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\section{Introduction}
\label{sec:intro}
Cooperative societies are ubiquitous in nature~\cite{axelrod1981evolution}, yet the cooperation or the mutual assistance between members
of a society is also likely to generate conflicts~\cite{schelling1980strategy}. Potential for conflicts is commonplace even in insect
species~\cite{ratnieks2006conflict} and so is conflict management through policing and negotiation in groups of
primates~\cite{waal2000primates,flack2006policing}. In human societies cooperation goes further not only in its scale and
range, but also in the available mechanisms to promote conflict resolution~\cite{melis2010human,rand2011dynamic}.
Collaborative and conflict-prone human endeavors are numerous, including public policy-making in globalized
societies~\cite{quirk1989cooperative,buchan2009globalization}, open-source software development~\cite{lerner2002some},
teamwork in operating rooms~\cite{rogers2011teaching}, and even long-term partnerships~\cite{minson2011two}. Moreover,
information communication technology opens up entirely new ways of collaboration.
With such a diversity in system size and social interactions between individuals, it seems appropriate to study this phenomenon
of social dynamics in the framework of statistical physics~\cite{castellano2009statistical,helbing2010quantitative}, an approach
benefiting greatly from the availability of large scale data on social interactions~\cite{onnela2007structure,ratkiewicz2010characterizing}.
As a relevant example of conflicts in social cooperation we select Wikipedia (WP), an intriguing example of value
production in an online collaborative environment~\cite{yasseri2013value}. WP is a free web-based encyclopedia
project, where volunteering individuals collaboratively write and edit articles about any topic they choose.
The availability of virtually all data concerning the visiting and editing of article pages provides a solid
empirical basis for investigating topics such as online content popularity~\cite{ratkiewicz2010characterizing,mestyan2013} and
the role of opinion-formation processes in a peer-production environment~\cite{ciampaglia2011bounded}.
The editing process in WP is usually peaceful and constructive, but some controversial topics might give rise to extreme cases
of disagreement over the contents of the articles, with the editors repeatedly overriding each other's contributions and
making it harder to reach consensus. These `edit wars' (as they are commonly called) result from complex online social dynamics, and recent
studies~\cite{yasseri2012dynamics} have shown how to detect and classify them, as well as how they are related to
burstiness and what are their circadian patterns in editing activity~\cite{yasseri2012circadian}.
Although collaborative behavior might appear without direct interactions between individuals, communication tends to have a positive effect on cooperation and trust~\cite{kollock1998social}. Indeed, more immediate forms of communication (voice as opposed to text, for example) have been seen to increase the level of cooperation in online environments~\cite{jensen2000effect}. In WP, direct communication is implemented via `talk pages', open forums where editors may discuss improvements over the contents of articles and exchange their related opinions~\cite{wiki:talk}. Discussions among editors are not mandatory~\cite{wiki:using_talk},
but there is a significant correlation between talk page length and the likelihood of an edit war, indicating that many debates happen in articles and talk pages, simultaneously~\cite{yasseri2013value,kaltenbrunner2012there}.
Overall, a minimal model aimed at reproducing the temporal evolution of a common medium (i.e. a product collectively modified by a group of people, like an article in WP) requires at least the following two ingredients:
\begin{enum}
\item \textit{agent-agent dynamics}: Individuals share their views and opinions about changes in the article
using an open channel accessible to all editors (the talk page or some other means of communication), thus effectively participating in an
opinion-formation process through information sharing.
\item \textit{agent-medium dynamics}: Individuals edit the article if it does not properly summarize their views
on the subject, thus controlling the temporal evolution of the article and coupling it to the opinion-formation mechanism.
\end{enum}
We describe the opinion-formation process taking place in the talk page by means of the
well-known \textit{bounded confidence} mechanism first introduced by Deffuant \textit{et al.}~\cite{deffuant2000mixing},
where real discussions take place only if the opinions of the people involved are sufficiently close to each other.
Conversely, we model article editing by an `inverse' bounded confidence process, where individuals change the current
state of the article only if it differs too much from their own opinions. Particularly, we focus our attention on how
the coupling between agent-agent and agent-medium interactions determines the nature of the temporal evolution of an article.
This we consider as a further step towards the theoretical characterization of conflict in social cooperative systems
such as WP~\cite{torok2013opinions}.
The text is organized as follows: In Section~\ref{sec:model} we introduce and discuss the model in detail. In Section~\ref{sec:results}
we describe our results separately for the cases of a fixed editor pool and a pool with editor renewal, and finally make a comparison with
empirical observations on WP conflicts. In Section~\ref{sec:conc} we present concluding remarks.
\section{Model}
\label{sec:model}
Let us first assume that there is a system of $N$ agents as potential editors for a collective medium. The state
of an individual $i$ at time $t$ is defined by its scalar, continuous opinion $x_i(t) \in [0, 1]$, while the medium
is characterized by a certain value $A(t)$ in that same interval. The variable $x$ represents the view and/or
inclination of an agent concerning the topic described by the common medium, while $A$ is the particular position
actually represented by the medium.
Although it may seem too reductive to describe people's perceptions by a scalar variable $x$, many topics can actually be projected to a one-dimensional struggle between two extreme, opposite options. In the Liancourt Rocks territorial dispute between South Korea and Japan~\cite{liancourt:dispute}, for example, the values $x = 0,1$ represent the extreme position of favoring sovereignty of the islets for a particular country. Other topics are of course multifaceted, generating discussions that depend on the global affinity of individuals and multiple cultural factors~\cite{axelrod1997dissemination}. While this complexity could be tackled by the use of vectorial opinions~\cite{lorenz2007continuous,sznajd2005left}, our intention here is not to describe extremism as realistically as possible, but to study the rise of collaborative conflict even in the simplest case of binary extremism.
In the case of WP, the scalar variable $A$ represents the opinion expressed by the written contents of an article, which carries the assumption that all agents perceive the medium in the same way. Real scenarios of public opinion might be more complex, given the tendency of individuals to attribute their own views to others and thus perceive false consensus~\cite{wojcieszak2009underlies}, usually out of a social need to belong~\cite{morrison2011socially}. Even so, we consider $A$ to be a sensible description of a WP article, one that could initially be measured by human judgment in the form of expert opinions, or in an automated way by quantifying lexical features and the use of certain language constructs. We note, however, that the actual value of $A$ is not the main concern of our study. Instead, we are interested in how opinion differences in collaborative groups may eventually lead to conflict, specifically when such opinion differences are perceived with respect to a common medium that all
individuals modify collectively.
\subsection{Agent-agent dynamics}
\label{ssec:AAD}
For the agent-agent dynamics (AAD) we consider a generic bounded-confidence model over a complete
graph~\cite{deffuant2000mixing,weisbuch2002meet}, that is, a succession of random binary encounters among
all agents in the system. We initialize every opinion $x_i(0)$ to a uniformly-distributed random value in
the interval $[0, 1]$. The initial medium value $A(0)$ is chosen uniformly at random from the same interval.
This way, even an initially moderate medium $A \sim 1/2$ may find discord with extreme opinions at the boundaries.
For each interaction we randomly select two agents $i$, $j$ and compare their opinions. If the difference in
opinions exceeds a given threshold $\epsilon_T$ nothing happens, but if $|x_i - x_j| < \epsilon_T$ we update as follows,
\begin{equation}
\label{eq:deffuant}
(x_i, x_j) \mapsto (x_i + \mu_T [ x_j - x_i ], x_j + \mu_T [ x_i - x_j ]).
\end{equation}
The parameter $\epsilon_T \in [0, 1]$ is usually referred to as the \textit{confidence} or \textit{tolerance} for
pairwise interactions, while $\mu_T \in [0, 1/2]$ is a \textit{convergence} parameter. AAD is then a symmetric
compromise between similarly-minded individuals: people with very different opinions simply do not pay attention
to each other, but similar agents debate and converge their views by the relative amount $\mu_T$.
The dynamics set by Eq.~(\ref{eq:deffuant}) has received a lot of attention in the past~\cite{castellano2009statistical},
starting from the mean-field description of two-body inelastic collisions in granular gases~\cite{ben2000multiscaling,baldassarri2002influence}.
Its final, steady state is comprised by $n_c \sim 1/(2\epsilon_T)$ isolated opinion groups that arise due to the instability of the initial
opinion distribution near the boundaries. Furthermore, $n_c$ increases as $\epsilon_T \to 0$ in a series of bifurcations~\cite{ben2003bifurcations}.
In the limit $\mu_T \to 0$ corresponding to a `stubborn' society, the asymptotically final value of $n_c$ also depends
on $\mu_T$~\cite{laguna2004minorities,porfiri2007decline}. The bounded-confidence mechanism has been extended in many ways over the years,
considering interactions between more than two agents~\cite{hegselmann2002opinion}, vectorial opinions~\cite{lorenz2007continuous,fortunato2005vector,jacobmeier2005multidimensional,lorenz2008fostering},
and coupling with a constant external field~\cite{gonzalez2010spontaneous}.
\subsection{Agent-medium dynamics}
\label{ssec:AMD}
For the agent-medium dynamics (AMD) we use what could be thought of as an asymmetric, inverse version of the bounded-confidence mechanism
described above. When the opinion of a randomly chosen agent $i$ is very different from the current
state of the medium, namely if $|x_i - A| > \epsilon_A$, we make the update,
\begin{equation}
\label{eq:article}
A \mapsto A + \mu_A [ x_i - A ],
\end{equation}
where $\epsilon_A$, $\mu_A \in [0, 1]$ are the tolerance and convergence parameters for AMD. In other words, individuals that
come across a version of the medium portraying a radically different set of mind will modify it by the relative
amount $\mu_A$, where the threshold to define similarity is given by $\epsilon_A$. Conversely, if $|x_i - A| < \epsilon_A$ we update,
\begin{equation}
\label{eq:opinion}
x_i \mapsto x_i + \mu_A [ A - x_i ].
\end{equation}
meaning that individuals edit the medium when it differs too much from their opinions, but adopt the medium's
view when they already think similarly. Observe that the maximum meaningful value of $\mu_T$ is 1/2 (i.e. convergence
to the average of opinions), while the maximum $\mu_A = 1$ implies changing the medium (opinion) so that it completely
reflects the agent's (medium's) point of view.
The previous rules comprise our model for the dynamics of conflicts in WP given a \textit{fixed agent pool},
that is, without agents entering or leaving the editing process of the common medium. In a numerical implementation
of the model, every time step $t$ consists of $N$ updates of AAD given by Eq.~(\ref{eq:deffuant}) and of AMD
following Eqs.~(\ref{eq:article}) and~(\ref{eq:opinion}), so that time is effectively measured in number of edits
and the broad inter-event time distribution between successive edits (observed in empirical studies~\cite{yasseri2012dynamics})
does not have to be considered directly. Given a fixed agent pool, AAD favors opinion homogenization in intervals of
length $2\epsilon_T$ and can thus create several opinion groups for low tolerance, while AMD makes the medium value follow the
majority group. Then, for a finite system there is a nonzero probability that any agent outside the majority group
will be drawn by the medium to it, and the system will always reach consensus after a transient regime characterized
by fluctuations in the medium value~\cite{torok2013opinions}.
However, in real WP articles the pool of editors tends to change frequently. Some editors leave (due to
boredom, lack of interest or fading media coverage on the subject, or are banned from editing by editors at a higher hierarchical level)
and newly arrived agents do not necessarily share
the opinions of their predecessors. Such feature of \textit{agent renewal} during the process or writing an article may
destroy consensus and lead to a steady state of alternating conflict and consensus phases, which we take into account by
introducing thermal noise in the model. Along with any update of AAD/AMD, one editor might leave the
pool with probability $p_{\text{new}}$ and be substituted by a new agent with opinion chosen uniformly at random from the
interval $[0, 1]$. The quantity $1/(Np_{\text{new}})$ then formally acts as the inverse temperature of the system, signaling
a dynamical phase transition between different regimes of conflict~\cite{torok2013opinions}.
\section{Results}
\label{sec:results}
\subsection{Fixed agent pool}
\label{ssec:fixedPool}
In the presence of a fixed agent pool ($p_{\text{new}}=0$) with finite size $N$, the dynamics always reaches a peaceful state where
all agents' opinions lie within the tolerance of the medium. To show this, let us calculate the probability that
an unsatisfied editor $i$ changes the medium $A$ for $n$ consecutive times, such that afterwards $|x_i - A'| < \epsilon_A$ and
the agent can finally stop its stream of edits. For fixed $x_i$ and following Eq.~(\ref{eq:article}), the final
distance between editor and medium is $|x_i - A'| = (1 - \mu_A)^n |x_i - A|$, so the inequality $|x_i - A'| < \epsilon_A$ is
satisfied if $n > \ln\epsilon_A / \ln(1-\mu_A)$. The probability of agent $i$ not participating in AAD for $n$ time
steps is $(1 - 2/N)^n$, while the probability of choosing it for AMD is $1/N^n$. Then the total probability of this
stream of edits is $(1 - 2/N)^n / N^n$, which for large $N$ and $\mu_A \sim 0$ might be very small, but always finite.
After editor $i$ gets into the tolerance interval of the medium, it will not perform additional edits and will
eventually adopt the majority opinion close to the medium value. Similar events with other unsatisfied agents will
finally result in full consensus and put an end to the dynamics.
The existence of a finite relaxation time $\tau$ to consensus (for finite systems) contrasts drastically with the behavior of the bounded confidence mechanism alone, where consensus is never attained for $\epsilon_T < 1/2$~\cite{castellano2009statistical}. In other words, the presence of agent-medium interactions
promotes an agreement of opinions that would otherwise not exist in the agent-agent dynamics, even though it may happen after a very long time (i.e. $\tau \gg 0$). If we think of the medium as an additional agent with maximum tolerance (in the sense that it always interacts with the rest no matter what) and against which agents have a different tolerance $\epsilon_A$ (as opposed to $\epsilon_T$), this result is reminiscent of previous observations for a bounded-confidence model with heterogeneous thresholds~\cite{weisbuch2002meet,lorenz2010heterogeneous}. There, even a small fraction of `open-minded' agents with relatively high tolerance may bridge the opinion difference between the rest of the agents and lead to consensus.
In order to analyze all possible typical behaviors of the fixed agent pool dynamics, we perform extensive numerical simulations in systems of
size ranging from $N = 10$ to $10^4$, letting the dynamics evolve for a maximum time $\tau_{\text{max}} = 10^4$. We then characterize the temporal evolution
of medium and agent opinions as a function of $\epsilon_T$, $\epsilon_A$ and $\mu_A$, while keeping $p_{\text{new}} = 0$ for all results in this Section. Finally, since the
value of $\mu_T$ has no major effect other than regulating the convergence time of AAD~\cite{laguna2004minorities,porfiri2007decline}, from now on
we fix it to the maximum value $\mu_T = 1/2$ in order to speed up the simulations as much as possible.
A sample time series of medium and agent opinions is shown in Fig.~\ref{fig:tseries_figure}. As a function of the medium convergence $\mu_A$ the
temporal evolution of the system shows three distinctive behaviors. In regime $\mathbf{I}$ where $\mu_A$ is typically very small (Fig.~\ref{fig:tseries_figure}
A and D), there is one or more `mainstream' opinion groups near $x \sim 1/2$ with a majority of the agents in the system, and a number of
smaller, `extremist' opinion groups at positions closer to the boundaries $x = 0, 1$. The medium opinion stays on average at the center of the
opinion space, close to the mainstream group(s), and although continuously contested by editors with extremist views, it remains stable and leads
to a very slow convergence towards consensus. The reason for a long relaxation time in regime $\mathbf{I}$ is intuitively clear: for low $\mu_A$ any change
in AMD is small and thus both medium and extremist opinions fail to converge quickly. When the tolerance $\epsilon_T$ decreases the effect is even more striking;
even though the number of opinion groups is larger (according to the approximation $n_c \sim 1/[2\epsilon_T]$), the article is quite stable and
remains close to the mainstream view.
\begin{figure}[ht!]
[width=0.95\linewidth]{Figure1}
\caption{\csentence{ Temporal evolution of opinions and medium.} (A, B, C) Time series of both the
density distribution $P(x)$ of agents' opinions $x$ (color map) and the medium value $A$ (line) for $\epsilon_T = 0.2$ and several $\mu_A$
values, signaling the three different regimes found in the dynamics. (D, E, F) The same but for $\epsilon_T = 0.04$.
Simulations correspond to $\epsilon_A = 0.1$ and $N = 10^4$.}
\label{fig:tseries_figure}
\end{figure}
In regime $\mathbf{II}$ identified with intermediate values of $\mu_A$ (Fig.~\ref{fig:tseries_figure} B and E), the fixed pool dynamics produces quasi-periodic
oscillations in the medium value $A$, which appear after an initial stage of opinion group formation and end up very quickly in total consensus.
Quite surprisingly, the final consensual opinion is not $x \sim 1/2$ (as in regime $\mathbf{I}$) or that of the initial mainstream group, but some
intermediate value closer to the extremist groups at the boundaries. This is indicative of a symmetry-breaking transition: as $\mu_A$ increases,
a symmetric stationary state at $x \sim 1/2$ is replaced by a final state close to 0 or 1. The oscillations in regime $\mathbf{II}$ can initially be
understood as a struggle over
medium dominance among the different opinion groups created by AAD. The AMD mechanism couples the medium dynamics with these groups, exchanging
agents between them and thus modifying their positions, until the majority group wins over the rest and consensus is achieved. For small $\epsilon_T$
oscillations are more well-defined and last for longer, while extremist groups tend to diffuse towards the mainstream.
In regime $\mathbf{III}$ for large $\mu_A$ (Fig.~\ref{fig:tseries_figure} C and F), extremist agents directly converge to a mainstream group and an article
at the center. Since in this case $\mu_A$ is so large, after any jump of the article extremist agents can enter its tolerance interval and start
drifting inwards. The limiting condition for this behavior is $\mu_A=1-\epsilon_A/(1/2-\epsilon_A)$~\cite{torok2013opinions}, a line separating regime $\mathbf{III}$ from
the rest. A smaller $\epsilon_T$ value produces a more erratic medium evolution, with occasional jumps up and down.
The regimes of the fixed agent pool dynamics can be quantified on average by taking a look at the cumulative distribution $P_c(\tau)$ of the
relaxation time $\tau$ (Fig.~\ref{fig:scaling_figure}). In regime $\mathbf{I}$ the tail of $P_c(\tau)$ is quite flat, getting flatter as $\mu_A$ decreases.
In contrast, the distribution has a power-law and an exponential tail in regimes $\mathbf{II}$ and $\mathbf{III}$, respectively, signaling shorter relaxation
times. The only exception is the transition between $\mathbf{II}$ and $\mathbf{III}$, where $\tau$ might be as large as in $\mathbf{I}$. Since $P_c(\tau)$ tends to be
broad, the average value of $\tau$ is not very meaningful and we opt instead for the probability $P(\tau > \tau_{\text{max}})$ that the relaxation time is
larger than a fixed maximum time. Numerically, we estimate $P(\tau > \tau_{\text{max}})$ as the fraction of realizations of the dynamics that have not reached
consensus after $\tau_{\text{max}}$ time steps,
out of a large total of $10^4$ realizations. In regimes $\mathbf{II}$ and $\mathbf{III}$, $P(\tau > \tau_{\text{max}})$ remains small as $N$ increases, indicating that $\tau$ is roughly
independent of system size. On the other hand, $P(\tau > \tau_{\text{max}})$ scales with $N$ for $\mathbf{I}$ and for the boundary between $\mathbf{II}$ and $\mathbf{III}$, even reaching 1 for
appropriate values of $\mu_A$ and $N$. A corollary is that even modestly-sized systems may only reach consensus after an astronomical time, if
the medium convergence value is appropriate.
\begin{figure}[ht!]
[width=0.95\linewidth]{Figure2}
\caption{\csentence{Distributions of relaxation time.} (A, B, C) Cumulative
distribution $P_c(\tau)$ of the relaxation time $\tau$ necessary to reach consensus and thus end the dynamics,
for different values of the medium convergence $\mu_A$. Insets: Probability $P(\tau > \tau_{\text{max}})$ that the relaxation
time is larger than $\tau_{\text{max}} = 10^4$ (the maximum time allowed in the numerical simulations), as a function of $N$
for selected values of $\mu_A$. The symbols $\mathbf{I}$, $\mathbf{II}$ and $\mathbf{III}$ denote the three
different regimes found in the dynamics. Simulations correspond to $\epsilon_T = 0.2$, $\epsilon_A = 0.1$ and $N = 10^4$,
with averages over $10^4$ realizations.}
\label{fig:scaling_figure}
\end{figure}
The transition between regimes becomes even clearer when we consider the effect of the medium tolerance $\epsilon_A$, resulting in a phase
diagram for $P(\tau > \tau_{\text{max}})$ in $(\epsilon_A, \mu_A)$ space (Fig.~\ref{fig:phasediag_figure} A). It turns out that regimes $\mathbf{I}$ and $\mathbf{II}$ cover most
of the low $\epsilon_A$ values, while the line $\mu_A=1-\epsilon_A/(1/2-\epsilon_A)$ roughly signals the transition to regime $\mathbf{III}$, which covers a broad area of
large $\epsilon_A$. As $N$ increases, the transition to $\mathbf{I}$ from either $\mathbf{II}$ or $\mathbf{III}$ (Fig.~\ref{fig:phasediag_figure} B and C) becomes sharper:
a consensual final state reached after a very short time gives way to a stationary state that remains stable for really long times.
Such features of the phase diagram remain qualitatively unchanged if we substitute $P(\tau > \tau_{\text{max}})$ with another measure giving
robust statistics, such as the median relaxation time of the dynamics.
\begin{figure}[ht!]
[width=0.95\linewidth]{Figure3}
\caption{\csentence{Phase diagram for a fixed agent pool.} (A) Phase diagram in $(\epsilon_A, \mu_A)$ space of the
probability $P(\tau > \tau_{\text{max}})$ that the relaxation time is larger than $\tau_{\text{max}} = 10^4$, in a system of size $N = 10^4$. Points
give the $(\epsilon_A, \mu_A)$ values used in Fig.~\ref{fig:scaling_figure},
corresponding to regimes $\mathbf{I}$, $\mathbf{II}$ and $\mathbf{III}$. (B, C) Cross sections of the phase diagram along the dashed lines in (A) for
varying $N$. Simulations correspond to $\epsilon_T = 0.2$, with averages over $10^4$ realizations.}
\label{fig:phasediag_figure}
\end{figure}
Finally, we can consider the symmetry-breaking transition between regimes $\mathbf{I}$ and $\mathbf{II}$ by taking a look at the density distribution $P(A)$
of the final medium value (Fig.~\ref{fig:symmetry_figure} A and B). After either $\tau$ or $\tau_{\text{max}}$ has passed, the majority of opinions are
in consensus with $A$, making $P(A)$ a good approximation for the final opinion distribution $P(x)$ as well. In regime $\mathbf{I}$ the medium
distribution is roughly unimodal and peaked at $A \sim 1/2$, signaling a stable and moderate medium. Here the relaxation time is quite long and for most realizations $\tau > \tau_{\text{max}}$.
In regime $\mathbf{II}$, however, $P(A)$ becomes
bimodal, meaning that the medium is more likely to end up close to the extremes rather than in the center. When $N$ is large, the main peaks in $P(A)$ correspond to consensual final states with $\tau \leq \tau_{\text{max}}$, while the secondary peaks are made up of long-lived realizations with long relaxation time. Larger values of $\tau_{\text{max}}$, although computationally expensive, would therefore let us see a strictly bimodal medium distribution for regime $\mathbf{II}$.
As $N$ increases the distribution peaks become sharper and we
can use the standard deviation $\sigma (A)$ of the final medium value as an order parameter for the transition (Fig.~\ref{fig:symmetry_figure} C).
In the thermodynamic limit $N \to \infty$, a vanishing $\sigma (A)$ for $\mathbf{I}$ implies a stationary stable state with $A \sim 1/2$ and no consensus.
As $\mu_A$ increases this symmetry gets broken, $\sigma (A)$ becomes nonzero and a true final state of consensus appears.
\begin{figure}[ht!]
[width=0.95\linewidth]{Figure4}
\caption{\csentence{ Symmetry-breaking transition.} (A, B) Distribution $P(A)$ of the final medium value $A$ reached after a
time $\min(\tau, \tau_{\text{max}})$ has elapsed, for varying $N$. The selected $\mu_A$ values represent regimes $\mathbf{I}$ (A) and $\mathbf{II}$ (B). (C)
Standard deviation $\sigma(A)$ of the final medium value as a function of $\mu_A$, for several values of $N$. This order parameter
signals a symmetry-breaking transition between regimes $\mathbf{I}$ and $\mathbf{II}$. Simulations correspond
to $\epsilon_T = 0.2$, $\epsilon_A = 0.0375$ and $\tau_{\text{max}} = 10^4$, with averages over $10^4$ realizations.}
\label{fig:symmetry_figure}
\end{figure}
This symmetry-breaking mechanism may be understood analytically via a rate equation formalism~\cite{torok2013opinions}. The resulting rate equation
can be solved numerically assuming three editor groups: a mainstream at $x \sim 1/2$ and two extremists with opinions close to the boundaries. The
solution shows stability for the medium at the mainstream opinion when $\mu_A$ is small, but becomes unstable and oscillating for $\mu_A \simeq 3\epsilon_A\pm0.1$.
The bifurcation transition is very sensitive on the position of the extremists, depending not only on $(\mu_A,\epsilon_A)$ but also on the initial conditions.
This is in part the cause of the `noisy' landscape of regime $\mathbf{II}$ in Fig.~\ref{fig:phasediag_figure} A, which appears regardless of the measure used to draw the phase diagram.
\subsection{Agent renewal}
\label{ssec:openPool}
In real systems the pool of collaborators is usually not fixed: Editors come
and go and very often the number of editors fluctuates in time as
external events may incite more or less attention. To keep things
simple we only focus on systems with a fixed number of editors ($N$
agents), but we allow agent replacement with probability $p_{\text{new}} \neq 0$. In our numerical simulations this
happens prior to editing, and new agents have initially random opinions coming from a uniform distribution.
If $\epsilon_A < 1/2$ there is always an opinion range outside the article
tolerance region $[A-\epsilon_A, A+\epsilon_A]$ and new agents may enter such range and edit the article. From WP data we know
that even peaceful articles have few disputes now and then so such a
scenario is realistic. This is thus in contrast with the case of a fixed
opinion pool, where consensus is theoretically always achieved.
A stronger statement can be shown \cite{torok2013opinions},
namely that if
\begin{equation}
\epsilon_A>\epsilon_A^*=\frac{1}{2-\mu_A}
\end{equation}
then consensus is always reached after a finite number of steps, but if
$\epsilon_A < \epsilon_A^*$ there are realizations that do not reach consensus ever.
We show here an example: if the medium value is $A = \epsilon_A^*$, then for
$\epsilon_A = \epsilon_A^*-\varepsilon$ an editor at $x=0$ will disagree with
the article and change it by $\Delta = \epsilon_A^*\mu_A$, so the new medium value would be $A = 1-\epsilon_A^*$. Afterwards an agent at $x=1$ can
restore the article to its previous state and avoid consensus.
The lack of full consensus does not mean that the system is always in
a conflict state. There are periods when $A$ remains
unchanged and these peaceful times are ended by conflicts in which the
opinion of the article is continuously disputed between agent groups
of different opinion. If the dispute is settled (i.e. all agents are
satisfied by the article) a new peaceful period may start. The ratio of
these peaceful and conflicting periods changes with the parameters and
may be considered as a good candidate for an order parameter. Thus we
define the order parameter $P$ as the relative length of the peaceful
periods.
The order parameter is plotted for two different initial conditions in
Fig.~\ref{Fig:3d_phase}. The top figure shows the value of the order
parameter $P$ for a `peaceful' initial condition when all agents had the opinion
$x_i = 1/2$. The bottom figure was instead obtained for a system with `conflict'
initial conditions, namely one with 20\% of agents divided between two
extremist groups of opinions 0 and 1 (and the rest at $x_i = 1/2$)
before the start of the dynamics.
\begin{figure}[ht!]
[width = .7 \linewidth]{Figure5}
\caption{\label{Fig:3d_phase}\csentence{Order parameter for the agent
renewal case.} Order parameter $P$ as a function of the medium tolerance $\epsilon_A$ and
the agent replacement rate $p_{\text{new}}$ for systems of size $N = 80$. The
chosen initial condition is consensus for the top diagram and conflict for the
bottom one.}
\end{figure}
It is clear that there are two distinct regimes in the phase diagram
of Fig.~\ref{Fig:3d_phase}: one characterized by $P=1$ (`peaceful' regime), the other with $P=0$ (`conflict' regime) and a
sharp transition in between. There is a region which is different in
the two cases and will be discussed later. We then identify the transition
point with the largest gradient of $P$ by using the lower plot in
Fig.~\ref{Fig:3d_phase}. The resulting phase diagram is shown
in Fig.~\ref{Fig:noisyphasediag}.
\begin{figure}[ht!]
[width = .7 \linewidth]{Figure6}
\caption{\label{Fig:noisyphasediag}\csentence{Phase diagram for a system with agent renewal.}
Largest gradient of $P$ by using the lower plot in
Fig.~\ref{Fig:3d_phase}, for varying $\mu_A$. Simulations correspond to
$\epsilon_T=0.2$ and system size ranging from $N = 10$ to $640$. The article
convergence parameter was $\mu_A=0.1$, $0.2$, $0.45$, $0.7$ for red,
green, blue and magenta respectively. The curved black line is the
analytical result for $\mu_A=0.1$. The horizontal line limiting the
prepetual peace domain is at $\epsilon_A=0.15$. The eternal peace is limited
by $\epsilon_A^*$ (shown with dashed lines for the same color) which depends
on $\mu_A$.}
\end{figure}
This transition is further illustrated in
Fig.~\ref{Fig:noisyevolsample} where we display sample time evolutions of the opinions
of agents and medium. The left panel shows an example
of a peaceful regime. As mentioned before, from time to
time new agents arrive with incompatible views with respect to the
article but they are pacified very fast, i.e. the conflict periods are
short. In the transition regime (middle panel) the scenario of
peaceful times interrupted by short conflicts is still observable,
but periods of continuous conflict occasionally appear. In the conflict regime exemplified by the right panel, these conflict bursts become
persistent and the peaceful periods tend to disappear.
\begin{figure}[ht!]
[width=.95\linewidth]{Figure7}
\caption{\label{Fig:noisyevolsample}\csentence{Time evolution of
opinions.}
Samples of medium/agent opinions as a function of time for $\epsilon_A=0.42$,
and for three different regimes represented by $p_{\text{new}}=0.001, 0.002,
0.003$ (from left to right respectively). Colour coding is as follows:
Red points (opinion of the article), green dots (agents who are
satisfied with the article), blue points (agents whose opinion is
outside the medium tolerance interval), and light blue background
(conflict regions).}
\end{figure}
The above transition is the result of a competition between two timescales. New
agents arrive outside of the article's tolerance interval with an `insertion'
timescale $\tau_\mathrm{ins}\propto Np_{\text{new}}$. In order to have $P > 0$
the conflicts must be resolved before a new extremist agent arrives.
Let us note that the convergence is very fast if there is only one
extremist group. The problem is solved by displacing the article
opinion by the required amount, which can be done in few ($N$
independent) steps. This is what happens in the left panel of
Fig.~\ref{Fig:noisyevolsample}. On the other hand, if we have two
extremist groups on both sides of the opinion interval the relaxation
is much slower and this is manifested in a much longer relaxation time.
Thus, at the transition the insertion timescale is equal to the
relaxation time of the case with two extremist groups, which is analogous to the
fixed agent pool version of the model.
The task here is to determine the relaxation time of the fixed pool
version of the model and relate it to $\tau_\mathrm{ins}$.
For large values of the medium tolerance ($\epsilon_A > 1/4$), the relaxation
time can by calculated analytically \cite{torok2013opinions},
\begin{equation}
\tau(e)= c(\mu_A)N\left([2 e^2+e_0^2 (n-1)] n - e e_0 (n-1) (2 + n)\right),
\end{equation}
where $e = \epsilon_A^*-\epsilon_A$, $e_0 = \epsilon_A^*-1/2$, $n$ denotes the integer
part of $e/e_0$ (which is actually the number of steps the medium can
make in one direction) and $c$ is a constant depending on $\mu_A$.
The above approach works well for $\epsilon_A>0.3$ and $\mu_A<0.3$ (regime
$\mathbf{III}$ of the fixed pool case). If the mainstream group gets dissatisfied
either by the large jump ($\mu_A$ is too large) or by the small
tolerance ($\epsilon_A$ too small) of the article, the reasoning presented in
\cite{torok2013opinions} breaks down and new effect comes into play,
namely the relaxation times of the fixed pool system becomes be
enormous (regime $\mathbf{I}$).
As we enter regime $\mathbf{I}$ of the fixed pool dynamics the relaxation time
increases sharply (see Fig.~\ref{fig:phasediag_figure} B and C). This
means that if the system gets into a conflict state it will remain
there for ever, which happens for,
\begin{equation}
\epsilon_{A,\mathrm{lim}}=\frac{1}{4}-\frac{\epsilon_T}{2}.
\end{equation}
This is why, starting from a conflict initial condition, the lower phase diagram in
Fig.~\ref{Fig:3d_phase} shows $P = 0$ for $\epsilon_A<0.15$. On the other
hand, in order to initiate such a conflict one needs to have a
situation where two extremists appear on both ends of the opinion space
outside of the article tolerance interval. If we have a single extremist
then the consensus will be reached within a few time steps,
independently of $N$. So the probability that we create a long-lasting
conflict state decreases proportionally to the agent replacement
probability. This is why we see only peace on the finite-time realizations
leading to the upper phase diagram in Fig.~\ref{Fig:3d_phase}. Had we waited long enough, a
conflict would have been formed for $\epsilon_A<1/4-\epsilon_T/2$ and would have persisted
further on.
In summary, the typical behavior of our model in the presence of agent renewal may be divided into four distinct regimes:
\begin{enum}
\item {\em Eternal peace} ($\epsilon_A>\epsilon_A^*$): The system reaches
consensus very fast and remains there for ever.
\item {\em Peace} ($\epsilon_A>\frac{1}{4}-\frac{\epsilon_T}{2}$ and above the phase transition
line): The system is mainly in a consensual state and only
interrupted by short disputes.
\item {\em War} ($\epsilon_A>\frac{1}{4}-\frac{\epsilon_T}{2}$ and below the phase transition
line): The system is mainly in a state of disagreement.
\item {\em Perpetual war} ($\epsilon_A<\frac{1}{4}-\frac{\epsilon_T}{2}$): In this
regime and in the thermodynamic limit $N \to \infty$ no consensus may exist.
\end{enum}
\subsection{The case of Wikipedia}
\label{ssec:wikipedia}
Although the model described and analyzed above is simplified enough to be extendable to various
cases of collaboration, we specially intend to use it to explain some of the empirical
observations regarding edit wars in WP.
Wikipedia is huge, not only in its number of articles and users but in the number of times articles are
edited. In most cases articles are not written in a collaborative way, i.e., they have single
authors or a few authors who have written and edited different parts of the article without any significant
interaction~\cite{kimmons2011understanding}. In contrast, a few cases show significant
constructive and/or destructive interactions between editors. The latter situation has been named `edit war'
by the WP community and defined as follows: ``An edit war occurs when editors who disagree about the content
of a page repeatedly override each other's contributions, rather than trying to resolve the
disagreement by discussion''~\cite{wiki:war}.
To start an empirical analysis of such opinion clashes and the way they are entangled with collaboration, we need to
be able to locate and quantify edit wars.
\subsubsection{Controversy measure}
An algorithm to quantify edit wars and measure the amount of social clashes for WP articles
has been introduced and validated before~\cite{sumi2011edit}, and then used to study extensively the
dynamical aspects of WP conflicts~\cite{yasseri2012dynamics}. An independent study~\cite{sepehri2012leveraging}
has also shown that this measure is among the most reliable in capturing very controversial articles.
We quantify the `controversiality' of an article based on its edit history by focusing on `reverts' (i.e.
when an editor completely undoes another editor's edit and brings the article back to the state just before the last version).
Reverts are detected by comparing all pairs of revisions of an article
throughout its history, namely by comparing the MD5 hash code~\cite{rivest1992md5} of the revisions. Specifically, a revert is
detected when two versions in the history line are exactly the same. In this case the latest edit (leading
to the second identical revision) is marked as a revert, and a pair of editors, referred to as reverting and
reverted editors, are recognized.
Very soon in our investigation we noticed that reverts can have different reasons and not in all cases
signalize a conflict of opinions. For example, an editor could revert personal edit mistakes or someone else's.
Reverts are also heavily used to suppress vandalism, in itself a different type of destructive social behavior,
but with no collaborative intention and therefore out of our interest. Thus we narrowed down our analysis
to `mutual reverts'. A mutual revert is recognized if a pair of editors $(x, y)$ is observed once with $x$ as the reverter and once with $y$.
We also noticed that mutual reverts between pairs of editors at different levels
of expertise and experience in WP editing could contribute differently to an edit war. Two
experienced editors getting involved in a series of mutual reverts is usually a sign of a more serious conflict, as
opposed to the case when two newbies or a senior editor and a newbie bite each other \cite{halfaker2011bite}.
As a solution we introduced a `weight' for each editor, and to sum up all reverts within the history of an article we counted each revert
by using the smaller weight of the pair of editors involved in it. The weight of an editor $x$ is defined as the
number of edits performed by him or her, and the weight of a mutually reverting pair is defined as the
minimum of the weights of the two editors. The controversiality $M$ of an article is then defined by summing
the weights of all mutually reverting editor pairs, multiplying this number by the total number of editors $E$
involved in the article. Overall,
\begin{equation}\label{Eq:M}
M = E \sum_{\text{all mutual reverts}} min(N^{\rm d}, N^{\rm r}),
\end{equation}
where $N^{\rm r}$, $N^{\rm d}$ are the number of edits for the article committed by the reverting/reverted editor. This
measure can be easily calculated for each article, irrespective of the language, size, and length of its history.
Before starting our discussion about the empirical dynamics of conflict and its comparison with theoretical results, a remark on
the most controversial articles in WP. We have calculated $M$ for all articles in 13 different languages, from the start of each language WP up to March 2010. In Table~\ref{top-10} we show the list of the top-10 most controversial articles. A more complete and detailed analysis of the lists of the most controversial WP articles in different languages and differences and similarities between them can be found elsewhere~\cite{yasseri2014controversial}.
\begin{table}[ht!]
\caption{List of the most controversial articles in different language WPs according to $M$.}
\begin{tiny}
\begin{tabular}{p{.0cm}p{2.2cm}p{2.2cm}p{2.2cm}p{2.2cm}p{2.2cm}}
\hline
& \bf{English} & \bf{German} & \bf{French} & \bf{Spanish} & \bf{Portuguese} \\
\hline
1 & George W. Bush & Croatia & S\'gol\`ene Royal & Chile & S\~ao Paulo\\
2 & Anarchism & Scientology & Unidentified flying object & Club América & Brazil \\
3 & Muhammad & 9/11 conspiracy theories & Jehovah's Witnesses & Opus Dei & Rede Record \\
4 & List of WWE personnel & Fraternities & Jesus & Athletic Bilbao & José Serra \\
5 & Global warming & Homeopathy & Sigmund Freud & Andrés Manuel López Obrador & Grêmio Foot-Ball Porto Alegrense \\
6 & Circumcision & Adolf Hitler & September 11 attacks & Newell's Old Boys & Sport Club Corinthians Paulista\\
7 & United States & Jesus & Muhammad al-Durrah incident & FC Barcelona & Cyndi Lauper \\
8 & Jesus & Hugo Chávez & Islamophobia & Homeopathy & Dilma Rousseff \\
9 & Race and intelligence & Minimum wage & God in Christianity & Augusto Pinochet & Luiz Inácio Lula da Silva \\
10 & Christianity & Rudolf Steiner & Nuclear power debate & Alianza Lima & Guns N' Roses \\
\hline
& \bf{Czech} & \bf{Hungarian} & \bf{Romanian} & & \\
\hline
1 & Homosexuality & Gypsy Crime & FC Universitatea Craiova & & \\
2 & Psychotronics & Atheism & Mircea Badea & & \\
3 & Telepathy & Hungarian radical right & Disney Channel (Romania) & & \\
4 & Communism & Viktor Orb\'an & Legionnaires' rebellion \& ucharest pogro & & \\
5 & Homophobia & Hungarian Guard Movement & Lugoj & & \\
6 & Jesus & Ferenc Gyurcsány's speech in May 2006 & Vladimir Tismăneanu & & \\
7 & Moravia & The Mortimer case & Craiova & & \\
8 & Sexual orientation change efforts & Hungarian Far- right & Romania & & \\
9 & Ross Hedvíček & Jobbik & Traian Băsescu & & \\
10 & Israel & Polgár Tamás & Romanian Orthodox Church & & \\
\hline
& \bf{Arabic} & \bf{Persian} & \bf{Hebrew} & \bf{Japanese} & \bf{Chinese} \\
\hline
1 & Ash'ari & Báb & Chabad & Koreans in Japan & Taiwan \\
2 & Ali bin Talal al Jahani & Fatimah & Chabad messianism & Korea origin theory & List of upcoming TVB series \\
3 & Muhammad & Mahmoud Ahmadinejad & 2006 Lebanon War & Men's rights & TVB \\
4 & Ali & People's Mujahedin of Iran & B'Tselem & internet right-wing & China \\
5 & Egypt & Criticism of the Quran & Benjamin Netanyahu & AKB48 & Chiang Kai-shek \\
6 & Syria & Tabriz & Jewish settlement in Hebron & Kamen Rider Series & Ma Ying-jeou \\
7 & Sunni Islam & Ali Khamenei & Daphni Leef & One Piece & Chen Shui-bian \\
8 & Wahhabi & Ruhollah Khomeini & Gaza War & Kim Yu-Na & Mao Zedong \\
9 & Yasser Al-Habib & Massoud Rajavi & Beitar Jerusalem F.C. & Mizuho Fukushima & Second Sino-Japanese War \\
10 & Arab people & Muhammad & Ariel Sharon & GoGo Sentai Boukenger & Tiananmen Square protests of 1989 \\
\end{tabular}
\end{tiny} \label{top-10}
\end{table}
\subsubsection{Dynamics of conflict and war scenarios}
Measuring $M$ can not only lead us to rank the articles based on their cumulative controversy measure,
but also enables us to follow edit wars in time as they emerge and get resolved, by investigating
the evolution of $M$ as time passes and the article develops. In the top row of
Fig.~\ref{Fig:war-scenario} we show the time evolution
of $M$ for three different sample articles.
\begin{figure}[ht!]
[width=0.95\linewidth]{Figure8}
\caption{\label{Fig:war-scenario} \csentence{War scenarios for WP and our model.} Top: Empirical controversy measure $M$ as a
function of the number of article edits in three different war scenarios. From left to right, sample articles
are `Jyllands-Posten Muhammad cartoons controversy', `Iran', and `Barack Obama'; and correspond to the
regimes of `single war', `war-peace cycles', and `never-ending war' respectively. Bottom: Theoretical conflict
measure $S$ in the case of agent renewal, reproducing the qualitatively analogue evolution
of WP articles with parameter values $N=640$, $\epsilon_T=0.2$ and $\mu_A=0.1$, as well
as $\epsilon_A=0.35, 0.42, 0.30$ and $p_{\text{new}}= 0.001, 0.001, 0.002$ for the three war scenarios,
respectively. Continuous lines correspond to selected single runs of the model, while the shading indicates the density of $S$ over an ensemble of $10^4$ realizations.}
\end{figure}
Based on the way $M$ evolves in time, we may categorize almost all controversial
articles into three categories:
\begin{enum}
\item {\it Single war to consensus}: In most cases controversial articles can be included in this category. A single
edit war emerges and reaches consensus after a while, stabilizing quickly. If the topic of the article is not particularly dynamic, the
reached consensus holds for a long period of time (top left in Fig.~\ref{Fig:war-scenario}).
\item {\it Multiple war-peace cycles}: In cases where the topic of the article is dynamic but the rate of new events (or production
of new information) is not higher than the pace to reach consensus, multiple cycles of war and peace may
appear (top center in Fig.~\ref{Fig:war-scenario}).
\item {\it Never-ending wars}: Finally, when the topic of the article is greatly contested in the real
world and there is a constant stream of new events associated with the subject, the article tends not to reach a
consensus and $M$ increases monotonically and without interruption (top right in Fig.~\ref{Fig:war-scenario}).
\end{enum}
The empirical war scenarios described previously are in qualitative agreement with the theoretical regimes of our model in the case of
agent renewal, as seen from both the sample time series in Fig.~\ref{Fig:noisyevolsample} and the regimes of war and peace in the phase
diagrams of Fig.~\ref{Fig:3d_phase} and Fig.~\ref{Fig:noisyphasediag}. Unfortunately, the theoretical order parameter $P$ is quite difficult to
measure in real systems as editor opinions are not known. What we know
instead is the controversy measure $M$ of Eq.~\ref{Eq:M}. As mentioned before, $M$
counts conflict events (i.e. mutual reverts) and weights them by the
maturity of the editor. This process can actually be repeated for the model:
The editor maturity $T_i$ is then defined as the number of time steps an agent has been in
the pool of editors (a quantity constantly reset by agent replacement), and a
conflict event is considered as the time an editor modifies the article, since this implies the agent is not satisfied with the state of the medium.
Thus a theoretical counterpart $S$ to the WP controversy measure $M$ may be defined as follows: Let $S=0$ at the beginning of the dynamics. Then in each update $t^*$ (out of the $N$ that constitute a time step in the dynamics), when editor $i$ changes the state of the article by the amount $\Delta = |A(t^*+1)-A(t^*)|$ we increment $S$ by $T_i\Delta$, where $T_i$ measures the time $i$ has been in the editorial pool. Examples of the temporal evolution of $S$ (lower row in
Fig.~\ref{Fig:war-scenario}) closely reproduce the qualitative
behavior of $M$ for different war scenarios. To further compare empirical observations in WP with our model predictions, we measure the
typical length of a constant `plateau' in the $M$ and $S$ time series, i.e. the number of edits between two successive increments. As seen in the distribution of plateau length for WP and the model (Fig.~\ref{Fig:plateau}), a statistical agreement for all three war scenarios is clear.
\begin{figure}[ht!]
[width=0.8\linewidth]{Figure9}
\caption{\label{Fig:plateau} \csentence{Peace periods in WP and our model.} Distribution of plateau lengths for selected
articles in WP (squares) and tuned parameters in our model (lines) for the three war scenarios shown in Fig.~\ref{Fig:war-scenario}.
The length of a plateau or peace period is defined as the number of edits between two successive increments in either $M$ or $S$.}
\end{figure}
A last word on WP banning statistics. A way of estimating the number of extremists is to count the number of editors who have been `banned'
from editing. Explicitly, ``a ban is a formal prohibition from editing some or all WP pages, either temporarily
or indefinitely''~\cite{wiki:ban}. Usually banning is used against vandals and/or editors who violate WP
policies, especially those related to edit wars. In Table~\ref{table:ban} we give some statistics of editors at
different classes of editing activity, according to their number of edits. Interestingly, the
relative population of banned editors is larger among more experienced editors (i.e. editors with more than 1000 edits).
In other words, up to almost 20\% of experienced editors could have been involved in edit wars.
This is in complete accord with the choices we have made for the modeling setup, namely having two active extremist groups with roughly 20\% of the total number of editors.
\begin{table}[ht!]
\caption{Percentage of banned users to the total number of editors at three different classes.}
\begin{tiny}
\begin{tabular}{p{.9cm}p{1.3cm}p{1.2cm}p{1cm}p{1.2cm}p{1.2cm}p{1cm}p{1.2cm}p{1.2cm}p{1cm}}
\hline
& Num. Editors w. \textgreater 1000 Edits & Ban. Editors w. \textgreater 1000 Edits & \% ban. w. \textgreater 1000 edits & Num. Editors w. \textgreater 100 Edits & Ban. Editors w. \textgreater 100 Edits & \% ban. w. \textgreater 100 edits & Num. Editors w. \textgreater 1 Edits & Ban. Editors w. \textgreater 1 Edits & \% ban. w. \textgreater 1 edits\\
\hline
English & 36280 & 6114 & 0.17 & 189174 & 20342 & 0.11 & 4552685 & 403851 & 0.09 \\
German & 8714 & 1561 & 0.18 & 34777 & 3458 & 0.10 & 511291 & 31996 & 0.06 \\
French & 5286 & 694 & 0.13 & 21940 & 1700 & 0.08 & 394385 & 16681 & 0.04 \\
Spanish & 3834 & 765 & 0.20 & 19135 & 2404 & 0.13 & 479305 & 21850 & 0.05 \\
Portuguese & 1733 & 345 & 0.20 & 8077 & 1015 & 0.13 & 194584 & 7486 & 0.04 \\
Czech & 700 & 112 & 0.16 & 2439 & 236 & 0.10 & 48030 & 2663 & 0.06 \\
Hungarian & 844 & 138 & 0.16 & 3107 & 276 & 0.09 & 49024 & 1201 & 0.02 \\
Romanian & 437 & 53 & 0.12 & 1675 & 130 & 0.08 & 36631 & 914 & 0.02 \\
Arabic & 610 & 96 & 0.16 & 2736 & 198 & 0.07 & 80498 & 1085 & 0.01 \\
Persian & 580 & 151 & 0.26 & 2531 & 406 & 0.16 & 56805 & 2544 & 0.04 \\
Hebrew & 1009 & 233 & 0.23 & 3898 & 515 & 0.13 & 53318 & 4341 & 0.08 \\
Japanese & 4010 & 786 & 0.20 & 19090 & 2845 & 0.15 & 242621 & 21995 & 0.09 \\
Chinese & 2106 & 378 & 0.18 & 9002 & 1072 & 0.12 & 160579 & 9387 & 0.06 \\
\end{tabular}
\end{tiny}
\label{table:ban}
\end{table}
\section{Discussion and Conclusion}
\label{sec:conc}
Here we have studied through modeling the emergence, persistence and resolution of conflicts in a collaborative environment of humans such as
WP. The value production process takes place through interaction between peers (editors for WP) and through direct modification of
the product or medium (an article). While in most cases this process is constructive and peaceful, from time to time severe conflicts emerge.
We modeled the dynamics of conflicts during collaboration by coupling opinion formation with article editing in a generalized bounded-confidence
dynamics. The simple addition of a common value-production process leads to the replacement of frozen opinion groups (typical of the
bounded-confidence dynamics)
with a global consensus and a tunable relaxation time. The model with a fixed pool shows a rich phase diagram with several characteristic
behaviors: a) an extremely long relaxation time, b) fast relaxation preceded by oscillating behavior of the medium opinion, and c) an even
faster relaxation with an erratic medium. We have observed a symmetry-breaking, bifurcation transition between regimes a) and b), as well as
divergence of the relaxation time in the transition between regimes b) and c).
If the pool is not fixed and editors are exchanged with new ones at a given rate, we obtain two different phases:
conflict and peace. A conflict measure can be defined for the modeled system and be directly compared to its empirical counterpart in
real WP data. It is then possible to follow the temporal evolution of this measure of controversy and obtain a good qualitative agreement
with the empirical observations. These results lead us to plausible explanations for the spontaneous emergence of current WP policies,
introduced to moderate or resolve conflicts.
Two remarks are at place here. In this study we have used a particular collaboration environment and compared our results with WP.
The main reason behind is that for the free encyclopedia we have a full documentation of actions; however, we should emphasize that as web-based
collaborative environments are abundant, we believe that our approach and results are much more general. Second, we are aware of the fact that
the model contains a number of stringent simplifications: There are cultural differences between the WPs (e.g., in the usage of the talk
page), and as in all human-related features there are large inhomogeneities in the opinions, in the tolerance level and in the activity of
editors. Some of these aspects are under current study and will be taken into account for future research.
\begin{backmatter}
\section*{Competing interests}
The authors declare that they have no competing interests.
\section*{Author's contributions}
All authors designed the research and participated in the writing of the manuscript. GI and JT
performed the numerical calculations and analytical approximations. TY analyzed the empirical data.
\section*{Acknowledgements}
The authors acknowledge support from the ICTeCollective EU FP7 project. JK thanks FiDiPro (TEKES)
and the DATASIM EU FP7 project for support. JT thanks the support of
European Union and the European Social Fund through project
FuturICT.hu (grant no.: TAMOP-4.2.2.C-11/1/KONV-2012-0013).
\bibliographystyle{bmc-mathphys}
| {
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Вилямовице:
Вилямовице — малый город в Бельском повете Силезского воеводства Польши.
Вилямовице — городско-сельская гмина (волость) в Польше, входит в Бельский повят (силезский), Силезское воеводство. | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,038 |
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Do you work for Inspiring Interns? Contact us to upload your company profile and reach a wide audience of relevant, industry professionals.
In this guest post, Alex Towney from Inspiring Interns, which specialises in finding graduates internships in London and throughout the UK, shares his view of internships.
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Patria 6x6 Unveiled June 13, 2018
Patria, based in Finland, has introduced the new armored personnel carrier (APC) called Patria 6x6 in Eurosatory 2018. The vehicle weighs 24 tons. Patria 6x6 can carry up to 8,5 tons payoad.
According to the statement made by the company, vehicle can be equipped with a wide range of weapons, including the AMOS 120 millimeter mortar system, which is already in is use Finnish Army mounted on the AMV vehicles. In the version of Patria 6x6 introduced in the Eurosatory, vehicle equipped with 12.7 millimetres M2 machine gun in a shielded gun station. Vehicle can also be equipped pintle mounted 5.56 millimetres and 7.62 millimetres machine guns on the rear side of the upper part of the vehicle. APC is powered by a five-cylinder engine producing 294 kW and it has seven forward and two reverse gearbox. The maximum speed of a vehicle capable of 700 kilometers with a single tank is 100 kilometers per hour. The body of vehicle which has 10 seats for troops is made of steel and it can be reinforced with additional armor plates and the protection level of the vehicle can be increased to STANAG 4569 standards up to Level 4.
Tags : 6x6 armor armored army carrier company engine equipped eurosatory finland finnish gun guns increased introduced kilometers machine mortar mounted new personnel powered protection range speed station system tank troops vehicle vehicles version weapons
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Q: Missing parameter username error in Zap API I have been running Zap authenticated scans using a Zest login script, but auth have broken after I updated Zap docker image - seems like it's due to a change in API.
Here is the output I get:
5309955 [ZAP-ProxyThread-3963] INFO org.parosproxy.paros.control.Control - New session file created
zap | 5313051 [ZAP-ProxyThread-3971] INFO org.zaproxy.zap.authentication.ScriptBasedAuthenticationMethodType - Loaded script for API:login.zst
zap | 5313633 [ZAP-ProxyThread-3975] WARN org.zaproxy.zap.extension.api.API - Bad request to API endpoint [/JSON/users/action/setAuthenticationCredentials/] from [10.254.0.6]:
zap | Missing Parameter (missing_parameter) : Username
And this is how I supply auth parameters:
authmethod_params = ('scriptName=' + auth_script_name + '&'
'Submission Form URL={0}/{1}&'
'Username field=username&'
'Password field=password&'
'Target URL=http://www.example.com/login')
# setup authentication
auth = zap.authentication
auth.set_authentication_method(
contextid=context_id,
authmethodname=auth_method_name,
authmethodconfigparams=authmethod_params)
For some reason, the API does not recognize the username parameter and, subsequently, login fails. Can you please provide a current example of how to pass login parameters for script-based auth to Zap API?
Many thanks
A: Found the reason: the auth broke on a new user because I did not update base 64-encoded credentials in the request.
| {
"redpajama_set_name": "RedPajamaStackExchange"
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Cleveland, OH (May 16, 2016) – Following the successful open house event hosted by Howard Hanna in April, the company is offering home buyers another unique open house experience. Beginning on Wednesday, May 18 in Pennsylvania, Virginia, Michigan and North Carolina and on Thursday, May 19 in Ohio, offices throughout our market areas will be hosting mid-week Twilight Open House events from 5:00 p.m. to 7:00 p.m.
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For a chance to view these great open houses in Pennsylvania, Virginia, Michigan and North Carolina, stop by an event on June 22, July 20, August 17, or September 14. In Ohio, the events are on June 23, July 21, August 18, and September 15. | {
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Take a look at 10 surfing films that are available now on Red Bull TV. Following surfers who go in search of the biggest and most fearsome waves, as well those who prefer to break from convention; you don't want to miss these cinematic treats.
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{"url":"https:\/\/www.encyclopediaofmath.org\/index.php?title=Simply-connected_group&oldid=39777","text":"# Simply-connected group\n\nA topological group (in particular, a Lie group) for which the underlying topological space is simply-connected. The significance of simply-connected groups in the theory of Lie groups is explained by the following theorems.\n\n1) Every connected Lie group $G$ is isomorphic to the quotient group of a certain simply-connected group (called the universal covering of $G$) by a discrete central subgroup isomorphic to $\\pi_1(G)$.\n\n2) Two simply-connected Lie groups are isomorphic if and only if their Lie algebras are isomorphic; furthermore, every homomorphism of the Lie algebra of a simply-connected group $G_1$ into the Lie algebra of an arbitrary Lie group $G_2$ is the derivation of a (uniquely defined) homomorphism of $G_1$ into $G_2$.\n\nThe centre $Z$ of a simply-connected semi-simple compact or complex Lie group $G$ is finite. It is given in the following table for the various kinds of simple Lie groups.\n\n<tbody> <\/tbody>\n\nIn the theory of algebraic groups, a simply-connected group is a connected algebraic group $G$ not admitting any non-trivial isogeny $\\phi : \\tilde G \\rightarrow G$, where $\\tilde G$ is also a connected algebraic group. For semi-simple algebraic groups over the field of complex numbers this definition is equivalent to that given above.","date":"2019-02-16 01:30:13","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\": 0.9310033321380615, \"perplexity\": 107.29041995610254}, \"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-2019-09\/segments\/1550247479729.27\/warc\/CC-MAIN-20190216004609-20190216030609-00461.warc.gz\"}"} | null | null |
Can Jones, like Key, rise from the fire?
Maori Party won't take Key's F&S deal
Written By: Marty G - Date published: 1:34 am, June 12th, 2010 - 42 comments
Categories: foreshore and seabed, Maori Issues, maori party - Tags: pita sharples, Tariana Turia, te ururoa flavell
'We don't know if we can support this'
It's a very delicate title for the Maori Party's press release on National's foreshore and seabed offer but it reveals much. On the one hand, they know they can't accept a deal that doesn't give title to iwi. On the other hand, the co-leaders really don't want to leave government.
It's very telling that the Maori Party's press release said "the caucus" doesn't think it can accept Key's offer and Te Ururoa Flavell fronted for the media calling Key's deal "a bridge too far". Tariana Turia and Pita Sharples haven't stated their personal views. The press release pleas for Key to meet with the Iwi Leadership Group: "We have got to a point where it is critical that the Prime Minister hear directly from the iwi leaders". As if their positions can magically be made reconcilable is a sign of desperation, is a prayer that the inevitable can be avoided.
This is obviously very difficult for the Maori Party's co-leaders.
By making them ministers, Key very cleverly co-opted Turia and Sharples. They have given his government an illusion of centrism and allowed him to play one coalition partner against the other. He has also made it very difficult for the Turia and Sharples to walk away. Leaving the government means a pay cut and a loss of power, and losing what little 'wins' they have gained, like Whanau Ora. All Key loses is a partner that was becoming a liability with his base anyway.
The backbenchers, especially Hone Harawira, are obviously pushing hard for the Party to stand true to its principles.
Which is why they should never have gone into the deal in the first place.
But there's no option for the Maori Party here. They can't get the deal they want from National. They can't buy into a deal that fails to meet their basic objectives on their key issue. They can't stay in government after failing to make a deal because the relationship would be all give for no gain.
42 comments on "Maori Party won't take Key's F&S deal "
mummybot 1
I have to say, the inevitability of it all is quite depressing, like watching a slow moving train wreck. At least when Winnie and NZ First sold out to National in the '96 election it was theatric – while against his own personal stance (given the history) – the decision wasn't a complete anathema to his base. This. This is just a mess.
Jenny 2
Honestly Marty what choice did they have?
Isn't it true Marty, that up to now the Labour Party has refused to take the Maori Party seriously? Ruling out any accommodation with them and even infamously seeks to "destroy the Maori Party" and that when it comes to coalition time, the Maori Party are to be considered "the last cab off the rank".
Realising that this sectarian stance by Labour was never going to allow the Maori Party any seat at the table, the sectarian stand of the Labour drove the Maori Party into an alliance with National in a hope of getting some gains for their people.
Despite what some on this site have claimed, (unfairly in my opinion) that "the Maori Party props up the government", in fact the Maori Party position is far more subtle than that.
The Maori Party have admitted from the beginning that they would rather have formed a coalition to the left. But realising that, this had been taken off the table, and knowing that National, with Act had the overall majority to rule with, or without them, the Maori Party attempted with some admittedly modest success to turn this no win situation into some gains for their people.
It seems that things may be changing, As has been shown on this site, Labour the Greens and the Maori Party are currently working together in practice, to build a protest campaign powerful enough to defeat National's attack on local body democracy.
felix 2.1
What choice did they have? Opposition of course.
Surely the only honourable choice given that the party oppose most of the government's policy.
Sarge 2.1.1
To what end?? You don't tend to acheive much in opposition…….
Marty G 2.1.1.1
you can stay true to your principles.
Basically, you guys are saying any political party should back the biggest party… one party state
Lew 2.1.1.1.1
Bollocks. What you're arguing is that every generally-left party should always back Labour, no matter how egregiously Labour screwed them. That breeds impunity and entitlement.
The Voice of Reason 2.1.1.1.1.1
Who's saying that the Maori Party is any kind of left, Lew? They have been conservative since their formation and willingly chose to go into Government with ACT and their support party, National. I haven't seen any evidence of them proposing, let alone winning, any left wing policy since taking the keys to the limos. Mind you, they have helped lift the living standards of Maori. Well, five of them, anyway.
Lew …
If that's so, why is the left so cut up that they went into government with National?
Oh, right. It isn't so. It's just more jilted bitterness.
The Voice of Reason …
Well, I don't speak for the left, Lew, just from the left. I'm not sure that too many from the left are cut up about the MP's current position other than those of their supporters who naively thought they were a progressive alternative.
It turns out that they aren't progressive at all, of course, though I hope that in the future they may move leftward, once the ideologically crippled leaders they currently have exited the scene.
Because it's possible to be progressive without supporting indigenous rights to self-determination?
No, it's not. Sorry about that. Progressivism includes indigenism and opposing racism, just like it includes feminism.
Er, what are you on about, Lew?
Of course it's possible to be progressive without supporting indigenous rights to self determination. It's a more 'perfect' political approach to be progressive on all matters, but a party could be progressive on peace, women's rights, animal rights, racism and a whole host of other things, without a specific commitment to self determination.
A failure or weakness in one specific policy area does not mean that overall a party is not progressive.
I disagree. I think you'd disagree, too, if it were a different issue — such as class, for instance. Can a party be progressive without a commitment to economic justice? If so, how?
The Voice of (un)Reason on the Maori Party:
I haven't seen any evidence of them proposing, let alone winning, any left wing policy since taking the keys to the limos. Mind you, they have helped lift the living standards of Maori. Well, five of them, anyway.
Putting aside VOR's bigoted depiction of Maori Party MPs as self serving opportunists only in parliament for the perks. I will instead point to left wing policy VOR claims that he hasn't "seen any evidence of them proposing….".
However in attempting to do this, I am mindful of the saying that there are none so blind, as those who choose not to see.
Off the top of my head, (others might like to add more):
The Maori Party are the main leaders in parliament calling for the removal of GST from healthy food. A Maori Party initiative that Phil Goff says Labour will consider supporting.
The Maori party also strongly opposed the Three Strikes Law and made a statement that they are prepared to work with any others to remove this law.
Recently the Maori Party has joined with Labour and the Greens in a protest campaign against National's attack on Local Body democracy.
And of course the Maori Party is opposed to the statutory removal of legal and internationally recognised, traditional indigenous people's customary rights and usage, specifically in New Zealand, around the issue of the seabed and foreshore.
I challenge any supporter of this enactment to try and justify that this was a left wing move by the last Labour Government.
VOR if you can stop spewing your irrational sectarian hatred for even 5 minutes maybe you would like to have a go.
It would also be good if (for a nice change) you refrained from making stuff up and instead supplied some facts or even links to back up your argument.
Terrific, Jenny. And things they have actually achieved since being handed the keys to the limos? Other than significantly increasing the incomes of 5 MP's?
And, by the way, I support the left wing party that 30-40% of NZ voters also prefer. I don't support a race based splinter party, who, by definition, are sectarian. So stop misusing the term and put up some facts about the Maori Party in Government that don't show them to be either incompetent underachievers or more accurately, pretty damn happy with their bawbees and Beemers.
VOR in your earlier comment you stated that:
I haven't seen any evidence of them proposing, let alone winning, any left wing policy
So I showed you the left wing policy they have proposed.
But still you couldn't see it.
Of course you also mentioned "winning" any left wing policy.
The United Nations Declaration on the Rights of Indigenous People is one left wing policy that the Maori Party championed and won from a minority position over opposition from within both Labour and National.
On the question of GST off food. The Maori Party have managed to move the debate to the left. So much so, that it looks likely that Labour will support Rahui Katene's private members bill for the removal of GST from healthy food. This also is a win.
Getting Labour's support for the removal of GST off food is far more than just a symbolic win, because by voting for this in opposition, Labour becomes committed to supporting this left wing proposal when they are returned to government. Which I hope will be as soon as possible.
The inescapable truth is, that a Labour Greens Maori Party electoral accommodation would be an unbeatable combination.
All it requires is a bit of good will and an open mind.
VOR, the only reason Labour may not be returned to the treasury benches next year, is, if blind sectarians like you have their way in the Labour Party.
This in my opinion would be a disaster.
I am of the firm opinion that a second term of National led Government during the continuing W recession will be extremely destructive for this country, and must be avoided if at all possible.
VOR as you yourself point out, Labour has the support of "30-40% of NZ voters", which, without coalition partners is not a majority.
To not even consider the Maori Party as a future coalition partner would be irresponsible.
When conservative parties like United Future and New Zealand First are considered perfectly acceptable coalition partners by Labour, the question must be asked why is the Maori Party considered by people like you to be beyond the pale?
Going on past record, I don't expect to get any rational explanation from you VOR. But this is still a worthwhile question that needs to be discussed.
felix 2.1.1.1.1.2
Lew,
All I suggested was that the maori party would be more true to their principles by sitting in opposition to the govt.
I don't see this as "backing Labour".
Frankly, it's you who seems a little bitter this morning.
My response wasn't to you, Felix, because while I disagree with your view (I don't think going into government in and of itself was contrary to the māori party's principles, and I think anyone who claims it is just doesn't understand those principles very well), it's an arguable position. I was reversing Marty's idiotic reductive "if you're not with us, you're against us" generalisation.
ghostwhowalksnz 2.1.1.2
Thats why its called 'opposition' Duhhh
Jenny 2.1.1.3
To what end?? You don't tend to acheive much in opposition .
I agree with what you are saying, here Sarge.
Effectively because of Labour's opinion of the Maori Party, Felix is not just asking the Maori Party to go into opposition, but effectively, to go into opposition permanently, no matter which ever of the two major parties holds the Treasury benches.
As this would be rather pointless.
As you asked, the question is, "To what end??"
Maybe some Labour Party supporters who want to continue the policy of snubbing the Maori Party might like to answer?
How about you, Voice of Unreason?
felix 2.1.1.3.1
Um, not permanently. Just while they, you know, oppose the govt.
But Jenny, they were just overreacting about the FSA. They should have realised that it was just the tough-love of realpolitik, it was for their own good really, and if they'd just sucked it up like good little subalterns in the knowledge that the master would eventually throw a few scraps down to even up the ledger, the world would have been at rights.
Lew 2.1.2
The crucial thing was to demonstrate their independence from Labour. They did that — it's the reason why most of the folk around here hate and revile them (when they're not pretending pity and regret, of course). They were clear from the beginning that they would work in good faith with the FSA repeal and replacement with something more agreeable as the medium-term goal, and now — supposing they do in fact walk away — they'll be able to do so having done what they said they'd come to do. Not to succeed in that goal, since that was never within their control — but to push hard for it against a party which only a few years ago declared the FSA too generous.
As long as they do walk away, they can do so with heads held pretty high. They gave the government no reason to renege on the agreement to work in good faith, and yet, renege they did. Can't do much about that. National's bad faith toward tangata whenua may have been inevitable, but now it's proven, and it won't soon be forgotten.
And as Sarge says, they'd have gotten nothing in opposition, and demonstrated that Labour treat them like shite with impunity. There's no mana in that.
The crucial thing was to demonstrate their independence from Labour." it's like a teenager getting into drugs to teach their parents a lesson.
It's nothing praiseworthy.
and don't you accuse me of only pretending regret. my regret is genuine.
if they walk away, they will do so having given away so much and got bugger all back. and they will be admitting they were wrong all along.
and don't you fall into this 'always back the govt" authoritarian bullshit
At least now Labour will get the message — hopefully, anyway — that they can't crap all over their oldest and most loyal voting bloc without consequences. By the same token, the full extent of National's poor faith is also crystal clear — I think that's a result everyone can be happy with.
I don't think they should always back the government — only to the extent where it is compatible with their principles or where there's a chance of achieving a major policy concession. That was previously the case, is no longer the case, and now I'm calling for them to walk away just as strongly as you are. That's the difference: regardless of what might have been possible, you think they should have foregone it and sided with Labour on ideological and historical loyalty grounds. I don't. That's what I mean by independence.
Marty G 2.1.2.1.1.1
"That's the difference: regardless of what might have been possible, you think they should have foregone it and sided with Labour on ideological and historical loyalty grounds. "
no, lew. I didn't think they should take the deal because I could see this future. Everyone could but those in lalaland.
It wasn't so much that Labour wouldn't take MP seriously. There was a huge level of antagonism between them – specially Tariana and Helen. It turns out this partly because Tariana is essentially a Tory.
Also (though I think Labour were gutless about this) whenever Labour did anything that smacked of pandering to Maori, a racist National opposition used it to good effect – mobilising the racist heartland very effectively.
IF Laour had included the MP in government we never would have heard the end of it. Whanau Ora? Special rules for kura kaupapa? Can you imagine National's response to those initiatives?
I think it was politically untenable for Labour to include the MP in government and it points to the cynical racism of National that they did.
Lew 3.1
But now, that door is open. That's an important thing to come from this dalliance.
ianmac 3.2
Hence canning of Closing the Gaps?
The Voice of Reason 4
Not sure that I agree that they can't stay in Government, Marty. What reason do they have to leave? The Nats have followed the agreement to the letter, given them their 'review' of the F&S Act and even though the review has predictably turned out badly for the Maori Party, it is still not an excuse to break their word.
Whatever they do, this shows up the Maori Party MP's as naive at best, useful idiots at worse. It's all mana reduction from here on in.
Fisiani 5
The National Government is hororably offering to Repeal the F+S Act , give up government ownership and make the land public domain and restore to Maori the opportunity to test any claims to ownership in the Courts.
This would give the Maori Party their founding aim.
Any reasonable person would accept.
Marty G 5.1
iwi can't get title under National's offer. Public domain is crown ownership in drag.
"hororably"
Freudian slip? 😉
ghostwhowalksnz 5.3
So 12000 other titles for the foreshore are OK ( mostly pakeha or business), but Maori become a special class who cant get it.?
Who is 'honourable' that offers such a deal?
Tiger Mountain 5.3.1
So true Ghost, there are literally hundreds of such titles on peninsulas and beach front properties all around Northland, no go zones for Maori and pakeha alike, gated and fenced by the sometimes overseas based owners.
No claims of "ownership" are even considered. Maybe customary rights which is available now.
Craig Glen Eden 6
The Maori Party have some pretty deep divisions at present and I think it will only be with the retiring of Tariana that this Party will be able to move forward and align itself with Parties on the left.
Maori politics is very complicated and very personal. Ron's comment is correct (See above) and as a result Tariana has actively caused division between Labour and the Maori Party. Tariana is a Tory, this is why she never fitted in Labours ranks. At the time she entered politics she had no other strong vehicle for her to get to power, she went with Labour because that was her best vehicle at the time. National would certainly not of had anything to do with her. Many Maori gave this Party a chance but I think the Maori Party will have their work cut out for them in the next election.
For this Party to have any chance of survival Tariana will have to go she is not popular in her own Parties base out side of the Whanganui Region. Interesting times ahead for the Maori Party I think the Seabed and foreshore issue will prove a double edged sword for Tariana.
ghostwhowalksnz 7
Reading the MP press release, the MP are throwing up their hands, asking for a face to face meeting with Key.
You an't getting it.
Key is the salesman, sell the sizzle and then leave it to the hard faced bastards to trap you in the fine print.
There is no way he will meet with this Iwi leadership group. Not. Ever.
treat them as equals ?
Letterman yes . Maori No
You can almost feel their desperation, hiding behind a door , saying we have done all we were asked, now its up to ( insert scapegoat here) to take it further. Anyway the BMW is waiting to take me to ( insert minor function here).
Foreshore & seabed is MP signature issue ??
J Mex 7.1
Shrek the Sheep – Yes.
Maori – No
ianmac 8
As a sometimes viewer of Maori Television, I have watched recent interviews with leaders saying that Public Ownership is going to be Ok. From that small step comes gradual improvement to "title" and thence to commercial operations like aquaculture. Small steps but forward.
This may not be the falling out of Nat v MP at all.
Its a good negotiation tactic to say we are walking away.
But while the MP may say yes, the iwi ( its 'their' foreshore) are putting a line in the sand as they do seem to not be able to get what private title all ready have.
The reality is Nationals first offer is Crown ownership with a bone carving necklace wrapped around it. Next up they will offer muskets and blankets to go with it.
J Mex 9
The problem for Labour is that their first offer to the MP was an extended middle finger.
Yeah. They didnt get them into government on a promise of a 'new' deal either. At least MP knew where they stood. The iwi groups can see now where MP support gets them . SFA as Turia wont walk away
Pat to Nic the NZer on | {
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In gridiron football, the chain crew (commonly known as the "chain gang") is a crew that manages signal poles on one of the sidelines. There are three primary signal poles: the "rear rod" that marks the beginning of the current set of downs, the "forward rod" that marks the line to gain, and the "box" that marks the line of scrimmage. The two rods are attached at the bottom by a chain exactly ten yards long, while the "box" displays the current down number.
The chain crew, under the direction of the head linesman/down judge, signals the officials' decisions; it does not make decisions. Players look to the chain crew to see the line of scrimmage, the down number, and the line to gain. Officials may rely on the chain crew after a play (incomplete pass or penalty) whose outcome depends on the original spot of the ball. This also includes bringing the chains onto the field whenever an accurate measurement is needed to determine if a first down has been made.
Members
Three members of the chain crew hold poles upright. The bottom of each pole is placed along a sideline to denote a line across the gridiron to the opposite sideline.
A "rod man" holds the "rear rod" that marks the beginning of the current set of downs.
Another "rod man" holds the "forward rod" ten yards toward the defense's goal-line from the rear rod. This marker indicates the line to gain, which the offense must reach in their series of four downs in order to retain possession of the ball. The two rods (sometimes known as "sticks") are attached at the bottom by a chain exactly ten yards long. The chain is always taut so that the rods are ten yards apart.
The "box man" holds a pole that marks the line of scrimmage.
There may be additional chain crew members. A "clip man" is discussed below. In the NFL, additional chain crew members have additional tasks, such as to relieve the line judge of the clerical task of recording all assessed penalties. Despite the use of "man" in the colloquial terms for the chain crew positions, women can perform any of them.
Members of the chain crew are usually picked by the offices of the home team instead of the league or conference. In the NFL, members of the chain crew must have credentials entitling them to access to the field, and must wear white shirts. The home team pays them; some teams pay an hourly wage and others pay a flat rate to work a game.
The chain crew does not wear protective gear as players do. A routine instruction by officials to the chain crew is to withdraw or drop their signals, and move back, if the play comes toward them so as to endanger them. Often, the signals use bright orange color, are padded, and have break-away components for safety.
Location
For games at all levels except the NFL, the chain crew operates on the side of the field opposite the press box (usually the visiting team's sideline).
In the NFL, the chain crew switches sides at halftime; the referee determines their initial placement.
In the NCAA, the chains are located opposite the press box for the entire game. In the first half, the line judge is located opposite the press box and supervises the chain crew, with the head linesman on the press box side of the field. In the second half, the head linesman and line judge swap sides of the field like in the NFL, with the linesman supervising the chain crew. This practice started in 2014.
In the NFL and other venues where there is a zone behind the sidelines, all three poles are placed somewhere along the back line of this zone. Otherwise, the poles are placed along the sideline.
Auxiliary chain crew
For professional and college football games, an auxiliary chain crew operates on the opposite side of the field, supervised by the line judge. Their presence lets players and officials look to either side of the field for information. The auxiliary chain crew also includes the drive start indicator, which is placed at the beginning of a team's drive and stays there until the team loses possession. This indicator is only used for statistical purposes to calculate the distance of each drive. It looks similar to a "stick" and has an arrow (or occasionally a large "X") that points in the direction the offensive team is going.
The NFL previously used an additional fourth chain crew member, which held a rod marked with an X to mark the spot of the last drive start. The X marker was eliminated in 2018.
Operations
At the start of a series of downs, the linesman stands so that the heel of one foot marks the initial line of scrimmage. The box man places his indicator to mark this position and sets the box to display "1". The operator of the rear rod marks the same position, while the other rod man moves ten yards toward the defense's goal line to mark the line to gain.
The linesman, the box man, or a fourth member of the chain crew attaches a "clip" to the chain to line up with the rear edge of the closest five-yard line to the rear rod. A device on the clip indicates which numbered line this is. The clip and the device let the chain crew restore the position of the rods after a mishap. In leagues such as the NFL with Instant Replay, there may be multiple clips to let the rods be repositioned after a play is reviewed and reversed.
After a typical play, the box man increments the displayed number and realigns that pole to the new line of scrimmage, again as directed by the linesman. After a play that results in a first down, all three members move and reset their signals to mark a new series of downs.
The chain crew must not move until the referee or linesman signals whether the play finished without a penalty. On a penalty, the chain crew stays put so that the officials can see the original state. When the referee and linesman walk off the appropriate number of yards, the box man moves as well. The box man does not change the number displayed, except on a penalty that results in a loss of down. On a penalty that results in a first down, the entire chain crew moves and resets.
When possession of the ball switches to the other team, the forward rod becomes the rear rod and vice versa to minimize the distance the rod men have to move. However, at the end of the first and third quarters, when players switch directions on the field, the chain crew also moves (for example, a marker may move from one 32-yard line to the other 32-yard line). The rear rod man moves past the forward rod man and continues to mark the start of the series of downs, in the new orientation. The linesman and other officials supervise this movement, using one or more clips to exactly reposition the chains.
On plays where there is no line to gain (a series of downs that starts within 10 yards of the goal line, a try after touchdown, or a kickoff), the rod men lower or lay down their signals, but the box man continues to mark the line of scrimmage.
On-field measurements
The chains are brought onto the field whenever the referee needs an accurate measurement to determine if a first down has been made. A team may also request an accurate measurement to determine how far they have to reach for the first down.
5-yard mark
Before the game, many linesmen attach a piece of tape at the midpoint of the chain. The linesman can compare the line of scrimmage to this mark at the start of a play and know whether a 5-yard penalty against the defense will result in a first down. If so, the linesman's typical hand signal to the line judge across the field is to extend the arms with the thumbs pointing toward one another. Such a gesture with thumbs pointing away signals that there are more than 5 yards to gain.
History
All levels of organized football use the chain crew. One notable exception at the professional level was the World Football League of 1974 to 1975, which used the "Dicker-rod," a proprietary, 90-inch stick that allowed measurements to be made with one person instead of three. The Dicker-rod was never used outside the WFL.
The "box" (down marker) has evolved over time. In the pre-television era, it was a rod (shorter than the height of the operator) with a triangular pointer that rotated to show the official the down number. It was replaced with a much larger, two-sided flipper system when television became widespread; flipper-style down markers are still in use in scholastic and amateur football. A more modern model is the Dial-a-Down, in which compact levers display a new down number over the entire face of the "box"; this model is used at most college and professional games. Electronic down markers using LEDs are emerging as the next advance. However, further application of technology to measure the lengthwise position of the football, such as sensors inside the football, may be resisted based on affection for the human element. Early attempts and proposals to use precision automatic chain instruments were hindered both by costs and potential hazards (early proposals required metal rails; a 1990s system used visible lasers). Lazser Down, a system that uses wideband radio waves to precisely spot and measure distances, has seen some rollout in college football, the Alliance of American Football and the XFL.
Notes
References
Further reading
American football terminology | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,638 |
Jesup is a railroad station in the city of Jesup, Wayne County, Georgia, United States. Located at 176 Northwest Broad Street, the station is currently in use for service on Amtrak's Silver Meteor and bypassed by their Silver Star. Amtrak service began on October 1, 1979, when the Silver Meteor was realigned away from a station on State Route 32 at Thalmann, Georgia.
The station was built in 1899 as part of the Atlantic Coast Line Railroad. In February 2003, the station was damaged in a fire and subsequently boarded up as the town sought funds for restoration. In 2005, Jesup received $836,000 in federal funds after the rehabilitation was designated a High Priority Project under the federal transportation bill. The city also purchased the building and land from CSX Transportation, owner of the adjacent railroad line. The city decided to return the building to its early 20th-century appearance.
The completion of the rehabilitation project was celebrated in October 2012 during the city's annual Arch Festival, an event started in 2003 to highlight the renewed downtown. In addition to a passenger waiting room, the depot now also includes a community meeting space and new offices and a welcome center for the Wayne County Board of Tourism. The interior is decorated with historic photographs and memorabilia that demonstrate the strong ties between Jesup and the railroads. A formal ribbon-cutting ceremony was held on March 8, 2013 and included speeches by the mayor and an Amtrak representative.
Between January 24 and October 14, 2022, the Silver Star temporarily stopped in Jesup due to the suspension Silver Meteor, which is normally the only train that stops at that station. This was due to a resurgence of the Omicron variant of COVID-19 as well as a further delay caused by Hurricane Ian.
References
External links
Jesup Amtrak Station (USA Rail Guide -- Train Web)
Jesup ACL Depot (Georgia's Railway History & Heritage)
Amtrak stations in Georgia (U.S. state)
Atlantic Coast Line Railroad stations
Buildings and structures in Wayne County, Georgia
Transportation in Wayne County, Georgia | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,948 |
\section{Introduction}
A set of dispersion relations for $\pi\pi \to \pi\pi$
scattering amplitudes incorporating crossing symmetry
were presented by Roy in 1971 \cite{Roy71} (hereafter called the Roy equations).
Two subtractions were used for faster convergence of the dispersive
integrals. These equations are a very efficient tool
in testing the $\pi\pi$ experimental data.
In the last few years, several analysis of $\pi\pi$ amplitudes using
Roy equations have appeared with different aims. For instance, to
predict the low energy $S$ and $P$ waves below 800 MeV with the aid of
Chiral Perturbation Theory
(ChPT), which is used to fix the threshold behavior of amplitudes \cite{A4,CGLNPB01}.
Or, for example, to eliminate the long standing "up-down"
ambiguity in scalar-isoscalar $\pi\pi$ amplitudes below 1 GeV \cite{klr}.
Later on, they were used by our group, together with forward dispersion relations (FDR)
to describe data and also test predictions of ChPT \cite{KPYII,KPYIII}.
All these works provide very precise
determinations of $\pi\pi$ amplitudes for the $S$ and $P$ waves
below about 1 GeV and very precise predictions or determinations of scattering
lengths and parameters of the $\sigma$ meson \cite{KPYIII,Caprini,GPY}.
More recently, together with our FDR and Roy
equations analyses \cite{KPYIII} we have developed
a set of once subtracted
dispersion relations that also incorporate $\pi\pi$ crossing symmetry
(hereafter called GKPY).
Due to the single subtraction, the higher $\pi\pi$ partial waves
and the high energy region contributions are less
suppressed in these equations than in Roy's, although
integrals in the GKPY equations still converge.
In this presentation we briefly analyze and
compare the structure and cancellations
that occur in Roy equations versus those in the GKPY eqs.
\section{Twice subtracted dispersion relations (Roy equations).}
Roy equations can be expressed as a sum
\begin{equation}
{\rm Re} f_l^I(s) = ST(s) + KT(s) + DT(s),
\label{Decomposition}
\end{equation}
where $ST(s)$, $KT(s)$ and $DT(s)$ are called subtraction, kernel and driving
terms, respectively.
The ${\rm Re} f_l^I(s)$ on the left hand side is called ``output'' amplitude
throughout this paper
and can be calculated for the $S$ and $P$ waves up to about 1 GeV.
The subtraction terms read
\begin{equation}
ST(s)= a_{0}^{0}\delta_{I0} \delta_{\ell 0} + a_{0}^{2}\delta_{I2} \delta_{\ell 0} +
\displaystyle \frac{s-4m_{\pi}^2}{12}(2a_{0}^{0}-5a_{0}^{2})
(\delta_{I0}\delta_{\ell 0}+
\frac{1}{6}\delta_{I1}\delta_{\ell 1}
-\ \frac{1}{2}\ \delta_{I2}\delta_{\ell 0})
\label{ST.Roy}
\end{equation}
where $a_{0}^{0}$ and $a_{0}^{2}$ are the $S0$ and $S2$
scattering lengths. Let us remark that
the $ST(s)$ contain a piece that grows with $s-4m_\pi^2$.
The $KT(s)$ are singular integrals of some known kernels $K_{\ell \ell^\prime}^{I I^\prime}(s,s')$ multiplied by
imaginary parts of the ``input'' amplitudes ${\rm Im }f_{\ell'}^{I^\prime}(s')$
\begin{equation}
KT(s) = \displaystyle \sum\limits_{I'=0}^{2}
\displaystyle \sum\limits_{\ell '=0}^{1}
\hspace{0.25cm}-\hspace{-0.55cm}
\displaystyle \int \limits_{4m_\pi^2}^{s_{max}}\ ds'
K_{\ell \ell^\prime}^{I I^\prime}(s,s') \, \mbox{Im }f_{\ell'}^{I^\prime}(s').
\label{KT.Roy}
\end{equation}
For twice subtracted dispersion relations the kernels are proportional to
$1/s'^2(s'-s)$.
In our analysis
(see for example \cite{KPYIII}) $s_{max}^{1/2} = 1.42$
GeV, which is the maximum energy
for which we can
parameterize experimental $S$ and $P$ wave
data in terms of phase shifts and inelasticities.
The so called driving terms $DT(s)$ collect
the $s^{1/2} > 1.42$ GeV contributions
from all waves -- parameterized in terms of
Regge theory -- together with
the contributions from $\ell\geq 2$ partial waves below 1.42 GeV.
Our fits of $\pi\pi$ amplitudes to
data are then constrained to minimize, within uncertainties,
the difference between
``input'' and ``output'' amplitudes for the $S$, and $P$ waves at 25
equidistant energy values $s_i^{1/2}$ below 1 GeV~\cite{KPYIII}.
A similar method using only forward dispersion relations
was used in~\cite{PY} to show that
many of the presently available experimental data sets dot not fulfill
well enough the analyticity constraints.
\section{Once subtracted dispersion relations (GKPY equations)}
The general structure of the GKPY equations is similar to that of the Roy
equations in Eq. (\ref{Decomposition}).
However, the
subtraction terms are now constant for each wave
and are expressed as combinations of scattering lengths
\begin{equation}
ST(s) = \sum_{I'}C^{st}_{II'}a_0^{I'}
\label{ST.GKPY}
\vspace*{-0.3cm}
\end{equation}
with
$a_0 = (a_0^0, 0, a_0^2)$ and $C^{st}$ the usual crossing matrix.
Since there is just one subtraction, the integral kernels
are now proportional to $1/s'(s'-s)$. Consequently,
the high energy contributions to kernel and particularly to the
driving terms are now
less suppressed compared with the Roy equations case.
Nevertheless, we will see in the next section
that the effect of driving terms is still
smaller than the kernel terms for the $P$, $S2$ and $S0$
waves in almost the whole energy region of interest,
which allows us to obtain a reliable calculation.
\section{Comparison of the Roy and GKPY dispersion relations}
In Table (\ref{Table.Thr.Exp}) we compare
the structure of the different terms of Roy and GKPY equations
for threshold parameters (TP), defined as:
\begin{equation}
Re f_{\ell}^I(s\approx 4m_{\pi}^2) = (s-4m_{\pi}^2)^{\ell} \left[a_{\ell}^I + b_{\ell}^I(s-4m_\pi^2) + ...\right].
\label{Thr.Exp}
\end{equation}
\begin{table}[b!]
\begin{center}
\begin{tabular}[b]{|c|c|r|c|c|c|}
\hline
& & \multicolumn{2}{|c|}{Roy} & \multicolumn{2}{|c|}{GKPY} \\
wave & TP & \multicolumn{1}{|c|}{$ST$} & $KT \& DT$ & $ST$ & $KT \& DT$ \\
\hline
&&&&& \\
$S0$ &$a_0^0$& $a_0^0 + \alpha(s-4)$ & $\beta(s-4)$ &
$a_0^0 + 5a_0^2$ & $\delta(s-4)-5a_0^2 $\\
&&&&& \vspace{-0.3cm}\\
$P$&
$0$ & \hspace{0.8cm}$\alpha'(s-4)$ & $\beta'(s-4)$ &
$a_0^0 - \frac{5}{2}a_0^2$ &$\delta'(s-4)-a_0^0 + \frac{5}{2}a_0^2$\\
&&&&& \vspace{-0.3cm}\\
$S2$&
$a_0^2$ & $a_0^2 +\alpha''(s-4)$ & $\beta''(s-4)$ &
$a_0^0 + \frac{1}{2}a_0^2$ & $\delta''(s-4)-a_0^0+\frac{1}{2}a_0^2 $ \\
&&&&& \\
\hline
\end{tabular}
\end{center}
\vspace{-0.5cm}
\caption{Comparison of the threshold expansion
parameters (TP) of the "output" amplitudes for Roy and
GKPY equations ($m_\pi$ units). Greek letters stand for constants
whose precise value is irrelevant for the discussion. Note that
the GKPY value at threshold is obtained from a
cancellation between $ST,KT$ and $DT$ terms.
}
\label{Table.Thr.Exp}
\end{table}
As is seen from the Table (\ref{Table.Thr.Exp})
in the case of Roy equations, not only the linear terms in $ST(s)$,
but also the whole kernel and driving terms vanish at
$s=4m_{\pi}^2$.
Thus, the constant terms in $ST(s)$ are the ones that ensure
the correct values of the threshold parameters in the "output" amplitudes.
In contrast, for the GKPY equations
the $KT(s)$ and $DT(s)$ do not vanish at
threshold and it is a combination of their nonzero constant parts
with the $ST(s)$ terms that yield the correct threshold value.
Hence, GKPY uncertainties around threshold are expected to be larger
than for Roy equations.
In Fig.~(\ref{fig:decomposition})
we show the decomposition of Roy and GKPY equations
into subtraction, kernel and
driving terms.
Error bands are obtained from a Monte Carlo
with $10^5$ Gaussian samplings,
within three standard deviations of their central values,
of all parameters used to describe
the different input (for details see \cite{KPYIII}).
Let us remark that, above
$\sqrt{s}\simeq 450\,$MeV ($s\simeq10$ in $m_\pi$ units),
the $ST(s)$ and $KT(s)$ terms
in Roy equations suffer a very strong cancellation to give the total
output amplitudes that, as seen in Fig.(\ref{fig:Results}), satisfy
$\mbox{Re } f^I_{\ell} < 0.6$ (note that the vertical
scale for the Roy equations figures is much bigger than 1).
In contrast, for GKPY equations, the kernel terms are
dominant and there is no such strong cancellation. It is also clear from Fig.(\ref{fig:decomposition})
that, above $\sqrt{s}\simeq400\,$ MeV,
the errors in Roy equations are significantly bigger
than those in the GKPY ones.
The main source of Roy equations uncertainties
is the experimental error on $a_0^{2}$, that propagates
through a term in $ST(s)$ proportional to $s$.
In contrast,
the $ST(s)$ and their errors in the GKPY equations are constant.
Fig.(\ref{fig:Results}) compares the size of the uncertainties for
a preliminary data fit constrained to satisfy
forward dispersion relations,
sum rules,
Roy and GKPY equations (see \cite{KPYIII}).
We also give preliminary values of an average $\chi^2/NP$
for each wave, where $NP = 29$ is number of points where "input" and
"output" amplitudes are compared.
In conclusion, for the same input, GKPY equations
have much smaller errors than standard Roy equations
above $\sqrt s \approx $ 400 MeV and
thus they become a
very promising tool to obtain a precise
data analysis of $\pi\pi$
amplitudes in the 400 to 1100 MeV region.
\begin{figure}[ht!]
\vspace{9pt}
\includegraphics*[width=6.0cm]{./figures/Roy.Decomp.MC2.S0.eps}
\includegraphics*[width=6.0cm]{./figures/Paco.Decomp.MC2.S0.eps}
\includegraphics*[width=6.0cm]{./figures/Roy.Decomp.MC2.P1.eps}
\includegraphics*[width=6.0cm]{./figures/Paco.Decomp.MC2.P1.eps}
\includegraphics*[width=6.0cm]{./figures/Roy.Decomp.MC2.S2.eps}
\hspace{0.5cm}\includegraphics*[width=6.0cm]{./figures/Paco.Decomp.MC2.S2.eps}
\caption{Subtraction ($ST$), kernel ($KT$) and driving ($DT$) terms for
the $S0$, $P$ and $S2$ waves from Roy equations (left panel) and
from the GKPY ones (right panel).
Dashed bands denote the errors of these terms. Note that we use $m_\pi$ units.}
\label{fig:decomposition}
\end{figure}
\begin{figure}[ht!]
\vspace{9pt}
\includegraphics*[width=6.2cm]{./figuresfromRuben/cdf-roys0all.eps}
\includegraphics*[width=6.2cm]{./figuresfromRuben/cdf-pacos0all.eps}
\vspace{0.5cm}
\includegraphics*[width=6.2cm]{./figuresfromRuben/cdf-roypall.eps}
\includegraphics*[width=6.2cm]{./figuresfromRuben/cdf-pacopall.eps}
\vspace{0.5cm}
\includegraphics*[width=6.2cm]{./figuresfromRuben/cdf-roys2all.eps}
\includegraphics*[width=6.2cm]{./figuresfromRuben/cdf-pacos2all.eps}
\caption{Comparison of preliminary results from
a data fit constrained to satisfy Forward dispersion relations,
Roy and GKPY equations for the $S0$, $P$ and $S2$ waves.
The dark bands show errors of these equations.
Dashed and solid lines represent "input" and "output"
amplitudes respectively. The $\bar d^2$ are averaged values of
$\chi^2$ for the Roy or GKPY equation corresponding to given wave.}
\label{fig:Results}
\end{figure}
\vspace{-0.1cm}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 252 |
namespace Silphid.Showzup
{
public interface IPostShow
{
void OnPostShow();
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 6,475 |
Getting Started Lists of Recommendations Search Recommendations Hematology Critical Care – Regular diagnostic tests
Critical Care Societies Collaborative – Critical Care
View all recommendations from this society
Don't order diagnostic tests at regular intervals (such as every day), but rather in response to specific clinical questions.
Many diagnostic studies (including chest radiographs, arterial blood gases, blood chemistries and counts and electrocardiograms) are ordered at regular intervals (e.g., daily). Compared with a practice of ordering tests only to help answer clinical questions, or when doing so will affect management, the routine ordering of tests increases health care costs, does not benefit patients and may in fact harm them. Potential harms include anemia due to unnecessary phlebotomy, which may necessitate risky and costly transfusion, and the aggressive work-up of incidental and non-pathological results found on routine studies.
These items are provided solely for informational purposes and are not intended as a substitute for consultation with a medical professional. Patients with any specific questions about the items on this list or their individual situation should consult their physician.
How The List Was Created
This document was prepared as an initiative of the Critical Care Societies Collaborative, which includes the American Association of Critical-Care Nurses, the American College of Chest Physicians, the American Thoracic Society and the Society of Critical Care Medicine. Each of these four societies was invited to nominate up to three members to join the taskforce. The final taskforce included 10 members representing all four societies and the disciplines of internal medicine, surgery, anesthesiology, emergency medicine and critical care nursing. Taskforce members initially proposed 58 items for consideration. The taskforce evaluated each item on five criteria (evidence, prevalence, cost, relevance, innovation), and agreed to narrow the list to 16 items. The taskforce debated the conceptual merits of these 16, and selected nine in which to pursue in-depth evidence reviews and consultations with external content experts. Taskforce members then independently scored each item on a scale from 1-9, rating each item on its overall impact as well as on each of the five criteria. The five items with the best mean overall scores were retained in the "penultimate" list. The taskforce then reviewed and edited the wording of items on the penultimate list, and submitted it to the 4 societies' executive committees. The executive committees sought feedback from additional experts in the field, debated the items, and provided written comments to the taskforce. The taskforce deliberated and incorporated these suggestions where appropriate to create the final list, resolving any conflicts through discussion. All four societies endorsed the final list.
Members of the taskforce were: Scott D. Halpern, MD, PhD (Chair), Deborah Becker, PhD, RN, J. Randall Curtis, MD, MPH, Robert Fowler, MD, Robert Hyzy, MD, Jeremy M. Kahn, MD, MSc, Lewis Kaplan, MD, Nishi Rawat, MD, Curtis Sessler, MD and Hannah Wunsch, MD, MSc.
The disclosure and conflict of interest policies for the American Association of Critical Care Nurses, American College of Chest Physicians, the American Thoracic Society and the Society of Critical Care Medicine can be found at www.accn.org, www.chestnet.org,www.thoracic.org and www.sccm.org respectively.
Flabouris A, Bishop G, Williams L, Cunningham M. Routine blood test ordering for patients in intensive care. Anaesth Intensive Care. 2000;28(5):562–5.
Ganapathy A, Adhikari NKJ, Spiegelman J, Scales DC. Routine chest x-rays in intensive care units: A systematic review and meta-analysis. Crit Care. 2012;16(2):R68.
May TA, Clancy M, Critchfield J, Ebeling F, Enriquez A, Gallagher C, Genevro J, Kloo J, Lewis P, Smith R, Ng VL. Reducing unnecessary inpatient laboratory testing in a teaching hospital. Am J Clin Pathol. 2006;126(2):200–6. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,245 |
\section{Introduction}
Atrial fibrillation (AF) is the most common sustained cardiac arrhythmia, characterized by a rapid and irregular contraction of the upper chambers of the heart, the atria. AF affects more than 33 million people worldwide, is associated with great increases in morbidity and mortality, and typically has a negative impact on patients' quality of life.
Although AF is mainly managed with medical therapy, catheter ablation is arguably the gold standard treatment to directly terminate AF in selected patients. In their current form, ablations are only first-time effective in approximately $50\%$ of AF patients \cite{Ganesan2013}.
Treatment efficacy for AF could be greatly increased if biomarkers capable of characterising atrial function and predicting treatment outcome were available. Left atrial (LA) dimensions and shape have been shown to be reasonable predictors of post-ablation patient outcome
\cite{Varela2017}. It is expected that dynamic characterisations of atrial dimensions and volumes across the cardiac cycle may be even more informative \cite{Hoit2017}. In particular, LA ejection fraction (EF) and active atrial contraction ejection fraction (aEF) contain important clinical information that can contribute to the management of AF.
The LA EF characterises the LA global function across the cardiac cycle, whereas the aEF assesses the LA pump function, which is likely to provide important additional clues about atrial tissue health. Both these biomarkers rely on ratios of LA volumes across the cardiac cycle. LA volumes are usually estimated by applying standard formulae derived from assumptions on the LA shape obtained from 2D atrial echocardiography or dynamic (CINE) Magnetic Resonance Images (MRI) \cite{ERBEL,UJINO20061185}. Volume estimation from 3D images is expected to be more accurate and precise. Furthermore, aEF relies on the identification of the onset of active atrial contraction (preA), which is difficult to perform visually in a single 2D view.
CINE MRI combines good spatial and temporal resolution with large cardiac coverage and is thus ideally suited for assessing LA function. Nevertheless, detailed volumetric temporal analyses of atrial volumes are not currently available for clinical use for two key reasons. First, atrial CINE MRI images are typically acquired on single-slice 2-chamber and 4-chamber views, which do not sample the full atrial volume \cite{Kowallick2015}. Second, reliable automatic techniques for segmenting the atria in short axis views across the entire cardiac cycle are not yet available. This is in contrast with the segmentation of ventricular structures from short axis CINE MRI and the LA in 2- and 4-chamber views~\cite{Chen2019}. We expect that automatic processing tools for short axis atrial images may lead to an increased interest in imaging this chamber in this orientation.
In this work, we propose a dedicated neural network for fully automatic SEGmentation of the left Atrium based on a convolutional neural Network (SEGANet) to address this important clinical gap. We acquired short-axis CINE images with full ventricular and atrial coverage and used SEGANet to segment the LA. The quality of the SEGANet LA segmentation is assessed using the Dice coefficient (DC), median contour distances (MCD) and Hausdorff distances (HD). We additionally compare the SEGANet results with the inter-observer variability of manual segmentations. To demonstrate the clinical utility of our method, we use SEGANet to estimate LA volumes across all cardiac phases and automatically calculate LA EFs and aEFs in both healthy subjects and AF patients.
\section{Methods}
\subsection{Data Acquisition}
Short axis CINE MR image stacks with full cardiac coverage were acquired in a 1.5T Philips Ingenia scanner with a 32-channel cardiac coil. Imaging was performed in 60 AF patients (31-72 years old, $75 \%$ male) and 12 healthy volunteers (24-36 years old, $50 \%$ female) under ethical approval and following informed written consent.
A 2D bSSFP protocol (flip angle: $60^{\circ}$, TE/TR: 1.5/2.9 ms, SENSE factor 2) was used. Images were captured with ECG-based retrospective gating with a typical field of view of 385 x 310 x 150 mm$^3$, acquisition matrix of 172 x 140 and slice thickness of 10 mm. Images were reconstructed to a resolution of 1.25 x 1.25 x 10 mm$^3$ and 30-50 cardiac phases with $60-70\%$ view sharing. These acquisitions provide full coverage of the ventricles and atria, with typically 4-6 slices covering the atria. Each slice was acquired in a separate breath hold.
Due to the large slice thickness in all datasets, it can be difficult, even for an expert, to identify the separation between the atria and ventricles.
In order to solve this challenge, we used a pre-trained left ventricular (LV) segmentation network \cite{Kerfoot2018} to identify the slices containing ventricular tissue.
The most basal atrial slice was automatically identified as the slice contiguous to the top ventricular slice segmented by this LV network.
Ground truth (GT or M1) segmentations were obtained by a consensus of two medical experts, who manually segmented the LA on a slice by slice basis at 3 phases of the cardiac cycle.
The LA appendage was included in the segmentation, but the pulmonary vein insertions were not.
\subsection{SEGANet}
The proposed neural network is based on the U-Net architecture~\cite{DBLP:journals/corr/RonnebergerFB15} with the following modifications: 1) the addition of residual units~\cite{DBLP:journals/corr/HeZR016} throughout the encode and decode paths, which prevent vanishing gradients by allowing some measure of the original input to be included in each layer's output; 2) instance layer-normalization, which minimises the influence outlier images may have in the whole batch; 3) Parametric Rectified Linear Unit (PReLU) activation, which allows the network to learn from negative values.
The network is built as a stack of layers which combine the encode and decode paths as illustrated in Figure \ref{fig:unet}. Four layers are stacked together using convolutions with a stride of 2 to downsample data in the encode path, and with output tensors to the layers below with channel dimensions of 16, 32, 64, 128, and 256.
The network was trained for LA segmentation on short axis CINE MRI in $50,000$ iterations with mini-batches of 300 slices drawn randomly from the 715 slices of the training dataset.
We used a binary formulation of the Dice loss function
and the Adam optimiser
with a learning rate of 0.0001.
To extract more generalised information from our relatively small dataset and to regularise the network to prevent overfitting, we used a number of randomly-chosen data augmentation functions to apply to each slice. These data augmentations were chosen to replicate some of the expected variation in real images without modifying the cardiac features of interest. They include: 1) rotations, translations and flips; 2) croppings and rotations; 3) additive stochastic noise; 4) k-space corruption to simulate acquisition artefacts;
5) smooth non-rigid deformations encoded using free-form deformations
and 6) intensity scalings by a random factor.
\begin{figure}[t]
{\includegraphics[width=0.75\linewidth]{unet}\includegraphics[width=0.18\linewidth]{unet_stack}}
\caption{{The proposed LA segmentation network SEGANet is based on a U-Net architecture. The segmentation network is built as a stack of layers (shown on the right), which combine the encode path of the network on the left and the decode path on the right. Subsequent layers, or the bottom connection, are denoted by ``Next Layer''. The bottom connection is composed of a single residual unit including two sets of convolution/normalisation/regularisation sequences.}} \label{fig:unet}
\end{figure}
\subsection{Data Analysis}
In order to assess the quality of the automatic segmentations, an additional medical expert was asked to provide manual LA segmentations (M2) in 13 AF patients. Segmentation quality metrics (DC, HD and MCD) were estimated relative to the ground truth for both the SEGANet segmentations and the manual segmentations M2.
We also estimated the agreement between the two sets of manual segmentations.
For a complete visualisation of the heart volume variations throughout the cardiac cycle, LA volumetric time curves were plotted. Using these, maximal ($V_{max}$) and minimal ($V_{min}$) LA volumes, as well as the LA volume at the onset of atrial contraction ($V_{pre A}$) were automatically computed. EF and aEF were also estimated using $ \textrm{EF} = \frac{V_{max}-V_{min}}{V_{max}} \times 100$ and $ \textrm{aEF} = \frac{V_{pre A}-V_{min}}{V_{pre A}} \times 100$.
LA EFs and aEFS obtained from SEGANet segmentations were calculated for both AF patients in sinus rhythm and healthy subjects. We used paired Student t-tests to assess whether we could detect a significant difference in these metrics between the two groups.
\begin{figure}[t]
\begin{center}
\includegraphics[width=1\linewidth, height=3.5cm]{atria_seg.png}
\caption{Segmentations obtained with the proposed method for one representative subject during atrial diastole, overlaid on the CINE \textbf{a)} short axis, \textbf{b)} pseudo 2-chamber, and \textbf{c)} pseudo 4-chamber views. The acquired short axis CINE image stacks include both ventricles and atria.}
\label{fig:3D}
\end{center}
\end{figure}
\section{Results}
\hspace{1em} SEGANet generated very good quality LA segmentations. This can be qualitatively observed in Figure \ref{fig:3D}, which depicts, in three orthogonal views, the CINE MRI for one representative patient overlaid with the automatic LA segmentations in red.
Figure \ref{fig:abs2} shows that automatic segmentations are on par with manual segmentations, with DC: $0.93 \pm 0.04$, HD: $4.59 \pm 2.06$ mm; MCD: $0.75 \pm 0.31$ mm for the SEGANet segmentations when compared to the GT. These values are comparable to those of the additional manual segmentations M2, further highlighting the good performance of the network (Figure \ref{fig:abs2}).
In previous studies, the network for LV segmentation had demonstrated accurate results when it was tested using other datasets \cite{Kerfoot2018} and the method allowed us to automatically select the slices that covered the atria.
The obtained LA volumes across the cardiac cycle for AF patients ($V_{min}: 79.40 \pm 25.34$ mL; $ V_{max}: 111 \pm 24.00$ mL; $ V_{pre A}: 103.40 \pm 25.34$ mL) and for healthy subjects ($V_{min}: 22.43 \pm 25.34$ mL; $ V_{max}: 44.23 \pm 24.73$ mL; $ V_{pre A}: 35.47 \pm 19.48 $ mL) show high inter-subject variability and agree well with the literature \cite{MORI201189}.
The LA volume varies smoothly across the cardiac cycle, further suggesting the good quality of segmentations throughout the different cardiac phases (Figure \ref{fig:h_vs_p}).
