighters. Congress tried to attract more mature firemen by promising them exemption from militia duty, but the measure proved worthless when the militia system collapsed. By the 1850s the fire company gangs had grown more powerful, extending their mayhem into local politics and using their pull to keep officials from regulating them. (But some still courted irony when even their own firehouses burned down.) It took until 1856 for Washington City to establish basic safety and operational standards for volunteer firefighters, and a professional, salaried fire department didn't come into existence until the Civil War.
Tourists from Mobtown
Some of the firehouse lads had ties to Washington's most notorious political party, the Know-Nothings, a virulently anti-Catholic and anti-immigrant group that meddled in District politics, usually for the worse. The most visible sign of their menace was the beleaguered Washington Monument, planned for decades but unfinished due to slow fund-raising and, later, their overt lawbreaking. In early 1854 they broke into the monument site at night, locked up the watchman, removed a memorial block of marble donated by Pope Pius IX, defaced and broke the stone, and threw the pieces into the Potomac. Soon after, they took control of the Washington National Monument Society by holding a sham "public meeting" in which they elected their own officers to its board and seized possession of its books and property. This bold act of thuggery aroused such public ire that Congress withdrew its funding, and other donors followed suit. The Know-Nothings added several shoddy layers to the monument but gave up control of the society a few years later. The obelisk, however, remained an embarrassing granite stump for another quarter of a century.
Nearby Baltimore had an even worse problem with the Know-Nothings, who matched their anti-immigrant hysteria with armed intimidation at the polls and seized city government in several disputed elections. (In so doing, they offered cheeky campaign slogans that reminded voters of the tools they had used to menace voters, such as "Come up and vote: there is room for awl.") The Know-Nothings found firm and brutal allies in the thugs that filled the ranks of the firehouse gangs, who in turn spread so much turmoil that the violence spread beyond Baltimore and into the capital itself.
The gangsters' use of violence had deep roots in the Maryland city, going back to 1812 and before. Even Alexis de Tocqueville had heard of its fearsome riots on a trip to America. The gangs caused unchecked havoc in subsequent years and gave Baltimore the well-deserved nickname of "Mobtown." One visitor estimated that Baltimore had "a greater number of black-guards, for its population, than any other city in the Union."
Baltimore's gangsters had many colorful names: the Rip Raps, Rough Skins, Ranters, Rattlers, Black Snakes, Thunderbolts, Little Fellows, Blood Tubs, and Decaturs. But it was the Plug Uglies who took a break from their Maryland violence in 1857 and paid a visit to Washington City. Their local allies in the Know-Nothing Party joined them in an effort to intimidate the District's voters and prevent those deemed "foreigners" from voting. The joint force attacked a naturalized citizen trying to vote in one ward, wounding the ward commissioner in the fracas, and then fired a volley of pistol shots at other voters. As Michael Shiner saw it, the out-of-town rioters "raised such an excitement that the mayor and the whole police force could not stop them." Desperate for help and unable to control the mayhem, Mayor William Magruder wrote to President Buchanan that hooligans armed with "firearms, clubs, knives, and stones" had managed to drive the voters from the polls, chased off the election commissioners, and were threatening further violence.
At the president's behest, the secretary of the Navy had to call out the Marines again, as in 1835, but this time the rioters didn't disperse so easily. Some in the crowd seized control of a "six pounder swivel gun"—a cannon—and hurled stones and fired revolvers at the Marines who tried to capture it. According to Shiner, "one of the Marines was shot in the face and severely wounded, and it was supposed that the Marines fired through a mistake of order, and there was several people killed and wounded." When the carnage ended, eight people lay dead, twenty-one injured, almost all of them citizens of Washington City. The Plug Uglies escaped back to Baltimore that night.
The election riot of 1857 offered yet another example of how the town had no real defense against disorder. A visiting goon squad easily overwhelmed the capital's police force to indulge in a bit of mob tourism. To quell the protests of residents over the threat of such violence, six months after the riot the city council authorized expanding the daytime police force by the grand number of just ten men, for a total of fifty-seven officers—twenty-seven policemen during the day and thirty Auxiliary Guardsmen at night—to patrol a city of sixty thousand people. A Senate committee summed up the terrible state of affairs in an 1858 report:
The police force is both feeble and inefficient. Riot and bloodshed are of daily occurrence. Innocent and unoffending persons are shot, stabbed, and otherwise shamefully mistreated, and not unfrequently the offender is not even arrested. It is hardly necessary to add, that such acts are a disgrace to a civilized society, and, if not put down, must result in disastrous consequences to society, and bring a lasting reproach on this Federal city.
But Congress had little interest in turning the DC police into an effective crime-fighting force. This impasse derived from its usual lack of action in passing legislation that could help the District in any way and from legislators' inability to approve almost anything because of the growing enmity among them. Indeed, by the middle of the 1850s, the "riot and bloodshed" on the capital's streets had once again moved into the halls of Congress itself.
House of Combat
The most infamous bloodletting was the assault by South Carolina congressman Preston Brooks on Massachusetts senator Charles Sumner in 1856. The attack developed from the ongoing battle over the admission of Kansas as a free or slave state, which produced great invective between abolitionists of the North and slavery apologists in the South. Infuriated by Sumner's speeches against human bondage, Brooks found him at his desk in the Senate and, in his own words, took action:
I struck him with my cane and give him about 30 first-rate stripes with a gutta percha cane which had been given me a few months before . . . Every lick went where I intended it. For about the first five or six licks he offered to make a fight, but I plied him so rapidly that he did not touch me. Towards the last he bellowed like a calf. I wore my cane out completely but saved the Head which is gold. The fragments of the cane are begged for as sacred relics.
Brooks did in fact become a hero to the South, just as Sumner became a martyr to the North, drenched in his own blood and nearly dying in the assault. Northerners saw Brooks as a demonic figure and called for quick justice, but he received no jail time for his attack and was reelected to the House after he made the voluntary gesture of resigning from it. (Before Brooks could retake his seat, however, he died of a respiratory disease. By contrast, Sumner recovered, lived long enough to see the South lose the Civil War, and helped oversee Reconstruction.)
Another brawl occurred two years later, again over slavery, as Brooks's ally Laurence Keitt called Galusha Grow a "black Republican puppy." Grow responded by calling his accuser a "negro-driver." Keitt tried to choke Grow, and the House exploded into a melee of bodies and fists flying. The speaker wielded the ceremonial House mace as a weapon, and one congressman even tried to brain people with a heavy stone spittoon. The fracas finally ended when one member tried to grab another by the hair to punch him in the face but pulled off his toupee instead. The chamber erupted in laughter, and the internecine battle ended—for the moment. But no amount of mirth could make people forget that, throughout six decades, the violence between "gentlemen" had degenerated in Congress just as it had around the country. What had begun with mortal contests to preserve honor had devolved into a grotesque spectacle of cane beatings and open brawling.
The infamous 1858 battle in Congress that included punching, choking, and even toupee pulling.
Final Pages of a Diarist
As the 1850s ended, Michael Shiner surprisingly managed to steer clear of much of the era's violence. He saw plenty of mayhem on the streets, but he personally experienced less of it as the years passed—or at least he grew less fond of writing about it in his journal. Quitting drinking helped him avoid conflict more easily, as did his manumission in 1840. Like some other urban bondsmen, he paid for his freedom through years of labor in the slave-hiring system, but afterward he continued to work at the Navy Yard until he was age sixty-five, living another ten years after that. During that time, he rose to prominence as a successful businessman, a leader in Republican Party politics, and a well-known figure in the black community. His journal provides but a glimpse of the Civil War and the years that followed. What remains, then, are his vivid anecdotes of an earlier era of socially sanctioned violence—a time when duelists, mobs, and gangs ruled by gun, club, and knife, and community bonds frayed and civil order nearly collapsed.
Seven
Illicit Congress
Washington City had another socially sanctioned activity that, like street violence, is almost always illegal today but was practiced openly then. It had a devoted class of customers from all stations of society, prominent locations near the Capitol and the White House, de facto impunity from any kind of effective prosecution, and intelligent, driven promoters who became some of the best-known figures in the underworld. Its employees went by a variety of colorful euphemisms, from "painted Jezebels" and "fallen angels" to "daughters of Eve" and "gay young ducks" in their pursuit of the "illicit congress" of profiting from human desire.
Prostitution wasn't technically illegal, but it did operate in a gray zone that enabled police to make busts when needed (usually due to political pressure) under the charge of "keeping a bawdy house" or a "disorderly house." The houses weren't dangerous themselves necessarily, but they did attract rougher types of crime since they operated in neighborhoods rife with thievery and street violence. Despite the danger of visiting a brothel in a bad neighborhood, countless men did so in Washington City, helping to make the capital one of the prime centers of the sex trade on the East Coast during the nineteenth century. Opportunities for sin lay within easy reach of any wayward politician, businessman, or merchant, and this vice became one of the capital's most pervasive.
Boardinghouses to Brothels
Although records are scarce, prostitution likely dated to the earliest days of the District, when brothels emerged from some of the lower-end boardinghouses in town. Of course these weren't the same houses that hosted legislators and executive staff members in individual state and party delegations—as far as we know. Instead, they were another sort of rooming house. Tenants included young, single women employed in shops and factories and often impoverished, earning about half the salary of their male counterparts. Many struggled through economic crises, the disappearance or death of a breadwinning spouse or parent, and other financial problems. To make ends meet, some turned to friends and family for support; others became "charity girls" who accepted material gifts in return for sexual favors. In time, the boardinghouses where they lived housed both working girls and "working girls." The latter had some of the highest incomes in the house and quietly conducted their business from their rooms.
An older woman typically operated the house, and, if sufficiently impressed by her tenants' underworld revenue, she might boot out the aboveboard residents and become a madam. In so doing, her boardinghouse became a brothel. Soon, enough boardinghouses had turned into whorehouses that critics saw prostitution as one of the capital's most prominent and regrettable industries. John Ellis, in his salacious guide to town, Sights and Secrets of the Nation's Capital, remarked:
Boarding-house life is not pleasant anywhere. In Washington it is simply abominable. . . . The "young ladies" are devoted to you, and expect you to take them around, and spend your spare cash on them in the most liberal manner . . . your peace of mind, if you are at all sensitive, is destroyed by the scandal which is soon set afloat about you. You meet with sundry women, who have no visible means of support, and sometimes in the effort to be civil to them, you compromise yourself in a manner you little dream of at the outset.
Tax and census records euphemistically called prostitutes "boarders," "substitutes," or "inmates," and the line between boardinghouse owner and brothel keeper was often so thin as to be imperceptible.
The Rise of a Madam
Among the several women who owned or managed property in town, Mary Ann Hall ranked among the most notable—or notorious—as a pioneer in the sex trade. She began her career in the 1840s, then in her twenties, and built a three-story brick edifice on The Island when most of the surrounding structures were little more than tumbledown wooden shacks. Government records don't reveal the source of the initial capital for her investment, but there's little doubt it came from sex. While most single women in the neighborhood worked as seamstresses or laundresses, Hall's official title was "substitute," an occupation shared by her housemates, who included her sister and several other women. It didn't take her long to create the biggest and possibly the most profitable operation in town. Early records list some eighteen "inmates" working at her establishment, with potentially more sex workers showing up for part-time duty.
Located at what was then 349 Maryland Avenue, Hall's brothel was erected at some distance from the central red-light district north of the Mall. This isolation proved profitable for Hall and her employees because here she could construct a sexual fantasyland for her elite clientele of bankers, merchants, and congressmen, who easily could afford the expensive rates and tastes on offer.
Capital Inmates
Upon entering, a visitor would find a house exquisitely furnished with oil paintings, silver-plated candlesticks, mahogany and rosewood furniture, marble tables, porcelain and ironstone dishes, plush lounges, and Brussels carpets. Escorted to one of the bedrooms, he'd find the decor no less eye-catching: French mirrors, brass candelabra, Chinese vases, assorted decanters and wineglasses, finely carved wooden beds—and of course the women.
It's hard to know exactly how Ms. Hall's prostitutes appeared or how they entertained visitors, but a few artifacts and baubles recovered from the brothel site by Donna Seifert and other archaeologists in the last few decades provide a clue. One might expect the mirror fragments, hairpins, combs, and jewelry, but the array of black-glass buttons that the ladies wore stand out as totems of high-priced dresses that few working-class women could afford.
The clothing of the "inmates" wasn't the only expensive aspect of the place. The food and drink that they and their clients enjoyed were consistently among the best in town: expensive steaks and roasts, fish, turtle, wild game and mutton, not to mention berries, peaches, grapes, figs, and even coconuts. Tea and coffee filled porcelain cups, pipes and later cigarettes held the finest local tobacco, and copious amounts of champagne flowed. All of these details suggest that Hall's clients weren't just popping in for a quickie. Clearly they expected to spend substantial time at her house, enjoying a fine meal, drinking tea, smoking, perhaps even conversing after a long day at the office. Her brothel thereby functioned more like an upscale, European-style salon with benefits rather than a stereotypical whorehouse with drunken johns chasing trollops in bloomers.
Although we know precise details of the fashion, food, and flair of Hall's elite (or "upper-ten") brothel, the identities of her johns remain mysterious. Doubtless she drew visitors from the Washington business district and the plantations of Virginia and Maryland, but uncovering the names of her Capitol Hill customers requires more speculation since no "little black book," if ever one existed, has survived. Suffice it to say, though, that the proximity of Capitol Hill gave Hall a ready and eager clientele, which contemporary sources indicate wouldn't have been unusual.
Tales from the Cattery
J. W. Buel, in his sensationalistic Mysteries and Miseries of America's Great Cities, describes how "the assignation houses of Washington are sustained almost wholly by members of the two houses of Congress." Buel even claims that within the House of Representatives there was "a reception room, which has been denominated by newspaper correspondents as the 'Cattery'. . . . In many respects it is an assignation place, maintained at public expense for the benefit of salacious congressmen." Of the Senate side, he reveals even more:
It is well known that upon special occasions, through the influence of senators, women of easy virtue are admitted, and that they give receptions therein to those who write notes on official [desks] underneath. Queens of the lobby have entre there, and from this lofty and flattering perch they become objects of unctuous admiration, displaying to excellent advantage their gorgeous apparel, with half revealing monuments of maternity peeping over brilliant bodies, and arms dressed in a rouge that helps nature amazingly.
Official Capitol records don't report the presence of prostitutes in the galleries, but other published accounts hint at their presence, including that certain enterprising women manipulated politicians to effect policy changes. One Lucy Cobb, for example, could "get a pardon [for her customers] where anybody else would fail. She probably picked up a few hundred dollars in this precarious way. . . . Policemen, folders, pages, and Congressmen all knew her, and she would walk through the Capitol unannoyed by the stare of people, and was able to make her way into almost any of the committee rooms." The author of this passage, George A. Townsend, reports similar tales, as do comparable salacious books of the time that covered any scrap of Washington scandal and intrigue that their writers could find.
A Division of Hookers
During the tumult of the Civil War, the sex trade expanded, and Washington City became well known for its illicit congress. The town attracted not only johns from the East Coast but prostitutes from as far away as the Midwest looking for a new place to set up shop, drawn by the capital's lax enforcement of vice laws, overwhelmed police force, willing clientele, and plentiful brothels. At their peak, more than 450 such houses of ill repute operated in the metropolitan area, with "ladies of easy virtue" plying their trade in bordellos, hotel rooms, gambling dens, music halls, saloons, private apartments, even parks and alleys. Much of the activity took place around Pennsylvania Avenue between Capitol Hill and the White House. One government inventory listed some eighty-five known brothels along with their locations and proprietors. Some of the more memorable establishments included the Haystack, the Ironclad, the Wolf's Den, the Devil's Own, the Blue Goose, Madame Russell's Bake Oven, and Madam Wilton's Private Residence for Ladies.
Modern estimates of the number of DC prostitutes range from 3,900 to 15,000, and with so many sex workers in town the city council briefly considered licensing them to exert some control over their industry. However, General Joseph Hooker, head of the Army of the Potomac, had a simpler plan: He herded them into an area below Pennsylvania Avenue, near the Treasury building, where he could keep an eye on any troops who might pay a visit. This consolidation of downtown brothels was known as "Joe Hooker's Division," then "Hooker's Division" or just "The Division," which gradually became the name of the neighborhood over the years, along with the old moniker of Murder Bay.
Red Light, Green Light
Though the general's name didn't give rise to the synonym for prostitute—a dubious honor that goes to New York several decades earlier—Hooker made official what was already developing in practice. Most boardinghouses left in the area already had switched to housing mainly prostitutes, or else they acted as safe houses for petty thieves, fugitives, thugs, and other miscreants. Guides to Washington, if they mentioned The Division at all, predictably thundered against it, as do modern histories of the era. When mentioned, it's described as a place where "shrieks and revelry rent the midnight air," and, outside one brothel, "the hacks of the sporting men were thickly ranked, and saucy women flounced in and out in full view of the horrified churchgoers on Sunday," which raises the question of why anyone was going to church there in the first place.
Some of the many brothels of the downtown red-light district known as The Division.
There's little doubt that the red-light district was a bleak, downtrodden area where criminals outnumbered police and poverty ran rampant. But the grim conditions of the zone did little to deter business, and a trip to The Division became something of a rite of passage. Its bordellos, music halls, and markets always had plenty of customers from beyond the neighborhood, and even its gambling halls saw their fair share of military officers and government officials. Slumming was as popular in the nineteenth century as it is today, and otherwise upstanding middle-class men weren't above getting a few cheap thrills from venturing into the rough part of town. Since the district lay conveniently between the White House and Capitol Hill, an enterprising john could easily take in the town's major sights in an afternoon. Pennsylvania Avenue, "America's Main Street," connected them all.
Of course, the brothels in The Division didn't quite reach the level of Mary Ann Hall's establishment. They came much closer to our modern conception of an old-fashioned cathouse than anything resembling an intimate salon. One visitor's testimony describes a brothel so clichéd that it could have come from Central Casting: In an elegant parlor featuring a sleek velvet couch and gas lights, an overdressed madam appeared in jewels and other finery while half a dozen prostitutes stood by in scanty garments and thick makeup. Only the fringy red lampshades and a player piano were missing.
War, Debauchery, and Reaction
The consolidation of downtown prostitution into Hooker's Division didn't bring the trade under control. Instead, as Washington City exploded during the war with troops, camp followers, and support staff, the underworld followed suit and tailored its gambling, thievery, and sex-trading operations to the new martial class.
Brothels expanded into the better parts of town, into elegant mansions with gardens and smart brick houses in the more upscale neighborhoods around Lafayette Square, the White House, and churches. Among the more elite sex-trading sites were Sal Austin's brothel near City Hall and Julie Dean's bordello in Marble Alley, a prostitution enclave three blocks west of the Capitol. Both establishments provided close and convenient access for the rich and powerful clients they entertained.
Many neighbors of these bordellos, however, took issue with all the activity taking place there. The press seized on stories of prostitutes consorting with army officers and exploited the tales to lurid effect, as described by Margaret Leech:
Painted equestriennes, in riding dresses and gaily feathered hats galloped beside their spurred and booted cavaliers. In satin and pinchbeck, the women of the town staggered boisterously into the restaurants; and the attendance of respectable citizens at the theatre was disturbed by scenes of bawdry in the audience. One officer attended the Campbell Minstrel Show at the Odd Fellows' Hall with a harlot on each arm.
As the spectacle of drinking and whoring grew louder and more chaotic, the upper crust of Washington City rose up to demand a crackdown on prostitution in general and Hooker's Division in particular. In due course, the army's Provost Guard, led by former clergyman Lieutenant W. G. Raymond, made a public show of raiding the brothels, arresting johns and prostitutes, and hauling them before a judge, night after night.
March of the Rogues
As the Civil War developed, Washington City had become a home base not only for prostitutes but for criminals drawn there because of the money to be had from the luckless soldiers in town, who proved to be willing dupes for various kinds of fraud and chicanery. There were the expected counterfeiters and con men, as well as all manner of pickpockets, from gentleman thieves to the lowliest handkerchief snatchers. In this lively carnival of vice centered around the brothel districts, the streets and houses of amusement thronged with "dancers and singers and comedians, prize fighters and gamblers, vendors of obscene literature and proprietors of 'rum-jug shops,' " who fueled the spectacle with free-flowing illegal liquor, all combining to create what one observer called the "wildest and wickedest city in the history of the world.'"
To control all the vice, the Provost Guard wasn't above a few publicity stunts. An early effort involved a roundup that paraded suspects through the streets with red signs identifying each troublemaker's crime while a band followed along playing "The Rogue's March." A more famous event saw six hundred secessionist-minded criminals receive an offer of safe passage across the border into the South, regardless of whether the Confederacy wanted them. (Some seventy prostitutes happily accepted.) Then came the dozens of sensational, well-publicized arrests. The infamous Light family, for example, featured a mother and three daughters all engaged in the sex trade. To entertain their clients, they hired an organ grinder and his excitable monkey and "danced their clothes off to the rhythm of mechanical melodies, until the racket brought the police, and they were carried, monkey and all, before the magistrate."
Madam in Trouble
One madam who had no need for such primate antics was Mary Ann Hall, who during the war maintained her Island brothel's status as the largest and most well-funded operation in DC. For years prior, the police had considered Hall and other upscale madams off-limits, likely on account of the embarrassment that might ensue if they found a wealthy banker or senator among the rest of the johns. But one indignant madam by the name of Maria Kauffman argued in court that the police were focusing obsessively on brothels like hers, in poorer neighborhoods, while pointedly ignoring the "upper-ten" houses of Austin and Hall. Spurred by the press, the authorities finally took action.
Hall was arrested and brought before a judge in a two-day trial. Nothing exceptional was stated for the record: Women were seen lounging on her property without any visible means of support. Carriages brought strange men at all hours of the night. The house was decorated with suspicious luxury. No legitimate work seemed to be going on there. Many of the witnesses were police officers and detectives who curiously betrayed a rather intimate knowledge of the place. Hall was summarily convicted, yet no record of her punishment survives. Given the typical penalties of the time, she likely paid a fine of just a few dollars.
Ultimately, despite brash headlines and dramatic activity, the Provost Guard and other police agencies failed to stamp out prostitution. By the end of the war, more bordellos were operating than at the beginning, and countless madams and prostitutes prospered even if they had to pay a small fine or spend a night in jail now and then. They even learned a trick or two from their well-paid lawyers and could navigate the legal system much better the next time around—or could offer a well-placed bribe to keep from being hauled in at all.
The authorities, however, were far from the only issue that denizens of Hooker's Division or The Island had to contend with. A much bigger threat was the ubiquitous pollution of such neighborhoods, which had only gotten worse during the war and now threatened to overwhelm the capital with disease and decay.
Filth in the City
No matter how many fine cuts of steak or magnums of champagne a madam bought or how exclusive her guest list, she still had to deal with the surrounding neighborhood, and in most cases that neighborhood was dreadful. Upper-shelf bagnios could front such major streets as Pennsylvania Avenue and Ohio Avenue, but the nastiest dives lay in the alleys behind. In the slum geography of nineteenth-century Washington City, hundreds of these cramped little roads interlaced the interiors of the wider blocks, giving access to the capital's most wretched gambling halls, saloons, shacks, and rubbish piles.
Filthy and decrepit alleys lined many interior blocks of the city, persisting well into the twentieth century.
The Island, for example, contained the forbidding Louse Alley, regularly mentioned as the worst street in town, which lacked running water and featured dozens of unkempt privies and piles of garbage. Predictably, it hosted all types of crime and of course vermin. But this wretched urban lane didn't lie just down the street from Mary Ann Hall's elite brothel—it ran right outside her back door. Indeed, Hall's fantasyland for the upper crust stood in an area that was home to half the crimes committed in the entire District. One particular concentration of alley housing lay south along F Street, where many migrants with little money or job prospects settled. An 1854 report by the town's Board of Health found a high death rate for children living in such squalid conditions, and "The higher proportion of these deaths are among the children of negro, of foreign, and of destitute native parents."
Overall, though, Hooker's Division was the bleakest of all. It too had plenty of alleys, making it an underworld warren where criminals could practice their crafts with impunity, but its biggest problem was the city canal, that fearsome "miasmatic swamp." When last we encountered it, in the 1830s, the underfunded and poorly designed waterway was silting up at both ends as garbage collected in the center section near downtown. By midcentury, the canal had worsened considerably. Poor funding meant a lack of even basic maintenance. Sedimentation virtually prevented end-to-end navigation. Garbage and sewage turned the shallow channel into an ongoing health menace. Some critics called it a "death-ditch," responsible for the town's regular outbreaks of disease, its "green, stinking water" making the capital noxious to the nose and eyes during the summer months. During spring rains, the canal often flooded, sending the whole vile stew into The Division's streets and basements as far north as 7th Street.
Economics of the Oldest Profession
Despite the toxic, crime-riddled zones where most of the brothels stood, no amount of pollution or violence seemed to limit their appeal, as they grew and expanded during and after the war and remained among Washington City's top attractions, licit or illicit. They also provided one the few reliable sources of employment for thousands of women.
Sordid, lower-class houses in The Division barely paid their sex workers enough to survive, but midrange brothels offered adequate salaries to their employees, plus regular meals and serviceable lodging. They in turn bought goods from vendors who specialized in selling overpriced wares to prostitutes—everything from cosmetics and perfume to laundry services and medicine. The patent medicines that they bought also encompassed narcotics, such as cocaine and morphine. (The more unusual cure-alls included Putnam's White Satin Bouquet, Mrs. Winslow's Soothing Syrup, and something called Valentine's Meat Juice, meant to relieve venereal disease as well as influenza and tuberculosis.) Houses of prostitution functioned as what economists call a "multiplier," creating new jobs for traders doing business with a house and establishing an economic incentive for the expansion of the sex-trading market.
The market continued to draw new employees because, for many young women who didn't come from middle-class or elite families, selling sex provided a decent wage. Ruth Rosen's groundbreaking study The Lost Sisterhood makes it plain: For women doing aboveboard work in shops and factories, salaries averaged about six dollars a week by the end of the nineteenth century; for prostitutes, the pay was forty to fifty dollars a week. The downsides were the moral qualms one might have about undertaking such work, the risks of venereal disease and vice arrests, and the physical discomfort and potential danger of fornicating with strange, possibly violent men.
Intelligent critics, then as now, were not ignorant of the links between economic desperation and prostitution for the capital's underprivileged women. William Sanger, in 1876, saw a widespread bias against women as contributing to their financial troubles that led to the sex trade. That same decade the Women's Christian Association undertook a groundbreaking series of interviews with sex workers and public hearings on the trade. The group successfully convinced the police vice squad to delay its brothel raids to allow time to create a health dispensary and charity that catered to the needs of these working women. Establishing the dispensary was a forward-thinking idea and proved to be controversial in its time. However, it was only in operation for a few years before it had to close due to the death of its landlord, Mary Ann Hall.
Hall's End
Hall met her end in 1886, and by all accounts her life had been a success: Aside from a brief tussle with the law, she avoided jail and the pitfalls of disease, addiction, and bankruptcy. She owned property throughout DC and a farm in Virginia, and her assets at the time of her death were valued at $67,000, about $2 million today. Her estate was large enough for her heirs to fight over it—and luckily so, because court records preserved a description of what her house of ill repute featured and a hint of how it operated.
As a final touch, Hall honored herself with a prominent funerary monument in Congressional Cemetery. On its capital kneels the plaintive figure of a woman lost in thought, which could be mistaken for an emblem of grief or some virtue or another. In reality she represents a lady of the night who ran one of the most lucrative enterprises in town. Thus, through death and with time, Mary Ann Hall finally became legitimate. In a touch of irony that she might have enjoyed, she lies in peaceful repose under her column, in a well-tended plot of land, close to the grave of J. Edgar Hoover.
Angelic statue in Congressional Cemetery memorializing Mary Ann Hall.
Twilight of a Fantasy
The rise and triumph of prostitution in the District of Columbia offers a telling case study of how far the original plan of the capital had fallen. The carefully laid blueprints of its designers, both physical and moral, had turned to mud. Pierre L'Enfant and the Founding Fathers had envisioned the city as a political lodestar and glistening centerpiece of the new republic. Instead, Washington City inverted that dream.
Between the Capitol and the White House, where L'Enfant imagined elegant mansions for statesmen and diplomats, there were filthy tenements and hovels. Where he saw useful canals and beautiful fountains, there were sewers and stagnant water. Where he saw grand avenues for strolling, there were dirty lanes and broken pavements. Where he saw smart theaters, churches, banks, and salons, there were squalid alleys, gambling halls, and bordellos catering to criminals and johns. The city had become a grotesque parody of everything that he and his contemporaries had envisioned, the inevitable legacy of seven decades of congressional indifference and incompetence, and the dangers posed by unelected, unaccountable leaders. And at the dawn of war, the capital was about to enter its darkest and most tumultuous period of all.
Eight
Seeing the Elephant
By 1862 the antebellum landscape of Washington City had vanished. The old town—long derided as a failed blueprint, a stillborn utopia, a national disgrace—suddenly became the key to victory for the Army of the Potomac and the Union itself. Holding and fortifying the capital became critical, as did making it a base for the federal government's prosecution of the war against the rebel states. The transformation wasn't hard to see: Barracks peppered the hillsides, hospitals occupied public spaces, nearby cemeteries began filling up, and camps for runaway slaves sprang up in ever larger numbers.
The textbook history of the capital's role in the Civil War usually focuses on the life and actions of Abraham Lincoln. It makes for epic, stirring biography, but it barely describes what Washington City resembled during these dark years or what its residents saw and experienced inside the battle lines. As the war moved the center of power from the halls of Congress to the White House and the War Department, the entire District of Columbia experienced more dramatic change from 1861 to 1865 than perhaps any other urban center in the North. Accordingly, the federal government unleashed its full, formidable might to fight secessionists and subversives—even if that meant ignoring more than a few constitutional liberties—and forced Washingtonians to confront the legacy of slavery by engineering its abrupt conclusion.
Volunteer Work
Trouble began almost as soon as South Carolina seceded on Christmas Eve, 1860. It readily became apparent that other slaveholding states would follow quickly in its wake, forming a daunting bloc ready to defend its actions by force. The national government knew it would have a hard time stopping it. Worse, many residents of the new Confederate states had their eye on the District of Columbia as a great prize in the coming battle; the rebel secretary of war even planned to fly the Stars and Bars over the Capitol once they had captured it. Southern armies would have plenty of sympathizers too if they invaded the capital. Members of aristocratic, slaveholding families held many positions in the Buchanan administration, from high-ranking politicians and diplomats to military officers and an array of midlevel clerks. Nearly half the residents of the District had family ties of one kind or another to the South.
More depressing for Unionists in the capital, the new Lincoln administration wouldn't be taking the reins until March 1861—and as was customary for the timing of the transfer of power then—leaving the town's defense in the hands of the doddering lame-duck president Buchanan and "Old Fuss and Feathers" general Winfield Scott, whose service to the country began in the War of 1812. Scott, however, astutely recommended that Buchanan promote US Army topographical engineer Charles Stone to the rank of colonel and to the role of inspector general of the District so he could provide an overview of what defenses the capital possessed. What Stone found wasn't pretty.
While there were three hundred to four hundred Marines at their barracks and fifty-six officers and ordnance men at the Arsenal, the local militia looked suspect. Units such as the National Rifles swarmed with secessionists, and outgoing Secretary of War John Floyd had supplied them plentifully with arms and ammunition, including a few howitzers. Moreover, instead of obeying General Scott's order to reinforce federal garrisons in the Southern states, Floyd shipped 115,000 muskets and rifles to rebel arsenals and planned to send 120 cannons from Pittsburgh to the Deep South as well. Luckily, Floyd's latter order was overturned before it went into effect—after which he resigned and took up arms for the Confederacy. (Floyd later became known for helping lose the Battle of Fort Donelson, which handed an obscure Union commander named Ulysses S. Grant his first major victory.)
Despite the efforts of turncoats like Floyd, Charles Stone did his job well, and by February he had organized twenty-five militia companies and purged the National Rifles and other companies of their subversives. He brought together two thousand infantrymen, two hundred cavalrymen, two batteries of artillery, and a company of engineers for militia training and service. This complement of citizen-soldiers formed a critical defense for the capital when it lay almost completely exposed to hostile forces. It wouldn't be strong enough to fight off a Southern army, but at least it provided a better defense against the pro-slavery mobs and other hooligans who had run riot in earlier years.
More drama came in short order, including a twelve-day threat to the capital in April, when Maryland secessionists isolated the town from the North by cutting telegraph wires and burning bridges near Baltimore. The Seventh New York and other regiments saved Washington City by arriving just in time to populate the capital with its first major complement of Union troops. Many more arrived in the coming months as the US military transformed the District of Columbia from a sleepy, dysfunctional village into a smart and efficient martial colony.
Source: Albert Boschke, topographical map of the District of Columbia, 1861.
Oaths of Iron
Even before the Northern troops arrived in the capital, the more overt secessionists made a quick exit, including hundreds of families of Southern slaveholders, government clerks, and army officers. Despite the disappearance of the more vocal rebels, a climate of fear and paranoia took hold of the capital as rumors abounded over conspiracies involving saboteurs trying to deliver the District into the hands of the Confederacy. The federal reaction was swift, imposing, and effective—some even called it dictatorship.
Lincoln began to suspend the writ of habeas corpus during 1861, and the following year he denied it to all persons detained under military order. Confederate sympathizers were labeled "Copperheads" and found their houses searched, their property confiscated, and themselves carted off to prison with no expectation of trial, legal counsel, or often any explanation of the charges against them. Secretary of State William Seward led the charge in hunting down potential rebels with a team of crack detectives to do his dirty work. (Secretary of War Edwin Stanton later took over responsibility for this branch of state security and released a number of the wrongly imprisoned.)
By August, Congress provided an additional tool for rooting out subversives by imposing an oath to the Constitution and the Union on all government employees. Among them was the mayor himself, James Berret, a Southern Democrat. Initially declining to take the oath, Berret sat in prison for three weeks until he changed his mind . . . and relinquished his office. More than a hundred other officeholders refused the oath and were driven from their positions, along with more than three hundred army officers in 1861 alone. The following May, an even more "iron-clad oath" applied to all residents of Georgetown and Washington City trying to vote in municipal elections.
The Fallen Capitol
Wartime paranoia reached ridiculous extremes—some even imagined Secretary of the Smithsonian Joseph Henry sending covert signals to secessionists in his castle turrets—but Southern spies did operate in Washington City and did anything they could to mine information on troop movements, battle plans, public morale, and anything else of value to the Confederate leadership. The most famous spy in town, Rose O'Neal Greenhow, a holdover from the old Southern gentry, hadn't left town like so many of her peers. Instead, she relayed secrets from her sources in the federal government to Confederate general P. G. T. Beauregard, which helped the South rout the North in the First Battle of Bull Run. She was summarily arrested and imprisoned, but even from her cell she was said to be adept at passing information to her associates outside the prison walls.
Taking the lead in the arrest and detention of potential and actual spies was the army's provost marshal, who—for enemies of the state, including Rose Greenhow—favored the ominous and much-feared Old Capitol Prison, a building with a long and unexpected history.
Thomas Law and others had conceived it as the Brick Capitol, the temporary home for Congress after the British burned the town in 1814. The sturdy three-story brick structure played a valuable role in the late 1810s, temporarily housing the legislature when countless schemers tried to displace Washington City as the national capital. In the years following it became a private school and a boardinghouse for congressmen, as well as the publishing site of Anne Royall's newspaper The Huntress, until the federal government purchased it and converted it to a prison in spring 1861. A block south stood a line of tumbledown wooden buildings known before the war as Carroll Row, the site of one of the capital's first hotels and boardinghouses. Rechristened Carroll Prison, the structures took their name from civic leader and property speculator Daniel Carroll. The jail also employed runaway slaves from Virginia as an ad hoc labor force.
Postwar view of the former Carroll Prison and Southeast DC.
Virginia Lomax, wrongly imprisoned at Old Capitol Prison for inquiring about her friends held there, later wrote a famous account of her ordeal and described her "accommodations" as follows:
The room was one mass of dirt; spiderwebs hung in festoons from the ceiling, and vermin of all kinds ran over the floor. The walls had been papered, but dampness had caused most of it to fall off, while all over that which was left were great spots of grease . . . The furniture consisted of an iron bedstead, pillows, and mattress of straw, a pair of sheets, and a brown blanket. Between the windows stood a small table, on which was a stone jug containing water, and a tin cup. A tin basin was on the floor. One wooden chair completed the inventory.
The prison held a surprising number of women prisoners, not only Lomax and actual spies Greenhow and Belle Boyd but all manner of upper-crust matrons—"ladies of education and refinement," according to the prison superintendent—whose sympathies lay on the wrong side of the conflict. The warden, William Wood, found it useful to detain such Southern sympathizers, since they could serve as useful sources of information about rebel spies and other activity. Wood employed a complex system of intercepting and reading prisoners' mail, used his own spies within the prison to figure out what the inmates were doing, and allowed Colonel Lafayette Baker, like "a tiger on the loose," to interrogate suspects in the fearsome Room 19.
Baker took over the job of Union spymaster and intelligence director from the famous Allan Pinkerton in 1862. Using a force of two thousand men, Baker essentially ran his own secret police, investigating anyone alleged to be committing treason, fraud, counterfeiting, profiteering, or bounty jumping, along with gamblers, prostitutes, their johns, and dealers in black-market medicine and illicit liquor. For his efforts, Baker's enemies branded him a tyrant, but few doubted the efficacy of his organization. He had a knack for offending those in power, usually by spying on them, and then getting fired; federal officials then decided they once again needed his special brand of skills and rehired him. (He most famously tracked down the conspirators in the Lincoln assassination.)
As a result of all of this activity, the capital veered closer to a police state than perhaps any major city in American history. Democracy still flickered here and there in the sharp protests from well-protected members of the upper class and in the vigorous dissent in Congress over the conduct of the war. But the executive branch exercised almost unchecked rule in most areas of civic life. Not surprisingly, newspapers in the early years of the war represented only a narrow slice of acceptable politics, from the National Intelligencer and National Republican (moderate to conservative Republican views) to the Daily Chronicle (radical Republican views). Even the strongly Democratic-leaning and widely read Evening Star quickly came around to supporting the Lincoln administration, though it maintained its criticisms of the dismal state of urban infrastructure.
Rise of a New Force
Paradoxically, even as the federal government was expanding its power over spies, secessionists, and saboteurs, the local government was proving thoroughly inept in dealing with garden-variety criminals. The District of Columbia had fallen far behind other US cities in law enforcement. New York created a formal police department in 1844, as had Boston, Philadelphia, Chicago, Baltimore, and New Orleans in the 1850s. When the Metropolitan Police finally came into being in August 1861, covering Washington City and Georgetown, it bore some of the hallmarks of those other forces: The District had ten precincts, each under the control of a police sergeant; station houses administered each precinct; and a superintendent oversaw the entire department, the first being William Webb.
It looked good on paper, and almost anything would have been an improvement on the city's dysfunctional constables and Auxiliary Guard. But the DC force faced significant challenges, thanks to the unwillingness of Congress—once again—to fully fund or staff an organization it had created. For a start, the department had far fewer patrolmen than it needed: only 161 officers to cover 75,000 people in 1860 and 140,000 people at the wartime height of 1864. An early report from the police commission in 1862 didn't gloss over the daunting challenge of having one officer for every 625 citizens, most spread out across 307 miles of roads and alleys. Allowing for sickness, absences, and double beats, the average officer beat stretched four miles, and covering it proved next to impossible. The town, the report claimed, needed a minimum of 545 officers to patrol such a huge, crime-ridden place, which also contained "the very worst and most disorderly class of residents from other cities."
The duties of these beleaguered officers didn't extend just to preserving the peace and tracking down lawbreakers. Instead, Congress made sure to pile on the work, directing them to fix just about everything that made the District of Columbia unpleasant. Some of these labors included cracking down on pawnbrokers, auctioneers, gamblers, drunks, vagrants, and disorderly citizens; guarding firefighters and property around burning buildings; maintaining blue laws on the Sabbath; looking after visitors new to town at docks and rail depots; protecting the public from illness and disease; and dealing with all manner of public nuisances, from "dead horses, bone factories, and garbage," to filthy stables and hog pens, leaking privies, broken sewers, and manure and ash heaps.
Malicious Mischief
The appearance of the police didn't exactly inspire fear in the hearts of criminals. At first the officers didn't even have weapons, badges, or uniforms. They were given a small oil band reading Metropolitan Police to drape around their hats, and for protection they had to create their own clubs or mallets from whatever woodpile they could find. They were better outfitted as the months went on, but the difficulty and brutality of the work didn't change.
More than half a century later, veteran patrolman Lingan Anderson gave an interview to the Washington Post in which he detailed the raw, barbaric nature of early police work. One of the biggest challenges was trying to corral enraged or drunk suspects and take them back to the station house. Sometimes they used horses for the task, but other times they had to force a suspect to walk a great distance, even as he tried "to straddle your chest so he can beat your head off." In one case, Anderson recalled having to strong-arm one brute, nearly a foot taller, a mile and a half to the station, trying to keep the man from escaping or punching him along the way. Finally, armed with a club, Anderson "belted him so hard that he had to lay down for a little while before he could get up and go on." Anderson ended up hauling him in a wheelbarrow for the rest of the journey, during which the suspect's mood brightened considerably: "All the way to the station the prisoner kept singing 'Nelly Gray' at the top of his voice, and when we finally landed him [at the station] he told us he'd had a fine evening."
Anderson was shot in the leg during one of the worst episodes of violence he witnessed, a ferocious barroom brawl and gunfight between pro-Southern sympathizers and abolitionists. He tangled again with the Copperheads when a group of them paraded down 4th Street, "up to devilment." Their infernal strategy included outnumbering the cops, one hundred to one, and trying to pull them from their horses to beat them. The police responded with guns and clubs and finally rode down the rioters on horseback.
The levels of street crime could be staggering. During Election Day skirmishes in June 1862, the force separated crowds from their knives, clubs, and guns in one part of town, halted scattered fighting between partisan zealots in another, and joined the army in stopping a fusillade of bricks and stones near City Hall in yet another.
Despite their meager numbers, the Metropolitan Police force arrested a huge number of people: 22,000 in the first year and 24,000 in 1863, amounting to a rate three and a half times that of Brooklyn. Most of the offenses, however, didn't concern violent crimes but drunk and/or disorderly conduct. Assaults, burglaries, and various kinds of fraud and thievery made up most of the rest of the offenses, along with a handful of arrests for adultery, bigamy, fast driving, vagrancy, and the catchall "malicious mischief."
Cops versus Cops
With so many people up to devilment, the task of keeping public order strayed well beyond the ability of the Metropolitan Police. But they weren't the only cops in town. As soon as the war began, the army's Provost Guard began patrolling the town at night to keep soldiers from committing crimes—including a law passed by Congress to keep liquor out of their hands—then arresting them when they did break the law. A few months later the Provost Guard expanded its mission to include daytime patrols and arrested citizens of the District along with army personnel.
The Metropolitan Police force arrested its own share of soldiers, nabbing 5,750 of them during its first year of operation, more than a quarter of its total arrests. As Lingan Anderson recalled, the soldiers "filled up on forty-rod liquor . . . and if we interfered we were their meat." Not all the offenses related to possessing illegal liquor, though. Sometimes rogue soldiers raced their carriages down Pennsylvania Avenue at breakneck speed and the police tried to stop them—despite the risk of being dragged by their horses or sustaining broken ribs. Other times garrulous troops fought with citizens. The police interceded, only to be beaten themselves by the soldiers, who often escaped arrest or court-martial. The War Department increased the potential conflict by ordering the police to hunt down army deserters and anyone resisting the wartime draft. While some officers did their duty, others exploited their power and became "substitute brokers," pocketing a handsome fee for finding someone willing to enlist in lieu of the draftee. One particular cop managed to pocket $125 for each substitute he found.
The hostility between the Metropolitan Police and rogue soldiers peaked in September 1862, when a full-scale riot broke out downtown after some drunken troops got into a dispute with a merchant and beat him. Soon the furious soldiers vented their rage on passersby and then on area blacks. A trio of police officers tried to intervene, but a volley of bricks and stones greeted them, and the mob chased them for several blocks. The Provost Guard made a belated appearance and arrested more than twenty-five malefactors. It was one of the most violent riots in wartime DC, made even worse because members of a military force who had sworn oaths to protect the Union had instead disgraced it.
Muddy Footprints
The lawless character of the town matched its physical appearance. Margaret Leech, in her magisterial history of wartime Washington City, described the place as "sour as a medieval plague spot," thanks to its rank odors and lack of ventilated buildings. The increased presence of military wagons and foot traffic buried some streets in almost a foot of mud, and great dust clouds arose in the dry months to envelop the town in a hot, choking atmosphere.
The lack of proper sanitation for soldiers garrisoned in the capital posed a particular challenge. The local Board of Health declared many of the barracks to be filthy and a public health hazard. (It didn't help that some soldiers new to town bathed in the fetid waters of the city canal.) Such poor living conditions, combined with a meager diet in the early war years, kept the men "half-starved, living on crackers and cold water." Soon enough, illnesses such as measles, whooping cough, and diarrhea claimed the good health of a number of the soldiers regardless of whether they had experienced combat. Adding insult to injury, the military located Camp Fry, one of its largest encampments, in the capital's own disease central, Foggy Bottom, best known for its equally large encampments of infectious mosquitoes. Here they put thousands of troops in barracks, supplies in warehouses, and horses and mules in stables.
The Union Army used the forlorn grounds of the Washington Monument as a livestock corral, with slaughterhouses nearby.
A great necessity for military transport and provision, livestock also created major sanitation problems, including the excrement of thousands of draft animals matched with a lack of effective measures to deal with it. The army built slaughterhouses for its droves of cattle, butchered them freely within city limits, and pastured its herds on the grounds of the Washington Monument. Soon enough, the stench of feces from the live animals and of the carcasses of the dead ones left in the street overwhelmed the town.
To the army, these concerns paled in comparison to the more critical mission of keeping the country together and subduing the rebellion. Accordingly, the war forced the city to grow and expand as a vital supply base and staging point for battle. The most visible examples of this change included not only the countless soldiers billeted here on their way to campaigns in the South, but also the hospital workers who attended to them when they came back.
Under the Blade
The waves of casualties came by land, rail, and sea. They arrived over rutted roads from Virginia in two- and four-wheeled horse-drawn ambulances. They came via the railroad depot on The Island, in boxcars and flatcars on mattresses or bare boards. They arrived at the wharves at 6th and 7th Streets on riverboats, where they lay in cabins and on decks, in saloons and on stairs. But few general hospitals existed to care for all the wounded, so the army had to improvise. It requisitioned schools, hotels, barns, homes, and even boats to the task of keeping soldiers alive.
Hospital wards and operating rooms sprang up inside the old Braddock House, where George Washington once held councils of war. Wounded men found themselves in the Insane Asylum, the halls of Congress, and the Patent Office—where they shared space with miniature models of inventions. Even churches saw their pulpits, cushions, and hymnals stashed away, their pews covered with boards for operating tables, and their doors greeting ambulances of the dying instead of the carriages of the pious. The amenities for the wounded were as spartan as the facilities themselves. Sacks of straw or corn shucks doubled as mattresses, and, where there were no mattresses, old boxes, benches, and woodpiles had to suffice.
Nor were there enough surgeons for all the casualties—at most, one doctor per every seventy-five—so an injured soldier might have to wait three to five days before seeing a physician. When he did receive care, he might expect a mixture of chloroform and whiskey to disinfect his wounds, if anything at all, and the same kinds of fluids to be consumed as painkillers. In the days before germ theory, elementary hygiene suffered: Soiled bandages were reused, wax and lard were applied to suppurating wounds, and sponges were dipped in dirty water and applied to multiple patients. Predictably, gangrene ran rampant, and when necrosis developed a surgeon could saw off a damaged limb in as few as forty seconds. Such speed barely lessened the terror of the blade, though. Some hospitals had piles of severed arms and legs outside, and after particularly bloody battles, such as Fredericksburg, a given hospital could become "a house full of amputated limbs."
Infectious diseases also afflicted the Army of the Potomac, both when its soldiers occupied the field and when they had gone to the District for treatment. In the early years, typhoid fever, malaria, and measles posed the major threats, and as the carnage continued diarrhea, chronic dysentery, tuberculosis, and an unsettling typhoid-malaria combination also ravaged the troops and those who tended to them. (Typhoid in its various forms was one of the top killers of the war, felling an estimated 81,360 in the Union army alone.) Shockingly, soldiers had a greater chance of survival on the battlefield than in the hospital. More soldiers died from infections than bullets.
At various times, up to fifty-six hospitals operated in the capital and held some fifty thousand soldiers—more than the town's entire population just a dozen years earlier. Of varying sizes, the facilities usually employed a team of doctors, stewards, chaplains, clerks, cooks, launderers, gardeners, grave diggers, and guards. But for many of the wounded, the most visible and benevolent presence belonged to the nurses.
Dix's Legions
Our modern conception of nurses doesn't quite fit who they were and what they did in the Civil War. The majority of nurses were men, but for women the term usually applied to white ladies of the middle and upper class. "Matron" was a more generic term for a woman who assisted in medical care and also cooked and did laundry. If such women were black or working-class white, they were called "cooks" or "laundresses," even though many performed nursing duties. Some of the latter found the designation financially crippling after the war. Maria Bear Toliver, who had worked in camps for runaway slaves and risked her life in a smallpox hospital, tried for more than three decades to get a pension from the federal government—to no avail.
Nurses handled a great number of tasks. They changed wound dressings, assisted in surgical operations, and provided medicine to patients. They acted as personal secretaries for injured men, writing their letters home or reading to them. They provided what we now call physical therapy or psychiatric care to soldiers suffering physical or mental trauma. They listened to the confessions of dying men, and they sang and played music to lighten the otherwise grim proceedings. They worked sixteen-hour days, sleeping in designated quarters if they were lucky or, if they weren't, making do with luggage or supply rooms as bedchambers. Most were aging widows with sons in the military or were longtime activists for abolition or women's rights.
At the head of Union nursing efforts was Dorothea Dix, already nationally well known and admired for her reform efforts in jails, almshouses, and asylums. The supervisor for the hiring and assignment of all nurses for the army, she had a reputation for being conscientious and driven as well as rigid, brusque, and capricious. She insisted that any nurse brought into service have strong morals, dress plainly, know how to cook, and look unattractive (the last to ensure that bedridden men would avoid sexual temptation—even as they struggled to breathe). Other prospective nurses went through Protestant organizations like the Christian Commission, Catholic groups like the Sisters of Charity (which provided a steady supply of nuns), and most importantly the US Sanitary Commission.
The commission united the work of charitable groups and individuals to provide food, medicine, and care to the sick, anything from "sugar, shirts, crackers, farina, drawers, and some chicken and oysters" to woolen underclothing and head rests. The commission also operated soldiers' homes for rehabilitation and recovery, home lodges that offered convalescent care for soldiers just out of the hospital, sanitary fairs throughout the country to raise funds for veterans, and a nurses' home in Washington City that provided rest and relief to medical workers overwhelmed by all the bloodshed and suffering. It also published regular bulletins that detailed its work and issued meticulous, pedantic recommendations for nurses: using a "noiseless step" when walking, ensuring "no door or window in the patient's room shall rattle or creak," being "as motionless as possible" when speaking to patients, and never speaking to an invalid from behind.
Tales of the Armory
Armory Square Hospital, the capital's highest-profile facility, sat on the eastern side of the Mall between the Smithsonian Castle and the city canal alongside a militia armory. It featured fifty white wooden buildings grouped into ten wards, each of which acted as its own mini-hospital. Unlike other local facilities, the Armory Square was well lit and ventilated, which made it one of the most modern hospitals around. The facility certainly needed to provide the best care in town, because it saw the worst casualties of the war. It lay a short distance from the railroad depot at Maryland Avenue and the wharves to the south. As such, it served as the hospital of first resort for grievously injured and dying men who needed immediate attention as soon as they returned from the battlefield. Not surprisingly, it also had the greatest number of wartime deaths of any facility in the region.
Contemporaries realized the significance of Armory Square, and it attracted some of wartime Washington City's most able chroniclers. One was Amanda Akin, the "Lady Nurse of Ward E," whose diary details the mortal struggles faced by the men and her challenges in providing care to them. While she considered her hospital "the most complete and best conducted institution of its kind during the Civil War," she had no illusions about the suffering of the soldiers, which ranged from hemorrhages and violent headaches to "neuralgic pain" and limb amputations.
But Akin doesn't dwell on the misery of her patients. Instead she details what she did to provide mirth and distraction. She played backgammon with them, staged impromptu classical concerts, delivered new and interesting foods such as "guava jelly," read literature and poems aloud, and even composed goofy rhymes for her coworkers. Her purpose in entertaining the wounded was clear: "anything that will keep them from despondency, and will not add to anyone's sufferings is welcomed with pleasure."
A ward at Armory Square Hospital, the most renowned of Washington City's many wartime hospitals.
Armory Square's most famous chronicler was Walt Whitman, who composed some of the war's most poignant and memorable descriptions of death and suffering. Working as a nurse in several of the capital's wards, he spent much time at Armory Square, which attracted him "because it contains by far the worst cases, most repulsive wounds, has the most suffering & most need of consolation—I go every day without fail, & often at night—sometimes stay very late—no one interferes with me, guards, doctors, nurses, nor any one—I am let to take my own course.
The hospital tolerated Whitman, but it didn't exactly welcome him. The controversial poet's then-scandalous work Leaves of Grass challenged conventional notions of moral propriety and poetic form. It made him a celebrated figure in some literary quarters, but the more devout ladies at the Armory Square had their doubts, Akin among them. She called him an "odd-looking genius" who "has written some very queer books about 'Free Love,' etc. . . . When he stalks down the ward I feel the 'prickings of my thumbs,' and never speak to him. . . . With all his peculiar interest in our soldier boys he does not appeal to me."
But propriety had its limits, and throughout her book Akin exhibits a strange fascination with America's bold new poet and itinerant nurse, however much she disapproves of his ways. She tellingly gives an entire chapter in her diary to an excerpt from Whitman's work, in which he praises a hospital concert featuring convalescent soldiers and nurses: "I am not sure but I received as much pleasure under the circumstances sitting there as I have had from the best Italian compositions. . . . The sounds and scene altogether have made an indelible impression on my memory."
Camp Misery and Beyond
The conditions at other Washington-area hospitals were much worse: no concerts, games, guava jelly, or famous poets. Julia Wheelock, another author of a fine memoir, The Boys in White (named for the shrouded bodies of the dead), found herself at Camp Convalescent, aka "Camp Misery," near Alexandria. She unsparingly recorded her contempt for it:
Pen would fail to describe one-half its wretchedness. Here were ten to fifteen thousand soldiers—not simply the convalescent, but the sick and dying—many of them destitute, with not even a blanket or an overcoat . . . sick with fever, pneumonia, or chronic diarrhea, eating raw pork and lying upon the cold, damp ground . . . the wonder will be, not that they died, but that any recovered.
Only after several soldiers froze to death in winter 1862 did the camp finally close and relocate.
Camp Convalescent represented the nadir of hospitals in the capital area, but many run-of-the-mill facilities were almost as bleak. One of the most well chronicled was Georgetown's Union Hospital, a converted hotel. Its darkened hallways and cold floors provided a sense of "universal depression" to the enlisted men confined there and to the nurses who dealt with living conditions almost as bad as those of the patients. A Sanitary Commission report in 1861 described "narrow, tortuous and abrupt" hallways, a lack of functional sinks and bathrooms, decaying woodwork, undrained cellars, and worst of all no morgue. Louisa May Alcott, who worked there briefly as a nurse before Little Women made her famous, called it the "Hurly Burly Hotel," a place where "disorder, discomfort, bad management . . . reduced things to a condition I despair of describing." Her patients stood "ragged, gaunt and pale, mud to the knees, with bloody bandages untouched since put on days before; many bundled up in blankets, coats being lost or useless; and all wearing that disheartened look which proclaimed defeat." Hospital typhoid afflicted Alcott herself, forcing her to leave the hospital. She survived, but at the physical expense of a long and painful recovery.
The grim confines of Camp Convalescent, also known as "Camp Misery," represented the worst of DC's hospitals.
Soldier of God
Another trenchant wartime diarist at Union Hospital, Alcott's boss Hannah Ropes, a Christian activist, had a background in abolitionist politics that gave her a radical stance on injustice where she found it. Ropes hailed from Massachusetts, wife of one William Ropes, who abandoned his family and left her and their son and daughter to fend for themselves. Her son, Edward, became a homesteader in the worst possible place: Kansas during its "Bleeding Kansas" phase of internecine guerrilla warfare over slavery. She and her daughter followed him there, and, as she described in her book Six Months in Kansas, they soon found themselves under the threat of pro-slavery Missourians, for whom "To kill a man is not much more than to shoot a buck." In response, she had no qualms about the reality of self-preservation: "How strange it will seem to you to hear that I have loaded pistols and a bowie-knife upon my table at night, three of Sharp's rifles, loaded, standing in the room," and "Now the hour for action has come . . . and may Heaven speed the RIGHT!"
Six years later, after Edward enlisted in the Union army, Ropes entered the fray again, this time a bit farther from the front lines. She came to the capital—"the ugliest and dirtiest city I ever saw"—with no proper experience in nursing, armed only with her knowledge of Florence Nightingale's influential Notes on Nursing. Despite her inexperience and lack of training—typical for most nurses in the war, before the development of professional organizations and proper licensing—Dorothea Dix accepted her as a ward matron for Union Hospital. Ropes started in July 1862.
Frightful Grandeur
Ropes had great sympathy for the soldiers in her care and great impatience for the cogs of bureaucracy that hampered that care. She gathered supplies from donations, the Sanitary Commission, and anyone with influence and recorded her observations of the men in their bleakest hour. The workers around her generally provided good care, but the head surgeon's treatment of the soldiers disgusted her. She claimed that he cared "no more for a private than for a dog" and that he released soldiers not fully healed or recovered: "the poor men in all the hospitals barely escape with life or clothes or money." She had already encountered the darkest side of human nature in Kansas, had "seen the elephant"—a popular nineteenth-century term for an intense emotional experience, often in combat—and didn't shrink from it. Thus, she resolved to act even if doing so meant upsetting the hierarchy of the medical system.
At Union Hospital, as with others in the capital, the top surgeon, A. M. Clark, reported to US Surgeon General William Hammond and, above him, Secretary of War Edwin Stanton. Below the chief was an array of assistants, contract physicians, medical students, and wardmasters who assisted both doctors and nurses. Hannah Ropes's main nemesis, though, was the hospital steward, a devious (unnamed) character who withheld food from the injured men, stole their clothes, and sold their rations. After he suggested to Ropes that they form a ring to purloin hospital food and supplies, she reported him to Clark, but the high-handed surgeon dismissed her complaints. She went over his head to Surgeon General Hammond, who referred her complaint back to Clark, who again dismissed it out of hand. Finally, when the steward attacked a patient with a chisel and created his own little prison for disfavored patients in the damp, rat-infested cellar, Ropes took dramatic action. She ignored the chain of command entirely and set up a meeting with the secretary of war.
At Stanton's office, as Ropes mentally prepared herself to be locked away for insubordination among "the rats and cockroaches," the secretary entered: "a large man with dark beard, bald head, and legal brow" whose eyes "gleamed with the fire of a purpose." Ropes stated the case about the problems at her hospital as succinctly as she could.
Stanton's response: "Call the Provost Marshal."
The marshal charged into Union Hospital with his investigators in "a frightfully grand scene." He released one of the steward's victims from the cellar and arrested the steward and sent him to the Old Capitol Prison—to the "pale terror of the head surgeon" and the fearful reaction of his subordinate officers. Soon after, head surgeon Clark himself went to prison, and a medical inspector came to the hospital. He looked around and questioned Ropes about the relationship of the steward and chief surgeon. She compared the former to a whispering devil and the latter to a tyrant, "harsh and unsympathizing." Her words kept them imprisoned a while longer.
Ropes had engineered a shocking, unexpected outcome. Not only had she upended the protocols between surgeons and their supposed subordinates, she had struck a powerful blow against the culture of greed and corruption that had held sway for decades in Washington City. What replaced it, at least for a few years, was a new military efficiency, intolerance for bureaucratic incompetence, and frightening use of absolute power.
Within the Fray
Countless other nurses and support staff took on miscreants in the medical system where they found them, from administrators unfairly withholding food and supplies from needy patients to rogue surgeons threatening and harassing their staff. Even though many surgeons acted heroically and diligently to save the lives of soldiers, they had fraught relationships with the female nurses below them. Nurse diarist Georgeanna Woolsey wrote, "Hardly a surgeon of whom I can think received or treated them with even common courtesy . . . [they] determined to make their lives so unbearable that they should be forced in self-defense to leave."
Joining the nurses in the wartime workforce were great numbers of women who filled jobs throughout the capital. These included clerks at the US Treasury and other departments—unheard of before the war—workers at the Government Printing Office, and weapons makers at the Navy Yard and Arsenal. Their pay predictably was low, and in some professions they earned about half what their male colleagues did. Still, the war helped challenge antebellum notions of the role of women, and it did so in combination with social reform movements and Christian charitable work. Hannah Ropes had ably chronicled and actively participated in both. Perhaps a bit too actively.
Because of her regular proximity with sick and infected patients, she regularly took ill with one disorder or another, complaining to her daughter, "We get lousy! and dirty. We run the gauntlet of disease from the disgusting itch to smallpox!" In her last journal entry, dated December 29, 1862, in her description of a dying soldier, she had a sense of something darker on the horizon:
two eyes like live coals roll, gleam, recede in terror behind their own pupils, or soften to tears before mine; two cheeks, purple with fever, a sweet mouth and beardless chin, teeth a girl might envy, and a wide fair brow, from which light brown hair, dank and curlless, falls away . . . .[The doctor] pronounces him very sick and orders an anodyne—still, no closing, hardly to wink, of these bright, restless, beautiful blue eyes.
Typhoid finally did what the medical bureaucracy couldn't do and conquered Hannah Ropes in January 1863.
Rise of the Contrabands
Ropes wouldn't have said her death was in vain. She had a keen sense of what the war was really about, and why soldiers like her son were fighting. As she wrote the month before her death, "If in the beginning our President had declared freedom for all, and armed all, the rebellion would not have lasted three months . . . the only way out of this trouble remains just where it did before, only to be gained by immediate, unreserved emancipation." Instead, freedom for slaves proceeded piecemeal, by moderate gestures and accidents. One of the biggest such accidents, however, fundamentally reshaped the racial and social landscape of the District.
Slaves had been coming to the capital even before the war started. Their masters and other Southern whites fled and either abandoned their "property" or made keeping track of it difficult in the growing chaos. Farther south, in May 1861, three slaves escaped to the Union lines at Virginia's Fort Monroe, one of the few federal installations still held by the national government. General Benjamin Butler decided not to send them back to their masters as required by the Fugitive Slave Act of 1850. Instead, improvising his own military law, he held them as "contraband of war," or commandeered enemy property. After Lincoln reluctantly confirmed Butler's decision, thousands of "contrabands" escaped their plantations in the South to take shelter behind Union lines, a number that grew to half a million by the end of the war.
The District of Columbia, not far from the fighting in Virginia, became a major draw for escaped slaves, who arrived via the Long Bridge and within two years formed a community of ten thousand people in Washington City and three thousand more in Alexandria. They took exceptional risks in the first year of the contraband policy, when Maryland slaveholders could have them held as fugitive slaves if they had come from that state and when they could be arrested for the slimmest of reasons and confined to the municipal jail (and the whims of its racist warden).
This situation changed on April 16, 1862, when President Lincoln signed the Compensated Emancipation Act, which freed slaves held within the District of Columbia and provided up to three hundred dollars for their owners, the only time such an act occurred during the war in any US city or state. This act predated Lincoln's much more famous Emancipation Proclamation—which freed slaves only behind enemy lines and didn't apply to slave states that remained within the Union—by nine months, and 996 slaveholders came forward to get their recompense. All they had to do was prove their ownership and take a loyalty oath, so the federal government essentially rewarded them for owning human chattel and staying in town. The total cost ran to more than two million dollars—owners typically claiming their slaves were young, sprightly, and in excellent health, while bondsmen argued the opposite—but the act was much less sweeping than it sounded. Slaveholding whites composed only 2 percent of the District's population in 1862. In the end, while it did free 3,100 slaves in the District, compensated emancipation also provided an undeserved treat for slaveholders. Abolitionists knew as much at the time and endeavored to make sure the policy was never repeated anywhere else in the future.
Camps and Villages
The Emancipation Proclamation went into effect at the beginning of 1863 and only increased the flow of slaves across Union lines. In response, the army used them as workers in trenches, kitchens, hospitals, and even plantations. In Washington City, the federal government employed thousands more, hiring them as "carpenters and masons, teamsters and blacksmiths, nurses and orderlies, and laborers of every description to move supplies, chop wood, haul coal, tend animals, build roads, and dig fortifications." For such work, the government paid them up to thirty dollars a month, the same as whites, but with an unpopular monthly tax of five dollars deducted to defray the costs of operating the sites where many of them lived.
The Department of War tried to provide at least a minimum amount of assistance, which included clothing, food, shelter, medicine, and education for the former bondsmen, consigning them to on-site settlements known as contraband camps. Conditions there were often grim, though. The camps faced a lack of sanitation and supplies, a surfeit of poverty and disease, and an inability to handle the seemingly endless flood of new arrivals. In due course, the healthier men and women with contacts elsewhere in the region departed the camps, leaving behind the poorest and sickest individuals. One of the most prominent outposts was Camp Barker, near Washington City's northern boundary. Built over a former brickyard and cemetery, its swampy conditions made it notorious as a plague center. In one of the camp's deadliest outbreaks, the six hundred residents suffered through a smallpox epidemic in 1863 that killed three to five people a day, worsened by the lack of access to water and vaccines.
Encampments closer to town didn't fare much better. Just a few blocks from the heart of Pennsylvania Avenue, freedmen found dreadful accommodation in the disease-ridden shacks and hovels that lined the poisonous city canal, making for a shantytown between the White House and Capitol known as Murder Bay.
The shanties of Murder Bay, where escaped slaves, or "contrabands," took refuge amid deplorable conditions.
Such dismal living conditions shocked the residents of the capital but persisted for years afterward. As late as 1866 the superintendent of the Metropolitan Police reported to Congress that whole families packed into shanties "without light or ventilation," barely protected from rain or snow, exposed to the "most disgustingly filthy and stagnant water." Even if sanitary standards were ever fully enforced, "these places can be considered as nothing better than propagating grounds of crime, disease, and death; and in the case of a prevailing epidemic, the condition of these localities would be horrible to contemplate." (The Bureau of Refugees, Freedmen, and Abandoned Lands—the "Freedmen's Bureau"—had the postwar task of improving this and other substandard conditions for blacks, and we'll see in chapter ten.)
By the summer of 1863, the military had to address the crisis. As a partial solution, it created Freedmen's Village, a mini-town with fifty houses and two families per residence, just across the river in Virginia. It also had schools, churches, a home for the elderly and disabled, streets and parks, and a tailor and other artisan shops. It provided job training for men in such fields as blacksmithing and for women in sewing, which paid the meager wage of ten dollars per month, minus five dollars for the contraband tax. Freedmen were charged rents of one to three dollars per month, which didn't leave much money to spare, so many African Americans there found other sources of income, including working as military laborers, defending the siege works of the District, and working in local fields and gardens. Eventually the army constructed barracks to hold 250 families at much lower rental costs, and the village ultimately grew to 1,500 people.
Life in the quasi town was marginal, but at least it improved on the awful conditions of the contraband camps. It also held great symbolic value. The village sat on the Custis-Lee estate, where Robert E. Lee lived before the war in Arlington House. On this former slave manor, African Americans now lived willingly and earned pay for their labors, where once they would have lived as prisoners at the behest of the Confederates' top general.
New Authorities
The Union army also opened Freedmen's Hospital on the site, a groundbreaking facility where African Americans could receive treatment for diseases and other ailments in the camps. Its most famous employee was the legendary Sojourner Truth, who before the war had been an activist for abolition and women's rights, an agent on the Underground Railroad, a preacher, and a lecturer. Already in her mid-sixties, she helped bring about the integration of the horse-drawn street railway by riding in whites-only cars, had a private audience with President Lincoln, and lobbied Congress for establishing proper training for doctors and nurses. During her time in Washington City, she also organized the cleaning of Freedmen's Hospital to help prevent disease at a time when few recognized, and most ignored, the need for medical sanitation at other hospitals in the District.
Other employees of Freedmen's Hospital may not have shared her fame, but they proved just as critical to the health of black soldiers and former slaves who needed care there. One of them, Dr. Alexander Augusta, had fought widespread racism directed at black professionals to become an army major and the surgeon in chief at Camp Barker. In 1863 his authority was transferred to the new three-hundred-bed Freedmen's Hospital, where he and eight other doctors became part of a select fraternity: African-American physicians who worked in a District medical facility. Augusta's second in command was Dr. Anderson Abbott, a prominent Canadian who attended levees held at the White House, became an acquaintance of the president, and fit well into local middle-class black society, despite his foreign origins. He was even present at Lincoln's deathbed, and the first lady later gave him the president's plaid shawl, "a most precious heirloom," as a reminder of his time in the capital and friendship with the chief executive.
Unlike the more reserved Abbott, hospital director Augusta cut a controversial figure in some circles because of his activism for racial equality. Like Sojourner Truth, he protested segregation on the capital's street railway and helped force the integration of the "c'yar boxes," as the streetcars were known, by lobbying Congress for action. Augusta's actions raised his public profile just as they raised the jealousy of his white peers. In 1864, these doctors forced his removal as chief surgeon, and Abbott assumed control of Freedmen's Hospital, continuing Augusta's policies.
Fighting Old Demons
Charles Sumner aided Augusta's antisegregation cause by bringing it up in the US Senate and by threatening to revoke the streetcar company's charter if it didn't remedy the problem. Other abolitionist politicians joined him in such attempts to lessen racial bias in public accommodations and helped pass laws that gave black-oriented schools a proportion of the municipal school fund and expunged some parts of the Black Code, including the hated ten o' clock curfew. However, racism remained alive and well: White District residents protested any assistance shown to African Americans, and laws like the one funding black schools existed more on paper than in reality thanks to the recalcitrance of the City Council.
The crazed mobs that had enforced the racial status quo before the war returned with a vengeance too. After such events as the Emancipation Proclamation or the enlistment of African-American troops, crowds of reprobates hurled stones and shattered glass at black churches, convalescing soldiers attacked minorities at random on the street, and interracial hostility increased throughout the capital. The law often gave sanction to such violence. Not only could blacks not testify against whites in many courts or even take the stand as witnesses, but they could be held as lawbreakers just for defending themselves from mob attack.
Similar prejudice existed in the military, as black troops became more visible defenders of the Union in 1863 and after. Many in the city and the nation resisted the idea of sending African Americans to fight in the war, and even Lincoln had his doubts. The army didn't enlist black troops out of magnanimity; it just needed more men, 150,000 more. Surprisingly, despite being offered less money than white soldiers and severely limited in rank and command, more than the requested number of African Americans enlisted, including many ex-slaves. It made for dangerous service, even when the bullets weren't flying. Local thugs occasionally attacked camps where these soldiers were billeted, and, if Southerners captured any of them, they stood a good chance of being massacred on the spot—infamously so at Fort Pillow in 1864. Nonetheless, black troops proved themselves to be able, vigorous combatants in the field, and their courageous service in such battles as Port Hudson and Milliken's Bend in the Deep South made their detractors less vocal if not necessarily more tolerant.
Village No More
By the end of the war, the racial landscape in Washington City had changed dramatically. No longer was the capital a backward village of plantation owners and white gentry with a minority of free blacks and slaves bound by law and custom. Instead, according to a special census in 1867, the capital boasted 106,000 people, a third of them black and none of them slaves.
At least one general in Washington City knew the value of African Americans as soldiers, laborers, and citizens of the Union. He happily employed contraband labor against the Southern enemy. He ordered that black soldiers buried at the humble Freedmen's Cemetery be reinterred in a more prominent facility. He developed a plan to give slaveholders' property to freed slaves, and he understood how "the loyal inhabitants of the country, white or black, must be compelled to assist" in the war since they were "animated by the strong desire not merely for political but for personal liberty." He was the city's greatest master builder, Montgomery Meigs.
An Engineer's Apotheosis
An officer in the US Army Corps of Engineers, Meigs cultivated an interest in just about everything: architecture, engineering, fine art, history, languages, literature, photography, and science. No ordinary engineer, he held thirteen patents on innovations from fire hydrants to file cases. Most importantly, Meigs devised and constructed the huge Washington Aqueduct that utilized only gravity (not steam pumps or other devices) to bring freshwater from Great Falls, Maryland, through 18.6 miles of reservoirs, bridges, conduits, tunnels, and pipes at a cost of more than two million dollars. His aqueduct had a capacity of sixty-seven-million gallons, twice what New York City needed and four times what Paris required. In the history of Washington City, only the Capitol itself had a higher price tag—which Meigs himself, as chief engineer, had helped reconstruct in the 1850s, the great white iron dome the most visible example of his exceptional ability.
The ingenious arches of the Washington Aqueduct, which doubled as pipes carrying water into the city.
Before the war, the turncoat Secretary of War John Floyd had shipped Meigs to the distant Dry Tortugas island chain. Instead of moping about his fate, Meigs instituted an immediate campaign to strengthen the defenses of the federal post there, Fort Jefferson. By February 1, 1861, he had bolstered the fort against potential attack, and three weeks later his political allies aided his return to Washington City.
In June, Lincoln promoted him to brigadier general and gave him the title of quartermaster general of the US Army, overseeing the administration, procurement, and supply of military troops. When he arrived, the shambling, debt-ridden condition of the quartermaster's office didn't help the massive organizational task, nor did the insidious fraud and corruption of federal contractors. Yet Meigs succeeded beyond expectation and helped the Union army dramatically improve its logistical planning and deployment of troops, equipment, and supplies—everything from shipping food, clothing, tents, and blankets to delivering gunboats and expediting railroad construction. Meigs also succeeded in the monumental feat of delivering huge numbers of horses, mules, wagons, and ambulances to the capital to aid the Union cause (while, more regrettably, tramping the town's roads into muck). But that wasn't the only way he altered the local landscape.
In fall 1862, Stanton named him to a commission to fortify the District of Columbia against Confederate assault. By the end of the war, it had become the most fortified city in the world, with sixty-eight forts and ninety-three batteries manned by twenty thousand troops along a thirty-seven-mile defensive line. Countless battles took place in the Chesapeake region, but only Jubal Early's July 1864 raid breached this line when the rebel cavalry general attacked Fort Stevens in Washington County. Meigs participated in the battle, commanding a force of some fifteen hundred men in rifle pits between Fort Stevens and Fort Totten, the latter appropriately named for the general who first brought Meigs to Washington City in 1852 to fix the town's water supply. Union troops repulsed Early's raid, and the capital remained secure.
During fifteen years, Montgomery Meigs built an aqueduct, engineered a new US Capitol, and helped the Union Army win the Civil War.
Ghosts of War
For all he did to provide clean water, engineer the Capitol, and help win the war, Meigs's most lasting contribution lay not within Washington City but across the river in Arlington, Virginia. Here the great engineer made a mark on the landscape of the capital that remained long after the war ended, the hospitals and military camps closed, and the decrepit antebellum village of Washington City disappeared from view and memory.
On the huge Custis-Lee estate, in a neoclassical manor rising above the Potomac, Robert E. Lee had once held court. His wife, Mary, had luxuriated under blooms of honeysuckle and jasmine here, and old George Custis had danced and cavorted with his wealthy guests. But Meigs had very different plans for the estate.
The federal government confiscated the property shortly after the outbreak of the war and claimed outright ownership of it in 1864 after Mary Lee failed to pay her property tax in person (though she had tried to do so via courier). With battles in Virginia causing eighty thousand casualties a month, local hospitals bursting with wounded and dying men, and the dozen Union cemeteries in the capital filling up rapidly, Meigs recommended the estate become the grounds for a new national cemetery to hold the bodies of deceased soldiers. Edwin Stanton concurred, and by the summer of 1864 plots for the Union dead began to populate the grounds.
Meigs's resolve only strengthened when he learned that his son had died in the Shenandoah Valley on an army scouting mission. He vowed that Lee's estate would never again serve as a leisurely retreat or pleasure garden. Instead, with its sarcophagi, memorials, and tombstones, it would stand as a testament to sacrifice and death. He located one of the biggest pits near the manor house, ordering Mary Lee's garden excavated and filled with the remains of two thousand unknown soldiers. Mary Lee fought for decades afterward in Congress and court for the return of her estate,** but Meigs served just as long as quartermaster general, continuing to expand and develop the property as the nation's foremost burial ground, adding temples, arches, and an amphitheater to the landscape. As he did on the aqueduct he created, Meigs took care to have his name engraved prominently and proudly on a column near the entrance, so all the world could see who had built this grand tribute to the fallen.
** Mary Lee achieved her aim in an 1882 Supreme Court case, after which she sold her estate back to the federal government for $150,000. The official buyer was the Secretary of War—Robert Todd Lincoln. (Robert M. Poole, "How Arlington Cemetery Came to Be," Smithsonian (November 2009): 4, accessed at www.smithsonianmag.com/history-archaeology/The-Battle-of-Arlington.html)
Conceived as revenge, Arlington National Cemetery in many ways became the ideal gesture. This estate, which sat on some of the area's most scenic property, never saw the Confederate general and his wife live out their twilight years in splendor. Instead, the hillsides embraced thousands of American heroes and warriors, officers and enlisted men, Supreme Court justices and presidents, explorers and reformers, black and white, North and South. And as Arlington grew, so too did the town on the flatlands below. Through terrible carnage and tumult, the capital city stood bloody but unbroken, straining to live and grow, watched over by armies of the dead.
Nine
Suspicious Characters
As the Civil War ended in 1865, many of the bodies filling up cemetery plots in the capital weren't only casualties of battle. A good number of the newly deceased were victims of cruel and often random attacks that epitomized the postwar explosion of violent crime and brutality. Murders, stabbings, and shootings became a daily occurrence, and rampant fighting and assaults gave the capital a well-earned reputation for mindless bloodshed and thuggery. Thieves robbed their victims in their hotels or on the streets, con artists and counterfeiters enjoyed a profitable trade, and houses of gambling and prostitution experienced a surge in popularity. The District turned from being the cornerstone of the Union to "a perfect Gomorrah of sin, violence, and corruption."
The wartime growth and military importance of the capital attracted a range of newcomers: discharged soldiers without jobs, former slaves without homes, army camp followers, vagrants, and troubled youth without any prospects at all. More than a few of these arrivals turned to crime in the absence of work or opportunity, while others came to town for the express purpose of preying on the local citizenry, whether by making a killing off them in thievery or just killing them outright. In later years, some compared the conditions in the capital to the worst corners of the Wild West, with levels of lawlessness as bad as Cripple Creek, Colorado, or Tombstone, Arizona.
Long, Hard Beats
During the fifteen years that followed the war, Congress expanded the Metropolitan Police force to 238 men, but time and again it refused to provide adequate funding and then salted the wound by cutting officers' salaries and their already meager benefits. In 1876 policemen went without half their full pay (six hundred dollars per year) for two months, and some of their station houses slid into such a deplorable condition that they actually collapsed. In later years, with the District's growing population, only one cop patrolled the streets for every nine hundred residents, and a beat could stretch for as long as ten to fifteen miles. An 1880 police report, summing up the era, decried "the total inadequacy of the force" to cover a city that had little to no police protection on most of its streets and alleys. One police officer walking seven blocks to the Capitol witnessed fourteen fights along the way. Another became exhausted from the endless conflict:
Like the others, I used to spend the entire day in making arrests. As fast as I would return from taking one prisoner to the station-house I would make another arrest, and sometimes I used to leave two or three people calling "Help!" and "Police!" simply because I had my hands full and could not tend to any more. . . . I remember that one night the old Central Guard House contained seventy-one prisoners arrested within a space of six hours for disorderly conduct, fighting, shooting, &c.
Deep in the Hole
The Metropolitan Police made countless arrests, but just because they took criminals off the street didn't mean they ended up in jail. Many faced lenient judges or juries at trial, but just as many faced unfair or inconsistent sentences. As an example, David Barnett stole a few hundred dollars and received a year in prison, while Samuel Uber received a five-dollar fine for assault and battery. Anyone unlucky enough to go to jail experienced conditions nearly on par with the the Old Capitol Prison. The Washington County jail held twice the capacity for which it was designed in 1830 and stuffed up to ten men into each of its eight-by-ten-foot cells. It had a filthy jail yard and an unsanitary lack of toilets and windows. Each corridor of cells had only a single daily tub of water for washing up. The secretary of the interior himself compared it to the Black Hole of Calcutta and with good reason. Delinquent teens convicted of minor offenses went into the same cells as the worst criminals, which provided them with little rehabilitation but extensive training in other, more savage kinds of crime. They emerged in a state of "precocious villainy."
Elsewhere, so-called "workhouses" combined the functions of jails and poorhouses, giving those in poverty the added humiliation of having to share their living quarters with actual criminals. Near the Arsenal, the federal penitentiary closed during the war for conversion into a storehouse for military ordnance and ammunition. Although some convicts headed north to a state prison in Albany, New York, the closure ultimately resulted in an even greater lack of space to house local criminals, inevitably allowing them once more to take to the streets. One police board report charged that no other city in America was so "inadequately supplied with prison accommodations," yet a congressional bill in 1864 to fund a new penitentiary failed, and many years passed before the legislature even attempted to build a new one.
Far-Flung Duties
Congress and police superintendents made the work of already overwhelmed police officers even more arduous by piling on extraneous duties. One of the most tedious was upholding strict enforcement of liquor laws even after the war had ended and most of the soldiers—the original targets of the Provost Guard for their drinking habits—had left. Temperance advocates demanded that officials strictly control or else reject liquor licenses. The police brass responded by detailing officers to crack down on illicit saloons and tippling shops, forcing patrolmen to chase down rogue bartenders instead of thugs and murderers.
The Metropolitan Police continued to take charge of one far-flung duty after another, no matter how far each stood from the primary goal of law enforcement. In a government town with ironically few government agencies, the police often served as the only recourse for fixing problems. The department's annual report from 1880 provides a detailed list of some of the many tasks—or "incidentals"—performed by officers, who in many cases acted as much as repairmen, utility workers, and social service agents as enforcers of the law:
* • abandoned infants found (26)
* • broken lamps reported (174)
* • dead infants found (47)
* • dangerous holes in carriageways and sidewalks (106)
* • filthy alleys reported (67)
* • hydrants out of repair (123)
* • loads of coal weighed (1,171)
* • lodgers accommodated (7,461)
* • lost children restored to parents (195)
* • owners of insecure buildings notified (13)
* • sewers in bad condition (46)
* • trees and tree boxes broken (1,121)
* • water notices served by police (7,017)
Age of the Swindle
With the police distracted by their ever more varied assignments, underpaid and exhausted from their labors, and outnumbered by lawbreakers, crime increased in frequency and complexity. In just the category of fraud and thievery, thousands of shady characters concocted schemes to steal goods and money from the public. While pickpockets and shoplifters were a strictly local menace, forgers, con artists, and fencers of stolen goods conducted elaborate operations across state boundaries, sometimes using aliases and disguises. Professional Criminals of America by Thomas Byrnes provides a key look at the assorted thieves in the Gilded Age with whom the urban police in America dealt:
bank burglar: the "intelligent and thoughtful rogue" who invades a bank and attacks its safe with "patience, intelligence, mechanical knowledge, industry, determination, fertility of resources, and courage—all in high degree."
bank sneak: part of a group of bank burglars, "who stealthily steals behind the counter and robs the cash box or a bundle of bonds."
confidence and bunco men: those who practice "the safest, pleasantest, and most amusing way for a shrewd thief to make his living," employing all types of subterfuge, fraud, and gamesmanship "in helping themselves to other people's money."
forgers: falsifiers or counterfeiters "of a writing, bill, bond, will, or other document" who "prostitute their talents by imitating the handwriting and workmanship of others."
receivers of stolen goods: middlemen thieves "extremely careful in their negotiations with professional rogues" in buying purloined "bonds, securities, diamonds or silks," among other commodities.
sawdust men: operators of get-rich-quick schemes who solicit rubes to purchase bags of stolen or counterfeit money at a discount before switching bags and leaving them with a sack of worthless blank paper sometimes weighed down by sawdust.
sneak thieves or house thieves: "Daring and desperate rascals" known to invade homes by breaking through doors and windows, some of them housebreaking at night "in search of plunder and with masks on their faces and murder in their heart."
One of the most notorious operations was the "circular swindle" or illicit lottery. In this scheme, thieves mailed handbills proclaiming the easy money to be had from buying tickets to a random drawing. There was no such drawing, however, and the criminal pocketed the money, changed his or her address, and moved on to the next group of marks. More traditional underworld gambling also proved popular and used various methods of cheating either through stacked odds or confidence games. Gambling houses became so pervasive that an 1876 congressional investigation revealed widespread police corruption in protecting such illegal establishments, the detectives either on the payroll or receiving money under the table.
Murder Bay to Hell's Bottom
In an era of unprecedented corruption, the White House perhaps appropriately lay near the heart of District crime. Most police arrests, about one-quarter, came in the First Precinct, roughly a ten-block arc east and southeast of the White House, which included one of the District's bleakest neighborhoods: Murder Bay. Here in 1869, a lunatic wielding a club with a glass insulator strapped to it attacked President Grant and tried to smash his head in. After police apprehended the assailant they found a loaded revolver on him. (Other unconventional weapons of the era included an umbrella to gouge out a man's eye, a gas-pipe bomb meant for a judge, a "cheeser" to scourge someone's flesh, a walking cane used by a rapist, and a "bogus infernal machine" used for God knows what. The police sometimes responded in kind with medieval-style weaponry, in one case with a nightstick that deployed steel barbs with a turn of its handle.)
A contraband camp had arisen in Murder Bay during and just after the war, but the area's material conditions hadn't improved much since then. Thick with thieves, cardsharps, and pickpockets, it stood within close, uncomfortable view of the White House, roughly bounded by 11th and 15th Streets NW, Pennsylvania Avenue, and the city canal. Murder Bay had its own main street, Ohio Avenue, which paralleled Pennsylvania Avenue to the north—though with a decidedly more dismal aspect: thick with low-rent industries like foundries and industrial works, numerous gambling halls and saloons, and the ubiquitous brothels. Looking back on the neighborhood's worst years, the Washington Post described the area as a place "where life itself was frequently sacrificed on the turning of a card [and] Thieves and unprincipled men and women, as ready to cut a throat as pick a pocket, flourished and walked the streets in certain sections in open daylight."
The old "Island" slums stood southwest of the Capitol.
Murder Bay wasn't even the worst of the District's neighborhoods, though. Some of them were so fearsome that the public didn't dare venture into them by day nor the police at night. The canal and railroad tracks cut off stretches of The Island from the rest of town and made it an expansive slum, with shanties and crowded tenements home to some of the town's most pervasive crime. Bloodfield near the Navy Yard and Swampoodle north of the Capitol were equally grim, packed with gambling houses and assorted thieves and thugs. But the most shameful was Hell's Bottom.
Located above the major boulevards, at the northern tip of Washington City, this down-at-heel neighborhood sat on low-lying marshy ground that bred malaria and other waterborne diseases and fostered dense criminal activity. It had evolved from a contraband camp at the close of the war to a forbidding enclave ignored by the police and left to the control of criminals preying on the predominantly black residents. In this forlorn place, "Money was scarce and whiskey was cheap." Fights routinely turned into riots, but no police court existed to try suspects. It had little in the way of elementary housing or sanitation, and the local and national governments provided almost nothing in funding or services to alleviate the misery. If highly visible areas like Murder Bay suffered from dreadful crime and poverty, then of course more distant neighborhoods like Hell's Bottom would be much worse.
Revolving Door
Not confined to just a few dangerous neighborhoods, crime existed everywhere, in areas rich and poor and practiced by criminals of a variety of looks, methods, and backgrounds. The National Archives holds several volumes of arrest books for the Metropolitan Police during the postwar era. Better than any dry statistics, they explain who these suspects were and what they were accused of doing. A few scattered violations concerned rarely enforced laws against abortion and profanity, but most of the offenses related to some form or other of stealing, drinking, and fighting—often in combination. A few of the listings are quite telling for what they reveal about the capital's standard of law and order, including the following cases from a sample page of the arrest books, during the late summer of 1874:
August 14: Mary Adams (servant), intoxicated and disorderly
Like many of those arrested, Ms. Adams was brought in for being drunk and, we can assume, causing a spectacle or threatening someone. Her case was dismissed, possibly after she spent a night in jail to sober up.
August 14: John S. Mosby (lawyer), suspicion of dueling
Times had changed dramatically in half a century for would-be duelers as the crime drew closer to a capital offense than an "affair between gentlemen." Mr. Mosby was held on a five thousand dollar bond to await requisition.
August 31: Tom White (thief), grand larceny
The arrest ledger lists Mr. White's occupation as a thief, so he may have been well known to authorities. Despite being accused of a major crime, he was given only ninety days in the workhouse.
September 6: George Nickens, John Talbert, Richard Queen, Frank Bell (laborers), affray
These four were hauled into the station just before noon for fighting and received the light but not uncommon fine of five dollars each.
September 7: John T. Matthews (merchant), receiving stolen goods; Charles Kennar (servant), petit larceny; William Henry (liquor dealer), obtaining goods under false pretenses
These three suspects were booked consecutively for unrelated crimes of thievery (though the order of their arrest does suggest an air of complicity). As with so many nonviolent criminals at a time when fraud ran rampant, they were not prosecuted, marked as "nolle prosequi" in the books.
September 12: William J. Dees (schoolmaster), insanity
The ledger doesn't reveal what led police to charge this teacher with madness, but they nonetheless arrested him and sent him to the Insane Asylum, the inevitable repository of the mentally ill.
September 14: Susan Simpkins (prostitute), assault and battery with intent to kill
Unlike the madams and prostitutes occasionally arrested in the sex trade, Ms. Simpkins was accused of a more serious crime and remanded to authorities in Virginia, most likely where the act was committed.
Of the forty-nine suspects on this page of the ledger—arrested from August 14 to September 16, 1874—only ten faced serious charges of a stint in jail or a later court date. The thirty-nine others either had their cases dismissed or not prosecuted, spent a night in jail, or paid a small fine, usually five dollars. It wasn't that almost 80 percent of these suspects were innocent or deserved only a light slap on the wrist. The beleaguered justice system simply couldn't prosecute so many accused criminals and had to focus on the worst violators by letting lesser offenders go.
Criminal Trading Cards
The National Archives contain many vivid images of area suspects as well, from steely-eyed murderers to winsome pickpockets, in a series of cabinet cards that police once used to identify persistent wrongdoers. Mostly dating from the 1880s, these pocket-size mug shots resemble criminal trading cards, with the suspect's image on the front and biographical details, including alleged crimes, on the back.
Police "cabinet cards" identifying alleged criminals. From left to right, starting at top left: Agostino Caliagno, known for his "false pretense." Charles Leonard, a "suspicious character." Pint-size pickpocket Ida Prather. William Johnson, "false pretenses." The swindler George Gardiner. Horse thief Harry Smith. Jack Wilson, aka "Boston Charley," a suspicious character. Isaac Vail, the very image of a confidence man.
Here we see long-forgotten figures like the portly and goofy "swindler" George Gardiner and his walrus mustache; Harry Smith, an ancient horse thief who looks barely able to steal a pencil, let alone a draft animal; the cane-bearing, top-hat-wearing Isaac Vail, a dapper confidence man; the sullen figure of pickpocket William Johnson; the surly Italian immigrant Agostino Caliagno, who "can't speak English" but is notorious for "false pretense"; and little Ida Prather, a petty thief only five-foot, four-inches tall but who "carries herself erect." Numerous figures are listed as "suspicious character," a catchall term for criminals clearly up to something or otherwise familiar and notorious to law enforcement. Some of them do indeed look suspicious, especially Charles Leonard with his "long thin fingers" and freakish eyeglasses and Jack Wilson, aka "Boston Charley," with a face like an Old Testament prophet.
Especially telling is the line for "Color" on the back of the cards. For most African Americans, it records a highly specific shade. Some of the descriptors are quite inventive and include anything from "bright yellow," "copper," and "dark copper mulatto" to "dark ginger" and "gingerbread." Such adjectives, for all their vagueness today, could be useful to nineteenth-century police in recognizing a suspect, but of course no comparable descriptions exist for Caucasian suspects, such as "milky," "eggshell," or "ivory." Instead, the line simply remains blank.
Racial Conflict Redux
The majority of suspects during the war were either Irish immigrants or African Americans, but, as the years went on and the number of black residents increased in the capital, so too did their arrests, up to half of all District arrests in 1888. Statistically black crime was no greater than white crime, but African Americans received most of the blame, especially when Reconstruction was winding down and segregation and Jim Crow laws were increasing. The Washington Post even blamed blacks for a "reign of terror" involving murder, rape, thievery, and arson, seeing them as the primary culprits for all crime in the capital.
In fact, blacks more often fell victim to crime than perpetrated it. Violent criminals attacked them in their own neighborhoods knowing that police would turn a blind eye. Angry mobs still targeted them even years after the abolition of slavery and the Black Code. In one example, in the summer of 1865—after the war had ended—the soldiers of the army's 20th corps descended upon blacks on The Island. After guzzling "bad whiskey," smashing doors and windows, and assaulting citizens, the soldiers had free rein to destroy as much of the slum as they wanted until a different group of soldiers interceded and arrested them. Four years later, almost to the day, another mob attacked black voters on Election Day. The police almost quelled the disturbance, but soon the crowd swelled and erupted in an antipolice riot, hurling rocks and wielding sticks at officers until the cops fired on them. The only person killed in the melee was black.
A New Class of Officers
Despite police inability to protect African Americans from the fury of racist mobs or from opportunistic criminals in their neighborhoods, one point had changed. Blacks had joined the force itself. A month after the 1869 Election Day riot, the Metropolitan Police swore in its first black officers, Charles Tillman and Calvin Caruthers. However noble the move may have seemed, it had less to do with the open-mindedness of local officials than with the difficulty that white officers had in patrolling minority neighborhoods and the need to find any policemen who could.
The new class of officers faced great hostility at times. Many residents in minority districts—who of course had reason to distrust all police—didn't accept them. The amount of crime in their precincts was overwhelming, and newspapers and public officials chastised them for being too lenient when they arrested black suspects and for being too firm when they arrested white ones. Within the department, they faced discrimination from their peers, rarely received promotions, and sometimes were forced to quit the force altogether.
An early group photo of Metropolitan Police, including several black officers.
Nonetheless, despite these drawbacks and challenges, it was a significant step that African Americans entered the force. Beginning in 1869, their presence as enforcers of the law dramatically reversed the grim situation of just a decade earlier, when the Auxiliary Guard rounded up blacks after dark and whipped them when they broke the rules or were thought to be disobedient. African Americans had become agents of executive authority, not just objects of it, and were expanding their roles beyond the servants, cooks, drivers, and laborers of the prewar years. That they met strong, often violent opposition on the streets and hostility within the department was perhaps inevitable, but their status as members of the police force—an arm of the national government—ensured that they had achieved a small but critical foothold on power in the capital.
Indeed, the hiring of blacks for the police force and the federal government's control of that force gave a clear sign that the old Washington City was changing. The war had introduced the most dramatic transformations—the expulsion of the pro-slavery elite, the rise of Republican power, the martial efficiency—but the threat of backsliding remained. At any time, the city could slip back into the shadows of a poor, benighted village underfunded by Congress and ignored by national politicians. The creation of the Metropolitan Police attempted to push the changes forward as these officers of the law, with all their thankless duties, tried to remake the capital into a modern, functional city, even as they patrolled a landscape almost feudal in its violence and poverty.
Ten
The Fall Of Washington City
On February 20 and 21, 1871, the capital threw a big party. It didn't celebrate the end of a bloody uprising or the abolition of slavery but something much more prosaic: the laying of new wooden pavement across Pennsylvania Avenue to replace the old stone pavers.
The stretch between the White House and the Capitol stood packed with ten thousand spectators who reveled under flags, streamers, and Chinese lanterns as fireworks erupted overhead. The entertainment included spirited races between citizens on foot and in sacks, horses in teams of four and six, and even contests between goats and wheelbarrows. Lively floats paraded down the avenue, including one depicting the inauguration of a female president. Along with a bevy of games and tournaments, a carnival delighted the spectators during the day, and masked balls enchanted the elite at night. As one newspaper remarked of the spectacle, taking place amid unexpected winter sunshine, "The very heavens lent the charm of their approval," marking "a complete transformation of the city into a thing of happy life, the beginning of a new era." However, this celebration wasn't honoring just the new era of a wood-paved Pennsylvania Avenue. It also marked the repeal of the charters of Washington City and Georgetown, the dissolution of their mayors and city councils, and the institution of a new form of territorial government.
The festival marked the end of a failed era of local government and its replacement with a fresh regime that many hoped would illuminate the benighted capital with major new projects and improvements. Indeed, the changes of the 1870s did begin the reinvention of the capital from embarrassing Chesapeake backwater to locus of national power and prestige. Yet the sacrifice proved harsh. In exchange for a bold modern city, Washingtonians lost the right to choose their local leaders, mired themselves in webs of debt and corruption, and relinquished the power to shape their city's image and infrastructure. Through dramatic twists and turns, the new capital emerged from the tragicomedy of its history as a markedly different place that scarcely resembled the old Washington City. It wouldn't even be called Washington City anymore.
The 1871 public gala that celebrated the long-awaited paving of Pennsylvania Avenue . . . as well as the official end of Washington City.
Postwar Capital
In the years after the Civil War, the capital lay in tatters. Inadequate sewage and an unreliable water supply crippled the city, darkness cloaked the streets, roads and bridges were falling into disrepair, and Congress wouldn't pay for any significant upkeep or improvement. Henry Latham, a visiting Englishman, described a patchwork landscape still reminiscent of the 1820s, with its scattered marble public buildings surrounded by brick and wooden houses, while beyond stood blighted sheds and fields. Unlike the rest of the country, "It is the only place we have seen which is not full of growth and vitality."
Barnyard animals still roamed at will despite laws that forbade the practice, and it wasn't uncommon to see cows grazing on the commons or unregulated slaughterhouses plying their trade throughout the capital. Hogs still had free rein and delighted in destroying people's gardens, creating wallowing holes in the streets, and scattering mud and feces everywhere. Municipal attempts to control waste of the human variety also failed. Citizens dumped "night soil" in unclean pits and privies and helped give the town's streets and alleys a ghastly odor. Some city lots still lacked privy boxes and even plumbing, and decaying offal and organic matter in the streets only helped spread infectious disease. The situation was worst in the poor and working-class parts of the capital, which held low-rent houses and tenements with deplorable sanitation and barely livable conditions.
GOP on the Rise
Once again, the dismal state of local affairs fired the enthusiasm of critics to move the capital elsewhere. Such detractors had never really disappeared in the half a century since the British had burned Washington City in 1814, and with the town in such a ragged condition after the chaos of war, many felt the time had come to relocate the capital farther west. New York Tribune publisher Horace Greeley thought St. Louis an excellent location for a world-class capital, and he wasn't alone. Former Union general John Logan also felt the Mississippi Valley would make for a fruitful site, imagining that the nation's archives, art, and even federal buildings could be carted off wholesale to the Midwest, leaving the District home only to the "maiden ladies and widows who kept boarding houses."
But the critics had a formidable enemy in the White House: Ulysses S. Grant, former head of the Union armies and, as of March 1869, president of the United States of America. He opposed any congressional scheme to relocate the capital from Washington City and threatened to veto any such measure that proposed it. He realized, however, that it would require an intensive campaign of public investment to make the town a worthy site for the seat of government. His Republican Party had reconstructed the capital as the political and constitutional heart of the reunified country, and there was no way that he'd lose such a potent symbol of federal supremacy over the states to the Midwest or to the clutches of his political enemies.
The GOP dominated the legislative branch with two major wings: Radical Republicans, who came from safe districts and favored civil rights for blacks and harsh Reconstruction measures for the white South, and more moderate Republicans from swing districts regularly contested by Democrats. After Grant replaced Andrew Johnson, the GOP ruled the executive branch as well. That meant that the party could dole out choice Washington jobs to such Northerners as bureaucrats seeking opportunities in the federal government and entrepreneurs seeking contracts for business with that government. Those Yankee Republican newcomers, derisively called "carpetbaggers," secured political and economic control over the District and further marginalized the old Southern ruling class—many of whom had absconded to Richmond and other points south, and returned now in the hopes that their unfortunate sympathies could be forgotten or, for the right price, overlooked.
But there was no getting around the fact that, for the first time in the capital's history, Southerners were in the minority. During the 1860s, the capital grew from 56,000 to 131,700 people, both the fastest numerical and percentage rise of the nineteenth century. Among these arrivals came a fresh new class of well-connected politicians, merchants, bankers, and robber barons who refashioned high society in the District in their own image.
Antiques and Parvenus
With the emergence of this new ruling class, the town's upper crust soon divided into mutually suspicious camps. On one side stood the "Antiques," the old-line, Southern-oriented, secessionist-friendly Democratic stalwarts who privileged rank, status, and lineage above all else. On the other stood the "Parvenus," the neophyte, Northern, pro-Union Republicans who valued money and property above the quality of a name or family line. The Parvenus threw notoriously lavish balls "overflowing with roses, heliotropes, and camellias" while "On the buffet sparkling with gold, silver and crystal sat the bottles of red Bordeaux and Burgundy and the buffet tables were loaded with terrapin and truffle, spiced meat and salads, pastries, elaborate confections and choice fruits." The only items missing from the old days were the canvasback ducks, minuets, and enslaved servants.
Madeleine Dahlgren's Etiquette of Social Life in Washington, an essential guide at the time, codified the social rules of the great men and women to prevent any unusual or untoward behavior among the unknowing. Among many other topics, Dahlgren detailed the proper manner by which to enter a ballroom, the ideal way to leave a calling card, the preferred gastronomy for a feast, and the most tasteful forms of attire and presentation—which did not include a gentleman wearing white gloves with his black dress suit instead of the more sensible choice of "lavender or any delicate tint."
On the plus side, few of these gentlemen were slapping each other in the face with their lavender gloves as a prelude to a duel, and the elevation of money over honor did much to diminish the importance of rank and status. However, the reign of the Parvenus appalled the Antiques, who avoided contact with such philistines—especially if they were "upstarts and grafters" in Congress.
Nonetheless it took a great deal of money for the average congressman to keep up with high society. After all, a politician had to make a good show among his peers. Luckily, he had ample opportunity through bribery. In their novel The Gilded Age, Mark Twain and Charles Dudley Warner helpfully tallied the costs of buying public servants for business magnates who wished to secure favors—such as a handy change of law or a lucrative appropriation—from the legislature:
majority of Senate committee members: $40,000
committee chairman: $10,000
male lobbyist: $3,000
female lobbyist: $10,000
"high moral" congressman or senator: $3,000
backbenchers: $500
In possibly the most avaricious era in American history, providing under-the-table payments represented part of the cost of doing business. This laissez-faire style of corruption helped fund the indulgent lifestyles of the region's richest citizens, fueled many of the major projects of the time, and created a strong, if perverse, incentive for the reconstruction of the District of Columbia. Its greatest practitioner was Alexander Shepherd.
The Making of a Boss
Like many of his upstart Republican peers, Shepherd came from humble circumstances, born in Washington City to an unexceptional middle-class family in 1835. After his father died, the teenaged Shepherd had to find work to support his mother and six younger siblings. He did drudge work for a time until a plumbing and gas-fitting company employed him in the 1850s and 1860s, giving him a hands-on understanding of public infrastructure that shaped his perspective in years to come. (During this time he also served a brief stint as a soldier in the Union army, for which he was eminently unsuited.)
Life in the plumbing business was good, and he eventually became the owner of the company. Like any good bootstrapper, he parlayed his business success into other areas, securing a seat on the boards of directors of banks and paving, construction, and railway companies and entering the political field with a seat on Washington County's governing Levy Court.
Shepherd also took partial ownership of the Evening Star newspaper, had a knack for speculative real estate, and belonged to several prestigious gentlemen's clubs. A champion glad-hander, he had a keen understanding of human politics, though partisan ideology engaged him less. He shifted from a pro-Southern stance in his early years, to a more pro-Union—though still conservative—perspective in his middle years, to an ardent Republican posture in his peak years. Self-made magnates such as Shepherd particularly attracted the attention of President Grant, who took him into his confidence as a member of his secretive "Kitchen Cabinet," even though Shepherd had worked to defeat his nomination for president in 1868.
A transient political partisan, Shepherd did have one ongoing commitment as a businessman: the development of the material conditions of the District. As many citizens were beginning to understand, if urban progress were to take place, it had to happen in a functional and well-built capital that could stave off threats of relocation to the Midwest. While Shepherd stood out as the most prominent figure to advocate for major capital improvements, he certainly wasn't the first. The Army Corps of Engineers had been doing so for decades.
The most powerful figure in the history of DC politics, Alexander "Boss" Shepherd laid the groundwork for the future city.
Capital Designers
Montgomery Meigs—engineer of the US Capitol, builder of the Washington Aqueduct, wartime quartermaster general—helped prompt Congress in 1867 to transfer control of the Office of Public Buildings and Grounds from the Interior Department to the War Department. This was no small feat. Henceforth the corps oversaw all public buildings in town and designed the blueprints for the modernization of the capital—for which later politicians like Shepherd were only too happy to take credit.
Meigs spent a crucial year in Europe, from 1867 to 1868, investigating the cities of Germany, Austria, Italy, and the UK, with a stop in Paris for the World's Fair. He made extensive sketches and notes on infrastructure with an eye toward using some of the best ideas to improve Washington City. He wrote of the proper layout of pavements, laid "at right angles to the line of travel." He detailed the color and composition of stone walkways and the effect of weather on them. He described boulevards featuring trees, paths, promenades, and parking as a means of reducing the scale of roadways. All while keeping an eye to the possibility of exporting the functional aesthetics of the Old World to the New. He sent his observations to Nathaniel Michler, the superintendent of public grounds and buildings of the army corps, who took Meigs's notes and recommended them to Congress as a starting point for capital improvements.
Michler, an engineer and brigadier general, had distinguished himself in running the Topographical Department of the Army of the Potomac. He created defensive works for Grant's bloodiest battles in the last phase of the war and even witnessed Lee's surrender in 1865. After the war he had the responsibility of finding a new home for the White House, which sat on a swampy site prone to malaria, with the filthy city canal running nearby. (An 1864 engineering report called the site "a dangerous miasmatic swamp . . . the noxious exhalations from which during the summer and early autumn months [have] made the Presidential mansion so notoriously unhealthy as a place of residence.") Michler issued a report proposing to locate the president's new residence to a pastoral setting such as Harewood, far from the grit and grime of downtown Washington City. Despite Michler's considerable efforts, though, Congress ultimately disregarded them because, as one historian wrote, "The men who were in the process of trying to impeach the President [Andrew Johnson] would hardly be enthusiastic about building or buying him a new home."
Michler's other proposals met with more success. He detailed a way to modernize Pennsylvania Avenue and other thoroughfares, based partially on Meigs's recommendations, with streetside parks, abundant trees, and graceful promenades. He recommended the creation of a network of public parks, centered around a great "National Park," perhaps at Rock Creek, which would give residents the opportunity to "seek its shades for the purpose of breathing the free air of Heaven and admiring nature." He developed a plan for the town's public parks, squares, and reservations—most in notorious disrepair—proposing to enclose and cover them with foliage while removing the decrepit structures that littered them. He also advocated for the replacement of the "dilapidated and unsightly" Centre Market with a new structure. The building burned down in 1870, and two years later Adolph Cluss designed a new structure acclaimed as "the largest and most modern food market in the country." (Further out on a limb, he envisioned ornamenting the bedraggled Mall with walkways, equestrian paths and gateways, and graceful water features such as "jets d'eau, fountains, miniature lakes" amid artistic statuary.)
With more immediate and practical application, he argued for a bevy of ambitious goals that came to pass in the coming decades: converting the city canal into a sewer, dredging the Potomac to improve navigation, repairing and remodeling DC bridges, and reclaiming the disease-ridden Potomac Flats as dry and healthful public lands. The Flats—the shallow sections of the Potomac River where low tide exposed higher ground as mudflats—notoriously hosted legions of disease-breeding mosquitoes and, in the popular imagination, "gazeous miasms, which, absorbed by the body, produce weakness, sickness, and death."
Few of Michler's ideas came to fruition during his tenure, aside from fixing up some small public parks and public reservations. Nonetheless, Washington City had found in him, like Meigs before, an urban planner who combined romantic visions with a knack for practical application. He also provided the Army Corps of Engineers even more credence as the capital's preeminent designers. In 1871 Michler stepped down as superintendent to make way for the more industrious and controversial Orville Babcock. Before he left, however, Michler served as one of the commissioners overseeing the successful paving of Pennsylvania Avenue and the high-spirited carnival that followed—as good a sendoff as any.
Struggle for a New Era
Along with the continued efforts of the Army Corps of Engineers and the new Republican elite, the dramatic changes of the 1870s couldn't have taken place without the increased presence of African Americans. The black population of the capital was expanding rapidly: from 14,316 before the war to 38,663 in 1867, a growth rate driven by former slaves and free black migrants looking for work. During this and subsequent decades in the nineteenth century, blacks composed around a third of the population, and lived in all wards of the capital, with particular concentrations in northwest and southwest DC, sometimes in racially mixed neighborhoods. Most worked as laborers, launderers, seamstresses, masons, and plasterers as well as the old antebellum jobs of waiters, drivers, servants, and midwives. A small but growing number of wealthy African Americans was emerging too, including hotel and drugstore owner James Wormley, lawyers John Cook and Charles Thomas, and hoteliers John Gray and Alfred Cook. Business magnate and early trade unionist George Downing even opened a restaurant at the Capitol, pushing for both races to be served there, and lobbied for African-American access to public galleries in the building as well.
The most famous black citizen of the District was Frederick Douglass—escaped slave, renowned autodidact, abolitionist, activist for equal rights for women as well as blacks, correspondent of Abraham Lincoln, newspaper publisher, lecturer, and author of several famed memoirs. He retired to his home in Rochester, New York, after the war and the abolition of slavery, but Washington City drew him back as the publisher of the reformist New National Era. Despite the newspaper's failure—a "misadventure" as he called it, which cost him nearly ten thousand dollars—Douglass stayed in town and came as close to an icon as a Washingtonian could get without serving as president. Douglass also involved himself in local politics, a turn of events that could humble any legend, as we'll see.
Although Douglass had educated himself, many other notable black professionals had studied at Howard University, chartered by Congress in 1867 to provide higher education and opportunity to students regardless of race. Endowed with funding from the Freedmen's Bureau and helmed by militant Christian general Oliver Howard, the university attracted pupils from around the world, including a wide range of black students as well as poor whites.
Howard became a valuable ally of Radical Republicans in Congress, who helped create the Freedmen's Bureau to assist blacks in the postwar era. During its existence, from 1865 to 1872, it had a huge array of tasks assigned to it: protecting the civil rights of African Americans, reuniting families separated by war and slavery, maintaining hospitals and settlements in the District (such as Freedmen's Village on the former Lee estate), overseeing and operating black schools, and supporting industrial and vocational schools that provided job training. It also had the monumental job of trying to improve the sanitation and livability of tenements in such neighborhoods as The Division and, failing that, razing the buildings and moving their residents to new facilities, including some remodeled from old hospital wards. It later provided food, fuel, blankets, and clothing to the destitute and coordinated with private aid societies for ongoing relief—sorely needed in view of the high death rate and infant mortality for local African Americans.
The bureau was controversial at the time. The idea of a government agency overseeing social welfare and services was almost unheard of in the mid-nineteenth century, much less one directed toward the betterment of blacks, whom so many of the town's white citizenry still viewed with suspicion and contempt. Nonetheless, the Freedmen's Bureau, like the Army Corps of Engineers, operated with military efficiency and stood as yet another example of the War Department forcing change on the capital while most other public institutions stood idle.
Rise of the Black Vote
Oddly enough, the other institution improving the capital was Congress. The Republican Party swept the national elections of 1866, and the GOP found itself with two-thirds majorities in both the Senate and House and therefore the ability to pass anything it liked. Near the top of the list for the Radical Republicans, the most active and dominant force in the party, was black suffrage in the District. In short order they passed the measure and easily overrode President Johnson's veto. Some, such as Charles Sumner, saw the measure as a test vote for extending suffrage to blacks nationwide, despite its broad unpopularity with local whites.
Thomas Nast cartoon of "the Negro at the Ballot Box," watched over by President Johnson holding a suffrage veto like a club.
The GOP didn't flinch at this disapproval, since it continued to see most native white Washingtonians as potential secessionists and saboteurs. The suffrage bill even included a plank denying the vote to anyone "convicted of any infamous crime or persons who may have given aid and comfort to the rebels in the late rebellion." In this way, the politics of the "Old Democracy" had turned on their head: Congress had come under the control of New Englanders instead of Southerners. Former abolitionists ruled instead of slaveholders, nationalists instead of regionalists, moguls and generals in place of planters and gentry.
Black enthusiasm for suffrage was immediate. Political clubs for African Americans met in assembly halls and churches, and the new voters organized into groups such as the Radical Republican Association with the goal of entrenching and extending the power of Lincoln's party. The franchise expanded considerably, and by the close of registration for the next election, nearly as many blacks as whites had registered.
Reaction from the other side was predictably livid. The National Intelligencer, guardian of the hidebound customs of the old DC, claimed a modest number of whites had registered because they feared having to sit alongside blacks in jury boxes drawn from voter rolls. Mayor Richard Wallach asserted that no "pauper race" should ever rule the capital. Other entrenched politicians charged black voters with fraud and other crimes. Later, the Daily Patriot, a local paper with funding from pro-secessionist banker and art collector W. W. Corcoran, bemoaned that the District ever became a beachhead for black suffrage and "an experimental garden for Radical plants."
Frederick Douglass had a markedly different view, that "to guard, protect, and maintain his liberty, the freedman should have the ballot; that the liberties of the American people were dependent upon the Ballot-box, the Jury-box, and the Cartridge-box; that without these no class of people could flourish in this country."
The Brief Reign of a Reformer
As it had in the 1830s, violence broke out at the polls in the city elections of 1868. Each party exaggerated the extent of the chaos and blamed the other side's voters for it. One conservative newspaper imagined a "Carnival of Blood" taking place as African Americans went out to vote, and Democrats accused Republicans of importing nonvoting blacks by the boatload from Maryland and Virginia to swing the elections. The Georgetown Courier, a Democratic mouthpiece, even envisioned a sort of Gilded Age horror movie arising from the interracial vote: "The races are now pitted against each other in deadly animosity and but very little added excitement is required to drench the streets of the capital with human blood."
After the bloody carnival had ended, former abolitionist and city postmaster Sayles Bowen became mayor by a margin of just eighty-three votes, a narrow victory for the Republican Party. The closeness of the count prompted the usual charges of fraud from Democrats, and lame-duck mayor Richard Wallach even refused to hand over the keys to his office. Bowen had to use a locksmith to claim his rightful title.
A prime figure in the Freedmen's Aid Society, which sent assistance to former slaves in the South, Bowen controversially used the Republican spoils system to reward his allies with key positions in local government, which prompted Democratic newspapers to dub him "Six Teat Bowen." He employed African Americans as laborers on urban improvement projects, and he continued his previously private support of black schools with mayoral efforts to fund and promote them citywide, even proposing to integrate public schools, which alarmed moderates as much as it heartened radicals. He also helped pass laws that forbade discrimination in public accommodations such as theaters and hotels and levied fines of fifty dollars on businesses refusing to serve blacks as customers.
Despite his noble efforts and good intentions, though, Bowen was a disappointment as mayor. He found it difficult to fund his many projects. He depleted the city treasury after increasing pay for local officials. He met with unrelenting hostility from white residents and many newspapers. He even oversaw a city election in 1869 as violent as the one the year before, featuring the familiar stone-throwing mobs that attacked passersby and ransacked people's houses. He lost support from his allies, both black and Republican, and in 1870 the more moderate Matthew Emery deposed him in a landslide.
The Territory Emerges
Voicing the attitude of the capital's upper crust in her memoir Ten Years in Washington, journalist Mary Clemmer Ames decried the "extravagance and venality" of Bowen's administration, which stood uncorrected by his successor, Emery. The elite didn't have the numbers to sway an election, so their only recourse was "the absolute necessity of a vigorous and radical reform." In other words, they wanted to scrap the old system of government altogether. In this instance, the Antiques and the Parvenus united in their contempt for politicians like Bowen and Emery, but they needed a champion to push forward a solution to the messy complications of local democracy. Alexander Shepherd was more than ready to meet their needs.
There had been efforts in Congress to eliminate the franchise for Washington City citizens completely, even for city elections, as early as 1865. Two years later, Shepherd, in his position on the local Board of Trade, proposed stripping the cities of the District of their charters and replacing elected representatives with appointed commissioners. In 1868, in laying down his position on democracy and progress in the District, he affected an air of a disgruntled king more than that of a former plumber: "The taxpayers of this city did not want elections of any kind, and had not wanted them for more than 20 years. If the people trifled with these petty little elections, the city never would come to anything. . . . A board of Commissioners of men of the right stamp could do better than any elected officials . . . in ten years the oldest inhabitants would scarcely recognize the city."
The incompetence of the Bowen regime immeasurably aided his cause. Bowen had led the city into such desperate fiscal straits that an 1870 legal judgment resulted in the seizure of the furniture in the mayor's own offices. In an atmosphere of yawning social need and an expectation for comprehensive public improvements, Bowen squandered his opportunity: City debt mushroomed while the streets lay unpaved. Shepherd attacked Bowen's failures through the newspapers over which he had influence and proposed once again scrapping the current system of government. The city charter had expired in 1868—to be renewed one meager year at a time—and critics again were pressing their demands to move the capital farther west. More than anything, though, what aided Shepherd's cause was the desire of white Washingtonians to relinquish their own suffrage completely to skirt the electoral power of newly enfranchised blacks.
Even before the wheels of local democracy had run over Sayles Bowen and replaced him with Matthew Emery, Alexander Shepherd was busy lobbying Congress to revoke the charters of the District cities and institute a new form of government. Both Shepherd, a Republican, and W. W. Corcoran, a Democrat, lobbied congressmen with treats and favors, including a ride on a Potomac yacht complete with champagne, food, and music. In a telling sign, outside Democratic politicians like New York ward heeler Fernando Wood—known for his vehemently racist rhetoric—praised a bill restricting the franchise in the District, as did a good number of the town's Republican newspapers, power brokers, and upper-crusters. Some, like the soon-to-be jobless Matthew Emery, derided the lack of democracy in such proposals, but to no avail. Emery was doomed to be the capital's last mayor for more than a century.
On February 21, Congress created the Territory of the District of Columbia in the Organic Act of 1871, which stripped Georgetown and Washington City of their charters, removed the jurisdiction of the Levy Court over Washington County, created a unified District of Columbia ruled by an appointed governor, and consigned the name of Washington City to history's dustbin. On the very same day, the parades and grand masques of the great carnival of Pennsylvania Avenue were taking place over clean wooden pavements. The festivities celebrated a brave new capital progressing inevitably toward urban glory, and its citizens had little power to stop it even if they wanted to. The carnival was the last great gasp of Washington City, which on June 1, 1871, would conclude its seven dark decades and cease to exist.
Eleven
A Gilded Cage
Local democracy in the District didn't die overnight. The new territory had twenty-two wards, each allowing voters to send a representative to a lower chamber of the legislature, the House of Delegates. But the president appointed the upper chamber, the Legislative Council, and all executive offices including the governor. This arrangement gave the chief executive a great deal of power over local matters, which Ulysses S. Grant was only too happy to use.
A month after the creation of the territory, Grant installed financier Henry Cooke, brother of Republican banker and power broker Jay Cooke, as territorial governor and appointed other Republican stalwarts to major offices. Democrats fumed, and in April they raged even more when Norris Chipman, Grant's handpicked and nonvoting delegate to Congress, was elected to the House of Delegates along with fifteen Republicans, among them two African Americans. The reactionary newspaper The Patriot—the instrument of W. W. Corcoran, who turned against the Republicans who had helped him lobby for the Organic Act—cried fraud, the first in a long string of verbal brickbats that it leveled against its enemies.
But battles over DC voting habits had become passé. Everyone knew the real power lay not with the territorial legislature, the congressional delegate, or even the governor. Instead, the Board of Public Works flexed the muscle behind the capital government, and its new vice president was Alexander Shepherd.
The Ruling Ring
Henry Cooke frequently left town to attend to financial matters in the Northeast, and his stand-in, Edwin Stanton—eponymous son of the former secretary of war—happily acted as rubber-stamp governor. (Technically the territorial governor acted as president of the Board of Public Works, and Stanton, like Cooke, acted as chief executive in name only.) When the Board of Public Works took control of the executive machinery of the District, The Patriot and other old-line interests took alarm, warning of "Ring Rule" if Shepherd and his cronies were allowed to dictate policy from their perch on the board. In response, Shepherd assumed the rhetoric of an Old Testament patriarch, warning that if his extensive program for the improvement of the District weren't enacted:
You shall continue the same old patchwork system which has rendered the nation's metropolis a disgrace and an eye-sore at home and a by-word and reproach abroad. You shall continue to drive over unpaved streets and exposed ravines and be as successfully lost in the blinding dust as was Elijah of old in the clouds which enveloped him as he ascended into the sky.
To tamp down any such dust, Shepherd advocated a series of proposals for the capital that cost six million dollars, a third of it coming from increased taxation on properties adjoining the improvements and the rest through a loan. Opponents had a US district judge issue an injunction against the plan, but Cooke and Shepherd appealed the decision and went for broke by calling a snap election in November, gambling that voters might approve four million dollars themselves in a plebiscite. As part of their high-risk strategy, they put all of the seats in the House of Delegates up for a revote—just seven months after the last election. The gambit paid off: The Republicans enjoyed a landslide victory and won all but two seats in the House. At nearly the same time, the US Supreme Court overturned the injunction. The Board of Public Works was in business.
Fractured Franchise
Shepherd still faced the suspicions of African Americans in the District, though, who had won the vote only four years earlier and now saw their franchise dramatically crimped, having to settle for five seats in the neutered House of Delegates. It didn't help his cause that Shepherd's own father had owned slaves or that many black leaders had protested Shepherd's rise to executive power as a politician hostile to their interests. Still-bitter Sayles Bowen even charged that Shepherd opposed equal education for blacks in the District as well as mainstream Republicanism. In response, early in 1871, Shepherd engaged in a Gilded Age version of spin control, exchanging a series of public letters with O. O. Howard in which he called himself a friend to African Americans, a supporter of "unified" education for both white and black students, and an opponent of racial discrimination in any form—while conspicuously avoiding the topic of black suffrage.
In reality, Shepherd was no more or less prejudiced than any white mainstream Republican of the era, and he didn't count race his primary concern anyway. He wanted to limit the franchise of any voter without property—white or black—on the dubious premise that anyone whose votes could be bought with "whiskey and money" inevitably would abuse the local elites. In this way his views mirrored those of other Parvenus in the GOP, who had little patience with old-fashioned ideas of democracy. Seven decades of District voting had resulted only in stagnation and decay, and these merchants and magnates didn't want to wait any longer to force change upon the decrepit capital.
Still, Shepherd knew that he had to appeal to core supporters of the Republican Party in the city, most of them African American. He accordingly made a vocal effort to support striking black railway workers in summer 1871 and later steered a good number of construction jobs to blacks and other party loyalists. He also had the good fortune to have a firm, notable ally in the black community.
The Ship and the Sea
Frederick Douglass had been appointed to one of the seats on the Legislative Council. The position was one of five appointed jobs in District government that Douglass filled in the postwar era, but probably the least important of them. (He served only two months before turning the job over to his son Lewis.) Nonetheless, despite his minor role in the chamber, Douglass remained an important figure, both for his prominence and for his allegiance to the GOP, of which he said, "The Republican Party is the ship and all else the sea."
Initially the newspaper that Douglass had purchased, the New National Era, vented hostility at Shepherd and his Board of Public Works, but it soon came around to argue that they "deserve the earnest, active support of the city, and the earnest, active, practical support of Congress." "Practical" was the key word here, for if blacks and other citizens of the District lost their voting rights, Congress had to provide something in return, such as sufficient funding for urban improvements and full political support for civil rights. In due course, Lewis Douglass introduced a bill into the Legislative Council that outlawed segregation and discrimination in restaurants, saloons, and soda fountains. A year later the bill passed, and the governor approved it. In 1873 the law was strengthened, and that same year a theater antisegregation bill passed the council too. Realistically, the Republican Party represented the only real alternative. Local Democrats remained wedded to antebellum notions of racial relations and the white supremacy that went along with them, and the GOP had demonstrated more than once at least a passing interest in the black voters who regularly helped it win elections in the District—even as those elections counted for less and less. With the firm support of Frederick Douglass and other African Americans, along with the already fervent backing of the nouveau riche Parvenus and the president, Alexander Shepherd had a clear road to change the capital, starting with the roads themselves.
Capitalizing the District
Emboldened by his success in court and at the ballot box, Shepherd threw his Board of Public Works into hasty action. Major property owners wanted him and his board to pay for public improvements as they went, but the man increasingly known as "Boss" Shepherd was having none of it. In autumn 1871, he ordered work to start in all wards of the city at once and enlarged the board's staff to more than two hundred employees. They took on the huge challenge of leveling the roads—a dream project if ever there was one. The District's streets had long been a hodgepodge of different slopes and angles, and clear perspectives down the thoroughfares had proved elusive because only Pennsylvania Avenue had ever been leveled. Shepherd demanded that asphalt or wood be used for the paving instead of a cheaper macadam surface, and he ordered uniform grades on the major boulevards and avenues, including those directly around the US Capitol, without authorization from Congress.
The board's work on the roads went beyond just making them functional. Employing three arborists, the board planted sixty thousand trees during two years, which helped narrow the giant, inhumanly scaled boulevards with green strips and foliage. It also provided new street parking for horses and carriages. Shepherd further ensured that major roads had illumination by ornamenting them with thousands of gas lamps, the largest street-lighting program in the city's history to date. Never one to miss an opportunity, Shepherd allowed for his own plumbing and gas-fitting company to submit bids for the work, including placing fifty-eight lampposts around the Capitol itself.
In earlier decades, fixing and lighting the roads would have presented an enormous enough task, requiring years to get started. But the board wasn't working only on the streets. It was adding even more duties to its agenda, including a redesign of the water system.
Water Work
The grand aqueduct of Montgomery Meigs had been a good start, but large parts of the capital on higher ground still didn't have access to water. The board addressed this problem by laying 180 miles of new water mains, largely in 1872, and giving residents of the District more water per capita than any other city in the world. New sewer lines followed as the old inadequate system of drainage gave way to a more streamlined network that included freshly laid conduits like those along Slash Run. Doing so turned one of the capital's last major creeks, with all of its bogs and marshes, into a channel for the filth and runoff of the city.
To scrape up more funds for his water projects, Shepherd created new sewer districts and assessed each a tax, then levied additional taxes on those areas improved by the conduits. As a further sanitary measure, the territory passed new laws in 1871 to control barnyard animals. Two years later it outlawed scavenging and began cleaning privies with the aid of the Odorless Evacuating Apparatus Company. It was one business Shepherd thankfully didn't have a hand in.
However, one dirty bit of business he couldn't help but be involved in was the town's longest-standing problem: the pestiferous ditch known as the Washington City Canal. In 1864 former mayor Richard Wallach had commissioned a comprehensive survey illustrating just how noxious the open sewer running through the center of town was. Even for a dry civil engineering report, the conclusions were damning. Not only was the canal dysfunctional and stagnant, it posed an active and ongoing health hazard. Rich with "putrescent and decomposing organic matters" that were "tough and viscous," it was enriched by runoff from "the offal of kitchens, and the soil and filth from water closets which are brought in by the sewers discharging in the canal." It was strewn with "carcasses of all kinds, from the bloated horse to the skeleton kidden which have found their way into the canal by divers modes." The canal's rank pollution extended beyond the water: "The accumulated filth and excrement of the city is constantly held in a state of semi-solution in this hot-bed of putrefaction, by means of the ebb and flow of the tides, over a surface of more than a million square feet . . . the miasma from which contaminates every breath of air which passes, from that direction, through or over the city."
With powerful members of Congress threatening to withhold funding for urban improvement unless the canal was removed, Shepherd and his board took quick action. By the end of 1871, Shepherd's men had filled in a large stretch of the ditch from 3rd to 14th Streets. They followed that with halving the width of the canal flowing south of the Capitol and making an actual sewer out of it. Within two years, the old canal vanished beneath pavement. Taking its place was an enlarged B Street, which was later named Constitution Avenue.
Orville's Industry
Shepherd wasn't alone in cleaning up the capital. Orville Babcock, head of the Office of Public Buildings and Grounds for the Army Corps of Engineers, nearly matched Shepherd in his undertakings. A former aide-de-camp to Ulysses S. Grant when he was a Union general and his executive secretary as president, Babcock rose in power above his predecessor, Nathaniel Michler, thanks to Grant's influence, becoming more heavily involved in the Republican machine than almost any engineer up to that time. A buddy of Shepherd, Babcock helped establish an almost incestuous relationship between the Army Corps of Engineers and the Board of Public Works, including giving Shepherd thirty-five thousand dollars in 1872 to install a new copper roof on the White House, one of many actions that invited scrutiny in future years.
The industrious Babcock aggressively steered the corps into remodeling and beautifying the "reservations"—the ugly plots of dirt, mud, and weeds in various circles, squares, and triangles—created by L'Enfant's plan. In just his first year, Babcock oversaw the laying of forty-six thousand square feet of sod, ten thousand yards of pavement, and four miles of drains. He oversaw the installation of countless fences, fountains, and trees, plus gaslights and running water, and rustic furniture and decor. He even created tree nurseries and mini-zoos thick with deer and prairie dogs and imported eagles, owls, and European sparrows to perch above the parks, paying for some of the new critters from his own pocket when funds ran short.
Turning his attention to the forlorn site of the stumpy, unfinished Washington Monument, Babcock improved the grounds by draining and grading them, installing ponds and a fish hatchery, planting trees, and constructing a scenic drive, all of which quickly helped people forget that the site had served as an ugly cattle pen during the Civil War. Just east, he planned to add greenery, walkways, and a unified layout to the jumble of uneven turf and rutted pathways of the decrepit Mall. Babcock also smartly oversaw the publication of a comprehensive survey of the park system, showing how the corps had made "green and beautiful" sites from "places of sand and mud."
Height of Hubris
Despite Babcock's accomplishments, there was still but one boss in town, and that was Alexander Shepherd. In a town that had never had party bosses, Shepherd ran an electoral machine that turned out core supporters to ensure victory at the polls and applied a heavy hand to control appointed boards and assemblies. Construction jobs and political patronage served as the carrot that went with the electoral stick, and Shepherd expertly glad-handed legislators in the local and national governments to do his bidding, trading their support of his costly projects with helping them gain admission to the upscale clubs and organizations they wanted to join.
He regularly favored bids from contractors smart enough to buy materials and services from companies in which he had a stake. To publicize his projects, he used government funds to buy advertising in local newspapers that promoted the sale of the board's construction bonds. He purchased $140,000 in ads from November 1871 to March 1872, more than all the state governments in New England spent on advertising combined. Of course, with near-absolute power came great hubris, and Shepherd took actions by fiat that no local DC politician had attempted before or since.
On September 3, 1872, Shepherd aimed to have the shambling Northern Liberties Market north of downtown razed and replaced with new structures. Only one judge in the District could stop him with an injunction, so Shepherd cheerfully invited him to dinner while leveling the structure. But he didn't warn the vendors that their building was going to come down. A butcher was killed in the demolition along with the son of a former court justice, and thieves descended on the chaotic scene to purloin whatever the unprepared merchants hadn't managed to secure. The public reacted with outrage: The funeral train for those killed stretched half a mile, and local opinion soon turned furiously against the Boss, to the point where an armed guard had to escort him from his office.
In November, his fortunes improved when his staunch ally President Grant won reelection in a landslide and his nemesis, The Patriot, went out of business. Having a free hand once more, Shepherd single-handedly altered the Mall without requesting permission from anyone. His men tore up the tracks of the B&O Railroad near Capitol Hill while other workers laid new tracks across the Mall at 6th Street. The head of the railroad expressed his annoyance, but Shepherd placated him with a friendly meeting, after which the B&O chief allegedly offered the Boss a position as vice president of the railroad itself. With its new ally in the Board of Public Works, the B&O received permission in 1873 to build a grand new station on the Mall itself, putting smoke-belching locomotives and rail yards on land once designated for trees and gardens.
Indomitable Perseverance
A greedy but benevolent tyrant, Shepherd resembled the party bosses and ward heelers who ran most cities in the northern US at the time, minus the benevolence. A master builder in the style of his contemporary Baron Haussmann in Paris, Shepherd had fewer than three years to execute his plans, whereas Haussmann had seventeen. But, driven by Shepherd's domineering attitude and boundless energy, the magnitude of the territorial government's achievement was stunning:
150 miles of road graded and paved
208 miles of sidewalks created
120 miles of sewer lines installed
30 miles of water lines laid
39 miles of gas lines laid
60,000 trees planted
1,000 buildings renovated
1,073 houses constructed
Other departments of the territorial government achieved their share of accomplishments too. Most notably, the Board of Health made some headway with disease control and sanitary inspections, along with condemning unsafe houses, inspecting meat and produce, controlling polluting businesses, and outlawing barnyard animals in the streets. The health department didn't have an Alexander Shepherd at its helm, however, so its efforts didn't receive as much publicity.
Ultimately, according to one estimate, the District had by the mid-1870s become the "best-lit and best-paved city in the United States and its water supply was more plentiful than that of New York." Shepherd and the board trumpeted their achievements in the press and through their own publications, and their allies in the Parvenu class were just as breathless. Mary Clemmer Ames saw Shepherd as a figure of "unvarying integrity and fearless independence," as well as "positive manliness" approaching the stature of a demigod, "with a large, well formed head, sharply-defined features, massive under jaw and square chin, indicative of [his] indomitable perseverance and firmness."
The square-chinned hero capped his career in late 1873 by becoming governor of the Territory of the District of Columbia following Henry Cooke's retirement. It should have been the crowning triumph in the career of the civil servant turned urban savior. Instead, the District was already sinking, and the former plumber was underwater.
Mudholes and Money Traps
The problems had begun soon after the Board of Public Works came into being. Since the board was undertaking so much work throughout the District simultaneously, construction activity tore up streets and sidewalks on nearly every block. The Patriot alleged that three-quarters of the capital's streets were damaged or inaccessible, and that "Mudholes and mantraps, dangerous alike by day and by night, swarm in all directions . . . a putrid stench comes from all sections of the city, offensive to the sense and dangerous to the public health." This situation caused turmoil for residents, who found their roadways and sidewalks ripped up, their street grades dramatically altered, and their houses perched twenty feet above the sidewalk in some cases. Construction so damaged the foundations of some houses that they risked collapsing, and the city brazenly issued condemnation warnings to their owners if they didn't repair them within thirty days. Influential citizens benefited from the usual favoritism—in this case reimbursing repair costs—while most homeowners received nothing for their trouble.
Many pavements that the board laid down were inadequate or, worse, dangerous. Chunks fell out of the wooden roadways, or they rotted altogether in a short time. The quality of the work had little to do with the amount the board paid for it. Shepherd steered work to his contractor friends for inflated amounts and even rejected bids when they came in too low. He set high financial floors for these "straw bids" and did all he could to ensure they would enrich his cronies.
In slapdash fashion, Shepherd often graded city streets without regard to those who lived along them.
Congressional investigations of the board began in early 1872, and the charges were myriad: The board met infrequently and without oversight, overpaid on project bids, spent more funds and carried more debt than was legally allowed, arrogated power from other agencies, acted with haste and secrecy, lacked effective recordkeeping, and used construction work—and the jobs that went with it—to win elections and reward friends. The Republicans who controlled the committees that oversaw the District naturally found little wrong with the Board of Public Works or the "high-minded" men who ran it.
But Congress did set a limit to the borrowing authority of the District at ten million dollars. Including preexisting debt and the four million dollars that voters had approved, that left only one million dollars to complete all of Shepherd's projects. The Boss didn't let minor concerns like debt or legality deter him, though, and he went ahead with his plans. Congress raised its appropriation for the District by $3.25 million in 1872 and 1873, and Shepherd pushed through an increase in local property taxes to their legal maximum, hiked the sewer tax, and looked into tightening tax exemptions for churches and other institutions.
In the end, it wasn't enough. With the territory spending money faster than it could take it in, the board resorted to increasingly creative means of financing, including issuing "certificates of indebtedness," or bonds backed by the estimated increase in taxes on improved land. They sold poorly, but that didn't stop the board from using them as collateral in lieu of cash to pay contractors, who later learned they were redeemable for eighty-five cents on the dollar rather than for their full face value.
Bubble Economy Redux
Undeterred by controversy, Shepherd made a brash, conspicuous target for his critics. His three-hundred-acre "Bleak House" farm, six miles from the city, boasted its own orchard, fish pond, rustic barns, and pony rides for kids. In 1872 he constructed a great bluestone mansion at K Street and Connecticut Avenue, featuring a towering mansard roof, rooms with blue-satin curtains and red-velvet walls, crystal chandeliers, an art gallery, and a billiard room. The mansion sat, not coincidentally, in the northwest quadrant of the capital, which saw the most development and improvement during the Boss's tenure and became home to a wide array of politicians, magnates, merchants, professionals, bureaucrats, generals, and admirals—some of whom later worked in the State, War, and Navy Building, west of the White House, yet another symbol of the board's corruption for its inflated costs and construction graft. (Mark Twain thought it the nation's ugliest building, which we know today as the Eisenhower Executive Office Building.) Shepherd and his allies stood to make a killing on the appreciation of their holdings as the capital expanded northwestward, and the Board of Public Works raked in even more taxes from higher assessments on property in the area.
The board-approved expansion of the street railway up Connecticut Avenue intentionally drove wealthier residents from the central city to develop lots on the fringes of town. Land near the avenue doubled or quadrupled in value in a short time, creating a dizzying property boom not seen in the District since the eighteenth century. Only the ghost of James Greenleaf could match Alexander Shepherd in his flair for speculative building, but Shepherd proved much more successful at it, overseeing the development of twelve hundred buildings in 1872 alone.
But in improving this section of the capital and the neighborhoods that became Dupont Circle, Embassy Row, and Kalorama, Shepherd largely ignored the part of town south and east of Capitol Hill, ensuring that it remained poor and underdeveloped for years to come. Indeed, while the west was booming, property in the eastern half of the capital either stagnated or depreciated. The imbalance of construction was obvious: From November 1872 to November 1873, Northwest DC saw the addition of 603 houses, 134 more than all the rest of the capital combined.
The Terra Firma of Hell
The building frenzy came to a sudden end with a financial collapse. This disaster, the Panic of 1873, even had a direct link to the territorial government, as Henry Cooke's brother, power broker Jay Cooke, forced him to resign as governor to attend to the desperate straits of their teetering Northern Pacific Railroad Company. The firm collapsed anyway, and a six-year national depression ensued. Unemployment exploded, banks failed and suspended customers' credit, and the market for municipal bonds and the payment of local taxes fizzled. An angry public and the public servants in their thrall quickly demanded solutions to the economic mess. Another congressional investigation of the territorial government began in February 1874.
Whereas Shepherd's smooth talk and glad-handing overcame the earlier, cursory congressional review of the District, he couldn't thwart this one. The year before, on his way out of Congress, reform Democrat Robert Roosevelt, uncle of future president Theodore, leveled particularly bitter scorn on the board. He claimed it operated on "the terra firma of Hell" and estimated the District would buckle under a debt of twenty million dollars to pay for the board's actions. He was right. After countless hours of research and investigation and a three-thousand-page report, congressional examiners determined that the District did indeed carry that colossal amount of debt, twice the legal amount allowed.
To get the District back in the black, Congress increased property taxes, cut municipal salaries by 20 percent, and authorized fifty-year bonds for the rest of the debt. It abolished the Board of Public Works, the territorial government as a whole, and the roles of governor and legislature, giving a three-person commission temporary but total charge of District affairs. In an embarrassing footnote, members of the House of Delegates tried to spirit away the legislature's desks, chairs, and office supplies on their way out the door. One politician even stuffed a feather duster down his pant leg, giving his legislative body, as well as the territorial government in general, the nickname "feather-duster legislature."
Ballot Box and Blame
Unfortunately, one of the most honest former members of that government was a prime victim of the economic collapse. In 1874, Frederick Douglass accepted a position as president of the Freedmen's Savings and Trust Bank, taking a job in public service as he had always done, not knowing that the bank was about to default.
Founded at the close of the Civil War as a depository for the funds of black citizens, the bank operated well for five years. In 1870, though, it began investing in riskier ventures, and when Shepherd's associates, including Henry Cooke, took seats on its finance committee, disaster was all but inevitable. The bank's managers schemed to find an unwitting scapegoat for their own bad investments in the Northern Pacific Railroad and other failed enterprises, and they found their mark in Douglass. Losing ten thousand dollars, he called being tied to the bank like being "married to a corpse" and castigated those who had brought the bank to ruin by "squandering in senseless loans on bad security the hard-earned moneys of my race."
The meltdown of the Freedmen's Bank wasn't the only example of territorial leaders abusing the trust of their African-American constituents. Shepherd and his peers used them to win elections and in return provided temporary construction jobs and passed the occasional civil rights bill. But the Boss and his board did almost nothing in the long term to build up the poor and working-class parts of town where most blacks lived, especially east and south of the Capitol. With their real estate improvements focused in Northwest DC, they actually stifled the development of such neighborhoods as The Island, East Capitol Hill, and parts of downtown. Even worse, Congress, which had offered the opportunity for black voters to become major players in local elections in the late 1860s, rolled back their franchise in 1871 with the creation of the territory and then, when the territory folded three years later, curtailed their suffrage entirely.
The Demise of Suffrage
In 1874 Senator Justin Morrill of Vermont introduced a bill to reorganize the District and permanently strip voting rights from its citizens. Senator Allan Thurman of Ohio, like others supporting the bill, tried to blame the failings of the territory on the African Americans who had supported the Board of Public Works. He made the specious claim that the previous municipal governments of the District did "tolerably well," and "There was never any great complaint about them until Negro suffrage came." Thomas Bayard of Delaware spoke more bluntly as a representative of a former slave state: "negro suffrage has been a very sickening business to the unhappy people of this District and to those who brought it here; and I have no doubt that as a matter of fact this bill seeks to accomplish the complete abandonment of that most absurd attempt to govern this District though the instrumentality of its most ignorant and degraded classes."
The elderly Frederick Douglass: icon of America, victim of DC bankers.
Old-line white supremacists of course supported removing the franchise from DC citizens, but they had company. Outside Congress, even the stalwart National Republican went along with the antivoting camp, saying the Republican Party should acknowledge the "failure" of suffrage. If it didn't, "The Party would be putting a sword in the hands of the enemy to slay itself." Many local whites spoke grimly of a return to suffrage in the District, and the emergence of "Murder Bay politicians," that is, blacks who would rise to power if it occurred.
A few brave politicians did speak out against the tide of reaction, noting the odium of permanently removing all voting rights for District residents. Senator Oliver Morton of Indiana said of the Morrill bill:
It takes from them the right of local self-government; it takes from them the power of considering and acting upon their own local and, so to speak, domestic affairs . . . In that respect this bill is anti-republican; it is anti-democratic; and I do not feel that I could vote for it without violating the very spirit of our institutions. . . . when we undertake to disenfranchise 100,000 people we are taking a step backward, and I know what will be said about it . . . that it is intended to get clear of colored suffrage. In this District, where it was first established, it is to be the first stricken down.
The Shepherd Legacy
Congress wrestled with a permanent form of District government for a few more years but rendered a verdict on Alexander Shepherd much more quickly: In 1874 it exonerated him from charges of fraud or any other misdeeds. He was simply too likable, too influential, and had too many friends in the Republican Party to be held liable for the failings of the territory, however grievous and however much his fault they were. Ulysses Grant even had the nerve to nominate him as one of the District's temporary commissioners, but for once the Senate didn't assent to the president's dubious choice.
But as the myth took hold that the failures and fraud of the territorial government derived from "degraded" African-American voters and a few corrupt public servants, Alexander Shepherd's reputation grew. In later years he was hailed a "latter-day L'Enfant, with more brains and more power," and an engineering genius who had "cautiously and carefully" reconstructed and improved the city. Although Shephred declared personal bankruptcy in 1876, he amazingly restored his fortunes six years later with a speculative gold mine in Mexico, and returned to the capital in 1882 to be "feted, honored, and commemorated in a deluge of congratulatory parties, parades, and balls." By then memories of the nasty little village of Washington City had faded, and writers sang the praises of the national capital as a hub of political power and prestige, with its "dazzling vistas and public edifices reminiscent of grand European capitals."
Real District Power
In the end, Shepherd received more credit than he deserved. The far-sighted vision of Montgomery Meigs and Nathaniel Michler provided the underlying template for the improvement of the District, even as the Board of Public Works took credit for their ideas and gloried in them. In subsequent years the popular press added to the legend that the board alone had driven all change in the capital, even assigning credit for the army corps' major accomplishments—such as replacing the wood pavers in the street with asphalt—to the board years after Congress had abolished it.
One figure who bridged the divide between the Army Corps of Engineers (as a superintendent) and the Board of Public Works (as an advisor) was Orville Babcock. Linked to nearly as many accomplishments and as much corruption as Shepherd, Babcock was indicted in 1875 and tried for his role in the Whiskey Ring to evade federal liquor taxes. A year later he was tried again for planting evidence on one of Shepherd's enemies. In both cases he was acquitted, though a later historian said that he "fished for gold in every stinking cesspool, and served more than any other man to blacken the record of Grant's administration."
Capital Emergent
Disregarding Babcock's antics, Congress elevated the role of the corps when it passed the Organic Act of 1878. This act codified the District of Columbia as the capital's sole governing entity, subject to the will of Congress, and made the federal government responsible for funding half of the city's budget, with the other half raised from local taxation. It was a long-overdue change from those dreadful decades when citizens had to beg the legislature for any scrap of funding at all.
The Grant administration featured a high-wire act of corruption, with two prominent DC officials—Shepherd and Babcock—key players.
In executing its plan for the city, Congress handed control of municipal affairs to three appointed commissioners. Leaders of each major party chose one, and the third, by law, would be an "Engineer Commissioner" from the US Army. With all former boards of the city abolished, the new commissioners had direct responsibility for the capital, a power they retained for nearly a century.
This was the ultimate payoff for the Army Corps of Engineers' steady role in building up the capital, which had only increased since the war until it now gained "almost total control over Washington's public buildings, infrastructure, and physical environment." In due course, it executed plans to correct the flaws in Shepherd's shoddy construction work, expand the water supply, extend the sewer system, pave and grade more streets, and reclaim the dreaded Potomac Flats. It even began finishing the embarrassing stump of the Washington Monument, finally completing the massive obelisk in 1884, a great triumph for the city. Indeed, as it acquired unprecedented power in the peacetime governance of the American capital, the corps seemed capable of achieving almost anything.
The End of the Franchise
But there was one thing the corps couldn't and wouldn't do: provide the citizens of the District of Columbia with a shred of power to choose their own leaders or run their own government. Early versions of the Organic Act of 1878 called for a local elective council and a member in Congress, but these disappeared from the final version of the bill and ensured that DC residents had the same influence over their local leaders as their federal ones—none. Surprisingly, the act passed with the support of a racially retrograde House of Representatives run by Democrats and a nominally more progressive Senate under Republican control. Both parties stripped the vote from capital residents because, at their core, there wasn't much difference in their motivations. A quick look back shows why.
Two rival forces had whipsawed Washington City throughout its troubled history. Initially Southern congressmen paralyzed the growth of the capital to keep it weak and undeveloped so the national government, by extension, remained feeble and inhibited with respect to the states. After the war, Northern congressmen emboldened the growth of the capital so the federal government would stand dominant and uninhibited over those states.
In both cases, the interests of local voters were irrelevant. Southerners didn't care to aid a city for which they had so little use. Residents' rights became even more constricted once Northerners decided to use their power to develop the capital. Any threat to that power—even voting in municipal elections—had to be stymied. Racial politics only added to the equation and ensured that white residents could, through statutory and constitutional law, keep African Americans from exercising their franchise in the District, even as they grew to a residential majority in future decades. In stripping away the franchise, Congress ensured that the District remained a ward of the nation, the sole province of national politicians. The day-to-day rulers changed, their motivations differed, but the disenfranchisement stood.
A Founder's Legacy
Ultimately the victor was Alexander Hamilton's political philosophy, which proved remarkably resilient. Nearly a century had passed since he pontificated on the dangers of relinquishing power to the mob, imagining a place where the federal government would reign supreme. Although the capital had suffered more than seven decades of misery, his dream had come to pass by the Gilded Age. The city changed for the better, as grand new buildings, parks, infrastructure, and neighborhoods took shape. The once dysfunctional village emerged as the world-class capital that—if not quite the baroque fantasy of Pierre L'Enfant—at least kept critics at bay and gave us a respectable urban center for the nation. As part of the deal, the city's residents stood no closer to having a stake in their governance than they had a century before. The light of their democracy was finally extinguished.
In the end, the language of Hamilton's philosophy may have been dressed up in legalese and constitutional purpose, but at root it involved two simple motivations: fear of the masses and need for dominion over them. Washington, DC, acted as the test case. It took decades of mud, chaos, and struggle, but by the end of the nineteenth century the city emerged as the paradigm for Hamilton's idea of urban development as well as his imperial, profoundly antidemocratic perspective.
Little has changed since then but for one striking mood swing: Regardless of political faction, US citizens have come to view the capital as an example of everything wrong with their national governance. The reasons may stem from the imperious attitudes of American politicians, inflated delusions of grandeur, or an ongoing frustration with the elephantine federal bureaucracy. Or perhaps the public understands something deeper about the nature of political power—perhaps realizing the darker motivations of their leaders and the absurdity of running a democracy from a place that has no use for it.
Epilogue
The Sea of Pavement
By the 1920s the District of Columbia looked brand new. The commissioners oversaw a city rapidly becoming the heart of a regional metropolis, the growth of the federal government providing its lifeblood. The Gilded Age had brought new commerce and industry, the Army Corps of Engineers had overseen a wealth of infrastructure improvements and public works projects, and the McMillan Commission Plan of 1901 had redesigned the capital to its core. The Mall now conformed much more closely to Pierre L'Enfant's original design. Outmoded train stations gave way to the Beaux-Arts colossus of Union Station. Stately bridges and presidential memorials added classical dignity to the landscape. Charming parks encouraged urban leisure. New roads, streetlights, sewers, and construction codes provided the essential building blocks for a modern American city.
But the one neighborhood that hadn't changed much or benefited from the City Beautiful campaigns that reshaped the rest of the capital was the former Murder Bay. This triangular precinct bordered by Pennsylvania Avenue NW, 15th Street, and B Street north of the Mall still lay in the heart of the city—between the White House and the Capitol—and it still sheltered the working class and the working poor. Congress may have outlawed prostitution in the District in 1914, but the neighborhood was still known as The Division, and crime remained deeply rooted.
Nonetheless, even for a down-at-heel area, The Division was quite busy, lively even. A foundry, power plant, machine shops, plumbers, and lumberyards operated in abundance here—precisely the industrial operations that old Washington City lacked—and these businesses employed a wide range of ethnic laborers who lived in the wood and brick row houses that lined the streets. Italian immigrants sold fruit from their stores and carts, and "gas stations, tattoo parlors, chop suey [restaurants], rooming houses, and cheap hotels" made a busy trade along Pennsylvania Avenue and alongside the now-illegal brothels operating on Ohio Avenue.
Although The Division may have resembled a Northern city, Washington society had retrenched since the carpetbagger days of the Gilded Age, as the capital once more returned to the cultural orbit of the South. From 1870 to 1930 the proportion of Northerners in town increased by 28 percent, but it doubled for Southerners, who now played a much greater role in the city's commercial and civic life and put a greater stamp on its social landscape.
Freedom's Descent
In the 1920s African Americans composed a quarter of the city's population. The return to power of the old Southern gentry fell upon these residents the hardest, beginning with the segregation of most public facilities at the turn of the century, and, when former Southerner Woodrow Wilson came to power in 1913, the segregation of federal offices and restriction of black hiring or advancement in government employment. Black schools went underfunded; discrimination widely affected theaters, department stores, and restaurants; and whites-only neighborhoods kept black home buyers out with restrictive covenants. As Constance Green writes, "The national government took the line of the Deep South, and white persons as private citizens now looked upon Negroes scarcely as citizens at all."
Then it got worse. The Washington episodes of the national "Red Summer" riots of 1919 included military servicemen attacking blacks in the streets. The police could do little to stop the violence and arrested the victims instead. That same year, health reports showed that local African-American levels of infectious disease were three to six times those of whites, infant mortality rates were also high, and the life span of a black person, male or female, was only forty-four years. The squalid housing conditions in precincts such as The Division obviously had a lot to do with it, since subpar health and sanitation were legion and poverty was endemic. This was especially the case in the increasingly nightmarish alley dwellings, which had plagued the city since the nineteenth century and stood just as filthy and dilapidated as ever—if conveniently out of sight to most of official Washington.
In the face of such unfair treatment, blacks had no recourse to the ballot box to demand change. They, like their white counterparts, couldn't vote in the capital or do anything to change the policies of those in power. This became most evident when, instead of improving The Division, the federal government decided to tear it down.
Dignified Ideas
In 1918 the Public Buildings Commission presented a report that harshly evaluated the neighborhood: "The character of the occupancy of the area between [Pennsylvania] Avenue and the Mall is low. . . . Nothing short of radical measures to bring this area into a higher grade of occupation will save the situation." Congress responded with the Public Buildings Act of 1926, which provided fifty million dollars for the construction of new federal buildings. Half the amount went to redevelop the Division, both to provide more office space for government workers and to engage in an early form of urban renewal. After all, as writer Mildred Adams said, there was no place for "the little shops with slovenly fronts that offend citizens with more dignified ideas."
The US government duly purchased nearly all of the land in The Division in 1927 and planned for a new "Federal Triangle" of superblocks to rise in its place. Answering critics who questioned whether such colossal structures would suit the area, federal builders promised great parks and plazas between the buildings. Two years later, Treasury Secretary Andrew Mellon funded a propaganda film to win over the remaining detractors. It extolled the virtues of the huge new buildings while deriding the old neighborhood as a decrepit patch unworthy of saving. During the next eight years, the government destroyed the old neighborhood.
Some of the notable buildings that came down included Harvey's restaurant, renowned for its piles of steamed clams; such popular entertainment venues as Ford's Grand Opera House, Albaugh's Opera House, and the Bijou and President Theatres; the US Electric Lighting Company, the great powerhouse built like a brick castle; and, most lamented of all, the Centre Market. Although a market had been included on early city plans in the 1790s and George Washington himself had picked out the site for it, neither public protests nor lawsuits could stop the government from demolishing it. On January 1, 1931, two thousand vendors and their employees—who sold meat, produce, and countless other goods—were forced from their stalls. Two months later the Victorian arches and turrets of Centre Market fell. The market was not rebuilt.††
†† Thankfully federal developers ran out of funds before they could tear down the great Romanesque revival post office at Pennsylvania Avenue and 12th Street.
The heart of the old city was demolished to make way for the Federal Triangle.
The Triangle Rises
In place of the diverse, polyglot old neighborhood rose the oversized buildings of the Federal Triangle, a hodgepodge of vaguely classical structures, each six stories high and faced in stone. Their designs mixed Classical Greek with Italian Renaissance and threw in Beaux-Arts and Art Deco motifs as well. The Public Buildings Commission called it the ideal way to show "the revival of classical architecture for the use of modern business demands." Official Washington rejoiced, but not everyone was impressed. Some architects later derided the Triangle for embracing "façadism" and "brutal masses . . . built in an eclectic style as boring as it was massive and unoriginal." Moreover, the development completely ignored L'Enfant's original street grid, wiped out thirty-one city blocks, and removed dozens of streets that had existed since the birth of the capital, replacing them with just a few north-south corridors. Eight giant buildings occupied the rest of the space, and the promised parks never came. Not only did the Triangle stand apart from the rest of the city's layout, it acted as a wall between the redesigned Mall and the active commercial district north of Pennsylvania Avenue, making for a crowded space for federal workers during the day but an unfriendly dead zone at night.
Despite its gargantuan blandness, the Federal Triangle made more than an architectural statement. Its planners intended it as a dramatic gesture to erase the embarrassing legacy of the capital by removing the shambling homes and businesses of its antique core and erecting in their place an icon to an empire on the rise. In this way, the capital's leaders succeeding in rewriting their city's visual history, replacing broken cobbles with a sea of pavement, trading ramshackle hotels and markets for imperial monuments, and helping people forget that a place called Washington City ever existed.
Walking from Pennsylvania Avenue to Constitution Avenue now, you'd never guess that colorful street life once thrived in the neighborhood—or that it had ever been a neighborhood at all. But in a previous age, before the wrecking ball arrived, life hummed along these streets. A ragtime band played in a music hall on one corner, a bordello piano on the next. Shouts and laughter from gambling dens and saloons filled the air. By contrast, these days, if you come to the area at night, you'll only hear tourists running to catch the next subway train, as the wind whistles through the Triangle's gaping arches and barren plazas past statues of people who never lived there.
Acknowledgments
Empire of Mud took five years from conception to completion, and there were a lot of people who helped along the way. The most prominent were my manager, Adam Chromy, at Movable Type Management, whose energy, insight, and acumen were essential to the project; editor James Jayo, who guided the book skillfully and offered critical feedback and revisions; project editor Meredith Dias, who oversaw the book with great dexterity; and everyone else at Lyons Press who contributed their skill and energy to the endeavor. I'd also like to thank Jason Ashlock, who provided essential help in getting the project started.
A few dozen librarians and archivists offered key assistance. The most important of these were Marilyn Ibach at the Library of Congress's Prints and Photographs Division; Mark Greek, photo archivist of the Washingtoniana Collection at the DC Public Library; Laura Barry, research services librarian of the Kiplinger Research Library at the Historical Society of Washington; Julia Downie, media librarian of Special Collections at the Alexandria Library; Lieutenant Nicholas Breul, historian of the Metropolitan Police; Audrey Davis, director of the Alexandria Black History Museum; Ruth Reeder, education coordinator at the Alexandria Archaeology Museum; Frances McMillen, preservation specialist for the District's Historic Preservation Office; and various staff members at the National Archives. Also helpful were DC historian Mark Herlong, who offered a bevy of colorful tales from the late nineteenth century; librarian Clara Stemwedel, who helped uncover key dissertations and research papers; and cartographer Daniel Rosen and his tireless, expert abilities.
Others who have provided valuable assistance include the authors James Howard Kunstler, George Pelecanos, Ron Franscell, Ro Cuzon, Zora O'Neill, and Andrew Rosenberg, as well as Scott Hoffman, for the initial push forward. Finally, my friends provided useful feedback on the text, among them Matt McMillen, Noel Ponthieux, Brenna Dickey, John Miller, Teresa Christie, Leopoldo Marino, Robin Richardson, and Lisa Scarpelli. Great praise too goes to my family members and especially my parents, who continue to provide valuable thoughts, insights, and love.
Notes
Introduction: Capital Movers
Mary A. Y. Gallagher, "Reinterpreting the 'Very Trifling Mutiny' at Philadelphia in June 1783," Pennsylvania Magazine of History and Biography 119:1/2 (1995): 8–11, 12–13.
Kenneth R. Bowling, "New Light on the Philadelphia Mutiny of 1783: Federal-State Confrontation at the Close of the War for Independence," Pennsylvania Magazine of History and Biography 101:4 (Oct. 1977): 425.
Bowling, "New Light," 426.
Ibid., 428.
Ibid., 431.
Ibid., 430.
Gallagher, "Reinterpreting," 24.
Bowling, "New Light," 433–34.
Ibid., 433.
Gallagher, "Reinterpreting," 25.
Bowling, "New Light," 437–38, 448.
William C. di Giacomantonio, "'To Sell Their Birthright for a Mess of Potage': The Origins of D.C. Governance and the Organic Act of 1801," Washington History 12:1 (Spring/Summer 2000): 32.
Bowling, Creation of Washington, 34.
Bowling, "New Light," 445.
Ibid., 449.
Rubil Morales Vasquez, "Imagining Washington: Monuments and Nation Building in the Early Capital," Washington History 12:1 (Spring/Summer 2000): 17; Donald R. Kennon, review of Congress and the Governance of the Nation's Capital, in Washington History 7:2 (1995/1996): 80.
Bowling, Creation of Washington, 198; Bowling, "New Light," 420.
Bowling, "New Light," 419.
Trollope, North America, 449, 450.
Chapter 1: The Capital Archipelago
Green, Washington: Village and Capital, 18, 20.
Gutheim, Worthy of the Nation, 21.
Highsmith and Landphair, Pennsylvania Avenue, 53.
Hurd, Washington Cavalcade, 58.
C. M. Harris, "Washington's 'Federal City,' Jefferson's 'Federal Town,' " Washington History 12:1 (2000): 49–53.
Ibid., 50.
Gutheim, Potomac, 12.
Priscilla W. McNeil, "Rock Creek Hundred: Land Conveyed for the Federal City," Washington History 3:1 (1991): 42–51.
Gutheim, Potomac, 327.
Smith, Washington at Home, 33.
Gutheim, Potomac, 327.
Vlach, " Mysterious Mr. Jenkins."
Margaret Brent Downing, "Significant Achievements of the Daniel Carrolls of L'Enfant's Era," Catholic Historical Review 16:3 (1930): 227–28.
Bob Arnebeck, "Tracking the Speculators: Greenleaf and Nicholson in the Federal City," Washington History 3:1 (1991): 113.
Ibid.
Gutheim, Potomac, 327.
Junior League of Washington, City of Washington, 48.
Arnebeck, "Speculators," 116.
Ibid., 117–18.
Ibid., 121; Reps, Washington on View, 32.
Reps, Washington on View, 32.
Arnebeck, "Speculators," 119.
Allen C. Clark, Thomas Law: A Biographical Sketch (Washington, DC; W. F. Roberts, 1900): 15
Bryan, History of the National Capital, 1:280.
Reps, Washington on View, 32.
Arnebeck, "Speculators," 120–21.
Gutheim, Potomac, 327.
Goode, Capital Losses, 5, 171
Reps, Washington on View, 32; Janson, Stranger in America, 214.
Gibbs, Memoirs of the Administrations, 2:44.
Janson, Stranger in America, 212, 214.
Goode, Capital Losses, 7.
Highsmith and Landphair, Pennsylvania Avenue, 50.
Ethel M. B. Morganston, "Davy Burnes, His Ancestors and Their Descendants," Records of the Columbia Historical Society, Washington, D.C. 40 (1948/1950): 110; Priscilla W. McNeil, "Rock Creek Hundred: Land Conveyed for the Federal City," Washington History 3:1 (1991): 42–51.
Morganston, "Davy Burnes," 111, 113.
Susan L. Klaus, " 'Some of the Smartest Folks Here': The Van Nesses and Community Building in Early Washington," Washington History 3:2 (1991/1992): 25; Morganston, "Davy Burnes," 112–13.
Allen C. Clark, "General John Peter Van Ness, a Mayor of the City of Washington, His Wife, Marcia, and Her Father, David Burnes," Records of the Columbia Historical Society, Washington, D.C. 22 (1919): 136.
Allen B. Slauson, "Curious Customs of the Past as Gleaned from Early Issues of the Newspapers in the District of Columbia," Records of the Columbia Historical Society, Washington, D.C. 9 (1906): 114.
Gutheim, Potomac, 13.
Frances Carpenter Huntington, "The Heiress of Washington City: Marcia Burnes Van Ness, 1782–1832," Records of the Columbia Historical Society, Washington, D.C. 47 (1969/1970): 80, 98.
Alison K. Hoagland, "Nineteenth-Century Building Regulations in Washington, D.C.," Records of the Columbia Historical Society, Washington, D.C. 52 (1989): 58–59.
Goode, Capital Losses, 5.
Gutheim, Federal City, 78; Letter to George Washington from Pierre L'Enfant, Nov. 21, 1791. National Archives, Founders Online, accessed at http://founders.archives.gov/documents/Washington/05-09-02-0124.
Goode, Capital Losses, 5.
Young, Washington Community, 22.
Reps, Washington on View, 32.
Pamela Scott, " 'This Vast Empire': The Iconography of the Mall: 1791–1848," in Longstreth, Mall in Washington, 54, n12.
Harris, "Washington's 'Federal City,' " 49, 51.
John W. Reps, "Thomas Jefferson's Checkerboard Towns," Journal of the Society of Architectural Historians 20:3 (1961): 108.
Rubil Morales Vasquez, "Imagining Washington: Monuments and Nation Building in the Early Capital," Washington History 12:1 (2000): 21.
Ibid., 24.
Harris, "Washington's 'Federal City,' " 52.
Hines, Early Recollections, 61–62; Washington Federalist, April 14, 1802, and November 23, 1802.
Hines, Early Recollections, 62–63.
Goode, Capital Losses, 23.
Hurd, Washington Cavalcade, 19.
Gutheim, Potomac, 326.
Weld, Travels through the States, 72–89.
Gutheim, Potomac, 327.
Reps, Washington on View, 60.
Young, Washington Community, 21.
Reps, Washington on View, 57.
Scott, " 'This Vast Empire,' " 40–41.
Smith, Washington at Home, 55–56.
Bergheim, Washington Historical Atlas, 128–29.
Smith, Washington at Home, 57.
Green, Washington: Village and Capital, 36.
Janson, Stranger in America, 215.
Young, Washington Community, 23.
Smith, Washington at Home, 66.
Kay Fanning, "The Mall: National Mall & Memorial Parks," in Cultural Landscape Inventory (Washington, DC: National Park Service, 2006), 25–26.
Green, Washington: Village and Capital, 106.
Scott, " 'This Vast Empire,' " 46.
National Intelligencer, March 24, 1841. Address of Joel R. Poinsett before the National Institution.
Gibbs, Memoirs of the Administrations, 2:377.
Diane K. Skvarla, "Nineteenth Century Visitors," Washington History 1:1 (1989): 10.
Reps, Washington on View, 70–74.
Dickens, American Notes, 279.
Green, Washington: Village and Capital, 38.
Bryan, History of the National Capital, 2:14.
Smith, First Forty Years, 10.
Highsmith and Landphair, Pennsylvania Avenue, 53.
Ibid., 55.
Mackay, Western World, 2:110–11.
Goode, Capital Losses, 492.
Hurd, Washington Cavalcade, 57.
Passonneau, Washington through Two Centuries, 68.
Green, Washington: Village and Capital, 41.
Gutheim, Federal City, 15.
Green, Washington: Village and Capital, 41.
Hurd, Washington Cavalcade, 27; Green, Washington: Village and Capital, 41.
Hurd, Washington Cavalcade, 58.
Vasquez, "Imagining Washington," 145–46.
Gutheim, Potomac, 332–33.
Bryan, History of the National Capital, 2:16.
Ibid., 18.
Green, Washington: Village and Capital, 140.
Young, Washington Community, 23.
Green, Washington: Village and Capital, 40.
Ibid., 39, 89–90.
Young, Washington Community, 24.
Gutheim, Potomac, 17.
Bryan, History of the National Capital, 2:20.
Arnebeck, Through a Fiery Trial, 626.
Ibid., 627.
Ibid.
Young, Washington Community, 24.
Hurd, Washington Cavalcade, 26–27.
Young, Washington Community, 25.
Thomas Moore, "To Thomas Hume, Esq., M.D., On the City of Washington," in The Poetical Works of Thomas Moore (London: Oxford University Press, 1915): 117.
Chapter 2: A Plague of Waters
District of Columbia Dept. of the Environment, et al. Federal Triangle Stormwater Drainage Study (Washington, DC: Oct. 6, 2011): 7. Accessed at www.ncpc.gov/ DocumentDepot/Planning/flooding/federal_triangle_drainage_study_presentation.pdf
Gutheim, Federal City, 8.
Hines, Early Recollections, 45.
Ibid., 47–48.
Ibid., 44, 67, 95.
Julie D. Abell and Petar D. Glumac, "Beneath the MCI Center: Insights into Washington's Historic Water Supply," Washington History 9:1 (1997): 26.
Garnett P. Williams, "Washington D.C.'s Vanishing Springs and Waterways," in Moore and Jackson, Geology, Hydrology and History, 77, 84–85
Ibid., 82.
Don Alexander Hawkins, "The Landscape of the Federal City: A 1792 Walking Tour," Washington History 3:1 (1991): 23.
John C. Reed Jr. and Stephen F. Obermeier, "The Geology Beneath Washington, D.C.—The Foundation of a Nation's Capital," in Moore and Jackson, Geology, Hydrology and History, 28; Gutheim, Worthy of the Nation, 41; Robbins and Welter, Building Stones, 6–7.
Gutheim, Worthy of the Nation, 19.
Robbins and Welter, Building Stones, 41.
Gutheim, Potomac, 8, 24.
Williams, "Vanishing Springs," 90.
Green, Washington: Village and Capital, 6.
Warden, Chorographical and Statistical Description, 11.
Hawkins, "Landscape," 16.
Harrison, History of the Commercial Waterways, 10.
Reed and Obermeier, "Geology Beneath Washington, D.C.," 28.
Cornelius W. Heine, "The Chesapeake and Ohio Canal: Testimony to an Age Yet to Come," Records of the Columbia Historical Society, Washington, D.C. 66, 68 (1966/1968): 58.
Richard J. Dent, "On the Archaeology of Early Canals: Research on the Pawtomack Canal in Great Falls, Virginia," Historical Archaeology 20:1 (1986): 52.
Heine, " Chesapeake and Ohio Canal," 58.
Dent, "Archaeology of Early Canals," 52.
Ibid., 50, 52.
Heine, " Chesapeake and Ohio Canal," 58.
Dent, "Archaeology of Early Canals," 53.
Gutheim, Potomac, 328.
Warden, Chorographical and Statistical Description, 7; Hibben, Navy-Yard, Washington, 26.
Warden, Chorographical and Statistical Description, 24.
Zach Spratt, "Ferries in the District of Columbia," Records of the Columbia Historical Society, Washington, D.C. 53/56 (1953/1956): 190–92.
Gutheim, Federal City, 4.
Williams, "Vanishing Springs," 87.
Ibid.
Cornelius W. Heine, "The Washington City Canal," Records of the Columbia Historical Society, Washington, D.C. 53, 56 (1953/1956): 2.
Bryan, History of the National Capital, 1:289.
Ibid., 288.
Heine, "Washington City Canal," 3.
Green, Washington: Village and Capital, 28.
Clark, Greenleaf and Law, 257.
Law, "Observations on the Intended Canal," 161–62.
Heine, "Washington City Canal," 5–7.
Frederick May, Letter to William H. Crawford, Secretary of the Treasury, December 2, 1818.
Reps, Washington on View, 54.
Bryan, History of the National Capital, 2:104.
Heine, "Washington City Canal," 9.
Bryan, History of the National Capital, 2:113.
Cowdrey, City for the Nation, 14; Williams, "Vanishing Springs," 87.
Gutheim, Worthy of the Nation, 40–41.
Green, Washington: Village and Capital, 72.
Heine, "Washington City Canal," 10.
Harrison, History of the Commercial Waterways, 14.
Harrison, United States Waterways and Ports, 10
Clark, Greenleaf and Law, 257.
Junior League of Washington, City of Washington, 146.
Green, Washington: Village and Capital, 116.
Ibid., 114–15.
Bryan, History of the National Capital, 2:111.
Vasquez, "Monuments, Markets, and Manners," 244.
Green, Washington: Village and Capital, 114.
Arthur G. Peterson, "The Old Alexandria-Georgetown Canal and Potomac Aqueduct," Virginia Magazine of History and Biography 40:4 (1932): 310.
Heine, "Washington City Canal," 13.
Ibid., 12.
Green, Washington: Village and Capital, 128.
Harzbecker, "Life and Death," 73.
Tindall, Standard History of the City of Washington, 245.
Ibid.; Bryan, History of the National Capital, 2:125.
Charles Augustus Murray, Travels in North America During the Years 1834, 1835 & 1836, Vol. 1 (London: Richard Bentley, 1839): 146.
Green, Washington: Village and Capital, 129.
Ibid.; Bryan, History of the National Capital, 2:126.
Heine, "Chesapeake and Ohio Canal," 59–60.
Gutheim, Potomac, 260.
Goode, Capital Losses, 454; Bryan, History of the National Capital, 2:115–17.
Gutheim, Potomac, 331.
Warden, Chorographical and Statistical Description, 63.
Ibid., 10.
Ibid., 24; Gutheim, Worthy of the Nation, 50.
George J. Moorhead, "Overflows from Combined Sewers in Washington, D.C.," Journal of the Water Pollution Control Federation 33:7 (1961): 713.
Abell and Glumac, "Beneath the MCI Center," 29.
Bryan, History of the National Capital, 2:303.
Chapter 3: A Mechanic's Guide to Washington City
Joint Force Headquarters–National Capital Region and The US Army Military District of Washington, "History of Fort Lesley J. McNair," accessed at http://mdwhome.mdw.army.mil/docs/media-documents/history-of-fort-mcnair-fact-sheet.pdf?sfvrsn=2.
Pitch, Burning of Washington, 20, 82–85, 117.
Smith, Forty Years, 115.
Junior League of Washington, City of Washington, 146
Pitch, Burning of Washington, 150–51.
Warden, Chorographical and Statistical Description, 31.
Smith, Forty Years, 115.
M. I. Weller, "Unwelcome Visitors to Early Washington," Records of the Columbia Historical Society, Washington, D.C. 1 (1897): 56.
Royall, Sketches of History, 156, 158.
Sarah Harvey Porter, "The Life and Times of Anne Royall, 1769–1854," Records of the Columbia Historical Society, Washington, D.C. 10 (1907): 10.
Elizabeth J. Clapp, " 'A Virago-Errant in Enchanted Armor'?: Anne Royall's 1829 Trial as a Common Scold," Journal of the Early Republic 23:2 (summer 2003): 209–10.
Porter, "Life and Times," 17.
Royall, Sketches of History, 156.
Ibid.
Warden, Chorographical and Statistical Description, 42.
Margo, Wages and Labor Markets, 12.
Delano, Washington Directory, 2–84.
Ibid., 21, 59, 104, 109.
Margaret H. McAleer, " 'The Green Streets of Washington': The Experience of Irish Mechanics in Antebellum Washington," in Cary, Washington Odyssey, 42–45.
Warden, Chorographical and Statistical Description, 27.
Charles H. Leedecker, et al., Phase I Archaeological Investigation for the National Museum of African American History and Culture (Washington: Smithsonian Institution, 2007), 39; Harzbecker, "Life and Death," 173.
Smith, Forty Years, 336.
McAleer, " 'Green Streets,' " 47.
Ibid., 48.
Royall, Sketches of History, 182.
Hamilton, Men and Manners, 2:70–72.
Carson, Ambitious Appetites, 137.
Gibbs Myers, "Pioneers in the Federal Area," Records of the Columbia Historical Society, Washington, D.C. 44/45 (1942/1943): 136.
Hamilton, Men and Manners, 2:71, 72.
Mona E. Dingle, "Gemeinschaft and Gemutlichkeit: German American Community and Culture, 1850–1920," in Cary, Washington Odyssey, 115–18.
Harzbecker, "Life and Death," 87.
Smith, Forty Years, 336–37.
Porter, "Life and Times," 13; Cynthia Earman, "An Uncommon Scold: Treasure-Talk Describes Life of Anne Royall," Library of Congress Information Bulletin 59:1 (2000), accessed at www.loc.gov/loc/lcib/0001/royall.html.
Porter, "Life and Times," 14.
Royall, Sketches of History," 156.
Cable, Avenue of the Presidents, 52.
Green, Washington: Village and Capital, 70, 90.
Plummer, "History of Public Health," 26.
Green, Washington: Village and Capital, 91.
Royall, Sketches of History, 143, 144.
David R. Goldfield, "Antebellum Washington in Context: The Pursuit of Prosperity and Identity," in Gillette, Southern City, National Ambition, 15–16.
Myers, "Pioneers," 149.
Elliot, Historical Sketches, 211.
Byron Sunderland, "Washington as I First Knew It, 1852–1855," Records of the Columbia Historical Society, Washington, D.C. 5 (1902): 204.
Royall, Black Book, 93.
Ibid., 20, 246.
Clapp, " 'Virago-Errant,' " 216.
Earman, "An Uncommon Scold."
James, Anne Royall's U.S.A., 253.
Earman, "An Uncommon Scold."
Clapp, " 'Virago-Errant,' " 216–17, 229.
Ibid., 219, 221.
Porter, "Life and Times," 25.
Clapp, " 'Virago-Errant,' " 224.
Ibid., 226–27.
James, Anne Royall's U.S.A., 257.
Earman, "An Uncommon Scold."
Porter, "Life and Times," 158.
Bernard L. Herman, "Southern City, National Ambition: Washington's Early Town Houses," in Gillette, Southern City, National Ambition, 45.
Carson, Ambitious Appetites, 4.
McAleer, " 'Green Streets,' " 48–50.
Carson, Ambitious Appetites, 4.
Herman, "Southern City," 31.
Busey, Pictures of the City, 218–22; Green, Washington: Village and Capital, 160.
Royall, Sketches of History, 130
E. D. Merrill, "Changing Fashions in Transportation," Records of the Columbia Historical Society, Washington, D.C. 48/49 (1946/1947): 160.
William Tindall, "Beginnings of Street Railways in the National Capital," Records of the Columbia Historical Society, Washington, D.C. 21 (1918): 25.
Warden, Chorographical and Statistical Description, 53–54.
Oliver W. Holmes, "Stagecoach Days in the District of Columbia," Records of the Columbia Historical Society, Washington, D.C. 50 (1948/1950): 17.
Twining, Travels in America, 95–97.
Carson, Ambitious Appetites, 34, 36.
Watterston, New Guide to Washington, 87.
Carson, Ambitious Appetites, 6–7.
Faux, Memorable Days in America, 394.
Walter F. McArdle, "The Development of the Business Sector in Washington, D.C., 1800–1973," Records of the Columbia Historical Society, Washington, D.C. 49 (1973/1974): 564.
Watterston, New Guide to Washington, 87.
Junior League of Washington, City of Washington, 101.
Goode, Capital Losses, 302.
Highsmith and Landphair, Pennsylvania Avenue, 77.
Bryan, History of the National Capital, 2:335.
Goode, Capital Losses, 302.
Thomas A. Bogar, "The Origins of Theatre in the District of Columbia," Washington History 22 (2010): 8–9, 11.
Roger Meersman and Robert Boyer, "The National Theatre in Washington: Buildings and Audiences, 1835–1972," Records of the Columbia Historical Society, Washington, D.C. 48 (1971/1972): 191, 194–95.
A. I. Mudd, "Early Theatres in Washington City," Records of the Columbia Historical Society, Washington, D.C. 5 (1902): 64, 65.
Meersman and Boyer, "National Theatre," 204.
Ibid., 217.
Trollope, Domestic Manners, 2:29–30.
Aloysius I. Mudd, "The Theatres of Washington from 1835 to 1850," Records of the Columbia Historical Society, Washington, D.C. 6 (1903): 239.
Richard Moody, quoted in Meersman and Boyer, "National Theatre," 218.
James Waldo Fawcett, "The Circus in Washington," Records of the Columbia Historical Society, Washington, D.C. 50 (1948/1950): 269.
Meersman and Boyer, "National Theatre," 195.
Joseph Earl Arrington, "Henry Lewis' Moving Panorama of the Mississippi River," Louisiana History: The Journal of the Louisiana Historical Society 6:3 (1965): 250, 266, 267.
Hines, Early Recollections, 42–43.
Quoted in Bryan, History of the National Capital, 1:610.
Larkin, Reshaping of Everyday Life, 283.
Poore, Reminiscences of Sixty Years, 1:61.
Royall, Sketches of History," 158.
Porter, "Life and Times," 29, 30, 32.
James, Anne Royall's U.S.A., 273, 307.
Ibid., 379.
Chapter 4: Driving Souls
James, Anne Royall's U.S.A., 63, 242.
James Oliver Horton, "The Genesis of Washington's African American Community," in Cary, Washington Odyssey, 20, 21.
Green, Secret City, 13, 33.
H. Con. Res., 111th Congress, 1st session, May 21, 2009: 1–3.
Edward E. Baptist, " 'Cuffy,' 'Fancy Maids,' and 'One-Eyed Men': Rape, Commodification and the Domestic Slave Trade in the United States," American Historical Review 106:5 (2001): 1636.
James Cox, "Corporations Challenged by Reparations Activists," USA Today, February 21, 2002.
Virginia Groark, "Slave Policies," New York Times, May 5, 2002.
Warden, Chorographical and Statistical Description, 44–46.
Green, Secret City, 20.
David R. Goldfield, "Antebellum Washingtonin Context: The Pursuit of Prosperity and Identity," in Gillette, Southern City, National Ambition, 9–10.
Harrold, Subversives, 30.
Alexandria Ship Records, 1732–1861, transcribed 1973–1989 by Betty Harrington Macdonald. Alexandria Library, Local History/Special Collections, Boxes 218, 219. "Inward Manifests, Alexandria Port," 1800–1809. Horne record from March 25, 1809.
John Michael Vlach, "From Slavery to Tenancy: African-American Housing in Washington, D.C., 1790–1890," in Longstreth, Housing Washington, 3, 6.
John Michael Vlach, "Evidence of Slave Housing in Washington," Washington History 5:2 (1993/1994): 66–67.
Wade, Slavery in the Cities, 59–60.
Vlach, "From Slavery to Tenancy," 7–9.
Lionel Moses, "The Octagon, Washington, D.C. Headquarters of the American Institute of Architects," Art World 2:3 (1917): 296.
Torrey, Portraiture of Domestic Slavery, 57; Andrews, Slavery and the Domestic Slave Trade, 113–14.
"Domestic Slave Trading Businesses," Collection of Freedom House Museum (Franklin & Armfield site), Alexandria, VA, accessed at www.nvul.org/freedomhouse.
Baptist, " 'Cuffy,' 'Fancy Maids,' " 1619, 1629, 1634, 1638–39.
Collection of Freedom House Museum (Franklin & Armfield site), Alexandria, VA, accessed at www.nvul.org/freedomhouse.
Andrews, Slavery and the Domestic Slave Trade, 138–43.
Northup, Twelve Years a Slave, 42–43.
Walter C. Clephane, "The Local Aspect of Slavery in the District of Columbia," Records of the Columbia Historical Society, Washington, D.C. 3 (1900): 237.
Baptist, " 'Cuffy,' 'Fancy Maids,' " 1634.
Abdy, Journal of a Residence, 100.
Clephane, "Local Aspect of Slavery," 239–40.
Abdy, Journal of a Residence, 97.
Goode, Capital Losses, 198.
Vlach, "From Slavery to Tenancy," 11.
Jeannie Tree Rives, "Old-Time Places and People in Washington," Records of the Columbia Historical Society, Washington, D.C. 3 (1900): 75–76.
Torrey, Portraiture of Domestic Slavery, 42–44.
Wilhelmus Bogart Bryan, "A Fire in an Old Time F Street Tavern and What It Revealed," Records of the Columbia Historical Society, Washington, D.C. 9 (1906): 208.
Abdy, Journal of a Residence, 91.
Green, Secret City, 29–30.
Cable, Avenue of the Presidents, 51.
Clephane, "Local Aspect of Slavery," 243.
Torrey, Portraiture of Domestic Slavery, 57.
Green, Secret City, 29.
Cable, Avenue of the Presidents, 51.
Bryan, "Fire in an Old Time F Street Tavern," 209; Green, Secret City, 23.
Green, Washington: Village and Capital, 77.
Harrold, Subversives, 18, 28.
Ibid., 18, 23.
Lundy, Life, Travels, and Opinions of Benjamin Lundy, 30.
William Lloyd Garrison, editorial, The Liberator, January 1, 1831.
Harrold, Subversives, 56.
Ibid., 45–46.
Gilje, Rioting in America, 89.
Jefferson Morley, "The 'Snow Riot,' " Washington Post, February 6, 2005.
Mary Beth Corrigan, "The Ties That Bind: The Pursuit of Community and Freedom Among Slaves and Free Blacks in the District of Columbia, 1800–1860," in Gillette, Southern City, National Ambition, 79–80.
Morley, " 'Snow Riot.' "
Corrigan, "Ties That Bind," 80.
John Davis, "Eastman Johnson's Negro Life at the South and Urban Slavery in Washington, D.C.," Art Bulletin 80:1 (1998): 72, 74.
Bryan, History of the National Capital, 2:143.
Harrold, Subversives, 31–32.
Martin Van Buren, First Inaugural Address, March 4, 1837.
H. Siebert, Underground Railroad, 125–26.
Goldfield, Cotton Fields and Skyscrapers, 45.
Harrold, Subversives, 46, 55.
Sylvester, District of Columbia Police, 29.
Harrold, Subversives, 91.
Hilary Russell, "Underground Railroad Activists in Washington, D.C.," Washington History 13:2 (2001/2002): 30–31.
Smallwood, Narrative of Thomas Smallwood, 21.
Ibid., 32.
Harrold, Subversives, 82, 90.
Smallwood, Narrative of Thomas Smallwood, 32.
Russell, "Underground Railroad Activists," 31.
Smallwood, Narrative of Thomas Smallwood, 46.
Torrey, Memoir of Rev. Charles T. Torrey, 81.
Harrold, Subversives, 86, 90.
Horton, "Genesis,"23.
Allen, History of Slave Laborers, 8–9.
Bob Arnebeck, "The Use of Slaves to Build the Capitol and White House, 1791–1801: Part One, Stumbling to a Policy of Hiring Slave Laborers," accessed at http://bobarnebeck.com/slaves.html.
Letitia W. Brown, "Residence Patterns of Negroes in the District of Columbia," Records of the Columbia Historical Society, Washington, D.C. 69/70 (1969/1970): 71.
Phillips, Freedom's Port, 25.
Wade, Slavery in the Cities, 38.
Brown, "Residence Patterns," 73.
Vlach, "From Slavery to Tenancy," 11.
Horton, "Genesis," 25; Green, Secret City, 16.
Wade, Slavery in the Cities, 48.
Douglass, My Bondage and My Freedom, 318, 328.
Green, Secret City, 16.
Jonathan D. Martin, Divided Mastery: Slave Hiring in the American South (Cambridge, MA: Harvard University Press, 2004), 46.
Green, Secret City, 33.
Corrigan, "Ties That Bind," 73.
Ibid., 73–76.
Harrold, Subversives, 14.
Corrigan, "Ties That Bind," 73.
Gibbs Myers, "Pioneers in the Federal Area," Records of the Columbia Historical Society, Washington, D.C. 44/45 (1942/1943): 139.
Fields, Slavery and Freedom on the Middle Ground, 4.
Green, Secret City, 53–54.
Dorothy Provine, "The Economic Position of the Free Blacks in the District of Columbia," The Journal of Negro History 58:1 (1973): 63.
Melvin R. Williams, "A Statistical Study of Blacks in Washington, D.C., in 1860," Records of the Columbia Historical Society, Washington, D.C. 50 (1980): 175.
Brown, "Residence Patterns," 75–76.
Provine, "Economic Position," 64.
Harrold, Subversives, 40–42.
Horton, "Genesis," 33.
Ibid.
Green, Washington: Village and Capital, 43–44, 162.
Harrold, Subversives, 26–27.
Horton, "Genesis," 36.
Druscilla J. Null, "Myrtilla's Miner's 'School for Colored Girls': A Mirror on Antebellum Washington," Records of the Columbia Historical Society, Washington, D.C. 52 (1989): 258, 259, 262.
Harrold, Subversives, 192; Green, Secret City, 51.
Null, "Myrtilla's Miner's 'School for Colored Girls,' " 259, 264, 266–68.
Horton, "Genesis," 29.
The Black Code of the District of Columbia (New York: William Harned, 1848).
Brown, "Residence Patterns," 70.
Vlach, "Evidence of Slave Housing," 67.
Green, Secret City, 43.
J. Valerie Fifer, "Washington, D.C.: The Political Geography of a Federal Capital," Journal of American Studies 15:1 (1981): 9–10.
Green, Secret City, 175.
Corrigan, "Ties That Bind," 83.
Harrold, Subversives, 141.
Ibid., 166.
Chapter 5: The Company They Kept
George Alfred Townsend, "Thomas Law, Washington's First Rich Man," Records of the Columbia Historical Society, Washington, D.C. 4 (1901): 237, 239.
William Wirt, letter to Laura H. Wirt, May 23, 1820.
Townsend, "Washington's First Rich Man," 237.
Gibbs Myers, "Pioneers in the Federal Area," Records of the Columbia Historical Society, Washington, D.C. 44/45 (1942/1943): 134.
Ibid., 134–35.
Logan, "Redemption of a Heretic," 7.
Martineau, Retrospect of Western Travel, 238.
Ibid., 235.
Carson, Ambitious Appetites, 88, 90.
Royall, Black Book, 122.
Elizabeth J. Clapp, "'A Virago-Errant in Enchanted Armor'?: Anne Royall's 1829 Trial as a Common Scold," Journal of the Early Republic 23:2 (summer 2003): 230.
Susan L. Klaus, " 'Some of the Smartest Folks Here': The Van Nesses and Community Building in Early Washington, Washington History 3:2 (1991/1992): 35.
Ibid., 38–40.
Royall, Black Book, 139.
Goode, Capital Losses, 23.
Myers, "Pioneers," 156.
Gutheim, Potomac, 328–29.
Carson, Ambitious Appetites, 108.
Mary Bailey Tinkcom, "Caviar Along the Potomac: Sir Augustus John Foster's 'Notes on the United States,' 1804–1812," William and Mary Quarterly, third series 8:1 (1951): 77.
David Hosford and Mary Bagot, "Exile in Yankeeland: The Journal of Mary Bagot, 1816–1819," Records of the Columbia Historical Society, Washington, D.C. 51 (1984): 36.
Crowninshield, Letters of Mary Boardman Crowninshield, 20.
Carson, Ambitious Appetites, 69–70.
Smith, Forty Years, 389–90.
Green, Washington: Village and Capital, 82.
Watterston, New Guide to Washington, 140.
Carson, Ambitious Appetites, 126–27.
Poore, Reminiscences of Sixty Years, 74, 75.
Ibid., 74
Aloysius I. Mudd, "The Theatres of Washington from 1835 to 1850," Records of the Columbia Historical Society, Washington, D.C. 6 (1903): 227.
Steven C. Bullock, "A Pure and Sublime System: The Appeal of Post-Revolutionary Freemasonry," Journal of the Early Republic 9:3 (1989): 361, 364.
Steven C. Bullock, "Remapping Masonry: A Comment," Eighteenth-Century Studies 33:2 (2000): 277.
Steven C. Bullock, "The Revolutionary Transformation of American Freemasonry, 1752–1792," William and Mary Quarterly 47:3 (1990): 367–68.
Ibid., 351; Bullock, "Remapping Masonry," 278.
Kathleen Smith Kutolowski, "Freemasonry and Community in the Early Republic: The Case for Antimasonic Anxieties," American Quarterly 34:5 (1982): 547.
H. Paul Caemmerer, "The Sesquicentennial of the Laying of the Cornerstone of the United States Capitol by George Washington," Records of the Columbia Historical Society, Washington, D.C. 44/45 (1942/1943): 177.
Ronald P. Formisano and Kathleen Smith Kutolowski, "Antimasonry and Masonry: The Genesis of Protest, 1826–1827," American Quarterly 29:2 (1977): 142; Bullock, "Pure and Sublime System," 359–60.
Formisano and Kutolowski, "Antimasonry and Masonry," 160.
William Wirt, letter to the Anti-Masonic Convention, September 28, 1831.
William Wirt, letter to Judge Dabney Carr, January 12, 1832.
Watterston, New Guide to Washington, 112–13; Green, Washington: Village and Capital, 101, 133–34.
Klaus, " 'Some of the Smartest Folks Here,' " 33.
Green, Washington: Village and Capital, 135.
Ibid., 64–65.
Vasquez, "Monuments, Markets, and Manners," 173; Goode, Capital Losses, 329.
Green, Washington: Village and Capital, 65–67.
Townsend, "Washington's First Rich Man," 234.
Clark, Greenleaf and Law, 221.
Ibid., 228.
Ibid., 236.
Twining, Travels in America, 109–10.
Clark, Greenleaf and Law, 245.
Townsend, "Washington's First Rich Man," 230–31.
Clark, Greenleaf and Law, 245.
Ibid., 256; Townsend, "Washington's First Rich Man," 226–27.
Clark, Thomas Law, 20.
Thomas Law, letter to President James Madison, November 26, 1814.
Clark, Greenleaf and Law, 315.
Ibid., 260.
Clark, Thomas Law, 11.
Ibid., 27.
Clark, Greenleaf and Law, 305.
Smith, Forty Years, 4.
Townsend, "Washington's First Rich Man," 236.
Clark, Greenleaf and Law, 287; Clark, Thomas Law, 26.
Townsend, "Washington's First Rich Man," 235; Twining, Travels in America, 110.
Hosford and Bagot, "Exile in Yankeeland," 37.
Townsend, "Washington's First Rich Man," 241.
Scott, " 'This Vast Empire,' " 47.
Junior League of Washington, City of Washington, 188–89.
Bryan, History of the National Capital, 2:324.
Martineau, Retrospect of Western Travel, 314–15.
Vasquez, "Monuments, Markets, and Manners," 251, 253.
The Journal of the House of Delegates of the Commonwealth of Virginia, 1831–1832 (Richmond: Thomas Ritchie, 1831): 163; Willie P. Mangum to Charity A. Mangum, February, 18, 1832, The Papers of Willie Person Mangum 1807–1832 (Raleigh: North Carolina State Deptartment of Archives and History, 1950): 486–87.
Bryan, History of the National Capital, 2:328–29.
Ibid., 245–46, 325.
Green, Washington: Village and Capital, 172.
Carson, Ambitious Appetites, 138.
Young, Washington Community, 71.
Carson, Ambitious Appetites, 138–41.
Young, Washington Community, 24.
Delano, Washington Directory, vii–xiv.
Young, Washington Community, 100–102.
Cable, Avenue of the Presidents, 56–57.
Smith, Forty Years, 192.
Young, Washington Community, 47.
Cable, Avenue of the Presidents, 54; Green, Washington: Village and Capital, 107.
Royall, Black Book, 126–27.
Green, Washington: Village and Capital, 107.
Young, Washington Community, 73–74, 224–25.
Hutchins and Moore, National Capital, Past and Present, 59–60.
Young, Washington Community, 73.
Plumer, Life of William Plumer, 354.
Faux, Memorable Days in America, 153.
Young, Washington Community, 76–77.
Myers, "Pioneers," 151-52
Young, Washington Community, 50.
Ibid.
David R. Goldfield, "Antebellum Washington in Context: The Pursuit of Prosperity and Identity," in Gillette, Southern City, National Ambition, 8.
Green, Washington: Village and Capital, 66.
Gillette, Introduction, Southern City, National Ambition, iv.
Constance McLaughlin Green, "The Jacksonian 'Revolution' in the District of Columbia," The Mississippi Valley Historical Review 45:4 (1959): 604–5.
Clark, Thomas Law, 12–13.
Clark, Greenleaf and Law, 286.
Ibid., 304, 307, 312, 313.
Wharton, Social Life in the Early Republic, 68.
Clark, Greenleaf and Law, 334.
Chapter 6: Coming to the Scratch
Twining, Travels in America, 91, 108.
Myra L. Spaulding, "Dueling in the District of Columbia," Records of the Columbia Historical Society, Washington, D.C. 29/30 (1928): 126.
Roger Lane, "Criminal Violence in America: The First Hundred Years," Annals of the American Academy of Political and Social Science, Crime and Justice in America: 1776–1976 423 (1976): 6.
Spaulding, "Dueling in the District of Columbia," 125.
Force, Picture of Washington and Its Vicinity, 102.
Spaulding, "Dueling in the District of Columbia," 156.
Ibid., 132–35.
Ibid., 140–41, 157.
Faux, Memorable Days in America, 125.
Spaulding, "Dueling in the District of Columbia," 150.
Ibid., 160–61.
Ibid., 172–76.
Ibid., 172–77.
Jeffrey L. Pasley, "Minnows, Spies, and Aristocrats: The Social Crisis of Congress in the Age of Martin Van Buren," Journal of the Early Republic 27:4 (2007): 629–30.
Hone, Diary of Philip Hone, 179.
Lane, "Criminal Violence in America," 6.
David Grimsted, "Rioting in Its Jacksonian Setting," American Historical Review 77:2 (1972): 367.
Smith, Forty Years, 295–96.
Grimsted, American Mobbing, 3–4.
Gilje, Rioting in America, 63.
Pasley, "Minnows, Spies, and Aristocrats," 627.
Carl E. Prince, "The Great 'Riot Year': Jacksonian Democracy and Patterns of Violence in 1834," Journal of the Early Republic 5:1 (1985): 18–19.
Grimsted, American Mobbing, 4; Prince, "Great 'Riot Year,' " 19.
Grimsted, American Mobbing, 181–82.
Abraham Lincoln, "The Perpetuation of Our Political Institutions," Address before the Young Men's Lyceum, Springfield, IL, January 27, 1838.
Hezekiah Niles, editorial, Niles Weekly Register, September 5, 1835, 1.
John G. Sharp, Preface, The Diary of Michael Shiner Relating to the History of the Washington Navy Yard, 1813–1869, Library of Congress MSS 20.957.
Shiner, Diary of Michael Shiner, 31–33.
Ibid., 35, 52, 52.1.
Ibid., 60, 61–73.
Grimsted, "Rioting in Its Jacksonian Setting," 365, 368.
Shiner, Diary of Michael Shiner, 26–27, 41–44, 66–70.
Donald Yacovone, "The Transformation of the Black Temperance Movement, 1827–1854: An Interpretation," Journal of the Early Republic 8:3 (1988): 288–91.
Ibid., 294; Brown, Strain of Violence, 206–7.
Shiner, Diary of Michael Shiner, 74.
Wilhelmus Bogart Bryan, "Hotels of Washington Prior to 1814," Records of the Columbia Historical Society, Washington, D.C. 7 (1904): 71–72.
Oliver W. Holmes, "The City Tavern: A Century of Georgetown History," Records of the Columbia Historical Society, Washington, D.C. 50 (1980): 8–9.
Grimsted, American Mobbing, 186.
Poore, Reminiscences of Sixty Years, 52.
Delano, Washington Directory, 146; Goode, Capital Losses, 193, 196–97.
Rorabaugh, Alcoholic Republic, 7–8.
Lane, "Criminal Violence in America," 12; Grimsted, American Mobbing, 97.
Greenberg, Cause for Alarm, 68.
Ibid.
Scott A. G. M. Crawford, "Blood Sport," from Guide to United States Popular Culture, ed. Ray B. Browne and Pat Browne (Madison, WI: Popular Press, 2001): 99.
Smyth, Tour in the United States of America, 67.
Poore, Reminiscences of Sixty Years, 191–92.
E. Lee Shepard, " 'This Being Court Day': Courthouses and Community Life in Rural Virginia," Virginia Magazine of History and Biography 103:4 (1995): 465.
William L. Ellis, "Home Rule in Action: Georgetown, 1789 to 1871," Records of the Columbia Historical Society, Washington, D.C. 66/68 (1966/1968): 53.
Hines, Early Recollections, 70–72.
Timony, American Fistiana, 3–4.
Ibid., 22–25.
Ibid., 25–27.
Sharp, "Metropolitan Police Department."
Green, Washington: Village and Capital, 160; Alfers, Law and Order, 13.
Sharp, "Metropolitan Police Department."
Alfers, Law and Order, 13.
Sylvester, District of Columbia Police, 29.
Alfers, Law and Order in the Capital City, 16.
Sylvester, District of Columbia Police, 29.
Michael A. Bellesiles, "The Origins of Gun Culture in the United States, 1760–1865," Journal of American History 83:2 (1996): 441.
Alfers, Law and Order in the Capital City, 18.
James Croggan, "Christmas in 1849; Day Celebrated in Washington with Much Noise, Drinkables in Plenty," Evening Star, December 25, 1909.
James Croggan, "Christmas Long Ago; How Washington Celebrated Before the Civil War; Riotous Day for Youth; Noise Continued from Dawn Until Late at Night," Evening Star, December 25, 1908.
Bryan, History of the National Capital, 2:147.
Cable, Avenue of the Presidents, 71.
Shiner, Diary of Michael Shiner, 57.
Bryan, History of the National Capital, 2:148.
Grimsted, American Mobbing, 267.
Pasley, "Minnows, Spies, and Aristocrats," 628–29, 647.
F. Regis Noel, "Some Notable Suits in Early District Courts," Records of the Columbia Historical Society, Washington, D.C. 24 (1922): 69–70.
Spaulding, "Dueling in the District of Columbia," 186–93.
Pasley, "Minnows, Spies, and Aristocrats," 649.
Spaulding, "Dueling in the District of Columbia," 193–98.
Green, Washington: Village and Capital, 94.
District of Columbia Fire Department, "History of the D.C. Fire Department: The Volunteers," accessed at www.dcfire.com/custom.html?id=173.
Green, Washington: Village and Capital, 160.
Bryan, History of the National Capital, 2:276–77.
Busey, Pictures of the City, 222.
Sharp, "District of Columbia Volunteer Fire Companies."
Bryan, History of the National Capital, 2:278.
National Intelligencer, September 25, 1844.
National Intelligencer, November 11, 1839.
Bryan, History of the National Capital, 2:277.
National Intelligencer, March 20, 1850.
David R. Goldfield, "Antebellum Washington in Context: The Pursuit of Prosperity and Identity," in Gillette, Southern City, National Ambition, 16.
Bryan, History of the National Capital, 2:277.
Washington Topham, "Centre Market and Vicinity," Records of the Columbia Historical Society, Washington, D.C. 26 (1924): 44.
Capitol Fire Museum, Firefighting in Washington, D.C., 14; Goldfield, "Antebellum Washington," 17.
Bryan, History of the National Capital, 2:403–4, 427.
Grimsted, American Mobbing, 238.
Gilje, Rioting in America, 69.
Paul Gilje, "The Baltimore Riots of 1812 and the Breakdown of the Anglo-American Mob Tradition," Journal of Social History 13:4 (1980): 556.
Greenberg, Cause for Alarm, 86.
Fields, Slavery and Freedom on the Middle Ground, 46.
Benjamin Tuska, "Know-Nothingism in Baltimore 1854–1860," Catholic Historical Review 11:2 (1925): 239.
Star, June 3, 1857, quoted in Barry, "The Know Nothing Party," 34.
Sylvester, District of Columbia Police, 16.
Shiner, Diary of Michael Shiner, 156.
Star, June 1, 1857, quoted in Barry, "The Know Nothing Party," 32–33.
Sylvester, District of Columbia Police, 17.
Shiner, Diary of Michael Shiner, 156.
Sylvester, District of Columbia Police, 17.
Bryan, History of the National Capital, 2:430; A.G. Brown, Report of the Senate Committee on the District of Columbia, US Senate, 35th Congress, First Session, reprinted in Congressional Globe, April 5, 1860, 1460.
Brown, Report of the Senate Committee on the District of Columbia, 1460.
Preston S. Brooks, letter to J. H. Brooks, May 23, 1856.
Allan L. Damon, "Filibuster," American Heritage 27:1 (1975): 4.
Sharp, Diary of Michael Shiner.
Chapter 7: Illicit Congress
Leech, Reveille in Washington, 260–61; Elizabeth Barthold O'Brien, "Illicit Congress in the Nation's Capital: The History of Mary Ann Hall's Brothel," Historical Archaeology 39:1 (2005): 47–58.
Donna J. Seifert, "Within Sight of the White House: The Archaeology of Working Women," Historical Archaeology 25:4 (1991): 87, 88.
Ellis, Sights and Secrets of the National Capital, 445–46.
"Biography—Mary Ann Hall, 19th Century Entrepreneur, "Smithsonian Associates, Civil War E-Mail Newsletter 4:1 (2005), accessed at http://civilwarstudies.org/articles/Vol_4/mary-ann-hall.shtm; O'Brien, "Illicit Congress," 48.
Elizabeth J. Himelfarb, "Capitol Sex," Archaeology 52 (July/August 1999): 18.
O'Brien, "Illicit Congress," 55.
Donna J. Seifert and Joseph Balicki, "Mary Ann Hall's House," Historical Archaeology 39:1 (2005): 65.
Ibid., 66–71; Smithsonian Institution, "Madam on the Mall" (Washington, DC, 2005), accessed at www.si.edu/oahp/madam.
O'Brien, "Illicit Congress," 49.
Buel, Mysteries and Miseries, 167, 176, 180.
Townsend, Washington, Outside and Inside, 457.
Leech, Reveille in Washington, 261.
Ibid., 264.
Green, Washington: Village and Capital, 251.
Ibid.
Leech, Reveille in Washington, 264.
Gutheim, Worthy of the Nation, 69.
Neil L. Shumsky, "Tacit Acceptance: Respectable Americans and Segregated Prostitution, 1870–1910," Journal of Social History 19:4 (Summer 1986): 666.
Seifert, "Within Sight of the White House," 82.
Leech, Reveille in Washington, 263–64.
Lowry, Thomas P., Sexual Misbehavior in the Civil War: A Compendium (Bloomington, IN: Xlibris, 2005), 98.
Leech, Reveille in Washington, 260–61.
Ibid., 265.
Ibid., 121.
Ibid.; Policemen's Association News, September 1861, quoted in Alfers, Law and Order, 26.
Leech, Reveille in Washington, 262–63.
O'Brien, "Illicit Congress," 50, 52.
Ibid., 52.
Charles D. Cheek and Amy Friedlander, "Pottery and Pig's Feet: Space, Ethnicity and Neighborhood in Washington, D.C.: 1880–1940," Historical Archaeology 24:1 (1994): 34.
De Gaffenreid, Typical Alley Houses, 10–11.
Green, Washington: Village and Capital, 363.
Borchert, Alley Life in Washington, 19, 23–24.
Green, Washington: Village and Capital, 255.
Garnett P. Williams, "Washington D.C.'s Vanishing Springs and Waterways," in Moore and Jackson, Geology, Hydrology and History, 87–88.
Porter, "Life and Times," 154; "The Washington Canal—Report to Major Generals Gilmore, Warren and Tower," Sen. Ex. Doc. 35, US Senate, 39th Congress, First Session, 1866, quoted in National Republican, April 7, 1866.
Seifert, "Within Sight of the White House," 83; Shumsky, "Tacit Acceptance," 666.
Rosen, Lost Sisterhood, 98–99.
Donna J. Seifert, "Mrs. Starr's Profession," in Scott, Those of Little Note, 161–62; Advertisement, Boston Medical and Surgical Journal, November 27, 1913, 2.
Rosen, Lost Sisterhood, 147–48.
Sanger, History of Prostitution, 640–642.
O'Brien, "Illicit Congress," 54.
Ibid., 55.
Chapter 8: Seeing the Elephant
Leech, Reveille in Washington, 56.
James H. Whyte, "Divided Loyalties in Washington During the Civil War," Records of the Columbia Historical Society, Washington, D.C. 60/62 (1960/1962): 104.
Green, Washington: Village and Capital, 231.
Benjamin Franklin Cooling, "Civil War Defenses During the Civil War," Records of the Columbia Historical Society, Washington, D.C. 71/72 (1971/1972): 316–17; Ed Hendrickson, "Defending Washington: The District of Columbia Militia," Washington History 23 (2011): 38.
Cooling, "Civil War Defenses," 317.
Hendrickson, "Defending Washington," 39; Whyte, "Divided Loyalties," 105.
Miller, Second Only to Grant, 75–76.
Cooling, "Civil War Defenses," 317.
Whyte, "Divided Loyalties," 106.
Cooling, "Civil War Defenses," 318; Leech, Reveille in Washington, 55–65.
Whyte, "Divided Loyalties," 108.
Leech, Reveille in Washington, 143, 145.
Whyte, "Divided Loyalties," 120.
Green, Washington: Village and Capital, 248.
Whyte, "Divided Loyalties," 120.
Green, Washington: Village and Capital, 287.
Leech, Reveille in Washington, 134–35.
Green, Washington: Village and Capital, 250–52.
Goode, Capital Losses, 329–30.
Curtis Carroll Davis, "The 'Old Capitol' and Its Keeper: How William P. Wood Ran a Civil War Prison," Records of the Columbia Historical Society, Washington, D.C. 52 (1989): 207, 211–12.
Lomax, Old Capitol and Its Inmates, 66–67.
Davis, " 'Old Capitol' and Its Keeper," 219–22.
Leech, Reveille in Washington, 266, 408.
Ibid., 143–45.
Whyte, "Divided Loyalties," 119.
Donal E. J. MacNamara, "American Police Administration at Mid-Century," Public Administration Review 10:3 (Summer 1950): 181.
Sylvester, District of Columbia Police, 36–37, 42.
Donald E. Press, "From Murder Bay to the Federal Triangle," Records of the Columbia Historical Society 51 (1984): 57; Green, Washington: Village and Capital, 21, 264.
Report of the Board of Metropolitan Police, House Ex. Doc. 1, 37th Congress, 2nd Session (1861), US Serial Set 1157: 649; Alfers, Law and Order, 27.
Alfers, Law and Order, 27.
Report of the Board of Metropolitan Police, 649.
Sylvester, District of Columbia Police, 36, 49; Report of the Board of Metropolitan Police, 651–52.
"Seven of the Finest, They Have Seen Nearly Thirty Years' Service; Origin of the Police Force," Evening Star, March 8, 1890.
Robert Hill, "Eighty-Four Years of Washington Life by a Man Who Has Seen Them All," Washington Post, August 19, 1917.
Ibid.
Leech, Reveille in Washington, 243.
Report of the Board of Metropolitan Police, 655; Green, Washington: Village and Capital, 251.
Report of the Board of Metropolitan Police, 658.
Alfers, Law and Order, 24.
Report of the Board of Metropolitan Police, 660.
Hill, "Eighty-Four Years of Washington Life."
Sylvester, District of Columbia Police, 247.
"Old Coppers' Stories; Two Original Members of the Force Tell Some Good Tales; Lively Times in the Sixties," Washington Post, October 7, 1895.
Alfers, Law and Order, 25–26.
Sylvester, District of Columbia Police, 245.
Leech, Reveille in Washington, 77.
Bryan, History of the National Capital, 2: 496–97.
Michael A. Cooke, "The Health of the Union Military in the District of Columbia, 1861–1865," Military Affairs 48:4 (1984): 195.
James M. Goode, "Civil War Washington: Rare Images from the Albert H. Small Collection," Washington History 15:1 (2003): 74.
Cooke, "Health of the Union Military," 195; Leech, Reveille in Washington, 71.
Cooke, "Health of the Union Military," 195.
Leech, Reveille in Washington, 209.
Marilyn Mayer Culpepper and Pauline Gordon Adams, "Nursing in the Civil War," American Journal of Nursing 88:7 (1988): 983.
Wheelock, Boys in White, 37.
Green, Washington: Village and Capital, 261.
Leech, Reveille in Washington, 205–6; Culpepper and Adams, "Nursing in the Civil War," 983.
Culpepper and Adams, "Nursing in the Civil War," 983; Wheelock, Boys in White, 201.
Martin G. Murray, "Traveling with the Wounded: Walt Whitman and Washington's Civil War Hospitals," Washington History 8:2 (1996/1997): 66.
Culpepper and Adams, "Nursing in the Civil War," 983.
Wheelock, Boys in White, 208; Ropes, Civil War Nurse, 116.
Cooke, "Health of the Union Military," 196–98.
Bray, Armies of Pestilence, 191.
Newby, Anderson Ruffin Abbott, 52.
Murray, "Traveling with the Wounded," 64; Green, Washington: Village and Capital, 261.
Culpepper and Adams, "Nursing in the Civil War," 982.
Jane E. Schultz, "The Inhospitable Hospital: Gender and Professionalism in Civil War Medicine," Signs 17:2 (1992): 369–70.
Ibid., 370.
Culpepper and Adams, "Nursing in the Civil War," 982, 984.
Leech, Reveille in Washington, 209.
John R. Brumgardt, "Introduction: Mother, Author, Antislavery Reformer," in Ropes, Civil War Nurse, 32.
Culpepper and Adams, "Nursing in the Civil War," 982.
Cooke, "Health of the Union Military," 196; Ropes, Civil War Nurse, 102, 105; G. C. Caldwell, "The Hospitals of Washington," from United States Sanitary Commission Bulletin (New York: 1866): 243.
Donald H. Mugridge, "The United States Sanitary Commission in Washington," Records of the Columbia Historical Society, Washington, D.C. 60/62 (1960/1962): 144; J. Foster Jenkins, "Report of Special Relief Department: Washington, D.C.," from United States Sanitary Commission Bulletin (New York: 1866): 19.
"Notes on Nursing," United States Sanitary Commission Bulletin (New York: 1866): 217–18.
Goode, Capital Losses, 351.
Murray, "Traveling with the Wounded," 65–66, 67.
Stearns, Lady Nurse of Ward E, 7–8, 86, 101.
Ibid., 52–53, 88, 150, 161.
Murray, "Traveling with the Wounded," 67.
Stearns, Lady Nurse of Ward E, 56–57.
Ibid., 60.
Wheelock, Boys in White, 39.
Ropes, Civil War Nurse, 89–90; Brumgardt, "Introduction: Mother, Author, Antislavery Reformer," 41.
Brumgardt, "Introduction: Mother, Author, Antislavery Reformer," 40.
Alcott, Hospital Sketches, 34, 72.
Brumgardt, "Introduction: Mother, Author, Antislavery Reformer," 12.
Ropes, Six Months in Kansas, 111, 116, 117.
Ropes, Civil War Nurse, 50.
Brumgardt, "Introduction: Mother, Author, Antislavery Reformer," 29–33.
Ropes, Civil War Nurse, 69.
Brumgardt, "Introduction: Mother, Author, Antislavery Reformer," 45.
Culpepper and Adams, "Nursing in the Civil War," 984.
Schultz, "Inhospitable Hospital," 384, 385.
Ropes, Civil War Nurse, 84.
Ibid., 84–85, 87.
Schultz, "Inhospitable Hospital," 382–83, 389.
Culpepper and Adams, "Nursing in the Civil War," 982.
Elden E. Billings, "Social and Economic Conditions in Washington During the Civil War," Records of the Columbia Historical Society, Washington, D.C. 63/65 (1963/1965): 196–97.
Barbara Welter, "The True Cult of Womanhood, 1820–1860," American Quarterly 18:2 (1966): 174.
Ropes, Civil War Nurse, 115.
Ibid., 119.
Ibid., 121–22.
Ropes, Civil War Nurse, 114–15.
Joseph P. Reidy, "Coming from the Shadow of the Past: The Transition from Slavery to Freedom at Freedmen's Village, 1863–1900," Virginia Magazine of History and Biography 95:4 (1987): 404.
Eric Wills, "The Contraband of America and the Road to Freedom," Preservation: The Magazine of the National Trust for Historic Preservation (May/June 2011): accessed at www.preservationnation.org/magazine/2011/may-june/the-forgotten.html.
Green, Washington: Village and Capital, 273, 277.
Damani Davis, "Slavery and Emancipation in the Nation's Capital: Using Federal Records to Explore the Lives of African American Ancestors," Prologue Magazine, National Archives 42:1 (2011): accessed at www.archives.gov/publications/ prologue/2010/spring/dcslavery.html.
Mary Mitchell, "I Held George Washington's Horse: Compensated Emancipation in the District of Columbia," Records of the Columbia Historical Society, Washington, D.C. 63/65 (1963/1965): 221, 222, 225–26.
Green, Washington: Village and Capital, 274.
Wills, "Contraband of America."
Reidy, "Coming from the Shadow of the Past," 408–9.
Rebecca K. Sharp, " 'Their Bedding Is Wet, Their Floors Are Damp': 'Pre-Bureau' Records and Civil War African American Genealogy," Prologue Magazine, National Archives 39:2 (2007): accessed at www.archives.gov/publications/prologue/2007/summer/pre-bureau.html.
Reidy, "Coming from the Shadow of the Past," 407.
Holt, Smith-Parker, and Terborg-Penn, Special Mission, 2–3.
Press, "From Murder Bay to the Federal Triangle," 58.
US Congress, Senate, Sen. Morrill introduction of Superintendent Report, Office of Metropolitan Police, 39th Congress, 1st Session, March 20, 1866, Congressional Globe, 1508.
Harper's Weekly, May 7, 1864; Reidy, "Coming from the Shadow of the Past," 409–11.
Reidy, "Coming from the Shadow of the Past," 413–14.
US Congress, Senate, Report of the Bureau of the Refugees, Freedmen, and Abandoned Lands, S. Ex. Doc. 6, 39th Congress, 2nd Session, October 22, 1866, p.36; Robert M. Poole, "How Arlington Cemetery Came to Be," Smithsonian (November 2009): 1, accessed at www.smithsonianmag.com/history-archaeology/The-Battle-of-Arlington.html.
Reidy, "Coming from the Shadow of the Past," 411.
Newby, Anderson Ruffin Abbott, 62–65.
M. Elizabeth Carnegie, "Black Nurses at the Front," American Journal of Nursing 84:10 (1984): 1251.
Newby, Anderson Ruffin Abbott, 60–65, 83–84.
Ibid., 80–81.
Ibid., 81; Bryan, History of the National Capital, 2:531.
Bryan, History of the National Capital, 2:512–13.
Green, Washington: Village and Capital, 280–82.
Leech, Reveille in Washington, 250–52.
US Congress, Senate, Report of the Bureau of the Refugees, Freedmen, and Abandoned Lands, S. Ex. Doc. 6, 39th Congress, 2nd Session, October 22, 1866,34–35.
Leech, Reveille in Washington, 251.
Newby, Anderson Ruffin Abbott, 53; Leech, Reveille in Washington, 253–54.
Green, Secret City, 88.
Sherrod E. East, "Montgomery C. Meigs and the Quartermaster Department," Military Affairs 25:4 (Winter 1961–1962): 194.
Wills, "Contraband of America."
Miller, Second Only to Grant, 264; East, "Montgomery C. Meigs," 195.
Cynthia R. Field, "A Rich Repast of Classicism: Meigs and Classical Sources," pp. 73–75, and Barbara A. Wolanin, "Meigs the Art Patron," pp. 138–143, in Dickinson, Montgomery C. Meigs and the Building of the Nation's Capital.
Dean A. Herrin, "The Eclectic Engineer: Montgomery C. Meigs and His Engineering Projects," in Dickinson, Montgomery C. Meigs and the Building of the Nation's Capital, 13.
Miller, Second Only to Grant, 20; Harry C. Ways, "Montgomery C. Meigs and the Washington Aqueduct," in Dickinson, Montgomery C. Meigs and the Building of the Nation's Capital, 22–23.
Miller, Second Only to Grant, 20.
Bryan, History of the National Capital, 2:306.
Miller, Second Only to Grant, 72–74.
East, "Montgomery C. Meigs and the Quartermaster Department," 187–90.
Cooling, "Civil War Defenses," 324–25.
Goode, "Civil War Washington," 64.
Miller, Second Only to Grant, 18–19, 239.
Poole, "How Arlington Cemetery Came to Be," 2.
Ibid., 3.
Miller, Second Only to Grant, 259–60.
Poole, "How Arlington Cemetery Came to Be," 3.
Chapter 9: Suspicious Characters
"Rival to Boom Towns; Washington Has Had Its Wild and Woolly Days," Washington Post, September 7, 1902.
Sylvester, District of Columbia Police, 53–54.
"Rival to Boom Towns; Washington Has Had Its Wild and Woolly Days," Washington Post, September 7, 1902.
Ibid.
Alfers, Law and Order, 35–37.
William G. Brock, Report of the Major and Superintendent of Police of the District of Columbia: The Year Ending June 30, 1880 (Washington, DC: Government Printing Office, 1881): 3.
"Rival to Boom Towns; Washington Has Had Its Wild and Woolly Days," Washington Post, September 7, 1902.
The Evening Union, July 3, 1863, quoted in John G. Sharp, "The Metropolitan Police Department, District of Columbia: Law, Crime and Policing in the District, 1790–1900," Washington D.C. Genealogy Trails (April 2, 2010), accessed at www.genealogytrails.com/washdc/lawsprisons/historyofpolicedept.html.
Green, Washington: Village and Capital, 252, 363.
Alfers, Law and Order, 27.
Leech, Reveille in Washington, 262.
David K. Sullivan, "Behind Prison Walls: The Operation of the District Penitentiary, 1831–1862," Records of the Columbia Historical Society, Washington, D.C. 71/72 (1971/1972): 262.
Green, Washington: Village and Capital, 253; Sullivan, "Behind Prison Walls," 266.
Sylvester, District of Columbia Police, 62, 67–69.
Brock, Report of the Major and Superintendent of Police, 14.
Byrnes, Professional Criminals of America, 1–2, 8, 12, 22, 30, 40, 44, 47–49.
David R. Johnson, "The Origins and Structure of Intercity Criminal Activity, 1840–1920: An Interpretation," Journal of Social History 15:4 (Summer 1982): 595.
Alfers, Law and Order, 38–39.
Moore, Report of the Major and Superintendent of Police, 8.
Sylvester, District of Columbia Police, 237.
Ibid., 228–31
Collection of Lt. Nicholas Bruel, Historian of the Metropolitan Police, Washington, DC, interview on June 26, 2012.
Donald E. Press, "From Murder Bay to the Federal Triangle," Records of the Columbia Historical Society 51 (1984): 51, 55, 62.
Washington Post, July 8, 1888.
Green, Washington: Village and Capital, 363.
"Rival to Boom Towns; Washington Has Had Its Wild and Woolly Days," Washington Post, September 7, 1902.
Washington Post, February 4, 1900.
Arrest Books, 1869–1906 (August 14–September 16, 1874); Law Enforcement Records, Metropolitan Police; Records of the Government of the District of Columbia, RG 351, National Archives and Records Administration.
Ibid.
Identification Books, 1883–90; Law Enforcement Records, Metropolitan Police; Records of the Government of the District of Columbia, Vols. 1–2, RG 351, National Archives and Records Administration.
Ibid.
Report of the Board of Metropolitan Police, House Ex. Doc. 1, 37th Congress, 2nd Session (1861), US Serial Set 1157: 659; Moore, Report of the Major and Superintendent of Police, 8.
Alfers, Law and Order, 33.
Sylvester, District of Columbia Police, 213.
Ibid., 216; Alfers, Law and Order, 34.
Borchert, Alley Life in Washington, 7, 26.
Alfers, Law and Order, 35.
Cecily Hilleary, "Noah E. Sedgwick: A Black Cop in D.C.'s Gilded Age," pt. 1, from Quondam Washington: A Compendium of Tales from Forgotten City Archives; accessed at http://quondamdc.wordpress.com.
Chapter 10: The Fall of Washington City
James H. Whyte, "The District of Columbia Territorial Government, 1871–1874," Records of the Columbia Historical Society, Washington, D.C. 51/52 (1951/1952): 87–88; Washington Topham, "Centre Market and Vicinity," Records of the Columbia Historical Society, Washington, D.C. 26 (1924): 69–70; William van Zandt Cox, "Matthew Gault Emery, The Last Mayor of Washington, 1870–1871," Records of the Columbia Historical Society, Washington, D.C. 20 (1917): 41–42.
Cox, "Matthew Gault Emery," 41–42.
Ibid., 43.
Whyte, "District of Columbia Territorial Government," 88–89.
Brian D. Crane, "Filth, Garbage, and Rubbish: Refuse Disposal, Sanitary Reform, and Nineteenth-Century Yard Deposits in Washington, D.C.," Historical Archaeology 34:1 (2000): 22.
Michael A. Cook, "Physical Environment and Sanitation in the District of Columbia, 1860–1868," Records of the Columbia Historical Society, Washington, D.C. 52 (1989): 295–98.
Crane, "Filth, Garbage, and Rubbish," 31; Cook, "Physical Environment and Sanitation," 299.
Maury, Alexander "Boss" Shepherd, 2.
Kenneth R. Bowling, "From 'Federal Town' to 'National Capital': Ulysses S. Grant and the Reconstruction of Washington, D.C.," Washington History 14:1 (2002): 15.
Ibid., 9, 15–16.
Carl Abbott, "Dimensions of Regional Change in Washington, D.C.," American Historical Review 95:5 (1990): 1375–76.
Whyte, Uncivil War, 17.
John Nolen Jr., "Some Aspects of Washington's Nineteenth Century Economic Development," Records of the Columbia Historical Society, Washington, D.C. 49 (1973/1974): 528–29.
Whyte, Uncivil War, 181–82.
Dahlgren, Etiquette of Social Life, 18–26.
Whyte, Uncivil War, 182.
Twain and Warner, Gilded Age, 254–55.
William M. Maury, "Alexander Shepherd and the Board of Public Works," Records of the Columbia Historical Society, Washington, D.C. 71/72 (1971/1972): 394.
Ibid., 396, 399.
Ibid., 399.
Whyte, Uncivil War, 92.
Scott, Capital Engineers, 71.
Pamela Scott, "Montgomery C. Meigs and Victorian Art Traditions," p. 62, and Cynthia R. Field, "A Rich Repast of Classicism: Meigs and Classical Sources," p. 75, in Dickinson, Montgomery C. Meigs and the Building of the Nation's Capital.
Montgomery C. Meigs, Letter to Brig. Gen. Nathaniel Michler (July 27, 1867), in Annual Report of Nathaniel Michler, Office of Public Buildings, Grounds, and Works, Capitol of the United States, Appendix T, Report of the Secretary of War (1867): 544–48.
Scott, Capital Engineers, 112–13.
In Memory of Nathaniel Michler, Funeral Program (Washington, DC, 1881): 8–10.
Ellen Robinson Epstein, "The East and West Wings of the White House," Records of the Columbia Historical Society, Washington, D.C. 48 (1971/1972): 598.
William D. Wise, Letter to the Board of Aldermen and the Board of Common Council, January 23, 1864.
Nathaniel Michler, Report in Relation to Public Park and Site of Presidential Mansion (January 29, 1867), in Annual Report of Nathaniel Michler, 535–38.
Epstein, "East and West Wings of the White House," 599.
Gutheim, Worthy of the Nation, 81.
Nathaniel Michler, Report in Relation to Public Park and Site of Presidential Mansion (January 29, 1867), in Annual Report of Nathaniel Michler, 532.
Nathaniel Michler, Annual Report of Nathaniel Michler, 523–25.
National Park Service, Historic American Buildings Survey: Market Square (Washington, DC: Department of the Interior, 1969): 3–4.
Nathaniel Michler, Annual Report of Nathaniel Michler, 525–26.
Gordon Chappell, Historic Resource Study: East and West Potomac Parks, A History (Denver, CO: US Department of Interior, 1973), 11–17.
Warden, Chorographical and Statistical Description, 18.
Cox, "Matthew Gault Emery," 41.
Robert Harrison, "Welfare and Employment Policies of the Freedmen's Bureau in the District of Columbia," Journal of Southern History 72:1 (2006): 75–76.
Nolen, "Some Aspects," 528–29; Frances J. Powell, "A Statistical Profile of the Black Family in Washington, D.C., 1850–1880," Records of the Columbia Historical Society, Washington, D.C., 52 (1989): 278–79.
Powell, "Statistical Profile of the Black Family," 277.
Whyte, Uncivil War, 251–52.
Edward Tang, "Rebirth of a Nation: Frederick Douglass as Postwar Founder in 'Life and Times,' " Journal of American Studies 39:1 (2005): 33–34.
Douglass, Life and Times of Frederick Douglass, 352.
Whyte, Uncivil War, 258–62.
Harrison, "Welfare and Employment Policies," 80–83, 86–87; Plummer, "History of Public Health," 154.
Robert C. Lieberman, "The Freedmen's Bureau and the Politics of Institutional Structure," Social Science History 18:3 (1994): 427.
Whyte, Uncivil War, 54–57.
Whyte, "District of Columbia Territorial Government," 89–90.
Thomas R. Johnson, "Reconstruction Politics in Washington: 'An Experimental Garden for Radical Plants,' " Records of the Columbia Historical Society, Washington, D.C. 50 (1980): 181.
Melvin R. Williams, "A Blueprint for Change: The Black Community in Washington, D.C., 1860–1870," Records of the Columbia Historical Society, Washington, D.C. 71/72 (1971/1972): 380–82.
Ibid., 381.
Whyte, Uncivil War, 62–63.
Johnson, "Reconstruction Politics in Washington," 180.
Douglass, Life and Times of Frederick Douglass, 333.
Whyte, Uncivil War, 67–68.
Ibid., 68–69.
Johnson, "Reconstruction Politics in Washington," 82–83; Williams, "Blueprint for Change," 383; Maury, Alexander "Boss" Shepherd, 3.
Whyte, Uncivil War, 74–75.
Ibid., 71–73; Cox, "Matthew Gault Emery," 26.
Williams, "Blueprint for Change," 384–87.
Ames, Ten Years in Washington, 77–78.
John Richardson, "Alexander Shepherd and the Race Issue in Washington," Washington History 22 (2010): 25.
Washington Star, January 16, 1868, quoted in Richardson, "Alexander Shepherd and the Race Issue in Washington," 25.
Whyte, "District of Columbia Territorial Government," 91.
Maury, "Alexander Shepherd and the Board of Public Works," 397–98.
Maury, Alexander "Boss" Shepherd, 4.
Ibid.
Cox, "Matthew Gault Emery," 43.
Tindall, Standard History of the City of Washington, 247.
Chapter 11: A Gilded Cage
Maury, Alexander "Boss" Shepherd, 6–7.
James H. Whyte, "The District of Columbia Territorial Government, 1871–1874," Records of the Columbia Historical Society, Washington, D.C. 51/52 (1951/1952): 94.
Maury, Alexander "Boss" Shepherd , 6.
Evening Star, August 7, 1871, quoted in Whyte, Uncivil War, 119.
Maury, Alexander "Boss" Shepherd, 9, 10.
Whyte, Uncivil War, 125–26.
Maury, Alexander "Boss" Shepherd, 30.
John Richardson, "Alexander Shepherd and the Race Issue in Washington," Washington History 22 (2010): 17–18.
Ibid., 22–23.
Maury, Alexander "Boss" Shepherd, 29.
Merline Pitre, "Frederick Douglass: The Politician vs. the Social Reformer," Phylon 40:3 (1979): 270–71.
Richardson, "Alexander Shepherd and the Race Issue in Washington," 30–31.
Whyte, Uncivil War, 243–46.
Ibid., 114–15.
Green, Washington: Village and Capital, 247, 249; Maury, Alexander "Boss" Shepherd, 34.
Maury, Alexander "Boss" Shepherd, 30.
Noreen, Public Street Illumination, 14–15.
William M. Maury, Alexander "Boss" Shepherd and the Board of Public Works (Washington, DC: George Washington University, 1975): 30.
Ibid., 30–31.
Ibid., 43.
Brian D. Crane, "Filth, Garbage, and Rubbish: Refuse Disposal, Sanitary Reform, and Nineteenth-Century Yard Deposits in Washington, D.C.," Historical Archaeology 34:1 (2000): 22.
Cluss & Kammerhueber Engineering, "Report on the Present State, and the Improvement of the Washington City Canal," (Washington City: May 12, 1865): 8–10.
Col. Silas Seymour, letter to Richard Wallach (April 26, 1864), in "Report on the Present State, and the Improvement of the Washington City Canal," (Washington City: May 12, 1865): 46.
Maury, Alexander "Boss" Shepherd, 30–31.
Gutheim, Worthy of the Nation, 86.
Scott, Capital Engineers, 81.
Cowdrey, City for the Nation, 26; Gutheim, Worthy of the Nation, 86–87.
Gutheim, Worthy of the Nation, 86–87; Scott, Capital Engineers, 77.
Cowdrey, City for the Nation, 26.
Gutheim, Worthy of the Nation, 86–87.
Scott, Capital Engineers, 75.
Maury, Alexander "Boss" Shepherd, 20.
Ibid., 21, 37.
Whyte, Uncivil War, 147–48; Whyte, "District of Columbia Territorial Government," 41.
Green, Washington: Village and Capital, 352; Maury, Alexander "Boss" Shepherd, 41–42.
Maury, Alexander "Boss" Shepherd, 42.
Green, Washington: Village and Capital, 354.
Maury, Alexander "Boss" Shepherd, 51.
Plummer, "History of Public Health," 143, 161–66.
Whyte, "District of Columbia Territorial Government," 99.
Ames, Ten Years in Washington, 78, 81.
Maury, Alexander "Boss" Shepherd, 46.
Whyte, Uncivil War, 128.
Barton, Historical and Commercial Sketches, 29–30.
Maury, Alexander "Boss" Shepherd, 35–36.
Ibid., 39–40.
Green, Washington: Village and Capital, 350.
Whyte, "District of Columbia Territorial Government," 97.
Ibid., 98–99; Whyte, Uncivil War, 163–64.
Maury, Alexander "Boss" Shepherd, 42.
Whyte, Uncivil War, 143–44.
Melissa McLoud, "Craftsmen and Entrepreneurs: Builders of the Red Brick City, 1880–1900," in Longstreth, Housing Washington, 26.
Whyte, Uncivil War, 146–47.
Green, Washington: Village and Capital, 355.
Bryan, History of the National Capital, 2:619; Green, Washington: Village and Capital, 355.
Gutheim, Worthy of the Nation, 86; Whyte, Uncivil War, 147.
Maury, Alexander "Boss" Shepherd, 51.
Whyte, Uncivil War, 168–69.
Green, Washington: Village and Capital, 358; Whyte, "District of Columbia Territorial Government," 99.
Whyte, Uncivil War, 159.
Green, Washington: Village and Capital, 359.
Whyte, "District of Columbia Territorial Government," 100.
Green, Washington: Village and Capital, 360.
Tindall, Standard History of the City of Washington, 268.
Richardson, "Alexander Shepherd and the Race Issue in Washington," 30.
Whyte, Uncivil War, 257; Richardson, "Alexander Shepherd and the Race Issue in Washington," 30.
Douglass, Life and Times of Frederick Douglass, 357.
Sen. Allan Thurman, Debate on the Morrill Bill, US Senate, 43rd Congress, Second Session, Congressional Record, December 17, 1874: 128.
Sen. Thomas Bayard, Debate on the Morrill Bill, US Senate, 43rd Congress, Second Session, Congressional Record, December 17, 1874: 126.
National Republican, November 17, 1874.
Green, Washington: Village and Capital, 361.
Sen. Oliver Morton, Debate on the Morrill Bill, US Senate, 43rd Congress, Second Session, Congressional Record, December 17, 1874: 120.
William M. Maury, "Alexander Shepherd and the Board of Public Works," Records of the Columbia Historical Society, Washington, D.C. 71/72 (1971/1972): 406.
Tindall, Standard History of the City of Washington, 271.
Moore, Picturesque Washington, 52; Scott, Capital Engineers, 114.
Maury, Alexander "Boss" Shepherd, 50, 51.
Scott, Capital Engineers, 114.
Poore, Reminiscences of Sixty Years, 313–14.
Scott, Capital Engineers, 81.
Tindall, Standard History of the City of Washington, 278.
Ibid., 277; Scott, Capital Engineers, 114–15.
Alan Lessoff, "Review of Montgomery C. Meigs and the Building of the Nation's Capital," by William C. Dickinson et al., in Washington History 15:1 (2003): 89.
Cowdrey, City for the Nation, 27–29.
Scott, Capital Engineers, 116.
Bryan, History of the National Capital, 2:641.
Epilogue: The Sea of Pavement
Goode, Capital Losses, 375.
Donald E. Press, "From Murder Bay to the Federal Triangle," Records of the Columbia Historical Society, Washington, D.C. 51 (1984): 68.
Ibid., 66.
Highsmith and Landphair, Pennsylvania Avenue, 107.
Carl Abbott, "Dimensions of Regional Change in Washington, D.C.," American Historical Review 95:5 (1990): 1378–79.
Green, Secret City, 200.
Abbott, "Dimensions of Regional Change," 1383.
Donald Roe, "The Dual School System in the District of Columbia," Washington History 16:2 (2004/2005): 31.
Green, Secret City, 214.
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Scott, Elizabeth M., ed. Those of Little Note: Gender, Race and Class in Historical Archaeology. Tucson: University of Arizona Press, 1994.
Scott, Pamela. Capital Engineers: The U.S. Army Corps of Engineers in the Development of Washington, D.C., 1790–2004. Alexandria, VA: US Army Corps of Engineers, 2011.
Sharp, John. "The District of Columbia Volunteer Fire Companies: 1800–1870." Washington, DC Genealogy Trails, http://genealogytrails.com/washdc/fire&police/fireco.html.
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Sherwood, Suzanne Berry. Foggy Bottom, 1800–1975: A Study of an Urban Neighborhood. Washington, DC: George Washington University Press, 1978.
Smith, Kathryn Schneider. Washington at Home: An Illustrated History of Neighborhoods in the Nation's Capital. Northridge, CA: Windsor Publications, 1988.
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Stover, John F. History of the Baltimore and Ohio Railroad. West Lafayette, IN: Purdue University Press, 1987.
Sylvester, Richard. District of Columbia Police: A Retrospect of the Police Organizations in the Cities of Washington and Georgetown and the District of Columbia. Washington, DC: Gibson Bros., 1894.
Tindall, William. Origin and Government of the District of Columbia. Washington, DC: Judd & Detweiler, 1902.
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Periodicals
Daily Chronicle, 1862–1874
Daily Patriot, 1870–1872
Evening Star/Washington Star, 1852–1981
Georgetown Courier, 1865–1876
National Era, 1847–1860
National Intelligencer, 1800–1869
National Republican, 1860–1888
New National Era, 1870–1874
Niles Weekly Register (Baltimore, Md.), 1811–1848
Records of the Columbia Historical Society, Washington, D.C., 1897–1989
Sunday Herald, 1866–1887
Washington Critic/Daily Critic, 1868–1896
Washington Globe, 1831–1873
Washington History, 1989–
Washington Post, 1877–
Washington Sentinel, 1873–1910
Index
Abbott, Anderson, 185
abolitionists, 68, 71, 79–85, 88, 90, 94, 129, 177, 182, 185. See also slaves/slavery
Adams, John, 100, 130
Adams, John Quincy, 39, 57, 58, 124
Adams, Mildred, 243
African Americans, 68–94, 184–85, 202. See also slavery; slaves/slavery
and Alexander Shepherd, 222–23
in DC in 1920s, 242–43
deaths, 215, 242
education, 90
and failure of Freedmen's Bank, 234
in military, 186
as physicians, 184–85
as police officers, 203–4
religion, 89–90
sources of income, 184
and voting, xv, 215–17, 224, 234–36
in Washington City during 1870s, 214–17
African Methodist Episcopal church, 89–90
Akin, Amanda, 174–75
alcohol, 126, 129–30, 135, 168
Alcott, Louisa May, 177
Alexandria, VA, 29, 31, 40, 72, 73, 94, 135, 176, 181
alley housing, 154, 242–43
American Anti-Slavery Society, 82
American Colonization Society, 78–79
American Fistiana (Timony), 132
American Notes (Dickens), 19
American Tract Society, 56
Ames, Mary Clemmer, 218, 229
amputations, 171–72
Anderson, Lingan, 167, 168
Andrews, E. A., 75
Anti-Masonic Party, 103
Antiques, 208–10, 218
aqueduct, 40, 187, 225
Arlington, VA, 188
Arlington National Cemetery, 190–91
Armfield, John, 74
Armory Square Hospital, 173–75
Army Corps of Engineers, US, 187, 211–12, 213, 215, 226, 237, 239, 241
Army of the Potomac, 172
arrests, 198–200, 202
Arsenal, US, 45, 194
assassinations, 127, 165
Augusta, Alexander, 184–85
Auxiliary Guard, 83, 133–34, 166, 204. See also police
Babcock, Orville, 213, 226–27, 237, 238
Bagot, Mary, 96, 100
Baker, Lafayette, 165
Ballard, Rice, 74
balls, 97, 101, 209
Baltimore, Lord, 3
Baltimore, MD, 21–22, 139–40, 162
Baltimore and Ohio (B&O) Railroad, 42, 228
bank failures, 233
Banneker, Benjamin, 68
banquets, 97, 99
Barnett, David, 193
Barron, James, 123–24
Bayard, James A., Sr., 19
Bayard, Thomas, 235
Beauregard, P. G. T., 163
Beecher, Henry Ward, 90
Berret, James, 163
Black Code, 83, 91–92, 185
blacks. See African Americans
Bladensburg, MD, 46, 122, 123, 136
Bloodfield, 198
blood sport, 63, 121, 130–32
boardinghouses, 24, 59, 114–16, 144
Board of Health, 169, 229
Board of Public Works, 221, 222, 223–25, 226, 229–33, 237
Boundary Avenue, 28
Bowen, Sayles, 217–18, 219, 223
Bowling, Kenneth, xi
boxing, 132–33
Boyd, Belle, 165
Boys in White, The (Wheelock), 176
Braddock, Edward, 28
Braddock House, 171
Braddock's Rock, 28–29
Brent, Robert, 96
bribery, 209–10
Brick Capitol, 163
bridges, 22–23, 35, 213, 241
Brooks, Preston, 141–42
brothels. See prostitution
B Street, 241
Buchanan, James, 140, 159
Buel, J. W., 147
Bulfinch, Charles, 50
Bull Run, Battle of, 163
Bureau of Refugees, Freedmen and Abandoned Lands, 183
Burnes, David, 9–10, 97
Burnes, Marcia, 97–98. See also Van Ness, Marcia
Burr, Aaron, 19, 122
Busey, Samuel, 60
Butler, Benjamin, 181
Byrnes, Thomas, 195–96
cabinet cards, 200–202
Camp Barker, 182, 184
Camp Convalescent, 176–77
Camp Fry, 169
canals, 18, 30–31, 32–33, 33–35, 37–40, 154, 213. See also Washington City Canal
problems, 35–37, 40–42
workers, 50–51
Capitol, US, 1, 18–19, 20, 29, 45, 69, 85, 111, 114
Capitol Hill, 3, 4, 10, 114, 228, 234
carpetbaggers, 208
Carroll, Charles, 17, 39, 100
Carroll, Daniel, 3–4, 4–5, 6, 8, 11, 33–35, 164
Carroll Prison, 164
Carroll Row, 8, 163
Caruthers, Calvin, 203
Catholics, 3, 51, 54, 173
cemetery, 190–91
Centre Market, 62–63, 213, 243–44
certificates of indebtedness, 231
charitable organizations, 54, 104–9
Chesapeake and Ohio Canal, 37–40, 42, 44
Chipman, Norris, 221
Christian Commission, 173
churches, 54, 89–90
Cilley, Jonathan, 136
circular swindle, 196
circuses, 65
civil disturbances, 126
Civil War, 94, 158–91
casualties, 171–72
and slaves, 158–59, 180–82
Clark, A. M., 178, 179
Clark Allen, 108
class, social. See social class
Clay, Henry, 78, 103, 124–25
Cluss, Adolph, 213
Cobb, Lucy, 148
cock-fighting, 131
Columbian Institute, 90, 108
"common scold," 56–57
Compensated Emancipation Act, 181
Confederate states, 158–59, 162
Congress, US
authorizes funds to rebuild Washington City, 46–47
capital improvements, 215
creates Territory of District of Columbia, 219
and DC government, 238
limits borrowing power of DC, 230–31
passes measure to control slavery, 94
pays Washington City debt, 41
petitioned to end slave transport in Washington City, 78
and prostitution, 147–48
refusal to fund police, 166
refusal to pass law against rioting, 135–36
refusal to upkeep District's infrastructure, 118–19
responds to massive DC debt, 233
and rioting, 141–43
Congressional Cemetery, 157
Congress of the Confederation, x, xii–xiii
Connecticut Avenue, 232
constables, 133–34, 166
Constitution, US, xiv, 162–63
Constitution Avenue, 226, 245
contraband, 181–82, 182–83, 184, 197, 198
Cook, Alfred, 214
Cook, John F., 89, 214
Cooke, Henry, 221, 222, 229, 233, 234
Cooke, Jay, 221, 233
Copperheads, 162, 167
Corcoran, W.W., 217, 219, 221
corruption, 196, 210, 232, 238
Coyle, John, 56
Crandall, Reuben, 81
crime, 21, 144, 165, 168, 192–204, 241. See also Metropolitan Police; police; violence
Crowninshield, Mary Boardman, 96
Cumberland, MD, 30, 39
curfews, 83, 133, 185
Custis, Eliza Parke, 107
Custis, George, 101, 190
Custis-Lee Estate, 184, 190, 215
Dahlgren, Madeleine, 209
Daily Chronicle, 165
Daily Patriot, 217
death rate, 215, 242
Decatur, Stephen, 123–24
defense, wartime, 45
Delano, Judah, 48–49, 115
Democratic Party, 51, 58, 127, 165, 208, 217, 219, 221
Democratic-Republican Party, xvi, 13
depression, national, 233
deserters, army, 168
Dickens, Charles, 19
Dickinson, John, xi, xii, xiii, xiv, xvi
discrimination, 203, 223, 224, 242
diseases, 17, 21, 25, 104, 154, 171, 172, 182, 198, 229, 242
District of Columbia, ix, xiv, 219. See also Washington City
arrests, 202
debt, 233
defense during Civil War, 162
end of franchise in, xv, 234–36, 239–40
and escaped slaves, 181
fortifications, 188
funding of city budget, 237–38
and law enforcement, 166
neighborhoods, 198 (See also specific neighborhoods)
and Organic Act of 1878, 237–39
population, 242
water system, 225–26
Division, The, 149–51, 154, 215, 241–42, 243–44
Dix, Dorothea, 173, 178
domestic workers, 73
Douglass, Frederick, 82, 86, 88, 90–91, 129, 214, 217, 223–24, 233–34, 235
Douglass, Lewis, 224
Downing, George, 214
draft, wartime, 168–69
drainage basin, 25
drinking water, 28
drunkenness. See alcohol
Dudley, Charles, 209
dueling, 121–26, 136
Dupont Circle, 232
Early, Jubal, 188
Early Recollections of Washington City (Hines), 25
Eastern Branch, 14, 17, 28, 33, 36, 42
Eaton, John, 23
education, 22, 90, 214–15
Eisenhower Executive Office Building, 232
election riots, 140–41
elections, 140–41, 217
11th Street, 63, 197
elite, Washington City. See upper class
Ellicott, Andrew, 1, 3, 16, 33, 68
Ellis, John, 145
Ely, Ezra Stiles, 56
Emancipation Proclamation, 181–82
Embassy Row, 232
Emery, Matthew, 218, 219
entertainment, 63–66, 130–32
Etiquette of Social Life in Washington (Dahlgren), 209
Evening Star, 165, 210
execution, public, 14–15
executive branch, 116–17, 165, 208
Executive Mansion, 18, 45
Fall Line, 29–30
Faux, William, 117, 119, 123
feather-duster legislature, 233
federal buildings, 19, 243
Federal Triangle, 243, 244–45
feminism, 90
15th Street, 197, 241
fighting, 63, 121, 132
fires, 20, 21, 136–39
Flats, The, 213
flooding, 25
Floyd, John, 159, 187
Foggy Bottom, 17, 32, 169
food, 61–63, 99–100, 145–47
Forrest, Edwin, 65
Fort Donelson, Battle of, 159
fortifications, 188
Fort Jefferson, 188
Fort Monroe, 181
Fort Pillow, 186
Fort Stevens, 188
Fort Totten, 188
Foster, Augustus John, 14, 99–100
14th Street, 35
Franklin, Benjamin, 102
Franklin, Isaac, 74
free blacks, 49, 68, 72, 83, 86, 87, 94, 181–82. See also African Americans; slaves/slavery
behavior code for, 91–92
and churches, 89–90
kidnapping of, 77–78
and marriage, 88
population in Washington City, 92–93
Freedmen's Aid Society, 217
Freedmen's Bureau, 183, 214, 215
Freedmen's Cemetery, 186
Freedmen's Hospital, 184–85
Freedmen's Savings and Trust Bank, 234
Freedmen's Village, 183–84
Freemasons, 101–3
F Street, 154
Fugitive Slave Act, 181
Funk, Jacob, 17, 52
gag rule, 81
gambling, 65–66, 196
gangrene, 171
gangs, 121, 136–39
garbage, 36, 41, 154
Garrison, William Lloyd, 79, 80, 82
Genius of Universal Emancipation (Lundy), 79–80
Georgetown, 28, 29, 31, 37, 131, 135
housing in, 59–60
and land speculation, 39–40
repeal of charter of, 205, 219
Georgetown Courier, 217
German immigrants, 52
Giacomantonio, William di, xiii
Giddings, Joshua, 93–94
Gilded Age, The (Twain), 209
Gilje, Paul, 126
government, central, xiii–xiv
Grant, Ulysses S., 159, 196, 208, 210, 221, 226, 228, 236, 238
Graves, William, 136
Gray, John, 214
Greeley, Horace, 207
Green, Constance, 19, 60, 116, 242
Greener, Jacob, 79, 88
Greenhow, Rose O'Neal, 163, 165
Greenleaf, James, 5–8, 33, 34, 95
Greenleaf's Point, 15, 17–18, 28, 45
Greenough, Horatio, 111–12
Grow, Galusha, 142–43
Gutheim, Frederick, 31–32
Hall, Mary Ann, 145–47, 152, 154, 155–57
Hamilton, Alexander, xi–xii, xiii–xiv, xvi, 122, 240
Hamilton, Thomas, 51, 52
Hammond, William, 178
Harewood, 212
Harrison, William Henry, 130
Haussmann, Baron, 228
Hell's Bottom, 198
Henry, Joseph, 163
Hines, Christian, 25–29, 43, 65–66, 131
Hone, Philip, 125
honor, 121, 122
Hooker, Joseph, 148–49
"Hooker's Division." See Division, The
hospitals, 53, 171–79
House of Delegates, 221, 222, 233
housing, 11, 58–61, 99, 154, 242
Houston, Sam, 136
Howard, Oliver, 214, 223
Howard, Thomas, Sr., 127
Howard University, 214–15
Huntress, The, 163
Hurd, Charles, 21
Hyer, Tom, 132
immediatism, 79
immigrants, 35, 50–51, 52, 88–89, 202
incendiarism, 136–39
infant mortality, 215, 242
infections, 172
infrastructure, 212
insurance, 70
Interior Department, US, 212
Irish immigrants, 35, 50–51, 202
Island, The, 18, 36, 146, 154, 198, 202, 234
Jackson, Andrew, 51, 58, 102, 125–27, 128, 131, 135
jail, 53, 193–94
James Creek, 28, 33
jams, 101
Janson, Charles, 8, 17, 119
Jefferson, Thomas, xvi, 12–14, 19, 33, 51–52, 63, 100
Jenkins Hill, 3, 4, 32
Jennings, Paul, 93
Jim Crow laws, 202
jobs, 48–50
for freed slaves, 88–89, 182
for women, 154, 172–73, 179–80 (See also prostitution)
Johnson, Andrew, 208, 212, 215
Johnson, Thomas, 5
Kalorama neighborhood, 232
Kauffman, Maria, 152
Keitt, Laurence, 142–43
Key, Francis Scott, 45, 81
Key of All Keys, 28
"Kitchen Cabinet," 210
Know-Nothing Party, 112, 139–41
Latham, Henry, 207
Latrobe, Benjamin, 15, 23, 108
Law, Thomas, 7, 33–35, 36, 37, 95, 104–9, 119–20, 163
law enforcement, 21, 166. See also police
Leaves of Grass (Whitman), 175
Lee, Robert E., 101, 184, 190
Leech, Margaret, 151, 169
legislative branch, 208
Legislative Council, 221, 223–24
L'Enfant, Pierre, ix, x, xvi, 1, 3, 11, 16–19, 23–24, 32–33, 157, 241
Levy Court, 210
Liberator, The, 80
Liberia, 79
lighting, street, 22, 225, 241
Lincoln, Abraham, 127, 158, 159, 165, 181, 186
Lincoln, Robert Todd, 190
liquor. See alcohol
liquor laws, 194
Little Falls, 30, 31
livestock, 170
Logan, John, 207
Lomax, Virginia, 164, 165
Long Bridge, 181
Lost Sisterhood, The (Rosen), 155
lotteries, 31, 34, 196
Louse Alley, 154
Lundy, Benjamin, 79–80
madams, 145–47, 152. See also prostitution
Madison, James, xii, xiv, xvi, 14, 107–8
Magruder, William, 140
malaria, 17, 172, 198, 212
Mall, The, 18, 32, 110, 173, 213, 227, 228, 241
Mangum, Willie, 111
markets, 62–63, 213, 228, 243–44
marriage, 88
Marshall, John, 112
Martin, Jonathan, 87
Martineau, Harriet, 96–97, 110
Masons, 101–3
matrons, 172
May, Frederick, 35
mayors, Washington City, 96, 217–20
McGirk, James, 14–15
McMillan Commission Plan of 1901, 241
mechanics, 45–67, 81
Meigs, Montgomery, 186–90, 211–12, 237
Mellon, Andrew, 243
Methodism, 89–90
Metropolitan Police, 166–69, 192–93, 194–95, 198–200, 203–4
Michler, Nathaniel, 212–13, 226, 237
militia, 134–35
Mills, Robert, 112
Miner, Myrtilla, 90–91
mobs, 80–81, 121, 135, 185–86
"Mobtown," 139
Monroe, James, 14, 50, 79
monuments, 13, 241. See also Washington Monument
Moore, Thomas, 24
Morgan, William, 102
Morrill, Justin, 234
Morris, Robert, xi, 5
Morsell, James, 78
Morton, Oliver, 236
mosquitoes, 17, 213
Mott, Lucretia, 90
Mount Vernon, 110, 111
Mount Zion Negro Church, 89
mug shots, 200–201
municipal bonds, 233
Murder Bay, 182–83, 196–98, 241
murders, 121, 133–34, 192
Mysteries and Miseries of America's Great Cities (Buel), 147
Nast, Thomas, 216
National Archives, 198, 200
national cemetery, 190–91
National Institute, 108
National Intelligencer, 58, 96, 107, 165, 216–17
national park, 213
National Republican, 165, 236
National Rifles, 159
Navy Yard, 14, 17, 34, 45
neighborhoods, 60, 198, 232, 241. See also specific neighborhood
New Jersey Avenue, 7, 11, 33
New National Era, 214, 223–24
newspapers, 80, 165, 214, 216–17, 227–28
Nicholson, John, 5
Niles, Hezekiah, 127
19th Street, 17
Northerners, 94, 208, 209
Northern Liberties Market, 228
Northern Pacific Railroad Company, 233, 234
Northup, Solomon, 75
nurses, 172–79
Octagon house, 74, 96
Odorless Evacuating Apparatus Company, 225
Office of Public Buildings and Grounds, 211–12, 226
Ohio Avenue, 197
Old Capital Prison, 163–65, 179, 193
Organic Act, xiv, 219, 221, 237–39
orphans, 54
Panic of 1837, 42
Panic of 1873, 233
parks, public, 213, 241
parties, 100–101
partisan politics, 13
Parvenus, 209–10, 218, 223, 224, 229
Patent Office, 19, 46, 59
Patriot, The, 221, 222, 228, 230
Pawtomack Canal Company, 30, 38
Payne, Daniel Alexander, 89
Pearl (schooner), 93–94
Pennsylvania Avenue, 10, 20, 23, 63, 66, 197, 205, 241, 245
beggars on, 53
leveling of, 224
paving of, 212–13
and prostitution, 148
Peter, Thomas, 96
Philadelphia, PA, x–xiv, xvi, 15
philanthropy, 104–9, 112, 114
Phillips, Wendell, 90
Pictures of the City of Washington in the Past (Busey), 60
Pinkerton, Allan, 165
plantations, 99
Plug Uglies, 140
police, 133–34, 165, 166–69, 192–93, 194–95. See also Auxiliary Guard; Metropolitan Police
African American officers, 203–4
and corruption, 196
political parties. See specific party
politicians, 114–16, 135–36, 209–10
pollution, 25, 226
poorhouse, 53, 194
Porter, David, 99
Portraiture of Domestic Slavery in the United States (Torrey), 77
Post Office, 19
Potomac Flats, 213, 239
Potomac River, 17, 28, 29–30, 33, 36, 42, 213
poverty, 52–54
prejudice, 185–86, 223
prisons, 76–77, 82, 93, 163–65, 193, 194
Professional Criminals of America (Byrnes), 195–96
prostitution, 17, 24, 144–57. See also Division, The; madams
Protestants, 55
Prout, John, 79
Provost Guard, 151–52, 168–69
Public Buildings Act of 1926, 243
Public Buildings Commission, 243, 244–45
public health, 44, 169
public transportation, 22, 61, 232
public works projects, 33, 37, 226–27, 229–30
Quakers, 90
quarry, 28–29
racecourses, 65–66
racism, 80–81, 184, 185, 223
Radical Republicans, 165, 208, 215–16
Randolph, John, 78, 79, 116, 124–25
Raymond, W. G., 151
real estate
construction rules and regulations, 10–12, 241
speculation, 4, 5–7, 8, 15, 17, 33, 39–40, 232
red-light district, 149–50. See also prostitution
Red Summer riots, 242
religion, 51, 54–57, 89–90
Reps, John, 16
Republican Party, xv, 165, 208, 209, 210, 215–16, 217, 219, 221, 222, 223, 224, 230, 236
reservations, 227
Residence Act of 1790, ix, xiv, 2
Richmond, VA, 208
Riggs, Elisha, 96
"Ring Rule," 222
Rioting in America (Gilje), 126
riots, 93–94, 125, 126–27, 128, 129, 135–36, 138, 140–43, 169, 198, 202, 242
rivers, 42–43
roads. See streets and roads
Rock Creek, 28, 213
Roosevelt, Robert, 233
Ropes, Hannah, 177–79, 180
Rosen, Ruth, 155
Royall, Anne, 47–48, 51, 53–54, 55–58, 61, 66–67, 68, 97, 98, 102, 116, 163
safe houses, 83
Sanger, William, 155
Sanitary Commission, US, 173, 177, 178
sanitation, 169–70, 225, 229
sawdust men, 196
schools, 22, 90, 185
Scott, Winfield, 159
Seaton, William, 96, 108
secessionism, 159, 162
Second Great Awakening, 54, 55
secret police, 165
secret societies, 101–3
sedimentation, 154
segregation, 97, 185, 202, 224, 242
Seifert, Donna, 146
17th Street, 10, 28
7th Street, 25, 62
sewage/sewers, 43, 154, 213, 225–26, 241
Seward, William, 162
sex-trade. See prostitution
shantytowns, 182–83
Shepherd, Alexander, 210–11, 218–19, 221–33, 238
legacy of, 236–37
Shiner, Michael, 127–29, 134, 140, 143
sidewalks, 22
Sisters of Charity, 173
Six Months in Kansas (Ropes), 177
Slash Run, 28, 225
Slatter, Hope, 80, 84–85
slaughterhouses, 170
Slavery in the Cities (Wade), 86
slaves/slavery, 12, 68–94. See also abolitionists; African Americans; contraband; free blacks; Underground Railroad
auctions, 76
and Civil War, 158–59, 180–82
cruelty, 77–78
decline of, 92–94
and Emancipation Proclamation, 181–82
employment in Washington City, 182
escaped, 181
fugitive, 181
hired-out, 85–89, 92
and liquor, 129
runaways, 83, 84
slaveholders' insurance, 70
slave-trading, 74–76, 80
value of, 70–73
slums, 153–54, 197, 198
smallpox, 182
Smallwood, Thomas, 83–84, 88
Smith, Margaret Bayard, 46, 47, 50, 96, 109, 115, 126
Smithsonian Institution, 108, 110, 112
Snow, Beverly, 81, 128
Snow Riot, 128, 135
social class, 48, 51–52, 58, 95–120, 165, 172, 208–10, 218
social life, 96–97
Southard, Samuel, 41, 118
Southerners, 94, 165, 208, 242. See also Confederate states
Southwest neighborhood, 18
speculation, real estate, 4, 5–7, 8, 15, 17, 33, 39–40, 232
spies, 163, 165
squeezes, 101
Stanbery, William, 136
Stanton, Edwin, 162, 178–79, 188, 190, 221–22
State Department, US, 19
states' rights, 78
St. Louis, MO, 207
Stone, Charles, 159
Story, Joseph, 126
streets and roads, 10, 19–20, 22–23, 41, 212–13, 224–25, 241
Stuart, David, 5
suffrage, 215–16, 234–36. See also voters/voting
sugar, 107
Sullivan, James, 132
Sumner, Charles, 141–42, 185, 215
Swampoodle, 198
Tanner, Althea, 86, 89
taverns, 59, 61, 63, 129–30
taxes, 22, 41, 225, 231, 232, 233
Tayloe, John, 74, 96
Taylor, Zachary, 65
temperance movement, 129, 194
Ten Years in Washington (Ames), 218
Territory of the District of Columbia, 219, 229. See also District of Columbia
theaters, 63–65
thieves, 196
Thomas, Charles, 214
Thomas Law House, 120
Thornton, William, 1, 46, 74, 108, 114
Thurman, Allan, 234
Tiber Creek, 25, 28, 32, 34, 62
tides, 35–36, 226
Tidewater region, 30
Tillman, Charles, 203
Timony, Patrick, 132
Toliver, Maria Bear, 172
Torrey, Charles, 84–85
Torrey, Jesse, 77, 78
Townsend, George A., 148
transportation, 22, 61, 232. See also streets and roads
Travels in America 100 Years Ago (Twining), 61
Travels in the United States (Royall), 48
Treasury Building, 19
Trollope, Frances, 18, 64–65
Truth, Sojourner, 184, 185
turnpikes, 21
Twain, Mark, 209, 232
12th Street, 35
Twelve Years a Slave, 75
24th Street, 17
Twining, Thomas, 61, 107, 121
typhoid, 172, 177, 180
Uber, Samuel, 193
Underground Railroad, 82–85, 88. See also African Americans; slaves/slavery
unemployment, 233
Union, 159, 162
Union Hospital, 177–79
Union Station, 241
Unitarian Church, 108–9
upper class, 95–120, 150–51, 165, 208–10, 218
urban planning, 16–17, 213
urban renewal, 243
Van Buren, Martin, 82
Van Ness, Marcia, 10, 97–98, 104
violence, 121–43, 185–86, 192–204. See also crime
election of 1868, 217
racial, 80–81
virago, 57–58
voters/voting, 21, 52
African Americans, 215–17, 224
DC residents, 234–36, 239–40
Wade, Richard, 86
Wallach, Richard, 217, 225–26
Warden, D. B., 46–47, 50, 70
War Department, US, 182, 212, 215
War of 1812, 34, 45
Washington, George, x, xiv, 1, 5–6, 9, 17, 65, 101, 102, 243–44
and canals, 30–31, 33
fires L'Enfant, 11
reasons for locating capital in Potomac region, 29–30, 45
and Residence Act of 1790, 2
Washington Aqueduct, 187
Washington Asylum, 53–54
Washington City, ix. See also District of Columbia
after Civil War, 186, 207
burned by British, 45, 46, 105
capital improvements to, 15–16
and Civil War, 158–91
critics of, 46–47
debt, 41
development of, 15
dissolution of, 205–20
education and schools, 90
entertainment, 63–66, 130–32
firefighting, 138–39
fiscal problems, 22–23
food, 61–63, 99–100, 145–47
government of, xv
housing, 11, 58–61, 99, 154, 242
how and where people lived, 58–61
infrastructure, 212
jobs, 48–50
maps, 26–27, 160, 161
mayors, 96, 217–20
neighborhoods, 18, 60 (See also specific neighborhood)
parties and balls, 100–101
physical appearance, 169–71
police (See police)
population, 24, 87, 92–93
poverty in, 52–54
prostitution, 17, 24, 144–57
reliance on philanthropy, 112, 114
repeal of charter, 205, 219–20
roots of trouble in, 2–24
and slavery (See slaves/slavery)
slums, 153–54
social life, 96–97
streets (See streets and roads)
transportation (See transportation)
upper class (See social class)
violence (See violence)
voters (See voters/voting)
why it became US capital, x
Washington City Canal, 18, 33–35, 40–42, 44, 50–51, 154, 197, 213, 225–26
Washington County Jail, 53, 193–94
Washington Female Orphan Asylum, 104
Washington Infirmary, 53
Washington Monument, 13, 110–12, 113, 139, 170, 227, 239
wastewater, 43
water problems, 25–44
water system, 20, 225–26
waterways, 42–44
Watkins, William, 79
Watterston, George, 63, 100–101
wealth. See social class
Webster, Daniel, 78, 93
Webster, Noah, 5
Wesley Zion Church, 89–90
Wheelock, Julia, 176–77
Whig Party, 97, 127
Whiskey Ring, 237
White House, 20, 28–29, 212
Whitman, Walt, 175
whorehouses. See prostitution
Williams Slave Pen, 76–77
Wilson, Woodrow, 242
Wirt, William, 99, 103
Wolcott, Oliver, 1, 8
women, 145. See also prostitution
"disorderly," 56–57
employment, 154, 179–80
as nurses, 172–79
as prisoners, 165
upper class, 96
Women's Christian Association, 155
Wood, Fernando, 219
Wood, William, 165
Woolsey, Georgeanna, 179
workhouses, 53, 194
working classes, white, 51–52, 58, 172. See also social class
Wormley, James, 214
Wright, Benjamin, 38–39
writ of habeas corpus, 162
Young, James Sterling, 11, 116
Young, Notley, 73
| {
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Q: Limit Windows 8 "Automatic Maintenance" to single CPU core? Windows 8's Automatic Maintenance has the nasty trait of hijacking my machine when I leave it idle. It becomes completely unresponsive after a while. In lieu of a proper solution by Microsoft, I thought maybe it's possible to limit the number of CPU cores used by Automatic Maintenance, so I can still use my machine when it happens. (To access Task Manager and kill the damned Maintenance, for example.)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,532 |
{"url":"https:\/\/labs.tib.eu\/arxiv\/?author=M.%20Volkerts","text":"\u2022 ### Suppression of soft nuclear bremsstrahlung in proton-nucleus collisions(nucl-ex\/0111021)\n\nNov. 30, 2001 nucl-ex\nPhoton energy spectra up to the kinematic limit have been measured in 190 MeV proton reactions with light and heavy nuclei to investigate the influence of the multiple-scattering process on the photon production. Relative to the predictions of models based on a quasi-free production mechanism a strong suppression of bremsstrahlung is observed in the low-energy region of the photon spectrum. We attribute this effect to the interference of photon amplitudes due to multiple scattering of nucleons in the nuclear medium.\n\u2022 ### The Isoscalar Giant Dipole Resonance in 208Pb and the Nuclear incompressibility(nucl-ex\/0109009)\n\nSept. 12, 2001 nucl-ex\nThe isoscalar giant dipole resonance (ISGDR) has been investigated in 208Pb using inelastic scattering of 400 MeV alpha particles at forward angles, including 0deg. Using the superior capabilities of the Grand Raiden spectrometer, it has been possible to obtain spectra devoid of any \"instrumental\" background. The ISGDR strength distribution has been extracted from a multipole-composition of the observed spectra. The implication of these results on the experimental value of nuclear incompressibility are discussed.\n\u2022 ### Hard photon and neutral pion production in cold nuclear matter(nucl-ex\/0109005)\n\nSept. 10, 2001 nucl-ex\nThe production of hard photons and neutral pions in 190 MeV proton induced reactions on C, Ca, Ni, and W targets has been for the first time concurrently studied. Angular distributions and energy spectra up to the kinematical limit are discussed and the production cross-sections are presented. From the target mass dependence of the cross-sections the propagation of pions through nuclear matter is analyzed and the production mechanisms of hard photons and primordial pions are derived. It is found that the production of subthreshold particles proceeds mainly through first chance nucleon-nucleon collisions. For the most energetic particles the mass scaling evidences the effect of multiple collisions.\n\u2022 ### Evidence for Thermal Equilibration in Multifragmentation Reactions probed with Bremsstrahlung Photons(nucl-ex\/0012009)\n\nJune 6, 2001 nucl-ex\nThe production of nuclear bremsstrahlung photons (E$_{\\gamma}>$ 30 MeV) has been studied in inclusive and exclusive measurements in four heavy-ion reactions at 60{\\it A} MeV. The measured photon spectra, angular distributions and multiplicities indicate that a significant part of the hard-photons are emitted in secondary nucleon-nucleon collisions from a thermally equilibrated system. The observation of the thermal component in multi-fragment $^{36}$Ar+$^{197}$Au reactions suggests that the breakup of the thermalized source produced in this system occurs on a rather long time-scale.\n\u2022 ### Thermal bremsstrahlung probing the thermodynamical state of multifragmenting systems(nucl-ex\/0007006)\n\nJuly 6, 2000 nucl-ex\nInclusive and exclusive hard-photon (E$_\\gamma >$ 30 MeV) production in five different heavy-ion reactions ($^{36}$Ar+$^{197}$Au, $^{107}$Ag, $^{58}$Ni, $^{12}$C at 60{\\it A} MeV and $^{129}$Xe+$^{120}$Sn at 50{\\it A} MeV) has been studied coupling the TAPS photon spectrometer with several charged-particle multidetectors covering more than 80% of 4$\\pi$. The measured spectra, slope parameters and source velocities as well as their target-dependence, confirm the existence of thermal bremsstrahlung emission from secondary nucleon-nucleon collisions that accounts for roughly 20% of the total hard-photon yield. 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Hello all, long time no see!
I posted my last walk in 2014. After that, I walked elsewhere.
The walk from my home to Rome in 2015, changed something: I no longer preferred the illusion of wilderness, but had learned to appreciate rural areas, city centers and even the 'in between' zone of industrial estates, shopping centers and apartment blocks.
So when in 2018, my love for the Highlands begged to be rekindled, I looked for a mix of rough and inhabited.
April 17, I arrived on Barra. A walk north to Harris seemed to fit my idea of a balanced walk.
To set the scene: I saw an eagle within half an hour after departure from Castlebay.
I crossed sunny Barra via the Virgin and the Child, the summit of Heabhal, a chambered cairn and a dun. My route touched the Hebridean Way and crossed over to Loch an Duin, where it was windy and un-campsite-looking. In Thiarabhagh, a pleasant looking village and harbor, I walked over to the Hotel, looking for a meal, but didn't like the look of it and walked back, soon accompanied by a family of four. He worked at the airport, she was in childcare business. Friendly people, relaxed. After a life on the mainland, they had settled on Barra, where they were born. They advised me to find a camping spot beyond the airport. Too far out for my taste. When I saw a wooded hillside a mile up the road, I camped on a flat spot between trees higher up.
Two nuns boarding the Twin Otter to Barra, one blaming the other "you do not pay me enough for this!"
Craignish Point and Garbh Reisa.
In the morning, I caught the ferry over to Eriskay. The sea looked choppy, but the crossing was alright, with great views all around. I climbed Ben Scrien, a nice little hill, hardly mentioned in any guidebook, but characterful and well worth the climb. Very windy on the summit. In the village shop I bought a snack and crossed the causeway to South Uist. I followed various paths along the coastline north. At an aisled house at 733203 my route turned inland, aiming for the Coop at Daliburgh, a well sorted shop. Walking along the road to Lochboisdale was quite boring, and quite wet lateron. With some 2 miles to go a driver relieved me of the drudgery and drove me to the pier.
Near a farm called Lasgair I crossed the river northward to connect to a track to the foot of Triuirebhein. At a water work, a group of concrete basins, I tried to pitch the tent. The first spot was too windy, but I cooked dinner at least, the second spot was on the lee side of a basin, but still too windy, and the last attempt was without tent in just a flysheet bivouac. In the meantime, it had started to rain. When rain and wind picked up a notch, I decided to walk back out and wished I had paid more attention to navigation on the way in. I arrived at the Lochboisdale Hotel around 11pm. Hot bath, hot chocolate and a good night sleep would recuperate me nicely..
After the rains, the weather felt clear and fresh. I retraced my path to the water intake and on to the foot of Triuirebheinn. The terrain could not be called solid ground in any way. I took my time climbing the hill. On the connecting ridge northward, the walking was much better, drier underfoot. Since I did not plot a route, and just decided to find my way, I was surprised by very steep heathery steps on the way down, which called for a lot of weaving in and out.
In the Bealach a'Chaolais lies a Souterrain. I could see it had been a nice spot to live in. Warm, less windy than elsewhere.
Stulabhal is a nice hill. From the south, one climbs onto a small plateau with two lochans, with an attractive buttress right above them. You climb a broad gully, and come out on the summit. Great views, at only 384m.
The way down was across curved gneiss banks, like a pod of whales. I had a good lunch on the shores of Loch Snigiscleit. To reach Loch Ainort, I needed to climb Beinn Aleinn almost to the top, and cross no man's land to the shores of the sea loch, which was to be rounded clockwise. A long way on asphalt, I kept myself entertained by looking at the farms and houses and the materials/mess around them. On the north shore of the loch the houses get quainter, until you reach an arboretum, a tree garden. Meanwhile, low tide turned the narrow loch into a labyrinth of skerries with oystercatchers flying on and off to try and pry shellfish from between the kelp.
I pitched the tent in full view of Beinn Mhòr. The summit became visible, and the mountain bathed in sunshine for the rest of the afternoon. I could not be seduced to climb it though.
Stulaval trig point, looking north to Beinn Mhòr, South Uist.
I departed after the early morning drizzle ended. Higher up, I picked up a path, which would lead me to the Bealach Crosgaird, I was sure. Naturally, this confidence was not based on navigational rigour, or so I found out on a bealach more than one kilometer to the south, near Beinn na Tobha.
No visibility, so the climb up to Beinn Mhòr was not too pleasant. A trig point can improve such a mood, because of the locational certainty it gives, but in this case also because this particular one looks very good, made from local stone. After this, I followed the ridge north. When the mist swirled the right way, I could see that the summit of the hill is perched above a steep drop.
I skipped Beinn Choradail, meandered through a labyrinth of rocky outcrops on the way to the foot of Hecla and had a good look down Gleann Uisinis, looking very wild. Originally I had planned to camp there, but this didn't fit my other plans. Coming down the north side of Hecla, the views opened up: blindingly bright in browns and blues after the previous clag, the cliffs of Skye in the distance.
Crossing the floodgate at NF814402, Hecla at the horizon.
Hearty breakfast & good conversations got me underway along the coastline and across the causeway to the shop at Creagorry. I was on Benbecula now, the flattest island. My route took a turn north through Torlum and Griminis. There, a faint track is shown to cross the moss to Baile na Cailleach, but the Cicerone guide I read discourages its use and my eyes gave me the evidence. It might be on the map, but it is a ribbon of water so no, it is not fit for walking, I concluded. I rounded the coast to the bay of Culla, a nice beach with lots of birds. I ate my locally produced hot-smoked salmon and called home.
On top of dykes of big round stones I reached Balivanich. Now I like my villages and towns 'real' even when it involves 'ugly' to ensure authenticity (yes, a snobby tourist's reasoning ), but this town is beyond charming ugliness, and so this tourist just visited the supermarket and decided to take a look at the timetable in a bus stop. It was 3pm, at 3.02 a bus across the causeway to North Uist appeared. Therefore, I landed on North Uist at 3.15. Hurray for opportunism . I followed the road eastward to Cladach Chairinis, hoping for a nice camping spot on farmland. No-one to be seen, so I ended up in a ruined sheiling on the peninsula of Calternis.
Rain passed by in the night. I waited for it to subside and left at 10.30. I could see the foot of the hill, so took my time climbing it, slow enough for the views to have appeared when I arrived on the summit at one.
In my humble opinion Eaval is the best hill of this trip . Its setting, its shape and in particular its views are grand. The view towards the sea is across a patchwork of lochans and rocky banks. Benbecula shows its likeness to a drenched and worn fiber kitchen cloth and on the southern horizon sit Hecla and Beinn Mhor, whose summits never ever were without cloud since my day 3 camp. A puzzle can be played comparing view and map: say if a loch is salt or fresh.
I descended the hill eastward, to find a natural arch in the cliffs at 926606. The walking on the cliff tops is fine. Dry underfoot, with the dark sea and the white foam, the petrels, the short grass. I lunched near the arch to watch the swell hit the rocks.
My route turned northwest towards Burabhal. I met two islanders and their Belgian friend near its summit, who questioned my sanity (or praised my attitude) for being on this hill. They were regulars.
The walk to the head of Loch Euphort is long, since this sealoch cuts Uist almost in two. Rain set in halfway. I visited a stone circle, just to distract, and reprimanded myself for postponing finding a place to camp. One of the tricks of wild camping in inhabited areas is to find the right mood to go and ask for water and permission. Eventually, I rang a doorbell and asked if the derelict harbor building on the pier would be a convenient spot. Inside a roofless building I pitched, only to find out the grass was underlaid by concrete. I repitched outside for a windy night.
This day I remember as one of many miles of walking along the A865. On these islands, a bike is the best transport, followed by a kayak. Walking across the land one will resort to use of the main roads, sooner or later. Fortunately, there's not very many cars on them.
I walked on to the Bayhead shop where a shop assistant got me coffee from the machine. I crossed Balranald, an RSPB-reserve. Not many birds here, but in general I've seen a lot, mostly snipe. A farmer, turning the ground, stopped his tractor for a chat when he saw me taking pictures of his work. He reminded me of my granddad, who was an expert with tractor and plough, me sitting on the fender of the tractor, next to him, long ago.
I walked along a wide beach and visited a headland (Gearraidh Gall) with another natural arch. Here, petrels soar above the cliffs, dropping down to the waves to gain speed, only to return to same apex again and again. The flying petrels watched the raven, who tried to find out whether there's eggs underneath the sitting petrels, operating in a sly manner.
Upon returning to the A865 I fantasized that history would repeat itself and I would bump into a bus stand minutes before the bus arrived. There was no bus, the road is long and undulating, and it started to rain rather continuously. I looked over my shoulder to see cars coming (I could see miles of road) but a) no-one came and b) those who drove by didn't pick me up and c) those who tried (a BMW Z4 roadster) discovered I wanted to go the other way. But d) an American pensioner in a rental car had all the time of the world to bring me to the Berneray Causeway, chatting all the while . I had planned to camp, but the Gatliff Trust hostel was warm, dry, cheap and I would have a room to myself. Ian and Dorothy, Glaswegian cyclists, provided good company. I hope I did, too.
I woke to sunshine and blue skies at 6. Before the ferry to Harris, I wanted to have walked round the island, so I ate and packed quickly and was on my way at 7. Very pleasant walk to the road end, and then up Beinn Sleibhe and anti-clockwise down the west coast. Fabulous beaches, windy seas, dark skies, stunning views across to Harris. The south-west side of Berneray is where dunes fade into machair and meadowland beautifully, and across the stony beach of Loch Buirgh I made the ferry with 15 minutes to spare.
Peat was harvested near Loch Langavat, where I turned straight north into the wild of Harris. The walk in was enjoyable, especially when a sea eagle came to circle me. I video-ed it, but soon felt like an intruder and moved on. After that I got tired, and couldn't find a place to camp in the usual type of terrain: none of the grassy patches in river bends were dry enough, no ridges were still enough, and no plateau was flat enough. I ended up on a heathery promontory, the tent pitched so skewed and crooked, the inside was shaped like a beach chair. The place is called Loch Dubh Màs Holasmul, doesn't it sound like a desert?
The South harris interior is not seen as being of any interest to hillwalkers, not a single line is written about it in my SMC guide. But try the satellite view and you'll see: these hills are rough. They were in the path of glaciers many times, hence the elephant skin look. Try climbing them and you'll notice the lack of any logic in the terrain, and when you stand on a summit and look across to the next hill, you'll notice the hills are covered as thin as possible by soil and vegetation, rock jutting through the tattered skin everywhere. Many false summits too. Heileasbhal Mor, An Coileach (with a curious notch in its skyline between the high point and the trig point) and Ceann Reamhar na Sroine are quite a handful. A feast for lovers of empty, pathless terrain. To finish it off, an exciting gully in the cliffs of Creag nan Eòin lands one on the path through Bealach Eòrabhat, a good track (coffin road?) to Luskentyre. Some heavy showers rolled in so I took a longish break on the doorstep of a white shed/house where the Abhainn Lacasdail joins the sands.
My route turns north-east across Ceann Reamhar and down to Tarbert. Again, not many suitable camping spots, so I walked into Tarbert. The hotels were woefully expensive, but the fish'n'chips were quite good and the backpackers Hostel was kinda perfect, with the company of two Americans of the intrepid kind. One was a guide in Denali National Park, the other planning to write a book about Beaujolais. I dried the gear for the journey home and took the bus to Stornoway in the morning.
Looking south from Heileasbhal Mòr, Roineabhal top right.
The route on the map was reconstructed from my gpx-files, using less waypoints.
Long, straight bits are ferry crossings and in one place a lift in a car or a short bus-ride.
The metres of ascent recorded here are calculated by the WH map, but please be reminded any route on these islands is winding, with a great many ups and downs just because of all those tussocks, hillocks, lochans and stream beds.
In 2019, in a few weeks, I'll be visiting Islay, Jura and possibly Colonsay. Looking forward to it, I love islands!
Ideal day out: A longish walk through a wooded glen, camping high up, climbing a hill in the evening and returning to the tent to cook. | {
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t.throws(fn, TypeError);
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Interest in midterms may be low, but local TV awash in political ad spending
By Katerina Eva Matsa
The upcoming midterm elections might be underwhelming for many Americans, but it could shape up to be one of the most profitable for local TV stations – one of the sources Americans turn to most for news about politics. Local TV has been receiving the largest portion of political media spending for at least a decade, but the share it consumes and the total dollars reaped continue to grow.
Through mid-October, local TV stations have captured 95% of the television political ad spending, which includes spot, national cable, national network broadcast (local cable political ad spending is not part of this analysis). In 2012, during the last presidential elections, local TV stations captured 92% of total political TV ad spending, based on the same analysis.
From January to mid-October 2014, total political ad spending for local TV was about $1.3 billion, according to a Television Bureau of Advertising (TVB) analysis of Kantar CMAG data. Those dollars, though, are far from evenly distributed across the states. More than half of that has gone to 10 states with the most competitive races (Florida, California, Texas, Colorado, Illinois, Michigan, Georgia, Pennsylvania, North Carolina and New York). In Florida, a state with a closely-watched governor's race pitting incumbent Rick Scott against former Republican-now Democrat Charlie Crist, the political ad spending has topped $100 million dollars, the highest among all states.
In the 2012 presidential campaign – the first one conducted after the Supreme Court's landmark 2010 Citizens United ruling – a record $3.1 billion in political ad revenue was spent in local television. That $3.1 billion was 48% higher than the old record set in 2010, and more than double the amount spent in 2008, the previous presidential election year.
A reason local TV is a magnet for political ad dollars is that it is among the sources turned to most for news about politics and government, according to a recent Pew Research survey. Nearly half (49%) of web-using adults say they got news about government and politics from local TV in the past week.
Local TV is also one of the few news sources turned to by Americans from both the left and right ends of the political spectrum. About four-in-ten or more of respondents from each of five ideological groups spanning the political spectrum said they turned to local TV for politics and government news in the previous week.
Correction: An earlier version of this blog post incorrectly said that local TV stations captured 95% of total television ad spending in 2014 and over 80% in 2012. It has been corrected to indicate that the 95% in 2014 is of all television spending other than local cable. The comparable figure for 2012 is 92%.
TelevisionState of the News MediaMedia Economics2016 ElectionNews Media Sectors
Katerina Eva Matsa is an associate director of journalism research at Pew Research Center.
Market is still hot for buying up local TV stations
5 facts about the state of local TV newsrooms
Media & NewsJune 15, 2016
5 key takeaways about the State of the News Media in 2016
Media & NewsMay 11, 2017
Buying spree brings more local TV stations to fewer big companies
Local TV stations post mixed results as some feel loss of political ads | {
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Francesc Domingo Ibáñez (València? 1934? - València, 1 de gener de 1996) va ser un empresari i polític valencià.
Com a president de Valencia 2000, va ser l'organitzador de les primeres manifestacions anticatalanistes a la Ciutat de València durant la Batalla de València, i va formar part de la Junta Permanent d'Unió Valenciana, òrgan que acabaria fundant el partit blaver. Les seues postures properes al Nacionalisme valencià el portarien a crear el Partido Coalición Valenciana, formació de curta vida que s'allunyà de l'anticatalanisme del blaverisme per a practicar un discurs més conciliador i menys crispat que el d'Unió Valenciana. Com a empresari, es dedicà al sector de la jardineria, fundant la fira internacional Iberflora a la Fira de Mostres de València.
Referències
Militants d'Unió Valenciana
Empresaris valencians contemporanis | {
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Russia says it's not to blame for poisoning of former spy
Police in the UK have asked the military for help in its investigation of the poison attack on Sergei Skripal and his daughter.
By JILL LAWLESS and DANICA KIRKAassociated press
Personnel in hazmat suits work at the scene of a nerve agent attack on a former Russian spy and his daughter in Salisbury, England, on Sunday. Andrew Matthews/PA via AP
LONDON — British police asked the military on Friday to help investigate the nerve-agent poisoning of a former spy, as investigators' attention increasingly focused on the victim's house in a quiet suburban street.
Meanwhile, Russia's foreign minister said his country might be willing to help with this investigation, but expressed resentment at suggestions Moscow was behind the attack on Sergei Skripal. The ex-agent was found unconscious on a bench in the English city of Salisbury on Sunday alongside his daughter Yulia.
The pair are in a critical condition in a local hospital. A police officer who helped investigate is in serious condition, and a total of 21 people have received medical treatment.
Counterterrorism detectives have called in military help "to remove a number of vehicles and objects from the scene" of the attack, the Metropolitan Police force said.
About 180 soldiers, marines and air force personnel have been called in because "they have the necessary capability and expertise," police said. They said health advice remains the same — that there is no broader risk to the public.
Detectives are retracing the movements of Sergei and Yulia Skripal as they try to discover how the toxin was administered and where it was manufactured. British authorities have not disclosed what nerve agent was involved.
Police have cordoned off sites including Skripal's house, a car, the cemetery where his wife is buried, a restaurant and a pub.
Former London police chief Ian Blair said Friday that a police officer who is in serious condition visited Skripal's house — perhaps a hint that the nerve agent may have been delivered there.
Blair told BBC radio that Det. Sgt. Nick Bailey "has actually been to the house, whereas there is a doctor who looked after the patients in the open who hasn't been affected at all. There may be some clues floating around in here."
Highly toxic and banned in almost all countries, nerve agents require expertise to manufacture — leading some to suspect whoever poisoned Skripal had the backing of a state.
"A well-equipped lab and a very experienced analytical chemist can do it, but it's not the sort of thing a chancer doing kitchen-sink chemistry can get away with," said chemical weapons expert Richard Guthrie.
Skripal, a former Russian military intelligence officer, was convicted in his home country in 2006 of spying for Britain and released in 2010 as part of a spy swap. He had been living quietly in Salisbury, a cathedral city 90 miles (140 kilometers) southwest of London.
Russian Foreign Minister Sergey Lavrov said Moscow was "ready to consider" lending a hand, "whether it's poisoning of some British subjects, whether it's rumors about interference in the U.S. election campaign."
"But in order to conduct such cases, it is necessary not to immediately run out on TV screens with unfounded allegations," Lavrov was quoted as saying by Russian state news agency Tass in the Ethiopian capital, Addis Ababa.
The U.K. has vowed to take strong action against whoever was responsible for the "brazen and reckless" attack.
British authorities say it's too soon to lay blame, but suspicions have fallen on Russia.
Those branded enemies of the Russian state have sometimes died mysteriously abroad, and the Skripal case echoes the death of Alexander Litvinenko, a former Russian agent who was poisoned in London in 2006 with radioactive polonium-210.
A British public inquiry found that Russia was responsible for Litvinenko's killing, and that Russian President Vladimir Putin probably approved it.
Blair, the former London police chief, called for a review of the deaths of 14 Russians in the U.K. amid suggestions they were targeted by the Russian state.
Blair, who led the London force when Litvinenko was fatally poisoned, told the BBC it is important to find out "whether there is some pattern here."
A BuzzFeed News investigation claimed U.S. spy agencies have linked 14 deaths to Russia, but U.K. police shut down the cases.
Russian media have mocked suggestions of Moscow involvement in the Skripal attack — but also noted that those who betray Russia seem to come to a bad end.
One anchorman on a Russian state television news show began a report on Skripal's poisoning with a warning to anyone considering becoming a double agent.
Channel One anchorman Kirill Kleimenov said in the Wednesday broadcast that he didn't wish death or suffering on anyone but wanted those "who dream of such a career" to know that traitors rarely live long.
"Alcoholism, drug addiction, stress and depression are inevitable professional illnesses of a traitor, resulting in heart attacks and even suicide," Kleimenov said.
Jim Heintz in Moscow contributed to this story. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 457 |
because they are trendy and trendy, they quickly discover likely also comfortable, well-made footwear. Not only are that they tough, but the natural puppy skins and fibers assist in keeping the feet toasty in addition to dry.
fashion will always become their core customers, knowning that means girls and women.
the larger brands sometimes offer boots or booties to get infants and babies.
are available in a group of styles and colors to get female customers. In addition for the classic slip-on version, nowadays there are lace-up boots and heights that go from above the ankles about the knee. The two preferred styles are the Short boots as well as Classic Tall.
: chocolate, pink, sand, paisley, chestnut, terracotta, metal gold, gray, magenta, and also eggplant. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,447 |
I'm trying to create a custom file upload control in WPF 4.0 and I'm stuck in one point.
// Now I want save this file to my image folder.
Now I want to save file in image folder which is inside my Solution explore. For ASP.NET we use Server.Mappath for mapping the specified relative or virtual path to the corresponding physical directory on the server. But I'm not sure what we can use in WPF for achieving the same thing. I'm new in WPF so please help me.
If you are talking about WPF, and not Silverlight, then it is important to understand the distinction between WPF and ASP.NET. ASP.NET is a hosting platform for the HTTP protocol. Paths in an ASP.NET site are not necessarily directly represented on disk, so Server.MapPath provides a way to map an ASP.NET path to a phsyical path.
WPF, on the other hand, is plain and simply a UI framework. It is not a hosting environment like ASP.NET, so the concept of mapping paths is irrelevant in the context of WPF. Based on the code you provided, you are not "uploading" a file, you are simply opening a file. In WPF, your applications logic is running directly on a users system, and therefor you have access to the file system via the System.IO namespace. You can create a new file using the FileStream class and copy bytes from the source to your new file manually, or simply copy the "opened" file using the File class. Your WPF UI is providing a window into a normal "desktop" application, so uploading files need not (and most likely will not) occur when you open or save a file.
Keep in mind, as your application is a desktop application, you will be limited by the permission set of the user running your application. If the user running your application does not have permission to write somewhere on disk, then you will encounter exceptions when trying to write. The same goes if they do not have permission to read or delete files from somewhere. Make sure any file activities you perform are done in areas of the file system that the user has permission, such as their documents folder. | {
"redpajama_set_name": "RedPajamaC4"
} | 311 |
Q: tensorflow restore variables when batch_size in testing is different from the batch_size in training I am new to TensorFlow. I have trained the inception_v3 model successfully with my training data; now I want to predict the output of several images, but the number of them is different from the batch_size in training. I did it as follows:
from tensorflow.contrib.slim.nets import inception_v3 as inception
checkpoint_dir =os.path.join('runs', configure_name, 'checkpoints')
checkpoint_file = tf.train.latest_checkpoint(checkpoint_dir)
graph = tf.Graph()
with graph.as_default():
session_conf = tf.ConfigProto(
allow_soft_placement=True,
log_device_placement=False)
sess = tf.Session(config=session_conf)
with sess.as_default():
# Load the saved meta graph and restore variables
saver = tf.train.import_meta_graph("{}.meta".format(checkpoint_file))
saver.restore(sess, checkpoint_file)
x = tf.placeholder(tf.float32, [batch_size,input_size,input_size,num_channels], name='images')
_, end_points = inception.inception_v3(x,num_classes=num_classes, is_training=False)
outputs = end_points['Predictions']
scores = sess.run(outputs, feed_dict={x: x_eval})
predictions = np.argmax(scores,axis=1)
It gave me the errors as follows:
FailedPreconditionError: Attempting to use uninitialized value InceptionV3/Conv2d_1a_3x3/weights_1
It seems that the model parameters in "outputs" are not fed in successfully, but I do not know how to do it. Any ideas? Thanks.
A: Here you explicitly set the first dim of input placeholder x batch_size, so each time you need to feed a numpy.array type tensor with the same dim or your program will go wrong.
A solution can be setting the first dim of any placeholder(input and label) None so that this dim can be any int or different during training and validation
UPDATE:
if you have already trained your model with a fixed first dim placeholder input(and label), you can change it when restore this graph with tf.train.import_meta_graph(grapg_def=your_graph_def, input_map={'your_train_input_placedholer_name':new_placeholder})
here new_placeholder is a placeholder you newly create with unfixed first dim.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,146 |
The second season of the Fox American television psychological thriller series The Following premiered on January 19, 2014 and concluded on April 28, 2014, with a total of 15 episodes.
Plot
The second season centers on former FBI agent Ryan Hardy (Kevin Bacon) and his niece, NYPD detective Max Hardy (Jessica Stroup) and their attempts to find serial killer Joe Carroll (James Purefoy) following Joe's faked death. After a new group, led by Lily Gray (Connie Nielsen) and her sons Mark and Luke (Sam Underwood), begins to develop and make public statements to lure Joe out of his hiding, Mike Weston (Shawn Ashmore) is re-recruited in order to find the new potential cult and teams with Ryan and Max to track down Joe and Lily.
Meanwhile, Joe is back to his old ways as he, along with his right-hand Emma (Valorie Curry), begin to draw plans to turn a new group of followers to his will. Things take a turn when Joe's ex-wife and the woman Ryan had an affair with, Claire Matthews (Natalie Zea), again enters the picture after Ryan and Joe believed her to be dead.
Cast
Main cast
Kevin Bacon as Ryan Hardy, a former FBI agent (15 episodes)
Shawn Ashmore as Mike Weston, a young FBI agent (15 episodes)
Valorie Curry as Emma Hill, a follower and close friend of Joe Carroll (14 episodes)
Sam Underwood as Luke and Mark Gray, twins that are both followers and sons of Lily Gray (12 episodes)
Jessica Stroup as Max Hardy, niece of Ryan Hardy and a New York City Police Department detective (13 episodes)
Tiffany Boone as Mandy Lang, daughter of Judy, and daughter-figure to Joe Carroll (11 episodes)
Natalie Zea as Claire Matthews, Joe Carroll's ex-wife and long-time love interest of Ryan Hardy (8 episodes)
Connie Nielsen as Lily Gray, once-admirer of Carroll, and mother to Luke and Mark (10 episodes)
James Purefoy as Joe Carroll, a former professor turned serial killer and cult leader (15 episodes)
Recurring
Valerie Cruz as Agent Gina Mendez, head of the investigation on Carroll and the new cult formed a year after his supposed death (8 episodes)
Sprague Grayden as Carrie Cooke, a tabloid reporter and author of The Havenport Tragedy (8 episodes)
Shane McRae as Robert, a leader in the Korban cult (8 episodes)
Mackenzie Marsh as Tilda, Korban member and follower of Carroll (6 episodes)
Felix Solis as Agent Clarke, FBI agent (6 episodes)
Camille De Pazzis as Gisele, a follower of Lily Gray, working closely with Luke and Mark (5 episodes)
Kyle Barisich as Hopkins, FBI information and computer specialist (5 episodes)
Montego Glover as Agent Lawrence, FBI information and computer specialist (5 episodes)
Susan Heyward as Hannah, one of Joe Carroll's followers (5 episodes)
John Lafayette as Marshal Scott Turner, former head of the Marshal's detail participating in the investigation of Carroll's cult; provides protection for Claire Matthews (4 episodes)
Tom Cavanagh as Kingston Tanner, televangelist who denounces Carroll (4 episodes)
Carter Jenkins as Preston Tanner, Kingston Tanner's son (4 episodes)
Carrie Preston as Judy, admirer of Carroll with whom Carroll lives for a year after going into hiding; Judy's daughter regards Joe Carroll as a father figure (3 episodes)
Bambadjan Bamba as Sami, Lily Gray's illegitimate son (3 episodes)
Rita Markova as Radmilla, Lily Gray's illegitimate daughter (3 episodes)
Jacinda Barrett as Julia, Micah's wife and second-in-command of Korban (3 episodes)
Jake Weber as Micah, the leader of the Korban cult (3 episodes)
J.D. Williams as Carlos, a follower of Carroll, working closely with Luke and Mark (3 episodes)
Josh Salatin as Lucas, Korban member and follower of Carroll (3 episodes)
Liza de Weerd as Angela, Korban member and follower of Carroll (3 episodes)
Leslie Bibb as Jana Murphy, Gina Mendez's ex-partner, follower of Joe Carroll (2 episodes)
Gregg Henry as Dr. Arthur Strauss, Joe Carroll's mentor and introducer to killing (2 episodes)
Episodes
Ratings
References
External links
2014 American television seasons
The Following | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 856 |
\section{Introduction}
Understanding the origin of Earth and life on it was one of the most important and daring questions since ancient times. These questions still did not loose their actuality. Predictions about the existence of planets orbiting other stars, currently called extrasolar planets or exoplanets, have been expressed already for several centuries \citep[e.g.][]{fontenelle_entretiens_1686}. Moreover, the RV and transiting methods, the two methods that are currently the most successful ones in terms of planet detection counts and are responsible for about 95\% of all the known exoplanets, were proposed to detect these planets around other stars already 80 years ago \citep{belorizky_soleil_1938, struve_proposal_1952}.
Starting from 1980s, thanks to the developments of high-precision spectrographs and CCD cameras, the search for exoplanets received a new impulse. Given the predictions that planets outside of our Solar System should exist numerously and the intensive search for these extrasolar planets, the detection of a planet around other stars should not have came as a surprise. However, it came: the first exoplanets\footnote{Two planets were first discovered around this neutron star in 1992 \citep{wolszczan_planetary_1992} and one additional planet was detected later in 1994 \citep{wolszczan_confirmation_1994}.} were discovered around a pulsar PSR1257 + 12 \citep{wolszczan_planetary_1992}. The existence of planets around neutron stars made a very difficult question to answer: i) did these planets form around a massive precursor star and survived the supernova explosion, ii) or they formed in a protoplanetary disk which was left over immediately after the neutron star was formed, iii) or
these planets were formed from a disk consisting of an already disrupted binary companion \citep[see][for different formation scenarios]{podsiadlowski_planet_1993}. The first confident detection of an exoplanet around a solar-type stars was made in 1995: Michel Mayor and Didier Queloz discovered a giant planet orbiting its host star with a period of only about 4 days \citep{mayor_jupiter-mass_1995}. The discovery of such a planet, which does not have an analog in our Solar System, rose more questions about formation of planets in and out of our system.
\subsection{Diversity of exoplanet properties and their formation scenarios}
Since the discoveries of first exoplanets via \textit{radial velocity} \citep[51 Pegasi b ][]{mayor_jupiter-mass_1995}, \textit{transiting method} \citep[HD209458 b ][]{charbonneau_detection_2000, henry_transiting_2000}, and by \textit{direct/indirect imaging} \citep[2M1207 b/Fomalhaut b ][]{chauvin_giant_2004, kalas_optical_2008}\footnote{The ``List of exoplanet firsts'' can be found from \url{https://en.wikipedia.org/wiki/List_of_exoplanet_firsts}} almost 4000 planets have been detected\footnote{\url{http://exoplanet.eu/}} and more than 4000 candidates awaiting for validation \citep{thompson_planetary_2018}. Right panel of Fig.~\ref{period_mass} shows the masses (for planets detected by RV method only the minimum mass is available) of the so far discovered planets as a function of discovery time labeled according to detection technique. The data is extracted from Extrasolar Planets Encyclopaedia \citep{schneider_defining_2011}. Thanks to the increasing number of ground based and space based planet search surveys the number of exoplanets has increased significantly during the last years. The plot also shows that the detection of planets with masses as low as the one of Earth became possible.
\begin{figure}[H]
\centering
\includegraphics[width=15cm]{figures/period_mass.pdf}
\caption{The distribution of discovered planets (exoplanet.eu) in the period--mass diagram (left). Mass of the known planets as a function of the discovery year (right). The planets
detected by different detection techniques are shown by different symbols. The planets of our Solar System are shown as a reference.
The two low-mass and short-period planets detected by direct imaging, Kepler-70b and Kepler-70c, are found to orbit a post-red-giant star \citep{charpinet_compact_2011}.}
\label{period_mass}
\end{figure}
Left panel of Fig.~\ref{period_mass} the distribution of exoplanets in the period -- mass diagram is plotted. The planets of our Solar System are also shown for a visual comparison. This figure suffers from selection effects and observational biases of different planet detection techniques. However, it still contains very valuable information about the processes of formation and evolution of the detected planets. In particular one can easily see that most of the exoplanets are clustered in three groups: i) hot-Jupiters with M $_{p}$ $\sim$1-2~M$_{\jupiter}$, ii) gas and ice giants with~M$_{p}$ $\sim$1-2~M$_{\jupiter}$ and P $\sim$1000 days, and iii) hot super-Earths with~M$_{p}$ $\sim$10~M$_{\oplus}$ and P $<$ 100 days. The observed lack of giant planets with periods between 10-100 days, so called ``period-valley'' \citep[][]{udry_statistical_2003, santerne_sophie_2016} is probably related to the disk migration \citep[see][for a discussion]{dawson_origins_2018} and the relative paucity of intermediate mass planets with masses between 10 to 100 M$_{\oplus}$ (so called ``planetary desert'' \citep[e.g.][]{ida_toward_2004})\footnote{The recent surveys of microlensing planets suggest about 10 times more intermediate-mass (20 -- 80 M$_\oplus$ for a median host star mass of 0.6 M$\odot$) planets than the CA models of \citet{ida_toward_2004} and \citet{mordasini_extrasolar_2009} predict \citep{suzuki_microlensing_2018}.} is explained as a consequence of the rapid increase in mass through runaway accretion when the planet core and envelope mass reach to about 30M$_{\oplus}$ \citep[e.g.][]{ida_toward_2004, mordasini_harps_2011}. Note, that the recent CA population synthesis of \citet[][]{mordasini_planetary_2018} suggest not as strong ``planetary desert'' as was previously proposed \citep[e.g.][]{ida_toward_2004}. The reason that the planets of our SS occupy the empty regions of the diagram is partly due to detection biases. At the same time, in our SS there are no short period (shorter than about 100 days) super-Earths\footnote{I note that using the term 'super-Earth' can be misleading or confusing for a reader (especially for a reader outside of the field or for public audience) \citep{moore_how_2017}. That is not our intention. By super-Earth I mean (as almost everywhere in the literature) planets more massive or larger than the Earth. I do not imply that more information about the properties of these planets are known that makes them similar to the Earth.}, which are very common around other stars. This property makes our SS somehow special \citep{martin_solar_2015}\footnote{It was also proposed that Jupiter's periastron is atypical making the SS an outlier \citep[e.g.][]{beer_how_2004}. However, the Jupiter's 'atypical' periastron is probably due to the observational biases \citep{martin_solar_2015}.}. For more details about the distribution of planets on the period -- mass diagram and on the architecture of exoplanetary systems I refer the reader to the recent excellent review by \citet{winn_occurrence_2015}.
\begin{figure}[H]
\centering
\includegraphics[width=14cm]{figures/radius_mass.pdf}
\vspace{-0.3cm}
\caption{The mass-radius relation for the discovered exoplanets (exoplanet.eu) with mass and radius determination better than 30\%.
The planets of our Solar System are shown for comparison.}
\label{radius_mass}
\end{figure}
Fig.~\ref{radius_mass} shows the mass--radius diagram of the extrasolar planets with precise measurements of mass and radius better than 30\%. Similar to Fig.~\ref{period_mass} I see large diversity of the physical characteristics of these exoplanets. In particular it is apparent the large number of Jupiter mass planets with radii much larger than that of Jupiter. Most of these bloated planets have very short orbits receiving incident flux of 2-3 magnitudes higher than the Earth receives \citep{demory_lack_2011, miller_heavy-element_2011}. Several theoretical explanations have been proposed \citep{bodenheimer_radii_2003, guillot_evolution_2002, chabrier_heat_2007} that can efficiently explain the radii of individual planets, but they have difficulties to explain the properties of the entire population of these puffed-up planets. The recent work by \citet{sestovic_investigating_2018} suggests that the inflation extent depends on the mass of the planets. In the figure it is also clear that there is a transition mass at which the mass-radius relation changes its functional form. Statistical studies of the mass--radius relation can provide valuable information about the bulk composition and structure of these planets, and even information about their formation and evolution \citep{seager_massradius_2007, fortney_planetary_2007, hatzes_definition_2015}.
\begin{figure}[H]
\centering
\includegraphics[width=11cm]{figures/mordasini_nayakshin_planet_metallicity.pdf}
\vspace{-0.3cm}
\caption{(Bottom panel): Dependence of the mass of synthetic planets predicted by the CA \citep{mordasini_extrasolar_2012} and TD/GI \citep{nayakshin_tidal_2016} planet formation models against the metallicity of their host stars. The running mean of [Fe/H] as a function of mass of CA planets (in red), TD/GI planets (in blue), and observed planets (in black) is shown in the top panel. The running means were calculated using windows of 50, 500, and 1000 for observed, TD/GI, and CA planets, respectively. These numbers reflect the sizes of each sample.}
\label{nayakshin_mordasini}
\end{figure}
The radius-mass (Fig.~\ref{period_mass}) and period-mass (Fig.~\ref{radius_mass}) diagrams (among other parameter spaces) contain enormous information about the physical processes acting during the formation and evolution of (exo)planets. Thus the reproduction of these diagrams is the ultimate goal of any planet formation theory. The models developed to explain the formation of SS planets did not predict such an enormous diversity of exoplanets that we observe in Figs.~\ref{period_mass} and ~\ref{radius_mass} \citep[e.g.][]{boss_proximity_1995, lin_orbital_1996}. The two most commonly used exoplanet formation scenarios are the core accretion \citep[CA; e.g.][]{safronov_evoliutsiia_1969, pollack_formation_1996, ida_toward_2004, alibert_models_2005, mordasini_extrasolar_2009, hasegawa_origin_2011} and gravitational instability \citep[GI; e.g.][]{kuiper_origin_1951, boss_evolution_1998, boss_stellar_2002, boley_clumps_2010, vorobyov_gravitational_2018}. In the CA scenario the low-mass planets and cores of massive planets form from the coagulation of small grains in the protoplanetary disc. When these cores reach to a critical mass of about 5-10M$_{\oplus}$ \citep{ikoma_formation_2000, hasegawa_planet_2014, mordasini_grain_2014} they undergo runaway accretion of gas. Giant planets then will be formed if the critical core mass is reached before the dissipation of the protoplanetary disk \citep[e.g.][]{tychoniec_vla_2018}, which has a typical lifetime of several Myr \citep{haisch_disk_2001, mamajek_initial_2009}. Since the phase of runaway accretion is very fast the planet formation time is essentially defined by the time of core-formation \citep[e.g.][]{alibert_models_2005}. In the GI scenario, the massive and cold disks fragment into a few Jupiter mass clump which then contracts to form giant planets \citep[e.g.][]{boss_giant_1997}. These massive planets are formed quickly, much before the gas in the disk depletes \citep[see][and references therein]{durisen_gravitational_2007}. If the GI is followed by tidal stripping during the migration of the clumps, then even a rocky planet (including objects in the SS \citep{nayakshin_tidal_2011, nayakshin_differentiation_2014}), can be formed \citep[see][for a recent
review on ``Tidal Downsizing'']{nayakshin_dawes_2017}.
Both the classical CA and GI theories have experienced substantial development and modifications during the last decades \citep[e.g.][]{alessi_formation_2018, johansen_forming_2017, boss_effect_2017, nayakshin_tidal_2015}. They include important processes such as pebble accretion \citep[e.g.][]{johansen_rapid_2007, ida_radial_2016, alibert_formation_2018} and/or migration in the disk \citep[e.g.][]{alibert_migration_2004}. Both theories have their strengths and weaknesses \citep[][]{helled_giant_2014} and might operate efficiently under different physical conditions and different parameter space \citep{matsuo_planetary_2007}. The planetary population synthesis calculations \citep{ida_toward_2004, mordasini_global_2015, forgan_towards_2013, ndugu_planet_2018} based both on recent CA \citep[e.g.][]{mordasini_extrasolar_2009,hasegawa_planetary_2013, ndugu_planet_2018} and TD \citep[e.g.][]{nayakshin_dawes_2017, forgan_towards_2018} are already able to reproduce some of the main structures of Figs.~\ref{period_mass} and \ref{radius_mass}.
In the bottom panel of Fig.~\ref{nayakshin_mordasini} I plot the mass of synthetic planets formed through CA of \citet{mordasini_extrasolar_2012}\footnote{The data is downloaded from \url{http://www.mpia.de/~mordasini/Site7.html}.} and through TD/GI of \citet{nayakshin_tidal_2016}\footnote{The data is kindly provided by Sergei Nayakshin.} against the metallicity of their host stars. The plot shows that the two conceptually different models cover very similar areas in this diagram. On the top panel of the figure I plot running mean of the host metallicity as a function of planetary mass for CA synthetic planets, TD/GI synthetic planet, and confirmed planets with hosts metallicities derived in a homogeneous way in SWEET-Cat (see Sect.~\ref{sweetcat}). This panel clearly shows that when one looks at the populations of planets as a whole, the two models show significant deviation from each other and from the observed planet populations in some metallicity regions. Although in the two considered models the absolute values of the mean [Fe/H] may change with population synthesis parameters, the trends should still remain since they are based on solid physical principles. Thus testing the predictions of the planet formation models with observations is the way to identify the weaknesses in the models and to provide insightful information for their further development.
\section{Motivation and the outline of this review}
As discussed in the previous section, the modern planet formation theories need to consider many different physical phenomena (e.g. migration of planets, evaporation, pebble accretion) in order to reproduce the main properties of the detected exoplanets. Besides these physical processes that directly affect the characteristics of the planets and their
orbital architecture, one should also consider the environmental conditions where these planets are formed \citep[e.g.][]{adibekyan_formation_2017}.
Linking the properties of exoplanets with the properties of protoplanetary disks where they have been formed will provide important insights about planet formation in different environments. Studying the dependencies of exoplanets properties on environmental conditions are usually performed indirectly by looking at the physical properties of the host stars that are linked to the characteristics of the proto-stellar/planetary disk.
Since the planets and their host stars are formed from the same molecular clouds, some global environmental properties such us chemical composition of some important mineralogical abundance ratios \citep[e.g. Mg/Si, Fe/Si][]{bond_compositional_2010, thiabaud_stellar_2014, dorn_can_2015}\footnote{Note that the C/O ratio, that controls the amount of the carbides and silicates in planet building blocks, varies in the protoplanetary disk and might be different from the value of the parent star \citep[][]{madhusudhan_toward_2014, thiabaud_gas_2015}.}, can be determined from the spectroscopic studies of their host stars. Moreover, precise characterization of the planet host stars is crucial for the characterization of the planets themselves \citep{adibekyan_characterization_2018}.
In this manuscript I will review the main observational correlations between the properties of exoplanets and the metallicity of their host stars. I will discuss the most-studied correlation between occurrence rate of different types of planets with metallicity (iron content) of their host stars and its link to different planet formation processes and models. Sine some of the correlations reported in the literature are based on heterogeneous data (for example compilation of properties of hosts stars from different literature sources), whenever possible, I will revisit them using the largest homogeneous catalog of exoplanet host stars called SWEET-Cat \citep[see Sect.~\ref{sweetcat},][]{santos_sweet-cat:_2013}.
\subsection{SWEET-Cat} \label{sweetcat}
There are four exoplanet catalogs that exoplanetologists commonly use \citep{bashi_quantitative_2018}. Despite small biases and discrepancies between these catalogs, on average they provide a good compilation of properties of exoplanets and their host stars \citep{bashi_quantitative_2018}. All these catalogs, however, suffer from heterogeneous literature compilations of stellar parameters. This heterogeneous compilation makes significant discrepancies when comparing with parameters derived in a homogeneous way \citep[e.g.][]{sousa_homogeneous_2015}. Moreover, homogeneous and uniform spectral analysis is essential to minimize the uncertainties in stellar atmospheric properties \citep[e.g.][]{torres_improved_2012}.
\citet{santos_sweet-cat:_2013}, presented a catalog of stellar parameters for stars with planets (SWEET-Cat\footnote{https://www.astro.up.pt/resources/sweet-cat/}) listed in the Extrasolar Planets Encyclopaedia \citep[exoplanet.eu][]{schneider_defining_2011}. This catalog provides a compilation of atmospheric stellar parameters (see Fig.~\ref{fig-sweetcat}) from literature and, whenever possible, derived using the same uniform methodology \citep[see e.g.][]{santos_spectroscopic_2004,sousa_spectroscopic_2008, sousa_ares_2014}. The catalog is regularly updated \citep[][]{andreasen_sweet-cat_2017, sousa_homogeneous_2015} and after the last major update \citep{sousa_sweet-cat_2018} it contains uniformly derived stellar parameters of $\sim$80\% of bright stars ($V<$12 mag) hosting RV detected planets. Besides the main stellar parameters, SWEET-Cat will soon provide abundance of different chemical abundances of the host stars again derived in a homogeneous and uniform way [Sousa et al. in prep.].
\begin{figure}[H]
\centering
\includegraphics[width=15cm]{figures/sweetcat.png}
\vspace{-0.2cm}
\caption{Screenshot showing the structure of the SWEET-Cat.}
\label{fig-sweetcat}
\end{figure}
It is worth to note that different groups also intensively work on homogeneous derivation of stellar parameters of Kepler stars hosting planets and planet candidates e.g. The Kepler Follow-up Observation Program \citep[][]{furlan_kepler_2018} and The California-Kepler Survey \citep[][]{petigura_california-kepler_2017}. Moreover, during the past few years dedicated communities\footnote{SAG-14 (https://exoplanets.nasa.gov/exep/exopag/sag/).} and web interfaces\footnote{ ExoFOP (https://exofop.ipac.caltech.edu/).} have been created to optimize the resources in exoplanet follow-up studies and characterization of their host stars.
\subsection{Nomenclature: the term 'metallicity' in astronomy} \label{nomenclature}
The term 'metallicity' is very widely used in the literature. Although it is always used to quantify the amount of 'metals', its nomenclature and scales are not the same in different fields of astronomy. In this subsection I will very briefly present the definitions of metallicity, its scales, and the quantities that are derived in practice as a proxy of metallicity in different fields of stellar astronomy.
\paragraph{Mass fraction}
In astronomy, all the chemical elements heavier than hydrogen and helium are called metals\footnote{This definition should not be confused with the definition of metals in the period table: \url{https://en.wikipedia.org/wiki/Properties_of_metals,_metalloids_and_nonmetals}.}. The composition of the stars can be characterized by the mass fraction of hydrogen (denoted as $X$), helium (denoted as $Y$), and metals (denoted as $Z$). The sum of these three abundances is normalized to unity i.e. $X$ + $Y$ + $Z$ = 1. This definition is convenient when dealing with the models of stars. However, direct derivations of these quantities from observations is impossible. Note, that in the literature $Z$ is sometimes called ``metal mass fraction'' \citep[e.g.][]{nsamba__2018} and sometimes ``metallicity'' \citep[e.g.][]{bressan_parsec:_2012}.
\paragraph{The solar ($\log \varepsilon(H) \equiv 12$) scale}
Atomic abundances of different metals (elements with atomic number greater than 2) in stars vary over several magnitudes, and thus, it is convenient to express them in a logarithmic scale. In stellar astrophysics, the atomic abundances of elements are usually presented relative to H\footnote{Note that for example the meteoritic abundances are usually pegged to Si abundance which is fixed to $N_{Si} \equiv 10^{6}$.}. Traditionally the logarithmic abundance (number of atoms) of H is set to 12 i.e. $\log \varepsilon(H) \equiv 12$. Atomic abundance of any other element El, then will be
$$ \log \varepsilon(El) = \log \bigg(\frac{N_{El}}{N_{H}}\bigg) + 12$$
where $N_{El}$ and $N_{H}$ are the number of atoms of element X and H ($\log (N_{H})$ = 12). The unit used for the abundances is the ``dex'' which is contraction of ``decimal exponent''.
Sometimes it is more convenient to derive the atomic abundances of stars relative to Sun using the $\log \varepsilon(H) \equiv 12$ scale. In this case square braces are used to express the abundance of an element El
$$ [El/H] = \log \bigg(\frac{N_{El}}{N_{H}}\bigg)_{star} - \log \bigg(\frac{N_{El}}{N_{H}}\bigg)_{sun} $$
Obviously for the Sun [El/H] $\equiv$ 0 for any element. Following this definition, abundance ratio of any two elements El1 and El2 can be expresses as
$$ [El_{1}/El_{2}] = \log \bigg(\frac{N_{El_{1}}}{N_{El_{2}}}\bigg)_{star} - \log \bigg(\frac{N_{El_{1}}}{N_{El_{2}}}\bigg)_{sun}$$
The conversion from solar scaled to absolute abundances requires the knowledge of the reference solar abundances \citep[e.g.][]{lodders_solar_2003, asplund_chemical_2009, lodders_abundances_2009, caffau_solar_2011}.
Metallicity of a star [m/H] is related to the metal mass fraction Z in the following form
$$ [m/H] = \log \bigg(\frac{Z}{X}\bigg)_{star} - \log \bigg(\frac{Z}{X}\bigg)_{sun}$$
Unfortunately, it is very difficult to derive atomic abundances of all the metals for a given star. Thus, in stellar astrophysics, the iron content ([Fe/H]) is commonly used as a tracer of overall stellar metallicity.
Although iron is not the most abundant metal in the Universe, the visible spectra of solar-type stars contain many strong iron lines which are easy the measure\footnote{In nebular astrophysics oxygen abundance is usually
used as the standard scale. This is simply because oxygen emission lines are among the strongest ones in nebular spectra.}. The usage of iron abundance as a proxy of overall meallicity assumes that the abundances of all the metals change proportionally to iron content. Thus under the assumption that the distribution of heavy metals in a given star is the same as in the Sun $\{X_{i}/Z\}$ = $\{X_{i}/Z\}_\odot$ (solar-scaled distribution) one can write
$$ [m/H] = [Fe/H] = \log \bigg(\frac{Z}{X}\bigg)_{star} - \log \bigg(\frac{Z}{X}\bigg)_{sun}$$
Taking into account the solar abundance \citet{bertelli_theoretical_1994} suggests the following approximate relation between [Fe/H] and Z \citep[see also][]{bonfanti_age_2016}
$$ \log(Z) = 0.977[Fe/H]-1.699 \quad \textrm{or} \quad [Fe/H] = 1.024\log(Z) + 1.739$$
The assumption about the universality of solar-scaled heavy element distribution is not always valid, especially for metal-poor stars that are enhanced in $\alpha$ elements \citep[e.g.][]{fuhrmann_nearby_1998, reddy_elemental_2006, adibekyan_chemical_2012, adibekyan_kinematics_2013, recio-blanco_gaia-eso_2014}. To account for the $\alpha$-enrichment the following correction is proposed \citep{yi_toward_2001}
$$ [m/H] = [Fe/H] + \log(0.694f_{\alpha} + 0.306) \quad \textrm{where} \quad f_{\alpha} = 10^{[\alpha/Fe]} $$
For a recent review on the derivation of stellar metallicities and other spectroscopic parameters of exoplanet hosting stars I refer the reader to \citet{adibekyan_characterization_2018}.
\section{Metallicity of planet host stars} \label{pl_occur_metal}
The first observed correlation that linked the presence of planets and a property of their host stars was the giant planet -- stellar metallicity correlation \citep[e.g.][]{gonzalez_stellar_1997,santos_metal-rich_2001}. The discovery of this correlation played a crucial role for the advancement of planet formation theories \citep[e.g.][]{ida_toward_2004, mordasini_extrasolar_2012, nayakshin_dawes_2017}. Until now, studies of the possible correlations between different types of planets (e.g. low-mass or massive planets at short or long period orbits) and metallicities of stars of different spectral types and evolutionary stages intensively continue, and provide new constraints for the models of planet formation and evolution. Planet--metallicity correlation is the subject of the discussion of this section.
It is very important to note, that in this manuscript the iron content is used as a proxy of overall metallicity\footnote{It is important to remember that the stellar chemical abundances and metallicities are usually derived from photospheric absorption lines thus they represent the composition of the photosphere.}. This approximation is very commonly used in the literature and is well justified for solar metallicity stars. However, as already mentioned, at low metallicities the iron abundance does not necessarily equal to the overall metal content in stellar atmospheres. There is another limitation that is typically ignored when studying the metallicity distribution of planet hosting stars. There are some astrophysical processes, such as atomic diffusion due to concentration and thermal gradients \citep[e.g.][]{mowlavi_stellar_2012}, that can affect the stellar metallicity. Moreover, engulfment of planetisimals under specific conditions \citep[e.g. depending on the number of accretion episodes][]{theado_metal-rich_2012} and/or non-accretion of metal-rich material as a consequence of planet formation \citep[again, depending on the time of planet formation and the composition of the formed planets][]{kunitomo_revisiting_2018} may also change the original metallicity of the planet hosting stars. Thus, the present-day stellar metallicity can be slightly different from the metallicity of the stars at the time of their formation \citep[e.g.][]{asplund_chemical_2009}.. Finally, it is important to note, that the key parameter in the core-accretion models of planet formation is the solid surface density \citep[e.g.][]{ida_toward_2004, mordasini_extrasolar_2009}. This parameter is proportional to the dust-to-gas ratio in the disk and is very difficult to constrain by observations. In turn, average dust-to-gas ratio in the protoplanetary disks is proportional to the metal abundance of the ISM \citep[e.g.][]{ruffle_galactic_2007} and is usually assumed to be proportional to the atmospheric metallicity of the host stars \citep[e.g.][]{murray_stellar_2001,mordasini_extrasolar_2009, ercolano_metallicity_2010}. The validity of this assumption was very recently revisited by \citet[][]{liu_migration_2016}. The authors concluded that although the metallicity of the disk can change significantly as the disks evolve, the dust-to-gas ratio (within an order of magnitude) is comparable with the heavy element content in the atmosphere of the host stars. However, for particular cases and in particular locations the dust-to-gas ratio can be significantly different from the host star metallicity \citep[e.g.][]{dawson_metallicity_2015} because of particles being decoupled from gas and radially drifting inwards \citep[e.g.][]{andrews_tw_2012, birnstiel_outer_2014}.
\subsection{Giant planets and metallicity} \label{giant_planet_metal}
Detection of only four giant planets required from \citet{gonzalez_stellar_1997} to notice that these planets tend to appear around metal-rich stars. This hint was very soon confirmed using relatively larger samples \citep[e.g.][]{laughlin_mining_2000, santos_metal-rich_2001, gonzalez_parent_2001} and become a well established correlation \citep[e.g.][]{santos_spectroscopic_2004, fischer_planet-metallicity_2005, johnson_giant_2010, sousa_spectroscopic_2011, mortier_functional_2013} known as giant planet -- metallicity correlation.
At the end of 1990s and beginning of 2000s, when only handful of hot-Jupiters have been detected, two hypotheses have been proposed to explain the metal excess of massive exoplanet host stars: self enrichment (aka pollution) mechanism and primordial origin \citep[e.g.][]{gonzalez_stellar_1997}. In the self enrichment scenario the high metallicity of planet hosts was explained by the pollution of outer convective envelope of the hosts due to accretion of gas-depleted material. This pollution could be a result of inward migration of massive planets that sweep metal-rich material with them. In the alternative, primordial scenario, the over-abundance of metals in massive planet hosts was considered to represent the high metallicity of the primordial cloud where the stars have been formed and was assumed that giant planets form more readily in high metallicity environments.
The two aforementioned scenarios provide different observationally testable signatures for the host stars. In particular, in case of pollution by rocky material, the increase of atmospheric metallicity of the host stars should depend on the mass of convective zone, thus on the mass and temperature of the stars \citep[][]{gonzalez_stellar_1997, laughlin_possible_1997, pinsonneault_mass_2001, murray_stellar_2001}. Going one step further, \citet{gonzalez_stellar_1997} proposed that if the accreting material is fractionated then a trend between chemical abundances and condensation temperature of the elements is expected. \citet{gonzalez_stellar_1997} also noted that the high-metallicity accretion signature should be lost for evolved stars which have larger convective zones where the accreted heavy metals will be mixed and diluted. When the number of detected planets increased, several systematic abundance studies on stars with and without planets have been performed focused on the aforementioned predictions. The results of these studies favored the primordial cloud as the most likely origin for the metal-rich nature of giant planet host stars \citep[e.g.][]{santos_spectroscopic_2004, fischer_planet-metallicity_2005, valenti_stellar_2008, johnson_giant_2010}. This hypothesis is supported by models of planet formation and evolution based on CA \citep[e.g.][]{ida_toward_2004, mordasini_extrasolar_2012} and tidal downsizing \citep{nayakshin_tidal_2015}.
In Fig.~\ref{fig-giant_planet_metal} I plot the metallicity distribution of stars hosting high mass planets (hereafter, HMPH) and stars known to host no detected planet (hereafter, SnoP). Only FGK dwarf hosts ($\log g$ \ $>$ 4.0 dex, and 0.6~M$_{\odot} <$ M $<$ 1.5~M$_{\odot}$) stars with with stellar parameters derived in a homogeneous way in SWEET-Cat are considered. The comparison sample of stars without detected planets consists of 954 FGK dwarf stars observed within the HARPS GTO program and are taken from \citet{adibekyan_chemical_2012}. In this figure only planets with masses between 50~M$_{\oplus}$ and 13~M$_{\jupiter}$\footnote{13M$_{\jupiter}$ approximately corresponds to the deuterium-burning mass limit for BDs at solar metallicity \citep[e.g.][]{spiegel_deuterium-burning_2011} and is usually used as a border line between giant planets and BDs. The exact deuterium-burning mass limit depends on several parameters \citep[see e.g.][for more details]{chabrier_giant_2014, caballero_review_2018}.} are considered. In case of multiplanetary systems the mass of the most massive planet is considered. I note that there is no clear definition for what should be the low mass limit of giant planets, thus the choice for lower limit of mass M = 50~M$_{\oplus}$ is somewhat semi-arbitrary. Different authors chose different definitions\footnote{I refer the readers to \citet{chabrier_giant_2014} and \citet{schneider_defining_2011} for an interesting discussion about the classifications of planets and BDs based on physical observable properties and formation mechanisms.} for giant planets and the choice of the low-mass limit varies (typically between 30 to 90~M$_{\oplus}$) depending on the aim of the study \citep[e.g.][]{cumming_keck_2008,russell_geophysical_2013, hatzes_definition_2015, brucalassi_search_2016, pinotti_zero_2017, bashi_two_2017, sousa_sweet-cat_2018}. In any case I choose this limit since it is close to the mass 'gap' observed in Fig.~\ref{period_mass} and \ref{radius_mass}. At the same time the planet core-accretion based population synthesis models by \citet{mordasini_extrasolar_2009} predicted such a minimum in the mass-distribution at about this mass. It is important to note that presented results are not sensitive to the choice of these limits. Here I should also comment that the classifications of different types of planets based on their radii is not straightforward as well, and varies from work to work \citep[e.g.][]{buchhave_three_2014, fulton_california-kepler_2017, narang_properties_2018, petigura_california-kepler_2018, berger_revised_2018}.
\begin{figure}[H]
\centering
\includegraphics[width=13cm]{figures/giant_planet_metal.pdf}
\vspace{-0.2cm}
\caption{Metallicity distribution of stars hosting giant planets detected via RV method (skyblue) and Transit method (blue), and stars without any detected planets (red). The KDE fit of the cumulative distribution of [Fe/H] for the three sample of stars is also shown with the curves of corresponding colors.}
\label{fig-giant_planet_metal}
\end{figure}
Although some theoretical works based on CA models propose that the critical metallicity for giant planet formation is in the range of $-$1.8 to $-$1.5 dex\footnote{Note that GI based model of \citet{johnson_constraints_2013} suggests a critical metallicity of about $-$4 dex for planet formation to happen.} \citep[][]{hasegawa_planet_2014, johnson_first_2012}, the lowest metallicity of the giant planet host in Fig.~\ref{fig-giant_planet_metal} is -0.65 dex. In fact, the lowest metallicity of a confirmed sub-stellar companion host currently listed in exoplanet.eu is $-$1.00$\pm$0.07 dex derived for BD+202457\footnote{BD+202457 is known to host two companions with masses of 12.47~M$_{\jupiter}$ and 21.42M$_{\jupiter}$ \citep{niedzielski_substellar-mass_2009}.} \citep{niedzielski_substellar-mass_2009}. However, the more recent spectroscopic analysis of this star suggests a higher metallicity of [Fe/H] = $-$0.79 \citep{maldonado_metallicity_2013}. Besides BD+202457, the lowest (spectroscopically derived) metallicity star hosting a giant planet in exoplanet.eu is the 24 Bo\"{o}tis with a metallicity of $-$0.77$\pm$0.03 dex \citep[][]{takarada_planets_2018}. Observationally determining the metallicity limit below which giant planets do not form can provide a very important insights for the planet formation theories. Indeed, some programs are focused on the metal-poor regime trying to tackle this issue \citep[e.g.][]{sozzetti_keck_2009, santos_harps_2011, mortier_frequency_2012}.
From Fig.~\ref{fig-giant_planet_metal} it is clear that the SnoP and HMPH samples have different metallicity distributions, the latter ones being more metallic. In particular the mean metallicity of SnoP is $-$0.159$\pm$0.009 dex, while the average metallicity of the stars hosting high mass transiting and RV planets are 0.117$\pm$0.013 dex and 0.112$\pm$0.013 dex, respectively. Here the errors represent the standard error of the mean i.e. standard deviation divided by the square root of the sample size. To evaluate the significance of this difference more quantitatively I applied a two--sample KS test to the samples. The results presented in Table~\ref{table_KS_metal_HMPH} show that stars hosting giant planets have significantly different metallicity distribution when compared to the stars without planets. Interestingly, the two samples of HMPH of transiting and RV planets have metallicity distributions that come from the same parent distribution. This is somehow surprising since the distributions of the orbital periods of the transiting and RV planets are statistically different. The transiting planets orbit their stars on average in 11 days (std = 66 days), while the RV detected planets have an average orbital period of 1202 days (std = 1775 days), and the KS tests suggests a p-value of 3.5$\times10^{-61}$ for the two orbital period distributions being similar.
As already mentioned the giant planet -- metallicity relation provides a general but very important information for planet formation models. The knowledge of the exact functional form of this relation can provide additional important constraints for the existing planet formation theories. However, a large, unbiased, and volume-limited sample of stars surveyed for planets is required to study the details of this relation. Usually, the dependence of planet fraction ($f$) on stellar metallicity is described by the following functional form: $f$ = $\alpha 10^{\beta [Fe/H]}$, where $\alpha$ and $\beta$ are the coefficients to be derived. To include the dependence of planet occurrence rate on stellar metallicity usually the $f([Fe/H])$ is fitted with the functional form of $f$ = $\alpha 10^{\beta [Fe/H]}$.
On the left panel of Fig.~\ref{fig-giant_planet_metal_harps2} I plot the metallicity distribution of SnoP and HMPH (again only planets 50~M$_{\oplus}$ $<$ M $<$ 13~M$_{\jupiter}$ are considered) taken from the HARPS volume-limited (up to about 60 pc from the Sun) survey \citep{lo_curto_harps_2010}. This sample consist of 582 FGK stars, for which the stellar parameters, including the stellar metallicities, were homogeneously derived in \citet{sousa_spectroscopic_2011}. The figure shows that the mean metallicity of the HMPH sample (0.046$\pm$0.035) is again higher than the mean metallicity of the SnoP ($-$0.112$\pm$0.010). The performed KS test also suggest a significantly different metallicity distributions for the two samples (see Table~\ref{table_KS_metal_HMPH}).
\begin{table}[H]
\caption{The results of the KS tests comparing the metallicity distributions of stars with and without planets. The p-values smaller than 0.05 are highlighted in boldface.}
\centering
\begin{tabular}{p{6cm}p{2cm}p{2cm}}
\toprule
{Samples} & {KS statistic} & {KS p-value}\\
& & \\
\textbf{Figure~\ref{fig-giant_planet_metal}} & & \\
\midrule
HMPH Transit vs HMPH RV & 0.089 & 0.392 \\
HMPH RV vs SnoP & 0.47 & \textbf{1.12e-40} \\
HMPH Transit vs SnoP & 0.49 & \textbf{1.60e-30}\\
\end{tabular}
\bigskip
\begin{tabular}{p{6cm}p{2cm}p{2cm}}
\textbf{Figure~\ref{fig-giant_planet_metal_harps2}} & & \\
\midrule
HMPH vs SnoP & 0.339 & \textbf{0.003} \\
\end{tabular}
\bigskip
\begin{tabular}{p{6cm}p{2cm}p{2cm}}
\textbf{Figure~\ref{fig-very_giant_planets_homo}} & & \\
\midrule
GPH vs SGMP & 0.152 & \textbf{0.026} \\
GPH dwarfs vs SGMP dwarfs & 0.067 & 0.935 \\
GPH giants vs SGMP giants & 0.288 & 0.061 \\
GMP dwarfs vs SnoP dwarfs & 0.450 & \textbf{1.92e-50}\\
GMP giants vs SnoP giants & 0.281 & \textbf{0.007}\\
SGMP dwarfs vs SnoP dwarfs & 0.480 & \textbf{2.45e-14}\\
SGMP giants vs SnoP giants & 0.187 & 0.105\\
\end{tabular}
\bigskip
\begin{tabular}{p{6cm}p{2cm}p{2cm}}
\textbf{Figure~\ref{fig-low_mass_planet_metal}} & & \\
\midrule
LMPH vs SnoP & 0.120 & 0.484 \\
Only LMPH vs SnoP & 0.252 & \textbf{2.06e-4}\\
\bottomrule
\end{tabular}
\label{table_KS_metal_HMPH}
\end{table}
The right panel of Fig.~\ref{fig-giant_planet_metal_harps2} shows the dependence of giant planet frequency (number of stars with planets relative to number of all surveyed stars) on stellar metallicity. The plot clearly shows that the frequency sharply increase with metallicty. If for sub-solar metallcities about 5\% of the stars have giant planets, at super-solar metallicities the relative frequency reaches to about 20\%. It is important to note that this giant-planet -- metallicity relation is practically unaffected by the possible dependence of RV precision on [Fe/H]. In principle, metallicity affects the strength of spectral lines, and thus RV precision. However, for the stars with [Fe/H] $\gtrsim$ $-0.8$ dex, the RV precision is practically independent of metallicity\footnote{To my knowledge there is no study on the dependence of photometric precision on stellar metallicity for transiting planet surveys. However, the detectability of transiting planets slightly depends on metallicity through the relationships between transit depth, stellar radius, and stellar metallicity: transiting planets are slightly easier to detect around metal-poor dwarf stars than around metal-rich ones \citep[][]{gaidos_objects_2013}.} \citep[][]{valenti_stellar_2008}.
\begin{figure}[H]
\centering
\includegraphics[width=14cm]{figures/giant_planet_occurence_harps2.pdf}
\vspace{-0.2cm}
\caption{(Left panel): Metallicity distribution of stars hosting giant planets (blue) and stars without any detected planets (red) from the HARPS planet search program. The KDE fit of the cumulative distribution of [Fe/H] for the two samples is also shown with the curves of corresponding colors. (Right panel): The dependence of giant planet frequency on stellar metallicity. The binomial errors of the planet fractions in each bin are estimated following \citet{cameron_estimation_2011}.}
\label{fig-giant_planet_metal_harps2}
\end{figure}
In Fig.~\ref{fig-giant_planet_metal_harps2} (right panel) I also show the functional form of the planet occurrence -- metallicity relation derived in several works using different samples \citep{fischer_planet-metallicity_2005, udry_statistical_2007, johnson_giant_2010}. One can see that there is, at least, qualitative agreement between the fitted curves obtained by different authors for stars with metallicities above the solar value. These curves also describe well the increase of planet frequency for solar and super-solar metallicity stars observed for the HARPS sample in the figure. The main difficulty and disagreement between the different works come for sub-solar metallicities. \citet{udry_statistical_2007}, based on the CORALIE sample from \citep{santos_spectroscopic_2004} and the sample from \citet{fischer_planet-metallicity_2005}, proposed that at sub-solar metallicities the giant planet frequency might be constant rather than exponential, which is clearly the case for solar and super-solar metallicities. This result has been contested by \citet{johnson_giant_2010} who used a larger sample of 1266 stars with and without planets from the California Planet Survey. Based on a Bayesian analysis the authors found that giant planet occurrence rate is a strong exponential function of metallicity that continues to sub-solar metallicities. More recently, \citet{mortier_functional_2013} performed a statistical Bayesian analysis on large volume-limited samples of CORALIE, HARPS\footnote{This HARPS sample is the same as the one shown in Fig.~\ref{fig-giant_planet_metal_harps2}. The only difference is that a few planets have been discovered around these stars after the study of \citet{mortier_functional_2013}.}, and CORALIE+HARPS (the combined sample) to test between different functional forms of the planet--metallicity correlation. While confirming the general correlation between giant planet incident and metallicity, they concluded that the samples are simply too small to be able to distinguish between a constant or an exponential form in the low-metallicity region. The authors pointed out that a sample of about 5000 stars (about a factor of 3 larger than the sample they used) is required to distinguish between different models (functional forms). Hopefully, this question will get its answer soon with the arrival of the ongoing and upcoming missions such as Gaia\footnote{The name "Gaia" was initially derived as an acronym for Global Astrometric Interferometer for Astrophysics.} \citep{sozzetti_detection_2001}, TESS \citep{ricker_transiting_2015}, and PLATO \citep{rauer_plato_2014}.
Using well defined samples one can determine the occurrence rate of given type of planets around given type of stars. Occurrence rate calculations require corrections for the detectability of a given type of planets. In case of transit surveys in addition one should take into account the geometric probability for seeing a transit of a given type of planet. For a recent review on planet occurrence in RV and transit surveys I refer the reader to \citet{deeg_planet_2018}. The main properties of giant planets detected by RV and transit methods was recently reviewed by \citet{santerne_populations_2018}. The latter author compiled a list of occurrence rate estimations of giant planet at different orbital periods: hot-Jupiters (P $<$ 10 days), period-valley giants (10 $<$ P $<$ 85 days), and temperate giants (85 $<$ P $<$ 400 days). Their results show that the average occurrence rate increases from about 1\% for the shortest period giants to about 3\% for giant planets with orbital periods of several hundred days \citep[see][and references therein]{santerne_populations_2018}. It is interesting to note that the occurrence rate calculations for hot-Jupiters detected by transit method are about factor of two lower than the one calculated for RV planets \citep[e.g.][]{santerne_sophie_2016}. The exact reason for this discrepancy is still unclear, but can be related to properties of the stars (e.g. binary rate) monitored in RV and transit surveys and/or (in)ability of accurate characterization of these stars \citep[e.g.][]{guo_metallicity_2017}. The integrated occurrence rate of giant planets (M $>$ 50~M$_{\oplus}$) with orbital periods shorter than 10 years is estimated to be 13.9$\pm$1.7\% \citep{mayor_harps_2011}.
\subsection{Metallicity of sub-Jupiters} \label{sub-Jupiters}
In Fig.~\ref{nayakshin_mordasini}, where I qualitatively compare the metallicities of different types of observed and synthetic planets, one can clearly see that there are two dips in the metallicity of observed planets at masses of $\sim$ 0.8~M$_{\jupiter}$ and 2~M$_{\jupiter}$. In this subsection I study these dips more in detail to understand whether they have an astrophysical origin or are due to different observational biases and selection effects.
In the leftmost panel of Fig.~\ref{fig-massive_planets_running_mean} I show the dependence of planet host metallicity on the mass of planets with masses between 50~M$_{\oplus}$ and 4~M$_{\jupiter}$. These planets are selected to be orbited around FGK dwarf stars ($\log g$ \ $>$ 4.0 dex, 0.6~M$_{\odot} <$ M $<$ 1.5~M$_{\odot}$) with stellar parameters derived in a homogeneous way in SWEET-Cat. The running means of hot- (P $<$ 10 days) and cold-Jupiters (P $>$ 100 days) with masses above about 1.5~M$_{\jupiter}$ have very different behaviors (see the middle panel). This is most probably due to small number of such planets in the sample. The small number of planets with masses above $\sim$ 1.5~M$_{\jupiter}$ and the change of the relative number of hot- and cold-Jupiters at 2~M$_{\jupiter}$ are probably responsible for the dip in metallicity observed at 2~M$_{\jupiter}$. The number of hot- and cold-Jupiters with masses between 0.3 and 1.5~M$_{\jupiter}$ (see the middle panel) is relatively large and their relative fractions are quite balanced. This means that the metallicity dip observed at $\sim$ 0.8~M$_{\jupiter}$ might have a physical origin and deserves further exploration.
In the middle column of Fig.~\ref{fig-massive_planets_running_mean} one can see that both hot- and cold-Jupiters show a dip in metallicity at about $\sim$ 0.8~M$_{\jupiter}$, although the dip of cold Jupiters is more apparent. The main reason of separating hot and cold Jupiters is that orbital periods of giant planets correlate with the host star metallicity: long-period Jovians tend to orbit more metal-poor stars than hot-Jupiters \citep[e.g.][]{sozzetti_possible_2004, adibekyan_orbital_2013, narang_properties_2018, maldonado_chemical_2018}. This correlation can be seen in Fig.~\ref{fig-massive_planets_running_mean} as well, where the red squares and red curve lie above the blue circles and the blue curve. To make the description of planets inside and outside of the metallicity dip easier and shorter, the planets inside the dip will be called 'sub-Jupiters', and the planets with masses higher and lower than the sub-Jupiters will be called 'Jupiters' and 'Saturns', respectively.
I tried to identify the lower and upper mass limits of sub-Jupiters by looking at a mass range for which the metallicity of their hosts stars is significantly lower than the metallicity of the'Jupiters' and 'Saturns'. Performed KS tests showed that the most significant difference between sub-Jupiters and non-sub-Jupiters is observed when sub-Jupiters are defined as planets with masses between about 200~M$_{\oplus}$ ($\sim$0.6~M$_{\jupiter}$) and 290~M$_{\oplus}$ ($\sim$0.9~M$_{\jupiter}$). However, when comparing the metallicities of the hosts of sub-Jupiters with those of the Saturns no statistically significant difference can be seen, while the difference from the hosts of Jupiters is always significant (see Table~\ref{table_KS_sub_jupiters}).
\begin{figure}[H]
\centering
\includegraphics[width=15cm]{figures/massive_planets_running_mean.pdf}
\vspace{-0.2cm}
\caption{(Bottom panel): Dependence of the mass of hot giant planets on the metallicity of their host stars. The large symbols represent the mean metallicities and standard error of the mean (which does not include the measured uncertainty of [Fe/H] for individual points) for each mass bin (bin size is equal to 0.2~M$_{\jupiter}$). The running mean of [Fe/H] as a function of mass of hot giants (P $<$ 10 days; red), cold giants (P $>$ 100 days; blue), and all giant planets (in black) is shown in the middle panel. The running means were calculated using windows of 30, 30, and 40 for hot, cold, and all planets, respectively. The number of planets in each mass bin is plotted on the top panels. In the middle column I show all the planets with masses between 0.3 and 1.5~M$_{\jupiter}$. In the leftmost column only the most massive planet in a system is considered.}
\label{fig-massive_planets_running_mean}
\end{figure}
The next step was to investigate whether the sub-Jupiters (and/or their hosts) are different from the Jupiters and Saturns (and/or their hosts) in parameters that are linked to planet formation processes (e.g. orbital period, eccentricity, multiplicity, host star mass). To test whether the obtained results are sensitive to the multiplicity of the planets, I also considered the most massive planet for each planetary system (see rightmost panel of Fig.~\ref{fig-massive_planets_running_mean} and Table~\ref{table_KS_sub_jupiters}). The results did not differ significantly from the case where all the planets in each planetary system were considered. The most significant difference was observed for orbital periods of hot giant planets (Table~\ref{table_KS_sub_jupiters}). In the left panel of Fig.~\ref{fig-subJupiters_period_mass} the dependence of orbital periods on the mass of the sample of hot giant planets is plotted. The observed clear correlation is the cause of the different orbital periods observed for planets with different masses. The lack of very short period (P $<$ 2 days) sub-Jupiters probably cannot be explained by photoevaportation as these planets loose very small fraction of their mass \citep[e.g.][]{murray-clay_atmospheric_2009, adams_magnetically_2011, owen_planetary_2012}. Worth mentioning that this process is invoked to explain the lack of super-Earths and Neptunes at very short orbits \citep[e.g.][]{owen_kepler_2013, lundkvist_hot_2016, mazeh_dearth_2016}. Most of the mechanisms proposed to explain the orbital distribution and the observed lower boundary of hot-Jupiters include disk migration \citep[e.g.][]{nelson_evidence_2017, dawson_origins_2018} and high-eccentricity migration \citep[e.g.][]{matsakos_origin_2016, nelson_evidence_2017, owen_photoevaporation_2018}, both followed by tidal dissipation. Very recently, \citet{bailey_hot_2018} proposed that the lower boundary of the periods of hot-Jupiters can be a result of their \textit{in-situ} formation followed by tidal decay for the most massive planets. Whatever is the mechanism shaping the orbital architecture of the hot-Jupiters, it is not straightforward to link it with the significant metallicitiy differences observed between the sub-Jupiter and Jupiter host stars.
\begin{table}[H]
\caption{The results of the KS tests comparing the orbital periods and host stellar masses of giant planets of different masses. The number of planets in each sub-sample is presented in parenthesis. The p-values smaller than 0.05 are highlighted in boldface.}
\centering
\begin{tabular}{p{6.5cm}p{2.5cm}p{2cm}p{2cm}}
\toprule
{Samples} & {Parameter} & {KS statistic} & {KS p-value}\\
\textbf{Cold planets (P $>$ 100 days)} & & & \\
\midrule
Sub-Jupiters (28) vs Saturns (25) & [Fe/H] & 0.34 & 0.061 \\
Sub-Jupiters (28) vs Saturns (25) & Period & 0.24 & 0.366 \\
Sub-Jupiters (28) vs Jupiters (44) & [Fe/H] & 0.38 & \textbf{0.009} \\
Sub-Jupiters (28) vs Jupiters (44) & Period & 0.24 & 0.240\\
\end{tabular}
\smallskip
\begin{tabular}{p{6.5cm}p{2.5cm}p{2cm}p{2cm}}
\textbf{Most massive cold planets (P $>$ 100 days)} & & & \\
\midrule
Sub-Jupiters (21) vs Saturns (18) & [Fe/H] & 0.31 & 0.231 \\
Sub-Jupiters (21) vs Saturns (18) & Period & 0.43 & \textbf{0.034} \\
Sub-Jupiters (21) vs Jupiters (35) & [Fe/H] & 0.37 & \textbf{0.039} \\
Sub-Jupiters (21) vs Jupiters (35) & Period & 0.26 & 0.260 \\
\end{tabular}
\smallskip
\begin{tabular}{p{6.5cm}p{2.5cm}p{2cm}p{2cm}}
\textbf{Hot planets (P $<$ 10 days)} & & & \\
\midrule
Sub-Jupiters (26) vs Saturns (51) & [Fe/H] & 0.22 & 0.332 \\
Sub-Jupiters (26) vs Saturns (51) & Period & 0.39 & \textbf{0.005}\\
Sub-Jupiters (26) vs Jupiters (50) & [Fe/H] & 0.34 & \textbf{0.023} \\
Sub-Jupiters (26) vs Jupiters (50) & Period & 0.42 & \textbf{0.002}\\
\end{tabular}
\smallskip
\begin{tabular}{p{6.5cm}p{2.5cm}p{2cm}p{2cm}}
\textbf{Most massive hot planets (P $<$ 10 days)} & & & \\
\midrule
Sub-Jupiters (24) vs Saturns (47) & [Fe/H] & 0.28 & 0.134 \\
Sub-Jupiters (24) vs Saturns (47) & Period & 0.37 & \textbf{0.018} \\
Sub-Jupiters (24) vs Jupiters (47) & [Fe/H] & 0.36 & \textbf{0.021} \\
Sub-Jupiters (24) vs Jupiters (47) & Period & 0.45 & \textbf{0.002} \\
\bottomrule
\end{tabular}
\label{table_KS_sub_jupiters}
\end{table}
Besides the metallicity, other characteristics of the protoplanetary disks, such as disk lifetime, disk accretion rate and the disk mass, have very strong influence on the formation and evolution of giant planets \citep[e.g.][]{mordasini_extrasolar_2012, hasegawa_planetary_2013, hasegawa_planet_2014}. In fact all these parameters strongly inter-correlate \citep[e.g.][]{mordasini_extrasolar_2012, hasegawa_planetary_2013}. While no direct information is available about the protoplanetary disk properties where the observed planets have been formed, as a proxy one can consider the stellar mass. The disk mass linearly \citep[e.g.][]{andrews_mass_2013, mohanty_protoplanetary_2013} or superlinearly \citep[M$_{disk}$ $\propto$ (M$_{star})^{>1}$; e.g.][]{barenfeld_alma_2016, ansdell_alma_2016, pascucci_steeper_2016} correlates with the mass of the host star with an average disk-to-star mass ratio of $\sim$0.2\%--0.6\% \citep[e.g.][]{andrews_mass_2013}. Thus massive stars holding massive disks should have higher probability to form giant planets \citep[e.g.][]{kennedy_planet_2008}. However, these massive disks disperse earlier \citep[e.g.][]{ribas_protoplanetary_2015}, which makes the formation of massive cores of gas giant planets difficult. At the same time, the migration of giant planets formed in these short-lived disks is supposed to be very limited \citep[][]{burkert_separation/period_2007, currie_semimajor_2009}. To make the picture more complex one should remember that the disk mass also correlates with the disk accretion rate \citep{manara_evidence_2016}, a parameter which might be important for the fast formation of the cores of giant planets \citep{liu_migration_2016}.
Interestingly, no significant difference of stellar mass was found for the subsamples of giant planets suggesting that for a given stellar mass Jupiters tend to form around more metallic stars than their lower mass counterparts. This is somehow surprising since the stellar mass correlates with the stellar metallicity as shown in the right panel of Fig.~\ref{fig-subJupiters_period_mass}. This correlation is a consequence of stellar evolution, stellar age -- metallicity relation, and the typical color and magnitude cuts used in the selection of target in planet search programs \citep[][]{santos_statistical_2003, fischer_planet-metallicity_2005, ghezzi_stellar_2010, johnson_giant_2010}. With such results at hand, one might argue that the higher metallicity of Jupiter hosts would mean longer disk lifetime \citep{ercolano_metallicity_2010} and higher amount of planet building material \citep[e.g.][]{mordasini_extrasolar_2012}. These two parameters can directly affect the formation efficiency of giant planets and their migration rate. For cold giant planets no significant difference in orbital periods between sub-Jupiters and Jupiters is observed. This might be due to difference in starting positions of planet formation in disks with different metallicities \citep[e.g.][]{mordasini_extrasolar_2012}.
\begin{figure}[H]
\centering
\begin{tabular}{cc}
\includegraphics[width=7.5cm]{figures/p_m_metal_hot_jup.pdf}
\includegraphics[width=7.5cm]{figures/Mstat_metal_SubJup_Jup.pdf}
\vspace{-0.4cm}
\end{tabular}
\caption{Orbital period against the mass of hot giant planets with 0.3 $<$~M$_{p}$ $<$ 1.5~M$_{\jupiter}$ (\textit{left panel}). In each planetary system, only the most massive planet is considered. Stellar mass against metallicity for sub-Jupiters and Jupiters (\textit{right panel}).}
\label{fig-subJupiters_period_mass}
\end{figure}
While in this section a very qualitative and somewhat speculative discussion was developed to explain the low metallicity of sub-Jupiter hosts when compared to the stars hosting Jupiter-mass planets, a more quantitative analysis is necessary to understand the origin of this metallicity difference. Perhaps, even before such an analysis it is necessary to study the influence of different selection and observational biases on this finding.
\subsection{Very massive giants and metallicity} \label{super-giants}
In this subsection I will discuss the dependence of very massive planet formation on stellar metallicity. However, such a discussion requires a knowledge of the upper mass boundary of planets, which is still an open question. As mentioned in Sect.~\ref{giant_planet_metal}, depending on the goal of the study, different authors use different lower and upper mass limits when defining giant planets. 13~M$_{\jupiter}$ is usually used as an upper mass limit for giant planets to separate from sub-stellar mass objects with significant central deuterium burning \citep[e.g.][]{spiegel_deuterium-burning_2011}. However, as already mentioned in the manuscript, the exact deuterium burning mass-limit depends on several parameters of the object. Another possible limitation of mass-limit based definition is that it does not involve formation mechanism of the object. Finally, the mass distribution of sub-stellar objects show no any special feature around this mass limit \citep[e.g.][]{udry_detection_2010}. \citet{schlaufman_evidence_2018} proposed that the separation between giant planets and BDs should be somewhere between 4~M$_{\jupiter}$ to 10~M$_{\jupiter}$, assuming that the sub-stellar objects formed via CA and GI can be statistically well separated. In particular, \citet{schlaufman_evidence_2018} assumed that the giant planets preference for metal-rich host stars is an indication of their formation through CA \citep[but see][]{nayakshin_dawes_2017}. \citet{schneider_defining_2011}, in exoplanet.eu set an upper limit of 25~M$_{\jupiter}$ for giant planets. Although appreciating the importance of having a formation-based definition for planets, the authors correctly noted about the difficulty (or at this point even probably impossibility) of knowledge about the formation mechanism for the planets. The choice of 25~M$_{\jupiter}$ the authors justified by the start of a dip at around this mass in the observed distribution in $M\sin i$ of substellar mass objects \citep[e.g.][]{mayor_hot_2005, grether_how_2006, udry_detection_2010, sahlmann_possible_2011}.
Exoplanets are sometimes categorized into different populations defined by distinct metallicity distributions \citep[e.g.][]{buchhave_three_2014}. \citet{ribas_eccentricity-mass_2007} found that the average metallicity of stars with planets of mass $<$ 4~M$_{\jupiter}$ is lower than that of higher mass planet hosts by about 0.15 dex. However, in their comparison the authors did not separate the super-Earth and Neptune mass planets from giant planets. Moreover, these low mass planets in their sample mostly had super-solar metallicities, while the majority of later-on detected low-mass planets hosts have subsolar or solar metallicities \citep[e.g.][]{mayor_harps_2011, buchhave_abundance_2012} if not orbiting their stars at very short periods \citep{adibekyan_orbital_2013, mulders_super-solar_2016}. Using a significantly larger sample of giant planets with masses greater than 0.1~M$_{\jupiter}$ and with homogeneously derived host metallicities derived in SWEET-Cat, \citet{adibekyan_orbital_2013} revisited the metallicity distribution of very massive giants. The authors found that the stars hosting massive Jupiters (mass $>$ 4~M$_{\jupiter}$) have an average metallicity of 0.083 $\pm$ 0.032 dex, while the stars hosting planets with masses between 1 and 4~M$_{\jupiter}$ had an average metallicity of 0.149 $\pm$ 0.016 dex. Despite the lower average metallicity (lower by 0.066 $\pm$ 0.036 dex) of massive Jupiter hosts when compared to the relatively lower mass Jupiter (1 $<$ M$_{p}$ $<$ 4~M$_{\jupiter}$) hosts, the performed KS statistics suggested a probability of about 15\% that the two subsamples have the same underlying metallicity distribution. \citet{adibekyan_orbital_2013} concluded that a simple separation in mass at 4~M$_{\jupiter}$ does not reveal two different populations in metallicity.
Recently, \citet{santos_observational_2017} using the SWEET-Cat database also addressed the question whether very massive Jupiters tend to form at metallicities lower than their less massive counterparts. The authors found a convincing observational evidence that giant planets with masses above and below $\sim$4~M$_{\jupiter}$ constitute two distinct populations\footnote{Recently, when studying mass-radius relation for exoplanets, \citet{bashi_two_2017} also found an evidence of existence of a transition at a planetary mass of $\sim$ 5~M$_{\jupiter}$.}. They showed that the hosts of giant planets with masses $<$ 4~M$_{\jupiter}$ have metallicities on average higher than that of the fields stars without planets. At the same time, the hosts of their most massive planets were more massive stars with relatively low metallicities, similar to that observed in field stars of similar mass. Compensation of the lack of metallicity by higher stellar mass (thus high disk mass and availability of larger amount of planet building material) was not considered as a convincing explanation. Based on the aforementioned observational results \citet{santos_observational_2017} proposed that the planets in the two mass regimes may form in different ways: low-mass giant planets are formed in metal-rich disks through CA \citep[e.g.][]{mordasini_extrasolar_2012} and the more massive planets are formed in massive and metal-poor disks via GI \citep[e.g.][]{rafikov_can_2005, cai_effects_2006}.
It is interesting to see that the transiting planets with a radii larger than about 10 R$_{\oplus}$ (note that the radius of Jupiter is 11.2 R$_{\oplus}$) also seem to have an average metallicity slightly (perhaps statistically not significant) lower than the giant planets with smaller radii \citep[see Fig.3, Fig. 7, and Fig. 6 of][ respectively]{petigura_california-kepler_2018, narang_properties_2018, wang_giant_2018}. However, the number of transiting planets with very large radii and precise host metallicities is small and it is difficult to conclude whether there is a break-point radius above which planet hosts show low metallicities. Perhaps, besides the sample size and precision in metallicity, the main limitation of testing the aforementioned hypothesis is the very weak correlation between mass and radius for these H/He dominated giant planets \citep[e.g.][]{weiss_mass_2013, hatzes_definition_2015, chen_probabilistic_2017}.
Very recently, \citet{schlaufman_evidence_2018} also studied the upper mass limit of exoplanets in connection with metallicity distributions of planets and sub-stellar mass objects. The author used a sample of 119 systems with planetary-mass companion having both RV and transit signals and true masses\footnote{Observations of the transits ensures that the inclination is about 90$^\circ$ and thus $\sin i \approx 1$.} $>$ 0.1~M$_{\jupiter}$ . These planets had orbits mostly within 10 days. His sample of subs-stellar objects consisted of 27 objects with masses $<$ 300~M$_{\jupiter}$. The constrain of having RV and transit signal restricted the orbital periods of the subs-stellar mass objects to be mostly within 50 days. First, \citet{schlaufman_evidence_2018} applied a clustering algorithm to separate the giant planets and non-planets based on the metallicities of their host/primary stars. The objects with M $<$ 4~M$_{\jupiter}$ and M $>$ 10~M$_{\jupiter}$ the algorithm unanimously classified as belonging to two different groups: giant planets and BD/low-mass stars, respectively. The clustering analysis of \citet{schlaufman_evidence_2018} using the SWEET-Cat sample suggested a separation at a similar mass of 4 ~M$_{\jupiter}$ (note the similarity in the separation mass proposed by \citet{santos_observational_2017}). In the second part of the analysis, ``Moving Median Analysis'', the author estimated the mass that separates the giant planets that are formed exclusively through CA and objects that do not show preference towards the high metallicity of their hosts and thus, cannot be formed through CA. Besides the assumption that the giant planets form only through CA, \citet{schlaufman_evidence_2018} also build the analysis on the theoretical prediction of \citet{mordasini_extrasolar_2012} that ``massive objects formed by core accretion should only occur around the most metal-rich primaries''. He found that the point at which secondaries do not preferentially orbit metal-rich primary stars occurs at about 10~M$_{\jupiter}$.
Inclusion of stellar mass binary systems in the sample of \citet{schlaufman_evidence_2018} might decrease the average metallicity of the massive secondaries sample, which in turn, would impact on the estimation of the breakpoint mass separating the giant planets from BDs. Recent observations suggest that the close (period $<$ 100 - 10,000 days, depending on the work) binary fraction of solar type stars strongly anti-correlates with metallicity \citep{raghavan_survey_2010, gao_binarity_2014, moe_close_2018}. In particular, \citet{moe_close_2018} showed that the binary fraction decreases from 40\% to 10\% in the mtallicity range of $-$1.0 dex and 0.5 dex. It is interesting to note that the wide orbit binary fraction of solar-type stars and close binary fraction of O- and B-type stars does not significantly depend on the metallicity across $-$1.5 $<$ [Fe/H] $<$ 0.5 dex range.
In the bottom panel of Fig.~\ref{fig-schlaufman_mordasini_planet_metallicity} I show the dependence of mass of giant planets (yellow) and sub-stellar objects (green) on the metallicity of the host star from the sample of \citet{schlaufman_evidence_2018}. In the same figure I also plot the giant planets (masses between 50~M$_{\oplus}$ and 4~M$_{\jupiter}$) and super-giant planets (masses greater than 4~M$_{\jupiter}$) orbiting around stars with metallicities homogeneously derived in SWEET-Cat. I note that while the masses of the objects from the sample of \citet{schlaufman_evidence_2018} are true masses, the masses for the SWEET-Cat objects are mostly the minimum masses ($M\sin i$). For a comparison, I also show the CA predicted synthetic planets of \citet{mordasini_extrasolar_2012}. The figure clearly shows that most of the giant planets and super-giant planets/BD with masses bellow about 20~M$_{\jupiter}$ share the area occupied by the synthetic CA planets. This means that, in principle, CA model of \citet{mordasini_extrasolar_2012} can explain the most metallic super-giant planets/BDs. The figure also shows that the area of M $\gtrsim$ 4~M$_{\jupiter}$ and [Fe/H] $\lesssim -$ 0.1 dex is very sparsely populated by the CA planets and the formation of the observed super-giant planets and/BDs in this area cannot be easily explained with the CA model of \citet{mordasini_extrasolar_2012}: at least not with the parameters (e.g. disk lifetime, disk mass) that were adopted in that specific model. It is interesting to see that almost all the sub-stellar objects with masses below about 60-70~M$_{\jupiter}$ of the sample of \citet{schlaufman_evidence_2018} are observed at super-solar metallicities. At the same time, almost all the low-mass stars\footnote{The hydrogen-burning mass limit for stars is at about 85~M$_{\jupiter}$ depending on the metallicity \citep[e.g.][]{hayashi_evolution_1963, baraffe_evolutionary_1998, nakano_pre-main_2014}.} with masses above about 150~M$_{\jupiter}$ have sub-solar metallicities. This latter trend is expected as the stellar binary fraction decreases with metallicity \citep[e.g.][]{moe_close_2018}. It is also interesting to see (compare the yellow and black/blue curves on the top panel of Fig.~\ref{fig-schlaufman_mordasini_planet_metallicity}) that the giant planets of \citet{schlaufman_evidence_2018} are on average more metallic (0.119 $\pm$ 0.015 dex) when compared with the giant planets from SWEET-Cat (0.091 $\pm$ 0.009 dex). This difference is probably due to the different orbital period distributions of the two samples. As discussed in Sect.~\ref{sub-Jupiters}, the short period Jupiters tend to orbit around more metallic stars than their longer period counterparts \citep[e.g.][]{ adibekyan_orbital_2013, maldonado_chemical_2018}.
\begin{figure}[H]
\centering
\includegraphics[width=14cm]{figures/schlaufman_mordasini_planet_metallicity.pdf}
\vspace{-0.2cm}
\caption{(\textit{Bottom panel}) Stellar metallicity against mass of giant planets and super-giant planets/sub-stellar objects discussed in \citet{schlaufman_evidence_2018} (yellow and green) and available in the SWEET-Cat database (black and blue). The synthetic planets predicted by the CA model of \citet{mordasini_extrasolar_2012} (red) are also plotted for a visual comparison. (\textit{Top panel}) The running mean of [Fe/H] as a function of mass of the aforementioned objects. The running means were calculated using windows of 20, 50, and 200 for the \citet{schlaufman_evidence_2018}, SWEET-Cat, and CA \citep{mordasini_extrasolar_2012} planets, respectively. These numbers reflect the sizes of each sample. For the \citet{schlaufman_evidence_2018} and SWEET-Cat samples the 1$\sigma$ uncertainty in the moving mean is also shown as a yellow-green and black-blue regions, respectively.}
\label{fig-schlaufman_mordasini_planet_metallicity}
\end{figure}
Fig.~\ref{fig-very_giant_planets_homo} shows the metallicity distributions of stars hosting giant planets (GPH) with masses 50~M$_{\oplus}$ $<$ M $<$ 4~M$_{\jupiter}$ and super-giant planet (SGPH) with masses 4~M$_{\jupiter}$ $<$ M $<$ 20~M$_{\jupiter}$. The figure and performed KS statistics suggest that the giant planet hosts are significantly more metallic (see Table~\ref{table_KS_metal_HMPH}) than the hosts of more massive planets. The average metallicity of GPH is 0.091 $\pm$ 0.009 dex and the average metallicity of SGPH is 0.021 $\pm$ 0.022 dex. Despite the significant differences in the average metallicity distributions of giant planets and super-massive planets and/or BDs one probably should not make a bold conclusion about their different formation channels. These planets might have formed via the same mechanisms in different environments. As discussed in \citet{santos_observational_2017}, the hosts of super-giant planets on average are more massive than the hosts of Jupiter-like planets which means that the super-giant planets have been formed in more massive disks.
\begin{figure}[H]
\centering
\includegraphics[width=12cm]{figures/very_giant_planets_homo.pdf}
\vspace{-0.2cm}
\caption{The KDE fit of the cumulative distributions of [Fe/H] for stars hosting giant (red) and super giant planets/BDs (blue) together with the samples of solar neighborhood single dwarf and giant stars are shown in curves of different colors that are indicated in the plot. The planet hosting dwarf stars with masses less than 1.5~M$_{\odot}$ and giant stars with masses greater than 1.5~M$_{\odot}$ are shown with dotted and dashed curves, respectively.}
\label{fig-very_giant_planets_homo}
\end{figure}
In order to study the impact of stellar mass on the obtained results I divide the samples into dwarf host stars (M $<$ 1.5~M$_{\odot}$) and giant host stars (M $>$ 1.5~M$_{\odot}$). The stellar masses were derived using the calibration presented in \citet{torres_accurate_2010}. This calibration is based on stellar temperature, surface gravity, and metallicity of the stars. Fig.~\ref{fig-very_giant_planets_homo} and Table~\ref{table_KS_metal_HMPH} show that when considering only dwarf stars the metallicity distribution of GPH and SGPH are almost identical. The average metallicity of SGP dwarf hosts is 0.106 $\pm$ 0.024 dex and the average metallicity of GP dwarf hosts is 0.100 $\pm$ 0.009 dex. Almost all the dwarf stars hosting super-giant planets have solar and super-solar metallicities (see Fig.~\ref{fig-mass_metallicity}). Such a metallicity distribution is expected for planets formed through CA \citep[e.g.][]{mordasini_extrasolar_2012} rather than GI/TD \citep{nayakshin_tidal_2015-2, nayakshin_dawes_2017}. Only four dwarf stars (HD111232, HD114762, HD181720, and HD22781) hosting SGP have metallicities bellow $-$0.3 dex. It is worth noting that most of the dwarf stars hosting planets with [Fe/H] $<$ $-$0.3 dex are enhanced in $\alpha$-elements, such as Mg and Si \citep{haywood_peculiarity_2008, adibekyan_exploring_2012, adibekyan_overabundance_2012}. $\alpha$-enhanced iron-poor stars are also enhanced in oxygen \citep[e.g.][]{bertran_de_lis_oxygen_2015} and carbon \citep[e.g.][]{delgado_mena_chemical_2010}. Enhancement in such abundant elements as O, C, Mg, and Si makes these stars not very metal-poor, but iron-poor. Interestingly, the picture is drastically different when comparing the metallicity distributions of SGP and GP giant hosts. The average metallicity of SGP giant hosts is $-$0.122 $\pm$ 0.031 dex and the average metallicity of GP giant hosts is $-$0.005 $\pm$ 0.027 dex. The performed KS test suggest a probability of 0.06 that the metallicies of the two samples come from the same parent distribution. In general, the data shows that giant stars hosting planets (giant and super-giant) are less metallic than the dwarf hosts and that practically there are no giant stars hosting planets with super solar metallicities [Fe/H] $>$ 0.2 dex (see Fig.~\ref{fig-mass_metallicity}).
To understand better the reason of dwarf and giant stars hosting planets having different metallicity distributions, in Fig.~\ref{fig-mass_metallicity} I show the distribution of stars with and without planets in the stellar mass -- metallicity diagram. It is important to note that the stars without planets have been searched for planets. The FGK field dwarf stars without detected planets have been observed within the HARPS GTO planet search program \citep{adibekyan_chemical_2012} and GK field giant stars without planets have been observed as part of the CORALIE planet search program \citep{alves_determination_2015} and the Okayama Planet search program \citep{takeda_stellar_2008}. The masses of these field stars were derived using the same calibration formulae \citep{torres_accurate_2010} as for the exoplanet host stars. Fig.~\ref{fig-mass_metallicity} clearly shows that all the giant stars with and without planets have a limiting maximum metallicity of about 0.2 dex and the fraction of very low metallicity (e.g. [Fe/H] $<$ -0.4 dex) giant stars is much less when compared with the lower mass dwarf stars in the same metallicity region. Several studies have already observed this tendency of evolved, giant stars lacking the metal-rich and very metal-poor stars \citep[e.g.][]{taylor_widths_2005,luck_giants_2007,takeda_stellar_2008, ghezzi_metallicities_2010, adibekyan_chemical_2015}. Due to their shorter main sequence lifetimes, most of these giant and evolved (the stars with M $>$ 1.5~M$_{\odot}$ have surface gravities between 1.5 and 3.0 dex) stars are younger than their dwarf counterparts. The younger age together with the age--metallicity dispersion relation \citep[e.g.][]{da_silva_basic_2006, casagrande_new_2011} might explain the narrower metallicity distribution of the
giant stars. These young stars are mostly local since they do not have time to migrate within the Galaxy \citep[e.g.][]{wang_influence_2013, minchev_chemodynamical_2013}. If the lifetime of the stars is long, then the radial migration in the disc would bring them from the inner,
metal-rich Galaxy \citep[e.g.][]{wang_influence_2013, minchev_chemodynamical_2013}. In addition, it is important to note that most large programs to search for planets around giant stars make a sample selection based on a cut-off in the B -- V colour. This B -- V cut-off result in the lack of low-gravity and massive stars with high-metallicities \citep[][]{mortier_new_2013}.
\begin{figure}[H]
\centering
\includegraphics[width=14cm]{figures/mass_metallicity.pdf}
\vspace{-0.2cm}
\caption{Dependence of stellar mass on [Fe/H] for stars hosting giant (red) and super giant planets/BDs (blue) together with the samples of solar neighborhood single dwarf and giant stars (black).}
\label{fig-mass_metallicity}
\end{figure}
Besides comparing the metallicitis of the hosts of massive and very massive planets, it is very informative to compare their metallicity distributions with the distribution of stars with not detected planets. The cumulative distribution of [Fe/H] for FGK field dwarf stars of \citet{adibekyan_chemical_2012}, and GK field giant stars of \citet{alves_determination_2015} and \citet{takeda_stellar_2008} is shown in Fig.~\ref{fig-very_giant_planets_homo}. The figure and the performed KS statistics (see Table~\ref{table_KS_metal_HMPH}) suggest that the dwarf hosts of both GP and SGP are significantly more metallic than the single field dwarf stars. This is a very important result suggesting that metallicity plays a very important role in the formation of massive planets independent of mass. When comparing the metallicity distributions of GP and SGP hosting giant stars with the metallicity distribution of filed giant stars without planets, the KS statistics suggests probabilities of 0.007 (for GPH) and 0.105 (for SGPH) that the samples come from the same parent distribution. However, it is very important to note that while the GPH are more metallic than the field giant stars (the mean metallicity of the \citep{adibekyan_chemical_2012} + \citep{alves_determination_2015} sample is $-$0.094 $\pm$ 0.007 dex), the giant hosts of SGP are slightly less metallic. This result suggest that giant planet (at least up to 4~M$_{\jupiter}$) formation around massive stars is more efficient if the disk is more metallic. Contrary, it seems that the most massive giant planets and/or BDs do not need metal-rich disks to be formed around massive stars.
Since our sample of planet hosting and single stars do not consist a single, well defined sample, it is not possible to determine the occurrence rate of very massive planets and test whether it depends on metallicity and stellar mass. Perhaps, a precise knowledge about a dependence (or absence of a dependence) of very massive planets and BD occurrence rate on stellar mass would help to better understand planet formation in massive disks. Different independent studies suggest that giant planet occurrence rate increases with the mass of the host star \citep[e.g.][]{reffert_precise_2015, jones_four_2016, ghezzi_retired_2018} for up to masses of about 2~M$_{\odot}$ and rapidly drops for masses larger than about 2.5~M$_{\odot}$ \citep[e.g.][]{reffert_precise_2015}\footnote{For a discussion about the possibility of planet engulfment producing a lack of close-in planets orbiting intermediate mass stars see e.g. \citet{sato_planetary_2008, villaver_orbital_2009, kunitomo_planet_2011}.}. This dependence is well explained by planet formation models based on CA \citep[e.g.][]{ida_toward_2005, kennedy_planet_2008, mordasini_extrasolar_2012}. GI models also predict an increase of giant planet formation efficiency with stellar mass\footnote{GI predict formation of more massive and more protoplanets as the disk/stellar mass increases \citep[][]{boss_formation_2011, vorobyov_formation_2013}.} \citep[][]{boss_formation_2011, vorobyov_formation_2013, kratter_gravitational_2016}. However, the short lifetime of massive disks (for stars with intermediate masses) affecting the formation efficiency of giant planets in the CA models should not be a problem for the giant planets formed through GI. Unfortunately, the limited number of BD detections does not permit to firmly conclude whether BD occurrence rate is a function of stellar mass or not. The occurrence rate of relatively short-period (within a few years) BDs around solar-mass stars is estimated to be between 0.5\% and 1\% \citep[e.g.][]{grether_how_2006, sahlmann_search_2011, grieves_exploring_2017}. \citet{borgniet_extrasolar_2018} did not find any BD mass companion within about 1000 days around a sample of 225 AF-type main sequence stars observed with SOPHIE and/or HARPS spectrographs. These authors estimated the upper limit of the occurrence rate of BDs around these stars to be below 4\%. An occurrence rate of 1.6\% for BDs around intermediate-mass giant and main-sequence stars was estimated by \citet[][]{jones_eccentric_2017}, which is slightly higher than the rate around lower mass stars. A similar occurrence rate of about 2\% for BDs orbiting white dwarfs (these are typically progeny of AF-type main sequence stars) was determined by \citet{girven_da_2011}\footnote{Note that \citet{girven_da_2011} adopted an indirect detection method of BD based on the existence of near-infrared excess emission in the spectral energy distributions of white dwarfs.}, again giving a tentative evidence that BD formation might be more efficient around massive stars. Interestingly, the parent stars of the BD candidates detected in \citet[][]{jones_eccentric_2017} are metal-rich. According to the CA model of \citet{mordasini_extrasolar_2009} the formation of super-massive planets and BDs are possible in massive and metal-rich disks at large distances.
In summary, our data and results do not support the previous hints and claims \citep[e.g.][]{santos_observational_2017, narang_properties_2018, schlaufman_evidence_2018} about the existence of a breakpoint planetary mass at 4~M$_{\jupiter}$ above and bellow which planet formation channels are different. iant planet formation (independent of their mass) around solar-like stars preferentially occurs in metal-rich disks. These planets thus can be result of CA process or be formed by TD model of \citet{nayakshin_dawes_2017}. In contrast, it seems that the most massive planets and BDs orbiting massive stars can be formed regardless of the disk metallicity. Such planets are not typical outcome of CA models and it is natural to suggest that they might have been formed via GI which efficiently produce very massive planets in massive and metal-poor disks \citep{rafikov_can_2005, nayakshin_dawes_2017}. Interestingly, several studies suggest that BDs with masses above and bellow $\sim$ 42~M$_{\jupiter}$ might have formed by different processes \citep[e.g.][]{sahlmann_possible_2011, ma_statistical_2014, mata_sanchez_chemical_2014, maldonado_searching_2017}. In particular, low-mass BDs can be formed by disk instability and the high-mass BDs via cloud fragmentation as stars \citep{ma_statistical_2014}.
\subsection{Low-mass planets and metallicity}
Ever since the first giant exoplanet was discovered orbiting a Sun-like star, the search has been ongoing for small, rocky planets around other stars, evocative of Earth and other terrestrial planets in the Solar System. Several ongoing and upcoming missions (e.g. TESS: \citet{ricker_transiting_2015}; CHEOPS \citet{fortier_cheops:_2014}; PLATO \citet{rauer_plato_2014}) and instruments (e.g. HARPS \citet{mayor_setting_2003}; HARPS-N \citet{cosentino_harps-n:_2012}; SOPHIE \citet{perruchot_sophie_2008}; CARMENES \citet{quirrenbach_carmenes_2014}; ESPRESSO \citet{pepe_espresso_2013}; SPIRou \citet{artigau_spirou:_2014}) are developed to search and characterize low-mass exoplanets, which should ultimately help us to understand the formation and evolution of these planets. However, the detection of low-mass/small-sized planets is not an easy task not only because of the very small photoelectric and RV signals, but also because of the activity signals coming from the host stars that often have the same magnitude as the planetary signal and can strongly perturb the detection of these planets and/or mimic a planetary signal \citep[e.g.][]{queloz_no_2001, oshagh_effect_2013, dumusque_earth-mass_2012, santos_harps_2014, hatzes_periodic_2016, faria_uncovering_2016, tal-or_carmenes_2018}. These difficulties not only limits the number of detected low-mass planets, but also make very hard to construct a control sample of stars without low-mass planets for RV surveys and make practically impossible\footnote{Transit method detects only planets which orbital planes are very close to the line of sight, thus all the stars with planets in inclined (with respect to the line of sight) orbital planes will appear as single stars.} for transit surveys \citep{buchhave_metallicities_2015}. Obviously, this makes the comparison of the properties of stars with and without low-mass/small-sized planets very difficult. Such a comparison is crucial to constrain the models of low-mass planet formation and for understanding environmental conditions required for their formation. In fact no strong correlation between low-mass planet frequency and metallicity is predicted by most of the CA based models \citep[e.g.][]{mordasini_extrasolar_2012, hasegawa_planet_2014}. However, there are subtle differences in the relation between the frequency of these planets and metallicity predicted by different CA models. For example, recent N-body simulations of planet formation via pebble accretion by \citet{matsumura_n-body_2017} suggest that the formation efficiency of low-mass planets subtly depends on the stellar metallicitiy. Their simulations show that at high metallicities large number of low-mass planets can be formed, but majority of them leave the systems because of dynamical instabilities. In the CA model of \citet[][]{hasegawa_planet_2014} formation of low-mass planets is almost independent and their frequency slightly decrease towards a minimum (at [Fe/H] of about $-$0.2 dex) and then increases again with increasing metallicity. In their model low-mass planets are considered as failed cores of giant planets and the observed minimum in their frequency is related with the rise in the frequency of giant planets at that metallicity. Unlike most of the GI models \citep[e.g.][]{boss_giant_1997, galvagni_early_2014}, GI/TD model of \citet{nayakshin_tidal_2015} can also explain the formation of low-mass planets. The model of \citet{nayakshin_tidal_2015}, as the CA models, also predicts high occurrence rate of these planets at low metallicities. However, in their model the frequency of low-mass planets decreases at super-solar metallicities.
Despite the aforementioned difficulties many groups tried to study the metallicity distribution of low-mass stars. Based only on a sample of seven short-period Neptune-mass ($M\sin i$ $<$ 21~M$_{\oplus}$) planets, \citet{udry_harps_2006} suggested that their formation efficiency may not depend on the host metallicity. This hint was later supported by the results of \citet{sousa_spectroscopic_2008} who used a sample of 17 low-mass planets ($M\sin i$ $<$ 25~M$_{\oplus}$) orbiting FGK and M-type dwarf stars. With the increasing number of RV detected low-mass planets, several independent studies confirmed that these planets (with masses bellow 30-40~M$_{\oplus}$) do not show any preference towards metal-rich FGK \citep[e.g.][]{ghezzi_stellar_2010, mayor_harps_2009, sousa_spectroscopic_2011, mayor_harps_2011, jenkins_hot_2013, sousa_sweet-cat_2018} and M-type stars \citep[e.g.][]{rojas-ayala_metallicity_2012, neves_metallicity_2013, gaidos_they_2016, hobson_testing_2018}. However, it seems that the maximum mass of super-Earth/Neptune-class planets ($M\sin i$ $\lesssim$ 40~M$_{\oplus}$) shows a dependence on metallicity \citep{courcol_upper_2016, petigura_four_2017}. As for the massive planets, when studying the metallicity distributions of low-mass planet hosts, the chosen upper planetary mass limit varies from work to work, mostly depending on the sample size. The mass below which planet formation does not depend on metallicity (if there is such a limit) is still not well known. It is worth to note, that both observations \citep{mayor_harps_2011} and CA based models \citep[e.g.][]{mordasini_extrasolar_2012, brugger_metallicity_2018} suggest a strong minimum starting at about 30~M$_{\oplus}$ in the mass distribution of low-mass planets.
The left and right panels of Fig.~\ref{fig-low_mass_planet_metal} show the metallicity distributions of FGK type stars hosting planets or planetary systems with only low-mass detected planets ($<$ 30~M$_{\oplus}$) and systems where at least one of the planets have a mass of less than 30~M$_{\oplus}$. The comparison of these distributions with that of FGK type single dwarfs from the HARPS sample \citep{adibekyan_chemical_2012} shows that the systems with only low-mass planets are less metallic ($-$0.101 $\pm$ 0.031 dex) than the systems of low-mass planets accompanied by more massive planets ($-$0.021 $\pm$ 0.026 dex), but are slightly more metallic than the single stars ($-$0.159$\pm$0.009 dex). KS tests show that the difference in the metallicity distributions between stars with only low-mass planets and single stars is not statistically significant, while the metal excess of systems including low-mass planets when compared to the single stars is statistically significant (Table~\ref{table_KS_metal_HMPH}). As it is well known, and already discussed in this manuscript, giant planets tend to orbit stars with high metallicities. Therefore, exclusion of low-mass planet hosting systems that also contain giant planets will artificially reduce the number of metallic planetary systems with low-mass planets. However, the occurrence rate of giant planets is several times less than the occurrence rate of low-mass planets \citep[e.g.][]{mayor_harps_2011}. Thus, when using a well defined volume limited sample of stars with and without planets, where the fraction of low- and high-mass planet hosts reflect their occurrence rates, exclusion of stars hosting high-mass planets probably should not significantly affect the study of low-mass planet -- metallicity relation, at least for metallicities (e.g. [Fe/H] $\lesssim$ 0.1 dex) at which the giant planet frequency is not extremely high. When excluding super-metallic stars ([Fe/H] $>$ 0.1 dex) and comparing the metallicity distributions of single stars and low-mass planet hosts accompanied by massive planets, the KS tests provides a p-value of 0.17 that the two samples come from the same parent distribution. This test shows that the statistically significant difference in metallicity obtained for the single stars and stars hosting simultaneously low- and high-mass planets was due to the presence of super-metallic stars with giant planets. In Fig.~\ref{fig-low_mass_planet_metal} one can see that in our SWEET-Cat sample, the number of stars hosting only low-mass planets is 49 and the number of stars hosting low- and high-mass planets is 75-49 = 26. This relatively large number of multiple planetary systems with low-mass and giant planets is due to selection effects towards giant planets and the fact that about 90\% of cold giant planets accompanied by a low-mass planet \citep{zhu_super_2018}.
\begin{figure}[H]
\centering
\begin{tabular}{c}
\includegraphics[width=7.5cm]{figures/low_mass_planet_metal.pdf}
\includegraphics[width=7.5cm]{figures/lowest_mass_planet_metal.pdf}
\end{tabular}
\vspace{-0.2cm}
\caption{ Metallicity distributions of FGK type stars hosting exclusively low-mass planets (left panel, skyblue), stars hosting at least one low-mass planet (right panel, skyblue), and stars without any detected planets (left and right panels, red). The KDE fit of the cumulative distribution of [Fe/H] for the sample of stars is also shown with the curves of corresponding colors.
}
\label{fig-low_mass_planet_metal}
\end{figure}
Majority of the planets in the Earth-like to Neptune-like regime have been discovered via transit method (see Fig.~\ref{period_mass}). The large number of such planets detected by $Kepler$ provides a good base for a statistical studies of these small worlds. However, an important limitation of $Kepler$ planet studies is the faintness of their host stars which makes difficult to characterize them very accurately. Most of the early studies based on transiting planets reached to a conclusion that stars hosting exoplanets with radii smaller than about 4 R$_{\oplus}$ show wide range of metallicities, indistinguishable from the distribution of field stars without known planets \citep[e.g.][]{buchhave_abundance_2012, everett_spectroscopy_2013, buchhave_metallicities_2015}. Here I should remind again that a star without known planets does not necessarily mean that the star does not have planets.
Mass determination of the small-sized planets (R $<$ 4 R$_{\oplus}$) revealed the existence of two sub-populations: rocky and gaseous. A division between rocky planets and small-sized planets with gaseous envelopes was suggested to occur at about 1.6 R$_{\oplus}$ \citep{weiss_mass-radius_2014, rogers_most_2015}. Recently, \citet{fulton_california-kepler_2017} found a bimodal distribution for radii of Kepler short period ($<$ 100 d) small-sized planets with a clear lack of planets with radii between 1.5 and 2.0 R$_{\oplus}$. Later, it was shown that the position of the gap (sometimes called ``Fulton gap'') depends on orbital distance of the planets \citep{fulton_california-kepler_2018} and the mass/type of the hosts \citep{zeng_exoplanet_2017, fulton_california-kepler_2018}. In fact, \citet{jin_compositional_2018} showed that the location of the gap should depend on the composition of these planets. They argued that the observed gap is best explained by their cores being rocky (rather than icy) and that most close-in low-mass planets may be formed within the snow line. The presence of the gap is mostly explained by photoevaporaton of the atmospheres of these low-mass planets \cite[][but see also \citep{ginzburg_core-powered_2018,lehmer_rocky_2017} for alternative explanations]{owen_kepler_2013, lopez_understanding_2014, jin_planetary_2014, owen_evaporation_2017, fulton_california-kepler_2018}, which may depend on metallicity \citep{owen_metallicity-dependent_2018}. In addition, CA based \textit{in-situ} planet formation model of \citet{dawson_metallicity_2015} suggest that the presence or absence of gaseous atmosphere depends on the solid surface density of the protoplanetary discs where they have been formed. Similarly, \citet{owen_metallicity-dependent_2018} found that the core masses of low-mass planets are larger at high metallicities allowing to accreate larger H/He envelopes. If the photoevaporaton is the mechanism producing the ``Fulton gap'' then the aforementioned results indicates that the metallicity distribution of the rocky planet hosts should be contaminated by the metallicities of the hosts of the photoevaporated cores that before the photoevaporaton had larger sizes.
Using a sample of about 400 $Kepler$ exoplanet candidate host stars with homogeneously derived metallicities \citet{buchhave_three_2014} found that there are three regimes of exoplanets - terrestrial-like planets (R $<$ 1.7 R$_{\oplus}$), gas dwarf planets (1.7 R$_{\oplus}$ $<$ R $<$ 3.9 R$_{\oplus}$), and ice or gas giant planets (R $>$ 3.9 R$_{\oplus}$) - that show different mean metallicities. In particular, \citet{buchhave_three_2014} showed that the terrestrial-like planets have a mean metallicity close to the solar value, while the hosts of gas dwarfs and ice/gas giants are more metallic than stars without known planets \citep{buchhave_metallicities_2015}. \citet{schlaufman_continuum_2015} using the sample of \citet{buchhave_three_2014} did not find a convincing evidence of the boundary at 1.7 R$_{\oplus}$, and argued that the data are better fitted by a continuous relation between radius and metallicity.
Most of the studies based on a relatively large number of transiting exoplanets with spectroscopically derived metallicities indicate that small-sized rocky planets (smaller than about 1.7 R$_{\oplus}$) show no preference towards high metallicities \citep[e.g.][]{buchhave_three_2014, mulders_super-solar_2016, narang_properties_2018, petigura_california-kepler_2018}, while the occurrence rate of larger transiting planets (1.7--3.9 R$_{\oplus}$) show a correlation with metallicity \citep[e.g.][]{buchhave_three_2014, mulders_super-solar_2016, petigura_california-kepler_2018}. By comparing the metallicity distribution of long-period ($>$ 25 days) small-sized (1--1.8~R$_{\oplus}$) planet hosts with the metallicity distribution of stellar hosts of planets with radii between 1 and 6 R~$_{\oplus}$ (independent of the orbital period) \citet{owen_metallicity-dependent_2018} found that the terrestrial-like planets are more common around low-metallicity stars and might have been formed after the gas disc was dispersed. However, to confirm or infirm whether rocky planet formation is more prevalent around lower metallicity stars one needs to study the dependence of occurrence rate of this planets on metallicity. \citet[e.g.][]{petigura_california-kepler_2018} showed that the occurrence rate of warm super-Earths (P = 10--100 days and R = 1.0--1.7~R$_{\oplus}$) almost independent of metallicity, showing slight (insignificant) decrease with metallicity. However, it is important to note that for transiting planets it is very hard to estimate the fraction of stars with planets \citep[][]{youdin_exoplanet_2011} and \citet[e.g.][]{petigura_california-kepler_2018}, as most of the works, used the average number of planets per star when studying the planet occurrence -- metalliciy dependence. Obviously, these two estimates of the occurrence rates are different (they would be the same if there was no star with more than one planet), and show different dependencies on stellar metallicity \citep{zhu_influence_2018}. Contrary to aforementioned results, \citet{wang_revealing_2015} suggested a universal planet--metallicity correlation for planet of all sizes. It is important to note that, while the stellar metallicites of their planet candidate hosts were derived spectroscopically, the metallicities of their control sample stars were based on photometric stellar parameters with further conversion to more ``representative'' stellar parameters \citep{wang_revealing_2015}. \citet{zhu_dependence_2016} suggested that the high occurrence rate and low detection efficiency of low-mass planets can explain the discrepant results regarding the small-sized planet -- metallicity correlations obtained by different authors.
When studying the metallicity dependence of low-mass/small size planets it is very important to take into account the relation between orbital periods of planets and their host stars metallicities \citep{adibekyan_orbital_2013, beauge_emerging_2013, dawson_metallicity_2015, adibekyan_which_2016, mulders_super-solar_2016, petigura_california-kepler_2018, wilson_elemental_2018, dong_lamost_2018}. In particular, \citet{adibekyan_orbital_2013} found that the super-Earth-like planets ($M\sin i$ $<$ 10~M$_{\oplus}$) orbiting metal-rich stars have orbital periods shorter than about 20 days, whereas planets orbiting metal-poor stars span a wide range of orbital periods \citep[see also][]{dawson_metallicity_2015, adibekyan_which_2016}. However, these results were contested by \citet{mulders_super-solar_2016} who argued that the observed trends might be due to selection effects. A systematic excess of short period ($\lesssim$ 10 days) rocky planets ($<$ 1.7 R$_{\oplus}$) around metal-rich stars was reported in several works \citep{mulders_super-solar_2016, petigura_california-kepler_2018, wilson_elemental_2018}. The metallicity preference of hot rocky planets is explained by the possible dependence of efficient inward migration of solids on metallicity \citep{petigura_california-kepler_2018}, higher
rates of planet-planet scattering in metal-rich disks \citep{petigura_california-kepler_2018}, and/or dependence of planet trap at the inner age on metallicity \citep{mulders_super-solar_2016, wilson_elemental_2018}. An alternative possibility is that hot rocky planets and hot Jupiters might share the same formation mechanism \citep{mulders_super-solar_2016}.
Despite aforementioned results suggesting that low-mass/small planet formation can be efficiently occur around stars with wide range of metallicities there seems to be an observational evidence that at a given metallicity these planets prefer to orbit stars with high [Mg/Si] abundance ratio \citep{adibekyan_stellar_2015, adibekyan_mg/si_2017} and at low-iron regime preferably orbit stars enhanced in $\alpha$-elements such as Mg and Si \citep{adibekyan_exploring_2012}. These results suggest that low-mass planet formation is not completely independent of the composition of the protoplanetary disk.
\section{Summary and conclusion} \label{conclusion}
In this manuscript I reviewed and discussed the dependence of planet occurrence on stellar metallicity (iron abundance). In the upcoming manuscripts I will review i) the dependencies observed between exoplanet properties (e.g. orbital properties, multiplicity) and the metallicity (iron abundance) of their host stars (Paper II: 'Heavy metal rules II. Exoplanet properties and stellar metallicity') and ii) the role of individual heavy and light elements in the formation of exoplanets and the link between composition of exoplanets and their hosts stars (Paper III: 'Heavy metal rules III. Exoplanets and elements other than iron').
\subsection{Questions to answer or to think about}
Before starting to write this review, I was hoping that by gathering/collecting all the available information and evidences coming from observations and theoretical predictions about formation of exoplanets of different types, I and/or the reader will get closer in answering to some important questions that I had in my mind. I hope the reader will be more successful in answering to this questions than the writer.
The origin of giant planet -- metallicity correlation. As discussed in the manuscript, formation of giant planets depends on several characteristics of the protoplanetary disks that are inter-correlated and all can produce a correlation between giant planet occurrence and metallicity. The most direct explanation of the correlation would go as, large amount of metals in the disk means large amount of material to build cores of giants which would translate into higher probability to form gas giants. However, at high metallicities the disk lifetime is longer \citep{ercolano_metallicity_2010} which makes easier (enough time) to build cores of giants and hence means higher probability to form gas giants as well. Besides the disk lifetime and metallicity, the mass of the disk also plays an important role for the formation of giant planets \citep[e.g.][]{kennedy_planet_2008}. As discussed in the manuscript, the disk mass, in turn correlates with the metallicity (due to selection effects) and disk lifetime \citep[e.g.][]{ribas_protoplanetary_2015}. The frequency of massive planets is lower than the frequency of systems with super-Earth-like planets. The latter systems, in principle, should have had enough material to build a core for giant planets. This may suggest that not the availability of core building blocks in the disk, but the conditions for planetary embryos to merge and acquire the critical core mass for giant planet formation is what might determine the formation probability of gas giants. \citet[][]{liu_migration_2016} suggested that the parameter determining these conditions is the critical disk accretion rate, which correlates with metallicity and disk mass. Finally, as a very alternative explanation, it was proposed that the giant planet -- metallicity correlation can have a secondary origin \citet{haywood_correlation_2009}. Because of the radial metallicity gradient in the Galaxy \citep[e.g.][]{lemasle_galactic_2008,anders_red_2017}, the giant planet -- metallicity correlation can be easily recovered if the planet formation is more efficient in the inner Galaxy than in the solar neighborhood. \citet{haywood_correlation_2009} suggested that giant planet formation might be related to the surface density of molecular hydrogen H$_{2}$ in the Galaxy.
\textbf{Low-mass/small-sized planets and metallicity.} Until the recent advancement of the TD model \citep[e.g.][]{nayakshin_dawes_2017} terrestrial planet formation was explained exclusively by CA. Most of the CA models and the TD model of \citet[][]{nayakshin_tidal_2015}\footnote{The typical outcome of most TD based models \citep[e.g.][]{forgan_towards_2013, galvagni_early_2014} are massive planets and BDs while terrestrial planets are formed very rarely and their survival is not guaranteed \citep{forgan_towards_2018}.} suggest practically no dependence of low-mass planet formation on disk metallicity, although still small differences exist in the predicted exact form of this dependence. The current observations seem to support the absence of correlation between the lowest-mass/smallest-sized planets and metallicity, at least for orbital periods longer than about 10 days \citep[e.g.][]{mulders_super-solar_2016, petigura_california-kepler_2018}. However, because of the very high frequency and low detectability of these planets it is still very difficult to firmly conclude whether terrestrial planet formation depends on metallicity or not \citep[e.g.][]{zhu_dependence_2016}. Very large samples of stars with and without planets will help to tackle this issue and help to select the model that explains the observations best.Hopefully such samples can be constructed in the near future with the ongoing and upcoming surveys and missions.
\subsection{The main new results and conclusions}
Besides making questions and extensive literature review about the role of metallicity on the formation of planets of different types, in this manuscript I also revisited most of the correlations related to metallicity of planet host stars reported in the literature. I used the SWEET-Cat database \citep{santos_sweet-cat:_2013} that provides homogeneously derived stellar parameters (including metallicities) for a very large sample of planet host stars, especially planets detected through RV method. Among the many findings discussed in the manuscript, I highlight two main new results and findings.
\begin{itemize}
\item The study of the dependence of planet masses on the mean metallicity of their hosts revealed (see Sect.~\ref{sub-Jupiters}) that the hosts of sub-Jupiter mass planets ($\sim$0.6 -- 0.9~M$_{\jupiter}$) are systematically less metallic than the hosts of the Jupiter-like planets.
The results seem to suggest that at high metallicities, the longer disk lifetime \citep{ercolano_metallicity_2010} and higher amount of planet building material \citep[e.g.][]{mordasini_extrasolar_2012}, allows a formation of more massive Jupiter-like planets than at lower metallicities.
\item Recently, several authors suggested that planets more massive than about 4~M$_{\jupiter}$ tend to orbit around low-metallicity stars and might have formed in a different way than Jupiter-mass planets with $<$ 4~M$_{\jupiter}$ \citep[e.g.][]{santos_observational_2017, schlaufman_evidence_2018}. The results of this study show that giant planets with masses above and bellow 4~M$_{\jupiter}$ orbiting solar-like stars are preferentially metal-rich, which does not support the previous hints about the different formation mechanisms of these two groups of planets. Formation of these planets and the observed metallicity trend can be explained by the CA models \citep[e.g.][]{mordasini_extrasolar_2012} more easily than by the GI and TD models \citep[e.g.][]{boss_giant_1997, nayakshin_dawes_2017}. The results also show statistically significant difference in the metallicity distributions of giant stars ($>$ 1.5~M$_{\odot}$) hosting planets with masses greater or less than 4~M$_{\jupiter}$. Perhaps, GI based models should be able to explain the formation of the most massive giant planets ($>$ 4~M$_{\jupiter}$) in low-meallicity environment more easily than CA based models. It is thus suggested that planets of the same mass can be formed through different channels depending on the disk mass i.e. environmental conditions.
\end{itemize}
Summarizing all the results and trends discussed in the manuscript one can conclude that there is no yet a single CA nor GI/TD model that can effectively explain the formation (and the observed trends with metallicity) of planets of all types. CA models can qualitatively explain the formation and observed trends with metallicity for all planets, but the super-massive planets ($>$ 4~M$_{\jupiter}$) orbiting metal-poor giant stars. GI can be responsible for the formation of these later planets, but will not explain the formation of low-mass planets and the giant planet -- metallicity correlation. The TD model of \citet[][]{nayakshin_dawes_2017} can qualitatively explain most of the metallicity trends discussed in this manuscript, but will fail in explaining the super-giant planet -- metallicity correlation observed for solar-type stars.
The planet formation models constrained by the observations undergo significant improvements on how different physical processes are implemented. Observational exoplanetology does not stand still as well. Several ongoing and up-coming ground-based surveys and space-based missions (sometimes driven by theoretical predictions) are planned that will provide the exoplanet community with unprecedented amount of high quality data. Everything speaks about the bright future of exoplanetology. My very general conclusion, thus is that \textit{heavy metal rules}!
\vspace{6pt}
\funding{This work was supported by FCT - Fundação para a Ciência e a Tecnologia through national funds and by FEDER through COMPETE2020 - Programa Operacional Competitividade e Internacionalização by these grants: UID/FIS/04434/2013 \& POCI-01-0145-FEDER-007672; PTDC/FIS-AST/28953/2017 \& POCI-01-0145-FEDER-028953 and PTDC/FIS-AST/32113/2017 \& POCI-01-0145-FEDER-032113. I also acknowledge the support from FCT through Investigador FCT contract nr. IF/00650/2015/CP1273/CT0001.}
\acknowledgments{I would like to thank the EXO-Earth team members for working together on the subject of this manuscript for many years. It is my special pleasure to thank Pedro Figueira, Jo\~{a}o Faria, Nuno Santos, Elisa Delgado Mean, S\'{e}rgio Sousa, Olivier Demangeon, Susana Barros, and Vardan Elbakyan for very interesting conversations and discussions. My double thanks to Mahmoud Oshagh for the very interesting discussions and for inviting me to review this topic. I also thank Sergei Nayakshin for the provided data and for very interesting discussion about the formation of planets through GI. I would also like to thank David Adibekyan for his critical comments that were sometimes difficult to figure out and to implement. Finally, I would like to thank the referees for very constructive comments that helped to improve the quality of the manuscript.}
\conflictsofinterest{The author declares no conflict of interest.}
\abbreviations{The following abbreviations are used in this manuscript:\\
\noindent
\begin{tabular}{@{}ll}
RV & radial velocity \\
CCD & Charge-Coupled Device \\
SS & Solar System \\
CA & core accretion\\
GI & gravitational instability \\
TD & Tidal Downsizing \\
ISM & interstellar medium \\
BD & brown dwarf \\
GTO & Guaranteed Time Observations \\
HARPS & High Accuracy Radial velocity Planet Searcher \\
HMPH & High Mass Planet Host \\
SnoP & Stars with not Planets \\
GPH & Giant Planet Host \\
GP & Giant Planet \\
SGPH & Super-Giant Planet Host \\
SGP & Super-Giant Planet \\
KS & Kolmogorov-Smirnov \\
std & standard deviation \\
TESS & Transiting Exoplanet Survey Satellite \\
PLATO & PLAnetary Transits and Oscillations of stars \\
AU & Astronomical Unit \\
KDE & Kernel Density Estimate
\end{tabular}}
\externalbibliography{yes}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,125 |
Q: fotorama click trigger thumbnails from select I used to fotorama plugin in my web site. My issue is when I select other product via selectbox, the thumbnails doesnt changes.
I need to add data-serialid="xxx" on thumbnails.
Any suggestions are realy good.
Thank you very much.
<!-- jQuery, -->
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<!-- Fotorama -->
<link href="http://cdnjs.cloudflare.com/ajax/libs/fotorama/4.5.2/fotorama.css" rel="stylesheet">
<script src="http://cdnjs.cloudflare.com/ajax/libs/fotorama/4.5.2/fotorama.js"></script>
<select>
<option>Thumb 1 Need Select</option>
<option>Thumb 2 Need Select</option>
<option>Thumb 3 Need Select</option>
<option>Thumb 4 Need Select</option>
</select>
<p>I need to change thumbnails with selectbox.</p>
<div class="fotorama"
data-width="700"
data-ratio="3/2"
data-nav="thumbs"
data-thumbheight="48">
<a href="1-lo.jpg"><img src="http://s.fotorama.io/okonechnikov/1-thumb.jpg" width="144" height="96"></a>
<a href="2-lo.jpg"><img src="http://s.fotorama.io/okonechnikov/2-thumb.jpg" width="144" height="96"></a>
<a href="3-lo.jpg"><img src="http://s.fotorama.io/okonechnikov/3-thumb.jpg" width="144" height="96"></a>
<a href="4-lo.jpg"><img src="http://s.fotorama.io/okonechnikov/4-thumb.jpg" width="144" height="96"></a>
<a href="5-lo.jpg"><img src="http://s.fotorama.io/okonechnikov/5-thumb.jpg" width="144" height="96"></a>
<a href="24-lo.jpg"><img src="http://s.fotorama.io/okonechnikov/24-thumb.jpg" width="144" height="214"></a>
<a href="6-lo.jpg"><img src="http://s.fotorama.io/okonechnikov/6-thumb.jpg" width="144" height="96"></a>
<a href="7-lo.jpg"><img src="http://s.fotorama.io/okonechnikov/7-thumb.jpg" width="144" height="96"></a>
</div>
A: Try this:
var fotorama = $('.fotorama').fotorama();
changeThumb = function(obj){
var fotoramaApi = fotorama.data('fotorama');
fotoramaApi.show($(obj).val());
}
<!-- jQuery, -->
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<!-- Fotorama -->
<link href="http://cdnjs.cloudflare.com/ajax/libs/fotorama/4.5.2/fotorama.css" rel="stylesheet">
<script src="http://cdnjs.cloudflare.com/ajax/libs/fotorama/4.5.2/fotorama.js"></script>
<select onchange="changeThumb(this)">
<option value="0">Thumb 1 Need Select</option>
<option value="1">Thumb 2 Need Select</option>
<option value="2">Thumb 3 Need Select</option>
<option value="3">Thumb 4 Need Select</option>
</select>
<p>I need to change thumbnails with selectbox.</p>
<div class="fotorama"
data-width="700"
data-ratio="3/2"
data-nav="thumbs"
data-thumbheight="48">
<a href="1-lo.jpg"><img src="http://s.fotorama.io/okonechnikov/1-thumb.jpg" width="144" height="96"></a>
<a href="2-lo.jpg"><img src="http://s.fotorama.io/okonechnikov/2-thumb.jpg" width="144" height="96"></a>
<a href="3-lo.jpg"><img src="http://s.fotorama.io/okonechnikov/3-thumb.jpg" width="144" height="96"></a>
<a href="4-lo.jpg"><img src="http://s.fotorama.io/okonechnikov/4-thumb.jpg" width="144" height="96"></a>
<a href="5-lo.jpg"><img src="http://s.fotorama.io/okonechnikov/5-thumb.jpg" width="144" height="96"></a>
<a href="24-lo.jpg"><img src="http://s.fotorama.io/okonechnikov/24-thumb.jpg" width="144" height="214"></a>
<a href="6-lo.jpg"><img src="http://s.fotorama.io/okonechnikov/6-thumb.jpg" width="144" height="96"></a>
<a href="7-lo.jpg"><img src="http://s.fotorama.io/okonechnikov/7-thumb.jpg" width="144" height="96"></a>
</div>
Available image change options in Fotorama are:
//Using index
fotorama.show(2);
// Next:
fotorama.show('>');
// Previous:
fotorama.show('<');
// Last:
fotorama.show('>>');
// Arbitrary id:
fotorama.show('some-id');
see Official Documentation for more information.
A: I found this whilst hunting for a Magento 2 solution.
Might be helpful for some:
jQuery("#product-options-wrapper .super-attribute-select").click(function() {
jQuery('.fotorama').on('fotorama:ready', function (e, fotorama) {
fotorama.show(0);
});
});
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,942 |
\section{Introduction}
Nowadays, tourists are increasingly involved in creating the travel experience, becoming promoters of what they experience first-hand and consequently contributing to the improvement of a destination. In other words, they become protagonists of a process of co-creation of value that can affect both the destination in general and individual companies operating in the sector; examples are "Expedia", one of the largest worldwide Online Travel Agencies (or OTA), and "TripAdvisor", a travel platform that offers the opportunity of reviewing the tourist services that you have enjoyed on holiday (not just accommodations, restaurants, or airlines, but also experiences and attractions). In fact, through the involvement of their customers / travellers, they have managed to increase their importance in the travel industry.
With the spread of the Internet, the world of tourism has undergone a first transformation, leading to the spread of the so-called e-tourism. More precisely, according to the definition provided by Buhalis (2003)\cite{buhalis2003}, e-tourism means "the digitization of all processes and value chains in the tourism, travel, hospitality and catering sectors that allow organizations to maximize their efficiency and effectiveness ". This situation has given a strong impetus to the tourism sector, as it has allowed the various destinations to exploit this technology to improve their attractiveness by implementing appropriate online communication strategies. Recently, however, we are witnessing the transition from e-tourism to smart tourism.
In truth, however, rather than smart tourism it would be more right to talk about smart destinations, which Lopez de Avila (2015)\cite{lopez2015} defines as: "an innovative tourist destination built on a state-of-the-art technology infrastructure, which ensures the sustainable development of tourist areas, accessible to all, and which facilitates the visitor's integration with its environment, increasing the quality of the experience and improving the quality of life of residents". This definition clearly shows the importance of ICTs for their integration into the physical infrastructure of the destinations.
The use of information technologies is therefore an essential requirement of new forms of tourism. On the one hand, they help tourists in identifying and purchasing the tourist products they prefer, making them increasingly involved in co-creation and co-promotion of travel experiences, and on the other hand they allow suppliers of such products to make their offerings known around the world.
One of the problems arising from the use of new technologies in tourism is the lack of public confidence. Blockchain technology would seem to provide a solution, as the strengthening of trust represents one of the potential effects deriving from its application to tourism, especially in a period of great uncertainty like the one we are currently experiencing. The formation of trust in the hospitality industry, in fact, is still a little-known aspect, since it depends on the subjectivity of individual tourists, or rather on the risk that they are willing to accept in travel experiences. In the specific case of blockchain technology, the protocols on which it is based are structured in such a way as to ensure greater involvement by the various tourism stakeholders and thus improve their experience in the sector.
As highlighted by Porru et al. (2017)\cite{porru2017}, the growing focus on the world of blockchain technology has led to the need to create tools for the development of specific software oriented towards it (called blockchain-oriented software, or BOS). In general, BOS is defined as a system that works through the implementation of a blockchain. An example is the Ethereum platform, which can be defined as the largest decentralized digital platform in the world that uses blockchain technology for the realization not only of transactions, but also of particular programs called smart contracts, ensuring security, reliability and transparency\cite{pierro2020,fenu2018}. More precisely, "Smart Contracts" are programs written in a programming language and registered in the blockchain that self-execute when certain predetermined conditions occur. Pinna et al. (2019)\cite{pinna2019} define Smart Contracts as programs stored within the public register of Ethereum and associated with a particular blockchain address, aimed at implementing a logical sequence of steps according to some well-defined rules.
In this work we want to investigate the use of innovative IT technologies by DMOs, focusing attention on blockchain technology. In particular, we intend to verify the potential offered by these tools in the management and monitoring of a destination, without forgetting the implications for the other stakeholders involved. Such technologies, in fact, can offer a wide range of services that can be useful throughout the entire destination life-cycle. They represent an indispensable tool both to provide DMOs with different advantages from the management point of view (for example in monitoring or marketing) in order to achieve the sustainability objective\cite{pinna2021}, both to ensure that tourists and operators in the sector have a satisfactory experience.
The investigation discussed in this paper is guided by the following research questions.
RQ1: to what extent does the scientific community address the problems relating to the use of blockchain technology in tourism? and
RQ2: what is the state of the art of the practical use of blockchain technology in tourism and DMOs?
To answer the first question, we examined the scientific literature on the SCOPUS database, and we deepened the study by examining the content of the works more related to technical and socio-economic issues, the results of which are presented in Section \ref{literature}.
To answer the second question, we collected information regarding the most relevant blockchain-oriented projects for tourism, analyzing both the functionalities and the technology used. Section 3 presents the study of eleven software projects currently operational or under development.
Through the study of the scientific literature of reference and documentation on specialized websites, it is intended to firstly evaluate the contribution of these technologies to tourism managers, by laying the foundations for subsequent implementations.
Furthermore, the Section 4 of the paper allows us to discuss the two directions towards which the tourism industry is moving towards thanks to the use of blockchain technology, i.e disintermediation and coordinaion \& coopetition, as is arising from our investigation. Finally, Section 5 concludes the paper.
\section{Literature Review}\label{literature}
Although the scientific literature on the topic of blockchain is increasingly extensive, there are still few contributions that analyse it in relation to the tourist industry, but all are suitable for new insights. To confirm this, in Fig. \ref{research} you can check the number of articles published (or added to the lists of papers in press) annually dealing with the issue of blockchain related to tourism. The data were recovered in November 2020 through the use of the Scopus database, setting the search by query $TITLE-ABS-KEY ( "blockchain" \ AND \ "tourism" )$ with which were extracted scientific papers containing the words "blockchain" and "tourism" in the title, in the abstract or among the keywords. The graph shows that since 2016, with no article published on this theme, the number has doubled from year to year, which highlights the growing interest of the scientific community towards the application of blockchain technology in the tourism sector.
\begin{figure}[t]
\begin{center}
\includegraphics[width=0.95\linewidth]{img/publications.pdf}
\end{center}
\caption{Number of resulting publication per year by quering \textit{TITLE-ABS-KEY ( "blockchain" AND "tourism" )} in SCOPUS. For the years 2020 and 2021, the symbol * indicates the presence of incomplete data, updated to November 2020.}
\label{fig:process}
\end{figure}
\subsection{Selected literature}
The selection process consisted of the following steps. From the list of 65 papers obtained from the above described query, the papers whose abstracts dealt with the application of blockchain technology to tourism as the main topic of the study were selected. Of these, the availability of the full text was verified (either by publishers' websites and by courtesy of the authors).
Then, we have focused our attention on the scientific contributions of the last two years in relation to the general principles of the BOSE \cite{porru2017}. In particular, we chose the papers that discussed the opportunities offered by blockchain technology applied in the tourism sector. We have also included the papers that discussed the challenges that the tourism industry will have to face with the adoption of blockchain technology, both from a technological point of view and from an economic-organizational point of view. Tab. \ref{research} reports the summary of the scientific literature chosen and analysed in this work about the application of blockchain technology in tourism.
\begin{table*}[]
\caption{Summary of the research papers analyzed in this study}
\begin{tabular}{|l|l|l|l|}
\hline
\textbf{YEAR} & \textbf{TITLE} & \textbf{AUTHORS} & \textbf{MAIN CONTRIBUTIONS} \\ \hline
2018 & Blockchain and Tourism: Three Research Propositions & \cite{onder2018} Önder I. \& Treiblmaier H. & \begin{tabular}[c]{@{}l@{}}Authors formulate three research hypotheses \\ about the impact of blockchain on tourist\\ industry.\end{tabular} \\ \hline
2019 & \begin{tabular}[c]{@{}l@{}}The Impact of Blockchain on the Tourism Industry: \\ A Theory-Based Research\end{tabular} & \cite{treiblmaier2019} Treiblmaier H. \& Önder I. & \begin{tabular}[c]{@{}l@{}}Understanding the potential impacts of \\ blockchain technology on tourist facilities and\\ how to cope with the changes induced by it.\end{tabular} \\ \hline
2019 & \begin{tabular}[c]{@{}l@{}}Is blockchain technology a watershed for tourism \\ development?\end{tabular} & \cite{kwok2019} Kwok A. O. J. \& Koh S. G. M. & \begin{tabular}[c]{@{}l@{}}Opportunities and main challenges arising \\ from the use of blockchain technology for\\ small island economies.\end{tabular} \\ \hline
2019 & \begin{tabular}[c]{@{}l@{}}Blockchain technology for smart city \\ and smart tourism: Latest trends and challenges\end{tabular} & \begin{tabular}[c]{@{}l@{}} \cite{nam2019} Nam K., Dutt C. S., \\ Chathoth P. \& Khan M. S.\end{tabular} & \begin{tabular}[c]{@{}l@{}}Latest blockchain technology trends and\\ challenges for smart cities and smart tourism \\ and their influences for the sector.\end{tabular} \\ \hline
2019 & \begin{tabular}[c]{@{}l@{}}Assessment of blockchain applications in travel and \\ tourism industry\end{tabular} & \cite{ozdemir2020} Ozdemir A. I., Ar I. M. \& Erol I. & \begin{tabular}[c]{@{}l@{}}A basic set of blockchain criteria is proposed \\ for the comparison of various decentralized\\ applications.\end{tabular} \\ \hline
2019 & \begin{tabular}[c]{@{}l@{}}Blockchain Technology in Tourism: \\ Applications and Possibilities\end{tabular} & \cite{rejeb2019} Rejeb A. \& Rejeb K. & \begin{tabular}[c]{@{}l@{}}Potential effects and applications offered by \\ blockchain technology to the tourism\\ industry.\end{tabular} \\ \hline
2019 & \begin{tabular}[c]{@{}l@{}}A blockchain approach for the sustainability in \\ tourism management in the Sulcis area\end{tabular} & \begin{tabular}[c]{@{}l@{}} \cite{baralla2019} Baralla G., Pinna A., Tonelli R., \\ Marchesi M. \& Mannaro K.\end{tabular} & \begin{tabular}[c]{@{}l@{}}A blockchain platform is proposed for \\ traceability and certification of agri-food \\ products origin and for the promotion of \\ tourist activities of a destination.\end{tabular} \\ \hline
2020 & Blockchain and Tourism & \cite{treiblmaier2020} Treiblmaier H. & \begin{tabular}[c]{@{}l@{}}Economic potential of blockchain technology\\ for the future of the tourism industry.\end{tabular} \\ \hline
2021 & \begin{tabular}[c]{@{}l@{}}Applications of Blockchain and Smart Contract \\ for Sustainable Tourism Ecosystems\end{tabular} & \cite{joo2021} Joo J., Park J. \& Han Y. & \begin{tabular}[c]{@{}l@{}}Analysis of some cases of blockchain \\ technology application and smart contracts to \\ the tourism industry and identification of \\ opportunities to innovate existing companies.\end{tabular} \\ \hline
\end{tabular}
\label{research}
\end{table*}
The analysis of the articles in Tab. \ref{research}, aims to be an opportunity to present the general framework of studies that address the relationship between blockchain technology and the tourism sector, to identify what may be its contribution to the development of this industry. In our survey, the important contribution of Önder and Treiblmaier stands out. They are among the most prolific authors dealing with the issue of the application of blockchain technology in tourism and enrich the ideas of reflection on this issue. In 2018, Önder and Treiblmaier \cite{onder2018} conducted a study in which they formulated three research hypotheses concerning the impact of the blockchain on the tourist industry, claiming that this will bring:
the activation of reliable systems for evaluating tourism products through the use of new forms of assessment and review technologies;
the creation of new consumer-to-consumer (C2C) markets through the adoption of cryptocurrencies;
disintermediation of the tourist industry.
Before buying a trip and its related services online, it is normal for any traveller to first read the reviews of those who have already used the same service, considering this information more up-to-date and reliable than that given directly by travel service providers. Indeed, it is well known that online reviews of tourism products have a significant influence on potential consumers. However, these reviews are often subject to falsification by industry players themselves (such as hotel or restaurant owners). They seek to orient customers to their advantage by creating a not entirely truthful evaluation of their products by posting fake reviews; this is complicated by the fact that anyone can publish travel reviews without being asked for proof of having completed the tourist experience. To overcome this situation, and thus have correct online reviews, through blockchain technology it is possible to create evaluation systems that provide individuals with traceable identities through unique private keys, in order to avoid distortions in reviews and make them more reliable. This would create a decentralized, impartial, and transparent system that guarantees authentic and reliable reviews to potential travellers, which once entered in the blockchain register would no longer be possible to modify or delete. In such a system, would still be guaranteed the privacy of users, who could also be more encouraged in making reviews with any financial rewards in the form of tokens and cryptocurrencies to be received as a reward.
Most tourism products often involve the transfer of money between partners located in different countries. This may require intervention by trusted intermediaries to conclude the transaction, with the consequence of having to pay additional large commissions; think for example of the 20\% charged by Booking to hoteliers, overpricing which inevitably affects final consumers. Using cryptocurrencies, however, it is possible to ensure an easy exchange of money without the help of third parties intermediaries and participate in the emergence of new forms of C2C markets of tourism products. Cryptocurrencies could therefore change the way tourists and operators exchange money and avoid the intervention of third parties (banks) in transactions, with consequent cost reductions. This is especially important where tourists' personal information, including financial data, cannot be entrusted to intermediaries. There are many systems that use blockchain to ensure high standards of security in transactions and at the same time greater protection of travellers' information. One of these is TripEcoSys (10), which aims to be the largest decentralized tourism platform in the world based on the Ethereum blockchain. It is a system in which it is possible to find in a single space all the providers of the different travel services (flights, accommodation, excursions, etc.) that normally the visitor should book independently of each other, and where you can earn cryptocurrency rewards by sharing your own experiences. Furthermore, given the characteristics of cryptocurrencies, through blockchain networks it is also possible to avoid the problem of converting foreign currencies and, consequently, further limit the influence exerted by intermediaries, making transactions safer. If, on the one hand, tourists would no longer have to convert money when travelling, thus eliminating all the risks associated with the exchange of foreign currencies, on the other hand companies would be free to adjust their prices according exchange rate variability.
The advent of information technologies also in the tourism sector can therefore significantly reduce the intermediation chain towards the fruition of the tourist offer. The removal and replacement of intermediaries (also called disintermediation) is just one of the prerogatives of blockchain technology that in a short time will revolutionize the distribution and use of travel products and services, bringing significant benefits not only of an economic nature (cost savings). In general, it can be said that consumers will be more independent in organizing their travels. This disintermediation, however, does not only concern money transactions, but also directly affects the supply of tourism products. An initial form of disintermediation has already occurred with the advent of OTAs, but now also these could be replaced by blockchain-based, open source and decentralized travel platforms, such as WindingTree as discussed in the next section, which can eliminate the power exercised by intermediaries on the market. Another example is the Locktrip platform (see Table 2), which allows travellers to book hotels and other travel services without the intervention of any intermediary and, at the same, time provide feedback on the quality of the service. All this by using blockchain technology. From these simple examples, one can already understand the extent of the blockchain in the future of the tourist industry.
In another study, Treiblmaier \& Önder \cite{treiblmaier2019} also set out to analyse the potential impacts of blockchain technology on tourism facilities and how organizations could cope with the changes it induces. In general, by interviewing the managers of ten European Destination Management Organizations (DMOs), they highlighted that blockchain can be an important resource for many tourist organizations because it has the potential to change market structures. However, this is still a complex technology as it requires a certain investment by organizations, but they may not have the necessary financial resources and appropriate know-how to exploit it adequately. It follows, therefore, that this technology can be a new (important) resource only for those organizations that are in a position to exploit it for their own benefit, especially in a sector such as tourism. In 2020, Treiblmaier \cite{treiblmaier2020} summarizes and discusses the current state of the art, describing a list of twelve use cases of blockchain adoption in tourism, and the most relevant theoretical aspects, according to the academic literature. It focuses attention on the economic aspects of tourism disintermediation, highlighting this use case as looming in the tourism sector, and as a challenge that the tourism organization must be ready to face.
\begin{table*}[ht]
\caption{Active or proposed blockchain oriented software system for tourism industry}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
\multicolumn{2}{|l|}{\textbf{NAME AND URL}} & \textbf{NATIONALITY} & \textbf{ACTIVITY STATUS} & \textbf{KIND OF APPLICATION} & \textbf{BLOCKCHAIN} \\ \hline
\multicolumn{2}{|l|}{\begin{tabular}[c]{@{}l@{}}(1) WindingTree\\ https://windingtree.com/\end{tabular}} & Switzerland & Operating & Booking hotels and flights & Ethereum \\ \hline
\multicolumn{2}{|l|}{\begin{tabular}[c]{@{}l@{}}(2) LockTrip\\ https://locktrip.com/\end{tabular}} & Bulgaria & Operating & Booking hotels, holiday homes and flights & Ethereum \\ \hline
\multicolumn{2}{|l|}{\begin{tabular}[c]{@{}l@{}}(3) FoodChain\\ https://food-chain.it/\end{tabular}} & Italy & Operating & Traceability of food products & Quadrans \\ \hline
\multicolumn{2}{|l|}{\begin{tabular}[c]{@{}l@{}}(4) Bagtrax\\ https://bagtrax.eu/\end{tabular}} & United Kingdom & Operating & Baggage tracking & ND \\ \hline
\multicolumn{2}{|l|}{\begin{tabular}[c]{@{}l@{}}(5) Yookye\\ https://yookye.com/it\end{tabular}} & Italy & Operating & \begin{tabular}[c]{@{}l@{}}Organization of the holiday \\ (holiday home, services, experiences)\end{tabular} & Ethereum \\ \hline
\multicolumn{2}{|l|}{\begin{tabular}[c]{@{}l@{}}(6) DTCM Tourism 2.0\\ https://dubai10x.ae/\end{tabular}} & United Arab Emirates & Announcement & \begin{tabular}[c]{@{}l@{}}Check occupancy status of hotel in Dubai\end{tabular} & ND \\ \hline
\multicolumn{2}{|l|}{\begin{tabular}[c]{@{}l@{}}(7) WICKET\\ https://www.wicketevents.com/\end{tabular}} & Italy & Operating & Ticketing & Ethereum \\ \hline
\multicolumn{2}{|l|}{\begin{tabular}[c]{@{}l@{}}(8) Trippki\\ https://trippki.com/\end{tabular}} & United Kingdom & Operating & Hotel booking & Ethereum \\ \hline
\multicolumn{2}{|l|}{\begin{tabular}[c]{@{}l@{}}(9) Travelchain\\ https://travelchain.io/\end{tabular}} & Russia & Prototype & Travel ecosystem & ND \\ \hline
\multicolumn{2}{|l|}{\begin{tabular}[c]{@{}l@{}}(10) TripEcoSys\\ https://www.tripecosys.com/\end{tabular}} & United Kingdom & Prototype & Travel ecosystem & Ethereum \\ \hline
\multicolumn{2}{|l|}{\begin{tabular}[c]{@{}l@{}}(11) Sardcoin\\ https://www.sardcoin.eu/\end{tabular}} & Italy & Prototype & Smart coupon ecosystem & Hyperledger Fabric \\ \hline
\end{tabular}
\label{projects}
\end{table*}
Kwok and Koh (2018)\cite{kwok2019} confirm the high potential of blockchain technology, analysing its opportunities in relation to the economies of small islands, which could exploit it to their advantage to compete with larger and often more renowned destinations. According to the two authors, in fact, blockchain technology represents a valid aid for such economies, strongly limited by their small size and their insularity, to implement tourism policies that encourage their economic growth. For example, Aruba is seeking to increase tourism revenue through the creation of a blockchain-based platform for travel bookings, while the Caribbean islands are promoting the adoption of their own regional cryptocurrency. In particular, the effects resulting from the application of the blockchain to small island tourism can be traced back to four categories that can create beneficial effects for both tourists and destinations. In summary, these are: the general offer of a better tourist experience to visitors; greater speed and security in transactions with foreign countries thanks to the use of cryptocurrencies; diversification of the financial offer and use of state-owned cryptocurrencies; finally, a reduction in costs for host destinations. All this, however, can only be possible if foreign tourists are able to understand it and if local operators are able to accept it, thus avoiding limiting its use to a restricted group of experienced users.
Nam et al. (2019)\cite{nam2019} analysed the latest trends and challenges regarding blockchain technology for smart cities and smart tourism, focusing their attention on the comparison of thirteen decentralized applications (Dapps) of the tourism industry. In particular, scholars have formulated some research proposals about its evolution and influence in the industry, coming to the conclusion that the adoption of blockchain technology, and especially Dapps, will lead in the future to the creation of new business models and new market structures. Although a limited number of solutions have been analysed, especially when compared to the totality of existing blockchain solutions, their analysis revealed three characteristics common to all Dapps: cost reduction, increasing adoption of cryptocurrencies and development of new all-encompassing ecosystems. More precisely, a market will be created with strong competition between new online travel platforms based on blockchain and those already existing on the market, that to survive will be forced to change their business models and adapt to new emerging trends. Furthermore, since it will not be easy to ensure the adoption of blockchain technology by travellers and other stakeholders, some operators may also provide for the granting of incentives for the use of cryptocurrencies (the greater the incentives, the faster the adoption of blockchain technology). This will therefore lead to the identification of some "dominant players", that is those platforms with the largest number of users, which will impose themselves on the market.
Ozdemir et al. (2019)\cite{ozdemir2020} also made a comparison between several DApps, providing some practical examples of how these are used in tourism. In particular, they have focused, however, on proposing a basic set of blockchain technology criteria that may prove useful for evaluating decentralized applications. For this purpose, according to the authors, it is necessary to consider the governance model of the blockchain, the platform on which it is implemented, the type of consent, the use of cryptocurrencies\cite{}, the use of smart contracts and finally tokens. They argue that understanding these elements is the key to understand and improve any blockchain application. For example, the identification of the governance model applied to the blockchain is of fundamental importance to determine its characteristics, as well as the type of platform on which it is implemented can affect its performance\cite{destefanis2018}. However, their considerations need further development, especially considering the sample of DApps analysed: some of these applications, in fact, seem to no longer exist.
The study conducted by Baralla et al. (2019)\cite{baralla2019}, however, aims at proposing a blockchain platform for traceability and certification of origin of Sardinian agri-food products and for the promotion of tourist activities in Sulcis area, in Sardinia, with a view to a sustainability. Thanks to the blockchain characteristics, in fact, it is possible to guarantee secure and transparent information and ensure that it reaches all the stakeholders involved. Following this logic, the system proposed by Baralla et al. makes use of a series of smart contracts to ensure traceability and provenance of products, giving tourist/consumer the opportunity to verify their authenticity and provide their own feedback by posting messages, photos, and videos. In this way, tour operators can simultaneously improve their services and enrich the tourist offer of the area. Although the proposed system is still in progress and limited to a finite territory, it is still very promising also for the future tourist management of much larger territories.
Finally, Joo et al. (2021)\cite{joo2021} focused their attention on the study of blockchain technology and related smart contracts in the sustainable tourism sector and on identifying the best opportunities to innovate existing companies, providing some application examples. They also confirm the evidence already highlighted by other scholars about the usefulness of the blockchain to improve the transparency and safety of travel operations, users' trust, and the reduction of transaction costs. The proposed examples can also help as a stimulus for tour operators who want to make their businesses more innovative.
\section{Projects and applications of blockchain technology in tourism}
\subsection{Relevant Business initiatives and Research Projects }
In Tab. \ref{projects} we report eleven blockchain oriented software that are used in the tourism industry. The list presented is the result of two considerations: there are some software that are cited as relevant examples in the reference literature, and others that have emerged from a specific research on the main uses of blockchain technology in the tourism sector. In addition to the name and their URL, for each of them are indicated: the nationality, the activity status (distinguishing the operating software, from the announcements and the prototypes), their main functionality and, where available, the type of blockchain technology used.
\subsection{Fields of application of blockchain technology}
Although some of them have already been mentioned previously, in the tourism and hospitality industry there may be many potential applications of blockchain technology, some of which may also integrate with each other.
Some of the main applications of blockchain in tourism and those that could be implemented to add value to the sector are summarized below.
\subsubsection{Inventory management}
Blockchain technology can be used in an inventory management system which in the hospitality sector can refer to the number of rooms available in hotels or the number of seats available on airplanes. Specifically, it can provide information on availability and coverage rate by sharing it with the various interested stakeholders, thus replacing any Property Management System (PMS) and CRS, with the consequent removal of intermediaries and related expenses. An example of this is the Swiss platform WindingTree (1) , which allows hoteliers and airlines to list their availabilities, and tourists to book them. Another example is given by "BedSwap", a project on which the German group TUI (Tourism Union International) is working for an effective management of the hotel rooms of its partners in the markets served by the company itself. The Dubai Department of Tourism and Commerce (6), on the other hand, in 2018 launched "Tourism 2.0", with the aim of making Dubai the world's first destination for global travel and events by 2020. It is a system that allows you to check hotel occupancy and room rates, allowing other tour operators to prepare their offers more effectively for customers.
\subsubsection{Traceability of food products}
In an increasingly globalized tourism context, it is important to provide destinations with tools to ensure traceability in the supply of food chain products, especially in those sectors of food and wine tourism whose competitive advantage derives from the use of organic, local, and sustainable products. Here blockchain can be used to create a system that allows people to access data on the origin of food products and then reconstruct the path of products from the field to the table. In practical, this could be done by scanning a QR Code or directly barcodes of products through devices registered in the blockchain. For example, Foodchain (3) is an Italian system that, also using the Internet of Things (IoT), traces food products from origin to the final consumer using blockchain technology. The information made public by the participating companies is accessible to end consumers through a QR Code applied on the packaging of products. This helps to increase their confidence in companies given the possibility to check all the information on the product.
\subsubsection{Baggage tracking}
Despite the progress made by airlines in handling luggage, many travellers continue to experience problems with lost luggage, which leads to a loss of time and money for both passengers and airlines themselves. Blockchain technology is proposed as a solution in this sense since it allows the tracking of baggage, which can be monitored at various essential points, through the automatic entry of the data collected in a public register, thus also speeding up check-in and effectively reducing waiting times at the airport. For example, Bagtrax (4) uses a sensor which, once attached to suitcases, allows you to locate your luggage during transfers and to claim immediate compensation in case of loss. This system uses blockchain technology to make tracking sequences protected and guarantee the data security of all the actors involved in the service: passengers, airlines, airport managers and insurance companies.
\subsubsection{Reservations and ticketing}
In this case, the blockchain's usefulness lies in possible uses related to making reservations, for the issuance of tickets and to contrast the black market, for example by creating standard protocols allowing buyers to use their electronic wallets to prove ownership of the ticket. This includes WICKET (7), an app launched by an Italian startup that uses a special protocol based on blockchain technology to digitize tickets and limit the phenomenon of speculation. It uses the GET (Guaranteed Entrance Token) protocol, already used in the Netherlands and Singapore for the sale of tickets for sporting events or other events such as concerts, fairs and congresses. This year, however, following the pandemic that has affected the entire planet, was proposed to bathing establishments to allow bathers to book their place on the beach and pay directly online. The system associates the ticket with the buyer's phone number, generating a unique QR code in a special wallet, and will make it accessible to the user via an app to allow the latter to access the facility.
\subsubsection{Travellers loyalty}
Travel industry operators can benefit from the creation of dedicated loyalty programs that issue tokens as rewards to travellers. In fact, it has been demonstrated that companies that use such systems are able to obtain a competitive advantage over their competitors, reach new potential customers and improve the perception of the brand in their eyes, thus strengthening the link between travellers and destinations. The startup Loyyal has launched a blockchain-based platform through which companies can manage their loyalty programs by offering various types of reward systems. The Arab Group Jumeirah, in collaboration with Dubai Holding, uses this platform to improve the efficiency of its loyalty programs. Trippki (8) , on the other hand, has devised a loyalty program to allow customers and companies in the tourism sector to enter directly into contact with each other, thus promoting the disintermediation of the sector. Specifically, customers are given some tokens (that are registered in the blockchain without expiration date) to stay in a certain hotel, thus ensuring the possibility to redeem them at any time.
\subsubsection{Identity, credential management and privacy}
In order to improve the sector safety and protect the privacy of travellers, we could think of the definition of a (digital) global traveller identity through a system that allows to determine unequivocally the identity of a person. At the same time, it is also possible finding a solution to the problem of identity theft that tourists often encounter. For example, it will be possible to add biometric information (especially fingerprints and facial recognition) to the other registered information thus also simplifying the work of hotels, that will have only to record in the blockchain the arrival and departure dates of guests, without having to report them to the police or other authorities. From this point of view, the telecommunications company of air transport SITA (Société Internationale de Télécommunications Aéronautiques) is studying how the use of virtual or digital passports can reduce document checks during passenger journeys, thus eliminating the need to possess various travel documents. Through a single token containing biometric data and other personal information, and stored on mobile or wearable devices, travellers can in fact be quickly identified only once by any authority.
\subsection{Technology}
Apart from their functionality in the tourism sector, there are two main blockchain technologies adopted: smart contracts and DApps.
\subsubsection{Smart contracts}
Their programmability and automated execution independently of human interference offers many potentials for the tourism industry. For example, these allow: the activation of immediate payment systems in transactions, thus facilitating collaboration between hotels and travel agencies; the allocation of rooms to guests via digital keys on the blockchain; airlines can facilitate flight insurance by paying automatically as agreed in case of delay or cancellation. Most of the applications mentioned as an example in this section use, in fact, different smart contracts in their systems.
\subsubsection{dApps for smart tourism}
Are in the process of defining projects for online review systems, travel planning, direct communication with property owners, personalized marketing. For example, the innovative Italian startup Yookye (5) aims to offer tourists travel proposals tailored by local experts on the needs and aspirations of users. On the basis of the preferences found, the local experts, making use of their territorial knowledge and artificial intelligence, then create some travel proposals from which the user can choose. Everything is made more reliable thanks to the blockchain technology, which guarantees transactions in total security. In this way, users enjoy a secure and reliable short-term property booking service, which combines traditional payment methods with the most famous cryptocurrencies and the YOOK token of the same platform.
\subsubsection{Breaking technological barrier}
Through the promotion of transparent transactions, blockchain technology guarantees a higher level of trust and security in online travel platforms, since all data will only be upgradable through a consensual agreement between all participants in the network. From this, it is clear that blockchain can be a valid tool for neutrality and objectivity in travel information systems. In this kind of system, in fact, customers/tourists feel more comfortable in sharing their travel experiences in a more open and sincere way. Examples include TravelChain (9) and WindingTree(1). The first is a blockchain-based travel business that rewards travellers for the transparent sharing of information regarding their experiences; the other, instead, is a decentralized and open-source platform that aims to find a solution to several problems in the travel industry (such as high commissions, obsolete technology, high entry barriers and lack of innovation), all linked to a high degree of centralization. This is a system in which transaction data is grouped into blocks and replicated among all participants to ensure greater transparency and control of the travel package. In this way, customers are able to ascertain the actual value of a tourism product and gain more control and power over the planning of their travel experience.
\section{Discussion}
The analysis carried out revealed two main effects that blockchain technology can bring to the tourism sector.
\subsubsection{Disintermediation}
The progressive removal of intermediaries has already been widely discussed.
Today, travel agencies add a level of intermediation to the tourism chain, capable of generating end-to-end trust, that is, between the consumer (the tourist) and the tourist operator (i.e the DMO). Thanks to the presence of a trustless mechanism, blockchain technology makes the role of travel agencies accessory, that will have to review their role in the tourism system (as experts in the sector or as facilitators). This is a challenging opportunity for traditional travel agencies (which will be able to count on direct human relations).
What has not been said, however, is that, specifically in the tourism sector, blockchain can lead to the replacement of Global Distribution Systems (GDS) that allow transactions between different service providers (for example hotels, airlines, travel agencies , etc.) and OTAs through systems that allow peer-to-peer communications and transactions.
\subsubsection{Coordination and coopetition}
Thanks to the blockchain technology it is possible to create systems that see the aggregation of different travel products and services in such a way as to reduce any inefficiencies and achieve greater coordination between the various proposals. The aforementioned Yookye platform (5), for example, brings together in a single system numerous services and utilities for tourists, simplifying the organization of their vacation. Its users, therefore, will no longer need multiple Apps, but can find and book accommodation, tours and other services in a single App. Similarly, Sardcoin (11), a project of the University of Cagliari, offers a platform for the sale of Sardinian tourist services based on blockchain technology. That typology of systems implements the concept of \textit{coopetition}, that is the constructive and collaborative competition between companies from which both benefit: participating companies will be able to use the infrastructure to include services, integrate their offers or to set up tourism promotion strategies with other existing infrastructures.
\section{Conclusions}
On the basis of what has been said so far, it can be also said that tourism is one of the most promising sectors for the development of blockchain technology.
According to the results reported in this paper, we are able to answer the research questions which guided us in this investigation. In particular, for what concerns the first research question we can say that even if the number of the published research paper is still limited (to a total of 65 in the SCOPUS database), the number of published paper per year doubles every year. We examined the content of nine selected paper from which we can analyze the directions of scientific research in this domain. The second research question allowed us to explore the blockchain-oriented software projects for tourism. We reviewed 11 software projects, many of them operational, providing a classification of their core functionality and the related technological aspects.
However, regardless of what the scope of the investigation, some other important aspects need to be taken into account in further research.
First of all, it is necessary to consider that the blockchain is just a collective term that synthesizes a series of different tools; in fact, there are numerous blockchain protocols that determine as many implementations. Secondly, it must be borne in mind that it is a constantly developing technology which involves from the simplest protocols that form the basis of it, up to real new applications. This progress is aimed above all at reducing the complexity of the technology regarding the difficulties of understanding (and consequently also of application). Finally, it must be said that, despite continuous progress, blockchain technology cannot be tied to a single use but lends itself to numerous purposes, even if sometimes conflicting with each other. In addition, it can also be combined with other technologies, such as the Internet of Things (IoT) or artificial intelligence, which integrate with each other to achieve increasingly innovative applications. This is confirmed by the blockchain technology application cases reported in this paper. This is the case of FoodChain (3) and Bagtrax (4), which integrate blockchain with the IoT to achieve their goals, or even of the startup Yookye (5), which combines blockchain technology and artificial intelligence tools.
In this work we highlighted the most relevant issues of the blockchain technology applied to the tourism industry. However, it has emerged that the uses of blockchain technology are limited to initiatives by individual companies, so we recommend destination managers to deepen and encourage its application in the tourist management of the territories. Researchers could conduct empirical studies to assess the design of comprehensive systems that help managers in promoting this innovative tool.
\bibliographystyle{plain}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,872 |
# The Last Time I Saw Paris
ELLIOT PAUL
_To Flora, my wife_
# _Contents_
_Title Page_
_Dedication_
_List of Characters_
_Silhouette of rue de la Huchette_
_Map of rue de la Huchette and Ile de la Cité_
_PART ONE_ _The Post-War Twenties_
_A Narrow Street at Dawn_
_A Stairway down to Antiquity_
_The Women in Black Who Moved in Pairs_
_Of Public Opinion_
_Of Winter, and Minding One's Own Business_
_The News and the Barber's Itch_
_Of Community Entertainment_
_The Maiden's Prayer_
_To the Memory of a Second-Hand Accordian_
_Of High and Low Art, and Inflation_
_Of, for and by the People_
_Of Non-Essentials_
_The Prevailing State of Grace_
_Of Clothes and How They Make the Man_
_The Shock Felt round the World_
_Mostly About Whores and Music_
_The Card That Slipped from the Deck of the Past_
_Of Western Culture_
_The Central Markets_
_A Bevy of Reds_
_Mene Mene Tekel_
_PART TWO_ _The Pre-War Thirties_
_Excerpts from a Series of Letters_
_To be Read on an Island_
_Less Brightness Every Year_
_Of Hospitality_
_The Heart to Resolve_
_One Bitter Pill Deserves Another_
_Of Property and Fraternity_
_Of 'Non-Intervention'_
_A Dead Man on the Pavement_
_PART THREE_ _The Death of a Nation_
_Between Relief and Shame_
_Boards across a Doorway_
_'Unto the Least of These'_
_'Woe to the Weak'_
_'A Time to Sow and a Time to Reap'_
_Of Aid and Comfort to the Poles_
_'A Time of Snow in All Endeavour'_
_A Few are Chosen_
_Black Rain_
_About the Author_
_Copyright_
# _List of Characters_
_Hotel and Café Keepers_
---
| _Hôtel du Caveau_ |
| Julliard, Henri | _proprietor_
| Marie | _his wife_
| Berthe | _his sister-in-law_
| Thérèse | _cook_
| Georges | _garçon_
| Claude & Philomèle | _Julliard's predecessors_
| |
| _Hôtel Normandie_ |
| Sara | _proprietress_
| Guy | _her husband_
| Louis | _one-armed garçon_
| Mocha | _the dog_
| |
| _Café St. Michel_ |
| M. and Mme. Trévise | _proprietors_
| Eugénie | _drudge_
| |
_Shopkeepers and Storekeepers_
| Luttenschlager | _articles of piety_
| Salmon | _beef-and-lamb butcher_
| Villières | _the paint man_
| Achille & |
| Geneviève Taitbout | _stationery and newspapers_
| Noël | _taxidermist_
| Dorlan | _bookbinder_
| Mme. Absalom | _yarn and thread_
| Odette and Jean | _dairy_
| Colette | _their delivery girl_
| Monge | _horse butcher_
| Laniers | _laundry_
| Mariette | _bordel_
| Mireille |
| Consuela |
| Daisy |
| Armandine |
| Mado |
| Gillottes | _bakery_
| Lunevilles | _drapers_
| Julien & Mme. Julien | _barber/hairdresser_
| Saint-Aulaire | _tailor_
| Joli | _cleaner and dyer_
| Mme. Durand | _flower shop_
| Dominique | _stamps_
| André and Alice | _coal and wine_
| Gion and Bernice | _music shop_
| Corres | _groceries_
| Maurice | _goldfish_
| |
_Public Employees_
| Hortense Berthelot | _clerk in prefecture_
| Frémont | _postman_
| Benoist | _policeman_
| Masson | _policeman_
| Pissy | _railway worker_
| Antoine | _his son_
| The Navet | _petty official in prefecture_
| Jeanne | _his wife_
| Eugène | _his son_
| |
_Professional Men_
| Dr. Clouet | _doctor_
| Dr. Roux | _dentist_
| |
_Private Employees_
| The Satyr | _chef_
| Claire | _artificial flower maker_
| Léonard | _accordion player_
| Panaché | _floor-walker_
| Nadia | _model_
| |
_Priests_
| Abbé Alphonse Lugan |
| Father Panarioux |
| Father Gaston |
| Father Desmonde |
| |
_Miscellaneous_
| Hyacinthe Goujon |
| Mme. Goujon | _her mother_
| Judge Lenoir | _her grandfather_
| Mary the Greek |
| Milka | _Communist_
| Stefan | _Communist_
| Pierre Vautier | _Communist_
| Daniel | _restaurateur_
| Elvira and Roberta | _Alsation old maids_
| M. de Malancourt | _bon vivant_
| Mme. Spook (Root) | _Englishwoman_
| _L'Hibou_ | _Tramp_
| _L'Oursin_ | _The Chestnut Man_
PART ONE
# _The Post-War Twenties_
_Rue de la Huchette and Ile de la Cité_
# _A Narrow Street at Dawn_
DAWN, THE SUN RISING behind the cathedral, Notre Dame de Paris, sent its first feeble rays directly down the rue de la Huchette to be reflected from the windows of the place St. Michel. A few yards away, running almost parallel to the little street, the south branch of the Seine skirted the Ile de la Cité, and on its yellow-brown waters, in which clouds were mirrored upside down, laden barges drifted, from the north of France or Belgium, bound for Rouen and Le Havre. The Latin quarter and the Cluny lay eastward; across the river stood the grim Conciergerie, the bleak and vast Hôtel Dieu, or hospital, and the Palais de Justice.
In the place St. Michel, with its dripping fountain and stone dolphins, the Café de la Gare was the first to open, to take care of early customers who arrived by underground railway from Versailles and the workers of the neighbourhood who snatched their coffee and _croissants_ at the counter before descending into the Métro, near the entrance of which stood a dingy international news stand, with a profusion of provincial and local French papers on sale, as well as the Paris journals. The first comers seldom bought newspapers; they couldn't afford to spend four sous. Across from the Café de la Gare on the corner nearest the book and music stalls that lined the quai, stood the famous restaurant Rouzier, the corrugated shutters of which were not raised until later in the day.
Midway down the rue de la Huchette, which was about three hundred yards long, the Bureau de Police was always open but never active. All night a sickly blue gas lamp marked its location; by day a cinder-stained tricolour flag drooped from its mast. The Café St. Michel, next door to the Café de la Gare, opened about five a.m. The proprietor had the tobacco concession for the neighbourhood, which brought in many customers and gave the place an air of prosperity. The odour of what the Third Republic called tobacco was purified, somewhat, by the slops and disinfectant used for cleaning the café.
While some of the early risers huddled around the counter to swallow their coffee, often spiked with cheap, watered rum or cognac, and to munch fresh crisp rolls, Eugénie, a pale, brown-eyed scrub-woman not yet forty, was on her knees beside her ill-smelling pail, faithfully scrubbing the back room floor in dimness. She wore drab grey, formless clothes which reeked of Eau de Javel; her breasts sagged; her hands and wrists were raw and red from the caustic; her feet were clad in worn felt slippers. When she was facing away from the crowd, and a little of her white leg showed, some gruff-voiced teamster or bargeman would joke about her _derrière_. One could not quite overlook it. Eugénie would turn her head and fling over her shoulder a gem of reproachful repartee. She slept in a sort of mop closet in the rear of the establishment, with the door bolted tightly, and while it was still dark she slunk over to the church of St. Séverin for an early morning prayer. After meal-times she ate of the leavings in the kitchen, when the cook and waiters had been fed. She had not had a day off in thirteen years, not since her mother had died of bronchitis and Eugénie had timorously left a more arduous job to take her deceased parent's place at the Café St. Michel.
Eugénie's chastity, her virginity in fact, was one of the matutinal subjects of conversation, a sort of perpetual challenge to the five-o'clock customers (male). It also served as a sort of springboard from which sly propositions could be launched towards the less virtuous customers (female). But the sharp-eyed Madame Trévise, the proprietress, who was every inch what the French called a _commerçante_ , or business woman, kept this daily ritual within bounds. There was practically nothing the men could or did not say to Eugénie, but none of them was ever permitted by Madame to lay his hand on her. The proprietress was not moved by moral considerations; she merely wanted to avoid the inconvenience of having a drudge who periodically became pregnant and had to be fired. So Madame Trévise added to Eugénie's native armour of fear and piety her matronly authority. Once a bashful country boy, much younger than Eugénie, tried to approach her and even went so far as to lie in wait for her in the church at dawn in order to escape the merciless tongues of the café customers. Eugénie ran a high fever and for the only time in her life had to spend two days in bed, so startled was she by the stammered proposition.
I first wandered into the rue de la Huchette in 1923, on a soft summer evening, and entirely by chance. It was possible then to do things without premeditation. An evening lay before me, so I merely dined and strolled. Granite lions and an empty fountain dozed by the ill-matched towers of St. Sulpice; men, women and children sat on kerbs and doorsteps of the rue des Ciseaux and grumbled as a stray taxi inconvenienced them. The broad leaves of the plane trees along the boulevard St. Germain were still, almost drooping. Activity seemed to have been gently suspended.
Avoiding the Deux Magots, I skirted along the old abbey of St. Germain and in the secluded place de Furstenburg, then the hideout of the budding group of Communists to whom no one – least of all, Moscow – paid the slightest attention, I paused in front of the old studio of Delacroix where a street lamp revealed a pencil drawing of a panther in the window.
In the place St. André des Arts I found myself staring with awe into a taxidermist's window. Like all the other citizens of France, the taxidermists of France were individualists. Even French mothballs seemed to have slight differences, one from the other. The taxidermist in the place St. André des Arts made a speciality of stuffing pet dogs and cats with which their owners could not bear to part. Monsieur Noël, the tall stuffer of birds and animals, whom I learned to know very well in later days, made them look, if not lifelike, decidedly unique. The bourgeois French called parrots 'Coco', cats 'Minou', small dogs 'Frou-frou' and police dogs 'Hanibal', or something corresponding. Monsieur Noël, before undertaking to skin the beasts, would try to divine their character. Since he had a mild class consciousness, the expressions on the faces of his masterpieces reflected something of M. Noël's sardonic philosophy. Noël pointed out to me once, over a bottle of Pouilly, that men and women, like gods, choose pets in their own image. My friend took sly delight in accentuating these resemblances.
On the corner, facing the boulevard St. Michel, was a pharmacy of the second class. That, as pharmacies went in France, was fairly high. A first-class pharmacy was an analytical and quantitative chemist's laboratory plus emergency clinic and dispensary of serums, prophylactics and specifics. The pharmacy in question was closed that evening, but on the front door was a placard explaining that another pharmacy, a couple of blocks distant, was open.
According to the law of February 4, 1896 – probably because on February 3rd of that same year some senator's wife had kept him awake with a toothache – pharmacists were obliged to take turns in handling night and holiday trade.
Among some very modern white enamel and red rubber accessories on display in the window in front of me, what caught my eye was a pair of crude mittens made of yellow cat's fur, with the fur side outside. Afterwards, when I got to know M. Noël well enough, I asked him about those incongruous articles.
'They are in no way exotic,' he said.
The very poor in Paris, naturally, do not keep cats. On the contrary, they frequently stalk them, feed them up in seclusion and eat them. The moderately poor (say, in the $250 to $300 a year bracket), if they have no children, sometimes permit themselves the extravagance of a pet; but when Minou dies, they do not have her stuffed. Instead, they skin her with a kitchen knife, salt down her hide and sell it for a small sum to a dealer in mittens. He, in turn, sells the finished product to drug stores. In winter those Parisians whose houses or rooms have no heating manage to keep warm by rubbing themselves with cat's fur.
Before the days of Police Commissioner Chiappe, there were no lanes studded with brass discs across the boulevards. Pedestrians simply ventured out and crossed in traffic as best they could. Experienced Parisians usually exercised a modicum of caution, but the provincial French had no background that equipped them to deal with the physics of scurrying taxis, lumbering buses and iconoclastic private cars, interspersed with market wagons drawn by stallions, old-fashioned fiacres, rubber-tyred bicycles and improvised delivery carts with three or more wheels.
In 1923 there were thousands of taxis, many of them driven by former cabmen who resented motors and used them with a minimum of mechanical consideration. Between the general public and the taximen a continual feud was carried on, with vehemence and sharp eloquence on both sides.
That first evening I was preceded into the traffic of the boul' Mich' by a dignified Frenchman from Mayenne, who wore an old-fashioned black felt hat and a string tie. A chauffeur jammed on his faulty brakes to avoid hitting the man, and the running board of the taxi barked his shins. Taxi No. 1 was promptly telescoped by another, which in turn was narrowly missed by a bus. If I quote him correctly, the taxi-driver called the incautious pedestrian a 'kind of harlot'. The Frenchman dispassionately reminded the chauffeur that the streets had belonged to the people since the fall of the Bastille. When a cop stepped reluctantly into the picture, glancing disgustedly at the traffic jam, the pedestrian calmly handed him his card. The _agent_ read it noncommittally and tucked it into his pocket.
_'Alors, toi!'_ ('Well! You!') the _agent_ said to the chauffeur.
The latter retorted at the top of his voice. It was thanks to his presence of mind, he said, that the 'type' with the string tie and card had not been annihilated and his family left disconsolate.
'Since the days of the Bastille...' began the party of the second part.
'That's a long time ago, Monsieur,' cackled a drunken old woman from the pavement.
It all ended with the _agent's_ escorting me and the professor from Mayenne to the opposite curb, in front of a reeking public _pissoir_. Then he waved majestically for traffic to proceed. As the taxi sped away, the _agent_ noticed that it had no tail-light. He blew his whistle furiously, to which the retreating chauffeur paid no attention. Unfortunately, several other drivers thought the whistle might be meant for them. They looked back, swerved, and one of them clipped the heavy market wagon, so that over the ensuing hubbub, the peasant on the wagon seat bellowed that his assailant was a _cochon_ and _voyou_ , or a 'pig' and a 'thug'.
I bowed to the professor from Mayenne, who lifted his hat in acknowledgment and then turned towards the _pissoir_ , unbuttoning his fly en route. In order to do this the Frenchman had to start about midway between his waist and his chin. In a land of passionate economy, the high trouser top was a baffling extravagance.
My meditations on style were cut short when, after proceeding along a narrow pavement, I heard and saw, respectively, the sharp, merry sound of an accordion and the dim silhouette of the most perfect small Gothic church in France, St. Séverin. All I can say is that as I stood there, seeing it outlined against the taller buildings of the street beyond, I breathed more freely.
No ambitious ornament intrudes as one stands before St. Séverin. The carvings of the arch at the entrance are integral parts of the whole; the gargoyles have less literary taint than those of Notre Dame. The little church does not dominate the scene but rests among secular buildings with modesty and restraint. I was to learn that, while in other localities the Church of Christ had wandered far afield, St. Séverin had remained truly the refuge and consolation of the poor. Its congregation consisted of workmen and their families, and its priests had no bank accounts, were never known to publish books, or to mix in politics. Three of them, I was to learn, played the neatest game of bridge I have yet encountered. At the end of each session they dropped my money into the poor box.
When I emerged from St. Séverin's candlelight and incense, having listened to Father Panarioux play the Bach B-minor fugue on the adequate little organ, I let myself be drawn across the street by the accordion band and into the Bal St. Séverin.
The waiter was at the bar, receiving from the proprietor a few drinks in glasses the size of thimbles. These he put on his tray and glanced towards me in response to a whispered admonition from his boss. Tray in hand, he guided me a distance of fifteen feet to a bench and table at the far corner of the crowded room, skirting the dancers, each couple of whom seemed to have achieved a sort of plastic unity. Someone had been occupying the table destined for me, as was evidenced by a handbag and an ashtray on the rim of which rested a cigarette butt that had been prudently extinguished with reference to the future. The waiter, still balancing his tray on which the tiny glasses were overflowing in an oily way, picked up the handbag with one hand and tossed it on the bench near another table. Then he said to me _'Voilà, monsieur_ ' and with unbelievable daintiness lifted the half-cigarette between thumb and forefinger and deposited it on the empty ashtray nearest the transferred handbag.
The only other occupant of the room who was not dancing, not counting the proprietor and waiter, was a young girl in a flame-coloured dress and nothing whatever underneath. She had large brown eyes with long curved lashes, a rosebud mouth with petulant corners, and bare legs, very shapely, the pallor of which was accentuated by black high-heeled shoes, size three and wide. As our glances crossed, she tilted her gaze towards the low mezzanine balcony where the three-piece orchestra played. The drummer nodded curtly.
When the orchestra struck up another tune the male customers rose indolently, blew cigarette smoke from the corners of their mouths, and let it be known with a minimum of ceremony that they chose to dance and with whom. The flame-coloured dress was left partnerless once more; so I stood up, glanced up at the drummer, and made my way to her corner.
'Would you care to dance?' I asked in American French.
'If monsieur wishes,' she replied, doubtfully.
I tried holding her circumspectly, but she did not seem at ease that way, and had difficulty in following. So I fitted our bodies together in the prevailing style, as best I could.
'What is your name?' I asked. Up came her long curved eyelashes, and she stared at me in surprise. It was not usual to talk while dancing.
'Suzanne,' she said, and that was the extent of the conversation. She was young, about seventeen I thought, and not muscular like a chambermaid or servant girl. Her high forehead and reddish-brown hair suggested Normandy. As we danced I learned that she used unscented Castile soap, that her hands and arms were cool while her torso was supple and warm.
_'Anglais, vous?'_ she asked, as if she were speaking to a child, when we were seated again. Marcel, the _garçon_ , without prompting, brought my unfinished _dégustation_ and placed it in front of me, resting on its saucer marked 2 fr. It was the 2 fr. label that got the first reaction from Suzanne. She raised her eyebrows and looked at my tie.
_'Anglais, ça?'_ she asked.
'What will you have?' I asked.
She ordered a cherry, which baffled me until Marcel brought her a neat brown one pickled in brandy. Then I tried to explain that I was not English but American. The task I had undertaken was not so easy as I had thought it would be. Suzanne had seen the sea once and had mistaken it for a continuation of the sky. That America was across the ocean meant nothing to her because she understood but dimly what an ocean was. Americans and Englishmen both spoke English. That was enough for her.
Having started dancing with Suzanne and buying her brandied cherries, it was pleasant to continue. The arrangement seemed to please the drummer and the proprietor, and had the sanction also of Marcel, the garçon, who was the real director of the establishment. The Bal St. Séverin was orderly in the extreme. There was no drunkenness, no open quarrels, and if the talk was loud between dances, it was uniformly so. The liquor wasn't bad. Although diluted, it was stimulating. I drank four or five fines, and each time Marcel laid another 2 fr. saucer on top of my modest stack, Suzanne began to show respect, if not alarm. Suspecting that she might be hungry, I suggested a sandwich. With a quick warning pressure of her cool little hand, which absentmindedly I seemed to be holding beneath the table, and a fearful glance towards the drummer, she whispered swiftly: 'Not here, Monsieur.'
I paid the bill, gave Marcel a generous tip and left the Bal St. Séverin. Once out on the pavement, Suzanne walked fearfully just ahead of me. There was not room for us to move abreast. To our right was St. Séverin. We saw the huge bulk of Notre Dame across the misty river. In the middle ground was the walled churchyard of St. Julien le Pauvre. Moorish music sounded faintly from the Hotel Rossignol – or Nightingale Hotel – which faced the exit from our street. Algerian and Moroccan rug peddlers convened there, and sometimes smuggled in a nautch dancer who performed by the hour.
_'Les Sidis!'_ Suzanne whispered, contemptuously. 'I should not like to sleep with them, as Renée does. Robert hasn't made me yet.'
Suzanne told me, later: 'Germaine is a droll one. She likes to have Robert try to break her arm – Not I. I don't like to be hurt.'
Suzanne was steering me at that moment into the rue de la Huchette. I don't know where she is today. It is difficult for me to think of her as thirty-five years old, and torn with suffering. I can only hope she has enough to eat and doesn't understand too much about current events. She led me to the Hôtel du Caveau, and for that I shall eternally thank her.
# _A Stairway down to Antiquity_
THE RUE DE LA HUCHETTE, in time and space, had a beginning, a middle and an ending. Centuries ago, when Paris was a walled city on the Ile de la Cité and cows were pastured in what is now the place St. Germain, some of the first Parisians to quit the fortified island area settled along the left bank of the Seine. The rue de la Huchette runs parallel to the river, just a few yards south of the quai. No one seems to be clear about the meaning of its name, least of all its modern inhabitants.
Most of the traffic moved through the little street in an easterly direction, entering from the place St. Michel. This consisted mainly of delivery wagons, make-shift vehicles propelled by pedaling boys, barrows of itinerant vendors, knife-grinders, umbrella menders, a herd of milch goats and the neighbourhood pedestrians. The residents could sit in doorways or on curbstones, stroll up and down the middle of the way, and use the street as a communal front yard, in daylight hours or in the evening, without risk of life or limb from careening taxis. In fact, at dawn and dusk, a pair of bats, never more nor less than two, zigzagged back and forth at the level of the second-story windowsills and, when confronted by noise and lights in the _place_ , or the rue des Deux Ponts, faltered, wheeled and started back again.
The two large corner cafés, Café St. Michel and the Brasserie Dalmatienne, belonged to the boulevard St. Michel. They were flanked by staid apartment buildings, four or five stories high, with attic dormers for chambermaids. Hard times, during and after World War I, had caused most of the families to dispense with servants, so the lofty undersized bedrooms, cut in odd irregular shapes by jutting roofs, skylights and rickety tile chimneys, were rented to impecunious tenants who lived alone, except possibly on Saturday or Sunday nights, and who liked a fairly good address at which to receive their mail.
The middle section of the street was cut, but not crossed, by two streets even smaller than the rue de la Huchette – the rue Zacharie and the rue du Chat Qui Pêche (street of the cat who fishes), so named because in the early days before the quai was built, a cat used to fish in the cellars when the Seine was high. He must have caught nearly all there were to catch, for although I have seen patient fishermen on Sundays and holidays lining the quai with well-rigged poles and tackle (including a straw fish basket with cover and green leaves inside, a lunch of bread, sausage and cheese, and a bottle of _pinard_ , or strong red wine) it was seldom if ever that a _goujon_ (or edible minnow) was landed. The rue du Chat Qui Pêche had the distinction of being the narrowest and shortest in the world, with only one window not more than a foot square and no doors at all.
On one corner of the rue du Chat Qui Pêche stood the Bureau de Police, not important enough to rate a police car. It was lucky to have a telephone. The _flics_ , or cops, used bicycles or patrolled soundlessly on foot, invariably in pairs.
Not oftener than twice a year a troublesome drunk, crazed with hunger and lack of sleep, would wander into the precinct from the slums to the east. If it proved impossible for the easy-going _agents_ to ignore him or chase him into another precinct, he (or she) was mauled and lectured mildly and locked in a damp granite cell, about six by six.
Once, however, in 1926, a small-time burglar tried to break into the grocery store at No. 31. When surprised by the even more astonished _agents_ , who unwittingly had popped around the corner, the marauder fired two shots at them, wounding one in the groin. He was kicked to death that night, on the cold stone floor of our little local station, and, with intestines steamingly exposed, was lugged under a cheap stiff blanket to the morgue behind Notre Dame. That ended the unfortunate affair. The Paris police, almost saintly as a rule in their gentleness and understanding, got tough only when their opponents made attempts on their lives.
_Le Panier Fleuri,_ the neighbourhood bordel run by Madame Mariette, was opposite the station house on the corner of the rue Zacharie. The south-east corner was occupied by a laundry which employed three hard-working girls and also served as a _clandestin_. That is to say, men who found it banal to patronize the orthodox establishment could, if they were known to Mme. Lanier, go upstairs with the laundress of their choice. This illegal arrangement increased the income of Mme. Lanier, her non-productive husband, and the girls, and, in the opinion of the easy-going sergeant, did no one any harm. Edouard Lanier, the husband, was a war veteran (Croix de Guerre with two palms), and because he was ' _gueule cassée_ ' (a soldier whose face had been disfigured), he was treated with indulgence.
The eastern end of the rue de la Huchette revolved around the Hôtel du Caveau. It was there Suzanne led me in search of a meal.
There I found Paris – and France.
When we entered the Caveau, by means of the door leading directly into the bar and restaurant, a dark-haired Greek woman, somewhat disheveled, was leaning on a marble-topped table stained with Dubonnet, and staring into space. Behind the bar stood a _garçon_ , with collarless white bosom shirt, the brass stud of which had stained his Adam's apple, and a slate-coloured apron that hung down to his knees. His twinkling blue eyes rested shrewdly on Suzanne, then noted my American felt hat and four-in-hand tie. His moustaches were sandy and red, with a spread from tip to tip of at least six inches. A glance at Georges could not fail to bring forth a merry smile. I soon learned that he was chronically cheerful – except about twice a month. Quite regularly each fortnight, after he had drunk Homerically, he tried to cut his throat, at which he was extremely clumsy. He always woke up the next morning and was shyly ashamed.
Georges was not a native Frenchman, but a Serb who had deserted the Austrian army and miraculously made his way to Paris. In 1917 he was picked up by the French authorities, who inducted him without further ceremony into the French army, where he proved to have a wonderful way with horses. After the war he had found a job in the Cirque d'Hiver. The Fratellini Brothers, princes of all clowns, were then the artistic directors. Georges cared for the semi-trained horses of the equestrian acts. He could do more with the troublesome beasts than their trainers, but one evening he found the Fratellinis' performance so excruciatingly funny that he forgot all else and stood, pail in hand, watching Albert, Paul and François go through their barbershop act. A long-legged roan with a Dutch disposition observed that Georges was off guard and kicked him half way across the ring. When Georges got out of the charity hospital, three months later, the Fratellinis were on tour in another country. So he loafed about for eighteen months and then became _garçon_ in the Hôtel du Caveau.
Suzanne did not choose a table in the small dining room, but led the way into an empty backroom, opened a small narrow door, and started descending a spiral stone stairway that smelled of antiquity. Below was a cool stone cellar with Roman and Byzantine arches. In Paris one soon learned that relics of all the centuries were shuffled together, if not scrambled. In the same block one would find Roman, Gothic, rococo, fake Greek, Byzantine, modern plaster shacks and bourgeois inadvertencies.
Suzanne found a light switch and turned it. The arches and pillars cast perfect shadows across a clean gravel floor of river pebbles.
_'Par ici, monsieur,'_ she said. She then led the way to another stone stairway, slightly wider than the first. This we descended hand in hand. Enough light leaked from above to reveal another arched hallway with a graveled narrow corridor ahead. The place appeared less likely to produce a sandwich than any I had seen in my life.
In the narrow corridor my guide found another light switch, and I saw at my immediate left what unquestionably had been a medieval dungeon cell in which wine was stored. That such a medieval cellar could belong to the dingy bar and dining room upstairs was hard to believe, but it proved to be a fact.
Facing us at the end of the corridor, beyond the dungeon wine cellar, was a massive studded-oak door spiked with large iron drift pins in impressive design. Suzanne lifted the heavy latch. As the heavy door swung outward, I saw that a light was burning inside, flickering like a taper. The least I expected when I looked into that sealed stone chamber was a Black Mass or hooded conspirators adjusting a torture rack. Instead, the two occupants of the subterranean vault turned out to be a fat middle-aged Frenchwoman and a medium-sized Turk, the latter in waiter's garb. In entering without knocking Suzanne and I had startled them, and both had half risen, the woman fearfully, the Turk guiltily, although between them was a huge magnificent oak table made of three-inch planks and seasoned by the centuries.
'Hello, mister,' said the Turk, in acquired American.
Suzanne looked at him, then at me.
_'Anglais, lui?'_ she asked. I had begun to expect it of her. The buxom woman, in a drab grey dress and wearing an old-fashioned crocheted shawl, sat down. She looked nervous and perpetually afraid. The Turk smiled reassuringly. He had identified the origin of hat and tie.
'Sit down,' he said, indicating the heavy oak benches that ran the length of the table on both sides. Suzanne thanked him with perfunctory politeness and sat next to the woman. I sat beside Suzanne. All three of us faced the Turk who resumed his place and leaned comfortably on his elbows.
'Good place,' he said, with a nod and gesture which included the raftered ceiling, the massive stone walls, the oak door, the ponderous table, the wavering taper in a wrought-iron holder and the gravel floor. 'One could make a lot of money here.'
As he made the last remark, he glanced meaningfully at the pale plump woman who drew her shawl tighter and shivered.
'You're cold,' I said to madame. 'Would you join us in a drink?'
'Me, I'm hungry,' said Suzanne.
The Turk excused himself and departed.
'Do you live here?' I asked madame, and when slowly it dawned on her that I had spoken a kind of French and that she had understood it, she rested her startled gaze on me and murmured, softly: _'Oui, monsieur.'_ It turned out that she owned the place, insofar as a married woman in France could own anything. It had been her dowry – stone dungeons, ancient arches and all.
When the Turk returned, with four glasses, a bottle containing _Marc de Bourgogne,_ a small carafe of red wine, a steaming generous portion of _ragoût_ and a large chunk of bread for Suzanne, I learned that he had worked in Athens, Genoa, Barcelona, Ceuta, London, France, and America.
'Where in America?'
'Boston, Mass.,' he said. 'Do you know Coco?'
I did know Coco. We reminded each other what a fine man Coco was. He ran the Ararat on Kneeland Street.
While the Turk and I chatted in American, the two women, aged 42 and 17, respectively, looked on with polite relief, the former sipping dutifully at the fiery liqueur and the latter doing justice without mercy to the excellent lamb stew. It was easier for them not to understand American than to understand Turkish or American French with effort. The _marc_ was undiluted – stupendous, in fact. As soon as my glass was empty the Turk filled it from the bottle near at hand. Meanwhile he talked and drank sparingly but with relish. It seemed that Madame's name was Philomèle, at each mention of which she looked startled and tried to smile. Her husband, the Turk told me, was no good. He was trying to steal the hotel away from Philomèle but the property could not be sold or divided without her consent. The husband had tried beating her but her skin was white and thin and bruised very easily, and she had cried all the time for a while. This caused the customers to complain.
Philomèle, by that time, had divined that we were talking about her, and grew so restive that the Turk assured her that I was an educated man and could be trusted. That caused her to relax a little.
Suzanne had eaten the stew, a huge dish of string beans cooked with bacon in North country style, about four hundred calories of French fried potatoes, a salad of chicory with oil and vinegar, a large loaf of bread, and was starting in on a soft slab of Brie. She ate so heartily that my own appetite was aroused. I ordered a double portion of the cheese and, curious to know whether that wine cellar was as good as it appeared to be from outside the grill, was escorted there by Madame Philomèle, who opened the medieval padlock with a hefty key she kept on a ring slung from her waist. While I was reading labels, observing dust on bottles and expressing my sincere admiration, we heard heavy footsteps on the gravel and Philomèle in a panic extinguished the light, clutched my arm, began to tremble and silently to pray.
The head of her husband, whose face and unkempt hair seemed to fit the Turk's unflattering description of him, lurched past the grilled Judas window. The man was very drunk, had an ugly look, and muttered threats as he proceeded towards the council chamber. When he entered he saw, not his cringing wife and the imaginary lover he had always sworn to catch _in flagrante delicto,_ but his swarthy waiter and a strange girl in a flame-coloured gown. She was on his side of the bench, so he made a grab for her. Suzanne made no resistance, but in her woman's way tried to pacify him and make him feel at home. The Turk, always the diplomat, did nothing to discourage this budding friendship, but tactfully faded from the scene leaving the bottle of _marc_ about half full.
Meanwhile Philomèle and I had tiptoed away from the danger zone. When her head appeared through an iron trap-doorway behind the bar, the friendly Georges smiled with such sincere relief and pleasure that wrinkles appeared on his forehead and his luxurious mustache wagged up and then down. An instant later, when my head followed Madame's felt-slippered feet, Georges not only smiled but beamed, and his knowing blue eyes rested not on my necktie, but looked straight into mine with mischievous congratulation. He had expected Madame Philomèle to be tearful and bruised.
Madame, without stopping to say farewell to me, moved swiftly towards the hallway. I was sure she did not intend for me to follow.
'Have a drink,' I said to Georges, whose beatific smile rewarded me. Under its spell I could find no reason for leaving that eventful small hotel. In fact, I had my meagre effects transferred the next day from the St. Sulpice quarter and was a guest at the Hôtel du Caveau, if 'guest' is not too distant and formal a term, off and on for eighteen years.
That first evening I was not in the mood for drinking alone, so I paused tentatively by the small table where the Greek woman with the luminous dark eyes was still staring into space. Slowly my American necktie found its way into her clouded consciousness. Mary drew from somewhere inside her waist a dog-eared American passport of a model no longer in vogue, together with some old snapshots and a sheaf of official papers, letters and several certificates from the Paris Mont-de-Piété, or municipal pawnshop. She had the illusion that she remembered her English, but after a few brief exchanges we both lapsed into such French as we could command. Hers was the more unacademic, since she persisted in using the letter 'G' for 'H' (which does not exist in the Greek alphabet) so that words like 'hospital' came out 'gopital', a harmless switch to which I rapidly grew accustomed.
When Mary first had come to the hotel almost any of the denizens would listen to her story, but, for a long time preceding my first appearance there she had not had a chance to unburden her troubled mind. She accepted another Dubonnet and quite pitifully smiled.
Mary's misfortunes and hardships had worked havoc with her wardrobe and had weakened her resistance to Dubonnet. It had not destroyed the almost celestial beauty of her face, which would have served as model for any painter in need of an olive-skinned Madonna, nor had it ruined her mature and memorable figure. As best I could gather, Mary had been brought up in Athens in comparatively easy circumstances. After an exchange of photos she had been sent for by a naturalized Greek fruit-dealer of Detroit to be his bride. In Detroit he had welcomed her gallantly and she had been a dutiful and faithful wife. The fruit business flourished, and two sons were born. Then an Irish girl in a hotel barbershop had attracted the husband's attention, and Mary had been sent back to Europe for a visit to her folks, via Le Havre and Paris. Her husband had escorted her as far as New York, seen her aboard with tenderness, had given her her passage as far as Paris and had assured her that additional funds for her journey to Greece (and return to America) would be waiting for her in a Paris bank. The two children had remained with him.
When the funds failed to materialize, the disinterestedness of the French officials in Mary's case was equalled only by that of the employees of the American Consulate in Paris. In some ingenious manner, symbolized but not fully described by the legal papers she carried, Mary found herself divorced, and learned that her two children belonged to the father, who had married the Irish manicure girl. Mary had subsisted in Paris while haunting government offices until she was forbidden entrance and threatened with arrest, by pawning her jewelry, now symbolized by the out-of-date pawn tickets to which she tenaciously clung. Her parents in Athens, unable to rescue her, had died and were now represented by some tear-stained letters, indicating that the distant ex-husband had led them to believe that Mary had wantonly deserted him after misbehaving with icemen, letter carriers and casual passers-by.
That Mary had suffered intensely and was in a grave international plight (having no work card or even a prostitute's yellow license) was all too apparent. Also it was plain that she looked to me, as an American of heart and education, to do something about it. I was feeling inadequate and useless in the extreme when an incident on the pavement, quite clearly visible through the hotel windows, attracted my eye, as well as the amused attention of Georges, the _garçon_.
An angry well-dressed Frenchman about fifty years of age, who looked out of place on the rue de la Huchette, was pummeling with his folded umbrella a young man who bore him a strong family resemblance. The recipient of the informal 'correction' was taller than his father, equally well dressed (in the French manner) and, although offering no physical resistance, was unyielding to the point that he broke away from the grasp of his indignant parent and entered our hotel. His father did not follow.
The young man (whose name was Pierre Vautier) had a sensitive, not quite effeminate face, and an erect military bearing. It turned out that, in defiance of his father, he had, some time before, quit the army engineering school of St. Cyr, to which only young men of high family and church influence had access, in order to enter the employ of an art gallery on the near-by rue de Seine. It was a small gallery that specialized in ultra-modern paintings of the neo-Cubistic school, the sight or mention of which had, on many occasions, nearly proven disastrous to the father's brittle arteries. Vautier the Elder's aversion to the gallery and its wares had been heightened by the indisputable fact that practically all of the other employees, the owner, most of the artists whose work was on display, and four-fifths of the customers were homosexual.
# _The Women in Black Who Moved in Pairs_
HORTENSE BERTHELOT, when I first met her, was an inconspicuous middle-aged woman who worked in the enormous prefecture, one of the tens of thousands who, because of widowhood or bereavement in World War I, were allowed, for very small pay, to sit at shabby desks, stand behind grilled windows or splintered counters, and in a sort of perpetual twilight, write words with bent stubpens and violet ink (thick with dust and sometimes dead gnats) on government forms which had been printed in such a way that there was never enough space in which to provide answers to ambiguous questions. One cannot exaggerate the inefficiency of a French public office, especially those to which members of the public were forced, all too often, to present themselves for heckling and abuse.
Methods of clerical work in twentieth-century France would not have been tolerated in America in the earliest colonial days, and surely not before then by the Indians.
It was easy to pass by Madame Berthelot without noticing her. In her long years of public service, she had practised being inconspicuous. Her eyes were soft and brown, her face lined and appealing. She spoke, infrequently, in a low-pitched voice that placed her instantly as a lady of quality who had lost none of it in descending the ladder of fortune. One did not notice at first that she must have been a wistfully beautiful girl in her twenties. Her shoulders were narrow, her hands were eloquent, but thin. Her clothes were colourless, out of date in style, and never had been coquettishly chosen. Only her gloves and shoes had style and distinction. She bought her gloves, she told me, in the Magasin du Louvre, where she knew a woman who had worked with her in the World War. This friend was able to sequester from the large department-store stock 'seconds' which had no detectable imperfections.
'Ah! You worked in the war?' I asked. I was surprised, having assumed from her manner that she had been sheltered until after that epoch.
'The last two years,' she said, without bitterness.
We were lunching together in the Hôtel du Caveau, the day after my arrival. Already I had a strong desire to know everyone in the quarter. Our conversation was interrupted in the salad course (of celery root Lyonnaise) by the sullen entry into the bar and restaurant of the pimp, Robert, of the Bal St. Séverin.
Georges, the _garçon_ , was serving drinks to a couple of officials and an oyster vendor from the Café de la Gare. Robert's small eyes were rimmed with red from anger and apple-jack, his face was pastier than it had looked by lamplight, his pinch-back coat was tighter, his purple scarf of a more poisonous shade, his cap at a more aggressive angle. The pimp, reptilian at best, was at his worst in the light of noonday. Georges, who knew what was the matter and was smiling behind his pale blue eyes, looked as non-committal and innocent behind the bar as a porcelain bust on an upright piano.
'What will you have?' Georges asked.
_'Il est méchant, le numéro'_ (He's a bad one, that fellow), whispered Madame Berthelot.
At that time I did not know with what exactness Hortense spoke French, and did not realize that for her to call a man a ' _numéro_ ' was equivalent to what three women who peddle fish in Marseilles would have meant after screaming all the words in the argot. A ' _numéro_ ' (number), in Mme. Berthelot's exquisite vocabulary, was one degree lower than a ' _type_ ', but less severe than ' _individu_ ' or 'individual'. A ' _type_ ' implies that the person to whom the word is applied is of little consequence. A ' _numéro_ ' may be a chap who is dangerous and antisocial, or a droll fellow or Merry Andrew who can be counted on for harmless fun. But a woman with the regard Mme. Berthelot had for the spoken word would not apply the epithet ' _individu_ ' to anyone less villainous than Landru.
The wide gulf between French slang and Academy French was not as confusing as it might have been, due to the fact that a Frenchman ordinarily stuck to one system of expression or the other. Some baffling French _argot_ resulted from nouns made up of pure sounds and having no linguistic roots whatever. Other stumbling blocks to the French of the streets involved the use of the names of certain objects to indicate other objects which had names of their own. For instance, a cooker was called a 'piano' and a _bidet_ , a 'violin'.
In the year 1923, the 'immortals' or members of the French Academy had progressed as far as the letter 'm' in their revision of the official French dictionary, and, at the moment the pimp, Robert, was leaning vindictively on the bar at No. 5 rue de la Huchette, the savants a few blocks west were arguing as to whether the word 'mimosa' was masculine or feminine. In the former event, it would be called ' _le_ mimosa', and in the latter ' _la_ mimosa'. Madame Berthelot was of the last-named faction. ' _la_ mimosa' to her delicate ear sounded more euphonious than ' _le_ mimosa'. Pierre Loti, Hortense said, used ' _la_ mimosa'. That clinched it for me.
With his mind on Suzanne in a sadistic way, Robert, _le mecque_ or 'mackerel', ignored George's question, 'What will you have?' and simply snarled:
'Where is that girl?'
Had I not noticed Claude, the proprietor, lurching upstairs the night before, with Suzanne in tow, or rather one step ahead, I should have believed Georges' profession of ignorance myself. Georges liked to be believed, and almost always I humoured him, making it easy for him to tell me about the minor misfortunes that forced him to ask for the loan of a couple of francs (5 cents) now and then. Robert, evil eyes gleaming, started for the stairway leading to the rooms upstairs, in one of which, no doubt, was sprawled the drunken patron and Suzanne. Madame Philomèle, it developed, had not had access to her conjugal bedroom that night but had been obliged to weep in another and smaller chamber.
Before Robert had reached the doorway, Georges, with twice the distance to travel, was suddenly in front of him, still smiling, moustaches waving up, then down. With the utmost precision he took hold of Robert's pointed nose, which he twisted, clockwise, about forty degrees. He was still smiling.
Robert, as he backed through the door to the sidewalk, uttered threats to both Georges and Suzanne. I have never seen a Serb less worried.
The bloodless incident put Mme. Berthelot in a sunny humour. She was always gentle and accommodating, but seldom looked otherwise than sad. As the salad course progressed and cheese was forthcoming (a Port Salut that increased my respect for the fat cook who did the daily marketing), Hortense told me about her World War job with her friend who now sold gloves in the Magasin du Louvre.
It seemed that the families of Frenchmen who died in the service of their country (when they had one) had in past years been notified by mail, telegraph or telephone. This had proved to be uneconomical. Little or nothing was accomplished, in homes, shops, cafés or factories, within an hour or more of the moment when the postman was due to heave into sight at the corner of a street. Every woman, also every old man and young child, had dear ones at some front (1914-1918), and the more nervous and less resistant among them frequently fainted or had fits of hysteria while watching the snail-like progress of the postman from door to door. There were, in those days, certain grey-blue postcards that meant someone had been wounded or missing, and some black-rimmed white ones that spelled stark death. The women at the far end of streets would, if they saw that the postman's pouch contained no black-rimmed messages, wave and sometimes cheer with an edge of fear diminishing in their voices, and up and down the street the watchers would relax. Very often no such reassurance was forthcoming, and everyone had to wait, breath caught, nerves throbbing, until someone let out a shriek, or turned wordlessly away or dropped in her tracks and the postman wiped a tear from his eye with the back of his hand before continuing.
So the _Gouvernement français_ , which had its soft as well as inept moments, in late 1916 hired tactful well-bred women who had friends in high office and needed a job to break the news in person to the nearest relatives in case a soldier was killed in action. These harbingers of sorrow were carefully chosen, and the qualifications were severe. They must present a dignified appearance, and neither be attractive enough to take men's thoughts away from grief nor ugly enough to scare the stricken children. They must have a smattering of practical nursing, in case the recipients of their tidings collapsed, and must be reasonably agile in cases of _folie furieuse_ , or fits of grief-inspired madness. These women dressed in heavy mourning, spoke softly and always went forth in pairs.
Thus, trudging from house to house, making a quota of six calls a days, Hortense Berthelot had spent the last two years of the war, after her husband, a captain in the artillery, had been killed by a truck he had tried to crank while still in gear, in the heroic defence of Verdun. When she was no longer needed in the 'archives' department, which supervised the 'women in black', she, being a second cousin by marriage of a petty official called 'The Navet' (turnip), was given a job, at lower wages (about $26.50 a month) in the passport department of the prefecture. There she had worked five years without once losing her head, when those about her were fairly bouncing theirs from wall to wall and blaming it on the nearest foreigner who chanced to have asked for something he was forced by law to have and could seldom obtain.
In order to reach her room at our hotel, Hortense had to walk up four steep and narrow flights of stairs, but she had moved there from the second floor in order to be out of hearing each night late, when Claude settled accounts with Philomèle. Mme. Berthelot got little exercise, having neither time nor means nor energy, and if she was awakened between one and three each morning by sounds or thuds, entreaties, sobs and curses, it made her eyes ache the next day after hours of squinting in the dingy misplaced prefectorial light and trying to make out the illegible scrawls of all nations. The first two years in the passport department, Madame Berthelot had had the toughest job: that of interviewing foreigners the first time in. But The Navet, after culling evidence of a particularly rare pastime to which one of his chiefs was addicted, got Hortense transferred to the desk where renewals of permission to stay in France were sometimes granted, after months or years of delay, with a rubber stamp.
The fundamental cause of Mme. Berthelot's promotion (without increase of pay) was a unique establishment on the Ile St. Louis, namely, the only house of ill-fame in the world whose 'girls' were all more than seventy years old. There were men all over Europe who doted on the grandmotherly type. The Navet's immediate chief, a third secretary of a cabinet minister, was one of the regulars at the aforementioned semi-public institution. How The Navet found out about this, Mme. Berthelot did not say, but she willingly admitted that she owed her advancement to his confidential information.
About one o'clock, just before Mme. Berthelot had to rise, shake hands, put on her gloves and walk, hurriedly but with dignity, across the bridge and along the avenue de la Justice to the prefecture, the door from the hotel stairway was pushed gently open and Mary, the badly hyphenated Greek, stepped in. She was followed by young Pierre Vautier, the St. Cyr alumnus, who was adjusting his necktie in a touchingly self-satisfied way. Mary was wearing, not the seamy and shiny blue-serge skirt of her heyday in Detroit, but a new one, more in style, which her hands touched fondly.
The evening before, when I had seen at a glance that, in mysterious ways known only to God, the abandoned Greek wife and disinherited French prodigal had some affinity, I had withdrawn from Mary's table to the bar, to further my acquaintance with Georges.
Pierre, it seemed, had slept with his mother from the time of his birth up to his entry, at the age of 19, into the exclusive army school of St. Cyr. In order to give the lie to the premature and bitter accusation of homosexuality his father had showered on him, between strokes of the umbrella, the lad had made up his mind to take a mistress, publicly. Having seen Mary so forlorn and unattached, he had acted without delay. They made a touching couple, because Mary, unselfish in the extreme, was able to put aside her own troubles (set forth in numerous documents retained) and turned her ready sympathy to the handsome young boy. So when the Turk brought their lunch from the kitchen, Mary inspected carefully the two portions of _boeuf bordelais_ , decided that the one that had been placed in front of her was the more attractive and nourishing and deftly exchanged plates with Pierre, who smiled fondly and made no objection.
Both Mary and Pierre were absolutely broke, having bought the new skirt, but The Navet, who entered the hotel bar at least twice a day in order to set the folks right about national affairs, had whispered to Madame Philomèle that Vautier, père, notwithstanding his impetuous nature, would never let the family name be tainted with small debts. Thus the lovers enjoyed credit and had no pressing need of cash. On my way to the kitchen, where I intended to compliment the fat drunken cook on the quality of the menu she had prepared, I paused briefly to give the pair my blessing, which was disguised by the conventional _'bonjour', 'bon appétit', 'Comment allez-vous, madame et monsieur'_ and _'à tout à l'heure'_. Pierre politely asked me to sit down, to which I replied that I would do so a little later. Such rituals as these were spoken with warmth, in inverse proportion to the likelihood of their fulfillment. The celebrated _politesse française_ had nuances and ramifications equal to any and all occasions, and enabled one, if used with skill, to keep just the right distance and leave things unsaid which could be implied, while employing euphonious sound effects that did much to enhance the charm of everyday intercourse.
The cook, Thérèse, was a ' _numéro_ ' in all senses of the word. Armed with a butcher knife and fortified with three litres of strong red wine (her daily consumption was about five), she could be as dangerous as a truckload of scoundrels like Robert. On the other hand, when rubbed the right way, she could be infinitely more amusing than the Deputies in the Chamber and fifty times more loyal. Luckily, I was admitted at once into her small circle of friends and confidants.
This vigorous woman, who weighed about 250 pounds, was harder than nails, and had to splice with rope the largest apron strings she could buy in a bazaar, had endeared herself to the wags of the quarter by having served The Navet stuffed cat ( _chat farci_ ) just after he had tried to tell her how ' _oeufs au vin_ ' or 'eggs in wine' were prepared on Sunday mornings in the Haute Marne, Thérèse's native province. That The Navet was from the Midi and had never seen the Haute Marne (up near the Vosges mountains) did not deter him. The Navet was like that. He had not been told about the cat he had eaten until a week later, his informant being the oyster and chestnut vendor from the Loire and the Café de la Gare, the provocation being that The Navet had insisted that the oyster man, who loved to sing and had a lusty natural voice, had garbled the words of one of the marvellous songs of the fertile Loire region. Between the oyster man and The Navet a feud had long smouldered. When it finally broke out, The Navet spent hours in his office, and with his underlings searched books of laws and old ordinances in order to find a statute that could be invoked against the oyster man's way of gaining his livelihood. The oyster man, less vengeful, held up his end by roaring louder than The Navet could talk and expressing political and social opinions that would often destroy The Navet's appetite and inflame him into abusing his deaf wife, Jeanne, and their son, Eugène.
It is related by Rabelais how Panurge, in calling on Herr Trippa, the fortune teller, for information concerning the future, stumbled over Herr Trippa's wife and a page on the narrow stone stairway. Panurge, the reader will remember, had some doubts about the ability of a fortune teller who professed to know the secrets of the future and was the only man in the neighbourhood unaware that he was being cuckolded at lease thrice daily. In an analogous way, the inhabitants of the rue de la Huchette distrusted the pronouncements of the voluble Navet and relished with glee the local intrigue between his sweet and patient wife, Jeanne, and a champion of social reform from Dijon.
Even to a greater extent than Georges, Thérèse, the cook, was responsible for the solvency of the hotel under the management of the ineffectual Philomèle. And if anyone did not know about Thérèse's triumph over The Navet, or thought she had gone too far, he or she approved _in toto_ the cook's contempt for Claude, the _patron_ , her refusal to take orders from him or even to allow him to enter the kitchen, and her physical defence, on one occasion, of Philomèle when the latter was being kicked below the belt of a Saturday night. Thérèse's code was 'an eye for an eye', and the result of her interference was salutary in the extreme, for when Claude had appealed to the police sergeant on the corner, three days later when he was able to walk that far, the officer told him that he had caused enough trouble in the precinct already and then threatened to lock him in either the cell or the toilet of the station (there was little choice between them) if he opened his _margoulette_ (trap) again.
I must make it clear that mingling in affairs between husband and wife was not the custom in Republican France. My friend, and fellow-labourer in the vineyard of various arts, Wolfe Kaufman, learned an early lesson in that respect in his first month in Paris. Traversing the place St. Sulpice he saw a motorman in heated conversation with a woman conductor. When the motorman kicked the dame resoundingly in the buttock, Wolfe, mild by nature and fresh from America, automatically became Sir Galahad. Instead of taking a sock at Wolfe, the motorman assumed an expression of injured innocence and dignity and began enumerating in a pained dispassionate way the long list of provocations the woman, his lawful wife, had given him before, patient law-abiding man that he was, he had yielded to an irresistible and justifiable impulse. The gathering crowd, always judicious as well as curious in Paris, in this instance including two policemen and one official from the near-by _mairie_ , nodded in approval as point after point was made by the first speaker, the motorman. At the conclusion of the opening argument, the onlookers turned to Wolfe to hear his rebuttal. All he could do was to look around for the woman and try to decide whether or not to kick her himself. Having decided against any physical demonstration, he did the handsome thing and apologized, inviting the motorman and the most promising members of the crowd to join him in a drink at a near-by bar. Thus the incident, which at first had threatened Franco-American amity (just then very much talked about, since Poincaré wanted Harding's support against England for his seizure of the Ruhr), ended up by cementing the traditional friendship personified by Lafayette.
# _Of Public Opinion_
ONE OF THE COLOURFUL TOUCHES among the shop windows of the rue de la Huchette was the yarn shop of Madame 'Absalom'. Ranged in coverless pasteboard boxes, her wares ran the gamut of commercial dyes, from the most vibrant orange through vermilions, carmines, emerald, turquoise, ultramarine and gamboge to the assortment of sickly pale pinks and watery blues that mothers buy for infants. The crotchety old woman, who had been left the shop by an aunt she had detested, scorned knitting as a waste of time and disliked needlework to the point that she would not mend her cotton stockings. No one called her anything but Absalom, except a few other old women who tottered from the suburbs, now and then, to quarrel with her on minor matters, exchange kisses on leathery cheeks and depart. To them she was Lucie.
Madame Absalom was thus nicknamed because of her hair, which was salt-and-pepper grey and wiry, and which, when it was not tied up with a black corset string in a knot on the back of her head, reached down to her prominent collar bones. She had been married once, about twenty five years before (she married late) to a pharmacist of the second class (not the one on the boulevard St. Michel near by), and when I first knew her she was scanning avidly the local newspapers from Clermont-Ferrand in gleeful anticipation of the demise of her 'ex', as she called him spitefully, who had become a fairly important man in Clermont and was suffering from rheumatism, combined with a tic that spasmodically distorted the left side of his face. I never saw the 'ex' himself, but Madame Absalom was a good mimic.
She was always reading newspapers and drying her bristling hair in a patch of sun that slashed one side of her little shop. Her views about French politicians and the prospect of a reformation of the German national character which might bring about a harmonious and peaceful Europe seemed to me, in the middle 1920s, to be pessimistic in the extreme.
Madame Absalom insisted each day, after reading all the Paris papers, that nothing could be done to improve matters or prevent them from getting worse. The French politicians were scoundrels with their hands in the till; the employers blood-suckers; the employees, ruffians; the peasants, thick-headed fools who were 'good for nothing but work'. Germany couldn't pay. And if Germans starved, what of it? Plenty of Frenchmen had been gassed and shot on their account. France was bankrupt and couldn't pay America. So what was the use of talking about it, and wasting money sending 'commissions' for a joy-ride?
As Madame Absalom orated amidst her multi-hued wools and small cabinets of cotton threads on spools, there appeared twice weekly from an apartment in No. 32 (the building in which The Navet also lived) a dainty girl of six, most carefully dressed, well-mannered and self-possessed, and pushing in a small rattan carriage a doll which looked like her. Her name was Hyacinthe Goujon, and her large round eyes glanced at me appraisingly before she extended her hand and smiled. First she had bowed to Madame Absalom with the courtesy due her in the capacity of hostess and the condescension her status as tradeswoman justified. I, being a foreigner, did not come into any category little Hyacinthe had learned to recognize. The fact that I did not work in the afternoon indicated that I was not a business or professional man. My clothes seemed to her inelegant, my French more so.
'It would be disturbing to marry a foreigner,' Hyacinthe remarked to Madame Absalom after I had gone. 'One wouldn't know how to behave in his country, and he wouldn't be at home in France.' The old woman replied that it was better than marrying a second-class pharmacist.
Hyacinthe, aged six, had a tiny box of face powder and a small stick of rouge, chose her own perfume, had quite astonishing ideas about her clothes and those of other 'women', and told me, without a flicker of her violet-blue eyes or a vulgar inflection of her well-trained voice, that she remained with Madame Absalom on Tuesday and Friday afternoons because her mother, Madame Goujon, entertained her 'lover' on those days.
'He's married, but, distinguished,' Hyacinthe said. Around Hyacinthe's neck hung an ornate cross. Its duplicate, slightly smaller, was around the doll's neck. The forms of religious observance were important to the child, but she would not have thought of entering St. Séverin, which was for the _canaille_ or rabble. Instead, she was taken by her mother, also devout, to the Madeleine by bus. Hyacinthe would have preferred a _voiture_ or taxi but understood that, on a small income, one must be careful and not wasteful, in common with some of the best names in France.
'Fewer people who matter attend vespers,' she told me, on returning from church one Sunday evening, when from the pont St. Michel, one could see reflections of the sunset, between historic bridges, in dove colours shot with carnation and ripples of molten gold, all the way from the Jardin des Plantes with its roaring beasts at feeding time, past the pont du Louvre, the pont du Carrousel, the pont Royal, to the Trocadéro overlooking the Champ de Mars, where little Hyacinthe loved to go, pay her small fee for a metal chair, and sit along the bridle path to see the handsome army officers ride by on mettled and well-bred horses.
Hyacinthe, of course, would not have been permitted to sit in a park alone, had Madame Goujon known about it. But the cousin (male) to whom the little girl was entrusted had a passion for a card game named _belotte_ and knew some cronies in the Gros Cailloux quarter. So he took a chance that nothing would happen to Hyacinthe, and nothing did. Defective as it was, this arrangement was better than those of families who sent their young children to the Luxembourg Gardens with servant girls. In that quarter, an enterprising public dance hall had installed a check-room into which children were herded for small fees paid by nurse girls, who danced with pinch-backed and scarved young men all afternoon, then collected their babies and returned home.
Little Hyacinthe never noticed the grooms along the bridle path. The man she could love, if the families could agree and his parents would accept her on account of her looks and distinction, without a large dowry, was a captain, tall, a good horseman, soft-spoken but accustomed to being obeyed, with dark blue eyes, a good forehead, slender shoulders, and a black moustache. Hyacinthe, very tactfully, had bribed the old woman who rented the chairs in the park, to find out the officer's name, and the sound of it had thrilled the little girl, and confirmed her sure instincts. It was Costa de la Montaigne who, when the time arrived, would again use the title of Count his fathers had possessed.
Madame Goujon, the mother of this precocious girl, had one lodger who rented a small room off the hallway, next to the salon in her apartment. In the rear of this she had installed what she and the neighbourhood plumbers believed to be a bathroom, the only one with running hot water in the rue de la Huchette. The tub was enormous and had been smeared with boat paint a shade of grey that suggested wet clay. It stood on four legs like the feet of the fabulous firebird. These legs were equal in length, but the floor boards were uneven, so that the tub, when one stepped in it, rocked from side to side like a cradle. The gas heater had been purchased second-hand by Madame Goujon at the Flea Market.
The tenant of this room and bath was a floor-walker from the Samaritaine, the only building in Paris ever ugly enough to be razed on aesthetic grounds by the public authorities. Monsieur Panaché was a pale severe man about twenty-eight years old, fussy and disagreeable, thoroughly hated by the girls who worked under him, and tolerated by his superiors because he was able to drive his inferiors with relentless meanness. Once when Hyacinthe caught him using one of the Goujon towels to rub dust from his shoes she made him pay and told him that if he wished to do that sort of thing he should move three doors down the street, to the Hôtel Normandie. Panaché detested Madame Goujon from the top of her authentic bosom to her thick ankles and bunioned feet. Madame blushed easily when annoyed, not that she was ever embarrassed. The floorwalker kept the blood surging up to Madame Goujon's face with his daily remarks about the bathroom for which he paid an extra fifty francs a month. Panaché had been goaded to this extravagance because the superintendent at the Samaritaine had complained that he stank.
The day it was installed, Panaché had filled the tub. When he got in, the water flooded the floor and seeped through to The Navet's ceiling below, which brought an argument that was historic in the street, having been overheard by Marie, Madame Goujon's deaf _bonne à tout faire,_ or maid servant. The result was a cash settlement amounting to two dollars ten cents, which Madame Goujon got back by scrimping on the daily lunches she served a lawyer-clerk from the Palais de Justice who could not digest restaurant food. Then Panaché insisted that the gas heater was dangerous and refused to light it himself. Madame Goujon tried to demonstrate that it was not, and the resulting explosion burned off her eyebrows and some of her frizzled hair, which made the floor-walker so happy that he failed that same afternoon to discharge a new girl at the store who dropped a French fountain pen on the floor while showing it to a customer.
In World War I, Anne Goujon had served as a voluntary nurse in a base hospital, up to the day when, turning the pages of a surgical textbook for a young intern in the act of performing an emergency operation he had never seen or attempted, she had turned two pages instead of one, so that the patient, a private of infantry (Croix de Guerre, one palm) had been given the first half of one operation and the second or final phase of another. That he lived was a tribute to the hardihood of the good French stock in the Ain.
Anne's father, 'the Judge' and the doting grandfather of little Hyacinthe, used to taxi to the rue de la Huchette from the avenue de la Bourdonnais. He was seventy years old, wore a pointed white beard and spoke as if he were St. Francis addressing the birds: that is to say, very softly and kindly but not expecting much in the way of rebuttal from the congregation. Honoré François René Martin Lenoir was the way he was described on his birth record. 'Lenoir' was the way he signed his name – not even deigning to prefix an initial. He had resigned his judgeship in order to better himself, and also in protest of the official separation of the Church and State, when the now buxom Anne was about twelve years old. Nevertheless, she seldom referred to him, except to his face, as 'papa' but always called him proudly 'the judge'.
When the Judge came to the rue de la Huchette, his taxi entering from the place St. Michel, veered over to the wrong side of the street, since he always chose either Tuesday or Thursday and these days were among those the municipality of Paris had set aside for parking on the lefthand side of the street. In order to give even breaks to shopkeepers and cafés on both sides of the city street, the municipal government had decreed that on Monday, Wednesday, Friday and Sunday, one should park on the right-hand side, and on Tuesday, Thursday and Saturday, the left. This was one of the few things the police were strict about. A friend of mine was stopped by the same cop on the same bridge six nights running, at about the same hour, and advised to turn on his headlights, but had he once parked on the right on Monday he would have been haled before the local commissar of police, and official documents would have started to accumulate. In those carefree years, only two other local ordinances were enforced according to the letter. A prostitute was not permitted to stand under a street lamp, and sisters were not allowed to work in the same _lupanar_.
Often The Navet would leave his office early and slyly on the chance of encountering the Judge. When the Judge entered the dimness of the hallway, being watched with furtive pride by the sharp-eyed concierge, The Navet would step out from some dark corner, raise his black derby hat and say obsequiously:
_'Bonjour, monsieur le juge!'_
If the Judge were thrown off his reverie by this, paused to exchange a few polite and guarded remarks, or on rare days extended his hand, and if only a few of the passers-by witnessed this mark of The Navet's distinction, the latter would consider his risky exit from his post of duty well hazarded. The Navet would have liked to have a few persons think that the Judge called at that address to see him. He never offered the Judge his arm to aid him while ascending the steep stairway because he had done so once, seven years before, when the Judge was only sixty-four, and the old man seemed to have resented the inference that he was infirm.
This was the extent of the association between The Navet and the Judge, but around the prefecture and in the bar of the Hôtel du Caveau, The Navet spoke of his old friend, Judge Lenoir, and quoted the old boy in frequent instances when he wished to publicize an idea of his own.
The Judge, when he achieved the landing of the third floor, paused as many minutes as were necessary before pushing his daughter's bell, in order that she might remark, after kissing him on each cheek perfunctorily, that he 'supported' those dreadful stairs much better than she did. The Judge seldom heard this distinctly, because he made it a custom to totter out to the diminutive kitchen in order to offer a cordial greeting to the humble Marie, whose morning had been made hideous on his account. Madame Goujon was an exacting employer, at best. When she was expecting her father but was not quite sure (the Judge would have no traffic with telephones, or even _pneumatiques_ ) she kept old Marie hopping and ' _Parfaitement, madame_ -ing' like a character doll with a concealed spring. Marie was hired by the hour, at a rate of pay that for most of us would barely sustain life for that length of time if we remained in bed. She was seventy-two years old, but neither Madame Goujon nor the Judge seemed to be aware of it.
The Judge was not worried about Germany in those days, and even less about England and the United States, where, according to _L'Action Française_ , one ate for breakfast something about the size of a small pumpkin that was coloured like a lemon but had a smoother skin. Some radical that year (they called them anarchists, not Communists, then) had taken a pot shot at Léon Daudet, the Royalist leader whose youth organization, the Croix de Feu, was given to rioting. From this Judge Lenoir concluded that Paris was honeycombed with dangerous characters who were coddled by the godless Republic.
Marie, the Goujon servant, was deaf, but very respectful. Her life had been so blameless that she had never confessed oftener than once a year, even when adolescent. That did not deter Madame Goujon, a cautious person if ever there was one, from keeping the butter, sugar, wine, etc., under lock and key while old Marie was on duty. When those articles were needed for cooking, Marie had to find Madame and ask her for the keys to the _placard_. The only time Marie ever considered quitting Madame Goujon was once when the latter left four sous (an eighth of a cent) on a dresser quite by accident. The old servant assumed that her mistress was suspecting her of theft and had set a trap for her. On that one occasion, Madame Goujon actually put her arm around the old woman's shoulder and blushed to the roots of her hair. Marie, deeply touched, had wept and begged Madame's pardon, and for a day or two was not scolded because she was continually, in trying to serve meals hot, raising blisters on her fingers, which might be infected from the dishwater, in which case Madame Goujon might have to pay for medical treatment.
After lunching with his daughter, whom he treated as if she were about fourteen, Judge Lenoir would allow her to help him take off his coat and shoes and would doze for an hour and a quarter. Then he would say good-bye and descend the stairway. When the concierge saw his spats at the head of the first flight she would hasten to the kerb to wake the dozing chauffeur, or, if he were already awake and were reading the _Paris-Midi_ , she would merely announce that the Judge was on his way. The chauffeur would mutter under his breath a five-letter word frequently paired with _alors_ , fold his newspaper, belch, pry himself out of his seat at the wheel, touch his cap as His Honour hove into view and open the door for him. In return he would be courteously given an address in the rue Cadet where lived the Judge's mistress, an ample type named Victoria, who played small parts at the Odéon.
The Odéon, the second national theatre of France, was in a bad way after World War I. There were no funds, even for the first national theatre, the Comédie Française, which went to pot artistically and remained a travesty of its former self until reorganized about 1938. The drafts at the Odéon were traditional, and had not been over-publicized. The French clung to the superstition that air in motion, however balmy, was detrimental to the human constitution. Let a Frenchman or woman feel what he or she called _'un courant d'air'_ and something had to be done about it. A French physician in attendance at the American Hospital at Neuilly once paused in the act of delivering a child to complain about a _'courant d'air'_ in the operating room, and nearly lost both mother and child while windows and screens were being adjusted to insure him against catching cold.
The Judge's income amounted to about one thousand dollars a year. Of course, the day set aside for making calls was one of his more active days. Between times, often for a week at a time, he would merely read the _Action Française_ , write a chapter of his memoirs, which no one had ever read, and drink one _apéritif_ in a Royalist café in the nearby place de l'École Militaire.
It was not until 1925, the year he had his first stroke, that Judge Lenoir came, feet first, to the rue de la Huchette to live with his daughter, Anne. This made it necessary for the latter to relinquish Monsieur Panaché and deprive herself of the room rent for the first two months when the Judge was so ill that she could not tactfully suggest that he make up the financial loss to her from his personal funds.
That the Judge made a fair recovery may or may not have been due to old Marie's devotion and her habit of dumping into the kitchen sink various medicines the doctor had prescribed and substituting other things she stewed up herself, according to formulae long honoured in the Aube.
# _Of Winter, and Minding One's Own Business_
ONE OF THE TOASTS offered by Americans to their French friends was: _'Vive la France et les pommes de terre frites!'_ (Long live France and her fried potatoes!)
This phrase was spoken in jest but had an undercurrent of seriousness, too. A French chef or housewife habitually created minor miracles with that humble Irish vegetable introduced into the country by the great gastronomist, Parmentier – the tones of golden brown, the exact degree of crispness on the outside with the inside left mealy and delicate! It involved the deft touch, the incomparable flair, applied to a basic supply and filling a utilitarian need with artistic overtones.
The French reply was even more sincere and heartfelt.
_'Vive l'Amerique et le chauffage central!'_ (Long live America and central heating!)
Winter, in Paris, did not occur in hotels like the Ritz, nor even in the Plaza-Athénée, the Georges V, or that buyers' happy hunting ground, the Continental. There the daily rates charged American guests would have kept a French family almost indefinitely. In order to attract such guests, hotels had to be heated with mountains of coal and cubic yards of steam. This expensive heating made protestive grunts, groans, whines, whimpers, knocks, thuds and unauthorized drips and bubbles. Its radiators were likely to be off when the indicator said 'on' and vice versa. But it warded off, in part, the dampness of the rainy season, and although the electric lights were invariably placed haphazardly, sometimes in the middle of a ceiling, they dispelled the gloom.
In New York, for instance, the best hotels are not designed to please an exotic race of millionaires from a legendary continent across the ocean, with foreign ways only partially conceivable, manners that are strange (therefore rude) and voices that rise above and cut through the din of native voices like unoiled brakes jammed on. The worst period of our depression, as bad as it seemed, would have appeared to the average European as a sort of heyday of prosperity.
The heating arrangements on the rue de la Huchette were typical of Paris and of France. To all intents and purposes there were none. One of the two hotels, the Hôtel Normandie, advertised ' _Confort_ _Moderne_ ', including central heating and electric light. That was as far as the comfort was supposed to go. The toilets, concealed by curved doors (concave) at the bend of each narrow stairway, were of the type known as Turkish: they consisted of an enamelled metal crater in the floor with a circular hole four inches in diameter in the not-exact centre. Two foot rests were ineptly placed near the front corners, usually of some material that offered little friction to the damp soles of one's shoes. In the rear corner, on the left-hand side, to make it harder for righthanders to grab, hung a rusty chain. From this the knob had disappeared, leaving a jagged edge or two on which fingers were easily cut. Somewhere on the damp, soggy wall was a nail from which had fallen an out-of-date copy of a Paris newspaper that used particularly vile ink that smeared. More than half the time there was no newspaper at all.
The trick was, after one had been black-jacked by nature into using one of these conveniences, to get oneself thoroughly buttoned up and in order, to open the curved door, stand as far outside the _cabinet_ as one could, and still reach the chain, give it a quick tug and then retreat in fairly good order down the stairs. The resulting flood or angry cascade swept over the entire floor of the _cabinet_ , about two inches deep, sparing only the area most in need of cleansing. The real job of cleaning was done by a one-armed _garçon_ who had distinguished himself on the Somme and who joined the chestnut and oyster man in singing of the Loire on happy evenings.
In contrast with the Hôtel du Caveau, the residents and personnel of the Hôtel Normandie did not seem like one weirdly assorted family. The Gentile _patron_ did not beat his wife, a sad-faced Jewish woman from the Temple quarter, but he let her do practically all the work that the one-armed _garçon_ , Louis, did not volunteer to do, when his own huge share had been accomplished. There were plenty of anti-Semites in the rue de la Huchette, the most insidious of whom was The Navet and the most vociferous, the pimp, Robert. Louis, the Normandie's _garçon_ , was not of this faction. He had found that Madame Sara, as he called his _patronne_ , was one of the gentlest and most patient women alive, and as years rolled by and I got to know her better, I agreed with him unreservedly. There might have been some time, late at night or early in the morning, when Sara was not tending her small zinc bar, or trying to make her cash and the figures in her notebook balance, or showing a room to some prospective client, or making out a bill for some departing guest. When anyone passed her window, at No. 18, she glanced up as the shadow crossed the pane of glass. Her face spelled resignation. In the infrequent cases when the passerby nodded, she smiled dutifully in return, then sighed and resumed her work.
Sara had been born in the rue de l'Hospitalier St. Gervais, upstairs over a kosher butcher shop, but World War I had transplanted her to a munitions factory, where her face and hands were stained yellow (and still were not exactly pale). Her protective colouring did not prevent Guy, now her husband, from seducing her rather forcibly, on a sort of wager with fellow munitions makers, none of whom had ever slept with Jewesses and had culled some bizarre notions as to what it would be like. Sara became pregnant, and it developed that an uncle of hers had influence, through a small private bank, with the director of the munitions factory. Guy was hauled up, put on the carpet, and when he learned that the uncle was willing to make a rather generous cash settlement, considered that he had the last laugh on his fellow workers who had been teasing him about his predicament. Guy, having done the handsome thing in the Mairie of the Fourth Arrondissement, considered that his life's work was done, and so, apparently, did Sara, for she never rebuked him. In fact, when he awoke as late as nine in the morning, she prepared his breakfast with care and sent Louis upstairs to his room with it, knowing that the sight of her so early in the day had the effect of irritating her taciturn husband.
The respectable apartment building at No. 32, where Madame Goujon and The Navet were the prize tenants, had no central heating whatsoever. In the winter months, one shivered as God had evidently intended. Or, in extreme cases, when company was expected, maybe on Sunday evenings or to cheer the _réveillon_ on Christmas and New Year's Eve, the tenants bought kindling wood in little bundles about the size and shape of a bunch of asparagus. These neat little sticks had been dipped in resin at one end, and were bound with haywire. The main fuel was usually soft coal dust, pressed into briquettes the shape of huge black tear drops and just about as ignitable. Wood suitable for use in the small marble fireplaces was on sale, both hard and soft, by the kilogram, and was so expensive that the sight of it burning was a calamity in miniature. So pans of hot coals and ashes from the kitchen were nearly always substituted. Also cat's fur mittens had their use for rubbing chilled members and limbs. Small charcoal braziers were much in vogue.
This brings us to André and his blue-eyed young wife with honey-coloured hair, who was named Alice and called by her huge husband from the Auvergne, _mon coeur._ This was taken up by the lower-class clients who came in to buy wine and could not afford wood and coal. It was traditional in France that _amarchand de charbon_ (or coal dealer) should also handle wine in bulk. The speciality of André's coal and wood store was Mâcon, a most satisfactory wine from the Rhône valley, on the edge of the Burgundy district.
André, the coal man, whose hands, arms and face were always black, almost like those of an old-time minstrel, was the largest and best-natured man in the rue de la Huchette, and because he served also the rue de la Harpe (former residence of Madame de Staël) and several large buildings in the place St. Michel and along the boulevard, he laboured prodigiously in winter. In some of the buildings there were what the French mistook for elevators, some of which would sometimes carry passengers down as well as up and therefore were labelled _'Ascenseur et descenseur'_. But coal men, carrying on their powerful backs and shoulders one hundred kilos (more than two hundred pounds) of coal briquettes or fire wood were not allowed to use the passenger elevators, reserved for middle-class tenants and white-collar visitors. Neither were they permitted the use of service elevators in the rear, if there were any, because the service elevators were even more dangerous than the others, so it was said, and were not designed for heavy loads. Besides, if the elevator should drop with a coal man and his wares, the owners of the building could be held responsible.
So André carried the fuel up the steep narrow stairways that caused normal men to puff and blow when merely carrying themselves and their clothes four or five flights. He made enough money in the winter to be able each summer to send his wife, or 'heart', back to her mamma in the country (on the coast of Brittany) with their blue-eyed boy, aged nine, and named also André, who was destined to be 25 years old in 1939, and therefore needed plenty of fresh sea air.
Once André broke the skin on his thumb on a rusty nail, and the thumb swelled, then the hand and arm. Doggedly, with Auvergnat stubbornness, wearing linseed poultices bound on by blue-eyed Alice, at whose frown he trembled, this mountain of a man, leaning far to one side to maintain an awkward new balance, lugged up endless flights of stairs, ears roaring and pounding, sweat streaking the coal dust on his brow, tons of coal and wood and gallons of Mâcon wine, counting hours like days and minutes like hours and stairs like stations of the cross. He tossed and muttered with fever in the night, to such a point that Alice appealed in despair to the chestnut vendor to reason with André and persuade him to go to the city hospital, or at least call a ten-franc doctor.
Spring came early that year, and when the coal trade petered out, André, getting back the use of his hand which was stiff as a board, went fishing from the bridge near the book stalls, and watched the barges go by, with gay-coloured cheap clothing hung to dry on fluttering clothes-lines, and geraniums in cabin windows, dogs and children on the decks. Some were loaded with cement, and André dimly imagined lugging cement-laden barges up the stone stairs of the quai and the battlements of the Conciergerie, whose history he did not know, and over the chipped gargoyles of the Tour St. Jacques, and brushed from his now non-coal-stained temple a clean yellow bee, and dip went his bright red float, but it was a false alarm. There was no tiny fish, but only gleaming wet line and dangling of hook and lead sinker. There André sighed and fished with no success but indescribable pleasure, with that nightmare of winter dissolving behind him and summer coming on, when he would miss his 'heart' and the boy, but decipher their letters, word for word, by the light of a candle in his bedroom.
What André remembers, at the time of this writing, in a convict gang somewhere in Germany, building roads, he being so well preserved that no Storm Trooper would ever believe he was nearly sixty years old – how much of his 'heart', of bees in spring or narrow stairs or septicaemia, is mingled with the dim murder in his simple candid mind, I cannot say, nor whom he blames, nor whom he should blame, nor how it will all end.
Men who carry heavy loads, and on Sunday get time and a half or double pay, remember André, and please give him a hand! It is very much your own and strictly personal affair, and if you don't lend a shoulder, no one will.
# _The News and the Barber's Itch_
THE NEWS WAS VITAL to the life of the rue de la Huchette, where each inhabitant, like other Parisians, chose the newspaper which confirmed his prejudices and fixed ideas.
The larger of the local distribution centres was the international news stand in front of the Café de la Gare in the place St. Michel. This vendor served the métro patrons, the customers of the three large cafés, and the respectable apartment houses near the boulevard. At the eastern end, however, next door to the Hôtel du Caveau, was the tiny stationery shop of Achille and Geneviève Taitbout, a small squint-eyed couple who shuffled around wearily, maintaining a perpetual relationship in their movements, like figures on a stage. Their daily routine involved getting up at five in the morning to receive a bundle of newspapers brought by a lad on a bicycle. On the infrequent occasions when the delivery boy did not show up, or was late, they pottered and muttered collectively, like a mechanical toy running down.
Monsieur Achille, as he was called, could make a surprising number of mistakes as he ambled from door to door each morning with copies of the _Petit Journal, L'Intransigeant, Le Journal, Le Temps, Le Matin, L'Action Française_ or _L'Oeuvre_. The two daily copies of _L'Humanité_ (the Socialist organ) he handled gingerly, as if he half expected them to burst into sulphurous flame.
In spite of the fact that his tiny shop was distant from No. 32, Achille delivered _L'Action Française_ to The Navet and Madame Goujon each day, timing his call so that the concierge could take up The Navet's paper in time for his breakfast at 8:20 o'clock. Once Achille inadvertently left _L'Oeuvre_ , a mildly liberal sheet containing the mildly anti-clerical column of Georges de la Fouchardière. By an unfortunate set of coincidences, neither the concierge nor the watchful deaf wife, Jeanne, spotted the substitution in time. As a result, The Navet outdid himself, giving the tremulous old couple such a frightful half-hour that they remembered it with a shudder for several days. The Navet wormed out of the old folks the information that two of their customers bought _L'Humanité_ and ended up by jotting down a checklist covering the entire street. He liked to give the impression that he was connected with the secret police.
The three daily copies of _L'Oeuvre_ went to Monsieur Noël, the taxidermist, Madame Mariette, of _Le Panier Fleuri_ , and Madame Absalom. The two _Humanités_ were delivered to the oyster man and Madame Absalom, respectively. Madame Absalom's only extravagance was to subscribe to practically all the papers and, like an editor on a holiday, gloatingly to compare their errors and discrepancies. The Navet, of course, did not dare to bother his superiors with his private black list, but he forbade his wife, Jeanne, to buy wool or thread from _'cette vieille crotte'_. Thereafter, Jeanne, who had never cared particularly where she bought her sewing supplies, took pleasure in patronizing Madame Absalom, who never knew the cause of her slight boom in trade.
An avid reader of the papers was Henri Julliard, who in 1924 purchased the Hôtel du Caveau from the taciturn Claude and his wife, Philomèle. Monsieur Henri, as he was affectionately called, was an understanding man of well-considered judgment. That he was able to combine a sweet forgiving nature with the ability to run a restaurant and hotel is an indication of his scope and versatility. It was due also, in a measure, to his short, stout wife, Marie, who made the harsh decisions about credit, etc., and carried them out during the hours when Monsieur Henri was getting his hard-earned sleep.
It came about thus that the Julliards bought the Hôtel du Caveau. The former _patron_ , Claude, disappeared one morning, along with the girl, Suzanne, for whom he had bought a more adequate wardrobe. They were last heard of in Chambéry, where Claude had placed Suzanne in a local bordel while he busied himself by smuggling absinthe from Switzerland. Philomèle took up with the well-meaning Turk, who treated her with impersonal kindness.
Monsieur Henri was a Savoyard with moustaches a little like those of the _garçon_ , Georges, but grey instead of red and only half as busy. He had dark brown eyes that twinkled, angular knees and elbows that were tireless and capable, and a wealth of human kindness. His partner, the first year, was his brother Jacques, who wanted also to be a good fellow but was too awkward and shy, and who had a slim wife, Berthe, whose character was much like Henri's. Many who knew the brothers and their wives said it was a pity that Henri had not married Berthe, and Jacques had not paired with Marie. In that, they all were very wrong. Henri and Berthe, in combination, would have given their shirts away. And the cranky old Marie, a caricature beside her distinguished husband, loved Henri with a devotion that was the stronger because of her apparent distaste for the rest of humankind.
It was with Monsieur Henri that I discussed the news events in those days and patiently, from his stock of sound information, he improved my grasp of French affairs. There was much to talk over during Poincaré's regime. France broke with England concerning the Ruhr, moved in, and filled the Paris papers with news about German civilian atrocities, in order to justify its own brutality. Unable to collect reparations, on account of German poverty and 'passive resistance' which became spasmodically impassive, Poincaré declared an embargo on iron and steel into Germany. The German police in the large industrial city of Essen were demobilized, and no police at all were substituted. Respectable inhabitants did not dare leave their homes after dark. Baron Krupp von Bohlen was arrested and sentenced to fifteen years by a French court martial. American troops were withdrawn from Coblenz, to the despair of the German population, and French troops took over, with resulting bloodshed and wholesale hatred.