Regarding the LA EF, we obtained $31.1\% \pm 9.9 \%$ in AF patients and $49.8\% \pm 7.6 \%$ in healthy volunteers, which is in good agreement with published echocardiographic and 2D CINE MRI values \cite{Chubb2018,MORI201189,DELGADO20081285}.
The obtained values for aEF (AF patients: $24.3\% \pm 9.0 \%$, healthy volunteers: $37.9\% \pm 10.1 \%$) are also in accordance with the literature
\cite{Kowallick2015,MORI201189,DELGADO20081285}.
As expected, both LA EF and aEF are significantly higher ($p<1\textrm{e}^{-4}$ and $p<1\textrm{e}^{-7}$, respectively) in healthy subjects than in AF patients (Figure \ref{fig:h_vs_p}).
\begin{figure}[t]
\centering
\includegraphics[width=1\textwidth]{box_plots_seg_2.png}
\caption{ \textbf{a)} Dice coefficient, \textbf{b)} Hausdorff distance and \textbf{c)} mean contour distance comparing automatic (SEGANet) and manual (M2) LA segmentations with the ground truth (GT/M1) in 13 subjects. \textbf{d)} Contours indicating the results of the manual and automatic LA segmentations in a representative slice: yellow is the SEGANet automatic segmentation, red is the manual M2 segmentation, and green is the GT/M1.}
\label{fig:abs2}
\end{figure}
\begin{figure}[h]
\centering
\includegraphics[width=1\textwidth]{h_vs_p_4.png}
\caption{Left atrium (LA) volume throughout the cardiac cycle for two representative subjects: \textbf{a)} an AF patient and \textbf{c)} an healthy subject . Three LA volumes are indicated: the maximal volume ($V_{max}$), the minimal volume ($V_{min}$) and the second peak volume, corresponding to the volume at the onset of the P wave, just before active atrial contraction ($V_{pre A}$). LA EF and aEF values are shown in each subfigure. Moreover, box plots of \textbf{b)} aEF and \textbf{d)} LA EF for AF patients and healthy subjects show that values are significantly higher in healthy subjects than in patients (LA EF p-value: $<1\textrm{e}^{-4}$; aEF p-value $<1\textrm{e}^{-7}$).}
\label{fig:h_vs_p}
\end{figure}
\section{Discussion}
\hspace{1em}
We present SEGANet, a
convolutional neural network that allows automatic LA segmentation in short-axis CINE MRI across the whole cardiac cycle. To the best of our knowledge, there are currently no
fully automatic segmentation methods designed for this important clinical application. We demonstrate the clinical potential of our technique by automatically estimating atrial biomarkers of interest, such as atrial ejection fractions.
The proposed method shows a very good segmentation performance for the LA (Figures \ref{fig:3D}-\ref{fig:abs2}), on par with the performance of other neural networks: for the segmentation of ventricular structures in CINE-MRI \cite{Chen2019};
and for LA segmentations in static MRI with a different resolution and contrast to ours. In particular, our results for CINE MRI compare well with the metrics for the segmentation of delayed enhacement MRI in the STACOM 2018 Left Atrial Segmentation Challenge (DC: $0.90 \pm 0.93$, HD: $14.23 \pm 4.83$ mm)\cite{inbook} .
In this work, we rely on a modified short axis CINE MRI acquisition that provides volumetric and functional information for the LA, as well as for the ventricles.
To keep our analysis pipeline fully automatic, we employed a pre-trained LV segmentation network \cite{Kerfoot2018} to identify the most basal atrial slice. This approach was found to be extremely reliable for all images and carried a negligible time penalty.
We chose to segment multi-slice CINE MRI data on a slice-by-slice basis. Although this setup does not make direct use of the 3D spatial and temporal correlations of this dataset, this approach has other advantages, as highlighted previously \cite{Chen2019}.
One of the advantages is the comparative simplicity and low parameter numbers of the SEGANet compared to its 3D or 3D+time counterparts and its immunity to misregistrations across slices caused by variations in breath hold positions. Additionally, treating each slice independently allows us to train the network with comparatively fewer number of patient datasets than for 3D (or 3D+time) networks. Furthermore, due to the relatively small size of the training dataset (715 slices), we applied an extensive data augmentation strategy, which was crucial for the good performance shown by the network. We add that our segmentation also uniquely includes the LA appendage, which is relevant for assessing stroke risk in AF.
To demonstrate the clinical utility of our work, we used SEGANet to obtain fully automatic estimates of clinical biomarkers such as LA volumes, LA EFs and aEFs. Up until now, LA volumes and functional markers have been estimated in CINE MRI by applying empirical formulae to single-slice long axis views \cite{ERBEL,UJINO20061185}, after manual annotation. These shortcomings have contributed to a comparative lack of interest in imaging left atrial function using CINE MRI.
Our method allows instead for biomarker estimates from volumetric CINE MRI, which are expected to be more accurate, reproducible and thus more clinically useful.
Estimates of LA volumes from long axis 2D slices typically rely on manual delineations of left atrial apex-base dimensions and assume, unrealistically (see Fig. \ref{fig:3D}), that the LA shape is as geometrically regular as that of the LV. Furthermore, given that atrial deformations across the cardiac cycle are not isotropic, it is not clear whether single 2D views allow for the accurate identification of the cardiac phases corresponding to maximal LA and minimal LA volume, as required for EF estimation. It is particularly difficult to identify the onset of atrial contraction ($V_{preA}$), required for aEF estimation, which our method performs automatically.
We thus expect that SEGANet will improve the clinical usefulness of atrial CINE MRI imaging and ultimately
make an important contribution to the stratification and treatment of AF patients.
\section{Conclusion}
\hspace{1em}
We have presented SEGANet for fully automatic segmentation of the LA from CINE MRI and showed it can accurately segment the LA across the cardiac cycle. SEGANet provides reliable automatic estimates of clinical biomarkers such as LA volumes, LA EF and aEF.
\vspace{2em}
\noindent \textbf{\large{Acknowledgments}}
\vspace{2em}
This research was supported by the Wellcome EPSRC Centre for Medical Engineering at the School of Biomedical Engineering and Imaging Sciences, King's College London [WT203148/Z/16/Z] and the National Institute for Health Research (NIHR) Biomedical Research Centre at Guy's and St Thomas' NHS Foundation Trust and King's College London. We also acknowledge funding from the Engineering and Physical Sciences Research Council [EP/N026993/1] and the British Heart Foundation [RE/18/4/34215].).
\section{First Section}
\subsection{A Subsection Sample}
Please note that the first paragraph of a section or subsection is
not indented. The first paragraph that follows a table, figure,
equation etc. does not need an indent, either.
Subsequent paragraphs, however, are indented.
\subsubsection{Sample Heading (Third Level)} Only two levels of
headings should be numbered. Lower level headings remain unnumbered;
they are formatted as run-in headings.
\paragraph{Sample Heading (Fourth Level)}
The contribution should contain no more than four levels of
headings. Table~\ref{tab1} gives a summary of all heading levels.
\begin{table}
\caption{Table captions should be placed above the
tables.}\label{tab1}
\begin{tabular}{|l|l|l|}
\hline
Heading level & Example & Font size and style\\
\hline
Title (centered) & {\Large\bfseries Lecture Notes} & 14 point, bold\\
1st-level heading & {\large\bfseries 1 Introduction} & 12 point, bold\\
2nd-level heading & {\bfseries 2.1 Printing Area} & 10 point, bold\\
3rd-level heading & {\bfseries Run-in Heading in Bold.} Text follows & 10 point, bold\\
4th-level heading & {\itshape Lowest Level Heading.} Text follows & 10 point, italic\\
\hline
\end{tabular}
\end{table}
\noindent Displayed equations are centered and set on a separate
line.
\begin{equation}
x + y = z
\end{equation}
Please try to avoid rasterized images for line-art diagrams and
schemas. Whenever possible, use vector graphics instead (see
Fig.~\ref{fig1}).
\begin{figure}
\includegraphics[width=\textwidth]{fig1.eps}
\caption{A figure caption is always placed below the illustration.
Please note that short captions are centered, while long ones are
justified by the macro package automatically.} \label{fig1}
\end{figure}
\begin{theorem}
This is a sample theorem. The run-in heading is set in bold, while
the following text appears in italics. Definitions, lemmas,
propositions, and corollaries are styled the same way.
\end{theorem}
\begin{proof}
Proofs, examples, and remarks have the initial word in italics,
while the following text appears in normal font.
\end{proof}
For citations of references, we prefer the use of square brackets
and consecutive numbers. Citations using labels or the author/year
convention are also acceptable. The following bibliography provides
a sample reference list with entries for journal
articles~\cite{ref_article1}, an LNCS chapter~\cite{ref_lncs1}, a
book~\cite{ref_book1}, proceedings without editors~\cite{ref_proc1},
and a homepage~\cite{ref_url1}. Multiple citations are grouped
\cite{ref_article1,ref_lncs1,ref_book1},
\cite{ref_article1,ref_book1,ref_proc1,ref_url1}.
| {
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Менту́-Кутю́р () — муніципалітет у Франції, у регіоні Центр-Долина Луари, департамент Шер. Населення — осіб (2011).
Муніципалітет розташований на відстані близько 210 км на південь від Парижа, 125 км на південний схід від Орлеана, 40 км на схід від Буржа.
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Розподіл населення за віком та статтю (2006):
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У 2010 році в муніципалітеті числилось 164 оподатковані домогосподарства, у яких проживали 377,0 особи, медіана доходів виносила євро на одного особоспоживача
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Список муніципалітетів департаменту Шер
Примітки
Муніципалітети департаменту Шер | {
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Lord Hardinge II (1910–16):Lord Hardinge served as India's Viceroy
From 1910 to 1916, Lord Hardinge served as India's Viceroy. He had entered the diplomatic service in 1880 and had served in Tehran as first secretary and Ambassador to Russia. But his administrative experiences were next to nothing. This young viceroy was sympathetic towards the Indians and wished to win their goodwill. The important event during his tenure were Delhi Durbar of 1911, annulment of the partition of Bengal (1911), Transfer of capital from Calcutta to Delhi (1911), Delhi Conspiracy Case (1912), Departure of Mahatma Gandhi to South Africa, Outbreak of the First World War (1914), Formation of the Home Rule League by Tilak, Foundation of Benaras Hindu University, Foundation of Ghadar Party, Komagatamaru incident, Foundation of Indian Independence League at Berlin (1914) etc.
Delhi Durbar of 1911
In 1910, there was a succession in England where King George V ascended the throne. In 1911, he paid a visit to India and a Darbar was held to commemorate the coronation of King George V and Queen Mary. This Darbar brought back the pomp and show of the Mughals once again in Delhi. The King and the Queen attired in the coronation robes with thousands of diamonds and precious gems appeared in the Jharokha of the red fort to give Darshan to 5 Lakh Indian people who gathered to greet the sovereign couple.
The Congress passed a resolution condemning the pomp and show of this Darbar at the cost of the poor Indians. King declared that Capital of India will be transferred from Calcutta to Delhi. In the same Darbar it was also declared the Partition of Bengal is cancelled.
Delhi Conspiracy case 1912
Delhi Conspiracy Case or Delhi-Lahore Conspiracy Case or Hardinge Bomb Case happened in 1912 when some members of Yugantar threw bomb in Chandni Chwok of Delhi to kill Lord Harding. The Viceroy survived with minor wounds but his mahawat {keeper of elephant} was killed. It was thought that this conspiracy was hatched by Ras Behari Bose, who then went underground and fled to Japan. In the trial, Basant Kumar Biswas, Amir Chand and Avadh Behari were convicted and executed.
B.H.U. Act 1915
In 1915, under Lord Hardinge, BHU act was passed by which Pandit Madan Mohan Malviya established the Banaras Hindu University.
Foundation of Ghadar Party 1913
It was after 1910, when the activities of India House had declined and the cradle of activities shifted from Europe to America. One of its members, Lal Hardayal settled in San Francisco and indulged in Industrial Unionism. In 1913, he set up Pacific Coast Hindustan Association with Sohan Singh Bhakna as its president, which was called Ghadar Party. The members of this party were the immigrant Sikhs of US and Canada.
Begin of World War I June 1914
On 28 June 1914, World war-I started and India naturally became a belligerent in the war. The British Government sought support of the Indians and most sections of the Indian society were with the empire. The moderates supported the war because, who knows their demands of self Government may be fulfilled after the war.
Return of Gandhi from South Africa
On 8 January 1915, Mahatma Gandhi returned to India. In May 1915, he laid the foundation of Sabarmati Ashram at Ahmadabad. Till 1917, Gandhi had no official leadership or role or agenda and British could easily tolerate his presence.
Tags: Civil Service, Conspiracy, conspiracy case, Current Affairs, delhi durbar, GK, hardinge, History, IAS, lord hardinge, lord hardinge 2, Mughal, Prelims, Sabarmati Ashram, UPSC
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Mícheál Ó Cléirigh (1590 – 1643) fue un cronista irlandés, y el autor principal de los Anales de los cuatro maestros. Estuvo asistido por otros historiadores como, Peregrine O'Clery, Fergus O'Mulconry y Peregrine O'Duignan. Nació en Kilbarron, cerca de Greevy, entre Rossnowlagh y Ballyshannon, en la bahía de Donegal. Era nieto de un jefe de Uí Chléirigh y fue bautizado como Tadhg, pero se cambió el nombre por Michael cuando se convirtió en fraile franciscano. Era primo de Lughaidh Ó Cléirigh (1595-1630), el cual junto a su hijo Cacrigcriche Ó Cléirigh, uno de sus colaboradores, es también conocido como un afamado historiador de Irlanda.
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#include "WaitForCondition.h"
namespace fiberdyne {
WaitForCondition::WaitForCondition(Scheduler &sched)
: m_ContinueRunning(true)
, m_Scheduler(sched)
{
}
size_t WaitForCondition::tasksPending()
{
return m_FibersAwaitingCondition.size();
}
bool WaitForCondition::tasksArePending()
{
return tasksPending()>0;
}
void WaitForCondition::yieldForCondition( std::function<bool()> f, const std::shared_ptr<TEXTask> &atask)
{
//printf("waitForCondition.yieldForCondition: \n");
m_FibersAwaitingCondition.push(std::make_pair(atask, f));
atask->suspend();
}
// each time we get CPU cycles, perform the following
void WaitForCondition::operator()()
{
size_t nPredicates = m_FibersAwaitingCondition.size();
//print("waitForCondition.step ==> ", nPredicates)
// BUGBUG - Not actually popping off of queue
// so we're doubling the size each time through
while (nPredicates) {
// Get the current front entry
auto entry = m_FibersAwaitingCondition.front();
m_FibersAwaitingCondition.pop();
if (entry.second()) {
entry.first->setStatus(TASK_READY);
m_Scheduler.ScheduleTask(entry.first);
//printf("Conditional FIBER To Be RESCHEDULED\n");
} else {
// stick the fiber back in the queue if it does not
// indicate true as yet.
m_FibersAwaitingCondition.push(entry);
}
nPredicates--;
}
}
/*
void WaitForCondition::operator()(AProcessor *proc)
{
while (m_ContinueRunning) {
this->operator()();
proc->yield();
}
}
*/
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"redpajama_set_name": "RedPajamaGithub"
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TrainUp.com offers instructor-led VoIP training courses in Yellowknife, Northwest Territories and VoIP training seminars in Yellowknife NT.
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\section{Introduction}
\label{sec:introduction}
Ultrasound (US) imaging is a safe imaging modality with high temporal resolution,
so it is considered as a first choice for various clinical applications such as echo-cardiography, fetal scan, etc.
To form an US image, individual channel RF measurements are back-propagated and accumulated after applying specific delays \cite{TimeReversal1}.
Accordingly, the quality of US images is limited by number of factors such as inhomogeneous sound speed, limited number of channels, frame rate, etc. For instance, in conventional focused B-mode ultrasound, lateral and axis resolutions depend on the number of scan-lines and axial sampling frequency,
whereas in planewave B-mode imaging the the quality of image is defined by the number of planewaves used in coherent-planewave compounding (CPC) \cite{montaldo2009coherent}. In addition, sonographic signals are inherently susceptible to speckle noises, which appear as granule patterns in US images and reduce the contrast-to-noise ratio (CNR) significantly \cite{zhang2020despeckle}.
To address these issue, model-based methods have been developed to remove the noises. These methods include
classical methods such as
adaptive filtering, deconvolution, etc.\cite{NLLR_Despeckle, zhang2020despeckle, coupe2009nonlocal,chen2015compressive, jensen1992deconvolution, 7565583, schretter2017ultrasound}.
However, these methods are usually associated with high computation cost
and may be subject to the model inconsistency \cite{chen2015compressive, jensen1992deconvolution, 7565583, schretter2017ultrasound}.
A promising direction to mitigate these issues is a deep learning approach. In the recent past, deep learning has emerged as a promising tool for variety of medical imaging related inverse problems \cite{kang2017deep, ye2017deep, han2017deep, aggarwal2017modl, khan2019deep, wurfl2016deep}. In particular, for high-quality ultrasound imaging there are number of solutions proposed by various researchers, which can be categorized into i) channel data based solutions \cite{yoon2018efficient,khan2020adaptive}, and ii) image domain based solutions \cite{feigin2018deep, yoon2018efficient, nair2018fully, khan2019universal, jafari2020cardiac, vedula2018high, nair2019generative, yu2018deep, ozkan2018inverse, cohen2018sparse}.
Typically, channel domain approaches
such as deep beamformers \cite{khan2020adaptive} show better generalization in diverse imaging conditions, but
image domain approaches are more easier to implement
for various applications without accessing the channel data.
The
existing deep learning strategies mostly rely on the paired dataset for supervised training. However, in many real world imaging situations, access to paired images (input image and its desired output pair) is not possible. For example, to improve the visual quality of US images acquired using a low-cost imaging system we need to scan exactly the same part using a high-end machine, which is not possible.
In another example,
the conversion of the plane wave imaging to the focused B-mode image quality is not applicable by supervised learning
as we should obtain the same image using two different
acquisition modes.
One could use simulation data for supervised training, but it is prone to bias to simulation environment.
Therefore, we are interested in developing an unsupervised learning strategy where low quality images from one scan can be used as inputs, whereas high quality images from different anatomy and imaging conditions can be used as target images, by doing so we can successfully train an image enhancement model.
We are aware that there are recent approaches in US literature that aim at similar unsupervised learning set-up \cite{jafari2020cardiac, huang2019mimicknet}. For example, the authors in \cite{jafari2020cardiac} employed cycleGAN network to improve the image quality from portable US image using high-end unmatched image data to improve the accuracy of cardiac chamber segmentation. Similar image domain cycleGAN approach has been recently proposed \cite{huang2019mimicknet}.
However, it is not clear whether such quality improvement is real or a cosmetic change.
Moreover, although there are potentially many applications beyond the conversion of the low-end image to high-end image,
these additional applications have been never investigated.
Therefore, one of the most important contributions of this study is an application
of recent theory of unsupervised learning using the optimal transport driven cycleGAN (OT-cycleGAN) \cite{Reference:sim2019optimal} for unsupervised artifact removal. Unlike the black-box application of cycleGAN, the OT-cycleGAN
was derived using optimal transport theory \cite{villani2008optimal,peyre2019computational} that transports a probability distribution of noisy images
to clean image distribution \cite{Reference:sim2019optimal}. Therefore, if properly trained, the theory guarantees that
the image improvement is not a cosmetic changes, but a real improvement by learning the distribution of the clean image data distributions.
Another important contribution of this paper is the extension of unsupervised learning to
various US artifact removal problems, such as speckle noise removal, deconvolution, limited measurements
artifact removal, plane wave to focused B-mode imaging conversion, etc, which verify that
our method provides near comparable results in both qualitative
and quantitative manners. Furthermore, our framework is so general that it can be used for various applications of
US image quality improvement without concerning about collecting paired reference data.
The rest of the paper is organized as follows. In Section \ref{sec:theory}, we briefly
review the recent theory of OT-cycleGAN for unsupervised deep learning applications.
The
detailed information of the proposed method are presented in Section \ref{sec:methods}, which
is followed by the results and discussion in Section \ref{sec:results}. Finally the paper is concluded in Section \ref{sec:conclusion}.
\section{Theory}
\label{sec:theory}
Here, we briefly introduced OT-CycleGAN \cite{Reference:sim2019optimal} to make the paper self-contained.
However, our derivation is different from \cite{Reference:sim2019optimal}, since here we focus on the general geometry
of unsupervised learning and explain why cycleGAN is a natural way to address this problem.
\subsection{Wasserstein Metric and Optimal Transport}
{Optimal transport (OT) provides a mathematical means to compare two probability measures} \cite{villani2008optimal,peyre2019computational}.
Formally, we say that $T:\mathcal{X} \mapsto \mathcal{Y}$ transports the probability measure $\mu \in P(\mathcal{X})$ to another measure $\nu \in P(\mathcal{Y})$, if
\begin{eqnarray}\label{eq:constraint}
\nu(B) = \mu\left(T^{-1}(B)\right),\quad \mbox{for all $\nu$-measurable sets $B$},
\end{eqnarray}
{Suppose there is a cost function $c:\mathcal{X} \times \mathcal{Y} \rightarrow {\mathbb R}\cup\{\infty\}$ such that $c(x,y)$ represents the cost of moving one unit of mass from $x \in \mathcal{X}$ to $y \in \mathcal{Y}$.}
Monge's original OT problem \cite{villani2008optimal,peyre2019computational} is then to find a transport map $T$ that transports $\mu$ to $\nu$
at the minimum total transportation cost.
Kantorovich relaxed the assumption to consider probabilistic
transport that allows mass splitting from a source
toward several targets:
\begin{align}\label{eq:OTcost}
&\min_{\pi \in \Pi (\mu, \nu)} \int_{\mathcal{X} \times \mathcal{Y}} c(x,y) d\pi(x,y)
\end{align}
where $\Pi(\mu, \nu)$ is the set of joint distributions whose marginal distribution is $\mu$ and $\nu$, respectively.
If we choose a metric $d$ in $\mathcal{X}$ as a transportation cost $c$, then
the optimal transport cost in \eqref{eq:OTcost} becomes
Wasserstein-1 distance between two probability measures $\mu$ and $\nu$:
\begin{align}\label{eq:Wp}
W_1(\mu,\nu):= &\inf\limits_{\pi \in \Pi(\mu,\nu)}\int_{\mathcal{X}\times \mathcal{Y}} d(x,y)d\pi(x,y) \\
=& \inf\limits_{\pi \in \Pi(\mu,\nu)} {{\mathbb E}}_\pi\left[d(X,Y)\right]
\end{align}
where
$X,Y$ are the random vectors with the joint distribution $\pi$,
and ${{\mathbb E}}_\pi[\cdot,\cdot]$ is the expectation with respect to the joint measure $\pi$.
Therefore, the meaning of the Wasserstein-1 metric is that
the minimum average distance between samples in two probability distributions $\mu$ and $\nu$,
the optimal transport theory is concerned about minimizing the average distance.
Unlike Kullback–Leibler (KL) divergence \cite{kullback1997information},
Wasserstein metric is a real metric that satisfies all properties of a metric in the metric space \cite{villani2008optimal,peyre2019computational}. Therefore, it provides a powerful way of measuring
distance in the probability space, which is useful for unsupervised learning as described in the next section.
\subsection{Geometry of Unsupervised Learning}
Our geometric
view of unsupervised learning is shown in Fig.~\ref{fig:cycleGANgeom}.
Here, the target image space
$\mathcal{X}$ is equipped with a probability measure $\mu$, whereas
the original image space is $\mathcal{Y}$ with a probability measure $\nu$.
Since there are no paired data, the goal of unsupervised learning is to match the probability distributions rather than each individual samples.
This can be done by finding transportation maps that transport the measure $\mu$ to $\nu$, and vice versa.
More specifically, the transportation from a measure space $(\mathcal{Y},\nu)$ to another measure space $(\mathcal{X},\mu)$ is done by a generator $G_\theta: \mathcal{Y} \mapsto \mathcal{X}$, realized by a deep
network parameterized with $\theta$. Then, the generator $G_\theta$ ``pushes forward'' the measure $\nu$ in $\mathcal{Y}$ to a meaure $\mu_\theta$ in the target space $\mathcal{X}$ \cite{villani2008optimal,peyre2019computational}. Similarly, the transport from $(\mathcal{X},\mu)$ to $(\mathcal{Y},\nu)$ is performed by another neural network generator $F_\phi$,
so that the generator $F_\phi$ pushes forward the measure $\mu$ in $\mathcal{X}$ to $\nu_\phi$ in the original space $\mathcal{Y}$.
Then, the optimal transport map for unsupervised learning can be achieved by minimizing the statistical distances between $\mu$ and $\mu_\theta$, and
between $\nu$ and $\nu_\phi$, and our proposal is to use the Wasserstein-1 metric as a means to measure the statistical distance.
\begin{figure}[!hbt]
\center{
\includegraphics[width=5cm]{cycleGAN_geom.png}
}
\caption{Geometric view of unsupervised learning.}
\label{fig:cycleGANgeom}
\end{figure}
More specifically, for the choice of a metric $d(x,x')=\|x-x'\|$ in $\mathcal{X}$, using the change of measure formula \cite{villani2008optimal,peyre2019computational},
the Wasserstein-1 metric between $\mu$ and $\mu_\theta$ can
be computed by
\begin{align}\label{eq:Wmu}
W_1(\mu,\mu_\theta
=&\inf\limits_{\pi \in \Pi(\mu,\nu)}\int_{\mathcal{X}\times \mathcal{Y}} \|x-G_\theta(y)\|d\pi(x,y)
\end{align}
Similarly, the Wasserstein-1 distance between $\nu$ and $\nu_\phi$ is given by
\begin{align}\label{eq:Wnu}
W_1(\nu,\nu_\phi
=&\inf\limits_{\pi \in \Pi(\mu,\nu)}\int_{\mathcal{X}\times \mathcal{Y}} \|F_\phi(x)-y\|d\pi(x,y)
\end{align}
Here, care should be taken, since we should minimize the two statistical distances simultaneously for unsupervised learning.
More specifically, rather than minimizing \eqref{eq:Wmu} and \eqref{eq:Wnu} separately with distinct joint distributions,
a better way of finding the transportation map is to minimize them together with the same joint distribution $\pi$:
\begin{align}\label{eq:unsupervised}
\inf\limits_{\pi \in \Pi(\mu,\nu)}\int_{\mathcal{X}\times \mathcal{Y}} \|x-G_\theta(y)\|+ \|F_\phi(x)-y\|d\pi(x,y)
\end{align}
This is our unsupervised learning formulation from optimal transport perspective \cite{Reference:sim2019optimal}.
\subsection{Optimal transport driven cycleGAN (OT-CycleGAN)}
One of the most important contributions of our companion paper \cite{Reference:sim2019optimal} is to show that
the primal formulation of the unsupervised learning in \eqref{eq:unsupervised}
can be represented by a dual formulation. More specifically, the following primal problem
\begin{align}\label{eq:primal}
\min_{\theta,\phi}\inf\limits_{\pi \in \Pi(\mu,\nu)}\int_{\mathcal{X}\times \mathcal{Y}} \|x-G_\theta(y)\|+ \|F_\phi(x)-y\|d\pi(x,y)
\end{align}
is equivalent to the following dual formulation which we call the optimal
transport driven CycleGAN (OT-cycleGAN):
\begin{eqnarray}\label{eq:OTcycleGAN}
\min_{\phi,\theta}\max_{\psi,\varphi}\ell_{cycleGAN}(\theta,\phi;\psi,\varphi)
\end{eqnarray}
where
\begin{eqnarray
\ell_{cycleGAN}(\theta,\phi):= \gamma \ell_{cycle}(\theta,\phi) +\ell_{Disc}(\theta,\phi;\psi,\varphi)
\end{eqnarray}
where $\gamma>0$ is the hyper-parameter, and the cycle-consistency term is given by
\begin{align*}
\ell_{cycle}(\theta,\phi) =& \int_{\mathcal{X}} \|x- G_\theta(F_\phi(x)) \| d\mu(x) \\
&+\int_{\mathcal{Y}} \|y-F_\phi(G_\theta(y))\| d\nu(y
\end{align*}
whereas the second term is
\begin{align*}
&\ell_{Disc}(\theta,\phi;\psi,\varphi) \\
=&\max_{\varphi}\int_\mathcal{X} \varphi(x) d\mu(x) - \int_\mathcal{Y} \varphi(G_\theta(y))d\nu(y) \\
& + \max_{\psi}\int_{\mathcal{Y}} \psi(y) d\nu(y) - \int_\mathcal{X} \psi(F_\phi(x)) d\mu(x) \notag
\end{align*}
Here, $\varphi,\psi$ are often called Kantorovich potentials and satisfy 1-Lipschitz condition (i.e.
\begin{align*}
|\varphi(x)-\varphi(x')|\leq \|x-x'\|,&~\forall x,x'\in \mathcal{X} \\
|\psi(y)-\psi(y')|\leq \|y-y'\|,&~\forall y,y'\in \mathcal{Y}
\end{align*}
In machine learning context, the 1-Lipschitz potentials $\varphi$ and $\psi$
correspond to the Wasserstein-GAN (W-GAN) discriminators \cite{arjovsky2017wasserstein}.
Specifically,
$\varphi$ tries to find the difference between the true image $x$ and the generated image $G_\Theta(y)$,
whereas $\psi$ attempts to find the fake measurement data that are generated by the synthetic
measurement procedure $F_\phi(x)$.
In fact, this formulation is equivalent to the cycleGAN formulation \cite{zhu2017unpaired} except for the use of 1-Lipschitz discriminators.
Here, care should be taken to ensure that the Kantorovich potentials become 1-Lipschitz.
There are many approaches to address this. For example, in the original W-GAN paper \cite{arjovsky2017wasserstein}, the weight
clipping was used to impose 1-Lipschitz condition.
Another method is to use the spectral normalization method \cite{miyato2018spectral}, which utilizes the power iteration method to impose
constraint on the largest singular value of weight matrix in each layer.
Yet another popular method is the WGAN with the gradient penalty (WGAN-GP), where
the gradient of the Kantorovich potential is constrained to be 1 \cite{gulrajani2017improved}.
Finally, in our companion paper \cite{lim2019cyclegan}, we also showed that the popular LS-GAN approach \cite{mao2017least}, which is often used in combination of standard
cycleGAN \cite{zhu2017unpaired}, is also closely related to
imposing the 1-Lipschitz condition.
In this paper, we therefore consider LS-GAN variation as our implementation for discriminator term where
the discriminator loss is given by
\begin{align}\label{eq:ourLSnonblind}
&\ell_{Disc}(\theta,\phi;\psi,\varphi)= \notag \\
&-\int_\mathcal{X} (\varphi(x)-1)^2d\mu(x) - \int_\mathcal{Y} \left(\varphi(G_\Theta(y))+1\right)^2d\nu(y) \notag\\
&-\int_\mathcal{Y} (\psi(y)-1)^2d\nu(y) - \int_\mathcal{X} \left(\varphi(F_\theta(x))+1\right)^2d\mu(x) \notag\\
\end{align}
\subsection{Unsupervised US Artifact Removal}
Based on the mathematical background of unsupervised learning
and its implementation using OT-cycleGAN,
we are interested in solving the following unsupervised learning problems in US:
\begin{enumerate}
\item Deconvolution.
\item Speckle noise removal.
\item Planewave image enhancement using high quality focused B-mode target.
\item Multi-line acquisition (MLA) block artifact and noise removal in cardiac imaging.
\item Missing channel artifact removal
\end{enumerate}
For each type of enhancement, we generated target data starting from the fully-sampled RX data i.e., $64$ channels from unmatched data set. The details of each application is given below.
\subsubsection{Deconvolution Ultrasound}
The axial resolution of ultrasound imaging is limited by the bandwidth of the transducer. Conventional beamforming methods such as delay-and-sum (DAS) are limited by the accuracy of ray approximation of the wave propagation \cite{jensen1992deconvolution}. In order to overcome these issues, many researchers have explored the deconvolution of US images \cite{7565583, chen2015compressive,jensen1992deconvolution}. Deconvolution ultrasound may help in dealing with modeling inaccuracies and finite bandwidth issues, which will eventually improve the spatial resolution of an ultrasonic imaging system.
Specifically, the received signal is modeled as a convolution of tissue reflectivity function (TRF) $x$ with a point spread function (PSF) $h$, where tissue reflectivity function represents scatter's acoustic properties, while the impulse response of the imaging system is modeled by point spread function.
The estimation of $x$ from the DAS measurement is known as a deconvolution US problem. In most practical cases, the complete knowledge of $h$ is not available, and therefore both unknown TRF $x$ and the PSF $h$ have to be estimated together, which is called the blind deconvolution problem \cite{taxt1999noise}. One strategy is to estimate $h$ and $x$ jointly \cite{yu2012blind}, and another strategy is to estimate them separately \cite{jensen1991estimation}, i.e., first $h$ is estimated from $y$, and then $x$ is estimated based on $h$ \cite{jirik2008two}.
In this paper, for unmatched target distribution data generation, the second strategy is used first with small number of DAS images, which is followed by training the DeepBF \cite{khan2020adaptive, 7565583} to perform deconvolution-based beamforming. This way a large number of target data can be
generated easily without solving deconvolution problems for large number of data set.
\subsubsection{Speckle-noise removal}
The granular patterns appears in US images due to constructive and destructive interference of ultrasonic wave. These are called `speckle' noise. The speckle noise is a multiplicative impulse noise. It is a major reason of quality degradation and removal of it can improve the visual quality and subsequently enhance the structural details in US images \cite{NLLR_Despeckle}. In recent past, a variety of reasonably good de-speckling algorithms have been proposed for US imaging \cite{NLLR_Despeckle, coupe2009nonlocal, zhang2020despeckle}. However, most of them are either too slow to use for run-time application or require complicated configurations of parameter for each image. These issues hinder the utilization in real world scenarios.
One such algorithm is proposed by Zhu \textit{et al} \cite{NLLR_Despeckle}, which is based on the principal of non-local low-rank (NLLR) filtering. To generate speckle free target data herein, we used NLLR method. In NLLR, the image is pre-processed to generate a guidance map and later non-local filtering operations are performed on the candidate patches that are selected using that guidance map. For further refinement of filtered patches, a truncated nuclear norm (TWNN) and structured sparsity criterion are used \cite{zhang2012matrix, gu2014weighted}. This algorithm
is used to generate our target samples for despeckle images.
\subsubsection{Planewave image enhancement using high quality focused B-mode target}
Planewave (PW) imaging is an emerging mode of US scanning. It offers ultra-fast scanning capabilities with comparable image quality. In PW imaging the quality of the acquired scan depends on the number of planewaves (PWs) used to generate the final image.
For most of the clinical applications, multiple PWs are combined using the CPC method to produce a desired quality image. However, there is a trade-off in the quality and speed of the scan as each PW scanning require additional scanning time, limiting the application of PWI for high quality accelerated imaging \cite{tanter2014ultrafast}.
To find an optimal trade-off between speed and visual quality, there are number of deep learning based PW compounding methods \cite{gasse2017high, khan2019universal}. However, these method require access to fully-sampled ($31\sim75$) planewaves data to train a supervised model. Typical lower-end commercial systems are not equipped with such hardware complexity to produce such a high quality label dataset.
Therefore, we propose to use an unsupervised learning in which high-quality label images are obtained using focused B-mode imaging.
For further quality improvement, the target focused B-mode images are processed using deconvolution and filtering with NLLR \cite{NLLR_Despeckle} speckle denoising algorithm.
\subsubsection{MLA block artifact and noise removal in cardiac imaging}
Echocardiography (ECHO) require fast scan time, and it is typically performed by a phased array probe operating in focused scanning mode in which multiple scan-lines are combined to form a complete image. Therefore, to scan a large region of interest, high number of scan-lines are required resulting in reduced temporal resolution.
For accelerated echocardiography, conventional acceleration methods like multi-line acquisition (MLA) are used, where each transmit/receive event's data is used to generate multiple scan-lines. The limitation of the MLA is that it works only for limited acceleration factor and produces blocking artifacts for high frame rate \cite{matrone2017high,vedula2018high}.
In addition to measurement's limitation, sonographic signals from echocardiography are susceptible of speckle noise which is also a major factor for the degradation of visual quality.
As such, this visual quality and temporal resolution trade-off is a bottle neck for many echocardiography applications.
A variety of deep learning based block artifact removal methods exist, but they are designed for supervised training and require access to high quality labelled channel data \cite{yoon2018efficient,matrone2017high,vedula2018high}. In this study we proposed an image domain unsupervised MLA artefact and noise removal deep neural network method. Unpaired target image distributions are generated with single-line-acquisition (SLA) and filtered using NLLR \cite{NLLR_Despeckle} filtering technique.
\subsubsection{ Missing channel artifact removal}
The power consumption, size, and cost of the US system are mainly dependent on the number of measurement channels. Therefore, in portable and three dimension ultrasound imaging system, there is an increasing demand for computational algorithms which can produce high quality images using fewer receive channels. Conventional beamforming methods are not designed for sub-sampled RF data and standard DAS is highly susceptible to sub-sampling in measurements. On the other hand, advance compressive beamforming methods \cite{wagner2012compressed,burshtein2016sub,cohen2018sparse} are computationally expensive and require hardware modifications limiting their use as generalized solution.
Recently a deep learning based compressive beamformer was proposed \cite{khan2020adaptive}, which can help reconstruct high quality images from limited measurements. However, the method in \cite{khan2020adaptive} requires an access to fully-sampled label data which is not accessible for low-cost imaging system. In this study, we proposed to design an image domain quality enhancement method that can directly process corrupted images to remove missing channel artefact, and improve the contrast and resolution of the B-mode images.
For the generation of unpaired target data distribution,
unmatched target images are generated using DeepBF \cite{khan2020adaptive}.
\begin{figure*}[!hbt]
\centerline{\includegraphics*[width=0.8\textwidth]{network_arch.png}}
\caption{Proposed network architecture: (a) Generator network, (b) Discriminator network.}
\label{fig:architecture}
\end{figure*}
\section{Method}
\label{sec:methods}
\subsection{Dataset}
In this study, we used four different dataset, all were acquired using an E-CUBE 12R US system (Alpinion Co., Korea). For data acquisition, we used a linear array (L3-12H), and phased array (SP1-5) transducers and their configuration are given in Table \ref{probe_config}.
\begin{table}[!hbt]
\centering
\caption{US Probes Configuration}
\label{probe_config}
\resizebox{0.48\textwidth}{!}{
\begin{tabular}{c|c|c}
\hline
{Parameter} & {Linear array} & {Phased array} \\ \hline\hline
Probe Model No. & L3-12H & SP1-5 \\
Carrier wave frequency & 8.48/10.0 MHz & 3.1 MHz\\
Sampling frequency & 40 MHz & 40 MHz\\
Scan wave mode & Focused/ 31-Planewaves & Focused\\
No. of probe elements & 192 & 192\\
No. of Tx elements & 128 & 128\\
No. of TE events & 96 & 96 \\
No. of Rx elements & 64 (from center of Tx) & 64 (from center of Tx)\\
Elements pitch & 0.2 mm & 0.3 mm\\
Elements width & 0.14 mm & 0.22 mm\\
Elevating length & 4.5 mm & 13.5 mm\\
Axial depth range & 20$\sim$80 mm & 75 mm\\
Lateral length & 38.4 mm & 57.6 mm \\
Focal depth range & 10$\sim$40 mm & 45 mm\\\hline
\end{tabular}}
\end{table}
\subsubsection{Linear array focused B-mode dataset}
The first data consist of $400$ \textit{in-vivo} and $218$ phantom frames scanned using a center frequency of $8.48$ MHz. The \textit{in-vivo} dataset acquired from the carotid/thyroid area of $10$ volunteers, $40$ temporal frames were scanned from each subject. For phantom dataset, we acquired $218$ frames from ATS-539 multipurpose tissue mimicking phantom. The phantom was scanned from different views angles. Second dataset was scanned from the calf and forearm regions of two volunteers using $10$ MHz carrier frequency. There are total $100$ images were scanned $50$ from each body part.
For deconvolution and denoising experiments, the training was performed using only the first data. In particular, for training purpose the dataset of $8$ individuals consist of $320$ in-vivo and $192$ phantom images were used, while remaining $80$ images from two different individuals and $26$ images from completely different region of phantom were used for testing. For additional validation, second independent dataset is used. Note that all models were trained on same $508$ images and no additional training is performed on any of the testing or independent dataset.
For missing channel artifact experiments the above mentioned data set is expanded into six subsets of input data each consist of $4$, $8$, $16$, $24$, $32$, and $64$ channels representing $16\times$, $8\times$, $4\times$, $2.667\times$, $2\times$, and $1\times$ sub-sampling rates respectively.
\subsubsection{Linear array planewave B-mode dataset}
For planewave imaging experiments, we collected the third dataset. For this dataset, we used the same (L3-12) operating at center frequency of $8.48$ MHz in a planewave mode. There are total $309$ scans acquired, $100$ from ATS-539 phantom and $209$ from \textit{in-vivo} carotid/thyroid area of $10$ volunteers. The dataset is expanded by using different subsets of PWs to simulate different imaging configurations. In particular, four subsets were used each consist of $31$PWs, $11$PWs, $7$PWs and $3$PWs. For planewave image enhancement experiments $508=127\times4$ images were used. All PW images were processed using standard DAS and CPC method \cite{montaldo2009coherent}. The training dataset is composed of $127$ images $50$ of which were acquired from ATS-539 phantom and remaining $77$ from \textit{in-vivo} dataset of $4$ volunteers. The remaining dataset of phantom and $6$ volunteers was used for testing purpose only.
\subsubsection{Phased array B-mode dataset}
To design MLA artifact removal experiment, we designed an additional dataset. This dataset was acquired using (SP1-5) phased array probe and it consist of $105$ scans of different regions of ATS-539 phantom and $489$ scans from the cardiac region of $7$ volunteers. Five subsets of images are generated using $16$, $24$, $32$, $48$ and $96$ transmit events representing $6$-MLA, $4$-MLA, $3$-MLA, $2$-MLA and a single line acquisition (SLA). The target images are generated from SLA images filtered with NLLR \cite{NLLR_Despeckle} algorithm. The training dataset used in this study consists of $55$ phantom scans, and $297$ \textit{in-vivo} scans acquired from $5$ individual, while remaining dataset were used for testing. Total number of images in training and test datasets are $1760=5\times(55+297)$, and $1210=5\times(50+192)$ respectively.
\subsection{Network specification}
\subsubsection{Generator Model}
The generator model has a U-Net architecture as shown in Fig.~\ref{fig:architecture}(a). The model comprises of $9$ modules, which consists of $27$ convolution layers with batch-normalization, pooling, up-sampling and concatenation blocks for skip connections. For all convolution layers ReLu activation function and 2D filters of kernel size $(3\times3)$ were used, except for the output layer, where $(1\times 1)$ filter size is used. The number of filters $G_f$ is doubled in every next module of encoder part and halve in every next decoder module, expect for the output layer where only a single layer is used to produce single channel output. For example, in deconvolution US and despeckle (speckle noise removal) experiments the number of channels starts from $8$ i.e., in the first module there were $8$ channels (number of filters) and in the next module the number of filters increased to $16$, $32$ and so forth. For missing channel and MLA artifact removal experiments, the number of channels starts from $64$ and $16$ respectively.
\subsubsection{Discriminator Model}
The discriminator model is a fully convolution neural network model to implement PatchGAN \cite{zhu2017unpaired}. Unlike conventional discriminator where mapping between an input image to a single scalar vector is performed, PatchGAN learns the mapping of sub-array (Patch) representing individual elements and their relative position in an image. The model comprises of $4$ convolution blocks each consist of a set of two convolution layers having stride-size of $2$ with batch normalization and Leaky ReLu activation function. The number of filters $D_f$ are doubled in every next module, expect for the output layer where only a single layer is used to produce single channel output. The filter size in all layers was again $(3\times3)$ except for the last layer where $(1\times1)$ filter size is used. For all experiments the number of filter was $256$, except for the MLA artifact experiment where it was chosen to be $512$. A detailed schematic of discriminator model is shown in Fig.~\ref{fig:architecture}(b).
\subsection{Performance metrics}
For quantitative evaluation of our proposed method, the standard quality metrics of ultrasound imaging are used.
Specifically, as the local anatomical structure or region of interest are important in US,
we used contrast statistics. The contrast between the two regions of interests ($R_a$) and ($R_b$) in the image is quantified in terms of contrast-recovery (CR), contrast-to-noise ratio (CNR), and generalized CNR (GCNR) \cite{rodriguez2019generalized}. To select region ($R_a$) and ($R_b$), we manually generated separate ROI masks for each image.
More specifically, the contrast recovery is quantified as
\begin{equation}
{\hbox{CR}}(R_a,R_b) = |\mu_{R_a}-\mu_{R_b}|
\end{equation}
where $\mu_{R_a}$, and $\mu_{R_b}$, are the local means of region ($R_a$) and ($R_b$) respectively.
The CR measure is a standard measure for contrast. However, it does not consider the SNR loss. In typical contrast enhancement methods, the contrast is usually improved at the cost of SNR; therefore, to estimate the overall gain in contrast with respect to noise level, we used CNR measure which is defined as
\begin{equation}
{\hbox{CNR}}(R_a,R_b) = \frac{|\mu_{R_a}-\mu_{R_b}|}{\sqrt{\sigma^2_{R_a} + \sigma^2_{R_b}}},
\end{equation}
where $\sigma_{R_a}$, and $\sigma_{R_b}$ are the standard deviations of region ($R_a$) and ($R_b$) respectively.
Recently, a more reliable measure of contrast is proposed called generalized-CNR (GCNR) \cite{rodriguez2019generalized}. The GCNR is supposed to be an unbiased measure of contrast in which the overlap between the intensity distributions of two regions are compared as
\begin{equation}
{\hbox{GCNR}}(R_a,R_b) = 1- \int \min \{p_{R_a} (i), p_{R_b} (i) \} di,
\end{equation}
where $i$ is the pixel intensity, and $p_{R_a}$ and $p_{R_b}$ are the probability distributions region ($R_a$) and ($R_b$) respectively. If the intensities of both regions are statistically independent, then GCNR will be equals to one, whereas, if they completely overlap then GCNR will be zero \cite{rodriguez2019generalized}.
In addition to image quality, we also compared the reconstruction time of proposed method.
\subsection{Network training}
In the supervised learning of the network for comparative study,
match image pairs are used to minimize the $l_1$ loss and SSIM loss between target and the network output.
For unsupervised learning, the loss function defined in \eqref{eq:OTcycleGAN} is minimized.
Both the supervised and unsupervised methods were implemented using Python on TensorFlow platform \cite{abadi2016tensorflow}. For parameter optimization the Adam optimizer is used \cite{kingma2014adam}. For supervised training the default values of adam were used, while for unsupervised case the learning rate is linearly changed from $5\times10^{-4}$ to $1\times10^{-4}$ in $200$ epochs.
\begin{figure}[!hbt]
\centerline{\includegraphics*[width=9cm]{deepDeconv_Full_Bmode.png}}
\caption{Deconvolution results on fully-sampled RF data. B-Mode images from tissue mimicking phantom (left), and from \textit{in-vivo} data of carotid region (center \& right).}
\label{fig:results_deconv_full}
\end{figure}
\begin{figure*}[!hbt]
\centerline{\includegraphics*[width=16cm]{ALL_images_deepDeconv_Graphs.png}}
\caption{Comparison of performance metrics by various methods.}
\label{fig:dist_deepDeconv}
\end{figure*}
\begin{figure}[!hbt]
\centerline{\includegraphics*[width=9cm]{das_Despeckle_Full_Bmode.png}}
\caption{Speckle removal results on fully-sampled RF data. B-Mode images from tissue mimicking phantom (left), and from \textit{in-vivo} data of carotid region (center \& right).}
\label{fig:results_despeckle_full}
\end{figure}
\begin{figure*}[!hbt]
\centerline{\includegraphics*[width=16cm]{ALL_images_das_despeckle_Graphs.png}}
\caption{Comparison of performance metrics by various methods.}
\label{fig:dist_das_despeckle}
\end{figure*}
\section{Results }
\label{sec:results}
In the following, we verify the performance of the algorithm for the following experiments:
\begin{enumerate}
\item Deconvolution ultrasound.
\item Speckle noise removal.
\item Planewave image enhancement using high quality focused b-mode target.
\item MLA block artifact and noise removal in cardiac imaging.
\item High quality ultrasound imaging from sub-sampled channel data.
\end{enumerate}
For the calculation of contrast metrics two regions are selected as highlighted with red and blue dotted lines in respective figures. The same regions are magnified as inset figure for better visualization.
\subsubsection{Deconvolution}
Fig.~\ref{fig:results_deconv_full} show example results from \textit{in-vivo} and phantom scans. From the figures it can be easily seen that the deconvoluted target images have better contrast and anatomical structures are quite prominent compared to the input DAS images.
Furthermore, both supervised and unsupervised deep learning method successfully learn the deconvolution filtering and improve the visual quality of das images.
For quantitative comparison, the improvement in visual quality is quantified and it is prominent in the contrast distribution plots shown in Fig.~\ref{fig:dist_deepDeconv}. In particular, using unsupervised learning method, CR values are comparable to the supervised method. As expected, contrary to CR, the CNR and GCNR values are reduced in deconvolution targets, this is because the deconvolution enhances resolution at the cost of noisy high-frequency components. Therefore, the contrast to noise ratio drops substantially, however it is worth noting that at the same CNR and GCNR the CR gain in unsupervised method is much higher compared to label and supervised method. In particular, compared to input (DAS) the proposed unsupervised method recover $3.28$ dB, $2.96$ dB, and $1.66$ dB better CR in Calf and Forearm, Phantom and Thyroid and Carotid regions scans respectively, which is $71.60\%$, $162.02\%$, and $16.11\%$ higher than supervised method.
\subsubsection{Speckle removal}
In this experiment, we perform the speckle de-noising from DAS images using NLLR \cite{NLLR_Despeckle}, supervised, and
unsupervised learning methods. In Fig.~\ref{fig:results_despeckle_full} one phantom and two in-vivo examples are shown. As for comparison, DAS input images are filtered using NNLR\cite{NLLR_Despeckle} method. Compared to the DAS images, the speckle noise in output images is noticeably reduced. The granular patterns in output images are well suppressed, and resultant images from both supervised and unsupervised
learning methods are similar to the target speckle free images. Here it is noteworthy to point-out that the reconstruction time of deep
learning methods is several magnitude lower than the NLLR\cite{NLLR_Despeckle} method, and unlike NLLR no parameter tuning is needed.
In order to quantify the performance gain, we utilized the same performance metrics used in deconvolution experiments, and the results are shown in Fig.~\ref{fig:dist_das_despeckle}. Interestingly, the CNR values in despeckle methods are significantly improved.
The reason for high CNR and GCNR is that the despeckle methods suppresses the noises while maintain the contrast and structural details.
In particular, compared to input DAS image, the proposed unsupervised method enhance the CNR by $0.89$ units, $0.28$ units, and $0.23$ units in Calf and Forearm, Phantom and Thyroid and Carotid regions scans respectively, which is comparable to supervised methods which shows $1.22$, $0.34$, and $0.23$ units gain, and NLLR \cite{NLLR_Despeckle} method which show $0.85$, $0.35$, and $0.26$ units gain in Calf and Forearm, Phantom and Thyroid and Carotid regions scans, respectively.
\subsubsection{Planewave image enhancement using high quality focused B-mode target.}
\begin{figure*}[!hbt]
\centerline{\includegraphics*[width=\textwidth]{DeconvDespeckle_Full_Bmode_PWI.png}}
\caption{Planewave ultrasound images enhancement. B-Mode images from \textit{in-vivo} data of carotid regions.}
\label{fig:DeconvDespeckle_Full_Bmode_PWI}
\end{figure*}
In this experiment, we design a model to improve the quality of planewave images using high quality focused B-mode images as target images. In particular, different sets of PWs were used to generate low quality input images. In Fig.~\ref{fig:DeconvDespeckle_Full_Bmode_PWI}, three example results are shown. From the figure it can be seen that the contrast of the input images has been improved.
It is remarkable that for each type of enhancement, a single trained model is used for all acceleration factors (PWs combinations). In Table~\ref{tbl:results_PWI_enhacement}, three different measures of contrast are shown. From the results it can be clearly seen that the statistics of the output images are substantially improved. When
the deconvoluted B-mode images are used as target distribution, on average there is a $3.60$ dB gain in CR;
when deconvoluted and speckle removed B-mode images are used as targets,
on average there is a $4.20$ dB, $0.565$ units and $0.04$ units gain in terms of CR, CNR and GCNR respectively.
\begin{table}[!hbt]
\centering
\caption{Comparison of performance statistics on test data in the planewave image enhancement.}
\label{tbl:results_PWI_enhacement}
\resizebox{9cm}{!}{
\begin{tabular}{c|ccc|ccc|ccc}
\hline
number of & \multicolumn{3}{c|}{CR (dB)} & \multicolumn{3}{c|}{{CNR}} & \multicolumn{3}{c}{{GCNR}} \\
{PWs} & \textit{a} & \textit{b} & \textit{c} & \textit{a} & \textit{b} & \textit{c} & \textit{a} & \textit{b} & \textit{c} \\ \hline\hline
3 & 13.36 & 17.42 & 17.73 & 2.05 & 2.09 & 2.55 & 0.8405 & 0.8434 & 0.8904 \\
7 & 15.24 & 18.64 & 19.81 & 2.29 & 2.29 & 2.86 & 0.8739 & 0.8742 & 0.9162 \\
11 & 16.23 & 19.65 & 20.54 & 2.48 & 2.46 & 3.11 & 0.8962 & 0.8949 & 0.9312 \\
31 & 17.17 & 20.69 & 20.73 & 2.65 & 2.62 & 3.21 & 0.9164 & 0.9165 & 0.9388 \\ \hline
\end{tabular}
}
\\
\tiny{$^a$ Input, $^b$ Deconvolution targets, $^c$ Deconvolution + despeckle targets}
\vspace{0cm}
\end{table}
\subsubsection{High quality accelerated Echocardiograph}
In Fig.~\ref{fig:results_cardiac_MLA}(a) reconstruction results of conventional MLA (referred to as input) and the proposed methods are compared for different number of acceleration factors (transmit events),
which are referred as SLA, 2-MLA, 3-MLA, 4-MLA, and 6-MLA respectively. For better visualization of the noise suppression effect of our proposed method, a region selected in target image is zoomed out and shown as an inset image. From the example results, it is quite evident that the reconstructed images are very much similar to the target image and have less noise/artifacts compared to input image. Our method sufficiently enhance the visual quality of the input images by eliminating both the speckle and block artifacts for all acceleration factors. It is noteworthy to point out that the proposed method is trained in an unsupervised fashion and a single one-time trained model is used for all acceleration factors. From reconstructions error statistics in Table~\ref{tbl:results_cardiac_MLA}, it is evident that the quality degradation in input images is much higher than the output images. In particular, on average there is $0.1372$ gain in GCNR.
Here we would like to emphasize that the proposed method is based on a single universal model which is one-time trained for multi-tasks i.e., blocking artifact and speckle noise removal and it works for variable MLA schemes without retraining.
Since in real in-vivo case it is difficult to decide between anomalies and true structures, to ensure structural preservation we provided additional results using tissue mimicking phantom in Fig.~\ref{fig:results_cardiac_MLA}(b). The results confirm that our method can accurately recover the phantom for most cases. However, with higer acceleration factors e.g., $6$-MLA the block artefacts are becoming prominent and recovery to target quality is not ideal.
Apart from reconstruction quality improvement one major advantage of our method is the fast reconstruction time.
This is especially important for real time echocardiography that requires fast image reconstruction.
Once a model is successfully trained, on average reconstruction time for a single image is around $7.92$ (milliseconds), which is same for all acceleration factors and it could further reduce by optimized implementation.
\begin{figure*}[!hbt]
\centerline{\includegraphics*[width=\textwidth]{cardiac_MLA.png}}
\caption{Reconstruction of high quality accelerated imaging: (a) B-modes images from echocardiograph. (b) B-Mode images from a tissue mimicking phantom.}
\label{fig:results_cardiac_MLA}
\end{figure*}
\begin{table}[!hbt]
\centering
\caption{Comparison of performance statistics on test data for noise and block artifact removal from MLA.}
\label{tbl:results_cardiac_MLA}
\resizebox{4cm}{!}{
\begin{tabular}{c|cc}
\hline
SLA/MLA & \multicolumn{2}{c}{GCNR} \\
{factor} & \textit{Input} & \textit{Output} \\ \hline\hline
SLA & 0.8221 & 0.9422 \\%& 25.26 & 29.95 & 0.6752 & 0.9160 \\
2-MLA & 0.8173 & 0.9380\\% & 25.08 & 29.93 & 0.6686 & 0.9135 \\
3-MLA & 0.8072 & 0.9361 \\% & 24.48 & 29.38 & 0.6521 & 0.9002 \\
4-MLA & 0.7797 & 0.9313 \\%& 23.78 & 28.65 & 0.6318 & 0.8824 \\
6-MLA & 0.7263 & 0.8911 \\%& 22.55 & 27.13 & 0.6055 & 0.8493 \\
\hline
\end{tabular}
}
\vspace{0cm}
\end{table}
\subsubsection{High Quality Ultrasound Imaging From Sub-Sampled Channel Data}
In this experiment, six sets of RF data at different down-sampling rates is generated. For each case a separate image is generated, mimicking low-quality/low-powered imaging conditions. For all sub-sampling configurations a single universal model is used, i.e., no separate training is performed for individual sub-sampling case.
Fig.~\ref{fig:results_deconv_sub} shows the results on example images generated for proposed unsupervised learning method and DAS method using sub-sampled RF data. The trained models are evaluated for standard quality measures. Overall a single model (one-time trained using either supervised/unsupervised approach) produces significant performance gain in terms of contrast, and resolution for all RF sub-sampling configurations and the performance is comparable with the supervised learning (see Table~\ref{tbl:deconv_sub}).
\begin{figure}[!hbt]
\centerline{\includegraphics*[width=9cm]{deepDeconv_SUB_Bmode.png}}
\caption{Reconstruction of high quality ultrasound image from sub-sampled RF data. B-Mode images from \textit{in-vivo} data of carotid artery region.}
\label{fig:results_deconv_sub}
\end{figure}
\begin{table}[!hbt]
\centering
\caption{Comparison of performance statistics on test data for compressive deconvolution ultrasound.}
\label{tbl:deconv_sub}
\resizebox{0.4\textwidth}{!}{
\begin{tabular}{c|ccc}
\hline
sub-sampling & \multicolumn{3}{c}{CR (dB)}\\
{factor} & \textit{Input} & \textit{Supervised} & \textit{Unsupervised}
\\ \hline\hline
1 & 8.32 & 9.80 & 11.06 \\
2 & 7.10 & 9.24 & 9.83 \\
4 & 6.39 & 8.54 & 8.64 \\
8 & 6.13 & 8.39 & 7.87 \\% & 14.13 & 19.27 & 18.63 & 0.63 & 0.76 & 0.73 \\
16 & 6.09 & 8.34 & 7.35\\% & 13.39 & 18.32 & 17.89 & 0.58 & 0.72 & 0.68
\hline
\end{tabular}
}
\vspace*{-0.3cm}
\end{table}
\section{Conclusion}
\label{sec:conclusion}
Medical ultrasound imaging is prone to variety of artifacts such as resolution and contrast loss due to insufficient measurement, speckle noise, etc. These artifacts are the major reasons of quality degradation in ultrasound imaging.
To address this issue, we proposed a robust unsupervised deep learning approach that can help generate high-quality US images from low quality noisy images. Compared to the black-box approaches, our approach was derived based on the rigorous formulation of unsupervised learning using optimal
transport theory, so with proper training, the method provided reliable reconstruction results without creating any artificial features.
Since our method does not require paired data for training, the method can be applied for various US image enhancement applications, providing
an important platform for further investigation.
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Хи́зер Линэ́й Пэйн (), в девичестве — Флойд (; 18 января 1970, Абилин, Техас, США) — американская певица.
Биография
Хизер Линэй Флойд родилась 18 января 1970 года в Абилине (штат Техас, США), а выросла и окончила среднюю школу в Нормане (штат Оклахома).
Хизер начала свою музыкальную карьеру в 1991 году, став участницей женской музыкальной поп-группы «Point of Grace», которую она покинула 17 лет спустя — в 2008 году. В 2010 году Пэйн начала сольную карьеру.
С 30 апреля 1999 года Хизер замужем за Брайаном Пэйном. У супругов есть четверо детей: дочь Элла Райли Пэйн (род.16.09.2002), сыновья Натаниэль Грэм Пэйн (род.12.09.2004) и Сет Хадсон Пэйн (род.17.04.2006) и ещё одна дочь — Ава Коринн Пэйн (род.12.11.2007).
Примечания
Ссылки | {
"redpajama_set_name": "RedPajamaWikipedia"
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\section{Introduction}
The crucial role of entanglement as a fundamental resource for quantum
information tasks that transgress the classical limits is particularly
evident and has been experimentally verified in such protocols like
teleportation \cite{Zeilinger,Boschi}, cryptography and secure key
distribution \cite{Gisin}, and quantum communication \cite{Communication}.
Typically, the {}``most natural way'' to create entanglement between
parties is by means of direct interactions. Since, intuitively, large
amounts of entanglement should be associated to the presence of strong
correlations, low-dimensional systems, as, for instance, spin chains,
offer a natural source of entanglement. However, in most systems with
short-range interactions, the entanglement between a pair of particles
decays rapidly with the distance. For instance, in the Ising model
with transverse field \cite{XX} the two-spin concurrence vanishes
for distances larger than two neighboring sites, while in the Heisenberg
model \cite{Jin}, it is restricted only to single nearest neighbors.
A first exception to this behavior was found by Amico {\em et al}
\cite{Amico}, who established that close to factorization points,
the range of entanglement grows indefinitely. However, in this case,
the entanglement strength between two spins rapidly vanishes as the
range increases. In fact, this behavior appears to be natural, recalling
that monogamy of entanglement \cite{Coffman} implies that if entanglement
is enhanced between two given subsystems, then the entanglement between
any of the two subsystems and a third one must necessarily be suppressed.
From a general quantum informatic perspective, a much desired goal
would be the ability to create a large amount of entanglement between
distant subsystems, simultaneously avoiding direct interactions between
them and single-subsystem addressing. Along this line of thought,
the first requirement can be satisfied by introducing the concept
of localizable entanglement, with the aim of exploiting spin chains
as quantum channels \cite{Verstraete}. The localizable entanglement
measures the average entanglement that can be concentrated on a pair
of distant subsystems by performing optimal local measurements onto
the rest of the system. More recently, it was shown that the ground
state of some spin models with finite correlation length defined
on one-dimensional chains with open ends can support large values
of long-distance entanglement between the end points of the chain
\cite{Bologna}. This approach, i. e.
to look for systems whose ground state can support long-distance entanglement
\textit{prima facie}, without the need of performing operations and
measurements, is clearly very appealing. However, it appears that
models which exhibit true long-distance entanglement are characterized
by energy gaps above the ground state that vanish exponentially as
the length of the chain is increased \cite{Bologna}. Hence, this
interesting phenomenon seems doomed to survive only in the physically
unattainable situation of zero temperature. In the effort to overcome
this problem, it was shown that a kind of long-distance entanglement,
very slowly decreasing with the length of the chain, can be supported
by the ground state of spin models with infinite correlation length defined
on one-dimensional open chains with small end bond interactions,
and that these systems allow for robust finite-temperature teleportation
across finite distances \cite{Bologna2}. This {}``quasi long-distance
entanglement'' between the end points of the chain is associated
to an energy gap that vanishes algebraically with the size of the
system. As a consequence, it is more resilient to thermal excitations,
and can be used to engineer realistic protocols of qubit teleportation,
as has been explicitly demonstrated, by numerical DMRG simulations,
in the case of the Heisenberg ($XXX$) chain with small end interactions
\cite{Bologna2}.
In the present paper we will show that both true long-distance and
quasi long-distance entanglement can be supported by very simple isotropic
$XX$ models of open spin chains. These models present some interesting
advantages over the ones that have been previously studied. At variance
with the Heisenberg case, they are amenable to exact analytical treatment
both in the case of alternating couplings, corresponding to dimerization
of the ground state and true long-distance entanglement, and in the
case of small end bonds, corresponding to a ground state that supports
quasi long-distance entanglement. In this way, one achieves a full
grasp of the physical mechanism responsible for long and quasi-long
distance entanglement, and the possibility to identify unambiguously
the optimal range of parameters for teleportation with maximal fidelity.
Moreover, having in mind possible experimental realizations, for instance
in suitably engineered optical lattices \cite{Duan}, $XX$ chains
are in principle more easily realizable or simulatable than Heisenberg
interactions. The exact solvability of the open-end $XX$ chains is
possible thanks the methods introduced by Lieb and coworkers \cite{Lieb}.
We will first study the fully dimerized $XX$ open spin chain with
alternating couplings, discuss the exact behavior of the end-to-end
concurrence in the ground state at zero temperature, and show analytically
that for this kind of model the energy gap between the ground and
the lowest excited state falls off exponentially with the size of
the system. Therefore, this system cannot be exploited for quantum
teleportation in realistic situations at finite temperature. We then
study the $XX$ open spin chain with small end bonds and determine
analytically the exact expression for the zero temperature end-to-end
concurrence in some physically relevant limits. We determine the exact
scaling of the energy gap with the length of the chain and show that
it dies off algebraically with the size of the system. Finally, we
determine the behavior of the teleportation fidelity as a function
of the temperature for different strengths of the small end bonds,
and show that qubit teleportation with fidelities well above the classical
threshold, and in some cases close to unity, is supported even at
moderately low temperatures.
The paper is organized as follows: In Section II we introduce the
general $XX$ spin chain Hamiltonian with arbitrary site-dependent
couplings, and solve it analytically for the end-to-end two-point
reduced density matrix, correlation, and concurrence (entanglement
of formation). We calculate the fully entangled fraction and establish
the analytical expression for the fidelity of teleportation of an
unknown qubit state between the two end points of the chain. In Section
III we specialize the model to the case of perfectly alternating couplings
and fully dimerized ground state. We determine the single particle
dispersion law, establish the exponential scaling behavior of the
energy gap, and determine the analytical expressions for the ground
state end-to-end concurrence and fidelity. We show that, depending
on the values of the coupling strength, high or even maximal entanglement
and fidelity can be achieved for chains of arbitrary length. In Section
IV we turn to the case of open $XX$ chains with small end bonds,
establishing the single particle dispersion law, the algebraic scaling
of the energy gap, and the analytic expressions for the concurrence
and the fidelity. We then investigate the behavior of the end-to-end
teleportation fidelity as a function of the temperature for different
values of the small end bonds, and conclude that teleportation with
unit fidelity at very low temperature and with high fidelity above
the classical threshold at moderately low temperature are both supported
by the $XX$ channel with small end bonds. Finally, in the conclusions
we summarize our findings and discuss some outlooks on possible future
developments along this line of research.
\section{The general model}
\label{Generalmodel}
As already anticipated in the introduction, we will focus our analysis
on one-dimensional lattices with open ends, described by $XX$ models
with different types of nearest neighbor interactions. Such models
are all special instances of the general $XX$ Hamiltonian
\begin{equation}
H=\sum_{i=1}^{L-1}J_{i}\left(S_{i}^{x}S_{i+1}^{x}
+ S_{i}^{y}S_{i+1}^{y}\right)\; ,
\label{HamiltonianaGenerica}
\end{equation}
where $J_{i}$ is the interaction strength between nearest neighboring
sites $i$ and $i+1$, $S_{i}^{\alpha}$ are the spin operators defined
at site $i$, and $L$ is the total number of sites (spins) or the
length of the chain. The spectrum of this Hamiltonian can be determined
exactly by a straightforward application of the standard methods introduced
in Ref. \cite{Lieb}. The first step in the procedure is to perform
a Jordan-Wigner transformation \cite{JordanWigner},
\begin{eqnarray}
& & S_{i}^{+}=c_{i}^{\dagger}e^{i\pi\sum_{j=1}^{i-1}c_{j}^{\dagger}c_{j}}\;,\qquad S_{i}^{-}
=e^{-i\pi\sum_{j=1}^{i-1}c_{j}^{\dagger}c_{j}}c_{i}\;,\nonumber \\
& & S_{i}^{z}=c_{i}^{\dagger}c_{i}-\frac{1\negthickspace{\rm I}}{2}\;,
\end{eqnarray}
where $S_{j}^{\pm}=S_{j}^{x}\pm iS_{j}^{y}$. As a result, the Hamiltonian
(\ref{HamiltonianaGenerica}) is mapped in the free fermion Hamiltonian
\begin{equation}
H=\frac{1}{2}\sum_{i=1}^{L-1}J_{i}\left(c_{i}^{\dagger}c_{i+1}+
c_{i+1}^{\dagger}c_{i}\right)=\mathbf{c}^{\dagger}M\mathbf{c}\;,
\label{Trasformata}
\end{equation}
where $\mathbf{c}^{\dagger}=\left(c_{1}^{\dagger},\ldots,c_{L}^{\dagger}\right)$
($\mathbf{c}$) is the vector of the $L$ creation (annihilation)
operators, one for each site of the lattice, and the adjacency matrix
$M$ reads
\begin{equation}
M=\frac{1}{2}\left|\begin{array}{cccccc}
0 & J_{1} & 0 & \cdots & & 0\\
J_{1} & 0 & J_{2}\\
0 & J_{2} & 0 & & & \vdots\\
\vdots & & & \ddots & J_{L-2} & 0\\
& & & J_{L-2} & 0 & J_{L-1}\\
0 & & \cdots & 0 & J_{L-1} & 0\end{array}\right|\;.
\label{Mgenerica}
\end{equation}
We will investigate two particular realizations of Hamiltonian (\ref{HamiltonianaGenerica})
that, as we will show, in the ground state allow for high or even
maximal entanglement between the end spins of the chain, and thus
naturally provide a channel with high or even unit fidelity for qubit
teleportation. To evaluate the teleportation fidelity, one needs to
determine the spin-spin concurrence (entanglement of formation) between
the end points of the chain. This quantity can be computed exactly
for any two-qubit state (pure or mixed), thanks to the celebrated
formula of Wootters \cite{Wootters}, and the task is left to obtain
its explicit expression in the reduced state of the two end-point
spins. To this purpose, we need to calculate explicitly all the possible
forms of two-point correlations in the ground state. The Hamiltonian
(\ref{HamiltonianaGenerica}) is symmetric under rotations of the
spins around the $z$-axis, so that the only nonvanishing correlations
are $\langle S_{i}^{x}S_{j}^{x}\rangle=\langle S_{i}^{y}S_{j}^{y}\rangle$,
$\langle S_{i}^{z}S_{j}^{z}\rangle$ and $\langle S_{i}^{z}\rangle$.
In the absence of external magnetic fields, $\pi$-rotations around
the $x$ and $y$ axes are symmetries of the model, which additionally
implies $\langle S_{i}^{z}\rangle=0$ at every site. Thanks to the
aforementioned symmetries, the two-point reduced density matrix $\rho_{i,j}$,
obtained by tracing the full density matrix of the system over all
sites except the pair $\{ i,j\}$, has the form
\begin{equation}
\rho_{i,j}=\frac{1\negthickspace{\rm I}}{4}+\langle S_{i}^{x}S_{j}^{x}\rangle\left(\sigma^{x}\otimes\sigma^{x}
+ \sigma^{y}\otimes\sigma^{y}\right)+\langle S_{i}^{z}S_{j}^{z}\rangle\sigma^{z}\otimes\sigma^{z},
\label{ReducedDensity}
\end{equation}
where $\sigma^{x,y,z}$ are the Pauli matrices and $\langle\cdot\rangle$
is the ground state average at temperature $T=0$, or the thermal
one at finite temperature $\beta=(k_{B}T)^{-1}$ with respect to the
Gibbs state $\rho=e^{-\beta H}Z^{-1}$. We are interested in the case
in which $i$ and $j$ are the two end points of the chain. In this
instance, we have
\begin{eqnarray}
& & S_{1}^{+}S_{L}^{-}+S_{1}^{-}S_{L}^{+}=-e^{i\pi\mathcal{N}}\left(c_{1}^{\dagger}c_{L}+
c_{L}^{\dagger}c_{1}\right)\;,\nonumber \\
& & S_{1}^{z}S_{L}^{z}=\left(c_{1}^{\dagger}c_{1}-\frac{1}{2}\right)\left(c_{L}^{\dagger}c_{L}
-\frac{1}{2}\right)\;,
\label{Correlazionigeneriche}
\end{eqnarray}
where $\mathcal{N}=\sum_{i=1}^{L}c_{i}^{\dagger}c_{i}$ is the total
number operator. Using Wick's theorem and taking into account that
$\langle c_{i}^{\dagger}c_{i}\rangle=1/2$, we obtain
\begin{eqnarray}
& & \langle S_{1}^{+}S_{L}^{-}+S_{1}^{-}S_{L}^{+}\rangle=
-e^{i\pi L/2}\left(\langle c_{1}^{\dagger}c_{L}\rangle
+ \langle c_{L}^{\dagger}c_{1}\rangle\right)\;,\nonumber \\
& & \langle S_{1}^{z}S_{L}^{z}\rangle=-\langle c_{1}^{\dagger}c_{L}\rangle\langle
c_{L}^{\dagger}c_{1}\rangle.\end{eqnarray}
Setting $x\equiv\langle c_{1}^{\dagger}c_{L}\rangle$ we see that
the end-to-end reduced density matrix depends uniquely on this parameter.
All the physical informations about model (\ref{Trasformata}) can
now be obtained by diagonalizing the one-body matrix $M$. Let $\xi_{k}$
be the eigenvector with eigenvalue $\Lambda_{k}$, where $k$ is a
quasi-momentum label. Then, passing to new fermionic operators via
the transformation $c_{i}=\sum_{k}\xi_{k}^{\left(i\right)}c_{k}$,
the Hamiltonian takes the form \begin{equation}
H=\sum_{k}\Lambda_{k}c_{k}^{\dagger}c_{k}\;.\end{equation}
The evaluation of the two-point correlation $x$ is then straightforward,
and one obtains
\begin{eqnarray}
x & = & \sum_{k,q}\xi_{k}^{\left(1\right)}\xi_{q}^{\left(L\right)} \langle
c_{k}^{\dagger}c_{q} \rangle \nonumber \\
& & \nonumber \\
& = & \left\{ \begin{array}{ll}
\sum_{\Lambda_{k}<0}\xi_{k}^{\left(1\right)}\xi_{k}^{\left(L\right)} & \mbox{for }T=0 \\
\rule{0mm}{5mm}\sum_{k}\xi_{k}^{\left(1\right)}\xi_{k}^{\left(L\right)}\frac{1}{1+e^{\beta\Lambda_{k}}}
& \mbox{for }T>0 \; . \end{array} \right.
\label{correlationgeneral}
\end{eqnarray}
For reduced states of the form (\ref{ReducedDensity}), the end to
end concurrence is easily computed, and we have \cite{Zanardi02}
\begin{equation}
C_{1,L}=2\max\left\{ 0,\, x^{2}+\left|x\right|-\frac{1}{4}\right\} \; .
\label{equazioneconcurrence}
\end{equation}
The above expression of the concurrence is nonvanishing for $|x|>(\sqrt{2}-1)/2\simeq0.207$,
and it reaches the maximum value $C_{1,L}=1$ for $|x|\rightarrow1/2$.
It is natural to expect that the existence of a strong quantum correlation
between the two end spins of the chain can be conveniently exploited
for performing tasks in quantum information, in particular considering
teleportation schemes. In the standard quantum teleportation protocol,
two parties A and B share a maximally entangled state (Bell state). Party
A holds also a third qubit, whose unknown state is to be teleported.
If the two end points of our $XX$ chain share a highly entangled
state, that in some limit may even be asymptotically close to a Bell
state, they can be identified as the two parties, sender and receiver,
for a long-distance, high-fidelity teleportation protocol. The efficiency
of a quantum channel in teleporting an unknown state is quantified
by the fidelity $f$ between the output and the input states, averaged
over all input realizations. The fidelity depends on the actual properties
of the entangled resource $\rho_{1,L}$ (Cfr. \eq{ReducedDensity})
shared by the end spins of the chain. In fact, it has been demonstrated
that the optimal fidelity depends only on the {}``fully entangled
fraction'' $F_{full}$, according to the formula $f=(2F_{full}+1)/3$
\cite{Horodecki}. The fully entangled fraction is defined as the
fidelity between the resource $\rho_{1,L}$ and a maximally entangled
state, maximized over all possible maximally entangled states. For
states of the form \eq{ReducedDensity} it can be easily computed,
and reads $F_{full}=\frac{1}{4}+|x|+x^{2}$ \cite{Badziag}.
The associated teleportation fidelity is thus
\begin{equation}
f=\frac{2\left(\frac{1}{4}+|x|+x^{2}\right)+1}{3} \; .
\label{generalfidelity}
\end{equation}
This expression highlights the crucial interplay between entanglement
and efficiency in quantum information protocols. In fact, due to the
high symmetry of states of the form \eq{ReducedDensity}, a nonvanishing
entanglement implies a nonclassical teleportation fidelity exceeding
the classical threshold $2/3$, and viceversa. In the limit $|x|\rightarrow1/2$
of maximally entangled resource, the maximum teleportation fidelity
reaches unity.
\section{Long-distance entanglement}
\label{LDE}
In analogy with previous work on the dimerized Heisenberg model \cite{Bologna},
we consider first the open end $XX$ chain with bonds of alternating
strengths $(1-\delta)$ (weak bond), and $(1+\delta)$ (strong bond),
with $0\le\delta\le1$. \begin{equation}
H = J \sum_{i=1}^{L-1}(1+(-1)^{i}\delta)\left(S_{i}^{x}S_{i+1}^{x} +
S_{i}^{y}S_{i+1}^{y}\right) \; .
\label{LDEHamiltonian}
\end{equation}
Choosing $L$ even and $0\le\delta\le1$ assures that the spins at
the end of the chain interact with a weak bond of strength $(1-\delta)$
with their respective neighbors.
Let us first comment on the general features of the model (\ref{LDEHamiltonian})
in the thermodynamic limit. For $\delta=0$ the model in the fermionic
picture reduces to a simple tight binding with dispersion $\Lambda_{k}=J\cos\left(k\right)$.
The ground state is given by a half filled band and vanishingly small
excitations are present near the Fermi points. Upon the introduction
of a nonvanishing $\delta$ translational invariance by one site is
broken, the Brillouin zone is correspondingly halved, and a gap of
width $\delta$ opens up in the single particle spectrum. Two bands
develop with dispersion
\begin{equation}
\Lambda_{k,\pm} = \pm J \sqrt{\cos^{2}\left(k\right) +
4\delta^{2}\sin^{2}\left(k\right)} \; .
\label{eq:dimer_bands}
\end{equation}
Upon increasing the value of $\delta$, the growing difference between
the alternating coupling constants allows the creation of dimers between
pairs of strongly interacting spins. The dimers, in turn, are very
weakly interacting with each other. Hence, because the two end spins
of the chain interact very weakly with their nearest neighbors, dimerization
and monogamy of entanglement force the creation of a strong quantum
correlation between the end points, in analogy with what happens in
the Heisenberg case \cite{Bologna}.
The above qualitative picture can be supplemented by a detailed quantitative
analysis both in the thermodynamic limit and at finite length $L$.
The eigenvectors of the adjacency matrix $M$ are given by \cite{Kuznetsova}
\begin{equation}
\xi_{k,\mu_{k}}^{\left(j\right)}=\left\{ \begin{array}{cl}
A_{k}\sin\left(kj\right) & j\,\,\mathrm{even}\;,\\
\mu_{k}A_{k}\sin\left(k\left(L-j+1\right)\right) & j\,\,\mathrm{odd} \; ,
\end{array} \right. \label{LDEeigenvector}
\end{equation}
where $\mu_{k}=\pm1$ is the parity (left-right symmetry) of the
eigenstate $\xi_{k}$, and $A_{k}$ is a normalization constant that
reads
\begin{equation}
A_{k} = 2 \left[2\left(L+1-\frac{\sin2k\left(L +
1 \right)}{\sin\left(2k\right)}\right)\right]^{-1/2} \; .
\label{LDEAk}
\end{equation}
The quasimomenta are given by the solution of the following equation
\begin{equation}
\frac{\sin k\left(L+2\right)}{\sin\left(kL\right)}=
-\frac{1+\delta}{1-\delta}\equiv-\frac{1}{a} \; .
\label{LDEQuasimomenta}
\end{equation}
For each quasimomentum we have two eigenvectors corresponding to
opposite parity. Hence we seek for $L/2$ solutions of (\ref{LDEQuasimomenta}).
When $a<L/\left(L+2\right)$ (roughly $\delta>0$, when $L$ is large)
we have $L/2-1$ real solutions for which the energy dispersion has
the form (\ref{eq:dimer_bands}). The missing solution is complex
(and plays a very important role) and has the form $k_{0}=\pi/2+ip$.
For this mode the equation reads
\begin{equation}
\cosh\left(2p\right) + \coth\left(Lp\right)\sinh\left(2p\right) =
\frac{1}{a} \; .
\end{equation}
At leading order the solution is given by
\begin{equation}
e^{2p}=\frac{1}{a}-\left(1-a^{2}\right)a^{L-1} \; .
\end{equation}
The appearance of a complex quasimomentum is crucial for the existence
of long-distance entanglement (LDE) in the ground state and can be
understood as follows. The eigenvectors $\xi_{k_{0},\pm}$ are localized
at the boundaries of the chain. For instance, for site $j$ close
to the left border of the chain ($j\simeq1$), one has
$\left|\xi_{k_{0},\pm}^{\left(j\right)}\right|\simeq e^{(L-j+1)/\zeta}$,
with a localization length $\zeta$ that, for an asymptotically large
chain, reads
\begin{equation}
\zeta = 2/\ln\left[\left(1+\delta\right)/\left(1-\delta\right)\right] \; .
\label{localizationlength}
\end{equation}
The energy of this mode, for both value of the parity, is exponentially
small:
\begin{equation}
\Lambda_{k_{0},\pm}\simeq\pm2\left(1-a\right)e^{-L/\zeta} \; ,
\label{eq:LDE_gap}
\end{equation}
and we thus see that the onset of LDE in the dimerized ground state
of the $XX$ chain with open ends is strictly linked to the existence
of an energy gap above the ground state that vanishes exponentially
fast with the length of the chain.
At zero temperature and zero external field, all negative energy modes
are filled, up to $\Lambda_{k_{0},-}$. The mode $k_{0}$ is responsible
for the appearance of a state localized at the end of the chain in
the many-body ground state. This means that the ground state resemble
$\Psi\simeq\psi_{1,L}\otimes\psi_{\mbox{rest}}$. As we have dimer
order at sites $1$ and $L$, we expect $\psi_{1,L}$ to be highly
entangled. Because factorization will not be exact, $\psi_{1,L}$
will not be exactly a pure state but rather a weakly mixed reduction
$\rho_{1,L}$ that becomes maximally entangled only in the asymptotic
regime of perfect dimerization. In fact, knowing the eigenvectors
of the adjacency matrix, we can evaluate exactly the end-to-end LDE
between the borders of the chain. Using Eq.~(\ref{LDEeigenvector}),
the fermionic correlation function $x$ reads
\begin{equation}
x = \langle c_{1}^{\dagger}c_{L}\rangle =
\sum_{k,\,\Lambda_{k}<0}\mu_{k}A_{k}^{2}\left[\sin\left(Lk\right)\right]^{2} \; .
\label{LDEx}
\end{equation}
To evaluate this sum we first isolate the contribution coming from
the complex momentum. The remaining set of terms defines a sum with
alternating signs of a periodic function analytic on the real axis.
The rate of convergence to its asymptotic vanishing value is dictated
by the width of the largest strip, around the imaginary axis, where
the function is analytic. The inverse of this width is precisely given
by the localization length \eq{localizationlength}. Such contribution
is exponentially suppressed, and the final result is
\begin{eqnarray}
x & = & \left(-1\right)^{L/2}\frac{1}{2}\left(1-a^{2}\right) +
O\left(e^{-L/\zeta}\right) \nonumber \\
& = & \left(-1\right)^{L/2}\frac{2\delta}{\left(1 +
\delta\right)^{2}} + O\left(e^{-L/\zeta}\right) \; .
\label{endtoendcorrelation}
\end{eqnarray}
We have checked this approximation against exact numerical data and
the results are plotted in Fig.~\ref{figesatta}. It turns out that
the remainder has the form $\left(-1\right)^{L/2}A_{0}L^{2}\exp\left(-L/\zeta\right)
+ \ldots$, where $A_{0}$ is a positive constant. This implies that, in modulus,
the asymptotic value of the end-to-end correlation is in fact approached
from below: In this type of systems, correlations \textit{increase}
as the length $L$ of the chain is increased.
We see that, for any nonvanishing value of the dimerization, the ground
state of the system develops a constant, non-zero correlation between
the end points of arbitrarily large chains, a phenomenon known as
surface order. Using Eq.~(\ref{equazioneconcurrence}), we deduce
that this surface order, present whenever $\delta>0$ (and $\delta<1$)
allows for LDE between the end spins as soon as
$\delta>\delta_{0} =
\left(1-\sqrt{2-\sqrt{2}}\right)/\left(1+\sqrt{2-\sqrt{2}}\right)=0.132$,
i.e.~for moderately low values of the dimerization. The corresponding
threshold localization length is $\zeta_{0}=7.479$. The localization
length $\zeta$ rapidly decreases from the threshold value $\zeta_{0}$
with increasing $\delta>\delta_{0}$.
As a consequence, the asymptotic regime for the corresponding end-to-end
concurrence (LDE) is reached already for chains with a size of few
tens of sites.
\begin{figure}[t]
\includegraphics[width=8cm]{xx_dimer_x_scaling.eps}
\caption{(Color online) Absolute value of the zero-temperature correlation
$x_{L}=|\langle c_{1}^{\dagger}c_{L}\rangle|$
as a function of the size $L$ of the chain according to the scaling
$x_{L}=x_{\infty}-A_{0}L^{2}\exp(-L/\zeta)$. The different
curves reproduce $\ln[(x_{\infty}-x_{L})/L^{2}]$ as a function of
$L$ for different values of the dimerization parameter $\delta$.
Symbols denote the exact numerical values. The values of $\zeta$
are obtained from \eq{localizationlength}.}
\label{figesatta}
\end{figure}
Finally, by substituting in \eq{equazioneconcurrence} and in \eq{generalfidelity}
the expression of $x$ \eq{endtoendcorrelation}, we obtain the analytic
expressions of the LDE (end-to-end concurrence) and of the teleportation
fidelity as functions of the dimerization ratio $a=(1-\delta)/(1+\delta)$
in the asymptotic regime of chains of large size $L\gg\zeta_{0}$.
One has:
\begin{eqnarray}
C_{1,L} & = & 2\max\left\{ 0,\frac{1}{2}-a^{2}+\frac{a^{4}}{4} \right\} \; , \\
& & \nonumber \\
f & = & \frac{2}{3}\left[1+\left(\frac{1}{2}-a^{2} +
\frac{a^{4}}{4}\right)\right] \; .
\label{formulefinaliLDE}
\end{eqnarray}
\begin{figure}
\begin{centering} \includegraphics[width=75mm,keepaspectratio]{concurrence_dimer.eps}
\par\end{centering}
\caption{End to end concurrence $C_{1,L}$, for long chains of length $L\gg\zeta_{0}$
in the dimer model (\ref{LDEHamiltonian}), as a function of the dimerization
parameter $\delta$. Nonvanishing LDE is achieved and is rapidly growing
as soon as $\delta>\delta_{0}=0.132$.}
\label{fig:concurrence_dimer}
\end{figure}
In Fig. \ref{fig:concurrence_dimer} we report the behavior of the
LDE between the end points of the chain as a function of the dimerization
parameter $\delta$ for large chains. We see that as soon as the dimerization
is above the threshold value $\delta_{0}$, the LDE grows very rapidly
with $\delta$, reaching saturation in the limiting situation $\delta\rightarrow1$.
Before ending this section we should remark that, although extremely
interesting, the true LDE picture, derived at zero temperature, does
not survive, even qualitatively, at finite temperature. We have seen
that the presence of LDE in the dimerized $XX$ is connected to the
presence of an eigenstate of the adjacency matrix with complex quasimomentum.
From Eq.~(\ref{eq:LDE_gap}) it follows that the energy gap between
the ground state and the lowest excited state vanishes exponentially
as the size of the chain increases. Hence, even for small chains and
very low temperatures, the first excited levels get significantly
populated, contributing to the correlation $x$ with values of opposite
sign with respect to that of the ground state. The total effect is
to lower $x$ down to zero even at very low temperatures. In conclusion,
we have determined that LDE can be supported at zero temperature by
relatively simple, dimerized $XX$ chains with open ends. However,
in close analogy with more complex systems analyzed previously \cite{Bologna},
the zero temperature LDE does not survive as soon as temperature is
switched on.
\section{Quasi long-distance entanglement}
\label{QLDE}
In this section we discuss a second type of model that can support
highly entangled reduced states at the end points of a spin chain.
In all generality, spin models that can allow for strong end-to-end
correlations are characterized by interactions between the end points
and their nearest neighbors that are smaller compared to the interactions
in the bulk of the chain. Otherwise, if the system does not meet this
criterion, the end points would become strongly entangled with their
neighbors, excluding, due to monogamy constraints \cite{Coffman},
the possibility of LDE. We then consider a model of open $XX$ spin
chain formed by $L-2$ spins with uniform coupling strengths, plus
two weakly interacting probes placed at the two end points. Such a
models is described by the following Hamiltonian
\begin{eqnarray}
H & = & J\sum_{i=2}^{L-2}\left[S_{i}^{x}S_{i+1}^{x}+S_{i}^{y}S_{i+1}^{y} \right.
\label{QLDEHamiltoniana} \\
& & + \left. \lambda \left(S_{1}^{x}S_{2}^{x}+S_{1}^{y}S_{2}^{y}+
S_{L-1}^{x}S_{L}^{x}+S_{L-1}^{y}S_{L}^{y} \right) \right] \; , \nonumber
\end{eqnarray}
where $0<\lambda<1$. The presence of the $\lambda$-term in Eq.~(\ref{QLDEHamiltoniana})
can be understood as a kind of generalized boundary condition, reducing
to the standard $XX$ model with uniform couplings and open ends for
$\lambda=0,1$. It is then not surprising that the eigenvalues of
the corresponding adjacency matrix $M$ have the form $\Lambda_{k}=J\cos\left(k\right)$.
The eigenvalue equation determining the quasimomenta for a generic
$\lambda$ reads \cite{Woj05}
\begin{equation}
\mu_{k}\cot\left(k\right)\left[\cot\left(\frac{L-1}{2}k\right)\right]^{\mu_{k}} =
\, \frac{\lambda^{2}}{2-\lambda^{2}} \; ,
\label{QLDEquasimomenti}
\end{equation}
where $\mu_{k}=\pm1$ is again the parity of the corresponding eigenstate.
The eigenstate $\xi_{k}$ associated to the quasimomentum $k$ has
the following components:
\begin{eqnarray}
\xi_{k}^{\left(1\right)} & = & \frac{\lambda}{A_{k}}\sin(k) \; , \nonumber \\
\xi_{k}^{\left(i\right)} & = & \frac{1}{A_{k}}\left(\sin((i+1)k)\right. \nonumber \\
& & \left.+(1-\lambda^{2})\sin((i-1)k)\right)\;,\;\;\;1<i<L \; , \nonumber \\
\xi_{k}^{\left(L\right)} & = & \mu\frac{\lambda}{A_{k}}\sin(k) \; ,
\label{eq:QLDE_vector}
\end{eqnarray}
where the normalization $A_{k}$ reads
\begin{equation}
A_{k}^{2}=(L-1)\left[2(1-\lambda^{2})\cos^{2}(k) +
\frac{\lambda^{4}}{2}\right]+2\lambda^{2}-\lambda^{4} \, .
\label{QLDEomega}
\end{equation}
Eq.~(\ref{QLDEquasimomenti}) admits $L$ distinct real solutions
in the interval $\left(0,\pi\right)$ for $\lambda\neq0$. Using Eq.~(\ref{eq:QLDE_vector})
the zero temperature end-to-end correlation $x$ reads
\begin{equation}
x=\sum_{\pi/2<k<\pi}\mu_{k}\frac{\lambda^{2}}{A_{k}^{2}}\sin^{2}k \; .
\label{QLDEx}
\end{equation}
The sum is limited to the $L/2$ quasimomenta that lie in the half-interval
$\pi/2<k<\pi$. This condition takes into account the fact that, at
exactly zero temperature, all levels below the Fermi energy are occupied,
while all the others are empty.
\begin{figure}[t]
\begin{centering} \includegraphics[width=75mm,keepaspectratio]{qlde_e2e_conc.eps}
\par\end{centering}
\caption{(Color online) End-to-end concurrence $C_{1,L}$ at zero temperature
as a function of $\lambda$ for different lengths $L$ of the chain.
Curves from right to left are, respectively, for $L=26$; $L=50$;
$L=100$; $L=200$; and $L=400$.}
\label{fig:QLDE_conc}
\end{figure}
The value of the end-to-end concurrence $C_{1,L}$ is readily obtained
by inserting expression (\ref{QLDEx}) for the end-to-end correlation
$x$ in Eq.~(\ref{equazioneconcurrence}). In Fig. \ref{fig:QLDE_conc}
we show the behavior of the end-to-end entanglement as a function
of $\lambda$, for different lengths of the chain. At fixed length
$L$ of the chain, $C_{1,L}\rightarrow1$ as $\lambda\rightarrow0$.
At a fixed value of $\lambda$, the end-to-end concurrence slowly
dies off as $L\rightarrow\infty$. The $XX$ spin chain with small
end bonds is thus characterized by what we may name \textit{{}``Quasi
Long-Distance Entanglement} (QLDE) because, at variance with the dimerized
case considered in the previous section, the end-to-end entanglement,
although able to reach asymptotically maximal values in the limit
of vanishing end-couplings, slowly decreases as the size of the chain
is increased. These considerations can be made quantitative by investigating
in detail the exact expressions for $x$ that are obtained from Eq.~(\ref{QLDEx})
in the two limiting cases $\lambda\rightarrow0,1$.
In the limit of vanishing small end bonds ($\lambda\rightarrow0)$,
the quasimomenta assume the expressions
\begin{eqnarray}
k_{n} & \simeq & \frac{n\pi}{L-1} -
\lambda^{2}\frac{\tan\left(\frac{n\pi}{L-1}\right)}{L-1},\quad n=1,2,\dots,L-2 \, ,
\nonumber \\
& & \nonumber \\
k_{\pm} & \simeq & \frac{\pi}{2}\pm\frac{\lambda^{2}}{2} \; .
\label{eq:QLDE_momenta}
\end{eqnarray}
Isolating the dominating contributions in the sum (\ref{QLDEx}),
and keeping terms up to second order in $\lambda$, in the limiting
case $\lambda\rightarrow0$, one obtains
\begin{equation}
x_{\lambda\rightarrow0}=\left(-1\right)^{L/2}\left[\frac{1}{2} -
\lambda^{2}L\overbrace{\left(\frac{1}{4}+\frac{2\mathcal{C}}{\pi^{2}}\right)}^{c} +
O\left(\lambda^{4}\right)\right] \, ,
\label{eq:QLDE0}
\end{equation}
where $\mathcal{C}$ is Catalan's constant $\mathcal{C}=0.915$,
and the constant in brackets is $c=0.435$. The above result provides
the quantitative content of the qualitative picture sketched above:
At fixed size $L$ of the chain, one can always choose $\lambda$
small enough so that $\left|x\right|\rightarrow1/2$ and the end-to-end
concurrence approaches unity. Depending on the length of the chain,
the condition to be satisfied to achieve large values of the end-to-end
concurrence is $\lambda\ll1/\sqrt{L}$.
For completeness, let us now consider the opposite situation of strong
end bonds $\lambda\rightarrow1$. In this case, all the $L$ quasimomenta
can be approximated by $k_{n}\simeq\pi n/(L+1)$ with $n=1,\ldots,L$.
Exploiting the fact that, at leading order, the alternating Riemann
sum of a function is equal to (one-half of) the value of the function
at the extrema, we obtain
\begin{equation}
x_{\lambda\rightarrow1}\simeq\left(-1\right)^{L/2}\frac{1}{\lambda^{2}\left(L-3\right)+4} \; .
\label{QLDEXapprossimata1}
\end{equation}
In Fig.~\ref{fig:comparison} we compare the exact expression of
$x$ as a function of $\lambda$, obtained by direct numerical diagonalization,
with the two analytic limiting expressions and an interpolating {\it ansatz}
for a chain of $L=100$ sites.
\begin{figure}[t]
\begin{centering} \includegraphics[width=75mm,keepaspectratio]{test_quasi_LDE_N100.eps}
\par\end{centering}
\caption{(Color online) Comparison between the exact numerical evaluation
and the analytic approximations for the end-to-end correlation function
$x=\langle c_{1}^{+}c_{L}\rangle$ for a chain of $L=100$ sites.
The intepolating curve is given by $x_{int}=\left(-1\right)^{L/2}/\left(2+4cL\lambda^{2}\right)$.
It is exact up to $O\left(\lambda^{2}\right)$ when $\lambda\rightarrow0$,
but retains its validity also for higher values of the coupling.}
\label{fig:comparison}
\end{figure}
We will now show that the phenomenon of QLDE is intimately related
to an algebraic scaling behavior of the energy gap that is radically
different from the one, exponentially decreasing with the size of
the chain, exhibited by the fully dimerized $XX$ chain. This feature
turns out to play a crucial role at finite temperature, allowing QLDE
to be more resilient to thermal fluctuations not only at very low
but even at moderately low temperatures.
\begin{figure}[t]
\begin{centering}\includegraphics[width=78mm,keepaspectratio]{gaps_qlde.eps}
\par\end{centering}
\caption{(Color online) Behavior of the energy gap $\Delta_{L}$ as a function
of the length $L$ of the chain for different values of $\lambda$.
Diamonds denote the exact numerical data. Continuous curves display
the approximate expression for the gap (Eq. (\ref{eq:QLDE_gap_approx})
in the text).}
\label{fig:gaps_qlde}
\end{figure}
As already pointed out, the single-particle dispersion law has the
form $\Lambda_{k}=J\cos k$. The lowest gap is then given by $J\cos\left(k^{\ast}\right)$
where $k^{\ast}$ is the solution of Eq. (\ref{QLDEquasimomenti})
closest to $\pi/2$ with $k^{\ast}<\pi/2$. For sufficiently large
values of $L$, the LHS of Eq. (\ref{QLDEquasimomenti}) has a vertical
asymptote arbitrarily close to $\pi/2$. Expanding the function around
this point we obtain for the desired solution \[
k^{\ast}\simeq\frac{\pi}{2}-\frac{\pi}{2\left(L-1\right)}+
\frac{\pi}{\left(L-1\right)^{2}\lambda^{2}\left(2-\lambda^{2}\right)^{-1} +
2\left(L-1\right)} \, . \]
Then, at leading order in inverse powers of the length of the chain
$L$, the lowest energy gap reads
\begin{eqnarray}
& & \frac{\Delta_{L}}{J}\simeq\frac{\pi}{2\left(L-1\right)} -
\frac{\pi}{\left(L-1\right)^{2}\frac{\lambda^{2}}{2 -
\lambda^{2}}+2\left(L-1\right)} \label{eq:QLDE_gap_approx} \\
& & = \frac{\pi}{2}L^{-1}-\left(\frac{\pi}{2} -
\frac{\pi\left(2-\lambda^{2}\right)}{\lambda^{2}}\right)L^{-2} +
O\left(L^{-3}\right) \, . \nonumber
\end{eqnarray}
We have compared the asymptotic analytic behaviors for different
$\lambda$ and chains of length up to $L=1000$ sites with the exact
numerical solutions. The results of this comparison are plotted in
Fig.~(\ref{fig:gaps_qlde}), showing excellent agreement of the exact
data with the algebraic scaling (\ref{eq:QLDE_gap_approx}).
The existence of a lowest energy gap slowly falling off algebraically
with the size of the system is to be compared with the exponentially
fast vanishing of the same quantity in the case of the dimerized $XX$
chain. Looking at the structure of the quasimomenta in the two cases,
we immediately realize that the reason for this very different behavior
lies in the absence of complex quasimomenta in the spectrum of the
$XX$ model with small end bonds. On the one hand, this is an undesired
feature, because it is exactly the presence of a complex quasimomentum
that allows for true LDE in the dimerized $XX$ model. On the other
hand this very same feature allows for true LDE and at the same time
is responsible for the exponentially fast vanishing of the energy
gap.
Moving to finite temperature, the exact numerical evaluation of the
fermionic end-to-end correlation function $x$ is obtained using \eq{correlationgeneral}.
After having determined the value of $x$, we can again use Eqs. (\ref{equazioneconcurrence})
and (\ref{generalfidelity}) to evaluate both the end-to-end concurrence
and the teleportation fidelity.
\begin{figure}[t]
\begin{centering}\includegraphics[width=75mm,keepaspectratio]{qlde_fidelity_T_N50.eps}
\par\end{centering}
\caption{(Color online) Teleportation fidelity for different values of $\lambda$
as a function of the rescaled temperature $T/J$ for a $XX$ chain
with small end bonds, supporting QLDE. Here the length of the chain
is fixed at $L=50$ sites. The horizontal dashed line $f=2/3$ is
the maximum attainable fidelity using a classical teleportation channel.}
\label{fvst}
\end{figure}
In \fig{fvst} we report the behavior of the teleportation fidelity
$f$ for different values of $\lambda$ as a function of the normalized
temperature $T/J$ for a chain of $L=50$ spins. We see that the higher
the limiting value of the fidelity at vanishing temperature, the faster
$f$ falls off below the classical threshold $f=2/3$. This behavior
is obviously due to the fact that a larger zero-temperature $f$ corresponds
to a smaller energy gap, and hence the system is more sensitive to
the disruptive effect of thermal fluctuations.
We can compare the results reported in \fig{fvst} for an $XX$ chain
with small end bonds with the ones obtained for an Heisenberg antiferromagnetic
chain with two weakly interacting end probes \cite{Bologna2}. The
teleportation efficiency at finite temperature for both models has
been investigated at the same fixed length of the chain $L=50$. From
this comparison, one sees that the behavior of the teleportation fidelity
as a function of the temperature in the two models is qualitatively
similar. This fact is of relevance, because it shows that the QLDE
due to the presence of weakly interacting probes at the and of a uniformly
interacting chain is an effect not restricted to a particular Hamiltonian
model, but can be supported by systems endowed with different bulk
interactions and different symmetries. The only important ingredient
for the realization of a QLDE and a teleportation channel that are
robust against thermal fluctuations is the availability of efficient
control on the interactions at the end points of the channel. Similar
conclusions can be drawn about LDE: In this work we have demonstrated
that existence of true LDE at zero temperature is a phenomenon not
restricted to a particular model and, in fact, does not crucially
depend on the mechanism of dimerization. Preliminary studies indicate
that gapped, anisotropic models in non critical regimes can sustain
LDE even in the absence of a clear pattern of dimerization.
Finally, it is worth noticing that even if the Heisenberg model with
small end bonds analyzed in Ref. \cite{Bologna2} sustains a teleportation
fidelity that remains above the classical threshold for larger values
of the end coupling parameter $\lambda$, the $XX$ channel with small
end bonds assures teleportation with nonclassical fidelities for larger
values of the temperature. Depending on the realistic experimental
settings, if the temperature can be controlled down to sufficiently
low values, it is more convenient to engineer a channel based on the
Heisenberg-like Hamiltonian proposed in Ref. \cite{Bologna2}. Otherwise,
if control on the external temperature cannot be implemented with
high precision down to sufficiently low temperatures, it may then
turn out more convenient to engineer $XX$ chains of the type discussed
in the present paper.
\section{Conclusions and outlook}
In conclusion, we have studied models of open quantum spin chains
endowed with $XX$-like Hamiltonians with nearest-neighbor interactions.
We have discussed two types of models, according to different engineerings
of the spin-spin couplings. In the first case considered, a chain
with bonds of alternating strengths, we have shown how the exact solution
for the ground state implies the existence of long-distance entanglement
between the end spins of the chain, independent of the size of the
system and asymptotically close to unity (maximal entanglement) in
the limit of exact dimerization. This system is therefore perfectly
suited for \textit{bona fide} long-distance quantum teleportation
with ideal fidelity at zero temperature. However, the limiting maximal
values of the fidelity are obtained for an exponentially small energy
gap above the ground state. Therefore, this system is \textit{de facto}
useless for efficient quantum teleportation at finite temperature.
We have then moved on to discuss another class of $XX$ open spin
chains with uniform bulk interactions and small end bonds. In this
case, we have shown that for sufficiently small values of the end
couplings, the ground state of the system supports a quasi long-distance
entanglement between the end spins of the chain, asymptotically close
to unity (maximal entanglement) in the limit of vanishing coupling,
but slowly decreasing as the length of the chain is increased. An
interesting feature of this model is that the lowest energy gap above
the ground state vanishes only algebraically, as the first power of
the inverse of the size of the system. Therefore, in principle, it
can be exploited as a quantum channel for teleportation with nonclassical
fidelity at finite temperature, both very low and moderately low.
Considering future research along these lines of investigation, it
will be interesting to consider practical schemes for the realization
of this kind of spin chains in highly controllable situations, for
instance resorting to ultracold atomic mixtures in optical lattices.
Another interesting open problem worth further study is to assess
the existence and the possible location of a crossover between true
long-distance and \textit{prima facie} quasi long-distance
entanglement behaviors.
\acknowledgments
It is a pleasure to thank Cristian Degli Esposti Boschi and Marco
Roncaglia for many insightful and frutiful discussions. S. M. G. and
F. I. acknowledge financial support from MIUR under PRIN National
Projects 2005, INFN, and CNR-INFM Coherentia. F. I. acknowledges financial
support from the ISI Foundation.
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Q: Run -jar with args and use args in Spring I need to run jar with static parameter, for example, java -jar myapp-1.0.0.jar /path/static/myfolder, and use this path "/path/static/myfolder" in my code. So, I know how to get this parameters in PSVM (String..args), but how to get it in Spring? Is there annotation for this or may be in properties file>
A: For example: java -jar -Dtest=abcd myapp-1.0.0.jar.
You can use System.getProperty("test") to get value.
-D{parameter} needs to be before that jar
A: It is really answer for my question:
create special @Component that implements CommandLineRunner and override method Run, like this:
@Component public class StartupPrintRunner implements CommandLineRunner {
private String folder;
@Override public void run(String... args) throws Exception {
this.folder = Arrays.deepToString(args); }
}
Inject bean StartupPrintRunner where you need and get parameters. It returns String looks like an array: [parameter1, parameter2.., parameter n] and we can parse it to get necessary paarameter.