The death of President Harding got a scant few lines on the inside pages of most of the French newspapers, and many European editors confused Calvin Coolidge, of whom they never had heard, with Professor Archibald Coolidge of Harvard, who had travelled in Europe, spoke several languages, and was hailed as a possible saviour until the illusion was dispelled.
Each Monday morning, Poincaré's Sunday 'sermons' were printed in full, their import being always that the Treaty of Versailles must be carried out to the letter, at the point of the bayonet if necessary. None of the papers, Catholic, Communist or otherwise, informed their subscribers that the American war debt which the new President Coolidge wished to collect was not money loaned to the French for carrying on the war while it was in progress, but had to do with a payment for American supplies left in France after the Armistice by agreement with the French Government. The United States was derided as a Shylock, exacting its pound of flesh from ruined France, who could not get the reparations money due from Germany because England would not help put the screws on the Boche.
Monsieur Henri saw through a great deal of the camouflage under which various interests, each with a newspaper or two at its disposal, were operating for selfish ends. He believed that France would have to work out her own salvation by making it possible for Frenchmen and women to share more equally in the national income, and all civic rights and prerogatives. His social outlook was broader and less provincial than that of most Frenchmen, but undoubtedly he thought of France as the important and civilized part of an otherwise exotic world. Of a planet without France he could never conceive.
While Jacques Julliard lived, Monsieur Henri took the early morning shift, from six until after lunch was served, slept a while in the afternoon, supervised the dinner and about nine o'clock turned over the bar to Jacques again. But after Jacques died suddenly, leaving Berthe a slim widow who looked like an elder sister of La Gioconda in the Louvre, Henri was on duty before breakfast and again from dinner time until after two in the morning. In the mid-morning and mid-afternoon the two women, one homely as a toad in grey, the other mature and lovely in black, carried on.
Green vegetables, meat, poultry, fish, etc., were purchased by Monsieur Henri in Les Halles, or central markets, with skill and discrimination. Some of his staple groceries he bought at the local _épicerie_ , or grocery, at No. 27, called 'L'Épicerie Danton' and owned by Jean-Baptiste Emile Denis Emanuel Corre and his wife, Gabrielle, who looked like a porcelain doll. Mme. Corre had style without chic, and a kind of beauty without savour that remained constant throughout the years.
It must not be assumed from the name 'Danton' on M. Corre's neat grocery store that the proprietor admired that revolutionary hero who came to revolutionary grief on the guillotine. M. Corre was stolid Breton, where Catholicism was still in a medieval stage more like that of Spain than the rest of France. He read _Le Matin_ because his wife, a business woman, thought it was better to have a newspaper less offensive to free thinkers than _L'Action Française._
In Paris, an _épicerie_ did not have green vegetables displayed near the front of the store, and a meat counter in the rear, with glass cases for fish and a large icebox filled with eggs, milk and butter. Meat was sold in the butcher shop, which was marked with red and white awnings, striped vertically, and matching the curtains on the bloodstained cart that drove up with reeking carcasses, un-iced, four mornings a week. And the butcher's shop was not authorized to sell pork, sausage or horse meat – only beef and lamb. Not even poultry was displayed there, but could be purchased in the _laiterie_ , or dairy shop. The pork store handled delicatessen, with sausages from Lyons and Genoa, _rillettes_ and _pâtés_ , head cheese, pink sausage dotted with green pistachio, the French equivalent of bologna, salami and superb concoctions made of rabbit meat, truffles, etc. A golden horse above the green and white awning at No. 13, near the rue Zacharie, was the emblem of the horse butcher, M. Monge, who sold only horse meat, and very good horse meat, too.
It was one of the many superstitions in France that horse _hamburg_ , cooked in thin bouillon, was good for invalids and convalescents. Anyway, horse meat was cheaper than beef and was used in low-priced restaurants in dishes that were not specifically labelled 'beef' on the menu. The menu, in those places, consisted of a blackboard or a slate on which the bill of fare was chalked. For a first course, these small establishments (which always served the prescribed number of courses, an appetizer, soup, fish, meat, salad, cheese and dessert) frequently resorted to what was known as Belgian _pâté_ , half horse meat, half rabbit; that is to say, one horse to one rabbit.
The horse butcher in the rue de la Huchette, No. 13, also had a sideline of mending hunting horns, so that when one passed his awninged and curtained doorway with the golden horse's head aloft, one frequently heard their flourishes or plaintive moans. This same M. Monge also played an obsolete type of horn, like Hoffman's famous _chapeaux chinois_ , in an amateur orchestra connected with the Society for the Preservation of Ancient Music. He was of middle height, broad and fat, with a couple of extra necks and chins, so that, when he walked or sat with the gaunt taxidermist, M. Noël, they looked like a caricature by Wilette.
The butter-and-egg store was almost across the street from L'Épicerie Danton, at No. 24, and was operated by Odette, a worthy woman with a long triangular face, sloe-brown eyes, large feet and bony wrists. She wore green-black clothes and looked pious and demure. Actually she was an infidel and a Socialist. Her meek little husband, Jean, had a small voice and a scraggly moustache. Once he had run fifth in a six-sided contest for deputyship in his native town in the valley of the Chevreuse. The milk sold at specified hours by M. and Mme. Odette was brought in large dented cans from a wholesale dealer in Les Halles, who received the cans by cart from the country about twenty miles away. To American eyes it was bluish and watery in appearance and tasted even paler than its faint sickly odour. To regular customers in the rue, this was delivered in converted wine or brandy bottles which had been washed in non-running not-cold water and not thoroughly rinsed.
The deliverer was a milk-smelling, well-rounded girl of sixteen who wore cloth slippers and no stockings, and most certainly no brassière and whose firm behind was playfully slapped or pinched by every _garçon_ in the quarter at least twice a day. Her name was Colette and she shared with the drudge, Eugénie, at the Café St. Michel, a reputation for chastity. Colette would discuss what was uppermost in the minds of the men with frankness and disarming wit. She was saving her money, a few pennies at a time, to take a course in nursing, because nurses wore stout strong shoes she never could afford and worked in an atmosphere of chemical odours that bore no resemblance to the smell of milk or cheese. She admired the trim, determined Madame Mariette, who kept order in the bordel a few doors away.
Colette was not hesitant in telling the men and boys who tweaked her buttocks as she sped up or down dark stairs that if only she were the 'type' she would sell what the good God gave her, and not dish it out to the likes of them for nothing.
The eggs on sale _chez_ Odette often bore unmistakable evidence of having been near hens. In some dairy shops in more expensive residential quarters, the eggs were white and were carefully scrubbed. Madame Odette and her customers believed that a dealer who scrubbed eggs must have an ulterior purpose, and that, once scrubbed, a fresh egg and a stale one looked altogether too much alike.
One had to choose between doing without milk worthy of the name or suffering the disapproval of thrifty servants and neighbours by dealing with the Necessary Luxuries Company. In rare cases the French could forgive such extravagance in the interest of an ailing male child. But for healthy adults to pay ten times the price of store milk and use it unboiled was tactless in the extreme.
In the last decade, a few of the higher-priced cafés and restaurants achieved ice cream that might have passed at a county fair in the American dust belt. Up to that time, except at Rumpelmayer's and a few pastry or confectioner's shops intended for the _haut monde_ , the ice cream was like snow over which something melancholy had been spilled.
The vegetable supply of the rue de la Huchette was displayed on barrows in the rue Zacharie, which had a small ancient square. Cabbages, cauliflowers, onions, carrots, parsnips, turnips, potatoes, lettuce, romaine, _chicorée_ and other salad leaves, tomatoes and peppers, and other products of the soil, made up in sightliness and freshness for the unattractive meat and dairy products whose prices were unreasonably high. Vegetables were so cheap and plentiful and diverse that it was scarcely worth while for a vendor to cheat a customer. Nevertheless they tried it, in a half-hearted way.
The barrow men and women bought their goods at five in the morning in the marvellous central markets and sold them in the forenoon in the little side streets. Most of the green stuff had been picked the afternoon before and hauled in trucks, neatly loaded, to Les Halles, in the night.
It will be readily understood that by the time the vegetable dealers, the milk store, the beef and lamb butcher, the pork and delicatessen man, the horse butcher and a few other specialists got through, there was little left but dried beans, peas, canned goods, spices, and preserves for the grocer, M. Corre, to sell. As anyone could see, his speciality was dried beans, which he handled and arranged with loving care, squinting at them as they lay in thousands in the shallow wooden boxes. These he had labelled painstakingly, so that a yellow-eyed pea bean seldom got into the bin intended for small kidney beans, and the mauve Indian bean, shaped like an elongated pearl, was seldom found with the _flageolets_ or _soissons_. It was seldom M. Corre had a call for the giant _fèves_ , four times the size of the large old-fashioned lima beans, but he kept them in stock just the same, and was repaid two or three times a year when some wandering Spaniard or Catalan would enter, saying he was sent by so-and-so, whom M. Corre had forgotten.
_'Mais, oui,'_ M. Corre would say with pride, when asked if he had _fèves_. Of course, the Épicerie Danton had limas, normal-sized and 'baby', Canterbury, scarlet runners, pintos, tropical turtle beans, snapping beans, chick peas, shell beans marbled with onyx, blue beans veined with gold, as well as cracked corn (red, orange and white), rice from the best fields of Annam, wild rice from Valencia, whole wheat, potato flour to relieve barber's itch, and two American articles. The first American item was corn meal, which was said to be used by Americans for frying fish and veal cutlets. From time to time, M. Corre let a little of this slip over his stubby fingers which afterwards he sniffed knowingly. No one had bought corn meal for cooking during the years of his proprietorship of the Épicerie Danton, but Monsieur the Horse Butcher (M. Corre was not good at names, not even his neighbours' and clients') had once tried it for barber's itch, there being no potato meal available.
Barber's itch, quite prevalent in Paris, was not always contracted in a barber shop, but often in a public bath or sometimes in a church. With barber's itch, one itches all over, as a sort of background or accompaniment to the principal and truly diabolical he-itch that crawls over and around one's shoulders, back and torso. It is caused by a microscopic creature which has little else to do. The poor, when afflicted with this horror, went to the hospital St. Louis, where the skin specialists had worked out a cure. The patient stood naked in a sulphurous shower bath (containing other mysterious ingredients) and then allowed himself or herself to dry while reading back numbers of _The Catholic World_ or _La Vie Parisienne_. Finally, the victim put on clean and different underwear and clothes (except shoes which do not carry the bug) and went home feeling like Lazarus in reverse. The contaminated underwear and clothes should have been burned, but not one in a hundred clients of the free clinic at St. Louis could afford that, even if they itched perpetually. Therefore, the beneficent doctor in charge asked the engineers who ran the heater to rig up a steam sterilizer that would kill the bacteria of the itch without destroying the garments. As so often happened in latter-day France, one branch of science could not keep pace with another. The sterilizer, while it killed the itch bugs and whatever else moved around, shrunk cheap coats, pants, shirts and underwear and blended the inexpensive dyes into a dismal neutral tone.
The middle-class sufferers, too proud to mingle with the lowly in the Hôpital St. Louis, called on a local ten-franc doctor, who advised the patient to sprinkle potato meal on his bed sheets and roll when the itch got unbearable.
I don't know by what clairvoyance Madame Absalom found out whenever anyone on the rue de la Huchette got the barber's itch. She, herself, being in league with the evil spirits which produce such minor torments, was immune. But the moment one of her neighbours showed the first furtive symptom, Madame Absalom was alert and gleeful.
'Won't he look pretty, that one, flopping around in meal like a frog? He's got hair all over, of that I'm sure. _Pas?_ It's worse for a _type_ like that.' And the old girl would chuckle off and on throughout the days ensuing. One of her best 'cases' was M. Panaché, the floor-walker from the Samaritaine, who got the itch and tried to blame it on Mary the Greek. M. Panaché, after losing his room and bath with Madame Goujon at No. 32, moved into the renovated Hôtel du Caveau under Monsieur Henri Julliard's new management. The chestnut vendor loathed Panaché on sight because the floor-walker pandered to The Navet.
The chestnut vendor, to keep M. Panaché in a perpetual hell of suspicion and rage, whispered to him that Monsieur Henri, who would not have cheated a fly, rented Panaché's room now and then for twenty-minute periods to street-walkers who did not draw the colour line. Monsieur Henri merely laughed, thinking Panaché was joking, when the outraged floor-walker confronted him. But once a suspicion entered Panaché's mind, it festered there. He contrived to enter at unexpected hours, which was difficult because he didn't dare leave the store. He sniffed, got down on his knees to look at the dust, left toothpicks leaning against the door, listened behind panels before entering the hallway, tried to pump Georges, who understood what was up and was purposely non-committal. At last, Panaché got the itch and Madame Absalom, that time, didn't wait for customers to come in order to spread the good tidings. Swiftly she made the rounds, up and down the street. Whenever Panaché appeared, heads popped into windows and out of doors. Madame Absalom went to Panaché's department at the Samaritaine and cackled the story to one of the salesgirls. The latter informed the chief, who summoned Panaché to the dreaded _bureau_ and, at a markedly safe distance, had a heart-to-heart talk with him. For the safety of the Samaritaine, the chief said, he should fire Panaché, but since that would ruin the latter's career, he would give him three days off, without pay, to be deducted from the annual week's vacation-without-pay, in order that he might go to the Hôpital St. Louis for treatment. Panaché, before being admitted to the store again, would have to present a medical certificate that he had no itch or contagious disease of any kind whatsoever, he was told.
'Now we'll find out if that _salaud_ has the pox or not. The doctor'll soak him twenty-five francs for the certificate, even if he hasn't. That's what they did to _mon ex_ in Clermont when he asked for insurance, the old cod-fish,' Madame Absalom said.
Panaché proceeded, more dead than alive, from the store across the Seine to the place St. Michel, where from the bars of the café de la Gare and the Café St. Michel sly and malicious eyes were glued on him and followed his course. Along the rue de la Huchette, shopkeepers spoke to him politely, but too politely. Ordinarily they almost ignored him. In every inflection of their voices and expression on their faces he detected an awareness and a relish of his predicament. When he entered the Hôtel du Caveau, Mary the Greek was sitting in the chair he used habitually.
Panaché did not speak directly to Mary. He grew livid, clenched his fists, wheeled and addressed Monsieur Henri: 'That foreign girl of the gutters has communicated to me a foul disease for which she, or you, will have to pay,' Panaché said.
Monsieur Henri merely smiled and stroked his grey moustaches.
'You exaggerate, Monsieur,' he said, not entirely without a warning undertone. Panaché, in his rage, missed the warning.
'That girl is sitting in _my_ chair,' said Panaché.
'The chairs belong to everybody,' said Monsieur Henri.
The chestnut vendor, who had overheard, stopped laughing long enough to start singing the Marseillaise.
Mary, only half understanding that the row was in some way connected with her, rose and turned her expressive eyes on Monsieur Henri.
'Does _Monsieur_ want this chair?' she asked, and accommodatingly extended it towards M. Panaché.
Georges, the _garçon_ , stepped in with a towel and playfully dusted off the chair seat, pretending to catch a few small hopping things with his free hand. Madame Marie's small terrier called 'Maggie' started scratching herself furiously, rolling over and biting her side. That set off Panaché, whose white-hot rage had stirred up the itch bugs. Buffeted by roars and squeals of tearful laughter, Panaché retreated up the stairs and that night appeared, naked, in the disconsolate line of patients in the Hôpital St. Louis. Twelve hours later he was pronounced cured, but when he asked for a certificate to that effect, the overworked clerks of the hospital were annoyed. It had taken less than two hours for Panaché to become the most unpopular patient of the year. He got as far as the third assistant to the head doctor before he was ordered to leave the premises.
The doorman at the Samaritaine was equally adamant. He had had instructions not to admit Panaché without a clean bill of health. No certificate, no admittance. Panaché demanded to see his chief.
'You'll have to call at his home. No doubt he has one,' the doorman said.
Late that night, when there was no one else at the bar, Panaché told his troubles to The Navet, who had been attending a Rightist meeting and had stopped for a nightcap on his way home, hoping at last to surprise Jeanne with a lover. He had cunningly told Jeanne that he would not be home that night at all. The Navet got so little of the respect he craved in the rue de la Huchette, that he liked it from the abject Panaché. So he told Panaché that he would get the necessary certificate from one of the prefectorial doctors (strictly in confidence, of course), not for the full price of insurance certificates, namely, twenty-five francs, but for only twenty francs. Panaché wrote out his full name, age, and whatever else The Navet wanted to know, and the next day The Navet brought back, very secretly, the certificate. It set forth that Gaston Panaché (whom the doctor had never seen) was free from contagious or infectious disease and in good physical condition.
'I might have known,' said Madame Absalom, when she learned that Panaché was back at work. 'He's too mean to get the clap. Or, more likely, the certificate was _truqué_ (fixed).'
# _Of Community Entertainment_
THE APARTMENT ON THE fourth floor of No. 32, above that of Madame Goujon, was rented by a jolly _bon vivant_ of uncertain age named Monsieur de Malancourt, whose frequent arrivals at all hours by taxicab were the more conspicuous after Judge Lenoir had taken to his bed. Monsieur de Malancourt had a more elaborate domicile in one of the expensive Right Bank hotels, a chateau with moat in the Chevreuse and was the nominal head of a private bank from which he drew as much money as he could spend and for which he gave no accounting. He was thought by his friends and employees to be eccentric because he had no sense of responsibility, no fear of the hereafter, no alarm about the state of France, and enjoyed himself hugely from day to day, having that rarest of blessings among Frenchmen: a robust constitution.
Monsieur de Malancourt might never have seen the rue de la Huchette, which would have been too bad for it and for him, had he not been persuaded by an American millionaire who gave out trophies for automobile races to drop in at a fashion show at Maggy Rouff's one afternoon. As the two gay old boys stepped into the salon, a Polish model, Nadia Visnovska, was standing, hands on hips, in front of a triple mirror, naked as a goddess and many times as beautiful. She had ivory skin and blue-black hair, a body that could be young and strong without muscles or bulges, tapering hands and feet and a rich mezzo voice that made her Polish-French electric.
'The chief cutter tells me she's a virgin,' the American philanthropist whispered, to Monsieur de Malancourt.
From that time onward de Malancourt had something to occupy his imaginative mind. He followed Nadia, discreetly, to the rue de la Huchette, where she turned in at No. 32. It would have been too crude to bribe the concierge, and he did not want to risk embarrassing the girl, and perhaps be the cause of having her deported, by inquiring from the Ministry of Justice about the details of her domicile. So he visited a flower shop in the place Vendôme, where for years he had been a generous customer, and arranged for a boy to deliver, just before Nadia was due to reach No. 32 each evening, not a vulgar display of flowers, but carefully chosen small and exquisite bouquets, with pale forget-me-nots, rosebuds or lilies-of-the-valley.
Nadia, in the course of her work, had been approached by all kinds of males, from American buyers to lesbian actresses. Being fastidious and independent, and as non-mercenary as only a Slav can be, she had held herself aloof to such a point that the virginity legend which had reached the ears of de Malancourt was fairly current in the dressmaking trade. She was naturally affectionate and companionable and was touched by the lavish delicacy of Monsieur de Malancourt's approach. When she saw him, after the most complicated arrangements for a rendezvous at La Poire Blanche, a tea room in the boulevard St. Germain, she liked him whole-heartedly and thoroughly. She had loved once or twice, with all her heart and Slavic passion, but in each instance the recipient of this amorous flood had been a poor man, and proud, and both parties had known that the affair must eventually come to an end. Monsieur de Malancourt was not only handsome, vigorous, tender, cultured and essentially fine, but apparently had all the money in the world. Nevertheless, Nadia insisted on continuing her work, which in turn inflamed the old roué's respect and tormented him with jealous thoughts of her peeling off her clothes in the presence of all and sundry in the couturier's establishment.
To make things more cosy, de Malancourt rented the apartment below Nadia's attic room and fitted it up for her in a style that staggered the concierge.
So imagine the excitement in the rue de la Huchette the afternoon its residents saw in all the newspapers the genial smiling countenance of their neighbour, Monsieur de Malancourt. The accompanying story dealt with the kind of racy occurrence that periodically stirred Paris and awakened in its population a feeling of kinship and unity, transcending class lines.
The bare facts were these: Monsieur de Malancourt, who disliked to do anything banal, had in this instance we cannot say 'sat' for a photographer, because de Malancourt had instructed the astonished camera artist to take an art photo of his plump and symmetrical backsides, without drapery. After selecting the best from a dozen proofs or so, de Malancourt had had expensive prints made and mounted, had autographed them and sent them by mail and messenger to his intimate friends and some other persons to whom he wished to convey his regards in a subtle and accurate manner. One pompous gentleman of the latter group who fancied himself an art expert received his copy enclosed with an oil painting signed Watteau which he had tried to sell Monsieur de Malancourt. Incidentally, false Watteaux were plentiful in Europe at that time, to such an extent that even the Louvre, manned by France's most renowned experts, had bought two fakes allegedly from the brush of that master.
Monsieur Latour Latour, the art expert who received Monsieur de Malancourt's token, interpreted it as an implication that the returned Watteau was not genuine, and was highly insulted. His dignity and reputation had suffered irreparable damage, M. Latour Latour contended. Had he been ten years younger, he would have challenged de Malancourt to a duel in the Bois at dawn. As it was, he sent by Negro messenger a letter to de Malancourt, demanding an apology. By some chance, the letter got into the hands of a gossip writer for Figaro, and all Paris started chuckling behind Latour Latour's learned back.
There was a lively exchange of correspondence before the story appeared in the popular press, but when Latour Latour entered suit for libel against de Malancourt, the affair became public property. That is, it was considered public property elsewhere than in the rue de la Huchette. There it was local and private property, giving each inhabitant a sense of distinction and participation in the life, of the haut monde. When Mademoiselle Nadia (no one ever attempted her Polish last name) appeared on the pavement, way was made for her as if she were a queen. The arrival of Monsieur de Malancourt's taxi after he had attended a session of the trial (which lasted ten days, to the increasing delight of judges, lawyers, journalists, spectators and the Parisians of all walks of life), was watched from doorways and windows with awe and approbation. Monsieur de Malancourt, enjoying the approval of his neighbours, bowed, smiled and lifted his hat courteously when he descended from the cab. His words and phrases, gems of wit and humour, were on everyone's lips, and Nadia's employer, the already famous couturier, did such an estate-agent's business that he (don't be deceived by the 'Maggy') turned clients away daily, considering that more dignified for a house of his reputation than building an annexe or hiring a hall.
Monsieur de Malancourt, disdaining the aid of counsel, defended himself, and his defence was worthy of the grand French tradition, exemplified by Rabelais and Voltaire. A picture of one's backsides, he argued, was more intimate and personal than a photograph of one's face. To send it to a friend or acquaintance, therefore, was not an insult, but a mark of affection and esteem. Furthermore, it was a token more permanent and honest than the conventional photograph, since one's bottom changes less rapidly and radically than one's face, the latter being exposed to wind and weather as well as the ravages of time. The human face, Monsieur de Malancourt remarked, is like that of a fish and has been much over-rated as an art object, being painted by artists from time immemorial principally out of regard to the model's convenience when posing for hours at a time. No such consideration was necessary, he pointed out, now that cameras could be adjusted quickly and even the longest exposures required only a few seconds.
Before the first day of the trial was over, the jury could no longer keep up a pretence of neutrality. Monsieur Latour Latour's rage was more comical, the higher it mounted. He had with him a battery of the stuffiest lawyers in the Paris bar, and that is saying a lot. The judge and his two assistants entered into the spirit of the thing and permitted a wide range of discussion. Always the gentleman, de Malancourt publicly offered not to raise the question of the genuineness of the Watteau he had failed to purchase. Latour Latour, vibrant with outraged dignity, demanded that the painting be brought into court and expertized. It was, and three out of five experts agreed that it was not by Watteau. It developed that Latour Latour had exchanged it with another expert for a Corot, which he insisted be returned to him. Four out of five experts declared the Corot was a forgery, too.
Each succeeding triumph scored by de Malancourt was enjoyed in the rue de la Huchette as its very own. Madame Absalom hobbled from shop to shop with glee. Monsieur Noël, the taxidermist, and his stout pal, the horse butcher and horn player, talked art with Monsieur Henri at the Caveau bar until far into the night, with Mary the Greek, Madame Berthelot, Pierre Vautier, the cook, Thérèse, and Georges, the garçon, hanging on their words and drinking happily the while. The Navet insisted that he had known about the fake Watteaux bought by the Louvre before the deal was made and would have warned the director had the latter not in his youth been a Dreyfus supporter and therefore a Jew-lover and a traitor.
The chestnut vendor suggested that Monsieur Panaché follow the example of de Malancourt, and even carry it farther than mere photography. He recommended, in fact, that the floor-walker cut a hole in the seat of his pants and make a practice of walking on his hands, in order to improve his appearance and present a more amiable exterior.
In times of excitement and general good feeling in our little street, human fellowship and tolerance blossomed and penetrated dim corners with a wholesome fragrance. A drink with a friend became a symbol reaching back into time and forward into the future. A nod or conventional greeting was accompanied by a warmer smile. Enmities, if not forgotten, were temporarily laid aside. One of the most important elements in national or community life is public entertainment, not the formal kind that is presented, like canned food, for sale at a price, but piquant incidents the people make their own and in which they have the illusion, at least, of being participants.
In the rue de la Huchette, while the procès de Malancourt was under way, Madame Mariette of Le Panier Fleuri used to leave her joint in charge of the big good-natured, middle-aged 'girl' named Armandine and steal a half hour just after midnight in our little bar, listening to the talk, joining in half-wistfully at times, and always with ready wit. Mariette was beloved in all the quarter, and a few years before had caused almost as much of a stir in Paris as had Monsieur de Malancourt's trial. She was short and petite but womanly and not doll-like. She was neatly shaped, with rosy cheeks and frank grey-blue eyes with lashes not too short nor too long. Her voice was rich in timbre and well modulated, her wrists and ankles small but not fragile. In repose her face was sad but instantly grew animated and responsive when one spoke to her.
Madame Mariette had saved her money quite a few years in order to attract a respectable and worthy husband, who would share her dream of a home in the country with plants and domestic animals, after her years in the bordel were over. She had never worked as a prostitute in the brothels she had directed; the clients called her 'Madame' and respected her person as well as her acumen. So when the time came for Mariette to marry the railway conductor of her choice, there was a difference of opinion among the priests of St. Séverin as to whether, technically, she could be married in white, the emblem of purity. Mariette, when she heard about this, solved the problem herself. She had a bridal gown made by one of the best couturiers in Paris and instructed him to use every colour of the spectrum. The resulting creation, for use only in the church, became fashionable for a time. Mariette also had a white bridal gown made for the wedding breakfast in the upstairs salon of the Café St. Michel. As soon as the church ceremony was over, she changed from the rainbow creation into the white one and all the neighbours attended the breakfast and drank champagne, including Father Panarioux and Father Desmonde, who feasted at a special table set for them in a little alcove.
# _The Maiden's Prayer_
NOT LONG AFTER I ARRIVED in the rue de la Huchette the newspapers announced the deaths of several important foreign leaders all of whose passing aroused more comment, pro and con, than did that of our handsome Harding. The first of these was Lenin, known to nobody on our street as Vladimir Ilyich, except a couple of exiled Serbian students (male and female) who shared a room at the Hôtel du Caveau. The female, Milka (or Amélie to the French), was grief-stricken and disturbed and tried to explain in halting French what the world had lost. Being overheard by Panaché, who told The Navet, she was visited by the police the next day, held forty-eight hours for questioning, and narrowly escaped being shipped back to Yugoslavia for torture and execution.
Notwithstanding that Lenin's political and social significance was little understood in the rue de la Huchette, nearly everyone was fascinated by the tales of his embalming. Tut-Ankh-Amen was excavated and publicized about the same time, and most Parisians thought Vladimir Ilyich would be trimmed up like Tut and were disappointed when news pictures showed him wearing a collar and tie. The treatment of bodies after death was a lively subject in Paris whenever it arose. When the beloved American Ambassador Herrick was embalmed by Bernard Lane, the American mortician and publicity hound, one of the French dailies carried a two-column interview setting forth in detail how Herrick's inner organs were removed and pickled.
The next celebrity on Charon's list that year was Hugo Stinnes, German multi-millionaire capitalist who made his fortune while others in Germany were starving in the streets. Madame Absalom was in favour of sending a French expeditionary force into Germany to appropriate Stinnes' money, and when informed by Monsieur Henri that the said money was scattered all over the world in banks much safer than those of Germany, the old woman accepted the story as another proof of German perfidy. The Navet, right for once, insisted that a substantial chunk of the Stinnes loot was in Paris, and would be held there safely for the heirs. The big shots stuck together, he contended, regardless of frontiers.
No one in the street was aware that an Austrian paperhanger named Shicklgruber, and calling himself Hitler, had been arrested in Munich and thrown into jail. The death of Eleanora Duse completely overshadowed that little item.
The Matteotti murder had little impact in the rue de la Huchette, there being few Italians in the quarter. Italians and Serbs do not mix, and when they do, the Italian has about as much chance as the rabbit matched against a horse in a Belgian paté.
Woodrow Wilson's death was associated in the minds of the news-conscious group in the rue de la Huchette with what seemed to Monsieur Henri a scrambled policy announced by the new President Coolidge: to the effect that war debts should be collected from France, loans made to Germany, that the United States would never join the League of Nations, which seemed to exist in a half-hearted way, but would support a non-existent or renovated 'world court' in some other city than Geneva. Meanwhile, Vice-President Dawes, according to the Paris press, was formulating a plan whereby France was to get less and less and Germany was to be financed and rehabilitated.
The Navet insisted that Harding's death had been a carefully staged plot so that Dawes and Coolidge might play Germany's game.
I noticed that in the Caveau bar, where nightly men and women gathered for conversation, the few foreigners like myself who had seen other countries said almost nothing, being so badly handicapped in a free-for-all talk by a few inelastic facts that it would have seemed almost bad taste to inject them into the discussion. My French friends preferred to hear about strange things like grapefruit and tinted toilet paper. These items did nothing to improve the standing of an American as an informant on more serious subjects.
It was no coincidence that the French writer who gave the most enchanting picture of distant Africa had never been nearer that continent than St. Cloud. Parisians loved to dream of distant lands but seldom visited them. M. Corre, the grocer, whose practicality was represented by his assortment of dried beans, had a romantic side to his nature. He would stand by the hour, hands behind his back, head tilted upward, sighing and looking longingly at his spices. Cinnamon would start him dreaming, so would the miracle of ginger, and as for nutmeg...
The day I told him that in a small American _département_ wooden nutmegs had been manufactured and sold, the pained astonishment of M. Corre was impressive to behold. His onion eyes bulged behind his thick-lensed glasses. He puffed and blew. His chubby hands twitched spasmodically.
_'Sans blague!'_ (No joking!) was all he could manage in the way of comment, but after I left the shop, according to Gabrielle, his porcelain madame, he minutely examined every nutmeg in his stock, scratching each one with a pocket knife and dropping it on the hardwood counter at the cash-desk, in the hope of finding a wooden or 'American' specimen for a souvenir.
The Épicerie Danton carried cassia, cloves, caraway and coriander; mace, cumin, anise, capers; cardamom, chervil, basil, tarragon, savory, curcuma, fennel and other treasures of Arabia, but on days his business took him near the Madeleine, M. Corre would treat himself to an hour or two with the peerless importers of that quarter. There he would stare and sigh at bean sprouts from China, canned tamales from Mexico, fabulous products in cardboard boxes from America, labelled 'Quaker Oats' and in extreme cases something allegedly shot from guns. M. Corre had come to Paris, not in _sabots_ but the same kind of shoes with elastic sides he wore until the end, from a small Breton village called Erquy, which has a tiny beach and crayfish (Zola's liquid fire) and a kind of serpent called 'vipers' no living man had seen but in which all inhabitants believed. He had always wanted to go to Versailles. After thirty-two years of waiting in Paris for the opportunity, he got there thirty minutes before German Panzers caught up with the wagon he had hired.
This fell far short of requiting him for the loss of his son, his stock, his business, his country and the only kind of medicine that would keep his diabetes in control and which was needed in Berlin.
M. and Madame Corre had had other plans for their son, who was one of the few French boys who stood his ground when deserted by his officers near Sedan. They had sent him to Berlin to learn German, to London to learn English and to Rome to learn Italian, hoping that he would not have to sell only beans, canned goods and spices, but would branch out into the importing trade and carry, in a larger store in some other quarter, Chinese bean sprouts, American breakfast foods and a yellow substance like snuff used by Hindus in making curry. The son had married a tall quiet Catholic country girl of good family from somewhere outside of Dijon who is quietly starving and sitting very still in a chair, alone in a room with lace on the cushions, lace antimacassars on the chairs and a hand-painted green velvet cover on the top of an upright piano she now never plays. This young woman, dutiful and obedient from birth, is trying to dull the pangs of hunger and bereavement with a bewildered hope that she has not been misled about the future life, which cannot be far away, and that somewhere beyond the clouds one can hear Gottschalk's 'Last Hope' or the 'Liebestraum' or angels singing _Madame Butterfly_ and that her resurrected young husband will not be a _gueule cassée_ (disfigured face) throughout Eternity.
# _To the Memory of a Second-Hand Accordian_
ONE SUMMER IN THE late twenties, when it rained practically every day and the city drooped and dripped under clouds that leaked like French plumbing, a witty street ballad appeared, entitled: _'Il n'y a plus de saisons!'_ (There are no more seasons.) That was true in certain years, but usually the Paris seasons were defined in traditional ways that transcended accidents of weather.
In spring one would be aware of a fragrance or balm in the air, sharpened by gasoline fumes. Suddenly, on the way to lunch, one would see a small irresponsible dog rolling over in a patch of sunshine. New leaves would appear on the plane trees and horse-chestnuts. Turtles, pigeons, hens, canaries and love birds would be placed on the pavements in front of pet shops and feed stores. The first _bateaux mouches_ (small passenger steamers) would pass under a bridge with a load of shivering passengers. Café terraces would spread in area and show sudden animation. Pale children would emerge from winter hiding with nurses in regional costumes or flat-faced women in pyjamas from Annam. There would be a few weeks' respite before tourists from the United States would show up, and take possession of their smug regions on the Right Bank, centering about the American Express, the Café de la Paix, and the de-luxe shops in the place Vendôme. In the rue de la Huchette there were no trees or tourists, but just across the rue des Deux Ponts, and clearly visible from the top windows of the Hôtel du Caveau, lay the quiet walled garden of St. Julien le Pauvre – grass and trees, old stone benches and a few, not many, neighbours who liked the quiet shelter. Earlier each day the morning sun would stream through the little street, making dancing miracles of dust batted from rugs held out of windows. For the beef and lamb butcher, M. Monge, the radical-socialist horse butcher, Madame Absalom and others, the coming of spring would mean a slump in trade, therefore less confinement. The barrow men and women, the milk dealer and the café keepers would get ready for a boom, as did the pimp, Robert, Madame Mariette of _Le Panier Fleuri_ , and Madame Lanier in the _clandestin_ and laundry.
France at that time was increasingly athletics-conscious. One heard the word 'sport' even in byways like the rue de la Huchette, where the son of M. Corre set out now and then for a soccer football game and the son of M. Henri Julliard (who had been established in a struggling typewriter repair shop) put on a _costume de tennis_ and batted soiled balls to his fiancée, who squealed happily and showed more good will than co-ordination. Paris was host to the Olympic Games in 1924 and while German athletes were barred, which was just as well since they were underfed to such a degree as to make competition unsportsmanlike, Austrian and Hungarian athletes were welcomed with self-conscious hospitality.
In sport as in music, individual Frenchmen were likely to be brilliant, if undependable, performers. Their team work left something to be desired. They were in continual subconscious rebellion against regimentation and, because of this, they fell steadily behind the progress of an age in which concerted effort and mass production were essentials. They did not bet as heavily on horse races as the English do, but they took the defeat of their prize horse, Épinard, very much to heart when he was beaten by Wise Counsellor at Belmont Park. Monsieur Henri, of course, could never have been a bad loser, but he thought Épinard must have been the faster horse and had been thrown off form by the long sea voyage. He, himself, mackerel fishing off Erquy with M. Corre one holiday week-end, had had a taste of seasickness which made him understand with a shudder what Épinard had to endure for eight days at sea.
The summer in Paris, in quarters like that of St. Michel, where tourists never swarmed, was marked by closed shutters. Most shops were sealed during August. The poorest tradesmen stopped making or losing money, as the case might be, one month out of twelve and went to the country. Sometimes the 'country' was only a half hour away; again it might be all the way across France. Many small restaurants also closed, and in the rue de la Huchette the two hotels were minus half their guests, the lupanar was under-staffed, the morning mass at St. Séverin was sparsely attended, the neighbourhood street walkers were more conspicuous in the evening hours, the laundry was closed, the sound of The Navet's voice and the ring of his pompous footsteps were absent. The taxidermist was in Normandy, the butcher in the Alpes-Maritimes, the beans and spices at Corre's grocery lay dormant in boxes and on shelves, the students were away, also most of the professors.
On account of her disabled father, Madame Goujon could not leave her apartment, and little Hyacinthe, who disliked the country because the trees and flowers seemed to distract attention from her dainty costume and precocious remarks, was taken frequently by Madame Absalom, and, after I had gained her mother's confidence, by me, to the children's theatre in the Luxembourg Gardens where La Absalom and I were obliged to sit around the rim of the auditorium so as not to obstruct the view of the small spectators. The children, as a whole, entered into the spirit of the Punch and Judy shows. The puppets behaved as the kids longed to do, being tough, uninhibited, unbreakable and subject only to their own perverse law. The most demure and quiet little boys and girls were enthusiastic when retribution caught up with the villain. But it was Madame Absalom who most enjoyed the show. She whooped and protested, shouting warnings and advice when the hero was in danger, and pounded her bony knees, her eyes gleaming, when the cop's resounding stick was whacking Punch's head. Punch, I am sure, she always identified with her 'ex' in Clermont. Little Hyacinthe did not like the show at all. It was not romantic. But the day I took her to a matinee in a variety theatre and Loie Fuller's girls performed their scarf dance, I began to love Hyacinthe wholeheartedly, forgiving freely her snobbishness, her relentless practicality, her selfish outlook on the social world. Her intensity was touching and tremulous. Then and there she resolved to be an actress.
Autumn was signalled by the re-opening of the schools, with wan tired children in drab smocks trooping in early and returning late. The French school system imparted considerable standard knowledge to its victims, but it cast a pall over childhood and exacted from frail bodies as much as it placed in submissive or rebellious minds. Discipline was strict, and imposed for the convenience of underpaid teachers without reference to the needs of the child. In the Catholic schools scholarship was subordinated to memorization of the Catechism without understanding it, and if the kids undressed in pitch dark, the duty of the sisters was done.
In the Luxembourg, a short walk from our dingy street, the head gardener made a speciality of late-blooming flowers. The gardens were riotous with rich autumn colours, shrubs with garnet leaves, dahlias, asters, chrysanthemums, exotic foliage and flowers in neat designs, others less symmetrical, in scarlet and vermilion, plum-colour and damask-purple, mahogany, ebony, amethyst and ochre, resplendent in the cooling sun, resistant to the deepening chill of night.
Along the Seine, not far from the Louvre, a colony of giant sagacious crows returned from the suburban grain fields to their town quarters in the ancient trees along the quais. These crows had learned that living in Paris, near the central markets where, at dawn each day, scraps of nearly everything a crow likes and needs were easily obtainable, was easier than rustling in the country, exposed to the farmers' shotguns.
One of the features of a Paris winter was the annual rise of the Seine. This provided a flood of conversation whenever talk lagged anywhere, any time, between December and April.
Much has been written about the dangers of the Arctic cold and the heat of Calcutta, but I have known many husky adventurers who could tolerate any climate without weakening except that of Paris, France. The thermometer seldom fell below zero; there was almost never any snow. Some days it failed to rain, and occasionally the sun came through the clouds. Nevertheless, it was impossible to get warm and keep warm and even harder to get dry. Dampness was everywhere. Walls were mouldy, pavements soggy, clothing humid. Worse than that, everyone had colds, ranging from simple ones through laryngitis and bronchitis to pneumonia. I could walk with my eyes shut through the rue de la Huchette and identify each cough as I passed.
That these respirational afflictions were communicable was a modern fact that neither the Church, State nor the population of Paris was willing to take into account. Cooks and waitresses sneezed, snuffled and coughed without stint. So did clerks in stores. Business was complicated by fevers, flushed cheeks, running noses, watery redrimmed eyes, voices that squeaked and scraped, inflamed tonsils, choked tubes and raw-papered lungs.
When the Seine was high, the cellars in the rue de la Huchette would be flooded, and this tendency of water to seek its level always caught the inhabitants unaware, ruined some vegetables and, occasionally, a few bottles of wine. The newspapers would recount each day how a certain number of families down river had been driven from their homes, and would print a few pictures of them being rescued in rowboats very clumsily manned.
One morning before dawn, when I was crossing the place Notre Dame on my way to the Hôtel du Caveau, I heard angry voices over the parapet and, looking down, I saw a disgruntled cop holding one end of a rope and leaning over the dark angry water. I descended the stone stairs, glanced over the edge and saw that on the other end of the rope was a tramp who had either fallen in, had been pushed or had tried to commit suicide. He invoked some kind of constitutional right not to tell us which. During ten minutes the tramp and the cop abused each other. Then I saw dimly a boatman struggling with a top-heavy dory.
'What kind of service is this?' the tramp asked. 'When a citizen is in the river, how long does it take to bring up a boat? '
'If you don't shut up, I'll let you drown,' shouted the cop.
'That's the way you _flics_ do your duty! Who pays you? The citizens. If you can't hold a rope, while this other lout is learning to row, let go! I didn't ask you to throw it to me, anyway!'
River traffic had to stop when the waters of the Seine reached the knees of a granite Zouave on the abutment of the pont de l'Alma. All tugs had smoke-stacks that could be tilted flat when the craft passed under a bridge, but after the flood had reached a certain height, recorded faithfully by the stone Zouave, there was danger that the entire superstructure might be swept away. During this short season when the flow of goods to Le Havre had to be suspended, a marvellous community came into being around the place de la Bastille. Barges by the dozen were tied up there, side by side, so closely that one could hop from one deck to another. The hardy river men, women, children and dogs renewed acquaintance, rested, drank, danced and frolicked, and enjoyed their only respite from months of strenuous toil.
Monsieur Léonard, the mild little Belgian who played the accordion in the Bal St. Séverin and occupied the attic room next to mine on the sixth floor of the hotel, knew many of the barge people, especially his own countrymen, and used to stroll over to the Bastille on winter afternoons carrying his accordion. Now and then he took me with him, and the memory of some of those afternoons still causes coloured shirts to flutter beneath my eyelids, and petticoats and cabin geraniums and kids and terriers and snatches of Javas, one-steps and foxtrots, legs in cotton stockings, strong wine drunk from mugs and jugs, cheese and fresh bread and all the bits and trifles now swept into the ash heap of history and progress.
It was on a narrow side street on the way to the Bastille quarter where I found the laundry for men with only one shirt.
One winter week-end, Georges, the _garçon_ , always depressed by stretches of bad weather, got boiled on Saturday night, and in attempting to cut his throat spilled blood all over my laundry, which was in his room at the time. I found myself with no clean linen and confided my predicament to Monsieur Léonard, the accordion player, who said it would be all right to start out with a soiled shirt – that we would have it washed and ironed on the way. Monsieur Léonard then led me to the _Blanchisserie des Imprévoyants_ (Laundry for the Non-foresighted), where conversing or reading, naked from the waist up, on crude benches placed around the wall, about a dozen men were waiting unhurriedly. They ranged in ages from twenty-two or -three to sixty. Some looked wasted, a few depraved, others thoughtful and resentful, one or two philosophic. A cadaverous hairy man was drawing a caricature of another with carpenter's chalk on the wall. A small old man with stained silver beard was murmuring over a volume of Verlaine. Four tramps were playing _belotte_ with greasy cards.
As Léonard and I entered, a villainous-looking man in a striped sweater and rakish cap appeared from the steaming kitchen with an immaculate white shirt, washed, starched and ironed, which he handed to the old amateur of Verlaine. The latter wiped a tear from his eye, which glittered like the Ancient Mariner's, accepted the clean shirt and, before he put it on, took four sous from a coin belt of onion skin. These he handed over to the sweater and cap, who started to put them in his pocket, then glanced at the doorway in which was standing a huge belligerent woman. Smiling at the woman, the sweater and cap changed his mind. He dropped the coins one by one into the cash box.
The other occupants of the room had gathered around Monsieur Léonard and his accordion.
Their desire for music was too insistent to be denied; so Léonard unslung his instrument and played one after another the pieces of his repertoire. He could play a fair accordion part in a small orchestra from a marked piano score, but in a long life of accordion playing he had learned only three pieces by ear.
One of the most depraved of the tramps, with deep, dirty lines in his face, a hoarse whisky bass for a voice, scars on his arms and torso, and one ear chewed off, grabbed the suds-slippery madame, who yielded, although she could have tossed her partner all the way across the room. A cop looked in, hesitated, then grinned. He had come to check the 'papers' of the vagrants. Seeing that everyone was enjoying himself the cop contented himself with asking me for my credentials. I showed him my American passport and he went his way. I went out for liquor and brought back a bottle of cognac and a gallon of red wine.
At seven o'clock that evening, four of the tramps were still standing. The big washerwoman had dragged her tramp somewhere out of sight but not completely out of hearing. So I strolled into the back room where the tubs were, washed my own shirt, and after hanging it on a line near the back of the stove to dry, decided to take a nap. I awoke, cold and stiff, to find that it was four o'clock in the morning and that the fire had gone out. The prudent sweater and cap was fast asleep on a bench in the front room. Léonard had tottered as far as a barge and had been laid away by some Belgians he knew, who had taken care not to puncture his accordion.
I became dissatisfied with the well-meant efforts of Monsieur Léonard on the accordion and resolved to take up the instrument myself. So I bought one in the place Clichy.
After struggling with it a while, to the mild amusement of Georges, the _garçon,_ I went back to the place Clichy to inquire about a teacher. I had got farther in a few days than Monsieur Léonard had in several years, but I wanted to play well. To my astonishment, I was given an address in the rue Zacharie, not two hundred yards from my hotel.
The teacher turned out to be a large, dignified, gruff Frenchman who had a Marseilles accent on which he could have hung his derby hat. His first admonition was that I should buy a leather apron, like those the blacksmiths wear, to protect my trouser legs. Then he played me an exercise which I repeated by ear at once. He looked annoyed.
'You have little patience,' he said reproachfully, and dug up another and more difficult exercise. By that time I realized that I was dealing with a sensitive man. So I refrained from playing the second exercise too easily and said I would practise it faithfully at home.
The fact of the matter is that Monsieur Trexel taught me little that I wanted to know about the accordion. He had other pupils who were very poor and pathetically anxious to be able to hold down jobs in dance halls, and his instruction tended to make one into a shrill component of a small dance combination. However, there was something big and expansive and musician-like about M. Trexel that inspired me to practise hard and learn for myself. Curious to find out what could be done with two accordions, I arranged the slow movement of the Beethoven violin and piano sonata in E-flat, took him the manuscript, and we played it side by side. Monsieur Trexel was impressed and amazed. He had never heard accordions sound like that before. We played the piece again and again, but when at the end of the lesson I tried to pay him the customary ten francs (twenty cents) he looked at me with injured dignity.
We hit on a compromise, finally, which worked well for everyone except my city editor. Twice weekly I went to M. Trexel for a lesson. We played standard and classical selections together. Then we went down to the sub-cellar of the Hôtel du Caveau, and I spent my ten francs for refreshments. In those days one could get a powerful lot of refreshments for ten francs. At 7.45 he staggered eastward towards the Panthéon and I sashayed westward to the rue Lafayette to the _Chicago Tribune_ office, where another drunken re-write man, more or less, made no difference at all.
# _Of High and Low Art, and Inflation_
AS THE SEINE WENT UP that year (1925) the franc went down. The middle-class French, accustomed from birth to count the sous, were pained and confused by the amended price tags. The government machinery creaked and fell farther behind. Farmers refused to produce. Industrial workers grew sullen and put fear into the hearts of their employers, who grudgingly handed out increases of pay that did not correspond to the mounting cost of living. The poor listened more readily to the Marxists; the rich were disquieted by the rumblings of the poor. The French Deputies, reflecting the naiveté of the French voter, assumed that the way to cure inflation was to change prime ministers.
Poincaré gave way to Herriot. Herriot was succeeded by Aristide Briand, an orator with a face that looked like a composite of all the earnest animals in the zoo. His voice ranged from a guttural growl to a baritone legato. For sound effects and pure malarky in the Chamber, no French politician had the edge on Aristide Briand, who was sincerely devoted to the idea that peace was a wonderful thing.
Certain news items of that period were, indeed, revealing, although given scant attention at the time. Two clerks of the Bank of France, during Herriot's incumbency, were arrested, tried and jailed for having advised some farmers to dump their holdings in French Government bonds and invest their money elsewhere. This pair of martyrs to the truth did not suffer in vain. Their message was not lost on the men and women of the rue de la Huchette. Madame Corre, who made the important decisions after her plodding husband had spent hours on the ledger, sold the family debentures and put the funds into Dutch securities. The beef and lamb butcher sold his bonds (amounting to $325) and stuffed the francs into a pewter pitcher on the mantelpiece, sweating daily when he read about their shrinkage in purchasing power. Monsieur Henri applied every franc he could get to paying off his indebtedness on the Hôtel du Caveau. For this purpose 'inflated' francs were just as good as any. Madame Absalom tried to put the screws on her 'ex' to make him jack up the small sum he had agreed, in writing, to pay her monthly, and her failure to get results kept her hopping like a roach in a skillet.
The Navet, fatuously pleased with himself because he was making paper profits by speculating secretly on the exchange, passed on a tip now and then to Monsieur Panaché. Madame Mariette, of _Le Panier Fleuri,_ bought Swiss francs on the Q. T. Madame Sara, of the Hôtel Normandie, made pilgrimages weekly to the Ghetto and handed her receipts to her old uncle, who was spurred to shrewder activities by anxiety. The milk store, run by Odette and the mild little Jean, raised prices as fast as the authorities would permit. In their tiny stationery shop, the aged Taitbouts dozed more fitfully.
The French army completed a sloppy evacuation of the Ruhr and Franco-German negotiations about trade and customs receipts floundered and finally bogged. Kellogg, known to American newspapermen as 'Nervous Nellie', was promoted from the Court of St. James's to the Secretaryship of State, where he played harmless trans-Atlantic ball with the eloquent Briand.
Having given up the invasion of Germany as a bad job, France joined Spain in a war against Abd-el-Krim, and was aided by some intrepid veterans of the American Lafayette Escadrille. These fliers, like the late son of Mussolini, saw flower-like beauty in bombs bursting below on the non-air-minded natives of Africa.
In spite of all the foregoing, life on the rue de la Huchette continued to be charming and abundant. The sun glowed in the east behind the towers of Notre Dame and three inhabitants of our little street, including myself, attended a magnificent performance of the Berlioz Requiem in that majestic cathedral. I refer to Milka, the Communist student, and a lonely man from an attic of No. 8, known in the neighbourhood as 'The Satyr' because of an alleged tendency to self-exposure. His accusers were two sisters from Alsace who jointly ministered to the needs of a retired lieutenant-colonel on the fourth floor of No. 7.
The Requiem, which Berlioz had written for the French Government in the late 1860's and which had been refused by the politicians who had ordered it from the composer, had been played not more than three times: once at Berlioz' own funeral as the first mark of national recognition; again in the spacious chapel at Les Invalides, or the national soldiers' home; and once previously at Notre Dame. The kindly old French musician, Gabriel Pierné, whose gentle little 'serenade' is known to piano pupils everywhere, organized and directed this top-flight musical event. At the head of his male and female chorus and full orchestra supplemented by a military band and several extra trumpeters, old Papa Pierné looked like Santa Claus in mufti. His benign appearance was the more incongruous because of the breadth and vigour of his interpretation. The horse butcher, Monsieur Monge, was ill with bronchitis at the time, with such a high fever that he was obliged to surrender his priceless ticket to the Satyr. My extra press ticket went to Milka because of her hunger for good music and the slander to which she was subjected on The Navet's account.
I will not say that, while being swept by surges of glorious sound, I did not, with tears in my eyes, subscribe to the notion that France and French genius could never pass away and by no means could be dispensed with. And when later I told my Marseilles accordion teacher that the experience had disabled me from practising the squeeze-box for a week, he nodded, blew his nose, and understood. We consumed twenty francs worth of refreshments on that lesson day, almost wordlessly, and as I drank all graves were opening at the blast of twenty of the best French trumpeters, plus the Archangel Gabriel, and the resurrection and the life were roaring in my ears.
On another day, I would stroll with Pierre Vautier to the Renoir exhibition in the rue la Boëtie and see deathless French blues and captured sunlight and flesh tones that had eluded the Academy. And again the rumblings of workers and economics and the sinking of the franc and the twitterings of 'Nervous Nellie' went out of earshot, and France was vital and indestructible.
My disinherited friend, Pierre, recently of St. Cyr, was having soul-storms which had little to do with world affairs. He confided in me that Mary the Greek was taking an attitude, lovingly and firmly, that had much in common with that of his unreasonable father. She had visited, on one unfortunate occasion, the art dealer's store in the rue de Seine, to bring him a registered letter. There she had formed the same uncharitable opinion of Pierre's co-workers that Vautier, _père,_ had forcibly expressed. Particularly she had viewed with misgivings the dainty and pink-cheeked middle-aged proprietor who wore corsets and addressed Pierre as 'lovey'. The proprietor took a corresponding aversion to the dark female beauty from the Mediterranean.
Pierre, flushed and earnest, insisted that Monsieur Bertrand, the art dealer, had made no improper advances. Also he confided in me that, since Bertrand had mentioned it, he could not deny to himself that Mary exuded a faint gamey odour, unresponsive to soap. Also, hips and breasts were essentially non-aesthetic, were they not? Was he unnatural, and lost? Or should he go back to military school and impose a self-discipline that would enable him to stand apart from women, men, boys and whatever else life had to offer?
'If only I were a believer,' he said, wistfully, 'but faith is the most disgusting of all delusions. I cannot be a hypocrite, and unluckily I am not a fool.'
I could offer no solution. Pierre soon broke with Mary, and she drifted back to Dubonnet before our eyes. She could seldom pay her room rent, but Monsieur Henri let her stay in the hotel, in spite of the protests of Marie, his wife.
Georges, the _garçon_ , was tender to Mary, not selfishly or with veiled intent. Strange as it may seem, Georges had no difficulty in enjoying more girls than his poverty and humility would seem to rate. When any one of the neighbourhood women got lonesome, which was often, and had no other place to go, Georges would be likely to find her in his cot. Naturally he would accept the situation manfully and philosophically.
In an ideal civilization most of us would have to be radically altered. I believe Georges would remain unchanged, the most wayward follower of Jesus and, perhaps, the most beloved.
# _Of, for and by the People_
FRÉMONT, THE LETTER CARRIER, his wife, Mathilde, and their blue-eyed daughter, Yvonne, lived in the cramped concierge's quarters on the ground floor of No. 11, a narrow four-story apartment house between M. Monge's horse-butcher shop and Dorlan's bindery.
Many of the families along the rue de la Huchette were set at odds by occasional quarrels. The Frémonts were always in accord. Monsieur Frémont sometimes on Sundays and holidays laid aside his letter-carrier's uniform for a light-grey cotton suit from the Bon Marché. He bought his shirts on the boulevard St. Germain in one of a chain of stores called '100,000 Chemises' and his socks were knitted by his wife, who bought wool from Madame Absalom. His passion was social justice, his weakness strong red wine. Frémont's mail route was near the Porte St. Martin. In our quarter he performed odd jobs with a screw driver, oil can, pair of tweezers, a bit of putty, beeswax, fishline, scraps of tin or zinc, a used paint brush, and, in extreme instances, a hammer and saw.
He would respond good-naturedly when summoned from his home or the Caveau bar, brush dampness from his forehead after taking off his cap, and then deny any knowledge, technical or practical, of the object or apparatus in need of repair. Readily he would accept a tumbler of red wine, which he relished as an owl loves baby mice, chat a while about the national predicament, amble home for material and tools, and finally get to work.
One of his creditable successes was to glue together the Colonel's bed pan which had been dropped by one of the Alsatian old maids in No. 7. This he did so neatly that the ex-officer never knew that it had been broken and consequently never deducted the 1907 value of it from Elvira's 1905 rate of pay. In 1926 he repaired a hole which had been punched with a broomstick through an oil painting of Judge Lenoir. About once in three years, he fixed Madame Corre's Singer (pronounced _san jhay_ , with the accent on the last syllable), and it was he who set up the Café St. Michel's complicated nickel-plated coffee machine after the man from the dealer's had bungled the job.
Of the men and women in our little street, an inordinate number was directly in the employ of the Republic. In addition to The Navet, Hortense Berthelot, the policemen in the little station, an inspector of gas meters who lived at No. 9, a Gentile inspector of kosher meat at No. 22, the driver of a watering cart, a telephonist, and numerous others, there were Frémont and his friend, Pissy, who checked trains in and out of the Gare St. Lazare.
These _fonctionnaires_ or government employees were the hardest hit by the fall of the franc. Unlike the industrial workers, they could not strike, and neither had they the farmers' facility for producing their own food. Their immediate bosses were small-minded men who had risen through superior meanness. The higher-ups did not know them by name. After twenty years of service (1919 to 1939) Monsieur Frémont drew down, for himself and his family, about one dollar per day. Monsieur Pissy did just about as poorly, but he had a son, and not a daughter, so he was in the better position to 'defend himself' as times got worse and worse.
Looking wistfully at Yvonne, his handsome daughter, Monsieur Frémont said one day:
'What a pity! She's too good-looking to marry a working man.'
By practising the strictest economy and because of his odd jobs, the Frémonts were able to put aside a dowry for Yvonne, from their dollar a day, minus dues to the union. In 1920 this nest egg amounted to 2,000 francs ($286) and in 1926, to 4,500 francs ($100). Of such mathematics are world disasters made.
Yvonne, as a girl, could not go out without her mother or father, and neither of them had much time, so she met few young men. She learned to embroider and make her own clothes with an aptitude for copying good models but no talent for original design. She got average grades in school, tried to read some of her father's Marxist pamphlets and failed to understand them, and her only small sin was sipping secretly at the family Benedictine. This made her feel warm, excitedly patient and expectantly calm.
Class-conscious and aggressive types like The Navet, the floor walker Panaché, and the small-souled beef and lamb butcher, who believed his francs, concealed in the pitcher, were losing value because of the growth of labour unions, denounced Frémont as a drunkard and a dangerous radical. Frémont dismissed them as victims of circumstances, blinded by their capitalist education for which they could not be blamed.
The Navet was afraid of practically everybody, but especially of Madame Mariette, whose grey eyes could be as cold as death on occasion, and who had some nugget of information stored away that kept The Navet within bounds.
Men of all sorts strayed into Mariette's establishment. It was equipped with a small schoolroom with school desks and blackboards on the walls for very small women who could make up and act like schoolgirls in their teens. Also it had a small salon where noncommercial motion pictures (for which the costume bill had been the smallest item in the cost of production) were displayed. Also a sound-proof chamber where a creditable flagellation act was staged when prosperous customers felt that way. Old Armandine and a tough young woman named Mireille were on the receiving end of the black snake whip on those gala evenings, and it was said that Mireille really liked it and Old Armandine did not. Madame Mariette's high-class clients were able, in those days of unbalanced budgets and inflation, to buy champagne at fifty francs a bottle (the first round being genuine) and often confided their little secrets to Madame, which, for the most part she guarded with professional discretion.
Under the oppressive Code Napoléon, framed to keep Frenchwomen in subjection, and which did not permit them to have bank accounts, or to buy or sell property, or to travel without their husband's consent, if they were married, or their father's if they were not, Madame Mariette was better able to hold her own than many of her more conventional sisters. She had a husband who made few demands, and enough state secrets to protect her from petty persecution.
A piquant illustration of the Code Napoleon comes to mind. A woman of my acquaintance received a telegram to the effect that her husband, a captain in the French army, was dying in Algeria. When she applied for permission to go to his deathbed, the police officials ruled that she could not do so without her husband's permission. Since the husband was too far gone to sign the necessary permission, he had to die without her, while she remained in Paris.
France, a nation of 40,000,000 people, maintained a huge standing army, the officers of which were, for the most part, contemptuous of republican ideals. On top of this, the French supported an even larger and less efficient horde of public employees who sapped the public morale and resources. These civil servants were so underpaid that they had no spirit except of resentment, no purchasing power, no prospects of anything but slow defeat.
'After all, in France there is no unemployment,' The Navet said to me, during the period of our American depression. The fact of the matter was that while few Frenchmen were out of work, a large percentage of them were unproductively employed. In the long run that is worse than having them jobless. It costs less to support an idle man than one who is perpetually in the way.
One might have thought that with this huge swarm of public employees drawing pay, however inadequate, the public services in France would be passable. Nothing could be farther from the truth. On our little street, there were less than a half dozen telephones. The population of the quarter was about 2,500 souls. If one of them wished to speak with some distant person, usually he saved time and trouble by taking a bus, the subway, or even a train. The semi-public phone in the Café St. Michel was out of order about half the time. Madame Trévise, busy woman that she was, liked it better that way. In order for a client to use the phone he had to buy from her a metal disc or jeton. This was good for a local call, in case one could (a) decipher the complicated directions as to when to take off the receiver, drop the jeton, etc., etc.; (b) attract the attention of an overworked and semi-hysterical operator who hated foreigners like poison and natives like medicine; (c) obtain the right number, if it hadn't been changed or listed incorrectly; (d) and provided that one's party was at home, and (unlikeliest of all) had a phone.
The unlucky Parisian who was forced to walk, as a last resort, to call long-distance, had to walk to the nearest branch post office and wait in line anywhere from thirty minutes to three hours.
The installation in Paris of dial telephones took several years and for a while complicated the already faulty system to such a point that telephoning almost went out of vogue. When it was resumed, the improved apparatus proved recalcitrant to a high degree.
Frenchmen took these things as a matter of course. Parisians who would deny their grandmothers a set of false teeth in order to 'save money' never grasped the idea of 'saving time'. Never in the history of France had the ordinary citizen received good service of any kind. The finest collection of paintings in the world, housed in the Louvre museum, were so placed that daylight never reached them and the artificial lighting was atrocious. The Métro, or tube system, when constructed, had been modern and fine. After World War I it was overcrowded and inadequate.
The railway system was antiquated, badly directed, under-manned and hazardous. In 1925 there was such an epidemic of railway accidents that the entire personnel got panicky. Engineers ran through signals. Signals were incorrectly manipulated. Rails spread; roadbeds settled; switchmen had nervous breakdowns after they had caused disasters; and one engineer was so relieved at having successfully brought his train from Nancy into a Paris terminal that he forgot to apply the brakes and crashed through the final bumper. Result: 6 dead, 44 injured. When one escaped with life and limb from a railway journey, one had been jolted and blown full of cinders, taken on detours and generally discommoded and delayed to a fantastic degree. In first class, one was slighted by the poverty-stricken employees, and served sloppily in the dining car, if any. Second class was jammed with bourgeois, third class with peasants and soldiers. Travelling became an ordeal and a hardship, and one was considered eccentric and vulgar if one did not assume it would be that way. Trains were dirty, unheated, irregular and late. Once, when employees were goaded into striking for less inhuman conditions, the then prime minister of France (I believe it was Briand, the lover of peace) found some old law under which he could induct them into the army as reservists, and then as soldiers have them shoot themselves for high treason.
The post office was no better. Mails were slow and unreliable; the offices were unsanitary and under-manned. Street cleaning was confined to the tourist sections. In the little streets debris was washed from gutters up on the pavements by old-fashioned waterwagons that blew like porpoises. Dustbins were systematically overturned and picked over by scavengers about four o'clock in the morning with such an attendant clatter that sleep was interrupted. Then about six o'clock the official collectors thumped and banged.
Gas meters leaked and sometimes exploded; electric lights wavered and ran up disproportionate bills; installations were outmoded and defective; and the whole maudlin process was complicated by trick systems of switches and fuses like an apprentice's nightmare. City water was unfit for drinking. Taxes piled on taxes. Government tobacco was impure, malodorous and unsuitable for smoking. Government matches had a sulphurous stench that brought tears to one's eyes, or came in little boxes labelled 'safety'. The stalk of a safety match was splintered and brittle; the head would not ignite, or it glowed without flame, hopped to one's trousers or shirt where it burned a hole, then had to be found and extinguished forcibly on the carpet, which thereafter bore a charred spot for which one had to pay when the inventory was taken, if one leased an apartment.
One can easily imagine how such services could become inadequate and extremely annoying. An American with a nostalgia for the efficiency of his homeland might indeed nourish a feeling of resentment over such minor inconveniences. Here he would search in vain for the well-ordered streets of his own country. Shaded lights and gadgets, modern and infallible, belonged to another world. Telephones and iceboxes and sound-proof bathrooms were far, far away from the rue de la Huchette.
But it had the finest and bravest and most companionable of men and women! It had two dusk-faring bats and mound upon mound of fresh vegetables that glowed on the barrows, and the haunting cries of itinerant vendors. It had life that streamed like the rays of warming sunshine. It had, above all, men and women of warmth and compassion, and also some of the lowest types extant. It had a scholar who read Plato by the light of a street-lamp through his dusty window and an old harlot who knitted for her nieces in the country. Behind the façades of its houses and shops were to be found the treasures of tradition and the fine or ignoble predicaments of living in the present. Love and hunger and hope and kindness and fear and humour and the struggle to survive on the rue de la Huchette, as elsewhere in France and the world, were the components of the drama frequently called human and now and then divine.
# _Of Non-Essentials_
MOST OF THE MEN AND WOMEN of the rue de la Huchette were active, if not productive. They sold food and produce, shelter, sex or refreshment, or scribbled in large ledgers. There were some others, equally interesting, who seemed at first glance to be a part of the scenery. The barrows around the corner in the rue Zacharie swarmed with customers and gave rise to lively chatter and hoarse invective. Men strayed in and out of bars, women in and out of stores and shops. Children trooped to and from school, pale and subdued, having been regaled with chocolate and a breakfast egg.
Even the florist at No. 23 had steady customers from large restaurants and hotels. The shop of Madame Durand was situated within easy walking distance of the fragrant _Marché aux Fleurs_ , or central flower market, behind the prefecture. Two mornings a week this market spilled over its boundaries on the quai and flooded the nearby bridges with potted plants and cut flowers, not to mention shrubs and, in season, Christmas trees. Therefore Albertine Durand could undersell other florists who could not have their wares transported so cheaply and easily. So Mme. Durand did a business quite out of proportion to the size of our street. She got up at five each morning, dressed without waking her husband, the Gentile inspector of kosher meat, whose hours were from eight to six.
Having selected fresh flowers for her shop, Madame Durand would hire a couple of tramps. These derelicts would borrow a kind of hod with shoulder hooks; the flower merchant would load them down until they looked like floats in a spring parade; and, herded by Madame, they would trudge to the rue de la Huchette. For this service Madame paid five cents per tramp regardless of the cost of living.
_La Vie Silencieuse_ (Silent Life) at No. 78, was a goldfish shop and, like its name, was peaceful. Passers-by paused to marvel at the fish and sea plants in glass tanks in the windows (the shop was only twelve feet wide) and about as often as the Seine fishermen along the quai caught a minnow a customer would stray in. Of course, the shop was poorly located, from a commercial point of view. In order to find it, one had to know positively where it was and how to get there.
The proprietor, Monsieur Maurice, was never called by any other name. Of all the shopkeepers in the rue de la Huchette, only two allowed themselves the luxury of getting to their place of business as late as nine in the morning. The two late risers were Monsieur Maurice, who appeared as if by magic each morning on a bicycle, and Monsieur Noël, the gaunt taxidermist.
'Man and boy I have been a taxidermist like my father and his father before him,' Monsieur Noël remarked one day. 'In the course of those three generations,' he added, 'no one ever came with an animal or bird to be stuffed, or to buy one already stuffed, before ten o'clock in the morning!'
Monsieur Maurice must have felt the same way about tropical fish, which are purchased during mankind's mellower hours, towards the last of the afternoon, when the fishes of _La Vie Silencieuse_ had the sun on them and were shimmering appreciation. He brought his lunch to our street each day, having strapped it under the seat of his bicycle in a rack provided for the purpose. When the suspended activities of the street seemed to indicate that it was lunch-time, Monsieur Maurice moved his one kitchen chair, the only non-piscine furniture in his shop, about twelve feet to the rear, unwrapped his package and started munching a sandwich (French style, with a long split crusty roll) and some knobby little pickles moist with wine vinegar. Then he locked his shop, strolled over to the book stalls and bought at random a second-hand volume which he would read, from cover to cover, in those exceptional cases when both the front and back cover of the book remained. Having read the book, he would turn it in next day in part payment for another. In all the years I knew him, he never found one he wished to retain and read a second time. He was a medium-sized man with wavy hair, dressed drably and quietly, responded politely with a warm smile when addressed and had a habit, when greeting a customer, of ungreedily rubbing his hands together. His taste in reading matter was catholic in the extreme. One day he would follow the adventures of some pioneer priest in the wilds of Canada, the next would find him mildly astonished by Mademoiselle de Maupin. In order, he would read with polite attention and quiet relish: a text book on the care of bees, a volume from Fi to Kl of an obsolete encyclopedia, and _Les Soeurs Marx_ (The Marx Sisters) by Louisa May Alcott.
To British readers this requires a word of explanation. 'Little Women' translated directly into French as _'Petites Femmes'_ would have a meaning which would have distressed Louisa May, of Concord, Massachusetts. The Frenchman of the street confused the name 'March' (the family name of Miss Alcott's _Little Women_ ) with Marx, made famous in France as elsewhere by the inimitable Groucho, Harpo and Chico. So _Little Women_ was named _The Marx Sisters_ and was believed by many purchasers, who were later disappointed, to have the zany qualities which have become synonymous with America's distinguished comedians.
No one knew where Monsieur Maurice went after crossing the place St. Michel at the height of evening traffic on his bicycle. The apéritif clients of the Café St. Michel and the Café de la Gare marveled at his co-ordination and judgment of distances, for nightly he steered a zigzag course between roaring buses, honking autos, rogue taxis, ambulances and harassed pedestrians without ever so much as nicking a delivery boy or sustaining a minor injury himself. Drinkers paused to watch his hair-raising performance, told their friends about it and even made bets on his chances. Of this Maurice seemed to be oblivious. He had to get somewhere on his bicycle at precisely that hour. His route, as a crow would have flown, involved crossing the busy _place_. Therefore, he did it.
One morning in 1927, Maurice's shop did not open, although a strange sad-faced boy arrived about noon to feed the fishes and arrange the sea plants in the tanks. The next day Maurice appeared with his bicycle loaded down with bundles and a straw hamper. A barrow with a few other effects followed later. Maurice purchased at the small bazaar or dry-goods store at No. 19 several yards of flowered cretonne, choosing a semi-oriental pattern that did not clash with fish. From the _Marchand de Couleur_ (paint and dye shop) at No. 4, he bought some picture wire. Meanwhile, because of the black band around his upper left arm and the black ribbon around his derby hat and the black tie against his clean white shirt front, the neighbours paused and expressed their condolences, not knowing exactly for what. It was not a mother, father, sister or brother who had died. Probably an aunt. Anyway, from that day on, until February, 1939, Maurice slept on a cot in the rear of _La Vie Silencieuse_ and within a month he sold his bicycle to one of the apprentices of the bookbinder's shop at No. 9. The apprentice, who lived up-river, across from the Halles aux Vins, did not cross the place St. Michel of an evening, but left the rue de la Huchette by the eastern gate, facing Notre Dame. This lad was so far below Maurice in skill that he was clipped by a siphon wagon, on his third night out, sustaining a broken collar bone.
It was exceptionally hard luck for Maurice that the book or pamphlet he had hit upon that day in 1919 was entitled _The Communist Manifesto_ and that his initiation into the poetry of Karl (not Groucho or Louisa) Marx was interrupted by special plain-clothes investigators from the Sûreté Générale who were making a routine check-up. These investigators, who had been able to make little showing in the neighbourhood, since so many inhabitants were already gone, disbelieved Maurice's story as to how he came by the volume, and booked him as a 'red'. His papers were years out of date, since no official of any kind had ever paid him the slightest attention before.
Two doors eastward, on the same side of the street with _La Vie Silencieuse_ , was a shop only ten feet wide with a sign reading: _Au Philatelogue_ (To Him Who Knows about Used Postage Stamps). The proprietor, Monsieur Dominique, was a grizzly, villainous-appearing old man in felt slippers and in frayed shirt-sleeves. He wore glasses which fitted him so badly that he took them off whenever he examined one of his prize stamps or filled small envelopes with assorted specimens and marked in ink the price of the lot, which ran from five to eighty francs. The valuable stamps he kept in a small old-fashioned safe, and were said to be worth as high as 1,500 francs apiece, having been expertized and labelled in 1907 when the franc was worth five to the dollar.
It was Monsieur Noël. who discovered that Monsieur Dominique was known throughout the stamp-collecting world as an authority, that he contributed articles under a pen name to several international magazines devoted to that hobby, and that he had been called to London on one occasion to testify in a British court (through an interpreter) and there had exposed a clever forgery.
In mid-summer, when the kind of people who like stuffed cats were away and when all kinds of animals, benefiting from the vitamins in the sunshine, were unusually healthy anyway, Noël had lots of spare time. The mortality of pets, he told us, was highest in the months of April, May, and in early June. In that season their fancy lightly turns to thoughts of love, makes them restless and incautious and leads them to their doom.
Mocha, the sleek black dog of the Hôtel Normandie, was not a thoroughbred, but he was the same colour (soot-blue-black) all over. His short healthy coat did not shine or glisten but seemed to absorb the sunlight. He had a noble head, with brown tranquil eyes, a nose neither blunt nor pointed, and a long tail he was careful not to sling around promiscuously. Mocha was a careful dog. He had to be, in a narrow cheap hotel where much drinking was done, in order not to be trodden upon. He was never kicked. Frenchmen of the city were extremely considerate of dumb animals, and in the country animals like horses, cows, pigs or oxen were too expensive to be abused or neglected. It always astonished me how well the city-bred French understood their pets, refrained from hurting their feelings, condoned their foibles and treated them like honoured guests. In return, the dogs and cats responded according to their individual temperaments. Maggie, the unspeakable terrier beloved by the grouchy Madame Marie at the Caveau, took every advantage of her mistress' indulgence. She scratched and chewed furniture, tore rugs and antimacassars, refused baths when she smelled to heaven, splashed in mud when she was clean. But the moment Marie was safely in bed and Monsieur Henri took over, Maggie became circumspect, performed tricks, kept out of the customers' way, did not snap at strangers or beggars, and became a she-angel.
Mocha, of the Normandie, was always the same, rain or shine, day or night, in sickness or in health. He was attached to three persons: Louis, the one-armed _garçon_ , Sara and the worthless Guy. With respect to Guy, I learned that Mocha, who respected him, was right, and that I had been hasty in my judgment.
One evening when a drunken client made some slighting remark about Jews, Guy rose in wrath, strode over to his table and said firmly: 'My wife is a Jew, Monsieur!'
Not content with that, Guy delivered a concise impassioned talk against race prejudice.
Of course, the next morning, Guy complained that Sara had sent him a rumpled napkin, and seemed to blame her because the baker's crescent rolls got smaller as the franc went down.
It was astonishing how Parisians reacted to flowers. One had only to carry an exposed bouquet or even a single rose or chrysanthemum along any Paris pavement, to see passers-by turn their heads and often gasp and exclaim aloud in admiration. Louis Aragon, an imaginative Frenchman if ever there was one, once gave an old beggar woman fifty francs and an orchid, on condition that she would memorize, and never forget as long as she lived, the name of the woman he loved. I would stake my life on it that the miserable old witch kept her part of the bargain. For the French, so penny wise in the midst of colossal folly, knew the value of gestures. I once saw a most prosaic-looking man in a public bus in Paris brush tears from his eyes as he read an article in _La Semaine Littéraire_. At the next news stand I got off the bus to purchase a copy. The story was an excerpt from a little-known diary of Oscar Wilde, who at the time he was trying to recover from the ordeal of his imprisonment was crossing a Paris bridge and saw a man drowning. Wilde was a strong swimmer and was about to plunge into the Seine when it occurred to him that his act would be interpreted as a theatrical gesture and a bid for public favour. In his pathologically sensitive state that thought held him back and left another burden on his troubled soul.
The barber shop and hairdressing salon in the rue de la Huchette (No. 20) was on the borderline between essentials and luxuries. Our local barber-in-chief was named Julien, who had worked for the famous Riess, near the place St. Germain des Prés, and whose tireless wife, Elaine, had been watched and prodded by Madame Riess, until she knew what surveillance really meant. When one got shaved, chez Julien, Julien tucked a sheet around one's collar and then lighted a gas jet, over which he warmed about a cupful of water. The lather was about like the meringue on a lemon pie at room temperature, and smelled of various things like bitter almonds. It dried quickly and thoroughly, especially around one's ears. The razor was stropped adequately, and Julien was pretty good with it, but once he had taken off the whiskers his part in the operation was over. One groped one's way to the sink, washed in tap water and dried oneself with a diminutive stiff towel, which had a way of resisting dampness almost entirely.
Julien's haircuts made one look like a nineteenth-century ad for hot chocolate, but they had an artistic touch, just the same. They bore the stamp of their creator.
Like most barbers, Julien had his favourite story. and his was a good one and true. His former employer, the great Riess, had commanded top prices for 'styling' women's hair and had attracted many rich Americans for whom the tariff was special. One of these, an advertising woman built short and stocky like an embroidered pine tree with head and shoulders, consulted Monsieur Riess and paid her large fee in advance. The master walked around her several times, patted her head, exclaimed, called his wife to witness and then said:
'Madame! You already are perfect! It would be a sacrilege to disarrange one hair.'
Julien used this story as a mental test for his clients. If they looked blank when he had finished, he gave them scant attention thereafter. Those who chuckled wholeheartedly were treated with special solicitude.
Madame Goujon had a routine all her own which she used on any men who strayed into her salon. It was not a funny story, but merely a way of getting the conversation on risqué ground. It seems that while her husband had still been alive (and that is all she ever said about him) they had been invited to a party at which parlour games were played. The hostess had a leaning towards literature of the Paul Bourget variety and had asked each guest to write a short composition, later to be read to the assembly, on piquant subjects drawn from a decorative spun-glass basket. Madame Goujon had been asked to describe _les frissons_ (the thrill that authors frequently describe by the use of asterisks).
'Now how could one do that, Monsieur?' she would ask.
All I could say was that many great writers had tried it, and almost always had come a cropper.
'Perhaps Proust,' I said, casually.
On the strength of those two words, Madame Goujon, an economical but emotional woman, bought the entire seventeen volumes of _Remembrance of Things Past._
# _The Prevailing State of Grace_
TO SAY THAT THE FRENCH had lost their religion or wandered after false gods is inaccurate in the extreme. I have never lived in a country where the church caused less trouble than in twentieth-century France. The famous 'separation' from the State occurred early in the century and broke the hold of the clergy on general education. The Jesuits did not dominate big business, as they did in Spain, and the priests, when they meddled in politics, did so discreetly, following a time-worn Vatican policy of lying low when years were lean.
Generally speaking, priests were not ignorant or bestial in France. In fact, they were sometimes better informed on worldly affairs than the average run of secular politicians. One of the best of them, the Abbé Alphonse Lugan of St. Germain des Prés, who had travelled the world as a missionary and had written several books in English about American government, offered a daily prayer which struck me as profound.
'Merciful God, make me neither rich nor poor.'
In France there was little Protestant influence. Either one was a Catholic and went through the motions or a free thinker and thought less about heaven or hell than who was prime minister or whether his mistress was to be trusted. The farmers and their wives were mostly church-goers. Industrial workers were not. The civilian employees of the government were good Catholics or not, according to the zeal of their superiors.
But in the army organized Catholicism was powerful indeed. High officers, if they were not conspicuously Catholic, had to be brilliant, almost phenomenal, to get along. The Catholic officers formed a powerful clique, and private soldiers who wanted leave or favours made it a point to attend mass with more regularity than sincerity.
But even among the most influential supporters of the Church, there was little fanaticism. The year that the Archbishop of Paris sprained his ankle when stepping from his limousine, which he had brought to the church of St. Christophe, the patron saint of vehicles to be blessed according to the annual custom, no one laughed harder than the bishops and generals.
Cardinal Verdier, who was renowned as a builder of churches in Paris, was visiting one in the process of construction and overheard a mason who had bruised his finger with a stone say: _'Nom de Dieu'._
'You mustn't say that, my good man,' the Cardinal said. 'When things don't go right, say _merde_ , as, everybody else does.'
As far as I know, the only things the Parisians were not willing to laugh about were the price of bread and the Tomb of the Unknown Soldier. The night that the eternal flame went out in a most irreverent way and the plumbers couldn't get it lighted again for fourteen hours, there was little irreverent comment. Editors and journalists continued to refer to the flame as 'eternal' and most of them did not mention its hours of non-eternality for fear of stirring up the touchy war veterans (anciens combattants).
The most pious inhabitant of the rue de la Huchette was a sad handsome woman of thirty who lived on the fifth floor, front, of the Hôtel du Caveau. Madame Claire dressed in deep mourning, kept her eyes to the floor and spoke to no one except Monsieur Henri, who treated her with divine consideration. For twelve hours each day Madame Claire made artificial flowers in a large dressmaker's establishment, and the rest of the time she prayed, either in St. Séverin or St. Augustin. She rose early, so as to be alone in the café with Monsieur Henri as she swallowed her coffee and bread. She felt unclean, like a leper, and destined to the sulphurous flames of hell because her husband, to whom she had been utterly faithful, had left her and divorced her in defiance of the Church.
The capacity for suffering of this gentle woman was frightening, if not shocking. She cringed as she put on or took off her clothes. The sharp wicked eyes of men and the remarks they made as she passed stung her like barbs of cat-o'-nine-tails. Her world and the world to come had crashed around her ears, and nothing Father Panarioux could say or do would induce her to relax. Monsieur Henri prevented her from starving herself, feeding her as if she were a sick child, as indeed she was.
'The trouble with Madame Claire,' said the cook, Thérèse, with finality, 'is that she has no sins of her own to weep about.'
'She doesn't know what she wants,' Georges said, as if he knew quite well.
A drunken American reporter who miscounted the stairs blundered into Claire's room one night and did not discover that she had practically swooned until too late. As is often the case, the mysterious ways of Providence turned apparent evil into miraculous good, for after floods of tears and protests, and a three-day bout of incessant praying, the clouds seemed to lift from Claire's troubled soul. Thereafter she went to mass, but not to excess, got a better job and one Easter morning showed up in coloured clothes and said 'bonjour' to everyone.
The store at No. 1 rue de la Huchette sold crucifixes, prayer books, stained-glass windows, altar trappings and other supplies for the faithful and the churches. The proprietor was a mild Alsatian who was meticulous in his religious observances because otherwise he would lose his neighbourhood monopoly. I think Monsieur Luttenschlager was a thwarted sculptor or painter, for he turned out the most amazing assortment of _crèches_ , or holy cradles, in the Christmas season. These little mangers, with baby dolls representing Jesus, porcelain Josephs and Marys, wide-eyed cows of papier-mâché, and excelsior for straw, were purchased by pious parents for well-behaved children at Christmas-tide.
In France the custom of exchanging elaborate Christmas presents was not in vogue. Small tokens such as flowers or decorative cards were sent to one's friends on New Year's Day.
Monsieur Luttenschlager could be seen early in December on his knees, in his shirtsleeves, in his window, giving the last artistic touch to his gems of representative and symbolic art. Had Salvador Dali taken a good look at a Luttenschlager creation he would have spared the world much hooey.
The carpenter next door went to church when some relative died. After years of 'Republicanism', France still had well-defined classes for funerals. One day I happened into St. Séverin just after a second-class funeral and found one of the younger priests matter-of-factly going the rounds and blowing out every other taper. We were good enough bridge companions so that I didn't mind asking him why.
'We're having a third-class funeral right away,' he said.
The line-up as regards believers and infidels on our street was about as follows:
Hôtel du Caveau (No. 5) Madame Claire... all other residents neutral or indifferent; No. 7 contained the very pious and aged Taitbout couple who sold newspapers, and the middle-aged Alsatian old maids and their army colonel (retired). All of these were pious.
The bookbinder who was alleged to use human skin was a free thinker, whenever he had time. Frémont was a Socialist infidel; so was Monge. Monsieur and Madame Lanier (of the laundry and _clandestin_ ) went to mass each Sunday morning and then took a trip on the Seine boats or a bus in the afternoon. Most of the girls of _Le Panier Fleuri_ went scuttling to St. Séverin, trembling, whenever bad news arrived.
On the north side of the street, the line-up was about like this:
The beef butcher had been born a Catholic and decided to let it go at that.
The paint dealer (who rented superbly beautiful copper kettles for two francs a day in the preserving season) went to mass about three times a year and sent his son to a parochial school.
The pork butcher, a pal of Luttenschlager's, approved but did not attend, being too tired of a Sunday.
The Satyr's habits were not known to anyone among his neighbours, but he would have been more likely to patronize a black mass than a white one.
Noël, the taxidermist, was a highly intelligent man who had no superstitions whatsoever, so he insisted.
Madame Absalom had ceased to believe in God as she got better and better acquainted with her slippery 'ex' in Clermont years before.
Odette and Jean, of the dairy store, were Socialists, and called religion the 'narcotic of the people'.
Had one asked Monsieur Corre whether or not he was a Christian he would have blinked and said, ' _Évidemment_ _!_ '
Madame Corre was as neatly religious as one of Luttenschlager's porcelain Marys. Dr. Clouet (of whom we shall hear much more) was an infidel who drank but did not take dope in any form. The dentist, on the other hand, was fairly meticulous in his religious observances, and consequently was given a small rake-off from parish funds for examining the teeth of the pupils in parochial schools.
Naturally, the spade-bearded military tailor, who looked like Tolstoy, was a churchman _sans rapproche_. Otherwise he would have had to make a speciality of sport or hunting outfits, or evening clothes. Julien the barber was a free non-thinker; the stamp collector was a scholar and scoffer; the owner and clerks at the music store confessed now and then; Maurice of _La Vie Silencieuse_ had not made up his mind; the publisher at No. 30 was commercially pious, since he handled semi-religious books; The Navet was a pillar of religion. You already know about Judge Lenoir, Madame Goujon and little Hyacinthe.
However backward the Church is in Spain or was in Mexico or is in South America, and notwithstanding the equivocal political manoeuvres of the Vatican, the Church in France behaved circumspectly. The French clergy, intensely patriotic and comparatively urbane, did not foster or encourage fanaticism. The priests, high and low, deplored it. I have heard many Americans express shocked surprise at the perfunctory and seemingly casual way in which a French congregation went through the motions while mass was being sung. They knelt or crossed themselves as if they were thinking about something else, mumbled their responses, strolled in and out during services and were dealt with sternly by the beadle only when they failed to come through with the requisite small change. A Frenchwoman, with grave pale face and black clothes, veiled and gloved on one hand, would skim the other over the Holy Water font like a sparrow wetting the tip of its wings, in about the same manner and spirit as if she were flicking a speck of dust from her skirt. There was neither the fervent intensity nor the crude brutality of a Spanish church in Paris, and the decorations were not in such atrocious taste at their worst, or nearly as magnificent as Burgos or Toledo at their best. One of the chapels at St. Germain des Prés had murals by Delacroix, another by the neglected master of Poussin, a tramp genius who was the real father of French painting. This was mentioned in guide books, but nothing was ever done to light the paintings properly, so they never could be seen.
The general run of French priests was far above the average of the Irish-American clergy in mental capacity and education, psychological understanding, tolerance and everything but warmth. The French priest did not see himself as a higher type of policeman. There was very little scandal involving priests and women of the congregations, and if a clergyman wandered now and then, in plain clothes, into a public establishment like _Le Panier Fleuri,_ safely removed in distance from his parish, no one in this world seemed to care a hang. There was no outward evidence that the Church was a burden to the poor. It seemed to derive its money and prestige from the rich. In fact, in no land as in France had Catholicism adapted itself to modern conditions with more grace and fewer incongruities.
Father Lugan told me, with a twinkle in his wise old eyes, that for several days before taking a boat for America he 'practised' wearing trousers so that he would not be continually walking around with his fly unbuttoned, accustomed as he was to robes in France. In whatever costume, he was the same good intelligent man. When German priests came to St. Sulpice, the missionary headquarters, Father Lugan spoke Latin to them and sometimes good-naturedly rebuked them for their lack of fluency in the grand old mother language.
The French people do not, like the suffering Spaniards, carry hatred in their hearts for the clergy. They know their priests are with and behind them, sharing their hardships and their ignominy, contributing to their dignity, but never wanting to betray them and prey upon their misery. They know that Frenchmen in robes, ordained and sanctified, would not persecute or condone or encourage the persecution of their helpless countrymen. Father Lugan's prayer, 'Let me be neither rich nor poor', struck a response from his communicants because, simply, they knew he meant it in all sincerity and humility.
# _Of Clothes and How They Make the Man_
IN THE MIDDLE 1920s it began to dawn on the people of the rue de la Huchette that France had not won the war, in fact, that nobody had won it. Early in 1926 Painlevé introduced a bill to reorganize the French army from thirty-two to twenty divisions. To this was attached a joker, increasing the term of universal compulsory military service from one year to eighteen months. The mothers of our quarter, particularly Madame Corre, Madame Marie of the Caveau, the baker's wife, and Madame Trévise of the Café St. Michel, grew haggard and tearful. This economy measure was accompanied in the French Senate by a bill to impose an 'income' tax on all foreigners resident in France (and not earning but spending money).
Each day the reactionary French columnists and editors came out more vituperatively against foreigners, particularly Americans. Since I was the only American on the rue de la Huchette (and many of the inhabitants did not know whether I came from North or South America), I was asked all too often to explain these scurrilous items and to make it clear what Coolidge, Dawes, Owen Young, Kellogg, J. P. Morgan, the monkey trialists of Tennessee, the Ku Klux Klan, Al Capone, the Fundamentalists, Henry Cabot Lodge, et al, were about. In each instance I had to start, not from scratch, but several yards behind the line.
On the Right Bank, floods of American tourists were arriving with each incoming liner, spending dollars that had multiplied in value because of the lop-sided exchange, eating expensive food badly chosen, drinking avidly because of Prohibition at home, purchasing objects of art and carting them away and enriching the owners of the big hotels. This had little effect in the rue de la Huchette, except through the daily papers.
It was at that time that an enterprising American newspaperman temporarily out of journalistic employment organized what were known as 'whoopee' tours, of thirty days' duration, on which fifty to one hundred thirsty countrymen of mine (without their wives) were treated to a protracted bout of inebriation and debauch unequalled by a Shriners' convention or an annual meeting of the American Legion.
An American Negro, wearing a full-feathered head-dress and a blanket, and representing himself as the Chief of all the American Indians, deposited a wreath on the Tomb of the Unknown Soldier on behalf of our sympathetic red men.
The Mellon-Berenger war-debt pact, giving France sixty-two years in which to pay a small fraction of a fabulous amount, was signed, and the State Department promptly lifted the ban on private loans to France.
Dr. Coué died at the age of sixty-two; Nicholas Murray Butler predicted a Franco-German entente in the near future; eighteen naturalized Americans were conscripted into the French army; Chamberlain and Mussolini staged a love-feast in Rome; Paul Claudel, a French writer, was sent to Washington as ambassador; our own Ambassador Herrick threw the weight of his amazing popularity into the balance against the rising tide of anti-American feeling that the press was feeding throughout France. Caillaux was publicly exonerated of the charge of traitorous complicity with the enemy, reinstated in political life and petitioned the United States Government to spare the lives of Sacco and Vanzetti. The Nobel Peace prize was divided between Aristide Briand and Dr. Stresemann, whose Locarno peace pact was sidestepped by Calvin Coolidge. Typewritten documents were officially admitted as evidence and for purposes of record in the French courts.
There was much comment, pro and con, because the American institution known as the 'cocktail hour' was being taken up in tourist hotels on the Right Bank. One afternoon I was urged by my friends at the Caveau bar to mix an American cocktail so that they would be in a better position to judge between the xenophobes who denounced the New World _apéritif_ and those milder critics who said it made no difference what Americans drank before the kind of meals they habitually ate.
Deeply aware of my responsibility as an 'unofficial ambassador' I shook up a pint of Gordon's Gin with a quart of dry vermouth, ignoring the observations that the gin was English, according to its label, and the vermouth was a product of France. That the pint of gin cost enough to feed a French family for a week or more was another point I refrained from discussing. When I sprinkled in the Angostura bitters, for which I had been obliged to journey a mile or more, all of my friends had to sniff the mysterious little bottle and taste the contents cautiously.
Monsieur Henri was the first to taste the Martini sec. He was polite but reserved.
'It's strong,' he said.
The chestnut vendor choked on the olive, which got stuck in his windpipe. Monsieur Noël thought the drink would be better without the vermouth or bitters.
Hastily I explained that this was not the only kind of American cocktail, that most bartenders could make at least twenty different varieties, and I tried, in vain, to translate such names as 'Side-car' and 'Bronx'. The affair wound up with Georges, the _garçon_ , drinking what was left of the pitcherful, about fifty per cent, and none of the Frenchmen or women was converted to the 'cocktail hour'. They preferred a drink before dinner that did not paralyse the taste, make them suddenly fond of strangers and hostile to members of their families, induce them to sleep with their clothes on, and miss buses and trains.
When I cooked oysters in milk my French acquaintances were adamant; they simply would not taste the stew. When I brought a package of Quaker Oats into the hotel, the well-meaning cook Thérèse made a soup, following a recipe she used for soup made of squash or pumpkin, convinced, in spite of what I had told her, that I had something else in mind.
The younger French, some intellectual and others not, made a fetish of everything American and 'modern'. What a French tailor turned out when he tried to imitate the cut of an American 'business' suit was equalled only by the output of a professional French instrumentalist when he attacked _le hot_ or American jazz.
The spade-bearded Monsieur Saint-Aulaire, who presided over the two-man tailor shop at No. 21, could not afford an atelier on the boulevard. He had never prospered, and never had gone broke. So he acted as if he were tailor by appointment to the Duc de Guise (pretender to the throne), and although his manners were impeccable, he did not consider it as much of an honour to make a chalk mark on the shoulder of Senator Berenger as on that of the penniless Honoré de Senlis, who played billiards with a duke.
The first time I entered the shop of Monsieur Saint-Aulaire to order a suit, being a devotee of the neighbourhood idea, I did not know all this about the owner and director. And now, years afterwards, I chuckle and gasp whenever I try to guess what Saint-Aulaire must have thought of me, a shabby uninformed and obscure foreigner (an American to boot), who wanted, not one of Saint-Aulaire's impressive creations for morning or afternoon or evening wear, but a copy of what I took to be a suit that had been made by a fair New York tailor.
'Can you make a suit like that?' I asked, after the required _bonjours_ and amenities.
I learned what a pair of eyebrows, fairly bushy, were able to express. Monsieur Saint-Aulaire looked at the garments I had laid on his table, half covering his illustrated style book, and made a superb effort to control himself. He did, to a certain extent. Picking up the coat (blue serge and shiny) as if it were Exhibit 'A' in a trial for treason, he glanced at it and put it down again.
'Exactly like that?' he asked.
'Exactly,' I said.
'Unfortunately I have no American cloth,' he said, and hoped politely that the incident was closed.
I told him French cloth would be all right if it didn't shrink, or English cloth if it were not too expensive. He must have needed money badly, for he called his assistant, who lifted down the bolts of cloth from the shelves. In order to break the ice that was rapidly forming, I said what a shame it was that the Empress Carlotta had died.
'She was 86,' said Monsieur Saint-Aulaire, dispassionately.
My selection was a serge from Lyons which Monsieur said 'naturally' would shrink, but before it was cut. I left my old suit for him to copy, agreeing to return a week from the following Thursday. I left a deposit of 200 francs (the price was to be 450 francs, or about nine dollars) and then was measured. I had not counted on that. My old suit fitted me, and I assumed in my innocence that a tailor could measure the suit and let me go free.
The eyebrows outdid themselves, and the assistant looked positively alarmed, as if he were to be arrested or fired. He was a meek little man who held rows of pins in his mouth, slouched a bit like Groucho Marx and glanced frequently at his master like a dog who is performing tricks while needing urgently to be taken out to the sidewalk. The measuring did not take more than an hour, and meanwhile, as a sort of challenge, I tried one subject of conversation after another, in the hope of causing Saint-Aulaire to thaw. The sixth or seventh try hit the jackpot. This superb champion of mind over matter was fond of amateur theatricals, which consisted, in his mind, of Molière, Racine and Shakespeare. He had played Hamlet at a benefit staged by the Duchesse de Rohan, and Shylock according to his own interpretation, which, I learned, was at odds with that of the director of the Odéon.
At this point I took the long chance that won me Saint-Aulaire's friendship.
'One could hardly go wrong, in disagreeing with him,' I said, timidly. Even the assistant smiled, and Saint-Aulaire decided that in spite of my sartorial inelegance and atrocious French pronunciation, I was susceptible to cultivation and refinement. From then on, things were better – all except the suit.
'Jews,' said Monsieur Saint-Aulaire, 'have been deprived of everything except their laughter. When they lose their money or property, one does not feel it in his heart. One is provoked into laughter.'
Saint-Aulaire's Shylock, then, was a comic character, and his audience fairly split their sides when his wench of a daughter got fed up with him and consorted with a Christian. As for the ducats – 'Monsieur, there is where the woe becomes lyrical. One assumes when a Jew makes money – he and you both know, Monsieur – that someone will take it from him when the time comes, _n'est-ce pas?'_
I got him away from Shylock with some deft cape work, and up north into Denmark. The French version of _Hamlet_ most in vogue has been embroidered into rhyme, so that the immortal 'to be or not to be' comes out something like this:
_'Être, ou ne pas être?_
_Dormir, rêver, peut-être?'_
From a third-story window of her 'salon', Hyacinthe Goujon had her eyes fixed on the tailor's window, since the legendary Count Costa de la Montaigne habitually ordered his uniforms there. Perhaps I should not have, but since little Hyacinthe was so frank with me, I talked to her as if she were a sophisticated adult. Hyacinthe was determined to remain a virgin until such time as she reached the age when Costa de la Montaigne might be given the opportunity to try to seduce her. Where this child got all her knowledge or information I never was able to understand. She told me candidly that when she went to Madame —'s select school she intended to have an affair with one of the young teachers (female) in order that she might not become too nervous on account of chastity unnaturally prolonged.
When the distinguished but Nazi-minded author of _Journey to the End of the Night_ set forth that French schoolboys ten years old sometimes kept themselves in pocket money by blackmailing innocent men they had spotted as homosexuals, many American readers were incredulous. In that instance, the Americans were wrong.
The second Thursday after my first visit to his shop at No. 21, I began to have misgivings about the coat that was process of creation. The assistant, it seemed, could not cut a coat so it would fall straight down in the back. The force of long habit was too strong. Monsieur Saint-Aulaire had not taken me at my word when I said my American suit was to be copied. That, from his point of view, would have been an unfriendly act. My new suit had a waist line and hips, not to mention trousers that were too tight in the legs and came up four inches too high. Also the shoulders were padded coyly, there was no watch pocket, and an array of practically indestructible buttons intended for suspenders had replaced the belt straps of the original model.
Either I had to refuse to go through with the deal, lose my 200 francs and be sued for 250 more, or modify my notions about style. I might have been obdurate had I not been reluctant to wound Monsieur Saint-Aulaire's professional pride.
'It's not your _genre_ , Monsieur Elliot,' Hyacinthe said thoughtfully. 'But it will make you less conspicuous.'
# _The Shock Felt round the World_
THE ONLY OCCASION on which I felt utterly ashamed and lonely in the rue de la Huchette was the night of August 22, 1927. For in distant Massachusetts that evening, my native state, a 'good mason and a poor fish peddler' were put to death, after seven years of mental torture, for a crime they had not committed.
What had been confused and distorted on Beacon Hill was perfectly clear to the inhabitants of my little street, and to the workers of Paris generally, namely, that Sacco and Vanzetti were being murdered because they had been 'anarchists' and foreigners and that Judge Thayer and Alvan T. Fuller destroyed them for the good of their privileged kind.
Previously it had seemed to me that the slogan of 'Frenchman first and partisan afterwards' had retained its force, but in little side streets like mine and on the broad boulevard Sebastopol, the hand that turned the switch in the Massachusetts prison that night started the preliminary rumblings of a series of quakes that jarred France's hostile inimical classes apart and ended in the death of a nation.
Monsieur Henri Julliard was tending bar that evening, and grouped silently around it were the oyster vendor, Messrs. Noël and Monge, Frémont, meek little Jean (the dairyman), Madame Mariette (who was too nervous to stay in her bordel that evening), the tough and courageous Mireille, Georges the _garçon_ , and Maurice of _La Vie Silencieuse._ At a near-by table sat Hortense Berthelot, all in black, Madame Berthe Dossot, and the drunken old woman who thought she sang like Yvette Guilbert.
A hush fell over the company when Monsieur Henri, who had gone to the corner to telephone, returned with incredulous sorrow on his face, looked apologetically at me and dropped his eyes.
'They have killed those men?' asked Noël, in his deep bass voice, almost a whisper.
Monsieur Henri's head inclined itself a little more. The women gasped.
'That was ignoble,' said Madame Berthe Dossot.
Conspicuously absent from our little street that night were The Navet, Monsieur Panaché, the beef and lamb butcher, spade-bearded Monsieur Saint-Aulaire, and all others of the extreme right who had expressed themselves on the case perhaps too freely. Shutters of certain shops were drawn at dusk; pilgrimages to safer quarters where men who worked were not predominant in numbers had started that afternoon. _Le Panier Fleuri_ had few high-class customers; the merchants and factory executives who patronized it ordinarily were reluctant to show themselves in public.
'The _canaille_ will make this a pretext for a night of thievery and disorder,' The Navet told his son. He added, smugly: 'I have it from someone close to the commissioner that the police will shoot them down. It's time they had a lesson.'
The son promptly went out to join the manifestants in the boulevard Sebastopol. The indignant mob, somehow, with bare hands and Vanzetti's dying words for inspiration, pulled out of their concrete beds some iron street-lamp posts and tossed them through plate-glass windows.
Had I been with The Navet's son and other prisoners of various kinds of starvation, I should have had an outlet for my grief and shame. As it was, I was the man from Boston, and wherever I went, to paraphrase the English poet, a bit of Massachusetts went with me.
It was no new thing to the French to have undesirables railroaded and executed on one flimsy pretext or another. But, somehow, they had hoped it was different in America, and so, in my innocence, had I. It would have been easier to bear if my friends in the café had not been so considerate.
There was little drunkenness that evening. The drinkers started recklessly and soon found that the stuff did not have its usual kick, and that made them listless and discouraged. I stood at the bar a decent interval, then started for my room, and decided half way up the first flight of stairs that I did not want to be alone, and could think of no one I wanted with me. I returned to the café and sat with Hortense Berthelot, and she consented, concealing her astonishment, to go with me somewhere in a taxi, in which she had not ridden since her pre-war days. We went to a Russian night club in the rue Henri-Martin, where there were rugs on all the walls and a large balalaika band and a Caucasian who danced with a hoop and sang a song I shall always remember about a tame bear which could not see a woman suffer so he went away into a forest – and she was hurt and wondered why. Mme. Berthelot and I drank near-champagne at high prices, she very sparingly but willing to do her part. At dawn we taxied to the Bois de Boulogne and drove slowly around the lake (tall silent trees and green moss on trunks and a swan on the water), and Mme. Berthelot, whose gloved hand rested on my forearm, said calmly:
'He spoke with exactness, _le pauvre_ Vanzetti. "I forgive _some_ of these people..."'
In that same season Papa Doumer, one of the most harmless Presidents of the late Third Republic, signed a bill authorizing the construction of six new warships for the French Navy, and Briand, on the other hand, cooked up a treaty with Kellogg and the wary Coolidge 'outlawing' war between France and the United States. The French Chamber voted to 'nationalize' all industry in time of war.
'We are _foutus_ ,' said Monsieur Henri Julliard. 'When there is so much talk about peace, we are sure to have another war.'
'It will be beyond our means,' the horse butcher said.
'We will have it just the same,' Monsieur Henri said, sadly.
Within a week seven billions of francs were earmarked for the construction of what turned out to be the Maginot Line.
All these events had an impact in the rue de la Huchette but did not hamper its traditional activities. Articles of piety, cabinet making, public women, paints and dyes, haircuts, yarn, goldfish, soap, felt slippers, used postage stamps, sheet music, flowers, spices, medical and dental treatment, and other local commodities and services were, as always, in demand. The man least affected by world trends and portents was probably Monsieur Dorlan, the bookbinder.
While at work, which seemed to be almost any time between seven a.m. and midnight, Monsieur Dorlan wore a smock soiled with ink, glue and other materials of his exacting trade, also a pair of ill-fitting spectacles which had to be pushed upward or laid aside when he had to be most careful. Neither he nor his two pale apprentices spoke, except to customers, during working hours. Each was preoccupied with seemingly unrelated tasks. The window was filled with battered worn volumes waiting their turn for parchment or leather bindings. So were all the shelves and corners and a large share of the floor area, and the tiny back room.
My own experience was probably characteristic. Time, for Monsieur Dorlan, did not exist. What mattered was doing his work as well or better than anyone else in the world. In the course of a year he handled precious books in Hebrew, Sanskrit, Babylonian, Arabian, Latin, Provençal and all the modern languages. He knew only French.
The job I had for him was to bind into two volumes twelve monthly copies of a modern magazine, containing among other baffling items several plates or reproductions of paintings by contemporary experimental artists and which his apprentices were just as likely as not to turn upside down in the hope of making their message more intelligible. I gave the volumes to Monsieur Dorlan one afternoon in February, and we spent several hours together, he questioning and making notes on torn fragments of used envelopes, and I explaining what I wanted done.
We agreed on a price which troubled my conscience, it was so low.
April 1st was the date we set for me to call for the books. On April 15th I glanced through the dusty window and saw by the light of a street lamp that my magazines were stacked just where Dorlan had put them two months previously. Delicacy prevented me from prodding the conscientious old man. When the leaves began to fall that year I was strolling one Sunday along the quai St. Michel and was halted by a man in a black suit and derby hat (late Empire) surrounded by his sizable middle-class family, consisting of large wife, and assorted children ranging in ages from twenty-four to nine. Only when he began speaking did I realize that he was Monsieur Dorlan. It was his wedding anniversary, he said, to explain his absence from his shop. Furthermore, there was a question he wanted to ask me about the periodicals I had left with him. Would I drop in some time within a fortnight or so?
I waited another decent interval, and just before Christmas I called on him (having walked past the shop at least twice daily in the interim) and agreed that the table of contents should be in the front of the book, not in the back, according to English and not French custom.
In March I observed that some of my magazines, enough for Volume One, had left their dusty places in the righthand corner of the front room.
Soon afterwards I had to make a short visit to America, about a year in duration.
On my return, Monsieur Dorlan sent one of his hardworking boys to the Hôtel du Caveau to inform me that my books were almost finished, and early in the following January I went to claim them, paying fifty francs the volume, which at the prevailing exchange was about two dollars each.
Just then I was having my daily lunches with Madame Goujon, whose tottering, deaf Marie put up memorable grub. As a contributor to the Goujon budget, I was given wider latitude in escorting Hyacinthe to the Comédie Française, the Grand Guignol, and tea at Rumpelmayer's or the Poire Blanche.
Call it what you like, I was deeply attached to that phenomenal young girl, who could witness with relish a stage performance in which a man's head was chopped off and spouted blood all over the footlights, or an episode in which a mad old hag gouges out the eyes of a young woman in the violent ward, using a knitting needle for the purpose. Hyacinthe also could vibrate like a sensitive viol when the company turned in a moving performance at the Comédie. Without musical training, and reared in the midst of her mother's atrocious taste, she could drink in modern or classical masterpieces and make, right off the bat, more intelligent comments than nine-tenths of the professional Paris critics.
Madame Goujon's newly acquired volumes of Proust did not benefit her, but they transformed Hyacinthe. In turn she devoured Villon, Rimbaud and Baudelaire, rejecting lesser poets with a sureness of instinct.
'You, my friend,' she said to me one afternoon as we looked up and down the Champs Elysées from the terrace of Fouquet's, 'will want to possess me one of these days. We have so much in common. You have looked so deeply into my heart, have had so much patience with my immaturity – such flattering confidence in my latent qualities you discern, and only you, dear Elliot.
'But I foresee that it may be wiser, more stimulating, yes, more satisfactory in the end, if we remain as we are. I swear that no one shall ever be closer. You know that. With us, it is not necessary to say everything. To define is to destroy. After all, you have no lack of mistresses. That is one respect in which I envy you, as a man. I shall understand, and there never will be anyone like Hyacinthe.'
It would have been brutal not to have replied in kind, and in so doing I cribbed from Huysmans. She knew it and overlooked it and lost no respect for me. It was all in the game.
'You tempt me,' I said, 'since I have had a share in creating you. Sin at all times is delightful, but a new sin, involving one's own creation, would be a refinement of incest, requiring theological interpretation...'
'Please. Don't be sacrilegious,' she said, earnestly.
# _Mostly About Whores and Music_
IN SOME WAYS the French were the least musical people in the world. Perhaps that statement is too dogmatic, and not just. What I mean is that there was no folk music that was part and fibre of Frenchmen, anywhere, any time, like the Spanish _flamenco_ , or American jazz. Tastes were individual and varied; there were cliques and schools and genres. Concerts were cheap in Paris, and mediocre. A crystalline, rather brittle school of piano playing, exemplified by Alfred Cortot, was taught by a few high-priced piano teachers to rich and ambitious pupils. On Saturdays and Sundays three or four orchestras like the Pasdeloup organization rendered German classics half-heartedly, Russian pieces in a Gallic style, and neglected the sound French music of the eighteenth and early nineteenth centuries in favour of trite selections familiar to the crowd.
News items leaked through to America how Koussevitzky had cancelled an engagement in Paris because the French musicians would not rehearse (since no one could afford to pay them). I once saw poor Schneevoigt do everything but throw his baton at the Frenchmen under his command, without attracting anything but their superficial attention. The Opéra Comique existed for American tenors or sopranos who wanted clippings about a European success, and practically anyone with a thousand dollars to spend could sing Mimi or Madame _Boot er flee_ (with the accent on the last syllable) once. French critics were so corrupt and cynical that for anything ranging from a lunch to a ten-dollar bill a performer could get a press notice that was not abusive. In the same way, authors could purchase literary praise and painters could get a canvas into the Luxembourg Museum. There is much just complaint in America about a corrupt press. In Paris individual newspapers were even more venal and unscrupulous, but no one expected them to be any different, and there were so many of them that every group had its say in one or another.
A cross-section of music in the rue de la Huchette is characteristic of the Paris of the Parisians, which had no resemblance, I cannot repeat often enough, to the American Express, the café de la Paix, the Hotel Ritz, onion soup at the Escargot, the Dôme, etc., etc. Moving from east to west along the street, the state of musical development, habits and preferences was about as follows:
The beef and lamb butcher had no awareness of music at all. He was like old Papa Doumergue, ex-president of the former Republic, who had to have a special secretary at his side on state occasions to nudge him when the Marseillaise was being played, so he could make the appropriate official gesture.
M. Luttenschlager, the dealer in articles of piety, hummed Alsatian (mostly Germanic) songs of poignant beauty and charm, and kept fairly well on the key, but could not keep time.
The proprietor of the paint-and-dye shop, Monsieur Villières, was neutral, and the carpenters across the street in No. 3 had no work songs to ease the monotony of saw and plane. The pork butcher strung along with Luttenschlager, specializing in children's songs about the snow, as he handled strings of sausages in a city where winter meant mud, influenza and a drizzling rain.
The Hôtel du Caveau had several assorted musicians among its residents, but most of these were foreign and they seldom got together when sober. Monsieur Léonard, the incompetent accordion player was a Belgian; Mary the Greek sang the Missouri Waltz without words in her cups; Pierre Vautier went in for 'The Six' French moderns who stemmed from Satie and were friendly with Ravel until his Bolero became a public nuisance with the advent of the radio, or _T.S.F._ Georges the _garçon_ hummed circus music; Thérèse, the cook, liked bawdy songs consisting mostly of words and gestures.
The Satyr, like Monsieur Noël, was a devotee of the splendid and neglected French music leading up to Rameau and Couperin. The Taitbouts were tone deaf; the Alsatian old maids never sang because it would have annoyed the ex-Colonel. Madame Absalom disliked music because it competed with her gossip. Dorlan, the bookbinder, thought of it in terms of early Catholic notation in old manuscripts. Lanier, war veteran and father of a family, sang 'Madelon' now and then.
Where music meant the most, in a limited way, was in _Le Panier Fleuri_. Mireille, with the indestructible hide and roguish blue eyes, had once been in the chorus at the Casino de Paris, before the days of Josephine Baker ( _Baa care_ ). She did much to relieve the gloom that stole into the parlour of joy so frequently. She would sit on the sagging sofa, beside old Armandine, who also was somewhat of a clown, singing and imitating the chorus girl's come-on tricks. And when rich customers wanted a living-picture show, a grave demure-faced girl with dark hair wound around her head in a braid like the halo of St. Cecelia, played Chaminade's 'Scarf Dance' on a cheap ornate piano, wearing a bathing suit cut rakishly to expose one breast and cover the scar of her Caesarian.
Sara, the Jewess at No. 18, when alone in her small café late at night, sang nostalgic laments like 'Eli, Eli'. But her faithful _garçon_ and platonic worshipper, the one-armed Louis, loved to sing, as a Spaniard or a Swede or Russian does, and when Monsieur Henri Julliard tried to exploit his medieval sub-cellars which had been frequented by Robespierre, Louis was given an old French costume and allowed, for a small fee, to sing songs like 'My Wife Is Dead' (familiar to American tourists who were taken to the Lapin à Gil [not _Agile_ ] near Sacré-Coeur).
Nothing much ever came of Monsieur Henri's attempt to make a night club of his splendid property, the Caveau, because the place, the songs and the neighbourhood were genuine. Tourists had become so accustomed to a certain amount of flim-flam that they could not be happy without it. This, Monsieur Henri could never grasp or understand. So his subterranean night club became a neighbourhood hang-out which was truly interesting and colourful but not profitable.
Of the man, wife and son who ran the little dry-goods shop at No. 19, where the neighbourhood servants and workers got their felt slippers, aprons, overalls and articles of plain clothing, I have said little because there was little to say. The family name was Luneville, they all were from the north and used the guttural r. They paid decent attention to their stock and customers, had their meals in the back room on time, and all three slept in the cellar. Their conversation was confined to 'yea, yea' and less frequently 'nay, nay'. They took no part in protest strikes, did not drink in cafés, read the _Intransigeant_ (known as the janitor's newspaper), closed the store in August to spend the vacation near Lille, and otherwise were the backbone of a decaying and disappearing France.
Monsieur Saint-Aulaire, essentially the artistic type, had views on music as well as drama and society.
'Mozart,' he said, pontifically, _'a fait une belle petite musiquette, mais, pour la vraie musique, donnez moi Massenet.'_ (Mozart wrote pretty little tunes, but for real music give me Massenet.)
Monsieur and Madame Corre had never had time for music, but they had a piano and liked it when their young daughter-in-law, homesick in Paris to a pitiful degree, played Gottschalk and Nevin's 'Narcissus' in a lady-like way.
It is needless to say that The Navet had no music in whatever he had in place of a soul. His kind the world over do not go for the arts, except to destroy them.
So the only men who sang with a will were Louis, the _garçon_ , and the chestnut and oyster man from the Loire, and the only creditable performer on any musical instrument was Monsieur Monge who played hunting horns and an old-fashioned instrument like a Chinese hat. The best French composers had always been taken up first by the Germans, the kind of Germans now extinct or in hiding. That was true of the works of modern French painters, too. When the struggling German Republic in 1923 took over the former palace of the Crown Prince for an art museum, the new directors acquired a fine collection of Cézannes, Renoirs, Vlamincks, Utrillos, Picassos (nearly always confused with the 'French school' he practically destroyed), Braques, Matisses, and good lesser artists like Masson, Chirico and the fantastic Alsatian meat cutter, Hans Arp.
Not as much could be said for any French museum. One of the last places the French impressionists got into was the Louvre.
The death of Jean de Reszke caused no flutter in the rue de la Huchette, whereas the death of the great actor, Lucien Guitry, whose only lapse from high art was Sacha, his son, was respectfully felt and acknowledged.
'All our great men are dying,' Monsieur Henri said, sadly. 'One hopes that some others are now being born.'
'Not likely,' cackled Madame Absalom.
When Rudolph Valentino died and fantastic reports about the demonstrations by American women in connection with the funeral of the great screen lover leaked into our quarter, well dressed up by the avid anti-American columnists who had a field day, again I had to proceed up my street as if I were running a gauntlet.
'Hey, American,' yelled Madame Absalom as I passed No. 10. 'What did that _type_ have that other men have not? He must have rogered half the women in your country.'
By that time Madame Absalom and I were on such terms that I was able to reply: 'He would have passed you up, you old battleaxe.'
'If I'd known when I was young what I know now,' the old woman said, 'I'd have _cocu mon_ 'ex' every afternoon and morning. I wasn't so bad. Just like the rest, I suppose, when all is said and done.'
'Some are better than others, just the same,' said Monsieur Maurice, smiling and descending from his bicycle.
When I passed No. 27, the Épicerie Danton, I was hailed by a troubled Monsieur Corre, flanked by his porcelain Madame. They were not concerned with the defunct Sheik of Araby and Hollywood. Madame's Singer or _San jhay_ , had broken down, and since I had informed them it was of American origin, they had hoped I might know how to fix it. The Corres, like other middle-class Parisians and Frenchmen, thought of the world as if it were a sort of dish, the bottom being France and all foreign lands and peoples being grouped together around the narrow slanting rim, so that stray objects and personalities slid down into their ken now and then. They expected all Americans to know one another, and to know all the answers about American occurrences and American machines.
The music shop at No. 26, owned by a non-musical bachelor named Gion who, like Madame Absalom, had received his means of livelihood by inheritance from an aunt, also had a small selection of early coloured engravings in the window. These Monsieur Gion picked up from clients who wanted to exchange them for sheet or bound music, and sold them to collectors, buyers from Right Bank art shops, and occasional stray foreigners like me. When I first saw the shop there was in the window, below a string of second-hand violins suspended like beautifully varnished hams above the level of the eye, a set of prints depicting the home life of the American _peaux rouges_ or Indians. Broke as I was, I simply had to have them.
The Indians were very shapely, the women being built about like Gaby Deslys and the men like the Christian saint who is portrayed leaning against a Corinthian pillar being shot full of arrows without showing the strain. All of them were the colour of Josephine Baker, with a touch of lavender powder. The she-Indians were all in their late teens, wore bands around their foreheads to keep their hair in place, had rings and bracelets on their fingers, arms, and ankles and skipped from place to place like Mary Pickford used to do before she was saved. The he-Indians fell into poses reminiscent of the Russian ballet, and in one of the best prints had strung hammocks of plaited deer sinews for the girls, who lay in them with one perfect leg exposed, while the braves swung the hammock gently.
My favourite was an old chief sending his sons off to war. He stood very straight and dignified, and the boys were lined up, in feathers and war paint, being embraced and kissed on both cheeks by the gruff old sachem, while squaws were turning their backs and weeping beneath trimmed willow trees. The engraver and artist, being a Parisian, had never seen an unpruned tree.
Monsieur Gion was a bloodless young man, something on the order of the floor-walker, M. Panaché. He expressed no political opinions, but one knew instinctively that those he had were all wrong. His mistress was an awkward, almost furtive, soft-spoken young girl who also was clerk in the store. This girl, Bernice, was an orphan who had worked in two department stores from which she had been fired for acting as the sisters in the orphanage had urged her to when approached by predatory males.
Monsieur Gion had hired her because she would work for two francs a day less than anyone else he had interviewed. She dusted well, which is essential in a music store. One day, however, when her hands were icy cold she dropped a violin worth 200 francs and got so rattled that, in trying to explain to the boss how it happened, she stepped on the instrument and stove in the fragile belly.
From that day onward she did the dusting and kept house in a very faithful way for Monsieur Gion, sharing his room on the fourth floor of the HôteI Normandie. Her pay ceased, and she learned how right the sisters of charity had been in warning her about original sin.
The very poor among the Parisians had learned that a certain poisonous drug, which I shall not name but which is obtainable without prescription in French and other drug stores, would, if administered a drop or two at a time, in a glass of white wine, make a woman quite ill for a few days, and sometimes produce a desirable result. Bernice was treated to this miraculous draught about three times a year, until queer things began happening to her digestion and her memory (never exceptionally good). This disturbed Monsieur Gion, who was afraid he might get himself into trouble. So he threw her out in 1932, after four years of unwedded non-bliss, and she tried to drown herself in the Seine, near the little park named for Henri IV, and merely caught pneumonia. Bernice looked so fresh and well, after her long rest in the Hôtel Dieu, that Monsieur Gion took her back on one condition which practically removed the possibility of pregnancy.
There was no nonsense preached in France about the dignity of labour and not much outside the church concerning the possibility of being content and happy although poor. That might be possible in the country, but not in Paris. The daughters of the poor, if they were ugly, would naturally be drudges. If they were pretty, or not repulsive, it was assumed that they would amplify their incomes, and the family income more often than not, by furnishing what men seemed to need and for which they would pay when they had to. The lucky girls, or the clever ones, landed kind or indulgent men. It was all a part of the system, and helped keep it in gear until it fell apart. It was accepted as a matter of course. That it was better or worse than any other system is beyond my judgment. In many instances it seemed to work hardships, and in quite as many others it seemed to turn out delightfully, with resulting benefits to all concerned. It was a part of French thrift, of ecclesiastical compromise, of a society highly civilized and poorly supplied with natural resources, of dangerous national boundaries and national enmities.
Madame Mariette, of _Le Panier Fleuri_ might permit old Armandine to get the hide whaled off her back for fifty francs, knowing the bruises would heal and that Armandine, at her age, could not make fifty francs as easily any other way. But the atmosphere of her establishment, from the point of view of the employees, was heavenly compared with that in Madame Durand's flower shop, Monsieur Gion's music shop, the sweatshop where Madame Claire did piece work ten hours a day, or the office in the prefecture where Hortense Berthelot was employed.
Officially, the bordel opened up at two o'clock in the afternoon, and remained open until two o'clock in the morning. But for men who had not got to bed, or had found themselves restless and had time on their hands in the morning, one girl came in at ten o'clock, in modest street clothes, peeled them off, washed herself all over with the aid of a bidet, was given a perfunctory O.K. by the _sous-maîtresse,_ or assistant hostess, who had early duty that day, and sat in a little triangular waiting room on a red velvet upholstered bench and chatted with the hostess until the bell in the hallway indicated that someone had entered without knocking, in obedience to the sign on the door.
The hostess, who was always fully and conservatively dressed, with the keys to the champagne closet dangling from her belt as a badge of office, would step into the hallway and greet the customer politely. _'Bonjour, Monsieur'_ , she would say, or, if she knew him as a steady customer who liked a certain amount of familiarity, she would say _'Bonjour, Monsieur Albert'._ Then she would usher him into a small reception room or parlour across the hall from where the girl was waiting.
'Mademoiselle,' the hostess would call, in a carefully modulated voice. Mireille or Mado or Suzie or Daisy or Claude or Germaine would cross the hall and pause a moment, smiling brightly, in the doorway.
_'Bonjour,'_ she would say to the man, or now and then sincerely pleased, _'Ah, c'est vous! Mais, vous êtes matinal aujourd'hui.'_ (Ah, it's you. My, you're up early today.)
The visit was described as 'a little moment', _une demi-heure_ (a half hour) or an 'hour', and was priced accordingly. For a short time, the client paid ten francs (about a quarter); a half hour cost twenty francs, and an hour thirty. The hostess mounted the short steep stairs with the happy pair, indicated which room they were to use: 'the red room', 'the blue room', 'the Oriental room', etc., and left two small freshly laundered towels on the bed table.
Only white girls, neither in the 'heavy' class like Armandine, nor the little women who posed as schoolgirls, nor the coal-black Negress from Martinique named Dora, took their turn on early duty. Wandering drunks or fitful sleepers might or might not be in the mood for something unusual in size or colour, and the chance that a tiny restless girl would be the only one available when Monsieur had set his mind on a fat complaisant type was too great. So morning customers got medium-sized beauties and had to wait until two o'clock if they had bizarre ideas that day.
At two o'clock the downstairs waiting room took on its lively air. Some of the girls slept in lofty little attic rooms upstairs in the establishment, but about half of them either had to meet their pimps and turn over the day's receipts at two in the morning or take a late bus or a taxi to their family homes. Even when business was dull, they never read. The only literature on the premises was six or eight illegal books with illustrations tending to stimulate certain customers who liked to browse through an obscene chapter or two before settling down to business. The girls never read these. Neither did they peruse the 'album' which was kept on hand and passed out discreetly by the hostess when a client asked for it. The 'album' had a collection of photographs which left little or nothing to the imagination except to make one wonder, when half way through, what possibly could be left for the remaining pages to portray. To what extent the 'album' at Madame Mariette's place made things easier for fading clients I cannot say, but it changed the course of the life of a young Frenchman I knew who was attending the Sorbonne in the early 1920s. Jacques was brilliant but had no ambition and no plans for the use of his excellent mind. He was at school because his parents could pay for it and university life was more carefree and less onerous than a job in a bank or the executive offices of some factory. One day when he was idling away an afternoon at Mariette's, in perusing the 'album' he was struck with the infinite number of variations contained in a few simple acts involving two, three, and in extreme cases four parties. He began thinking in terms of numbers: permutations and combinations. That same evening he plunged avidly into his neglected mathematics text books and soon led his class in higher algebra and integral calculus. Today he is one of the most distinguished theoretical mathematicians in London and freely admits that he owes it all to Mariette.
One of the features of _Le Panier Fleuri_ was what Mariette called 'the chamber of detached divertissement' in which a client (if he were well known or officially vouched for) might sit in an easy-chair, with a drink at his elbow, and watch through a hole in the wall, cleverly camouflaged by a figure in the flamboyant wall paper and covered on the observer's side by a picture when not in use, the behaviour of unsuspecting fellow men who entered the 'red' room with the girl or girls of their choice. The girl or girls, of course, knew all about the red room, and when the grave-faced and dignified hostess led them thither, she or they chuckled inwardly and shed all inhibitions with the scant and flimsy garments they wore downstairs for display.
Many students of psychology and human behavior patronized her chamber of detached divertissement, Madame Mariette told me. She had no affection for these professors who pretended a scientific interest in her spectacle because, when they had got through with their observations, instead of finishing the afternoon or evening in her salon they went to another one, in the rue de la Harpe or the rue Mazet, in order to leave with Mariette an illusion of sincerity in their detachment.
One client, who dressed like the late Berry Wall, used to show up every other Monday afternoon, that being the day of the doctor's visit. He would sit on the terrace of the Café de la Gare, sipping vermouth cassis, with the coins for payment of his drink already on the table. The moment he saw Dr. Clouet leave _Le Panier,_ this gay old party would grab his gloves and stick and would hobble to No. 17. He knew that on Mondays the girls were forbidden by law to receive any clients before the doctor came, and it pleased the old boy to be the first on the order of the day. This man, during the years Consuela was with Mariette, chose her invariably and complained indignantly when she left Paris for Madrid. Consuela was a thin Spanish girl with an appealing dignified face, black hair piled high with a Spanish comb, and she was 'the bride' of the establishment. That is to say, she did not appear in the line-up with the other girls when a chance customer arrived, but waited in a dim room for the initiated who were hard to please. She wore a white bridal gown, a white lace mantilla, longwhite gloves and carried a bouquet of small rosebuds and forget-me-nots (artificial but very bridal).
One of the most popular specialities at Mariette's was a Scandinavian type of blonde who dyed her hair, and I mean all of it, pale green and appeared naked except for a transparent cellophane raincoat tinted green.
All this was for the trade. The girls themselves were much like any other girls. The same ones used to work for a while in the cheaper houses like Mariette's, where things were more lively, and then would be graduated to the high-class houses in the Montholon or Madeleine or Étoile quarters and receive one hundred francs instead of ten for the same _quid pro quo._ They made about the same amount of money, since at Mariette's there was more activity, and they preferred that, not because they enjoyed it, but because in the expensive houses they had to wear expensive clothes and be careful of them, and were obliged to watch their grammar. The cheap busy places were less 'lonesome'.
Let no man think that he and his actions were not described gleefully and in piquant detail in that red plush reception room where the waiting girls gathered. Generally speaking the girls got along with one another. If one girl got in trouble or needed money, or was bereaved or discarded by a lover she doted on, the others rallied round. They all knew that if two girls in a house took a dislike to each other, and could not control it and be polite, one would have to go. Men reacted badly to an atmosphere of discord. And the one the Madame would send away would invariably be the one who was least popular with the clients.
I liked Madame Mariette. I think of her as a friend, an interesting and beautiful woman with genuine understanding, wide experience and something deep inside her that no man has yet aroused or even touched and but rarely suspected. On our street she was second to none, unless it was Monsieur Henri, in her love and solicitude for France. Of her profession, which many despise and deplore, this cleareyed shapely woman was neither ashamed nor proud. It existed. It was wanted. She tried to direct her establishment efficiently and well. No one was ever clipped at Mariette's, and most of her clients remained her customers for years. But when France's Mr. Blum knuckled under to England's appeasers and stood idly by while the decent men and women of Spain were destroyed and martyrized, Madame Mariette wept and bit her lips constantly for shame, the deep fundamental kind of shame that sweeps from head to foot and through all the nerves and fingers and intestines and glands like a foul disease made instantaneous. By the time Munich came along, her eyes had no more tears but were hot and dry and smarted.
What fascinated me most about _Le Panier Fleuri_ , after Mariette and the others had accepted me as a neighbour and a comrade, was the little record book and what it contained in the way of statistics. I tried to look at the astonishing Mireille with dispassionate scientific eye and decide why it was that, day in and day out, in sunshine or in rain, in May or in December, about three-fifths of the men in search of physical and spiritual solace would, when eight shapely, sweet, skilled and accommodating girls were lined up before them, nod or point or smile towards Mireille. Mireille was not the most attractive, from the magazine-cover standpoint. In fact, she was somewhat bony, lean, with long feet and hands and breasts slightly shrunken. Her face was not beautiful, and not particularly interesting. True, her eyes were large and the lashes were long and curved, but they did not reveal her dry sense of humour or her perverse and very ribald wit. Her voice was unforgettable, but a large percentage of the clients had never heard it when they selected her the first time.
In the case of most of the girls, clients stuck with them two or three visits, then tactfully switched to a contrasting type. Not so with Mireille. They would have no other, even if they had to wait, which all of them detested.
Conversely, there was one little girl, a small _chic_ brunette who had had one baby without leaving a mark, and who could have served as a model for any commercial artist. As Mariette expressed it, she was _'extrêmement gentille et caressante'_. Her name was Mado, and her average was the lowest in the house, come what may. Every man who chose her liked her, assured Madame that Mado was very nice, but they did not want her again.
In all public or private lupanars, there was always one favourite, another badly out of luck, while the rest of the girls maintained a fair average. In order to keep their unfortunate sister in funds, each girl, when asked by a man which among the others she preferred to have with her on a 'double date' said promptly, 'Mado', and promised all sorts of hitherto undreamed-of delights.
The girls of _Le Panier Fleuri_ grossed about 150 francs apiece per day, half of which went to Mariette, who footed the bills of the establishment, furnished the meals (and excellent ones) in the attic dining room, arranged police protection and gave the place its personality and reputation for fair play. Her profit as owner and proprietress amounted to about 100,000 francs a year (from $2,000 to $5,000 dollars). This she doubled by tips on the market and the exchange received from bankers who patronized her place.
Mireille averaged about 65,000 francs a year; poor Mado had to struggle along with 12,000, as did Monsieur Frémont, the letter carrier, Hortense Berthelot and others of our acquaintance who worked for a living.
# _The Card That Slipped from the Deck of the Past_
THE READER ALREADY KNOWS how little the neighbourhood grocery in the rue de la Huchette resembles an A and P in America, M. Corre having been surrounded by specialists who took care of the meat, fish, milk and dairy products, vegetables, delicatessen, etc. It was equally astonishing to the American observer how many more articles than might have been expected were to be found at No. 4 in the store of the _marchand de couleur_ or paint store. Like the carpenter at No. 3, Monsieur Villières, the paint dealer, lived among his neighbours amicably without expressing his political or religious convictions. Monsieur Villières carried his non-partisanship to a degree of refinement which made a purchase in his store quite difficult at times. He would not choose between rival brands of brads or screws, or advise a customer about a suitable colour for woodwork. Patterns and thicknesses of oil cloth all had their virtues and drawbacks, nicely balanced, in his cautious mind.
Monsieur Villières carried small tools and minor items of hardware, artists' materials and drafting supplies, school supplies, flower and vegetable seeds, what the French mistook for modern office supplies and book-keeping equipment, toys, jigsaw puzzles, novelties that mooed like cows when concealed in drawers, tin frogs that bided their time before leaping disconcertingly into the air, jack straws, chess and checkers (French style), dominoes, household disinfectants, furniture polish, machine oil – the list is inexhaustible. Furthermore, Monsieur Villières knew exactly what was in his store and where to find it. The customer had to know and say just what he wanted. In that respect he was given no help whatsoever. Once the client had stated his desire or pleasure, the paint man would respond, even if he knew that the kind of hook the chap was buying would not fit the eyes already in his possession. His was not to reason why.
His personal life consisted of meals at the Hôtel du Caveau, during which he was careful not to raise his eye-brows no matter what was being said at the bar, evenings occupied with endless inventories of his stock, his eight hours on a cot in the back room, now and then a bath in his portable tub (which he rented out for a small fee to neighbourhood exponents of bathing, of which there were not many). He attended an American Western or Chaplin movie whenever one came to the neighbourhood cinema on the boulevard St. Michel, enjoyed old Armandine every fortnight at half past eight, and spent alternate Sundays with relatives in St. Germain.
The paint dealer simply doted on counting camel's hair brushes, boxes of thumb tacks, the three tubes of a most unpleasant oil colour called 'Italian pink', not one of which he had sold in twenty years of strict application to business, and whatever else was on his shelves. He proceeded methodically, wrote figures in his ledger, checked them with notations he had slipped into the cash drawer during the day, and considered that all was well with the world when the whole proved to be equal to the sum of its parts, and vice versa. The only information he ever volunteered to me, in the course of sixteen years' acquaintance, was a flat statement to the effect that one could not mix aniline dyes but had to use them as they had been created in the package. This proved to be erroneous, and I was tempted to tell him so. Some good instinct halted me in time. One had to respect the beliefs of others and not continually be setting folks right about this or that, if one wished to live serenely in Paris.
In the canning or preserving season, taken very seriously in thrifty France, in Paris as well as in the country, every _marchand de couleur_ trotted out a most beautiful array of huge copper and bronze kettles which he rented to housewives and others for two francs a day. I rented one once for two months and kept it on a table in my attic room, so beautiful did the otherwise unsightly objects around me appear in resplendent reflection. This bothered Monsieur Villières more than anything that had happened to him since World War I. I paid regularly, by the week, in order to enjoy his perplexity. I assured him that I was using his marvellous example of the coppersmith's lost art for no ulterior or unworthy purposes, that I never bathed in it, or used it as a chamber pot. I liked the look of it, that was all. Undoubtedly I contributed to the French belief that all Americans are crazy.
Imagine my surprise when, one day at the Caveau, Monsieur Villières, with flushed face and indignant eyes, stopped at the bar on his way to the luncheon table with a weekly paper clutched in his hand. He confronted me with such asperity and personal reproachfulness in his manner and tone that I was taken aback, as were my drinking companions, the chestnut vendor, Monsieur Frémont, and the _garçon_ , Georges.
'This is an outrage,' the paint man said, beating the bar with his folded periodical. 'America is barbarous and uncivilized.'
As soon as I could, I ascertained the cause of his unique spasm of partisanship. One glance at the paper made it all too plain. Charlie Chaplin was in trouble. He was, according to the text, being victimized and persecuted and robbed by a designing woman who had used her young daughter as bait, bamboozled the world's greatest pantomime artist into marriage with the child, and now was demanding a huge fortune out of Charlie's earnings.
The way in which the American male seemed to be pushed around by his womenfolk left Parisians goggle-eyed. There was a feeble women's suffrage movement in France but it never came to anything because Frenchmen and women did not think in terms of abstract justice. None of the sentimental arguments in favour of sex equality had much weight in France. Clever women got everything they wanted, if they were lucky, and often manipulated high statesmen, financiers and streamlined executives as if the men were marionettes. The French wife did not think the end of the world had come if her man made an occasional trip to the neighbourhood bordel; she did not expect to live without work or worry forever afterwards if she caught him in a hotel room with another woman standing by _déshabillé_. What she was to get, under any and all circumstances, was carefully specified in a marriage contract written by the head of her family and the head of her husband's family.
Men in public life, except clergymen, did not have to scuttle and hide like waterbugs if they felt the urge for some good loose feminine society. I never heard a Frenchwoman complain about any action of her husband's that she did not know about. Most of them knew just how much or how little of a hold they had on their man, and arranged their lives accordingly. If a jealous woman lost her head and shot an unfaithful lover, a French jury, 999,999 times out of 1,000,000 would acquit her, and in the remaining instance the President of the Republic would pardon her. That this had any deterrent effect on men's philandering was not noticeable.
Charlie Chaplin's predicament was kept in the public eye of Paris several days, and the comment was uniformly sympathetic with Charlie, indignant towards the mother, and scarcely mentioned the girl, who was thought of as a sort of stage 'property' which could serve in one kind of show as well as another. I saw the chestnut vendor staring with wrinkled brow at a newspaper cut depicting the girl wife of the comedian one day.
'I've picked up better ones than that in the place Zacharie on the 14th of July,' he said.
Pierre Vautier expressed the neighbourhood idea of middle-aged American females when shown a photograph of a club woman from Ohio or Wisconsin.
'What impudence!' Pierre exclaimed.
'The French they are a funny race,' is a household phrase in America. Having witnessed the American Legion parade in Paris (on the day of Isadora Duncan's funeral), I began to understand that we are as comical as anyone could be.
Something deterred me from taking Hyacinthe Goujon to see that Legion performance, where drunken veterans in miscellaneous costumes that had everything except art and imagination streamed and staggered along, with female drum majors who would not have been allowed to polish doorknobs in the Moulin Rouge. Instead, I escorted Madame Frémont and Yvonne, and neither of them laughed or cried when those middle-aged men, looking more incongruous when they had preserved part of an athletic shape than when they had let themselves go, gave one of the world's most amazing exhibitions of goodwill and bad taste. The ex-doughboy faces in a foreign setting looked almost depraved; the costumes were ill-chosen; the average veteran wasn't drunk enough to be clownish or sober enough to be dignified. But, if neither Mlle. nor Mme. Frémont brushed tears from her eyes, I must admit that I did. For there was something in the beat of that old march step, echoing between French buildings, some relentless and jaunty and effective rhythm in the drums, that made me see my former comrades as they had been in khaki, years before. I remembered standing in the door of a freight car in a troop train, very early in the morning, in some region of France where the cattle were snow white in green fields, and an old peasant woman, seeing strong young men swarming over that string of box cars, dropped down on her knees in gratitude to pray, as naturally as she would have reached for a pitchfork.
About the time the Legion was parading in Paris, Briand and Kellogg were outlawing war, by means of a series of complicated multilateral pacts which now are useful, one hopes, for carpet lining. France accepted the Kellogg plan (which before it had become apparent that it was to prove a dud had been called the Briand plan) with the reservation that France should have 'the right to fight' if the Rhineland non-military zone were militarized.
The rue de la Huchette knew only this about the American presidential campaign: namely, that Al Smith habitually wore a brown _'chapeau melon'_ and that he was against Prohibition, as who wasn't.
'Smith can't be elected because he is a Catholic,' I said to Monsieur Monge, who was all for Al and a glass of wine with his meals.
Monsieur Monge tried to remember whether Papa Doumergue, then President of the French Republic, was a Catholic or a freethinker. He could not be sure, and neither could anyone else in the bar.
I went on further to say that Al habitually mispronounced some well-known American words when campaigning over the T.S.F.
'That's nothing,' said Madame Berthelot. 'I heard Tardieu the other day and he made three mistakes in syntax. Blum had good schooling, it seems. He makes practically no mistakes at all.'
'All Jews make a mistake in being born,' The Navet said. 'It makes life hard for them and for us.'
Somehow the fall of Jericho does not seem as remote as the carefree 1920s. One has long lived with the fact that those walls came tumbling down. Likewise we accept the fact that a hero's dead body was dragged around the ramparts of Troy. Not so familiar is the fearful twilight over France. I can hear those voices in the rue de la Huchette. Blindfolded I could identify the clasp of Madame Berthelot's gloved hand, the tough palm of the chestnut vendor, the intonations of little Hyacinthe's lost voice, the lift of Mireille's unquenchable spirit. Of Monsieur Henri Julliard I think each day with gratitude. Or is it gratitude to death itself? Monsieur Henri, who had lived so well, knew just when to die.
I am telling you in advance that Henri Julliard died while dying was still good, because that is satisfying news, and so much I have to tell will undermine your faith in evolution.
That remote and historical post-war period (1918-1930) has slipped from the pack of time and lies face downward on the floor. For when the 1920s collapsed and fell, they took with them all that was worth while in the nineteenth century.
In 1929 Poincaré, the only living mathematician who could not figure out that what went up must come down and that money is labour (nothing more or less), was still at what one calls loosely 'the helm' of France. He had a majority of two or three votes in the Chamber, the support of the pactingest politician in the world (Aristide Briand) and a financier named Charon who had one of the softest hands under a hen of any gent who ever balanced a budget.
It was during 1929 that two new figures appeared in the Chamber of Deputies, both destined to play important, if ignoble, roles in French affairs. No. 1 was Léon Blum, and the other was Marty, the Communist who led the French Black Sea Revolt. In the German elections of that period, both the Communists and the Hitler party made gains at the expense of the centre. In England, Ramsay MacDonald got in again, having proved to the ruling clique that he was the world's worst false alarm as a labour leader. In the United States, in case you don't remember, the camphorous sage from Vermont was in the White House and was busily saying nothing, because he could think of nothing whatever to say.
Marshal Foch died and was given a magnificent state funeral. Ambassador Herrick died, and with him the last vestige of Franco-American co-operation or understanding. Then, when everyone in Paris was weary of superlatives having to do with death or interment, an obscure marshal named Sarrail discovered two years late that he had passed the Biblical age. All the properties and phrases had to be trotted out again for his public funeral.
Dr. Stresemann, who had agreed with Briand to end Franco-German wars, died and got less notice than Serge Diaghileff of the Russian ballet. The _Bremen_ made her maiden trip to New York and set a speed record. General Maginot declared that the Franco-German frontier must be fortified on the French side before the Rhineland could safely be evacuated.
In the Radical-Socialist Party, a hot contest was going on which kept Monsieur Noël, the Satyr and Monsieur Monge, the horse butcher, on their toes. Herriot, the Lyons local politician, littérateur, and amiable gentleman who came about as close to being honest as a practical statesman can, was opposed for the leadership of the powerful conservative centre party by a baker's son named Daladier. There was practically nothing left of socialism in the Radical-Socialist Party, and Daladier wanted even less of it. Daladier was a non-prepossessing man with little personal charm or intellectual distinction, but he had never been Premier and had therefore made fewer enemies than Herriot, who had held the office several times.
The three 'radical-socialists' on our street all voted for Herriot – and Daladier won. Little did anyone suspect what that would mean to France or even Czechoslovakia. To The Navet and Monsieur Panaché, the beef butcher, Monsieur Saint-Aulaire, Madame Durand the florist, and even the inoffensive Monsieur and Madame Corre, Daladier was a dangerous radical who would undermine business and the home. On the other hand, to Milka and the chestnut vendor, Daladier was beneath contempt as a reactionary blunderer who was in public life because working in a baker's shop was harder and less profitable. Daladier made a bid for the premiership and lost out because Briand would not play ball with him. So Tardieu, a reactionary patriot who believed in big business, got in, just after Clemenceau, the tiger, died. Hoover became President of the United States, and Senator Edge came to Paris as Ambassador. The Parisians never even learned his name.
My connection with the press entitled me to tickets for various state funerals and other functions. The stirring pageant when Foch was laid away was made to order for Hyacinthe. We stood side by side on a balcony in the rue de Rivoli and saw the procession pass three stories below. There is nothing I can say that will describe how my companion of the day reacted, when the dead Marshal's snow white horse, blanketed with a flowing black robe, and riderless, was led past, towards the place de la Concorde. Cardinals marched in their red trappings, the Coldstream Guards shipped over for the purpose wore their bearskin shakos. Crack French troops marched with their nervous hurried step. They kept time with the heart beats of a thirteen-year-old girl, becomingly pale, most tastefully dressed in deepest black, not Joan of Arc, but a daughter of France who had sprung from her decaying class like an orchid in a tropical swamp.
When the lesser marshal named Sarrail had his turn I could not resist taking Mireille. When she lighted a ready-made cigarette, not far from the casket, while a solemn part of the ceremony was in progress, my first impulse was to take it from her gently and step on it, eyeing the police and military guards and hoping for the best. My second and sounder impulse was to mind my own business.
While spending freely on the epidemic of public funerals the Government of France made spasmodic attempts at minor economies, one of which alarmed the Paris police department to such an extent that, after a lively tilt in the newspapers which spread to all our neighbourhood cafés, the plan was promptly abandoned. The French army had on hand several hundred thousand rifles of obsolete types. In fact, that was about the only kind of rifles available for the national defence. In order to cash in on the old-fashioned shooting irons, some ordnance officers, backed by the Deputies in the Chamber who liked to vote for anything their constituents might interpret as a move to reduce the mounting taxes, proposed a huge national bargain sale – at which the old rifles were to be auctioned off to the highest bidders.
The police commissioner howled to heaven, and his arguments found favour with all propertied middle-class citizens who already had weapons. Factory owners and executives joined in the protest. These prudent members scented sure disaster if every Tom, Dick and Harry could purchase a gun. The weapon might not stand up in competitive test with those new ones Germany was manufacturing in open secrecy, but it would still be effective in riots and uprisings in the narrow city streets.
What became of the obsolete firearms was never disclosed, but they were not put up at public auction.
What had become of French unity, security, solidarity, and spirit is today more apparent than it was then. Clemenceau had sabotaged the only promising world peace proposal since the Sermon on the Mount. The bunglers of the Quai d'Orsay abused all of France's former allies. They had failed in an attempt to grab the Ruhr, the Rhineland and the Saar. France was economically unsound, financially bankrupt, morally ill and physically tottering. From a first-class power she had slipped to a third-class relic.
How was this debacle reflected in the rue de la Huchette?
Meat was higher and tougher, and the families in average circumstances could not afford it more than twice a week.
Across the street from the meat shop, piety collected dust in the windows. It is not before, but after, wars and national collapses that piety abounds.
At No. 4 less paint was sold; inventories, consequently, became simpler.
At No. 3 timber was prohibitive in price, hence little carpenter work was attempted. One of the two apprentices was sacked.
At No. 6 expensive sausages and delicatessen became unsaleable.
At No. 5 hotel bills were harder to collect, and no tourists came to the cabaret.
At No. 10 wool and cotton touched fantastic all-time heights. So did Madame Absalom's invective.
At No. 9 Dorlan, the bookbinder, scarcely noticed any change. His clients were eccentric anyway.
At No. 12 milk was paler, eggs smaller and dirtier. The delivery girl tried what all the men had long been after and was not impressed.
At No. 15 the Lanier _clandestin_ raised prices from 5 to 10 francs. Twenty percent drop in volume of trade. Laundry prices also doubled.
At No. 14 the pay received by the police officers had shrunk so much in relation to the cost of living that the wife of one of the officers, unable to buy pretty underwear, formed the habit of picking up rich gentlemen in department stores. The family life became insupportable.
At No. 17 the neighbourhood men who worked for wages stopped patronizing _Le Panier Fleuri_ , which attracted increasingly well-to-do clients from the textile manufacturers and dealers near the Châtelet and the boulevard Sebastopol.
At No. 16 an Englishwoman at No. 25 (third floor) complained that the bread left at her door each morning was not wrapped in paper, and therefore was dirty. Thereafter the delivery girl carried inside her blouse, next to her rather clear skin, a sheet of newspaper, with which she wrapped Madame Spook's loaf before standing it against the door. Madame Spook's real name was Root, but the French could not seem to manage that.
At No. 18 Sara's rich uncle from the Temple quarter sent her two clients, distant cousins from Germany who wished to transfer some assets out of Germany, in case the anti-Jewish feeling mounted.
At No. 19 the son of M. and Mme. Luneville left the dry-goods shop to begin his eighteen months of military service. Mme. Luneville, who had been a World War I bride, wept when she saw Jacques in uniform. Her veteran husband rebuked her.
At No. 20 Julien, the barber, received a call from his old employer, Monsieur Riess, the famous hair dresser. Riess told him about the American bank holiday which had frightened away his best paying clients from abroad. The old man was puzzled and discouraged. Money was no good anywhere, he said.
At No. 21 Monsieur Saint-Aulaire found himself overstocked with horizon-blue material, the Chamber having decreed that French soldiers and officers should wear, khaki in the future. This, like all modern innovations, the spade-bearded tailor deplored.
At No. 27 the cleaner and dyer had less cleaning and more dyeing to do. This was always true in hard times, he said, so he raised his prices for dyeing to make up for the cleaning he lost.
At No. 23Madame Durand discharged Amélie, her nineteen-year-old clerk and assistant for having angered a steady client by refusing to spend a night in the country with him.
At No. 24M. Dominique made a journey to Bayonne to buy stamp collections from Jesuit exiles from Spain who needed ready cash. He found some very good bargains.
At No. 25 André, the coal man, intending to go to the Auvergne, for the first time in eighteen years, to attend his sister's funeral, got on the wrong train at Langres and found himself at Bourbon-les-Bains. The station-master would not let him sleep in the depot after two. The park was closed, so he walked back and forth on the platform, then took the morning train back to Paris. He was non-communicative for several days after he got home and once spoke crossly to his little son.
At No. 26 Bernice, because trade fell off in the music shop, started embroidering on a piece-work basis and used the proceeds to buy food for M. Gion, knowing that it would make him sullen and harsh if he had to tap his money in the bank. Because M. Gion did not like to have her use the electric light when he was away, she worked at the window, in the glow of a street lamp. This made it necessary for her to wear spectacles, which she purchased for ten francs, selecting them from an open basket of assorted glasses on a counter in the Bon Marché.
At No. 27 M. and Mme. Corre, who had planned to take a commodious apartment in the avenue du Maine, after their son was married and took over the grocery, decided to be content, instead, when the time came, with a smaller apartment in the rue du Bac.
At No. 28 the goldfish trade, always desultory, was slow in reflecting the general depression. Maurice discovered Fenimore Cooper and, for once, tried to get another book by an author he had chanced upon. This he was unable to do along the quai.
At No. 29 Dr. Clouet attended a meeting of French physicians and voted in favour of restricting sales of iodine to Germany. He would have voted with equal relish to restrict the sale of anything to Germany.
At No. 32 The Navet wangled a raise in pay by joining a secret organization against communism, favoured by Chiappe, the police commissioner, and dedicated to the proposition that all men are not born free and by no means equal.
At the Brasserie Dalmatienne, which belonged to the boulevard and was patronized by prosperous Serbs and other Balkan people, the police were on watch with instructions to pick up foreigners who might be Reds and did not have identity cards. The Serbs in this café were reactionary, not Red, but the police did not know the difference, where Slavs were concerned.
At the Café St. Michel, when customers complained that the crescent rolls were smaller than before, Mme. Trévise blamed War Minister Maginot, who had just asked for twelve billion francs yearly for the army.
# _Of Western Culture_
ONCE IN DORCHESTER, MASSACHUSETTS, lived a huge fat undertaker, a veritable Man Mountain Dean _sans_ whiskers, who had a beautiful black cat. The cat was sleek and well-fed, with glossy fur and agate-yellow eyes. When business was slack, the undertaker used to doze for hours in a swivel chair, his feet on a littered roll-top desk, in full view of the passing crowds from the elevated railway terminal near by. The cat stretched comfortably on her master's commodious belly, slept when it pleased her, and at other times followed the movements, left to right, of the stream of pedestrians that never seemed to dwindle during daylight hours.
When the undertaker died, and was stretched out in the back room among the materials and implements of his lugubrious trade, the black cat paid no attention whatsoever to the body, but paced nervously back and forth, tail switching, yellow eyes distended peevishly, in front of the empty swivel chair. From time to time she uttered a soft complaining cry.
A discerning friend of mine, observing this, pointed out to me that the cat had thought of the deceased mortician not as a person but a place. The place was gone.
The attitude of the average foreigner towards Paris and its people was much like that of the undertaker's cat. The city was a refuge. That it was staffed with people who, beneath their inefficient exteriors, were toiling and aspiring human beings escaped the casual visitors.
It was the sad-eyed Monsieur Noël, the taxidermist, who said one evening in 1931: 'If France goes down, so much of Western culture will go, too.'
Monsieur Noël and his two friends, Monsieur Monge, the horse butcher, and the maligned Satyr, were among those in our little street who were concerned with culture and with France.
As my companions knew, I was planning just then to leave Paris very soon for Spain and what turned out to be the most soul-stirring adventure of my disorderly life. Each one of my French friends envied me, in a way, but most of them would not have travelled if they could.
'The French do not travel,' Monsieur de Malancourt said to me. And he added: 'Why should they?'
There was little I could say in reply. But it always gave me an odd sensation when I talked with Frenchmen about foreign lands, even if they had seen the countries in question. It was as if I and they were speaking, simultaneously, of two different entities, both of which were removed from what is loosely known as reality.
Pierre Vautier, who, the moment he had broken loose from his family ties, had developed mentally before our eyes, and who thought in terms of the arts, took up Monsieur Noël's remark about the decline of Western culture.
Being primarily interested in painting, Pierre started with that. France, he said, had taken over the art of painting from the Italians – with Poussin in the seventeenth century. Like so many other amateurs of painting, young Vautier ignored the Spanish development in that field, which reflects as truly the course of history and world and national affairs, believing that all Spanish painting had been done by El Greco, Velasquez and Goya, and had died in Napoleon's time.
Pierre was eloquent in his résumé of French achievements with palette and brush, and he was well informed. But when he remarked that the Italians had civilized the French, and that Poussin, the first great French painter, had learned painting in Rome, Father Panarioux spoke up gently from the doorway.
'You're forgetting Clément Vautel,' the priest said. Vautel was a wandering painter, almost a tramp, who went from village to village and earned small sums by repairing church decorations or painting murals of his own on chapel walls. Vautel had visited Poussin's native village in Normandy when Poussin was twelve years old and had let the boy clean his brushes and watch him while he worked. The old vagrant also did one job in Paris, a mural which is still intact in St. Germain des Prés and which shows many of the salient characteristics of Poussin's best painting, notably _le cri parmi les gris_ (the cry among the greys).
'So French painting may be French after all,' the priest said, smiling.
Pierre told of Claude Lorrain, and described the blossoming of French genius in the hands of Watteau, Fragonard, Chardin, David, Ingres, Courbet, Corot and Delacroix. His eyes shone and his voice trembled when he got to the impressionists, who let sunlight into art (in the path of the pioneer Claude Lorrain). He spoke of Manet, Monet, then – nearer home – Renoir and the great Cézanne. He told of Gauguin and Van Gogh, of the moderns Derain, Vlaminck, Utrillo. But there he struck the snag that made Henri Julliard, who had never seen the inside of the Louvre or the galleries in the rue la Boëtie except on Sunday mornings, look worried and puff at his pipe.
For modern painting, beginning with World War I, had been taken in hand, revolutionized and stamped with the vigour of his race by a Spaniard named Picasso. And the French petered out. It is true, said Pierre, that Picasso has a studio in Paris and that his paintings were sold by the yard by the dealers of France. His art is Spanish, nevertheless, and what few Frenchmen who have not thrown up the sponge are influenced by Picasso to a degree which amounts to imitation. French painting, glorious as it was, will have on its tombstone the dates 1594 (Nicolas Poussin) to 1914, when Picasso came forward with his first 'cubistic' landscape.
'After all,' said Thérèse the cook, who was drunk but attentive, 'what is painting? One can't eat it, or even make a living at it, unless one has pull.' She had fed too many art students, on the cuff, in her time.
Concerning music, the floor was held by Monsieur Monge, purveyor of horse meat and the world's best performer on some kind of antique horn. He was aided and prompted by the Satyr and Monsieur Noël. The Society for the Preservation of Ancient Instruments, it seemed, took the long view in connection with its art and, before and after hours of ancient practise, played 'for fun' whatever scores the leader could obtain from the contemporary 'Six' and other living French composers.
The great misunderstood genius of modern French music (although he did his best work in the 1860s) was Berlioz. He was ridiculed and neglected by his contemporary Parisians and had to go to the Rhineland for his first success. Liszt stood up in his might in his theatre box in Budapest and roared for Berlioz, carrying with him the Hungarian crowds. But the French Government refused to pay for the great Mass evoking the resurrection and the life, and, even in the year 1931 sloppily played Beethoven numbers were seldom set aside to make room for Berlioz in French concert halls. The once great French opera had, for lack of funds, become a travesty. Rameau and Couperin were 'revived' from time to time and atrociously misinterpreted.
Debussy? When it came to Debussy, Monsieur Monge grew lyrical, and the faces of my friends were alight with hope. But, said the horse butcher, Debussy's genius (which was prophetic of the impressionistic movement in all the arts) led into a _cul de sac._
'Debussy,' said Monsieur Monge, 'did all there was of its kind. No use to imitate or copy. His music was fresh, inspiring, in a word – it was French. But it had a beginning, a middle and an end – a verdant island around which flows the main stream.'
'Satie?' suggested young Vautier.
'The best toy music ( _musiquette_ ),' said the Satyr. 'That is all. It goes well with motion pictures.'
Ravel, according to our academy of the rue de la Huchette, brought into France an African and Spanish influence as Manet did into French painting. He was good, but of the nineteenth century, which 'the big shots' of European governments (official, financial and otherwise) were out to sink without trace.
The Six? Honneger (with his 'King David' on the one hand and his 'Locomotive' on the other), Poulenc, Auric, Milhaud, Durey and Tailleferre. Jacques Benoit-Mechin, who wrote tone poems about South America? The music after World War No. 1?
It was entertaining, derivative and slight. On a programme with an early masterpiece like Monteclaire's _Plaisirs Champêtres_ it sounded like the decorations on a department-store Christmas tree.
Of literature?
Another drink all around, and while Georges the _garçon_ did fine feats of serving to supplement Monsieur Henri's masterful pouring, the eyes of our company turned first to young Vautier, who deferred to Monsieur de Malancourt.
'Alas,' said Monsieur de Malancourt, looking slightly ashamed. 'I haven't got a step beyond Proust. And _his_ marvellous works, I must confess, were brought to my attention by a schoolgirl, in my apartment house, a young girl, I assure you, my friends, who should be locked behind convent walls for the good of her soul and my own, and God knows how many others.' He glanced at me uneasily as he was speaking, knowing that I knew he was referring to Hyacinthe Goujon, at that moment staring thoughtfully at the ceiling in her still virginal bedroom on the third floor of No. 32.
Now in that small smoky bar-room, there were perhaps six of us who had read Marcel Proust. Pierre, Milka (with impatience because Proust was class-conscious in the unapproved way, that is, from birth quite snobbish and aesthetic), Madame Berthelot (who read behind official ledgers and files, when business was dull in the prefecture), Maurice, the goldfish man, who had chanced upon _Sodom and_ _Gomorrah_ in the second-hand bookstalls, Monsieur de Malancourt and your author. But even the cook Thérèse had heard of Proust and knew he was a Frenchman and of the élite.
'A genius is neither an invalid nor a pederast,' said Monsieur de Malancourt. 'He transcends all disabilities.'
_'Ce ne sont pas les pédérastes qui manquent,'_ said Thérèse.
The priest glanced at her disapprovingly and smiled.
'A genius makes no mistakes,' I quoted from Joyce. 'His errors are the portals of discovery.'
'It would be better if your geniuses were less arrogant and more humble,' said Father Panarioux. 'And, furthermore, a genius does not flaunt his twisted sex, except unconsciously, as an ambi-sexual genius does. In the days when Frenchmen were more vigorous, and content with wholesome sins for which they could be forgiven with less distaste, French writers were not preoccupied with vagueness or monstrosities. There was something quite solid in between. A Christian reading Proust will find much truth and exact observation, precisely expressed with care and, good taste. Sin is not glorified – true, it is not castigated either. That would interrupt the flow.
'The result of modern corruption will be,' the priest continued, 'that our artists and then our countrymen will turn from warmth and sentiment altogether. They will become hard and godless, without scruples or pity.'
'Our enemies are that way already, or so they would have us believe,' said Henri Julliard.
'Poor men,' the priest said, sadly.
'The bastards,' said Thérèse.
Céline's _Voyage au Bout de la Nuit_ had not yet shocked the world with its uncompromising vista of Paris, New York and Detroit.
Rolland had doddered into a senile pacifism. Gide was in a _cul de sac;_ de Montherlant dealt only with a devastated aristocracy. The writer with the widest historical scope was Jules Romains. It still remained for a young man who wrote so simply that his prose was disarming to achieve the utmost in brutal prophecy, and portray, in advance of its general appearance, the fascist type in _The Young European._
In the Caveau bar that night, I was the only one who had read Pierre Drieu la Rochelle; so I produced a copy of _The Young European_ and handed it to Mme. Berthelot who, shuddering, read passages like the following:
'Man need never have left the forest. He is a degenerate nostalgic animal.'
'The violence of men! They are born only for war as women are made to have children. All the rest is a tardy detail of the imagination which has already shot its bolt.'
'I felt only the civilized side of war, in that odour of feet which pervades all monasteries, that rancid smell of men alone.'
'I had seen no women for several months. A large girl entered my office each morning (in America).... Here was the great white race I had sought throughout the world. I no longer looked at her face.... I ate, I slept, I got a child under way... she had no face. Her features merely prolonged the long lines of her body.... I brought her a love from Europe, precise and tender.'
'The skyscraper seemed no higher to me than the trajectory of our cannon and this mass of humanity hurled itself to the assault of unknown impregnable positions in blind columns, obeying an absurd order dictated by an anonymous telephone. I was not astonished by the grandeur of the American material apparatus, since the war had sickened me forever with the prestige of masses. I was intrigued only by the sight of so many wholesome bodies.... I turned the great body of my wife over and over, admiring those limbs firm with exercise, the calves of her legs, her thighs, her shoulders.... One evening I did not return home.'
'It is necessary to have killed with the hands in order to understand life. The only life of which men are capable, I tell you again, is the spilling of blood: murder and coitus. All the rest is decadence.'
(This was written in 1926, about the time that Mother's Day was first celebrated in France.)
I have seldom seen a man with a sadder face than that of Father Panarioux when Hortense finished reading, but he stepped resolutely forward and copied on a slip of paper the name of the author and the book.
Jules Romains, after starting out adventurously, gave up looking for new paths and tried to be Balzac, Zola _and_ Proust. He lacked the incisiveness of the first, the fire of the second, and the sensitivity of the third. His _Men of Good Will_ is a work of patience. Of the Nobel prize winner, Roger Martin Du Gard, it need only be said that his forceful work centres around the period of the Dreyfus case. The contemporary problems he has passed by without a sign of awareness.
In World War I, Monsieur Henri had read _Le Feu_ of Barbusse, as many Americans did. Barbusse's effectiveness stopped with that indictment of force.
The man who is the most likely to match the work of the nineteenth-century giants is Louis Aragon, but his talent is scattered and his contempt for the race too near the surface of his prose. After years as a Surrealist clown, he did heroic work as editor of the newspaper _Ce Soir_ , presenting the Communist view with clarity and brilliance. Only when confronted with the Hitler-Stalin pact did he flounder and shelve his intelligence.
Malraux went to China and wrote _Les Conquérants_ before he had had time to digest his observations. Six years later he made a splendid work of the same material, under the title of _La Condition Humaine._ He went to Spain and turned out _L'Espoir._
François Mauriac, a Catholic, wrote of the decline of Catholicism and took a brave stand for the Spanish republicans. He is silent now.
Morand was never worth mentioning; Duhamel was a the phony who hoodwinked the Americans but never the French; Cocteau was a playboy and good light entertainment; Cendrars a fascist dupe; Jean-Richard Bloch essentially a journalist. Maurois was superficial enough for the English and never found out what his century was like.
The survey makes it all too clear that France had no twentieth-century Proust, not even a Gide, who belongs before World War I; not even a poet to compare with Paul Valéry. Literary giants must have a solid country under them, or the stables of Hercules.
An exception to the general decline in France's share of Western culture was the cinema. The medium was perfectly suited to the modern French temperament, to their instinctive taste and quick reactions, their adult approach to life, their wit and adaptability. Georges Méliès turned out the first story-films in 1912, with Sarah Bernhardt as co-pioneer. On their trials and errors much has been built that is sound. The First World War gave the producers, directors, writers and actors a change of occupation and Hollywood four years in which to demonstrate what should not be done. Immediately after the armistice, the French took the lead with Abel Gance, Louis Delluc, Marcel I'Herbier and René Clair.
Even the Clair contributions that have been stolen or imitated elsewhere have increased his stature. His wit and finesse no one could borrow or debauch, until he was forced to submit to the Hollywood conventions. Then he debauched himself. His _Chapeau de Paille d'Italie, Sous les Toits de Paris, A Nous la Liberté_ (which Chaplin took over in _Modern Times_ ), _Le Dernier Milliardaire_ are film classics such as America could never produce.
With the best French directors, the play is the thing. Not only Clair and Renoir, but Duvivier, Chénal, Camé, and Feyder, respect the writers like Giono, Jacques Prévert ( _Quai des Brumes_ ) not to mention Anatole France. The French producers were willing to give cultured adults a break, and not make films exclusively for backward children. When the output was bad, it was consciously bad, and not standardized mediocrity.
The best French films reflected the most interesting French life in one or many of its phases. The characters were not automatons, their motives were not trite or over-simplified, their words were not wisecracks like raisins in a dough of banalities.
Bergson's philosophy, based on the impulse of living ( _élan vital_ ) and the conception that one creates whenever one acts freely, is essentially a product of the best thought of the nineteenth century, and dates before World War I. It is the antithesis of the fascist idea, the most dangerous doctrine for a totalitarian state. No philosophy comparable to Bergson's sprang from the postwar twenties or the prewar thirties. It breathes of the life of France in the days of the now dead Third Republic.
The restaurants of France, which led the world during the nineteenth century, came into being with the revolution, an outgrowth of republicanism. As freedom faded, so did the restaurants, and with the Third Republic they died. In no totalitarian country is good eating encouraged, but only the kind of food that makes for soldierly stamina without mental health or elasticity. A restaurant was a meeting place, and meetings are taboo.
The famous restaurants of Paris which flourished before World War I – Boulanger, Verdier, Véry, Legacque, Les Frères Provenceaux, the Café Anglais, Véforn, Café de Paris, La Vachette, Bignon, La Maison d'Or, Philippe, Brébant, to name but a few of the leaders – were creative institutions. The famous chefs, such as Véry, André, Terrail, Casimir, Mourier, Burdel and other artists, did not merely turn out copies of the great creations of Bechamel, Parmentier and the giants of the monarchy. They made contributions of their own. Two revolutionary writers and philosophers, Brillat-Savarin and Grimod de la Reynière, made food articulate. Gauclair perfected _aioli_ ; old Alfred Prunier learned to cook oysters; Close invented _paté de foie gras._
Between World War I and World War II there were fine restaurants in Paris, like Pharamond's in the market district, Foyot's and Prunier's and Lapérouse, Weber's, Larue, the Café de Paris, the Tour d'Argent, Chez Francis, etc., and most of them were hangovers from pre-war days. But they lost their republican quality and became hangouts of the newly rich. They kept up the quality of pre-war food but evolved few new sauces or dishes. Like piano music, the last of which was written in 1870, French cooking coasted along on its former greatness, marvellous but not living or modern.
No restaurateurs in the 1920s or 30s had the stature of old M. Frédéric (Delvain), or Gauclair, or old Marguéry or Noël Peter. Escoffier, the last of the major chefs, died in 1935. No successor is in line. Neither will there be any young man to take the place of such a _maître d'hôtel_ as Olivier of the Ritz.
French cooking, like French painting, music and literature, was cherished by the monarchy and adapted itself to the Republic. All these arts, by stagnating and dying after World War I, foretold the fall of France.
French couture reached its artistic apogee in the years immediately preceding World War I; it achieved its greatest commercial success and the maximum of its influence on world fashions in the early twenties. In the years just before World War II, Parisian dress houses had become a fair of samples which buyers bought piecemeal, pooling their purchases so as to pay less and reduce the cost of copying. From the eighteenth century, when Rose Bertin, whose most famous client was Marie Antoinette, decreed styles, through the period dominated by Charles Frederick Worth, who was the first to display his creations on live mannequins and induced the Empress Eugénie to wear a dress made of Lyons silk, to the time of Paul Poiret, the leadership of the fashion world remained in France. Poiret was the first to make use of modern artists. Under the influence of Bakst he restored brilliant colours to fashion and released women from the armour of corsets and petticoats. By the introduction of the short skirt Poiret gave impetus to the present hosiery industry.
Chanel created the one-piece jersey dress. This started a trend that eventually developed into modern sports clothes. The influence of Jeanne Lanvin, Jean Patou, Lucien Lelong and Molyneux on fashion was to feminize it. Schiaparelli, with a thought for her less attractive sisters, provided ornaments and surrealist gadgets that distracted attention from the face – when necessary.
The French couturiers borrowed without stint from their fellow-artists, the painters, and used colour and form as lavishly for their creations.
Unlike the United States and Germany, where scientific education has run so far ahead of artistic culture and general knowledge that adults with the mentality of children are playing with phenomenally powerful toys, France laid emphasis on matters of the spirit and let modern science go hang. A few brilliant exceptions among French scientists, therefore, had to work under handicaps imposed by an indifferent public and a penny-pinching Government. Pasteur, in pioneer days, was hooted and obstructed. Joliot had to squander his invaluable time raising money for his _cyclotron_ , which cost about one-eighth as much as a small destroyer. The entire French appropriation for scientific research after World War I was about 2,000,000 francs, and there was no crop of private millionaires to rally round. In 1924, when World War I's victory had slipped away, Emile Borel, the famous mathematician, persuaded Parliament to set aside a special tax for the support of laboratories. About that time, the Rothschilds, alarmed because their interests in France were falling behind their interests in other countries where science was encouraged, created a foundation of 10,000,000 francs for fellowships, and thus aided the work of the chemist, André Job; the physicist, Claude Bernard; and the distinguished scientists, Jean Perrin, Pierre Garerd and André Meyer.
In 1930, long after it was too late, Herriot, then Premier, got across an annual appropriation of 5,000,000 francs for encouragement to science. This amount, about $1,250,000, represents the receipts of the Childs' restaurants in New York for about four weeks.
In 1935, the French deputies took a long step backwards, and, in the interest of economy, abolished the Borel tax. In 1936, Léon Blum appointed Irene Joliot-Curie under-secretary of scientific research, and in 1937, the budget for modern science was boosted to 32,500,000 francs. An observatory for astrophysics was set up at Forcalquier; a national chemical institution was started at Ivry; a laboratory for atomic transformation in connection with the Collège de France, a laboratory for low temperatures at Bellevue, and a magnificent collection of documents known as the 'Institut des Textes,' all were established just in time for Hitler to grab them, transport their contents into Germany and, where that was not possible, to replace their personnel with storm professors from the Reich.
# _The Central Markets_
PERHAPS THE MOST VITAL PART of Paris the Germans have soiled and ruined was Les Halles, or the central market, which belonged to all quarters and streets alike and from which the rue de la Huchette, like the others, got its sustenance. I mean the city acres between the rue du Louvre and the boulevard Sebastopol, extending west from the rue de Rivoli all the way to the rue Étienne Marcel, where fresh food – fruit, cheese, eggs, vegetables, meat, fish, game and poultry – poured in daily from the fertile countryside and was distributed and sold to the hotels and restaurants, as well as the little local markets, and, without formality, to the lucky retail pedestrian who chanced to be out that night or who got up with the sun in the morning.
The above-mentioned parcel of former France had colours and shapes as exciting as the walls of the renowned long gallery of the Louvre Museum, had movement that exceeded in grace the undulations of Loie Fuller's pastel robes, had vigour surpassing the action of molecules under a microscope, smells that put to shame the scent shops and verdant gardens – also brutality, avarice, stench, confusion. In short, the foremost necessity and historical privilege of mankind known as food.
There at two in the morning one could stand in the shadow of the flying bastions of St. Eustache (where the Christmas music was so inspiring that tickets were sold at least one year in advance) and could, if one could bear it, look south-eastward. The fragrance of wild strawberries forced one to breathe deeply and to lower the lids of one's eyes. There were in the middle distance lanes between pyramids of carrots under lamplight (henna by orange by green by gold) and of stacked cauliflower (buff and cream with blue-grass setting), but first – the strawberries!
France, in her wisdom, ordained that all the strawberries for miles and kilometers around should convene near a grand old church just after midnight, and should be ranged there neatly in straw baskets or in boxes, garnished greenly with their leaves. If one man can smell one wild strawberry at a distance of eight inches, how far can four million men enjoy the perfume of one million five hundred thousand strawberries with cool leaves all around, laid out on ancient cobblestones?
I know many tourists and even foreign residents of Paris who rode through the market district in the daytime fairly often, seeing nothing but shabby stores and sheds on uninteresting and not quite tidy streets. There was traffic in the day, and retail business of a sort, but no fresh food in sight. The miracle of each time of darkness was hauled, swept, washed and brushed away before nine o'clock in daylight. The farmers and produce men had by that time scattered back into the country, on roads like the spokes of a wagon wheel, with Paris as the hub. To come in before midnight and depart when their stuff was sold or stored, these citizens of France who made such a solid contribution employed a multitude of vehicles of widely assorted kinds, periods and conditions of practicability and servitude.
It was a pleasant reassuring sight to see streaming into Paris in the late evening, and departing in the early morning over avenues and bridges whose names were known around the world, the farmers and outdoor workers driving enormous stallions between high heavy shafts, made slightly more tractable by heavy collars and double-plated harness. These vegetable and produce carts were not exactly of our century. A number of them rumbled past our little street on the Boul' Mich' end and crossed the pont St. Michel. Others jolted by the eastern extremity of the rue and crossed the two bridges ahead of the rue Deux Ponts. In the late thirties, many of these horse-drawn supply chariots were replaced with cheap trucks, burning an atrocious-smelling petrol which counteracted the earth and vegetable odours.
At midnight the rue Montmartre and the rue de Montorgeuil just northward and all the streets around Les Halles were lined with carts in front of which and on which stallions and peasants were slumbering. Some had been unloaded, but most of them were awaiting their turn. In some of the small or cheap restaurants near by, an upstairs room was provided where incoming farmers could snatch an hour or two, sitting tightly side by side on a bench with their elbows on a rope or a rail. The food in all the market restaurants was good. It had to be for hungry farmers and jolly produce dealers.
The beef and mutton were displayed in huge high-roofed sheds like giant airplane hangars, suet and flesh and tubs of blood and miles of tripe and lights and livers, hung from hooks in endless files and rows. If Rembrandt found one carcass notable and paintable, who would sneer at fifty thousand? Butchers, roustabouts and helpers, cashiers and clerks, women whose faces and hands were ruddy from exposure toiled steadily in the lamplight amid sharp shadows and customers in inexhaustible throngs. At 5 A.M. on certain days one would see there the surly Monsieur Salmon, the butcher from No. 2 rue de la Huchette, complaining and pinching pennies as he made his purchases, but using good business judgment and getting the most for his coin.
Along the rue Ferronerie were waiting in line the barrow men and women who would appear in the rue de la Huchette and the rue Zacharie as soon as the inhabitants got up and were ready to buy their day's provender. The chestnut man (who sold oysters, clams and periwinkles, as well as pistachio nuts, castañas and the very best peanuts from Perpignan) frequented a small bar called the Café Jean Bart, an excellent spot for a nocturnal drink or snack. Around the counter, and seated at the tables in the main room of the Jean Bart were men and women who worked in the markets near by. Not infrequently one saw the old red stocking cap of the French revolutionaries, and more often wide blue sashes and wooden sabots. The back room was devoted to occasional tourists, for whom the prices were slightly raised, and the neighbourhood whores who worked in the four-o'clock houses across the rue du Louvre and in the Quartier St. Paul, or across the Seine in the rue des Rosiers. The pimps drifted in, sleekly dressed in tight-fitting coats and coloured mufflers, or with second-hand army raincoats if the weather were inclement, arriving about quarter to four. In case of heavy rain, they brought rubbers or umbrellas for their non-foresighted providers.
Everybody in that neighbourhood ate heartily and well, excepting the trembling ill-smelling vagrants the police had chased out from under bridges. They had to pick up what they could, which somehow kept them alive.
On the morning the death of Willette, the famous cartoonist, was announced in the press, I met l'Hibou (the owl) as he was sitting on the stone doorstep of No. 30 rue de la Huchette, the semi-religious publishing house. It was about five minutes to two. L'Hibou was not a sound sleeper. He was the one among the throng of vagrants who had chosen our street as his own, that is, for a sleeping place. On the pavement, snug against No. 30, was a grill covering a vent from the Métro or subway; from this issued a sluggish current of air that was warm and had been purified somewhat, let us hope, in rising from the depths of the St. Michel station to the level of the ground. This was I'Hibou's bed, and pedestrians on the northern pavement (not more than two and one-half feet wide) were careful to step around his slumbering form when walking that way between the hours of eleven at night and two in the morning.
It was noteworthy of I'Hibou that he considered himself entitled to his share of public service, for on the occasions when he awoke before the hour of tramps' reveille, when the police throughout the city roused sleeping tramps and, started them towards the central markets to rustle scraps of food, our rue de la Huchette representative among the hoboes would sit calmly on the publisher's doorstep and wait to be summoned in the formal way. Consequently, some cop had to walk all the way from the police station at No. 14 to the publishing house at No. 30 in order to do the job. The dialogues that resulted nightly have been lost to posterity, but I had the luck to overhear one now and then.
The cop, sometimes the sarcastic _Agent_ Benoist who had trouble with his liver, would stride self-consciously along the narrow stonepaved pavement, listening to his own footsteps and their echoes. Formerly the police had shouted to l'Hibou across several intervening street numbers, but the residents had beefed about that, since it broke their sleep, and I'Hibou would never recognize the validity of an order to move on if it were delivered at an unconventional distance. He had done his military service just after World War I, mostly in Coblenz and Ehrenbreitstein (where the guardhouse was) and he knew that a man should be addressed from not more than four paces, when given the orders of the day.
_'Dis donc, toi. Tu t'es bien reposé?'_ _Agent_ Benoist would inquire, rocking back and forth on the heels of his well-polished regulation shoes.
_'Pas mal, je vous remercie,'_ l'Hibou would reply.
_Agent_ Benoist: 'Then flag your dirty arse to hell out of here! Why can't you vamoose of your own accord, when the clock strikes? Why do I have to come out in the cold...?'
L'Hibou: 'Monsieur, you have a frivolous idea of duty. Come out in the cold, indeed! The public is not paying you to toast your _derrière_ on a brazier. You should be out of doors making life complicated for the helpless and homeless whom nightly you abuse, while the rich, Monsieur...
Madame Absalom (From the second-floor window of No. 28, where she slept): _'Alors, bavardeurs. Est-ce que vous allez trompeter pendant toute la nuit, pour embêter les gens honnêtes? Foutez le camp, tous les deux. Vous valez également à deux fois rien.'_ (Now then, windbags. Do you intend to trumpet all night, to annoy honest folk? Scram, both of you. You are equally not worth a whoop!)
_Agent_ Benoist (with severity): 'Madame. My duty...'
At that l'Hibou would break out with derisive laughter.
L'Hibou: 'I know where you do your duty, Monsieur l'Agent. Up against the door of No. 15 rue Zacharie. One, of these nights that trollop will get the doorlatch in her behind and you'll have to...'
Madame Absalom (nightcap appearing at window, gleefully): 'Respect yourselves. What kind of talk is that for a serious woman's ears?'
What l'Hibou suggested, with exaggerated politeness, that Madame Absalom should do with her ears had best be omitted from this _reportage_.
On the night or morning of which I started to write, I found I'Hibou, who was usually quite self-possessed if not gay, sitting dejectedly on the doorstep staring at an early edition of the Petit Journal. Tears were coursing down his cheeks. Because they furrowed the dust from the subway exhaust, they were more easily discernible.
'Something wrong?' I asked.
_'Il est mort,'_ said I'Hibou simply, and bowed his head, _'Un grand homme,'_ he continued. _'Il n' y a plus comme lui en France, Monsieur Heliot_ (that was as near as any Frenchman could come to Elliot). _Nous sommes tombés dans les jours maigres...'_
I wish I could convey the eloquent way in which he growled out the words like ' _maigres_ '. Villon, in reciting _'Ma pauvre mère'_ , could not have hit a richer diapason. Briand would have been jealous. (In translation, l'Hibou said: 'He is dead! A great man! There are no more like him in France, Monsieur Heliot. – We have fallen on lean days.')
'Who is dead?' I asked. I had within an hour made up the old _Tribune's_ front page and the only death of note was that of Willette. 'You mean Willette?' I added, puzzled.
L'Hibou rose with dramatic dreariness. 'Who else?' he asked. _'Ah, les gosses!_ The poor kids of Montmartre! Who will now interpret them, their laughter, their pranks, their heartbreaks, to the world?'
L'Hibou and his small circle of friends and social equals who gathered around the open fire on the riverside between the pont du Louvre and the pont du Carrousel passed over the political news of national and world affairs with scant attention. But whatever was Parisian, like the cartoons of Willette, belonged to them.
Once I told Henri Julliard that I had never had enough mushrooms at one time. Mushrooms, undoubtedly the miraculous manna of Holy Writ, are used for garniture, are chopped and lost in sauces and omelettes, on rare days are stuffed and roasted and served on toast. But I had always had in mind a meal consisting mostly of mushrooms, fresh from the earth and replete with earthy tastes and odours.
'Come with me,' said Monsieur Henri.
It was about four o'clock in the morning, just as the sky behind Notre Dame was clearing to form an impressive morning background for that majestic example of French Gothic art. The air was crisp and cool, the timeless city (we thought) was silent and slumbering. In heavy darkness the street lamps of Paris, along important avenues or boulevards and across bridges of the Seine, glowed alternately with a pink and lemon tone. Every other lamp gave out pink-toned light, and the odd ones were tinged with yellow. As dawn approached, those contrasting colours drew nearer to each other, as if seeking a common factor. Instead of heading for the Châtelet, towards the central area of Les Halles, my No. 1 Frenchman led me westward to the rue du Louvre. I remember that we both halted, on the same strong impulse, to look at the large beds of _fleurs de lys_ (blue iris) that beautified the northern end of the former palace of the Bourbons, in the days of the Third Republic the most important national museum. There was something in the slowly blending light, a combination of natural pre-sunrise and dwindling artificiality of man-made incandescence, that caused shades of blue to radiate, on the borderline between warmth and coolness, and made one feel that, in stumbling around the world for many years, and seeing red and yellow, one had overlooked the essence of blueness, because of its remoteness in the sky.
' _Formidable!_ ' was Monsieur Henri's comment.
The official gardener, a most competent one, must have been near by because the black soil around the iris plants had been troweled and its fragrance (for the hardy) was an excellent preparation for what I was about to experience.
Ironically enough, the space in Les Halles devoted to heaven-sent mushrooms is backed up against the Bourse, where men toil and moil for paper which they make believe is gold. There, in a clear area about fifty yards square, were mushrooms displayed in boxes and baskets – not only the common or restaurant variety ( _Agaricus campestris_ ), but pungent little _cèpes_ from the south that incite to abandon and the wholesomeness of sin, large pine-needle mushrooms from up near Lille, the special medium mushrooms from outside Rouen with the flesh tones of Jeanne d'Arc to be ravished by irreverent teeth and swallowed as substitute magic. Twenty-five hundred square yards of mushrooms back to back, as neatly matched as dancers by Degas, each basketful consistent, clean (without washing), and with a brimming convex surface, like a cream-coloured sea.
_'C'est bien la France,'_ said Monsieur Henri. 'How do you do this in America?'
I tried to describe the Washington market in New York, the Fulton fish market, the Faneuil Hall area in Boston, the markets of Mexico City, to which bare-footed Indians come from many miles with desert cacti. But nowhere else in the pre-war world was there a square, backed up by a temple of Mammon like a roundhouse, where at dawn those interested in mushrooms met together, and found assembled for their benefit all the mushrooms that had sprung up and been picked and brushed with understanding fingers and placed just so in clean and uniform containers.
I hope some day when the damage done by tanks, tractors, trucks, artillery and the tramp of foreign feet over fields and farms is computed that the statisticians will add an item for the ruined mushrooms.
In France as in Spain, but to a lesser degree, the outsides of old churches were likely to be beautiful. The edifice had been well designed by men who knew what they were doing and felt it, too. Unfortunately the interior was likely to be packed with the tawdriest of gimcracks, of cheap material with a cheaper veneer, showing taste that surpassed the grotesque. In Les Halles, the buildings were ugly and shoddy, _per se,_ while the sheer loveliness of what was inside took one's breath away. To reach the central area, one plunged into the teeming markets, in lamplight or thin daylight, from the rue de Rivoli. One abandoned one's taxi near a series of shops in front of which were crates of doves and pigeons, clucking hens behind lathe-work, cockerels of henna, with vermilion combs, sardonyx eyes, old ivory beaks, Rousseau (the Douanier) tails, and on their necks a turquoise sheen, squat ducks, obese frogs, prone sleeping puppies, love birds, parakeets, and frequently, in small tanks equipped with moss and stones, some tiny turtles.
Between poultry and pet shops a narrow alley led westward to a small street where pushcarts were being loaded. Suddenly one was aware of a ravine of colour, variegated and profuse, fragrant above human and vegetable smells, velvet in tone, suffused with green and revealing a semblance of order. I refer to a passageway between two sheds where cut flowers were on display.
There one frequently met Julien the barber, who, because he had a feud with Albertine Durand at No. 23, would not buy from her the small bouquet M. Riess, the master coiffeur, had taught him should grace any well-appointed ladies and gents hairdressing parlour. Julien had some kind of kidney trouble that woke him, if he was lucky, very early in the morning. Since he was a sensitive man, the general air of oncoming disaster in the Paris atmosphere prevented him from going back to sleep again. So he left his handsome wife (who was equally restless at the beginning of the night but who slept like death itself in the morning) and passed the time wandering around the markets, until the Café St. Michel opened.
Julien's quarrel with Mme. Durand arose over a bunch of dahlias. He bought them (six in all, of purple and garnet shades) from Jacqueline, a lame girl who worked for the exigent Albertine about ten days. The dahlias wilted almost before Julien got them to his shop in No. 20. He complained and took them back, which threw Mme. Durand into a white-hot rage. She fired the crippled Jacqueline on the spot for having failed to burn the dahlia stems after she had broken them off to the length indicated by Julien, but madame did not offer to give Julien his money back. Instead, she gave him a bunch of yesterday's petunias which didn't last long either.
From that time on, dahlias were Julien's favourite flower and he had a few in his shop every day in the long dahlia season. He found that practically none of his clients knew that dahlias will wilt, if the broken-off stems are not treated with heat. He loved to collect such odd bits of information and give them out gratis to his customers. When he learned from Monsieur Luttenschlager, who sold prayer books and crucifixes (increasingly less often), that rabbits do not drink, either milk or water or anything whatsoever, Julien added this fact to his repertoire. No client Julien esteemed was deprived of this jewel of knowledge. I did my best to stock Julien with a few Americana, such as the Kentucky breakfast (straight whisky and raw beefsteak), scented and tinted bathroom tissue, and the requirement that couples renting rooms for short periods in American hotels be equipped with suitcases, which could be rented cheaply, loaded down with a few bricks and wadded newspapers, in pawnshops near the large terminal railway stations. What really got Julien down, however, was my insistence that playing cards, sheet music and typewriter ribbons were on sale in United States pharmacies.
Upon entering the market shed with the galvanized roof beside the alley filled with flowers, one found on gently inclined counters prodigious numbers and assorted specimens of fish of the sea, not to mention lakes, ponds, brooks and rivers and even hatcheries.
Salt-water fish streamed into Les Halles from the Channel ports, and the Mediterranean. Cod, or _morue_ , came to France by the boatload from Iceland and Newfoundland. Trout were shipped from the Vosges, the Pyrenees and Alps and the streams and mountains of Alsace-Lorraine. Eels came from Brittany, the long low marshes, or from Normandy, a region rich in foodstuffs of all kinds and inhabited by the world's hardiest _gourmets_.
So in the great shed in Les Halles one saw the shapes and colours and patterns of sea creatures from the Maritime Provinces. The great _langouste_ , one of the best of shellfish (like our Pacific lobster), the _homard_ (somewhat like the lobster of Maine), huge pink crabs, turquoise king crabs, transparent soft-shelled crabs, the small flat but tasty European oysters ranging from the green-tinged Portuguese to the marennes, and the matchless belons (pride of Prunier's). Ugly John Dorys with faces like Raimu, bluefish with faces like Hoover, silver smelts, _dorades_ with golden flecks of false sunshine to camouflage their predatory eyes, slabs of smoked haddock, skates and sting rays and Portuguese men-of-war; a dozen kinds and sizes of shrimps, crayfish, cockles and periwinkles; mussels of Tyrian purple; steak salmon; _lottes_ (the only freshwater fish fit for chowder); flat turbots; philosophic eels in plate glass tanks; _calmars_ or ink-fish; roguish young shark, which seemed to be slumbering; mackerel (God's idea of quantity production) perfectly matched and matchlessly marked.
The sole, being tough enough to be mauled by waiters and having boneless fillets to be served with sauce, were bought by the large hotels and restaurants, which did their best with them. The sweet flounders, more breakable, went to the housewives' kitchens.
Importunate hardy women sang hoarse praises of their wares as one passed from counter to counter, for when Nature has produced a school of mackerel impossible to distinguish one from the other, the personal element enters into salesmanship. The local fish store of the rue de la Huchette was just around the corner, in the truly provincial rue Zacharie. Quite naturally, none of the small merchants of our street wanted a fish store (with elementary ideas of icing) next door or fifteen feet away across the street.
Thérèse, the cook at the Caveau, was fond of fish, because it stimulated her thirst. She prepared fish in a talented manner. Nightly she would leave her door open so Monsieur Henri could shake her by the shoulder in the morning (about 5.30), knowing that a mere banging on the panel or a siren or artillery fire would never rouse her from her drunken sleep. Like so many manless women, Thérèse was extraordinarily sensitive and hostile to the masculine touch. Had anyone but Monsieur Henri put his hand on her bare shoulder (she slept in her low-cut chemise) he might have lost his life. An unsuspecting client of the hotel, good-naturedly drunk, had pinched her once as she passed with a dish of stew and had remembered the incident dimly but with almost pious regret for years afterwards.
The day, for Thérèse, began with a tug at her shoulder, a bleary opening of protesting eyes, and the sight of the fine Savoyard countenance of Henri Julliard. Very often he would linger while she struggled out of bed and into the rest of her clothes, talking casually about the weather, or the menu for the day. Down at the bar, he would serve her coffee spiked with rum. Then she would grab her huge basket and start on foot for the market. At the çafé Jean Bart, she would pause for a glass of red wine and a word with the chestnut man, whom she treated like a comrade. Then she would buy her vegetables along the street. The tramp of her choice would follow her from stand to stand with a barrow and would be taken under her wing into the various bars at which she stopped to refresh herself _en_ _route_. Fruit, vegetables and other bulky and perishable supplies would be entrusted to the tramp and his barrow, but the precious meat, fish and poultry she lugged in her own large basket. By the time she got back to the rue de la Huchette, Thérèse was feeling warm inside and all right with the world, and the tramp was even more so. But whatever had been on Monsieur Henri's list was on hand and intact, if it were obtainable, and if not, something just as good.
In the market shed of incomparable beauty, the zone between the fish and the fruit was given over to the kingdom of poultry. There the fowls of the air, by long habit or coercion grounded, were ranged side by side, and row on row, bereft of feathers and showing thin tender skin and plump meat beneath and just enough fat and not too much. Their eyes were closed; their necks and heads showed resignation and a long sweet last repose. Their very neat feet were tucked under them. The fryers and roasters of Bresse, browned over poplar and willow twigs, impaled on spits, cooked in ovens or boiled or served cold on cool plates in the heat of the day; the birds, paired with bottles that aided in seductions and persuasions, that gladdened little children on Sunday, that bolstered convalescents in the grim Hôtel Dieu, that yielded broth and curry, that graced expensive banquets – all are now a mirage of forsaken years of plenty.
# _A Bevy of Reds_
EVEN IN THE LATE 1920s, while France was still assumed to be a first-class power, by Frenchmen and others, the Communists had started making themselves unnecessarily conspicuous and unpopular. If there is contained in the works of Karl Marx an admonition to his followers to make life hard for themselves and to add to the almost insuperable difficulties attendant on social reform the handicap of offensive personalities, it has escaped my cursory examination. Nevertheless, in all the countries I have visited, and in the United States where I properly belong, the so-called Reds have conspired, perhaps unwittingly, with reactionary traitors and die-hards to place the blame on Communists for all of man's ineptitudes and Nature's sorrows. They will never utter a word but hem and haw when a clear explanation or avowal would be helpful, and it is impossible for them to keep their traps shut when discretion would be the better part, not only of valour, but of strategy and tactics as well.
A group of talented literary clowns known as Surrealists, with an associated handful of painters whose works are just now sifting into the consciousness of New York (sixteen years after their purposes have been served), adopted in 1926 a policy of protest. Members of the group, including such outstanding and authentic talents as Louis Aragon, Paul Éluard, the painters Masson, Chirico and others, and led by a windbag named André Breton (who could write like hell, when he wanted to) were not encouraged to write or to paint too much. It was passé, Breton decided, to spend one's time making beautiful objects. Instead they issued manifestos concerning this or that, and into them went so much wit and perversity that invariably they stirred up a squall. The only Communists, at that time, on our little street were Milka, the Serbian student, her lover and disciple, Stefan Koltko, and later, Pierre Vautier.
Pierre's conversion from being the wayward son of a rich aristocrat and manufacturer to a champion of the prisoners of starvation took place in a characteristic way (for Paris of that period). The boy detested military life and engineering and he had always disliked his father, who exploited his employees in a bald-faced and arrogant manner that should have offended less sensitive men than Marx. When Pierre found refuge in the art gallery infested with homosexuals, their combined influence disrupted his wholesome liaison with Mary the Greek. The group of painters whose work was shown in the Galerie Peret included several minor Surrealists and others who were independents. Along about 1926, André Breton decided that his followers could not permit their works to be exhibited in galleries which also included conservatives, or still worse, non-Surrealist radicals. Bertrand Brun, proprietor of the Galerie Peret, and who had succeeded Mary the Greek in Pierre's warm affections, had to make a choice. For various reasons he elected to become pure Surrealist.
Then Breton made another grandstand play. The Communist Party in France had been founded and nurtured in its infancy, as in other countries, by a few exiles and refugees with no special interest in France but only solicitude for the workers of the world. Discontented French industrial workers, in small numbers, were induced to join and did so, principally because the other parties were obviously so corrupt and ineffectual. To this unfortunate nucleus, the Surrealists decided to attach themselves, and proclaimed themselves Communists in a bombastic manner by public manifesto. The only hitch was that Moscow would have none of them, and let this be known.
Years later, after tragic events and longer experience, more calmly assimilated, a few of the former Surrealists became bona-fide Communists, and some of them, like Aragon, did heroic work. Breton, the pontifical sachem, turned to Trotsky and became an enemy. Most of the Surrealists eased themselves back into the _intelligentsia_ or the _bourgeoisie_ , or both, and now are indistinguishable from other French citizens.
Pierre Vautier was a fine intelligent young man. His effeminate instincts were congenital and had been fostered by an idiotic doting mother, and were brought into high relief by a mutton-headed obstinate father who was not an impressive example of mankind. In spite of their differences in breeding and temperament, not to mention race, nationality and point of view, Pierre did his best to maintain solidarity with Milka and Stefan, his fellow Reds, after Breton had read him and his gallery into the Party. I have seen him turn white with embarrassment when his comrades exhibited abrupt and bad manners. I observed with what effort he bore the odour of Stefan's unwashed body and infrequently laundered clothes. Had there been a barricade, just then, Pierre would have defended it calmly. Later, his behaviour in the valley of the shadow of death entitles him to forgiveness and acceptance by the most bigoted and righteous of critics.
But from 1926 until the end, Pierre's days and nights were beset with problems which far wiser and older men could not have batted back and forth between conflicting theories, facts and policies like tennis balls in a champion doubles match. He knew the rottenness of his class, and hoped the workers would prove sounder and better, as they did.
His first jolt was when his _Führer_ (M. Breton) forced his lover (M. Brun) to eject the works of his friends, whom I need not name, from the Galerie Peret. That he swallowed in the name of discipline, group discipline. When he was read into the Communist Party with his brother Surrealists, he went humbly to Milka, who was nothing if not articulate, and sat at her feet for hours, while she tried to make him class-conscious (which he was) and politically minded (which he was not). Pierre, having lived in an atmosphere of petty jealousies all his life, was warmed and impressed because Stefan showed no jealousy when Milka took him under her shapely wing and was closeted with him far into the night and sometimes all night. Milka had a theory that a two-sided conversation is infinitely more effective than a three-cornered one. So she banished Stefan during Pierre's apprenticeship and let him do Party work in the rue des Écoles while she was supplementing Pierre's education. The spice of jealousy, however, was amply supplied by M. Brun, who, although technically a comrade by force of Breton's decree, nearly lost his mind. On two occasions he stormed into the Caveau, rushed hatless upstairs and burst into the room where Pierre and Milka were deep in Party lore. Both times they had their clothes on and were sitting at least a foot apart, but that did not comfort M. Brun.
A short time afterwards, when the Surrealists discovered that they were not, in fact, Communists and that Moscow was leery of their antics, Pierre went through a double crisis which faded the roses on his cheeks and cost him at least ten pounds of much-needed weight. M. Brun was ecstatic. Pierre, he believed, would now put that foreign menace and her mackerel in their places and spend all his evenings with him. He had not reckoned with Pierre's sterling qualities. For Milka's eloquent interpretations of Marx had taken root in Pierre's logical mind. He could not discard them at the casual behest of an absent chief – even Joe Stalin, himself.
The result was a soul-storm such as only homosexual young Frenchmen can achieve, but it resulted in a victory of Milka over Brun and the loss of Pierre's job. The pay had been small but steady, and was all Pierre had had with which to eat.
Milka came through splendidly. She vouched for Pierre as a promising convert, notwithstanding his Surrealist affiliations (which were shattered by the influential Brun) and got him into the C.P. rank and file through regular channels. For the sake of economy, since every franc was needed for the cause, she persuaded Pierre to give up his expensive room, which cost $7.50 a month, and move in with her and Stefan. This he did, at what cost to his squeamishness about perfumes and sartorial elegance no one else will ever know. There was only one double bed and a moth-eaten upholstered chair, and what the trio did or how they managed, I have no idea. I wondered from time to time but could not, with delicacy, inquire directly. Georges insisted that they all slept together, most often with Milka in the middle, also that Milka mothered and lectured her two room-mates and kept them both busy from morning until night. Once in a while, when stray comrades entered the Caveau by the side entrance, Milka would send both Pierre and Stefan down to the bar while she conferred on matters too desperate for their ears.
Mary the Greek, who had been reduced to prostitution and was allowed to sit in a dingy café in the rue St. André des Arts from six in the evening until two in the morning, did not rebuke Pierre openly, but she whispered insidious things about Milka and sang sad maudlin songs in her cups every night. Her drinking interfered somewhat with trade, for which she was not at all suited. But she was patient, her face and body were beautiful, and in spite of the fact that she had only one skirt and two blouses, she made enough in good weeks to pay her rent and board to Monsieur Henri. Marie wanted to eject her while she still was not quite destitute, knowing Monsieur Henri would never do it later when she became entirely helpless.
An example of Red tact occurred early in 1931, and put Pierre on an uncomfortable spot in the Caveau bar. The beloved Marshal Joffre died, and while public feeling for and gratitude to the grand old soldier was at its height, the handful of Communists in the Chamber of Deputies refused to join in a eulogy. Nothing whatever was gained for the prisoners of starvation by such a surly gesture, and its effect was to inflame public opinion against all the sound causes the Communists were favouring at the time or would sponsor in the future. Milka, in private, to me, excused the blunder on the ground that the French were only in the kindergarten stage, as far as Marxism was concerned. It was the country in which the middle class was the stuffiest and most influential, she said, with more justice than relevance. Pierre was acutely sick, and for days did not show himself in the street; so the kindhearted Stefan, to cheer him, took a bath and had his hair cut and promised to be neater in the future, which he sincerely tried to do.
It appeared to me and nearly everyone in the rue de la Huchette that reform and regeneration of society was retarded when small minorities with some good ideas (and a lot of absurd ones) did everything they could from day to day to antagonize that great body of nonpartisan citizens without whom no action can be made to stick. Nevertheless, the French C.P. overlooked not the minutest opportunity to make itself loathed and detested. From its inception until this very day, the American C.P. has followed suit, with the exception of a short period in 1936 when, acting on instructions from above, the American comrades whooped it up for 'democracy'.
For the last fifteen years in France, every pretext furnished by _événements_ (events) large or small, has started the so-called government on a Red hunt which has helped camouflage the real issues. In the rue de la Huchette the general feeling was so strong against Communists that it would be simpler to list those who tolerated them than to enumerate their enemies. Of course, Henri Julliard, humanitarian that he was, was willing for everyone to have his say, and would listen respectfully even if he were not taken in. So would Mme. Berthelot.
Monsieur Henri, it is true, housed all three of the Communists in our street, and defended them against flank attacks by The Navet and his henchman, the floor-walker Panaché.
Maurice, the goldfish man, who accidentally was martyred in the name of Lenin, Marx and Stalin, had a smile for everyone and listened just as respectfully when Milka held forth against class compromise between workers and employers as when The Navet insisted that he had inside information to the effect that munition makers like Schneider spent all their profits, and more, in patriotic and charitable endeavour while labour leaders drew down fabulous salaries and sat with their feet on desks of pure mahogany, with 100-franc courtesans, half-dressed, as office help and thugs out in the alleys, garrotting helpless respectable citizens who refused to let themselves be blackmailed.
'Those _maudit_ Reds are no worse than the rest,' Maurice said, but he added, with characteristic emphasis, 'and no better, either.'
# _Mene Mene Tekel_
THE PEOPLE OF THE rue de la Huchette were fairly representative of Parisians and other Frenchmen who lived in cities. The _garçons_ , chambermaids and many vegetable and fruit peddlers were peasants. They treated our street as if it were a lane in the country and were bewildered by gas light, telephones and the traffic in the place St. Michel.
It was necessary to walk only a few minutes towards the place St. Germain or the Ile de la Cité or into Notre Dame, when it was open, to find French people with more money than those in the rue de la Huchette. On the other hand, a shorter trip across the rue des Deux Ponts would take one to a quarter that was even poorer, probably poorer than any place a non-travelling American has seen or ever dreamed about. Into the eastern gate, as it were, whose pillars were the butcher shop and the crucifix store, came savants and students from the Latin Quarter and the Sorbonne. The clergy was much in evidence, on account of the proximity of St. Séverin, church of the workers; St. Julien le Pauvre, church of transients; and Notre Dame, cathedral of the greedy gang who ultimately sold out the country.
At the western end, our street was guarded by the two large and prosperous cafés, the Brasserie Dalmatienne and the Café St. Michel. From that direction came the respectable middle- and even upper-class white-collar and professional men, business men from the place St. Michel and the boulevard St. Germain, and customers for such shops as Maurice's _La Vie Silencieuse_ , the stamp collector's, book lovers bearing volumes under their arms, writers blinking in the sun as they looked for No. 30, the publisher's headquarters, and twenty-franc patients for Dr. Clouet and the dentist, Dr. Roux. The neighbourhood shops had staples and perishables for neighbourhood needs, and the quarters of recreation and supply that belonged to all Paris (like Les Halles and the zoological and botanical display in Le Jardin des Plantes) were used by inhabitants of our street and were really a part of it. The public transportation system served it from the western end, the Metro station being not twenty-five feet from the corner; the railway station a hundred feet farther on. Several lines of street cars passed through the _place_ , and buses radiating in all directions had their terminal in the place St. André des Arts, in front of Noël's taxidermist's shop.
When the Oustric bank scandal (the first rumble of the Stavisky affair to follow) could not be kept out of the papers, no matter who owned them, several prominent politicians, including members of the Chamber and of the Bank of France, a Cabinet Minister and an Under Secretary, were involved and could not squirm out from under. As usual, when anything sinister happened, his enemies tried to pin everything on Caillaux, who cleared himself promptly.
The faces around the Caveau bar, when news like this was read, sometimes aloud, more often over a drinking companion's shoulder, showed mild disgust which deepened into resentment. Thérèse and the chestnut man called the absconders and crooks foul names; Monsieur Henri and Madame Berthelot dropped their eyes and turned away. Frémont and Pissy worked harder to get government employees into the union, but the opposition against them was forming on all sides because they were Socialists and were beginning to be reviled by the Communists on their left and the Radical-Socialists led by Daladier on their right.
Early in 1931, the jackal Pierre Laval got himself elected Prime Minister, after much chicanery and some hedging by the peace-maker Aristide Briand. On January 26, 1931, Briand stated publicly that he would not serve with Laval, for Briand was honest though weak. On January 27th, Briand grew a little less honest and much weaker, and by his co-operation made it possible for Laval to worm his way into the No. 1 position. Included in that cabinet of lilies was Tardieu, who a week or two before had been ousted because of the Oustric affair.
Daladier, in the Chamber, assailed Maginot for asking military appropriations which were, in Daladier's opinion, 'too high'. Coincidentally a huge loan was granted to Romania. Also, the Verdun forts were restored. A hen with her head cut off could not have behaved more erratically than the French Government did.
All the foregoing news items were discussed and added to the encircling gloom. But what really shook the rue de la Huchette was Alfonso's fall in Spain and the proclamation of the Spanish Republic. The reader has seen how certain minerals, dull in colour to the naked eye, will glow with intense reds, purples, greens, blues and yellows when violet rays are turned on them. A similar transformation takes place in the aspect of a population when the announcement of a historical event is made. Political enmities which had been smoldering burst into flame. And ideological affinities that had been scarcely apparent unite men and women who had ignored or avoided one another.
The Navet stormed and stamped with rage, denouncing the Spanish patriots as jailbirds and cut-throats. Even a likeable roué like Monsieur de Malancourt turned pale and shook his head sadly. He definitely did not believe in a people's reign. He was smart enough not to expect a monarchy to return to France, but he preferred to have one handy across the border in Spain, and not a land where the terrible Reds would swarm like locusts in preparation for world conquest.
Monsieur Panaché blamed the Spanish uprising on the Jews, and when reminded that Jews had been chased out of Spain six hundred years before, he redoubled his accusations, declaring that the Jews outside Spain had manoeuvered the revolution in order to extend their hunting grounds.
Of course, our three Communists, Milka, Stefan and Pierre Vautier, were overjoyed. They did not consider that the Spanish Socialists were really revolutionaries, but assumed that they soon would be liquidated and replaced by proletarian leaders who would surely spring up.
Our Radical-Socialists, Monsieur Monge, Monsieur Noël and the Satyr, being good fellows, were one hundred per cent for the liberated Spaniards, although their party was, as usual, on the fence.
The Socialists, Monsieur Frémont, the chestnut man, Monsieur Pissy, and Odette and Jean of the dairy shop were heart and soul for freedom. In _Le Panier Fleuri_ , Consuela, the Spanish girl who dressed daily as a bride, was loaned money by her fellow workers to hurry back to Madrid to breathe the free air again.
There was rejoicing for the Spaniards in every little bar along our street that evening. André, the coal man, his blue-eyed Alice and his little son stayed up until long after midnight, with their friends around them, drinking applejack in moderation, and talking, heads nodding thoughtfully, eyes shining happily, of the things that Americans are taught to love in the primary grades of school: no taxation without representation, no cruel and unusual punishments, the separation of Church and State, free speech, universal suffrage, and the right of eminent domain. The proprietors of the Café St. Michel were reactionary, but the customers at the bar were working men, and when they talked that night about a republic, for once Madame Trévise did not contradict them sharply and inject some warning wisdom of her own.
I wish you could have seen the face of Sara, the soft-eyed Jewess, at the Hôtel Normandie that night. For not only the _garçon_ , Louis, was humming and whistling as he worked, but Guy, Sara's husband, actually took off his coat and helped his wife with the work, smiling on her affectionately from time to time. Happiness is beautiful.
The date was April 14, 1931. That April 14th has passed away and with it the memory of other more and less important days. July 14th (Bastille Day) has passed away. So have dates honoured in Poland, Czechoslovakia, Holland, Belgium, Norway, Greece and almost everywhere else on this sad earth. Little is left intact.
If only that tiny thoroughfare, the rue de la Huchette, a few hundred yards in length, could be resurrected, there would be enough of France alive today to stir a spark of hope in the hearts of men. If we could call back from degradation and disaster that small array of citizens and foreigners; the shops, the apartments; the beds, stoves, meals and draperies; the soap and olive oil; the wine, the bread, the piety and wit; the crimes and sacrifices; the knowledge, ignorance, love and hate; the indifference and the prejudice; if those faces could smile, those hands gesticulate, those dripping taps make music through the night; if those priests could walk, hands behind their backs clasping prayerbooks, under the trees at St. Julien le Pauvre; if the girls at _Le_ _Panier Fleuri_ could once again say, _'Avec plaisir, Monsieur';_ if Frémont the Postman could tinker with rusty latches; if the chestnut man could roar a song of the Loire; if l'Hibou could sleep on the grill over the Métro; if Sara could chew her pencil as she totted up accounts; if Dorlan could bind books and Monge sell horse meat and the cops loaf in the station; if only death were not the ultimate relief and birth the worst disaster – in short, if fate or history or progress or God could have spared the rue de la Huchette, from it another France might grow.
PART TWO
# _The Pre-War Thirties_
# _Excerpts from a Series of Letters_
[Received by the writer in Madrid, Alicante, Barcelona, Palma de Majorca and Santa Eulalia, Ibiza, Spain, from residents of the rue de la Huchette, Paris, France, from July 1931 to November 1934.]
THIS PERIOD WAS MY longest absence from the rue de la Huchette in the course of the past eighteen years. So from the time of the Spanish revolution that unseated Alfonso until just after the United States had recognized the sixteen-year-old revolution in Russia I had to depend for news of my friends in Paris on their own talent for letter writing and what I could read between the lines of the corrupt and scattered French press. On the island of Ibiza I received the Paris papers two or three weeks late, but I had plenty of leisure in which to read them and assimilate their contents.
A city one loves exists at no matter what distance, and its symphony is sometimes heard more clearly when one is away, as the music of an orchestra is more lucid to an audience than it sounds to the performers on the stage. Had I been in another European country, the local events might have confused me and blurred my understanding of the Parisian scene. But France was decaying Europe, and Spain was an awakening new world. The Pyrenees and not the Straits of Gibraltar form the real boundary between the continents. The short journey from Biarritz to Burgos this very day takes one back across a gulf of about six centuries.
_Paris, 17 July, 1931_
_Cher ami,_
My hour of escape at noon from this dingy barrack is not what it was before you deserted us, or, rather, found it necessary to exercise your sharp curiosity in fresh flelds. You were right and I would do the same if I could. Instead I look forward to a report from you of what you have found in Spain and to talking with you hours on end when you return. You will pardon me for telling you how much I have missed you, especially in the noon hour when you were gallant enough to share my table and so many of my doubts. Before you appeared, I had accustomed myself to eating alone, but never could I enjoy it. There is something in the taste of food that requires joint appreciation. One is impelled to glance across the table, and since you went away I have done that so often that my eyes must have worn some varnish from the empty chair.
The only gossip I can relay to you is a development that troubles Monsieur Henri, although, saint that he is, he does not complain. A young boxer, formerly champion of Yugoslavia, I believe, has come to our hotel – in Room No. 6 where I used to be before I moved upstairs to escape the sound of blows and cries. He has become attentive, for what motive I cannot say, to Madame Berthe, our widow who looks daily more like a Botticelli madonna. His name is Daniel. He is handsome, gay, neat and smartly dressed, and he speaks French with an accent that makes it almost too emphatic.
Our French language, which you have almost succeeded in Americanizing – you know that I adore your accent and the way in which you find expressive words and phrases incorrectly – should not always be used at the summit of its exactness. It is capable of nuances, of hints and suggestions, of subtle implications. Monsieur Daniel employs none of the aforesaid.
[Note: The Berthe to whom my correspondent refers is the widow of Jacques, Henri Julliard's brother, who formerly shared with Henri the ownership of the Hôtel du Caveau. She was then about forty years old and always dressed in black, which set off her somewhat Italian style of – not beauty but comeliness. Since Jacques' sudden death, Madame Berthe had tended her bar, while Monsieur Henri slept in the afternoons, and otherwise made herself useful around the hotel of which she was half-owner.]
The change in our madonna without child is astonishing. Each day she looks younger, like a wilted plant being revived with water. This is not an illusion; it is an actual physical change. The lines in her face are disappearing; her figure, in the same black dress, is more supple. Madame Julien has done wonders with her hair, which is still black – and not grey. She smiles at customers, talks aloud to Maggie [the troublesome terrier]. Georges [the _garçon_ ] smiles knowingly and a little maliciously all day long and waves his moustaches when Berthe and Daniel come into view.
How will it end? Who can say? How will anything end, or will anything end? Certainly not the prefecture, where large and small we berate the foreigners more churlishly each day. The Navet is in such a rage about foreign loans the Government has made that the other day he struck poor Jeanne on one of her useless ears. Of course they are ornamental. Luckily. Her Socialist Lothario has quit her, to take some minor post in the Midi, I believe. So the day after her conjugal beating she took up with a Turk, a painter, if I am not mistaken.
Somehow – forgive me for being chauvinistic – I cannot visualize a Turk with palette and brushes. Probably because when I was young I loved madly a tall Turkish illusionist, I think of Turks perpetually bashing in silk hats (chapeaux de forme) or tearing coloured cloth into ribbons, threading needles and swallowing them, and never doing anything banal. Would that it were so, and that some Turk would speak to me and rush me to a transient hotel. I am past that age, and never enjoyed a clandestine situation. That is not a boast, _cher Heliot,_ but a regret.
Perhaps it is better just to sit obscurely in corners and smile inwardly. Anyway, I never received a box on the ear. When I heard about Jeanne's, I tried one gently to see how it would feel. I confess that I didn't like it.
The Navet's fat son, I understand from la _petite Hyacinthe_ who knows everything, far too much, advised his mother to quit The Navet. 'I know you have put up with him on my account and it hurts me,' he said. 'Leave so I may show my loathing openly and take your side in court.'
At the risk of losing my position, I am reading in secret these days _L'Humanité,_ to help me imagine what you are seeing down in Spain. It would be too much to hope all the glowing accounts _L'Humanité_ prints of the revolution in Madrid are true, but they err on the side of my heart, and that is always agreeable.
Spare me a moment when you can, if only for a postcard.
Your more or less faded friend, ( _Votre amie, plus ou moins fanée_ ),
Hortense Berthelot
_Paris, 3 August, 1931_
_Cher Américain,_
I have just returned from a long walk and still feel quarrelsome, so I am avoiding Milka, who always gets the best of every argument. What set me off is the Matisse exhibition which I visited for the third and last time today. The effect on each occasion has been to make me faintly ill with uncertainty. To what purpose those long walls covered with odalisques only slightly lop-sided and all in terms of pink and blue, with also some green and yellow, and eyes of such dark grey that they look like holes burned in a baby's blanket?
That is unjust, I know. When I paused in front of any one of them, I said to myself, 'A superb colourist, a gentle facile composer who will do no one any harm.' There are many paintings by Matisse that I should like to own, if I had an apartment – but then, what should I put in it for furniture? The chairs and sofas in the gallery are Louis XIV, clashing weirdly with the pinks and blues because of the pale lavender and gold. You will not credit the statement, but on the opening evening (to which your _New York Times_ sent McBride all the way across the sea, not to bury the artist but to praise him) the ceremony was opened and accompanied with music. Modern music? No, indeed. Ancient music. Music for a large auditorium? By no means. Chamber music. And the bourgeois fools ( _poires_ ) noticed nothing incongruous.
I honestly believed I had changed when I dedicated myself to the logic and decency of our party programme. I wonder. I would have relished Matisse if I could have seen his works alone, or with you, the only American with taste and humour. You would deny that if you were present and I should have to retract, as usual. Either I do not go far enough in my judgments, or I go too far. That is why I thrive in the party. Such questions are decided for me. The wisdom of St. Karl is old, and I am young; the doctrine of Lenin and Milka is reinforced and rigid, and I am flexible.
Apropos of art and doctrine, I find it hard to accept the idea that the painting I have loved is all useless and anti-social and should be replaced by propaganda. Am I incorrigible? In the Independent Show this year, one of the worst ever, I stood in front of a canvas quite ably painted and depicting a dead workman in a village gutter being nibbled on by swine. The red was red, the mud quite worthy of a pupil of Courbet. The composition answered to the rules of dynamic symmetry, derived, I believe, from the proportions of the Pantheon. I was moved to indignation, not with the Cossack who murdered the deceased worker, or because of the cowardice of the other workers who fled and left their dead upon the field. I felt an irrepressible hostility towards the painter and whoever had convinced him that photographic representation of ignoble incidents in colour and illusory three-dimensional form is good art, however well executed, or good propaganda either. Seldom does a worker visit the _Salon des Indépendants,_ and how right they all are. But should one of our wage slaves stray into the Grand Palais and see the painting in question, the lesson he would derive, in all probability, is that the capitalist police are still too powerful to be successfully crossed and that proletarian solidarity is as yet far over the horizon.
You are discreet as well as sympathetic, and will not think me disloyal to the principles I have embraced in all sincerity if I confess to you my lack of clarity. My intense French sense of proportion (how I detest it!) and my grasp of reality, which has been strengthened by my unwholesome excursion into surreality, reminds me softly and persistently from time to time that my comrades, so few of them French, are ahead of actualities. I mean to say that they see the kind of progress they know would be just, and which Marx foresaw in advance of its materialization. Probably, they are sound in this eagerness to anticipate developments. The progress must come, or else we are lost, and humanity cannot be lost. Or can it? Shaw, the Irishman, points out that a thing must be imagined before it can be made, but that does not mean that imagining a thing is making it.
I was not a good member of the vile ruling class of my country. Evidently I was wrong in thinking of country, and not in terms of strata of society. I was a fizzle as a soldier and an engineer. In the realm of art I floundered and ranted like a gander. Shall I be more worthy as a member of the party rank and file?
Please tell me frankly.
Yours for the revolution,
Pierre (Vautier)
P.S. In my state of uncertainty I do not even know when I am finished with a letter. I started to tell you of my long walk, which I hoped would numb and exhaust me to a greater degree than it has. The only suitable day for walking in Paris is the first of May, when taxi drivers take a holiday and the streets are not dangerous. Next best is any day in August, when our stupid bourgeoisie flocks out into the country to suffer sunburn, insect bites and hives. So many shops are closed and customers are absent that walking in what quarters are left in which one sees none of your tourists – thank God there are fewer of these parasites each year – is almost a pleasure.
You want news of our mutual friends. At least half of them are away. The only ones remaining are the whores, the serfs and the few Parisians who have no relatives outside the city gates. It may be hotter in Madrid than it is here, but the atmosphere could not be more oppressive. Milka is anxious to go to Spain, lacking only the funds, the pretext, the passport and visa, the invitation and the means of livelihood when she would arrive. I hope the new government, made up mostly of middle-class drips ( _fripouilles_ ) with a sprinkling of professors, will forbid Republican Spaniards from visiting France. Should a Spanish patriot see what we have come to, after a century of capitalistic L.E.F. (Liberty, Equality, Fraternity), he would clamour for the soursmelling Alfonso and his gaga queen again.
Is it true that when the people took over the royal palace not one book except the breviary was found and that the royal _salaud_ used a scooped-out horse's hoof for an inkwell?
P.
(Undated)
_Cher confident,_
I am writing to you, not at Mama's desk but in front of her triple mirror, which is kinder to me than to her. As yet I have nothing of my own. Mama is away with D. for the afternoon. Since grandfather came to live with us, by force of necessity she goes with D. to a small hotel in the rue Papillon, leaving me to soothe the Judge when he taps on the floor with his cane. That, dear friend, is often.
You, as a man of letters [Hyacinthe never referred to me as a mere newspaperman or writer] are not wanting in visual imagination. You can project yourself into characters and situations which unfortunately I cannot share, being ignorant of English and of life. I am studying the language, however, and my first use of it, once the grammar and syntax are mastered, will be to read your works. Meanwhile, try, with me, to imagine what Mama must look like, blushing kittenishly as she takes off her clothes behind a screen – I trust there is one – and hiding coyly beneath the sheets until they are accidentally dislodged. D. is no Adonis, but he comes around twice each week and has done so over a period of years, as you know. That is something. Just what he gets out of it, that he could not arrange more cheaply and with a younger partner, I cannot fathom. Mama must be inept. She could not be otherwise. She has no money, and D. doesn't need it anyway. His handbags are sufficiently renowned to yield him a good income even when France is bankrupt and America has millions of unemployed. You never explained to me why there are so many.
_Cher maître!_ [Untranslatable but the utmost in flattery]. You know very well that, as I write, I am glancing at my reflection between phrases, full-face, left profile, right profile, half profile, from over my own shoulder; head tilted forward, chin lowered, eyelashes raised; head leaning backward – I have a good throat – and eyes half closed. I see myself physically, a sort of animate shell, and compared with other women I am beautiful. But am I desirable in the more compelling ways? Men look at me as I pass, but they stare at my legs. I suspect that if I were irresistible they would look at me in such a way that my hands would steal up to shield my breasts – such as they are – and that I would, having passed, feel their glances somewhere near my shoulder blades and not around my hips. Are my hips really right, or must I get rid of them like an American girl? I shall not. To the last, and at any cost, I shall remain French.
What I miss in my reflection is what you supply when you are near at hand. I shall never be able to tell you how much I owe to your candid and critical attitude, not spiteful and never abusive – one counsel I can always count on and always heed.
I have news for you, my – what? You are not a lover yet, exactly, and may never be. That is as much for you to decide as for me, for if you should look at me tenderly and say: 'Hyacinthe. It is time, and I need you', there is nothing, utterly nothing, I would withhold or deny. The news I have is for you alone, not even to be shared by Mama just now. I am a _woman_. The proof of it I find not as unpleasant or mildly disgusting as I had expected, but I do not want Mama to giggle and whisper about it or to give me advice. Whatever she would advise, I should have to discard, pretending to be obedient.
What am I and where do I come from? Surely not from Mama. I must have come through her, but practically unchanged. Of my father I know so little, except also through Mama, and therefore my information is false. How do men make daughters? What qualities of theirs can be transformed or transmuted?
You may write me in English, for although I think I never shall be able to speak your language, I have reached the stage where your written words, so well arranged, mean more to me than your piquant French, which only expresses what you have equivalents for in French and therefore leaves much to be desired. In justice, I must add that frequently your French is more incisive and striking ( _frappant_ ) than that of any disciple of Racine.
I have much to thank you for, but nothing more important than your having cured me of Racine. Elliot, I shudder to think what I must have been when you first knew me (at the age of six), what opinions I must have expressed that would have closed the mind of a less receptive clairvoyant. When I open Racine and mumble the meter of that spiceless abracadabra, I wonder if I am not as silly as Mama and if simply you have not poured into an empty pitcher the wine of discernment. You tell me to the contrary, not so much with words, but with light pressure of your hand or understanding glances at just the moment when they reveal unmistakably that we are seeing or hearing or feeling and sharing the same sensation.
The same satisfying contact of spirit occurs with others, a very few others, but not nearly as often as with you. What does that mean? To me it means that I am not alone, that life lies beyond my degrading _milieu_. You have taught me to feel at one with Mozart and Beethoven, Corot and Cézanne, Rimbaud and Baudelaire, Balzac and Proust, so many others that I cannot list one-tenth of them. You have made me believe that, were those sensitive men alive, they would smile at me and press my hand as you do in the concert hall or in the Louvre or the rue de la Boëtie.
Elliot, sometimes I am afraid. What has existence in store for me? To what purpose am I developing? I used to be certain that I loved the Count Costa de la Montaigne and that some day he would come for me and solve everything. That is not likely, my friend. Life is not as simple as that, and I would not have it so. You know as well as I do that no man is going to see me as you and I do, that I am only an incident of your rich and eventful career [nothing to brag of, I assure the reader, especially in 1931], that, no one man will be everything to me, that I must either work or create. I cannot vegetate. What is happening to France? Is France recovering? Is Honneger another Berlioz? Is Gide another Proust? I'm always prattling about art, but is it indicative and prophetic or isn't it? Is Coué another Pasteur? Is Blum another Moses? At least, he speaks wonderful French, even if I cannot understand what he is driving at.
I saw la petite Yvonne [Frémont] sitting in her window yesterday. She is pale, listless, with no orientation, not chic, not clever. But she might have been as beautiful as I am had she had the help I have had from you. Or would she, in defiance of instruction, still have looked upon Antoine Pissy, who has pimples and a uniform now, as another Count Costa de la Montaigne, and think of life with Pissy in a damp concierge's corner as a low-priced paradise in a country that guards the heritage of Pericles and Charlemagne with Citroën and a _crétin_ called Daladier.
I am uneasy. As I passed _La Vie_ today, another goldfish, spotted unhealthily with rusty black, was dead and M. Maurice fished it out of the tank and walked to the quai to throw it in the Seine, then finished his lunch without washing his fingers. I wish I hadn't seen the incident.
Hyacinthe
_Hôtel du Caveau, Paris vie
4 Oct. (1931)_
_Cher M. Paul,_
I am ashamed to have waited so long to thank you for the _saucisse_ _de vieille Castille._ It was truly excellent, with a sound body and flavour of some Spanish herb not unlike _basil_. Also for that _espèce de Jerez_ (manzanilla), so pale and dangerous, to wash it down. The whole experience was surprising to me, as we others are not in the habit of thinking of our neighbours across the Pyrenees as gourmets. A cousin of mine, visiting near Biarritz once, went out mackerel fishing with some Spanish Basques and was served, at the moment when he was trying to uphold our national honour by not revealing his _mal de mer,_ a cold fish pie ( _tarte au poisson_ ) about four days old. In spite of himself he promptly sprinkled the lugubrious snack ( _casse-croûte_ ) with the cognac and coffee he had injudiciously taken before embarking. The result was that he cut his visit short and came back to Paris four days before his annual vacation was over. Foolishly I had formed an idea of Spanish cooking from his report. No doubt we French are libelled and misunderstood in reciprocal ways.
My delay in writing you has had other causes than negligence. Notwithstanding that the season has been the dullest since I entered the hotel business so many years ago I do not like to count them, I have been immersed in complicated book-keeping, filling out innumerable papers, tax forms, etc., and trying to take an inventory which events have made necessary.
[Note: The veiled passage just quoted is Monsieur Henri's only reference to the fact that Berthe's approaching marriage to the young Serbian boxer was threatening him with ruin, since in order to divide the common property he would be obliged to sell the Hôtel du Caveau at a sacrifice, if he could find a buyer.]
The inventory in question reminded me that the stove and stovepipe in the room you used to occupy belong to you. In case I should leave here, what do you want me to do with them? If you wish, I could have them transported to my house in Montmorency, unless I have to dispose of that, too. Also your bicycle is in the cellar. Shall you be needing it in Spain?
Your new war minister must be a man of wit ( _homme d'esprit_ ).
[Note: The new minister of war to whom Henri refers was Azaña, who later organized the Popular Front, at least on paper, and then deserted it and his countrymen in order to live in security near Chambery while they were slaughtered and starved. Azaña made a ruling the day he took office that civilian clerks in the war department who could not show that they had had a chair in which to sit should be stricken from the payrolls. This cut the departmental budget by a large percentage and filled the garrison towns with malcontents who started conspiring against the Republic which had refused to pay them for doing nothing, as the monarchy had cheerfully done.]
Our minister of war [Maginot] is, as you know, still draining the public funds to build a sort of Chinese wall along the border of Alsace-Lorraine and the western provinces. Young Corre has been sent there because he speaks German, although his technical training is by no means finished. His mother was so saddened by this that she was confined to her bed three days. The poor women! While their sons are of military age, they are always afraid of war.
Julliard
(Undated)
_Cher camarade,_
[Note: In case Mr. Dies or the F.B.I. care to make an issue of this salutation, I wish to swear, on my honour as an American-born citizen of American-born parentage, as a war veteran and member (not paid up to date) of the American Legion, and the titular head of an American family that I am not, never was and am not likely to be affiliated with the Communist Party or any organization whatsoever that advocates or has advocated or is likely to advocate the violent overthrow of any government the United States has had yet, except the British rule in the time of the Colonies. Of this I would have disapproved, very probably, had I been born soon enough. I did not relish Harding or Coolidge or Hoover, but I was willing to let nature take its course. Milka's use of the word _camarade_ , a word which was freely used as a term of respect and affection in our war between the States, was intended as a compliment, and a mild rebuke because I was not of the fold.]
I saw with indignation in the news reel last night the parade of murderers through the streets of Madrid and the deceived populace cheering and waving from the kerbstones, trees and the windows and steps of near-by buildings. If you were in that crowd, as you must have been, I'm sure you did not applaud the Foreign Legion, remembering how they slaughtered honest men, women and children at Barcelona.
Your so-called revolution, which is turning out not to be a revolution at all, is a deep disappointment. That old _fumiste_ (windbag) Zamora! He would not be too intelligent even for the Cabinet in France. Somehow he reminds me of Briand, only he is better educated and not so gay with the women, because of his two sisters who are some kind of nuns, are they not?
I have heard from you indirectly through Comrade Vautier, who is brave and conscientious but handicapped to a staggering degree by his _haute bourgeoise_ education. He is a sensitive young man, too sensitive perhaps for what lies ahead. I assigned him to help draw some posters, and after trying all night long, poor Pierre ran a fever of 104 degrees during forty-eight hours. In Zagreb it would be unheard of to take affairs of art so much to heart.
Is there a chance for me in Spain, Comrade Paul? Perhaps I am foolish to want to visit Madrid and see another country, and even if I could get a job my superiors might not approve. I am much needed here, they say. Still, I am blackly discouraged, not at the petty persecutions which crop out each day anew, but at the lack of progress we are making in educating the government employees. We cannot exclude them from the central union, or do otherwise than urge them to form larger and more powerful organizations. But men who are so basely underpaid, and who may be read into the army and shot as traitors if they try to strike, are difficult material. All tasks worth while are hard, I suppose.
Did Pierre tell you that I passed my finals in history and economics? I know it is foolish, or seems foolish, to attend classes at the capitalist Sorbonne, but in order to elude the police and remain here I have to attend lectures, and since I must attend them I feel ashamed not to pass.
Thank you for the Avila blanket. I feel that it belongs to me especially, being made of black sheep's wool streaked with red.
Yours for the real revolution,
Milka
_3 November, 1931_
_Cher maître,_
Not long ago I wrote you that I had nothing of my own. That is no longer the case. I have a lovely protection between me and the chill autumn air which this year is particularly vicious [an Avila blanket I sent her]. And every time I feel its warmth, through the family linen which before it comes to me will be so patched and frayed that I shall have to use it to cover chairs in summer, I am reminded of a subtler protection, an enveloping solicitude that shelters me, in bed or out – the love of a friend who, although distant, is closer than any other.
Elliot, my dear, what are you leaving – not for your successor but your substitute, who will be my fiancé? Surely the one little attribute, so important in most men's eyes, can mean next to nothing if it has been dissolved from within and is merely a deceptive mask.
Perhaps I burden you with too intimate confidences. It seemed to me that I detected a new tone in your last letter – it might have been nostalgia but I don't think so. The phrase you used, concerning what I told you about – my inevitable development – was not entirely clear, my understanding of written English is still inadequate. You urged me to study and to guard against 'the nervous or psychological crises' which might make me 'behave erratically and either act more like myself or less like myself, according to my mood'. The good God should have made women a little harder to influence, or else much easier, but doubtless He knows best.
For my satisfaction I tried to read a suggestion of jealousy into your admonitions. Sometimes I am sure that you want me to wait for you to be the first, which I gladly will do if you ask me to – providing you do not stay in Spain too long.
Yours tentatively,
Hyacinthe
I lie. Yesterday I saw the Count Costa de la Montaigne on his slim sorrel horse, in uniform, and I am sure I do not love him as I did. Concerning you I am sure of nothing whatsoever.
_17 rue de la Huchette,
Paris 6e,
2 Jan, 1932_
Monsieur Paul Heliot,
29 Calle de Velasquez,
Madrid, Espagne
It was considerate of you to think of me on New Year's day. Little Daisy did not get her card until the day after the rest of us received ours and when we made fun of her she cried. Later when the postman brought hers, she was so happy that we all had to treat her and she got tipsy and had to be put to bed. Mariette did not scold her, because it happened on your account, I suppose. Mariette's husband gave her a radio which she has brought to the _boîte_ (joint). Armandine plays it all the time, having little else to do. But then, we all grow old.
Mireille
(Mlle. Marie Verneuil)
P.S. In case I move I will send you my new address.
(Date blurred)
_Cher M. Heliot,_
Seeing Monsieur Stoff [Leland Stowe, then of the _New York Herald_ _Tribune_ and a frequent visitor at the Caveau bar] reminded me of you the other day and now a pretext has arisen for me to ask a little of your valuable time, or is time not so valuable in Spain. I hope not. Spain must be a happy land.
In one of the _bouquins_ [little book, no doubt a magazine like the _Scientific American]_ Georges [the Serbian _garçon_ ] found when he cleaned out your room, I have tardily noticed an article about my own profession and it has deeply interested me. It seems that in America, where well enough is never let alone, a new method of 'mounting' animals has been in use some time. According to the illustrations, the results are excellent, far beyond anything we can achieve here by means of stuffing. Madame Franz [wife of Ralph Franz of the _Herald Tribune_ who then was city editor of the _Chicago Tribune_ in Paris] was kind enough to explain the text to me, but the information is not complete enough to allow me to try the American method without instruction.
I applied at the central school of taxidermy and was shown the door by an angry old fathead who cursed me and all the Americas for disturbing his afternoon nap.
Can you refer me to any one in America who could conduct a course in this modern taxidermy in French, for which I will gladly pay within my means, which sink lower and lower;
Noël
_13 February, 1932_
_Cher M. Paul,_
I remember that today is your birthday, as who wouldn't who took part in that _soulographie presque historique_ (almost historical binge) that marked it last year in the cellar.
Your compatriot who plays the mandolin like His Majesty the Devil [Fulton Grant, formerly of the _New York Herald_ ] had lunch at my table today and was very entertaining. How is it that when an American undertakes to play a mandolin he is not content with merely strumming out a few tunes but will not rest until he can do the Czardas de Monte at full speed without missing a note? I shall never forget that performance, although how M. Grant could have found the strings or you could have balanced on that piano stool after what you both had drunk, I can never understand. Americans are a race apart. Of that I am convinced. Or do they send only their hardiest specimens to the rue de la Huchette?
Excuse my cramped handwriting as I have finally contracted a kind of neuritis or rheumatism because of the dampness and drafts at the prefecture. I am the last one in our department – that is, I held out longer than any of the others. Old Madame Lefarge fairly cackles with satisfaction. She detests me because I can keep my temper and, on their second visit, the foreigners wait in line or ask for me, rather than be reviled by her. She is an ideal public servant, having all the minor ailments possible, a fiendish disposition, short stature and a healthy dislike for mankind. The thing about her is that she is impartial. She hates her own sister quite as bitterly as the most abject illiterate Italian labourer who applies for a renewal of his identity card on the day after Monsieur Mussolini has taken over the Mediterranean – verbally, it goes without saying. Unfortunately for the wayfaring Italian, he does not know that, and thinks Lefarge detests him personally and without provocation.
In my last letter I gave you incorrect information about Jeanne, The Navet's wife. It was not a Turk with whom she consoled herself after her husband had slapped her ear because of our loan to Romania. L'Absalom, backed by Mlle. Nadia, insists the chap is a Persian. Also that he wants Jeanne to go with him, to Baghdad I suppose, and marry him in Persian style. The son is not opposed to this, but he wants his mother first to get a divorce and an accounting from The Navet, who, the boy is sure, has misused and appropriated funds which, according to the marriage contract, should have been kept intact for Jeanne. Poor woman. I'm afraid she won't go, or that if she does she will be homesick and find it hard to adopt the Persian customs. I've no idea what they are, but surely they are different from ours.
Your story about the Prado I have relayed to the faithful here.
Hortense Berthelot
[Note: The story to which Madame Berthelot refers concerns an American couple, middle-aged and Middle Western, on the steps of the national museum in Madrid, where the French paintings, not very good examples, are on display in the basement. The American woman, guide book in hand, said to her husband: 'We haven't seen the French school downstairs.'
'To hell with cooking, my feet are tired,' was her husband's reply.] The following card was written at Georges' dictation by Daniel, the Serbian boxer who was wooing Madame Berthe at the Caveau. That Georges, who could never read or write, would ask this service of Daniel convinced me that the latter was strictly _pukka_ and a real _sahib_ , as the British would say. From then on I felt easier about the romance which was causing Monsieur Henri so much inconvenience and the fear of financial ruin.
(Undated)
_Cher Mister Paul,_
Thanks for the white shirt and _faux-col_ (white collar) I found under the bed. Amuse yourself well.
Respectfully,
Georges
# _To be Read on an Island_
THE COMMON PEOPLE of France knew little about high finance. Neither do the people of the Blue Ridge mountains of Virginia, the pavements of New York or those called the salt of the earth or the toilers of the sea. Each slightly out-of-date newspaper I received in Spain in late 1931 and 1932 made it clear that plain French citizens could not understand why, with one hand, the Government was piling up a tremendous deficit and, with the other, was shovelling out loans to Poland, Rumania, Germany, Hungary and Monarchist Spain.
While I was actually in Paris, I thought of the city and of France in terms of my acquaintances and neighbours and friends. What happened to them also happened to me. When one is in another country, among different friends, one must depend upon what can be read in and between the lines of letters and newspapers. The report that political rows were breaking out in all parts of Paris was only an indication of what was seething beneath the surface on the rue de la Huchette and every other street and avenue and country lane in France. As usual, when anything happened at all, some 'Reds' were arrested, about one hundred on February 5th. Twenty citizens were injured in Montparnasse in a clash between Royalists and Socialists. In the Chamber it was voted that members should not be permitted to bring in canes, for fear that they would be used as weapons. The entire neighbourhood along the quai, across the wide bridge and in the place de la Concorde across the river was filled with manifestants who shouted and cat-called. Two thousand of them were arrested by the police and the so-called _Garde-Républicaine_. But merely throwing two thousand indignant citizens into jail for a few hours apiece and breaking a few of their heads did little or nothing to soothe the unrest. The damage had been done. The handwriting on the wall was becoming more legible every day.
In far-off Spain, separated not so much by the Pyrenees as by centuries, I could evoke the city of light and oncoming darkness. The last time I see Paris will be on the day I die. The city was inexhaustible, and so is its memory. I can stand in dazzling sunshine and experience an eclipse all my own, with Paris in dim blue lights and shrieking sirens between me and the sun and the landscape. I can recall the first moment I realized there was moonlight on the dingy old Gare St. Lazare and the surrounding streets and buildings. Before the débâcle, when street lamps were alight, soft pink and old gold, their reflection in the night sky dimmed the moon.
The same moon shone over Ibiza, in the days when life there was wonderful and free, and letters from my friends in Paris lent moonlight to my thoughts of them and of my little street and what we were all coming to.
_17 June, 1932_
_Cher Monsieur Paul,_
The Abbé Lugan is much upset because on his return from Canada he finds numerous letters from one of his former parishioners now living in Troyes, asking frantically for some papers concerning the pedigree of a certain hunting dog. You are, I think, involved. A month ago I gave the Abbé your address, and now I find that you are not captivating Madrid, as I had supposed, but are in the Balearic Islands. _Formidable!_
The Abbé is away again, but is coming back Monday, according to his letter. He writes that he sent you a letter to the calle Velasquez which has not been returned, and still he has no word from you. The Trojan ( _Troyen_ ) is out of his mind. It seems that in 1929, about three years ago, he forwarded M. l'Abbé the pedigree of a setter named Pompier, by Debureau out of Zuleika, with the request that the Abbé have these records authenticated at some sort of canine prefecture in the boulevard Haussmann. The Abbé insists that he gave the papers to you and that you agreed to attend to the matter and forward them to Troyes. According to the dog fancier from Troyes, these records cannot be replaced and without them the setter called Pompier might just as well be Daladier.
Knowing your habits, Monsieur Paul, and remembering that you lost important manuscripts of your own on more than one occasion, I suspect your having retained dog papers three years, in as many different lands, is about as likely as that Jesus Christ will appear on earth again next 14th of July. I promised M. Lugan, however, to add my supplications to his own, in order to authenticate the dog Pompier, pacify the citizen of Troyes and vindicate our good friend of the cloth who, in spite of his dingy robes, is not a bad fellow.
I am writing this not from the hotel, which I have sold to a worthy chap ( _brave type_ ) from Chatillon-sur-Seine, but from my house in Montmorency where I spend much time in the garden. It is a long time since I tried gardening, and most of the herbs and vegetables will not grow according to the illustrations on the packages of seeds. I have one pumpkin vine, however, so healthy that I have built a platform in the crotch of a small pear tree on which rests the pumpkin, just high enough to perplex the few folks who pass by outside the wall. Marie has been ailing since we left the Caveau. She misses the drafts and dampness, and the lack of sun and fresh air. Luckily she is able to sleep most of the time. She sends you her regards.
Berthe, as you know, is married and has bought a restaurant in the rue de la Harpe. Her husband, whom you do not know, will not allow her to work there, or even to act as cashier. He is _tout à fait sérieux_ and has not yet deceived her, as far as you and I are aware.
Sometimes I wish he would take over this pesky garden and let me manage the restaurant. We would both do better that way – but when are things disposed ideally?
Thanks for the postcards showing the Balearic women in their native costume. I trust you find them reasonable. No doubt you do or you wouldn't stay.
Julliard
The Abbé Alphonse Lugan was a Breton, who, if such a thing is possible, are more stubborn than Basques. He had acted as confessor many times in his long years of service, and in the name of the Father, Son and Holy Ghost had forgiven sins which must have outweighed the losing of a set of dog papers. Nevertheless he could not quite forgive me for having misplaced the pedigree of Pompier, who remained unauthenticated to the end of the Third Republic. I saw Abbé Lugan many times afterwards, and he was always polite, but a little too polite, considering the fairly intimate relationship we had maintained over a period of years.
I know that if I should see him now, while he is working day and night to help and console his people, his immense sorrow would have dissolved the little grudge he held against me. His hollow eyes would sparkle as he lowered his heavy eyebrows in mock severity. Would he now repeat, morning and evening, his simple prayer: 'Let me be neither rich nor poor'? Even that would be asking too much of any Deity now presiding over France.
_5 September, 1932
7 rue de la Huchette
Paris VIe_
_Cher ami,_
You will notice that I have progressed along our street from No. 5 to No. 7. Existence is not the same with Monsieur Julliard away, but I have grown accustomed to it, and at my age one makes as few changes as possible. No use competing with Nature.
The HôteI du Caveau is much changed, under the proprietorship of M. and Mme. Amance from the Haute-Marne. Or rather should I say, Mme. and M.? The latter is an easy-going countryman for whom Chatillon (sur Seine) was too large a metropolis and to whom Paris will always be an enemy. He lurks behind the bar, smoking his vile pipe and squinting out from time to time to see if the sun is still shining. It seldom is, this summer.
Thérèse is gone, and with her the distinction of the Caveau cuisine. Mme. Amance, a real shrew, would not trust her to do the morning marketing and complained about the quantity of wine she drank from the store left by Monsieur Henri. Thérèse chased her from the kitchen, using as a threat the small kerosene stove which, as she waved it through the air, flared up and burned her hand. Mme. Amance was screaming for the police, who naturally paid no attention, as it was near the time for changing shifts. Luckily the stove landed in the middle of the street, right side up and still burning. Georges, the only witness present, calmly retrieved it while the two women were reviling each other, the honours going to Thérèse, I am glad to say.
Georges will stay at the hotel in the soothing belief, so characteristically Slavic, that the Amances surely will fail in business and that Monsieur Henri will be obliged to return when they are unable to make their payments. I had not thought of that possibility, but since Georges expressed it I have been unable to put it from my mind. Perhaps that is why I moved only as far as next door, above the Taitbouts, who grow more owl-like each day.
No one knows how I detest living alone, and preparing my own breakfast. The coffee at the Hôtel Normandie is not to my liking and the Café St. Michel is too far. Someone is opening a new café, with a blinking henna light, across the rue des Deux Ponts. Once or twice I have tried to enter but the place is newly varnished, with a clientele entirely strange to me. I was always timid and unadventurous, and what little courage I had was used up in 1917 and 1918. Does that seem ages ago to you? Probably not, since you have done so many things and seen so many places.
As to the clientele at the Caveau, that has shifted, too. Mme. Amance, as you may well imagine, is of Tardieu's party (the old one called humorously 'Left' republican). Milka, Stefan and young Vautier have crossed over to the Hôtel Normandie, where Sara and Louis have moved in a cot into their room to supplement the narrow three-quarter bed. We all have lunch and dinner chez Daniel, in the rue de la Harpe.
Our Radical-Socialist trio have removed their patronage to the Café St. Michel, where they sit for hours each evening in the small side room and are increasingly disgusted with Daladier. Monsieur Frémont practically made over my little room here, with a door latch in American style that slides over and bars it securely while I am inside. I have a gas jet over which I can boil coffee and the girl from Gillotte's delivers my _croissant_ in time so that I can arrive punctually at the prefecture.
Now that I think over my life, and I have plenty of time, it seems like a weed, that was bent but not quite severed when I married Berthelot. My three sisters, especially Anne who was older, were envious of me. But how many times have I wished it were she whom my husband had chosen? Not that he treated me unkindly. He was gentle but preoccupied and inattentive, or perhaps I was difficult to approach. Who knows? It has always troubled me that when I received his papers and the Croix de Guerre with two palms I thought of him lying in his grave as he had lain on his side of our bed, no more or less remote. Soon after, when I found myself alone, I realized how much he had done to shelter me from practical affairs and how excellent he was, in negative ways. It is all very well to say that love and marriage are not necessarily interdependent, but I would have liked to experience what is written and talked about incessantly. The two Alsatians who roost above us on the fifth floor and minister to the colonel have a more valid claim to spinsterhood than I have, and yet I feel more like them than I do like Jeanne with her Persian, who seems to adore her, or Mlle. Nadia, who still is alluring to Monsieur de Malancourt.
There was a time when I wanted to grow old as fast as possible, to hasten the day when I should not have to practice a charitable deception, which, in passing, fooled no one, least of all poor Berthelot. Now that I find myself perspiring and shivering by turns and expect to dry up like a herring and become as crotchety as old Mme. Lefarge, I am dismayed. I feel like one of those sad-faced preoccupied children who, riding the merry-go-round in the Luxembourg Gardens, discover only when the mechanism is slowing down that there were brass rings to be grabbed for another free ride. I shall not descend sobbing from my carved wooden horse, but lately I have become more aware of the principle of death and I see it all around me. I notice that leaves are wilting in the gutters and will turn in the autumn, that the window sash is decaying, that an ageing waterbug moves stiffly and finds it hard to scurry out of sight when the hall light is switched on (and responds).
In writing of Frémont, I neglected to say that he, too, has quit the Caveau bar. That leaves the field to The Navet, who is admired as only _he_ likes to be admired, by Madame Amance; the specimen from the Samaritaine; Gion and his martyred mistress from the music shop; and the eternal Georges. All the aforementioned except Georges are moderate in everything but meanness and talk, both of which have no price attached, so the bar is losing money. So is the restaurant, and half the rooms are unoccupied. They have closed the dungeons downstairs, using only the wine cellar. Georges has to snatch his drinks unobserved and seems to be more clever than Mme. Amance, as watchful as she is, for Saturday he tried to cut his throat again, in company with the poor Greek (Mary), who was dragged to the station and kept in the cell overnight. Perhaps it is best that she got bronchitis and will have a week of care, such as it is, in the HôteI Dieu.
You, my friend, are on your little coral beach, in the sun and sea air, surrounded by the gentle people you describe with such affection, and the creatures of your own imagination. What would it be like to be free from routine and squalor, to have _your_ energy and zest for life? I am not covetous, in the sense that I would take your good fortune from you. I shouldn't know what to do with it, most likely, if I had it. But, dear friend, I would like to try.
Hortense Berthelot
P.S. It has taken me the better part of a week to write this, and two days more to decide that it should be mailed, it is so much like a lament.
_14 October, 1932_
_Cher M. Paul,_
Thank you so much for the radio [my wedding present to Madame Berthe and Daniel] which I enjoy each afternoon and evening. My husband wishes also to extend his thanks and is sorry he didn't meet you, as so many of his customers speak of you.
We have taken the apartment formerly occupied by M. and Mme. Corre, who have retired at last and live in the rue du Bac. The son and his wife did not want it, as young Corre has modern ideas.
I want you to know, Monsieur Paul, that I am very content.
Berthe Petrovitch
(formerly Julliard)
[Note: In a letter from Mrs. Ralph Franz she told me that Berthe and her young Serbian boxer, Daniel, were deeply in love, that Berthe looked ten years younger and even more angelic, and that Daniel, who worked like a trooper from early morning until the bar closed at night, would not permit his wife to raise her hand. At first, Berthe tried to discard her mourning and to buy brightly coloured clothes. Daniel had preferred that Berthe remain exactly as she was. He had met and admired her in black and was opposed to any change. Also he had the firm conviction that modern women who tried to look half their age were inferior to the old school who matured gracefully.]
_Paris, 11 December, 1932
18 rue de la Huchette_
_Cher Américain,_
Sunday, while I was walking along the quai Voltaire for a reason I will disclose later, I was seized with an irresistible desire to enter the Louvre and make the stations of the cross as we used to do.
[Note: 'The stations of the cross' means a number of French paintings we liked to see in chronological order, a tour of several miles through the galleries of the Louvre. The masterpieces were:
'Rebecca' by Poussin; 'Seaport at Sunset' of Claude Lorrain, with the sun low in the sky and flooding the sea, masts, spars and buildings; Watteau's 'Embarkation to Cythera', and then his 'Gilles' which we liked much better; Corot's 'Woman with Pearl'; Fragonard's 'Inspiration'; Courbet's 'Burial at Ornans'; Daumier's 'Washerwoman'; Ingres' 'Portrait of Mme. Rivière'. David's portrait of his mother and father; Chardin's crayon self-portrait, and his still life: 'The Copper Fountain'; Delacroix's 'Death of Sardanapalus'; the fresco portrait of a woman painted for practice on his studio wall by Mottez and later transferred to the Louvre; Manet's 'Olympia'; Monet's 'Bridge at Argenteuil'; Renoir's 'Woman Combing Her Hair'; Van Gogh's 'The Gypsies'; Pissaro's 'Red Roofs'; Gauguin's 'Landscape at Arles'; Sisley's 'Bateau à l'Écluse de Bougival'; Toulouse-Lautrec's 'Jane Avril Dancing' and Cézanne's 'Home of the Hanged'.]
I had never been in that palace of eternal twilight on Sunday before, when it is filled with Sunday Frenchmen and yokels from the provinces who could not have been less comfortable in church or on a witness stand.
[Note: A 'Sunday Frenchman' was one who has no regular work, being untrained and incapable of getting a job. He lived from a small inheritance, conservatively invested, and was allowed to occupy a room and eat meagrely in the home of some relative. For this he paid, the amount of his contribution and the service he received being subjects of continual bickering. On Sunday when the other menfolk were at home there was no room for him around the house, so he frequented the museums, the public parks and the quais along the Seine – whatever cost little or nothing. This kept him out of the cafés, where he would be likely to unbalance his diminutive budget.]
I had read, in some silly book Maurice had picked up, of how Watteau was a poet and created a dream world of his own that transcended reality. Having always held other ideas about Watteau, I went straight to the vaunted ( _fameux_ ) 'Embarkation'. There was no dream world at all. Watteau, as I had always believed, painted exactly what he had seen and was familiar to him, namely, the foliage of the Luxembourg Gardens and backstage of the Opéra Comique where he spent the other half of his time.
Two Frenchmen, both bourgeois and smug, but trying to be properly awed, were staring at the painting.
'What poetry! What soul!' said one of them, looking nervously at the other. Having seen a Watteau, he felt that he had to say something to somebody, the most common error encountered in galleries. The other fellow was more honest.
'For me it's just macaroni,' he said.
Even you cannot deny, for all your admiration of Watteau, that his brush strokes have many of the qualities of cooked vermicelli. I began to like art lover No. 2.
No. 1 was indignant and started to remonstrate, but in repeating the word 'macaroni' he began thinking about macaroni, glanced at his watch, saw that it was nearly lunch-time, and hastily excused himself without further defence of poetry or art.
Questions of art have long since ceased to stir me. I like to look at good paintings but I try to attach no importance to them, unless, like the 'Interment' (Courbet), they contain some peasants or industrial workers, preferably both. What started me out was another problem which will haunt me longer, I am afraid. I mean bed bugs.
There is no use dissembling. In the Hôtel Normandie, in practically every room, there are bedbugs. They troop along the ceilings and walls, hide themselves between the sheets, and feed on the clients who are hardier than I am. Not that they do not feed on me, but I cannot seem to ignore them.
Milka says that bedbugs have been forced on the proletariat. It seems to me as if the bedbugs prefer the underfed, underpaid and unfortunate. She and Stefan can sleep among them, and even snore. Fortunately, however, she does not disapprove of my efforts to get rid of them. She believes that the proletariat should chase them back to the oppressors or, if that is impracticable, may take the time to kill them and sprinkle kerosene and powder to discourage them. Being occupied with important matters, she leaves insects entirely to me. So does Stefan, who has little or nothing to do, having bungled an assignment or two and got himself into mild disgrace. My skin is streaked and raw from scratching; my clothes are infested. Only this morning I found a bedbug on my tie, and wept in the street, entering a pissoir so nobody would notice and stare. The pissoir stench has killed my appetite. So I am writing to you.
That is not intended in a derogatory sense, my friend. You are sane, and many times I wish you were here to listen to my muddled ravings. I have lost much sleep, but no determination. I believe, and I shall see the thing through. Oh, to hell with these heroics!
Pierre
Extracts from three letters received from Hyacinthe Goujon in 1933 (January to July):
_Cher voyageur,_
As you know, the Judge has been volunteering information and giving me 'instruction' ever since I reached the age when I could listen respectfully. He has had his second stroke, poor Grandfather, and is, to all intents and purposes, already dead. Watching by his bedside in the night I began to review, as best I could, the advice and counsel he has uttered in the last twelve years. Perhaps I was tired, or exasperated with him because in so many respects he resembles Mama, but out of the infinity of talk which has issued in a rhythmic stream from his lips since I can remember, only one instance came to my mind in which what he told me proved useful. I don't think the Judge is more foolish or inconsequential than most of our public men, or our private ones, either, allowing for brilliant exceptions. My conclusion, subject always to your revision, is that what men or women say has a very indirect relation to what they think, and what they think is again many spheres removed from what they are. You told me, once, infidel that you are, in order to explain away some manifestation of the supernatural, that we have many undeveloped senses. I wish we had unexplored organs to supplement our feeble brains.
The Judge's gem of information, which he tossed off as gossip, making me promise not to tell anyone, had to do with Vladimir de Pachmann who has recently died. I wept, and you know that I do not often indulge in that low-priced relief, when I read that the grand old poet of the piano, one of the few besides your incredible Percy Grainger who seemed to have understood Chopin, had gone to his reward at the age of eighty-five. Monsieur de Pachmann once paid me a tribute, or rather, an attention, that was so precious and individual that I think it removed the last barrier between me and the 'feeling' of music. Now that he is dead, and the Judge is paralysed, it will do no harm to stretch my oath of secrecy in a matter that soon will be retailed to the public and, like linen on a bargain counter, will be rumpled and soiled.
In an issue of _Figaro_ , Grandfather noticed a small advertisement (with, of course, the accompanying complimentary notice as a part of the _quid pro quo_ ) to the effect that de Pachmann, after an absence of fifty years from the Paris concert stage, was about to play a recital for charity in the Salle Gaveau. Fifty years! Half a century, my friend! Why, only sixty years ago, Franz Liszt was alive, and de Pachmann could have been listening at his side.
Why the Judge had suddenly taken an interest in matters of art, which had made no noticeable impression on him previously, fascinated me. I had formed the habit of appearing to listen without taking in what he said, so that he had spoken several sentences before I became aware that he was talking of de Pachmann's one romance. Romance had always been ignored by the Judge, or had neglected him, in so far as I know. Still, he knew about de Pachmann because the drama involved a colleague, or member of the bar with whom Grandfather was on intimate terms. This is what he told me. That de Pachmann in all his long career had had only one pupil, a French girl, now living in Paris (as an aged woman) and who had such pianistic genius and such an appeal to the master that he took time from his own practice and performance to develop her. He would entrust her to no one else. Of course he was in love with her. No one can ever convince me that a man and a woman can share, day by day, what is magic and the breath of life to them, without the kind of harmony that would create a deep and fervent love. Sometimes the art would outlast the passion, and occasionally the respect. Of what importance is duration?
De Pachmann and the pupil were married, and then began to lose the harmony and counterpoint in that ghastly endurance contest which must be, at once, a rivalry and a hash made from the remnants of initial raptures. One reads of men who love once, and never afterwards. Apparently de Pachmann was one of those phenomena. They parted; de Pachmann swore he would never again set foot in Paris, and after a couple of years the pupil married a respectable lawyer (who later became famous), gave up the piano, and ploughed through heavier courses after having eaten her dessert and sipped her liqueur.
I began to hate that woman.
At first Mama was unwilling to spend the necessary amount so that I could hear that recital. She has refused me almost as many things as her father has told me, but in the three or four instances where refusal would have meant that I never would have forgiven her, and would have borne an implacable hatred all the rest of my life, she has yielded from instinct. She has instincts, although most of them are unsound.
Elliot! You will understand! I cannot even try to write how I felt in the Salle Gaveau. Mama and I were among the first to enter, and I examined breathlessly each woman's face who came in afterwards. At last I saw _her_ and her lawyer husband, distinguished in appearance I must confess, and looking uneasy and protective as men do when they know they are in the presence of something more important to a woman than ever they could be. She was small, chicly dressed, if a woman of seventy can be so described.
Forgive me if I do not try to write you in detail about the programme. That will be reserved for me to tell you, close by your side and vibrating with your kind receptivity. Naturally, it was all Chopin, excepting a little Brahms. Out of it, one gem will never be lost in my memory, the nocturne in F-minor. He played the E-minor sonata with all the fervour of Paderewski plus delicacy, accuracy, breadth and power. Just before the cavalry movement I thought how much indebted Chopin was to de Pachmann for being understood; how much de Pachmann was indebted to me for listening so intently; and how much I was indebted to you for having shown me what my ears and nerves and mind are for. During the finale, the presto, I didn't think at all, as hooves were pounding over me, no stupid onomatopaeia but the spiritual impact.
But the nocturne. He did not play it, he evoked it. One did not hear a thump and twang but suddenly the music was around one in the room. Time was suspended as it grew and flowered, and then, like all our dearest hopes, dispersed like a drop of wine in a lake of obscurity. I was not fully conscious the rest of the evening, until... That wonderful old man – now dead – with the back of his coat slit under him. What died when de Pachmann ceased breathing? Not that smug detestable woman who had been inadequate, doubtless ranting about her own career, as if a woman could have a more sacred career than to sustain a genius.
After the recital, another instance in which Mama did not dare refuse me, I went _alone_ – that is without Mama – and stood in the line before his dressing room and inch by inch moved nearer. I have forgotten to tell you the most touching incident. My heart is thumping as I write and the blood is rushing to the front of my brain to confuse me. After the nocturne, not hearing the applause, de Pachmann stood looking at his hands as if they were miracles that did not belong to him.
'You've done well tonight, my hands,' he said, and waited as if he expected them to answer.
That, dear Elliot, was not fanciful. It was exact, as his sonata of Chopin was exact and not blurred with the pedal. Notwithstanding all his heart and understanding, his hands might have played him false, and not done precisely everything that he wanted from them. Every artist must have disappointments like that.
When I came face to face with him, in the dressing room, and extended my hand, my eyes on his, he must have felt what the moment was meaning to me. I am sure that he must always have been kind as well as difficult, and I am thankful that in a lifetime of tribute and gratitude and appreciation he realized what my silence and vertigo meant. What he did was take my hand, and to the consternation of his manager, an offensive little man, and the throng of admirers, he led me into a small room near by and locked the door. There was a piano, a bench and one piano chair. Through the door and the walls I could hear mild clamouring outside. He paid no attention. With amazing vigour, considering that he was eighty years old, he pushed the bench away from the piano and indicated with a gesture of that inspired left hand that I was to sit there. The piano chair he placed in front of the keyboard.
'Which? For you?' he asked.
'The nocturne,' I said, surprised that my voice was audible.
He had played three nocturnes that evening, but he knew which one I meant, and he rose from his chair to clasp me in his arms and kiss me on the cheek. Then he played the F-minor, as exquisitely as before and even more personally. He had forgotten his former wife and pupil and her stuffed shirt of a husband ( _vieux fumiste_ ).
Today he is dead, or rather yesterday, for I have written long past midnight.
Hyacinthe
There is no one listening to music in France today as little Hyacinthe did, and Poland, which was being crushed when Chopin wrote his passionate protests, is the scene of brutality and misery and suffering, the news of which would have overwhelmed the composer entirely.
The following passage is from a letter addressed 'Cher fainéant' (dear lazy one) because, on account of winter rains, I had been remiss in writing.
... I was allowed today to have an ice in any café within reason, which I was to choose, in company with Cousin Dagobert.
[Note: Her cousin Émile she called Dagobert because he was absent-minded, if not gaga, and often tried to put his right arm in his left coat sleeve. In the French children's song _Le Roi Dagobert_ the king gets his trousers on backwards and is chided by the good St. Eloi.]
I had intended to drag poor Émile to the rue St. Sulpice, one of your discoveries, and where the pastry and ice cream cannot be surpassed even at Rumpelmayer's for ten times or at least twice the price. Your American use of exaggeration for emphasis leads me, who has contracted it from you, too far at times. On descending into the street, however, I found that all the shops were on strike, except mercifully a few cafés. Some matter of taxes.
Your Spaniards are magnificent when it comes to taxes, if you were not deceiving me when you wrote that they pay their governmental expenses indirectly, by conducting huge lotteries in which a few win large sums and everybody has a sporting chance at whatever minute percentage.
What I wanted to say was that I chose the Café St Michel, which I have passed thousands of times, and have entertained and stimulated with the view of my legs – which I hope you will find are improving – since I was eight years old. Émile was relieved because along with the other shopkeepers and _commerçants_ the ladies of joy from _Le Panier Fleuri_ had joined the strikers. Their impressario, Madame Mariette herself, whom I understand wields the black snake whip in an illusion or tableau which is part of the entertainment, and four of the 'girls' were on the terrace in street clothes. They appeared ill at ease, the girls, but not Madame Mariette, who always looks self-possessed. Their costumes were not in fashion; in fact, seemed to be a mixture of several outmoded fashions. They had no skill in out-of-doors make-up, and to my surprise seemed utterly without coquetry.
Elliot, I looked them over more carefully than any man for ten or twenty francs has ever done, I am sure. The tall slim one [It must have been Mireille] had plenty of spirit, if a rather meagre physique, and exchanged banter with the men that would have put to shame the chatter that goes on in Mama's little club where she learned about _frissons_. A wide-eyed little blonde looked exactly like the cover of _La Vie Parisienne._ Hitherto I had thought the popular artists draw caricatures on magazine covers. Now I understand it is impossible. [Daisy must have inspired this.]
On that subject alone you have been unkindly reticent. Elliot, I know you could smuggle me into one of those establishments, not in our quarter, it goes without saying, where, protected by you, I could see for myself what really takes place. No one will tell me. I have come dangerously near inquiring from men I should not give any hold upon me. If my curiosity gets the better of me and I get into trouble, it will be chargeable to you.
Thank God I shall not be reduced to extremes in finding pleasure. With me, I am certain, it is always near the surface, perhaps too ready for the keenest enjoyment. Shall I gain control with practice? Or anything at all? Even prostitutes can strike, with their neighbours. What have I, or Mama, or the Judge, whose second stroke did not, as the doctor had predicted, finish him? Please. I'm not heartless. I tremble with sympathy when he seems to be suffering, which is seldom. It is when he does nothing at all except defecate and breathe that I am impatient. It seems purposeless and undignified.
Hyacinthe
Elliot,
I am crushed and disappointed. I did not win the grand prize in the lottery. As if that in itself were not enough of a blow to my vanity, and to undermine what little faith I had in my destiny – I didn't win any prize at all, not even one of the contemptuous ten thousand which enable one to get one's money back, minus tax, I believe.
My ticket is crisp and unsoiled, so freshly printed, with the number 364825. I slept, or more often lay with my eyes open in the darkness... and I prayed to God sincerely – I know you cannot comprehend this – to send me a sign. In René Clair's wonderful film, the star actress got the million. I asked God if she were more beautiful or more intelligent than I am, or will be when I have reached her age, which must be considerable. All the stories, books and plays dealing with lotteries have given me the prize, since in order to get it I was willing to identify myself with an inferior heroine.
This whole affair has left me desolate – but really desolate. Having asked for a sign, I cannot ignore the one which was sent me – a blank, an insult, a rebuke.
My ticket, of course, was not a whole ticket, but only one tenth. A whole one would have cost 100 francs and never have I had 100 francs – never, Elliot. Monsieur de Malancourt, who, next to you, is the nicest man on earth, brings large sums of money purposely when he comes to see Nadia, increasingly seldom – ah, God, time and men. De Malancourt likes to encounter me on the stairway, and I frequently permit him to do so, for, if only he knew it, the meeting excites me as much or more than it does him. Then he lets me hold and handle a few thousand-franc bills. He has offered to let me keep some of them – not as a gift or a proposition – because he knows I would enjoy dreaming over them and would return them when the fancy had spent itself. This, Elliot, I have not quite dared to do.
If any other men had made similar gestures, both you and I would know what was behind them. I assure you – I swear to you, Elliot – de Malancourt is acting in the friendliest spirit. He has confined our flirtation to the realms of wit and does not pinch, paw, or stare, or make insidious dirty remarks to test how much I know or would stand for. In short, he is a gentleman, with the _politesse française_ of which you have spoken sarcastically, and with reason. I wish there were more like de Malancourt and that France were not pocked with ruined and inadequate types of men of family, the kind Grandfather mostly knew, and who have been immortalized in de Montherlant's faithful writing.
All roads lead straight to me, as you have so often remarked. When I write of de Montherlant and his faded bachelors or of Proust and his Odette, I wonder – do not smile – if I shall ever be the subject... You are the only writer I know, and doubtless profound and brilliant, but who could write about me in English? Elliot, I am old enough now [sixteen]. Will you promise to introduce me to some French writers you know, so I will not be lost to posterity, even if I am unimportant in my own generation? Who shall they be? Not Gide. He loathes women. Even if he didn't, I would find him stale and unsatisfactory. Not Leon-Paul Fargue, because he has a mistress who not only must be superb in bed but does the most artistic – I mean, actually composed – embroidery.
Céline? Decidedly no. He writes of the depraved middle and lower classes and uses taxi-driver's language. I know how chauffeurs would describe me, having overheard their remarks in the place St. Michel for the past eight years, whenever I appeared. Their voices carry, and my ears are tuned especially for whatever is said concerning me. Please do not think I have a disparaging thought for the historic _Voyage au Bout de la Nuit_ , [Journey to the End of the Night, Céline's masterpiece].
Shall I confide whom I would like to sit, or even lie for? Philippe Soupault. His story about Nijinski and the tree has haunted me, and his picture, even in the vile ink of the _Semaine Littéraire_ looks handsome. If you will not have what so many men would die for – I shall offer it freely to Soupault, who, if he is the Frenchman I think he is, will not hesitate or quibble. Then he will write it all, if he recovers.
Hyacinthe
# _Less Brightness Every Year_
ON THE ISLAND OF IBIZA my small group of French friends followed with me the increasingly corrupt offerings of the Paris press and exchanged bits of news from their letters. Among them was Drieu la Rochelle, whose _Young European_ had disturbed Father Panarioux and the others at the Caveau bar.
Nor must I forget a sailor named Jean, who later in a desperate year stood alone on the deck of a destroyer, speeding through a storm, while everyone about him was all washed up. I mention Jean because he was French Catalan, and tough as nails, and fought for Spain willingly and died futilely for France.
We read about Japan's refusal to withdraw from Manchuria, of Great Britain's prompt embargo on arms for China and Japan.
Daladier had formed a cabinet consisting entirely of Radical Socialists, and Blum, always given to gestures when there was little or no risk attached, quit the Socialist Party because its other leaders helped Daladier for whatever they could get in return.
The Little Entente, consisting of Czechoslovakia, Yugoslavia, Rumania and Poland, was formed (by France) and agreed (with France) that there should be no revision of the Treaty of Versailles. To counteract Mussolini's threats, the French Navy held manoeuvres off Corsica, and Daladier visited that historic island to assure the Corsicans (who, after all, are practically pure Italian) that their mother-country, France, would never let them down. This was agreeable to the Corsicans, since any able-bodied man among them could always get a job on the Paris police force, as the Irish do in Boston and New York.
A new batch of taxes stirred up riots in the Madeleine quarter and on the very steps of that famous Catholic church with the outward form of a Greek pagan temple. The uneasy deputies had a cement blockhouse built at the approach to the Chamber, just in time for the Stavisky affair.
Stavisky was the director of the municipal pawnshop (Mont-de-Piété) in Bayonne, near the border of Spain. In France there were no private pawnshops, with three golden balls suspended over the doorways and windows filled with old clothes, musical instruments, watches and jewellery and other objects of comparatively little value. Any French citizen or foreigner with his papers in order, and any woman with the written consent of her husband or male head of the family, could take to the municipal loan office movable and nonperishable articles of value. These would be appraised by experts who always kept on the safe side, and a fixed percentage of their cautiously estimated value would be loaned the pawner, who was given a ticket which must be returned when the pledge was redeemed or else revalidated periodically.
In America, pawnshops are used by the poor or the temporarily needy student or reveler who wants to borrow ten dollars, or less. Not so in France. Every municipality, excepting small villages, had its official Mont-de-Piété, and the sky was the limit. The loan office had behind it the Bank of France and the credit of the Third Republic. An astonishing percentage of pledges was never redeemed, for the larger the loan the harder it was to raise the money later. The sum received had nearly always been spent or earmarked in advance, for fur coats, abortions, gambling debts, petty blackmail, etc.
Stavisky, whose name is now notorious the world over and heads the Pantheon of swindlers, was a talented financier and only lacked capital and credit. These he obtained in an ingenious way. He used the valuables which had been deposited with him and otherwise would have lain fallow, as it were, as security for large private loans on his own account. The bankers and brother-financiers in question had an idea where the stuff came from but did not ask embarrassing questions, since the supply was larger, the harder the times. Stavisky paid high rates of interest, promptly, and if some client called at the Bayonne pawnshop for a diamond that was in re-hock, Stavisky redeemed it from the banker.
With the money Stavisky borrowed he floated several companies and sold stock, pyramiding one concern upon the other until he had a finger in practically every financial pie in France. If the pawned articles in Bayonne proved inadequate to sustain his expanding affairs, Stavisky drew upon similar pledges in the hands of some pals in Orléans and elsewhere, until the financial machinery of the Third Republic was spinning like a clock with its mainspring off the peg.
Late in 1933, _L_ _'Oeuvre,_ a comparatively liberal Paris newspaper which developed such talents as those of Geneviève Tabouis and Georges de la Fouchardière (the former liberal and anti-fascist to the core, the latter a reactionary who detested Americans and America but had such wit that one forgave him anything) began to print accusations almost daily against the hitherto unknown Stavisky. According to _L'Oeuvre,_ Stavisky was not only a crook in his own right but had corrupted nearly all the officials of the Third Republic.
Since no one paid any attention at first, _L'Oeuvre_ gained confidence in itself and made larger and better accusations. Just before Christmas, Stavisky and a few of his associates threatened to sue the newspaper for libel, but the suits were never filed. This gave _L' _Oeuvre__ still more confidence, and the sluggish public began to scent the No. 1 scandal of the century. If everyone involved in stock transactions in the United States in the year 1928 had been acting in a way he knew was punishable by law, although it seemed at first glance to be doing no one any harm, the situation would have been in some ways comparable to the Stavisky affair, which had roots and tendrils in nearly every business establishment or prosperous French home.
Chautemps was Premier in January, 1934, the year of the Stavisky shake-up. Public clamour following the long campaign of _L' _Oeuvre__ forced the Prime Minister to take some action. Chautemps ordered the police to bring in Stavisky, but Stavisky had disappeared. Debate broke out in the Chamber. One does not have to say 'heated', since French deputies could scarcely discuss the weather or sing 'Sur le pont d'Avignon' in that epoch without getting into fist fights. The Minister of Commerce, M. Dalimier, was accused of being a Stavisky accomplice, but Premier Chautemps stood by him and let him keep his job for a day or two. Naturally, the Prime Minister was in with Stavisky, too.
Comparatively few men in French public life slept soundly between January 5th, the day the official inquiry started, and January 8th, when Stavisky was found dead in a villa near Chamonix. It goes without saying that the coroner's verdict was 'suicide', and that the mystery of how and by whose hand Stavisky died has never been cleared up. That must not be held against the _Sûreté Générale_. Any working detective who got too close to the facts would have committed the same kind of 'suicide' that Stavisky did; that is, he would have known too much to live.
On that same historic day Monsieur Garat, the mayor of Bayonne, was arrested. Scandals and disclosures followed in rapid succession, and French official integrity cracked up like the surface of a mudhole in the heat of the sun.
Dalimier, since Chautemps could no longer protect him, resigned. Deputies and Paris editors were forced to admit that their campaigns and newspapers, respectively, had been financed by Stavisky. M. Georges Bonnet, who was soon to be Ambassador to the United States, called undue attention to himself unwisely by protesting his innocence too much. Everyone in Paris knew that if Bonnet was not guilty, it was because no smart man like Stavisky would trust him as far as he could kick a steamroller. That did not prevent him from making an impression on our State Department and in Washington society.
Some daring French detective produced Stavisky's chequebook. Its contents revealed clearly that the self-righteous M. Tardieu, darling of big industry and respectability, had been paid large sums from the Stavisky trough. Even Fabre, head of the Comédie Française, had been well-subsidized, so that Stavisky could have his favourite actress. The Minister of Agriculture was involved. Attorney General Pressard was caught in the act of sabotaging the investigation. There were a few tardy suicides among the deputies. A former Cabinet Minister, Renault, was mobbed by his fellow lawyers in open court. Judges, keepers of gambling houses, financiers and minor politicians fell like ninepins. Among the innocent bystanders to suffer was Mlle. Jeanne Chautemps, niece of the Premier. She upheld the family self-respect by killing herself.
Perhaps the most far-reaching disclosure in the Stavisky affair was the fact that the super pawnbroker of Bayonne had been financing the Radical-Socialist party (again I must remind the reader that the party was neither radical nor socialist but opportunist-centre). Whether or not M. Daladier knew about it depends on how well he was informed about his own party affairs. Anyway, when the smoke cleared away, the patriot Daladier was appointed Prime Minister to succeed Chautemps, now thoroughly in disgrace.
Will the most ardent advocate of law and order blame the citizens of Paris if I add that this appointment was more than they could bear? They rioted. The lower-middle-class merchants and shopkeepers had been impoverished by taxes, the proceeds of which had been squandered; the nation had been maneuvered into bankruptcy; parliamentary wrangling and graft had become the order of the day. Even such traditional enemies as the Royalist _Croix de Feu_ and the Communists joined hands against the police, the unfortunate symbol of corrupt authority.
On February 6th the first major riot occurred and some shots were fired which, like other historic shots, were heard around the world. Only in this instance, with the aid of modern press and radio, the sound waves made the world circuit in record time. Seventeen Parisians died instantly, and five more lingeringly when the police fired into the mob.
Daladier resigned. The same day, national censorship was clamped down and newspapers became skeletons of their former inadequate selves. The national federation of labour called a general strike, which was blamed on the Communists. In Herriot's city of Lyons, rioting occurred. War veterans joined the indignant citizens, standing side by side with Royalists and Communists against the so-called government.
Old Papa Doumergue, who could not recognize the national anthem when it was played, was called upon to save France. He formed a Cabinet consisting of six former Prime Ministers and got a promise of co-operation from every party excepting the Socialists (who were just left of the Radical Socialists in the fantail of parliamentary opinion).
To quiet the rioters, Doumergue announced that their 'leaders' would not be arrested. The Comédie Française came through handsomely in the programme of national unity by taking off the boards a play called _Coriolanus_ which makes light of parliamentary procedure, and substituting, I swear to you, reader, Molière's _Malade Imaginaire_. Seventy-five percent of the French workers answered the general strike call as a 'warning to fascists!' In Rome Mussolini made a speech pointing out that the French riots were an argument for fascist discipline. France was still breathing, but vultures were wheeling in a leadcoloured sky.
I received in the next mail this short note from Pierre Vautier: _Cher ami,_
Three nights I have passed in the streets to no purpose. I was not killed, so it's just as well that I wasn't wounded.
_Vive la France!_
Pierre
In another letter, two weeks later, he told me that Milka had been stepped on by a horse and afterwards had been clubbed by a hysterical policeman. Messieurs Monge, Noël and the Satyr quit Daladier's party and joined the Socialists. Pissy announced at the Café St. Michel that henceforth he was a Communist, then tried to make good through the regular channels. He knew very dimly about Marx, Lenin and Stalin, but, to him, the air seemed less foul towards the left, so stalwartly he shuffled over. Frémont got drunk and lost a full day's pay.
Police Commissioner Chiappe, one of the ringleaders of Pétain's Cagoulards, the hooded order conspiring for a fascist dictatorship, was ousted on February 2nd.
The Stavisky scandal and the ensuing riots were high spots, or low spots, of 1934. However, other news events leaked out through the strictest peace-time censorship suffered by the Third French or any other republic (unless one includes the U.S.S.R.).
Whenever an article in the newspapers touched on American interests, I was called upon to explain. Sometimes it was harder than others. When a statement from Moscow charged that the United States and England were selling huge quantities of war material to Japan, which had become the world's foremost purchaser (with money) of arms and ammunition, I could only say that industrialists were the same the whole world over and that it was a bleeding shame.
Hitler signed a ten-year non-aggression pact with Poland, using the best German ink.
The French Government caused three-minute propaganda films to be shown in all movie theatres, to bolster the public morale. In a letter from Mme. Berthelot she told me that Monsieur Monge, after hearing the Marseillaise played badly in so many cinemas, had written a letter to Doumergue offering to conduct a free school for union musicians in which they would be instructed to play the stirring national anthem intelligently. He received an answer from a secretary that the matter would be referred to the appropriate department. Two weeks later M. Monge received an unannounced visit from two officers of the Sûreté Générale, who searched his small room and horse-butcher shop for Russian propaganda.
The Royalist youth organization ( _Croix de Feu_ ) came out in favour of a 'corporate' state.
Doumergue's plan for saving France had one main feature in common with all previous plans for saving France, by no matter what Premier. It decreed a salary cut and reduction in personnel in public offices and institutions, including postal and railway workers. Strikes broke out; meetings of protest were held. More riots occurred in Paris suburbs. The lower-middle-class _Intransigeant_ placed the blame for the disorders squarely on the narrow sloping shoulders of Leon Trotsky, for a change.
The Radical-Socialist party had been thoroughly discredited by the Stavisky exposure and its numerical strength was diminished. Herriot had replaced Daladier as its titular head.
In the international field, events were moving faster. The disarmament conference at Geneva, with representatives from ten nations, agreed on a blanket arms embargo plan _contingent on acceptance by Japan._ Japan turned it down.
With great pomp and oratory, Mussolini received Hitler in Venice for their first get-together, on June 15, 1934. A couple of weeks later, Hitler, buoyed up by promises of solidarity from his brother dictator, ordered the blood purge which knocked off Roehm, Von Schleicher, and others among his former pals.
Steadily, since the Stavisky scandal, the Socialist Party had been gaining at the expense of the centre, and in July the Communists joined the Socialists in a 'united front' against fascism. The bankers and industrialists, whose sharpest tool was Bonnet, were thoroughly aroused and started sniping in all quarters, not in favour of fascism, but _against its enemies_. In the controlled press, 'united front' adherents henceforth were referred to as Communists or 'Reds'. In 1934, following the assassination of the King of Yugoslavia in Marseilles, a Cabinet shake-up made a place for the wily Laval. The _Berliner Tageblatt_ became lyrical over the appointment and foresaw untold benefits in Franco-German relations. In Paris, Monsieur Herriot, not so well pleased, walked out of Doumergue's coalition, and Flandin, to make confusion more confounded and for ironic climax, was boosted to the leadership of the 'democratic alliance'. Political parties, in the interest of clarity, should not have names but numbers, like football players on the field.
# _Of Hospitality_
THE NIGHT TRAIN from Barcelona, via Cerbere and Perpignan, arrived in Paris about nine o'clock in the morning. That did not prevent me from waking about four o'clock and dressing in my lower berth as noiselessly as possible. I had had an experience the night before when the train stopped at Narbonne that prompted me to avoid disturbing my travelling companion by raising the window shade.
The express was crowded that trip and all the way from the Catalan capital across the border into France I had felt lucky because I had a compartment all to myself. At Narbonne, I was awakened by voices just outside. One of them, that of the conductor, was hushed and apologetic. The other, that of a Frenchwoman who sounded vigorous if not young, was raised in protest, and must have been harsh and uncompromising under the best of circumstances.
'This is the only upper,' the conductor said, and I felt sure he must have said it to the same party many times before.
'Impossible!' said the woman. 'How much extra for a lower?'
'I assure you there is no lower unoccupied.'
'I shall not accept this one,' the woman said, and there was just enough of a pause to indicate that the conductor was shrugging his shoulders. If she wanted to stand in the draughty corridor all night, it was her own affair.
'But, Monsieur. There's a man inside,' the woman continued.
' _Ça ne fait rien, madame. C'est un Anglais_ ,' the conductor reassured her. (What of it? He's an Englishman.)
I didn't relish being tagged as an Englishman just then, having tangled with a rather foul collection of them in Spain, men and their peevish angular wives who had had some kind of gravy under the Habsburg monarchy with a British queen. The members of that faction spoke of republicans in scathing terms George III could not have topped.
Furthermore, I didn't know how to take the conductor's well-meant remark, whether to feel that a Sir Galahad quality showed through my gruff exterior and had aroused the Frenchman's awe and admiration, or whether he thought of Anglo-Saxons as an inferior and unenterprising race from whom women in distress had little or nothing to fear. Anyway, the woman decided to risk my company and at dawn was sleeping soundly when I wrestled into my clothes.
My eyes smarted and my skin was rough with cinders. The water in the first-class gentleman's lavatory was not running or even dripping from the tap. Cold air blew down my neck and up my sleeves and trousers' legs. I was shivering. My teeth were chattering. There was no prospect of breakfast or even coffee for hours to come. Nevertheless I tingled and caught my breath with excitement as the unseen but familiar landscape of France rushed past me in the darkness and mist. By the time dawn tinged the eastern sky, I could make out the shapes of long files of trees, with white streaks of road, plaster houses with red tiled roofs, giant haystacks, and walled gardens in which the Brussels sprouts were still standing.
When we reached the Paris suburbs I strained my eyes so as not to miss a sign or building. Commuters were flocking to the depots to take the local trains; shutters were being hoisted; the cobbled streets were stirring with desultory traffic. Sleepy chambermaids, servants, factory men and women, white-collar workers, bakers' boys and dairy girls were going drowsily about their business. Cafés were filled with customers who huddled around the counters for their meagre breakfast of coffee and crescent rolls. I felt ghostly and at the same time conspicuous. All those people were dear to me, and I was alien to them. I could have jumped from the train to shake hands with them all, but knew that had I done so I should have been dismissed as eccentric. I was elated, and at the same time blackly depressed. Everywhere I looked I detected a dogged air, a slowing up of reflexes, a sullenness of demeanour that was new to me in France. Daily I had been reading of France's trials and the humiliations, the cupidity of her leaders, the futility of the people's protests, the arrogance of France's enemies, the imbecility of her allies. Still I was shocked when I saw the results, as one recoils and tries to hide one's dismay when encountering a friend who has been ill or has been stricken with some staggering misfortune.
There was no one to meet me in the Gare d'Orléans, since no one knew I was coming. Had the Hotel du Caveau not passed from the hands of Henri Julliard, I should have hurried there without hesitation. As things were, I was not at ease, and proceeded cautiously. I checked my hand luggage in the parcel room and took a taxi to the place St. Michel, and with every click of the meter and jolt over unrepaired streets my heart beat faster. I was empty-handed, inconspicuous, unkempt from the journey, and with no plans for the morning.
I thought of the bats that zigzagged back and forth in the rue de la Huchette at dusk and dawn and wondered if they flew perpetually, like souls condemned to restlessness and torment, without respite or repose. It was too late in the day to see them, but still I imagined that they must be there, hiding beneath some window-ledge or eave. Of the men, the women and the children I did not dare to think before I was sure that they were safely where they should be.
The taxi pulled up in front of the restaurant Rouzier, on the opposite side of the _place_ from my street. I got out and paid the driver and was standing on the kerb, undecided as he drove away. Then I saw the drudge, Eugénie, with the slate-coloured hair. She was standing in the rear of the terrace of the Café St. Michel and wheeled quickly as no doubt the sharp voice of Madame Trévise called her back to her duties. I crossed over to the international news stand; the proprietor reached for _L_ _'_ _Oeuvre_ and handed it to me absent-mindedly as I drew alongside. I was startled, then relieved. He had recognized me, but had not realized that I had been away. But when I paid him the former price of the paper, he reminded me that now the bandits charged 50 centimes. Evidently many of his customers, from force of habit, made the same mistake.
When I walked a few paces towards the Seine and paused in front of the booth of the chestnut man, I was brought up short again. My friend from the Loire was absent, but the price tags on the turquoise-green Portugaises and the flat grey Marrennes of incomparable flavour would have caused a traffic jam a few years before. I hadn't been in Paris half a day before it was clear to me that the rich had become richer and the poor much poorer, as a result of the recent events.
That morning I entered my street from the western, or St. Michel gate. The militant concierge of No. 32 was muttering curses as she tried to erase a violent political slogan that had been chalked on the wall. The publishing house at No. 30 looked as if it were closed, with the same dusty books stacked in the front windows. Whoever read such books ( _The Attitude of the Faitbful towards Immodesty, The Trutb about the Cburch in Spain_ , etc., etc.) I have always been at a loss to understand.
Maurice had gone with his bucket to the Seine to draw water for his exotic fishes, who, according to Maurice, found river water more to their liking than that from Paris taps.
Only Bernice was in the music shop at that hour. She always got up early, swept the place, and dusted the shelves and instruments before she prepared Gion's breakfast and called him from his morning sleep. In my absence, a friendship had sprung up between the pale Bernice and the equally subdued mistress of Panaché. The two men, who liked each other in so far as they could like any member of the human race, had forbidden their respective girls to speak to each other beyond 'Good morning' or 'Good evening', fearing that if Bernice and Louise compared notes they might find common grounds for complaint.
M. Dominique was at his littered desk, squinting through a jeweller's single eyeglass at a stamp, so I got past No. 24 unnoticed. The cleaner and dyer, Madame Joli, who looked like a lesbian and called her little husband _Mon Trésor_ , nodded absent-mindedly. I had seen her infrequently, so she had not missed me.
The day being Monday, Julien and Mme. Julien had not raised the shutters of the barber shop. Monday morning was the only time during the week they could seem to get together in bed, and that was possible only because Julien took his usual morning walk in the markets, then returned, undressed and crawled back about the time his handsome wife was awakening.
On the other side of the street I caught a glimpse of young Mme. Corre, the pale homesick girl from Burgundy, in the grocery store.
The blue-eyed Alice, wife of André the coal man, was busy serving teamsters at the bar. The tailor, Saint-Aulaire, was deep in _L_ _'Action Française_ and its tirade on the menace of communism.
Abreast of the window of No. 18, the Hôtel Normandie, I caught the eye of Sara, the Jewess, as she glanced up from her ledger. A flash of recognition stirred highlights in her warm brown eyes. Her face, while preserving its essential sadness, relaxed into a welcoming smile.
'Monsieur Paul!' she said, extending her hand.
'Madame Sara!' I replied.
As she reached for the bottle of cognac and two tiny glasses, I felt suddenly at home. It was seldom, unless pressed by a drunken client, that Sara clinked glasses with anyone. We did not say much about Spain, where the enemies of the Republic were in clover once again (without the King and Queen and haemophiliac princes, with assorted relics of their royal parentage 100 percent non-Spanish). To a hardworking woman with soft eyes and neat shoulders who has seen only a ghetto, a munitions factory, a mayor's office (to be married) and a third-class hotel with bedbugs and modern comfort, it is hard to be lucid about distant lands. But I sensed as we chatted and drank that Sara was happier than she had been for many years, and soon afterwards, when Guy came in, buttoning his trousers, his hair tousled from sleep, he kissed his wife on the cheek as she poured him a glass of cognac to join our little feast.
Through all the years Guy had overworked and neglected Sara, he had focused his better qualities on one humanitarian hobby. He was a rabid anti-anti-Semite, a baiter of Jew-baiters. The recent news of German pogroms had inflamed Guy to such a point that he had seen, however tardily, that his Jewish wife was an angel and, as such, should be comforted and cherished. On that November morning, Guy entered definitely into my friendship. Love marches on.
Before I knew it, I was surrounded by Milka, Pierre; Georges, the Caveau _garçon_ ; Monge; Frémont (who had the day off); the pimp, Robert; and Madame Absalom. At noon miraculously appeared in the small and already overcrowded café, Hortense (a little grey); Noël, looking gaunter than ever; Lanier, the _gueule cassée_ ; officer Flammarion from the _Poste de Police_ ; Mary the Greek (who was still lovelier than Mona Lisa but pitifully in need of clothes); and timid Jean, the Socialist butter-and-eggs man. Someone had gone across to No. 5 (I never got beyond No. 18 that first day) for Leonard's accordion, which they took without ceremony from his room for me to play. And the day was filled with music, and somehow most of us missed our lunch but ate onion soup and sausage with sauerkraut in mid-aftemoon. I cannot say just how it happened that I took time off for a dance or two at the Bal St. Séverin, and to teach Robert, my brother musician (I disclaim his other profession) how to play _España Cani_ and a Spanish sailor's song called ' _No Te Vayas_ '. Naturally, we could not slight Madame Mariette and Mireille, not to mention Armandine and little Daisy, who could not leave their place of business.
There was little work performed or business transacted in the rue de la Huchette that day, but money changed hands in a healthy hearty way, each paying according to his ability and receiving according to his needs. I awoke the next morning in one of the first-floor front rooms of the Hôtel Normandie (there were only two) which ordinarily was reserved for couples in a hurry. So my eyes, growing accustomed to the thin light, rested on a bland white _bidet_ , and an area of wallpaper figured with either jellyfish or chrysanthemums. Pierre, in writing me of bedbugs, had indulged in understatement. I did not complain about them, since Sara refused to accept a franc for the night's lodging or my transportation on the shoulders of Guy from the back room up the stairs and into bed.
Louis, the one-armed garçon, who had sung _Zoum La La, Auprès de ma Blonde, Les Montagnards, Aubreville, Mon Lazare,_ and other French songs and ballads had passed out two hours before I did. Neither he nor anyone else seemed to find it strange that I had come all the way from Spain without baggage. Louis travelled lightly himself, when he travelled at all. When he offered to buy me a shirt, however, I remembered my suitcase, typewriter, and canvas overseas bag at the gare d'Orléans and sent him to retrieve them.
My problem was to get dressed without allowing my head to tip too far forward, and find lodgings before he got back. I didn't think the bedbugs could get into my suitcase or typewriter unless I opened them, but the duffle bag was pregnable. Georges, the Serb, had convinced me that the Caveau, without M. Julliard, was out of the question. Some woman and her grown son who was studying the violin were in my room with my stove.
In No. 8, an attic room was vacant next to that of the Satyr. I rented it and as I unpacked my stuff, in full view through the open window, I could see the two Alsatian old maids across in No. 7, peering through the lace curtains and nodding busily to each other. I shall never forget these two old maids, of whom I had thought with ridicule over a period of years. As a matter of fact, when I first went to the rue de la Huchette in 1923, Elvira and Roberta were not very old maids. They kept too much to themselves, fearing otherwise that their tyrant, the colonel, would discharge them.
On the day after my return, we all took it easy. I walked with Pierre Vautier all the way to Notre Dame de Lorette, near which there is a national museum left to France by Gustave Moreau. The museum is filled with Moreau's own works, the least said about which the better, except for some portfolios of animal drawings. The curator or director was Georges Rouault, one of the most gifted modern French painters, who drew a small salary for guarding the worthless junk of Moreau in order to eat while painting splendid works of his own. Rouault was a master of _gouaches_ , a kind of watercolour, into which he instilled a vigour the medium had not known before his time. He worked in the museum, since no one ever visited the place except by accident or to see him.
As Pierre and I walked, we talked about Laval and Flandin.
Flandin was the most outspoken Nazi among French politicians, one who loathed a working man to such a point that he turned pale whenever he saw one. When Papa Doumergue, the last duffer in France who should have been selected to save it when the people rioted against Stavisky and Daladier, tumbled off his perch on the issue of a budget to be balanced largely from the lower brackets of government employees, Flandin was chosen Prime Minister. That was a kind of political accident that frequently occurs in democracies. The French politicians of the Right were afraid a Left Leader would get in, and started talking for social justice and against monopolies. The leaders of the Left, especially Blum and Daladier, were afraid of one another.
From whatever causes, Flandin got in just in time to have Pétain reinstated 'permanently' as a member of the superior council of national defence. Modernity, personified by a brilliant officer named Charles de Gaulle, was buried. Promptly, aboard the fastest train, Laval was sent to confer with Mussolini and give him all aid and comfort in big plans to invade Abyssinia. If Stavisky had lived, this might not have happened, since the Bayonne financier had put up the funds for Haile Selassie's resistance.
Laval admired Mussolini with all his heart, and Il Duce got him into the good graces of Hitler. On the visit in question, Laval promised a slice of French territory in Africa and a share in the French railway from Abyssinia to French Somaliland.
In a similar spirit, Flandin and Laval sent a French trade commission to do business with the Japs in Manchukuo. Meanwhile the army put its dead hand on De Gaulle and his fellow exponents of mobile warfare, as against sitting behind the Maginot line until Hitler thought of the bright idea of walking around the end.
# _The Heart to Resolve_
VICTOR HUGO, on the barricades when the Second French Republic was being scotched by the ancestors of the same industrialists and bankers (with figureheads out in front to distract the populace with a false show of government), remarked that he could only take part in battle half way. His conscience would permit him to expose himself to death but not to kill his enemies. So he was out there unarmed.
As I walked that day in 1934 across the city we both loved with Pierre Vautier he was in a somewhat analogous predicament.
'I can go along with my comrades in despising all the fakers and their chicanery,' he said. 'I can accept the logic of Marxian socialism. Why can I not confuse hope with reality?
One of Pierre's duties as a Communist had been to conduct noonday meetings in factory yards and near-by cafés. He was no longer the bewildered boy of twenty who had been struck by his father with an umbrella, but an earnest man of thirty-one. He spoke in public well but dispassionately, in an even tone of voice, giving excellent reasons for what he asked the workers to do but without conviction that any great number of his hearers was responding. The men he was trying to help and to organize, with little success, were suffering injustices and were being herded to slaughter and slavery. This he understood. Meanwhile, Laval and Sir Samuel Hoare, in the name of the class which was born tightly organized and had the funds, arms and ammunition, were building up Mussolini and giving away Abyssinia. The futility of it all was consuming Pierre, like a loathsome disease he had innocently contracted. He had been weak in many ways, but his intellect burned steadily, like a night lamp in the sickroom of his soul. He craved gestures of protest as an addict longs for drugs, knowing they would not cure him or uplift society.
At dinner that night, we talked with Milka, who ordered and ate what she needed, nothing more or less, and moved in her incisive sphere of revolutionary practicalities, as surely and cheerfully as ever. She would no more have thought of glancing to one side at doubts or hesitations than a racing driver would have taken his eyes from the road on a bend to sneer at hostile rooters in the crowd. The girl I had known as a student was a drably dressed woman of thirty-five, more constant than fanatic, and very much alive. Her father had been a revolutionist in Zagreb, in constant danger of the police. He had been a goldsmith by trade and must have been practical, like Milka, because he had chosen his profession deliberately as being best suited to his political activities. Goldsmiths were highly paid; so he had to work only a few hours a week to live and maintain his family. The rest of his time was for the workers of the world.
When Milka was seventeen years old, and handsome in her candid way, her father sent her to a dentist. There were no dentists who also were revolutionists in Zagreb then, so he had to patronize a reactionary one who had an excellent reputation. The dentist took a fancy to Milka and one day, after the dental treatment was over, he made her a clear proposition. Either she was to be his mistress or he would denounce her father to the dread police. She had to make her first big decision and, like St. Mary of Egypt, she came to the conclusion that her body was not of sufficient importance to keep intact at the cost of her father's torture and subsequent death.
I could imagine Milka going about her distasteful duties with contempt she could conceal only because of the obtuseness of her blackmailer. But after three years the dentist tired of her, anyway, or found a more alluring young patient; so he denounced both the father and Milka. The father was arrested, and died without divulging the names of his comrades, in spite of the fact that a wooden wedge was driven with a mallet slowly into his rectum, he being given a chance to rat after every stroke of the hammer. Milka escaped, and without money or friends, somehow, got into France. From Chambery she was able to contact her father's co-revolutionists whose lives he had saved while splitting slowly up the middle, and they got her enrolled at the Sorbonne and sent her a meagre allowance with which to carry on the family tradition.
She had never told me, until that evening _chez_ Daniel, in the shadow of the former home of Madame de Staël, about her antecedents and the way in which she had stood where the brook and river meet with feet more reluctant than our kindly Longfellow ever dreamed of. Even then she did not take off her drab blouse and show me what Pierre must have noticed but never had mentioned: an ugly seared area under her smooth left arm where the police had placed a red hot coal and kept it there until it had been extinguished by her blood. And not until much later did I learn that, having been arrested when her father was, she had been obliged to purchase her safety by consorting with a plain-clothes man whose uncle had influence in the court of old Franz Josef, who was then Milka's sovereign and protector and defender of the faith.
So, if the reader finds it hard to understand why, starving and rotting under the grandstand of that Paris stadium converted by Premier Daladier, and later used by Reynaud and Hitler as a concentration camp, Milka, now forty-two years old, is looked on as a rock in a weary land by fellow prisoners she keeps from despair by the force of her spirit, having lost, of the 135 pounds she carried in there, exactly fifty pounds, he must concede, at least, that she came up the hard way and is a chip off a commendable old block. (Milka Petrovna died of dysentery on September 12, 1941.)
I had a chance that same evening to size up Madame Berthe's young husband, who was presentable and energetic, well-liked in the quarter and whole-heartedly in love. In the midst of the meal, I saw Berthe enter, still in black but radiant, and pause at the doorway to smile as Daniel kissed her respectfully on one soft cheek, then the other. As Hortense had written me, her wrinkles had disappeared, all except the becoming crow's feet at the corners of her eyes. I hastened to her, and Daniel beamed as I too kissed her cheeks and told her how glad I was that someone was happy and that she was the one who had been chosen.
I am sure it was because she was so engrossed with her first real passion that she did not seem depressed on account of what her Indian summer idyll had meant to Monsieur Henri. Henri had been willing, when he saw how things were going between the handsome young boxer and his infatuated sister-in-law, to continue running the Hôtel du Caveau with Daniel as a partner. This Daniel was not willing to do. With the arrogance of youth, he thought of Monsieur Henri as quaint and old-fashioned because he was lax about bill collecting and hesitated to raise prices in proportion to the fall of the franc. Instead of the traditional French menu, dear to the heart of Henri Julliard, and consisting of _hors d'oeuvres_ , soup, fish, meat, vegetable, salad, cheese, dessert and coffee, Daniel served a more modern meal, in Dalmatian style, with meat, mashed potatoes and sweet and sour cabbage on the same plate, requiring fewer dishes to be washed, less help to he paid, and yielding a comparable amount of nourishment in a briefer space of time.
Neither Daniel nor Berthe was worrying about Abyssinia or even France. They were wrapped up in their profitable restaurant business, which was succeeding beyond their hopes, and in each other. It is true that Berthe found the hours long, between six in the morning when Daniel went to market and two in the morning when he came home eagerly and with plenty of what it took, after closing the bar. Of course, he slept four hours in the afternoon, leaving the establishment in charge of the cashier, the pious Mme. Claire whom Monsieur Henri and the American reporter had rehabilitated. Claire had turned out to be a first rate _commerçante_ and, after the American had left her to work in Detroit, she had entered a liaison with the neighbourhood physician, Dr. Alphonse Clouet. They planned to get married years later, when they could afford to buy a place in the country and raise rabbits and poultry, in preparation for which the unbusy doctor had littered his private office with pamphlets about trap-nests, weasel-proof warrens, and a kind of 'American home' that had been shown at the Colonial exhibition and was portable, economical, easy to set up, and could be shipped compactly, via Le Havre, for only 50,000 francs. The doctor had about 4,000 in French Government bonds, and Claire was saving twenty-five a day from her thirty-franc salary, since Daniel furnished her board and the doctor had a large double bed.
So while Flandin, Laval, Bonnet and the others were selling the country out from under them, a lot of French men and women were making plans for a future which resembled other futures of which they had known.
When I returned to my attic room at No. 8 about three in the morning, l'Alouette (the Lark), as the statuesque concierge was called, having pressed the button controlling the door latch to let me in, opened her door and, standing unembarrassed in her beige flannel nightgown, bare feet on the tiles, handed me with a sly sleepy smile a letter smelling enticingly of musk or some rare perfume. The Lark was so called because she sang in a lusty and rather metallic soprano, arias from _La Bohème, Louise, La Tosca_ and _La Traviata_ while performing her duties as janitress and guardian of the gate. The neighbours and tenants could set their clocks at ten a.m. when the Lark started singing, that being the hour when she considered that whoever was not already stirring had forfeited his right to quiet in the home.
I knew, with a sinking of the heart, that the letter was from Hyacinthe, whom the Lark envied and admired, envied because of her youth and normal size (the Lark was five feet eleven in her bare feet) and her excellent diction. The Lark had never been able to lose her Marseille accent, even when singing in Italian. A quick reading of the message, however, set me at ease again, and made me ashamed for having feared, if only for a moment, that Hyacinthe would prove untactful or demanding. The letter is typical of the finest French tolerance and understanding, with an undertone of banter and a play of wit, a reproach so gentle as to be acceptable without resentment, and enough protective vanity to save the face of all parties concerned.
'Elliot,' the letter began, 'I understand very well that because with you safely at a distance I revealed myself so completely, you have not wished to startle me by claiming abruptly the familiarity to which I have made you feel entitled. That is delicate of you, and endears you to me all the more. At first I was hurt when I heard you were back and even saw you pass my window without a glance upward – no doubt because you were afraid of breaking your chivalrous resolution.
'I reasoned thus: You could not be heedless or cruel. Nothing I had written could have offended you. Then your aloofness must be deliberate. Suddenly the truth broke through the clouds of my obtuseness. You were _waiting for a sign from me_. A cruder man would have rushed up the stairs, risking to find me unprepared. A vainer one would have embraced me overbearingly, as if he already owned me. You – the Frenchman who pretends to be an American, even to the point of improving on our vocabulary at the expense of pronunciation – were perfect.
'But come now, quickly. Please! Tomorrow morning. Not in this stupid barracks, it goes without saying, where Mama spills daily more powder as her blood pressure makes her face more russet and autumnal. In the Café de la Régence, inside, against the southern wall, no later than half past nine.
'Your devoted Hyacinthe'
I doubt if ever a man was pardoned more subtly for having got boiled and, as a result, having slighted a dear friend.
Some tourists will remember the Café de la Régence in the rue St. Honoré, not far from the Comédie Française, the Hôtel du Louvre and the Palais Royal (in which the expatriate who wrote 'Home Sweet Home' lived in 1840). There was a table in the centre at which Napoleon had played chess, and chess champions from all quarters of the world frequented the Régence. The terrace afforded a good view of the Opéra, at the end of the broad busy avenue, at just about the right distance to keep between a music lover and that degenerate institution in France, after World War I. Between the terrace and the inner café, a trio of musicians (violin, 'cello and piano) played at dinner time (the food was good if not excellent) selections like the 'Barcarolle' from _The Tales of Hoffmann_ , Nevin's 'Narcissus', Dvorák's 'Humoresque' and Saint Saën's 'My Heart at Thy Sweet Voice'. The Régence was not a political café, and the memento of Napoleon did not bring too many tourists. It was a favourite rendezvous for men like Monsieur de Malancourt, or who wanted to be like him, and the women of their temporary choice. Usually a French _bon vivant_ invited his light of love to the Régence _before_ the seduction, so the couples to be seen there were attentive, from the male angle, and coy or reserved on the part of the female.
At late breakfast time, however, there were a few English and Americans, on account of a house speciality called _'oeuf à cheval'_ (egg on horseback), which consisted of an egg on a layer of Gruyère cheese on a slice of _pain mie_ (something like American bread, but not much) neatly toasted in a hot oven until the white of the egg was cooked firm, the yolk still soft and fluid, and the cheese partly melted. Hyacinthe adored eggs on horseback, and watching her enjoy herself is one of the lost pleasures I mourn from the bottom of my heart.
I had first taken Hyacinthe to the Café de la Régence, when she was almost fourteen, because her mother kept her in black most of the time out of respect for distant relatives who seemed to know just when to die, in turn, in order to prevent Hyacinthe from wearing the colours she loved and understood. Not that she was not ravishing in black, so pale and demure, with those haunting hazel eyes and curved lashes, not too long. But black does not compose well with pastel colours; so I selected for Hyacinthe the best cafés where the chairs or benches would supply her black clothes and white skin with a strong intermediary red, ultra-marine, gold- or corn-yellow, and sometimes royal purple or violet. Oh, yes, and in the Café de Rohan, so safe and select if one knew which room to patronize, a Veronese green that brought out the warm highlights in her eyes and, reflected in her throat, and her dainty but capable hands, lent her an eerie quality she liked now and then to exercise.
Make of it what you will. Hyacinthe loved her shapely body and wanted not even its reflections wasted, not a curve or a surface, not a single fine-spun wisp of hair, or a gesture of a crooked finger, or a swish of silken knee. Behind her smooth forehead, and revealed by her hazel eyes, was a mind that balked at nothing, that was more sensitive than a seismograph and more supple and resistant than a Toledo blade.
She was perfume and morning and rest and atmosphere and sky, and she honoured me with her friendship because, a stranger from a distant land, I wandered into the little street where she, too, was a stranger. She gave me her confidence because, with a zest for life like hers, and so much she had to share, it was imperative to extend it to someone, and no one else was available.
On the morning of which I write she was just turned seventeen. She had left home early in order to pray in the shrine of the Virgin in the Madeleine. I doubt if the Virgin was accustomed to commune with supplicants as highly intelligent, or who asked Her for guidance with more sincerity.
'I know it annoys you, Elliot, when you are reminded that I cling to a form of worship which seems to you quite empty and illogical,' she said, after I had ordered our hearty breakfast. The perfume she had selected that morning was Molyneux No. 5, which is not obtrusive in the aroma of food. Her gloves were of black suede, as were her high-heeled narrow shoes. She sat on the bench beside me at precisely the right distance, so that I could feel dimly her warmth and not be hampered in my movements.
'When you need rest from yourself and the turning of your restless mind, you get drunk, my friend. Religion is my repose, and it comforts me. I know the Church has strayed far from the thoughts of Jesus and the humble, who must have been more attractive in pastoral lands and ancient times than we find them today. The fact remains, I am a Catholic and it comforts me.'
'I am almost converted,' I said, not sarcastically. 'I wish you would send some of your tolerant French clergy to Spain, armed with flit guns.'
Hyacinthe looked at me closely. 'Elliot. What has hurt you so?' she asked.
She knew that had everything been well, I should not have introduced an acid note into our reunion.
'Things are going very badly down there,' I said, meaning Spain.
'The Church has often been corrupt and its priests have been bestial and greedy; worse, they have been short sighted. It is not the impurity of Her human agents one worships, but Her spiritual perfection,' said Hyacinthe.
'Perfection is the ultimate. Why not worship it plain?'
'It needs to be dramatized,' she said.
That brought us to the subject nearest to her mind. She had decided on a career, from which neither her family nor all the archbishops, nor rebuffs nor discouragements of any kind would dissuade her.
'The cinema,' she said, 'while manufactured in quantity by the Americans [she spoke of Americans sometimes to me as if I were French or Siamese], is produced with style and significance in France. The medium is characteristically French. Molière himself wrote cinema before the day of the camera. American pictures are like American food, wasteful and rich in material, haphazard and boorish in conception. Why, Elliot, the exceptions, the first-rate films you have produced [I had become American again because the remark was complimentary] provide the most devastating criticism of the run of the mill, for illiterates who know the alphabet and arithmetic, but never literature or algebra.
'The German films are strong, sometimes, but they have no sense of tempo or of timing. You remember the one we saw at the Ursulines in which the switch-tender's daughter was betrayed and everybody died – but everybody. Where was the crescendo of seduction, the presto of rage, the adagio of disappointment? No. The whole piece was a dogged persistent largo.
'The English cannot make pictures because as a race they are incurably frivolous, and think the middle ground conceals truth as a tropical island has hidden treasure buried some distance from the shore. When they portray love, they talk about lust or kippered herring and chase each other across lawns where the girl, had she not tripped over a croquet wicket, might never have known that the cold exterior of the rather bony hero, who talks as if he had a hot potato in his mouth, covered a rather decent income and a willingness to be married in a church that is neither Catholic nor Protestant, but on the fence, like everything English!'
The _oeufs à cheval_ had been placed in front of us but were still too hot to taste. So she continued. I would not have stopped her for the world.
'One reason for the superiority of French films,' she said, 'aside from the Gallic instinct for ensemble and synchronization, for atmosphere and restraint, is the acceptance by our public of middle-aged heroes. Hollywood sends out on the screen either callow youths who not only have not lived long enough to learn what acting means, but have not seen or felt enough to interpret a script; or men with four or five children and three wives – only one at a time, perhaps – who play opposite _cocottes_ cast as gentle young ladies or college graduates with breeding who have to try to act like hard-boiled creatures of the slums. In either case, one leaves the theatre before the show is finished, to spare oneself the sight of a heroine who is going to suffer a calf-like honeymoon with a fresh young bungler or, worse, is going to have to learn about love from a settled middle-aged party who needs the tricks of a professional to arouse him at all.'
There was nothing I could say in rebuttal, except that our photography was tops.
'Your Carnegie Institute, or some philanthropic institution, should ship it over here,' she said, 'without your producers or censorship.'
Her plan of campaign took my breath away, as familiar as I was with her determination and ruthless realistic approach. She knew, she said, that in order to get quickly to the top she would have to become the mistress of some influential producer or director or both, or if not, some backer or male star who could stand in her way. But since she was a virgin, and could offer this rare attraction as bait, when most of the actresses could not compete on those terms, if any one of them could (her words), she believed she was justified in proceeding, as follows:
The system was unjust, the men who took advantage of it were unchivalrous and mean. Therefore she was within her rights in duping them. A hymen was too great a price for anyone to demand merely for a chance to be an extra. So she was going to select the man or men who could do the most towards getting her to stardom, promise them the prize when she should reach the goal, which, with her physique, brains and talent could not be long in achievement, and then, when the moment came to deliver, she, having established herself, would laugh in his or their face or faces.
'I believe you can do it, Hyacinthe,' I said.
'If you will be patient and help me,' she answered, and I thought when she looked straight into my eyes that I saw in hers an infinite sadness.
# _One Bitter Pill Deserves Another_
NOT EVEN THE REACTIONARIES in the rue de la Huchette came out openly in defence of Laval's blessing to Mussolini's Abyssinian campaign or the League of Nation's abject attitude in the face of Japan and Fascist Italy who mocked and defied the hypocrites of Geneva. From one end of the street to the other, my decent and well-meaning friends were ashamed of what their Government was doing, and worried not only about the ethics involved but also the practical consequences.
'What can one do?' asked Madame Berthelot, as we lunched that day. My appetite had not been sharpened by what Hyacinthe had told me at breakfast, but I kept the engagement. It would be hard for me to say for which of those two women, so disparate in age and temperament and natural gifts and talent for companionship, I had the deepest affection.
In spite of my desire to be of service, I could suggest nothing that Hortense could do to stop Laval and Mussolini, short of assassination. Neither of us would have objected to that, but neither of us had the necessary zeal to attempt it, either.
'We are as helpless to control our Government as we are to change the weather,' she said. That was literally true. No matter how many Frenchmen voted, or how they voted, the same predatory combination ran the country for the benefit of large employers and speculators on a colossal scale. Voters in a so-called democracy may depose tyrants or crooks in isolated cases but they cannot give birth, full grown like Minerva, to honest and experienced statesmen to take their places.
Those of us who were familiar with France between the two world wars knew that there was continual agitation among Frenchmen for a restoration of the monarchy supported by a dictatorship. In that way the co-operation of the monarchists and their social influence was secured in a manoeuvre which was really intended to break the rising power of labour and reduce the general standard of living in order to keep the workers helpless and the police all powerful. Even Lyautey, one of the most unscrupulous colonial administrators who has in modern times been given sway over a subject population, was mentioned as the possible iron man of France before he died in 1934. In January, 1935, a Paris newspaper conducted a poll to choose a most likely dictator, and Pétain won, hands down, so by the time he wrote his first proclamation in 1940 and started it, 'We, —' in the style of the Bourbon kings, the idea of governing France by absolute decree was not new to him. Of course, he had not counted on having the decrees he signed dictated by a German Führer, or at least O.K.'d, when their hearts beat exactly as one.
A letter from Pierre Vautier which I received in Mexico City in April of that year (1935) contained sidelights on Pétain's growing influence and the way in which the army was being prepared, not to defend the country, but for police work in reducing parliamentary control and as a bulwark against organized labour. While Pierre had not enjoyed his year at St. Cyr, he had not left his brains behind when he entered, and in spite of his distaste for military studies and engineering, he had learned to keep track of the score.
_Paris, 16 April, 1935_
_Cher voyageur,_
Milka, who is too busy to write you just now, asks me to thank you for the Mexican embroidery. As you know you seem to notice everything – our red Jeanne d'Arc (without army and with the 'voices' safely written down) has not, in her passion for reform, lost her Slavic taste for bright colours. She is having your material made into a blouse by one of the Croatian comrades in the rue de Serpent and plans to wear it a day or two after you return, knowing that the first two days will be spent in drunkenness and music and that any new clothes would be stained with cognac or otherwise ruined.
Today, when she was holding the embroidery across her shoulders, to help her guess what it would look like when the comrade seamstress got through, I stepped up behind her and saw in the small cracked mirror that I was definitely getting bald. In the first days I knew you, even then I thought of you as old enough to be a colonel, which would by now have put you so far in your dotage that you would be eligible for our general staff. The machinations and absurdities of those _vieux_ _crétins_ (it rhymes with Pétain) are beginning to take form.
You have read, no doubt, how Laval, who has befouled us in Africa and the Mediterranean and prefers Il Duce to young Eden – both are gallows-meat; so are Laval and Flandin. Anyway, Laval, before his conference with Mussolini to celebrate the New Year, dissolved the league opposing conscription. That was one of the little signs, of course, that the term of conscription was to be lengthened, and the money ground out of the workers in prices and the small shopkeepers in taxes was to be spent on more soldiers instead of modern arms. That suits old Pétain to a T, also Gamelin and Weygand, and Chiappe [the Paris police commissioner] who is part of the same dirty gang.
When a few weeks ago the students of the technical schools staged a strike, it was blamed on the Party, as a matter of routine. Actually we had nothing to do with it, or it would have been better organized. I have read so much lately, in the books Milka hands out to me, of how people rise up and protest spontaneously and afterwards prove to have been perspicacious and sound that I was intrigued with the students' demonstration. What was behind it was simple enough. A few young patriots, backwards in their studies, resented the fact that they had to compete with Germans, Italians and examples of God-knows-what Central European races. Our engineering schools have been filling up with foreigners, practically all of whom are potential enemies in war. The least amount of thought by our Paris editors would have convinced them that Communists are not whooping it up for any _national_ movement. I have noticed, as little as I am permitted to know of Party affairs, that we are blamed mostly for what we have no hand in, and our most telling coups pass unnoticed altogether. Perhaps, after all, it is good strategy to be systematically misunderstood.
There has been an agitation for a longer term of military service ever since the Left started gaining in the elections. It is not against Mussolini or Hitler, who eventually will destroy us unless Russia steps in. They are building highly mechanized and mobile armies, as one of my old professors said, 'like navies on land'. The mobility of such forces enables them to avoid grave risks, as well as to strike quick and telling blows before an enemy is ready. Who cannot see that the war will depend on tanks and airplanes? Instead we are piling up more soldiers to be fed, while they learn squads right and left and infect servant girls, or vice versa.
Colonel P. (the Colonel is still alive) got drunk in a café one evening when I was at St. Cyr and talked quite freely about Gamelin, who has been promoted to chief of staff.
Gamelin is fifty percent like Caesar and Napoleon, according to P. Those great generals of the past made quick clear decisions and carried them out with dispatch. Gamelin will say yes to anything half-way reasonable, but that is as far as the matter ever goes. Weygand, of course, still thinks the year is 1917 and that Americans will be superfluous in the new 1918. He has been retired to an honourary position where he will have more time for church politics.
Pétain thinks he is the Saviour, and he has behind him all the Cagoulards and too many of the army officers. Milka insists the rank and file, or ordinary soldiers, will not obey right-wing traitors but only revolutionists of the Left. If you ask me, in confidence, I think the privates will chuck them both into the nearest river or well. Our famous _poilu_ thinks mostly of girls he can lay and the pinard (red wine) allowance, and of the day when he can put away his badly fitting uniform and take injections in the family W.C. without a sentry looking on. If he can be made class-conscious, and can remember what it means, we are saved. I expect a sure remedy for baldness to come sooner.
I saw Bernard [Brun] the other day, because I was wearing the scarf you forgot to pack and he mistook me for someone else from behind. He almost fainted. Then, when he saw I was unmoved, he told me, out of spite, that he and Breton are supporting Trotsky. Aragon is with us; so is Jean-Richard Bloc. You'll agree that we have the best of the bargain.
When you get back to the United States, send me a consignment of faith, which seems to come so easily to your countrymen. By the way, I saw one of your lady evangelists the other night. She was being shown the sins of Paris in the Oubliette Rouge.
Pierre
It is a striking coincidence that Laval, who got into office in January, 1935, just in time to give Mussolini the all-clear signal for his adventure in Africa, wormed his way back into the trough precisely at the moment to let down the English, who for once were ready to act and to put Il Duce in his place. Their strongest argument, their fleet, was already in the Mediterranean with a large force of submarines so that a British undersea craft was within striking distance of every Italian warship. Laval spiked all this, in the name of France, notwithstanding the fact that all up and down streets like the rue de la Huchette the voters and their wives were indignant and ashamed, and behind any kind of a leader would have given their last drop of blood or the money they had saved to stop Mussolini's arrogant strutting forever.
Mussolini sounded off on May 7th, warning the 'powers' not to interfere in his theft of Abyssinia. The only powers in question were England, France, the United States and Russia.
The farce in the League of Nations is familiar to everyone who can remember back that far. The Negus made a dignified speech; the League appointed an undignified committee. Mussolini gassed and bombed the Abyssinians; Laval stuck by him. In order to save its face, the League voted sanctions, omitting the only one that would have stopped the campaign, namely, an embargo on petrol. The United States Department of State could not see its way clear to persuade American dealers not to sell fuel. So what could the British and French dealers do? Laval got together with his moral equal and social superior, Sir Samuel Hoare, who still is around somewhere back of Churchill, and they gave away the Abyssinians and their territory.
In Concord, Massachusetts, in June, I received the following note from Hyacinthe:
_Cher maître,_
Hurry back, for I need you worse than ever. Elliot, I can no longer ignore what is known as politics, although I scarcely understand the meaning of the word. These pronouncements and conferences of names – it is hard for me to think of them as men – are poisoning the atmosphere. I take up the newspaper – no longer _L'Action Française,_ but any newspaper; I choose them at random. Something terrible is happening and, ignorant as I am, I tremble for our beautiful France.
Elliot, are we or are we not in danger? Have we not been insulted and imposed upon? Who should act?
Last night I bought all the papers and, after reading column after column, confused and contradictory and utterly untruthful, I began to cry. And I couldn't stop; so today my eyes are still swollen. Perhaps my headache resulted from breathing that unhealthy odour of ink. I thought I never should get the smudges off my fingers.
I try to be calm. After all, the Italians can't do anything worse to Africans than I have heard Cousin Émile tell about the government of Lyautey. That is not the point. Africa, to me, exists in the paintings of Rousseau (the _Douanier_ ), an ordered jungle somewhat flat, each leaf and frond in place, with monkeys in full-face, never profile, for inhabitants. How disgusting that is! How abominable for French families to treat their daughters to such an education! I attended the most exclusive school in Paris, and Mama, whom I have ill-naturedly disparaged and whom I might try to love if I didn't have to see and hear her every hour of every day, spent more than she could spare so that I might be equipped for life.
Look at me, or, rather, examine my equipment. Looking at me is deceptive. I am beautiful, and sometimes I believe my eyes have in their depths the mysteries of existence. My grammar and syntax are impeccable. My taste is fairly sure. In the eighteenth or the nineteenth century I should have made my mark. What can I know today? No one cares for society any more, the _haut monde_ , I mean. Intelligent men and women are trying to blunt and not develop their wit and understanding.
These politicians have become important, and I cannot grasp what they mean. Please come. I know from what you have said that you despise them. So do I, without being able to define my grounds. That doesn't mean we can shut our eyes to their threat to us and our enjoyments.
I _will_ succeed. I _will_ become somebody or something. If, to do it, I must vote, I will vote. Forgive me, I am becoming hysterical.
Hyacinthe
Hyacinthe's sensitive awareness of danger and the crumbling of the only society she had been taught to recognize was symptomatic. Everywhere one went, after Japan's aggression was topped by Mussolini's defiance of all so-called democratic governments, men and women who had got along well hitherto without knowing a plebiscite from an alderman were beginning to read what they could find on international affairs and to talk a modern Mother Goose in which the words 'communism' and 'fascism' fitted into all the rhymes.
When I found myself again in the rue de la Huchette, my friends were trying to forget the recent humiliation to which they had, in common with the rest of the French, been subjected by the double play, Laval to Hoare to Mussolini.
'Now he's got the poor Negroes ( _les pauvres nègres_ ), let him be quiet for a while,' said Madame Absalom, apropos of Il Duce.
Monsieur Noël and his cronies felt about the same way. They had disapproved of the treachery and the abject attitude in the face of Mussolini's empty threats, but once it was over they wanted to settle down in peace again, and take up life where it had been flowing steadily, so they thought, before World War I. Like victims of blackmail who make the first few payments on the promise that they will be left unmolested forever afterwards, my French friends hedged and dissimulated. What else could they do, except revolt? And the army, equipped for police duty against unarmed civilians, but not for modern war, had machine-guns, tear-gas bombs and authority to coerce and murder in the name of the law.
Opinions differed as to the willingness of soldiers in the ranks to shoot, gas or bayonet French workmen. There was no doubt that the high officers and most of the low ones (liberals having been carefully weeded out) would carry out the wishes of the large employers if they could. The Navet; Madame Durand, the florist; the tailor, Monsieur Saint-Aulaire; and Madame Absalom expected a military _coup d'état_ , but each for different reasons.
The Navet believed in absolute authority vested in an individual approved by the clerical and capitalistic clique with which he had for years curried favour.
Madame Durand, under a law favoured by the Socialists, had been forced to pay the balance of a week's wages to the lame Jacqueline when she had fired her on the spur of the moment. A firm hand in government, she believed, would not countenance an outrage like that, which encouraged worthless girls to be lazy and impudent.
In case Pétain and Weygand and their disciples took over and dissolved Parliament, Monsieur Saint-Aulaire would get all the business he could handle, making new uniforms, and expected the high officers who already had patronized him to recommend him, perhaps, to a brigadier general, if not the marshal, himself. He visualized himself standing on a balcony in the rue de Rivoli and watching Pétain ride by at the head of a column, on a snow-white horse, wearing a uniform of horizon blue which fitted so perfectly that it received a cheer from the crowd, a uniform by Saint-Aulaire. No French dictator would wear khaki, of that Saint-Aulaire was sure.
Madame Absalom thought the army would disperse and subdue the workmen, not because she stood to gain in that event.
'The _salauds_ always get the best of things in the end,' she said to me.
I did not smile. Already I was beginning to wonder.
The group that gathered in the Caveau bar before the Julliards were forced to sell now patronized the Café St. Michel, which had a larger bar, of which they appropriated the end near the rue de la Huchette. There was not so much argument as there had been in former years, since the reactionary members had stuck with Madame Amance in No. 5, and only the former Radical Socialists – now just plain Socialists – the former Socialists – some of whom had moved over to the Left and called themselves Communists – and the old-line Communists remained.
Monsieur Henri, when he came back to the quarter to collect payments from the Amances, who never were able to pay in full and frequently had to pass up payments altogether, had one glass of brandy with his successors at the Caveau, as a matter of politeness, then called at the Café St. Michel. The women who were politically conscious all adhered to the Left contingent. Mme. Berthelot seldom left her room after dark, but Mariette quit the Caveau cold and took her midnight recess with her former companions, ignoring the dark looks she received from Mme. Trévise, who suspected that her husband strayed down to _Le Panier Fleuri_ on occasion and entered the small side door in the rue Zacharie.
When Mme. Trévise said as much to Madame Absalom, another fellow-traveller with the Left group, the old woman cackled knowingly.
'Between you and me,' she said, 'the men are all alike. And who can blame them?'
When I entered the street from the rue des Deux Ponts in 1936, on my way from New York to Spain, the old carpenter was sitting in the middle of his shop filing a saw with utter disregard for the hideous sounds he was producing. I noticed that the place was nearly empty and not littered with new work redolent with the fragrance of lumber and sawdust. The one apprentice he had retained when No. 2 was dismissed in 1929 had left to take a job in the Schneider ammunition factories near Rouen, and the old carpenter had not replaced him. There was less and less demand for the services of a good but slow cabinet maker.
It was impossible for me to pass the Hôtel du Caveau. When I entered, the café was empty, except for a stranger (M. Amance) behind the bar who spoke to me politely. I snatched a quick drink and hurried away. At the other end of the street I received another shock, for standing in front of the grocery store at No. 27, looking very dignified and self-conscious in a brand-new linen duster, was Monsieur Noël.
The gravity of his face deterred me from asking why he was clerking in young Corre's grocery instead of stuffing cats and dogs. I shook hands, as if nothing were changed, and was on the point of suggesting that he step across to the Café St. Michel for a snifter when it occurred to me that Etienne Corre might be a strict employer. He had been a schoolboy in a smock when first I had known him in 1923.
The small group at the bar, dominated by the alert Mme. Trévise, was not thinking of Noël just then. Like Frenchmen the length and breadth of the land, they were talking about Hitler, who had sent his troops all the way to the Rhine, in defiance of France. Mme. Trévise and Lanier, whose face had been seared and twisted in World War I, were blaming the English, Mr. Baldwin in particular, who had refused to back up their French Allies in military action to oust the German forces from the kilometre neutral zone. The Satyr, the horse butcher and Monsieur Pissy, who because of his union activities had been given night duty in the gare St. Lazare and had not learned to sleep in the daytime, were denouncing Pierre Laval. Laval had let down England when Eden wanted to keep Italy out of Abyssinia.
'It was a dirty Englishman [Sir Samuel Hoare] who gave Abyssinia to the macaronis,' Mme. Trévise insisted.
'Laval made him do it,' Pissy said.
From the small back room came a weary voice I recognized as that of Pierre Vautier.
'They're both pisspots,' he said, and let his head sink down again on his arms, which rested on the table.
'At least, pisspots are useful,' said the gloomy Satyr.
I heard from both Frémont, the postman, and The Navet that day, and from many other sources throughout Paris, that Gamelin, the new Chief of Staff, had wanted to attack the German forces at once, with all the military strength of France, with or without the backing of the Cliveden set in England. Had this course of action been followed, the rising power of Hitler could easily have been overthrown.
It is interesting to note that on January 22nd, just before Hitler took over the Rhineland in March, Laval got out from under and left Sarraut, a colourless stop-gap, holding the bag against the outburst of popular indignation. Laval stepped aside just in time to avoid being the target of the huge Leftist demonstrations in February of that crucial year, and in March the Chamber adjourned until after the elections, when the Popular Front swept the country and Léon Blum took charge, or rather took office, as Prime Minister.
In the rue de la Huchette, I found many of my friends who agreed with Gamelin that the Germans should be subdued right then and there, before it was too late. I did not find a man or woman among them who believed for a moment that this would be done. They knew the politicians were against it, because they were fighting their own war against labour, and for once the going was hard. The French bankers were afraid to oppose Downing Street because London controlled the franc and might devaluate it, in reprisal, if the French did not behave.
The families who had sons in the army were in a special category, having their own flesh and blood directly at stake. Pissy and young Pissy were eager to go, but they had no property. Madame Corre, who had held her age so well through trying years, began to fade at the prospect of Etienne's having to abandon the business his father left him and the education, including travel in Italy, England and Germany in order to acquire languages, they had given him at a sacrifice. Etienne, himself, while anxious to get rid of the grocery business, did not want to waste any more years in the army, having served his eighteen months. He wanted to become an export broker and was trying to establish himself in that line. That was why Noël, whose taxidermist trade was at a standstill, had been hired as clerk, to assist young Madame Corre, the homesick girl from Dijon, in the no-longer thriving Épicerie Danton, from which the beans in trays, pride of Corre the elder, and the spices of Arabia had gone like the snows of yesteryear. A breath of old France had gone with them.
As soon as the group in the Café St. Michel found out that I had crossed on the _Normandie_ , they set aside politics for a while. The _Normandie_ was the pride, not only of the French marine, but of all the French, from the poorest to the most influential and prosperous. Shop girls, delivery boys, sisters of charity, clerks, even the pathetic old Taitbouts, would pour over columns in the newspapers and cheap magazines, or listen to descriptions on the radio whenever the _Normandie_ was mentioned. Hyacinthe, who already, at 19 was attracting attention by her work on the screen and who had become the local celebrity, eclipsing even Monsieur de Malancourt, had dozens of folders and pamphlets and saved clippings about the great ship that was to rule the ocean, not with force but with elegance, and put the British and the Germans to shame.
'We French have done so little lately that the _Normandie_ has become the symbol of our race. As long as we can be predominant in comfort and taste, and match the speed of the Americans, we are not lost,' she said.
I did not have the heart to tell them that my trip on the _Normandie_ , because of the frightful vibration caused by her powerful engines, had been my all-time low in Atlantic crossings. The liner was taken out of service for six months, following that maiden voyage and return, and the French engineers succeeded in correcting what was wrong with the original design, so that after 1936 the Normandie fulfilled the dreams and hopes the French had placed on the ship in advance.
# _Of Property and Fraternity_
THE SONGS OF THE LOIRE which formerly issued from the Caveau, roared by l'Oursin (the oyster and chestnut man), came nightly from the little bar of André, the coal man, after the split in our street between adherents of the Right and Left when Monsieur Henri sold his hotel. That meant that the blue-eyed Alice was obliged to stay up each night until closing time, 2 A.M., or later. André, of course, with his day's work ahead, had to go to bed right after supper.
L'Oursin got his nickname, meaning 'little bear' or 'sea-urchin', because in season he sold those cheap and prickly delicacies. The name fitted him perfectly, much better than Léon Saleil, which appeared on his identity card. He came from a fishing village not far from Perpignan, and years of good eating and drinking, combined with the open air, had given him a globular figure from which hair grew stiffly in profusion. The wine and cognac he had drunk, interspersed with applejack and _marc_ , had given his voice a bucolic timbre, and his powerful lungs lent it volume and carrying power. He never spoke or sang in an ordinary tone but always histrionically, as if he were ringmaster of a circus, introducing his own act.
Each morning he scrubbed himself from the waist up with something like saddle soap, only stronger, and once a week he borrowed a bar towel from the _patronne_ of the Café de la Gare and went to the public bath near the Cluny. But oyster shells are muddy and roasted chestnuts sooty. Also his beard, blue-black and stiff, grew so fast it showed an hour after he had shaved. He wore a turtle-neck sweater, inside coarse baggy corduroy trousers which were held up by a wide blue sash. On rainy days he wore sabots. If the sun shone, he wore leather brogans. Socks he considered effete and useless.
I do not wish to give the impression that l'Oursin was brutish or unmusical, or that mingled with the badinage he shouted was not a lot of common sense. His bulk was forbidding, his costume utilitarian and his means of livelihood was not conducive to fastidiousness. In fact, he looked about as black as the coal man did, except when he lumbered from the bath. His walk made it plain that in his youth he had gone to sea.
The discerning women liked him; the others were mildly afraid of him for no reason whatever except his epic masculinity. Madeleine, the proprietress of the Café de la Gare, kept him roaring with her shrewish tongue when he was attending to his business. Blue-eyed Alice, the coal man's wife, leaned against the bar and simply watched him with an understanding smile, and let him rave. She was the kind of woman who liked to please a man, and understood his needs; so in spite of her drowsiness she was reluctant to send him out into the cold when two o'clock came. L'Oursin was seventy years old and looked fifty. She was forty and looked thirty-five. If he drank too much (for him) after midnight, when they had the bar to themselves, she would gently dissuade him. On rare occasions when she was afraid he would fall in the street if left to his own devices, she accompanied him to his door on the quai a block away. A disrespectful thought of Alice never once crossed his mind. She was the wife of his good friend, André, a man like himself.
Way back in the early 1920s, l'Oursin had seen from an expression on The Navet's face that the latter was afraid of him and, while he had never followed up the advantage, it lurked in his mind. When he chanced to pass The Navet he would take up his full share of the pavement, with perhaps a little to spare. In the evening at the Caveau he would shout down The Navet's opinions if he felt in an expansive mood. Along with the garçon, Georges, he had taken a healthy dislike for The Navet's satellites, Messieurs Gion and the floorwalker, Panaché.
One night, just before the Popular Front election in 1936, when class feeling was high and campaign talks were violent, Alice had such a severe migraine that l'Oursin, although well along in drink, insisted that she close her small bar and go to bed.
_'Alors, fiche le camp, grosse fainéante',_ 'Come on, get to blazes out of here, lazybones' was the way he put it.
The Normandie bar was filled with Jews who had fled from Germany, and while l'Oursin was by no means an anti-Semite, he disliked hearing a foreign language to which he could not reply. The rooms in Sara's hotel, in those days, were mostly occupied by refugees sent her by her rich uncle in the Temple quarter. The uncle had paid for their transportation, in many instances, and kept them afloat while they tried to adjust themselves to Paris and find a way to keep alive on their own initiative. This was hard because the French, feeling the pinch of unemployment, would not give foreigners permission to work and taxed them heavily if they tried to do business.
Passing up the Normandie, l'Oursin saw that the only fight was in the Caveau. So he headed that way. Gathered around the bar were The Navet, M. Gion, M. Panaché, and the neighbourhood dentist, Dr. Roux. As the chestnut man barged in there was a sudden hush in the conversation, which had been carried on in confidential whispers, and the conservative quartet looked away with distaste and murmured when l'Oursin bellowed lustily:
_'Bonsoir, Messieurs!'_
Only Georges, the Serb, looked pleased and stroked his wide moustaches.
The Navet and his cronies hoped that the chestnut man would swallow a quick one and beat it, which might have been l'Oursin's first intention had he not seen so clearly that the Right was eager to be rid of him. Anyway, he spread himself over a generous section of the zinc, lighted a particularly vile cigarette, and asked for a shot of red. Georges grinned and poured out a large tumblerful from the high-priced bottle, charging only the price of lowgrade Pinard. No one spoke for as long as a minute. The Navet tried to look unconcerned. He would have liked to leave the place, but in front of his satellites, especially the dentist who had good connections, he could not afford to appear timid or undignified. Then l'Oursin started talking to Georges. The parties of the Left, he said, at last had got together. They would win the election and start a house cleaning in the ministries. Almost anybody, even in the lousy prefecture, might find himself out of a job, the chestnut man said.
Then he spread out a little farther, jostling Panaché ever so slightly, begged his pardon with elaborate politeness, and treated the company to another heavy silence, broken only by the ticking of the wooden Swiss clock. Sweat began to show on The Navet's forehead. The dentist paid for his unfinished drink and, after shaking hands with The Navet, made his getaway.
L'Oursin resumed his talk about the Popular Front, and what Blum would do when he got the premiership, with the working men behind him. He wouldn't break his promises like that _salaud_ , Tardieu.
The Navet could stand it no longer. The veins on his forehead stood out, and he swelled like a pouter pigeon.
'Monsieur, you exaggerate,' he said, turning to confront the chestnut man, who broke into such a roar of laughter that the watchdog in the carpenter shop next door started barking.
The chestnut man paid not the slightest attention.
'Blum is a gentleman,' he continued, pretending not to notice the effect of his words. 'He'll put through the forty-hour week – [louder] _the forty-hour week,_ and a law to protect the unions, so the dirty skunks can't fire the committees. The minimum wage...'
'Do you know what that will cost? Twelve percent, Monsieur,' said The Navet, white with rage.
'Who'll have to pay?' l'Oursin asked, but directly of Georges, who shyly disclaimed any knowledge.
'Monsieur!' piped The Navet. He was hopping like a snap-dragon and waving his arms, but the chestnut man remained as if unaware of his existence.
'You don't know who'll have to pay?' l'Oursin demanded of Georges.
Georges sweetly shook his head and wiped his moustaches.
'We'd better go,' Panaché said in an undertone to Gion.
L'Oursin began describing the employers and bankers who'd pay the extra twelve percent, and take fifteen percent out of the public like the stinking bastards they were.
'Stay,' said The Navet to his two supporters. 'This place is public.'
'Exactly,' said l'Oursin, glad that The Navet had played right into his hand. 'This place is not only for measly, little pencil-stiffs and cuckolds...'
Georges could contain himself no longer. He tried not to look at The Navet when he burst out laughing, but somehow he made his effort too conspicuous. Everyone knew that Panaché and Gion kept their girls in such a state of submission and spied on them so carefully that they could not possibly have cheated. The Navet had been hit in his most sensitive spot. He had laid traps for Jeanne, beaten and bruised her, given her the third degree for hours on end, and not a shred of tangible evidence had he been able to find. Yet he was aware that somehow she had got the best of him, and that the neighbours knew what he could only surmise.
That night was an active one in No. 32. The Navet had burst into his apartment in a maniacal state, not noisily, but with silent venom. Without taking time to remove his coat and hat, he had rushed to the bedroom, switched on the light, torn the bedclothes off his wife as she lay sound asleep and accused her as she opened her eyes. He had caught her at last, he said, and knew everything.
'Don't talk so loud. Eugène will hear,' Jeanne said.
'You admit you've been a whore,' said The Navet, burning with incredulous satisfaction and triumphant rage.
'I've never accepted money,' Jeanne said, coolly.
The Navet lost all reason. Grasping a large blue vase, he shattered it on the floor. He began to throw Jeanne's toilet articles at her, perfume atomizer, box of powder, lipstick, mirror. The latter made a gash above her eye.
'Tell me his name,' shouted The Navet.
_'Penses-tu,'_ said Jeanne. (Imagine!)
He began to yell and rave, advancing with a trunk strap on which was a heavy metal buckle. Jeanne screamed. Windows were flung open, upstairs, across the street. The footsteps of Officer Masson echoed hurriedly in the street below. From the pavement l'Oursin was shouting:
'Sure. You'll beat up a woman. Come down here. I'll show you. I'll fix you up for Tardieu! '
'What's up?' cackled Madame Absalom.
'The Navet thinks he's _cocu_ ,' roared the chestnut man.
'Who doesn't?' asked the shrewd old woman, reaching for a shawl.
'Less noise. Chiappe'll hear you,' said Officer Masson, addressing himself to l'Oursin and Madame Absalom and disregarding the diminishing sounds from The Navet's apartment. The chestnut man lowered his voice to a whisper; Madame Absalom merely chuckled; and the neighbours, whose heads were protruding from various windows, talked less and listened harder as the commotion abruptly ceased with a scream and a thud.
What had happened did not leak out until the following day, through the sensitive grapevine of the servants. Eugène, the fat son, who had always sided with his mother against The Navet, had picked up the crockery umbrella stand in the hallway, the only weapon that came to his hand, and had floored his father from behind as the latter was lashing Jeanne with the strap and buckle.
'After all, he's his father,' said Mme. Durand, the florist, who, being virtuous although a hard employer, sided with The Navet because she detested pretty women and feared the Popular Front. Alice, the coal man's wife, blamed herself for l'Oursin's drunken exhibition of himself and took him to task quite severely. She had heard much talk around her little bar of how the Left, when Blum got in, was going to help the working men. She knew all too well how badly the working men needed help. Nevertheless, she was timidly conservative and afraid of reform; so she kept her huge and gentle husband out of all political movements and wished she could do the same for l'Oursin, Monsieur Frémont, Pissy and the rest of her radical customers. Since Pissy had turned Communist, Alice served him with the same ready smile, but she chided him when he spoke against the Church which she attended perfunctorily, although she sent little André to the public school.
In The Navet's home, matters had reached a stalemate. Dr. Clouet had taken a few stitches in the back of his scalp, and as long as the adhesive showed, The Navet went to and from the prefecture via the place St. Michel instead of walking the length of our street night and morning. Eugène, who believed he was now his father's match in strength, started taking boxing lessons secretly in order to improve his chances when the combat came. Jeanne, who was welted but not badly hurt, continued to meet her Persian at the Café Cluny two blocks away. Of course, the difference was that The Navet had positive knowledge of what he had long suspected, and still could not find out the name of the man who had dishonoured him. That he did not throw Jeanne out into the street convinced everyone in the neighbourhood that he had, as Eugène contended, misappropriated funds from Jeanne's dowry and could not replace them in case of a showdown.
The chestnut man lapsed into ordinary correct behaviour for a while; the conservatives were not molested as they gathered nightly in the Hôtel du Caveau. The Socialists held forth in the Café St. Michel; the Jewish refugees scurried in and out of the Hôtel Normandie; and because Milka, the local leader, had her dinner with Stefan and Pierre Vautier _chez_ Daniel, just around the corner in the rue de la Harpe, visiting Communists and comrades from other quarters began to think of the little Dalmatian restaurant as a safe and comfortable rendezvous. Neither Daniel, an athlete and businessman, nor Madame Berthe, his demure wife in black, was alarmed at this, since Milka's friends always paid their bills, were seldom drunk or noisy, and formed a steady nucleus for their growing clientele. There was still a friendly and neighbourly feeling in the rue de la Huchette, but class alignments became more sharply defined. It was as if a hand of cards that had been dealt at random had been sorted into suits.
It took the elections of April 26th, the overwhelming Left victory that provoked fascists everywhere to turn against a democracy they could no longer dominate and control, to draw the class lines sharper.
The Popular Front consisted (reading from left to right) of Communists, Socialists and the misnamed Radical Socialists. These parties got 381 seats in the Chamber, as against 237 for the Right. They were pledged to a programme of social reform. Léon Blum, a well-to-do Jewish aesthete and scholar, with prosperous business interests on the side, became Prime Minister and formed a Cabinet of Socialists and Radical Socialists (led by Herriot and Daladier, whose Stavisky connections seemed to have been pardoned or forgotten by his party and the public). The Communists promised to support Blum, but would not join his Cabinet until they had a chance to see him in action. Their numerical strength in the Chamber had risen from 10 to 72.
Blum had been converted to socialism by Jean Jaurès, and with him had founded _L'Humanité,_ the socialist organ that had become Communist in the middle twenties. His elegant French was admired by Hyacinthe and Mme. Berthelot. It was less effective with factory hands or railway employees, but the workers respected him and cheered him without following in detail what he said.
One evening just after Blum's occupation of the Hôtel Matignon (the Premier's headquarters), the Satyr failed to come home, and next morning the papers were filled with violently coloured accounts of the first sit-down strikes. In scanning the list of factories, department stores and mines affected, I noticed the name of the restaurant in the Bois de Boulogne where the Satyr was assistant chef.
That same morning, in the concierge's lodge at No. 11, a bitter argument took place between M. and Mme. Frémont, who ordinarily were affectionate and in accord. The pale blonde Yvonne, dressed neatly for work, handbag in hand, stood by to wait tearfully for the outcome.
'You can do as you please and lose your job and go to prison,' Mathilde Frémont said to her husband. 'My daughter shall stay at home today.'
'No daughter of mine will desert her fellow workers,' said Frémont, and, turning to Yvonne, said: 'Go – and stay until it's over.'
Madame Frémont tried to clutch at Yvonne's sleeve; Frémont, more brusquely than he had intended, jerked her arm away. His face suffused with anger, he repeated to his daughter: 'Go.'
Sobbing helplessly, Madame Frémont sank down on the bed. The postman glanced at her with pity a moment, shrugged his shoulders, picked up his uniform cap and started down the street.
Yvonne had just recently got a job as sales girl in the Galeries Lafayette, which enabled her to dress more attractively and help increase her own dowry, which in 1936 had reached the sum of 6,000 francs ($240). She had heard some of the other girls say there was to be a sit-down strike that day and had asked her parents what to do.
The sit-down strikes, although none of them occurred in the rue de la Huchette, and only the Satyr and the gentle Yvonne were directly involved as participants, shocked every inhabitant. While the movement spread and the Government, bewildered, was unable to decide how to act, everyone in our street took sides, with increasing tenseness and excitement and flaring animosities. The right of property had been attacked and was not being officially defended, with blood and iron and discharge slips and broken heads and funerals. That the sit-down strikers were acting in an orderly fashion and had been careful not to destroy or steal seemed to make the concerted demonstrations more ominous. At first the Communists were accused of organizing the movement, until it spread so far and had so many adherents that the red baiters could no longer admit the reds had so much power.
The Navet and his group were yelling for martial law and an overthrow of Blum by the army and the Right. On one point, the street was unanimous. The strikes were illegal. The strike sympathizers, in the minority, smiled and said 'What of it?' whenever this argument was advanced as conclusive.
In the rue de la Huchette, the men and women who came out frankly in support of the 'sitdowns' were: Henri Julliard; Georges the _garçon_ ; Thérèse, former cook; Hortense Berthelot; Léonard, the accordion player; Milka, Stefan and Pierre, in a block; Noël, Monge and the Satyr (who sat and struck); Madame Absalom, who relished novelty and illegality; Odette and Jean in the dairy shop; and Colette the delivery girl; Frémont (not his wife); Officer Masson; Madame Mariette, Mireille, Suzie and little Daisy, of _Le Panier Fleuri_ ; Sara, Guy, Louis the one-armed _garçon_ , the dog, Mocha, and all the refugees in the Hôtel Normandie; Mme. Julien, the barber's wife (but not the barber); Maurice of _La Vie Silencieuse;_ Pissy, the railway employee; Nadia, the beautiful model; Hyacinthe, the beautiful young actress; the roaring chestnut man, and l'Hibou, the tramp.
Since the same sharp alignment held intact through the crises that followed, and persists even today under invasion and persecution, I am listing the members of the other faction, omitting only the listless and indifferent and sub-normal who were capable of no affiliation and who had no tangible opinions.
The Navet was the most vociferous; Father Desmonde and Father Panarioux were more influential. Other rightists follow: M. and Madame Trévise and the drudge, Eugénie; M. de Malancourt; Judge Lenoir and Anne Goujon; Dr. Clouet; Dr. Roux; M. and Mme. Corre, both elder and younger; the religious publisher; Alice, the coal man's wife; Gion of the music shop and Bernice; M. and Madame Durand, the florist; the tailor, M. Saint-Aulaire; Mme. Joli, cleaner and dyer; M. and Mme. and young Jacques Luneville, of the dry-goods shop; M. Dominique, the stamp man; Julien the barber; M. and Mme. Gillotte, the bakers; Mme. Spook (Mrs. Root), the Englishwoman; Officer Benoist; M. and Mme. Lanier, of the _clandestin_ ; Mme. Frénont; Dorlan the bookbinder; the aged Taitbouts; the Alsatian old maids and the retired Colonel at No. 7; Mme. Claire, at the Caveau; Marie Julliard; Daniel and Berthe Petrovich; the floor walker Panaché; the delicatessen proprietor; Villières, the paint dealer; the old cabinet maker at No. 3; M. Salmon, the butcher; and M. Luttenschlager, who sold church supplies.
# _Of 'Non-Intervention'_
THERE COMES vividly to my memory an evening in November. My friends in France were gathered around me in the Caveau bar to hear about my friends in Spain, who, fighting gallantly, already were doomed to destruction. We were still in the compass of that most terrible of all years, 1936. It was not so discouraging that fascists in every land were scheming and battling for fascism. What else could be expected? What dealt our pre-war world its mortal blow was the supine cowardice and hypocrisy of so-called democrats who played into their hands and sealed the death warrants of countless innocent millions.
France might have recovered from Manchukuo and Abyssinia, the Stavisky scandals and the sit-down strikes and Hitler in the German Rhineland. From the treachery called non-intervention, forced on the weeping Blum and willing Delbos by Baldwin-Chamberlain-Halifax Simon, neither France nor liberty could raise their heads or staunch the flow of life's blood from their hearts.
In October, Italian troops, airplanes, tanks, artillery and ammunition were being rushed to the support of Franco, and German technicians, materials and supplies were freely at the Rebels' disposal. The ruling clique of England had already made its choice and was keeping France and the United States in line. The elected government of Spain and the republican Spaniards were to be sacrificed to the monarchists, medieval Catholic hierarchy, landowners, rich manufacturers, generals (there were 257 of them, and 21,000 army officers), Italian fascists, Moorish mercenaries and Hitler-heiling Germans.
The excuse was 'communism', which did not then exist in Spain, and the slogan was 'war must be prevented from spreading at any cost'. That the cost was the annihilation of free men and innocent women in a rising republic, the surrounding of France on all sides by fascist armies and governments (Germany, Belgium, Italy and Spain), the opportunity for the dictators to train their armies, try out and perfect their equipment and experiment on a helpless civilian population (as at Guernica), and the despair of workers everywhere, did not deter the Cliveden group, assisted by their counter-parts in France, including Bonnet, Delbos, Laval and Pétain.
How far from the chancellories of Washington and of Europe was the rue de la Huchette! How much better informed were my friends in their shops and cafés than the statesmen seemed to be! The fascists of the St. Michel quarter wanted Franco to win in Spain; they wanted the doctrine of fascism to spread, and looked forward to its influence in France. The republicans knew that what was happening to their brothers across the Pyrenees was going to descend on them, and who was behind it, and that Blum, their hope, and the Popular Front, their duly elected bulwark against reaction, were showing the white feather.
In late 1936 French patriots like Henri Julliard, Pierre Vautier, Frémont or Noël had not given up resisting, but inwardly they could not continue hoping, as did Hortense Berthelot, the steadfast Milka, Mariette, Maurice, the budding Hyacinthe or the roaring chestnut man.
In 1936 the night was falling fast and as yet there are no streaks of dawn, no cleavage, no clarity, no consecration.
I had escaped from Ibiza a few hours before the Italians came, on a German mine layer, _Die Falke_. This I managed by representing myself and my wife as neutrals, along with the Spanish leader of the Left, Cosmi Mari, who I said was my cook, and a German girl who passed as governess to my step-son, Peanut. The story of those years in Spain and my reportage of the early days of the war are included in my _The Life and Death of a Spanish Town._ The immediate sequel, in which my fugitive party, ill-equipped with money, clothes or papers, was shunted back and forth between the world's most powerful navies before we landed finally at Marseille, was told, on the evening in question, at the Hôtel du Caveau.
Henri Julliard was back behind the little bar; Madame Marie was sleeping upstairs. The _garçon_ , Georges, had been rewarded for his patience and was happily on the job. As Georges had predicted, the Amances had been unable to make a go of the hotel, and Monsieur Henri had been obliged to take it over. In spite of the financial loss involved. I think Henri was glad to be in his element once again.
His old customers, who had been scattered among the other cafés, all except The Navet's diehards, came straggling back, but the two inimical elements, for and against the Popular Front, did not clink glasses as in former years. The conservatives showed up right after dinner, between seven-thirty and eight o'clock, and dispersed about ten. During those hours, if Mme. Berthelot, Mme. Absalom or Mary the Greek wished to linger in the restaurant, they sat quietly at the tables, pretending not to listen, no matter what they heard. This was easier for the others than for Mme. Absalom, who sometimes flung a challenge at The Navet, who haughtily continued what he was saying, without a glance around.
About eleven, after the Rightists were safely out of the way, the chestnut man, Frémont, Noël, Monge, the Satyr, and often Milka and her two faithful comrades, Stefan and Pierre, would drift into the Caveau and the session would begin. Father Panarioux, although an anti-Marxist, got through playing the organ at St. Séverin, where he had many talented pupils, about the time Mariette of _Le Panier Fleuri_ took her nightly recess. More than once I have seen them approach the entrance simultaneously, from opposite directions, and do a kind of hesitation dance at the doorway, each insisting that the other take precedence, although for different reasons.
'You both wear skirts. So what's the difference?' cackled Mme. Absalom on one such occasion, and the chestnut man led the roar of laughter in which the priest benignly joined.
The situation in France was so similar to that in Spain that my friends reacted to events there as if they were seeing themselves in a dream. Against them was the same line-up, the enemies of the democratic ideal:
(a) the military clique who were fascist-minded.
(b) the bankers, large employers, and landlords.
(c) the reactionary Catholic clergy.
(d) Italy, Germany, Portugal and Japan.
(e) a vengeful subject race in Africa.
(f) a deposed aristocracy.
The Spanish military rebels were not as powerful as the corresponding group in France. They struck because they had more support from abroad and a more helpless opposition. Relatively, the Spanish capitalists were as strong as the industrialists and financiers of France. The Spanish clergy had never been put in its place, as had the French. Neither had the Spanish aristocrats. The Germans and Italians did not want France to be fascist and therefore better organized for resistance. The time had not come to wipe France out entirely. Spain was the logical first step in European conquest, sealing the Mediterranean and threatening the Channel, opening the road to Africa.
By the time I reached Paris from Spain in November, the republican element in the rue de la Huchette was in profound discouragement. Franco's failure to seize power, as he and the dictators had planned, was not considered a defeat, and every acre of territory his Moors overran was chalked up as a victory. That Madrid, Valencia, Alicante and Barcelona were still in the legitimate Government's hands became day by day less impressive, as Italy stepped in, then Germany, then Portugal – and then England.
The gloating satisfaction of the enemies on the street – there was no further use for pretending the existence of a 'united' France – was hard to bear, and fanned the ill-feeling that was transforming the formerly charming and harmonious neighbourhood into two hostile camps, one already triumphant, the other resentful and desperate.
As Franco took Toledo, continued the defence of the Alcazar, made possible simply because the Government had no artillery, and the rebels advanced nearer to Madrid, The Navet grew bolder. He smiled, waved patronizingly to republicans along the street, and encouraged other fascists to come out of their shells and breathe more easily. The first to respond was Mme. Durand, the florist, whose customers were all entrenched against a popular regime. The girl who worked for her after she had discharged Amélie, then the lame Jacqueline, was crying one morning, after seeing in the paper a picture of some dead Spanish children, killed by Mussolini's intrepid bombers from Majorca. Her eyes were blurred and she made a mistake in change. The cash did not balance that night; Hélène, the tender-hearted clerk, could not make up the difference. Madame Durand dragged her, accusing her of theft loudly the while, to the police station at the corner of the rue du Chat Qui Pêche. Little Colette, the dairy girl, a friend of Hélène, tried to find out what was the matter and Madame Durand slapped her. Colette dropped the bottle rack she was holding and dragged the screaming florist from the station, while Officer Masson hopped ineffectually around and the sergeant bellowed for order. Before she was subdued, Colette tore out a handful of Madame Durand's crisp hair and raked her cheek with fingernails. Colette was arrested, her socialist employers bailed her out and hired a socialist lawyer. The night after Madame Durand recovered damages amounting to fifty francs, her plate-glass windows were broken with paving stones at an hour when both Hélène and Colette had airtight alibis.
Had not Franco's forces been drawing closer each hour to the suburbs of Madrid, the tension in our street might have abated. As it was, the anticipation of easy victory and the prospects for a similar triumph at home goaded those who had property or privileges endangered by the Popular Front into a spontaneous show of force against their neighbours on the losing side. The inhabitants of the rue de la Huchette, for the most part narrow and egocentric in their outlook, like people everywhere who move in restricted circles, did not realize that their line-up extended over all the continents, representing two irreconcilable ideologies about to tear the world apart in the act of devouring each other.
One evening in the course of those terrible days in November, when Madrid was hanging in the balance and free men everywhere had become Madrid, a young man entered the Caveau bar in khaki. He was not a prepossessing youth, and his suit was not exactly a uniform. He had no cartridge belt or gun, and only an ordinary cloth cap, a conspicuous plaid with a long sharp visor.
_'Mais, Antoine. Tu es tout à fait en militaire!'_ (But, Antoine, you're rigged up like a soldier!) said Henri Julliard.
The chestnut man spilled a little of the red wine he was about to drink and set down the glass, embracing the embarrassed young man like a bear.
_'Tu vas te faire casser la gueule là-bas?'_ (You're going to get your face smashed in down there?)
Young Pissy nodded. He was neither shy nor bold, and certainly not excited or emotional. What he had decided to do had been the result of two weeks' meditation while tending a machine in the Renault factory up river.
His life did not pass through my mind in an instant, like that of a person drowning, but my first view of him returned like a flash to my mind. His father, then as now a railway worker stationed in the Gare St. Lazare, had been holding him over the gutter near the west end of the street, and, blinking absently at the uninspiring passers-by, Antoine had been pissing. I had seen him, a pale schoolboy for whom his mother bought one egg every Wednesday and Saturday, _chez_ Odette and Jean. The parents had had no eggs, being fully grown and not needing them.
Antoine, knowing I had just escaped from the fascists in Spain and how I felt about it, looked straight at me and smiled.
'When do you leave? – Excuse me,' said Milka, in a business-like way. She would have torn off her own ears and slept with Georges Bonnet for the chance Antoine was taking, but instead she jerked her own ridiculous cap down farther on one side of her forehead. The 'Excuse me' was intended to convey that she knew the orders were not to be divulged. The Blum Government had not yet posted sentries to prevent republican Frenchmen from going to fight with the Spaniards, but no permits to travel were issued if it was known that the traveller was going somewhere the Germans and Italians might not approve of.
I beckoned for Antoine to step aside with me, not knowing what to say or how to say it. Of the men and women in that room, only I knew what he was headed for.
'You know you're likely to be bumped off?' I asked. 'Things are tough down there, and they won't get any better.'
He nodded. 'Sure,' he said.
Pierre Vautier was standing very still, erect, almost at attention. He was staring at Antoine as if he were a ghost. I could almost see the working of his mind. He had also seen Antoine playing on the pavement with his father, who, with a tray and glass could imitate a drum, who told of a horse named Senator he had ridden in the cavalry. Pierre was wondering why this lad, whose pimples were clearing and who was filling out well after a lanky, stringy youth, had thought of the right thing to do while Pierre, with all his education and culture, had missed the obvious. I saw Pierre withdraw quietly and leave by the side door, and I knew that he would be with young Pissy on the train for Perpignan. Stefan was a little slower in making his decision, about ten minutes slower, since he had come to depend on Milka to tell him what to do.
There was no demonstration when the three volunteers went away. Pissy the elder, Milka, the chestnut man, and, hobbling at my side, Madame Absalom accompanied them from the Caveau bar to a taxi in the place St. Michel. Stefan was slightly drunk, Antoine was sleepy and Pierre self-conscious.
'Cut the throats of the macaronis,' Madame Absalom said. She disliked Italians slightly more than the rest of the human race. But under her arm was a package she shoved crossly into the taxi when the men had entered and were about to he driven away. She never mentioned what was in it, but Pierre wrote me a few weeks later that Absalom's woollen muffler had served as a tourniquet.
While Madrid was making her heroic stand, Englishmen of the ruling class were helping to put non-intervention across. Only one Frenchman might have stopped it. His name was Blum, and he failed to act, or rather he acted like a craven. It is all very well to say that he might have believed he was keeping France out of war. War is bad, but it is better for self-respecting men to die while they still feel like men than to become cowards and hypocrites and the laughing stock of an unscrupulous enemy who will make them fight or enslave them after they are demoralized.
The British leaders decided on an embargo against sending arms, planes, tanks or ammunition to 'either side' in Spain, knowing that the republicans were represented by the legitimate Government elected by popular will and that Italy and Germany, through Portugal, were supplying and would continue to supply the rebels with everything they needed, including fully equipped units of troops and technical advisers.
The Spanish Government could get supplies only through France, even if they were sold to Spain by Russia. The British policy, in effect, was to permit Franco to obtain, without putting up cash but by mortgaging future Spain, all the arms and soldiers and food he needed, while the republicans were to be shut off from supplies and slaughtered. Not only did the British plan this chicanery, but they forced the French to take the initiative, under pain of a double threat:
(a) a refusal to guarantee the eastern frontier on the Rhine.
(b) a devaluation of the franc, controlled by the London exchange.
In other words, an invitation to Hitler to dominate France and set up a fascist rule, and the ruin of the Popular Front Government, which would fall if the franc collapsed.
As if this were not enough, the British coerced twenty-six other nations into signing the non-intervention pact, including Italy and Germany. The former celebrated the agreement by landing 5,000 troops in Cadiz the day after it was signed, and the latter by persuading the rebel General Mola to swing his offensive north, where the minerals and coal were that Germany needed. Who cared about Madrid just then? Aggressors, the world over, were given _carte blanche._
It will be hard for future generations to credit the fact that while the rue de la Huchette and the rest of the world were squaring off for a life and death struggle, the merchants of France and their politicians were planning a World's Fair. This was conceived originally to revive the tourist trade which had dwindled in Paris since the American depression. Shoddy exhibition buildings were erected in the Champ de Mars and complicated systems of entrances and raised passageways were built, until the quarter around the Trocadero and the place de l'Alma looked like the New York subway above ground and exposed to view. Just below the old theatre near the main gate, the Soviet exhibit, housed in an ultra-modern building and topped with a rather bad statue holding a star aloft, faced the Nazi entry.
The fact that many needy Jews were able to get temporary employment enraged The Navet to the point that he spent most of his evenings at the Fair, counting them and making remarks they could overhear if they were not too busy. The restaurant in the Bois where the Satyr was second chef had a branch near enough to the Rumanian and Czech exhibit so that French visitors who did not care to risk foreign food, but liked foreign music, could hear the gypsies play violins and tympanums on one side, while refugees from Prague played Strauss waltzes on the other.
That the Fair was a failure was evident from the opening day. The only exhibit that attracted any permanent attention or has survived was Picasso's mural called 'Guernica', which only a few artists and labourers could understand. Only the Germans seemed enthusiastic. Of course, the French Government lowered the bars for tourist traffic and admitted anyone without question or surveillance who said he came to see the Fair. On the boulevards and avenues of the Right Bank, one heard German more frequently than French for a while, and the square-headed, owl-like Nazis, all with guide books and cameras, swarmed methodically from one end of the city to the other, and took long tours through provincial France.
In those days of 1937, no one had heard the term 'fifth column' except a few Spaniards in the region of Madrid, where Franco had boasted that he would find in that city, to support the four columns of his quadruple attack, a fifth within the city limits. Nevertheless, it was the Exposition that gave the Nazis their chance to establish and organize their supporters, look over and survey the ground they were soon to occupy, and honeycomb France with spies and traitors. This may have been in the minds of the French officers or members of the Sûreté Générale, but none of them protested openly. The Germans were well behaved, and seemed to have plenty of money. As Hitler had intended, the bourgeois French were impressed and began to whisper that the Führer was, after all, looking after his own and to express quite freely the wish that France had such a man.
Not many of the German tourists wandered into the rue de la Huchette. A few of the most thorough did, however. A trio of them, all men and all cropped closely and wearing rimmed spectacles, peered into the Caveau one day when Milka was there. When one of them asked in halting French if there were any points of interest near by, Milka spoke up in good German. There was nothing worth seeing she said. They had wandered into a slum where frequently the housewives dumped pisspots out of the windows. They had better keep their heads up as they walked back to the place St. Michel.
The three Nazis nodded gravely and thanked her. One of them scribbled a word or two in his notebook, and as they passed along the street they walked rather hurriedly, glancing uneasily towards the upper windows.
# _A Dead Man on the Pavement_
AS THE WAR IN SPAIN went worse and worse, and it slowly dawned on the republicans, even the honourable Henri Julliard and the hopeful Mme. Berthelot, that the Italian and German invasion was to be condoned by France, the enemies of the Popular Front wore an air of relief and satisfaction. My friends sank deeper in despair.
Pierre Vautier, who had just fought at Jarama, wrote me:
_Cher Elliot,_
It's wonderful to be surrounded by noble people for a change. As for me, I am still without faith. Even in the midst of a battle, I am haunted by the conviction that decency and unselfishness are dreams from which men are forcefully awakened or which end in oblivion.
I cannot say what my comrades felt or thought when they started out of a ditch and, rifles in hand, began to trot across a field. There were a few bare fig trees, some rocks, a rolling and desolate terrain. I saw, two hundred yards away, the flash of rifles, a machine-gun, heads and shoulders appearing and disappearing above a sand-bag parapet. The enemy. I heard the whine of bullets and the sharp, insistent rat-tat-tat. St. Cyr! I had not heard a machine-gun since my miserable days in school. I began to be aware of an undertow that slowed my progress forward, a slowing down of time. Each clod of earth, tuft of grass, ping of bullet, slap of feet on turf became distinct. I found myself standing quite still, looking at the smallest almond tree I had ever seen, thin, helpless and awkward, like a colt. Elliot, it was in blossom. Two blossoms. The sight of them made me cry.
'Come on, _mon vieux_ , they'll shoot you.' It was the voice of one of my American comrades. I roused myself, started trotting again and, as I ran, discharged my rifle. It slammed viciously against my shoulder.
'Get down, you fool,' another comrade said. He must have been French because I did not, as in the instance just preceding, remember your appalling accent. God, what a hash is one's mind!
'Get down!' This time more insistently, with a blow on my shins of a rifle barrel. It was hot. It hurt dimly, as if I had been anaesthetized in between. Before I dropped, I realized that my comrades were flat on the ground – all except me. One American was clutching his abdomen and hiccoughing blood. Another was dead. How did I know? I cannot say. It was my first sight of a corpse, but there was no mistaking that life was not in that deflated uniform. No blood.
My comrades rose again. So did I. When we got to a ditch, the one with sandbags on the parapet, we stumbled in and my rifle was discharged again; luckily it was pointing in the air.
Later, I could not say how long, I was huddled in a deserted shed which smelled of manure. In my hand was a mug of coffee. Stefan came running in. He was jubilant. A victory. We had advanced under fire, routed the enemy and taken his first line of defence. His second line he had given us free of charge. What will Milka say? How glad she will be! That was Stefan. I did not ask him if he had remembered to keep trotting, or had aimed before he fired....
Elliot, three nights now I have lain awake because of the cold, and have been sure that I love Milka. Can that be possible? I don't mean that I love her solicitude and integrity. I am gnawed with regret that I have not clasped her knees and kissed her all over. Twice I dreamed of her and she became poor Mary. I beg of you, in the name of our friendship, do something for Mary. Why is it, here in Spain, I am aware of everything I have done or left undone? Was there ever such a fool?
Two days later. Antoine has been taken to Villa Paz with a bullet through his jaw. We have heard that the surgeon is an American. God, I hope so. Tell M. Pissy, if he hasn't heard already. You will know what to say. He will know how to act.
Elliot, I have slept on a concrete floor with my head on a sill and water running down my neck. I have eaten spoiled tomatoes cooked in rancid oil. I have covered with her skirt the body of a woman, ripped with a bayonet, four days dead. What I cannot stand, mon vieux, are the glad voices and hopeful eyes of the Spaniards and the orations of Comrade M., who prates about victory as if it were baking in some oven and had only to be removed when nicely browned. I shouted ' _Merde_ _!_ ' at the top of my voice – and was sent to the doctor.
Who can possibly fail to see that we are _foutus_? Not those leprous Socialists or that slimy Blum!
Pierre
I found M. Pissy with l'Oursin and André the coal man. Alice was behind the bar. Pierre was quite wrong. I did not know at all what to say.
'You have a letter from down there?' Pissy asked.
The letter was in my hand. Perhaps he saw the oddly ruled paper on which it was written.
'Yes. Your son got hit – nothing serious,' I said.
'In the belly or the legs?' Pissy asked. The faces of André and l'Oursin, stained and streaked, eyes staring dumbly, seemed suspended in the smoky atmosphere.
'It's shameful. You had no right...' said Alice, eyes hard, lips tight.
'Hold your tongue,' said André, gruffly. She looked up at him in astonishment.
' _Oui_ ,' she said, as if she were in school.
'In the legs or in the belly? It makes a difference,' said Pissy, setting down his drink because his hand was trembling.
'In the head.'
'Ah, the head. Is that letter in English?'
'No, in French.'
I folded over the page and handed it to Pissy. No one spoke. All breathed hard as he read.
'Happily the surgeon is American,' he said, and drank his applejack, wiping off his lips with the back of his hand. 'They're handy ( _commodes_ ), those Americans.'
The news of the victory of Guadalajara reached the rue de la Huchette about eight o'clock in the evening, by radio in the Café St. Michel. Mme Trévise, as bitterly as she distrusted the Popular Front, was more contemptuous of Italians. By and large, the French loathed Italians as thoroughly as the Germans hate Jews, but not for the same reasons or from similar causes. The antipathy of the French for the 'macaronis' was not induced by government leadership and propaganda. It was as natural as the liking for red wine. Of course, Noël, Monge and the Satyr were jubilant. They had had no victories before and were quite boyish and uninhibited. Not knowing what else to do, they drank and called on their friends, up and down the street. The republicans came out of their shells.
Frémont defiantly went to the pitcher where his savings were kept and took out ten francs, looking at Mme. Frémont in such a way that she did not dare remonstrate.
'Be careful, Papa,' said Yvonne, putting her arms around his neck.
He smiled. He still had hopes of convincing his daughter that her mother was a foolish short-sighted woman.
Madame Absalom was by that time definitely committed to the weaker side, not because she believed in socialism or popular government, but because her 'ex' was a toady of Pierre Laval, who practically owned Clermont-Ferrand. L'Oursin was in an expansive mood and had gathered under his wing l'Hibou, the tramp, and the old woman whose name no one ever knew and who thought she sang like Yvette Guilbert. When the crowd left André's place to drop in at the Hôtel Normandie, André, who had taken one or two drinks more than usual, was moved to join his friends. Alice was worried, but made no objection. Her huge husband had shown signs of impatience with her anti-Blum opinions, and had taken the position that Blum was doing the best he could. Milka was attending one of her meetings; she seldom had fewer than three a day.
Instead of turning in at the Hôtel Normandie, which was filled with gloomy refugees, l'Oursin beckoned his followers to continue to the Caveau. It was the hour when The Navet, Gion, Salmon, Dr. Roux and Panaché had gathered for their after-dinner chat. They had not heard about Guadalajara.
Somehow the chestnut man had gained control of his group, to the point that the others were doing as he did, as if they were playing a game of follow the leader. He entered the Caveau with his hearty booming laugh and started singing 'Les Montagnards' at the top of his voice. I heard Noël's firm bass, the off-key voice of the drunken old woman, the whisky tenor of the tramp, Frémont, Pissy and the others carrying the air. Since the bar space was limited and occupied, l'Oursin's group lined up behind them and reached for their drinks over their shoulders. Monsieur Henri looked worried but not disapproving, and Georges, the Serbian _garçon_ , beamed.
The Navet was livid with fright. Behind him, and between him and the door, was the big reckless man he had openly reviled, and l'Oursin was drunk and knew of old that The Navet was afraid of him. The situation seemed to amuse the chestnut man no end.
_'Tu es au courant, toi?'_ (equivalent to 'Have you heard the news, old chap?') asked l'Oursin. The Navet pretended not to realize that the chestnut man was addressing him. He turned to leave the café, but l'Oursin was in front of him. The latter roared with laughter, spilled his drink on The Navet's derby hat and repeated his question.
'What news?' asked Monsieur Henri, to divert l'Oursin's attention.
'The victory!' roared the chestnut man. He burst into the Marseillaise, half his companions joined raggedly. Panaché started for the side door and, in doing so, jostled Mme. Absalom. The chestnut man grabbed him by the shoulder and spun him around.
'I beg your pardon,' tardily said Panaché to Mme. Absalom. The chestnut man roared approval.
In a dim corner, seated alone at her table, Mme. Berthelot was smiling. The tableau, indeed, was ridiculous. The Navet's crowd was afraid to make a move; the popular front was circumspect enough but showed no signs of relenting. They edged close to the bar, increasingly careless about crowding their opponents, stepping on their well-polished shoes or staining their clothes with wine and alcohol. André, the coal man, trying to find the W.C., stumbled into the kitchen and awakened Thérèse, the cook, who had passed out in her chair. She was a forceful woman, even when half asleep, and insisted that André help her finish the bottle of Pinard on the floor beside her.
As suddenly as he had taken the notion to scare The Navet, l'Oursin decided to leave him in peace and led his cohorts away. The following evening however, the wife of Julien the barber told the chestnut man what The Navet had said he was going to do at the prefecture: have 'the dirty Communists' cleared out of the _quartier St. Michel_. The political rift between Julien, anti-Socialist, and his handsome wife, had not then become public knowledge; so The Navet, while getting shaved, had not been overcautious. The chestnut man waited until eight o'clock; then he swaggered alone and cold sober to the Hôtel de Caveau, entered the bar, shoved
The Navet to one side as if he were a window dummy, reached for the drink that had been in front of The Navet and was about to drink it when Dr. Roux, cane in hand, stepped up to him. L'Oursin's hearty laughter shook the bottles on the shelves. While the dentist's cane played a soft tattoo on his unheeding shoulders, l'Oursin took Dr. Roux' head under one hairy arm and forced it, face downward, into the little sink in the middle of the bar. This was filled with dirty water. The Navet rushed out of the Caveau shouting ' _Police! Au secours!_ ' The dentist followed, dripping, his cane broken. Gion and Panaché had vanished in the short course of the _mêlée_.
' _Vive la France et les pommes de terre frites!_ ' boomed the chestnut man when Officer Masson came in, followed by the Rightists. Monsieur Henri was about to explain what had happened when Hortense Berthelot stepped forward.
'This man,' she said, pointing to The Navet, 'and this one,' indicating Dr. Roux, 'attacked Monsieur l'Oursin, set on him with a cane.'
Georges smiled and nodded confirmation.
'Is that true?' asked Officer Masson of Monsieur Henri.
'Evidently,' said Henri.
The Navet began to splutter.
'I won't prefer charges,' roared the chestnut man, and reverted to the Marseillaise.
'I know where we shall get satisfaction,' The Navet said, leading the dentist away.
That was the last of the Rightists in the Hôtel du Caveau. The Navet and his friends gave all the cafés in the rue de la Huchette a wide berth and gathered nightly in the new place with neon signs across the rue des Deux Ponts. The freshly upholstered back room there became a meeting place, not only for the local enemies of the Popular Front, but others who arrived in private cars, and whose faces were crafty and determined, sometimes exultant.
The exception was the 11th September, 1937. I was in Madrid and received news of the affair on my next visit to Valencia. I had seen no French newspapers for several weeks and had not opened the American papers I found waiting for me. The first communication to receive my attention was a letter from Hortense Berthelot. It had been opened by the government censors and showed signs of having been read repeatedly and with satisfaction.
_Paris, 13 Sept
_
_Cher voyageur,_
Bloodshed at last! A corpse on the pavement of our little street!
The Navet, Julien and the dentist – the three who have become inseparable – came into the hotel last night about 9 o'clock with an inspector of the Sûreté Générale. The latter was not on duty, but our grand _cocu_ made it clear that his friend was armed with automatic and authority. He was looking for the chestnut man, or said he was. Instead he found Milka.
'You dirty cut-throats. You've all found your match. You thought you'd have an easy time, didn't you?' The Navet said to her.
_'Monsieur, je ne vous salue pas!'_ she replied. (Monsieur, I do not care to speak to you.)
At that moment Thérèse the cook came shouting out of the kitchen, a bottle in her hand.
'Don't talk that way to your betters,' she yelled, advancing on The Navet.
'This man is an officer,' The Navet said.
Thérèse took a deep drink of wine, then sprayed it in the face of the Sûreté Générale. The three intruders and the moistened officer retreated, The Navet brandishing his cane. He and his friends are never seen without canes, now. Georges says they have swords concealed inside.
'Don't deny you know nothing about dynamite,' The Navet said to Milka, as he closed the door behind him.
At ten o'clock, Frémont came running from the Café St. Michel. Two buildings had been blown up near the Étoile. Milka hurried out to use a telephone. I could only think of what _le cocu_ had said about dynamite.
This morning _Le Matin_ and, of course, the party journals of the Right accused the Communists. The buildings had been destroyed, with the loss of only one life, that of a policeman. Not only were the bombed premises empty of regular employees but the caretakers had luckily taken a short walk at the exact moment necessary to prolong their lives. One structure belonged to the Confédération du Patronat Français (Employers' Association), the other to the Associated Metal Industries.
_L'Humanité_ attributed the incident to Rightist provocations.
After dinner, l'Oursin and his friends, Pissy, Frémont, the three ex-Radicals (Noël, Monge and the Satyr), decided, for some reason I do not know, to venture across the street and annoy The Navet in the new café. Some kind of meeting was in progress, attended not only by our neighbours, including the barber and Monsieur Saint-Aulaire, but the Prefect of the Seine. Seeing the Prefect was closeted with the Right, l'Oursin did not persist, but in re-crossing the street he encountered a gang of young men, former Croix de Feu, now some political party with another name.
'Down with Moscow!' 'Death to Communists!' they were shouting, and other remarks about the _Front Populaire_ not convenient to write down. Without hesitation, l'Oursin picked up one student by the legs and began knocking down others, using the first as a sort of bludgeon. The free-for-all that resulted involved not only Frémont, Pissy, the aging Satyr who did yeoman service, but the barber and the new café proprietor, our own mild Georges and the musical pimp-macquereau from the Bal St. Séverin. [That was Robert.]
Because of the proximity of the Prefect, no doubt, police cars with sirens charged into the _mêlée_. Our friends scattered into the rue de la Huchette, the dishevelled Right contingent formed on the pavement in front of the new café. There was much screaming and opening of windows.
When the confusion subsided, I saw, sprawled on the pavement directly beneath my window, a young man, flat on his face. He was dead. Stabbed once, deeply, in the heart. More police came on the scene; all night there was searching and scuffling of feet. Georges had been bruised but not cut, and his razor, so often wet, was dry. Julien the barber received only a black eye until he got home, where his wife split his head with some hair-curling device and expelled him forever from her bed.
Monsieur Henri suspects that Robert did the stabbing but no one arrested him, since he has no political affiliations. The chestnut man has served notice that no Cagoulard, as The Navet and his associates are now called, shall use the rue de la Huchette with impunity after dark. The sergeant gave him a severe talking to, but our neighbours of the Right keep very much out of sight just now. There are rumours of a plot, not by Moscovites, but financed by Michelin and some other industrialists. Lefarge [the old woman at the prefecture] is heartily in sympathy with the Cagoulards and hints that Pétain and Weygand are in it, too. Laval and Tardieu are implicated; so is that count with the bizarre Italian name, and, of course, de La Rocque.
Milka tells me the dead student was the son of a wallpaper manufacturer. I cannot forget how he looked on our pavement.
Your devoted friend,
Hortense
P.S. (the 14th) Lefarge is a fountain of information. It seems the Government has found an arsenal in Clermont-Ferrand and has questioned several hundred members of the new Ku Klux Klan, meanwhile afraid to detain the principals who are out on bail, or publicly denounce the hero of Verdun and his former chief of the secret service who is one of the ringleaders of the plot.
The Prime Minister is moving heaven and earth to hush up the scandal and minimize its importance. Only _Ce Soir_ and _Humanité_ are triumphant, and, of course, Milka, in her energetic way.
We have no more honour, no more authority.
Young Pissy has malaria. His ward was not screened. Perhaps you saw him. If so, write. His mother no longer tastes the little food she swallows.
PART THREE
# _The Death of a Nation_
# _Between Relief and Shame_
THE POPULAR FRONT ELECTION, April 16 to 21, 1936, was the last held in France, as the Popular Front election in February of that same year was the last held in Spain. In France the civil war that broke out when Blum took office was not conducted with armies and explosives, but the French anti-republicans were promptly aided by foreign fascist Governments which planned to dominate them openly later, when democracy had been destroyed. The Cagoulard movement was financed largely by Italian and German funds, and Blum's Government (whether Blum or Chautemps was the premier) was so demoralized by the farce of non-intervention in Spain that the widespread plot to overthrow the Republic was hushed up. The leaders went scot free, and the political murders the hooded conspirators had committed were not investigated.
The Right, in France, was able to take over without the formality of a general election by means of a politician named Daladier, a baker's son who went to school under Herriot and later undermined his teacher in the Radical-Socialist Party. Daladier's record, on reexamination, seems to have fitted him ideally for Munich. Briefly, it is as follows:
He first became Prime Minister, to succeed Paul-Boncour's brief regime, on January 30, 1933, the same day that Hitler first became Chancellor of Germany. France already was bankrupt and disrupted, but not hopelessly.
Daladier lasted until October, and showed no grasp of either the internal or general European situation. His idea was to cut salaries and increase taxes in the lower brackets. His Cabinet consisted entirely of members of his own party, and his policies were attacked consistently by Léon Blum. His party was supported by Stavisky funds.
In January, 1934, Daladier took over for the second term of office, just in time to order the police and military to fire on the citizens who were rioting in protest at the Stavisky exposure. He lasted seven days, and in that time earned the nickname 'the murderer'. The popular outcry against him frightened him so badly that he promptly resigned, making way for Doumergue.
An outsider not familiar with French politics might have thought that Daladier was through. Not at all. He got himself elected by the Popular Front (Communists, Socialists and Radical-Socialists) when Blum, after non-intervention, resigned, a broken man, in April, 1938.
That date marks the second great victory for the Right in the French civil war, the first being the support of Franco in Spain against the Spanish republicans. Daladier, while the rest of the world was worrying about the Czechs, busied himself with the repeal of the labour laws and social reforms enacted under Blum and Blum-Chautemps.
'Nowhere else but in France and Mexico,' Daladier said, 'do employees work only forty hours a week.'
The Communists, Socialists and some of his own Radical-Socialists denounced Daladier for his _volte-face_ , but the parties of the Right warmed to him instantly and gave him the support he needed to remain in office. To the enemies of the Popular Front Daladier seemed to have been transformed for their purposes by heavenly intervention. Daladier left French foreign affairs entirely to Chamberlain, whose umbrella had already become the symbol of humility and double-dealing throughout the world. If the workers would work longer hours for less money, Daladier said, France would be safe; the national defence would be adequate.
Before he put across the repeal of the Blum reforms, on the basis of which the Congress, still sitting, had been elected, Daladier (having been left out of the conference at Berchtesgaden because, as he put it, 'some other powers might have wanted to be represented if I attended') was invited to Munich, with the result which the world knows now and all but the imbeciles knew then. American movie-goers will remember, standing uneasily on the edge of the group consisting of Hitler, Mussolini, Chamberlain, Goering and others, a short unprepossessing man who looked like Napoleon, only stouter, and who seemed to be trying to maintain his dignity and keep out of everybody's way. That man was Daladier, representing the Third Republic. He signed, when the time came and when he was told, on the dotted line. What is noteworthy is that of all those present he was the only one whose country had pledged itself in writing to stand by the Czechs and defend them against aggression. Hitler had never promised to guarantee the Czechs against attack; neither had Mussolini _or_ Chamberlain. The British were not committed irrevocably. Only France.
When, returning to Paris, Daladier saw the field at Le Bourget crowded with people, he thought he was going to be mobbed and was afraid, according to the story that spread through all France.
'I am torn between shame and relief,' said Léon Blum.
So were my friends in the rue de la Huchette, whose husbands and sons had been mobilized. Even to those who have not seen it or felt it directly, war is such a terrible thing that any immediate avoidance or postponement raises hopes and gratitude in their hearts. What it means to a generation which has already suffered it is many times more poignant.
The effect on Daladier of sudden popularity, in place of the contempt he had suffered because of the February riots and his taint of Stavisky, was to inflate the man. Because he had signed away the honour and safety of France, he considered himself a hero and was beginning to see himself a dictator.
How far removed are the selfish and traitorous activities of a Laval, a Bonnet or a Daladier, or the cowardice of a Blum, from their victims in a sheltered little street!
A week before Munich, Étienne Corre, son of the retired grocer, was called to the colours and sent into the Maginot Line. He was selected, along with other specialists, because he knew German, which still was in current use along the Alsatian frontier. His sad young wife, with the aid of Monsieur Noël, had been carrying on the business in l'Épicerie Danton for some time and trade had been falling off progressively as times got harder. When Étienne went away, his wife lost her strength and appetite, and, after she had fainted in the store, was persuaded to take to her bed.
In his apartment in the rue du Bac, old man Corre could no longer be content with pacing the floor and escorting his wife to parks and museums. So he and Gabrielle came back to the store and, in the interest of economy, were obliged to dismiss Monsieur Noël. The latter, for want of anything better to do, went back to his taxidermist's shop in the place St. André des Arts. Trade in the grocery store was at a standstill, since no one bought fancy groceries when war was just over the doorstep. Noël's twenty francs a day earned as a grocer's clerk could not be made up in his taxidermist's shop. No one brought cats or dogs to be stuffed when reservists were being summoned to the border to face the German army which had been holding manoeuvres across from the Maginot fortifications.
Throughout the years I had known the rue de la Huchette, I had seldom passed l'Épicerie Danton without stopping for a word with the Corres, especially if I had just returned from a journey. The bug-eyed old Breton, continually puffing at his short-stemmed pipe, was so wistful about distant lands, so appreciative of any travelogue I could throw his way, that his attitude made my adventures seem piquant and important, even to me. That time, although I had just disembarked from the _Normandie_ , he did not ask me about New York or London or Spain.
'You're back at work,' I said.
He glanced uneasily at his wife, who was seated on the stool behind the cash drawer.
'Do you think things will arrange themselves?' he asked. 'What do you hear at the newspaper office?'
I had not been connected with a Paris newspaper for about eight years, but Corre had never been strong on chronology.
Madame Corre, of the alabaster skin, the trim well-rounded figure, the lavender perfume, white well-kept hands and curly light-brown hair, seemed to age in front of me. Her hazel eyes, undimmed since young womanhood, were dull with fright. Her lips were blue. The skin sagged around her determined jaws. Her voice was thin and shrill.
'My son is in the Maginot Line,' she said.
_'Dis donc_ , it's safe down there,' grunted Corre.
A sudden gust of anger distorted her usually placid face.
'It was for that we spent our money, having him taught German. If only he had not studied that accursed language someone else might have been chosen,' she said.
'Who could have figured anything like that?' asked the old grocer, defensively.
'While I was nursing him, you were on the Somme,' she said, her voice rising. Both of them seemed to have forgotten I was still there. 'You were buried in a trench...'
'Our trenches weren't much good in those days,' he said. 'The walls are of concrete in the Maginot Line, two metres of concrete reinforced with rails.'
'And what if all that crumbles? On you there were only a few shovelfuls of dirt.'
'No need to get nervous,' he said. 'Perhaps everything will arrange itself. I read, just this morning, that the Cabinet has been meeting. Perhaps we'll not bother about the Czechs, after all. Is that possible, Monsieur Paul?'
Just then it didn't seem possible, but I hadn't the heart to say so. As I proceeded down the street, I saw signs of panic and uncertainty. The publisher in No. 30 had closed his metal shutters. The windows of the flower shop at No. 23 were devoid of colour and the door was padlocked. Madame Absalom, having heard that I was back, before I got near No. 10, sent Mary the Greek to summon me to her bedside. The peppery old woman, some time between the Cagoulard exposure and Hitler's seizure of Austria, had decided not to get up any more. She had bought some second-hand clothes for poor Mary, still beautiful and tragic at forty, and installed her in the yarn shop, where the Greek madonna did the leg work faithfully while La Absalom cackled orders through a rift in the portières that screened her bed from the front of the establishment.
What impelled Madame Absalom to give her ancient legs a permanent vacation no one ever learned. She simply announced one morning that she was going to stay in bed the rest of her years, and she did. Even more thoroughly than formerly she kept track of the happenings in our street and neighbourhood. She kept Mary jumping and fetching from dawn until late in the evening, and often in the night. She insisted there was nothing wrong with her, except the general lassitude that had poisoned all of France.
I entered her little alcove and pulled up a kitchen chair. I had no news for her, being as uncertain as the rest of the public as to when war was coming. She knew I had been predicting its outbreak all along. But Madame Absalom had a rare item for me. It seemed that Julien the barber was on the list of reservists quite likely to be called. A few evenings before, when young Corre and young Luneville had both received marching orders, Elaine, the barber's wife, had spoken her mind. She had been faithful to Julien, fool that she was, all the years they had been married, including the recent period when she would not let him come near her in bed. There would be war and Julien would be called away, of that Elaine was sure.
'The moment you are out of sight, I shall find a real man,' she said to Julien. 'I shall be his slave. He shall do with me as he likes, all the tender tricks I couldn't bear from you. Nothing that he asks will be too much, or half enough. Do you understand?'
Madame Absalom's mimicry was at its best as she sat up in bed, her wiry grey hair in a tangle, her flannel nightgown flapping as she gesticulated and turned.
'She'll be a hot piece, that one. Some poor idiot won't know what's struck him, _n'est-ce pas?_ She's been saving it up quite a while,' said the gleeful old woman. Then she added, almost wistfully, 'Now why couldn't I have thought of something like that for my 'ex'? He would have bitten off his nails. He would have been beside himself. Ah, well, it's good to see _some_ woman get the best of one of them.'
I could not resist dropping into the barber shop for a haircut, just to size up the situation. Julien was pale and wan; his hands were trembling. Elaine was watching him, covertly, with a mischievous glint in her eye. As she hovered at my side and smiled at me provocatively, I could see Julien adding me to the list of possible undoers. No doubt she let him think the same of every man who entered the door.
'How soon will the war commence in earnest?' Elaine asked me, in a tone quite different from that of the despairing Madame Corre.
'It can't be long,' I said. 'Will you stay in Paris? The stations already are crowded with people running to the country.'
'Not for me, the country,' she said. 'I'm not afraid.'
'And if there isn't any war?' asked Julien, trying to be defiant.
'Then I'll start an offensive of my own,' she said, and looked at me so invitingly that it would have been inhuman not to respond.
In the music shop, Gion and Bernice were taking an inventory. He also might be mobilized, in which case he intended to hold her strictly to account for each article in stock. He had agreed that she was to take out enough from the receipts to buy her food each day, within the limit of six francs (fifteen cents). Bernice, terrified at the idea of remaining in the city alone, in the midst of gas and bombing attacks, could not count or add. She was wishing for the one kind sister in the orphanage who had shielded her, years ago, from the strict mother superior.
From Father Panarioux I learned about the drama that was taking place in the back room of the Luneville's dry goods store, _Au Beau_ _Marocain_. The priest was haggard from incessant prayer and shared with me, his infidel friend and bridge partner, the problem he had taken to his God.
M. Luneville, just turned forty-four, had been an orderly to General de Castelnau, the defender of Nancy, in World War I. His son, Jacques, in 1938, was twenty-one. Mme. Luneville had urged her husband to visit his old chief, who had influence with the General Staff, and obtain for Jacques a safe place behind the lines. The boy was in the infantry. Luneville the elder had refused point blank. All through the other war he had been taunted because he was an _embusqué_. His son was not going to suffer the same humiliation. He would fight like a man, if war had to come, said Luneville, and the boy was of the same opinion.
Both husband and wife had appealed to the priest, who, a fervent patriot himself, could come to no decision.
'Poor woman. This will undermine her faith,' he said. He did not mention that he had asked permission to become a chaplain at the front and had been told that he could not be spared from the organ.
M. and Mme. Frémont, who had never become reconciled since their bitter dispute about Yvonne and the sit-down strike, continued their struggle for the timid girl's allegiance. Mme. Frémont brought in all the newspapers of the Right, which praised Daladier for his stand against the forty-hour week and the unions, and read the editorials aloud while Frémont choked over his dinner.
'Frenchmen will have to choose between the forty-hour week and the one-hundred-hour week imposed by the enemy's cannon,' was _Figaro's_ comment.
'The national defence is another term for the profits of Schneider,' said Frémont. 'Daladier will never fight Hitler, but only the workers of France.'
'Your cronies would rather fight for the Moscovites in Spain than do their duty here,' she retorted.
Without answering, Frémont strode to the pitcher on the shelf and took out another ten francs. His wife began to cry, turning to let her tears fall into the dishpan as she struggled with her growing resentment.
'Be careful, Papa,' said the gentle Yvonne as her father paused at the door.
'Drunkard!' said her mother.
_'Sotte!'_ said Frémont, and slammed the door.
# _Boards across a Doorway_
DALADIER TOOK ADVANTAGE of his popularity just after Munich to repeal Blum's forty-hour week, as a warning to labour that French workmen must work as hard and as long, and for as low wages, as Germans and Italians did in the totalitarian countries.
'If peace is assured in our time, as Chamberlain says, why work overtime to build cannon?' asked Henri Julliard.
'Hitler and Mussolini need the cannon. We'll either sell them, at a good fat profit, or they'll come and take them free of charge,' said Milka.
Milka, however, a true revolutionist of a family of revolutionists, was privately disgusted because of a blunder made by Marcel Jouhaux, head of the C.G.T., or _Confédération Générale du Travail_ , who had announced, two weeks in advance, a general strike of protest against the breaking down of labour laws. A general strike could only be an effective weapon if it came without warning. Give the capitalists, politicians, the press and the army two weeks in which to prepare, and the workers would simply walk into a trap, she insisted, and all of us agreed. It proved embarrassing to Milka a little later when her party leaders added a worse error to Jouhaux's original one. Jouhaux, who could have carried with him at that point the directors of the C.G.T., foresaw that he was going to lose and that Daladier would add to his power at the expense of the underpaid workers, especially the government employees. He wanted to back down and call off the strike. The Communists wouldn't let him; so Milka, having seen the situation clearly, worked hard and faithfully against her own better judgment.
It was then that I noticed the profound change that had come over Pierre. He had come back with the disfigured Antoine after Negrin, the Spanish leader, had, like the gentleman he was and is, ordered the foreign volunteers who had risked their lives for Spanish freedom to leave the country before the débâcle. Stefan had stayed, not far from Belchite, where a hand grenade, exploding prematurely, had blown off his hands and his head.
I remembered Stefan as a gay young student, hypnotized by the headstrong Milka, running her errands, understanding her moods and whims. I had never heard him disagree with her or resent her reproaches or neglect a task she had set for him. His devotion was not to her womanhood, but to her strength, which he lacked. She did not cry when Pierre brought her the news, but nodded grimly. In the months that followed I saw her more than once drop a tear in memory of her disciple and room-mate, but in each instance it was not out of regret that he was dead. She wept when, late at night, after hours of untiring work, she was confronted with some colossal stupidity, some chance remark of a non-class-conscious neighbour, a headline to mislead the geese, a poster about gas masks or a bucketful of sand. At such moments death covered itself with an alluring garment and life was endless and discouraging.
Whenever we met, Pierre was courteous but I could not fail to see that he was avoiding me. I had heard his first uncertainties. He had written me of all his doubts. His contact with the noble Spaniards had uplifted him at first, until he saw what nobility without machine-guns really meant. He had seen the bravest die and the jackals feast on their bodies. He had seen reason stabbed to death and fanaticism drink the blood. The faith and conviction that had eluded him when he was stronger, he seized upon in desperation. There was no more rigid follower or defender of the party line. Like Antoine, Pierre had been disfigured, and like Stefan, he had died.
There was no trace of his battlefield passion for Milka. They spoke to each other curtly, like an officer to a soldier. He obeyed without question, as she obeyed her own superior. They had little use for me. Each evening they dined _chez_ Daniel, in company with other Communists who were as busy as they were. Two of the regulars turned out later to be agents of the Sûreté Générale.
On the eve of the general strike of November, two things were apparent. Daladier, Bonnet and the saboteurs of the Popular Front, including on our street The Navet, Saint-Aulaire, Madame Durand, who had returned from the country after the Munich exodus, and Julien the barber – all were eager that the strike should take place. On the other hand, the non-communist unionists were willing to make concessions and did not want to go through with the premature threat Jouhaux had made. That could only mean one thing. The Government, the Communists _and_ the non-communist leaders all assumed the strike would be a failure.
Why should the Communists want the strike to fail?
Because if it did, Daladier would be sure to take excessive revenge. The workers would suffer, but it would make them more resentful, and therefore more revolutionary.
The workers on our street who had the most to lose, in each case a government job with nearly twenty years of seniority, were Frémont and Pissy. That they would obey the call was sure. When the unlucky day arrived, they were joined by Eugène, The Navet's son, who had a small job in a gymnasium; Hyacinthe Goujon, on her way to be a star; Elaine, the barber's wife, who threatened to walk the boulevard and offer herself to the first presentable man who spoke to her if her husband raised the shutters that day; Louis, garçon at the Normandie; the girls in Lanier's laundry; and the butcher boy who worked for Salmon. Had she not been prevented by an attack of bronchitis Hortense would have risked her job with the others. Of that number, totalling ten, one, M. Pissy, was a member of the Communist Party. Frémont was a Socialist. The remaining eight had no affiliations whatsoever.
Afraid of 'communist' disorders, Gion, Madame Durand, Madame Joli, the cleaner, and Luttenschlager, purveyor of articles of piety, closed their shops. André, the coalman, in spite of the tears of his wife, closed in sympathy with the workers; as did Maurice of _La Vie Silencieuse_ , Monge, the horse butcher, Odette and Jean in the dairy shop, and Monsieur Henri Julliard.
I could not repress a smile as I passed old Dorlan, the bookbinder, working away on orders eight months overdue. I am sure he did not know what was happening outside. Corre came down to open his grocery, then changed his mind and spent the day in the Café St. Michel. Of the taxis usually lined up in front of the Brasserie Dalmatienne, only two put in an appearance.
The bus lines, the tramways and the Metro were unimpeded, and before noon the taxi drivers began to drift back to their places. The tory _Petit Journal_ came out as a handbill, prepared by scabs. Nearly all the newspapers were abbreviated. Still, those of the right proclaimed the strike a failure, while _Ce Soir_ and _Humanité_ exaggerated its success. It was not until the next day or the day after that the news became public to the effect that in the large factories around Paris and in the other important cities, the tie-up had been almost complete, that the ports of Le Havre, Rouen, Cherbourg and Marseille had been at a standstill and that even among the brow-beaten government employees the turn-out had been impressive.
Instead of emerging triumphant, the tories were badly frightened, and while Daladier set all the government agencies in motion to disrupt the unions and play the non-communist element against the small minority of Reds, all the resources of the large employers and war speculators were pooled in a concerted drive. Another battle in the French civil war was in full progress, and again the Germans and Italians threw their weight with their fascist brethren who were fighting the Third Republic.
The Communist Party at that time was second in numerical strength in the Chamber. That does not mean that the Reds were predominant. They were second in a list of nineteen, and all the other eighteen were lining up against them. Daladier tried to outlaw the Communists and disband the party, planning later to arrest the leaders and put them out of action.
When the butcher boy appeared for work, the day after the strike, Monsieur Salmon would not let him enter the shop and refused to pay him the two days' wages due. The boy asked the police sergeant to help him collect, and was referred to a special court for 'commercial disputes'. Madame Lanier locked out the girls for a week and then took them back at a reduction in pay. Their percentage of earnings 'upstairs' remained the same. Eugène, The Navet's son, got his job back without question, since his mother's Persian lover was one of the gymnasium's best customers.
The reason the general strike was not a complete victory for the Left, as the 1936 elections had been, was because a large percentage of the members of the C.G.T. were government employees, receiving less than a dollar a day with which to support themselves and their families. This horde of subhuman victims of a corrupt bureaucracy had been systematically demoralized. They had no security beyond the whims of their superiors, who, in turn, were beholden to secretaries who licked the boots of Cabinet Ministers. Half of the public employees in the C.G.T. were afraid to strike, and on the braver half Daladier, Bonnet and Co. visited their revenge. The Communists again had manoeuvred themselves into an unpopular attitude. With justice on their side, they had jeopardized another honourable cause, lacking tact as well as a grasp of popular psychology. They were unquestionably right in holding out against the Munich fraud, and they knew the repeal of the labour laws was designed for private gain and not for national defence. Their obtuseness in forcing a losing general strike caused a split in the ranks of labour, turning non-communists against them. That was what Daladier wanted.
The general strike offered Daladier an excuse for news suppression and censorship that never was relaxed again.
When I first went to the rue de la Huchette there was little drunkenness in evidence. Mary the Greek would drink a few Dubonnets and sing, Georges would try to cut his throat, and the old woman who imitated Yvette Guilbert would sometimes fall in the gutter and be taken to the police station for the night. The wreck of the Popular Front brought so much dissension and discouragement to the little street that friendliness all but disappeared; there was no longer love and harmony in all the houses, and dirt and dissipation got the upper hand.
It was not for the purpose of reforming her that Madame Absalom befriended Mary the Greek. The old witch did not drink herself, except now and then a sip of benedictine after meals. Nevertheless, she seemed to enjoy, as a weird accompaniment to her nightly monologues on the worthlessness of man, the off-key wailing of poor Mary, who declaimed about her home and children in Detroit, shuffled the torn remnants of the papers she still retained, and mourned the days of love with Pierre who had left her for a _tapette_ and a foreign ' _anarchiste_ '. In the daytime, Mme. Absalom made Mary toe the mark. The orderly regime of desultory work in the yarn shop, the regular meals and the comfort of a staunch protector did wonders for Mary and made her better able to stand a mild evening's debauch. Early in 1939, the two women were joined each evening by Frémont, who had been discharged from the post office on Daladier's instructions, Pissy, the railway worker, also out of work as a result of the strike, and young Pissy, who because of his record in Spain could not find employment. No middle-class employer would trust a 'Red'.
A few francs came Frémont's way because of his knack as a tinker, but none of the conservative inhabitants of the rue de la Huchette would call on him to enter their houses. Each night, following the strike, he would take ten francs from the pitcher containing the savings for Yvonne's dowry, until Mme. Frémont took what remained, 2,500 francs ($62.00) and fled, with her daughter, to her mother in the country. Thus Frémont lost the job of concierge of No. 11, since a man and wife are required for that semi-official post. Throughout Paris, the police department was encouraging landlords to get rid of concierges who had radical tendencies and who might shelter questionable characters. This was in preparation for the outlawing of the Communist Party, which Daladier manoeuvred just after the Stalin-Hitler pact. The ambitious Premier had been working on the project since the first big hand he received when he got home from Munich.
The Spanish republicans were being slaughtered by Franco's well-armed Moors and Mussolini's Italians, aided by German technicians and British duplicity. In the side streets of the entire world, as in the rue de la Huchette, the finest citizens were heart and soul with the champions of freedom and human dignity in Spain. Not so the landlords, manufacturers, clergymen, army officers and financiers. The London press was as hypocritical as the Paris press and the New York press. All over the world, the helpless workers were losing influence in their respective governments.
In 1923, just after Suzanne led me to the Hôtel du Caveau, Henri Julliard was fifty years of age, and I was thirty-two. In 1939, when he showed the first symptoms of Bright's disease, he was sixty-six and I was forty-eight. It was a long rough road we had travelled together, friends from the first, sometimes understanding, often misunderstanding. Yet in all that time I can remember no major issue on which we had disagreed. A remark overheard, a headline, a glimpse through the window of the dingy little bar, and I would look over at him, and he would raise his eyebrows to look across at me. Had I not been so numb with misery on account of the brutal injustices in Spain I should have been more deeply depressed when the Hôtel du Caveau closed its door. Madame Marie, frightened and loyal, could not keep it going. She took her sick husband to their house in Montmorency where quietly, in isolation and the hope for France he never could relinquish, Henri Julliard started slowly to die, day by day, as shells and bombs from Italy and Germany raked the helpless bodies of Spanish patriots, as the clubs of police and the bayonets of Senegalese battered and pricked the outraged French workers, as the day came nearer when no Frenchman could raise his head, when Liberty, Equality and Fraternity were stripped from the public buildings, when the land that had been civilization's darling became the orphan of rampant violence.
The windows of No. 5 were boarded; the door was chained and padlocked. I saw my old friend ride away in the small truck his son used for delivering typewriters. Marie, hunched up like a marsh bird in the rain, was by his side. He had around his neck a woollen muffler. His luxuriant Savoyard moustaches were white, not grey.
_'À bientôt,_ Paul,' he said, simply.
# _'Unto the Least of These'_
IT WAS A GREY DAY, sharp but not cold, with a minimum of dampness in the air. Hyacinthe, my wife Flora, and I were seated in the stuffy old Comédie Française witnessing a performance of _Le Chapeau de Paille d'Italie._ Just outside the traffic was streaming into the avenue de l'Opéra, from the swirling Palais Royal, the pont du Louvre, and the rue faubourg St. Honoré. We did not then look away and hide our tears at the mention of those names and places but already they had taken on a quality of unreality. Most reassuring was the inside of the national theatre, which belonged to the rue de la Huchette and the other side streets as did the central markets, the museums, the grand boulevards and the parks and gardens, now bleak and cloaked with dead leaves. It was a Thursday matinée and all the subscribers were in their places, among them the wistful sad-faced woman in the first balcony box, stage left, accompanied by her watchful chaperone. Year in, year out I had seen that woman, passed close to her purposely in the corridor, inhaled her perfume, always elusive and individual, remarked her clothes of old-fashioned velvet and stiff silk. She was France, inscrutable, mysterious. So was the old critic who brought his niece on Thursdays; Jeanne and her Persian lover who sat four rows ahead; the dowager who commented aloud, but so piquantly and naively that one accepted her interruptions as a super-performance.
The company, as is often the case in desperate days, outdid itself in that graceful farce-comedy on the one and only French theme, the cocu. French women were betrayed so often that their situation was practically devoid of dramatic material. Not so the gentlemen on whom had been glued the fatal horns, the badge of ridicule and unrest. Some took it calmly, others ranted and raved. They were comical, just the same.
There was something uncanny about the gaiety that afternoon on the drafty old stage, with the national hams cavorting and the mistresses of Cabinet Ministers in period costumes holding up their end of the show. They also were accomplished actresses, in the Comédie tradition. It was as if that performance had been dropped, like an orchid on the pavement, in the midst of disaster. A few days before, the remnants of the Spanish army had crossed the border into France, the most despairing ones tearing from their families at the last moment and rushing back to be killed by the fascists. A few days later, Hitler was to annex Bohemia, according to pre-arrangement with M. Georges Bonnet.
Always my mind dwelt on the army of Spanish children down on the Catalan border as they crossed over into France. Much that I had seen was too terrible, even for me, an observer trained in mass heartbreaks and modern frightfulness, to retain. I can only record, in passing, a certain mudhole in which starving children of patriots were croaking and peeping like frogs; a woman so weak with hunger that she could scarcely hold her baby in her arms, who went through the Spanish convention of refusing twice, insisting she was not hungry, before accepting food from me.
Just a few days later, after a performance at the Comédie, Hyacinthe and I sat silently in the Café de Rohan, across the street from the theatre.
'Was I as intelligent as your son at his age?' she asked, and then answered for herself: 'No. I was a prude, a dupe and a snob.'
'You liked vespers at the Madeleine,' I said, because I was thinking of something else.
Only two days before I had visited a dingy dining room in Perpignan, a little-used hall of a small cheap hotel where the proprietor was one of the understanding ones and had opened his pocketbook and his establishment to the children whom Franco and Mussolini had driven from their homes, after trying repeatedly to kill them, from the land, the sea and the air. A few, in fact, wore bloody bandages where intrepid aviators, fresh from mass, had spattered the helpless refugees with machine-gun bullets, in order to demonstrate to each other a new method of diving. Children are volatile and resistant, especially when eating after a long interval of hunger. But in one corner was a pale, grave-faced little boy with hair closely cropped and large dark eyes, who was trying to eat his soup and lagged behind the others. It had been the same in every camp of refuge for children I had seen in Spain, in every dining room, in every dormitory, in every group on the beach for a swim or in the classroom to learn the alphabet. There was always one child, wiser than the rest, less demonstrative, less hopeful, more obedient. An irreconcilable. He knew the grown-ups were trying to make it easier, and responded as best he could. With the best of good will, he could not sing or smile or feel in the air that the earth was the place for the likes of him.
Hyacinthe, beside me on the plush bench in the Café de Rohan, did not come at once to the subject that was preying on her mind. That was not her way. Instead she told a story that summarized fascist venom and cruelty.
In Hyacinthe's building, No. 32, the second floor apartment had been rented to a Spanish refugee, one of the few who were permitted by Georges Bonnet to live in Paris, since the German Embassy had registered an objection to having republicans close by. He was a tall ascetic man with lean jaws and thin hands and eyes that were sadly humorous.
This exile had a wife and little son, and the boy had a bicycle. Hyacinthe caught the concierge of No. 32, who thought the sun rose and set in The Navet, puncturing the tires of the bicycle of the 'dirty Spanish Red' (aged 7) with an old-fashioned hat pin.
As she was telling me about the hospitality accorded a child without a country, I suddenly understood what was on her mind.
'Hyacinthe, you should save yourself,' I said.
My remark took her completely by surprise. ' _Vous dites?_ ' (What's that?) she asked.
'Get away from here, while you can. Go to America,' I said. 'You could succeed there.'
She sighed. I could see that she had thought the matter over and had made her decision.
'I am lost, like the rest of France,' she said. 'I have spent my life developing two qualities which seemed to me the most characteristic and important. First of all, I have been French, night and day, asleep and awake. Second, I have occupied myself with my femininity.'
'You can be French in America,' I said. 'Everyone will like it. Only the boors Americanize themselves, as the worst type of Americans here imagine they have become French.'
'I'm afraid to be a foreigner,' she said. 'I have thought of them, always, as monstrosities – except, of course, you, the cosmopolitan.'
No agony or indecision was acute enough to make Hyacinthe forget to be gracious. Perhaps there were other young women in the world who were, in certain ways or by other standards, more beautiful and desirable than Hyacinthe. Not many. Unluckily her manners, her tact, her feeling for nuances, could not live after her as an example to a brusque and boorish world.
'How different it must be to be a boy!' she said. 'I find that in trying so consciously to be feminine, I have failed to be human. Your Spaniards are human, from birth.'
'Don't be severe with yourself,' I said. Indeed, her humanity had grown warmer in recent years with each succeeding day. Her director, who had cast her first as a clothes' horse and light comedienne, already had corrected his error. She had an almost effortless dramatic appeal. In one role, I could have sworn she was Yvonne Frémont, the girl of another class and kind she had watched through two intervening windows. Later she told me she had impersonated Yvonne: and that had been her first real triumph.
'We are human in America,' I said.
'You are sentimental. But human, also. Americans, of all the people of the world, are good-hearted, frank, like children. Among them, as a relic of France, I should be anachronistic. A curiosity.'
She took my hand and looked at me with devastating sadness.
'I have thought about it, hour upon hour. and Elliot, I cannot go away. I am a part of Paris, of the stifling soul of France. When France goes, I go. When Daladier sells France, he sells me. I am part of the bargain. When Flandin sends his telegrams to Hitler, he sends me. I could make fabulous sums in Hollywood; I could lose myself in the swirl of New York. I should make conquests, gain fame – I cannot do it.'
'You know best,' I said sadly.
'Oh, Elliot, make me go!' She rose as she spoke, and her tears made it plain that she did mean what she said, but that it would be useless to try to persuade her.
'You Americans are alive. You have your share of the future. Flora will go on from day to day, thinking mostly of others, _avec sa clarté aussi forte que sa timidité est pénible_. (With her clarity which is as strong as her shyness is painful.) Peanut will grow to be a man. I have the gift of prophecy today. He will be important to his friends, disdainful of ambition or glory. You, like Moses, will slip quietly out of this world at the age of one hundred and twenty, as deftly as you disappear from salons or cafés when conversation bores you.
'I love the screen. The screen loves me. It welcomes me and enfolds me. I love the public, and am loved a little in return. Only, when I think of what is ahead, I am afraid. In my profession, one is supplied with lines, sometimes well-written, often inspired. When Paris dies, I shall not know what to say. Please, Elliot, do not let me be banal.'
Hyacinthe's reference to Flandin's telegram touched on an incident that was typical of French politics in the fatal thirties. At the time of the Munich pact, Flandin, formerly Prime Minister and one of the outstanding fascists of France, sent a telegram of congratulations to Hitler, doubtless having in mind that he should make himself solid with his future Führer.
Before the smoke of Hitler's seizure of Bohemia had cleared away, President Lebrun sent Marshal Pétain as Ambassador to Franco. Like so many under-sized men, Franco thought of little ways in which to make himself appear impressive. He kept the aged Pétain, already in his dotage, cooling his heels a week in Santander and then made him motor all the way to Burgos for a twenty-minute interview. That was indicative of the level to which France had descended; the France of the Bourbons and the Bastille, of Balzac and Zola, Voltaire and Rousseau, of Pasteur and Curie, Lucien Guitry and Debureau, Bernhardt and de Reszke. The list is so long, but no longer can be said to be endless. Franco's discourtesy was the harder to excuse in view of the fact that Pétain and his Cagoulards had been working for Franco all along.
It was about that time that Von Ribbentrop came to Paris with a pact which bound Germany and France to keep the peace for ten years. He was received with open arms by his collaborator, Georges Bonnet. I walked with Pierre that morning around the Gare des Invalides, as near as we could get to the scene of Von Ribbentrop's official welcome. I had thought, until that day, that in the course of my years as a newspaperman I had seen police precautions. I was very wrong. The place de la Concorde, the Quai d'Orsay, and all the streets leading in or out or around were packed with soldiers and police, shoulder to shoulder, and there were thousands of plain-clothes men to form a solid circle around the soldiers. The peace envoy's train had been shunted from the Gare de Lyon, where trains from Germany came in, to the Gare des Invalides, only a stone's throw from the foreign office where Daladier and Bonnet were waiting to sign once more on the dotted line.
Ribbentrop was kept at all times out of sight or reach of the Paris population. There was not a cheer or a hearty sound of any kind as his bullet-proof limousine rolled two hundred yards between the station and the grey stone building which had been decked with French and German flags, the tricolor and the swastika, so lovingly entwined.
I remembered a remark made years before by Henri Julliard. 'When they talk too much about peace, there's sure to be a war.'
# _'Woe to the Weak'_
THE FALL OF MADRID was the signal for organized massacres throughout Spain that for sheer barbarity have not been surpassed in history. Alexander the Great had an entire city put to the sword; men, women and children, because the inhabitants had resisted his armies too bravely. That was an act of rage, on the impulse of the moment. Franco and his Phalanx went about their revenge coolly and methodically. The priests, their consciences salved by the promise that henceforward there should be no more secular schools in Spain and that Jesuit business monopolies should be restored, closed their eyes to the bloodshed, their ears to the cries of anguish, and their mouths to their co-religionists beyond the borders. In Barcelona, 80,000 republicans were jailed, pending execution.
I have been told recently by refugees from Vienna who suffered under Hitler and, in escaping, had to pass through Spain, that the impoverished Central Europeans shuddered at the sights of famine and ruin they saw as the train traversed the land of Franco. José, whose son's bicycle had felt the anti-republican disapproval of The Navet's concierge, was able to get news, and all of it was appalling. Not a line got into the newspapers through regular channels and no word has issued from fascist Spain since. Within that wall of silence and censorship are horrors no medieval dungeons ever witnessed.
Day after day, with her divine resignation, Madame Berthelot crossed the place Notre Dame to her job at the prefecture. At noon she ate her lunch _chez_ Daniel, in a corner as far removed as possible from the noisy group of comrades, who could not relish their food without free-for-all arguments on the interpretation of Marxian paragraphs. Their brave comrades in Madrid were dying by hundreds and thousands, not being able to talk back to machine-guns. Milka warned her companions that their own hour was approaching and that they could expect no easier fate.
I joined Hortense the day that the abject _Paris-Midi_ came out with the headline to the effect that Mussolini's speech of the evening before had taken a 'moderate tone'. With a mirthless smile, she handed the paper across to me and I read:
'If the democracies weep over the death of their dearest creature [the Spanish Republic] we have no reason to join them. Let's have no more talk about Latin cousinship. Relations between states are relations of force.
'The watchword is: more cannon, more ships, more planes, at any price, even if it should mean wiping out what is known as civil life.
'Woe to the weak.'
'I find that not moderate, but even a little strong,' she said. 'To wipe out civil life. – We are civil life, Monsieur, or rather, I am. You, as an American, see this carnival of unreason from a grandstand seat.'
'Not necessarily,' I said. 'We can't have civil life in America, all by ourselves.'
'I can form no idea of America,' she said. 'To us it is represented as a paradise with klaxons replacing harps and steel instead of streets of gold, with seraphim forbidden to teach evolution, and cherubs weighing seven pounds apiece, exactly, and fed on some cereal preparation that they relish in appropriate doses and eat in unison, as the violins bow together in an orchestra.'
Behind his counter, inhaling the fragrance of his peanut roaster, the smoke of which was blown his way by the breeze from the Seine, l'Oursin greeted passers-by and customers alike. In the summer season he had spread before him the delicacies of the coast of Normandy and Brittany, from the Pas de Calais, the Côte d'Or and Marseille. He rose about three in the morning, sauntered over to the central markets, and selected his wares between pauses in the bistros. Prawns and langoustines; tiny pale shrimp and the black-tails as big as the diminishing crescent rolls; clams, periwinkles and cockles when he could get them; razorfish, goose barnacles; baby sea snails to be picked out with a pin; huge _palourdes_ and giant snails; the tender coquilles St. Jacques. L'Oursin took pride in his assortment, as old M. Corre had been proud of his dried beans and spices. Often l'Oursin lost money by having so many strange kinds of shellfish, but he made up for the financial loss in conversation. His life was a succession of conversations, and that was what meant most to him. At certain times they were acrimonious, but for the most part they were companionable and gay.
The period during which the husky chestnut man had championed the Popular Front, as against The Navet and the Cagoulards, had slipped away. Like a storm, the class hostility had gathered slowly in the rue de la Huchette, had burst in fury on the night the student had been stabbed and left dead on the pavement, and after spending itself had drifted away.
_'Comme les curés, il faut se taire quand on est dans le cirage,'_ l'Oursin said to me, the day Mussolini had bombed the Albanians and taken over their small country as a gateway to Yugoslavia. The Duce had been so puffed up over his success in Abyssinia and his defiance and defeat of the French in Spain that he had brought out once again his dream of dominating his share of the Balkans.
A literal translation of l'Oursin's exact words would read like this: 'Like the priests, it's necessary to shut up when you're in the shoe-blacking,' or 'When things are going against you, it 's better to keep quiet as the priests do.'
In the summer of 1938, l'Oursin no longer roamed the street at night bellowing threats to traitors and reactionaries. He had ceased worrying Alice by dragging André, the coal man, from bar to bar in search of opposition. The situation had taken such a turn that just then no one, not even the voluble Navet, was self-satisfied.
Concerning the dangers of popular government and social reform, the Right contingent had no further cause for worry. The 'haves' were firmly in control again. The Spanish refugees were not allowed to show themselves in Paris, but had been segregated into unsanitary concentration camps, surrounded by barbed wire and African sentries who had been brutalized for just such purposes by Lyautey and the French High Command. What had been a brave anti-fascist army had been starved and beaten into a resentful mob. Daladier was well along with his minor-league Kampf. He had repealed the forty-hour week, reduced the wages for overtime and removed the limit of hours. His backers were selling him the leavings of the arms and munitions not purchased by Hitler in Germany. His secret police were hounding the dissenters from Munich. The President of the Republic, the only man who could call an election and give the people a chance to vote Daladier out of office, was belching dutifully every time Daladier ate _choucroute garnie_. His Finance Minister, Reynaud, had put over some of the neatest tax swindles ever suffered by a democratic population, decreasing the assessments of the upper brackets and penalizing the poor for working or trying to do business. Bonnet, his Minister of Foreign Affairs, was paving the way for French fascism by coddling the dictators. His wife, the ravishing Odette who made up in looks and animation for her grotesque husband with his monstrous nose, was entertaining daily the female head of German espionage in Paris, one of the contacts of the notorious Otto Abetz, who organized the Franco-German youth movement and used it for fifth-column activities.
On July 29th, Daladier went the whole hog, and adjourned Parliament for two years, after having railroaded through the authority to govern France by decree, as Hitler governs Germany.
From the foregoing hints of what was happening in official France, against the rights of labour and parliamentary government, it will readily be seen that the chestnut man was wise in holding his peace for the time. The Left, still technically by virtue of the will of the voters in control, had been reduced to impotence. Labour unions were split wide open. The representatives of the people had been sent home. My liberal friends, crushed and disappointed, were accustomed to defeat. What awed the Right and frightened the rank and file of fascist followers was the certainty of war. Their leaders had told them Hitler would behave, if appeased, that he did not want their land and goods but only 'living room'. Now, even the most stupid of the reactionaries had to face the fact that Hitler had hoodwinked Chamberlain and Daladier and that war was nearer each day.
On July 14, I was again aboard the _Normandie_ , bound for France. Just after I landed Hyacinthe described the pageant the Government had staged to bolster up morale. With her gift for the exact phrase she said:
'The whole display was political, not military. Compared with the Russians or the Germans in a newsreel, our quick-stepping _chasseurs_ and resplendent Spahis, with bands and trumpet corps that never can quite keep time, are _opéra bouffe_.'
In the early days of the summer it was Milka who was most hopeful, and because all our neighbours were so anxious to find something to cling to, all up and down the rue de la Huchette men and women who had looked askance at the Serbian 'Red' and had declared she should have been deported long ago, became respectful and asked her to explain. The hope of France, according to Milka, was the Russian army. After she had said this so convincingly and repeatedly that the idea seemed to belong to her alone, Daladier, in a speech, was quoted thus in all the papers.
'The participation of the U.S.S.R. in a mutual assistance pact is essentially desirable.'
It was generally accepted in our street after that that France was eager to sign up with Russia against Hitler. My friends were able to forget, for the moment, that Georges Bonnet was in their Foreign Office and that Chamberlain and his set still were doing business at the same old stand.
'Why Poland?' asked Maurice, the goldfish man. 'The old umbrella didn't care about the Chinese, the Africans, the Spaniards or the Czechs. Now he wants to guarantee Poland. Is that feasible? What can the British navy do so far away?'
'The Poles are the bitterest enemies of Russia, that's why,' said Milka. Ironically, about the time she had convinced all her neighbours that Russia would stand by, Milka herself had learned through her various channels of information that England would have none of it. In the first place, instead of sending an important or competent ambassador to Moscow, Chamberlain had dispatched a group of third-rate army and naval officers. Bonnet had followed suit, with a cynicism only he could achieve.
After having listened to the dangers that beset France and England, which Stalin understood much better than Chamberlain or Daladier did, the red leader pointed out that the Russian frontiers were vulnerable, too. His staff officers explained to the British and French mission what precautions were necessary, involving concessions by Finland, Estonia, Latvia, etc. Would England and France undertake to guarantee the Baltic States against German infiltration or invasion, if Russia pledged herself to march against Hitler in case of further aggression in the west? That, for the Clivedens and Cagoulards, was a horse of another colour.
Long before the Stalin-Hitler pact was announced, Madame Mariette was sure the Franco-British negotiations with Russia would come to nothing, and that view was accepted up and down our street. The newspapers of the extreme Left, _Ce Soir_ and _L'Humanité,_ kept up a daily bombardment against Bonnet and Daladier, insisting that a mutual assistance pact with Russia, with like obligations and guarantees on either side, be consummated.
'Whatever those people want is often right but never happens,' Mariette said, sadly.
The plucky little woman, who had worked so hard and surmounted so many obstacles, knew that her hopes for a peaceful retirement on a little farm, where no one entered without knocking, were being shattered. Her husband, for whom she had fairly paid and who had learned to like her and respect her and never chiselled her money, had struck with the other railway workers in November, 1938, had lost his job, and instead of waiting to be forgiven by Daladier had got other work as an automobile mechanic in a garage. In case of a general mobilization, he had to report for duty on the third day. Mariette's steel-grey eyes were seldom warm and gay, but remained resentful and cold. The rich clients from across the place du Châtelet were received politely, and if they got drunk and left their money and papers behind, Mariette took care of them. But in her heart was burning a steady hatred for those who were profiting by France's downfall.
'If I had known that I would have to stay in this life forever...' she said, the day that Chamberlain made his Albanian deal with Mussolini.
'I often wondered why you wanted to go to the country. It's so lonesome there,' said the naïve little Daisy.
'You'll go running to the country yourself, when the bombs begin to fall,' said Mireille.
Daisy opened her pale-blue eyes very wide.
'Tell me, Mireille,' asked the shapely little creature who did so well with the 'difficult' cases. 'Why isn't it better to have a big tall house over you, if those people are going to be _méchant_ and drop things from the air.'
Daisy was a victim of the general débâcle, a little ornament of peace-time France, a candid girl who expected men to be amenable and honest in return. What she understood of the state of France and Europe, if it had been mascara, would not have sufficed for one of her long, curved eye-lashes, and still she was not ridiculous like Chamberlain. The bargain the sage of the umbrella had to swallow that day would have been too transparent for our little nymphomaniac friend of _Le Panier Fleuri_ , who ranked low in the Binet scale and as high in the judgment book as Abou ben Adhem. Mussolini, swollen with arrogance like a pouter pigeon, told Chamberlain that if the British would countenance the theft of Albania, the fascist troops, who under the non-intervention agreement were never in Spain, would be withdrawn from that stricken country, not just then, but some time.
'That's nothing,' said Mireille, when the Albanian deal was under discussion. 'The French still have more _culot_ [nerve or effrontery] than the big macaroni.' She handed over her local paper from Marseilles and pointed out an item. A very old woman had been arrested for selling beggar's licenses for twenty francs apiece on the Canebière. The licenses she had made herself on a hand printing press. When asked by the detectives how she happened to be in that business she said she had inherited it from her mother.
# _'A Time to Sow and a Time to Reap'_
ON AUGUST 26, THE DAY three classes of French reservists were called into the army, the crisis that had been simmering at No. 19 rue de la Huchette, in the little dry-goods shop, came to a head. Tension had been mounting in the quarter, as war stalked nearer in the mists of the river and the shadows of the rue du Chat Qui Pêche. There was little hysteria, but an ominous quiet in which all events, large and small, restrained or violent, reverberated between the walls of the buildings like whisperings or shoutings in a well.
One heard screams of 'My son! My poor boy!' from Madame Luneville as the post man approached the door with a grey postcard in his hand. That meant the summons to the colours, and Jacques, the young son, was still in the infantry. Point blank, the father had refused again and again to intercede with General de Castelnau. Increasingly bitter and frantic, the mother had threatened and raved. There was a crash of overturned furniture, followed by the voices of Jacques pleading with his mother to calm herself, the gruffer voices of Luneville the elder (45 years of age), and the letter carrier who had laid the summons on the counter near the cash box.
For a moment the quarrel subsided, and Madame Luneville, sobbing and praying, rushed upstairs. Luneville, a sad eyed, patient man, started picking up scattered goods and articles from the floor. Jacques helped him.
From above came the tearing sound of a window flung open, a whimper that rose to a scream. Across the street Maurice, the goldfish man, started pointing upward and supplicating ineffectively. As the Lunevilles, father and son, reached the pavement Madame Luneville flung herself from the window and dropped like a plummet, but before anyone could shout or move again, her skirt caught on some kind of steel spike that had been imbedded into the plaster wall between floors. The material held and, upside down, shrieking in fear and agony, she was helplessly suspended.
The police, _Agents_ Masson and Benoist, came running. There were calls for a ladder. Frémont appeared with a step-ladder which was too short by six feet. Luneville the elder rushed upstairs and tried to climb down where his wife was dangling, but could find no foothold. The two-voiced klaxon of the fire-department truck was heard in the boulevard, and the red wagon veered around the corner just as with a slow ripping sound the cloth of Madame Luneville's skirt gave way and she crashed to the pavement, twenty feet below. She never moved. She was quite dead.
A summons to the army was a summons, and a death in the family was no excuse. When the body of Madame Luneville had been taken to the cot in the little back room, and the two priests, Fathers Panarioux and Desmonde, had followed, with faces grave and strained, Jacques picked up the fatal postcard. His jaw dropped, his face assumed an almost imbecile expression. Like a sleepwalker he turned to his father, who was sweating and trembling, and muttering something about whose fault it was that his wife was dead.
_'Mais, c'est pour toi, Papa,'_ Jacques said. ('But it's for you, Papa.')
That proved to be accurate. It was the father, not the son, who had been mobilized, in accordance with the policy of Daladier's Government to send middle-aged and experienced soldiers to the German frontier, so that they could rest quietly in the Maginot Line and would not be likely to fire off guns or high explosives that might provoke 'incidents' or otherwise annoy or anger Herr Hitler.
Intermittently that night the boulevard lights flashed on and off, as electricians who had not been mobilized tried to dim the street lamps. Methylene blue paint was daubed on the windows of the railway station and the corner cafés. The radio blared out recorded repetitions of Daladier's speech, stating that France, this time, would stand firm and honour her promises. Again, in bars and doorways, I heard bewildered men and women ask one another why it was so important to save the Poles when the Spaniards and Czechs had been abandoned. They knew they were in the war, which was to be declared almost any hour, but they would have liked to understand better the immediate necessity for action, after two decades of dilly-dallying.
About five in the morning, the residents of the eastern end of the street were aroused by a lusty thumping and indignant cackling like a Punch and Judy show. Madame Absalom, who slept fitfully at best, had opened one baleful eye just in time to catch a city worker in a white 'monkey suit', or one-piece overalls and jumper, shovelling sand onto her pavement from the back of a small truck. Mary the Greek, on the other narrow bed, sat up and blinked, exposing her dusky shoulders and one shapely breast, to the delight of the sand man and driver, who, in expressing their appreciation, caused Mary to giggle and l'Absalom to pound on the floor with her cane and lay about her as if the clutterers-up of her pavement were within striking distance.
'Don't get all nerved up, Grandmother,' said one of the men. 'We don't do this for fun. The sand must be taken in buckets to your roof, so if the Boches set the house on fire...'
What Madame Absalom suggested be lugged upstairs in buckets and dumped on the disturbers of the peace who should be at the front or else in jail can well be left unrecorded. The old woman's proposal, however, got a big laugh from _Agent_ Benoist who sauntered into view, just as Mocha, the black dog from the Hôtel Normandie, made the first use of Madame Absalom's anti-incendiary sand pile. That threw the old woman into another tantrum. Mary, by that time, had snuggled under the covers and gone to sleep again.
All up and down the side streets that morning sand was distributed, and the early editions of the newspapers contained new decrees about wearing gas masks.
Most of the residents of the rue de la Huchette who were native born Frenchmen or Frenchwomen had already obtained gas masks from the commissariat, and had been informed after the fact that they were to be taxed eighty francs apiece for the same. Father Panarioux, who had spent the long night with Jacques Luneville at his dead mother's bedside, came out from the dry-goods shop at six, gas mask in a long cylindrical tin can slung over his shoulder.
'Do you think they'll use gas, Father?' asked Mme. Lanier, as the weary priest trudged past.
'Probably not,' replied Father Panarioux. 'One seldom is prepared against the weapons actually employed either by the enemy or Satan, my daughter.'
'Just the same, eighty francs,' the laundress grumbled.
She closed her establishment, later in the day, and, dismissing the girls without waiting to finish the work already started, fled to the Seine-et-Oise in a taxi that had been commandeered by one of the army lieutenants who patronized her _clandestin_.
In the French Cabinet meeting, Reynaud found out that while he had been trying to arouse the sluggish Daladier sufficiently to effect mobilization, Georges Bonnet had 'secretly' telephoned Warsaw to make the Poles promise not to fight, even if Danzig was taken over by Hitler. The Poles, quite naturally, thought Bonnet was speaking with governmental authority.
Whether justly or not, all the Frenchmen, Right or Left in opinion, in the rue de la Huchette believed that the Soviet-Nazi pact was an all-clear signal from Stalin to Hitler to start war in Poland, and against France and England. Feeling was high against the Communists who, not having been informed of the amazing somersault on the part of their chief, suddenly began whooping it up for the Nazis and against what, even before it got officially started, was termed by the comrades 'an imperialist war'.
This gave Daladier the pretext he had long awaited. He had been determined to destroy the Communist Party in France, not because he cared whether Russian churches were open or closed, or were Greek Catholic or Roman Catholic. The Communists constituted the only opposition in the Chamber and the press to his dictatorship and his war against labour. So he sent the secret police to take over the two Communist papers, _Ce Soir_ and _L'Humanité,_ a few hours in advance of issuing a decree to make such action, shall we say, 'legal'. Milka, Pierre and (to a lesser degree) Pissy complained and got ready for martyrdom. The rest of the neighbours thought it served the Reds right. Even the gentle Hortense Berthelot was resigned to having the Communists silenced since, as she expressed it, 'One could no longer be sure from day to day which side of the street they were parking on.'
In the prefecture, The Navet was busy with his superior, organizing what became known as 'passive defence'. This consisted of marking cellars suitable for air shelters, instructing concierges how to make them gas proof, issuing and enforcing rules about lights in store or residence windows, and the appointment of deputies who were given to understand they had far-reaching authority to compel civilians to take the precautions prescribed. For the rue de la Huchette, The Navet nominated two deputies who were to patrol the quarter and wear a band marked 'D.P.' on their sleeves. One was Panaché, the floorwalker, who had not been called into military service, the other was Gion, of the music shop.
The first victim was Madame Absalom, who threatened to throw her coffee mug at anyone who dared carry sand up her stairs towards the attic, and thereby furnish a W.C. for bugs and rats. At Panaché's request, she was fined eight francs for civil disobedience. In the confusion, however, the sand itself was left untouched, except by dogs, on the narrow pavement.
As the last week of 'peace' wore on, the tramp of soldiers' feet and the rumble of trucks, tanks and caissons was heard more frequently in the night. Troops were not much in evidence in the daytime, except in the neighbourhood garages which had been utilized as mobilization stations.
Since the Caveau had closed, Georges, the _garçon_ , had worked smilingly in the kitchen _chez_ Daniel. But as preparations multiplied and word got around that foreigners, anti-fascist or fascist without distinction, were to be sent to concentration camps, the amiable Serb decided it was time for him to get himself set for a long and comfortable war. Somewhere he got a French uniform and a set of papers, and on the night of August 29th, he put on khaki slyly, said good-bye to me and a few chosen friends and slipped out the back door, to escape the surveillance of M. Panaché. I was told in confidence by Daniel what Georges did that night. He had figured out that he would rather fight Italians than Germans, if he had to fight at all, and that he wanted to be attached to some unit that still used horses, so he would not be lonesome. Georges felt sure that eating and shelter would be better in the army than in the barbed-wire enclosures and prisons, and the freedom of circulation much more satisfactory. He sat in the avenue de la Motte-Picquet, near the place de l'École Militaire about two hours, letting regiment after regiment pass by until he saw one that not only had horses but seemed to be headed south and not east. When the order to halt was given, at the corner, to let traffic pass in the busy _place_ , Georges looking to all intents and purposes like a regular French soldier, attached himself unofficially to the outfit of his choice by shuffling over and sitting on the back of a caisson. No one paid the slightest attention, and, moustaches waving up and down, Georges rode away. I have not been able to get further word of him, but would place any bet within reason that my old friend and servitor is as well as can be expected to this very day.
# _Of Aid and Comfort to the Poles_
ON THE EVENING OF SEPTEMBER 2ND, the day before war was declared, a French friend of mine who ran a short-wave radio station which broadcast in French and English for the benefit of England and America telephoned me. We had always spoken English together, because, having lived so long in foreign lands, I preferred whenever possible to be mildly startled by foreign dialects of my own tongue than to run the risk of antagonizing foreigners by misusing their language. A sharp voice of an operator interrupted:
'Speak French, if you please, or I shall cut you off.'
My friend told me that nearly all the men in his establishment had been mobilized and asked me if I would makeshift as a broadcaster until he could do better. Like Diogenes of old, I was ashamed to be idle in the midst of such feverish preparations for war; so I consented.
At 5 P.M. September 3rd, therefore, when the die was cast that spelled ruin and desolation for millions of my fellow-creatures all over the earth, I was cooped up in a small broadcasting room waiting my turn to read the most stuffy essay on Racine that it has ever been my misfortune to encounter. A lean French soprano of uncertain age and shop-worn features was mugging into the microphone and gesticulating as she sang: _'Parlez-moi d'amour_ '.
As I followed her with my bit about Racine, I could imagine with what breathless interest the radio audience of New York and London was hanging on my words. I volunteered to write a daily description of Paris under stress of war, nothing censorable or informatory to the enemy, but local colour that would keep the customers awake. No one had time to answer yes or no. I heard a few brief bars of the Marseillaise only once that day, sung by a few departing French boys who were riding in a truck.
A few sharp memories of that day persist. It was announced in the press that no gas masks were available for children under two years of age, or for foreigners. My own consulate could do nothing for me, so I got one from the Rumanian consulate, where fifty francs looked bigger than a gas attack to one of the young attachés. In one's third war, one begins to learn how to shift for oneself.
It was not that I expected Paris to be gassed, or believed, in case the Nazis did use gas, that the French masks would prove efficacious. The danger, or rather inconvenience, lay in another direction, namely, the new and over-zealous 'passive defence' workers who might pick one up any moment if one did not have a gas mask in a can conspicuously slung over one's shoulder.
All up and down the narrow streets of the St. Michel quarter, and the wide streets of the Champ de Mars district where I had, and still have, I think, an apartment, concierges were working hard and arguing harder, trying to seal up their air-raid shelters and tape their windows, so that in case of explosions the danger from falling glass would be reduced. In the rue de la Huchette, the aged stamp collector, M. Dominique, contributed one of the humorous classics of the war. In the window of his little shop, before he closed it forever, he placed a placard reading:
_'Fermé à cause de la mobilisation annuelle.'_ ('Closed because of the annual mobilization.') It was announced that the markets which had made night beautiful would henceforth be open only in the afternoon. Parisians were urged to leave the city. Street crossings were painted white so that pedestrians and stray drivers of vehicles could see them in a blackout.
After the stamp collector shut up shop, Luttenschlager, who had not sold an article of piety in a fortnight, followed suit. Closed shutters, like blinded eyes, appeared up and down the rue de la Huchette. Dorlan, the bookbinder, departed for the south of France. The Laniers had left in style several days before. In the Hôtel Normandie, the Jewish refugees stared out with frightened faces, trying to convince one another that Daladier and Bonnet would not treat them like enemies. Julien the barber was obliged to depart on the fourth day of mobilization, and Elaine did not relent. She promised him he would be horned like a mountain goat before his train had left the suburbs. Actually, he was not – not until several days later. The dry goods shop, from which a small funeral cortège had passed, gave up and the stock was placed by Jacques in storage. The flower shop again was colourless and this time remained so. Young André, son of the coal man, drove away in a Renault truck, as did the husband of Mme. Mariette of _Le Panier Fleuri._ Dr. Clouet put on a uniform again and was assigned to a base hospital in Stenay. Dr. Roux, the dentist, moved his office to Nice, on the advice of Pierre Laval. The ageing Corres continued as usual in the Épicerie Danton. The publisher at No. 30 had never opened for business since Munich.
Having said good-bye to his son, who was a sergeant in the ordnance department, Henri Julliard in his lonely stucco home in Montmorency uncomplainingly died, and the yearly pumpkin he had trained to grow in the crotch of a pear tree rotted on the little platform. The tree died some months later.
I noticed that Bill Shirer, coming back to Paris with the German army for a little private Gethsemane and the public benefit in his own groping country, passed through the rue de la Huchette and stood a moment in front of No. 5, where he had been served and enlightened by Monsieur Henri in happier days. Jay Allen, having been released from the Nazi jail which was no prison to a man of Jay's guts and curiosity, spent some of the precious last minutes in Paris in the rue de la Huchette, and also paused at No. 5 and remembered, through dissolving shutters, what some of us had known there. Leland Stowe, that sterling American who reports men's spirit with gusto, no matter what luck they have, did not forget No. 5 or Monsieur Henri when he said good-bye to the town.
A circular was sent to me just the other day announcing an important new American newspaper in Chicago. On the list of talent was Wolfe Kaufman, who taught the late Monsieur Henri to make potato cakes. Also I saw the name Rex Smith as editor. Likewise a chap named Pickering who ate the largest slice of a certain fish one night in our cellar of Robespierre, and helped Monsieur Henri lug in the roast goat that followed.
At the picture desk of the _New York Herald Tribune_ sits a man named Ralph Franz, who found his splendid little wife at No. 5 rue de la Huchette. He is one of the old guard who has the same wife now, and they talk together about Monsieur Henri Julliard.
Waverly Root would not look blankly if one mentioned No. 5 rue de la Huchette, which never got into any tourist pamphlet, or guide book, or even _La Semaine à Paris_. Johnny White, of the new Chicago daily; half the boys on _Newsweek_ ; Kenneth Stewart of _PM_ ; Eugene Jolas; Robert N. Linscott, the late Sherwood Anderson who, I remember, was very wistful and envious because I could chat with the neighbours of the rue de la Huchette while he was helpless because of his lack of French. It was just the thing Sherwood loved to do and he felt the genuineness of the atmosphere and its relation to communities in America he had known. With their usual discernment, the people in the hotel sized up Anderson as a good fellow and significant man. Their judgment of foreigners whom I brought there was uncanny. Of the large number who were my guests or who came to call on me there at No. 5, the people of our book elected two as outstanding Americans without knowing a word they said or a thing they had done. The first was Sherwood and the second, our old friend, Horace Liveright who, incidentally, took a passing shine to Elaine, the wife of Julien.
To continue with my list: Gertrude Stein and Alice B. Toklas, Virgil Geddes, Eva Gautier, Bravig Imbs, Edgar Calmer, and Robert M. Coates, who is now art editor of the _New Yorker_. Also Jim Thurber, Dave Darrah, Hendrik Van Loon and E. E. Cummings, Jim Farrell, Helena Rubenstein; Whit Burnett and Martha Foley, editors of _Story_ magazine; Bettina Bedwell, Dora Miller, Allen Updegraff, Louis Atlas, Jim Tully, Holger Cahill, who became National Director of Art; Archibald MacLeish, Librarian of Congress; Duke Ellington, Louis Armstrong, Josephine Baker, Paul Robeson, Morley Callaghan, Sonia Himmel, Catherine Huntington, Creighton Hill, Ernest Hemingway, Harold Stearns, and the late F. Scott Fitzgerald.
The painters got around, too. Stuart Davis, Guy du Bois, Buck Warshawsky, Joe Stella, Marsden Hartley, Ivan Opfer, Norman Jacobsen, Pop Hart, Mahonri Young, Howard Simon. And the musicians: Georges Antheil, Irving Schwerke, Edgar Varese, Carlos Salzedo.
Paris, under blue light, with ghosts of regiments in dark streets and refugees in swarms in public places, and such patriots as Gion and Panaché (and thousands of others who were better men) roaming alleys to find fault with householders and wayfarers alike, fascinated me and kept me from sleep. On the night of the first air alarm, I was near the rue de la Huchette and stepped into the shelter marked '92 persons' at No. 7. The first inhabitants to come, bewildered and shivering, into the cellar, were the aged Taitbouts, blinking like hoot owls and muttering to each other what probably was intelligible to someone. There were fourteen chairs, one of which was a stuffed easy-chair in bad repair.
'That is for the Colonel,' Madame Taithout said reproachfully, when M. Taitbout was about to sit on it. He muttered and shifted over. She remained standing, explaining to me that, when erect, one offered less of a target to a marksman in the sky. Father Panarioux entered with a punctilious ' _Bonsoir, mesdames et messieurs._ '
Two pretty Catalan girls, both servants, appeared from somewhere, followed by one cop, Benoist, who could not stay, but promised to return later. The early days of the war meant grief and hardship to many of the French. What they brought to the young and good-looking, or middle-aged and vigorous, members of the Paris police force and to abandoned cooks and chambermaids has survived a lot of slander through the centuries, but still goes on.
The din of sirens had died away before a new arrival was announced. Frémont, no longer having a family, a job, or a concierge's lodge of his own, had helped his neighbours rig up their cellars with an eye to comfort. He acted as a sort of doorman, as if No. 7 were a night club, as indeed it was for a while. So when my old accordion teacher, instrument in hand, put in an appearance, Frémont welcomed him heartily, introduced him enthusiastically and then braved the dangers of the outdoors, evoking prayers from Madame Taitbout, in order to entice Pissy, who played the flute, from his own and proper dugout. Up and down the street boomed the voice of The Navet, who knew the 'raid' was being staged to test air defences and therefore was exceptionally brave.
There is always one big moment, and we had it when the aged colonel, who was nearly ninety, was ushered in by his faithful Alsatian old maids. Colonel Montalban nodded politely to the priest, and then in a blanket way to the others, including the servant girls and me. He was neatly dressed in a World War I uniform, and could by no means take possession of the only easychair when there were women present. In fact, no one would take the largest chair that evening and it remained unoccupied.
Moment No. 2 occurred when in came little Daisy of _Le Panier Fleuri_ , eyes wide with wonder and apology. She had been off duty that evening, had visited a friend in another quarter and had been herded into No. 7 by Panaché, who would not permit her to join her co-workers in No. 17, a few steps farther up the street.
The Alsatian old maids glanced at the priest and at each other, not knowing whether a _fille publique_ and an ex-colonel could sit in the same shelter. The colonel did not seem to mind. He was sleepy, but cocked his eye appreciatively at the frightened and embarrassed little Daisy and said, simply:
'Sit down, my daughter. It's cold outside!'
Elvira and Roberta not only smiled, but giggled. The accordion player struck up a tune, joined by Pissy. Somehow, a flute seems like a singularly inappropriate instrument for an air raid, since it has to be approached from the side with a grimace which makes a man look like an ant-eater. Then softly, from somewhere down in Elvira, came a throaty Alsatian song, and instead of restraining her or discharging her without notice, the colonel roused himself and looked at her reproachfully.
'Why didn't you tell me you could sing?' he asked crossly. (She had been in his service eighteen years.)
'Excuse me, Monsieur le Colonel. We thought it would annoy you,' said Elvira and Roberta, practically in unison.
'On the contrary, I like music,' said the colonel.
From then on, we had music, until five in the morning, when the air whistles and horns wailed in reverse and we all were released by Panaché.
As she departed for No. 17. little Daisy held out her hand politely and quite formally and said, with the utmost candour, to the colonel, who was just opening his eyes from an hour's sound nap: 'You are very kind, Monsieur. It is true that in time of war we should all approach closer to one another.'
Then she forgot herself, turned to the rest of us, and said, from force of habit: _'Au revoir, mes lapins.'_ (Until next time, my rabbits.)
Daladier, it seemed to me, fell far below the standard of eloquence set by little Daisy, just as Chamberlain had shown less understanding of Mussolini than did Mireille. Daladier's contribution to national defence and world malarkey that day read as follows, as well as I can translate it:
'France commands today, and never have her orders been clearer or more imperious. Without hatred for people whoever they may be, with love for the victims... France is conscious of her power.
'Every Frenchman is ready to do his duty, to give his life.... What would life be worth in an oppressed France?'
Across the rue des Deux Ponts from the Hotel du Caveau, where the slums were, a street cleaner with no wife and five kids left his dependents in the local commissariat of police when he was forced to rejoin the army. This was made illegal by decree. A loyal widow raised a terrific rumpus because no steps were taken to protect her husband's grave from air attack. The newspapers were so demoralized by Giraudoux's literary censorship that in more than one instance they even got the date of the issue wrong, to the despair of future historians. Through all this, the members of the French Academy continued pottering with the official dictionary which fell so far behind the vocabulary of the ordinary taxi driver that it was useless except as a curiosity, and had been a joke for years. Duhamel, who had set himself up as an authority on America, made a touching address which said exactly nothing. That was possible with Academic French. According to the _Paris-Soir_ , which smelled to heaven whether censored or uncensored and whether or not its editors were in France or America, German storm troops were taught to sing the 'International'.
Of course, the censorship pressed harder on the Left than on the Right, which was beginning to inhale the fragrance of clover.
In an air-raid shelter, an officious deputy of the passive defence arrested a man who had lost his gas mask to a neighbour during an air raid in a game of _belotte_. The winner, as so often is the case, was not molested. There was no law to prevent having two gas masks, but a definite penalty attached to having none at all.
British troops, according to the censored papers, which not only had items deleted but other items supplied, were beginning to pour into France. One saw them rarely, but a few strayed into Paris and were described as follows by M. Giraudoux's enthusiastic publicists:
'One sees again the English officers on the _grands boulevards_ , a familiar sight in 1914, with their impeccable boots, bamboo swagger sticks under their arms. Officers of 1939 prefer the Rond Point and Étoile to the Opera and the Madeleine of the other war.'
The writer describes three Britishers sitting on a _terrasse_ in the Champs Élysées:
'... with their sportive allure, their brick-red complexions, their clear eyes and that aspect of the "gentleman" which all of them have... the three lieutenants smiled benignly on Paris over their three whisky-sodas, traditional like their elegance and _bon ton.'_
This is a fair sample of what my neighbours read, while wondering prayerfully what was happening in Poland and elsewhere. Madame Absalom, to whom newspapers had always been so important, cut the air with her cane almost constantly and developed arm muscles in indirect proportion to the shrinkage of her neglected legs.
The municipal pawnshop issued hurry calls to those who had pledges in Paris depositories, warning the clients that valuables would be transported to the country. Every experienced Frenchman knew that meant they would probably never be found again in any man's lifetime.
Pierre Vautier, in uniform, sought me out one day. Already Milka had been sent to a concentration camp, along with all the refugee Jews from the Hôtel Normandie, and Mary the Greek. Also the model, Nadia, who, because of de Malancourt's intervention, remained less than three days. Pierre was still secretive but he wanted to make amends for having broken off our friendship after the Spanish adventure. I understood all too well. He had been hurt too badly by the colossal injustice of it all, as I had. What Pierre had in mind I did not learn until later. Knowing, as Aragon did, that all Reds would be used as decoys, Pierre offered his services in advance of being called and started sending affectionate notes to certain homosexual French officers who were rabidly anti-Left. These missives were so worded that any casual reader would have suspected they were in code. One by one, these pansy reactionaries began to disappear from their units, and, in many cases, nothing was heard of them until after the armistice, if at all. Pierre, knowing he was safe as long as the spy hunt continued, outdid himself in the use of his fertile imagination, which he had so long stifled with party dogma. I am sure his influence was salutary for his dying France.
# _'A Time of Snow in all Endeavour'_
ONE CLEAR AUTUMN MORNING in that most unreal phase of war where the enemy was busy in some distant land and all the news was bright and cheery from the office of M. Giraudoux, and the sun, slanting from its autumn angle, gilded oblongs and slits so familiar in the rue de la Huchette, catching glints of goldfish in the windows, of chrysanthemum wallpaper, scarlet and white, of children too poor to be evacuated sitting in dark smocks on stone doorsteps, of rugs slung over railings to be beaten, of the signs of the shops, the customers and proprietors, vegetable carts (there still were green vegetables) and unreal realities patching indelible memories, I wondered, walking slowly up and down, staring at those housefronts, greeting and being greeted, being seen and not noticed, heard and not seen, existent and non-existent, in short, a ghost or pilgrim – I could not dislodge from my mind the question: 'How would these building fronts impress a man who had not been here before, a photographer, a traveller, a dweller in another quarter or country?'
Like a cold wind between me and the sun came the vision of another street, not a side street but the Grand Calle of Madrid, and how I had returned there breathless and shaking to see for myself what bombs and shells and inter-class hatred had done. From the street, except for broken windows and sandbags and not so many pedestrians and no song, the buildings looked about the same. Each one had been hit from above, or had been damaged in the upper stories, but from the street so little of the destruction was visible, so utterly nothing of the broken friendships, dispersed families, days gone by that ne'er return again, mistakes, achievements – life.
War, then, is a cancer, fatal before it shows, and sure of its victims before they feel the symptoms.
Two spots of colour, which is light, were the favourites of the sun in the rue de la Huchette: the window of Maurice, in _La Vie Silencieuse_ where moved in deliberate constellations the exotic fishes, and the yarn shop of Madame Absalom. The former was of nature, the latter of man's artifice; hues from the mysterious eternal, human answers in the form of dyes.
These two were among the last to be extinguished – one by chance, the other by design.
It was at the time that Russia was attacking Finland, a procedure that was played up in the Paris press as one of history's basest atrocities. This is not the time to try to discover what was behind it, what prompted the Finns, or the Soviet leaders, or what it meant to soldiers frozen stiff as ramrods before they could bleed to death at thirty below zero. In Paris it meant gravy for Daladier, who still had not been able to outlaw a political party among whose offenses was a strong distaste for him. Of course, as Prime Minister and Minister of War and also Foreign Affairs, he did not make all the calls in little side streets. For that he called upon the Sûreté Générale. And the best and brightest and most discerning men of the famous Sûreté were sent after bigger game than we had in the rue de la Huchette.
Two Sûreté agents, in the big Red hunt of that period, came into our street by the western gate and made a perfunctory check-up in the Café St. Michel. They were told by Madame Trévise that the Communists had quit her bar long before and were thick _chez_ Daniel. In No. 32 the concierge who had punctured the Spanish child's bicycle, in the name of the true religion, assured the inspectors that if any Red had dared enter the doorway, the respectable Navet who worked in the prefecture would have reported the incident, and the venerable Judge Lenoir would have risen from his bed like Lazarus from the grave. The publisher at No. 30 was closed. Next came _La Vie Silencieuse._
In his goldfish shop, as usual, was Maurice. He had not sold a fish since Albania, or Austria, but, as I have mentioned earlier, his booklet, chosen at random for the day, was entitled _The Communist Manifesto_ _,_ and the author was one Karl Marx. The book was bewildering to the candid-minded Maurice, since the text sounded fine, but he couldn't quite understand what it meant. With his usual politeness he greeted the callers, and gently rubbed his hands in anticipation of a sale. One of the detectives picked up the book, and in doing so disclosed his badge.
Now Maurice, although a man of simple tastes, was no fool. He had read a few papers, listened to Henri Julliard and Lucie Absalom and Father Panarioux in neighbourhood cafés, and was aware that official investigations led to trouble, in nine cases out of nine.
'Where did you get this?' asked Detective No. 1.
On the point of answering, Maurice suddenly recalled that the honest old woman who had sold him the book, without glancing at anything but the price, had been in business a long time and was having hard sledding.
'I don't remember,' said Maurice.
There followed an abusive dialogue, in which the abuse came from the detectives and was received with increasing calm by Maurice. These men were mistaken, he knew. He was not a Red. Finally, when asked how he could prove he was not a Red he nearly made a slip.
'Ask them. Ask the Communists themselves,' he suggested, then caught himself in time.
The detectives beamed. 'Ah, you know some Communists?'
'No, but surely you do. That's your _metier_.'
Three days later, after Maurice had been taken to prison and held incommunicado, _Agent_ Masson went sadly to the shop, the door of which was still open. The fishes were dead and had begun to smell. The tenants of No. 32 were beginning to complain. The policeman took the tanks of dead fish and dying plants to the quai St. Michel and dumped the contents, then washed them at a public spigot in front of l'Épicerie Danton, where bug-eyed old Corre, in smock, murmured and glanced across the street regretfully.
Father Panarioux and Father Desmonde, appealed to by a group of the neighbours, went patiently from office to office to give testimony for Maurice, but they never found anyone who had Maurice on his mind just when they called. Father Panarioux, almost as persistent as the Abbé Lugan, went firmly to The Navet and came out, very pleased, as The Navet, who seemed to be able to do anything in war time, had promised to intercede for the goldfish man.
' _Pense-toi!_ ' (Imagine!) The Navet said to Jeanne, after the priest had departed. 'The _type_ [meaning Maurice] spent all his time with those rowdies like the chestnut man. Of course, he'd land in jail. So will they, in time.'
And The Navet picked his teeth with a hairpin.
The same raid in our street struck a telling blow at Madame Absalom. The old woman had come to depend entirely on the loving care of Mary the Greek, who simply would not, in spite of a life of worry and privation, give up her beauty in Mediterranean style. The detectives found that Mary had no papers of more recent date than 1925 and took her in so that her status might be investigated.
No source of mine has disclosed to this day where she landed, after leaving the stadium outside of Paris for a camp in the south. I hope someone gives her Dubonnet, which is not good for her but makes her smile and sing, and that if anyone makes use of her shapely olive-tinted body he does it with gentleness and without contempt. Today her two boys in Detroit must be about 22 and 24 years old, respectively, and if they read this book they may rest assured that, in so far as I know, their mother never did a fellow-creature any harm.
Milka had long been imprisoned in the stadium; Pierre was in the service, as were Pissy and his son. The raid _chez_ Daniel netted the investigators precisely nothing, but it frightened badly the good Madame Berthe, Monsieur Henri's sister-in-law. The restaurant remained open, and did as well as any, considering the new restrictions, the high prices and the lack of customers.
Being left alone, and still unwilling to get out of bed, Madame Absalom tried hiring a servant girl, but no girl would stay with her at night and sleep on a cot on the ground floor. So a close and mutually helpful relationship developed between the peppery old woman and the lonely Frémont, who had been taken back as letter carrier soon after mobilization and now had some pay to spend but few companions with whom to spend it. From his wife in the country he heard nothing, although Yvonne wrote him faithfully once a week, urging him not to do the two things he most enjoyed: namely, to drink and to play cards for money.
Frémont came to the yarn shop early every morning, built a fire, got Absalom's breakfast, fed it to her, brought her the papers and then went to work. At noon, a hearty meal was brought by Sara of the Hôtel Normandie. All evening Frémont would argue with the old woman, and to an outsider it might have appeared they were coming to blows. Actually, she never struck him with her cane and he never threw a bottle at her head. They fought about everything except the imbecility of French politicians and the prospects of winning the war. On those points they were as one: the French had no leader, civil or military; the Germans would surely take what they wanted, now that Poland was finished.
When the Stalin-Hitler peace proposals came forward, however, both Madame Absalom and Frémont were indignant and agreed that the war must go on.
One December evening, down came the snow, so rarely seen in Paris. It touched the rooftops of the rue de la Huchette, and from doorways and open windows, what few of the inhabitants were left looked upward in awe, caught large flakes in their hands, saw crystals melt on windows, woke the children, and in a cracked voice some woman sang: _'Noël, Noël'._ She was joined by the drunken voice of the chestnut man, who used the word _'merde'_ all the way through, but did well with the tune. And then the fat horse-butcher Monge, and the lean Noël sang too, swaying drunkenly.
In the yarn shop, Frémont, singing off-key, dragged the bed of Madame Absalom through the doorway and up to the front window, as she never in her life had seen the snow when it really lasted. And for a short time the footprints of l'Oursin, Monge, Noël and Frémont were discernible as they paced up and down, serenading her from the pavement. All the rest of the street was softly carpeted with white, with blue haze from the street lamps, until Mariette, calling from the doorway of _Le Panier Fleuri,_ invited the singers in for a glass of brandy – 'if you drunkards can hold another one,' she added, and dodged a snowball that went wide of its mark.
Even for the early mass at St. Séverin there was still some snow; so footprints of old men and women, and some small ones that still had not been evacuated, led the way to the working man's church. Father Panarioux said mass that morning and afterwards could not remember whether there were eleven or twelve to hear him, and after trying to imagine where some others were just then he started to pray, then changed his mind and asked the beadle not to sweep away the snow from the old church doorsteps.
Across the street, where the Bal St. Séverin used to be, old Germaine was wailing, having heard that day that Robert, the pimp, had died outside Forbach – shall we say for France? Anyway, he had worn the same kind of uniform as the worthier soldiers, had done what his officer told him and a little bit more, and had fallen facing the Siegfried Line, for which, the week before, the German High Command had ordered 100,000 rose bushes from Holland, to be planted in the spring.
Daladier's Christmas address had the following passage: 'It is our pride to conduct the war with method.'
The French losses, he said, were 1,136 on land, 256 on the sea and 42 in the air. In the other war, for the corresponding period, the losses were 450,000.
Whether the Prime Minister, so soon to resign so late, included our local pimp in his list, I cannot say, so perhaps the correct total should have been 1,137.
Way up on the fourth floor of No. 9, a child was born to the wife of the gas inspector who was one of the first French parents to benefit by the new law providing a bonus of 2,000 francs ($50) for the first child. For decades the French officials had known that France was slipping behind Italy and Germany in the birth rate, and at last something was being done about it.
Early in January, Madame Absalom had another visit from the officials. The only casualty was a bruise on the hand suffered by one of the government inspectors, but the visor of _Agent_ Benoist's cap was cracked and the old woman's large coffee bowl was smashed. A short time before, a decree had been issued requiring dealers in yarn to declare their stocks, since wool was badly needed for the soldiers in the Maginot Line.
Madame Absalom had heard about it from Frémont, who offered to take the inventory, but she would have none of it. When the inspectors came she simply grabbed up her cane and started swinging, sitting up in bed and calling them whatever came to her still active mind.
The matter was resolved by _Agent_ Benoist, who had known l'Absalom many years. He winked at the inspectors, beckoned them into the Normandie bar and suggested that they make a fair guess as to how much wool the old lady had, since she was an eccentric and very excitable. Not only did the inspectors comply in the case of Madame Absalom, but they stayed at the Normandie all day and guessed at the amount of wool in six other shops on their list, marking in the figures with Sara's calm help before staggering home.
Her newspaper brought to Madame Absalom the information that same evening that it had been decided to hold the Olympic Games the following August, notwithstanding the international situation.
# _A Few are Chosen_
THE WARM SPRING AT LAST stirred the winter of inaction and discontent. Pétain was hobnobbing with Franco in Madrid and receiving such eulogistic press notices for home consumption that the big deal of the season escaped his eye. The little generalissimo arranged to purchase from England six million pounds' worth of war supplies, some of which could be obtained only in Egypt, for reshipment to Germany. The same device had worked well with American oil.
As ignominiously as he had risen to leadership, Daladier resigned as French Prime Minister, after receiving in the Chamber a vote of no-confidence 279 to 1. Three hundred of the deputies refused to vote at all. The dapper Reynaud, who spoke English after a fashion and had a neat way of turning phrases which, on analysis, proved to contain no meaning, took over the job. Reynaud's promise to the bewildered French was that he would 'pursue the war with energy'.
'Our only hope is that Germany might fail to attack. Is that possible?' asked Hortense Berthelot. There was little talk in those last days in the rue de la Huchette; so many of the talkers were away or dead or afraid to speak their minds. Daniel, the Serb, who had the only good restaurant left in the quarter, was not anxious to give credit to Noël, who was too proud to ask for it. In fact, since Daniel had got into trouble innocently enough with the Communist group headed by Milka, he had been increasingly careful not to encourage the old customers of the Caveau to patronize his modern place. Berthe, the sweet-faced sister-in-law of the late Henri, said nothing. She never crossed her husband.
Monge still sold a little horse meat and the Satyr had found another job in a small hotel in Montparnasse when the luxury restaurant in the Bois had faded. These two could have eaten chez Daniel, but knowing Noël could not afford it, they joined him at the Normandie, where now there was plenty of room.
As often as she dared, the patient Jewess, Sara, cooked special nourishing food and wrapped it warmly in clean napkins, and her husband, Guy, who started so slowly and was coming up so fast, pushed a three-wheeled delivery cart out to the Stadium, where the refugees, their former clients, had huddled in coldest winter with thin shiny black clothes and one blanket apiece and for that reason were grateful for the warm spring sun. They had a way of sitting on benches, side by side, and not in groups but rows, as if they were in a synagogue waiting for services to begin. When they spoke, infrequently, two or three others nodded, and the rest stared silently ahead. They were dirty and had no water, bewildered and no one explained, and tired without sleep for nights and days until at last, once or twice in a fortnight, oblivion came and for hours they had the inestimable relief of non-obligation to exist at all. If the people in our street who were not Jewish were uncertain as to whether Hitler would attack, the refugees were not. They knew, and waited, coughing in the night and shivering in the sun and opening their eyes as slowly as they could, to prolong the sensation.
At No. 15, a situation had developed in the laundry that kept the neighbourhood in ferment for weeks. Edouard Lanier, the gueule cassée, had returned from the country and had left his wife behind. No one knew why. They had always been congenial and affectionate, and although Edouard had done no work of any kind since World War I, Madame Lanier had not complained. On the contrary, she had encouraged his idleness. There was a small room in the cellar of No. 15, at the back of the building, and in this Lanier lived all alone, washing infrequently, drinking red wine constantly and having no traffic with his neighbours. The front door of the establishment was locked and boarded, the cellar windows were covered with sandbags, the upper windows stained blue and criss-crossed with narrow strips of paper.
Clients of the legitimate laundry and the secret bordel pounded on the boards, but Lanier would not answer, or, if they persisted, he would shout for them to go away. He wept and roared sometimes about the other war, saying one was enough and that he shouldn't be called upon to fight another. No one had called him, but he objected just the same.
A few of the clients who had had laundry in the place when the Laniers had fled before Munich had retrieved their bundles on a day when Madame Lanier had put in an appearance. On that day Lanier had stayed in the cellar and refused to see her. She wept and pleaded, and told the neighbours her husband was ill and that she didn't know what to do. But when all comers had been satisfied, there remained a lot of clothes, washed but not ironed, and so badly mixed up that Madame Lanier was not certain to whom they belonged.
Mireille, of _Le Panier Fleuri_ , had been ill at the time, and Madame Durand, of the flower shop, did not venture back to Paris until later. When these women, so disparate in temperament, returned to the street, each one tried to get a word with Lanier, who would not listen to them. Mireille appealed to her friend, _Agent_ Masson, who braved the disfigured veteran on one of his trips to André's wine shop. Lanier went into a rage and threatened to shoot, with his old service revolver, the first one who tried to enter his shop. He knew nothing about laundry. His wife had always taken care of that. Now she was gone.
Madame Durand tried to reason with Lanier herself and was called by him some names that more accurately might have been applied to Mireille.
When Mireille heard that Madame Durand had applied to the court and that Lanier had been served with a paper, she called on a lawyer friend and, on payment of fifty francs, preferred a similar charge. Lanier appeared in court and wept about World War I and the injustice of having two wars in one lifetime until the judge was quite impatient with the women who wanted a stricken patriot to bother about laundry. Nevertheless he sent a court officer with them to Lanier's place, and the _gueule cassée_ was forced to unlock the main door.
Madame Durand, when she saw that her respectable laundry had been scrambled together with Mireille's sinful underclothes, refused to accept her linen unless Lanier would agree, in the presence of the officer, to have it laundered again at his expense. Mireille began to laugh, and as the infuriated florist turned on her, she picked up her dainties and hurried across the street to tell the other girls. The court officer could not terminate the affair until Madame Durand could be induced to go, since he had been instructed by the court to lock the premises and leave them as he found them.
Swaying and growling, eyes red with rage, Lanier lurched down to his cellar. In World War I he had used hand grenades, and having none handy, he lighted a small kerosene lamp and ascended the steep stairs. This he tossed between the laundry, the screaming Madame Durand and the officer, where it exploded, setting fire to the clothes and singeing off the eyebrows of his adversaries.
For the second time in twenty years, the fire department came to the rue de la Huchette and put out the small blaze. Seven days later, a squad of attendants lured Lanier from his cellar and took him in an ambulance to some kind of institution.
The story of Hitler's _Blitzkrieg_ through Holland and Belgium, and the collapse of France, has not been told and never will, but the grand lines are familiar. When the breakthrough near Sedan occurred, Étienne Corre had been stationed in a clump of trees with a machine-gun unit and didn't know, when the enemy approached, that his officers had started back for safety some hours before. He fired. The enemy fired. Some of the enemy died. He died. That was the end of the German, the English and the Italian he knew, and the hopes of being an important export broker.
Young Antoine Pissy, who had fought in Spain with officers and soldiers who would fight with rocks or their bare hands and die together, managed to avoid being caught by the Nazi troops, although they were all around him. He entered the Épicerie Danton, cap in hand, some days later, and told Monsieur Corre, and old Corre told Gabrielle, and they both told the young widow from Dijon.
There was the night when no one was left in the rue de la Huchette except Madame Absalom, Hortense Berthelot, Frémont, Monge, Mariette, Mireille and Daisy, Sara, Guy and Mocha, and Eugénie in the Café St. Michel. And detached from the others, on the third floor of No. 32 Judge Lenoir, Madame Goujon and the screen star, Hyacinthe. In the afternoon, Elvira and Roberta borrowed the baby carriage from the gas inspector in No. 9 (the baby having died) and pushed away some of the valuables, including four decorations for valour in World War I, of Colonel Montalban. The colonel, dignified in uniform, in spite of his 88 years, walked down the street and away by the eastern gate in a military manner.
Hortense had been invited to take refuge with a relative of her dead husband near Orléans and had been on the point of doing so when she heard the cackle of Madame Absalom and decided to remain with her. Frémont sat with them, and, for once, was sober.
'How do you explain that, Mesdames?' he asked. 'I try to drink and can't.'
'Too late,' croaked l'Absalom, scowling at him shrewdly.
Sara, the Jewess, sat at her bar, all alone, while Guy was sweeping upstairs. No one passed on the pavement, until Monge came along.
'Hadn't you better go and get Noël?' Sara asked.
'No use. He won't come,' Monge said, and cursed under his breath. The lean taxidermist was sitting among his stuffed cats and dogs and tossing up and down in his hand a can of cyanide of potassium. He wouldn't swallow the stuff, but he wouldn't put it down, either.
Sara looked at her worn hands and broken fingernails, and then at the dog-eared account book in which figures were scribbled on each page. Without rancour she picked up the ledger and tossed it with the dust rag on the shelf behind the bar.
Somehow The Navet got possession of a public bus, and into it he had loaded whatever he could carry, his unfaithful wife, Jeanne, his concierge, Gion and Bernice, Panaché, and the tailor, Saint-Aulaire. There was one other man, a stranger, who said he could drive, and having been tipped off that the Government was about to steal away to Tours, was as eager as The Navet was to travel that way. The bus, loaded beyond its normal capacity, got a start over the bulk of fleeing refugees, but progress was impeded because the frightened women asked the driver to stop now and then so they could relieve themselves. After two such delays, The Navet, always in command, put an end to the practice.
'Mesdames! In the midst of a war one cannot stop every five minutes!' he said.
And back on the rue St. Séverin two dogs howled and howled, abandoned in an empty building.
# _Black Rain_
IN FUTURE YEARS THE DAY of the black rain will always be remembered, when all those who could or would had fled, and the others were waiting. Some said it was because of oil from blown-up tanks and others believed it might be a deadly gas sent by the Germans. A few thought, and tens of thousands hoped, it was the end of the world.
It was the end of a world in which Paris was supreme, in which France was alive, in which there was a breath of freedom. There was oil in the blackened air, and soot in the rain, and the wretched city was pressed upon by the lowering sky. Greasy buildings, empty. Dingy pavements, bare.
One of the first Nazi tank units to roar across the Ile de la Cité must have been directed by someone who had misread a map, for the Panzers rumbled over the Pont St. Michel and, instead of proceeding along the vast and empty boulevard, No. 1 tank turned into the rue de la Huchette and then, sharp right, to the rue Zacharie to get back to the Boul' Mich' again. The opening between Mariette's _Le Panier Fleuri_ and the charred laundry of the Laniers was not wide enough for the turn, the old buildings being set at an angle, and the jocular driver at first was about to push off a corner of the bordel to make room.
Another German shouted something gay in German; so, the tank spared Mariette's place, in which, wide-eyed, was cowering little Daisy with Mireille's arms around her. Instead, the Panzer crashed into the Lanier corner and broke down enough of it to pass along and out of sight, followed by four others which crunched over the unimportant ruins.
The news of the armistice terms found the chestnut man sitting on the parapet of the pont St. Michel. He had a few francs left and bought a paper as a man with a club foot lurched along with a few under his arm. The Café de la Gare had closed and the area in front, where l'Oursin had sold moist treasures of the sea, in shell pink and mauve and dark seaweed green, flat Portuguese oysters and others from the channel coast, was swept clean. Gone, too, was the sharp aroma of roasting chestnuts. The neighbouring news stand in front of the Café St. Michel had blown down, and the first German troops, quartered in the larger hotels along the quai, had gathered up the scattered papers. De Gaulle's appeal had spread, even in advance of its publication.
L'Oursin did not go drunkenly in search of his adversaries of the Right, since all of them were far away and about to be enthroned. (Practically the entire roster of the Cagoulards was in the new Vichy Government.) Instead he walked, with his sailor's gait that swayed him from side to side, and found Frémont with Madame Absalom. At the corner of the rue de la Huchette, near the place, stood a pair of German sentries, one with phrase book in hand. Two more were in front of the Bureau de Police at the rue du Chat Qui Pêche. The gruff old man and the lonely middle-aged man set out on foot in the general direction of the Norman coast, where l'Oursin said they could get jobs in a fishing boat. The Boche already had announced in _Paris-Soir,_ which was taken over instantly by the invader, that producers of food, on land or off the coast, should get to work for all concerned as soon as possible.
'Why should you work for the Boche?' the old woman demanded. 'Can't you starve, like the rest of us?' L'Oursin winked and nodded to the grim old party who sat, ragged, in her untidy bed.
'To fish one must have petrol,' he said.
'What does that get you?' asked Absalom.
'One can sell the petrol for more than the fish.'
'You want to get rich, you _salaud_? What kind of son of a _putain_ comes here to my shop to torment respectable citizens of the...' Then she caught herself and frowned. 'The citizens of _merde_ _!_ ' she added.
L'Oursin winked again and slapped Frémont on the shoulder. 'With money one can get across to the English, and maybe now they'll fight,' he said.
All the spite left Absalom's wrinkled face. Chuckling and coughing she smiled.
'They're a thick-headed lot, but go ahead, _mon vieux!'_ she said.
And when Frémont hesitated at the door she growled:
'Don't you hang around. You're no good here. You're both a pair of boozefighters beyond help. Go on, little rabbits! Get your faces busted in with the bloody English! Ha! Ho!' The rest was lost in coughing and gurgling which they heard a short way down the street.
Monsieur de Malancourt, a week before, had taken Nadia, who had spent three days in the dread Stadium, to his swell hotel on the Right Bank and before a priest and then the only _mairie_ he could find, he had married her once in church, kissed her hand, walked debonairly with her to the back door of the _mairie_ , married her again in civil style, and kissed her on the cheek. He had gathered together as much money as he could, which filled a large part of his baggage, bought at a fabulous price the broken-down last year's auto from the Hotel Ritz, and, stopping almost momentarily to give francs to those who needed them along the crowded highways where trooped the refugees, had proceeded on his one and only honeymoon. This took him through Vichy, where he had friends in high places he was willing to use just once more. There he signed over enough assets to Nadia to keep her almost anywhere for any length of time.
At the Swiss border, as soon as her passport (a new one and as legally French as any document could be) was stamped and she was safely through the gate, de Malancourt held out his hand gallantly.
'I couldn't explain, for fear of worrying you, my dear. I must remain behind – just a day or two. In Geneva, stop at the Grand Hotel,' he said.
Nadia made a touching Polish scene and meant it, but once across the border she couldn't get back without formalities. When her tears and sobs subsided a little, he held out his hands a little distance towards her and said:
'I've never commanded you!'
'No, _chéri_ ,' she said.
'This time I command. Please go!'
The weeping Nadia, as lovely at thirty-six as she had been at twenty-one, when de Malancourt had found her, was led, almost fainting, into the station. De Malancourt nodded to the chauffeur, tipped the attendants generously, and turned his head towards France, and his celebrated rear towards Vichy. The last heard of him he was in Lyons, with no more francs to give away.
Soon the police were back on duty in the rue de la Huchette, but not for patrolling the neighbourhood in pairs, as in luckier days. Instead they tried to teach pedestrians and pushers of handcarts and children's carriages not to interrupt a German column when troops were marching down the boulevard.
The German command designated the Brasserie Dalmatienne as the suitable café for German officers in the quarter, and at meal times these busy directors of occupation, for which the French paid more than they had for their own defence, convened chez Daniel. It was not the fault of the handsome Serb, now too old for the ring. Just what could he do?
The Navet and the tailor, Saint-Aulaire, were sworn in by a new agency from Vichy to carry on in Paris under the direction of Pierre Laval, and to his concierge The Navet said, when she returned to No. 32: 'You see now what those cowardly English have brought to us. At the most, they sent ten divisions, and all of them ran!'
The Nazi-controlled press contained editorials of that nature every day.
The Navet, outside his apartment, shows a rather self-satisfied air, and talks about the sufferings ahead and that France must work and pay for Bolshevik waste and English perfidy. In his bedroom, he still tries, with threats and cajoling, to make Jeanne name the man who dishonoured him, always referring to him in the singular. Madame Spook heard that Jeanne is denying herself what little sugar comes her way, in order to save it up until the quantity is impressive enough to denounce her husband to the Boche for hoarding. I shudder whenever I think of the individualist, Saint-Aulaire, in charge of a department of quantity production of convict and working clothes, to be made from substitutes for cloth.
Of the able-bodied men who were sent by the Germans to work in Germany – including André the coal man, Monge and Louis, the one-armed _garçon_ – Guy, of the Hôtel Normandie fares the hardest, not counting the dead l'Hibou. For when Sara was sent, for Jewishness and trying to feed other Jews in secret, to take a place on the bench beside her former clients in the Stadium, who had lost 'nearly half their pounds', Guy ran amok and was clubbed into insensibility while Mocha, protesting, was shot and his sleek black body tossed into the Seine. It must not be inferred that the visiting Gennans, with wanton brutality, set upon this man and destroyed his ageing dog. Guy attacked them, in defiance of regulations, and was the partial cause of Maurice and some other hostages being threatened with death if their compatriots did not behave.
When informed that _Le Panier Fleuri_ was to be taken over for the use of German non-coms., Mariette had what is known as a _crise de nerfs_ , or nervous breakdown, and Mireille broke some regulations on her own account. She set fire to the joint, after warning Mado, Armandine and little Daisy, and, when arrested, was dragged away singing the Marseillaise. The fire engine came for the third time to the rue de la Huchette and put out the fire in time, and the first evening the noncoms drank too much champagne and were warned by the officer of the day that any further disorder would be punished severely.
Of Hortense Berthelot there is little to say. The office in the prefecture in which she worked for years was discontinued; so she was sent upstairs to another one and still received patiently such citizens as were sent to her desk. She is yellow and thin, having eaten little else but chick peas and turnips in the course of last winter. Morning and evening she feeds what she can get to Madame Absalom, now seventy-eight years old and of very sound mind.
The Nazis made a fair haul in the rue de la Huchette, taking over the canned goods of l'Épicerie Danton, for which they paid in printing-press marks; the soap and cosmetics in Julien's barbershop; the wine from Alice, wife of André; the cotton goods of the Lunevilles; whatever was of metal in the paint shop; and the entire stock of dogs, cats and stuffing materials owned by the gaunt Noël. These were wanted for some weird _ersatz_. In each instance an inventory was made by a German, an estimate of value was made by another German, and a slip of paper was given to the owner or owners which entitled them to call at an office where they could exchange it for a given number of marks, computed at twenty francs to the mark.
Noël, with the money he received, has been able to eat frugally for about four months. He has volunteered to labour, no matter for whom, to take his mind from other things, but his gauntness makes him look unhealthier than he is, so no one will accept him.
When two German soldiers, both non-coms., came to the shop of Madame Absalom to take away her coloured yarns, she reached for her cane. One of the Germans, a blond young man from Hanover, having a grouchy grandmother of his own, was reluctant to carry out his orders. He prevailed on the other, a country boy from Westphalia, to ask Madame Absalom, in phrasebook French, if, in case they were lax in Nazi duty, she would hide the stuff away so they would not be shot at sunrise.
That brought about a change of mood in the indignant old woman.
'Oh, take the blasted stuff, _mes lapins,'_ she said. 'We're all in the soup together, and you're younger. You'll suffer more than I do. Ha! He! Ho!'
_Les Dernières Nouvelles_ , four months after the Nazis came, was about to go to press when the censor caught the following item which, since he held it to be discouraging and suggestive of discontent among the French, did not appear:
'Mlle...... [the screen name of Hyacinthe Goujon] was found dead in her bedroom, and in the adjoining chambers of her apartment, 32 rue de la Huchette, her mother, Anne Goujon, and her grandfather, formerly a judge, were also asphyxiated by the fumes of a charcoal brazier. The windows were tightly closed and the doors were sealed with old theatre programmes. The loss of Mlle...... is a severe blow to the French cinema which has been showing an impressive recovery under government encouragement.'
It was two months later that a brief letter was delivered to me.
'My friend. I am afraid. I cannot convey to you the fear that is freezing like paralysis. You know how I wanted to live.... I shall wait for a glimpse of the bats.
'I cannot be accused of self-destruction. It is not Hyacinthe who dies, but the life all around her...'
# _About the Author_
ELLIOT PAUL WAS BORN IN MASSACHUSETTS IN 1891 and graduated from the University of Maine. After working in the construction camps of the American North-west, he returned to New England and worked on a Boston newspaper. During World War I he served in the Signal Corps of the American Expeditionary Force, and decided to stay on in Europe where he worked on the Paris editions of the _Chicago Tribune_ and the _New York Herald_. While living in rue de la Huchette, in 1927 he co-founded an experimental modernist review, _transition_ , with Eugene Jolas. It gave space to many struggling artists who were later to become famous. Work by Samuel Beckett, Franz Kafka, Gertrude Stein, Dylan Thomas and James Joyce sat between covers by Miro, Picasso, Kandinsky and Man Ray.
Between 1931 and 1936 Elliot Paul lived on Ibiza, whence he was rescued at the height of the Spanish Civil War by a man-o-war. At the outbreak of the Second World War he returned to New York and began a series of successful detective novels. Readers of this book will not be surprised to hear that he once introduced into the Massachusetts Legislature a bill (defeated) forcing book & play censors to pass an intelligence test and to prove that their sex lives were normal.
61 Exmouth Market, London EC1R 4QL
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# Copyright
First published by Random House Inc in 1942
First published by Eland Publishing Limited
61 Exmouth Market, London EC1R 4QL in 2011
This ebook edition first published in 2012
All rights reserved
Copyright © the Estate of Elliot Paul
The right of Elliot Paul to be identified as author
of this work has been asserted in accordance with the
Copyright, Designs and Patents Act 1988
This ebook is copyright material and must not be copied, reproduced, transferred, distributed, leased, licensed or publicly performed or used in any way except as specifically permitted in writing by the publishers, as allowed under the terms and conditions under which it was purchased or as strictly permitted by applicable copyright law. Any unauthorised distribution or use of this text may be a direct infringement of the author's and publisher's rights, and those responsible may be liable in law accordingly
ISBN 978–1–78060–003–1
Cover Image: _Police Station on the corner of rue de la Huchette and rue du Chat-qui-Pêche_ by Brassaï, pseudonym of Halasz Gyula (1899–1984) © Brassaï Estate RMM/Collection Centre Pompidou, Dist. RMN/Adam Rzepka
| {
"redpajama_set_name": "RedPajamaBook"
} | 5,180 |
\section{Introduction}
Among many ways of generalizing the ordinary derivative $\frac{d}{dx}$,
the notion of the so-called Laguerre derivative \cite{Dattoli1} seems to be particularly fruitful.
The idea is to extend the operator $\frac{d}{dx}$ to a simple homogeneous counterpart $D_x$,
which we define as in \cite{Dattoli2},\cite{Dattoli3}
(note that here we omit the factor $(-1)$ present in these references):
\begin{eqnarray}
D_x=\frac{d}{dx}x\frac{d}{dx}.
\end{eqnarray}
In Refs.\cite{Dattoli1},\cite{Dattoli2},\cite{Dattoli3} many important consequences of the replacement $\frac{d}{dx}\rightarrow D_x$
in the integral transform methods and in the operational calculus were investigated.
The link between $D_x$ and the Laguerre polynomials becomes clear if one notices the operational
relation (see Eq.(5) of Ref.\cite{Dattoli3}) which is easy to get using the amusing identity $D_x^{n}=\left(\frac{d}{dx}\right)^{n}x^{n}\left(\frac{d}{dx}\right)^{n}$ \cite{turbiner}
\begin{eqnarray}
\label{ELaguerre}
e^{yD_x}x^n=n!\;y^nL_n(-\frac{\displaystyle x}{\displaystyle y}),
\end{eqnarray}
where $L_n(z)$ are Laguerre polynomials. This justifies \textit{a posteriori} the name Laguerre derivative for $D_x$.
Using Eq.~(\ref{ELaguerre}) we may obtain the action of $e^{\lambda D_x}$ on various functions, using the different generating functions of Laguerre polynomials listed in Section 5.11 of \cite{Prudnikov}. In particular, using the well known ordinary generating function of $L_n(x)$ (formula 5.11.2.1 for $\alpha=0$ of \cite{Prudnikov} ) one obtains \cite{Dattoli5}
\begin{eqnarray}
\label{2}
e^{\lambda D_x}e^{-bx}=\frac{1}{1+b\lambda}\exp\left(-\frac{bx}{1+b\lambda}\right)
\end{eqnarray}
valid for $|b\lambda|<1$ \cite{Dattoli5}. Analogously, using the formula 5.11.2.6 of \cite{Prudnikov}, one gets
\begin{eqnarray}
e^{\lambda D_x}{_{1}F_{1}}\left([b],[1],x\right)=\frac{1}{(1-\lambda)^{b}} \ {_{1}F_{1}}\left([b],[1],\frac{x}{1-\lambda}\right),
\end{eqnarray}
with $_{1}F_{1}$ the hypergeometric function\footnote{We use a convenient and self-explanatory notation for the hypergeometric functions of type ${_p}F_{q}$: ${_p}F_{q}$([List of $p$ upper parameters],[List of $q$ lower parameters],$x$).} which for many values of $b$ specializes to elementary or known special functions. Note that for both these examples the action of $e^{\lambda D_x}$ results in a substitution and a prefactor which is reminiscent of the so-called Sheffer-type operators \cite{PLA1}.
We now employ the operational equivalence
\begin{eqnarray}
\label{aa}
[\frac{d}{dx},x]=1\longleftrightarrow[a,a^\dag]=1,
\end{eqnarray}
where $a$, $a^\dag$
are boson annihilation and creation operators respectively and rewrite $D_x\longleftrightarrow D$ as
\begin{eqnarray}
\label{aaa}
D=aa^\dag a.
\end{eqnarray}
By going one step further we extend Eq.(\ref{aaa}) by defining the generalized Laguerre derivative $D(r,M)$ as
\begin{equation}
\label{araM}
\begin{array}{l}
\hskip -52pt
{\displaystyle D(r,M)=a^r(a^\dag a)^M \sim D_{x}(r,M) =(\frac{d}{dx})^r(x\frac{d}{dx})^M\ ,
\ \ r=1,2,...\ \ ,M=0,1,...\ .}
\end{array}
\end{equation}
These operators are the object of our present study. Although the equivalence in Eq.(\ref{araM}) between $D(r,M)$ and $D_{x}(r,M)$ is formal since the domains of $a$, $a^\dag$ and $\frac{d}{dx}$, $x$ are different, we shall show that it provides one with an effective calculational tool.
Since $(a^\dag a)^M$ conserves the number of bosons, the operators $D(r,M)$ act as monomials in boson operators which annihilate $r$ bosons. Recent experiments in quantum optics have shown how one may produce quantum states with specified numbers of photons. This in turn raises the interesting possibility of producing exotic coherent states; that is, states other than the standard ones which satisfy $a|z\rangle = z|z\rangle$
\cite{Klauder}. The current work introduces operators whose eigenstates may be used to model new coherent states which have many of the features of the standard ones, and still permit explicit analytic description. The explicit forms of these new generalized coherent states can be used to evaluate relevant physical parameters, such as the photon distribution and the Mandel parameter, squeezing factors and signal-to-noise ratio, etc.
Much theoretical work has been devoted to the description of nonstandard coherent states; for example, the so-called nonlinear coherent states \cite{Vogel}, multiphoton coherent states \cite{Solomon1} and $q$-deformed coherent states \cite{Solomon2}. The structure embodied in definition Eq.(\ref{araM}) is a special case of the extension of boson operators proposed in the construction of nonlinear coherent states \cite{Vogel}. In this latter reference one defines the generalized boson annihilator $b$ by
\begin{eqnarray}
\label{noncoh}
b=af(a^{\dag}a)
\end{eqnarray}
choosing the $f(x)$ that most suits the problem in question. Evidently for this identification $r=1$ and $f(x)=x^M$. In this case the commutator is equal to
\begin{eqnarray}\label{D1D1}
[D(1,M),D^\dag(1,M)]=(a^\dag a+1)^{2M+1}-(a^\dag a)^{2M+1}.
\end{eqnarray}
This emphasizes the fact that although $D(1,M)$ and $D^{\dag}(1,M)$ annihilate and create one boson, respectively, they are \textit{not} canonical boson operators (unless $M=0$). Eq.(\ref{D1D1}) is a special case of
\begin{eqnarray}
\label{10}
[D(r,M),D^\dag(r,M)]&=&(a^\dag a+r)^{2M}\left(\sum_{k=1}^{r+1}|\sigma(r+1,k)|(a^\dag a)^{k-1}\right)-\nonumber\\
&&-
(a^\dag a)^{2M}\left(\sum_{k=1}^{r}|\sigma(r,k)|(a^\dag a)^{k}\right),
\end{eqnarray}
where the $\sigma(r,k)$ are Stirling numbers of the first kind \cite{Comtet}.
Eq.(\ref{10}) was obtained by using the following two equations
\begin{equation}
\label{11}
\begin{array}{rcl}
a^{r}(a^{\dag})^{r} &=& \prod\limits_{p=1}^{r}{(a^{\dag}a + p)}=\\
&=&\sum\limits_{k=1}^{r+1}|\sigma(r+1,k)|(a^{\dag}a)^{k-1}.
\end{array}
\end{equation}
The first part of Eq.(\ref{11}) is readily proved by induction. To prove the second part of Eq.(\ref{11}) we use the generating function for $|\sigma(r+1,k)|$ in the form \cite{Weisstein}
\begin{equation}
\begin{array}{rcl}
\sum\limits_{k=1}^{r+1}|\sigma(r+1,k)|x^{r+1-k} &=&\prod\limits_{p=1}^{r}(1 + px)\label{13}
\end{array}
\end{equation}
from which, by substituting $x = 1/n$ and using the first part of Eq.(\ref{11}), the second part of Eq.(\ref{11}) follows.
The basic objective of this work is the investigation of arbitrary powers
of $D(r,M)$ which in turn will allow one to evaluate Taylor-expandable functions of $D(r,M)$. We achieve our goal following recently developed methods of construction of normally ordered products \cite{PLA}, \cite{AnnComb}, \cite{JMP}, \cite {Bugs}.
As we shall show, results derived in this way have a combinatorial flavour and lend themselves to a
combinatorial interpretation.
The paper is organized as follows.
In Section \ref{NormalOrd} we introduce generalizations of the Stirling and Bell numbers which are well known from classical combinatorics and relate them to the normally ordered powers
of operators $D(r,M)$. These numbers, as shown in Section \ref{Dobinski}, may be explicitly found using generalized Dobi\'nski relations. In Section \ref{Combinatorics} we compare calculations of purely analytical origin with those based on methods of graph theory and give a combinatorial interpretation of our results. Examples of various applications of our approach are presented in Section \ref{Examples} while Section \ref{Conclusions} summarizes the paper.
\section{Normal ordering: Generalized Stirling and Bell Numbers}
\label{NormalOrd}
The \emph{normally ordered} form of $F(a,a^\dag)$, denoted by $F_{\mathcal{N}}(a,a^\dag)$
\cite{Louisell} is obtained by moving all annihilators to the right using the canonical commutation
relation of Eq.(\ref{aa}). It satisfies $F_{\mathcal{N}}(a,a^\dag)=F(a,a^\dag)$. On the
other hand the \emph{double dot} operation $:G(a,a^\dag):$ means that we are applying the
same ordering procedure but without taking account of the commutation relation.
Conventionally the solution to the normal ordering problem is obtained if a function
$G(a,a^\dag)$ is found satisfying
\begin{eqnarray}\label{NFG}
F_{\mathcal{N}}(a,a^\dag)=\ :G(a,a^\dag):\ \ .
\end{eqnarray}
A large body of research has been recently devoted to finding the solution of
Eq.(\ref{NFG}) \cite{AmJPhys}. A general approach which facilitates a combinatorial interpretation of
quantum mechanical quantities is to use the coherent state representation. Standard
coherent states
\begin{equation}\label{scs}
|z\rangle=e^{-|z|^2/2}\sum_{n=0}^\infty\frac{z^n}{\sqrt{n!}}|n\rangle
\end{equation}
with the number states $|n\rangle$ satisfying $a^\dag a|n\rangle=n|n\rangle$, $\langle
n|n'\rangle=\delta_{n,n'}$ and $z$ complex, are eigenstates of the annihilation operator,
i.e. $a|z\rangle=z|z\rangle$. The latter eigenstate property shows that having solved the
normal ordering problem Eq.(\ref{NFG}) for an operator $F(a,a^\dag)$ we immediately find
\begin{eqnarray}
\label{NFG2} \langle z|F_{\mathcal{N}}(a,a^\dag)|z\rangle =\ G(z,z^{*}) \ .
\end{eqnarray}
An early observation on how to extract combinatorial content from normally ordered forms
\cite{Katriel} was based on the formula $e^{\lambda a^\dag a}=\ :e^{a^\dag
a(e^\lambda-1)}:$ \cite{Cahill}. It led to the identification
\begin{eqnarray} \label{Bell}
\langle z|(a^\dag a)^n|z\rangle\stackrel{z=1}{=}B(n),
\end{eqnarray}
where the $B(n)$ are conventional Bell numbers described in \cite{Comtet}. Eq.(\ref{Bell})
may be taken as a {\em definition} of the Bell numbers. For Stirling numbers of the
second kind we have \cite{Comtet},
\begin{equation}\label{stirling}
( a^\dag a)^n= \sum_{k=0}^{n}S(n,k)(a^\dag)^ka^k
\end{equation}
(which may also be used as a practical definition) in terms of which one defines the
Bell polynomials by
\begin{equation}\label{Bellpoly}
B(n,x)=\sum_{k=0}^{n}S(n,k)x^k.
\end{equation}
We have extended and developed the coherent state
methodology for operators other than $a^\dag a$ in \cite{PLA}, \cite{AnnComb} and \cite{JMP}.
After the seminal observation by Katriel \cite{Katriel}, combinatorial methods found
widespread application in this context \cite{PLA},\cite{AnnComb},\cite {JMP},\cite{Bugs},\cite{Mikhailov}. We apply these methods to $F(a,a^\dag)=[D(r,M)]^n$, $n=1,2,...$ .
Formally, we write $[D(r,M)]^n$ in normally
ordered form as
\begin{eqnarray}
\label{Saa} [D(r,M)]^n=\left[\sum_{k=0}^{Mn}S_{r}^{(M)}(n,k)(a^\dag)^ka^k\right]a^{rn}.
\end{eqnarray}
Clearly, from Eq.(\ref{Saa}) the integers $S_{r}^{(M)}(n,k)$ are generalizations of
the conventional Stirling numbers of the second kind (which are recovered for $r=0,
M=1$). Analogously to Eq.(\ref{Bellpoly}) the numbers $S_{r}^{(M)}(n,k)$ serve to define
the generalized Bell polynomials
\begin{eqnarray}
\label{B} B_{r}^{(M)}(n,x)=\sum_{k=0}^{Mn}S_{r}^{(M)}(n,k)x^k.
\end{eqnarray}
Finding the explicit form of these generalized Stirling numbers will give the normally
ordered form of $[D(r,M)]^n$. We proceed to do this in the next section by use of a
generalization of the famous Dobi\'nski formula.
\section{Generalized Dobi\'nski formula}\label{Dobinski}
We first write Eq.(\ref{Saa}) in derivative form as
\begin{eqnarray} \label{Sdd}
[D_x(r,M)]^n=
\left[\sum_{k=0}^{Mn}S_{r}^{(M)}(n,k)x^k\left(\frac{d}{dx}\right)^k\right]\left(\frac{d}{dx}\right)^{rn}.
\end{eqnarray}
Acting with the r.h.s. of Eq.(\ref{Sdd}) on $e^x$ one obtains $B_{r}^{(M)}(n,x)e^x$. The
action of the l.h.s. of Eq.(\ref{Sdd}) on $e^x$ is obtained by acting with generalized
Laguerre derivatives on monomials $x^p$
\begin{eqnarray}
D_x(r,M)\ x^p=p^{\underline{r}}p^Mx^{p-r},
\end{eqnarray}
where $p^{\underline{r}}=p(p-1)...(p-r+1)$ is the falling factorial, then extending it to the $n$-th power
\begin{eqnarray}
\label{Dpxn}
\left[D_x(r,M)\right]^nx^p=\left[\prod_{j=0}^{n-1}(p-rj)^{\underline{r}}(p-rj)^M\right]
x^{n-rp},
\end{eqnarray}
and next summing up contributions for $x^p/p!$
\begin{eqnarray}
\label{Dpxn1}
\sum\limits_{p=0}^{\infty}\left[D_x(r,M)\right]^n{\displaystyle{\frac{x^p}{p!}}}=\sum\limits_{p=rn}^{\infty}\left[\prod_{j=0}^{n-1}(p-rj)^{\underline{r}}(p-rj)^M\right]{\displaystyle{\frac{x^{p-rn}}{p!}}}\ .
\end{eqnarray}
Upon simplifying Eq.(\ref{Dpxn1}) leads to the Dobi\'nski-type
representation of generalized Bell polynomials \cite{Bugs},\cite{Lognormal},\cite{Dobinski}:
\begin{eqnarray}
\label{Dob} B_{r}^{(M)}(n,x)=e^{-x}\sum_{l=0}^\infty
\left[\prod_{i=1}^n(l+ir)\right]^M\frac{x^l}{l!}\ ,
\end{eqnarray}
verified by direct calculation of $\langle z|[a^{r}(a^{\dag}a)^{M}]^{n}|z\rangle$.
The classic Dobi\'nski formula \cite{Comtet} corresponds to $r=0,M=1$:
\begin{eqnarray}
\label{classDob} B(n,x)=e^{-x}\sum_{l=0}^\infty \frac{l^n x^l}{l!}.
\end{eqnarray}
From Eq.(\ref{Dob}) the generalized Stirling numbers are obtained by standard Cauchy
multiplication of series
\begin{equation}
\label{SrM}
\begin{array}{l}
\hskip -25pt {S_{r}^{(M)}(n,k)={\displaystyle\frac{1}{k!}\sum_{j=0}^k\left(\begin{array}{c}{k}\\{j}\end{array}\right)(-1)^{k-j}
\left[\prod_{i=1}^n(j+ir)\right]^M}\ ,
\ \ \ k=0,1,\dots,Mn.}
\end{array}
\end{equation}
We point out that Eqs.(\ref{Dob}) and (\ref{SrM}) are the central results we need for further
calculations. For practical applications it is useful to note that the
generalized Stirling and Bell numbers, as well as generalized Bell polynomials, can be
expressed through generalized hypergeometric functions $_{p}F_{q}$.
Below we quote some examples of such relations.
\begin{equation}
\label{stgen}
S_{1}^{(M)}(n,k)= \frac{(-1)^k (n!)^M}{k!}\cdot\!\!\ _{M+1}F_{M}([-k,\underbrace{n+1,...,n+1}_{M\ times}],[\underbrace{1,...,1}_{M\ times}],1)
\end{equation}
\begin{equation}
\label{bellgenpol}
B_{1}^{(M)}(n, x)= e^{-x}(n!)^M\cdot\!\!\ _{M}F_{M}([\underbrace{n+1,...,n+1}_{M\ times}],[\underbrace{1,...,1}_{M\ times}],x)
\end{equation}
The numbers $B^{(M)}_{1}(n)= B^{(M)}_{1}(n,1)$ can be shown to be related to the numbers $B_{p,p}(n)$ (introduced in Refs.\cite{PLA} and \cite{AnnComb}) characterizing the normal order of $[(a^{\dag})^{p}a^{p}]^{n}$ by the formula
\begin{equation}
\label{bellgenpol1a}
B^{(M)}_{1}(n)=B_{n,n}(M+1)\ ,
\end{equation}
as seen by comparing Eq.(2.6) in Ref.\cite{AnnComb} with Eq.(\ref{Dob}) of the present work.
\begin{equation}
\label{bellgenpol1}
\begin{array}{l}
\hskip -78pt{B_{2}^{(M)}(n, x)= \frac{1}{{\pi}^{M/2}}2^{Mn}e^{-x}\left((n!)^M\cdot\!\!\ _{M}F_{M+1}([\underbrace{n+1,...,n+1}_{M\ times}],[\!\underbrace{1,...,1}_{M\ times}\!,1/2],x^2/4){\pi}^{M/2}+\right.}\\
\hskip -78pt{\left.+2^{M}\left[{\Gamma(n+3/2)}\right]^M\cdot\!\!\ x \cdot {_{M}F_{M+1}}([\underbrace{n+3/2,...,n+3/2}_{M\ times}],[\underbrace{3/2,...,3/2}_{M+1\ times}],x^2/4)\right) \ ,}
\end{array}
\end{equation}
\begin{equation}
\hskip -1pt{\label{bellgenpol2}}
\begin{array}{l}
\hskip -78pt{B_{3}^{(M)}(n,x)= \frac{1}{2^{M+1}[\pi\Gamma(2/3)]^{M}}e^{-x}\ \times}
\\
\hskip -78pt{\times\ \left(2^{M+1}3^{Mn}[\pi n! \Gamma(2/3)]^{M}\cdot\!\!\ _{M}F_{M+2}([\underbrace{n+1,...,n+1}_{M\ times}],[\!\underbrace{1,...,1}_{M\ times}\!,1/3,2/3],x^3/27) + \right. }\\\\
\hskip -78pt{\left.+ 2\cdot 3^{M(n+3/2)} \left(\Gamma^{2}(2/3)\Gamma(n+4/3)\right)^M\right.\times} \\\\
\hskip -78pt{\left. \times\ x\cdot {_{M}F_{M+2}}([\underbrace{n + 4/3,...,n + 4/3}_{M\ times}],[\underbrace{4/3,...,4/3}_{M+1\ times},2/3],x^3/27)\ + \right. }\\
\hskip -78pt{\left.+ 3^{M(n+1)}\left[\pi{\Gamma(n+5/3)}\right]^M\cdot x^{2}\cdot\!\!\ {_{M}F_{M+2}}([\underbrace{n+5/3,...,n+5/3}_{M\ times}],[\underbrace{5/3,...,5/3}_{M+1\ times},4/3],x^3/27)\right)\ .}
\end{array}
\end{equation}
We conjecture that in general $B^{(M)}_{r}(n,x)$ is a combination of $r$ hypergeometric functions of type $_{M}F_{M+r-1}$ of argument $x^{r}/{r^{r}}$.
Examples of numbers resulting from Eqs.(\ref{bellgenpol})-(\ref{bellgenpol2}) for $n=0,\dots,6,\dots$ are
\begin{equation}
\label{numbers}
\begin{array}{l}
\hskip -78pt{M=1\ \ \ \ B_{1}^{(1)}(n) = 1,2,7,34,209,1546,13227\dots\ ,}\\\\
\hskip -78pt{M=2\ \ \ \ B_{1}^{(2)}(n) = 1,5,87,2971,163121,12962661\dots\ ,}\\\\
\hskip -78pt{M=3\ \ \ \ B_{1}^{(3)}(n) = 1,15,1657,513559,326922081,363303011071\dots\ ,}\\\\
\hskip -78pt{M=2\ \ \ \ B_{2}^{(2)}(n) = 1,10,339,23395,2682076,457112571,107943795145\dots\ ,}\\\\
\hskip -78pt{M=3\ \ \ \ B_{2}^{(3)}(n) = 1,37,9415,7063615,11360980081,33040809105661,}\\\\
\hskip -78pt{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 156151310977544887\dots\ ,}\\\\
\hskip -78pt{M=3\ \ \ \ B_{3}^{(3)}(n) = 1,77,39839,62310039,214107236041,1358185668416501,} \\\\
\hskip -78pt{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 14247249149298651007\dots\ ,}\\\\
\hskip -78pt{M=4\ \ \ \ B_{3}^{(4)}(n) = 1,372,1905633,43249617004,2805942285116705,}\\\\
\hskip -78pt{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 411223445534704016116,117428972441699060660584977\dots\ ,}
\end{array}
\end{equation}
which are positive integers and as such admit combinatorial interpretation. The first two sequences in Eq.(\ref{numbers}) may be identified as A002720 (which enumerates matching numbers of a perfect graph $K(n,n)$) and A069948, respectively, in Ref.~\cite{sloane}.
We note in passing that the numbers $B_{r}^{(M)}(n)$ are solutions of the Stieltjes moment problem, \textit{i.e.} they are the $n$-th moments of positive weight functions on the positive half axis. This can be deduced from their Dobi\'nski-type relations Eq.(\ref{Dob}), whose form allows one to obtain the weight functions for any $r$ and $M$. For the first two sequences in Eq.(\ref{numbers}) the Stieltjes weights are given in \cite{sloane} under their entries.
As a second illustration of our approach we shall apply it to $D(r,1)$. Note that
\begin{equation}
\label{bbb}
\left[a^r(a^\dag a)^M\right]^n=\,:B_r^{(M)}(n,a^\dag a)\,a^{rn}:\ ,
\end{equation}
which upon using the Dobi\'nski relation Eq.(\ref{Dob}) for $M=1$ leads to
\begin{eqnarray}
\label{shef}
e^{\lambda D(r,1)}=\ :\frac{1}{1-\lambda ra^r}\exp\left(\frac{a^\dag a}{(1-\lambda ra^r)^{1/r}}-a^\dag a\right):\ .
\end{eqnarray}
The operator $D(r,1)$
is of Sheffer-type viewed through hermitean conjugation (see Refs. \cite{PLA1},\cite{turbiner2}) and Eq.(\ref{shef}) can also be obtained through the methods developed in Ref.\cite{PLA1} (see Appendix). Consequently,
\begin{eqnarray}
\label{E}
\langle z| e^{\lambda D(r,1)}|z\rangle&\stackrel{z=1}{=}&\frac{1}{1-r\lambda}\exp\left(\frac{1}{(1-r\lambda)^{1/r}}-1\right)\equiv \\
&\equiv&\sum_{n=0}^\infty B_{r}^{(1)}(n)\frac{\lambda^n}{n!},
\end{eqnarray}
where
\begin{eqnarray}
\label{Bsigma}
\langle z|\left(a^ra^\dag a\right)^n|z\rangle\stackrel{z=1}{=}B_{r}^{(1)}(n)=\sum_{p=1}^{n+1}|\sigma(n+1,p)|r^{n-p+1}B(p-1)\ .
\end{eqnarray}
In Eq.(\ref{Bsigma}) $\sigma(n,k)$ are Stirling numbers of the first kind, $B(n)$ are conventional Bell numbers, and in obtaining Eq.(\ref{Bsigma}) we have again used Eq.(\ref{11}).
Using Eqs.(\ref{Saa}) and (\ref{bellgenpol}) we obtain for $r=1$ the following formula in a compact notation
\begin{eqnarray}
\label{BBB1}
\!\!\!\!\!\!\left[D(1,M)\right]^n=\ (n!)^M :e^{-a^\dag a}\cdot\!\!\ _{M}F_{M}([\underbrace{n+1,...,n+1}_{M\ times}],[\underbrace{1,...,1}_{M\ times}],a^\dag a)a^n:\ .
\end{eqnarray}
The last formula can be used to normally order $H(\lambda D(1,M))$ for any Taylor-expandable $H(x)$.
\section{Combinatorics of normally ordered Laguerre derivatives}\label{Combinatorics}
In previous Sections we considered the normal ordering of Laguerre derivatives for which the results heavily exploited combinatorial identities stemming from the underlying iterative character of the problem. Indeed, the reordering of the operators $a$ and $a^{\dag}$ is a purely combinatorial task which can be interpreted in terms of graphs \cite{Bugs},\cite{arXiv},\cite{HW} and analyzed by the use of combinatorial constructors \cite{flajolet}. Briefly, to each operator in the normally ordered form
$H=\sum_{r,s}\alpha_{r,s}\,(a^{\dag})^{r}a^s$ one associates a set of one-vertex graphs such that each vertex $\bullet$ carries weight $\alpha_{r,s}$ and has $r$ outgoing and $s$ incoming lines whose free ends are marked with white $\circ$ and gray ${\color{light-gray}\bullet}\!\!\!\circ$ spots respectively. Multi-vertex graphs are built in a step-by-step manner by adding one vertex at each consecutive step and joining some of its incoming lines with some the free outgoing lines of the graph constructed in the previous step. Additionally, one keeps track of the history by labeling each vertex by the number of steps in which it was introduced. As a result, one obtains a set of increasingly labeled multi-vertex graphs with some free incoming and outgoing lines. It can be shown that the normal ordering of powers of the operator $H$ can be obtained by enumeration of such structures. Namely, the coefficient of $({a}^{\dag})^{k}a^l$ in the normally ordered form of the operator $H^n$ is obtained by counting all possible graphs with $n$ vertices $\bullet$ and having $k$ white $\circ$ and $l$ gray ${\color{light-gray}\bullet}\!\!\!\circ$ spots respectively. For illustration, we give two examples of Laguerre derivatives $D(1,1)=aa^{\dag}a=a^{\dag}a^2+a$ and $D(2,1)=a^2a^{\dag}a=a^{\dag}a^3+2\,a^2$ and their graph representation leading to the solution of the normal ordering problem by simple enumeration (see Fig.~\ref{LaguerreFig}).
\begin{figure}[h]
\resizebox{\columnwidth}{!}{\includegraphics{LaguerreFig.eps}}
\caption{\label{LaguerreFig} Building blocks (in the inset) and the associated graphs of order $n=1,2$ for Laguerre derivatives: (a) $H=D(1,1)=a^{\dag}a^{2}+a$ and (b) $H=D(2,1)=a^{\dag}a^{3}+2a^{2}$.}
\end{figure}
One should compare these ``graphical results'' with the explicit formulas of Eqs.(\ref{SrM}) and (\ref{Dob}) or the expansion coefficients of the generating function in Eq.(\ref{E}) for $r=1,2$ and $M=1$. Thus, using Eq.(\ref{numbers}), the coefficients multiplying the operators in Fig.(1a) are the first two terms in $B^{(1)}_1(n) = 2,7,34,209$ for $n=1,2,\ldots$ (A002720). Similar coefficients in Fig.(1b) are the first two terms in $B^{(1)}_2(n) = 3,16,121,1179$ for $n=1,2,\ldots$ (A121629).
\section{Examples}\label{Examples}
1. For $r=M=1$, i.e. for $D(1,1)=aa^\dag a$\, one obtains (see \cite{Riordan} for a similar calculation):
\begin{eqnarray}
\label{DL}
\left[D(1,1)\right]^n=n!:L_n(-a^\dag a):a^n,
\end{eqnarray}
where $L_n(y)$ are Laguerre polynomials and Eq.(\ref{DL}) is derived from Eq.(\ref{BBB1}) and using the definition of $L_n(y)$ via the function $\ _1F_1$. Then
\begin{equation}
\label{xxxx}
\begin{array}{rcl}
e^{\lambda D(1,1)}&=&{\displaystyle\sum_{n=0}^\infty \frac{\lambda^n}{n!}\left[{D(1,1)}\right]^n = }\\
&=&{\displaystyle\ :\sum_{n=0}^\infty L_n(-a^\dag a)(\lambda a)^n:\ =\ :\frac{1}{1-\lambda a}\exp\left(\frac{\lambda a^\dag a^2}{1-\lambda a}\right):\ ,}
\end{array}
\end{equation}
where in Eq.(\ref{xxxx}) we have used the ordinary generating function for the Laguerre polynomials \cite{Prudnikov}.
Using other generating functions listed on p.704 of Ref.\cite{Prudnikov} one can
derive further formulas of type Eq.(\ref{xxxx}). ( In a) and b) below: $\lambda\neq0,\ p=1,2,...$).
a) Formula $5.11.2.6$ of \cite{Prudnikov} for $\alpha=0$ provides the normal ordering of
\begin{eqnarray}
\label{example1}
_{1}F_{1}\left([b],[1],\lambda D(1,1)\right) = {\displaystyle :\!\frac{1}{(1-\lambda a)^{b}}{_{1}F_{1}}\left([b],[1],\frac{\lambda a^{\dag} a^{2}}{1-\lambda a}\right)\!:\ ,}
\end{eqnarray}
which for $b$ integer and half-integer can be written down in terms of known functions. Examples are:
\begin{equation}
{\hskip -19pt\label{example2}}
\begin{array}{l}
\hskip -50pt{{_{1}{F}_{1}}\left([3],[1],\lambda D(1,1)\right) = {\displaystyle :\!\frac{1}{(1-\lambda a)^{3}}
L_{2}\left(-\frac{\lambda a^{\dag} a^{2}}{1-\lambda a}\right)\exp{\left(\frac{\lambda a^{\dag} a^{2}}{1-\lambda a}\right)}\!:\ ,}}\\\\
\hskip -50pt {{_{1}{F}_{1}}\left([\frac{3}{2}],[1],\lambda D(1,1)\right) = {\displaystyle :\exp{\left(\frac{\lambda a^{\dag} a^{2}}{2(1-\lambda a)}\right)}\times}}\\\\
\hskip 78pt {\displaystyle{\times\left[I_{0}\left({\frac{\lambda a^{\dag} a^{2}}{2(1-\lambda a)}}\right )(1+\frac{\lambda a^{\dag} a^{2}}{1-\lambda a}) + I_{1}\left({\frac{\lambda a^{\dag} a^{2}}{2(1-\lambda a)}}\right)\right]\!:\ .}}
\end{array}
\end{equation}
where $I_0(y)$ and $I_1(y)$ are modified Bessel functions.
b) Similarly, we consider the formula $5.11.2.8$ of \cite{Prudnikov}:
\begin{eqnarray}
\sum_{n=0}^\infty\left(\begin{array}{c}{n+p}\\{n}\end{array}\right)t^nL_{n+p}(x)=\frac{1}{(1-t)^{p+1}}e^{-\frac{tx}{1-t}}L_p\left({\frac{x}{1-t}}\right)\ .
\end{eqnarray}
Using Eq.(\ref{DL}) we obtain the normally ordered form of $[\lambda D(1,1)]^p\exp(\lambda D(1,1))/p!\,$:
\begin{equation}
\label{example3}
\begin{array}{rcl}
{\displaystyle
\frac{1}{p!}\sum_{n=0}^\infty\frac{[\lambda D(1,1)]^{n+p}}{n!}}&=&{\displaystyle\sum_{n=0}^\infty\frac{(n+p)!}{p!n!}:L_{n+p}(-a^\dag a)(\lambda a)^{n+p}: \ =}\\
&=&{\displaystyle :\frac{1}{(1-\lambda a)^{p+1}}e^{\frac{\lambda a^\dag a^2}{1-\lambda a}}L_p(-\frac{a^\dag a}{1-\lambda a}):\ (\lambda a)^p\ .}
\end{array}
\end{equation}
2. The normal order of the modified Bessel function of the first kind $I_0\left(2(\lambda D(1,1))^{1/2}\right)$ may be derived:
\begin{equation}
\label{example4}
\begin{array}{rcl}
I_0(2(\lambda D(1,1))^{1/2})&\!=\!&\!{\displaystyle :\sum_{n=0}^\infty \frac{L_n(-a^\dag a)(\lambda a)^n}{n!}: =}\\
&\!=\!&\!{\displaystyle :e^{\lambda a}J_0(2\sqrt{\lambda(-aa^\dag a)}):\ =\ :e^{\lambda a}I_0(2\sqrt{\lambda a^\dag a^2}):
\ ,}
\end{array}
\end{equation}
where in the last line we have used the exponential generating function of Laguerre polynomials \cite{Prudnikov}. The analogous formula for $J_0\left(2(\lambda D(1,1))^{1/2}\right)$ reads
\begin{equation}
\label{example5}
\begin{array}{rcl}
J_0(2(\lambda D(1,1))^{1/2})&=&{\displaystyle\ :\sum_{n=0}^\infty \frac{L_n(-a^\dag a)(-\lambda a)^n}{n!}:} =\\
&&{\displaystyle =\ :e^{-\lambda a}I_0(2\sqrt{\lambda a^\dag a^2}):\ .}
\end{array}
\end{equation}
3. We quote here the eigenfunctions of $D_x(r,M)$ with eigenvalue 1 satisfying $D_x(r,M)E(r,M;x)=E(r,M,x)$,
with the following $r$ boundary conditions:
\begin{eqnarray}
E(r,M;0)= 1,\ \ \ \ \ \ \ \left.\left[\frac{d^p}{{dx}^{p}}E(r,M;x)\right]\right|_{x=0}=0,\ \ \ p=1,\dots,r-1
\end{eqnarray}
which are
\begin{eqnarray}\label{EEEEE}
E(r,M;x)=\ _0F_{M+r-1}([\; \;],[\underbrace{1/r,2/r,...,(r-1)/r,}_{{r-1}\ times}\underbrace{1,...,1}_{M\ times}],x^r/r^{r+M})\ .
\end{eqnarray}
Useful normal ordering formulas can be obtained by applying the Dobi\'nski relations
to the eigenfunctions of $D_x(1,M)$ {\em with the argument taking operator values}, see Eq.(\ref{EEEEE}), i.e. $E(1,M;D_x(1,M))$. We briefly show the calculation, in boson notation, for $E(1,2;\lambda D(1,2))=_0\!\!F_2([\; \;],[1,1],\lambda D(1,2))$, see Eq.(\ref{BBB1}) :
\begin{equation}
\label{52}
\begin{array}{l}
_0F_2([\; \;],[1,1],\lambda D(1,2))=\sum\limits_{n=0}^\infty{\displaystyle\frac{\lambda^n}{(n!)^3}}[a(a^\dag a)^2]^n=\\\\
=\ :e^{-a^\dag a}\sum\limits_{l=0}^\infty{\displaystyle{\frac{(a^\dag a)^l}{l!}}}\sum\limits_{n=0}^\infty{\displaystyle\frac{((n+l)!)^2}{(l!)^3}}(\lambda a)^n:\ =\\\\
=\ :e^{-a^\dag a}\sum\limits_{l=0}^\infty{\displaystyle\frac{(a^\dag a)^l}{l!}}\ _2F_2([1+l,1+l],[1,1],\lambda a):\ ,
\end{array}
\end{equation}
and similarly
\begin{equation}
\label{a1}
\begin{array}{l}
E(1,M;\lambda D(1,M))=\ _0F_M([\; \;],[\ \underbrace{1,1,...1}_{M\ times}\ ],\lambda D(1,M))=\\
={\displaystyle\ :e^{-a^\dag a}\sum_{l=0}^\infty\frac{(a^\dag a)^l}{l!}\ _MF_M([\ \underbrace{1+l,1+l,...,1+l}_{M\ times}\ ],[\underbrace{1,1,...,1}_{M\ times}],\lambda a):\ ,}
\end{array}
\end{equation}
which indicates a pattern appearing in the course of this procedure.
Indeed, by evaluating the coherent state expectation value of Eq.(\ref{a1}) between $\langle z=1|\dots|z=1\rangle$ in the spirit of Eq.(\ref{Bell}) we obtain the hypergeometric generating functions of the numbers $B^{(M)}_{1}(n)$ as then
\begin{equation}
\label{a2}
\begin{array}{l}
{\displaystyle e^{-1}\sum\limits_{l=0}^{\infty}\frac{1}{l!}\ _MF_M([\underbrace{l+1, l+1, \dots, l+1}_{M\ times}],[\underbrace{1,1,...1}_{M\ times}],\lambda)=}\\
= {\displaystyle \sum_{n=0}^\infty B^{(M)}_{1}(n)\frac{\lambda^n}{(n!)^{M+1}}, \ \ \ \ \ M=1,2,\dots\ .}
\end{array}
\end{equation}
The hypergeometric generating function of $B_{r}^{(M)}(n, x)$ for arbitrary $r$ and $M$ can also be obtained from Eq.(\ref{Dob}), and reads:
\begin{equation}
\label{a3}
\begin{array}{l}
{\displaystyle e^{-x}\sum\limits_{l=0}^{\infty}\frac{x^l}{l!}\ _MF_M([\underbrace{l/r+1, l/r+1, \dots, l/r+1}_{M\ times}],[\underbrace{1,1,...1}_{M\ times}],r^M\lambda)=}\\
{\displaystyle= \sum_{n=0}^\infty B^{(M)}_{r}(n,x)\frac{\lambda^n}{(n!)^{M+1}}\ .}
\end{array}
\end{equation}
In spite of their apparent complexity the l.h.s of the above equations can be straightforwardly handled by computer algebra systems \cite{Maple}.