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{"url":"https:\/\/www.mathdoubts.com\/cos-0-degrees\/","text":"$\\cos{(0^\u00b0)}$ value\n\n$\\cos{(0^\u00b0)} \\,=\\, 1$\n\nThe value of cosine in a zero degrees right triangle is called the cosine of angle zero degrees.\n\nIntroduction\n\nThe cosine of angle zero degrees is a value, which represents the quotient of length of adjacent side by the length of hypotenuse when the angle of a right triangle is equal to zero degrees.\n\nIn Sexagesimal system, the cos of angle zero degrees is written as $\\cos{(0^\u00b0)}$ and the exact value of cosine of angle zero degrees is equal to one. It is written mathematically in the following form in trigonometry.\n\n$\\cos{(0^\u00b0)} \\,=\\, 1$\n\nThe cosine of angle zero degrees is also expressed in two other forms in trigonometric mathematics.\n\ncircular system\n\nThe cosine of zero degrees is expressed as cosine of zero radian. In circular system, it is written in mathematical form as $\\cos{(0)}$.\n\n$\\cos{(0)} \\,=\\, 1$\n\nCentesimal system\n\nIn the same way, the cosine zero degrees is also expressed as cosine of angle zero grades and it is written in mathematical form as $\\cos{(0^g)}$ in Centesimal system.\n\n$\\cos{(0^g)} \\,=\\, 1$\n\nProofs\n\nThe exact value for cosine of zero degrees can be derived in three different methods in mathematics.\n\nLatest Math Topics\nApr 18, 2022\nApr 14, 2022\nMar 18, 2022\nLatest Math Problems\nApr 06, 2022\n\nA best free mathematics education website for students, teachers and researchers.\n\nMaths Topics\n\nLearn each topic of the mathematics easily with understandable proofs and visual animation graphics.\n\nMaths Problems\n\nLearn how to solve the maths problems in different methods with understandable steps.\n\nLearn solutions\n\nSubscribe us\n\nYou can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.","date":"2022-05-28 17:09:30","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 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\": 0.7337191700935364, \"perplexity\": 1151.8146210721866}, \"config\": {\"markdown_headings\": false, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 20, \"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-2022-21\/segments\/1652663016949.77\/warc\/CC-MAIN-20220528154416-20220528184416-00065.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.physicsforums.com\/threads\/processors-chipsets-and-sockets-oh-my.214929\/","text":"# Processors, chipsets, and sockets (oh my!)\n\nHomework Helper\nI was trying to compare processors for a computer that I might get\/make eventually, and I determined that I don't know enough about the various chipsets to make an informed choice. To begin, I want to be able to compare processor prices including motherboards, since if a motherboard has a new\/uncommon socket that's compatible only with a few expensive motherboards, that's an effective increase in the price of the chip. Further, insofar as I have a choice in buying a motherboard (several that all work with a given processor) I'm not sure how to compare them. RAM expandability is one clear difference, but what else is there and how much does it matter?\n\nI could really use a good resource on the topic -- I feel a little out of my league here.\n\nvincentm\nAre you building a PC? If so, what will uit be used for? What's your budget? Right now i'd stick with Intel Chipsets, on ASUS motherboards. X38 seems to be the latest, but ASUS boards having this can be quite spendy, you also need to know which RAM you're going to slap in. DDR3 seems to be the fastest thus far.\n\nHomework Helper\nWell... I've been thinking about Microwulf and just testing the waters of budgetary feasibility. I'd need at least four motherboards and processors, maybe more. What do you think?\n\nvincentm\nuhm ok, i'm not familair with Microwulf cluster\n\nHomework Helper\nuhm ok, i'm not familair with Microwulf cluster\n\nIt's all on the link I gave. The manifest should give a pretty good overview. Basically, it's four dual-core processors, one a master with a hard drive, CD drive, and Internet connection, and the other three compute nodes. The compute nodes have small boot partitions on the main hard drive -- just enough to get Linux started -- and they're all linked with a fast Ethernet connection.\n\nsl1solo76\nGiven youd be planning on using the same parts, itd be cheaper... alot cheaper at least with the CPU's and RAM for the MB....\n\nas far as bang for your buck and universality goes, i think the AMD AM2 platform would be good for a budget project like this. Everything in that line has gotten ALOT cheaper in the last few..\n\ntaking from your question that your asking about motherboards- To be completely honest, motherboards are really only as good as what you put on them, given you pay a decent price. most run a universal 1000mhz Hyper threading frequency under 100 bucks, and after that, its all preference of what sound\/North and South Bridge\/ and possibly integrated video chips they run.\n\nPersonally, i love either AMD or nvidia Nforce on the bridge(S)\n\nGold Member\nHere is a good site for you http:\/\/www.clustermonkey.net\/\/content\/view\/211\/1\/\n\nI have also been considering building one to run SETI on.\n\nHomework Helper\nGiven youd be planning on using the same parts, itd be cheaper... alot cheaper at least with the CPU's and RAM for the MB.\n\nYes, there's a more recent price estimate on the site I linked to, something like $1200 as of six months ago. But I would use faster chips, so the price wouldn't necessarily be lower. as far as bang for your buck and universality goes, i think the AMD AM2 platform would be good for a budget project like this. Everything in that line has gotten ALOT cheaper in the last few. This is why I wanted to know about motherboards. Right now I have a spreadsheet comparing MHz per dollar and the cheap chips are given an unfair advantage because I'm not considering motherboard cost (or RAM, but that's less straightforward to compare). That's why I want information on motherboards: so I can more fairly compare CPUs. Ideally I'd find the 'best' (cheapest? highest performance?) motherboard for a given chip and compare them to other motherboard + CPU bundles. taking from your question that your asking about motherboards- To be completely honest, motherboards are really only as good as what you put on them, given you pay a decent price. most run a universal 1000mhz Hyper threading frequency under 100 bucks, and after that, its all preference of what sound\/North and South Bridge\/ and possibly integrated video chips they run. So you'd recommend getting the cheapest motherboard that can support the chip, yes? Science Advisor Homework Helper Here is a good site for you http:\/\/www.clustermonkey.net\/\/content\/view\/211\/1\/ I have also been considering building one to run SETI on. I read that before posting. Good article. If you do build it or something similar, I'd love to hear how it goes -- plus get any information from you on what did and didn't work. B. Elliott IMO, I would opt for an Intel processor over an AMD if the intention is for raw number crunching. I would save AMDs for gaming machines. The bang for the buck on the mid-range Intel's is unbeatable... faster performance when compared to a same speed AMD. It's also getting harder to compare processor performance if all you're looking at is just the clock speed. How the data is actually being handled can be a considerable tie breaker between two same-speed processors. I know you've probably had quite a few people tell you that you can build the same system for much cheaper now than you could back then, but let me recommend this. The system parts that I found were all on Newgg. Better motherboard, 2GB of ram vs. 1GB (also runs the memory in dual channel mode), a 25watt increase in the P\/S output, 52x vs a 16x cd-rom speed and a hard drive with the same capacity only a larger memory cache which has been shown to improve performance with large-file transfers. I'll admit that the cd-rom drive performance will most likely be insignificant considering your application so you may be fine with an older, slower drive. The lesser price just nabbed my attention. That and i've never had any major issues with Asus products. ASUS P5VD2-VM SE$46.99 + 5.85 x 4 = $223.32 Core2DuoE4600 2.4GHz$144.99 x 4 = $579.96 Kingston pc25300 2x1GB$38.99 + 4.99 x 4 = $175.92 P\/S PS350MA 350w$17.99 + 6.54 x 4 = $98.12 WDSE16 WD2500KS250GB$69.99 x 1 = $69.99 ASUS CD-S520B 52X$11.99 x 1 = $11.99 +_________ =$1159.30\n\nIntel PRO\/1000 PT PCI-Express NIC 164.00\nIntel PRO\/100 S PCI NIC 15.00\nTrendware TEG-S80TXE 8-port Gigabit Switch 75.00\nZalman ZM-F3 120mm Case Fans 32.00\nGeneric NET12 Fan Grill (120mm) 10.00\n36\" x 0.25\" threaded rods 5.00\nLots of 0.25\" nuts and washers 10.00\n12\" x 11\" polycarbonate pieces 0.00\n1159.30\n+________\nTotal = $1470.30 Although slightly greater than your last cost update, the performance increase would be considerable for your app, but that's just MO. Last edited: B. Elliott Forgot to add that if you happen to consider overclocking, the E4600s are good overclockers. I was able to hit 2.8GHz with one on stock voltage and a standard 775 cpu cooler. The motherboard is also overclock friendly. Both allowing an extra bit of headroom without stressing any components... if you feel like squeezing a bit more out of them. Science Advisor Homework Helper Could I just scavenge old power supplies? Forgot to add that if you happen to consider overclocking, the E4600s are good overclockers. I was able to hit 2.8GHz with one on stock voltage and a standard 775 cpu cooler. The motherboard is also overclock friendly. Both allowing an extra bit of headroom without stressing any components... if you feel like squeezing a bit more out of them. Since I'm doing math instead of gaming, I've always been a little wary of overclocking. My understanding is that overclocked machines tend to have (at least) floating-point mistakes -- one every trillion, quadrillion, or hundred quadrillion cycles, perhaps -- and while these mistakes don't matter when you're just rendering polygons real-time in a game, I can't tolerate the mistakes doing math. Can you correct any misunderstandings of mine here? Is there a safe zone for overclocking? And yes, RAM errors are just as bad and harder to avoid due to cosmic rays, but hopefully I can make a system with ECC? B. Elliott Could I just scavenge old power supplies? Since I'm doing math instead of gaming, I've always been a little wary of overclocking. My understanding is that overclocked machines tend to have (at least) floating-point mistakes -- one every trillion, quadrillion, or hundred quadrillion cycles, perhaps -- and while these mistakes don't matter when you're just rendering polygons real-time in a game, I can't tolerate the mistakes doing math. Can you correct any misunderstandings of mine here? Is there a safe zone for overclocking? And yes, RAM errors are just as bad and harder to avoid due to cosmic rays, but hopefully I can make a system with ECC? With the newer processors they require an additional four or eight pin power plug for additional processor power. As long as you find a p\/s with enough juice and the additional plug, it should work fine. The floating point errors is definitely a concern for you, but as long as you don't try to really 'push' the limits of the cpu you shouldn't experience any random, fluke errors. One thing that i've noticed over the past few years is that Intel's processors have come a long way as far as providing enough headroom for overclocking without stress. It seems as though when they test the processors and are about to stamp them with their rating, they drop the final rating a considerable amount. Back when I was playing with overclocking Celeron 500s i'd be amazed to get anywhere near a stable 18 to 19% overclock. Using Intels E6700 as an example, i'm now able to hit a stable 25% overclock. This is also without any additional voltage increase or a huge aftermarket heatsink. Some people have been able to clock them higher, but that's were having \"the pick of the crop\" comes in. When you try to push the envelope is where problems start to show. I'd say the safe margin for avoiding any errors would be around a 10-15% overclock... upping it from 2.4GHz to 2.64 or 2.76GHz. While not exactly an Earth-moving increase, it's added performance without any negatives. You should also have no problem finding ECC memory for whatever motherboard you use. The only issue is that it's more expensive than non-ECC. Science Advisor Homework Helper With the newer processors they require an additional four or eight pin power plug for additional processor power. As long as you find a p\/s with enough juice and the additional plug, it should work fine. I have power supplies with extra 4-pin plugs, but not with an extra 8-pin. How can I tell which need 4 and which need 8? I'd say the safe margin for avoiding any errors would be around a 10-15% overclock... upping it from 2.4GHz to 2.64 or 2.76GHz. While not exactly an Earth-moving increase, it's added performance without any negatives. You should also have no problem finding ECC memory for whatever motherboard you use. The only issue is that it's more expensive than non-ECC. Sounds good. I'll overclock just a bit, and shell out the extra$ for ECC memory. Is there anything extra I have to do in BIOS to turn on the ECC?\n\nB. Elliott\nI have power supplies with extra 4-pin plugs, but not with an extra 8-pin. How can I tell which need 4 and which need 8??\n\nIf it's a motherboard made within the last few years it'll most likely have an 8-pin female mounted on it. It's a little iffy, but as long as the voltage supplied to each pin number is the same there shouldn't be any problems, except for a possible lack of CPU power. The motherboard manual should show the voltage layout for the pins though. I've seen adapters out there, but to be honest I haven't run into a situation where i've had to convert. Here's one I found with a quick Google search.\n\nhttp:\/\/www.performance-pcs.com\/catalog\/index.php?main_page=product_info&products_id=3204\n\nSounds good. I'll overclock just a bit, and shell out the extra $for ECC memory. Is there anything extra I have to do in BIOS to turn on the ECC? When I tried looking for the BIOS options on that motherboard I realized that it doesn't support ECC memory. Well, it may see the memory and be able to use it, but the ECC capability won't be recognised. Usually there is an option in the BIOS though. I'll look around tonight to see if I can find any other good, cheap boards... with ECC in mind this time. It would be nice to find a decent priced motherboard with a 975X chipset. That way you could later upgrade to a quad core when the prices really fall. That and the ECC support. g33kski11z ... This is why I wanted to know about motherboards. Right now I have a spreadsheet comparing MHz per dollar and the cheap chips are given an unfair advantage because I'm not considering motherboard cost ... So you'd recommend getting the cheapest motherboard that can support the chip, yes?... It really depends on your budget, experience, and what you are trying to actually accomplish. Lets assume you've got the pc experience to put this all together {hardware & software}, and your trying to calculate data sets that require at least 2 gb ram. Option 1: {the low budget build} - you go bottom dollar on your equipment, meaning lowest priced board, cpu, and ram. With some research, it could be done for$1,000. You would probably get by just fine, but things might seem to take a little longer than you want.\n\nOption 2: {mid level built}\n- something along the lines that has been discussed. Intel Core Dou cpu's, decent gigabyte {my personal favorite} boards, fast ram... this would be in the $1,100 -$1,300 range. This is probably where your best bang for the buck is at. You would be able to notice a difference between this type of system and your budget build.\n\nOption 3: {the beast}\n- you wait about 3-4 months and Intel releases their new Q9xxx cpu's. You could easily spend $1,500 -$2,000. Higher end boards, 4 Gb ram each. Something in this area could easily double option 1's output. This would be a huge number crunching beast.\n\nI've been overclocking for +5 years.. it's a fun hobby. It can be done safely with out compromising your equipment or the validity of your results. You just have to be careful with what you do. Here is the link to my work machine. I built it about a yr ago and its been running 24\/7 at my office as my primary pc. { I'm a system analyst for a local university} http:\/\/valid.x86-secret.com\/show_oc?id=213938 [Broken]. If you really want to know how to safely overclock, we can open another thread.\n\nLast edited by a moderator:\nHomework Helper\nSome motherboards have unusual features:\n\nIntel D975XBX2 motherboard: 2 Sata controllers, 4 ports each for a total of 8 hard drives. Two independent sets of striped or raid drives can be setup. 3 PCI Express slots. DDR2 up to 800mhz. ATI crossfire (dual video card) support.\n\nIntel DX38BT - 2 Sata controllers, 6 ports on internal with raid, 2 ports on external, also raid. 3 PCI Express slots. DDR3 up to 1333mhz. ATI and Nvidia dual video card support.\n\nI have an older D975XBX motherboard (uses Silicon Image for second SATA controller instead of Marvell), with 4 hard drives, setup as 2 sets of striped drive since I do some video editing and also use the 2nd pair of hard drives to back up (also backup \/ compare \/ reformat \/ restore \/ compare for full defrag) paritions from the primary harddrives, so streaming transfer rate helps. I'm using a X6800 CPU. To upgrade from this, I'd have to get a new motherboard, DX38TBT, QX9650 CPU, and 2GB of DDR3 ram. My current setup is more than good enough for gaming, but for video rendering, more speed always helps. Since Adobe Premiere Pro CS3, which I use, supports quad core cpus, the QX9650 should help there. HD video work requires striped hard drive (or raid with 3 or more drives). Depending on when I do my next upgrade, this is what I'll consider.\n\nFor math purposes, this stuff isn't needed, unless speed is an issue, and your software can utilize dual or quad core cpu's.\n\nLast edited:","date":"2022-10-02 07:38:21","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 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\": 0.2777809202671051, \"perplexity\": 3398.318323648863}, \"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\/1664030337287.87\/warc\/CC-MAIN-20221002052710-20221002082710-00447.warc.gz\"}"} | null | null |
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Davies takes home major award, four others named All-CCC in men's soccer
salvetoday Posted On January 4, 2023
The Commonwealth Coast Conference (CCC) recently announced its 2022 Men's Soccer All-Conference Teams and major award winners.
Salve Regina senior James Davies '22 was selected as the CCC Scholar-Athlete.
Davies is a two-year captain that has compiled a 3.843 GPA while pursuing a degree in business administration. He has been named to the CCC Academic All-Conference team three times and is in line to make his fourth appearance on the list. He has also been recognized by United Soccer Coaches (USC) as a Scholar All-East Region nominee.
On campus, Davies was the recipient of the Salve Regina University Presidential Scholarship multiple times and has been named to the Dean's List in every semester of his collegiate career. He holds membership in the Chi Alpha Sigma National College Athlete Honor Society, the Sigma Beta Delta International Honor Society for Business, Management, and Administration, and the Economic and Global Business Club. Davies graduated magna cum laude in December 2022.
Along with Davies, four other members of the Salve Regina men's soccer program made All-CCC: Evan Arpin '24, Jordan Borges '24, Kendy Prince '24, and Ben Tomas '26.
"It's always nice to see the individual quality within our roster recognized by these sorts of awards," said Craig O'Rourke II, head coach of men's soccer.
Voting for the All-CCC Teams and major awards was conducted by the 10 CCC head men's soccer coaches following the conclusion of the regular season and do not take postseason play into consideration.
For the full release from the CCC, go here.
The Commonwealth Coast Conference, founded in 1984, is an NCAA Division III athletic conference comprised of 10 full member and two associate member institutions throughout the New England region. Its membership aims to provide student-athletes with a positive experience in their pursuit of excellence through high academic standards, quality competition, and a meaningful student life. The conference administers championships in 19 intercollegiate sports.
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{"url":"https:\/\/www.gurobi.com\/downloads\/license-detail\/","text":"Information and installation instructions\n\nNo ID is set\n\nTo install a license key automatically, the grbgetkey program needs to be able to communicate with the Gurobi website (http:\/\/www.gurobi.com). It may fail if the computer:\n\n\u2022 has no Internet connection\n\u2022 has restricted access due to a firewall\n\u2022 uses a proxy server\n\nAlternately, here are manual instructions to obtain or update a license key file for your computer.\n\n1. Run the grbprobe command on the computer where the license will be installed.\n2. Complete the following form using the output from the grbprobe command:\nHOSTNAME win32 win64 linux32 linux64 mac64 power64 Not reported by grbprobe 2 4 8 16 24 32","date":"2022-10-06 16:06:22","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 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\": 0.30797097086906433, \"perplexity\": 5557.184249836991}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-40\/segments\/1664030337853.66\/warc\/CC-MAIN-20221006155805-20221006185805-00779.warc.gz\"}"} | null | null |
Q: OutOfRangeError: RandomShuffleQueue '_1_shuffle_batch/random_shuffle_queue' is closed and has insufficient elements (requested 8, current size 7) firstly, I'm really thankful for you to read my problem.
TensorFlow version: TensorFlow-GPU 1.14
os: ubuntu 16.04
tensorflow.python.framework.errors_impl.OutOfRangeError: RandomShuffleQueue '_1_shuffle_batch/random_shuffle_queue' is closed and has insufficient elements (requested 8, current size 7)
[[{{node shuffle_batch}}]]
I'm testing a kind of CNN called "Goturn", and I implement it with TensorFlow. When I use 100,000+ images to train my net, it always displays this error. the strange thing is that the error displays during the training other than at the first circle of training.
I've already tried a lot of solutions from stackoverflow、CSDN and the other websites, but it is no use. most of the suggestion is to modify the elements of tf.train.shuffle_batch(), whereas how I should choose them, is there any regulation to obey? Thanks for reading. Any suggestion will be appreciated
def next_batch(input_queue):
min_queue_examples = 8
num_threads = 2
[search_tensor, target_tensor, box_tensor] = data_reader(input_queue)
[search_batch, target_batch, box_batch] = tf.train.shuffle_batch(
[search_tensor, target_tensor, box_tensor],
batch_size=8,
num_threads=num_threads,
seed=88,
min_after_dequeue=min_queue_examples,
capacity=min_queue_examples+3*BATCH_SIZE)
print("next_batch!!!!!")
return [search_batch, target_batch,
box_batch, input_queue[0], input_queue[1]]
A: OK, I make such a stupid mistake, in fact, my dataset has a horrible error: some images are null, and when I delete those images, the code runs well!!!!!
| {
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Q: GUI file compressors What GUI file compressors are available for Ubuntu ?
I prefer one that offers LZMA2 to speed up file compression since I have multiple cores.
Thanks.
A: File Roller is Ubuntu's default application for handling the creation, modification and extraction of archives.
To launch it by itself, press Alt+F2 and type file-roller.
The following archive formats are well supported, and installed by default in File Roller:
tar - gzip - bzip - bzip2 - LZMA - zip - jar - iso
| {
"redpajama_set_name": "RedPajamaStackExchange"
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Pre-Requiste & Technology
1.Maven
2.SpringBoot
3.Hibernate - To presist data
4.PostMan - To test the Rest service
5.MySQL - DB
6.Eclipse
Execute Method and URL.
1.Deploy the latest code from GITHUB and Build project using Maven
2.Run the server from eclipse, no need to add any server as all configuration taken care inside maven.Refer the POM.XML to cross check on the dependency for the project to build.
4.http://localhost:8080/points - GET- To pull all the data
5.http://localhost:8080/points - POST - calculate the score and insert the data
6. For POST, take the input from the files and trigger the request in POSTMAN (Which can be used as plugin in chrome browsers)
7.First trigger the POST request so as to have data in DB
8. In application properties spring.jpa.hibernate.ddl-auto=create - So that evertime the table gets created (We can have this as UPDATE so to manintain previous data)
Assumptions
1.Its only for single players but it can be extended.
2.More logic handled in Java and made the DB side simple.(Can be done other way around)
3.Junit is included, but test suit not implemented to test the scenario as it is carried out by postman.
4.Done for single match , but can be extended for more matches.
5.There are scopes for betterment of the existing code, but concentrated more on the core and technology as other parts little more time consuming.But happy to structure it more if this soultion is acceptable.
Sampleout Response in JSON format for POST Request(TESTED FOR 3 GAMES):
{
"matchid": 1,
"players": [
{
"players1": "John",
"players2": "Adam"
}
],
"matchWinner": "John",
"gameScores": [
{
"gameID": 1,
"gameWinner": "John",
"gameScores": {
"Adam": 1,
"John": 21
}
},
{
"gameID": 2,
"gameWinner": "John",
"gameScores": {
"Adam": 1,
"John": 21
}
},
{
"gameID": 3,
"gameWinner": "Adam",
"gameScores": {
"Adam": 21,
"John": 1
}
}
]
}
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Progressive Ears Forums
Progressive Ears MUSIC Forums
Off-Topic (OT) - Music And Arts
Vintage TV thread
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Thread: Vintage TV thread
Dave (in MA)
42°09′30″N 71°08′43″W
Originally Posted by frinspar
I'm looking for my digital version of Taxi. It's time to watch that series again.
WHAAAAAAAAAAAAAAAAAAAAT... DOOOOOOOOES... A...
GuitarGeek
Most recently I ran through the Bob Newhart Show from the 70s during my lunch breaks at work. Now I'm on season 2 of the Newhart series he did set in Vermont.
I was watching The Bob Newhart Show last year, I think it was, on FETV that was showing it on the weekends. Suzanne Pleshette was actually kinda hot. Lots of good episodes on that show.
I actually remember watching Newhart when it was originally on. There was a good episode where they show the dreams everyone is having. Dick has a dream that everyone is acting normal. He pinches himself, to make sure he's not having a dream, and when he wakes up, he decides to ask his wife there's a way to pinch yourself back into a dream. When she says no, he simply says, "Damn!".
And of course, Newhart had the greatest series finale ever. "Honey, wake up! I had this dream that I was an inn keeper in Vermont!"
Originally Posted by Proglodite
Re: Buck Rogers - one of the reasons the second season was so bad was Gil Gerard insisted on toning down the sex; that just made Buck's character too bland.
I wonder if that's why Erin Grey went from wearing those skin tight lycra jumpsuits in the first season to wearing an outfit that actually more or less looks like it might be a military uniform. Needless to say, I prefered the lycra.
Wasn't Twiki played by Felix Silla?
His physical performance was, yes. Silla was also Cousin Itt on The Addams Family. Twiki's voice was done in the first season by the legendary Mel Blanc. I'm not sure I knew who Mel Blanc was at the time, though it's kind of a moot point, as I believe he was uncredited. They had some kind of dispute between seasons, and Mel quit, so they had to get someone else who didn't sound anything like Mel, to do Twiki's voice for the second season.
Barney Miller and Hogan's Heroes are two of my favorites among others
I was watching Barney Miller, All In The Family, Archie Bunker's Place, and a couple other shows FamilyNet channel a few years ago. FamilyNet has since morphed into the Cowboy Channel, and well, I guess they decided those shows didn't fit into "the new look" or whatever.
I forget which channel I was watching The Bionic Woman on. I was watching The Six Millon Dollar Man on something called The ESquire Channel, but that turned out to be a short lived affair (the Esquire Channel is now defunct).
Fracktured
Philadelphia Area
Originally Posted by Dave (in MA)
When I was in elementary school I had a Hogan's Heroes lunch box. One end had Lebeau digging a tunnel right under an "Escaping is Verboten!" sign, and the other had Newkirk giving Schultz a hotfoot.
You must be about the same age as me. I'm 60 and I had that box also. It's now worth a lot of money as a collectors lunch box. My mother threw it out. Ugh.
Halmyre
Originally Posted by Fracktured
Those are two that made it across to the UK. HH was shown in a prime time early evening slot. Barney Miller was one of those programmes I found tucked away in a late-night slot.
ronmac
Originally Posted by SteveSly
One I always liked was "Green Acres". Lots of subtle humor in that one.
Hilarious show. Lots of not-so-subtle humor, too.
"A conspiracy of silence speaks louder than words."
- Dr. Winston O'Boogie
Any more obscure shows? Maybe Highway Patrol or Peter Gunn. Why doesn't, The FBI, get more rerun play. Not seen it in years but I liked the ones I saw. Watching the original, The Outer Limits on Prime. Bring back, Thriller.
The older I get, the better I was.
Speaking of Dragnet. I remember the blue boy episode.
Sturgeon's Lawyer
...blattid...
"Hogan's Heroes" - the "Nazis were kind of cute and not all bad" show.
Maka ki ecela tehani yanke lo!
Originally Posted by ronmac
I thought it was funny that Oliver's Mother didn't like him but liked Lisa much more. Mr. Kimball? Oh man .
Originally Posted by Sturgeon's Lawyer
How could they do all the things they did with no one catching on? The bad guys had great uniforms though.
I prefer to think of it as the "the Nazis were stupid and that's why they lost the war" show. I've occasionally heard talk of how "disrespectful" the show was, but there's three things to consider:
1. Robert Clary, the actor who played LeBeau, was himself a concentration camp survivor.
2. All four of the main Nazis (i.e. Schultz, Klink, Burkhalter, and Hockstetter) were all played by Jewish actors.
3. The show was set in a POW camp, not a concentration camp, which as I understand, is a significant difference.
If the show is disrespectful to anyone or anything, it's the Nazis, but if you ask me, that's as it should be. It's a funny show, that's all it needs to be. And from what I gather, it was popular with people who actually served in WWII, too.
I saw Hogan's Heroes mostly in reruns, and almost never a full episode, because it was used as already-in-progress filler after Boston Bruins games to just fill up the remaining portion of a half hour until they could resume their regular schedule. Later on they switched to using The Odd Couple for the same purpose. And then they took the Bruins off free TV...
Side note: I've never comprehended why, with the glut of pay TV sports channels, they still need to show sports on broadcast TV.
Yeah, they're crowding out important schedule time that could be used for more wonderful "reality" shows...
progmatist
Man of repute
That may be why German TV canceled Seinfeld and replaced it with Hogan's Heroes.
"Well my son, life is like a beanstalk, isn't it?"--Dalai Lama
In grade school, a police officer visited and talked to the class. One kid asked him what he thought of Adam 12, which at the time was still in first run episodes. He said it wasn't very realistic because police officers spend most of their time doing paperwork. But then, that wouldn't make for very compelling television.
SunRunner2
"Run For Your Life", anyone?
There's an interview with Werner Klemperer in which he said he would only play a nazi if they were made fools of. He also served in the US Army. His father Otto of course the great conductor fled Germany when Hitler came to power I believe. And yes they we're Jewish. So was John Banner I believe.
Originally Posted by Staun
Funny, because that's the episode I always think of first. a couple of weeks ago, I put the show on for the first time in many years and guess which episode was on?
Ya know, I never liked the unrealistically dumb characters in shows. Even Edith Bunker until I realized how well Jean Stapleton played the role. But, with Green Acres, EVERY character is dumb and Oliver is the only "smart" one. That show still cracks me up. My favorite episode is one where Arnold Ziffel goes missing.
Mr. Haney cracks me up. He even has a double in Washington.
Good point. I know what I'd put in there instead of sports, but what some jackass TV executive would put in there is another matter.
I guess with sports, I just get annoyed about programs being pre-empted and such. Remember when The Simpsons did that "Who Shot Mr. Burns" thing? I recall they actually did a special, that aired before the season premiere, with the guy who hosts America's Most Wanted "investigating" all the evidence in the Burns shooting. Unfortunately, because it was football sesaon, whichever game it was ran over, and we never got to see the first half of it. Now that I think about it, I bet it's on Youtube these days, I'll have to look for it.
Actually, it's not even the games themselves running over that bothers me. I get it, there's lots of money to be made in sports, and you have an ironclad contract that says you can't interrupt the game (as Heidi-Gate), but once the game is over, that should be it, announce the final score, then go to whatever you're supposed to be showing. No, they gotta have these dumbfucks come on and spend another half hour talking about the game that just ended. That's what really irritates me. I went through a phase where I was DVRing David Letterman, and I'd go tow atch it the next day, and I'd maybe five minutes of game, 20 minutes of post-game, 30 minutes of local news, then maybe 10 minutes of Letterman! Oy!
Another one that pissed me was David Letterman being interrupted so they could go to the press conference after a Cavaliers game, I guess so that LeBron James could explain what they did wrong that caused them to be eliminated from the playoffs. Again. (This was a few years before they finally did win the championship, giving Cleveland it's third pro sports championship since 1965 or whenever it was).
Well, that's the line you always heard about police shows, none of them are particularly realistic. There's even an episode of Barney Miller, where Yemana reiterates the typical commentary about the lack of realism. When the guy he's talking to says "Ya know, on TV, they usually catch the crook", Yemana fires back with, "Good example!"
But I've also heard that Barney Miller was the one show that actually was more or less realistic, in that it portrayed the day to day life of a police detective, in terms of dealing with small change disputes or just plain weird incidents (e.g. a guy going nuts in a department store because of the piped in Muzak), bureaucracy, etc. One episode had a plot that hinged on an officer dealing with his own feelings after fatally shooting a bank robber. Heavy stuff for a sitcom, and I'm not sure there were even "serious" cop shows that dealt with that kind of back then.
But I still say the best episode of Barney Miller was the one where Wojo brought the brownies to work. That one and the one where Fish got shot "in the cheek" (i.e. ass).
I was watching that for awhile, via a download off I got off a torrent site about 7 or 8 years ago, I think. I dont' think I ever finished the series, but it was a good program. I think one of the vintage TV channels was showing it for awhile too.
As I posted yesterday, (post #30), Klemperer, Banner, Leon Askin (who played General Burkhalter) and Howard Caine (Major Hockstetter) were all Jewish. Klemperer, Banner, and Askin had all fled Nazi Germany. And I believe all four of them served in the US military. Wikipedia says that Kemperer insisted that Hogan had to always win at the end of each episode, no matter happened, the outcome had to be in the favor of the Allies.
Ooooh, cut man, cut man .
Originally Posted by SunRunner2
Was that like a Fugitive kind of set up?
Andy Griffith would be nothing without Don Knotts.
I don't see Barney Fife as the same type of character. More of a fool than just a clueless dummy.
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, spesso abbreviato in Nijigaku o semplicemente Nijigasaki, è un progetto multimediale giapponese, nato come spin-off del fanchise di Love Live! e la sua serie di giochi Love Live! School Idol Festival. Il gruppo è stato introdotto per la prima volta nel 2017 come "Perfect Dream Project" ed è stato inizialmente creato come parte del gioco Love Live! School Idol Festival All Stars. A differenza delle μ's e delle Aqours, i precedenti gruppi del franchise, le Nijigasaki non sono un gruppo ma, piuttosto studentesse idol che competono per mantenere vivo il loro club idol scolastico.
Sono presenti nel gioco spin-off Love Live! School Idol Festival All Stars, insieme alle μ's e alle Aqours. Appaiono anche come carte rarità SR in Love Live! School Idol Festival. Le ragazze sono state divise in gruppi di tre per diverse app prima della loro aggiunta al gioco: un gruppo sul sito web Dengeki Online (Kasumi, Karin, Setsuna), sul sito web dell'app Famitsu (Ayumu, Ai, Rina) e sul sito web ufficiale del gioco (Emma, Shizuku, Kanata). Ogni luogo funziona come una stanza separata o una filiale per la Nijigasaki High School. È stato realizzato un adattamento anime della Sunrise; la prima stagione è uscita nel 2020 e la seconda sta per uscire nel 2022.
Personaggi
Nijigasaki High School Idol Club
Doppiata da Hinaki Yano.
Collegamenti esterni
Sito ufficiale
Serie televisive anime del 2020 | {
"redpajama_set_name": "RedPajamaWikipedia"
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Produced by Turgut Dincer, Charlie Howard, and the Online
Distributed Proofreading Team at http://www.pgdp.net (This
file was produced from images generously made available
by The Internet Archive)
NAPOLEON
[Illustration]
[Illustration: _Napoleon._
_From a portrait by Lassalle._]
NAPOLEON
A Sketch of
HIS LIFE, CHARACTER, STRUGGLES, AND
ACHIEVEMENTS
BY
THOMAS E. WATSON
AUTHOR OF "THE STORY OF FRANCE," ETC.
_ILLUSTRATED WITH PORTRAITS AND FACSIMILES_
New York
THE MACMILLAN COMPANY
LONDON: MACMILLAN & CO., LTD.
1903
_All rights reserved_
COPYRIGHT, 1902,
BY THE MACMILLAN COMPANY.
Set up and electrotyped February, 1902. Reprinted May, 1902; January,
1903.
Norwood Press
J. S. Cushing & Co.--Berwick & Smith
Norwood Mass. U.S.A.
TO MY WIFE
Georgia Durham Watson
PREFACE
In this volume the author has made the effort to portray Napoleon as he
appears to an average man. Archives have not been rummaged, new sources
of information have not been discovered; the author merely claims to
have used such authorities, old and new, as are accessible to any
diligent student. No attempt has been made to give a full and detailed
account of Napoleon's life or work. To do so would have required the
labor of a decade, and the result would be almost a library. The
author _has_ tried to give to the great Corsican his proper historical
position, his true rating as a man and a ruler,--together with a just
estimate of his achievements.
THOMSON, GEORGIA,
Dec. 24, 1901.
CONTENTS
CHAPTER PAGE
I. CORSICA 1
II. BOYHOOD 17
III. LIEUTENANT 37
IV. REVOLUTION 47
V. RETURNS HOME 58
VI. FIRST SERVICE 70
VII. AT MARSEILLES 86
VIII. 13TH OF VENDÉMIAIRE 94
IX. THE YOUNG REPUBLIC 115
X. JOSEPHINE 123
XI. THE ARMY OF ITALY 135
XII. MILAN 148
XIII. MANTUA 159
XIV. CAMPO FORMIO 175
XV. JOSEPHINE AT MILAN 188
XVI. EGYPT 196
XVII. THE SIEGE OF ACRE 211
XVIII. THE RETURN TO FRANCE 221
XIX. THE REMOVAL OF THE COUNCILS 230
XX. THE FALL OF THE DIRECTORY 242
XXI. FIRST CONSUL 256
XXII. MARENGO 275
XXIII. THE CODE NAPOLÉON 294
XXIV. PLOT AND CONSPIRACY 310
XXV. EMPEROR 329
XXVI. DISTRIBUTION OF HONORS 349
XXVII. JENA 355
XXVIII. ENTRY INTO BERLIN 363
XXIX. WARSAW 372
XXX. HABITS AND CHARACTERISTICS 386
XXXI. HIGH-WATER MARK 412
XXXII. SPAIN 425
XXXIII. WAGRAM 435
XXXIV. THE DIVORCE 450
XXXV. MOSCOW 470
XXXVI. THE RETREAT 491
XXXVII. IN PARIS AGAIN 502
XXXVIII. METTERNICH 514
XXXIX. DRESDEN AND LEIPSIC 523
XL. RETREAT FROM LEIPSIC 543
XLI. THE FRANKFORT PROPOSALS 557
XLII. THE FALL OF PARIS 571
XLIII. ELBA 583
XLIV. ELBA 598
XLV. LOUIS XVIII 612
XLVI. THE RETURN FROM ELBA 628
XLVII. REORGANIZATION 635
XLVIII. WATERLOO 647
XLIX. WATERLOO 657
L. ST. HELENA 672
LI. ST. HELENA 687
INDEX 705
LIST OF ILLUSTRATIONS
NAPOLEON. From a portrait by Lassalle _Frontispiece_
FACING PAGE
NAPOLEON. From an engraving by Tomkins of a drawing from life
during the campaign in Italy 70
LETTER FROM NAPOLEON TO GENERAL CARTEAUX, DATED AT TOULON. In
facsimile 80
NAPOLEON. From a print in the collection of Mr. W. C. Crane.
The original engraving by G. Fiesinger, after a miniature
by Jean-Baptiste-Paulin Guérin. Deposited in the National
Library, Paris, 1799 136
LETTER FROM NAPOLEON IN ITALY TO JOSEPHINE. In facsimile 160
JOSEPHINE IN 1800. From a pastel by P. P. Prud'hon 188
NAPOLEON. From the painting by Paul Delaroche entitled "General
Buonaparte crossing the Alps" 200
NAPOLEON AS FIRST CONSUL, AT MALMAISON. From a painting by
J. B. Isabey 256
JOSEPHINE IN 1809. From a water-color by Isabey 338
MARIA LOUISA. From the portrait by Gérard in the Louvre 460
LETTER FROM NAPOLEON TO COUNTESS WALEWSKI, DATED APRIL 16,
1814. In facsimile 562
THE KING OF ROME. From the painting by Sir T. Lawrence 690
NAPOLEON
CHAPTER I
Corsica, an island in the Mediterranean Sea, has an extreme width of
52 miles and length of 116. It is within easy reach of Italy, France,
Spain, Sardinia, and the African coast. Within 54 miles lies Tuscany,
while Genoa is distant but 98, and the French coast at Nice is 106.
Across the island strides a chain of mountains, dividing it into two
nearly equal parts. The <DW72>s of the hills are covered with dense
forests of gigantic pines and chestnuts, and on their summits rests
eternal snow. Down from these highlands rapid streams run to the sea.
There are many beautiful valleys and many fine bays and harbors.
The population of the island was, in the eighteenth century, about
130,000. The Italian type predominated. In religion it was Roman
Catholic.
The history of Corsica has been wonderfully dramatic. Peopled
originally by the Celts, perhaps, the island has been so often
war-swept, so often borne down under the rush of stronger nations,
that the native race almost disappeared. The Greeks from Asia Minor,
back in the dim ages, seized upon a part of the coast and colonized
it. Carthage, in her day of greatness, was its mistress; and then
came Rome, whose long period of supremacy left its stamp upon the
people, bringing as it did multitudes of Italians, with their language,
customs, and religion.
After the day of Rome came Germans, Byzantine Greeks, Moors, Goths,
Vandals, and Longobards. For centuries the island was torn by incessant
war, the Corsicans doing their utmost to keep themselves free from
foreign masters. The feudal system was fastened upon the struggling
people by the chiefs of the invaders. The crags were crowned with
castles, and half-savage feudal lords ruled by the law of their own
fierce lusts. They waged war upon each other, they ground down the
native races. Unable to defend themselves, miserably poor, but full of
desperate courage, the Corsicans fled from the coasts to escape the
pirate, and to the mountains to resist the feudal robber. In their
distress the peasants found a leader in Sambuccio, who organized them
into village communities,--a democratic, self-ruling confederation.
There were no serfs, no slaves, in Corsica; freedom and equality the
people claimed and fought for; and under Sambuccio they totally routed
the barons.
The great leader died; the barons took up arms again; the peasants
appealed to the margrave of Tuscany for aid; an army came from Italy,
the barons were beaten, and the village confederation restored. From
A.D. 1020 to A.D. 1070, Tuscany protected the Corsicans; but the popes,
having looked upon the land with eyes of desire, claimed it for the
Church, and, through skilful manipulations (such as are common in
cases of that kind), the people were persuaded to submit. In the year
1098 Pope Urban II. sold the island to Pisa, and for one hundred years
Corsica remained under the dominion of that republic.
Genoa, however, envied Pisa this increase of territory, claimed the
island for herself, and backed her claim by arms. Corsica was rent by
the struggle, and the Corsicans themselves were divided into hostile
camps, one favoring Pisa, the other Genoa.
The leader of the Pisan faction, Guidice della Rocca, kept up, for
many years, an unequal struggle, showing wonderful courage, fertility
of resource, rigorous justice, and rare clemency. He killed his own
nephew for having outraged a female prisoner for whose safety he, Della
Rocca, had given his word. Old and blind, this hero was betrayed by his
bastard son, delivered to the Genoese, and died in a wretched Genoese
dungeon; and with his downfall passed away the Pisan sovereignty.
A period of anarchy followed the death of Della Rocca. The barons were
unmerciful in their extortions, and the people were reduced to extreme
misery. After many years appeared another valiant patriot of the Rocca
race, Arrigo della Rocca (1392). He raised the standard of revolt, and
the people rallied to him. He beat the Genoese, was proclaimed Count of
Corsica, and ruled the land for four years. Defeated at length by the
Genoese, he went to Spain to ask aid. Returning with a small force, he
routed his enemies and became again master of the island. Genoa sent
another army, Arrigo della Rocca was poisoned (1401), and in the same
year Genoa submitted to France.
Corsica kept up the struggle for independence. Vincentello, nephew
of Arrigo della Rocca, was made Count of Corsica, and for two years
maintained a gallant contest. Genoa poured in more troops, and the
resistance was crushed. Vincentello left the island. Soon returning
with help from Aragon, he reconquered the county with the exception of
the strongholds of Calvi and Bonifaccio. Inspired by the success of
Vincentello, the young king of Aragon, Alfonso, came in person with
large forces to complete the conquest. Calvi was taken, but Bonifaccio
resisted all efforts. The place was strongly Genoese, and for months
the endurance of its defenders was desperately heroic. Women and
children and priests joined with those who manned the walls, and all
fought together. Spanish courage was balked, Spanish pride humbled, and
Alfonso sailed away. Vincentello, bereft of allies, lost ground. He
gave his own cause a death-blow by abusing a girl whose kinsmen rose to
avenge the wrong. The guilty man and indomitable patriot determined to
seek aid once more in Spain; but Genoa captured him at sea, and struck
off his head on the steps of her ducal palace (1434).
Then came anarchy in Corsica again. The barons fought, the peasants
suffered. Law was dead. Only the dreaded vendetta ruled--the law of
private vengeance. So harried were the people by continued feuds,
rival contentions, and miscellaneous tumult, that they met in general
assembly and decided to put themselves under the protection of the
bank of St. George of Genoa. The bank agreed to receive this singular
deposit (1453). The Corsican nobles resisted the bank, and terrible
scenes followed. Many a proud baron had his head struck off, many of
them left the country. Aragon favored the nobles, and they came back to
renew the fight, defeat the forces of the bank, and reconquer most of
the island.
In 1464 Francesco Sforza of Milan took Genoa, and claimed Corsica as
a part of his conquest. The islanders preferred Milan to Genoa, and
but for an accidental brawl, peaceful terms might have been arranged.
But the brawl occurred, and there was no peace. Years of war, rapine,
and universal wretchedness followed. Out of the murk appears a valiant
figure, Giampolo, taking up with marvellous tenacity and fortitude the
old fight of Corsica against oppression. After every defeat, he rose to
fight again. He never left the field till Corsican rivalry weakened and
ruined him. Then, defiant to the last, he went the way of the outlaw to
die in exile.
Renuccio della Rocca's defection had caused Giampolo to fail. After a
while Rocca himself led the revolt against Genoa, and was overthrown.
He left the island, but came again, and yet again, to renew the
hopeless combat. Finally his own peasants killed him to put an end
to the miserable war, there being no other method of turning the
indomitable man (1511).
Resistance over, the bank of Genoa governed the island. The barons
were broken, their castles fell to ruin. The common people kept up
their local home-rule, enjoyed a share in the government, and were in
a position much better than that of the common people in other parts
of Europe. But the bank was not satisfied to let matters rest there; a
harsh spirit soon became apparent; and the privileges which the people
had enjoyed were suppressed.
Against this tyranny rose now the strongest leader the Corsicans had
yet found, Sampiero. Humbly born, this man had in his youth sought
adventures in foreign lands. He had served the House of Medici, and in
Florence became known for the loftiness and energy of his character.
Afterward he served King Francis I., of France, by whom he was made
colonel of the Corsican regiment which he had formed. Bayard was his
friend, and Charles of Bourbon said of him, "In the day of battle the
Corsican colonel is worth ten thousand men"; just as another great
warrior, Archduke Charles of Austria, said of another great Corsican,
serving then in France (1814), "Napoleon himself is equal to one
hundred thousand men."
In 1547 Sampiero went back to Corsica to select a wife. So well
established was his renown that he was given the only daughter of the
Lord of Ornano, the beautiful Vannina. The bank of Genoa, alarmed by
the presence of such a man in the island, threw him into prison. His
father-in-law, Francesco Ornano, secured his release.
Genoa, since her delivery from French dominion by Andrea Doria, was in
league with the Emperor of Germany, with whom the French king and the
Turks were at war. Hence it was that Sampiero could induce France and
her allies to attack the Genoese in Corsica. In 1553 came Sampiero, the
French, and the Turks; and all Corsica, save Calvi and Bonifaccio, fell
into the hands of the invaders. Bonifaccio was besieged in vain, until,
by a stratagem, it was taken. Then the Turks, indignant that Sampiero
would not allow them to plunder the city and put all the Genoese to the
sword, abandoned the cause, and sailed away. Calvi still held out. The
Emperor sent an army of Germans and Spaniards; Cosmo de Medici also
sent troops; Andrea Doria took command, and the French were everywhere
beaten. Sampiero quarrelled with the incapable French commander, went
to France to defend himself from false reports, made good his purpose,
then returned to the island, where he became the lion of the struggle.
He beat the enemy in two pitched battles, and kept up a successful
contest for six years. Then came a crushing blow. By the treaty of
Cambray, France agreed with Spain that Corsica should be given back to
Genoa.
Under this terrible disaster, Sampiero did not despair. Forced to leave
the island, he wandered from court to court on the continent, seeking
aid. For four years he went this dreary round,--to France, to Navarre,
to Florence. He even went to Algiers and to Constantinople. During this
interval it was that Genoa deceived and entrapped Vannina, the wife
of the hero. She left her home and put herself in the hands of his
enemies. One of Sampiero's relatives was fool enough to say to him, "I
had long expected this."--"And you concealed it!" cried Sampiero in a
fury, striking his relative to the heart with a dagger. Vannina was
pursued and caught, Sampiero killed her with his own hand.
Failing in his efforts to obtain foreign help, the hero came back to
Corsica to make the fight alone (1564). With desperate courage he
marched from one small victory to another until Genoa was thoroughly
aroused. An army of German and Italian mercenaries was sent over,
and the command given to an able general, Stephen Doria. The war
assumed the most sanguinary character. Genoa seemed bent on utterly
exterminating the Corsicans and laying waste the entire country.
Sampiero rose to the crisis; and while he continued to beseech France
for aid, he continued to fight with savage ferocity. He beat Doria
in several encounters, and finally, in the pass of Luminada, almost
annihilated the enemy. Doria, in despair, left the island, and Sampiero
remained master of the field. With his pitifully small forces he had
foiled the Spanish fleet, fifteen thousand Spanish soldiers, and an
army of mercenaries; and had in succession beaten the best generals
Genoa could send. All this he had done with half-starved, half-armed
peasants, whose only strength lay in the inspiration of their
patriotism and the unconquerable spirit of their leader. Few stronger
men have lived and loved, hoped and dared, fought and suffered, than
this half-savage hero of Corsica. With all the world against him
Sampiero fought without fear, as another great Corsican was to do.
In open fight he was not to be crushed: on this his enemies were
agreed, therefore treachery was tried. Genoa bribed some of the
Corsican chiefs; Vannina's cousins were roused to seek revenge;
Vittolo, a trusted lieutenant, turned against his chief; and a monk,
whom Sampiero could not suspect, joined the conspirators. The monk
delivered forged letters to Sampiero, which led him to the ambuscade
where his foes lay in wait. He fought like the lion he was. Wounded in
the face, he wiped the blood out of his eyes with one hand while his
sword was wielded by the other. Vittolo shot him in the back, and the
Ornanos rushed upon the dying man, and cut off his head (1567).
The fall of Sampiero created intense satisfaction in Genoa, where there
were bell-ringings and illuminations. In Corsica it aroused the people
to renewed exertions; but the effort was fitful, for the leader was
dead. In a great meeting at Orezzo, where three thousand patriots wept
for the lost hero, they chose his son Alfonso their commander-in-chief.
After a struggle of two years, in which the youth bore himself bravely,
he made peace and left the country. Accompanied by many companions
in arms, he went to France, formed his followers into a Corsican
regiment, of which Charles the Ninth appointed him colonel. Other
Corsicans, taking refuge in Rome, formed themselves into the Pope's
Corsican guard.
Thrown back into the power of Genoa, Corsica suffered all the ills of
the oppressed. Wasted by war, famine, plague, misgovernment, a more
wretched land was not to be found. Deprived of its privileges, drained
of its resources, ravaged by Turks and pillaged by Christians, it bled
also from family feuds. The courts being corrupt, the vendetta raged
with fury. In many parts of the country, agriculture and peaceful
pursuits were abandoned. And this frightful condition prevailed for
half a century.
The Genoese administration became ever more unbearable. A tax of twelve
dollars was laid on every hearth. The governors of the island were
invested with the power to condemn to death without legal forms or
proceedings.
One day, a poor old man of Bustancio went to the Genoese collector
to pay his tax. His money was a little short of the amount due--a
penny or so. The official refused to receive what was offered, and
threatened to punish the old man if he did not pay the full amount.
The ancient citizen went away grumbling. To his neighbors, as he met
them, he told his trouble. He complained and wept. They sympathized and
wept. Frenzied by his own wrongs, the old man began to denounce the
Genoese generally,--their tyranny, cruelty, insolence, and oppression.
Crowds gathered, the excitement grew, insurrectionary feelings spread
throughout the land. Soon the alarm bells were rung, and the war
trumpet sounded from mountain to mountain. This was in October, 1729.
A war of forty years ensued. Genoa hired a large body of Germans from
the Emperor, and eight thousand of these mercenaries landed in Corsica.
At first they beat the ill-armed islanders, who marched to battle bare
of feet and head. But in 1732 the Germans were almost destroyed in the
battle of Calenzala. Genoa called on the Emperor for more hirelings.
They were sent; but before any decisive action had taken place, there
arrived orders from the Emperor to make peace. Corsica had appealed
to him against Genoa, and he had decided that the Corsicans had been
wronged. Corsica submitted to Genoa, but her ancient privileges were
restored, taxes were remitted, and other reforms promised.
No sooner had the Germans left the island than Genoese and Corsicans
fell to fighting again. Under Hyacinth Paoli and Giafferi, the brave
islanders defeated the Genoese, at all points; and Corsica, for the
moment, stood redeemed.
In 1735 the people held a great meeting at Corte and proclaimed their
independence. A government was organized, and the people were declared
to be the only source of the laws.
Genoa exerted all her power to put down the revolt. The island was
blockaded, troops poured in, the best generals were sent. The situation
of the Corsicans was desperate. They stood in need of almost everything
requisite to their defence, except brave men. The blockade cut off any
hope of getting aid from abroad. English sympathizers sent two vessels
laden with supplies, and keen was the joy of the poor islanders. With
the munitions thus obtained they stormed and took Alesia.
But their distress was soon extreme again, and the struggle hopeless.
At this, the darkest hour, came a very curious episode. A German
adventurer, Theodore de Neuhoff, a baron of Westphalia, entering the
port with a single ship, under the British flag, offered himself to the
Corsicans as their king. Promises of the most exhilarating description
he made as to the men, money, munitions of war he could bring to
Corsican relief. Easily believing what was so much to their interest,
and perhaps attaching too much importance to the three English ships
which had recently brought them supplies, the Corsican chiefs actually
accepted Neuhoff for their king.
The compact between King Theodore and the Corsicans was gravely reduced
to writing, signed, sealed, sworn to, and delivered. Then they all
went into the church, held solemn religious services, and crowned
Theodore with a circlet of oak and laurel leaves. Theodore took himself
seriously, went to work with zeal, appointed high dignitaries of the
crown, organized a court, created an order of knighthood, and acted as
if he were a king indeed. He marched against the oppressors, fought
like a madman, gained some advantages, and began to make the situation
look gloomy to the Genoese.
Resorting to a detestable plan, they turned loose upon the island a
band of fifteen hundred bandits, galley-slaves, and outlaws. These
villains made havoc wherever they went. In the meantime, the Corsican
chiefs began to be impatient about the succors which Theodore had
promised. Evasions and fresh assurances answered for a while, but
finally matters reached a crisis. Theodore was told, with more or less
pointedness, that either the succors must come or that he must go. To
avoid a storm, he went, saying that he would soon return with the
promised relief. Paoli and the other Corsican chiefs realized that in
catching at the straw this adventurer had held out to them, they had
made themselves and Corsica ridiculous. They accordingly laid heavy
blame on Theodore.
Cardinal Fleury, a good old Christian man, who was at this time (1737)
minister of France, came forward with a proposition to interfere in
behalf of Genoa, and reduce the Corsicans to submission. Accordingly
French troops were landed (1738), and the islanders rose _en masse_ to
resist. Bonfires blazed, bells clanged, war trumpets brayed. The whole
population ran to arms. The French were in no haste to fight, and for
six months negotiations dragged along. Strange to say, the Corsicans,
in their misery, gave hostages to the French, and agreed to trust
their cause to the king of France. At this stage who should enter but
Theodore! The indefatigable man had ransacked Europe, hunting sympathy
for Corsica, and had found it where Americans found it in a similar
hour of need--in Holland. He had managed to bring with him several
vessels laden with cannon, small arms, powder, lead, lances, flints,
bombs, and grenades. The Corsican people received him with delight,
and carried him in triumph to Cervione, where he had been crowned; but
the chiefs bore him no good-will, and told him that circumstances had
changed. Terms must be made with France; Corsica could not at this time
accept him as king--oaths, religious services, and written contract to
the contrary notwithstanding. Theodore sadly sailed away.
The appeal to the French king resulted in the treaty of Versailles,
by whose terms some concessions were made to the Corsicans, who were
positively commanded to lay down their arms and submit to Genoa.
Corsica resisted, but was overcome by France. In 1741 the French
withdrew from the island, and almost immediately war again raged
between Corsican and Genoese.
In 1748 King Theodore reappeared, bringing munitions of war which
the island greatly needed. He seems to have succeeded in getting the
Corsicans to accept his supplies, but they showed no inclination to
accept himself. Once again he departed--to return no more. The gallant,
generous adventurer went to London, where his creditors threw him into
prison. The minister, Walpole, opened a subscription which secured his
release. He died in England, and was buried in St. Anne's churchyard,
London, December, 1756.
Peace was concluded between Genoa and Corsica, whose privileges were
restored. For two years quiet reigned. Family feuds then broke out, and
the island was thrown into confusion. Following this came a general
rising against the Genoese, in which the English and Sardinians aided
the Corsicans. Genoa applied to France, which sent an army. Dismayed
by the appearance of the French, the island came to terms. Cursay, the
commander of the French, secured for the unfortunate people the most
favorable treaty they had ever obtained. Dissatisfied with Cursay, the
Genoese prevailed on France to recall him. Whereupon the Corsicans rose
in arms, Gaffori being their chief. He displayed the genius and the
courage of Sampiero, met with the success of the earlier hero, and like
him fell by treachery. Enticed into an ambuscade, Gaffori was slain
by Corsicans, his own brother being one of the assassins. The fall
of the leader did not dismay the people. They chose other leaders,
and continued the fight. Finally, in July, 1755, the celebrated
Paschal Paoli was chosen commander-in-chief. At this time he was but
twenty-four years old. Well educated, mild, firm, clear-headed, and
well balanced, he was very much more of a statesman than a warrior. His
first measure, full of wisdom, was the abolition of the vendetta.
Mainly by the help of his brother Clemens, Paoli crushed a rival
Corsican, Matra, and established himself firmly as ruler of the island.
Under his administration it flourished and attracted the admiring
attention of all European liberals. Genoa, quite exhausted, appealed
to France, but was given little help. As a last resort, treachery was
tried: Corsican was set against Corsican. The Matra family was resorted
to, and brothers of him who had led the first revolt against Paoli took
the field at the head of Genoese troops. They were defeated.
Genoa again turned to France, and on August 6, 1764, was signed an
agreement by which Corsica was ceded to France for four years. French
garrisons took possession of the few places which Genoa still held.
During the four years Choiseul, the French minister, prepared the way
for the annexation of Corsica to France. As ever before, there were
Corsicans who could be used against Corsica. Buttafuoco, a noble of
the island, professed himself a convert to the policy of annexation.
He became Choiseul's apostle for the conversion of others. So adroitly
did he work with bribes and other inducements, that Corsica was soon
divided against herself. A large party declared in favor of the
incorporation of the island with France. In 1768 the Genoese realized
that their dominion was gone. A bargain was made between two corrupt
and despotic powers by which the one sold to the other an island it
did not own, a people it could not conquer,--an island and a people
whose government was at that moment a model of wisdom, justice, and
enlightened progress. Alone of all the people of Europe, Corsica
enjoyed self-government, political and civil freedom, righteous laws,
and honest administration. Commerce, agriculture, manufactures, had
sprung into new life under Paoli's guidance, schools had been founded,
religious toleration decreed, liberty of speech and conscience
proclaimed. After ages of combat against awful odds, the heroic people
had won freedom, and, by the manner in which it was used, proved that
they had deserved to win it. Such were the people who were bargained
for and bought by Choiseul, the minister of France, at and for the sum
of $400,000. The Bourbons had lost to England an empire beyond seas--by
this act of perfidy and brutality they hoped to recover some of their
lost grandeur.
Terrible passions raged in Corsica when this infamous bargain became
known. The people flew to arms, and their wrongs sent a throb of
sympathy far into many lands. But France sent troops by the tens of
thousands; and while the Corsicans accomplished wonders, they could not
beat foes who outnumbered them so heavily. Paoli was a faithful chief,
vigilant and brave, but he was no Sampiero. His forces were crushed at
Ponte Nuovo on June 12, 1769, and Corsica laid down her arms. The long
chapter was ended, and one more wrong triumphant.
Chief among the painful features of the drama was that Buttafuoco and a
few other Corsicans took service with France, and made war upon their
own people.
Paoli with a band of devoted supporters left the island. From Leghorn,
through Germany and Holland, his journey was a triumphal progress.
Acclaimed by the liberals, honors were showered upon him by the towns
through which he passed; and in England, where he made his home, he was
welcomed by the people and pensioned by the government.
The French organized their administration without difficulty. The
Buttafuoco element basked in the warmth of success and patronage.
For a while all was serene. Later on the French grip tightened, the
Corsican time-honored privileges were set aside, the old democracy
was no longer the support of a government which relied more and more
on French soldiers. Power, taken from the village communities, was
placed entirely in the hands of a military governor and a council of
twelve nobles. Frenchmen filled all the important offices. The seat of
government was moved from Corte to Bastia and Ajaccio. The discontent
which these changes caused broke into open rebellion. The French
crushed it with savage cruelty. After that Corsica was a conquered
land, which offered no further resistance; but whose people, excepting
always those who had taken part with France, nursed intensely bitter
feelings against their conquerors.
Of this fiery, war-worn, deeply wronged people, Napoleon Bonaparte was
born; and it must be remembered that before his eyes opened to the
light his mother had thrilled with all the passions of her people, her
feet had followed the march, her ears had heard the roar of battle. As
Dumas finely says, "The new-born child breathed air that was hot with
civil hates, and the bell which sounded his baptism still quivered with
the tocsin."
CHAPTER II
"From St. Charles Street you enter on a very small square. An elm tree
stands before a yellowish gray plastered house, with a flat roof and
a projecting balcony. It has six front windows in each of its three
stories, and the doors look old and time-worn. On the corner of this
house is an inscription, _Letitia Square_. The traveller knocks in vain
at the door. No voice answers."
Such is the picture, drawn in 1852, of the Bonaparte mansion in
Ajaccio. Few tourists go to see it, for Corsica lies not in the direct
routes of the world's trade or travel. Yet it is a house whose story
is more fascinating, more marvellous, than that of any building which
cumbers the earth this day.
We shut our eyes, and we see a picture which is richer than the richest
page torn from romance. We see a lean, sallow, awkward, stunted lad
step forth from the door of the old house and go forth into the world,
with no money in his pocket, and no powerful friends to lift him over
the rough places. He is only nine years old when he leaves home, and
we see him weep bitterly as he bids his mother good-by. We see him at
school in France, isolated, wretched, unable at first to speak the
language, fiercely resenting the slights put upon his poverty, his
ignorance, his family, his country--suffering, but never subdued. We
see him rise against troubles as the eagle breasts the storm. We see
him lay the better half of the civilized world at his feet. We see him
bring sisters and brothers from the island home, and put crowns on
their heads. We see him shower millions upon his mother; and we hear
him say to his brother on the day he dons the robes of empire, "Joseph,
suppose father were here--!"
As long as time shall last, the inspiration of the poor and the
ambitious will be the Ajaccio lawyer's son: not Alexander, the born
king; not Cæsar, the patrician; but Napoleon, the moneyless lad from
despised Corsica, who stormed the high places of the world, and by his
own colossal strength of character, genius, and industry took them!
As long as time shall last his name will inspire not only the
individual, but the masses also. Wherever a people have heard enough,
read enough, thought enough to feel that absolutism in king or priest
is wrong; that special privilege in clan or clique is wrong; that
monopoly of power, patronage, wealth, or opportunity is wrong, there
the name of Napoleon will be spoken with reverence, despot though he
became, for in his innermost fibre he was a man of the people, crushing
to atoms feudalism, caste, divine right, and hereditary imposture.
* * * * *
As early as the year 947 there had been Bonapartes in Corsica, for
the name of one occurs as witness to a deed in that year. There were
also Bonapartes in Italy; and men of that name were classed with the
nobles of Bologna, Treviso, and Florence. It is said that during the
civil wars of Italy, members of the Bonaparte family took refuge in
Corsica, and that Napoleon's origin can be traced to this source. It is
certain that the Bonapartes of Corsica continued to claim kindred with
the Italian family, and to class themselves as patricians of Italy;
and both these claims were recognized. In Corsica they ranked with the
nobility, a family of importance at Ajaccio.
At the time of the French invasion the representatives of the family
were Lucien, archdeacon of Ajaccio, and Charles Bonaparte, a young man
who had been left an orphan at the age of fourteen.
Born in 1746, Charles Bonaparte married, in 1764, Letitia Ramolino,
a Corsican girl of fifteen. She was of good family, and she brought
to her husband a dowry at least equal to his own estate. Beautiful,
high-spirited, and intelligent, Madame Letitia knew nothing of books,
knew little of the manners of polite society, and was more of the proud
peasant than of the grand lady. She did not know how to add up a column
of figures; but time was to prove that she possessed judgment, common
sense, inflexible courage, great loftiness and energy of character.
Misfortune did not break her spirit, and prosperity did not turn her
head. She was frugal, industrious, strong physically and mentally,
"with a man's head on a woman's shoulders," as Napoleon said of her.
Charles Bonaparte was studying law in Italy when the war between France
and Corsica broke out. At the call of Paoli, the student dropped
his books and came home to join in the struggle. He was active and
efficient, one of Paoli's trusted lieutenants. After the battle of
Ponte Nuovo, realizing that all was lost, he gave in his submission
(May 23, 1769) to the French, and returned to Ajaccio.
The policy of the French was to conciliate the leading Corsicans, and
special attention seems to have been given to Charles Bonaparte. His
mansion in Ajaccio, noted for its hospitality, became the favorite
resort of General Marbeuf, the bachelor French governor of the
island. With an ease which as some have thought indicated suppleness
or weakness of character, Bonaparte the patriot became Bonaparte the
courtier. He may have convinced himself that incorporation with France
was best for Corsica, and that his course in making the most out of the
new order of things was wisdom consistent with patriotism.
Resistance to France having been crushed, the policy of conciliation
inaugurated, and the Corsicans encouraged to take part in the
management of their own affairs, subject to France, one might hesitate
before condemning the course of Charles Bonaparte in Corsica, just as
we may hesitate between the policies of Kossuth and Déak in Hungary,
or of Kosciusko and Czartoryski in Poland. We may, and do, admire the
patriot who resists to the death; and, at the same time, respect the
citizen who fights till conquered, and then makes the best of a bad
situation.
In 1765 Madame Letitia Bonaparte gave birth to her first child; in
1767, to her second, both of whom died while infants. In 1768 was born
Joseph, and on August 15, 1769, Napoleon.[1]
[1] During the period of this pregnancy, Corsica was in
the storm of war; and Madame Bonaparte, following her
husband, was in the midst of the sufferings, terrors, and
brutalities which such a war creates. The air was still
electrical with the hot passions of deadly strife when the
young wife's time came. On the 15th of August, 1769, Madame
Bonaparte, a devout Catholic, attended service at the
church; but feeling labor approaching, hastened home, and
was barely able to reach her room before she was delivered
of Napoleon on a rug upon the floor.
The authority for this statement is Madame Bonaparte herself,
who gave that account of the matter to the Permons in Paris,
on the 18th of Brumaire, the day on which the son thus born
was struggling for supreme power in France.
The story which represents the greatest of men and warriors
as having come into the world upon a piece of carpet,
or tapestry, upon which the heroes of the "Iliad" were
represented, is a fable, according to the express statement
made by Madame Bonaparte to the American General Lee, in
Rome, in 1830.
Other children came to the Bonapartes in the years following, the
survivors of these being: Elisa, Lucien, Louis, Pauline, Caroline, and
Jerome. To support this large family, and to live in the hospitable
fashion which custom required of a man of his rank, Charles Bonaparte
found a difficult matter, especially as he was a pleasure-loving,
extravagant man whose idea of work seemed to be that of a born
courtier. He returned to Italy after the peace; spent much of his
patrimony there; made the reputation of a sociable, intelligent,
easy-going gentleman; and took his degree of Doctor of Laws, at Pisa,
in November, 1769.
It was his misfortune to be cumbered with a mortgaged estate and a
hereditary lawsuit. Whatever surplus the mortgage failed to devour
was swallowed by the lawsuit. His father had expensively chased this
rainbow, pushed this hopeless attempt to get justice; and the steps of
the father were followed by the son. It was the old story of a sinner,
sick and therefore repentant; a priest holding the keys to heaven and
requiring payment in advance; a craven surrender of estate to purchase
the promise of salvation. Thus the Jesuits got Bonaparte houses and
lands, in violation of the terms of an ancestor's will, the lawsuit
being the effort of the legal heirs to make good the testament of the
original owner.
In spite of all they could do, the Bonapartes were never able to
recover the property.
Charles Bonaparte, a man of handsome face and figure, seems to have
had a talent for making friends, for he was made assessor to the
highest court of Ajaccio, a member of the council of Corsican nobles,
and later, the representative of these nobles to France. With the
slender income from his wife's estate and that from his own, aided by
his official earnings, he maintained his family fairly well; but his
pretensions and expenditures were so far beyond what he was really able
to afford that, financially, he was never at ease.
It was the familiar misery of the gentleman who strives to gratify a
rich man's tastes with a poor man's purse. There was his large stone
mansion, his landed estate, his aristocratic associates, his patent of
nobility signed by the Duke of Florence; and yet there was not enough
money in the house to school the children.
The widowed mother of Madame Letitia had married a second husband,
Fesch, a Swiss ex-captain of the Genoese service, and by this marriage
she had a son, Joseph Fesch, known to Napoleonic chronicles as "Uncle
Fesch." This eleven-year-old uncle taught the young Napoleon the
alphabet.
In his sixth year Napoleon was sent to a dame's school. For one of the
little girls at this school the lad showed such a fondness that he was
laughed at, and rhymed at, by the other boys.
_Napoleon di mezza calzetta
Fa l'armore a Giacominetta._[2]
[2]Napoleon with his stockings half off
Makes love to Giacominetta.
The jeers and the rhyme Napoleon answered with sticks and stones.
It is not very apparent that he learned anything here, for we are told
that it was the Abbé Recco who taught him to read; and it was this
Abbé whom Napoleon remembered in his will. As to little Giacominetta,
Napoleonic chronicles lose her completely, and she takes her place
among the "dream children" of very primitive poesy.
Just what sort of a boy Napoleon was at this early period, it is next
to impossible to say. Perhaps he did not differ greatly from other
boys of his own age. Probably he was more fractious, less inclined to
boyish sports, quicker to quarrel and fight. But had he never become
famous, his youthful symptoms would never have been thought to indicate
anything uncommon either for good or evil.
At St. Helena, the weary captive amused himself by picturing the young
Napoleon as the bad boy of the town. He quarrelled, he fought, he bit
and scratched, he terrorized his brothers and sisters, and so forth. It
may be true, it may not be; his mother is reported as saying that he
was a "perfect imp of a child," but the authority is doubtful.
The Bonaparte family usually spent the summer at a small country-seat
called Milleli. Its grounds were beautiful, and there was a glorious
view of the sea. A large granite rock with a natural cavity, or grotto,
offered a cool, quiet retreat; and this is said to have been Napoleon's
favorite resort. In after years he improved the spot, built a small
summer-house there, and used it for study and meditation.
It is natural to suppose that Napoleon as a child absorbed a good deal
of Corsican sentiment. His wet-nurse was a Corsican peasant, and from
her, his parents, his playmates, and his school companions he probably
heard the story of Corsica, her wrongs, her struggles, and her heroes.
Della Rocca, Sampiero, Gaffori, and Paoli were names familiar to his
ears. At a very early age he had all the passions of the Corsican
patriot. The French were masters, but they were hated. While the
Bonapartes had accepted the situation, they may not have loved it.
The very servants in the house vented their curses on "those dogs of
French."
General Marbeuf, the warm friend of the family, encouraged Charles
Bonaparte to make the attempt to have the children educated at the
expense of France. In 1776 written application was made for the
admission of Joseph and Napoleon into the military school of Brienne.
At that time both the boys were on the safe side of the age-limit of
ten years. But the authorities demanded proofs of nobility,--four
generations thereof,--according to Bourbon law; and before these proofs
could be put into satisfactory shape, Joseph was too old for Brienne.
Chosen in 1777 by the nobles of Corsica as their deputy to France,
Charles Bonaparte set out for Versailles in 1778, taking with him his
sons Joseph and Napoleon. Joseph Fesch accompanied the party as far as
Aix, where he was to be given a free education for the priesthood by
the seminary at that place. Joseph and Napoleon both stated in after
years that their father visited Florence on the way to France, and was
given an honorable reception at the ducal court.
The Bishop of Autun, nephew of General Marbeuf, had been interested
in behalf of the Bonapartes; and it was at his school that Joseph was
to be educated for the Church. Napoleon was also placed there till he
could learn French enough for Brienne. On January 1, 1779, therefore,
he began his studies.
The Abbé Chardon, who was his teacher, says that he was a boy of
thoughtful and gloomy character. "He had no playmate and walked about
by himself." Very naturally. He was a stranger to all the boys, he was
in a strange country, he could not at first speak the language, he
could not understand those who did speak it--how was the homesick lad
to be sociable and gay under such conditions? Besides, he was Corsican,
a despised representative of a conquered race. And the French boys
taunted him about it. One day, according to the teacher, the boys threw
at him the insult that "the Corsicans were a lot of cowards." Napoleon
flashed out of his reserve and replied, "Had you been but four to one
you would never have conquered us, but you were ten to one." To pacify
him the teacher remarked, "But you had a good general--Paoli."--"Yes,"
answered the lad of ten, "and I would like to resemble him."
According to the school register and to Napoleon's own record, he
remained at Autun till the 12th of May, 1779. He had learned "enough
French to converse freely, and to make little themes and translations."
In the meantime, Charles Bonaparte had been attending his king, the
young Louis XVI., at Versailles. Courtier in France as in Ajaccio, the
adroit lawyer had pleased. A bounty from the royal purse swelled the
pay of the Corsican delegates, a reward for "their excellent behavior";
and for once Charles Bonaparte was moderately supplied with funds.
On May 19, 1779, Napoleon entered the college of Brienne. Its teachers
were incompetent monks. The pupils were mainly aristocratic French
scions of the privileged nobility, proud, idle, extravagant, vicious.
Most of these young men looked down upon Napoleon with scorn. In him
met almost every element necessary to stir their dislike, provoke
their ridicule, or excite their anger. In person he was pitifully thin
and short, with lank hair and awkward manners; his speech was broken
French, mispronounced and ungrammatical; it was obvious that he was
poor; he was a Corsican; and instead of being humble and submissive, he
was proud and defiant. During the five years Napoleon spent here he was
isolated, moody, tortured by his own discontent, and the cruelty of his
position. He studied diligently those branches he liked, the others he
neglected. In mathematics he stood first in the school, in history and
geography he did fairly well; Latin, German, and the ornamental studies
did not attract him at all. The German teacher considered him a dunce.
But he studied more in the library than in the schoolroom. While the
other boys were romping on the playground, Napoleon was buried in some
corner with a book.
On one occasion Napoleon, on entering a room and seeing a picture of
Choiseul which hung therein, burst into a torrent of invective against
the minister who had bought Corsica. The school authorities punished
the blasphemy.
At another time one of the young French nobles scornfully said to
Napoleon, "Your father is nothing but a wretched tipstaff." Napoleon
challenged his insulter, and was imprisoned for his temerity.
Upon another occasion he was condemned by the quartermaster, for some
breach of the rules, to wear a penitential garb and to eat his dinner
on his knees at the door of the common dining-room. The humiliation was
real and severe; for doubtless the French lads who had been bullying
him were all witnesses to the disgrace, and were looking upon the
culprit with scornful eyes, while they jeered and laughed at him.
Napoleon became hysterical under the strain, and began to vomit. The
principal of the school happening to pass, was indignant that such a
degradation should be put upon so dutiful and diligent a scholar, and
relieved him from the torture.
"Ah, Bourrienne! I like you: you never make fun of me!" Is there
nothing pathetic in this cry of the heart-sick boy?
To his father, Napoleon wrote a passionate appeal to be taken from
the school where he was the butt of ridicule, or to be supplied
with sufficient funds to maintain himself more creditably. General
Marbeuf interfered in his behalf, and supplied him with a more liberal
allowance.
The students, in turn, were invited to the table of the head-master.
One day when this honor was accorded Napoleon, one of the
monk-professors sweetened the boy's satisfaction by a contemptuous
reference to Corsica and to Paoli. It seems well-nigh incredible
that the clerical teachers should have imitated the brutality of
the supercilious young nobles, but Bourrienne is authority for the
incident. Napoleon broke out defiantly against the teacher, just as
he had done against his fellow-students: "Paoli was a great man; he
loved his country; and I will never forgive my father for his share in
uniting Corsica to France. He should have followed Paoli." Mocked by
some of the teachers and tormented by the richer students, Napoleon
withdrew almost completely within himself. He made no complaints,
prayed for no relief, but fell back on his own resources. When the boys
mimicked his pronunciation, turned his name into an offensive nickname,
and flouted him with the subjection of his native land, he either
remained disdainfully silent, or threw himself single-handed against
his tormentors.
To each student was given a bit of ground that he might use it as he
saw fit. Napoleon annexed to his own plat two adjacent strips which
their temporary owners had abandoned; and by hedging and fencing made
for himself a privacy, a solitude, which he could not otherwise get.
Here he took his books, here he read and pondered, here he indulged his
tendency to day-dreaming, to building castles in the air.
His schoolmates did not leave him at peace even here. Occasionally they
would band together and attack his fortress. Then, says Burgoing, one
of his fellow-students, "it was a sight to see him burst forth in a
fury to drive off the intruders, without the slightest regard to their
numbers."
Much as he disliked his comrades, there was no trace of meanness in
his resentments. He suffered punishment for things he had not done
rather than report on the real offenders. Unsocial and unpopular, he
nevertheless enjoyed a certain distinction among the students as well
as with the teachers. His pride, courage, maturity of thought, and
quick intelligence arrested attention and compelled respect.
When the students, during the severe winter of 1783–84, were kept
within doors, it was Napoleon who suggested mimic war as a recreation.
A snow fort was built, and the fun was to attack and defend it with
snowballs. Then Napoleon's natural capacity for leadership was seen.
He at one time led the assailants, at another the defenders, as
desperately in earnest as when he afterward attacked or defended
kingdoms. One student refusing to obey an order, Napoleon knocked him
down with a chunk of ice. Many years after this unlucky person turned
up with a scar on his face, and reminded the Emperor Napoleon of the
incident; whereupon Napoleon fell into one of his best moods, and dealt
liberally with the petitioner.
During the whole time Napoleon was at Brienne he remained savagely
Corsican. He hated the French, and did not hesitate to say so. Of
course the French here meant were the pupils of the school--the big
boys who jeered at his poverty, his parentage, his countrymen. It
is worth notice that he never by word or deed sought to disarm his
enemies by pandering to their prejudices. He made no effort whatever to
ingratiate himself with them by surrendering any of his own opinions.
He would not even compromise by concealing what he felt. He was a
Corsican to the core, proud of his island heroes, proud of Paoli,
frankly detesting those who had trampled upon his country. It must have
sounded even to the dull ears of ignorant monks as something remarkable
when this shabby-looking lad, hardly in his teens, cried out,
defiantly, "I hope one day to be able to give Corsica her freedom!"
He had drunk in the wild stories the peasants told of Sampiero; he had
devoured the vivid annals of Plutarch, and his hopes and dreams were
already those of a daring man.
During these years at Brienne, General Marbeuf continued to be
Napoleon's active friend. He seems to have regularly supplied him with
money, and it was the General's interference which secured his release
from imprisonment in the affair of the duel. Through the same influence
Napoleon secured the good-will of Madame de Brienne, who lived in the
château near the school. This lady warmed to the lad, took him to her
house to spend holidays and vacations, and treated him with a motherly
kindness which he never forgot.
The character which Napoleon established at Brienne varied with the
point of view. To the students generally he appeared to be unsocial,
quarrelsome, and savage. To some of the teachers he seemed to be mild,
studious, grateful. To others, imperious and headstrong. M. de Keralio
reported him officially as submissive, upright, thoughtful, "conduct
most exemplary." On all he made the impression that he was inflexible,
not to be moved after he has taken his stand. Pichegru, afterward
conqueror of Holland, and after that supporter of the Bourbons, was a
pupil-teacher to Napoleon at Brienne, and is thought to have been the
quartermaster who put upon him the shame of eating on his knees at the
dining-room door. Bourbon emissaries were eager to win over to their
cause the brilliant young general, Bonaparte, and suggested the matter
to Pichegru. "Do not try it," said he. "I knew him at Brienne. His
character is inflexible. He has taken his side, and will not change."
When Napoleon, in his last years, came to speak of his school days,
he seemed to have forgotten all that was unpleasant. Time had swept
its effacing fingers over the actual facts, and he had come to believe
that he had not only been happy at Brienne, but had been a jolly,
frolicksome fellow--a very cheerful, sociable, popular lad. It was
some other youth who had shunned his fellows, fenced himself within a
garden wall, combated all intruders with sticks and stones, and hated
the French because they teased him so. The real Napoleon, according to
the captive Emperor, was a boy like other boys, full of fun, frolic,
tricks, and games. One of the sportive tricks of the merry and mythical
Bonaparte was this: An old commandant, upward of eighty, was practising
the boys at target-shooting with a cannon. He complained that the aim
was bad, none of the balls hit the target. Presently, he asked of
those near him if they had seen the ball strike. After half a dozen
discharges, the old general bethought himself of counting the balls.
Then the trick was exposed--the boys had slipped the balls aside each
time the gun was loaded.
Another anecdote told by the Emperor brings him more immediately within
the circle of our sympathies. Just above his own room at the college
was a fellow-student who was learning to play on the horn. He practised
loudly, and at all hours. Napoleon found it impossible to study.
Meeting the student on the stairs, Napoleon feelingly remonstrated.
The horn player was in a huff at once, as a matter of course. His room
was his own, and he would blow horns in it as much as he pleased. "We
will see about that," said Napoleon, and he challenged the offender to
mortal combat. Death could have no terrors compared to the incessant
tooting in the room above, and Napoleon was determined to take his
chances on sudden sword thrust rather than the slow tortures of the
horn practice. Fellow-students interfered, a compromise was reached,
and the duel did not come off. The student who roused the ire of
Napoleon in this extreme manner was named Bussey, and in the campaign
of 1814 Napoleon met him again, received offers of service from him,
and named him aide-de-camp. It is a pleasure to be able to record that
this fellow-student of Brienne remained faithful to Napoleon to the
very last, in 1814 and again in 1815.
In the year 1810 the Emperor Napoleon, divorced from Josephine, was
spending a few days in seclusion in the Trianon at Versailles, awaiting
the coming of the Austrian wife, "the daughter of the Cæsars." Hortense
and Stephanie Beauharnais were with him, and Stephanie mischievously
asked him if he knew how to waltz. Napoleon answered:--
"When I was at the military school I tried, I don't know how many
times, to overcome the vertigo caused by waltzing, without being able
to succeed. Our dancing-master had advised us when practising to take a
chair in our arms instead of a lady. I never failed to fall down with
the chair, which I squeezed affectionately, and to break it. The chairs
in my room, and those of two or three of my comrades, disappeared one
after another."
The Emperor told this story in his gayest manner, and the two ladies
laughed, of course; but Stephanie insisted that he should even now
learn to waltz, that all Germans waltzed, that his new wife would
expect it, and that as the Empress could only dance with the Emperor,
he must not deprive her of such a pleasure.
"You are right," exclaimed Napoleon. "Come! give me a lesson."
Thereupon he rose, took the merry Stephanie in his arms, and went
capering around the room to the music of his own voice, humming the
air of _The Queen of Prussia_. After two or three turns, his fair
teacher gave him up in despair; he was too hopelessly awkward; and she
flattered him, while pronouncing him a failure, by saying that he was
made to give lessons and not receive them.
* * * * *
Toward the close of 1783 a royal inspector of the military schools,
Keralio by name, examined the students at Brienne for the purpose
of selecting those who were to be promoted to the higher military
school at Paris. M. de Keralio was greatly impressed by Napoleon, and
emphatically recommended his promotion. This inspector having died, his
successor examined Napoleon the second time, and passed him on to the
Paris school, which he entered on October 30, 1784. On the certificate
which went with him from Brienne were the words, "Character masterful,
imperious, and headstrong."
When Napoleon alighted from the coach which brought him from Brienne to
Paris, and stood, a tiny foreign boy, in the midst of the hurly-burly
of a great city, he must have felt himself one of the loneliest and
most insignificant of mortals. Demetrius Permon found him in the Palais
Royal, "where he was gaping and staring with wonder at everything he
saw. Truly, he looked like a fresh importation." M. Permon invited
the lad to dine, and found him "very morose," and feared that he had
"more self-conceit than was suitable to his condition." Napoleon made
this impression upon Permon by declaiming violently against the luxury
of the young men at the military school, denouncing the system of
education which prevailed there, comparing it unfavorably to the system
of ancient Sparta, and announcing his intention of memorializing the
minister of war on the subject.
Napoleon, at the military school of Paris, continued to be studious,
and to read almost constantly. He was obedient to the authorities,
and defiant to the young aristocrats who surrounded him and looked
down on him. The extravagance, indolence, and superciliousness of the
noble students, together with the general luxury which prevailed in
the establishment, disgusted and enraged a scholar who had no money to
spend, and who had come there to study. When he, as head of the State,
came to reorganize the educational system of France, he did not forget
the lessons taught by his own experience. As a man he adopted a system
which avoided all the abuses which as a boy he had denounced.
During this period he may have occasionally visited the Permons in
Paris and his sister Elisa, who had been admitted into the State
school at St. Cyr. Madame D'Abrantes so relates in her _Memoirs_;
and while there is a difficulty about dates, her narrative is,
perhaps, substantially correct. It is a lifelike picture she paints
of Napoleon's gloom at Paris and Elisa's sorrow at St. Cyr: Napoleon
wretched because he could not pay his way among the boys; Elisa
miserable because she could not keep step with the girls. Napoleon
sulked and denounced luxury; Elisa wept and bewailed her poverty. Elisa
was consoled by a tip given by Madame Permon. As for Napoleon, he
refused to borrow: "I have no right to add to the burdens of my mother."
On final examination, August, 1785, Napoleon stood forty-second in his
class--not a brilliant mark, certainly, but it sufficed. He received
his appointment of sub-lieutenant with joy unbounded. His days of
tutelage were over: henceforth he was a man and an officer. Having
chosen the artillery service, he set out with Des Mazis, a friend he
had made at the military school, to join the regiment of La Fère, which
was stationed at Valence. According to one account, Napoleon borrowed
money from a cloth merchant to make this journey; according to another,
Des Mazis paid the way of both. However that may be, it seems that when
the young officers reached Lyons, a gay city of the south, they relaxed
the rigors of military discipline to such an extent that their money
all vanished. The remainder of the distance to Valence was made on foot.
* * * * *
Those biographers who devote their lives to defaming Napoleon, lay
stress on the alleged fact that he was educated by the King. In
becoming an adherent of the Revolution, these writers say that he
betrayed an amount of moral obliquity quite appalling. Louis XVI. was
king while Napoleon was at Brienne, and the suggestion that Napoleon
owed a debt of gratitude to Louis XVI. is amusing. The tax-payers, the
people, educated Napoleon; and whatever debt of gratitude he owed, he
owed to them. In going with the Revolution, he went with those who had
paid his schooling. He himself drew this distinction at the time. When
M. Demetrius Permon rebuked him for criticising royalty, throwing the
alleged debt of gratitude in his teeth, the boy replied, "The State
educates me; not the King."
Of course Permon could not admit the distinction, he being a noble of
the Old Order; nor can biographers who write in the interest of modern
Toryism admit it. But the distinction is there, nevertheless; the boy
saw it, and so does impartial history.
CHAPTER III
Napoleon carried with him to his new home a letter of introduction
from the Bishop of Autun to the ex-Abbot of St. Ruffe, and with this
leverage he made his way into the best society of Valence. For the
first time circumstances were favorable to him, and the good effects
of the change were at once evident. Occupying a better place in life
than before, he was more contented, more sociable. He mingled with the
people about him, and made friends. No longer a waif, a charity boy
from abroad, thrust among other boys who looked down upon him as a
social inferior, he was now an officer of State, housed, fed, clothed,
salaried at the public expense. No longer under the wheels, he held
a front seat in that wondrous vehicle which men call government, and
in which a few so comfortably ride while the many so contentedly wear
harness and pull. No longer subject to everybody's orders, Napoleon
had become one of the masters in God's world here below, and could
issue orders himself. Glorious change! And the sun began to look bright
to "Lieutenant Bonaparte of the King's Royal Academy." He cultivated
himself and others socially. He found some congenial spirits among the
elderly men of the place; also some among the young women. In the hours
not spent in study, and not claimed by his duties, he could be found
chatting at the coffee-house, strolling with brother officers, dancing
at the neighborhood balls, and playing the beau amid the belles of this
high provincial circle.
To one of these young ladies, according to tradition and his own
statement, he lost his heart. But when we seek to know something more
definite, tradition and his own statements differ. If we are to accept
his version, the courtship led to nothing beyond a few promenades, and
the eating of cherries together in the early morning. According to the
local tradition, however, he proposed and was rejected. Her parents
were local aristocrats, and had so little confidence in the future of
the little officer that they married their girl by preference to a M.
de Bressieux--a good, safe, commonplace gentleman of the province. In
after years the lady reminded Napoleon of their early friendship, and
he at once made generous provision for both herself and husband.
If possible, Napoleon studied more diligently at Valence than at
Brienne. Plutarch's _Lives_ and Cæsar's _Commentaries_ he had already
mastered while a child; Rousseau had opened a new world of ideas to
him in Paris: he now continued his historical studies by reading
Herodotus, Strabo, Diodorus. Anything relating to India, China, Arabia,
had a peculiar charm for him. Next he learned all he could of Germany
and England. French history he studied minutely, striving to exhaust
information on the subject. In his researches he was not content
merely with ordinary historical data: he sought to understand the
secret meaning of events, and the origin of institutions. He studied
legislation, statistics, the history of the Church, especially the
relation of the Church to the State. Likewise he read the masterpieces
of French literature and the critical judgments which had been passed
upon them. Novels he did not disdain, and for poetry of the heroic cast
he had a great fondness.
He read also the works of Voltaire, Necker, Filangieri, and Adam
Smith. With Napoleon to read was to study. He made copious notes, and
these notes prove that he bent every faculty of his mind to the book
in hand. He analyzed, commented, weighed statements in the balance of
his own judgment--in short, doing everything necessary to the complete
mastery of the subject. A paper on which he jotted down at that time
his ideas of the relations between Church and State appear to show that
he had reached at that time the conclusions he afterward embodied in
the Concordat. Rousseau he studied again, but the book which seems to
have taken his fancy more than any other was the Abbé Raynal's famous
_History of the Institutions and Commerce of the Europeans in the Two
Indies_. This book was a miscellany of essays and extracts treating of
superstition, tyranny, etc., and predicting that a revolution was at
hand in France if abuses were not reformed.
How was it that Napoleon, with his meagre salary, could command so many
costly books? A recent biographer patly states that he "subscribed to a
public library." This may be true, but Napoleon himself explained to an
audience of kings and princes at Erfurth, in 1808, that he was indebted
to the kindness of one Marcus Aurelius, a rich bookseller, "a most
obliging man who placed his books at my service."
The personal appearance of the young lieutenant was not imposing. He
was short, painfully thin, and awkward. His legs were so much too small
for his boots that he looked ridiculous--at least to one young lady,
who nicknamed him "Puss in Boots." He wore immense "dog's ears," which
fell to his shoulders, and this style of wearing the hair gave his dark
Italian face a rather sinister look, impressing a lady acquaintance
with the thought that he would not be the kind of man one would like
to meet near a wood at night. Generally he was silent, wrapped in
his own thoughts; but when he spoke, his ideas were striking and his
expressions energetic. He rather affected the laconic, oracular style,
and his attitude was somewhat that of a man posing for effect. In
familiar social intercourse he was different. His smile became winning,
his voice soft and tender, and his magnetism irresistible. He loved to
joke others and play little pranks with them; but he could not relish a
joke at his own expense, nor did he encourage familiarity. He had none
of the brag, bluster, or roughness of the soldier about him, but in a
quiet way he was imperious, self-confident, self-sufficient. So little
did his appearance then, or at any other time, conform to the popular
ideal of the soldier, that one old grenadier of the Bourbon armies, on
having Napoleon pointed out to him, after the Italian campaign, could
not believe such a man could possibly be a great warrior. "That a
general!" said the veteran with contempt; "why, when he walks he does
not even step out with the right foot first!"
Extremely egotistic he was, and so remained to his last hour. He had
no reverence, looked for fact in all directions, had almost unerring
judgment, and believed himself superior to his fellow-students, to his
teachers, and to his brother officers. At the age of fifteen he was
giving advice to his father--very sound advice, too. At that early
age he had taken family responsibilities upon his shoulders, and was
gravely disposing of Joseph and Lucien. In a remarkable letter he
elaborately analyzed Joseph's character, and reached the conclusion
that he was an amiable nonentity, fit only for society. It had been
well for Napoleon if he had always remembered this, and acted upon it.
In August, 1786, Napoleon spent a short time in Lyons. After this he
was perhaps sent to Douay in Flanders, though he himself has written
that on September 1, 1786, he obtained leave of absence and set out for
Corsica, which he reached on the fifteenth of the same month.
* * * * *
Napoleon found the condition of the family greatly changed. Charles
Bonaparte had died in France in February, 1785. General Marbeuf,
also, was dead. The French officials were not now so friendly to the
Bonapartes. Madame Letitia had been growing mulberry trees in order
to obtain the governmental bounty--the government being intent upon
building up the silk industry. Madame Bonaparte had apparently been
giving more thought to the bounty than to the trees, and the result was
that the officials had refused payment. Hence the supply of cash in
the household was cut down to Napoleon's salary (about $225), and such
sums as could be teased out of the rich uncle--the miserly archdeacon.
Desperately worried as he must have been by the condition of the family
finances, Napoleon put a bold face upon it, strutting about town so
complacently that he gave much offence to the local magnates--the town
oracles whose kind words are not easily won by the neighborhood boys
who have gone to distant colleges for an education and have returned
for inspection and approval. To the sidewalk critics, who only nine
years ago had jeered at the slovenly lad and his girl sweetheart,
Napoleon's style of walk and talk may have seemed that of inflated
self-conceit.
Like a good son, Napoleon exerted himself to the utmost in behalf of
his mother, making every effort to have the mulberry bounty paid, and
to wring revenue out of the family property. He met with no success in
either direction, though it appears that he prevailed upon the local
authorities to grant some slight favor to the family. At one time
Madame Letitia was reduced to the necessity of doing all her housework
with her own hands.
At Elba, the Emperor related a story which belongs to this period of
his life. He said that one day his mother's mother was hobbling along
the street in Ajaccio, and that he and Pauline followed the old lady,
and mimicked her. Their grandmother, happening to turn, caught them
in the act. She complained to Madame Letitia. Pauline was at once
"spanked" and disposed of; Napoleon, who was rigged out in regimentals,
could not be handled. His mother bided her time. Next day, when her
son was off his guard, she cried, "Quick, Napoleon! You are invited to
dine with the governor!" He ran up to his room to change clothing--she
quietly followed. When she judged that the proper time had come, she
rushed into the room, seized her undressed hero before he guessed
her purpose, laid him across the maternal knees, and belabored him
earnestly with the flat of her hand.
In October, 1787, Napoleon was again in Paris, petitioning the
government in behalf of his mother, and seeking to have his furlough
extended. Failing as to his mother, succeeding as to himself, he
was back home in January, 1788, and remained there until June of the
same year. While in Corsica, Napoleon frequently dined with brother
officers in the French army. Between him and them, however, there was
little congeniality. He was hotly Paolist, and his talk was either of
Corsican independence or of topics historical and governmental. His
brother officers did not enjoy these conversations. His patriotism
offended; his learning bored them. What did the average French officer
of that day know or care about history and the science of government?
The upshot of such a dinner-party usually was that Napoleon got into a
wrangle with that one of the officers who imagined he knew something
of the subject, while the others, who honestly realized that they did
not, would walk off in disgust. "My comrades, like myself," says M. de
Renain, one of the officers in question, "lost patience with what we
considered ridiculous stuff and pedantry."
So far did Napoleon carry his patriotic sentiments that he rather
plainly threatened to take sides with the Corsicans if any collision
should occur between the French and his countrymen. Upon this, one of
the officers who disliked him asked sharply, "Would you draw your sword
against the soldiers of the King?"
Napoleon, dressed in the King's uniform, had the good sense to remain
silent. The officers were offended at his tone, and, says Renain, "This
is the last time he did me the honor of dining with me."
Not for a day had Napoleon neglected his books. To escape the household
noises, he went to the attic, and there pursued his studies. Far
and wide ranged his restless mind, from the exact sciences, dry and
heavy, to Plato and Ossian, rich in suggestions to the most opulent
imagination nature ever gave a practical man. To the very last,
Napoleon remained half mystic; and when he stood in the storm the night
before Waterloo, and cast into the darkness the words, "We are agreed";
or when he remained silent for hours at St. Helena watching the vast
wings of the mist whirl, and turn, and soar around the summit of the
bleak, barren mountain of rock, we feel that if pens were there to
trace his thought, Ossian would seem to live again. From his youth up
the most striking characteristic of his mind was its enormous range;
its wide sweep from the pettiest, prosiest details of fact to the
sublimest dreams and the most chimerical fancies. Not wholly satisfied
with reading and commentary, he strove to compose. Under the Bourbons,
his outlook in the army was not promising. He might hope, after many
tedious years of garrison service, to become a captain; after that it
would be a miracle if he rose higher. Hence his lack of interest in the
routine work of a soldier, and hence his ambition to become an author.
He wrote a story called _The Count of Essex_, also a novel founded on
Corsican life, and pulsing with hatred of France. Another story which
he called _The Masked Prophet_, is the same which Moore afterward used
in _The Veiled Prophet of Khorassan_.
His greatest exertions, however, were spent upon the _History of
Corsica_. To this work he clung with a tenacity of purpose that is
touching. All the long, tragic story of Corsica seems to have run
like fire in the boy's veins, and the heroes of his country--Paoli,
Sampiero, Della Rocca--seemed to him to be as great as the men of
antiquity, as perhaps they were. Therefore, the young man wrote and
rewrote, trying to get the book properly written, his thoughts properly
expressed. He had turned to Raynal, as we have seen, and the Abbé had
kindly said, "Search further, and write it over." And Napoleon had done
so. At least three times he had recast the entire book. He sought the
approval of a former teacher, Dupuy; he sent "copy" to Paoli. Dupuy
had a poor opinion of the performance; and Paoli told him flatly he
was too young to write history. But Napoleon persevered, finished the
work, and eagerly sought publishers. Alas! the publishers shook their
heads. Finally, at Paris was found a bold adventurer in the realm of
book-making, who was willing to undertake half the cost if the author
would furnish the other half. But for one reason or another the book
was never published.
The passionate earnestness with which Napoleon toiled at his book on
Corsican history, the intense sympathy with which he studied the lives
of Corsican heroes, the fiery wrath he nursed against those who had
stricken down Corsican liberties, were but so many evidences of the set
purpose of his youth--to free his country, to give it independence.
There is no doubt that the one consuming ambition of these early years
was as pure as it was great: he would do what Sampiero and Paoli had
failed to do--he would achieve the independence of Corsica!
Napoleon rejoined his regiment at Auxonne at the end of May, 1788.
That he did so with reluctance is apparent from the manner in which
he had distorted facts to obtain extension of his furlough. Garrison
duty had no charms for him; the dull drudgery of daily routine became
almost insupportable. It appears that he was put under arrest for the
unsatisfactory manner in which he had superintended some work on the
fortifications. When off duty he gave his time to his books. He became
ill, and wrote to his mother, "I have no resource but work. I dress but
once in eight days. I sleep but little, and take but one meal a day."
Under this regimen of no exercise, hard work, and little sleep he came
near dying.
In September, 1789, came another furlough, and the wan-looking
lieutenant turned his face homeward. In passing through Marseilles he
paid his respects to the Abbé Raynal.
CHAPTER IV
The French Revolution was now (1789–90) getting under full headway.
The States-General had met on May 5, 1789; the Third Estate had
asserted and made good its supremacy. The King having ordered up
troops and dismissed Necker, riots followed; the Bastille was taken
and demolished. The nobles who had persuaded Louis XVI. to adopt the
measures which provoked the riots, fled to foreign lands. Louis was
brought from Versailles to Paris, Bailly was made mayor of the city,
Lafayette commander of the National Guard, and on the night session of
August 4, feudalism, losing hope, offered itself up as a sacrifice to
the Revolution.
Liberty, fraternity, equality, freedom of conscience, liberty of the
press, were proclaimed; and the mighty movement which was shaking down
the Old Order was felt at Auxonne as in Paris. The officers, as a
rule, were for the King; the soldiers for the nation. Society ladies
and governmental officials were royalists, generally; so, also, the
higher clericals. The curés and the masses of the people were for the
Revolution.
Instinctively, and without the slightest hesitation, Napoleon took
sides with the nation. He needed no coercion, no change of heart; he
was already an enemy of the Ancien Régime, and had been so from his
first years in France.
"How does it happen that you, Napoleon, favor democracy? You are a
noble, educated at a school where none but nobles can enter; you are
an officer, a position none but nobles may hold; you wear the King's
livery; you are fed on his bounty: where did you get your republican
principles?"
Supposing such a question to have been put, we can imagine the answer
to have been something like this:--
"I go with the reformers partly because I hate the Old Order, partly
because I see in the coming changes a chance for me to rise, and partly
because I believe the reformers are right. I have read books which
gave me new ideas; I have thought for myself, and reached conclusions
of my own. The stupid monk who threw my schoolboy essay into the fire
at Brienne because it criticised royalty, only stimulated my defiance
and my independence. I have seen what your system of education is,
and condemn it; have learnt what your nobles are, and detest them. I
have seen the Church, which preaches the beauties of poverty, rob my
family of a rich inheritance, and I loathe the hypocrisy. I have read
Rousseau, and believe in his gospel; have studied Raynal, and agree
that abuses must be reformed. I have looked into the conduct of kings,
and believe that there are few who do not deserve to be dethroned. The
privileged have combined, have closed the avenues of progress to the
lower classes, have taken for a few what is the common heritage of all.
The people are the source of power--those below not those above. I am
poor, I hate those above me, I long to be rich, powerful, admired. If
things remain as they are, I shall never be heard of: revolution will
change all. New men will rise to make the most of new opportunities.
Hence I am a Jacobin, a democrat, a republican--call it what you will.
I am for putting the premium on manhood. The tools to him who can use
them! As to the King's uniform and bounty--bah!--you must take me for a
child. The King gives nothing, is nothing; the nation gives all, and is
everything. I go with the nation!"
With such thoughts fermenting in his head, Napoleon reached home,
and at once began to agitate the politics of the island. Corsica
was far out of the track of the Revolution, and the people had not
been maddened by the abuses which prevailed in France. The one great
national grievance in Corsica was French domination. Therefore to
arouse the island and put it in line with revolutionary France, was
a huge task. Nevertheless Napoleon and other young men set about
it. Copying the approved French method, he formed a revolutionary
committee, and began to organize a national guard. He became a violent
speaker in the Jacobin club, and a most active agitator in the town.
Soon the little city of Ajaccio was in commotion.
Paoli's agents bestirred themselves throughout the island. In some
towns the patriot party rose against the French authorities. In Ajaccio
the royalist party proved the stronger. The French commandant, De
Barrin, closed the democratic club and proclaimed martial law. The
patriots met in one of the churches, on the night of October 31, 1789,
and signed a vigorous protest and appeal to the National Assembly of
France. This paper was written by Napoleon, and he was one of those who
signed.
Baulked in Ajaccio, Napoleon turned to Bastia, the capital. Agitating
there and distributing tricolored cockades which he had ordered
from Leghorn, he soon got matters so well advanced that he headed a
deputation which waited upon the royal commandant and demanded that
he, too, should adopt the national cockade. De Barrin, the commandant,
refused. A riot broke out, and he consented. Napoleon agitated for
a national guard. Deputations sought the governor and requested his
sanction. He refused. One morning the streets were thronged with
patriots, armed, marching to one of the churches to be enrolled. De
Barrin called out his troops, trained cannon on the church, and set his
columns in motion to attack. Shots were exchanged, two French soldiers
killed, two wounded, and an officer got a bullet in the groin. Several
Bastians, including two children, were wounded. De Barrin lost his
head, yielded at all points, and ordered six hundred guns delivered to
the insurgents. Prompt obedience not having been given to his order,
the Bastians broke into the citadel, armed themselves, and insisted
that they, jointly with the French, should garrison the fortress. When
quiet was restored, the governor ordered Napoleon to leave, and he did
so.
This episode in Napoleon's career is related by an enemy of Napoleon,
and it is to be received with caution. Yet as it is a companion piece
to what he had attempted at Ajaccio, there is nothing violently
incredible about it. It is certain he was very active at that time, and
that he was often at Bastia. What was his purpose, if not to foment
revolutionary movements?
On November 30, 1789, the National Assembly of France decreed the
incorporation of Corsica with France, and amnesty for all political
offenders, including Paoli. Bonfires in Corsica and general joy greeted
the news. The triumph of the patriots was complete. A democratic town
government for Ajaccio was organized, a friend of Napoleon was chosen
mayor, and Joseph was put in place as secretary to the mayor. A local
guard was raised, and Napoleon served as private member of it. At the
club and on the streets he was one of the loudest agitators.
Paoli, now a hero in France as well as in Corsica, was called home
by these events, received a magnificent ovation from the French,
and reached Corsica, July, 1790. When he landed, after an exile of
twenty-one years, the old man knelt to the ground and kissed it.
Supported by the town government, Napoleon renewed his activity, the
immediate object aimed at being the capture of the citadel. He made
himself intensely disagreeable to the royalists. Upon one occasion,
during a religious procession, he was attacked by the Catholics, as an
enemy of the Church. His efforts to seize the citadel came to nothing.
There was an uprising of the revolutionists in the town, but the French
officials fled into the citadel and prepared to defend it. Napoleon
advised an attack, but the town authorities lost heart. They decided
not to fight, but to protest; and Napoleon drew up the paper.
The people of Corsica met in local district meetings and chose
delegates to an assembly which was to elect departmental and district
councils to govern the island. This general assembly met at Orezzo,
September 9, 1790, and remained in session a month. Among the delegates
were Joseph Bonaparte and Uncle Fesch. Napoleon attended and took an
active part in the various meetings which were held in connection with
the work of the assembly. He was a frequent speaker at these meetings,
and, while timid and awkward at first, soon became one of the most
popular orators.
It was while he was on his way to Orezzo, that Napoleon first met
Paoli. The old hero gave the young man a distinguished reception.
Attended by a large cavalcade, the two rode over the fatal field of
Ponte Nuovo. Paoli pointed out the various positions the troops had
occupied, and related the incidents of that lamentable day. Napoleon's
comments, his peculiar and original thought and speech, struck Paoli
forcibly; and he is said to have remarked that Napoleon was not modern,
but reminded him of Plutarch's heroes. Napoleon himself, when at St.
Helena, represents Paoli as often patting him on the head and making
the remark above mentioned.
The assembly at Orezzo voted that Corsica should constitute one
department, and that Paoli should be its president. He was also made
commander-in-chief of the National Guard. The conduct of Buttafuoco and
Peretti who had been representing Corsica in France, was condemned.
Pozzo di Borgo and Gentili were chosen to declare to the National
Assembly the loyalty of Corsica to the principles of the French
Revolution.
Napoleon had endeavored to secure the election of Joseph Bonaparte to
the general directory of the department. In this he failed, but Joseph
was chosen as one of the district directory for Ajaccio.
During the sitting of the convention Napoleon wiled away many an hour
in familiar intercourse with the peasantry. He visited them at their
huts, made himself at home by their firesides, and interested himself
in their affairs. He revived some of the old Corsican festivals, and
the target practice which had long been forbidden. Out of his own
purse he offered prizes for the best marksmen. In this manner he won
the hearts of the mountaineers--a popularity which was of value to him
soon afterward.
Returned to Ajaccio, Napoleon continued to take prominent part in the
debates of the club, and he also continued his efforts at authorship.
He threw off an impassioned "open letter" to Buttafuoco. This was his
first successful writing. With imperial pride, it is dated "from my
summer house of Milleli." Stimulated perhaps by the applause with which
young Corsican patriots hailed his bitter and powerful arraignment of
a traitor, Napoleon ventured to compete for the prize which Raynal,
through the Academy of Lyons, had offered for the best essay on the
subject "_What truths and ideas should be inculcated in order best to
promote the happiness of mankind_." His essay was severely criticised
by the learned professors, and its author, of course, failed of the
prize.
It was on the plea that his health was shattered, and that the waters
of Orezzo were good for his complaint, that Napoleon had been enabled
to prolong his stay in Corsica. In February, 1791, he rejoined his
regiment at Auxonne. His leave had expired long since, but his colonel
kindly antedated his return. Napoleon had procured false certificates,
to the effect that he had been kept in Corsica by storms. To ease his
mother's burden, he brought with him his little brother Louis, now
twelve years old, whose support and schooling Napoleon proposed to take
upon himself. To maintain the two upon his slender pay of lieutenant
required the most rigorous economy. He avoided society, ate often
nothing but bread, carried on his own studies, and taught Louis. The
affectionate, fatherly, self-denying interest he took in the boy
beautifully illustrates the better side of his complex character.
During the Empire an officer, whose pay was $200 per month, complained
to Napoleon that it was not enough. The Emperor did not express the
contempt he felt, but spoke of the pittance upon which _he_ had been
made to live. "When I was lieutenant, I ate dry bread; but I shut the
door on my poverty."
It was at Dôle, near Auxonne, that the letter to Buttafuoco was
printed. Napoleon used to rise early, walk to Dôle, correct the proofs,
and walk back to Auxonne, a distance of some twenty miles, before
dinner.
In June, 1791, Napoleon became first lieutenant, with a yearly salary
of about $260, and was transferred to the Fourth Regiment, stationed
at Valence. Glad of the promotion and the slight increase in salary,
he did not relish the transfer, and he applied for leave to remain at
Auxonne. Permission was refused, and he quitted the place, owing (for
a new uniform, a sword, and some wood) about $23. Several years passed
before he was able to pay off these debts.
Back in Valence, he again lodged with old Mademoiselle Bou, he and
Louis. He continued his studies, and continued to teach Louis. His
former friends were dead, or had moved away, and he did not go into
society as he had done before; his position was too dismal, his poverty
too real. He lived much in his room, reading, studying, composing.
Travels, histories, works which treated of politics, of ecclesiastical
affairs and institutions, attracted him specially. No longer seen
in elegant drawing-rooms, he was the life of the political club. He
became, successively, librarian, secretary, and president.
All this while the Revolution had been rolling on. The wealth of the
Church was confiscated. Paper money was issued. The Festival of the
Federation was solemnized. Necker lost his grip on the situation, and
fled. Mirabeau became the hope of the moderates. Danton, Robespierre,
Marat, became influential radicals. The Jacobin club rose to power.
There developed the great feud between the Church and the Revolution,
and factions began to shed blood in many parts of France. The old-maid
aunts of the King fled the realm, causing immense excitement.
In April, 1791, Mirabeau died. His alliance with the court not being
then known, his death called forth universal sorrow and memorial
services. At Valence the republican club held such a service, and
Napoleon is said to have delivered an address. Then came the flight of
the King to Varennes. Upon this event also the club at Valence passed
judgment, amid excitement and violent harangues.
In July, 1791, the national oath of allegiance to the new order
of things was taken at Valence with imposing ceremony, as it was
throughout the country. The constitution had not been finished; but the
French of that day had the faith which works wonders, and they took the
oath with boundless enthusiasm.
There was a monster meeting near Valence: a huge altar, a grand coming
together, on common ground, of dignitaries high and low, officials
of Church and State, citizens of all degrees. Patriotism for one
brief moment made them all members of one fond family. "We swear to
be faithful to the Nation, the law, and the King; to maintain the
constitution; and to remain united to all Frenchmen by the bonds of
brotherhood." They all swore it, amid patriotic shouts, songs, cannon
thunder, band music, and universal ecstasy. Mass had begun the
ceremony, a _Te Deum_ ended it. At night there was a grand banquet, and
one of those who proposed a toast was Napoleon. Of course he was one of
those who had taken the oath.
"Previous to this time," said he, later, "had I been ordered to fire
upon the people, habit, prejudice, education, and the King's name would
have induced me to obey. With the taking of the national oath it was
otherwise; my instinct and my duty were henceforth in harmony."
Kings and aristocrats throughout the world were turning black looks
upon France, and an invasion was threatened. The Revolution must be
put down. It was a fire which might spread. This threat of foreign
intervention had an electrical effect upon the French, rousing them to
resistance.
Paris was the storm centre, Napoleon was highly excited, and to Paris
he was most eager to go. Urgently he wrote to his great-uncle, the
archdeacon, to send him three hundred francs to pay his way to Paris.
"There one can push to the forefront. I feel assured of success. Will
you bar my road for the lack of a hundred crowns?" The archdeacon did
not send the money. Napoleon also wrote for six crowns his mother owed
him. The six crowns seem not to have been sent.
* * * * *
This anecdote of Napoleon's sojourn at Valence is preserved by the
local gossips: Early one morning the surgeon of the regiment went to
Napoleon's room to speak to Louis. Napoleon had long since risen, and
was reading. Louis was yet asleep. To arouse the lad, Napoleon took his
sabre and knocked with the scabbard on the ceiling above. Louis soon
came down, rubbing his eyes and complaining of having been waked in
the midst of a beautiful dream--a dream in which Louis had figured as a
king. "You a king!" said Napoleon; "I suppose I was an emperor then."
The keenest pang Napoleon ever suffered from the ingratitude of those
he had favored, was given him by this same Louis, for whom he had acted
the devoted, self-denying father. Not only was Louis basely ungrateful
in the days of the Napoleonic prosperity, but he pursued his brother
with vindictive meanness when that brother lay dying at St. Helena,
publishing a libel on him so late as 1820.
A traveller in Corsica (Gregorovius, 1852) writes: "We sat around a
large table and regaled ourselves with an excellent supper.... A dim
olive-oil lamp lit the Homeric wanderers' meal. Many a bumper was drunk
to the heroes of Corsica. We were of four nations,--Corsicans, French,
Germans, and Lombards. I once mentioned the name of Louis Bonaparte,
and asked a question. The company suddenly became silent, and the gay
Frenchman looked ashamed."
* * * * *
In August, 1791, Napoleon obtained another furlough, and with about
$80, which he had borrowed from the paymaster of his regiment, he and
Louis set out for home. Again he left debts behind him, one of them
being his board bill.
CHAPTER V
Soon after Napoleon reached home, the rich uncle, the archdeacon,
died, and the Bonapartes got his money. The bulk of it was invested in
the confiscated lands of the Church. Some of it was probably spent in
Napoleon's political enterprises.
Officers of the Corsican National Guard were soon to be elected,
and Napoleon formed his plans to secure for himself a lieutenant
colonelship. The leaders of the opposing faction were Peraldi and Pozzo
di Borgo.
Three commissioners, appointed by the Directory of the Island, had the
supervision of the election, and the influence of these officers would
have great weight in deciding the contest. Napoleon had recently been
over the island in company with Volney, inspector of agriculture and
manufactures, and had personally canvassed for votes among the country
people. He had made many friends; and, in spite of powerful opposition
in the towns, it appeared probable that he would win. It is said that
he resorted to the usual electioneering methods, including bribes,
threats, promises, and hospitality. Napoleon made a good combination
with Peretti and Quenza, yielding to that interest the first lieutenant
colonelship. The second was to his own. But one of the commissioners,
Murati, took up lodgings with Bonaparte's rival candidate, Peraldi.
This was an ominous sign for Napoleon. On the night before the
election, he got together some of his more violent partisans, sent
them against the house of Peraldi, and had Murati seized and brought
to the house of the Bonapartes. "You were not free at Peraldi's," said
Napoleon to the amazed commissioner; "here you enjoy liberty." Murati
enjoyed it so much that he was afraid to stir out of the house till the
election was over.
Next morning Pozzo di Borgo commenced a public and violent harangue,
denouncing the seizure of the commissioner. He was not allowed to
finish. The Bonaparte faction rushed upon the speaker, knocked
him down, kicked him, and would have killed him had not Napoleon
interfered. In this episode is said to have originated the deadly
hatred with which Pozzo ever afterward pursued Napoleon, who triumphed
over him in the election.
Ajaccio was torn by revolutionary passion and faction. Resisting the
decrees of the National Assembly of France, the Capuchin friars refused
to vacate their quarters. Riotous disputes between the revolutionists
and the partisans of the Old Order ensued. The public peace was
disturbed. The military ousted the friars, and took possession of the
cloister. This added fuel to the flames, and on Easter day there was a
collision between the factions. One of the officers of the militia was
killed. Next morning, reënforcements from outside the town poured in to
the military. Between the volunteer guards on the one hand, the citadel
garrison and the clerical faction on the other, a pitched battle seemed
inevitable. Commissioners, sent by Paoli, arrived, dismissed the
militia, and restored quiet by thus virtually deciding in favor of the
Capuchins.
Napoleon was believed by the victorious faction to have been the
instigator of all the trouble. The commander of the garrison bitterly
denounced him to the war office in Paris. Napoleon, on the contrary,
published a manifesto in his own defence, hotly declaring that the
whole town government of Ajaccio was rotten, and should have been
overthrown. Unless Ajaccio differed radically from most towns, then and
now, the indictment was well founded.
At all events, his career in Corsica was at an end, for the time. He
had strained his relations with the French war office, had ignored
positive orders to rejoin his command, had been stricken off the list
for his disobedience, had exhausted every resource on his Corsican
schemes, and was now at the end of his rope. And what had he gained?
He had squandered much money, wasted much precious time, established
a character for trickiness, violence, and unscrupulous self-seeking;
and had aroused implacable enmities, one of which (that of Pozzo) had
no trifling share in giving him the death-wound in his final struggles
in 1814–15. What, after it all, must he now do? He must get up a lot
of certificates to his good conduct during the long time he had been
absent from France; he must go to Paris and petition the central
authority to be taken back to the French army. There was no trouble
in getting the certificates. Paoli and his party, the priests and the
wealthy towns-people, were so eager to get rid of this dangerous young
man that they were ready to sign any sort of paper, if only he would go
away. Armed with documentary evidence of his good behavior, Napoleon
left Corsica in May, 1792, and reached Paris on the 28th of that month.
Things were in a whirl in France. War had been declared against
Austria. Officers of royalist principles were resigning and fleeing the
country. Excitement, suspicion, alarm, uncertainty, were everywhere. No
attention could be given to Napoleon and his petition just then. He saw
that he would have to wait, be patient and persistent, if ever he won
reinstatement. Meanwhile he lived in great distress. With no money, no
work, no powerful friends, Paris was a cold place for the suppliant.
He sauntered about with Bourrienne, ate at the cheapest restaurants,
discussed many plans for putting money in his purse--none of which put
any there. He pawned his watch to get the bare necessaries of life.
Bearing in mind that Napoleon had been so active in the republican
clubs at Valence and Ajaccio, and recalling the urgent appeal for three
hundred francs which he had made to his great-uncle in order that he
might go to Paris and push himself to the front, his attitude now that
he was in Paris is a puzzle. According to his own account and that
of Bourrienne, he was a mere spectator. A royal officer, he felt no
inclination to defend the King. A violent democratic agitator, he took
no part in the revolutionary movements. Seeing the mob marching to the
Tuileries in June, his only thought was to get a good view of what was
going on; therefore he ran to the terrace on the bank of the river
and climbed an iron fence. He saw the rabble burst into the palace,
saw the King appear at the window with the red cap on his head. "The
poor driveller!" cried Napoleon. And according to Bourrienne he said
that four or five hundred of the mob should have been swept away with
cannon, and that the others would have taken to their heels.
During the exciting month of July, Napoleon was still in Paris. He
was promenading the streets daily, mingling with the people; he was
idle, discontented, ambitious; he was a violent revolutionist, and was
not in the habit of concealing his views: therefore the conclusion is
well-nigh irresistible that he kept in touch with events, and knew
what was in preparation. Where was Napoleon when the battalion from
Marseilles arrived? What was his attitude during Danton's preparation
for the great day on which the throne was to be overturned? Was an
ardent, intensely active man like Napoleon listless and unconcerned,
while the tramp of the gathering thousands shook the city? He had long
since written "Most kings deserve to be dethroned": did he by any
chance hear what Danton said at the Cordeliers,--said with flaming
eyes, thundering voice, and wild gesticulation,--"Let the tocsin sound
the last hour of kings. Let it peal forth the first hour of vengeance,
and of the liberty of the people! To arms! and it will go!"
However much we may wish for light on this epoch of Napoleon's career,
we have no record of his movements. We only know that on the 10th of
August he went to see the spectacle, and saw it. From a window in
a neighboring house, he looked down upon the Westermann attack and
the Swiss defence. He saw the devoted guards of the palace drive the
assailants out, doubtless heard Westermann and the brave courtesan,
Théroigne de Méricourt, rally their forces and renew the assault; was
amazed perhaps, when the Swiss ceased firing; and looked on while the
triumphant Marseillaise broke into the palace. After the massacre, he
walked through the Tuileries, piled with the Swiss dead, and was more
impressed by the sight than he ever was by the dead on his own fields
of battle. He sauntered through the crowds and the neighboring cafés,
and was so cool and indifferent that he aroused suspicion. He met a
gang of patriots bearing a head on a pike. His manner did not, to this
gang, indicate sufficient enthusiasm. "Shout, 'Live the nation,'"
demanded the gang; and Napoleon shouted, "Live the nation!"
He saw a man of Marseilles about to murder a wounded Swiss. He
said, "Southron, let us spare the unfortunate."--"Art thou from the
South?"--"Yes."--"Then we will spare him."
According to Napoleon, if the King had appeared on horseback,--that is,
dared to come forth and lead the defence,--he would have won the day.
Other days of wrath Napoleon spent in Paris--the days of the September
massacres. What he saw, heard, and felt is not known. Only in a general
way is it known that during the idle summer in Paris, Napoleon lost
many of his republican illusions. He conceived a horror of mob violence
and popular license, which exerted a tremendous influence over him
throughout his career. He lost faith in the purity and patriotism of
the revolutionary leaders. He reached the conclusion that each man
was for himself, that each one sought only his own advantage. For the
people themselves, seeing them so easily led by lies, prejudices, and
passions, he expressed contempt. The Jacobins were, he thought, a
"parcel of fools"; the leaders of the Revolution "a sorry lot."
This sweepingly severe judgment was most unfortunate; it bore bitter
fruit for Napoleon and for France. He never ceased to believe that each
man was governed by his interest--an opinion which is near the truth,
but is not the truth. If the truth at all, it is certainly not the
whole truth.
Napoleon, with the independence of his native land ever in mind, wrote
to his brother Joseph to cling to Paoli; that events were tending to
make him the all-powerful man, and might also evolve the independence
of Corsica.
During this weary period of waiting, Napoleon was often at the home
of the Permons. On the 7th or 8th of August an emissary of the
revolutionary government made his way into the Permon house without a
warrant, and, because M. Permon refused to recognize his authority and
threatened to take a stick to him, left in a rage to report against
Permon. Napoleon, happening to call at this time, learned the fact,
and hurried off to the section where he boldly denounced the illegal
conduct of the officer. Permon was not molested further.
* * * * *
The King became a prisoner of the revolutionists, the moderates fell
from power, the radicals took the lead. Napoleon's case had already
received attention, he had already been pronounced blameless, and
he was now, August 30, 1792, restored to his place in the army, and
promoted. He was not only made captain, but his commission and pay were
made to date from February 6, 1792, at which time he would have been
entitled to his promotion had he not fallen under official displeasure.
Such prompt and flattering treatment of the needy officer by the
radicals who had just upset the monarchy, gives one additional cause to
suspect that Napoleon's relation to current events and Jacobin leaders
was closer than the record shows. It became good policy for him in
after years to suppress the evidence of his revolutionary period. Thus
he burnt the Lyons essay, and bought up, as he supposed, all copies
of _The Supper of Beaucaire_. The conclusion is irresistible that the
efforts to suppress have been more successful as to the summer of 1792
than in the other instances. It is impossible to believe that Napoleon,
who had been so hot in the garrison towns where he was stationed in
France, and who had turned all Corsica topsy-turvy with democratic
harangues and revolutionary plots, should have become a passionless
gazer at the show in Paris.
Whatever share he took, or did not take, in the events of the summer,
he now turned homeward. The Assembly having abolished the St. Cyr
school, where his sister Elisa was, Napoleon asked and was given leave
to escort her back to Corsica. Travelling expenses were liberally
provided by the State. Stopping at Valence, where he was warmly greeted
by local friends, including Mademoiselle Bou to whom he owed a board
bill, Napoleon and Elisa journeyed down the Rhone to Marseilles, and
sailed for Corsica, which they reached on the 17th of September, 1792.
The situation of the Bonaparte family was much improved. The estate was
larger, the revenues more satisfactory. Joseph was in office. Lucien
was a leading agitator in the Jacobin club. The estate of the rich
uncle had helped things wonderfully. It must have been from this source
that Napoleon derived the fine vineyard of which he spoke to Las Cases,
at St. Helena, as supplying him with funds--which vineyard he afterward
gave to his old nurse. The position which his promotion in the army
gave him ended the persecution which had virtually driven him from
home; and a reconciliation was patched up between him and Paoli.
Napoleon insisted upon holding both his offices,--the captaincy in the
regular army and the lieutenant colonelship in the Corsican National
Guard. Paoli strongly objected; but the younger man, partly by threats,
carried his point. It may have been at this period that Paoli slightly
modified the Plutarch opinion; he is said to have remarked: "You see
that little fellow? Well, he has in him the making of two or three men
like Marius and one like Sulla!"
During his sojourn in Corsica, Napoleon took part in the luckless
expedition which the French government sent against the island of
Sardinia. The Corsican forces were put under the command of Paoli's
nephew, Colonna-Cæsari, whose orders, issued to him by Paoli, who
strongly opposed the enterprise, were, "See that this expedition ends
in smoke." The nephew obeyed the uncle to the letter. In spite of
Napoleon's good plan, in spite of his successful attack on the hostile
forts, Colonna declared that his troops were about to mutiny, and he
sailed back home.
Loudly denouncing Colonna as a traitor, Napoleon bade adieu to his
volunteers, and returned to Ajaccio.
There was great indignation felt by the Jacobins against Paoli. He
was blamed for the failure of the Sardinian expedition, for his
luke-warmness toward the French Revolution, and for his alleged leaning
to England. The September massacres, and the beheading of the King, had
been openly denounced by the old hero, and he had exerted his influence
in favor of conservatism in Corsica. The Bonaparte faction was much
too rabid, and the Bonaparte brothers altogether too feverishly eager
to push themselves forward. The friendship and mutual admiration which
Napoleon and Paoli had felt for each other had cooled. Paoli had thrown
ice water on the _History of Corsica_, and had refused to supply the
author with certain documents needed in the preparation of that work.
Neither had he approved the publication of the _Letter to Buttafuoco_;
it was too bitter and violent. Again, his influence seems to have been
thrown against the Bonapartes at the Orezzo assembly. All these things
had doubtless had their effect; but the radical difference between
the two men, Napoleon and Paoli, was one of Corsican policy. Napoleon
wished to revolutionize the island, and Paoli did not. If Corsican
independence could not be won, Napoleon favored the French connection.
Paoli, dismayed by the violence of the Revolution in France, favored
connection with England.
It is said that Lucien Bonaparte, in the club at Ajaccio, denounced
Paoli as a traitor. The club selected a delegation to go to Marseilles
and denounce the old hero to the Jacobin clubs there. Lucien was a
member of the delegation; but after delivering himself a wild tirade
against Paoli in Marseilles, he returned to Corsica. The delegation
went on to Paris. In April, 1793, Paoli was formally denounced in the
National Convention, and summoned to its bar for trial.
At first Napoleon warmly defended Paoli, and drew up an impassioned
address to the Convention in his favor. In this paper he expressly
defends his old chief from the accusation of wishing to put Corsica
into the hands of the English.
Within two weeks after writing the defence of Paoli, Napoleon joined
his enemies. What brought about this sudden change is not certain. His
own excuse was that Paoli was seeking to throw the island to England.
As a matter of fact, however, Napoleon's course at this period seems
full of double dealing. For a time he did not have the confidence of
either faction.
Sémonville, one of the French commissioners then in Corsica, related to
Chancellor Pasquier, many years later, how Napoleon had come and roused
him, in the middle of the night, to say: "Mr. Commissioner, I have
come to say that I and mine will defend the cause of the union between
Corsica and France. People here are on the point of committing follies;
the Convention has doubtless committed a great crime"--in guillotining
the King--"which I deplore more than any one; but whatever may happen,
Corsica must always remain a part of France."
As soon as this decision of the Bonapartes became known, the Paolists
turned upon them savagely, and their position became difficult. The
French commissioners, of whom the leader was Salicetti, appointed
Napoleon inspector general of artillery for Corsica. He immediately
set about the capture of the citadel of Ajaccio, the object of so much
of his toil. Force failed, stratagem availed not, attempted bribery
did not succeed; the citadel remained untaken. Ajaccians bitterly
resented his desertion of Paoli, and his life being in danger, Napoleon
in disguise fled to Bastia. Indomitable in his purpose, he proposed
to Salicetti's commission another plan for the seizure of the coveted
citadel. Some French war vessels then at St. Florent were to surprise
Ajaccio, land men and guns, and with the help of some Swiss troops,
and of such Corsicans as felt disposed to help, the citadel was to be
taken.
Paoli was warned, and he prepared for the struggle. The French war
vessels sailed from St. Florent, Napoleon on board, and reached Ajaccio
on May 29. It was too late. The Paolists, fully prepared, received the
assailants with musketry. Napoleon captured an outpost, and held it
for two days; but the vessels could not coöperate efficiently, and the
assailants abandoned the attempt. Napoleon joined his family at Calvi.
They had fled from Ajaccio as Napoleon sailed to the attack, and the
Paolists were so furiously enraged against them that their estates were
pillaged and their home sacked. Paoli had made a last effort to conquer
the resolution of Madame Letitia, but she was immovable. On June 11
the fugitives left Corsica for France, escaping from their enemies by
hiding near the seashore till a boat could approach in the darkness
of night and take them away. Jerome and Caroline were left behind,
concealed by the Ramolinos.
Napoleon himself narrowly escaped with his life. He was saved from
a trap the Peraldis had set by the faithfulness of the Bonaparte
tenants. He was forced to disguise himself, and lay concealed till
arrangements could be made for his flight. Far-seeing was the judgment
and inflexible the courage which must have sustained him in cutting
loose entirely from his first love, Corsica, and casting himself upon
revolutionary France. For it would have been an easy matter for him to
have gone with the crowd and been a great man in Corsica.
In his will Napoleon left 100,000 francs to Costa, the loyal friend to
whom he owed life at the time the Paolists were hounding him down as a
traitor.
CHAPTER VI
The French revolutionists had overturned the absolute monarchy of the
Bourbons, but they themselves had split into factions. The Moderates
who favored constitutional monarchy had been trodden under foot by
the Girondins who favored a federated republic; and the Girondins, in
their turn, had been crushed by the Jacobins who favored an undivided
republic based upon the absolute political equality of all Frenchmen.
To this doctrine they welded State-socialism with a boldness which
shocked the world at the time, and converted it a few years later. The
Girondins did not yield without a struggle, drawing to themselves all
disaffected elements, including the royalists; and the revolt which
followed was supported by the English. Threatened thus from within and
without, the Revolution seemed doomed to perish.
It was in the midst of this turmoil that the Bonapartes landed at
Toulon in June, 1793. In a short while they removed to Marseilles.
Warmly greeted by the Jacobins, who regarded them as martyrs to the
good cause, the immediate necessities of the family were relieved by a
small pension which the government had provided for such cases. Still,
as they had fled in such haste from their house in Ajaccio that Madame
Letitia had to snatch up the little Jerome and bear him in her arms,
their condition upon reaching France was one of destitution.
[Illustration: NAPOLEON
From an engraving by Tomkins of a drawing from life during the campaign
in Italy. In the collection of Mr. W. C. Crane]
"One of the liveliest recollections of my youth," said Prince Napoleon,
son of Jerome Bonaparte, "is the account my father gave of the arrival
of our family in a miserable house situated in the lanes of Meilhan,"
a poor district of Marseilles. "They found themselves in the greatest
poverty."
Having arranged for the family as well as he could, Napoleon rejoined
his regiment at Nice. To shield himself from censure, on account of
his prolonged absence, he produced Salicetti's certificate to the
effect that the Commissioner had kept him in Corsica. The statement was
false, but served its purpose. So many officers had fled their posts,
and affairs were so unsettled, that it was no time to reject offers of
service; nor was it a good time to ride rough-shod over the certificate
of so influential a Jacobin as Salicetti.
Napoleon's first service in France was against the Girondin revolt. At
Avignon, which the insurgents held, and which the Convention forces had
invested, Napoleon, who had been sent from Nice to secure necessary
stores, was appointed to the command of a battery. Mr. Lanfrey says,
"It is certain that with his own hands he pointed the cannons with
which Carteaux cleared Avignon of the Marseilles federates."
About this time it was that Napoleon came in contact with Augustin
Robespierre, brother of the great man in Paris. The Convention
had adopted the policy of sending commissioners to the armies to
stimulate, direct, and report. Robespierre was at the head of one of
these formidable delegations, and was now at Avignon in his official
capacity. With him, but on a separate commission, were Salicetti and
Gasparin.
To these gentlemen Napoleon read a political pamphlet he had just
finished, and which he called _The Supper of Beaucaire_. The pamphlet
was a discussion of the political situation. The author threw it into
the attractive and unusual form of a dialogue between several guests
whom he supposed to have met at an inn in the town of Beaucaire. An
actual occurrence of the sort was doubtless the basis of the pamphlet.
A citizen of Nismes, two merchants of Marseilles, a manufacturer
of Montpellier, and a soldier (supposed to be Napoleon), finding
themselves at supper together, fell naturally into conversation and
debate, the subject being the recent convulsions. The purpose of the
pamphlet was to demonstrate the weakness of the insurgent cause, and
the necessity of submission to the established authorities at Paris.
The Commissioners were so well pleased with Napoleon's production that
they ordered the work published at the expense of the government.
Exerting himself in behalf of his family, Napoleon secured positions in
the public service for Lucien, Joseph, and Uncle Fesch.
* * * * *
Into the great seaport town of Toulon, thousands of the Girondin
insurgents had thrown themselves. The royalists and the Moderates of
the city made common cause with the revolting republicans, and England
was ready to help hold the place against the Convention.
The royalists, confident the counter-revolution had come, began to
massacre the Jacobins in the town. The white flag of the Bourbons was
run up, displacing the red, white, and blue. The little boy, son of
Louis XVI., who was lying in prison at Paris, was proclaimed king
under the name of Louis XVII. Sir Samuel Hood, commanding the British
fleet, sailed into the harbor and took possession of about twenty-five
French ships, "in trust" for the Bourbons; General O'Hara hurried
from Gibraltar with troops to aid in holding this "trust"; and to the
support of the English flocked Spaniards, Sardinians, and Neapolitans.
Even the Pope could not withhold his helping hand; he sent some priests
to lend their prayers and exhortations.
When it became known throughout France that Toulon had revolted,
had begun to exterminate patriots, had proclaimed a Bourbon king,
had surrendered to the British the arsenal, the harbor, the immense
magazines, and the French fleet, a tide of furious resentment rose
against the town. There was but one thought: Toulon must be taken,
Toulon must be punished. The hunger for revenge said it; the promptings
of self-preservation said it; the issue was one of life or death to the
Revolution.
The Convention realized the crisis; the Great Committee realized
it; and the measures taken were prompt. Commissioners hurried to
the scene, and troops poured in. Barras, a really effective man in
sudden emergencies, Fréron, Salicetti, Gasparin, Ricord, Albitte,
and Robespierre the Younger were all on hand to inspirit the army
and direct events. Some twenty odd thousand soldiers soon beleagured
the town. They were full of courage, fire, and enthusiasm; but
their commander was a painter, Carteaux, whose ideas of war were
very primitive. To find where the enemy was, and then cannonade him
vigorously, and then fall on him with muskets, was about the substance
of Carteaux' military plans. At Toulon, owing to peculiarities of the
position, such a plan was not as excellent as it might have been at
some other places. Besides, he had no just conception of the means
needed for such a work as he had undertaken. Toulon, with its double
harbor, the inner and the outer, its defences by land and by sea, to
say nothing of the fortresses which Lord Mulgrave had constructed
on the strip of land which separated and commanded the two harbors,
presented difficulties which demanded a soldier. Carteaux was brave and
energetic, but no soldier; and week after week wasted away without any
material progress having been made in the siege.
Near the middle of September, 1793, Napoleon appeared at Toulon,--at
just the right moment,--for the artillery service had well-nigh broken
down. General Duteuil, who was to have directed it, had not arrived;
and Dommartin had been disabled by a wound. How did Napoleon, of the
army of Italy, happen to be at Toulon at this crisis? The question is
one of lasting interest, because his entire career pivots on Toulon.
Mr. Lanfrey states that, on his way from Avignon to Nice, Napoleon
stopped at Toulon, was invited by the Commissioners to inspect the
works, and so won upon them by his intelligent comments, criticisms,
and suggestions, that they appointed him at once to a command.
Napoleon's own account of the matter was that the Minister of War
sent him to Toulon to take charge of the artillery, and that it was
with written authority that he confronted Carteaux, who was not at
all pleased to see him. "This was not necessary!" exclaimed Carteaux.
"Nevertheless, you are welcome. You will share the glory of taking the
town without having borne any of the toil!"
But the biographers are almost unanimous in refusing to credit this
account. Why Napoleon should have falsified it, is not apparent. Mr.
Lanfrey says that Napoleon's reason for not wishing to admit that the
Commissioners appointed him was that he was unwilling to own that he
had been under obligations to Salicetti. But Salicetti was only one
of the Commissioners; he alone could not appoint. So far was Napoleon
from being ashamed to acknowledge debts of gratitude that he never
wearied of adding to the list. In his will he admits what he owed to
the protection of Gasparin at this very period, and left a legacy of
$20,000 to that Commissioner's son. Hence Mr. Lanfrey's reasoning is
not convincing. Napoleon surely ought to have known how he came to be
at Toulon, and his narrative is natural, is seemingly truthful, and is
most positive.
But these recent biographers who dig and delve, and turn things over,
and find out more about them a century after the occurrences than the
men who took part in them ever knew, assert most emphatically that
both Mr. Lanfrey and Napoleon are wrong. They insist that the way it
all happened was this: After Dommartin was wounded, Adjutant General
Cervoni, a Corsican, was sent to Marseilles to hunt around and find
a capable artillery officer. Apparently it was taken for granted by
whoever sent Cervoni, that capable artillery officers were straggling
about at random, and could be found by diligent searchers in the lanes
and by-ways of towns and cities. We are told that Cervoni, arrived in
Marseilles, was strolling the streets, his eyes ready for the capable
artillery officer,--when, who should he see coming down the road,
dusty and worn, but his fellow-Corsican, Napoleon Bonaparte! Here,
indeed, was a capable artillery officer, one who had just been to
Avignon, and was on his way back to Nice.
That Cervoni should at once invite the dusty Napoleon into a café
to take a drink of punch was quite as natural as any other part of
this supernatural yarn. While drinking punch, Cervoni tells Napoleon
his business, and urges him to go to Toulon and take charge of the
artillery. And this ardently ambitious young man, who is yearning
for an opening, is represented as at first declining the brilliant
opportunity Cervoni thrusts upon him! But at length punch, persuasion,
and sober second thought soften Napoleon, and he consents to go.
All this you may read in some of the most recent works of the diggers
and delvers; and you may believe it, if you are very, very credulous.
* * * * *
The arrival on the scene of an educated artillery officer like
Napoleon, one whose handling of his guns at Avignon had achieved
notable success, was a welcome event. His friends, the Commissioners,
took him over the field of operations to show him the placing and
serving of the batteries. He was astonished at the crude manner in
which all the arrangements had been made, and pointed out the errors
to the Commissioners. First of all, the batteries were not in range of
the enemy; the balls fell into the sea, far short of the mark. "Let us
try a proof-shot," said Napoleon; and luckily he used a technical term,
_coup d'épreuve_. Favorably impressed with this scientific method of
expression, the Commissioners and Carteaux consented. The proof-shot
was fired, and the ball fell harmlessly into the sea, less than
halfway to its mark. "Damn the aristocrats!" said Carteaux; "they have
spoilt our powder."
But the Commissioners had lost faith in Carteaux' management of the
artillery; they determined to put Napoleon in charge of it.
On the 29th of September, Gasparin and Salicetti recommended his
promotion to the rank of major, and on the next day they reported that
Bonaparte was "the only artillery captain able to grasp the operations."
From the first Napoleon threw his whole heart into his work. He never
seemed to sleep or to rest. He never left his batteries. If exhausted,
he wrapped himself in his cloak, and lay down on the ground beside the
guns.
From Lyons, Grenoble, Briançon, he requisitioned additional material.
From the army of Italy he got more cannon. From Marseilles he took
horses and workmen, to make gabions, hurdles, and fascines. Eight
bronze guns he took from Martigues; timbers from La Seyne; horses from
Nice, Valence, and Montpellier. At the ravine called Ollioules he
established an arsenal with forty workmen, blacksmiths, wheelwrights,
carpenters, all busy making those things the army needed; also a
gunsmith's shop for the repair of muskets; and he took steps to
reëstablish the Dardennes gun foundry.
Thus he based his hopes of success upon _work_, intense, well-directed,
comprehensive work. All possible precautions were taken, all
possible preparations made, every energy bent to bring to bear those
means necessary to the end. Nothing was left to chance, good luck,
providence, or inspiration. Cold calculation governed all, tireless
labor provided all, colossal driving force moved it all. In ever so
short a time, Napoleon was felt to be "the soul of the siege." In
November he was made acting commander of the artillery. Carteaux had
been dismissed, and to the painter succeeded a doctor named Doppet.
The physician had sense enough to soon see that an easier task than
the taking of Toulon would be an agreeable change, and he asked to be
sent elsewhere. To him succeeded Dugommier, an excellent soldier of
the old school. Dutiel, official commander of the artillery, at length
arrived, and he was so well pleased with Napoleon's work that he did
not interfere.
The Committee of Public Safety, sitting in Paris, had sent a plan of
operations, the main idea of which was a complete investment of the
town. This would have required sixty thousand troops, whereas Dugommier
had but twenty-five thousand. But he dared not disobey the terrible
Committee. Between the loss of Toulon and his own head he wavered
painfully. A council of war met. The Commissioners of the Convention
were present, among them Barras, Ricord, and Fréron. Officers of the
army thought the committee plan bad, but hesitated to say so in plain
words. One, and the youngest, spoke out; it was Napoleon. He pointed to
the map lying unrolled on the table, explained that Toulon's defence
depended on the British fleet, that the fleet could not stay if a land
battery commanded the harbor, and that by seizing a certain point, the
French would have complete mastery of the situation. On that point on
the map he put his finger, saying, "There is Toulon."
He put his plan in writing, and it was sent to the war office in Paris.
A second council of war adopted his views, and ordered him to put them
into execution.
The English had realized the importance of the strategic point named by
Napoleon, and they had already fortified it. The redoubt was known as
Fort Mulgrave; also as Little Gibraltar.
On the 30th of November the English made a desperate attempt to storm
Napoleon's works. They were repulsed, and their leader, General O'Hara,
was taken prisoner. At St. Helena Napoleon said that he himself had
seized the wounded Englishman and drawn him within the French lines.
This statement appears to have been one of his fancy sketches. Others
say that General O'Hara was taken by four obscure privates of Suchet's
battalion.
A cannoneer having been killed by his side, Napoleon seized the rammer
and repeatedly charged the gun. The dead man had had the itch; Napoleon
caught it, and was not cured until he became consul.
Constantly in the thick of the fighting, he got a bayonet thrust in the
thigh. He fell into the arms of Colonel Muiron, who bore him to a place
of safety. Napoleon showed the scar to O'Meara at St. Helena.
It was at Toulon that fame first took up that young dare-devil, Junot,
whom Napoleon afterward spoiled by lifting him too high.
Supping with some brother officers near the batteries, a shell from
the enemy fell into the tent, and was about to burst, when Junot rose,
glass in hand, and exclaimed, "I drink to those who are about to die!"
The shell burst, one poor fellow was killed, and Junot drank, "To the
memory of a hero!"
Some days after this incident Junot volunteered to make for Napoleon a
very dangerous reconnoissance. "Go in civilian's dress; your uniform
will expose you to too much risk."--"No," replied Junot, "I will
not shrink from the chance of being shot like a soldier; but I will
not risk being hanged like a spy." The reconnoissance made, Junot
came to Napoleon to report. "Put it in writing," said Napoleon; and
Junot, using the parapet of the battery as a desk, began to write. As
he finished the first page, a shot meant for him struck the parapet,
covering him and the paper with earth. "Polite of these English," he
cried, laughing, "to send me some sand just when I wanted it." Before
very long Napoleon was a general, and Junot was his aide-de-camp.
On December 17 everything was ready for the grand assault on the
English works. Between midnight and day, and while a rainstorm was
raging, the forts, which for twenty-four hours had been bombarded by
five batteries, were attacked by the French. Repulsed at the first
onset, Dugommier's nerve failed him, and he cried, "I am a lost man,"
thinking of that terrible committee in Paris which would cut off his
head. Fresh troops were hurried up, the attack renewed, and Little
Gibraltar taken. Thus Napoleon's first great military success was won
in a fair square fight with the English.
[Illustration: LETTER FROM BONAPARTE, COMMANDANT OF ARTILLERY, TO
GENERAL CARTEAUX.]
Assaults on other points in the line of defence had also been made, and
had succeeded; and Toulon was at the mercy of Napoleon's batteries. The
night that followed was one of the most frightful in the annals of war.
The English fleet was no longer safe in the harbor, and was preparing
to sail away. Toulon was frantic with terror. The royalists, the
Girondins, the refugees from Lyons and Marseilles, rushed from their
homes, crowded the quays, making every effort to reach the English
ships. The Jacobins of the town, now that their turn had come, made the
most of it, and pursued the royalists, committing every outrage which
hate and lust could prompt. Prisoners broke loose, to rob, to murder,
to ravish. The town became a pandemonium. Fathers, mothers, children,
rushed wildly for safety to the quays, screaming with terror, and
plunging into the boats in the maddest disorder. And all this while the
guns, the terrible guns of Napoleon, were playing on the harbor and
on the town, the balls crashing through dwellings, or cutting lanes
through the shrieking fugitives on the quays, or sinking the boats
which were carrying the wretched outcasts away. The English set fire
to the arsenal, dockyard, and such ships as could not be carried off,
and the glare shone far and wide over the ghastly tumult. Intensifying
the horror of this hideous night came the deafening explosion of the
magazine ships, and the rain of the fragments they scattered over all
the surrounding water.
Some fourteen thousand of the inhabitants of Toulon fled with the
English; some other thousands must have perished in the bombardment
and in the butcheries of the days that followed. Toulon's baseness had
aroused the ire, the diabolism of the Revolution, and the vilest men of
all her ravening pack were sent to wreak revenge. There was Barras, the
renegade noble; Fréron, the Marat in ferocity without Marat's honesty
or capacity; Fouché, the renegade priest. And the other Commissioners
were almost as ferocious; while from the Convention itself came the
voice of Barère demanding the total destruction of Toulon. Great
was the sin of the doomed city; ghastly was its punishment. Almost
indiscriminately people were herded and mown down with musketry.
On one of the days which ensued, Fouché wrote to his friend, Collot
d'Herbois: "We have sent to-day 213 rebels to hell fire. Tears of joy
run down my cheeks and flood my soul." Royalist writers do not fail
to remind the reader that this miscreant, Fouché, became minister of
police to Napoleon. They omit the statement that he was used by Louis
XVIII. in the same capacity.
Napoleon exerted himself to put a stop to these atrocities, but he
was as yet without political influence, and he could do nothing. Some
unfortunates he rescued from his own soldiers, and secretly sent away.
He was forced to witness the execution of one old man of eighty-four,
whose crime was that he was a millionnaire. "When I saw this," said
Napoleon afterward, "it seemed to me that the end of the world had
come."
In his spiteful _Memoirs_, Barras labors hard to draw a repulsive
portrait of the Napoleon of Toulon. The young officer is represented
as bustling about with a bundle of his _Supper of Beaucaire_, handing
copies right and left to officers and men. He is made to profess rank
Jacobinism, and to allude to Robespierre and Marat as "my saints."
He pays servile court to the wife of Commissioner Ricord, and to the
Convention potentates generally. Of course he was on his knees to
Barras. That lofty magnate stoops low enough to mention, as a matter
detrimental to Napoleon, that his uniform was worn out and dirty--as
if a tattered and soiled uniform at the close of such a siege, such
herculean work, could have been anything but a badge of honor to
the soldier who wore it! Dugommier's official report on the taking
of Toulon contains no mention of Napoleon by name, but he uses this
expression, "The fire from our batteries, directed with the greatest
talent," etc. This allusion could have been to no other than to
Napoleon.
To the minister of war Duteil wrote on December 19, 1793, "I cannot
find words to describe the merit of Bonaparte; a considerable amount
of science, just as much intelligence, and too much bravery, such is a
feeble outline of the virtues of that rare officer."
The Commissioners themselves, whose names crowded the name of Bonaparte
out of the official report, recognized his services by at once
nominating him to the post of general of brigade.
* * * * *
English authors dwell extensively on Napoleon's hatred of their
country: do they never recall the origin of the feeling? Had not
England deceived old Paoli, crushed the opposite faction, and treated
Corsica as a conquest? Was it not the English faction which had sacked
the home, confiscated the property, and sought the lives of the
Bonaparte family? Had not England been striving to force the Bourbons
back on France; had it not seized the French ships at Toulon "in
trust"; had it not then given to the flames not only the ships, but
dockyards, arsenals, and magazines? Did not William Pitt, in the King's
speech of 1794, include among the subjects of congratulation "the
circumstances attending the evacuation of Toulon"? Had not England,
in 1793, bargained with Austria to despoil France and divide the
booty: Austria to have Alsace and Lorraine; and England to have the
foreign settlements and colonies of France? "His Majesty" (of England)
"has an interest in seeing the house of Austria strengthen itself by
acquisitions on the French frontier; the Emperor" (of Austria) "must
see with pleasure the relative increase of the naval and commercial
resources of this country" (England) "over those of France."
Historians have long said that England's war with France was forced
upon her, that it was defensive. Does the language just quoted
(official despatches) sound like the terms of self-defence? It is the
language of aggression, of unscrupulous conquest; and the spirit which
dictated this bargain between two powers to despoil a third is the
same which gave life to each successive combination against the French
Republic and the Napoleonic Empire.
Like master, like man: the British ministry having adopted the policy
of blind and rancorous hostility in dealing with France, the same
fury of hatred pervaded the entire public service. Edmund Burke and
William Pitt inoculated the whole nation. "Young gentlemen," said
Nelson to his midshipmen, "among the things you must constantly bear
in mind is to hate a Frenchman as you would the devil." At another
time, the same illustrious Englishman declared, "I hate all Frenchmen;
they are equally the object of my detestation, whether royalists or
republicans." Writing to the Duke of Clarence, he stated: "To serve my
king and to destroy the French, I consider the great order of all....
Down, down with the damned French villains! My blood boils at the name
of Frenchman!" At Naples he exclaimed, "Down, down with the French! is
my constant prayer."
I quote Nelson simply because he was a controlling factor in these
wars, a representative Englishman, a man in full touch with the policy,
purpose, and passion of his government.
Consider England's bargain with Austria; consider her bribes to Prussia
to continue the struggle when even Austria had withdrawn; consider the
animus of such leading actors as Burke and Nelson--is it any wonder
that Napoleon regarded Great Britain as the one irreconcilable and
mortal enemy of France?
And what was England's grievance? Her rival across the Channel had
overturned a throne, slain a king, and proclaimed principles which were
at war with established tyranny. But had England never upset a throne,
slain a king, and proclaimed a republic?
Was it any matter of rightful concern to Great Britain that France had
cast out the Bourbons, and resorted to self-government? Did England, by
any law human or divine, have the right to impose her own will upon a
sister state? Was she right in seizing and destroying the French fleet
at Toulon, which she had accepted as a trust? Unless all these can be
answered Yes, Napoleon deserves no deep damnation for his hatred of
Great Britain.
CHAPTER VII
The Mediterranean coast of France being almost at the mercy of the
English fleet, Napoleon was sent, immediately after the fall of Toulon,
to inspect the defences and put them into proper condition. He threw
into this task the same activity and thoroughness which had marked him
at Toulon, and in a short while the coast and the coasting trade were
secure from attack.
His duties carried him to Marseilles, where he found that a fortress
necessary to the defence of the harbor and town had been dismantled by
the patriots, who detested it as a local Bastille. Napoleon advised
that the fortifications be restored "so as to command the town." This
raised a storm. The Marseilles Jacobins denounced Bonaparte to the
Convention. By that body he was summoned to appear at its bar. He had
no inclination to take such a risk, and hastened to Toulon, where he
put himself under the protection of Salicetti and Augustin Robespierre.
At their instance he wrote to the Paris authorities an exculpatory
letter, and the storm blew over.
In March, 1794, Napoleon returned to headquarters at Nice. By his
influence over the Commissioners of the Convention, young Robespierre
in particular, he became the dominant spirit of the army of Italy.
General Dumerbion, commander-in-chief, a capable officer but too old,
had been wasting time, or the strength of his troops, for several
months, in attacks upon the enemy (Piedmontese and Austrians) who were
intrenched at the foot of the maritime Alps. Despondent after repeated
failures, officers and men were contenting themselves with holding
their positions, and conducting such operations as were consistent with
extreme prudence. Napoleon had no sooner made a careful study of the
positions of the opposing forces, than he drew up a plan of campaign,
and submitted it to the commander-in-chief and the Commissioners. In
a council of war it was discussed and approved. Early in April, the
army was in motion; the position of the enemy was to be turned. Masséna
led the corps which was to do what fighting was necessary. The enemy
was beaten in two engagements, and Piedmont entered by the victorious
French, who then turned back toward the Alps. The communications
between Piedmont and the fortified camps of the enemy being thus
endangered, they abandoned them without a fight; and thus in a campaign
of a month the French won command of the whole range of the Alps, which
had so long resisted every attack in front.
At this time the Bonaparte family was living in Nice, and Napoleon,
during the months of May and June, 1794, spent much of his time with
his mother and sisters. Uncle Fesch, Joseph, and Lucien were in good
positions; and Napoleon secured for Louis, by the telling of some
falsehoods and the use of the influence of Salicetti, the rank of
lieutenant in the army. Louis was represented as having served as a
volunteer at Toulon, and as having been wounded there. As a matter of
fact, Louis had visited Napoleon during the siege, but had not served,
and had not been wounded.
Joseph Bonaparte was made war commissioner of the first class.
Napoleon, in securing him the place, represented Joseph as being the
holder of the commission of lieutenant colonel of Corsican volunteers,
the commission which Napoleon had won for himself at such a cost in his
native land. The fraud was discovered later on; but, for the present,
his brother Joseph was snugly berthed.
In July, 1794, Napoleon went to Genoa on a twofold mission. That
republic, which was wholly controlled by a few rich families, had been
giving aid and comfort to the enemies of republican France. The English
and the Austrians had been allowed to violate Genoa's neutrality.
Also, the English had been permitted to set up an establishment for
the manufacture of counterfeit assignats--that peculiar policy of the
British ministry which had been used with good effect against the
revolted American colonies. Besides, there was a complaint that certain
stores bought from Genoa, and paid for, had not been delivered to the
French.
Ostensibly, therefore, Napoleon's mission was about the stores which
Genoa withheld, and about the neutrality which she was allowing to
be violated. But within this purpose lay another. Genoa, and her
neutrality was an obstacle to French military plans; she was weak, and
the temptation to seize upon her was strong. Napoleon while at Genoa
was to look about him with the keen eyes of a military expert, and to
form an opinion as to the ease with which the little republic could be
made the victim of a sudden spring.
This mission, which bears an unpleasant resemblance to that of a spy,
was undertaken at the instance of the younger Robespierre. Salicetti
and Albitte had not been consulted, and knew nothing of the secret
instructions given to Napoleon. Suddenly recalled to Paris by his
brother, Robespierre wished to take with him the young officer whose
"transcendent merit" he had applauded. With Napoleon to command the
Paris troops, instead of Henriot, the Robespierres might confidently
expect victory in the crisis they saw coming. But it was a part of
Napoleon's "transcendent merit" to possess excellent judgment, and he
declined to go to Paris. So the friends parted: the one to visit little
Genoa and bully its feeble Doge, the other to return to the raging
capital and to meet sudden death there in generous devotion to his
brother.
Napoleon reached Nice again, July 21, 1794, after his successful
mission to Genoa, and in a few days later came the crash. The
Robespierres were overthrown, and the Bonapartes, classed with that
faction, fell with it. Napoleon was put under arrest; his brothers
thrown out of employment. For some reason Salicetti and Albitte,
previously so friendly to Napoleon, had turned upon him, had denounced
him to the Convention, and had signed the order of arrest--an order
almost equivalent to a death warrant.
It was a stunning, unexpected blow. Madame Junot, in her _Memoirs_,
hints that the traditional woman was at the bottom of it; that the
younger man, Napoleon, had found favor in the eyes of a lady who
looked coldly upon the suit of Salicetti. But this explanation does
not explain the hostility of other commissioners, for members of two
separate commissioners signed against Napoleon. Surely he had not cut
them all off from the smiles of their ladies. No; it would seem that
Napoleon owed his tumble to the fact that he was standing upon the
Robespierre scaffolding when it fell. He merely fell with it.
He was known as a Robespierre man, and to a very great extent he
was. He had been put under heavy obligations by the younger brother
whom he liked, and he did not believe that the elder was at heart
a bad man. He had seen private letters which the elder brother had
written to the younger, in which letters the crimes of the more rabid
and corrupt revolutionists were deplored, and the necessity for
moderation and purity expressed. Among those who befouled the names
of the Robespierres, either then or afterward, Napoleon is not to be
found. He understood well enough that the convulsion of July 27, 1794
(Thermidor), was the work of a gang of scoundrels (Barras, Fouché,
Carrier, Tallien, Billaud, Collot), who took advantage of circumstances
to pull down a man who had threatened to punish them for their crimes.
Napoleon believed then and afterward that Robespierre had been a
scapegoat, and that he had not been responsible for the awful days of
the Terror in June and July 1794. The manly constancy with which he
always clung to his own estimates of men and events is shown by the
way in which he spoke well of the Robespierre brothers when all others
damned them, and by his granting Charlotte Robespierre a pension at a
time when the act could not have been one of policy. Marvellous was
the complexity of Napoleon's character; but like a thread of gold runs
through all the tangled warp and woof of his life the splendid loyalty
with which he remembered those who had ever been kind to him. Not once
did he ever pursue a foe and take revenge so far as I can discover;
not once did he ever fail to reward a friend, so far as the record is
known.
Napoleon's arrest created such indignation among the young officers of
the army of Italy that a scheme for his forcible release was broached.
Junot, Marmont, and other ardent friends were to take him out of prison
and flee with him into Genoese territory. Napoleon would not hear of
it. "Do nothing," he wrote Junot. "You would only compromise me."
Junot the hot-headed, Junot the tender-hearted, was beside himself
with grief; and he wept like a child as he told the bad news to Madame
Letitia.
But Napoleon himself was not idle. He knew that to be sent to Paris
for trial at that time was almost like going to the scaffold, and he
made his appeal directly to the Commissioners. By name he addressed
Salicetti and Albitte, in words manly, bold, and passionate, protesting
against the wrong done him, demanding that they investigate the case,
and appealing to his past record and services for proofs of his
republican loyalty. This protest had its effect. Salicetti himself
examined Napoleon's papers, and found nothing against him. The
suspicious trip to Genoa was no longer suspicious, for his official
instructions for that trip were found.
After an imprisonment of about two weeks, he was released, but his
employment was gone. He still held his rank in the army, but he was
not on duty. It was only as an adviser and spectator that he remained,
and, at the request of Dumerbion, furnished a plan of campaign, which
was successful to the extent that Dumerbion pushed it. He did not push
it far enough to gain any very solid advantages, much to Napoleon's
disgust.
It was at this time that the incident occurred which he related at
St. Helena. He was taking a stroll with the wife of the influential
Commissioner Turreau, when it occurred to him to divert and interest
her by giving her an illustration of what war was like. Accordingly he
gave orders to a French outpost to attack the Austrian pickets. It was
a mere whim; the attack could not lead to anything. It was done merely
to entertain a lady friend. The soldiers could but obey orders. The
attack was made and resisted. There was a little battle, and there were
soldiers wounded, there were soldiers killed. And the entertainment
which the lady got out of it was the sole other result of the attack.
It was Napoleon who told this story on himself: he declared that he had
never ceased to regret the occurrence.
Corsican affairs now claimed attention for a moment in the counsels of
the government at Paris (September, 1794). For after the Bonapartes had
fled the island, Paoli had called the English in. The old hero intended
that there should be a protectorate, thought that England would be
satisfied with an arrangement of that sort, and that he, Paoli, would
be left in control as viceroy or something of the kind. But the English
had no idea of putting forth their strength for any such halfway
purpose. They intended that Corsica should belong to England, and that
an English governor should rule it. They intrigued with Paoli's stanch
friend, Pozzo di Borgo, and Pozzo became a convert to the English
policy. King George III. of England wrote Paoli a polite and pressing
invitation to visit England, and Paoli accepted.
England bombarded and took the remaining French strongholds (February,
1794), went into quiet and peaceable possession of the island, and
appointed Sir Gilbert Elliott, governor. Of course Paoli's stanch
friend, Pozzo di Borgo, was not forgotten; he was made president of the
state council under Elliott.
When commissioners from Paris came to the headquarters of the army of
Italy, instructed to suspend the operations of the army and to prepare
for an expedition against Corsica, Napoleon saw an opportunity to get
back into active service again. He sought and obtained, perhaps by the
favor of Salicetti, command of the artillery for the expedition. Great
preparations were made at Toulon to organize the forces and to equip
the fleet. In this work Napoleon was intensely engaged for several
months. His mother and the younger children took up their residence in
pleasant quarters near Antibes, and he was able to enjoy the luxury
of the home circle while getting ready to drive the English out of
Corsica. In due time the French fleet set sail; in due time it did what
French fleets have usually done--failed dismally. The English were on
the alert, swooped down, and captured two French vessels. The others
ran to shelter under the guns of shore forts. The conquest of Corsica
was postponed.
CHAPTER VIII
It must have been a sadly disappointed young man who rejoined his
family, now at Marseilles, in the spring of 1795. Gone was the Toulon
glory; gone the prestige of the confidential friend of commissioners
who governed France. Barely escaping with his life from the Robespierre
wreck, here he now was, stranded by the failure, the miserable
collapse, of an expedition from which so much had been expected. Very
gloomy must have been Napoleon's "yellowish green" face, very sombre
those piercing eyes, as he came back to his seat at the hearth of the
humble home in Marseilles. Ten years had passed since he had donned his
uniform; they had been years of unceasing effort, painful labor, and
repeated failure. A demon of ill-luck had dogged his footsteps, foiled
him at every turn, made null all his well-laid plans. Even success had
come to him only to mock him and then drop him to a harder fall. Not
only had he lost ground, but his brothers had been thrown out of the
places he had obtained for them. In the midst of these discouragements
came another: Lacombe St. Michel, a commissioner who bore him no
good-will, urged the government to remove him from the army of Italy
and to transfer him to the West. An order to that effect had been
issued. This transfer would take him away from an army where he had
made some reputation and some friends, and from a field of operations
with which he was thoroughly familiar. It would put him in La Vendée,
where the war was the worst of all wars,--civil strife, brother against
brother, Frenchman against Frenchman,--and it would put him under the
command of a masterful young man named Hoche.
Absolutely determined not to go to this post, and yet desperately
tenacious in his purpose of keeping his feet upon the ladder, Napoleon
set out for Paris early in May, 1795, to exert himself with the
authorities. In the capital he had some powerful friends, Barras and
Fréron among them. Other friends he could make. In a government where
committees ruled, and where the committees were undergoing continual
changes, everything was possible to one who could work, and wait, and
intrigue. Therefore to Paris he hastened, taking with him his aides
Junot and Marmont, and his brother Louis.
Lodged in a cheap hotel, he set himself to the task of getting the
order of transfer cancelled. A general overhauling of the army list had
been going on recently, and many changes were being made. Napoleon's
was not an isolated case. The mere transfer from one army to the other,
his rank not being lowered, was, in itself, no disgrace; but Aubrey,
who was now at the head of the war committee, decided upon a step which
became a real grievance. The artillery service was overstocked with
officers; it became necessary to cut down this surplus; and Napoleon,
as a junior officer, was ordered to the army of the West as general of
a brigade of infantry.
Napoleon regarded this as an insult, a serious injury, and he never
forgave the minister who dealt him the blow. Aubrey had been a
Girondin, and was at heart a royalist. He knew Napoleon to be a
Jacobin, if not a Terrorist. Without supposing that there were any
causes for personal ill-will, here were sufficient grounds for positive
dislike in times so hot as those. In vain Napoleon applied in person,
and brought to bear the powerful influence of Barras, Fréron, and the
Bishop of Marboz. Either his advocates were lukewarm, or his cause was
considered weak. Neither from the full committee nor from Aubrey could
any concession be wrung. Aubrey, himself a soldier of the perfunctory,
non-combative sort, believed that Napoleon had been advanced too
rapidly. "You are too young to be commander-in-chief of artillery," he
said to the little Corsican. "Men age fast on the field of battle," was
the retort which widened the breach;--for Aubrey had not come by any of
his age on fields of battle.
Foiled in his attempt on the committees as then constituted, Napoleon's
only hope was to wait until these members should go out and others come
in by the system of rotation.
In the meantime he stuck to Paris with supple tenacity. By producing
certificates of ill-health, he procured and then lengthened leave of
absence from this obnoxious post in the West. He clung to old friends,
and made new ones. Brother Lucien having been cast into prison as a
rabid Jacobin, Napoleon was able to secure his release. Peremptory
orders were issued that Napoleon should go to his post of duty, but he
succeeded, through his friends, in evading the blow. Louis, however,
lost his place as lieutenant, and was sent back to school at Châlons.
In spite of all his courage and his resources, Napoleon became, at
times, very despondent. He wrote his brother Joseph that "if this
continues, I shall not care to get out of the way of the carriages
as they pass." The faithful Junot shared with his chief the money he
received from home, and also his winnings at the gaming table;--for
Junot was a reckless gambler, and, being young, sometimes had good
luck. Bourrienne and Talma may also have made loans to Napoleon in
these days of distress, but this is not so certain. There is a letter
which purports to have been from Napoleon to Talma, asking the loan
of a few crowns, and offering repayment "out of the first kingdom I
win with my sword." But Napoleon himself declared that he did not meet
Talma before the time of the consulate.
Idle, unhappy, out of pocket, Napoleon became morose and unsocial. If
he seemed gay, the merriment struck his friends as forced and hollow.
At the theatre, while the audience might be convulsed with laughter,
Napoleon was solemn and silent. If he was with a party of friends,
their chatter seemed to fret him, and he would steal away, to be seen
later sitting alone in some box of an upper tier, and "looking rather
sulky."
Pacing the streets from day to day, gloomy, empty of pocket, his career
seemingly closed, his thoughts were bitter. He envied and hated the
young men who dashed by him on their fine horses, and he railed out at
them and at fate. He envied his brother Joseph, who had married the
daughter of a man who had got rich in the business of soap-making and
soap-selling. "Ah, that lucky rogue, Joseph!" But might not Napoleon
marry Désirée, the other daughter of the soap man? It would appear
that he wished it, and that she was not unwilling, but the soap-boiler
objected. "One Bonaparte in the family is enough."
Napoleon traced his misfortunes back to the date of his arrest:
"Salicetti has cast a cloud over the bright dawn of my youth. He has
blighted my hopes of glory." At another time he said mournfully,
striking his forehead, "Yet I am only twenty-six." Ruined by a
fellow-Corsican! Yet to all outward appearance Salicetti and Napoleon
continued to be good friends. They met at Madame Permon's from time to
time, and Salicetti was often in Napoleon's room. Bourrienne states
that the two men had much to say to each other in secret. It was as
though they were concerned in some conspiracy.
On May 20, 1795 (1st of Prairial), there was a riot, formidable and
ferocious, directed by the extreme democrats against the Convention
and its moderates. The Tuileries was forced by the mob, and a deputy
killed. Intending to kill Fréron, the crowd slew Ferraud. The head of
the deputy was cut off, stuck on a pike, and pushed into the face of
Boissy d'Anglas, the president. Gravely the president took off his hat
and bowed to the dead. The Convention troops arrived, cleared the hall,
and put down the riot.
Napoleon was a witness to this frightful scene. After it was over, he
dropped in at Madame Permon's to get something to eat. The restaurants
were all closed, and he had tasted nothing since morning. While eating,
he related what had happened at the Tuileries. Suddenly he inquired,
"Have you seen Salicetti?" He then went on to complain of the injury
Salicetti had done him. "But I bear him no ill-will." Salicetti was
implicated in the revolt, and the conspiracy which preceded it may have
been the subject of those private conversations he had been having at
Napoleon's room--conversations which, according to Bourrienne, left
Napoleon "pensive, melancholy, and anxious."
The conspiracy had ripened, had burst into riot, and the riot had
been crushed. "Have you seen Salicetti?" A very pertinent inquiry
was this, for Salicetti was being hunted, and in a few days would be
proscribed. If caught, he would probably be executed. Madame Junot says
that while Napoleon spoke of Salicetti he "appeared very abstracted."
Briefly to conclude this curious episode, Salicetti was proscribed,
fled for refuge to Madame Permon's house, was hidden by her, and was
finally smuggled out of Paris disguised as her valet. Napoleon had
known where Salicetti lay concealed, but did not betray him. Was his
conduct dictated by prudence or by generosity? There was something
generous in it, no doubt; but the conclusion is almost unavoidable that
there was policy, too. If driven to the wall, Salicetti could have
disclosed matters hurtful to Napoleon. Those private interviews, secret
conferences, daily visits to Napoleon's room on the days the conspiracy
was being formed--would they not look bad for a young officer who
was known to have a grievance, and who had been heard frequently and
publicly to denounce the government? This may have been what was on
Napoleon's mind while he was so much buried in thought at Madame
Permon's.
It was fine proof of Napoleon's judgment that he did not allow himself
to be drawn into the conspiracy. Angered against the government,
despising many of the men who composed it, restlessly ambitious, and
intensely yearning for action, the wonder is that he came within the
secrets of the leaders of the revolt and yet kept his skirts clear.
Napoleon at this period was sallow and thin; his chestnut hair hung
long and badly powdered. His speech was generally terse and abrupt.
He had not yet developed grace of speech and manner. When he came to
present Madame Permon a bunch of violets, he did it awkwardly--so much
so that his ungainly manner provoked smiles. His dress was plain. A
gray overcoat buttoned to the chin; a round hat pulled over his eyes,
or stuck on the back of his head; no gloves, and a black cravat, badly
tied; boots coarse, and generally unclean. When the weather was bad,
these boots would be muddy and wet, and Napoleon would put them on
the fender to dry, to the irritation of those who had exacting noses.
Madame Permon's being a nose of that class, her handkerchief rose to
her nose whenever the Bonaparte boots rose to the fender. Napoleon, an
observant man, took the hint, and got into the habit of stopping in
the area for the chambermaid to clean his boots with her broom. His
clothes had become threadbare, his hat dilapidated. The bootmaker who
gave him credit in this dark hour was never forgotten. The Emperor
Napoleon persisted in patronizing the clumsy cobbler whose heart had
not hardened itself against the forlorn brigadier.
One night at St. Helena, when Napoleon, unable to sleep, was trying
to rob time of its tedium by recalling the vicissitudes of his past,
he related this incident: "I was at this period, on one occasion,
suffering from that extreme depression of spirits which renders life
a burden too great to be borne. I had just received a letter from
my mother, revealing to me the utter destitution into which she was
plunged. My own salary had been cut off, and I had but five francs
in my pocket. I wandered along the banks of the river, tempted to
commit suicide. In a few moments I should have thrown myself into the
water, when I ran against a man dressed like a mechanic. 'Is that you,
Napoleon?' and he threw himself upon my neck. It was my old friend, Des
Mazis, who had emigrated, and who had now returned in disguise to visit
his mother. 'But what is the matter, Napoleon? You do not listen to me!
You do not seem to hear me!'
"I confessed everything to him.
"'Is that all?' said he, and unbuttoning his coarse waistcoat and
taking off a belt which he handed me, 'Here are 30,000 francs which I
can spare; take them and relieve your mother.'"
Napoleon told how he was so overjoyed that he rushed away to send the
money to his mother, without having waited to thank his friend. Ashamed
of his conduct, he soon went back to seek Des Mazis, but failed to find
him anywhere. It was under the Empire that the two again met. Napoleon
forced ten times the amount of the loan upon Des Mazis, and appointed
him to a position which paid him 30,000 francs per year.
Low as he was in purse and spirit, Napoleon was too young, too strong,
too self-reliant to yield to despair for any length of time. His active
brain teemed with schemes for the future. His airy fancy soared all
the way from plans which involved a book store, and a leasing and
sub-letting of apartment houses, to service in Turkey and an empire in
the East. Sometimes his friends thought him almost crazy. Going with
Bourrienne, who was looking about for a suitable house, Napoleon took
a fancy to the house opposite, and thought of hiring it for himself,
Uncle Fesch, and his old Brienne teacher, Patrault: "With that house,
my friends in it, and a horse and cabriolet, I should be the happiest
fellow in the world."
Junot relates that one evening when the two were walking in Jardin
des Plantes, Napoleon appeared to be overcome by the beauties of
his surroundings and the charms of the night. He made Junot his
confidant--he was in love, and his affection was not returned.
Junot listened, sympathized, condoled, and then made Napoleon _his_
confidant. Junot was also in love--he loved Pauline Bonaparte,
and wished to wed her. At once Napoleon recovered himself. Firmly
he rejected the proposition: Junot had no fortune, Pauline had
none--marriage was out of the question.
"You must wait. We shall see better days, my friend.--Yes! We shall
have them even should I go to seek them in another quarter of the
world!"
But where should he go? This question he put to himself and to the
few friends who felt interest in his fate. One of his former teachers
at Brienne, D'Harved, met him at this time in Paris, and was struck
by his dejected appearance. "Chagrin and discontent were vividly
painted on his face. He broke out into abuse of the government."
D'Harved was afraid that such talk would endanger listener as well
as speaker, and at his instance they retired into the garden of the
Palais Royal, accompanied by an Englishman named Blinkam or Blencowe.
Napoleon continued to complain of the manner in which the authorities
had treated him, and he declared his purpose of leaving the country.
The Englishman proposed that they enter a restaurant. There the
conversation was resumed. Napoleon did not favor D'Harved's suggestion,
that he offer his services to England. Nor did Germany attract him.
Spain might do, for "there is not a single warrior in that country."
Then the Englishman proposed Turkey, promising to write letters which
would favorably dispose certain influential persons in Constantinople
to the luckless adventurer. Napoleon jumped at the idea. "His
countenance beamed with delight and hope." He exclaimed, "I shall at
once solicit permission to depart to Constantinople." And he did so.
At the end of July, Aubrey went out of office, and was succeeded in
the war committee by Doulcet de Pontécoulant. One of the first matters
which engaged his attention was the condition of the army of Italy.
It had been losing ground. Doulcet needed the advice of some one who
was familiar with the situation there; and Boissy d'Anglas recommended
Napoleon. Summoned to the war office, Napoleon answered all questions
promptly, and made suggestions as to what ought to be done, which so
dazzled the minister that he said to Napoleon, "General, take time
and write out what you propose, so that it may be laid before the
Committee."
"Time!" cried Napoleon, "give me a couple of sheets of paper and a pen.
In half an hour I will have the plan of campaign ready." He sat down
and wrote, but who could read that awful writing? Taking it home with
him, he made Junot copy it, and the plan was submitted to the full
committee, which sent it on to the army. Doulcet, favorably impressed
by Napoleon, retained him in the topographical bureau, where he and
three others drew up plans and directions for all the armies.
On the 16th of August the order was issued peremptorily, that Napoleon
should proceed to the post assigned him in the army of the West.
He did not obey, and powerful friends screened him. On August 30 he
applied to be sent to Turkey to increase the military resources of the
Sultan. On September 15 or 25 (for authorities differ painfully on the
date), a report signed by Cambacérès and others decreed that his name
be stricken from the list of generals in active service.
One reason given for the sudden harshness of the Committee in striking
his name off the list is that he had pressed for payment of fraudulent
accounts. He had claimed and received mileage from Nice to Paris, when
he had come from Marseilles only. He had also claimed pay for horses
sold by him according to orders, when he set forth on the Corsican
expedition. The authorities had no faith in these horses, considered
them purely imaginary; and, in consequence, Napoleon was spoken of very
harshly by government officials. Letourneur, who had succeeded Doulcet
on the Committee, was one of those who disliked and opposed him.
On September 15 a subcommittee reported to the full committee in favor
of the proposition, that Napoleon be sent, with officers of his suite,
to reorganize the military system of the Turks. Only in government by
committee could such a contradictory series of orders and resolutions
be possible. Napoleon had seriously canvassed the officers who were
to compose his suite on the mission to Turkey, when symptoms of
another revolutionary convulsion attracted his notice and halted his
preparations.
The Convention, which had reeled and rocked along for three years, was
now about to adjourn. It felt that it must, and yet it did not wish to
do so. They therefore decreed that two-thirds of the next legislature
should be composed of themselves. The other third, the people might
elect. One reason for this strange law was that the royalist reaction
had become extremely threatening. The Count of Artois was said to be
hovering on the coast, ready to land an expedition from England, and to
march on Paris. The army of Condé was expecting to coöperate from the
Rhine. Paris was to give the signal by a revolt which should upset the
Convention.
Besides the royalists, there were other formidable malcontents. There
were the poorer classes, who had been deprived of their votes by the
property qualification of the new constitution. In the revolt which
ensued, however, the royalists were the soul of the movement. The
extreme democrats, though hotly opposed to the property qualification,
hated royalism worse. Santerre was ready to sustain the Convention,
and did so. The very prisoners who had been lying in chains since the
democratic revolt of May (1st of Prairial) were now willing to fight
for the Convention, and did fight for it.
The centre of the insurrection against the Convention, its new
constitution, and its decrees was the Section Lepelletier, the home
of the rich men of the middle class. The National Guards from this
section, it will be remembered, had fought in defence of the King on
the famous 10th of August. It was now ready to fight for royalty again.
On the 4th of October (12th of Vendémiaire) the Section Lepelletier
declared itself in insurrection, and it became the rallying-point for
insurgents from all the sections of Paris. The National Guard, forty
thousand strong, had been so reorganized that it was now with the
insurgents. To the royalists the situation seemed full of promise,
for the Convention had but seven or eight thousand troops upon which
it could rely. General Dumas was selected by the Convention to take
command of its forces, but he had left town three days before.
General Menou, in command of the Convention forces, was ordered to
go and disarm and disperse the insurgents. For some reason, either
because he failed to realize the gravity of the crisis, or because he
was unnerved by it, he did the worst thing possible. He parleyed, and
compromised. He agreed to withdraw his troops on the promise of the
insurgents to withdraw theirs. He then retreated, and the insurgents
held their ground and their arms, loudly proclaiming their triumph.
As the nerveless and witless Menou was drawing off his men, a young
officer, on the steps of the Feydau Theatre, exclaimed to his
companion, "Where can that fellow be going?" It was Napoleon speaking
to Junot. And he continued: "Ah, if the sections would only let me lead
them, I would guarantee to place them in the Tuileries in two hours,
and have all those Convention rascals driven out!" Then he hurried to
the Tuileries to see what the Convention would do next.
It was evident that on the morrow the insurgents would attack. They
proclaimed their intention of doing so, and they were confident of
success.
The Convention removed Menou from command, and placed him under arrest.
They then chose Barras commander-in-chief, remembering his vigor and
success in July, 1794, when Robespierre fell. Napoleon was made second
in command.
Just how this appointment came to be made, will always be a matter of
dispute. It is certain that Barras suggested Bonaparte's name to the
Committee in the words: "I have precisely the man we want. It is a
little Corsican officer, who will not stand on ceremony." Baron Fain
states that Napoleon was at this time in the topographical office, that
he was sent for, and sworn in by the Committee in the committee-room.
Napoleon himself, in one of his different versions, relates that he was
at the Feydau Theatre, was told what was happening at the Lepelletier
section, left the theatre, witnessed Menou's retreat, and then hurried
to the Convention to see how the news would be received. Arrived at the
Tuileries, he mixed with the crowd in the galleries, and heard his name
called. Announcement was made that he had been appointed as aide to
Barras.
Barras, in his turn, says that on this fateful evening Bonaparte could
not be found at any of his usual haunts, that he came to the Tuileries
late, looking confused, and that in answer to sharp questions he
admitted that he had come from the section Lepelletier, where he had
been reconnoitring the enemy. Barras charges that he had been dickering
with the other side.
By whatever means it came about, Napoleon Bonaparte was acting chief in
the famous 13th of Vendémiaire (5th of October, 1795). It was he whose
genius converted the Tuileries, which the Parisian mobs had time and
again stormed, into a fortress an army could not have taken. Cannon
were at Sablons, cannon he must have, and Murat at the head of three
hundred horse went in a gallop to bring the guns. In the nick of time
the order was given, for the insurgents had sent also. Murat's mounted
men reached Sablons in advance of the unmounted insurgents, and the
cannon were whirled away to the Tuileries. Planted so as to command
all avenues of approach, they made the position invulnerable, for the
insurgents had no cannon.
General Thiébault says: "From the first, his activity was astonishing:
he seemed to be everywhere at once, or rather he only vanished at
one point to reappear instantly. He surprised people further by his
laconic, clear, and prompt orders, imperative to the last degree.
Everybody was struck also by the vigor of his arrangements, and passed
from admiration to confidence, and from confidence to enthusiasm."
Morning came, and with it the insurgents; but at sight of the
formidable defences which had been the work of the night, they halted.
Hour after hour passed away in hoots, yells, threats, negotiation.
Toward evening it seemed that the Convention troops might be brought
to fraternize with the insurgents. Suddenly a musket was fired, and
the battle opened; or rather the cannonade commenced, for battle it
could not be called. The insurgents showed courage, but had no chance
of success whatever. It was cannon against muskets, an army intrenched
against a packed mob in the streets. The firing commenced at about four
in the evening. By six all was over.
A few attempts to rally the insurgents were made, but were easily
frustrated. The Convention forces carried out the orders Menou had
received by disarming the turbulent sections. A few of the ringleaders
of the revolt were tried and punished, but only one, Lafond, was
executed.
During this disarmament, which recent writers say never happened, but
which Menou had been officially instructed to effect, and which both
Napoleon and Barras say they _did_ effect, the victorious conventionals
made one of those mistakes incident to the prevailing darkness and
confusion. The house of Madame de Beauharnais was entered, the sword of
her late husband, the Viscount Beauharnais, was carried off. In a day
or so the son of the widow Beauharnais went to Napoleon and asked for
the return of his dead father's sword. His request immediately granted,
and the sacred relic being placed in his hands, the boy covered the
handle of the weapon with kisses, and burst in tears. Napoleon's
interest was deeply aroused, and he treated the lad with that winning
kindness which fascinated all who came within its influence. Such
report did Eugène Beauharnais carry home that his mother felt bound
to call upon the General, and thank him in person; and it was thus,
perhaps, that these two first met.
Later biographers scout this story as a romance fashioned by Napoleon
himself, and they say that (1) no disarmament took place; and (2)
that if such disarmament did take place, Madame Beauharnais, a friend
of Barras, would not have been molested. To say nothing of further
proof, the contemporaneous letter of Napoleon to Joseph shows that the
sections _were_ disarmed; and as to Madame Beauharnais being screened
by her friendly relations with Barras, _that_ presupposes every soldier
in the Convention army to have known all about Barras's private
affairs. How could the thousands of Convention troops, fifteen hundred
of whom were democrats just out of jail, know who was or was not a
personal friend of Barras? The Convention was in the minority; it had
less than eight thousand troops: would it have left arms in the hands
of the majority and the forty thousand National Guards?
Captious critics call attention to the fact that Napoleon elsewhere
stated that he met his future wife at the house of Barras. This
assertion does not necessarily conflict with the other. A call at
the office of an official does not constitute a social meeting. When
Napoleon said he met Madame Beauharnais at the house of Barras, his
meaning probably was that he there first knew her socially. And why
should a man like Napoleon, who could lie so superbly when he tried,
invent so bungling a hoax as one which involved a disarmament of Paris
which did not take place, and the return of a sword which had never
been seized?
General Thiébault says: "A few days after the 13 of Vendémiaire
I happened to be at the office of the general staff when General
Bonaparte came in. I can still see his little hat surmounted by a
chance plume badly fastened on, his tricolor sash more than carelessly
tied, his coat cut anyhow, and a sword which did not seem the kind of
weapon to make his fortune. Flinging his hat on a large table in the
middle of the room, he went up to an old general, named Krieg, a man
of wonderful knowledge of military detail and author of a soldier's
manual. He made him take a seat beside him at the table, and began
questioning him, pen in hand, about a host of facts connected with the
service and discipline. Some of his questions showed such complete
ignorance of some of the most ordinary things that several of my
comrades smiled. I was myself struck by the number of his questions,
their order, and their rapidity, no less than by the way in which the
answers were caught up, and often found to resolve themselves into
new questions, which he deduced as consequences from them. But what
struck me still more was the sight of a commander-in-chief perfectly
indifferent about showing his subordinates how completely ignorant
he was of various points of the business which the junior of them was
supposed to know perfectly, and this raised him a hundred cubits in my
eyes."
Here we see Napoleon drawn to the life. Instead of sitting down to
gloat over his recent brilliant success, he had gone to work with the
devouring zeal of a man who had done just enough to encourage him to
do more. He did not idle away any time listening to congratulations.
His cannon having opened one door in his advance, his eager eyes were
already fixed far ahead on another, and his restless feet were in
the path. In his garrison days he had not loved the details of his
profession. Dull routine had been hateful, keeping him away from his
books and his solitary musings. Now it was different. He saw the need
of mastering everything which related to war, and, before he had even
arrayed himself in new uniform, he had sought the old officer, Krieg,
and was exhausting that source of information. In such direct, honest,
practical way he came by that knowledge of war which justified him in
saying in later years: "I know my profession thoroughly. Everything
which enters into war I can do. If there is no powder, I can make
it. If there are no cannon, I will cast them." He knew better how to
construct a road or a bridge than any engineer in the army. He had the
best eye for ground, could best estimate distances, could best tell
what men could do on the march or in the field. Down to the pettiest
details, he studied it all. "Do you know how the shirts which come in
from the wash should be placed in the drawer? No? Then I will tell you.
Put them always at the bottom of the drawer, else the same shirts will
be constantly in use." This advice he volunteered to the astonished
matron who had charge of the soldiers' linen at the Invalides.
On October 12, 1795, Napoleon was restored to his grade in the
artillery, and was named second commandant in the Army of the Interior.
Ten days later, Barras having resigned his generalship, Napoleon became
general of division and commander-in-chief of the Army of the Interior.
On October 26, 1795, the Convention finally adjourned; and on the next
day it began to govern the country again with its two-thirds of the
new legislatures (councils of Ancients and of Five Hundred) and its
five regicide directors,--Barras, Carnot, Rewbell, Letourneur, and
Larévellière-Lépaux.
Napoleon had become one of the dominant men of the State. In his every
movement was the sense of his power. His position good, he lost no
time in making it better. He took up suitable quarters in the _Rue
des Capuchines_, surrounded himself with a brilliant staff, donned a
handsome uniform, sported carriages and fine horses, and appeared in
society.
He did not narrow himself to any clique or faction, but sought friends
in all parties. He protected and conciliated royalists, called back to
the service officers who had been retired, found good places for his
friends, sent bread and wood to famishing families in the districts of
the poor. At the same time he held down lawless outbreaks with a hand
of iron, and went in person to close the great club of the Panthéon,
the hot-bed of political agitation. He thoroughly reorganized the
Army of the Interior and the National Guard, formed guards for the
legislative councils and for the Directory, acting almost always on
his own responsibility, and consulting his superiors but little.
Uncle Fesch came to town to be nominally Napoleon's secretary. Joseph
received money and the promise of a consulship. Lucien was reinstalled
in the fruitful commissary. Louis was once more lieutenant, and Jerome
was placed in school in Paris. Of course Madame Letitia and the sisters
basked in the sunshine also; for Napoleon could never do too much
for his family. Nor did he overlook the Permons. According to Madame
Junot, he had always liked them in the days of his poverty. Now that
prosperity had come, he loved them better than ever: so much so indeed
that he proposed that the Bonapartes should matrimonially absorb the
entire Permon family. Jerome was to be married to Laura Permon, Pauline
to Albert Permon, and Napoleon, himself, was to wed the widow Permon.
According to Laura (afterward Madame Junot), this proposition was
formally made by Napoleon, and laughed out of court by Madame Permon.
The baffled matchmaker continued his visits, however, and frequently
came to the house, accompanied by members of his staff.
One day as he stepped from his carriage, a poor woman held out toward
him a dead child in her arms--the youngest of her six children. It had
died of starvation, and the others would die if she could not get help.
Napoleon was deeply moved, gave the woman kind words and money, and
followed the matter up by getting her pensioned.
There was widespread squalor and misery in Paris during the winter
of 1795, and Napoleon showed tact as well as kindness and firmness
in preventing tumult. Consider that little picture which is usually
passed over so lightly: an angry mob of the unemployed, hungry,
desperate, threatening, and on the brink of violence. They suffer,
their wives starve, their children die in the garrets. Of course they
blame the government. How could such misery exist where there was
so much wealth and food, if the government was treating all fairly?
Furious women stir about in the crowd lashing the upper classes with
bitter tongues, and goading the men on to the point of rioting.
Napoleon and his escort arrive. One fat fisherwoman bustles and
bawls: "Don't mind these dandies in uniform with epaulettes on their
shoulders! Don't disperse! They care not if the poor people starve, if
they can but eat well and grow fat."
Think of Napoleon, the leanest of all lean men, "the thinnest and
oddest object I ever laid eyes on," sitting there on his horse
representing the unpopular "they"! "Madame, pray look at me: tell us
which of us two is the fatter." The paunchy fisherwoman was stunned;
the crowd laughed, and fell to pieces.
CHAPTER IX
The young Republic found itself beset by the old governments of Europe.
Because the Revolution proclaimed a new gospel, because it asserted the
divine right of the people to govern themselves, because it made war
upon caste and privilege, because it asserted the equal right of every
citizen to take his share in the benefits as well as the burdens of
society, because it threatened the tyranny of both Church and State, it
was hated with intense bitterness by the kings, the high-priests, and
the aristocracy of Europe.
In 1793 the first great league was formed to crush it, and to restore
the Old Order in France. The strong member of this combination against
human progress was Great Britain. Rendered secure from attack by her
ocean girdle and her invincible fleets, she nevertheless dreaded what
were called "French principles." In these principles she saw everything
to dread; for they were most insidious, and few were the men of the
masses who, having learned what the new doctrine was, did not embrace
it.
The common man, the average man, the full-grown man, the man who had
not been stunted by the Orthodox pedagogue or priest, could not listen
to the creed of the French republicans without feeling in his heart of
hearts that it offered to the world an escape from the system which
then enslaved it. Into Great Britain, in Germany, in Italy, in the
Netherlands, in Russia itself, the shock with which the Old Order had
fallen in France sent its vibrations--tremors which made the kings,
princes, and privileged who dwelt in the upper stories of the social
fabric quake with terror for the safety of the entire building.
The controlling man in England was William Pitt, able, proud,
cold, ambitious. Personally honest, his policy sounded the deepest
depravities of statecraft. Under his administration India was looted,
ravaged, enslaved; Ireland coerced and dragooned; France outlawed
because she dared to kill a king and call into life a republic; Europe
bribed to a generation of war; freedom of thought, and speech, and
conduct denied, and the cause of feudalism given a new lease of life.
The aims and ends of this man's statesmanship were eternally bad; his
methods would have warmed the heart of a Jesuit. He would not stoop to
base deeds himself, would not speak the deliberately false word, would
not convey the bribe, would not manufacture counterfeit money, would
not arm the assassin, would not burn cities nor massacre innocent women
and children. No, no!--he belonged to what Lord Wolseley complacently
calls "the highest type of English gentleman," and his lofty soul
would not permit him to do things like these himself. He would not
corrupt Irish politicians to vote for the Union; but he would supply
Castlereagh with the money from which the bribes were paid. He would
not himself debauch editor or pamphleteer to slander a political foe,
and deceive the British nation; but he supplied funds to those who
did. Nor would he have put daggers into the hands of fanatics that
they might do murder; but he protected and aided in England those who
did. Not a political criminal himself, he used criminals and garnered
the harvest of their crimes. Not himself capable of political theft,
he countenanced the political thief, approved his success, and as a
receiver of stolen goods, knowing them to have been stolen, haughtily
added huge gains to his political wealth.
The same lofty-minded minister who had debauched Ireland--an enemy to
Irish independence--made war upon free speech and political liberty in
England, and exhausted the resources of diplomacy and force to stamp
out the revolutionary movement of France. Under his sanction, his
emissaries attacked the French Republic by forging and counterfeiting
her paper currency; by arming her factions the one against the other;
by corrupting her trusted leaders; by nerving the hand of the assassin
when the corruptionist could not prevail. That London harbored the
Bourbon and his paid assassin was due to the influence of William Pitt.
That the Bourbon could land on the French coast the emissaries who came
to rouse Vendeans to revolt, or to murder Bonaparte in Paris, was due
to the position of William Pitt.
To the same eminent statesman was due the fact that for a whole
generation British newspapers were so filled with falsehoods against
France and Napoleon that an Englishman could not know the truth without
leaving his country to hear it. To the same cause was due the league
after league of Europe against France, which, beginning in 1793,
reunited and renewed the struggle as often as opportunity offered until
France was crushed, and the hands upon the clock of human progress put
back a hundred years.
Without England, the coalitions against republican France would have
had trifling results. It was England which furnished inexhaustible
supplies of money; England which scoured the ocean with her fleets and
maintained the blockade.
There had been a time when the French Revolution was not unpopular in
Great Britain. This was when the reform movement was under the control
of leaders who proclaimed their purpose to be to model the monarchy
in France upon that of England. So long as professions of this sort
were made, there was nothing to awaken distrust in staid, conservative
England. Even aristocracy loves a fettered king. But when more radical
men wrested leadership from the constitutionals, and boldly declared
that the work of reform must strike deeper, must destroy feudalism
root and branch, must consign a corpulent Church to the poverty whose
beauties it preached, the lords and the bishops of Great Britain
realized that the time had come when they must legislate, preach, pray,
and fight against inovations which, if successful in France, would
inevitably cross the narrow Channel.
All the machinery of repression was put to work. Books were written
against the Revolution, and paid for by pensions drawn from the common
treasury. Sermons were preached against the Revolution, and paid for
in salaries drawn from the State funds. Parliament was set in motion
to enact rigorously oppressive laws, and courts were set in motion to
enforce the statutes. The political system in England might be ever
so bad, but the people should not discuss it. Public meetings became
criminal; public reading rooms, unlicensed, were criminal. By the
plain letter of the law of Christian England, if any citizen opened
his house or room "for the purpose of reading books, or pamphlets,
or newspapers," such citizen became a criminal and such house "a
disorderly house." Before the citizen could permit others to use his
books for pay, he must secure the approval and the license of bigoted
Tory officials. No public meeting at all could be held unless a notice
of such meeting signed by a householder, and stating the object of the
meeting, should be inserted in a newspaper at least five days previous
to the meeting. And even then the Tory justice of the peace was
empowered to break up the meeting and imprison the persons attending
it, if he thought the language held by the speaker of the meeting was
calculated to bring the King or the government into contempt. Not even
in the open fields could any lecture, speech, or debate be had without
a license from a Tory official.
The government spy, the paid informer, went abroad, searching,
listening, reporting, persecuting, and prosecuting. No privacy was
sacred, no individual rights were respected, terrorism became a system.
Paine's _Rights of Man_ threw the upper classes into convulsions; his
_Common Sense_ became a hideous nightmare. Men were arrested like
felons, tried like felons, punished like felons for reading pamphlets
and books which are now such commonplace exponents of democracy that
they are well-nigh forgotten. It was a time of misrule, of class
legislation, of misery among the masses. It was a time when the laborer
had almost no rights, almost no opportunities, almost no inducement
to live, beyond the animal instinct which preserves the brute. It was
a time when the landlord was almost absolute master of land and man;
when the nobleman controlled the King, the House of Lords, and the
House of Commons. It was a time when a duke might send half a dozen of
his retainers to take seats in Parliament, or when he might advertise
the seats for sale and knock them down to the highest bidder. It was
a time when a close corporation of hereditary aristocrats controlled
England like a private estate, taxed her people, dictated her laws,
ruled her domestic and foreign policies, and made war or peace
according to their own good pleasure. It was a time when it might have
been said of most English towns as the town-crier reported to his Tory
masters in reference to the village of Bolton--that he had diligently
searched the place and had found in it neither _The Rights of Man_ nor
_Common Sense_.
There was one class which shared with the nobles the control of
English national policies, and this was that of the great merchants
and manufacturers. The exporter, The Prince of Trade, was a power
behind the throne, and in foreign affairs his selfish greed dominated
England's policy.
This governing class, as Napoleon said, looked upon the public, the
people, as a milch cow; the only interest which they had in the cow was
that it should not go dry. Offices, dignities, salaries, were handed
down from sire to son. By hereditary right the government, its purse
and its sword, belonged to these noble creatures whose merit frequently
consisted solely in being the sons of their sires. To fill the ships
which fought for the supremacy of this oligarchy, press-gangs prowled
about the streets on the hunt for victims. Poor men, common laborers,
and people of the lowlier sort were pounced upon by these press gangs,
and forcibly carried off to that "hell on earth," a British man-of-war
of a century ago. One instance is recorded of a groom coming from the
church where he had just been married, and who was snatched from the
arms of his frantic bride and borne off--to return after many years to
seek for a wife long since dead, in a neighborhood where he had long
been forgotten.
In the army and in the fleet soldiers and sailors were lashed like dogs
to keep them under; and it was no uncommon thing for the victims to die
from the effects of the brutal beating.
Considering all these things, the reader will understand why England
made such determined war upon republican France. Against that country
she launched armies and fleets, bribed kings and ministers, subsidized
coalitions, straining every nerve year in and year out to put the
Bourbons back on the throne, and to stay the advance of democracy. She
temporarily succeeded. Her selfish King, nobles, and clericals held
their grip, and postponed the day of reform. But the delay was dearly
bought. The statesmanship of Pitt, Canning, Castlereagh, and Burke
strewed Europe with dead men, and loaded nations with appalling debts.
Upon land and sea, in almost every clime, men of almost every race were
armed, enraged, and set to killing each other in order that the same
few might continue to milk the cow.
In forming an opinion about Napoleon, it must be remembered that
when he first came upon the scene he found these conditions already
in existence,--Europe in league against republican France. With the
creation of those conditions he had had nothing to do. Not his was
the beginning of the Revolution; not his the execution of Louis XVI.;
not his the quarrel with England. If Great Britain and her allies
afterward concentrated all their abuse, hatred, and hostility upon him,
it was because he had become France; he had become, as Pitt himself
said, "the child and champion of democracy"; he had become as Toryism
throughout the world said, the "embodiment of the French Revolution."
This is the great basic truth of Napoleon's relations with Europe; and
if we overlook it, we utterly fail to understand his career. In an
evil hour for France, as well as for him, the allied kings succeeded
in making the French forget her past. It was not till the Bourbons
had returned to France, to Spain, to Italy; it was not till feudalism
had returned to Germany with its privilege, its abuses, its stick for
the soldier, its rack and wheel for the civilian; it was not till
Metternich and his Holy Alliance had smashed with iron heel every
struggle for popular rights on the Continent; it was not till Napoleon,
dead at St. Helena, was remembered in vivid contrast to the soulless
despots who succeeded him, that liberalism, not only in France, but
throughout the world, realized how exceeding great had been the folly
of the French when they allowed the kings to divorce the cause of
Napoleon from that of the French people.
CHAPTER X
The French Revolution was no longer guided by the men of ideals. With
the downfall of Robespierre had come the triumph of those who bothered
themselves with no dreams of social regeneration, but whose energies
were directed with an eye single to their own advantage. Here and there
was left a relic of the better type of revolutionist, "a rose of the
garden left on its stalk to show where the garden had been"; but to one
Carnot there were dozens of the brood of Barras.
The stern, single-minded, terribly resolute men of the Great Committee,
who had worked fourteen hours a day in a plainly furnished room of the
Tuileries, taking their lunch like common clerks as they stood about
the table at which they wrote,--smiling perhaps, as they ate, at some
jest of Barère,--with no thought of enriching themselves, intent only
upon working out the problems of the Revolution in order that France
might find her way to a future of glory and happiness--these men were
gone, to come no more. Fiercely attached to variant creeds, they had
warred among themselves, destroying each other, wearying the world with
violence, and giving the scoundrels the opportunity to cry "Peace!"
and to seize control. True, the work of the Revolution had been done
too well to be wholly undone. Feudalism had been torn up root and
branch; it could never be so flourishing again. Absolutism, royal
and papal infallibility, had been trodden into the mire where they
belonged; they might be set in place again, but they would never more
look quite so dazzling, nor be worshipped with quite such blindness
of devotion. Great principles of civil and religious liberty had been
planted; they could never be wholly plucked out. The human race had
for once seen a great people fill its lungs and its brain with the air
and the inspiration of absolute freedom from priest, king, aristocrat,
precedent, conventionality, and caste-made law; the spectacle would
never be forgotten, nor the example cease to blaze as a beacon,
lighting the feet and kindling the hopes of the world.
But, for the time, the triumph of the venal brought with it shame
and disaster to the entire body politic. The public service corrupt,
the moral tone of society sank. Ideals came into contempt, idealists
into ridicule. The "man of the world," calling himself practical,
and priding himself on his ability to play to the baser passions
of humanity, laughed revolutionary dogmas aside, put revolutionary
simplicity and honesty out of fashion, made a jest of duty and
patriotism, and prostituted public office into a private opportunity.
Hordes of adventurers, male and female, stormed the administration,
took it, and looted it. The professional money-getter controlled the
Directory: the contractor, stock-jobber, fund-holder, peculator, and
speculator. In all matters pertaining to finance, the Bourse was
the government. The nobility of the Old Order had monopolized the
State's favors under the kings; the rich men of the middle class, the
Bourgeoisie, did so now. The giver and the taker of bribes met and
smiled upon each other; the lobbyist hunted his prey and found it.
Once again the woman, beautiful, shrewd, and unchaste, became greater
than the libertine official who had surrendered to her charms; and she
awarded fat contracts, trafficked in pardons and appointments, and
influenced the choice of army chiefs.
The government no longer concerned itself with chimeras, dreams of
better men and methods, visions of beneficent laws dealing impartially
with an improving mass of citizenship. Just as the Grand Monarch's
court had revelled in the fairyland of joy and light and plenty at
Versailles while peasants in the provinces fed on grass and roots,
dying like flies in noisome huts and garrets; just as the Pompadour of
Louis the XV. had squandered national treasures upon diamonds, palaces,
endless festivities, while the soldiers of France starved and shivered
in Canada, losing an empire for want of ammunition to hold it! so,
under the Directory, Barras held court in splendor, while workmen died
of want in the garrets of Paris; and he feasted with his Madame Tallien
or his Josephine Beauharnais, while the soldiers on the Rhine or on
the Alps faced the winter in rags, and were forced to rob to keep from
starvation.
This wretched state of things had not reached its climax at the period
I am treating, but the beginnings had been made, the germs were all
present and active.
In this revival of mock royalty, Barras outshone his peers. He was of
most noble descent, his family "as old as the rocks of Provence"; his
manners redolent of the Old Régime, and much more so his morals. His
honesty, like his patriotism, delighted in large bribes; and he never
by any chance told the truth if a lie would do as well. His person
was tall and commanding; his voice, in a crisis, had sometimes rung
out like a trumpet and rallied the wavering, for the man was brave and
capable of energetic action. But he was a sensualist, base to the core,
vulgar in mind and heart, true to no creed, and capable of no high,
noble, strenuous rôle. Rotten himself, he believed that other men were
as degraded. As to women, they never stirred a thought in him which
would not, if worded in the ears of a true woman, have mantled her
cheek with shame.
This was the man to whom Napoleon had attached himself; this was the
man in whose house Josephine was living when Napoleon met her. Barras
was the strong man of the hour; Barras had places to give and favors to
divide; Barras was the candle around which fluttered moths large and
small; and to this light had come the adventurer from Corsica, and the
adventuress from Martinique. Usually it is the candle which singes the
moth; in this case it was the moths which put out the candle.
Napoleon had become a thorough man of the world. Hard experience had
driven away sentimental illusions. The visionary of the Corsican
sea-lulled grotto, the patriotic dreamer of the Brienne garden-harbor,
had died some time ago. The man who now commanded the Army of the
Interior was different altogether. Reading, experience, observation,
the stern teachings of necessity, had taught him to believe that the
Italian proverb was true, "One must not be too good, if one would
succeed." He believed now that rigid principles were like a plank
strapped across the breast: not troublesome when the path led through
the open, but extremely detrimental to speed in going through a wood.
He had studied the lives of great men,--Alexander, Cæsar, Richelieu,
Frederick, Cromwell,--and the study had not tended to his elevation
in matters of method. He had studied the politics of the world, the
records of national aggrandizement, the inner secrets of government,
and his conceptions of public honor had not been made more lofty.
He had come to believe that interest governed all men; that no such
things as disinterested patriotism, truth, honor, and virtue existed on
earth. He believed that life was a fight, a scramble, an unscrupulous
rush for place, power, riches; and that the strongest, fleetest, most
artful would win--especially if they would take all the short cuts.
Idealogists he despised.
Cold, calculating, disillusioned, he took the world as he found it.
New men and women he could not create, nor could he create other
conditions, moral, social, political, or material. He must recognize
facts, must deal with actualities. If bad men alone could give him what
he wanted, he must court the bad men. If bad men only could do the
work he wanted done, he must use the bad men. Barras, Fréron, Tallien,
being in power, he would get all he could out of them, just as he had
exhausted the friendship of Robespierre and Salicetti, and just as he
afterward used Fouché and Talleyrand.
Nor was he more scrupulous in his relations with women. He must have
known the character of Madame Tallien, mistress and then wife of the
man of July, and now mistress of Barras; but nevertheless he sought
her acquaintance, and cultivated her friendship. Knowing the character
of Madame Tallien, he must have felt that her bosom friend, Madame
Beauharnais, could not be wholly pure. He saw them together night and
day, he witnessed their influence with Barras; it is impossible that he
did not hear some of the talk which coupled their names with that of
the libertine Director. He must have heard of the early life of this
creole widow, whose husband, the Viscount Beauharnais, had separated
from her, accusing her of scandalous immorality. He must have heard
that after her husband had been guillotined, and she herself released
from prison by the overthrow of Robespierre, she had begun a life of
fashionable dissipation. He must have heard the talk which coupled her
name with that of such women as Madame Tallien, Madame Hamelin, and a
dozen other Aspasias of like kind. The names of her lovers were bruited
about like those of Madame Tallien, one of these lovers having been
General Hoche. Now that she, a widow just out of prison, having no
visible income or property, and whose children had been apprenticed at
manual labor, sported a magnificent establishment, wore most expensive
toilets, led the life of the gayest of women,--the favorite of those
who had recently beheaded her husband,--the world classed her with
those with whom she was most intimate, and thought her morals could
not be purer than those of her associates. Justly or unjustly, she was
regarded as one of the lights of the harem of Barras; and people were
beginning to hint that she and her extravagance had become a burden of
which the Director would gladly be rid.
Napoleon had never come under the spell of such society as that which
he had now entered. That fleeting glimpse of polite society which
he had caught at Valence bore no comparison to this. In his limited
experience he had not met such women as Madame Tallien and Josephine.
He moved in a new sphere. Around him was the brilliance of a court. In
apartments adorned with every ornament and luxury, night was turned
into day; and with music, the dance, the song, the feast, men and
women gave themselves to pleasure. He, the unsocial man of books and
camps, was not fitted to shine in this social circle. He was uncouth,
spoke the language with an unpleasant accent, had no graces of manner
or speech, had nothing imposing in figure or bearing, and he felt
almost abashed in the high presence of these elegant nullities of the
drawing-room.
Shy, ill at ease, he was not much noticed and not much liked by the
ladies of the directorial court, with one exception--Josephine. Either
because of the alleged return of the sword, and the good impression
then made, or because of her natural tact and kindness of heart, Madame
Beauharnais paid the uncouth soldier those little attentions which
attract, and those skilful compliments which flatter, and almost before
he was aware of it Napoleon was fascinated. Here was a woman to take a
man off his feet, to inflame him with passion. She was no longer young,
but she was in the glorious Indian summer of her charms. Her perfect
form was trained in movements of grace. Her musical voice knew its own
melody, and made the most of it. Her large, dark eyes with long lashes
were soft and dreamy. Her mouth was sweet and sensuous. Her chestnut
hair was elegantly disordered, her shoulders and bust hid behind no
covering, and of her little feet and shapely ankles just enough was
seen to please the eye and stimulate the imagination.
As to her costume and her general toilet, it was all that studied art
and cultivated taste could do for generous nature. Madame Tallien was
more beautiful and more queenly than Josephine, many others excelled
her in wit, accomplishments, and mere good looks; but it may be doubted
whether any lady of that court, or other courts, ever excelled the
gentle Josephine in the grace, the tact, the charm, which unites in the
make-up of a fascinating society woman.
Add to this that she was sensual, elegantly voluptuous, finished in
the subtle mysteries of coquetry, fully alive to the power which the
physically tempting woman exerts over the passions of men, and it
can be better understood how this languishing but artful widow of
thirty-three intoxicated Napoleon Bonaparte, the raw provincial of
twenty-seven.
That he _was_ madly infatuated, there can be no doubt. He loved her,
and he never wholly ceased to love her. Never before, never afterward,
did he meet a woman who inspired him with a feeling at all like that
he felt for her. If he did not know at that time what she had been,
he knew after the marriage what she continued to be, and he made a
desperate effort to break the spell. He could not completely do so.
She might betray his confidence, laugh at his love-letters, neglect
his appeals, squander his money, sell his secrets, tell him all sorts
of falsehoods, underrate his value, misconceive his character, and
befoul his honor with shameless sin; but against her repentance and her
childlike prayers for pardon, the iron of his nature became as wax.
Before those quivering lips, before those tear-filled eyes, before
that tenderly sweet voice, all broken with grief, he could rarely
stand. "I will divorce her!" he said fiercely to his brothers, when
they put before him proofs of her guilt, after the Egyptian campaign.
But through the locked door came the sobs of the stricken wife, came
her plaintive pleadings. "_Mon ami!_" she called softly, called hour
after hour, piteously knocking at the door. It was too much; the cold
resolution melted; the soldier was once more the lover, and the door
flew open. When the brothers came next day to talk further about the
divorce, they found little Josephine, happy as a bird, sitting on
Napoleon's knee, and nestling in his arms.
"Listen, Bourrienne!" exclaimed Napoleon, joyously, on his return to
Paris from Marengo, "listen to the shouts of the people! It is sweet to
my ears, this praise of the French--as sweet as the voice of Josephine!"
Even when cold policy demanded the divorce, it was he who wept the
most. "Josephine! my noble Josephine! The few moments of happiness I
have ever enjoyed, I owe to you!"
And in the closing scene at St. Helena it was the same. The dying
man thought no more of the Austrian woman. Even in his delirium, the
wandering memory recalled and the fast freezing lips named "Josephine!"
* * * * *
Yet calculation played its part in Napoleon's marriage, as it did in
everything he undertook. He was made to believe that Josephine had
fortune and high station in society. He weighed these advantages in
considering the match. Both the fortune and the social position would
be valuable to him. In fact, Josephine had no fortune, nor any standing
in society. Men of high station were her visitors; their wives were
not. All the evidence tends to show that Barras arranged the match
between his two hangers-on, and that the appointment to the command of
the Army of Italy became involved in the negotiation. Napoleon received
this coveted commission March 7, 1796; two days later the marriage
occurred.
On the register both Napoleon and Josephine misrepresented their ages.
He had made himself one year older, and she three years younger, than
the facts justified. There was a difference of six years between them,
and Madame Letitia angrily predicted that they would have no children.
In forty-eight hours after the marriage, Napoleon set out for Italy. At
Marseilles he stopped, spending a few days with his mother and sisters.
On March 22, 1796, he was at Nice, the headquarters of the army with
which he was to win immortality.
Almost at every pause in his journey Napoleon had dashed off hot
love-letters to the languid Josephine whom he left at Paris. The bride,
far from sharing the groom's passion, did not even understand it--was
slightly bored by it, in fact. Now that he had gone off to the wars,
she relapsed into her favorite dissipations, she and her graceful
daughter Hortense.
Madame Junot gives an account of a ball at the banker Thellusson's,
which not only illustrates the social status of Josephine, but also the
mixed conditions which the Revolution had brought about in society.
Thellusson was a rich man, and not a nobleman; one of those unfortunate
creatures who, in the eyes of lank-pursed aristocrats, have more money
than respectability. In our day he would be called a plutocrat, and
he would hire some bankrupt imbecile with a decayed title to marry
his idiotic daughter. For Thellusson, just like a plutocrat with
more money than respectability, craved what he did not have, and was
giving entertainments to foist himself up the social height. Of course
he crowded his sumptuous rooms with a miscellany of people, most of
whom despised him, while they feasted with him. It was one of these
entertainments, a ball, at which took place the incidents Madame Junot
relates.
It seems that a captious, querulous, nose-in-the-air _Grand Dame_,
Madame de D., had been decoyed to this Thellusson ball by the assurance
of the Marquis de Hautefort that she would meet none but the best
people--her friends of the Old Régime. Very anxious to see former
glories return, and very eager to meet her friends of this bewitching
Old Régime, Madame de D. not only came to the ball herself, but
consented to bring her daughter, Ernestine. As all high-born people
should, Madame de D. and her daughter Ernestine arrived late. The
ballroom was brilliant, but crowded. The high-born late comers could
find no seats, an annoyance which the Marquis de Hautefort, who was on
the lookout for them, at once tried to remedy.
A sylph-like young lady, who had been divinely dancing, was being led
to her place beside another beautifully dressed woman who seemed to be
an elder sister. So charming was the look of these seeming sisters that
even Madame de D. admired.
"Who are those persons?" she inquired of the Marquis, before the seats
had been brought.
"What!" he exclaimed, "is it possible that you do not recognize
Viscountess Beauharnais, now Madame Bonaparte, and her daughter
Hortense? Come, let me seat you beside her; there is a vacant place by
her, and you can renew your acquaintance."
Madame de D. stiffened with indignation and made no reply. Taking the
old Marquis by the arm, she led him to a side room and burst forth:
"Are you mad? Seat me beside Madame Bonaparte! Ernestine would be
obliged to make the acquaintance of her daughter. I will never connect
myself with such persons--people who disgrace their misfortunes!"
Presently there entered the ballroom a woman, queen-like, lovely as
a dream, dressed in a plain robe of Indian muslin, a gold belt about
her waist, gold bracelets on her arms, and a red cashmere shawl draped
gracefully about her shoulders.
"Eh! my God! who is that?" cried Madame de D.
"That is Madame Tallien," quoth the Marquis.
The high-born relic of the Old Régime flamed with wrath, and was
beginning a tirade against the Marquis for having dared to bring her to
such a place, when the door flew open, and in burst a wave of perfume
and--Madame Hamelin, the fastest woman of the fastest set in Paris. All
the young men crowded around her.
"And now in heaven's name, Marquis, who may _that_ be?"
At the words demurely uttered, "It is Madame Hamelin," the high-born
Madame de D. unfurled the red banner of revolt. It was the one shock
too much.
"Come, Ernestine! Put on your wrap! We must go, child. I can't stand
it any longer. To think that the Marquis assured me I should meet my
former society here! And for the last hour I have been falling from the
frying-pan into the fire! Come, Ernestine!"
And out they went.
CHAPTER XI
The year 1796 found the Republic in sorry plight. The treasury was
empty, labor unemployed, business at a standstill. So much paper
money, genuine and counterfeit, had been issued, that it almost took a
cord of assignats to pay for a cord of wood. Landlords who had leased
houses before the Revolution, and who had now to accept pay in paper,
could hardly buy a pullet with a year's rental of a house. There was
famine, stagnation, maladministration. The hope of the Republic was its
armies. Drawn from the bosom of the aroused people at the time when
revolutionary ardor was at its height, the soldiers, after three years
of service, were veterans who were still devoted to republican ideals.
Great victories had given them confidence, and they only needed proper
equipment and proper direction to accomplish still greater results. At
the end of 1795, Moreau commanded the army of the Rhine, Jourdan that
of the Sambre and Meuse, Hoche that of the West. Schérer commanded the
Army of Italy, where, on November 24, 1795, he beat the Austrians and
Sardinians in the battle of Loano. He did not follow up his victory,
however, and the Directory complained of him. On his part he complained
of the Directory. They sent him no money with which to pay his troops,
no clothing for them, and only bread to feed them on. The commissary
was corrupt; and the Directory, which was corrupt, winked at the
robbery of the troops by thievish contractors. Schérer, discouraged,
wished to resign. It was to this ill-fed, scantily clothed, unpaid, and
discouraged army that Napoleon was sent; and it was this army which he
thrilled with a trumpet-like proclamation.