\section{Conclusions and outlook}
\label{Conclusions}
We have found exact analytical expressions for the generalized Stirling numbers and generalized Bell polynomials which appear in the normal ordering of powers of Laguerre-type derivative operators, and have provided a complete set of hypergeometric generating functions for these quantities. The combinatorial aspect of the problem was demonstrated by finding an exact mapping between the normal ordering and an enumeration of increasingly labelled, multivertex forests constructed according to a two-parameter $(r, M)$ prescription. In this way analytical, numerical and combinatorial facets of this problem have been given a very complete treatment. We have also used generalized Dobi\'nski relations to investigate the properties of these Laguerre-type differential operators. We provided a large number of operational formulas involving functions of Laguerre derivatives, which can alternatively be applied using the boson language. The framework developed above enables one to construct and analyze new coherent states relevant to nonlinear quantum optics, which will be the subject of forthcoming research.
\section{Acknowledgments}
We wish to acknowledge support from Agence Nationale de la Recherche (Paris, France) under programme no. ANR-08-BLAN-0243-2.
Two of us, P.B. and A.H., wish to acknowledge support from the Polish Ministry of Science and Higher Education under grants no. N202 061434 and 202 107 32/2832.
\section{Appendix: Sheffer-type operators}\label{Appendix}
We derive Eq.(\ref{shef}) with the help of methods developed in Ref.\cite{PLA1}.
First, observe that $D(r,1)=a^\dag a^{r+1}+r a^r$ from which it follows that
$D^\dag(r,1)=(a^\dag)^{r+1} a +r (a^\dag)^r$ is an operator of Sheffer-type:
$D^\dag(r,1)=v(a^\dag)+q(a^\dag)a$ with $q(x)=x^{r+1}$ and $v(x)=rx^r$.
The normally ordered form of $\exp(\lambda D^\dag(r,1))$
is obtained by solving the linear differential equations (Eqs.(2) and (3) of Ref.\cite{PLA1})
for $T(\lambda,x)$ and $g(\lambda,x)$ yielding
\begin{eqnarray}
T(\lambda,a^\dag)=\frac{a^\dag}{(1-\lambda r (a^\dag)^r)^{1/r}},{\hskip 207pt{(A1)}}\nonumber
\end{eqnarray}
and
\begin{eqnarray}
g(\lambda,a^\dag)=\frac{1}{1-\lambda r (a^\dag)^r}\ .{\hskip 230pt{(A2)}}\nonumber
\end{eqnarray}
According to Eq.(29) of \cite{PLA1} the normally ordered form of $e^{\lambda D(r,1)}$ is
\begin{eqnarray}
e^{\lambda D(r,1)}=\left[e^{\lambda D^\dag(r,1)}\right]^\dag=\ :g(\lambda,a)e^{a^\dag(T(\lambda,a)-a)}:{\hskip 121pt{(A3)}}\nonumber
\end{eqnarray}
which gives Eq.(\ref{shef}).
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\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,142 |
\section{ABD Kinematics}
\label{sec:affine}
We begin by constructing a flat kinematics via affine coordinates. We equip each simulated body $b$ in our domain with a time-varying linear transform $\mathsf{A}_b(t) \in \R^{3 \times 3}$, and a translation $p_b(t) \in \R^3$. In the following we often store per-body configuration in the vector form as: $
q = \left(p^T, a_1^T, a_2^T, a_3^T\right)^T \in \R^{12}$, with the transform $\mathsf{A} = [a_1, a_2, a_3]^T$, then stored in row order.
Each material point $k$ in body $b$ has a body frame (equivalently rest) position $\bar{x}_k$ with its corresponding world frame coordinates given by the affine map:
\begin{equation}\label{eq:kinematic}
x_k = \mathsf{A}_b \bar{x}_k + p_b = \mathsf{J}(\bar{x}_k) q,
\end{equation}
and its velocity,
\begin{equation}\label{eq:kinematic-vel}
{\dot x}_k = \dot{\mathsf{A}}_b \bar{x}_k + \dot{p}_b = \mathsf{J}(\bar{x}_k) \dot q.
\end{equation}
Here note that $\mathsf{J}(\bar{x}) = [ \mathsf{I}_3, \mathsf{I}_3 \otimes \bar{x}]$ is \emph{constant} across all configuration changes, where $\mathsf{I}_3$ is a 3 by 3 identity matrix.
\subsection{Kinetic Energy}
Given a mass density distribution, $\rho$, over the body domain, $\Omega$, the kinetic energy of each affine body is then
\begin{align}
\begin{split}
\frac{1}{2} \int_\Omega \rho \dot{x}^T \dot{x} \> \mathrm{d}\Omega &= \frac{1}{2} \int_\Omega \rho (\dot{\mathsf{A}} \bar{x} + \dot{p})^T (\dot{\mathsf{A}} \bar{x} + {\dot p})\> \mathrm{d}\Omega \\
&= \frac{1}{2} \dot{q}^T \left( \int_\Omega \rho \> \mathsf{J}(\bar{x})^T \mathsf{J}(\bar{x}) \> \mathrm{d}\Omega \right) \dot{q},
\end{split}
\end{align}
with the generalized mass matrix for each affine body defined as:
\begin{align}
\label{eq:mass}
\mathsf{M} = \int_\Omega \rho \> \mathsf{J}(\bar{x})^T \mathsf{J}(\bar{x}) \> \mathrm{d}\Omega.
\end{align}
Here we note an additional convenience of ABD: for flat affine coordinates we obtain a constant mass matrix. In turn this ensures that the equations of motion for affine bodies, unlike rigid bodies, \emph{do not} add nonlinear Coriolis-type forces. Instead, they are embodied as generalized internal forces.
With $V$ the total potential energy the free ABD is then simply the equations of motion:
\begin{align}
\label{eq:EL}
\mathsf{M} \ddot{q} =-\nabla V(q) + f,
\end{align}
where external forces $f_k \in \R^3$, applied at material points $k$, are included as $f = \sum_k \mathsf{J}(\bar{x}_k)^T f_k$.
\subsection{Orthogonality Potential}
In place of SE(3) coordinates we rigidify each affine body with a stiff orthogonality potential
\begin{equation}\label{eq:orthogonality}
V_{\perp}(q) = \kappa \nu \| \mathsf{A}\mathsf{A}^T - \mathsf{I}_3 \|^2_{F},
\end{equation}
scaled by the stiffness $\kappa$ and the body's volume $\nu$. We apply a large stiffness ($\kappa >100$GPa) to ensure the deformation on the body is sufficiently suppressed and negligible.
As we relax the rigidity constraint, we instead apply a highly stiff penalty term. Generally engineering rule of thumb suggests that stiff penalties should be avoided in simulation, as they tend to exacerbate the numerical difficulties of computing with nonlinear potentials. However, we observe that contact and collision forces (irrespective of whether they are treated via constraints, penalties springs, or barriers) introduce a much more dominant stiffness to the system. In our case this already requires handling system solves with a robust Newton-type algorithm so that the overhead of a single, additional stiff orthogonality potential per body is indifferent. In practice, as we show in Section\ \ref{sec:result}, directly stiffened affine systems significantly improve in performance over comparable systems that resolve rigid motion explicitly.
The stiff potential itself provides the effective constitutive model for the affine bodies -- modulating their collision response upon impact (and so intrinsically handling restitution). While $V_{\perp}$ is a natural choice for close-to-rigid motion~\cite{moser1991discrete}, it is never exclusively suited. Indeed affine bodies could alternately be equipped with the ARAP energy~\cite{igarashi2005rigid,alexa2000rigid,sorkine2007rigid}, i.e., $\| \mathsf{A} - \mathsf{R}(\mathsf{A}) \|^2_F$ for $\mathsf{A} = \mathsf{R}\mathsf{S}$ being the polar decomposition, to enforce rigidity, or else neo-Hookean, or any number of other rotation-invariant hyperelastic energies~\cite{bonet1997nonlinear}. However, we find that the orthogonality potential is both effective and efficient. $V_{\perp}$ requires no expensive decompositions (as opposite to ARAP) -- it can be computed as a polynomial
\begin{equation}\label{eq:ortho-energy}
V_{\perp} = \kappa \nu \left(\sum ( a_i \cdot a_i - 1)^2 + \sum_{i \neq j} (a_i \cdot a_j)^2\right),
\end{equation}
leading to more efficient evaluations of energy gradient and Hessian:
\begin{align}\label{eq:ortho-poly}
\begin{split}
\frac{\partial V_{\perp}}{\partial a_i} &= 2 \kappa \nu \left(2(a_i \cdot a_i - 1) a_i + 2\sum(a_j \otimes a_j)a_i\right), \\
\frac{\partial^2 V_{\perp}}{\partial a_i^2} &= 2 \kappa \nu \left(4a_i \otimes a_i + 2(\|a_i\|^2-1) \mathsf{I}_3 + 2\sum a_j \otimes a_j \right).
\end{split}
\end{align}
In comparison, energy operations for affine bodies with $V_{\perp}$ are over $43\%$ and $178\%$ faster than applying ARAP and neo-Hookean models respectively.
\section{Affine IPC}
We simulate systems of affine bodies with triangulated boundaries. Following Li and colleagues~\shortcite{li2020incremental}, for each affine body $b \in \mathscr{B}$, we construct a discrete incremental potential (IP), $E_b$, whose stationary points give the unconstrained time step update:
\begin{equation}
q_b^{t+1} = \arg\min_{q_b} E_b(q_b), \quad E_b = \frac{1}{2} \|q_b - \widetilde{q}_b\|_{\mathsf{M}}^2+ \Delta t^2 V_{\perp}(q_b).
\end{equation}
Here, $\Delta t$ is the time step size. $\widetilde{q}_b = q_b^t + \Delta t \dot{q}_b^t + \Delta t^2 \mathsf{M}^{-1} f_b^{t+1}$ is a known vector depending on the body state from the previous step. $f_b$ is the per-body external force (i.e., in Eq.~\eqref{eq:EL}). Unlike rigid body dynamics\footnote{Rigid body models require Poisson or constrained Lagrangian methods for numerical time integration~\cite{hairer2006preprocessed}.}, flat equations of motion of ABD allows us to directly apply IPs for a broad range of standard implicit time integration methods~\cite{li2020incremental,li2020codimensional}.
Setting $q = \big(q_1^T,\cdots,q_{|\mathscr{B}|}^T\big)^T$ as the stacked vector of all the bodies, we construct IPC potentials for contact, $V_C(q)$, and dissipative friction, $V_F(q)$, to model inter-body contact forces. The contact potential
\begin{align}
\label{eq:barrier}
V_C(q) = \kappa \sum_{i \in \mathscr{C}} B\left(d_{i}(q)\right),
\end{align}
(stiffness $\kappa$) resolves contacts between all possible pairings $i \in \mathscr{C}$ of inter-body surface geometry primitives (e.g., edge-edge, vertex-face pairs between body meshes -- but no self-contact because of body's high stiffness). Here the smoothly clamped logarithmic barrier function
\begin{equation}
B(d, \hat{d}) =
\begin{cases}
\displaystyle -(d - \hat{d})^2 \ln \left(\frac{d}{\hat{d}}\right), &0 < d < \hat{d} \\
\displaystyle 0 & \quad \> \> \> d \geq \hat{d}
\end{cases},
\label{eq:clamped-b}
\end{equation}
needs to evaluate the unsigned distances for all primitive pairs in $\mathscr{C}$. Smooth clamping ensures that proximities beyond $\hat{d}$ can be safely culled from evaluation without harming convergence, while surface pairs within the small, prescribed contact accuracy $\hat{d}$ are activated to receive contact forces.
Likewise, the friction potential is defined as:
\begin{align}
\label{eq:barrier}
V_F(q) = \sum_{j \in \mathscr{F}} \mu \lambda_j m_j(q),
\end{align}
where $\mathscr{F} \subseteq \mathscr{C}$ is the active subset of contact pairs with positive contact force magnitude $\lambda_j = - \kappa \nabla_q B\left(d_{j}(q)\right)$. $\mu$ is the coefficient of friction, and $m_j$ returns a mollified norm of the relative sliding velocity, orthogonal to the distance vector, between geometric pairs $j$. Li and colleagues~\shortcite{li2020incremental} demonstrated that $V_F$ provides smooth approximation of the nonsmooth Coulomb friction model with user-controlled accuracy. In turn, this obtains effective and accurate capture of frictional stick and slip behaviors for both maximal and reduced body models~\cite{li2020incremental,ferguson2021intersection}.
At each time step we then construct a global IP for the full contact-coupled system as: $E = \sum E_b + V_C + V_F$, and solve for its minimizer as the updated system configuration.
\subsection{Affine CCD}
To ensure that every search fulfils the nonintersection guarantee, a significant (and for rigid bodies dominant) cost of each time step's Newton solve is the repeated evaluation of CCD for primitive pairs in $\mathscr{C}$. Edge-edge or vertex-face pairs are defined on vertices $x_j \in \R^3$ for $j = 1$ to $4$ belonging to one of two bodies in $\mathscr{B}$. At any iteration $\ell$ of a Newton solve, new positions of these vertices $x_j$ are proposed, per participating body $b$, as $\mathsf{A}_b^{\ell} \bar{x}_j + p_b^\ell$, and so we search along the direction formed by $\Delta \mathsf{A}_b^{\ell} = \mathsf{A}_b^{\ell} - \mathsf{A}_b^{\ell - 1}$ and $\Delta p_b^{\ell} = p_b^{\ell} - p_b^{\ell-1}$. The corresponding trajectories are then just $(\mathsf{A}_b^{\ell - 1} + \alpha \Delta \mathsf{A}_b^{\ell}) \bar{x}_j + p_b^{\ell} + \alpha \Delta p_b^{\ell - 1}$, with $\alpha \in [0,1]$. In other words, we are testing displacements (from $0$ to $1$) along $\Delta \mathsf{A}_b^{\ell} \bar{x}_j + \Delta p_b^{\ell}$ starting from $x_{j}^{\ell-1} = \mathsf{A}_b^{\ell-1} \bar{x}_j + p_b^{\ell-1}$ i.e., the previous iteration footstep and so can apply standard linear CCD rather than the expensive, curved CCD required for rigid-body trajectories. Throughout we employ Additive CCD (ACCD) method~\cite{li2020codimensional} for all affine body CCD evaluations.
\subsection{Contact Culling via i-AABB}
\label{subsec:ibvh}
The IPC framework inverts traditional contact-processing practices by integrating collision detection within every iterate, inside each nonlinear time step solve (rather than once per time step, after completing a solve -- as has been a standard practice in rigid body pipelines). Above we have already seen the implications of this choice on CCD and the advantages for ABD. We next address culling of contact pair evaluations and then below, in the following section, an integrated approach to efficiently compute the local energy Hessian evaluations and their assembly.
\begin{figure}[h!]
\centering
\includegraphics[width=\linewidth]{figs/iBVH/iBVH.pdf}
\caption{\textbf{i-AABB.}~~Intersection-AABB (i-AABB) is a simple and more effective culling strategy than per-object BVHs traditionally employed for rigid bodies. In this example, we collide helicopter and ship models with well over $343$K surface triangles for the system. Culling with full body BVHs leads to $1.3$M AABB intersection tests. Instead, we build a shallow, three-level i-AABB based on the models' overlapping AABB volume. With i-AABB, the total number of AABB intersection tests reduces to $120$K, $90\%$ fewer than regular BVH-based culling.}\label{fig:iBVH}
\end{figure}
With the affine bodies' stiff potentials applied to model close-to-rigid motion, we eliminate, as in rigid body models, the need for self-collision processing on intra-body surface primitives pairs. To further cull inter-body surface pairs from downstream collision processing, Rigid body methods commonly employ precomputed per-body (or per unique mesh instance) BVH which only requires a rigid (or, in our setting, affine) transform to evaluate at each configuration update. To further improve collision detection queries, most popular rigid body libraries (e.g., \texttt{Bullet}, \texttt{Mujoco}, \texttt{PhysX}, \texttt{Flex}) additionally require that all nonconvex surface meshes be replaced by approximations -- convex decompositions~\cite{mamou2016volumetric} so that evaluations can utilize convexity assumptions.
In the context of stiff-body models we propose a simple strategy that significantly enhances contact-pair culling. We start with the observation that contact-dense regions between close-to-rigid meshes are most often local. Unlike deforming meshes (e.g., consider a cloth model), in common, contact-rich configurations we see that a large portion of each body's surface remains free of contacts. A BVH evaluation over each body's full surface is then a bit too aggressive (and a potentially unnecessarily expensive precomputation cost) -- especially as we consider higher resolution models and/or increasing numbers of bodies.
We instead begin with a coarse AABB per body, offset to account for the small $\hat{d}$ parameter of the contact accuracy. While clearly not providing a tight bound we only need to evaluate potential contacts in each pairwise overlap between these initial, \emph{intersecting} AABB (i-AABB) volume. With stiff affine transformations the overlap volume of each i-AABB is most often sufficiently small -- the total number of surface primitives within our i-AABB is often one order smaller than that obtained from full-mesh BVH queries. Then, utilizing the guarantee that i-AABBs will not intersect one another, this already provides effective culling for us to directly proceed with parallel (multi-threaded) primitive-pair collision-check evaluations within each i-AABB.
In the most extreme, heavily entangled configurations, e.g., see Fig.~\ref{fig:iBVH}, we find i-AABB volumes can be too conservative for CPU implementations. Here we simply build a shallow, three-level AABB hierarchy (a binary AABB tree) for each i-AABB. Our observation is that for GPU implementations and most (even contact-intense) CPU examples the single-level i-AABB is highly effective (and exceedingly simple to implement). We utilize the i-AABB hierarchies solely for CPU examples where dense, entangled contacts are consistently encountered, such as the geared system in Fig.~\ref{fig:teaser} and the interlocked collision of complex models in Fig.~\ref{fig:iBVH}. As a representative improvement we note that in the latter example the ship and the helicopter models have $227$K and $116$K surface triangles respectively; here the three-level hierarchical i-AABB is over $90\%$ more efficient in culling surface pairs in comparison to per-body BVH.
\subsection{Contact-Aware Hessian Construction}
It is, by far, most efficient to simulate a set of noncontacting affine bodies. Along with reduced cost for collision detection, the global (system-wide) Hessian for $E$ is then simply a $12|\mathscr{B}| \times 12|\mathscr{B}|$ block-diagonal matrix with just a \emph{separable} $12 \times 12$ block for each affine body's mass and orthogonality energy ($V_{\perp}$) contributions. When the system includes contacts, however, off-diagonal terms from active, inter-body contact and friction potentials necessarily pollute the Hessian to account for contact coupling.
Standard FEM-type evaluation and assembly would suggest iterating across all active contact potentials. However, here the surface mesh resolution, and so the corresponding number of surface pairs forming contact potentials, is generally much larger than the number of affine bodies we simulate. Traditional assembly, in this contact-oblivious way, is neither necessary nor efficient. We instead integrate our Hessian evaluation and assembly with the i-AABB hierarchy for contact-aware parallelization in both multi-core CPU and GPGPU implementations.
We start with the easiest part. The global Hessian's default non-zero diagonal blocks are given by a constant mass term and the orthogonality potentials' Hessian (Eq.~\eqref{eq:ortho-poly}). This can be computed trivially in parallel. Next comes the expensive part. The Hessian of the contact potential, $V_C$, then has an unpredictable pattern which varies widely with contact states. Recall that, when bodies $i$ and $j$ are sufficiently close ($\leq \hat d$), barrier and friction forces between them activate, resulting in non-zero contributions to both their respective $i$-th and $j$-th $12 \times 12$ diagonal blocks \emph{and} to the off-diagonal blocks linking the corresponding body coordinates in the Hessian.
Here we observe that the configuration-varying sparsity of the global Hessian is effectively determined by our i-AABB culling. If the leaves of the i-AABB tree between bodies $i$ and $j$ are empty, they certainly do not contact, and the barrier and friction potentials make no contribution to the Hessian. Otherwise, we can conservatively allocate space for the corresponding $12 \times 12$ off-diagonal blocks to store all potential (active contacts are not yet certain) non-zero contact Hessian contributions between bodies $i$ and $j$. Thus, utilizing the i-AABB structures we apply a two-pass strategy to compute and assemble barrier and friction terms for the global Hessian. The first pass iterates across all surface primitives pairs within each i-AABB; their local Hessians are computed in parallel and cached. Here we also account for the Hessian's symmetry to reduce total memory consumption. Our second pass then accumulates the local Hessians from the surface pairs. Here, as each culled i-AABB is independent and non-intersecting, accumulation is parallelized at each corresponding non-zero element of the global Hessian.
We find that i-AABB Hessian construction is significantly faster than default sequential parallelization of Hessian computation (e.g., as applied in rigid-IPC). We observe speedups of up to two orders, especially when the contacting system is composed of large numbers of bodies. Here, for example, the simulation in Fig.~\ref{fig:wrecking} provides a representative example, with a $188\times$ speedup over contact-oblivious, sequential Hessian construction.
\begin{figure*}[t!]
\centering
\includegraphics[width=\linewidth]{figs/wrecking/wrecking.pdf}
\caption{\textbf{Wrecking ball.}~~A metal ball linked to a chain of rigid rings hits a stack of $560$ wooden blocks. There are in total $575$ bodies including the ball, rings on the chain, and blocks in this example. ABD and rigid-IPC yield nearly identical simulation results but ABD is $124\times$ faster than rigid-IPC (both on CPU). The time step is $\Delta = 1/100$~sec. We also tested ABD using $\Delta = 1/50$~sec and $\Delta = 1/25$~sec respectively. The results are similar -- all are free of inter-penetration.}\label{fig:wrecking}
\end{figure*}
\section{Conclusion}
We have introduced a new, simple affine dynamics model and a carefully customized, easy-to-implement affine IPC algorithm for the simulation of extremely stiff materials with fidelity, convergence and reliability. The resulting method is highly suited for simulating all scenarios and applications where currently rigid body methods are now popularly employed \emph{without}, as we have shown, the current limitations that rigid body models impose. Here we have demonstrated that ABD obtains orders of magnitude speedup over state-of-the-art rigid body simulation with comparable guarantees of non-intersection and convergence. At the same time we have also shown that ABD obtains both comparable (for easy examples) and improved (as scene complexity grows) speeds when compared with highly optimized rigid body libraries that do not have guarantees and so suffer from artifacts and all-out failures that limit their automated use.
ABD is custom-suited for parallelization, is also differentiable, and automatically and directly simulates all input triangulated geometries. We have shown that, when leveraging the GPU, ABD can simulate complex contacting systems at interactive rates. With these combined properties it is then exciting to consider future applications where ABD's automation, reliability, and differentiability can be utilized for computational design, machine learning, and robotics. In these cases consistent, artifact-free simulation behavior across shape, material and contact variations, without algorithm parameter tuning, should accelerate development. We have also shown a few initial, proofs-of-concept for extensions of ABD to both complex, jointed stiff multibody systems, and to hybrid stiff/flexible multibody systems. Here there also clearly remain significant opportunities for further development and application. Finally, looking ahead, with the popularity and diverse applications of physical modeling we hope that ABD will provide the rapidly growing and diverse community of simulation users with a reliable, differentiable and exceedingly efficient framework suitable to swap in for all rigid body-type applications.
\section{Introduction}\label{sec:intro}
The simulation of highly stiff and so close-to-rigid materials remains a critical task in diverse applications ranging from animation and computer vision to robotics and geomechanics. A long-standing and natural strategy then is to model these bodies at the limit of stiffness and so treat them as exactly rigid. Equipped with just rotational and translational degrees of freedom (DOFs) this simplification enables the computational efficiency of classic rigid body methods as they utilize orders of magnitude fewer DOFs when deformations can be excluded.
At the same time this minimal representation for rigid bodies poses several fundamental difficulties of its own in exchange for optimized system size. The first being that moving from a flat continuum model to rigid (SE(3))
coordinates introduces significant nonlinearities that must be resolved. The second being that infinite stiffness implies applied forces, and especially contact responses, are communicated instantaneously across the material domain. In combination these two issues have long challenged both rigid body models (e.g., Painlev\'e's paradox) and the downstream simulation methods derived from them. State-of-the-art rigid body methods have long focused on efficient velocity (twist) level solutions. However, in doing so, these methods tend to generate undesired positional errors in the form of intersections and instabilities.
To address these issues a \emph{position-level} barrier method for rigid bodies was recently introduced by Ferguson and colleagues~\shortcite{ferguson2021intersection}. Applying the incremental potential contact (IPC) model~\cite{li2020incremental} to the rigid body formulation, the resulting rigid-IPC method provides robust intersection-free simulation of rigid solids with frictional contact. However, here a third challenge posed by rigid body models limits the efficiency and applicability of rigid-IPC: accurately tracing a piecewise-rigid trajectory is much more difficult than for a piecewise-linear trajectory. Unfortunately, doing so across numerous continuous-collision detection (CCD) operations throughout computation is a must for the non-intersecting guarantee. Rigid-IPC addresses this third challenge by conservatively subdividing rigid transformations into piecewise-linear subsequences i.e., the curved CCD. While proven to be viable, the expense remains substantial -- especially as CCD is invoked heavily throughout each simulation step. As a result, the overall performance of rigid-IPC is close to (and occasionally slower than) comparable (appropriately stiffened) fullspace finite element method (FEM) IPC simulations~\cite{li2020incremental}. Here the curved CCD in rigid-IPC severely undermines the advantage of its small DOF representation.
Beginning with this analysis, our takeaways are that the key advantage of rigid body models is \emph{not} the rigidity assumption but rather the compact representation. Indeed, the rigidity assumption is neither necessary, efficient, nor particularly accurate since no material is perfectly rigid. Following this reasoning, we approach the classic stiff-body problem from a different perspective, without the dedicated constraint and resultant limitations that the motion be exactly rigid. Specifically, we construct an affine-body dynamics (ABD) model, directly stiffened to obtain close-to-rigid trajectories and augmented with an IPC-type barrier. ABD preserves all guarantees of the IPC model including solution convergence, guaranteed non-intersection, and accurate frictional contact. However, discrete steps in ABD are now, as in the FEM case, piecewise linear, enabling us to utilize efficient linear CCD routines. Likewise ABD remains compact, utilizing 12 DOFs per body -- a bit more than rigid bodies but still compact enough for efficient system solves. In turn the relaxation from the rigidity constraint allows ABD to significantly outperform the rigid-IPC method across all benchmarks (ranging from two- to three-order speedups for side-by-side comparison on the CPU, and an order-of-magnitude further improvement enabled by our GPU implementation), and to likewise successfully simulate problems where rigid-IPC fails.
At the same time, by combining compact representation and efficient collision processing, ABD also exhibits clear advantages in quality, reliability and even performance when compared to off-the-shelf rigid body simulation libraries. Here these libraries (we use \texttt{Bullet}~\cite{coumans2015bullet} as our baseline for comparison; see Section\ \ref{sec:result} for a discussion of this choice) are often optimized for speed over robustness and guarantees. Nevertheless, without requiring the precomputation of collision proxies (e.g., the convex decompositions required by \texttt{Bullet}, \texttt{Mujoco}~\cite{todorov2012mujoco}, \texttt{PhysX} and \texttt{Flex}~\cite{nvidia2011physx}), ABD remains closely competitive in performance on small-scale examples, while obtaining significantly faster simulations on larger and/or more challenging scenarios.
ABD is also able to simulate a wide range of challenging modeling problems where existing rigid body methods and libraries fail altogether. As an example, in Fig.~\ref{fig:teaser} we demonstrate a driven mechanical system with all gear-to-gear interactions processed directly via frictional contact. As we apply an external torque to the driving gear, the entire mechanism moves with well over a quarter of the mesh's $2.45$M triangles actively in contact during each time step. Here we find rigid-IPC (curved CCD failures) and \texttt{Bullet} (severe intersections) are both unable to simulate this mechanism even as we adjust algorithm settings and time step sizes conservatively. ABD simulates the scene robustly without algorithm tuning. Under a time step of $\Delta t = 1/100$~sec, ABD simulates each step/frame in $12$~sec on the CPU (multi-threaded) and reaches an interactive speed on the GPU ranging from $5$ to $10$ FPS.
In a nutshell, ABD provides a new stiff-body simulation framework suitable for all rigid-body-type modeling problems that offers similar (or improved) performance when compared to existing rigid body libraries (optimized for performance), while providing guarantees of non-intersection, accurate contact, and convergent implicit solves that they do not. ABD does not require pre-computed convex part proxies for simulation geometries; frees users from time-consuming per-scene parameter sweeps to find parameters that work; and ensures successful simulation completion in challenging cases where prior methods fail altogether.
Our technical contribution is simple and highly effective -- a relaxation replacing strictly rigid bodies by stiff affine bodies. This ``trivial'' strategy leads to non-trivial improvements on a fundamental simulation problem in terms of both efficiency and robustness. Here, based our above analysis of prior methods, we see that our resulting ABD framework balances tradeoffs between compact representation, nonlinearity, rigidity, and reliable guaranteed contact resolution.
In addition to this high-level idea, we also design a novel collision culling algorithm dedicated for our simulation and a corresponding parallel matrix assembly strategy. We demonstrate the efficacy and efficiency of ABD across extensive benchmark testing and comparisons. Keeping all favored guarantees, the observed speedup over the state-of-the-arts is often two- to three-order, i.e., over $1,000\times$ faster, and reaches $10,000\times$ on a GPU. We hope ABD will provide the rapidly growing and diverse community of simulation users with a reliable and efficient tool suitable to swap in for all rigid body-type applications.
\section{Related Work}\label{sec:related}
A rigid body is an idealization, which simplifies a highly stiff object. External stimulus like forces or impulses are propagated almost instantaneously across the object eliminating relative deformations. This property is normally handled \emph{kinematically} i.e., by directly formulating rigid body models with SE(3) coordinates. Rigid body models have been extensively studied by the graphics community dating back to the pioneering work of Baraff\ \shortcite{baraff1989analytical}. We refer the reader to a comprehensive survey from Bender and colleagues~\shortcite{bender2014interactive}, which covers a wide spectrum of classic rigid body simulation techniques.
The primary focus of rigid body problems is typically at the resolution of the collision and contact. Intuitively, objects should never intersect with each other at any instance during the simulation. Enforcing this requirement has traditionally lead to algorithms based on linear complementarity programming (LCP)~\cite{baraff1994fast,baraff1995interactive,trinkle2001dynamic,stewart2000rigid}. One needs to carefully search within the combinatorial space for an approximation of a feasible configuration, while the interaction among bodies in contact is generally based on impulses rather than forces~\cite{baraff1989analytical}. The LCP-based contact problem is known to be NP-Hard due to the indeterminacy of which contacting nodes are contributing the collision impulse~\cite{baraff1991coping}. Alternate solvers formulated on approximations of velocity-level LCPs have also been popular ~\cite{erleben2007velocity,kaufman2005fast,anitescu1997formulating} for improved solvability. Yet, the resulting system remains non-convex and challenging to solve with accuracy for complex scenes. Irrespective of the accuracy of the solution, here the required constraint linearization means that intersections leading downstream to artifacts like drifting and tunneling can and will result. To reduce these artifacts, additional constraint stabilizations are often employed~\cite{cline2003post,baumgarte1972stabilization,moreau1988unilateral} however this, in turn can introduce new instability artifacts like popping. In addition to rigid bodies, LCP modles are also widely used for contact modeling among non-rigid objects~\cite{hauser2003interactive,pauly2004quasi,song2003distributed,duriez2005realistic,otaduy2007adaptive}.
For small-scale problems, a direct LCP solver could be used. When the complexity and the dimensionality increase, iterative LCP solvers stand as a more efficient option. Here successful designs of various iterative methods for LCP-based contacts such as Gauss-Seidel~\cite{erleben2007velocity}, PROX (iterative proximal operator)~\cite{erleben2017rigid}, surrogate constraints~\cite{kaufman2005fast}, accelerated gradient descent~\cite{mazhar2015using}, staggered projection~\cite{kaufman2008staggered}, and adaptive merging~\cite{coevoet2020adaptive} have all been applied.
Penalties are also another popular option widely used to process collisions~\cite{terzopoulos1987elastically,teschner2005collision}. Instead of imposing inequality constraints, a penalty method often chooses a spring-like repulsion mechanism based on the penetration depth between two objects~\cite{fisher2001fast,hasegawa2004real,drumwright2007fast}. While computationally simple, the penalty method fails for fast-moving models or simulations under large time steps and often requires significant manual tuning of stiffness parameters per scene. Its stability can be significantly enhanced using implicit formulations coupled with CCD~\cite{xu2014implicit,tang2012continuous}. Nevertheless, interpenetration still can and will result. This defect limits its wider use beyond graphics, where visual plausibility is not the only concern. Recently, M\"uller and colleagues also proposed a position-based rigid body framework~\cite{muller2020detailed}. Unlike classic rigid body algorithms, this method uses PBD-like constraint projection~\cite{muller2007position,macklin2016xpbd} to process multiple-body dynamics.
Collision detection is another important procedure for modeling rigid bodies with contacts. In general, a collision could occur between any triangle pair of two objects, and an exhaustive triangle-based collision detection is infeasible for high-resolution models. To this end, a commonly adopted method is to use some bounding volume hierarchy (BVH)~\cite{zachmann2003geometric} to avoid excessive triangle-triangle intersection tests. This pre-screening procedure is known as collision culling. Different BV types have been explored such as AABB~\cite{bergen1997efficient}, OBB~\cite{gottschalk1996obbtree}, bounding sphere~\cite{hubbard1995collision,james2004bd}, Boxtree~\cite{zachmann2002minimal}, spherical shell~\cite{krishnan1998rapid} and so on. As the geometry of the model does not change in rigid body models, BVH updates become particularly convenient -- the per-body rigid transformation can be directly applied to update the BVH instead of re-building it from scratch (as opposite to deformable objects). In some existing rigid body packages e.g., \texttt{Bullet} library~\cite{coumans2015bullet}, the collision detection does not apply to the surface triangles directly but rather to a volumetric proxy of the model, formed of convex components -- most often obtained by via a convex decomposition. While methods like \texttt{Bullet} require these convex proxies for robust processing this proxy also helps as an acceleration for collision detection. In this paper, we provide a new culling method to accelerate for collision detection for rigid bodies and ABD. Our method leverages the fact that the colliding region between two rigid bodies often constitutes a very small fraction of their surfaces. Based on this observation, we create a BVH only covering the overlapping region of two bodies for a more effective culling.
Discrete collision detection (DCD) checks for collisions or penetrations at a specific time instance. This method could miss inter-penetrations if the detection is not performed frequently enough. Alternatively, CCD checks the possible overlap of the trajectories of the surface primitives and returns the first time of impact (TOI)~\cite{bridson2002robust,redon2005fast}. The overlap test for triangle-vertex and edge-edge becomes a cubic polynomial, and there are several root-finding algorithms are available for solving the TOI~\cite{redon2005fast,brochu2012efficient,tang2014fast}. In a recent contribution from Wang and colleagues~\shortcite{wang2021large}, a more stable root-finding algorithm was proposed based on an improved inclusion.
Lastly in this section, we would like to discuss our most closely related work on rigid-IPC from Ferguson and colleagues~\shortcite{ferguson2021intersection}. Rigid-IPC features a new rigid body formulation, where contact is modeled with a barrier-based potential i.e., the IPC~\cite{li2020incremental,li2020robust} model. Conceptually, IPC is similar to the implicit penalty method (e.g., as in~\cite{tang2012continuous}), which produces a repulsion force pushing apart two contacting objects. However, due to the dedicated design of the barrier function, IPC provides guaranteed intersection-free collision resolution when appropriately combined with a CCD-filtered linear search. When compared to existing contact handling methods, IPC has demonstrated a superior performance -- it is significantly faster than LCP-based solutions for complicated contacts where LCP-based methods often fail altogether and much more robust than regular penalty methods with user-specified accuracy bounds. This method has been broadly applied to elastodynamics simulation~\cite{li2020incremental}, codimensional models~\cite{li2020codimensional}, embedded interfaces~\cite{choo2021barrier}, FEM-MPM coupling~\cite{li2021bfemp}, deformation processing~\cite{Fang2021IDP}, and reduced models~\cite{lan2021medial}. Rigid-IPC transplants classic rigid body models to the framework of IPC providing significantly improved reliability in contact processing. Unfortunately, this also comes at a cost -- strictly rigidity motion imposes significant computational challenges. The trajectory in rigid-IPC becomes curved. In order to successfully compute TOI in curved CCD, Ferguson and colleagues~\shortcite{ferguson2021intersection} subdivide the rigid trajectory into piece-wise line segments, which becomes the new bottleneck of the simulation. We argue that the success of IPC has already proven the feasibility of using smooth approximation to substitute hard constraints (even the approximation itself could be stiff), why not use another smooth approximation for the rigidity constraint in traditional rigid body modeling? ABD is then devised following this intuition. The results are exciting: ABD is three-order faster than rigid-IPC. With our novel culling algorithm and parallel Hessian assembly, the speedup over rigid-IPC scales even further. Likewise, as ABD provides stiff compliance (as in real-world stiff materials) tight almost rigid parts robustly fit together where an absolutely strict rigidity model can fail. Finally, as in rigid-IPC, ABD provides user-controllable solution and contact accuracies with solutions always reaching the specified tolerances.
\section{Evaluation}\label{sec:result}
Our implementation platform is a desktop PC with an \texttt{intel i9 11900K} CPU (8 cores, 3.5GHZ), $64$G memory and an \texttt{nVidia~3090} GPU. All the numerical methods were implemented using \texttt{C++} on CPU, and we chose \texttt{Eigen}~\cite{guennebaud2010eigen} as our primary linear algebra library, including all sparse linear system solves. Our CPU parallelization utilizes \texttt{intel TBB}. We understand that some other BLAS libraries may be better optimized for our hardware (e.g., \texttt{intel MKL}~\cite{wang2014intel}). This choice is to ensure an objective comparison with rigid-IPC, whose multi-thread CPU implementation is also based on \texttt{Eigen} and \texttt{TBB}. We use Cholesky factorization~\cite{dereniowski2003cholesky} i.e., \texttt{SimplicialLLT} routine shipped with \texttt{Eigen} as our primary linear solver. In hybrid simulation problems, we may occasionally resort to \texttt{SimplicialLDLT} in case when LLT scheme fails (see more discussions in Section~\ref{subsec:hybrid}).
\begin{figure}[ht!]
\centering
\includegraphics[width=\linewidth]{figs/Net_small/net.pdf}
\caption{\textbf{Small chain net.}~~We simulate a small-size chain net consisting of $8$ by $8$ rings using both ABD and rigid-IPC. The exterior rings are bound with a loop of fixed blue rings. In this simple test, ABD is $34\times$ faster than rigid-IPC on the CPU. An increase of the time step size from $1/100$~sec to $1/50$~sec does not noticeably slow down our method (from $0.059$~sec to $0.065$~sec per frame), but rigid-IPC will be significantly slower (by $350\%$).}\label{fig:net}
\end{figure}
For benchmarking we focus on rigid-IPC~\cite{ferguson2021intersection} as comparison to the ``quality-oriented'' rigid body simulator with comparable guarantees to ABD and, as a representative baseline for comparison to state-of-the-art, optimized rigid body libraries we use \texttt{Bullet}~\cite{coumans2015bullet}. There are certainly numerous other, highly effective rigid body libraries with varying capabilities. However, trade-offs with respect to \texttt{Bullet} among alternatives have been extensively documented in~\cite{ferguson2021intersection}. In their comprehensive analysis and benchmark testing of rigid body libraries \texttt{Bullet} most consistently succeeds across challenging examples and, at the same time, we also note that \texttt{Bullet} is probably the most widely deployed rigid body solution.
\subsection{Comparison with Rigid-IPC}\label{subsec:comp_ripc}
Both ABD and rigid-IPC~\cite{ferguson2021intersection} exploit the IPC~\cite{li2020incremental} model for contact processing and friction modeling. Here we carefully compare ABD with rigid-IPC across several representative simulation scenarios of varying complexities, as illustrated in Figs.~\ref{fig:wrecking}~through~\ref{fig:cards}.
\begin{figure}[h!]
\centering
\includegraphics[width=\linewidth]{figs/friction/friction.pdf}
\caption{\textbf{Friction test.}~~While ABD and rigid-IPC use the same barrier-based friction processing method, ABD is much faster than rigid-IPC under the same simulation settings. The screw example (left) is a representative demonstration of dynamic friction/contact. Our speedup is $30\times$. On the other hand, the arch example (right) is dominated by static frictions, and ABD is $77\times$ faster than rigid-IPC.} \label{fig:friction}
\end{figure}
The snapshots of the first comparison are given in Fig.~\ref{fig:wrecking}. In this test, a heavy ball linked by a chain of metal rings dashes into a stack of wooden blocks, which are scattered by the collision. There are in total $575$ bodies in this example. Both rigid-IPC and ABD produce high-quality simulation results without any inter-penetration. However, ABD is $124\times$ faster. The performance of ABD is not sensitive to the time step size. Doubling or even quadrupling the time step size (from $1/100$~sec to $1/50$~sec and $1/25$~sec) lead to similar results and performance with ABD. Detailed timing statistics can be found in Section~\ref{subsec:timing}. Similar observations are received in chain net examples. For the small chain net case (Fig.~\ref{fig:net}), we have few bodies, and the relative velocities among bodies are small. In this ``entry-level'' test, ABD offers a $34\times$ speedup.
\begin{figure*}[t!]
\centering
\includegraphics[width=\linewidth]{figs/friction/cards.pdf}
\caption{\textbf{House of cards.}~~The 10-level stack of cards is initially balanced by frictions among cards. Two falling boxes break the balance and crash the stack. This experiment mixes static and dynamic frictions involving $158$ bodies. Our method is $103\times$ faster than rigid-IPC.}\label{fig:cards}
\end{figure*}
An ``upgraded'' experiment is reported in Fig.~\ref{fig:net_big}, where the resolution of the chain net is set to $16 \times 16$. We also drop a ball, which bounces back and forth on the net triggering interesting dynamics. The collisions and contacts also become more complicated than the plain simple chain net in Fig.~\ref{fig:net}. The difference between our method and rigid-IPC becomes more significant. At some instances when sharp collisions occur under high relative velocities, rigid-IPC could take multiple hours to simulate one frame ($\Delta t = 1/100$~sec). On the other hand, our method needs seconds at most. On average, ABD is over $1,200\times$ faster than rigid-IPC. This speedup exceeds $4,000\times$ from time to time during the simulation. In ABD, affine CCD, i-AABB, as well as the integrated Hessian assembly are all parallelization-ready. Therefore, ABD typically receives one more orders performance gain on \texttt{CUDA}. That makes ABD over $10,000\times$ faster than rigid-IPC in the example of Fig.~\ref{fig:net_big}.
The friction handling in ABD and rigid-IPC is similar as both follow the variational friction model originally proposed in~\cite{li2020incremental}. Nevertheless, ABD still exhibits superior performance in simulations dominated by frictions. We hereby report three more experiments in Figs.~\ref{fig:friction} and~\ref{fig:cards}. In those comparisons, both ABD and rigid-IPC use the same simulation settings with the time step size of $1/100$~sec. The screw example (Fig.~\ref{fig:friction} left) is relatively simple -- the surface geometry only has $7$K triangles and $5$K edges. We rotate the bolt into the nut. On average, rigid-IPC needs $2.59$~sec to simulate one step, and our method only needs $87$~ms. The arch (Fig.~\ref{fig:friction} right) consists of $100$ brick blocks. In this example, we mainly have static friction to deal with. Rigid-IPC runs faster than the screw case and needs $0.67$~sec for simulating one frame. Our method however, only uses $8.7$~ms. The card of house example starts with a 10-level stack of $155$ cards. The stack is first held up under the frictions between cards and gets crashed by two falling boxes. In this example, it takes about $8.9$~sec for rigid-IPC to simulate one frame, and ABD needs $86$~ms.
\begin{figure}[th!]
\centering
\includegraphics[width=\linewidth]{figs/bullet/bullet.pdf}
\caption{\textbf{ABD vs. \texttt{Bullet}.}~~We compare simulation results using ABD and \texttt{Bullet} with varying numbers of bodies and time step sizes. \texttt{Bullet} often produces interpenetrations between bodies even under small time steps. Interpenetrations becomes increasingly severe with growing body counts and/or time step size. On the other hand, ABD remains intersection-free across changing parameters and scene complexities. All timing statistics are reported in Tab.~\ref{tab:bullet}.} \label{fig:bullet}
\end{figure}
\subsection{Comparison with \texttt{Bullet}}
\texttt{Bullet} is a widely used rigid body engine known for the simplicity and efficiency. \texttt{Bullet} is also based on the classic rigid body model formulation. However, \texttt{Bullet} uses the so-called convex collision resolution, which approximates the geometry of the body via convex decomposition proxies. The collision is resolved using impulse-based method at the convex proxies. Therefore, it is not surprising to see \texttt{Bullet} fails in simulations under lasting and intense collisions and contacts. We have shown that our method is orders of magnitude faster than rigid-IPC with further improved robustness. For smaller simulation problems, ABD is nearly as efficient as \texttt{Bullet}. It quickly outperforms \texttt{Bullet} from almost all perspectives as the complexity of the simulation escalates.
We compare ABD and \texttt{Bullet} using the wrecking ball setup (i.e., see Fig.~\ref{fig:wrecking}) but under different block counts and time step sizes. In this set of comparisons, the ball is no longer attached to the chain as in Fig.~\ref{fig:wrecking}. This is because under high-velocity movements, collision resolution in \texttt{Bullet} frequently fails, and the rings on the chain would ``break out'' so that the ball may not hit the stack. The results are reported in Fig.~\ref{fig:bullet}, where we have three configurations: light, medium, and full. The light test only has $16$ blocks on the stack; the medium test has $142$ blocks; and the full test is the same as in Fig.~\ref{fig:wrecking} with $560$ blocks.
\begin{table}[th!]
{\small \fontfamily{ppl}\selectfont
\begin{center}
\begin{tabular}{c|c|c|c|c|c}
\whline{1.15pt}
Test & $\#$ Bdy & $\#$ Tri./Edg. & $\Delta t$ (sec) & $\#$ Iter. & Time (ms)\\
\whline{0.5pt}
Light & $16$ & 1.2K/796 & \begin{tabular}{@{}c@{}}1/100 \\ 1/240 \\ 1/1000\end{tabular}
& \begin{tabular}{@{}c@{}}1.9 \\ 1.5 \\ 1.1\end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{3} | \red{2} \\ \textbf{2.2} | \red{1.5} \\ \textbf{2} | \red{3} \end{tabular} \\
\whline{0.5pt}
Medium & 142 & 3.5K/2.3K & \begin{tabular}{@{}c@{}}1/100 \\ 1/240 \\ 1/1000\end{tabular}
& \begin{tabular}{@{}c@{}}7.6 \\ 2.9 \\ 1.3\end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{92} | \red{68} \\ \textbf{41} | \red{58} \\ \textbf{19} | \red{82} \end{tabular} \\
\whline{0.5pt}
Full & 562 & 11K/7.3K & \begin{tabular}{@{}c@{}} 1/100 \\ 1/240 \\ 1/1000\end{tabular}
& \begin{tabular}{@{}c@{}}11.0 \\ 4.4 \\ 1.8\end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{657} | \red{629} \\ \textbf{328} | \red{809} \\ \textbf{102} | \red{804} \end{tabular} \\
\whline{1.15pt}
\end{tabular}
\end{center}
}
\caption{\textbf{ABD vs. \texttt{Bullet} timing.}~~We record timing information of simulating the wrecking ball scenarios under different block counts and time step sizes using ABD and \texttt{Bullet}. \textbf{$\#$~Bdy} is the number of bodies in the test. \textbf{$\#$~Tri./Edg.} gives the total numbers of triangles and edges on the surface of the models. $\bm{\Delta t}$ is the time step size. \textbf{$\#$~Iter.} is the average iteration counts in ABD simulation. \textbf{Time} reports the average computation time for each frame using \textbf{ABD} and \red{\texttt{Bullet}}. This timing comparison is reported on a single thread implementation.}\label{tab:bullet}
\vspace{-20 pt}
\end{table}
\begin{figure*}[t!]
\centering
\includegraphics[width=\linewidth]{figs/bone_dragon/bone_dragon.pdf}
\caption{\textbf{Bone dragon.}~~In addition to the simulation algorithm, another difference between ABD and \texttt{Bullet} is the collision detection. ABD allows triangle-level collision detection to capture local contacts between fine geometries. \texttt{Bullet} is mesh-based and relies on convex decomposition of the model. In some cases, the decomposition is not accurate enough to approximate concave shapes. This figure shows one of such examples. Both bone dragons and rock spikes are sharp and concave.} \label{fig:bone_dragon}
\end{figure*}
The detailed timing comparison is listed in Tab.~\ref{tab:bullet}. In order to ensure the comparison is fair, we turn off multi-threading in ABD and \texttt{Bullet}. This is because our method processes collision on the surface triangles, which will receive more acceleration under parallelization. It is noted that under the light test ($\Delta t = 1/100$~sec), \texttt{Bullet} is rather efficient and only needs $2$~ms to simulate one frame. Our method is slower than \texttt{Bullet} and takes $3$~ms to simulate one frame. This difference diminishes under a smaller time step. For instance, when the time step size is set as $1/240$~sec, which is the default setting in \texttt{Bullet}, the difference of per-frame simulation time is less than one millisecond ($2.2$~ms for ABD and $1.5$~ms for \texttt{Bullet}). If the time step size is more conservatively set to $1/1000$~sec, ABD becomes faster than \texttt{Bullet} by a small margin ($2$~ms for ABD and $3$~ms for \texttt{Bullet}). However, \emph{simulations using \texttt{Bullet} in all time step sizes have intersections} (even with $\Delta t = 1/1000$~sec). Our method on the other hand is guaranteed to be free of inter-penetration. Another interesting observation is per-frame simulation using ABD consistently becomes more efficient under smaller time steps, which is not the case for \texttt{Bullet}. This may be because a smaller time step could expose more collisions to \texttt{Bullet} solver, which are otherwise missed under a bigger step. In addition, \texttt{Bullet} fails all the friction experiments including the screwing bolt, arch, and house of cards (Figs.~\ref{fig:friction}~and~\ref{fig:cards}) even with highly conservative time step size ($\Delta t = 1/10000$~sec).
The story is similar for the medium/full test: ABD ($92$~ms in medium and $657$~ms in full) is slightly slower than \texttt{Bullet} ($68$~ms in medium and $629$~ms in full) when $\Delta t = 1/100$~sec\footnote{Basically, ABD and \texttt{Bullet} have the same FPS in the full test with $\Delta t = 1/100$~sec}. Yet ABD takes the lead under smaller time steps of $1/240$~sec and $1/1000$~sec. In addition, \texttt{Bullet} has significantly more inter-penetration instances in the medium/full tests than in the light test, which could end up with undesired artifacts in many simulation tasks.
As discussed, ABD's collision processing directly handles each body's input surface mesh boundary with all guarantees, including non-intersection, applying directly to those meshes. This means that control of resolution and so quality is available via standard, well optimized geometry pipelines, e.g. mesh decimation. \texttt{Bullet}, however, requires pre-processing to convert all input meshes body into convex decompositions. In turn \texttt{Bullet} will then simulate these decomposed, simplified models as proxies, resolving collision handling on them, for each rigid body's surface rather than the original mesh. \texttt{Bullet} users often use V-HACD~\cite{mamou2016volumetric}, an automated library for computing convex decomposition, for this process. Utilizing libraries like V-HACD, can be a slow and often time-consuming iterative process to hand-tune quality parameters in order to obtain a reasonable a reasonable geometric approximation and resolution. Even so important features can be lost while details and symmetries are often unnecessarily broken. As such, many advanced users often resort to laborious hand-crafting of proxies when capturing important surface features is critical in an application (e.g., for design or robotics). Here, we demonstrate a comparative example of utilizing detailed, bone dragons in Fig~\ref{fig:bone_dragon} dropped on a highly featured geometry. After careful hand-tuning of V-HACD parameters, we present in Fig~\ref{fig:bone_dragon} right the resulting simulation using our best resulting V-HACD proxies. Here we see the convex decomposition geometry is still insufficiently detailed to capture local collision behavior between sharp asperities and convexities. In contrast, in Fig~\ref{fig:bone_dragon} left, ABD directly simulates the detailed geometry with tight tolerance so that all the original input meshes' detailed affordances are kept. In turn we see that this allows the dragons' concavities to tightly entangle and also slide directly onto and be caught by the sharp points -- all while remaining intersection free.
\subsection{Joint Constraints are Linear for Affine Bodies}\label{subsec:constraint}
An additional benefit of ABD is convenient constraint handling -- especially for the those prescribing rotational DOFs. For instance, it is common to require multiple objects to obey a given kinematic relation following the joint connecting them. Such constraints are often nonlinear as they are formulated from rigid body rotational DOF. Enforcing them would then require computing the derivatives of the rotational DOFs (either via constrained Lagrangian methods or generalized coordinates). Here relaxation from rigidity to affinity also eases the processing of such constraints.
It is known that a non-degenerate tetrahedron uniquely defines an affine transform. This suggests our generalized coordinate $q$ can be mapped to \emph{any} linear tetrahedron. From this perspective, an affine body simulation can also be viewed as a single-element FEM (with a simplified strain energy). The geometry of this element however, can be setup flexibly even its position deviates away significantly from the object. Let $\phi$ denote the map between $q$ and this virtual tetrahedron such that $q = \phi(\mathsf{P})$. $\mathsf{P}\in\mathbb{R}^{3 \times 4}$ stores the deformed vertex positions (i.e., $p_1$, $p_2$, $p_3$, and $p_4$) of the element. Let the rest shape position of the element be $\bar{\mathsf{P}}$, and one can easily verify that:
\begin{equation}\label{eq:phi}
\phi(\mathsf{P}) = \left[\frac{1}{4}\sum_i(p_i - \bar{p}_i)^T,\text{vec}^T\left(\mathsf{P}\bar{\mathsf{P}}^T(\bar{\mathsf{P}} \bar{\mathsf{P}}^T)^{-1}\right)\right]^T.
\end{equation}
Here, $\text{vec}(\cdot)$ denotes the vectorization of a matrix. Since $\bar{\mathsf{P}}$ is given, we could use $\text{vec}(\mathsf{P})$ as the new generalized coordinate of the system. Clearly $\phi$ is a linear function of $\mathsf{P}$. $\partial \phi/\partial p_i$ only depends on $\bar{\mathsf{P}}$. Therefore, the Jacobi of the system remains constant:
\begin{equation}\label{eq:tet_jacobi}
\mathsf{J}_i = \frac{\partial x_i}{\partial q} \cdot \frac{\partial \phi}{\partial \text{vec}(\mathsf{P})}\in\mathbb{R}^{3\times12}.
\end{equation}
\begin{figure}[ht!]
\centering
\includegraphics[width=\linewidth]{figs/rotation/rotation.pdf}
\caption{\textbf{Constrained simulation.}~~Prescribing rotation freedom in ABD is convenient. We visualize the generalized coordinate as a virtual tetrahedron, and most rotational constraints are linearized. We show two examples of such simulation in this figure. Both pendulum and octopus tentacles are made of multiple bodies connected via hinge joints. ABD remains significantly faster than rigid-IPC: ABD achieves a $371\times$ speedup for the pendulum and a $28\times$ speedup for the octopus.} \label{fig:rotation}
\end{figure}
\begin{figure*}[t!]
\centering
\includegraphics[width=\linewidth]{figs/hybrid/hybrid.pdf}
\caption{\textbf{Hybrid simulation.}~~ABD is particularly convenient for simulating hybrid object with both rigid and deformable parts. Both the barbarian ship ($225$K triangles, $341$K edges) and helicopter ($116$K triangles, $176$K edges) are such hybrid objects with a rigid main body appended by several deformable parts (canvas, rotors, and wheels). We use standard neo-Hookean FEM to simulate deformable parts, which are constrained to the virtual tetrahedron corresponding to the rigid body. Due to the involvement of massive DOFs from deformable parts, the simulation uses about $16$~sec for one frame under $\Delta t = 1/100$~sec.} \label{fig:hybrid}
\end{figure*}
\setlength{\columnsep}{10 pt}
\begin{wrapfigure}{r}{0.35\linewidth}
\includegraphics[width = \linewidth]{figs/constraint/tet.pdf}
\caption{\textbf{Convenient constraint handling.}~~An axis constraint becomes a linear one and can be easily enforced in A-IPC framework.}
\vspace{-5 pt}
\label{fig:tet}
\vspace{-5 pt}
\end{wrapfigure}
In practice, we exploit the fact that $\bar{\mathsf{P}}$ could be any tetrahedron to manipulate such constraints intuitively. For instance as shown in Fig.~\ref{fig:tet}, the gear is constrained to rotate around a prescribed axis (blue dash line). In ABD, we map $q$ to a tetrahedron. Since the tetrahedron can be chosen freely, we make sure that one of its edges is parallel to the rotation axis. After that, the axis constraint can be simply posed as a linear equality constraint fixing two vertices of the edge ($p_2$ and $p_4$ in the figure). Indeed, such formulation is over-constraining as it eliminates six freedoms instead of two (we should also allow $p_2$ and $p_4$ to move laterally along the edge). However, such ``over-constrainment'' still gives correct simulation because ABD uses more DOFs to simulate a rigid object. Other types constraints can be dealt with in a similar way (e.g., the constraint over the rotation angle can be converted to a linear shearing constraint).
Two of such examples are reported in Fig.~\ref{fig:rotation}. The pendulum is a basic mechanism structure with two rigid links constrained by a hinge. The octopus has eight tentacles, and each of it consists of five joints. We also compared ABD with rigid-IPC with these models. ABD does not only enjoy a more handy formulation but also runs significantly faster ($371\times$ and $28\times$ speedups for the pendulum and octopus respectively). A more challenging experiment is reported in Fig.~\ref{fig:teaser}, where we simulate a more complex mechanism device of a set of 28 gears. Those gears are coupled by tooth contacts and shafts (see Fig.~\ref{fig:gear}). There are totally $2,450$K triangles and $3,090$K edges on the surface (i.e., those could participate in culling and CCD). A component-wise breakdown showing the inter-connectivity of gears is given in the right of the figure. As the driving torque is applied at one of the gear (the one with red arrow), the entire device moves forward. This simulation is very demanding for the robustness of the simulation algorithm. Because gear tooth are close to each other, highly localized and detailed CCD is massively used. All rigid body simulation algorithms we have tested fail in this case including rigid-IPC, \texttt{MuJuCo}, and \texttt{Bullet}. As mentioned, \texttt{Bullet} requires building a convex proxy for collision processing, which does not capture the zigzag geometry at the gear tooth. \texttt{MuJuCo} fails the test even under highly conservative settings (e.g., very small time step size). Rigid-IPC also fails this experiment: after first few steps, the Newton iteration loops infinitely because the cured CCD is unable to find a usable TOI (time of impact). ABD manages to simulate this scene without any issues. Each frame takes about $12$~sec on the CPU. As the majority of the computation is at CCD processing, we port our i-AABB algorithm to \texttt{CUDA}, and the simulation of the gear set reaches an interactive rate (at 5 -- 10 FPS).
\begin{figure*}[t!]
\centering
\includegraphics[width=\linewidth]{figs/net_huge/net_huge.pdf}
\caption{\textbf{Huge chain net.}~~When the body count increases, the disadvantage of using redundant DOFs in the simulation may become more obvious. Following this thought, we up scale the chain net to have $27,645$ bodies. In this stress test, A-IPC takes about $5$~min to simulate one frame on average. The entire simulation takes about five \emph{days} with A-IPC. We are never able to finish this test with rigid-IPC. Based on our observation, A-IPC is at least $2,000\times$ faster than rigid-IPC. This means it will need several \emph{years} for rigid-IPC to finish this experiment.} \label{fig:net_huge}
\end{figure*}
\subsection{Hybrid Simulation}
\label{subsec:hybrid}
Another benefit of ABD, when viewed as a reduced single-tetrahedron FEM, is to simulate models with both rigid and soft components. Such objects are vastly available in real world. While existing rigid body methods can also be augmented to incorporate such hybrid simulations, it is particularly effortless in the framework of ABD. We show a simulation of such scene. The barbarian ship has a rigid ship body and two deformable canvas. Each ship has $225$K surface triangles and $341$K edges. The helicopter is also hybrid with a rigid body, two soft rotors, and four soft wheels. There are $116$K triangles and $176$K edges on each helicopter. After two ships fall into the glass tank, five helicopters follow, producing interesting animation effects of both rigid and deformable dynamics. Note that the collision between rigid and soft bodies can be handled uniformly using barrier-based penalties. In such hybrid simulation, the Hessian of elastic potential on the deformable components are much smaller (by several orders) than the Hessian of the orthogonality potential ($V_{\perp}$), and the positive definiteness of the global system matrix is numerically compromised. Therefore, LLT factorization (\texttt{SimplicialLLT}) may fail occasionally. In this case, we switch to LDLT Cholesky for each Newton solve. A possible remedy for increase numerically stability is to use Schur complement like formulation~\cite{peiret2019schur} to somehow decouple DOFs from rigid (affine) and deformable components.
\begin{figure}[h!]
\centering
\includegraphics[width=\linewidth]{figs/gear_collision/gear_collision.pdf}
\caption{\textbf{Contact forces at teeth.}~~With the assistance of i-AABB, ABD efficiently and accurately model the contact forces among gear teeth. This figure visualizes the force distribution over the gear teeth.} \label{fig:gear}
\end{figure}
\begin{table*}[th!]
\caption{\textbf{Time statistic.}~~Detailed time statistics of our experiments. In most experiments, we tested ABD under three different $\Delta t$ settings namely $1/100$, $1/50$, and $1/25$. \textbf{$\#$~Bdy} (number of bodies), \textbf{$\#$~Tri./Edg.} (numbers of triangles and edges), $\bm{\Delta t}$ (time step size), \textbf{$\#$~Iter.} (average per-frame iteration counts), and \textbf{Time} (total time for each frame) are the same measures as in Tab.~\ref{tab:bullet}. This table also reports computation time used for Hessian assembly (\textbf{Hess.}), total time used for solving the linear system in Newton method at each frame (\textbf{Sol.}), time used for triangle-level CCD (\textbf{CCD}), time used for building the collision pairs (\textbf{Cons.}), and other computations (\textbf{Misc.} e.g., variables initialization, convergence check etc. In many examples (except for the last four examples), we give comparative timing information of both \textbf{ABD} and \teal{rigid-IPC}. The \textbf{\blue{GPU FPS}} is also reported for $\Delta t = 1/100$ ABD simulations.}\label{tab:time}
{\footnotesize \fontfamily{ppl}\selectfont
\begin{center}
\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c}
\whline{1.15pt}
Test & $\#$ Bdy & $\#$ Tri./Edg. & $\Delta t$ (sec) & $\#$ Iter. & Hess. (sec) & Sol. (ms) & CCD (sec) & Cons. (sec) & Misc. (ms) & Time (sec)\\
\whline{0.5pt}
\begin{tabular}{@{}c@{}} Wrecking ball \\ (Fig.~\ref{fig:wrecking}) \end{tabular}
& 575 & 14K/20K & \begin{tabular}{@{}c@{}}1/100 \\ 1/50 \\ 1/25\end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{8.8} | \teal{17.1} \\ \textbf{19.4} \\ \textbf{42.6} \end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{0.023} | \teal{10.3} \\ \textbf{0.067} \\ \textbf{0.18} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{53} | \teal{47} \\ \textbf{160} \\ \textbf{444} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.028} | \teal{4.9} \\ \textbf{0.078} \\ \textbf{0.23} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.031} | \teal{2.3} \\ \textbf{0.092} \\ \textbf{0.027} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{8} | \teal{53} \\ \textbf{18} \\ \textbf{43} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.14} | \teal{17.6} | \blue{\textbf{18}{\tiny{ FPS}}}\\ \textbf{0.41} \\ \textbf{1.1} \end{tabular}\\
\whline{0.5pt}
\begin{tabular}{@{}c@{}} Small chain net \\ (Fig.~\ref{fig:net}) \end{tabular}
& 144 & 63K/95K & \begin{tabular}{@{}c@{}}1/100 \\ 1/50 \\ 1/25\end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{2.1} | \teal{4.0} \\ \textbf{2.4} \\ \textbf{2.8} \end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{0.011} | \teal{0.18} \\ \textbf{0.014} \\ \textbf{0.018} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{6} | \teal{2} \\ \textbf{7} \\ \textbf{9} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.016} | \teal{1.1} \\ \textbf{0.023} \\ \textbf{0.29} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.017} | \teal{0.73} \\ \textbf{0.023} \\ \textbf{0.032} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{9} | \teal{6} \\ \textbf{10} \\ \textbf{10} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.059} | \teal{2.1} | \blue{\textbf{143}{\tiny{ FPS}}}\\ \textbf{0.07} \\ \textbf{0.08} \end{tabular}\\
\whline{0.5 pt}
\begin{tabular}{@{}c@{}} Big chain net \\ (Fig.~\ref{fig:net_big}) \end{tabular}
& 673 & 445K/297K & \begin{tabular}{@{}c@{}}1/100 \\ 1/50 \\ 1/25\end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{13.5} | \teal{169} \\ \textbf{24.9} \\ \textbf{26.3} \end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{0.13} | \teal{109} \\ \textbf{0.25} \\ \textbf{0.27} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{241} | \teal{437} \\ \textbf{440} \\ \textbf{464} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.41} | \teal{305} \\ \textbf{0.82} \\ \textbf{0.93} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.43} | \teal{388} \\ \textbf{0.87} \\ \textbf{0.96} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{62} | \teal{1336} \\ \textbf{83} \\ \textbf{86} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.78} | \teal{944} | \blue{\textbf{5}{\tiny{ FPS}}} \\ \textbf{2.4} \\ \textbf{2.7} \end{tabular}\\
\whline{0.5 pt}
\begin{tabular}{@{}c@{}} House of cards \\ (Fig.~\ref{fig:cards}) \end{tabular}
& 158 & 336/816 & \begin{tabular}{@{}c@{}}1/100 \\ 1/50 \\ 1/25\end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{9.8} | \teal{66.5} \\ \textbf{13.3} \\ \textbf{25.2} \end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{0.014} | \teal{2.49} \\ \textbf{0.024} \\ \textbf{0.045} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{24} | \teal{41} \\ \textbf{37} \\ \textbf{64} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.009} | \teal{5.1} \\ \textbf{0.014} \\ \textbf{0.035} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.035} | \teal{1.1} \\ \textbf{0.043} \\ \textbf{0.074} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{4} | \teal{46} \\ \textbf{20} \\ \textbf{9} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.086} | \teal{8.9} | \blue{\textbf{42}{\tiny{ FPS}}} \\ \textbf{0.13} \\ \textbf{0.24} \end{tabular}\\
\whline{0.5 pt}
\begin{tabular}{@{}c@{}} Screw \\ (Fig.~\ref{fig:friction}, left) \end{tabular}
& 2 & 7.9K/5.2K & \begin{tabular}{@{}c@{}}1/100 \\ 1/50 \\ 1/25\end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{4.1} | \teal{8.2} \\ \textbf{3.2} \\ \textbf{5.7} \end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{0.0004} | \teal{0.028} \\ \textbf{0.0007} \\ \textbf{0.001} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.1} | \teal{0.1} \\ \textbf{0.1} \\ \textbf{0.1} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.039} | \teal{2.5} \\ \textbf{0.068} \\ \textbf{0.11} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.039} | \teal{0.096} \\ \textbf{0.068} \\ \textbf{0.12} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{9} | \teal{1} \\ \textbf{10} \\ \textbf{10} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.087} | \teal{2.6} | \blue{\textbf{1K}{\tiny{ FPS}}} \\ \textbf{0.14} \\ \textbf{0.23} \end{tabular}\\
\whline{0.5 pt}
\begin{tabular}{@{}c@{}} Arch \\ (Fig.~\ref{fig:friction}, right) \end{tabular}
& 101 & 1.2K/1.8K & \begin{tabular}{@{}c@{}}1/100 \\ 1/50 \\ 1/25\end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{1.9} | \teal{6.2} \\ \textbf{3.2} \\ \textbf{5.7} \end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{0.002} | \teal{0.13} \\ \textbf{0.003} \\ \textbf{0.005} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{2} | \teal{44} \\ \textbf{2} \\ \textbf{3} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.001} | \teal{0.44} \\ \textbf{0.001} \\ \textbf{0.003} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.002} | \teal{0.099} \\ \textbf{0.003} \\ \textbf{0.006} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{2} | \teal{3} \\ \textbf{2} \\ \textbf{3} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.0087} | \teal{0.67} | \blue{\textbf{500}{\tiny{ FPS}}}\\ \textbf{0.013} \\ \textbf{0.022} \end{tabular}\\
\whline{0.5 pt}
\begin{tabular}{@{}c@{}} Pendulum \\ (Fig.~\ref{fig:rotation}, left) \end{tabular}
& 4 & 1.3K/2.0K & \begin{tabular}{@{}c@{}}1/100 \\ 1/50 \\ 1/25\end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{4.1} | \teal{4.3} \\ \textbf{4.3} \\ \textbf{4.7} \end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{0.001} | \teal{0.018} \\ \textbf{0.001} \\ \textbf{0.001} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.1} | \teal{0.1} \\ \textbf{0.1} \\ \textbf{0.1} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.003} | \teal{2.5} \\ \textbf{0.004} \\ \textbf{0.005} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.003} | \teal{0.03} \\ \textbf{0.003} \\ \textbf{0.004} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{1} | \teal{1} \\ \textbf{1} \\ \textbf{1} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.007} | \teal{2.6} | \blue{\textbf{1K}{\tiny{ FPS}}}\\ \textbf{0.009} \\ \textbf{0.01} \end{tabular}\\
\whline{0.5 pt}
\begin{tabular}{@{}c@{}} Octopus \\ (Fig.~\ref{fig:rotation}, right) \end{tabular}
& 41 & 33K/49K & \begin{tabular}{@{}c@{}}1/100 \\ 1/50 \\ 1/25\end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{4.6} | \teal{4.3} \\ \textbf{5.6} \\ \textbf{6.7} \end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{0.012} | \teal{0.071} \\ \textbf{0.014} \\ \textbf{0.017} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{2} | \teal{0.5} \\ \textbf{0.2} \\ \textbf{0.2} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.02} | \teal{0.97} \\ \textbf{0.03} \\ \textbf{0.04} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.019} | \teal{0.34} \\ \textbf{0.025} \\ \textbf{0.03} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{5} | \teal{3} \\ \textbf{6} \\ \textbf{6} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{0.05} | \teal{1.4} | \blue{\textbf{333}{\tiny{ FPS}}}\\ \textbf{0.07} \\ \textbf{0.09} \end{tabular}\\
\whline{0.5 pt}
\begin{tabular}{@{}c@{}} Hybrid sim. \\ (Fig.~\ref{fig:hybrid}) \end{tabular}
& 19+8 & 1.1M/1.6M & \begin{tabular}{@{}c@{}}1/100 \\ 1/50 \\ 1/25\end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{16.7} | \teal{--} \\ \textbf{19.3} \\ \textbf{25.9} \end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{4.3} | \teal{--} \\ \textbf{5.8} \\ \textbf{7.9} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{4600} | \teal{--} \\ \textbf{5311} \\ \textbf{7083} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{3.5} | \teal{--} \\ \textbf{4.8} \\ \textbf{7.2} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{3.4} | \teal{--} \\ \textbf{4.5} \\ \textbf{6.9} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{490} | \teal{--} \\ \textbf{562} \\ \textbf{836} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{16.4} | \teal{--} | \blue{\textbf{0.4}{\tiny{ FPS}}} \\ \textbf{21.3} \\ \textbf{30.0} \end{tabular}\\
\whline{0.5 pt}
\begin{tabular}{@{}c@{}} Gear set \\ (Fig.~\ref{fig:teaser}) \end{tabular}
& 28 & 2.5M/3.1M & \begin{tabular}{@{}c@{}}1/100 \\ 1/50 \\ 1/25\end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{16.7} | \teal{--} \\ \textbf{19.3} \\ \textbf{25.9} \end{tabular}
& \begin{tabular}{@{}c@{}} \textbf{4.3} | \teal{--} \\ \textbf{5.8} \\ \textbf{7.9} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{4} | \teal{--} \\ \textbf{4} \\ \textbf{6} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{5.4} | \teal{--} \\ \textbf{6.3} \\ \textbf{9.3} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{6.0} | \teal{--} \\ \textbf{7.9} \\ \textbf{11.2} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{211} | \teal{--} \\ \textbf{219} \\ \textbf{43} \end{tabular}
& \begin{tabular}{@{}c@{}}\textbf{11.7} | \teal{--} | \blue{\textbf{7.3}{\tiny{ FPS}}} \\ \textbf{14.5} \\ \textbf{20.1} \end{tabular}\\
\whline{0.5 pt}
\begin{tabular}{@{}c@{}} Bone dragon \\ (Fig.~\ref{fig:bone_dragon}) \end{tabular}
& 29 & 1.2M/1.7M
& 1/100
& \textbf{6.3}
& \textbf{0.003}
& \textbf{0.2}
& \textbf{2.3}
& \textbf{0.56}
& \textbf{74}
& \textbf{2.8} \\
\whline{0.5 pt}
\begin{tabular}{@{}c@{}} Huge chain net \\ (Fig.~\ref{fig:net_huge}) \end{tabular}
& 27,645 & 12M/18M
& 1/100
& \textbf{14.2}
& \textbf{37.2}
& \textbf{87~sec}
& \textbf{95}
& \textbf{94}
& \textbf{7.2~sec}
& \textbf{310} \\
\whline{1.15pt}
\end{tabular}
\end{center}
}
\end{table*}
\subsection{Timing and Breakdown}\label{subsec:timing}
Detailed time statistics of other the experiments is reported in Tab.~\ref{tab:time}. In all the experiments, we uniformly scale the scene to a $1 \times 1 \times 1$ box and set $\hat{d}$ as $1/1000$. In other words, if the size of the model is around one meter, the contact accuracy is guaranteed to be less than one millimeter, and all the models do not intersect with each other at any time during the simulation. We report comparative timing benchmark of ABD and rigid-IPC under $\Delta t = 1/100$ in most experiments. Normally, rigid-IPC is numerically robust under larger time steps. However, its performance is highly sensitive to a bigger $\Delta t$. This is because the underlying curved CCD quickly becomes prohibitive when examining over a wider trajectory gap. Therefore, we do not report our speedup over rigid-IPC for any time steps bigger than $\Delta t = 1/100$~sec. For chain net example shown in Fig.~\ref{fig:net_big}, the literal speedup exceeds four orders in general if we set $\Delta t = 1/25$. It is not our intention to oversell just by tweaking the time step size.
The majority portion of our performance improvement is brought by relaxing the rigidity constraint. This can be reflected by two important metrics from Tab.~\ref{tab:time}: the iteration count (\textbf{$\#$ Iter.}) and the time needed for CCD processing (\textbf{CCD}). It is clearly shown that as long as the contact frequency in the simulation is intense, ABD always requires much fewer iterations to converge than rigid-IPC does. This difference is ``extremized'' in the gear set example (Fig.~\ref{fig:teaser}), where ABD needs $17$ iterations for each time step, and rigid-IPC needs infinite iterations. CCD processing is another major game changer. As mentioned, rigid-IPC strictly follows the rigidity constraint making per-step trajectory curved. This curved trajectory is split and converted back to piece-wise line segments again during the CCD. This conversion is fully avoided in ABD, and one can use any existing CCD algorithm to detect potential intersection between primitives and compute TOI. We would like to remind that CCD needs to be carried out at each Newton iteration in order to make sure the line search does not introduce inter-penetrations. Therefore, the performance gap between A-IPC and rigid-IPC is further scaled by the iteration count. Together, those two factors contribute to $90\%$ of our speedup in complex simulations such as the big chain net (Fig.~\ref{fig:net_big}), house of cards (Fig.~\ref{fig:cards}) and wrecking ball (Fig.~\ref{fig:wrecking}). In other relatively lighter simulation experiments, our improved culling and Hessian assembly become more profitable. Our culling is up to to $90\%$ more effective than conventional BVH-based strategy for models with complex geometry. It is on average $30\%$ more effective for simpler shapes (e.g., the chain net or the octopus). In terms of system solve, ABD is typically slower than existing rigid body methods due to inflated DOFs. However, this disadvantage is invisible because ABD always enjoys a much fewer iterations and much faster CCD processing. This is our core inspiration of designing ABD.
We suspect increasing the body count will grant the lead to rigid-IPC at a certain point and simulate a huge chain net model with $27,645$ bodies. The result is opposite -- we estimate ABD has a $\sim5,000\times$ speedup (on CPU). This is just a rough assessment as we are never able to finish rigid-IPC in this stress test, which will need \emph{several years} while ABD finishes the simulation in \emph{five days}.
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Coenotephria pistacieti är en fjärilsart som beskrevs av Edward P. Wiltshire 1952. Coenotephria pistacieti ingår i släktet Coenotephria och familjen mätare. Inga underarter finns listade i Catalogue of Life.
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"redpajama_set_name": "RedPajamaWikipedia"
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{"url":"https:\/\/axiomsofchoice.org\/fugacity","text":"## Fugacity\n\n### Function\n\n definiendum $z(\\beta,\\mu):=\\mathrm e^{\\beta\\cdot\\mu}$\n\n#### Discussion\n\nNot to be confused with the fugacity coeffient $\\phi$, which is a pressure value used to model abbaviations from the ideal gas model pressures. The unitless normalized fugacity coeffient is called thermodynamic activity $a$, which is closer to $z$. The so called activity $a_B$ on the other hand is the non-ideal analogue of a concentration.","date":"2022-09-28 22:51:23","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8820794224739075, \"perplexity\": 2016.4126666316722}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-40\/segments\/1664030335286.15\/warc\/CC-MAIN-20220928212030-20220929002030-00002.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.nature.com\/articles\/s41597-021-00796-z?error=cookies_not_supported&code=2fd70788-f4bd-4e7b-894e-d15883ae662f","text":"Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.\n\n# Estimation of waste outflows for multiple product types in China from 2010\u20132050\n\n## Abstract\n\nMaterial flow has been accelerated from underground natural minerals and is accumulating as aboveground waste stock. China is not only the largest producer and consumer of material-driven products, but also the largest generator of product waste. No official annual product waste data are released for China, which creates challenges especially in light of China\u2019s emerging waste management policies. Previous studies have presented only estimations of waste streams for single products. In this study, we considered three product types and 33 technological products and collected all the available data. A Kuznets curve and Bass diffusion model were employed to forecast their future consumption. Based on urban consumption metabolism, we created one systematic estimation model of product waste generation related to material flow and social regulation. Typical technological product waste outflows were estimated from 2010 to 2050, which can assist further material flow and environmental impact research, as well as waste management policy-making and technology development. The created model can be potentially extended to other types of product waste estimation.\n\n Measurement(s) waste generation \u2022 waste material Technology Type(s) digital curation \u2022 Mathematical Model Factor Type(s) year of data collection Sample Characteristic - Location China\n\nMachine-accessible metadata file describing the reported data: https:\/\/doi.org\/10.6084\/m9.figshare.13277732\n\n## Background & Summary\n\nMaterials derived from biotic, mined and secondary sources are fundamental to the functioning of modern technologically advanced society1. Since 1970, global material consumption in four main categories (e.g., metal ores, biomass, fossil fuels, and non-metallic mineral) has grown from 27 Pg (1 Pg\u2009=\u20091015\u2009g) to 90 Pg in 20172, and is projected to more than double from 79 Pg in 2011 to 167 Pg in 20603. More and more underground materials are consumed in the technological product and finally \u201cstored\u201d in product waste. The rapid shortage of primary resources and the serious degradation of the environment from their extraction is one of the great challenges we face in transitioning to a more sustainable society4,5.\n\nChina\u2019s rapid development has led to the growth of an unprecedented industrial metabolism in the past four decades. Driven by the national call for an \u201cecological civilization\u201d6, China has embarked on an effort to implement solid waste management regulations and policies since 2010, particularly covering waste electrical & electric equipment regulation (WEEE), waste import ban, solid waste sorting, revised end-of-life vehicle (ELV) regulation, and zero-waste city. A major evolution of the environmental industry from informal to formal and from illegal to legal is emerging in the field of urban mining7 and circular economy8 paradigms. Lack of basic data related to typical technological product waste is severely frustrating the sound implementation of these regulations and policy.\n\nNational Development and Reform Commission regulated anthropogenic minerals for typical technological products waste, consisting of electrical & electric equipment (EEE), vehicle, and wiring & cable. Currently, China has no annual, officially released data of technological product waste generation. Only a few scholars previously attempted to forecast a certain type of product waste for a short duration; for instance, e-waste9,10,11 and ELV12. There is still no systematic estimation of solid waste generation, especially for typical technological product waste like WEEE, ELV, and waste wiring & cable (WWC). The chemical composition of materials stocks is scattered due to the fact that data collection tends to focus on single categories of materials. Therefore, after considering the consumption principle and the restrictive regulation, we firstly collected the available data of three types of technological product (i.e., EEE, vehicle, and wiring & cable) consumption from 1990s to now. Next, a Kuznets curve and Bass diffusion model will be employed to forecast their consumption from now to 2050. Finally, we provide the accurate estimation of product waste generation from the three technological product types and thirty categories from 2010 to 2050. Strict validation is also adopted with the detailed comparison and uncertainty analysis.\n\n## Methods\n\nTo estimate China\u2019s technological product waste, we designed four steps combining: (1) data collecting and pre-mining for product consumption, (2) regression simulation for future consumption, (3) estimating the product waste generation, and (4) validating the obtained results. Figure\u00a01 shows the detailed research diagram of product waste estimation with the datasets and methods which we employed for this study.\n\n### Step 1. Data collecting and pre-mining for product consumption\n\nBased on the product classification of EEE, vehicle, and wiring & cable in China (Table\u00a01), we collected all the available data of their production (Dataset, D1-D3 attached at figshare13), importation, and exportation (D4 attached at figshare13) from the 1990s to 2018\/2019. All the data sources are primarily from China National Bureau of Statistics (http:\/\/data.stats.gov.cn\/english\/) and China Customs Statistics (http:\/\/www.tradedata.hk\/). The domestic consumption amount in this period can be easily determined by the equation (Domestic consumption\u2009=\u2009Domestic production\u2009+\u2009Importation - Exportation). Seventeen types of EEEs and eight types of vehicles are involved here. Some products like mobile phones are still increasing, while a couple of products such as single-machine telephone and cathode-ray tube (CRT) monitors are dropping (Fig.\u00a02).\n\n### Step 2. Regression simulation for future consumption\n\nIn natural ecological systems, the inverted-U shape of a Kuznets curve is an adequate simulation model to address the evolution and succession of species, respectively14,15. This theoretical model has been well transplanted into industrial ecology to forecast the future product use16,17,18. But in reality, the consumption of technological products is dependent on total population, urbanization, and technology. China is projected to encounter the population peak in the 2020s19,20 and maintain a rapid urbanization in the 21st century. At the micro level, the consumption from emergence to peak can be addressed appropriately by the Bass diffusion model21,22, which is innovatively considered for future consumption prediction in this study. Driven by emerging technologies, the dramatic decline or obsolescence of the consumption of one product is predominately subject to the substitution of another product23. For instance, the Cathode Ray Tube (CRT) has been replaced by liquid crystal display (LCD) so that the use of CRT has been sharply cut down24,25. Therefore, the rapid growth, stable growth, stagnation, and eventual decrease shown in the consumption model could be described approximately by exponential regression, linear regression, constant value, and linear regression, respectively.\n\nWith these principles, we deliberately drew the regression simulation equation based on the recent-year data (F1 attached at figshare13) and forecasted the future consumption of those products between the years of 2019\/2020 and 2050. Accordingly, the domestic consumption of EEEs and vehicles from 1990 to 2050 is demonstrated in D6-D8 (see the detail at the below data code). Meanwhile, we also consider them to fit for normal distribution with standard deviations as 10% (of mean) between the years of 2019\/2020\u20132030, 15% for 2030\u20132040, and 20% for 2040\u20132050. Additionally, we also create the weight dataset for all the concerning products (D5 attached at figshare13) based on the reported and self-determined data. The experienced evolution of the product weight appropriately encloses them as the Beta distribution26.\n\n### Step 3. Estimating the technological product waste outflows\n\nThe Weibull distribution function is adequately sophisticated to express the durable product lifespan27. We use it to model the lifetime of the product. For no regulated-lifespan products like EEEs and bicycles, the probability density function (PDF) of the Weibull distribution is given by Eq.\u00a0110,28. Regarding the regulated-lifespan products like vehicles, and wiring & cable, the regulated lifespan should be considered and embedded into the conventional PDF for Eq.\u00a02.\n\n$$f(t)=\\left\\{\\begin{array}{cc}\\frac{\\beta }{\\eta }{\\left(\\frac{t}{\\eta }\\right)}^{\\beta -1}{e}^{-{(t\/\\eta )}^{\\beta }} & (t\\ge 0)\\\\ 0 & (t < 0)\\end{array}\\right..$$\n(1)\n$$f(t)=\\{\\begin{array}{cc}0 & (t > L)\\\\ {e}^{-{(t\/\\eta )}^{\\beta }} & (t=L)\\\\ \\frac{\\beta }{\\eta }{\\left(\\frac{t}{\\eta }\\right)}^{\\beta -1}{e}^{-{(t\/\\eta )}^{\\beta }} & (0\\le t < L)\\\\ 0 & (t < 0)\\end{array}.$$\n(2)\n\nwhere \u03b2 is the shape parameter (\u03b2\u2009>\u20090), \u03b7 is the scale parameter (\u03b7\u2009>\u20090), and L is the maximum lifetime of products regulated in China\u2019s legislation system (y). EoL units for a particular duration time t can be mathematically described as ref. 29. Based on net product production (as inflow) and the lifespan function, the annual technological product waste generation (as outflow) can be determined by Eq.\u00a0330,31:\n\n$$\\begin{array}{ccc}D(x) & = & \\underset{0}{\\overset{n}{\\int }}f(x)P(x)dx\\\\ & = & \\mathop{\\sum }\\limits_{i=1}^{30}[{P}_{i}(2000)\\times {f}_{i}(x-2000)+{P}_{i}(2001)\\times {f}_{i}(x-2001)+\\cdots +{P}_{i}(x-1)\\times {f}_{i}(1)].\\end{array}$$\n(3)\n\nwhere x is the year; D(x) is the total weight of technological product waste generation in the year x (in Mg); i is the ith category of product; n is the total number items in the product category; Pi(20yy) is the net weight of the ith product in the year 20yy (in Mg); and fi(x\u2009-\u20092000) is the obsolescence rate of the ith product since the year 2000.\n\n### Step 4. Validating the obtained results\n\nTwo approaches are enabled to validate the obtained results. Firstly, we compare the estimated technological product waste generation to the partially real data and previous studies. Secondly, based on all the equations, the uncertainty of the technological product waste generation and their materials stock is not only caused by the variables, including each product weight and Weibull function parameters, but also on the methods like the direct linear regression simulation. Here we consider their interactive influences and adopt a Monte Carlo simulation (105 iterations) to examine the uncertainty of the obtained results.\n\n## Data Records\n\nAfter the deep data mining, we created the database containing a total of 5,478 data records (consumption and generation) for mainland China. Of these\n\n\u2022 922 are seventeen types of EEE consumption unit amount (from 1990 to 2050; D6 online at figshare13);\n\n\u2022 1,421 are twenty-four types of vehicle consumption unit amount (from 1990 to 2050; D7 online at figshare13);\n\n\u2022 320 are weight amount of six types of wiring & cable production, import, and export (from 1996 to 2050; D8 online at figshare13);\n\n\u2022 68 are the collected parameters of Weibull lifespan distribution and the regulated maximum lifetime (D9 online at figshare13);\n\n\u2022 697 are seventeen types of WEEE generation unit amount (from 2010 to 2050; D10 online at figshare13);\n\n\u2022 697 are seventeen types of WEEE generation weight amount (from 2010 to 2050; D10 online at figshare13);\n\n\u2022 615 are fifteen types of ELV generation unit amount (from 2010 to 2050; D11 online at figshare13);\n\n\u2022 615 are fifteen types of ELV generation weight amount from 2010 to 2050; D11 online at figshare13); and\n\n\u2022 123 are total three types of technological waste product generation weight amount (from 2010 to 2050; D12 online at figshare13).\n\nChina\u2019s domestic consumption of EEE, vehicles, and wiring & cable from 2010 to 2050 is projected and demonstrated in Fig.\u00a03. After 2030, the total amount of EEE consumption will reach the peak of 2500 million units. The total consumption of vehicles and wiring & cable, however, will grow constantly during this period of time.\n\nWe also visualize the evolution of various WEEE and ELVs outflows from 2010 to 2050 (Fig.\u00a04). Regarding WEEE, the total unit and weight amount will grow from 635 million and 4 Tg (1Tg\u2009=\u20091012g) in 2010 to approximately 4,000 million and 28 Tg in 2040, respectively. The peak time is projected to be around 2040\u20132045 year. With respect to ELVs, the total unit and weight will maintain a rise driven by economic growth and rapid urbanization. The total weight amount will grow from 11 Tg in 2010 to 42 Tg in 2020 and 100 Tg in 2050.\n\nThe obtained data could be applied directly in a variety of fields. For instance, the estimated product waste generation can indicate the future recycling potential of a resource: how about the economic benefit and the ascending size of the waste recycling industry? Thus, potential energy conservation and associated greenhouse gas emission reduction can be enclosed from the recycling of product waste. Last but not least, the future consumption and obsolescence of electronics and vehicles will indicate a promising consumer electronics and automobile industry in a planned way32.\n\n## Technological Validation\n\n### Comparison with existing works\n\nWe compared our obtained results with the existing research and real values. Regarding five typical types of WEEE (e.g., TV, air conditioner, refrigerator, washing machine, and personal computer), their total quantity from 2010\u20132016 from this estimation is somewhat lower than the values reported by others previous studies (Fig.\u00a05). The difference can be attributed to two aspects of the previous works: old used data sources and different estimating methods. Moreover, in weight, the gaps among these studies are not significant. Regarding typical ELV quantity, some previous works indicate no distinct difference to this study. The biggest difference is given from Xi et al.33 only using a simple linear regression. The latest data until 2019 and the scientific methods such as Bass diffusion model and Weibull lifespan distribution were employed in this study to realize an accurate estimation. Additionally, the registered vehicle data has been estimated in this study for further comparison with real value released by the government. With the variance analysis, they demonstrate almost the same value without significant difference. The difference in 2009 is much larger than one in 2016 because the available consumption data of vehicle is initialed from 1995 (Fig.\u00a02). The data in 2009 is more sensitive to the unknown information before 1995. All the discussions can verify and validate the above results of this study, and further consolidate the relevant results.\n\n### Data error and uncertainty analysis\n\nThe error or range of the obtained results is primarily related to two points: one is the estimating waste methods of the Weibull distribution and the other is the projected future consumption of technological products. The error in the data of product waste outflows from 2010 to 2019 is provided from the Weibull distribution, but the error for the year of 2020 to 2050 is afforded by the two mixed points. Perhaps the projected future consumption method plays a bigger role.\n\nWe adopted the Monte Carlo simulations to further validate the obtained results. The uncertainty of waste product generation mainly depends on each product weight (Beta distribution) and the Weibull lifespan parameters (Normal distribution). Normal distribution was assumed for the forecasted data of EEE and vehicle consumption (see Online D6 and D7 at figshare13) with the standard deviation of 10%, 15%, and 20% for the data in 2020\u20132030, 2031\u20132040, and 2041\u20132050, respectively. We chose the WEEE weight and ELV weight in 2010, 2030, and 2050 as the examples. The increase of standard deviation indicates a growth in the uncertainty of waste product weight (Fig.\u00a06). Nevertheless, all 100% certainties can fully verify the robustness of the waste product outflows.\n\n## Code availability\n\nAll relevant data (D1-D12) and figure (F1) presented in this article are available online at figshare13. They were developed using the collecting data and Eqs. (13) in detail described in the methods. Equation (1) was employed for EEE and wiring & cable to measure the waste outflows, and Eq. (2) was adopted for vehicle to measure the waste outflows. It should be highlighted here that some obtained data covers the year until the year of 2018 or 2019 (D1-D8), which has updated the given data until the year of 2015 or 2016 at the published article in Nature Communication34.\n\n## References\n\n1. 1.\n\nGulley, A. L., Nassar, N. T. & Xun, S. China, the United States, and competition for resources that enable emerging technologies. Proc. Natl. Acad. Sci. USA 115, 4111\u20134115 (2018).\n\n2. 2.\n\nIRP. Assessing global resource use: a systems approach to resource efficiency and pollution reduction. Report No. 978-92-807-3677-9, (United Nations Environment Programme, Nairobi, 2017).\n\n3. 3.\n\nOECD. Global Material Resources Outlook to 2060. (OECD Publishing, 2019).\n\n4. 4.\n\nReid, W. V. et al. Earth System Science for Global Sustainability: Grand Challenges. Science 330, 916\u2013917 (2010).\n\n5. 5.\n\nNAE & NASEM. Environmental Engineering for the 21st Century: Addressing Grand Challenges. (The National Academies Press, 2018).\n\n6. 6.\n\nXiao, L. & Zhao, R. China\u2019s new era of ecological civilization. Science 358, 1008\u20131009 (2017).\n\n7. 7.\n\nZeng, X., Mathews, J. A. & Li, J. Urban Mining of E-Waste is Becoming More Cost-Effective Than Virgin Mining. Environ. Sci. Tech. 52, 4835\u20134841 (2018).\n\n8. 8.\n\nMathews, J. A. & Tan, H. Circular economy: Lessons from China. Nature 531, 440\u2013442 (2016).\n\n9. 9.\n\nBald\u00e9, C. P., Forti, V., Gray, V., Kuehr, R. & Stegmann, P. The Global E-waste Monitor 2017: Quantities, Flows, and Resources. (International Telecommunication Union & International Solid Waste Association, 2017).\n\n10. 10.\n\nDuan, H. et al. Systematic characterization of generation and management of e-waste in China. Environ. Sci. Pollut. Res. 23, 1929\u20131943 (2016).\n\n11. 11.\n\nZeng, X., Gong, R., Chen, W.-Q. & Li, J. Uncovering the Recycling Potential of \u201cNew\u201d WEEE in China. Environ. Sci. Tech. 50, 1347\u20131358 (2016).\n\n12. 12.\n\nYu, L., Chen, M. & Yang, B. Recycling policy and statistical model of end-of-life vehicles in China. Waste Manag. Res. 37, 347\u2013356 (2019).\n\n13. 13.\n\nZeng, X., Ali, S. H. & Li, J. Source code for: Estimation of waste outflows for multiple product types in China from 2010\u20132050. figshare https:\/\/doi.org\/10.6084\/m9.figshare.12129303\u00a0(2020).\n\n14. 14.\n\nLaw, R., Murrell, D. J. & Dieckmann, U. Population growth in space and time: spatial logistic equations. Ecology 84, 252\u2013262 (2003).\n\n15. 15.\n\nArrow, K. et al. Economic Growth, Carrying Capacity, and the Environment. Science 268, 520\u2013521 (1995).\n\n16. 16.\n\nHoornweg, D., Bhada-Tata, P. & Kennedy, C. Waste production must peak this century. Nature 502, 615\u2013617 (2013).\n\n17. 17.\n\nBald\u00e9, C. P., Wang, F., Kuehr, R. & Huisman, J. The global e-waste monitor -2014. (United Nations University, IAS-SCYCLE, 2015).\n\n18. 18.\n\nLebreton, L. & Andrady, A. Future scenarios of global plastic waste generation and disposal. Palgrave Commun. 5, 6 (2019).\n\n19. 19.\n\nLiu, Q. & Liu, X. Forecasting on China\u2019s population size and structure during 2018-2100 with the background of family planning policy adjustment (in Chinese). Mathematics in Practice and Theory 48, 180\u2013188 (2018).\n\n20. 20.\n\nUNDESA. World Population Prospects 2019, Volume II: Demographic Profiles. Report No. ST\/ESA\/SER.A\/427, (United Nations, made available under a Creative Commons license (CC BY 3.0 IGO), 2019).\n\n21. 21.\n\nBass, F. M. A New Product Growth for Model Consumer Durables. Manage. Sci. 50, 1825\u20131832 (2004).\n\n22. 22.\n\nDong, C., Sigrin, B. & Brinkman, G. Forecasting residential solar photovoltaic deployment in California. Technol. Forecast Soc. 117, 251\u2013265 (2017).\n\n23. 23.\n\nParajuly, K. et al. Future E-waste Scenarios. (StEP Initiative, UNU ViE-SCYCLE, UNEP IETC, 2019).\n\n24. 24.\n\nAlthaf, S., Babbitt, C. W. & Chen, R. Forecasting electronic waste flows for effective circular economy planning. Resour. Conserv. Recycl. 151, 104362 (2019).\n\n25. 25.\n\nDebnath, B., Chowdhury, R. & Ghosh, S. K. Sustainability of metal recovery from E-waste. Front. Env. Sci. Eng. 12, 2 (2018).\n\n26. 26.\n\nKuong, I. H., Li, J., Zhang, J. & Zeng, X. Estimating the Evolution of Urban Mining Resources in Hong Kong, up to the Year 2050. Environ. Sci. Tech. 53, 1394\u20131403 (2019).\n\n27. 27.\n\nCastillo, E. & Fern\u00e1ndez-Canteli, A. A unified statistical methodology for modeling fatigue damage. Vol. 80 (Springer, 2009).\n\n28. 28.\n\nZhang, L., Yang, J., Cai, Z. & Yuan, Z. Understanding the Spatial and Temporal Patterns of Copper In-Use Stocks in China. Environ. Sci. Tech. 49, 6430\u20136437 (2015).\n\n29. 29.\n\nLam, C. W., Lim, S.-R. & Schoenung, J. M. Linking Material Flow Analysis with Environmental Impact Potential. J. Ind. Eco. 17, 299\u2013309 (2013).\n\n30. 30.\n\nBusch, J., Steinberger, J. K., Dawson, D. A., Purnell, P. & Roelich, K. Managing critical materials with a technology-specific stocks and flows model. Environ. Sci. Technol. 48, 1298\u20131305 (2014).\n\n31. 31.\n\nDu, X. & Graedel, T. E. Global in-use stocks of the rare Earth elements: a first estimate. Environ. Sci. Technol. 45, 4096\u20134101 (2011).\n\n32. 32.\n\nKim, H., Jang, Y.-C., Hwang, Y., Ko, Y. & Yun, H. End-of-life batteries management and material flow analysis in South Korea. Front. Environ. Sci. Eng. 12, 3 (2018).\n\n33. 33.\n\nXi, H., Yang, Y. & Chen, Y. Forecasting the near-future obsolescence, increase, and stock of vehicle in China (in Chinese). Highways & Automotive Applications, 30\u201334 (2014).\n\n34. 34.\n\nZeng, X., Ali, S. H., Tian, J. & Li, J. Mapping anthropogenic mineral generation in China and its implications for a circular economy. Nat. Commun. 11, 1544 (2020).\n\n35. 35.\n\nYang, J. X., Lu, B. & Xu, C. WEEE flow and mitigating measures in China. Waste Manage. 28, 1589\u20131597 (2008).\n\n36. 36.\n\nLi, J. et al. Status quo of e-waste management in mainland China. J. Mater. Cycles Waste Manage. 8, 13\u201320 (2006).\n\n37. 37.\n\nLiu, X., Tanaka, M. & Matsui, Y. Generation amount prediction and material flow analysis of electronic waste: a case study in Beijing, China. Waste Manage. Res. 24, 434\u2013445 (2006).\n\n38. 38.\n\nVeenstra, A., Wang, C., Fan, W. & Ru, Y. An analysis of E-waste flows in China. Int. J. Adv. Manuf. Technol. 47, 449\u2013459 (2010).\n\n39. 39.\n\nXue, J., Hu, S. & Yang, Q. Potentials of the Renewable Resource of Scrapped Cars in China (in Chinese). China Population Resources and Environment 23, 169\u2013176 (2013).\n\n40. 40.\n\nJin, X. et al. Analysis on Modeling of Utilization System of Automobile Renewable Resources (in Chinese). Systems Engineering 26, 69\u201373 (2008).\n\n## Acknowledgements\n\nThe work is financially supported by National Key R&D Program of China (2018YFC1900101) and Asia Research Centre in Tsinghua University (2018-B1). We sincerely acknowledge the four anonymous reviewers for their valuable comments and suggestions.\n\n## Author information\n\nAuthors\n\n### Contributions\n\nX.Z. collected data and wrote the paper; S.A. contributed the insight and polished the article; X.Z. and J.L. supervised this study.\n\n### Corresponding author\n\nCorrespondence to Xianlai Zeng.\n\n## Ethics declarations\n\n### Competing interests\n\nThe authors declare no competing interests.\n\nPublisher\u2019s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.\n\n## Rights and permissions\n\nThe Creative Commons Public Domain Dedication waiver http:\/\/creativecommons.org\/publicdomain\/zero\/1.0\/ applies to the metadata files associated with this article.\n\nReprints and Permissions\n\nZeng, X., Ali, S.H. & Li, J. Estimation of waste outflows for multiple product types in China from 2010\u20132050. 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Douglas Moss AIA, LEED AP is an American architect, who practices in New York City. He was a founding partner of Holzman Moss Bottino Architecture. In October 2019 Holzman Moss Bottino Architecture merged with California-based Steinberg Hart and Moss became a partner of Steinberg Hart.
He is involved in both the administration of the office and the development of planning and building projects that include performing arts center, museums, civic facilities, and student centers.
Life and career
Douglas Moss, AIA, LEED AP, a partner of Steinberg Hart, directs the development of planning and building projects that include performing arts centers, libraries, museums, and student centers. Prior to the merging of the firm in late 2019 with Steinberg Hart, Moss was a founding partner of Holzman Moss Bottino Architecture. Active in numerous professional associations, he is a member of the American Institute of Architects, the U.S. Green Building Council, the National Trust for Historic Preservation, and the Urban Land Institute Small Scale Developer Forum. Moss is on the board of Bogardus Plaza in New York City; Co-Chair of Westside Center for Community Life; and past President of the Emerging Artists Theatre board. He has served as a guest lecturer at several universities, and as a board member of the Texas Tech University Architecture Alumni Association. Moss received his Bachelor of Architecture degree from Texas Tech University and was awarded the prestigious Alumni of the year award in 2018.
Moss has also been a panelist and speaker at the Association of College Unions International, the Society for Campus and University Planning, the International Council of Fine Arts Deans and the United States Institute for Theatre Technology conferences. He received his Bachelor of Architecture degree from Texas Tech University, where he was awarded the prestigious Alpha Rho Chi Medal of Architecture. He is a LEED Accredited Professional and is certified by the National Council of Architectural Registration Boards. In 2018 Moss was awarded the Texas Tech University College of Architecture Distinguished Alumni award, which identifies graduates who have clearly defined excellence in their profession as well as dedication to the field of architecture.
Works (partial list)
Steinberg Hart
See also
Malcolm Holzman
Nestor Bottino
References
External links
Holzman Moss Bottino Architecture Website
Douglas Moss Tribeca Loft
Douglas Moss International Council of Fine Arts Deans
Year of birth missing (living people)
Living people
20th-century American architects
Texas Tech University alumni
21st-century American architects
People from Taylor, Texas
Architects from Texas | {
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\section{Introduction} Networks of elastoplastic springs are increasingly used in the modeling of the distribution of stresses in elastopastic media \cite{buxton,chen}, swarming of mobile router networks \cite{robot2,robot1}, and other physical phenomena. According to Moreau \cite{moreau}, the stresses of springs of such a network can be described by a differential inclusion
({\it Moreau sweeping process})
\begin{equation}
-y'(t)\in N_{C(t)}(y(t)),\quad y(t)\in\mathbb{R}^m,
\label{eq:MSP0}
\end{equation}
where $C(t)\subset\mathbb{R}^m$ is a closed polyhedron that plays the role of a constraint,
\begin{equation}\nonumber
N_{{C}}(x)=\left\{\begin{array}{ll}\left\{\zeta \in \mathbb{R}^n:\langle\zeta,c-x\rangle\leqslant 0,\ c\in {{C}}\right\},& {\rm if}\ x\in {{C}},\\
\emptyset,& {\rm if}\ x\not\in {{C}},
\end{array}\right.
\end{equation}
and the dimension $m$ equals or smaller than the number of springs in the network.
\vskip0.2cm
\noindent Periodicity of the constraint $C(t)$ corresponds to periodicity of the external loading applied to the given network of springs. The fundamental result by Krejci \cite[Theorem 3.14]{Krejci1996} says that for $C(t)$ of the form $C(t)=C+c(t)$, where $C$ is a convex closed bounded set and $t\mapsto c(t)$ is a $T$-periodic vector-function, any solution of sweeping process (\ref{eq:MSP0}) converges to some $T$-periodic regime. For a class of continuum elastoplastic media with $T$-periodic loading the uniqueness of $T$-periodic response is established in Frederick-Armstrong \cite[p.~159]{frederick}. Sufficient conditions for the uniqueness of the response in sweeping processes can be drawn based on Adly et al \cite{adly}.
The non-uniqueness of the response for sweeping processes can of course be easily designed, see Fig.~\ref{fig1}a, where one gets a family of periodic solutions by moving a rectangle normal to its sides back and worth. However, as shown at Fig.~\ref{fig1}b, small perturbation of such a rectangle destroys the attracting family of
orbits of Fig.~\ref{fig1}a leaving only a single attracting solution.
\begin{figure}[h]
\begin{center}
\includegraphics[scale=0.78]{fig1.pdf}
\end{center}\vskip0.0cm
\caption{Sample trajectories (solid curves) of Moreau sweeping process with a moving constraint (dashed rectangle) that moves back and forth. The bold points are the initial conditions of sample trajectories. The figure illustrates the type of attractor (solid black curves) when (a) the moving constraint is just a rectangle, (b) the moving constraint is a pentagon with a corner that accumulates all the trajectories.}
\label{fig1}
\end{figure}
\noindent That is why a natural question arises:
\begin{itemize}
\item[] whether or not any network of elastoplastic springs can always be slightly perturbed in way that destroys any potential family of periodic orbits in the respective sweeping process (\ref{eq:MSP0})?
\end{itemize}
\begin{figure}[h]\center
\vskip-0.7cm
\includegraphics[scale=0.78]{example2-sping-Ivan.pdf}\vskip-0.0cm
\caption{\footnotesize A one-dimensional network of 5 springs on 5 nodes with one displacement-controlled loading. The circled digits stand for numbers of nodes. The regular digits are the numbers of springs. The thick bar is the displacement-controlled loading $l_1(t)$. The stress-controlled loadings $f_1(t),...,f_5(t)$ are applied at nodes.
} \label{ex2newfig}
\end{figure}
\noindent As uniqueness of the response lies in the core of reliability of modeling prediction (see e.g. \cite{bouby,brazil}), the above-stated question is not of merely academic value. We introduce a simple example that answers this question negatively. Specifically, we show that the cyclically loaded network of elastoplastic springs of Fig.~\ref{ex2newfig} leads to a sweeping process with a family of attracting periodic orbits.
\vskip0.2cm
\noindent The paper is organized as follows. In the next section we define a network of elastoplastic springs formally. In section~\ref{eq:sweepProcess} we derive a sweeping process \eqref{eq:MSP0} that governs the quasi-static evolution of such a network.
Section~\ref{step-by-step} is based on Moreau \cite{moreau} and Gudoshnikov-Makarenkov \cite{G-M}. It compiles a guide for closed-form computation of the quantities required for construction of a sweeping process of a given network of elastoplastic springs. This guide is then used in Section~\ref{sect:structStab} to construct the sweeping process of the network of elastoplastic springs of Fig.~\ref{ex2newfig}. We rigorously proof (Proposition~\ref{prop1} and Corollary~\ref{corr1}) that such a sweeping process admits a family of periodic orbits that persists under perturbations of the mechanical parameters of the network.
\section{A concise definition of a general network of elastoplastic springs}\label{defined}
\noindent We consider a network of $m$ elastoplastic springs on $n$ nodes that are connected according to a directed graph given by the $n\times m$ incidence matrix $D^\top$. The Hooke's coefficients $a_1, ..., a_m$ of the springs are arranged into an $m\times m$-matrix $A={\rm diag}\left\{a_1,...,a_m\right\}.$ The elastic limits $[c_i^-,c_i^+]$ of springs are used to introduce a parallelepiped $C\subset\mathbb{R}^m$ as $C=[c_1^-,c_1^+]\times...\times[c_m^-,c_m^+].$ In addition the network comes with a collection of stress-controlled and displacement-controlled loadings $\{f_i(t)\}_{i=1}^n$ and $\{l_i(t)\}_{i=1}^q$ respectively. The stress-controlled loadings are simply applied at the $n$ nodes of the network and are supposed to satisfies the equation of static balance
\begin{equation}\label{balance!}
f_1(t)+...+f_n(t)=0.
\end{equation}
As for the displacement-controlled loading $l_k(t),$ $k\in\overline{1,q}$, we consider a chain of springs which connects the left node $I_k$ of the constraint $k$ with its right node $J_k.$
To each displacement-controlled loading $l_k(t)$ we, therefore, associate a so-called {\it incidence vector} $R^k\in\mathbb{R}^m$ whose $i$-th component $R^k_i$ is $-1,$ $0,$ or $1$ according to whether the spring $i$ increases, not influences, or decreases the displacement when moving from node $I_k$ to $J_k$ along the chain selected, see Fig.~\ref{figR}.
\begin{figure}[h]\center
\vskip-0.3cm
\includegraphics{drawing1-Ivan1.pdf}\vskip-0.0cm
\caption{\footnotesize Illustration of the signs of the components of the incidence vector $R^k\in\mathbb{R}^m.$ The dotted contour stays for the chain of the springs associated with the vector $R^k$.
} \label{figR}
\end{figure}
We assume that the displacement-controlled loadings $\{l_i(t)\}_{i=1}^m$ are independent in the sense that
\begin{equation}\label{A2}
{\rm rank}\left(D^\top R\right)=q.
\end{equation}
Mechanically, condition (\ref{A2}) ensures that the displacement-controlled loadings don't contradict one another. For example, (\ref{A2}) rules out the situation where two different displacement-controlled loadings connect same pair of nodes.
\section{A concise formulation of the sweeping process of a general network of elastoplastic springs}
\label{eq:sweepProcess}
\noindent In this section we follow Moreau \cite{moreau} (see also Gudoshnikov-Makarenkov \cite{G-M}). If condition (\ref{balance!}) holds, then there exists a function
$\bar h:\mathbb{R}\to\mathbb{R}^m$, such that
\begin{equation}\label{fh}
f(t)=-D^\top \bar h(t).
\end{equation}
Then, under condition (\ref{A2}), there exists an $n\times q-$matrix $L$, such that
\begin{equation}
R^\top D L=I_{q\times q}.
\label{barxi}
\end{equation}
\sloppy
\noindent Introducing
\begin{equation}\label{U} U=\left\{x\in D\mathbb{R}^n:R^\top x=0\right\},\qquad V=A^{-1}U^\perp,
\end{equation}
where $U^\perp=\left\{y\in\mathbb{R}^m:\left<x,y\right>=0,\ x\in U\right\},$
the space $V$
becomes an orthogonal complement of the space $U$ in the sense of the scalar product
\begin{equation}\label{product}
(u,v)_A=\left<u,Av\right>.
\end{equation}
Therefore, any element $x\in\mathbb{R}^m$ can be uniquely decomposed
as
$$
x=P_U x+P_V x,
$$
where $P_U$ and $P_V$ are linear (orthogonal in sense of \eqref{product}) projection maps on $U$ and $V$ respectively.
Define
\begin{align}
g(t)&=P_V DL l(t),\label{g(t)}\\
h(t)&=P_U A^{-1}\bar h(t),\label{h}\\
N_C^A(x)&=\\
&\hskip-1cm =\left\{\begin{array}{ll}\left\{\xi\in\mathbb{R}^m:\left<\xi,A(c-x)\right>\le 0,\ c\in C\right\},&\quad {\rm if}\ x\in C,\\
\emptyset,& \quad {\rm if}\ x\not\in C,
\end{array}\right.\nonumber\\
\Pi(t)&=A^{-1}C+h(t)-g(t),\label{Pi(t)}
\end{align}
Assuming that both $f:\mathbb{R}\to\mathbb{R}^n$ and $l:\mathbb{R}\to\mathbb{R}^q$ are Lipschitz continuous, we get that $h(t)$ and $g(t)$ are Lipschitz continuous as well, so that the function
$$
y(t)=A^{-1}s(t)+h(t)-g(t)
$$
is absolutely continuous for any absolutely continuous $t\mapsto s(t).$
\begin{theorem}\label{thm1} {\rm \cite{moreau} (see also \cite{G-M})} Assume that the network of elastoplastic springs $(D,A,C,R,f(t),l(t))$ of section~\ref{defined} satisfies the conditions (\ref{balance!}) and (\ref{A2}). Assume that
$h:\mathbb{R}\to\mathbb{R}^m$ and $g:\mathbb{R}\to\mathbb{R}^m$ given by
(\ref{g(t)})-(\ref{h}) are Lipschitz continuous. Assume that safe load condition
\begin{equation}\label{A4}
\left(C+Ah(t)\right)\cap U^\perp\not=\emptyset
\end{equation}
holds on some time interval $[0,T].$
Then,
the function $s(t)=(s_1(t),...,s_m(t))$ defines the evolution of stresses of
the network $(D,A,C,R,f(t),l(t))$ for $t\in[0,T]$ if and only if the function
$$
y(t)=A^{-1}s(t)+h(t)-g(t)
$$
satisfies the differential inclusion (called {\it sweeping process})
\begin{eqnarray}
-\dot y&\in& N^A_{\Pi(t)\cap V}(y),\quad {\rm for\ a.a.\ }t\in[0,T], \label{sw1}\\
y(0)&\in & \Pi(0)\cap V.\label{eq:initialElastic}
\end{eqnarray}
\end{theorem}
\noindent It remains to note that, for Lipschitz continuous
$h:\mathbb{R}\to\mathbb{R}^m$ and $g:\mathbb{R}\to\mathbb{R}^m$,
sweeping process (\ref{balance!})-(\ref{A2}) has a unique Lipschitz-continuous solution for any initial condition (see e.g. Kunze and Monteiro Marques \cite[sect. 3]{kunze}).
\section{The shakedown condition}
\label{sect:conditions}
\noindent {The following} conditions will rule out the existence of constant solutions.
\begin{proposition}\label{prop3} {\rm \cite[Proposition~3]{G-M}} Assume that conditions of Theorem~\ref{thm1} hold. If
\begin{equation}\label{formulaprop3}
\|A^{-1}c^--A^{-1}c^+\|_A<\left\|g(t_1)-g(t_2)\right\|_A,
\end{equation}
for some $0\le t_1< t_2$,
where
\begin{eqnarray*}
\|x\|_A&=&\sqrt{\left<x,Ax\right>},\\
c^-&=&(c_1^-,...,c_m^-)^\top,\\
c^+&=&(c_1^+,...,c_m^+)^\top.
\end{eqnarray*}
then sweeping process (\ref{sw1}) doesn't have any solutions that are constant on $[t_1,t_2].$
\end{proposition}
\begin{remark}\label{remarkprop3} Note, the left-hand-side in the squared inequality \eqref{formulaprop3} from the statement of Proposition~\ref{prop3} can be computed as \newline
$\|A^{-1}c^--A^{-1}c^+\|_A^2=
\left<c^--c^+,A^{-1}(c^--c^+)\right>.$
\end{remark}
\section{A step-by-step guide to compute the quantities of the sweeping process from a network of elastoplastic springs}\label{step-by-step}
\noindent In this section we again follow Moreau \cite{moreau}, but use the notations and additional properties established in Gudoshnikov-Makarenkov \cite{G-M}. In particular, \cite[Lemma~1]{G-M} and \cite[formula~(49)]{G-M} say that
\begin{eqnarray}
\dim U&=&n-q-1.\label{dimU}\\
\dim V&=&m-n+q+1,\label{dimV}
\end{eqnarray}
provided that (\ref{A2}) is satisfied.
\vskip0.2cm
\noindent {\boldmath{\bf Step 1. The matrix $M.$}} According to (\ref{dimU}), there should exist an $n\times (n-q-1)-$matrix $M$ such that
\begin{equation}\label{RTDM}
R^\top DM=0 \quad {\rm and}\quad {\rm rank}(DM)=n-q-1
\end{equation}
which allows to introduce $U_{basis}$ as
\begin{equation}\label{Ubasis}
U_{basis}=DM.
\end{equation}
\noindent {\boldmath{\bf Step 2. The matrix $V_{basis}.$}}
According to (\ref{U}), $V_{basis}$ is an arbitrary matrix of $m-n+q+1=\dim V$ linearly independent columns that solves
\begin{equation}\label{Vbasis}
(U_{basis})^\top AV_{basis}=0.
\end{equation}
\noindent {\boldmath{\bf Step 3. The matrix $D^\perp.$}} Define $D^\perp$ to be an $m\times(m-n+1)-$matrix of full rank that solves the equation
\begin{equation}\label{Dperp}
(D^\perp)^\top D={\color{black}0_{(m-n+1)\times(m-n+1)}}.
\end{equation}
\noindent {\bf Step 4. Other quantities.} Using Steps 2 and 3, we can compute an $(m-n+q+1)\times q$-matrix $\bar L$ as
\begin{equation}\label{barLnew}
\bar L=\left(\left(\begin{array}{c}
R^\top \\
(D^\perp)^\top\end{array}\right)V_{basis}\right)^{-1}\left(\begin{array}{c}
I_{q\times q}\\ 0_{(m-n+1)\times q}\end{array}\right).
\end{equation}
It turns out that formula (\ref{g(t)}) can now be rewritten in closed-form as
\begin{equation}\label{g(t)ex}
g(t)=V_{basis}\bar L l(t).
\end{equation}
To account for all possible functions $h(t)$ from (\ref{h}) we will simply take $h(t)$ as
\begin{equation}\label{h(t)}
h(t)=U_{basis}H(t),
\end{equation}
where $H(t)$ is an arbitrary Lipschitz continuous control input. It is possible to compute $H(t)$ in terms of $f(t)$, but it is not of added value here.
\vskip0.2cm
\noindent Finally, for $\Pi(t)\cap V$ we have
\begin{equation}\label{222}
\Pi(t)\cap V=\bigcap_{i=1}^{m}V_i(t),
\end{equation}
\noindent where
\begin{equation}\label{normals}
\begin{array}{rcl}
V_i(t)&=&\left\{x\in V:c_i^-\hskip-0.05cm+\hskip-0.05cma_ih_i(t)\hskip-0.05cm\le\right.\\
&&\hskip1cm \left.\le\hskip-0.05cm\left<n_i,Ax\hskip-0.05cm+\hskip-0.05cmAg(t)\right>\hskip-0.05cm\le c_i^+\hskip-0.05cm+\hskip-0.05cma_ih_i(t)\right\},\\
n_i&=&V_{basis}\bar n_i,\\
n_i&=&\left(\left(\begin{array}{c} R^\top\\ (D^\perp)^\top\end{array}\right)V_{basis}\right)^{-1}\left(\begin{array}{c} R^\top\\ (D^\perp)^\top\end{array}\right)e_i,
\end{array}
\end{equation}
and $e_i\in\mathbb{R}^m$ is the vector with 1 in the $i$-th component and zeros elsewhere.
\section{The sweeping process of the network of elastoplastic springs of Figure~\ref{ex2newfig}}
\label{sect:structStab}
The network of elastoplastic springs of Fig.~\ref{ex2newfig} is given by
\begin{equation}\label{Dex2new}
D\xi=
\left(\begin{array}{ccccc}
-1 & 1 & 0 & 0 & 0\\
0 & -1 & 1 & 0 & 0\\
0 & 0 & -1 & 1 & 0\\
0 & 0 & 0 & -1 & 1\\
0 & -1 & 0 & 1 & 0
\end{array}\right)
\left(\begin{array}{c}\xi_1\\
\xi_2\\
\xi_3\\
\xi_4\\
\xi_5
\end{array}\right), \quad R=\left(\begin{array}{l} 1 \\ 1 \\ 1 \\ 1 \\ 0\end{array}\right),
\end{equation}
\noindent some $5\times 5$ diagonal matrix $A$ of Hooke's coefficients and some intervals $[c_i^-,c_i^+]$, $i\in\overline{1,5}$, of elasticity bounds
\vskip0.2cm
\noindent Formula (\ref{dimU}) leads to
$$
\dim U=5-1-1=3.
$$
The $5\times 3-$matrix $M$ that solves (\ref{RTDM}) and the respective $5\times 3-$matrix (\ref{Ubasis}) are found as
\begin{equation}\label{UbasisEx2new}
M=\left(\begin{array}{ccc}
0 & 0 & 0\\
1 & 0 & 0\\
0 & 1 & 0\\
0 & 0 & 1\\
0 & 0 & 0
\end{array}\right),
\quad U_{basis}=\left(\begin{array}{ccc}
1 & 0 & 0\\
-1 & 1 & 0\\
0 & -1 & 1\\
0 & 0 & -1\\
-1 & 0 & 1
\end{array}\right),
\end{equation}
and
$H(t)$ in (\ref{h(t)}) is an arbitrary Lipschitz continuous function from $[0,T]$ to $\mathbb{R}^3.$
\vskip0.2cm
\noindent
According to (\ref{dimV}) and (\ref{Vbasis}), one gets
\begin{equation}\label{VbasisEx2}
\begin{array}{rcl}
\dim V&=&5-5+1+1=2,\\
V_{basis}&=&\left(\begin{array}{ccc}
1/a_1 & \ &0\\
1/a_2 &\ &-1/a_2\\
1/a_3 &\ &-1/a_3\\
1/a_4 &\ & 0\\
0 &\ & 1/a_5
\end{array}\right)
\end{array}
\end{equation}
\noindent Following Step~3 of section~\ref{step-by-step}, we compute $\dim D^\perp=5-5+1=1$ and the $5\times 1$-dimensional solution of (\ref{Dperp}) is
{\color{black}\begin{equation}\label{0110-1}
D^\perp=\left(\begin{array}{c}
0\\ 1\\ 1\\ 0\\ -1
\end{array}\right).
\end{equation}}
Therefore, according to formula (\ref{barLnew}), the $2\times1-$matrix $\bar L$ computes as
\begin{equation}
\bar L=\left(\left(\begin{array}{ccccc}
1 & 1 & 1 & 1 & 0\\
0 & 1 & 1 & 0 & -1\\
\end{array}\right)V_{basis}\right)^{-1}\left(\begin{array}{c}
1\\0\end{array}\right)
\label{eq:LBarEx2new}
\end{equation}
and by (\ref{g(t)ex}) we get
\begin{equation}\label{relation1}
g(t)=V_{basis}\left(\left(\begin{array}{ccccc}
1 & 1 & 1 & 1 & 0\\
0 & 1 & 1 & 0 & -1\\
\end{array}\right)V_{basis}\right)^{-1}\left(\begin{array}{c}
1\\0\end{array}\right)l(t).
\end{equation}
On the other hand, formula (\ref{normals}) says that for each $i\in\overline{1,5}$, the normal vector $n_i$ is given by $n_i=$
\begin{equation}\label{relation2}
V_{basis}\left(\left(\begin{array}{ccccc}
1 & 1 & 1 & 1 & 0\\
0 & 1 & 1 & 0 & -1\\
\end{array}\right)V_{basis}\right)^{-1}\hskip-0.2cm\left(\begin{array}{ccccc}
1 & 1 & 1 & 1 & 0\\
0 & 1 & 1 & 0 & -1\\
\end{array}\right)e_i.
\end{equation}
Note, formulas (\ref{relation1}) and (\ref{relation2}) hold for any $a_i,$ $i\in\overline{1,5}$ and any $c_i^-,c_i^+$, $i\in\overline{1,5}.$ Therefore, we see from formulas (\ref{relation1}) and (\ref{relation2}) that $n_1\parallel g(t)$ and $n_4\parallel g(t)$ for any values of the physical parameters of the network of Fig.~\ref{ex2newfig}. However, at this point we don't know whether or not the normals $n_1$ and $n_4$ have anything to do with the sides of the shape $\Pi(t)\cap V$ given by (\ref{222}), as it may happen that the constraints of \eqref{222} provided by $n_1$ and $n_4$ become redundant for a particular $h(t)$.
\begin{proposition}\label{prop1} There is an open set of the parameters $a_i,$ $c_i^-,c_i^+$, $i\in\overline{1,5}$, and an open set of Lipschitz-continuous functions $H:[0,T]\mapsto\mathbb{R}^3,$ for which the vectors $n_1$ and $n_4$ are the normal vectors of the two opposite sides of the shape $\Pi(t)\cap V$. In particular, this open set of the parameters contains the point
\begin{equation}\label{para}
\begin{array}{l}
c_i^-=-1,\ c_i^+=1,\ a_i=1,\\
H(t)\equiv(-0.5,-0.8,-1)^\top.
\end{array}
\end{equation}
Here $[0,T]$ is an arbitrary chosen domain of the functions $t\mapsto H(t).$
\end{proposition}
\noindent {\bf Proof.} Without loss of generality we can consider $g(t)\equiv 0$. Indeed, since $g(t)$ acts along $V$, $g(t)$ simply translates $\Pi(t)\cap V$ within $V$, so that $g(t)$ doesn't change the shape of $\Pi(t)\cap V$.
\vskip0.2cm
\noindent Plugging (\ref{para}) into (\ref{UbasisEx2new}) and using (\ref{h(t)}) we get
$$
h(t)\equiv (-0.5,-0.3,-0.2,1,-0.5)^\top.
$$
Therefore, for the parameters (\ref{para}), formula (\ref{222}) says that $x\in\Pi(t)\cap V$ if and only if
\begin{equation}\label{system}
\left\{\begin{array}{lllll}
-1-0.5&\le&\left<n_1,x\right>&\le& 1-0.5,\\
-1-0.3&\le&\left<n_2,x\right>&\le& 1-0.3,\\
-1-0.2&\le&\left<n_3,x\right>&\le& 1-0.2,\\
-1+1&\le&\left<n_4,x\right>&\le& 1+1,\\
-1-0.5&\le&\left<n_5,x\right>&\le& 1-0.5,
\end{array}\right.
\end{equation}
where
\begin{equation}\label{n1} \renewcommand\arraystretch{2}
\begin{array}{l}n_1=n_4=\dfrac{1}{d}\left(-3,-1,-1,-3,-2\right)^\top,\\
n_2=n_3=\dfrac{1}{d}\left(-1,-3,-3,-1,2\right)^\top,\\
n_5=\dfrac{1}{d}\left(-2,2,2,-2,-4\right)^\top,\\
d=-8.
\end{array}
\end{equation}
Based on (\ref{relation2}), $n_1=n_4$ and $n_2=n_3$. Therefore, 1st and 4th lines of system (\ref{system}) as well as 2nd and 3rd lines combine, that reduces the number of double-sided inequalities to 3. Substituting the expressions (\ref{relation2}) with parameters (\ref{para}) into (\ref{system}) and plugging $x=V_{basis}v,$ where $v\in\mathbb{R}^2,$ system (\ref{system}) reduces to the following system
\begin{equation}\label{system2}
\left.\begin{array}{lrlcll}
{\rm normals}\ n_1\ {\rm and}\ n_4: \quad& 0&\le&v_1&\le& 0.5,\\
{\rm normals}\ n_2\ {\rm and}\ n_3: \quad& -1.2&\le&v_1-v_2&\le& 0.7,\\
{\rm normal}\ n_5: & -1.5&\le&v_2&\le& 0.5.
\end{array}\right.
\end{equation}
\begin{figure}[h]\center
\vskip-0.5cm
\includegraphics[scale=0.6]{shape.pdf}\vskip-0.2cm
\caption{\footnotesize The gray region stays for the set of $(v_1,v_2)$ given by inequalities (\ref{system2}). The dotted lines denote the sets of $(v_1,v_2)$ where equalities of (\ref{system2}) are attained (the dotted line $v_1=0$ coincides with the vertical axis and another dotted line $v_2=-1.5$ is not shown).
} \label{figshape}
\end{figure}
\noindent Fig.~\ref{figshape} illustrates that the two constraints from \eqref{222} corresponding to normal vectors $n_1$ and $n_4$ constitute the opposite sides of the shape
$\Pi(t)\cap V$. This properties persists under small perturbations of the parameters (\ref{para}). Indeed, formulas (\ref{222}) and (\ref{relation2}) imply that small perturbations of the parameters (\ref{para}) lead to small parallel displacements of the dotted lines of Fig.~\ref{figshape} (without rotations), so that the two opposite parallel sides will stay. The proof of the proposition is complete. \qed
\vskip0.2cm
\noindent In order to obtain the existence of a structurally stable family of non-stationary periodic solutions it is now remains to apply the displacement-controlled loading (\ref{relation1}) of sufficiently large amplitude. We will now use Proposition~\ref{prop3} to give an estimate for the required amplitude. In the case of a 5-spring network, formula (\ref{formulaprop3}) of Proposition~\ref{prop3} follows from
\begin{equation}\label{fofo}
\sum_{i=1}^5\dfrac{1}{a_i}\left(c_i^+-c_i^-\right)^2<\left\|V_{basis}\bar L\right\|^2_A\cdot\left(l(t_1)-l(t_2)\right)^2.
\end{equation}
In the case of parameters (\ref{para}), formula (\ref{fofo}) reduces to
$$
\sum_{i=1}^5 2^2<\|n_1\|^2\cdot\left(l(t_1)-l(t_2)\right)^2,
$$
where $n_1$ is given by (\ref{n1}), or simply
$$
\dfrac{160}{3}<\left(l(t_1)-l(t_2)\right)^2.
$$
Since $\frac{160}{3}\approx 53.3,$ we introduce $l(t)$ as follows
\begin{equation}\label{loadt}
l(t)=\left\{\begin{array}{ll}
t, & \ {\rm if}\ t\in[0,54],\\
-t+54, & \ {\rm if}\ t\in[54,108],
\end{array}\right.
\end{equation}
extended to $[0,\infty)$ by 108-periodicity.
\begin{corollary} \label{corr1} Consider the network of elastoplastic springs of Fig.~\ref{ex2newfig} with the parameters (\ref{para}). Assume the displacement-controlled loading given by (\ref{loadt}), so that $T=108.$ Then, for any parameters $a_i,$ $c_i^-,c_i^+$, $i\in\overline{1,5}$, and any Lipschitz-continuous functions $T$-periodic $H:[0,T]\mapsto\mathbb{R}^3,$ that are close to those in (\ref{para}), and for any Lipschitz-continuous $T$-periodic $l(t)$ close to (\ref{loadt}), the sweeping process
(\ref{sw1})-(\ref{eq:initialElastic}) admits a structurally stable family of non-stationary $T$-periodic solutions (swept by the opposite parallel sides of Fig.~\ref{figshape}). Accordingly, the mechanical model of Fig.~\ref{ex2newfig} admits an entire family of co-existing stress distributions that evolves $T$-periodically in time.
\end{corollary}
\section{Conclusions} In this paper we showed that sweeping processes of networks of elastoplastic springs (elastoplastic systems) inherit a designated structure that restrict possible dynamic transitions. Specifically, we gave an example of an elastoplastic system whose sweeping process admits a structurally stable family of non-stationary periodic solutions. Specifically, the structure given by the elastoplastic system locks the family of periodic solutions of the associated sweeping process, so that it persists under all such small perturbations of the sweeping process that come from small perturbations of the physical parameters of the elastoplastic system.
\sloppy
\section*{Compliance with Ethical Standards}
\noindent {\bf Conflict of Interest:} The authors have no conflict of interest.
\bibliographystyle{plain}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,343 |
Research at Computer Systems concerns development of computer networks, parallel computer architectures, and embedded systems, spanning specification, verification, and experimental systems development.
Computers and computer systems have become a natural part of our lives: on our desks, built into our cars, etc. Computer Systems is all about developing new and better computer systems, and there are several challenges both in building the systems and in programming them. The systems must be efficient and electricity-saving, and we need to be able to test and verify that they work as intended. Communication in real-time and in networks is also becoming more and more important, and in that field we need new technology for better security and function.
At the Division of Computer Systems we conduct research within several related areas: computer architecture, communication, real-time systems, formal methods for analysis of computer programs, and machine learning. We also conduct research on developing pedagogical methods in computer systems.
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Director of UPMARC is professor Bengt Jonsson and co-ordinator is Roland Grönroos.
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\section{Introduction}
Spectroscopic and imaging surveys suggest that a majority of young stars are formed in binary/multiple systems \citep{1993AJ....106.2005G,1993A&A...278..129L,1997ApJ...481..378G,2008ApJ...683..844L,2011ApJ...731....8K}. Theoretical and observational studies indicate that the interaction between disks and companions is an efficient mechanism to dissipate disks \citep{1993prpl.conf..749L,2009ApJ...696L..84C,2012ApJ...745...19K}. Thus, it is very important to investigate disks around the binary or multiple stellar systems, in order to understand disk evolution, as well as planet formation. The triple system GW~Ori is an ideal target for such study.
GW~Ori is located at $\lambda$~Ori \citep[$\sim$400\,pc,][]{2013MNRAS.434..806B}, and was revealed as a triple stellar system recently \citep[GW~Ori~A/B/C,][]{1991AJ....101.2184M,2011A&A...529L...1B}. The primary GW~Ori~A is a G8 pre-main sequence star with a mass of $\sim$4\,$M_{\odot}$, which makes it a very interesting system between Herbig~Be stars and classical T~Tauri stars \citep{2014A&A...570A.118F}. The close companion GW~Ori~B was discovered as a spectroscopic binary with an orbital period of $\sim$242\,days and a separation of $\sim$1\,AU \citep{1991AJ....101.2184M,2014A&A...570A.118F}. The second companion GW~Ori~C, located at a projected separation of $\sim$8\,AU from GW~Ori~A, was detected with near-infrared interferometric technique \citep{2011A&A...529L...1B}. The sub-millimeter and millimeter observations show that GW~Ori is still harboring a massive disk \citep{1995AJ....109.2655M}, which is one of the most massive disks around a G-type star. Strong ongoing accretion activity ($\dot M_{\rm{acc}}$$\sim$3--4$\times$10$^{-7}$\,$M_{\odot}$\,yr$^{-1}$ ) from the disk to the central star(s) in the GW~Ori system was suggested from the $U$-band excess, and strong and broad H$\alpha$ and H$\beta$ emission lines on the spectrum of GW~Ori \citep{2004AJ....128.1294C,2014A&A...570A.118F}.
In \citet[][hereafter Paper\,I]{2014A&A...570A.118F}, we presented a study of the inner disk in the GW~Ori system based on the infrared data. We reproduced the spectral energy distribution (SED) of GW~Ori using disk models with gaps sized 25--55\,AU. We found that the SED of GW~Ori exhibited dramatic changes on timescales of $\sim$20\,yr in the near-infrared bands, which can be interpreted as the change in the amount and distribution of dust particles in the gap due to a ``leaky dust filter''. Due to its brightness { at submillimeter and millimeter wavelengths}, the disk mass and size has been subject to lot of speculation with sizes up to 500\,AU radius and masses that could render it gravitational unstable \citep{1995AJ....109.2655M,2009A&A...502..367S}. In this work, we present an investigation of the outer disk around GW~Ori using the new millimeter data obtained from the Submillimeter Array \citep[SMA,][]{2004ApJ...616L...1H}. These new observations have spatially resolved the disk around GW~Ori for the first time. We arrange this paper as follows: In Sect.~\ref{Sec:data} we describe the observations and data reduction. In Sect.~\ref{Sec:obs_result} we present our observational results, and in Sect.~\ref{Sec:modeling} we describe the disk modeling, and compare the model results with the observations, which are then discussed in~\ref{Sec:discussion}. We summarize our results in Sect.~\ref{Sec:summary}.
\begin{figure*}
\centering
\includegraphics[width=1.\columnwidth]{cont.ps}
\includegraphics[width=1.\columnwidth]{dust_model_test.ps}
\includegraphics[width=1\columnwidth]{EW_dust.ps}
\includegraphics[width=1\columnwidth]{SN_dust.ps}
\caption{(a) The observed map of the continuum emission observed toward GW~Ori at the wavelength of 1.3~mm, with contours (solid lines) drawn at 9.5\,mJy~beam$^{-1}$ (10\,$\sigma$) intervals, starting at 4.8~mJy~beam$^{-1}$ (5\,$\sigma$). The synthesized beam is shown in the lower left corner. The position of the central star is indicated with the star symbol. (b) The modeled map of the continuum emission for the GW~Ori disk system at the wavelength of 1.3~mm. The contour levels are same as in Panel~(a). (c, d) The distribution of the observed intensities (filled circles) along the east-west (c) and north-south (d) direction cross the center of the map compared with the our model (solid lines). The dash lines show the expected profiles for an unresolved object. \label{Fig:cont}}
\end{figure*}
\section{Observations, data reduction}\label{Sec:data}
The object GW~Ori was observed with the SMA on January 5, 2010 in the compact configuration with six antennas, on January 19, 2011 in the very extended configuration with six antennas, and February 2, 2011 in the extended configuration with seven antennas. The phase center of the field was RA=05h29m08.38s and Dec=$+11^{\circ}52^{\prime}12.7^{\prime\prime}$ (J2000.0). The SMA has two spectral sidebands, both 4\,GHz wide and separated by 10\,GHz. The receivers were tuned to 230.538 GHz in the upper sideband ($v_{\rm lsr}$ = 11~km~s$^{-1}$) with a maximum spectral resolution of 1.1\,km\,s$^{-1}$\ on the upper sideband and 1.2~km~s$^{-1}$ on the lower sideband. The system temperatures ($T_{\rm sys}$) were around $\sim$80--200~K during the observation on January 5, 2010, $\sim$100--200~K on January 19, 2011, and $\sim$110--300~K on February 2, 2011. For the compact configuration on January 5, 2010, the bandpass was derived from the quasar 3c273 observations. Phase and amplitude were calibrated with regularly interleaved observations of the quasar 0530+135 (1.7$^{\circ}$ away from the source). The flux calibration was derived from Titan observations, and the flux scale is estimated to be accurate within 20\%. For the very extended configuration on January 19, 2011, the bandpass was derived from the quasar 3c279 observations. Phase and amplitude were calibrated with regularly interleaved observations of the quasar 0530+135 and 0423--013. The flux calibration was derived from Ganymede observations, and the flux scale is estimated to be accurate within 20\%. For the extended configuration on February 2, 2011, the bandpass was derived from the quasar 3c279 observations. Phase and amplitude were calibrated with regularly interleaved observations of the quasar 0530+135 and 0423--013. The flux calibration was derived from Titan observations, and the flux scale is estimated to be accurate within 20$\%$.
We merged the three configuration data sets, applied different robust parameters for the continuum and line data, and got the synthesized beam sizes between 1.03$^{\prime\prime}$ $\times$0.70$^{\prime\prime}$ (PA$\sim$89.5$^\circ$) and 1.15$^{\prime\prime}\times0.83^{\prime\prime}$ (PA$\sim-$88.6$^\circ$), respectively. The rms of 1.3~mm continuum image is 0.96 mJy beam$^{-1}$, and the rms of the $^{12}$CO$~J=2-1$ data is 0.05~Jy~beam$^{-1}$ at 1.1\,km\,s$^{-1}$\ spectral resolution, 0.04~Jy~beam$^{-1}$ at 1.2\,km\,s$^{-1}$\ spectral resolution for $^{13}$CO~$J=2-1$, and 0.03~Jy~beam$^{-1}$ at 1.2\,km\,s$^{-1}$\ spectral resolution for C$^{18}$O~$J=2-1$. The flagging and calibration was done with the IDL superset MIR \citep{1993PASP..105.1482S}, which was originally developed for the Owens Valley Radio Observatory and adapted for the SMA\footnote{The MIR cookbook by Chunhua Qi can be found at \url{http://cfa-www.harvard.edu/~cqi/mircook.html}.}. The imaging and data analysis were conducted in MIRIAD \citep{1995ASPC...77..433S}.
\section{Observational Results}\label{Sec:obs_result}
\subsection{Dust continuum emission}
In Fig.~\ref{Fig:cont}(a), we show the continuum emission map of GW~Ori with contours starting at 4.8\,mJy~beam$^{-1}$\ (5$\sigma$) and increasing at 9.5mJy~beam$^{-1}$\ (10$\sigma$) intervals. Considering a 20\% systematic calibration uncertainty, the integrated continuum flux density in this map is 320$\pm$64\,mJy, consistent with the result (255$\pm$60\,mJy) in \citet{1995AJ....109.2655M}. From a two-dimensional Gaussian fit to the image, the full width at half maximum (FWHM) of the continuum emission is 1$\farcs$4($\pm0\farcs004$)$\times$1$\farcs$3($\pm0\farcs004$), suggesting that the continuum emission of GW~Ori is resolved given the synthesized beam size of 1.03$^{\prime\prime}$ $\times$0.70$^{\prime\prime}$. After the deconvolution of the synthesized beam, the FWHM of the continuum emission map is 0$\farcs$9$\times$1$\farcs$1 which is corresponding to 360$\times$400\,AU at a distance 400\,pc. In Fig.~\ref{Fig:cont}(c, d) we show the distribution of the intensities for the the continuum emission map along the east-west and north-south directions cross the center of the map, and the expected distrubutions for an unresolved object according to the spatial resolutions of our observations. We note that the emission of GW~Ori along the east-west direction is marginally resolved, but the one along the north-south direction is well resolved.
\begin{figure*}
\centering
\includegraphics[width=2\columnwidth]{allCO_cont_test.ps}
\caption{Top panels: The velocity-integrated intensities (contours) for the $^{12}{\rm CO}~J=2-1$, $^{13}{\rm CO}~J=2-1$, and ${\rm C^{18}O}~J=2-1$ line emission, overlaid on the the continuum emission. For $^{12}{\rm CO}~J=2-1$, the intensities are integrated over the velocity range between 6.5 and 20.8\,km\,s$^{-1}$, and the contours are drawn at 0.69\,Jy~beam$^{-1}$~km\,s$^{-1}$ (3\,$\sigma$) intervals, starting at 0.69\,Jy~beam$^{-1}$~km\,s$^{-1}$ (3\,$\sigma$). For $^{13}{\rm CO}~J=2-1$, the intensities are integrated over the velocity range between 7 and 20\,km\,s$^{-1}$, and the contours start at 0.48\,Jy~beam$^{-1}$~km\,s$^{-1}$ (3\,$\sigma$) with an interval of 0.16\,Jy~beam$^{-1}$~km\,s$^{-1}$ (1\,$\sigma$). For ${\rm C^{18}O}~J=2-1$, the intensities are integrated over the velocity range between 7 and 20\,km\,s$^{-1}$, and the contours begin at 0.24\,Jy~beam$^{-1}$~km\,s$^{-1}$ (3\,$\sigma$), and increase in 0.08\,Jy~beam$^{-1}$~km\,s$^{-1}$ (1\,$\sigma$) increments. In each panel, the negative contours, shown with the dashed lines, are drawn at $-$1\,$\sigma$ intervals, starting at $-$3\,$\sigma$. The synthesized beam for each line emission is shown in the lower left corner in each panel. Bottom panels: The modeled velocity-integrated intensities (contours) for the $^{12}{\rm CO}~J=2-1$, $^{13}{\rm CO}~J=2-1$, and ${\rm C^{18}O}~J=2-1$ line emission, overlaid on the modeled continuum emission, for the GW~Ori disk system. The contour levels are same as in the top panels at the corresponding molecular lines. \label{Fig:CO_cont}}
\end{figure*}
\subsection{Molecular line emission}\label{Sect:Molecular_line_emission}
In the top three panels in Fig.~\ref{Fig:CO_cont} we show the integrated intensity maps of $^{12}{\rm CO}~J=2-1$, $^{13}{\rm CO}~J=2-1$, and ${\rm C^{18}O}~J=2-1$ lines. The $^{12}{\rm CO}~J=2-1$ line emission map shows an elongated structure extended from the north-east to the south-west direction with a single peak coincided with the center of the continuum emission. The $^{12}{\rm CO}~J=2-1$ line emission map is clearly spatially resolved. A two-dimensional Gaussian fit to the $^{12}{\rm CO}~J=2-1$ integrated intensity map gives an FWHM size of 2$\farcs$5$\times$3$\farcs$4 after the deconvolution of the synthesized beam, corresponding to 890$\times$1300\,AU at a distance 400\,pc, which is much more extended than the continuum emission map. The $^{13}{\rm CO}~J=2-1$ line integrated intensity map of GW~Ori is more compact than the $^{12}{\rm CO}~J=2-1$ one, and comparable to the continuum emission map. From the disk of GW~Ori, we only marginally detect ${\rm C^{18}O}~J=2-1$ line.
\begin{figure*}
\centering
\includegraphics[width=1.\columnwidth]{vel1.ps}
\includegraphics[width=1.\columnwidth]{COmodel_test.ps}
\caption{(a) $^{12}{\rm CO}~J=2-1$ velocity (1st) moment map. The contours are for the $^{12}{\rm CO}~J=2-1$ velocity-integrated intensities (see Fig.~\ref{Fig:CO_cont}), starting at 0.69\,Jy~beam$^{-1}$~km\,s$^{-1}$\ (3\,$\sigma$) with an interval of 0.69\,Jy~beam$^{-1}$~km\,s$^{-1}$\ (3\,$\sigma$). The synthesized beam is shown in the lower left corner. (b) Same as in Panel~(a), but for the predicted map from modeling. \label{Fig:vel1}}
\end{figure*}
In Fig.~\ref{Fig:vel1}(a) and Fig.~\ref{Fig:vel2}(a), we show the $^{12}{\rm CO}~J=2-1$ and $^{13}{\rm CO}~J=2-1$ velocity (1st) moment maps, respectively, suggesting northern and southern parts of the disk are redshifted and blueshifted with respect to the relative velocity of GW~Ori, respectively. Fig.~\ref{Fig:channel} displays the channel maps of $^{12}{\rm CO}~J=2-1$ line emission with contours starting at 0.127\,Jy~beam$^{-1}$ (3$\sigma$) with intervals of 0.127\,Jy~beam$^{-1}$. The velocity moment maps and the channel maps are generally consistent with the expected kinematic pattern for gas material in Keplerian rotation with substantial inclination to our line of sight. The disk inclination can be constrained using the position-velocity (PV) diagram of the molecular lines. In Fig.~\ref{Fig:PV}(a), we present the PV diagram from the $^{12}{\rm CO}~J=2-1$ map along the north-south direction cross the peak of the integrated intensity maps of $^{12}{\rm CO}~J=2-1$. In the figure, we plot the expected Keplerian rotation curves for a disk inclined by 20$^{\circ}$, 40$^{\circ}$, and 60$^{\circ}$ around a star with a mass of 3.9\,$M_{\odot}$\ for comparison. From the comparison, we infer that the disk inclination should be between 20$^{\circ}$ and 60$^{\circ}$.
Fig.~\ref{Fig:channel} shows the channel maps of $^{12}{\rm CO}~J=2-1$ line emission. In the figure, at the channels with velocities of 12.0 and 13.1\,km\,s$^{-1}$, we note a tail structure originating from the outer disk and pointing to the north-western direction. Such a tail is also evident as the blueshifted structure in the $^{12}{\rm CO}~J=2-1$ velocity moment map. One explanation for the structure could be the cloud contamination which can be severe for CO lines. If it is the case, it is required that the velocity of the parental cloud around GW~Ori is $\sim$1\,km\,s$^{-1}$\ bluer than GW~Ori. A Gaussian fit to the $^{12}{\rm CO}~J=2-1$ spectrum at the peak of { the integrated line intensity map} suggests that the velocity of GW~Ori with respect to the local standard of rest (LSR) is around 13.6\,km\,s$^{-1}$, and the LSR velocity of the parental cloud of GW~Ori is around 12.7\,km\,s$^{-1}$\ \citep{2000A&A...357.1001L}, which supports the above explanation of the blueshifted tail structure.
\begin{figure*}
\centering
\includegraphics[width=1.\columnwidth]{vel2.ps}
\includegraphics[width=1.\columnwidth]{13COmodel_test.ps}
\caption{(a) $^{13}{\rm CO}~J=2-1$ velocity (1st) moment maps. The contours are for the $^{13}{\rm CO}~J=2-1$ velocity-integrated intensities (see Fig.~\ref{Fig:CO_cont}), starting at 0.48\,Jy~beam$^{-1}$~km\,s$^{-1}$\ (3\,$\sigma$) with an interval of 0.16\,Jy~beam$^{-1}$~km\,s$^{-1}$\ (1\,$\sigma$). The synthesized beam is shown in the lower left corner. (b) Same as in Panel~(a), but for the predicted map from modeling. \label{Fig:vel2}}
\end{figure*}
\begin{figure*}
\centering
\includegraphics[width=2.\columnwidth]{Channel_CO_cont.ps}
\caption{The channel maps of the $^{12}{\rm CO}~J=2-1$ emission toward GW~Ori. Channels are 1.1\,km\,s$^{-1}$\ wide with the synthesized beam marked in the bottom left corner. Contour levels are drawn at intervals of 0.127\,Jy~beam$^{-1}$ (3$\sigma$), starting at 0.127\,Jy~beam$^{-1}$. The dashed contours are the negative features with the same contours as the positive ones in each panel. The synthesized beam is shown in the lower left corner in each panel. \label{Fig:channel}}
\end{figure*}
\section{Disk modeling}\label{Sec:modeling}
{ In this section, we use a simple disk model to reproduce the SMA observations of GW~Ori. Given that our data has low spatial resolution, any model involves a strong simplification of the very complex GW~Ori disk system \citep{2014A&A...570A.118F}. Furthermore, the complexity of disks means that the parameter space is highly degenerated and non-continuous \citep{2016PASA...33...59S}. Our aim is thus to explore the global gas and dust content of the GW~Ori disk in the light of typical disk models, and to compare it to other similar objects. Any further modeling is beyond the scope of this paper and worth only when higher resolution data becomes available. }
\subsection{Continuum emission}
\subsubsection{Parameters for modeling continuum emission}
We define a global dust surface density in the same form as in \citet{2009ApJ...700.1502A},
\begin{equation}
\Sigma=\Sigma_{\rm c}~\bigg(\frac{R}{R_{\rm c}}\bigg)^{-\gamma}~{\rm exp}\Bigg[-\bigg(\frac{R}{R_{\rm c}}\bigg)^{2-\gamma}\Bigg],\label{Equ:sigma}
\end{equation}
\noindent where $\Sigma_{\rm c}$ is the normalization parameter at the characteristic scaling radius $R_{\rm c}$, and $\gamma$ is the gradient parameter. The above profile, which has been used to successfully model different types of disks in the literature \citep{2009ApJ...700.1502A,2011ApJ...732...42A,2012ApJ...744..162A}, is the similarity solution for a simple accretion disk with time-independent viscosity ($\nu$) and $\nu\propto R^{\gamma}$ \citep{1974MNRAS.168..603L,1998ApJ...495..385H}. In this work, we do not take $\Sigma_{\rm c}$ as the free parameter. Instead, we use the disk dust mass ($M_{\rm dust}$), and $\Sigma_{\rm c}$ can be calculated when we set up other parameters about the disk structure. We set $\gamma$ as a free parameter.
{ We include a vertical gradient in the dust size distribution in disk modelling, to simulate the dust settling in disks. In practice, we use two dust populations: small dust population, and large dust population, as did \citet{2011ApJ...732...42A}. The dust density structure for each dust population in a spherical coordinate system ($R$, $\theta$, and $\phi$) is parameterized as
\begin{equation}
\rho_{\rm small}=\frac{(1-f)\Sigma}{\sqrt{2\pi}Rh}~{\rm exp}\Bigg[-\frac{1}{2}\bigg(\frac{\pi/2-\theta}{h}\bigg)^{2} \Bigg],\label{Equ:rhos}
\end{equation}
\begin{equation}
\rho_{\rm large}=\frac{f\Sigma}{\sqrt{2\pi}R\Lambda h}~{\rm exp}\Bigg[-\frac{1}{2}\bigg(\frac{\pi/2-\theta}{\Lambda h}\bigg)^{2} \Bigg],\label{Equ:rhol}
\end{equation}
\noindent where $\rho_{\rm small}$ is the density for the small dust population, $\rho_{\rm large}$ is the one for the large dust population, and $h$ is the angular scale height. Following \citet{2011ApJ...732...42A}, we assume the large grains are distributed to 20\% of the scale height ($\Lambda$=0.2), and account for 85\% of the total column ($f$=0.85). We do not explore the parameter space of $\Lambda$ and $f$ since our observational data cannot provide an efficient constraint on them. The angular scale height $h$ is defined as
\begin{equation}
h=h_{\rm c}~\bigg(\frac{R}{R_{\rm c}}\bigg)^{\Psi},
\end{equation}
\noindent where $h_{\rm c}$ is the angular scale height at the scaling radius $R_{\rm c}$, and $\Psi$ characterizes the flaring angle of the disk.
}
In Paper\,I, we have shown that a gap sized at 25--55\,AU needs to be included in the disk model. A small population of tiny dust particles (sizes 0.005--1\,$\mu$m) is also needed to distribute in the gap, in order to reproduce the moderate excess emission at near-infrared bands and the strong and sharp silicate feature at 10\,$\mu$m\ on the SED of GW~Ori. In this work, we include a dust depletion factor ($\xi_{\rm gap}$) to modify the surface density within the gap. We simply set the gap size $R_{\rm gap}$=45\,AU, according to the results in Paper\,I, since our SMA data cannot provide any constraints on the inner disk. { The inner radius of the gap ($R_{\rm in}$) is fixed to be 1.2\,AU, which is the orbital semi-major axis of the close companion GW~Ori~B (see Paper\,I).} When the disk radius $R\le R_{\rm gap}$, the modified surface density is $\Sigma=\xi_{\rm gap}\Sigma$, where $\Sigma$ is obtained from Equation~\ref{Equ:sigma}.
\begin{figure*}
\centering
\includegraphics[width=1.\columnwidth]{pv.ps}
\includegraphics[width=1.\columnwidth]{mpv_test.ps}
\caption{(a) The observed position-velocity diagram from the $^{12}{\rm CO}~J=2-1$ map along the north-south direction cross GW~Ori. The offset refers to the distance along cut from GW~Ori. The contours start at 0.15\,Jy~beam$^{-1}$ (3$\sigma$) with an interval of 0.05\,Jy~beam$^{-1}$ (1$\sigma$). The dotted, dashed, and dash-dotted lines show a Keplerian rotation curve with a central mass of 3.9\,$M_{\odot}$\ with disk inclinations of 20$^\circ$, 40$^\circ$, and 60$^\circ$, respectively. (b) Same as in Panel~(a) but for the modeled position-velocity diagram with a disk inclination of 35$^{\circ}$. \label{Fig:PV}}
\end{figure*}
In the disk models, we use two populations of amorphous dust grains (25\% carbon and 75\% silicate) with a power-law size distribution with an exponent of $-3.5$ and a minimum size of 0.005\,$\mu$m. The maximum size of dust grains is set to be 1\,$\mu$m\ in the gap, as suggested in Paper\,I, and { to be 1\,$\mu$m\ for the small dust population and 1000\,$\mu$m\ for the large dust population in the outer disk ($R>R_{\rm gap}$). In Fig.~\ref{Fig:dust_opa}, we show the opacity spectra for the two dust populations derived from Mie calculations.}
The stellar parameters adopted in the models are $T_{\rm eff}$=5500\,K, $R_{\star}$=7.6\,$R_{\odot}$, and $M_{\star}$= 3.9\,$M_{\odot}$, taken from Paper\,I. We use the RADMC--3D code \citep[version~{ 0.40},][]{2012ascl.soft02015D} to do the radiative transfer in the disk models, and vary the free parameters to calculate the continuum emission maps at 1.3\,mm and the SEDs. For simplicty, we convolve the model continuum emission maps with the synthetical beam for the SMA continuum emission map to simulate the observations.
{ \subsubsection{Scheme for modeling continuum emission}
In order to model the continuum emission from the disk of GW~Ori, we have 10 parameters. Among them, the 8 parameters, $R_{\rm in}$, $R_{\rm gap}$, $\xi_{\rm gap}$, $R_{\rm c}$, $\gamma$, $h_{\rm c}$, $\Psi$, and $M_{\rm dust}$, are for the disk structure. As discussed above, we have fixed $R_{\rm in}$=1.2\,AU, $R_{\rm gap}$=45\,AU. To compare the model results with the observations, we need to know the orientation of the disk with respect to the observer, which can be characterized with two more parameters, the inclination ($i$) of the disk with respect to the line of sight ($i=90^\circ$ for edge-on disks), and the position angle (PA) of the disk major axis. The disk of GW~Ori is well resolved in the $^{12}{\rm CO}~J=2-1$ line. From the integrated intensity map of the $^{12}{\rm CO}~J=2-1$ line, we derive an inclination of $\sim$40$^{\circ}$ and a position angle$\sim$10$^{\circ}$. In disk modelling, we allow the inclination to change from 30$^{\circ}$, 40$^{\circ}$, to 50$^{\circ}$, and fix position angle to be 10$^{\circ}$.
The exploration of the parameter spaces is divided into three steps. At the first step, we calculate the continuum emission map at 1.3\,mm for a coarse and wide grid of parameters listed in Table~\ref{Tab:disk_par_grid}. Here we fix $\xi_{\rm gap}$=3$\times10^{-3}$, according to the SED modelling in Paper\,I, since it only insignificantly affects the 1.3\,mm continuum emission modelling. In total, we obtain 9360 modeled 1.3\,mm continuum emission maps. We compare the calculated continuum emission maps with the observation, which can efficiently constrain $M_{\rm dust}$ and $R_{\rm c}$. For each model, the goodness of the fit $\chi^2_{\rm mm}$ is calculated by
\begin{equation}
\chi^2_{\rm mm}=\frac{\frac{1}{N}\sum^{N}_{i=1}(\mu_{i}-\omega_{i})^2}{\sigma^2} \label{Equ:equa5}
\end{equation}
\noindent where $\sigma$ is the noise of the observed 1.3\,mm map, $N$ the number of pixels with the values above 3$\sigma$, $\mu$ the modeled data, and $\omega$ the observed data. By comparing with the observations, we obtain sets of disk models providing a good fit which we define as $\chi^2_{\rm mm}-\chi^2_{\rm mm,~best}<2$ where $\chi^2_{\rm mm,~best}$ is the minimum $\chi^2_{\rm mm}$ among all the models. In total, we have 102 good-fit models. Then, we calculate the SEDs of the good-fit disk models in the range from 70\,$\mu$m\ to 1.3\,mm, and compare them with the one of GW~Ori. The goodness of the fit of the SED $\chi^2_{\rm SED}$ is calculated by
\begin{equation}
\chi^2_{\rm SED}=\frac{1}{N}\sum^{N}_{i=1}\frac{(\mu_{i}-\omega_{i})^2}{\sigma_{i}^2}
\end{equation}
\noindent where $N$ is the number of the observed wavelengths, $\mu$ the synthetic flux density, $\omega$ the observed flux density, and $\sigma$ the observational uncertainities. The total goodness of the fit $\chi^2_{\rm total}$ is given by
\begin{equation}
\chi^2_{\rm total}=\chi^2_{\rm mm}+\chi^2_{\rm SED}
\end{equation}
We derive the ranges for the free parameters of the models providing a good fit with $\chi^2_{\rm total}-\chi^2_{\rm total,~best}<2$ where $\chi^2_{\rm total,~best}$ is the minimum $\chi^2_{\rm total}$ among the 102 models. The parameters of the good-fit models are listed in Table~\ref{Tab:disk_par_grid}.
\begin{figure}
\centering
\includegraphics[width=1.\columnwidth]{opa.ps}
\caption{Opacity spectra ($\kappa_{\rm abs}$ for absorption and $\kappa_{\rm sca}$ for scattering) for the small dust population (solid line) and the large dust population (dash line) used in our disk modeling. \label{Fig:dust_opa}}
\end{figure}
\begin{table*}
\caption{Coarse grids of the parameters for modeling disk continuum emission.\label{Tab:disk_par_grid}}
\centering
\begin{tabular}{ccc}
\hline\hline
& & Range \\
Parameters & Input & ($\chi^2_{\rm total}-\chi^2_{\rm total,~best}<2$) \\
\hline
\multicolumn{3}{c}{{\bf Central star}}\\
\hline
Effective temperature ($T_{\rm eff}$)\tablefootmark{a} &\multicolumn{1}{c}{5500\,K}\\
Stellar radius\tablefootmark{a} &\multicolumn{1}{c}{7.5\,$R_{\odot}$}\\
Stellar mass ($M_{\star}$)\tablefootmark{a} &\multicolumn{1}{c}{3.9\,$M_{\odot}$}\\
\hline
\multicolumn{3}{c}{{\bf Disk}}\\
\hline
Inner radius ($R_{\rm in}$)\tablefootmark{a} &1.2\,AU \\
Gap size ($R_{\rm gap}$)\tablefootmark{a} &45\,AU\\
Dust depletion factor ($\xi_{\rm gap}$)\tablefootmark{a} &3$\times10^{-3}$ \\
Characteristic scaling radius ($R_{\rm c}$) &250, 270, 290, 310, 330, 350, 370, 390 \,AU & 290--350\,AU \\
Surface density gradient parameter ($\gamma$) & 0.1, 0.3, 0.5, 0.7, 0.9, 1.1 & 0.1--0.5\\
Angular scale height ($h_{\rm c}$) & 0.15,0.17,0.19,0.21,0.23 & 0.15--0.19 \\
$\Psi$\tablefootmark & 0.1, 0.15, 0.2 &0.1--0.2 \\
Disk mass & [1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.7, 7]$\times10^{-2}\,M_{\star}$ &3--3.5$\times10^{-2}\,M_{\star}$ \\
Disk inclination ($i$) & 30$^\circ$, 40$^\circ$, 50$^\circ$ & 30$^\circ$--40$^\circ$\\
Position angle\tablefootmark{a} & 10$^\circ$ \\
\hline
\end{tabular}
\tablefoot{\tablefoottext{a}{Fixed parameters.}}
\end{table*}
At the second step, we refine the grid of parameters with knowledge of the above good-fit models, and list them in Table~\ref{Tab:disk_par_refined_grid}. We repeat the procedure in the first step, but require $\chi^2_{\rm mm}-\chi^2_{\rm mm,~best}<0.5$ and $\chi^2_{\rm total}-\chi^2_{\rm total,~best}<0.5$. We obtain the ranges for the free parameters of the models providing a fit with $\chi^2_{\rm total}-\chi^2_{\rm total,~best}<0.5$. The disk model with minimum $\chi^2_{\rm total}$ is considered as the best-fit model.
At the final step, we will constrain the dust depletion factor ($\xi_{\rm gap}$) by fitting the full SED of GW~Ori. We calculate a set of model SEDs by varing $\xi_{\rm gap}$ from 1$\times10^{-3}$ to 1$\times10^{-2}$ with other parameters from the above best-fit model. Since the change of $\xi_{\rm gap}$ can only obviously vary the shape of the SED within near- and mid-infrared wavelengths, we compare the model SEDs with the observed one within the within the wavelengths ranging from 1\,$\mu$m\ to 37\,$\mu$m. We find the model SEDs with $\xi_{\rm gap}=1.5-4\times10^{-3}$ can reproduce the observations, and the one with $\xi_{\rm gap}=2.5\times10^{-3}$ can give the best fit to the data. { As mentioned before, our model is highly simplified and the low resolution does not allow us to expore in depth the degenerated and non-continuous parameter space of this very complex system. Thus the $\chi^2$ approach has to be taken as a tool to measure the goodness of fit, but it cannot be used to derive statistics on the significance of any particular model.}
\begin{table*}
\caption{Refined Grids of the parameters for modeling disk continuum emission.\label{Tab:disk_par_refined_grid}}
\centering
\begin{tabular}{cccc}
\hline\hline
& & Range & \\
Parameters & Input & ($\chi^2_{\rm total}-\chi^2_{\rm total,~best}<0.5$) & Best-fit \\
\hline
Characteristic scaling radius ($R_{\rm c}$) &290, 300, 310, 320, 330, 340, 350 \,AU &300--340\,AU &320\,AU \\
Surface density gradient parameter ($\gamma$) & 0.1, 0.2, 0.3, 0.4, 0.5 &0.1--0.4 & 0.2\\
Angular scale height ($h_{\rm c}$) & 0.15, 0.16, 0.17, 0.18, 0.19 &0.15--0.19 & 0.18\\
$\Psi$\tablefootmark & 0.1, 0.15, 0.2 &0.1-0.2 &0.1 \\
Disk mass & [3.0, 3.1, 3.2, 3.3, 3.4, 3.5]$\times10^{-2}\,M_{\star}$ &3.0--3.4$\times10^{-2}\,M_{\star}$&3.1$\times10^{-2}\,M_{\star}$ \\
Disk inclination ($i$) & 30$^\circ$, 35$^\circ$, 40$^\circ$ & 30$^\circ$--35$^\circ$ & 35$^\circ$\\
\hline
\end{tabular}
\end{table*}
}
\subsection{CO emission}
{ With the parameters of the above best-fit model, we can compute the model map of the $^{12}{\rm CO}~J=2-1$ velocity-integrated intensities, and compare it with the observation. However, to calculate the CO emission, one needs to know the gas temperaure distribution in the disk. At the first step, we assume that the gas and dust has equal temperatures, and ignore that CO molecules are frozen out of the gas phase when $T_{\rm gas}<20$\,K and that the gas temperatures may be higher than the dust temperatures near the disk surface. The velocity fields of gas material in the disk models are assumed to be Keplerian. The thermal line broadening is automatically included in the RADMC--3D code. Besides it, we also include the turbulent line broadening by assuming a constant linewidth of 0.01\,km\,s$^{-1}$\ from turbulence. Taking { an abundance ratio} $^{12}{\rm CO}/H_{2}=10^{-4}$, which is the canonical abundance of interstellar medium (ISM), we calculate the $^{12}{\rm CO}~J=2-1$ line emission using the RADMC–3D code with an assumption of local thermal equilibrium (LTE) conditions. The resulting maps are simply convolved with the corresponding synthetical beams, and then compared with the observation. We find that the predicted peak intensity of $^{12}{\rm CO}~J=2-1$ is about 3 time weaker than the observation. We vary the parameters among the good-fit models listed in Table~\ref{Tab:disk_par_refined_grid}, and the model emission for $^{12}{\rm CO}~J=2-1$ line are all 2--3 time weaker than the observation. The previous studies have shown that the gas temperatures could exceed the dust temperatures in the disk surface layers \citep{2006ApJ...636L.157Q,2009A&A...501..269P}, possibly due to additional ultraviolet or X-ray heating from central stars \citep{2004ApJ...615..972G,2004A&A...428..511J}. In order to reproduce the observed CO emissions of GW~Ori, following \citet{2012ApJ...744..162A}, we parameterize the gas temperature as}
\begin{equation}
T_{\rm gas} = \left\{
\begin{array}{l l}
T_{\rm atm}+(T_{\rm mid}-T_{\rm atm})~\Bigg[{\rm cos}\bigg(\frac{\pi}{2}\frac{\pi/2-\theta}{h_{\rm q}}\bigg)\bigg]^{2\delta} & \quad \text{if $\pi/2-\theta<h_{q}$}\\
T_{\rm atm} & \quad \text{if $\pi/2-\theta\ge h_{q}$}
\end{array} \right.
\end{equation}
\noindent Where $T_{\rm mid}$ is the midplane temperature derived from the RADMC--3D simulations of the dust, $\delta$ describes the steepness of the vertical profile, and $h_{\rm q}=4H_{\rm p}$ where $H_{\rm p}$ is the angular pressure scale height determined from $T_{\rm mid}$. We calculate $H_{\rm p}$ as $H_{\rm p}=(kT_{\rm mid}R/GM_{\star}\mu m_{\rm H})^{1/2}$ where $k$ is the Bolzmann's constant, $G$ is the gravitational constant, and $\mu=2.37$ is the mean molecular weight of the gas. $T_{\rm atm}$ is the temperature in the disk atmosphere, parameterized as
\begin{equation}
T_{\rm atm}=T_{\rm atm, 100\,AU}\bigg(\frac{R}{\rm 100\,AU}\bigg)^{\zeta}
\end{equation}
\noindent For gas temperatures, we only set $T_{\rm atm, 100\,AU}$ as a free parameter and fix $\delta=2$ and $\zeta$=$-$0.5. We assume that the CO molecules are frozen out of the gas phase when $T_{\rm gas}<20$\,K. { Since $^{12}{\rm CO}~J=2-1$ line emission can be used to constrain the disk inclination better than dust continuum emission, we calculate the $^{12}{\rm CO}~J=2-1$ line emission using three disk inclinations, 30$^\circ$, 35$^\circ$, and 40$^\circ$. The $^{12}{\rm CO}~J=2-1$ line emission are computed using RADMC-3d assuming non-local thermal equilibrium (non-LTE) conditions for different $T_{\rm atm, 100\,AU}$. The result integrated intensity maps of $^{12}{\rm CO}~J=2-1$ are simply convolved with the corresponding synthetical beams, and then compared with the observations to characterize $T_{\rm atm, 100\,AU}$. For each model, the goodness of the fit $\chi^2_{\rm CO}$ is calculated in the similar way as Equation~\ref{Equ:equa5}, but only for the pixels with values above half of the peak intensity to reduce the possibility of CO contamination by the parental cloud. We also compare the PV diagrams from the observation and from the models to constrain the disk inclination. from a $\chi^2$ test, we find a disk model with $T_{\rm atm, 100\,AU}$=200$\pm$10\,K and $i=35^\circ-40^\circ$ can fit the observations. In Table~\ref{Tab:disk_par}, we list the best-fit parameter for modeling continuum and gas emission of GW~Ori.}
\subsection{Model results}\label{Sect:model_ressult}
In our disk models, we have { 8} free parameters. The dust depletion factor ($\xi_{\rm gap}$) are mainly constrained by comparing the model SEDs with the observed one at near- and mid-infrared wavelengths, $h_{\rm c}$ can be estimated by fitting the SED at mid- and far-infrared bands, and $M_{\rm dust}$ can be constrained by fitting the SED of GW~Ori at submillimeter and millimeter wavelengths and the 1.3\,mm continnum emission map. The parameters $R_{\rm c}$ and $\gamma$ are mainly constrained by comparing the model continuum emission map at 1.3\,mm with the observations. { The disk inclination ($i$) is constrained by fitting the 1.3\,mm continuum emission map, the $^{12}{\rm CO}~J=2-1$ line emission map, and the PV diagram. And the gas temperature parameter $T_{\rm atm, 100\,AU}$ is constrained by fitting the $^{12}{\rm CO}~J=2-1$ line emission map. } In Table~\ref{Tab:disk_par}, we list the disk model which can satisfactorily reproduce both the 1.3\,mm continnum emission, the SED, and the $^{12}{\rm CO}~J=2-1$ line emission of GW~Ori. In the following, we compare the model results using these parameters with the observations.
\begin{table}
\caption{Disk model parameters for modeling dust and gas emission of GW~Ori.\label{Tab:disk_par}}
\centering
\begin{tabular}{cc}
\hline\hline
Parameters & Values \\
\hline
\multicolumn{2}{c}{{\bf Central star}}\\
\hline
Effective temperature\tablefootmark{a} &\multicolumn{1}{c}{5500\,K}\\
Stellar radius\tablefootmark{a} &\multicolumn{1}{c}{7.5\,$R_{\odot}$}\\
Stellar mass\tablefootmark{a} &\multicolumn{1}{c}{3.9\,$M_{\odot}$}\\
\hline
\multicolumn{2}{c}{{\bf Disk}}\\
\hline
Inner radius ($R_{\rm in}$)\tablefootmark{a} &1.2\,AU \\
Gap size ($R_{\rm gap}$)\tablefootmark{a} &45\,AU\\
Dust depletion factor ($\xi_{\rm gap}$) &2.5$\times10^{-3}$ \\
Characteristic scaling radius ($R_{\rm c}$) &320\,AU \\
Surface density gradient parameter ($\gamma$) & 0.2 \\
Angular scale height ($h_{\rm c}$) & 0.18 \\
$\Psi$ & 0.1 \\
Disk mass & 0.12\,$M_{\odot}$ \\
$T_{\rm atm, 100\,AU}$ & 200\,K\\
Power index for $T_{\rm atm}$ ($\zeta$)\tablefootmark{a} &$-$0.5 \\
$\delta$\tablefootmark{a} & 2 \\
Disk inclination ($i$) & 35$^\circ$ \\
Position angle\tablefootmark{a} & 10$^\circ$ \\
\hline
\end{tabular}
\tablefoot{\tablefoottext{a}{Fixed parameters.}}
\end{table}
In Fig.~\ref{Fig:cont}(b), we show the model continuum emission at 1.3\,mm. In Fig.~\ref{Fig:cont}(c, d), we compare the distribution of the intensity along the east-western and south-northern direction across the center of the map, respectively, from the model. The model results can fit the observations well. In Fig.~\ref{Fig:SED}, we compare the model SED with the observed one. The observed SED in the figure is the type~1 SED for GW~Ori in Paper\,I, and constructed using the $UBVR_{\rm C}I_{\rm C}$ photometry from \citet{2004AJ....128.1294C}, the $JHK_{\rm s}$ photometry from the 2MASS survey \citep{2006AJ....131.1163S}, the photometry at 3.4, 4.6, 12, and 22\,$\mu$m\ from the WISE survey \citep{2010AJ....140.1868W}, the photometry at 9 and 18\,$\mu$m\ from the AKARI survey \citep{2010A&A...514A...1I}, the MIPS 70\,$\mu$m\ photometry from Paper\,I, the fluxes at 350, 450, 800, 850, 1100, 1360\,$\mu$m\ from \citet{1995AJ....109.2655M}, and the 5$-$37\,$\mu$m\ low-resolution IRS spectrum from paper\,I. In Fig.~\ref{Fig:SED}, it can be seen that our simple disk model can well reproduce the observed SED of GW~Ori. In Fig.~\ref{Fig:CO_cont}, we show the model map of the $^{12}{\rm CO}~J=2-1$ velocity-integrated intensities calculated with the parameters in Table~\ref{Tab:disk_par}, which reproduces the observation very well. Figure~\ref{Fig:vel1}(b) displays the model $^{12}{\rm CO}~J=2-1$ velocity moment map, and Fig.~\ref{Fig:PV}(b) shows the model PV diagram for the $^{12}{\rm CO}~J=2-1$ lines\footnote{The LSR velocity of GW~Ori is assumed to be 13.6\,km\,s$^{-1}$\ (see Sect.~\ref{Sect:Molecular_line_emission}).}.
Using the disk parameters listed in Table~\ref{Tab:disk_par}, and taking the typical abundances of ISM for $^{13}{\rm CO}$ and ${\rm C^{18}O}$, $^{13}{\rm CO}/{\rm H_{2}}=1.43\times10^{-6}$ and ${\rm C^{18}O}/{\rm H_{2}}=1.82\times10^{-7}$, i.e. $^{12}{\rm CO}/^{13}{\rm CO}$=70 and $^{12}{\rm CO}/{\rm C^{18}O}$=550 \citep{1994ARA&A..32..191W}, we calculate the the predicted emission of the $^{13}{\rm CO}$ and ${\rm C^{18}O}$ lines using RADMC--3D assuming Non-LTE conditions. { We note the predicted line emission of $^{13}{\rm CO}~J=2-1$ is consistent with the observations (see Fig.~\ref{Fig:CO_cont} and Figure~\ref{Fig:vel2}(b)), but the model line emission of ${\rm C^{18}O}~J=2-1$ is three time stronger than the observational data. A simple solution to reduce the model line emission is to decrease the abundance of ${\rm C^{18}O}$ in gas phase, which can be due to the real reduction in their abundances or more freezing than we assumed. We find that a satisfactory fit to the SMA data required that ${\rm C^{18}O}/{\rm H_{2}}\sim2.3\times10^{-8}$. In Fig.~\ref{Fig:CO_cont}, we show the model map of ${\rm C^{18}O}~J=2-1$ velocity-integrated intensities calculated using the above abundances. Such global ${\rm C^{18}O}$ gas-phase depletion in circumstellar disks has been suggested before \citep{1994A&A...286..149D,1996A&A...309..493D,2003A&A...399..773D,2007A&A...469..213I}, which can be due to a selective photodissociation of CO and its isotopes in disks \citep{2009A&A...503..323V}. However, we must stress that the constraint on the abundance of ${\rm C^{18}O}$ in the disk of GW~Ori based on the SMA data is just tentative since the detection of ${\rm C^{18}O}$ is marginal. Furthermore, an underestimate of the dust absorption of the line emission in the disk modelling or over-subtraction of continuum around ${\rm C^{18}O}~J=2-1$ could complicate the issue.}
\begin{figure}
\centering
\includegraphics[width=1.\columnwidth]{SED_test.ps}
\caption{The observed SED of GW~Ori. The broad band photometry is shown with the filled circles, and the IRS spectrum of this source is displayed in solid line. The open circle show the flux from our SMA observations. The thick gray line shows our model SED. The photospheric emission level is indicated with a thin gray curve.\label{Fig:SED}}
\end{figure}
We have shown that our disk model can reproduce the SMA observations of GW~Ori. However, multi-parameter disk models are known to be highly degenerated and non-continuous. In addition, there are other sources of uncertain in disk modeling. The dust growth and settling in disks can change the dust properties vertically and radially \citep{2010A&A...513A..79B,2012A&A...539A.148B}. And it is unknown whether the gas and dust are well mixed in the GW~Ori disk, and the gas-to-dust ratio may vary vertically and radially \citep{2010A&A...513A..79B}. All these put strong limitations on the interpretations of the results from our disk modeling. The inferred disk masses can be strongly dependent on the assumed dust model (size distribution) and gas-to-dust ratio. { In addition, it should be expected that the structure of the disk, vertical scale height, dust distribution, and heating may differ from typical cases due to the interaction between the two companions and the very massive disk in GW~Ori.}
\section{Discussion}\label{Sec:discussion}
The disk inclination of GW~Ori is constrained by the gas kinematics in the disk traced by the $^{12}{\rm CO}$ line, which gives an intermediate inclination ($\sim$35$^\circ$). In Paper\,I we have estimated the inclination of the stellar rotation axis of the primary star (GW~Ori~A), which is around 35--50$^\circ$. Thus the stellar rotation axis of GW~Ori~A and the disk spin axis could be aligned. It is still unclear if the the binary orbital plane and the disk is aligned in the GW~Ori system. If it is the case, the mass of the close companion GW~Ori~B is estimated to be { 0.44}\,$M_{\odot}$\ using the minimum companion mass ($m_{2}{\rm sin}~i_{*}=0.25$, $i_*$ is the inclination of the orbit) derived in Paper\,I. In this case, the expected $H$-band flux ratio between the primary GW~Ori~A (3.9\,$M_{\odot}$) and GW~Ori~B (0.44\,$M_{\odot}$) is 30:1 at age of $\sim$0.9\,Myr from the pre-main-sequence evolutionary tracks of \citet{2000A&A...358..593S}. On the contrary, the near-infrared interferometric observations show that the two stellar components may have near-equal $H$-band fluxes (2:1), which requires a low inclination of the orbit ($\sim$10$^{\circ}$) for GW~Ori to have a massive close companion GW~Ori~B. { However, an inclined orbit of a massive companion can drastically disturb the disk \citep{1996MNRAS.282..597L}.} In addition, \citet{1998AstL...24..528S} detected the eclipses toward GW~Ori during 1987-1992, which may suggest a nearly edge-on inclination of the the orbit for GW~Ori~A/B. { However, recent observation with Kepler/K2 observations detect many quasi-periodic or aperiodic dimming events from young stars with disks, which are not edge-on, and could be due to inclined and variable inner dust disk warps \citep{2016ApJ...816...69A,2016MNRAS.462L.101A,2016MNRAS.463.2265S}. Thus, an intermediate disk inclination of GW~Ori does not contradict with the observation from \citet{1998AstL...24..528S}.}
\section{Summary}\label{Sec:summary}
Using the SMA we have mapped the disk around GW~Ori both in continuum and in the $J=2-1$ transitions of $^{12}{\rm CO}$, $^{13}{\rm CO}$, and ${\rm C^{18}O}$. The dust and gas properties in the disk are obtained by comparing the observations with the predictions from disk models with various parameters.
We find a clear evidence that the circumstellar material in the disk is in Keplerian rotation around GW~Ori with a disk inclination of $\sim$35$^\circ$.
{ We present a disk model which can reproduce the dust continuum and line emission of CO and its isotopes from the disk of GW~Ori. To reproduce the line emission of ${\rm C^{18}O}$, we may need the substantially depleted abundances of ${\rm C^{18}O}$ in gas phase.}
GW~Ori is one of the most remarkable disks regarding its mass, and one of the most remarkable stellar systems (a massive G8 star with two companions). This object is bright at the whole electromagnetic spectrum and well studied, and an ideal target for future observations with ALMA.
\begin{acknowledgements}
MF acknowledges support of the action "Proyectos de Investigación fundamental no orientada", grant number AYA2012-35008. ASA support of the Spanish MICINN/MINECO "Ramón y Cajal" program, grant number RYC-2010-06164, and the action "Proyectos de Investigación fundamental no orientada", grant number AYA2012-35008. YW acknowledges the support by NSFC through grants 11303097. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. 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 the National Aeronautics and Space Administration and the National Science Foundation. This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. This research is based on observations with AKARI, a JAXA project with the participation of ESA. This work is in part based on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA.
\end{acknowledgements}
\bibliographystyle{aa}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,246 |
\section{Introduction}
Question generation (QG) aims to create natural questions from a given a sentence or paragraph.
One key application of question generation is in the area of education --- to generate questions for reading comprehension materials~\cite{heilman2010good}. Figure~\ref{fig:problem}, for example, shows three manually generated questions that test a user's understanding of the associated text passage.
Question generation systems can also be deployed
as chatbot components ({\em e.g.}, asking questions to start a conversation or to request feedback~\cite{nasrin2016vqg}) or, arguably,
as a clinical tool for evaluating or improving mental health~\cite{Weizenbaum1966eliza, parry1971colby}.
In addition to the above applications, question generation systems can aid in the development of annotated data sets for natural language processing (NLP) research in reading comprehension and question answering. Indeed the creation of such datasets, {\em e.g.}, SQuAD~\cite{rajpurkar2016squad} and MS MARCO~\cite{nguyen2016msmarco}, has spurred research in these areas.
For the most part, question generation has been tackled in the past via rule-based approaches ({\em e.g.},~\newcite{mitkov2003computer, rus2010first}. The success of these approaches hinges critically on the existence of well-designed rules for declarative-to-interrogative sentence transformation, typically based on deep linguistic knowledge.
\begin{figure}[t]
\centering
\begin{tabular}{p{6.5cm}}
\toprule
\small \textbf{Sentence}:\\
{
\small
\fontfamily{phv} \selectfont
Oxygen is used in cellular respiration and released by \textcolor{LimeGreen}{photosynthesis}, which uses the energy of \textcolor{red}{sunlight} to produce oxygen from \textcolor{blue}{water}.
}\\[4pt]
\small \textbf{Questions}: \\
{
\small \fontfamily{phv}\selectfont
-- What life process produces oxygen in the presence of light?
}\\
{
\small \fontfamily{phv}\selectfont
\quad \emph{\textcolor{LimeGreen}{photosynthesis}}
}\\[4pt]
{
\small
\fontfamily{phv}\selectfont
-- Photosynthesis uses which energy to form oxygen from water?
}\\
{
\small
\fontfamily{phv}\selectfont
\quad \emph{\textcolor{red}{sunlight}}
}\\[4pt]
{
\small \fontfamily{phv}\selectfont
-- From what does photosynthesis get oxygen?
}\\
{
\small \fontfamily{phv}\selectfont
\quad \emph{\textcolor{Blue}{water}}
}\\[2pt]
\bottomrule
\end{tabular}
\caption{Sample sentence from the second paragraph of the article \textit{Oxygen}, along with the natural questions and their answers. \label{fig:problem}}
\vspace{-0.2cm}
\end{figure}
To improve over a purely rule-based system, \newcite{heilman2010good} introduced an overgenerate-and-rank approach that generates multiple questions from an input sentence using a rule-based approach and then ranks them using a supervised learning-based ranker. Although the ranking algorithm helps to produce more acceptable questions, it relies heavily on a manually crafted feature set, and the questions generated often overlap word for word with the tokens in the input sentence, making them very easy to answer.
\newcite{vanderwende2008importance} point out that learning to ask good questions is an important task in NLP research in its own right, and should consist of more than the syntactic transformation of a declarative sentence.
In particular, a natural sounding question often compresses the sentence
on which it is based ({\em e.g.},~question 3 in Figure~\ref{fig:problem}), uses synonyms for terms in the passage ({\em e.g.},~``form'' for ``produce'' in question 2 and ``get'' for ``produce'' in question 3), or refers to entities from preceding sentences or clauses ({\em e.g.},~the use of ``photosynthesis'' in question 2).
Othertimes, world knowledge is employed to produce a good question
({\em e.g.},~identifying ``photosynthesis'' as a ``life process'' in question 1).
In short, constructing natural questions of reasonable difficulty would seem to require an~\emph{abstractive} approach that can produce fluent phrasings that do not exactly match the text from which they were drawn.
As a result, and in contrast to all previous work, we propose here to
frame the task of question generation as a
sequence-to-sequence learning problem that directly maps a sentence from a text passage to a question. Importantly, our approach is
fully data-driven in that it requires no manually generated rules.
More specifically, inspired by the recent success in neural machine translation~\cite{sutskever2014sequence, bahdanau2014neural}, summarization~\cite{rush2015namas, iyer2016code}, and image caption generation~\cite{xu2015show}, we tackle question generation using a conditional neural language model with a global attention mechanism~\cite{luong2015effective}.
We investigate several variations of this model, including one that takes into account paragraph- rather than sentence-level information from the reading passage as well as other variations that determine the importance of pre-trained vs.\ learned word embeddings.
In evaluations on the SQuAD dataset~\cite{rajpurkar2016squad} using three automatic
evaluation metrics, we find that our system
significantly
outperforms a collection of strong baselines, including an information retrieval-based system~\cite{robertson1994bm25},
a statistical machine translation approach~\cite{koehn2007moses}, and the overgenerate-and-rank approach of ~\newcite{heilman2010good}.
Human evaluations also rated our generated questions as more grammatical, fluent, and challenging (in terms of syntactic divergence from the original reading passage and reasoning needed to answer) than the state-of-the-art ~\newcite{heilman2010good} system.
In the sections below we discuss related work (Section~\ref{sec:related}), specify the task definition (Section~\ref{sec:task}) and describe our neural sequence learning based models (Section~\ref{sec:model}). We explain the experimental setup in Section~\ref{sec:experiment}. Lastly, we present the evaluation results as well as a detailed analysis.
\section{Related Work}
\label{sec:related}
\textbf{Reading Comprehension} is a challenging task for machines, requiring both understanding of natural language and knowledge of the world~\cite{rajpurkar2016squad}. Recently many new datasets have been released and in most of these datasets, the questions are generated in a synthetic way. For example, bAbI~\cite{weston2015towards} is a fully synthetic dataset featuring 20 different tasks.~\newcite{hermann2015teaching} released a corpus of cloze style questions by replacing entities with placeholders in abstractive summaries of CNN/Daily Mail news articles.~\newcite{danqi2016exam} claim that the CNN/Daily Mail dataset is easier than previously thought, and their system almost reaches the ceiling performance.~\newcite{richardson2013mctest} curated MCTest, in which crowdworker questions are paired with four answer choices. Although MCTest contains challenging natural questions, it is too small for training data-demanding question answering models.
Recently,~\newcite{rajpurkar2016squad} released the Stanford Question Answering Dataset\footnote{\url{https://stanford-qa.com}} (SQuAD), which overcomes the aforementioned small size and (semi-)synthetic issues. The questions are posed by crowd workers and are of relatively high quality. We use SQuAD in our work, and similarly, we focus on the generation of natural questions for reading comprehension materials, albeit via automatic means.
\textbf{Question Generation} has attracted the attention of the natural language generation (NLG) community in recent years, since the work of~\newcite{rus2010first}.
Most work tackles the task with a rule-based approach. Generally, they first transform the input sentence into its syntactic representation, which they then use to generate an interrogative sentence. A lot of research has focused on first manually constructing question templates, and then applying them to generate questions~\cite{mostow2009generating, lindberg2013online, mazidi2014linguistic}.~\newcite{labutov2015deep} use crowdsourcing to collect a set of templates and then rank the relevant templates for the text of another domain. Generally, the rule-based approaches make use of the syntactic roles of words, but not their semantic roles.
~\newcite{heilman2010good} introduce an overgenerate-and-rank approach: their system first overgenerates questions and then ranks them. Although they incorporate learning to rank, their system's performance still depends critically on the manually constructed generating rules.~\newcite{nasrin2016vqg} introduce visual question generation task, to explore the deep connection between language and vision.~\newcite{serban2016factoid30m} propose generating simple factoid questions from logic triple (subject, relation, object).
Their task tackles mapping from structured representation to natural language text, and their generated questions are consistent in terms of format and diverge much less than ours.
To our knowledge, none of the previous works has framed QG for reading comprehension in an end-to-end fashion, and nor have them used deep sequence-to-sequence learning approach to generate questions.
\section{Task Definition}
\label{sec:task}
In this section, we define the question generation task. Given an input sentence $\mathbf{x}$, our goal is to generate a natural question $\mathbf{y}$ related to information in the sentence, $\mathbf{y}$ can be a sequence of an arbitrary length: $[ y_1, ..., y_{|\mathbf{y}|}]$. Suppose the length of the input sentence is $M$, $\mathbf{x}$ could then be represented as a sequence of tokens~$[ x_1, ..., x_M]$. The QG task is defined as finding $\mathbf{\overline{y}}$, such that:
\begin{equation}
\label{equ:task}
\mathbf{\overline{y}} = \argmax_{\mathbf{y}} P \left( \mathbf{y} \vert \mathbf{x} \right)
\end{equation}
where $P \left(\mathbf{y} \vert \mathbf{x} \right)$ is the conditional log-likelihood of the predicted question sequence $\mathbf{y}$, given the input $\mathbf{x}$. In section~\ref{ssec:decoder}, we will elaborate on the global attention mechanism for modeling $P \left(\mathbf{y} \vert \mathbf{x} \right)$.
\section{Model}
\label{sec:model}
Our model is partially inspired by the way in which a human would solve the task. To ask a natural question, people usually pay attention to certain parts of the input sentence, as well as associating context information from the paragraph. We model the conditional probability using RNN encoder-decoder architecture~\cite{bahdanau2014neural, cho2014phrase}, and adopt the global attention mechanism~\cite{luong2015effective} to make the model focus on certain elements of the input when generating each word during decoding.
Here, we investigate two variations of our models: one that only encodes the sentence and another that encodes both sentence and paragraph-level information.
\subsection{Decoder}
\label{ssec:decoder}
Similar to~\newcite{sutskever2014sequence} and~\newcite{chopra2016abstractive}, we factorize the the conditional in equation~\ref{equ:task} into a product of word-level predictions:
\begin{equation}
\nonumber
P \left( \mathbf{y} \vert \mathbf{x} \right) = \prod_{t=1}^{\vert y \vert} P \left( y_{t} \vert \mathbf{x}, y_{ <t}\right)
\end{equation}
where probability of each $y_t$ is predicted based on all the words that are generated previously ({\em i.e.}, $y_{ <t}$), and input sentence $\mathbf{x}$.
More specifically,
\begin{equation}
P \left( y_{t} \vert \mathbf{x}, y_{ <t}\right) = \textnormal{softmax} \left(\mathbf{W}_s \textnormal{tanh}\left( \mathbf{W}_t [ \mathbf{h}_t; \mathbf{c}_t] \right )\right)
\end{equation}
with $\mathbf{h}_t$ being the recurrent neural networks state variable at time step $t$, and $\mathbf{c}_t$ being the attention-based encoding of $\mathbf{x}$ at decoding time step $t$ (Section~\ref{ssec:encoder}). $\mathbf{W}_s$ and $\mathbf{W}_t$ are parameters to be learned.
\begin{equation}
\mathbf{h}_t = \textnormal{LSTM}_1 \left( y_{t-1} , \mathbf{h}_{t-1}\right)
\end{equation}
here, $\textnormal{LSTM}$ is the Long Short-Term Memory (LSTM) network~\cite{hochreiter1997long}. It generates the new state $\mathbf{h}_t$, given the representation of previously generated word $y_{t-1}$ (obtained from a word look-up table), and the previous state $\mathbf{h}_{t-1}$.
The initialization of the decoder's hidden state differentiates our basic model and the model that incorporates paragraph-level information.
For the basic model, it is initialized by the sentence's representation $\mathbf{s}$ obtained from the sentence encoder (Section~\ref{ssec:encoder}). For our paragraph-level model, the \emph{concatenation} of the sentence encoder's output $\mathbf{s}$ and the paragraph encoder's output $\mathbf{s}'$ is used as the initialization of decoder hidden state. To be more specific, the architecture of our paragraph-level model is like a ``Y''-shaped network which encodes both sentence- and paragraph-level information via two RNN branches and uses the concatenated representation for decoding the questions.
\subsection{Encoder}
\label{ssec:encoder}
The attention-based sentence encoder is used in both of our models, while the paragraph encoder is only used in the model that incorporates paragraph-level information.
\vspace{0.3cm}
\noindent \textbf{Attention-based sentence encoder}:
\vspace{0.01cm}
We use a bidirectional LSTM to encode the sentence,
\begin{equation}
\nonumber
\begin{split}
\overrightarrow{\mathbf{b}_t} &= \overrightarrow{{\textnormal{LSTM}_2}} \left( x_{t}, \overrightarrow{\mathbf{b}_{t-1}}\right) \\
\overleftarrow{\mathbf{b}_t} &= \overleftarrow{{\textnormal{LSTM}_2}} \left( x_{t}, \overleftarrow{\mathbf{b}_{t+1}}\right)
\end{split}
\end{equation}
where $\overrightarrow{\mathbf{b}_t}$ is the hidden state at time step $t$ for the forward pass LSTM, $\overleftarrow{\mathbf{b}_t}$ for the backward pass.
To get \emph{attention-based} encoding of $\mathbf{x}$ at decoding time step $t$, namely, $\mathbf{c}_t$, we first get the context dependent token representation by $\mathbf{b}_t = [\overrightarrow{\mathbf{b}_t}; \overleftarrow{\mathbf{b}_t} ]$, then we take the weighted average over $\mathbf{b}_t$ ($t = 1, ..., |\mathbf{x}|)$,
\begin{equation}
\mathbf{c}_t = \sum_{i=1,..,|\mathbf{x}|} a_{i,t} \mathbf{b}_i
\end{equation}
The attention weight are calculated by the bi-linear scoring function and softmax normalization,
\begin{equation}
a_{i,t} = \frac{\exp \left( \mathbf{h}_t^{T} \mathbf{W}_b \mathbf{b}_i\right)}{\sum_{j} \exp \left( \mathbf{h}_t^{T} \mathbf{W}_b \mathbf{b}_j\right)}
\end{equation}
To get the sentence encoder's output for initialization of decoder hidden state, we concatenate last hidden state of the forward and backward pass, namely, $\mathbf{s} = [\overrightarrow{\mathbf{b}_{|\mathbf{x}|}}; \overleftarrow{\mathbf{b}_1} ]$.
\vspace{0.3cm}
\noindent \textbf{Paragraph encoder}:
\vspace{0.01cm}
Given sentence $\mathbf{x}$, we want to encode the paragraph containing $\mathbf{x}$. Since in practice the paragraph is very long, we set a length threshold $L$, and truncate the paragraph at the $L$\textsuperscript{th} token. We call the truncated paragraph ``paragraph'' henceforth.
Denoting the paragraph as $\mathbf{z}$, we use another bidirectional LSTM to encode $\mathbf{z}$,
\begin{equation}
\nonumber
\begin{split}
\overrightarrow{\mathbf{d}_t} &= \overrightarrow{{\textnormal{LSTM}_3}} \left( z_{t}, \overrightarrow{\mathbf{d}_{t-1}}\right) \\
\overleftarrow{\mathbf{d}_t} &= \overleftarrow{{\textnormal{LSTM}_3}} \left( z_{t}, \overleftarrow{\mathbf{d}_{t+1}}\right) \\
\end{split}
\end{equation}
With the last hidden state of the forward and backward pass, we use the concatenation $[\overrightarrow{\mathbf{d}_{|\mathbf{z}|}}; \overleftarrow{\mathbf{d}_1} ]$ as the paragraph encoder's output $\mathbf{s}'$.
\subsection{Training and Inference}
Giving a training corpus of sentence-question pairs: $\mathcal{S} = \left\{ \left( \mathbf{x}^{(i)}, \mathbf{y}^{(i)}\right) \right\}_{i=1}^{S}$, our models' training objective is to minimize the negative log-likelihood of the training data with respect to all the parameters, as denoted by $\theta$,
\begin{equation} \label{equ:loss}
\nonumber
\begin{split}
\mathcal{L} & = - \sum_{i=1}^{S} \log P \left( \mathbf{y}^{(i)}\vert \mathbf{x}^{(i)}; \theta \right) \\
& = - \sum_{i=1}^{S} \sum_{j=1}^{\vert \mathbf{y}^{(i)} \vert} \log P \left( y_{j}^{(i)}\vert \mathbf{x}^{(i)}, y_{ <j}^{(i)} ; \theta \right)
\end{split}
\end{equation}
Once the model is trained, we do inference using beam search. The beam search is parametrized by the possible paths number $k$.
As there could be many rare words in the input sentence that are not in the target side dictionary, during decoding many \verb|UNK| tokens will be output. Thus, post-processing with the replacement of \verb|UNK| is necessary. Unlike~\newcite{luong2015addressing}, we use a simpler replacing strategy for our task. For the decoded \verb|UNK| token at time step $t$, we replace it with the token in the input sentence with the highest attention score, the index of which is $\argmax_{i} a_{i,t}$.
\section{Experimental Setup}
\label{sec:experiment}
We experiment with our neural question generation model on the processed SQuAD dataset. In this section, we firstly describe the corpus of the task. We then give implementation details of our neural generation model, the baselines to compare, and their experimental settings. Lastly, we introduce the evaluation methods by automatic metrics and human raters.
\subsection{Dataset}
\label{ssec:dataset}
\begin{figure}[t]
\centering
\includegraphics[scale=.52]{./figures/overlap.pdf}
\vspace{-0.4cm}
\caption{Overlap percentage of sentence-question pairs in training set. $y$-axis is \# non-stop-words overlap with respect to the total \# tokens in the question (a percentage); $x$-axis is \# sentence-question pairs for a given overlap percentage range.}
\vspace{-0.4cm}
\label{fig:overlap}
\end{figure}
With the SQuAD dataset~\cite{rajpurkar2016squad}, we extract sentences and pair them with the questions. We train our models with the sentence-question pairs. The dataset contains 536 articles with over 100k questions posed about the articles. The authors employ Amazon Mechanical Turks crowd-workers to create questions based on the Wikipedia articles. Workers are encouraged to use their own words without any copying phrases from the paragraph. Later, other crowd-workers are employed to provide answers to the questions. The answers are spans of tokens in the passage.
Since there is a hidden part of the original SQuAD that we do not have access to, we treat the accessible parts ($\sim$90\%) as the entire dataset henceforth.
We first run Stanford CoreNLP~\cite{manning2014corenlp} for pre-processing: tokenization and sentence splitting. We then lower-case the entire dataset. With the offset of the answer to each question, we locate the sentence containing the answer and use it as the input sentence. In some cases (<~0.17\% in training set), the answer spans two or more sentences, and we then use the concatenation of the sentences as the input ``sentence''.
Figure~\ref{fig:overlap} shows the distribution of the token overlap percentage of the sentence-question pairs. Although most of the pairs have over 50\% overlap rate, about 6.67\% of the pairs have no non-stop-words in common, and this is mostly because of the answer offset error introduced during annotation. Therefore, we prune the training set based on the constraint: the sentence-question pair must have at least one non-stop-word in common. Lastly we add \verb|<SOS>| to the beginning of the sentences, and \verb|<EOS>| to the end of them.
We randomly divide the dataset at the article-level into a training set (80\%), a development set (10\%), and a test set (10\%). We report results on the 10\% test set.
Table~\ref{tab:data} provides some statistics on the processed dataset: there are around 70k training samples, the sentences are around 30 tokens, and the questions are around 10 tokens on average. For each sentence, there might be multiple corresponding questions, and, on average, there are 1.4 questions for each sentence.
\begin{table}[t]
\centering
\begin{tabular}{lc}
\toprule
\# pairs (Train) & 70484\\
\# pairs (Dev) & 10570\\
\# pairs (Test) & 11877\\ \cmidrule(r{2pt}){1-2}
Sentence: avg. tokens & 32.9\\
Question: avg. tokens & 11.3\\\cmidrule(r{2pt}){1-2}
Avg. \# questions per sentence& 1.4\\
\bottomrule
\end{tabular}
\caption{Dataset (processed) statistics. Sentence average \# tokens, question average \# tokens, and average \# questions per sentence statistics are from training set. These averages are close to the statistics on development set and test set.}
\label{tab:data}
\vspace{-0.2cm}
\end{table}
\subsection{Implementation Details}
\begin{table*}[htb]
\centering
\resizebox{\textwidth}{!}{%
\begin{tabular}{l|cccc|c|c}
\toprule
Model & BLEU 1 & BLEU 2 & BLEU 3 & BLEU 4 & METEOR & ROUGE\textsubscript{L}\\\midrule
IR\textsubscript{BM25} & 5.18 & 0.91 & 0.28 & 0.12 & 4.57 & 9.16 \\
IR\textsubscript{Edit Distance} & 18.28 & 5.48 & 2.26 & 1.06 & 7.73 & 20.77 \\
MOSES+ & 15.61 & 3.64 & 1.00 & 0.30 & 10.47 & 17.82 \\
DirectIn & 31.71 & 21.18 & 15.11 & 11.20 & 14.95 & 22.47 \\
H\&S & 38.50 & 22.80 & 15.52 & 11.18 & 15.95 & 30.98 \\
Vanilla seq2seq & 31.34 & 13.79 & 7.36 & 4.26 & 9.88 & 29.75 \\\midrule
Our model (no pre-trained) & 41.00 & 23.78 & 15.71 & 10.80 & 15.17 & 37.95 \\
Our model (w/ pre-trained) & \textbf{43.09} & \textbf{25.96} & \textbf{17.50} & \textbf{12.28} & \textbf{16.62} & \textbf{39.75} \\
\quad + paragraph & 42.54 & 25.33 & 16.98 & 11.86 & 16.28 & 39.37\\
\bottomrule
\end{tabular}}
\caption{Automatic evaluation results of different systems by BLEU 1--4, METEOR and ROUGE\textsubscript{L}. For a detailed explanation of the baseline systems, please refer to Section~\ref{ssec:baselines}. The best performing system for each column is highlighted in boldface. Our system which encodes only sentence with pre-trained word embeddings achieves the best performance across all the metrics.}
\label{tab:results}
\end{table*}
We implement our models~\footnote{The code is available at~\url{https://github.com/xinyadu/nqg}.} in Torch7~\footnote{\url{http://torch.ch/}} on top of the newly released~OpenNMT system~\cite{2017opennmt}.
For the source side vocabulary $\mathcal{V}$, we only keep the 45k most frequent tokens (including \verb|<SOS>|, \verb|<EOS>| and placeholders). For the target side vocabulary $\mathcal{U}$, similarly, we keep the 28k most frequent tokens. All other tokens outside the vocabulary list are replaced by the \verb|UNK| symbol. We choose word embedding of 300 dimensions and use the \verb|glove.840B.300d| pre-trained embeddings~\cite{pennington2014glove} for initialization. We fix the word representations during training.
We set the LSTM hidden unit size to 600 and set the number of layers of LSTMs to 2 in both the encoder and the decoder. Optimization is performed using stochastic gradient descent (SGD), with an initial learning rate of 1.0. We start halving the learning rate at epoch 8. The mini-batch size for the update is set at 64. Dropout with probability 0.3 is applied between vertical LSTM stacks. We clip the gradient when the its norm exceeds 5.
All our models are trained on a single GPU. We run the training for up to 15 epochs, which takes approximately 2 hours. We select the model that achieves the lowest perplexity on the dev set.
During decoding, we do beam search with a beam size of 3. Decoding stops when every beam in the stack generates the \verb|<EOS>| token.
All hyperparameters of our model are tuned using the development set. The results are reported on the test set.
\subsection{Baselines}
\label{ssec:baselines}
To prove the effectiveness of our system, we compare it to several competitive systems. Next, we briefly introduce their approaches and the experimental setting to run them for our problem. Their results are shown in Table~\ref{tab:results}.
\vspace{0.1cm} \noindent \textbf{IR} stands for our information retrieval baselines. Similar to ~\newcite{rush2015namas}, we implement the IR baselines to control memorizing questions from the training set. We use two metrics to calculate the distance between a question and the input sentence, {\em i.e.}, BM-25~\cite{robertson1994bm25} and edit distance~\cite{levenshtein1966binary}. According to the metric, the system retrieves the training set to find the question with the highest score.
\vspace{0.1cm} \noindent \textbf{MOSES+}~\cite{koehn2007moses} is a widely used phrase-based statistical machine translation system. Here, we treat sentences as source language text, we treat questions as target language text, and we perform the translation from sentences to questions. We train a tri-gram language model on target side texts with KenLM~\cite{KenLM2015}, and tune the system with MERT on dev set. Performance results are reported on the test set.
\vspace{0.1cm} \noindent \textbf{DirectIn} is an intuitive yet meaningful baseline in which the longest sub-sentence of the sentence is \emph{directly} taken as the predicted question.~\footnote{We also tried using the \emph{entire} input sentence as the prediction output, but the performance is worse than taking sub-sentence as the prediction, across all the automatic metrics except for METEOR.} To split the sentence into sub-sentences, we use a set of splitters, {\em i.e.}, \{``?'', ``!'', ``,'', ``.'', ``;''\}.
\vspace{0.1cm} \noindent \textbf{H\&S} is the rule-based overgenerate-and-rank system that was mentioned in Section~\ref{sec:related}. When running the system, we set the parameter \verb|just-wh| true (to restrict the output of the system to being only wh-questions) and set \verb|max-length| equal to the longest sentence in the training set. We also set \verb|downweight-pro| true, to down weight questions with unresolved pronouns so that they appear towards the end of the ranked list. For comparison with our systems, we take the top question in the ranked list.
\vspace{0.1cm} \noindent \textbf{Seq2seq}~\cite{sutskever2014sequence} is a basic encoder-decoder sequence learning system for machine translation. We implement their model in Tensorflow. The input sequence is reversed before training or translating. Hyperparameters are tuned with dev set. We select the model with the lowest perplexity on the dev set.
\subsection{Automatic Evaluation}
We use the evaluation package released by~\newcite{chen2015microsoft}, which was originally used to score image captions. The package includes BLEU 1, BLEU 2, BLEU 3, BLEU 4~\cite{papineni2002bleu}, METEOR~\cite{2014meteor} and ROUGE\textsubscript{L}~\cite{lin2004rouge} evaluation scripts. BLEU measures the average $n$-gram precision on a set of reference sentences, with a penalty for overly short sentences. BLEU-$n$ is BLEU score that uses up to $n$-grams for counting co-occurrences. METEOR is a recall-oriented metric, which calculates the similarity between generations and references by considering synonyms, stemming and paraphrases. ROUGE is commonly employed to evaluate $n$-grams recall of the summaries with gold-standard sentences as references. ROUGE\textsubscript{L} (measured based on longest common subsequence) results are reported.
\subsection{Human Evaluation}
We also perform human evaluation studies to measure the quality of questions generated by our system and the H\&S system. We consider two modalities: \emph{naturalness}, which indicates the grammaticality and fluency; and \emph{difficulty}, which measures the sentence-question syntactic divergence and the reasoning needed to answer the question. We randomly sampled 100 sentence-question pairs. We ask four professional English speakers to rate the pairs in terms of the modalities above on a 1--5 scale (5 for the best). We then ask the human raters to give a ranking of the questions according to the overall quality, with ties allowed.
\begin{table}[t]
\centering
\resizebox{\columnwidth}{!}{%
\begin{tabular}{lccccc}
\toprule
& Naturalness & Difficulty & Best \% & Avg. rank\\\midrule
H\&S & 2.95 & 1.94 & 20.20 & 2.29 \\
Ours & \textbf{3.36} & \textbf{3.03}\textsuperscript{*} & \textbf{38.38}\textsuperscript{*} & \textbf{1.94}\textsuperscript{**} \\\midrule
Human & 3.91 & 2.63 & 66.42 & 1.46 \\
\bottomrule
\end{tabular}}
\caption{Human evaluation results for question generation. Naturalness and difficulty are rated on a 1--5 scale (5 for the best). Two-tailed t-test results are shown for our method compared to H\&S (statistical significance is indicated with $^{*}$($p$ < 0.005), $^{**}$($p$ < 0.001)).}
\label{tab:human}
\vspace{-0.2cm}
\end{table}
\section{Results and Analysis}
\label{sec:discussion}
\begin{figure}[!tb]
\begin{framed}
\small
\noindent \textbf{Sentence 1}: the largest of these is the eldon square shopping centre , one of the largest city centre shopping complexes in the uk .
\vspace{0.02cm}\noindent \textbf{Human}: what is one of the largest city center shopping complexes in the uk ?
\vspace{0.02cm} \noindent \textbf{H\&S}: what is the eldon square shopping centre one of ?
\vspace{0.02cm} \noindent \textbf{Ours}: what is one of the largest city centers in the uk ?
\par
\vspace{0.4cm}
\noindent \textbf{Sentence 2}: free oxygen first appeared in significant quantities during the paleoproterozoic eon -lrb- between 3.0 and 2.3 billion years ago -rrb- .
\vspace{0.02cm}\noindent \textbf{Human}: during which eon did free oxygen begin appearing in quantity ?
\vspace{0.02cm} \noindent \textbf{H\&S}: what first appeared in significant quantities during the paleoproterozoic eon ?
\vspace{0.02cm} \noindent \textbf{Ours}: how long ago did the paleoproterozoic exhibit ?
\par
\vspace{0.4cm}
\noindent \textbf{Sentence 3}: inflammation is one of the first responses of the immune system to infection .
\vspace{0.02cm}\noindent \textbf{Human}: what is one of the first responses the immune system has to infection ?
\vspace{0.02cm} \noindent \textbf{H\&S}: what is inflammation one of ?
\vspace{0.02cm} \noindent \textbf{Ours}: what is one of the first objections of the immune system to infection ?
\par
\vspace{0.4cm}
\noindent \textbf{Sentence 4}: tea , coffee , sisal , pyrethrum , corn , and wheat are grown in the fertile highlands , one of the most successful agricultural production regions in Africa.
\vspace{0.02cm}\noindent \textbf{Human}: (1) where is the most successful agricultural prodcution regions ? (2) what is grown in the fertile highlands ?
\vspace{0.02cm} \noindent \textbf{H\&S}: what are grown in the fertile highlands in africa ?
\vspace{0.02cm} \noindent \textbf{Ours}: what are the most successful agricultural production regions in africa ?
\par
\vspace{0.4cm}
\noindent \textbf{Sentence 5}: as an example , income inequality did fall in the united states during its high school movement from 1910 to 1940 and thereafter .
\vspace{0.02cm}\noindent \textbf{Human}: during what time period did income inequality decrease in the united states ?
\vspace{0.02cm} \noindent \textbf{H\&S}: where did income inequality do fall during its high school movement from 1910 to 1940 and thereafter as an example ?
\vspace{0.02cm} \noindent \textbf{Ours}: when did income inequality fall in the us ?
\par
\vspace{0.4cm}
\noindent \textbf{Sentence 6}: however , the rainforest still managed to thrive during these glacial periods , allowing for the survival and evolution of a broad diversity of species .
\vspace{0.02cm}\noindent \textbf{Human}: did the rainforest managed to thrive during the glacial periods ?
\vspace{0.02cm} \noindent \textbf{H\&S}: what allowed for the survival and evolution of a broad diversity of species?
\vspace{0.02cm} \noindent \textbf{Ours}: why do the birds still grow during glacial periods ?
\par
\vspace{0.4cm}
\noindent \textbf{Sentence 7}: maududi founded the jamaat-e-islami party in 1941 and remained its leader until 1972.
\vspace{0.02cm}\noindent \textbf{Human}: when did maududi found the jamaat-e-islami party ?
\vspace{0.02cm} \noindent \textbf{H\&S}: who did maududi remain until 1972 ?
\vspace{0.02cm} \noindent \textbf{Ours}: when was the jamaat-e-islami party founded ?
\end{framed}
\vspace{-0.5cm}
\caption{Sample output questions generated by human (ground truth questions), our system and the H\&S system. }
\vspace{-0.4cm}
\label{fig:example}
\end{figure}
\begin{table*}[!htb]
\centering
\footnotesize
\begin{tabular}{lp{1.5cm}p{.9cm}p{.9cm}p{.9cm}p{.9cm}p{.9cm}p{.9cm}p{.9cm}p{.9cm}p{.9cm}p{.9cm}}
\toprule
\multirow{2}{*}{Category} & \multirow{2}{*}{(\%)} & \multicolumn{3}{c}{H\&S} & \multicolumn{3}{c}{Ours} & \multicolumn{3}{c}{Ours + paragraph} \\ \cmidrule(r{4pt}){3-5} \cmidrule(l){6-8} \cmidrule(l){9-11}
& & {\scriptsize BLEU-3}& {\scriptsize BLEU-4}& {\scriptsize METEOR} & {\scriptsize BLEU-3}& {\scriptsize BLEU-4}& {\scriptsize METEOR} & {\scriptsize BLEU-3}& {\scriptsize BLEU-4} & {\scriptsize METEOR} \\ \midrule
w/ sentence & 70.23 (243) & 20.64 & 15.81 & 16.76 & \textbf{24.45} & \textbf{17.63} & 17.82 & 24.01 & 16.39 & \textbf{19.19} \\
w/ paragraph & 19.65 (68) & 6.34 & < 0.01 & 10.74 & 3.76 & < 0.01 & 11.59 & \textbf{7.23} & \textbf{4.13} & \textbf{12.13} \\\midrule
All\textsuperscript{*} & 100 (346) & 19.97 & 14.95 & 16.68 & 23.63 & \textbf{16.85} & 17.62 & \textbf{24.68} & 16.33 & \textbf{19.61} \\ \bottomrule
\end{tabular}
\caption{An estimate of categories of questions of the processed dataset and per-category performance comparison of the systems. The estimate is based on our analysis of the 346 pairs from the dev set. Categories are decided by the information needed to generate the question. Bold numbers represent the best performing method for a given metric. ${}^{*}$Here, we leave out performance results for ``w/ article'' category (2 samples, 0.58\%) and ``not askable'' category (33 samples, 9.54\%).}
\label{tab:category}
\vspace{-0.2cm}
\end{table*}
Table~\ref{tab:results} shows automatic metric evaluation results for our models and baselines. Our model which only encodes sentence-level information achieves the best performance across all metrics. We note that IR performs poorly, indicating that memorizing the training set is not enough for the task. The baseline DirectIn performs pretty well on BLEU and METEOR, which is reasonable given the overlap statistics between the sentences and the questions (Figure~\ref{fig:overlap}). H\&S system's performance is on a par with DirectIn's, as it basically performs syntactic change without paraphrasing, and the overlap rate is also \linepenalty=1000 high.
Looking at the performance of our three models, it's clear that adding the pre-trained embeddings generally helps. While encoding the paragraph causes the performance to drop a little, this makes sense because, apart from useful information, the paragraph also contains much noise.
Table~\ref{tab:human} shows the results of the human evaluation. We see that our system outperforms H\&S in all modalities. Our system is ranked best in 38.4\% of the evaluations, with an average ranking of 1.94. An inter-rater agreement of Krippendorff's Alpha of 0.236 is achieved for the overall ranking. The results imply that our model can generate questions of better quality than the H\&S system. An interesting phenomenon here is that human raters gave higher score for our system's outputs than the human questions. One potential explanation for this is that our system is trained on {\em all} sentence-question pairs for one input sentence, while we randomly select one question among the several questions of one sentence as the human generated question, for the purpose of rating. Thus our system's predictions tend to be more diverse.
For our qualitative analysis, we examine the sample outputs and the visualization of the alignment between the input and the output. In Figure~\ref{fig:example}, we present sample questions generated by H\&S and our best model. We see a large gap between our results and H\&S's. For example, in the first sample, in which the focus should be put on ``the largest.'' Our model successfully captures this information, while H\&S only performs some syntactic transformation over the input without paraphrasing. However, outputs from our system are not always ``perfect'', for example, in pair 6, our system generates a question about the reason why birds still grow, but the \emph{most related} question would be why many species still grow. But from a different perspective, our question is more challenging (readers need to understand that birds are one kind of species), which supports our system's performance listed in human evaluations (See Table~\ref{tab:human}). It would be interesting to further investigate how to interpret why certain irrelavant words are generated in the question. Figure~\ref{fig:heatmap} shows the attention weights ($\alpha_{i,t}$) for the input sentence when generating each token in the question. We see that the key words in the output (``introduced'', ``teletext'', etc.) aligns well with those in the input sentence.
\begin{figure}[t]
\centering
\small
\includegraphics[scale=.48]{./figures/heatmap3.pdf}
\vspace{-0.5cm}
\caption{Heatmap of the attention weight matrix, which shows the soft alignment between the sentence (left) and the generated question (top).}
\label{fig:heatmap}
\vspace{-0.1cm}
\end{figure}
Finally, we do a dataset analysis and fine-grained system performance analysis. We randomly sampled 346 sentence-question pairs from the dev set and label each pair with a category.~\footnote{The IDs of the questions examined will be made available at~\url{https://github.com/xinyadu/nqg/blob/master/examined-question-ids.txt}.} The four categories are determined by \emph{how much} information is needed to ask the question. To be specific, ``w/ sentence'' means it only requires the sentence to ask the question; ``w/ paragraph'' means it takes other information in the paragraph to ask the question; ``w/ article'' is similar to ``w/ paragraph''; and ``not askable'' means that world knowledge is needed to ask the question or there is mismatch of sentence and question caused by annotation error.
Table~\ref{tab:category} shows the per-category performance of the systems. Our model which encodes paragraph information achieves the best performance on the questions of ``w/ paragraph'' category. This verifies the effectiveness of our paragraph-level model on the questions concerning information outside the sentence.
\section{Conclusion and Future Work}
We have presented a fully data-driven neural networks approach to automatic question generation for reading comprehension. We use an attention-based neural networks approach for the task and investigate the effect of encoding sentence- vs. paragraph-level information. Our best model achieves state-of-the-art performance in both automatic evaluations and human evaluations.
Here we point out several interesting future research directions. Currently, our paragraph-level model does not achieve best performance across all categories of questions. We would like to explore how to better use the paragraph-level information to improve the performance of QG system regarding questions of all categories. Besides this, it would also be interesting to consider to incorporate mechanisms for other language generation tasks ({\em e.g.}, copy mechanism for dialogue generation) in our model to further improve the quality of generated questions.
\section*{Acknowledgments}
We thank the anonymous ACL reviewers, Kai Sun and Yao Cheng for their helpful suggestions. We thank Victoria Litvinova for her careful proofreading. We also thank Xanda Schofield, Wil Thomason, Hubert Lin and Junxian He for doing the human evaluations.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,567 |
\section{Introduction}
Early-type galaxies are strongly clustered \citep[e.g.,][]{Lov95,
Her96, Will98, Shep01}, making galaxy clusters an ideal place for
their study.
Stellar population studies have shown that both, local and high-redshift
early-type galaxies follow tight correlations between the colors and line-strength
features and other properties of the galaxies (mostly related with their masses)
\citep[e.g.][]{Bow92, K00, T00b, Ber05, SB06a}
The mere existency of these correlations, as well as their evolution with redshift,
seem to be consistent with a very early (z$\ge$2) and coordinated formation
of their stars \citep{VS77, Bow92,
Ell97,KA98, SED98, Kel01, Ben98, Zie01}.
However, the evolution of the
cluster red-sequence luminosity function with redshift challenges this
view (De Lucia et al.\ 2004; De Lucia et al.\ 2007; Kodama et
al.\ 2004, Rudnick et al. 2008, in preparation; although see
\citet{And08} for contradictory results), and so does the
morphological evolution since $z=0.4$ \citep[e.g.,][]{Dres97}, and the
evolution of the blue/star-forming fraction (Butcher \& Oemler 1984;
Poggianti et al.\ 2006) in clusters.
A deeper understanding of the nature of the evolution of the cluster
red-sequence requires to go beyond colors (affected by the age-metallicity degeneracy)
and derive the stellar
populations parameters (age and chemical abundances) with time, using stellar population models.
However, breaking the age-metallicity
degeneracy requires a combination of indices with different
sensitivities to both parameters (see, e.g., Rabin 1982)\nocite{Rab82}.
\footnote{Combination of optical and near-IR colours have also been probed useful
to break the age-metallicity degeneracy (e.g., Peletier, Valentijn \& Jameson 1990;
MacArthur et al. 2004; James et al. 2005, among others), although dust reddening is
still a problem.}
Unfortunately, instrumental limitations have
long prevented accurate measurements of absorption line indices at
high redshift. Recent observational advances, on the ground and
in space, now allow such measurements in intermediate and high
redshift galaxies, both in clusters and in the field \citep[][]{Zie01,
Barr05, Sch06, J05}. The analysis of these data have revealed that, indeed, the
age-metallicity degeneracy is confusing the interpretation of the
scaling relations: large spreads in galaxy luminosity weighted ages
and metallicities at high redshift have been found in datasets showing
very tight Faber-Jackson, Mgb-$\sigma$ and Fundamental plane (FP)
relations, challenging the classical interpretation of the tightness
of the scaling relations.
High redshift spectroscopic samples are, however, still restricted to a
maximum of $\sim$30 galaxies. Moreover, they often target a single
cluster \citep[][]{Kel01,J05, Tran07, Kel06}. This could be biasing the
results, as studies at low redshift have shown that the star formation
histories of early-type galaxies might depend on cluster properties
\citep[e.g., compare][]{KD98, CRC03, SB03, J99, Nel05, T08}.
Therefore, a study based on a large sample of galaxies in
clusters covering a large range in cluster masses is necessary to obtain
a complete picture of galaxy evolution.
The present work is based on 24 clusters with
redshifts between 0.39 and 0.8 from the ESO Distant Cluster Survey
(hereafter, EDisCS). The major novelty of the present work is that we
do not only consider very massive structures; our sample spans a large
range in cluster velocity dispersions. Therefore, we minimize
possible biases due to the relationship between galaxy properties and
environment.
It is now common to
study red-sequence galaxies rather than morphologically classified
early-type galaxies, as
colours are easier to measure in large datasets than
morphology, and they appear to be more correlated with environment
\citep[][]{Kauff04, Blan05, MM06}. Nonetheless, observations have also revealed the
existence of an intrinsic spread in morphology at given colour
\citep[e.g.,][]{Con06, Bal04, Cross04}. This stress the need for
investigating the relation between morphology and colour, and their
evolution with redshift and, therefore, this is the strategy we adopt.
Our sample of
red-sequence galaxies is much larger than those used in previous
efforts. It encompasses 337 galaxies, distributed in 24 clusters and
groups, for which we study stellar populations and morphologies.
Our sample of red-sequence galaxies is not restricted to the most massive,
but span a wide range of internal velocity dipsersion (100-350 km/s),
comparable to the samples analysed at low-redshift.
Throughout the paper, we adopt a concordance cosmology with $\Omega_{\rm
M}=0.3$, $\Omega_{\Lambda}=0.7$, H$_0$=70~km~s$^{-1}$ Mpc$^{-1}$. All
magnitudes are quoted in the Vega system.
\section{The sample}
\label{sec.sample}
The ESO Distant Cluster Survey
(EDisCS) is a photometric and spectroscopic survey of galaxies
in 20 fields containing clusters with redshifts between 0.39 and 0.96.
These fields were selected from the Las Campanas Distant Cluster Survey
\citep{Gon01}, specifically from the 30 highest surface
brightness candidates. A full description of the sample selection can
be found in \citet{White05}. EDisCS includes structures
with velocity dispersions from $\sim$150 to $\sim$1100~km~s$^{-1}$,
i.e. from small groups to clusters.
Deep optical photometry with VLT/FORS2 \citep{White05}, near-IR
photometry with SOFI on the ESO/NTT (Arag\'on-Salamanca et al., in
preparation), and deep-multi-slit spectroscopy with VLT/FORS2 were
acquired for each field. The same high-efficiency grism was used
in all observing runs (grism 600RI+19, $\lambda_0$ = 6780\AA~).
The wavelength range varies with the field and
the x-location of the slit on the mask \citep[see][for details]{MJ08}, but
it was chosen to cover, at least, a rest-frame wavelength range
from 3670 to 4150~\AA~(in order to include [OII] and H$\delta$ lines)
for the assumed cluster redshift.
The spectral resolution is $\sim$6 \AA~(FWHM), corresponding to
rest-frame 3.3 \AA~ at $z=0.8$ and 4.3 \AA~at $z=0.4$. Typically,
four- and two-hour exposures were obtained for the high$-z$ and
mid$-z$ samples, respectively. The
spectroscopic selection, observations, data reduction and catalogs are presented
in detail in \citet{Hall04} and \citet{MJ08}.
In brief, standard reduction procedures (bias subtraction, flat fielding, cosmic-ray removal,
geometrical distortion corrections, wavelength calibration, sky subtraction and flux calibration)
were performed with IRAF. Particular attention was paid to the sky-subtraction that was performed
before any interpolation or rebinning of the data \citep[see][for details]{MJ08}.
This dataset has also been complemented with 80 orbits of HST/ACS imaging in F814W of the highest
redshift clusters \citep{Des07}, H$\alpha$ narrow-band imaging
\citep{Finn05}, and XMM-Newton/EPIC X-ray observations \citep{Jon06}.
26 structures (groups or clusters) were identified in the 20 EDisCS fields
\citep{Hall04, MJ08}. Two of these structures
were not considered in this paper. The first
one, cl1103.7-1245,
because its spectroscopic redshift (0.96) is too far away from the
redshift targeted by the photo-z-based selection (0.70). This can
introduce observational biases.
The second one, cl1238.5-1144, because it could only be observed
for 20 minutes and the S/N of the spectra is not sufficient for our analysis.
To define the red-sequence, we use total-I magnitudes, estimated
by adding, to the Kron magnitudes, a correction appropriate
for a point source measured within an aperture equal to the galaxy's Kron
aperture. These corrections are obtained empirically from
unsaturated and isolated stars on each convolved I-band image
(see White et al.\ 2005 for details).
A galaxy is considered a member of a given cluster (or group) if its
redshift falls within 3$\times \sigma_{\rm cluster}$ of the cluster
redshift, where $\sigma_{\rm cluster}$ is the cluster velocity
dispersion presented in \citet{Hall04} and \citet{MJ08}. Similarly to
all other EDisCS analyses, galaxy groups are identified by
$\sigma_{\rm cluster} < 400 $ km/s. We define red-sequence galaxies
as those with {\it secure} redshifts, and colours between $\pm$0.3~mag
from the best linear fit (with slope fixed to $-0.09$) to the colour-magnitude
relation (V-I vs. I) of the objects without emission lines. This
definition coincides with that of \citet{White05} and De Lucia et al.\ (2004,
2007). The width of the region corresponds to $\sim$3 times the
RMS-dispersion of the red-sequence colours of our two most populated
clusters, cl1216.8-1201 and cl1232.5-1250.
Table \ref{tb:clusterlist} lists the structures selected for the present work
and the total number of galaxies on the red-sequence.
Figure~\ref{colo-mag}
displays the $V-I$ vs $I$ colour-magnitude diagrams of the 24 EDisCS
structures studied in the present paper.
\begin{figure*}
\resizebox{\textwidth}{!}{\includegraphics[angle=0.]{CMDVI.ps}}
\caption{$V$, $I$ colour-magnitude diagrams for the 24 EDisCS
structures considered in this study. Galaxies with no- or weak-
emission are represented by red circles, while galaxies with strong
emission are marked as blue circles. The fit, with a fixed slope of
$-0.09$, of the secure cluster members with no or only weak emission
is shown as a solid line. The dashed lines trace the $\pm$ 0.3 mag
boundary taken into account to select the red-sequence galaxies. This
corresponds to the measured dispersions of cl1232.5-1250 and
cl1216.8-1201, our two most populous galaxy clusters. When photo-z
membership is available, we show the photo-z selected cluster galaxies
as small black dots.}
\label{colo-mag}
\end{figure*}
To study the evolution of the galaxy population properties with redshift,
we divide our galaxies in 3 different redshift intervals : (1) $0.39 < z < 0.5$; (2)
$ 0.5 \leq z < 0.65$; and (3) $0.65 \leq z < 0.81$. For convenience, we
refer to these intervals by their median redshifts, $z=0.45$,
$z=0.55$, and $z=0.75$. Figure~\ref{Groups} shows the redshift
distribution of our sample of galaxies.
\begin{table*}[h]
\begin{tabular}{clcrrrcr}
Group & Cluster Name & z & ACS & N$_{reds}$ & N$_{N+W}$ & $\sigma\pm err$ & R$_{200}$\\
& & & & & & (kms$^{-1}$) & Mpc \\
\hline
\hline
0.45 &cl1018.2-1211 & 0.4734 & & 17 & 9 & 486$^{+59}_{-63}$ & 0.93\\
&cl1037.9-1243a & 0.4252 & x & 18 & 9 & 537$^{+46}_{-48}$ & 1.06\\
&cl1059.2-1253 & 0.4564 & & 26 & 18 & 510$^{+52}_{-56}$ & 0.99 \\
&cl1138.2-1133 & 0.4796 & x & 17 & 8 & 732$^{+72}_{-76}$ & 1.40 \\
&cl1138.2-1133a & 0.4548 & x & 8 & 3 & 542$^{+63}_{-71}$ & 1.05 \\
&cl1202.7-1224 & 0.4240 & & 18 & 7 & 518$^{+92}_{-104}$ & 1.02 \\
&cl1301.7-1139 & 0.4828 & & 19 & 10 & 687$^{+81}_{-86}$ & 1.31 \\
&cl1301.7-1139a & 0.3969 & & 13 & 6 & 391$^{+63}_{-69}$ & 0.78 \\
&cl1420.3-1236 & 0.4962 & & 18 & 13 & 218$^{+43}_{-50}$ & 0.41 \\
\hline
0.55 &cl1037.9-1243 & 0.5783 & x & 7 & 5 & 319$^{+53}_{-52}$ & 0.57\\
&cl1103.7-1245a & 0.6261 & x & 9 & 6 & 336$^{+36}_{-40}$ & 0.59 \\
&cl1119.3-1129 & 0.5500 & & 17 & 9 & 166$^{+27}_{-29}$ & 0.30 \\
&cl1227.9-1138 & 0.6357 & x & 14 & 8 & 574$^{+72}_{-75}$ & 1.00 \\
&cl1227.9-1138a & 0.5826 & x & 4 & 1 & 341$^{+42}_{-46}$ & 0.61 \\
&cl1232.5-1250 & 0.5414 & x & 41 & 20 &1080$^{+119}_{-89}$ & 1.99 \\
&cl1353.0-1137 & 0.5882 & & 10 & 7 & 666$^{+136}_{-139}$& 1.19 \\
&cl1354.2-1230a & 0.5952 & x & 8 & 5 & 433$^{+95}_{-104}$ & 0.77 \\
&cl1411.1-1148 & 0.5195 & & 18 & 12 & 710$^{+125}_{-133}$& 1.32 \\
\hline
0.75&cl1040.7-1155 & 0.7043 & x & 14 & 8 & 418$^{+55}_{-46}$ & 0.70 \\
&cl1054.4-1146 & 0.6972 & x & 36 & 16 & 589$^{+78}_{-70}$ & 1.06 \\
&cl1054.7-1245 & 0.7498 & x & 20 & 6 & 504$^{+113}_{-65}$ & 0.70\\
&cl1103.7-1245b & 0.7031 & x & 3 & 2 & 252$^{+65}_{-85}$ & 0.42 \\
&cl1216.8-1201 & 0.7943 & x & 38 & 23 &1018$^{+73}_{-77}$ & 1.61 \\
&cl1354.2-1230 & 0.7620 & x & 7 & 5 & 648$^{+105}_{-110}$& 1.05 \\
\hline
\end{tabular}
\caption{Col. (1) Redshift interval in which the galaxy structure falls
(see text for details).
Col. (2): Cluster name. Following \citet{MJ08}, we label the secondary
structures with letters "a" and "b". Col. (3): Cluster redshift.
Col. (4): marked with x if ACS images are
available. Col.(5): Number of secure spectroscopically confirmed red-sequence
galaxies. Col. (6) Number of red-sequence galaxies with no or
negligible emission, full-filling our signal-to-noise ratio criterion.
Col. (7) Velocity dispersion of the cluster. Col. (8) R$_{200}$,
calculated as in \citet{Finn05}.}
\label{tb:clusterlist}
\end{table*}
\begin{figure}
\resizebox{0.5\textwidth}{!}{\includegraphics[angle=-90]{Groups.ps}}
\caption{Redshift distribution of the red-sequence galaxies in
the 3 redshifts-bins with no or negligible emission lines, before
any signal-to-noise selection.}
\label{Groups}
\end{figure}
Dust reddened star-forming galaxies
are estimated to make up $\sim$20\% of galaxies in low-redshift
clusters \citep{Strat01, Gav02, Bell04, Fran07}. This contamination
is likely to be more important in the strong-emission line regime
To avoid contamination from these galaxies that do not have red stellar populations,
and due to the difficulty of measuring reliable absorption line indices
in galaxies with emission lines, we discard, for our absorption line
analysis, galaxies showing
evidence of emission lines.
Our selection is based both on visual
inspection of the 2D- spectra and on measurements of the line
equivalent widths (EWs). These measurements were taken from
\citet{Pog06}. We also measured the [OII] and H$\beta$ emission-line
EWs after carefully subtracting the underlying stellar continuum (see
Moustakas \& Kennicutt \citeyear{2006ApJS..164...81M} for details).
After comparing the visual inspection with the quantitative measurements,
we keep galaxies with equivalent widths of
[OII]$\lambda$3727 $ < 7$\AA.
In Fig.~\ref{colo-mag} we distinguish between galaxies with strong
emission lines and those with no- or weak- emission lines (N+W,
hereafter) in the spectroscopic sample of red-sequence galaxies.
Figure~\ref{STypes} shows the fraction of N+W red-sequence galaxies as
a function of redshift and structure velocity dispersion. The scatter
is large and there is no trend with either $\sigma_{\rm cluster}$
or redshift. On average, 24\% of the red-sequence galaxies show
EW[OII]3727$>$7\AA. Section~\ref{sec.emiss} discusses the nature of
the emission in these galaxies.
We also remove the brightest cluster
galaxies (BCGs) from the sample, as their position in the cluster may
lead to a different evolution from the rest of the red population (De
Lucia \& Blaizot 2007)\nocite{dLB07}. A photometric study of the BCGs
in the EDisCS clusters is presented in Whiley et
al.\ (2008)\nocite{Whiley08}.
\begin{figure*}
\resizebox{0.8\textwidth}{!}{\includegraphics[angle=-90]{STypes.ps}}
\caption{Fraction of red-sequence galaxies that have no or only weak
emission lines (EW[OII] $<$7$\AA$) as a function of redshift and
group/cluster velocity dispersion. This fraction is calculated as the
ratio between the N+W red-sequence galaxies and the total number of
red-sequence galaxies in the spectroscopic sample.}
\label{STypes}
\end{figure*}
Our initial sample includes a total of 337 N+W red-sequence
galaxies. Their mean spectral signal-to-noise ratio per \AA~ (S/N), measured
between 4000 and 4500 \AA~ (rest-frame) is $\sim$ 17, 19 and 12 per
\AA~ at redshift 0.45, 0.55 and 0.75, respectively. We
consider all galaxies independently of their distance to the cluster
centers except for the morphological analysis. The radial cuts, when
applied, will be stated
explicitly. However, to measure line-strength indices, we require a minimum signal-to-noise ratio of 10 per
\AA~, measured between 4000 and 4500\AA~ (rest-frame). Thie leave us, for our spectroscopic analysis, with a
total of 215 galaxies satisfying our selection criteria, i.e, 70\% of the initial sample (see Table
\ref{tb:clusterlist} for their distribution).
\section{Source of ionization for the emission line red-sequence galaxies}
\label{sec.emiss}
As inferred from Fig.~\ref{STypes}, a non negligible fraction of
red-sequence galaxies exhibit emission lines, with equivalent widths
reaching $\sim$30\AA~ for [OII] and $\sim$12\AA~ for H$\beta$.
Although these galaxies are discarded from further investigation, we
are interested in trying to unveil their nature. We investigate below the
various possible ionization sources and look for evidence of
evolution with redshift.
We perform a similar analysis than \citet{Yan06}.
\citet{Yan06} studied
a large sample of red galaxies from the
Sloan Digital Sky Survey (SDSS) finding emission in 52.2\%
of them. They showed that they could be classified in two
main groups: galaxies with high [OII]$\lambda 3727\AA$/H$\alpha$
(LINER-like and quiescent galaxies, representing 20.6\% of the
total red populution with emission) and low-[OII]/H$\alpha$ galaxies
(mostly dusty-starforming ones, with a small fraction of Seyferts, accounting
for 9\% of the red-sequence galaxies with emission).
Counting galaxies
with only [OII] seen in emission (instead of both [OII] and
H$\alpha$) increases the fraction of LINERS to 28.8\%. Finally, 14\%
of the red galaxies have H$\alpha$ detected but no [OII], making them
difficult to classify. Nevertheless, Yan et al.\ (2006) show that the
majority of these galaxies have [NII]/H$\alpha > 0.6$ suggesting a
non-starforming origin for their emission lines.
In the present case, the determination of the ionization sources is
hampered by the fact that the wavelength coverage of the spectra does
not include H$\alpha$. We consider H$\beta$ instead. For each
galaxy, the stellar continuum has been fitted and the [OII] and
H$\beta$ equivalent widths subsequently measured.
Figure~\ref{OIIoverHbeta} illustrates the distribution of [OII] and
H$\beta$ EWs for the red-sequence galaxies and for the full EDisCS spectroscopic sample.
\begin{figure}
\resizebox{0.5\textwidth}{!}{\includegraphics[angle=-90]{OIIoverHbeta.ps}}
\caption{Ratio between [OII] and H$\beta$ for the full EDisCS sample
of cluster members (black dots). Red, green, and blue stars indicate
the red-sequence galaxies in the 0.45, 0.55, and 0.75 redshift bins,
respectively. The[OII]/H$\beta$ distribution is also presented in the
form of a histogram: the black-filled zone represents the red-sequence
galaxies, to be compared to the full sample. Dashed lines indicate the
[OII]/H$\beta$ = 6.7 limit above which the galaxy emission is
considered to be due to mechanisms other than star formation.}
\label{OIIoverHbeta}
\end{figure}
Out of the EDisCS full sample of red-sequence galaxies (393), 243 have
spectra with a wavelength range appropriately centered and wide enough
to include both [OII]$\lambda\lambda 3727$\AA~ and H$\beta$. The
redshift distribution of these galaxies has a mean of 0.52 and a
standard deviation of 0.09. We count 57 galaxies with a 2-$\sigma$
detection (threshold identical to \citet{Yan06}) of both [OII] and
H$\beta$, 68 with only one of the two lines detected, and 118 with no
detection at all (at the 2-$\sigma$ level). Hence, very similarly to
\citet{Yan06}, we obtain 51.4\% of emission line red-sequence
galaxies.
Following \citet{Kew04}, we consider that star formation cannot
induce [OII]/H$\alpha$ larger than 1.5. This value is derived before
any reddening correction and was independently confirmed by
\citet{2006ApJS..164...81M}. We assume a mean value of
H$\alpha$/H$\beta$=4.46, which was derived by \citet{Yan06} before
any reddening correction, and which corresponds to a median
extinction of A$_{\rm V}$=1.40, assuming Type B recombination. Under
this condition, [OII]/H$\beta$= 6.7 draws a boundary between star
forming galaxies and those with emission powered by an AGN. As shown
in figure~11 of \citet{Yan06}, this limit is very conservative.
Indeed, one hardly finds any star forming galaxies with
[OII]/H$\beta$ $>$ 5. However, it does eliminate most Seyferts and
selects mostly LINER-type galaxies. Interestingly, the limit of 6.7
seems to represent a
natural upper limit for the bulk of the whole cluster galaxy
population (see the histogram part of Figure~\ref{OIIoverHbeta}).
For our statistics below, we use the empirical bimodal demarcation
advised by \citet{Yan06}, i.e., EW([OII])=18EW(H$\beta$)$-$6 rather
than a constant [OII]/H$\beta$ ratio. We have checked, however, that
both methods lead to identical results (within 1-2\%).
Table~\ref{emission.lines} shows the emission-line properties of the
red-sequence galaxies with spectra wide enough to cover H$\beta$ and [OII]. To go beyond upper and lower limits we would
need, at least, another set of two lines to build more diagnostic
diagrams (e.g., Kewley et~al.\ 2006). However, we believe that our counts
give reliable hints on the major trends for the ionization processes
at play in our sample. The fraction of quiescent red galaxies is very
much the same as the percentage reported by \citet{Yan06} in the local
Universe. The obvious difference between the two studies resides in
the nature of the galaxies which do have detections of both H$\beta$
and [OII]. While \citet{Yan06} find that only 9\% of those galaxies
have low-[OII]/H$\beta$ ratios, we obtain more than twice this percentage, 19\%.
In addition, only 4\% of
our red-sequence galaxies have high-[OII]/H$\beta$ ratios
characteristic of LINERS. This fraction might increases up to 8\% if we
include galaxies with [OII] detected and H$\beta$ undetected. However, this
is still a factor of 3 smaller than
the fraction of high-[OII]/H$\beta$ galaxies in the red-sequence reported
by \citet{Yan06}, 29\%.
The conclusion for this tentative identification of the ionizing
sources in the EDisCS emission line red-sequence galaxies is that most
of them are dusty star forming ones. We can not disentangle, at this
stage, whether time or environment, or even more technically the use
of H$\beta$ instead of H$\alpha$, leads to the difference with the
results of \citet{Yan06}. Further investigation, both in field
intermediate redshift galaxies and in low redshift cluster galaxies,
is required to shed light on this matter.
\begin{table}
\centering
\begin{tabular}{ll|lr}
[OII] & H$\beta$ & [OII]/H$\beta$ & Fraction \\
\hline
N & N & & 48.5 \% \\
N & Y & uncertain & 24 \% \\
Y & N & high & 4\% \\
Y & Y & high & 4\% \\
Y & Y & low & 19.5\% \\
\hline
\end{tabular}
\caption{Emission line properties of the red-sequence
galaxies for which the spectra covers both [OII] and H$\beta$. The
first two columns indicate whether or not [OII] and H$\beta$ have been
detected (at 2-$\sigma$ level). High and low [OII]/H$\beta$ stand for
EW([OII])$>$18EW(H$\beta$)$-$6 and EW([OII])$<=$18EW(H$\beta$)$-$6, respectively.
\label{emission.lines}}
\end{table}
\section{Stellar velocity dispersions}
\label{sec.sigma}
Velocity dispersions were measured in all our spectra using the IDL
routine PPXF developed by \citet{CE04}. This routine, based on
maximum penalized likelihood with optimal template, is specially suited to extract as much
information as possible from the spectra while suppressing the noise
in the solution and, therefore, is perfect to measure the kinematics
in low S/N data. This algorithm estimates the best fit to a galaxy spectrum
by combining stellar templates that are convolved with the appropiate
mean galaxy velocity and velocity dispersion.
The final values of these parameters are sensitive to the template
missmatch and, therefore, the use of this technique requires templates which
match closely the galaxy spectrum under scrutiny.
This is achieved with the use of extensive stellar library spanning a large range of
metallicities and ages. We use 35 synthetic spectra from the library of single stellar population
models from Vazdekis et al. (2009, in preparation), which makes use of the new stellar library MILES
\citep{SB06_miles}, degraded to the resolution of EDisCS spectra. The library contains spectra spanning
an age range from 0.13 to 17 Gyr and metallicities from $[$Z/H$]=-0.68$ to $[$Z/H$]=+0.2$.
Errors were calculated by means of Monte
Carlo simulations, in which each point was perturbed with the typical
observed error, following a Gaussian distribution. Because the template mistmach
affects the measure of the velocity and $\sigma$ determined with PPXF,
a new optimal template was derived in each simulation. The errors were obtained as the
standard deviation of a total of 50 simulations. The mean uncertainty
in the velocity dispersion calculated in our spectra with S/N $>$ 10
is $\sim$25\%. Given the signal-to-noise ratio and the resolution of
our spectra, $\sigma$ values below 100 kms$^{-1}$ are considered
untrustworthy and, consequently, galaxies with $\sigma <100$
kms$^{-1}$ are eliminated in all analysis involving the comparison
with $\sigma$.
\section{Line-strength indices}
For all of the galaxies in the red sequence, we measure Lick/IDS
indices as defined by \citet{T98} and \citet{WO97}. The strength of
the Lick/IDS as a function of age, metallicity, and individual
chemical abundances has been calibrated by many authors for a simple
stellar population, i.e. a population formed in a single,
instantaneous burst \citep[e.g.][TMB03 hereafter]{w94, V99, TMB03},
and for more complicated star formation histories
\citep[e.g.][]{BC03}. These indices remain the most popular way to
extract information about the stellar ages and metallicities from the
integrated light of galaxies.
The errors on the indices were estimated from the uncertainties caused
by photon noise using the formula by \citet{Car98} and from
uncertainties due to the wavelength calibration, derived using
Monte-Carlo simulations. The variances were estimated from the
residuals between the observed spectrum and the $"$best template$"$,
which was obtained in the calculation of the velocity dispersion, and
which was previously broadened to match the line width of each galaxy.
For the clusters with $z> 0.6$, indices redward of 4500~\AA~ were
affected by telluric absorption in the atmosphere and by sky
subtraction residuals and were not measured. For the clusters with $z
\sim 0.45$ all Lick/IDS indices from H$\delta_A$ to H$\beta$ were
measured, as well as D4000. Each individual spectrum was visually
examined to check for indices affected by sky residuals or telluric
absorption in the atmosphere. All affected indices were discarded
from any subsequent analysis.
Line-strength indices are sensitive to the line broadening due to both
instrumental resolution and the stellar velocity dispersion. In order
to compare the galaxy spectra with stellar population models and to
compare the line-strength indices of galaxies with different velocity
dispersion, the indices need to be corrected to identical levels of
intrinsic Doppler and instrumental broadening.
Because the models we are using (see Sec.~\ref{sec.indices}) predict,
not only line-strength indices, but the whole spectral distribution,
we can degrade the synthetic
spectra to the resolution of the data. We decided to broaden all of
the observed and synthetic spectra to a final resolution of
325~km~s$^{-1}$ (including the velocity dispersion of the galaxy and
the instrumental resolution) before measuring the indices. Galaxies
with a velocity dispersion higher than $\sim$ 315~km~s$^{-1}$ could
not be broadened, but the number of galaxies with velocity dispersions
above this limit is very small and, therefore, we decided to include
them on the plots, although they have not been included in the data
analysis.
One of the problems of using Lick/IDS-based models
(e.g., Worthey 1994; Thomas, Maraston \& Bender 2003)
is that the data need to be transformed to the spectrophotometric system of
the Lick/IDS stellar library.
To do this, it is common to observe stars from the Lick/IDS library using the
same instrumental configuration than for the science objects and to derive
small offsets between the indices measured in those stars and the ones from Lick/IDS. When
analyzing data at high redshift, this is of course impossible.
In principle, no further corrections to the indices are required when
comparing data with stellar population models using flux-calibrated
libraries.
Although we do not have to apply the offsets to our indices, we have
computed them using the stars in common between MILES and the Lick/IDS
library because it may be useful for other studies. The final offsets
and the comparison can be found in Appendix~\ref{lickoffsets}
\footnote{Note that these offsets will not correct for any systematic
effect due to a not-perfect calibration in the data. They are only
useful to correct the fitting-function-based models from the
non-perfect calibration of the Lick/IDS stars.}.
Some of the Lick/IDS indices are affected by emission lines. In
particular, emission, when present, fills the Balmer lines, lowering
the values of the indices and, hence, increasing the derived age.
High-order Balmer indices (H$\delta$ and H$\gamma$) are much less
affected by emission than the classic index H$\beta$ \citep{WO97}, but
nevertheless still affected. To correct for
emission, two different approaches are normally adopted: First,
assume a correlation between the equivalent width of some other
emission line and the emission in the Balmer line
\citep[e.g.][]{T00b}. Second, fit an optimal template and
subtract the emission directly from the residuals. \citet{Nel05} have
shown that the first approach suffers from significant uncertainties,
in part because there are almost certainly several competing sources
of ionization in early type galaxies. The second approach requires
that the fit of the optimal template to the individual spectrum is
very good. The S/N of our individual spectra simply do not allow us to
explore that option. Therefore, instead of trying an emission
correction to the Balmer lines, we have analyzed the differences in
the results by first eliminating {\it all} the galaxies showing {\it
any} emission. It is re-assuring to see that none of our conclusions
change when the (weak)
emission line galaxies are excluded (we remind the reader than the
galaxies with strong emission lines have been excluded from the
analysis).
Table \ref{line-strength}, available at the CDS, lists the measured line-strength indices in our sample
of galaxies with non-or weak emission lines. A portion of the table
is shown here to show its content an structure.
\begin{table*}
\caption{Line-strength indices in our sample of red-galaxies with S/N(\AA)$>$10 and no- or weak-emission lines. The number between brackets after
the indices values indicates the presence (1) or not (0) of sky-subtraction residuals or telluric absorptions inside the definition passband of the
index. Only those indices with labels (0) are used in our analysis. Type: Indicate the presence (2) or not (1) of weak ([OII]$<$7\AA) emission
lines. Last column lists the measured velocity dispersion and its error.
This is only a portion of
the Table, shown for guidance regarding its format and content. The full table is electronically
available at CDS and at http://www.ucm.es/info/Astrof/psb/ediscs.html.}\label{line-strength}
\begin{tabular}{lrrrrrrrrrrrrr}
\hline\hline
& \multicolumn{1}{c}{D4000}& \multicolumn{1}{c}{H$\delta_A$}&\multicolumn{1}{c}{H$\delta_F$}&
\multicolumn{1}{c}{CN$_2$}&\multicolumn{1}{c}{Ca4227}&\multicolumn{1}{c}{G4300}&\multicolumn{1}{c}{H$\gamma_A$}\\
\hline
1018471-1210513&1.83$\pm$0.01 (1) &1.28$\pm$0.41 (0) &2.11$\pm$0.27 (0) &0.027$\pm$0.015 (0)&
1.27$\pm$0.23 (0) &2.71$\pm$0.43 (0) &$-1.53\pm$0.47 (0)\\
1018464-1211205&2.22$\pm$0.02 (1) &$-0.18\pm$0.69 (0) &0.84$\pm$0.47 (0) &0.038$\pm$0.024 (0)&
0.87$\pm$0.38 (0) &4.86$\pm$0.65 (0) &$-4.75\pm$0.81 (0)\\
1018467-1211527&2.13$\pm$0.01 (0) &$-0.97\pm$0.29 (0) &0.63$\pm$0.19 (0) &0.108$\pm$0.010 (0)&
0.48$\pm$0.16 (0) &5.10$\pm$0.26 (0) &$-5.55\pm$0.33 (0)\\
1018401-1214013&1.98$\pm$0.02 (0) &$-0.57\pm$0.65 (0) &0.40$\pm$0.45 (0) &0.072$\pm$0.022 (0)&
0.53$\pm$0.37 (0) &7.13$\pm$0.57 (0) &$-4.71\pm$0.76 (0)\\
\hline\hline
&\multicolumn{1}{c}{H$\gamma_F$}&\multicolumn{1}{c}{Fe4383}&\multicolumn{1}{c}{Ca4455}&\multicolumn{1}{c}{Fe4531}&
type&\multicolumn{1}{c}{$\sigma\pm$err}&\\
1018471-1210513 & 0.52$\pm$0.28 (0) &3.71$\pm$0.68 (0) &0.67$\pm$0.38 (0) &3.28$\pm$0.58 (0) &2 &245.9$\pm$15.8&\\
1018464-1211205 &$-2.01\pm$0.52 (0) &4.10$\pm$1.09 (0) &0.91$\pm$0.60 (0) &3.47$\pm$0.93 (0) &1 &279.9$\pm$27.6&\\
1018467-1211527 &$-1.73\pm$0.21 (0) &3.27$\pm$0.44 (0) &0.98$\pm$0.24 (0) &3.03$\pm$0.38 (0) &1 &211.1$\pm$14.8\\
1018401-1214013 &$-0.29\pm$0.45 (0) &1.77$\pm$1.06 (0) &0.71$\pm$0.57 (0) &1.37$\pm$0.91 (0) &1 &129.2$\pm$21.0\\
\hline
\end{tabular}
\end{table*}
\subsection{The local sample \& aperture correction}
\label{localsample}
To increase the time baseline of our analysis, we compare the EDisCS
spectra with 36 early-type galaxies (ellipticals and
lenticulars) in the Coma cluster at redshift $z=0.02$. The
characteristics of this sample are described in \citet{SB06a}. Because
the galaxies were selected morphologically we
checked first that all the objects belong to the red-sequence of this
cluster, using the colours and magnitudes from \citet{Mob01}. We are
aware that the comparison with the Coma cluster is probably not the
most appropriate, as the the velocity dispersion of this cluster
exceeds that of all the clusters in our sample at intermediate
redshifts. For this reason, we will base all the conclusions of this paper in the
intercomparison of the EDisCS clusters. The local sample is included here
to show that some of our results can be extrapolated to
the local Universe, where higher S/N spectra can be obtained. One of the
main problems when comparing observations at different redshifts is
that, for a fixed aperture, one is sampling different physical regions
within the galaxies. Early-type galaxies show variations in their
main spectral characteristics with radius and, therefore, a correction
due to these aperture differences is necessary. In order to compare
directly with the sample at medium- and high-redshift, we extracted
the 1D spectra in the same way as the EDisCS spectra, inside an
aperture equal to the FWHM of the spatial profile. However, aperture
effects are not entirely mitigated via such an extraction, as the
EDisCS spectra were observed with a 1$^{\prime\prime}$-wide slit,
equivalent to a much larger physical aperture at the redshift of the
Coma cluster. \citet{Jor95}, \citet{Jor97} and \citet{J05} derived
aperture corrections using mean gradients obtained in the
literature.
The index corrected for aperture effects
can be obtained as $\log (\rm index)_{\rm corr}=\log(\rm index)_{\rm ap}+
\alpha \log \frac{\rm r_{\rm ap}}{\rm r_{\rm nor}}$ for those indices
measured in \AA~ and ${\rm index}_{\rm corr}= {\rm index}_{\rm ap} + \alpha \log
\frac{\rm r_{\rm ap}}{\rm r_{\rm nor}}$ for molecular indices measured in
magnitudes, where ${\rm r_{\rm nor}}$ is the final normalised aperture,
and $r_{\rm ap}$ is the equivalent circular aperture, obtained
as 2 ${\rm r}_{\rm ap} = 1.025\times 2(xy/\pi)^{1/2}$, being ${x}$ and ${y}$
the width and length of the rectangular aperture.
J{\o}rgensen (1995, 1997) calculated $\alpha$ parameters
for a large subset of Lick indices but, in some cases, using the gradients
measured in a very small sample of galaxies.
In this work, we have taken advantage of the large sample
of galaxies with measured line-strength gradients published in
\citet{SB06c}, \citet{SB07} and \citet{Jab07} to calculate new
aperture corrections. These also include corrections for the
higher-order Balmer lines that have not been published before, as far
as we are aware.
Appendix~\ref{appendix.aperture}
lists the new $\alpha$ parameter calculated in this paper.
We correct all our indices to
mimic the physical aperture of the slit used to observe the galaxies
at $z=0.75$. The aperture corrections ($\alpha \log \frac{\rm r_{\rm ap}}
{\rm r_{\rm nor}}$) for all the indices at the
different redshift bins are listed in Table
\ref{aperture.corrections}.
\begin{table*}
\centering
\begin{tabular}{rrrrrr}
Index & Coma & $z=0.45$ & $z=0.55$ & $z=0.75$ &correction type\\
\hline
\hline
H$\delta_A$ & 1.031 & 0.063 & 0.016 & 0.00 & additive\\
CN$_1$ & $-0.083$ &$-0.005$ &$-0.001$& $0.00$ & additive\\
Ca4227 & 0.856 & 0.990 & 0.997 & 1.0 & multiplicative\\
G4300 & 0.914 & 0.995 & 0.998 & 1.0 & multiplicative\\
H$\gamma_F$ & 0.623 & 0.038 & 0.009 & 0.0 & additiva\\
Fe4383 & 0.817 & 0.987 & 0.996 & 1.0 & multiplicative\\
Ca4455 & 0.726 & 0.980 & 0.995 & 1.0 & multiplicative\\
Fe4531 & 0.876 & 0.992 & 0.998 & 1.0 & multiplicative\\
C4668 & 0.676 & 0.976 & 0.994 & 1.0 & multiplicative\\
H$\beta$ & 1.179 & 1.010 & 1.000 & 1.0 & multiplicative\\
\hline
\end{tabular}
\caption{Aperture correction for Lick/IDS indices measured in our sample.
The correction for the molecular indices and for the higher-order Balmer lines
is additive while the correction for
the atomic indices is multiplicative. The aperture correction was only applied
to the Coma galaxies, as it is very small for the other redshifts.
The type of correction is indicated
in the last column.\label{aperture.corrections}}
\end{table*}
Line-strength gradients show large variations between early-type
galaxies \citep[see, e.g.][among others]{Car93, Gor90, DSP93, Hall98, SB06c, Kun06, Jab07},
and the slope of the
gradients does not seem to correlate clearly with any of their other
properties. For this reason, we use the mean gradient to compute the
aperture corrections for all the galaxies. However, in order to
calculate the error in the aperture correction due to the fact that
early-type galaxies show a large variation in the slope of their
gradients, we perform a series of Monte Carlo simulations where the
mean index-gradient was perturbed by a random amount, given by a
Gaussian distribution with $\sigma$ equal to the typical RMS-
dispersion in the gradients
The errors in the aperture correction calculated this way are also
indicated in Table~\ref{aperture.corrections}. In some cases
(e.g., higher-order Balmer lines), these errors are very large. In fact,
despite the large mean aperture correction for H$\delta$ and
H$\gamma$ indices, the aperture correction is compatible, within
those errors, with being null. These errors have been
added quadratically to the errors of the indices for the Coma
galaxies.
For the 0.45 and 0.55 bins, the error in the aperture
correction due to the scatter among the mean gradients is negligible
(less than 1\% of the total correction) and we do not list them.
Gradients might evolve with redshift. That is the reason why we
correct the indices in the Coma cluster to the same equivalent
aperture as the highest redshift bin instead of correcting the highest
redshift measurements as is commonly done. This way, the correction is
performed to the galaxies where the gradients used to derive the
aperture correction have been measured.
\subsection{Stacked spectra}
\label{sec.stacked}
The degeneracy between age and metallicity effects on galaxy
colours could well affect the interpretation of their colour-magnitude
diagrams. This degeneracy can be partially broken by using a
combination of two or more spectral indices chosen for their
different sensitivities to age and metallicity. The S/N of our galaxy
spectra is not high enough to do this analysis on an
individual basis. Therefore, in order to derive the evolution with
time of the galaxy mean ages and chemical abundances, we stacked the
galaxy spectra in each of the 0.45, 0.55 and 0.75 redshift bins.
We made sure that the distribution of galaxy velocity dispersions ($\sigma$)
in all the different redshift intervals is similar (Fig.~\ref{distribut.sigma.fig}).
This a prerequisite to any further
comparison between the three redshift bins, as most line-strength
indices are strongly correlated with this parameter
\citep[e.g.][]{G93}. To explore the possible dependence of star
formation history on galaxy mass, we distinguish between galaxies with
$\sigma$ higher and lower than 175km~s$^{-1}$ in all three redshift
groups. We perform a Kolmorogov-Smirnov test comparing the
distribution of $\sigma_{\rm s}$ at different redshifts to look for
possible significant differences. We performed the test separately
for galaxies with $\sigma $ larger and smaller than 175~km~s$^{-1}$ and found
them compatible with being drawn from the same distribution.
Before adding them, we normalize all spectra by their mean flux in the region between
3900\AA~ and 4400\AA, to avoid a bias towards the indices of the most
luminous galaxies. Finally, we co-add them, clipping out all the
pixels deviating more than 2-$\sigma$ from the mean.
Figure~\ref{StackedSpectra.fig} displays the resulting 6 stacked
spectra for the three redshift bins and the two velocity dispersion
regimes.
\begin{figure}
\centering
\resizebox{0.4\textwidth}{!}{\includegraphics[angle=-90]{distribution.sigma.new.ps}}
\caption{Velocity dispersion distribution of the individual spectra stacked
in the different redshift bins. From bottom to top:
$z$=0,0.45,0.55,0.75.}
\label{distribut.sigma.fig}
\end{figure}
\begin{figure}
\resizebox{0.5\textwidth}{!}{\includegraphics[angle=-90]{StackedSpectra.ps}}
\caption{Final stacked spectra for our three redshift and velocity
dispersion bins. The shaded areas identify the central bands of the
four indices used in our spectral analysis.}
\label{StackedSpectra.fig}
\end{figure}
Earlier works have studied the evolution of red-sequence galaxies as a
function of magnitude (e.g. De Lucia et~al. 2004; De Lucia et~al.\
2007; Rudnick et~al.\ 2008, in preparation). These studies have put
the boundary between faint and bright galaxies at Mv$=-20$. Assuming
a formation redshift of 3 followed by passive evolution, our
$\sigma$=175~km~s$^{-1}$ cut corresponds to Mv$\sim-$20.0, $-20.2$ and
$-20.2$ mag at $z=0.45$, 0.55 and 0.75, respectively (see
Figure~\ref{faber.jackson}). As can be seen, the magnitude cut is not
very different between our study and the above mentioned photometric
studies. However, those studies reach much fainter magnitudes in
their $"$faint$"$ bin.
\begin{figure}
\resizebox{0.4\textwidth}{!}{\includegraphics[angle=-90]{faber.jackson.wf.ps}}
\caption{Relation between the absolute magnitude Mv and the velocity
dispersion for our sample of galaxies in the three considered redshift
bins. The right label shows the absolute magnitude Mv evolved
passively to $z=0$ using \citet{BC03} models at solar
metallicity. The vertical dashed line indicates the position corresponding
to our $\sigma$-cut (175 km~s$^{-1}$) while the horizontal line marks
the mean magnitude for the galaxies with a sigma between 160 and 180
km~$^{-1}$.}
\label{faber.jackson}
\end{figure}
Velocity dispersions and line-strength indices for the stacked spectra
were measured using the same techniques as for the individual spectra.
Errors on the indices were calculated with the formula of
\citet{Car98}, using the signal-to-noise of the stacked spectra.
These errors do not reflect the differences between the spectra added
in each bin, which are larger than the formal errors obtained using
the signal-to-noise ratio. However we do not intend to study the
distribution of galaxy properties but rather their mean values. To
explore the robustness of our results to errors in velocity
dispersion, we performed 20 Monte Carlo simulations in which the
individual galaxy velocities were randomly perturbed following a
Gaussian error distribution. After each simulation, the spectra were
stacked again, indices were measured, and their mean and
RMS-dispersion were calculated. Fig.~\ref{sim} compares the indices
obtained in the original stacked spectra with the mean indices
obtained from the 20 simulations. The separation in low- and
high-$\sigma$ galaxies is robust to the errors in velocity dispersion.
When the RMS-dispersion for all the simulated galaxies is larger than
the error we have calculated for the individual indices, we add the
quadratic difference as a residual error to the original error in the
index. We have also checked that the mean values of the individual
indices for all the stacked galaxies is compatible, within the errors,
with the index measured in the stacked spectra.
The Lick/IDS indices measured in the stacked spectra as well as their errors are listed in
Table~\ref{Lick.stacked}.
\begin{table*}
\begin{tabular}{l|rrrrrrrrrrr}
\hline\hline
Redshift group & &\multicolumn{1}{c}{D4000}&\multicolumn{1}{c}{H$\delta_A$}&\multicolumn{1}{c}{H$\delta_F$}&
\multicolumn{1}{c}{CN$_2$}&\multicolumn{1}{c}{Ca4227}&\multicolumn{1}{c}{G4300}&\multicolumn{1}{c}{H$\gamma_A$}&
\multicolumn{1}{c}{H$\gamma_F$}&\multicolumn{1}{c}{Fe4383}&\multicolumn{1}{c}{$\sigma$} \\
\hline
& &\multicolumn{1}{c}{\AA}&\multicolumn{1}{c}{\AA}&\multicolumn{1}{c}{\AA}&\multicolumn{1}{c}{mag}&
\multicolumn{1}{c}{\AA}&\multicolumn{1}{c}{\AA}&\multicolumn{1}{c}{\AA}&\multicolumn{1}{c}{\AA}&\multicolumn{1}{c}{\AA}&\multicolumn{1}{c}{kms$^{-1}$}\\
0.45 & $\sigma>175$ km/s & 2.044 &$-0.433$ &0.894 &0.067&0.932 &4.589& $-4.114$ & $-0.704$ & 3.662 & 233.1\\
& & 0.004 & 0.140 &0.094 &0.005&0.076 &0.133& 0.161 & 0.098 & 0.220 & 7.2\\
0.45 & $\sigma<175$ km/s & 2.045 &0.103 &1.074 &0.036&0.841 &4.053& $-3.145$ & $-0.177$ & 3.380 & 122.3\\
& & 0.004 &0.139 &0.094 &0.005&0.077 &0.136& 0.158 & 0.096 & 0.222 & 12.0\\
0.55 & $\sigma>175$ km/s & 2.051 &$-0.075 $&1.143 &0.065&0.847 &4.600& $-3.779$ & $-0.437$ & 3.534 & 218.1 \\
& & 0.002 & 0.087 &0.058 &0.003&0.048 &0.083& 0.100 & 0.061 & 0.137 & 9.0\\
0.55 & $\sigma<175$ km/s & 1.995 & 0.045 &0.960 &0.028&0.757 &4.341& $-3.138$ & $-0.114$ & 3.138 & 134.9\\
& & 0.004 & 0.140 &0.095 &0.005&0.078 &0.135& 0.159 & 0.096 & 0.224 & 10.1\\
0.75 & $\sigma> 175$ km/s & 2.008 & 0.699 &1.400 &0.057&0.824 &4.381& $-3.061$ & $-0.234$ & 2.877 & 233.2\\
& & 0.003 & 0.104 &0.070 &0.004&0.059 &0.102& 0.120 & 0.073 & 0.171 & 6.2\\
0.75 & $\sigma< 175$ km/s & 1.987 & 0.453 &1.163 &0.034&0.826 &4.244& $-2.963$ & $-0.016$ & 2.796 & 154.2\\
& & 0.003 & 0.130 &0.089 &0.004&0.073 &0.128& 0.149 & 0.091 & 0.213 & 8.1\\
\hline
\end{tabular}
\caption{Line-strength indices and velocity dispersion measured in the stacked spectra. The second row of
each line lists the errors. Last column show the velocity dispersion measured in the different stacked spectra.\label{Lick.stacked}}
\end{table*}
\begin{figure}
\centering
\resizebox{0.25\textwidth}{!}{\includegraphics[angle=-90]{compara.cn2.new.ps}}
\resizebox{0.25\textwidth}{!}{\includegraphics[angle=-90]{compara.fe4383.new.ps}}
\resizebox{0.25\textwidth}{!}{\includegraphics[angle=-90]{compara.hgf.new.ps}}
\caption{Comparison between the indices measured in the stacked
spectra and the mean index calculated in the 20 stacked spectra
obtained with Monte Carlo simulations as described in the text to
analyze the robustness of our separation of galaxies with $\sigma$ due
to errors in this parameter. The errors in the $y$-direction represent
the rms of all the 20 measured indices, while the errors in the
$x$-direction represent the errors in the index due to the S/N of the
stacked spectra. Big and small symbols show the indices measured in
the stack with $\sigma$ larger than 175 kms$^{-1}$ and smaller than $\sigma< 175$ kms$^{-1}$
respectively. The meaning of the different symbols is indicated in the
inset.}
\label{sim}
\end{figure}
\section{Stellar population models}
\label{sec.indices}
In this study we compare our measured values with the models by
Vazdekis et al.\ (2008, in preparation, V08 hereafter\footnote{The models are
publicly available at
http://www.ucm.es/info/Astrof/miles/models/models.html}). These
models are based on the MILES stellar library \citep{SB06_miles}. The
spectra from this library have a resolution of 2.3\AA~, constant along
the whole wavelength range, and are flux-calibrated. Thanks to this,
the models predict not only individual indices, but the whole spectral
energy distribution from 3500 to 7500\AA~ as a function of age and
metallicity, for ages between 0.1 and 17.78 Gyr and metallicities from
[Z/H]=$-1.68$ to +0.2 dex\footnote{In the normalization to the solar values
a solar metallicity Z$_{\odot}$=0.02 has been used}.
However, the chemical composition of stars in the MILES library (as
in the rest of empirical libraries included in stellar population models)
matches that of the solar-neighborhood.\footnote{Although the
detailed chemical composition of all the stars in the MILES is
unknown, it is reasonable to assume that this is the case.} This
means that the models, in principle, can only predict accurate ages
and metallicities for stellar populations with the same chemical
patterns as the solar vicinity. We know that this
condition does not apply to bright nearby early-type galaxies
\citep[see review by][]{W98}), where Mg/Fe and maybe Ti/Fe, Na/Fe, N/Fe
and C/Fe are enhanced with respect to the solar values. This may
result in systematics errors in the measured ages and metallicities
\citep[see][] {W98, TMB03}. In order to overcome this problem, we
calibrate the models for different chemical compositions using the
method first introduced by \citet{Tan98} and \citet{T00b}. This method uses stellar
atmospheres to characterize the variation of the different indices to
relative changes of different chemical species. We first interpolate
the existing models to make a grid with 168 ages from 1 Gyr to 17.8
Gyr in steps of 0.1 Gyr and 209 metallicities from $-1.68$ to +0.4 in
steps of 0.1. Then, we modify each index according to their
fractional response to variations of different elements using (from
Trager et al.):
\begin{equation}
\frac{\Delta I}{I}=\left (\prod_i (1+R_{0.3}(X_i))^{[X_i/H]/0.3} \right) -1,
\end{equation}
where $R_{0.3}(X_i)$ is the response function for element $i$ at
$[X_i/H]=+0.3$ dex. As in Trager et al.\ , we also consider that the
fractional light contribution from each stellar component is 53\% from
cool giant stars, 44\% from turnoff stars and 4\% from cool dwarfs
stars. We use the calibrations by \citet{Korn05} instead of the ones
by \citet{TB95} (used by Trager et al.) because they include the
higher order Balmer lines H$\delta$ and H$\gamma$, and they are
computed at other metallicities different from solar. However, the
differences between the two studies are very small \citep{Korn05}. Following the approach of several
previous authors, we do not change all the elements individually but
we assume than some of them are linked by nucleosynthesis and,
therefore, change them in lock-step. We built models where N, Ne, Na,
Mg, Si and S are enhanced by 0.3 dex with respect to Fe while C is
enhanced by +0.15 dex. The reason that C is only enhanced by +0.15
is that enhancing C by +0.3 dex brings the C/O ratio very close to
the values at which a carbon star is formed \citep[see][for a
discussion]{Hou02, Korn05}. Ca and the Fe peak elements are
depressed to keep the overall metallicity constant.
\footnote{Despite the fact that Ca is an $\alpha$-element, theoretically linked
with the overabundant elements as Mg, measurements show that it may be
depressed in elliptical galaxies (although see \citet{Pro05} for a
different point of view). We follow Trager et al.\ 2000 and include
this element in the depressed group.} To obtain response functions
for enhancements different from +0.3 dex we, again, follow \citet{T00a}:
We first calculate $\Delta$[Fe/H] and $\Delta$[E/Fe] using
$\Delta$[Fe/H]=$-$A$\Delta$[E/Fe] = $-\frac{A}{1-A}\Delta$[E/H], where E
represents the {\it enhanced elements}. $A$ is the response of the
enhanced elements to changes in [Fe/H] at fixed [Z/H]. For the chosen
enhanced model, $A =0.929$ (Trager et al. 2000). Then, we scale
exponentially the response functions by the appropriate element
abundance.
We built models with enhancements from [E/Fe]=$-0.1$ to $0.5$ in steps
of 0.05.
Because we are not working at the Lick/IDS resolution, in principle,
we should not be using \citet{Korn05} response functions to compute
the sensitivity of different indices to variations of chemical
abundance ratios, as they were computed at this resolution. However,
\citet{Korn05} showed that the influence of the resolution on the
response functions is very small.
Note that the models used here (as well as most existing models in the
literature) {\it do not} include isochrones with chemical abundance
ratios different from solar. The effect of the different chemical
abundance ratios is only included in the atmospheres. The influence
that the inclusion of $\alpha$-enhanced isochrones may have in the
final predictions is still unclear, especially at super-solar
metallicities, but some studies have shown
that it is
much smaller than the one in the model atmospheres \citep{Coel07},
at least for line-strength indices at wavelengths shorter than
$\sim$5750.
We want to caution the reader that the absolute values of ages
obtained directly with stellar population models are subject, not only
to errors in the data (which are taken into account) but also to
errors in the stellar population models. Stellar evolutionary models
are still affected by uncertainties that leave room for improvement
\citep[see, e.g.][]{Cas05}, as illustrated by the {\it non-negligible}
differences still existing among the results provided by different
theoretical groups. Furthermore, it must be noted that the oldest
ages of the models we are using (17.78 Gyr) are older than the current
age of the Universe. The derivation of very old spectroscopic ages,
inconsistent with the ages derived from colour-magnitude diagrams for
globular clusters and with the age of the Universe, was first pointed
out by \citet{Gib99} and is a well-known problem in the community.
Some solutions have been proposed, such as the inclusion of atomic
diffusion in the stellar evolutionary models or the use of
$\alpha$-enhanced isochrones \cite[see][] {V01}, although none of
these have been implemented in publicly available stellar population
models. \citet{Sch02} showed, for the particular case of 47Tuc, that
the luminosity function of the red giant branch is underestimated in
the stellar evolutionary models and that the use of the observed
luminosity functions instead of theoretical ones results in derived
ages for this cluster consistent with the age of the Universe and with
those derived directly from the colour-magnitude diagram. A similar
effect in super-solar metallicity models would cause spectroscopic
ages to be 30\% too high (see Schiavon et~al.\ 2002 for details). It
is beyond the scope of this paper to discuss these uncertainties in
stellar population models, but it is clear that conclusions based on
the absolute values of age are simply too preliminary. Relative
differences in age and metallicity are more reliable than absolute
values, and we will therefore base our interpretations on relative
values.
Lick/IDS indices, as well as colours,
respond to variations in both age and chemical abundances, but the
relative sensitivity of the different indices to these two parameters
is not the same. In order to break the existing degeneracy between age
and metallicity, it is necessary to combine two or more indices. In
what follows, for the main analysis, we use 4 indices: Fe4383, CN$_2$,
H$\delta_A$ and H$\gamma_F$. We choose these because, of all the
Lick/IDS indices that could be measured in {\it all} galaxies, they
are the most sensitive to variations of age (H$\delta$ and H$\gamma$)
and total metallicity (CN$_2$, Fe4383). TMB03 recommend CN and Fe4383
as the best blue indices to calculate $\alpha$/Fe abundance ratios.
Furthermore, we choose H$\gamma_F$ instead of H$\gamma_A$ because the
ages measured with H$\gamma_A$ are systematically younger than those
measured with H$\gamma_F$ or H$\beta$ when $\alpha$-enhanced models
are used \citep[][]{TMK04}. As the origin of these differences is
unclear, we follow the advice by \citet{TMK04} and use H$\gamma_F$,
despite the higher photon noise in this index compared to its wider
version (H$\gamma_A$).
\section{Age \& Metallicity}
We derive age, metallicity and the ratio of $\alpha$-element
enhancement [E/Fe] for our stacked spectra comparing our
four selected indices (H$\delta_A$, H$\gamma_F$, CN$_2$, and Fe4383) with the models
by V08 using a $\chi^2$ minimization routine.
We find that the
derived ages are independent of the chosen Balmer index (H$\delta_{\rm A}$
or H$\gamma_{\rm F}$). The resulting ages, metallicities, and [E/Fe]
are listed in Table~\ref{alphayz}. Index-index
diagrams comparing the indices measured in the stacked spectra with
the predictions for single stellar population models
by V08 are shown Fig.~\ref{index.index.v07}. In each panel, [E/Fe] is chosen to be as close as
possible to the values given in Table~\ref{alphayz}.
\begin{figure*}
\resizebox{0.4\textwidth}{!}{\includegraphics[angle=-90]{cn2.hgf.massive.new2.v07.ps}}
\resizebox{0.4\textwidth}{!}{\includegraphics[angle=-90]{cn2.hgf.nomassive.new2.v07.ps}}
\resizebox{0.4\textwidth}{!}{\includegraphics[angle=-90]{fe4383.hgf.massive.new2.v07.ps}}
\hspace{3.3cm}
\resizebox{0.4\textwidth}{!}{\includegraphics[angle=-90]{fe4383.hgf.nomassive.new2.v07.ps}}
\caption{Index-index diagrams for the indices measured in the stacked
spectra at different redshifts. Left panels (big symbols) show
measurements on the stacked spectra of galaxies with $\sigma$ larger than 175
km~s$^{-1}$ while right panels (small symbols) show the same measurement for galaxies with
$\sigma$ smaller than 175 km~s$^{-1}$. The different redshifts bins are
represented as different colours (and different symbol shapes);
$z=0.75$: blue triangles; $z=0.65$: green stars; $z=0.45$: red
circles; $z=0.02$: orange squares. Model grids of constant age (solid
lines) and constant metallicity (dashed lines) from V08 with
[E/Fe]=+0.35 (for the most massive galaxies ) and [E/Fe]=+0.1 (for the
lower sigma bins) are superimposed. The ages and metallicities of the
different models are indicated in the Figure.}
\label{index.index.v07}
\end{figure*}
Although the selection of our sample has been done using colours, many
previous studies of the red-sequence were restricted to
morphologically classified early-type galaxies. To compare with those,
the analysis in this section has been repeated for
the subset of red-sequence galaxies that are morphologically
classified as E or S0 galaxies. For the clusters imaged with the ACS
(see Table \ref{tb:clusterlist}), we use their visual classification
\citep{Des07}. For the others, we apply the selection criterion of
Simard et al. (2008), based on the bulge fraction derived from our VLT
I-images (see Sec.\ref{sec.morph} for the criteria to select
early-type galaxies).
The last three rows of Table~\ref{alphayz} show the SSP-parameters derived
for the red-early-type galaxies. The first thing that can be seen is that the SSP-parameters
for the whole red-sequence and for the morphologically classified early-type galaxies are
compatible within the errors. Therefore, we will not discuss further the possible differences
and will restrict our analysis to the complete red-sequence sample.
\begin{table*}
\centering
\begin{tabular}{lrrr|rrr}
\hline
& \multicolumn{3}{c}{$\sigma> 175$ km~s$^{-1}$} & \multicolumn{3}{c}{$\sigma < 175$ km~s$^{-1}$} \\
& Age~~~~~~ & [Z/H]~~~~~~ & [E/Fe]~~~~~ & Age~~~~~~ & [Z/H]~~~~~~ & [E/Fe]~~~~~\\
& Gyr~~~~~~ & & & Gyr~~~~~~ & & \\
\hline
\hline
Coma & $7.90\pm 1.81$ & $-0.03\pm 0.06$&$0.40\pm 0.03$ & $5.80\pm 0.36$ &$-0.11\pm 0.03$&$0.31\pm 0.04$\\
$z=0.45$ & $5.60\pm 1.05$ & $-0.01\pm 0.07$&$0.35\pm 0.09$ & $3.20\pm 0.64$ &$-0.05\pm 0.13$&$0.16\pm 0.12$\\
$z=0.55$ & $3.40\pm 0.52$ & $ 0.11\pm 0.07$&$0.35\pm 0.06$ & $3.40\pm 0.81$ &$-0.13\pm 0.09$&$0.11\pm 0.13$\\
$z=0.75$ & $2.70\pm 0.38$ & $ 0.18\pm 0.11$&$0.46\pm 0.06$ & $3.10\pm 0.83$ &$-0.08\pm 0.14$&$0.30\pm 0.21$\\
\hline
$z=0.45$ & $5.70\pm 2.42$& $ 0.02\pm 0.12$&$0.45\pm 0.10$ &$2.80\pm 0.46 $ &$ 0.01\pm 0.11$& $0.23\pm 0.14$\\
$z=0.55$ & $3.10\pm 0.62$& $ 0.11\pm 0.12$&$0.30\pm 0.10$ &$2.90\pm 0.42$ & $-0.04\pm 0.10$& $0.25\pm 0.11$ \\
$z=0.75$ & $4.60\pm 2.32$& $-0.07\pm 0.14$&$0.55\pm 0.10$ &$2.50\pm 0.34$ &$ 0.11\pm 0.13$& $0.24\pm 0.15$\\
\hline
\end{tabular}
\caption{First 4 rows: Ages (measured in Gyr), metallicities [Z/H] and [E/Fe]
abundances for the stacked spectra, in different redshift bins,
of the red-sequence galaxies, measured using V08 models and the indices H$\gamma_F$, Fe4383 and
CN$_2$. The spectra have been stacked separating galaxies with
$\sigma$ lower than 175 km~s$^{-1}$ (right side) and larger than 175
km~s$^{-1}$ (left side). The parameters have been obtained iteratively as
described in the text. Last three rows: Ages, metallicities
and [E/Fe] derived for the stacked spectra, at different redshifts, of
morphologically classified E and S0 galaxies.\label{alphayz}}
\end{table*}
\subsection{Massive galaxies}
It can be seen in Table~\ref{alphayz} and Fig.~\ref{index.index.v07}
that the age difference between the redshift bins of the most massive
galaxies ($\sigma > 175$ kms$^{-1}$) corresponds to the expected age
difference of the Universe at those redshifts. The absolute age
obtained from the models for these galaxies corresponds to a redshift
of 1.4. In other words, they are compatible with being formed at
$z>1.4$ and evolving passively since then. The metallicity measured
from CN$_2$ does not evolve either, as expected in a passive evolution
scheme.
When we look at the panels using Fe4383 instead of CN$_2$ we can see
that the most massive galaxies at $z=0.75$ seem to have a lower Fe4383
than predicted by passive evolution. \citet{J05} similarly found a
weaker Fe4383 index for more than half of the galaxies in a sample of
red-sequence galaxies (including those with $\sigma$ larger than 175 km~s$^{-1}$)
in the cluster RX J101522.7-1357 at redshift $z=0.83$. This result,
if confirmed, could be indicating that at least some massive galaxies
have experienced some chemical enrichment since $z=0.75$. It will be
necessary to measure other Fe-sensitive indices to confirm this
trend. Unfortunately, the wavelength range covered by our spectra does
not allow us to do this and, therefore, we will not discuss this further.
\subsection{Less-massive galaxies}
Contrary to their massive counterparts, galaxies with $\sigma <$
175~km~s$^{-1}$ do not show any evolution, within the errors, in age
or in metallicity between $z=0.75$ and $z=0.45$. They also evolve
less than expected from a pure passive scenario between $z=0.45$ and
$z=0.0$. A similar result was reported by \citet{Sch06} with a {\it
field} galaxy sample. Comparing galaxies from the DEEP2 survey around $z=0.8$ with an
SDSS local galaxy sample, they showed that the H$\delta_F$ variation
was less than predicted by passively evolving models. However, they do
not group galaxies by mass. Along the lines discussed by the authors,
our results suggest that either individual low-mass galaxies
experience continuous low levels of star formation, or that the
red-sequence is progressively built-up with new and younger small
galaxies. This latter hypothesis is supported by a number of recent
works \citep[e.g.][]{Bell04, Pog06, dL07, Har06, Fab07}. This
differential evolution for massive and less massive galaxies implies
that the {\it mean} difference in luminosity-weighted mean-age between
massive and intermediate-mass red-sequence galaxies increases with
time. This should be taken into account when studying the evolution
of the colour-magnitude relation with redshift.
Low-$\sigma$ galaxies show a lower value of [E/Fe] than high-$\sigma$
galaxies, in agreement with the results at low redshift. Most of the
$"$enhanced$"$ (E) elements we are considering here arise from massive
stars and the bulk of their mass is released in Type II supernova
explosions, while at least 2/3 of the Fe is released to the
interstellar medium by Type Ia supernovae, with a delay of $\sim$ 1
Gyr. Therefore, the ratio [E/Fe] has classically been used as a cosmic
clock to measure the duration of the star formation. The lower [E/Fe]
in low-$\sigma$ galaxies can be interpreted as a more extended star
formation history, just as found locally.
Table~\ref{alphayz} also shows that, within the errors, [Z/H] and
[E/Fe] do not vary with redshift for low-$\sigma$ galaxies.
Whether galaxies have experienced low-level star formation or new
galaxies have entered the red-sequence from the blue cloud, it is
still unclear how galaxies that have been forming stars until recently
have the same chemical composition as those where star formation was
quenched 2 Gyr previously (the lookback time between z$\sim$0.45 and
z$\sim$0.75). Answering this question is not trivial, as there are
multiple paths by which a galaxy may enter and leave the red-sequence.
Furthermore, one has to be careful when interpreting single-stellar
population equivalent parameters. While galaxy mean ages are biased
towards their last episode of star formation, the chemical composition
depends more strongly on the oldest population (see Serra \& Trager
2007 for a quantitative study). Therefore, galaxies with different
star formation histories can have similar [E/Fe] and [Z/H] if they
have formed the {\it bulk} of their stars on similar time-scales and with a
similar efficiency.
\section{Evolution of the index-$\sigma$ relations with redshift}
\label{sec.indices.mv}
The outcome of the previous section seems to contradict earlier
studies, in which the evolution of the index-$\sigma$ relation was
found compatible with a high-redshift formation and subsequent passive
evolution for all red-sequence galaxies, irrespective of their mass
range (Kelson et al. 2001). We will now demonstrate that our
index-$\sigma$ relation is also consistent with this scenario, but
that this analysis cannot provide robust constraints on the
star-formation histories of red galaxies. In fact, the evolution of
the index-$\sigma$ relation is also compatible with a more extended
star formation history for the intermediate-mass galaxies if the
progenitor-bias (i.e. the fact that the galaxies with more extended
star formation history (or quenched at later times) drop out of the red-sequence at high redshift
\citet{2000ApJ...541...95V}) is taken into account.
Figure~\ref{indices.sigma} displays the relation between H$\gamma_A$,
H$\gamma_F$, CN$_2$, and Fe4383 and the galaxy velocity dispersion,
for the Coma cluster and our EDisCS sample.
\begin{figure*}
\resizebox{0.5\textwidth}{!}{\includegraphics[angle=-90]{hda.sigma.todas.new2.ps}}
\resizebox{0.5\textwidth}{!}{\includegraphics[angle=-90]{cn2.sigma.todas.new2.ps}}
\resizebox{0.5\textwidth}{!}{\includegraphics[angle=-90]{hgf.sigma.todas.new2.ps}}
\resizebox{0.5\textwidth}{!}{\includegraphics[angle=-90]{fe4383.sigma.todas.new2.ps}}
\caption{Relation between line-strength indices and the velocity
dispersion for the galaxies in the three different bins. Solid
coloured lines represent the result of a linear fit to the data
forcing the slope to be the same as the one obtained for the galaxies
in the redshift bin at $z=0.45$. The black lines represent the
expected relation assuming that galaxies formed at $z_{\rm f}$=1.4
(dotted-dashed line), $z_{\rm f}=2$ (thick, dashed line), and $z_{\rm
f}$=3 (dotted line), and have evolved passively since then and
assigning a solar metallicity for galaxies with velocity dispersion of
300~km~s$^{-1}$. As can be seen, the evolution of the index-$\sigma$
relation is compatible with a scenario in which the stars formed at
$z> 1.4$ and evolved passively since then, except for the CN$_2$ index,
which cannot be reproduced by any of the proposed models (see text for details)}. However, the evolution of
these relations are also compatible with more complex scenarios (see
Sec.~\ref{ops}).
\label{indices.sigma}
\end{figure*}
Following \citet{Kel01} and \citet{J05}, among others, we first
calculate the best linear fit to the data using the galaxy sample at
$z=0.45$. Then, keeping the slope of the relation fixed, we evolve
its zero point with look-back-time.
This approach assumes that, if galaxies were coeval and evolving passively, the
slope of the relation would not change. In reality, {\it if} all the
galaxies in the red-sequence were coeval and evolving passively, we
would expect a small variation in the slope of the index-$\sigma$
relation, as the variation of the indices is not completely linear
with age. However, this variation would be {\it very} small over the
range of ages considered.
To calculate the lines of passive
evolution, we used the V08 models, assigning solar metallicity to the
galaxies with $\sigma=300$~km~s$^{-1}$, to match the observed
value of the metal-sensitive index Fe4383 at $z=0.45$. We show the best linear fits in
Fig.~\ref{indices.sigma}, obtained by minimizing the residuals in the
$y$-direction. We also show the expected evolution of the
index-$\sigma$ relation assuming three different formation redshifts:
$z_{\rm f}=$1.4, 2, and $3$. The value $z_{\rm f}=1.4$ is chosen as
it corresponds to the mean age measured in the stacked spectra of the
massive galaxies in the 0.75 galaxy group (see
Sec.~\ref{sec.stacked}). We only plot models with solar-scaled
chemical abundances.
Figure~\ref{indices.sigma} shows that a scenario where all stars form
at $z_{\rm f}>1.4$ and evolve passively afterwards is compatible with the
observations. The exception is CN$_2$ which we discuss below. In
order to analyze this more quantitatively, we performed a $t-$test,
comparing the linear fit values at $\sigma=200$~km~s$^{-1}$ (which is
approximately the mean of the distribution of $\sigma$) with the ones
predicted by passive evolution. The results are shown in
Table~\ref{table.t}. $t$-values higher than 1.9 would indicate that
the probability that we have rejected the null-hypothesis (prediction
and measurement are equal) by chance is less than $\sim$5\%, i.e., a
$t$-value higher than 1.9 implies that the passive scenario does not
reproduce our relations within the errors. We do not obtain such
$t$-values, implying that indeed a passive evolution model can
reproduce the evolution of the zero-point of the index-$\sigma$
relations from $z=0$ to, at least, $z$$\sim$0.75. Although we obtain
a slightly better agreement between model and data if we assume a
formation redshift above $2$, we do not find any statistically
significant difference from a formation redshift of 1.4. Noticeably,
formation redshifts lower that 1.4 produce an evolution of the
index-$\sigma$ relation significantly larger than the one observed.
The relation of the other indices with $\sigma$ is presented in
Appendix~\ref{appendix.indices}. The analysis of these indices gives
consistent results without adding any new information to our study,
but we show it for comparison purposes with eventual following
studies. We did not include CN$_2$ in the $t$-test procedure as the
stellar population models with solar-scaled chemical abundances cannot
reproduce the absolute values of this index. This is a well known
effect in nearby early type galaxies \citep{W98, SB03, Kel06, Sch06,
Grav07} and it is attributed to differences in the chemical
composition of these galaxies compared to the solar values. (Note that
in Sect.~\ref{sec.stacked} we used models where C/Fe and N/Fe are
enhanced with respect to the solar values in order to reproduce this
index).
Summarizing, we show here that, in agreement with previous works, the
evolution of the index-$\sigma$ relation is compatible with a scenario
where the red galaxies formed their stars at z$>$1.4 and have evolved
passively since. However, this conclusion has been reached assuming
that all red galaxies formed at the same time independently of their
mass. The results of Sec.~\ref{sec.stacked} argue against this.
Furthermore, numerous works \citep{dL04,dL07,Kod04} indicate that the
red sequence was not yet fully in place at z$\sim$1 and that it has
been growing since then. If this effect is taken into account, a more
complex star formation history is allowed while keeping the slope and
the tightness of the index-$\sigma$ relations. This was proposed by \citet{vDF01}
to explain the evolution of the magnitude
and the constancy and scatter of the colours on the red sequence.
\citet{Har06} showed that quenched models, where a constant star
formation is truncated at evenly spaced time intervals can explain the
evolution of the {\it mean} H$\delta$ of all the field red galaxies
between $z=1$ to $z=0$. However, they did not explore the dependence
of this evolution on galaxy mass. In order to study this aspect, we
have used the \citet{BC03} population synthesis models with a Salpeter
IMF and solar metallicity. We built a series of star-formation
histories starting at z$_{\rm f}$=2 where a constant rate of star
formation of 1 M$_{\odot}$/yr is quenched at different look-back
times. Whenever a galaxy satisfies our criteria to belong to the
red-sequence, we measure its indices.
Figure~\ref{SFH} shows the resulting line-strength indices assuming 3
different metallicities, $Z=$0.001, 0.004 and 0.02. We display, again,
the relation of the indices with $\sigma$ for each redshift bin
discussed in Sec.~\ref{sec.indices.mv}. While the index-$\sigma$
relations of the most massive galaxies are only well reproduced by a
scenario where star formation is truncated after 1 Gyr (i.e. the rest
of the star formation histories produce relations systematically
shifted compared to the observed one), less massive ones can be
described by a variety of star formation histories, in agreement with
our results of Sec.~\ref{sec.stacked}. Furthermore, this variety of
star formation histories is supported by the larger scatter in
metallicity and age values at a given mass of low-$\sigma$ galaxies
compared to that of the most massive ones \citep[e.g.][]{CRC00}. Some
studies have claimed that star formation histories of this nature
would have problems reproducing the colours of red-sequence galaxies.
As a sanity check (see Fig.~\ref{colors.sfh}) we verify that these
star formation histories reproduce the colours of the red-sequence.
\begin{figure*}
\resizebox{0.5\textwidth}{!}{\includegraphics[angle=-90]{hda.sfh.new3.ps}}
\resizebox{0.5\textwidth}{!}{\includegraphics[angle=-90]{hgf.sfh.new3.ps}}
\resizebox{0.5\textwidth}{!}{\includegraphics[angle=-90]{fe4383.sfh.new3.ps}}
\caption{Evolution of the relation of line-strength indices with
$\sigma$. We show with coloured, solid lines, the best linear fits to
the observations, fixing the slope to that obtained for the redshift
bin $z=0.45$ (see Sec.~\ref{sec.indices.mv}). Squares, diamonds,
and black stars represent the predicted indices for a constant star
formation rate starting at $z_{\rm f}=2$, for stellar populations with
metallicities Z=0.001,0.004 and 0.02, respectively. At each of these
metallicities, the sta r formation is truncated after 1 (largest
symbols), 2, 3, 4 and 5 (smallest symbols) Gyr.}
\label{SFH}
\end{figure*}
\begin{figure*}
\resizebox{0.5\textwidth}{!}{\includegraphics[angle=-90]{evolution.colors.new.ps}}
\caption{Measured $V-I$ vs $\sigma$ for the galaxies in the different
redshift bins. Symbols are the same as in Fig.~\ref{SFH}.}
\label{colors.sfh}
\end{figure*}
This, of course, does not prove that different galaxies have different
star formation histories, but it does demonstrate that more
complicated scenarios than pure passive evolution are compatible with
the index-$\sigma$ relations.
\begin{table*}
\centering
\begin{tabular}{rr rr| rr| rr|rr}
\hline
& & \multicolumn{2}{c}{linear fit}&\multicolumn{2}{c}{ $z_{\rm f}=1.4$} &\multicolumn{2}{c}{ $z_{\rm f}=2$}
&\multicolumn{2}{c}{ $z_{\rm f}=3$}\\
Index & redshift & @200~km/s & $\sigma$ & @200~km/s & $t$& @200~km/s & $t$ & @200~km/s & $t$ \\
\hline
\hline
Fe4383 & 0.02 &$ 4.70$ & 0.41 & $ 4.09$ & 1.5 & $ 4.33$ & 0.9& $ 4.38$ & 0.8\\
& 0.45 &$ 3.58$ & 0.82 & $ 3.39$ & 0.2 & $ 3.57$ & 0.0& $ 3.65$ & 0.1\\
& 0.55 &$ 3.73$ & 0.38 & $ 3.06$ & 1.7 & $ 3.40$ & 0.8& $ 3.47$ & 0.8\\
& 0.75 &$ 2.77$ & 1.24 & $ 2.56$ & 0.2 & $ 3.19$ & 0.3& $ 3.34$ & 0.4\\
H$\delta$A & 0.02 &$-1.40$ & 0.79 & $ -1.37$ & 0.0 & $-1.85$ & 0.6& $-1.93$ & 0.7\\
& 0.45 &$-0.23$ & 1.12 & $ -0.08$ & 0.1 & $-0.47$ & 0.2& $-0.64$ & 0.4\\
& 0.55 &$ 0.09$ & 1.09 & $ 0.58$ & 0.4 & $-0.02$ & 0.1& $-0.26$ & 0.3\\
& 0.75 &$ 0.63$ & 1.10 & $ 1.54$ & 0.8 & $ 0.33$ & 0.3& $ 0.05$ & 0.5\\
H$\gamma$F & 0.02 &$-1.48$ & 0.44 & $ -0.86$ & 1.4 & $-1.09$ & 0.9& $-1.13$ & 0.8\\
& 0.45 &$-0.61$ & 0.66 & $ 0.10$ & 1.1 & $-0.36$ & 0.4& $-0.48$ & 0.2\\
& 0.55 &$-0.48$ & 0.66 & $ 0.31$ & 1.1 & $-0.09$ & 0.6& $-0.21$ & 0.4\\
& 0.75 &$0.04$ & 0.97 & $ 0.96$ & 0.9 & $ 0.16$ & 0.12& $-0.04$ & 0.0\\
\hline
\end{tabular}
\caption{Comparison between the indices predicted by the linear fit
to the data at $\sigma=200$~km~s$^{-1}$ and the ones predicted -- at the
same velocity dispersion-- in a passively evolving model with redshift
formations $z_{\rm f}=1.4$, $z_{\rm f}=2$ and $z_{\rm f}=3$. Column 3 shows the predicted
value by the linear fit at $\sigma=200$~km~s$^{-1}$, column 4 the
standard deviation among the relation; columns 5, 7 and 9 show the value
predicted by the model with redshift formations of 1.4, 2 and 3 respectively.
Columns 6, 8 and 10 shows the $t$-parameter
of comparing these two values (fitted and predicted) using a Student's t-test. A $t$ value higher than 1.96 would
indicate that the probability that the two values are different by chance
is less than 5\% (for samples larger than 40 and 6\% for smaller samples). As can be seen, none of the
values show significant
differences from the model.\label{table.t}}
\end{table*}
\section{Morphological content of the red-sequence}
\label{sec.morph}
Table~\ref{tb:clusterlist} lists the EDisCS structures wich have been
observed with the HST/ACS in the F814W band, i.e, all six in the 0.75
redshift bin, six at $z=0.55$, and three at $z=0.45$.
In the following, we use the visual classifications of \citet{Des07}, which
has been performed down to $I_{auto}$\footnote{SExtractor Kron magnitudes}=23 mag.
Since we concentrate on the EDisCS spectroscopic sample, the actual magnitude cuts for the
morphological classification are I (r $\le$ 1$"$) $\sim$ 22 mag at
$z=0.45$ and I(r $\le$ 1$"$) $\sim$ 23~mag at z=0.75. This translates
into restframe magnitudes of Mv$\sim -18.7$ and $\sim -$19.3 mag at
z=0.45 and z=0.75, respectively. Once we account for the dimming due
to passive evolution (0.5 mag from z=0.75 to 0.45 assuming an age of
3.1 Gyr at z=0.75), the intrinsic magnitude cut is the same at
all redshifts. We note that some secondary structures at low redshift
were discovered in high-redshift targeted fields. Consequently, they
were observed down to lower magnitude limits than the primary targets
at similar redshifts. As such, they are exceptions to the above
general rule. However, they represent a small percentage of the
total number of galaxies.
Interestingly, only 15 E/S0 galaxies out of 168 (i.e., 9\%) are not on
the red-sequence. This is similar to the fraction of blue early-type
galaxies found at low redshift \citep{Bam08}, which is highly
dependent on local density but varies between 12 and 2\%.
We concentrate on the N+W red-sequence galaxies, the same for which we
have analyzed the stellar population. Figure~\ref{Hubble.Sigma.Type12}
shows their Hubble type distribution. We also indicate the
distribution of galaxies with $\sigma$ $<$ 175km/s. There is no
apparent morphological segregation as a function of galaxy mass, i.e,
whatever the galaxy mass range, the dominant morphological types on
the red-sequence are clearly E and S0, although the entire Hubble
sequence is covered.
\begin{figure}
\resizebox{0.5\textwidth}{!}{\includegraphics[angle=-90]{Hubble.ps}}
\caption{The distribution of Hubble types among the N+W emission line
red-sequence galaxies in redshift bins: E(T=-5), S0(T=$-2$), Sa
(T=1), Sab(T=2), Sd(T=7). The solid line histograms trace the
morphological distribution for the entire sample. The dashed areas
trace the histograms for the galaxies with velocity dispersions lower
than 175 km~s$^{-1}$.}
\label{Hubble.Sigma.Type12}
\end{figure}
In order to look for possible evolution with time, we now restrict the
sample to the EDisCS clusters (galaxy structures with $\sigma$ larger than 400
km~s$^{-1}$) and fix the area of analysis to the region falling inside
a radius of 0.6R$_{200}$ from the cluster centers, where R$_{200}$ is
the radius within which the average cluster mass density is equal to
200 times the critical density. R$_{200}$ values were derived using
equation (8) in \citet{Finn05} and are listed in Table
\ref{tb:clusterlist}. These restrictions are governed by the need to
have the same spatial coverage in all structures
given that a morphology-radius relation is observed in clusters
(e.g. Whitmore \& Gilmore 1991; Postman et al. 2005).
The fraction of galaxies from each morphological type
have been corrected for magnitude and spatial
incompleteness \citep{Pog06}. Errors in these fractions are calculated using the formulae in
\citet{1986ApJ...303..336G}, since Poissonian and binomial statistics
apply to our small samples.
The fraction of early-type galaxies (E and S0) at
redshifts $z=0.45$, 0.55 and 0.75 are:
56$^{+12}_{-13}$\%, 61$^{+9}_{-9}$\% and 75$^{+9}_{-9}$\%,
respectively. In other words, our calculations suggest that,
in the red-sequence, the fraction of early-type galaxies
{\it decreases} from $z=0.75$ to $z=0.45$.
In order to check the
robustness of this result, we also consider another technique of
morphological classification. In particular
the GIM2D decompositions presented in Simard et al. (2008, in
preparation), where early-type galaxies are identified by their bulge
fraction ($B/T$$\ge$ 0.35) and the ACS image smoothness within two
half-light radii ($S2$ $\le$ 0.075). This method leads to
33$^{+14}_{-12}$\%, 62$^{+8}_{-9}$\%, and 80$^{+5}_{-6}$\% of
early-type galaxies at $z=0.45$,0.55 and 0.75, respectively, in
agreement with our previous finding. As mentioned earlier, only 3
clusters have ACS data in the 0.45 bin, and only 22 galaxies within
0.6R$_{200}$, as these clusters did not constitute our primary targets
for HST. This most likely explains the large difference found at this
redshift between the two classification techniques. Nevertheless, the
decrease of early-types fractions in the red-sequence
is confirmed. It is worth noting that even when
strong emission line galaxies are kept in the sample, the fractions of
early-type galaxies are very much the same, i.e., 62$^{+10}_{-9}$\%
and 72$^{+5}_{-7}$\% at z=0.55 and z=0.75.
The mean redshift of the MORPHS sample is 0.45 \citep{Dress99}, hence
allowing direct comparison with our lowest redshift group and
increasing the statistical significance (10 clusters). After
selection of the red galaxies (g$-$r$>$1.4) without emission lines,
i.e, a selection comparable to ours, the fraction of MORPHS E+S0s is
57$\pm$9\% (B. Poggianti, private communication), i.e, very close to
the initial value coming from our visual classification. Additional
evidence of a decrease in early-type fraction with time on the
red-sequence comes from \citet{2006ApJ...642L.123H} who measured a
total fraction of E/S0 galaxies in two clusters at z=0.83 (MS
1054.4--0321 and Cl 0152.7--1357) of 74\% and 82\%, for their
selection in mass ( $ > 10^{10.9}$ M$_{\odot}$ ), best corresponding
to our red-sequence criteria. Note that our selection extends to
lower masses or accordingly to fainter limits, i.e., $3-6\times
10^{10}$ M$_{\odot}$ (derived from stellar M/L with the calibration by
\citet{2001ApJ...550..212B} and the re-normalization proposed by
\citet{dJB07} for elliptical galaxies). However, in this fainter
regime, Holden et~al.\ take into account all cluster galaxies, rather
than only those on the red-sequence, making impossible a direct
comparison. Anyhow, their figure~2 shows that their early type
fraction can not vary much along the red-sequence.
Figure~\ref{Hubble.Fraction} summarizes our results.
\begin{figure}
\resizebox{0.5\textwidth}{!}{\includegraphics[angle=-90]{HubbleFraction.ps}}
\caption{Variation of the fraction of early-type galaxies in the red-sequence with
redshift. Black and red symbols show the fraction derived from the
EDisCS data. Black triangles show the results for the morphological
classification based on visual inspection. Red squares stand for the
GIM2D bulge and disk decomposition method, where early-type galaxies
are selected upon their bulge-to-total light fractions and image
smoothness. The green circle represents MORPHS and the blue star
indicates the results of Holden et al. (2006), for their two X-ray
selected clusters.}
\label{Hubble.Fraction}
\end{figure}
The decrease, on the red-sequence, of the early-type fraction represents a
remarkable synthesis between the results of \citet{Des07} who detect
no evolution in the cluster {\it total} fraction of E/S0 galaxies
between redshift 0.4 and 1.4, and those of \citet{dL07} who measure a
decrease of the {\it red-sequence} faint-to-luminous galaxy ratio of
$\sim$40 \% between redshift 0.45 and 0.75. Indeed, if the
red-sequence keeps building up, as suggested by \citet{dL07}, it must
find its supply in the cluster blue galaxies. These EDisCS blue
galaxies are composed of only 20$\pm$7\% early-types and of 80\%
spiral galaxies. This distribution in types is constant with
redshift. Hence, provided that galaxy colours redden before any
morphological transformation occurs, an increase in the number of
spirals on the red-sequence is naturally expected when new galaxies
reach it. By restricting our analysis to the EDisCS spectroscopic
sample, we do not reach as faint magnitudes as \citet{dL07}. As a
consequence, our 20\% variation in the fraction of E/S0 galaxies on
the red-sequence between redshifts 0.45 and 0.75 most certainly
constitutes a lower limit.
It is interesting to estimate the subsequent evolution of the
red-sequence population, i.e., from $z=0.45$ to $z=0$. \citet{Dres97}
and \citet{Fas00} found that, while the elliptical fraction does not
evolve in the redshift range 0.5 to 0.0, the fraction of lenticular
galaxies doubles. This increase in the number of S0s is accompanied by
a drop in the fraction of (Sp+Irr) type galaxies. Combining these
results together with those of \citet{Post05} and EDisCS,
\citet{Des07} conclude that $z\sim 0.4$ must constitute a special
epoch after which the {\it total} fraction of S0-type galaxies in
clusters begins to increase. Meanwhile, \citet{dL07} measure only
$\sim 10$ \% variation of the red-sequence faint-to-luminous galaxy
ratio between redshift 0.45 and 0. As a consequence, at the time the
red sequence reduces its growth ($ z \le 0.45$), one can expect a rise
in its E/S0 fraction as well.
\section{Discussion}
\label{ops}
We have shown that the rate at which red-sequence galaxies evolve
depends on their mass range. In particular, less massive galaxies show
evidence for a more extended star formation history. Two possibilities
are considered: i) the sequence is in place at redshift $z\sim 0.8$,
but a low level of star formation continues in galaxies on the faint
end \citep[e.g.][]{CC02}; or ii) the red-sequence is continuously
built-up by new incomers, preferentially selected among faint systems.
We examine both hypotheses.
\citet{Geb03} explore, in the context of the first model, the maximum
amount of low-level star formation that the galaxies can experience
without leaving the red-sequence. They found that, to keep the
colours of the red-sequence galaxies almost constant since $z=1$, in
agreement with observations, only 7\% \footnote{the percentage varies
between 4 and 10\% depending on the chosen metallicities} of the mass
could have been formed after the initial burst (assumed to be at
$z=$1.5) using exponential star formation histories with e-folded time
of 5 Gyr. We did a similar experiment, and calculated the maximum
amount of low-level star formation that the galaxies could experience
from $z=0.75$ to $z=0.45$ in order to reproduce the evolution of the
index-$\sigma$ relations with redshift measured in
Sect.~\ref{sec.indices.mv}. The exact percentage depends on the
chosen metallicity but we also find that this fraction has to be
always less than $\sim$10\% (note that our redshift baseline is
smaller). However, recent results of the evolution of the UV colours
in early-type galaxies suggest that this percentage is higher:
\citet{Kav08} found that, at intermediate luminosity (M$_{\rm v} <
-20.5$), early-type galaxies in the red-sequence have formed 30-60\%
of their mass since $z=1$. However, this study does not sample
exclusively galaxies in dense clusters, but in a wide range of
different environments.
\citet{Fab07, Pog06} proposed a mixed scenario where red-sequence
galaxies form through by two different channels. \citet{Pog06}
discussed a scenario where the red-sequence is composed of primordial
galaxies formed at $z_{\rm f}>$2.5 on the one hand and of galaxies
that quenched their star formation due to the dense environment of
clusters on the other hand. They calculate that, of the 80\% of
passive galaxies at z=0, 20\% are primordial and 60\% have been
quenched. With regards to this later aspect, \citet{Har06} could
reproduce the evolution of $U-B$ and the H$\delta$, as well as the
galaxy number density, by assuming models of constant star formation
histories truncated at evenly spaced intervals of 250 Myr up to now.
Along this line, we calculate the number of new quenched galaxies that
have to enter the red sequence to reproduce the results obtained in
Sec.~\ref{sec.stacked}. We start with a population of galaxies with a
formation redshift of $z_f=1.4$ and solar metallicity, both derived
for the low-mass galaxy bin at $z=0.75$. Then we consider galaxies
that started forming stars at $z=2$ at a constant rate of
1M$_{\odot}$/yr and start quenching them at regular intervals of 250
Myr. Once a galaxy is red enough to pass our red-sequence selection
criteria at $z=0.45$ and 0.55, we add its normalized spectrum to the
that of the initial population. If we assume that all the new
galaxies have velocity dispersions lower than 175 km~s$^{-1}$, we need
$\sim$40\% of new arrivals in the interval z=0.75 to z=0.45 in order
to reproduce the constant luminosity-weighted age of the low-$\sigma$
galaxy bins with redshift. This is in surprisingly exact
correspondence with the result of \citet{dL07}, who measure a decrease
of the red-sequence faint-to-luminous galaxy ratio of $\sim$40 \%
between redshifts 0.45 and 0.75. Note that \citet{dL07} deal with
photometric data and therefore their dataset reaches fainter
magnitudes than our spectroscopic sample. The exercise presented here
is of extremely simple nature and is not intended to represent the
true star formation histories of the galaxies. Apart form quenching,
disk galaxies can merge and have bursts of star formation before
becoming red. By merging with other galaxies, our objects can also
move from the low-$\sigma$ bin to the high-$\sigma$ bin, which is
something not considered here. However, simple models similar to this
one have proved to be very successful in reproducing the evolution of
the colours and H$\delta$ index and the evolution of the luminosity
function (e.g., Harker et al. 2007).
Linking these constraints to our morphological results, it appears
that the mechanism that quenches star formation does not necessarily
produce a morphological transformation {\it at the same} time, but
certainly, it favors it. Most likely, the mechanism that quenches star
formation also produces the morphological transformation, but on a
different time-scale. Indeed, the fraction of spiral galaxies evolves
by 20\% and not by the 40\% calculated in the spectroscopic analysis.
Splitting between stellar population and morphologies was also raised
by MORPHS \citep{Dress99,Pog99}.
\section{Summary}
\label{sec.summary}
We addressed the questions of the epoch of formation of the reddest
galaxies in clusters, the extent of their period of star formation and
the link between morphological and stellar population evolution time
scales.
Our analyses are primarily based on 215 red-sequence galaxies,
selected from the EDisCS spectroscopic database, that we divided into
three redshift bins, $z=0.75$, $0.55$, and $0.45$. We considered their
mass range, via the proxy of their velocity dispersions; their stellar
population properties derived from absorption line features; and their
morphologies, thanks to HST/ACS imaging. We have been able to trace
the evolution of the red-sequence from $z=0.75$ to $z=0.45$ in a
homogeneous dataset, the largest to date, extracted from a single
survey, hence avoiding a mix of different systematic errors.
$\bullet$ Before discarding red-sequence galaxies with strong emission
lines from our absorption line analysis, we investigated the nature of
their ionizing sources. Most of the EDisCS red-sequence galaxies with
emission lines seem to be forming stars. The proportion of dusty star
forming galaxies among our total sample is larger than the fraction
reported by \citet{Yan06} at $z=0$ in the SDSS field red
population. Whether this difference is due to evolution or to
environment is worth clarifying in the future.
$\bullet$ We measured 12 Lick/IDS indices, carefully visually
inspecting the spectra in order to eliminate those possibly affected
by sky subtraction residuals or any other systematic effect. To
compare with our local sample of Coma galaxies, we derived new
aperture corrections. We used state-of-the art stellar population
models to derive ages, metallicities, and chemical abundance ratios.
These models make predictions over the whole spectral energy
distribution, allowing us to analyze our data at a resolution of 325
km/s, avoiding any spurious correction for the galaxy velocity
dispersion.
$\bullet$ After selecting on secure redshifts and signal-to-noise
ratios, we stacked the galaxy spectra in redshift bins. In each bin,
we also distinguished galaxies with respect to their velocity
dispersions, dividing at $\sigma = 175$~km~s$^{-1}$. We derived the
age, metallicity (Z), and $\alpha$-element abundance ([E/Fe]) of each
redshift and velocity dispersion group.
\begin{itemize}
\item Massive galaxies ( $\sigma > 175$~km~s$^{-1}$ ) show a variation
in age corresponding to the expected cosmological variation between
redshifts, a mean solar metallicity and an overabundance [E/Fe] with
respect to the solar values. Therefore, they are well represented by
a scenario of formation at high redshift, followed by passive
evolution. Conversely, the properties of less massive galaxies
($\sigma< 175$ kms$^{-1}$) require longer star formation, at low
level. Indeed, their luminosity weighted ages is found constant with
time in our redshift range. An immediate consequence is that the age
difference between low- and high-$\sigma$ galaxies increases with
time. This need to be taken into account in studies of the evolution
of the colour-magnitude diagrams.
\item Values of [E/Fe] and [Z/H] are constant with time, independent
of $\sigma$. This implies that the bulk of the galaxy stellar
population is formed on a time-scale and with efficiency fixed by the
galaxy mass. Possible subsequent episodes of star formation, which
change the age of the less-massive galaxies, can not account for a
large fraction of the galaxy mass.
\end{itemize}
$\bullet$ We confirm that the evolution of the zero-points of the
index-$\sigma$ relationships with redshift is compatible with a
scenario in which galaxies formed all their stars at high redshift and
evolved passively since then. However, we demonstrate that it is also
compatible with more complex star formation histories. In particular,
galaxies can progressively enter the red-sequence as their star
formation is quenched. In this scenario, galaxies with lower $\sigma$
enter the red-sequence at lower redshift than more massive galaxies.\\
The two more important results of this work are:
$\bullet$ The morphological analysis, based on visual or automated
classification, indicates that red sequences are composed of types
covering the entire Hubble sequence, irrespective of the redshift,
with, however, a very clear plurality of Es and S0s. The fraction of
red-sequence early type galaxies decreases between $z=0.75$ and
$z=0.45$ by about 20\%. This means that spiral galaxies get first
redder, stopping their star formation, before they turn into earlier
morphological types. This evolution is however lower than the rate at
which new galaxies enter the red-sequence, meaning that quenching and
morphological transformation operate on different time-scales.
$\bullet$ We found that the evolution of the line-strength indices with
redshift can be reproduced if 40\% of the galaxies with $\sigma$ lower than 175 kms$^{-1}$
entered the red-sequence between $z=0.75$ and $z=0.45$, in agreement
with the fraction derived in studies of the luminosity function.
In summary, a number of works dedicated to the evolution of the luminosity
function of red galaxies in clusters (Rudnick et al. 2008, in
preparation; De Lucia et al.\ 2004; De Lucia et al.\ 2007) and in the
field (Faber et al.\ 2007; Brown et al.\ 2007) report an increase of
the galaxy number density since $z\sim$1. Conversely,
colour-magnitude diagrams and index-$\sigma$ relations of cluster
red-sequence galaxies at intermediate- and high-redshift usually
describe them as in place very early, passively evolving,
independently of their mass \citep[e.g.,][]{Ell97, Dres97, vD98,
SED98, K00c, Zie01, Blak03, Wuy04, Tran07}. The present work
reconciles the luminosity functions and stellar content outcomes.
\begin{acknowledgements} We thank the anoymous referee for useful suggestions
that have improved the final presentation of the paper.
PSB is supported by a Marie Curie
Intra-European Fellowship within the 6th European Community Framework
Programme. The Dark Cosmology Centre is funded by the Danish National
Research Foundation. \end{acknowledgements} \bibliographystyle{aa}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,262 |
President George Bush may have hoped that a weekend in Argentina would be a respite from the successive scandals suffered by his administration at home. But as has happened often during his presidency, Bush was greeted at the Summit of the Americas in Mar del Plata by tens of thousands of peaceful demonstrators, and street violence by a smaller group in the seaside resort.
President Bush, the most unpopular U.S. president in recent Latin American history, met with 33 heads of state representing every nation in the Western Hemisphere except Cuba. Among the top issues addressed at the summit was Washington's long running effort to implement the hemisphere-wide Free Trade Area of the Americas. But in the end, progress on FTAA was blocked by five nations: Brazil, Argentina, Uruguay, Paraguay and Venezuela, who opposed a deadline of April 2006 for a new round of talks. Venezuela's president Hugo Chavez, a staunch opponent of free trade, dominated coverage of the summit when he led a rally with soccer star Diego Mardona against President Bush, attended by 25,000.
Between The Lines' Scott Harris spoke with Tom Barry, policy director with the International Relations Center, who assesses the popular opposition to the FTAA across Latin America and the viability of progressive alternatives for economic development and integration.
©2005 Between The Lines. All Rights Reserved. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,184 |
Bone Frog Bachelor Series
Back for More!
About the Bone Frog Bachelor Series
This series involves the same couple: former billionaire and Navy SEAL Marco Gambini and his new love, Shannon Marr, as they traverse oceans and play in the dangerous world of assassins and mercenaries while clawing their way back from the brink of destruction, restoring Marco's powerful fortune earned through his successful shipping, real estate and protection businesses. With each book in this series, Shannon grows into the partner he's always wanted: someone worthy of his trust as his right-hand woman, as well as the woman who can match him in every way in the bedroom.
I have done it all. I have built three global security companies, including foreign subsidiaries which include an airline company and a shipping conglomerate, partnered with some of the biggest industry titans in the realm of international trade. But my…
Armed with new focus and passion for restoring his rightful place atop his shipping, consulting and private security empire, former Navy SEAL Marco Gambini takes his new love on a dangerous and romantic pre-honeymoon to the Pink Pasha on a… | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,872 |
GOP bill that would eliminate Miami-Dade wage theft ordinance passes in the House
The Florida House of Representatives on Wednesday passed a bill filed by state Rep. Tom Goodson, R-Titusville, that prohibits local governments from adopting or maintaining in effect law, ordinance, or rule for purpose of addressing wage theft, the practice of employers stiffing workers out of the wages they are owed.
Goodson's bill would preempt the existing Miami-Dade anti-wage theft ordinance that has successfully recovered $400,000 since September 2010.
An amendment to Goodson's bill (proposed by Rep. Cynthia Stafford, D-Miami) that aimed to exempt the existing Miami-Dade county wage theft ordinance failed.
Rep. Darren Soto, D-Orlando, filed two amendments – one that "would create a statewide study to determine what the proper solution is for wage theft in the state" and a second that would "provide for a statewide authorization of the Miami-Dade solution regarding the wage theft ordinance." Both failed.
Rep. Luis Garcia, D-Miami, said that the bill would allow the state legislature to take away Miami-Dade county's rights to "protect [its] citizens," urging legislators from Miami to vote against the bill.
A Florida International University report released in January states what many supporters of local anti-wage theft ordinances have previously told the Independent: Existing federal workplace laws do not protect millions of workers, including "hospital, school, or government workers or workers at small, local firms, including contractors for larger companies." Florida's minimum wage law also excludes millions of workers "from protections against employers who withhold their earnings."
Rep. Carlos Trujillo, R-Miami, told the committee that legislators "are arguing about nothing," adding that attorneys love wage theft cases because they often collect thousands of dollars in fees from taking them on. Trujillo added that these cases can be brought in the county, circuit, or federal court and that Miami should "not have a quasi-judicial administrative court."
According to Rep. Stafford, the bill "will hurt workers and place an unfair burden on them" and "on employees who are trying to get what is legally due to them." Further, said Stafford, it requires a worker to file a "costly, timely, and intimidating" civil action in court, which would only silence them.
Rep. John Julien, D-Miami, said that the Miami-Dade County wage theft ordinance that passed the board of County Commissioners unanimously in 2010 "was trying to protect the least amongst us, the employees that work the fields in Homestead, the members that work the hospitality industry in Miami-Beach."
Julien added that wage-theft ordinances act as an avenue for those who have had wages of $60 or more stolen from them so that they don't have to go to court, "where a lot of these poor people [can] does not afford to go."
"I'm concerned about what we have done here today, and now that we know we don't have enough jobs, we are about to pass a bill that will no longer allow workers to get their just pay," said Rep. Barbara Watson, D-Miami Gardens. "If we have an employer who is constantly ripping off his employees, this bill will prohibit employees from filing a class-action lawsuit."
Rep. Keith Perry, R-Gainseville, argued that such ordinances can hurt businesses and make fraudulent activity easy, adding "help the businesses and they'll help the workers."
Rep. Rick Kriseman, D-St Petersburg, said the bill is problematic in that it requires that workers come up with court costs and filing fees. "If you're a business with over $500,000 in gross volume sales you can go ahead and steal the wage from your employee, [and] you'll [still] have immunity," he said.
Rep. Lori Berman, D-Delray Beach, said the bill eliminates a victim's right to a jury trial, forbids class action suits "even when you have numerous workers victimized by the same employer," and only grants victims the "wages their employer failed to pay."
"What happens when it results in the person being put out of their apartment?" Berman asked. "Under this law, they wouldn't be entitled to get those items recovered."
"In this chamber, we want to help the big guy, we want to do something for the corporations, the job creators," said Rep. Mark Pafford, D-West Palm Beach, adding that "this bill takes the boot and puts it on the throat of the most desperate folks who need to get paid to feed their family…we're telling them, 'you are not important.'"
To close the debate, Goodson said that voting against his bill was akin to voting against the Florida constitution, because "no other courts may be established."
"This bill doesn't do anything to your rights, you still have your federal rights, state rights," said Goodson. "This is only doing exactly what I hear they want to do – municipalities set up their own little non-judiciary hearing to help collect wages."
Majority of Florida voters support bill to spend BP fines on gulf restoration
Van Zant anti-abortion bill echoes 'personhood' language
Leon supervisor of elections says new elections law will cost county $112,000 more
Leon County Supervisor of Elections Ion Sancho warned advocates attending a State of Black Florida 2012 event today that last year's elections law is costing Leon County money.
McCollum, bucking his own party and allies, refuses to endorse Scott
Florida Attorney General Bill McCollum refused to endorse his Republican primary opponent Rick Scott for governor (at least,… | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3 |
Teopantecuanitlan è un sito archeologico situato nello stato messicano di Guerrero, esempio di sviluppo inaspettatamente precoce in questa regione di una società complessa.
Il sito viene datato al primo o medio periodo formativo, e le prove archeologiche dimostrano chiaramente l'esistenza di connessioni tra Teopantecuanitlan e la terra degli Olmechi sulla Costa del Golfo degli Stati Uniti. Prima della scoperta di Teopantecuanitlan nei primi anni degli anni ottanta si sapeva poco dello sviluppo socio-culturale e dell'organizzazione esistente durante il periodo formativo della Mesoamerica.
Posizione geografica
Teopantecuanitlan si trova nello Stato di Guerrero, situata alla confluenza dei fiumi Amacuzac e Balsas, e ad 8 km da dove l'Amacuzac si immette nel Balsas. Teopantecuanitlan occupa circa tra 1,6 e 2 km², e si trova ai piedi di una collina che si eleva 200 metri sopra al sito.
Teopantecuanitlan era il centro della regione che comprendeva Oxtotitlán, Juxtlahuaca, Xochipala, Zumpango del Río e Chilpancingo.
Arte ed architettura
Teopantecuanitlan fu occupata tra il 1400 a.C. ed il 500 a.C., periodo diviso generalmente in quattro fasi, con il picco della popolazione e la complessità del sistema raggiunti durante la seconda fase, tra il 1000 e l'800 a.C. L'insediamento consisteva in gran parte di edifici residenziali caratterizzati da quattro strutture disposte attorno ad un cortile o piazza condivisa. Le strutture stesse erano fatte di materiale deperibile, costruite su fondamenta in pietra. Artefatti importati costruiti con conchiglie ed ossidiana, così come le ceramiche olmeche, sono stati trovati nei vari complessi residenziali. Questi oggetti forniscono le prove del fatto che la comunità di Teopantecuanitlan faceva parte di una rete interregionale che collegava la costa del Golfo alle alture del Messico centrale.
Patio affondato
Oltre alle aree residenziali, Teopantecuanitlan è interessante per la sua architettura monumentale, l'arte, le terrazze agricole, ed in particolare per una delle prime strutture cerimoniali civili della Mesoamerica, El Recinto, noto anche come il Patio affondato, costruito durante la seconda fase (1000-800 a.C.). Il Patio affondato prende il nome dal fatto di trovarsi 2 metri sotto al normale livello del suolo, eretto su una base di argilla gialla e ornato da blocchi di travertino.
Quattro monumenti in travertino, pressoché identici, adornano i lati orientale ed occidentale del Patio affondato. Questi blocchi sono scolpiti in modo da raffigurare creature antropomorfe, probabilmente giaguari Olmechi con occhi a mandorla e bocche rivolte verso il basso. Si tratta di monumenti pesanti da 3 a 5 tonnellate citate nel nome dato al sito dall'archeologo Guadalupe Martinez Donjuán, Teopantecuanitlan, termine nahuatl per "luogo del tempio del giaguaro". Secondo Martinez Donjuán queste sculture si trovano lì per segnare l'equinozio ed il solstizio, e "simobleggiano le forze opposte che governano il mondo".
Il muso di uno di questi monumenti (Monumento 2) contiene simboli che Martinez Donjuán interpreta come "10 Fiore". Se questa interpretazione è corretta si tratterebbe del più antico riferimento conosciuto ad un calendario mesoamericano.
Il sito archeologico contiene anche due campi del gioco della palla. Uno piccolo si trova nel Patio affondato mentre l'altro si trova 900 metri a nord-est. Ad un'estremità di quello piccolo si trova una sauna costruita in adobe. Questa sauna era probabilmente usata come ritrovo sociale delle classi agiate di Teopantecuanitlan.
Altre caratteristiche
Teopantecuanitlan è anche la più antica diga mesoamericana conosciuta. Questa diga fu costruita attorno al 1200 a.C. con rocce grezze non tagliate. Sfrutta la gravità per portare l'acqua all'interno del terreno agricolo. Anche alcuni canali, fatti con grandi pietre piatte, si trovano a Teopantecuanitlan. Questi canali permettevano la coltivazione domestica delle piante tramite un sistema di irrigazione. Evitavano anche i danni causati dall'erosione, e le acque che fuoriuscivano venivano usate come fogna.
Il sito è anche uno dei primi conosciuti in Mesoamerica ad utilizzare una tecnica architettonica nota come arco a mensola. Questa volta permetteva i soffitti molto alti senza l'uso di pietre tagliate con forma trapezoidale. Venivano usate nelle antiche strutture quali le tombe delle classi potenti ed i templi.
La società di Teopantecuanitlan non era paritaria, altrimenti certe strutture monumentali non sarebbero state costruite. Vi era un capo che controllava la costruzione di queste strutture, che insegnava ai lavoratori e che assicurava la fornitura di tutte le risorse necessarie.
Scoperta e scavi
Teopantecuanitlan fu scoperta da Martinez Donjuán nel 1983, in seguito a notizie di saccheggi in questo sito di Guerrero. Tra gli altri, fu aiutato anche da Christine Niederberger. Niederberger si preoccupò soprattutto delle aree residenziali note come zona Lomerios, o Tlacozotitlán.
Il sito di Teopantecuanitlan è aperto al pubblico dal martedì al sabato, dalle 10 alle 17.
Influenza olmeca
L'influenza olmeca è visibile in molti dei monumenti di Teopantecuanitlan. Oltre ai quattro monumenti già discussi, lo stile olmeco si trova in tutto il resto del sito.
Vi sono molte teorie riguardo a come le decorazioni olmeche (anche le divinità) siano giunte a centinaia di chilometri dalla loro terra natale. Martinez Donjuán crede che le radici della cultura olmeca siano a Teopantecuanitlan, e che un gruppo di abitanti sia partito da qui per colonizzare quella che oggi è ritenuta la patria naturale degli Olmechi., e si tratta di una rivisitazione dell'ipotesi avanzata da Miguel Covarrubias.
L'archeologo Michael D. Coe disse che la sua "opinione viene smentita dai vincoli ambientali" imposti dalle alture semi-aride dello Stato di Guerrero. La Niederberger trova influenze olmeche solo nell'architettura dei monumenti, mentre il resto deriverebbe secondo lei da fonti indigene.
Note
Bibliografia
Michael Coe Mexico: From the Olmecs to the Aztecs, 1994, quarta edizione, Thames & Hudson, New York
Richard A. Diehl, The Olmecs: America's First Civilization, 2004, Thames & Hudson, New York
Susan Toby Evans, Ancient Mexico & Central America: Archaeology and Cultural History, 2004, New York, Thames & Hudson
F. K. Reilly, "Tlacozotitlán (Guerrero, Mexico)", 2000, in Susan Evans, Archaeology of Ancient Mexico and Central America, Taylor & Francis
V. H. Malmström, "A Survey of Teopantecuanitlán, Guerrero, Mexico"
Guadalupe Martinez Donjuan, "Teopantecuanitlan", 2000, in The Oxford Encyclopedia of Mesoamerican Cultures, David, Carraso, Oxford University Press
Guadalupe Martinez Donjuan, "Teopantecuanitlan", 1986, in Arqueologia y Etnohistoria del Estado de Guerrero, Roberto Cervantes-Delgado, Instituto de Antropologia e Historia of Mexico, pp 55–80
Altri progetti
Collegamenti esterni
Sito ufficiale su INAH
Siti archeologici del Guerrero
Siti archeologici olmechi | {
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{"url":"https:\/\/academy.vertabelo.com\/course\/common-table-expressions\/final-quiz\/quiz\/single-cte","text":"Introduction\nQuiz\n5. Single CTE\nSummary\n\n## Instruction\n\nFine. Let's get started with a single CTE.\n\n## Exercise\n\nFor each project, show project_id and an average number of hours an employee spent on a project.","date":"2019-04-25 09:54:35","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.834163248538971, \"perplexity\": 7855.621787397137}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-18\/segments\/1555578716619.97\/warc\/CC-MAIN-20190425094105-20190425120105-00063.warc.gz\"}"} | null | null |
Q: BundleConfig.cs using bootstrap.min.css My BundleConfig.cs file looks like this (CSS):
bundles.Add(new StyleBundle("~/Content/css").Include(
"~/Content/bootstrap.css",
"~/Content/site.css",
"~/Content/bootstrap-switch.css",
"~/Content/datepicker.css",
"~/Content/bootstrap-duallistbox.css",
"~/Content/fullcalender.css",
"~/Content/fullcalender.print.css"));
BundleTable.EnableOptimizations = true;
No where am I calling bootstrap.min.css, however, when I updated only the bootstrap.css file none of my changes were recognized. I started to make the changes in the .min file and then I noticed my changes.
I get that the BundleTable.EnableOptimizations = true; takes all of the .css files and minimizes them, but I don't understand why I had to update the .min file for it to recognize my style changes.
I expected the bootstrap.css file to be minimized in memory and used that way.
Can someone explain why this is occurring?
Just for more information I'm using MVC5 in VS2013
A: When you include stylesheet.css in an bundle and there is already a stylesheet.min.css file in your project, the optimization framework will use the .min file when BundleTable.EnableOptimizations == true.
It does the same thing for script.min.js files.
BundleTable.EnableOptimizations = true; // when this is not false
bundles.Add(new StyleBundle("~/Content/css").Include(
"~/Content/bootstrap.css", // will look for bootstrap.min.css
"~/Content/site.css", // will look for site.min.css
"~/Content/bootstrap-switch.css", // will look for bootstrap-switch.min.css
"~/Content/datepicker.css", // will look for datepicker.min.css
"~/Content/bootstrap-duallistbox.css", // will look for bootstrap-duallistbox.min.css
"~/Content/fullcalender.css", // will look for fullcalender.min.css
"~/Content/fullcalender.print.css")); // will look for fullcalender.print.min.css
If you would rather have the optimization framework minify for you, just remove bootstrap.min.css from your project.
From the docs:
public static void RegisterBundles(BundleCollection bundles)
{
bundles.Add(new ScriptBundle("~/bundles/jquery").Include(
"~/Scripts/jquery-{version}.js"));
// Code removed for clarity.
}
The preceding code creates a new JavaScript bundle named ~/bundles/jquery that includes all the appropriate (that is debug or minified but not .vsdoc) files in the Scripts folder that match the wild card string "~/Scripts/jquery-{version}.js". For ASP.NET MVC 4, this means with a debug configuration, the file jquery-1.7.1.js will be added to the bundle. In a release configuration, jquery-1.7.1.min.js will be added. The bundling framework follows several common conventions such as:
*
*Selecting ".min" file for release when "FileX.min.js" and "FileX.js" exist.
*Selecting the non ".min" version for debug.
*Ignoring "-vsdoc" files (such as jquery-1.7.1-vsdoc.js), which are used only by IntelliSense.
| {
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My name is Marie-Eve Vallieres and I travel the world for a living. I'm a full-time travel writer, amateur photographer and translator born, raised and based full-time in Montreal, Canada. At age 19 I quit my boring data entry job and moved to England for a year – an experience that would leave a permanent mark on my life path.
This blog is not just any run-of-the-mill travel blog; it's a travel journal encompassing over a decade of travel across Europe and the rest of the world from the eyes of an architecture-obsessed, latte-lover female traveller.
With this space I aim to encourage millennial women to discover the world on their own using my recommendations, practical tips, and ready-to-use itineraries in the far ends of Scotland, the bustling metropolises of Japan, the beaches of Mexico, and the charming streets of my hometown.
The world's our oyster, ladies. Let's get out there. | {
"redpajama_set_name": "RedPajamaC4"
} | 5,748 |
\section{\Large Supplementary material}
\subsection{Theory basics}
At this point we will sketch the derivation of the equations of motion and the coupling constants. The force on a dipole is given by the gradient of the scalar product of its dipole moment with the incident electric field, where the gradient only acts on the electric field, treating the dipole moment as a constant. We can express the dipole moments inside of a $j$-th dielectric particle via the particles polarizability $\alpha_j=\varepsilon_0 V_j \chi$ and the drive (trapping) field $\mathbf{E}_0(\mathbf{r})$, with the particle volume $V_j$ and $\chi=3(\varepsilon-1)/(\varepsilon+2)$ with the permittivity $\varepsilon$. The incident field at the position $\mathbf{r}_j$ away from a particle is a sum of $\mathbf{E}_0(\mathbf{r})$ and the scattering fields of all other particles, which can be expressed by the Green's tensor $\mathbf{G}(\mathbf{r})$ of the transverse Helmholtz equation:
\begin{align}
\mathbf{G}(\mathbf{r}) = \frac{e^{ikr}}{4\pi}\left[ \frac{3\mathbf{r}\otimes\mathbf{r} - r^2}{r^5}(1 - ikr) + k^2 \frac{r^2 - \mathbf{r}\otimes\mathbf{r}}{r^3} \right],
\end{align}
with $r=|\mathbf{r}|$ and where we omitted the unity matrix for simplicity.
By expanding the force to the second order in the particle volume, one can identify three contributions to the total force acting on one particle. The first is a sum of the well-known gradient force and the non-conservative radiation pressure originating only from the trapping field. The second contribution comes from the scattering fields of the other particles acting on the dipole moment due to the laser field, while the third contribution can be interpreted as the laser acting on the dipole moment induced by the scattering fields of the other particles. The second and third contribution together condense in what is called the optical binding force:
\begin{align}
\mathbf{F}_j^{\rm bind} = \nabla_j \text{Re} \left[ \sum_{j'\neq j} \frac{\alpha_j \alpha_{j'}}{2\varepsilon_0} \mathbf{E}^*_0(\mathbf{r}_j)\cdot \mathbf{G}(\mathbf{r}_j - \mathbf{r}_{j'})\mathbf{E}_0(\mathbf{r}_{j'}) \right],
\end{align}
with the nabla operator $\nabla_j$ acting on the coordinate $\mathbf{r}_j$. Expanding the forces to the third order in the particle volume would add the gradient force of scattering fields alone, as well as the interaction of the trapping field with the second order scattering fields. However, we will neglect these higher order terms ($\sim \mathcal{O}(V^3)$) in this work.
The coupling rates used in this work can be derived by expanding the optical binding forces on the particles around their respective equilibrium positions given by the gradient force of the trapping field. Here, we approximate the trapping fields as focused Gaussian beams. We take only the contributions to the optical force that are $\propto d_0^{-1}$. We consider two spherical dielectric particles of equal mass, each trapped in an optical trap with frequencies $\Omega_j$ along the optical axis and optical phases $\phi_j$.
The linearized dynamics along the optical axis with particle coordinates $z_{1,2}$ is then, in leading order of the trap separation $d_0$, determined by the coupling constants $k_1$ and $k_2$,
\begin{eqnarray}
m\ddot{z}_1 &=&- \left( m\Omega_1^2 + k_1 + k_2 \right) z_1 + (k_1 +k_2)z_2 \nonumber\\
m\ddot{z}_2 &=& - \left( m\Omega_2^2 + k_1 - k_2 \right) z_2 + (k_1-k_2)z_1.\label{lang}
\end{eqnarray}
The coupling constant $k_1$ describes the conservative part of the optical binding forces, while $k_2$ describes a non-conservative interaction, as indicated by the opposite sign in the equations of motion. They depend on the relative local phase $\Delta\phi_0 = \phi_1-\phi_2$ and the tweezer separation $d_0$ as $k_1 = G \cos(kd_0) \cos(\Delta\phi_0)/kd_0$ and $k_2 = G \sin(kd_0) \sin(\Delta\phi_0)/kd_0$. Constant $G= \alpha^2 k^5 \sqrt{P_1 P_2}/(2c w_0^2\pi^2\varepsilon_0^2)/m$ is a positive function of the particle polarizability $\alpha$ and optical powers $P_{1,2}$, where $w_0$ is the trap waist, $\varepsilon_0$ is the vacuum permittivity and $c$ is the speed of light. The distance $d_0$ and the relative tweezer phase $\Delta\phi_0$ allow tuning between purely conservative and non-conservative interactions.
The non-conservative contribution to optical binding emerges from the radiation pressure induced by the scattered fields, which constantly pumps energy into the system, thus it can't be derived from a Hamiltonian. This is also observed with curl-forces \cite{berry2013}, in ro-translational oscillators \cite{AritaBinding2,Nanowires} or for binding of particles of different sizes \cite{KarasekAssymetric,DogariuAssymetric,ChvatalAssymetric}. The equations of motion along the x and y axes follow the same form.
\subsubsection{Eigenfrequencies of the coupled system}
We diagonalize Eqs. \ref{lang} in order to obtain the eigenfrequencies of the normal modes for arbitrary intrinsic mechanical frequencies $\Omega_1$ and $\Omega_2$:
\begin{equation}
\Omega_{\pm}^2=\frac{1}{2}\left(\Omega_2^2+\Omega_1^2+2k_1/m\mp\sqrt{(\Omega_2^2-\Omega_1^2)^2+4(k_1/m)^2-4(\Omega_2^2-\Omega_1^2)k_2/m}\right).
\end{equation}
The splitting is minimal for $\Omega_2^2-\Omega_1^2=2k_2/m$. This is reached for the control parameter $\eta_{\rm m}=k_2/(m\Omega^2)$, where $\Omega$ is the mean mechanical frequency for $\eta=0$. For small $k_1\text{, }k_2\ll m\Omega_1^2$ the eigenfrequencies are:
\begin{equation}
\Omega_\pm=\sqrt{\Omega_1^2+(k_1+k_2)/m\mp\sqrt{k_1^2-k_2^2}/m}\approx \Omega_1+\frac{(k_1+k_2)/m\mp\sqrt{k_1^2-k_2^2}/m}{2\Omega_1},
\end{equation}
with the minimal splitting of:
\begin{equation}
\Omega_--\Omega_+\approx \frac{\sqrt{k_1^2-k_2^2}}{m\Omega\sqrt{1-\eta_{\rm m}}}.
\end{equation}
The conservative interaction has to be larger than the non-conservative interaction $k_1^2>k_2^2$ in order to have an avoided crossing. In the case of purely conservative interaction ($k_2\equiv 0$) the splitting is minimal for $\Omega_2=\Omega_1\equiv \Omega$:
\begin{eqnarray}
\Omega_{\pm}=\sqrt{\Omega^2+(k_1\mp k_1)/m} &\Rightarrow& \Omega_+=\Omega\text{, }\Omega_-\approx \Omega+\frac{k_1}{m\Omega}\nonumber\\
\Omega_--\Omega_+&\approx& \frac{k_1}{m\Omega}=2g.
\end{eqnarray}
\subsubsection{Interaction suppression by polarization}
The radiated electric field for an arbitrary polarization angle $\Theta$ consists of a radial and an azimuthal contribution:
\begin{eqnarray}
E_R(R)&=&-E_0\frac{\alpha k^2\sin\Theta}{4\pi\varepsilon_0 R}e^{ikR}\left(\frac{2}{k^2R^2}-\frac{2i}{kR}\right)\nonumber\\
E_\varphi(R)&=&-E_0\frac{\alpha k^2\cos\Theta}{4\pi\varepsilon_0 R}e^{ikR}\left(\frac{1}{k^2R^2}-\frac{i}{kR}-1\right).
\end{eqnarray}
If the light is polarized along the x axis ($\Theta=90^\circ$), the azimuthal component of the radiated field disappears $E_{\varphi}\equiv 0$. However, the near-field radial component $E_R$ yields the following conservative coupling rate:
\begin{equation}
g_{\text{near}}(d_0,\Delta\phi_0=0)=\frac{G}{2\Omega}\left(-\frac{2}{k^3d_0^3}\cos(kd_0)+\frac{2}{k^2d_0^2}\sin(kd_0)\right).
\end{equation}
For $d_0\sim 3\lambda$ the coupling rate is a factor of $2/(36\pi^2) \approx 5.6\times 10^{-3}$ of the coupling rate for $\Theta=0^\circ$.
\subsubsection{Electrostatic interaction}
Electrostatic interaction between dielectric objects is purely conservative with the interaction energy:
\begin{equation}
H_{C}=\frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{\sqrt{(d_0+x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}},
\end{equation}
where $q_1$ and $q_2$ are particle charges, $d_0$ is the trap separation and particle motions $x_{1,2}$, $y_{1,2}$ and $z_{1,2}$. We expand the Hamiltonian to the second order in $z_{1,2}$ and obtain:
\begin{equation}
H_{C}=\frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{d_0}\left(1-\frac{(z_1-z_2)^2}{2d_0^2}\right)\equiv \frac{k_1}{2}(z_1^2+z_2^2)-k_1z_1z_2,
\end{equation}
where we have defined $k_1=-\frac{q_1 q_2}{4\pi\varepsilon_0 m}\frac{1}{d_0^3}$ in analogy to the conservative optical interaction. The coupling rate due to the electrostatic interaction is given by:
\begin{equation}
g_C=\frac{k_1}{2m\Omega'}=-\frac{q_1 q_2}{8\pi\varepsilon_0 m\Omega'}\frac{1}{d_0^3},
\end{equation}
where $\Omega'=\sqrt{\Omega^2-\frac{q_1 q_2}{8\pi\varepsilon_0 m d_0^3}}$ is the modified mechanical frequency due to the electrostatic interaction.
\subsection{Experimental setup}
The experimental setup is shown in Fig. \ref{Schematic}. The trapping beam ($\lambda=1064$ nm, Keopsys fiber amplifier seeded by a Mephisto laser) is expanded to a diameter of $8.7$ mm in order to overfill the apertures of the spatial light modulator (SLM, Meadowlark Inc.) and the microscope objective. We imprint a phase profile with the SLM into the trapping beam that transforms into an amplitude profile in the Fourier plane of the trapping optics. The phase profile is calibrated to compensate for aberrations, nonlinearities of the SLM response and non-flatness of the SLM surface. Inset of Fig. \ref{Schematic} shows the phase profile used to generate two traps spaced by $3.4~\mu\text{m}$. This phase profile is imaged onto the trapping optics using a 1:1 telescope set in a 4f configuration (focal length of lenses $300$ mm). The trap is then generated using a microscope objective (NA$=0.8$, WD $= 1$mm, Nikon Corp.), focusing the beam to two traps of waist $\approx 730nm$. The total power used in front of the vacuum chamber is $\approx 1.2$ W. We maintain a stable pressure of $p\approx 1.5$ mbar in the vacuum chamber, at which a single particle is in a thermal equilibrium with the environment.
\begin{figure}[!ht]
\includegraphics[width=\linewidth]{SupplementSetup.pdf}
\caption{Setup for generating multiple traps using a spatial light modulator. 1064 nm laser light, with a diameter of 8.7mm, is reflected on a Spatial Light Modulator (SLM Meadowlark Inc.) where a phase profile is imprinted. In the Fourier plane of the trapping objective the phase profile is translated into an amplitude profile with correct imaging being ensured via a 4f configuration using a 1:1 telescope. The light is recollimated and split for detection, with the traps being selected using movable pin holes in 1:1 telescopes.}
\label{Schematic}
\end{figure}
A pair of electrodes mounted on a 3D piezo stage (MX25, Mechonics Inc.) is placed around the beam focus, with a spacing of $D_c=(230\pm 15)~ \mu\text{m}$. The light is recollimated using an aspheric lens (C660TME-C, Thorlabs) and split at a polarization beamsplitter (PBS2) for power monitoring. The reflected arm is split with a $50:50$ beamsplitter. We mount a pinhole on a translation stage in the focus of a 1:1 telescope ($f=125$ mm) in each of the beamsplitter outputs, which we use to select individual laser beams in order to separate the detection. In each arm the trapping beam goes onto one photodiode of a balanced photodetector (PDB425C, Thorlabs), while the reference beam of equal power (taken from PBS1) is focused onto the other photodiode in order to suppress the intensity noise. We acquire $2$ seconds of data at a sampling rate of $2.5~\text{MSa}/\text{s}$ with an oscilloscope (PicoScope 5444D).
\subsection{Charge calibration}
In order to estimate the magnitude of the electrostatic interaction between the particles, we performed charge calibration for each particle used in the experimental runs. We increase the trap separation to approximately $18~\mu\text{m}$ in order to minimize all interactions and cross-talk in the detection. We subsequently apply a sinusoidal voltage ($F_d(t)=F_0 \sin (\Omega_d t)$) to the electrodes set along the x axis, with the driving frequency $\Omega_d$ close to the mechanical frequencies along the x axis $\Omega_x$. We measure the particle displacement as a function of the driving frequency \cite{Magrini2}:
\begin{equation}
\label{1}
\langle x_d^2\rangle =\frac{\langle F_d^2\rangle}{m^2(\Omega_{x}^2-\Omega_{d}^2)^2}
\end{equation}
Here, $\langle \cdot \rangle$ is the time average, $\langle F_d^2\rangle= F_0^2/2$ is the applied half-amplitude force, $m=(7.0\pm 0.7)$ fg is the particle mass, $\Omega_x$ is the trap frequency (in rad/s) along the x axis, $\Omega_d$ is the drive frequency (in rad/s).
Assuming a model for a massive point charge in a parallel-plate capacitor, we get $F_0 = \frac{qV}{D_c}$ where $q=Ne$ is the particle charge, $V$ is the applied voltage and $D_c=(230\pm 15)~\mu\text{m}$ is the distance between the electrodes. We can express Eq. \ref{1} in terms of the number of charges to get:
\begin{equation}
N = \frac{\sqrt{2}mD_c}{eV}\left|\Omega_{x}^2-\Omega_{d}^2\right|\sqrt{\langle x_d^2\rangle}
\end{equation}
After a position-displacement calibration \cite{NovotnySensing2018}, we extract $\langle x_d^2\rangle$ by integrating over the drive frequency in the spectrum. Table \ref{table1} lists the number of charges for each particle used in the main text.
\begin{figure}[!ht]
\label{2}
\includegraphics[width=\linewidth]{PeaksAndSigns.pdf}
\caption{a) Example spectra with the drive frequency $\Omega_d=2\pi\times200$ kHz. The mechanical frequencies are set to be different in order to check that we have independent readout of the particles. b) Time trace of the driven particle motion at the drive frequency. The phase between the particles is indicative of the sign of the charges. Equal and opposite sign of charges is reflected in the in-phase or out-of-phase response to the drive, respectively. }
\end{figure}
\begin{table}[h!]
\begin{tabular}{ |c|c|c|c|c| }
\hline
Figure in the main text & $|N_1|$ & $|N_2|$& sign($N_1 N_2$)&$g_C/\Omega'$\\
\hline
3a & $23\pm5$ &$5\pm 2$ &1&$-(4.6\pm 2.1)\times 10^{-4}$\\
\hline
3b & $3\pm 1$ & $1\pm 1$ &-1&$(1.2\pm1.3)\times 10^{-5}$\\
\hline
4c & $1\pm 1$ & $0 \pm 1 $&n.a.&$(0\pm4)\times 10^{-6}$\\
\hline
4d & $110 \pm 24$ & $96 \pm 21$ &-1&$0.047 \pm 0.015$\\
\hline
\end{tabular}
\caption{Results of the charge calibrations performed on 4 sets of particles. $N_1$ and $N_2$ are the number of elementary charges on the particles. Each row represents a set of particles used for measurements in the main text. We provide the coupling rate due to the electrostatic interaction at a distance of $3.2~\mu\text{m}\approx 3\lambda$ and for the mechanical frequency $\Omega=2\pi\times 50$ kHz.}
\label{table1}
\end{table}
\subsection{Interaction model used for fitting}
We correct for aberrations \textit{in situ} with the SLM, however the trapping field still has the shape of an Airy function in the focus due to the high numerical aperture of the microscope objective. This leads to a small overlap of the trapping fields at distances larger than the trap waist, therefore we are unable to separate the trapping fields in the description of the total interaction. This leads to a "self-interference" effect, where for example at the position of particle 2 the scattered field of particle 1 interferes with the tail of the trapping field for particle 1 \cite{WeiLateralBinding}. We model this with a standing wave in the focal plane with a relative electric field magnitude $A$. Already a weak tail of the trapping potential can have a large impact as it becomes comparable to the magnitude of the dipole radiation. This effect leads to a slight modification of the trap positions.
Furthermore, the radiation pressure of the scattered fields displaces the particles from the desired trap positions. The actual distance between the particles is smaller (larger) in the presence of an attractive (repulsive) force. This is confirmed when we compare coupling rates obtained for $\Delta\phi_0=0$ and $\Delta\phi_0=\pi$ in Fig. 3a in the main text; the period between the zero crossings of the coupling rate is larger for positive coupling rates, which is a result of the displacement by the optical force.
We include both effects in the model of the dipole-dipole interaction and find an excellent fit between the model and the experimental data for distances larger than $\sim 2.4~\mu\text{m}$ in Figure 3a in the main text. We point out that at smaller trap separations we neglect several features of the trap potential and the near-field optical interaction, as well as the (small) effect of the aerodynamic coupling. In future experiments at closer trap separations we will have to investigate the trap potential shape, as well as include the dipole radiation component $\propto d_0^{-2}$ which is non-negligible at trap separations $d_0\sim \lambda$.
\subsection{Normal mode splitting of the x and y motions}
In the main text we have presented the results obtained only for the motion along the optical axes (z axes). However, standard optical binding interaction exists for all three directions of the particle motion due to the modification of the interparticle distance $d^2=(d_0+x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2$. The coupling rate between the x motions has the following form: $g_x\sim G/(2\Omega_x kd_0))$. We observe an avoided crossing between the x motions at a distance $d_0\approx 2.2~\mu\text{m}$ (Fig. \ref{nmsx}). We extract the coupling rate of $g_x/\Omega'_x=0.013\pm 0.002$, which is significantly smaller than the coupling rate between the z motions from the main text as expected. The coupling rate $g_x/\Omega'_x$ scales $\propto \Omega_x^{-2}$, thus the higher mechanical frequency by a factor of $\Omega_x/\Omega\approx 4$ yields a smaller ratio $g_x/\Omega_x$ by a factor of $\sim 16$ in comparison to $g/\Omega$, which fits to the measured value of $g/\Omega'\approx 0.186$ from the main text. We are unable to observe the avoided crossing between the y motions as the coupling rate is smaller than the mechanical damping.
\begin{figure}[!ht]
\includegraphics[width=0.4\linewidth]{SINormalModeSplittings.pdf}
\caption{Normal mode splitting of the x motion due to the dipole-dipole interaction between two particles at a distance $d_0\approx 2.2~\mu\text{m}$.}
\label{nmsx}
\end{figure}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,373 |
require "CSV"
def load_airports
airports_file = "airport-data/airports.csv"
CSV::Converters[:blank_to_nil] = lambda do |field|
field && field.empty? ? nil : field
end
CSV.new(File.open(airports_file), :headers => true, :header_converters => :symbol, :converters => [:all, :blank_to_nil])
.map { |a| a.to_h }
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,301 |
Q: How to make Flutter HTTP partial (range) request? Code
I have this main.dart Flutter code:
import 'package:http/http.dart' as $http;
Future main() async {
await hit();
}
Future hit() async {
const url = 'https://data.wikibulary.com/data/plain/index/en/0.bin';
const len = 10000024;
final resp = await $http.get(url, headers: {
'range': 'bytes = ${len - 1}-${len - 1}',
'cache-control': 'no-cache',
});
final headers = resp.headers.entries.fold('', (r, i) => '$r\n${i.key}: ${i.value}');
print('length: ${resp.bodyBytes.length}\n-------------\nheaders:\n$headers');
}
Problem
Range request header is ignored for Windows desktop and Android. For Flutter Web it works great.
Response headers for all three platforms:
WEB:
statusCode: 206
length: 1
-----------
cache-control: public, max-age=86400000
content-length: 1
content-type: application/octet-stream
date: Sat, 09 Jan 2021 11:12:22 GMT
etag: 0x8D8B4749CC587E6
last-modified: Sat, 09 Jan 2021 08:00:21 GMT
WINDOWS:
statusCode: 200
length: 10000024
-----------
connection: keep-alive
last-modified: Sat, 09 Jan 2021 08:00:21 GMT
cache-control: public, max-age=86400000
access-control-allow-origin: *
date: Sat, 09 Jan 2021 11:09:00 GMT
vary: Accept-Encoding
age: 6367
content-type: application/octet-stream
accept-ranges: bytes
content-length: 10000024
etag: 0x8D8B4749CC587E6
ANDROID EMULATOR:
I/flutter ( 5528): statusCode: 200
I/flutter ( 5528): length: 10000024
I/flutter ( 5528): -----------
I/flutter ( 5528):
I/flutter ( 5528): connection: keep-alive
I/flutter ( 5528): last-modified: Sat, 09 Jan 2021 08:00:21 GMT
I/flutter ( 5528): cache-control: public, max-age=86400000
I/flutter ( 5528): access-control-allow-origin: *
I/flutter ( 5528): date: Sat, 09 Jan 2021 11:10:42 GMT
I/flutter ( 5528): vary: Accept-Encoding
A: Problem solved, space char matter in 'bytes = ${len - 1}-${len - 1}'
Correct code is:
final resp = await $http.get(url, headers: {
'range': 'bytes=${len - 1}-${len - 1}',
'cache-control': 'no-cache',
});
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,427 |
Q: How to count specific characters in all lines in notepad ++ I need to count the number of | symbol and make sure that each line contains 6 of them. How do i do it in notepad++ to highlight the lines that contains less or more than 6 | symbol?
For example:
1.The F in TGIF means?|Fish|Fort|Friday|Father|Fan|3
2.The T in TGIF means?|Thank|Tooth|Tank|Tiger|1
3.The G in TGIF means?|Gundam|Go-pro|Genetics|Google|God|Goldfish|5
Line 2 and 3 need to be highlighted to inform me that there is more/less than 6 of the symbol |
A: you can try this pattern that checks in a lookahead that the line doesn't contain exactly 6 pipes:
^(?!(?:[^|\n]*\|){6}[^|\n]*$).+
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 590 |
{"url":"https:\/\/www.hackmath.net\/en\/math-problem\/5190","text":"# Calories\n\nA large order of McDonald\u2019s french fries has 500 calories. Of this total, 220 calories are from fat. Find the ratio of the calories from fat to total calories in a large order of McDonald\u2019s french fries.\n\nCorrect result:\n\nx = \u00a011:25\n\n#### Solution:\n\n$x=220\\mathrm{\/}500=\\frac{11}{25}=0.44=11:25$\n\nWe would be pleased if you find an error in the word problem or inaccuracies and send it to us. Thank you!\n\nTips to related online calculators\nCheck out our ratio calculator.\n\n## Related math problems and questions:\n\n\u2022 Ounce\n749 calories in a 7 - ounce serving . What is the unit rate?\n\u2022 Fewer than 500 sheep,\nThere are fewer than 500 sheep, but if they stand in a double, triple, quadruple, five and sixth order, one sheep will remain. But they can stand in the seventh order. How many are sheep?\n\u2022 Moneys in triple ratio\nMilan, John and Lili have a total 344 euros. Their amounts are in the ratio 1:2:5. Determine how much each of them has?\n\u2022 Ratio\n6 numbers are in the ratio 1:5:1:5:5:5. Their sum is 242. What are the numbers?\n\u2022 Dividing money\nMilan divided 360 euros in the ratio 4: 5, Erik in the ratio 500: 625. How many euros did the individual parts of Milan and how many Erik?\n\u2022 Salary raise\nThe monthly salary was 620 Eur. During the year it was raised to 727 Eur. Calculate the month from salary was increased that employee earned 7547 Eur during the whole year.\n\u2022 Plot\nThe plot on which Mr. Kalous is to build a house has the shape of a rectangle. On a 1: 500 scale, its dimensions are 7cm and 5.5cm. Find out the dimensions of the plot. Calculate the parcel size.\n\u2022 Two machines\nPerformances of two machines are in a ratio of 7:12. A machine with less power produced 406 pieces of products per shift. a) How many pieces produced per shift second machine? b) How many pieces produced two machines together for five shifts?\n\u2022 School books\nAt the beginning of the school year, the teacher distributed 480 workbooks and 220 textbooks. How many pupils could have the most in the classroom?\n\u2022 Ratios\nReduce the numbers: 50 in a 1:2 ratio 111 at a ratio of 2:3 70 at 10:50 560 at a ratio of 3:8\n\u2022 A family\nA family of four consumes 220 liters of water a day. How many hectoliters of water are consumed by 68 tenants per day?\n\u2022 Building\nAt the building, we divided 240 boards into two piles in a 5: 3 ratio. How many were fewer boards in the lower pile?\n\u2022 Ratio three numbers\nThree numbers SUV are in the ratio 1:2:3. Their sum is 24. Find this numbers and write their add and sum.\n\u2022 Natural gas in kWh\nGas consumption for 2017 was 11,301 kWh I paid 532 \u20ac How much 1 m3?\n\u2022 Lcm simple\nFind least common multiple of this two numbers: 140 175.\n\u2022 Ratios\nDivide: a) 250 CZK in the ratio 2:3 b) 1000 CZK in the ratio 4:7:9\n\u2022 Two villages\nTwo villages are 11 km and 500 m away. On the map, their distance is determined by a 5 cm long line. Find the scale of the map.","date":"2021-02-28 10:36:29","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 1, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.38490214943885803, \"perplexity\": 2796.474067415939}, \"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-2021-10\/segments\/1614178360745.35\/warc\/CC-MAIN-20210228084740-20210228114740-00466.warc.gz\"}"} | null | null |
Fondatore della Brookings Institution, con il suo supporto finanziario e gestionale portò l'Università Washington di St. Louis ed in particolare la scuola di medicina a diventare un ateneo di rilevanza nazionale.
Con un finanziamento acquisì un terreno da cento acri che divenne il Campus Hilltop dell'università, la cui sede centrale fu nominata "Brookings Hall" in suo onore, mentre agli amici William K. Bixby, Adolphus Busch e Edward Mallinckrodt furono intitolati altrettanti palazzi ai lati del campus.
Dopo aver fatto fortuna con cartello nel settore degli articoli per la casa fra la sua ditta famigliare e la Cupples & Marston, si ritirò dagli affari molto giovane. Nel 1917 il presidente Woodrow Wilson lo volle dapprima nel War Industries Board, e in seguito lo nominò presidente del comitato prezzi statunitense.
La città di Brookings, nell'Oregon, porta ancora il suo nome.
Biografia
Figlio del Dr. Richard e di sua moglie Mary Eliza (Carter) Brookings, trascorse l'infanzia a Little Elk Creek nella contea di Cecil, vicino a Baltimora. Il padre morì quando Robert aveva solo due anni e la famiglia venne a trovarsi in difficoltà economiche.
Robert Brookings dovette abbandonare la scuola dopo il primo anno. Nel 1867, si trasferì a St. Louis, nel Missouri, per unirsi a suo fratello Harry come impiegato della Cupples & Marston, un grossista di articoli per la casa. Lavorando anche al chiaro di luna come contabile, riusciva a portare a casa un salario di $ 10 al mese aggiuntivi rispetto alla paga base impiegatizia di 25 dollari.
Abile venditore, persuase Samuel a dargli una posizione da commerciale, che gli guadagnò il soprannome di batterista.
Dopo quattro anni di esperienza con la Cupples e Marston, i fratelli Brookings decisero di mettersi in proprio. Cupples propose a Robert di diventare partner e socio in affari, piuttosto che perderlo in una nuova compagnia. Robert rifiutò la controproposta e fondò una nuova azienda con e Harry. I Brookings viaggiarono in tutto il Paese (per promuovere i loro prodotti), mentre la Cupples acquisì una posizione dominante nel commercio di articoli in legno. A trent'anni, Robert Brookings divenne il milionario vicepresidente della compagnia.
Una delle maggiori intuizioni imprenditoriali di Brookings fu la costruzione della Cupples Station, completata nel 1895. Egli notò che le compagnie pagavano per spedire merci dalle ferrovie nel centro di St. Louis ai magazzini lungo il fiume, Brookings ebbe l'idea di localizzare i magazzini direttamente lungo la ferrovia, in modo che i treni potessero compiere le operazioni di carico-scarico merci direttamente all'interno dei magazzini stessi. La Cupples Station aveva diciotto magazzini progettati da William Eames e Thomas Young. La stazione rivoluzionò il trasporto marittimo a St. Louis e divenne un modello logistico implementato anche in altre città. La sua costruzione richiese l'acquisto di otto blocchi di proprietà e la società non riuscì a evitare il fallimento. poiché non trovò nessuna banca americana disposta a oncedergli un prestito. Brookings, infine, trovò una banca britannica lo che salvò la ditta con un prestito di 3 milioni di dollari.
Nel 1895, ormai tranquillo dal punto di vista finanziario, Brookings si ritirò dagli affari a quarantasei anni, decisendo di dedicarsi ad attività di beneficenza e filantropiche, ed in particolare all'istruzione. Dopo aver supportato la propria università, indirizzò i propri contributi alla Washington University, divenendo presidente del consiglio di fondazione dell'ateneo. Con una donazione di oltre 5 milioni di dollari in contanti e proprietà (pari ad 82 attualizzati al 2017) acquisì un posto nel consiglio di amministrazione, dove rimase fino alla morte. Brookings prese in affitto molti dei nuovi edifici universitari di St. Loius, in vista dell'Esposizione mondiale del 1904.
Nel 1917, il presidente Woodrow Wilson nominò Brookings nel War Industries Board, e in seguito lo nominò presidente del suo comitato per l'amministrazione dei prezzi e il contingentamento delle quote di mercato, fungendo da facilitatore e punto di raccordo fra il governo degli Stati Uniti e i diversi settori dell'economia nazionale, pur molto diversi tra loro. Il ruolo del consiglio era quello di coordinare gli sforzi per fornire e distribuire cibo e beni materiali ai militari. Brookings fu insignito della Distinguished Service Medal degli Stati Uniti, della Legione d'Onore francese e dell'Ordine della Corona d'Italia per le attività prodigali svolte in tempo di guerra.
Nel 1916 Brookings divenne il primo presidente del consiglio di amministrazione dell'Institute for Government Research, un'organizzazione indipendente dedicata agli studi politici. Anni dopo, Brookings ottenne dalla Carnegie Corporation i fondi necessari per creare l'Istituto di Economia. Nel 1928, Brookings destinò il suo denaro alla nascita di una scuola di specializzazione in economia e management.
Nello stesso anno, queste tre organizzazioni confluirono nella Brookings Institution, la quale influenzò la politica del governo federale per più di mezzo secolo: dal bilancio degli anni '20 al Tax Reform Act del 1986.
Brookings si spense nel 1932 a Washington e fu sepolto nel cimitero Bellefontaine di St. Louis.
Ancora negli anni 2000, la Brooking Institution era uno dei principali gruppi di riflessione negli Stati Uniti. L'influsso nella vita democratica ed economica statunitense fu tale che la presidenza Nixon nel '73 progettò di mettervi fine.
Vita privata
A gennaio del 1876, Robert Brookings divenne il compagno di una vita di Isabel Valle (m. 1965).
Brookings rimase scapolo fino all'età di settantasette anni. Costruì tre palazzi a St. Louis e divenne proprietario anche una tenuta di campagna. Con una certa degli altri amici, nel 1927 fuggì con Isabel January, allora cinquantunenne, che conosceva da anni e con la quale aveva costruito un palazzo della scuola forense della Washington di St. Louis e il quartier generale della Brookings Institution.
Opere
Brookings scrisse tre libri:
Industrial Ownership (1925);
Economic Democracy (1929);
The Way Forward (1932).
Note
Voci correlate
Università Washington a Saint Louis
Woodrow Wilson
Complesso militare-industriale e politico
Jimmy Carter
Altri progetti
Collegamenti esterni
Decorati con la Legion d'onore | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,584 |
<?php
use Roots\Sage\Setup;
use Roots\Sage\Wrapper;
?>
<!doctype html>
<html <?php language_attributes(); ?>
<?php get_template_part('templates/head'); ?>
<body id="page-top" class="index">
<?php include Wrapper\template_path(); ?>
<?php
do_action('get_footer');
get_template_part('templates/footer');
wp_footer();
?>
</body>
</html>
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,677 |
In this Instructable I'm going to show you how I made a concrete and acrylic LED lamp with a wooden base.
Here I'll try to embed tiny acrylic pieces into concrete, which will guide the light from the LED light source to the concrete surface.
Step 1: Cutting the Acrylic and the Styrofoam.
The acrylic piece that I'm using is 5 mm thick. I cut around 60 tiny pieces of it on my table saw using the crosscut sled.
For the mold I'm using 10 mm thick Styrofoam board. I marked all the dimensions and cut it using a metal ruler and a utility knife for more precision.
Step 2: Inserting the Acrylic Into the Styrofoam.
The most complicated thing I need to do is combining acrylic and concrete. But, I found a pretty good way to do that.
I created random holes into each Styrofoam piece with a hot screwdriver, which I heated up onto a portable gas stove.
Then, I inserted the acrylic into the smallest Styrofoam piece, which will actually be the bottom of the mold, and secured them in place with zip tie.
Step 3: Bending the Acrylic Pieces.
When it comes to inserting the acrylic into the sides of the mold, there's one important step that will make that possible. And that step is bending the acrylic.
So, I bent the acrylic using a simple technique that requires only a gas stove and a lighter. I turned the gas stove on, reduced the heat and placed a piece of acrylic above, waiting for about 20 seconds until it softened so that I can easily bend it.
This way I bent all the pieces of acrylic and inserted them into the holes that I previously made. To make the next step easier I tied them up with zip ties.
Now, I can secure the acrylic in place with hot glue.
Applying cooking oil over the Styrofoam surface will prevent the concrete from sticking to the mold.
Step 4: Assembling the Mold.
Finally, I can assemble the mold.
Instead using an adhesive for Styrofoam, I went with toothpicks and hot glue. The toothpicks served as dowels, and the hot glue helped me fill in all the gaps between the joints.
Additionally, I used a corner clamp, a masking tape and a duct tape to secure the mold.
Step 5: Mixing Up Some Concrete.
Now I can mix up some concrete. I mixed one part sand with one part cement, and gradually added water until I got a thick consistency. Then, I poured the concrete into the mold. Here I needed to vibrate the mold by hand to fill in all the voids.
I poured concrete into the mold until it reached around 20 cm height. At the end, I additionally vibrated the mold to release the air pockets.
When I was done, I let the concrete cure for 2 days.
Step 6: Removing the Mold and Cutting the Extra Length of the Acrylic.
Removing the mold was very easy, I only had a difficulty with the hot glue which stuck onto the acrylic. But, I removed that easily with a utility knife.
All acrylic pieces need to be flush with the concrete surface. So, I cut all the parts of the acrylic that were sticking out of the concrete with a coping saw.
Also, I needed to cut the extra length of the acrylic on the bottom, and left only 3 cm of it.
Then, I sanded the concrete surface with my random orbit sander to remove all the imperfections.
Step 7: Creating the Wooden Base.
Now, I can move on to the wooden base. The base I made out of beech wood. I cut 4 identical pieces at a 45 degree angle in order to get a clean look, because I want the focus to be on the concrete and the acrylic.
When I placed the wooden pieces onto the concrete, I realized that some of the acrylic pieces were closer to the edge which doesn't allow the wood to sit flush with the concrete. So, I needed to remove parts of the thickness of the wood on the crosscut sled.
It took me a while until I finished, because I needed to adjust the blade all the time, but I was really satisfied with the end result. I made just enough space for the acrylic to fit inside the base.
On the bottom of the base I'll attach a fiberboard piece, so I need to make rabbets on each wooden piece, 5 mm wide and 7 mm deep. These rabbets will give a cleaner look to the base.
Step 8: Making Space for the LED Controller.
I took the wooden piece that will go on the back side of the lamp, and made a space for the LED controller. I drilled two holes, on for the power plug, and the other for the infrared receiver. On the other side I made enough space for the controller with a Forstner bit and a chisel.
Next, I'm going to glue up the base. Using masking tape as a clamp when gluing mitered corners together works pretty well.
Step 9: Applying Finish to the Concrete and the Wood.
While the base is drying, I can protect the concrete surface with a transparent finish. First, I cleaned the surface with a wet rug, and then sprayed all over the concrete.
Now I can go back to the base.
One corner had a gap on the joint, so I filled in the gap with a combination of wood glue and saw dust. I was surprised of how good it turned out.
After that, I hand sanded the base, first with 120, and then with 220 grit sandpaper. To protect the wood, I applied one coat of transparent finish.
Step 10: Installing the Light.
Next, I can work on the light. I cut 1 meter RGB LED strip on the predetermined cutting points. Then, I took the connector, stripped off the wires, and soldered them on the LED strip appropriately. I'm using 12 V power adapter.
Before gluing everything in place, I made a test to see how it works.
Everything was OK, so I hot glued the controller and the infrared receiver in place.
Then, I stuck the LED strip into the base.
Step 11: Joining All the Parts Together.
To cover the bottom I used 3 mm thick fiberboard, and attached it only with 2 screws, so that I can easily remove it if needed.
All the pieces are ready for assembly. I applied a large amount of epoxy to make a strong connection between the wood and the concrete.
The last thing I need to do is to attach silicone cabinet bumpers on the bottom to protect the surface where the lamp will be placed on.
Now I can insert the plug, turn the lamp on, and enjoy the fascinating effect.
Don't forget to watch the video for full experience!
If you like this project please follow me on social media and subscribe to my YouTube channel.
This project is so beautiful and your video presentation was amazing!
very competent technical skills! Very much enjoyed your fabrication techniques. I think this design can lend itself to outdoor objects e.g. garden lighting features. as the voltage is low and concrete is robust enough to withstand the weather. Have you considered optical fibers instead of acrylic strips? Acrylic will work well but a lot of work involved especially if you consider that a more polished end is required to capture optimal light from the LED source. In any case, well done on a well executed project! | {
"redpajama_set_name": "RedPajamaC4"
} | 8,541 |
START_ATF_NAMESPACE
namespace Info
{
using _qry_case_select_guild_master_lastconnctor__qry_case_select_guild_master_lastconn2_ptr = void (WINAPIV*)(struct _qry_case_select_guild_master_lastconn*);
using _qry_case_select_guild_master_lastconnctor__qry_case_select_guild_master_lastconn2_clbk = void (WINAPIV*)(struct _qry_case_select_guild_master_lastconn*, _qry_case_select_guild_master_lastconnctor__qry_case_select_guild_master_lastconn2_ptr);
using _qry_case_select_guild_master_lastconnsize4_ptr = int (WINAPIV*)(struct _qry_case_select_guild_master_lastconn*);
using _qry_case_select_guild_master_lastconnsize4_clbk = int (WINAPIV*)(struct _qry_case_select_guild_master_lastconn*, _qry_case_select_guild_master_lastconnsize4_ptr);
}; // end namespace Info
END_ATF_NAMESPACE
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,291 |
\section{INTRODUCTION}
The Cherenkov Telescope Array (CTA) \citep[e.g.,][]{acharya2013} is a next-generation ground-based observatory for gamma rays in the energy range from a few tens of GeV to beyond 300 TeV. The CTA concept combines a large number of imaging atmospheric Cherenkov telescopes of different sizes in two sites in the Northern and Southern hemispheres to observe the whole sky over this large energy range with unprecedented sensitivity and angular resolution.
The CTA Southern array will include 70 Small-Sized Telescopes (SSTs) \citep[e.g.,][]{montaruli2015} spread over an area of $\sim$7~km$^2$ that dominate the sensitivity in the energy range from a few TeV to 300 TeV and beyond. Multi-TeV gamma-ray showers generate a large amount of Cherenkov light, thus SSTs (with $\sim$4~m diameter reflectors) are sufficient for efficient detection. A large number of these SSTs spread over an area of $\sim$7~km$^2$ provides the huge effective area needed to achieve the desired sensitivity at the highest energies given the rapidly declining numbers of gamma rays from sources with power-law energy spectra. With a field of view $\gtrsim 8^\circ$ and an angular resolution of a few arcminutes, the SSTs will provide the highest-resolution survey ever of the sky in this energy domain that is crucial, e.g., to understanding extreme particle accelerators in the Universe, establish the nature of the sources of Galactic cosmic rays up to the knee, and look for potential signals of new physics at the highest energies.
The Gamma-ray Cherenkov Telescope (GCT) is one of the proposed telescope designs for the CTA SST array. In this contribution we provide an overview of the GCT project, and describe the status of the prototyping effort undertaken by the GCT team. We conclude with an outlook including future plans toward the realisation of CTA.
\section{OVERVIEW OF THE GCT PROJECT}
The GCT telescope (shown in Figure~\ref{gcttel}) features a dual-mirror design with Schwarzschild-Couder optics to achieve at the same time large aperture and optimal optical performance. The primary mirror diameter is 4 m, the secondary 2 m, and the focal length is 2.3 m. The GCT camera has a photodetector surface of size $\sim$0.4~m with 2048 pixels of physical size 6-7~mm. This provides an $\sim$8$^\circ$ field of view with pixels of angular size $\sim$0.2$^\circ$.
\begin{figure}[!hbt]
\centerline{\includegraphics[width=0.7\linewidth]{figures/GCT.jpg}}
\caption{A rendition of the GCT telescope.}\label{gcttel}
\end{figure}
The GCT telescope structure consists of a foundation which supports an alt-azimuth structure controlled through drive motors. This holds the optical support structure, including support for primary and secondary dish, as well as the camera, and counterweights. For the mirrors we are considering solutions based on polished and coated aluminium or cold-slumping glass. The primary is formed of six independent petals, while the secondary is assembled as monolithic unit.
The GCT camera is based on commercially available photodetectors. The two options considered are multi-anode photomultipliers (MAPMs) and Geiger-mode avalanche photodiodes, also known as Silicon photomultipliers (SiPMs). The signal, after pre-amplification and shaping, is processed by custom electronics modules based on application-specific integrated circuits (ASICs) of the TARGET family \citep{bechtol2012target,tibaldo2015TARGET}. The TARGET ASICs sample the signal at a high and configurable rate (typically 1~Gsample~s$^{-1}$) and form trigger signals (of adjustable length) based on the analog sum of the signals in four adjacent pixels (superpixels) exceeding a configurable threshold. Analog samples, stored in a buffer with depth of 16384 cells, can be digitised and transmitted off ASIC on demand, with typical readout windows of 96 to 128 samples. Backplane electronics control power distribution and form the trigger signals for the whole camera, based on the trigger signals from the TARGET modules (typically, from the coincidence of triggers from two neighbour superpixels). The camera trigger initiates digitisation and data transmission from the TARGET modules. Data Acquisition (DACQ) boards act as a switch for transmission off camera of the data packets (in UDP format) through an optical fibre. The camera also includes LEDs for calibration purposes \citep{Brown2015flashers}, and a liquid cooling system for temperature control.
\section{THE FIRST PROTOTYPE, COMMISSIONING CAMPAIGN, AND FIRST LIGHT}
The first prototype of the GCT camera based on MAPMs, also known as CHEC-M, Compact High-Energy Camera with MAPMs, was assembled and tested in the laboratory in 2015. CHEC-M employs H10966B MAPMs from Hamamatsu and ASICs of the fifth generation of the TARGET family. Figure~\ref{T5module} shows one of the 32 camera modules that compose CHEC-M. The backplane was custom produced, while the two 1 Gbit~s$^{-1}$ DACQ boards are commercial devices from Seven Solutions. The characterisation of the camera in the laboratory included calibration of the trigger and digitiser ASICs, calibration of the photodetector-readout chain gain, and gain equalisation of the different photodetectors through tweaking of the MAPM bias voltages.
\begin{figure}[!hbt]
\centerline{\includegraphics[width=0.75\linewidth]{figures/T5Module.pdf}}
\caption{One of the 32 camera modules of CHEC-M. The MAPM has 64 pixels. After pre-amplification the 64 analog signals are processed by 4 TARGET~5 ASICs (with 16 channels each). The module also produces on board the high-voltage (HV) bias for the MAPM. A single companion FPGA controls operations of the whole module and assembles data packets in UDP format to be transmitted off camera through the DACQ boards. The total module length is $\sim$40~cm.}\label{T5module}
\end{figure}
After laboratory testing, CHEC-M was installed in November 2015 on the prototype GCT telescope built at the Observatoire de Paris, in Meudon (see Figure~\ref{telescope}). The prototype telescope features only two out of six petals in the primary mirror (the other petals were replaced by dummies), and the primary petals are round rather than trapezoidal.
\begin{figure}[!hbt]
\centerline{\begin{tabular}{cc}
\includegraphics[width=0.45\linewidth]{figures/telescope.jpg}&
\includegraphics[width=0.45\linewidth]{figures/camera.pdf}
\end{tabular}}
\caption{On the left, the prototype telescope at the Observatoire de Paris-Meudon with the CHEC-M camera installed during the commissioning campaign of November/December 2015 (note the circular petals used that will be replaced by trapezoidal ones in the final system). On the right, closeup of the camera.}\label{telescope}
\end{figure}
After mechanical integration, the camera functionality tests were repeated on telescope, including checks on temperature stability. Data acquisition was initially tested using the calibration LEDs shining on the secondary mirror or a portable laser shining on the primary as light sources.
Owing to small delays in the system commissioning procedure, the final stage of the 2015 campaign, consisting of observations of the night sky, took place during a few nights that were closer to full moon than anticipated, with a night-sky-background light level estimated to be 20 to 100 times brighter than at the actual CTA site. The harsh observing conditions required the use of an MAPM bias voltage of 750~V, lower than values tested earlier in the laboratory (950~V and 1100~V). This implied that the gain and trigger calibration constants were not known. Trigger thresholds were therefore set through an empirical scan, resulting in a trigger rate of a few~Hz.
After data acquisition lasting for $\sim$10 minutes, we found a few tens of events that bore the unmistakeable appearance of Cherenkov shower images, like that shown in Figure~\ref{Cevent}.
\begin{figure}[!hbt]
\centerline{\includegraphics[width=1\linewidth]{figures/event.png}}
\caption{A Cherenkov event recorded by CHEC-M during the on-telescope campaign of November/December 2015 at the Observatoire de Paris-Meudon. Right: a full-camera image showing the amplitude of the digital signal in each pixel (after pedestal subtraction) corresponding to the 1-ns frame when the recorded Cherenkov flash peaks. Left: waveforms from two pixels labeled as 1, top, and 2, bottom, in the right plot. The waveforms show the signals from the two pixels that were digitised and recorded over 96~ns. The vertical lines mark the time corresponding to the image on the right. Only very preliminary calibration (pedestal subtraction) was applied.}\label{Cevent}
\end{figure}
For some of the events it was also possible to see a few~ns shift in light arrival time across the camera as expected for a Cherenkov flash from a shower inclined with respect to the telescope focal plane. The measurement of shower images by the prototype GCT telescope represents the first Cherenkov light detection using a telescope proposed for CTA, as well as the first measurement ever of Cherenkov shower images with a dual-mirror telescope. The results are discussed in more detail in these proceedings in the paper by J.~Watson et al.
\section{TOWARD THE 2016 COMMISSIONING CAMPAIGN}
After the first on-telescope campaign, CHEC-M was taken back to the laboratory to understand in more detail its performance and solve some issues that were discovered in the field.
\begin{itemize}
\item We are investigating the output data rates and the factors limiting these due to the different camera subsystems to address some issues with data packet loss; a revision of the TARGET modules and backplane electronics firmware, along with upgraded slow control and data acquisition software, solves the issue of packet loss up to a sustained data rate of 700~Hz (at the level foreseen for the GCT camera in normal operations).
\item We are characterising in more detail the triggering of the camera using a collimated light source with tuneable intensity.
\item A first prototype of a new safety board, that implements an improved safety and slow control concept (see below for a short description), will be integrated in CHEC-M for testing.
\end{itemize}
In the mean time, the telescope prototype drive system has been fully commissioned. Optical alignment of the system was perfected, and characterisation of its optical and pointing performance is now ongoing. Preliminary results indicate that the size of the optical point-spread function on the camera focal plane is $\sim5$~mm (80\% containment diameter), which is less than the transverse size of a pixel. Additional ongoing measurements include:
\begin{itemize}
\item optical transmission of the instrument;
\item quality of the alignment of mirrors on the telescope;
\item measurement of the quality of the optical surface.
\end{itemize}
A new campaign with CHEC-M back on the prototype telescope is anticipated for the fall of 2016. More details on the studies of the telescope prototype, and how Monte~Carlo simulations are being developed to inform the next on-telescope campaign, can be found in these proceedings in the paper by H.~Costantini et al.
\section{THE SECOND GCT CAMERA PROTOTYPE WITH SILICON PHOTOMULTIPLIERS}
We are currently developing a second camera prototype based on SiPMs, CHEC-S (Compact High-Energy Camera with SiPMs). This camera features S12642-1616PA-50 SiPMs from Hamamatsu, and a number of other upgrades and improvements:
\begin{itemize}
\item an improved mechanical design that includes focal-plane cooling to compensate for the power dissipation from the SiPMs and pre-amplifier boards, as well as a revised lid design with motorised control;
\item a new generation of TARGET ASICs, TARGET~C and T5TEA (see below for more details);
\item an improved safety and slow control concept, that includes a safety board with the capability to autonomously protect the camera subsystems from damage due to high temperature, over voltage, and high-current;
\item an upgrade to the DACQ boards to support data transmission at 10 Gbit~s$^{-1}$.
\end{itemize}
In addition to the different photodetectors, the latest-generation TARGET ASICs will provide a big step forward in performance. The original concept of a single ASIC combining sampling, digitisation, and triggering was posing a problem due to coupling between sampling and triggering operations that limited the trigger sensitivity to $\gtrsim 5$~ p.e. (with the photodetector and preamplifier gain planned for GCT). Therefore, the two functionalities were split into two separate ASICs. T5TEA provides triggering based on the same concept as TARGET~5, with a sensitivity reaching the single~p.e. level and trigger noise $\lesssim 1/4$~p.e. TARGET~C performs sampling and digitisation, with a dynamic range of 1.9~V and improved resolution with respect to TARGET 5 (cf. TARGET~7, used in the SCT telescope prototype for CTA). For more details on TARGET~C and T5TEA and the characterisation of their performance see the paper by D.~Jankowsky et al. in these proceedings.
\section{SUMMARY AND PLANS}
We have built a full prototype of the GCT telescope proposed for CTA as well as a first camera prototype based on MAPMs. The prototype assessment and characterisation is ongoing. The full system was tested in the field at the end of 2015, achieving the first detection of Cherenkov light from atmospheric showers with an instrument proposed for CTA. A new campaign in the field is planned by the end of 2016. In the mean time, a second camera prototype is being built. This new camera uses a different type of photodetector, SiPMs, and features many improvements to the camera mechanics and electronics. It will be assembled in early 2017, and tested in the laboratory and subsequently on the prototype telescope. Thereby, we will verify that GCT meets all the requirements for CTA.
CTA observatory construction is planned to start in 2017. The first phase, dubbed pre-production, will consist of the deployment of $\sim$10\% of the total number of each type of telescope on the final site for final testing and characterisation before the mass production phase. We propose to deploy 3~GCT telescopes on site in 2018 as part of the pre-production phase for CTA. Later, we propose to contribute up to 35 SST to the CTA array.
\section{ACKNOWLEDGMENTS}
We gratefully acknowledge support from the agencies and organisations
listed under Funding Agencies at this website: http://www.cta-observatory.org/.
\bibliographystyle{aipnum-cp}%
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,168 |
Wenas Wildlife Area is a protected area managed by the Washington Department of Fish and Wildlife located in Yakima and Kittitas counties. The property was acquired in the mid-1960s to provide wintering grounds for the Yakima elk herd and is managed with the chief purpose of providing healthy wildlife habitat.
References
External links
Wenas Wildlife Area Washington Department of Fish and Wildlife
Nature reserves in Washington (state)
Protected areas of Kittitas County, Washington
Protected areas of Yakima County, Washington | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,851 |
SONY at CES 2020: Amazing Content, Tech and Even a New Concept Car
by Editor | Jan 17, 2020
The world's biggest consumer tech event – CES 2020 – just came and went. CES which began in 1967 as the Consumer Electronics Show – basically a small gadget fair – has now become a really big gadget fair and a lot more with 170,000 attendees and 4,500 exhibitors. The world counts on it to debut what's new in technology from 5G and transportation advancements to IoT and virtual reality. But like everything else these days, CES continues to morph.
One change – some of the bigger companies like Apple and Amazon now introduce their new stuff at their own private events. Another change – visitors are happily more and more interested not just in new products, but also how these products affect security, privacy and human rights. A perfect example – Salesforce co-CEO Marc Benioff spoke on a panel called "Good for Business, Good for the Planet: How Companies Drive Positive Impact."
Know what's also morphing? How our largest customer at CES – Sony – is evolving its brand. A few years ago, Sony was all about showing products and letting visitors "touch and try" them. A visitor walking this year's Sony exhibit would have noted at least two important changes.
First, the continued evolution of Sony from product manufacturer to content creator. Think Jumanji: The Next Level and Once Upon a Time in Hollywood. Second, there is way less product, and in its place, Sony now focuses on showcasing the newest technologies it's pioneering to power both it's own products as well as those of others in many industries. And a big part of that is the technology it continues to develop to empower other content creators – both professionals and individuals – to create and share their own original content.
Here are two examples. One area of the exhibit was used for a surprise introduction of SONY's Vision S concept car (see photos). SONY's not selling it. Instead it's a vehicle (pun intended) that showcases all kinds of new tech, including Sony's imaging technology which provides the Vision-S with a 360-degree view of its environment.
Another area headlined "The Future of Movie Magic" featured the Ghostbusters' Ecto 1 converted ambulance (see photo) surrounded by a digital green screen. This was used to demo Sony's new Atom View technology which replaces the traditional green screen background with a giant Crystal LED display so that the background image is actually there while filming takes place (instead of a just a giant green wall). Even more impressive, that background changes angle and perspective with perfect realism as the camera moves around the set. All of which is a huge plus for actors, directors and cinematographers.
Other featured technology included Sony's 360 Reality Audio Technology. You have to hear this to believe it. There was also new AI technology that enhances sports training demoed by two people playing ping pong in the booth. Cool new TV technology including the "Frame Tweeter" was on display. This technology actually vibrates the TV's frame to make it part of the sound system. There was also a video demo of how Sony helped capture the first live football game in 5G last December showing how a 5G-connected camera can allow for more creative, untethered camerawork in live broadcast production. .
Sony's booth, of course, is dramatically different each year, although it remained it usual massive 25,000 square feet. The overall concept uses S-shaped curtains of different colors and materials to gracefully section off each of the exhibit's main demonstration areas without impeding access. The concept was conceived by Sony's Tokyo-based in-house design team, rendered by Blumlein Associates and then turned into executable reality and a beautiful finished booth by us. Credit for the amazing lighting goes to Illumination Production Services.
A simple bird eye's view of the overall exhibit layout are part of the slide show above. All photos by Mark Woudsma.
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,857 |
Q: php str_replace умлаут Как сделать на php замену умлаута в строке?
Обычные символы функция str_replace меняет, а вот умлауты нет.
Делал так:
$city = str_replace('ü','u',$city);
A: Вопрос решился изменением кодировки php файла.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,715 |
Q: Java Lucene 4.5 how to search by case insensitive We have implemented Java Lucene search engine 4.5, I am trying to search the content even if the field value is case insensitive (e.g., if I search a city with name "Banglore" I get a result, but when I search a city with name "banglore" I get 0 results).
I have used StandardAnalyzer for analyzing the data and WildcardQuery to match a Like condition (I tried as mentioned here without success).
I am not sure where I have gone wrong. I appreciate any guidance on fixing this case sensitivity problem.
public SearchHelper
{
Analyzer analyzer;
Directory index;
public IndexSearcher searcher = null;
public IndexWriter indexWriter = null;
public QueryParser parser = null;
private static int hitsPerPage = 100;
/**
* @param indexFileLocation
* @throws IOException
*/
public SearchHelper(String indexFileLocation) throws IOException
{
// this.analyzer =new StandardAnalyzer();
this.analyzer = new CaseStandardAnalyzer();
// analyzer = new ThaiAnalyzer();
this.index = FSDirectory.open(java.nio.file.Paths.get(indexFileLocation));
}
/**
* @param create
* @return
* @throws IOException
*/
public IndexWriter getIndexWriter(boolean create) throws IOException
{
if (indexWriter == null)
{
IndexWriterConfig iwc = new IndexWriterConfig(this.analyzer);
this.indexWriter = new IndexWriter(this.index, iwc);
}
return this.indexWriter;
} //End of getIndexWriter
/**
* @throws IOException
*/
public void closeIndexWriter() throws IOException
{
if (this.indexWriter != null)
{
this.indexWriter.commit();//optimize(); LUCENE_36
this.indexWriter.close();
}
} //End closeIndexWriter
/**
* @param indexFileLocation
* @throws CorruptIndexException
* @throws IOException
*/
public void startSearch(String indexFileLocation) throws CorruptIndexException, IOException
{
// searcher = new IndexSearcher(FSDirectory.open(new File(indexFileLocation)));
IndexReader reader = DirectoryReader.open(FSDirectory.open(java.nio.file.Paths.get(indexFileLocation)));
// IndexReader.open(this.index);
// open(getIndexWriter(true), true);
this.searcher = new IndexSearcher(reader);
}
/**
* @param fieldNames
* @param fieldValues
* @return
* @throws IOException
* @throws ParseException
*
* <p></p>
* https://stackoverflow.com/questions/2005084/how-to-specify-two-fields-in-lucene-queryparser
*/
public ScoreDoc[] searchSEO(String[] fieldNames, String[] fieldValues, int limitSize) throws IOException, ParseException
{
this.analyzer = new StandardAnalyzer();
int searchFieldSize = (null == fieldNames) ? 0 : fieldNames.length;
BooleanQuery booleanQuery = new BooleanQuery();
for (int i = 0; i < searchFieldSize; i++)
{
Query query1 = searchIndexWithWildcardQuery(fieldNames[i], fieldValues[i]);
addQueries(booleanQuery, query1, 2);
}
TopScoreDocCollector collector = null; // Or use by default hitsPerPage instead limitSize
if (limitSize > 0)
{
collector = TopScoreDocCollector.create(limitSize);
} else {
collector = TopScoreDocCollector.create(hitsPerPage);
}
this.searcher.search(booleanQuery,collector);
return collector.topDocs().scoreDocs;
}
/**
* @param whichField
* @param searchString
* @return
* @throws IOException
* @throws ParseException
*/
public Query searchIndexWithWildcardQuery(String whichField, String searchString) throws IOException, ParseException
{
Term term = addTerm(whichField, "*" + searchString + "*");
Query query = new WildcardQuery(term);
return query;
}
/**
* @param whichField
* @param searchString
* @return
*/
public Term addTerm(String whichField, String searchString)
{
Term term = new Term(whichField, searchString);
return term;
}
/**
* @param searchString
* @param operation
* @return
* @throws ParseException
*/
public Query addConditionOpertaion(String searchString, String operation) throws ParseException
{
Query query = null;
if ("and".equals(operation))
{
parser.setDefaultOperator(QueryParser.AND_OPERATOR);
} else if("or".equals(operation)) {
parser.setDefaultOperator(QueryParser.AND_OPERATOR);
}
query = parser.parse(searchString);
return query;
}
/**
* @param booleanQuery <code>BooleanQuery</code>
* @param q <code>Query</code>
* @param type <code>int</code> , 1--> Must, 2-->Should, 3 --> Must Not
*/
public void addQueries(BooleanQuery booleanQuery, Query q, int type)
{
switch(type)
{
case 1: booleanQuery.add(q, Occur.MUST);
break;
case 2: booleanQuery.add(q, Occur.SHOULD);
break;
default:booleanQuery.add(q, Occur.MUST_NOT);
break;
} //End of switch
}
public QueryParser getParser()
{
return parser;
}
public void setParser(String fieldName)
{
this.parser = new QueryParser(fieldName, this.analyzer);
}
public void getDefaultByStatus(int status)
{
this.analyzer = new StandardAnalyzer();
this.parser = new QueryParser("status", this.analyzer);
}
protected void doClear(File dir,boolean deleteSubDir)
{
for (File file: dir.listFiles())
{
if (file.isDirectory() && deleteSubDir)
{
doClear(file,deleteSubDir);
}
file.delete();
}
} //End of doClear();
protected void doClose() throws IOException
{
this.searcher.getIndexReader().close();
}
public boolean add(Object Obj) throws Exception
{
User currentUser = (User)Obj;
boolean isAdded = false;
org.apache.lucene.document.Document luceneDoc = new org.apache.lucene.document.Document();
luceneDoc.add(new IntField("oid", currentUser.getOid(), Field.Store.YES));
luceneDoc.add(new IntField("status", currentUser.getStatus(), Field.Store.YES));
luceneDoc.add(new StringField("login", currentUser.getLogin(), Field.Store.YES));
luceneDoc.add(new StringField("fName", currentUser.getFirstName(), Field.Store.YES));
luceneDoc.add(new StringField("lName", currentUser.getLastName(), Field.Store.NO));
luceneDoc.add(new StringField("email", currentUser.getEmailId(), Field.Store.YES));
luceneDoc.add(new StringField("city", currentUser.getCity(), Field.Store.YES));
// addRelatedFields(luceneDoc,city.getStateCode());
IndexWriter writer = getIndexWriter(false);
writer.addDocument(luceneDoc);
closeIndexWriter();
isAdded = true;
System.out.println(isAdded);
return isAdded;
} // End of add
public boolean update(Object Obj) throws Exception
{
boolean isUpdated = false;
User currentUser = (User) Obj;
org.apache.lucene.document.Document luceneDoc = new org.apache.lucene.document.Document();
// luceneDoc.add(new IntField("oid", currentUser.getOid(), Field.Store.YES));
luceneDoc.add(new IntField("oid", currentUser.getOid(), Field.Store.YES));
luceneDoc.add(new StringField("login", currentUser.getLogin(), Field.Store.YES));
luceneDoc.add(new IntField("status", currentUser.getStatus(), Field.Store.YES));
luceneDoc.add(new StringField("fName", currentUser.getFirstName(), Field.Store.YES));
luceneDoc.add(new StringField("lName", currentUser.getLastName(), Field.Store.NO));
luceneDoc.add(new StringField("email", currentUser.getEmailId(), Field.Store.YES));
luceneDoc.add(new StringField("city", currentUser.getCity(), Field.Store.YES));
// addRelatedFields(luceneDoc,city.getStateCode());
IndexWriter writer = getIndexWriter(false);
writer.updateDocument(new Term("login", currentUser.getLogin()),luceneDoc);
closeIndexWriter();
isUpdated = true;
return isUpdated;
} // End of update
public boolean delete(Object Obj) throws Exception
{
boolean isDeleted = false;
User currentUser = (User) Obj;
Term deleteTerm = new Term("login", currentUser.getLogin());
IndexWriter writer = getIndexWriter(false);
writer.deleteDocuments(deleteTerm); // Or use Query
writer.forceMergeDeletes();
closeIndexWriter();
isDeleted = true;
return isDeleted;
} // End of delete
@Override
public Object search(String[] fieldNames, String[] fieldValues, int returnType, int limit) throws Exception
{
Object obj = null;
org.apache.lucene.search.ScoreDoc[] hits = searchSEO(fieldNames,fieldValues, limit);
int hitSize = (null == hits) ? 0 : hits.length;
System.out.println("total:" + hitSize);
doClose();
return obj;
} // End of search
public void addThreadUser()
{
User user = new User();
addUserPojo(user);
add(user);
}
public void updateThreadUser()
{
User user = new User();
addUserPojo(user);
update(user);
}
public void deleteThreadUser()
{
User user = new User();
addUserPojo(user);
delete(user);
}
private void addUserPojo(User user)
{
user.setOid(3);
user.setLogin("senthil");
user.setFirstName("Semthil");
user.setLastName("Semthil");
user.setStatus(1);
user.setCity("Combiatore");
user.setEmailId("semthil@xyz.com");
}
public void searchUser()
{
searchUser(new String[] {"login"}, new String[] {"Se"}, null);
}
public static void main(String[] args)
{
SearchHelper test = new SearchHelper();
test.searchUser();
}
}
A: You are usingStringField to index your data but this field will bypass the analyzer chain and always index your term verbatim as one token, regardless of your analyzer. You should use TextField if you want to have your data analyzed and the StandardAnalyzer already does lower-casing.
Other than that, the WildcardQuery does not analyze its term, so if you search for Banglore, it won't match the now-lower-case banglore from the index. You have to lowercase the searchterm yourself (or use an analyzer on it).
A: Use the LowerCaseFilter as the post you referenced suggests:
TokenStream stream = new StandardFilter(Version.LUCENE_CURRENT, tokenizer);
stream = new LowerCaseFilter(Version.LUCENE_CURRENT, stream);
A more complete example is in this post.
A: You can use custome compare class
class CaseIgonreCompare extends FieldComparator<String>{
private String field;
private String bottom;
private String topValue;
private BinaryDocValues cache;
private String[] values;
public CaseIgonreCompare(String field, int numHits) {
this.field = field;
this.values = new String[numHits];
}
@Override
public int compare(int arg0, int arg1) {
return compareValues(values[arg0], values[arg1]);
}
@Override
public int compareBottom(int arg0) throws IOException {
return compareValues(bottom, cache.get(arg0).utf8ToString());
}
@Override
public int compareTop(int arg0) throws IOException {
return compareValues(topValue, cache.get(arg0).utf8ToString());
}
public int compareValues(String first, String second) {
int val = first.length() - second.length();
return val == 0 ? first.compareToIgnoreCase(second) : val;
};
@Override
public void copy(int arg0, int arg1) throws IOException {
values[arg0] = cache.get(arg1).utf8ToString();
}
@Override
public void setBottom(int arg0) {
this.bottom = values[arg0];
}
@Override
public FieldComparator<String> setNextReader(AtomicReaderContext arg0)
throws IOException {
this.cache = FieldCache.DEFAULT.getTerms(arg0.reader(),
field , true);
return this;
}
@Override
public void setTopValue(String arg0) {
this.topValue = arg0;
}
@Override
public String value(int arg0) {
return values[arg0];
}
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,660 |
{"url":"https:\/\/dsp.stackexchange.com\/questions\/10430\/preserving-integral-through-downsampling","text":"# Preserving integral through downsampling\n\nI've got a high-resolution image segmentation, which I'm downsampling (and non-linearly deforming) to fit on an ROI image. I typically blur the high-res image before downsampling with a Gaussian-fwhm related to the downsampling factor. The result is high-res and low-res images with the same mean.\n\nI'd like now for my high-res and low-res images to have the same sum. If I scale up the low-res image by the downsampling factor, will local sums be preserved across the image? Is there a better way to downsample and preserving local sums?\n\n\u2022 If I understand you correctly, that seems impossible! If my high resolution image is $[100\\ 100]$ and my low resolution image is $[100]$ (same mean value) then there is no way the two can also have the same sum. Perhaps I'm missing something! :-? \u2013\u00a0Peter K. Aug 22 '13 at 14:38\n\u2022 Oh, I mean make another low-resolution image; one which preserves the mean, and the other which preserves the sum! \u2013\u00a0Andrew Wood Aug 22 '13 at 14:46\n\u2022 :-) Thanks. In that case, just scaling by the downsampling factor should get very close to what you need. It probably won't be precisely correct, though. \u2013\u00a0Peter K. Aug 22 '13 at 15:24","date":"2019-08-18 11:58:00","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\": 0.8638538718223572, \"perplexity\": 1561.05432414178}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-35\/segments\/1566027313803.9\/warc\/CC-MAIN-20190818104019-20190818130019-00187.warc.gz\"}"} | null | null |
Ста́рая Салау́сь () — село в Балтасинском районе Республики Татарстан, административный центр Салаусского сельского поселения.
География
Село находится на реке Шошма, в 8 км к востоку от районного центра, посёлка городского типа Балтаси.
История
Село основано в период Казанского ханства.
В XVIII – первой половине XIX века жители относились к категории государственных крестьян. Основные занятия жителей в этот период – земледелие и скотоводство.
В начале XX века в селе функционировали мечеть, мектеб. В этот период земельный надел сельской общины составлял 1226,2 десятины.
В 1918 году в селе открыта начальная школа. В 1929 году — организован колхоз «Кызыл яшляр».
До 1920 года село входило в Янгуловскую волость Малмыжского уезда Вятской губернии. С 1920 года в составе Арского кантона ТАССР. С 10 августа 1930 года в Тюнтерском, со 2 марта 1932 года в Балтасинском, с 1 февраля 1963 года в Арском, с 12 января 1965 года в Балтасинском районах.
Население
Национальный состав села: татары.
Известные уроженцы
Ф. С. Баязитова (р. 1942) – языковед, доктор филологических наук.
Х. Г. Галимуллин (р. 1932) – заслуженный агроном ТАССР, председатель колхоза «Татарстан» (в 1971–1996 годах).
Экономика
Жители работают преимущественно в ООО «Татарстан», занимаются полеводством, овощеводством, мясо-молочным скотоводством.
Социальные объекты
В селе действуют многопрофильный лицей, спортивный комплекс (с 1992 года), дом культуры (с 1989 года), детский сад (с 1983 года), фельдшерско-акушерский пункт (открыт в 1942 году как медпункт), библиотека.
Религиозные объекты
Мечеть (с 1995 года).
Примечания
Литература
Ссылки
Населённые пункты Балтасинского района | {
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Transtecs implements active, standardized processes and commercial software packages as part of our Base and Facilities Operations Support system. We provide our customers' solutions to meet cost, schedule, and quality goals, mitigate risks, and manage key processes in supporting multiple scopes and responsibilities.
Our strategy includes implementing management control structures to Federal Government installation and facilities operations, through governance control boards as well as the tactical workforce level controls. Transtecs' Earned Value Management (EVM) and International Organization for Standardization (ISO) quality systems were developed to actively manage and measure operations and scope plans, recommend appropriate services and projects to support plan execution, monitor workforce and subcontractor performance and cost, and provide our customers visibility into program support status. | {
"redpajama_set_name": "RedPajamaC4"
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Q: Selenium - Running Firefox as root in a regular user's session is not supported I am very new to Selenium and all of the sudden for no reason an error is stopping me from running ANY Selenium tests.
This is the error I am getting when I run my Python script:
2018-05-14 12:07:52,766 [INFO ] Getting Selenium setup here.
Traceback (most recent call last):
File "test.py", line 308, in <module>
webcrawler.crawl()
File "test.py", line 177, in crawl
self.web_crawl.setup()
File "/test/src/webcrawlers/utils/webcrawl_lib.py", line 83, in setup
self.browser = webdriver.Firefox(firefox_profile=profile)
File "/usr/local/lib/python2.7/dist-packages/selenium/webdriver/firefox/webdriver.py", line 162, in __init__
keep_alive=True)
File "/usr/local/lib/python2.7/dist-packages/selenium/webdriver/remote/webdriver.py", line 154, in __init__
self.start_session(desired_capabilities, browser_profile)
File "/usr/local/lib/python2.7/dist-packages/selenium/webdriver/remote/webdriver.py", line 243, in start_session
response = self.execute(Command.NEW_SESSION, parameters)
File "/usr/local/lib/python2.7/dist-packages/selenium/webdriver/remote/webdriver.py", line 312, in execute
self.error_handler.check_response(response)
File "/usr/local/lib/python2.7/dist-packages/selenium/webdriver/remote/errorhandler.py", line 242, in check_response
raise exception_class(message, screen, stacktrace)
selenium.common.exceptions.WebDriverException: Message: Process unexpectedly closed with status 1
Now I can usually debug these issues. However, the geckodriver.log is not giving me much to work with:
1526299672891 geckodriver INFO geckodriver 0.20.1
1526299672895 geckodriver INFO Listening on 127.0.0.1:48641
1526299673899 mozrunner::runner INFO Running command: "/usr/bin/firefox" "-marionette" "-profile" "/tmp/rust_mozprofile.YNIc2l05QiIr"
Running Firefox as root in a regular user's session is not supported. ($HOME is /home/test which is owned by test.)
Environment:
*
*Geckodriver: 0.20.1
*Selenium: 3.12.0
*Python: 2.7. And I tried using 3 as well
*Firefox: 60.0
I even tried switching out to using Chrome, and the setup would just hang and give a unique error as well.
A side note is that this is on Amazon AWS, and I am not the administrator on the account. Maybe something was changed on that end.
A: I had the same problem with geckodriver 0.21.1, Selenium 3.12.0, and Python 3.5.2. It worked for me on Ubuntu 17.04 to remove Firefox and (firefox-dev) with sudo apt-get purge firefox, firefox-dev and then I install Firefox version 50.0 manually with:
wget http://ftp.mozilla.org/pub/firefox/releases/50.0/linux-$(uname -m)/en-US/firefox-50.0.tar.bz2
tar -xjf firefox-50.0.tar.bz2
sudo mv firefox /opt/
sudo mv /usr/bin/firefox /usr/bin/firefox_old
sudo ln -s /opt/firefox/firefox /usr/bin/firefox
After those steps it also worked with root.
| {
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} | 7,902 |
layout: tagpage
title: "Tag: calico"
tag: calico
---
| {
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} | 96 |
\section{Introduction}
A \emph{Littlewood polynomial} is a polynomial whose coefficients
are all in $\{-1,1\}$. By a random Littlewood polynomial of degree
$n$ we mean a Littlewood polynomial chosen uniformly among all the
$2^{n+1}$ Littlewood polynomials of degree $n$. In this paper we
investigate the probability that a random Littlewood polynomial has
a double root and show that it is $O(n^{-2})$, and compute it up to an error of
order $o(n^{-2})$.
Our result concerning random Littlewood polynomials is a corollary of
a more general theorem that we now state.
Let $(\xi_j)$, $j\ge 0$, be an independent, identically distributed
sequence of random variables taking values in $\{-1,0,1\}$. Let
$n\ge 1$ and define the random polynomial $P$ by
\begin{equation*}
P(z):=\sum_{j=0}^n \xi_j z^j.
\end{equation*}
For a
complex number $z$ define the event
\begin{equation*}
D_z := \{z\text{ is a double root of }P\}.
\end{equation*}
\begin{theorem}\label{thm:double_root}
If
\begin{equation}\label{eq:coefficient_condition}
\max_{x\in\{-1,0,1\}} \P(\xi_0 = x) < \frac{1}{\sqrt{3}}
\end{equation}
then
\begin{equation}\label{eq:thm_conclusion}
\P(P\text{ has a double root}) = \P(\cup_z D_z)=\P(D_{-1}\cup D_0\cup D_1) +
o(n^{-2})\quad\text{as $n\to\infty$}.
\end{equation}
\end{theorem}
Thus, up to a $o(n^{-2})$ factor, the probability of having a double
root is dominated by the probability that either $-1,0$ or $1$ are
double roots. Here and later in the paper we write $o(a_n)$ to
denote a term $\delta_n$, where the sequence $(\delta_n)$ depends
only on the distribution of $\xi_0$ and satisfies $\lim_{n\to\infty}
\delta_n/a_n = 0$. Similarly, $\delta_n=O(a_n)$ means that
$\limsup_{n\to\infty} |\delta_n|/a_n<\infty$.
Our next theorem calculates the asymptotics of the double root
probability.
\begin{theorem}\label{thm:double_root_asymptotics}
Assume condition~\eqref{eq:coefficient_condition}. First,
\begin{equation}\label{eq:double_root_prob_limit}
\lim_{n\to\infty} \P(P\text{ has a double root}) = \P(\xi_0 = 0)^2.
\end{equation}
Second, if
\begin{equation}\label{eq:no_atom_at_0}
\P(\xi_0=0)=0
\end{equation}
then
\begin{equation}\label{eq:double_root_prob_asymptotics}
\P(P\text{ has a double root}) = \frac{L_n}{n^2} + o(n^{-2})
\quad\text{as $n\to\infty$},
\end{equation}
where $L_n$ denotes the periodic sequence
\begin{equation}\label{eq:limit_constant_value}
L_n := \begin{cases}
\frac{8\sqrt{3}}{\pi \var(\xi_0)}& \text{if $\E(\xi_0) = 0$
and $n+1$ is divisible by $4$},\\
\frac{4\sqrt{3}}{\pi \var(\xi_0)}&\text{if
$\E(\xi_0) \neq 0$ and $n+1$ is divisible by
$4$},\\
0&\text{if $n+1$ is not divisible by $4$}.
\end{cases}
\end{equation}
\end{theorem}
We make a few remarks regarding the theorems.
\begin{enumerate}
\item The event that $P$ possesses a double root is the same as the
event that $P$ and $P'$ have a common root, which necessarily
must lie in the annulus ${\cal A}=\{1/2\leq |z|\leq 2\}$ or at $0$.
Since the
correlation coefficient between $P(z)$ and $P'(z)$ is
bounded away from $1$
as $n\to \infty$ uniformly in ${\cal A}$,
a natural heuristic is that
the probability that $P$ possesses a double root
is up to a multiplicative constant
asymptotically the same as the probability that $P$ and an
independent copy of $P'$ possess a common root, which by local
CLT considerations and some analysis should be at most
of order
$n^{-2}$
when $\P(\xi_0=0)=0$ (in case one considers $P$ and
an independent copy $\tilde{P}$ of $P$, such an analysis was
carried out in \cite{KZ13}). Directly carrying out this heuristic seems, however, challenging.
\item We do not know if condition \eqref{eq:coefficient_condition},
or a condition of a similar kind, is necessary for the conclusion
\eqref{eq:thm_conclusion} of Theorem
\ref{thm:double_root} to hold; the theorem does cover the
interesting cases where the distribution of the
coefficients $\xi_i$ is uniform on
all three of $\{-1,0,1\}$ or uniform on any two of these values.
See the open problems section for further information.
\item In case $n+1$ is not divisible by $4$, our results for $\P(\xi_0=0)=0$
do not yield the
leading term in the asymptotic expansion of the left side
of \eqref{eq:thm_conclusion}; by parity consideration,
in that situation,
$\pm1$ cannot be a
double root of $P$. In that situation, one needs to
consider also roots of unity of algebraic degree larger than $1$. The
asymptotics
then depend on further arithmetic properties of $n$. While
our methods could in principle be adapted to yield such results,
we do not attempt to do so.
We note, however, that under certain number theoretic
assumptions, there exist infinitely many $n$ for which the
polynomial $P$ is deterministically irreducible, indeed, even the
deterministic polynomial $P\bmod 2$ is irreducible mod $2$, see
\cite{MO09}.
\item Our methods could also be used in evaluating the
probability that $P$ possesses a root of multiplicity $k$. We
expect that under the condition
\eqref{eq:coefficient_condition}, the probability of
having a root of multiplicity $k \ge 2$ (fixed) equals
$\P(\text{either $-1, 0$ or $+1$ is a root of order of } k)
+ o(n^{-k^{2}/2})$.
We have, however, not verified the details
of this assertion.
Note that, as described in the next remark, it is known
\cite{FL99} that the probability that $1$ is a root of
multiplicity $k$ is of order $O(n^{-k^2/2})$ for random Littlewood
polynomials.
\item When dealing with random Littlewood polynomials and when $n+1$ is divisible by $4$, the asymptotic
probability that $-1$ or $1$ are double roots of $P$ is already known
and has an interesting history which we briefly sketch. It
suffices, as one may check simply (see
\eqref{eq:1_and_minus_1_equality_in_distribution} and
\eqref{eq:simultaneous_double_root}), to show that
\begin{equation}
\label{eq-of1}
\P(P(1)=P'(1)=0) = \frac{4\sqrt{3}}{\pi n^2} +
o(n^{-2}).\end{equation}
That is, one needs to count the number of $\pm 1$
sequences $\{a_i\}_{i=0}^n$
such that $\sum_{i=0}^n a_i=0$ and $\sum_{i=1}^{n} i a_i=0$.
Setting $b_i=a_{i-1}$, this is the same as counting the number of
solutions of the system of equations $\sum_{i=1}^{n+1} b_i=0$ and
$\sum_{i=1}^{n+1} ib_i=0$, with $b_i\in \{-1,1\}$.
The latter is a quantity appearing in coding theory, namely, the number
of spectral-null codes of second order and length $n+1$,
denoted ${\cal S}(n+1,2)$, which was
evaluated (non rigorously, and with a slightly different motivation) already
in \cite{SR}, and rigorously in \cite{FL99}.
Both derivations start from the substitution
$X_i=(b_i+1)/2$ to show that
${\cal S}(n+1,2)$ equals the number of partitions with distinct parts
of $(n+1)(n+2)/4$
into $(n+1)/2$ parts with largest part at most $n+1$.
The authors in \cite{FL99} then derive a local CLT, which implies the
required asymptotics.
Our proof proceeds
with a somewhat different approach to the local CLT, using some ideas from
\cite{KLP13}.
\end{enumerate}
\subsection{Overview of the proof of Theorem \ref{thm:double_root}}
Recall that the minimal polynomial of an algebraic integer $\alpha$
is the monic polynomial in $\mathbb{Z}[x]$ of least degree such
that $\alpha$ is a root of that polynomial. We denote by
$\deg(\alpha)$ the algebraic degree of an algebraic integer
$\alpha$, i.e., the degree of its minimal polynomial.
The first and perhaps most crucial step of our argument is the following lemma which allows us to discard the algebraic integers with sufficiently high degrees.
The proof of the lemma is based on an
idea appearing in a work of Filaseta and Konyagin \cite{FK96}.
\begin{lemma}\label{lem:high_degree}(High degree)
Under the assumption \eqref{eq:coefficient_condition} there exist
constants $C,c>0$ such that for any $1\le d\le n$,
\begin{equation*}
\P(P\text{ has a double root $\alpha$ with $\deg(\alpha)\ge
d$})\le C\exp(-cd).
\end{equation*}
\end{lemma}
As we are aiming for an error of size $o(n^{-2})$, as in
\eqref{eq:thm_conclusion}, the lemma allows us to restrict attention
to algebraic integers $\alpha$ with $\deg(\alpha) = O(\log n)$. We
shall
then make use of Dobrowolski's result on Lehmer's conjecture
\cite{D79} to further restrict attention to two cases: the case
when $\alpha$ is a root of unity or $\alpha = 0$ and the case when
there is a conjugate $\beta$ of $\alpha$ such that $\beta$ lies a
bit far away
from the unit circle, more precisely
$|\beta| > 1 + \frac{c}{\log n} \big(\frac{\log\log n}{\log n}\big)^3$.
The first case is addressed in the following lemma whose proof relies on a classical anti-concentration result of S\'ark\"ozi and
Szemer\'edi \cite{SS65}.
\begin{lemma}\label{lem:root_of_unity}(Roots of unity)
Under the assumption \eqref{eq:coefficient_condition} there exists
a constant $C>0$ such that if $\alpha$ satisfies $\alpha^k = 1$ for some $k\ge 1$ then
\begin{equation*}
\P(\alpha\text{ is a root of $P'$})\le
\left(\frac{C}{\lfloor\frac{n}{k}\rfloor}\right)^{\frac{3\deg(\alpha)}{2}}.
\end{equation*}
\end{lemma}
Using Lemma~\ref{lem:root_of_unity}, we will show that if $\alpha$
is a root of unity with $\deg(\alpha) = O(\log n)$ and $\deg(\alpha)
\ge 2$, then $ \P(\alpha\text{ is a root of $P'$}) \le
O\left(\left(\frac{\log n\log\log \log n}{n}\right)^{3}\right)$.
Since there are not many such roots of unity, in fact $O\big((\log n
\log \log \log n)^2\big)$ of them, a simple union bound implies that
\[ \P( P' \text{ has a root $\alpha$ such that $\alpha$ is a root of unity and } 2 \le \deg(\alpha) = O(\log n)) = o(n^{-2}).\]
Finally, we deal with the second case as follows. We will show that
the probability that $\alpha$ is a root of $P$ decreases very
rapidly with the distance of $\alpha$ from the unit circle.
\begin{lemma}\label{lem:off_circle}(Far from the unit circle)
Under the assumption \eqref{eq:coefficient_condition}, for any algebraic integer $\alpha\neq 0$,
\begin{equation*}
\P(\alpha\text{ is a root of $P$})\le e^{-\frac{n\log 3}{2\lceil \log 3 /|\log
|\alpha||\rceil}}.
\end{equation*}
\end{lemma}
The proof of the above lemma is elementary and is based on a
sparsification argument. We shall apply the lemma for $\alpha$
satisfying $|\alpha| > 1 + \frac{c}{\log n} \big(\frac{\log\log
n}{\log n}\big)^3$. Since there are only $\exp(O((\log n)^2))$
potential roots of $P$ with algebraic degree $O(\log n)$ (see
Lemma~\ref{lem:number_of_minimal_polynomials}), a union bound yields
an error estimate of $o(n^{-2})$ for the second case too. Therefore,
we conclude that the probability that $P$ has a double root is the
same as the probability that $P$ has a double root at $-1, 0$ or $1$
up to an error of $o(n^{-2})$.
\subsection{Structure of the paper}
Section \ref{sec:high_alg_degree} is dedicated to handling roots of
high algebraic degrees, i.e., to the proof of Lemma
\ref{lem:high_degree}. Section \ref{sec:roots_unity} treats roots of
unity and provides the proof of Lemma \ref{lem:root_of_unity}.
Section \ref{sec:far_roots} handles roots that are far away from the
unit circle, providing the proof of Lemma \ref{lem:off_circle}.
Section \ref{sec:double_root} is dedicated to the deduction of
Theorem~\ref{thm:double_root}. Section \ref{sec:A_double_root} is
dedicated to the local CLT and proof of Theorem
\ref{thm:double_root_asymptotics}. The paper ends with a few open
questions.
\subsection{Acknowledgements}
We are grateful to Van Vu for mentioning the relevance of Lehmer's conjecture and Hoi H. Nguyen for the reference to Filaseta and
Konyagin \cite{FK96}. Also, AS is indebted to Manjunath Krishnapur for many insightful discussions.
\section{High algebraic degree}
\label{sec:high_alg_degree}
In this section we prove Lemma~\ref{lem:high_degree}. We start with
two preliminary claims.
\begin{claim}\label{clm:jensen}
There exists a constant $M$ such that for any $n \ge 1$ and any
non-zero polynomial $f$ of the form $f(z) = \sum_{i=0}^n a_i z^i$
with $a_i \in \{-1,0,1\}$ for all $0 \le i \le n$, the number of
$z\in\C$ for which $f(z) = 0$ and $|z|\ge\frac{3}{2}$ is at most
$M$.
\end{claim}
\begin{proof}
Assume, without loss of generality, that $|a_n| = 1$. Let $\tilde
f(z) = z^n f(z^{-1}) = \sum_{i=0}^n a_i z^{n-i}$ be the reciprocal
polynomial of $f$. Denote by $N(f)$ the number of $z\in\C$ for which
$f(z) = 0$ and $|z|\ge\frac{3}{2}$. Then $N(f)$ is also the number
of $z\in\C$ for which $\tilde f(z)=0$ and $|z|\le \frac{2}{3}$.
Noting that $|\tilde{f}(0)|=1$ we may apply Jensen's formula (see,
e.g., \cite[Chapter 5.3.1]{A78}) and obtain for any $r> \frac{2}{3}$
that
\begin{equation*}
\max_{0\le \theta\le 2\pi} \log|\tilde{f}(re^{i\theta})| \ge
\frac{1}{2\pi}\int_0^{2\pi} \log|\tilde{f}(re^{i\theta})|d\theta =
\log|\tilde{f}(0)| + \sum_{z\colon \tilde{f}(z)=0,\, |z|\le r} \log\left(\frac{r}{|z|}\right) \ge N(f)
\log\left(\frac{r}{2/3}\right).
\end{equation*}
Observe that when $r<1$ we have $|\tilde{f}(re^{i\theta})|\le
\frac{1}{1-r}$ for all $\theta$. Thus
\begin{equation*}
N(f)\le \frac{1}{(1-r)\log(3r/2)},\quad \frac{2}{3}<r<1
\end{equation*}
and substituting $r=0.82$, say, yields that $N(f)\le 26$, finishing
the proof.
\end{proof}
\begin{claim}\label{clm:integer_divisibility}
Let $P$ be the random polynomial from
Theorem~\ref{thm:double_root} and assume
\eqref{eq:coefficient_condition}. There exist constants $C, c>0$
such that for any $B>0$ we have
\begin{equation*}
\P\left(\text{P(3) is divisible by $k^2$ for some integer $k\ge B$}\right)\le C
B^{-c}.
\end{equation*}
\end{claim}
\begin{proof}
Let $k\ge 1$ be an integer and let $r$ be the integer satisfying
$3^r\le k^2<3^{r+1}$. By conditioning on $\xi_r, \xi_{r+1}, \ldots, \xi_n$ we have
\begin{align}\label{eq:P3ad}
\P\left(P(3) \bmod k^2 = 0\right) \le \max_{m\in \mathbb Z} \P\left(
\sum_{j=0}^{r-1} \xi_j 3^j \bmod k^2 = m\right) = \max_{m \in
\mathbb Z} \P\left(\sum_{j=0}^{r-1} \xi_j 3^j = m\right),
\end{align}
where the last equality follows from the fact that
$\left|\sum_{j=0}^{r-1}\xi_j 3^j\right|\le\frac{1}{2}(3^r-1)$
deterministically and $k^2\ge 3^r$ by the definition of $r$. Write
$\max_{x\in\{-1,0,1\}} \P(\xi_0 = x) = \frac{1}{\sqrt{3}} -
\delta\in\left[\frac{1}{3},\frac{1}{\sqrt{3}}\right)$ by the
assumption \eqref{eq:coefficient_condition}. Observe that
\begin{equation}\label{eq:ternary_expansion}
\text{the mapping $(a_0,\ldots, a_{r-1})\mapsto \sum_{j=0}^{r-1}
a_j 3^j$ is one-to-one on $\{-1,0,1\}^r$}
\end{equation}
as the ternary expansion of an integer is unique. Thus,
\begin{equation}\label{eq:P3bd}
\max_{m \in
\mathbb Z} \P\left(\sum_{j=0}^{r-1} \xi_j 3^j = m\right) \le
\left(\frac{1}{\sqrt{3}} - \delta\right)^r.
\end{equation}
Combining \eqref{eq:P3ad} and \eqref{eq:P3bd} with the fact that
$r>\frac{2\log k}{\log3} - 1$ we deduce that
\[ \P\left(P(3) \bmod k^2 = 0\right) \le 3\left(\frac{1}{\sqrt{3}} - \delta\right)^{\tfrac{2 \log k}{\log 3}} = 3k^{-\gamma},\]
where $\gamma := - \log\left(\frac{1}{\sqrt{3}} - \delta\right) /
\log \sqrt 3
>1$. Summing over $k \ge B$ we obtain
\begin{equation*}
\P\left(\text{P(3) is divisible by $k^2$ for some integer $k\ge B$}\right) \le C B^{-(\gamma -
1)},
\end{equation*}
for some suitable constant $C>0$, as required.
\end{proof}
We now complete the proof of Lemma~\ref{lem:high_degree}.
Let $P$ be the random polynomial from
Theorem~\ref{thm:double_root} and assume
\eqref{eq:coefficient_condition}. Fix $1 \le d \le n$. Let
$\alpha$ be an algebraic integer of degree $d$ with (monic) minimal
polynomial $g$. Denote by $C(\alpha)$ the set of
algebraic conjugates of $\alpha$ (i.e., the set of roots of
$g$). Suppose that $\alpha$ is a double root of $P$.
Then, necessarily $g$ divides $P$ and therefore
$|\beta|\le 2$ for all $\beta\in C(\alpha)$ and, by
Claim~\ref{clm:jensen}, all but at most $M$ of the $\beta\in
C(\alpha)$ satisfy
$|\beta|\le \frac{3}{2}$. We conclude that
\begin{equation*}
|g(3)| = \prod_{\beta\in C(\alpha)} |3-\beta| \ge (\tfrac{3}{2})^{d - M} \ge c_1 (\tfrac{3}{2})^{d},
\end{equation*}
where $c_1 := (\tfrac{3}{2})^{-M}>0$. In addition, the facts that
$\alpha$ is a double root of $P$ and that $\alpha$ cannot be a
multiple root of $g$, since in that case $\alpha$ is also a root of
$g'$ violating the minimality of $g$, imply that $g^2$ divides $P$
in $\mathbb{Z}[x]$ so that, in particular, the integer $P(3)$ is
divisible by $g(3)^2$. Putting the above facts together we arrive at
the inclusion of events
\begin{equation*}
\left\{\text{$\alpha$ is a double root of $P$}\right\}\subseteq\left\{\text{$P(3)$
is divisible by $k^2$ for some integer $k\ge
c_1(\tfrac{3}{2})^d$}\right\}.
\end{equation*}
Lemma~\ref{lem:high_degree} now follows from
Claim~\ref{clm:integer_divisibility}.
\section{Roots of unity}
\label{sec:roots_unity}
In this section we prove Lemma~\ref{lem:root_of_unity}. We make use
of the following anti-concentration result of S\'ark\"ozi and
Szemer\'edi \cite{SS65}.
\begin{theorem}\label{thm:Sarkozy_Szemeredi}
Let $(\eps_j)$, $1\le j\le N$, be independent random variables
with $\P(\eps_j = 0) = \P(\eps_j = 1) = \frac{1}{2}$. There exists
a constant $C>0$ such that for any \emph{distinct} integers $(a_j)$, $1\le j\le N$, we have
\begin{equation*}
\max_{m\in\Z} \P\left(\sum_{j=1}^N \eps_j a_j = m\right) \le
\frac{C}{N^{3/2}}.
\end{equation*}
\end{theorem}
Clearly, by a linear change of variable, the theorem continues to
hold when $\P(\eps_j = a) = \P(\eps_j = b) = \frac{1}{2}$ for any
$\{a,b\}\subset\Z$. The following corollary extends this to our
non-symmetric setting.
\begin{corollary}\label{cor:Sarkozy_Szemeredi}
Let $(\xi_j)$ be as in Theorem~\ref{thm:double_root}. There exists a constant $C>0$
such that for any \emph{distinct} integers $(a_j)$, $1\le j\le N$, we have
\begin{equation*}
\max_{m\in\Z} \P\left(\sum_{j=1}^N \xi_j a_j = m\right) \le
\frac{C}{N^{3/2}}.
\end{equation*}
\end{corollary}
\begin{proof}
Using the assumption \eqref{eq:coefficient_condition} there exists
some $p> \left(1 - \frac{1}{\sqrt{3}}\right)$,
$a\neq b\in \{-1,0,1\}$ and a random variable
$\eta$ supported in $\{-1,0,1\}$ such that if we let $\eps$ be uniform on $\{a,b\}$
then the distribution of $\xi_1$ has the distribution of the mixture obtained by
sampling $\eps$ with probability $p$ and sampling $\eta$ with
probability $1-p$. Let $(\eps_j)$, $(\eta_j)$, $j\ge 1$, be
independent identically distributed sequences with the
distributions of $\eps$ and $\eta$ respectively.
Independently, couple each
$\xi_j$ to $(\eps_j, \eta_j)$ as the above mixture. Let $T$ be the
random set of indices $1\le j\le N$ in which we sampled $\eps_j$
to obtain $\xi_j$. Thus $T$ is distributed as a binomial with
$N$ trials and success probability $p$. Using
Theorem~\ref{thm:Sarkozy_Szemeredi} we have
\begin{align*}
\max_{m\in\Z} \P\left(\sum_{j=1}^N \xi_j a_j = m\right) &= \max_{m\in\Z}
\E\P\left(\sum_{j=1}^N \xi_j a_j = m\,\Big|\,T, (\xi_j)_{j\notin T}\right)\le \E\max_{m\in\Z}\P\left(\sum_{j\in T} \xi_j
a_j = m\,\Big|\,T\right) =\\
&= \E\max_{m\in\Z}\P\left(\sum_{j\in T} \eps_j a_j =
m\,\Big|\,T\right) \le \E\left(\min\left(1,\frac{C}{|T|^{3/2}}\right)\right).
\end{align*}
It remains to note that by standard concentration estimates for
binomial random variables there exists some universal constant
$c>0$ for which $\P(|T| \le \frac{1}{2} Np) \le \exp(-cNp)$. Thus
\begin{equation*}
\E\left(\min\left(1,\frac{C}{|T|^{3/2}}\right)\right) \le
\exp(-cNp) + \frac{C}{\left(\frac{1}{2}Np\right)^{3/2}}.\qedhere
\end{equation*}
\end{proof}
We complete now the proof of Lemma \ref{lem:root_of_unity}.
Let $\alpha$ be such that $\alpha^k = 1$ for some $k\ge 1$.
Observe that necessarily $\deg(\alpha)\le k$. Set
\begin{align*}
J&:=\{j\colon 1\le j\le n\text{ and }0\le (j -1) \bmod k\le
\deg(\alpha) -1\},\\
\bar{J}&:=\{1,\ldots, n\}\setminus J.
\end{align*}
Define the random variables $(S_r)$, $0\le r\le\deg(\alpha) - 1$, by
\begin{equation*}
S_r := \sum_{\substack{j\in J\\
j-1\bmod k = r}} \xi_j j \alpha^{j-1} = \alpha^r \sum_{\substack{j\in J\\
j - 1\bmod k = r}} \xi_j j
\end{equation*}
and
\begin{equation*}
\bar{S} := \sum_{j\in \bar{J}} \xi_j j
\alpha^{j-1}.
\end{equation*}
Observe that
\begin{equation*}
P'(\alpha)=\sum_{j=1}^n \xi_j j \alpha^{j-1} = \sum_{j\in J} \xi_j j
\alpha^{j-1} + \sum_{j\in \bar{J}} \xi_j j
\alpha^{j-1} = \sum_{r=0}^{\deg(\alpha)-1} S_r + \bar{S}.
\end{equation*}
Now, by definition, $(S_r)$, $0\le r\le\deg(\alpha)-1$, are
independent and also independent of $\bar{S}$. In addition,
$(\alpha^r)$, $0\le r\le \deg(\alpha)-1$, are linearly independent
over the rational numbers, and therefore the equation
$\sum_{i=0}^{\deg(\alpha)-1} a_i \alpha^i=z$
has at most one integral solution $(a_0,\ldots,a_{\deg(\alpha)-1})$
for
a given
$z\in \C$. Hence
\begin{align*}
\P(P'(\alpha)=0) &= \E\P\left(\sum_{r=0}^{\deg(\alpha)-1} S_r=-\bar{S}\,\Big|\,\bar{S}\right)
\le \max_{z\in\C} \P\left(\sum_{r=0}^{\deg(\alpha)-1} S_r = z\right) =\\
&= \prod_{r=0}^{\deg(\alpha)-1}\max_{z\in\C} \P(S_r = z) =
\prod_{r=0}^{\deg(\alpha)-1}\max_{m\in\Z} \P\Bigg(\sum_{\substack{j\in J\\
j-1\bmod k = r}} \xi_j j = m\Bigg).
\end{align*}
Applying Corollary~\ref{cor:Sarkozy_Szemeredi}
and the fact that $|J|\geq \lfloor n/k\rfloor$ we conclude that
\begin{equation*}
\P(P'(\alpha)=0) \le
\left(\frac{C}{\lfloor\frac{n}{k}\rfloor}\right)^{\frac{3\deg(\alpha)}{2}}.
\end{equation*}
\section{Roots off the unit circle}
\label{sec:far_roots} In this section we prove
Lemma~\ref{lem:off_circle}. Let $\alpha\neq 0$ be an algebraic
integer. We assume $|\alpha|\neq 1$ as otherwise the lemma is
trivial. We note also that the probability that $\alpha$ is a root
of $P$ is the same as the probability that $1/\alpha$ is a root of
$P$ since $P(\alpha)$ has the same distribution as $\alpha^n
P(1/\alpha)$. Thus we assume without loss of generality that
$|\alpha|>1$. Define $j_0$ as the minimal positive integer for which
\begin{equation}\label{eq:j_0_prop}
|\alpha|^{j_0} \ge 3.
\end{equation}
Write $P(z) = P_1(z) + P_2(z)$ with
\begin{equation*}
P_1(z):=\sum_{k=0}^{\lfloor n/j_0\rfloor} \xi_{kj_0} z^{k
j_0}\quad\text{and}\quad P_2(z):=P(z) - P_1(z).
\end{equation*}
The assumption \eqref{eq:j_0_prop} implies that the mapping
$T:\{-1,0,1\}^{\lfloor n/j_0\rfloor+1}\to\C$ defined by
\begin{equation*}
(a_0, \ldots, a_{\lfloor n/j_0\rfloor})\mapsto \sum_{k=0}^{\lfloor n/j_0\rfloor} a_k \alpha^{k
j_0}
\end{equation*}
is one-to-one (similarly to \eqref{eq:ternary_expansion}). Thus, as
$P_1(\alpha)$ and $P_2(\alpha)$ are independent,
\begin{align*}
\P(\alpha\text{ is a root of $P$}) &= \E\left[\P(\alpha\text{ is a root of
$P$}\,|\,P_2(\alpha))\right] =\\
&= \E\left[\P(P_1(\alpha) =
-P_2(\alpha)\,|\,P_2(\alpha))\right]\le
\left(\max_{x\in\{-1,0,1\}}\P(\xi_0=x)\right)^{\lfloor
n/j_0\rfloor+1}.
\end{align*}
Finally, assumption~\eqref{eq:coefficient_condition} and the
definition of $j_0$ imply that
\begin{equation*}
\P(\alpha\text{ is a root of $P$})< \left(\frac{1}{\sqrt{3}}\right)^{\lfloor
n/j_0\rfloor+1}\le e^{-\frac{n\log 3}{2j_0}} = e^{-\frac{n\log 3}{2\lceil \log 3 / \log
|\alpha|\rceil}}.
\end{equation*}
\section{Probability of double root}
\label{sec:double_root}
In this section we prove Theorem~\ref{thm:double_root}.
By definition, any root of a monic polynomial with integer
coefficients is an algebraic integer. Thus, unless all coefficients
of $P$ are zero, the equation $P(z)=0$ is satisfied only by
algebraic integers $z$. We note this explicitly for later reference,
\begin{equation}\label{eq:double_root_zero_polynomial_estimate}
\P\left(P\text{ has a root which is not an algebraic integer}\right) = \P(\xi_0 = 0)^{n+1} < 3^{-n/2}
\end{equation}
by assumption \eqref{eq:coefficient_condition}.
Let $c$ be the constant appearing in Lemma~\ref{lem:high_degree} and
note first that this lemma implies that
\begin{equation}\label{eq:double_root_high_degree_estimate}
\P\left(P\text{ has a double root $\alpha$ with $\deg(\alpha)\ge \frac{3\log n}{c}$}\right)\le Cn^{-3}.
\end{equation}
Thus we may restrict attention to the following set of potential
roots,
\begin{equation*}
A:=\left\{\alpha\in \C\colon \alpha\text{ is a root of a monic polynomial with coefficients in $\{-1,0,1\}$
and $\deg(\alpha)<\frac{3\log n}{c}$}\right\}.
\end{equation*}
We now use use another argument of Filaseta and Konyagin
\cite{FK96} to bound the cardinality of $A$.
\begin{lemma}\label{lem:number_of_minimal_polynomials}
There exists a constant $C>0$ such that
\begin{equation*}
|A| \le C^{(\log n)^2}.
\end{equation*}
\end{lemma}
\begin{proof}
Let $\alpha\in A$ and denote by $C(\alpha)$ the set of its algebraic conjugates (including $\alpha$ itself). Since $\alpha$ is a root of a monic polynomial
with coefficients in $\{-1,0,1\}$ it follows immediately that
\begin{equation}\label{eq:conjugates_bound}
|\beta|<2\;\;\text{ for each $\beta\in C(\alpha)$}.
\end{equation}
Now suppose $\deg(\alpha)=d$, let $g$ be the minimal polynomial of $\alpha$
and denote
\begin{equation*}
g(z) = z^{d} + \sum_{j=0}^{d-1} a_j z^j = \prod_{\beta\in
C(\alpha)} (z - \beta).
\end{equation*}
From this representation and \eqref{eq:conjugates_bound} we deduce
that $|a_j|\le 4^{d}$ for each $j$, whence the integral vector $(a_0,\ldots,
a_{d-1})$ has at most $4^{d^2}$ possibilities. We conclude that
the number of $\alpha\in A$ with $\deg(\alpha) = d$ is at most
$4^{d^2}$ and the lemma follows by summing over $d$.
\end{proof}
We continue by recalling the Mahler measure of an algebraic integer.
If $\alpha$ is an algebraic integer having minimal polynomial
\begin{equation*}
g(z) = \prod_{\beta\in C(\alpha)}(z - \beta),
\end{equation*}
where $C(\alpha)$ is the set of algebraic conjugates of $\alpha$,
then the Mahler measure $M(\alpha)$ of $\alpha$ is
\begin{equation*}
M(\alpha):=\prod_{\substack{\beta\in C(\alpha)\\|\beta|\ge 1}}
|\beta|.
\end{equation*}
In particular, if $\alpha$ is an algebraic integer then
$M(\alpha)=1$ if and only if $\alpha=0$ or $|\beta|=1$ for all
$\beta\in C(\alpha)$. Moreover, it follows from a classical theorem of
Kronecker \cite{K57} that if
$\alpha$ is an algebraic integer with $|\beta|=1$ for all $\beta\in
C(\alpha)$ then $\alpha$ is a root of unity. Finally, Lehmer's
conjecture \cite{L33} states that there exists some absolute constant $\mu>1$
such that
\begin{equation*}
M(\alpha)=1\text{ or }M(\alpha)\ge\mu\text{ for all algebraic
integers $\alpha$}.
\end{equation*}
We will make use of Dobrowolski's result on Lehmer's conjecture
\cite{D79} which says that
\begin{equation*}
M(\alpha)=1\text{ or }\log(M(\alpha))\ge c'\left(\frac{\log\log(\deg(\alpha)+2)}{\log(\deg(\alpha)+2)}\right)^3\text{ for some $c'>0$ and all algebraic
integers $\alpha$}.
\end{equation*}
We remark that earlier weaker results on Lehmer's conjecture such as those
of Blanksby and Montgomery \cite{BM71} or Stewart \cite{S78} would
also have sufficed for our purposes.
Now let $\alpha\in A$ and denote $d := \deg(\alpha)$. Assume that
$\alpha$ is neither $0$ nor a root of unity. It follows from the
preceding discussion that
\begin{equation*}
\log(M(\alpha))\ge c'\left(\frac{\log\log(d+2)}{\log(d+2)}\right)^3
\end{equation*}
and hence, using that $e^x\geq 1+x$ for $x\geq 0$,
one concludes that
$\alpha$ has some algebraic conjugate $\beta$ satisfying
\begin{equation*}
|\beta|\ge 1 +
\frac{c'}{d}\left(\frac{\log\log(d+2)}{\log(d+2)}\right)^3.
\end{equation*}
Since $P(\alpha)=0$ if and only if $P(\beta)=0$ we may apply
Lemma~\ref{lem:off_circle} to deduce that
\begin{equation*}
\P(\alpha\text{ is a root of $P$})\le e^{-\frac{n\log 3}{2\lceil \log 3 /\log
|\beta|\rceil}}\le e^{-c''\frac{n(\log\log(d+2))^3}{d(\log(d+2))^3}}
\end{equation*}
for some $c''>0$. Putting this estimate together with
Lemma~\ref{lem:number_of_minimal_polynomials} and the fact that
$\deg(\alpha)<\frac{3\log n}{c}$ for $\alpha\in A$ yields that
\begin{equation}\label{eq:double_root_non_root_of_unity_estimate}
\P\left(P\text{ has a root $\alpha\in A$ with $\alpha\neq 0$ and $\alpha$ not a root of
unity}\right)\le C^{(\log n)^2}e^{-c'''\frac{n(\log\log \log n)^3}{\log n(\log
\log n)^3}}
\end{equation}
for some $c'''>0$. It remains to consider the probability that $P$
has a root which is a root of unity. Let $\alpha$ be a root of unity
with $k$ being the minimal positive integer for which $\alpha^k = 1$
and $d := \deg(\alpha)$. By Lemma~\ref{lem:root_of_unity},
\begin{equation}\label{eq:root_of_unity_double_root_estimate}
\P(\alpha\text{ is a double root of $P$})\le
\left(\frac{C}{\lfloor\frac{n}{k}\rfloor}\right)^{\frac{3d}{2}}.
\end{equation}
Since the minimal polynomial of $\alpha$ is given by the $k$th cyclotomic polynomial $$\Phi_k(x):= \prod_{\substack{ 1 \le j \le k, \\ \gcd(j, k)=1}} (1- e^{ 2 \pi i j/k})$$ (see, for example, Lemma~7.6 and Theorem~7.7 of \cite{M96}), we have that
$d = \deg(\Phi_k) = \varphi(k)$
where $\varphi$
is Euler's totient function, i.e., $\varphi(k)=|\{1\le j\le k\colon
\gcd(j,k) = 1\}|$. By standard estimates (see \cite[Theorem 2.9]{MV07}) there exists
some constant $c_1>0$ for which
\begin{equation*}
d = \varphi(k) \ge \frac{c_1k}{\log\log (k+2)}.
\end{equation*}
Thus if $\alpha\in A$, so that in particular $\deg(\alpha) <
\frac{3\log n}{c}$, then
\begin{equation}\label{eq:root_of_unity_k_estimate}
k \le C_1 \log n \log\log \log n
\end{equation}
for some $C_1>0$. Substituting back in
\eqref{eq:root_of_unity_double_root_estimate} yields
\begin{equation*}
\P(\alpha\text{ is a double root of $P$})\le
\left(\frac{C_2\log n\log\log \log n}{n}\right)^{\frac{3d}{2}}
\end{equation*}
for some $C_2>0$. In particular, since there are at most $k$ numbers
$\alpha$ for which $k$ is the minimal positive integer such that
$\alpha^k=1$ we conclude from the last two inequalities that
\begin{multline}\label{eq:double_root_root_of_unity_estimate}
\P\left(P\text{ has a double root $\alpha\in A\setminus\{-1,1\}$ which
is a root of
unity}\right)\le\\
\le (C_1\log n \log\log\log n)^2 \left(\frac{C_2\log n\log\log \log n}{n}\right)^{3} =
o(n^{-2}).
\end{multline}
Theorem~\ref{thm:double_root} now follows by putting together
\eqref{eq:double_root_zero_polynomial_estimate},
\eqref{eq:double_root_high_degree_estimate},
\eqref{eq:double_root_non_root_of_unity_estimate} and
\eqref{eq:double_root_root_of_unity_estimate}.
\section{Asymptotics of the double root probability}
\label{sec:A_double_root} In this section we find asymptotics in
many cases for the probability that
the random polynomial $P$ has a
double root, proving Theorem~\ref{thm:double_root_asymptotics}.
We start with the proof of \eqref{eq:double_root_prob_limit}. By
Theorem~\ref{thm:double_root} we may focus on the probability that
either $-1, 0$ or $1$ are double roots of $P$. We have
\begin{equation}
\P(0\text{ is a double root of $P$}) = \P(\xi_0 = 0)^2
\end{equation}
since $0$ is a double root of $P$ if and only if the free
coefficients of $P$ and $P'$ vanish. Thus,
\eqref{eq:double_root_prob_limit} follows by noting that the
probability that either $-1$ or $1$ are double roots of $P$ tends to
zero with $n$ by Lemma~\ref{lem:root_of_unity}.
In the rest of the section we assume \eqref{eq:no_atom_at_0} and
proceed to prove \eqref{eq:double_root_prob_asymptotics}. By
Theorem~\ref{thm:double_root} it suffices to find the asymptotics of
the probability that either $-1$ or $1$ are double roots of $P$.
We start with some simple observations. Note that
\begin{equation}\label{eq:parity_restrictions}
\begin{aligned}
P(1) &\equiv P(-1) \equiv n+1 \bmod 2,\\
P'(1) &\equiv P'(-1) \equiv \left\lceil\frac{n}{2}\right\rceil \bmod
2.
\end{aligned}
\end{equation}
Thus,
\begin{equation}\label{eq:non-divisibility_conclusion}
\P(-1\text{ or }1\text{ are double roots of $P$}) = 0\;\;\text{if
$n+1$ is not divisible by $4$}.
\end{equation}
Together with Theorem~\ref{thm:double_root} this establishes the
case $L_n=0$ in \eqref{eq:double_root_prob_asymptotics} and
\eqref{eq:limit_constant_value}. We henceforth make the assumption
that
\begin{equation}\label{eq:divisibility_condition}
\text{$n+1$ is divisible by $4$}.
\end{equation}
Next we note that $P(1)=0$ if and only if exactly half of the
$(\xi_j)_{0\le j\le n}$ are $1$. Thus, by standard large deviation
estimates for binomial random variables,
\begin{equation}\label{eq:non_zero_mean_estimate}
\text{if $\E(\xi_0)\neq 0$ then }\P(P(1) = 0)\le C\exp(-cn)
\end{equation}
for some constants $C,c>0$. Additionally, it is straightforward to
check that
\begin{equation}\label{eq:1_and_minus_1_equality_in_distribution}
\text{if $\E(\xi_0) = 0$ then $(P(1), P'(1)) \eqd (P(-1), P'(-1))$}.
\end{equation}
Lastly, since we have the equality of events
\begin{equation*}
\{P'(1) = P'(-1) = 0\} = \left\{\sum_{k=1}^{\lceil\frac{n}{2}\rceil}
(2k-1)\xi_{2k-1} = \sum_{k=1}^{\lfloor \frac{n}{2}\rfloor}
2k\xi_{2k} = 0\right\},
\end{equation*}
it follows from Corollary~\ref{cor:Sarkozy_Szemeredi} that
\begin{equation}\label{eq:simultaneous_double_root}
\P(P'(1) = P'(-1) = 0) = \P\left(\sum_{k=1}^{\lceil\frac{n}{2}\rceil}
(2k-1)\xi_{2k-1}=0\right)\P\left(\sum_{k=1}^{\lfloor \frac{n}{2}\rfloor}
2k\xi_{2k} = 0\right)\le \frac{C}{n^3}
\end{equation}
for some constant $C>0$. Putting together
Theorem~\ref{thm:double_root}, \eqref{eq:non_zero_mean_estimate},
\eqref{eq:1_and_minus_1_equality_in_distribution} and
\eqref{eq:simultaneous_double_root} we see that the remaining parts
of Theorem~\ref{thm:double_root_asymptotics} will follow by showing
that
\begin{equation}\label{eq:minus_1_double_root_asymptotics}
\left|\P(-1\text{ is a double root of $P$}) - \frac{4\sqrt{3}}{\pi \var(\xi_0)n^2}\right| =
o(n^{-2}).
\end{equation}
This asymptotics will be established via a local central limit
theorem. We rely on some ideas from \cite{KLP13}, but aim to give a
short proof tailored for our case rather than a general statement.
We wish to compare the probability distribution of $(P(-1), P'(-1))$
to the density of a Gaussian random vector with the same expectation
and covariance matrix. To this end we denote
\begin{equation}\label{eq:X_def}
X:=(P(-1),P'(-1)) = \left(\sum_{j=0}^n \xi_j(-1)^j,\, \sum_{j=0}^n j\xi_j(-1)^{j-1}\right) = \sum_{j=0}^n (1,\, -j)\xi_j(-1)^j.
\end{equation}
A short calculation, using our standing assumption
\eqref{eq:divisibility_condition}, yields the expectation $\mu$ and
covariance matrix $\Sigma$ of $X$,
\begin{equation}\label{eq:mu_and_sigma_def}
\begin{aligned}
&\mu=\left(0, \frac{n+1}{2}\E(\xi_0)\right),\\
&\Sigma =\begin{pmatrix}
\var(\xi_0)(n+1)&-\frac{\var(\xi_0)}{2}n(n+1)\\
-\frac{\var(\xi_0)}{2}n(n+1)&\frac{\var(\xi_0)}{6}n(n+1)(2n+1)
\end{pmatrix}.
\end{aligned}
\end{equation}
We also let $Y$ denote a Gaussian random vector in $\R^2$ having
expectation $\mu$ and covariance matrix $\Sigma$. By standard facts
regarding Gaussian random vectors, the characteristic function
$\hat{Y}:\R^2\to\C$ of $Y$ is
\begin{equation}\label{eq:Y_Fourier_transform}
\hat{Y}(\theta)=\E e^{2\pi i\langle \theta, Y\rangle} = e^{2\pi i
\langle \theta, \mu\rangle - 2\pi^2 \theta^t \Sigma \theta}
\end{equation}
and the density $f_Y:\R^2\to\R$ of $Y$ is
\begin{equation}\label{eq:Gaussian_density_with_Fourier transform}
f_Y(y) = \frac{1}{2\pi\sqrt{\det(\Sigma)}}e^{-\frac{1}{2}(y -
\mu)^t\Sigma^{-1}(y-\mu)} = \int_{\R^2} e^{-2\pi i
\langle \theta, y\rangle}\hat{Y}(\theta)d\theta.
\end{equation}
The characteristic function $\hat{X}:\R^2\to\C$ of $X$ is also
simple to calculate, as $X$ is given in \eqref{eq:X_def} as a sum of
independent random vectors,
\begin{equation}\label{eq:Fourier_transform_of_X}
\hat{X}(\theta)=\E e^{2\pi i \langle \theta, X\rangle} =
\prod_{j=0}^{n}\left(p e^{2\pi i ((-1)^j\theta_1 + j(-1)^{j-1}\theta_2)}
+ (1-p) e^{-2\pi i ((-1)^j\theta_1 + j(-1)^{j-1}\theta_2)}\right).
\end{equation}
where we denote $\theta = (\theta_1, \theta_2)$ and let
\begin{equation*}
p:=\P(\xi_0 = 1).
\end{equation*}
In addition, we note that by the parity restrictions
\eqref{eq:parity_restrictions} the values of $X$ lie in the lattice
$2\Z^2$ (again, using our standing assumption
\eqref{eq:divisibility_condition}). Therefore we have the
representation
\begin{equation}\label{eq:double_root_as_Fourier_transform_integral}
\P(-1\text{ is a double root of $P$}) = \P(X = (0,0)) = 4\int_{\left[-\frac{1}{4},\frac{1}{4}\right]^2}
\hat{X}(\theta)d\theta.
\end{equation}
The following proposition relates $\hat{X}$ to $\hat{Y}$ near zero
and shows that both are small away from zero.
\begin{proposition}
\label{prop:6.2}
Denote
\begin{equation*}
D:=\left[-n^{-5/12},
n^{-5/12}\right]\times\left[-n^{-17/12},n^{-17/12}\right].
\end{equation*}
There exists an absolute constant $C>0$ and constants $C_p,c_p>0$ depending only on $p$ such that
\begin{enumerate}
\item\label{it:X_and_Y_near_zero} For every $\theta\in D$ we have $|\hat{X}(\theta) -
\hat{Y}(\theta)|\le Cn^{-1/4}$.
\item\label{it:X_far_from_zero} For every $\theta\in[-1/4,
1/4]^2\setminus D$ we have $|\hat{X}(\theta)| \le
C\exp\left(-c_pn^{1/6}\right)$.
\item\label{it:Y_far_from_zero} $\int_{\R^2\setminus D}
|\hat{Y}(\theta)|
d\theta \le C_p\exp\left(-c_pn^{1/6}\right)$.
\end{enumerate}
\end{proposition}
\begin{proof}
We start with the proof of part~\ref{it:X_and_Y_near_zero}. Define a
function $f:\R\to\C$ by
\begin{equation*}
f(x):=pe^{ix}+(1-p)e^{-ix}.
\end{equation*}
A simple calculation using the Taylor expansion of the logarithm
(see \cite[Claim 4.10]{KLP13} for a similar claim) shows that for $0\le p\le 1$ and
$|x|\le \frac{\pi}{4}$ we have
\begin{equation*}
f(x) = e^{(2p-1)ix - 2p(1-p)x^2+\delta(p,x)}
\end{equation*}
where $|\delta(p,x)| \le C' |x|^3$ for some absolute constant
$C'>0$.
Plugging this into \eqref{eq:Fourier_transform_of_X} for
$\theta\in D$ yields
\begin{align*}
\hat{X}(\theta) &= \exp\left(2\pi(2p-1) i\sum_{j=0}^n((-1)^j\theta_1 + j(-1)^{j-1}\theta_2) - 8\pi^2 p(1-p)\sum_{j=0}^n ((-1)^j\theta_1 + j(-1)^{j-1}\theta_2)^2 +
\delta'\right)\\
&=\exp\left(2\pi i\langle\theta, \mu\rangle -
2\pi^2\theta^t\Sigma\theta +
\delta'\right)=\hat{Y}(\theta)e^{\delta'}
\end{align*}
where the error term $\delta' = \sum_{j=0}^n \delta(p, 2\pi((-1)^j\theta_1 + j(-1)^{j-1}\theta_2))$ satisfies
\begin{equation*}
|\delta'|\le C''\sum_{j=0}^n |(-1)^j\theta_1 +
j(-1)^{j-1}\theta_2|^3 \le C'''n^{-1/4}
\end{equation*}
and $C'',C'''>0$ denote absolute constants. This finishes the
proof of part~\ref{it:X_and_Y_near_zero}.
We now continue with the proof of part~\ref{it:Y_far_from_zero}. It is useful to proceed by finding a diagonal matrix which
$\Sigma$ dominates. Since, for all $(\theta_1, \theta_2) \in\R^2$,
\begin{equation*}
n\theta_1\theta_2 =
\left(\frac{\sqrt{7}}{2}\theta_1\right)\left(\frac{2n}{\sqrt{7}}\theta_2\right)\le\frac{1}{2}\left(\frac{7}{4}\theta_1^2
+ \frac{4n^2}{7}\theta_2^2\right) \le \frac{7}{8}\theta_1^2 +
\frac{1}{7}n(2n+1)\theta_2^2
\end{equation*}
we conclude that
\begin{equation*}
\theta^t\Sigma\theta = \var(\xi_0)(n+1)\left(\theta_1^2 +
\frac{1}{6}n(2n+1)\theta_2^2 - n\theta_1\theta_2\right) \ge
\var(\xi_0)(n+1)\left(\frac{1}{8}\theta_1^2 + \frac{n(2n+1)}{42}
\theta_2^2\right).
\end{equation*}
Thus, by \eqref{eq:Y_Fourier_transform}, we have
\begin{equation*}
\int_{\R^2\setminus D} |\hat{Y}(\theta)|d\theta = \int_{\R^2\setminus D} e^{-2\pi^2 \theta^t \Sigma
\theta}d\theta\le \int_{\R^2\setminus D} e^{-2\pi^2\var(\xi_0)(n+1)\left(\frac{1}{8}\theta_1^2 + \frac{n(2n+1)}{42}
\theta_2^2\right)}d\theta.
\end{equation*}
Now, letting $G_1, G_2$ be independent centered normal random variables with
$\var(G_1) = \sigma_1^2:=\frac{2}{\pi^2\var(\xi_0)(n+1)}$ and $\var(G_2)
= \sigma_2^2:=\frac{21}{2\pi^2\var(\xi_0)n(n+1)(2n+1)}$ we have that
\begin{align*}
\int_{\R^2\setminus D} |\hat{Y}(\theta)|d\theta \le
2\pi\sigma_1\sigma_2\P((G_1,G_2)\notin D) &\le
2\pi\sigma_1\sigma_2\left(\P(|G_1|> n^{-5/12}) + \P(|G_2| >
n^{-17/12})\right)\\
&\le \frac{C}{\var(\xi_0)^2}e^{-c\var(\xi_0)n^{1/6}}
\end{align*}
for some absolute constants $C,c>0$. This finishes the
proof of part~\ref{it:Y_far_from_zero}.
Finally we turn to part~\ref{it:X_far_from_zero}. By taking the constant $C$ sufficiently large we may assume that $n$ is large. Fix $\theta\in\left[-\frac{1}{4},\frac{1}{4}\right]^2$. Write
\begin{equation*}
x_j := 2((-1)^j\theta_1 + j(-1)^{j-1}\theta_2),\quad 0\le
j\le n.
\end{equation*}
For a real number $x$, denote by $d(x,\Z)$ its distance to
the nearest integer. Let
\begin{equation*}
J = J(\theta) :=\left\{0\le j\le n\colon d(x_j,\Z)\le
\frac{1}{8}n^{-5/12}\right\}.
\end{equation*}
Using \eqref{eq:Fourier_transform_of_X}, if $|J|\le 9(n+1)/10$ then
\begin{align*}
|\hat{X}(\theta)| &=
\prod_{j=0}^{n}\left|p e^{2\pi i x_j}
+ (1-p)\right| = \prod_{j=0}^n \sqrt{1 - 2p(1-p)(1-\cos(2\pi x_j))} \\
&\le \left(1 - 2p(1-p)\left(1-\cos\left(\frac{\pi}{4} n^{-5/12}\right)\right)\right)^{\frac{n+1 - |J|}{2}} \le \left(1 - 20c_p n^{-5/6}\right)^{\frac{n+1}{20}}\le \exp\left(-c_pn^{1/6}\right).
\end{align*}
for some constant $c_p>0$ depending only on $p$.
Hence it suffices to show that if
\begin{equation}\label{eq:J_large}
|J|\ge 9(n+1)/10
\end{equation}
then $\theta\in D$.
Assume \eqref{eq:J_large}. We claim
that there necessarily exist $j_1, j_2$ such that $j_1, j_2, j_1 +
j_2\in J$. Indeed, we may take $j_1:=\min J\le \frac{n+1}{10}$ and
we then have $J\cap(j_1 + J)\neq \emptyset$ by \eqref{eq:J_large} and the pigeonhole
principle since both $J$ and $j_1 +
J$ are contained in $\left[0,\frac{n+1}{10}+n\right]$.
Thus,
\begin{align}\label{eq:theta_1_integer_distance}
d(2\theta_1, \Z) &= d((-1)^{j_1+j_2-1}x_{j_1+j_2} + (-1)^{j_1}x_{j_1} + (-1)^{j_2}x_{j_2}), \Z) \notag \\
&\le
d(x_{j_1+j_2}, \Z) + d(x_{j_1}, \Z) + d(x_{j_2}, \Z) \le \frac{3}{8}n^{-5/12},
\end{align}
whence, as $|\theta_1|\le \frac{1}{4}$,
\begin{equation*}
|\theta_1| = \frac{1}{2}d(2\theta_1, \Z) \le \frac{3}{16}n^{-5/12}.
\end{equation*}
Now, if $|\theta_2|\le n^{-17/12}$ then $\theta\in D$ and we are
done. Assume, in order to obtain a contradiction, that
$|\theta_2|>n^{-17/12}$.
Let $I:=\{0\le j\le
n\colon d(2j\theta_2, \Z)>\frac{1}{2}n^{-5/12}\}$. We claim that $|I|\ge n/3$. To see this let $k$ be the minimal positive
integer for which $2k|\theta_2|>n^{-5/12}$. Since $|\theta_2|\le
1/4$ it follows that $2k|\theta_2|\le 1/2$. Thus,
if $j\not\in I$ and $j\leq n-k$ then necessarily $j+k\in I$.
In addition, $k\le \frac{1}{2n^{5/12}|\theta_2|}+1< n/2+1$.
In particular, $|I|\geq k$ which shows the claim when $k\geq n/3$.
Otherwise, assume $k<n/3$ and define $T:=\{j\in
[0,n-k]\cap\Z:\lfloor j/k\rfloor \, \mbox{\rm is even}\}$. We have
that $T$ and $T+k$ are disjoint subsets of $\{0,\ldots,n\}$ and for
each $j\in T$, either $j$ or $j+k$ belong to $I$. Hence $|I|\geq
|T|\geq (n-k+1)/2> n/3$, as claimed.
Now the assumption \eqref{eq:J_large} and the above claim imply that
there exists some $j_3\in J$ for which $d(2j_3\theta_2, \Z)>
\frac{1}{2}n^{-5/12}$, whence by \eqref{eq:theta_1_integer_distance},
$d(x_{j_3}, \Z) > \frac{1}{8}n^{-5/12}$, contradicting the fact that $j_3\in J$.
\end{proof}
The asymptotics \eqref{eq:minus_1_double_root_asymptotics} are an
immediate consequence of Proposition \ref{prop:6.2}. Indeed, by
\eqref{eq:Gaussian_density_with_Fourier transform} and
\eqref{eq:double_root_as_Fourier_transform_integral}, and the proposition,
\begin{multline*}
|\P(-1\text{ is a double root of $P$}) - 4f_Y((0,0))| = 4\left|\int_{\left[-\frac{1}{4},\frac{1}{4}\right]^2}
\hat{X}(\theta)d\theta - \int_{\R^2} \hat{Y}(\theta)d\theta\right| \\
\le 4\left(\int_{D} |\hat{X}(\theta) - \hat{Y}(\theta)|d\theta + \int_{\left[-\frac{1}{4},\frac{1}{4}\right]^2\setminus D} |\hat{X}(\theta)|d\theta +
\int_{\R^{2}\setminus D}
|\hat{Y}(\theta)|d\theta\right) \\
\le 4Cn^{-1/4}\area(D) + C\exp\left(-c_pn^{1/6}\right) +
\frac{4C}{\var(\xi_0)^2}e^{-c\var(\xi_0)n^{1/6}} = o(n^{-2}).
\end{multline*}
In addition, by \eqref{eq:Gaussian_density_with_Fourier transform}
and \eqref{eq:mu_and_sigma_def} we have
\begin{align*}
f_Y((0,0)) &=
\frac{1}{2\pi\sqrt{\det(\Sigma)}}e^{-\frac{1}{2}\mu^t\Sigma^{-1}\mu}
=
\frac{\sqrt{12}}{2\pi\var(\xi_0)(n+1)\sqrt{n(n+2)}}e^{-\frac{3(n+1)^2}{2n(n^2+3n+2)}}
=\\
&=\frac{\sqrt{3}}{4\pi p(1-p)n^2} + o(n^{-2}).
\end{align*}
This finishes the proof of
\eqref{eq:minus_1_double_root_asymptotics} and completes the proof
of Theorem~\ref{thm:double_root_asymptotics}.
\qed
\section{Open questions}
We conclude the paper by listing down several open questions.
\begin{enumerate}
\item As mentioned in the introduction, we do not know if the assumption \eqref{eq:coefficient_condition} or any similar condition is
necessary for Theorem~\ref{thm:double_root} to hold. Recall that the
assumption enters into the proof mainly through
Claim \ref{clm:integer_divisibility} which, in turn, is used to
obtain the crucial Lemma~\ref{lem:high_degree}.
\noindent
{\bf Remark.} Mei--Chu Chang \cite{Ch} has kindly pointed out to the authors that for Claim \ref{clm:integer_divisibility}
to hold, in Assumption
\eqref{eq:coefficient_condition} the constant $1/\sqrt{3}=0.5774\ldots$ can be replaced by the supremum of $\rho$s so that there exists $q\in (1,\infty)$ such that $3^{(q-1)/2q}<\rho^q+(1-\rho)^q$, leading to the value $0.7615\ldots$. This still leaves open the question of whether \textit{any} assumption of the type \eqref{eq:coefficient_condition}
is needed for Theorem~\ref{thm:double_root} to hold.
\item It is natural to try and extend Theorem~\ref{thm:double_root}
to more general coefficient distributions. This would require a
non-trivial modification of our approach as we relied in several
places on the fact that the potential roots of our random polynomial
are algebraic integers rather than the more general algebraic
numbers. A significant issue is to deal with potential roots of high
degree, providing an analogue of Lemma~\ref{lem:high_degree}.
\item The following question does not involve any probability. Are there examples of Littlewood polynomials with at least one non-cyclotomic double root? The same question had been asked by Odlyzko and Poonen \cite{OP93}
for polynomials with $0/1$ coefficients with the constant term equal
to one. That question was later answered by Mossinghoff \cite{M03}
who found examples of several such polynomials
with non-cyclotomic repeated roots.
\item Another interesting question is
to bound the probability that a random Littlewood polynomial is reducible. This is somewhat related to our original question regarding double roots - note that the probability of having a double root is dominated by the probability of being reducible. But handling irreducibility seems to be much harder. To the best of our knowledge, it is open whether this probability goes to zero as $n$ increases. See
the thread \cite{MO09} for some partial results on this question.
\end{enumerate}
\noindent
{\bf Acknowledgments} We thank an anonymous referee for spotting an error in
our original proof of Proposition \ref{prop:6.2}, and Mei--Chu Chang
for correspondence \cite{Ch} concerning Assumption
\eqref{eq:coefficient_condition}.
| {
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Rozszerzający draft odbył się 15 czerwca 1989 r., z okazji przyjęcia do ligi NBA nowych klubów – Orlando Magic i Minnesota Timberwolves. Kluby wybrały z pozostałych drużyn, odpowiednio, 12 i 11 zawodników.
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Japan Protected With SPY-7, Lockheed Martin's Latest Generation Radar Technology That Defends Against Ballistic Missile Threats
Hits 587
Provides continuous protection toJapan
Lockheed Martin's Solid State Radar has been designated as AN/SPY-7(V)1 by the United States government. SPY-7 and Aegis Ashore will defend against ballistic missile threats and provide continuous protection of Japan.
Tokyo. 18 November 2019. Lockheed Martin and its trading partner in Japan recently contracted with the Japanese Ministry of Defense to produce two Solid State Radar (SSR) antenna sets for Aegis Ashore Japan.
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\section{Introduction}
A variety of dimension reduction techniques have been developed for representing and analyzing data. Most of the dimension reduction techniques are focused on Euclidean space data. Recently there has been a growing interest in the analysis of non-Euclidean data; some dimension reduction techniques for non-Euclidean data have been studied for shape analysis or motion analysis. For example, Siddiqi and Pizer (2008) and Cippitelli et al. (2016) considered a Cartesian product of SO(2) (i.e., sphere) and $\mathbb{R}$ for medial representation and skeleton data analysis, respectively. For these representations, existing dimension reduction methods have been modified by considering geodesic distance. There have been several generalizations of principal component analysis (PCA) suited for non-Euclidean data, which contain Fletcher et al. (2004), Huckemann and Ziezold (2006), Huckemann et al. (2010), Jung et al. (2011), Jung et al. (2012), Panaretos et al. (2014), and Hauberg (2016). Fletcher et al. (2004) proposed a tangent plane approach of dimension reduction for manifold data, termed principal geodesic analysis (PGA). However, PGA is somewhat limited in scope because it can only perform the dimension reduction of spherical data onto the great circle. Along with this generalization, Jung et al. (2011) proposed a dimension reduction that extracts a circle on a sphere, and Jung et al. (2012) suggested principal nested spheres that can be considered as a high-dimensional version of Jung et al. (2011). Huckemann et al. (2010) suggested an extension of PCA using the intrinsic manifold structure and obtained their principal geodesic component as the best approximating the data does not necessarily pass through a predetermined intrinsic mean.
As a study that is closely related to our proposal, Hauberg (2016) developed principal curves on Riemannian manifolds. To be specific, Hauberg (2016) used an approximation to construct principal curves by a projection of the data onto the discrete points, unlike the original principal curve by Hastie and Stuetzle (1989) that projects the data onto a continuous curve. This approximation of finding closest points instead of projections on a curve causes a problem that may project different data points onto a single point mistakenly. In this study, we propose a new principal curve approach for spherical data by a projection of the data onto a continuous curve on a sphere instead of approximation, which improves dimension reduction and its stability. Our proposed approach is two-fold: One is the extrinsic approach that requires an additional space setting to the given manifold. In the case of the sphere, there exists a unique natural embedding space (three-dimensional space), and there is no question of the subjectivity of the extrinsic approach. The extrinsic approach is computationally efficient. The other is the intrinsic approach without any embedding space. Although this approach is difficult to calculate and impractical (Srivastava and Klassen, 2002), it is necessary to develop principal curves to a generic manifold. Furthermore, we investigate the stationarity of spherical principal curves obtained by both proposed approaches.
To sum up, the main contributions of this study can be summarized as follows: (a) We present a new principal circle defined on a sphere for initialization of the proposed principal curves. (b) We propose both extrinsic and intrinsic approaches to construct principal curves on a sphere. (c) We develop median principal curves that might be resistant to outliers, which can be considered as a robust extension of the proposed principal curves. (d) We verify the stationarity of all the proposed principal curves on the sphere.
The remainder of this paper is organized as follows. Section 2 briefly reviews conventional principal curves and intrinsic and extrinsic means on manifolds. In Section 3, a newly developed exact principal circle on a sphere is studied, which is used for the initialization of the proposed principal curves. Section 4 presents the proposed principal curves with a practical algorithm and investigates the stationarity of them theoretically. In Section 5, the experimental results of the proposed method are provided through earthquake data from the U.S. Geological Survey and simulation examples. Section 6 discusses a robust extension of intrinsic principal curves, termed median principal curves. Finally, concluding remarks are given in Section 7. The detailed proofs of properties of the principal curve on the sphere are given in Appendix.
Before closing this section, we remark that, as a significant extension of canonical interpretation of principal component analysis on Riemannian manifolds, Panaretos et al. (2014) introduced a smooth curve on the manifold, termed principal flow, which passes through the mean of given data and allows for non-geodesic flexibility of curve fitting of the data. Along with this line, the concept of principal flows can be shared with that of our method. Nevertheless, in this study, we focus on a direct extension of principal curves from Euclidean space to Riemannian manifolds, such as a sphere.
\section{Backgrounds}
\subsection{Principal Curves}
Principal curves of Hastie and Stuetzle (1989) can be considered as a nonlinear generalization of PCA that finds an affine space that maximizes the variance of the projected data. The curve is a function from a one-dimensional closed interval to a given space, and further, curve $f$ is said to be self-consistent or a principal curve of $X$ if the curve satisfies
\begin{equation}
\label{pc}
f(\lambda) = E\big(X|\lambda_{f}(X)=\lambda\big),
\end{equation}
where $f(\lambda_f(x))$ is the projection of the point $x$ to the function $f$. It implies that $f(\lambda)$ is the average of all data points projected onto $f(\lambda)$ itself. One of the most important consequences of self-consistency is that the principal curve is a critical point of the reconstruction error for small perturbations (Hastie and Stuetzle, 1989).
The existence of principal curves satisfying the self-consistency for a given distribution is not guaranteed. It is also difficult to formulate the principal curve by solving the self-consistent equation of (\ref{pc}). Thus, by the algorithm of Hastie and Stuetzle (1989), we set the principal curve as the first order spline connected by $T$ points, where the points are initialized by the given rule. The $T$ points of the principal curve are updated so that the curve reaches the self-consistency condition by iterating the following two steps, projection and expectation: (a) In the projection step, the given data are projected onto the curve. If the projection index is not unique, it is set to be the maximum value among them. (b) In the expectation step, the curve is updated to satisfy the self-consistency.
In practice, the projection indices of the data are likely to be different. Thus, each point of the curve is updated to the local weighted mean of data points projected near the point of the curve. These two steps are iterated until the reconstruction error is converged.
As related works, Banfield and Raftery (1992) proposed a modification of the original algorithm by Hastie and Stuetzle (1989) to reduce bias when segments of function $f$ have high curvature. Tibshirani (1992) presented a different definition of principal curves based on a mixture model and suggested an EM algorithm for estimation to reduce bias.
\subsection{Means on Manifolds}
The self-consistency of principal curves on Euclidean space implies that the conditional expectation of random variable $X$ given a projection index coincides with the point of the curve at the projection index. On the one hand, the concept of the expected value of a distribution is expandable in a smooth manifold and is called as \textit{Fr\'echet mean}. Given a probability distribution $Q$ on a smooth Riemannian manifold $M$ with a distance $\rho(\cdot, \cdot)$, the Fr\'echet mean $m\in M$ is defined as
\begin{equation}
\label{frechetmean}
\argmin\limits_{m\in M} \int \rho^2(m, x) Q(dx).
\end{equation}
The natural distance on a manifold is geodesic distance $d_{Geo}(\cdot, \cdot)$. The Fr\'{e}chet mean of (\ref{frechetmean}) using $d_{Geo}$ as distance is termed as \textit{intrinsic mean} (Bhattacharya and Patrangenaru, 2003). However, in general, it is difficult to solve geodesic distance and to ensure the uniqueness of intrinsic mean (Le and Kume, 2000).
On the other hand, by embedding a given manifold $M$ into a higher dimensional Euclidean space $\mathbb{R}^p$, the Fr\'echet mean can be calculated using Euclidean distance in $\mathbb{R}^p$, which is called as \textit{extrinsic mean}. With letting $\xi$ denote embedding from $M$ to $\mathbb{R}^p$, the extrinsic mean is defined as
\begin{equation}
\label{frechetmean1}
\argmin\limits_{m\in M} \int \|\xi(m) - \xi(x)\|^2 Q(dx).
\end{equation}
It is equivalent to the projection of the mean value of data points in $\mathbb{R}^p$ to $M$ (Bhattacharya and Patrangenaru, 2003). With a projection mapping $\pi: \mathbb{R}^p \to M$ as $\pi(y) = \argmin\limits_{m\in M} \|\xi(m) - y\|$, the extrinsic mean of (\ref{frechetmean1}) can be calculated as
\begin{equation}
\label{extrinsic}
\mbox{extrinsic mean} = \pi\big( \int \xi(x) Q(dx)\big).
\end{equation}
We remark that the extrinsic mean obtained by Euclidean distance holds a computational advantage, compared to the intrinsic mean (Bhattacharya et al., 2012). Moreover, the extrinsic mean is indistinguishable from the intrinsic mean in the case that the distribution has support in a small region (Bhattacharya and Patrangenaru, 2005).
\subsection{Existing Principal Curves on Riemannian Manifolds}
Hauberg (2016) developed principal curves on Riemannian manifolds by extending the previous work of Hastie and Stuetzle (1989). The principal curve by Hauberg (2016) is represented as a set of points, $f = \{C_1,\ldots, C_{T} \}$, joined by geodesic segments. These points are initialized with the principal geodesic. The fitting algorithm of the curves follows that of Hastie and Stuetzle (1989). More specifically, the mean operation in the expectation step of Hastie and Stuetzle (1989) is replaced with the intrinsic mean, and in the projection step, each data point is projected onto the closest points in $f$ as
\[
\mbox{proj}(x) = \argmin_{C_i\in f} d_{Geo}\big(x, C_i\big).
\]
Note that Hauberg's algorithm does not perform accurate projection on a principal curve.
\section{Enhancement of Principal Circle for Initialization}
In this section, we improve the principal circle to use the initialization for the proposed principal curves in Section 4.
\subsection{Principal Geodesic and Principal Circle}
The principal curve algorithm of Hastie and Stuetzle (1989) uses the first principal component as the initial curve, which is easily calculated by singular value decomposition (SVD) of the data matrix in Euclidean space. Along with this line, the proposed principal curve algorithm in Section 4 requires an initial curve.
Principal geodesic analysis (PGA) by Fletcher et al. (2004) can be considered as a generalization of PCA, which performs dimension reduction of data on the Cartesian product of simple manifolds. For this purpose, Fletcher et al. (2004) projected each manifold component of data onto the tangent space at the intrinsic mean of each component. As a result of the tangent space approximation of each component, the given data are approximated by points on Euclidean space; thus, by applying PCA, the dimension reduction can be performed through the inverse process of the tangent projection. For a spherical case, they particularly perform tangent space projection using an inverse exponential map, which is called as {\it log map}. The log map at (0,0,1) of the unit sphere centered at the origin of $\mathbb{R}^3$ is given by Fletcher et al. (2004) as
\[
\log \mbox{map}_{(0,0,1)}(x_1,x_2,x_3) = \Big(x_1\frac{\theta}{\sin\theta}, x_2\frac{\theta}{\sin\theta}\Big),
\]
where $(x_1,x_2,x_3)$ is a point on the unit sphere and $\theta=\arccos(x_3)$.
Principal curves on manifolds by Hauberg (2016) employ PGA for the initialization of a curve without endpoints and use a circle by tangent approximation for initialization of a closed curve. The first principal component obtained by the projection of manifolds into the tangent space corresponds to the geodesic in the existing manifolds (Fletcher et al., 2004). Thus, principal curves by Hauberg (2016) are initialized as great circles or approximated circles that do not minimize a reconstruction error for the representation of spherical data. However, geodesic on a sphere is limited to represent data on the sphere. Figure~\ref{fig1} shows earthquake data from the U.S. Geological Survey that represent the locations (blue dots) of significant earthquakes of Mb magnitude 8+ around the Pacific ocean since 1900. The data will be analyzed detailedly Section 5. In Figure~\ref{fig1}, the result (pink) by PGA does not fit the data appropriately, while our principal circle (red) in Section 3.2 improves the representation of the data.
\begin{figure}
\centering
\includegraphics[scale=1.0]{figures/principal_circle.JPG}
\vspace{-3mm}
\caption{Spherical distribution of significant earthquakes, the result (pink) by PGA, and the result (red) by our proposed principal circle.}
\label{fig1}
\end{figure}
In literature, there exists an attempt by Jung et al. (2011) that generalizes PGA to a circle on a sphere. The circle on the sphere that minimizes a reconstruction error is called \textit{principal circle}, where the reconstruction error is defined as the total sum of squares of geodesic distances between curve and data. Jung et al. (2011) used a doubly iterated algorithm that finds the principal circle after projecting the data onto the tangent space by using the log map. However, this approach suffers from two problems. First, using the tangent approximation in minimizing the distance causes numerical errors. In the case that data points are located far away from the mean, the numerical errors increase considerably because there is no local isometry between the sphere and its tangent plane from the \textit{Gauss's Theorema Egregium}. For instance, the left panel in Figure~\ref{fig2} shows simulated data distributed in the range of longitudes from 0.7 to 0.8, where the underlying structure is a great circle. Suppose that the intrinsic mean of the dataset is $(0,0,1)$. It means that even if the structure is a circle, data points are mainly concentrated on around the north pole, which looks like an inhomogeneous great circle. The middle panel shows projected points of the dataset onto the tangent plane at $(0,0,1)$. Although the data points around the south pole are dense, they become somewhat scattered after mapping onto the plane, as shown in the middle panel, which causes numerical errors (non-isometricity). Secondly, owing to a topological difference between sphere and plane, the existence of principal circles in the plane is not guaranteed. Even though the sphere is compact, the tangent plane is not compact, merely open. From the compactness of the sphere, the least square circle always exists regardless of the data structure; however, it does not work in the plane. In the right panel of Figure~\ref{fig2}, the blue dotted points are the projected ones onto the plane, which form a non-periodic line. Because a small arc of a big circle looks like a line, there are infinitely many circles that minimize the reconstruction error to be sufficiently close to 0. Hence, the least square circle does not exist in this case.
\begin{figure}
\centering
\includegraphics[scale=0.7]{figures/ex.JPG}
\includegraphics[scale=0.7]{figures/proj.JPG}
\includegraphics[scale=0.7]{figures/plane_circle.JPG}
\vspace{-3mm}
\caption{(Left) Simulated data points that are located in longitudes $[0.7, 0.8]$ with the intrinsic mean $(0,0,1)$. (Middle) The projected points from the sphere onto the tangent plane at (0,0,1). (Right) A case that the principal circle does not exist.}
\label{fig2}
\end{figure}
In this study, for a better initialization of the proposed principal curves in Section 4, we propose a new principal circle that does not depend on tangent projection. This attempt was previously made by Gray et al. (1980), which embeds a sphere into three-dimensional space and then find a circle that minimizes the reconstruction error through an iterative quadratic approximation of geodesic distances in the three-dimensional spatial coordinate system. Specifically, Gray et al. (1980) expressed the center of the circle as three-dimensional coordinates $(x_1, x_2, x_3)$ with a constraint of $x_1^2 + x_2^2 + x_3 ^2=1$.
On the other hand, we obtain the constraint-free optimization problem by expressing the center of the circle using a spherical coordinate system in Section 3.2; hence, our principal curve can be obtained through a simple algorithm.
\subsection{Intrinsic Principal Circle}
For our principal circle, we consider an intrinsic optimization algorithm that does not use an approximation; thus, it is simple and is applicable to some situations focused on a two-dimensional sphere instead of a high-dimensional one. Let $d_{Geo}(x, y)$ denote the minimal geodesic distance between two points $x$ and $y$ on a sphere. For a given dataset $D$ and a circle $C$ on a sphere, let $\delta(D,C)$ be the sum of squares of distances between circle and data, defined as
\[
\delta(D,C) = \sum_{x\in D} d_{Geo}\big(x, \mbox{proj}_C(x)\big)^{2},
\]
where $\mbox{proj}_C(x)$ denotes a projection of $x$ on $C$. The goal is to find a circle $C$ on the sphere that minimizes $\delta(D,C)$. To solve this optimization problem, we represent a circle $C$ by a center $c$ of the circle and a radius $r\in [0, \pi]$ that is a geodesic distance between the center $c$ and the circle $C$. This representation is not unique. For example, let $c^\prime$ be the antipode of $c$, then $(c,r)$ and $(c^\prime, \pi-r)$ represent the same circle $C$. Nevertheless, it is not crucial to the optimization problem since we simply find a representation of the least square circle. See Figure~\ref{fig3}. By using a spherical coordinate system, it is able to parameterize $c$ as $(\theta, \rho)$, where $\theta$ denotes the azimuth angle and $\rho$ is the polar angle. By symmetricity of the circle, $d_{Geo}\big(x, \mbox{proj}_C(x)\big)$ can be easily calculated by
\begin{figure}
\centering
\includegraphics[scale=0.8]{figures/circle_d.JPG}
\vspace{-3mm}
\caption{$d_{Geo}\big(x, \mbox{proj}_C(x)\big)$ is expressed as $d_{Geo}(x,c) - r$.}
\label{fig3}
\end{figure}
\[
d_{Geo}\big(x, \mbox{proj}_C(x)\big) = d_{Geo}(x,c) - r.
\]
Thus, we have
\begin{equation}
\label{ss1}
\delta(D,C) = \sum_{x\in D} \big(d_{Geo}(x,c) - r\big)^{2}.
\end{equation}
With letting $c = (\theta_{c}, \rho_{c})$ and $x = (\theta_{x}, \rho_{x})$ in the spherical coordinate system, the geodesic distance $d_{Geo}(x,c)$ is given by the spherical law of cosines with three points $c$, $x$ and the polar point (see Appendix for details)
\begin{equation}
\label{dgeo1}
d_{Geo}(x,c) = \arccos\big(\cos\rho_{c}\cos\rho_{x} +\sin\rho_{c}\sin\rho_{x}\cos(\theta_{c}-\theta_{x})\big).
\end{equation}
By putting (\ref{dgeo1}) into (\ref{ss1}), it follows that $\delta(D,C)$ is represented as a three-parameter differentiable function $\delta_{D}(\theta_{c}, \rho_{c},r)$ in domain $S^1\times S^1 \times [0,\pi]$. Since $S^1\times S^1 \times [0,\pi]$ is compact, the function $\delta_{D}(\theta_{c}, \rho_{c},r)$ holds global minimum value; hence, it can apply the gradient descent method to find the solution. Here is the algorithm to find a principal circle by the above description.
\vskip 3mm
\begin{algorithm}[H]
\caption{Intrinsic Principal Circle by Gradient Descent}
\begin{algorithmic}
\State Initialize $(\theta_{c}, \rho_{c}, r)$ as ($\overline{\theta}, \, \overline{\rho}, \, \pi/2$)
\While{ ($\Delta \delta(D,C) \ge \mbox{threshold}$) }
\State $(\theta_{c}, \rho_{c}, r) \leftarrow (\theta_{c}, \rho_{c}, r) - \beta \nabla \delta_{D}(\theta_{c}, \rho_{c},r) $
\EndWhile
\end{algorithmic}
\end{algorithm}
Notice that the algorithm can converge to a local minimum since $\delta_D(\theta_c, \rho_c, r)$ is not a convex function. Therefore, the intrinsic mean of the data set $D$ is recommended for the initial setting. Denote ($\overline{\theta}, \, \overline{\rho})$ as spherical coordinates of the intrinsic mean. Besides, $\beta$ denotes the step size of the algorithm, which works well unless $\beta$ is too large.
\section{Proposed Principal Curves}
In this section, we propose both extrinsic and intrinsic principal curves on a sphere and present practical algorithms for implementing the procedures. We further investigate the stationarity of the proposed principal curves.
\subsection{Extrinsic Principal Curves}
As mentioned previously, Hauberg's algorithm does not perform exact projection on a principal curve. On the other hand, when we focus on a sphere, by using the series of rotations, it is able to perform exact projection on the geodesic segments, and hence, obtain a continuous and sophisticated dimension reduction, which is our main feature that is distinguished from Hauberg's principal curves. Like the original one of Hastie and Stuetzle (1989), we consider performing the projection and expectation steps iteratively to obtain principal curves on a sphere.
\begin{figure}[!h]
\centering
\includegraphics[height=0.24\textheight,width=1.0\textwidth]{figures/proj_plot.JPG}
\vspace{-10mm}
\caption{Projecting a point (blue) onto the geodesic segment (red) by using rotations. (Left) Initial position of the point and the geodesic segment. (Middle) Rotating one of the end points of the geodesic segment to the north pole. (Right) Rotating the center of the circle to the north pole.}
\label{fig4}
\end{figure}
In the projection step, each data point is projected on the curve along a geodesic. To project a point on an arbitrary geodesic segment, we rotate the geodesic segment to be aligned on the equator. Next, we project the rotated data point on the rotated geodesic segment and re-rotate the result to get coordinates of the projection that we want. Figure 4 shows this procedure that projects a point to the geodesic segment by using rotations. In the left panel of Figure 4, the initial position of the point (blue) and the corresponding geodesic segment (red) are displayed. The middle panel shows a rotated result obtained after rotating one of the endpoints of the geodesic segment to the north pole. As a result of this rotation, the geodesic becomes a part of a great circle perpendicular to the $xy$-plane. By adding $\pi$/2 to the azimuth angle of the geodesic, it is able to get the center (green) of the great circle, which contains the geodesic segments. The right panel shows a rotated result from rotating the center of the circle to the north pole. As one can see, the geodesic segment is now aligned on the equator, so we can easily calculate the coordinates of projection from the point (blue) using a spherical coordinate system. By the inverse process of these rotations, we obtain the coordinates of the projection in the original coordinate system. Finally, after projecting the data point on each geodesic segment of the principal curve, we obtain the projection on the curve by choosing the closest geodesic segment. Let $\lambda_f(x)$ denote the projection index of a point $x$ to the curve $f(\lambda)$, where $\lambda \in [0,1]$. Then, the projection of $x$ can be expressed as
\[
\mbox{projection of }x = f\big(\lambda_f(x)\big), \quad \lambda_f(x) = \argmin_\lambda d_{Geo}\big(x, f(\lambda)\big).
\]
In the expectation step, we find the mean of data points. Mean on a sphere can be obtained from both intrinsic and extrinsic perspectives. We first focus on the extrinsic approach. The extrinsic approach is advantageous in that it has a smaller computational complexity compared to the intrinsic algorithm, and further, the stationarity of the spherical principal curves can be held. The expectation step follows that of the principal curve of Hauberg (2016), i.e., updating the weighted average by smoothing that makes the curve closer to the self-consistency condition.
Suppose that we have $n$ data points $\{x_i\}_{i=1}^n$ and the corresponding projection indices $\{\lambda_i\}_{i=1}^n$, where $\lambda_i=\lambda_f(x_i)$ for $i=1,\ldots,n$. Let $T$ denote the number of points in an initial curve.
The local weighted smoother updates the $t$th point of the principal curve $C_t$ with the weighted extrinsic mean of data points for $t=1,\ldots,T$. We use a quadratic kernel $k(\lambda) = (1-\lambda^2)^2\cdot \delta_{|\lambda|\le 1}$, as Hauberg (2016), and the weights are given by $w_{t, i}= k(|\lambda_f(C_t) - \lambda_i| / \sigma)$, where $\sigma = q \cdot \mbox{length\ of\ curve}$ for fixed $q$.
Here are the detailed steps for obtaining the proposed extrinsic principal curve.
\begin{algorithm}[H]
\caption{Extrinsic Principal Curve}
\begin{algorithmic}
\State 1. Initialize principal curve $f = \{C_1,...,C_{T}\}$ as principal circle.
\State 2. Parameterize the curve as $f(\lambda)$ by the unit speed in the geodesic distance.
\State 3. Do projection $\lambda_f(x_i) = \argmin_{\lambda} d_{Geo}\big(x_i, f(\lambda)\big)$, $i = 1,\ldots,n$.
\State 4. Calculate $ \delta(D,f) = \sum_{i=1}^n d^2_{Geo}\bigr(x_i, f\big(\lambda_f(x_i)\big)\bigr)$.
\While{ ($\Delta \delta(D,f) \ge \mbox{threshold}$) }
\State - {\underline{Expectation}} $C_t =\sum_{i=1}^n w_{t,i}x_i / \lVert \sum_i w_{t,i}x_i \rVert$, $t=1,\ldots, T$.
\State - Reparameterize the curve as $f(\lambda)$ by the unit speed in the geodesic distance.
\State - {\underline{Projection}} $\lambda_f(x_i) = \argmin_{\lambda} d_{Geo}\big(x_i, f(\lambda)\big)$, $i = 1,\ldots,n$.
\State - Calculate $\delta(D,f) = \sum_{i=1}^n d^2_{Geo}\bigr(x_i, f\big(\lambda_f(x_i)\big)\bigr)$.
\EndWhile
\end{algorithmic}
\end{algorithm}
We remark that, for principal curves on a sphere, we can choose the curves to have either the endpoints or not. Through our experiments, we observe that there is no significant difference in empirical performance. As far as Euclidean space is concerned as embedding space, the extrinsic approach is advantageous in computational efficiency. However, if data points, in the expectation step, are not contained in local regions, then the intrinsic way may have better performances than the extrinsic one. Moreover, the intrinsic manner might be appealing owing to its inherent metric.
\subsection{Intrinsic Principal Curves}
Intrinsic principal curves can be obtained by using the intrinsic mean in the expectation step of Algorithm 2. In our case, the intrinsic mean is the point that minimizes the sum of square of the geodesic distances $\sum_{x \in data} d^2_{Geo}(x, \, \cdot)$; thus, the minimum cannot be solved explicitly; instead, it can be approximately obtained by an iterative algorithm (Fletcher et al., 2004). Although the intrinsic mean exists due to the compactness of the sphere, uniqueness is guaranteed only in a restricted region. Specifically, the intrinsic mean is determined uniquely for a random vector $X$ on the unit sphere $S^2$ satisfying $d_{Geo}(X, p) < \frac{\pi}{2}$ for some $p \in S^2$ (Pennec, 2006).
Here are the detailed steps for obtaining the proposed intrinsic principal curve.
\begin{algorithm}[H]
\caption{Intrinsic Principal Curve}
\begin{algorithmic}
\State 1. Initialize principal curve $f = \{C_1,\ldots,C_{T} \}$ as principal circle.
\State 2. Parameterize the curve as $f(\lambda)$ by the unit speed in the geodesic distance.
\State 3. Do projection $\lambda_f(x_i) = \argmin_{\lambda} d_{Geo}\big(x_i, f(\lambda)\big)$, $i = 1,\ldots,n$.
\State 4. Calculate $ \delta(D,f) = \sum_{i=1}^n d^{2}_{Geo}\bigr(x_i, f\big(\lambda_f(x_i)\big)\bigr)$.
\While{ ($\Delta \delta(D,f) \ge \mbox{threshold}$) }
\State - {\underline{Expectation}} $C_t=\argmin_{x}\sum_{i=1}^n w_{t,i} \cdot d^2_{Geo}(x, x_i)$, $t=1,\ldots, T $.
\State - Reparameterize the curve as $f(\lambda)$ by the unit speed in the geodesic distance.
\State - {\underline{Projection}} $\lambda_f(x_i) = \argmin_{\lambda} d_{Geo}\big(x_i, f(\lambda)\big)$, $i = 1,\ldots,n$.
\State - Calculate $\delta(D,f) = \sum_{i=1}^n d^{2}_{Geo}\bigr(x_i, f\big(\lambda_f(x_i)\big)\bigr)$.
\EndWhile
\end{algorithmic}
\end{algorithm}
\subsection{Stationarity of Principal Curves}
For a random vector $X$ on $\mathbb{R}^p$ for $p \in \mathbb{N}$, the stationarity of the principal curve of $X$ is given by Hastie and Stuetzle (1989) as
\begin{equation}
\label{eq:stat}
\frac{dE_X d^2(X,f+\epsilon g)}{d\epsilon} \Bigr|_{\epsilon = 0} = 0,
\end{equation}
where $f$ and $g$ are smooth curves on $\mathbb{R}^p$ satisfying $\norm{g} \le 1$ and $\norm{g^\prime} \le 1 $, and $d(X,f)$ denotes the distance from $X$ to the curve $f$.
However, unlike $\mathbb{R}^p$, it is not easy to define addition on a sphere. Thus, it is necessary to redefine some concepts, such as addition and perturbation, in order to extend the properties of the principal curves on Euclidean space to a spherical surface.
We conversely consider $f+g\ (\small{:=}h)$ firstly, instead of $g$. Specifically, let $f$ and $h$ be infinitely differentiable smooth curves on a sphere that are parameterized with $\lambda \in [0, 1]$. From these assumptions, we define the perturbation $f + \epsilon g$ shown in Figure~\ref{fig5} as follows:
\begin{definition}
$\epsilon$-internal division of the geodesic from $a$ to $b$ means a point that contracts by $\epsilon$ times along the geodesic from $a$ to $b$, that is, $\epsilon\cdot d_{Geo}(a,b) = d_{Geo}\big(a,\epsilon-internal\ division\big).$
\end{definition}
\begin{figure}
\centering
\includegraphics[scale=1]{figures/math1.JPG}
\vspace{-3mm}
\caption{Perturbation of $f$ along geodesic to $f+g$.}
\label{fig5}
\end{figure}
For $\epsilon < 0$, $\epsilon$-internal division of the geodesic from $a$ to $b$ can be defined in the same manner. We note that when $a$ and $b$ are located on the opposite sides, the shortest geodesic is not unique. Thus, we only consider the case that the distance between $f (\lambda)$ and the perturbation function $(f+g)(\lambda)$ is less than $\pi$ when the curves are on the unit sphere. It is reasonable since we aim to show the stationarity for small $\epsilon$.
\begin{definition}
Let $f$ and $f+g$ be smooth curves on a sphere that are parameterized with $\lambda \in [0,1]$ satisfying $\norm{g}:= \max_{\lambda \in [0,1]} d_{Geo}\bigr(f(\lambda), (f+g)(\lambda)\bigr) \ne \pi$. Then, we define $(f+\epsilon g)(\lambda)$ as $\epsilon$-internal division of the geodesic from $f(\lambda) $ to $(f+g)(\lambda)$ \ $\forall \lambda \in [0, 1]$.
\end{definition}
The following two properties can be obtained from the definition.
\begin{proposition}
Under the same conditions in Definition 2, $f+\epsilon g$ is a smooth curve on a sphere and $\lim\limits_{\epsilon \to 0}(f+\epsilon g)(\lambda) = f(\lambda)$ uniformly on $\lambda \in [0, 1]$.
\begin{proof}
From the assumption that $f(\lambda)$ and $(f+g)(\lambda)$ are smooth functions and the uniqueness assumption of $(f+\epsilon g)(\lambda)$, the smoothness of $(f+\epsilon g)(\lambda)$ with respect to $\lambda$ follows. Moreover, it is easy to see that $f+\epsilon g\bigr(=f(\epsilon, \lambda)\bigr)$ is infinitely differentiable on $[-1, \, 1] \times [0, \, 1]$. In addition, from the definition of $\epsilon$-internal division and $\norm{g} \ne \pi $, the uniform continuity of $(f+\epsilon g)(\lambda)$ on $\lambda \in [0,1]$ with respect to $\epsilon$ follows.
\end{proof}
\end{proposition}
In Euclidean space, we have $g(\lambda)= \frac{\partial}{\partial \epsilon} f_{\epsilon}(\lambda)$, where
$f_{\epsilon}(\lambda):=f+\epsilon g$. From this fact, the magnitude of perturbation $\norm{h-f}$ is defined as $g(\epsilon_0,\lambda) := \frac{\partial}{\partial \epsilon} \bigr|_{\epsilon=\epsilon_0} f_{\epsilon}(\lambda)$, $\norm{g(\lambda)} := d_{Geo}\bigr(f(\lambda),g(\lambda)\bigr) = \ \bigr|g(\epsilon_0, \lambda) \bigr|$, $\norm{g}:=\max_{\lambda} \norm{g(\lambda)}$, and $\norm{h-f} := \norm{g} \ne \pi.$ The boundedness of $\norm{g}$ guarantees that $\epsilon$-internal division of the geodesic from $f$ to $h$ converges to $f$ uniformly on $\lambda \in [0,1]$ as $\epsilon$ goes to zero. Notice that from the compactness of the unit sphere, $\norm{h-f}$ is inherently equal or less than $\pi$; thus, the assumption of $\norm{h-f} \ne \pi $ implies that $\norm{h-f} < \pi $.
Moreover, the norm of derivative of perturbation $\norm{(h-f)'}$ is defined as $g'(\epsilon, \lambda_0) := \frac{\partial}{\partial \lambda} \bigr|_{\lambda=\lambda_{0}} g(\epsilon,\lambda)$, $\norm{g'(\lambda_0)} := \max_{|\epsilon| \le 1} \norm{g'(\epsilon,\lambda_0)}$, $\norm{g'}:=\max_{\lambda_0} \norm{g'(\lambda_0)}$, and $\norm{(h-f)'} := \norm{g^\prime}$. It is easy to check that a constraint $\norm{g^\prime} \le 1$ ensures a finite length of $f+\epsilon g$ and well-definedness of $\lambda_{f+\epsilon g}$ for $|\epsilon| \le 1$. In addition, $(f+\epsilon g)(\lambda)$ is extended to a small open interval containing $[-1, 1]$ for differentiability on $[-1,1]$.
Let $x$ be a point on a sphere. By the continuity of $f$ and the compactness of the domain set, it follows that $\inf_{\lambda \in [0,1]} d_{Geo}\big(x,f(\lambda)\big)$ can be attained. Let $d(x,f)$ denote the geodesic distance between $x$ and $f$, i.e., $d(x,f):=\min_{\lambda \in [0,1]} d_{Geo}\big(x,f(\lambda)\big)$. By the continuity of $f$ again, $\{\lambda \in [0,1] \ | \ d_{Geo}\big(x,f(\lambda)\big)=d(x,f)\}$ is closed and therefore compact. Thus, the projection index $\lambda_f(x) = \inf\{\lambda \ | \ d_{Geo}\big(x,f(\lambda)\big)=d(x,f)\}$ is well defined. When $\mbox{card}\{\lambda \ | \ d_{Geo}\big(x,f(\lambda)\big)=d(x,f)\}>1$, the point $x$ is called an ambiguity point of $f$. The set of ambiguity points of the smooth curve has spherical measure 0; thus, the ambiguity points are negligible when calculating the expected value.
Let $X$ be a random vector on a sphere that has a probability density. We define that $f$ is an extrinsic principal curve of $X$ when $f$ satisfies the following self-consistency of $X$,
\[
\pi\big(E\big(\xi(X)|\lambda_f(X)=\lambda\big)\big) = f(\lambda),~\mbox{for}~\mbox{a.e.}~\lambda,
\]
where $\xi$ denotes the natural embedding from the unit sphere to $\mathbb{R}^3$ and $\pi$ is a projection mapping from $\mathbb{R}^3$ to the sphere, which are used in (\ref{extrinsic}) for the definition of extrinsic mean.
In the principal curve algorithm, it is natural that the projection is made along the geodesic, and therefore, it is reasonable to calculate the distance of (\ref{eq:stat}) as the geodesic distance. However, it is difficult to show that the equation (\ref{eq:stat}) is valid in the spherical surface directly. It seems that the square is a natural operation in the Euclidean space, but not in the spherical surface. Here, by using the spherical law of cosine, we obtain the following result.
\begin{theorem}
Suppose that $f$, $f+g: [0,1] \to S^2$ are finite-length smooth curves satisfying $\norm{g} \ne \pi$ and $\norm{g^\prime} \le 1$ and $X$ is a random vector on $S^2$. Then, $f$ is an extrinsic principal curve of $X$ if and only if
\begin{equation}
\label{eq:thm1}
\frac{dE_X\bigr(\cos\big(d_{Geo}(X,f+\epsilon g)\big)\bigr)}{d\epsilon} \Bigr|_{\epsilon = 0} = 0.
\end{equation}
\end{theorem}
A proof is provided in Appendix. We remark that since $2-2\cos x \approx x^2$ for small $x$, the above result (\ref{eq:thm1}) has a similar meaning to (\ref{eq:stat}). Based on this, it is able to consider the sum of $2-2\cos\big(d_{Geo}(x, f)\big)$ in the extrinsic principal curve as the reconstruction error (distance) $\delta(D, f)$. However, $2-2\cos\big(d_{Geo}(x, f)\big)$ is a monotonically increasing function of $d_{Geo}(x, f)$, if $d_{Geo}(x, f) \in [0,\pi]$; hence, there is no difference in which one is used as an evaluation measure or a threshold in the algorithm.
Furthermore, we find a necessary and sufficient condition of intrinsic principal curves on a sphere below.
\begin{theorem}
Suppose that $f$, $f+g: [0,1] \to S^2$ are finite-length smooth curves satisfying $\norm{g} \ne \pi$ and $\norm{g'} \le 1$ and that a random vector $X$ on $S^2$ satisfies $X \in B(\zeta)$, where $B(\zeta) := \{x \in S^2 \ | \ |f''(\lambda_{f}(x)) \cdot x| > \zeta \}$ for a small $\zeta > 0$. Then, $f$ is an intrinsic principal curve of $X$ if and only if
\begin{equation}
\label{eq:thm2}
\frac{dE_X\big(d^{2}_{Geo}(X,f+\epsilon g)\big)}{d\epsilon} \Big|_{\epsilon = 0} = 0.
\end{equation}
\end{theorem}
In contrast to the extrinsic stationarity, an additional constraint $X \in B(\zeta)$ is necessary for guaranteeing that the projection index $\lambda_{f_{\epsilon}}(X)$ is differentiable for $\epsilon$ and its derivative is uniformly bounded, which is verified by Lemma 5 in Appendix. Furthermore, the measure of $S^2 \setminus B(\zeta)$ goes to 0 as $\zeta \rightarrow 0$ by Lemma 4 in Appendix. Thus, the constraint of random vector $X$ could be almost negligible by setting $\zeta$ infinitesimally small since $X$ has a probability density.
We remark that the stationarity of principal curves in Euclidean space provides a rationale for the principal curves of Hastie and Stuetzle (1998) that is a nonlinear generalization of the linear principal component. Along the same line, the above stationarity results provide theoretical justifications that the proposed approaches extend the principal curves in Euclidean space to the sphere.
\section{Numerical Experiments}
In this section, we conduct numerical experiments with real data analysis and several simulated examples to assess the practical performance of the proposed methods, which are implemented by the algorithms in Section 4. The Python codes used to implement the methods and to carry out some experiments are available at \url{https://github.com/Janghyun1230/Spherical-Principal-Curve} in order that one can reproduce the same results.
\subsection{Real Data Analysis: U.S. Geological Earthquake Survey}
Here we present a real data analysis of the proposed principal curves on a sphere. For this purpose, we consider earthquake data from the U.S. Geological Survey in Figure~\ref{fig6} that represent the distribution of significant earthquakes (8+ Mb magnitude) around the Pacific Ocean since the year 1900. As shown in Figure~\ref{fig6}, we observe some features of the data: (a) the observations are scattered on the surface of Earth, and (b) they are non-linear one-dimensional structure on the sphere. It seems that the proposed principal curve might be applicable to the data for extracting the feature.
\begin{figure}
\centering
\includegraphics[scale=0.5]{figures/earth1.JPG}
\hspace{1cm}
\includegraphics[scale=0.95]{figures/earth2.JPG}
\caption{The distribution of significant earthquakes (8+ Mb magnitude), and their three-dimensional visualization.}
\label{fig6}
\end{figure}
We now perform the proposed extrinsic principal curve over different values of hyperparameter $q$. As $q$ decreases, the resulting curve becomes wiggly and overfits the data. Figure~\ref{fig7} shows the results with $q=0.01$ and 0.2. The determination of the parameter $q$ is not easy. Duchamp and Stuetzle (1996) showed that a principal curve is always a saddle point of the expected squared distance function, which explains why cross-validation is not reliable for choosing hyperparameter $q$. In Euclidean space, Biau and Fischer (2012) suggested the parameter selection by empirical risk minimization via penalization of length and the number of points in curves. In a spherical domain, this topic is left for future work.
\begin{figure}
\centering
\includegraphics[scale=0.5]{figures/curves/earth_extrinsic_q001_n500.jpg}
\hspace{0.0cm}
\includegraphics[scale=0.5]{figures/curves/earth_extrinsic_q02_n500.jpg}
\vspace{-3mm}
\caption{Principal curves (extrinsic) of $T=500$ points with $q=0.01$ (left) and $q=0.2$ (right). Blue points represent the earthquake data and red points represent the points of the fitted curve.}
\label{fig7}
\end{figure}
As mentioned earlier, the proposed algorithm is required to have an initialization. The results in Figure~\ref{fig7} are obtained by using $T=500$ uniformly sampled points from the intrinsic principal circle in Section 3.2 as an initialization.
\comment{On the other hand, Figure~\ref{fig} shows results by taking the principal geodesic as initialization in Figure~\ref{fig1}. The initial and final states of the principal curve with $q=0.05$ are shown in the left and right panels, respectively. In this case, the principal curve cannot represent the feature of the observations well.
\begin{figure}[h]
\centering
\includegraphics[scale=0.5]{figures/curves/PGA_init.jpg}
\hspace{0.0cm}
\includegraphics[scale=0.5]{figures/curves/PGA_init_q005.jpg}
\vspace{-3mm}
\caption{A result of principal curve with the initialization as the principal geodesic ($T= 77$, $q= 0.05$). The initial and final states of the principal curve.}
\label{fig}
\end{figure}
}
\begin{figure}
\centering
\includegraphics[scale=0.5]{figures/curves/projected_earth_extrinsic_q01_n77.jpg}
\hspace{0.0cm}
\includegraphics[scale=0.5]{figures/curves/projected_earth_hauberg_q01_n77.jpg}
\vspace{-3mm}
\caption{Projection results by the proposed method (left) and Hauberg's method (right), $T=77$ and $q=0.1$.}
\label{fig8}
\end{figure}
\begin{table}[h]
\caption{Comparison of extrinsic principal curve and Hauberg's.}
\vspace{-3mm}
\centering
\label{table1}
\small{
\begin{tabular}{c||c|c|ccc}
\hline
\multicolumn{3}{c|}{} & extrinsic & intrinsic & Hauberg \\ \hline \hline
& \multirow{2}{*}{q=0.2} & Reconstruction error & 2.662 & 4.391 & 12.067 \\
\multirow{6}{*}{T=77} & & \# of distinct projection & 74/77 & 72/77 & 22/77 \\ \cline{2-6}
& \multirow{2}{*}{q=0.1} & Reconstruction error & 0.463 & 0.467 & 4.920 \\
& & \# of distinct projection & 76/77 & 76/77 & 9/77 \\ \cline{2-6}
& \multirow{2}{*}{q=0.05} & Reconstruction error & 0.359 & 0.359 & 1.313 \\
& & \# of distinct projection & 74/77 & 73/77 & 16/77 \\ \cline{2-6}
& \multirow{2}{*}{q=0.01} & Reconstruction error & 0.061 & 0.061 & 0.227 \\
& & \# of distinct projection & 75/77 & 75/77 & 27/77 \\ \hline
& \multirow{2}{*}{q=0.2} & Reconstruction error & 2.193 & 3.460 & 11.300 \\
\multirow{6}{*}{T=500} & & \# of distinct projection & 75/77 & 72/77 & 30/77 \\ \cline{2-6}
& \multirow{2}{*}{q=0.1} & Reconstruction error & 0.715 & 0.732 & 3.903 \\
& & \# of distinct projection & 75/77 & 74/77 & 18/77 \\ \cline{2-6}
& \multirow{2}{*}{q=0.05} & Reconstruction error & 0.298 & 0.200 & 0.963 \\
& & \# of distinct projection & 75/77 & 75/77 & 27/77 \\ \cline{2-6}
& \multirow{2}{*}{q=0.01} & Reconstruction error & 0.036 & 0.036 & 0.121 \\
& & \# of distinct projection & 75/77 & 75/77 & 37/77 \\ \hline
\end{tabular}%
}
\end{table}
We further compare the proposed extrinsic principal curves with the principal curves of Hauberg (2016). Figure~\ref{fig8} shows both results with $q= 0.1$, where the purple lines represent the fitted curves by each method, and the blue lines represent the projections from the data onto the curve. As one can see, the proposed extrinsic principal curve continuously represents the given data on the curve, whereas the principal curve of Hauberg (2016) projects some local data points to a single point. The results are further summarized in Table~\ref{table1}. When 77 earthquake observations are projected on the principal curve, the number of distinct projections by our method is much larger than that of Hauberg's method. It implies that our principal curve represents the data continuously, compared to Hauberg's principal curve that tends to cluster the data. Moreover, through a reconstruction error defined as $\sum_{i=1}^n d^2_{Geo}\bigr(x_i,\hat{f}\big(\lambda_{\hat{f}}(x_i)\big)\bigr)$
with the observations $x_i$ and fitted values $\hat{f}\big(\lambda_{\hat{f}}(x_i)\big)$, we compare both methods and observe that our method outperforms Hauberg's method.
\subsection{Simulation Study}
To evaluate the empirical performance of the proposed method, we conduct a simulation study. For this purpose, we consider two types of form on the unit sphere with spherical coordinates $(r=1,\theta,\phi)$, where $\theta$ is the azimuthal angle, and $\phi$ denotes polar angle.
\begin{itemize}
\item Circle: It is formed of $(r=1,\theta,\phi)$ with $0\le \theta < 2\pi$ and $\phi=\pi/4$. It is an ideal case for the extrinsic principal curve as well as the improved principal circle.
\item Wave: It is defined as $(r=1,\theta,\phi)$ with $0\le \theta < 2\pi$ and $\phi=\alpha\sin(2\pi\theta f)+\pi/2$. It has a complicated structure with varying frequency ($f=4,8$) or amplitude of waveform ($\alpha=1/3,1/6$).
\end{itemize}
\begin{figure}
\centering
\includegraphics[scale=0.5]{figures/curves/simulation/circle_true.jpg}
\hspace{0.0cm}
\includegraphics[scale=0.5]{figures/curves/simulation/circle_extrinsic_q005_n500.jpg}
\vspace{-5mm}
\caption{True circular curve and blue noisy data (left), and the extrinsic principal curve with $T= 500$ and $q=0.05$ (right).}
\label{fig9}
\end{figure}
\begin{figure}
\centering
\includegraphics[scale=0.5]{figures/curves/simulation/wave_true.jpg}
\hspace{0.0cm}
\includegraphics[scale=0.5]{figures/curves/simulation/wave_extrinsic_q005_n500.jpg}
\hspace{0.0cm}
\caption{True waveform curve and blue noisy data (left), and the extrinsic principal curve with $T= 500$ and $q=0.05$ (right). }
\label{fig10}
\end{figure}
For each dataset, we generate $n=100$ data points from each form by sampling $\theta$ equally in $[0,2\pi]$, and add normal noises from $N(0,\sigma^2)$ on $\phi$ with a certain noise level $\sigma$. Figure~\ref{fig9} shows a realization of noisy circular data with $\sigma=0.07$ marked by blue and the extrinsic principal curve by the proposed method with $T= 500$ and $q=0.05$ that represents the underlying structure well.
We now consider a dataset with the wave structure, in which the principal circle cannot reveal the wave feature, while the proposed principal curve might be capable of extracting the feature. To conduct various experiments, we use several forms of wave, parameterized by amplitude $\alpha=1/6,~1/3$ and frequency $f=4,~8$. In addition, a sampling rate of the data point is considered for the experiment setting.
Firstly, a waveform dataset with the amplitude of $\alpha=1/3$ and the frequency of $f=8$ is generated. Figure~\ref{fig10} shows the underlying structure, noisy data, and the extrinsic principal curve with $T= 500$ and $q=0.05$ that represents the underlying waveform efficiently.
Notice that the amplitude of principal curves is reduced owing to the locally weighted averaging in the expectation step of the algorithms when segments of the underlying structure have high curvature, which is a general phenomenon of the original principal curves (Banfield and Raftery, 1992). Secondly, we consider a waveform dataset with amplitude $\alpha=1/3$ and relatively low frequency $f=4$ in Figure~\ref{fig11}. We compare our methods with Hauberg's method under the same condition $T= 500$ and $q=0.05$. As one can see, both extrinsic and intrinsic principal curves extract the true waveform effectively, while Hauberg's method yields rather a sharp curve. Thirdly, Figure~\ref{fig12} shows a noisy waveform dataset with relatively low amplitude $\alpha=1/6$ and frequency $f=8$ and the true waveform. The result by the proposed method represents the waveform feature well, as shown in the right panel. Lastly, in Figure~\ref{fig13}, we use a waveform with high amplitude $\alpha=1/3$ and high frequency $f=8$ as the first case, but take a low sampling rate that the number of data points is small, $n=50$, compared to the case of Figure~\ref{fig10}. In other words, the generated data are rather sparse. The result by the proposed method in the right panel produces a sawtooth form, but it still represents the up-down pattern roughly on the sphere.
\begin{figure}[!h]
\centering
\includegraphics[scale=0.5]{figures/curves/simulation/wave_freq_true.jpg}
\hspace{0.0cm}
\includegraphics[scale=0.5]{figures/curves/simulation/wave_freq_extrinsic_q005_n500.jpg}
\hspace{0.0cm}
\includegraphics[scale=0.5]{figures/curves/simulation/wave_freq_intrinsic_q005_n500.jpg}
\hspace{0.0cm}
\includegraphics[scale=0.5]{figures/curves/simulation/wave_freq_hauberg_q005_n500.jpg}
\vspace{-5mm}
\caption{From left to right and top to bottom: True waveform and noisy data, the extrinsic principal curve, the intrinsic principal curve, and the curve by Hauberg's method.}
\label{fig11}
\end{figure}
\begin{figure}
\centering
\includegraphics[scale=0.5]{figures/curves/simulation/wave_amp_true.jpg}
\hspace{0.0cm}
\includegraphics[scale=0.5]{figures/curves/simulation/wave_amp_extrinsic_q005_n500.jpg}
\vspace{-5mm}
\caption{True waveform of low amplitude and noisy data (left), and the extrinsic principal curve with $T= 500$ and $q=0.05$ (right).}
\label{fig12}
\end{figure}
\begin{figure}
\centering
\includegraphics[scale=0.5]{figures/curves/simulation/wave_sparse_true.jpg}
\hspace{0.0cm}
\includegraphics[scale=0.5]{figures/curves/simulation/wave_sparse_extrinsic_q005_n500.jpg}
\vspace{-5mm}
\caption{True waveform and a spare dataset with 50 data points (left), and the extrinsic principal curve with $T= 500$ and $q=0.05$ (right).}
\label{fig13}
\end{figure}
For further evaluation, we conduct a Monte Carlo simulation. For this purpose, we generate noisy data that consist of two true curves and Gaussian noises from $N(0,\sigma^2)$ with a noise level of $\sigma=0.07$ or 0.1. The number of data points is $n=100$, and data points are equally spaced. We consider three methods for feature extraction, the proposed extrinsic, intrinsic principal curves, and the principal curve by Hauberg (2016). As an evaluation measure, we consider a reconstruction error defined as $\sum_{i=1}^n d^2_{Geo}\bigr(x_i,\hat{f}\big(\lambda_{\hat{f}}(x_i)\big)\bigr)$, where $x_i$ denote sample values of the true function and $\hat{f}\big(\lambda_{\hat{f}}(x_i)\big)$ are the fitted values. In addition, we use the number of distinct projection points as another evaluation measure. It can be conjectured that the resulting curve with a large number of distinct projection points represents data continuously.