"Soldiers! You are naked, badly fed. The government owes you much; it
can give you nothing. Your endurance, and the courage you have shown,
do you credit, but gain you no advantage, get you no glory. I will lead
you into the most fertile plains in the world. Rich provinces, great
cities, will be in your power; and there you will find honor, glory,
and riches. Soldiers of Italy, can you be found wanting in courage?"
The army was electrified by this brief address, which touched
masterfully the chords most likely to respond. Courage, pride,
patriotism, and cupidity were all invoked and aroused. For the first
time the soldiers of the Revolution were tempted with the promise of
the loot of the vanquished. "Italy is the richest land in the world;
let us go and despoil it." Here, indeed, was the beginning of a new
chapter in the history of republican France.
[Illustration: NAPOLEON
From a print in the collection of Mr. W. C. Crane. The
original engraving by G. Fiesinger, after a miniature by
Jean-Baptiste-Paulin Guérin. Deposited in the National Library,
Paris, 1799.]
Not without a purpose did Napoleon so word his proclamation. There had
been an understanding between himself and the Directory that his army
must be self-sustaining; he must forage on the enemy as did Wallenstein
in the Thirty Years' War. The government had exerted itself to the
utmost for Napoleon, and had supplied him with a small sum of specie
and good bills; but, this done, he understood that the Directors could
do no more. As rapidly as possible he put his army in marching order,
and then marched. From the defensive attitude in which Schérer had
left it, he passed at once to the offensive. The plan of campaign
which Napoleon, the year before, had drawn up for the revolutionary
committee, and which, when forwarded to the army, Kellermann had
pronounced "the dream of a madman," was about to be inaugurated by the
lunatic himself.
The generals of division in the Army of Italy were older men, older
officers than Napoleon, and they resented his appointment. Masséna,
Augereau, Sérurier, Laharpe, Kilmaine, Cervoni, but especially the two
first, murmured discontentedly, calling Napoleon, "one of Barras's
favorites," a "mere street general," a "dreamer" who had "never been in
action."
Napoleon, aware of this feeling, adopted the wisest course. He drew
around himself the line of ceremony, repelled with steady look all
inclination toward familiarity, abruptly cut short those who ventured
to give advice, adopted a stern, imperative, distant manner, took the
earliest opportunity of showing his absolute self-confidence and his
superiority, indulged in no levity or dissipation, and issued his
orders in a tone so laconic and authoritative that, after his first
formal interview with his division commanders at Albenga, his power
over them was established. On leaving the tent of the new chief,
Augereau remarked to Masséna, "That little ---- of a general frightened
me," and Masséna confessed to the same experience.
The military plans of the Directory, emanating from such men as
Carnot and Bonaparte, were bold and practical. Austria, which had
invaded France from the Rhine, was to be held in check there by
Moreau and Jourdan at the same time that she was assailed by way of
Italy. The three armies of the republic, operating far apart, were to
coöperate in general design, and were finally to converge upon Vienna.
Incidentally to this plan of campaign, Genoa was to be brought to terms
for violations of neutrality; the Pope was to be punished for his
constant encouragement to La Vendée and the royalists generally; and
also because he had screened the assassins of the French ambassador,
Basseville. Sardinia (whose king was father-in-law to the Counts of
Provence and Artois, afterward respectively Louis XVIII. and Charles
X.) was to be humbled for its alliance with Austria against France.
The armies opposed to Napoleon were commanded by old men, excellent
officers so long as war was conducted with a sword in one hand and a
book of etiquette in the other. Opposed to a man like Napoleon, who
set all rules at naught, and put into practice a new system, they were
sadly outclassed and bewildered.
Napoleon intended to force his way into Italy at the point where the
Alps and the Apennines join. From Savona on the Mediterranean to Cairo
it is about nine miles by a road practicable for artillery. From Cairo
carriage roads led into Italy. At no other point could the country be
entered save by crossing lofty mountains. Therefore Napoleon's plan
was to turn the Alps instead of crossing them, and to enter Piedmont
through the pass of Cadibona.
Putting his troops in motion, he threw forward toward Genoa a
detachment under Laharpe. The Austrian commander, thinking that
Bonaparte's plan was to seize Genoa, divided his forces into three
bodies,--the Sardinians on the right at Ceva, the centre under
D'Argenteau marching toward Montenotte, and the right under Beaulieu
himself moved from Novi upon Voltri, a town within ten miles of Genoa.
Between these three divisions there was no connection; and, on account
of the mountainous country, it was difficult for them to communicate
with each other, or be concentrated.
On April 10, 1796, Beaulieu attacked Cervoni, leading the van of the
French in their march toward Genoa, and drove him.
But D'Argenteau, who had advanced on Montenotte, was less fortunate.
Colonel Rampon, who commanded twelve hundred Frenchmen at this point,
realized the immense importance of checking the Austrian advance,
to prevent it from falling upon the flank of Napoleon's army as it
moved along the Corniche road. Throwing himself into the redoubt
of Montelegino, Rampon barred the way of the Austrians with heroic
gallantry. Three times he threw back the assault of the entire
Austrian-Sardinian division. During the combat he called upon his
little band to swear that they would die in the redoubt rather than
give it up, and the oath was taken with the greatest enthusiasm.
Had D'Argenteau continued his efforts, the oath-bound defenders would
probably have been exterminated, but he did not persevere. He drew off
his forces in the evening, to wait till next morning, and then renew
the attack. Morning came, but so did Napoleon. D'Argenteau looked
around him, and lo! he was a lost man. Three French divisions enveloped
the one division of their foe, and to the discomfited Austrians was
left the dismal alternative of surrender or a desperate fight against
overwhelming odds. The battle was fought, and Napoleon won his first
individual and undivided triumph, the victory of Montenotte. The enemy
lost colors and cannon, a thousand slain, and two thousand prisoners.
Napoleon had kept the divisions of his army so skilfully placed
that each could support the other, and all could concentrate. Thus
he crushed the Austrian centre, which could get no support from its
two wings, and with his small force triumphed over the larger armies
opposed to him.
But in this his first campaign, Napoleon's tactics presented that weak
point which was in the end to be his ruin; he risked so much that one
slip in his combination was too likely to bring about a Waterloo.
Had Rampon been merely an average officer, or had D'Argenteau been a
Rampon, or had the gallant twelve hundred been merely average soldiers,
the road through the pass at Montenotte would have been cleared, the
Austrians would have been on Napoleon's flank, and only a miracle could
have saved him from disaster. But Napoleon was young, and luck was with
him: the time was far distant when he himself was to be angrily amazed
at seeing Fortune mock his best combinations, and trivial accidents
ruin his campaigns.
Swiftly following up his advantage, Napoleon pushed forward to Cairo,
to wedge his army in between the separated wings of the enemy. At Dego,
lower down the valley of the Bormida, in which the French were now
operating, were the rallying Austrians, guarding the road from Acqui
into Lombardy. To the left of the French were the Sardinians in the
gorges of Millesimo, blocking the route from Ceva into Piedmont. It was
necessary for Napoleon to strike the enemy at both points, drive them
farther apart, so that he might combat each in detail.
On April 13 the French moved forward, Augereau to the attack of the
Sardinians, Masséna and Laharpe against the Austrians. The Sardinians
were strongly posted on high ground, but the onset of the French
carried all before it. So impetuous had been the rush of Augereau, that
one of the divisions of the enemy under General Provera was cut off.
That brave soldier threw himself into the old castle of Cossario, and
could not be dislodged. Napoleon in person came up and directed three
separate assaults, which were heavily repulsed. Provera was then left
in possession, the castle blockaded, and the strength of the French
reserved for the remaining divisions of the Sardinian army. On the
next day (April 14) General Colli, commander-in-chief of the Sardinian
army, made every effort to relieve Provera, but was repulsed and driven
back upon Ceva, farther than ever from the Austrians. Provera then
surrendered.
While the battle raged at Millesimo, Laharpe had crossed the Bormida,
his troops wading up to their waists, and attacked the Austrian
flank and rear at Dego; at the same time Masséna struck the line of
communication between the two armies on the heights of Biastro. Both
attacks succeeded; and as Colli retreated on Turin, Beaulieu drew off
toward Milan.
On the morning after these victories a fresh Austrian division, which
had come from Voltri on the seacoast to join the main army, reached
Dego, and drove out the few French they found there. The appearance
of this force in his rear gave Napoleon a surprise, and a feeling of
alarm ran through his army. He immediately marched upon the town, and
gave battle. The French were twice beaten off. A third charge led by
Lanusse, waving his hat on the point of his sword, carried all before
it.
For his gallantry in this action, Lanusse was made brigadier general on
the recommendation of Napoleon, under whose eyes the splendid charge
had been made. Lieutenant Colonel Lannes distinguished himself greatly
also, and Napoleon made him colonel on the field.
The result of these battles were nine thousand of the enemy taken
prisoners, other thousands killed, besides thirty cannon taken, and
a great quantity of baggage. Napoleon was now master of the valley
of the Bormida, and of all the roads into Italy. It was his duty,
for Carnot had so ordered, to leave the Sardinians and pursue the
Austrians. He took just the opposite course. Turning to his left, he
entered the gorges of Millesimo, and followed the road to Piedmont.
Laharpe's division was left to watch the Austrians. On April 28 the
French were in full march upon Mondovi. When they reached the height of
Mount Lemota, "the richest provinces in the world" lay beneath them,
stretching from the foot of the height as far as eye could reach. The
troops, so wonderfully led and so daringly fought, were in raptures
with themselves and their chief.
As they looked down upon the lovely Italian plains, dotted with towns
and silvered with rivers, they broke into enthusiastic cheers for the
young Napoleon. For him and for them it was a proud moment. "Hannibal
forced the Alps; we have turned them."
Passing the Tanaro, the French entered the plains, and for the first
time cavalry was in demand. On April 22 the Sardinians made a stubborn
fight at Mondovi. They had repulsed Sérurier with heavy loss on the
day before; but now Sérurier was joined by Masséna and the Sardinians
routed. The Piedmontese cavalry, however, turned upon the French
horse, which had pursued too far, and General Stengel, its commander,
was killed. Murat, at the head of three regiments, dashed against
the Sardinian cavalry with such reckless courage that they broke.
The Sardinians, defeated at all points, lost three thousand, slain
or prisoners, eight cannon, ten stand of colors. Colli requested an
armistice which Napoleon refused to grant. The French continued their
advance upon Turin. The king of Sardinia, Amadeus, wished to prolong
the struggle; but his courtiers clamored for peace, and prevailed.
Overtures were made, Napoleon gladly accepted. Such terror had Napoleon
inspired by his rapid and brilliant victories that he practically
dictated his own terms to the king. The "Keys of the Alps," Coni and
Tortona, besides Alessandria and other fortresses, were surrendered to
him pending negotiations, and the immense magazines they contained were
appropriated to the use of the French army. The Sardinian army was to
be retired from the field, and the roads of Piedmont were to be opened
to the French. The Austrian alliance should cease, and the royalist
émigrés from France should be expelled. This armistice was signed April
29, 1796. As to a definitive peace, plenipotentiaries were to be sent
at once to Paris to conclude it.
Napoleon had violated both the letter and the spirit of his
instructions in virtually making peace with the king of Sardinia. The
Directory, many republicans in France, and many in the army maintained
that Amadeus, a kinsman of the Bourbons, should have been dethroned,
and his country revolutionized. Augereau and others boldly declared
their disapproval of Napoleon's course. He himself was serenely certain
that he had done the proper thing, and he gave himself no concern about
the grumblers.
To Paris he sent his brilliant cavalry-officer, Murat, with twenty-one
flags taken from the enemy. To his troops he issued a stirring address,
recounting their great achievements, and inspiring them to still
greater efforts.
With hands freed, Napoleon turned upon the Austrians. Deceiving them as
to the point at which he would cross the Po, they prepared for him at
one place while he dashed at another. While Beaulieu waited at Valenza,
Napoleon was crossing at Placenza, May 7, 1796. On the next day an
Austrian division arrived at Fombio, a league from Placenza. Napoleon
attacked and routed it, taking two thousand prisoners and all their
cannon. Beaulieu put his troops in motion, hoping to catch the French
in the act of crossing the river.
As the Austrians, preceded by a regiment of cavalry, approached,
they struck the advance posts of Laharpe. That general rode forward
to reconnoitre, and, returning by a different road, was fired upon
and killed by his own troops, in almost precisely the same manner
as the great Confederate soldier, Stonewall Jackson, was slain at
Chancellorsville.
The Austrians, realizing that they were too late, drew off toward Lodi.
On May 10, Napoleon overtook them there. The town was on that side of
the river Adda on which were the French, and Napoleon drove out the
small detachment of Austrians which held it.
On the opposite side of the river Beaulieu had stationed twelve
thousand infantry, two thousand horse, and twenty cannon to dispute
the passage. A single wooden bridge, which the retreating Austrians
had not had time to burn, spanned the river. In the face of an army
sixteen thousand strong, and twenty pieces of artillery ready to rain
a torrent of iron on the bridge, Napoleon determined to pass. Behind
the walls of the town of Lodi the French army was sheltered. Napoleon,
under fire, went out to the bank of the river to explore the ground and
form his plan. Returning, he selected six thousand grenadiers, and to
these he spoke brief words of praise and encouragement, holding them
ready, screened behind the houses of the town, to dash for the bridge
at the word. But he had also sent his cavalry up the stream to find a
ford to cross, and to come upon the Austrian flank. Meanwhile his own
artillery rained a hail of deadly missiles upon the Austrian position,
making it impossible for them to approach the bridge. The anxious
eyes of Napoleon at last saw that his cavalry had forded the river,
and were turning the Austrians' flank. Quick as a flash the word went
to the waiting grenadiers, and with a shout of "Live the Republic,"
they ran for the bridge. A terrific fire from the Austrian batteries
played upon the advancing column, and the effect was so deadly that it
hesitated, wavered, seemed about to break. The French generals sprang
to the front,--Napoleon, Lannes, Masséna, Berthier, Cervoni,--rallied
the column, and carried it over the bridge. Lannes was the first man
across, Napoleon the second. The Austrian gunners were bayoneted before
the infantry could come to their support. In a few minutes the Austrian
army was routed.
The moral effect of this victory, "the terrible passage of the bridge
of Lodi," as Napoleon himself called it, was tremendous. Beaulieu
afterward told Graham that had Napoleon pushed on, he might have taken
Mantua without difficulty--no preparations for its defence having then
been made. The Austrians lost heart, uncovered Milan in their retreat;
and, five days after the battle, Napoleon entered the Lombard capital,
under a triumphal arch and amid thousands of admiring Italians.
It was after this battle that some of the soldiers got together and
gave Napoleon the name of the "Little Corporal," an affectionate
nickname which clung to him, in the army, throughout his career. His
personal bravery at Lodi, and his readiness to share the danger, made
a profound impression on his troops, and when he next appeared he was
greeted with shouts of "Live the Little Corporal."
Napoleon asked a Hungarian prisoner, an old officer, what he now
thought of the war. The prisoner, not knowing that Napoleon himself
was the questioner, replied: "There is no understanding it at all. You
French have a young general who knows nothing about the rules of war.
To-day he is in your front, to-morrow in the rear. Now he is on your
left, and then on your right. One does not know where to place one's
self. Such violation of the rules is intolerable."
Upon the victor himself Lodi made a lasting impression; it was the
spark, as he said afterward, "which kindled a great ambition." Already
Napoleon had begun to levy contributions and to seize precious works
of art. The Duke of Parma, pleading for peace and protection, had been
required to pay $400,000, to furnish sixteen hundred horses and large
quantities of provisions. His gallery was stripped of twenty of its
best paintings, one of which was the "Jerome" of Correggio. The Duke
offered $200,000 to redeem this painting, but Napoleon refused. The
offence which this duke had committed was his adhesion to the coalition
against France, and his contributing three thousand soldiers to aid in
the glorious work of maintaining feudalism.
In France the effect of Napoleon's victories upon the excitable,
glory-loving people was prodigious. His name was on every tongue.
Crowds gathered around the bulletins, and the streets rang with
acclamations. Murat and Junot, bringing to Paris the captured
colors, were given enthusiastic ovations by government and people.
But the Directors began to be uneasy. They would have been more or
less than human had they relished the autocratic manner in which
Napoleon behaved. He had ignored their plans and their instructions.
He had developed an imperiousness which brooked no control. His fame
was dwarfing all others to an extent which gave rise to unpleasant
forebodings. All things considered, the Directors thought it would be
a good idea to divide the Italian command. To that effect they wrote
Napoleon. In reply he offered to resign. A partner he would not have:
he must be chief, or nothing. The Directors dared not make such an
issue with him at a time when all France was in raptures over his
triumphs; and they yielded.
CHAPTER XII
Throughout Italy the principles of the French Revolution had made
considerable progress, and in every province there were intelligent men
who welcomed the advent of Napoleon as the dawn of a new era. The young
warrior was an astute politician, and he assumed the pose of liberator.
With the same pen he wrote proclamations to Italy and letters to
France: in the one he dwelt on the delights of liberty; in the other
on the amount of the loot. And while apparently there was shameful
inconsistency here, really there was much sincerity. He was in earnest
when he spoke of tributes to be levied upon princes and municipalities;
he was also in earnest when he spoke of planting in Italy the
principles of the French Revolution. The extreme type of misgovernment
which prevailed throughout the Italian peninsula shocked his reason,
his sense of justice.
He despised the pampered nobles who could neither govern, fight, nor
die like men. He loathed an idle, ignorant, ferocious priesthood which
robbed the peasantry in the name of religion, and which compelled rich
and poor to bow before such idols as the black doll of Loretto. Hence,
while he compelled the defeated enemies of France, the ruling princes,
to pay heavy sums by way of indemnity, he did, in fact, replace the old
feudal institutions with new ones and better ones.
Napoleon has been heartily abused because he stripped the art galleries
of Italy of their gems--statuary and paintings. French writers of
the royalist school swell the cry and emphasize the guilt. Lanfrey,
particularly, calls the world to witness the fact that he hangs
his head in shame, so much is his conscience pricked by Napoleon's
seizure of pictures. How absurd is all this! If to the victor belong
the spoils, where is the line to be drawn? If one may take the purse
of the vanquished, his jewels, his house, his lands, why are his
pictures sacred? If the civilized world insists upon maintaining the
trained soldier, and continues to hunger after the alleged glories
of wars of conquest, we must get accustomed to the results. Wars of
conquest are waged for very practical purposes. We combat the enemy
because he happens to be in possession of something which we want
and which we mean to have. When we have taken the trouble to go up
against this adversary, prepared to smite him hip and thigh, in robust,
Old-Testament style, and have prevailed against him by the help of the
Lord, shall we not Biblically despoil him of all such things as seem
good in our own eyes? Are we to allow the vanquished heathen--heathen
because vanquished--to choose for us those things which we shall take
with us when we go back home? If mine enemy has a golden crown, or a
golden throne, the appearance and the weight and the fineness of which
please me exceedingly, shall I not take it? If I happen to be a king,
shall I not include such trophies among my "crown jewels" in my strong
"Tower of London"?
And if by chance there should be in the land of mine enemy, the land
which the Lord has given me as the conquest of my sword, a diamond of
surpassing size and purity,--a gem so rich and rare that the mouth of
the whole world waters at the mere mention of Kohinoor--the heathen
name thereof,--shall I not take this rare gem from among unappreciative
heathen, and carry it to my own land, where people worship the only
true and living God and cultivate ennobling fondness for the best
diamonds? If I should chance to be king of my native land, shall I not
gladden the heart of my queen by the gift of the marvellous gem, so
that she may wear it upon her royal brow, and so outshine all royal
ladies whomsoever?
Between such trophies as these and paintings, Napoleon could see
no difference in principle. Numerous are the historians, tracking
dutifully after other historians, who have been, these many years,
heaping abuse upon Napoleon concerning those Italian paintings. It so
happens that while the present chronicler has been engaged with this
book, the world has witnessed quite a variety of warfare. There has
been battle and conquest in China, South Africa, the Philippines; and
the Christian soldiers of Europe and America have prevailed mightily
against the heathen and the insurgent. There has been much victory and
much loot; and with the record of what our Christian soldiers took in
Africa, Asia, and the islands of the sea fresh in mind, it seems to me
that we might all become silent about Napoleon's Italian "works of art."
* * * * *
Lombardy, in 1796, was a possession of the house of Austria, and was
nominally ruled by the Archduke Ferdinand, who lived at Milan in
magnificent state. The victorious approach of the French filled him
and his court with terror, and he called on the Church for help.
The priests aroused themselves, put forth the arm ecclesiastic, and
endeavored to avert the storm by religious ceremonies. The bones of
the saints were brought out, processions formed, and street parades
held. Also there were chants, prayers, mystical invocations. Heaven
was implored to interfere and save the city. Heaven, as usual, had
no smiles for the weak; the angels, who save no doves from hawks, no
shrieking virgin from the ravisher, concerned themselves not at all
(so far as any one could see) with the terrors of the priests and the
nobles of Milan. The Archduke with his Duchess, and the ever faithful
few, deserted his beautiful capital; and Count Melzi went forth with a
deputation to soften the wrath of the conqueror.
Napoleon's terms were not hard. Money he needed to pay his troops,
also provisions, clothing, munitions of war. These he must have, and
these Milan could supply. About $4,000,000 was the sum demanded, but
he allowed this to be reduced by payments in such things as the army
needed. The conquered province was reorganized on a liberal basis, a
national guard enrolled, new officials appointed, and a constitution
framed for it--all this being provisional, of course.
The Duke of Modena sued for peace, and was made to pay $2,000,000,
furnish provisions and horses, and to give up many precious works of
art.
During the negotiations with Modena, Salicetti came into Napoleon's
room one day and said: "The brother of the Duke is here with four
coffers of gold, 4,000,000 francs. He offers them to you in his
brother's name, and I advise you to accept them."
"Thank you," answered Napoleon, "I shall not for that sum place myself
in the power of the Duke of Modena."
Such rivulets of gold as Napoleon had set flowing into the army chest
had far-reaching influence. First of all, the army itself was put
into first-class condition. The troops were newly clothed, well fed,
punctually paid. The pockets of the generals were filled with coin. The
cavalry was splendidly mounted; the artillery brought to perfection. As
a war machine, the Army of Italy was now one of the best the world ever
saw. The Directors were not forgotten. Napoleon gladdened the souls of
Barras and his colleagues with $1,000,000 in hard cash. Other millions
followed the first, Napoleon doling out the sums judiciously, until his
contributions exceeded $4,000,000.
To Moreau, sitting idly on the Rhine, purse empty and spirit low,
Napoleon sent a million in French money. To Kellermann, commanding in
Savoy, he sent 1,200,000 francs. It is hardly necessary to add that he
kept the lion's share of all his booty for his own army chest. Austria
was rousing herself to renew the struggle, France could send him no
supplies, and it would have been lunacy for him to have emptied his
pockets at the opening of another campaign.
After a rest of a week in Milan, the French army was pushed forward
toward Austria. Napoleon advanced his headquarters to Lodi on the
24th of May, 1796. Shortly after his arrival, he learned that a
revolt had broken out behind him, that the French garrison at Pavia
had surrendered, and that insurrection had spread to many towns of
Lombardy, and that in Milan itself there was revolt.
He immediately turned back with a small force, reëntered Milan, fought
the insurgents at Binasco, where Lannes took and burned the town,
and then with fifteen hundred men stormed Pavia, defended by thirty
thousand insurgents, forced his way in, and gave it over to pillage,
butchery, and the flames. The French officer who had signed the order
of capitulation was court-martialled and shot.
Why had the Italians risen against their liberator? There are those who
say that his exactions in money, provisions, horses, paintings, and
so forth caused it. This could hardly have been the sole cause, for
Napoleon's exactions did not directly reach the peasants. His heavy
hand was felt by the rich men of the Church and the State; but upon the
poor he laid no burden. A more reasonable explanation seems to be that
the priests, encouraged by aristocrats, preached a crusade against the
French marauders, who looted rich temples, and made spoil of things
that were believed to be holy. Besides, these marauders were infidel
French who had trampled upon the Church in France, confiscating the
riches thereof, and ousting fat clericals from high, soft places. The
Pope knew that his turn would come,--Basseville's ghost not yet being
laid,--and that he would have to suffer for all the cruel blows he
had aimed at republican France. Therefore as Napoleon marched off to
meet the Austrians, who were reported to be mustering in overwhelming
numbers, it was thought to be a good time to kindle flames in his rear.
Priests rushed frantically to and fro, the cross was lifted on high,
church bells pealed from every steeple, and the ignorant peasants flew
to arms to win a place in heaven by shedding the blood of heretics.
The insurrection stamped out, Napoleon proved what _he_ thought of
its origin. He demanded hostages, not from the peasants, but from the
nobles. The hostages were given, and there was no further revolt.
The Austrian army, in its retreat from Lodi, had taken up the line
of the Mincio, its left at Mantua and its right at Peschiera, a city
belonging to Venice. This violation of neutral ground by Beaulieu gave
Napoleon an excuse, and he seized upon the Venetian town of Brescia. He
proclaimed his purpose to do nothing against Venice, to preserve strict
discipline, and to pay for whatever he might take. Pursuing his march,
he again deceived the aged Beaulieu as to the place where he meant
to cross the river; and he was over the Mincio before the Austrians
could mass sufficient troops to make any considerable resistance. On
the other side of the river, Napoleon, in passing with a small escort
from the division of Augereau to that of Masséna, narrowly missed
falling into the hands of an Austrian corps which was hastening up the
river to join Beaulieu. Napoleon, after having ridden some distance
with Augereau, had returned to Valeggio, where he stopped to get a
foot-bath to relieve a headache. At this moment the light cavalry of
the enemy dashed into the village. There was barely time to sound the
alarm, close the gates of the carriage-way, and to post the escort to
defend the place. Napoleon ran out the back way with only one boot on,
made his escape through the garden, jumped on his horse, and galloped
as hard as he could to Masséna, whose troops, near by, were cooking
their dinner. Masséna promptly aroused his men, rushed them against the
enemy--and then it was the turn of the Austrians to run.
The danger which he had incurred caused Napoleon to form a personal
guard for his own protection. Called by the modest name of _Guides_
at first, the force swelled in numbers and importance until it became
the immortal Imperial Guard. Its commander was Bessières, a young
officer of humble birth, who had attracted Napoleon's notice during the
campaign by his coolness and courage. He became Marshal of France and
Duke of Istria.
In the fighting which took place at Borghetta, the cavalry began
to show its capacity for achieving brilliant results. It was young
Murat, the innkeeper's son, who inspired, led it, and impetuously
fought it. A finer cavalier never sat a horse. A better leader of
cavalry never headed a charge. It was a sight to see him,--brilliantly
dressed, superbly mounted, on fire with the ardor of battle, leading
his magnificent squadrons to the charge. Even Napoleon thrilled with
unwonted admiration in looking upon Murat in battle. "Had I been at
Waterloo," said Murat, the outcast, in 1815, with a flash of his old
pride, "the day had been ours."
And the sad, lonely man of St. Helena assented:--
"It is probable. There were turning-points in that battle when such a
diversion as Murat could have made might have been decisive."
Beaulieu fell back to the Tyrol, and Napoleon occupied Peschiera. He
was furiously angry with Venice because she had allowed Beaulieu to
take possession of this town, which cost the lives of many Frenchmen
before it was retaken. The Venetian Senate, bewildered and dismayed,
sent envoys to propitiate the terrible young warrior. Napoleon assumed
his haughtiest tone, and threatened vengeance.
Finally, when the Venetians had opened to him the gates of Verona, and
had agreed to supply his army, he began to soften, and to talk to the
envoys of a possible alliance between Venice and France.
On June 5, 1796, one of these envoys wrote of Napoleon, in a letter to
Venice, "That man will some day have great influence over his country."
The French were now masters of the line of the Adige, which Napoleon
considered the strongest for the defence of Italy. This line was of
vast importance to him, for he knew that Austria was recruiting her
strength and preparing to retrieve her losses. He had won Italy; could
he hold it? That was now the issue.
Before reënforcements from Austria could arrive, Napoleon calculated
that he would have time to punish the Pope and to humble Naples.
Leaving Mantua invested, and the line of the Adige well defended, he
took one division and turned to the South. There were many reasons
why he should do so. The Bourbons of Tuscany had welcomed the English
to Leghorn, and in Naples preparations were being made to equip a
large force to act against the French. Genoa was giving trouble, her
nobles being very unfriendly to France. In Genoese territories troops
of disbanded Piedmontese soldiers, escaped Austrian prisoners and
deserters, infested the Apennine passes, stopped couriers, plundered
convoys, and massacred French detachments.
Reaching Milan, Napoleon directed Augereau upon Bologna, and Vaubois
on Modena. To the Senate of Genoa was sent a haughty letter demanding
to know whether that state could put down the disorders of which the
French complained. Murat, the bearer of the message, read it to the
trembling Senate. It had the effect desired: Genoa promised, and did
all that was asked.
Lannes, with twelve hundred men, sent to chastise the feudatory
families of Austria and Naples, resident in Genoese territories, did
the work with energy and success. Châteaux of conspiring nobles were
burnt; and wherever any of the bands which had been molesting the
French could be found, they were summarily shot down.
Naples was cowed before she had been struck, and she sent in her
submission to the conqueror. He dealt with her leniently. She must
abandon the coalition against France, open all her ports to the
French, withdraw her ships from England, and deliver to Napoleon
the twenty-four hundred cavalry which she had furnished to Austria.
This armistice signed, he turned his attention and his troops in the
direction of Rome. Bologna, a papal fief, was seized. Ferrara, another
papal domain, threw off the papal yoke.
The Pope, smitten with fear, sent Azara, the ambassador of Spain, to
negotiate terms; and again Napoleon was mild. He required that Ancona
should receive a French garrison, that Bologna and Ferrara should
remain independent, that an indemnity of 21,000,000 francs should
be paid, that one hundred statues and paintings should be given up,
besides grain and cattle for the army. The Pope consented. Here again
Napoleon gave great offence to the Directory, and to many republicans
in France, as well as in the army.
The Pope had been the centre of the hostility against the Revolution
and its principles. He had actively coöperated with the enemies of
France, had torn her with civil strife, had suffered her ambassador
to be brutally murdered, and had given aid, comfort, blessings, and
pontifical inspiration to her enemies wherever he could. The Directory
wished that the papal power should be totally destroyed. Napoleon had
no such intention. Catholicism was a fact, a power, and he proposed to
deal with it accordingly. He accepted the money and the paintings and
the marbles: Basseville's ghost being left to lay itself as best it
could. In delicate compliment to the Pope, the young conqueror did not
enter Rome. In all his passings to and fro, this modern Cæsar, this
restorer of the Empire of the West, never set his foot in the Sacred
City.
On June 26, 1796, Napoleon crossed the Apennines into Tuscany. By
forced marches, a division was thrown forward to Leghorn, where, it
was hoped, the English ships would be taken. Warned in time, they had
sailed away, but the French seized large quantities of English goods.
Leaving a garrison at Leghorn, Napoleon proceeded to Florence, where
the grand-duke fêted him royally. The grand-duchess did not appear at
the banquet: she was "indisposed." Italy having been pacified in this
swift manner, Napoleon returned to his army headquarters near Mantua.
CHAPTER XIII
Even Austria could now see that Beaulieu was no match for Napoleon. In
his place the Emperor sent the aged Wurmser, another officer excellent
in the old leisurely cut-and-dried style of campaigning. If Napoleon
would rest satisfied to wage war according to the rules laid down in
the books, Wurmser would perhaps crush him, for to the 34,000 French
there would be 53,000 Austrians in the field, not counting the 15,000
Austrians who were blockaded in Mantua by 8000 French.
Napoleon was at Milan when news came that Wurmser had issued from the
mountain passes and was in full march to envelop the French below Lake
Garda. Hastening back to the front, Napoleon established headquarters
at Castel-Nuovo. Wurmser was confident; Napoleon anxious, watchful, and
determined. The Austrians were divided into three columns,--one came
down the western bank of Lake Garda, and the other two down the eastern
shore. At first the Austrians drove the French at all points, and
Napoleon's line was broken, July 30, 1796. This brought on the crisis
in which it is said that he lost his nerve, threw up the command, and
was saved by doughty Augereau. The evidence upon which this alleged
loss of nerve is based is of the frailest, and the undisputed record
of the campaign discloses Napoleon's plan, Napoleon's orders, and
Napoleon's presence throughout. His only hope was to prevent the
junction of the Austrian divisions. Could he hold two off while he
concentrated on the third? Practically the same tactics which won
at Montenotte prevailed again. While Wurmser was passing forward to
Mantua by forced marches, Napoleon had already called in Sérurier;
and when the Austrians arrived, expecting to capture the besiegers,
no besiegers were there. They had spiked their siege guns, destroyed
surplus ammunition, and gone to join the main army of Napoleon, and to
aid in crushing one of Wurmser's lieutenants while Wurmser was idling
uselessly at Mantua. Almost identically the same thing had occurred at
Montenotte, where Beaulieu had rushed upon Voltri to capture French who
had been withdrawn, and who were destroying Colli at Montenotte while
Beaulieu at Voltri talked idly with Lord Nelson of the English fleet,
devising plans whereby Napoleon was to be annihilated. Napoleon struck
the first blow at Quasdanovitch, who led the Austrian division which
had come down the western side of the lake. At Lonato, July 31, 1796,
the French beat the Austrians, driving them back, recovering the line
of communication with Milan which had been cut. Then Napoleon hastened
back to confront the Austrian centre. Twenty-five thousand Austrians,
marching to join Quasdanovitch, reached Lonato. On August 3, Napoleon
threw himself upon this force, and almost destroyed it. So demoralized
were the Austrians that a force of four thousand surrendered to twelve
hundred French.
[Illustration: LETTER TO JOSEPHINE.]
Next day Wurmser came up offering battle. Stretching his line too far
and leaving his centre weak, Napoleon struck him there, beat him with
heavy loss, and sent him flying back toward the mountains. In these
various operations, Austria had lost about forty thousand men; France
about ten thousand. Mantua had been revictualled, and the French now
invested it again. Their siege outfit having been destroyed, they could
only rely upon a blockade to starve the enemy out.
Both armies were exhausted, and there followed a period of rest.
Reënforcements were received by Wurmser, and by Napoleon also. The
Austrians still outnumbered him, but Napoleon took the offensive.
Wurmser had committed the familiar mistake of dividing his forces.
Napoleon fell upon Davidovitch at Roveredo and routed him. Then turning
upon Wurmser, who was advancing to the relief of Mantua, Napoleon
captured at Primolano the Austrian advance guard. Next day, September
8, 1796, he defeated the main army at Bassano.
Wurmser was now in a desperate situation. Shut in by the French on one
side and the river Adige on the other, his ruin seemed inevitable.
By the mistake of a lieutenant colonel, Legnano had been left by the
French without a garrison, and the bridge not destroyed. Here Wurmser
crossed, and continued his retreat on Mantua. He gained some brilliant
successes over French forces, which sought to cut him off, and he
reached Mantua in such good spirits that he called out the garrison and
fought the battle of St. George. Defeated in this, he withdrew into the
town. He had lost about twenty-seven thousand men in the brief campaign.
At length the armies on the Rhine had got in motion. Moreau crossed
that river at Kehl, defeated the Austrians, and entered Munich. Jourdan
crossed at Dusseldorf, and won the battle of Alten Kirchen. Then the
young Archduke Charles, learning a lesson from Napoleon, left a
small force to hold Moreau in check, and massed his strength against
Jourdan. The French were badly beaten, and both their armies fell back
to the Rhine. The original plan of a junction of Jourdan, Moreau, and
Bonaparte for an advance upon Vienna was, for the present, frustrated.
Encouraged by the success, Austria sent a new army of fifty-three
thousand men, under Alvinczy, to recover the lost ground in Italy.
Napoleon had about forty thousand troops, several thousand of whom were
in hospitals, and once more his safety depended upon preventing the
concentration of the enemy.
As in the former campaign, Austria won the first encounters. Vaubois
was driven to Trent, and from Trent to Roveredo, and from thence to
Rivoli. Masséna fell back, before superior numbers, from Bassano.
Napoleon, with the division of Augereau, went to Masséna's support.
All day, November 6, 1796, Augereau fought at Bassano, and Masséna at
Citadella. Alvinczy gave ground, but the French retreated, because of
the defeat of Vaubois. It seemed now that the two Austrian divisions
would unite, but they did not. At Rivoli a French division, eager to
win back the respect of their chief, who had publicly reproved them
and degraded their commander, held Davidovitch in check, and prevented
his junction with Alvinczy. Fearful that Rivoli might be forced, and
the Austrian divisions united, Napoleon again attacked Alvinczy. This
time the French were repulsed with heavy loss, some three thousand men
(November 13, 1796). Napoleon now had a fresh Austrian army on each
flank, and Wurmser on his rear.
Should the three Austrian commanders coöperate, the French were lost.
But Napoleon calculated upon there being no coöperation, and he was
correct. Nevertheless, he almost desponded, and in the army there was
discouragement.
As night closed round the dejected French, Napoleon ordered his troops
to take up arms. Leaving a garrison to hold the town, he led his troops
out of Verona, and crossed to the right side of the Adige. Apparently
he was in retreat upon the Mincio. Down the Adige he marched as far
as Ronco. There he recrossed the river on a bridge of boats which he
had prepared. On this march the French had followed the bend which the
river here makes to the Adriatic. Therefore he had reached the rear of
the enemy simply by crossing the Adige and following its natural curve.
Arrived at Ronco and crossing the river again, the troops saw at a
glance the masterly move their chief had made; their gloom gave way to
enthusiastic confidence.
It is a marshy country about Ronco, and the roadways are high dikes
lifted above the swamp,--one of these raised roads leading to Verona
in Alvinczy's front, another leading from Ronco to Villanova in the
Austrian rear. Early in the morning, November 15, 1796, Masséna
advanced from Ronco on the first of these roads, and Augereau on the
other. Masséna passed the swamp without opposition, but Augereau met
an unforeseen and bloody resistance at the bridge of Arcole, a town
between Ronco and Villanova, where the little river Alpon crosses the
road on its way to the Adige. Two battalions of Croats with two pieces
of artillery defended this bridge, and so bravely was their task done
that Augereau's column was thrown back in disorder. There was no
better soldier in the army than he, and Augereau seized the standard
himself, rallied his men, and led them to the bridge. Again the Croats
drove them back with enfilading fire. The bridge must be taken; it was
a matter of vital necessity, and Napoleon dashed forward to head the
charge. Seizing the colors, he called upon the troops to follow, and
with his own hands planted the flag on the bridge. But the fire of the
enemy was too hot, their bayonets too determined: the Croats drove the
French from the bridge, and in the confusion of the backward struggle,
Napoleon got pushed off the dike into the swamp where he sank to his
waist. "Forward! forward! To save our general!"
With this cry the French grenadiers rallied their broken line, made a
desperate rush, drove back the Croats, and pulled Napoleon out of the
mud.
It was in the charge led by Napoleon that Muiron, his aide, threw
himself in front of his chief, as a shield, saved Napoleon's life, and
lost his own.
It was not till a French corps, which had crossed the Adige lower down
at a ferry, came upon the Austrian flank, that the French were able
to carry the bridge and take Arcole. By this time, owing to stubborn
fight at the bridge, Alvinczy had had time to get out of the trap which
Napoleon had planned. The Austrians took up a new position farther
back, and were still superior in numbers and position to the French.
If Davidovitch would only brush Vaubois out of his way and come upon
Napoleon's flank, and if Wurmser would only bestir himself against the
weakened blockading force at Mantua and make trouble in Napoleon's
rear, it would be the French, not the Austrians, who would feel the
inconvenience of the trap! But Davidovitch did nothing; Wurmser did
nothing; and Alvinczy continued to make mistakes. For when Napoleon,
after the first day's fighting before Arcole, fell back to Ronco in
fear that Davidovitch might come, Alvinczy took up the idea that the
French were in full retreat, and he started in pursuit, using the
raised roads for his march. On these dikes only the heads of columns
could meet, the Austrian superiority in numbers was of no advantage,
and Napoleon could not have been better served than by the offer of
battle under such conditions. Again there was a day of fighting.
Napoleon attempted to get to Alvinczy's rear by crossing the Alpon, but
failed. Night came, both armies drew off, and nothing decisive had been
done.
Again Napoleon fell back to Ronco to be prepared for Davidovitch, and
again the son of David was not at hand. Neither was Wurmser doing
anything in the rear. In front, Alvinczy, stubbornly bent on staying
just where Napoleon wanted him, came upon the narrow dikes again. Once
more it was a battle between heads of columns, where the veteran French
had the advantage of the recent recruits of Austria. For a moment the
giving way of part of the bridge the French had made over the Adige
threatened them with disaster. The Austrians came forward in force to
cut off a demi-brigade left on their side of the broken bridge. But the
bridge was repaired, French troops rushed over, and threw the Austrians
back on the marsh. Napoleon laid an ambuscade in some willows bordering
the Alpon, and when the enemy, in retreat, passed along the dike, the
soldiers in the ambuscade poured a deadly fire on their flank, and
then charged with the bayonet. Taken by surprise, assailed on front
of flank, some three thousand Croats were thrown into the swamp, where
most of them perished.
Calculating that in the battles of the last three days Alvinczy had
lost so many men that his army did not now outnumber the French,
Napoleon determined to leave the swamps, advance to the open, dry
ground, and beat the Austrians in pitched battle. Crossing the Alpon by
a bridge built during the night, the French fought a sternly contested
field on the afternoon of the 17th of November, 1796, and finally
won it. Napoleon had sent about twenty-five mounted guides with four
trumpets to the swamp on which rested the Austrian left, and this
trifling force breaking through the swamp, and making a tremendous
noise with their trumpets, caused the Austrians to think that another
ambuscade was being sprung. This fear, falling upon them at a time when
they were almost overcome by the stress of actual battle, decided the
day. Alvinczy retreated on Montebello, and the long struggle was ended.
It is said that Napoleon, who had not taken off his clothes for a week,
and who for nearly three days had not closed his eyes, threw himself
upon his couch and slept for thirty-six hours.
At last Davidovitch roused himself, swept Vaubois out of his path, and
came marching down to join Alvinczy. There was no Alvinczy to join;
Davidovitch was some three or more days too late. And Wurmser down at
Mantua made brilliant sally, to create apprehension in the rear. The
old man was a week or so behind time. The grip of Napoleon still held;
the line of the Adige was intact.
But while Napoleon had succeeded in holding his own, he had done so
by such desperate straits and narrow margins, leaving the Austrian
armies unbroken, that the Emperor decided on another great effort.
Recruits and volunteers were enrolled to reënforce Alvinczy, and
hurried forward, bearing a banner embroidered by the Empress. Once more
the Austrians took the field with superior numbers; once more these
forces were divided; once more Napoleon beat them in detail by skilful
concentration.
General Provera was to lead a division to the relief of Mantua;
Alvinczy was to overwhelm Napoleon. Provera was to follow the Brenta,
pass the Adige low down, and march across to Mantua. Alvinczy was to
move along the Adige from Trent, and fall upon the main French army,
which it was hoped would have been drawn to the lower Adige by the
demonstration of Provera.
The heights of Rivoli on Monte Baldo command the valley of the Adige;
and no sooner had the preliminary movements of the enemy revealed their
plan of campaign, than Napoleon sent orders to Joubert to seize and
fortify the plateau of Rivoli, and to hold it at all hazards. This was
on January 13, 1797. That night Napoleon himself marched to Rivoli with
twenty thousand men, reaching the heights by a forced march at two in
the morning.
Alvinczy felt so confident of enclosing and capturing the small force
of Joubert that he had gone to sleep, ranging his army in a semicircle
below to await the dawn, when Joubert was to be taken immediately after
breakfast.
When Napoleon arrived, between midnight and day, he looked down
from the heights, and there below, peacefully snoring and bathed in
moonlight, were the confident Austrians--five divisions strong. Leaving
them to slumber, he spent the balance of the wintry night getting
ready for the battle that would come with the day. As morning broke,
the Austrians attacked the French right at St. Mark, and the contest
soon raged along the whole line as far as Caprino, where the French
left was driven. Berthier and Masséna restored order, and repulsed
every charge. Strongly posted on the heights, the French had all the
advantage. Alvinczy found it impossible to use his cavalry or artillery
with effect, and many of his troops could not be brought into action.
In relative position, Napoleon held the place of Meade at Gettysburg,
and Alvinczy that of Lee. Perhaps Napoleon was even better intrenched
than Meade, and Alvinczy less able to bring his forces up the heights
than Lee. The result was what it was almost bound to be--the Austrians
were routed with terrible loss, and fled in disorder. So great was
the panic that a young French officer, René, in command of fifty men
at a village on Lake Garda, successfully "bluffed" and captured a
retreating body of fifteen hundred Austrians. Joubert and Murat pursued
vigorously, and in two days they took thirteen thousand prisoners.
It was not till the battle of Rivoli had raged for three hours that
Alvinczy realized that he was attempting the foolhardy feat of storming
the main French army, posted by Napoleon himself, in almost impregnable
positions.
Leaving Joubert and Murat to follow up the victory, Napoleon went at
full speed to head off Provera. That gallant officer had fought his way
against Augereau and Guieu, and had reached the suburb of St. George,
before Mantua, with six thousand men. He had lost the remainder on the
way--some twelve thousand. Throughout the day of January 15, 1797, he
was held in check by Sérurier. Next morning the battle was renewed;
but Napoleon had arrived. Provera attacked the French in front; Wurmser
in the rear. Sérurier threw Wurmser back into Mantua; and Victor,
who had come with Napoleon, vanquished Provera so completely that he
laid down his arms. This action is known as that of La Favorita (the
name of a country-seat of the Dukes of Mantua near by), and threw
into the hands of the French six thousand prisoners, including the
Vienna volunteers and many cannon. One of the trophies was the banner
embroidered by the Empress of Austria.
A few days later Mantua capitulated, and the last stronghold of the
Austrians in Italy was in the hands of the French.
Critics who understand all the mysteries of Napoleon's character
say that there was not a trace of chivalry or generosity in him.
Yet at Mantua he, a young soldier, would not stay to gloat over the
humiliation of the veteran Wurmser. He praised that old man by word and
by letter, he granted him liberal terms, and he left the older Sérurier
to receive Wurmser's sword. Was not this delicate, even chivalrous to
Wurmser? Was it not even more generous to Sérurier? Mr. Lanfrey hints
"No"; but Wurmser thought "Yes," for he warmly expressed his admiration
for Napoleon; and out of gratitude warned him, while he was at Bologna,
of a plot the papal party had made to poison him--a warning which
probably saved his life.
The Pope, believing that Napoleon could not possibly escape final
defeat at the hands of Austria, had broken their friendly compact.
A crusade had been preached against the French, sacred processions
paraded, and miracles worked. The bones of martyrs bled, images of the
Virgin wept. Heaven was outspoken on the side of Rome beyond all doubt.
Aroused by these means, the peasants flocked to the standard of the
Pope; and an army, formidable in numbers, had been raised.
Leaving Sérurier to receive the capitulation of Mantua, Napoleon
hastened to Bologna, and organized a force of French, Italians, and
Poles to operate against the papal troops. Despatching the greater part
of his little army to Ancona, he advanced with about three thousand
men into the States of the Church. Cardinal Busca with an army of
mercenaries, fanatical peasants, and miscellaneous Italian recruits was
intrenched on the banks of the Senio to dispute its passage. The French
came marching up in the afternoon of a pleasant spring day; and the
Cardinal, with a solicitude which did honor to his conscience, sent a
messenger, under flag of truce, to notify Napoleon that if he continued
to advance, he would be fired upon. Greeting this as the joke of the
campaign, the French became hilarious; but Napoleon gravely returned
a polite answer to the Cardinal, informing him that as the French had
been marching all day, were tired, and did not wish to be shot at,
they would stop. Accordingly, camp was struck for the night. Before
morning, Lannes had taken the cavalry, crossed the river above, and
got in the Cardinal's rear. Day broke, and there was some fighting. In
a short while the Cardinal fled, and the greater part of his motley
army were prisoners. Advancing on Faenza, which had closed its gates
and manned its ramparts, the French battered their way in with cannon,
and routed the defenders. Napoleon's policy with the Pope was not that
of the Directory; it was his own, and it was subtle and far-sighted.
Prisoners were kindly treated and released. Cardinals and influential
priests were caressed. Papal officers recently captured were visited,
soothed by conciliatory speech, assured that the French were liberators
and desired only the welfare of a regenerated Italy--redeemed from
papal thraldom and rusty feudalism. For the first time modern Italians
heard a great man outlining the future of a united Italy.
At Loretto were found the relics which made that place one of the
holiest of shrines. The very house in which Mary, the mother of Jesus,
had received the visit of Gabriel was at Loretto. Had you asked how
came it there, the answer would have been that the angels carried
it from Nazareth to Dalmatia to keep the Saracens from getting it.
From Dalmatia the angels, for reasons equally good, had carried it
to Loretto. Within this holy hut was a wooden image of Mary, old,
blackened, crudely carved. The angels had carved it. In times of
clerical distress this image of Mary was seen to shed tears. As there
had been quite an access of clerical woe recently, in consequence
of Napoleon's brutal disregard of papal armies led by priests with
crucifixes in their hands, the wooden Virgin had been weeping profusely.
Napoleon had doubtless familiarized himself with the methods by which
pagan priests had kept up their stupendous impostures, and he had a
curiosity to see the old wooden doll which was worshipped by latter-day
pagans at Loretto. He found a string of glass beads so arranged that
they fell, one after another, from the inside, athwart the Virgin's
eyes, and as she was kept at some distance from the devotees, and
behind a glass case, the optical illusion was complete. Napoleon
exposed the trick, and imprisoned the priests who had caused the
recent tears to flow.
To add to the sanctity of the shrine at Loretto, there was a porringer
which had belonged to the Holy Family, and a bed-quilt which had
belonged to Mary, the mother of Jesus. Thousands of devout Catholics
prostrated themselves every year before these relics, and countless
were the rich offerings to the shrine.
Napoleon took from the church pretty much all the treasure which the
priests had not carried off; and the wooden Madonna was sent to Paris.
In 1802 he restored it to the Pope, and it was put back in its old
place in the Virgin's hut.
Many of the French priests who had refused the oath of allegiance
to the new order of things in France had taken refuge in the papal
States. The Directory wished Napoleon to drive these men out of
Italy. He not only refused to do that, but he gave them the benefit
of his protection. In a proclamation to his troops he directed that
the unfortunate exiles should be kindly treated; and he compelled the
Italian monasteries, which had indeed grown weary of these come-to-stay
visitors, to receive them and supply all their wants.
The breadth and depth of Napoleon's liberalism was also shown by the
protection he gave to the Jews. These people had, at Ancona, been
treated with mediæval barbarity. Napoleon relieved their disabilities,
putting them upon an exact political equality with other citizens. In
favor of certain Mohammedans, who resided there, he adopted the same
course.
Capturing or dispersing the Pope's troops as he went, and winning by
his clemency the good-will of the people, Napoleon drew near Rome. The
Vatican was in dismay, and the Pontiff listened to those who advised
peace. The treaty of Tolentino was soon agreed upon, and the papal
power once again escaped that complete destruction which the Directory
wished. A mere push then, an additional day's march, the capture of
another priest-led mob, would have toppled the sovereignty which was
at war with creed, sound policy, and common sense. It cost torrents of
blood, later, to finish the work which Napoleon had almost completed
then.
By the treaty of Tolentino, February 19, 1797, the Pope lost $3,000,000
more by way of indemnity; the legations of Bologna and Ferrara,
together with the Romagna, were surrendered; papal claims on Avignon
and the Venaisson were released, and the murder of Basseville was to be
formally disavowed. To his credit be it said that Napoleon demanded the
suppression of the Inquisition; to his discredit, that he allowed the
priests to wheedle him into a waiver of the demand.
"The Inquisition was formerly a bad thing, no doubt, but it is harmless
now--merely a mild police institution. Pray let it be." Napoleon
really was, or pretended to be, deceived by this assurance, and the
Inquisition remained to purify faith with dungeon, living death in
foul tombs, torture of mind and of body in Italy, in Spain, in South
America, in the far Philippines.
"Most Holy Father," wrote Bonaparte to the Pope; "My Dear Son," wrote
the Pope to Bonaparte; and so they closed _that_ lesson.
Amid all the changes made and to be made in Italy there was one
government Napoleon did not touch. This was the little republic of San
Marino, perched upon the Apennines, where from its rain-drenched,
wind-swept heights it had for a thousand years or more looked
tranquilly down upon troubled Italy. Governed by a mixed council of
nobles, burgesses, and farmers, it was satisfied with itself, and asked
only to be let alone. Now and then a pope had shown a disposition to
reach out and seize the little republic, but it had always managed to
elude the fatherly clutch. Napoleon respected the rights of San Marino,
and offered to increase its territory. San Marino declined; it had
enough. More would bring trouble. Presenting it with four cannon as
a token of his esteem, the great Napoleon got out of the sunshine of
this Italian Diogenes, and left it in peace. In 1852 the Pope again
hungered for San Marino; but Napoleon III. interfered, and the smallest
and oldest republic in the world was left to its independence in its
mountain home.
CHAPTER XIV
The hope of Austria was now the Archduke Charles, who had so
brilliantly forced the two French armies on the Rhine to retreat. He
was a young man, younger even than Napoleon, being but twenty-five
years of age. The Aulic Council at Vienna decided to pit youth against
youth, and the Archduke was ordered to take chief command in Italy.
Aware of the fact that the Archduke was waiting for reënforcements from
the army of the Rhine, Napoleon decided to take the initiative, and
strike his enemy before the succors arrived.
Masséna was ordered up the Piave, to attack a separate division under
Lusignan, while Napoleon moved against the Archduke on the Tagliamento.
By forced marches, the French reached the river before they were
expected (March 16, 1797). Making as if they meant to force a passage,
they opened upon the Austrians, who awaited them upon the other side,
and gave them a soldierly reception. Then, as if he had suddenly
changed his mind and meant to bivouac there, Napoleon drew back his
troops, and preparations for a meal were made. The Archduke, deceived
by this, drew off also, and returned to his tent. Suddenly the French
sprang to arms, and dashed for the fords. Bernadotte's division led,
and before the Austrians could get into line, the French were safely
over, and prepared for action. The Austrians fought, and fought well;
but they were outnumbered, as they had been outgeneralled, and they
were beaten, losing prisoners and cannon. Masséna, equally successful,
had defeated and captured Lusignan, and was nearing the Pass of Tarvis,
which leads into Germany from the Italian side. The Archduke hurried
to the defence of this vital point, gathering in all his forces as he
went. Taking position in front of the pass, he awaited Masséna. By
forced marches that intrepid soldier, "the pet child of victory," came
up, battle was joined, and desperately contested. Masséna won; and the
road to Vienna was cleared. The Archduke fell back to Villachi; Masséna
waited at Tarvis, hoping to capture an Austrian division which was
advancing to the pass, pursued by General Guieu. Not till the Austrians
reached Tarvis did they perceive that they were enclosed, front and
rear. Demoralized, they surrendered after feeble resistance.
Bernadotte and Sérurier took Gradisca and its garrison, after the
former had sacrificed several hundred men in reckless assault upon the
ramparts.
On March 28, 1797, Napoleon, with the main body of his army, passed
into Corinthia by the Col de Tarvis. Pressing on, he reached
Klagenfurth, from which he wrote to the retreating Archduke a letter
suggesting peace, March 31, 1797. In reply, the Austrian commander
stated that he had no authority to treat. The French continued a
vigorous advance, and near Newmarket the Archduke, having received
four battalions of the long-expected reënforcements, stood and fought.
He was beaten with a loss of three thousand men. He then asked for an
armistice, which was refused. Napoleon would treat for peace, but a
truce he would not grant. At Unzmark the Archduke was again worsted,
and his retreat became almost a rout. On April 2, 1797, the advance
guard of Napoleon was at Leoben, and the hills of Vienna were in sight
from the outposts. Then came officers to ask a suspension of arms to
treat for peace; and the preliminaries of Leoben, after some delays,
were signed.
Many reasons have been suggested for Napoleon's course in tendering
peace when he was apparently carrying all before him. It is said that
he became alarmed at non-coöperation of the armies of the Rhine; again,
that he was discouraged by Joubert's want of success in the Tyrol;
again, that he feared insurrection in his rear. Whatever the motive,
it is difficult to avoid the conclusion that he made a huge mistake.
The French on the Rhine had moved. Desaix was driving one Austrian army
through the Black Forest; Hoche had beaten and was about to surround
the other. Austria's situation was desperate, and Vienna must have
fallen. There are those who suggest that Napoleon hastened to suspend
the war to deprive rival generals, Hoche especially, of a share in his
glory. This is far-fetched, to say the least of it. Month after month
he had done all in his power to get those rival generals to move. To
the Directory he sent appeals, one after another, to order the Rhine
armies to cross and coöperate. He even sent money from his own army
chest; and for fear the funds might lodge somewhere in Paris, he sent
them directly to the Rhine.
Bourrienne is not an authority friendly to Napoleon, and yet Bourrienne
states that when Napoleon, after the truce, received the despatches
announcing the progress of Desaix and Hoche, he was almost beside
himself with chagrin. He even wanted to break the armistice, and his
generals had to remonstrate. This testimony would seem to conclusively
prove that Napoleon offered peace because he had lost hope in the
coöperation which had been promised him, and which was necessary to his
triumph. Singly he was not able to hold disaffected Italy down, guard
a long line of communications, and overthrow the Austrian Empire. The
preliminaries of Leoben and the treaty of Campo Formio will always be
subject of debate. The part which Venice was made to play--that of
victim to the perfidy of Napoleon and the greed of Austria--aroused
pity and indignation then, and has not ceased to be a favorite pivot
for Napoleonic denunciation. Austria was very anxious to hold Lombardy.
Napoleon was determined to hold both Lombardy and Belgium. Venice was
coldly thrown to Austria as compensation, because it was easier to
seize upon decrepit Venetia than to meet another effort of the great
Empire whose courage and resources seemed inexhaustible. Perhaps a
clearer case of political hard-heartedness had not been seen since
Russia, Prussia, and Austria cut up Poland and devoured it.
But after this has been said, let the other side of the picture be
viewed. Venice had undertaken to maintain neutrality, and had not
maintained it. She had allowed both belligerents to take her towns,
use her fortresses, eat her supplies, and pocket her money. Trying to
please both, she pleased neither; and they united to despoil her.
Again, there was the quarrel between the city of Venice and the
Venetian territories on the mainland. Venice had its Golden Book
in which were written the names of her nobles. Aristocrats on the
mainland craved the writing of their names in this Golden Book, and
were refused that bliss; hence heartburnings, which were referred to
Napoleon. He advised the Venetian Senate to write the names in the
book, and the Senate refused. Venice had long been governed by a few
families, and these few had the customary obstinacy and prejudice of a
caste. They treated Venetia simply as a fief--an estate belonging to
the nobles.
Again, republican leaven had been at work throughout Venetia, and
Napoleon had advised the Senate to remodel its mediæval institutions.
Other states in Italy were yielding to the trend of the times, and
Venice should do likewise. The Senate refused, until its consent came
too late to avert its doom.
Again, Napoleon had warned Venice that she was too weak to maintain
neutrality, and had advised her to make an alliance with France. She
had refused.
Again, as Napoleon was about to set out to join his army for the
invasion of Germany, he warned Venice to make no trouble in his rear.
Things he might forgive were he in Italy, would be unpardonable if
done while he was in Germany. Venetia could not, or would not, profit
by this warning. While Napoleon was in Germany, tumults arose in the
Venetian states, and the French in considerable numbers were massacred.
At Verona the outbreak was particularly savage, three hundred of the
French have been butchered, including the sick in the hospitals. To
leave nothing undone which could be done to give Napoleon the excuses
he wanted, a French vessel, which, chased by two Austrian cruisers, had
taken refuge in the harbor at Venice, was ordered to leave (according
to the law of the port), and when she refused, was fired upon. Her
commander and others were killed, and some horrible details aggravated
the offence.
Napoleon may have had his intentions from the first to sacrifice
Venetia. He may have been insincere in offering the weak old oligarchy
the protection of liberal institutions and a French alliance. Letters
of his, inconsistent with each other, have been published. They prove
his duplicity, his craft, his cunning, his callousness; but this was
long after Venice had provoked him.
However cold-blooded Napoleon's treatment of Venice may have been, the
European conscience could not have been as much shocked as royalist
writers pretend, for after Napoleon's overthrow, Venice, which he had
reformed and regenerated, was thrown back as a victim to Austria.
* * * * *
It was a brilliant gathering which surrounded Napoleon and Josephine
in the summer of 1797. Diplomats, statesmen, adventurers, soldiers,
men of science and literature, thronged Milan, and paid court at
beautiful Montebello, the palatial country-seat where Napoleon had
taken up his residence after the preliminaries of Leoben. Many subjects
of importance needed his thought, his fertile resources, his ready
hand. His republics needed guidance, the affairs of Genoa and Venice
were unsettled, German princelets from along the Rhine had a natural
curiosity to know just who they belonged to, and details of the coming
treaty of Campo Formio needed to be worked out. It was a busy and a
glorious season for Napoleon. He stood on the highest of pinnacles,
his renown blazing to the uttermost parts of Europe; and to him was
drawn the enthusiastic admiration which turns so warmly to heroes
who are young. He had, as yet, made few enemies. All France was in
raptures over him; even Austrians admired him. The aristocrats, lay and
clerical, in Italy doubtless wished him dead; but the masses of the
people looked up to him in wonder and esteem. Of Italian extraction, he
spoke their language, knew their character, despised it, imperiously
dominated it, and was therefore loved and obeyed.
Miot de Melito, an unfavorable witness, declares that Napoleon already
harbored designs for his own sovereignty, and made no secret thereof.
"Do you think I am doing all this for those rascally lawyers of the
Directory?" He may possibly have said so, but it is not probable. A
man like Napoleon, meditating the seizure of power and the overturn of
government, does not, as a rule, talk it to the Miots de Melito. Had
Napoleon had any such clearcut design as Miot records, he would not
have allowed the wealth of Italy to roll through his army chest, while
he himself was left poor. Like Cæsar, he would have returned laden with
spoil, to be used in furthering his plans. Napoleon doubtless took
something for Napoleon out of the millions which he handled, but the
amount was so inconsiderable that he keenly felt the burden of debt
which Josephine had made in furnishing his modest home in Paris. And
when the time _did_ come to overturn the "rascally lawyers," he had
to borrow the money he needed for that brief campaign. No; the simple
truth is that Napoleon indulged no sordid appetites in his Italian
campaign. He made less money out of it than any of his lieutenants,
than any of the army contractors, than any of the lucky spoilsmen who
followed in his wake. If he had harbored, the designs attributed to
him by Miot, it was obviously a mistake for him to have declined the
$800,000 in gold secretly offered him by the Duke of Modena. At St.
Helena he uttered something which sounds like an admission that, in
view of his subsequent necessities in Paris, he should have accepted
the money. For wealth itself Napoleon had no longing--glory, power,
fame, all these stood higher with him. The 7,000,000 francs Venice
offered were as coolly refused as the smaller sum tendered by Modena,
and the principality offered by the Emperor of Germany.
* * * * *
The elections of 1797 were not favorable to the Directory. Many
royalists found seats in the Assembly, and the presiding officer of
each legislative body was an opponent to the government. Two of the
Directors, Carnot and Barthélemy, joined the opposition.
Openly and boldly, the malcontents, including royalists,
constitutionals, and moderates, declared their purpose of upsetting
the Directory. Barras, Rewbell, and Larévellière were united, and
Barras still retained sufficient vigor to act promptly at a crisis.
Seeing that bayonets were needed, he called on Hoche for aid. Hoche was
willing enough, but he involved himself in a too hasty violation of
law, and became useless. Then Barras turned to Napoleon, and Napoleon
was ready. Angry with the legislative councils for having criticised
his high-handed conduct in Italy, and feeling that for the present
his own interest was linked with that of the Directory, he did not
hesitate. He sent Augereau to take command of the government forces
at Paris, and Augereau did his work with the directness of a bluff
soldier. "I am come to kill the royalists," he announced by way of
public explanation of his presence in town. "What a swaggering brigand
is this!" cried Rewbell when he looked up from the directorial chair
at Augereau's stalwart, martial figure. Augereau marched thousands of
troops into Paris at night, seized all the approaches to the Tuileries
where the councils sat, and to the guard of the councils he called out
through the closed gates, "Are you republicans?" and the gates opened.
Augereau broke in upon the conspirators, seized with his own hand
the royalist commander of the legislative guard, tore the epaulettes
from his shoulders, and threw them in his face. Roughly handled like
common criminals, the conspirators were carted off to prison. Carnot
fled; Barthélemy was arrested at the Luxembourg palace. With them
fell Pichegru, the conqueror of Holland. While still in command of
the republican army, he had entered into treasonable relations with
the royalists, and had agreed to use his republican troops to bring
about a restoration of the monarchy. This plot, this treason, had not
been known when Pichegru, returned from the army, had been elected to
one of the councils and made its president. Moreau had captured the
correspondence from the Austrians, and had concealed the facts. After
Pichegru's arrest by Augereau, the secret of the captured despatches
came to light. Moreau himself made the report, and the question
which sprang to every lip was, Why did he not speak out before? This
universal and most natural query became the first cloud upon the career
of the illustrious Moreau. As Napoleon tersely put it, "By not speaking
earlier, he betrayed his country; by speaking when he did, he struck
a man who was already down." After having saved the government, as
Augereau fancied he alone had done, that magnificent soldier's opinion
of himself began to soar. Why should he not become a director, turn
statesman, and help rule the republic? Very influential people, among
them Napoleon and all the Directors, were able to give good reasons
to the contrary, and Augereau was compelled to content himself with
remaining a soldier. Although he bragged that he was a better man than
Bonaparte, he yielded to the silent, invisible pressure of the little
Corsican, and he went to take command of the unemployed army of the
Rhine. In a few months the same fine, Italian hand transferred him to
the command of the tenth division in Perpignan, where he gradually, if
not gracefully, disappeared from the political horizon.
The negotiation for final peace between Austria and France continued
to drag its slow length along. Diplomats on either side exhausted
the skill of their trade, each trying to outwit the other. How many
crooked things were done during those weary months, how many bribes
were offered and taken, how many secrets were bought and sold, how much
finesse was practised, how many lies were told, only a professional
and experienced diplomatist would be competent to guess. Into all
these wire-drawn subtleties of negotiation Napoleon threw a new
element,--military abruptness, the gleam of the sword. Not that he
lacked subtlety, for he was full of it. Not that he was unable to
finesse, for he was an expert. Not that he scorned to lie, for he
delighted in artistic deception. But on such points as these the
veteran Cobentzel and the other old-time diplomats could meet him on
something like an equality. To throw in a new element altogether,
to hide his perfect skill as a machinator under the brusque manners
of a rude soldier, was to take the professionals at a disadvantage.
Just as the Hungarian veteran had complained that Napoleon would not
fight according to rule, Cobentzel and his band were now embarrassed
to find that he would not treat by established precedent. Wearied with
delays, indignant that they should threaten him with a renewal of the
war, and determined to startle the antiquated Austrian envoys into a
decision, Napoleon is said to have sprung up from his seat, apparently
in furious wrath, exclaiming, "Very well, then! Let the war begin
again, but remember! I will shatter your monarchy in three months, as
I now shatter this vase," dashing to the floor a precious vase which
Catherine II. of Russia had given Cobentzel.
This story, told by so many, is denied by about an equal number.
Cobentzel himself contradicted it, but he makes an admission which
almost amounts to the same thing. He says that Napoleon became
irritated by the delays, worked himself into a passion, tossed off
glass after glass of punch, became rude to the negotiators, flung out
of the room, and required a good deal of pacification at the hands of
his aides. Says Cobentzel: "He started up in a rage, poured out a flood
of abuse, put on his hat in the conference room itself" (an awful thing
to do!), "and left us. He behaved as if he had just escaped from a
lunatic asylum."
Between this Austrian admission and the Austrian denial the substantial
difference is not great. Reading between Cobentzel's lines, one sees
that the brutal young soldier ran over Austria's delicate old diplomat
just as he had been running over a lot of Austria's delicate old
generals.
The next day after this violent scene, the treaty of Campo Formio was
signed. By its terms Austria ceded Lombardy, Belgium, and the German
principalities on the Rhine. It recognized the Italian republic; the
Cisalpine, composed of Lombardy, Modena, Ferrara; the Romagna, Mantua,
Massa-e-Carrara; the Venetian territory, west of the Adige and the
Valtelline. It also recognized the Ligurian republic, recently formed
by Napoleon out of Genoa and its states. France kept the Ionian Isles,
and the Venetian factories opposite on the mainland. To Austria was
given the Italian lands eastward from the Adige. Within this concession
was embraced the venerable city of Venice.
In the treaty of Campo Formio, Napoleon insisted that Austria should
liberate the prisoner of Olmutz, Lafayette, who had been lying in a
dungeon since 1793.
To regulate the redistribution of German territory, made necessary by
the treaty, a congress was to be convened at Rastadt. It may as well be
stated in this place that the congress met, remained in session a long
while, and could not reach an agreement. Napoleon having gone to Egypt,
Austria renewed the war, broke up the congress, and murdered the French
envoys.
The Directors were strongly opposed to the terms of the Campo Formio
treaty, but they were powerless. Napoleon disregarded their positive
instructions, relying for his support upon the enthusiasm with which
the French would hail peace. His calculations proved correct. The
nation at large welcomed the treaty as gladly as they had done his
victories. It seemed the final triumph and permanent establishment of
the new order. Against so strong a current in Bonaparte's favor, the
Directory did not venture to steer.
Setting out for Paris, November 17, 1797, Napoleon passed through
a portion of Switzerland, where he was encouraging the democratic
movement which led to the formation of the Helvetian republic. At
Geneva and Lausanne he was given popular and most hearty ovations. He
put in appearance at Rastadt, where the congress was in session, and
remained just long enough to exchange ratifications of the Campo Formio
treaty with Cobentzel; and to hector, insult, and drive away Count
Fersen, the old friend of Marie Antoinette. Count Fersen had come as
Swedish envoy; and to Napoleon his presence seemed improper, as perhaps
it was.
CHAPTER XV
Military critics agree that the Italian campaign was a masterpiece; and
many say that Napoleon himself never surpassed it. At no other time was
he perhaps quite the man he was at that early period. He had his spurs
to win, his fame to establish. Ambition, the thirst for glory, his
youth, his intense activity of mind and body, the stimulus of deadly
peril, formed a combination which did not quite exist again. To the
last a tremendous worker, he probably never was on the rack quite as he
was in this campaign. In Italy he did all the planning, and saw to all
the execution. He marched with his troops night and day, fair weather
and foul. He shared the dangers like a common soldier, pointing cannon,
leading charges, checking retreat, taking great risks in reconnoitring.
He went without food, sleep, or shelter for days at a time. Horses
dropped under him, some from wounds, some from fatigue. He marched
all night before the battle of Rivoli, directed his forces during the
battle, galloped himself to bring up support at critical points; and
then, at two or three in the afternoon, when Alvinczy was beaten, he
set out to the relief of Sérurier, marched again all night, and again
directed a battle--that of La Favorita. This was but one instance;
there were dozens of others, some even more remarkable. For Napoleon
never seemed to tire: mind and body were like a machine. He was thin,
looked sickly, and indeed suffered from the skin disease caught from
the dead cannoneer at Toulon; but his muscles were of steel, his
endurance phenomenal, his vitality inexhaustible. The impression he
made upon one close observer at this period was condensed in the words,
"the little tiger."
[Illustration: JOSEPHINE IN 1800
From a pastel by P. P. Prud'hon]
Inexorably as he marched and fought his men, he as carefully looked
after their proper treatment. He was tireless in his efforts to
have them shod, clothed, fed as they should be; when sick or
wounded, he redoubled his attention. Oppressed as he was by work and
responsibility, he found time to write letters of condolence to the
bereaved, those who had lost husbands, sons, or nephews in his service.
Quick to condemn and punish negligence, stupidity, or cowardice, he was
as ready to recognize and reward vigilance, intelligence, and courage.
He cashiered General Vallette in the field, but Rampon, Murat, Junot,
Marmont, Bessières, Lannes, and hundreds of others he picked out of the
ranks and put in the lead. "I am ashamed of you. You no longer deserve
to belong to the army. Let it be written on your colors, 'They no
longer belong to the army of Italy.'" Thus in stern tones he spoke to
Vallette's troops, who had done too much running as compared to their
fighting. The soldiers were in despair. Some groaned; some wept; all
were ashamed. "Try us again, General. We have been misrepresented. Give
us another chance, General!" Napoleon softened, spoke as his matchless
tact suggested, and in the battles that followed no troops fought
better than these.
Complete genius for war Napoleon displayed in the campaign:
masterly plans, perfection of detail, penetration of the enemy's
plan, concealment of his own, swift marching, cautious manœuvring,
intrepidity in fighting, absolute self-possession, sound judgment,
inflexible will power, capacity to inspire his own army with confidence
and the enemy with almost superstitious terror.[3] An incident occurred
after the battle of Lonato, attested by Marmont and Joubert, which
reads like fiction. Napoleon with twelve hundred men was at Lonato
making arrangements for another battle. An Austrian column of four
thousand, bewildered in the general confusion, strayed into the
neighborhood, and were told by some peasants that only twelve hundred
French were in the place. The Austrians advanced to capture this band
and sent a summons. Napoleon ordered that the herald should be brought
in blindfolded. When the bandage was removed, the herald found himself
in the presence of Napoleon, around whom stood his brilliant staff.
"What means this insolence? Demand my surrender in the midst of my
army? Go tell your commander that I give him eight minutes to lay down
his arms." And the Austrian commander had time to his credit when his
surrender of his four thousand had been made.
[3] It was a curious remark Napoleon made at St. Helena, that
his whole military career had taught him nothing about a
battle which he did not know at the time he fought his
first; subsequent campaigns taught him no more than the
first.
It was at this period that Napoleon developed his wonderful fascination
of manner. As he could intimidate by frowns, harsh tones, fierce looks,
and cutting words, he could charm with the sweetest of smiles, the
kindest of glances, the most caressing words. If he wished to please,
he could, as a rule, do so; if he wished to terrify, it was rarely
he failed. Already there were hundreds of young officers who swore
by him, lived for his praise, and were ready to die for him. Muiron
had done so; Lannes, Junot, Marmont, Bessières, Berthier, Murat, were
as ready. As to the army itself, Cæsar had never more completely the
heart of the Tenth Legion than the young Napoleon that of the army
of Italy. No higher reward did his soldiers crave than his words of
praise. His proclamations intoxicated them like strong wine. They were
ready to dare all, endure all, to please him, win his smile, wear his
splendid tribute. "I was at ease; the Thirty-second was there;" and the
delighted regiment embroidered the words on its flag. "The terrible
Fifty-seventh" were proud to see on their banner that battle name given
them by their "Little Corporal"; just as, at Toulon, he had kept the
most exposed of the batteries filled with men by posting the words,
"The Battery of those who are not afraid."
Planning, executing, marching, fighting, organizing new states,
Napoleon was still the ardent lover. Josephine he never neglected.
Courier sped after courier, bearing short, hasty, passionate
love-letters to Josephine. He was in all the stress and storm, often
cold, drenched by wintry rains, pierced by wintry winds, hungry,
overwhelmed with work and care, yet not a day did he forget his bride.
She was lapped in luxury at Paris,--warmth, light, pleasure, joyous
ease, and companionship about her; and she laughed at the love-letters,
thinking them wild, crude, extravagant. "Bonaparte is so queer!"
In June, 1796, Napoleon was made to believe that Josephine was in
a fair way to become a mother. His raptures knew no bounds. The
letter which he then wrote her is certainly the most ardently tender,
furiously affectionate scrawl ever penned. It drives in upon the
impartial reader the conviction that this strange man possessed the
uxorious and paternal spirit in its most heroic form; and that had
he been fitly mated, his developing character would have reached a
perfect harmony and equilibrium. It was in him to have found exquisite
enjoyment in home-life; it was in him to have bent caressingly over
wife and child, to have found at the fireside repose and happiness.
As it was, his marriage was one source of his ruin. In Josephine he
found no loyalty, no sympathy of the higher sort, and she bore him no
children. She froze his hot affection with that shallow amiability
which smiled on him as it smiled on all the others. She outraged his
best feelings by her infidelities. She destroyed his enthusiasm, his
hopes, his ideal of pure and lofty womanhood. He waited on her too
long for children. His character, undeveloped on that side, hardened
into imperial lines, until he himself was the slave of political
necessities. The second marriage, and the son he idolized, came too
late.
Napoleon, the lover-husband, who had quitted his bride in forty-eight
hours after the marriage, repeatedly implored her to join him at
headquarters. Josephine had no inclination to obey: Paris was too
delightful. Upon various excuses she delayed, and it was not till July,
1796, that she reached Italy.
Arrived in Milan, she was rapturously welcomed by Napoleon, and found
herself treated by the Italians almost as a queen. She was lodged in
a palace, surrounded with luxury, and flattered by the attentions of
thronging courtiers. She moved from place to place as the months
passed on, shared some of the dangers of the campaign, and by her
grace, amiability, and tact made many a conquest useful to her
many-sided lord. One conquest she made for herself, and not for her
lord. A certain officer named Hypolite Charles, attached to Leclerc's
staff, was young, handsome, gallant,--_such_ a contrast to the wan,
wasted, ungainly, skin-diseased Napoleon! Josephine looked upon Charles
and found him pleasing. The husband, engrossed by war and business,
was often absent. Charles was not engrossed with war, was present, and
was not a Joseph. Here was youth, inclination, opportunity--and the
old result. Scandal ensued, Napoleon's sisters made shrill outcry, the
husband heard the story, and Charles joined the absent. It was thought
for a while that Napoleon would have him shot, but apparently there was
some invincible reason to the contrary. He went to Paris and obtained a
good position--rumor said by the influence of Josephine.
If Napoleon was imperious at school, a tyrant in his childhood,
self-willed and indomitable when out of employment and threatened with
starvation, how were the Directors to curb him now? Just as natural as
it seemed to be for him to command when among soldiers, it was for him
to treat king, duke, and pope as equals, lay down the law of national
relations, and create new governments in Italy. He assumed the power
as a matter of course, and his assumption of authority was nowhere
questioned. "Bless me! I was made that way," exclaimed Napoleon. "It is
natural for me to command."
The Directors would gladly have dismissed him, for they doubted,
disliked, and feared him; but they dared not face him and France
on such an issue. He rode rough-shod over their policies and their
instructions, and they could do nothing. They had thought of sending
Kellermann, had actually appointed him to share the command; Napoleon
flatly said the command could not be shared, and Kellermann had to go
elsewhere.
They sent General Clarke as agent to manage negotiations, treaties,
and to supervise matters generally. Napoleon said to Clarke, "If you
have come here to obey me, well and good; but if you think to hamper
me, the sooner you pack up and leave, the better." Clarke found himself
completely set aside and reduced to nothing. The Directory itself,
overawed by Napoleon's tone, wrote Clarke, in effect, that he must not
oppose the imperious commander-in-chief.
There were official commissioners in the field, Salicetti and others.
How powerful and dreaded these commissioners had formerly been! Had not
Napoleon courted them and their wives with all the haughty cajolery of
a proud nature which stoops to conquer? Now he would stoop no more; he
had conquered. Salicetti and company did the stooping; and when, at
length, their doings displeased the conqueror of Italy, he ordered them
off.
The Milanese, historic Lombardy, was the first province which he
fashioned into a republic. Here he met Count Melzi, almost the only
_man_ Italy could boast. Working with Melzi and others, the Transpadane
republic was established--the child of Napoleon's brain and energy.
Afterward as liberalism spread, and the papal yoke was thrown off,
Bologna, Reggio, Ferrara, clamored for republican institutions. The
dream of Italian unity began to be a reality.
Modena caught the infection; its miserly duke had already run away,
carrying his treasure. He had failed to pay 500,000 francs of his fine;
and, seizing upon this pretext, Napoleon granted the petitions of the
people, grouped Modena with the papal legations, and gave organization
under a liberal constitution to the Cispadane republic. At a later day
the two republics were united into one, and became the Cisalpine.
In the wake of the victorious army skulked the hungry civilian, the
adventurer seeking gain, the vultures grouping to the carcass. It was
feast-day for the contractor, the speculator, the swindler, the robber,
the thief. It threw Napoleon into rage to see himself surrounded by a
horde of imitators, puny plunderers doing on a small scale, without
risking battle, what he did in grand style, after a fair fight.
Soldiers who brought scandal on the army by too notorious pillage he
could shoot, and did shoot; he resented the limitations of power which
kept the civilian buccaneers from being shot.
An indirect result of Napoleon's victories in Italy was the loss
of Corsica to England. The rule of Britannia had not pleased the
Corsicans, nor been of any special benefit to England. Toward the close
of 1796 the islanders revolted, and the English withdrew. Corsica
became again a province of France.
CHAPTER XVI
On December 5, 1797, Napoleon returned to Paris. With studious eye for
effect, he adopted that line of conduct most calculated, as he thought,
to preserve his reputation and to inflame public curiosity. He was
determined not to stale his presence. Making no display, and avoiding
commonplace demonstrations, he doffed his uniform, put on the sober
dress of a member of the Institute, to which he was elected in place of
Carnot, screened himself within the privacy of his home, and cultivated
the society of scholars, authors, scientists, and non-combatants
generally. When he went out, it was as a private citizen, his two-horse
carriage unattended by aides or escort. He demurely attended the
meetings of the Institute, and on public occasions was to be found in
his place, in his class, among the savants, just as though he had set
his mind now on literary matters and was going to write a book. His
brother Joseph gave it out that Napoleon's ambition was to settle down
and be quiet, to enjoy literature, friends, and, possibly, the luxuries
of the office of Justice of the Peace. It must have been a queer sight
to have seen the little Corsican dress-parading as a guileless man
of letters; it is very doubtful whether many were deceived by his
exaggerated modesty. Those who were in place and power, the men whom he
would have to combat and overcome, were not for a moment duped. They
suspected, dreaded, and watched him. Prepare for him they could not,
for they had not the means. He had said nothing and done nothing which
they had not indorsed; with hearts full of repugnance, with faces more
or less wry, they had sanctioned even when their instructions had been
disobeyed. They could not seize him by brute force, or put him out of
the way. They were too weak; he too strong. He was the idol of soldiers
and civilians alike; the Directors were not the idols of anybody.
They could not even have him poisoned, or stabbed, for he was on his
guard against that very thing. Soon after his return to Paris he had
received warning of a plot to poison him; he had caused the bearer of
the note to be accompanied by a magistrate to the house of the woman
who had furnished the information, and she was found lying dead on the
floor, her throat cut and her body mutilated. The would-be murderers
had, doubtless, discovered her betrayal of them, and had in this manner
taken vengeance and assured their own safety. After such an occurrence,
Napoleon was not the man to be caught napping; and it was noticed that
at the official banquets to which he was invited he either ate nothing,
or slightly lunched on wine and bread brought by one of his aides.
The Directory gave him, in due time, a grand public reception at the
Luxembourg, which was attended by immense numbers, and which was
as imposing as the pomp of ceremony and the genuine enthusiasm of
the people could make it. But the part played by the Directory and
Talleyrand was theatrically overdone, and gave a tone of bombast and
insincerity to the whole.
What now must Napoleon do? There was peace on the Continent; he was
too young for a place in the Directory, and if he remained in Paris
too long, France would forget him. This was the reasoning of Napoleon,
the most impatient of men. Evidently the reasoning was unsound; it was
dictated only by his feverish, constitutional need of action. There was
no danger of his sinking out of notice or importance in France. There
was the danger of his being identified with a party, but even this
peril has been exaggerated. Astute and coldly calculating as he was,
the party he would have chosen, had he seen fit to choose one at all,
would probably have been the strongest, and political success comes to
that in the long run.
He had been too impatient in Corsica in his earlier struggles; he
had there alienated the wise and lovable Paoli, who wanted to be his
friend, but could not sympathize with his too violent, too selfishly
ambitious character. He had been too impatient to get on in France, and
had been perilously near losing his head as a terrorist in the fall
of Robespierre. Too anxious for social recognition and independent
military command, he had fallen into the snares of Barras and the shady
adventuress of whom the libertine Director was tired, and had rushed
into a marriage which proved fatal to him as a man and a monarch. The
same feverish haste was again upon him, and was to continue to be upon
him all the days of his life, until his final premature rush from Elba
was to lead him, through the bloody portals of Waterloo, to his prison
on the bleak rock of St. Helena.
How could a few months of quiet in Paris have tarnished his fame? Had
he not seen the heart of liberalism throughout all Europe warm to
Paoli,--the time having come,--although the patriot exile had been
sitting quietly at English firesides for twenty-one years?
Who in France was likely to outstrip Napoleon in one year, two years,
ten years? Hoche was dead, Moreau in disgrace, Jourdan under the cloud
of defeat, Augereau on the shelf, Carnot an exile, Pichegru banished.
In the Directory there was not a man who could give him the slightest
concern.
But to Napoleon it seemed absolutely necessary that he must be actively
engaged--publicly, and as master. He could not get the law changed so
that he could become a director; he could not quite risk an attack in
the Directory. _That_ pear was not yet ripe. He had wished to be sent
to Rastadt to straighten matters there, but the Directory chose another
man. Napoleon, resenting the slight, threatened, once too often, to
resign. A Director (some say Rewbell, others Larévellière) handed him a
pen, with the challenge, "Write it, General!" Moulins interposed, and
Napoleon beat a retreat, checkmated for the time.
Apparently, as a last resort, the expedition to Egypt was planned, both
Napoleon and the Directory cordially agreeing upon one thing--that it
was best for him to leave France for a while.
The attack on Egypt suggested itself naturally enough as a flank
movement against England. The idea did not originate with Napoleon; it
was familiar to the foreign policy of France, and had been urged upon
the Bourbon kings repeatedly. With his partiality for the East, whose
vague, mysterious grandeurs and infinite possibilities never ceased
to fascinate him, the oft-rejected plan became to Napoleon a welcome
diversion. Veiling his design under the pretence of a direct attack
upon England, he bent all his energies to the preparations for the
invasion of Egypt. Nominally belonging to Turkey, the ancient ally
of France, Egypt was in fact ruled by the Mamelukes, a military caste
which had, in course of time, evolved from the personal body-guard of
Saladin. The reign of the Mamelukes was harsh and despotic; they paid
little respect to religion, and none to law; and Napoleon thought that
by telling the Sultan he would overthrow the Mamelukes in the Sultan's
interest, while he assured the subject Egyptians that he came to
liberate them from Mameluke tyranny, he would deceive both Sultan and
Egyptians. As it happened, he deceived neither.
It was a part of the scheme agreed on by Napoleon and the Directors
that Talleyrand should go to Constantinople and gain over the Sultan
to neutrality, if to nothing more favorable. With this understanding,
Napoleon gathered up the best generals, the best troops, the best
vessels, swept the magazines, cleaned out the directorial treasury, and
even borrowed from the Institute its best savants, and weighed anchor
at Toulon, May 18, 1798, for Alexandria. The wily Talleyrand did not go
to Turkey, had apparently never intended to go, and that part of the
plan failed from the beginning. English diplomats took possession of
the Sultanic mind; and what they saw, the heir of the Prophet saw. To
save herself from a movement which threatened her in the East, Great
Britain warmed to the infidel, forgot crusading vows and traditions,
guided infidel counsels, supplied infidel needs, and aimed infidel
guns. So that from the day he set sail, Napoleon had against him all
the resources of England, all the power of Ottoman arms, all the
strength of Mameluke resistance, all the discouragement of native
Egyptian hostility.
[Illustration: NAPOLEON
From the painting by Paul Delaroche entitled "General Buonaparte
crossing the Alps"]
To reach Egypt at all it was necessary that he should run the extreme
risk of encountering the British fleet. By the victory England had
won over the Spanish allies of France off Cape St. Vincent (February,
1797), and over the Dutch at Camperdown (October, 1797), France was
left without naval support. In a sea-fight between herself and England,
all the advantage would have been with her foe. Conscious of this,
Nelson did his utmost to come upon Napoleon during his voyage, and the
two fleets passed each other once in the night; but Napoleon's rare
luck favored him, and Nelson missed his prey.
The capture of Malta was a part of Napoleon's plan. This island
fortress belonged to the Knights of St. John, a belated remnant of
the ancient orders of chivalry, created for the purpose of retrieving
Palestine from the infidel. These soldiers of the Cross had fallen
upon evil days and ways; their armor very rusty indeed, their banners
covered with dust, their spurs very, very cold. In a world which had
seen a new dispensation come, the knights were dismally, somewhat
ludicrously, out of place. Asked, What are you doing here? What do you
intend to do? What is your excuse for not being dead? the knights would
have been stricken dumb. No intelligible reply was possible. Camped
there upon a place of strength and beauty, a fortress girdled by the
Mediterranean, they were, in theory, Christendom's outpost against
the infidel. Christendom, in theory, was yet intent upon raising
up champions who would tread in the steps of Godfrey, of Tancred,
of Richard Cœur de Lion. In theory, Christendom was never going to
rest till the tomb of Jesus had been redeemed, till the shadow of
Mahomet should be lifted from the Holy Land. And so it happened that
the knights had stopped at Malta, long ages ago, resting upon their
arms, until such time as Christendom should rouse itself and send
reënforcement. The time had never come. The knights, they waited; but
the crusader of Europe had gone home to stay. Once and again, as the
centuries crept slowly by, the Church had turned in its sleep and
mumbled something about the tomb of Christ; but the Church was only
talking in its sleep, and the knights had continued to wait. A king,
now and then, suddenly awakened to the fact that he was a very great
scoundrel, must finally die, would probably go to hell, and therefore
needed to redeem himself at the expense of the infidel, swore a great
oath to renew the crusades; but such vows bore no fruit; the spasm of
remorse passed over, and the knights continued to wait. Really, it
was not so hard upon them. They had a royal home, a royal treasury, a
royal standing and a sacred. They lived a pleasant life; they doffed
iron armor, and wore silks, velvets, and other precious stuffs more
congenial to the flesh than metallic plates. They came to love such
things as good eating, joyous entertainments, the smiles and the favors
of fair ladies, and the sweetness of doing nothing generally.
Malta being defended by such decadent champions, it was easily captured
by such a man as Napoleon Bonaparte. There was, perhaps, bribery; there
was, certainly, collusion, and the resistance offered was but nominal.
General Caffarelli probably voiced the general sentiment when he said,
looking around at the vast strength of the fortress, "It is lucky we
had some one to let us in."
Leaving a garrison under Vaubois to hold the place, Napoleon again set
sail for Egypt.
Nelson was flying hither and thither, on the keenest of hunts, hoping
to pounce upon the crowded vessels of the French, and to sink them.
Storms, fog, bad guessing, and Napoleonic luck fought against the
English, and they missed the quarry completely. Napoleon hastily landed
near Alexandria, July 2, 1798, marched upon the city, and easily took
it. After a short rest, the army set out by the shortest route for
Cairo. The sun was terribly hot, the desert a burning torment, water
it was almost impossible to supply, food failed, and the skirmishes of
the enemy from behind sandhills, rocks, or scraggy bushes harassed the
march, cutting off every straggler. Bitterly the soldiers complained,
contrasting this torrid wilderness to the fertile beauty of Italian
plains. Even the generals became disheartened, indignant, almost
mutinous. Men like Murat and Lannes dashed their plumed and braided
hats on the ground, trampled them, and damned the day that had brought
them to this barren Hades.
The common soldiers bitterly recalled Napoleon's promise that each of
them should make enough out of the campaign to buy seven acres of land.
Was this desert a fair sample of the land they were to get? If so, why
the limit of seven acres?
The trying march was over at last, the Nile was reached, and then
came the relief of battle and easy victory. The Mamelukes were great
horsemen, the best in the world, perhaps; but they had no infantry
and no artillery worth the name. In the hands of Napoleon they were
children. Battle with Mamelukes was target practice, during which
French marksmen, in hollow square, shot out of their saddles the
simple-minded Mamelukes, who fancied that they could do everything with
horses.
In all of the battles which took place, the tactics of the French
were the same: "Form square: savants and asses to the centre." Then,
while the baggage, the learned men, and the long-eared donkeys rested
securely within the lines, a steady fire of musketry and cannon emptied
the saddles of the heroes of the desert.
To see the Mamelukes come thundering on to the attack, was magnificent;
to see them drop in the sand without having been able to reach the
French, was pitiful.
After a skirmish at Shebreis, in which the Mamelukes were driven off
without any difficulty (July 13), came the encounter known as the
Battle of the Pyramids (July 21), chiefly remembered now as that in
which Napoleon dramatically exclaimed to his troops as they were being
made ready for the struggle, "Soldiers, from yonder pyramids forty
centuries look down upon you!" The telescope had revealed to him the
fact that the artillery of the enemy consisted of guns taken from
their flotilla on the river. These guns were not on carriages, like
field artillery, and therefore they could not be moved at will during
battle. This suggested to him a change in his own dispositions. A
portion of his army being left to deal with the stationary artillery
and the infantry which manned the feeble, sand-bank intrenchments,
he directed the other to march out of the range of the guns, for
the purpose of throwing against the Mameluke horse his own cavalry,
supported by infantry and artillery. Murad Bey, the commander-in-chief
of the opposing army, seized the moment when this change was being made
by Napoleon to launch against him a mass of seven thousand Mameluke
horse. This mighty host struck the division of Desaix when it was
in motion, and therefore unprepared for cavalry. For an instant the
French, at least of that column, were in peril. So quickly, however,
did the veterans of Desaix form squares, so quickly did Napoleon see
the point of danger and send relief, that the battle was never in
real doubt. The camp of the Arabs was stormed, the Mameluke cavalry
slaughtered; and, inflicting a loss computed at ten thousand on the
enemy, the French had but a score or two killed and one hundred and
twenty wounded.
The Mameluke power was shattered by the Battle of the Pyramids, and the
conquest of Egypt was practically achieved. For some days Frenchmen
fished the Nile for dead Mamelukes, to secure the wealth which those
warriors carried on their persons.
Arrived in Cairo, Napoleon did his utmost to assure the permanence
of his triumph. He caused the religion, the laws, the customs of the
country, to be respected. Pursuing his policy of trying to deceive
the Mahometans, he proclaimed that the French were the true champions
of the Prophet; that they had chastised the Pope, and conquered the
Knights of Malta; therefore the people of Egypt should be convinced
that they were the enemies of the Christians.
"We are the true Mussulmans!" read the proclamation. "Did we not
destroy the Pope because he had preached a crusade against the
Mahometans? Did we not destroy the Knights of Malta because they said
that God had directed them to fight the followers of Mahomet?"
He cultivated the influential men of the country, and encouraged the
belief that he himself might become a Mussulman. In truth, Napoleon
admired Mahomet greatly, and he never shrank from saying so, then or
afterward. In the classification of the books of his private library,
made in his own writing, he grouped under the same head the Bible, the
Koran, the Vedas, and Mythology, and Montesquieu's _Spirit of Laws_.
These he enumerated in the class of _Politics and Morals_. He reminded
his soldiers that the Roman legions had respected all religions. He
did not remind them that Roman rulers had considered all religions as
equally useful for purposes of government; nor that Roman philosophers
had regarded them all as equally sons and daughters of that primeval
pair, Fear and Fraud--fear of the unknown, and the fraud which
practises upon it.
Napoleon found that Mahometan priests were as eager to convert him
as Christian priests had been to capture Constantine and Clovis. In
the one case as in the other, the priests were willing to compromise
the creed to gain the convert. Napoleon did not quite join the
faithful himself, but he approved of General Menou's apostasy, and he
ostentatiously observed the Mahometan festivals.
Both Napoleon and Bourrienne denied, as others assert, that he went
into the mosque, sat cross-legged on the cushion amid the faithful,
muttered Koran verses as they did, and rolled head and body about as a
good Mussulman should. If he did not do so it was because he thought,
as a matter of policy, that the act would not compensate him for the
trouble and the ridicule. He afterward did just about that much for the
Christian religion; and faith had no more to do with his conduct in the
one case than in the other.
As he went farther with the Jacobins than it was pleasant to remember,
so he probably went farther with the Mahometans than he cared to
admit; for he certainly prevailed upon the priesthood to do that which
was forbidden by the Koran unless he was a convert. They officially
directed the people to obey him and pay him tribute. Nor is there
any doubt that the leaders among the priests liked him well enough,
personally, to watch over his personal safety. General Kléber, who
succeeded him in command, neglected to pay the chiefs those attentions
Napoleon had lavished upon them, and in turn they neglected him. To
this, perhaps, his assassination was due.
Regarding Egypt as a colony to be developed, rather than a conquest
to be despoiled, Napoleon devoted every attention to civil affairs.
He reorganized the administration, conforming as nearly as possible
to established customs. He set up a printing-press, established
foundries and manufactories, planned storage dams and canals to add to
the cultivable soil, organized an institute, and started a newspaper.
He sent his savants abroad to dig, delve, excavate, explore, map the
present and decipher the past of Egypt. Napoleon himself used his
leisure in visiting historic places and making plans for the material
progress of the benighted land. He discovered traces of the ancient
canal connecting the Nile with the Red Sea, and formed the resolution
of reopening it. He himself located the lines for new canals. He
crossed the Red Sea ford which the Israelites used in fleeing from
bondage, and, staying too long on the opposite shore, was caught by the
rising tide, and came near meeting the fate of Pharaoh and his host.
More self-possessed than Pharaoh, Napoleon halted when he realized his
peril, caused his escort to form a circle around him, and each to
ride outward. Those who found themselves going into deeper water drew
back, followed those who had found fordable places; and, by this simple
manœuvre, he deprived needy Christendom of a new text and a modern
instance.
While on the farther shore Napoleon visited the Wells of Moses,
and heard the petition of the monks of Sinai. At their request, he
confirmed their privileges, and put his name to the charters which bore
the signature of Saladin.
A terrible blow fell upon him in August when Nelson destroyed the
French fleet in the famous battle of the Nile. There is doubt as to
who was to blame for this calamity. Napoleon cast it upon Brueys, the
French admiral who lost the battle; and Brueys, killed in the action,
could not be heard in reply. He had drawn up his ships in semicircle
so close to the shore that he considered himself comparatively safe,
protected as he was by land batteries at the doubtful end of his line.
But Nelson, on the waters, was what Bonaparte was on land--the boldest
of planners and the most desperate of fighters. He came up at sunset,
and did not wait till morning, as Brueys expected. He went right to
work, reconnoitred his enemy, conceived the idea of turning his line,
getting in behind with some of his ships, and thus putting the French
between two fires. The manœuvre was difficult and dangerous, but
succeeded. Nelson rammed some of his ships in on the land side of the
amazed Brueys, who had made no preparations for such a manœuvre. Caught
between two terrible fires, Brueys was a lost man from the beginning.
It was a night battle, awful beyond the power of description. When it
ended next day, the English had practically obliterated the French
fleet; Napoleon was cut off from Europe. When the news reached him,
he was stunned, almost crushed; but rallying immediately, he wrote to
Kléber, "The English will compel us to do greater things in Egypt than
we had intended."
Desaix conquered Upper Egypt; organized resistance to the invaders
ceased for the time, and from the cataracts to the sea Napoleon held
the valley down. The administration began to work smoothly, taxes
seemed lighter because more equitably distributed, and the various
enterprises Napoleon had set on foot began to show some life. He
enrolled natives in his army, and formed a body of Mamelukes which
afterward appeared so picturesquely in France. Two young Mamelukes,
Roustan and Ibrahim, given him by one of the pachas, became his
personal attendants, and served him faithfully till his power was
broken in 1814.
The ruin of the fleet was not the only grief of Napoleon in the months
which followed. Junot had acted the part of the candid friend, and had
revealed to Napoleon the secret of Josephine's infidelities. Captain
Hypolite Charles had reappeared in the absence of the husband, and was
now living with the wife at Malmaison. So openly was this connection
kept up that the Director, Gohier, a friend of Josephine, advised her
to divorce Napoleon and marry Charles. The first shock of Junot's
revelation threw Napoleon into a paroxism of wrath, then into a stupor
of despair and dull disgust with everything. Then, by a reaction,
natural, perhaps, to a man of his temperament, he threw himself into
libertine excesses. Prior to this period his morals, considering the
times and the temptations, had been remarkably pure. Henceforth he
was occasionally to give himself a license which scandalized even the
French officers. Scorning subterfuge and concealment, he became as
bold as any born king, a rake by divine right, in the shamelessness
of his amours. He appeared in public at Cairo with Madame Foures, his
mistress, riding in the carriage by his side; and if Bourrienne tells
the truth on Napoleon, and Carlyle tells no lie on Peter the Great,
the one was about as obscene as the other while the lustful impulse
prevailed.
CHAPTER XVII
Carefully as Napoleon had cultivated the native authorities, deferred
to prejudice and custom, and maintained discipline, native opposition
to French rule seems to have been intense. A revolt in Cairo took him
by surprise. It had been preached from the minaret by the Muezzins in
their daily calls to prayer. It broke out with sudden fury, and many
Frenchmen were slaughtered in Cairo and the surrounding villages.
Napoleon quelled it promptly and with awful severity. The insurrection,
coming as it did upon the heels of all his attempts at conciliation,
filled him with indignant resentment, and, in his retaliation, he left
nothing undone to strike terror to the Arab soul. Insurgents were shot
or beheaded without mercy. Donkey trains bearing sacks were driven to
the public square, and the sacks being untied, human heads rolled out
upon the ground--a ghastly warning to the on-looking natives. Such is
war; such is conquest. The conquered must be tamed. Upon this principle
acted the man of no religion, Napoleon, in Egypt, and the Christian
soldier, Havelock, in Hindustan. The Christian Englishmen who put down
the Indian mutiny were as deaf to humanity as was the Deist who quelled
the revolt in Cairo. Like all the cruelty whose injury society really
feels, the crime is in the system, not the individual. War is war; and
as long as Christendom must have war to work out the mysterious ways
of God, we must be content with the thorns as well as the fruits. If
it be a part of the white man's burden to exterminate black and brown
and yellow races to clear the way for the thing we call Christian
civilization, Napoleon's course in Egypt was temperate and humane.
Upon all his deeds a blessing might be asked by the preachers who
incited the soldiers of America, Great Britain, Germany, Russia, in the
wars of the year 1900; and the chaplains who went, on good salaries,
to pray for those who shot down Filipinos, Chinamen, or even South
African Boers could just as easily have given pious sanction to the
murders-in-mass committed by Bonaparte.
Inspired by the result of the battle of the Nile, England, Turkey, the
Mamelukes, and the Arabs made great preparations to drive Napoleon out
of Egypt. A Turkish army was to be sent from Rhodes; Achmet, Pacha of
Acre, surnamed Djezzar, the Butcher, was raising forces in Syria, and
Commodore Sir Sidney Smith was cruising on the coast ready to help
Turks, Mamelukes, and Arabs against the French. Sir Sidney had been
a political prisoner in Paris, had recently made his escape, and had
been assisted in so doing by Napoleon's old schoolmate, Phélippeaux.
Following Sir Sidney to the East, Phélippeaux, a royalist, was now at
hand eager to oppose the republican army of Napoleon, and capable of
rendering the Turks valuable service. There is no evidence that he
was actuated by personal hatred of Napoleon. They had not liked each
other at school, and had kicked each other's shins under the table;
but, as men, they had taken different sides as a matter of policy or
principle, and it was this which now arrayed them against each other.
Napoleon's invariable rule being to anticipate his enemy, he now
marched into Syria to crush Djezzar before the Turkish army from Rhodes
could arrive. Leaving Desaix, Lanusse, and other lieutenants to hold
Egypt, he set out with the main army February 11, 1799. El Arish was
taken February 20, 1799, and Gaza followed. Jaffa, the ancient Joppa,
came next (March 6), and its name will always be associated with a
horrible occurrence. Summoned to surrender, the Arabs had beheaded
the French messenger. The place was stormed, and the troops gave way
to unbridled license and butchery. The massacre went on so long and
was so hideous that Napoleon grew sick of it, and sent his step-son,
Eugène, and another aide, Croisier, to put a stop to it. He meant, as
he claimed, that they were sent to save the non-combatants,--old men,
women, and children. He did not mean them to save soldiers, for, by the
benign rules of war, all defenders of a place taken by assault could
be slain. Misunderstanding Napoleon, or not knowing the benign rules,
Eugène and Croisier accepted the surrender of three or four thousand
Arab warriors, and brought them toward headquarters. As soon as
Napoleon, walking in front of his tent, saw these prisoners coming, he
exclaimed, in tones of grief: "Why do they bring those men to me? What
am I to do with them?" Eugène and Croisier were severely reprimanded,
and he again asked: "What am I to do with these men? Why did you bring
them here?"
Under the alleged necessity of the case, want of food to feed them,
or vessels to send them away, a council of war unanimously decided
that they should be shot. With great reluctance, and after delaying
until the murmurs of the troops became mutinous, Napoleon yielded, and
the prisoners were marched to the beach and massacred. That this was
a horribly cruel deed no one can deny; but the barbarity was in the
situation and the system, not the individual. Napoleon himself was
neither blood-thirsty nor inhumane. The last thing he had done before
quitting France had been to denounce the cruelty of the authorities in
dealing with émigrés who were non-combatants. His proclamation, which
really invited soldiers to disobey a cruel law, closed with the ringing
statement, "The soldier who signs a death-warrant against a person
incapable of bearing arms is a coward!"
In passing judgment upon Napoleon, we must adopt some standard of
comparison; we must know what military precedents have been, and what
the present practice is. Three days after the battle of Culloden the
Duke of Cumberland, being informed that the field was strewn with
wounded Highlanders who still lived,--through rain and sun and the
agony of undressed wounds,--marched his royal person and his royal
army back to the field and, in cold blood, butchered every man who lay
there. A barn, near the battle-field, was full of wounded Scotchmen;
the royal Duke set it on fire, and all within were burned to death.
During the conquest of Algiers, in 1830, a French commander, a
royalist, came upon a multitude of Arabs--men, women, children--who had
taken refuge in a cave. He made a fire at the cavern's mouth and smoked
them all to death.
In the year 1900, Russians, Germans, and other Christians invaded
China to punish the heathen for barbarities practised upon Christian
missionaries. A German emperor (Christian, of course) said, "Give no
quarter." Germans and Russians killed everything that was Chinese--men
and women and children. Armed or not armed, working in fields or idle,
walking in streets or standing still, giving cause or giving none,
the heathen were shot and bayoneted and sabred and clubbed, until the
streets were choked with dead Chinese, the rivers were putrid with
dead Chinese, the very waters of the ocean stank with dead Chinese.
Prisoners were made to dig their own graves, were then shot, tumbled
into the hole, and other prisoners made to fill the grave. Girls and
matrons were outraged in the presence of brothers, sons, husbands,
fathers; and were then shot, or stabbed to death with swords or
bayonets.
Were it not for examples such as these, the reader might feel inclined
to agree with the anti-Bonaparte biographers who say that the Jaffa
massacre was the blackest in the annals of civilized warfare.
Rid of his prisoners, Napoleon moved forward on the Syrian coast and
laid siege to St. Jean d'Acre. The town had strong, high walls, behind
which were desperate defenders. The lesson from Jaffa had taught the
Arab that it was death to surrender. To him, then, it was a stern
necessity to conquer or die. The English were there to help. Sir Sidney
Smith furnished guns, men to serve them, and skilled engineers.
Napoleon was not properly equipped for the siege, for his battering
train, on its way in transports, was stupidly lost by the captain in
charge. Sir Sidney took it and appropriated it to the defence. In vain
Napoleon lingered till days grew into weeks, weeks into months. He was
completely baffled. There were many sorties, many assaults, dreadful
loss of life, reckless deeds of courage done on both sides. Once,
twice, the French breached the walls, made good their assault, and
entered the town, once reaching Djezzar's very palace. It was all in
vain. Every house was a fortress, every street an ambuscade, every Arab
a hero,--the very women frantically screaming "Fight!"
With bitterness in his soul, Napoleon turned away: "that miserable hole
has thwarted my destiny!" And he never ceased to ring the changes on
the subject. Had he taken Acre, his next step would have been to the
Euphrates; hordes of Asiatics would have flocked to his banner; the
empire of Alexander would have risen again under his touch; India would
have been his booty; Constantinople his prize; and then, from the rear,
he would have trodden Europe into submission. He saw all this on the
other side of Acre, or thought he saw it. But the town stood, and the
château in Spain fell.
Once he had been drawn from the siege to go toward Nazareth to the
aid of Kléber, who was encompassed by an army outnumbering his own by
ten to one. As Napoleon came within sight, he could see a tumultuous
host of cavalry enveloping a small force of infantry. The throngs of
horsemen surged and charged, wheeled and turned, like a tossing sea. In
the midst was an island, a volcano belching fire. The tossing sea was
the Mameluke cavalry; the island in the midst of it was Kléber. Forming
so that his line, added to Kléber's, would envelop the enemy, Napoleon
advanced; and great was the rout and the slaughter of the foe. No
organized force was left afield either in Syria or Egypt.
Now that the siege of Acre was abandoned, the army must be got back to
Cairo, and the country laid waste to prevent Djezzar from harassing
the retreat. What could not be moved, must be destroyed. The plague,
brought from Damietta by Kléber's corps, had stricken down almost as
many as had perished in the siege. To move the wounded and the sick was
a heavy undertaking, but it was done. On the night of May 20, 1799,
Napoleon began his retreat. A terrible retreat it was, over burning
sands, under brazen skies, amid stifling dust, maddening thirst--and
over all the dread shadow of the plague. In their selfish fears, the
French became callous to the sufferings of the wounded and the sick.
The weak, the helpless, were left to die in the desert. Every hamlet
was fired, the fields laden with harvest were in flames, desolation
spread far and wide. "The whole country was in a blaze."
Napoleon doggedly kept his course, full of dumb rage--seeing all,
feeling all, powerless in the midst of its horrors. At Tentoura he
roused himself to a final effort to save the sick and the wounded.
"Let every man dismount; let every horse, mule, camel, and litter be
given to the disabled; let the able go on foot." The order so written,
despatched to Berthier, and made known through the camp, Vigogne,
groom to the chief, came to ask, "What horse shall I reserve for you,
General?"
It was the touch that caused an explosion. Napoleon struck the man with
his whip! "Off, you rascal! Every one on foot, I the first. Did you not
hear the order?"
The hungry desert swallowed horses and men. The heavy guns were
abandoned. The army pressed on in sullen grief, anger, despondency. The
chief trudged heavily forward, in grim silence.
On May 24, the French were at Jaffa again. Here the hospitals were full
of the plague-stricken and the wounded. Napoleon visited these men,
spoke encouraging words to them, and, according to Savary, touched
one of the victims of the plague in order to inspire confidence--the
disease being one with whose spread imagination is said to have much
to do. Bourrienne denies this story; but according to a report written
by Monsieur d'Ause, administrator of the army of the East, and dated
May 8, 1829, Napoleon not only touched the afflicted, but helped to
lift one of them off the floor. Substantially to the same effect is the
testimony of the chief surgeon of the army, Desgenettes. Bourrienne
also denies that the sick were taken away by the retreating French.
Monsieur d'Ause reports that the wounded and the sick were put on board
seven vessels (he names the vessels), and sent by sea to Damietta.
This statement is corroborated by Grobert, Commissioner of War, who
gives the names of the officers placed in charge of the removal. A few
of the plague-stricken were so hopelessly ill that Napoleon requested
the surgeon to administer opium. It would put the poor creatures out
of their misery, and prevent them from falling into the hands of
the enemy. Desgenettes made the noble reply which Napoleon himself
quoted admiringly, "My duty is to cure, not to kill." But Napoleon's
suggestion was really humane; as he says, any man in the condition of
these hopeless, pain-racked invalids would choose the painless sleep of
opium rather than the prolonged agony of the disease.
In the year 1900 the Europeans, beleaguered by the Chinese in
Tien-Tsin, adopted the view of Napoleon. They killed their own wounded
to prevent them from falling into the hands of the heathen. According
to reports published throughout Christendom and not contradicted,
Admiral Seymour of the British Navy issued orders to that effect. And
when the barbarities which the Christians inflicted upon the heathen
became worse than death, Chinamen did as Seymour had done--killed their
own friends to escape the torture.
Napoleon not insisting on poison, the few invalids who could not be
moved were left alive, and several of these yet breathed when Sir
Sidney Smith took possession of Jaffa.
After another dreadful desert-march, in which Napoleon tramped in
the sand at the head of his troops, the army reached Cairo, June 14,
1799. With all his art, Napoleon only partially made the impression
that he had returned victorious. During his absence there had been
local revolts, soon repressed, and he found the country comparatively
quiet. It was probably a relief to him when news came that the expected
Turkish army had arrived at Aboukir. In open fight on fair field he
could wipe out the shame of Acre. With all his celerity of decision,
movement, and concentration, he was at Aboukir on July 25, 1799,
where the Turkish army had landed. But for an accident, he would have
taken it by surprise. In the battle which followed, the Turks were
annihilated. Out of a force of twelve thousand scarce a man escaped.
Its commander, Mustapha, was taken prisoner by Murat, after he had
fired his pistol in the Frenchman's face, wounding him in the head. A
blow of Murat's sabre almost severed the Turk's hand. Carried before
Napoleon, the latter generously said, "I will report to the Sultan how
bravely you have fought."--"You may save yourself the trouble," the
proud Turk answered; "my master knows me better than you can."
The aid, counsel, and presence of Sir Sidney Smith had not availed the
enemy at Aboukir as at Acre. It was with difficulty that he escaped to
his ships. As to Phélippeaux, he had been stricken by the plague and
was mortally ill, or already dead.
On his return to Alexandria, Napoleon sent a flag of truce to Sir
Sidney, proposing an exchange of prisoners. During the negotiations,
the English commodore sent Napoleon a file of English newspapers and a
copy of the _Frankfort Gazette_. Throughout the night Napoleon did not
sleep; he was devouring the contents of these papers. The story which
they told him was enough to drive sleep away.
It is possible that Talleyrand, by way of Tripoli, may have been
corresponding with Napoleon; and it seems that a letter from Joseph
Bonaparte had also reached him; but Bourrienne, his private secretary,
positively denies that he knew of conditions in France prior to the
battle of Aboukir. Although it is possible he may have received letters
which his private secretary knew nothing about, it is not probable. It
would seem, therefore, that his knowledge of the situation in Europe
was derived from the newspapers sent him by Sir Sidney Smith.
CHAPTER XVIII
With the first coming of the armies of revolutionary France to Italy,
the establishment of republics in the peninsula, and the talk of
Italian unity, even Rome and Naples began to move in their shrouds.
Probably two systems of government more utterly wretched than those of
the Pope and the Neapolitan Bourbons never existed. While changes for
the better were taking place in the immediate neighborhood of these
misruled states, it was natural that certain elements at Rome and
Naples should begin to hope for reforms.
The support of the Pope and of the Bourbons was the ignorance of the
lowest orders and the fanaticism of the priests. The middle classes,
the educated, and even many of the nobles favored more liberal
principles. In December, 1797, the democratic faction at Rome came into
collision with the papal mob; and the papal troops worsted in the riot,
the democrats sought shelter at the French embassy, Joseph Bonaparte
being at that time the minister of France. The papal faction, pursuing
their advantage, violated the privilege of the French ministry, and
General Duphot, a member of the embassy, was killed. This was the
second time a diplomatic agent of France had been slain by the Pope's
partisans in Rome. Joseph Bonaparte left the city, and General Berthier
marched in at the head of a French army. The Pope was removed, and
finally sent to Valence, where he died in 1799. His temporal power
having been overthrown, the liberals of Rome, including many clericals
who were disgusted with the papal management of political affairs, held
a great meeting in the forum, renounced the authority of the Pope,
planted a liberty tree in front of the Capitol, and declared the Roman
republic, February 15, 1798.
In the spring of 1798 the democratic cantons in Switzerland had risen
against the aristocracy of Berne, had called in the French, and on
April 12, 1798, the Helvetic republic had been proclaimed.
This continued and successful advance of republican principles
profoundly alarmed the courts and kings of Europe. Great Britain,
having failed in her efforts to make favorable terms of peace with the
French Directory, and having gained immense prestige from the battle
of the Nile, organized a second great coalition in the autumn of 1798.
Russia, Turkey, Naples, and England combined their efforts to crush
republican France.
A Neapolitan army, led by the Austrian general, Mack, marched upon
Rome for the purpose of restoring the temporal power of the Pope. Its
strength was overwhelming, the French retreated, and Ferdinand of
Naples made his triumphant entrance into Rome in November, 1798. The
liberty tree was thrown down, an immense cross set up in its place,
many liberals put to death in spite of Ferdinand's pledge to the
contrary, and a few Jews baptized in the Tiber. The French, having left
a garrison in the castle of St. Angelo, General Mack issued a written
threat to shoot one of the sick French soldiers in the hospital for
every shot fired from the castle.
Ferdinand gave the credit of his victory to "the most miraculous
St. Januarius." To the King of Piedmont, who had urged Ferdinand to
encourage the peasants to assassinate the French, he wrote that the
Neapolitans, guided by Mack, had "proclaimed to Europe, from the summit
of the Capitol, that the time of the kings had come."
We do not know of any incident which more fully illustrates the meaning
of the gigantic efforts made by Europe against France and Napoleon
than this. Ferdinand called to the Pope to return, to sweep away
all reforms, to restore all abuses, to become master again of life,
liberty, and property: "The time of the kings has come!" And back of
the Bourbon king, back of these efforts of Naples to inaugurate the
return of the Old Order and all its monstrous wrongs, was Nelson and
the English government.
If "the most miraculous St. Januarius" had joined Ferdinand in his
Roman campaign, the saint soon wearied of it, for the conquest was
lost as soon as made. The Neapolitan forces were badly handled, and
the favorites of the saint fell easy prey to the heretic French. King
Ferdinand, losing faith in Januarius, fled, the French reëntered Rome,
the republic was set up again; and Championnet, the French general,
invaded Neapolitan territory. In December, 1798, the royal family of
Naples took refuge on Nelson's ship, and soon sailed for Sicily. The
republicans of Naples rose, opened communications with the French, who
entered the city, January 23, 1799; and the Parthenopean republic was
proclaimed. Representative government took the place of intolerant
priest-rule and feudalism. Against this new order of things the clergy
preached a crusade. The ignorant peasants of the rural districts and
the lowest rabble of the city flew to arms, and civil war in its worst
form was soon raging between the two factions--that which favored and
that which opposed the republic.
In the meantime the forces of the great coalition were getting under
way. A Russian army, led by the celebrated Suwarow, was on the march
toward Italy. Austria had recuperated her strength, and the Archduke
Charles beat the French, under Jourdan, at the battle of Stockach,
March 25, 1799. On the 28th of April of the same year, as the French
envoys to the Congress of Rastadt were leaving that place, they were
assailed by Austrian hussars, two of them killed, and the third left
for dead. The Archduke Charles commenced an investigation of this
crime, but was stopped by the Austrian Cabinet. The evidence which he
collected was spirited away, and has never since been found.
On April 5, 1799, the army of Italy, under Schérer, was defeated by the
Austrians, who recovered at one blow Italian territory almost to Milan.
In June, Masséna was beaten by the Archduke Charles at Zurich, and fell
back to a strong position a few miles from that city.
Suwarow having reached Italy in April, 1799, began a career of victory
which would have been followed by momentous results had not Austrian
jealousy marred the campaign. His impetuous valor overwhelmed Schérer;
and, by the time Moreau was put in command of the French, the army was
too much of a wreck for even that able officer to stand the onset of
the Russians. General Macdonald, hastening to Moreau's aid, was not
quite quick enough. The dauntless and vigilant old Russian commander
made a dash at Macdonald, struck him at the Trebbia, and well-nigh
destroyed him, June 18, 1799.
Southern Italy rose against the French. Cardinal Ruffo, at the head
of an army of peasants, ravaged Calabria and Apulia. On the 15th of
June, 1799, this army, assisted by the lazzeroni of Naples, attacked
the republican forces in the suburbs of that city, and for five days
there was a carnival of massacre and outrage. On the 19th the Cardinal
proposed a truce. The republicans who remained in possession of the
forts agreed; negotiations followed, and on the 23d terms of peace were
signed by Ruffo on behalf of the King of Naples, and guaranteed by the
representatives of Russia and Great Britain. It was agreed that the
republicans should march out with the honors of war, that their persons
and property should be respected, and that they should have the choice
of remaining, unmolested at home, or of being safely landed at Toulon.
On the faith of this treaty the democrats yielded up the forts, and
ceased all resistance. At this juncture, Nelson sailed into the harbor
and annulled the treaty. A reign of terror followed.
The Queen of Naples was the sister of Marie Antoinette,--a violent,
cruel, profligate woman. She and her friend, Lady Hamilton, wife of the
English minister and mistress of Lord Nelson, hounded on the avengers
of the republican revolt, and Naples became a slaughter-pen. Perhaps
the blackest of all the black deeds done in that revel of revenge was
the murder of Admiral Carraccioli.
This man was a prince by birth, a member of one of the noblest Italian
houses; his character was as lofty as his birth, and he was seventy
years old. He had joined the republicans, and had commanded their naval
forces. Involved in the failure of his cause, he was entitled to the
protection of the treaty of capitulation.
Nelson, returning from his Victory of the Nile, and inflated with
pride and political rancor, annulled the terms which Cardinal Ruffo
had accepted--doing so over the Cardinal's protest, be it said to his
honor. The republican garrisons of the castles were delivered by Nelson
to the vengeance of their enemies. As to Prince Carraccioli, Nelson
himself took charge of his case. The gray-haired man, who had honorably
served his country for forty years, was brought on board the English
vessel, with hands tied behind him, at nine o'clock in the forenoon.
By ten his trial had begun; in two hours it was ended. Sentenced to
death immediately, he was, at five o'clock in the afternoon of the same
day, hanged at the yard-arm, his body cut down at sunset, and thrown
into the sea. In vain the old man had pleaded that the president of
the court-martial was his personal enemy. In vain he had asked for
time, a rehearing, a chance to get witnesses. Nelson was unrelenting.
Then the victim of this cold-blooded murder begged that he might be
shot. "I am an old man, sir. I leave no family to grieve for me, and
therefore cannot be supposed to be very anxious to live; but the
disgrace of being hanged is dreadful to me!" And again Nelson refused
all concession.
Lady Hamilton, Nelson's mistress, looked on with unconcealed
satisfaction as the prince-republican was choked to death with a rope;
and if ever Nelson felt a pang because of his shocking inhumanity, it
has escaped the record.
Who has not had his ears deafened by royalist diatribes concerning the
murder of the Duke d'Enghien? And how silent are the same royalist
authors concerning the murder of the Prince Carraccioli!
The closer the facts of history are studied and compared, the less
certain the reader will be that Napoleon Bonaparte was a whit worse in
any respect than the average public man of his time.
* * * * *
From the newspapers which Napoleon read at Alexandria during the night
of July 25, 1799, he first learned the full extent of the disasters
which had befallen France in his absence.
"Great heavens, the fools have lost Italy! I must return to France!"
In the East his work was done. He had crushed organized resistance.
From the cataracts to the sea all was quietude. True, he had not
conquered Syria, but he had broken Djezzar's strength, and destroyed
the relieving army of Turks. What remained? What more had he to do in
Egypt? Was he, when France was in such dire distress, to stay at Cairo
running the newspaper, making pencils, supervising canals and schools,
and dawdling along the Nile as local governor?
In France itself there was no division of sentiment on the subject. All
felt that the best soldier of the Republic was needed at home. "Where
is Bonaparte?" was the cry throughout the country. The need for him was
felt in Italy as well as France, on the Rhine as on the Seine.
Even the Directory realized the necessity for the presence of the
one Frenchman who could restore courage, inspire confidence, assure
victory. They despatched a special messenger to call him home
(September, 1799). This courier did not reach Egypt, and the order
of recall was revoked; but the fact that it was issued, proves that
Napoleon, in returning to France, obeyed an impulse which even his
enemies shared.
Hastily and secretly making the necessary arrangements, and taking with
him a chosen few of his soldiers and his savants, Napoleon embarked in
four small vessels, August 23, 1799, and next morning made sail for
France.
In the army left behind there was a wail of despair, a burst of wrath.
Napoleon's name was cursed,--the traitor, the deserter, the coward!
This was very natural, and very unjust. Kléber himself, to whom
Napoleon had delegated the chief command, was as indignant as the rest.
In bitter, unmeasured terms he denounced Bonaparte in letters to the
Directory--despatches which, when opened, were opened by Bonaparte,
First Consul. Kléber had grossly exaggerated the difficulties of his
situation, and soon gave proof of that fact. He was in no real danger.
When other armies were thrown against him, he gloriously defeated them,
and held his ground.
Uncontrollable circumstances, the continued hostility of England, the
unforeseen inability of Napoleon to throw succors into Egypt, alone
defeated his plans, finally. Never did a man strive harder to send
relief to a lieutenant. There is something positively pathetic in the
strenuous and fruitless efforts made by Napoleon to triumph over the
incompetence of his naval commanders, and to compel them to exhibit
enterprise, courage, and zeal in the relief of Egypt. It was all in
vain. "I cannot create men," he said sadly. He certainly never was able
to find effective aid in his navy, and Egypt was finally lost, in spite
of all he could do.
That he was correct in his judgment in attaching so much importance to
the conquest of Egypt, subsequent events have proved. In seizing upon
the exhaustless granary of the East, the enormously important midway
station on the road to India, his was the conception of a far-sighted
statesman. It was his fate to teach the world, England especially, the
vital importance of Malta and of Egypt, and to lose both.
CHAPTER XIX
The seas were infested with hostile ships, and a more perilous voyage
than Napoleon's from Egypt few men ever risked. His little sailing
vessels had but one element of security--their insignificance. They
could hope to slip by where larger ships would be sighted; and they
could retreat into shoal water where men-of-war could not follow.
Napoleon had with him some four or five hundred picked troops and a
few cannon; his plan was to run ashore on the African coast, and make
his way overland, if he should find his escape cut off on the ocean by
English ships. Keeping close to the shore, he made tedious progress
against contrary winds, and did not arrive off Corsica till the last
days of September, 1799. He had not intended to land on his native
soil, but the adverse gales made it necessary to put into the harbor of
Ajaccio. Sending ashore for fruit and the latest journals, he sat up
all night on board reading. He now learned that the battle of Novi had
been fought, and Joubert killed.
The presence of Napoleon in the harbor of Ajaccio created a sensation
on shore, and the people thronged the streets and the quays, eager
for a sight of the hero of Italy and of Egypt. His victories in the
East were known, for he himself had dictated the reports, and had not
weakened them with any dashes of modesty. Around his name, therefore,
had formed a halo, and even those Corsicans who had scorned him when
feeble, admired him now that he was strong. Yielding to popular
pressure, Napoleon landed. His reception was enthusiastic. The square
was filled with shouting multitudes, the windows and the roofs crowded
with the curious, everybody wanting to catch sight of the wondrous
little man who had so quickly become the first soldier of the world.
Crowds of admiring islanders remembered that they were his cousins. The
number of god-children laid to him was immense. His old nurse hobbled
to him, hugged him, gave him a blessing, and a bottle of goat's milk.
He walked St. Charles Street, into the little square, and into the
old Bonaparte home, which the English troops had used as a barrack.
He visited the country-seat, the grotto of Milleli, all the old
familiar scenes. He showed his staff, with some pride, the estates of
his family; and to the tenants and the herdsmen he gave cattle and
land. The soldiers of the garrison, drawn up to receive him, were in
a wretched condition; they had received no pay for more than a year.
Napoleon gave them $8000, all he had, saving necessary travelling
expenses. To his nurse he gave a vineyard and a house in Ajaccio.
The Corsicans tell the story that during the time when the young
Lieutenant Bonaparte was trying to revolutionize the island, a priest,
standing at the window of a house overlooking the street, aimed a gun
at the little Jacobin's head. Napoleon, ever watchful, saw the movement
just in time to dodge. The bullet struck the wall, and Napoleon
scurried off.
This priest, having remained in Ajaccio, and the situation having
undergone a change, was very uncomfortable; for Napoleon now had it in
his power to make his old enemy do the dodging. But he bore no malice.
He offered the embarrassed priest his hand, made a joke of the shot out
of the window, and put the good man quite at his ease.
It was while attending a ball given in his honor in Ajaccio that
Admiral Ganteaume sent word that the wind had changed, and the voyage
could be resumed. Hurriedly bidding adieu to friends, he quitted
Corsica for the last time.
On October 8, 1799, the four vessels entered the roads of Fréjus, and
immediately upon its becoming known that Napoleon was on board, the
water was covered with the boats of hundreds crowding to meet him.
It was in this spontaneous rush of the people to greet the returning
hero that the quarantine law was violated. The joy of the people was
unbounded. They rang the bells, they filled the streets with shouting
multitudes, they hailed him as the deliverer of France. A king in the
best of Bourbon days had never drawn a warmer welcome. On his way from
the coast he met with a prolonged ovation. At Lyons it was as though
Napoleon had already become the ruler of France.
General Marbot, late commander of Paris, now passing through Lyons on
his way to Italy, was somewhat scandalized and offended to see that
Bonaparte was treated like a sovereign. Says his son in his _Memoirs_:--
"The houses were all illuminated, and decorated with flags, fireworks
were being let off; our carriage could hardly make its way through the
crowd. People were dancing in the open spaces, and the air rang with
cries of: 'Hurrah for Bonaparte! He will save the country!'"
The hotel keeper had given to Napoleon the rooms for which General
Marbot had spoken, and Napoleon was in them. Learning how General
Marbot had been treated, Napoleon invited him to come and share the
rooms comrade-like. Marbot went to another hotel, rather in a huff, it
would seem; and Napoleon, determined not to make an enemy out of such
an occurrence, went on foot and at once to apologize and express his
regrets to General Marbot in his rooms at the other hotel. As he passed
along the street he was followed by a cheering crowd.
"General Marbot," says his son, "was so shocked at the manner in which
the people of Lyons were running after Napoleon, as though he were
already king, that the journey to Italy was resumed as speedily as
possible."
Napoleon's route led him through Valence, where there was not only the
miscellaneous crowd to cheer him, but some true and tried personal
friends. For example, there was old Mademoiselle Bou, who had credited
him for board. Napoleon greeted her affectionately and made her some
valuable presents, which are now to be seen in the museum of the town.
Indeed, the news, flashed to all parts of France, "Bonaparte has come!"
created a kind of universal transport. One deputy, Baudin by name, died
of joy. Chancellor Pasquier relates that he was at the theatre one
evening in Paris, when he saw two very pretty women, sitting in the box
next to him, receive a message. They rose in excitement and hurried
away. These very pretty women, as Pasquier learned, were the sisters of
Bonaparte. A courier had brought the news that their brother had landed
at Fréjus. Béranger says in his autobiography: "I was sitting in our
reading room with thirty or forty others, when suddenly the news was
brought in that Bonaparte had returned from Egypt. At the words every
man in the room started to his feet, and burst into one long shout of
joy!"
By the signal telegraph of that day, the news had flown to the capital,
and in a short while carriages were rumbling along the road out of
Paris toward Lyons, bearing relatives and friends to meet the returning
hero. One of these lumbering vehicles bore the uneasy Josephine.
At Lyons, Napoleon, suspicious of political foes perhaps, changed
his course, and hastened toward Paris by a different road. Would-be
assassins, if there were any, as well as faithful friends, would fix
their plans for nothing.
When Napoleon got down from his carriage before his house in the street
which was called, in compliment to him, the street of Victory, there
was no wife, no relative, no friend to greet him. His home was a dismal
picture of darkness, silence, desertion; and it chilled him with a
painful shock which he never ceased to remember. The anxious Josephine,
the faithless wife, had gone to meet him, to weep away her sins on his
breast, had missed him because of his change of route; and Napoleon,
not knowing this, believed she had fled his home to escape his just
anger. Bitter days and nights this eminently human Bonaparte had known;
bitter days and nights he was to know again; but it may be doubted
whether any of them gave to him a bitterer cup to drink than this of
his return from Egypt.
Josephine came posting back as fast as she could, worn out with fear
and fatigue. Napoleon refused to see her. Locked in his room, he paced
the floor, his mind in a tempest of wrath, grief, mortification,
wounded love. The guilty wife grovelled at the door, assaulting the
barriers with sobs, plaintive cries, soft entreaties. Her friends,
Madame Tallien, the Director Gohier, her children, Eugène and Hortense,
and some of Napoleon's friends, besieged the infuriated husband,
appealing to his pride, his generosity, his self-interest, his fondness
for the children,--in short, using every conceivable inducement,--and
at length Napoleon, worn out and softened, allowed Eugène and Hortense
to put Josephine into his arms.
Bourrienne relates that many years afterward, strolling along the
boulevard with Napoleon, he felt the Emperor's hand suddenly close on
his arm with spasmodic grip. A carriage had just passed, and within
it Napoleon had recognized Hypolite Charles, Josephine's old-time
paramour. That this coxcomb still lived, is proof enough that Napoleon
the Great scorned personal revenge.
While the hope of the Bonaparte family was in the East, its interest
had not been neglected in France. Joseph had been established in
state at Paris (town house, country house, etc.) and had cultivated
influential men of all parties. Lucien had been elected in Corsica as
deputy to the Council of Five Hundred. Bold, and gifted with eloquence,
he had become a power in the council, and had been elected its
president. Josephine herself had been effective, so splendid had been
her establishment, so charming her tact and gracious ways. Therefore,
when the returning soldier cast his eye over the political field,
there was much to give him satisfaction. He was committed to no party;
he was weighed down by no record; he was held in no rigid grooves.
Towering above all other heads, he alone could draw strength from all
parties. As he himself said, in his march to power he was marching
with the nation. Barras admits that all France was rushing to him as
to a new existence. That he would become the ruler was expected, was
desired; it was only a question of when and how. The almost unanimous
voice of the people would have made him Director. Details alone caused
differences of opinion. Should the constitution be set aside? Should
Bonaparte be one of five Directors? Or should he be vested with a
virtual dictatorship? Should the powers of government be distributed,
as under the Directory, or should they be concentrated? It was on
details like these that differences arose; but as to the importance of
having the benefit of Napoleon's services, the great mass of Frenchmen
were agreed. True, the brilliant triumphs of Masséna around Zurich,
and the overthrow of the English and Russians in Holland, by Brune,
had saved the Republic from the pressing dangers of foreign invasion;
but the foreign invasion was not the only cause of disquiet in France.
The root of the evil was thought to be weakness of the government.
The constitution had been violated by the Directors in Fructidor when
Augereau had broken in upon the councils and arrested so many members.
Three Directors, it will be remembered, had driven out two, Carnot and
Barthélemy. Afterward, in Floréal (May 11, 1798), the elections had
been set aside to get rid of objectionable members. In each of these
cases the vacancies made by force had been filled by the victors.
Then, finally, the reaction had become too strong, and in Prairial
(June 18, 1799) the Fructidorians had in turn been beaten, and the
Directory changed by the putting in of Sieyès, Gohier, Moulins, and
Roger-Ducos.
People grew weary of so many convulsions, so much uncertainty, so much
vacillation, so much disorder. Besides, the finances were in hopeless
confusion. National bankruptcy virtually existed, and a forced loan
of 100,000,000 francs, the law of hostages, and the vexatious manner
in which the new Sunday law was enforced gave offence in all classes.
Barras had managed to keep his place in the Directory, but not his
power. Sieyès had entered the Directory, but wished to overthrow
it. Even had there been no Bonaparte to plan a change, a change was
inevitable. Sieyès had said, "France needs a head and a sword." With
Sieyès present, only the sword was lacking, and he had tried to find
one. Joubert was chosen, but got killed. Bernadotte was mentioned, but
he would not take the risk. Moreau was sounded, but would not agree to
act. Nevertheless, it was but a question of time when the man and the
opportunity would meet. It might possibly have happened that Sieyès
with his new constitution and his new executive would have saved the
Republic. Better men, coming to the front and casting out the scum
which had floated to the top of the revolutionary current, might have
established the Republic on a solid basis, and saved the world from the
hideous revel of blood and carnage which marked the era of Napoleon.
No one can tell. It is easy to say that the directorial régime had
failed; it is no less easy to say that a change could have been made
without rushing into imperialism. Republics, being merely human, cannot
be perfected in a day; and there is some injustice in cutting down the
tree because it is not laden with fruit as soon as it is planted.
While Napoleon was exploring the ground and selecting his point of
attack, the Directory adopted no measures of self-defence. In a general
way they suspected Bonaparte and dreaded him, but they had no proofs
upon which they could act. Their minister of war, Dubois de Crancé told
them a plot was brewing, and advised the arrest of Napoleon. "Where
are your proofs?" demanded Gohier and Moulins. The minister could not
furnish them. Then a police agent warned them. Locking the informer in
a room, the Directors began to discuss the matter. The agent became
alarmed for his own safety, and escaped through a window.
Anxious to get Napoleon away from Paris, the Directors offered him
his choice of the armies. He pleaded shattered health, and declined.
There were two parties, possibly three, with the aid of either of which
Napoleon might have won his way to power. There were the Jacobins, the
remnants of the thorough-going democrats, who had made the Revolution.
These were represented in the Directory by Gohier and Moulins, men of
moderate capacity and fine character. But Napoleon had been cured of
his youthful Jacobinism, and believed that if he now conquered with
the democrats, he would soon be called on to conquer against them.
Again, there were the moderates, the politicians, who were sincere
republicans, but who opposed the radicalism of the democrats on the
one hand, and the weakness of the Directory on the other. Sieyès and
Roger-Ducos represented these in the Directory, and their following
among the rich and middle-class republicans was very large. Lastly came
the Barras following, the Rotten, as Napoleon called them, who would
agree to pretty much any change which would not take from them the
opportunities of jobbery.
Each of these parties courted Napoleon, who listened to them all,
used them all, and deceived them all. Barras he despised, yet lulled
to the last moment. Gohier and Moulins were carefully manipulated and
elaborately duped. Sieyès and his associates were used as tools, and
then, after the bridge had been crossed, thrown over.
Even the royalists were taken in; they were beguiled with hints that
Napoleon was preparing a way for the return of the Bourbons--he to act
the part of Monk to the exiled King.
Napoleon's first plan was to oust from the Directory the hateful
Sieyès,--"that priest sold to Prussia," and this proposition he urged
upon Gohier and Moulins. As there were no legal grounds upon which
the election of Sieyès could be annulled, and as Napoleon himself had
not reached the age of forty, required by the constitution, Gohier
and Moulins refused to have anything to do with the scheme. Its mere
mention should have put them on guard; but it did not. Then Napoleon
seemed, for a moment, to consider an alliance with Barras. Fouché and
other friends of that Director brought the two together, and there
was a dinner which was to have smoothed the way to an agreement.
Unfortunately for Barras he blundered heavily in proposing an
arrangement which meant that he should have the executive power, while
Napoleon should merely be military chief. Napoleon, in disgust, looked
the Director out of countenance, and, taking his carriage, returned
home to tell Fouché what a fool Barras had made of himself. The friends
of the Director, going to him at once, were able to convince even him
that he had bungled stupidly; and next day he hastened to Bonaparte
to try again. He was too late. Napoleon, upon leaving Barras the day
before had called in to see Sieyès, and to tell him that the alliance
of the Bonapartes would be made with him alone.
Naturally these two men were antagonistic. When Napoleon, quitting
the army without orders, had landed at Fréjus, Sieyès had proposed to
his colleagues in the Directory to have the deserter shot. The weak
Directory had no such nerve as such a plan required, and the advice was
ignored. Sieyès detested the abrupt, imperious soldier; and Napoleon
despised the ex-priest as a confirmed, unpractical, and conceited
visionary. Before he had failed with Gohier and Moulins, Napoleon had
treated Sieyès with such contempt as to ignore his presence, when they
were thrown together at one of the official banquets. The enraged
ex-priest exclaimed to his friends, "See the insolence of that little
fellow to a member of the government which ought to have had him shot!"
Napoleon, intent upon the plan of ousting Sieyès from the Directory,
asked _his_ friends, "What were they thinking about to put into the
Directory that--priest sold to Prussia?"
Powerful as were these feelings of reciprocal dislike, they were
overcome. Talleyrand, Joseph Bonaparte, Cabanis, and others plied both
the warrior and the priest with those arguments best suited to each.
The promptings of self-interest, as well as the necessities of the
case, drew them together. With Sieyès--jealous, irritable, suspicious,
impracticable--the task had been most difficult. He knew he was being
ensnared,--emphatically said so,--but yielded.
"Once Napoleon gets in he will push his colleagues behind him, like
this," and Sieyès forcibly illustrated what he meant by bustling
between Joseph and Cabanis, and then thrusting them back. Among the
civilians the Bonaparte campaign at this crisis was actively aided
by Talleyrand, Cambacérès, Roger-Ducos, Roederer, Boulay, Regnier,
Cabanis, the friend of Mirabeau. Among the soldiery the leading
canvassers were Sébastiani, Murat, Leclerc, Marmont, Lannes, Macdonald.
The plan agreed on was that the Council of Ancients, a majority having
been gained over, should decree the removal of the legislative sessions
to St. Cloud, name Napoleon commander of all the troops in Paris,
appoint a provisional consulate (Napoleon, Sieyès, and Roger-Ducos),
during which the councils should stand adjourned and a new constitution
be framed. The day fixed upon was the 18th of Brumaire (November 9,
1799), and the Ancients were to meet at seven and pass the decrees
agreed on by the Bonaparte steering committee. The Five Hundred, a
majority of which had not been won, were to meet _after_ the Ancients
should have voted the removal of the councils to St. Cloud. Hence they
would be powerless to prevent Napoleon from doing what he proposed for
the 18th. Whether they would be able to resist him after they formed
themselves at St. Cloud on the 19th, was another matter.
CHAPTER XX
There were in Paris at this time certain battalions which had served
under Napoleon in Italy; also the directorial, legislative, and
national guards, which he had organized. Naturally these troops were
all favorably disposed toward him. They had been urging the great
soldier to review them. The officers of the garrison and of the
National Guard who had not been presented to him had asked him to
receive them. Napoleon had postponed action on these requests, thereby
increasing the eagerness of officers and men. Now that his plans were
matured, he named the 18th of Brumaire (November 9, 1799) for the
review, and invited the officers to call upon him early in the morning.
His excuse for this unusual hour was that he would have to leave town.
Other appointments of interest Napoleon made at about the same time. He
had agreed to have a conference with Barras on the night of the 17th of
Brumaire, and the Director had caught at the promise as the drowning
catch at anything within reach. When Bourrienne went, about midnight,
to plead headache for the absent Napoleon, he saw Barras's face fall
as soon as the door opened. The worn-out debauchee had no faith in the
headache of Napoleon; but yet he had lacked the wish, or the energy, or
the influence, to oppose the plot which he now felt sure was aimed at
him as well as the others.
Gohier also had his appointments with Bonaparte. The Director was to
breakfast, he and wife, with Napoleon on the 18th of Brumaire, and
Napoleon was to dine with Gohier on the same day. The minister of war,
Dubois de Crancé, had warned both Gohier and Moulins; but it was not
till this late day that Gohier became suspicious enough to stay away
from Bonaparte's house on the morning of the 18th. His wife went, found
the place thronged with officers in brilliant uniform, and soon left.
In this assembly of soldiers stood the conspicuous figure of Moreau.
Discontented with the government, and without plan of his own, he had
allowed Napoleon to win him by flattering words, accompanied by the
complimentary gift of a jewelled sword. He had joined the movement with
his eyes shut. He did not know the plan, and would not listen when
Napoleon offered to explain it.
Bernadotte, the jealous, had stood aloof. Inasmuch as he was, in some
sort, a member of the Bonaparte family (he and Joseph having married
sisters), earnest efforts had been made to neutralize him, if nothing
more. Napoleon afterward stated that Bernadotte would have joined him,
had he been willing to accept Bernadotte as a colleague.
Whatever efforts were made to gain this inveterate enemy of Napoleon
had no other result than to put him in possession of the secret, and
to fill him with a cautious desire to defeat the plot. Augereau and
Jourdan, both members of the Five Hundred, and known Jacobins, were not
approached at all. General Beumonville, the ex-Girondin, had joined.
Meanwhile the conspiracy was at work from the Sieyès-Talleyrand end of
the line. The Council of Ancients, convoked at seven in the morning in
order that unfriendly and unnotified deputies might not be present,
voted that the councils should meet at St. Cloud, and that Napoleon
should be invested with command of all the troops in Paris. This
decree, brought to him at his house, was immediately read by him from
the balcony, and heard with cheers by the officers below.
The Napoleonic campaign was based upon the assumption that the
country was in danger, that the Jacobins had made a plot to overthrow
everything, and that all good citizens must rush to the rescue. Upon
this idea the council had voted its own removal to a place of safety,
and had appointed Napoleon to defend the government from the plotters
who were about to pounce upon it. Therefore when Napoleon read the
decree, he called aloud to the brilliant throng of uniformed officers,
"Will you help me save the country?" Wildly they shouted "Yes," and
waved their swords aloft. Bernadotte and a few others did not like
the looks of things, and drew apart; but, with these exceptions,
all were enthusiastic; and when Napoleon mounted his horse, they
followed. He went to the Council of Ancients, where he took the oath
of office, swearing not to the constitution then in existence, but
that France should have a republic based on civil liberty and national
representation.
The councils stood adjourned to St. Cloud, and Napoleon went into the
gardens of the Tuileries to review the troops. He briefly harangued
them, and was everywhere hailed by them with shouts of "Long live
Bonaparte!" So strong ran the current that Fouché volunteered aid that
had not been asked, and closed the city gates. "My God! what is that
for?" said Napoleon. "Order the gates opened. I march with the nation,
and I want nothing done which would recall the days when factious
minorities terrorized the people."
Augereau, seeing victory assured, regretted that he had not been
taken into the confidence of his former chief, "Why, General, have
you forgotten your old comrade, Augereau?" (Literally, "Your little
Augereau.") Napoleon had no confidence in him, no use for him, and
virtually told him so.
The Directory fell of its own weight; Sieyès and Roger-Ducos, as it
had been agreed, resigned. Gohier and Moulins would not violate the
constitution, which forbade less than three Directors to consult
together; and the third man, Barras, could not be got to act. The plot
had caught him unprepared. He knew that something of the kind was
on foot, and had tried to get on the inside; but he did not suspect
that Napoleon would spring the trap so soon. He had forgotten one of
the very essential elements in Napoleonic strategy. Barras bitterly
denies that the calamity dropped upon him while he was in his bath. He
strenuously contends that he was shaving. When Talleyrand and Bruix
came walking in with a paper ready-drawn for him to sign, he signed. It
was his resignation as Director. Bitterly exclaiming, "That--Bonaparte
has fooled us all," he made his swift preparations, left the palace,
and was driven, under Napoleonic escort, to his country-seat of
Gros-Bois. His signature had been obtained, partly by threats, partly
by promises. He was to have protection, keep his ill-gotten wealth,
and, perhaps, finger at least one more bribe. It is said that
Talleyrand, in paying over this last, kept the lion's share for himself.
The minister of war, Dubois de Crancé, had been running about seeking
Directors who would give him the order to arrest Napoleon. How he
expected to execute such an order if he got it, is not stated. As
Napoleon was legally in command of eight thousand soldiers, who were
even then bawling his name at the top of their voices, and as there
were no other troops in Paris, it may have been a fortunate thing for
the minister of war that he failed to get what he was running after.
From this distant point of view, the sight of Dubois de Crancé, chasing
the Napoleonic programme, suggests a striking resemblance to the
excitable small dog who runs, frantically barking, after the swiftly
moving train of cars. "What would he do with it if he caught it?" is as
natural a query in the one case as in the other.
So irresistible was the flow of the Bonaparte tide that even Lefebvre,
commander of the guard of the Directory, a man who had not been taken
into the secret, and who went to Bonaparte's house in ill-humor,
to know what such a movement of troops meant, was won by a word, a
magnetic glance, a caressing touch, and the tactful gift of the sabre
"which I wore at the Battle of the Pyramids." "Will you, a republican,
see the lawyers ruin the Republic? Will you help me?" "Let us throw the
lawyers into the river!" answered the simple-minded soldier, promptly.
According to Fouché, it was about nine o'clock in the morning when
Dubois found the two Directors, Gohier and Moulins, and asked for the
order to arrest Bonaparte. While they were in doubt and hesitating,
the secretary of the Directory, Lagarde, stated that he would not
countersign such an order unless three Directors signed it.
"After all," remarked Gohier, encouragingly, "how can they have a
revolution at St. Cloud when I have the seals of the Republic in my
possession?" Nothing legal could be attested without the seals. Gohier
had the seals; hence, Gohier was master of the situation. Of such
lawyers, in such a crisis, well might Lefebvre say, "Let us pitch them
into the river."
Quite relieved by the statement about the seals, Moulins remembered
another crumb of comfort: he had been invited to meet Napoleon at
dinner that very day at Gohier's. Between the soup and the cheese,
the two honest Directors would penetrate the designs of the schemer,
Napoleon, and then checkmate him.
Moreau had already been commissioned to keep these confiding legists
from running at large. However, it was not a great while before
they realized the true situation, and then they came to a grotesque
conclusion. They would go to Napoleon and talk him out of his purpose.
Barras had already sent Bottot, his private secretary, to see if
anything could be arranged. Napoleon had sternly said, "Tell that man
I have done with him." He had also addressed the astonished Bottot a
short harangue intended for publication: "What have you done with that
France I left so brilliant? In place of victory, I find defeat"--and so
forth.
Gohier and Moulins were civilly treated, but their protests were set
aside. They reminded Napoleon of the constitution, and of the oath of
allegiance. He demanded their resignations. They refused, and continued
to remonstrate. At this moment word came that Santerre was rousing
the section St. Antoine. Napoleon said to Moulins, "Send word to your
friend Santerre that at the first movement St. Antoine makes, I will
have him shot." No impression having been made by the Directors on
Napoleon, nor by him on them, they went back to their temporary prison
in the Luxembourg.
Thus far there had been no hitch in the Bonaparte programme. The
alleged Jacobin plot nowhere showed head; the Napoleonic plot was
in full and peaceable possession. There was no great excitement in
Paris, no unusual crowds collecting anywhere. Proclamation had been
issued to put the people at ease, and the attitude of the public was
one of curiosity and expectancy, rather than alarm. Not a single man
had rallied to the defence of the Directory. Their own guard had
quietly departed to swell the ranks which were shouting, "Hurrah for
Bonaparte!" Victor Grand, aide-de-camp to Barras, did indeed wait upon
that forlorn Director at seven o'clock in the morning of the 18th, and
report to him that one veteran of the guards was still at his post. "I
am here alone," said the old soldier; "all have left."
Here and there were members of the councils and generals of the army
who were willing enough to check the conspiracy of Napoleon, if they
had only known how. With the Directory smashed, the councils divided
and removed, the troops on Napoleon's side, and Paris indifferent, how
could Bernadotte, Jourdan, and Augereau do anything?
They could hold dismal little meetings behind closed doors, discuss
the situation, and decide that Napoleon must be checked. But who was
to bell the cat? At a meeting held by a few deputies and Bernadotte in
the house of Salicetti, it was agreed that they should go to St. Cloud
next morning, get Bernadotte appointed commander of the legislative
guard, and that he should then combat the conspirators. Salicetti
betrayed this secret to Napoleon; and, through Fouché, he frustrated
the plan by adroitly detaining its authors in Paris next morning.
To make assurance doubly sure, orders were issued that any one
attempting to harangue the troops should be cut down.
Sieyès advised that the forty or fifty members of the councils most
violently opposed to the Bonaparte programme be arrested during the
night. Napoleon refused. "I will not break the oath I took this
morning."
By noon of the 19th of Brumaire (November 10, 1799) the members of
the councils were at St. Cloud, excited, suspicious, indignant. Even
among the Ancients, a reaction against Napoleon had taken place. Many
of the members had supported him on the 18th of Brumaire because they
believed he would be satisfied with a place in the Directory. Since
then further conferences and rumors had convinced them that he aimed
at a dictatorship. Besides, those deputies who had been tricked out of
attending the session of the day before, resented the wrong, and were
ready to resist the tricksters. During the couple of hours which (owing
to some blunder) they had to wait for their halls to be got ready,
the members of the two councils had full opportunity to intermingle,
consult, and measure the strength of the opposition. When at length
they met in their respective chambers, they were in the frame of mind
which produces that species of disturbance known as a parliamentary
storm. Napoleon and his officers were grimly waiting in another room of
the palace for the cut-and-dried programme to be proposed and voted.
Sieyès had a coach and six ready at the gates to flee in case of mishap.
In the Five Hundred the uproar began with the session. The overwhelming
majority was against Bonaparte--this much the members had already
ascertained. But the opposition had not had time to arrange a
programme. Deputy after deputy sprang to his feet and made motions, but
opinions had not been focussed. One suggestion, however, carried; they
would all swear again to support the constitution: this would uncover
the traitors. It did nothing of the kind. The conspirators took the
oath without a grimace--Lucien Bonaparte and all. As each member had to
swear separately, some two hours were consumed in this childish attempt
to uncover traitors and buttress a falling constitution.
In the Ancients, also, a tempest was brewing. When the men, selected
by the Bonaparte managers, made their opening speeches and motions,
opposition was heard, explanations were demanded, and awkward questions
asked. Why move the councils to St. Cloud? Why vest extraordinary
command in Bonaparte? Where was this great Jacobin plot? Give facts and
name names!
No satisfaction could be given to such demands. The confusion was
increased by the report made to the body that four of the Directors had
resigned. Proceedings were suspended until the Council of Five Hundred
could receive this report, and some action be suggested for filling the
places thus made vacant.
At this point Napoleon entered the hall. He could hear the wrangle
going on in the Five Hundred, but he had not expected trouble in
the Ancients. The situation had begun to look dangerous. Augereau,
thinking it safe to vent his true feeling, had jeeringly said to
Napoleon, "Now you are in a pretty fix."
"It was worse at Arcole," was the reply.
Napoleon had harangued sympathetic Jacobins in small political
meetings; but to address a legislative body was new to him. His
talk to the Ancients was incoherent and weak. He could not give the
true reasons for his conduct, and the pretended reason could not be
strengthened by explanation or fact. He was asked to specify the
dangers which he said threatened the Republic, asked to describe the
conspiracy, and name the conspirators. He could not do so, and after
rambling all round the subject, his friends pulled him out of the
chamber. Notwithstanding his disastrous speech, the conspiracy asserted
its strength, and the Council of Ancients was held to the Bonaparte
programme. Napoleon at once went to the Council of Five Hundred, and
his appearance, accompanied by armed men, caused a tumult. "Down with
the Dictator! For shame! Was it for this you conquered. Get out! Put
him out!" Excited members sprang to their feet shouting, gesticulating,
threatening. Rough hands were laid upon him. Knives may have been
drawn. The Corsican, Peretti, had threatened Mirabeau with a knife in
the assembly hall: Tallien had menaced Robespierre with a dagger; there
is no inherent improbability in the story that the Corsican, Arena,
a bitter enemy of Napoleon, now struck at him with a knife. At all
events, the soldiers thought Napoleon in such danger that they drew him
out of the press, General Gardanne (it is said) bearing him backward in
his arms.
"_Hors la loi!_" was shouted in the hall--the cry before which
Robespierre had gone down. "Outlaw him! Outlaw him!"
Lucien Bonaparte, president of the body, refused to put the motion.
The anger of the Assembly then vented itself upon Lucien, who vainly
attempted to be heard in defence of his brother. "He wanted to
explain," cried Lucien, "and you would not hear him!" Finding the
tumult grow worse, and the demand that he put the motion grow more
imperative, he stripped himself of the robe of office, sent for an
escort of soldiers, and was borne out by Napoleon's grenadiers.
While the council chamber rang with its uproar, there had been
consternation outside. For a moment the Bonaparte managers hesitated.
They had not foreseen such a check. Napoleon himself harangued the
troops; and telling them that an attempt had been made on his life,
was answered by cries of "Long live Bonaparte!" It was noticed that he
changed his position every moment, zig-zagging as much as possible,
like a man who feared some assassin might aim at him from a window in
the palace. He said to Sieyès, "They want to outlaw me!" Seated in his
carriage, ready to run, but not yet dismayed, the ex-priest is said
to have answered: "Then do you outlaw them. Put them out." Napoleon,
reëntering the room where the officers were sitting or standing,
in dismay and inaction, struck the table with his riding-whip, and
said, "I must put an end to this." They all followed him out. Lucien,
springing upon a horse, harangued the troops, calling upon them to
drive out from the hall the factious minority which was intimidating
the virtuous majority of the council. The soldiers hesitated. Drawing
his sword, Lucien shouted, "I swear that I will stab my brother to the
heart if ever he attempt anything against the liberties of the people!"
This was dramatic, and it succeeded. The troops responded with cheers,
and Napoleon saw that they were at length ready. "_Now_ I will soon
settle those gentlemen!" He gave Murat the signal; Murat and Le
Clerc took the lead; and to the roll of drums the file advanced. The
legislators would have spoken to the troops, but the drums drowned the
protest. Before the advancing line of steel, the members fled their
hall, and the Bonaparte campaign was decided.
But once more Sieyès was the giver of sage advice. Legal forms must
be respected. France was not yet ready for the bared sword of the
military despot. The friendly members of the Council of Five Hundred
must be sought out and brought back to the hall. The deputies were
not yet gone, were still lingering in astonishment and grief and rage
about the palace. Lucien Bonaparte, the hero of this eventful day,
contrived to assemble about thirty members of the Council of Five
Hundred who would vote the Bonaparte programme through. They spent most
of the night adopting the measures proposed. It was past midnight when
the decrees of this Rump Parliament were presented to the Ancients
for ratification. In that assembly the Bonaparte influence was again
supreme, and no bayonets were needed there. Napoleon, Sieyès, and
Roger-Ducos having been named provisional consuls, appeared before the
Five Hundred between midnight and day to take the oath of office.
The legislative councils then stood adjourned till February 19, 1800.
Commissions had been selected to aid in framing the constitution.
Lucien made the last speech of the Revolution, and, according to Mr.
Lanfrey, it was the most bombastic piece of nonsense and falsehood that
had been uttered during the entire period. He compared the Tennis Court
Oath to the work just done, and said that, as the former had given
birth to liberty, this day's work had given it manhood and permanence.
Not until the last detail of the work had been finished and put in
legal form, did Napoleon quit St. Cloud. He had even dictated a
proclamation in which he gave to the public his own account of the
events of the day. He again laid stress on the Jacobin plot which had
threatened the Republic, he again renewed his vows to that Republic, he
praised the conduct of the Ancients, and claimed that the violence used
against the Five Hundred had been made necessary by the factious men,
would-be assassins, who had sought to intimidate the good men of that
body. This proclamation was posted in Paris before day.
To humor the fiction, if it was a fiction, that Napoleon had been
threatened with knives, a grenadier, Thomas Thomé, was brought forward,
who said that he had warded off the blow. He showed where his clothes
had been cut or torn. As soon as the stage could be properly arranged
for the scene, the amiable and grateful Josephine publicly embraced
Thomé and made him a present of jewels. Napoleon promoted him later to
a captaincy.
The men who stood by Napoleon in this crisis left him under a debt
which he never ceased to acknowledge and to pay. With one possible
exception, he loaded them with honors and riches. The possible
exception was Collot, the banker, who, according to Fouché, supplied
the campaign fund. The bare fact that Napoleon did not at any time
treat Collot with favor, is strong circumstantial evidence that he
rendered no such aid at this crisis as created a debt of gratitude.
It was morning, but before daybreak, when Napoleon, tired but exultant,
reached home from St. Cloud. As he threw himself upon the bed by the
side of Josephine, he called out to his secretary:--
"Remember, Bourrienne, we shall sleep in the Luxembourg to-morrow."
CHAPTER XXI
On Sunday evening, Brumaire 19, Napoleon had been a desperate political
gambler, staking fortune and life upon a throw; on Monday morning
following he calmly seated himself in the armchair at the palace of the
Luxembourg and began to give laws to France. He took the first place
and held it, not by any trick or legal contrivance, but by his native
imperiousness and superiority. In genius, in cunning, in courage,
he was the master of the doctrinaire Sieyès, and of the second-rate
lawyer, Roger-Ducos; besides, he held the army in the hollow of his
hand.
The sad comfort of saying "I told you so," was all that was left to
Sieyès. "Gentlemen, we have a master," said he to his friends that
Monday evening; and the will of this imperious colleague he did not
seriously try to oppose. In the very first meeting of the consuls,
Napoleon had won the complete supremacy by refusing to share in the
secret fund which the Directors had hidden away for their own uses.
They had emptied the treasury, and had spent $15,000,000 in advance
of the revenues, yet they had laid by for the rainy day which might
overtake themselves personally the sum of 800,000 francs or about
$160,000. Sieyès blandly called attention to this fact, and proposed
that he, Ducos, and Napoleon should divide the fund. "Share it between
you," said Napoleon, who refused to touch it.
[Illustration: NAPOLEON
As First Consul, at Malmaison. From a painting by J. B. Isabey]
* * * * *
Without the slightest apparent effort, Napoleon's genius expanded to
the great work of reorganizing the Republic. Heretofore he had been
a man of camps and battle-fields; but he had so completely mastered
everything connected with the recruiting equipment and maintenance
of an army, had served so useful an apprenticeship in organizing the
Italian republics, and had been to school to such purpose in dealing
with politicians of all sorts, negotiating treaties, and sounding the
secrets of parties, that he really came to his great task magnificently
trained by actual experience.
In theory the new government of the three consuls was only
experimental, limited to sixty days. The two councils had not been
dissolved. Purged of about sixty violently anti-Bonaparte members,
the Ancients and the Five Hundred were but adjourned to the 19th of
February, 1800. If by that time the consuls had not been able to offer
to France a new scheme of government which would be accepted, the
councils were to meet again and decide what should be done. On paper,
therefore, Napoleon was a consul on probation, a pilot on a trial trip.
In his own eyes he was permanent chief of the State; and his every
motion was made under the impulse of that conviction.
Determined that there should be no reaction, that the scattered forces
of the opposition should have no common cause and centre of revolt, he
stationed his soldiers at threatened points; and then used all the art
of the finished politician to deceive and divide the enemy. To the
royalists he held out the terror of a Jacobin revival; to the Jacobin,
the dread of a Bourbon restoration. To the clergy he hinted a return
of the good old days when no man could legally be born, innocently
married, decently die, or be buried with hope of heaven, unless a
priest had charge of the functions. But above all was his pledge of
strong government, one which would quell faction, restore order, secure
property, guarantee civil liberty, and make the Republic prosperous and
happy. The belief that he would make good his word was the foundation
of the almost universal approval with which his seizure of power was
regarded. He was felt to be the one man who could drag the Republic
out of the ditch, reinspire the armies, cleanse the public service,
restore the ruined finances, establish law and order, and blend into a
harmonious nationality the factions which were rending France. Besides,
it was thought that a strong government would be the surest guarantee
of peace with foreign nations, as it was believed that the weakness
of the Directory was an encouragement to the foreign enemies of the
country.
One of Napoleon's first acts was to proclaim amnesty for political
offences. He went in person to set free the hostages imprisoned in the
Temple. Certain priests and émigrés who had been cast into prison, he
released. The law of hostages, which held relatives responsible for the
conduct of relatives, he repealed.
The victims of Fructidor (September, 1797) who had been banished, he
recalled--Pichegru and Aubrey excepted.
Mr. Lanfrey says that this exception from the pardon is proof of
Napoleon's "mean and cruel nature." Let us see. Pichegru, a republican
general, in command of a republican army, had taken gold from the
Bourbons, and had agreed to betray his army and his country. Not only
that, he had purposely allowed that army to be beaten by the enemy. As
Desaix remarked, Pichegru was perhaps the only general known to history
who had ever done a thing of the kind. Was Napoleon mean and cruel in
letting such a man remain in exile? Had Washington captured and shot
Benedict Arnold, would that have been proof that Washington's nature
was mean and cruel? In leaving Pichegru where he was, Napoleon acted as
leniently as possible with a self-convicted traitor.
As to Aubrey, he had held a position of the highest trust under the
Republic, while he was at heart a royalist; he had used that position
to abet royalist conspiracies; he had gone out of his way to degrade
Napoleon, had refused to listen to other members of the government in
Napoleon's favor, and had urged against Napoleon two reasons which
revealed personal malice,--Napoleon's youth, and Napoleon's politics.
To pardon such a man might have been magnanimous; to leave him under
just condemnation was neither mean nor cruel.
Under the law of that time, there were about 142,000 émigrés who
had forfeited life and estate. They had staked all in opposition to
the Revolution, had lost, and had been put under penalty. Almost
immediately, Napoleon began to open the way for the return of these
exiles and for the restoration of their property. As rapidly as
possible, he broadened the scope of his leniency until all émigrés had
been restored to citizenship save the very few (about one thousand) who
were so identified with the Bourbons, or who had so conspicuously made
war on France, that their pardon was not deemed judicious.
Priests were gradually relieved from all penalties and allowed to
exercise their office. Churches were used by Christians on the
seventh-day Sabbath, and by Theophilanthropists on the Decadi--the
tenth-day holiday. The one sect came on the seventh day with holy
water, candles, holy image, beads, crucifix, song, prayer, and sermon
on faith, hope, and charity,--with the emphasis thrown on the word,
Faith. The other sect came on the tenth day with flowers for the altar,
hymns and addresses in honor of those noble traits which constitute
lofty character, and with the emphasis laid upon such words as
Brotherhood, Charity, Mercy, and Love.
It was not a great while, of course, before the Christians (so recently
pardoned) found it impossible to tolerate the tenth-day people; and
they were quietly suppressed in the Concordat.
One of the Directors, Larévellière, was an ardent Theophilanthropist,
and he had made vigorous effort to enroll Napoleon on that side, soon
after the Italian campaign. The sect, being young and weak, found no
favor whatever in the eyes of the ambitious politician; and he who in
Egypt sat cross-legged among the ulemas and muftis, demurely taking
lessons from the Koran, had no hesitation in repelling the advances of
Theosophy.
Going, perhaps, too far in his leniency to the émigrés (Napoleon
said later that it was the greatest mistake he ever made!), the new
government certainly erred in its severity toward the Jacobins. Some
fifty-nine of these were proscribed for old offences, and sentenced to
banishment. Public sentiment declared against this arbitrary _ex post
facto_ measure so strongly that it was not enforced.
The men of the wealthy class were drawn to the government by the
repeal of the law called the Forced Loan. This was really an income
tax, the purpose of which was to compel the capitalists to contribute
to the support of the State. The Directors, fearing that the rich men
who were subject to the tax might not make true estimates and returns,
assessed it by means of a jury. Dismal and resonant wails arose from
among the stricken capitalists.
Although the government created the tax as a loan, to be repaid
from the proceeds of the national domain, the antagonism it excited
was intense. In England, Mr. Pitt had (1798) imposed a tax upon
incomes,--very heavy in its demands, and containing the progressive
principle of the larger tax for the larger income,--but the Directors
were too feeble to mould the same instrument to their purpose in
France. Faultily assessed, stubbornly resisted, irregularly collected,
it yielded the Directory more odium than cash.
The five per cent funds which had fallen to one and a half per cent
of their par value before the 18th of Brumaire, had risen at once to
twelve per cent, and were soon quoted at seventeen.
Confidence having returned, Napoleon was able to borrow 12,000,000
francs for the immediate necessities of the State. The income tax
having been abolished, an advance of twenty-five per cent was made in
the taxes on realty, personalty, and polls. Heretofore, these taxes
had been badly assessed, badly collected, imperfectly paid into the
treasury. Napoleon at once remodelled the methods of assessment,
collection, and accounting. Tax collectors were required to give bonds
in cash; were made responsible for the amount of the taxes legally
assessed; were given a certain time within which to make collection,
and were required to give their own bills for the amount assessed.
These bills, backed by the cash deposit of the collectors, became good
commercial paper immediately, and thus the government was supplied with
funds even before the taxes had been paid.
It was with this cash deposit of the collectors that Napoleon paid for
the stock which the government took in the Bank of France which he
organized in January, 1800.
There yet remained in the hands of the government a large amount of
the confiscated land, and some of this was sold. To these sources of
revenue were soon added the contributions levied upon neighboring and
dependent states, such as Genoa, Holland, and the Hanse towns.
Under the Directory, tax-collecting and recruiting for the army had
been badly done because the work had been left to local authorities.
The central government could not act upon the citizen directly; it
had to rely upon these local authorities. When, therefore, the local
authorities failed to act, the machinery of administration was at a
standstill. Napoleon changed all this, and devised a system by which
the government dealt directly with the citizen. It was a national
officer, assisted by a council, who assessed and collected taxes. The
prefects appointed by Napoleon took the place of the royal intendants
of the Bourbon system. Holding office directly from the central
government, and accountable to it alone, these local authorities became
cogs in the wheel of a vast, resistless machine controlled entirely by
the First Consul. So perfect was the system of internal administration
which he devised, that it has stood the shock of all the changes which
have since occurred in France.
Keeping himself clear of parties, and adhering steadily to the
policy of fusion, Napoleon gave employment to men of all creeds. He
detested rogues, speculators, embezzlers. He despised mere talkers
and professional orators. He wanted workers, strenuous and practical.
He cared nothing for antecedents, nor for private morals. He knew the
depravity of Fouché and Talleyrand, yet used them. He gave employment
to royalists, Jacobins, Girondins, Deists, Christians, and infidels.
"Can he do the work, and will he do it honestly?" these were the
supreme tests. No enmity would deprive him of the service of the honest
and capable. No friendship would tolerate the continuance in office of
the dishonest or incompetent. Resolute in this policy of taking men as
he found them, of making the most of the materials at hand, he gave
high employment to many a man whom he personally disliked. He gave
to Talleyrand the ministry of foreign affairs, to Fouché that of the
police, to Carnot that of war. To Moreau he gave the largest of French
armies; Augereau, Bernadotte, Jourdan, he continued to employ. "I
cannot create men; I must use those I find." Again he said, "The 18th
of Brumaire is a wall of brass, separating the past from the present."
If they were capable, if they were honest, it did not matter to
Napoleon whether they had voted to kill the King or to save him; he put
them to work for France. Once in office, they must work. No sinecures,
no salaries paid as hush money, or indirect bribe, or pension for past
service, or screen for the privileged; without exception all must
earn their wages. "Come, gentlemen!" Napoleon would say cheerfully
to counsellors of State who had already been hammering away for ten
or twelve hours, "Come, gentlemen, it is only two o'clock! Let us
get on to something else; we must earn the money the State pays us."
He himself labored from twelve to eighteen hours each day, and his
activity ran the whole gamut of public work,--from the inspection of
the soldier's outfit, the planning of roads, bridges, quays, monuments,
churches, public buildings, the selection of a sub-prefect, the choice
of a statue for the palace, the review of a regiment, the dictation of
a despatch, or the details of a tax-digest, to the grand outlines of
organic law, national policy, and the movements of all the armies of
the Republic.
Under the Directory, the military administration had broken down so
completely that the war office had lost touch with the army. Soldiers
were not fed, clothed, or paid by the State. They could subsist only by
plundering friends and foes alike. Frightful ravages were committed by
civil and military agents of the French Republic in Italy, Switzerland,
and along the German frontier. When Napoleon applied to the late
minister of war, Dubois de Crancé, for information about the army, he
could get none. Special couriers had to be sent to the various commands
to obtain the most necessary reports. Under such mismanagement,
desertions had become frequent in the army, and recruiting had
almost ceased. The old patriotic enthusiasm had disappeared; the
"Marseillaise" performed at the theatres, by order of the Directory,
was received with hoots. To breathe new life into Frenchmen, to inspire
them again with confidence, hope, enthusiasm, was the great task of the
new government. The Jacobin was to be made to tolerate the royalist,
the Girondin, the Feuillant, and the priest. Each of these in turn
must be made to tolerate each other and the Jacobin. The noble must
consent to live quietly within the Republic which had confiscated his
property, and by the side of the man who now owned it. The republican
must dwell in harmony with the emigrant aristocracy which had once
trodden him to the earth, and which had leagued all Europe against
France in the efforts to restore old abuses. In the equality created
by law, the democrat must grow accustomed to the sight of nobles and
churchmen in office; and the man of the highest birth must be content
to work with a colleague whose birth was of the lowest. Ever since the
Revolution began, there had been alternate massacres of Catholics by
revolutionists, and of revolutionists by Catholics. It is impossible
to say which shed the greatest amount of blood--the Red Terror of the
Jacobins, or the White Terror of the Catholics. Fanaticism in the
one case as in the other had shown a ferocity of the most relentless
description. The cruel strife was now to be put down, and the men who
had been cutting each other's throats were to be made to keep the peace.
Napoleon, in less than a year, had completely triumphed over the
difficulties of his position. The machinery of state was working with
resistless vigor throughout the realm. The taxes were paid, the laws
enforced, order reëstablished, brigandage put down, La Vendée pacified,
civil strife ended. The credit of the government was restored, public
funds rose, confidence returned. Men of all parties, of all creeds,
found themselves working zealously to win the favor of him who worked
harder than any mortal known to history.
Meanwhile Sieyès and the two commissions had been at work on the new
constitution. Dreading absolute monarchy on the one hand, and unbridled
democracy on the other, Sieyès had devised a plan of government which,
as he believed, combined the best features of both systems. There was
to be universal suffrage. Every tax-paying adult Frenchman who cared
enough about the franchise to go and register should have a vote.
But these voters did not choose office-holders. They simply elected
those from whom the office-holders should be chosen. The great mass
of the people were to elect one-tenth of their number, who would be
the notables of the commune. These would, in turn, elect one-tenth of
their number, who would be the notables of the department. These again
would elect one-tenth, who would be the national notables. From these
notables would be chosen the office-holders,--national, departmental,
and communal. This selection was made, not by the people, but by the
executive. There was to be a council of state working immediately with
the executive by whom its members were appointed. This council acting
with the executive would propose laws to the tribunate, an assembly
which could debate these prepared measures and which could send three
of its members to the legislative council to favor or oppose the law.
This legislature could hear the champions of the tribunate, and also
the delegates from the council of state; and after the speeches of
these advocates, pro and con, the legislature, as a constitutional jury
which heard debate without itself debating, could vote on the proposed
law. Besides, there was to be a Senate, named by the executive,
holding office for life. This Senate was to choose the members of the
legislative council and of the tribunate, as well as the judges of the
high court of appeals. In the Senate was lodged the power of deciding
whether laws were constitutional.
According to the Sieyès plan, there were to have been two consuls, of
war and of peace respectively; and these consuls were to have named
ministers to carry on the government through their appointees. Above
the two consuls was to be placed a grand elector, who should be lodged
in a palace, maintained in great state, magnificently salaried, but who
should have no power beyond the choice of the consuls. If the Senate
should be of the opinion, at any time, that the grand elector was not
conducting himself properly, it could absorb him into its own body, and
choose another.
Sieyès had been one of the charter members of the revolutionary party,
had helped to rock the cradle when the infant was newly born, had
lived through all the changes of its growth, manhood, madness, and
decline. Much of the permanent good work of the Revolution was his.
He now wished to frame for the French such a fundamental law as would
guard their future against the defects of their national character,
while it preserved to them what was best in the great principles of the
Revolution.
Once a churchman himself, he knew the Church and dreaded it. He feared
that the priests, working through superstitious fears upon the minds of
ignorant masses, would finally educate them into hostility to the new
order--train them to believe that the Old Régime had been the best, and
should be restored. To get rid of this danger (the peril of royalists
and priests from above acting upon the ignorant masses below), the
far-sighted statesman, dealing with France as it was, did not favor
popular sovereignty. Only by indirection were the masses to be allowed
to choose their rulers. The people could choose the local notables from
whom the local officers must be taken; and these local notables could
vote for departmental notables from whom departmental officers should
be chosen; and those departmental notables would select from their own
numbers the national notables from whom holders for national positions
must be taken.
These electoral bodies grew smaller as they went upward. The 5,000,000
voters of the nation first elected 500,000 local notables; these chose
from themselves 50,000 departmental electors; and these in turn took
by vote 5000 of their own number to constitute the electoral class for
national appointments. The executive filled all offices from these
various groups. From below, the masses furnished the material to be
used in governing; from above, the executive made its own selection
from that material.
This was far from being representative government; but it was far from
being mere despotism, military or otherwise. It was considered as free
a system as France was then prepared for; and he is indeed a wise man
who knows that she would have done better under a constitution which
granted unlimited popular control. The French had not been educated or
trained in republican government, and the efforts which had been made
to uphold a republic in the absence of such education and experience
had resulted in the dictatorship of the Great Committee and of the
Directory.
Napoleon and Sieyès were agreed on the subject of popular suffrage;
they were far apart on the question of the executive. By nature
"imperious, obstinate, masterful," the great Corsican had no idea of
becoming a fatuous, functionless elector. "What man of talent and honor
would consent to such a rôle,--to feed and fatten like a pig in a stye
on so many millions a year?" Before this scornful opposition the grand
elector vanished. In his place was put a First Consul, in whom were
vested all executive powers. Two associate consuls were given him, but
their functions in no way trenched upon his.
The constitution, rapidly completed, was submitted to the people by the
middle of December, 1799. It was adopted by three million votes--the
negative vote being insignificant.
"This constitution is founded on the true principles of representative
government, on the sacred rights of property, equality, and liberty."
"The Revolution is ended." So ran the proclamation published by the
provisional government.
It was a foregone conclusion that Napoleon would be named First Consul
in the new government which the people had ratified. It is no less
true that he dictated the choice of his two colleagues,--Cambacérès
and Lebrun. These were men whose ability was not of the alarming kind,
and who could be relied upon to count the stars whenever Napoleon, at
midday, should declare that it was night. Sieyès was soothed with the
gift of the fine estate of Crosne, and the presidency of the Senate.
Roger-Ducos also sank peacefully into the bosom of that august,
well-paid Assembly.
It was on Christmas Eve of 1799 that the government of the three
permanent consuls began; by the law of its creation it was to live for
ten years.
This consular government was a magnificent machine, capable of
accomplishing wonders when controlled by an able ruler. The gist of
it was concentration and uniformity. All the strength of the nation
was placed at the disposal of its chief. He could plan and execute,
legislate and enforce legislation, declare war and marshal armies,
and make peace. He was master at home and abroad. In him was centred
France. He laid down her laws, fixed her taxes, dictated her system of
schools, superintended her roads and bridges, policed her towns and
cities, licensed her books, named the number of her armies; pensioned
the old, the weak, and the deserving; censored her press, controlled
rewards and punishments,--his finger ever on the pulse-beat of the
nation, his will its master, his ideals its inspiration.
No initiative remained with the people. Political liberty was a
reminiscence. The town bridge could not be rebuilt or the lights of
the village changed without authority granted from the Consul or his
agents. "Confidence coming from below; power descending from above,"
was the principle of the new Sieyès system. Under just such a scheme
it was possible that it might happen that the power of the ruler would
continue to come down long after the confidence of the subject had
ceased to go up.
The Revolution had gone to the extreme limits of popular sovereignty
by giving to every citizen the ballot, to every community the right
of local self-government; and to the masses the privilege of electing
judicial and military as well as political officers. France was
said to be cut up into forty thousand little republics. The central
authority was almost null; the local power almost absolute. It was
this federative system carried to excess (as under the Articles of
the Confederation in our own country) which had made necessary the
despotism of the Great Committee. The consular constitution was the
reverse of this. Local government became null, the central authority
almost absolute. Prefects and sub-prefects, appointed by the executive,
directed local affairs, nominally assisted by local boards, which met
once a year. Even the mayors held their offices from the central power.
From the lowest round of the official ladder to the highest, was a
steady climb of one rung above the other. The First Consul was chief,
restrained by the constitution; below him, moving at his touch, came
all the other officers of state.
Under Napoleon the burden of supporting the State rested on the
shoulders of the strong. Land, wealth, paid the direct taxes; the
customs duties were levied mainly upon luxuries, not upon the
necessaries of life. Prior to the Revolution the taxes of the
unprivileged had amounted to more than three-fourths of the net produce
of land and labor. Under the Napoleonic system the taxes amounted to
less than one-fourth of the net income.
Before the Revolution the poor man lost fifty-nine days out of every
year in service to the State by way of tax. Three-fifths of the French
were in this condition. After the Revolution the artisan, mechanic,
and day laborer lost from nine to sixteen days per year. Before the
Revolution Champfort could say, "In France seven millions of men beg
and twelve millions are unable to give anything." To the same purport
is the testimony of Voltaire that one-third of the French people had
nothing.
Under Napoleon an American traveller, Colonel Pinkney could write,
"There are no tithes, no church taxes, no taxation of the poor. All the
taxes together do not go beyond one-sixth of a man's rent-roll."
Before the Revolution the peasant proprietor and small farmer, out
of 100 francs net income, paid 14 francs to the seigneur, 14 to the
Church, and 53 to the State. After Napoleon's rise to power, the same
farmer out of the same amount of income paid nothing to the seigneur,
nothing to the Church, very little to the State, and only 21 francs to
the commune and department. Under the Bourbons such a farmer kept for
his own use less than 20 francs out of 100; under Napoleon he kept 79.
Under the Bourbons the citizen was compelled to buy from the government
seven pounds of salt every year at the price of thirteen sous per
pound, for himself and each member of his family. Under Napoleon he
bought no more than he needed, and the price was two sous per pound.
Under the Bourbons the constant dread of the peasant, for centuries,
had been Famine--national, universal, horribly destructive Famine. With
Napoleon's rise to power, the spectre passed away; and, excepting local
and accidental dearths in 1812 and 1817, France heard of Famine no more.
Napoleon believed that each generation should pay its own way. He had
no grudge against posterity, and did not wish to live at its expense.
Hence he "floated" no loans, issued no bonds, and piled up no national
debt.
The best of the Bourbon line, Henry IV., lives in kindly remembrance
because he wished the time to come when the French peasant might, once
a week, have a fowl for the pot. Compare this with what Lafayette
writes (in 1800): "You know how many beggars there were, people dying
of hunger in our country. We see no more of them. The peasants are
richer, the land better tilled, and the women better clad."
Morris Birkbeck, an English traveller, writes, "Everybody assures
me that the riches and comfort of the farmers have been doubled in
twenty-five years.
"From Dieppe to this place, Montpellier, we have not seen among the
laboring people one such famished, worn-out, wretched object as may
be met in every parish in England, I had almost said on almost every
farm.... A really rich country, and yet there are few rich individuals."
As one reads paragraphs like these, the words of John Ruskin come to
mind, "Though England is deafened with spinning-wheels, her people have
no clothes; though she is black with digging coal, her people have no
fuel, and they die of cold; and though she has sold her soul for gain,
they die of hunger!"
* * * * *
How the government which was overthrown by Napoleon could have gone on
much longer even Mr. Lanfrey does not explain. It had neither money nor
credit; the very cash box of the opera had been seized to obtain funds
to forward couriers to the armies. It had neither honesty nor capacity.
Talleyrand, treating with the American envoys, declined to do business
till his hands had been crossed, according to custom; brigands robbed
mail coaches in the vicinity of Paris; the public roads and canals were
almost impassable; rebellion defied the government in La Vendée. The
Directory did not even have the simple virtue of patriotism; Barras was
sold to the Bourbons, and held in his possession letters-patent issued
to him by the Count of Provence, appointing him royal commissioner
to proclaim and reëstablish the monarchy. "Had I known of the
letters-patent on the 18th of Brumaire," exclaimed Napoleon afterward,
"I would have pinned them upon his breast and had him shot."
CHAPTER XXII
All honor to the ruler who commences his reign by words and deeds
which suggest that he has somewhere heard and heeded the golden text,
"Blessed are the peacemakers!"
There had been riots in France and the clash of faction; there had
been massacre of Catholic by Protestant and of Protestant by Catholic;
there had been civil war in La Vendée. Napoleon had no sooner become
master than his orders went forth for peace, and a year had not passed
before quiet reigned from Paris to all the frontiers. Royally he
pardoned all who would accept his clemency, giving life and power to
many a secret foe who was to help pull him down in the years to come.
France tranquillized within, the First Consul turned to the enemies
without,--to the foreign powers which had combined against her.
On Christmas Day, December 25, 1799, Napoleon wrote to the King of
England and to the Emperor of Austria nobly worded letters praying
that the war might cease. Written with his own hand, and addressed
personally to these monarchs, the question of etiquette is raised
by royalist writers. They contend that letters, so addressed, were
improper. Think of the coldness of nature which would make the lives
of thousands of men turn on a pitiful point like that! These letters
were not sincere, according to Napoleon's detractors. How they come to
know this, they cannot explain; but they know it. The average reader,
not gifted with the acumen of the professional detractor, can only be
certain of the plain facts of the case, and those are, that Napoleon
made the first overtures for peace; that his words have the ring of
sincerity, and the virtue of being positive; and that his conciliatory
advances were repelled, mildly by Austria, insolently by Great Britain.
So arrogant was the letter of reply which Grenville, the English
minister, sent to the French foreign office that even George III.
disapproved of it. With incredible superciliousness the French were
told by the English aristocrat that they had better restore the
Bourbons under whose rule France had enjoyed so much prosperity at
home and consideration abroad. Inasmuch as England had but recently
despoiled Bourbon France of nearly every scrap of territory she had in
the world,--Canada, India, etc.,--Grenville's letter was as stupidly
scornful of fact as it was of good manners. The Bourbon "glory" which
had sunk so low that France had not even been invited to the feast when
Poland was devoured; so low that the French flag had been covered with
shameful defeat on land and sea, was a subject which might have made
even a British cabinet officer hesitate before he took the wrong side
of it.
The honors of the correspondence remained with Napoleon; and by way
of retort to Grenville's plea, that the Bourbons were the legitimate
rulers of France, whom the people had no right to displace, the surly
Englishman was reminded that the logic of his argument would bring the
Stuarts back to the throne of England, from which a revolting people
had driven them. The truth is that Pitt's ministry believed France
exhausted. Malta and Egypt were both coveted by Great Britain, and it
was believed that each would soon be lost by France. It was for reasons
like these that Napoleon's overtures were rejected.
With the Emperor of Russia the First Consul was more fortunate. The
Czar had not liked the manner in which he had been used by his allies,
England and Austria. In fact, he had been shabbily treated by both.
Added to this was his dissatisfaction with England because of her
designs on Malta, in whose fate he took an interest as protector of the
Knights of St. John.
Napoleon cleverly played upon the passions of the Czar (who was more or
less of a lunatic), flattered him by releasing the Russian prisoners
held by France, and sending them home in new uniforms. Soon Napoleon
had no admirer more ardent than the mad autocrat Paul, who wrote him a
personal letter proposing a joint expedition against India.
Prussia had declared her neutrality. Napoleon sent Duroc and a letter
to the young King urging an alliance, Hamburg being the bait dangled
before the Prussian monarch's eyes. He was gracious, and he was
tempted, but he did not yield: Prussia remained neutral.
Great Britain had good reasons for wishing for the restoration of the
Bourbons, from whose feeble hands so much of the colonial Empire of
France had dropped; she had good reason to believe that a continuation
of the war would increase her own colonial empire, but the manner in
which she repelled Napoleon's advances gave to France just the insult
that was needed to arouse her in passionate support of the First Consul.
Forced to continue the war, his preparations were soon made.
* * * * *
It may be doubted whether any victory that he ever won held a higher
place in the memory of the great captain than that of Marengo. He never
ceased to recall it as one of the most glorious days of his life. We
see a proof of this in the Memoirs of General Marbot. The year was
1807, the battle of Eylau had been fought, the armies were in motion
again; and Lannes, hard-pressed by the Russian host at Friedland, had
sent his aide-de-camp speeding to the Emperor to hurry up support.
"Mounted on my swift Lisette, I met the Emperor leaving Eylau. His
face was beaming. He made me ride up by his side, and as we galloped
I had to give him an account of what had taken place on the field of
battle before I had left. The report finished, the Emperor smiled,
and asked, "Have you a good memory?"--"Pretty fair, sire."--"Well,
what anniversary is it to-day, the 14th of June?"--"Marengo."--"Yes,"
replied the Emperor, "and I am going to beat the Russians to-day as I
beat the Austrians at Marengo." And as Napoleon reached the field, and
rode along the lines, he called out to his troops, "It is a lucky day,
the anniversary of Marengo!" The troops cheered him as he rode, and
they won for him the great battle of Friedland."
The old uniform, sabre, spurs, hat, he had worn on that sunny day in
Italy, in 1800, he scrupulously kept. In the year he was crowned
Emperor he carried Josephine to see the plain he had immortalized,
fought again in sham fight the battle of Marengo, wearing the faded
uniform he had worn on that eventful day.
Even on his last journey to dismal St. Helena, it seems that these
relics of a glorious past were not forgotten. We read that when the
dead warrior lay stark and stiff in his coffin on that distant rock,
they spread over his feet "the cloak he had worn at Marengo."
* * * * *
It was indeed a brilliant campaign, great in conception, execution,
results.
Moreau's army lay upon the Rhine, more than one hundred thousand
strong. Masséna with the army of Italy guarded the Apennines, facing
overwhelming odds. From Paris the First Consul urged Masséna to hold
his ground, and Moreau to advance. Against the latter was a weak
Austrian commander, Kray, and forces about equal to the French. Much
time was lost, Napoleon proposing a plan which Moreau thought too
bold, and was not willing to risk. Finally the First Consul yielded,
gave Moreau a free hand, and the advance movement began. The Rhine was
crossed, and Moreau began a series of victories over Kray which brought
him to the Danube. But the Austrians, taking the offensive against the
army of Italy, cut it in two, and shut up Masséna in Genoa, where the
English fleet could coöperate against the French.
It was then that Napoleon, almost by stealth, got together another
army, composed partly of conscripts, partly of veterans from the armies
of La Vendée and Holland, and hurried it to the foot of the Alps. The
plan was to pass these mountains, fall upon the Austrian rear, and
redeem Italy at a blow. His enemies heard of the Army of the Reserve
which he was collecting at Dijon. Spies went there, saw a few thousand
raw recruits, and reported that Napoleon had no Army of Reserve--that
he was merely trying to bluff old Melas into loosening his grip on
Genoa. It suited Napoleon precisely to have his new army treated as a
joke. With consummate art he encouraged the jest while he collected,
drilled, and equipped at different points the various detachments with
which he intended to march.
Under the constitution the First Consul could not legally command the
army. He was not forbidden, however, to be present as an interested
spectator while some one else commanded. So he appointed Berthier,
General-in-chief.
Early in May, 1800, all was ready, and the First Consul left Paris to
become the interested spectator of the movements of the Army of the
Reserve. At the front, form and fiction gave way to actuality, and
Napoleon's word was that of chief. At four different passes the troops
entered the mountains, the main army crossing by the Great St. Bernard.
Modern students, who sit in snug libraries and rectify the arduous
campaigns of the past, have discovered that Napoleon's passage of the
Alps was no great thing after all. They say that his troops had plenty
to eat, drink, and wear; thousands of mules and peasants to aid in the
heavy work of the march; no foes to fight on the way; and that his
march was little more than a military parade. Indeed, it was one of
those things which looked a deal easier after it had been done than
before. And yet it must have been a notable feat to have scaled those
mighty barriers on which lay the snow, to have threaded those paths up
in the air over which the avalanche hung, and below which the precipice
yawned--all this having been done with such speed that the French were
in Italy before the Austrians knew they had left France. Much of the
route was along narrow ledges where the shepherd walked warily. To
take a fully equipped army over these rocky shelves,--horse, foot,
artillery, ammunition, supplies,--seems even at this admire-nothing
day to have been a triumph of organization, skill, foresight, and
hardihood. Only a few months previously a Russian army, led by Suwarow,
had ventured to cross the Alps--and had crossed; but only half of them
got out alive.
In less than a week the French made good the daring attempt, and were
in the valleys of Italy marching upon the Austrian rear. They had
brought cavalry and infantry almost without loss. Cannon had been laid
in hollowed logs and pulled up by ropes. The little fort of Bard, stuck
right in the road out of the mountains, had, for a moment, threatened
the whole enterprise with ruin. Napoleon had known of the fortress, but
had underrated its importance. For some hours a panic seemed imminent
in the vanguard, but a goat-path was found which led past the fort on
rocks higher up. The cannon were slipped by at night, over the road
covered with litter.
Remaining on the French side to despatch the troops forward as rapidly
as possible, Napoleon was one of the last to enter the mountains. He
rode a sure-footed mule, and by his side walked his guide, a young
peasant who unbosomed himself as they went forward. This peasant, also,
had his eyes on the future, and wished to rise in the world. His heart
yearned for a farm in the Alps, where he might pasture a small flock,
grow a few necessaries, marry a girl he loved, and live happily ever
afterward. The traveller on the mule seemed much absorbed in thought;
but, nevertheless, he heard all the mountaineer was saying.
He gave to the young peasant the funds wherewith to buy house and land;
and when Napoleon's empire had fallen to pieces, the family of his
old-time guide yet dwelt contentedly in the home the First Consul had
given.
So completely had Napoleon hoodwinked the Austrians that the Army of
the Reserve was still considered a myth. Mountain passes where a few
battalions could have vanquished an army had been left unguarded; and
when the French, about sixty thousand strong, stood upon the Italian
plains, Melas could with difficulty be made to believe the news.
Now that he was in Italy, it would seem that Napoleon should have
relieved Genoa, as he had promised. Masséna and his heroic band were
there suffering all the tortures of war, of famine, and of pestilence.
But Napoleon had conceived a grander plan. To march upon Genoa,
fighting detachments of Austrians as he went, and going from one
hum-drum victory to another was too commonplace. Napoleon wished to
strike a blow which would annihilate the enemy and astound the world.
So he deliberately left Masséna's army to starve while he himself
marched upon Milan. One after another, Lannes, leading the vanguard,
beat the Austrian detachments which opposed his progress, and Napoleon
entered Milan in triumph.
Here he spent several days in festivals and ceremonials, lapping
himself in the luxury of boundless adulation. In the meantime he threw
his forces upon the rear of Melas, spreading a vast net around that
brave but almost demoralized commander.
On June 4 Masséna consented to evacuate Genoa. His troops, after having
been fed by the Austrians, marched off to join the French in Italy.
Thus, also, a strong Austrian force was released, and it hastened to
join Melas.
When Bourrienne went into Napoleon's room late at night, June 8, and
shook him out of a sound sleep to announce that Genoa had fallen, he
refused at first to believe it. But he immediately rose, and in a short
while orders were flying in all directions, changing the dispositions
of the army.
On June 9, Lannes, with the aid of Victor, who came up late in the day,
won a memorable victory at Montebello.
Napoleon, who had left Milan and taken up a strong position at
Stradella, was in a state of the utmost anxiety, fearing that Melas was
about to escape the net. The 10th and 11th of June passed without any
definite information of the Austrian movements. On the 12th of June his
impatience became so great that he abandoned his position at Stradella
and advanced to the heights of Tortona. On the next day he passed the
Scrivia and entered the plain of Marengo, and drove a small Austrian
force from the village. Napoleon was convinced that Melas had escaped,
and it is queer commentary upon the kind of scouting done at the time
that the whereabouts of the Austrian army was totally unknown to the
French, although the two were but a few miles apart. Leaving Victor in
possession of the village of Marengo, and placing Lannes on the plain,
Napoleon started back to headquarters at Voghera. By a lucky chance
the Scrivia had overflowed its banks, and he could not cross. Thus
he remained near enough to Marengo to repair his terrible mistake in
concluding that Melas meant to shut himself up in Genoa. Desaix, just
returned from Egypt, reached headquarters June 11, and was at once put
in command of the Boudet division. On June 13 Desaix was ordered to
march upon Novi, by which route Melas would have to pass to Genoa.
Thus on the eve of one of the most famous battles in history, the
soldier who won it was completely at fault as to the position and the
purpose of his foe. His own army was widely scattered, and it was only
by accident that he was within reach of the point where the blow fell.
The staff-officer whom he had sent to reconnoitre, had reported that
the Austrians were not in possession of the bridges over the Bormida.
In fact they were in possession of these bridges, and at daybreak, June
14, they began to pour across them with the intention of crushing the
weak French forces at Marengo and of breaking through Napoleon's net.
About thirty-six thousand Austrians fell upon the sixteen thousand
French. Victor was driven out of the village, and by ten o'clock in
the morning his troops were in disorderly retreat. The superb courage
of Lannes stayed the rout. With the utmost firmness he held his troops
in hand, falling back slowly and fighting desperately as he retired.
At full speed Napoleon came upon the field, bringing the consular
guard and Monnier's division. Couriers had already been sent to bring
Desaix back to the main army; but before these messengers reached him,
he had heard the cannonade, guessed that Melas had struck the French
at Marengo, and at once set his columns in motion toward the field of
battle.
Napoleon's presence, his reënforcements, his skilful dispositions,
had put new life into the struggle; but as the morning wore away, and
the afternoon commenced, it was evident that the Austrians would win.
The French gave way at all points, and in parts of the field the rout
was complete. Napoleon sat by the roadside swishing his riding-whip
and calling to the fugitives who passed him to stop; but their flight
continued. A commercial traveller left the field and sped away to carry
the news to Paris that Napoleon had suffered a great defeat.
Melas, oppressed by age and worn out by the heat and fatigue of the
day, thought the battle won; went to his headquarters to send off
despatches to that effect, and left to his subordinate, Zach, the task
of the pursuit. But Desaix had come--"the battle is lost, but there is
time to gain another."
Only twelve pieces of artillery were left to the French. Marmont massed
these, and opened on the dense Austrian column advancing _en échelon_
along the road. Desaix charged, and almost immediately got a ball in
the breast and died "a soldier's beautiful death." But his troops
pressed forward with fury, throwing back in confusion the head of the
Austrian column. At this moment, "in the very nick of time" as Napoleon
himself admitted to Bourrienne, Kellermann made his famous cavalry
charge on the flank of the Austrian column, cut it in two, and decided
the day. The French lines everywhere advanced, the Austrians broke.
They were bewildered at the sudden change: they had no chief, Zach
being a prisoner, and Melas absent. In wildest confusion they fled
toward the bridges over the Bormida, Austrian horse trampling Austrian
foot, and the French in hot pursuit.
Some sixteen thousand men were killed or wounded in this bloody battle,
and very nearly half of these were French. But the Austrians were
demoralized, and Melas so overcome that he hastened to treat. To save
the relics of his army, he was willing to abandon northern Italy, give
up Genoa, and all fortresses recently taken.
From the field of Marengo, surrounded by so many dead and mangled,
Napoleon wrote a long letter to the Emperor of Austria, urgently
pleading for a general peace.
Returning to Milan, he was welcomed with infinite enthusiasm. He spent
some days there reëstablishing the Cisalpine republic, reorganizing the
administration, and putting himself in accord with the Roman Catholic
Church. Just as earnestly as he had assured the Mahometans in Egypt
that his mission on earth was to crush the Pope and lower the Cross, he
now set himself up as the restorer of the Christian religion. He went
in state to the cathedral of Milan to appear in a clerical pageant; and
he took great pains to have it published abroad that the priests might
rely upon him for protection.
Leaving Masséna in command of the army of Italy, Napoleon returned
to Paris by way of Lyons. The ovations which greeted him were as
spontaneous as they were hearty. Never before, never afterward, did
his presence call forth such universal, sincere, and joyous applause.
He was still young, still the first magistrate of a republic, still
conciliatory and magnetic, still posing as a public servant who could
modestly write that "he hoped France would be satisfied with its
army." He was not yet the all-absorbing egotist who must be everything.
Moreau was still at the head of an army, Carnot at the war office,
there was a tribunate which could debate governmental policies; there
was a public opinion which could not be openly braved.
Hence it was a national hero whom the French welcomed home, not a
master before whom flatterers fawned. All Paris was illuminated from
hut to palace. Thousands pressed forward but to see him; the Tuileries
were surrounded by the best people of Paris, all eager to catch a
glimpse of him at a window, and greeting him wherever he appeared with
rapturous shouts. He himself was deeply touched, and said afterward
that these were the happiest days of his life. The time was yet to come
when he would appear at these same windows to answer the shouts of a
few boys and loafers, on the dreary days before Waterloo.
With that talent for effect which was one of Napoleon's most highly
developed traits, he had ordered the Consular Guard back to France
almost immediately after Marengo, timing its march so that it would
arrive in Paris on the day of the great national fête of July 14. On
that day when so many thousands of Frenchmen, dressed in gala attire,
thronged the Field of Mars and gave themselves up to rejoicings, the
column from Marengo, dust-covered, clad in their old uniform, and
bearing their smoke-begrimed, bullet-rent banners, suddenly entered the
vast amphitheatre. The effect was electrical. Shout upon shout greeted
the returning heroes; and with an uncontrollable impulse the people
rushed upon these veterans from Italy with every demonstration of joy,
affection, and wild enthusiasm. So great was the disorder that the
regular programme of the day was thrust aside; the men of Marengo had
dwarfed every other attraction.
About this time the Bourbons made efforts to persuade Napoleon to play
the part of Monk in restoring the monarchy. Suasive priests bearing
letters, and lovely women bearing secret offers, were employed, the
facile Josephine lending herself gracefully to the intrigue. The First
Consul was the last of men to rake chestnuts out of the fire for other
people, and the Bourbons were firmly advised to accept a situation
which left them in exile.
Failing in their efforts to bribe him, the monarchists determined to
kill him; and the more violent Jacobins, seeing his imperial trend,
were equally envenomed. It was the latter faction which made the
first attempt upon his life. The Conspiracy of Ceracchi, Arena, and
Topino-Lebrun was betrayed to the police. Ceracchi was an Italian
sculptor who had modelled a bust of Napoleon. Arena was a Corsican
whose brother had aimed a knife at Napoleon on the 19th of Brumaire.
Topino-Lebrun was the juryman who had doubted the guilt of Danton, and
who had been bullied into voting death by the painter David. They were
condemned and executed.
A yet more dangerous plot was that of the royalists. An infernal
machine was contrived by which Napoleon was to have been blown up while
on his way to the opera. The explosion occurred, but a trifle too
late. Napoleon had just passed. The man in charge of the machine did
not know Josephine's carriage from Napoleon's, and approached too near
in the effort to make certain. A guard kicked him away, and while he
was recovering himself Napoleon's coachman drove furiously round the
corner. A sound like thunder was heard, many houses were shattered,
many people killed and wounded.
"Drive on!" shouted Napoleon; and when he entered his box at the opera,
he looked as if nothing had occurred. "The rascals tried to blow me
up," he said coolly as he took his seat and called for an opera-book.
But when he returned to the Tuileries he was in a rage, and violently
accused the Jacobins of being the authors of the plot. Fouché in vain
insisted that the royalists were the guilty parties; the First Consul
refused to listen. Taking advantage of the feeling aroused in his
favor by the attempts to assassinate him, he caused a new tribunal
to be created, composed of eight judges, who were to try political
offenders without jury, and without appeal or revision. By another law
he was empowered to banish without trial such persons as he considered
"enemies of the State." One hundred and thirty of the more violent
republicans were banished to the penal colonies.
For the purpose of feeling the public pulse, a pamphlet was put forward
by Fontanes and Lucien Bonaparte, called a "Parallel between Cæsar,
Cromwell, Monk, and Bonaparte." It was hinted that supreme power should
be vested in Napoleon, that he should be made king. The pear was not
quite ripe, the pamphlet created a bad effect. Napoleon, who had
undoubtedly encouraged its publication, promptly repudiated it; and
Lucien, dismissed from his office as Secretary of the Interior, was
sent to Spain as ambassador.
* * * * *
However willing Austria might be for peace, she could not make it
without the consent of England, her ally. The British ministry viewed
with the spirit of philosophy the crushing blows which France had
dealt Austria, and, secure from attack themselves, encouraged Austria
to keep on fighting. Not able to send troops, England sent money.
With $10,000,000 she bought the further use of German soldiers to
keep France employed on the Continent, while Great Britain bent her
energies to the capture of Malta and of Egypt. Thus it happened that
the armistice expired without a treaty having been agreed on; and the
war between the Republic and the Empire recommenced (November, 1800).
Brune defeated the Austrians on the Mincio; Macdonald made the heroic
march through the Splügen Pass; Moreau won the magnificent victory of
Hohenlinden (December 4, 1800).
It seems that, with a little more dash, Moreau might have taken Vienna,
exposed as it was to the march of three victorious armies. But Austria
asked for a truce, gave pledges of good faith, and the French halted.
On February 9, 1801, the Peace of Lunéville put an end to the war.
France had won the boundary of the Rhine; and, in addition to the
territory made hers by the treaty of Campo Formio, gained Tuscany,
which Napoleon had promised to Spain, in exchange for Louisiana.
Napoleon's position on the Continent was now very strong. Prussia was a
friendly neutral; Spain an ally; Italy and Switzerland little more than
French provinces; the Batavian republic and Genoa submissive subjects;
Portugal in his power by reason of his compact with Spain; and the
Czar of Russia an enthusiastic friend. England was shut out from the
Continent almost completely.
Her insolent exercise of the right of search of neutral vessels on the
high seas, a right which had no basis in law or justice, had provoked
the hatred of the world, and Napoleon took advantage of this feeling
and of Russia's friendship to reorganize the armed neutrality of the
northern powers for the purpose of bringing England to reason. Her
reply was brutal and effective. She sent her fleet, under Parker and
Nelson, to bombard Copenhagen and to destroy the Danish navy. The work
was savagely done, and the northern league shattered. The English party
at St. Petersburg followed up this blow by the murder of the Czar Paul.
Hardly had the young Alexander been proclaimed before he announced
his adhesion to the English and his antagonism to the French. He may,
possibly, have been free from the guilt of conniving at his father's
murder; but it is not to be denied that he continued to reward with the
highest offices the chief assassins--Bennigsen, for example.
* * * * *
Kléber, who had gloriously maintained himself in Egypt, was
assassinated on the day of Marengo. It is one of the mysteries of
Napoleon's career that he allowed the incompetent Menou to succeed
to a command where so much executive and administrative ability was
required. One is tempted to think that even at this early date the
genius of Napoleon was overtaxed. In trying to do so many things,
he neglected some. Egypt he certainly tried to relieve by sending
reënforcements; but he slurred all, neglected all, and lost all, by
allowing so notorious an imbecile as Menou to remain in chief command.
Why he did not appoint Reynier or Lanusse, both of whom were already
in Egypt, or why he did not send some good officer from France, can
only be explained upon the theory that his mind was so much preoccupied
with other matters that he failed to attach due importance to the
situation of the Army of the East.
Menou's administration was one dreary chapter of stupidities; and when
the English landed at Alexandria, they found an easy conquest. With
little effort and little bloodshed the French were beaten in detail,
and agreed to quit the country.
When the tidings reached Napoleon, his anger and chagrin were extreme.
He jumped upon his horse and dashed off into the forest of Bougival
as if the furies were after him. Hour after hour he rode frantically
in the wood, to the wonder of his staff, who could not guess what it
was all about. At last, when the storm had spent itself, he unbosomed
himself to the faithful Junot. That night Junot said to his wife,
"Ah, my General suffered cruelly to-day: Egypt has been taken by the
English!"
Malta having been captured also, Napoleon had the mortification of
realizing that his expedition to the East had had no other result than
to sow seed for an English harvest.
However, Great Britain was dismayed at the increase of her public debt,
oppressed by the load of taxation, and somewhat intimidated by the
energy which Napoleon began to show in building up the French navy. A
monster demonstration at Boulogne,--where he gathered an immense number
of armed sloops, apparently for the purpose of invading England,--and
the failure of an attack which Nelson made on this flotilla, had an
effect; and in March, 1802, to the joy of the world, the Peace of
Amiens was signed.
For the first time since 1792 universal peace prevailed in Europe.
CHAPTER XXIII
Nothing but memories now remains to France, or to the human race,
of the splendors of Marengo, of Austerlitz, Jena, and Wagram; but
the work which Napoleon did while Europe allowed him a few years of
peace will endure for ages. Had the Treaty of Amiens been lasting,
had England kept faith, had the old world dynasties been willing to
accept at that time those necessary changes which have since cost
so much labor, blood, and treasure, Napoleon might have gone down
to history, not as the typical fighter of modern times, but as the
peerless developer, organizer, administrator, and lawgiver. In his
many-sided character there was the well-rounded man of peace, who
delighted in improvement, in embellishment, in the growth of commerce,
agriculture, and manufactures; in the progress of art, science, and
literature; in the thorough training of the young, the care of the
weaker members of society, the just administration of wise laws, the
recognition of merit of all kinds. The orderly march of the legions of
industry was no less satisfying to him than the march of armies. We
have read so much of his battles that we have come to think of him as
a man who was never so happy as when at war. This view is superficial
and incorrect. It appears that he was never more energetic, capable,
effective, never more at ease, never more cheerful, contented, kind,
and magnetic than in the work connected with his schools, hospitals,
public monuments, public improvements of all sorts, the codification of
the laws, the encouragement and development of the various industries
of France. No trophy of any of his campaigns did he exhibit with more
satisfaction than he took in showing to visitors a piece of sugar made
by Frenchmen from the beet--a triumph of home industry due largely to
his stimulating impulse.
In all such matters his interest was intelligent, persistent, and
intense. Few were the months given to him in which to devote himself
to such labor; but he took enormous strides in constructing a new
system for France which worked wonders for her, and which has had its
influence throughout the civilized world.
The men of the Revolution had sketched a grand scheme of state
education, but it remained a sketch. Napoleon studied their scheme,
improved it, adopted it, and put it into successful operation. His
thorough system of instruction, controlled by the State, from the
primary schools to the Lyceums and the Technological Institute remain
in France to-day substantially as he left them.
Under the Directory society had become disorganized and morals corrupt.
Napoleon, hard at work on finance, laws, education, military and
civil administration, inaugurated the reform of social abuses also.
With his removal to the Tuileries, February 1800, may be dated the
reconstruction of society in France. The beginnings of a court formed
about him, and into this circle the notoriously immoral women could not
enter. It must have been a cruel surprise to Madame Tallien--coming to
visit her old friend Josephine--when the door was shut in her face by
the usher. Of course it was by Napoleon's command that this was done,
never by Josephine's. Applying similar rules to the men, Napoleon
compelled Talleyrand to marry the woman with whom he openly lived; and
even the favorite Berthier, too scandalously connected with Madame
Visconti, was made to take a wife. Sternly frowning upon all flaunting
immoralities, the First Consul's will power and example so impressed
itself upon the nation that the moral tone of society throughout the
land was elevated, and a loftier moral standard fixed.
Under the Directory the material well-being of the country, internally,
had been so neglected that even the waterways fell into disuse. Under
the consular government the French system of internal improvements soon
began to excite the admiration of Europe. Englishmen, coming over after
the peace, and expecting to see what their editors and politicians had
described as a country ruined by revolution, were amazed to see that
in many directions French progress could give England useful lessons.
Agriculture had doubled its produce, for the idle lands of former
grandees had been put into cultivation. The farmer was more prosperous,
for the lord was not on the lookout to seize the crop with feudal dues
as soon as made. Nor was the priest seen standing at the gate, grabbing
a tenth of everything. Nor were state taxes levied with an eye single
to making the burden as heavy as peasant shoulders could bear.
Wonder of wonders! the man in control had said, and kept saying,
"Better to let the peasant keep what he makes than to lock it up in
the public treasury!" The same man said, "Beautify the markets, render
them clean, attractive, healthy--they are the Louvres of the common
people." It was such a man who would talk with the poor whenever he
could, to learn the facts of their condition. In his stroll he would
stop, chat with the farmer, and, taking the plough in his own white
hands, trace a wobbly furrow.
Commerce was inspired to new efforts, for the First Consul put himself
forward as champion of liberty of the seas, combatting England's harsh
policy of searching neutral vessels and seizing goods covered by the
neutral flag.
Manufactures he encouraged to the utmost of his power, by shutting off
foreign competition, by setting the example of using home-made goods,
and by direct subsidies. He even went so far as to experiment with the
government warehouse plan, advancing money out of the treasury to the
manufactures on the deposit of products of the mills.
No drone, be he the haughtiest Montmorency, whose ancestor had been in
remote ages a murderer and a thief, could hold office under Napoleon.
Unless he were willing to work, he could not enter into the hive. For
the first time in the political life of the modern French, men became
prouder of the fact that they were workers, doers of notable deeds,
than that they were the fifteenth cousin of some spindle-shanked duke
whose great-great-grandfather had held the stirrup when Louis XIII. had
straddled his horse.
Having founded the Bank of France, January, 1800, Napoleon jealously
scrutinized its management, controlled its operations, and made
it useful to the State as well as to the bankers. He watched the
quotations of government securities, took pride in seeing them command
high prices, and considered it a point of honor that they should not
fall below eighty. When they dropped considerably below that figure,
some years later, the Emperor went into the market, made "a campaign
against the Bears," and forced the price up again--many a crippled bear
limping painfully off the lost field.
The First Consul also elaborated a system of state education. Here he
was no Columbus, no creator, no original inventor. His glory is that
he accomplished what others had suggested, had attempted, but had not
done. He took hold, gave the scheme the benefit of his tremendous
driving force, and pushed it through. It will be his glory forever
that in all things pertaining to civil life he was the highest type of
democrat. Distinctions of character, merit, conduct, talent, he could
understand; distinctions of mere birth he abhorred. The very soul of
his system was the rewarding of worth. In the army, the civil service,
the schools, in art and science and literature, his great object was to
discover the real men,--the men of positive ability,--and to open to
these the doors of preferment.
Remembering the sufferings he and his sister had endured at the Bourbon
schools where the poor scholars were cruelly humiliated, he founded his
training-schools, military and civil, upon the plan which as a boy he
had sketched. The young men at his military academies kept no troops
of servants, and indulged in no hurtful luxury. They not only attended
to their own personal needs, but fed, curried, and saddled their own
horses.
It was such a man as Napoleon who would turn from state business to
examine in person an ambitious boy who had been studying at home for
admission into one of the state schools, and who had been refused
because he had not studied under a professor. "This boy is competent;
let him enter the school," wrote Napoleon after the examination: and
the young man's career was safe.
It was such a man who would invite the grenadiers to the grand banquets
at the palace, and who would direct that special courtesies should be
shown these humblest of the guests.
It was such a man who would read every letter, every petition
addressed to him, and find time to answer all. Never too proud or
too busy to hear the cry of the humblest, to reward the merit of the
obscurest, to redress the grievance of the weakest, he was the man to
make the highest headed general in the army--Vandamme himself, for
instance,--apologized to the obscure captain who had been wantonly
insulted. Any private in the ranks--the drummer boy, the grenadier--was
free to step out and speak to Napoleon, and was sure to be heard as
patiently as Talleyrand or Murat or Cambacérès in the palace. If
any difference was made, it was in favor of the private soldier.
Any citizen, male or female, high or low, could count with absolute
certainty on reaching Napoleon in person or by petition in writing,
and upon a reply being promptly given. One day a careless secretary
mislaid one of these prayers of the lowly, and the palace was in terror
at Napoleon's wrath until the paper was found. Josephine might take a
petition, smile sweetly on the supplicant, forget all about it, and
suavely assure the poor dupe when meeting him next that his case was
being considered. Not so Napoleon. He might not do the sweet smile, he
might refuse the request, but he would give the man his answer, and if
his prayers were denied, would tell him why.
The Revolution having levelled all ranks, there were no visible
marks of distinction between man and man. Napoleon was too astute
a politician not to pander to mankind's innate craving for outward
tokens of superiority. The Legion of Honor was created against stubborn
opposition, to reward with ribbons, buttons, and pensions those who had
distinguished themselves by their own efforts in any walk of life. It
embraced merit of every kind,--civil, military, scientific, literary,
artistic. Men of all creeds, of every rank, every calling, were
eligible. The test of fitness for membership was meritorious service
to the State. Such at least was Napoleon's theory: whether he or any
one else ever strictly hewed to so rigid a line may be doubted. His
order of nobility had this merit: it was not hereditary, it carried
no special privileges, it could not build up a caste, it kept alive
the idea that success must be founded upon worth, not birth. In theory
such an order of nobility was democratic to the core. Lafayette, whom
Napoleon had freed from captivity, recalled to France, and reinstated
in his ancestral domain, scornfully declined to enter this new order
of nobility. So did many others--some because they were royalists,
some because they were republicans. In a few years the institution had
become so much a part of national life that the restored Bourbons dared
not abolish it.
* * * * *
"I will go down to posterity with the Code in my hand," said Napoleon
with just pride, for time has proven that as a lawgiver, a modern
Justinian, his work has endured.
Early in his consulate he began the great labor of codifying the laws
of France,--a work which had often been suggested, and which the
Convention had partially finished, but which had never been completed.