For each combination of the underlying curve and noise level, we generate equally spaced data points with size $n=100$ and then compute the reconstruction error and the number of distinct projection points by each method. Over 50 simulation data sets, Table~\ref{table2} lists the average values of reconstruction errors and their standard deviations. As listed, the proposed principal curves outperform the method of Hauberg (2016). Table~\ref{table3} provides average values of distinct projection points and their standard deviations. As one can see, the proposed method provides a much large number of distinct projection points, compared to that of Hauberg (2016). Overall, as listed in Tables~\ref{table2} and \ref{table3}, the proposed methods perform better than Hauberg's method, including the case that $T=500$ is much larger than $n=100$ in which Hauberg's method is improved. In addition, the results of both intrinsic and extrinsic principal curves are similar in terms of reconstruction error and the number of distinct projection points, which is along with the fact that the intrinsic and extrinsic means are almost identical in the local region (Bhattacharya and Patrangenaru, 2005).
\begin{table}
\caption{Averages of reconstruction errors and their standard deviations in the parentheses by each method.}
\vspace{-3mm}
\label{table2}
\centering
\resizebox{1\textwidth}{!}{%
\begin{tabular}{c||c|c|cccccc}
\hline
\multirow{3}{*}{} & \multirow{3}{*}{True form} & \multirow{3}{*}{Method} & \multicolumn{6}{c}{Noise level} \\
& & & \multicolumn{3}{c}{$\sigma=0.07$} & \multicolumn{3}{c}{$\sigma=0.1$} \\ \cline{4-9}
& & & $q=0.05$ & $q=0.03$ & \multicolumn{1}{c|}{$q=0.01$} & $q=0.05$ & $q=0.03$ & $q=0.01$ \\ \hline \hline
\multirow{6}{*}{$T=100$} & \multirow{3}{*}{Circle} & Proposed(extrinsic) & 0.093 (0.026) & 0.12 (0.026) & \multicolumn{1}{c|}{0.095 (0.013)} & 0.201 (0.049) & 0.218 (0.042) & 0.138 (0.025) \\
& & Proposed(intrinsic) & 0.093 (0.026) & 0.12 (0.027) & \multicolumn{1}{c|}{0.095 (0.013)} & 0.201 (0.048) & 0.216 (0.046) & 0.137 (0.025) \\
& & Hauberg & 0.117 (0.073) & 0.408 (0.149) & \multicolumn{1}{c|}{0.298 (0.038)} & 0.370 (0.205) & 0.74 (0.208) & 0.494 (0.063) \\ \cline{2-9}
& \multirow{3}{*}{Wave} & Proposed(extrinsic) & 0.703 (0.116) & 0.338 (0.092) & \multicolumn{1}{c|}{0.084 (0.026)} & 0.679 (0.136) & 0.353 (0.108) & 0.124 (0.037) \\
& & Proposed(intrinsic) & 0.71 (0.114) & 0.329 (0.097) & \multicolumn{1}{c|}{0.084 (0.023)} & 0.673 (0.150) & 0.346 (0.113) & 0.124 (0.038) \\
& & Hauberg & 2.444 (0.059) & 2.158 (0.155) & \multicolumn{1}{c|}{0.568 (0.055)} & 2.544 (0.118) & 2.103 (0.563) & 0.796 (0.094) \\ \hline
\multirow{6}{*}{$T=500$} & \multirow{3}{*}{Circle} & Proposed(extrinsic) & 0.088 (0.026) & 0.118 (0.023) & \multicolumn{1}{c|}{0.091 (0.018)} & 0.209 (0.049) & 0.212 (0.043) & 0.129 (0.018) \\
& & Proposed(intrinsic) & 0.088 (0.026) & 0.118 (0.023) & \multicolumn{1}{c|}{0.091 (0.018)} & 0.21 (0.050) & 0.207 (0.043) & 0.129 (0.018) \\
& & Hauberg & 0.089 (0.027) & 0.205 (0.079) & \multicolumn{1}{c|}{0.269 (0.034)} & 0.233 (0.087) & 0.453 (0.177) & 0.397 (0.079) \\ \cline{2-9}
& \multirow{3}{*}{Wave} & Proposed(extrinsic) & 0.531 (0.064) & 0.239 (0.058) & \multicolumn{1}{c|}{0.072 (0.020)} & 0.57 (0.094) & 0.237 (0.081) & 0.110 (0.031) \\
& & Proposed(intrinsic) & 0.535 (0.065) & 0.239 (0.056) & \multicolumn{1}{c|}{0.072 (0.020)} & 0.574 (0.094) & 0.237 (0.082) & 0.110 (0.031) \\
& & Hauberg & 2.006 (0.697) & 1.831 (0.146) & \multicolumn{1}{c|}{0.529 (0.043)} & 1.906 (0.847) & 1.756 (0.696) & 0.688 (0.073) \\ \hline
\end{tabular}%
}
\end{table}
\begin{table}[!h]
\caption{Averages of distinct projection points and their standard deviations in the parentheses by each method.}
\vspace{-3mm}
\label{table3}
\centering
\resizebox{\textwidth}{!}{%
\begin{tabular}{c||c|c|cccccc}
\hline
& \multirow{3}{*}{True form} & \multirow{3}{*}{Method} & \multicolumn{6}{c}{Noise level}
\\
& & & \multicolumn{3}{c}{$\sigma=0.07$} & \multicolumn{3}{c}{$\sigma=0.1$}
\\ \cline{4-9}
& & & $q=0.05$ & $q=0.03$ &\multicolumn{1}{c|}{$q=0.01$} &$q=0.05$ & $q=0.03$ & $q=0.01$ \\ \hline \hline
\multirow{6}{*}{$T=100$} & \multirow{3}{*}{Circle} & proposed(extrinsic) & 99.06 (0.31) & 98.96 (0.40) &\multicolumn{1}{c|}{98.80 (0.45)} &99.06 (0.31) & 98.6 (1.12) & 98.10 (1.05) \\
& & proposed(intrinsic) & 99.02 (0.32) & 98.92 (0.34) &\multicolumn{1}{c|}{98.84 (0.47)} &99.08 (0.34) & 98.72 (1.11) & 98.20 (1.12) \\
& & Hauberg & 87.70 (7.95) & 56.68 (17.99) &\multicolumn{1}{c|}{64.70 (3.22)} &69.80 (12.28) & 47.04 (15.44) & 60.42 (2.83) \\ \cline{2-9}
& \multirow{3}{*}{Wave} & proposed(extrinsic) & 93.36 (4.50) & 96.88 (1.96) &\multicolumn{1}{c|}{99.30 (0.54)} &94.98 (3.86) & 96.36 (2.34) & 99.00 (0.67) \\
& & proposed(intrinsic) & 93.36 (4.47) & 97.28 (2.13) &\multicolumn{1}{c|}{99.32 (0.51)} &95.82 (3.77) & 96.72 (2.22) & 99.10 (0.65) \\
& & Hauberg & 22.72 (2.77) & 25.94 (2.65) &\multicolumn{1}{c|}{62.14 (2.49)} &24.5 (3.63) & 32.16 (16.72) & 58.84 (3.04) \\ \hline
\multirow{6}{*}{$T=500$} & \multirow{3}{*}{Circle} & proposed(extrinsic) & 99.06 (0.24) & 99.08 (0.40) &\multicolumn{1}{c|}{98.72 (0.58)} &99.08 (0.27) & 98.94 (0.47) & 98.14 (1.03) \\
& & proposed(intrinsic) & 99.08 (0.27) & 99.02 (0.25) &\multicolumn{1}{c|}{98.76 (0.69)} &99.1 (0.30) & 99.04 (0.49) & 99.30 (1.09) \\
& & Hauberg & 97.8 (1.47) & 89 (8.63) &\multicolumn{1}{c|}{79.28 (4.60)} &93.64 (5.29) & 78.72 (13.08) & 73.86 (7.28) \\ \cline{2-9}
& \multirow{3}{*}{Wave} & proposed(extrinsic) & 99.16 (0.37) & 98.5 (1.40) &\multicolumn{1}{c|}{99.28 (0.64)} &99.18 (0.39) & 98.68 (1.22) & 99.30 (0.74) \\
& & proposed(intrinsic) & 99.18 (0.39) & 98.5 (1.27) &\multicolumn{1}{c|}{99.26 (0.56)} &99.22 (0.42) & 98.84 (1.20) & 99.18 (0.66) \\
& & Hauberg & 45.2 (24.8) & 43.38 (3.72) &\multicolumn{1}{c|}{73.20 (3.42)} &52.04 (26.81) & 50.64 (19.99) & 71.52 (4.38) \\ \hline
\end{tabular}%
}
\end{table}
\comment{
\begin{figure}
\centering
\includegraphics[scale=0.45]{figures/spiral.png}
\includegraphics[scale=0.45]{figures/spiral_init.png}
\includegraphics[scale=0.45]{figures/spiral_curve.png}
\vspace{-5mm}
\caption{
Left : Spiral structure (red) in which data (blue) is generated.
Middle : Initialization (principal circle) for the spiral data.
Right : Extrinsic principal curve of the spiral data ($q=0.2$).
}
\end{figure}
}
\section{Median Principal Curves: A Robust Extension}
The intrinsic mean is obtained by the minimization of the sum of square of the geodesic distances; thus, the intrinsic principal curves might be sensitive to outliers. By following the conventional way in Euclidean space, it is natural to consider the median as an alternative measure of the centrality of data. In particular, we replace the expectation step in Algorithm 3 with
\[
C_t=\argmin_{x}\sum_i w_{t,i} \cdot d_{Geo}(x, x_i), ~ t=1,\ldots, T.
\]
Then the resulting curves pass through the ``median" of the given dataset. We now define a median principal curve, by mimicking the principal curve of (\ref{pc}), as
\[
f(\lambda) = Median\big[X|\lambda_{f}(X)=\lambda\big] ~ \mbox{for}~ \mbox{a.e.} ~ \lambda,
\]
where the points projecting onto $f(\lambda)$ are contained in a set of a great circle on the sphere, $M_{\lambda} := \{x \in S^2: \lambda_{f}(x)=\lambda\}$, and a connected proper subset of $M_\lambda$ is isometric to a line with the same length in $\mathbb{R}$. Thus, the above-median can be found in the same way in $\mathbb{R}$. More specifically, for a given dataset $\{x_{1},x_{2},...,x_{n}\} \subset S^2$, the point on the sphere that minimizes the function $f(x) := {1 \over n} \sum_{i=1}^n d_{Geo}(x, x_i)$ is called \textit{geometric median}, which has no explicit form (Bajaj, 1988). Thus, it should be obtained by a numerical algorithm. By a similar way in Buss and Fillmore (2001), we have
\[
\nabla f(x) = - {1 \over n} \sum_{i=1}^n \log_{x}(x_i) / \lVert \log_{x}(x_i)\rVert
\]
for $x \notin \{x_1, x_2,..., x_n \}$. Here is a practical algorithm for finding geometric median on a sphere by gradient descent.
\vskip 3mm
\begin{algorithm}[H]
\caption{Geometric Median on Sphere}
\begin{algorithmic}
\State For given data $x_{1},\ldots,x_{n} \in S^2$ and their weights $w_{1},\ldots,w_{n} \ge 0$ such that $\sum_{i=1}^n w_{i} > 0$, select initial geometric median as $M_{1} = x_{1}$.
\While{ ($\Delta M \ge \mbox{threshold}$) }
\State - $\Delta M = {1 \over j} \cdot \underset{1 \le i \le n, \, x_{i} \ne M_{j}}{\sum} {w_{i} \over {\sum_{i=1}^n w_{i}}} \cdot \mathrm{\log}_{M_j}(x_i) / \lVert \mathrm{\log}_{M_j}(x_i) \rVert $.
\State - $M_{j+1} = \mathrm{\exp}_{M_{j}}(\Delta M)$.
\EndWhile
\end{algorithmic}
\end{algorithm}
In the case that a dataset on the unit sphere is contained in a convex region $U$ in which any geodesic distance between two points in $U$ is less than $\pi \over 2$, the geometric median exists and is unique (Fletcher et al., 2009). In practice, it is necessary to obtain the geometric median only on a small region in the expectation step of the principal curve algorithm, say Algorithm 3. Meanwhile, notice that we divide a gradient part by iteration $j$ to get $\Delta{M}$ for each iteration. In contrast to the intrinsic mean, $\Delta{M}$ is a weighted average of the unit vectors; thus, it is possible that its length does not go to 0, and the algorithm could oscillate and not converge. Heuristically, to cope with this problem, we divide it by the number of iterations $j$, so the length of $\Delta{M}$ goes to 0 as $j \rightarrow \infty$. Moreover, it is able to reach the goal finally because of $\sum_{j \in \mathbb{N}} {1 \over j}=\infty$. Algorithm 4 works and is empirically stable. To reduce the computational cost, the denominator could be considered as $j^\alpha$ ($0< \alpha < 1$) instead of $j$.
Furthermore, we investigate the stationarity of the median principal curves as follows.
\begin{theorem}
Under the same conditions on Theorem 2, $f$ is a median principal curve of $X$ if and only if
\begin{equation}
\label{eq:thm3}
\frac{dE_X\big(d_{Geo}(X,f+\epsilon g)\big)}{d\epsilon} \Bigr|_{\epsilon = 0} = 0.
\end{equation}
\end{theorem}
\begin{figure}[!h]
\centering
\includegraphics[scale=0.5]{figures/curves/simulation/circle_robust_init_cauchy.jpg}
\includegraphics[scale=0.5]{figures/curves/simulation/circle_extrinsic.jpg}
\includegraphics[scale=0.5]{figures/curves/simulation/circle_robust_median.jpg}
\vspace{-0.5cm}
\caption{True circular curve and noisy data (left), the extrinsic principal curve with $T = 100$ and $q = 0.1$ (right), and the median principal curve with $T = 100$ and $q = 0.1$ (bottom).}
\label{fig14}
\end{figure}
We now present a simulated example for the empirical performance of the proposed median principal curves. For this purpose, we consider the circular data on the sphere, which is formed of $(r=1,\theta,\phi)$ with $0\le \theta < 2\pi$ and $\phi=\pi/4$. We generate $n=200$ data points by sampling $\theta$ equally in $[0, 2\pi]$, and add random noises from Cauchy$(0, \, 0.05)$ on $\phi$. As shown in Figure~\ref{fig14}, the median principal curve implemented with $T= 100$ and $q = 0.1$ is robust to the outliers and represents the underlying structure well, compared to the extrinsic principal curve.
\section{Concluding Remarks}
In this paper, we have proposed new principal curves on a sphere for dimension reduction of spherical data. For this purpose, we have considered the extrinsic and intrinsic approaches and investigated the stationarity of the principal curves which supports that the proposed methods are a direct extension of principal curves (Hastie and Stuetzle, 1989) to a sphere.
As far as Euclidean space is concerned as embedding space, dimension, or location of the origin does not affect the distance, and hence, does not affect the extrinsic mean. Moreover, the extrinsic approach holds efficiency computationally. However, it is questionable whether an extrinsic approach is still effective in asymmetric manifolds. For some asymmetric manifolds, an intrinsic approach may yield better performance. Moreover, the intrinsic mean defined by a given geodesic distance might be attractive owing to its inherency. However, the iterative way for the intrinsic mean is computationally expensive since it takes time for the algorithm to converge.
In this study, the proposed principal curve algorithm is a top-down approach, in the sense that it approximates the structure of data as an initial curve and then improve the approximation gradually in an iterative manner. Thus, initialization plays a crucial role in the algorithm. The intrinsic principal circle in Section 3.2 has been used as the initialization of the proposed principal curve. It is capable of identifying some meaningful structure of spherical data. However, there exist some complex structures that cannot be represented only by a circle, for example, a structure divided into several pieces or a structure with intersections. To cope with this limitation, it is worth to study a ``bottom-up" approach, which is left for future work.
As final remarks, in shape analysis or motion analysis, data have been represented as a Cartesian product of $\mathbb{R}$, $\mathbb{R^{+}}$ and SO(2). PGA by Fletcher et al. (2004) and the principal arc analysis by Jung et al. (2011) perform dimension reduction on medial representation by mapping the given data space to Euclidean space. If the data are properly projected on geodesic segments, the proposed principal curve procedure can be applied for medial representation. Since the mean can be independently calculated for each component of the Cartesian product, there is no additional difficulty in the expectation step. Some problems of projecting from the Cartesian product of simple manifolds to geodesic segments are left for future study.
\section*{Appendix: Stationarity of Principal Curves}
Throughout this discussion, we cover finite-length smooth curve that does not cross on a sphere \big(i.e., $ \lambda_{1} \ne \lambda_{2} \in [0,\,1) \Rightarrow f(\lambda_1)\ne f(\lambda_{2})\big)$, including curves with end points as well as closed curves, which can be both parameterized by the closed interval $[0, 1]$. In the latter case, boundary condition is needed; any order partial derivatives of $f$ at 0 and 1 are the same, i.e., $f^{(k)}(0)=f^{(k)}(1) ~ \mbox{for}~\mbox{all} \ k \ge 0$. For a random vector $X$ on a sphere, we further assume that the curve $f$ is not short enough to cover $X$ well, that is, $\lambda_{f}(X) \in (0, 1) ~ \mbox{for}~\mbox{a.e.}~X$, which implies that $X$ is orthogonally projected on the curve $f$. Note that $f$ is infinitely differentiable on $[0, 1]$, i.e., $f$ is smoothly extended to open interval containing $[0, 1]$ and all the its derivatives on $[0, 1]$ are continuous. Our main purpose is to prove the stationarity of extrinsic, intrinsic, and median principal curves $f: [0,1] \to S^2$ that satisfies the equations (\ref{eq:thm1}), (\ref{eq:thm2}), and (\ref{eq:thm3}) in Theorems 1, 2, and 3.
When moving from Euclidean space to spherical surface, topological properties such as measurability and continuity are preserved, while the formula using specific distance should be modified. This modification could be obtained by embedding a spherical surface into a three-dimensional Euclidean space. Specifically, we embed a spherical surface as a unit sphere centered at the origin and investigate further derivations.
For a smooth curve $f: [0, 1] \to S^2$, suppose that $f$ is parameterized by a constant speed with respect to $\lambda$ and is expressed as three-dimensional coordinates $(f(\lambda)_1,f(\lambda)_2,$ $f(\lambda)_3)$. Then the following lemmas are held.
\begin{lemma}
The curve $f$ satisfies $f'(\lambda) \cdot f(\lambda) = 0$ and $f''(\lambda) \cdot f'(\lambda) = 0$, $\forall\lambda \in [0, \, 1]$, where $\cdot$ denotes inner product in $\mathbb{R}^3$.
\end{lemma}
\begin{proof}
It is directly obtained from $f(\lambda)\cdot f(\lambda)=1$ and $f'(\lambda)\cdot f'(\lambda) = constant$.
\end{proof}
\begin{lemma}
Suppose that $f(\lambda)$ and $x$ are expressed as three-dimensional vectors. Then, it follows that $d_{Geo}(f(\lambda),x)=\arccos(f(\lambda)\cdot x)$, where $\arccos(f(\lambda)\cdot x)$ is the angle between $f(\lambda)$ and $x$. Then, $\frac{df}{d\lambda} (\lambda_f(0,0,1))_3 =0$. Thus, it follows that $\frac{df}{d\lambda} (\lambda_f(0,0,1)) = a\big(-f(\lambda_f(0,0,1))_2, f(\lambda_f(0,0,1))_1, 0\big)$ for some $a \in \mathbb{R}$. Note that $\lambda_f(x) $ denotes the projection index of point $x$ to the curve $f$.
\end{lemma}
\begin{proof}
For $p = (0,0,1)$, it follows that $d_{Geo}(f(\lambda),p)=\arccos(f(\lambda)_3)$. From the assumption that $f(\lambda)$ is a smooth curve and the fact that $d_{Geo}(f(\lambda),p)$ has the minimum at $\lambda_f(0,0,1)$, the remaining part of the lemma follows by differentiation with respect to $\lambda$.
\end{proof}
\begin{lemma} (Spherical law of cosines)
Let $u$, $v$, $w$ be points on a sphere, and $a$, $b$ and $c$ denote $d_{Geo}(w,u)$, $d_{Geo}(w,v)$ and $d_{Geo}(u,v)$, respectively. If $C$ is the angle between $a$ and $b$, i.e., the angle of the corner opposite $c$, then,
$
\cos c=\cos a \cos b + \sin a \sin b \cos C.
$
Further, with three-dimensional vectors $u$, $v$, $w$, it follows that
$
\sin a \sin b \cos C=(w\times u)\cdot(w\times v),
$
where $\times$ denotes outer product in $\mathbb{R}^3$.
\end{lemma}
The next topological properties of the principal curves established in Euclidean space of Hastie and Stuetzle (1989) are still valid in spherical surfaces.
\begin{proposition} (Measurability of index function)
For a continuous curve f on a sphere, $\lambda_f(x)$ is measurable.
\end{proposition}
\begin{proposition} (Continuity of projection index under perturbation)
If $x$ is not an ambiguity point for continuous curve $f$, then $\lim\limits_{\epsilon \to 0}\lambda_{f+\epsilon g}(x) = \lambda_{f}(x)$.
\end{proposition}
In the proof of Proposition 3, we use the triangle inequality on a sphere. Moreover, by the smoothness and compact domain of $f$; $[0,1]$, we have a more efficient tool for verifying Theorem 2 and 3.
\begin{proposition} (Uniform continuity of projection index under perturbation)
$\lim\limits_{\epsilon \to 0}\lambda_{f+\epsilon g}(x) = \lambda_{f}(x)$ uniformly on the set of non-ambiguity points of $f$. That is, for every $\eta > 0$, there exists $\delta > 0$ such that for any non-ambiguity points $x$, if $|\epsilon| < \delta$, then $|\lambda_{f_{\epsilon}}(x)-\lambda_{f}(x)| < \eta$.
\end{proposition}
For guaranteeing uniform continuity of projection index, it is required that $|f''|$ is bounded. A proof is similar to that of Proposition 3; thus, we omit the proof, which can be provided on request.
\begin{proposition}
Spherical measure of the set of ambiguity points of smooth curve $f$ is 0.
\end{proposition}
Detailed steps for a proof of Proposition 5 are similar with those of Hastie and Stuetzle (1989); thus, we omit the proof, which can be provided on request.
Meanwhile, to prove Theorem 2 and 3, it is crucial to verify that $\lambda_{f_{\epsilon}}$ is differentiable for $\epsilon$ and its derivative is uniformly bounded. Thus, it is necessary to define a subset of $S^2$ as $B(\zeta) := \{x \in S^2 \ | \ |f''(\lambda_{f}(x)) \cdot x| > \zeta \}$ for $\zeta \ge 0$. Note that $B(\zeta)$ is increasing as $\zeta$ goes to 0 by definition.
\begin{lemma}
The image of smooth function from $[0,1]$ to $S^2$ has measure 0. Moreover,
\[
S^2\setminus B(0)=\{x\in S^2 \ | \ |f''(\lambda_{f}(x)) \cdot x | =0 \}
\]
is a union of images of two smooth functions from $[0,1]$ to $S^2$, which implies that $S^2\setminus B(0)$ are measure 0. Therefore, the measure of $S^{2} \setminus B(\zeta)$ goes to 0 as $\zeta \rightarrow 0$.
\end{lemma}
\begin{proof}
Suppose that $I$ is a smooth function on the sphere, that is, $I:[0,1] \rightarrow S^2$. The domain and range are the second countable differentiable manifolds whose dimensions are 1 and 2, respectively. Since $f$ is twice continuously differentiable function and the differential $dI$ has rank 1 which is less than dimension of $S^2$, by Sard's Theorem, the image $I([0,1])=\{I(x) \in S^2 \ | \ x \in [0,1] \}$ has measure zero. Next, each point of $S^2 \setminus B(0)$ is characterized by two equations $f'(\lambda) \cdot x=0$ and $f''(\lambda) \cdot x=0$ for some $\lambda \in [0,1]$. Therefore, we define functions $I_1, I_2$ as follows: For all $\lambda \in [0,1]$,
\[
I_{1}(\lambda)= f'(\lambda) \times f''(\lambda) / \norm{f'(\lambda) \times f''(\lambda)}, \quad I_{2}(\lambda)= -f'(\lambda) \times f''(\lambda) / \norm{f'(\lambda) \times f''(\lambda)},
\]
It is well known that the curvature of a smooth curve lying on the unit sphere is more than 1. It implies that $\kappa=\frac{|f''|}{s^{2}} \ge 1$, where $\kappa$ is the curvature of $f$ and $s := |f'(\lambda)| > 0$ for all $\lambda \in [0,1]$, and hence $f'' \neq 0$. We have already known that $f' \cdot f'' = 0$ by Lemma 1. Hence, it is obtained that $f' \times f'' \ne 0$, which means that $I_{1}$ and $I_{2}$ are well defined and smooth functions. Therefore, we have $S^2 \setminus B(0)= I_{1}([0,1]) \bigcup I_{2}([0,1])$, which completes the proof.
\end{proof}
Lemma 4 implies that the constraints of random vector $X$ in Theorems 2 and 3 are almost negligible by setting $\zeta$ infinitesimally small. It is also used for verifying Theorem 3. Denote the set of ambiguity points of smooth curve $f$ on a sphere as $A$, which is a measure zero set by Proposition 5.
\begin{lemma}
Let $A$ be the set of non-ambiguity points of smooth curve $f$ on a sphere. Suppose that $x \in A \cap B(\zeta)$ for some small $\zeta > 0$, and $\lambda_{f}(x) \in (0,1)$. Then $\lambda(\epsilon):=\lambda_{f_\epsilon}(x)$ is a smooth function for $\epsilon$ on an open interval containing zero. Moreover, $\frac{\partial \lambda(\epsilon)}{\partial \epsilon}$ is uniformly bounded on $A \cap B(\zeta)$. That is, there exists a constant $C > 0$ and $\delta > 0$ such that if $|\epsilon_0| < \delta $ and $x \in A \cap B(\zeta)$, then $\big|\ \frac{\partial \lambda_{f_{\epsilon}}(x)}{\partial \epsilon}\big|_{\epsilon=\epsilon_{0}} \big| < C$.
\end{lemma}
\begin{proof}
Since $x$ is a non-ambiguity point of $f$ and $\lambda_{f}(x) \in (0,1)$, $\lambda(\epsilon)$ is uniquely characterized by orthogonality between geodesic from $x$ to $f_{\epsilon}\big(\lambda(\epsilon)\big)$ and $f'_{\epsilon}\big(\lambda(\epsilon)\big)$ on a small $\epsilon$ near the zero, that is, $ f'_{\epsilon}(\lambda) \cdot \big(x-f_{\epsilon}(\lambda)\big) = f'_{\epsilon}(\lambda) \cdot x = 0$ by the same argument in Lemma 1. Then, we define a map $F:[-1, \, 1] \times [0, \, 1] \to \mathbb{R}$ as $F(\epsilon, \lambda)=f'_{\epsilon}(\lambda)\cdot x$. $F$ is a smooth function by Proposition 1. It follows by the definition of $B(\zeta)$ that
\begin{eqnarray}
\frac{\partial}{\partial \lambda} F(\epsilon,\lambda)\bigr|_{(0, \lambda_f)}
& = & f''(\lambda_f) \cdot x \ne 0. \nonumber
\end{eqnarray}
By implicit function theorem, for each $x \in A \cap B(\zeta)$, $\lambda(\epsilon)=\lambda_{f_{\epsilon}}(x)$ is a smooth function for $\epsilon$ and $F\big(\epsilon, \lambda(\epsilon)\big)=0$ in an open interval containing zero. Next, in order to prove uniform boundedness of $\frac{\partial \lambda(\epsilon)}{\partial \epsilon}$, we should verify that $f''_{\epsilon}\big(\lambda_{f_{\epsilon}}(x)\big)$ uniformly converge to $f''\big(\lambda_{f}(x)\big)$ on $A \cap B(\zeta)$ as $\epsilon$ goes to 0. First of all, for each $\lambda$, we have
\begin{eqnarray}
\label{unif_1}
f_{\epsilon_0}(\lambda)=f(\lambda)+ \int_{0}^{\epsilon_0} g(\epsilon_0,\lambda)\, d\epsilon
&\Rightarrow& f''_{\epsilon_0}(\lambda)=f''(\lambda)+\int_{0}^{\epsilon_0}g''(\epsilon,\lambda)\, d\epsilon \nonumber \\
&\Rightarrow& \norm{f''_{\epsilon_0}(\lambda)-f''(\lambda)} \le \int_{0}^{\epsilon_0}\norm{g''(\epsilon,\lambda)}\, d\epsilon \le \epsilon_0 \cdot M,
\end{eqnarray}
for some $M > 0$. Note that the above derivatives are differentiation by $\lambda$. Also, the second equation holds since $g(\epsilon, \cdot)$ is a twice continuously differentiable function for all $\epsilon$; thus, it is able to change the order of derivative and the integration. The last inequality holds because $g''(\epsilon, \lambda)\bigr(=\frac{\partial^2 g(\epsilon, \, \lambda)}{\partial \lambda^2}\bigr)$ is continuous on $[-1, \, 1] \times [0, \, 1]$. Hence, it follows that
\begin{eqnarray*}
\label{unif_2}
\norm{f''_{\epsilon}\big(\lambda_{f_{\epsilon}}(x)\big) - f''\big(\lambda_{f}(x)\big)} &\le& \norm{f''_{\epsilon}\big(\lambda_{f_{\epsilon}}(x)\big) - f''\big(\lambda_{f_{\epsilon}}(x)\big)} + \norm{f''\big(\lambda_{f_{\epsilon}}(x)\big)-f''\big(\lambda_{f}(x)\big)} \\
&\to& 0,
\end{eqnarray*}
as $\epsilon \rightarrow 0$ uniformly on $x \in A \cap B(\zeta)$, because the first term uniformly converges to 0 by (\ref{unif_1}) and the last one also converges to 0 uniformly by Proposition 4 and the boundedness of $f'''$. We have that $|x \cdot f''\big(\lambda_{f}(x)\big)| > \zeta$ owing to $x \in B(\zeta)$, and from (\ref{unif_2}), there exists a constant $\delta > 0$ such that $|\epsilon| < \delta$ $\Rightarrow$ $|x \cdot f''_{\epsilon}\big(\lambda_{f_{\epsilon}}(x)\big)| \ge \frac{\zeta}{2}$. Since $f_{\epsilon}(\lambda)=f(\epsilon, \, \lambda)$ has continuous second partial derivatives, it is able to change the order of partial derivatives by Schwarz's theorem, as
\begin{eqnarray}
\frac{\partial}{\partial \epsilon} \Big|_{\epsilon=\epsilon_0} f'_{\epsilon}\big(\lambda(\epsilon_0)\big) &=& \frac{\partial}{\partial \epsilon} \Big|_{\epsilon=\epsilon_0} \frac{\partial}{\partial \lambda} \Big|_{\lambda=\lambda(\epsilon_0)} f_{\epsilon}(\lambda) \nonumber \\
&=& \frac{\partial}{\partial \lambda} \Big|_{\lambda=\lambda(\epsilon_0)} \frac{\partial}{\partial \epsilon} \Big|_{\epsilon=\epsilon_0} f_{\epsilon}(\lambda) \nonumber \\
&=& g'\big(\epsilon_0, \, \lambda(\epsilon_0)\big), \nonumber
\end{eqnarray}
for all $|\epsilon_{0}| < \delta$. Therefore, if $|\epsilon_{0}| < \delta$ by applying implicit function theorem to $F$ again, then we obtain that $\lambda(\epsilon)$ is differentiable at $\epsilon=\epsilon_0$ and
\begin{eqnarray}
|\lambda'(\epsilon_0)| = \Big| \frac{-\partial F(\epsilon, \lambda)/ \partial \epsilon} {\partial F(\epsilon, \lambda) / \partial \lambda} \Big|_{\big(\epsilon_{0},\lambda(\epsilon_0)\big)} \Big| &=& \frac{\Big|x \cdot \frac{\partial}{\partial \epsilon} \big|_{\epsilon=\epsilon_0} f'_{\epsilon}\big(\lambda(\epsilon_0)\big)\Big|}{\Big|x \cdot f''_{\epsilon_0}\big(\lambda(\epsilon_0)\big)\Big|} \nonumber \\
&\le& \frac{\norm{g'}}{\zeta/2} \le \frac{2}{\zeta}, \nonumber
\end{eqnarray}
which completes the proof.
\end{proof}
\begin{figure}
\centering
\includegraphics[scale=1]{figures/math2.JPG}
\caption{Two curves are on a spherical surface and the lines orthogonal to the curves denote the shortest geodesics.}
\label{fig15}
\end{figure}
\vskip 5mm
\noindent{\bf Proof of Theorem 1}
\begin{proof}
If $f = h$, then nothing to prove. Thus, we assume that the curves $f$ and $f+g(\small = h)$ are not identical and further both are parameterized by $\lambda \in [0,1]$. To prove the result, we need to show that the conditional expectation is zero after exchanging the order of the derivative and expectation.
First, for order exchange, it is necessary to show that the following random variable
\begin{eqnarray}
\label{eq_z}
Z_\epsilon(X) & = & \frac{\cos\big(d_{Geo}(X,f+\epsilon g)\big)-\cos\big(d_{Geo}(X,f)\big)}{\epsilon}\nonumber\\
& = & \frac{\cos\big(d_{Geo}\big(X,(f+\epsilon g)(\lambda_{f+\epsilon g}(X))\big)\big)-\cos\big(d_{Geo}\big(X,f(\lambda_f(X))\big)\big)}{\epsilon}
\end{eqnarray}
is uniformly bounded for any sufficiently small $\epsilon>0$. Then we apply bounded convergence theorem. Since the projection index of $X$ represents the closest point in the curve, it follows that
\begin{equation}
\label{eql4}
Z_\epsilon(X) \le \frac{\cos\big(d_{Geo}\big(X,(f+\epsilon g)(\lambda_{f+\epsilon g}(X))\big)\big)-\cos\big(d_{Geo}\big(X,f(\lambda_{f+\epsilon g}(X))\big)\big)}{\epsilon}.
\end{equation}
For simplicity, let $f_g (\lambda_\epsilon):=(f+g)(\lambda_{f+\epsilon g}(X))$, $f_\epsilon (\lambda_\epsilon):=(f+\epsilon g)(\lambda_{f+\epsilon g}(X))$ and $f(\lambda_\epsilon):=f(\lambda_{f+\epsilon g}(X))$. By applying Lemma 3 to $\cos\big(d_{Geo}(X,f_\epsilon(\lambda_\epsilon))\big)$, as shown in Figure~\ref{fig15}, the inequality of (\ref{eql4}) becomes
\begin{eqnarray}
\label{ze_ub}
Z_\epsilon(X) &\le&\frac{\cos\big(d_{Geo}\big(X,f_\epsilon(\lambda_\epsilon)\big)\big)-\cos\big(d_{Geo}\big(X,f(\lambda_\epsilon)\big)\big)}{\epsilon}\nonumber\\
&=&\frac{\cos(d_{Geo}(X,f(\lambda_\epsilon))) (\cos(d_{Geo}(f_\epsilon (\lambda_\epsilon),f(\lambda_\epsilon)))-1) + (f(\lambda_\epsilon)\times f_\epsilon (\lambda_\epsilon))\cdot (f(\lambda_\epsilon)\times X)}{\epsilon}\\
&=&\frac{\cos(d_{Geo}(X,f(\lambda_\epsilon))) (\cos (\epsilon d_{Geo}(f_g(\lambda_\epsilon),f(\lambda_\epsilon)))-1) + A_\epsilon (f(\lambda_\epsilon)\times f_g (\lambda_\epsilon))\cdot (f(\lambda_\epsilon)\times X)}{\epsilon}\nonumber,
\end{eqnarray}
where $A_\epsilon = |f(\lambda_\epsilon)\times f_\epsilon (\lambda_\epsilon)|/|f(\lambda_\epsilon)\times f_g (\lambda_\epsilon)| = \sin(\epsilon d_{Geo}(f(\lambda_\epsilon), f_g(\lambda_\epsilon)))/|f(\lambda_\epsilon)\times f_g (\lambda_\epsilon)|$. The last equality is done by Definition 1. To get the upper bound of $Z_\epsilon(X)$, we further use the following fact, $|\frac{\sin \epsilon C}{\epsilon}| \le |C|$ and $|\frac{1-\cos \epsilon C}{\epsilon}| \le \frac{|\epsilon| C^2}{2}$ for $C\in\mathbb{R}$ and $\epsilon\in\mathbb{R}$. Then, we have
\[
Z_\epsilon(X) \le \big|\cos\big(d_{Geo}\big(X,f(\lambda_\epsilon)\big)\big)\big| \frac{|\epsilon| B^2}{2} + \frac{B}{|f(\lambda_\epsilon)\times f_g (\lambda_\epsilon)|}\big|(f(\lambda_\epsilon)\times f_g (\lambda_\epsilon))\cdot (f(\lambda_\epsilon)\times X)\big|,
\]
where $B = d_{Geo}\big(f(\lambda_\epsilon), f_g(\lambda_\epsilon)\big) \le \norm{g} < \pi$. Note that any smallest geodesic distance on a unit sphere is smaller than $\pi$. In addition, we can assume that $\epsilon$ is less than $1/\pi$ because we are only interested in $\epsilon$ near 0. Thus, we obtain the upper bound of $Z_\epsilon(X)$ in (\ref{ze_ub})
\[
Z_\epsilon(X) \le \ \frac{\pi}{2} + \pi = \frac{3\pi}{2}.
\]
A lower bound of $Z_\epsilon(X)$ can be similarly obtained. Let $f_g (\lambda):=(f+g)(\lambda_{f}(X))$, $f_\epsilon (\lambda):=(f+\epsilon g)(\lambda_{f}(X))$ and $f(\lambda):=f(\lambda_{f}(X))$. By following the same path, we have
\begin{eqnarray}
\label{ze_lb}
Z_\epsilon(X) & \ge & \frac{\cos\big(d_{Geo}\big(X,(f+\epsilon g)(\lambda_{f}(X))\big)\big)-\cos\big(d_{Geo}\big(X,f(\lambda_{f}(X))\big)\big)}{\epsilon}\nonumber\\
& =& \frac{\cos\big(d_{Geo}\big(X,f(\lambda)\big)\big) \big(\cos\big(d_{Geo}\big(f_\epsilon (\lambda),f(\lambda)\big)\big)-1\big) + (f(\lambda)\times f_\epsilon (\lambda))\cdot (f(\lambda)\times X)}{\epsilon} \\
& = &\frac{\cos\big(d_{Geo}\big(X,f(\lambda)\big)\big) \big(\cos\big(\epsilon d_{Geo}\big(f_g(\lambda),f(\lambda)\big)\big)-1 \big) + B_\epsilon (f(\lambda)\times f_g (\lambda))\cdot (f(\lambda)\times X)}{\epsilon}\nonumber,
\end{eqnarray}
where $B_\epsilon = |f(\lambda)\times f_\epsilon (\lambda)|/|f(\lambda)\times f_g (\lambda)| = \sin(\epsilon d_{Geo}(f(\lambda), f_g(\lambda)))/|f(\lambda)\times f_g (\lambda)|$. By the same way, it can be shown that
\[
Z_\epsilon(X) \ge -\frac{3\pi}{2}.
\]
Hence, we show that
\[
|Z_{\epsilon}(X)| \le \frac{3\pi}{2},
\]
which is bounded for any $ |\epsilon| \le 1/\pi$. Then, by the bounded convergence theorem, it follows that
\[
\frac{dE_X\cos(d_{Geo}\big(X,f+\epsilon g)\big)}{d\epsilon} \Big|_{\epsilon = 0} =
E_X\frac{d\cos(d_{Geo}\big(X,f+\epsilon g)\big)}{d\epsilon} \Big|_{\epsilon = 0}.
\]
Thus, the proof is completed provided that the following equation holds
\[
E_{X|\cdot}\Big(\frac{d\cos\big(d_{Geo}(X,f+\epsilon g)\big)}{d\epsilon} \Big|_{\epsilon = 0} \Big|\ \lambda_f(X) = \lambda\Big) = 0, ~\mbox{for}~\mbox{a.e.}~\lambda.
\]
By the definition of derivative,
\[
\frac{d\cos\big(d_{Geo}(X,f+\epsilon g)\big)}{d\epsilon} \Big|_{\epsilon = 0} = \lim\limits_{\epsilon \to 0}Z_\epsilon(X),
\]
and as shown, $Z_\epsilon(X)$ is bounded. Since $f$ and $f+g$ are continuous, by Proposition 3, if $X$ is not an ambiguity point of $f$ and $f+g$, then
\[
\lim\limits_{\epsilon \to 0}f_g(\lambda_\epsilon)= f_g(\lambda),~ \ \lim\limits_{\epsilon \to 0}f(\lambda_\epsilon) = f(\lambda).
\]
Next, to show the limit of $Z_\epsilon$, we use the fact that $\lim_{\epsilon\to 0}\frac{\sin\epsilon C}{\epsilon}=C$ and $\lim_{\epsilon\to 0}\frac{1-\cos\epsilon C}{\epsilon}=0$ for $C\in \mathbb{R}$ and $\epsilon\in\mathbb{R}$. When $f_g(\lambda) \ne f(\lambda)$, it follows that
\[
\lim\limits_{\epsilon \to 0}~\mbox{RHS of (\ref{ze_ub})} = d_{Geo}\big(f(\lambda), f_g(\lambda)\big)\frac{f(\lambda)\times f_g (\lambda)}{|f(\lambda)\times f_g (\lambda)|} \cdot (f(\lambda)\times X) = \mu(\lambda)\cdot (f(\lambda)\times X),
\]
where $\mu(\lambda) = d_{Geo}(f(\lambda), f_g(\lambda))(f(\lambda)\times f_g (\lambda))/|f(\lambda)\times f_g (\lambda)|$ if $f(\lambda) \ne (f+g)(\lambda)$ and $\mu(\lambda) =0$ otherwise. Similarly, we obtain that
\[
\lim\limits_{\epsilon \to 0}~\mbox{RHS of (\ref{ze_lb})} = \mu(\lambda)\cdot (f(\lambda)\times X).
\]
In summary, if $X$ is not an ambiguity point of $f$ and $f+g$, and $f(\lambda_{f}(X)) \ne (f+g)(\lambda_{f}(X))$, then we have
\begin{equation}
\label{limit1}
\frac{d\cos\big(d_{Geo}(X,f+\epsilon g)\big)}{d\epsilon} \Big|_{\epsilon = 0} = \mu(\lambda_{f}(X)) \cdot \big(f(\lambda_{f}(X))\times X\big).
\end{equation}
In the case of $f(\lambda_{f}(X)) = (f+g)(\lambda_{f}(X))$, the equation (\ref{limit1}) also hold because its left and right hand side are 0. From Proposition 4, the limit of (\ref{limit1}) is established for a.e. $X$. Since $X$ is a random vector, $\lambda_{f}(X)$ is also a random variable depending on X. Thus, the following equality holds
\begin{equation}
\label{result}
E_{X}\Big(\frac{d\cos\big(d_{Geo}(X,f+\epsilon g)\big)}{d\epsilon} \Big|_{\epsilon = 0}\Big) = E_{X}\Big(\mu(\lambda_{f}(X)) \cdot \big(f(\lambda_{f}(X))\times X \big) \Big).
\end{equation}
Finally, if $f$ is an extrinsic principal curve, then
\[
E_{X|\cdot}\big(X|\lambda_f(X)=\lambda\big)=cf(\lambda)
\]
for $\exists c \in \mathbb{R}$, and hence, it follows that
\begin{eqnarray*}
E_{X|\cdot}\big(\mu(\lambda_{f}(X)) \cdot \big(f(\lambda_{f}(X))\times X \big) \big| \lambda_f(X) = \lambda \big) &=& E_{X|\cdot}\big(\mu(\lambda) \cdot (f(\lambda)\times X) | \lambda_f(X) = \lambda \big) \\
&=& \mu(\lambda)\cdot (f(\lambda)\times cf(\lambda)) = 0.
\end{eqnarray*}
Hence, we have
\begin{eqnarray*}
\mbox{LHS of (\ref{result})} = E_{X}\big(\mu(\lambda)\cdot (f(\lambda)\times X)\big) = E_{\lambda}\big[E_{X|\cdot}\big(\mu(\lambda)\cdot (f(\lambda)\times X) | \lambda_f(X) = \lambda\big)\big] = 0.
\end{eqnarray*}
To prove the converse, we assume that $E_{\lambda}\big[E_{X|\cdot}\big(\mu(\lambda)\cdot (f(\lambda)\times X) | \lambda_f(X) = \lambda\big) \big] = E_{\lambda} \big[\mu(\lambda) \cdot E_{X|\cdot}\big(f(\lambda)\times X | \lambda_f(X) = \lambda\big)\big] = 0$ for all smooth $f+g$ satisfying $\norm{g} \ne \pi$ and $\norm{g'} \le 1$. Since $f+g$ is only included in $\mu(\lambda)$, it followed that
\[
E_{X|\cdot}\big(f(\lambda)\times X | \lambda_f(X) = \lambda\big) = f(\lambda)\times E_{X|\cdot}\big(X | \lambda_f(X) = \lambda\big) = 0 ~~\mbox{for}~\mbox{a.e.}~\lambda.
\]
Therefore, we have
\[
E_{X|\cdot}\big(X | \lambda_f(X)=\lambda\big)=cf(\lambda)
\]
for $\exists c \ge 0$, which completes the proof.
\end{proof}
\vskip 5mm
\noindent{\bf Proof of Theorem 2}
\begin{proof}
In the case of $f=h$, the result is obvious. We thus assume that $f$ and $f+g(\small = h)$ are not identical. Further, suppose that $X \in A \cap B(\zeta)$ for a small $\zeta > 0$ and $\lambda_{f}(X) \in (0,1)~ \mbox{for}~\mbox{a.e}~ X$. As the proof of Theorem 1, we use the bounded convergence theorem to change the order of derivative and expectation. For this purpose, we define
\begin{eqnarray}
\label{eq_z}
Z_\epsilon(X) & = & \frac{d^{2}_{Geo}(X,f+\epsilon g)-d^{2}_{Geo}(X,f)}{\epsilon} \nonumber\\
& = & \frac{d^{2}_{Geo}(X, f_{\epsilon}\big(\lambda_{f_{\epsilon} })\big)-d^{2}_{Geo}\big(X,f(\lambda_f)\big)}{\epsilon}, \nonumber
\end{eqnarray}
where $f_{\epsilon} := f + \epsilon g$ for $ | \epsilon | \le 1$. Let $\theta(\lambda,X)$ be a smaller angle between segments of geodesics from $f(\lambda)$ to $X$ and from $f(\lambda)$ to $(f+g)(\lambda)$. Then, from Lemma 3, it follows that
\begin{eqnarray}
F(\epsilon):=\cos\bigr(d_{Geo}\big(X, f_{\epsilon}(\lambda_{f_\epsilon})\big)\bigr)
& = &\cos\bigr(d_{Geo}\big(X,f(\lambda_{f_\epsilon})\big)\bigr) \cdot \cos\bigr(\epsilon \norm{g(\lambda_{f_\epsilon})}\bigr)\nonumber \\
& + &\sin\bigr(d_{Geo}\big(X,f(\lambda_{f_\epsilon})\big)\bigr) \cdot \sin\bigr(\epsilon \norm{g(\lambda_{f_\epsilon})}\bigr) \cdot \cos\bigr(\theta(\lambda_{f_\epsilon},X)\bigr),\nonumber
\end{eqnarray}
where $\norm{g(\lambda)} = d_{Geo}\big(f(\lambda), (f+g)(\lambda)\big) < \pi$.
Firstly, we verify that $Z_{\epsilon}(X)$ is uniformly bounded for a small $\epsilon > 0$. By Lemma 5, there are constants $C>0$ and $\eta > 0$ such that if $|\epsilon_0| < \eta$, then $\lambda(\epsilon)$ is differentiable at $\epsilon=\epsilon_0$ and $\big|\frac{\partial \lambda(\epsilon)}{\partial \epsilon} \big|_{\epsilon=\epsilon_0} \big| < C$, where $\lambda(\epsilon)=\lambda_{f_{\epsilon}}(X)$. For simplicity of notation, let $\lambda_{f_{\epsilon}}(X) = \lambda_{\epsilon}$ and $\lambda_f(X) = \lambda_0$. If $ 0 < |\epsilon_{0}| < \eta$, then by triangle inequality on sphere and mean value theorem, it follows that
\begin{eqnarray*}
|Z_{\epsilon_{0}}(X)| & = & \Bigg|\frac{d_{Geo}\big(X, f_{\epsilon_0}(\lambda_{f_{\epsilon_0} })\big)-d_{Geo}\big(X,f(\lambda_f)\big)}{\epsilon_0} \Bigg| \cdot \Big( d_{Geo}\bigr(X,f_{\epsilon_0}(\lambda_{f_{\epsilon_0}})\bigr) + d_{Geo}\big(X, f(\lambda_f) \big) \Big) \\
& \le & 2 \pi \cdot \frac{d_{Geo}\big(f(\lambda_0),f_{\epsilon_0}(\lambda_{\epsilon_0})\big)}{\epsilon_0} \\
& \le & 2\pi \cdot \frac{d_{Geo}\bigr(f(\lambda_0),f(\lambda_{\epsilon_0})\bigr)+d_{Geo}\bigr(f(\lambda_{\epsilon_0}),f_{\epsilon_0}(\lambda_{\epsilon_0})\bigr)}{\epsilon_0} \\
& < & 2\pi \cdot \bigr(s \cdot \frac{\norm{\lambda_{0}-\lambda_{\epsilon_0}}}{\epsilon_0} + \norm{g(\lambda_{\epsilon_0})} \bigr) \\
& \le & 2\pi \cdot (s \cdot C+ \pi),
\end{eqnarray*}
where $s:=|f'(\lambda)|$ for all $\lambda$. Therefore, $Z_{\epsilon}(X)$ is uniformly bounded on $X \in A \cap B(\zeta)$ for $0 < |\epsilon| < \eta $.
Secondly, we find the limit of $Z_{\epsilon}(X)$. For this purpose, we define a map $u:(-1,1] \to (1,\infty)$ by $u(x)=\arccos(x) \cdot \frac{1}{\sqrt{1-x^2}}$ if $x \in (-1, 1)$, and $u(1)=1$. By simple calculations, $u$ is a monotone decreasing continuous function on $(-1, 1]$. Note that $F(\epsilon)$ is differentiable for $|\epsilon| < \eta$. By the mean value theorem to find the limit of $Z_{\epsilon}(X)$, we have
\begin{eqnarray}
\label{r_eq}
Z_{\epsilon_{0}}(X) & = & \frac{d^{2}_{Geo}\big(X, f_{\epsilon_0}\big(\lambda_{f_{\epsilon_0} })\big)-d^{2}_{Geo}\big(X,f(\lambda_f)\big)}{\epsilon_0} \nonumber \\
& = & \frac{\arccos^{2}\bigr(F(\epsilon_0)\bigr)-\arccos^2\bigr(F(0)\bigr)}{\epsilon_0} \nonumber \\
& = & -2 \arccos\bigr(F(\epsilon_{1})\bigr) \cdot \frac{1}{\sqrt{1-F^{2}(\epsilon_{1})}} \cdot \frac{dF(\epsilon)}{d\epsilon}\Bigr|_{\epsilon = \epsilon_{1}}
\end{eqnarray}
for $0 < |\epsilon_1| < |\epsilon_0| < \eta$. When $F(\epsilon_{1})=1$, the last equality is considered as a limit that is well-defined, because $\lim_{x \to 1}u(x) = 1$ and $u(x)$ is smoothly extended on an open interval containing 1 such that $u(x)$ is differentiable at $x=1$. By applying chain rule to the derivative of $F$, we obtain
\begin{eqnarray}
\lim_{\epsilon_{0} \to 0} \frac{\partial F(\epsilon)}{\partial \epsilon} \Big |_{\epsilon=\epsilon_0}
& = & \lim_{\epsilon_{0} \to 0}{ \Big[ \sin\big(d_{Geo}\big(X,f(\lambda_{f_{\epsilon_0}})\big)\big) \cdot \cos\big(\theta(\lambda_{f_{\epsilon_0}},X)\big) \cdot \big(\lVert g(\lambda_{f_{\epsilon_0}}) \rVert + \epsilon_{0} \cdot \frac{\partial \norm{g(\lambda_{f_{\epsilon}})}}{\partial \epsilon} \Big |_{\epsilon=\epsilon_0} \big) \Big]} \nonumber \\
& - & \lim_{\epsilon_{0} \to 0}{ \Big[ \sin\big(d_{Geo}\big(X,f(\lambda_{f_{\epsilon_0}})\big)\big) \cdot \frac{\partial d_{Geo}\big(X,f(\lambda_{f_\epsilon})\big)}{\partial \epsilon} \big |_{\epsilon=\epsilon_0} \big] }. \nonumber
\end{eqnarray}
In addition,
\[
\frac{\partial \norm{g(\lambda_{f_\epsilon})}}{\partial \epsilon} \Big |_{\epsilon=\epsilon_0} = \frac{\partial \norm{g(\lambda)}}{\partial \lambda} \Big |_{\lambda=\lambda_{f_{\epsilon_0}}} \frac{\partial \lambda(\epsilon)}{\partial \epsilon} \Big |_{\epsilon=\epsilon_0},
\]
which exists and does not diverge as $\epsilon_{0}$ goes to 0, since $\norm{g(\lambda)}=d_{Geo}\bigr(f(\lambda), (f+g)(\lambda)\bigr)$ is continuously differentiable for $\lambda$ and $\frac{\partial \lambda(\epsilon)}{\partial \epsilon} \bigr |_{\epsilon=0}$ is bounded by Lemma 5. Moreover,
\begin{eqnarray}
\lim_{\epsilon_{0} \to 0} \frac{\partial d_{Geo}\bigr(X,f(\lambda_{f_\epsilon})\bigr)}{\partial \epsilon} \Big |_{\epsilon=\epsilon_0} & = & \lim_{\epsilon_{0} \to 0} \frac{\partial d_{Geo}\bigr(X, f(\lambda) \bigr)}{\partial \lambda} \Big |_{\lambda=\lambda_{f_{\epsilon_0}}} \frac{\partial \lambda(\epsilon)}{\partial \epsilon} \Big |_{\epsilon=\epsilon_0} \nonumber \\
& = & \frac{\partial d_{Geo}\bigr(X, f(\lambda)\bigr)}{\partial \lambda} \Big |_{\lambda=\lambda_{f}} \frac{\partial \lambda(\epsilon)}{\partial \epsilon} \Big |_{\epsilon=0} \nonumber \\
& = & 0, \nonumber
\end{eqnarray}
where $\lambda(\epsilon)= \lambda_{f_\epsilon}$. The last equality is done by the definition of $\lambda_f$. Therefore, we have
\begin{eqnarray}
\label{thm2_limit_F}
\lim_{\epsilon \to 0} \frac{\partial F(\epsilon)}{\partial \epsilon}=\norm{g(\lambda_f)} \cdot \cos\big(\theta(\lambda_{f},X)\big) \cdot \sin\big(d_{Geo}\bigr(X,f(\lambda_f)\big)\big).
\end{eqnarray}
Thirdly, it follows from (\ref{r_eq}) and (\ref{thm2_limit_F}) that
\begin{eqnarray}
\label{thm2_limit_1}
\lim_{\epsilon_{0}\to0}{Z_{\epsilon_{0}}(X)}
& = & \lim_{\epsilon_{1}\to0}\Bigr[-2\arccos{F(\epsilon_{1})}\cdot\frac{1}{\sqrt{1-F^{2}(\epsilon_1)}}\cdot\frac{dF(\epsilon)}{d\epsilon}\Bigr|_{\epsilon=\epsilon_{1}}\Bigr]\nonumber\\
& = & -2u\Big(\cos\big(d_{Geo}\big(X, f(\lambda_f)\big)\big)\Big) \cdot \norm{g(\lambda_f)} \cdot \cos\big(\theta(\lambda_{f},X)\big) \cdot \sin\big(d_{Geo}\big(X,f(\lambda_f)\big)\big) \\
& = & -2d_{Geo}\big(X,f(\lambda_f)\big) \cdot \frac{1}{\sin\big(d_{Geo}\bigr(X,f(\lambda_f)\big)\big)} \cdot \norm{g(\lambda_f)} \cdot \cos\big(\theta(\lambda_{f},X)\big) \cdot \sin \big(d_{Geo}\bigr(X,f(\lambda_f)\bigr) \big) \nonumber \\
\label{thm2_limit_2}
& = & -2d_{Geo}\bigr(X,f(\lambda_f)\bigr) \cdot \norm{g(\lambda_f)} \cdot \cos\bigr(\theta(\lambda_f,X)\bigr),
\end{eqnarray}
In the case of $d_{Geo}\bigr(X,f(\lambda_{f})\bigr) = 0$, the same result follows since both (\ref{thm2_limit_1}) and (\ref{thm2_limit_2}) are zero. Thus, by Proposition 5, the equation (\ref{thm2_limit_2}) is established for a.e $X \in B(\zeta)$. Next, we notice that, for a smooth curve $f$, it can be shown that $M_{\lambda}:=\{x \in S^2|\lambda_{f}(x)=\lambda \}$ is a subset of the great circle perpendicular to $f$ at $f(\lambda)$ by Lemma 2. Let $S_{\lambda}$ be the great circle perpendicular to $f$ at $f(\lambda)$. That is, $M_{\lambda} \subset S_{\lambda} \cong S^1$. Moreover, a connected proper subset of $S_{\lambda}$ is isometric to a line with the same length in $\mathbb{R}$, which makes the intrinsic mean on $M_\lambda$ feasible. Thus, $f$ is an intrinsic principal curve of $X$, by the definition of $\theta(\lambda_{f},X)$ and $\cos(\pi-\theta)= -\cos(\theta)$, if and only if
\[
E_{X|\cdot} \Big(d_{Geo}\bigr(X, f(\lambda_{f})\bigr) \cdot \cos\big(\theta(\lambda_{f},X)\big) \big | \lambda_{f}(X) = \lambda \Big) = 0 ~~ \mbox{for} ~ \mbox{a.e.}~ \lambda.
\]
Finally, it follows from (\ref{thm2_limit_2}) and bounded convergence theorem that
\begin{eqnarray*}
\frac{dE_{X}d^2_{Geo}(X, f+\epsilon g)}{d\epsilon} \Bigr |_{\epsilon=0} & = & \lim_{\epsilon \to 0} \frac{E_{X}d^2_{Geo}(X,f+\epsilon g) - E_{X}d^2_{Geo}(X,f)}{\epsilon} \\
& = & E_{X} \Big[\lim_{\epsilon \to 0} \frac{d^2_{Geo}(X,f+\epsilon g)-d^2_{Geo}(X,f)}{\epsilon} \Big] \\
& = & E_{\lambda}\Big[E_{X|\cdot}\Big(\lim_{\epsilon \to 0}Z_{\epsilon}(X) \big| \lambda_{f}(X)=\lambda \Big) \Big] \\
& = & -2 E_{\lambda} \Big[ E_{X|\cdot} \Big( d_{Geo}\bigr(X,f\big(\lambda_{f}(X)\big)\big) \cdot \norm{g\big(\lambda_{f}(X)\big)} \cdot \cos \big(\theta(\lambda_{f}, X) \big) \big| \lambda_{f}(X)=\lambda \Big) \Big] \\
& = & -2 E_{\lambda}\Big[\norm{g(\lambda)} \cdot E_{X|\cdot} \Big(d_{Geo}\big(X,f\bigr(\lambda_{f}(X)\big)\big) \cdot \cos\big(\theta(\lambda_{f},X) \big) \big| \lambda_{f}(X)=\lambda \Big) \Big] \\
& = & 0.
\end{eqnarray*}
Conversely, we assume that
\[ E_{\lambda}\Big[\norm{g(\lambda)} \cdot E_{X|\cdot}\Big(d_{Geo}\bigr(X,f\big(\lambda_{f}\big)\bigr) \cdot \cos\big(\theta(\lambda_{f},X)\big) \big| \lambda_{f}(X)=\lambda \Big) \Big] = 0,
\]
for all $f+g(=h)$ such that $\norm{g} \ne \pi$ and $\norm{g'} \le 1$. Then, we have
\[
E_{X|\cdot}\Big(d_{Geo}\big(X,f(\lambda_{f})\big) \cdot \cos\big(\theta(\lambda_{f}, X)\big) \big| \lambda_{f}(X) = \lambda \Big)=0 ~~ \mbox{for} ~ \mbox{a.e.} ~ \lambda,
\]
which is equivalent to that $f$ is an intrinsic principal curve of $X$.
\end{proof}
\vskip 5mm
\noindent{\bf Proof of Theorem 3}
\begin{proof}
The proof follows the same line of Theorem 2. For given $h \ne f$, we assume that $X \in A \cap B(\zeta)$ for a small $\zeta > 0$ and $\lambda_{f}(X) \in (0,1)~\mbox{for}~\mbox{a.e.} ~ X$. By Lemma 5, there are constants $C>0$ and $\eta > 0$ such that if $|\epsilon_0| < \eta$, then $\lambda(\epsilon)$ is differentiable at $\epsilon=\epsilon_0$ and $\big|\frac{\partial \lambda(\epsilon)}{\partial \epsilon} \big|_{\epsilon=\epsilon_0} \big| < C$, where $\lambda(\epsilon)=\lambda_{f_{\epsilon}}(X)$. For simplicity, let $\lambda_{f_{\epsilon}}(X) = \lambda_{\epsilon}$ and $\lambda_f(X) = \lambda_0$. If $ 0 < |\epsilon_{0}| < \eta$, by similar arguments in Theorem 2 we obtain
\begin{eqnarray}
|Z_{\epsilon_{0}}(X)| & = & \bigg|\frac{d_{Geo}\big(X, f_{\epsilon_0}\big(\lambda_{f_{\epsilon_0} })\big)-d_{Geo}\big(X,f(\lambda_f)\big)}{\epsilon_0} \bigg| \nonumber \\
& \le & \bigg| \frac{d_{Geo}\big(f(\lambda_0),f_{\epsilon_0}(\lambda_{\epsilon_0})\big)}{\epsilon_0} \bigg| \nonumber \\
& \le & \Bigg| \frac{d_{Geo}\big(f(\lambda_0),f(\lambda_{\epsilon_0})\bigr)+d_{Geo}\bigr(f(\lambda_{\epsilon}),f_{\epsilon_0}(\lambda_{\epsilon_0})\bigr)}{\epsilon_0}\Bigg| \nonumber \\
& \le & s \cdot \frac{\norm{\lambda_{0}-\lambda_{\epsilon_0}}}{\epsilon_0} + \norm{g(\lambda_{\epsilon_0})}, \nonumber \\
& \le & s \cdot C + \pi, \nonumber
\end{eqnarray}
where $s:=|f'(\lambda)|$ for all $\lambda$. The last inequality is done by mean value theorem. That is, $Z_{\epsilon}(X)$ is uniformly bounded on $X \in A \cap B(\zeta)$ for $0 < |\epsilon| < \eta $. Recall that, in the proof of Theorem 2, we have verified that
\[
\lim_{\epsilon \to 0} \frac{\partial F(\epsilon)}{\partial \epsilon}=\norm{g(\lambda_f)} \cdot \cos\big(\theta(\lambda_{f},X)\big) \cdot \sin\big(d_{Geo}\big(X,f(\lambda_f)\big)\big).
\]
By mean value theorem, for $0 < |\epsilon_0| < \eta$, we obtain that
\begin{eqnarray}
Z_{\epsilon_{0}}(X) & = & \frac{d_{Geo}(X, f_{\epsilon_0}\big(\lambda_{f_{\epsilon_0} })\big)-d_{Geo}\big(X,f(\lambda_f)\big)}{\epsilon_0} \nonumber \\
& = & \frac{\arccos\bigr(F(\epsilon_0)\bigr)-\arccos\bigr(F(0)\bigr)}{\epsilon_0} \nonumber \\
& = & -\frac{1}{\sqrt{1-F^{2}(\epsilon_{1})}} \cdot \frac{dF(\epsilon)}{d\epsilon}\Bigr|_{\epsilon = \epsilon_{1}}, \nonumber
\end{eqnarray}
where $0 < |\epsilon_1| < |\epsilon_0|$.
Hence, it follows that
\begin{eqnarray}
\label{thm3_limit}
\lim_{\epsilon_{0} \to 0}{Z_{\epsilon_{0}}(X)}
& = & \lim_{\epsilon_{1}\to0}\Bigr[-\frac{1}{\sqrt{1-F^{2}(\epsilon_1)}}\cdot\frac{dF(\epsilon)}{d\epsilon}\Bigr|_{\epsilon=\epsilon_{1}}\Bigr]\nonumber\\
& = & -\frac{1}{\sin\big(d_{Geo}\big(X,f(\lambda_f)\big)\big)} \cdot \norm{g(\lambda_f)} \cdot \cos\big(\theta(\lambda_{f},X)\big) \cdot \sin\big(d_{Geo}\big(X,f(\lambda_f)\big)\big) \nonumber \\
\label{limit}
& = & -\norm{g(\lambda_f)} \cdot \cos\big(\theta(\lambda_f,X)\big),
\end{eqnarray}
where the equation (\ref{thm3_limit}) holds for $X \in A \cap B(\zeta)$ such that $d_{Geo}\bigr(X, f(\lambda_{f})\bigr) > 0$. Because the trajectory of $f$, $\{f(\lambda) \in S^2 \ | \ \lambda \in [0,1] \}$, is a measure zero set by Lemma 4, the equation (\ref{thm3_limit}) holds for a.e $X \in B(\zeta)$ by Proposition 4. Moreover, $f$ is a median principal curve of $X$ if and only if
\[
E_{X|\cdot} \Big(\mbox{sgn}\big(\cos\big(\theta(\lambda_{f},X)\big)\big) \big | \lambda_{f}(X) = \lambda \Big) = 0 ~~ \mbox{for} ~ \mbox{a.e.}~ \lambda,
\]
where $\mbox{sgn}(x)=1$ if $x \ge 0$ and otherwise -1. Finally, the result can be obtained in a similar manner to the proofs of Theorem 1 and 2 by applying (\ref{limit}) and bounded convergence theorem. The converse is further proved in the same way as the proofs of Theorem 1 and 2.
\end{proof}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,493 |
\section{Introduction}
The origin of the ferromagnetism has been mystery for a long time.
We cannot show the ferromagnetism without quantum many body effect since
interactions for electrons are almost spin independent in the
microscopic point of view. Moreover, only a non-perturbative analysis
can predict the ferromagnetism since perturbative approaches such as the
Fermi liquid theory show only paramagnetism.
Hubbard model is one of the simplest models to describe itinerant
electrons in solids. This model is a lattice electron model which
considered only two effects. One is an
electron hopping between lattice points and the other is
an on-site repulsive interaction. We identify this interaction with the
Coulomb interaction.
Recently, Mielke and Tasaki
independently have proposed the models whose ground state has saturated
ferromagnetism by a rigorous constructive approach. These models are called
flat-band Hubbard model \cite{Mielke1,Mielke2,Mielke3,Tasaki92}.
Some remarkable results for ferromagnetic ground states have been
obtained in this class of models. Nishino, Goda and Kusakabe have extended
their result to more general models \cite{NGK}. Tasaki has proved also the
stability of the saturated ferromagnetism against a perturbation which
bends the electron band \cite{Tasaki95,Tasaki03}. Tanaka and Ueda have shown the
stability of the saturated ferromagnetism in a more complicated
two-dimensional model in Mielke's class \cite{TU}. Tasaki has studied
the energy of the spin-wave excitations in the flat-band Hubbard model
\cite{Tasaki96}. He has shown that the dispersion of the one-magnon
excitation is non-singular in the flat-band Hubbard model, contrary to
the Nagaoka ferromagnetism. The flat-band ferromagnetism is believed to
be stable against a small perturbation or change the electron number
density \cite{MT}.
We argue an anisotropy in a ferromagnetic Hubbard model
in this paper.
A realistic ferromagnet has anisotropies which have no SU(2)
symmetry. The Hubbard model has SU(2) symmetry and
therefore it has no anisotropy. One of the easiest ways
to introduce an anisotropy is adding a spin anisotropy term such as
the Ising term. However, this way gives us no information for
the origin of the anisotropies as well as the ferromagnetism.
It is believed that the anisotropy is originated from
non-trivial electron dynamics. Moriya has shown
that the spin-orbit coupling gives a spin-dependence of the electron
hopping and the effective spin model has the Ising and the Dzyaloshinski-Moriya
interactions. The hopping anisotropy induces the anisotropy in an effective
spin model. We expect that the spin-orbit coupling induces the
anisotropy even for strong ferromagnetic systems.
Recently, a deformed flat-band Hubbard model with an exact domain wall
ground state was proposed \cite{HI1,HI2,HI3}. The deformed model has a
hopping anisotropy which depends on a spin of an electron.
The ground states of
the model with open boundary condition has same degeneracy as that in
original SU(2) symmetric model. The anisotropy induces the deformation of
SU(2) spin algebra, and then a ground state has a domain wall. It
is also proven that there exists local gapless excitation above the
domain wall ground state \cite{HI3}. These properties of deformed
flat-band Hubbard model are very similar to those in the XXZ model with
critical boundary field. Therefore, we expect that the Ising anisotropy in
quantum spin models comes from hopping anisotropy in
a ferromagnetic Hubbard model.
In this paper, we study a deformed flat-band Hubbard model under a
periodic boundary condition. We can construct all exact ground
states. We find that the magnetization of ground states are fully
polarized, {\it i.e.}, the ground states are only two states: all-spin-up
state and -down state. We also obtain upper and lower
bounds of one-magnon spin-wave
excitation energy. We employ the method proposed by Tasaki.
He showed that the
spin-wave excitation in the SU(2) invariant
Tasaki model has the ordinary spin-wave dispersion
relation which has no energy gap above the ground state. We find that
the one-magnon spin-wave energy has the finite gap above the all-up
state in our deformed model. The dispersion relation is
the same as that in XXZ model in the certain
parameter region. These facts indicate that our model is related to XXZ
model which is non-singular spin model.
This paper is organized as follows.
In section \ref{sec:def}, we define a deformed flat-band Hubbard model
and show the main results which consist of three theorems.
In section \ref{sec:GS}, we prove the first theorem for ground
states. In section \ref{sec:SW_LB}, we show two lemmas and prove
the second theorem for the lower bound of spin-wave energy from these lemmas.
In section \ref{sec:calc_ME} and \ref{sec:est_ME},
we prove the lemmas. In section \ref{sec:SW_UB}, we prove the third theorem for the upper
bound of the spin-wave excitation.
\section{Definitions and Main Results \label{sec:def}}
In this section, we define the $d$-dimensional deformed flat-band
Hubbard model. We also show our main results and discuss their physical
meanings. The proofs of results are given in later sections.
\subsection{Lattice}
The lattice $\Lambda$ on which defined our deformed Hubbard model is
decomposed into two sublattices
\begin{equation}
\Lambda = \Lambda_o \cup \Lambda^\prime.
\end{equation}
$\Lambda_o$ is a $d$-dimensional integer lattice with linear size $L$
defined by
\begin{equation}
\Lambda_o :=
\left\{
x = (x_j)_{j=1}^d \in {\mathbb Z}^{d}
\biggl| |x_j| \leq \frac{L - 1}{2} \quad j = 1, 2, \cdots, d
\right\},
\end{equation}
where $(x_j)_{j=1}^d:=(x_1, x_2, \cdots, x_d)$.
$\Lambda^\prime$ can be further decomposed to
$\Lambda_j$ ($j=1, 2, \cdots, d$), {\it i.e.}
\begin{equation}
\Lambda^\prime = \bigcup_{j = 1}^{d}\Lambda_j.
\end{equation}
$\Lambda_j$ is obtained as a half-integer translation of $\Lambda_o$ to
$j$-th direction,
\begin{equation}
\Lambda_j := \left\{ x + e^{(j)} | x \in \Lambda_o \right\}
\end{equation}
where $e^{(j)}$ is defined by
\begin{equation}
e^{(j)} := (\tfrac{1}{2} \delta_{j, l})_{l=1}^d
= (0, \cdots, 0,
\begin{array}[t]{@{}l@{}}
\frac{1}{2}, 0, \cdots, 0 ).\\
\uparrow\\
j\mbox{-th}
\end{array}
\end{equation}
We show the two-dimensional lattice in
Fig. \ref{fig:2-dim_lattice} as an example.
\begin{figure}[htbp]
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\end{picture}
\end{center}
\vspace*{-1em}
\caption{The two dimensional lattice (with $L = 3$). The white circles are
sites in $\Lambda_o$ and the black dots are sites in
$\Lambda^\prime$. Electrons at a site can hop to another site if this
site is connected to the original site with a line or a curve.}
\label{fig:2-dim_lattice}
\end{figure}
\subsection{Electron Operators and the Fock Space}
The creation and annihilation operators for an electron
$c_{x, \sigma}^\dagger$ and $c_{x, \sigma}$ obey the standard
anticommutation relations
\begin{equation}
\{ c_{x, \sigma}, c_{y, \tau}^\dagger \}
= \delta_{x, y} \delta_{\sigma, \tau}, ~~
\{ c_{x, \sigma}, c_{y, \tau} \}
= 0 = \{ c_{x, \sigma}^\dagger, c_{y, \tau}^\dagger \},
\label{eq:anti-comm-rel_for_c}
\end{equation}
where $\{A, B\} = A B + B A$, for $x, y \in \Lambda$ and electron spin coordinates
$\sigma, \tau = \uparrow, \downarrow$.
We define the no-electron state $\Psi_{\rm vac}$ by
\begin{equation}
c_{x, \sigma} \Psi_{\rm vac} = 0
\mbox{ for } \forall x \in \Lambda
\mbox{ and }\sigma = \uparrow, \downarrow.
\end{equation}
We construct a Fock space spanned by a basis
\begin{equation}
\left\{
\left( \prod_{x \in A} c_{x, \uparrow}^\dagger \right)
\left( \prod_{x \in B} c_{x, \downarrow}^\dagger \right)
\Psi_{\rm vac}
\biggl| A, B \subset \Lambda
\right\}.
\end{equation}
We also define a number operator $n_{x, \sigma}$
by $n_{x, \sigma} = c_{x, \sigma}^\dagger c_{x, \sigma}$ whose
eigenvalue represents a number of electrons at site $x$ with spin $\sigma$.
Note anticommutation relations
$\{ c_{x, \sigma}^\dagger, c_{x, \sigma}^\dagger \} = 0$ {\it i.e.}
$c_{x, \sigma}^\dagger c_{x, \sigma}^\dagger = 0.$
This relation implies the Pauli principle. We employ the periodic
boundary condition. This is realized by
$c_{x+2L e^{(j)}, \sigma} = c_{x, \sigma}$ for $j=1,2,\cdots,d$.
\subsection{Deformed Flat-Band Hubbard Model}
The Hubbard model is a model which represents a many-electron system on
an arbitrary lattice. Here, we define a $d$-dimensional deformed
flat-band Hubbard model.
Our model is a generalization of the Tasaki model given in the reference
\cite{Tasaki92}
A generalized Hubbard Hamiltonian consists of two terms
\begin{equation}
H := H_{\rm hop} + H_{\rm int}.
\label{eq:hamiltonian}
\end{equation}
The hopping term $H_{\rm hop}$ is defined by
\begin{align}
H_{\rm hop} =
t \sum_{\sigma = \uparrow, \downarrow} \sum_{j=1}^{d}
\sum_{x \in \Lambda_j}
d_{x, \sigma}^\dagger d_{x, \sigma}
\label{eq:H_{hop}}
\end{align}
and the interaction term $H_{\rm int}$ is defined by
\begin{equation}
H_{\rm int} = U \sum_{x \in \Lambda}
n_{x, \uparrow} n_{x, \downarrow}
\end{equation}
where $d_{x, \sigma}$ is defined on $x \in \Lambda_j$
$(j=1,2, \cdots, d)$
\begin{equation}
d_{x, \sigma} :=
(q^{-p(\sigma)/4})^\ast c_{x - e^{(j)}, \sigma} +
\lambda c_{x, \sigma} +
(q^{p(\sigma)/4})^\ast c_{x + e^{(j)}, \sigma},
\end{equation}
with $t, U > 0$. $q$ is an complex parameter and $p(\sigma)$ is defined
by $p(\sigma)=\pm 1$ for $\sigma=\uparrow, \downarrow$.
We write the phase factor of $q$ by $\theta$.
The hopping Hamiltonian $H_{\rm hop}$ can also be written
in the following form
\begin{equation}
H_{\rm hop} = \sum_{x, y \in \Lambda} t_{x, y}^{(\sigma)}
c_{x, \sigma}^\dagger c_{y, \sigma}.
\end{equation}
Each term $t_{x, y}^{(\sigma)} c_{x, \sigma}^\dagger c_{y, \sigma}$
in the hopping Hamiltonian represents the hopping of an electron
with spin $\sigma$ from site $x$ to site $y$ with a probability
proportional to $|t_{x, y}^{(\sigma)}|^{2}$.
We expect that the spin-orbit coupling can induce this spin dependent
hopping amplitudes \cite{Moriya}.
Since the interaction Hamiltonian $H_{\rm int}$ represents a on-site
repulsive interaction, we regard this Hamiltonian as a simplification of
the Coulomb interaction between two electrons.
Note that this system conserves the number of electron. The total
electron number operator $\hat{N}_{e}$ is defined by
\begin{equation}
\hat{N}_{e} := \sum_{x \in \Lambda}
\sum_{\sigma = \uparrow, \downarrow} n_{x, \sigma}.
\end{equation}
Since the Hamiltonian commutes with this operator, we can set the
electron number to an arbitrary filling. In the
present paper, we consider only the case that the
electron number is equal to $|\Lambda_o|$.
We confine ourselves to the Hilbert space ${\cal H}$
spanned by the following basis
\begin{equation}
\left\{
\left( \prod_{x \in A} c_{x, \uparrow}^\dagger \right)
\left( \prod_{x \in B} c_{x, \downarrow}^\dagger \right)
\Psi_{\rm vac}
\biggl| A, B \subset \Lambda \mbox{ with }
|A| + |B| = |\Lambda_o|
\right\}.
\end{equation}
Let us discuss the symmetry of the model. An important symmetry is a
U(1) symmetry. We define spin operators at site $x$ by
\begin{equation}
S_{x}^{(l)} := \sum_{\sigma, \tau = \uparrow, \downarrow}
c_{x, \sigma}^\dagger
\frac{{\cal P}_{\sigma, \tau}^{(l)}}{2} c_{x, \tau},
\end{equation}
where ${\cal P}^{(l)}$ ($l = 1, 2, 3$) denote Pauli matrices
\begin{equation}
{\cal P}^{(1)} =
\begin{pmatrix}
0 & 1 \\ 1 & 0
\end{pmatrix}
, \quad
{\cal P}^{(2)} =
\begin{pmatrix}
0 & - i \\ i & 0
\end{pmatrix}
, \quad
{\cal P}^{(3)} =
\begin{pmatrix}
1 & 0 \\ 0 & -1
\end{pmatrix}
.
\end{equation}
The Hamiltonian commutes with the third component of total spin operator
\begin{equation}
[H, S_{\rm tot}^{(3)}] =
H S_{\rm tot}^{(3)} - S_{\rm tot}^{(3)} H = 0,
\label{good}
\end{equation}
with
\begin{equation}
S_{\rm tot}^{(l)} = \sum_{x \in \Lambda} S_{x}^{(l)}.
\end{equation}
Note that this symmetry is enhanced to an SU(2) symmetry in the case of
$q = 1$ {\it i.e.} Hamiltonian commutes with any component of total spin
operator.
In this case, this model becomes the original flat-band Hubbard
model given by Tasaki \cite{Tasaki92,Tasaki95}.
Another important symmetry is ${\mathbb Z}_2$ symmetry which is
generated by a product of a parity and spin rotation defined by
\begin{equation}
\Pi = \Pi^{-1} = P \exp \left( i \pi S_{\rm tot}^{(1)} \right),
\end{equation}
where $P$ is a parity operator defined by
$P c_{x, \sigma} P = c_{-x, \sigma}$ and
$P c_{x, \sigma}^\dagger P = c_{-x, \sigma}^\dagger$.
$\Pi$ transforms $c_{x, \sigma}$ and $c_{x, \sigma}^\dagger$ to
$c_{-x, \overline{\sigma}}$ and $c_{-x, \overline{\sigma}}^\dagger$,
where $\overline{\sigma} = \downarrow$ if $\sigma = \uparrow$ or
$\overline{\sigma} = \uparrow$ if $\sigma = \downarrow$.
Note the following transformation of the total magnetization
$\Pi S_{\rm tot}^{(3)} \Pi = - S_{\rm tot}^{(3)}$. An energy eigenstate
with the total magnetization $M$ is transformed by $\Pi$ into another
eigenstate with the total magnetization $-M$, which belongs to the same
energy eigenvalue.
\subsection{Ground States}
First, we introduce two states $\Psi_\uparrow$ and $\Psi_\downarrow$
defined by
\begin{equation}
\Psi_\uparrow =
\left(\prod_{x \in \Lambda_o} a_{x, \uparrow}^\dagger \right)
\Psi_{\rm vac}
\mbox{ and }
\Psi_\downarrow =
\left(\prod_{x \in \Lambda_o} a_{x, \downarrow}^\dagger \right)
\Psi_{\rm vac},
\end{equation}
where $a_{x, \sigma}^\dagger$ with $x \in \Lambda_o$ is
\begin{equation}
a_{x, \sigma} = - q^{p(\sigma)/4} \sum_{j = 1}^{d}
c_{x - e^{(j)}, \sigma}^\dagger
+ \lambda c_{x, \sigma}^\dagger
- q^{-p(\sigma)/4} \sum_{j = 1}^{d}
c_{x + e^{(j)}, \sigma}^\dagger.
\end{equation}
We can easily verify that the above two states are ground states of the
model since the Hamiltonian is positive semi-definite and
$[d_{y, \sigma}, a_{x, \tau}^\dagger]=0$ for $y \in \Lambda^\prime$ and
$x \in \Lambda_o$. The following theorem states that the ground states
of the model are only above two states.
{\theorem(Ground State of the Model)
In the deformed flat-band Hubbard model defined by
(\ref{eq:hamiltonian}) under a periodic boundary condition with a fixed electron
number $|\Lambda_o|$, the space of ground states are spanned by
two fully polarized states $\Psi_\uparrow$ and $\Psi_\downarrow$.
\label{th:GS}}\smallskip
The proof is given in the next section.
This theorem shows that the deformation of electron hopping destroys
the large degeneracy of ground state in the original SU(2) symmetric
Tasaki model and we obtain two ground states: all-up state and all-down
state. The ground states breaks ${\mathbb Z}_2$ symmetry.
This is similar to that Ising anisotropy effect of the Ising-like XXZ
model.
\subsection{Spin-Wave Excitations}
Before we discuss the spin-wave excitation, we remark properties of the
spin-wave state in quantum spin models. The one-magnon spin-wave state $\Phi_{\rm SW}(k)$
with a wave-number $k \in \ensuremath{{\cal K}}$ satisfies
\begin{equation}
T_{x} \Phi_{\rm SW}(k) = e^{- i k \cdot x} \Phi_{\rm SW}(k)
\label{eq:SW_1}
\end{equation}
and
\begin{equation}
S_{\rm tot}^{(3)} \Phi_{\rm SW}
= (S_{\rm max} - 1 ) \Phi_{\rm SW},
\label{eq:SW_2}
\end{equation}
where $x \in \Lambda_o$ and the translation operator $T_x$ is
defined by
\begin{equation}
T_x c_{y, \sigma} T_x^{-1} = c_{x + y, \sigma}
\quad \mbox{and} \quad
T_x c_{y, \sigma}^\dagger T_x^{-1} = c_{x + y, \sigma}^\dagger.
\end{equation}
$\ensuremath{{\cal K}}$ is the space of wave number vectors
\begin{equation}
\ensuremath{{\cal K}} :=
\left\{
\frac{2 \pi n}{L} ~\biggl|~
n \in {\mathbb Z}^d \cap \left[ -\frac{L-1}{2}, \frac{L-1}{2} \right]^d
\right\}.
\label{eq:def_of_K}
\end{equation}
Then, the one-magnon spin wave state should be in the following Hilbert
space ${\cal H}_k$
\begin{equation}
{\cal H}_k :=
\left\{
\Psi \in {\cal H} ~\Bigl|~
T_x \Psi = e^{-i k \cdot x} \Psi \mbox{ and }
S_{\rm tot}^{(3)} \Psi = \tfrac{1}{2} (|\Lambda_o| - 1) \Psi
\right\}.
\end{equation}
We define one-magnon spin-wave state as the lowest energy state
in ${\cal H}_k$. We denote the spin-wave energy with wave-number $k$ by
$E_{\rm SW}(k)$. We can show the following two theorems. Note that
$\theta \in {\mathbb R}$ which appears in followings is the phase factor of $q$,
{\it i.e.} $q=|q|e^{i\theta}$.
{\theorem(Lower Bound of the Spin-Wave Excitation)
There exist positive constants $t_1$, $\lambda_1$, $U_1$ and $A_1$
independent of the system size such that
\begin{equation}
E_{\rm SW}(k) \geq
\frac{2 U}{\lambda^{4}}
\left[
\frac{d(|q| + |q|^{-1})}{2}
- \sum_{j = 1}^{d} \cos \left( 2 k \cdot e^{(j)} + \theta \right)
- \frac{A_1}{\lambda}
\right]
\end{equation}
for $t \geq t_1$, $\lambda \geq \lambda_1$ and $U \geq U_1$.
\label{th:SW_LB}}
{\theorem(Upper Bound of the Spin-Wave Excitation)
There exists positive constant $A_2$ such that
\begin{equation}
E_{\rm SW}(k) \leq
\frac{2 U}{\lambda^{4}}
\left[
\frac{d(|q| + |q|^{-1})}{2}
- \sum_{j = 1}^{d} \cos \left( 2 k \cdot e^{(j)} + \theta \right)
+ \frac{A_2}{\lambda^2}
\right]
\end{equation}
for $t, \lambda, U>0$.
\label{th:SW_UB}}
\paragraph{Remark}
Theorems \ref{th:SW_LB} and \ref{th:SW_UB} show that the dispersion
relation of the spin-wave is asymptotically
\begin{equation}
E_{\rm SW}(k) \sim
\frac{2 U}{\lambda^{4}}
\left[
\frac{d(|q| + |q|^{-1})}{2}
- \sum_{j = 1}^{d} \cos \left( 2 k \cdot e^{(j)} + \theta \right)
\right]
\label{eq:SW_asymp}
\end{equation}
for large $\lambda$. This dispersion relation is the same as that in the
XXZ model with the Dzyaloshinski-Moriya interaction given by the
Hamiltonian
\begin{equation}
-J \sum_{x \in \Lambda_o} \sum_{j=1}^d
\left[
\cos \theta
\left( S_x^{(1)} S_{x+2e^{(j)}}^{(1)}
+
S_x^{(2)} S_{x+2e^{(j)}}^{(2)} \right)
+ \Delta S_x^{(3)} S_{x+2e^{(j)}}^{(3)}
-\sin \theta {\bm D}\cdot ({\bm S}_x \times {\bm S}_{x+2e^{(j)}})
\right]
\label{eq:H_eff}
\end{equation}
with an exchange parameter $J=2U/\lambda^4$, an Ising anisotropy
parameter $\Delta=(|q|+|q|^{-1})/2$ and a Dzyaloshinski-Moriya
vector ${\bm D} = (0,0,1)$. Furthermore we can obtain the
representation (\ref{eq:H_eff}) as an effective Hamiltonian by a
perturbation theory from our model with a perturbation parameter
$1/\lambda$.
{\corollary(Existence of the Spin-Wave Gap)
There exists positive constant $\lambda_3$ such that
\begin{equation}
\min_{k \in {\cal K}} E_{\rm SW}(k) \geq
\frac{2 U}{\lambda^{4}}
\left[
\frac{d(|q| + |q|^{-1}-2)}{2}
- \frac{A_1}{\lambda}
\right]
> 0
\end{equation}
\label{cor:SW_Gap}}
This means that there is a finite energy gap between
the fully polarized ground state and a spin flipped state. We expect that the
energy spectra have finite gap above the ground states. On the contrary,
there exists a gapless excitation in the model under an open boundary
condition. This drastic difference is also similar to the XXZ model.
\section{Ground States\label{sec:GS}}
In this section, we obtain ground states with the fixed
electron number $N_{e} = |\Lambda_o|$,
and prove the Theorem \ref{th:GS} on the basis of Tasaki's
construction method \cite{Tasaki92}.
\subsection{Localized Electron Operators}
First, We introduce localized electron operators, which are convenient to
construct a ground state and to prove the bounds of spin-wave
excitation energy. This representation was introduced by Tasaki\cite{Tasaki96} to
construct the bases of single electron state. We show the construction
of the operators in Appendix\ref{A:localized_bases}.
First we introduce a localized electron operator $a_{x, \sigma}^\dagger$
defined by
\begin{equation}
a_{x, \sigma}^\dagger = \sum_{ y \in \Lambda}
\psi_{y, \sigma}^{(x)} c_{y, \sigma}^\dagger,
\label{eq:def_of_a}
\end{equation}
where $\psi_{y, \sigma}^{(x)}$ is represented by
\begin{equation}
\psi_{y, \sigma}^{(x)} =
\begin{cases}
\displaystyle
-\frac{q^{p(\sigma)/4}}{\lambda}
\sum_{j=1}^{d} \delta_{x - e^{(j)}, y}
+ \delta_{x, y}
-\frac{q^{-p(\sigma)/4}}{\lambda}
\sum_{j=1}^{d} \delta_{x + e^{(j)}, y}
& \mbox{for }x \in \Lambda_o \\
\displaystyle
\frac{(q^{-p(\sigma)/4})^\ast}{\lambda}
\delta_{x - e^{(j)}, y}
+ \delta_{x, y}
+ \frac{(q^{p(\sigma)/4})^\ast}{\lambda}
\delta_{x + e^{(j)}, y}
& \mbox{for }x \in \Lambda_j
\end{cases}
.
\label{eq:local_basis}
\end{equation}
$a_{x, \sigma}^\dagger \Psi_{\rm vac}$ with $x \in \Lambda_o$ is a
ground state of single electron state. The single-electron ground state
has
$|\Lambda_o|$-fold degeneracy. This macroscopic degeneracy of
single-electron ground state is one of the origin of flat-band
ferromagnetism.
$\{ a_{x, \sigma}^\dagger \Psi_{\rm vac} \}_{x \in \Lambda_o}$ is
a basis of zero-energy single-electron states, and
$\{ a_{y, \sigma}^\dagger \Psi_{\rm vac} \}_{y \in \Lambda^\prime}$
is a basis of excited single-electron states. Furthermore, the ground state energy is 0 and the
lowest excitation energy eigenvalue is $t \lambda^2$ (See
Appendix\ref{A:localized_bases}).
We can also construct another localized electron operator
$b_{x, \sigma}$ which satisfies
\begin{equation}
\{ b_{x, \sigma}, a_{y, \tau}^\dagger \} = \delta_{x, y}
\delta_{\sigma, \tau}
\mbox{ and }
\{ b_{x, \sigma}, b_{y, \tau} \}
= 0 =
\{ a_{x, \sigma}^\dagger, a_{y, \tau}^\dagger \}.
\label{eq:a-com_a-b}
\end{equation}
We represent $b_{x, \sigma}$ in terms of the original electron operator
by
\begin{equation}
b_{x, \sigma} = \sum_{y \in \Lambda}
(\tilde{\psi}_{y, \sigma}^{(x)})^\ast c_{y, \sigma}.
\label{eq:def_of_b}
\end{equation}
(\ref{eq:def_of_a}), (\ref{eq:def_of_b}) and (\ref{eq:a-com_a-b}) means
\begin{equation}
\sum_{w \in \Lambda}
(\tilde{\psi}_{w, \sigma}^{(x)})^\ast \psi_{w, \sigma}^{(y)}
= \delta_{x, y}
\mbox{ and }
\sum_{w \in \Lambda}
(\tilde{\psi}_{x, \sigma}^{(w)})^\ast \psi_{y, \sigma}^{(w)}
= \delta_{x, y}.
\label{eq:dual_basis}
\end{equation}
Note, $\tilde{\psi}_{y, \sigma}^{(x)}$ cannot be represented closed form
but decay exponentially as $\|x-y\|_1$ becomes large, where
$\|x-y\|_1:=\sum_{j=1}^{d}|x_j-y_j|$. We can obtain the following
bounds.
{\lemma
There exists positive constant $B_1$ such that
\begin{align}
& \sum_{w \in \Lambda} |\tilde{\psi}_{w, \sigma}^{(x)}-\psi_{w, \sigma}^{(x)}|
\leq \frac{B_1}{\lambda^2},
\label{eq:bound_of_sum_psi-1}
\\
& \sum_{w \in \Lambda} |\tilde{\psi}_{x, \sigma}^{(w)}-\psi_{x, \sigma}^{(w)}|
\leq \frac{B_1}{\lambda^2}
\label{eq:bound_of_sum_psi-2}
\end{align}
for all $x, y \in \Lambda$.
\label{lemma:bound_sum_psi}}
{\lemma
There exist positive constants $B_2$, $B_3$ and $B_4$
\begin{align}
& |\tilde{\psi}_{y, \sigma}^{(x)}|
\leq B_2
\left[
\frac{2d}{\lambda^2 +d (|q|^{1/2}+|q|^{-1/2})}
\right]^{\|y-x\|_1}
\mbox{ for } \forall x, y \in \Lambda,
\label{eq:bound_of_psi} \\
& |\tilde{\psi}_o^{(o)} - \psi_o^{(o)}|
\leq
\frac{B_3}{\lambda^2},
\label{eq:bound_diff_psi00} \\
\intertext{and}
& |\tilde{\psi}_{\pm e^{(j)}}^{(o)} - \psi_{\pm e^{(j)}}^{(o)}|
\leq
\frac{B_4}{\lambda^3}.
\label{eq:bound_diff_psi01}
\end{align}
\label{lemma:bound_psi}}
The proofs of these lemmas are given in \ref{A:estimates_of_psi}.
The original electron operators can be written in terms of
$a_{x, \sigma}^\dagger$ and $b_{x, \sigma}$,
\begin{equation}
c_{x, \sigma}^\dagger
= \sum_{y \in \Lambda}
(\tilde{\psi}_{x, \sigma}^{(y)})^\ast a_{y, \sigma}^\dagger
\quad \mbox{and} \quad
c_{x, \sigma}
= \sum_{y \in \Lambda} \psi_{x, \sigma}^{(y)} b_{y, \sigma}.
\label{eq:c_i.t.o._a_or_b}
\end{equation}
The Hilbert space with $|\Lambda_o|$ electrons is also spanned by the
basis
\begin{equation}
\left\{
\left( \prod_{x \in A} a_{x, \uparrow}^\dagger \right)
\left( \prod_{x \in B} a_{x, \downarrow}^\dagger \right)
\Psi_{\rm vac}
\biggl| A, B \subset \Lambda \mbox{ with }
|A| + |B| = |\Lambda_o|
\right\},
\end{equation}
because $c_{x, \sigma}^\dagger$ can be written in terms of
$a_{x, \sigma}^\dagger$.
\subsection{Proof of Theorem \ref{th:GS}}
Here, we construct ground states of the model.
Let $\Psi$ be a ground state with $|\Lambda_0|$ electrons. First, we
expand a ground state $\Psi$ into the following series
\begin{equation}
\Psi = \sum_{A, B}
\psi(A, B)
\left(
\prod_{x \in A} a_{x, \uparrow}^\dagger
\right)
\left(
\prod_{y \in B} a_{y, \downarrow}^\dagger
\right)
\Psi_{\rm vac} \label{eq:exp-of-GS-1},
\end{equation}
where the summation is taken over all $A, B \subset \Lambda$ with
$|A|+|B|=|\Lambda_o|$. Note that $a_{x, \sigma}^\dagger$ for
$x \in \Lambda_o$ creates an electron which has the lowest energy of
$H_{\rm hop}$. For the lowest energy state of
$H_{\rm hop}$, $\psi(A, B)$ should vanish, if $A$ or $B$
contains a site in $\Lambda^\prime$.
Next, we consider the interaction Hamiltonian. If we find a state $\Psi$
such that $c_{x, \uparrow} c_{x, \downarrow} \Psi=0$ for
$\forall x \in \Lambda$, then the state is a ground state of
$H_{\rm int}$. For $x \in \Lambda_o$, we find that $\psi(A, B)$ survives
only for $A \cap B = \emptyset$, if
$A, B \subset \Lambda_o$. These facts allow us to represent $\Psi$ the
following form:
\begin{equation}
\Psi =
\sum_\sigma \phi(\sigma)
\left(
\prod_{x \in \Lambda_o} a_{x, \sigma_{x}}^\dagger
\right) \Psi_{\rm vac}
\label{eq:rep_of_GS_M}
\end{equation}
where the summation is taken over all possible spin configurations
$\sigma=(\sigma_{x})_{x \in \Lambda_o}$.
To satisfy the condition $c_{y, \uparrow} c_{y, \downarrow} \Psi=0$ for
$y \in \Lambda_j$ ($j=1,2,\cdots, d$), the coefficient holds
\begin{equation}
\phi(\sigma) = q^{\left[ p(\sigma_{y - e^{(j)}})
- p(\sigma_{y + e^{(j)}}) \right]/2}
\phi(\sigma_{y - e^{(j)}, y + e^{(j)}}),
\label{eq:cond_for_phi}
\end{equation}
where $\sigma_{x, y}$ is spin configuration obtained by the exchange
$\sigma_{x}$ and $\sigma_{y}$ in the original configuration $\sigma$.
The periodic boundary
condition allows no configuration which satisfies the condition
(\ref{eq:cond_for_phi}) except in the two cases: $\sigma_x = \uparrow$
for all $x \in \Lambda_o$ or $\sigma_x = \downarrow$ for all
$x \in \Lambda_o$. Thus, we conclude that all ground states in the
periodic boundary condition are only two fully polarized states
\begin{equation}
\Psi_\uparrow :=
\left( \prod_{x \in \Lambda_o} a_{x, \uparrow}^\dagger \right)
\Psi_{\rm vac}
\end{equation}
and
\begin{equation}
\Psi_\downarrow :=
\left( \prod_{x \in \Lambda_o} a_{x, \downarrow}^\dagger \right)
\Psi_{\rm vac}.
\end{equation}
This fact proves Theorem \ref{th:GS}. ~ \rule{0.8ex}{1.6ex}\smallskip
\section{Lower bound of the Spin-Wave Excitation \label{sec:SW_LB}}
In this section, we show that the one-magnon spin-wave excitation has the
same dispersion relation as that in the XXZ model. Our proof is based on
Tasaki's argument for the SU(2) invariant model \cite{Tasaki96}. He has
proved that the one-magnon spin-wave excitation in the Tasaki model has
the same dispersion relation as that in the ferromagnetic Heisenberg
model. These spin-wave excitations in both models have no energy gap,
since they are the Goldstone mode above the ground state which
spontaneously breaks the SU(2) spin rotation symmetry. On the contrary,
we will find an energy gap in our anisotropic model.
\subsection{Another Hopping Hamiltonian}
To estimate a lower bound, it is convenient to introduce a
new hopping Hamiltonian $\tilde{H}_{\rm hop}$ which satisfies
\begin{equation}
\tilde{H}_{\rm hop} a_{x, \sigma}^\dagger \Psi_{\rm vac} =0
\mbox{ for } x \in \Lambda_o
\end{equation}
and
\begin{equation}
\tilde{H}_{\rm hop} a_{x, \sigma}^\dagger \Psi_{\rm vac} =
t \lambda^2 a_{x, \sigma}^\dagger \Psi_{\rm vac}
\mbox{ for } x \in \Lambda^\prime.
\end{equation}
Note that $a_{x, \sigma}^\dagger \Psi_{\rm vac}$ with $x \in \Lambda_o$
is the basis of single electron ground states
and $a_{y, \sigma}^\dagger \Psi_{\rm vac}$ with $y \in \Lambda^\prime$ is
a basis of single electron
excited states. Moreover, the ground state energy
is 0 and the lowest excitation energy eigenvalue is $t \lambda^2$, {\it i.e.}
$H_{\rm hop} a_{x, \sigma}^\dagger \Psi_{\rm vac}=0$ for all
$x \in \Lambda_o$ and
$(\Psi, H_{\rm hop} \Psi)/\|\Psi\|^2 \geq t \lambda^2$ with
$\Psi = \sum_{y \in \Lambda^\prime} C_y a_{y, \sigma}^\dagger \Psi_{\rm vac}$
for any set of complex numbers $\{ C_y \}_{y \in \Lambda^\prime}$.
Then, we obtain that $\tilde{H}_{\rm hop} \leq H_{\rm hop}$.
$\tilde{H}_{\rm hop}$ is represented by
\begin{equation}
\tilde{H}_{\rm hop} = t \lambda^2
\sum_{x \in \Lambda^\prime} \sum_{\sigma=\uparrow,\downarrow}
a_{x, \sigma}^\dagger b_{x, \sigma}.
\end{equation}
Note that $\tilde{H}_{\rm hop}$ is not hermitian and therefore
its eigenvectors are not orthogonal systems.
Nevertheless, all eigenvalues of $\tilde{H}_{\rm hop}$ are real.
We define a new Hamiltonian
$\tilde{H} := \tilde{H}_{\rm hop}+H_{\rm int}$.
We use a representation of interaction Hamiltonian in terms of the
localized electron operators to evaluate the bounds
\begin{align}
H_{\rm int} = \sum_{x_1, x_2, x_3, x_4 \in \Lambda}
\widetilde{U}_{x_1, x_2; x_3, x_4}
a_{x_1, \uparrow}^\dagger a_{x_2, \downarrow}^\dagger
b_{x_3, \downarrow} b_{x_4, \uparrow},
\end{align}
where $\tilde{U}_{x_1, x_2; x_3, x_4}$ is defined by
\begin{equation}
\tilde{U}_{x_1, x_2; x_3, x_4}
:=
U \sum_{w \in \Lambda}
(\tilde{\psi}_{w, \uparrow}^{(x_1)}
\tilde{\psi}_{w, \downarrow}^{(x_2)})^\ast
\psi_{w, \downarrow}^{(x_3)} \psi_{w, \uparrow}^{(x_4)}
.
\end{equation}
\subsection{Basis for the Spin-Wave State}
To define convenient basis of ${\cal H}_k$, we define a state
$\Psi_{\mu, A}(k)$ for $\mu=0,1, \cdots, d$ and for a set
$A \subset \Lambda$ with $|A| = |\Lambda_o|-1$ by
\begin{equation}
\Psi_{\mu, A}(k) :=
\sum_{w \in \Lambda_o} e^{i k \cdot w} T_w
a_{e^{(\mu)}, \downarrow}^\dagger
\left(
\prod_{v \in A} a_{v, \uparrow}^\dagger
\right)
\Psi_{\rm vac},
\end{equation}
where $e^{(\mu)}=o=(0,0,\cdots, 0)$ for $\mu=0$ and $e^{(\mu)}=e^{(j)}$
for $\mu=j$ $(j=1, 2, \cdots, d)$.
This state satisfies both properties (\ref{eq:SW_1}) and
(\ref{eq:SW_2}). We define another state $\Omega(k)$ by
\begin{equation}
\Omega(k) = \frac{1}{\alpha}
\sum_{w \in \Lambda_o} e^{i k \cdot w} T_w
a_{o, \downarrow}^\dagger b_{o, \uparrow} \Psi_\uparrow(k)
\propto \Psi_{0, \Lambda_o \backslash \{ o \}},
\end{equation}
which is an approximation of the spin wave state. We will choose a
positive constant $\alpha$ in the proof. We define the following basis
of ${\cal H}_k$ by
\begin{align}
\ensuremath{{\cal B}}_{k} :=
\{ \Omega(k) \} \cup
\bigl\{
\Psi_{\mu, A}(k)
~\bigl|~
\mu = 0, 1, \cdots, d, \quad A \subset \Lambda
& \nonumber \\
\mbox{ with }
|A| = |\Lambda_o| -1
\mbox{ and }
(\mu, A) \neq (0, \Lambda_o \backslash \{ o \})
&
\bigr\}.
\end{align}
\subsubsection{Basic Lemma for Lower Bound}
We define matrix elements $h[\Psi, \Phi]$ between $\Psi, \Phi \in \ensuremath{{\cal B}}_k$
by the unique expansion
\begin{equation}
\tilde{H} \Psi = \sum_{\Phi \in \ensuremath{{\cal B}}_{k}}
h[\Phi, \Psi] \Phi.
\label{eq:def_ME}
\end{equation}
And we define $D[\Phi]$ by
\begin{equation}
D[\Phi] := \Re[h[\Phi, \Phi]]
- \sum_{\Psi \in \ensuremath{{\cal B}}_k \backslash \{ \Phi \}}
|h[\Phi, \Psi]|.
\end{equation}
We can prove the following lemma. The proof is given in
Appendix\ref{A:proof_SW-1}.
{\lemma \label{lemma:SW-1}
Let $\tilde{E}_0 (k)$ be the lowest energy eigenvalue of $\tilde{H}$ in
the Hilbert space ${\cal H}_k$. Then, we have
\begin{equation}
\tilde{E}_0 (k) \geq \min_{\Phi \in \ensuremath{{\cal B}}_k} D[\Phi].
\end{equation}
}
\subsection{Proof of Theorem \ref{th:SW_LB}}
First, we show the results of estimates. We obtain these bounds from the
direct evaluation (See Section \ref{sec:calc_ME} and \ref{sec:est_ME})
{\lemma
There exist positive constants $F_1$, $F_2$, $F_3$, $F_4$, $F_5$ and $F_6$
such that
\begin{align}
D[\Omega(k)] \geq &
\frac{2 U}{\lambda^4}
\left[
\frac{d (|q|+|q|^{-1})}{2}- \sum_{j=1}^d\cos(k \cdot 2e^{(j)} + \theta)
- \frac{F_1}{\lambda^2}
\right]
-
U \alpha \frac{F_2}{\lambda}
\label{eq:D[Omega]}
\\
D[\Psi_{0, x}(k)] \geq &
U
\left(
1 - \frac{F_2}{\lambda} - \frac{F_3}{\lambda^2}
\right)
-\frac{U}{\alpha} \frac{F_4}{\lambda^4}
\label{eq:D[Psi_0x]}
\\
D[\Psi_{\mu, A}(k)] \geq &
t \lambda^2 - U \frac{F_5}{\lambda}
-\frac{U}{\alpha} \frac{F_6}{\lambda^2},
\label{eq:D[Psi_gen]}
\end{align}
for $\mu\neq 0$ and $A \cap \Lambda^\prime \neq \emptyset$.
\label{lemma:D[Psi]}}\smallskip
We give the proof of this lemma in subsection
\ref{sec:estimates_of_D[Psi]}.
\paragraph{Proof of Theorem \ref{th:SW_LB} from Lemma \ref{lemma:SW-1} and \ref{lemma:D[Psi]}}
From these inequalities and good choice of $\alpha$,
$\min_{\Psi \in \ensuremath{{\cal B}}_k} D[\Psi]$ is given by $D[\Omega(k)]$.
If we choose $\alpha= U/\lambda^4$, then we find
\begin{align}
D[\Psi_{0, x}] \geq &
U
\left(
1 - \frac{F_2}{\lambda} - \frac{F_3}{\lambda^2}
\right)
-F_4
=
U
\left( 1 - \frac{F_2+F_3/\lambda}{\lambda} \right)
-F_4
\end{align}
and
\begin{equation}
D[\Psi_{\mu, A}] \geq
t \lambda^2
\left(
1- \frac{F_6}{t}
\right)
- U \frac{F_5}{\lambda}.
\end{equation}
If $\lambda \geq \lambda_2 = 4 (F_2+F_3/\lambda_2)$ and $U \geq U_1 = 4F_4$, then
\begin{equation}
D[\Psi_{0, x}] \geq \frac{U}{2}.
\end{equation}
If $t \geq t_1 = 4F_6$ and
$\lambda \geq \lambda_3 = [U F_5/(4t)]^{1/3}$, then
\begin{equation}
D[\Psi_{\mu, A}] \geq \frac{t \lambda^2}{2}.
\end{equation}
If
$\lambda \geq \lambda_4 = \max \left\{ [d(|q|+|q|^{-1}+2)]^{1/4},[d U(|q|+|q|^{-1}+2)/t]^{1/6}\right\}$,
then
\begin{equation}
D[\Omega] \leq \frac{d U}{\lambda^4}(|q|+|q|^{-1}+2)
\leq \frac{U}{2}
\end{equation}
and
\begin{equation}
D[\Omega] \leq \frac{d U}{\lambda^4}(|q|+|q|^{-1}+2)
\leq \frac{t \lambda^2}{2}.
\end{equation}
We set $\lambda_1 = \max \{ \lambda_2, \lambda_3, \lambda_4 \}$.
Thus we obtain
\begin{align}
\min_{\Phi \in \ensuremath{{\cal B}}_{k}} D[\Phi] = D[\Omega(k)]
\geq
\frac{2 U}{\lambda^{4}}
\left[
\frac{d(|q| + |q|^{-1})}{2}
- \sum_{j = 1}^{d} \cos \left( 2 k \cdot e^{(j)} + \theta \right)
- \frac{A_1}{\lambda}
\right]
\end{align}
for $\lambda \geq \lambda_1$, $U \geq U_1$ and $t \geq t_1$
where $A_1=F_2+F_1/\lambda_1$.
Lemma \ref{lemma:SW-1} and this show that
\begin{equation}
\tilde{E}_0(k) \geq
\frac{2 U}{\lambda^{4}}
\left[
\frac{d(|q| + |q|^{-1})}{2}
- \sum_{j = 1}^{d} \cos \left( 2 k \cdot e^{(j)} + \theta \right)
- \frac{A_1}{\lambda}
\right].
\end{equation}
Since $H \geq \tilde{H}$, then $E_{\rm SW}(k) \geq \tilde{E}_0(k)$.
Thus we obtain
\begin{equation}
E_{\rm SW}(k) \geq
\frac{2 U}{\lambda^{4}}
\left[
\frac{d(|q| + |q|^{-1})}{2}
- \sum_{j = 1}^{d} \cos \left( 2 k \cdot e^{(j)} + \theta \right)
- \frac{A_1}{\lambda}
\right].
\end{equation}
This concludes Theorem \ref{th:SW_LB}. ~ \rule{0.8ex}{1.6ex}\smallskip
\section{Calculation of Matrix Elements \label{sec:calc_ME}}
In this section, we calculate the matrix elements defined by
(\ref{eq:def_ME}) to estimate $D[\Phi]$ for $\Phi \in \ensuremath{{\cal B}}_k$. Before
showing the details of calculation, we list the summary formulae of matrix
elements. We often abbreviate the $k$-dependence of the states for
simplicity.
\subsection{Summary of Matrix Elements}
Here, we show only summary of the calculations. We define
$h_{\rm hop}[\Phi, \Psi]$ and $h_{\rm int}[\Phi, \Psi]$ by
\begin{equation}
\tilde{H}_{\rm hop} \Psi
= \sum_{\Phi \in \ensuremath{{\cal B}}_k} h_{\rm hop}[\Phi, \Psi] \Phi
\end{equation}
and
\begin{equation}
H_{\rm int} \Psi
= \sum_{\Phi \in \ensuremath{{\cal B}}_k} h_{\rm int}[\Phi, \Psi] \Phi.
\end{equation}
It is convenient to define $\Psi_{\mu, x}$ and $\Psi_{\mu, y, v, w}$
with $x, v, w \in \Lambda_o$, $v \neq w$ and $y \in \Lambda^\prime$ by
\begin{equation}
\Psi_{\mu, x}(k) :=
\sum_{w_1 \in \Lambda_o}
e^{i k \cdot w_1}
a_{w_1+e^{(\mu)}, \downarrow}^\dagger b_{w_1+x, \uparrow}
\Phi_\uparrow
\propto
\Psi_{\mu, \Lambda_o\backslash\{x\}}
.
\end{equation}
and
\begin{equation}
\Psi_{\mu, y, v, w}(k) :=
\sum_{w_1 \in \Lambda_o}
e^{i k \cdot w_1}
a_{w_1+e^{(\mu)}, \downarrow}^\dagger
b_{v+w_1, \uparrow} b_{w+w_1, \uparrow}
a_{y+w_1, \uparrow}^\dagger
\Phi_\uparrow
\propto
\Psi_{\mu, (\Lambda_o\backslash\{v, w\})\cup\{y\}}.
\end{equation}
Only $\Psi_{\mu, x}$ and $\Psi_{\mu, y, v, w}$ contribute to
matrix elements related to $\Omega$: $h_{\rm int}[\Omega, \Phi]$ and
$h_{\rm int}[\Phi, \Omega]$.
We summarize the calculations of the matrix elements.
\begin{equation}
h_{\rm hop}[\Psi_{\rho, B}, \Psi_{\mu, A}] = t \lambda^2
(|A\cap \Lambda^\prime| + \chi[\mu \neq 0])\delta_{\mu, \rho} \chi[A=B],
\label{eq:h_hop}
\end{equation}
\begin{align}
h_{\rm int}[\Psi_{\rho, y}, \Psi_{\mu, x}]
=
e^{-i k \cdot x}
\sum_{v \in \Lambda_o}
\left(
e^{i k \cdot y}
\tilde{U}_{v, e^{(\rho)}; y-x+e^{(\mu)}, v}
- e^{i k \cdot v}
\tilde{U}_{v, e^{(\rho)}; v-x+e^{(\mu)}, y}
\right),
\label{eq:h_int[1]}
\end{align}
\begin{equation}
h_{\rm int}[\Psi_{\rho, y, v, w}, \Psi_{\mu, x}]
=
e^{i k \cdot (v-x)} \tilde{U}_{y, e^{(\rho)}; v-x+e^{(\mu)}, w}
\chi[v \neq w],
\label{eq:h_int[2]}
\end{equation}
and
\begin{align}
h_{\rm int}[\Psi_{\rho, y}, \Psi_{\mu, x, w, w}]
e^{i k\cdot y}
\left(
e^{-i k \cdot v}
\tilde{U}_{w, y-v+e^{(\rho)}; e^{(\mu)}, x}
- e^{-i k \cdot w}
\tilde{U}_{v, y-w+e^{(\rho)}; e^{(\mu)}, x}
\right),
\label{eq:h_int[3]}
\end{align}
where the indicator function $\chi$ is defined by $\chi[{\rm true}]=1$
and $\chi[{\rm false}]=0$.
\subsection{Treatment of the Hopping Hamiltonian}
It is easy to calculate matrix elements of hopping Hamiltonian, since the
modified hopping Hamiltonian $\tilde{H}_{\rm hop}$ is ``diagonalized''
in terms of localized electron operators (\ref{eq:def_of_a}) and
(\ref{eq:def_of_b}). We can easily obtain the matrix element
(\ref{eq:h_hop}) from
\begin{equation}
\tilde{H}_{\rm hop} \Psi_{\mu, A}
=
t \lambda^2 ( |A \cap \Lambda^\prime|+\chi[\mu \neq 0])
\Psi_{\mu, A}.
\end{equation}
\subsection{Treatment of the Interaction Hamiltonian}
Here, we calculate the matrix elements.
\paragraph{Calculation of $h_{\rm int}[\Phi, \Psi_{\mu, x}]$}
First, we consider $H_{\rm int} \Psi_{\mu, x}$,
\begin{align}
H_{\rm int} \Psi_{\mu, x}
=
\sum_{w_1, w_2, w_3, w_4 \in \Lambda} \sum_{v \in \Lambda_o}
e^{i k \cdot v} \tilde{U}_{w_1, w_2; w_3, w_4}
a_{w_1, \uparrow}^\dagger a_{w_2, \downarrow}^\dagger
b_{w_3, \downarrow} b_{w_4, \uparrow}
a_{v+e^{(\mu)}, \downarrow}^\dagger b_{x+v, \uparrow}
& \Phi_\uparrow
\nonumber \\
=
\sum_{w_2 \in \Lambda} \sum_{v, w_4 \in \Lambda_o}
e^{i k \cdot v}
\Biggl[
\tilde{U}_{w_4, w_2; v+e^{(\mu)}, w_4}
a_{w_2, \downarrow}^\dagger b_{x+v, \uparrow}
-
\tilde{U}_{x+v, w_2; v+e^{(\mu)}, w_4}
a_{w_2, \downarrow}^\dagger b_{w_4, \uparrow}
\Biggr]
\chi[w_4 \neq x+v] & \Phi_\uparrow
+
\nonumber \\
\sum_{w_1 \in \Lambda^\prime}
\sum_{w_2 \in \Lambda} \sum_{v, w_4 \in \Lambda_o}
e^{i k \cdot v} \tilde{U}_{w_1, w_2; v+e^{(\mu)}, w_4}
a_{w_2, \downarrow}^\dagger
b_{w_4, \uparrow} b_{x+v, \uparrow}
a_{w_1, \uparrow}^\dagger
\chi[w_4 \neq x+v] & \Phi_\uparrow.
\label{eq:H_int_psi_mu-x:1}
\end{align}
Here, we decompose $w_2$ into $w \in \Lambda_o$ and $e^{(\rho)}$. We make
the change of variables $w_4=w+y$ and $v=w-x+v$ for first line. Then we
obtain
\begin{align}
& \sum_{\rho=0}^{d} \sum_{v, w, y \in \Lambda_o}
\Biggl[
e^{i k \cdot (v - x+w)}
\tilde{U}_{w+y, w+e^{(\rho)}; v -x+w+e^{(\mu)}, w+y}
a_{w+e^{(\rho)}, \downarrow}^\dagger b_{v+w, \uparrow}
-
\nonumber \\
& \qquad
e^{i k \cdot (w+v-x)}
\tilde{U}_{v+w, w+e^{(\rho)}; v-x+w+e^{(\mu)}, w+y}
a_{w+e^{(\rho)}, \downarrow}^\dagger b_{w+y, \uparrow}
\Biggr]
\chi[w+y \neq v+w] \Phi_\uparrow
\nonumber \\
& =
\sum_{\rho=0}^{d} \sum_{v, y \in \Lambda_o}
\chi[y \neq v]
\biggl[
e^{i k \cdot (v - x)}
\tilde{U}_{y, e^{(\rho)}; v-x+e^{(\mu)}, y}
\Psi_{\rho, v}
-
e^{i k \cdot (v-x)}
\tilde{U}_{v, e^{(\rho)}; v-x+e^{(\mu)}, y}
\Psi_{\rho, y}
\biggr]
\nonumber \\
& =
\sum_{\rho=0}^{d} \sum_{v, y \in \Lambda_o}
\chi[y \neq v]
\biggl[
e^{i k \cdot (y-x)}
\tilde{U}_{v, e^{(\rho)}; y-x+e^{(\mu)}, v}
-
e^{i k \cdot (v-x)}
\tilde{U}_{v, e^{(\rho)}; v-x+e^{(\mu)}, y}
\biggr] \Psi_{\rho, y},
\end{align}
where we used the relation
$\tilde{U}_{x + u, y + u; v + u, w + u} = \tilde{U}_{x, y; v, w}$ with
$u \in \Lambda_o$. Thus we find the representation
(\ref{eq:h_int[1]}). ~ \rule{0.8ex}{1.6ex}\smallskip
For second line of (\ref{eq:H_int_psi_mu-x:1}), we make the change of
variables $w_2=w^\prime+e^{(\rho)}$, $w_1=w^\prime+y$, $w_4=w^\prime+w$
and $v=w^\prime-x+v$. Then we obtain
\begin{align}
& \sum_{\rho = 0}^{d} \sum_{y \in \Lambda^\prime}
\sum_{v, w^\prime, w \in \Lambda_o}
e^{i k \cdot (v+w^\prime - x)}
\tilde{U}_{y+w^\prime, w^\prime+e^{(\rho)}; v+w^\prime - x+e^{(\mu)}, w^\prime+w}
\times
\nonumber \\
& \qquad
a_{w^\prime+e^{(\rho)}, \downarrow}^\dagger
b_{w^\prime+w, \uparrow} b_{v+w^\prime, \uparrow}
a_{y+w^\prime, \uparrow}^\dagger
\chi[w^\prime+w \neq v+w^\prime] \Phi_\uparrow
\nonumber \\
& = \sum_{\rho = 0}^{d} \sum_{y \in \Lambda^\prime}
\sum_{v, w \in \Lambda_o}
e^{i k \cdot (v-x)}
\tilde{U}_{y, e^{(\rho)}; v-x+e^{(\mu)}, w}
\chi[v \neq w]
\sum_{w^\prime \in \Lambda_o}
e^{i k \cdot w^\prime} T_{w^\prime}
a_{e^{(\rho)}, \downarrow}^\dagger
b_{w, \uparrow} b_{v, \uparrow}
a_{y, \uparrow}^\dagger
\Phi_\uparrow
\nonumber \\
& = \sum_{\rho = 0}^{d} \sum_{w \in \Lambda^\prime}
\sum_{v, y \in \Lambda_o}
e^{i k \cdot (v - x)}
\tilde{U}_{y, e^{(\rho)}; v - x+e^{(\mu)}, w}
\chi[y \neq v] \Psi_{\rho, y, v, w}.
\end{align}
Thus we find representation (\ref{eq:h_int[2]}). ~ \rule{0.8ex}{1.6ex}\smallskip
\paragraph{Calculation of $h[\Psi_{\rho, y}, \Psi_{\mu, x, v, w}]$}
Next, we consider $H_{\rm int}\Psi_{\mu, x, v, w}$,
\begin{align}
& H_{\rm int} \Psi_{\mu, x, v, w}
= \sum_{w_1, w_2, w_3, w_4 \in \Lambda} \sum_{w_5 \in \Lambda_o}
e^{i k\cdot w_5} \tilde{U}_{w_1, w_2; w_3, w_4}
\times
\nonumber \\
& \qquad
a_{w_2, \downarrow}^\dagger b_{w_3, \downarrow}
a_{w_5+e^{(\mu)}, \downarrow}^\dagger
a_{w_1, \uparrow}^\dagger
b_{w_5+w, \uparrow} b_{w_5+v, \uparrow}
b_{w_4, \uparrow} a_{w_5+x, \uparrow}^\dagger
\Phi_\uparrow
\nonumber \\
& = \sum_{\rho=0}^d \sum_{w_1 \in \Lambda} \sum_{w_2, w_5 \in \Lambda_o}
e^{i k\cdot w_5} \tilde{U}_{w_1, w_2+e^{(\rho)}; w_5+e^{(\mu)}, w_5+x}
\times
\nonumber \\
& \qquad
a_{w_2+e^{(\rho)}, \downarrow}^\dagger
a_{w_1, \uparrow}^\dagger
b_{w_5+w, \uparrow} b_{w_5+v, \uparrow}
\Phi_\uparrow
+ \mbox{other terms}
\nonumber \\
& = \sum_{\rho=0}^d \sum_{w_2, w_5 \in \Lambda_o}
e^{i k\cdot w_5} a_{w_2+e^{(\rho)}, \downarrow}^\dagger
\biggl(
\tilde{U}_{w, w_2+e^{(\rho)}-w_5; e^{(\mu)}, x}
b_{w_5+v, \uparrow}
-
\nonumber \\
& \qquad
\tilde{U}_{v, w_2+e^{(\rho)}-w_5; e^{(\mu)}, x}
b_{w_5+w, \uparrow}
\biggr)
\Phi_\uparrow
+ \mbox{other terms}
\nonumber \\
& = \sum_{\rho=0}^d \sum_{w_2, w_5 \in \Lambda_o}
e^{i k\cdot (w_5+w_2)} a_{w_2+e^{(\rho)}, \downarrow}^\dagger
\biggl(
\tilde{U}_{w, w_5+e^{(\rho)}; e^{(\mu)}, x}
b_{w_2+w_5+v, \uparrow}
-
\nonumber \\
& \qquad
\tilde{U}_{v, w_5+e^{(\rho)}; e^{(\mu)}, x}
b_{w_2+w_5+w, \uparrow}
\biggr)
\Phi_\uparrow
+ \mbox{other terms}
\nonumber \\
& = \sum_{\rho=0}^d \sum_{w_5 \in \Lambda_o}
e^{i k\cdot w_5}
\biggl(
\tilde{U}_{w, w_5+e^{(\rho)}; e^{(\mu)}, x}
\Psi_{\rho, w_5+v}
-
\nonumber \\
& \qquad \tilde{U}_{v, w_5+e^{(\rho)}; e^{(\mu)}, x}
\Psi_{\rho, w_5+w}
\biggr)
+ \mbox{other terms}
\nonumber \\
& = \sum_{\rho=0}^d \sum_{y \in \Lambda_o}
e^{i k\cdot y}
\biggl(
e^{-i k \cdot v}
\tilde{U}_{w, y-v+e^{(\rho)}; e^{(\mu)}, x}
-
\nonumber \\
& \qquad
e^{-i k \cdot w}
\tilde{U}_{v, y-w+e^{(\rho)}; e^{(\mu)}, x}
\biggr)
\Psi_{\rho, y}
+ \mbox{other terms},
\end{align}
where ``other terms'' do not contribute to the matrix elements
$h_{\rm int}[\Psi_{\rho, y}, \Psi_{\mu, x, v, w}]$. Thus we find the
representation (\ref{eq:h_int[3]}). ~ \rule{0.8ex}{1.6ex}\smallskip
\section{Estimates of the Matrix Elements \label{sec:est_ME}}
In this section, we show the estimates of matrix elements and to prove
Lemma \ref{lemma:D[Psi]}. Before showing the details of estimates, we
list the results of estimates and give the proof of Lemma
\ref{lemma:D[Psi]}.
\subsection{Summary of Estimates}
Here, we obtain following bounds:
\begin{align}
\Re[h_{\rm int}[\Omega, \Omega]] \geq &
\frac{2 U}{\lambda^4}
\biggl[
\frac{d (|q|+|q|^{-1})}{2}-
\sum_{j=1}^d\cos(k \cdot 2e^{(j)} + \theta)
-
\frac{G_1}{\lambda^2}
\biggr],
\label{eq:bound_h_int[1]}
\end{align}
\begin{equation}
\Re[h_{\rm int}[\Psi_{0, x}, \Psi_{0, x}]] \geq
U\left( \chi[x \neq o] - \frac{G_2}{\lambda^2} \right),
\label{eq:bound_h_int[2]}
\end{equation}
\begin{equation}
|h_{\rm int}[\Psi_{0, x}, \Omega]|
\leq
\frac{U}{\alpha} \frac{G_3}{\lambda^4},
\label{eq:bound_h_int[3]}
\end{equation}
\begin{equation}
|h_{\rm int}[\Psi_{\mu, y, v, w}, \Omega]|
\leq \frac{U}{\alpha} \frac{G_4}{\lambda^2},
\label{eq:bound_h_int[4]}
\end{equation}
\begin{equation}
\sum_{\rho=0}^d \sum_{v_1 \in \Lambda_o}
\chi[(\rho, v_1) \neq (0, x)]
|h_{\rm int}[\Psi_{0, x}, \Psi_{\rho, v_1}]|
\leq
U \frac{G_5}{\lambda},
\label{eq:bound_h_int[5]}
\end{equation}
\begin{equation}
\sum_{\rho=0}^d \sum_{y_1 \in \Lambda^\prime}
\sum_{v_1, w_1 \in \Lambda_o}
\chi[v_1 \neq w_1]
|h_{\rm int}[\Psi_{0, x}, \Psi_{\rho, y_1, v_1, w_1}]|
\leq
U \frac{G_6}{\lambda},
\label{eq:bound_h_int[6]}
\end{equation}
and
\begin{align}
& \Re[h_{\rm int}[\Psi_{\mu, A}, \Psi_{\mu, A}]]
-
\nonumber \\
& \sum_{\rho=0}^d \sum_{B \subset \Lambda}
\chi[(\rho, B) \neq (\mu, A)]
|h_{\rm int}[\Psi_{\mu, A}, \Psi_{\rho, B}]|
\geq
U \left[ \chi[e^{(\mu)} \in A] - \frac{G_7}{\lambda} \right],
\label{eq:bound_h_int[7]}
\end{align}
where $x, v, w \in \Lambda_o$ with
$v \neq w$, $y \in \Lambda^\prime$ and $\mu = 0, 1, \cdots, d$.
$G_{l}$ $(l=1, 2, \cdots, 7)$ are finite constants which do not depend
on the system size.
\subsection{Proof of Lemma \ref{lemma:D[Psi]} \label{sec:estimates_of_D[Psi]}}
Here, we show the estimates of each $D[\Psi_{\mu, A}]$. We start to
evaluate cases that $\mu=0$ and $A\subset \Lambda_o$.
\paragraph{Estimates of $D[\Omega]$}
Since $\tilde{H}_{\rm hop} \Omega=0$, we can represent
\begin{align}
D[\Omega] = &\Re [h_{\rm int}[\Omega, \Omega]]
-\sum_{\Psi \in \ensuremath{{\cal B}}_k\backslash\{\Omega\}} |h_{\rm int}[\Omega, \Psi]|
\nonumber \\
= & \Re[h_{\rm int}[\Omega, \Omega]]
- \sum_{\rho=0}^d \sum_{v_1 \in \Lambda_o}
\chi[(\rho, v_1) \neq (0, o)]
|h_{\rm int}[\Omega, \Psi_{\rho, v_1}]|
- \nonumber \\
& \qquad \sum_{\rho=0}^d \sum_{y_1 \in \Lambda^\prime}
\sum_{v_1, w_1 \in \Lambda_o}
\chi[v_1 \neq w_1]
|h_{\rm int}[\Omega, \Psi_{\rho, y_1, v_1, w_1}]|.
\end{align}
Note that $\Omega = \Psi_{0, o}/\alpha$ and $\alpha > 0$.
Then we obtain (\ref{eq:D[Omega]}), from eqs. (\ref{eq:bound_h_int[1]}),
(\ref{eq:bound_h_int[5]}) and (\ref{eq:bound_h_int[6]}). ~ \rule{0.8ex}{1.6ex}\smallskip
\paragraph{Estimates of $D[\Psi_{0, x}]$}
$\tilde{H}_{\rm hop} \Psi_{0, x}$ also vanishes, then we have
\begin{align}
D[\Psi_{0, x}] = & \Re[h_{\rm int}[\Psi_{0, x}, \Psi_{0, x}]]
- \sum_{\rho=0}^d \sum_{v_1 \in \Lambda_o}
\chi[(\rho, v_1) \neq (0, x)]
\chi[(\rho, v_1) \neq (0, o)]
|h_{\rm int}[\Psi_{0, x}, \Psi_{\rho, v_1}]|
- \nonumber \\
& \qquad
|h_{\rm int}[\Psi_{0, x}, \Omega]|
-
\sum_{\rho=0}^d \sum_{y_1 \in \Lambda^\prime}
\sum_{v_1, w_1 \in \Lambda_o}
\chi[v_1 \neq w_1]
|h_{\rm int}[\Psi_{0, x}, \Psi_{\rho, y_1, v_1, w_1}]|.
\end{align}
Thus we obtain (\ref{eq:D[Psi_0x]}) from (\ref{eq:bound_h_int[2]}),
(\ref{eq:bound_h_int[3]}), (\ref{eq:bound_h_int[5]}) and (\ref{eq:bound_h_int[6]}).
~ \rule{0.8ex}{1.6ex}\smallskip
\paragraph{Estimates of Other Contributions}
We estimate $D[\Psi_{\mu, A}]$ with $\mu\neq 0$,
$A \cap \Lambda^\prime \neq \emptyset$ or both.
Here, we regard $\Psi_{\mu, x}$ and $\Psi_{\mu, y, v, w}$ as
$\Psi_{\mu, \Lambda_o\backslash\{x\}}$ and
$\Psi_{\mu, (\Lambda_o\backslash\{v, w\})\cup\{y\}}$
since the differences between them are only sign factor which is
irrelevant to absolute value of off-diagonal matrix elements.
Thus we have
\begin{align}
D[\Psi_{\mu, A}] = &
\Re[h_{\rm hop}[\Psi_{\mu, A}, \Psi_{\mu, A}]+
h_{\rm int}[\Psi_{\mu, A}, \Psi_{\mu, A}]]-
\nonumber \\
&
\sum_{\rho =0}^d \sum_{B \subset \Lambda}
\chi[(\rho, B)\neq(0, \Lambda_o\backslash\{o\}),(\mu, A)]
|h_{\rm int}[\Psi_{\mu, A}, \Psi_{\rho, B}]|
-|h_{\rm int}[\Psi_{\mu, A}, \Omega]|.
\end{align}
Since only $\Psi_{\mu, y, v, w}$ has non-vanishing
off-diagonal matrix elements related $\Omega$:
$h_{\rm int}[\Psi_{\mu, A}, \Omega]$ with
$A \cap \Lambda^\prime \neq \emptyset$, we have
\begin{equation}
h_{\rm int}[\Psi_{\mu, A}, \Omega] < \frac{U}{\alpha} \frac{G_4}{\lambda^2}
\end{equation}
from (\ref{eq:bound_h_int[4]}). Then we have
\begin{align}
D[\Psi_{\mu, A}] \geq & t\lambda^2
+ U \left[ \chi[e^{(\mu)} \in A] - \frac{G_7}{\lambda} \right]
- \frac{U}{\alpha} \frac{G_4}{\lambda^2}
\nonumber \\
& \geq t\lambda^2 - \frac{U}{\lambda}G_7
- \frac{U}{\alpha} \frac{G_4}{\lambda^2}
\end{align}
from (\ref{eq:h_hop}) and (\ref{eq:bound_h_int[7]}), where we use
\begin{equation}
h_{\rm hop}[\Psi_{\mu, A}, \Psi_{\mu, A}] =
t \lambda^2 (\chi[\mu\neq 0] + |A \cap \Lambda^\prime|) \geq t \lambda^2
\end{equation}
for the cases $\mu\neq 0$, $A\cap\Lambda^\prime \neq \emptyset$ or both.
Thus, we find the bounds for all contributions and we conclude
Lemma \ref{lemma:D[Psi]}. ~ \rule{0.8ex}{1.6ex}\smallskip
\subsection{Estimates of Matrix Elements}
Here, we estimate the matrix elements.
To estimate the matrix elements, it is convenient to introduce
$\varphi_{x, \sigma}^{(y)}$ by
$\varphi_{x, \sigma}^{(y)} = \tilde{\psi}_{x, \sigma}^{(y)} - \psi_{x, \sigma}^{(y)}$.
Note that $\varphi_{x, \sigma}^{(y)} = \tilde{\psi}_{x, \sigma}^{(y)}$
for $|x - y| \geq 1$. Lemma \ref{lemma:bound_sum_psi} and
\ref{lemma:bound_psi} give us the bound of
$\sum_{x}|\varphi_{x, \sigma}^{(y)}|$ and $|\varphi_{x, \sigma}^{(y)}|$.
Then, we obtain bounds of the matrix elements from representations of
each matrix element in terms of $\varphi_{x, \sigma}^{(y)}$.
\paragraph{Estimates of $\Re [h_{\rm int}[\Psi_{0, x}, \Psi_{0, x}]]$}
First, we estimate the diagonal part of the matrix elements.
From the representation (\ref{eq:h_int[1]}), we can write
\begin{align}
& \frac{h_{\rm int} [\Psi_{0, x}, \Psi_{0, x}]}{U}
=
\frac{1}{U} \sum_{v \in \Lambda_o}
\left(
\tilde{U}_{v, o; o, v}
- e^{i k \cdot v}
\tilde{U}_{x+v, o; v, x}
\right)
\nonumber \\
& =
\sum_{v \in \Lambda_o} \sum_{w \in \Lambda}
\Biggl[
(\tilde{\psi}_{w, \uparrow}^{(v)} \tilde{\psi}_{w, \downarrow}^{(o)})^\ast
\psi_{w, \downarrow}^{(o)} \psi_{w, \uparrow}^{(v)}
-
e^{i k \cdot v}
(\tilde{\psi}_{w, \uparrow}^{(x+v)} \tilde{\psi}_{w, \downarrow}^{(o)})^\ast
\psi_{w, \downarrow}^{(v)} \psi_{w, \uparrow}^{(x)}
\Biggr].
\end{align}
From the explicit representation of $\psi_{x, \sigma}^{(y)}$, we obtain
\begin{align}
& \frac{h_{\rm int} [\Psi_{0, x}, \Psi_{0, x}]}{U}
=
(\tilde{\psi}_{o, \uparrow}^{(o)} \tilde{\psi}_{o, \downarrow}^{(o)})^\ast
-
e^{i k \cdot x}
(\tilde{\psi}_{-x, \uparrow}^{(o)} \tilde{\psi}_{x,
\downarrow}^{(o)})^\ast
+
\nonumber \\
& \quad
\frac{1}{\lambda^2} \sum_{j=1}^d
\left[
\tilde{\psi}_{-e^{(j)}, \uparrow}^{(o)} \tilde{\psi}_{-e^{(j)}, \downarrow}^{(o)}
+\tilde{\psi}_{e^{(j)}, \uparrow}^{(o)} \tilde{\psi}_{e^{(j)}, \downarrow}^{(o)}
\right]^\ast
-
\nonumber \\
& \quad
\frac{e^{i k \cdot x}}{\lambda^2} \sum_{j=1}^d
\biggl[
\tilde{\psi}_{-x-e^{(j)}, \uparrow}^{(o)} \tilde{\psi}_{x-e^{(j)}, \downarrow}^{(o)}
+
\tilde{\psi}_{-x+e^{(j)}, \uparrow}^{(o)} \tilde{\psi}_{x+e^{(j)}, \downarrow}^{(o)}
\biggr]^\ast
+
\nonumber \\
&
\frac{1}{\lambda^2} \sum_{j=1}^{d}
\Biggl\{
q^{-1/2}
\left[
\tilde{\psi}_{e^{(j)}, \uparrow}^{(o)} \tilde{\psi}_{-e^{(j)}, \downarrow}^{(o)}
-
e^{-i k \cdot (x+2e^{(j)})}
\tilde{\psi}_{-x-e^{(j)}, \uparrow}^{(o)} \tilde{\psi}_{x+e^{(j)}, \downarrow}^{(o)}
\right]^\ast +
\nonumber \\
& \quad
q^{1/2}
\left[
\tilde{\psi}_{-e^{(j)}, \uparrow}^{(o)} \tilde{\psi}_{e^{(j)}, \downarrow}^{(o)}
-
e^{-i k \cdot (x-2e^{(j)})}
\tilde{\psi}_{-x+e^{(j)}, \uparrow}^{(o)} \tilde{\psi}_{x-e^{(j)}, \downarrow}^{(o)}
\right]^\ast
\Biggr\},
\label{eq:h_int[Psi_0xPsi_0x]}
\end{align}
where we use the relation
$\tilde{\psi}_{x, \sigma}^{(y+u)} = \tilde{\psi}_{x-u, \sigma}^{(y)}$
for $u \in \Lambda_o$.
For $x = o$, we obtain
\begin{align}
& \frac{h[\Psi_{0, o}, \Psi_{0, o}]}{U}
=
\frac{d (|q|+|q|^{-1})-2\sum_{j=1}^d\cos(k \cdot 2e^{(j)} + \theta)}{\lambda^4}
+
\nonumber \\
&
\frac{1}{\lambda^2}
\sum_{j=1}^d
\Biggl\{
\left[
\frac{q^{-1/4}}{\lambda}
(\varphi_{e^{(j), \uparrow}}^{(o)}+ \varphi_{-e^{(j)}, \downarrow}^{(o)})
+
\varphi_{e^{(j)}, \uparrow}^{(o)} \varphi_{-e^{(j)}, \downarrow}^{(o)}
\right]^\ast \times
\nonumber \\
& \qquad
(q^{-1/2} - q^{1/2} e^{-i k \cdot 2e^{(j)}})
+
\nonumber \\
&
\left[
\frac{q^{1/4}}{\lambda}
(\varphi_{e^{(j), \downarrow}}^{(o)}+ \varphi_{-e^{(j)}, \uparrow}^{(o)})
+\frac{1}{\lambda^2}
\varphi_{e^{(j)}, \downarrow}^{(o)} \varphi_{-e^{(j)}, \uparrow}^{(o)}
\right]^\ast \times
\nonumber \\
& \qquad
(q^{1/2} - q^{-1/2} e^{i k \cdot 2e^{(j)}})
\Biggr\}.
\end{align}
Lemma \ref{lemma:bound_psi} means
$|\varphi_{\pm e^{(j)}, \sigma}^{(o)}|\leq B_3 \lambda^{-3}$, then we
find the bound (\ref{eq:bound_h_int[1]}).~ \rule{0.8ex}{1.6ex}\smallskip
For $x \neq o$, we find (\ref{eq:bound_h_int[2]}) from
$|\tilde{\psi}_{o, \sigma}^{(o)}| \leq 1-O(\lambda^{-2})$ and
$|\tilde{\psi}_{x, \sigma}^{(o)}| = O(\lambda^{-2})$ for $x \neq o$. ~ \rule{0.8ex}{1.6ex}\smallskip
\paragraph{Estimates of $h_{\rm int}[\Psi_{0, y}, \Psi_{0, o}]$}
Next, we estimate the off-diagonal part of the matrix elements.
To obtain (\ref{eq:bound_h_int[3]}), we calculate the following matrix element
\begin{align}
h_{\rm int} & [\Psi_{0, y}, \Psi_{0, o}] =
\sum_{v \in \Lambda_o}
\left[
e^{i k \cdot y} \tilde{U}_{v, o; y, v}
- e^{i k \cdot v} \tilde{U}_{v, o; v, y}
\right]
\nonumber \\
= &
\frac{U}{\lambda^2} e^{i k \cdot y}
\sum_{j=1}^{d}
\Biggl[
(q^{-1/2} - q^{1/2} e^{-2i k \cdot e^{(j)}})
(\tilde{\psi}_{e^{(j)}, \uparrow}^{(o)} \tilde{\psi}_{y-e^{(j)}, \downarrow}^{(o)})^\ast
+ \nonumber \\
& \quad
(q^{1/2} - q^{-1/2} e^{2i k \cdot e^{(j)}})
(\tilde{\psi}_{-e^{(j)}, \uparrow}^{(o)} \tilde{\psi}_{y+e^{(j)}, \downarrow}^{(o)})^\ast
\Biggr].
\end{align}
Since $|\tilde{\psi}_{w}^{(o)}| = O(\lambda^{-1})$ for
$w \in \Lambda^\prime$, we find the bound (\ref{eq:bound_h_int[3]}).
\paragraph{Estimates of $h[\Psi_{\mu, x, v, w}, \Psi_{0, o}]$}
Using the following bound
\begin{align}
|h[\Psi_{\mu, y, v, w}, \Psi_{0, o}]|
= &
\frac{U}{\lambda^2}
\biggl|
\sum_{j=1}^d
\biggl[
q^{-1/2} \delta_{v, w+2e^{(j)}}
(\tilde{\psi}_{w+e^{(j)}}^{(o)} \tilde{\psi}_{w+e^{(j)}}^{(e^{(\mu)})})
+ \nonumber \\
& \qquad
q^{1/2} \delta_{v, w-2e^{(j)}}
(\tilde{\psi}_{w-e^{(j)}}^{(o)} \tilde{\psi}_{w-e^{(j)}}^{(e^{(\mu)})})
\biggr]
\biggr|
\nonumber \\
& \leq O(U \lambda^{-2}),
\end{align}
we obtain (\ref{eq:bound_h_int[4]}).
\paragraph{Estimates of $h[\Psi_{0, x}, \Psi_{\mu, y}]$ with $x \neq o$}
Using the following bound
\begin{align}
& \sum_{\rho=0}^d \sum_{y \in \Lambda_o}
|h_{\rm int}[\Psi_{0, x}, \Psi_{\rho, y}]|
\chi[(\rho, y)\neq(0, x)]
\nonumber \\
& =
U \sum_{\rho=0}^d \sum_{y \in \Lambda_o}
\left|
\sum_{v, w \in \Lambda}
(\tilde{\psi}_{w, \uparrow}^{(v)}
\tilde{\psi}_{w, \downarrow}^{(e^{(\rho)})})^\ast
(\delta_{v, x-y} \delta_{w, x-y}
-e^{i k \cdot v} \delta_{v, x+y} \delta_{w, x})
\right| \times
\nonumber \\
& \qquad
\chi[(\rho, y)\neq(0, x)]
+ O(U \lambda^{-2})
\nonumber \\
& =
U \sum_{\rho=0}^d \sum_{y \in \Lambda_o}
\left|
\tilde{\psi}_{o, \uparrow}^{(o)}
\tilde{\psi}_{x-y, \downarrow}^{(e^{(\rho)})}
-
e^{-i k \cdot (x+y)}
\tilde{\psi}_{x, \uparrow}^{(x+y)}
\tilde{\psi}_{x, \downarrow}^{(e^{(\rho)})}
\right|
\chi[(\rho, y)\neq(0, x)]
+ O(U \lambda^{-2})
\nonumber \\
& =
U \sum_{y \in \Lambda_o}
\left|
\tilde{\psi}_{o, \uparrow}^{(o)}
\tilde{\psi}_{x-y, \downarrow}^{(o)}
-
e^{-i k \cdot (x+y)}
\tilde{\psi}_{x, \uparrow}^{(x+y)}
\tilde{\psi}_{x, \downarrow}^{(o)}
\right|
\chi[(\rho, y)\neq(0, x)]
+ O(U \lambda^{-1})
\nonumber \\
& =
U \sum_{y \in \Lambda_o}
\left|
\tilde{\psi}_{o, \uparrow}^{(o)}
\tilde{\psi}_{x-y, \downarrow}^{(o)}
-
e^{-i k \cdot (x+y)}
\tilde{\psi}_{x, \uparrow}^{(x+y)}
\tilde{\psi}_{x, \downarrow}^{(o)}
\right|
-
\left|
\tilde{\psi}_{o, \uparrow}^{(o)}
\tilde{\psi}_{o, \downarrow}^{(o)}
-
e^{-2 i k \cdot x}
\tilde{\psi}_{x, \uparrow}^{(2x)}
\tilde{\psi}_{x, \downarrow}^{(o)}
\right|
+ O(U \lambda^{-1})
\nonumber \\
& \leq
U \sum_{y \in \Lambda_o}
\left(
\left|
\tilde{\psi}_{o, \uparrow}^{(o)}
\tilde{\psi}_{x-y, \downarrow}^{(o)}
\right|
+
\left|
\tilde{\psi}_{x, \uparrow}^{(x+y)}
\tilde{\psi}_{x, \downarrow}^{(o)}
\right|
\right)
-
\left|
\tilde{\psi}_{o, \uparrow}^{(o)}
\tilde{\psi}_{o, \downarrow}^{(o)}
\right|
+
\left|
\tilde{\psi}_{x, \uparrow}^{(2x)}
\tilde{\psi}_{x, \downarrow}^{(o)}
\right|
+ O(U \lambda^{-1})
\nonumber \\
&
\leq O(U \lambda^{-1}).
\end{align}
for $x \neq o$, and using another bound
\begin{align}
& \sum_{\rho=0}^d \sum_{y \in \Lambda_o}
|h_{\rm int}[\Psi_{0, o}, \Psi_{\rho, y}]|
\chi[(\rho, y)\neq(0, o)]
\nonumber \\
& =
U \sum_{y \in \Lambda_o}
\left|
\tilde{\psi}_{o, \uparrow}^{(o)}
\tilde{\psi}_{-y, \downarrow}^{(o)}
-
e^{-i k \cdot y}
\tilde{\psi}_{o, \uparrow}^{(y)}
\tilde{\psi}_{o, \downarrow}^{(o)}
\right|
+ O(\lambda^{-1})
\nonumber \\
& \leq
U \sum_{y \in \Lambda_o}
\left(
\left|
\tilde{\psi}_{o, \uparrow}^{(o)}
\tilde{\psi}_{-y, \downarrow}^{(o)}
\right|
+
\left|
\tilde{\psi}_{o, \uparrow}^{(y)}
\tilde{\psi}_{o, \downarrow}^{(o)}
\right|
\right)
\chi[y \neq o]
+ O(U \lambda^{-1})
\nonumber \\
& =
U \sum_{y \in \Lambda_o}
\left(
\left|
\tilde{\psi}_{o, \uparrow}^{(o)}
\tilde{\psi}_{-y, \downarrow}^{(o)}
\right|
+
\left|
\tilde{\psi}_{o, \uparrow}^{(y)}
\tilde{\psi}_{o, \downarrow}^{(o)}
\right|
\right)
- 2 \left|
\tilde{\psi}_{o, \uparrow}^{(o)}
\tilde{\psi}_{o, \downarrow}^{(o)}
\right|
+ O(U \lambda^{-1})
\nonumber \\
&
\leq O(U \lambda^{-1}),
\end{align}
for $x=o$, we obtain (\ref{eq:bound_h_int[5]}).
\paragraph{Estimates of $h[\Psi_{0, x}, \Psi_{\mu, y, v, w}]$}
Using the following bound
\begin{align}
& \sum_{\mu=0}^d \sum_{y \in \Lambda^\prime}
\sum_{v, w \in \Lambda_o}
|h_{\rm int}[\Psi_{0, x}, \Psi_{\mu, y, v, w}]|
\nonumber \\
& \leq
U \sum_{j=1}^{d}
\sum_{y \in \Lambda_j} \sum_{v, w \in \Lambda_o}
\left|
e^{i k \cdot v} \tilde{\psi}_{e^{(j)}, \uparrow}^{(w)}
\tilde{\psi}_{e^{(j)}, \downarrow}^{(x-v)}
+
e^{i k \cdot w} \tilde{\psi}_{e^{(j)}, \uparrow}^{(v)}
\tilde{\psi}_{e^{(j)}, \downarrow}^{(x-w)}
\right| +
O(U\lambda^{-1})
\nonumber \\
& \leq
U \sum_{j=1}^{d}
\sum_{y \in \Lambda_j} \sum_{v, w \in \Lambda_o}
\left(
|\tilde{\psi}_{e^{(j)}, \uparrow}^{(w)}|
|\tilde{\psi}_{e^{(j)}, \downarrow}^{(x-v)}|
+
|\tilde{\psi}_{e^{(j)}, \uparrow}^{(v)}|
|\tilde{\psi}_{e^{(j)}, \downarrow}^{(x-w)}|
\right)
+ O(U\lambda^{-1})
\nonumber \\
& \leq O(U\lambda^{-1}),
\end{align}
we obtain (\ref{eq:bound_h_int[6]}).
\paragraph{Estimates of Other Matrix Elements}
To obtain (\ref{eq:bound_h_int[7]}), we calculate the
matrix elements of $H_{\rm int}$.
\begin{align}
& H_{\rm int} \Psi_{\mu, A}
=
\sum_{w_1, w_2, w_3, w_4 \in \Lambda} \tilde{U}_{w_1, w_2; w_3, w_4}
a_{w_1, \uparrow}^\dagger a_{w_2, \downarrow}^\dagger
b_{w_3, \downarrow} b_{w_4, \uparrow}
\times
\nonumber \\
& \qquad
\sum_{w \in \Lambda_o} e^{i k \cdot w}
a_{w+e^{(\mu)}, \downarrow}^\dagger
\left(
\prod_{v \in A} a_{v+w, \uparrow}^\dagger
\right)
\Psi_{\rm vac}
\nonumber \\
& =
\sum_{w \in \Lambda_o} \sum_{w_1, w_2, w_3, w_4 \in \Lambda}
e^{i k \cdot w}
\tilde{U}_{w_1, w_2; w_3, w_4}
a_{w_2, \downarrow}^\dagger
b_{w_3, \downarrow}
a_{w+e^{(\mu)}, \downarrow}^\dagger
a_{w_1, \uparrow}^\dagger
b_{w_4, \uparrow}
\left(
\prod_{v \in A} a_{v+w, \uparrow}^\dagger
\right)
\Psi_{\rm vac}
\nonumber \\
& =
\sum_{w \in \Lambda_o} \sum_{w_1, w_2, w_4 \in \Lambda}
e^{i k \cdot w}
\tilde{U}_{w_1, w_2; w+e^{(\mu)}, w_4}
\chi[w_4 \in A+w, w_1 \notin (A+w)\backslash \{ w_4 \}] \times
\nonumber \\
& \qquad {\rm sgn}[A+w, w_1, w_4]
a_{w_2, \downarrow}^\dagger
\left(
\prod_{v \in ((A+w)\backslash \{ w_4 \}) \cup \{ w_1 \} } a_{v, \uparrow}^\dagger
\right)
\Psi_{\rm vac}
\nonumber
\end{align}
Here, we make the change of the variables $w_2 \rightarrow y+e^{(\rho)}$,
$w \rightarrow w+y$, $w_1 \rightarrow w_1+y$ and
$w_4 \rightarrow w_4+y$. Then we obtain
\begin{align}
= &
\sum_{\rho = 0}^{d} \sum_{w, y \in \Lambda_o} \sum_{w_1, w_4 \in \Lambda}
e^{i k \cdot (w+y)}
\tilde{U}_{w_1+y, e^{(\rho)}+y; w+y+e^{(\mu)}, w_4+y} \times
\nonumber \\
& \quad \chi[w_4+y \in A+w+y,
w_1+y \notin (A+w+y)\backslash \{ w_4+y \}] \times
\nonumber \\
& \quad {\rm sgn}[A+w+y, w_1+y, w_4+y] \times
\nonumber \\
& \quad
a_{e^{(\rho)+y}, \downarrow}^\dagger
\left(
\prod_{v \in ((A+w)\backslash \{ w_4 \}) \cup \{ w_1 \}+y} a_{v, \uparrow}^\dagger
\right)
\Psi_{\rm vac}
\nonumber \\
= &
\sum_{\rho = 0}^{d} \sum_{w \in \Lambda_o} \sum_{w_1, w_4 \in \Lambda}
e^{i k \cdot w}
\tilde{U}_{w_1, e^{(\rho)}; w+e^{(\mu)}, w_4} \times
\nonumber \\
& \quad
\chi[w_4 \in A+w, w_1 \notin (A+w)\backslash \{ w_4 \}]
{\rm sgn}[A+w, w_1, w_4] \times
\nonumber \\
& \quad
\sum_{y \in \Lambda_o} e^{i k \cdot y}
a_{e^{(\rho)+y}, \downarrow}^\dagger
\left(
\prod_{v \in ((A+w)\backslash \{ w_4 \}) \cup \{ w_1 \}+y} a_{v, \uparrow}^\dagger
\right)
\Psi_{\rm vac}
\nonumber \\
= &
\sum_{\rho = 0}^{d} \sum_{w \in \Lambda_o} \sum_{w_1, w_4 \in \Lambda}
e^{i k \cdot w}
\tilde{U}_{w_1, e^{(\rho)}; w+e^{(\mu)}, w_4} \times
\nonumber \\
& \quad \chi[w_4 \in A+w, w_1 \notin (A+w)\backslash \{ w_4 \}]
{\rm sgn}[A+w, w_1, w_4] \times
\nonumber \\
& \quad
\Psi_{\rho, ((A+w)\backslash \{ w_4 \}) \cup \{ w_1 \}}.
\end{align}
Thus, we find
\begin{align}
h_{\rm int}
[\Psi_{\rho, ((A+w)\backslash \{ w_4 \}) \cup \{ w_1 \}},
\Psi_{\mu, A}]
= e^{i k \cdot w}
\tilde{U}_{w_1, e^{(\rho)}; w+e^{(\mu)}, w_4}
\chi[w_4 \in A+w, w_1 \notin (A+w)\backslash \{ w_4 \}]
\end{align}
Here, we neglect the sign of the matrix element,
since it is irrelevant to obtain the bounds. If we
define $A^\prime$ by $A^\prime = ((A+w)\backslash \{ w_4 \}) \cup \{ w_1 \}$, then
we obtain its solution $A=(A^\prime\backslash\{w_1\})\cup\{w_4\}-w$.
Thus, we obtain
\begin{align}
& h_{\rm int}
[\Psi_{\rho, A},
\Psi_{\mu, (A\backslash\{w_1\})\cup\{w_4\}-w}]
= e^{i k \cdot w}
\tilde{U}_{w_1, e^{(\rho)}; w+e^{(\mu)}, w_4}
\chi[w_1 \in A, w_4 \notin A\backslash \{ w_1 \}].
\end{align}
If $w_1=w_4$ and $w=o$, then $A=(A\backslash\{w_1\})\cup\{w_4\}-w$.
Since other $w_1, w_4$ and $w$ makes
$(A\backslash\{w_1\})\cup\{w_4\}-w=A$, we find
\begin{align}
& \Re[h_{\rm int}[\Psi_{\rho, A}, \Psi_{\rho, A}]]
- \sum_{\Phi \in \ensuremath{{\cal B}}\backslash\{\Psi_{\rho, A}\}}
|h_{\rm int} [\Psi_{\rho, A}, \Phi]|
\nonumber \\
& \geq
\Re\left[ \sum_{w_1 \in A}
\tilde{U}_{w_1, e^{(\rho)}; e^{(\rho)}, w_1}\right]
-
\sum_{w_1 \in A}
\sum_{w \in \Lambda} \sum_{w_4 \in (\Lambda\backslash A)\cup\{ w_1 \}}
|\tilde{U}_{w_1, e^{(\rho)}; w, w_4}|
\chi[(w, w_1)\neq(e^{(\rho)}, w_4)].
\label{eq:D[general-pre]}
\end{align}
To estimate the first term in (\ref{eq:D[general-pre]}), we use
\begin{align}
\Re\left[ \sum_{w_1 \in A} \tilde{U}_{w_1, e^{(\rho)}; e^{(\rho)}, w_1} \right]
\geq & U \Re
\left[ \sum_{w_1 \in A}
( \tilde{\psi}_{e^{(\rho)}, \uparrow}^{(w_1)}
\tilde{\psi}_{e^{(\rho)}, \downarrow}^{(e^{(\rho)})})^\ast
\right]
- O(U \lambda^{-2})
\nonumber \\
\geq & U \chi[e^{(\rho)} \in A] - O(U \lambda^{-1}).
\label{eq:D[general-R]}
\end{align}
We estimate the second term in (\ref{eq:D[general-pre]}). From the
explicit form of $\psi_{x, \sigma}^{(y)}$, we obtain
\begin{align}
&
\sum_{w_1 \in A}
\sum_{w \in \Lambda} \sum_{w_4 \in (\Lambda\backslash A)\cup\{ w_1 \}}
|\tilde{U}_{w_1, e^{(\rho)}; w, w_4}|
\chi[(w, w_1)\neq(e^{(\rho)},w_4)]
\nonumber \\
& \leq U
\sum_{w_1 \in A}
\sum_{w_4 \in (\Lambda\backslash A)\cup\{ w_1 \}}
|\tilde{\psi}_{w_4, \uparrow}^{(w_1)}
\tilde{\psi}_{w_4, \downarrow}^{(e^{(\rho)})}|
\chi[w_4, w_1\neq e^{(\rho)}]
+
O(U \lambda^{-2}).
\label{eq:tmp1}
\end{align}
Since $|\tilde{\psi}_{w_4, \uparrow}^{(w_1)}| \leq O(\lambda^{-1})$ for
$w_4 \neq w_1$, then (\ref{eq:tmp1}) is bounded by
\begin{equation}
\leq U
\sum_{w_1 \in A}
|\tilde{\psi}_{w_1, \uparrow}^{(w_1)}
\tilde{\psi}_{w_1, \downarrow}^{(e^{(\rho)})}|
\chi[w_1\neq e^{(\rho)}] + O(U \lambda^{-1}).
\label{eq:tmp2}
\end{equation}
Since $|\tilde{\psi}_{w_1, \uparrow}^{(e^{(\rho)})}| \leq O(\lambda^{-1})$ for
$w_1 \neq e^{(\rho)}$, we find the bound
\begin{align}
& \sum_{w_1 \in A}
\sum_{w \in \Lambda} \sum_{w_4 \in (\Lambda\backslash A)\cup\{ w_1 \}}
|\tilde{U}_{w_1, e^{(\rho)}; w, w_4}|
\chi[\overline{w=e^{(\rho)}, w_1=w_4}]
\nonumber \\
& \leq O(U \lambda^{-1}).
\label{eq:D[general-A]}
\end{align}
From (\ref{eq:D[general-R]}) and (\ref{eq:D[general-A]}), we find the
bound (\ref{eq:bound_h_int[7]}).
\section{Proof of Theorem \ref{th:SW_UB} \label{sec:SW_UB}}
In this section, we show the proof of the upper bound of spin-wave
energy. The proof is given by the standard variational approach.
If we can show
\begin{align}
\frac{(\Psi_{0,o}, H \Psi_{0,o})}{\|\Psi_{0,o}\|^2} \leq
\frac{2U}{\lambda^4}
\biggl[ &
\frac{d(|q|+|q|^{-1})}{2}-
\sum_{j=1}^{d} \cos \left( 2k\cdot e^{(j)} +\theta \right)+
\frac{const}{\lambda^2}
\biggr],
\end{align}
this concludes the Theorem \ref{th:SW_UB}. Here we evaluate
this quantity.
Since $H_{\rm hop} \Psi_{0,o}=0$, we obtain
\begin{align}
& \frac{(\Psi_{0,o}, H \Psi_{0,o})}{\|\Psi_{0,o}\|^2} =
h_{\rm int}[\Psi_{0,o}, \Psi_{0,o}] +
\nonumber \\
& \sum_{\mu=0}^d \sum_{x \in \Lambda_o}
\chi[(\mu, x) \neq (0,o)] h_{\rm int}[\Psi_{\mu, x}, \Psi_{0,o}]
\frac{(\Psi_{0,o}, \Psi_{\mu, x})}{\|\Psi_{0,o}\|^2} +
\nonumber \\
& \sum_{\mu=0}^d \sum_{y \in\Lambda^\prime}
\sum_{v, w \in \Lambda_o} \chi[v \neq w]
h_{\rm int}[\Psi_{u, y, v, w}, \Psi_{0,o}]
\frac{(\Psi_{0,o}, \Psi_{\mu, y, v, w})}{\|\Psi_{o,0}\|^2}.
\end{align}
Note $(\Psi_{0,o}, \Psi_{j, x})=0$ for $j=1, 2, \cdots, d$ because of the
representation of $a_{y, \sigma}$ with $y \in\Lambda^\prime$ in terms of
its dual
$$a_{y,\sigma}=\sum_{y^\prime \in \Lambda^\prime}C_{y, y^\prime;\sigma}b_{y^\prime,\sigma},$$
where $C_{y^\prime, y;\sigma}$ is a complex coefficient.
We also find $(\Psi_{0,o}, \Psi_{\mu, y, v, w})=0$ with the same
argument. Thus, we obtain
\begin{align}
\frac{(\Psi_{0,o}, H \Psi_{0,o})}{\|\Psi_{0,o}\|^2}
= h_{\rm int}[\Psi_{0,o}, \Psi_{0,o}] +
\sum_{x \in \Lambda_o\setminus\{o\}}
h_{\rm int}[\Psi_{0, x}, \Psi_{0,o}]
\frac{(\Psi_{0,o}, \Psi_{0, x})}{\|\Psi_{0,o}\|^2}.
\end{align}
We already have the bounds of the matrix elements. We concentrate to
estimate the inner product between $\Psi_{0,o}$ and $\Psi_{0, x}$.
We represent $(\Psi_{0, o}, \Psi_{0, x})$
\begin{align}
(\Psi_{0,o}, \Psi_{0,x})=\sum_{v, w \in \Lambda_o}
e^{-i k \cdot (v-w)}
(
a_{v, \downarrow}^\dagger b_{v,\uparrow} \Psi_{\uparrow},
a_{w, \downarrow}^\dagger b_{w+x, \uparrow} \Psi_{\uparrow}
)
\nonumber \\
=
\sum_{v, w \in \Lambda_o}
e^{-i k \cdot (v-w)}
\{b_{w+x,\uparrow}^\dagger, b_{v, \uparrow}\}
\{a_{v, \downarrow}, a_{w,\downarrow}^\dagger\}
\|\Psi_{\uparrow}\|^2
\end{align}
Using the relations
\begin{equation}
\{a_{x, \sigma}, a_{y, \sigma}^\dagger\}
= \sum_{w \in \Lambda} (\psi_{w, \sigma}^{(x)})^\ast
\psi_{w,\sigma}^{(y)}
\mbox{ and }
\{b_{x, \sigma}^\dagger, b_{y, \sigma}\}
= \sum_{w \in \Lambda} \tilde{\psi}_{w, \sigma}^{(x)}
(\tilde{\psi}_{w,\sigma}^{(y)})^\ast
\end{equation}
and the explicit representation of $\psi_{x, \sigma}^{(y)}$, we obtain
\begin{align}
& (\Psi_{0,o}, \Psi_{0,x})=L^d \sum_{w \in \Lambda}
\biggl[
\frac{\lambda^2+d(|q|^{1/2}+|q|^{-1/2})}{\lambda^2}
\tilde{\psi}_{w, \uparrow}^{(x)}(\tilde{\psi}_{w,\uparrow}^{(o)})^\ast
+
\nonumber \\
& \frac{1}{\lambda^2}\sum_{j=1}^{d}
\biggl(
e^{-i k\cdot 2e^{(j)}+i \theta/2}
\tilde{\psi}_{w, \uparrow}^{(x)}(\tilde{\psi}_{w,\uparrow}^{(2e^{(j)})})^\ast
+
e^{i k\cdot 2e^{(j)}-i \theta/2}
\tilde{\psi}_{w, \uparrow}^{(x)}(\tilde{\psi}_{w,\uparrow}^{(-2e^{(j)})})^\ast
\biggr)
\biggr] \|\Phi_\uparrow\|^2.
\end{align}
To obtain this, we have also used the translational invariance of
$\tilde{\psi}_{x, \sigma}^{(y)}$:
$\tilde{\psi}_{x, \sigma}^{(y)}=\tilde{\psi}_{x+w, \sigma}^{(y+w)}$ with
$w \in \Lambda_o$.
Thus we have
\begin{align}
\left| \sum_{x \in \Lambda_o\backslash\{o\}} h[\Psi_{0,x}, \Psi_{0,o}]
(\Psi_{0,o}, \Psi_{0,x}) \right|
\leq L^d \frac{U}{\lambda^4} G_3 \sum_{x \in \Lambda_o\backslash\{o\}}
|(\Psi_{0,o}, \Psi_{0,x})|
\leq L^d \frac{U}{\lambda^6} K_1 \|\Psi_\uparrow\|^2,
\end{align}
where we use (\ref{eq:bound_h_int[3]}) and Lemma \ref{lemma:bound_sum_psi}.
The norm of $\Psi_{0, o}$ can be estimated as
\begin{align}
&
\|\Psi_{0,o}\|^2 = L^d \sum_{w \in \Lambda}
\biggl[
\frac{\lambda^2+d(|q|^{1/2}+|q|^{-1/2})}{\lambda^2}
\tilde{\psi}_{w, \uparrow}^{(o)}(\tilde{\psi}_{w,\uparrow}^{(o)})^\ast
+
\nonumber \\
&
\frac{1}{\lambda^2} \sum_{j=1}^d
\biggl(
e^{-i k\cdot 2e^{(j)}+i\theta/2}
\tilde{\psi}_{w, \uparrow}^{(o)}(\tilde{\psi}_{w,\uparrow}^{(2e^{(j)})})^\ast
-
e^{i k\cdot 2e^{(j)}-i\theta/2}
\tilde{\psi}_{w, \uparrow}^{(o)}(\tilde{\psi}_{w,\uparrow}^{(-2e^{(j)})})^\ast
\biggr)
\biggr] \|\Phi_{\uparrow}\|^2
\geq L^d K_2 \|\Psi_\uparrow\|.
\end{align}
Then we have
\begin{align}
\frac{(\Psi_{0,o}, H \Psi_{0,o})}{\|\Psi_{0,o}\|^2}
\leq & |h[\Psi_{0,o}, \Psi_{0,o}]| + \frac{U}{\lambda^6} \frac{K_1}{K_2}
\nonumber \\
\leq &
\frac{2U}{\lambda^4}
\biggl[
\frac{d(|q|+|q|^{-1})}{2} -
\sum_{j=1}^d \cos (k \cdot 2e^{(j)}+\theta)
+\frac{K_1/K_2}{\lambda^2}
\biggr].
\end{align}
This completes the proof. ~ \rule{0.8ex}{1.6ex}\smallskip
\paragraph{Acknowledgments}
I would like to thank T. Koma, M. Oshikawa, A. Tanaka and H. Tasaki for
helpful suggestions and great encouragements. I also thank to C. Itoi
for carefully reading the manuscript and kind suggestions.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,488 |
_You Are Destined to Be Together Forever_ is a work of fiction. Names, characters, places, and incidents either are products of the author's imagination or are used fictitiously. Any resemblance to actual events, locales, or persons, living or dead, is entirely coincidental.
A Bantam Books eBook Original
Copyright © 2014 by Dean Koontz
All rights reserved.
Published in the United States by Bantam Books, an imprint of Random House, a division of Random House LLC, a Penguin Random House Company, New York.
BANTAM BOOKS and the HOUSE colophon are registered trademarks of Random House LLC.
eBook ISBN 9780804180931
Cover design: Scott Biel
Cover images: (man) Claudio Marinesco; (woman) © Stephen Carroll/Trevillion Images
www.bantamdell.com
v4.0_r1
ep
# Contents
Cover
Title Page
Copyright
Chapter One
Chapter Two
Chapter Three
Chapter Four
Chapter Five
Chapter Six
By Dean Koontz
About the Author
# One
My four-hundred-pound friend and mentor, P. Oswald Boone, the famous mystery writer, says that although he has in his refrigerator cheeses older than I am, sixteen is not too young to write worthwhile prose, as long as I write about what I know, which in my case means a girl named Stormy Llewellyn, the ghost of Elvis Presley, brutal murder, and revenge from beyond the grave.
In late May, the annual spring fair had come to Pico Mundo, California, where I had lived all my life, on the edge of the Mojave Desert. On Friday, I borrowed Terri Stambaugh's car so that I could take Stormy to the carnival that had set up its many attractions on the fairground midway. Terri was my boss, the owner of the Pico Mundo Grille, where I worked as a fry cook twenty-four hours each week during the school year, forty hours each week during the summer.
I couldn't borrow a car from my father, because he had walked out on us years earlier. I couldn't borrow a car from my mother, because such a request would stress her. When stressed, Mother made veiled references to suicide, and sometimes she retrieved the pistol from the nightstand drawer in her bedroom, caressing its contours with more affection than she'd ever shown me. When I was a child, which was a shorter period of time for me than it was for most people, my mother sometimes implied that she might take me with her if she decided to consummate her romance with Death. My mother is beautiful, and to anyone who never lived with her, she seems to be a genteel and pleasant lady, if slightly aloof. I moved out when I turned sixteen, into a tiny apartment above a garage, which I pay for by mowing the lawn and doing general maintenance chores for my landlady.
At 4:30, Stormy met me behind the Grille, where Terri's Mustang was parked. "Hey, odd one. You look better than a stack of your best pancakes."
"I take that as a compliment."
"As it was intended."
We kissed. It wasn't a wild, passionate kiss, but tender and sweet. In the matter of passion, she wanted to go slow, and I wanted whatever she wanted.
She had been orphaned at seven, when her parents died in a plane crash. After that, for a time, she had been an abused child, a victim of her adoptive parents. In spite of all that she had suffered, the world had not broken her.
With jet-black hair, a Mediterranean complexion, and mysterious dark eyes, she was straight out of a dream about an Egyptian queen regarded as a demigoddess by her subjects, which is how I would have regarded her if she wouldn't have punched me for daring to put her on a pedestal. Stormy Llewellyn didn't want a pedestal. She wanted only someone who would look her straight in the eyes and always tell her the truth.
As I opened the passenger door of the Mustang for Stormy, I said, "Mr. Presley is in the backseat."
"Elvis?"
"I thought you should know. Though he can't speak, he can hear whatever we say."
Stormy got into the car and looked behind her seat, but of course she couldn't see the King of Rock 'n' Roll because he had been dead for years, in fact, for decades, and it was only his spirit that was going with us to the carnival.
Most people leave the world when their bodies die. Some spirits linger, reluctant to cross over to the Other Side. They come to me because they know that I can see them and that I will help them if I can. Sometimes they want their murders avenged. Mr. Presley wasn't murdered—except by numerous movie critics when he was alive. But he, like some others, seemed to be afraid of what might await him in the Great Beyond.
He had been hanging out with me for some months, though he made no effort to explain himself. The dead don't talk. I don't know why. But they have ways of conveying their concerns and desires. Mr. Presley seemed content just to keep me company.
As I got behind the wheel of the Mustang, Stormy said, "What's he wearing this time?"
"That ridiculous Arab getup from _Harum Scarum._ Sorry, sir, but it is ridiculous."
All other lingering spirits that I had known were limited in their wardrobe to the clothes they had been wearing when they died. Mr. Presley, however, was capable of manifesting in anything he had worn during his storied career. He tended to avoid the flashy Vegas costumes that made him look like a less-well-coiffed Liberace.
Glancing over my shoulder, I saw that he had in an instant changed from the _Harum Scarum_ garb to the flamenco-dancer costume that he had worn in _Fun in Acapulco_ : tight black tuxedo pants, a two-thirds-length black jacket, and a ruffled white shirt with an elaborate black foulard at the throat.
"Better," I said.
He made a gun of his thumb and forefinger, pointed it at me, and winked.
You might wonder why Stormy Llewellyn would believe I can see spirits. She's a practical girl with a commonsense plan for her future. She works part-time behind the counter at Burke & Bailey's in the mall, scooping ice cream and mixing milkshakes. She intends to be an ice-cream entrepreneur with her own shop by the time she's twenty-four and to build a chain of six stores by the time she's thirty. She is already saving half her wages toward the financing of that plan. Stormy is not the kind of sixteen-year-old girl who believes everything—or anything—I say just because I'm her guy.
_I'm her guy._ I can't tell you how deeply it pleases me to write those three words. My father's a mess, my mother's psychotic, I'm a fry cook without his own car, a geek who lives in one room and a bath above a garage, and I see dead people and worse. She's the coolest girl in school, and every guy who sees her stands awestruck, with his tongue hanging out. Nevertheless, _I'm her guy,_ me and no one else, maybe because I'm able to keep my tongue in my mouth when I look at her and because I can make her laugh.
Anyway, she believes in my paranormal abilities because she's had some experiences in my presence that confirmed them. For example, she was with me when an angry poltergeist destroyed my brand-new stereo system for no good reason. And Wyatt Porter, chief of police, has vouched for me, because I have shared my prophetic dreams with him and have given him other paranormally obtained information that has helped him close cases. Only the chief and his wife, Stormy, Ozzie Boone, and Terri Stambaugh know about my sixth sense, and they all protect me from discovery by others.
Now, as I drove the Mustang along the alleyway behind the Pico Mundo Grille, Stormy said, "Maybe Elvis doesn't want to leave this world because so many people loved him here. The day of his funeral, over fifty thousand gathered at the gates to Graceland."
"Guess you've been talking to Terri," I said. My boss at the Grille was an obsessive Elvis fan, though she was fifteen when he died, and he was even then long past his prime.
"The lines waiting to view him in his casket totaled two miles," Stormy said.
Mr. Presley had come forward from the backseat, leaning over the console to see Stormy's face.
She said, "They needed one hundred vans and four hours to move all the flowers from the funeral at Graceland to the cemetery for the graveside service."
As I braked at the end of the alley, I glanced at Mr. Presley, and he looked at me, and in his spirit eyes were spirit tears. He had always treated his fans with respect until the last few years, when his drug use and health problems prevented him from giving them the high-quality performances for which they had paid.
We rode in silence for a block or so, and then Stormy said, "Eighty cops and forty sheriff's deputies weren't enough to control the grieving crowd. The governor had to call up thirty National Guardsmen to assist them."
Mr. Presley slipped once more into a corner of the backseat, gazing out a side window, clearly distraught.
At a red traffic light, I stopped and glanced at Stormy, aware that she was up to something with all those funeral details.
She met my eyes but spoke loud enough to be sure that my other passenger heard her. "Maybe he doesn't want to leave this world because so many people loved him here," she said again, but then she added, " _or_...or maybe he's embarrassed by how his life spun out of control, and he's afraid to cross over and face those fans who adored him but saw how he spiraled down in the end. It can be tough to be idolized by millions and even tougher if you can't live up to the image they have of you."
I wasn't surprised by her bluntness. She was, after all, Stormy Llewellyn. _Llewellyn_ is a variant of _Leo,_ which comes from the Greek _leon,_ meaning "lion" and implying abundant strength of character and will and physique, all of which applied to her. And you know what _stormy_ means. Although not surprised, I did feel some sympathy for Mr. Presley, and I said, "That was a little hard."
"Tough love," she said.
And of course what she'd told him was at least as much love as it was tough. He had died in 1977. Rare is the spirit who lingers here so long after death. He needed to understand and accept the reason that he had not yet moved on; and whatever words were required to bring him to his senses, even if tough, would be a kindness.
Instead of responding to what Stormy said, Mr. Presley did a little mime routine, first boring vigorously in his nose with one finger, then pretending to reel from his nostril a few yards of snot.
"How's he taking it?" Stormy asked.
"Immaturely."
Mr. Presley rolled the imaginary snot into a wad the size of a baseball and threw it at me.
A horn honked behind us. The light had changed. Nevertheless, I delayed long enough to pretend to catch the hideous but nonexistent ball of mucus and throw it over my shoulder, back at him, before I accelerated across the intersection.
"What was that about?" Stormy asked.
"Snotball."
"Again?"
"He always was a big child at heart."
You might think that the presence of the lingering dead would make of my life a solemn if not even sorrowful affair, grim and dark and shot through with fear. It _is_ at times grim and dark and shot through with fear—when it's not silly, amusing, and shot through with foolishness.
We had traveled a few miles and were in that area where Maricopa Lane passed from suburban neighborhoods into a semirural landscape, when a man with a meat cleaver embedded in his neck came out of nowhere and dashed in front of the car. Even if I had been driving the Batmobile, with its ability to stop on a dime and give six cents in change, I couldn't have avoided hitting the guy. Anyway, braking didn't matter, which I knew because of Stormy's failure to cry out in alarm. I drove through the spirit as he pointed at me. With the nimble grace of the lingering dead, he passed through the front of the car, boarding the vehicle at fifty miles per hour, folded to a sitting position, and settled into the backseat, beside Mr. Presley, the laws of physics no longer applicable to him.
As I slowed and pulled to the shoulder of the road, Stormy said, "What's up?"
"A dead guy just came aboard."
"What dead guy?"
"I don't know. Never saw him before. Covered in blood, meat cleaver in his neck, looks a little excited."
"Maybe he's an Elvis fan."
I parked along the side of the road and turned in my seat to confront our new passenger. He appeared to be about forty. Shaved head. Blue eyes. No beard. No tattoos. He wore khakis and a red-and-white checkered shirt that looked as though it had been made from the tablecloth in an Italian restaurant, but the stains all over it weren't spaghetti sauce.
"Tell me," Stormy said, because she couldn't see the new guy any more than she could see Mr. Presley.
"Well," I said, "his partially severed head wobbles like a bobblehead doll with a horizontal-motion feature. His eyes are so wide they look as lidless as fish eyes, and he's screaming at me as if he hasn't realized yet that the dead can't be heard, even by me."
"Vivid," Stormy said.
Although he had been capable of flamboyance on the stage, Mr. Presley looked appalled by the grotesque spectacle of the recently deceased passenger. He tapped the newcomer on the shoulder (a spirit can feel another spirit), and with the forefinger of his right hand, he made a wind-it-down gesture.
"I think he must have been murdered just minutes ago," I said. "That's why he's so excited."
Stormy sighed. "I thought we were going to the fair."
"We are."
"We are, huh? So you mean for once the dead guy doesn't want vengeance?"
"He'd probably call it justice."
"And I suppose he wants us to get it for him."
"Not us. Me. Then we'll go to the fair."
The spirit recently freed from his body had taken Mr. Presley's advice and had manifested as he appeared in life. No blood. No meat cleaver embedded in his neck. He nodded vigorously, to assure me that he wanted justice.
An instant later, he was outside of the car, running ahead of it, his feet never quite touching the ground.
I drove in pursuit of the spirit, turned left into a narrow country lane, and said to Stormy, "He's leading us to his murderer."
"I was looking forward to a snow cone with orange syrup."
"There'll be plenty of time for a snow cone," I assured her.
"And a cheeseburger and jalapeño french fries and a ride on the Tilt-a-Whirl."
"There'll be plenty of time for all of that and even time for you to throw up afterward, but we've got to deliver a little justice first."
"It's like being married to some Perry Mason lawyer with superpowers."
"I don't have superpowers."
"What would you call them?"
"Quirks."
# Two
The two-lane blacktop was so narrow that if we met oncoming traffic, I would have to drive partly on the graveled shoulder of the road. Following the sprinting spirit in khakis and checkered shirt, we passed a few humble houses that featured cacti as lawn shrubs and pebbles instead of grass, in recognition of the desert that, in these outskirts of Pico Mundo, couldn't be denied as easily as it could in the center of town.
"Call Chief Porter," I said, "and give me the phone when you have him on the line."
Stormy flipped open her cell phone and entered the number as I gave it to her.
The road sloped down for more than a mile, through an uninhabited area of mesquite and purple sage in full spring bloom, toward a hollow in which a grove of cottonwoods flourished because an aquifer lay within reach of their roots. At the trees, the paved road came to a dead end.
"There's no cell service out here," Stormy reported as she pocketed her phone. "No cell service, probably no cable TV, no public sewer hookup, most likely well water, no city water lines, but I bet they have plenty of chain saws."
An oiled-dirt driveway curved among the trees. Through the screen of branches, I could see a two-story house. Gliding toward that residence, the spirit of the murdered man disappeared into the cottonwood shadows.
As I parked across the narrow dirt lane to prevent anyone from escaping the house in a vehicle, I said, "Better stay here while I have a look around."
"I'm not a delicate flower," Stormy declared. "As soon as I'm old enough to buy a pistol, I'm going to get a license to carry a concealed weapon."
Because of the troubles in her childhood, she knew that true Evil walked the world.
"But you're not old enough yet," I said.
"Which is why I have this."
From her purse, she produced a six-inch-long stainless-steel tube about two inches in diameter, with a crosshatched grip. At the top was a stainless-steel knob as shiny as a mirror. She pressed a button, and in an instant the tube telescoped to eighteen inches and locked at that length. Smiling at me, she lightly rapped the palm of her left hand with the knob of the baton.
"Ordered it through an ad in a martial-arts magazine," she said. "It'll fracture a knee or even a skull."
Unconvinced, I said, "You should still stay here with the car."
"Oh, my adorable fry cook, I am either coming with you or I'm going in there alone."
"What does that mean? You're going to test that thing on my head?"
"I wouldn't _want_ to test it on your head," she assured me. "But we're either in this together or we're not, and I've been operating on the assumption that we _are_ in it together."
"In _what_ together?"
"Life."
She has these dark eyes as deep as galaxies. It's easy to get lost in them.
I said, "Well...see...it's just that...since caveman days it's been the man's job—"
"You're not a caveman."
"No. But traditionally—"
"I bet some of those cavewomen were totally tough mamas." She opened the passenger door and got out of the car. "Is Elvis coming with us?"
Mr. Presley was no longer in the backseat. I don't know where he goes when he's not with me. Being a spirit, he can't sing or play the guitar, and he can't eat his favorite deep-fried peanut-butter-and-banana sandwich even if he could get somebody to make one for him.
"He split," I said, "he's off ghosting somewhere," and I got out of the car.
As she joined me at the entrance to the driveway, Stormy said, "Why Elvis and not Buddy Holly?"
"I don't know."
"Buddy Holly was twenty-three when he died. So young. You'd think he'd be more reluctant than Elvis to cross over."
I said, "Buddy Holly went down in a plane crash one winter night. On the other hand, Elvis was sitting on a toilet when he died, maybe of an overdose, and he collapsed into a puddle of his own vomit."
"So you're saying maybe he lingers here out of mortification?"
"Not just that. But it's conceivably a factor."
As we followed the driveway into the cottonwood grove, she said, "I doubt that anyone on the Other Side cares how we died, only how we lived. Tell him that. I mean, if he comes around again."
"He'll come around. Even if he didn't want me to help him cross over, he'd come around to stare moon-eyed at you."
She was surprised. "He stares moon-eyed at me?"
"He's in love with you, I think."
"That's kind of weird."
"Regardless of his other faults, he was always a gentleman in life. He wouldn't materialize in your bathroom and watch you naked in the shower or anything. Anyway, I guess I'm glad he's dead, so I don't have to compete with him."
"If he wasn't dead, he'd be like sixty-five. You being a quarter his age, he wouldn't be much competition."
"I wish you'd said _any_ instead of _much._ "
She smiled and pinched my cheek. "Yes, my sweet griddle boy, I'm sure you do."
We followed the oiled-dirt driveway only twenty feet or so into the woods before leaving it for the cover of the trees. I wanted to circle the house, staying in the woods, to reconnoiter it from every angle, before deciding on an approach.
This being the Mojave in spring, the day was warm, the air oven-dry and very still. Dead leaves crunched underfoot, and occasionally a bird took wing through the branches overhead, startled into flight.
I felt someone watching me, but that didn't mean anything. Because of my paranormal abilities, because I had to make my way through the world of the living _and_ the dead, I sometimes felt that I must be under observation by a hostile presence when in fact I wasn't.
In a whisper, Stormy said, "I feel as if we're being watched."
To spare her the fear of being tracked by malevolent and unseen enemies, I said, "Watch out for rattlesnakes."
# Three
The house didn't look like the place where Norman Bates dressed in his mother's clothes and sharpened the cutlery with which he would stab women to death in the family motel. Neither was it constructed of gingerbread and gumdrops to lure unsuspecting children into the home of the woodland witch, there to be roasted in an oven.
The simple two-story residence was freshly painted white with pale-yellow trim. A swing on the front porch; basket ferns hanging from brass chains. A pair of bentwood rocking chairs on the back porch. Furnishing the green lawn were a birdbath, four ceramic garden gnomes seated at a table that was a giant ceramic mushroom, a half-dozen cast-concrete pastel-blue rabbits four or five times life-size, and a powder-blue wheelbarrow used as a planter that overflowed with vine geraniums offering a wealth of scarlet flowers.
If this had been Thanksgiving Day, I would have expected a Norman Rockwell grandmother to be standing at the open front door, costumed in a long apron over a gingham dress, a smear of flour on one cheek, waving to the arriving grandkids.
Deep in cottonwood shadows, Stormy said, "Creepy."
"Megacreepy," I agreed.
"Blue rabbits? What're they supposed to be—the product of nuclear waste?"
"Bunny Godzillas," I said.
"Are the gnomes playing poker?"
"I think they're having tea."
Wary of snakes, we continued through the trees until we could see up the back porch steps to the open kitchen door.
Stormy said, "Something's lying in the doorway."
I squinted and said, "Maybe a dead guy."
"What dead guy?"
"Probably the meat-cleaver-in-the-neck dead guy."
She tried using her cell phone again, but as before there was no service in this area. "I'm having second thoughts. Blue rabbits and now a corpse. Let's drive someplace the phone works and call Chief Porter from there."
As a chill crawled up my spine and stiffened the hairs on the nape of my neck, I said, "Too late."
"This isn't a stupid horror movie, odd one. It's never too late to do the intelligent thing."
"Someone in there needs our help right now. There's no time to waste."
"How do you know?"
"Intuition."
"Yeah? Well, _my_ intuition says we should leave this very minute or get a meat cleaver in the neck."
"When I say _intuition,_ " I reminded her, "I mean _sixth sense._ My intuition isn't like yours. No offense intended."
"I fall for a fry cook," she said, "and find myself with a clairvoyant."
" _Clairvoyant_ isn't the right word."
"Is there a right word for you?"
"Maybe not," I admitted.
Draperies or curtains covered most of the windows, and the house stood in silence, as if abandoned.
"She'll die if we don't go in there right now," I said.
"Who?"
"I don't know who or how or why, but I know we don't have much time to save her."
Whether or not fortune favored the bold, we crossed the lawn without darting from one point of cover to another. The four gnomes around the ceramic toadstool were neither playing poker nor having tea. Each of them held a beer stein, and judging by the expressions on their faces, the sole reason for their gathering was to drink themselves into a stupor.
Lying across the threshold between the porch and the kitchen was in fact the fortyish guy with the shaved head and the wide blue eyes, the same man whose anguished spirit had led us to this place. The cleaver had cut through his carotid artery, and he had bled onto the porch floor so recently that the pooled blood had not yet developed a skin.
To avoid tracking blood into the house, Stormy and I had to step on the dead man's back and then between his splayed legs. I'm not an admirer of bearskin rugs, but at least all the squishy-gooey parts of the bruin have been long removed before it is cast down to be trod upon. From the cadaver's torn throat issued rude wet noises that, it seemed to me, we deserved.
In the kitchen, Stormy brandished her stainless-steel baton, looking for a skull to fracture, and I snatched up a rolling pin that lay on a disk of pie dough, on the pastry-friendly marble slab inlaid in the butcher's-block island. We were ready for anything now, unless the anything had a gun.
"Pigurines," Stormy whispered.
Someone collected cute ceramic and glass and carved-wood pigs, which were lined up atop the refrigerator, peeking between bottles on the spice shelves, displayed on the windowsills, clustered on the center of the work island and on the dinette table. There were pigs in frock coats and bib overalls and Santa Claus costumes, in tuxedos and party dresses. Here a pig stood in mid-pirouette, and there a pig played a banjo.
Where the walls weren't hung with cabinets and appliances, they featured framed needlepoint samplers with decorative borders and clichés meant to comfort: _Home Is Where the Heart Is, Sunshine Always Follows the Rain...._
Abruptly the framed samplers rattled against the walls, and the pigs clinked against one another, as if a mild earthquake shook Pico Mundo.
Unnerved, I turned, and Stormy turned, and behind us stood the spirit, which manifested with his neck intact.
"You see something?" she asked.
"Dead guy."
"What's he doing?"
His blue eyes were gas-flame bright, his face tortured by conflicting emotions. As if demanding justice, he pointed at me. Baring his clenched teeth, he thrust the same finger toward the ceiling, and like Clark Kent in an emergency that allowed no time for changing into cape and tights, he shot out of the kitchen and through the plaster overhead, causing no damage in his sudden exit.
"What just happened?" Stormy whispered.
"Well, basically, pointing the way, he flew through the ceiling. The killer must be upstairs."
"Let's get him."
"I can handle this myself."
"Boyfriend, you're not going up there alone."
I raised the rolling pin. "This is all I need."
Raising the steel baton, she said, "And this is all _I_ need."
"Sometimes you make me nuts."
She smiled. "You wouldn't love me if I didn't."
We went upstairs.
# Four
The stairs creaked. They always creaked when creaking could lead to your death, and they never creaked when creaking didn't matter. The universe is anthropic, meaning that its design makes possible and sustains intelligent life, especially human beings. Nevertheless, I perceive some power, some presence, some adversary behind the scenes that by countless devices subtle or blunt seeks to destroy us. On the second floor, the master bedroom, a second bedroom, a bathroom, and a hall closet were deserted, but all the door hinges squeaked or rasped, or did both.
Two women were in the third bedroom, at the back of the house. They looked up, frightened, when I pushed open the door.
The youngest of the two was an attractive blonde in her late twenties. She was sitting on the edge of a bed, fully clothed but chained to a steel ring that had been welded to the bed frame.
The other woman fumbled with a collection of keys, trying to free the blonde from the manacle that connected her to the chain. She was gaunt, disheveled, her thin arms mottled with bruises, her right eye swollen shut. When she turned to me, terror and timidity were written large across her paper-pale face, but the tight corners of her mouth suggested determination, and in her green eyes I thought I read a wild scrawl of triumph.
In spite of the rolling pin that I carried and Stormy's martial-arts baton, the older woman's initial fright gave way to a kind of frantic but inconstant gladness. One moment, she seemed relieved and rejoicing, as if she had just disarmed a bomb, but an instant later, her face clouded and a frown briefly replaced her grin, as though she heard the bomb clock ticking again.
She scowled. "Who're you? What're you doin' in my house?"
"There's a dead man—" I began.
"Yeah, Kurt. He moved in on me, moved in smooth as butter. I didn't see the snake he was till too late. Bastard Kurt, stone dead now, sick bastard, stone dead." She grinned as though I had told her that she'd won the lottery. "I chopped on him real good, damn if I didn't. Me, useless old Roberta, I finally done it." She appeared to be amazed that she had been capable of killing Kurt. "I chopped him like he weren't but a rack of ribs. Wish I'd chopped him a couple hundred times, chopped him up and down, 'fore I killed him. Wish I'd had the nerve _years_ ago."
Apparently Stormy decided no threat existed here, or maybe she thought I looked ridiculous as I brandished the rolling pin, because she handed me the stainless-steel baton. The emotionally fragile Roberta, struggling with the manacle lock, had begun to cry. Stormy went to her, put a hand on her shoulder as though to console her, and relieved her of the keys.
Voice trembling more with anger than with fear, the blonde said, "I was on my way to work. It wasn't even dawn yet. He came up behind me. It happened so fast."
As Stormy examined the keys, Roberta explained herself through a veil of tears: "He brung this one other girl last year, just like he brung Kristen this mornin'. He beat me near to death 'cause I said just please let Hannah go. Hannah was her name. He kept her in this here same room. Treated her like she weren't nothin' but a _thing._ He broke that girl, just like he broke me, broke her bad."
Stormy was having trouble finding the key to the manacle.
Trembling, alert for some sudden attack, Kristen said, "Where are the cops? Why didn't you call the cops?"
"No cell-phone service out here," I said.
"Use the house line."
"There ain't none," Roberta declared, wiping away tears, still an unstable brew of emotions, phasing now from sorrow to anger in an instant. "The mean sonofabitch never let me have no phone. When he'd go out, he locked me down in the cellar, like you wouldn't even lock up some dog."
Stormy said, "Kurt had more keys than a prison warden, but none of them work." She looked at me. "Why would he lead us here?"
"Vengeance, I guess. Even the wicked feel justified in wanting vengeance."
I thought of the kitchen, the collection of "pigurines" and the needlework samplers that suggested a time before Kurt, when Roberta had evidently led a simple but happy life in this house. I recalled the moment when the framed samplers rattled against the walls and the pigs clinked against one another, as if in a mild earthquake—just as Kurt's angry spirit had manifested.
Evidently my expression revealed my alarm, because Stormy said, "What's wrong?"
Before I could reply, the spirit of Kurt rose into the room, as though for the past few minutes he'd been wandering and lost between the kitchen ceiling and the bedroom floor. Once more, he manifested with his mortal wounds, soaked in blood, a demonic figure around which the air was smoky, murky, as if he pulled with him some of the darkness from the realm of the dead where he belonged. Glaring at Roberta and then at me, he pointed repeatedly to the meat cleaver in his neck, as if I might have failed to notice it. Thrusting an accusatory finger at the woman who killed him, he looked equally furious and exasperated, having apparently reached the conclusion that I had the IQ of an amoeba.
"You've already gotten the justice you deserved," I told him. "You don't belong here anymore. Just move on."
Roberta said, "Who're you talkin' to?"
Enraged by my failure to beat the woman to death with either the martial-arts baton or the rolling pin, Kurt pulled the cleaver from his neck and threw it at me. Because it wasn't a real blade, only the idea of one, it passed harmlessly through me.
"You can't do any more damage in this world," I told him.
"Who's he talkin' to?" Roberta asked Stormy.
"Nobody," Stormy said. "He's just quirky. Are there other keys?"
"Quirky?" Kristen was alarmed by the possibility of an encounter with another homicidal lunatic. "What do you mean, _quirky_?"
"Peculiar," Stormy replied. "But in a good way. He's quirky but adorable." To Roberta, she said again, "Are there any other keys?"
His head now seated firmly on his neck, face contorted by fury, Kurt raised his hands, and from his palms issued concentric pulses of energy visible to me but to no one else.
I said, "Uh-oh."
Spirits lingering in this world have only one way to harm the rest of us. If their lives were marbled with many evil acts, if they are spiritually malignant to a sufficient degree, they are able to convert their demonic rage into destructive energy and vent it upon the inanimate.
Kurt was going poltergeist.
"There's no point in this," I counseled him. "All you're doing is delaying the inevitable and ensuring yourself greater suffering when you finally cross over."
"He's weird," Kristen said, referring to me.
"Quirky," Stormy insisted.
Not susceptible to my charms, Kristen said, _"Roberta! Are there other keys anywhere?"_
Roberta felt her pockets, looked surprised, "Maybe these," she said, producing a ring of ten or twelve keys.
The pulses of energy that Kurt emitted grew brighter, concentric ripples issuing from him faster, faster.
The bedroom door crashed shut before anyone could move toward it. Roberta dropped the new set of keys, hurried across the room, and wrenched the knob back and forth.
I scooped up the keys and tossed them to Stormy.
When the door wouldn't relent, Roberta returned to us, shivering and shaking her right hand as if the doorknob had been freezing.
"There!" Stormy declared, having found the right key to unlock the manacle.
Freed, Kristen sprang at once off the bed, as though it were saturated with some pestilence infinitely more horrific than the black plague. Although Roberta had saved her life, she shied from the woman, too, as if not convinced that everything was as it seemed to be. Stormy and I excited her suspicion, as well. She ran to the door, but she had no more success with it than had Roberta.
Nightstand drawers opened of their own accord, slammed shut, slid open, shut, and now the dresser drawers, whispering on their slides, banging shut, banging, banging. A mahogany highboy spat out its drawers entirely, spilling their contents as they clattered to the floor.
Roberta's stew of emotions—sorrow, anger, frantic gladness—had boiled down to a thick reduction of fear. She stood awestruck, turning this way and that, arguing against the clear evidence of her senses—"This ain't happenin', no way, no, no"—and raising her already bruised arms to ward off whatever missiles might come her way.
The six-foot length of chain fixed to the ringbolt on the bed frame rattled up from the mattress, weaving in the air as if it were a charmed serpent, the manacle like a cobra's head poised to bite.
A ginger-jar nightstand lamp levitated, its cord taut. The plug pulled from the wall socket. The lamp flew past my head, shattering against a wall, showering Kristen with ceramic shards.
In spite of all their violent thrashing and vindictive wrath, poltergeists cannot control the malevolent energy that issues from them, cannot target anyone or aim with precision. They are able to harm us only by indirection, by ricochet, by the luckiest of lucky blows. If, however, a flung fireplace poker spears through your eye, through your brain, and out the back of your head, the fact that it found you by sheerest chance will not be much consolation.
Roberta began to scream and Kristen joined her, which seemed to inspire the late, unlamented Kurt to new heights of supernatural ire. The mattress flipped off the bed, and the coils of steel in the box springs sang as though something with a thousand claws plucked and strummed them. Emptied of all its drawers, the highboy lurched away from the wall, rocked to its left, rocked to its right, as if it were the Frankenstein's monster of furniture, lumbering this way and that in search of a victim, before it suddenly rocketed to the ceiling with such force that it broke apart and brought down with it a hail of shattered plaster.
Over the cacophony, Stormy called to me: "Do something!"
"Do what?" I shouted.
"How would I know? I work in an ice-cream shop."
_"Do something!"_ Kristen demanded.
"I'm just a fry cook," I lied. "I don't know what's happening here."
The twanging steel coils in the box springs began to break free from their ties, unwinding as they tore loose, ripping through the covering fabric like baby snakes emerging from a nest, greeted by the manacle-and-chain serpent that still undulated like a cobra in the thrall of flute music.
# Five
The ceiling joists creaked and shuddered. Cracks appeared in the plaster overhead, from which a powdery debris rained down upon us. Within the walls of the room, the studs groaned as though they might buckle under some tremendous weight, and underfoot the floor began to thrum, so that I thought the room might implode upon us.
Kurt's angry spirit, a poltergeist of singular power unique in my experience, whirled like a tornado, careening around the debris-littered bedroom, vanishing into—and reappearing out of—the walls. He passed through the door, and when an instant later he rushed back into the bedroom, he split the door in two. The portion on hinges swung open, and the other half crashed to the floor.
None of us needed prompting. We rushed across the fallen half of the door, into the upstairs hallway, and sprinted toward the stairs. Retreating from a poltergeist is not cowardly any more than running with the bulls in Pamplona is courageous; the former is an act of reasoned prudence, and the latter is foolishness bordering on lunacy. I am pleased to report that, in my haste to escape Kurt's wrathful spirit, I only _considered_ muscling ahead of the three women, but in fact followed them through the door, down the stairs, and out of the house. Chivalry lives.
We departed by the front door and reached the yard in time to hear what sounded like second-floor windows exploding at the back of the house and a shower of glass raining upon the porch roof there. The thump-bang-rattle of Kurt's postmortem temper tantrum continued in our absence, though I hoped that in spite of his singular power, he would be unable to follow us. Having initiated its frenzied destruction, the average poltergeist thrashes mindlessly until exhausted, whereupon it wanders off into whatever purgatorial zone serves as its retreat between our world and the next, perhaps for a while as confused as any living person with advanced dementia.
Roberta's trembling right hand spidered across her face as if she expected to discover bleeding lacerations, and when she found nothing, she wrapped her pale bruised arms around herself, shivering as if the Mojave were as cold as the Alaskan tundra. "It's him," she said. "Ain't no way it's anythin' else."
"Him who?" Kristen asked. "What're you talking about?"
"I chopped him with the cleaver, so he come back for revenge."
"Came back from the dead?" Kristen said. "I don't believe in ghosts."
"I believe in what I seen," Roberta insisted.
"There's a word for a destructive spirit," I said. "Something like... _polyanthus._ "
"That's a flower," Stormy said.
"Or maybe it's _poltroon._ "
"That's a craven coward," she said.
" _Polonaise_?"
"A Polish dance."
"Well, I'm just a fry cook."
The fracas on the second floor seemed to be winding down.
" _Poltergeist,_ " said Roberta.
"No," I said, "I don't think that's it."
"That's it, all right," Stormy said.
" _Poltergeist,_ " Roberta insisted.
I shook my head. "No, I don't think so."
Kristen looked at me as if I were a candidate for the Idiots' Hall of Fame, which was a look that I had seen before on the faces of a number of pretty girls. "What the hell's wrong with you? Of course it's _poltergeist._ "
"I thought you didn't believe in ghosts," I said.
"I don't. We're not talking about what happened up there. We're just talking about a word."
"Well," I said, "if it wasn't a pollinosis up there, then what was it?"
"Hay fever," Stormy said, defining the word _pollinosis._
"Poltergeist," Roberta repeated. "But we ain't never gonna say what it was, if we know what's good for us."
_"Polonium,"_ I suggested.
Stormy said, "A radioactive element."
The battered woman continued: "What we best say is Kurt done trashed the room while alive. Knocked me around some, too, give me all these bruises, black eye. Then he tried takin' Kristen out to the shed, to the old cold cellar deep down under, where he done killed poor Hannah and hung her body, where he'd soon of killed and hung me, too. We say how I caught up with him, me all crazy with fear, and my mind snapped, and I chopped him to save Kristen."
Beginning to shake violently again, Roberta broke into tears.
Kristen put an arm around her and said, "You saved me."
In the house, all had gone quiet.
Before either of the women could start to wonder why Stormy and I had shown up in the first place, my girl said, "It's over now. You two wait here. We'll drive out to the highway, where there's cell-phone service, and we'll call the police."
In my experience, the spirits of truly evil people didn't linger long in this world, if at all. When they were reluctant to cross to the Other Side, they were soon _taken_ across against their will, as if by a bill collector for some lender to whom they owed a big debt.
Because I couldn't share that knowledge with these women without blowing my fry-cook cover, I worried that we were leaving them in a state of high anxiety. "Will you be all right here? The sun's pretty hot. You could move onto the shade of the porch. It'll be safe on the porch."
"I'll keep myself right here," Roberta said, "and to hell with the porch."
"It's over now," I assured them. "It really is. Or you could move into the shade of the cottonwoods. I mean, if you don't think the porch is safe. But it is safe. The porch, I mean."
Kristen regarded me with a mix of pity and exasperation. To Stormy, she said, "Do you usually drive or does he?"
"I will," Stormy said. "Let's go, Oddie."
Stormy and I started toward the cottonwoods, but then I had to hurry back to Roberta to return her rolling pin. I didn't look at Kristen again.
# Six
While Stormy drove us to the fairground, I called Chief Wyatt Porter, who was something of a surrogate father to me, and told him what had happened, when, and where. As usual, he would do his best to keep me out of the official story.
In the fairground parking lot, Stormy wanted to sit in silence, with the windows up and the air conditioner running. We watched the late-afternoon light darkle from peach to apricot to cherry, and after a few minutes she closed her eyes, whereupon I looked not at the colorful western sky but at her.
Eventually she said, "When high school's over and real life starts, can you go on being a fry cook?"
"Sure. Why not?"
"With everything...everything else in your life?"
"Because of everything else, being a fry cook keeps me sane."
"Sooner or later, it's all going to overwhelm you—what you see, what you can do, what you are."
"I'm getting a better handle on it all the time," I assured her. "If my messed-up parents couldn't drive me crazy, I'm not going to go nuts just because I can see the lingering dead."
"And have prophetic dreams."
"Not a big deal."
"And have psychic magnetism," she said, referring to another gift of mine that played no role in that day's adventure.
After a silence, I said, "Maybe what you're really wondering is if eventually it's all going to overwhelm _you._ "
"Maybe."
"I'm not an easy date."
She said nothing.
The next silence was excruciating, and I became the one who at last broke it. "What I want most of all isn't you. What I want most of all is for you to have a happy life."
Her thick eyelashes suddenly glistened with tears that she held back. "I really want that ice-cream shop of my own."
"I bet you'll have a chain of them."
"This far in life, I've been nobody."
"You've been somebody to me. You're everything."
"I want to be somebody, odd one. I want to have a business that I can be proud of, a place where people like to go. When people hear my name, I want them to think of ice cream. I want my name to make them happy, the way ice cream makes them happy."
If I assured her that she would achieve her dream, I would be failing to provide her with the one thing that she demanded of me: the truth, whether it was easy or hard to hear. I could not see the future. If I happy-talked her through this moment, if I insisted that my paranormal gifts would only enhance our lives together and would all but guarantee her success, if I minimized the difficulty of my own struggles with my sixth sense, I would be lying to her.
At last I said, "What do you want to do?"
Without opening her eyes, she reached out to me, and we held hands as the desert darkened and the carnival on the midway painted the night with more color than the aurora borealis.
After a minute, she opened her eyes, smiled at me, and answered my question with seven words that were a welcome reprieve. "I want to go to the carnival."
We ate snow cones with orange syrup, cheeseburgers, and jalapeño french fries. We rode not just the Tilt-a-Whirl but also the Whip, the Big Drop, and the Caterpillar. Neither of us threw up.
From time to time, I saw Mr. Presley wandering the midway. He was watching people eat the hot dogs, burgers, fried ice cream, fried Almond Joys, and french-fried butter that he could no longer consume.
In time, Stormy and I came to a large tent where fancy lettering above the entrance promised ALL THINGS FORETOLD. Within, a sawdust floor spread wall to wall. In five rows stood thirty-three fortune-telling machines. Some were quaint contraptions dating from previous and more magical eras of carnival life, but others were fully of the moment, digital.
In a shadowy corner of the tent stood a machine the size of an old-fashioned telephone booth. The lower three feet were enclosed. The upper four feet featured glass on three sides. In that display sat—so a placard declared—the mummified corpse of a Gypsy dwarf who, in the eighteenth century, had been renowned throughout Europe for her predictions.
Gypsy Mummy wore much cheap jewelry and a colorful headscarf. Her eyes and lips were sewn shut, and her mottled skin pulled tight across her face. For a fortune-teller who supposedly had been counsel to three kings, her price for a prognostication was remarkably reasonable: a mere quarter.
As we arrived at the machine, a couple in their early twenties sought revelation ahead of us. The woman put her mouth to the round grille in the glass and asked, "Gypsy Mummy, tell us, will Johnny and I have a long and happy marriage?"
The man, Johnny, pushed the ANSWER button. A card slid into a brass tray. He read its message aloud: "A COLD WIND BLOWS, AND EACH NIGHT SEEMS TO LAST A THOUSAND YEARS."
Stormy squeezed my hand, and we smiled at each other. Johnny and his date were not satisfied. They sought again the approval of the long-dead sage.
Gypsy Mummy's unrelenting negativity did not at first deter them from feeding additional quarters to the machine. They'd spent two bucks before, in frustration, they threw all eight cards to the sawdust floor and, bickering about the meaning of the predictions, left the tent. In answer to their question about a long and happy marriage, some of the other warnings they had received were THE FOOL LEAPS FROM THE CLIFF, BUT THE WINTER LAKE BELOW IS FROZEN; and more ominous still, THE ORCHARD OF BLIGHTED TREES PRODUCES POISONOUS FRUIT; and not least troubling of all, A STONE CAN PROVIDE NO NOURISHMENT, NOR WILL SAND SLAKE YOUR THIRST.
"Maybe this isn't such a good idea," Stormy suggested when we were alone before the centuries-old corpse, which was more likely to have been a figure constructed of plaster and wire and latex.
Nevertheless, I gave Gypsy Mummy a quarter, and she presented to us the message that Johnny and his fiancée had hoped to receive: YOU ARE DESTINED TO BE TOGETHER FOREVER.
"She just winked at me," Stormy said.
"Who did?"
"Gypsy Mummy."
"How could a sewn-shut eye wink?"
"I don't know, Oddie. But she did, she winked."
I am superstitious, for good reason. But you don't have to be superstitious to think that it's a bad idea to doubt the reliability of a fortune-teller's prediction when it is word for word the very assurance that you desperately wanted to hear. We had no doubts as, there in the arcade called ALL THINGS FORETOLD, we kissed each other to seal the promise.
I have written this brief memoir not merely at the encouragement of my friend and mentor, Ozzie Boone, but at his _insistence._ Because my paranormal talent must remain my secret, nothing that I write can be published in my lifetime. In fact, I doubt that I will ever write another piece like this, for my life with Stormy Llewellyn will be too full to allow time for memoirs. I will have my work as a short-order cook, the griddle and the deep fryer, and she will have her ice-cream career, and we will both have the needy spirits of the lingering dead to deal with in the years ahead. I believe there will be children, too, each of them as beautiful as she is, perhaps one or two as strange as their father. She and I will grow old together in Pico Mundo, too busy for the wider world beyond, grow old here with our many friends, in the warmth of family that she hardly knew before being orphaned, that I never knew with my troubled parents. We will grow old together, for so it is promised by Gypsy Mummy, and if God is good—which He is—I will be with Stormy on the distant day, decades hence, when she leaves this world. I will hold her hand at the end, and I will pass soon after, for we are one heart, and neither of us would be of use without the other.
**You've witnessed the beginning. Join us for the end.**
**Don't miss** _Saint Odd_ **, Dean Koontz's stunning conclusion to the Odd Thomas series.**
**Coming in hardcover and eBook on January 13, 2015.**
# BY DEAN KOONTZ
The City • Innocence • 77 Shadow Street • What the Night Knows • Breathless
Relentless • Your Heart Belongs to Me • The Darkest Evening of the Year
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1. Cover
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\section{Acknowledgements}
We thank CERN for the very successful operation of the LHC, as well as the
support staff from our institutions without whom ATLAS could not be
operated efficiently.
We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC,
Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP,
Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC,
China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic;
DNRF, DNSRC and Lundbeck Foundation, Denmark; EPLANET, ERC and NSRF, European Union;
IN2P3-CNRS, CEA-DSM/IRFU, France; GNSF, Georgia; BMBF, DFG, HGF, MPG and AvH
Foundation, Germany; GSRT and NSRF, Greece; ISF, MINERVA, GIF, I-CORE and Benoziyo Center,
Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; FOM and NWO,
Netherlands; BRF and RCN, Norway; MNiSW and NCN, Poland; GRICES and FCT, Portugal; MNE/IFA, Romania; MES of Russia and ROSATOM, Russian Federation; JINR; MSTD,
Serbia; MSSR, Slovakia; ARRS and MIZ\v{S}, Slovenia; DST/NRF, South Africa;
MINECO, Spain; SRC and Wallenberg Foundation, Sweden; SER, SNSF and Cantons of
Bern and Geneva, Switzerland; NSC, Taiwan; TAEK, Turkey; STFC, the Royal
Society and Leverhulme Trust, United Kingdom; DOE and NSF, United States of
America.
The crucial computing support from all WLCG partners is acknowledged
gratefully, in particular from CERN and the ATLAS Tier-1 facilities at
TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France),
KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain),
ASGC (Taiwan), RAL (UK) and BNL (USA) and in the Tier-2 facilities
worldwide.
\end{document}
\section{Introduction} \label{sec:introduction}
Heavy long-lived particles (LLP) are predicted in a range of extensions of the Standard Model (SM)~\cite{Fairbairn:2006gg}. $R$-parity-conserving supersymmetry (SUSY)~\cite{Miyazawa:1966, Ramond:1971gb, Golfand:1971iw, Neveu:1971rx, Neveu:1971iv, Gervais:1971ji, Volkov:1973ix, Wess:1973kz, Wess:1974tw, Fayet:1976et, Fayet:1977yc, Farrar:1978xj, Fayet:1979sa, Dimopoulos:1981zb} models, such as split SUSY~\cite{ArkaniHamed:2004fb, ArkaniHamed:2004yi}, gauge-mediated SUSY breaking (GMSB)~\cite{Dine:1981gu, AlvarezGaume:1981wy, Nappi:1982hm, Dine:1993yw, Dine:1994vc, Dine:1995ag, Kolda:1997wt, Raby:1997pb} and \lsusy~\cite{DeSimone:2009ws, DeSimone:lgm}, as well as other scenarios such as universal extra dimensions~\cite{Appelquist:2000nn} and leptoquark extensions~\cite{Friberg:1997nn}, allow for a variety of LLP states stable enough to be directly identified by the ATLAS detector. These states include long-lived super-partners of the leptons, quarks and gluons; sleptons ($\tilde{\ell}$), squarks ($\tilde{q}$) and gluinos ($\tilde{g}$), respectively; as well as charginos ($\tilde{\chi}^{\pm}_{1,2}$), which together with neutralinos ($\tilde{\chi}^{0}_{1-4}$) are a mixture of super-partners of the Higgs and $W$/$Z$ bosons, known as Higgsinos, winos and binos.
When travelling with a speed measurably slower than the speed of light, charged particles can be identified and their mass ($m$) determined from their measured speed ($\beta$) and momentum ($p$), using the relation $m=p/\beta\gamma$, where $\gamma$ is the relativistic Lorentz factor. Three different searches are presented in this article, using time-of-flight (TOF) to measure $\beta$ and specific ionisation energy loss (\dedx), to measure $\beta\gamma$.
The searches are based almost entirely on the characteristics of the LLP itself, but are further optimised for the different experimental signatures of sleptons, charginos and composite colourless states of a squark or gluino together with light SM quarks or gluons, called \rhads.
Long-lived charged sleptons would interact like muons, releasing energy by ionisation as they pass through the ATLAS detector. A search for long-lived sleptons identified in both the inner detector (ID) and in the muon spectrometer (MS) is therefore performed (``slepton search''). The search is optimised for GMSB and \lsusy models. In the former, the gravitino is the lightest supersymmetric particle (LSP) and the light tau slepton ($\stau_1$) is the long-lived, next-to-lightest supersymmetric particle (NLSP). The $\stau_1$, the lightest \stau mass eigenstate resulting from the mixture of right-handed and left-handed super-partners of the $\tau$ lepton, is predominantly the partner of the right-handed lepton in all models considered here. In addition to GMSB production, results are also interpreted for the case of direct pair production of charged sleptons, independently of the mass spectrum of other SUSY particles. The recent discovery of the Higgs boson with a mass of about 125~\GeV~\cite{Aad:2012tfa, Chatrchyan:2012ufa} disfavours minimal GMSB within reach of the Large Hadron Collider (LHC). For the Higgs boson to have such mass, the top squark mass would have to be several \TeV, and in GMSB the slepton masses are strictly related to the squark masses. However, modifications to minimal GMSB can easily accommodate the observed Higgs mass without changing the sparticle masses~\cite{Abdullah, EvansIbeYanigida, EvansIbeShiraiYanigida}. The \lsusy models, characterised by final states with high multiplicity of leptons and jets, are studied in the context of a simplified model, where all the neutralinos and charginos are decoupled with the exception of the $\tilde\chi_1^0$, and the sleptons are long-lived and degenerate, with a mass set to 300~\GeV, a value motivated by exclusion limits of previous searches~\cite{Aad:2012pra}. In these models a substantial fraction of the events would contain two LLP candidates, a feature also used to discriminate signal from background.
Charginos can be long-lived in scenarios where the LSP is a nearly pure neutral wino and is mass-degenerate with the charged wino. The chargino signature in the detector would be the same as for a slepton, but the dominant production is in chargino--neutralino ($\tilde{\chi}^{\pm}_1\tilde{\chi}^{0}_1$) pairs, where the neutralino leaves the apparatus undetected. As a result, the event would have one LLP and significant missing transverse momentum (\ptmiss, with magnitude denoted by \etmiss). This signature is pursued in a dedicated ``chargino search''.
Coloured LLPs ($\tilde{q}$ and $\tilde{g}$) would hadronise forming \rhads, bound states composed of the LLP and light SM quarks or gluons. They may emerge as charged or neutral states from the $pp$ collision and be converted to a state with a different charge by interactions with the detector material, and thus arrive as neutral, charged or doubly charged particles in the MS. Searches for \rhads are performed following two different approaches: using all available detector information (``full-detector \rhad search''), or disregarding all information from the MS (``MS-agnostic \rhad search''). The latter case is independent of the modelling of \rhad interactions with material in the calorimeters.
Previous collider searches for charged LLPs have been performed at LEP~\cite{Barate:1997dr,Abreu:2000tn,Achard:2001qw,Abbiendi:2003yd}, HERA~\cite{Aktas:2004pq}, the Tevatron~\cite{Abazov:2007ht,Aaltonen:2009kea,Abazov:2011pf}, and the LHC~\cite{Aad:2012pra,Chatrchyan:2013oca,Aad:2013gva}.
\section{Data and simulated samples}
The work presented in this article is based on \lumi of $pp$ collision data collected at a centre-of-mass energy $\sqrt{s} = 8~\TeV$ in 2012. Events are selected online by trigger requirements either on the presence of muons or large \etmiss. Events collected during times when a problem was present in one of the relevant sub-detectors are later rejected offline. A separate stream of \lumiZmumu $pp$ collision data and Monte Carlo (MC) simulation \zmumu samples are used for timing resolution studies. Simulated signal samples are used to study the expected signal behaviour and to set limits.
All MC simulation samples are passed through a detector simulation~\cite{Aad:1267853} based on \geant~\cite{Agostinelli:2002hh} and a model of the detector electronics. The effect of multiple $pp$ interactions in the same or a nearby bunch crossing (pile-up) is taken into account by overlaying additional minimum-bias collision events simulated using \pythiapp~\cite{Sjostrand:2007gs} v.\ 8.170 and reweighting the distribution of the average number of interactions per bunch crossing in MC simulation to that observed in data. All events are subsequently processed using the same reconstruction algorithms and analysis chain as the data.
The GMSB samples are generated, using \herwigpp~\cite{Bahr:2008pv} v.\ 2.5.2 along with the UEEE3~\cite{Gieseke:2012ft} tune and the CTEQ6L1~\cite{Pumplin:2002vw} parton distribution function (PDF) set, with the following model parameters: number of super-multiplets in the messenger sector, $N_5=3$, messenger mass scale, $m_{\rm{messenger}}=250~\TeV$, sign of the Higgsino mass parameter, $\rm{sign}(\mu)=1$, and $C_\mathrm{grav}$, the scale factor for the gravitino mass which determines the NLSP lifetime, set to 5000 to ensure that the NLSP does not decay inside the detector. The ratio of the vacuum expectation values of the two Higgs doublets ($\tan\beta$) is varied between 10 and 50. The SUSY-breaking scale ($\Lambda$) is chosen between 80 and 160~\TeV and the corresponding $\stau_1$ masses vary from 175 to 510~\GeV, in order to cover the regions of parameter space accessible to this analysis and not excluded by previous searches. The masses of the right-handed $\tilde{e}$ (or $\tilde{\mu}$) are larger than that of $\stau_1$ by 2.7--93~\GeV for $\tan\beta$ values between 10 and 50. The corresponding lightest neutralino ($\tilde{\chi}^{0}_{1}$) mass varies from 328 to 709~\GeV as a function of $\Lambda$ and is independent of $\tan\beta$. The lightest chargino ($\tilde{\chi}^{\pm}_{1}$) mass varies from 540 to 940~\GeV, and is 210 to 260~\GeV higher than the neutralino mass, with a small dependence on $\tan\beta$. The dependence of the mass splitting between the chargino and lightest neutralino on $\tan\beta$ varies from 1\% at $\Lambda=80$~\TeV to 3\% at $\Lambda=160$~\TeV.
The \lsusy samples are simulated in \madgraph~\cite{Alwall:2011uj} v.\ 1.5.4 using the CTEQ6L1 PDF set, with \bridge~\cite{Meade:2007js} v.\ 2.24 used for decaying the squarks, and \pythiapp v.\ 8.170 along with the AU2~\cite{ATL-PHYS-PUB-2011-008,ATL-PHYS-PUB-2011-009} tune for parton showering. The sleptons are long-lived and set to be degenerate with a mass of 300~\GeV. The third-generation squarks are assumed to be very heavy (10~\TeV).
The masses of the first- and second-generation squarks (gluinos) are varied between 600~\GeV and 3~\TeV (950~\GeV and 3~\TeV) assuming a fixed mass of the $\tilde{\chi}^{0}_{1}$ of 400~\GeV.
Samples of long-lived charginos are generated using \herwigpp v.\ 2.6.3 along with the UEEE3 tune and the CTEQ6L1 PDF set, according to simplified models where the lightest chargino and lightest neutralino are nearly degenerate, and the chargino is the LLP. Starting from a self-consistent model with a chargino/neutralino mass of about 658~\GeV (140~\MeV mass splitting), the simplified version is obtained by moving the chargino and neutralino masses up and down in a range between 100 and 800~\GeV, keeping the mass splitting constant. In addition, the chargino is forced to remain stable and the other particle masses are set to values too high to be produced at the LHC. Production of $\tilde{\chi}^{\pm}_{1}\tilde{\chi}^{\mp}_{1}$ ($\tilde{\chi}^{\pm}_{1}$$\tilde{\chi}^{0}_{1}$) constitutes about one third (two thirds) of the events generated in these samples.
For the \rhad samples, pair production of gluinos, bottom squarks (sbottoms) and top squarks (stops) is simulated in \pythia~\cite{Sjostrand:2006za} v.\ 6.4.27, incorporating specialised hadronisation routines~\cite{rasmusthesis,Kraan:2004tz} to produce final states containing \rhads~\cite{Aad:2011yf}, along with the AUET2B~\cite{ATL-PHYS-PUB-2011-014} tune and the CTEQ6L1 PDF set. Interactions of \rhads with matter are handled by dedicated routines for \geant based on different scattering models with alternative assumptions~\cite{Mackeprang:2009ad}. The model for gluino \rhad interactions, using a gluino-ball fraction of ten percent, is referred to as the generic model. For sbottom and stop \rhads a triple Regge interaction model is assumed.
Samples of \zmumu events are simulated using \powheg~\cite{Frixione:2007vw} r.\ 1556 and \pythiapp v.\ 8.170 along with the AU2 tune and the CT10~\cite{Lai:2010vv} PDF set and used only for calibration and studies of systematic uncertainties.
\section{ATLAS detector}
The ATLAS detector~\cite{Aad:2008zzm} is a multi-purpose particle detector with a forward-backward symmetric cylindrical geometry and near $4\pi$ coverage in solid angle.\footnote{ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point in the centre of the detector and the $z$-axis coinciding with the axis of the beam pipe. The $x$-axis points from the interaction point to the centre of the LHC ring, and the $y$-axis points upward. Cylindrical coordinates ($r$, $\phi$) are used in the transverse plane, $\phi$ being the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the polar angle $\theta$ as $\eta = - \ln \tan(\theta/2)$.} The search for heavy long-lived charged particles relies on measurements of ionisation and time-of-flight, therefore the detector components providing these observables are described below.
\subsection{Pixel detector} \label{sec:pixel}
As the innermost detector system in ATLAS, the silicon pixel detector typically provides at least three high-precision spatial measurements for each track in the region $|\eta|<2.5$ at radial distances from the LHC beam line of $r<15$~cm. The sensors in the pixel barrel ($|\eta|<2$) are placed on three concentric cylinders around the beam-line, whereas sensors in the end-cap ($|\eta|>2$) are located on three disks perpendicular to the beam axis on each side of the barrel. The data are only read out if the signal is larger than a set threshold.
\subsubsection{Specific ionisation measurement}
The charge collected in each pixel is measured using the time-over-threshold (ToT) technique. The calibration of the ToT to the charge deposition in each pixel is established in dedicated scans, and therefore the ToT measurement yields the energy loss of a charged particle in the pixel detector.
The maximum ToT value corresponds to 8.5 times the average charge released by a minimum ionising particle (MIP) with a track perpendicular to the silicon detectors and leaving all of its ionisation charge on a single pixel. If this value is exceeded, no hit is registered.
In LHC collisions the charge generated by a charged particle crossing a layer of the pixel detector is usually contained in a few pixels. Neighbouring pixels are joined together to form clusters and the charge of a cluster is calculated by summing the charges of all pixels after calibration correction. The specific energy loss (\dedx) is measured using the average of all individual cluster charge measurements for the clusters associated with the track, typically three measurements. To reduce the effect of tails in the expected Landau distribution, the average is evaluated after removing the cluster with the highest charge (the two clusters with the highest charge are removed for tracks having five or more clusters).
\subsubsection{Mass measurement}
The masses of slow charged particles can be measured using the ID information by evaluating a function that parameterises the expected behaviour of the specific energy loss as a function of the particle $\beta\gamma$. The parametric function describing the relationship between the most probable value of the specific energy loss (${\cal{MPV}}_{\mathrm{d}E\over \mathrm{d}x}$) and $\beta\gamma$ was found by searching for a functional form which adequately describes the simulated data~\cite{dedxnote}. ${\cal{MPV}}_{\mathrm{d}E\over \mathrm{d}x}$ is described via five fixed parameters $p_1$--$p_5$, evaluated separately for data and MC simulation, using
\vspace{-1em}
\begin{equation}
{\cal{MPV}}_{\mathrm{d}E\over \mathrm{d}x}(\beta\gamma) = {p_1\over \beta^{p_3}}\ln(1+(|p_2|\beta\gamma)^{p_5})-p_4.
\label{bbfun}
\end{equation}
The most probable value of \dedx for MIPs is about 1.2~\MeVgcm with a spread of about 0.2~\MeVgcm and a slight $\eta$ dependence, increasing by about 10\% from low-$|\eta|$ to high-$|\eta|$ regions~\cite{Aad:2011hz}. The measurable $\beta\gamma$ range lies between 0.2 and 1.5, the lower bound being defined by the overflow in the ToT spectrum, and the upper bound by the overlapping distributions in the relativistic-rise branch of the curve.
A mass estimate $m_{\beta\gamma} = p/\beta\gamma$ can be obtained for all tracks with a measured specific energy loss \dedx above the value for MIPs, using their reconstructed momentum $p$ and $\beta\gamma$ evaluated from \dedx. The stability of the measurement of the specific energy loss as a function of time is monitored through measurements of the masses of kaons and protons with percent-level precision and is found to have a variation of less than one percent. For LLPs considered in this article the expected \dedx values can be significantly larger than those of SM particles, allowing their identification based on this information. The RMS of the $m_{\beta\gamma}$ distribution obtained in this way is about 20\%.
\subsection{Calorimeters} \label{sec:calorimeters}
Liquid argon is used as the active detector medium in the electromagnetic (EM) barrel and end-cap calorimeters, as well as in the hadronic end-cap (HEC) calorimeter. All are sampling calorimeters, using lead plates as absorbers material for the EM calorimeters and copper plates as absorbers material for the HEC calorimeter. The barrel EM calorimeter covers the region $|\eta|<1.475$ and consists of a pre-sampler and three layers at radii from 150 to 197~cm. The EM end-cap calorimeter consists of three layers in the region $1.375<|\eta|<2.5$ (two for $2.5<|\eta|<3.2$) and a pre-sampler for $1.5<|\eta|<1.8$. The four layers of the HEC calorimeter cover the range $1.5<|\eta|<3.2$. The time of the energy deposition in each element of the calorimeter (cell) is measured. The typical cell time resolution is 1.5--2.0~ns for energy deposits of 1~\GeV in the EM, 2.0--2.5~ns for energy deposits of 10~\GeV in the HEC.
The ATLAS tile calorimeter is a cylindrical hadronic sampling calorimeter. It uses steel as the absorber material and plastic scintillators as the active material. It covers radii from 228 to 423~cm. The calorimeter is subdivided into a central barrel covering $|\eta| \lesssim 1.0$ and extended barrels covering $0.8 \le |\eta| \le 1.7$. Each barrel part is divided into 64 modules in $\phi$ and the cells in each module are divided into three layers. The typical cell time resolution is 0.6--0.8~ns for energy deposits of 1~\GeV. The time resolution is approximately proportional to $E^{-1/2}$.
\subsection{Muon system} \label{sec:muondetectors}
The muon spectrometer forms the outer part of the ATLAS detector, detects charged particles exiting the calorimeters and measures their momenta in the pseudorapidity range $|\eta| < 2.7$. It is also designed to trigger on these particles in the region $|\eta| < 2.4$. In the barrel the chambers are arranged in three concentric cylindrical shells around the beam axis with radii of 5 to 10~m, while in the two end-caps the muon chambers are arranged in three wheels that are perpendicular to the beam axis at distances between 7.4 and 21.5~m to the nominal interaction point.
The precision momentum measurement is performed by monitored drift tube (MDT) chambers. These chambers consist of three to eight layers of drift tubes covering the region $|\eta| < 2.7$, except in the innermost tracking layer of the forward region ($2.0 < |\eta| < 2.7$), where cathode strip chambers are used. Resistive plate chambers (RPC) in the barrel region ($|\eta|<1.05$) and thin gap chambers (TGC) in the end-cap ($1.05 < |\eta| < 2.4$) provide a fast first-level trigger (level-1). Muons typically have around 20 MDT hits and 10 RPC hits if they traverse the MS barrel, with a typical time resolution of 3.5~ns and 0.6--1.1~ns, respectively. In contrast to the standard ATLAS muon reconstruction, candidate tracks are refitted allowing their velocity to be less than the speed of light, in order to associate all the MDT hits produced by the LLP with the candidate.
\subsection{Measurement of $\beta$ based on time-of-flight} \label{sec:tofbeta}
\begin{figure*}[tb]
\centering
\includegraphics[width=0.49\linewidth]{fig_01a.pdf}
\includegraphics[width=0.49\linewidth]{fig_01b.pdf}
\caption{Distribution of the muon speed, $\beta$, from the calorimeter (left) and combined measurements of calorimeter and muon spectrometer (right) obtained for selected \zmumu events in data (points) and smeared MC simulation (line).}
\label{fig:beta}
\end{figure*}
The calorimeters, RPCs and MDTs have sufficiently accurate timing to distinguish between highly relativistic SM particles and slower LLPs of interest to the searches described in this article. The measured time-of-flight to calorimeter cells and MS hits crossed by the candidate track are used to measure the speed $\beta$. Custom calibration methods using \zmumu events are used to achieve optimal $\beta$ resolution. The times are first corrected collectively for any timing differences between the LHC and ATLAS in order to compensate for collective time-dependent effects (average for each LHC store) and then individually by detector element for any offsets. The calibration also provides a $\beta$ uncertainty for each detector element.
In order to obtain the correct signal efficiency, hit time measurements in simulated \zmumu samples are smeared to correspond to the distribution observed in data. Each hit is smeared by the time resolution observed in the detector element where it was measured.
The individual $\beta$ measurements are combined in a weighted average, using the errors determined per detector element in the calibration. The combination is done first for each sub-detector (calorimeters, MDT, RPC) separately, and then for the entire detector. At each step the measurements are required to be consistent, as described in section~\ref{sec:selection_offline_event_slepton}. Depending on $\eta$, the $\beta$ resolution for muons with $\beta=1$ is 2.4--2.6\% for the RPC, 3.7--4.9\% for the MDT and about 8\% for the calorimeter. Though the calorimeter $\beta$ resolution is less precise than that of the MS, it provides high efficiency and the model independence of the MS-agnostic \rhad search.
Figure~\ref{fig:beta} shows the $\beta$ from the calorimeter (left) and combined measurements (right) obtained for selected \zmumu events in data and smeared MC simulation. The mean values and resolution of the combined $\beta$ are $\bar\beta=0.999$ and $\sigma_\beta=0.024$, respectively, for both data and MC simulation. The RMS of the $m_{\beta}$ distribution obtained this way is about 10\% (20\% for the calorimeter only measurement).
\section{Online event selection} \label{sec:selection_trigger}
All searches are based on events collected by at least one of two trigger types: single-muon and \etmiss triggers.
\subsection{Single-muon trigger} \label{sec:selection_trigger_muon}
The muon trigger and its performance in 2012 data are described in detail in reference~\cite{Aad:2014sca}. The searches use un-prescaled muon triggers with a transverse momentum (\pT) threshold of 24~\GeV. Offline candidates are selected with $\pT > 70~\GeV$, well above the trigger threshold.
Events selected by level-1 muon triggers are accepted and passed to the high-level trigger only if assigned to the collision bunch crossing. Late triggers due to the arrival of particles in the next bunch crossing are thus lost. The trigger efficiency for particles arriving late at the MS cannot be assessed from data, where the vast majority of candidates are in-time muons and where low-$\beta$ measurements are due to mismeasurement. The trigger efficiency is thus obtained from simulated signal events. However, the quality of the estimate depends on the accuracy of the timing implementation in the simulation. A detailed emulation of the level-1 electronics circuits, including their timing, is applied to simulated events. The probability that an LLP triggers the event increases roughly linearly from zero at $\beta = 0.62$ to a maximum value of about 70\% at $\beta = 0.82$ for LLPs that reach the MS. A systematic uncertainty is assigned to account for differences in the input time measurements between data and simulated events (see section~\ref{sec:syst_signal}).
GMSB and \lsusy events have two LLPs and possibly muons present in the decay chain, so the likelihood of one of the penetrating particles arriving in the collision bunch crossing is high. Chargino events have no muons, and since in the majority of the chargino events there is only one LLP, the efficiency is lower. The estimated trigger efficiency for GMSB slepton events is between 65\% and 80\%, for \lsusy events between 75\% and 90\% and for stable-chargino events between 24\% and 64\%. Muon triggers are less efficient for \rhads (0--20\%), where one or both of the \rhads may be neutral as they enter the MS and $\beta$ is typically low.
\subsection{Missing transverse momentum trigger} \label{sec:selection_trigger_met}
The \etmiss quantity used at the trigger level is based on the calorimeter only and does not include any corrections for muon-like objects. LLPs deposit very little of their energy in the calorimeter, and therefore in most signal types \etmiss is dominated by initial state radiation (ISR) jets recoiling against the two LLPs. When charginos and neutralinos decay into long-lived sleptons, additional \etmiss may result from neutrinos.
The \rhad searches use un-prescaled \etmiss triggers~\cite{ATLAS-CONF-2014-002} with thresholds as low as 60~\GeV, while the other searches use thresholds between 70 and 80~\GeV. The onset of these triggers is at about 10~\GeV below the threshold, while full efficiency is reached at about 70--80~\GeV above the threshold. Unlike the single-muon trigger, there is no loss of efficiency for the \etmiss triggers when LLPs have low $\beta$.
\subsection{Trigger efficiency} \label{sec:selection_trigger_eff}
In all the searches, except the MS-agnostic \rhad search, a logical \texttt{OR} of the muon and \etmiss triggers described above is used. Depending on the mass of the LLP, the total trigger efficiency is between 80\% and 90\% for GMSB slepton events, between 40\% and 66\% for events with stable charginos, above 95\% for \lsusy events and between 22\% and 35\%, depending on mass and type, for events containing \rhads. In the MS-agnostic \rhad search only the \etmiss triggers are used, with an efficiency between 21\% and 26\%.
\section{Offline event and candidate selection} \label{sec:selection_offline}
Three different signal types are studied: sleptons, charginos and \rhads. An overall trigger and event-quality selection, common to all searches, is applied. Given the different expected interactions with the ATLAS detector, a dedicated selection, containing event-based as well as candidate-based criteria, is optimised and applied for each signal type. An overview of the signal regions can be found in table~\ref{tab:SignalRegions}.
\subsection{Common event and candidate selection} \label{sec:selection_offline_event}
\begin{table*}[tb]
\footnotesize
\def1.0{1.0}
\begin{center}
{\setlength{\tabcolsep}{0em}\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}}llccccccc}
\hline
\hline
Search &Signal &LLP mass &$N_\mathrm{cand}$ &Momentum &$|\eta|$ &\etmiss &$\beta$ &$\beta\gamma$ \\
®ions &[GeV] & &[GeV] & &[GeV] & & \\
\hline
Sleptons &\srslcc &175--510 &2 &$\pt > 70$ &$<2.5$ & &$<0.95$ &consistency \\
&\srslc &175--510 &1 &$\pt > 70$ &$<2.5$ & &$<0.85$ &consistency \\
Charginos &\srchcc &100--800 &2 &$\pt > 70$ &$<2.5$ & &$<0.95$ &consistency \\
&\srchcl &100--800 &1 &$\pt > 70$ &$<1.9$ &$>100^{***}$ &$<0.95$ &consistency \\
&\srchc &100--800 &1 &$\pt > 70$ &$<1.9$ & &$<0.85$ &consistency \\
\rhads &\srrhma &400--1700 &$\ge$1 &$p > 140$--$200^*$ &$<1.65$ & &$<0.88$--$0.74$ &$<2.3$--1.15 \\
&\srrhfd &400--1700 &$\ge$1 &$p > 140$--$200^*$ &$<1.65^{**}$ & &$<0.88$--$0.74$ &$<2.3$--1.15 \\
\hline
\multicolumn{4}{c}{\smaller \smaller $\phantom{ }^* \Delta R_{\mathrm{jet}, \pt > 40 \GeV} > 0.3$, $\Delta R_{\mathrm{track}, \pt > 10 \GeV} > 0.25$}
& \multicolumn{3}{c}{\smaller \smaller $\phantom{ }^{**}$ only for \idcalo candidates}
& \multicolumn{2}{c}{\smaller \smaller $\phantom{ }^{***} \Delta \phi_{\mathrm{LLP},\etmiss} > 1.0$}\\
\hline
\hline
\end{tabular*}}
\caption{Overview of signal regions (SRs), the covered mass range and selection requirements for different types of long-lived particles. The signal regions for the same search are mutually exclusive and combined in the limit setting, except for two \rhad SRs, which each probe a different hypothesis for the particle interactions with the detector. $N_\mathrm{cand}$ denotes the number of LLP candidates considered in the given SR. The $\beta$ and $\beta\gamma$ requirements listed for the \rhad SRs are due to their mass dependence. In addition, all selections have cosmic-ray muon and $Z$ vetoes. For sleptons and charginos $\beta\gamma$ is only used to check for consistency with $\beta$ by requiring $\beta(\mathrm{TOF})-\beta(\dedx)<5\sigma$.\label{tab:SignalRegions}}
\end{center}
\end{table*}
Collision events are selected by requiring a good primary vertex. Vertices are reconstructed requiring at least three tracks reconstructed in the ID and consistent with the beam spot. The primary vertex is defined as the one with the highest $\sum p^2_T$ of associated tracks.
Since the background increases significantly at high $|\eta|$, due to the large momenta of candidates and decreased ID momentum resolution, those regions are excluded from the definition of signal regions where they may add large backgrounds and where the signal is expected to be more centrally produced (high masses). High-$|\eta|$ regions are considered for selections where other stringent requirements reduce the background, such as two muons or LLP candidates in the event and/or a precise $\beta$ measurement.
Different requirements on \pt and $p$ are placed in the various searches, as \pt is more suitable to suppress very boosted SM background in cases including the high-$|\eta|$ regions, while the the use of $p$ is advantageous in searches focussing on low-$|\eta|$ regions (e.g.\ \rhads), as it is more closely related to mass.
Additional requirements on $\beta$ ($\beta\gamma$) and $m_{\beta}$ ($m_{\beta\gamma}$) are used to reduce background. The presence of an LLP signal is searched for in a distribution of $m_{\beta}$ ($m_{\beta\gamma}$), where the signal should peak and background be continuous.
\subsection{Slepton event and candidate selection} \label{sec:selection_offline_event_slepton}
In GMSB and \lsusy events, the weak coupling of the gravitino to the other particles implies that only the NLSP ($\stau_1$ for the models of interest) decays to the gravitino. As a result of this and of $R$-parity conservation, at least two $\stau_1$ sleptons are expected in each GMSB event, both with a high probability of being observed. Therefore the slepton searches require at least two loosely identified muon-like objects reconstructed using the techniques described in reference~\cite{Aad:2014rra}, which will be called LLP candidates in the following. By applying this selection criterion, background from $W$ and multi-jet events is reduced. Two sets of selection criteria are applied on a per-candidate basis with details given below. A loose selection with high efficiency is used to select candidates in events where there are two LLP candidates, since a background event would very rarely have two high-\pt~muons, both with poorly measured $\beta$ and a large reconstructed mass. Events having two loose candidates, independent of their charge, fall in the two-candidate signal region (\srslcc). In events where only one candidate passes the loose selection, that candidate is required to pass an additional, tighter selection. Such events are collected in a mutually exclusive one-candidate signal region (\srslc).
Candidates in the loose slepton selection are required to have $\pt > 70~\GeV$ and $|\eta| < 2.5$. Any two candidates that combine to give an invariant mass within $10~\GeV$ of the $Z$ boson mass are both rejected. Candidates are also required to have associated hits in at least two of the three layers of precision measurement chambers in the MS. Cosmic-ray muons are rejected by a topological requirement on the combination of any two candidates with opposite $\eta$ and $\phi$. The number of degrees of freedom in the $\beta$ measurement\footnote{The number of calorimeter cells plus MS hits contributing to the $\beta$ measurement minus the number of detector systems} is required to be larger than three. LLP candidates are expected to have low $\beta$ values and these values are expected to be consistent between individual measurements, both in the same detector system and between different detectors, while in the case of muons a low $\beta$ value would be due to a poor measurement in only one of the detectors.
The different detector system measurements of $\beta$ are required to be pair-wise consistent at the 3$\sigma$ level, and the combined $\beta$ to be consistent with the $\beta\gamma$ estimated in the pixel detector within 5$\sigma$. The $\beta$ resolution is estimated for each candidate, and the $\beta\gamma$ resolution is about 11\%. The $\beta\gamma$ measurement is translated to $\beta$ and compared to the value of $\beta$ based on time-of-flight for the consistency check. There is no requirement on the value of $\beta\gamma$ obtained from the pixel \dedx measurement in the searches that require consistency. As a result, many candidates are in the MIP region. Those are required to have $\beta$ consistent with the MIP hypothesis. Finally, in order to reduce the muon background, the combined $\beta$ measurement is required to be between 0.2 and 0.95.
To pass the tighter slepton selection used for \srslc, a candidate is additionally required to have at least two separate detector systems measuring $\beta$ and the number of degrees of freedom of the $\beta$ measurement is required to be at least six.
Events with one candidate are then divided between \srslc, where the combined $\beta$ measurement is required to be less than 0.85, and a control region with $0.85<\beta<0.95$, used to cross-check the background estimation.
Finally, the measured mass, $m_{\beta}=p/\beta\gamma$, calculated from the candidate's momentum and its measured $\beta$, is required to be above some value. The value is chosen according to the mass of the the hypothetical $\stau_1$ mass in the given model, so as to achieve 99\% signal efficiency with respect to the earlier selection. For \srslcc, both masses are required to be above the chosen value.
Typical efficiencies for signal events to satisfy all criteria including the mass requirement are 30\% for \srslcc and 20\% for \srslc, giving 50\% efficiency in total. The efficiencies are similar for events with pair-produced sleptons and events where sleptons arise from directly produced, decaying charginos and neutralinos.
\subsection{Chargino event and candidate selection} \label{sec:selection_offline_event_chargino}
Except for the two-muon requirement, the chargino event selection is the same as the slepton selection. For chargino-pair production, the events would be very similar to slepton events, while for chargino--neutralino production a single LLP candidate is accompanied by \etmiss caused by the neutralino. The chargino and neutralino are typically well-separated in $\phi$, therefore the \ptmiss is expected to point in the opposite direction to the reconstructed LLP. The events are divided into three signal regions. Events with two LLP candidates passing the loose selection, as before independent of their charge, are in the two-candidate signal region (\srchcc). This selection is motivated by pair production of charginos. Events with one candidate passing the loose selection must have \etmiss$>$100~\GeV and an azimuthal angular distance between the LLP candidate and the \ptmiss $\Delta\phi>1$, to be included in the one-loose-candidate signal region (\srchcl). \srchcl is motivated by the chargino--neutralino production mode. Finally if an event has neither two candidates nor large \etmiss, one given candidate has to pass the tighter selection and have $\beta<0.85$ to be included in the one-candidate signal region (\srchc). All three signal regions are mutually exclusive.
The requirements for a candidate to pass the loose or the tight selection are the same as for the slepton search. In addition, in both \srchcl and \srchc, candidates with $|{\eta}|>1.9$ are excluded.
A mass selection, chosen to achieve 99\% signal efficiency with respect the earlier selection, is applied to the candidate mass. This requirement depends on the hypothetical chargino mass and differs by model. For \srchcc, both masses are required to be above the chosen value.
Typical efficiencies for signal events to satisfy all selection criteria including the mass requirement are 5--6\% for \srchcc, 10--13\% for \srchcl and 3\% for \srchc, giving 18--22\% efficiency in total, depending on the mass of the chargino candidates. Looking separately at the two different production modes, the efficiency of \srchcc for chargino-pair production is 15--20\% and the efficiency of \srchcl for chargino--neutralino production is 12--17\%.
\subsection{\rhad event and candidate selection} \label{sec:selection_offline_event_rhadron}
Since the \rhad contains light quarks and gluons in addition to the squark or gluino, the charge of the \rhad can change following nuclear interactions with the detector material. This possibility makes it difficult to rely on a single detection mechanism without any loss of detection efficiency, as a neutral state would not be detected until the next nuclear interaction occurs. Some of the main hadronic states resulting from such charge exchange in the models considered are neutral. In a search for \rhads that are produced charged, it is therefore natural to take an inside-out approach, starting from the ID track and adding discriminators from outer detector systems, in case a signal is seen along the extrapolated track. This is reflected in the two different \rhad approaches.
In an \idcalo selection, candidates are required to have a good-quality ID track with $\pt > 50~\GeV$ and $|\eta| < 1.65$. To ensure reliable estimates of $\beta\gamma$ and $\beta$, candidates must not be within an $\eta$--$\phi$ distance $\Delta R = \sqrt{\left( \Delta \eta \right)^2 + \left(\Delta \phi \right)^2} = 0.3$ of any jet with $\pt > 40~\GeV$, reconstructed from calorimeter energy clusters using the anti-$k_t$ jet algorithm~\cite{jetalgo} with distance parameter set to 0.4. Furthermore, candidates must not have any nearby ($\Delta R < 0.25$) tracks with $\pt > 10~\GeV$ nor have pixel hits shared with other tracks. The $Z$ boson mass window and cosmic-ray muon rejection are applied in the same way as in the slepton searches. Candidates must have a good \dedx measurement and a good estimate of $\beta$. The uncertainty on the calorimeter-only $\beta$ is required to be less than 12\%.
In a \combined selection, candidates are required to have a combined track, reconstructed in both the ID and the MS. With the exception of the explicit $\eta$ requirement, the ID requirements for the \combined candidate as well as the $Z$ boson mass window, cosmic-ray muon rejection and \dedx measurement are the same as for the \idcalo selection. The estimate of $\beta$, based on a combination of internally consistent measurements in the calorimeter, the RPCs and the MDTs, is required to have an uncertainty of less than 5\%.
In the full-detector \rhad search, candidates are first checked for compatibility with the \combined selection and only when failing, for compatibility with the \idcalo selection. The two types of candidates are therefore mutually exclusive and events containing at least one candidate fulfilling either of the two selections are considered in the full-detector signal region (\srrhfd).
The independent MS-agnostic \rhad search, ignoring MS information, as well as the muon trigger, considers events containing at least one candidate passing the \idcalo selection (\srrhma).
In the approximately 15\% of events with more than one candidate, a candidate passing the combined selection is preferred; if there are two or more candidates from the same category, one is chosen at random and the others are discarded. In both \rhad searches, additional requirements on a minimum momentum and maximum values for $\beta$ and $\beta\gamma$ are set, depending on the mass hypothesis in question. The two \rhad mass estimates $m_{\beta\gamma}$ and $m_{\beta}$ are both required to be larger than the mass-peak value for the given hypothesis minus twice the width of the mass peak, which is typically around 20\% of the peak mass, leading to an efficiency of more than 95\%. All mass and momentum requirements are the same for gluinos, sbottoms and stops, while the requirements on $\beta\gamma$ and $\beta$ are optimised separately to account for the lower expected cross-section in the sbottom and stop cases. The signal efficiency for gluino, sbottom and stop \rhads is typically 8--12\%, 5--9\% and 8--13\%, respectively, in the MS-agnostic search and 8--15\%, 8--11\% and 15--18\%, respectively, in the full-detector search, depending on the mass hypothesis. While stops and sbottoms have the same cross-section, sbottoms tend to hadronise into neutral states (57\%) slightly more often than stops (43\%). In addition, more sbottom-based \rhads convert into neutral states, as they traverse material, than stop-based \rhads do, reducing the efficiency of the sbottom search compared to the stop one.
\section{Background estimation} \label{sec:background}
The background for all searches is almost entirely composed of high-\pt muons with mismeasured $\beta$ and/or large ionisation. Most of this instrumental background is rejected by requiring a $\beta$ measurement significantly smaller than one and by requiring consistency between the different, independent $\beta$ and $\beta\gamma$ measurements. The background estimate is derived from data in all cases. The background mass distribution can be estimated by producing random pairings of momentum and $\beta$ (and $\beta\gamma$ where applicable) according to the distributions seen in the data. The procedure relies on two validated assumptions: that the signal-to-background ratio before applying selections on $\beta$ ($\beta\gamma$) is small, and that the $\beta$ ($\beta\gamma$) distribution for background candidates is due to measurement resolution and is therefore independent of the source of the candidate and its momentum.
To avoid $\beta$--momentum measurement correlations arising from different detector systems and for different pseudorapidity regions, the detector is divided into eight $\eta$ regions so that the $\beta$ resolution within each region is similar.
\subsection{Slepton and chargino searches} \label{sec:background_sleptonchargino}
The muon $\beta$ probability density function (pdf) in each $\eta$ region is the distribution of the measured $\beta$ of muons in the region normalised to unity, and is obtained separately for each signal region from candidates passing the selection described in sections~\ref{sec:selection_offline_event_slepton} and \ref{sec:selection_offline_event_chargino}, but without the requirements on the value of $\beta$ or $m_{\beta}$.
The background is then estimated by drawing a random $\beta$ from the appropriate muon $\beta$ pdf and calculating $m_{\beta}$ using the momentum of the reconstructed LLP candidates only in cases where the $\beta$ satisfies the selection requirement. Events with two candidates before the $\beta$ requirement are used to estimate the background in \srslcc and \srchcc. The statistical uncertainty of the background estimate is reduced by repeating this procedure many times for each candidate and dividing the resulting distribution by the number of repetitions.
\subsection{\rhad searches} \label{sec:background_rhadron}
In the \rhad searches, the pdfs are produced from candidates in data, which satisfy the selection criteria, except those on $\beta$, $\beta\gamma$, $m_\beta$ and $m_{\beta\gamma}$. As each particle/mass hypothesis has a different selection, the background estimates are produced in each case.
The momentum pdf is produced from candidates that pass the momentum requirement, but have $\beta < 0.90$ and $\beta\gamma < 2.5$, while the $\beta$ and $\beta\gamma$ pdfs are produced by selecting candidates which pass the respective $\beta$ and $\beta\gamma$ selection and have momentum in the range $70~\GeV < p < 180~\GeV$. This ensures that enough events are selected for the background pdfs to reflect the signal region even at high masses.
The independence of $p$, $\beta$ and $\beta\gamma$ required for this approach to work is achieved by considering five equidistant regions in $|\eta|$. The typical number of events in the pdfs used for generating the background estimate is $O(10^{4})$.
\section{Systematic uncertainties} \label{sec:syst}
Several possible sources of systematic uncertainty are studied. The resulting systematic uncertainties are summarised in tables~\ref{tab:systematics1} and \ref{tab:systematics2}. The uncertainties given are those on the expected yields in the signal region.
\begin{table*}[tb]
\footnotesize
\begin{center}
{\setlength{\tabcolsep}{0em}\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}}lrrrr}
\hline\hline
& \multicolumn{2}{c}{GMSB} & \multicolumn{2}{c}{\lsusy} \\
Source & \srslc & \srslcc & \srslc & \srslcc \\
\hline
\hline
Signal size -- theory & 5 & 5 & 1--54 & 1--54 \\
\hline
Signal efficiency & & & & \\
~$\cdot$~Trigger efficiency & 3.2 & 3.2 & 3.1 & 3.1 \\
~$\cdot$~ISR & $\leq$0.5 & $\leq$0.5 & $\leq$0.5 & $\leq$0.5 \\
~$\cdot$~Pixel \dedx calibration & 1.1 & 1.1 & 1.1 & 1.1 \\
~$\cdot$~$\beta$ timing calibration & 1.0 & 2.0 & 1.0 & 2.0 \\
Total signal efficiency & 3.6 & 4.0 & 3.5 & 3.9 \\
\hline
Luminosity & 2.8 & 2.8 & 2.8 & 2.8 \\
\hline
Background estimate & 10--12 & 8.3--9 & 10--12 & 8.3--9 \\
\hline
\hline
\end{tabular*}}
\caption{Summary of systematic uncertainties for the slepton searches (given in percent). Ranges indicate a mass dependence for the given uncertainty (low mass to high mass).}
\label{tab:systematics1}
\end{center}
\end{table*}
\begin{table*}[tb]
\footnotesize
\begin{center}
{\setlength{\tabcolsep}{0em}\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}}lrrrr}
\hline\hline
& \multicolumn{3}{c}{Charginos} & \rhads \\
Source & \srchc & \srchcl & \srchcc & \srrhma \& \srrhfd \\
\hline
\hline
Signal size -- theory & 8.5 & 8.5 & 8.5 & 15--56 \\
\hline
Signal efficiency & & & & \\
~$\cdot$~Trigger efficiency & 3.4 & 3.4 & 3.4 & $\leq$2.4 \\
~$\cdot$~ISR & $\leq$1.0 & $\leq$1.0 & $\leq$1.0 & $\leq$9 \\
~$\cdot$~Pixel \dedx calibration & 1.1 & 1.1 & 1.1 & 1.1 \\
~$\cdot$~$\beta$ timing calibration & 1.0 & 1.0 & 2.0 & $\leq$3.6 \\
~$\cdot$~Offline \etmiss scale & 5.6--7.6 & 2--4.2 & & \\
Total signal efficiency & 6.8--8.5 & 4.3--5.7 & 4.2 & $\leq$10.2 \\
\hline
Luminosity & 2.8 & 2.8 & 2.8 & 2.8 \\
\hline
Background estimate & 3.5--6.8 & 4 & 8.7--20 & 3--15 \\
\hline
\hline
\end{tabular*}}
\caption{Summary of systematic uncertainties for the chargino and \rhad searches (given in percent). Ranges indicate a mass dependence for the given uncertainty (low mass to high mass).}
\label{tab:systematics2}
\end{center}
\end{table*}
\subsection{Theoretical cross-sections} \label{sec:syst_theo}
Signal cross-sections are calculated to next-to-leading order in the strong coupling constant, including the resummation of soft gluon emission at next-to-leading-logarithm accuracy (NLO+NLL)\footnote{The NLL correction is used only for strong squark and gluino production when the squark and gluino masses lie between 200~\GeV and 2~\TeV. Following the convention used in the NLO calculators the squark mass is defined as the average of the squark masses in the first two generations. In the case of gluino-pair (associated squark--gluino) production processes, the NLL calculations are extended up to squark masses of 4.5~\TeV (3.5~\TeV). For masses outside this range and for other types of production processes (i.e. electroweak and associated strong and electroweak), cross-sections at NLO accuracy obtained with \prospino~\cite{Beenakker:1996ch} are used.}~\cite{Beenakker:1997ut, Beenakker:2010nq, Beenakker:2011fu}. The nominal cross-section and the uncertainty are taken from an envelope of cross-section predictions using different parton distribution function sets and factorisation and renormalisation scales, as described in reference~\cite{Kramer:2012bx}.
The procedure results in an uncertainty of 5\% for the GMSB slepton search (dominated by electroweak production), between 1\% (low squark mass) and 54\% (high squark mass) in the \lsusy slepton search, 8.5\% in the stable-chargino search and from 15\% (at 400~\GeV) to 56\% (at 1700~\GeV) in the \rhad searches.
\subsection{Signal efficiency} \label{sec:syst_signal}
The muon trigger efficiency for muons is calculated using the tag-and-probe technique on \zmumu events as described in reference~\cite{Aad:2014sca}. The reduction in the muon trigger efficiency due to late arrival of particles is estimated from simulation. However, the quality of the estimate depends on the exact timing implementation in the simulation, and needs to agree well with the data in order to obtain a good estimate of the trigger efficiency. For events triggered by the RPC, a systematic uncertainty is estimated by smearing the hit times in the simulation according to uncalibrated data, and applying the trigger efficiency as a function of $\beta$. The uncertainty on events triggered by the TGC is negligible due to an accurate timing description in the simulation. The resulting systematic uncertainty on the muon trigger efficiency is between 2.9\% and 3.4\%, depending on the signal model.
The \etmiss triggers use calorimeter energy deposits to calculate the transverse energy, and are thus blind to muons. Therefore, \zmumu events can be used for calibration and to study systematic uncertainties. To evaluate the trigger efficiency, the trigger turn-on curve is obtained by fitting the measured efficiency as a function of \etmiss in \zmumu events, both in data and simulation. These efficiency turn-on curves are then applied to the expected \etmiss spectrum from simulated signal events. The total uncertainty is estimated from three contributions: the relative difference between the efficiencies obtained using the fitted threshold curves from \zmumu data and simulation\hide{ \raisebox{.5pt}{\textcircled{\raisebox{-.1pt} {\scriptsize 1}}}} as well as the differences in efficiency obtained from independent $\pm 1\sigma$ variations in fit parameters relative to the unchanged turn-on curve fit for both \zmumu data\hide{ \raisebox{.5pt}{\textcircled{\raisebox{-.1pt} {\scriptsize 2}}}} and MC simulation\hide{ \raisebox{.5pt}{\textcircled{\raisebox{-.1pt} {\scriptsize 3}}}}. The total estimated \etmiss trigger uncertainties are 1.2\%, 3.4\%, 2.5\%, 2.3\% and 2.3\% for sleptons, stable charginos as well as gluino, sbottom and stop \rhads, respectively. These uncertainties include effects of a 10\% variation of the \etmiss scale, motivated by comparing the calorimeter response in \zmumu events between data and simulation.
The trigger efficiency depends on the amount of ISR. To evaluate the associated uncertainty, a number of representative mass hypotheses are reproduced, setting the \pythia radiation level low and high~\cite[p.~391]{Sjostrand:2006za}. A simple threshold curve modelling of the trigger is applied to those and the nominal samples. The largest variation from the central sample is found to be between 0.5\% and 1\% for the slepton and chargino searches and below 9\% for the \rhad searches.
The systematic uncertainty on the efficiency of the offline \etmiss selection for \srchcl is determined by varying the energy or momentum scale of the individual components entering the calculation, and propagating these changes to the \etmiss calculation. The dominant contributions are the muon momentum scale (at low masses) and the jet energy scale~\cite{Aad:2014bia} (at high masses). A systematic uncertainty on the signal efficiency can be obtained by using those scaled values when applying the \etmiss requirement and is estimated to be between 2\% and 7.6\%. \srchc is affected by candidates migrating in or out of \srchcl.
The signal $\beta$ resolution is estimated by smearing the measured time of hits in the MS and calorimeter according to the spread observed in the time calibration. The systematic uncertainty due to the smearing process is estimated by scaling the smearing factor up and down, so as to bracket the distribution obtained in data. A 1\% (2\%) systematic uncertainty is found in \srslc and \srchc (\srslcc and \srchcc) for the slepton and chargino searches, respectively. The corresponding uncertainty for \rhads is estimated to be less than 3.6\% (1\%) in the full-detector (MS-agnostic) approach.
The $\beta\gamma$ measurement from the pixel \dedx carries a systematic uncertainty due to the difference between simulation (signal) and data (predominantly background). This difference can be measured using \zmumu events in data and simulation, and the scale between data and MC simulation is found to be different by 2.3\%. In addition, variations in the $\beta\gamma$ scale are checked, assuming tracking to be very stable, by monitoring the measured proton mass over time. This results in an RMS of 0.6\%, yielding a total scale uncertainty of 2.4\%. Applying this scale uncertainty in simulated signal events leads to uncertainties on the signal efficiency of
1.1\% at low \rhad masses (300~\GeV) and 0.4\% at higher masses (500 and 800~\GeV). For simplicity, a systematic uncertainty of 1.1\% is applied for all masses.
The uncertainty on the integrated luminosity is $\pm$2.8\%. It is derived, following the same methodology as that detailed in reference~\cite{Aad:2013ucp}, from a preliminary calibration of the luminosity scale derived from beam-separation scans performed in November 2012.
\subsection{Background estimation} \label{sec:syst_bkg}
To test the momentum dependence of the muon $\beta$ pdf, the candidates in each $\eta$ region are split into a high and a low momentum category with the same amount of events in each, and the background is estimated with the resulting $\beta$ pdfs. The effect on the background estimation due to residual $p$--$\beta$ correlations is assessed by using a finer $|\eta|$ division in the slepton searches. The detector is sub-divided into 25 $|\eta|$ regions instead of the 8 used in the analysis and the background is estimated with this division.
Similar tests are performed to determine the uncertainty on the background for the \rhad search. Unlike the slepton search, the range of mass hypotheses tested is very large, and it is found that the size of the systematic uncertainty on the background estimate grows with mass. In order to quantify the systematic uncertainty, the pdfs used to produce the background estimates are varied, both by changing the selection range used for producing them and also by dividing the selection ranges into two sub-ranges, and comparing the resulting background estimates from these sub-range pdfs.
The total uncertainties on the background estimate are 8.3--9\% for \srslcc increasing with mass, and 10--12\% for \srslc in the slepton searches. The uncertainties in the chargino searches are 3.5--6.8\% for \srchc, 4\% for \srchcl and 8.7--20\% for \srchcc. For \rhads the uncertainty is 3--15\%.