To realize the magnitude of the undertaking, we must bear in mind that,
under the Old Order, there were all sorts of law and all kinds of
courts. What was right in one province was wrong in another. A citizen
who was familiar with the system in Languedoc would have found himself
grossly ignorant in Brittany. Roman law, feudal law, royal edicts,
local customs, seigniorial mandates, municipal practices, varied and
clashed throughout the realm. The Revolution had prostrated the old
system and had proposed to establish one uniform, modern, and equitable
code of law for the whole country; but the actual carrying out of the
plan was left to Napoleon.
Calling to his aid the best legal talent of the land, the First Consul
set to work. Under his supervision the huge task was completed, after
the steady labor of several years. The Civil Code and the Code of
Civil Procedure, the Criminal Code and the Code of Criminal Procedure,
were the four parts of the completed system, which, adopted in France,
followed the advance of the Empire and still constitutes the law of a
large portion of the civilized world.
Every statute passed under Napoleon's eye. He presided over the
meetings when the finished work of the codifiers came up for sanction,
and his suggestions, reasoning, experience, and natural wisdom left
their impress upon every page. "Never did we adjourn," said one of the
colaborers of Napoleon, "without learning something we had not known
before."
It is the glory of this Code that it put into final and permanent shape
the best work of the Revolution. It was based upon the great principle
that all citizens were legally equals; that primogeniture, hereditary
nobility, class privileges, and exemptions were unjust; that property
was sacred; that conscience was free; that state employment should be
open to all, opportunities equal to all, state duties and state burdens
the same to all; that laws should be simple, and legal proceedings
public, swift, cheap, and just; and that personal liberty, civil right,
should be inviolable.
Recognizing his right as master-builder, his persistence, zeal, active
coöperation in the actual work, and the modern tone which he gave to
it, the world does him no more than justice in calling it the Code
Napoléon.
Another great distinctive work of the First Consul is the Concordat;
and here his claim to approval must ever remain a question. Those who
believe that the State should unite with the Church and virtually deny
to posterity the right to investigate the most important of subjects,
will always strain the language of praise in giving thanks to Napoleon
for the Concordat. On the contrary, those who believe that the State
should not unite with the hierarchy of any creed, but should let the
question of religion alone,--leave it to be settled by each citizen for
himself,--will forever condemn the Concordat as the colossal mistake of
Napoleon's career.
It will be remembered that the Revolution had confiscated the enormous,
ill-gotten, and ill-used wealth of the Catholic Church, but in lieu of
this source of revenue had provided ample salaries to the clergy, to
be paid from the public treasury. It is not true that the Christian
worship was forbidden or religion abolished. Throughout the Reign
of Terror the Catholic Church continued to be a state institution.
Only those priests who refused to take the oath of allegiance to
the New Order were treated as criminals. It was not till September,
1794, that the Convention abolished the salaries paid by the State,
thus separating Church and State. After this all creeds were on a
level, and each citizen could voluntarily support that which he
preferred,--Catholic, Protestant, or the Theophilanthropist.
It was the princely bishop, archbishop, and cardinal who had brought
reproach upon the Church under the Old Régime; it was the humble parish
priest who had maintained some hold upon the love and the respect
of the people. When the Revolution burst upon the land, it was the
prince of the Church who fled to foreign shores; it was the parish
priest who remained at the post of duty. Bravely taking up the cross
where the cardinals and bishops had dropped it, the curés reorganized
their Church, pledged themselves to the new order of things, and
throughout France their constitutional Church was at work--a voluntary
association, independent of Rome, and supporting itself without help
from the State. In one very essential particular it stood nearer to the
Christ standard than the Church it replaced--it charged no fees for
administering the sacraments.
This revived Gallican Church was distasteful to Napoleon, for he wished
the State, the executive, to be the head, centre, and controlling power
of everything. Voluntary movements of all sorts were his aversion.
To the Pope this independent Gallican Church was a menace, an
impertinence, a revolt. Catholicism, be it never so pure in creed,
must yield obedience and lucre to Rome, else it savors of heresy,
schism, and dire sinfulness.
Again, to the Pope and to the princes of the Church this equality
among the denominations in France was a matter that was almost
intolerable. Where creeds stand on the same footing, they will compete
for converts; where there is room for competition, there is license
for investigation, debate, reason, and common sense. And we have the
word of Leo XIII., echoing that of so many of his predecessors, that
religion has no enemy so subtle, so much to be dreaded, so much needing
to be ruthlessly crushed, as reason, investigation.
The Pope of Napoleon's day held this view, as a matter of course; and
in order to bring about a renewal of the union between the Catholic
Church and the government of France he was ready to concede almost
anything Napoleon might demand. Once the union had been accomplished,
no matter on what terms, the papacy would feel safe. Evolution and
time would work marvels; the essential thing was to bring about the
union. Napoleon was mortal, he would die some day, and weaker men
would succeed him--a stronger would never appear. Let the Pope bend a
little to that imperious will, let concessions be made while the Church
was getting fulcrum for its lever. Once adjusted, the lever would do
the rest. So it appeared from the point of view of the Pope: time has
proven him right.
On the part of Napoleon there were reasons of policy which lured him
into the toils of Rome. Immense results, immediate and personal, would
follow his compact with the Pope; for these he grasped, leaving the
future to take care of itself.
For Napoleon was personally undergoing a great transformation.
Gradually his mind had filled with dreams of empire. The cannon of
Marengo had hardly ceased to echo before he began to speak of "My
beautiful France." Between himself and those about him he steadily
increased the distance. His tone was that of Master. Tuscany having
been taken from Austria, he made a kingdom out of it, put a feeble
Bourbon upon its throne, dubbed the puppet King of Etruria, and brought
him to Paris where the people of France could behold a king playing
courtier to a French consul. At the Tuileries the ceremony and royalty
encroached constantly upon republican forms, and the lip service
of flatterers began to displace military frankness and democratic
independence.
Looking forward to supreme power, Napoleon was too astute a politician
to neglect the priest. As Alexander had bent his head in seeming
reverence at altars, and listened with apparent faith to Grecian
oracles; as Cæsar had posed as Roman chief priest, and leagued himself
to paganism; so Napoleon, who had been a Mussulman at Cairo, would now
become a Catholic in Paris. It was a matter of policy, nothing more.
"Ah, General," said Lafayette to him, "what you want is that the little
vial should be broken over your head."
It all led up to that.
Monarchy was to be restore, and its natural supports--the aristocrat
and the priest--were needed to give it strength. By coming to terms
with the Pope, Napoleon would win, and the Bourbons lose, the
disciplined hosts of the Catholic Church.
Therefore the Concordat was negotiated, and the French Church, which
even under the Bourbons had enjoyed a certain amount of independence,
was put under the feet of the Italian priest, under the tyranny of Rome.
By this compact the Pope held to himself the right to approve the
clerical nominees of the State, while the tax-payers were annually
to furnish $10,000,000 to pay clerical salaries. By this compact was
brought back into France the subtle, resistless power of a corporation
which, identifying itself with God, demands supreme control.
Napoleon himself soon felt the strength of this released giant, and the
France of to-day is in a death grapple with it.
The time may come when the Concordat will be considered Napoleon's
greatest blunder, his unpardonable political sin. It was not faith,
it was not even philanthropy which governed his conduct. It was cold
calculation. It was merely a move in the game of ambition. At the very
moment that he claimed the gratitude of Christians for the restoration
of religion, he sought to soothe the non-believers by telling them that
under his system religion would disappear from France within fifty
years.
It is not true that a majority of the French clamored for a return
of the old forms of worship. On the contrary, the vast majority
were indifferent, if not hostile. In the army it caused a dangerous
conspiracy among the officers, against Napoleon's life.
When the Concordat came to be celebrated by a pompous pagan ceremonial
in the cathedral of Notre Dame, it required all of his authority to
compel a respectful attendance, as it had required the utmost exercise
of his power to secure the sanction of the state authorities to the
Concordat itself. More than one saddened Frenchman thought what
General Delmas is reported to have said, when Napoleon asked his
opinion of the ceremonial at Notre Dame; "It is a fine harlequinade,
needing only the presence of the million men who died to do away with
all that."
Yes, a million Frenchmen had died to do away with that,--the worst
feature of the Old Order,--and now it had all come back again. Once
more the children of France were to have their brains put under the
spell of superstition. They were to be taught the loveliness of
swallowing every marvel the priest might utter, and the damnation of
thinking for oneself upon any subject ecclesiastical. They were to be
crammed from the cradle, on one narrow creed, and incessantly told that
hell yawned for the luckless wight who doubted or demurred.
With a line of writing, with a spurt of the pen, Napoleon reënslaved
the nation. So well had the image breakers of the Convention done
their work that it appeared to be only a question of time when France,
"having by her own exertions freed herself, would, by the force of her
example, free the world." As Méneval states, "Catholicism seemed at
its last gasp." Rapidly Europe was being weaned from a worn-out creed,
a threadbare paganism. Idols had been broken, miracles laughed out
of countenance, the bones of alleged saints allowed to rest, and the
mummeries of heathen ceremonial mocked till even the performers were
ashamed.
A few bigots or fanatics, chained by an education which had left them
no room for unfettered thought, longed for the return of the old
forms; but the mass of the French people had no more wish for their
reëstablishment than for the restoration of the Bourbons. France was
religiously free: every citizen could believe or not believe, worship
or not worship, just as he pleased.
Of all rulers, Napoleon had the best opportunity to give mental
independence an open field and a fair fight. No ruler less strong than
he could have achieved the task of lifting the Church from the dust,
and frowning down the ridicule which had covered with discredit idol,
shrine, creed, and ceremonial rite.
He did it--he alone! And verily he reaped his reward. The forlorn
prisoner of St. Helena, sitting in misery beside the cheerless hearth
in the night of endless despair, cursed himself bitterly for his huge
mistake.
Some who defend the Concordat say that it enabled Napoleon to make
alliances which otherwise he could not have made. The facts do not
support the assertion. He was at peace with Continental Europe already,
and Great Britain was certainly not influenced to peace by France's
agreement with the Pope. No alliances which Napoleon ever made after
the Concordat were stronger than those he had made before; and as
the restorer of Catholicism in France, he was not nearer the sincere
friendships of monarchs and aristocracies abroad than he had been
previous to that time.
In the murk of modern politics the truth is hard to find, but even a
timid man might venture to say that the question of religion is the
last of all questions to influence international relations. Comparing
the prolonged security which Turkey has enjoyed with the fate which
recently befell Catholic Spain and Protestant South African republics,
the casual observer might hazard the statement that it is at least as
safe to be Mahometan as Christian, so far as winning international
friendship is concerned.
"Don't strike! I am of the same faith as you--both of us hope for
salvation in the blood of the same Savior!" is a plea which is so
worthless among Christians that the weaker brother never even wastes
breath to make it.
CHAPTER XXIV
To say that the French were pleased with the consular government,
would convey no idea of the facts. France was delighted, France was in
raptures. Excepting the inevitable few,--some royalists, some Jacobins
and some lineal descendants of the Athenians who grew tired of hearing
Aristides called _The Just_,--all Frenchmen heartily united in praise
of Bonaparte.
As proudly as Richelieu, in Bulwer's play, stands before his king and
tells what he has done for France,--a nation found lying in poverty,
shame, defeat, deathly decay, and lifted by the magic touch of genius
to wealth, pride, victory, and radiant strength,--so the First Consul
could have pointed to what France had been and what she had become, and
justly claim the love and admiration of his people.
What reward should be given such a magistrate? In 1802 his consulship,
which had already been lengthened by ten years, was, by the almost
unanimous vote of the people, changed into a life tenure.
Consul for life (August, 1802), with the power to name his own
successor, Napoleon was now virtually the king of France.
* * * * *
In St. Domingo, the Revolution in France had borne bitter fruit. The
blacks rose against the whites, and a war of extermination ensued.
The <DW64>s, immensely superior in numbers, overcame the whites, and
established their independence. Toussaint L'Ouverture, the leader of
the blacks, and a great man, became president of the black republic,
which he patterned somewhat after Napoleon's consulate.
The rich French planters, who had the ear of Napoleon in Paris, urged
him to put down the revolt, or to bring the island back under French
dominion. Thus these Bourbon nobles led Napoleon into one of his worst
mistakes. He aligned himself with those who wished to reëstablish
slavery, put himself at enmity with the trend of liberalism everywhere,
and plunged himself into a ruinous war.
Mainly from the army of the Rhine, which was republican and unfriendly
to himself, he drew out of France twenty thousand of her best troops,
put them under command of Leclerc, his brother-in-law, and despatched
them to St. Domingo, to reconquer the island.
Here again it is impossible to escape the conclusion that Napoleon had
not duly considered what he was doing. There is evidence of haste,
want of investigation, lack of foresight and precaution. The whole
plan, from inception to end, bears the marks of that rashness which is
forever punishing the man who tries to do everything.
The <DW64>s gave way before Leclerc's overwhelming numbers; and, by
treachery, Toussaint was captured and sent to France to die in a
dungeon; but the yellow fever soon came to the rescue of the blacks,
and the expedition, after causing great loss of life, ended in shameful
failure. Leclerc died, the remnants of the French army were brought
back to Europe in English ships, and the <DW64>s established their
semi-barbarous Republic of Hayti (1804).
This much may be said by way of defence for Napoleon's treatment
of San Domingo: it had been one of the choicest possessions of the
French crown, and he wished to regain it for his country, just as he
regained Louisiana, and just as he yearned for the lost territories in
Hindustan. Visions of a vast colonial empire haunted his imagination,
and the spirit which influenced him in his efforts in the West Indies
was, perhaps, the same which lured him to Egypt, which caused him to
attach such extreme importance to Malta, and which caused him to send
men-of-war to South Australia to survey the coast for settlement.
* * * * *
Meantime the Peace of Amiens was becoming a very frail thing, indeed.
To all men, war in the near future seemed inevitable. Very positively
England had pledged herself to restore Malta to the Knights of St.
John; very emphatically she now refused to do so. By way of excuse
she alleged that France had violated the spirit of the treaty by her
aggressions on the Continent. In reply, Napoleon insisted that France
had done nothing which it was not well known she intended at the time
peace was made. He also reminded England that she had taken India.
And this was true, but truth sometimes cuts a poor figure in debate.
In vain such splendid types of English manhood as Charles Fox stood
forth boldly in the British Parliament, and defended the First Consul.
England was determined not to give up the Mediterranean fortress.
France had no navy, no sailor with a spark of Nelson's genius, and
Malta was safe. On the Continent Napoleon might rage and might destroy;
but England had proved how easy it was for her to bear the losses
inflicted upon Continental Europe, and she was prepared to prove it
again. Safe in her sea-girt isle, she was not to be intimidated by
armies hurled against her allies.
In this crisis, when conciliatory measures might have availed to avert
war, Lord Whitworth was sent to Paris as British ambassador. With his
coming all hope of accommodation vanished. He was a typical English
aristocrat, the very worst man who could have been sent if peace was
desired. From the first, his letters to his government show that he
was intensely hostile to Napoleon and to the consular government. To
his superiors at home he misrepresented the situation in France, and
where he did not misrepresent, he exaggerated. Finally, when Napoleon
went out of his way to have a long conference with him, and to urge
that England should keep her contract, he showed himself coldly
irresponsive, and hinted that Malta would not be given up. Following
this private and urgent conference came the public reception, in which
Napoleon, with some natural display of temper and with the frankness of
a soldier, asked Whitworth why England wanted war, and why she would
not respect treaties. Whereupon Whitworth represented to his court that
he had been grossly insulted, and all England rang with indignation.
A falser statement never caused more woe to the human race. Bismarck
cynically confessed that he it was who changed the form, the wording,
and the tone of "the Ems telegram" which caused the Franco-German War
of 1870–1. It is not too much to say that Whitworth's exaggerated
report, and the changes for the worse which the British ministry made
in it when making it public, was one of the controlling causes of the
wars, the bloodshed, and the misery which followed the year 1804.
During all this while the English newspapers were filled with the
bitterest abuse of Napoleon. The most shameful lies that were ever
published against a human being were constantly repeated against him
in the British journals. That he should be subjected to such treatment
during years of peace, and while he was giving most cordial welcome
to the thousands of Englishmen who were now visiting France, filled
Napoleon with wrath. He knew that by law the press of Great Britain was
free; but he also knew that these papers, especially the ministerial
papers, would not be filled with scurrilous personal abuse of him
unless the government encouraged it. He knew that the political press
reflects the views of the political party, and that when ministerial
journals hounded him with libels, the ministers had given the signal.
In vain he protested to the English ministry; he was told that in
England the press was free. Then, as all his admirers must regret, he,
also, stooped to libels and began to fill the official organs in France
with outrageous attacks upon England.
Another grievance Napoleon had against Great Britain--she harbored
men who openly declared their intention of assassinating him. English
protection, English ships, English money, were ever at the command
of the royalists who wished to stir up revolt in France, or to land
assassins who wished to creep to Paris. On this subject, also, the
English government would give no satisfaction. It coldly denied the
accusation, disavowed the assassins, and continued to encourage
assassination.
While relations were thus strained, a report of General Sébastiani
on the eastern situation was published. In the paper, Sébastiani
had ventured to say that six thousand French troops might reconquer
Egypt. Here was another insult to England. Here was another excuse for
editorial thunder, another provocative of parliamentary eloquence.
England did not choose to remember that Sir Robert Wilson had just
published a book, also on the eastern situation, and that in this
publication Napoleon had been represented as the murderer of prisoners
at Jaffa, and the poisoner of his own sick in the hospitals. This book
had been dedicated to the Duke of York by permission, and had been
presented by the author to George III., at a public levee.
England was bent on war; no explanations or remonstrances would
soothe her, and on May 18 war was declared. But she had already
seized, without the slightest warning, hundreds of French ships
laden with millions of merchandise--ships which had come to English
harbors trusting to her faith pledged in the treaty. This capture and
confiscation excited almost no comment, but when Napoleon retaliated
by throwing into prison thousands of Englishmen who were travelling
in France, England could find no words harsh enough to condemn the
outrage. Even so intelligent a historian as Lockhart is aghast at
Napoleon's perfidy. For, mark you, England had _always_ seized what she
could of the enemy's property previous to a declaration of war, whereas
Napoleon's counterstroke was a novelty. It had never been done before,
therefore it was an unspeakable atrocity--"It moved universal sympathy,
indignation, and disgust." So says Lockhart, repeating dutifully what
his father-in-law, Sir Walter Scott, had already said. And the most
recent British historian, J. H. Rose, writing of that period, falls
into the well-worn path of Tory prejudice, and ambles along composedly
in the hallowed footprints of Lockhart and Sir Walter.
Their style of putting the case is like this: It was wrong to seize an
enemy's ships and sailors previous to a declaration of war, but Great
Britain had always done it, and, consequently, she had a right to do
it again. It was right for France to retaliate, but France had never
retaliated, and, consequently, she had no right to do it now. Thus
England's hoary wrong had become a saintly precedent, while Napoleon's
novelty of retaliation was a damnable innovation. In this neat manner,
entirely satisfactory to itself, Tory logic makes mesmeric passes over
facts, and wrongs become rights while rights become wrongs.
The eminent J. H. Rose, Master of Arts, and "Late Scholar of Christ's
College, Cambridge," remarks:
"Napoleon showed his rancour by ordering some eight or ten thousand
English travellers in France to be kept prisoners." Why the eminent
Master of Arts and "Late Scholar of Christ's College" did so studiously
omit to state that England had already seized French ships and sailors
before Napoleon seized the travellers, can be explained by no one but a
master of the art of writing partisan history.
"Napoleon showed his rancour"--by hitting back when Britain dealt him
a sudden unprovoked and dastardly blow. Showed his rancour! "Sir, the
phrase is neat," as Mirabeau said to Mounier upon a certain historic
occasion.
Napoleon hastened to put Louisiana beyond England's reach. This
imperial, but undeveloped, province had been lost to France by the
Bourbon, Louis XV. and had only recently been recovered. Napoleon
profoundly regretted the necessity which compelled him to sell it to
the United States, for he realized its value.
The war recommenced with vigor on both sides. Great Britain seized
again upon all the colonies which she had released by treaty, and
French armies in Italy or Germany added territory to France.
Spain refusing to join the league against Napoleon, Great Britain made
war upon her, captured her treasure ships upon the high seas, and thus
forced her into the arms of France. She not only put her fleet at
Napoleon's disposal, but agreed to furnish him a monthly subsidy of
more than $1,000,000.
Definitely threatening to invade Great Britain, Napoleon made
preparations for that purpose on a scale equal to the mighty task.
Along the French and Dutch coasts 160,000 men were assembled, and vast
flotillas built to take them across the Channel. So great was the alarm
felt in England that her coasts were watched by every available ship,
and almost the entire manhood of the island enrolled itself in the
militia, and prepared for a desperate struggle.
So prominently did Napoleon stand forth as the embodiment of all that
monarchical Europe detested, so completely did he represent all that
England and the Bourbons most dreaded, that a mad determination to kill
him took possession of his enemies. The head of the conspiracy was the
Count of Artois, afterward king of France under the name of Charles X.
The meetings of the conspirators were held in London. The plan adopted
was that Pichegru (who had escaped from South America) and Moreau
should be brought together to head the malcontents in the army; Georges
Cadoudal, and a band of royalists equally resolute, should be landed
on the Norman coast, should proceed to Paris, and should kill the
First Consul; a royalist revolt should follow, and the Count of Artois
should then himself land on the Norman coast to head the insurrection.
The English minister to Bavaria, Mr. Drake, was actively at work in
the plot, and in one of his letters to a correspondent, wrote: "All
plots against the First Consul must be forwarded; for it is a matter
of little consequence by whom the animal be stricken down, provided
you are all in the hunt." Among others who were in the background and
winding sonorous horns to those who were "in the hunt," were certain
British agents,--Spencer Smith at Stuttgard, Taylor at Cassel, and
Wickham at Berne. Directly in communication with the heads of the
conspiracy in London was the under secretary of state, Hammond, the
same who was so intolerably insolent to the United States during the
second term of President Jefferson.
Lavishly supplied with money by the English government, a ship of the
royal navy was put at their service,--Captain Wright, an officer of
that navy, being in command.
The assassins were landed at the foot of a sea-washed cliff on the
coast of Normandy in the night. Using a secret path and the rope-ladder
of smugglers, they climbed the precipice and made their way secretly
to Paris. Here they spent some weeks in organizing the conspiracy. The
danger to Napoleon became so urgent that those who had the care of his
personal safety felt that no precautions could be too great. De Ségur,
captain of the body-guard, relates how Caulaincourt, Grand Marshal of
the palace _pro tem_, woke him up after twelve o'clock at night toward
the end of January, 1804, with: "Get up! Change the parole and the
countersign immediately. There is not an instant to lose. The duties
must be carried out as if in the presence of the enemy!"
Napoleon himself remained cool, but gradually became very stern. Asked
by one of his councillors if he were afraid, he replied: "I, afraid!
Ah, if I were afraid, it would be a bad day for France."
The first great object of the conspirators was to bring Pichegru and
Moreau together. It was hoped and believed that this could be readily
done. It was remembered that Moreau had concealed the treasonable
correspondence of Pichegru which had fallen into his hands in 1796. It
was known that Moreau heartily disliked Napoleon. It was known that
Moreau, sulking in his tent, and bitterly regretting his share in
Napoleon's elevation to power, was in that frame of mind which leads
men into desperate enterprises.
Nevertheless, the conspirators found him very shy. By nature he was
irresolute and weak, strong only when in command of an army. He
consented to meet Pichegru, and did meet him at night, and have a few
words with him in the street. Afterward Pichegru visited Moreau's
house, but the proof that Moreau agreed to take any part in the
conspiracy is not satisfactory. It seems that Moreau had no objection
to the "removal" of Napoleon and the overthrow of the government.
He even spoke vaguely of the support which he and his friends in
authority might bring to those who were conspiring; but Moreau was
a republican,--one of those ardent young men of 1789 who had left
school to fight for the Republic, and he was not ready to aid in the
restoration of the Bourbons. Willing to countenance the overthrow
of Napoleon, he was not willing to undo the work of the Revolution.
According to one account, he himself aspired to succeed Bonaparte. This
disgusted Cadoudal, who in scornful anger declared that he preferred
Napoleon "to this brainless, heartless Moreau." Inasmuch as Moreau had
already become disgusted with Cadoudal, the conspiracy could not knit
itself together.
Meanwhile, repeated conferences were held between the assassins and
various royalists of Paris who were in the plot, the most prominent of
these being the brothers Polignac and De La Rivière. Napoleon knew in
a general way that his life was being threatened, knowing just enough
to be convinced that he must learn more or perish. His police seemed
powerless, and as a last resort he tried a plan of his own. Causing
a list of the suspected persons to be brought to him, his attention
became fixed upon the name of a surgeon, Querel. In the belief that
this man must be less of a fanatic than the others, he ordered that the
surgeon should be brought to trial, and the attempt made to wring a
confession from him. Tried accordingly, condemned, sentenced, and about
to be shot, Querel broke down and confessed.
Learning from him that the most dangerous of the conspirators were
even then in Paris, a cordon of troops was thrown around the city,
and a vigilant search begun. Pichegu, after dodging from house to
house, was at length betrayed by an old friend with whom he had sought
shelter. Georges was taken after a desperate fight in the street.
Captain Wright was seized at the coast and sent to Paris. Moreau had
already been arrested. Many other of the Georges band were in prison.
Napoleon's fury was extreme, and not unnatural. He had been lenient,
liberal, conciliatory to his political foes. He had pushed to the
verge of imprudence the policy of reconciliation. Vendeans, royalists,
priests--all had felt his kindness. Some of the very men who were now
threatening him with assassination were émigrés whom he had relieved
from sentence of death and had restored to fortune. What had he done
to England or to the Bourbons that they should put him beyond the pale
of humanity? Had he not almost gone upon his knees in his efforts to
secure peace? Had he ever lifted his hand against a Bourbon save in
open war which they themselves had commenced? And now what was he to do
to put a stop to these plots hatched in London? To what court could he
appeal? With the Bourbons safely housed in England and supplied with
British money, ever ready to arm against him the fanatics of royalism,
what was he to do to protect his life? Was he to await the attack,
living in constant apprehension, never knowing when the blow would
fall, uncertain how the attack would be made, ignorant who the assassin
might be, and in eternal doubt as to whether he could escape the peril?
Can mortal man be placed in a position more trying than that of one who
knows that sworn murderers are upon his track, and that some one moment
of every day and every night may give the opportunity to the unsleeping
vigilance of the assassin?
Roused as he had never been, Napoleon determined not to wait, not to
stand upon literal self-defence. He would strike back, would anticipate
his enemies, would paralyze their plans by carrying terror into their
own ranks.
The head of the conspiracy, Artois, could not be reached. Expected on
the French coast, he had not come. But his cousin, the Duke d'Enghien
was at Ettenheim, close to the French border.
What was he doing there? He had borne arms against France, a crime
which under the law of nations is treason, and which under the law of
all lands is punishable with death. By French law, existing at the
time, he had forfeited his life as a traitor. He was in the pay of
England, the enemy of France. He was closely related by blood and by
interest to the two brothers, Provence and Artois, who were making
desperate efforts to recover the crown for the Bourbon family. What
was the young Bourbon duke doing so near to the French border at this
particular time?
Royalist authors say that he was there to enjoy the pleasures of the
chase; also to enjoy the society of the Princess de Rohan, to whom they
now say, without evidence, that he was secretly married.
Sir Walter Scott, a most unfriendly witness for Napoleon, admits that
d'Enghien "fixed himself on the frontier for the purpose of being ready
to put himself at the head of the royalists in East France, or Paris
itself."
That he was on the Rhine awaiting some event, some change in France
in which he would have "a part to play," was confessed, and cannot be
denied.
What was the movement at whose head he was waiting to place himself?
What other plan did the royalists have in progress at the time other
than the Georges-Pichegru plot? If d'Enghien was waiting on the
Rhine until they should have dealt the blow in Paris, was he not an
accomplice, a principal in the second degree? It does not matter
whether he knew the details of the Georges-Pichegru conspiracy or not.
If he had been instructed to hold himself in readiness on the French
frontier to enter the country and "act a part" therein, his common
sense told him that a plot was on foot, and if he did not wish to be
treated as an accomplice, he should not have acted as one. The cowardly
d'Artois had not left London, and the Duke d'Enghien was to enter
France as representative of the Bourbon family after the First Consul
should have been killed.
The rule in law and equity is that where one is put upon notice of a
transaction, he is to be held as knowing all that he could have learned
by reasonable inquiry. The instructions issued to d'Enghien put him
upon notice that something unusual was in progress, that it concerned
him, and that he had a part to play. Prudent inquiry made by him of his
Bourbon relatives in London would have put him in possession of the
facts. This inquiry he either made or he did not: if he made it, he
learned of the plot; if he did not make it, his was the negligence of
being ignorant of the plan in which he was to "act a part."
It is very improbable that the Count of Artois, who had sent word to
the Count of Provence at Warsaw asking his adhesion to the conspiracy,
should have given his cousin, d'Enghien, a "part to act" in it without
informing him of the nature of the drama itself.
The police reports made to Napoleon led him to believe that the young
duke was privy to the plot, and was waiting at Ettenheim ready to take
part in it. Here was a Bourbon he could reach. Through this one, he
would strike terror into the others. "Neither is my blood ditchwater!
I will teach these Bourbons a lesson they will not soon forget. Am I a
dog to be shot down in the street?"
After deliberating with his councillors, Talleyrand and all the rest,
the First Consul issued his orders. A French squadron rode rapidly to
the Rhine, crossed over to Ettenheim, seized the Duke, who had been
warned in vain, and hurried him to Paris. Stopped at the barrier, he
was sent to Vincennes, tried by court-martial that night, condemned
upon his own confession, sentenced to death, shot at daybreak, and
buried in the moat of the castle.
This harsh act of retaliation had met the approval of Talleyrand--an
approval given in a written paper which he was quick to seize and
destroy upon Napoleon's fall in 1814. During the day upon which the
Duke was being taken to Vincennes, Talleyrand was asked, "What is to be
done with the Duke d'Enghien?" and had replied to the questioner, "He
is to be shot."
The Consul Cambacérès, who had voted for death at the trial of Louis
XVI., opposed the arrest, giving his reasons at length. Napoleon
replied: "I know your motive for speaking--your devotion to me. I thank
you for it; but I will not allow myself put to death without defending
myself. I will make these people tremble, and teach them to keep quiet
for all time to come."
Poor Josephine, who could never meet a member of the old noblesse
without a collapse of spirit, a gush of adulation, and a yielding
sensation at the knees, made a feeble effort to turn her husband from
his purpose; but when Napoleon reminded her that she was a mere child
in politics, and had better attend to her own small affairs, she
dried her tears, and went into the garden to amuse herself with her
flower-beds.
Napoleon himself made a thorough study of the papers, taken with the
Duke at Ettenheim, and drew up a series of questions which were to
be put to the prisoner by Réal, state councillor. The messenger sent
by the First Consul did not see Réal, and the paper was not handed
him till five o'clock next morning. Worn out by continuous toil, the
councillor had gone to bed the evening before, leaving instructions
with his household that he was not to be disturbed. Next morning when
he was posting along the highway to Vincennes, he met Savary on his way
back to Paris. Savary had already carried out the death-sentence, and
the victim was in his grave.
It seems that the young Duke had not realized his danger. A term of
imprisonment, at most, was all he feared. In vain the court-martial
endeavored to hint at the fatal consequence of the admissions he was
making. Unconscious of the fact that he was convicting himself, he
repeated the statements that he had borne arms against France, that
he had been in the pay of England, that he had tampered with French
soldiers on the Rhine, that he had been instructed to place himself
near the Rhine where he could enter France, arms in hand, and be ready
for the part he was to play; and that he intended to continue to bear
arms against the government of France which he regarded as a usurpation.
It must not be forgotten that in sending the Duke d'Enghien before a
court-martial, Napoleon had before him certain documentary evidence
which we do not now possess. The Duke's own papers, Talleyrand's
opinion, and the reports of certain officials disappeared from the
archives after the Bourbons returned in 1814--just as the documentary
evidence against Marie Antoinette was destroyed, and the letters which
crowned heads of Europe had written Napoleon stolen and carried away.
Peculiarly awful must have been the vision of sudden death to this
youthful prince of the blood-royal, as he was dragged from bed in the
dismal darkness of early morning, and hurried to face a file of silent
soldiers beside an open grave. After the first shock and outcry of
amazement, the courage in which his race has rarely been wanting came
to the condemned, and he met his fate with a soldier's nerve.
In 1805, during the march upon Vienna, Napoleon received at his bivouac
M. de Thiard, who had known d'Enghien well. For a long while the
Emperor sat talking with this officer, asking many questions about the
Duke, and listening with interest to all that was told him.
"He was really a man, then, that prince?" he asked, and this casual
remark was his sole comment.
Among all those who believe that the life of a prince is more sacred
than that of a plebeian, among aristocrats of all countries, and among
the crowned heads of Europe, there was a burst of grief and rage when
it became known that Napoleon had shot a Bourbon duke. Thousands
of pages were written then, thousands have been written since, in
denunciation of this so-called murder. Men who had never uttered a word
in condemnation of Lord Nelson's treatment of Carraccioli, could find
no words harsh enough for Napoleon's usage of d'Enghien. Alexander of
Russia, who had whimpered in the palace while his father was being
stamped, choked, and smothered to death in the adjoining room, and who
had promoted the assassins to high trusts in his own service, took
Napoleon's conduct more to heart than did any of the royal fraternity.
Assuming the lofty moral attitude of one who is missioned to rebuke
sin, he broke off diplomatic relations with France and put the Russian
court in mourning. Napoleon launched at the Czar a crushing reminder on
the subject of Paul's death, and Alexander suffered the subject to drop.
Paris, stunned at first by the tragedy, recovered itself immediately;
and when Napoleon appeared at the theatre a few nights afterward, he
was acclaimed as usual. Talleyrand gave a ball, and society was there
with the same old stereotyped smile upon its vacuous face.
Nevertheless, it is certain that the death of this young Duke injured
Napoleon in public esteem, was of no political service to him, armed
his enemies with a terrible weapon against him, and gave to the exiled
Bourbons a sympathy they had not enjoyed since the Revolution. Said
Fouché, "It is worse than a crime; it is a blunder." But there is no
evidence that Napoleon ever regretted it. It is true that he became
enraged when Talleyrand denied his share in the transaction, and that
he always maintained that Talleyrand had advised it; but he never
shirked his own responsibility.
When he lay upon his death-bed at St. Helena, an attendant read to him
from an English publication a bitter attack upon those guilty of the
alleged murder of d'Enghien. The dying Emperor had already made his
will; but he roused himself, had the paper brought, and interlined
with his own hands these final words in which he assumed full
responsibility:--
"I had the Duke d'Enghien arrested and tried because it was necessary
to do so for the safety, the honor, and the interest of the French
people at a time when the Count of Artois openly admitted that he had
sixty paid assassins in Paris. Under similar circumstances I would do
so again."
The trials of Moreau, Georges, and the other conspirators did not take
place until Napoleon had become emperor. The prosecution was clumsily
managed; and as to Moreau, public opinion was divided. His services,
so recent and so great, gave some color to the story that Napoleon was
actuated by jealousy in having him classed with criminals. However,
Moreau weakened his defence by an exculpatory letter he wrote Napoleon,
and this together with such proofs as the government could furnish,
and such influence as it could bring to bear on the court, resulted in
a conviction and a sentence of two years in confinement. This penalty
Napoleon changed into one of banishment. Georges and a number of others
were shot. Pichegru and Wright committed suicide. The Polignacs and
Rivière, as guilty as the guiltiest, were pardoned--they being of
gentle birth, and being fortunate in having the friendship of some who
stood near Napoleon.
CHAPTER XXV
During the years of the peace (1801–1804), French influence upon the
Continent kept marching on. Napoleon's diplomacy was as effective as
his cannon. Holland became a subject state, with a new constitution
dictated by France, and a governing council which took guidance from
France (1801).
Lombardy dropped its title of the Cisalpine, and became the Italian
republic, with Napoleon for President. French troops entered
Switzerland, put down civil strife, and the country for ten years
enjoyed peace and prosperity under a constitution given it by Napoleon,
he being virtually its ruler under the name of Mediator of the Helvetic
League.
In Germany, a general shaking up and breaking up of political fossils
and governmental dry bones occurred. The territory ceded to France by
the treaty of Lunéville needed to be reorganized. The German princes,
who were dispossessed, required compensation. Prussia had to be paid
for her neutrality. Austria wished to recoup her losses. How was it
possible for diplomacy to satisfy at the same time France, which had
fought and won; Austria which had fought and lost; and Prussia, which
had not fought at all?
Napoleon was ready with his answer. Let the strong help themselves to
the territories of the weak. At Rastadt, Napoleon had remarked to
Marten, "Does not public law nowadays consist simply in the right of
the stronger?" Evidently it did, as it does yet, and ever has done.
Upon this theory the German complication was worked out. There were
fifty so-called Free Cities which, being weak and in debt, might be
forcibly absorbed. There were a number of ecclesiastical princes,
ruling wretchedly over wide and rich domains, whose tempting wealth
might be confiscated. There were hundreds of knights of the German
Empire, decayed relics of mediævalism, each holding as private property
a snug territory, whose people the knight taxed, judged, and outraged
at his own good pleasure. The Congress of Rastadt had been laboring
upon this German problem at the time Austria murdered the French envoys
(1798). The task was now resumed (1801) nominally by the Congress at
Ratisbon, but really by French diplomats in Paris. Talleyrand, as
Minister of Foreign Affairs, had a magnificent opportunity to feather
his nest with bribes, and he made the most of it. German diplomatists
posted to Paris, paid court to the corrupt minister, laughed at all
his good sayings, fondled his poodle, petted his supposed bastard, and
lavished their gold upon him to win his influence.
When the process of reorganization was completed, Germany had been
revolutionized. Most of the Free Cities were no longer free, but were
incorporated with the territory of the government in which they were
located. The ecclesiastical princes were reduced to the condition
of salaried priests, their domains confiscated to the governments.
Bavaria, Baden, Würtemberg, were given large increase of territory;
Prussia was not left unrewarded; France got all she was entitled to;
and Austria, the defeated nation, lost almost nothing. The happy
combination of France, Prussia, Austria, and Russia, to settle their
differences at the expense of the Free Cities and the Princes of the
German Catholic Church, had been blessed with brilliant success.
Following the redistribution of German lands came changes yet more
vital. The wretched little feudal sovereignties disappeared. The
imperial knights lost their out-of-date principalities. The leaven of
the French Revolution penetrated far beyond the Rhine. Offices ceased
to be bought, sold, and inherited. Regular systems of taxation, police,
and legal procedure came into use. The trades and professions were
thrown open to all: caste was breached, the peasant freed from some of
his heaviest burdens. Education, in some parts of Germany, was taken
out of the hands of the Church, and the clergy made amenable to the law.
In this manner Napoleon had, unconsciously perhaps, laid the foundation
for the union of the German peoples into one great empire, by the
suppression of so many of those small, jealous, and hide-bound
principalities which had divided the land, and which nothing but
overwhelming pressure from without could have reformed.
Thus, while still wearing the modest title of First Consul, the ruler
of France had grown to proportions which were imperial. To the French,
he was the necessary man without whom they might relapse into chaotic
conditions. The wondrous structure he had reared seemed to rest upon
his strength alone. His life was the sole guarantee of law and order.
Should assassins strike him down, what would be the situation in
France? To avoid such a danger, and to deprive royalist fanatics of
such a temptation, would it not be better to make Napoleon monarch,
and to settle the succession? In that event his death would not bring
about endless confusion and violent convulsions. Reasoning of this kind
seems to have moved the Senate to propose that the First Consul accept
a new title, and on May 18, 1804, he proclaimed himself Emperor of the
French.
Partly by the force of circumstances, partly by sincere conviction,
partly by the exertion of Napoleon's wonderful gift for the management
of men, France had been so well prepared for this change in her form
of government that she indorsed it by a practically unanimous vote.
Only such stalwart exponents of a principle as Carnot and Lafayette
protested.
With the Empire came all things imperial: a change of constitution;
a creation of high dignitaries; the ennobling of the Bonaparte
family, Lucien excepted; the creation of marshals in the army; the
establishment of court forms and etiquette in the palace.
Gorgeous and imposing were the ceremonies which ushered in the New
Order. Paris, France, Europe, were dazzled by the lavish expenditures,
the magnificent parade, with which the Consul became Emperor. He spared
no expense, no pains, no personal discomfort, to make the pageant a
success. Historians have sneered at the rehearsals by means of which he
prepared each actor in the coronation for his part; but the ridicule
would seem to be misplaced. His example has set the fashion; and not
only are private marriages rehearsed in our day, but royal funerals and
royal coronations perfect their functions by the same prudent process.
That nothing might be wanting to the solemnity and impressiveness of
the occasion, Napoleon insisted that the Pope should come from Rome
to Paris and officiate. So recent and so immense had been Napoleon's
services to the Church that the Pontiff could not refuse, more
especially as he had other favors to ask.
Brilliant as a dream was the coronation in the great cathedral of Notre
Dame. Paris never witnessed a civic and military display more splendid.
The Church, the State, princes foreign and native, grandees old and
new, blazed forth in the utmost that wealth and pride and vanity could
display. In a coach heavy with gold Napoleon and Josephine rode, amid
soldiers, to the church where the Pope had long awaited their coming;
and when the great Corsican had been conducted through the proper
forms, had prayed, had sworn, had been oiled and blessed, he proudly
took the crown out of the Pope's hands, crowned himself, and then
crowned the kneeling Josephine (December, 1804). His mother was not
there, she was in Rome with the revolted Lucien; but when the artist
David painted the picture of the coronation, Napoleon, with his never
failing eye for effect, had Madame Letitia put in. Just as he wished
for his mother on this the great day of his life, he did not forget his
father.
"Joseph, what would father have said!"
One who had lifted himself from a cottage to the White House in these
United States drew all hearts to himself when, after having taken the
oath of office, he turned to his old mother and kissed her. Not far
distant from the same creditable feeling was Napoleon's regret for his
father.
Mother Letitia could not be persuaded to leave Rome and the insurgent
Lucien; but the old nurse journeyed from Corsica to see her nursling
crowned. Napoleon hugged and kissed the old woman, lavished every
attention upon her, and kept her in Paris a couple of months. When she
returned to Ajaccio, she was laden with gifts.
Nor could Brienne be overlooked in these sunny days of triumph and
of happiness. The Emperor must return to the school grounds of his
boyhood, view the old familiar scenes, talk of old times with such
former acquaintances as might still be there. Behold him, then, soon
after his coronation, arriving at the château of Brienne, at six in
the evening, where Madame de Brienne and Madame Loménie await him at
the foot of the steps. He spends the night at the château, whose kind
mistress had so often made him welcome in the forlorn days of his
youth. He walks about the place, pointing out every spot familiar to
him when at school. He visits the field of La Rothière, a favorite
strolling place of his youth. He is so affable, so animated, so
interested, that his movements seem to say, See where I started from,
and where I have arrived. "And what has become of Mother Marguerite,
the peasant woman who used to sell milk, eggs, and bread to the boys?"
Mother Marguerite is still living, still to be found at the thatched
cottage in the woods. By all means, the Emperor must quit the fine
circle at the château and visit the old peasant in the hut. A man so
gifted with eye to effect could never miss a point like that. So the
horse is saddled and brought; the Emperor mounts and rides; and at the
cottage in the wood his Majesty alights and enters.
"Good day, Mother Marguerite!" The aged eyes are dim, and they
gleam with no recognition. She knows that the Emperor is in the
neighborhood; she expects to go to the château to see him; she will
carry him a basket of eggs to remind him of old times. Suddenly his
Majesty puts himself where the dim eyes can see him better, draws
nearer to her, and mimicking in voice and manner his schoolboy tone,
and rubbing his hands as he had used to do: "Come, Mother Marguerite!
Some milk and fresh eggs; we are dying of hunger."
A little more jogging of the memory, and the ancient dame, knowing now
who it is, falls at the Emperor's feet. He lifts her, and still insists
on the eggs and milk. She serves, he eats, both of them happy, and both
of them full of reminiscences of the years long ago. Though he left her
a purse of gold, Mother Marguerite probably was prouder of the fact
that he came to her house and ate.
One more visit the great Emperor will pay Brienne, the year of the last
visit being 1814. Foreign invaders will be encamped all round about the
playgrounds of his boyhood. Prussian Blücher will be taking his ease
and his dinner in the château. Prussian Blücher will give him battle
at Brienne, and will rout him at La Rothière. And to his companions,
the falling Emperor will again point out places of interest in the old
school-ground, but not in the happy vein of 1804.
* * * * *
What should be done with Italy? French arms had wrested her from
Austria and defended her from Russia. She was too weak to stand alone.
Take away the support of France, and she would again be cut up and
devoured by the stronger powers. On all sides she was threatened. The
English were at Malta, the Russians at Corfu, the Austrians in Venice,
while in Naples and Rome were apparent allies, but actual foes. Reasons
of state made it imperative that Napoleon's imperial system should
embrace Italy, and the Italians themselves favored the change.
Napoleon tendered the crown to his brother Joseph. To the amazement of
the world that preposterous egotist refused upon two grounds: first,
Italy was too near to France for its king to enjoy that complete
independence which Joseph felt necessary to his self-respect; second,
the crown of France belonged to him, in prospect, as heir of the
childless Napoleon; and Joseph would not exchange this selfish, shadowy
claim for the certainty offered him by his too partial brother! Surely
there never lived a man more be-cursed with ingrates of his own blood
than Napoleon!
"I am sometimes tempted to believe," said he, "that Joseph thinks I
have robbed my elder brother of his share of the inheritance of the
late king, our father!"
It was only after Joseph had resisted all persuasions that Napoleon
decided to make himself king of Italy "until the peace."
In April, 1805, taking Josephine with him, he crossed the Alps.
Everywhere he was greeted with enthusiasm. On the field of Marengo he
and Josephine sat upon a throne and viewed the splendid rehearsal of
the battle in which the young hero had crushed Austria and rescued
Italy at a blow.
In May, 1805, he placed upon his head, amid pomps and ceremonies in the
cathedral of Milan, the iron crown of the Lombards. Josephine looked
on from the gallery; she was not crowned queen of Italy; but her son,
the loyal and gallant Eugène Beauharnais, was made Viceroy of the new
kingdom. His Holiness, the Pope, was not present at the ceremony; his
Holiness was chagrined and unfriendly; he had left Paris a disappointed
man; he had asked many favors of Napoleon, "my son in Christ Jesus,"
which had been denied, and already was to be seen the slender line of
the rift between Napoleon and the Papacy which was to grow and grow,
widening year by year, until the yawning chasm was to ingulf much of
the strength of the Empire.
But, for the time being, the Pope went his way almost unnoticed, meekly
implacable, humbly vindictive, waiting his chance to strike the ruler
he had so recently oiled and blessed, while the vaulting Corsican,
using an archbishop to manipulate the clerical machinery instead of a
pope, inflated himself with pride as he felt upon his head the crown of
Charlemagne.
And had he no cause to be proud? Did the history of the world disclose
a more dazzling record than his? Not born to the throne, a stranger to
the purple and the gold of rank, the greatest Empire of modern times
was his; and, as heir to the Cæsars, he had now caught upon his arms
the grandeur and the glory of old Rome. Emperor of the West!--another
Theodosius, another Charles the Great! And only a few years ago he had
meekly stopped to scrape the mud of the streets off his coarse boots to
avoid offence to the nose of Madame Permon: had pawned his watch for
food; had moodily thought of drowning himself in the Seine because his
mother had pleaded for help which he was too poor to give!
If ever mortal was justly proud, it was he,--Napoleon, the penniless
son of the lawyer; Napoleon, tireless student, unwearied worker,
unconquerable adventurer, resistless soldier of Fortune,--Napoleon,
Emperor of France and King of Italy, whose crowns had come to him
unstained of blood! He was the strongest, the wisest, the best in
fight, in work, in council; and they had raised him aloft on their
bucklers as the strongest had been lifted in the valiant days of old.
Nothing in Napoleon's career was more brilliant than his triumphal
progress through the Italian cities. Everything which a passionate,
imaginative people could do to testify their admiration and affection,
they did; and during these brief, sunny weeks when he moved amid
ovations and splendors, amid rejoicings and blessings, amid music
and flowers, with Josephine by his side, he probably came as near to
happiness as his restless, craving nature could come. Everywhere he
left indelible footprints,--roads, canals, public buildings of all
sorts, mighty and useful works which made his tour memorable for all
time.
Genoa, following the lead of Italy, and friendly suggestions from
France, voted to unite her fortunes with those of the new Empire. The
Doge and the Senate went in state to Milan, were received by Napoleon
on his throne, and prayed that he would accept the ancient republic
as a part of France. Graciously the modern Cæsar consented; the Doge
became a French senator, and out of the territories of the republic
were carved three French departments.
The little republic of Lucca caught the general infection, sent a
deputation to Milan, begged at Napoleon's hands a government and a
constitution, was warmly welcomed by the Emperor, and was bestowed as
an imperial fief upon his sister Elisa, wife of a Corsican fiddler
named Bacciochi.
[Illustration: JOSEPHINE IN 1809
From a water-color by Isabey]
The horror and indignation with which European kings and cabinets
looked upon these encroachments can easily be imagined. With one accord
they began to cry out against Napoleon's "insatiable ambition." England
did not consider how she had despoiled France in Canada, on the Ohio,
in Hindustan. Russia and Austria made no account of provinces taken
from Poland or Turkey. All the great nations were growing greater; the
general balance of power had been disturbed: was France alone to be
denied the right to extend her system over states which asked for it,
and which were dependent upon her for protection?
In January, 1805, Napoleon had written directly to the King of England,
as he had done once before, asking for peace. As before, his advances
had been repelled. Great Britain had already begun to knit together the
threads of another coalition. An understanding existed between England,
Russia, Austria, and Sweden. Naples, through her Bourbon rulers, was
fawning at Napoleon's feet, flattering and servile, while secretly she
was plotting his downfall. Well aware of the storm which was gathering
on the Continent, Napoleon prepared for it, but did not for an instant
relax his efforts at Boulogne.
His plan was to send his fleet to sea, decoy Nelson into pursuit,
and then, while his own ships doubled and came back to the Channel,
to cross his army over to England, under its protection, in his
flat-bottomed boats. "Masters of the Channel for six hours, we are
masters of the world."
It was not to be. Wind and waves fought against him. The incapacity
of his navy fought against him. Into soldiers on land he could infuse
courage, confidence, sympathetic coöperation. But the navy baffled
him: all his efforts were vain. His admirals could not, or would
not, have faith; could not, or would not, obey orders; could not, or
would not, coöperate. Utterly wasted were all his labors, all his
expenditures. Austrian armies were marching against Bavaria, Napoleon's
ally; Russian hordes were moving down from the north; Prussia's
magnificent army of fifty thousand men was in the balance, wavering
ominously, and threatening to unite with the coalition.
Such was the situation on the Continent when the despatches reached
Napoleon that all his great plans for the invasion of England had gone
to wreck and ruin; that his admiral had misconceived or had disobeyed
positive orders; that the French fleet would not only be unable to give
him aid, but was so scattered and so placed that it must inevitably
fall a prey to the English.
"It was about four o'clock in the morning of August 13, that the news
was brought to the Emperor," says Ségur. "Daru was summoned, and
on entering gazed on his chief in utter astonishment." The Emperor
"looked perfectly wild"; his hat jammed down over his eyes, "his whole
aspect terrible." As soon as he saw Daru, he rushed up, and poured out
a torrent of pent-up wrath. He railed at his admiral, his imbecile
admiral, "that damned fool of a Villeneuve!" He paced "up and down the
room, with great strides for about an hour," venting his rage, his
disappointment, his reproaches. Then stopping suddenly and pointing
to a desk, he exclaimed: "Sit down there, Daru, and write!" And with
marvellous self-control, wresting his thoughts away from Villeneuve,
the fleet, the blasted plans of invasion, he dictated to the secretary,
hour after hour, as fast as pen could catch the rushing words, the
whole campaign of Ulm in its largest outline, in its smallest detail,
embracing, as it did, the movement of his own vast legions lying
along the coast for two hundred leagues, the movement of Masséna
from Italy, of Marmont from Holland, and of Bernadotte from Hanover.
Four hundred thousand soldiers were moving against the French; less
than half that number of French rushed to repel the attack. The vast
camps on the Boulogne coast vanished, the eagles set Rhineward, other
legions marched as they had never marched before--thousands speeding
along the roads in coaches. The Austrians had not waited for the
Russians; Bavaria had been overrun; and Mack, the Austrian general,
was now dawdling about Ulm. Before he suspected what was happening,
Napoleon's combination had been made, a circle of steel drawn about
his adversary; and the French armies, closing in upon front, rear, and
flanks, held the Austrians as in a mighty trap. With the exception of
a few squadrons which broke through the gaps in the French lines as
they advanced, the whole Austrian army laid down its arms (October 20,
1805). In the _Memoirs_ of de Ségur we are given a personal glimpse of
the Emperor which is perhaps more interesting to the average reader
than the dreary narrative of march, counter-march, manœuvre, and battle.
During the combats around Elchingen, Napoleon, soaked with rain, went
to a farmhouse at Hasslach to wait for Lannes and the Guard to come up.
There was a stove which threw out its comfortable heat, and before it
sat a drummer boy, wet, cold, and wounded. Napoleon's staff officers
told the boy to get out, and go somewhere else. The drummer would not
hear of it. The room was big enough for both the Emperor and himself,
he said, and he meant to stay. Napoleon laughed, and told them to let
the boy alone, "since he made such a point of it." In a few moments
the Emperor was dozing on one side of the stove and the drummer lad on
the other. Around the two sleepers were grouped the staff officers,
standing, and awaiting orders.
Louder roared the cannon, and every few minutes Napoleon would rouse
himself and send off messengers to hasten Lannes. While the Emperor was
thus napping, Lannes came up, entered the room abruptly, and exclaimed:
"Sire! What are you thinking about? You are sleeping while Ney,
single-handed, is fighting against the whole Austrian army!"--"That's
just like Ney, I told him to wait," said Napoleon, and springing on his
horse, he galloped off so fast that Lannes, afraid now that the Emperor
would rush into danger, roughly seized the bridle rein and forced
him back in a less dangerous position. Ney was reënforced, and the
Austrians routed.
* * * * *
In the midst of his own successes, Napoleon received the tidings from
Trafalgar. Nelson had fought the combined fleets of France and Spain,
had lost his own life, but had won so complete a triumph that England's
supremacy at sea was not disputed again throughout the Napoleonic wars.
The shock to Napoleon must have been stunning, but he only said, "I
cannot be everywhere."
Continuing his advance, he entered Vienna, November 13, 1805, and lost
no time in throwing his army across the Danube, in hot pursuit of the
retreating enemy.
By a trick and a falsehood, Murat and Lannes secured the great bridge,
and much precious time was saved. By a similar trick, the Russians
deceived Murat a few days later, and escaped the net Napoleon had
thrown around them, and thus "the fruits of a campaign were lost."
Murat gained the bridge by pretending that an armistice had been agreed
on; the Russians made good their escape by duping Murat with the same
falsehood. Napoleon's anger was extreme, the more so as a blunder of
Murat's had come within a hair's-breadth of spoiling the campaign of
Ulm.
Failing to trap the Russians as he had trapped the Austrians, there
was nothing for Napoleon to do but to press the pursuit. League after
league the French penetrated a hostile country, new armies mustering
on all sides to rush in upon them, until they were in the heart of
Moravia. The Emperor Francis of Austria had joined the Czar Alexander,
and the combined Russo-Austrian forces, outnumbering the French,
confronted Napoleon at Austerlitz. The position of the French, far
from home and surrounded by populations rushing to arms, was critical.
Napoleon realized it, and so did his foe. There is no doubt that he
would have welcomed an honorable peace, but the terms offered by the
Czar were so insulting that he indignantly rejected them. Hastily
concentrating his army, he made ready to fight. He artfully cultivated
the self-confidence of the enemy, and put them under the impression
that he was trying to escape. They had the hardihood to believe that
they could turn his position, cut him off from his line of retreat, and
do to him at Austerlitz as he had done to Mack at Ulm.
Indeed, the position of the French army demanded all of Napoleon's
firmness, all of his genius. He had about eighty thousand men; the
Emperors in his front had ninety thousand. His right was threatened
by the Archduke Charles with an army of forty thousand; his rear by
the Archduke Ferdinand with twenty thousand; on his left flank was
unfriendly Prussia with a magnificent force of one hundred and fifty
thousand. The combined armies in his front, taking the offensive,
attacked the French advance guard at Wischau, and routed it. Napoleon
was uneasy. He sent envoys to the Czar and sought a personal interview.
Surrounded by young hotheads, Alexander repulsed the overture, sending
Dolgorouki to meet the Emperor of the French. Full of the idea that the
French were frightened and would pay handsomely for the privilege of
getting back home, young Dolgorouki demanded of Napoleon the surrender
of Italy, Belgium, and the Rhine provinces.
"What more could you ask if you were in France?" exclaimed the
indignant Napoleon. The envoy's manner was as offensive as his
language, and Napoleon finally ordered him off. Violently irritated,
Napoleon stood talking to Savary for some time, striking the ground
with his riding-whip, as he dwelt upon the insolence of the Russians.
"Please God, in forty-eight hours I will give them a lesson!"
An old grenadier stood near, filling his pipe for a smoke. Napoleon
walked up to him and said, "Those fellows think they are going to
swallow us up."--"If they try it," said the veteran, "we'll stick in
their craws." Napoleon laughed, and his brow cleared.
Drawing his army back to a still better position, Napoleon studied
the ground thoroughly, reconnoitred diligently, and waited. He soon
guessed the plan of the enemy, to turn his right flank. But to do this
they must expose their own flank to him, and he would strike them as
they marched. So confident was Napoleon that he could destroy his enemy
if the turning movement across his front were attempted, that he lured
them still farther by withdrawing from the high-ground, the Pratzen
plateau--"a grand position," from which he could easily have inflicted
upon the Russians an ordinary defeat. But an ordinary defeat was not
what he wanted; he manœuvred to lead his foes into a false movement
where they could be annihilated.
On December 1, 1805, about four in the afternoon, Napoleon could see
through his field-glass that the great turning movement of the Russians
had commenced. He clapped his hands and exclaimed, "They are walking
into a trap; before to-morrow night that army will be mine!"
Ordering Murat to make a sham attack and then retire so as to confirm
the enemy in his delusion of a French retreat, Napoleon dictated a
stirring address to his troops, pointing out to them the Russian
mistake and the advantage the French could take of it. Everything done
that could be done, the great captain called his staff about him, and
sat down to dinner in the hut which served him for a bivouac. Seated
around the table on wooden benches were Murat, Caulaincourt, Junot,
Rapp, Ségur, Mouton, Thiard, and others. As serenely as though he were
in Paris, Napoleon led the conversation to literary topics, dramatic
poetry especially, and commented at length on the merits of various
authors and plays. From these subjects he passed on to Egypt, and again
spoke of the wonderful things he would have done had he taken Acre. He
would have gained a battle on the Issus, become Emperor of the East,
and returned to Paris by way of Constantinople. Junot suggested that
they might, even now, be on the road to Constantinople. But Napoleon
said: "No. The French do not love long marches. They love France too
well. The troops would prefer to return home." Junot questioned this;
but Mouton bluntly declared that the Emperor was right, that the army
was tired out, it had had enough: it would fight, but would do so
because it wished to win a battle which would end the war and allow the
men to return home.
Throwing himself upon some straw in his hut, Napoleon slept till far
into the night. Then he mounted his horse, and once more went the
rounds to see that all was right. He went too near the Russian lines:
roused some Cossacks, and escaped capture by the speed of his horse.
Getting back into his own lines, he was stumbling along on foot in the
darkness when he fell over a log. A grenadier, to light his way, made
a torch of some straw. The blaze showed to other soldiers the Emperor.
Upon a sudden impulse, more torches were made of straw, while the shout
arose, "Live the Emperor!" It was the anniversary of the coronation,
and the troops remembered. The one torch became a score, the score a
hundred, then thousands, until a blaze of light ran along the line for
miles, while the shout of "Live the Emperor!" roused even the Russian
hordes. It was such an ovation as only a Cæsar could inspire. It was
so unstudied, so heartfelt, so martial and dramatic, that Napoleon was
profoundly moved. "It is the grandest evening of my life," he exclaimed.
At dawn he called his staff to the hut, ate with them standing, and
then, buckling on his sword, said, "Now, gentlemen, let us go and begin
a great day!" A moment later he sat his horse on a hill that overlooked
the field, his staff and his marshals around him. As the sun cleared
itself of the mists, "the sun of Austerlitz," the final orders were
given, the marshals galloped to their posts, and the famous battle
began. By four o'clock that evening the Russo-Austrian army was a
wreck--outgeneralled, outfought, knocked to pieces. Napoleon had ended
"_this_ war by a clap of thunder." The Czar fled with the remnant of
his host, escaping capture at the hands of Davoust by the well-worn
falsehood of an armistice. The Emperor Francis came in person to
Napoleon to sue for peace, was kindly received, and was granted terms
far more liberal than he had any right to expect.
On December 27, 1805, the Treaty of Presburg was signed. Austria ceded
Venice, Friuli, Istria, and Dalmatia to Italy; Tyrol to Bavaria, which
Napoleon erected into an independent kingdom; Würtemberg and Baden
received cities and territory as rewards for adherence to France.
Austria sanctioned all of Napoleon's recent encroachments in Italy, and
agreed to pay an indemnity of $8,000,000.
In the battle of Austerlitz the Allies lost about fifteen thousand men,
killed and wounded, besides twenty thousand prisoners. The French loss
was about twelve thousand.
Marbot relates an incident which illustrates the character of Napoleon.
One of the familiar episodes of the battle of Austerlitz was the
retreat of the Russians over the frozen lakes. Napoleon himself ordered
the cannoneers to cease shooting at the fugitives, and to elevate
their pieces so that the balls would fall upon the ice. The balls fell,
the ice cracked, and some two thousand Russians sank to watery graves.
Next day Napoleon, being near this spot, heard feeble cries for help.
It was a Russian sergeant, wounded, adrift in the lake, supporting
himself on an ice floe. Napoleon's sympathies were at once aroused,
and he called for volunteers to save the Russian. Many attempts were
made, several Frenchmen came near being drowned, and finally Marbot and
Roumestain stripped, swam to the man, and brought him to the shore.
Napoleon had every attention shown to the poor fellow--the survivor of
the host which sank the day before under his pitiless orders.
CHAPTER XXVI
In England the wonderful triumph of Napoleon spread consternation and
bitter disappointment. So much hard cash had been wasted, so many
well-laid plans smashed, so much blind hatred brought to nothing!
Other faces besides Pitt's took on "the Austerlitz look." That most
arrogant of ministers had offered money to all who would unite against
France, had encouraged Austria to attack Bavaria because of the
refusal of Bavaria to enter the coalition against France, had landed
English troops in Calabria to stir up the priest-ridden peasantry to
insurrection, and had pledged himself to the task of driving the French
from Germany, from Switzerland, from Italy and Holland. A mightier ruin
had never fallen upon haughtier plans. The French were now masters of
more territory than ever; Napoleon's power greater than ever; England's
allies were being dismembered to strengthen the friends of France; and
the British troops which had been sent to Calabria, and which had won
the battle of Maida (July, 1806), abandoned the enterprise, and left
the peasantry to suffer all the vengeance of the French. Whether Mr.
Pitt's last words were, "My country! How I leave my country!" or, as
Mr. D'Israeli used to relate, "I think I could now eat one of Bellamy's
pork pies," it is certain that he took the news of Austerlitz as Lord
North took Saratoga, "like a ball in the breast."
On the Continent Napoleon was supreme, and he used his advantage
vigorously. The Bourbons of Naples had played him false, and he
dethroned them. In western Germany was organized the Confederation of
the Rhine, composed of Bavaria, Baden, Würtemberg, and thirteen smaller
principalities, and containing a population of eight million. Created
by Napoleon, it looked to him for protection, put its military forces
at his service, and became, practically, a part of his imperial system.
By these changes the Emperor of Austria was reduced to his hereditary
dominions, and his shadowy Holy Roman Empire ceased to exist, August 6,
1806.
Following Austerlitz came a grand distribution of crowns and coronets.
Brother Joseph condescended to become King of Naples, with the distinct
understanding that he waived none of his "rights" to the throne of
France, and that he should be treated as an "independent ally" of the
Emperor.
Holland was turned into a subject kingdom, and Louis Bonaparte put upon
its throne.
To his sister Elisa, Napoleon gave additional territory in Italy; and
to Pauline, who had married Prince Borghese, was given Guastalla.
Madame Bacciochi, who was morally another Caroline of Naples, was a
good ruler, and her government of her little kingdom was excellent. As
to Pauline, she cared for nothing but pleasure; and not knowing very
well what else to do with her Guastalla, she sold it.
Caroline Bonaparte, importunate in her demands for imperial
recognition, was offered the principality of Neufchâtel. She haughtily
declined it. Such a petty kingdom was obviously, even glaringly, less
than her share. Yielding to this youthful and self-assertive sister,
Napoleon had to create the Grand Duchy of Berg to satisfy her and her
no less aspiring husband, Murat.
The scapegrace Jerome Bonaparte, one of whose numberless freaks was
that of paying $3,000 for a shaving outfit long prior to the arrival
of his beard, was made to renounce his beautiful young American wife,
Miss Patterson; and was kept in imperial tutelage till such time as he
should be made king of Westphalia, with a Würtemberg princess for queen.
Eugène Beauharnais, Viceroy of Italy, was married to the daughter of
the king of Bavaria; and Stephanie Beauharnais, Josephine's niece, was
wedded to the son of the Elector of Baden.
In these grand arrangements for the Bonaparte family, Lucien was left
out. He and Napoleon had quarrelled, the cause being, chiefly, that
Lucien would not discard his wife, as the pusillanimous Jerome had
done. Napoleon was offended because Lucien at his second marriage had
selected a woman whose virtue was far from being above suspicion.
"Divorce her," demanded Napoleon; "she is a strumpet."
"Mine is at least young and pretty," retorted Lucien, with sarcastic
reference to Josephine, who was neither young nor pretty. Angrily the
brothers parted: the elder insisting on the divorce, and offering
a kingdom as a bribe: the younger scornfully spurning the bribe,
and cleaving to his wife. This manly and independent attitude was
the easier to maintain since Lucien had already amassed a fortune
in Napoleon's service. Taking up his residence in a grand palace in
Rome, surrounded by rare books, paintings, and statuary, comforted
by the preference and the presence of Madame Letitia, a favorite of
the Pope because an enemy of Napoleon, Lucien cultivated letters,
wrote the longest and the dullest epic of modern times, and called it
_Charlemagne_.
While elevating to thrones the members of his family, the Emperor could
not forget those who had served him in the army and in civil affairs.
From the conquered territories he carved various principalities,
duchies, and so forth, for distribution among the Talleyrands,
Bernadottes, and Berthiers, who were to betray him later. A new order
of nobility sprang up at the word,--a nobility based upon service, and
without special privilege, but richly endowed, and quick to arrogate to
itself all the prestige ever enjoyed by the old.
Surrounded as he was by hostile kings, Napoleon felt the need of
supports. In creating the Confederation of the Rhine, in putting his
brothers upon adjacent thrones, in bestowing fiefs upon his high
officials, he believed himself to be throwing out barriers against
foreign foes, and propping his empire with the self-interest and
resources of all these subject princes whom he had created, never
dreaming that in the day of adversity his own brothers and sisters
would think of saving themselves at his expense.
* * * * *
On the very night of Napoleon's return to Paris from the army, he
summoned his council. The finances were in confusion; there had been
something of a panic, and only the victory of Austerlitz restored
confidence. The minister, who had brought about this state of things
by his mismanagement, was Barbé-Marbois, a royalist whom Napoleon
had recalled from banishment and elevated to high office. During
the Emperor's absence the minister had allowed the contractors and
speculators to become partners in the management of the treasury,
had allowed these speculators to use public funds, and had carried
his complaisance to such an extent that they now owed the government
more than $25,000,000. Under the Old Régime it was quite the usual
thing to allow contractors and speculators to use and misuse public
funds. In our own day it is the universal rule. No well-regulated
Christian government would think of issuing a loan, undertaking public
improvements, or refunding its debt without giving to some clique
of favored capitalists a huge share of the sum total: just as it
would shock a modern government to its foundation if the principle
were enforced that public funds should be rigidly kept in public
depositories to be used for public purposes only.
Napoleon, however, was neither a ruler of the ancient Bourbon type,
nor a Christian governor of the modern sort. He would not float loans,
levy war taxes, nor allow his treasury to become the hunting-ground
of the Bourse. England was fighting Napoleon with paper money, was
floating loan after loan, was giving to speculators and contractors
golden opportunities to enrich themselves. In the end, England's paper
money, loans, and war taxes were to whip the fight; but in the meantime
Napoleon believed himself right and England wrong. He honestly believed
that England would sink under her debt, taxes, and worthless currency.
When he saw her grow in strength year by year, her manufactures
increase, her trade increase, her wealth, power, and population
increase, he was unable to comprehend the mystery. Mr. Alison, the
Tory historian, who chronicles the facts, explains, kindly, that this
growth of England was illusive and fictitious. To Napoleon, sitting
desolately on the rock at St. Helena, housed in a remodelled cow barn
and tormented by rats, it must have seemed that this paper-money growth
of English power was not quite so illusive as Mr. Alison declared.
Sternly adhering to his own system, Napoleon called the erring minister
and the greedy speculators to account. Marbois was dismissed from
office, the speculators thrown into jail, the property of the syndicate
seized, and the debt due the treasury collected. The Bank of France was
overhauled, the finances put into healthy condition, and the public
funds advanced until they commanded a higher price than ever before,
nearing par.
CHAPTER XXVII
After the treaty of Presburg the Archduke Charles, in paying off the
Austrian troops, said to them, "Go and rest yourselves until we begin
again." Even at that early date the European powers were acting upon
the fixed principle that the war against France was not to cease till
she had been forced back into her ancient limits. No matter what
battles might be fought, treaties made, and territories yielded, the
one thing upon which England, Austria, and Russia were agreed, was that
Napoleon must be crushed. He represented the New Order brought forth by
the Revolution. He represented liberalism, civil and religious freedom,
and progress in its modern sense of giving to every man a chance in
life. Such principles were destructive to the repose of Europe, and the
ruling classes in Europe were deeply attached to this repose. England's
ruling class, supported in lordly preëminence by the patient millions
below them, wanted no levelling tendencies to invade her caste-ridden
isles. Germany, whose nobles and landowners clung to all the privileges
and barbarities of feudalism, abhorred the Code Napoléon, and the
democratic germs of the Napoleonic system. Russia, almost as benighted
as Persia or Turkey, dreaded a trend of events which meant freedom
for the serf and civil rights for the common people. The nobleman in
Russia, the peer of Great Britain, the petty lord in Germany, was at
heart one and the same man. He had been born to wealth, privilege, and
power; he meant to keep what birth had given him, and he meant to pass
it on to his son, "forever in fee simple." Of course he explained that
God had ordained it so. And what the nobleman asserted, the priest
maintained. If Napoleon foresaw that as Consul war would be made upon
him continually by the opposing systems of Europe, how much less hope
was there for peace now, when he had begun to shatter the ancient
feudalisms?
Let crimination and recrimination exhaust itself, let Thiers write
bulky volumes in Napoleon's favor, while Lanfrey and Baring-Gould print
heavy pamphlets against him, the truth lies here:--
Napoleon represented principles which were considered ruinous to the
Old Order in Europe, and the beneficiaries of that Old Order were
determined not to surrender without a desperate fight. Just as the Old
Order in France resisted all efforts at reform, so on a wider field
the kings and aristocracies of Europe resisted Napoleon. They could
not believe themselves safe while he was aggressive and triumphant.
Therefore, while Austria might bow to the storm, while the Emperor
Francis might come to Napoleon's tent, pleading for mercy, and get it,
the true sentiment of Austria was voiced by the Archduke Charles, when
he said to the troops, "Go rest yourselves, my children, till we begin
again." It was only a question of time and opportunity when they would
begin again.
Prussia had been one of the first nations to arm against revolutionary
France. Lugged in by Austria, she had published the famous proclamation
of Brunswick, had invaded France, and had been beaten back at
Valmy. In due time Prussia had become disgusted with the French
royalists--tired of a contest in which, gaining no glory, she lost
men, money, and prestige. She had made peace with the Republic, and
had become honestly neutral. Harmonious relations had continued to
exist between the two nations until the rupture of the Peace of Amiens.
England had then done her utmost to draw Prussia into the third
Coalition, but had not quite succeeded. In the grand strategy leading
to the climax at Ulm, it had become necessary to march some French
troops through Anspach, a Prussian province. This violation of his
territory gave great offence to the young King Frederick William IV.,
and he threatened war.
Napoleon's crushing blows on Austria intimidated Prussia and made
her hesitate; but when the French risked themselves in Moravia, and
the outlook for Napoleon began to grow gloomy, Prussia sent him her
minister, Haugwitz, bearing an ultimatum. Napoleon realized his peril,
postponed immediate action, and fought the battle of Austerlitz.
His victory released him from danger, and Haugwitz, forgetting his
ultimatum, poured forth congratulations. Napoleon heard them with
a sardonic amusement he did not conceal, bluntly declaring that
Austerlitz had changed the Prussian tone.
When the Confederation of the Rhine was about to be formed, Napoleon,
by the treaty of Vienna, ceded Hanover to Prussia partly in return for
Anspach and Bayreuth. Hanover being the personal domain of the King of
England, its cession to Prussia was a fair guarantee against Prussian
and English coöperation. That he gave so rich a bribe to Prussia
proves his earnestness in seeking her friendship. Those who criticise
Napoleon's politics, dwell on his imprudence in not separating England
from the Continent. The critics say that he ought to have known that
he was not strong enough to combat combined Europe. The probabilities
are that Napoleon understood the situation quite as well as those
divines and college professors who now criticise him. How was he to get
Continental Europe on his side save by force of arms? Had he not tried
treaties with Naples and Austria? Had he not exhausted conciliation
with Russia and Prussia? In what way was he to <DW36> England if not
by shutting her out of the Continent, and how could he do that without
using force? His navy was gone; England had rejected his repeated
overtures for peace; her gold bribed European diplomats and cabinets to
wage war upon him: how was he to deal with armies hurled against him
if he did not fight them? Unite the Continent against England! That
was precisely what he was trying to do, and England knew it. Hence her
bribes, hence successive wars. Ever and ever it was Napoleon's hope to
win his way to a Continental league against England, forcing her to
peace, and to the terms she had made at Amiens.
The inherent antagonism of the European monarchs to Napoleon was shown
when the Czar visited Berlin in 1805, and at the tomb of Frederick the
Great vowed alliance and friendship to the Prussian king.
In 1806 that pledge was solemnly repeated, the Czar and the King having
broken it a good deal in the interval. Whether the last oath would
amount to more than the first, would depend upon circumstances; but
the formal act proved at least how instinctive and vehement was their
antagonism to Napoleon.
After Mr. Pitt's death, Fox succeeded him in the ministry, and almost
immediately Napoleon again made overtures for peace. There was much
less hope of it now, for the situation had greatly changed. Passions on
both sides the Channel were at white heat, territorial distributions
had been made which it would be difficult to unmake, and Fox, as a
known friend of Napoleon, might find himself unable to make concessions
which Pitt could safely have offered.
Of course, England would demand that Hanover be restored; Malta, she
would certainly keep. In the temper which the newspapers had created in
England, no minister would have dared now to surrender that island. But
still peace was possible. Equivalents for Malta might be arranged. As
to Hanover, Napoleon might take it from Prussia, giving her something
just as good in exchange. The negotiations were set on foot, through
Lord Yarmouth, one of the Englishmen who had been held in France at
the beginning of the war. When Prussia learned that Napoleon was using
Hanover as a bait to England, her smothered ill-will burst into flames.
Violent talk, violent pamphlets, broke out in Prussia, and Davoust
intensified matters by having Palm, the bookseller of Naumberg, shot,
because he had circulated incendiary documents against the French.
The war feeling rose irresistibly. Even had the King been inclined to
oppose it, he could not have done so. His Queen, his army chiefs, his
nobles, his troops, his people--they all clamored for war.
The young officers at Berlin whetted their swords on the steps of the
French embassy, and broke the windows of Prussian ministers who favored
peace.
Napoleon was at Paris when the news came that the Prussian hotheads had
been sharpening their blades in front of his embassy. His hand went to
his sword-hilt: "They will learn that our swords need no whetting--the
insolent braggarts!"
So confident were the Prussians, so impatient were they to hurl
themselves into the struggle, that they would not wait for Russian aid.
Apparently they feared that Prussia might have to divide the glory.
Was not theirs the army of Frederick the Great? Was not their cavalry
the finest in Europe? Had not General Rüchel announced on parade that
the army of his Majesty of Prussia possessed several commanders who
were the equals of Bonaparte? Why await Russia? The delay would put
Napoleon on his guard. At present he was unsuspicious of immediate
attack. Prussian diplomats had lulled him with assurances that their
preparations were a mere pretence. There were a few scattered French
forces in Bavaria; Prussia could hurl her two hundred thousand veterans
upon Saxony, absorb the Saxon forces, and brush the French out of
Germany before Napoleon could help himself. So thought the Prussian war
party, at the head of which was the Queen and Prince Louis, brother of
the King. On horseback, clad in uniform, Queen Louisa appeared at the
head of the army, fanning the war fever into flames. Prince Louis took
high command for active service, and the old Duke of Brunswick (he of
the famous manifesto of 1792 and of Valmy) tottered forth under the
weight of his fourscore years to suggest bold plans which he lacked the
vigor to prosecute. While Prussian cohorts were mustering and marching
upon Saxony, the Prussian ambassador in Paris was still playing a
confidence game on Napoleon. At last Prussia launched an ultimatum
giving the Emperor of the French until October 8 to save himself by
submission. The Prussian army, one hundred and thirty thousand strong,
concentrated near Jena; the French seemed at their mercy, the chief
dispute among the Prussian commanders being whether they should wait
till after the date fixed by the ultimatum to pass the Thuringian
Forest and attack the enemy. When the ultimatum reached Paris, Napoleon
was gone, was on the Rhine, was ready to launch two hundred thousand
men upon the now amazed and bewildered Prussians. The great Emperor had
not for a moment been deceived. All the time that he had been listening
with placid face to the lies of the Prussian diplomat, he had been
massing troops where they were needed. When the courier caught up with
him and delivered the ultimatum, he laughed at it. With masterly speed
he threw himself upon the Prussian flank and rear. Prussia had repeated
the mistake of Austria; her losses were even more ruinous. Prince
Louis, attacking Lannes at Saalfeld (October 10), was routed and killed.
When Napoleon reached Jena with his main army of ninety thousand men,
he supposed that the bulk of the Prussians were before him. Cautious
as ever, he sought the advantage of position, and secured it. A Saxon
parson showed him a secret path to the heights commanding the Prussian
position, and during the night this path was made practicable for
artillery. When day dawned (October 14, 1806), the unequal battle
commenced, the French outnumbering the enemy two to one. Hohenlohe, the
Prussian commander, was almost annihilated, the remnants of his army
fleeing in wild disorder.
At the same time Davoust with twenty-seven thousand French fought
the main Prussian force, about double his own, at Auerstädt. Badly
commanded by the Duke of Brunswick and the King of Prussia, the
Germans fought with desperate valor, but were utterly beaten. Broken
and driven, they fled from the field, making for Weimar, and ran
into the masses of fugitives who were flying from the field of Jena.
Murat's dreaded cavalry were in hot pursuit, and a scene of the wildest
confusion followed. To the beaten army all hope was lost. There was no
fixed line of retreat, no rallying-point, no master-mind in control.
In hopeless fragments the fugitive host fell apart, and the relentless
pursuit was never slackened until the last one of these bands had been
captured. With incredible ease and rapidity the Prussian monarchy had
been brought to the dust.
CHAPTER XXVIII
There is no doubt that Napoleon had more personal feeling against
Prussia than against any foe he had heretofore met, England excepted.
In fact, the manner in which Prussia had acted justified much of this
enmity. She had tried to blow hot and cold, run with the hare and hold
with the hounds in so shameless a manner that even Charles Fox, the
sweetest tempered of men, had denounced her to the English Parliament
in the bitterest of terms. She had toyed with England, sworn and broke
faith with Russia, dallied with and deluded Austria, trifled with and
played false to Napoleon, and finally, after taking the Hanover bribe
from him, had sent the Duke of Brunswick to St. Petersburg to assure
Alexander that Frederick William III. was still his friend, and that
the apparent alliance with Napoleon meant no more than that Prussia was
glad to get Hanover.
It is no wonder that Napoleon had declared that Prussia was for sale
to the highest bidder, and that she would be his because he would pay
most. He had paid the price,--Hanover. When he saw that Prussia meant
to keep the price, and not the contract, his feeling was that of the
average man who finds that where he thought he had made a good trade,
he has been swindled.
Therefore, when the Queen of Prussia, Prince Louis, the Duke of
Brunswick, and the war party generally, showed their determination to
break faith with him; when the young officers insulted his embassy;
when the Prussian army launched themselves against a member of his
Confederation of the Rhine, Napoleon was genuinely incensed. They had
shown him no consideration, and he was inclined to show them none.
He roughly denounced the conduct of the Duke of Weimar, when speaking
to the Duchess in her own palace; but when she courageously defended
her absent husband, Napoleon's better nature prevailed, he praised her
spirit, and became her friend.
The Duke of Brunswick, mortally wounded at Auerstädt, sent a messenger
to Napoleon praying that his rights as Duke of Brunswick might be
respected. Napoleon answered that he would not spare the _duke_,
but would respect the general; that Brunswick would be treated as
a conquered province, but that the Duke himself should have that
consideration shown him which, as an old man and a brave soldier, he
deserved. At the same time, and as additional reason for not sparing
the Duke as a feudal lord, Napoleon reminded him of the time when he
had advanced into France with fire and sword, and had proclaimed the
purpose of laying Paris in ashes. The son of the dying Duke took this
natural reply much to heart, and swore eternal vengeance against the
man who sent it.
Napoleon understood very well that the war had been brought on by
the feudal powers in Germany,--those petty lords who had dukedoms
and principalities scattered throughout the land, miniature kingdoms
in which these lords lived a luxurious life at the expense of the
peasantry. These feudal chiefs were desperately opposed to French
principles, and dreaded the Confederation of the Rhine. Every elector,
prince, duke, or what not, expected, with trembling, the day when he
might be "mediatized," and his little monopoly of a kingdom thrown into
the modernized confederation. Hence their eagerness for war, and hence
Napoleon's bitterness toward them. It went abroad that he said that
he would make the nobles of Prussia beg their bread. He may have said
it, for by this time he was no longer a mute, all-concealing sphinx.
He had become one of the most talkative of men; therefore, one of the
most imprudent. Unfortunately, he did nothing to separate the cause of
the German people from that of the German nobles. His heavy hand fell
upon all alike; and it was his own fault that the national spirit of
Germany rose against him finally, and helped to overthrow him. Not only
did he speak harshly, imprudently of the Prussian nobles, he committed
the greater blunder of reviling the Queen. True, she had well-nigh
said, as a French empress said later, "This shall be _my_ war!" She had
inspired the war party by word and by example. In every way known to
a beautiful young sovereign, she had made the war craze the fashion.
She had done for Prussia what Eugénie afterward did for France,--led
thousands of brave men to sudden death, led her country into a colossal
smash-up. Eugénie's husband, swayed by an unwomanly wife, lost his
liberty and his throne. By a mere scratch did Louisa's husband, as
blindly led, escape the same fate. A brazen but patriotic lie, told
by old Blücher to the French general, Klein,--"an armistice has been
signed,"--saved Frederick William III. from playing Bajazet to the
French Tamerlane. A political woman was ever Napoleon's "pet aversion."
In his creed the place held by women was that of mothers of numerous
children, breeders of stout soldiers, wearers of dainty toilets,
companions of a lustful or an idle hour, nymphs of the garden walks,
sirens of the boudoir, nurses of the sick, comforters of grief, censer
bearers in the triumphal progress of great men. A woman who would talk
war, put on a uniform, mount a horse, and parade at the head of an
army, aroused his anger and excited his disgust. This feeling was the
secret of his dislike to the Queen of Prussia, and of his ungentlemanly
references to her in his bulletins. But while those references were
such as no gentleman should have made, they were infinitely more
delicate than those in which the royalist gentlemen of Europe were
constantly alluding to Napoleon's mother, his sisters, his wife, his
step-daughter, and himself. It is only fair, in trying to reach just
conclusions, to remember the circumstances and the provocations under
which a certain thing is said or done. If we constantly keep in view
this standard in weighing the acts and words of Napoleon, it will
make all the difference in the world in our verdict. Napoleon was no
passionless god or devil. His blood was warm like ours; his skin was
thin like ours; a blow gave him pain as it pains us; slanders hurt him
as they hurt us; infamous lies told about his wife, sisters, and mother
wrung from him the same passionate outcries they would wring from us.
And this fact also must be kept in mind: before Napoleon stooped to
make any personal war upon his sworn enemies, he had appealed to them,
time and again, to cease their personal abuse of him and his family.
On October 27, 1806, Napoleon made his triumphal entry into Berlin,
giving to the corps of Davoust the place of honor in the march. It
was a brilliant spectacle, and the people of Berlin who quietly
looked upon the scene were astonished to see the contrast between the
Emperor's plain hat and coat, and the dazzling uniforms of his staff.
Says Constant: "We came to the square, in the middle of which a bust
of Frederick the Great had been erected. On arriving in front of the
bust, the Emperor galloped half around it, followed by his staff, and,
lowering the point of his sword, he removed his hat and saluted the
image of Frederick. His staff imitated his example, and all the general
officers ranged themselves in semicircle around the monument, with the
Emperor. His Majesty gave orders that each regiment as it marched past
should present arms."
The Prince Hatzfeldt brought the keys of the city to the conqueror,
and Napoleon at once organized a new municipal government, putting
Hatzfeldt at the head of it. The Prince, instead of being faithful to
the confidence Napoleon placed in him, used his position to gather
information about French forces and movements. This information he
forwarded to the fugitive king, Frederick William. Hatzfeldt may
not have realized that his conduct was that of a spy; may not have
understood that holding an office by Napoleon's appointment he must be
loyal to Napoleon. Serving two masters under such circumstances was
a risky business, and Hatzfeldt found it so. His letter to the King
was intercepted, and brought to Napoleon. The Prince was about to be
court-martialled and shot. Already the necessary orders had been given,
when the Princess Hatzfeldt, wife of the accused, gained access to
the palace, and threw herself at Napoleon's feet. A woman in tears--a
genuine woman and genuine tears--Napoleon could never resist; and
Hatzfeldt was saved, as the Polignacs had been, by the pleadings of a
devoted woman.
After Waterloo, the Duke of Wellington, confident now that he was the
greatest man that ever walked upon the earth, bought Canova's statue
of Napoleon, carried it to London, stood it up in his hall, and made
of it a hat-rack, umbrella-stand, and cloak-holder. It would seem that
the men who say that Napoleon had no generous, chivalrous instincts
have failed to see in Wellington's conduct any evidence of indelicacy
of feeling. These critics, however, are confident that, in seizing as
trophies the sword and sash of Frederick the Great, as Napoleon did at
this time, he committed a most outrageous act. It may fairly be argued
that the rule as to trophies is not so clear as it might be. The law
seems to be obscure, and the decisions conflicting. So far as can be
gathered from a reading of a number of authorities, the rule seems
to be that after a conqueror has overthrown his enemy, he can take
whatever his taste, fancy, and greed suggest.
Of course we are here speaking of Christians--civilized, complacent,
watch-me-and-do-as-I-do Christians. It will be found that they have
taken any sort of plunder which can be carted away. All over England
is the loot of India; all over Spain that of South America and Mexico;
and in sundry portions of these United States may be found articles of
more or less value which used to belong to China or the Philippines.
They--the Christians--have taken the ornaments from the bodies of the
wounded and the dead; have wrenched from arms, and fingers, and necks,
and ears, the jewels of man, woman, and child; have robbed the temple
and the shrine; have not spared the idol, nor the diamonds that blazed
in its eyes; have taken sceptre, and sword, and golden throne; have
stripped the palace, and robbed the grave. A dead man of to-day and a
dead man of thousands of years ago, are as one to the remorseless greed
of the Christians. In the name of science the mummy is despoiled; in
the cause of "advancing civilization" the warm corpse of the Chinaman
or the Filipino is rifled. When we find among the crown jewels of
Great Britain the "trophies" wrenched from the living and the dead in
Hindustan; when we see the proud people of the high places wearing the
spoil of Egyptian sepulchres, it is difficult to know where the line is
which separates legitimate from illegitimate loot. Consequently, we are
not certain whether Napoleon was right or wrong in robbing the tomb of
Frederick the Great of the sash and sword.
While at Berlin, Napoleon issued his famous Berlin Decree. The English,
repeating the blow they had aimed at France during the Revolution, had
(1806), by an "Order in Council," declared the entire coast of France
in a state of blockade. In other words, Great Britain arrogated to
herself the right to bottle up Napoleon's Empire, the purpose being to
starve him out.
By way of retaliation, he, in the Berlin Decree, declared Great Britain
to be in a state of blockade. It is curious to notice in the books how
much abuse Napoleon gets for his blockade, and how little England gets
for hers. Usually in trying to get at the merits of a fight for the
purpose of fixing the blame, the question is, "Who struck the first
blow?" This simple rule, based on plain common sense, seems to be lost
sight of here entirely.
When England struck at Napoleon with a sweeping blockade which
affected eight hundred miles of his coast, had he no right to strike
back? The Berlin Decree was no more than blow for blow.
There can be no doubt that in this commercial war Napoleon got the
worst of it. England suffered, but it was for the want of markets.
Continental Europe suffered, but it was for the want of goods.
Napoleon's Continental system, about which so much has been said, was,
after all, nothing more than a prohibitory tariff. In course of time
it would have produced the same effect as a prohibitory tariff. The
Continent would have begun to manufacture those goods for whose supply
it had heretofore depended upon England. In other words, the blockade,
shutting off the supply of certain cloths, leather goods, hardware,
etc., would have forced their production on the Continent. A moderate
tariff stimulates home production in the ratio that it keeps out
foreign competition. A prohibitive tariff, shutting off foreign wares
entirely, _compels_ the home production of the prohibited articles.
Napoleon's Continental system, prohibiting all English goods, would
inevitably have built up manufactories of these goods on the Continent.
During the years when these enterprises would have been getting under
way, the people of the Continent would have suffered immense loss and
inconvenience; but in the long run the Continent would have become
the producer of its own goods, and Great Britain would have been
commercially ruined. This Napoleon saw; this the English Cabinet saw:
hence the increasing bitterness with which this death struggle between
the two went on.
The great advantage of England was that she had the goods ready for
market, and the Continent wanted them. The enormous disadvantage of
Napoleon was that he neither had the goods nor the men ready to take
hold and manufacture them. The all-important _now_ was on the side of
England. The ink was hardly dry on the Berlin Decree before Napoleon
himself had to violate it. He needed enormous supplies for his army in
the winter campaign he was about to begin. Continental manufactories
did not produce what he wanted, England did, and Napoleon's troops were
supplied with English goods. What the master did, his minions could
imitate. All along the coast French officials violated the law, sold
licenses, winked at smuggling at so much per wink, and feathered their
nests in the most approved and gorgeous style. The Continental system
did great damage to England, since it drove her trade into tortuous,
limited channels. It did great damage to the Continent, since it worked
inconvenience to so many who needed English goods, and so many who
had Continental produce to sell to England. But it never had a fair
test, did not have time to do its work, and therefore has been hastily
called Napoleon's crowning mistake. Failing to get a fair trial for his
system, it collapsed, and must therefore be called a blunder; but it
must be remembered that its author believed he could get a fair trial
for it; that he worked with tremendous tenacity of purpose for many
years to bring Continental Europe to accept and enforce it. Could he
have done so, the candid reader must admit that he would have smitten
England's manufactures, her commercial life, as with a thunderbolt. It
should also be remembered that to Napoleon's policy, so much resisted
then, France owes many of those manufactures which constitute her
wealth at the present day.
CHAPTER XXIX
After allowing his army a brief rest, Napoleon set out against the
Russians. His troops entered Poland, and on November 28, 1806, Murat
took possession of Warsaw. The Poles received the French as deliverers.
They believed that the dismemberment of their country by Austria,
Prussia, and Russia was to be at last avenged, and Poland once more to
take its place among the nations. By thousands the bravest flocked to
the French standards, as enthusiastic for Napoleon as were the French
themselves.
It may be that in his treatment of Poland the Emperor made one of his
huge mistakes. It may be that he here lost his one great opportunity
of permanently curbing the three Continental powers, whose combined
strength finally wore him out. Had Poland's resurrection as a nation
been promptly proclaimed, had her crown been given to some born
soldier, like Murat, Lannes, Soult, or Poniatowski, he would have drawn
to his physical support every man of Polish blood, and to his moral
support the active approval of every liberal in the world.
Across the path of Russia he would have thrown the living rampart of
a gallant nation, fired by love of country and a passion for revenge.
With Turkey on one frontier, and united Poland on another, and the
mighty power of Napoleon ready to aid both, Russia's position would,
apparently, have been desperate. In like manner, a united Poland, on
the flanks of Austria and Prussia, would, apparently, have been the
very best guarantee that those two nations would not invade France.
In brief, had Napoleon decreed the liberty of Poland, he would have
secured an ally whose strength and position were of vast importance
to him, and whose need of his support would have kept her loyal. On
the other hand, he would have incurred the lasting hatred of the three
robber powers, and they would have had a common cause of union against
him. This is what he realized, and this is what held him back; but in
the end his temporizing, inconsistent, I-will-and-I-won't policy did
exactly that--brought upon him the lasting hatred of the three robber
powers, and lost him the united support of Poland. For in order that
his ranks might be recruited with Polish volunteers, he constantly
dangled before the eyes of the unfortunate nation the prospect of
independence. "Show yourselves worthy and then--." In other words, rush
to my eagles, fight my battles, die in my service, lavish your blood
and your treasures upon me, and I will then consider whether Poland
shall once more become a nation! It is a sorry picture--this of the
greatest man of history sporting with Polish hopes, rights, lives,
destiny.
Gallant men of this heroic nation gave him their lives--for Poland.
At least one beautiful Polish woman gave him her honor--for Poland.
He won part of the country because of his vague promises. He failed
to win united Poland because his promises _were_ vague. But the mere
fact that Poland looked to Napoleon as its liberator, the fact that
Poles trooped by thousands to fight for him, the fact that he erected
Prussian Poland into the Grand Duchy of Warsaw, bore just the bitter
fruit which Napoleon was so anxious the tree should not bear--the union
of the three powers which had despoiled Poland, and whose suspicion and
hatred had been aroused past all remedy by his dalliance with the Poles.
But these final results were all in the future as yet. For the time,
Napoleon's plan worked well enough. He got all the help he needed from
Poland without burning any bridges between him and the three powers.
His attitude seemed to say to Russia, Austria, and Prussia, "See what I
can do with these Poles if you provoke me too far!" Polish independence
was artfully utilized in two ways; to the Poles it was an aspiration
rousing them to rush to the French eagles; to the three powers it was a
threat, warning them to come to terms with Napoleon.
In the game of national chess, Poland thus became a mere pawn on the
board. From any moral point of view such a policy is infamous. And the
indignation of the historian is deepened when he is forced to add that
Napoleon's conduct was but an imitation of the statecraft of former
times, just as similar infamies of the present day are imitations
of time-honored precedents of kings and cabinets. Cavour one day
exclaimed, "What rascals we should be if we did for ourselves what
we are doing for our country!" He was referring to some especially
dirty work (dirt and blood being copiously mixed), which he had
been doing in copartnership with Napoleon III. in bringing about
Italian independence. The confession is worth remembering. Christian
civilization has certainly reached a curious pass when its leading
statesmen admit that in statecraft they are continually doing things
which would disgrace them as private citizens.
In the _Memoirs_ of the Princess Potocka there is a vivid picture of
the Polish situation in the winter of 1807, the writer being in Warsaw
at the time.
"The 21st of November, in the morning, the arrival of a French
regiment was announced. How shall I describe the enthusiasm with
which it was received? To understand such emotions properly one must
have lost everything and believe in the possibility of hoping for
everything--like ourselves. This handful of warriors, when they set
feet on our soil, seemed to us a guarantee of the independence we were
expecting at the hands of the great man whom nothing could resist.
"The popular intoxication was at its height: the whole town was lit
up as if by magic. That day, forsooth, the town authorities had no
need to allot quarters to the new arrivals. People fought for them,
carried them off, vied with each other in treating them best. Those
of the citizens who knew no French, not being able to make themselves
understood, borrowed the dumb language which belongs to all countries,
and by signs of delight, handshakings, and bursts of glee made their
guests comprehend that they freely offered all their houses contained,
_cellars included_.
"Tables were even laid in the streets and squares. Toasts were drunk
to Napoleon, to his Grand Army, to the Independence of Poland. There
was hugging and kissing, and a little too much drinking." Next day came
dashing Murat and his brilliant staff, with braided uniforms, gold and
silver lace, nodding plumes of red, white, and blue, and a good deal
of rattle and bang, fuss and bustle, generally. A noisy cavalier was
Murat, ostentatious, boastful, full of the reminiscences of his own
meteoric career.
Lodged at the Hotel Raczynski, where there was a vile chimney which
smoked, the Grand Duke of Berg left it, and quartered himself "in our
house,"--the palace Potocki,--where he bored the inmates with his loud
manners, his theatrical airs, and his too frequent reference to his
most recent feat of arms,--the storming and taking of Lubeck at the
head of his cavalry. Murat gave the Warsaw people to understand that
the Emperor would soon arrive, and would enter the city with a certain
degree of pomp. The authorities bestirred themselves; reared triumphal
arches, composed inscriptions, ordered fireworks, plaited wreaths, and
gave the usual warnings to poets and orators. The whole town was thrown
into the private agony which is the prelude to a public and joyful
reception.
And after all the toil and suffering of preparing for the Emperor's
triumphal entrance, what should he do but come riding into Warsaw on
a shabby little post-horse, between midnight and day, with no one in
attendance save Roustan, the Mameluke! The imperial carriage had mired
on the road, and Napoleon had left it sticking in the mud. When he
reached Warsaw, all were asleep, and "the Emperor went to the sentry
box himself to wake up the sentinel."
That same evening the authorities of the city were received by the
Liberator, who talked to them graciously and volubly upon all topics
excepting that of liberation. Upon this all-important subject he
uttered nothing more than what are called "glittering generalities."
Poland, it appeared, had not yet done enough. Poland must rouse
herself. "There must be devotion, sacrifices, blood." Otherwise Poland
would never come to anything. Running on in his nervous, rapid way,
Napoleon alluded to the great exertions he would have to make to bring
the campaign to a prosperous end. But he was sure that France would do
all he demanded of her. Putting his hands in his pockets, he exclaimed:
"I have the French _there_. By appealing to their imagination I can do
what I like with them!"
The Polish magnates listened to this statement with considerable
surprise, which pictured itself upon their faces. Observing this,
Napoleon added, "Yes, yes, it is just as I tell you," and took snuff.
Keenly disappointed as many of the Polish nobles were at Napoleon's
doubtful attitude, the country generally was enthusiastic in its faith
that he would, at the proper time, do the proper thing. Every want of
the French was supplied. Where voluntary offerings fell short, forced
contributions made good the difference.
Warsaw had never been more brilliant. The heart of the doomed nation
beat again. There were smiles, open hands, glad festivities. There were
brilliant balls at Murat's; brilliant balls at Talleyrand's; brilliant
balls at the palace of Prince Borghese; brilliant receptions held by
the Emperor. It must have been a spectacle worth seeing,--a ballroom in
reawakened Warsaw, where the loveliest ladies of Poland and the bravest
warriors of France danced the happy hours away. It must have been a
sight worth seeing,--Talleyrand entering a grand reception hall filled
with the notables of Poland and gravely announcing, "The Emperor!"
Well worth seeing was the stout, stunted figure, crowned by the
pale, set, marble-like face and large head, which came into view at
Talleyrand's announcement, and which stood within the doorway a moment
to see and to be seen.
Did lovely Polish women crowd about the mighty Emperor, listening for
the least word in favor of Poland's independence? Did fair patriots
appeal by look and word to him, yearning for the magic names, Liberty,
Freedom? Vain the ardent, beseeching look; vain the tender, seductive
voice. It would not do at all. He had suspected that--had steeled
himself against it; and eager patriotism, voiced by women never so
bewitching, could not break through that watchful guard. But as he
leaves the room, he pauses again, and says to Talleyrand in a tone loud
enough to be heard by all, "What pretty women!" Then the imperial hand
salutes the company, and the Liberator is gone!
It must have been a sight worth seeing,--that ball at Talleyrand's
where Napoleon danced, and cultivated Madame Walewski, and where the
imposing Talleyrand, with folded napkin under his arm, and gilt tray in
his hand, humbly served his imperial master with a glass of lemonade.
Army affairs called Napoleon to the front; but after the bloody
struggle at Pultusk, the weather stopped military movements. Continual
rains had ruined the roads. Cannon stuck in the mire, soldiers perished
in the bogs. Even Polanders had never seen anything equal to it.
Napoleon returned to Warsaw quite serene, remarking, "Well, your mud
has saved the Russians; let us wait for the frost."
Busy with French affairs, Polish and Russian affairs, busy also and
above all at this time with army affairs, the Emperor relaxed himself
socially to a greater extent than usual, and made himself exceedingly
agreeable.
He entered into all the amusements, gossiped familiarly with all comers
to his receptions, played whist, danced square dances, attended the
concerts of his Italian orchestra, and led the applause with zest and
good taste.
"How do you think I dance?" he smilingly inquired of the young Princess
Potocka. "I suspect you have been laughing at me."
"In truth, sire," answered the adroit lady, "for a great man your
dancing is perfect."
Sitting down to whist, Napoleon turned to Princess Potocka at the
moment the cards were dealt and asked:--
"What shall the stake be?"
"Oh, sire, some town, some province, some kingdom."
He laughed, looking at her slyly.
"And supposing you should lose?"
"Your Majesty is in funds and will perhaps deign to pay for me."
The answer pleased. He loved bold talk, prompt replies, definite
answers. Halting, uncertain, indefinite people he could never endure.
Answer quick and answer positively, and your reply, though untrue,
might please him better than if you hesitatingly told him the truth.
The same lively writer gives another lifelike picture of Napoleon in
one of his fits of ill temper.
One day at Warsaw he received information that General Victor, bearing
important despatches, had been captured by the Prussians. This piece of
news enraged the Emperor. It chanced that upon the same day a Dutch
delegation arrived to congratulate him upon the victory of Jena. They
were admitted to audience just before the Emperor's regular reception.
"It was near ten o'clock, and we (those in the reception room) had been
awaiting a long time ... when, the door being noisily thrown open, we
saw the fat Dutchmen, in their scarlet robes, roll rather than walk in.
The Emperor was prodding them, exclaiming in rather loud tones, 'Go on!
go on!' The poor envoys lost their heads, and tumbled all over each
other."
Princess Potocka says that she felt like laughing; but when she looked
at the Emperor's face, she did not dare.
"The music soothed him quickly; toward the end of the concert his
gracious smile returned, and he addressed pleasant words to the ladies
he liked best, before sitting down to his whist table.
"Excepting foreign ministers, and some of the high functionaries at
play, all stood while Napoleon sat. This did not displease Prince
Murat, who lost no opportunity to pose and to strike attitudes which
he judged appropriate to show off the beauty of his figure. But little
Prince Borghese was enraged and still had not the courage to sit down."
But the Emperor's amusements did not confine themselves to such things
as whist and quadrilles alone. A certain Madame Walewski, "exquisitely
pretty," "her laugh fresh, her eyes soft, her face seductive," caught
the attention of the imperial visitor. "Married at sixteen to an
octogenarian who never appeared in public, Madame Walewski's position
in society was that of a young widow." She was "lovely and dull,"
tempting and not unyielding. Talleyrand's diplomacy is said to have
done some very humble work as go-between, and the Madame was soon
known to be the Emperor's favorite.
Josephine, hearing vague rumors of high-doings at the Polish capital,
generously offered to brave the rigors of travel and season to join her
absent spouse. In the gentlest manner in the world he insisted that she
stay where she was.
The gay time at Warsaw ended abruptly. Ney having made a dash at
the Russians, without orders, Bennigsen roused himself to general
action, and Napoleon went forth to one of the bloodiest battles in
history--Eylau, February 8, 1807. Fought in a blinding snowstorm, the
losses on both sides were frightful. So doubtfully hung the result that
the Emperor himself escaped capture because he was concealed from view
in the old churchyard. Augereau's corps, caught in the snow-drift,
blinded by wind-driven sleet, and exposed point blank to deadly Russian
fire, was annihilated. Only a desperate cavalry charge, led in person
by Murat, checked the Russian advance. When darkness fell, the French
were about to retreat when Davoust, laying ear to ground, heard the
retiring rumble of Russian guns. So the French held their position and
claimed the victory. The Russians, in retreat, also claimed it.
On each side rose hymns and prayers of thanks and praise to God:
Russians grateful that they had won; French rejoicing that they had
prevailed. Bennigsen continued to retire; Napoleon went back into
winter-quarters; and the only distinct and undisputed result of the
battle was that some twenty-five thousand men lay dead under the snow.
Napoleon did not return to Warsaw, but made his headquarters at
Osterode, where he shared all the discomforts of his soldiers while
doing more work than any hundred men in the army. In spite of the
dreadful weather and boggy roads, he was constantly on horseback, going
at full speed from one outpost to another. Frequently he rode ninety
miles during the day. With his own eyes he inspected the military
situation down to the smallest details, untiring in his efforts to have
his men well placed, well clothed, well fed. The sick and the wounded
were indeed "his children." He spared no efforts in their behalf, and
this was one of the secrets of the cheerfulness with which his soldiers
made such sacrifices for him. Sometimes in the march when the weary
legions were weltering through the mud, drenched with rain or pelted
by sleet, or blinded by snow, hungry and homesick, murmurs would be
heard in the ranks, complaints would even be thrown at the Emperor
as he passed. But when the enemy was in sight, murmurs ceased. "Live
the Emperor!" was all the cry. They shouted it wherever they caught a
glimpse of him on the field; they shouted it as they rushed to battle;
and after the fight was over those who came forth unharmed, and those
who were mangled, and those who were about to die--all shouted, "Live
the Emperor!" Nothing like the devotion of the French soldier to
Napoleon had ever been known before, and not till another Napoleon
comes will be seen again.
The care of his army by no means filled all of the Emperor's time: he
ruled France from Poland, just as though he were at St. Cloud. Couriers
brought and carried ministerial portfolios, brought and carried
official reports and orders. Every detail of government passed under
the eye of the master, all initiative rested with him.
Madame Walewski was brought secretly to headquarters, an indulgence
Napoleon had never allowed himself before. While at Finckenstein, he
received envoys from Persia and Turkey, and gravely discussed plans for
an invasion of India.
In June the Russians again took the offensive. Their
commander-in-chief, Bennigsen, one of the murderers of the Czar Paul,
had shown great courage and ability. At Pultusk he had beaten Lannes
and Davoust; at Eylau he had fought the Emperor to a standstill, and
had carried away from that field twelve of the French eagles.
Bennigsen renewed the war by an attack on Ney, whom he hoped to cut
off. A hasty retreat of the French saved them. Then Napoleon came up,
and the Russians retired. At Heilsberg they stood and fought, both
sides losing heavily. At length the superiority of the French leader
made itself felt. He lured Bennigsen into a false position, closed
on him, and well-nigh crushed him, at the battle of Friedland, June
14, 1807. This victory ended the campaign. The Russians asked for an
armistice, which was promptly granted. The two emperors, Napoleon and
Alexander, met on a raft, moored in the Niemen, near Tilsit, June 25,
1807, embraced each other cordially, and, amid the rapturous shouts of
the two armies drawn up on opposite sides of the river, commenced those
friendly, informal conferences which led to peace.
The town of Tilsit, having been made neutral ground, became the
headquarters of the two emperors, who established their courts there,
and lived together like devoted personal friends. The poor fugitive,
Frederick William of Prussia, was invited to come, and he came. Later
came also his queen.