\section{Results}
The mass distributions observed in data together with the background estimate, its systematic uncertainty and examples of expected signal are shown in figures~\ref{fig:DSB}--\ref{fig:rhadronBkgDists} for the slepton, chargino and \rhad searches, respectively.
\begin{figure*}[p]
\centering
\includegraphics[width=0.48\linewidth]{fig_02a.pdf}
\includegraphics[width=0.48\linewidth]{fig_02b.pdf}
\includegraphics[width=0.48\linewidth]{fig_02c.pdf}
\caption{Reconstructed mass $m_\beta$ of one candidate ($m_2$) versus $m_\beta$ of the other candidate ($m_1$) for observed data and expected signal, in the GMSB slepton search in the two-candidate signal region (top-left). Observed data, background estimate and expected signal in the slepton search for the lower of the two masses ($m$) in the two-candidate signal region (GMSB $\stau_1$ masses of 344.5 and 437~\GeV; top-right) and for the one-candidate signal region (\lsusy $m_{\tilde q}$ = 2.0, 1.2 and 0.9~\TeV with $m_{\tilde g}$ = 1.2~\TeV; bottom).}
\label{fig:DSB}
\end{figure*}
\begin{figure*}[p]
\centering
\includegraphics[width=0.48\linewidth]{fig_03a.pdf}
\includegraphics[width=0.48\linewidth]{fig_03b.pdf}
\includegraphics[width=0.48\linewidth]{fig_03c.pdf}
\caption{Reconstructed mass $m_\beta$ in observed data, background estimate and expected signal ($\tilde{\chi}^{\pm}_1$ masses of 400 and 600~\GeV) in the chargino search for the lower of the two masses ($m$) in the two-candidate signal region (top-left), for the one-loose-candidate signal region (top-right) and the one-candidate signal region (bottom).}
\label{fig:chargino_results}
\end{figure*}
\begin{figure*}[tb]
\centering
\includegraphics[width=.48\linewidth]{fig_04a.pdf}
\includegraphics[width=.48\linewidth]{fig_04b.pdf}
\includegraphics[width=.48\linewidth]{fig_04c.pdf}
\includegraphics[width=.48\linewidth]{fig_04d.pdf}
\caption{Data and background estimates for the reconstructed mass based on time-of-flight, $m_{\beta}$, (top-left) and based on specific energy loss, $m_{\beta\gamma}$, (top-right) for \combined candidates in the full-detector 500~\GeV gluino \rhad search (\srrhfd), as well as $m_{\beta}$ (bottom-left) for the MS-agnostic 500~\GeV sbottom and $m_{\beta\gamma}$ (bottom-right) for the MS-agnostic 500~\GeV stop \rhad search (\srrhma). \label{fig:rhadronBkgDists}}
\end{figure*}
No indication of signal above the expected background is observed, and limits on new physics scenarios are set using the \CLs prescription~\cite{Read:2000ru}.
For each search, limits on the cross-section are calculated from the likelihood to observe the number of events found in each signal region with candidate mass $m_\beta$ (and $m_{\beta\gamma}$ for \rhads) above the required mass value, given the background estimate and signal efficiency. For each signal region the likelihood function is built assuming a Poisson counting model for the observed number of events with Gaussian constraints for the systematic uncertainties. For the slepton and the chargino searches a global extended likelihood, given by the product of the likelihood functions of the various signal regions, is used. The \CLs calculation uses a profile likelihood test statistic~\cite{Roostat}.
Mass limits are derived by comparing the obtained cross-section limits to the lower edge of the $\pm 1\sigma$ band around the theoretically predicted cross-section for each process. Examples of the observed and expected event yields, as well as efficiencies and uncertainties for data and some MC simulation signal samples, are shown in tables~\ref{tab:GMSBResults}--\ref{tab:RHADResults} for the various searches and signal regions.
\begin{table*}[tb]
\footnotesize
\begin{center}
{\setlength{\tabcolsep}{0em}\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}clrrr}
\hline
\hline
& $\stau_1$ mass [GeV] & 345 & 407 & 469 \\
\hline
\multirow{5}{*}{\begin{turn}{90}\srslcc\end{turn}}
& Minimum $m_{\beta}$ requirement [GeV] & 240 & 270 & 320 \\
& Expected signal & 12.5 & 5.1 & 2.1 \\
& Efficiency & 0.28$\pm$0.01 & 0.29$\pm$0.01 & 0.28$\pm$0.01 \\
& Estimated background & 0.43$\pm$0.05 & 0.25$\pm$0.03 & 0.10$\pm$0.01 \\
& Observed & 0 & 0 & 0 \\
\hline
\multirow{5}{*}{\begin{turn}{90}\srslc\end{turn}}
& Minimum $m_{\beta}$ requirement [GeV] & 240 & 280 & 320 \\
& Expected signal & 8.5 & 3.5 & 1.5 \\
& Efficiency & 0.19$\pm$0.01 & 0.20$\pm$0.01 & 0.21$\pm$0.01 \\
& Estimated background & 49$\pm$5 & 27$\pm$3 & 15$\pm$1 \\
& Observed & 47 & 28 & 20 \\
\hline
& Cross-section limit [fb] & 0.52 & 0.50 & 0.54 \\
\hline
\hline
\end{tabular*}}
\caption{Observed and expected event yields, as well as efficiencies and uncertainties for three MC simulation signal samples, in the two signal regions used in the GMSB slepton search. Cross-section upper limits are stated at 95\% CL.} \label{tab:GMSBResults}
\end{center}
\end{table*}
\begin{table*}[tb]
\footnotesize
\begin{center}
{\setlength{\tabcolsep}{0em}\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}clrrr}
\hline
\hline
& $\tilde{q}$ mass [GeV] & 1200 & 2000 & 3000 \\
& $\tilde{g}$ mass [GeV] & 1600 & 1400 & 1600 \\
\hline
\multirow{5}{*}{\begin{turn}{90}\srslcc\end{turn}}
& Minimum $m_{\beta}$ requirement [\GeV] & 190 & 190 & 190 \\
& Expected signal & 96.5 & 6.9 & 0.5 \\
& Efficiency & 0.27$\pm$0.01 & 0.30$\pm$0.01 & 0.19$\pm$0.01 \\
& Estimated background & 1.36$\pm$0.14 & 1.36$\pm$0.14 & 1.36$\pm$0.14 \\
& Observed & 0 & 0 & 0 \\
\hline
\multirow{5}{*}{\begin{turn}{90}\srslc\end{turn}}
& Minimum $m_{\beta}$ requirement [\GeV] & 210 & 210 & 210 \\
& Expected signal & 66.9 & 4.9 & 0.5 \\
& Efficiency & 0.190$\pm$0.007 & 0.207$\pm$0.007 & 0.181$\pm$0.006 \\
& Estimated background & 80$\pm$7 & 80$\pm$7 & 80$\pm$7 \\
& Observed & 73 & 73 & 73 \\
\hline
& Cross-section limit [fb] & 0.55 & 0.49 & 0.78 \\
\hline
\hline
\end{tabular*}}
\caption{Observed and expected event yields, as well as efficiencies and uncertainties for three MC simulation signal samples, in the three signal regions used in the \lsusy slepton search. Cross-section upper limits are stated at 95\% CL.} \label{tab:LSResults}
\end{center}
\end{table*}
\begin{table*}[tb]
\footnotesize
\begin{center}
{\setlength{\tabcolsep}{0em}\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}clrrr}
\hline
\hline
& $\tilde{\chi}^{\pm}_{1}$ mass [GeV] & 500 & 600 & 700 \\
\hline
\multirow{5}{*}{\begin{turn}{90}\srchcc\end{turn}}
& Minimum $m_{\beta}$ requirement [GeV] & 350 & 420 & 480 \\
& Expected signal & 16.9 & 4.9 & 1.5 \\
& Efficiency & 0.061$\pm$0.003 & 0.054$\pm$0.002 & 0.047$\pm$0.002 \\
& Estimated background & 0.053$\pm$0.006 & 0.018$\pm$0.003 & 0.008$\pm$0.001 \\
& Observed & 0 & 0 & 0 \\
\hline
\multirow{5}{*}{\begin{turn}{90}\srchcl\end{turn}}
& Minimum $m_{\beta}$ requirement [GeV] & 300 & 330 & 420 \\
& Expected signal & 35.0 & 10.7 & 3.3 \\
& Efficiency & 0.126$\pm$0.006 & 0.118$\pm$0.005 & 0.109$\pm$0.005 \\
& Estimated background & 29.6$\pm$0.3 & 21.1$\pm$0.3 & 8.6$\pm$0.3 \\
& Observed & 37 & 31 & 12 \\
\hline
\multirow{5}{*}{\begin{turn}{90}\srchc\end{turn}}
& Minimum $m_{\beta}$ requirement [GeV] & 340 & 430 & 450 \\
& Expected signal & 9.21 & 2.95 & 0.99 \\
& Efficiency & 0.033$\pm$0.002 & 0.033$\pm$0.002 & 0.032$\pm$0.002 \\
& Estimated background & 14.14$\pm$0.67 & 4.85$\pm$0.21 & 3.91$\pm$0.16 \\
& Observed & 14 & 6 & 6 \\
\hline
& Cross-section limit [fb] & 2.18 & 3.31 & 2.62 \\
\hline
\hline
\end{tabular*}}
\caption{Observed and expected event yields, as well as efficiencies and uncertainties for three MC simulation signal samples, in the three signal regions used in the chargino search. Cross-section upper limits are stated at 95\% CL.} \label{tab:CHARResults}
\end{center}
\end{table*}
\begin{table*}[tb]
\footnotesize
\begin{center}
{\setlength{\tabcolsep}{0em}\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}clrrr}
\hline
\hline
& \rhad type / mass [GeV] & $\tilde{g}$ / 1300 & $\tilde{b}$ / 800 & $\tilde{t}$ / 900 \\
\hline
\multirow{6}{*}{\begin{turn}{90}\srrhma\end{turn}}
& Minimum $m_{\beta\gamma}$ requirement [GeV] & 785.1 & 560.3 & 612.9 \\
& Minimum $m_{\beta}$ requirement [GeV] & 746.9 & 512.7 & 565.5 \\
& Expected signal & 3.09 & 4.63 & 2.54 \\
& Efficiency & 0.10$\pm$0.01 & 0.084$\pm$0.009 & 0.12$\pm$0.01 \\
& Estimated background & 0.010$\pm$0.001 & 0.27$\pm$0.02 & 0.18$\pm$0.02 \\
& Observed & 0 & 0 & 0 \\
\hline
& Cross-section limit [fb] & 1.53 & 1.8 & 1.23 \\
\hline
\hline
& & & & \\
\hline
\hline
& \rhad type / mass [GeV] & $\tilde{g}$ / 1300 & $\tilde{b}$ / 800 & $\tilde{t}$ / 900 \\
\hline
\multirow{6}{*}{\begin{turn}{90}\srrhfd\end{turn}}
& Minimum $m_{\beta\gamma}$ requirement [GeV] & 785.1 & 560.3 & 612.9 \\
& Minimum $m_{\beta}$ requirement [GeV] & 746.9 & 512.7 & 565.5 \\
& Expected signal & 3.50 & 5.90 & 3.50 \\
& Efficiency & 0.11$\pm$0.01 & 0.11$\pm$0.01 & 0.17$\pm$0.02 \\
& Estimated background & 0.051$\pm$0.006 & 0.73$\pm$0.06 & 0.40$\pm$0.03 \\
& Observed & 0 & 1 & 0 \\
\hline
& Cross-section limit [fb] & 1.33 & 1.80 & 0.84 \\
\hline
\hline
\end{tabular*}}
\caption{Observed and expected event yields, as well as efficiencies and uncertainties for three MC simulation signal samples, in the \rhad searches. Cross-section upper limits are stated at 95\% CL.} \label{tab:RHADResults}
\end{center}
\end{table*}
\subsection{Slepton limits}
The resulting production cross-section limits at 95\% confidence level (CL) in the GMSB scenario as a function of the $\stau_1$ mass are presented in figure~\ref{fig:limit_by_tanb} and compared to theoretical predictions.
A long-lived $\stau_1$ in GMSB models with $N_5=3$, $m_{\rm{messenger}}=250~\TeV$ and $\mathrm{sign}(\mu)=1$ is excluded at 95\% CL up to masses of 440, 440, 430, 410, 385\xspace~\GeV for $\tan\beta$ = 10, 20, 30, 40 and 50, respectively.
\begin{figure*}[tb]
\centering
\includegraphics[width=0.48\linewidth]{fig_05a.pdf}
\includegraphics[width=0.48\linewidth]{fig_05b.pdf}
\includegraphics[width=0.48\linewidth]{fig_05c.pdf}
\includegraphics[width=0.48\linewidth]{fig_05d.pdf}
\includegraphics[width=0.48\linewidth]{fig_05e.pdf}
\caption{Cross-section upper limits as a function of the mass of the lightest stau for the GMSB models organised by $\tan\beta$: 10 and 20 first row, 30 and 40 second row and 50 last row. The expected limit is drawn as a dashed black line with $\pm 1\sigma$ and $\pm 2\sigma$ uncertainty bands drawn in green and yellow, respectively. The observed limit is shown as solid black line with markers. The theoretical cross-section prediction is shown as a solid blue line with a shaded $\pm 1\sigma$ uncertainty band.} \label{fig:limit_by_tanb}
\end{figure*}
Limits on the rates of specific production mechanisms are obtained by repeating the analysis on subsets of the GMSB samples corresponding to each production mode. For GMSB models with parameters in this range, strong production of squarks and gluinos is suppressed due to their large masses. Directly produced sleptons constitute 30--63\% of the GMSB cross-section, and the corresponding $\stau_1$ production rates depend only on the $\stau_1$ mass and the mass difference between the right-handed $\tilde{e}$ (or $\tilde{\mu}$) and the $\stau_1$. Thus the same analysis constrains a simple model with only pair-produced sleptons which are long-lived, or which themselves decay to long-lived sleptons of another flavour. Such direct production is excluded at 95\% CL up to $\stau_1$ masses of 373 to 330~\GeV for models with slepton mass splittings of 2.7--93~\GeV. The slepton direct-production limits are shown in figure~\ref{fig:limits2d-DY}. Figure~\ref{fig:limitsSTAU-STAU} shows the cross-section limits on direct $\stau_1$ production for the case where the mass splitting from the other sleptons is very large. As the theoretical prediction as well as the according uncertainty bands overlap almost entirely for various values of $\tan\beta$, only the curve for $\tan\beta = 10$ is shown. Masses below 286~\GeV are excluded if only $\stau_1$ is produced. The values for direct $\stau_1$-only production are also used in figure~\ref{fig:limits2d-DY} at very high mass splittings.
Finally, in the context of the GMSB model, 30--50\% of the GMSB cross-section arises from direct production of charginos and neutralinos (dominated by $\tilde{\chi}^0_1 \tilde{\chi}^{\pm}_1$ production) and subsequent decay to $\stau_1$. Figure~\ref{fig:limitsCHI-EW} shows the 95\% CL lower limits on the $\tilde{\chi}^0_1$ and $\tilde{\chi}^\pm_1$ mass when the final decay product is a long-lived $\stau_1$. In the samples used to derive these limits, the $\tilde{\chi}^0_1$ and $\tilde{\chi}^{\pm}_1$ masses are closely related by GMSB, as represented by the values on the two $x$-axes. The mass of the $\stau_1$ decreases with increasing $\tan\beta$ and increases with the $\tilde{\chi}^0_1$ and $\tilde{\chi}^\pm_1$ masses. At low $\tilde{\chi}^0_1$ and $\tilde{\chi}^\pm_1$ masses and large $\tan\beta$, the cross-section limits are thus affected by the amount of background in the $\stau_1$ mass search region, which starts at 120~\GeV for $\tan\beta=50$ and at 170~\GeV for $\tan\beta=10$. The cross-section limits exclude $\tilde{\chi}^0_1$ masses below 537~\GeV, with corresponding $\tilde{\chi}^\pm_1$ masses 210--260~\GeV higher.
\begin{figure*}[tb]
\centering
\includegraphics[width=0.48\linewidth]{fig_06a.pdf}
\caption{95\% CL excluded regions for directly produced sleptons in the plane $m(\tilde{\ell})$--$m(\stau_1)$ vs. $m(\stau_1)$. The excluded region is is shown in blue. The expected limit is drawn as a solid black line with a $\pm 1 \sigma$ uncertainty band drawn as dashed black lines. The observed limit is shown as solid red line with a $\pm 1 \sigma$ uncertainty band drawn as dashed red lines.}
\label{fig:limits2d-DY}
\end{figure*}
\begin{figure*}[tb]
\centering
\includegraphics[width=0.48\linewidth]{fig_07a.pdf}
\caption{Cross-section upper limits as a function of the $\stau_1$ mass for direct $\stau_1$ production and three values of $\tan\beta$. The expected limit for $\tan\beta=10$ is drawn as a dashed black line with $\pm 1\sigma$ and $\pm 2\sigma$ uncertainty bands drawn in green and yellow, respectively. The observed limits for three values of $\tan\beta$ are shown as solid lines with markers. The theoretical cross-section prediction for $\tan\beta=10$ is shown as a coloured $\pm 1\sigma$ band, and does not vary significantly for the other $\tan\beta$ values.
}
\label{fig:limitsSTAU-STAU}
\end{figure*}
\begin{figure*}[tb]
\centering
\includegraphics[width=0.48\linewidth]{fig_08a.pdf}
\caption{Cross-section upper limits as a function of the $\tilde{\chi}_1$ mass for $\stau_1$ sleptons resulting from the decay of directly produced charginos and neutralinos in GMSB. Observed limits are given as a solid black line with markers. Expected limits for $\tan\beta=10$ are drawn as a dashed black line with $\pm 1\sigma$ and $\pm 2\sigma$ uncertainty bands drawn in green and yellow, respectively. The theoretical cross-section prediction (dominated by $\tilde{\chi}^0_1 \tilde{\chi}^+_1$ production) is shown as a coloured $\pm 1\sigma$ band. Depending on the hypothesis and to a small extent on $\tan\beta$, in these models, the chargino mass is 210 to 260~\GeV higher than the neutralino mass.}
\label{fig:limitsCHI-EW}
\end{figure*}
Limits on \lsusy scenarios are set on squarks and gluinos decaying to long-lived sleptons within the \lsusy model. The exclusion region in the plane $m(\tilde{g})$ vs. $m(\tilde{q})$ is shown in figure~\ref{fig:ls_limit}. Squark and gluino masses are excluded at 95\% CL up to a mass of 1500\xspace and 1360\xspace~\GeV, respectively, in simplified \lsusy models where sleptons are stable and degenerate, with a mass of 300~\GeV, and all neutralinos (except $\tilde{\chi}^0_1$) and charginos are decoupled.
\begin{figure*}[tb]
\centering
\includegraphics[width=0.48\linewidth]{fig_09a.pdf}
\caption{95\% CL excluded regions of squark mass and gluino mass in the \lsusy models. The excluded region is is shown in blue. The expected limit is drawn as a solid black line with a $\pm 1 \sigma$ uncertainty band drawn as dashed black lines. The observed limit is shown as solid red line with a $\pm 1 \sigma$ uncertainty band drawn as dashed red lines.}
\label{fig:ls_limit}
\end{figure*}
\subsection{Chargino limits}
Limits are set on long-lived charginos, which are nearly degenerate with the lightest neutralino in simplified SUSY models. The production cross-section limits at 95\% CL in this scenario as a function of the $\tilde{\chi}^{\pm}_1$ mass are presented in figure~\ref{fig:char_limit} and compared to theoretical predictions. Masses below 620\xspace~\GeV are excluded. The observed cross-section limit is found to be consistently one or two standard deviations ($\sigma$) above the expected limit, due to an excess of data events relative to the background estimate in \srchcl, as can be seen in figure~\ref{fig:chargino_results} (top-right).
\begin{figure*}[tb]
\centering
\includegraphics[width=0.48\linewidth]{fig_10a.pdf}
\caption{Cross-section upper limits for various chargino masses in stable-chargino models. The expected limit is drawn as a dashed black line with $\pm 1\sigma$ and $\pm 2\sigma$ uncertainty bands drawn in green and yellow, respectively. The observed limit is shown as solid black line with markers. The theoretical cross-section prediction is shown as a solid blue line with a shaded $\pm 1\sigma$ uncertainty band.}
\label{fig:char_limit}
\end{figure*}
\subsection{\rhad limits}
The \rhad limits in the MS-agnostic (left) and full-detector (right) searches are shown in figure~\ref{fig:RHad_limit}. In the full-detector search for \rhads a lower mass limit at $95\%$ CL of 1270\xspace~\GeV for gluinos, 845\xspace~\GeV for sbottoms and 900\xspace~\GeV for stops is obtained. A selection relying solely on the inner detector and calorimeters, thereby covering e.g.\ \rhads which change into neutral bound states in the calorimeters before reaching the MS, yields a lower mass limit of 1260\xspace~\GeV for gluinos, 835\xspace~\GeV for sbottoms and 870\xspace~\GeV for stops.
\begin{figure*}[tb]
\centering
\includegraphics[width=0.48\linewidth]{fig_11a.pdf}
\includegraphics[width=0.48\linewidth]{fig_11b.pdf}
\includegraphics[width=0.48\linewidth]{fig_11c.pdf}
\includegraphics[width=0.48\linewidth]{fig_11d.pdf}
\includegraphics[width=0.48\linewidth]{fig_11e.pdf}
\includegraphics[width=0.48\linewidth]{fig_11f.pdf}
\caption{Cross-section upper limits as a function of the LLP mass for the \rhad models for the MS-agnostic (left) and full-detector search (right). The expected limit is drawn as a dashed black line with $\pm 1\sigma$ and $\pm 2\sigma$ uncertainty bands drawn in green and yellow, respectively. The observed limit is shown as solid black line with markers. The theoretical cross-section prediction is shown as a solid blue line with a shaded $\pm 1\sigma$ uncertainty band.}
\label{fig:RHad_limit}
\end{figure*}
\begin{table}[tb]
\footnotesize
\begin{center}
{\setlength{\tabcolsep}{0em}\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}lr}
\hline
\hline
Search & Lower mass limit [GeV] \\
\hline
GMSB sleptons & \\
~$\cdot$~$\tan\beta=10,20,30,40,50$ & 440, 440, 430, 410, 385\xspace \\
\multicolumn{2}{l}{~$\cdot$~direct $\tilde{\ell}$ production {\scriptsize ($m_{\tilde{\ell}}-m_{\stau_1}=2.7$--93~\GeV)} \hfill 377--335} \\
~$\cdot$~direct $\stau_1$ production & 289 \\
~$\cdot$~$\tilde{\chi}^0_1\tilde{\chi}^{\pm}_1$ decaying to stable $\stau_1$ & 537 \\
\hline
\lsusy & \\
~$\cdot$~$\tilde{q}$,~$\tilde{g}$ & 1500\xspace, 1360\xspace \\
\hline
Charginos & \\
~$\cdot$~$\tilde{\chi}^{\pm}_1$ & 620\xspace \\
\hline
\rhads & \\
~$\cdot$~$\tilde{g}$, $\tilde{b}$, $\tilde{t}$ (full-detector) & 1270\xspace, 845\xspace and 900\xspace \\
~$\cdot$~$\tilde{g}$, $\tilde{b}$, $\tilde{t}$ (MS-agnostic) & 1260\xspace, 835\xspace and 870\xspace \\
\hline
\hline
\end{tabular*}}
\caption{Summary of the lower mass limits (95\% CL) from the various searches.} \label{tab:AllResults}
\end{center}
\end{table}
\section{Conclusion}
Searches for heavy long-lived charged particles are performed through measurement of the mass of candidates by means of time-of-flight and specific ionisation loss measurements in ATLAS sub-detectors using a data sample of \lumi from proton--proton collisions at a centre-of-mass energy of $\sqrt{s} = 8~\TeV$ collected by the ATLAS detector at the Large Hadron Collider. The data are found to match the Standard Model background expectation within uncertainties. The exclusion limits placed for various models impose new constraints on non-SM cross-sections.
An overview on all 95\% CL lower mass limits placed in this article is given in table~\ref{tab:AllResults}.
The upper limits placed on cross-sections and lower limits placed on the mass of long-lived particles in various supersymmetric models, thanks to increased luminosity and more advanced data analysis, substantially extend previous ATLAS limits, and are largely complementary to searches for promptly decaying SUSY particles.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,453 |
\section{Introduction}
In this note, we consider two different types of method that can be applied in searches for new particles
or new phenomena.
An example would be the search for some hypothesised particle, such as the recently discovered Standard
Model (S.M.) Higgs boson. For such a search, the data could be a mass
histogram or the corresponding individual mass values, but more realistically would be augmented
by other relevant kinematic variables. Then the aim is to try to distinguish between two hypotheses: that
the data are due to some background processes ($H_0$), or that there is also the production of some
new particle ($H_1$) \footnote{ Slightly confusingly, in this example the Higgs boson $H^0$ is not considered to be
part of the null hypothesis $H_0$. }. The former would result in some relatively smooth mass distribution, while the more exciting
production of a new particle would produce a fairly sharp peak in mass spectra.
We regard the new particle as being characterised by its mass $m_H$ and by its production
cross-section $\sigma \ $\footnote{We use the symbol $\sigma$ both for cross-section and for standard deviation.
The meaning should be abundantly clear from the context. }. We use this example through most of this note, but a
couple of other situations involving new physics are discussed in Section 2.
We consider two possible approaches:
\begin{itemize}
\item{ Raster scan. Here we search over the physically interesting range of masses, and at each one separately
we make a decision as to whether we can claim a discovery (i.e. decide that $H_0$ is excluded, and
that $H_1$ is acceptable); exclude the existence
of the new particle (reject $H_1$); or be unable to discriminate between them. This is done separately at each possible
mass in the range, before moving on to the next mass - see Section 3.1.}
\item{ 2-D approach. A parameter-determination method is used for $m_H$ and $\sigma$, and the choice between
$H_0$ and $H_1$ is based on the selected region in ($\sigma,m_H$) space - see Section 3.2. }
\end{itemize}
It is to be noted that these two approaches use essentially the same data statistic $t$ (e.g. a likelihood ratio). The
difference is that the 2-D approach looks for a 2-D region around the optimal values of $\sigma$ and $m_H$,
while the raster scan determines a best region of $\sigma$ at each $m_H$ separately.
Our aim is to compare the relative merits of these two approaches.
\section{Examples of Actual Searches}
Here we mention briefly 3 examples of searches for new physics. Throughout this note, we use the language
relevant for a Higgs search, but the `translation' to our other two examples can be achieved via Table 1.
These are not intended to be exact descriptions of the procedures used in actual searches, but more generic
principles of approaches. For example, real searches for the Higgs boson involve several possible different
decay modes; more data variables than just the mass $M$ for each event; uncertainties on energy scales,
backgrounds and other systematics; etc.
\begin{itemize}
\item{Higgs search.
This was performed using a raster scan \cite{CMS_Higgs, ATLAS_Higgs}. At each closely spaced mass
over the relevant range, a separate search was performed. Fig. 1 shows the $p$-values for the null
hypothesis as a function of $m_H$. Based on this (and on a comparison of $\sigma$ with the Standard Model
prediction, as well as branching ratios for various decay modes), the discovery of a Higgs particle with mass
around 126 GeV was claimed.}
\item{$B_s$ oscillations\cite{CDF_Bs, D0_Bs}.
These are parametrised by the amplitude $A$ of oscillations and their frequency, which is proportional
to the mass difference $\Delta m_s$ between the $B_s$ and its anti-particle. A raster
scan was performed to determine $A$ at each mass difference $\Delta m_s$ - see fig. 2. If such oscillations occur,
the value of $A$ should be unity at the relevant $\Delta m_s$, whereas otherwise $A$ is expected to be
close to zero. On the basis of the data,
the discovery of $B_s$ oscillations at a mass difference of $\sim 17 ps^{-1}$ was claimed.}
\item{Neutrino oscillations\footnote{In contrast to the other two types of searches, plots of the accepted regions in parameter space for neutrino
oscillations tend to have the (logarithm of the) mass parameter plotted on the $y$-axis.}.
In a simplified model with only two species of mixing neutrinos, their oscillations are specified by an
amplitude $\sin^2(2\theta)$ and by their frequency which is proportional to
$\Delta m^2$, the difference in mass squared of the two neutrino types. A given set of data can be analysed
by obtaining the best value of $\sin^2(2\theta)$ at each value of $\Delta m^2$ (i.e. a raster scan), and
seeing whether sin$^2(2\theta) \,= \, 0$ is excluded.
However, Feldman and Cousins\cite{F_C} point out that for extracting
$(\sin^2 (2\theta), \Delta m^2)$ a 2-D parameter determination is preferable (see Fig 3).
}
\end{itemize}
\begin{table}
\caption{Examples of searches for new physics, characterised by a strength $\phi_1$ and a mass parameter $\phi_2$.}
\vspace{0.3cm}
\centering
\begin{tabular}{|c| c| c | c| }
\hline
Data and params & Event variables & Strength $\phi_1$ & Mass param $\phi_2$ \\
Example & & & \\
\hline & & & \\
Higgs & Mass $M$ & Cross-section $\sigma$ & Mass $m_H$ \\ \hline & & & \\
$B_s$ oscillations & Length, energy, decay mode & Amplitude $A$ & Mass diff $\Delta m_s$ \\ \hline & & & \\
$\nu$ oscillations & Length, energy, interaction type &Amplitude $\sin^2(2\theta)$ & Diff in mass-sq $\Delta m^2$ \\
\hline
\end{tabular}
\end{table}
An interesting question is why the search for $B_s$ oscillations uses a raster scan, but for neutrino oscillations a 2-D approach is used.
The main reason is that the emphasis of the analysis in the neutrino oscillation case was to determine the values of the parameters
$\sin^2(2\theta)$ and $\Delta m^2$, while in the $B_s$ case it was whether the $B_s$ oscillations could be discovered. Also
the amplitude in the $B_s$ case is expected to be unity, while for the neutrinos any value from zero to unity is physically possible.
Another interesting contast between searches for these two types of oscillations is the difference in the
appearence of the raster scan in the two cases. At small mass differences, the raster scan for $B_s$ gives values
of the amplitude close to zero. In contrast, the neutrino oscillation amplitude in the corresponding region can be large. The
reason is that the range of observable times in the $B_s$ case covers several complete oscillations, while for some
neutrino experiments, only a small part of the first oscillation can be observed\footnote{In other neutrino experiments,
the distance and resolution are such that only a time-averaged oscillation rate is observed, giving rise to a widish range of
possible values for the mass parameter.}.
Thus the $B_s$ data tend to pick out the correct oscillation frequency, with the fitted
amplitude at smaller frequencies being close to zero; while neutrino experiments in this regime are sensitive essentially only to the
product $\ sin^2(2\theta)\times (\Delta m^2)^2$, so smaller $\Delta m^2$ values need a larger amplitude.
\section{Further Details}
There are several possible choices for the way a preferred region in parameter space is defined, whether this
is for just $\sigma$ for the raster scan, or for both $m_H$ and $\sigma$ for the 2-D approach. A partial
list of possible methods is:
\begin{itemize}
\item{Maximum likelihood approach, with the selected region being those parameter values for which
\begin{equation}
\Delta ln{\calligra L}\ = \ ln {\calligra L}_{max} - ln {\calligra L}(\sigma , m_H) \le C,
\end{equation}
where $ln {\calligra L}(\sigma , m_H)$ is the
logarithm of the likelihood for parameter values $(\sigma , m_H)$; ${\calligra L}_{max}$ is the maximum
of the likelihood as a function of $\sigma$ for the Raster Scan, or of both $\sigma$ and $m_H$ for the 2-D approach;
and $C$ is a constant whose value depends on
the desired nominal coverage level and on the number of free parameters. For example, for a $95 \%$ region
in a 1 or 2 parameter problem, $C$ would be 1.9 or 3.0 respectively. }
\item{An alternative
but related approach would be to define a $\chi^2$ region such that $\chi^2 (\sigma , m_H) - \chi^2_{best}$
is below some critical value.}
\item{Frequentist approach. This uses the Neyman construction, with parameter(s) $\mu$ as $\sigma$ for
the raster scan, or ($\sigma, m_H$) for the 2-D approach. For each value of $\mu$,
the probability density
for observing possible data $d$ is used in conjunction with an ordering rule to construct the confidence band
containing the likely range of data values
for the given $\mu$,
at the chosen confidence level. The observed data
are then used to determine the range of parameter values for which the data is likely.
With just one parameter, the ordering rule can be chosen to provide upper or lower limits, or central regions (e.g. equal tail probabilities).
In the Feldman-Cousins version of
the frequentist approach, a likelihood-ratio is used to define the ordering rule. This extends naturally to situations
with more than one parameter. The Feldman-Cousins approach is called `unified' as, depending on the data,
the pre-defined ordering rule
determines whether the 1-D preferred region will be single-sided (i.e. an upper or a lower limit), or double-sided.
Another feature of the Feldman-Cousins method is that, in contrast to the frequentist approach with
other ordering rules, empty intervals or those consisting just of the point $\sigma = 0$ are far less likely.}
\item{Bayesian methods. Here the likelihood function is multiplied by the prior probability density $\pi({\sigma , m_H})$ to obtain the
posterior probability density $p({\sigma , m_H})$. From this, a region can be selected in parameter space that contains the required
level $f_{Bayes}$ of integrated posterior probability density. As always the Bayesian approach requires the specification of the
(possibly multi-dimensional) prior, and it is advisable to perform a sensitivity analysis to see how much the result depends on the
choice of prior.
If there is only one parameter, even for a given $f_{Bayes}$, the region could be chosen for an upper limit, lower limit, central interval
with equal probability in each tail, shortest interval\footnote{A problem with the shortest interval is that it is not independent of
changing to a different function of the parameter
e.g. In the neutrino oscillation problem, choosing $\Delta m^2$ or $ln(\Delta m^2)$; or $\theta$ or
$\sin^2(2\theta)$ or $\tan\theta$.}, etc.
With more than one parameter, the obvious choice is to use a cut on the value of the posterior probability density, which in one dimension corresponds to the
minimum length interval. Again this produces regions which are not invariant with respect to
reparametrisations of $(\sigma , m_H)$. There is no such problem for the likelihood, $\chi^2$ or
Feldman-Cousins approaches.}
\end{itemize}
Frequentist methods have the advantage over other approaches that coverage is guaranteed i.e.
the procedure is such that for a series of repeated analyses each with new data,
in the absence of experimental biases, the fraction of times that the true value of the parameter(s) will be
contained within the preferred region will be at least that specified by the chosen confidence level.
In this note, we use the generic name `preferred region' for the 1-D or 2-D parameter regions produced by any of
these methods. Clearly, any test to see whether $\sigma$ is consistent with zero cannot employ a
lower or an upper limit technique; equi-tailed central intervals may be problematic too.
\subsection{Raster Scan}
\subsubsection{Procedure}
The characteristic of a raster scan is that it is performed at each mass $m_H$ separately, and independently of
what happens at any other mass. At each such mass, a decision is made
to exclude $H_1$, to reject the null hypothesis $H_0$ or to make no choice. Thus at each mass $m_H$, a region of
$\sigma$ is determined at the pre-defined confidence level, even though the overall fit to
the data using these parameters may be much
worse than fits at other masses; the raster scan
ignores the fact that there may be a discrepancy, and still provides a range for $\sigma$ at each mass.
It then checks whether these regions contain
zero (as a test of the null hypothesis $H_0$) or/and $\sigma_{SM}$, the predicted cross-section assuming
S.M. Higgs.
If the region excludes $\sigma = 0$, then $H_0$ is excluded at the relevant confidence level,
while if it does not contain $\sigma_{SM}$, the predicted cross-section, then $H_1$ is excluded.
It is thus possible to claim a discovery of the Higgs at a specific mass; to
claim discoveries at more than one mass\footnote{This demonstrates the slightly slippery approach
used by Particle Physicists in the definition of the New Physics involved in $H_1$. We start off by looking
for the S.M. Higgs, but would not be unhappy if we discovered more than the expected one such object.
Similarly if the observed production rate was very inconsistent with zero, but not really in agreement with
$\sigma_{SM}$, many (or most?) Particle Physicists would claim this as a discovery of a S.M.-like Higgs,
but with a production rate different from the predicted rate according to the S.M.};
to exclude the S.M. Higgs over a range of masses; to
have insufficient evidence for choosing between $H_0$ and $H_1$; or a combination of
these
An analogous procedure is used in the search for $B_s$ oscillations, where the amplitude $A$ is determined at each $\Delta m_s$.
Of course, a lot of detail has been ignored in the above brief description.
Further discussion of hypothesis testing techniques, including the so-called $CL_s$ method\cite{Read}
for excluding $H_1$, can be found in ref. \cite{H0vH1}.
\subsubsection{Features}
\begin{itemize}
\item{We have already mentioned that because the raster scan treats each mass separately, the conclusion
as to what the data tell us at one mass is completely unaffected by what is happening at other masses (Contrast
the 2-D approach below.)}
\item{Another consequence of dealing with each mass separately is that it may be possible to claim
discoveries of more than one `S.M.' Higgs.}
\item{The raster scan will provide a cross-section range for each mass, regardless of
the quality of the fit. }
\item{The prefered region defined by the raster scan for $\sigma$ at each possible $m_H$ is different
from what would have been obtaind by determining the $m_H$ range at each $\sigma$. In the case of
the Higgs (and $B_s$) searches, the former is used as it is more physically motivated, and it works better in practice; this
might not be the case in different sorts of analyses where the two parameters might have a more symmetric
status.}
\end{itemize}
\subsection{2-D Parameter Determination}
\subsubsection{Procedure}
As a result of a 2-D search for the preferred region at some level (see Fig 4, where some
possibilities are shown), some rules have to be formulated for deciding whether we can claim a discovery;
exclude/disfavour the existence at some or perhaps even all relevant masses; or be unable to distinguish
between these possibilities.
Even apart from the choice of confidence levels, there is some degree of arbitrariness in how the
procedure is defined. We consider the following as an example of a possible set of rules:
\begin{itemize}
\item{Discovery: We require the 2-D preferred region at the 5$\sigma$ level to exclude $\sigma = 0$;
and also require the predicted $\sigma_{SM}$ to be within the 95\% contour. This ensures that the
observed signal strength is as expected; a consequence of this is that an apparent signal which is
significantly smaller or larger than predicted does not count as a discovery.
It may also be reasonable to impose a requirement that the width in $m_H$ of the discovery region
be consistent with expectation. e.g. in a channel with good mass resolution such as $H \rightarrow \gamma\gamma$ or
$H \rightarrow ZZ \rightarrow 4$ charged leptons,
an apparent signal over a very wide mass region may be more
likely to correspond to a mis-modeled background than to a fundamental discovery. (This applies also to raster scans.)}
\item{Exclusion: Masses at which the 95\% region does not include $m_H$ are excluded. This includes the case where
the single S.M. Higgs boson has been discovered at some other mass. }
\item{No decision: This applies when the 95\% region includes both $\sigma=0$ and $\sigma =
\sigma_{SM}$}, unless the Higgs boson has been discovered at some other mass.
\end{itemize}
\subsubsection{Features}
\begin{itemize}
\item{Usually when we quote the mass uncertainty on a new particle state, this is interpreted as a 1$\sigma$
error region. In the 2-D approach, the discovery region is defined by a 5$\sigma$ contour, which will
usually correspond to a wider mass interval. This is not a big problem as, once the existence of the
particle is established, its mass could be determined in a separate analysis using any desired
criterion for defining the mass uncertainty.}
\item{Because the model used for analysing the data assumes that there is only one S. M. Higgs boson, a signal
at one mass ($m_1$) affects what happens at other masses\footnote
{It is possible that the 5$\sigma$ discovery region could consist of two or even more separate
regions, with more than one of these being consistent with Higgs discovery at that mass. Within the S. M., however,
this corresponds to an ambiguity in the location of the single Higgs, rather than to the existence of more than
one Higgs.}. Thus if there is another mass $m_2$ which in
a raster scan also shows a 5$\sigma$ signal, $m_2$ could appear in the exclusion region in the 2-D approach
if the signal at $m_1$ has larger significance. Similarly, because of discovery of the one and only Higgs boson at
$m_1$, other masses are excluded; this includes mass regions where the experimental data has only
very weak (or even no) discrimination to the presence or absence of a Higgs boson.
Thus the 2-D approach with the assumption of just one Higgs boson has a higher probability than the
raster scan has of excluding the Higgs at other masses. However, in the absence of a significant excess
throughout the mass range, the exclusion power of the raster scan is better, largely because of the higher cut on
the log-likelihood ratio needed in the 2-D scenario\cite{daniel}.}
\item{Similarly for discovery at the favoured mass, the 2-D $5\sigma$ region will include a wider range of cross-section
(and hence be less sensitive to discovery) than the corresponding region in a raster scan. For a frequentist method such as
Feldman-Cousins, the $p$-values for excluding zero cross-section will be global and local (for the 2-D and raster scan
approaches respectively). }
\item{There are other situations in which the above procedure is not logical. For example, the preferred region might
correspond to a low or a high signal rate, such that it does not qualify as a discovery claim, and yet we
still exclude all other masses outside the preferred region, even including those where we have little or no
sensitivity. }
\end{itemize}
\subsection{Absence of predicted signal strength}
In some searches for the New Physics embodied in the alternative hypothesis $H_1$, there might not be a
prediction for the signal strength. For example, the strength of gravitational waves observed on Earth depends
on various parameters of the source, including its distance from us. Similarly with neutrino oscillations, the
strength factor $\sin^2(2\theta)$ can take on any value between zero and 1. In such situations,
the procedures for exclusion of $H_1$ (and to some extent, its discovery too) are modified.
\subsubsection{Raster Scan}
Because we deal with each mass separately, we can make a discovery by finding that the strength factor is
inconsistent with zero. (Indeed it may be that this happens at more than one mass.) However, no check is possible
that the strength is consistent with expectation, as the latter does not exist.
In contrast, there can be no excluded mass region, basically because the phenomenon could have a very
weak strength, below the sensitivity of the experiment. It is possible, however, to produce an upper
limit on the possible strength at each mass, which can then be built up into an exclusion region in
(strength, mass) parameter space.
\subsubsection{2-D approach}
After the preferred region is found in 2-D parameter space, we can make the usual discovery claims, except
that as in the raster scan, there is no possible check that the strength of the observed effect is as expected.
However, we now can have excluded mass regions, being those that lie outside the preferred region. This is
possible even without a predicted signal strength, provided $H_1$ involves the assumption that
there is only one true set of values for the parameters.
\section{Conclusions}
Table 2 contains an overview of various features of the raster scan and $\!$ 2-D approaches to discovery
and exclusion. A few comments about some of the entries are worth emphasising.
\begin{table}
\caption{Relative merits of Raster Scan and 2-D approach}
\vspace{0.3cm}
\centering
\begin{tabular}{|p{5cm}| p{5.4cm}| p{4.5cm}| }
\hline
$\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; $ Method & Raster Scan & 2-D \\
Features & & \\
\hline
\hline
Aim & Determines $\sigma$ region at each $m_H$ & Determines $(\sigma,m_H)$ region \\ \hline
Discovery criterion & $\sigma$ region excludes 0 & 2-D region excludes $\sigma = 0$ \\ \hline
Multiple discoveries possible? & Yes & No \\ \hline
Discovery at $m_1$ affects other $m$? & No & Yes \\ \hline
Exclusion criterion & $p$ or $CL_s$ <5\% & Region excludes $\sigma = \sigma_{SM}$ \\ \hline
Exclusion at $m_1$ affects other $m$? & No & No \\ \hline
Possible to exclude at $m$ with no sensitivity? & No & Yes \\ \hline
Confidence levels & Separate for discovery, exclusion. Measure $m$ separately & Different for discovery, exclusion, measurement of $m$ \\ \hline
Local or global $p$? & Local. Needs LEE for global & Global \\ \hline
Good points & Treats each mass separately.\ \ \ \ \ \ \ \ \ \ \ \ \ \ Better sensitivity & Regions with poor Goodness of Fit not accepted \\ \hline
Bad points & Determines $\sigma$ at $m$ where fit is poor. Raster in $m$ different from in $\sigma$ & Can exclude where no sensitivity \\ \hline
Method best for... & Hypothesis testing & Parameter determination \\ \hline
\end{tabular}
\end{table}
The fundamental difference between the two methods is that the 2-D approach assumes that there
is (at most) one S.M. Higgs boson, while the raster scan is more flexible in that it treats each mass
separately. This then can result in the 2-D method excluding Higgs production at masses for which
there is essentially no sensitivity to Higgs production, simply because a discovery claim is made
at another mass. Another consequence is that part of the preferred region in $(\sigma,m_H)$ space
from the raster scan can correspond to very poor fits of the theory to the data; in the 2-D approach,
only the best fit region is obtained.
Both methods use separate confidence levels for searches and for exclusion. When a discovery
is claimed at the 5$\sigma$ level, the 2-D approach provides a mass region over which this occurs.
However a mass measurement should be performed separately as this traditionally uses a 68\%
confidence level for the uncertainty. In the raster scan, the mass measurement is clearly a separate
exercise from the Hypothesis Testing of discovery.
To associate a $p$-value with a discovery claim, we need to determine the (hopefully very low)
probability of a background fluctuation giving rise to an effect at least as large as the one observed.
If a frequentist approach is used to determine the preferred regions, the $p$-value for a discovery claim is
directly determined by the method, as coverage is guaranteed; otherwise a brute-force Monte Carlo
approach may be needed.
There are (at least) two $p$-values
to consider: the local one, which is the probability of such a fluctuation at the mass observed for the data
signal, and a global $p$-value which incorporates the Look Elsewhere Effect (LEE)\cite{LEE} i.e. the
chance of having such a fluctuation not only at the observed mass, but anywhere in the analysis.
The 2-D approach most naturally lends itself to calculating the global $p$-value over the range of masses
relevant for the analysis, while in the raster scan the local $p$-value is more easily calculated, and hence needs to
be corrected for the LEE.
\vspace{0.07in}
In conclusion, it appears that the raster scan provides a more natural approach to discovery or
exclusion of New Physics, while the 2-D approach is preferable for parameter determination.
\vspace{0.15in}
I would like to thank Bob Cousins, Jon Hays, Tom Junk, Richard Lockhart, Yoshi Uchida, Nick Wardle, Daniel Whiteson
and members of the CMS Statistics Committee for many useful discussions and patient explanations.
| {
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} | 4,110 |
MG Siegler talks portfolio management and fundraising 6 months into the COVID-19 pandemic – TechCrunch
by Our Source | Jan 3, 2021 | Startups | 0 comments
This week, GV General Partner (and TechCrunch alum) MG Siegler joined us on Extra Crunch Live for a far-ranging chat about what it takes to foster a good relationship between investor and startup, how portfolio management and investing has changed as the COVID-19 crisis drags on, and what Siegler expects will and won't stick around in terms of changes in behavior in investment and entrepreneurship once the pandemic passes.
We last caught up with Siegler on the heels of his investment in Universe, a mobile-focused, e-commerce business-building startup. The coronavirus pandemic was relatively new and no one was sure how long it would last or what measures to contain it would look like. Now, with a few months of experience under his belt, Siegler told me that things have relatively settled into a new normal from his perspective as an investor – sometimes for worse, sometimes for better, but mostly just resulting in differences that require adaptation.
This select transcript has been edited for length and clarity. Aside from section headers, all text below is taken from MG Siegler's responses to my questions.
Business impacts of coping with the pandemic six months on
Just talking about the business side of the equation, I do think that things have sort of stabilized in the day-to-day world here. For us, certainly, I think it's it's just as much of a factor though, of just learning how to operate in this in this weird and surreal environment, and knowing how to do remote meetings better. Knowing how to hop on quick Zoom calls, Hangouts, and phone calls, with portfolio companies, to help put out fires, and doing all board meetings remotely, and all that sort of stuff.
That seems like it's pretty straightforward on paper, but in day-to-day operations, these are all different little learning things that you have to do and come across. I do feel like things are operating in a pretty streamlined manner, or as much as they can be at this point. But, you know, there's always going to be some more wildcards – like we're a week away, today, from from the US election. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,937 |
What is Tarn?
You must have noticed or seen some lakes in the mountains which have been formed because of the melting of the glaciers. Lakes are generally found in any type of environment and all parts of the world. Here, in this article, we will be talking about a type of lake that is considered a small mountain lake or tarn. It is also known as Corrie loch. This article will help you to understand one of the types of lakes or one of the important geographical features. It will be helpful in Geography, Earth Sciences, Geology, Geomorphology and Physical Geography.
A body of water that is surrounded by land is called a lake. It is not a part of the ocean. Most of the lakes are browsed and drained by the rivers and streams. There are many lakes which are found in the world. They are found on every continent and in every type of environment. They are generally found in mountains, deserts, on plains, and near seashores. The still bodies of water are lake as compared to the river where the water flows. Lakes are generally deeper than ponds and have a large surface area. They can contain salt and freshwater. They are larger than the ponds.
There are different kinds of lakes found in the world. It is classified on the basis of its origin and mode of formation. The different kinds of lakes are organic lakes, volcanic lakes, glacial lakes, Tectonic lakes, fluvial lakes, Landslide lakes, Solution Lakes, Aeolian lakes, Shoreline lakes, Anthropogenic lakes, Meteorite lakes. Out of these, we came to know about the " Tarn" which is a type of glacial lake.
Formation of Lake
The lakes are formed by erosion. When the glaciers melted, water-filled the hollows, which formed the lake. Glaciers carved deep valleys and deposited high amounts of earth, pebbles and boulders as they melted. These materials sometimes formed dams that have water and formed more lakes.
Tarn Meaning
Tarn means a small mountain lake in a hollow area surrounded by steep slopes formed by a glacier. The word tarn comes from the old Norse tjorn which means "small mountain lake with no tributaries." It is a proglacial mountain lake which is formed in a cirque excavated by a glacier. It is found in corries which are the result of erosion of glaciers. After the glaciers have melted, it leaves behind circular hollows in the heads of the valleys up in the mountains. Such hollows are arm chaired shaped cirques and corries. The water collects on the floor of the cirques to form the tarn lakes. Both corries and tarns are typically located in higher topographies to match their glacial origins.
The word tarn is derived from the old Norse word tjorn which means a small mountain lake with no tributaries. Tarn is a small mountain lake which is set in a glaciated steep-walled amphitheatre known as a cirque. A cirque is formed by ice and indicates the head of a glacier. Some of the cirques are so furbished that a lake formed in the base of the cirque after the ice has melted. These are called tarn.
"It is a small steep-banked mountain lake or pool." - Merriam-Webster
"It is a small mountain lake in a hollow area surrounded by steep slopes formed by a glacier." - Cambridge dictionary.
"A tarn is a small lake in an area of mountains." - Collins dictionary.
There are some features of the tarn
Tarn is lakes that are formed in glacially carved cirques.
They are obstructed by moraines below a tarn.
Tarns are often full of tiny, glacially-ground sediment that pass the light and make the watercolour.
They are found in mountainous areas.
The highest tarns of the world are found in Snowdonia, Lake District and Scotland.
Some of the famous examples of tarn are mentioned below:
Lake Tear of the Clouds, Adirondack Mountains, New York.
Veľké Hincovo, a tarn in Slovakia
Lousy Lake (tarn) in North Cascades National Park, Washington, USA
Lakes of the Clouds, below Mount Washington in the White Mountains
Banderishka Chukar seen from the Banderishka Lakes (tarns), Pirin Mountain, Bulgaria
Gergiysko lake (tarn), Pirin Mountain, Bulgaria
The Dreadful Lake (tarn), Rila Mountain, Bulgaria
The Seven Rila Lakes (tarns), Rila Mountain, Bulgaria
Marichini lakes (tarns), Rila Mountain, Bulgaria
Sea Lion Tarn on Livingston Island in Antarctica
To conclude, we can say that tarn is nothing but a type of small mountain lake which is surrounded by steep slopes that are formed by a glacier. The word tarn comes from the old Norse tjorn which means "small mountain lake with no tributaries." It is a proglacial mountain which is formed in a circle and excavated by glaciers. A bowl-shaped feature in the centre of the glacier is called cirque which is formed by ice and indicates the head of the mountains. Here, we have learned tarn meaning, definition, basics of lakes or formation of lakes, famous examples of the tarn, etc. All these things will help you to learn one of the important geographical features of the Earth.
1. What are Tarns? How is it Formed?
Answer. Tarns are known as small mountain lakes which are surrounded by steep slopes which are formed by glaciers and are found in corries that are formed by glacial erosion. These types of lakes are found at the high elevation where when the glaciers have melted, water collects in the floor of the corries which leads to the formation of lakes or tarns. The tarns or corries are typically and generally located in higher topographies.
2. Where Lakes are Found?
Answer. A lake is a body of water that is surrounded by land. There are many lakes in the world. They are found on every continent and in every kind of environment. They are generally found in mountains, deserts, plains, and near seashores. If we talk about tarns, they are found in the mountains at high elevations. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,332 |
Q: how can I merge selected table cells using jquery How can I merge selected table cells using jquery? I have a dynamically created table and I need to merge the selected table cells horizontally and vertically.
<table cellpadding="0" cellspacing="1" id="our_table" class="jan">
<tr id="dte">
<th>head1</th>
<th>head2</th>
<th>head3</th>
<th>head4</th>
</tr>
<tr>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
</table>
A: So far, from my knowledge, jquery has no function for manipulating tables. But cells can be merged by manually by coding. Here is a sample idea. Same thing can be done for merging rows.
<html>
<head>
<script type="text/javascript" src="jquery-1.11.0.min.js"></script>
<script>
$("document").ready(function () {
$("table").delegate("td" , "click", function(){
var colSp = prompt("Number of cells to span");
$(this).attr("colspan", colSp);
var ptr = $(this).parent().children();
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ptr[ptr.length - i].parentNode.removeChild(ptr[ptr.length - i]);
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width: 50px;
height: 50px;
}
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</html>r code here
| {
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A New York Classic: Tavern on the Green, Upper West Side, NY
May 26, 2014 / Cheese, Manhattan Munchies, New York Food, Upper West Side / 0 comment
A long time ago, two Australians visited New York City while on holiday. They had a romantic lunch at Tavern on the Green, oohed and aahed at the over-the-top Versailles-like decor, then went on their merry journey. They got engaged, then married, and then, finally, moved to New York City and had an adorable (albeit crazy) toddler. All the while, Tavern on the Green was on its own journey.
Tavern was originally built to hold the sheep that lived in the Central Park Sheep Meadow. In the early 1930s, New Yorkers evicted the sheep, and the building was converted into a restaurant. The restaurant became famous for its decadent Crystal Room, a conservatory-like space decked out with colored-glass chandeliers, stucco embellishments on the ceiling, and numerous flower motifs.
In the restaurant's hey day, during the late 1970s and '80s, Tavern was the place for celebrities to be seen. John Lennon and Yoko Ono, Madonna and Michael Jackson were all guests.
In 2009, the owners of Tavern filed for bankruptcy and the restaurant closed its doors, opening again in April 2014 after a massive refurbishment. The new restaurant barely resembles the old one. Gone is the Crystal Room and abundance of flowers. In its place is a sleek, modern dining establishment with nods to its heritage, such as sheep heads by the fire place, and a carousel-resembling chandelier over the bar.
And so it was that this little family of three made their way back to the newly opened Tavern on an absolutely gorgeous spring day. Let me say this from the outset: the new Tavern has amazing staff. The efficient, friendly staff welcomed our wriggly toddler and her tired parents with open arms, and gave us a wonderful table in the courtyard.
We ordered Assorted Pastries with Cultured Vermont Butter and Preserves ($6) which contained two perfectly-sized plain croissants, two chocolate croissants, a lemon poppy seed scone, butter, and orange marmalade and raspberry jam by my favorite jam-makers, Bonne Maman. We had intended these for Missy E, but they were so good we all devoured them.
Alec and I both ordered the same dish off the brunch menu: the Scrambled Local Eggs with Fresh Goat Cheese and Chives with Applewood Smoked Bacon and a Sourdough Bruschetta ($21). It came with bacon, which I received on the side and added to Alec's eggs. We added cocktails to the brunch (what's brunch without a cocktail?) and were delighted to receive strong, well-made White Peach Bellinis and Brooklyn.
Our eggs on toast were really tasty – fluffy eggs on sourdough, as described. Even better — the meals all came quickly, before Missy E got totally bored.
We even went back for dessert – a Brownie Sundae for me, with Fudge Brownie, Caramel Ice Cream, Homemade "Cracker Jacks", Chocolate Sauce ($13), the Spring Pavlova for Alec, with Matcha Curd, Macerated Strawberries and Rhubarb, Chantilly Cream, Tarragon Oil ($12), and a single scoop of vanilla ice cream for E.
My brownie was rich and moist, but I would have liked a bit more ice cream to go with it. I really enjoyed the caramel ice cream however – it tasted like a salted caramel. Alec enjoyed his pavlova, but declared it nothing extraordinary. I think as Australians we're spoiled by the amazing home-cooked pavs we're used to back in Sydney!
After our lunch, we took a little tour around the restaurant to check it all out. I really liked the bar area with the big booths, so Central Park-goers can drop in just for a casual drink, but still be comfortable. I saw a lot of families with smaller kids in this area — a great idea when you want to stop somewhere nice in the afternoon, but know your kids can't handle full table service.
Last Bite: A great dining option in Central Park for families. Friendly staff make this an enjoyable outing — just be sure to make reservations first.
Tavern on the Green
Central Park West & 67th Street,
Prices: $$
Hours: Daily, Lunch 11am-3pm, Dinner 5pm-11pm, Late night 11pm-1am, Brunch Sat & Sun 9am-3pm,
Cuppa Flower Waterloo: Sydney's Prettiest Cafes
Eloise Afternoon Tea at the Plaza Hotel, New York
Afternoon Tea at the Plaza Hotel, New York
Two Sis & Co. Pyrmont: Sydney Cafe Reviews
Crowne Plaza Surfers Paradise: Best Family Resort Gold Coast
Sir Stamford at Circular Quay Hotel High Tea
« An Historical Day Trip With Kids to Roosevelt Island
Jack's Wife Freda: Kid-Friendly Restaurants, SoHo, New York » | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,337 |
A list of films produced in Argentina in 1987:
External links and references
Argentine films of 1987 at the Internet Movie Database
1987
Argentine
Films | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,538 |
{"url":"https:\/\/codereview.stackexchange.com\/questions\/229257\/dictionary-comprehension-with-nested-for-loop-and-conditional-if","text":"# Dictionary comprehension with nested for loop and conditional if [closed]\n\nLet's suppose I have two lists:\n\nlist_b = ['cat.2','dog.6','bear.10','zebra.13']\nlist_a = ['cat','dog','bear','zebra']\n\n\nI would like to create a dictionary with the desired output:\n\ndict_ = {'cat.2':'cat','dog.6':'dog','bear':'bear.10','zebra.13':'zebra'}\n\n\nI have two possible solutions. I am assuming the lists are not ordered so I cannot simply do a dict(zip(list_a,list_b)) or something along those lines.\n\nSolution 1:\n\ndict_ = {}\nfor i in list_a:\nfor j in list_b:\nif i.startswith(j):\ndict_[i] = j\n\n\nSolution 2:\n\ndict_ = {key:value for key in list_a for value in list_b if key.startswith(value)}\n\n\nI prefer solution two because, if I recall correctly, comprehensions should be much faster, but I do not know if there is a more efficient way of doing this.\n\n\u2022 Hey, welcome to Code Review! Here we take a look at complete and working code and try to make it better. For this it is paramount to see the code in its actual environment. The more code you can show, the better. Hypothetical code, code stubs without context or general best practice questions are off-topic here. Have a look at our help center for more information. \u2013\u00a0Graipher Sep 18 '19 at 17:30\n\u2022 I think the context is clear, even if implicit: \"for each key in list_b, split on '.' and find the corresponding partial-match from list_a and use it as the value\". Don't even need regex. Now if you mean the question is toy, that's different... \u2013\u00a0smci Sep 18 '19 at 22:52\n\u2022 As @Reinderien showed, can we totally ignore list_a and just assume each key in list_b has a match in list_a when we split on '.'? What should we do if key has no matches? multiple matches? \u2013\u00a0smci Sep 18 '19 at 22:54\n\n{k: k.split('.', 1)[0] for k in list_b}\n\np.s. don't call your variable dict_. Name it according to its application function - animals, or whatever.","date":"2020-07-13 15:04:14","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.3432130515575409, \"perplexity\": 1947.461384062082}, \"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-2020-29\/segments\/1593657145436.64\/warc\/CC-MAIN-20200713131310-20200713161310-00336.warc.gz\"}"} | null | null |
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This is the situation for rural farming families in the Dominican Republic, both in the trans border region and in communities of the central region. As agricultural productivity decreases, farmers who are desperate to feed their families turn to cutting trees either as a source of income or to clear land to farm. However, attempts to grow crops on cleared land are unproductive because the soil's fertility and ability to hold water has been compromised. The deforestation also leads to serious erosion, causing soil depletion, water pollution, and increased vulnerability to natural disasters. The continued decline in productivity paradoxically leads to more tree cutting, and the vicious cycle continues. The rural sector, which makes up 31 percent of the Dominican Republic's population, is affected by high poverty rates, and 56% of people in rural areas live below the poverty line (Source: CIA World Factbook, July 2012).
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The overarching goal of Plant With Purpose Dominican Republic's program is to equip rural communities to restore their environment, creating health and productivity for families and communities.
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Train 360 farmers in sustainable agriculture techniques. This will involve 60 workshops covering the following topics: soil conservation, environmental and economic benefits of trees, agroforestry, organic fertilizers, tree grafting, water conservation, and waste management.
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Educate 300 children in 13 schools in how to care for their environment.
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U.S. Patent No. 9,268,509 Japan Patent No. 6499651 International Patents Pending Privacy Policy Acceptable Use Policy | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,161 |
import os
import testscenarios
import nova.conf
from nova import test
from nova.tests import fixtures
from nova.tests.functional import api_paste_fixture
from nova.tests.functional import api_samples_test_base
from nova.tests.unit import fake_network
CONF = nova.conf.CONF
# API samples heavily uses testscenarios. This allows us to use the
# same tests, with slight variations in configuration to ensure our
# various ways of calling the API are compatible. Testscenarios works
# through the class level ``scenarios`` variable. It is an array of
# tuples where the first value in each tuple is an arbitrary name for
# the scenario (should be unique), and the second item is a dictionary
# of attributes to change in the class for the test.
#
# By default we're running scenarios for 2 situations
#
# - Hitting the default /v2 endpoint with the v2.1 Compatibility stack
#
# - Hitting the default /v2.1 endpoint
#
# Things we need to set:
#
# - api_major_version - what version of the API we should be hitting
#
# - microversion - what API microversion should be used
#
# - _additional_fixtures - any additional fixtures need
#
# NOTE(sdague): if you want to build a test that only tests specific
# microversions, then replace the ``scenarios`` class variable in that
# test class with something like:
#
# [("v2_11", {'api_major_version': 'v2.1', 'microversion': '2.11'})]
class ApiSampleTestBaseV21(testscenarios.WithScenarios,
api_samples_test_base.ApiSampleTestBase):
SUPPORTS_CELLS = False
api_major_version = 'v2'
# any additional fixtures needed for this scenario
_additional_fixtures = []
sample_dir = None
_project_id = True
scenarios = [
# test v2 with the v2.1 compatibility stack
('v2', {
'api_major_version': 'v2'}),
# test v2.1 base microversion
('v2_1', {
'api_major_version': 'v2.1'}),
# test v2.18 code without project id
('v2_1_noproject_id', {
'api_major_version': 'v2.1',
'_project_id': False,
'_additional_fixtures': [
api_paste_fixture.ApiPasteNoProjectId]})
]
def setUp(self):
self.flags(use_ipv6=False)
self.flags(glance_link_prefix=self._get_glance_host(),
compute_link_prefix=self._get_host(),
group='api')
# load any additional fixtures specified by the scenario
for fix in self._additional_fixtures:
self.useFixture(fix())
if not self.SUPPORTS_CELLS:
# NOTE(danms): Disable base automatic DB (and cells) config
self.USES_DB = False
self.USES_DB_SELF = True
# This is to enable the network quota which is being registered
# based on CONF.enable_network_quota. Need this to test the
# network quota in quota sample tests.
self.flags(enable_network_quota=True)
self.useFixture(fixtures.RegisterNetworkQuota())
# super class call is delayed here so that we have the right
# paste and conf before loading all the services, as we can't
# change these later.
super(ApiSampleTestBaseV21, self).setUp()
if not self.SUPPORTS_CELLS:
self.useFixture(fixtures.Database())
self.useFixture(fixtures.Database(database='api'))
self.useFixture(fixtures.DefaultFlavorsFixture())
self.useFixture(fixtures.SingleCellSimple())
super(ApiSampleTestBaseV21, self)._setup_services()
if not self.USE_NEUTRON:
# self.network is only setup if USE_NEUTRON=False
self.useFixture(test.SampleNetworks(host=self.network.host))
fake_network.stub_compute_with_ips(self.stubs)
self.useFixture(fixtures.SpawnIsSynchronousFixture())
# this is used to generate sample docs
self.generate_samples = os.getenv('GENERATE_SAMPLES') is not None
def _setup_services(self):
pass
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,517 |
\section{Introduction}\label{sec:intro}
Cataclysmic variables (CVs) are close binary systems
consisting of a companion late-type main-sequence star and a white dwarf (WD).
The late-type star fills the Roche lobe and
feeds its gaseous material to the WD through the inner Lagrange point.
CVs comprising a highly magnetized WD ($B > 0.1$~MG) are called magnetic CVs (mCVs), which are categorized as polar or intermediate polar (IP)
systems. In polar systems, the magnetic field is quite
strong ($B > 10$\,MG) and can channel the gaseous flow directly from the companion star.
In IPs, the magnetic field is moderate ($0.1 < B < 10$\,MG), and an accretion disk forms around the WD.
The magnetic field tears the gas from the accretion disk near the Alfv$\acute{\rm e}$n radius and channels it. The channeled gas
falls toward the WD at an almost free-fall velocity and is accelerated up to hypersonic speeds. A strong shock is formed close to the WD surface,
heats the gas, and generates highly ionized plasma.
In IP systems, the plasma flow is cooled by an X-ray thermal emission, and the plasma flow then settles onto the WD surface,
which is called the post-shock accretion column (PSAC).
The PSAC irradiates the WD with X-rays, and
the WD shines in the X-ray owing to the reflection.
The X-ray observation enables us to measure the WD mass independent of
the dynamical measurement and to determine the PSAC geometry.
The WD model is still controversial, particularly under extreme conditions (for example, \citealt{2004A&A...419..623Y,2013ApJ...767L..14D}),
and the WD mass is a fundamental physical parameter used to constrain the model.
However, the well-established dynamic WD mass measurement is difficult, except in systems showing an eclipse
because of the uncertainty in the orbital inclination angle.
By contrast, with X-ray spectroscopy, the WD mass can be measured by measuring the plasma temperature, which is correlated with the gravitational potential.
Moreover, the reflection enables us to measure the height of the PSAC and the angle between the PSAC and the line-of-sight.
Height is a fundamental parameter that specifies the PSAC and constrains the WD mass.
The PSAC angle is modulated by the WD spin, which allows us to estimate the spin axis angle.
The spin axis angle provides the direction of the angular momentum,
which is new information regarding the dynamics of a binary system.
The thermal X-ray spectrum of PSAC has been well studied.
The PSAC has been hydrodynamically modeled (\citealt{1973PThPh..49..776H}, \citealt{1973PThPh..49.1184A},
\citealt{1983ApJ...268..291I}, \citealt{1994ApJ...426..664W}, \citealt{1996A&A...306..232W}, \citealt{1998MNRAS.293..222C}
\citealt{1999MNRAS.306..684C}, \citealt{2005A&A...440..185C},
\citealt{2005MNRAS.360.1091S}, \citealt{2007MNRAS.379..779S} and \citealt{2014MNRAS.438.2267H}).
Such studies
involved various physical effects:\,gravitational potential release,
cross-section
convergence, and variation in the accretion rate per unit area (called the ``specific accretion rate''). PSAC models have been employed to measure the WD mass of the mCVs:
(\citealt{1991ApJ...367..270I},
\citealt{1997ApJ...474..774F},
\citealt{1998MNRAS.293..222C}
\citealt{1999MNRAS.306..684C},
\citealt{1999ApJS..120..277E},
\citealt{2000MNRAS.316..225R},
\citealt{2005A&A...435..191S},
\citealt{2009A&A...496..121B},
\citealt{2009MNRAS.392..630L},
\citealt{2010A&A...520A..25Y} and
\citealt{2014MNRAS.441.3718H}).
Less attention has been paid to the X-ray reflection from the WD surface
despite
its prominent spectral features.
The reflection consists of thermal X-rays escaping from the WD through scattering and/or fluorescence.
The reflection spectrum has distinctive features:\,fluorescent iron K$_\alpha$ lines,
a Compton hump at approximately 10--30keV, and Compton shoulders following the emission lines.
These features enable us to study the geometry between a PSAC and a WD. However, these features can be a nuisance when obtaining thermal plasma parameters unless they are correctly modeled.
Several studies have considered the reflection in their spectral analysis
(e.g., \citealt{1995MNRAS.272..749B}, \citealt{1998MNRAS.293..222C},
\citealt{2000MNRAS.315..307B}, \citealt{2011PASJ...63S.739H}, \citealt{2015ApJ...807L..30M}, and \citealt{2018MNRAS.476..554S}),
invoking reflection models developed for
active galactic nuclei (AGN) (e.g.,\,\citealt{1995MNRAS.273..837M} and \citealt{1991MNRAS.249..352G})
or for the mCV \citep{1996A&A...312..186V}.
However, these models do not incorporate the stratified structure of the PSAC, finite height of the PSAC, or the WD curvature.
Moreover, the features incurred by the scattering and fluorescence were handled separately.
Recently, we developed an IP reflection model using a Monte Carlo simulation \citep{2018MNRAS.474.1810H}.
In the model, a finite-length columnar source on a spherical reflector irradiated the reflector
with X-rays, the spectrum of which was determined by
the PSAC stratified structure calculated by \cite{2014MNRAS.438.2267H}.
The reflector was cold and neutral,
and its radius was determined based on the WD mass \citep{1972ApJ...175..417N}.
The simulation involved X-ray interactions with atoms, i.e.,
coherent/incoherent scattering and photoelectric absorption.
The photoelectric absorption by iron and nickel
is followed by K$_{\alpha1, 2}$ and K$_\beta$ fluorescent emissions with the corresponding fluorescent yield.
The reflection model has five fitting parameters:\,the WD mass ($M_{\rm WD}$),
specific accretion rate ($a$), elemental abundance ($Z$),
the angle between the PSAC and line of sight ($i$), and normalization.
These parameters are also common to the IP thermal model of \cite{2014MNRAS.438.2267H}.
We selected V1223\,Sagittarii (V1223\,Sgr) as the first target to
demonstrate how well the IP reflection model reproduces the observed spectrum
and the parameters that can be measured.
V1223\,Sgr is a typical IP and one of the brightest.
The other brightest IPs, EX\,Hydrae and V2400\,Ophiuchus, are
somewhat extraordinary owing to their extremely low X-ray luminosity \citep{2005A&A...435..191S}
and the discless feature \citep{1995MNRAS.275.1028B}, respectively.
V1223\,Sgr was observed for 190 and 20\,ks using the {\it Suzaku} and nuclear spectroscopic telescope array ({\it NuSTAR}) satellites,
respectively (\S\ref{sec:obs}), the data of which are publicly available.
The {\it Suzaku} data have a large effective area for fluorescent iron K$\alpha$ lines,
and the fluorescent line was resolved from the thermal K$_{\alpha}$ lines.
The {\it NuSTAR} data have a
high signal-to-noise ratio in the Compton hump energy band.
In this paper, we present an application of the IP reflection model to the
V1223\,Sgr data acquired by the {{\it Suzaku} } and
{{\it NuSTAR}}) satellites.
We describe the observations and data reduction in \S\ref{sec:obs}
and the model application in \S\ref{sec:app}.
We discuss the reflection spectral modeling, the effects of various parameters on the WD mass estimation, and the geometry in \S\ref{sec:dis}.
The conclusions are presented in \S\ref{sec:con}.
\section{Observations and Data reduction}\label{sec:obs}
We used
{\it Suzaku} \citep{2007PASJ...59S...1M} and {\it NuSTAR} \citep{2013ApJ...770..103H} archival data for V1223\,Sgr.
Table\,\ref{table:obs} shows a summary of the observation.
We applied a barycentric correction to each
dataset
\citep{2008PASJ...60S..25T}.
\subsection{\it Suzaku}
{\it Suzaku} has two instruments: \, an X-ray imaging spectrometer (XIS; \citealt{2007PASJ...59S..23K})
and a hard X-ray detector (HXD; \citealt{2007PASJ...59S..53K}; \citealt{2007PASJ...59S..35T}).
The XIS has an imaging capability with the aid of an X-Ray Telescope (XRT; \citealt{2007PASJ...59S...9S}).
The 2007 and 2014 observations (hereafter referred to as 07S and 14S) were conducted at the nominal positions of the HXD
and XIS, respectively.
The exposure time is tabulated in Table\,\ref{table:obs}.
The 07S and 14S data were screened through
the {\it Suzaku} processing pipeline version 3.0.22.43 and 3.0.22.44, respectively,
with the latest calibration database (20160607 for XIS, 20110630 for XRT, and 20110913 for HXD).
\begin{table*}
\centering
\caption{Observation summary of V1223\,Sgr by {\it Suzaku} and {\it NuSTAR}.}\label{table:obs}
\begin{tabular}{cccccc}
\hline
Observation ID & Observation date (UT) & data set name & Aim point & Detector & Exposure (ks)$^{\ast}$\\
\hline
\multicolumn{5}{c}{{\it Suzaku} }\\
402002010 & 2007 April 13--14th & 07S & HXD & XIS & 60.7\\
& & & & HXD & 46.3\\
\hdashline
408019010 & 2014 March 29--30th & \multirow{4}{*}{14S} & XIS & XIS & 29.4\\
& & & & HXD & 26.1\\
408019020 & 2014 April 10--14th & & XIS & XIS & 150.8\\
& & & & HXD & 146.3\\
\hline
\multicolumn{5}{c}{{\it NuSTAR}}\\
30001144002 & 2014 September 16 & 14N& - & FPMA/FPMB&20.4\\
\hline
$^{\ast}$ Exposure time after data screening.
\end{tabular}
\end{table*}
\subsubsection{XIS}
We extracted the source events from a circle of radius 4$\acute{.}$34 around the image center.
The background events fall in the annulus between radii of 4$\acute{.}$34 and 8$\acute{.}$68,
excluding those regions irradiated by the $^{55}$Fe calibration sources
and the detector edges.
One of the XIS sensors XIS0 in 14S has an unusable area owing to an anomaly
that
was also excluded from the background region.
The spectra of the two front-illuminated (FI) sensors (XIS0 and 3) were combined.
During all of the observations, the other FI sensor XIS2 was deemed
unusable because of an anomaly that occurred in November 2006.
Subsequently, the data acquired during the two periods in 2014 were combined.
\subsubsection{HXD-PIN}
We used the ``tuned'' non-X-ray background (NXB) spectrum version 2.0
provided by the instrument team \citep{2009PASJ...61S..17F} for the 07S HXD-PIN data.
The cosmic X-ray background (CXB) spectrum was generated by convolving the
spectral model of \cite{1987PhR...146..215B}
with the detector response.
The NXB and CXB spectra were subtracted from the HXD-PIN data.
We did not use the S14 HXD-PIN data because only a ``quick''
NXB spectrum was provided, which had larger systematic errors.
\subsection{\it NuSTAR}
{{\it NuSTAR}} has two co-aligned hard X-ray telescopes.
Each telescope focuses celestial X-rays onto
a focal plane module A or B (FPMA or FPMB).
The observation of V1223\,Sgr was conducted in September 2014 (hereafter referred to as 14N).
We reprocessed the data using {\it NuSTAR} data analysis software ({\tt NuSTARDUS} v.1.7.1)
and the calibration files of 20171002 to extract the cleaned events.
The source events were extracted within a circle of 2$\acute{.}$5
radii around the image center,
whereas the background events were extracted
within an annulus between radii of 2$\acute{.}$5 and 5$\acute{.}$0 by excluding the detector edges.
\section{Spectral model fitting}\label{sec:app}
The IP thermal model of \cite{2014MNRAS.438.2267H}
and the reflection model of \cite{2018MNRAS.474.1810H}
(hereafter referred to as {\sc acrad$_{\rm th}$} and {\sc acrad$_{\rm ref}$}, respectively)
have been compiled into table models that are available on the XSPEC \citep{1996ASPC..101...17A}.
We fitted the IP models to the V1223\,Sgr spectrum using {\sc XSPEC} version 12.9.1,
binding the same parameters in both models.
For comparison, we also fitted
an AGN reflection model ({\sc reflect} in {\sc XSPEC}; \citealt{1995MNRAS.273..837M})
or a partial covering absorption (PCA) model ({\sc pcfabs} in {\sc XSPEC})
instead of {\sc acrad$_{\rm ref}$}.
Phenomenologically, the PCA model may reproduce
the spectral shape of the Compton hump \citep{1998MNRAS.293..222C}.
With {\sc reflect} and {\sc pcfabs}, a narrow Gaussian model was added to the fluorescent iron K$_\alpha$ line,
whose central energy and width were fixed at 6.4 and 0\,keV, respectively.
The abundance of iron and other elements in {\sc reflect}
were bound to that of {\sc acrad$_{\rm th}$}.
For all cases, the photoelectric absorption was considered using
{\sc phabs}.
In summary, we used the three models of
{\sc phabs$\times$(acrad$_{\rm th}$+acrad$_{\rm ref}$)}, {\sc phabs$\times$(reflecting $\times$acrad$_{\rm th}$+Gaussian)}, and
{\sc phabs$\times$(pcfabs$\times$acrad$_{\rm th}$+Gaussian)}, which are
hereafter referred to as {\tt IP-reflect}, {\tt AGN-reflect}, and {\tt PCA-reflect}, respectively.
We excluded data below 5\,keV
to avoid the complicated absorption feature
created by the multicolumnar absorber
\citep{1999ApJS..120..277E}.
The exclusion of $<5$\,keV data is reasonable
because the main features of the maximum plasma temperature
depending on the WD mass and the reflection appear at above 5 keV.
\subsection{Spin averaged spectrum}\label{sec:ave_spe_fit}
First, we fitted each model to the spin-averaged spectra of all datasets.
Figures\,\ref{fig:ave_fit_acrad}, \ref{fig:ave_fit_reflect}, and \ref{fig:ave_fit_pc}
display the spectrum with the best-fit models, and
Table\,\ref{table:ave_spe_para} shows the best-fit parameters.
The three fittings are comparable in terms of the goodness of fit.
In other words, the {\tt PCA-reflect} model reproduces the Compton hump
as much as the {\tt IP-reflect} and {\tt AGN-reflect} models do,
although the parameters of {\sc pcfabs} in {\tt PCA-reflect} have no physical meaning.
Here, {\tt IP-reflect} estimated the WD mass $M_{\rm WD}$ to be $0.86\pm0.01$\,$M_{\odot}$,
which is consistent with
$M_{\rm WD}$ = $0.87\pm0.01$\,$M_{\odot}$ and $0.83\pm{0.02}$\,$M_{\odot}$
estimated by {\tt AGN-reflect} and {\tt PCA-reflect}, respectively.
All three models estimated an extremely high specific accretion rate, with log ($a$ [\,g\,cm$^{-2}$\,s$^{-1}]) > 2$, and were found to agree with each other.
In addition, {\tt IP-reflect} tightly constrained the viewing angle to $i = 54.2^{-2.2}_{+2.1}$$^\circ$,
which disagrees with the output of {\tt AGN-reflect} of $i < 42$$^\circ$.
The shock height $h$ and the maximum plasma temperature
$T_{\rm max}$ (i.e., the temperature just below the shock)
are hydrodynamically calculated \citep{2014MNRAS.438.2267H}
using the best-fit parameters, as shown in Table\,\ref{table:ave_spe_para}.
The luminosity of the thermal component within the 0.1--100\,keV band is estimated
as 1$\times10^{34}$\,erg\,s$^{-1}$ by all three models
with the distance $D = 580\pm16$\,pc set as per
{\it Gaia} DATA RELEASE 2 (DR2; \citealt{2016A&A...595A...1G}).
\begin{table*}
\centering
\caption{Best-fit parameters of the spectral fitting to the spin-averaged V1223\,Sgr spectra for all the data sets$^\ast$.
The parameters below the dashed line were hydrodynamically calculated with the best-fit parameters \citep{2014MNRAS.438.2267H}.}\label{table:ave_spe_para}
\begin{tabular}{cccc}
\hline
& {\sc phabs$\times$(acrad$_{\rm th}$+acrad$_{\rm ref}$}) & {\sc phabs$\times$(reflect$\times$acrad$_{\rm th}$+Gaussian)} & {\sc phabs$\times$(pcfabs$\times$acrad$_{\rm th}$+Gaussian)}\\
Nickname & {\tt IP-reflect} & {\tt AGN-reflect} & {\tt PCA-reflect} \\\hline
$N_{\rm H}$ ($\times10^{22}$\,cm$^{-2}$) & $6.5\pm0.5$ & $8.9\pm0.7$ & $8.2_{-2.5}^{+2.2}$ \\
$M_{\rm WD}$ (M$_{\odot})$ & $0.86\pm0.01$ & $0.87\pm{0.02}$ & $0.83\pm{0.02}$ \\
log($a$) (g\,cm$^{-2}$\,s$^{-1}$) & $> 2.5$ & $> 2.7$ & $> 2.0$\\
$Z$ (Z$_\odot^\dagger$) & $0.32\pm0.01$ & $0.29\pm0.01$ & $0.26_{-0.01}^{+0.02}$ \\
$i$ ($^\circ$) & $54.2_{-2.2}^{+2.1}$ & $< 42$ & -\\
$\Omega/2\pi$& - & $0.44_{-0.06}^{+0.10}$ & -\\
$N_{\rm H, PCA}^\ddagger$ ($\times10^{22}$\,cm$^{-2}$) & - & - & $90_{-29}^{+30}$\\
$CF_{\rm PCA}^\S$ & - & - & $0.30_{-0.05}^{+0.12}$ \\
$EW_{\rm FeI-K\alpha}^\parallel$ (eV)& - & $105_{-2}^{+15}$ & $104\pm4$ \\
$F_{\rm bol}^{\flat}$ ($\times$10$^{-10}$\,erg\,s$^{-1}$) & 2.8 & 3.2 & 3.3 \\
$L_{\rm bol}^\natural$ ($\times$10$^{34}$\,erg\,s) & 1.1 & 1.3 & 1.3\\
$f^\sharp$ & $<$ 4$\times$10$^{-5}$ & $<$ 3$\times$10$^{-5}$ & $<$ 1$\times$10$^{-4}$ \\
$\chi^2_{\rm red}$ (d.o.f.) & 1.38 (1196) & 1.31 (1194) & 1.34 (1194)\\
\hdashline
$T_{\rm max}^{\star}$ (keV) & 42 & 43 & 39 \\
$h^\P$ ($R_{\rm WD}$) & $<$ 4$\times$10$^{-4}$ & $<$ 3$\times$10$^{-4}$ & $<$ 1$\times$10$^{-4}$ \\
\hline
\multicolumn{4}{l}{$^{\ast}$ The errors indicate a 90\% statistical uncertainty.}\\
\multicolumn{4}{l}{$^\dagger$ Based on \cite{1989GeCoA..53..197A}.}\\
\multicolumn{4}{l}{$^\ddagger$ The hydrogen column density of PCA.}\\
\multicolumn{4}{l}{$^\S$ The covering fraction of PCA.}\\
\multicolumn{4}{l}{$^\parallel$ The equivalent width of the fluorescent iron K$_\alpha$ line.}\\
\multicolumn{4}{l}{$^\flat$ Unabsorbed flux in 0.1--100\,keV without the reflect component.}\\
\multicolumn{4}{l}{$^\natural$ Unabsorbed luminosity in 0.1--100\,keV without the reflect component.}\\
\multicolumn{4}{l}{$^\sharp$ The fractional accreting area.}\\
\multicolumn{4}{l}{$^\star$ The temperature just below the shock.}\\
\multicolumn{4}{l}{$^\P$ Height of the shock column from the WD surface.}\\
\end{tabular}
\end{table*}
\begin{figure}
\includegraphics[width=80mm]{fig/SP0-1_5-78keV_trefacradMa0G_walldata_fit.eps}
\includegraphics[width=80mm]{fig/SP0-1_5-78keV_trefacradMa0G_walldata_fit_5-9.eps}
\caption{Top: 07S-FI (black), 07S-BI (red), 07S-PIN (green),
14S-FI (blue), 14S-BI (light blue), 14N-FPMA (magenta), and 14N-FPMB (yellow) spectra
with the best-fit {\tt IP-reflect}
model.
The three lower panels show the residuals of 07S, 14S, and 14N from the top
in units of $\sigma$.
The dotted and dashed lines show the thermal ({\sc acrad$_{\rm th}$}) and reflection ({\sc acrad$_{\rm ref}$}) components, respectively.
Bottom: Blowup of top panel between 5 and 9\,keV.}
\label{fig:ave_fit_acrad}
\end{figure}
\begin{figure}
\includegraphics[width=80mm]{fig/SP0-1_5-78keV_tacradMa0G-reflect_walldata_extend100keV_fit_wref.eps}
\includegraphics[width=80mm]{fig/SP0-1_5-78keV_tacradMa0G-reflect_walldata_extend100keV_fit_wref_5-9.eps}
\caption{Same as Figure\,\ref{fig:ave_fit_acrad}, although the fitting model is
{\tt AGN-reflect}.
The dotted, dotted-dashed, and dashed lines show the thermal ({\sc acrad$_{\rm th}$}), fluorescent iron K$_\alpha$ line ({\sc Gaussian}), and reflection ({\sc reflect}) components, respectively.
}
\label{fig:ave_fit_reflect}
\end{figure}
\begin{figure}
\includegraphics[width=80mm]{fig/SP0-1_5-78keV_tacradMa0G-pcfabs_walldata_fixnorm-pcfabs-ga_fit_wref.eps}
\includegraphics[width=80mm]{fig/SP0-1_5-78keV_tacradMa0G-pcfabs_walldata_fixnorm-pcfabs-ga_fit_wref_5-9.eps}
\caption{Same as Figure\,\ref{fig:ave_fit_acrad}, although the fitting model is
{\tt PCA-reflect}.
Dotted, dotted-dashed, and dashed lines show the thermal ({\sc acrad$_{\rm th}$}), fluorescent iron K$_\alpha$ line ({\sc Gaussian}), and reflection ({\sc pcfabs}) components, respectively.}\label{fig:ave_fit_pc}
\end{figure}
The change in accretion rate affects the specific accretion rate and hydrogen column density.
With this in mind, we fitted {\tt IP-reflect} again,
separating the specific accretion rate and the hydrogen column density into different datasets.
Table \ref{table:ave_spe_para_sep-obs} shows the best-fitting parameters.
The fitting was found to improve statistically,
with the $F$-test indicating that the significance in separating the parameters is $1-2\times10^{-9}$.
The specific accretion rate and the hydrogen column density
are consistent between 07S and 14S.
By contrast, both parameters of 14N are less than those of the other datasets,
which is qualitatively self-consistent.
The WD mass $M_{\rm WD} = 0.92\pm0.02$\,$M_{\odot}$
is 0.06\,$M_{\odot}$ higher in mass than that
estimated by fitting
when binding
the specific accretion rate and the hydrogen column density across the entire dataset.
\begin{table*}
\centering
\caption{Best-fitting parameters of the spectral fitting to the spin-averaged V1223\,Sgr spectrum with
{\tt IP-reflect}$^\ast$ $a$, $N_{\rm H}$, and normalization separated into different datasets.
The parameters below the dashed line were hydrodynamically calculated using the best-fitting parameters
\citep{2014MNRAS.438.2267H}.
The superscript signs are the same as those in Table\,\ref{table:ave_spe_para}.
}\label{table:ave_spe_para_sep-obs}
\begin{tabular}{cccc}
\hline
data set & 07S & 14S & 14N\\\hline
$N_{\rm H} (\times10^{22}$\,cm$^{-2}$) & $6.3_{-0.9}^{+0.8}$ & $6.5\pm0.5$ & $5.5_{-1.1}^{+1.2}$ \\
$M_{\rm WD}$ (M$_{\odot})$ & \multicolumn{3}{c}{$0.92\pm0.02$} \\
log($a$) (g\,cm$^{-2}$\,s$^{-1}$) & $> 1.7$ & $> 2.3$ & $0.5_{-0.2}^{+0.3}$ \\
$Z$ (Z$_\odot^\dagger$) & \multicolumn{3}{c}{$0.34\pm0.01$} \\
$i$ ($^\circ$) & \multicolumn{3}{c}{$53.2\pm{2.1}$} \\
$F_{\rm bol}^\flat$ ($\times$10$^{-10}$\,erg\,s$^{-1}$) & 2.9 & 2.8 & 2.8\\
$L_{\rm bol}^\natural$ ($\times$10$^{34}$\,erg\,s) & 1.2 & 1.1 & 1.1 \\
$f^\sharp$ & $<$ 2$\times$10$^{-4}$ & $<$ 6$\times$10$^{-5}$ & 4$\times$10$^{-3}$\\
$\chi^2_{\rm red}$ (d.o.f.) & \multicolumn{3}{c}{1.33 (1192)} \\
\hdashline
$T_{\rm max}^\star$ (keV) & 48 & 48 & 46 \\
$h^\P$ ($R_{\rm WD}$) & $<4\times10^{-3}$ & $<9\times10^{-4}$ & $5_{-2}^{+4}\times10^{-2}$ \\
\hline
\end{tabular}
\end{table*}
\subsection{Spin phase-resolved spectrum}
We divided the spectrum based on the spin phase with a period of 745.63\,s \citep{1985SSRv...40..143O}.
We determined the temporal origin of each dataset by
cross-correlating the light curves
because there was no ephemeris to share among the datasets.
We used the 5--10\,keV energy band to establish cross-correlations among the
{\it Suzaku} and {\it NuSTAR} data.
As a result, we determined the origins of BJD = 2454203.48031,
2456745.50051, 2456757.50299, and 2456916.50652
for the data of 07S, 14S-March, 14S-April, and 14N, respectively.
Panel (a) of Figure\,\ref{fig:para_in_sp} shows the folded light curves.
We divided the spectrum into the following eight phases:\,0--0.25, 0.125--0.375, 0.25--0.5, 0.375--0.625, 0.5--0.75,
0.625--0.875, 0.75--1.0, and 0.875--1.125.
Note that these phases show a mutual overlap of 0.125.
First, we fitted the {\sc phabs$\times$(powerlaw + 3$\times$Gaussian}s) model to the spin-phase-resolved spectra.
The three {\sc Gaussian}s reproduced the fluorescent, He-like, and H-like iron K$_\alpha$ lines
at 6.40, 6.70, and 6.97\,keV in the rest
frames, respectively.
We kept the {\sc Gaussian}s narrow and used 5--23\,keV to reasonably reproduce the continuum using the power law.
Figure\,\ref{fig:sp-res_ga} shows the 0--0.25 spin phase spectrum with the best-fitting model.
This empirical model appropriately approximates the spectra.
The best-fitting energy centroid and the equivalent width (EW)
are listed in Table\,\ref{tab:para_in_sp} along with $\chi^2$.
Panels (c) and (d) of Figure\,\ref{fig:para_in_sp} show
the energy centroid and the EW, respectively, as functions of the phase.
Both parameters
modulate with the WD spin.
\begin{figure}
\includegraphics[width=80mm]{fig/SP0_pow_3g_noset0_gw0_fit_fe_la.eps}
\caption{
The 5--9\,keV spectra from the 0--0.25 spin phase
with the best-fitting {\sc phabs$\times$(powerlaw + 3$\times$Gaussians}) model
to the 5--23\,keV spectra.
The relations between the data and colors are the same as in Figure\ref{fig:ave_fit_acrad}.
The dotted and dashed lines show the {\sc powerlaw} and three {\sc Gaussians}, respectively.}\label{fig:sp-res_ga}
\end{figure}
Next, we fitted {\tt IP-reflect} to the spin-phase-resolved spectra.
We fixed the WD mass, abundance, and specific accretion at
their best-fitting quantities of the phase-averaged fitting
with the separated specific accretion rate (Table\,\ref{table:ave_spe_para}).
This is because the WD mass and abundance
should be independent of the spin phase
and the specific accretion is too insensitive to detect its spin modulation.
Moreover, we fixed the ratio of the hydrogen column densities of
14S and 14N to that of 07S at 1.03 and 0.88, respectively, which are the best-fitting hydrogen column densities of the phase-averaged fitting.
The consistent modulation profiles within the 5--10\,keV band across
all datasets (panel (a) of Figure\,\ref{fig:para_in_sp})
justifies fixing the hydrogen column density ratio.
Table\,\ref{tab:para_in_sp} shows the best-fitting parameters.
Panels (e) and (f) of Figure\,\ref{fig:para_in_sp} display
the hydrogen column density of 07S and the viewing angle, respectively, during the spin period.
Both parameters
modulate with the WD spin as well.
\begin{figure}
\includegraphics[width=80mm]{fig/sp_i_flc_gc_gw0_edit4.eps}
\caption{Modulations of several parameters in the spin period:
(a) 5--10\,keV folded light curves of 07S (black), 14S-March (red), 14S-April (green), and 14N (blue),
(b) 20--30\,keV folded light curve of 14N, (c) EW of the fluorescent iron K$_\alpha$ line,
(d)
Centroid of fluorescent iron K$_\alpha$ line,
(e) Hydrogen column density of S07,
and (f) the viewing angle.
The error bars in (a) and (b) denote a 68\% statistical uncertainty, and those of the other panels denote a 90\% statistical uncertainty.
(c) and (d) Outputs of the {\sc phabs$\times$(powerlaw + 3Gaussians)} fitting.
(e) and (f) Outputs of {\tt IP-reflect} fitting
}\label{fig:para_in_sp}
\end{figure}edit
\begin{table*}
\rotcaption{Best-fitting parameters of the spin-phase-resolved spectra with {\sc phabs$\times$(powerlaw + 3Gaussians)} and {\tt IP-reflect}.}\label{tab:para_in_sp}
\centering
\begin{sideways}
\begin{tabular}{ccccccccc}
\hline
Phase & 0.875-1.125 & 0-0.25 & 0.125-0.375 & 0.25-0.5 & 0.375-0.625 & 0.5-0.75 & 0.625-0.875 & 0.75-1\\\hline
&\multicolumn{8}{c}{\sc phabs$\times$(powerlaw + 3Gaussians)} \\
FeI-K$_\alpha$ line energy (keV) & $6.391\pm0.005$ &$6.388_{-0.004}^{+0.006}$ &$6.387_{-0.005}^{+0.007}$ &$6.386\pm0.007$ &$6.391_{-0.005}^{+0.007}$ &$6.398_{-0.008}^{+0.007}$ &$6.398_{-0.004}^{+0.001}$ &$6.399_{-0.006}^{+0.001}$\\
FeI-K$_\alpha$ line $EW$ (eV) & $109.7_{-4.4}^{+4.1}$ &$120.8_{-7.8}^{+7.4}$ &$130.1_{-6.0}^{+7.2}$ &$125.9_{-5.4}^{+6.9}$ &$113.1_{-7.2}^{+5.1}$ &$109.7_{-6.6}^{+8.2}$ &$102.5_{-5.9}^{+6.3}$ &$103.6_{-7.7}^{+8.8}$\\
$\chi^2$ (d.o.f.) & 1.17 (765) & 1.08 (762) & 1.13 (753) & 1.18 (741) & 1.15 (748) & 1.12 (752) & 1.05 (759) & 1.14 (760)\\\hline
&\multicolumn{8}{c}{\sc phabs$\times$(acrad$_{\rm th}$+acrad$_{\rm ref}$)} \\
$N_{\rm H,07S}$ ($\times10^{22}$\,cm$^{-2}$) & $4.3_{-0.3}^{+0.2}$ & $6.5_{-0.3}^{+0.2}$ & $9.6\pm0.3$ & $11.0\pm0.3$ & $8.6\pm0.3$ & $5.2_{-0.3}^{+0.2}$ & $3.8_{-0.3}^{+0.2}$ & $3.8_{-0.3}^{+0.2}$\\
$N_{\rm H,14S}$ ($\times10^{22}$\,cm$^{-2}$)$^{\S}$ & 4.4 & 6.6 & 9.9 & 11.3 & 8.9 & 5.3 & 3.9 & 3.9 \\
$N_{\rm H,14N}$ ($\times10^{22}$\,cm$^{-2}$)$^{\l}$ & 3.8 & 5.7 & 8.5 & 9.7 & 7.6 & 4.6 & 3.3 & 3.3 \\
$M_{\rm WD}$ (M$_{\odot})$ & \multicolumn{8}{c}{0.92$^{\ddagger}$} \\
log($a$)$_{07S}$ (g\,cm$^{-2}$\,s$^{-1}$) & \multicolumn{8}{c}{3.4$^{\ddagger}$} \\
log($a$)$_{14S}$ (g\,cm$^{-2}$\,s$^{-1}$) & \multicolumn{8}{c}{3.3$^{\ddagger}$} \\
log($a$)$_{14N}$ (g\,cm$^{-2}$\,s$^{-1}$) & \multicolumn{8}{c}{0.5$^{\ddagger}$} \\
$Z$ (Z$_\odot^\dagger$) & \multicolumn{8}{c}{0.34$^{\ddagger}$} \\
$i$ ($^\circ$) & $48.1_{-2.9}^{+2.6}$ &$47.6_{-3.2}^{+2.6}$ &$55.2_{-2.3}^{+2.3}$ &$63.0_{-2.0}^{+1.6}$ &$63.1_{-2.0}^{+1.6}$ &$59.1_{-2.0}^{+1.9}$ &$55.7_{-2.2}^{+2.2}$ &$52.1_{-2.6}^{+2.2}$ \\
$\chi^2_{\rm red}$ (d.o.f.) & 1.19 (797) & 1.12 (795) & 1.20 (785) & 1.24 (773) & 1.19 (779) & 1.18 (784) & 1.20 (791) & 1.26 (791) \\\hline
\multicolumn{9}{l}{$^{\ast}$The errors indicate a 90\% statistical uncertainty.}\\
\multicolumn{2}{l}{$^\dagger$Based on \cite{1989GeCoA..53..197A}.}\\
\multicolumn{9}{l}{\footnotesize $^{\ddagger}$Fixed at the quantity
best-fitted to the averaged spectrum with {\sc phabs$\times$(acrad$_{\rm th}$+acrad$_{\rm ref}$}) separating $a$ and normalization
using the dataset.}\\
\multicolumn{9}{l}{$^{\S}$Ratio of $N_{\rm H,07S}$ was fixed at 1.02984.}\\
\multicolumn{9}{l}{$^{\l}$Ratio of $N_{\rm H,07S}$ was fixed at 0.88017.}\\
\end{tabular}
\end{sideways}
\end{table*}
\section{Discussion}\label{sec:dis}
\subsection{Reflection component}\label{sec:dis_ref}
We found a remarkable discrepancy in the reflection parameters
(i.e., viewing and solid angles)
among the spin-phase-averaged spectral fittings
with the bound hydrogen column density and the specific accretion rate
(see Table\,\ref{table:ave_spe_para}).
The best-fitting viewing angles of {\tt IP-reflect} and {\tt AGN-reflect}
are $i = 54.2_{-2.2}^{+2.1}$$^\circ$
and $< 42$$^\circ$, respectively.
The best-fitting solid angle of the {\tt AGN-reflect} model was $\Omega/2\pi = 0.44_{-0.06}^{+0.10}$.
Assuming a point source, as in {\sc reflect} in {\tt AGN-reflect}, the solid angle is expressed as
\begin{equation}
\Omega/2\pi = 1 - \sqrt{1-\frac{1}{\left(\frac{h}{R_{\rm WD}}+1\right)^2}}.
\end{equation}
Thus, the PSAC height is calculated at 13\% of the WD radius.
Note that the PSAC should even be taller with its actual finite length.
However, the PSAC is shorter than 0.03\% of the WD radius
according to the hydrodynamical calculation \citep{2014MNRAS.438.2267H}
with the best-fitting parameters of {\tt AGN-reflect}, indicating that {\tt AGN-reflect} is seriously self-inconsistent.
As a major advantage of {\sc acrad$_{\rm ref}$} in {\tt IP-reflect} over other reflection models,
it utilizes the fluorescent iron K$_\alpha$ line to determine the reflection spectrum.
To do so, the other models use a Compton hump, which is a continuum, making it
difficult to separate from the thermal continuum.
In fact, the solid angle or the viewing angle is generally fixed when using {\sc reflect} (for example, \citealt{2011PASJ...63S.739H}, \citealt{2015ApJ...807L..30M}).
By contrast, we tightly constrained both parameters simultaneously using {\tt IP-reflect}.
To compare the reflection models, the ratios of the best-fit reflection spectra of
{\tt AGN-reflect} and {\tt PCA-reflect} to that of {\tt IP-reflect} are plotted in Figure\,\ref{fig:refspe_ratio}.
In the case of {\tt PCA-reflect}, the reflection spectrum
is the sum of the narrow Gaussian and
the thermal spectrum
strongly attenuated using the PCA model to mimic the Compton hump.
The reflection spectrum of {\tt AGN-reflect} includes a narrow Gaussian.
The ratios have numerous lines that
originating from the thermal emission.
{\tt IP-reflect} considers the energy loss to be due to incoherent scattering \citep{2018MNRAS.474.1810H}.
{\tt PCA-reflect} cannot reproduce the energy loss.
In addition, {\sc reflect} in {\tt AGN-reflect} does not calculate the energy loss at
below 10\,keV \citep{1995MNRAS.273..837M}.
Therefore, the
thermal-origin emission lines in the reflection spectrum
of {\tt PCA-reflect} and {\tt AGN-reflect}
stay at their original energy, and the total spectrum
overestimates the intensity of the thermal emission lines.
As a result, the reflection spectrum is inevitably suppressed
to match the overestimated model lines to the data.
Although either an increase of the viewing angle or a decrease of the solid angle
suppresses the reflection, only the latter
results in a strong curvature at approximately 20--30\,keV
\citep{1991MNRAS.249..352G,2018MNRAS.474.1810H}.
This stronger curvature reproduces the Compton hump better with the suppressed reflection.
As a result, the solid angle is decreased to suppress the reflection.
In fact, \cite{2015ApJ...807L..30M} reported that
the reflection spectrum reproduced by {\sc reflect} is suppressed
when the iron K$_\alpha$ lines are included in the fitting.
Meanwhile, the overestimated lines also suppressed the abundance, as shown in Table \ref{table:ave_spe_para_sep-obs}.
It should be noted that a better energy resolution would
strengthen the suppression of the reflection and
abundance
because it highlights the discrepancy in the overestimated line.
Another noticeable feature in the spectral ratios
is the Compton shoulder below the emission lines.
Neither PCA-reflect nor AGN-reflect reproduces the Compton shoulder, as described above.
Moreover, {\tt IP-reflect} has fluorescent lines of neutral iron and nickel,
unlike the PCA and {\sc reflect}.
Therefore, negative line structures are found at the energies of the
fluorescent lines (6.404, 6.391, 7.058, 7.478, 7.461, and 8.265\,keV
for iron K$_{\alpha1,2}$, iron K$_\beta$, nickel K$_{\alpha1,2}$, and nickel K$_\beta$, respectively).
\begin{figure}
\includegraphics[width=85mm]{fig/ratio_reflect-pcfabs_mo_5-70.eps}
\includegraphics[width=85mm]{fig/ratio_reflect-pcfabs_mo_5-9.eps}
\caption{Spectral model ratios of the reflection component reproduced by {\sc reflect} (black) and {\sc pcfabs} (red) to that by {\sc acrad$_{\rm ref}$}.
The model spectra above and below 10 keV are the best-fitting models for FPMA and XIS-FI, respectively.
The bottom panel shows a blowup of the top at between 5 and 9keV.}\label{fig:refspe_ratio}
\end{figure}
\subsection{WD mass estimation}
In this subsection,
we correct the estimated WD mass by considering the finite inner disk radius described in Section \ref{sec:finit_disk_r}.
In §\ref{sec:energy_band}--\ref{sec:ref}, we discuss several factors
that affect the WD mass measurement
and summarize the directions in Table \ref{tab:Mwd_measure_direction}.
We compare the results with an optical measurement technique in \ref{sec:opt}.
\subsubsection{Finite inner disk radius}\label{sec:finit_disk_r}
{\tt IP-reflect} assumes that accreting gas falls from infinity.
Therefore, a non-negligible
small inner radius results in a small shock energy release, a low shock temperature,
and an underestimation of the WD mass
(\citealt{2005A&A...435..191S,2019MNRAS.482.3622S}).
The inner disk radius may be approximated by the co-rotation radius,
\begin{equation}
R_{\rm co} = \left(\frac{GM_{\rm WD}P_{\rm spin}^{2}}{4\pi^2}\right)^{\frac{1}{3}}
\end{equation}
in the spin equilibrium systems \citep{1991ApJ...378..674K,1993MNRAS.261..144K,2018MNRAS.476..554S}.
With a spin period of 745.63\,s and our WD mass estimate of 0.92\,$M_{\odot}$,
the inner radius is estimated as $R_{\rm in} \sim R_{\rm co}$ = 20\,$R_{\odot}$,
where the WD radius is computed by the relation between the WD mass and radius by \cite{1972ApJ...175..417N}.
As a result, the WD mass should be corrected by 5\% to 0.97\,$M_{\odot}$.
\subsubsection{Energy band}\label{sec:energy_band}
\begin{table*}
\centering
\caption{Influence of different factors on the estimation of the WD mass.}
\label{tab:Mwd_measure_direction}
\begin{tabular}{lp{12cm}}
\hline
Parameter & Direction\\
\hline
\vspace{1mm}
Upper limit of the energy band & It can not be too high, and the higher, the better. It should be higher than the maximum plasma temperature at least. It should be adjusted to each target by confirming that the WD mass converges as by figure\,\ref{fig:highE_Mwd}. \\
\vspace{1mm}
Lower limit of the energy band & It should be high enough to approximate the multicolumnar absorber by a single-column absorber but include the iron K$_\alpha$ lines. It has to be adjusted to each target by confirming that the WD mass converges as by Figure \,\ref{fig:lowE_Mwd}.\\%, as shown in
\vspace{1mm}
Reflection & It can be reproduced by the AGN reflection model ({\sc reflect}) or by the PCA model instead of the IP reflection model. Note that this substitution is not necessarily valid, with a better energy resolution than that of the CCD.\\
\vspace{1mm}
Abundance & It should be parameterized and free in the spectral fitting.\\
\hline
\end{tabular}
\end{table*}
The fitting energy band is a major factor in measuring the WD mass.
Because the maximum temperature of an IP is generally higher than 10\,keV (for example, \citealt{2010A&A...520A..25Y}),
we selected the hard X-ray spectrum \citep{2016ApJ...826..160H}.
Figure\,\ref{fig:highE_Mwd} shows the relation between the computed WD mass
and the upper limit of the energy band fitted with {\tt IP-reflect}
by separating $a$, $N_{\rm H}$, and the normalization when applying the dataset.
The computed WD mass converges on 0.92\,$M_{\odot}$ at an upper limit of approximately 50\,keV.
This is natural because the maximum temperature of the plasma in V1223\,Sgr is approximately 40\,keV.
{\it NuSTAR} is sufficiently powerful to measure the WD mass in an IP
because it gives us high-quality
data of up to 78\,keV.
The lower limit of the energy band is also important.
The emission lines at below 10\,keV allow us to measure the metal abundance
and the emission measure distribution across the PSAC.
The absorption in
an IP is created by the complicated accretion curtain and is generally difficult to model.
From an observational view, a few partial covering absorbers are needed to
reproduce the IP spectra at even below 10\,keV \citep{1999ApJS..120..277E}.
One method used to avoid this difficulty is cutting off a lower energy band \citep{1999ApJS..120..277E}.
Figure\,\ref{fig:lowE_Mwd} shows the relation between the computed WD mass and the lower limit of the energy band.
Except for the lower limit, which is higher than 6\,keV, the WD mass converges to 0.92\,$M_{\odot}$.
At approximately the 5\,keV lower limit, the multicolumnar absorber
is approximated using our applied single-column absorber.
When the lower limit goes beyond 6\,keV (i.e., the iron K$_\alpha$ shell band),
the emission measure distribution in the temperature cannot
be determined and the WD mass estimation suffers from large systematic errors.
\begin{figure}
\includegraphics[width=85mm]{fig/trefacrad_upE_Mwd.eps}
\caption{WD mass computed by varying the upper limit of the fitted energy band.}\label{fig:highE_Mwd}
\end{figure}
\begin{figure}
\includegraphics[width=85mm]{fig/trefacrad_lowE_Mwd.eps}
\caption{WD mass computed by varying the lower limit of the fitted energy band.}\label{fig:lowE_Mwd}
\end{figure}
\subsubsection{Abundance}
The abundance is another major factor in measuring the WD mass.
In \cite{2018MNRAS.476..554S}, the authors measured the WD mass in V1223\,Sgr
to be $0.75\pm0.02$\,$M_{\odot}$ or $0.78\pm0.01$\,$M_{\odot}$,
which is less massive than our estimate by approximately 0.15\,$M_{\odot}$ with the {\tt IP-reflect} model.
The authors excluded the iron K$_\alpha$ band (5.5--7.5\,keV)
and fixed the abundance at 1\,$Z_{\odot}$.
Figure\,\ref{fig:Z_Mwd} shows the relation between the computed WD mass and the fixed abundance.
By excluding the iron K$_\alpha$ band and fixing the abundance at 1\,$Z_{\odot}$,
we obtained the WD mass of $M_{\rm WD}$ = 0.78$^{+0.02}_{-0.01}$\,$M_{\odot}$,
which agrees with \cite{2018MNRAS.476..554S}.
The lighter WD is computed with higher abundance
because the higher abundance leads to a harder reflection continuum
{\citep{2018MNRAS.474.1810H}.
The {\tt AGN-reflect} model includes this effect as well.}
However, when we include the iron K$_\alpha$ band,
such
a high abundance of 1\,$Z_{\odot}$ is rejected (reduced-$\chi^2$ = 2.9).
The circles in Figure\,\ref{fig:Z_Mwd} do not have an error bar because the
$\chi^2$ of the fittings was too large.
With the iron K$_\alpha$ band, an overabundance leads to
an overestimation of the WD mass
and an underestimation of the specific accretion rate,
and thus the emission line in the thermal and reflection spectra weakens and resembles the data.
\begin{figure}
\includegraphics[width=85mm]{fig/trefacrad_Z_Mwd.eps}
\caption{Computed WD mass with fixed abundance.
Squares show the data fitting without an iron K$_\alpha$ band.
Circles show the data fitting with the iron K$_\alpha$ band.
Errors of a part of circles are not shown (see text). }\label{fig:Z_Mwd}
\end{figure}
\subsubsection{Reflection component}\label{sec:ref}
To reproduce the reflection spectrum,
we used three models, that is, {\sc acrad$_{\rm ref}$} of {\tt IP-reflect}, {\sc reflect} of {\tt AGN-reflect}, and PCA of {\tt PCA-reflect}.
The differences in the best-fitting WD mass are only within 0.04\,$M_{\rm WD}$ among the models.
This result is consistent with that of \cite{1998MNRAS.293..222C}
in that the difference in the measured WD masses
is 0.04\,$M_{\odot}$ on average at over 13\,mCVs with and without the reflection model.
However, as mentioned in \S\ref{sec:dis_ref}, the {\tt reflect} and PCA models
suppress the reflection in the fitted model, and
the degree of the suppression depends on the energy resolution.
The data that we used had a modest energy resolution, whereas the {\it Ginga} data used in
\cite{1998MNRAS.293..222C} had an even worse energy resolution.
Therefore, we cannot judge whether reflection modeling generally influences the WD mass estimation.
\subsubsection{Comparison with optical estimation}\label{sec:opt}
\cite{1985ApJ...289..300P} estimated the WD mass at 0.4--0.6\,$M_{\odot}$
using an optical orbital modulation measurement.
However, in this study, the maximum plasma temperature of V1223\,Sgr is estimated as 48\,keV and is no less than 30\,keV in previous studies using a multi-temperature plasma model.
As long as the Rankine-Hugoniot relations and the theoretical WD mass-radius relation are valid, the WD of 0.6\,$M_{\odot}$ leads to 22\,keV plasma even if the shock is strong and formed at the WD surface.
Therefore, the 0.4--0.6\,$M_{\odot}$ should be an underestimation.
\subsection{Spin modulations of the parameters}
We discovered modulations of the EW of the fluorescent iron K$_\alpha$ line and viewing angle.
The viewing angle approximately correlates with the EW and flux within the 20--30\,keV energy band.
These anti-correlations are consistent with the fact that lowering the
viewing angle enhances the reflection and supports the discovery regarding the viewing angle modulation.
If the reflections are a unique factor leading to modulations of the EW
and the flux within the 20--30\,keV energy band, the modulations will correlate completely with those of the viewing angle.
However, the pre-shock gas may also contribute to the modulations, and
thus may shift the phase of the modulations.
The fluorescent iron K$_\alpha$ lines of the EW of $\sim$ 15 and 40\,eV are
emitted from the pre-shock gas
of $N_{\rm H}$ = 4$\times$10$^{22}$\,cm$^{-2}$
and 10$^{23}$\,cm$^{-2}$, respectively \citep{2011PASJ...63S.739H},
assuming that the pre-shock gas covers the plasma by 2$\pi$.
The pre-shock gas modulates the 20--30\,keV flux
by absorption and scattering by a few percentage points.
These effects are minor relative to the reflection but should shift the phase.
A sinusoid approximates the viewing angle modulation
with average and semi-amplitude values of 55$^\circ$ and 7$^\circ$, respectively.
Its minimum and maximum values are located at spin phases $\phi$ = 0.1 and 0.6, respectively.
Two combinations of the latitude of the PSAC ($l_{\rm PSAC}$)
and
the spin axis angle from the line-of-sight ($\theta_{\rm spin}$)
are possible, that is, ($l_{\rm PSAC}$, $\theta_{\rm spin}$) = (55$^\circ$, 7$^\circ$), and (7$^\circ$, 55$^\circ$),
as shown in Figure\,\ref{fig:geo}.
Both spin axes disagree with the reported system inclination of 17-47$^\circ$
\citep{2004A&A...419..291B}.
This disagreement implies that
WD does not receive a substantial fraction of the angular momentum of the accreting gas.
At this point, we cannot distinguish between the two geometries, but
we may see variations in the angle between the magnetic pole and the PSAC, and distinguish between them
if we measure $l_{\rm PSAC}$ and $\theta_{\rm spin}$ more precisely.
\begin{figure*}
\begin{minipage}{0.49\hsize}
\begin{center}
\includegraphics[width=80mm]{fig/a_orbplane.eps}
\end{center}
\end{minipage}
\begin{minipage}{0.49\hsize}
\begin{center}
\includegraphics[width=80mm]{fig/b_orbplane.eps}
\end{center}
\end{minipage}
\vspace{5mm}
\caption{Geometries of the WD, PSAC, spin axis, and line-of-sight in V1223\,Sgr.
(a) and (b) Cases of ($l_{\rm PSAC}$, $\theta_{\rm spin}$) = (55$^\circ$, 7$^\circ$), and (7$^\circ$, 55$^\circ$), respectively.
The system inclination is 24$^\circ$
\citep{2004A&A...419..291B} in both cases.}\label{fig:geo}
\end{figure*}
The maximum viewing angle phase does not correspond to that of the maximum X-ray.
The anti-correlation between the X-ray flux and hydrogen column density agrees with the standard scenario,
where the pre-shock gas leads to X-ray modulation by photoelectric absorption \citep{1988MNRAS.231..549R}.
This scenario expects that the X-ray flux reaches the maximum
when the PSAC points away from the observer and
the viewing angle is at its maximum.
However, we show that the viewing angle is close to its minimum, rather than its maximum.
Some complicated factors, such as unevenness in the density
and/or the accretion geometry, should exceed the path-length factor.
We confirmed the central energy modulation
of the fluorescent iron K$_\alpha$ line reported by \cite{2011PASJ...63S.739H}.
The authors suggested that the energy shift is due to the Doppler effect of the pre-shock gas accreting at $\sim$5$\times10^{3}$\,km\,s$^{-1}$.
By contrast, {\tt IP-reflect} does not require additional components around the 6.3\,keV energy band, as reported,
and the Compton shoulder compensates this component.
Higher-resolution data are required to distinguish between these scenarios.
\subsection{Specific accretion rate and shock height}
A fitting of the data with {\tt IP-reflect} by separating the specific accretion rate
shows that the parameter changes by the dataset as
log($a_{07S}$\,[g\,cm$^{-2}$\,s$^{-1}$]) $> 1.7$,
log($a_{14S}$\,[g\,cm$^{-2}$\,s$^{-1}$]) $> 2.3$,
and ($a_{14N}$\,[g\,cm$^{-2}$\,s$^{-1}$]) = $0.5_{-0.2}^{+0.3}$.
The luminosity of the three datasets is
1.1--1.2$\times$10$^{34}$\,erg\,s$^{-1}$,
indicating that the accretion rate hardly changes.
Therefore, the fractional accreting area ($f$, the
ratio of the PSAC cross section to the entire WD area) should be changed to explain the
change in the specific accretion rate.
Herein, we examine the consistency in the measured specific accretion rate, hydrogen column density, and area fraction.
With a free fall, the velocity of the pre-shock gas can be expressed as
\begin{equation}
v = \sqrt{\frac{2GM_{\rm WD}}{r}},
\end{equation}
where $r$ is the distance from the WD center.
The dipole geometry constrains the PSAC cross section as
\begin{equation}
S = S_0\left(\frac{r}{R_{\rm WD}}\right)^{3},
\end{equation}
where $S_0$ is the PSAC cross section at the WD surface.
From the mass continuity equation, $\rho v S$ = $a S_0$ = constant,
the density is calculated as
\begin{equation}
\rho = \frac{a R_{\rm WD}^3}{\sqrt{2GM_{\rm WD}}}r^{-\frac{5}{2}}.\label{eq:density}
\end{equation}
When the PSAC is sufficiently short,
we integrate equation\,\ref{eq:density} and obtain the mass column density as
\begin{equation}
\sigma = \frac{2 a R_{\rm WD}^3}{3\sqrt{2GM_{\rm WD}}}(R_{\rm WD}^{-\frac{2}{3}}-r^{-\frac{2}{3}}).
\end{equation}
The hydrogen column density can then be obtained as
\begin{equation}
n_{\rm H} = \frac{\sigma}{m_{\rm H}},
\end{equation}
where $m_{\rm H}$ is the hydrogen mass.
Assuming that the X-rays pass through a path whose length is the radius of the PSAC cross-section,
computed from $f$ in Table\,\ref{table:ave_spe_para_sep-obs},
the specific accretion rates of the datasets 07S, 14S, and 14N ($a$ in Table\,\ref{table:ave_spe_para_sep-obs})
produce hydrogen column densities of approximately
$7.9\times10^{22}$\,cm$^{-2}$,
$17\times10^{22}$\,cm$^{-2}$, and
$2.0\times10^{22}$\,cm$^{-2}$, respectively.
These quantities correspond to
their respective directly measured hydrogen column density by a factor of 2, and the parameters are approximately self-consistent.
In any case, it is difficult to determine
the specific accretion rate \citep{2014MNRAS.441.3718H}.
We will obtain new information on the specific accretion rate and the area fraction
with a higher energy resolution from the {\it X-ray imaging and spectroscopy mission (XRISM)}
and X-ray polarization from the {\it imaging X-ray polarimeter explorer (IXPE)}.
\section{Conclusion}\label{sec:con}
We applied the newly developed IP X-ray thermal and reflection spectral models ({\sc acrad}$_{\rm th}$ + {\sc acrad}$_{\rm ref}$
called {\tt IP-reflect}) to the V1223\,Sgr combined spectrum collected from the
{\it Suzaku} satellite in 2007 and 2014, and the {\it NuSTAR} satellite in 2014.
We compared our model with an AGN reflection model ({\sc reflect} with {\sc acrad}$_{\rm th}$, called {\tt AGN-reflect}),
and a partial covering absorption model
({\sc pcfabs} with {\sc acrad}$_{\rm th}$, called {\tt PCA-reflect}).
In this study, {\tt IP-reflect} agrees with other models for the estimated WD mass.
This result shows that the reflection modeling does not significantly influence the WD mass measurement
in the case of V1223\,Sgr, which has a moderate energy resolution ($\Delta E \protect\raisebox{-0.5ex}{$\:\stackrel{\textstyle >}{\sim}\:$} 150$\,eV).
In addition, {\tt AGN-reflect} shows a serious self-inconsistent behavior. The PSAC height determined by the best-fitting solid angle
was found to be higher than that calculated hydrodynamically
using the best-fitting WD mass and the specific accretion rate by a few orders of magnitude.
This problem is probably
due to the neglect of
the energy loss
by the incoherent scattering at below 10\,keV.
Data with better energy resolution may make the origin of this issue clearer.
We fitted {\tt IP-reflect} by separating
the specific accretion rate and hydrogen column density into different data sets.
The WD mass, metal abundance, and viewing angle were estimated
to be $M_{\rm WD}$ = 0.92$\pm$0.02\,$M_{\odot}$, $Z = 0.34\pm0.01$\,$Z_{\odot}$, and $i = 53.2\pm2.1$$^\circ$, respectively.
The three datasets agree on the hydrogen column density as
$N_{{\rm H,} 07S}$ = $6.3_{-0.9}^{+0.8}\times10^{22}$\,cm$^{-2}$,
$N_{{\rm H,} 14S}$ = $6.5\pm0.5\times10^{22}$\,cm$^{-2}$, and
$N_{{\rm H,} 14N}$ = $5.5_{-1.1}^{+1.2}\times10^{22}$\,cm$^{-2}$.
By contrast, the specific accretion rate of {\it NuSTAR} in 2014,
log($a_{14N}$ [\,g\,cm$^{-2}$\,s$^{-1}$]) = $0.5_{-0.2}^{+0.3}$,
is lower than that of the other data
(log($a_{07S}$ [\,g\,cm$^{-2}$\,s$^{-1}$]) $> 1.7$
and log($a_{14S}$ [\,g\,cm$^{-2}$\,s$^{-1}$]) $> {2.3}$).
These specific accretion rates constrain the PSAC height as
$h_{07S} < 4\times10^{-3}$\,R$_{\rm WD}$,
$h_{14S} < 9\times10^{-4}$\,R$_{\rm WD}$,
and $h_{14N} = 5_{-2}^{+4}\times10^{-2}$\,$R_{\rm WD}$.
If the inner disk radius is approximated by the co-rotation radius
$R_{\rm in} \sim R_{\rm co}$ = 20\,$R_{\rm \odot}$,
the WD mass should be corrected to 0.97$\pm$0.02\,$M_{\odot}$.
The change in the specific accretion rate results in a change in
the fractional accreting area as the thermal X-ray
luminosity is 1.1--1.2\,$\times10^{34}$\,erg\,s$^{-1}$ across all datasets.
The directly measured hydrogen column densities are approximately consistent with
those calculated with the specific accretion rate and fractional accreting area by a factor of 2.
The energy band and the metal abundance affect the WD mass measurement,
and the choice of incorrect value introduces large systematic errors (e.g., $\ltsimscript$\,0.2\,$M_{\odot}$ in the WD mass).
Without an energy of higher than 40 keV, it was difficult to measure the maximum temperature,
which is essential for the WD mass measurement.
The spectrum at below 5\,keV introduces a complication of the multicolumnar absorber.
The iron K$_\alpha$ energy band is also essential
to determine the emission measure as a function of temperature.
Incorrect metal abundance leads to over- or under-intensity of the hard X-ray continuum and emission lines,
resulting in a large error in the WD mass measurement.
We fitted an empirical model composed of a power law and three Gaussians or
{\tt IP-reflect} to the spin-phase-resolved spectra.
With {\tt IP-reflect}, the WD mass, metal abundance,
specific accretion rate, and ratio of the hydrogen column density between the data sets
were fixed to those of the best-fit parameters of the average spectral fitting.
We discovered for the first time the modulation of the EW and viewing angle.
The viewing angle correlates approximately with the EW and flux within the 10--30\,keV energy band.
This fact supports the discovery of the viewing-angle modulation by {\tt IP-reflect}.
The viewing angle modulation has average and semi-amplitude values of 55$^\circ$ and 7$^\circ$, respectively.
Two combinations of the latitude of the PSAC ($l_{\rm PSAC}$) and
the spin axis angle from the line-of-sight ($\theta_{\rm spin}$)
are possible, that is, ($l_{\rm PSAC}$, $\theta_{\rm spin}$) = (55$^\circ$, 7$^\circ$), or (7$^\circ$, 55$^\circ$).
In either case, the spin axis disagrees with the previously reported system inclination of 24$^\circ$
\citep{2004A&A...419..291B}.
The anti-correlation between the viewing angle and the flux is
inconsistent with the expectation of the standard model, which is called the accretion curtain model.
For V1223\,Sgr, a complex structure in the pre-shock gas, e.g.,
the unevenness of the density, should affect the X-ray modulation.
\section*{DATA AVAILABILITY}
The {\it Suzaku} and {\it NuSTAR} data used in this study are publicly available
in the HEASARC archive at https://heasarc.gsfc.nasa.gov/.
\section*{ACKNOWLEDGEMENTS}
The authors are grateful to all of the Suzaku and NuSTAR project members for developing
the instruments and their software, the spacecraft operations, and the calibrations.
We thank the anonymous referee and Dr. Yang Soong for their careful review and insightful comments,
and Editage (www.editage.com) for English language editing.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,354 |
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Εργασίες για CPM (Συνεχής Παθητική Κίνηση). Διαβάστε περισσότερα εδώ.
Παρασκευή, 05 Οκτωβρίου 2012 11:06
The effects of immediate continuous passive motion on the clinical signs of soft tissue healing following an anterior cruciate ligament reconstruction
The purpose of this study was to examine the effects of continuous passive motion (CPM) immediately following an arthroscopically assisted anterior cruciate ligament reconstruction (ACL) utilizing a bone patella bone (BPTB) autograft on the clinical signs of the inflammatory phase of soft tissue healing. The clinical signs that were examined are acute pain, swelling, and knee function. During the inflammatory phase, the study investigated the relationship between CPM and blood loss when utilizing a hemovac drain during the first post-operative 24 hours. Another purpose of this study was to determine the effects of CPM during the fibroplastic phase of soft tissue healing. During this phase, the relationship between CPM and swelling, and CPM and knee function was also investigated.
Thirty patients (15-45 yrs. old) participated in this study. The patients in this study were randomly placed into one of four groups. The first (chronic ACL) (n = 11) and second (acute ACL) (n = 4) groups used the CPM and began knee motion immediately following surgery. The third (chronic ACL (n = 9) and fourth (acute ACL) (n = 6) groups did not use the CPM following the surgery. All groups followed an identical post-operative rehabilitation program with the exception of the CPM groups using a CPM device. The design of this study included the collection of data during the inflammatory (1-3 days postsurgery) and fibroplastic phases (4-21 days postsurgery) of soft tissue healing.
The results indicated that the initiation of CPM immediately following an ACL reconstruction had a significant ($<$.05) effect on decreasing the amount of medication consumed by the patient, and a significant ($<$.05) decrease in the patient's need for medication during the inflammatory phase. There was no statistical significance in the level of perceived pain between the groups. Patients that received CPM had a significantly ($<$.01) greater decrease in joint ellusion and hemarthrosis during the inflammatory phase. The use of CPM during the fibroplastic phase resulted in a significant ($<$.025) decrease in hemarthrosis. There was no statistically significant difference in the amount of blood that was collected in the hemovac between groups. There was a statistically greater ($<$.05) increase in the degrees of active and passive knee flexion attained by patients that utilized CPM during the inflammatory and fibroplastic phases. No statistically significant difference was found between groups in the degrees of knee extension during these phases of soft tissue healing.
Bρείτε το άρθρο:
McCarthy, M. R. (1990). The effects of immediate continuous passive motion on the clinical signs of soft tissue healing following an anterior cruciate ligament reconstruction. University of Virginia). ProQuest Dissertations and Theses, , 128-128 p.
Retrieved from http://search.proquest.com/docview/303900953?accountid=36196;
Κατηγορία CPM
The effect of continuous passive motion on anterior cruciate ligament reconstruction stability
Burks, R., Daniel, D., & Losse, G. (1984).
This study was undertaken to examine the immediate effect of continuous passive motion (CPM) on anterior cruciate ligament (ACL) reconstruction stability. Ca daver knees were tested with a knee arthrometer with the anterior cruciate intact and then with the anterior cruciate sectioned. One of three anterior cruciate re constructions was then performed and stability was restored to the knee and it was again tested with the knee arthrometer. Stability was defined as being within 2 mm of the intact measurement. The three operations selected were the Marshall-Maclntosh "over-the-top," (OTT) a patellar bone-patellar tendon-tubercle bone (BTB) graft, and a semitendinosis reconstruction. The specimens were placed on a CPM device in a cooler at 38 degree F and put through a range of motion of 20 to 70 degree at 10 cycles per minute for 3 days. A success was less than a 2 mm increase in the post-CPM measurement compared to pre-CPM. All three bone-tendon-bone op erations failed. The semitendinosis operation was suc cessful in only three out of eight specimens. The OTT operation was successful in eight out of nine speci mens. The possible reasons for success and failure are discussed.Because of the potential problems with failure of an ACL with CPM it is suggested that the particular tech nique being used for an anterior cruciate reconstruction be tested prior to it being used with CPM clinically.
Βρείτε το άρθρο:
The effect of continuous passive motion on anterior cruciate ligament reconstruction stability. American Journal of Sports Medicine, 12(4), 323-327. doi: http://dx.doi.org/10.1177/036354658401200414
εξάρθρωση γόνατος
CPM--Continuous Passive Motion: treatment of injured or operated knee-joints using passive movement. A meta-analysis of current literature
Kirschner, P. P.
There is still a controversial discussion in literature about the use of motor driven splints in knee surgery--as the principle of continuous passive motion, CPM. For this reason it seemed useful for an evaluation to look through the papers which were published since 1990. It was obvious, that negative results were published often before this year, but this papers are still quoted standard works. In medical data bases subito-doc.de, medscape.com, medica.de and zbmed.de 230 papers were found by search CPM, continuous passive motion and arthromot. Coincidentally there was a search for authors who were already quoted in other papers. 36 papers concerning CPM after knee surgery were utilized. The role of CPM regarding the range of motion, swelling, duration of hospital stay, use of analgesics, costs, postoperative manipulations, wound healing and thrombo embolic complications was evaluated. Although the results of this partial retrospective, partial prospective, sometimes randomized or double blinded studies are in contradiction, there can only be found a trend to better results. New clinical studies for evidence based guidelines in the handling of continuous passive motion after knee surgery are necessary.
Βρείτε το πλήρες άρθρο:
Kirschner, P. P. (2004). [CPM--continuous passive motion: Treatment of injured or operated knee-joints using passive movement. A meta-analysis of current literature]. Der Unfallchirurg, 107(4), 328-340.
Retrieved from http://search.proquest.com/docview/71867567?accountid=36196;
Effectiveness of prolonged use of continuous passive motion (CPM), as an adjunct to physiotherapy, after total knee arthroplasty
Lenssen Ton AF, van Steyn, Mike JA, Crijns, Yvonne HF, Waltje Eddie MH, Roox, George M et al.
BMC Musculoskeletal Disorders 9 (2008): 60-60.
Background Adequate and intensive rehabilitation is an important requirement for successful total knee arthroplasty. Although research suggests that Continuous Passive Motion (CPM) should be implemented in the first rehabilitation phase after surgery, there is substantial debate about the duration of each session and the total period of CPM application. A Cochrane review on this topic concluded that short-term use of CPM leads to greater short-term range of motion. It also suggested, however, that future research should concentrate on the treatment period during which CPM should be administered. Methods In a randomised controlled trial we investigated the effectiveness of prolonged CPM use in the home situation as an adjunct to standardised PT. Efficacy was assessed in terms of faster improvements in range of motion (RoM) and functional recovery, measured at the end of the active treatment period, 17 days after surgery. Sixty patients with knee osteoarthritis undergoing TKA and experiencing early postoperative flexion impairment were randomised over two treatment groups. The experimental group received CPM + PT for 17 consecutive days after surgery, whereas the usual care group received the same treatment during the in-hospital phase (i.e. about four days), followed by PT alone (usual care) in the first two weeks after hospital discharge. From 18 days to three months after surgery, both groups received standardised PT. The primary focus of rehabilitation was functional recovery (e.g. ambulation) and regaining RoM in the knee. Results Prolonged use of CPM slightly improved short-term RoM in patients with limited RoM at the time of discharge after total knee arthroplasty when added to a semi-standard PT programme. Assessment at 6 weeks and three months after surgery found no long-term effects of this intervention Neither did we detect functional benefits of the improved RoM at any of the outcome assessments. Conclusion Although results indicate that prolonged CPM use might have a small short-term effect on RoM, routine use of prolonged CPM in patients with limited RoM at hospital discharge should be reconsidered, since neither long-term effects nor transfer to better functional performance was detected.
"Lenssen, T. A. F., van Steyn, M.,J.A., Crijns, Y. H. F., Waltje, E. M. H., Roox, G. M., Geesink, R. J. T., . . . De Bie, R.,A. (2008). Effectiveness of prolonged use of continuous passive motion (CPM), as an adjunct to physiotherapy, after total knee arthroplasty. BMC Musculoskeletal Disorders, 9, 60-60. doi: http://dx.doi.org/10.1186/1471-2474-9-60 "
αρθροπλαστική
1 σχόλιο
Πέμπτη, 04 Οκτωβρίου 2012 10:31
Devices for the prevention and treatment of knee stiffness after total knee arthroplasty
Mark J McElroy, Aaron J Johnson, Michael G Zywiel and Michael A Mont
Expert Rev. Med. Devices 8(1), 57–65 (2011)
Persistent pain and dysfunction following total knee arthroplasty require treatment beyond standard rehabilitation. This article discusses devices used to prevent and treat decreased range of motion. If deficits remain after initial standard therapy, multiple devices exist that can be used for nonoperative treatment. Load-control devices apply a constant force, producing variable soft-tissue displacement as tissues stretch. Static progressive stretch devices use the principle of stress relaxation by applying progressively increasing constant displacements. Both types of devices are reported to be effective in treating persistent knee stiffness. The authors feel that future developments will occur in improving treatment protocols for these devices.
..."Using CPM led to shorter hospital stays by a difference of approximately 1 day (95% CI: 0.03–1.35 days, based on 382 patients), improved active knee flexion at 2-week follow-up by a mean of 4.3° (95% CI: 2.0–6.6°, based on 286 patients) and lowered the incidence of postoperative manipulation by a relative risk of 0.12 (95% CI: 0.03–0.53, based on three trials). "...
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\section{Introduction }
Optical orientation of the electron spins can be used to cool the nuclear spin system (NSS) in semiconductors to very low spin temperatures, down to microkelvins \cite{OO1}. It becomes possible due to the fact that the NSS is thermally isolated from its environment. Indeed, thermalization within the NSS occurs on the $\mathrm{\sim}$100 µs scale, while spin-lattice relaxation takes seconds and even minutes \cite{OO1,PhysRevB.94.081201,PhysRevB.95.125312}. This means that the thermodynamic equilibrium in the NSS is established much faster than the equilibrium between the NSS and the lattice and the energy accumulated in spin degrees of freedom remains constant on this timescale. Thus, even at zero magnetic field when the NSS polarization is lost, its energy is not. This is the essence of the spin temperature concept, that is particularly important at low magnetic field \cite{AbragamProctor}.
The NSS can be efficiently cooled in the external magnetic field through the hyperfine interaction with optically oriented electron spins \cite{OO1,PhysRevLett.20.491}. But to achieve even lower temperatures of the NSS, such as fractions of microkelvin required to realize nuclear magnetic ordering \cite{Merkulov1982,Merkulov1987,Merkulov1998,vladimirova2021}, dynamic polarization under strong magnetic field has to be combined with adiabatic demagnetization to zero field \cite{JETP1982,CH11Spin2017,PhysRevB.97.041301}. Adiabatic demagnetization further decreases the nuclear spin temperature and allows one to reach temperatures of the order of few microkelvin in \textit{n}-GaAs \cite{JETP1982,PhysRevB.97.041301,kotur2021deep}. Indeed, the spin temperature ${\theta }^{ad}_N$ that can be reached using adiabatic demagnetization to zero field, if the NSS has been preliminary cooled to the temperature ${\theta }_N$ in the magnetic field $B$, is limited by the heat capacity of the nuclear spin reservoir. The heat capacity can be characterized in terms of the local nuclear field $B_L$. During adiabatic demagnetization of the NSS from the magnetic field $B$ to zero field, the spin temperature is reduced by the factor \cite{CH11Spin2017,Goldman}:
\begin{equation} \label{GrindEQ__1_}
\theta_N / \theta_N^{ad} = \sqrt{(B^2+B^2_L)/B^2_L}.
\end{equation}
\begin{figure}
\includegraphics[width=3.4in]{Fig1.png}
\caption{ Nuclear spin states splitted by quadrupole interaction induced by a uniaxial strain in the growth direction (black lines), as a function of longitudinal (a) and transverse (b) static magnetic field. Application of the OMF in \textit{x} and \textit{z} directions allows us to probe warm-up rates corresponding to transitions between any pair of spin energy levels. The allowed transitions in different configurations are shown by arrows. For comparison, red dotted lines show nuclear spin states in the absence of quadrupole effects.}
\end{figure}
In principle, the local field can be as low as $B_L \approx B_{dd}=1.5$~G, corresponding to the dipole-dipole interaction between nuclear spins \cite{PhysRevB.15.5780}. However, it appears that this ideal situation is rarely realized, since the nuclei of the two gallium isotopes as well as those of arsenic have quadrupole moments and are therefore sensitive to the electric field gradients (EFG) induced by the lattice deformations \cite{doi:10.1063/1.1923191} or electric fields \cite{PhysRevB.67.085308}. These kinds of perturbations result in quadrupole splitting of the four spin levels of each Ga or As nucleus into two Kramers doublets as illustrated in Fig.~1. A common source of the quadrupole effects in heterostructures like quantum dots \cite{Nat09,Chekhovich2012,Chekhovich2017}, quantum wells \cite{PhysRevLett.72.1368} or microcavities \cite{PhysRevB.97.041301}, and even in epitaxial layers \cite{Lit18}, is a lattice mismatch. It was shown that quadrupole effects can be so strong in certain quantum dots, that NSS fails to thermalize, and the concept of the nuclear spin temperature loses its sense and validity \cite{Nat09}. By contrast, in "unstrained" GaAs/(Al,Ga)As quantum dots, quantum wells, microcavities and epitaxial layers, which are characterized by a weaker quadrupole splitting, the thermalization has been demonstrated \cite{PhysRevB.97.041301,Chekhovich2012,Chekhovich2017,PhysRevLett.72.1368,kotur2021deep}. Nevertheless, even in epilayers of \textit{n}-GaAs local fields are of order of $B_L \approx 8$~G, i.e. approximately $5$ times larger than $B_{dd}$ \cite{PhysRevB.97.041301,Lit18,kotur2021deep}. This fact can be explained by sample deformation during its mounting and further cooling, or by electric field from surface charges or charged impurities \cite{RSI08}.
Motivated by the validity of the thermodynamic description of the NSS in presence of weak quadrupole effects, we propose to use the nuclear spin temperature as an universal indicator of the state of the NSS under external perturbations. To implement this idea, we investigate how the NSS absorbs the electromagnetic energy generated by the weak oscillating magnetic field (OMF) in the frequency range from zero to radiofrequencies (RF). The absorption of OMF power is proportional to the spectral density of magnetic moment fluctuations of the NSS at the frequency of OMF. This fact, which is a consequence of the general fluctuation-dissipation theorem \cite{LL5}, allows one to record fluctuation spectra by measuring the spin temperature difference induced by the OMF as a function of the OMF frequency. The spin temperature variation can be detected by measuring the NSS magnetization in a probe magnetic field, for which purpose the Hanle effect under optical orientation of electron spins can be used \cite{Lit18,JETP99,Bill83}. The RF absorption measurements can be considered as a new implementation of the optically detected nuclear magnetic resonance (NMR) spectroscopy, where NMR is probed via the changes of the spin temperature. Arrows in Fig.~1 show various spin transitions for one of the isotopes that can be probed by the OMF.
Pioneering experiments of this kind were performed back in 1980s in epilayers of \textit{n}-GaAs in zero magnetic field \cite{Bill83}, see also the review \cite{CH11Spin2017}. It that work the technique was termed as nuclear spin warm-up spectroscopy, because the magnetization does not make any sense at zero field, while the spin temperature does. The measured spectrum of OMF absorption (or, equivalently, warm-up spectrum) of \textit{n}-GaAs at $B\ $= 0 demonstrated two peaks at $6$ and $14$~kHz, in apparent contradiction with the theory of spin fluctuations predicting a single peak at about $2$~kHz due to magnetic dipole-dipole interactions within NSS. This result was quite a mystery at that time since no quadrupole effects were expected in a GaAs epilayer grown on GaAs substrate, and it remained so until very recently, when new techniques capable of measuring local fields has been developed \cite{PhysRevB.97.041301,Lit18}. Their application to the sample of Ref. \onlinecite{Bill83} yielded $B_L=8$~G, suggesting that quadrupole effects could be responsible for the high-frequency absorption of the NSS at $B=0$. Thus, the model case of NSS in \textit{n}-GaAs epilayers appears as an ideal candidate for comprehensive studies of the quadrupole effects by the warm-up spectroscopy in order to validate this approach.
In this work, we apply the warm-up spectroscopy detected by PL to the same \textit{n}-GaAs sample as in Ref. \cite{Bill83}. We address a wide range of static magnetic fields $B$ ranging from zero to $75$~G, oriented either along [100] ($B \parallel B_z$) or along [011] ($B \parallel B_x$) crystal axes, keeping the direction of the OMF, $B_1$, either perpendicular (as in traditional NMR experiments) or parallel to the direction of the static field. These four different experimental geometries differ by relative orientations of $B$ and $B_1$ (perpendicular or parallel), and by the field orientation with respect to the crystal axes. This way, we probe various NMR transitions, in particular those that are not allowed in orthogonal geometry, but can be accessed at weak static fields in the parallel geometry. This idea is illustrated in Fig.~1.
We analyze the ensemble of the experimental data in the framework of the model accounting for both Zeeman interaction of the nuclear magnetic dipole with the static magnetic field $B$ and the interaction of the nuclear electric quadrupole moment $Q$ with EFGs. This allows us to identify the contribution of different isotopes in the spectra and unravel in-plane and longitudinal components of the EFG tensor. Then, three possible sources of the EFGs are considered: (i) an uniaxial deformation either along the growth axis or in the plane, (ii) a shear strain in the plane, (iii) a static electric field perpendicular to the sample surface.
{However, characterization of the sample by electron beam induced current (EBIC) technique shows that this contribution is small enough compared to the strain effects and can be neglected.
Our results suggest that the} the ratio of diagonal and off-diagonal components of the elastic-gradient tensor $S_{11}/S_{44}$ for $^{75}$As reported recently in Ref.~\onlinecite{Griffiths2019} must be revisited.
The paper is organized as follows. The next Section presents the sample and experimental setup. It is followed by the presentation of the experimental protocol of the warm-up spectroscopy. Section IV is devoted to the experimental results, Section V to the model, and Section VI to the interpretation of the results in its light. Section VII summarizes and concludes the paper, {while EBIC characterization results are presented in Appendix, Section \ref{sec:appendix}}.
\section{Samples and experimental setup}
\begin{figure}
\includegraphics[width=3.1in]{Fig2.png}
\caption{Sketch of the experimental set-up. APD is the avalanche photodiode. GT is the Glan-Taylor prism. PEM is the photo-elastic modulator. Inset shows spectra of PL (black line) and PL polarization degree (red points) for \textit{n}-GaAs sample studied in this paper. Red arrows point the PL polarization degree ${\rho}_{0}$ measured at the wavelength $\lambda_m$=817 nm chosen for detection of the NSS warm-up rates.}
\end{figure}
We study the same GaAs layer as in Refs.~\onlinecite{Lit18,Bill83}. The details of the growth procedure are described in Ref.~\onlinecite{Sem89}. The layer of $77$~$\muup$m is grown by the liquid phase epitaxy on a \textit{p}-GaAs [100] substrate. The nominal donor concentration in the close-to-the-surface area addressed in PL experiments is $n_d \approx 10^{15}$~cm$^{-3}$. The half-width at half-maximum of the Hanle curve measured at power density $P=200$~W/cm$^{2}$ used in the warm-up experiments is $B_{1/2}=10$~G. This indicates electron spin relaxation time $T_s \approx 20$~ns, consistent with nominal donor density \cite{PhysRevB.66.245204}. Nuclear spin-lattice relaxation time
$T_1 \approx 80$~s was measured at lattice temperature $T_L=20$~K and at $B_x=1$~G by the technique of Ref.~\onlinecite{PhysRevB.94.081201}.
The experimental setup is sketched in Fig~2. The sample is cooled down to $T_L=20$~K in a closed-cycle cryostat. The cryostat cold finger is positioned inside two pairs of orthogonal coils, that create magnetic fields oriented along the growth axis ($B_z \parallel [100]$), and in the plane of the sample ($B_x \parallel [011]$). Optical pumping and PL excitation are realized with a laser diode emitting at $\lambda=780$~nm. After passing through a linear polarizer (a Glan-Taylor prism) and a quarter-wave plate, the light beam of $15$~mW power is focused on a $100$~$\muup$m diameter spot on the sample surface.
A typical PL spectrum and the corresponding {PL} polarization degree measured with a $0.55$-m spectrometer coupled to an avalanche photodiode are shown in Fig.~2, inset. One can see that the PL spectrum is rather broad, corresponding to overlapping emission of the free excitons, excitons bound to neutral donors (D$^{0}$X), and excitons bound to charged donors (D$^{+}$X). The polarization degree is the highest at the short-wavelength shoulder of the PL line \cite{PhysRevB.66.245204}. Therefore, in our measurements of the nuclear spin warm-up rate we choose $\lambda=\lambda_m=817$~nm to monitor PL polarization induced by the Overhauser field $B_N$. This ensures an optimum trade-off between PL intensity and polarization degree. At $B=0$ and in the absence of the nuclear spin polarization we get PL polarization degree $\rho_0 \approx 3$~\% at $\lambda=\lambda_m$.
The polarized PL obtained within the warm-up spectroscopy protocol (see next Section) is modulated at $50$~kHz by a photoelastic modulator (PEM) and spectrally dispersed by the spectrometer. The PL signal at $\lambda_m$ is detected by a silicon avalanche photodiode (APD) connected to a two-channel photon counter synchronized with the PEM. Three pairs of Helmholtz coils compensated for the laboratory fields with $0.005$~G precision. Two small coils, each comprising ten turns of the enameled copper wire, are placed inside the cryostat near the sample in order to apply OMF in the frequency range from zero to hundreds of kHz either along the growth axis ($B^1_z \parallel [100])$ or in the sample plane $(B^1_x \parallel [011])$.
\section{Warm-up spectroscopy method}
\begin{figure}
\includegraphics[width=3.3in]{Fig3.png}
\caption{(a) Timing diagram of the experimental cycle including thermalization with the lattice ($60$~s), optical cooling ($120$~s), adiabatic demagnetization ($20$~ms), application of the OMF (warm-up stage, $3$~s) and measurement. (b) Evolution of the PL polarization with (green line) and without (blue line) OMF during the cycle. Red curves are fits of the data to Eq.~\eqref{GrindEQ__3_}. The difference between $\rho_{\mathrm{dark}}$ values for blue and green curves characterizes the effect of OMF heating on the NSS.}
\end{figure}
The experimental protocol that we implement for warm-up spectroscopy is illustrated in Fig.~3. It starts from erasing any NSS polarization and setting up the NSS temperature $\theta_N^{\infty}$ such that $1/\theta_N^{\infty}\approx 0$. It comprises waiting "in the dark" (laser off) at $B=0$ during $60$~s in presence of the erasing OMF at the frequency $f=3$~kHz. The cooling stage starts at $t=t_p=60$~s. It consists of NSS cooling via optical pumping and adiabatic demagnetization. During $120$~s of optical pumping the longitudinal field $B_p=150$~G is applied, and the circularly polarized laser beam is switched on. Under optical pumping, nuclear magnetization builds up due to hyperfine interaction between electron spins localized at the donors and the underlying nuclei. This magnetization spreads out within the crystal by spin diffusion \cite{PhysRevB.25.4444}. Typical diffusion distance can be estimated as $l_d \approx 50$~nm. The time dependence of the Overhauser field in the external static magnetic field $B$ is controlled by the time dependence of the nuclear spin temperature. It is given by the expression \cite{OO1}:
\begin{equation} \label{GrindEQ__2_}
B_N(t)=B \frac{b_N h{\overline{\gamma}}_N}{k_B}
\frac{I(I+1)}{3} \beta_N(t),
\end{equation}
where
$\beta_N\left(t\right)={1}/{\theta_N\left(t\right)}$ is the inverse nuclear spin temperature that increases under optical pumping starting from ${1}/{\Theta_N^{\infty}}$; $b_N=5.3$~T is the Overhauser field at saturation of magnetization; ${\overline\gamma}_N$ is the average gyromagnetic ratio of the NSS of GaAs; \textit{h} and $k_B$ are Planck and Boltzmann constants, respectively. After $120$~s optical pumping the laser is switched off and magnetic field is adiabatically (in $20$~ms) swept down to zero. This reduces the nuclear spin temperature $\theta_N$ reached after optical cooling down to
$\theta_N^{ad}$, according to Eq.~\ref{GrindEQ__1_}.
Within the experimental procedure described above we obtain nuclear spin temperatures $\theta^{ad}_N \approx 300$~$\muup$K. Note that deep NSS cooling is not mandatory but quite useful to achieve high magnetic susceptibility of the NSS and increase its response to OMF \cite{Abragam}. Indeed, according to Eq.~\eqref{GrindEQ__2_}, nuclear magnetization in the external field is proportional to the inverse spin temperature $\beta_N$. Therefore, the Overhauser field that is measured in our experiments can be significant even in a very low external magnetic field, provided that NSS is cold. In this work after optical pumping and adiabatic demagnetisation to $B=0$, conducted within the protocol described above, the Overhauser field $B_N=10$~G builds up in the measurement field $B_m=1$~G. Moreover, cooling of the NSS results in the increase of the RF absorption by the NSS. Thus, the NSS cooling prior to the application of the RF field significantly increases the sensitivity of this method.
The heating of the NSS by the OMF is the shortest, but the most essential stage of this protocol. During this stage the laser remains switched off, so that there are no out-of-equilibrium carriers in the sample. The static field is set at a value of interest, $B$ (either $B_\mathrm{x}$ or $B_\mathrm{z}$), and the OMF $B_1=0.1 - 1$~G is applied during $t_\mathrm{RF}=3$~s at a fixed frequency \textit{f} ranging from $0.1$ to $100$~kHz. The amplitude of the OMF, $B_1$, is chosen for each static magnetic field in such a way, that it erases about $70$~\% of nuclear polarization at the frequency of absorption maximum. Then each spectrum was normalized to the square of $B_1^2$.
At the last stage we measure to which extent the NSS temperature is increased due to the presence of the OMF at a given frequency (measurement stage). At $t=t_\mathrm{m}=183$~s the pump beam and the static in-plane magnetic field $B_\mathrm{m}=1$~G are turned on. This results in the polarized PL that is carefully recorded during at least $180$~s, as illustrated in Fig.~3~(b). The PL polarization $\rho \left(t\right)$ increases starting from the value ${\rho}_{dark}$ to the PL polarization degree that is reached under optical pumping due to Hanle effect in the transverse field given by $B_\mathrm{tot}(t)=B_\mathrm{m} \pm B_N(t)$. The sign of $B_N$ depends on the sign of the nuclear spin temperature \cite{OO1}. In the experiments presented below NSS is cooled down to positive temperatures, so that Overhauser field is antiparallel to the external field, but we have checked that the results do not depend on the spin temperature sign. The Overhauser field $B_N$ decreases with the characteristic nuclear spin relaxation time $T_1$. The resulting evolution of the PL polarization can be written as
\begin{equation} \label{GrindEQ__3_}
\rho \left(t\right)=\frac{ \rho_0 B^2_{1/2}}
{{B^2_{1/2}+
\left(B_\mathrm{m}+b+(B_N(t)-b)\times \exp(-\frac{\left(t-t_\mathrm{m}\right)}{T_1})\right)}^2},
\end{equation}
where $b\approx 0.2$~G is the nuclear field that builds up in the Knight field created by carriers. By fitting Eq.~\eqref{GrindEQ__3_} to the experimental data we determine Overhauser field $B_N(t_\mathrm{m})$ and thus nuclear spin temperature induced by the OMF for each set of parameters of interest, that is static field value and direction, the OMF value, its frequency $f$ and orientation.
The rate of the NSS heating ${1}/T_\mathrm{RF}(f)$ induced by the OMF at frequency $f$, can be expressed in terms of the Overhauser field before ($B_{N0}$) and after ($B_N(f)$) application of the OMF \cite{OO1}:
\begin{equation} \label{GrindEQ__4_}
B_N(f)=B_{N0}\ \mathrm{exp}\left({-t_\mathrm{RF}\left(\frac{1}{T_1}+\frac{1}{T_\mathrm{RF}(f)}\right)}\right). \end{equation}
Measuring the calibration curve in the absence of the OMF (blue line in Fig.~3~(b)) allows us to use the following expression for the warm-up rate at each point of the absorption spectrum:
\begin{equation} \label{GrindEQ__5_}
\frac{1}{T_\mathrm{RF}}(f)=\frac{1}{t_\mathrm{RF}}{\mathrm{ln}\left(\frac{B^\prime_N}{B_N(f)}\right)}, \end{equation}
where $B^\prime_N$ is the Overhauser field at $t=t_\mathrm{m}$ in the absence of the OMF. By repeating the measurements for each frequency from $0.1$ to $100$~kHz with the step of $1$~kHz we obtain the warm-up spectrum at a given static field and orientation of OMF.
\section{Experimental results }
\begin{figure}
\includegraphics[width=3.1in]{Fig4.png}
\caption{Warm-up spectra measured at zero static magnetic field in four different points on the sample surface. Point 2 is the one studied throughout the paper. The significant difference between these spectra suggests that the deformation and electric field, which could contribute to the quadrupole interaction, are inhomogeneous in the sample plane. Dashed curves indicate the positions of the peaks denoted as $f_1$ and $f_2$.}
\end{figure}
\begin{figure}
\includegraphics[width=3.2in]{Fig5.png}
\caption{Warm-up spectra (symbols) measured in orthogonal configuration $B \parallel x$, $B_1 \parallel z$ at point 2 on the sample surface (\textit{cf} Fig.~4). Despite low spectral resolution as compared to the linewidth, one can guess multiple contributions in each spectrum, suggesting the presence of the quadrupole satellites. Green solid lines are Gaussian contributions and red line is their sum obtained via least squares fitting of the spectra. The peak positions identified within such procedure for each pair of static field/OMF are shown in the theoretically calculated Fig.~7 for convenient comparison with the data.}
\end{figure}
Warm-up spectra measured at zero static magnetic field in four different points on the sample surface are shown in Fig.~4. One can see that the spectra are not identical, but they always comprise two peaks centered at $f_1=4-7$~kHz and $f_2=12-22$~kHz, consistent with the result of Ref.~\onlinecite{Bill83}. The significant difference between these spectra suggests that the deformation and electric field that could contribute to the quadrupole interaction are inhomogeneous in the sample plane. Point 2 is the one that we discuss in details below.
The spectral features observed at $B=0$ can be interpreted as being due to purely quadrupole splitting: we attribute the peak at $f_1$ to $^{71}$Ga and $^{69}$Ga that are merged together since the values of their quadrupole moments $Q$ are quite close, and the peak at $f_2$ to $^{75}$As that has the highest quadrupole moment, see Table 1. Their behavior in an external magnetic field is \textit{a priori} determined by the ratio of the quadrupole and Zeeman energies. For each of three isotopes four different transitions are expected at $B \perp B_1$ and two when $B \parallel B_1$ (at least at $B \leq B_L$), see Fig.~6.
Several examples of the warm-up spectra measured in orthogonal ($B \parallel x$, $B_1 \parallel z$) configuration where up to $12$ different transitions can be anticipated are shown in Fig.~5. Despite relatively low spectral resolution as compared to the linewidth, one can guess multiple contributions in each spectrum, suggesting the presence of the quadrupole satellites. Green solid lines are Gaussian contributions (up to 9 features can be distinguished at $19.3$~G), while the red line is their sum obtained from the least squares fitting of the spectra.
Fig.~6 gathers waterfall-arranged warm-up spectra (points) measured at different relative orientations of static field and OMF, either perpendicular (top panels) or parallel (bottom panels) as well as their orientation with respect to the growth axis. For convenience of comparison between the spectra, each spectrum is normalized to its integrated intensity. {The corresponding values of the integrated intensity are shown in Fig.~7~(c) and (f)}. Gray spheres mark the peak positions that we could tentatively identify by multiple Gaussians fit, as those shown in Fig.~5.
In orthogonal geometries (Fig.~6~(a-b), $B \perp B_1$), the high-frequency $^{75}$As peak splits in two and fades out at $B_z \gtrsim 5$~G. The low-frequency peak splits into multiple peaks in a rather complex manner, see also Fig.~5. Experimental resolution does not allow us to follow the evolution of each isotope with magnetic field, but at high fields these peaks evolve into Zeeman transitions for $^{71}$Ga and $^{69}$Ga and two equidistant pairs of their satellites.
The particularity of the warm-up spectroscopy as compared to the traditional NMR experiments is an easy access to weak magnetic fields. Under magnetic fields $B \lesssim B_L$ the RF absorption is measurable even in parallel geometry (Fig.~6~(c-d), $B \parallel B_1$). If both fields lie in the plane of the sample, the low-frequency line associated with Ga isotopes fades out, while the $^{75}$As peak splits into two broad peaks. If the fields are perpendicular to the growth axis, the $^{75}$As peak does not split with the field, but its frequency grows quadratically with magnetic field. The frequency of the Ga peak increases much faster, eventually approaching the Larmor frequency with the double gyromagnetic ratio of $^{71}$Ga.
We show below that this dense forest of spectral features can be unraveled and understood as a result of the interplay between quadrupole and Zeeman interaction in the system with three different isotopes.
\section{Theory }
The quadrupole interaction of a nucleus with spin $I$ and quadrupole moment $Q$ with EFGs is described by the following Hamiltonian \cite{Abragam}:
\begin{equation}
\label{GrindEQ__6_}
\hat{H}_Q=
\frac{eQ}{6I(2I-1)}\sum_{j,k} V_{jk}
\left(
\frac{3}{2}
\left(\hat{I}_j\hat{I}_k+\hat{I}_k \hat{I}_j\right)
-\delta_{jk}\hat{I}^2
\right),
\end{equation}
where $V_{jk}$ is the EFG tensor at the nucleus location, $e$ is electron charge. In GaAs all isotopes are characterized by $I=3/2$.
In unperturbed cubic crystals, the elements of $V_{jk}$ are {equal to} zero. {But} EFG may arise due to lattice deformation and, because of absence of inversion symmetry in the zinc-blende lattice, due to homogeneous electric fields. Our sample is a relatively thin platelet with one of the axes of zinc-blende lattice directed along the \textit{z-}axis normal to the sample plane. In this case, one can expect shear strains in \textit{xz} and \textit{yz} planes to be zero. Electric fields, if present, created by the surface charge or doping gradient, are always directed along \textit{z}-axis \cite{PhysRevB.76.245301,King2012}. Under these assumptions, the Hamiltonian of the NSS in the presence of quadrupole interaction reads:
\begin{equation} \label{GrindEQ__7_}
\hat{H}_{Q}^i=\frac{E_{QZ}^i}{2}
\left(\hat{I}_z^2 -\frac{I(I+1)}{3}\right)+
\frac{E_{QR}^i}{4\sqrt{3}}
\left(\hat{I}_+^2 + \hat{I}_-^2\right)+
i\frac{E_{QI}^i}{4\sqrt{3}}
\left(\hat{I}_+^2 - \hat{I}_-^2\right),
\end{equation}
where $i=$ ${}^{71}$Ga, ${}^{69}$Ga and ${}^{75}$As. It is characterized by 9 parameters, 3 for each isotope.
The energy parameter $E_{QZ}$ {determines} the uniaxial deformation along \textit{z}-axis:
\begin{equation} \label{GrindEQ__8_}
E^i_{QZ} =\frac{3eQ^iS^i_{11}}{I(I+1)}\left({\varepsilon }_{zz}-\frac{{\varepsilon }_{xx}+{\varepsilon }_{yy}+{\varepsilon }_{zz}}{3}\right),
\end{equation}
where $S_{11}$ is a diagonal element of the fourth rank gradient-elastic tensor, ${\varepsilon }_{zz},{\varepsilon }_{yy}\ $and ${\varepsilon }_{xx}$ are diagonal components of the second rank elastic strain tensor.
The energy parameter $E_{QR}$ accounts for the uniaxial deformation along \textit{x} and \textit{y}-axes:
\begin{equation} \label{GrindEQ__9_}
E^i_{QR}=\frac{3\sqrt{3}eQ^iS^i_{11}}{I\left(I+1\right)}\left({\varepsilon }_{xx}-{\varepsilon }_{yy}\right).
\end{equation}
The energy parameter $E_{QI}$ is related to the shear strain in the $xy$-plane and/or to a built-in electric field $F$ along the growth axis:
\begin{equation} \label{GrindEQ__10_}
E^i_{QI}=\frac{3\sqrt{3}eQ^iS^i_{44}}{2I\left(I+1\right)}{\varepsilon }_{xy}+\frac{3\sqrt{3}eQ^iR^i_{14}}{2I\left(I+1\right)}F. \end{equation}
Here $S_{44}$ is an off-diagonal component of the gradient-elastic tensor, $R_{14}$ is the tensor component relating EFG with homogeneous electric field $F$ oriented along $z$-axis \cite{PhysRevB.20.4406}, and ${\varepsilon }_{xy}$ is a off-diagonal component of the elastic strain tensor. Elastic strain and electric field in these equations are common for all isotopes, while quadrupole moments and gradient-elastic tensors are different (see Table 1).
Note, that the values of the gradient-elastic tensor components $S_{11}$ and $S_{44}$ has been recently calibrated by nuclear magnetic resonance spectroscopy of GaAs/AlGaAs quantum dot structures \cite{PhysRevB.97.235311,Griffiths2019} and our experiments provide an opportunity to check them in another kind of experiments.
We can further assume that the stress experienced by {the} sample is a combination of a compressive pressure $p_1$ in \textit{xy} plane applied at some angle $\varsigma $ with respect to \textit{x}-axis and a decompressive pressure $p_2$ in the orthogonal direction. In this case all components of the strain tensor ${\varepsilon }_{jk}\ $can be calculated from $p_1$, $p_2$ and $\varsigma$ using the stiffness tensor $C_{iklm}$ and cubic symmetry of the crystal:
\begin{equation} \label{GrindEQ__11_}
{\varepsilon }_{xx}=\frac{\left(C_{11}+2C_{12}\right)\left(p_1{{\mathrm{cos}}^2 \varsigma \ }+p_2{{\mathrm{sin}}^2 \varsigma \ }\right)-C_{12}\left(p_1+p_2\right)}{\left(C_{11}-C_{12}\right)\left(C_{11}+2C_{12}\right)},
\end{equation}
\begin{equation} \label{GrindEQ__12_}
{\varepsilon }_{yy}=\frac{\left(C_{11}+2C_{12}\right)\left(p_1{{\mathrm{sin}}^2 \varsigma \ }+p_2{{\mathrm{cos}}^2 \varsigma \ }\right)-C_{12}(p_1+p_2)}{\left(C_{11}-C_{12}\right)\left(C_{11}+2C_{12}\right)},
\end{equation}
\begin{equation} \label{GrindEQ__13_}
\ {\varepsilon }_{zz}=-\frac{C_{12}(p_1+p_2)}{\left(C_{11}-C_{12}\right)\left(C_{11}+2C_{12}\right)}, \end{equation}
\begin{equation} \label{GrindEQ__14_}
{\varepsilon }_{xy}={\varepsilon }_{yx}=\left(p_1-p_2\right)\frac{{\mathrm{cos} \varsigma \ }{\mathrm{sin} \varsigma \ }}{C_{44}}\ .
\end{equation}
Remaining ${\varepsilon}_{lm}$ components are equal to zero. Thus, we can rewrite Eqs.~\eqref{GrindEQ__8_} - \eqref{GrindEQ__10_} in terms of pressure parameters $p_1$ and $p_2$ and the angle $\varsigma$:
\begin{equation} \label{GrindEQ__15_}
E_{QZ}^i=\frac{eQ^iS_{11}^i}{I\left(I+1\right)}\frac{1}{C_{11}-C_{12}}\left(p_1+p_2\right),
\end{equation}
\begin{equation} \label{GrindEQ__16_}
E_{QR}^i=\frac{3\sqrt{3}eQ^iS_{11}^i}{I\left(I+1\right)}\frac{{\mathrm{cos} \left(2\varsigma \right)\ }}{C_{11}-C_{12}}\left(p_1-p_2\right),\
\end{equation}
\begin{equation} \label{GrindEQ__17_}
E_{QI}^i=\frac{3\sqrt{3}eQ^iS_{44}^i}{4I\left(I+1\right)}\frac{{\mathrm{sin} \left(2\varsigma \right)\ }}{C_{44}}\left(p_1-p_2\right)+\frac{3\sqrt{3}eQ^iR_{14}^i}{2I\left(I+1\right)}F.
\end{equation}
\begin{table}
\begin{ruledtabular}
\begin{tabular}{|c c c c|}
\multicolumn{4}{|c|}{GaAs parameters} \\
\hline
\hline
$C_{11}\times {10}^{10}($ ${\mathrm{N}}/{{\mathrm{m}}^{\mathrm{2}}})$ \cite{SS73} & & 12 & \\
\hline
$C_{12}\times {10}^{10}$ (${\mathrm{N}}/{{\mathrm{m}}^{\mathrm{2}}})$ \cite{SS73}& & 5.4 & \\
\hline
$C_{44}\times {10}^{10}$ (${\mathrm{N}}/{{\mathrm{m}}^{\mathrm{2}}})$ \cite{SS73} & & 6.2 & \\
\hline
\hline
Isotope Parameters & ${}^{71}$Ga & ${}^{69}$Ga & ${}^{75}$As \\
\hline
\hline
{$A$}& {$0.2$}& {$0.3$}& {$0.5$ }\\
\hline
$S_{11}\times {10}^{-21}$ ( ${\mathrm{V}}/{{\mathrm{m}}^{\mathrm{2}}}$ ) \cite{PhysRevB.97.235311} & -22 & -22 & 24.2 \\
\hline
$S_{44}\times {10}^{-21}$ ( ${\mathrm{V}}/{{\mathrm{m}}^{\mathrm{2}}}$ ) \cite{PhysRevB.97.235311} & {\bf 14} & 14 & {\bf 48} \\
\hline
$S_{44}\times {10}^{-21}$ ( ${\mathrm{V}}/{{\mathrm{m}}^{\mathrm{2}}}$ ) [this work] & {\bf 14.6} & 14 & {\bf 22} \\
\hline
$R_{14}\mathrm{\times }{10}^{12}\ ({\mathrm{m}}^{\mathrm{-}\mathrm{1}})$ \cite{PhysRev.129.1965} & 2.1& 2 & 1.9\\
\hline
$Q\times {10}^{30}$ (m${}^{2}$) \cite{doi:10.1080/00268970802018367} & 10.7 & 17.1 & 31.4 \\
\hline
$\gamma_N $ (kHz/G) \cite{doi:10.1080/00268970802018367} & 0.82 & 0.64 & 0.45 \\ \hline
$E_{QZ}$/h (kHz) & -0.4 & -0.6 & 1.2 \\
\hline
$E_{QR}$/h (kHz) & -1.8 & -3 & 6 \\
\hline
$E_{QI}$/h (kHz) & 2.6 & 4 & -11.3 \\
\end{tabular}
\end{ruledtabular}
\caption{Values of the {abundance}, relevant gradient-elastic, electric field and stiffness tensors elements, quadrupole moments and gyromagnetic ratios for three GaAs isotopes.
Last three lines show the quadrupole frequencies resulting of the fitting procedure. }
\end{table}
The total energy of the NSS in the external magnetic fields is given by the sum of the quadrupole and Zeeman Hamiltonians for each isotope:
\begin{equation} \label{GrindEQ__18_}
\hat{H}^i=\hat{H}_{Q}^i+h\gamma_N^i(\hat{I}\cdot B), \end{equation}
were $\gamma_N^i$ are nuclear gyromagnetic ratios. The energy levels of each isotope are given by the eigenvalues of ${\hat{H}}^i$.
The dipole-dipole interaction which is known to broaden the NMR transitions, but does not lead to any shifts of their energies, is not included here\cite{Abragam}.
The eigenfunctions $\mid\Psi_m\rangle$ of the Hamiltonian ${\hat{H}}^i$ are superpositions of the states with angular momentum $\mid\pm 1/2\rangle$ and
$\mid \pm 3/2 \rangle$ that depend on the orientation of the pressure axes with respect to the crystallographic directions.
They can be found by numerical diagonalization of the Hamiltonian. The OMF induces spin transitions between {a pair of states} if its frequency matches the energy difference between {their} energy levels. Since all the states are mixed, the OMF can induce transitions between any pair of spin energy levels of a given isotope. The probability of transition $P_{kl}^i$ between energy levels $E_k$ and $E_l$ of $i$-th isotope is given by $P_{kl}^i \propto M^2_{kl,i}$, where $M_{kl}=\langle \Psi _k\left|H_{OMF}\right|\Psi_l\rangle$ is the matrix element of the Hamiltonian describing Zeeman interaction of the nuclear spins with the OMF. Thus, the warm-up rate associated with each transition reads
\begin{equation}
\label{eq:wurate_theor}
\frac{1}{T_{RF}}\bigg|_{i, kl}=
\frac{A^i P_{kl}^i \left| E^i_k-E_l^i \right|^2}
{\sum_i{A^i}\sum_{j=1}^{6}\left| E_j\right|^2},
\end{equation}
{where $A^i$ stands for the isotope abundance}. Note, that the denominator in Eq.~\eqref{eq:wurate_theor} represent the heat capacity of the NSS per one nucleus.
\section{Experiment versus theory: discussion}
\begin{figure*}
\includegraphics[width=6.02in]{Fig6.png}
\caption{Waterfall-arranged warm-up spectra (points) measured at different values of $B \parallel B_z$ (a, c) and $B \parallel B_x$ (b, d). OMF ($B_1$) is oriented either along \textit{z}-axis (b, c) or along \textit{x}-axis (a, d). For convenience of comparison between the spectra, each spectrum is normalized to its integrated intensity (indicated by symbols in Fig.~7~(c),~(f)). Gray balls point the peak positions that can be tentatively identified by multiple gaussians fit, as those shown in Fig.~5. Solid lines are the results of least squares fit of the model based on Eq.~\eqref{GrindEQ__7_} to these the spectra, assuming fixed transition linewidth $1.5$~kHz.}
\end{figure*}
\begin{figure*}
\includegraphics[width=6.80in]{Fig7.png}
\caption{Color-encoded warm-up spectra obtained by fitting of the experimental spectra shown in Fig.~6 to the model defined by Eqs.~\eqref{GrindEQ__7_} and \eqref{GrindEQ__18_} at different values of $B \parallel B_z$ (a, c) and $B \parallel B_x$ (b, d). OMF is oriented either along \textit{z}-axis (b, c) or along \textit{x}-axis (a, d). The corresponding parameters are given in Table 1. For the visual comfort of comparison with experiment, white open circles on top of the color maps point peak positions as indicated in Fig.~6. Their diameters are proportional to the integrated intensities of the corresponding spectral peaks. Integrated intensity of the warm-up spectra (circles) as a function of the static magnetic field in longitudinal (f) and transverse (c) experimental configurations. Solid lines show the same quantities obtained from the fit.}
\end{figure*}
To fit the above model to the experimental data (the ensemble of 35 spectra shown in Fig.~6) we proceed as follows.
First, using quadrupole energies as parameters, we calculate the transition frequencies and transition probabilities for all the values and orientations of magnetic fields and for all isotopes. To transform these values into theoretical spectra, we convolute them with Gaussians using an empirically defined half-width $\delta f=\ $1.5 kHz. It is determined by dipole-dipole interaction within NSS. Then, we iterate over fitting parameters $E_{QZ}$, $E_{QR}$ and $E_{QI}$, in order to minimize the total mean square difference between experimental and theoretical spectra. The best fit values are given in Table~1.
Theoretical spectra with these parameters are shown in Fig.~6 by solid lines, and the agreement is surprisingly good. Note, however, that to fit relative intensities of some peaks in the spectra at different fields we introduced a minor disorientation of the OMF with the crystal axes, $3^\circ$ for the in-plane field, and $7^\circ$ for the field along \textit{z}-axis. This misalignment is due to uncontrollable shifts of the small size RF coils that cannot be repositioned any more when the sample is cooled down.
For better understanding of the theoretically calculated spectra, Fig.~7 represents color-encoded theoretical spectra in four experimental geometries that we have studied. White symbols on top of the color maps indicate the peak positions deduced from the experiments (indicated by gray spheres in Fig.~6). In Fig.~7(c), (f) we compare the calculated integrated intensities with the experimentally measured total RF absorption. In this calculation we assume that spins of different isotopes are thermalized, so that the heat capacity is determined by the entire NSS. Under this assumption the magnetic field dependence of the total warm-up rate is well reproduced, suggesting that the thermodynamic description of the quadrupole-split NSS and its heating by OMF is, indeed, justified.
The fitting procedure points out that all the quadrupole energies $E_{QZ}$, $E_{QR}$ and $E_{QI}$ defined by Eqs.~\eqref{GrindEQ__8_}-\eqref{GrindEQ__10_} are different from zero. Thus, there should be at least two sources of the quadrupole interaction in our sample: tension/compression and either shear strain, or built-in electric field.
Mechanical deformations can be associated with different thermal expansion coefficients for GaAs sample and sapphire holder at $T=$ 20 K. Also, glue between the sample and the sample holder can induce some uncontrollable squeezing.
However, assuming the NSS parameters known from the recent work by Griffiths {\it et al} \cite{Griffiths2019} as summarized in Table 1, and in particular the ratio $S_{11}/S_{44}$ for different isotopes, this mechanical deformation is not sufficient, and both a shear strain and an electric field $F$ must be included in the model to account for the experimentally measured values of quadrupole energies $E_{QZ}$, $E_{QR}$ and $E_{QI}$.
We end up with the in-plane pressure parameters $p_1=2.5$~MP, $p_2=-0.95$~MP, $\varsigma=-30^\circ$, and electric field $F=5$~kV/cm.
Although the presence of electric fields close to the surface is not impossible due to the pinning of the Fermi level on the surface states in the middle of the GaAs bandgap \cite{PhysRevB.43.12138}, such electric field could, in principle, ionize the donors, preventing dynamic polarization of nuclear spins by localized electrons \cite{PhysRevB.76.245301,King2012}.
Moreover, we have conducted EBIC characterization of the sample.
These results, presented in Appendix suggest that there is no measurable surface-induced electric field.
The only region where an electric field is detected by EBIC technique is located at $77$~$\muup$m from the surface, close to the interface between $n$-GaAs layer and $p$-GaAs substrate.
Thus, we need to admit that the gradient-elastic tensor elements $S_{44}$ are different from the values estimated in Ref.~\onlinecite{Griffiths2019}. In this case our warm-up spectra can be consistently described by the deformation induced quadrupole effects only. The resulting values of $S_{44}$ tensor elements are given in Table 1, to be compared with Ref.~\onlinecite{Griffiths2019}.
The parameter $S_{44}$ for $^{71}$Ga was not measured in Ref.~\onlinecite{Griffiths2019}, but assumed to be identical to $^{69}$Ga value.
Here we also obtain very similar values for two Ga isotopes.
By contrast, for $^{75}$As the difference with Ref.~\onlinecite{Griffiths2019} is significant, exceeding a factor of two.
The resulting stress estimation yields $p_1=7$~MP, $p_2=-5.3$~MP and $\varsigma=-40^\circ$, that is both tensile/compression and a weak shear strain.
\section{Conclusions}
In conclusion, we have shown that nuclear spin temperature can be used as a probe of the NSS state in the presence of an oscillating magnetic field at various frequencies. This method is termed warm-up spectroscopy, because it is particularly fruitful at low magnetic fields, where magnetization of the NSS is low, and traditional optically detected NMR does not have enough sensitivity. The warm-up spectroscopy addresses precooled NSS to increase its sensitivity. The degree of heating of the NSS by the OMF in the dark is subsequently determined via the Overhauser field. We measured NMR spectra detected by such a thermometer for different mutual orientations of static external magnetic field and OMF, and with respect to \textit{n}-GaAs epilayer crystal axes. The analysis of the data within the model accounting for various sources of the quadrupole interaction and the NSS parameters from the literature suggests that both mechanical strain and built-in electric field contribute to the quadrupole splitting of different isotopes. Nevertheless, since we could not evidence the presence of such electric field, the off-diagonal element of the $^{75}$As gradient-electric tensor may need to be revisited. We obtained $S_{44}=22\times10^{21}$~V/m$^2$, that is $2.2$ times less than in Ref.~\onlinecite{Griffiths2019}. Thus, further experiments with in-situ control of the electric field and deformation will be a key to better understanding of their relative contributions and determination of the gradient-elastic tensors for $^{75}$As. %
Overall, our results validate warm-up spectroscopy as a new effective tool for studies of the quadrupole-split NSS.
\section{Acknowledgements}
The authors are grateful to M.~M.~Sobolev for inspiring discussions and acknowledge Saint-Petersburg State University for a research grant 73031758, financial support from the Russian Foundation for Basic Research (RFBR Project No. 19-52-12043) and Deutsche Forschungsgemeinschaft (DFG Project A6) in the framework of International Collaborative Research Center TRR 160.
{SEM and} EBIC characterization was performed using equipment owned by the Federal Joint Research Center "Material science and characterization in advanced technology".
V.M.L. acknowledges Russian Foundation for Basic Research for research Grant 19-32-90084 and the support of the French Embassy in Moscow (Ostrogradski fellowship for young researchers 2020).
\section{Appendix : Estimation of the built-in electric field by EBIC microscopy}
\label{sec:appendix}
\begin{figure}
\includegraphics[width=3.2in]{FigEBIC.png}
\caption{(a) {SEM image of sample in cross-sectional geometry. Variations of the grey shades (also marked by yellow arrows) point the positions of the sample surface, as well as the interface between the epitaxial layer and $p$-GaAs substrate.}
(b) Electron beam induced current (black line) and derivative of this current (blue line) as a function of the beam position on the cleaved sample edge. The electron beam energy is $15$~keV.
Pink area shows the SCR on the $n$-side of the $p-n$ junction. It expands from the position corresponding to the EBIC maximum (zero derivative) to the position of the EBIC inflection point (maximum of the derivative). SCR thickness is $z_n=1.7$~$\muup$m. }
Inset shows the cross-sectional geometry of the scan, where electron beam is perpendicular to the cleaved edge of the sample.
\label{fig:EBIC}
\end{figure}
EBIC is a powerful technique based on the collection of free charges generated within a semiconductor by an electron beam.
Cross-sectional EBIC is routinely applied to identify the location of $p$–$n$ or Schottky junctions, as well as the corresponding built-in electron fields \cite{FRIGERI20012557,Oelgart}. In the setup used in this work it is integrated in a scanning electron microscope (SEM).
The sketch of the cross-sectional EBIC experiment, SEM image of the sample cross-section, and the measured current are shown in Fig.~\ref{fig:EBIC}.
By analysing the contrast of the SEM image one can identify the surface of the sample, $n$-GaAs layer, as well as $p$-GaAs substrate at $77$~$\muup$m from the surface.
The peak of the current corresponds to increased electric field in the space charge region (SCR) on both sides of the $p$-$n$ junction, situated close to the interface with the substrate.
By contrast, there is no measurable variation of the signal in the vicinity of the sample surface, in the region probed by warm-up spectroscopy.
In order to estimate the maximum electric field of the $p-n$ junction $F_{p-n}$, we first determine the SCR width on the $n$-doped side of the junction. It is defined as the distance between the positions of the current maximum (zero derivative) and the inflection point (maximum derivative), which yields {$z_n=1.7$~$\muup$m}, pink area in Fig.~\ref{fig:EBIC}.
Then, the maximum electric field is given by \cite{Luth2015}
\begin{equation}
\label{eq:EBIC}
F_{p-n}=-\frac{e n_d z_n}{\epsilon \epsilon_0},
\end{equation}
where $\epsilon=12.9$ is GaAs dielectric permittivity, $\epsilon_0$ is vacuum permittivity. Assuming nominal donor density $n_d=10^{15}$~cm$^{-3}$ (consistent with measured electron and nuclear spin relaxation times) we obtain $F_{p-n}\approx 24$~kV/cm.
In contrast to the interface region, the EBIC signal has no peculiarities near the surface, suggesting that any field $F$ near the surface is less than $F_{p-n}$, if existing at all. One can reasonably assume that it does not exceed $1$~kV/cm. Thus we conclude that the electric field plays a minor role, while the deformation is the dominant source of the quadrupole splittings in the studied sample.
| {
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Farum is een plaats en voormalige gemeente in Denemarken.
Voormalige gemeente
De oppervlakte bedroeg 22,69 km². De gemeente telde 18.662 inwoners waarvan 8950 mannen en 9712 vrouwen (cijfers 2005). Op 1 januari 2007 is de gemeente toegevoegd aan de gemeente Furesø.
Plaats
De plaats Farum telt 18.102 inwoners (2007). Direct ten zuiden van Farum ligt het meer Farum sø. De plaats is met de auto bereikbaar over de Hillerødmotorvejen.
De kerkelijke gemeenschap van Farum behoort tot de gelijknamige parochie.
Sport
FC Nordsjælland is de betaaldvoetbalclub van Farum en speelt haar wedstrijden in het Farum Park. FC Nordsjælland werd in 2012 landskampioen van Denemarken.
Geboren in Farum
Laus Høybye (11 december 1978), acteur
Plaats in regio Hoofdstad
Voormalige gemeente in Denemarken
Furesø | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,598 |
Parental Guidance Prize Pack Giveaway!
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Previous Post: This made me smile….
Next Post: $100 Walmart Gift Card for the New Year GIVEAWAY! | {
"redpajama_set_name": "RedPajamaC4"
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/**
* @compiler Bridge.NET 17.10.1
*/
Bridge.assembly("TestProject", function ($asm, globals) {
"use strict";
Bridge.define("TestProject1.TestClassA", {
fields: {
Value1: 0
}
});
Bridge.define("TestProject2.TestClassB", {
fields: {
Value1: 0
}
});
});
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{"url":"https:\/\/cstheory.stackexchange.com\/questions\/2315\/why-ramanujan-graphs-are-named-after-ramanujan\/2319","text":"# Why Ramanujan graphs are named after Ramanujan?\n\nI recently taught expanders, and introduced the notion of Ramanujan graphs. Michael Forbes asked why they are called this way, and I had to admit I don't know. Anyone?\n\nTo add some content to the answers here, I'll explain briefly what Ramanujan's conjecture is.\n\nFirst of all, Ramanujan's conjecture is actually a theorem, proved by Eichler and Igusa. Here is one way to state it. Let $r_m(n)$ denote the number of integral solutions to the quadratic equation $x_1^2 + m^2 x_2^2 + m^2 x_3^2 + m^2 x_4^2 = n$. If $m=1$, that $r_m(n) > 0$ was of course proved by Legendre, but Jacobi gave the exact count: $r_1(n) = 8 \\sum_{d \\mid n, 4 \\not \\mid d} d$. Nothing similarly exact is known for larger $m$ but Ramanujan conjectured the bound: $r_m(n) = c_m \\sum_{d \\mid n} d + O(n^{1\/2 + \\epsilon})$ for every $\\epsilon > 0$, where $c_m$ is a constant dependent only on $m$.\n\nLubtozky, Phillips and Sarnak constructed their expanders based on this result. I'm not familiar with the details of their analysis but the basic idea, I believe, is to construct a Cayley graph of $PSL(2,Z_q)$ for a prime $q$ that $1 \\bmod 4$, using generators determined by every sum-of-four-squares decomposition of $p$, where $p$ is a quadratic residue modulo $q$. Then, they relate the eigenvalues of this Cayley graph to $r_{2q}(p^k)$ for integer powers $k$.\n\nA reference, other than the Lubotzky-Phillips-Sarnak paper itself, is Noga Alon's brief description in Tools from Higher Algebra.\n\n\u2022 nice ! great answer. Oct 19, 2010 at 22:08\n\nWikipedia delivers this answer rather promptly. Quoting\n\nConstructions of Ramanujan graphs are often algebraic. Lubotzky, Phillips and Sarnak show how to construct an infinite family of $p+1$-regular Ramanujan graphs, whenever $p = 1 \\mod 4$ is a prime. Their proof uses the Ramanujan conjecture, which led to the name of Ramanujan graphs.\n\nThe paper referred to is Ramanujan graphs A. Lubotzky, R. Phillips and P. Sarnak, COMBINATORICA Volume 8, Number 3 (1988), 261-277, DOI: 10.1007\/BF02126799.\n\n\u2022 the question is: what is the ramanujan conjecture Oct 19, 2010 at 21:51\n\u2022 It is sometimes much better to preserve links when you quote. Oct 20, 2010 at 2:21\n\u2022 Indeed. I underestimated the seriousness of the question. Oct 20, 2010 at 13:31","date":"2022-05-25 19:35:16","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\": 0.9080908298492432, \"perplexity\": 458.19653315359534}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-21\/segments\/1652662593428.63\/warc\/CC-MAIN-20220525182604-20220525212604-00286.warc.gz\"}"} | null | null |
package org.nd4j.parameterserver.distributed.messages;
/**
* @author raver119@gmail.com
*/
public interface DistributedMessage extends VoidMessage {
}
| {
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} | 6,111 |
{"url":"https:\/\/mathproblems123.wordpress.com\/2011\/05\/07\/traian-lalescu-contest-2009-problem-3\/","text":"Home > Analysis, Inequalities, Problem Solving > Traian Lalescu contest 2009 Problem\u00a03\n\n## Traian Lalescu contest 2009 Problem\u00a03\n\nSuppose $n \\in \\Bbb{N}, \\ n \\geq 2$ and $x_1,...,x_n >0,\\ x_1+x_2+...+x_n=1$.Prove that\n\n$\\displaystyle \\sum_{k=1}^n \\frac{x_k}{1+k(x_1^2+x_2^2+...+x_k^2)}< \\frac{\\pi}{4}$, and the constant $\\pi\/4$ is the best possible.\n\nTraian Lalescu contest 2009\n\n1. May 11, 2011 at 2:53 pm\n\nI don\u2019t have a solution for the inequality, but if one can show it then we can conclude $\\pi\/4$ is the optimal constant by picking $x_1 = x_2 = x_3 = ... = x_n = 1\/n$, which makes the sum a Riemann integral for $\\int_0^1 1\/(1+x^2) dx = \\pi\/4$, so we can make the sum arbitrarily close to $\\pi\/4$ by picking sufficiently large $n$.\n\n\u2022 May 11, 2011 at 6:29 pm\n\nThank you for your remark. If you noticed that, you are very close to solving the inequality. The idea is to apply Cauchy Schwarz and then see that the result is indeed a Riemann sum for the given integral, which is smaller than the integral itself.","date":"2017-11-18 13:48:17","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 9, \"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\": 0.9707891941070557, \"perplexity\": 367.7436805098275}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"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-2017-47\/segments\/1510934804965.9\/warc\/CC-MAIN-20171118132741-20171118152741-00363.warc.gz\"}"} | null | null |
{"url":"https:\/\/homework.cpm.org\/category\/CCI_CT\/textbook\/apcalc\/chapter\/3\/lesson\/3.2.2\/problem\/3-66","text":"### Home > APCALC > Chapter 3 > Lesson 3.2.2 > Problem3-66\n\n3-66.\n\nEvaluate each limit. If the limit does not exist due to a vertical asymptote, then add an approach statement stating if $y$ is approaching negative or positive infinity.\n\n1. $\\lim\\limits _ { x \\rightarrow 1 ^ { + } } \\large\\frac { x ^ { 2 } + 2 x - 3 } { x ^ { 2 } - 2 x + 1 }$\n\nThe denominator equals zero. Factor first to see if you can cancel out that zero. If so, the limit exists. If not, it DNE but approaches $+\\infty$ or $\u2212\\infty$.\n\n$\\lim\\limits _ { x \\rightarrow 1 ^ { + } } \\large\\frac { \\cancel{(x-1)}(x+3) } { \\cancel{(x-1)}(x-1) }$\u00a0Cancel out the x minus 1 on the top and bottom of the fraction.\n\nEven though some cancelling happens, there is still an $(x \u2212 1)$ on the bottom. That means that the limit DNE but $y \\rightarrow \\infty$ or $y \\rightarrow \u2212\\infty$. Which one?\n\nFor more guidance, refer to the hint in problem 3-51(a).\n\n1. $\\lim\\limits _ { x \\rightarrow \\infty } \\large\\frac { x ^ { 2 } + 6 x + 5 } { 3 x ^ { 2 } + 4 }$\n\nThe highest-power term in the numerator is $x^2$.\nThe highest-power term in the denominator is $3x^2$.\nWhen $x \\rightarrow \\infty$, only the highest-power terms need to be considered.\n\n1. $\\lim\\limits _ { x \\rightarrow 9 } \\large\\frac { \\sqrt { x } - 3 } { x - 9 }$\n\nThere appears to be a zero in the denominator. But can you factor and cancel?\n\nOr you could multiply the numerator and denominator by the conjugate of the numerator.\n\nOr you might have recognized that this is Ana's Definition of the Derivative:\n\n$f'(a)=\\lim\\limits_{x\\rightarrow a}\\frac{f(x)-f(a)}{x-a}$\n\nExamining closely,\u00a0$a = 9$\u00a0and\u00a0$f(x) = \\sqrt x$. Find\u00a0$f^\\prime (x)$\u00a0and finally\u00a0$f^\\prime (a)$.\n\n1. $\\lim\\limits _ { x \\rightarrow 2 } \\large\\frac { x ^ { 2 } + x + 1 } { \\sqrt { x + 7 } }$\n\nSometimes, a limit can be evaluated in just one step. In a case like this, the value of the limit is the same as the real value (there are no holes on this graph).","date":"2022-07-05 17:55:45","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 19, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9553967714309692, \"perplexity\": 428.42028838225383}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-27\/segments\/1656104597905.85\/warc\/CC-MAIN-20220705174927-20220705204927-00199.warc.gz\"}"} | null | null |
TEOS Confirmed To Support METAL CHURCH In South Jersey
American power metallers TEOS will support METAL CHURCH at the Pirate's Den in Gloucester, NJ on Monday November 29. TEOS will also introduce their new lead singer at the show.
Back with a new record and some new blood, METAL CHURCH are currently in the middle of a U.S. tour in support of their new CD, "The Weight of the World".
TEOS have recently shared the stage with MCBRAIN DAMAGE (featuring IRON MAIDEN drummer Nicko McBrain and ex-BLACK SABBATH/GREAT WHITE bassist Dave "The Beast" Spitz), PIGMY LOVE CIRCUS (featuring Danny Carey of TOOL), Josh Todd (ex-BUCKCHERRY), and THE ATOMIC BITCHWAX, and appeared at March Metal Meltdown IV.
Visit www.teosband.com for more info. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,020 |
{"url":"https:\/\/cs.ericyy.me\/laff-linear-algebra\/week-9.html","text":"# Week 9 - Vector Spaces\n\n## 1. When Systems Don\u2019t Have a Unique Solution\n\n\u2022 To solve $Ax = b$, we may face three different situations: Unique Solution, No Solution and Many Solutions.\n\u2022 For example $\\left(\\begin{array}{c c c} 2 & 2 & -2 \\\\ -2 & -3 & 4 \\\\ 4 & 3 & -2\\end{array}\\right) \\left(\\begin{array}{c}\\chi_0 \\\\ \\chi_1 \\\\ \\chi_2 \\end{array}\\right) = \\left(\\begin{array}{c} 0 \\\\ 3 \\\\ 4 \\end{array}\\right)$\n\u2022 We will end up with $\\left(\\begin{array}{c c c} 2 & 2 & -2 \\\\ 0 & -1 & 2 \\\\ 0 & 0 & 0\\end{array}\\right) \\left(\\begin{array}{c} 0 \\\\ 3 \\\\ 1 \\end{array}\\right)$\n\u2022 But $0 \\ne 1$ => No solution\n\u2022 For example $\\left(\\begin{array}{c c c} 2 & 2 & -2 \\\\ -2 & -3 & 4 \\\\ 4 & 3 & -2\\end{array}\\right) \\left(\\begin{array}{c}\\chi_0 \\\\ \\chi_1 \\\\ \\chi_2 \\end{array}\\right) = \\left(\\begin{array}{c} 0 \\\\ 3 \\\\ 3 \\end{array}\\right)$\n\u2022 $\\left(\\begin{array}{c}\\chi_0 \\\\ \\chi_1 \\\\ \\chi_2 \\end{array}\\right) = \\left(\\begin{array}{c} 3 \\\\ -3 \\\\ 0 \\end{array}\\right) + \\beta \\left(\\begin{array}{c} -1 \\\\ 2 \\\\ 1 \\end{array}\\right)$\n\u2022 Many solutions\n\n### 1.1. When we have many solutions\n\n\u2022 Consider $Ax=b$ and assume that we have\n\u2022 One solution to the system $Ax = b$, the specific solution we denote by $x_s$ so that $Ax_s = b$.\n\u2022 One solution to the system $Ax = 0$ that we denote by $x_n$ so that $Ax_n = 0$.\n\u2022 Then\n\u2022 $A(x_s + x_n) = Ax_s + Ax_n = b + 0 = b$\n\u2022 So $x_s + x_n$ is also a solution\n\u2022 Now $A(x_s + \\beta x_n) = Ax_s + A(\\beta x_n) = Ax_s + \\beta A x_n = b + 0 = b$\n\u2022 So $A(x_s + \\beta x_n)$ is a solution for every $\\beta \\in \\mathbb{R}$.\n\u2022 Recall the example $\\left(\\begin{array}{c c c} 2 & 2 & -2 \\\\ -2 & -3 & 4 \\\\ 4 & 3 & -2\\end{array}\\right) \\left(\\begin{array}{c}\\chi_0 \\\\ \\chi_1 \\\\ \\chi_2 \\end{array}\\right) = \\left(\\begin{array}{c} 0 \\\\ 3 \\\\ 3 \\end{array}\\right)$\n\u2022 After two steps of LU factorization, we get \\begin{aligned} \\chi_0 + \\chi_2 &= 3 \\\\ \\chi_1 - 2\\chi_2 &= -3 \\\\ 0 &= 0 \\end{aligned}\n\u2022 Set $\\chi_2 = 0$, we conclude that a specific solution is given by $x_s = \\left(\\begin{array}{c}\\chi_0 \\\\ \\chi_1 \\\\ \\chi_2 \\end{array}\\right) = \\left(\\begin{array}{c} 3 \\\\ -3 \\\\ 0 \\end{array}\\right)$\n\u2022 Now, to calculate $x_n$. If we choose the free variable $\\chi_2 = 0$, then it is easy to see that $\\chi_0 = \\chi_1 = 0$, and we end up with the trivial solution, $x = 0$. So, instead choose $\\chi_2 = 1$: \\begin{aligned} \\chi_0 + 1 &= 0 \\\\ \\chi_1 - 2(1) &= 0 \\\\ 0 &= 0 \\end{aligned}\n\u2022 $Ax = 0$: $x_n = \\left(\\begin{array}{c} -1 \\\\ 2 \\\\ 1 \\end{array}\\right)$\n\u2022 But if $Ax_n = 0$, then $A(\\beta x_n) = 0$. This means that all vectors $x_s + \\beta x_n = \\left(\\begin{array}{c} 3 \\\\ -3 \\\\ 0 \\end{array}\\right) + \\beta \\left(\\begin{array}{c} -1 \\\\ 2 \\\\ 1 \\end{array}\\right)$\n\n#### Some terminology\n\n\u2022 row-echelon form:\n\u2022 The boxed values are known as the pivots.\n\u2022 In each row to the left of the vertical bar, the left-most nonzero element is the pivot for that row.\n\u2022 Notice that the pivots in later rows appear to the right of the pivots in earlier rows.\n\u2022 reduced row-echelon form:\n\n### 1.2. Summary\n\n\u2022 Whether a linear system of equations $Ax = b$ has a unique solution, no solution, or multiple solutions can be determined by writing the system as an appended system $\\left(A | b\\right)$ and transforming this appended system to row echelon form, swapping rows if necessary.\n\n## 2. Review of Sets\n\n\u2022 A set is a collection of distinct objects.\n\u2022 The objects are the elements of the set.\n\u2022 $x \\in S$: (object) x is an element of set $S$. an element of S.\n\u2022 If S contains object x, y and z: $\\{x, y, z\\}$\n\u2022 Order doesn't matter.\n\u2022 The size of a set denoted by $|S|$.\n\u2022 $(S \\subset T) \\iff (x \\in S \\Rightarrow x \\in T)$\n\n### 2.1. Examples\n\n\u2022 $\\{1, 2, 3\\}$\n\u2022 $|\\{1, 2, 3\\}| = 3$\n\u2022 The collection of all integers denoted by $\\mathbb{Z}$ => $\\{\\ldots, -2, -1, 0, 1, 2, \\ldots\\}$. $|\\mathbb{Z}| = \\infty$\n\u2022 The collection of all real numbers denoted by $\\mathbb{R}$. $|\\mathbb{R}| = \\infty$\n\u2022 The set of all vectors of size $n$ whose components are real valued is denoted by $\\mathbb{R}^n$.\n\n### 2.2. Operations with Sets\n\n\u2022 Union of two set\n\u2022 Notation: $S \\cup T$\n\u2022 Formal definition: $S \\cup T = \\{ x | x \\in S \\vee x \\in T\\}$\n\u2022 Interaction of two sets\n\u2022 Notation: $S \\cap T$\n\u2022 Formal definition: $S \\cap T = \\{ x | x \\in S \\land x \\in T\\}$\n\u2022 Complement of two sets\n\u2022 Notation: $T \\backslash S$\n\u2022 Formal definition: $T \\backslash S = \\{ x | x \\notin S \\land x \\in T\\}$\n\n## 3. Vector Spaces\n\n### 3.1. Definition\n\n\u2022 a vector space is a subset, $S$, of $\\mathbb{R}^n$ with the following properties:\n\u2022 $0 \\in S$ (the zero vector of size n is in the set S); and\n\u2022 If $v, w \\in S$ then $(v+w) \\in S$; and\n\u2022 If $\\alpha \\in \\mathbb{R}$ and $v \\in S$ then $\\alpha v \\in S$.\n\n\u2022 Example: The set $\\mathbb{R}^n$ is a vector space:\n\n\u2022 $0 \\in \\mathbb{R}^n$\n\u2022 If $v, w \\in \\mathbb{R}^n$ then $(v+w) \\in \\mathbb{R}^n$; and\n\u2022 If $\\alpha \\in \\mathbb{R}$ and $v \\in \\mathbb{R}^n$ then $\\alpha v \\in \\mathbb{R}^n$.\n\n### 3.2. Subspaces\n\n\u2022 Subspaces of $\\mathbb{R}^n$ are the subsets of $\\mathbb{R}^n$, and also vector spaces.\n\u2022 Examples:\n\u2022 The set $S \\subset \\mathbb{R}^n$ described by $\\{\\chi a | \\chi \\in \\mathbb{R}\\}$, where $a \\in \\mathbb{R}^n$, is a subspace of $\\mathbb{R}^n$.\n\u2022 $0 \\in S$: (pick $\\chi = 0$).\n\u2022 If $u, w \\in S$ then $(u + w) \\in S$: Pick $u, w \\in S$. Then for some scalars $\\upsilon$ and some scalars $\\omega$, vector $v = \\upsilon a$ and vector $w = \\omega a$. Then $v+w = \\upsilon a+ \\omega a= (\\upsilon + \\omega)a$, which is also in S.\n\u2022 If $\\alpha \\in \\mathbb{R}$ and $v \\in S$ then $\\alpha v \\in S$: Pick $\\alpha \\in \\mathbb{R}$ and $v \\in S$. Then for some $\\upsilon$, $v = \\upsilon a$. But $\\alpha v = \\alpha (\\upsilon a) = (\\alpha \\upsilon) a$. which is also in S.\n\n#### The Column Space\n\n\u2022 Definition: Let $A \\in \\mathbb{R}^{m \\times n}$. Then the column space of A equals the set $\\{Ax | x \\in \\mathbb{R}^n\\}$. It is denoted by $\\mathcal{C}(A)$. $Ax = \\left(\\begin{array}{c|c|c|c} a_0 & a_1 & \\cdots & a_{n-1}\\end{array}\\right) \\left(\\begin{array}{c} \\chi_0 \\\\ \\chi_1 \\\\ \\vdots \\\\ \\chi_{n-1}\\end{array}\\right) = \\chi_0 a_0 + \\chi_1 a_1 + \\cdots + \\chi_{n-1} a_{n-1}$\n\u2022 Thus $\\mathcal{C}(A)$ equals the set of all linear combinations of the columns of matrix A.\n\u2022 Theorem: The column space of $A \\in \\mathbb{R}^{m \\times n}$ is a subspace of $\\mathbb{R}^m$\n\u2022 Theorem: Let $A \\in \\mathbb{R}^{m \\times n}, x \\in \\mathbb{R}^n$, and $b \\in \\mathbb{R}^m$. Then $Ax = b$ has a solution if and only if $b \\in \\mathcal{C}(A)$.\n\n#### The Null Space\n\n\u2022 Definition: Let $A \\in \\mathbb{R}^{m \\times n}$. The set of all vectors $x \\in \\mathbb{R}^n$ that have the property that $Ax = 0$ is called the null space of A.\n\u2022 Frankly speaking, all of the possible vector x that satisfy $Ax = 0$.\n\u2022 So $x$ should be perpendicular to $A$.\n\u2022 Notation: $\\mathcal{N}(A) = \\{x|Ax = 0\\}$\n\u2022 Theorem: Let $A \\in \\mathbb{R}^{m \\times n}$. The null space of $A, \\mathcal{N}(A)$, is a subspace.\n\u2022 Example:\n\u2022 $A = \\begin{bmatrix} 1 & 1 & 1 & 1 \\\\ 1 & 2 & 3 & 4 \\\\ 4 & 3 & 2 & 1 \\end{bmatrix}$\n\u2022 $\\text{rref }(A) = \\begin{bmatrix} 1 & 0 & -1 & -2 \\\\ 0 & 1 & 2 & 3 \\\\ 0 & 0 & 0 & 0 \\end{bmatrix}$\n\u2022 rref: reduced row-echelon form.\n\u2022 => $\\chi_0 - \\chi_2 - 2\\chi_3 = 0, \\chi_1 + 2 \\chi_2 + 3 \\chi_3 = 0$\n\u2022 => $\\begin{bmatrix} \\chi_0 \\\\ \\chi_1 \\\\ \\chi_2 \\\\ \\chi_3 \\end{bmatrix} = \\chi_2 \\begin{bmatrix} 1 \\\\ -2 \\\\ 1 \\\\ 0 \\end{bmatrix} + \\chi_3\\begin{bmatrix} 2 \\\\ -3 \\\\ 0 \\\\ 1 \\end{bmatrix}$\n\u2022 We defined: $\\chi_2 \\in \\mathbb{R}, \\chi_3 \\in \\mathbb{R}$\n\u2022 So, $\\mathcal{N}(A) = \\text{Span }\\left( \\begin{bmatrix} 1 \\\\ -2 \\\\ 1 \\\\ 0 \\end{bmatrix},\\begin{bmatrix} 2 \\\\ -3 \\\\ 0 \\\\ 1 \\end{bmatrix}\\right)$\n\u2022 $\\mathcal{N}(A) = \\mathcal{N}(\\text{rref }(A))$\n\n## 4. Span, Linear Independence, and Bases\n\n\u2022 Definition: Let $\\{v_0, v_1, \\cdots, v_{n-1} \\} \\subset \\mathbb{R}^m$. Then the span of these vectors, Span $\\{v_0, v_1, \\cdots, v_{n-1}\\}$, is said to be the set of all vectors that are a linear combination of the given set of vectors. $\\text{If}\\ V = \\left(\\begin{array}{c|c|c|c} v_0 & v_1 & \\cdots & v_{n-1} \\end{array}\\right)\\ \\text{then Span}\\left(\\begin{array}{c c c c} v_0, v_1, \\cdots, v_{n-1} \\end{array}\\right) = \\mathcal{C}(V).$\n\n\u2022 Linear Combination: Let $u,v \\in \\mathbb{R}^m$ and $\u03b1,\u03b2 \\in \\mathbb{R}$. Then $\u03b1u + \u03b2v$ is said to be a linear combination of vectors $u$ and $v$.\n\u2022 Let $u,v \\in \\mathbb{R}^m$. $\\text{Span }(u, v) = \\mathbb{R}^m$ means we can use the linear combination of vectors u and v to represent all of the vectors $\\in \\mathbb{R}^m$.\n\u2022 Definition: A spanning set of a subspace S is a set of vectors $\\{v_0, v_1, \\cdots, v_{n-1} \\}$ such that Span($\\{v_0, v_1, \\cdots, v_{n-1} \\}$) = S.\n\n\u2022 For example: $\\text{Span }\\{ \\left(\\begin{array}{c}1 \\\\ 2\\end{array}\\right), \\left(\\begin{array}{c}2 \\\\ 1\\end{array}\\right) \\} = \\mathbb{R}^2$\n\u2022 Definition: Let $\\{v_0, v_1, \\cdots, v_{n-1} \\} \\subset \\mathbb{R}^m$. Then this set of vectors is said to be linearly independent if $\\chi_0 v_0 + \\chi_1 v_1 + \\cdots + \\chi_{n-1} v_{n-1} = 0$ implies that $\\chi_0 = \\chi_1 = \\cdots = \\chi_{n-1} = 0$. A set of vectors that is not linearly independent is said to be linearly dependent.\n\u2022 In other words, the only solution for $Ax = 0$ is $\\overrightarrow{x} = \\overrightarrow{0}, \\text{ where, } A = \\{v_0, v_1, \\cdots, v_{n-1}\\}, x^T = \\{\\chi_0, \\chi_1, \\cdots, \\chi_{n-1} \\}$\n\u2022 For example: $\\text{Span }\\{ \\left(\\begin{array}{c}1 \\\\ 2\\end{array}\\right), \\left(\\begin{array}{c}2 \\\\ 4\\end{array}\\right) \\}$ is linearly dependent.\n\u2022 Because the set $\\left(\\begin{array}{c}2 \\\\ 4\\end{array}\\right)$ can be represent with $2 \\left(\\begin{array}{c}1 \\\\ 2\\end{array}\\right)$. We can do: $2 \\left(\\begin{array}{c}1 \\\\ 2\\end{array}\\right) - \\left(\\begin{array}{c}2 \\\\ 4\\end{array}\\right) = 0$ to make the linear combination to be 0. And don't have to make all $\\chi_n = 0$.\n\u2022 In other words, $\\left(\\begin{array}{c}2 \\\\ 4\\end{array}\\right)$ doesn't give us any new dimension, still the same as $\\left(\\begin{array}{c}1 \\\\ 2\\end{array}\\right)$.\n\u2022 So $\\text{Span }\\{ \\left(\\begin{array}{c}1 \\\\ 2\\end{array}\\right), \\left(\\begin{array}{c}2 \\\\ 4\\end{array}\\right) \\} = \\text{Span }\\{ \\left(\\begin{array}{c}1 \\\\ 2\\end{array}\\right) \\}$\n\u2022 $\\left(\\begin{array}{c}1 \\\\ 2\\end{array}\\right), \\left(\\begin{array}{c}2 \\\\ 1\\end{array}\\right)$ is linear independent set.\n\u2022 Also, we know that two vectors with different directions can span a plane. So if we add any vectors to $\\{ \\left(\\begin{array}{c}1 \\\\ 2\\end{array}\\right), \\left(\\begin{array}{c}2 \\\\ 1\\end{array}\\right) \\}$, it will be linear dependent set.\n\u2022 Theorem: Let the set of vectors $\\{ v_0, v_1 , \\ldots , v_{n-1} \\} \\subset \\mathbb {R}^ m$ be linearly dependent. Then at least one of these vectors can be written as a linear combination of the others.\n\n\u2022 In other words, the dependent vector $a_j$ can be written as a linear combination of the other n\u22121 vectors.\n\u2022 Theorem: Let $\\{ a_0, a_1 , \\ldots , a_{n-1} \\} \\subset \\mathbb {R}^ m$ and let $A = \\left(\\begin{array}{c|c|c|c} a_0 & a_1 & \\cdots & a_{n-1}\\end{array}\\right)$. Then the vectors $\\{ a_0, a_1 , \\ldots , a_{n-1} \\}$ are linearly independent if and only if $\\mathcal{N}(A) = \\{0\\}$.\n\n\u2022 aka $\\chi_0 = \\chi_1 = \\cdots = \\chi_{n-1} = 0$\n\u2022 Definition: A basis for a subspace S of $R^n$ is a set of vectors in S that\n\n1. is linearly independent and\n2. Spans S.\n\n3. Basis is the minimum set of vectors that spans the subspace.\n\n4. Let $\\{v_1, v_2, \\cdots, v_n\\} = \\text{ Basis of subspace U }$. Then $\\{v_1, v_2, \\cdots, v_n\\}$ are linear independent,\n5. And all of the linear combinations of $\\{v_1, v_2, \\cdots, v_n\\}$ can get all of the possible components of $U$. And each member of U can be uniquely defined by a unique combination of $\\{v_1, v_2, \\cdots, v_n\\}$.\n\u2022 Theorem: Let S be a subspace of $\\mathbb{R}^m$ and let $\\{v_0, v_1, \\cdots, v_{k-1} \\} \\subset \\mathbb{R}^m$ and $\\{w_0, w_1, \\cdots, w_{n-1} \\} \\subset \\mathbb{R}^m$ both be basis for S. Then $k = n$. In other words, the number of vectors in a basis is unique.\n\u2022 Definition: The dimension of a subspace S equals the number of vectors in a basis for that subspace.\n\u2022 For example: $A = \\begin{bmatrix}1 & 1 & 2 & 3 & 2 \\\\ 1 & 1 & 3 & 1 & 4\\end{bmatrix}$\n\u2022 $\\text{rref }(A) = \\begin{bmatrix}1 & 1 & 2 & 3 & 2 \\\\ 0 & 0 & 1 & -2 & 2\\end{bmatrix}$\n\u2022 => $\\begin{bmatrix} \\chi_0 \\\\ \\chi_1 \\\\ \\chi_2 \\\\ \\chi_3 \\\\ \\chi_4 \\end{bmatrix} = \\chi_1 \\begin{bmatrix} -1 \\\\ 1 \\\\ 0 \\\\ 0 \\\\ 0 \\end{bmatrix} + \\chi_3\\begin{bmatrix} -7 \\\\ 0 \\\\ 2 \\\\ 1 \\\\ 0 \\end{bmatrix} + \\chi_4\\begin{bmatrix} 2 \\\\ 0 \\\\ -2 \\\\ 0 \\\\ 1 \\end{bmatrix}$\n\u2022 set $v_0 = \\begin{bmatrix} -1 \\\\ 1 \\\\ 0 \\\\ 0 \\\\ 0 \\end{bmatrix} , v_1 = \\begin{bmatrix} -7 \\\\ 0 \\\\ 2 \\\\ 1 \\\\ 0 \\end{bmatrix}, v_2 = \\begin{bmatrix} 2 \\\\ 0 \\\\ -2 \\\\ 0 \\\\ 1 \\end{bmatrix}$\n\u2022 then $\\{v_0, v_1, v_2\\}$ is the basis of $\\mathcal{N}(A)$.\n\u2022 $\\mathcal{N}(A) = \\mathcal{N}(\\text{rref}(A)) = \\text{Span }(v_0, v_1, v_2)$.\n\u2022 the dimension of null space of A = 3, which also equals to the number of non-pivot columns of $\\text{rref}(A)$.\n\u2022 $\\mathcal{C}(A) = \\text{Span}(\\begin{pmatrix}1 \\\\ 1\\end{pmatrix}, \\begin{pmatrix}2 \\\\ 3\\end{pmatrix})$.\n\u2022 the dimension of A = 2, which also equals to the number of pivot columns of $\\text{rref}(A)$.\n\u2022 Definition: Let $A \\in \\mathbb{R}^{m \\times n}$. The rank of A equals the number of vectors in a basis for the column space of A. Denoted by $\\text{rank}(A)$.\n\n## 5. Showing that A^T A is invertible\n\n\u2022 Let $A \\in \\mathbb{R}^{m \\times k}$, and $\\{a_0, a_2, \\cdots, a_{m-1}\\}$ are linearly independent. Is $A^T A$ invertible?\n\u2022 $A^T A \\in \\mathbb{R}^{k \\times k}$.\n\u2022 So, we only need to prove $A^T A$'s columns also linear independent.\n\u2022 Because, $A^T A$ is a square matrix, if $A^T A$'s columns are linear independent, the reduced row-echelon form of $A^T A$ will be $I$.\n\u2022 Let $v \\in \\mathcal{N}(A^T A)$\n\u2022 then $A^T A v = 0$ => $v^T A^T A v = v^T \\overrightarrow{0} = 0$ => $(A v)^T A v = 0$\n\u2022 which means $\\lVert Av \\rVert _2 = 0$ => $A v = 0$\n\u2022 We've assumed $A$'s columns are linearly independent,\n\u2022 so $v \\in \\mathcal{N}(A) = \\{\\overrightarrow{0}\\}$ => $v = \\overrightarrow{0}$\n\u2022 So, the only solution of $A^T A v = 0$ is $v = \\overrightarrow{0}$\n\u2022 Then $A^T A$'s columns are linearly independent, which means $A^T A$ is invertible.\n\n## 7. Words\n\n\u2022 echelon ['e\u0283\u0259l\u0254n] n. \u68af\u5f62\uff1b\u68af\u6b21\u7f16\u961f\uff1b\u68af\u9635\uff1b\u9636\u5c42 vi. \u5f62\u6210\u68af\u961f vt. \u6392\u6210\u68af\u961f","date":"2018-06-19 14:09:14","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 201, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9964412450790405, \"perplexity\": 331.6069726252435}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-26\/segments\/1529267863043.35\/warc\/CC-MAIN-20180619134548-20180619154548-00324.warc.gz\"}"} | null | null |
Cathay Pacific was founded in 1946 by an American and an Australian, with each man putting up a single Hong Kong dollar in order to register the airline. Since then it has grown to be the tenth largest airline when measured by sales, and the world's largest airline in terms of cargo.
Cathay Pacific has won the "World's Best Airline" award four times and is generally among the very top in this category.
Hong Kong International Airport (HKG). Also known as Chek Lap Kok airport, and situated on that island, this airport is the primary airport for Hong Kong. The main buildings for passengers are Terminal 1, Terminal 2, the North Satellite Concourse and the Midfield Concourse. | {
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Q: Exchange Server 2007 message tracking log tuning? what is the best practice if I want to have a retention of let say 6 months ?
I'm confused which parameter that is should/can be changes.
Get-ExchangeServer | where {$_.isHubTransportServer -eq $true} | Get-TransportServer | select Name, *MessageTracking* | ft -AutoSize
Name MessageTrackingLogEnabled MessageTrackingLogMaxAge MessageTrackingLogMaxDirectorySize MessageTrackingLogMaxFileSize MessageTrackingLogPat h
---- ------------------------- ------------------------ ---------------------------------- ----------------------------- ---------------------
ExHTServer1 True 20.00:00:00 250MB 10MB D:\Program Files\M...
ExHTServer2 True 20.00:00:00 250MB 10MB D:\Program Files\M...
ExHTServer3 True 20.00:00:00 250MB 10MB D:\Program Files\M...
Thanks,
Albert
A: The MessageTrackingLogMaxAge parameter directly controls the length of time after which logs will be deleted; setting that to 180.00:00:00 will get you 6 months.
However, MessageTrackingLogMaxDirectorySize will also be a limiting factor. You will want to set the max directory size to large enough to fit all of the logs you'd like to keep, but keep the limit set to something reasonable - the last thing you want is for that drive to fill up if you have a reply-all storm.
I'd also recommend using a more robust log aggregation and search tool if you're gonna want to look at those logs; Splunk comes to mind.
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{"url":"https:\/\/forum.azimuthproject.org\/discussion\/1523\/crunch-time\/p5","text":"#### Howdy, Stranger!\n\nIt looks like you're new here. If you want to get involved, click one of these buttons!\n\nOptions\n\n# Crunch time\n\n\u2022 Options\n201.\nedited November 2014\n\nHow is Nino3.4 computed from the temperatures?\n\nAs an average.\n\nRight. The precise details are here:\n\nComment Source:Nad wrote: > How is Nino3.4 computed from the temperatures? WebHubTel answered: > As an average. Right. The precise details are here: * [ENSO - Niño 3.4 and SOI](http:\/\/www.azimuthproject.org\/azimuth\/show\/ENSO#Nino3.4), Azimuth Library.\n\u2022 Options\n202.\nedited November 2014\n\nAs an average.\n\nthanks Paul, by looking at that wind graphics I suddenly thought that the wind speeds might have eventually entered too, but now I found another graphic which says that the indices are sea surface temperature anomalies...at least if I interpret the abbreviation SST correctly.\n\nIn particular I wrote:\n\nwhich it is actually not what the graphic is supposed to show but rather that what I could suspect what it shows, that is the data mentioned in #163 is actually not about temperatures but about socalled wind indices, where I also don't know how these indices are computed from the actual wind speeds, in particular I haven't found anything on those in the frequently asked questions file next to the data and the graphic.\n\nComment Source:>As an average. thanks Paul, by looking at that wind graphics I suddenly thought that the wind speeds might have eventually entered too, but now I found another <a href=\"http:\/\/www.cpc.ncep.noaa.gov\/products\/analysis_monitoring\/enso_update\/ssta_c.gif\">graphic<\/a> which says that the indices are sea surface temperature anomalies...at least if I interpret the abbreviation SST correctly. In particular I wrote: >about the strange temperatures graphics which it is actually not what the graphic is supposed to show but rather that what I could suspect what it shows, that is the data mentioned in #163 is actually not about temperatures but about socalled wind indices, where I also don't know how these indices are computed from the actual wind speeds, in particular I haven't found anything on those in the <a href=\"http:\/\/www.cpc.ncep.noaa.gov\/data\/indices\/Readme.index.shtml\">frequently asked questions file<\/a> next to the data and the graphic.\n\u2022 Options\n203.\nedited November 2014\n\nYay! Blake computed Ludescher's \"average link strength\" on a daily basis, and I put the data here:\n\nThe second column in this file lists the average link strengths S as computed by Blake using a modified version of ludescher.R at daily intervals, starting from day 730, and going until day 24090, where day 1 is 1 January 1948. The first column numbers these items from 730 to 24090. For an explanation see Part 4 of the El Ni\u00f1o Project series.\n\nComment Source:Yay! Blake computed Ludescher's \"average link strength\" on a _daily_ basis, and I put the data here: * [https:\/\/github.com\/azimuth-project\/el-nino\/blob\/master\/average-link-strength-daily.txt](https:\/\/github.com\/azimuth-project\/el-nino\/blob\/master\/average-link-strength-daily.txt) The second column in this file lists the average link strengths S as computed by Blake using a modified version of ludescher.R at daily intervals, starting from day 730, and going until day 24090, where day 1 is 1 January 1948. The first column numbers these items from 730 to 24090. For an explanation see Part 4 of the El Ni\u00f1o Project series.\n\u2022 Options\n204.\nedited November 2014\n\nBlake also computed the average link strengths on a monthly basis, but he would like someone to check his work, e.g. by comparing it Daniel's existing estimates of monthly average link strengths, or recomputing it from the daily data.\n\nI put his work here:\n\nThe second column in this file lists the average link strengths S as computed by Blake using a modified version of ludescher.R at monthly intervals, starting from January 1950 and going until December 2013. The first column numbers these items from 1 to 768. For an explanation see Part 4 of the El Ni\u00f1o Project series.\n\nComment Source:Blake also computed the average link strengths on a _monthly_ basis, but he would like someone to check his work, e.g. by comparing it Daniel's existing estimates of monthly average link strengths, or recomputing it from the daily data. I put his work here: * [https:\/\/github.com\/azimuth-project\/el-nino\/blob\/master\/average-link-strength-monthly.txt](https:\/\/github.com\/azimuth-project\/el-nino\/blob\/master\/average-link-strength-monthly.txt) The second column in this file lists the average link strengths S as computed by Blake using a modified version of ludescher.R at monthly intervals, starting from January 1950 and going until December 2013. The first column numbers these items from 1 to 768. For an explanation see [Part 4](http:\/\/johncarlosbaez.wordpress.com\/2014\/07\/08\/el-nino-project-part-4\/) of the El Ni\u00f1o Project series.\n\u2022 Options\n205.\n\nNow I found another graphic which says that the indices are sea surface temperature anomalies\u2026at least if I interpret the abbreviation SST correctly.\n\nI gave a link to the precise definition of the Ni\u00f1o 3.4 index in comment 200. Now I just want to remind you (and everyone) of a non-obvious fact: \"SST\" means \"sea surface temperature\", but this means the temperature of the air slightly above the sea surface.\n\n(Apparently this is often very close to the temperature of the water, but anyway, it's the air temperature!)\n\nComment Source:Nad wrote: > Now I found another graphic which says that the indices are sea surface temperature anomalies\u2026at least if I interpret the abbreviation SST correctly. I gave a link to the precise definition of the Niño 3.4 index in comment 200. Now I just want to remind you (and everyone) of a non-obvious fact: \"SST\" means \"sea surface temperature\", but this means the temperature of the _**air**_ slightly above the sea surface. (Apparently this is often very close to the temperature of the water, but anyway, it's the air temperature!)\n\u2022 Options\n206.\n\nNad - our comments passed each other, but in comment 200 I pointed you to the definition of Ni\u00f1o 3.4 index:\n\nYes, SST means sea surface temperature.\n\nComment Source:Nad - our comments passed each other, but in comment 200 I pointed you to the definition of Niño 3.4 index: * [ENSO - Niño 3.4 and SOI](http:\/\/www.azimuthproject.org\/azimuth\/show\/ENSO#Nino3.4), Azimuth Library. Yes, SST means sea surface temperature.\n\u2022 Options\n207.\nedited November 2014\n\nNad - our comments passed each other, but in comment 200 I pointed you to the definition of Ni\u00f1o 3.4 index:\n\nyes sorry. I know I shouldn't have asked but look it up again, I guess that happened because I sort of wanted to have any reaction at all.\n\nwhat's with the blog post about the temperature data?\n\nComment Source:>Nad - our comments passed each other, but in comment 200 I pointed you to the definition of Ni\u00f1o 3.4 index: yes sorry. I know I shouldn't have asked but look it up again, I guess that happened because I sort of wanted to have any reaction at all. what's with the <a href=\"http:\/\/forum.azimuthproject.org\/discussion\/1501\/how-good-is-climate-science-temperature-data\/?Focus=13056#Comment_13056\">blog post about the temperature data<\/a>?\n\u2022 Options\n208.\n\nThe monthly figures linked to from #203 look very similar to ones I calculated by interpolating the ten day figures using the code from #164. So we both made the same mistakes, if any.\n\nMine:\n\n\"Year\",\"Month\",\"S\"\n1950,1,2.70178689291113\n1950,2,2.60221854718809\n1950,3,2.53372837232994\n1950,4,2.49447059052603\n1950,5,2.52343325029961\n...\n2013,7,2.73474337185331\n2013,8,2.82223182873403\n2013,9,2.87405506804477\n2013,10,2.93929845827353\n2013,11,2.98576616712402\n2013,12,3.024712642373\n\n\nBlake's:\n\n\"month\" \"S\"\n\"1\" 2.70389999886587\n\"2\" 2.60019196693804\n\"3\" 2.53369933967342\n\"4\" 2.4932572592701\n\"5\" 2.52305342960841\n...\n\"763\" 2.7349204284955\n\"764\" 2.82233374599453\n\"765\" 2.87416278205779\n\"766\" 2.93793110581363\n\"767\" 2.98613238800691\n\"768\" 3.02519852113451\n\nComment Source:The monthly figures linked to from #203 look very similar to ones I calculated by interpolating the ten day figures using the code from #164. So we both made the same mistakes, if any. Mine: ~~~~ \"Year\",\"Month\",\"S\" 1950,1,2.70178689291113 1950,2,2.60221854718809 1950,3,2.53372837232994 1950,4,2.49447059052603 1950,5,2.52343325029961 ... 2013,7,2.73474337185331 2013,8,2.82223182873403 2013,9,2.87405506804477 2013,10,2.93929845827353 2013,11,2.98576616712402 2013,12,3.024712642373 ~~~~ Blake's: ~~~~ \"month\" \"S\" \"1\" 2.70389999886587 \"2\" 2.60019196693804 \"3\" 2.53369933967342 \"4\" 2.4932572592701 \"5\" 2.52305342960841 ... \"763\" 2.7349204284955 \"764\" 2.82233374599453 \"765\" 2.87416278205779 \"766\" 2.93793110581363 \"767\" 2.98613238800691 \"768\" 3.02519852113451 ~~~~\n\u2022 Options\n209.\n\nFor #206, I would say the two analyses are identical for all intents and purposes.\n\nComment Source:For #206, I would say the two analyses are identical for all intents and purposes.\n\u2022 Options\n210.\nedited November 2014\n\nGreat! If the two ways of computing monthly link strengths differ by at most about 0.002, as they seem to here, there's no point in Daniel redoing any of his calculations.\n\nBut, it was worthwhile for Blake to do this crosscheck!\n\nComment Source:Great! If the two ways of computing monthly link strengths differ by at most about 0.002, as they seem to here, there's no point in Daniel redoing any of his calculations. But, it was worthwhile for Blake to do this crosscheck!\n\u2022 Options\n211.\nedited November 2014\n\nwhat's with the blog post about the temperature data?\n\nThanks for putting that article on the wiki! I hadn't even noticed it, because I'm busy preparing this talk for Dec. 10th.\n\nI edited your article a bit just now. I will get it ready to post shortly after Dec. 10th, or perhaps even sooner.\n\nComment Source:Nad wrote: > what's with the <a href=\"http:\/\/forum.azimuthproject.org\/discussion\/1501\/how-good-is-climate-science-temperature-data\/?Focus=13056#Comment_13056\">blog post about the temperature data<\/a>? Thanks for putting that article on the wiki! I hadn't even noticed it, because I'm busy preparing this talk for Dec. 10th. I edited your article a bit just now. I will get it ready to post shortly after Dec. 10th, or perhaps even sooner.\n\u2022 Options\n212.\nedited November 2014\n\nDaniel - what are the time intervals between the lines in this plot of the correlation between average link strength and Ni\u00f1o 3.4 index?\n\nAlso: what time does the maximum occur?\n\nThis appears below In [24] in your notebook. If I could read Python, I could probably figure it out. I figure the spacing between lines should either be 10 days or one month, but it makes a huge difference which one it is! 10 days seems more likely....\n\nComment Source:Daniel - what are the time intervals between the lines in this plot of the correlation between average link strength and Niño 3.4 index? <img width = \"500\" src = \"http:\/\/math.ucr.edu\/home\/baez\/climate_networks\/mahler_link_strength_nino3.4_correlation.png\" alt = \"\"\/> Also: what time does the maximum occur? This appears below In [24] in [your notebook](https:\/\/5619417f7fb3a489ed01c7f329cbd1e9b70a10d6-www.googledrive.com\/host\/0B4cyIPgV_VxrX0lxSUxHU2VLN28\/link-anom.html). If I could read Python, I could probably figure it out. I figure the spacing between lines should either be 10 days or one month, but it makes a huge difference which one it is! 10 days seems more likely....\n\u2022 Options\n213.\n\nI have posted a draft of my talk here:\n\nThe main thing it's missing is a summary of Dara Shayda's results. I want to get comments as soon as possible!\n\nI can't make the talk much longer, so as usual the comments I really need are not ones that suggest more material but ones that improve the clarity and effectiveness of what I'm saying... perhaps by omitting distracting irrelevant material.\n\n(For example, I will probably omit the names of other teleconnections when I give the actual talk.)\n\nComment Source:I have posted a draft of my talk here: * [Networks in Climate Science](http:\/\/johncarlosbaez.wordpress.com\/2014\/11\/29\/climate-networks\/), Azimuth, 29 November 2014. The main thing it's missing is a summary of Dara Shayda's results. I want to get comments as soon as possible! I can't make the talk much longer, so as usual the comments I really need are not ones that suggest more material but ones that improve the clarity and effectiveness of what I'm saying... perhaps by omitting distracting irrelevant material. (For example, I will probably omit the names of other teleconnections when I give the actual talk.)\n\u2022 Options\n214.\n\nre #210\n\nAlso: what time does the maximum occur?\n\nThe spacing is 1 month. The maximum correlation between link strength and the anomaly is at 10 month, but by then the correlation with the current anomaly is 0, so the overall predictability at 10 month will be lower since it will only come from the link strength which is already close to max at 6 months. The peak cross correlation of the combined regression model is actually at 0, but is skewed towards the future so the cross correlation does not decay as fast as for the anomaly alone. The anomaly is still the dominant effect and the links strength just modifies it.\n\nThis suggests it might be worthwhile to look at predicting the change in anomaly over the next six month rather that predicting the anomaly itself. It is possible that the link strength predicts the delta while the current anomaly provides the baseline through inertia. This would be consistent with the fact that ExtraRandomRegressor model based an the past 6 month anomaly values got .32 $R^2$, but using past 6 month combined anomaly and link strength did only marginaly better. This suggests that both anomaly history and the link strength provide information about the trajectory of the the anomaly. Also adding more then 6 month anomaly history did not improve the predictions.\n\nComment Source:re #210 > Also: what time does the maximum occur? The spacing is 1 month. The maximum correlation between link strength and the anomaly is at 10 month, but by then the correlation with the current anomaly is 0, so the overall predictability at 10 month will be lower since it will only come from the link strength which is already close to max at 6 months. The peak cross correlation of the combined regression model is actually at 0, but is skewed towards the future so the cross correlation does not decay as fast as for the anomaly alone. The anomaly is still the dominant effect and the links strength just modifies it. This suggests it might be worthwhile to look at predicting the change in anomaly over the next six month rather that predicting the anomaly itself. It is possible that the link strength predicts the delta while the current anomaly provides the baseline through inertia. This would be consistent with the fact that ExtraRandomRegressor model based an the past 6 month anomaly values got .32 $R^2$, but using past 6 month combined anomaly and link strength did only marginaly better. This suggests that both anomaly history and the link strength provide information about the trajectory of the the anomaly. Also adding more then 6 month anomaly history did not improve the predictions.\n\u2022 Options\n215.\nedited November 2014\n\nAha thanks to Johns talk summation I now realized that this mysterious STD DEV (while strictly speaking it is called ST DEV here) appears also for the Tahiti Darwin SOI - however again with cryptic explanations.\n\nComment Source:Aha thanks to <a href=\"http:\/\/johncarlosbaez.wordpress.com\/2014\/11\/29\/climate-networks\/\">Johns talk summation<\/a> I now realized that this <a href=\"http:\/\/forum.azimuthproject.org\/discussion\/1523\/crunch-time\/?Focus=13710#Comment_13710\">mysterious STD DEV<\/a> (while strictly speaking it is called ST DEV here) appears also for the Tahiti Darwin SOI - however again with <a href=\"http:\/\/www.cgd.ucar.edu\/cas\/catalog\/climind\/soiAnnual.html\">cryptic explanations.<\/a>\n\u2022 Options\n216.\n\nThe main thing it\u2019s missing is a summary of Dara Shayda\u2019s results.\n\nJohn let me know what you need so I could jut down something\n\nComment Source:>The main thing it\u2019s missing is a summary of Dara Shayda\u2019s results. John let me know what you need so I could jut down something\n\u2022 Options\n217.\n\nThe convention used is that anomalies are normalized against their RMS value, which is generated by computing the standard deviation over the sample size. Then one can get a feel for how big the outliers are with respect to the other values in the sample. So anytime one sees a significant outlier like a strong El Nino, it will be at least a few standard deviations in value. Other than for that use, the value is meaningless and you might as well call it A.U.\n\nComment Source:The convention used is that anomalies are normalized against their RMS value, which is generated by computing the standard deviation over the sample size. Then one can get a feel for how big the outliers are with respect to the other values in the sample. So anytime one sees a significant outlier like a strong El Nino, it will be at least a few standard deviations in value. Other than for that use, the value is meaningless and you might as well call it A.U.\n\u2022 Options\n218.\nedited December 2014\n\nJohn, I know you do not want more stuff, but ...\n\nI ran sparsity regularized linear models against the data and got performance comparable to the extra random trees from a model that only uses 5 pressure values. One nice aspect is that the degree of regularization was determined by cross validation on the training set, with no manual tuning of the hyperparameters.\n\nMore interesting are the locations and coefficients of the pressure values used (map at the veru bottom of the notebook): Two negatively weighted points in each of the north and south Horse Latitudes and one positively weighted point in the Indonesian region, between Borneo and Java.\n\nThis means the model is predicting high anomaly values when there is increased pressure in the west pushing back against the trade winds and the subtropical high pressure ridges are weakened or moved leading to reduced driving force behind the trade winds. This is in line with Walker Circulation mechanism discussed by others here before.\n\nHowever lots of theories are consisten with just 5 points. I tweaked the models to be less sparse to see what pattern emerges. More extensive negatively correlated regions emerge in the Horse Latitudes and the Eastern Pacifica and new positevely correlated regions emerge in the Central Pacific and Inindian Ocean. Here are some more norebooks. The most interesting part is the BW map at the bottom each notebook. The lighter regions are negatively correlated and darker regions are positively correlated.\n\nComment Source:John, I know you do not want more stuff, but ... I ran sparsity regularized linear models against the data and got performance comparable to the extra random trees from a model that only uses 5 pressure values. One nice aspect is that the degree of regularization was determined by cross validation on the training set, with no manual tuning of the hyperparameters. More interesting are the locations and coefficients of the pressure values used (map at the veru bottom of the [notebook](https:\/\/www.googledrive.com\/host\/0B4cyIPgV_VxrX0lxSUxHU2VLN28\/sl-pressure-anom-predict-omp.html)): Two negatively weighted points in each of the north and south Horse Latitudes and one positively weighted point in the Indonesian region, between Borneo and Java. This means the model is predicting high anomaly values when there is increased pressure in the west pushing back against the trade winds and the subtropical high pressure ridges are weakened or moved leading to reduced driving force behind the trade winds. This is in line with Walker Circulation mechanism discussed by others here [before](http:\/\/forum.azimuthproject.org\/discussion\/1360\/paper-ludescher-et-al-improved-el-nino-forecasting-by-cooperativity-detection\/?Focus=10890#Comment_10890). However lots of theories are consisten with just 5 points. I tweaked the models to be less sparse to see what pattern emerges. More extensive negatively correlated regions emerge in the Horse Latitudes and the Eastern Pacifica and new positevely correlated regions emerge in the Central Pacific and Inindian Ocean. Here are [some](https:\/\/www.googledrive.com\/host\/0B4cyIPgV_VxrX0lxSUxHU2VLN28\/sl-pressure-anom-predict-bag-omp.html) [more](https:\/\/www.googledrive.com\/host\/0B4cyIPgV_VxrX0lxSUxHU2VLN28\/sl-pressure-anom-predict-elnet0_2.html) [norebooks](https:\/\/www.googledrive.com\/host\/0B4cyIPgV_VxrX0lxSUxHU2VLN28\/sl-pressure-anom-predict-elnet0_1.html). The most interesting part is the BW map at the bottom each notebook. The lighter regions are negatively correlated and darker regions are positively correlated.\n\u2022 Options\n219.\n\nPosted this on the blog:\n\nJohn, I think that you should try to cobble together a more positive message in the introduction to the talk.\n\nTake a few steps back, and consider the question of why this material \u2014 at a very general level \u2014 could potentially be of interest to (1) you, and (2) the audience at NIPS. What would be the abstract for this talk?\n\nHere are some possible ingredients:\n\n\u2013 New area of application for network theory\n\n\u2013 New area of application for machine learning\n\n\u2013 Application area represents a pressing human concern\n\n\u2013 Azimuth project is searching for ways that mathematicians, scientists and programmers can contribute to the understanding of significant environmental problems\n\n\u2013 Made a decision to investigate a more concrete problem\n\n\u2013 In this talk, I will begin by giving background and context on the El Nino phenomenon and its physics; then discuss climate network structures that have been posited as indicators for the occurrence of El Nino events; then proceed to evaluate a specific paper which uses this framework, and makes specific testable hypotheses about the preconditions for the occurrence of an El Nino event.\n\nI would also suggest a section that talks about the role of machine learning in this study.\n\nGood Luck!\n\nComment Source:Posted this on the blog: John, I think that you should try to cobble together a more positive message in the introduction to the talk. Take a few steps back, and consider the question of why this material \u2014 at a very general level \u2014 could potentially be of interest to (1) you, and (2) the audience at NIPS. What would be the abstract for this talk? Here are some possible ingredients: \u2013 New area of application for network theory \u2013 New area of application for machine learning \u2013 Application area represents a pressing human concern \u2013 Azimuth project is searching for ways that mathematicians, scientists and programmers can contribute to the understanding of significant environmental problems \u2013 Made a decision to investigate a more concrete problem \u2013 In this talk, I will begin by giving background and context on the El Nino phenomenon and its physics; then discuss climate network structures that have been posited as indicators for the occurrence of El Nino events; then proceed to evaluate a specific paper which uses this framework, and makes specific testable hypotheses about the preconditions for the occurrence of an El Nino event. I would also suggest a section that talks about the role of machine learning in this study. Good Luck!\n\u2022 Options\n220.\n\nIn blog, John wrote:\n\nPreliminary throat-clearing\n\nI\u2019m very flattered to be invited to speak here. I was probably invited because of my abstract mathematical work on networks and category theory. But when I got the invitation, instead of talking about something I understood, I thought I\u2019d learn about something a bit more practical and talk about that. That was a bad idea. But I\u2019ll try to make the best of it.\n\nIt's disarmingly honest, but I don't think that starting with this is the best way to make the best of it.\n\nThere was a reason why we were drawn to this subject, and we performed some preliminary explorations, for the cause of the Azimuth project. Now, having been through this, what are your reflections on this subject, and its prospects for further research? Imagine you were drafting a research agenda for networks in climate science. Where, at all, would you fit the work that you have reviewed into this agenda?\n\nI think that at the end of your conclusion, you should add some statements that summarize your perspective as a scientist on further avenues to pursue for the application of climate network theory.\n\nComment Source:In blog, John wrote: > Preliminary throat-clearing > > I\u2019m very flattered to be invited to speak here. I was probably invited because of my abstract mathematical work on networks and category theory. But when I got the invitation, > instead of talking about something I understood, I thought I\u2019d learn about something a bit more practical and talk about that. That was a bad idea. But I\u2019ll try to make the best of it. It's disarmingly honest, but I don't think that starting with this is the best way to make the best of it. There was a reason why we were drawn to this subject, and we performed some preliminary explorations, for the cause of the Azimuth project. Now, having been through this, what are your reflections on this subject, and its prospects for further research? Imagine you were drafting a research agenda for networks in climate science. Where, at all, would you fit the work that you have reviewed into this agenda? I think that at the end of your conclusion, you should add some statements that summarize your perspective as a scientist on further avenues to pursue for the application of climate network theory.\n\u2022 Options\n221.\nedited December 2014\n\nCan anyone here who knows about machine learning, and the approach of Ludescher et. al, give a little blurb about the role of machine learning per se in this kind of research.\n\nThis could give John some ideas for his talk.\n\nTime is of the essence here.\n\n(Sorry I would have given these comments earlier, had the words come to me then.)\n\nComment Source:Can anyone here who knows about machine learning, and the approach of Ludescher et. al, give a little blurb about the role of machine learning _per se_ in this kind of research. This could give John some ideas for his talk. Time is of the essence here. (Sorry I would have given these comments earlier, had the words come to me then.)\n\u2022 Options\n222.\nedited December 2014\n\nThanks, David. I probably won't be as disarmingly honest and negative in my actual talk as I was in the blog version - maybe I just needed to get it out of my system. I've given about 200 talks in my life, and I've rarely felt so poorly in control of the material I'm presenting. For this talk I had to learn about El Ni\u00f1os, \"complex network theory\" (which is different than my network theory), and smidgens of programming in R, statistics and machine learning - a huge range of new stuff. I feel like a raw newbie in all these fields.\n\nThanks for your suggestions. Most of them are good. But I don't like the idea in comment 219. There's no way I'm going to say anything really interesting about machine learning to this crowd of experts on machine learning. If I try to parrot a short blurb, it will probably come off sounding wrong, and I'll just set myself up for questions that puncture my paper-thin veneer of knowledge. I haven't even had time to learn about the 9 different statistical approaches to El Ni\u00f1o prediction listed here:\n\nOn the other hand, there is enough material in my talk that I'll be hard-pressed to cover it in 50 minutes... I gave a version earlier this week in my seminar, and it took 90 minutes! So I don't really need more material. I just need to frame it better, zip through it, and make it sound exciting. But I'm pretty good at that; that's why people invite me to give lots of talks.\n\nOne thing I want to do is get the audience - experts on machine learning - to try their hand at El Ni\u00f1o prediction. So my actual strategy for disarming them - a bit different than in the blog article - will be to flatter them and say the world, and the Azimuth Project, needs their help.\n\nComment Source:Thanks, David. I probably won't be as disarmingly honest and negative in my actual talk as I was in the blog version - maybe I just needed to get it out of my system. I've given about 200 talks in my life, and I've rarely felt so poorly in control of the material I'm presenting. For this talk I had to learn about El Niños, \"complex network theory\" (which is different than my network theory), and smidgens of programming in R, statistics and machine learning - a huge range of new stuff. I feel like a raw newbie in _all_ these fields. Thanks for your suggestions. Most of them are good. But I don't like the idea in comment 219. There's no way I'm going to say anything really interesting about machine learning to this crowd of experts on machine learning. If I try to parrot a short blurb, it will probably come off sounding wrong, and I'll just set myself up for questions that puncture my paper-thin veneer of knowledge. I haven't even had time to learn about the 9 different statistical approaches to El Niño prediction listed here: <img src = \"http:\/\/math.ucr.edu\/home\/baez\/climate_networks\/2014-11-20-Nino34-predictions.jpg\" alt = \"\"\/> On the other hand, there is enough material in my talk that I'll be hard-pressed to cover it in 50 minutes... I gave a version earlier this week in my seminar, and it took 90 minutes! So I don't really need more material. I just need to frame it better, zip through it, and make it sound exciting. But I'm pretty good at that; that's why people invite me to give lots of talks. One thing I want to do is get the audience - experts on machine learning - to try their hand at El Niño prediction. So my actual strategy for disarming them - a bit different than in the blog article - will be to flatter them and say the world, and the Azimuth Project, needs their help.\n\u2022 Options\n223.\n\nBy the way, I hope to give more talks about roughly similar stuff after we do more work on it. I think in a year or two we could do something really interesting, like developing methods to predict El Ni\u00f1os and\/or rate existing El Ni\u00f1o prediction methods. That's if people here are interested in this, of course!\n\nI don't think the \"climate network\" stuff should be the central focus of further work if it's El Ni\u00f1os we're interested in. It suggests some interesting ideas but those ideas will probably wind up looking rather different by the time they've matured.\n\nComment Source:By the way, I hope to give more talks about roughly similar stuff after we do more work on it. I think in a year or two we could do something really interesting, like developing methods to predict El Niños and\/or rate existing El Niño prediction methods. That's if people here are interested in this, of course! I don't think the \"climate network\" stuff should be the central focus of further work if it's El Niños we're interested in. It suggests some interesting ideas but those ideas will probably wind up looking rather different by the time they've matured.\n\u2022 Options\n224.\nedited December 2014\n\nJohn wrote:\n\nBut I don\u2019t like the idea in comment 219. There\u2019s no way I\u2019m going to say anything really interesting about machine learning to this crowd of experts on machine learning. If I try to parrot a short blurb, it will probably come off sounding wrong, and I\u2019ll just set myself up for questions that puncture my paper-thin veneer of knowledge.\n\nEven if you didn't use it, I'd still be interested to read such a blurb, if anyone wants to take a shot at it.\n\nI'd liked to be convinced of the meaningfulness of machine learning.\n\nHere is a quote from an article Peter Norvig on Google's mistrust of machine learning:\n\nSo why isn't Google using this machine learning model for their search engine then? Well, Peter suggests that there are two reasons. The first is that those engineers who hand made the current algorithm don't think a machine could do better. The second, as Anand says, is more interesting. Google worries that machine-learned models may suffer \"catastrophic errors on searches that look very different from the training data\".\n\nBut, because I know so little about machine learning, I retain an open mind -- my skeptical instincts could be completely wrong!!\n\nComment Source:John wrote: > But I don\u2019t like the idea in comment 219. There\u2019s no way I\u2019m going to say anything really interesting about machine learning to this crowd of experts on machine learning. If I try to parrot a short blurb, it will probably come off sounding wrong, and I\u2019ll just set myself up for questions that puncture my paper-thin veneer of knowledge. I see your point. Even if you didn't use it, I'd still be interested to read such a blurb, if anyone wants to take a shot at it. I'd liked to be convinced of the meaningfulness of machine learning. Here is a quote from an article [Peter Norvig on Google's mistrust of machine learning](http:\/\/www.zdnet.com\/article\/peter-norvig-on-googles-mistrust-of-machine-learning\/): > So why isn't Google using this machine learning model for their search engine then? Well, Peter suggests that there are two reasons. The first is that those engineers who hand made the current algorithm don't think a machine could do better. The second, as Anand says, is more interesting. Google worries that machine-learned models may suffer \"catastrophic errors on searches that look very different from the training data\". But, because I know so little about machine learning, I retain an open mind -- my skeptical instincts could be completely wrong!!\n\u2022 Options\n225.\n\nSo why isn\u2019t Google using this machine learning model for their search engine then?\n\nThe price of their stock and their massive IPO was based upon the promise that there is a secrete sauce i.e. handmade algorithm that does much better than any other algorithm, do you think they risk their franchise to admit that machine learning algorithms could produce much better results?\n\nComment Source:>So why isn\u2019t Google using this machine learning model for their search engine then? The price of their stock and their massive IPO was based upon the promise that there is a **secrete sauce** i.e. handmade algorithm that does much better than any other algorithm, do you think they risk their franchise to admit that machine learning algorithms could produce much better results?\n\u2022 Options\n226.\nedited December 2014\n\nDavid wrote:\n\nI\u2019d liked to be convinced of the meaningfulness of machine learning.\n\nAre you convinced of the meaningfulness of animal learning? Say, human learning?\n\nFor all these things, it works when it work and it doesn't when it doesn't, and it's hard to say exactly when it does and when it doesn't... but it's still useful.\n\nAnyway, I won't try to spend any time trying to tell the people at this conference anything about machine learning - it's a huge conference of experts on the subject, and all I can do is learn. In my talk, it's more important to get a few interested in the Azimuth Project. I'm glad you pushed me away from that extremely humble self-introduction. If it were just me giving this talk, I might try it. But I'm speaking for the Azimuth Project, and some of you have done a lot of work leading up to this talk, so I shouldn't make it sound bad. I don't think the work we've done is bad... I just feel I'd need to do a lot more work myself to become an expert on the subjects I'm talking about here!\n\nComment Source:David wrote: > I\u2019d liked to be convinced of the meaningfulness of machine learning. Are you convinced of the meaningfulness of animal learning? Say, human learning? For all these things, it works when it work and it doesn't when it doesn't, and it's hard to say exactly when it does and when it doesn't... but it's still useful. Anyway, I won't try to spend any time trying to tell the people at this conference anything about machine learning - it's a huge conference of experts on the subject, and all I can do is learn. In my talk, it's more important to get a few interested in the Azimuth Project. I'm glad you pushed me away from that extremely humble self-introduction. If it were just _me_ giving this talk, I might try it. But I'm speaking for the Azimuth Project, and some of you have done a lot of work leading up to this talk, so I shouldn't make it sound bad. I don't think the work we've done is bad... I just feel I'd need to do a lot more work myself to become an expert on the subjects I'm talking about here!\n\u2022 Options\n227.\n\nHello John\n\nI hope your talk was a smash :)\n\nI would like to post the forecasts I made, as articles in GSJOURNAL.net, if ok with you. They allow me to post code in my writings.\n\nDara\n\nComment Source:Hello John I hope your talk was a smash :) I would like to post the forecasts I made, as articles in GSJOURNAL.net, if ok with you. They allow me to post code in my writings. Dara\n\u2022 Options\n228.\nedited December 2014\n\nHi -\n\nI'm giving my talk tomorrow morning at 9 am. I hope it's a smash too!\n\nYou can see the slides here:\n\nThe talk may also be videotaped; if it is, I'll tell the world.\n\nComment Source:Hi - I'm giving my talk tomorrow morning at 9 am. I hope it's a smash too! You can see the slides here: * [Networks in Climate Science](http:\/\/math.ucr.edu\/home\/baez\/climate_networks\/), NIPS 2014. The talk may also be videotaped; if it is, I'll tell the world.\n\u2022 Options\n229.\n\nRock on, as they say.\n\nComment Source:Rock on, as they say.\n\u2022 Options\n230.\n\nOne last minute thought. It may be worth explaining exactly what the anomaly is. Seasonal variations would easily account for more than 22% or even 36% percent of mean tempeature variatiation so people might think we are shooting fish in a barrel if they do not understand what it is a percentage of. Good Luck!\n\nComment Source:One last minute thought. It may be worth explaining exactly what the anomaly is. Seasonal variations would easily account for more than 22% or even 36% percent of mean tempeature variatiation so people might think we are shooting fish in a barrel if they do not understand what it is a percentage of. Good Luck!\n\u2022 Options\n231.\nedited December 2014\n\nThanks, David and Daniel! I certainly do explain what a temperature anomaly is - it's on page 4 of my slides, but I'll try to remind people a couple of times.\n\nThere are 2100 people at this conference - six hotels are completely sold out - and no other talks during mine. I'm giving my talk in a HUGE room, that can actually hold all these people, so it will be quite exciting.\n\n(I hope they don't all decide to stay in bed. Luckily the conference is serving breakfast on location - a clever incentive.)\n\nComment Source:Thanks, David and Daniel! I certainly do explain what a temperature anomaly is - it's on page 4 of [my slides](http:\/\/math.ucr.edu\/home\/baez\/climate_networks\/climate_networks.pdf), but I'll try to remind people a couple of times. There are 2100 people at this conference - six hotels are completely sold out - and no other talks during mine. I'm giving my talk in a **HUGE** room, that can actually hold all these people, so it will be quite exciting. (I hope they don't all decide to stay in bed. Luckily the conference is serving breakfast on location - a clever incentive.)\n\u2022 Options\n232.\n\nBest questions:\n\n1) How well can you do predicting Ni\u00f1o 3.4 using the entire matrix of link strengths, not just the average link strength?\n\n2) To what extent have people systematically checked that Ni\u00f1o 3.4 is the best quantity for predicting other El Ni\u00f1o-related quantities, e.g. ones that actually matter to farmers? There are a number of El Ni\u00f1o indices, but maybe machine learning could be used to look for optimal ones. (Optimal for different purposes.)\n\nComment Source:Best questions: 1) How well can you do predicting Niño 3.4 using the entire matrix of link strengths, not just the average link strength? 2) To what extent have people _systematically_ checked that Niño 3.4 is the best quantity for predicting other El Niño-related quantities, e.g. ones that actually matter to farmers? There are a number of El Niño indices, but maybe machine learning could be used to look for optimal ones. (Optimal for different purposes.)\n\u2022 Options\n233.\n\n1) How well can you do predicting Ni\u00f1o 3.4 using the entire matrix of link strengths, not just the average link strength?\n\nThere should be meaningful advantages to do this, since we had computed north-south trend for the temperature. My intuition tells me that the entire grid is far better than the averages.\n\nthe best quantity for predicting other El Ni\u00f1o-related quantities, e.g. ones that actually matter to farmers?\n\nJohn I am very very interested in this\n\nDara\n\nComment Source:>1) How well can you do predicting Ni\u00f1o 3.4 using the entire matrix of link strengths, not just the average link strength? There should be meaningful advantages to do this, since we had computed north-south trend for the temperature. My intuition tells me that the entire grid is far better than the averages. >the best quantity for predicting other El Ni\u00f1o-related quantities, e.g. ones that actually matter to farmers? John I am very very interested in this Dara\n\u2022 Options\n234.\n\nHello John\n\nCould you find if anyone is doing clustering algorithms for the climate data to create a network\/graph model?\n\nComment Source:Hello John Could you find if anyone is doing clustering algorithms for the climate data to create a network\/graph model?\n\u2022 Options\n235.\n\n1) How well can you do predicting Ni\u00f1o 3.4 using the entire matrix of link strengths, not just the average link strength?\n\n2) To what extent have people systematically checked that Ni\u00f1o 3.4 is the best quantity for predicting other El Ni\u00f1o-related quantities, e.g. ones that actually matter to farmers? There are a number of El Ni\u00f1o indices, but maybe machine learning could be used to look for optimal ones. (Optimal for different purposes.)\n\nThat is a a really excellent question. I have been thinking about that. I would like to do build models that try to predict economic\/agricultural statistics from the el nino index, link strenth or raw NOAA data. I asked about available data sets on the Open Data StachExchnge site and got a couple of pointers:\n\nand got potnters to the FOOD AND AGRICULTURE ORGANIZATION OF THE UNITED NATIONS - Statistics Division and to the USDA NASS site.\n\nComment Source:> 1) How well can you do predicting Ni\u00f1o 3.4 using the entire matrix of link strengths, not just the average link strength? Good one. I had tried a time window of avg link strength and anomalies, but had not thought about their spatial distribution. > 2) To what extent have people systematically checked that Ni\u00f1o 3.4 is the best quantity for predicting other El Ni\u00f1o-related quantities, e.g. ones that actually matter to farmers? There are a number of El Ni\u00f1o indices, but maybe machine learning could be used to look for optimal ones. (Optimal for different purposes.) That is a a really excellent question. I have been thinking about that. I would like to do build models that try to predict economic\/agricultural statistics from the el nino index, link strenth or raw NOAA data. I asked about available data sets on the Open Data StachExchnge site and got a couple of pointers: + [Historical monthly farm\/agricultural data 1950 to the present](http:\/\/opendata.stackexchange.com\/questions\/4085\/historical-monthly-farm-agricultural-data-1950-to-the-present) and got potnters to the FOOD AND AGRICULTURE ORGANIZATION OF THE UNITED NATIONS - Statistics Division and to the USDA NASS site.\n\u2022 Options\n236.\n\nI suggest we drop the grid and instead form the clusters and measure a link strength between them. Because I am sure the planet does not have a grid on its surface\n\nComment Source:>but had not thought about their spatial distribution. I suggest we drop the grid and instead form the clusters and measure a link strength between them. Because I am sure the planet does not have a grid on its surface\n\u2022 Options\n237.\n\nDear John\n\nThank you for mentioning my name for my minor contribution and I am honored to be a part of your publication and research, and my note of gratitude for everyone else.\n\nDara\n\nComment Source:Dear John Thank you for mentioning my name for my minor contribution and I am honored to be a part of your publication and research, and my note of gratitude for everyone else. Dara\n\u2022 Options\n238.\nedited December 2014\n\nMy intuition tells me that the entire grid is far better than the averages.\n\nSure. and you will see most probable even more if you look at different time delays. If someone should do the computations then please make images.\n\nComment Source:>My intuition tells me that the entire grid is far better than the averages. Sure. and you will see most probable even more if you look at different time delays. If someone should do the computations then please make images.\n\u2022 Options\n239.\n\nIf someone should do the computations then please make images.\n\nI did a bunch of them, but you need to run a Wolfram CDF on your machine, which is a free plugin to see the results.\n\nActually it is quite telling about the North-South+East-West oscillations.\n\nD\n\nComment Source:>If someone should do the computations then please make images. I did a bunch of them, but you need to run a Wolfram CDF on your machine, which is a free plugin to see the results. Actually it is quite telling about the North-South+East-West oscillations. D\n\u2022 Options\n240.\n\nYes thanks John for naming us on the talk.\n\nComment Source:Yes thanks John for naming us on the talk.\n\u2022 Options\n241.\nedited December 2014\n\nJohn wrote:\n\nAre you convinced of the meaningfulness of animal learning? Say, human learning?\n\nFor all these things, it works when it work and it doesn\u2019t when it doesn\u2019t, and it\u2019s hard to say exactly when it does and when it doesn\u2019t\u2026 but it\u2019s still useful.\n\nNow that I think about it, what was confusing me was the terminology, not the actual practice of ML. In this branch of computer science, the term \"learning\" has become very diluted, to the point where it many not involve any substantive knowledge representation.\n\nHere is a quote from Tom M. Mitchell in the Wikipedia article:\n\nA computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E.\n\nOk, but note that a consequence of this definition is that a linear regression function learn from the data points, though what it produces for its outputs are just a heuristic set of coefficients -- and these may be completely misguided, if the real relationship is not linear.\n\nTo me it makes more sense to think of learning as the process of building declarative models from data. This is no small feat. The weaker notion is the algorithmic optimization of parameters for a given model.\n\nI think I'll just call it ML :)\n\nComment Source:John wrote: > Are you convinced of the meaningfulness of animal learning? Say, human learning? > > For all these things, it works when it work and it doesn\u2019t when it doesn\u2019t, and it\u2019s hard to say exactly when it does and when it doesn\u2019t\u2026 but it\u2019s still useful. Now that I think about it, what was confusing me was the terminology, not the actual practice of ML. In this branch of computer science, the term \"learning\" has become very diluted, to the point where it many not involve any substantive knowledge representation. Here is a quote from Tom M. Mitchell in the Wikipedia article: > A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E. Ok, but note that a consequence of this definition is that a linear regression function learn from the data points, though what it produces for its outputs are just a heuristic set of coefficients -- and these may be completely misguided, if the real relationship is not linear. To me it makes more sense to think of learning as the process of building declarative models from data. This is no small feat. The weaker notion is the algorithmic optimization of parameters for a given model. I think I'll just call it ML :)\n\u2022 Options\n242.\n\nTo me it makes more sense to think of learning as the process of building declarative models from data.\n\nBut it seems these may be completely misguided as well - especially if they need to be nonlinear.\n\nComment Source:>To me it makes more sense to think of learning as the process of building declarative models from data. But it seems these may be completely misguided as well - especially if they need to be nonlinear.\n\u2022 Options\n243.\n\nI remember someone back in the 1980s saying that there were two reasons why people prefer 'learning' to 'parameter estimation' Firstly it is shorter. Secondly it looks much more impressive in grant proposals.\n\nComment Source:I remember someone back in the 1980s saying that there were two reasons why people prefer 'learning' to 'parameter estimation' Firstly it is shorter. Secondly it looks much more impressive in grant proposals.","date":"2021-04-20 14:10:50","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\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5430742502212524, \"perplexity\": 1177.877926640358}, \"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-2021-17\/segments\/1618039398307.76\/warc\/CC-MAIN-20210420122023-20210420152023-00441.warc.gz\"}"} | null | null |
Rindera austroechinata är en strävbladig växtart som beskrevs av Mikhail Grigoríevič Popov. Rindera austroechinata ingår i släktet Rindera och familjen strävbladiga växter. Inga underarter finns listade i Catalogue of Life.
Källor
Strävbladiga växter
austroechinata | {
"redpajama_set_name": "RedPajamaWikipedia"
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Q: How would I make ionic segment swipeable when I slide the slider of the content I'm trying to implement a slider feature whenever a user slides the page in ionic application. To elaborate, when I swipe the slider the segment button does highlights but the remaining segment buttons are hidden where I have to swipe the slider manually. Is there any way to make the whole segment slide as when I swipe the content?
A: I found the solution by using angular animation and translating the segment component horizontally. How you are going to use animation depends upon you.
| {
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Settle Rural District was an administrative district in the West Riding of Yorkshire, England. The rural district was named after the town of Settle and included the civil parishes of Bentham, Clapham cum Newby, Malham, Settle, Stainforth, Austwick, Giggleswick, Ingleton and Horton.
The rural district was disbanded in local government reorganisation in 1974 and transferred to the Craven district of North Yorkshire.
References
External links
Boundary map
Rural districts of the West Riding of Yorkshire | {
"redpajama_set_name": "RedPajamaWikipedia"
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