On the 7th of July, 1807, the Treaty of Tilsit was signed.
Prussia lost her Polish provinces, which were erected into the grand
duchy of Warsaw, and given to the Elector of Saxony. A slice of this
Polish Prussia, however, was bestowed on Alexander. Dantzic, which
the French had taken, was declared a free city, to be garrisoned with
French troops till maritime peace should be ratified. The Prussian
dominions in lower Saxony and on the Rhine, with Hanover, Hesse-Cassel,
and other small states were formed into the kingdom of Westphalia for
the profligate Jerome Bonaparte.
Ancient Prussia, as well as Silesia, was restored to Frederick William.
Much ado has been made over Napoleon's alleged harshness to Queen
Louisa at Tilsit; but a careful reading of the authorities proves that
his only harshness consisted in declining to give to her that for which
she asked. She went there to influence Napoleon by a beautiful woman's
persuasions; and she failed. In the nature of things, it could not
have been otherwise. Having provoked the war, and having lost in the
trial of arms, Prussia had to pay the penalty. The tears or cajoleries
of Queen Louisa could not of course obliterate the hard political
necessities of the case. Suppose the Empress Eugénie, in 1871, had gone
in tears to Bismarck or to the Emperor William, could she have saved
for France the provinces of Alsace and Lorraine? Could she have reduced
the war penalty from $1,000,000,000 to $1,000,000? Just such a task
Queen Louisa undertook in 1807.
Beyond his refusal to be influenced, Napoleon was not guilty of any
discourtesy to the Queen. On the contrary, he honored her with the most
studious politeness and deference.
By the Treaty of Tilsit, Russia bound herself to mediate between France
and Great Britain. On his part, Napoleon agreed to mediate between
Russia and Turkey.
In secret articles, Russia bound herself to adopt Napoleon's
Continental system in the event that Great Britain refused to make
peace.
Furthermore, in that case, there was to be a northern confederation
against England for the purpose of shutting her out of the Continent
and of breaking her tyranny over the seas.
Russia, in return for this promise, was to be allowed to conquer
Finland, a province of vast importance to her.
It is also stated by some authorities that Alexander agreed that
Napoleon should do as he liked with Spain and Portugal; while Napoleon
consented that Alexander should be allowed to strip Turkey of Moldavia
and Wallachia, provided Turkey refused his mediation.
CHAPTER XXX
At this period (1807) Napoleon was a strikingly handsome man. The "wan
and livid complexion, bowed shoulders, and weak, sickly appearance"
of the Vendémiaire period were things of long ago. The skin disease
of the Italian campaign had been cured. Not yet fat and paunchy as he
became toward the end, his form had rounded to a comely fulness, which
did not impair his activity. The face was classic in profile, and in
complexion a clear, healthy white. His chin was prominent, the jaw
powerful, the head massive, being twenty-two inches round, according
to Constant. The chestnut- hair was now thin, inclining to
baldness on the crown. Worn long in his youth, he cut it short in the
Egyptian campaign, and ever afterward continued to wear it so. His
ears, hands, feet, were small and finely shaped. The nose was long,
straight, well proportioned. His teeth were white and sound; the lips
beautifully moulded; the expression about the mouth, when he smiled,
being peculiarly sweet and winning. His eyes were gray-blue, and
formed the striking feature of his face. All accounts agree that his
glance was uncomfortably steady and penetrating; or, at other times,
intolerably fierce and intimidating; or, again, irresistibly soft,
tender, magnetic. One is struck with the fact that so many who knew
him, and loved him or hated him, feared him or defied him, should
emphasize the impression made upon them by his eyes. Before that steady
gaze, which seized and held attention, Lavalette said that he felt
himself turning pale; Decrés lost all desire to be familiar; Vandamme
became a coward; Augereau and Masséna admitted they were afraid;
Madame de Staël grew embarrassed; and Barras faltered into silence at
his own table. Not many years ago there lived in Michigan a battered
veteran of the Italian wars, one who had been with Napoleon the day
he reconnoitred Fort Bard, which had checked the army; and this old
soldier's recollection of Napoleon had dwindled down to the wonderful
eyes which had fixed him as though they would pierce the very innermost
fibre. During the year 1900 there died in London an aged man, who as a
boy had seen Napoleon at St. Helena; and his recollection of the fallen
Emperor hung upon the same feature,--the eyes.
Generally, the expression of Napoleon's face was that of a
student,--mild, pensive, meditative, intellectual. In moments of
good humor, his smile, glance, voice, were caressing, genial, even
fascinating. In anger, his look became terrible; a rotary movement
took place between the eyes, and the nostrils distended. All agree
that in conversation there was such a play of feature, such quick
changes of expression, such mirroring of the mind upon the face, that
no description or portrait could convey an idea of it. Only those who
had talked with him could realize it. But it is also agreed that when
he wished to banish all expression, he could do that also, and his face
then became a mask.
His voice was sonorous and strong. In anger it became harsh and cruelly
cutting. In his best mood it was as soft and wooing as a woman's.
His general appearance, then, at this time, was that of a well-built
man, below the medium height, but powerfully moulded, the bust, neck,
and head being massive, and the legs somewhat short for the trunk.
Unfriendly critics called him stunted, his stature being about five
feet, three inches.
He was inclined to be round-shouldered, and, when walking meditatively,
he slightly stooped. In talking he gesticulated freely, sometimes
violently; when in repose the hands were folded behind him, or across
the breast, or one would rest within the waistcoat and the other behind
him.
It is doubtful whether any true portrait of Napoleon exists. He has
been idealized and caricatured until the real Napoleon may have been
lost. If the death mask claimed to have been taken by Antommarchi
is genuine, one must surrender the belief that Napoleon's head was
massive, his brow imperial, his profile perfect; for this mask exhibits
a forehead which recedes, and which narrows above the temples. It shows
the high cheek-bones of the American Indian, and the skull itself is
commonplace. But this is not the Napoleon pictured in the portraits
and _Memoirs_ of his contemporaries. According to friend and foe, his
head was massive, in fact too large to be in symmetry with his body.
Madame Junot speaks of that "brow fit to bear the crowns of the world."
Bourrienne, Méneval, and numbers of others speak of the magnificent
forehead and classic face. And yet there are two or three fugitive
portraits of Napoleon which are so different from the orthodox copies,
and so much like the Antommarchi's death-mask, that one knows not what
to believe.
Napoleon was very temperate in eating and drinking. He preferred the
simplest dishes, drank but little wine, and that weakened with water.
Coffee he drank, but not to excess. He ate fast, and used his fingers
oftener than his fork. He was very sensitive to cold, and could not
bear the least light in his room at night. He slept a good deal, from
six to eight hours per day; and usually took a nap during the afternoon
or evening. His standing order to his private secretary was a model of
wisdom, "Never wake me to hear good news, that will wait; but in case
of bad news wake me at once, for there is no time to be lost." Another
rule of his was to sleep over a matter of doubt. "Night is a good
counsellor."
While his nerves were very irritable, his pulse was slow and regular.
He declared that he had never felt his heart beat. Medicine he detested
and would not take. When ill, he left off food, drank barley water,
and took violent exercise. He could not bear the least tightness in
his clothing. His garments were of the softest, finest material, and
cut loose. His hats were padded, his boots lined with silk, and both
hats and boots were "broken" for him before he wore them. His favorite
trousers were white cassimere, and a habit he had of wiping his pen on
his breeches made a new pair necessary every morning. His taking of
snuff consisted merely in smelling it. He used tobacco in no other form.
Extremely careful in business matters, he was disorderly in some
personal details. In undressing he flung his clothes all about the
room, and sometimes broke his watch in this way. Newspapers and books
which he had been reading were scattered around in confusion. In
shaving, he would never allow both sides of his face to be lathered
at the same time: one cheek was finished before the other was touched.
He had a habit of poking the fire with his foot, and burnt out many a
pair of boots in so doing. Excessively fond of the hot water bath, he
opened letters, read newspapers, and received callers while splashing
around in the tub. On leaving the bath, his valet rubbed him down,
using the flesh brush and coarse cloths, and then dressed him. The most
self-helpful of men in matters of importance, he was one of the least
so in this. He depended upon servants for almost everything connected
with the care of his person. "Rub me hard! Scrub me as though I were
an ass!" he would call to his valet, while he stood almost naked, and
with a red bandanna handkerchief knotted about his head. He loved
cologne-water and drenched himself with quantities of it. One of the
privations he keenly felt at St. Helena was the lack of cologne. Other
perfumes he detested, and Constant relates a curious incident of
Napoleon calling to him one night to take out of his room a certain
young lady who had been brought there, and who was "killing me with her
perfume."
With his elevation to empire, Napoleon became more stately, reserved,
dignified, and imposing; but perfect ease and repose of manner he never
acquired. The indolent, calm, and studied air of languor and fatigue
which, according to a well-known standard, constitutes good-breeding,
he did not have. Perhaps he did not realize its tremendous value.
Nervous, intense, electrical, pulsing with vital power, tossed by
colossal ideas, ambitions, purposes, it was never possible for
him to become a self-complacent formality, posing with studiously
indolent grace, and uttering with laborious ease the dialect of polite
platitude.
But the man never lived who knew better how to talk, how to write,
how to say what he meant. He could address mobs, committees, state
councils, senates, armies, peoples, and kings. Who that ever lived
excelled him in speaking to soldiers? Verily the lines are yet hot
in his proclamations, and he who reads them even now will feel the
magnetic thrill. How they must have inspired the soldiers _then_!
His speeches to the councils and the Senate were models in their way;
his state papers have not been excelled; his diplomatic correspondence
measures up the loftiest standards. In truth, his language varied
with the subject and the occasion. He could be as elegantly gracious
as any Bourbon, if the occasion required it. If it became needful
to call a spade a spade, he could do it, and with a vim which left
the ears tingling. In all of his talk, however, there was character,
individuality, and greatness. Wrong he might often be, weak never.
Whatever view he expressed, in youth or age, was stated clearly, and
with strength. Even when sifted through the recollections of others,
his sayings stand out as incomparably finer than those of any talker of
that age. Compare the few little jests and epigrams of Talleyrand, for
instance, with the numberless comments of Napoleon on men and things,
on matters social, political, industrial, financial, military, and
religious. It is like a comparison between a few lamps in a hallway
and the myriad stars of the firmament. On every topic he discussed
he said the best things that can be said on that side; and there is
no subject connected with human affairs in a state that he has not
touched. Upon every subject he had a word which shot to the core of the
matter. His talent for throwing into one dazzling sentence the pith of
a long discussion was unexcelled. Some of the best sayings attributed
to Talleyrand were really the sayings of Napoleon. It often happened
that these terse expressions were coarse, the language of men on the
street. At such sayings the "Lady Clara" tribe of men arched their
eyebrows in delicate protest, and said to one another, "This Bonaparte
is no gentleman; he was not so well brought up as we were,--we, the
Talleyrands, Metternichs, and Whitworths!"
In one humor, Napoleon was brusque, coarse, overbearing, and pitiless;
in another he was caressing, elegantly dignified, imperially generous
and gracious. Between these extremes ran the current of his life:
hence the varied impressions he made upon others. Charles Fox and Lord
Holland knew him personally, and they risked political and social
influence in England by defending him from the abuse which had become
the fashion there. Almost without exception the men who came into
personal relations with him loved him. The rare exceptions are such
people as Bourrienne and Rémusat, whom Napoleon had to rebuke for ways
that were crooked. Even to his valets he was a hero.
As Charles Fox said, "The First Consul at Malmaison, at St. Cloud, and
at the Tuileries are three different men, forming together the _beau
ideal_ of human greatness."
To these three Napoleons should be added at least one other,--Napoleon
at the head of his army.
In public, Napoleon trained himself to that majestic dignity, grace,
and thoughtfulness which his imposing position required. The Pope did
not act his part better at the coronation, nor Alexander at Tilsit. He
rarely, if ever, overacted or underacted a public part, but in private
there was a difference. In familiar converse he would pace up and down
the room, or twitch in his chair, or throw his feet up on the desk, and
open his penknife and whittle the chair arm, or sprawl on the floor
studying his big maps, or sit down in the lap of his secretary.
With the rough good humor of a soldier, he would call his intimates
"simpleton," "ninny," or even "fool"; he would pinch their ears, and
lightly flick them on the cheek with his open hand. Whereupon the
oversensitive biographers have unanimously shuddered, and exclaimed,
"See what a vulgar creature this Napoleon was!"
In his personal habits he was neat to the point of being fastidious.
If ever he wasted any time at all, it was the hours he spent in the
bath. Simple in his dress and in his tastes, no gentleman was ever more
scrupulously clean. Generally he wore the uniform of a colonel of his
guard; and his plain gray overcoat, and plain little hat with its cheap
tricolor cockade, formed a vivid contrast to the gaudy dress of foreign
diplomats, or of his own officers.
He pretended that anger with him never reached his head, that he had
his passions under perfect control. This was all nonsense. His temper
frequently burst all bounds, and for the moment he was as insane as
other men in a passion. Madame Junot states that when he fell into one
of these fits of anger, he was frightful.
Upon at least one occasion of this kind he kicked the dinner table
over, and smashed the crockery; at another he put his foot, in a
violent and tumultuous manner, against the belly of Senator Volney.
It was rumored around the palace, on his return from Spain in 1809,
that he gave Talleyrand a "punch on the nose"; and once when the
jealous and watchful Josephine came upon him as he was enjoying himself
with another woman, he sprang at her in such a fury that she fled the
room in terror.
At Moscow while the Emperor was in his blackest mood, everything going
wrong, and a general crash impending, Roustan, kneeling before him to
put on his boots, carelessly got the left boot on the right foot. The
next instant he was sprawling on his back on the floor. Napoleon had
kicked him over.
It is said that he threatened Berthier once with the tongs, and Admiral
Bruix with his riding-whip. On the road to Moscow he rode furiously
into the midst of some pillaging soldiers, striking them right and left
with his whip, and knocking them down with his horse.
But these occasions were rare. His control of himself was almost
incredible, and he learned to endure the most startling and calamitous
events without a word or a change of expression.
If you would see far, far into the heart of Napoleon, study his
relations with Junot. Not much brain had this Junot, not much
steadiness of character; but he was as brave as a mad bull, and he had
shared his purse with Napoleon in the old days of poverty and gloom.
More than this, he had believed in Napoleon at a time when Napoleon
himself had well-nigh lost heart. So it came to pass that Junot was
the beloved of the chief, and remained so in spite of grievous faults
and sins. Junot gambled, and Napoleon abhorred gaming; Junot drank
to excess, and Napoleon detested drunkards; Junot was a rowdy, and
Napoleon shrank from rowdyism; Napoleon loved order, and Junot was
most disorderly; Napoleon loved a strict relation between income and
outgo, and Junot was a marvel of extravagant prodigality. Napoleon
loved success, and Junot brought failure upon him where it hurt
dreadfully--in Portugal, in Russia. Yet through it all Napoleon never
flagged in his indulgence to Junot. He made the hot-headed grenadier
Governor of Paris, Duke of Abrantes, lapping him in honors and wealth.
Sometimes Junot would be angry at his chief, and Napoleon would coax
him back to good humor, as a father would a child. Sometimes Junot
would run to Napoleon with his griefs; and the busiest man in the world
would drop everything, take his suffering friend by the arm, walk him
up and down some quiet room or corridor, soothing him with soft words,
with caresses. One day when Junot had taken to his bed, because of a
fancied slight at the palace, Napoleon, hearing of it, slipped away
from the Tuileries, went to the bedside of his old comrade, comforted
him, reassured him, and stood by him until he was himself again.
When Madame Junot is in the throes of child-birth, it is to Napoleon
that the distracted husband flies. At the Tuileries he is soothed by
Napoleon himself, who sends off messengers to inquire after the wife;
and when the ordeal is safely over, it is Napoleon who congratulates
the now radiant Junot, finds his hat for him, and sends him off home to
the mother and babe.
At last there did come something like a rupture between these
two--and why? Junot had brought scandal on Napoleon's sister while
the brother was off with his army in Germany. "To bring shame upon
my sister--_you_, Junot!" and the great Emperor fell into a chair,
overcome with grief.
In his relations with Duroc, Berthier, Lannes, La Salle, Rapp, Méneval,
Eugène Beauharnais, we find the same traits. The indulgence with which
he treated those he liked, the pains he took to keep them in good
humor, his care not to wound their feelings, and his caressing way of
coaxing them out of their occasional sulks, shows a phase of Napoleon's
own character which is usually overlooked.
He had many boyish ways which never left him. He would hum a song and
whistle a tune to the last. During moments of abstraction he fell to
whittling his desk or chair, sat upon a table and swung his leg back
and forth, or softly whistled or hummed some favorite air. During the
great disaster at Leipsic, when all had been done and all had failed,
Napoleon, in a kind of daze, stood in the street and whistled "Malbrook
has gone to the wars."
He was fond of playing pranks. He tried to drive a four-in-hand at
Malmaison, struck a gate-post, and got thrown headlong to the ground,
narrowly escaping fatal injuries to himself and Josephine. He would
disguise himself, and go about Paris to hear the people talk, coming
back delighted if he had provoked angry rebuke by some criticism of his
on Napoleon. He would throw off his coat at Malmaison, and romp and
play like a schoolboy. After dinner, if the weather was fine, he would
call out, "Let's play barriers!" and off would go his coat, and in a
moment he would be racing about the grounds.
One afternoon while amusing himself in this way, two rough-looking
men were seen near the gate, loitering and gazing at the romping
group. The ladies saw fit to become frightened, and to make the usual
hysterical outcry. Gallant young officers sprung forward to drive off
the intruders, as gallant young officers should. But it turned out
that one of the men was a maimed veteran of the wars, come with his
brother, in the hope of catching a glimpse of the beloved form of his
general--Napoleon. Having seen, having heard, the First Consul put his
arm around Josephine, drew her toward the two men, gave them gracious
welcome, introduced them to his wife, and sent them under Eugène's
escort to the house to drink his health in a glass of wine. So promptly
was the thing done, so naturally, so warmly, so tactfully, that the
one-armed soldier was melted to tears.
In his rude horse-play, Napoleon taught his gazelle to chase the ladies
of the court, and when the animal caught and tore a dress, or caught
and pinched a leg, his delight was precisely that of the mischievous,
slightly malicious boy. In playing barriers he cheated, as he did at
all games, and violated all the rules. When he was unbent, when he was
at Malmaison, he could take a joke as well as any. One very rough piece
of horse-play he took a good deal more placidly than many a private
citizen would have done. Passing through a gallery at Malmaison, he
stopped to examine some engravings which were lying upon a table. Young
Isabey happening to come into the gallery behind Napoleon, and seeing
the back of the stooping figure, took it to be Eugène Beauharnais.
Slipping up softly, Isabey gave a jump, and leaped upon Napoleon's
shoulders, astraddle of his neck. Napoleon recovered from the shock,
threw Isabey to the ground, asking, "What does this mean?"
"I thought it was Eugène," cried Isabey.
"Well, suppose it was Eugène--must you needs break his shoulder bones?"
Without further rebuke Napoleon walked out of the gallery. Through the
folly of Isabey, the secret leaked out, and there was just enough of
the ludicrous about it to embarrass both the actors, and Isabey went to
play leap-frog elsewhere.
Napoleon was fond of children, knew how to talk to them, play with
them, and win their confidence. The man never lived who knew better
than he the route to the heart of a soldier, a peasant, or an ambitious
boy. With these he could ever use exactly the right word, look, smile,
and deed. He was familiar with his friends, joked them, put his arms
around them, and walked with them leaning upon them: he never joked
with men like Fouché, Talleyrand, Bernadotte, Moreau, and St. Cyr.
These men he used, but understood and disliked.
Fat women he could not endure, and a pregnant woman showing herself
when she should have been in seclusion, excited his disgust. One of the
pictures he most liked to gaze upon was that of a tall, slender woman,
robed in white, and walking beneath the shade of noble trees.
A fastidious, exacting busybody, he was forever on the lookout for
violations of good taste on the part of the ladies of his court. He
detested the low dresses which exposed the bosom to the vulgar gaze;
and if he saw some one dressed in peculiarly unbecoming style, he was
rude enough to give words to his irritation. "Dear me! are you never
going to change that gown?" This was very, very impolite, but the
costume was one which he abhorred, and the wearer had inflicted it upon
him "more than twenty times."
Possibly if there were a greater number of outspoken Napoleons, there
would be fewer absurdities in fashionable female attire.
To some of Napoleon's sharp sayings, the haughty dames and damsels
of the old aristocracy made some crushing replies--according to their
_Memoirs_. It is fairly safe to say that these crushing retorts were
made in the seclusion of the homes of the fair retorters. The man whose
stern look and bitter tongue awed into embarrassed silence such a
veteran in word-play as Madame de Staël, was not likely to be crushed
by such pert and shallow beings as Madame de Chevreuse and her kind.
For facts, events, his memory was prodigious; for names and dates, it
was not good. Sometimes he would ask the same man about court three or
four different times what his name was. In his later years his memory
became very fickle, and he was known to forget having given the most
important orders. He could not remember a charge he ordered Ségur to
make in Spain; nor could he recall that he had ordered the charge of
the heavy cavalry at Waterloo.
Noted at school for his skill in mathematics, and using that science
constantly in his military operations, it is said that he could rarely
add up a column of figures correctly.
He could not spell, nor could he write grammatically; and he took no
pains to learn. A busy man, according to his idea, had no time to waste
on such matters.
He loved music, especially Italian music; was fond of poetry of the
higher sort, and appreciated painting, sculpture, and architecture.
He loved the beauty and quietude of such country places as Malmaison,
never wearied of adding to their attractions, and was happy when free
from business, and taking a solitary stroll along garden walks amid
flowers and under the shade of trees.
In his work, Napoleon was all system. No clerk could keep papers in
better order. No head of a department could turn off business with such
regularity and despatch. He knew all about his army, down to the last
cannon; knew just what his forces numbered, where they were, and what
their condition. He was master of the state finances, of every branch
of the internal administration, of every detail of foreign affairs. He
kept up with everything, systematized everything, took the initiative
in everything. An extra plate of soup could not be served in the
palace without a written order from Duroc, the proper officer. An army
contractor could not render a false account without being exposed and
punished. An overcharge could not be made in the palace furnishings
without his finding it out. "He is a devil," said many a quaking
Beugnot.
One day, says Constant, the pontoon men were marching with about forty
wagons. The Emperor came along, and cried, "Halt!"
Pointing to one of the wagons, Napoleon asked of the officer in
charge:--
"What is in that?"
The officer answered, "Some bolts, nails, ropes, hatchets, saws--"
"How many of all that?"
The officer gave the number.
"Empty the wagon and let me see!"
The order was obeyed, bolts, nails, ropes, saws, everything taken out
and counted. But the Emperor was not satisfied. He got off his horse,
climbed into the wagon over the spoke to see that it had been emptied.
The troops shouted: "Bravo! That's right! That is the way to find out!"
He compared his mind to a chest of drawers, where each subject occupied
its separate space. In turn he opened each drawer. No one subject ever
got mixed with another. When all the drawers were shut, he fell asleep.
Of course this was not literally true, but during his best years it
came as near being literally true as is possible to the human brain.
After the day's work was done, he would enter into the amusements of
his domestic circle, would play and dance with the young people, would
read or listen to music, or would entertain the circle by telling some
romantic story which he composed as he talked. In the evening he loved
to have the room darkened while he threw the ladies into a gentle state
of terror with a ghost-story.
Napoleon's penetration in some directions was wonderfully keen; in
others remarkably dull. For instance, it was almost impossible to
deceive him in matters of account, the number of men in a mass, or
the plan of battle of a foe. He would converse with an engineer in
reference to a bridge he had been sent to build and which Napoleon
supposed he had built; after a few words he would turn away and say to
the prefect, "That man did not build the bridge--who did it?" The truth
would come out: an obscure genius had planned the work, and Napoleon
would say to this genius, obscure no more, "Come up higher."
He could scan a list of political prisoners, pounce upon the name of a
surgeon, decide at a flash that this man could not be a fanatic. "Bring
him to trial, order him to be shot, and he will confess." And it so
happened.
But it is marvellous that Napoleon, who revolutionized the strategy of
war, improved nothing, invented nothing, in the instruments of warfare.
A Prussian offered to him the original of the needle-gun, and he
totally failed to grasp the terrible effectiveness of the weapon. True,
he experimented with it, ordering that specimens should be made and
shown him. But when his armories turned out clumsy models, as at first
they were almost sure to do, he seemingly lost interest. The Prussian
carried his invention to Germany; and the Austrians and French of a
later day melted like snow before this new and fearful gun.
When Fulton came to France with his steam-boat discovery, offering
a means by which Napoleon might have destroyed with ease England's
all-powerful navy, his invention was not appreciated. True, Napoleon
gave him encouragement and money, and urged the wise men of the
Institute to look into the thing; but Napoleon himself did not "take
hold." When the sages of the Institute reported adversely to the
new invention, as sages almost always do, Napoleon let the subject
drop, apparently forgetting that it is usually the ignorant "crank"
and the untutored "tenderfoot" who stumbles upon great inventions
and the richest mines. So far-sighted in some directions, it seems
unaccountable that he did not realize immediately the vast importance
of the breech-loading gun, and the steam-propelled vessel. With the
same muzzle-loading muskets he fought the first battle and the last.
The same little cannon which could not batter down the old walls of
Acre, sent balls which rebounded from the farmyard enclosures at
Waterloo.
During all of his campaigns prior to 1812, Napoleon gave personal
attention to everything; no detail was neglected. He saw with his own
eyes, taking nothing for granted, nothing on trust. As far as possible
he followed up his orders, seeing to it that they were executed.
Thus on the night before Jena he risked his life and came near being
shot reconnoitring the Prussian position, and after he had selected
positions for his batteries, and marked out the path up which the guns
were to be drawn to the heights, he could not rest until he had gone in
person and seen how his orders were being executed. It was fortunate
that he did so. The foremost cannon carriage had got jammed between
the rocks of the passage and had blocked the way of all the others.
The whole battery was at a halt, and nothing being done to forward the
guns. Angry as he was, Napoleon at once took command, ordered up the
sappers, held a lantern while they were at work, and showed them how to
widen the road. Not until the first gun had passed through did he leave
the place. The failure to look after such things was one cause of the
disasters of his later years.
He spared himself no fatigue in war. Sensitive to cold, to evil smells,
to ugly scenes, to physical discomfort of all sorts, the Sybarite of
the palace became the Spartan on the campaign. He could stand as much
cold, or heat, or hunger, or thirst, camp hardships and camp nastiness
as any private. He could stay in the saddle day and night, could march
on foot by the hour in snow or mud, could stand the storms of rain,
sleet, and wind, made no complaint of filthy beds and disgusting
surroundings, and could eat a soldier's bread out of the knapsack with
all of a soldier's relish.
In later years he carried his habits of luxury to the army, and with
them came defeats. The general who in Italy could have taken all his
baggage in a cart was followed in 1812 by a train of seventy wagons. He
went to war then like Louis XIV., and the luck of Louis XIV. overtook
him.
On the field of battle his aspect was one of perfect composure. No turn
of the tide broke through his absolute self-control.
At Marengo, when the great plain was covered with the flying fragments
of his army, and fugitives were crying: "All is lost! Save himself
who can!" he was as calm as at a review. Berthier galloping up with
more bad news, Napoleon rebuked him with, "You do not tell me that
with sufficient coolness." When Desaix arrived, Napoleon took all the
time that was necessary to make proper dispositions for the attack,
exhibiting not the slightest nervousness under the galling Austrian
fire.
In the retreat from Russia he was stoically serene, save on the rarest
occasions. Only a few intimates knew how much, in private, he gave way
to his immense burden of care, of grief, of impotent rage. To the army
he appeared as cold, as hard, as unyielding as granite. When a general
brought him some unusually appalling news, Napoleon turned away as
though he did not wish to hear. The officer persisted; Napoleon asked,
"Why do you wish to disturb my equanimity?"
If his fatigues had been excessive in the preparation for battle, and
his dispositions had been made, and all was going as he had foreseen,
he could slumber restfully while the combat raged. Thus at Jena, Ségur
speaks of Napoleon asleep on the ground where his great map was
unrolled--asleep with the grenadiers standing in hollow square about
him.
Lord Brougham writes: "Lying under some cover in fire, he would remain
for an hour or two, receiving reports and issuing his orders, sometimes
with a plan before him, sometimes with the face of the ground in his
mind only.
"There he is with his watch in one hand, while the other moves
constantly from his pocket, where his snuffbox, or rather his snuff,
lies. An aide-de-camp arrives; tells of a movement; answers shortly,
some questions rapidly, perhaps impatiently, put; is despatched with
the order that is to solve the difficulty of some general of division.
Another is ordered to attend, and sent off with directions to make
some distant corps support an operation. The watch is again consulted;
more impatient symptoms; the name of one aide-de-camp is constantly
pronounced; question after question is put whether any one is coming
from a certain quarter; an event is expected; it ought to have
happened; at length the wished-for messenger arrives. 'Well! what has
been done yonder?'--'The height is gained; the Marshal is there.'--'Let
him stand firm--not to move a step.' Another aide-de-camp is ordered to
bring up the guard.
"'Let the Marshal march upon the steeple, defiling by his left--and all
on his right are his prisoners.' Now the watch is consulted and the
snuff is taken no more; the great captain indulges in pleasantry; nor
doubts any more of the certainty and of the extent of his victory than
if he had already seen its details in the bulletin."
Cruelty and kindness, selfishness and generosity, loyalty and
treachery, honesty and perfidy, are almost unmeaning terms if applied
without qualification to Napoleon. Where his plans were not involved,
he frequently manifested the human virtues in their highest form;
where those plans were involved, he practised all the vices without
scruple or pity. Naturally he was humane, charitable, kind, indulgent,
sympathetic, generous; if policy required it, he became as hard as
steel. He left no debt of gratitude unpaid; ignored none of the claims,
however slight, of kindred and old association. See how he behaves
toward Madame Permon, how tolerant he is of that intolerable woman,
how he forgets her snubs, how he forgives her a public insult, how he
follows her with respectful consideration all the days of her life--and
why? She had been kind to him when he was a poor boy, had nursed his
father on the death-bed. "It is a devil of a temper, but a noble
heart;" and the noble heart makes him forget the devil of a temper.
He gave place and pension to early sweetheart, to boyhood friends,
to schoolmates, to teachers. The son and daughter of General Marbeuf
found him delighted to serve them in remembrance of their father. The
widow of the Duke of Orleans who had chanced to be the giver of a prize
to him at Brienne, and who had forgotten all about it, was happily
surprised to find that he had remembered. He restored her confiscated
pension, and gave a relative of hers a place in the Senate. To the
daughter of Madame de Brienne he proved himself a vigilant guardian. So
the record runs throughout his life, and his last will is little more
than a monument of gratitude to those who had at any time done him a
service.
He was not free from superstition. What people called "omens" made an
impression upon him. He sometimes made the sign of the cross, as though
to ward off impending evil. When in Italy the glass over Josephine's
portrait was broken, Marmont says that he turned frightfully pale, and
exclaimed that his wife was either dead or unfaithful.
He was a man of insatiable curiosity. He wished to know everything,
and to have a hand in everything. His police infested every nook and
corner, and over his police he set spies, and over the spies he set the
informer. Thus he had two or three systems going at the same time. He
not only sought to know all about public affairs, but private matters
also. He delighted in gossip and scandal, hugely enjoying his ability
to twit some man or some woman with an amour which he had discovered.
Theatre talk, street talk, drawing-room talk, were reported to him
regularly. Copying the Bourbon example, he opened private letters to
ascertain what correspondents were saying to each other. He allowed no
freedom of the press, and no real freedom of speech. Journals which
showed the least independence he suppressed. Authors, actors, orators,
who ventured upon forbidden ground, felt the curb at once.
Lavish as he was in expenditures, there was method and economy
throughout. He was good at a bargain, exacted the worth of his money,
would tolerate no imposition or overcharge. His imperial displays were
more magnificent than those of the Grand Monarch, but they cost him
less than one-tenth as much.
It is not possible to dogmatize about a man like Napoleon, saying
positively just what he was. A more contradictory mortal never lived.
The man who massacred the prisoners at Jaffa was the same who perhaps
lost his crown because he would not consent to excite civil war in
Russia or in France. He who had just sent tens of thousands to death at
Borodino, angrily reproved a careless member of his staff for allowing
the hoof of his horse to strike one of the wounded, causing a cry of
pain.
"It was only a Russian," said the negligent rider.
"Russian or French, it's all the same," cried Napoleon, furiously; "I
want them all cared for."
His temper was despotic; he could not brook opposition, nor tolerate
independence. Hence he banished Madame de Staël, suppressed the
tribunate which had the power of debate, and frowned upon voluntary
movements of all kinds, whether clubs or schools. His treatment of
Toussaint was atrocious, filling the honest biographer with anger,
disgust, and shame: but, after all, Toussaint was a rebel, and the
way of the rebel is hard. In his own eyes the insurgent, striving for
national independence, is a hero: in the eyes of the world he is an
incendiary, unless he whips his master and becomes free.
From the grave of Robert Emmett, Ireland can speak of England's
treatment of rebels: from Cuba comes a voice choked with blood, which
vainly tries to do justice to Spain's treatment of the rebel; and
from Siberia, Hungary, Poland, Finland, Hindustan, Crete, Italy,
South Africa, come awful reminders of the well-known fact,--the way
of the rebel is hard. Toussaint L'Ouverture, regarded as a rebel, was
cast into prison: Jefferson Davis, regarded as a rebel, was cast into
prison: Davis, the white man, was put in irons and came near dying:
Toussaint, the black man, was ironed, and died. In each case the motive
was the same,--to degrade and to punish an alleged rebel.
Great has been the outcry made by the literary Scribes and Pharisees
against Napoleon because of his cruelty to the hero of St. Domingo
and to Andreas Hofer, the hero of the Tyrol; until these indignant
people indict also the kings and cabinets who have slain their hundreds
where Napoleon slew his dozens, we cannot feel much sympathy for the
prosecution.
Relentlessly selfish in the pursuit of power, it will be admitted by
those who impartially study his career that he used his power, not
for personal and selfish pleasures, but for the future welfare of the
peoples over whose destinies he presided. The laborious manner in which
he worked out the revolutionary principle of lifting the despised Jew
into full citizenship, will always be a striking illustration of the
liberality of his statesmanship.
He loved to tour the country, to see with his own eyes, to hear with
his own ears. He loved to meet the people face to face, to talk with
them familiarly, to get at the real facts about everything. The man
never lived who had such a passion for making things better. Harbors
must be widened, deepened, made more secure. Trade routes must be
improved, rivers linked to rivers, or rivers connected with seas.
Mountains must be conquered by broad, easy-grade roads; and villages
must be planted along the route for the convenience of the traveller.
He tore out old buildings to make way for new ones,--larger, better,
grander. Crooked streets--narrow, nasty, the homes of squalor, of
crime, and of pestilence--he replaced by broad avenues and handsome
buildings. Churches, schools, town-halls, arsenals, dockyards, canals,
highways, bridges, fortifications, manufactories, harbor works, new
industries, sprang up at his touch throughout the realms he ruled.
Had he never been known as a warrior, his work as administrator and
as a legislator would have made his name immortal. Had he never been
heard of as a legislator, his work in Europe as a developer of material
resources would have made it impossible for the world to forget him.
The manufactories which he encouraged were but the beginnings of a
mighty evolution which would have transferred to the Continent the vast
profits England had so long reaped. At every seaport, on every canal,
on all the highways, in every town from Venice to Brest and Cherbourg,
the traveller of the present day sees the footprints of Napoleon the
Great.
He rid Paris of the periodical nuisance of the Seine overflow, and
along the river ran his magnificent embankments. At St. Helena he
expressed a wonder that the Thames had never been thus controlled, and
England afterward embanked her river as the great Emperor suggested.
His natural instinct was to make improvements. The first thing he did
in Spain was to establish free-trade between her provinces, abolish
feudal burdens, suppress one-third of the monasteries where "those lazy
beasts of monks" lived in idleness at public expense, and to give the
people the right to be heard in fixing taxes and making laws. The first
thing the Bourbons did, on their return, was to restore all the abuses
Napoleon had abolished.
In Italy, the first thing he did, after overturning the temporal
power of the Pope, was to suppress the papal monopolies by which the
Albani family had the sole right to manufacture pins, Andrea Novelli
the exclusive privilege of selling oil for lamps, Alexandro Betti
the monopoly of ferry boats, and so forth. To these benighted Romans
he gave the Code Napoléon, trial by jury, home rule in local affairs,
equality before the law, and relief from all feudal abuses.
The first thing the Pope did when in 1814 he was restored to temporal
power was to abolish all things Napoleonic, and to reëstablish the
hateful monopolies, feudal burdens, and papal customs.
In Egypt he projected the mighty work of adding millions of acres to
the cultivable area by the construction of vast storage basins on the
Nile. England has but recently carried to successful completion the
magnificent plan he suggested.
In Milan he finished the gorgeous cathedral which had been commenced
hundreds of years before. To stagnant, pestilential Venice he gave new
life, dredging her lagoons, decreeing a Grand Canal, deepening her
harbor, overhauling her sanitary system--spending $1,000,000 during his
one visit. And the story is the same for almost every portion of his
huge empire.
Bad? Lord Wolseley says he was not only bad, but "superlatively" so.
Perhaps he was; but here is one publican and sinner who dares to say
that were the good men to work half as hard as Napoleon did to improve
the condition of _this_ world, its moral and material situation would
more nearly approximate the imagined perfection of that heavenly abode
in whose behalf _this_ poor planet and its poor humanity are so often
neglected.
CHAPTER XXXI
Tilsit is generally considered the high-water mark of Napoleon's
power. Not yet forty years of age, he was lord of lords and king of
kings. With Russia for an ally, Continental Europe was at his mercy.
Adding Westphalia and, also, enlarged Saxony to the Confederation of
the Rhine, the Empire was guarded upon the west, from the North Sea
to the Mediterranean, by an unbroken line of feudatory states. In all
these subject lands the principles of the French Revolution took the
form of law. The Code Napoléon, with its civil equality, jury trials,
uniformity of taxes, publicity of legal proceedings, drove out the
mediæval abuses which had so long robbed the people in the name of
government. To his brother Jerome Napoleon wrote: "Be a constitutional
king. Your people ought to enjoy a liberty, an equality, a well-being
unknown heretofore to the Germans." And the Emperor reminded Jerome
that if he gave his people the benefits of a wise and liberal
administration, they would never wish to return to the barbarous rule
of Prussia. Rule your kingdom wisely and liberally, said Napoleon,
and "this kind of government will protect it more powerfully than
fortresses or the armies of France."
Far-reaching as was the sweep of Napoleon's sword, that of his Code
went farther. The soldier of the Revolution could never go as far as
its principles. In the hour of its deepest humiliation Prussia dropped
the system of Frederick, a worn-out garment, and clad itself anew. She
freed the serf, abolished caste, opened all careers to merit, made
military service universal, and gave partial self-government to towns
and cities. Under the ministry of Stein, Prussia was born again, and
the greatness of modern Germany dates from the reorganization which
followed Jena--a greatness which, when analyzed, is seen to consist
in calling in the Prussian people to resurrect a nation which class
legislation and the privileged nobles had led to perdition.
In measuring the results of the French Revolution and of Napoleon's
victories, let us remember what Germany was in the eighteenth century.
Let us not forget that the great mass of the people were serfs chained
to the soil, mere implements of husbandry, burdened with the duty of
feeding the nation in time of peace, and fighting for it in time of
war, but uncheered by the hope of ever becoming more than serfs. Let us
remember that the great rights of the citizen had no legal existence,
that the arbitrary will of the lord was the peasant's law. In the very
provinces out of which Napoleon fashioned the kingdom of Westphalia a
legitimate, divine-right prince had sold to an equally God-appointed
king of Great Britain some thousands of soldiers to fight against the
revolted colonists in North America. In the very cities which the Code
Napoléon now entered and ruled, might still be seen the foul dungeons
where alleged culprits were secretly tried, secretly tortured, and
secretly done to death with atrocities which might have shamed a savage.
With Napoleon himself, however, imperialism had become a fixed creed.
Ever since Austerlitz, he had affected greater reserve, exacted a
greater deference, obeyed and enforced a more rigid etiquette. Oriental
baseness of flattery pampered his pride; opposition to his will was not
dreamt of in his empire; pestiferous intriguers like Madame de Staël
lived in exile; pert maids of honor like Mademoiselle de Chevreuse were
sent away and silenced; secret enemies, embryo traitors like Talleyrand
and Bernadotte, fawned and flattered like the others, greedily
clutching at all he flung to them,--money, titles, estates. The Grand
Monarch himself never lived in greater pomp than this "Corsican
upstart." The formulas of divine right usurped the old popular phrases,
and "Napoleon by the grace of God Emperor, etc.," was the style of
imperial proclamations. "Religious veneration" was claimed for the
eagles of the army; and the priests taught the children that "to honor
and serve the Emperor is to honor and serve God." No toil was spared
to make the ceremonial at the palace conform to Bourbon precedent. The
hero of Austerlitz and Jena consented to be tutored by the Campans, De
Ségurs, Narbonnes, and De Brézés of etiquette. When Louis XVIII. came
to the throne in 1814, he apparently discovered but one serious fault
in all of Napoleon's imitation Bourbonism--his dinner had not been
escorted from kitchen to dining room by a squad of soldiers.
* * * * *
Turkey had not nursed any very great degree of wrath against Napoleon,
on account of his attempt upon Egypt; she had recognized his greatness
and had become his ally. During the campaign in Poland, while
Napoleon's army was weltering in the mud, which caused indignant
French soldiers to exclaim, "Is this what the Poles have the impudence
to call their country?" England had sent a fleet to Constantinople to
bully the Sultan into joining the league against France.
The terror of the unprepared Turk was profound, and he was about
to submit; but it so happened that Napoleon was represented there
by a man of courage and ability--General Sébastiani. Through his
advice, and inspired by his confidence, the Sultan parleyed with the
English, temporized, gained time, manned defences, and prepared for a
struggle. A letter from Napoleon came at the right moment, exhorting
and promising, as no one but Napoleon could exhort and promise. French
diplomats steadied the nerves of the Commander of the Faithful, while
French officers directed the work on the fortresses, so that when the
English admiral was finally told that Turkey would resist his insolent
demands, the Turks were all ready for battle, and the English were not.
They had forced their way into Turkish waters, killing and wounding as
they came; they now sailed away, pursued and bombarded, losing many in
killed and wounded as they escaped.
Failing here, they determined to make sure of Denmark. By the Treaty
of Tilsit the two Emperors contemplated a union of all the Continental
powers against English commerce. Great Britain believed that Denmark
would be forced to enter this league--but she had no proofs, so far
as historians know. At any rate, no hostile steps had been taken by
either Emperor: Napoleon had merely instructed Talleyrand to enter
into negotiations with Denmark. Upon the plea that Napoleon meant to
seize the Danish fleet, Great Britain determined to take charge of
it herself, despite the fact that Denmark was at peace with her, had
given no cause for war, and was even then represented at London by
a resident, friendly minister. Concealing her purpose, smiling upon
this duped minister to the last, Great Britain launched fleet and army
against an unsuspecting people. Appearing before Copenhagen in force,
the British demanded that the Danish fleet be given up to England in
pledge, "until the peace."
Taken at disadvantage though they were, the Danes could not at once
yield to so shameful a humiliation, and the English opened fire. For
three days and nights the devoted city was shelled, and all the horrors
of war inflicted upon it. For three days the British guns roared,
strewing the streets with dead men, dead women, dead children; while
eight hundred homes were in ruins or on fire. Then the Danes yielded,
their city was looted, their ships taken away, and the exulting
marauders sailed back to England towing their prizes, to be welcomed
with rapturous enthusiasm.
* * * * *
To the Berlin Decree of Napoleon, Great Britain retorted with another
"Order in Council." She declared that she would search all merchant
vessels, and that neutrals should not be allowed to trade unless they
had touched at a British port and paid duties there. Here was another
violation of all law,--an insolent invasion of the right of neutrals
to do business, save in contraband of war. Napoleon's counter shot was
the Milan Decree, in which he very naturally declared that any ship
submitting to such demands as England had made, should be treated as
an English ship. Why not? It is apparent enough, that if neutral ships
did business under English rules, paying duties at English ports, such
ships were practically doing business as English ships.
Strange are the verdicts of history. Napoleon gets almost all the blame
for this commercial war, in which he was first struck by England, and
in which each of his decrees was but an attempt to ward off the blows
England aimed at him.
To make a success of his Continental system, it was necessary that the
entire seacoast of the Continent should be closed to English goods.
In theory, the system was in force throughout the Continent, with the
important exceptions of Spain and Portugal. To close the long line of
seaboard these countries presented, was Napoleon's first purpose in
meddling with their affairs.
Spain had been his ally, but had, perhaps, never had her heart in the
alliance. At all events, when the great Bourbon conspiracy against
Napoleon's life was on foot, in 1803, some of the accomplices of
Georges had entered France under the protection of Spanish passports.
Nevertheless, Spain had paid rich subsidies into Napoleon's coffers,
and had sent her ships to be destroyed by Nelson at Trafalgar. So
burdensome had become the alliance that Spain had grown tired of it.
While Napoleon was involved with Prussia, and previous to Jena, the
Spaniards had been called to arms by Godoy, the Prince of The Peace,
real ruler of the kingdom. Napoleon believed that this call to arms was
a measure of hostility to the French. The victory of Jena, however,
changed the situation, and Godoy humbly came to terms with the winner.
Now again, in 1808, a treaty was made between France and Spain.
Portugal, virtually an English colony, and ruled from London, was to
be conquered, and divided between France and Spain. A French army,
under Junot, marched through Spain into Portugal, and captured Lisbon
(November, 1807). The royal house of Braganza made its escape to
Brazil. Its throne was declared vacant by Napoleon, and the French took
full possession of the country. But for Junot's rashness and rapacity,
it seems that the Portuguese, as a general thing, would have been quite
contented with the change of masters.
In Spain itself fateful events were on foot. The old king, Charles IV.
was a Bourbon, densely ignorant, extremely religious, and devoid of
any real character. His queen was a woman of some ability and force of
character, but she had become infatuated with a common soldier, Manuel
Godoy, and both she and her husband were governed by the favorite.
The heir to the throne, Ferdinand, prince of the Asturias, was a young
man of obstinate temper, full of duplicity and cruelty. He was loved
by the Spanish people, partly because he was their handsome young
prince-royal, and partly because it was known that he hated Godoy.
The old king was made to believe that his son meant to have him
assassinated. He appealed to Napoleon for protection against Ferdinand.
At the same time this prince requested of Napoleon the hand of a
Bonaparte princess in marriage. Thus both factions looked to France,
and the French Emperor used each against the other.
The Spaniards rose against Godoy, a mob wrecked his palace, and he fled
for his life, hiding himself in a roll of matting in a loft. Forced out
by hunger, he was seen, captured, and about to be torn to pieces when
he was rescued by the guards of Ferdinand, and taken, amid blows and
curses, to the barracks. The terrified old king abdicated in favor of
his son; and on March 20, 1808, Ferdinand entered Madrid in triumph, to
the frantic delight of the people.
French armies had already been massed in Spain, and some of the
strongest fortresses seized by unscrupulous trickery. Murat was in
chief command, and he marched upon the Spanish capital in overwhelming
numbers--unresisted because the French were believed to be coming as
friends of Ferdinand.
The old king, Charles IV., protested to Napoleon that his abdication
had been made under duress; he prayed for help against his son. To
Napoleon applied Ferdinand, also; for Murat held Madrid with forty
thousand troops, and he had not yet recognized the title of the new
king.
In April, 1808, the Emperor himself came to Bayonne, moving soon into
the château of Marrac, which was surrounded by a lovely park "on the
banks of the silver Nive." The place is now a ruin, the house having
been gutted by fire in 1825, and the park being now used for the
artillery of the garrison. But when Napoleon came there in 1808, soon
to be joined by Josephine and the court, it was a place of beauty.
Biarritz, the fashionable watering-place of to-day, was then unknown;
but along the same shore where summer visitors now stroll, Napoleon
romped with Josephine, "chasing her along the sands, and pushing her
into the sea at the edge of the tide, until she was up to her knees
in water." They bathed and played together, "and the great Emperor,
England's 'Corsican Ogre,' used to hide her satin shoes on the sands
while she was in the water, and not allow us to bring them to her, but
made her walk from the beach to the carriage barefooted, which gave him
immense delight."
All was very gay at the château of Marrac, everything free, easy,
joyous, etiquette somewhat shelved. For instance, it is related that
Josephine's harpsichord needed tuning, that a man was called in to
tune it, that Josephine, who was unknown to the tuner, leaned her arms
on the harpsichord, chatting very familiarly with the tuner, that her
dress was so plain (and perhaps slovenly) that the amorous tuner took
her to be a lady's-maid, accessible to kisses, that he assured her
she was much prettier than the Empress, and that he was just about to
kiss her, when the door opened and in walked the Emperor! Josephine
laughed, Napoleon laughed, the tuner fled,--leaving his tools,--deaf to
Napoleon's call for him to come back.
Equally true, perhaps, is another story of the same date. There was a
ball at the château of Marrac, the windows were open, the night being
warm. At a pause in the music, a lady stepped out upon the balcony,
seen by the sentinels, who likewise saw an officer follow her and kiss
her. The sentinels knew him--it was the Little Corporal. But he saw
them also, and his sharp word of command rang out, "Shoulder arms!"
"Right about turn!" They turned, and they stayed turned, fixed and
immovable, until the relief came an hour or so later.
So much for the bright side of this famous picture.
* * * * *
By the most astonishing series of duplicities and perfidies, Napoleon
gathered into his snare at Bayonne _all_ the contending parties of the
Spanish trouble,--King Charles, the Queen, Godoy, Ferdinand, and Don
Carlos, Ferdinand's younger brother.
These Bourbons washed their dirty family linen in his presence,
appealing to him against each other. Ferdinand's royal father shook a
cane over his head and cursed him; Ferdinand's royal mother reviled
him, and told him that the king, her husband, was not his father; and
Godoy, the paramour of the wife and mother, sat down to meat with
King and Queen, indispensably necessary to both. Charles IV., fond of
pleasure and ease, resigned the crown of Spain to Napoleon; Ferdinand
was asked to do likewise. He refused, and it was not till there had
been an uprising in Madrid, cruelly suppressed by Murat, who lost
nearly a thousand men, that he yielded. The revolt had been laid at his
door, and Napoleon had threatened to treat him as a rebel.
Charles and Ferdinand became grandees of France, with princely
revenues; in return Napoleon received Spain and its magnificent
dependencies (May, 1808).
Calling Joseph Bonaparte from Naples to wear this new crown, Napoleon
wished to give to the transfer some show of national consent. He
summoned an assembly of Spanish prelates and grandees to Bayonne (June,
1808). They came, but as they came the ground upon which they walked
was hot with revolt. All Spain was spontaneously and furiously running
to arms. The assembly at Bayonne accepted Joseph and the constitution
which Napoleon had prepared.
In all courts and cabinets Napoleon's conduct was hotly discussed; in
most of them it was furiously condemned. True, he had not used Spain
much more unscrupulously than he had treated Venice; nor, indeed, more
perfidiously than England had dealt with India, Russia with Poland,
Prussia with Silesia. But there were two considerations which weighed
heavily against Napoleon: he was not a legitimate king, and he was
getting more than his share. The small men began to ask, one the other,
concerning the meat upon which this our Cæsar fed; and to say, one to
the other, that they, the small men, might, by union and patience and
perseverance, pull the big man down.
The more closely his statecraft is studied, the more clearly will it
be seen that in all things he conformed to orthodox standards. He was
neither better nor worse than others. His march to power was bridged
with broken promises, pitiless deeds, utter disregard of human life,
and the rights of other peoples. A foe was an obstacle, which must be
got out of the way. If fair means would answer, well and good; if fair
means would not answer, then foul methods would be used. Precisely the
same principles have been constantly practised by all conquerors, all
conquering nations. Russia, England, Prussia, France--the same policy
built empires for each. The Russian Czar, Alexander, fawned upon the
Swedish minister, swearing friendship and good intentions when the
Russian legions were already on the march to seize Finland. Russian
faith was solemnly pledged afterward to the Finns themselves, that
their autonomy, their local institutions, should never be destroyed. In
our own day, we have seen a most Christian Czar violate this written
contract and pitilessly Russianize helpless Finland.
England's empire is built on force and fraud; Prussia's greatness rests
on Frederick's crime against Silesia: France under Napoleon merely
conformed to the well-known precedents. Ambitious and despotic, he
made war upon the weak, to shut out English goods, to <DW36> English
commerce, and to bring her to terms of peace. This was bad enough,
but we have lived to see things that were worse. We have seen England
make war upon China to compel her to open her ports to the deadly
opium trade--deadly to the Chinese, but most profitable to the English
trader. We have lived to see a Dutch republic trampled out of existence
because it would not allow English gold-miners to rule it.
Let us put away cant and lies and hypocrisy; let us frankly admit
that Napoleon was a colossal mixture of the good and the bad, just as
Cromwell was, just as Richelieu, Frederick, and Bismarck were. Those
retained attorneys of royalism, clericalism, and absolutism, who
gravely compile huge books to prove that Napoleon was a fiend, an evil
spirit struggling against light, are the absurdest mortals extant.
Even Spain now knows better; and the national revolt there at this
era is against the very system the great democratic despot would have
overthrown. "Down with the Jesuits!" they cry in all the cities of
Spain in this year 1901. They are just a century behind time. Napoleon,
a hundred years ago, put down the Jesuit and his Inquisition, swept
feudalism away, gave just laws and representative government to a
priest-ridden, king-accursed people. They were not ready for the boon,
and repelled it. With mad infatuation Spaniards listened to monk and
grandee and English marplot. Passion flamed, and reason fled. Blind
hatred of all things French took possession of men, women, and children
throughout the land. Peasants were even more frantic than princes and
peers. Deeds of heroism, of self-sacrifice, of cruelty were done which
amazed the world. By desperate persistence, the Spaniards succeeded
in getting back their good old system--Bourbon king, privileged
aristocracy, priestly tyranny, feudal extortions. Great Britain kindly
sent armies and subsidies to aid the good work. Spain got the old
system back, and much good has it done her. It has eaten the heart out
of a great people, made her name a byword among nations, stranded her
in the race of human progress. To-day she comprehends what she lost a
hundred years ago.
CHAPTER XXXII
When Captain Marbot, bearing despatches from Murat announcing the riot
in Madrid, reached the château of Marrac, he found the Emperor in the
park, taking his after-dinner walk, with the Queen of Spain on his arm
and Charles IV. beside him, followed by the Empress Josephine, Prince
Ferdinand, Don Carlos, Marshal Duroc, and some ladies.
"What news from Madrid?" cried Napoleon, as Marbot, covered with dust,
drew near. The despatches were delivered in silence, and Napoleon drew
to one side to read them, and to overwhelm the officer with questions.
In vivid terms, Marbot described the despair of the Spanish people, the
fury with which they had fought, the threatening aspect of the populace
even after the revolt had been put down.
"Bah!" exclaimed Napoleon, cutting him short; "they will calm down
and will bless me as soon as they see their country freed from the
discredit and disorder into which it has been thrown by the weakest and
most corrupt administration that ever existed!"
When the Emperor had explained to the King and Queen of Spain what had
occurred in Madrid, they turned upon Ferdinand with an outburst of
rage. "Wretch!" cried the old King, "you may now be satisfied. Madrid
has been bathed in the blood of my subjects shed in consequence of your
rebellion against your father; their blood be on your head!" The Queen
was no less bitter, and even offered to strike her son. Napoleon put a
stop to the painful scene.
"Bah! they will soon calm down." So Napoleon thought, having no
fear whatever that a tumultuous rising of peasants would make head
against his troops. What his army had done in Italy and in Egypt, it
could do in Spain. It only annoyed him, and somewhat puzzled him,
to see that the people should reject his liberal constitution, and
devote themselves with such frantic zeal to the most worthless of
Bourbon kings. That Joseph would soon be in peaceful possession of
the peninsula, that his generals would soon sweep the peasant bands
out of the field, he did not doubt. Had he lacked faith as to this,
he would probably not have given the crown to Joseph,--the placid,
self-satisfied, comprehensively incapable Joseph. Had he dreamed of the
long years of war that were to follow, he might have hearkened to the
pleadings of Murat, and left that brilliant soldier to defend the crown
which he so ardently coveted.
Amid ovations the Emperor and Josephine toured the provinces, on the
return trip to Paris, everywhere welcomed with joy and admiration,
while in the peninsula the great storm was muttering. Throughout Spain,
in the highways and byways, from pulpit to market-place, Napoleon was
denounced, defied, and resisted. Priests led the crusade, cursing the
man of the Concordat as anti-Christ, minister of the devil, worthy
of death and damnation. Committees of defence, juntas, sprang up
everywhere; armies mustered almost at the stamp of the foot. Wherever
a Frenchman could be stabbed, shot from ambush, or taken and sawn
asunder, it was done. Roads were lined with ambuscades, stragglers and
detached parties cut off, and the French generals were soon thrown on
the defensive by this despised uprising of the people. At Saragossa
and Valencia the French troops were repulsed; in Andalusia hordes of
Spaniards surrounded Dupont's army of twenty thousand, beat it in
battle, and forced it to capitulate (Baylen, July, 1808).
In August the English landed troops in Portugal; and Junot, whose
forces were scattered, fought with only thirteen thousand men against
Wellington with sixteen thousand, was worsted at Vimeiro (August 21,
1808) and by the convention of Cintra (August 30, 1808) agreed to
evacuate Portugal. He, too, had wanted to become a king; he, too, had
thought of himself rather than of his master; he, too, had wrecked a
splendid plan by sheer mismanagement and monstrous rapacity.
The disaster in Spain and Portugal came upon Napoleon like a
thunderbolt; his grief and indignation knew no bounds; cries of rage
and pain were wrung from him; pointing to his uniform, he said, "There
is a stain here." At Aboukir, Brueys had at least fought and died like
a soldier; at Trafalgar Frenchmen had shown desperate valor; but at
Baylen an army of twenty thousand imperial troops had laid down their
arms to gangs of insurgents! Oh, the shame of it! Who could estimate
its effect in Europe? When the Emperor spoke of Baylen to his council
of state, his voice trembled, and his eyes were full of tears.
Conscious of the peril which menaced his supremacy, Napoleon determined
to go in person and put down the Spanish revolt. But before doing so
it was necessary that he and the Czar should have another conference,
smooth over certain points of difference which had arisen, and come
to a better understanding--hence the famous gathering at Erfurth
(October, 1808). This time Alexander was Napoleon's guest, and very
royally was he entertained. A more brilliant assembly was never seen
in Europe. Subject kings, vassals, lords of the Empire, civil and
military dignitaries, courtiers, ambassadors, diplomats, eminent men
of letters, surrounded the two great Emperors, and rendered homage.
Business and pleasure intermingled; and while frontiers of empire were
being arranged, there were banquets, balls, grand hunts, orchestral
music, and the drama. Actors brought from Paris played to the Emperors
and their trains, and the Czar stood up one night and took Napoleon's
hand at the line "the friendship of a great man is a gift from the
gods." Davoust used to say that Napoleon had been nodding till the Czar
improvised this little by-play.
If Napoleon was anxious for the future of his power, he concealed
it well; his face showed nothing but serenity, good nature, and
confidence. He found time to converse at length with Goethe and
Wieland; he found time to act the suave host to lords and ladies; he
was as firm with Alexander as he had been at Tilsit; and when the
conference broke up, he had arranged everything as completely to his
satisfaction.
In the _Memoirs_ of Marshal Oudinot, we find the following anecdote of
the Erfurth meeting:--
"Napoleon had occasional fits of forgetfulness which prevented him from
displaying, in his relations with the sovereigns, all the forethought
expected in a host.
"One day we were riding into the country, the two Emperors, Napoleon
and Alexander, riding side by side. At a given moment, the former,
carried away by his thoughts, took the lead, whistling, and seeming to
forget those he was leaving behind. I shall always remember Alexander,
turning stiffly toward his neighbor, and asking, 'Are we to follow?'
'Yes, sire.' I rejoined Napoleon and told him of this little scene. He
fell back, offered an explanation, and that was the end of it."
So Marshal Oudinot thought, but as the compiler of the _Memoirs_ asks,
who knows what influence this trifling incident may have had upon the
proud, sensitive, suspicious, and wavering Czar?
By the terms of the new agreement, Alexander was to have a free hand
on the Danube to take Moldavia and Wallachia; that much had been
understood at Tilsit, perhaps, but "Constantinople, never! That is the
empire of the world!" In return for the liberty to seize the Danubian
provinces, the Czar was to keep central Europe quiet, while Napoleon
conquered Spain and Portugal. Prussia was notified by the Czar that she
must remain quiet, bow to Napoleon's will, and agree to his demands,
one of which was that Stein should be dismissed.
To Germans, generally, the heavy hand of the Czar, coming down upon
Frederick William in this imperative fashion, must have suggested the
thought that it was high time the Lord's Anointed autocrat of Russia
was being sworn to friendship to Prussia, once more, at the tomb of the
great Frederick. The two oaths already taken seemed to have slipped
their hold.
Suppose that Napoleon had solemnly gone in state to the Escorial
and there, at night, had taken in his own the hand of the Spanish
king, and had, over the bones of dead Spanish monarchs, sworn eternal
friendship to Spain; suppose he had broken this vow as soon as made;
suppose he had gone the second time and sworn it all over again;
suppose he had violated his oath a second time:--would royalist and
clerical authors _ever_ have found ink black enough to fill their
righteously indignant pens?
If we would correctly judge Napoleon, let us keep our equilibrium and
our standards of comparison; let us throw him into contrast, not with
the ideal man, but with other rulers of his own time. By so doing we
may hope to come, in the humblest spirit and manner, to know the great
Corsican as he actually was.
Once more an effort was made to put an end to war. The two Emperors
sent couriers,--one French and the other Russian,--to England, bearing
offers of peace. These couriers were treated almost as spies by the
English, were kept under surveillance, and were finally sent back with
a note which gave no encouragement to the monarchs who sent them.
King Joseph had been driven out of Madrid, was now at Vittoria, and
the insurgents controlled the country with the exception of the soil
occupied by the French armies.
Losing no time after the Erfurth interview, Napoleon hastened to Spain,
took command of the troops at Vittoria (November 5, 1808), and moved
forward. In a few days the entire military situation was changed.
The Spaniards were out-generalled, beaten at all points, and escaped
complete annihilation by the too great haste of some of the French
generals. Within four weeks after the commencement of the campaign,
Madrid was retaken, and once more put into the possession of the feeble
Joseph.
On his march to the Spanish capital, Napoleon found his road blocked
at the mountain pass of Sommo-Sierra. The insurgents had fortified the
heights, their cannon completely controlling the defile. So strong was
the position that a handful of veterans there might have checked an
army.
But the impudence of these Spanish bands in presuming to resist his
march threw Napoleon into a fury. He would not wait till his infantry
could advance upon either side, turn the enemy, and almost certainly
secure a bloodless victory. He raged and stormed, "What! my army
stopped by armed bands, wretched peasants!"
"Patience, sire, I pray," pleaded General Walthour, who assured him
that in a few minutes the pass would be cleared by infantry, which was
even then advancing on either side. But no; the enemy must be charged
with cavalry--a bristling battery, on the crest of a mountain gorge,
must be swept out of the way by a cavalry dash.
"Go, Ségur! Go at once; make my Poles charge, make them take
everything!"
There was astonishment--but the order had to be obeyed. At full speed
the splendid soldiers of the Polish squadron dashed up the pass, to
melt away in an awful fire from the battery above. Historians say that
the cavalry charge succeeded. Ségur, who led the dash and was shot down
in it, relates that the flanking infantry columns did the work.
"Does anybody know how Ségur came to be hurt? Was he carrying an
order?" Napoleon asked, after the battle.
When reminded that he had himself given Ségur the order, he was silent,
and "fell into a very thoughtful mood."
An English army under Sir John Moore had entered Spain and was
advancing toward Madrid. When it learned that Napoleon was in the
field, it began a retreat to the coast, which is famous in military
history. The French, led by the Emperor, set out in hot pursuit; and
it would be hard to say with certainty which party suffered the more
frightful hardships,--the pursuers or the pursued. The weather was
bitterly cold, with cutting winds, chilly rains, blinding snowstorms.
In crossing the Gaudamara Mountains the storm was so fierce, the cold
and the snow so terrible, that the advance guard of Napoleon actually
began to retreat. It required all the Emperor's personal influence
and example to encourage the men onwards. Dismounting, he trudged
along on foot, Lannes and Duroc on either side, and hour after hour
he plodded thus through the snow, up the mountain, at the head of his
men. Near the summit, on account of the jackboots the officers wore,
they could go no farther. Napoleon was lifted on to a gun carriage,
and riding on a cannon, he reached the top, his generals similarly
mounted. By forced marches the French were pushed on in the hope of
cutting off the English retreat, but it could not be done. Horribly
as they suffered, the English were not wholly demoralized. There were
always some gallant thousands who would turn and fight when the French
pressed them too hard. In this way the pursuers met bloody repulses.
Many frightful scenes took place among the English; but General Marbot
relates an incident of the French pursuit which throws a vivid light
over the hideous character of this whole campaign. He saw three French
grenadiers kill themselves because they were tired out, could no
longer keep up, and chose death rather than the tortures which awaited
them if they fell into the hands of the Spanish peasants.
Napoleon was so deeply impressed by the suicide of his grenadiers that
in spite of the drenching rain and bitter cold he went the rounds of
the bivouac that night, speaking to the wretched soldiers and trying to
restore their courage.
At Astorga a courier arrived, bringing despatches from Paris which
warned Napoleon that Austria was ready now "to begin again." She had
completely reorganized her army, had patiently waited for the right
moment, and was sure that it had come. The veteran troops of France
were scattered over the Spanish peninsula; England had made good her
grip on Portugal; Austria had about five hundred thousand soldiers
ready, and now was the time to strike. The pursuit of the English
was turned over to Soult, and the race for the seacoast continued as
before. When the French could overtake the English at all, it was with
an advance guard too small to crush the English rear-guard. If there was
a clash, the French were repulsed. If the French came up in force, the
English continued the retreat. At last the coast was made. There was a
bloody fight, the battle of Corunna. Sir John Moore was killed, but his
army, or what remained of it, got on board the English ships and sailed
away.
As to Napoleon, he returned to Valladolid, where he busied himself
for several days regulating the affairs of Spain, and in sending off
innumerable despatches. Then springing upon his horse, he spurred
away for Bayonne, in perhaps the wildest ride an emperor ever made.
His escort clattered after him, strung out behind, and the wondering
peasants of Spain long remembered that meteoric vision. They heard in
the distance a faint noise as of frantic racing; there burst into view
a breathless cavalcade; it came on like a wind-driven cloud; there was
a rush, and a noise like thunder, a fleeting glimpse of bent riders and
straining steeds; there was, perhaps, a shout in passing; then it went
as it came, and in a moment it was gone.
General Thiébault, on his way to Vittoria, was in the road, with
carriage, aides, escort, and servants, when one of his attendants said,
"Here comes the Emperor, I think." The General was about to alight from
the carriage when he heard some one call:--
"Who is in that carriage?"
The servant hardly had time to answer "General Thiébault" before the
imperial party tore by. "Savary was first, after him the Emperor,
lashing Savary's horse, and digging the spurs into his own.... A good
minute afterward Duroc and the Emperor's Mameluke galloped by, and at
a like distance from them came a guide, exhausted with his efforts to
make up lost ground, and four more brought up the rear as best they
could."
From Valladolid to Burgos, some seventy-five miles, Napoleon rode in
three hours and a half (January, 1809).
CHAPTER XXXIII
When the Emperor reached Paris, he was in one of his worst moods.
Many causes had combined to mar his serenity. His brother Joseph had
violently found fault with him because he, Napoleon, had remodelled the
government, making it better for the people, and not quite so good for
the nobles and priests. Joseph resented this deeply. He, Joseph, was
King of Spain. He, Joseph, was the proper person to remodel government,
change laws, and manage the country. Napoleon was present merely as a
military expert, a general whose service was temporarily needed to pull
Joseph from beneath the enemy, and lead him by the hand back to the
throne; but when this had been done, Napoleon should have gone away,
leaving Joseph to do in Spain just as he thought best. This view was
not only held by Joseph at the time, but as long as his worthless life
lasted he never wearied of explaining to his friends how Napoleon had
lost him the crown of Spain by "interfering in his affairs" in 1809.
Not less high than this was the estimate which Louis Bonaparte placed
on his "rights" as King of Holland. No sooner had that morose, jealous,
ill-conditioned dolt been placed on a throne by his elder brother than
he arrogated to himself all the prerogatives of a dynastic king. The
"divine right" virus got into _his_ sluggish veins, and he began to
shift on to God the responsibility for such a creature as himself being
a king at all. He wished to rule Holland, not as a fief of the Empire,
not as part of the Napoleonic system, but as a piece of independent
property which had come to him, Louis, through a long line of
ancestors. When Napoleon gave him the crown, the conditions were made
plain. Holland was a part of France; must be governed with reference to
France; the friends and enemies of the one must be those of the other.
In other words, Holland was a planet in the French system, and Louis
a subordinate king. If Louis was too proud to rule as a lesser light
in the system of his great brother, he should have been as frank as
Lucien: he should have refused the crown. But he accepted the splendid
gift, and then violated the conditions. English goods poured into
his markets. To all intents and purposes he became the ally of Great
Britain, for it was her policy which he favored. It was her dearest
object to break down the Continental system, and Louis was aiding her
to the best of his slight ability. Could Napoleon be otherwise than
furious? Had Holland been won merely that England should be enriched?
Had he set his brother on a throne merely to weaken his own empire,
and to set an example of disloyalty to other allies? At a time when
Prussia, Austria, and even Russia were under contract to enforce
the Continental system, was it tolerable that his own brother, in
all-important Holland, should be throwing his ports open to the common
foe?
This cause of trouble, also, was worrying Napoleon and making it hard
to maintain good humor. And even this was far from being all. Murat,
his brother-in-law, was acting almost as badly as his brother. Murat,
who was grand duke, wanted to be king, had coveted the crown of Poland,
had claimed the Spanish throne, and in his disappointment, in both
instances, had fallen into a rebellious mood.
Napoleon had given him Joseph's vacant throne in Naples; but it
was rumored that he was still discontented, and had been holding
communications with conspirators in Paris. And who were these
conspirators? Talleyrand and Fouché, of course. These restless,
overrated, and chronic traitors had been sagely conferring in Paris,
as they had done previous to Marengo, for the purpose of agreeing upon
a successor to Napoleon, in case he should be killed in battle or
hopelessly defeated.
Nor was even this all: the funds had fallen, the treasury was drained,
murmurs had begun to be heard in France against the expansion of the
Empire; conscriptions, which had been called for in advance of the
legal time, began to be unpopular, desertions were frequent, and "the
refractory" grew ever more numerous. The Spanish war was not relished.
Generals ordered to Spain went, but went reluctantly. They carried no
zeal, none of that buoyant confidence which is half the battle. Troops
ordered there marched, but without enthusiasm. Compared with Italy and
Germany Spain was a barren land. Against armed peasant bands no glory
was to be won; little booty could be expected. Even the Guard grumbled
at such service. As Napoleon was holding a review at Valladolid just
before quitting Spain, the murmurs in the ranks grew so loud that he
lost control of himself, snatched the musket from one of the growlers,
jerked the man out of the line, threatened to have him shot, and then
pushed him back to his place while he sharply lectured the whole troop.
Once more at Paris, Napoleon's courtiers grouped themselves around him
with the same blandishments as before. A few, a very few, might venture
to speak frankly to him and to tell him the truth, but the many had
fallen into the ways natural to all courts: they spoke, not to inform,
but to please. And foremost among those who came to fawn and to flatter
was "that <DW36>" whom Josephine said she dreaded, Talleyrand.
Only dangerous to the weak, gifted with no constructive talent
whatever, incapable of sustained labor of any sort, strong only in
sudden emergencies, in the crises of political changes, Talleyrand was
known to Napoleon like an open book. Scorning him, rather than fearing
him, Napoleon's anger against him now was inflamed to the highest
pitch, not so much because of anything he had done, as because of what
his treachery implied. That so keen-eyed a time-server as Talleyrand
should begin to plot, meant that confidence was shaken in the
Napoleonic power. That the funds should fall, conscripts dodge the law,
allies shirk their obligations, and domestic enemies conspire, were but
various symptoms of the same malady.
When Talleyrand appeared at the levee, Napoleon boiled over. He began
to rebuke the false courtier, began in a moderate tone, but the more
he talked the less he could control himself. All the past perfidies
of this most perfidious of men came to mind, and in bitter words were
hurled at Talleyrand's head. His venalities, his bribe-takings, his
betrayal of state secrets--they all swelled the torrent of Napoleon's
excoriation. "You base wretch, you false-hearted minister. _You_
pretend that you advised against the trial of the Duke d'Enghien when
you urged it in writing; _you_ pretend that you advised against the
Spanish war when you urged me into it!"
And at each sentence Napoleon advanced, face distorted with passion,
hand raised in menace, while the guilty courtier slunk back step by
step as the Emperor advanced, until he reached the wall. There he
stood, with Napoleon's clenched hand in his face and Napoleon's blazing
eyes threatening death, warning him, as he loved life, to say nothing,
and let the storm pass.
When Talleyrand reached home, "he fell into a kind of fit," and the
doctors had to be called in. Only a few days elapsed, however, before
he was again at the levee, bending humbly before his master, and ready
again with his fawnings and flatteries. Napoleon's anger had passed: he
listened to the courtier's suave phrases with a smile of contemptuous
indifference.
France had given Austria no cause for war. It was not even claimed that
she had. Austria had causelessly provoked two wars already, had got
whipped in both, had lost much territory, much money, much prestige.
She now believed she was strong enough to win back all she had
lost--hence she had mustered her forces and commenced the march into
Bavaria. Her readiness to "begin again" had been accelerated by a bribe
of $20,000,000 paid her by England.
Napoleon had massed troops at the point of danger, but had trusted to
Berthier the direction of their movements. This officer had bungled
matters so badly that the different divisions were widely scattered;
and the troops, conscious that something was wrong, were becoming
demoralized. Summoned by the signal telegraph, Napoleon made all haste
to headquarters. He found the army so ill-posted that he said to
Berthier, "If I did not know you to be true to me, I should suspect
that you were a traitor."
The Archduke Charles, commanding the Austrians, had seen his advantage
clearly, and was hastening to throw himself between the separate
divisions of the French, to beat them in detail. He commenced his
campaign well, and it appeared certain that he would crush the corps
of Davoust before it could be supported. But the Archduke was almost
superstitiously afraid of Napoleon, and no sooner did he learn that
the Emperor was now in command of the French than the Austrians seemed
paralyzed. Time was given for Masséna and Davoust to support each
other, the one having been ordered to fall back while the other moved
forward. Calculating to the hour when these two wings could support
the centre, the great soldier fell upon his enemy. The risk was great;
for should his two lieutenants fail to come up, all would be lost. But
Davoust and Masséna were not Grouchys: they came, and the campaign was
saved. Never was Napoleon greater in plan and execution than in 1809;
not even in the Italian campaign did he work harder. For a week he was
almost constantly in the saddle, never having time to undress. But in
that week he wrought utter confusion among his enemies, and saved his
empire. At Abensberg, at Landshut, at Eckmühl, at Ratisbonne, he struck
the Austrians blow after blow, and shattered their army, killing and
wounding thirty thousand men, capturing an equal number, and taking
vast spoil in guns, ammunition, stores, war material of all sorts. The
Archduke drew off his broken army on Bohemia; Napoleon marched upon
Vienna, which fell May 12, 1809. The royal family fled to Hungary;
the French Emperor, quartered at the palace of Schönbrunn, made
preparations to cross the Danube. There were no bridges this time for
Lannes and Murat to win by stratagem; the river rolled broad and deep
between French and Austrians; bridges would have to be built, and the
French put across in face of an army ready to dispute the passage.
Had not victory declared for Napoleon, promptly and emphatically at
the opening of the campaign, his ruin would have come in 1809 as it
did in 1814. The national spirit was declaring against him in Germany,
as it had done in Spain. Prussia was honeycombed with patriotic secret
societies, pledged against him; and in anticipation of Austrian
success, the young Duke of Brunswick and Colonel Schill had raised the
standard of revolt. The decisive victory of the French at Eckmühl alone
prevented this abortive effort at a national uprising from being a
success. In the Tyrol, also, the people, intensely Catholic and opposed
to the reforms Bavaria had introduced, rose against the Napoleonic
power, and failed only because the French had been so prompt in
scattering the strength of Austria.
In the crisis, Napoleon's ally, Russia, had shown little zeal. She sent
a very small army where she had promised a large one; and a general of
their army wrote to the Austrian commander that he hoped they would
soon be acting in concert. Napoleon forwarded this letter to Alexander,
who contented himself with the recall of the writer. But for the heroic
conduct of Poniatowski and the Poles, it seems that the Austrian army
would have succeeded in wresting the Grand Duchy of Warsaw from Saxony.
But Napoleon's triumphs at the opening of the campaign changed the
aspect of affairs all around. Austrian armies had to be called in from
Warsaw, from Italy, from Bohemia, to concentrate and oppose Napoleon on
the Danube.
Choosing a position below Vienna, where the large island of Lobau
divides the stream into two unequal channels, the French threw bridges
across, and on May 20 commenced passing over, taking possession of
the villages of Aspern and Essling, almost without opposition. Next
day the Archduke Charles made a furious attack, first on Aspern, then
on Essling also. The struggle was very bloody. Only a portion of the
French had passed the river; the Austrians outnumbered them heavily;
and, realizing this vast advantage, pushed it with splendid energy.
Aspern was taken and retaken time after time; and when night put an
end to the carnage, the French held only a portion of the smouldering
ruins. Next day the battle was renewed, the French army still cut
in two by the Danube. The corps of Davoust had not passed, and the
Austrians were doing their utmost to break the bridges, which a sudden
rise in the river already threatened to carry away.
So strong had been the efforts of the enemy to carry Aspern on their
right, that Napoleon guessed they had weakened their centre too much.
He therefore massed heavy columns against it, and began to drive it
back. At this moment came the dreaded message,--"The bridges are gone!"
He might have pressed on and beaten his foe, but Napoleon thought
the risk too great. His columns halted, their fire slackened, and
the orders to retire were given. The wondering Austrians took fresh
courage, and followed the retiring French with terrible effect. Masséna
must hold Aspern, Lannes Essling, until the Emperor could get the army
back to the island of Lobau. Aspern was everything; it must be held at
all hazards.
"Hold your position! It is a question of saving the army--the bridges
are gone!" So ran the despatch, and the grim soldier who held Genoa
while Napoleon planned Marengo, now held Aspern while his Emperor
prepared for Wagram.
Poor Lannes! Brave, unselfish, plain-spoken, leonine Lannes! Here his
long march was to end. The same year that Madame Letitia in Corsica
had begun to rock the cradle of Napoleon, the wife of an humble dyer
in Gascony had begun to nurse the babe who became the Roland of
Bonaparte's army. He had little education, no influential friends; but
when the Revolution began to sound its tocsin and beat its drum, the
Gascon lad went forth to the wars. From 1791, when he volunteered as
grenadier, he had served without pause and with unsurpassed courage.
Augereau made him colonel for bravery in the Pyrenees; and Napoleon
made him general for brilliant service in Italy. He followed his
chief to Egypt, and was shot through the neck at Acre. On the famous
Sunday of Brumaire he aided in Napoleon's seizure of supreme power,
and at Montebello fought the prelude to Marengo. He had loved Caroline
Bonaparte, whom Murat won; and had Lannes instead of Murat been the
imperial brother-in-law, much disaster might have been averted. Raised
in rank, made marshal of the Empire, and Duke of Montebello, he was the
same intrepid, ever growing, ever loyal soldier. Great at Austerlitz,
great at Jena, great at Friedland, he was greater yet at Saragossa
where he overcame a resistance which challenged the wonder of the world.
From that ruined city in Spain he had hastened to Germany, and had
been again the right hand of the great captain who so well knew his
worth. Better courtiers there were than Lannes, gallants who better
graced a ballroom, flatterers who could better please the ear. But who
of all the brave men of France could walk the battle-field with surer,
steadier step than he?
Who at heart was more loyal to the chief--who so ready to forsake ease
and comfort and go forth at the call of the chief into rain or snow,
heat or cold, exhausting march or desperate battle? In all the long
record of French heroism, who had done deeds more lionlike than Lannes?
Who was first over the bridge at Lodi, outstripping Napoleon and all,
and slaying six Austrians with his own hand? Who led the vanguard
across the frozen Alps and held the rout at Marengo till Desaix could
come? Who, in this last campaign, had rallied the grenadiers beneath
the blazing walls of Ratisbonne, seized a scaling ladder, when the
bravest held back, and had rushed toward the battlements under a
withering fire, shouting to his halting men, "I'll show you that I've
not forgotten I was once a grenadier!" Who but Lannes had electrified
these troops by his fearless example, and had carried them over the
walls?
At Essling he had been in the thick of the fight, holding his ground
with old-time grip. The slaughter had been immense, and the sight of
the mangled body of General Pouzet, shot down at his side, had affected
him painfully. Sick of the hideous spectacle, he had gone a little to
one side, and had seated himself on the embankment of a trench.
A quarter of an hour later, four soldiers, laboriously carrying in a
cloak a dead officer whose face could not be seen, stopped in front of
Lannes. The cloak fell open, and he recognized Pouzet. "Oh!" he cried,
"is this terrible sight going to pursue me everywhere?" Getting up, he
went and sat down at the edge of another ditch, his hand over his eyes,
and his legs crossed. As he sat there a three-pounder shot struck him
just where his legs crossed. The knee-pan of one was smashed, and the
back sinews of the other torn. General Marbot ran to him; he tried to
rise, but could not. He was borne back to the bridge, and one of his
limbs amputated. Hardly was the operation over when Napoleon came up.
"The interview," says Marbot, from whose _Memoirs_ this account is
literally taken, "was most touching. The Emperor, kneeling beside the
stretcher, wept as he embraced the marshal, whose blood soon stained
the Emperor's white kerseymere waistcoat."
"You will live, my friend, you will live!" cried the Emperor, pressing
the hand of Lannes. "I trust I may, if I can still be of service to
France and to your Majesty."
The weather was terribly hot, and fever set in with Lannes; on May 30th
he died. In spite of the cares and dangers of his position, Napoleon
had found time to visit the wounded man every day. A few moments after
daybreak on the 30th, the Emperor came as usual, when Marbot met him
and told him of the sad event. The amputated limb had mortified, and
the stench was so strong that Marbot warned Napoleon against going in.
Pushing Marbot aside, the Emperor advanced to the dead body, embraced
it, wept over it, remained more than an hour, and only left when
Berthier reminded him that officers were waiting for orders.
"What a loss for France and for me!" Well may Napoleon have grieved and
wept: here was a gap in his line that could never be filled. Said the
Emperor at St. Helena, "I found him a pygmy; I lost him a giant."
* * * * *
The bridges connecting the island of Lobau with the bank of the Danube
upon which the army had been fighting were not broken: hence the
troops could be led back to the island. Once there, the position could
be fortified and held, until the Vienna arm of the river could be
rebridged.
This was done. Several weeks were spent in preparations, reënforcements
brought up, larger, better bridges built, and all made ready for
another attempt to cross.
The Archduke Charles, believing that Napoleon would direct his march
upon Aspern and Essling, as before, calmly waited, confident that he
could beat the French as before. On the night of July 4, 1809, while a
terrible thunderstorm was raging, Napoleon began his attack upon the
Austrian position at Essling and Aspern. This was a feint to hide his
purpose of crossing at another place, in front of Enzersdorf.
While the Archduke's attention was fixed on the two villages first
named, the French made a dash at Enzersdorf, and took it. Several
bridges, ready-made, had been thrown across the river here, and
Napoleon's army had passed almost before the Austrian knew what he
was about. Then the Archduke drew back into the vast plain of the
Marchfeld, and three hundred thousand men lined up for the great battle
of Wagram. From the roofs and ramparts of Vienna, excited thousands
gazed upon that vast wheat field, yellow in the summer sun, where the
harvester Death was to reap where humble peasants had sown.
For two days the tremendous struggle lasted. The Austrians never fought
better. In sight of fathers and sons, of wives, daughters, sisters,
sweethearts, who would not fight well for home and native land? What
did the Austrian soldier know of the cause of the war? He knew as much
as his masters chose to tell him; and in his heart he believed the
French to be aggressors, tyrants, marauders, come to loot and ruin and
enslave.
So they stood amid the burning wheat in the golden grain fields,
beneath the torrid sun, and fought as Napoleon had never seen them
fight--fought as men fight only when their souls are in it. And far
off on the housetops, steeples, and battlements of old Vienna were
straining eyes, beating hearts, hungry prayers, and the wild hope that
these marauders from France would be scattered as the Turks had been
scattered in that dread time long ago.
But in those olden days Christians could hear the cry of Christians,
could fly to the relief of Christians. What bannered host was that
which had burst like a storm upon the Moslem rear, scattering infidels
like so much dust, bringing salvation to the beleaguered town? Who
but the Polanders and John Sobieski had smitten the Turk and sent the
crescent backward in flight before the cross? That was many and many a
year ago. There would be no "Poland to the rescue!" this time. Poland
had been devoured--by Moslems? No; by Christians. And at the feast
Austria had sat, greedily eating her share.
The shells set fire to the wheat; the smoke and the flame from the
burning grain mingled with the smoke and flame of batteries. Troops
moving to the charge were halted or turned from their course; the
wounded fell in the midst of the blazing stubble, and were burnt to
death or suffocated.
Nothing could withstand the French. The Austrian leader outclassed by
his antagonist, the long trial of strength yielded victory at length
to the better soldier. The efforts made on the wings had weakened the
Archduke's centre. Masséna, though terribly shaken, was able to hold
the right, while Napoleon massed all his available force to hurl it
upon the Austrian centre. But he must wait. Nothing could be done
until Davoust on the enemy's left had succeeded. Motionless as a rock,
Napoleon kept his eyes riveted on Neusiedel, a village "which lies high
and is surmounted by a tall tower visible from all parts of the field."
Davoust must fling the Austrians back behind this village before the
attack on the centre could be made. "At last we suddenly saw the smoke
of Davoust's guns beyond the tower." Now the enemy's left was beaten.
"Quick! quick!" cried the Emperor to Aide-de-camp Marbot, who had come
from Masséna to ask instructions. "Tell Masséna to fall upon whatever
is in front of him, and the battle is won!" All along the line flashed
similar orders, while Macdonald, a hundred cannon blazing along his
front, made the famous charge which broke the Austrian centre.
It was a great fight, a great victory, and great were its results.
Austria sued for peace, and Napoleon, ready as he ever was to end a
war, granted her terms as generous as she had any right to expect. She
lost territory, and had to pay an indemnity; but out of wreck which she
herself had made, her empire came forth practically intact.
As indemnity, she was asked to pay $20,000,000. This was the amount of
the bribe she had taken from England to begin the war.
An indemnity of $20,000,000! How trivial this amount when compared to
the _one thousand millions_ which Bismarck levied upon France. How
modest it looks beside the $330,000,000 which China had to pay to
Christian missionaries and their supporting nations for the riots of
the year 1900!
CHAPTER XXXIV
After the French defeat at Aspern (May 22, 1809), and while they were
shut up in the island of Lobau, it had seemed that Napoleon's position
was almost desperate. The Tyrolese were in revolt, and had expelled
the French and Bavarians; the young Duke of Brunswick had invaded
Saxony and driven Napoleon's vassal king from his capital. Popular
insurrections broke out in Würtemberg and Westphalia; England was
holding her ground in Portugal, and was preparing an armament to fall
upon the Dutch coast. Prussian statesmen, officers, preachers, poets,
and patriots were clamoring for war. In this anxious crisis the courage
and confidence of Napoleon were perfect. To beat the Austrians in his
front was the one thing he must do. Succeeding in that, resistance
elsewhere would disappear. Failing in that, all was lost. Thus Napoleon
had reasoned, and he had judged rightly. After Wagram his peril passed.
Austria, after having pledged faith to the Tyrolese, coldly deserted
them, and they were crushed. Brunswick's effort failed as Schill's had
failed; popular insurrections were stamped out; Prussia dared not move;
and England's "Walcheren expedition" against Flushing and Antwerp ended
in utter failure and heavy loss. Everywhere Napoleon's Empire stood
the test: Eugène beat the Austrians in Italy; and Wellington, after
defeating Victor at Talavera, was driven back into Portugal by Soult.
Out of the storm which had threatened his very existence, Napoleon came
forth with frontiers extended to the borders of Turkey, cutting off
Austria from the sea--an empire stretching in unbroken line from Bosnia
to the straits of Calais.
Never had Napoleon's power seemed so great, nor his court so splendid.
His vassal kings came to Paris with brilliant retinues, the kings of
Saxony, Bavaria, Westphalia, Würtemberg, and Naples, the Viceroy of
Italy, the Queen of Holland, besides princes and dukes by the dozen.
Paris had become the capital of Continental Europe, and from Paris went
forth the law to eighty million people. All Frenchmen realized the
grandeur of this huge empire; but many a wise Frenchman was oppressed
by anxieties. What if the Emperor should suddenly die? Would the
succession go quietly to his brothers, or would the mighty fabric fall
to pieces? All this power, all this splendor, hung as by a single hair
upon the life of Napoleon; and there were others besides Talleyrand and
Fouché who speculated upon what should be done if the Emperor should
fall in battle. When the bullet struck his toe at Ratisbonne, the
troops broke ranks and crowded toward him in their breathless eagerness
to know whether he were seriously hurt; and the far-seeing said,
"Suppose the ball had struck two feet higher!" When it became known
that a young German fanatic, Staps, bent on assassinating the Emperor,
had almost reached him with his knife when stopped, the same uneasy
feeling prevailed. Too much depended on this one life. The Emperor had
no bodily heir; by Josephine he would never have one; the favorite
nephew, Hortense's son, the little Napoleon, might have been adopted,
but he died of croup in Holland.
* * * * *
His power in the north being now secure, it was expected that Napoleon
would take charge of the war in the south, and end it. He could easily
have done so. England had less than thirty thousand troops there,
and the native soldiers, Spaniards and Portuguese, could not have
stood against French veterans led by the greatest soldiers of all
time. Besides, he could have crushed resistance by the mere weight of
numbers. Why did he never return to Spain? Joseph was blundering as
stupidly as mortal could; the French commanders were not acting in
concert, but were pulling against each other; things were going as
badly as the English could reasonably expect; and nowhere in the Empire
was its Emperor needed worse than here. But Napoleon, once so quick
to rush to the point of danger, let the "Spanish ulcer" run, year in
and year out, with an apathy for which it is impossible to account.
Either he had grown fonder of his personal ease, or the dreary kind of
warfare necessary to reduce a national uprising did not appeal to his
imagination, or he feared that in his absence the north might again
give trouble, or he took an imperial pride in seeming to say to the
world that the insurrection in the south was too trifling a matter for
his personal attention and could be left to his lieutenants.
Whatever the motive, he astonished his enemies no less than his friends
by failing to follow up Wagram with the complete conquest of the
peninsula. Three hundred thousand French soldiers in Spain propped
feeble Joseph on his throne; but they were never able to put down
resistance or expel the English.
Another serious matter which might have been settled at this time was
his quarrel with the Pope.
The Concordat had accomplished great results for both contracting
parties, and at first both were highly satisfied. Napoleon complacently
rubbed his hands and declared, "With my soldiers, my prefects, and my
priests I can do as I like."
But, after all, the Concordat was a compromise. Neither party got quite
what was wanted. Napoleon expected that there would result a clergy
wholly dependent upon his will; a pope who would be a sort of clerical
lieutenant obeying imperial orders, content to move as a lesser light
in the Napoleonic system. The Pope, on the other hand, eagerly expected
a restoration, gradually, of the former spiritual prestige of the
Church. When Napoleon was seen to attend Mass, and kneel for blessing
or prayer, clerical fancy readily pictured the return of the good old
times when pious Bourbon kings and their official mistresses had fallen
on their knees at the feet of Jesuit confessors, and allowed the reins
of government to be pulled by the Church. Especially did the Pope look
for the restoration of his full temporal power, the return of the lost
legations in Italy.
Both parties found themselves in grievous error. Napoleon not only
believed he had done quite enough for the Church, but was inclined to
think he had done too much. At any rate, he flatly declined to do more.
He would not put priests in charge of the state schools; he would not
restore the legations. He was ready to lavish respectful attentions
upon the head of the Church, ready to aid him in restoring public
worship, ready to fill his coffers with cash; but in the Concordat, the
solemn contract already agreed on, he would make no change.
So the Pope had left Paris after the coronation in ill-humor. He
refused to crown Napoleon at Milan; refused to annul Jerome's marriage;
refused to recognize Joseph Bonaparte as King of Naples; refused to
close his ports to English commerce. Professing neutrality, he became
as much the enemy of France as he had been when an avowed member
of the European league against the Revolution. Enemies of Napoleon
flocked to Rome and found friendly welcome there. Fugitives from
French justice took refuge under papal immunity, and were protected.
The Roman court, as in the time of the Revolution, became a nucleus of
anti-French sentiment and intrigue. Papal animosity to the French did
not cool its ire when it saw him do in Spain what he had wished to do
in Italy--abolish the Inquisition. Napoleon complained, remonstrated,
threatened--all to no purpose. Meekly obstinate, piously implacable,
the Pope refused to come to terms, using God's name, of course, as a
sanction to his own line of conduct.
During the campaign of 1809 Napoleon proclaimed the abolition of the
temporal power of the Pope, and the papal territories were incorporated
in the kingdom of Italy. The Pope's spiritual powers were not
challenged: his revenues were largely increased. The Pope protested, as
usual, that the temporal power, lands, cities, rich revenues, were the
patrimony of St. Peter, of God, and that he, the Pope, had no right to
give them up. Napoleon, in effect, replied that what a French emperor
had given, a French emperor could take away; and that it ill became the
successor of Peter and the vicar of the homeless, moneyless Christ to
be making such eternal clamor about money, wealth, lands, and earthly
power and splendor. The situation at Rome, where French authorities
and papal authorities were in conflict, became so embarrassing that
the Pope was finally arrested, carried to Savona, and lodged in a
palace there. Later, he was transferred to the magnificent château of
Fontainebleau in France, where he was luxuriously lodged and treated as
a prince.
This complete rupture between Napoleon and the Church might never have
been more than an annoyance, a crab nibbling at the toe of Hercules,
had Napoleon continued fortunate. But when disasters thickened, and his
powers began to totter, the papal legions were not the weakest of those
who assaulted his wavering lines.
Well had it been for France had Napoleon, in 1810, given personal
attention to the Spanish war; equally well had he come to some terms
with the Pope, who had excommunicated him. The longer each trouble was
neglected, the more difficult its treatment became.
* * * * *
Napoleon would not go to Spain, he would not settle his differences
with the Pope; but he made up his mind to bring to an issue another
long-deferred and vitally important matter--that of divorcing Josephine.
The Emperor must have an heir, the question of succession must not be
left open longer: political necessity was inexorable: ambition would
tolerate no obstacle.
Great as a man may become, he is human after all; and Napoleon flinched
from saying the fateful word to Josephine. From time to time he shrank
from the pitiful task, and the way in which he led up to it is full of
the pathos which sometimes lies in small things. Whenever Napoleon
was at home, it was the custom for a page to bring in coffee for the
Emperor after dinner. Every day Josephine herself would take the
tray, pour the coffee, sweeten it, cool it, taste it, and hand it to
Napoleon. Years had come and gone, and the little domestic custom had
become as fixed as the relation of man and wife.
At length came the day of days for them both, the dismal evening upon
which Napoleon had resolved to speak. He was gloomy and sad; she
was red-eyed with weeping, wretched, waiting the word she dreaded
and expected. Dinner was served, but neither ate, neither spoke.
The Emperor rose from the table, she followed "with slow steps, her
handkerchief over her mouth, as if to stifle her sobs." The page came
with the coffee, offering the tray to the Empress, as he had always
done. But Napoleon, looking steadily at Josephine, took the tray,
poured the coffee, sweetened it, and drank; and Josephine knew that
they had reached the parting of the ways. The tray was handed back to
the page, the attendants withdrew at a sign from the master, Napoleon
closed the door, and then with face as cold and sad as death he spoke
of the divorce.
Constant, the valet, dreading "some terrible event," had sat down
outside by the door. He heard shrieks, and rushed forward. The Emperor
opened the door, the Empress was on the floor, "weeping and crying
enough to break one's heart." They lifted her and bore her to her room,
Napoleon assisting. There were tears in his eyes, and his voice was
broken and trembling. It was a bitter night to them both, and Napoleon
visited her room several times to inquire after her condition. He did
not sleep; he did not utter a word to his attendants. "I have never
seen him," writes Constant, "in such affliction."
But his resolution stood, and on December 16, 1809, the divorce was
formally pronounced. There was a final heart-breaking interview in
Napoleon's bedchamber, to which the stricken wife had come to say
good-by; there were sobs and tears and tender, regretful words; then
Josephine, weeping, went back to her room, leaving Napoleon "silent as
the grave, and so buried in his bed that it was impossible for one to
see his face."
The ex-Empress's humiliation was softened in every manner possible.
She was regally endowed with pensions and estates; she was treated
with the most delicate respect; the friendship between herself and
Napoleon remained uninterrupted; he delighted to do her honor; and her
place in the Empire remained one of dignity and grandeur. Once the
Emperor, returning from the chase with the kings of Bavaria, Baden,
and Würtemberg, stopped at Malmaison to pay the ex-Empress a visit,
and spent an hour in the château with her while the three little kings
waited and lunched at her gate.
* * * * *
Napoleon's first thought was to wed a sister of the Czar of Russia,
and proposals to that effect were made. The mother of the princess,
however, was bitterly opposed to Napoleon, and alleged that her
daughter was too young. Alexander, greatly embarrassed, asked for time.
To the impatient Emperor of the French this evasion seemed to cover a
refusal, and he would not grant the delay. In the meantime the Austrian
Cabinet, dreading the increased strength which such a marriage would
give to the Franco-Russian alliance, let it be known to Napoleon that
if he asked for the daughter of the Emperor Francis, she would be
promptly delivered. Irritated by the hesitation of the Romanoffs, and
flattered by the advances of the Hapsburgs, Napoleon put his foot upon
the "abyss covered with flowers." On March 11, 1810, he was married
by proxy to Maria Louisa in Vienna, and the bride set out at once for
Paris. "Take as your standpoint that children are wanted," Napoleon had
frankly written to his negotiator at St. Petersburg: and the Austrian
princess understood the situation thoroughly. After a triumphal
progress through the provinces of the Empire, she reached the French
frontier, was formally received, her clothing all changed, her Austrian
attendants relieved, and France, taking her precious person in custody,
reclothed her, surrounded her with a fresh lot of attendants, and
hastened with her in the direction of Compiègne, where by appointment
she was to meet her imperial spouse. Napoleon had himself dictated, to
the minutest detail, every movement of the bridal party, and he awaited
its coming with the utmost impatience, "cursing the ceremonial and the
fêtes which delayed the arrival of his young bride."
At length when Maria was within ten leagues of Soissons, Napoleon broke
from all restraint.
At the top of his voice he shouted to his valet: "Heigho, Constant!
Order a carriage without livery, and come and dress me!"
He bathed, he perfumed, he dressed, laughing all the time like a boy
at the effect which the surprise he was planning would produce on his
bride. Over his uniform he drew the gray overcoat he had worn at
Wagram; and calling Murat to go with him, he secretly left the park
of Compiègne, entered the plain carriage, and dashed along the road
beyond Soissons. The rain was pouring down when he and Murat reached
Courcelles, where they left the carriage and stood in the porch of
the church for the bridal train to come up. Signing to the postilions
to stop, Napoleon had intended to reach Maria Louisa unannounced; but
the equerry, recognizing him, let down the step and called out, "His
Majesty!"
"Didn't you see that I signed you to be silent?" exclaimed Napoleon,
in a pet. But his ill-humor vanished at once, he hastened into the
carriage, and flung his arms around the neck of his bride, who, nicely
tutored, was all graceful submission, and who, looking from his face
to his portrait which she held in her hand, remembered to say, "Your
portrait does not flatter you."
Napoleon was in ecstasies. He was a boy again, amorous, rapturous,
seeing everything with the eyes of a lover. Soissons had prepared a
magnificent reception and banquet, but Napoleon could not think of
tarrying. He must hasten on to Compiègne with the blushing Maria that
very night. "He made love like a hussar!" some have sneered. So he did,
and most men who are not invalids or frigid decadents make love like
hussars. Furthermore, most women who are young, healthy, and sane, have
a stealthy preference for the hussar style of love-making.
Etiquette had prepared a bed for Maria at the Chancellor's, and one for
Napoleon at the palace. Etiquette insisted that this separation was
decorous, was most essential, was demanded by precedent and custom.
"Not so," maintained Napoleon; "Henry IV. breached the custom, and so
will I."
Had not the marriage already taken place in Vienna? If that ceremony,
solemnized by the Archbishop of Vienna was valid, were not Napoleon
and Maria man and wife? Why, then, separate apartments? He decided
that a husband's rights were already his, and Maria made no strenuous
objection,--so well had she been tutored in Vienna. Read what the
imperial _valet-de-chambre_, Constant, writes:--
"The next morning at his toilet the Emperor asked me if any one had
noticed his change of the programme." Constant lied, like a good
servant, and "I told him, no." At that moment entered one of the
Emperor's intimates who was unmarried. Pinching his ears, his Majesty
said to him: "Marry a German, my dear fellow. They are the best women
in the world: gentle, good, artless and as fresh as roses." And
Constant states that Napoleon "was charmingly gay all the remainder of
the day."
With imperial pomp the civil and religious marriage was solemnized
at St. Cloud and Paris, April 1 and 2, 1810. The illuminations, the
processions, the festivities, were gorgeous beyond description. After
these were ended, there was a grand tour of the provinces by the
imperial couple. Returning to Paris, the Austrian ambassador, Prince
Schwarzenberg, tendered them the magnificent fête during which the
tapestries in the vast temporary ballroom caught on fire, the building
burned to the ground, and some of the revellers met fiery death.
[Illustration: MARIA LOUISA
From the portrait by Gérard in the Louvre]
As to Maria Louisa it may be said, once for all, that she was a
commonplace woman, with no talent, no character, no graces of manner,
and no beauty. She was strong, healthy, physically fresh and buxom,
therefore admirably suited to Napoleon's immediate purpose. She was
never a companion to him, never had any influence over him, never had
any love for him, never understood or appreciated him. Dull, indolent,
sensual, capable of no warm attachment, she simply yielded to her
father's policy, married where she was told to marry, obeyed Napoleon
as she was told to obey him, accepted his caresses, ate four or five
times per day, bore him a child, pleaded her health against the bearing
of more, gave herself little concern about his reverses, left him when
her father called for her to leave him, took up with another man whom
her father selected, lived with him in much contentment, and bore him
several children.
* * * * *
Increasingly heavy became to Napoleon the burden of his family. Joseph
in Spain required huge armies and huge subsidies to uphold him there,
and his correspondence with his brother was one long, lugubrious
howl for "more." Jerome's reckless dissipations and extravagance in
Westphalia scandalized Germany, bringing reproach upon the Empire.
Lucien contributed his share of mischief by encouraging the ill-temper
of the Pope. Pauline, Caroline, Elisa were so many thorns in the flesh,
so many annoyances more or less acute. Brother-in-law Murat, by his
pride and boasting and complaints, disgusted friends of the Emperor,
arousing jealousies among old comrades who had not been made kings.
Mother Letitia, like the mother of Washington, complained that the
illustrious son had not done enough for the author of his being. Uncle
Fesch, now a cardinal, had absorbed all the essence of his clerical
order, and maddened his nephew by opposition in the quarrel with Rome.
And to cap a climax and advertise family feuds to the world, Louis
Bonaparte vacated the throne of Holland, left the country privately,
and went, almost as a fugitive, to "drink the waters" at Teplitz in
Bohemia. For some days it was not even known what had become of him.
The Emperor's grief, anger, and mortification were extreme. Stunned by
the blow dealt him by his brother, he said in broken voice: "To think
that Louis should make me this return! When I was a poor lieutenant of
artillery, I divided my slender pay with him, fed him, taught him as
though he were my son." And this cross-grained, thankless Louis had
brought shame upon Emperor and Empire! Why? Because the brother who had
put the sceptre in his hand wished him to rule Holland as a province
of the Empire, in line with the policy of the Empire, sharing all the
benefits of the Empire, and sharing likewise its burdens! Because
Napoleon would not consent that Holland should violate the Continental
system, and become practically the ally of England in the great
struggle for national supremacy, Louis had dropped the crown and gone
away to drink mineral water in Bohemia.
A very aggravating mortal must have been this Louis, on general
principles. Yielding to his brother's influence, he had wedded
Hortense, the daughter of Josephine. There was no love prior to this
marriage, and none afterward. Despite Napoleon's repeated, patient
efforts, the two could never harmonize. With or without reason, Louis
suspected the virtue of his wife. Ugly rumor reported that the first
child of Hortense was not begotten by Louis, but by Napoleon. The
younger brother may not have believed the story, but the fondness of
the childless elder brother for the son of the younger, attracted
attention and excited remark. The child was a promising boy; he was
named after his uncle Napoleon, and he was devotedly fond of this
uncle. The little fellow would come into Napoleon's room, put on the
Emperor's hat, catch up his sword, put the belt over his shoulders,
and, whistling a military air, go marching about in military style,
with the sword dragging along on the floor. And Napoleon would be
thrown into ecstasy, and would cry out, rubbing his hands: "Look at
him! See the pretty picture!"
His love for the boy growing with the boy's growth, Napoleon had
offered to make him King of Italy, preparatory, doubtless, to adopting
him as heir to the Empire. Louis would not hear of it. Put his son
above _him_? Give his child a throne, when he himself had none? Never
in the world! So he objected flatly, saying to his brother with
unparalleled impudence, "Such a favor from you to this child would
revive the rumors that you are his father."
Is it any wonder that Napoleon's temper escaped control, and that he
caught Louis about the body and flung him out at the door?
The little Napoleon had died, Hortense had separated from her
impossible spouse, and was going a rapid pace of her own, with a
certain Duc de Flahaut, famous for his shapely legs,--so much so that
they wrung from the Emperor an exclamation on the subject of Flahaut
and "his eternal legs." Holland's throne was vacant: what was Napoleon
to do? Give it to some one else who would be as ungrateful as Louis
had been? Abandon it entirely, and see England get a foothold there?
To escape the dilemma, Holland was annexed to the Empire (July, 1810).
* * * * *
The royal line of Sweden was about to become extinct. It became
necessary to provide for the succession. The Swedes decided to choose
a Crown Prince from among the illustrious Frenchmen who stood around
Napoleon's throne. They wished to win Napoleon's good-will and
protection by selecting one of his favorites, and they were made to
believe that they could not please him better than by the choice of
Bernadotte.
Were not this a matter so gravely serious, it would be comical to the
last degree. The marshal whom Napoleon most detested and distrusted
was Bernadotte. The marshal who most envied the Emperor, most hated
him, most longed to betray him, was Bernadotte. He had plotted against
his chief during the Consulate, and escaped court-martial because he
and Joseph Bonaparte had married sisters. He had left Davoust in the
lurch at Auerstädt, imperilled the army, coldly leaving thirty thousand
French to combat sixty thousand Prussians, without lifting a hand to
help the French. Again he had escaped; he was a member of the Bonaparte
family.
At Wagram his conduct had been so darkly suspicious, his proclamation
claiming a victory where he had failed miserably to do his duty, had
been so insolent, that Napoleon ordered him home in disgrace. But again
family influence prevailed, and he was made Governor of Rome.
The Swedes had not kept the run of these events, and when Bernadotte's
agents plied them with the argument that he was a member of the
Bonaparte family, and a favorite with the Emperor, there were none to
deny. Napoleon knew what was going on. He alone could have set the
Swedes right, and nipped the intrigue in the bud. Why did he not do
so? Absolutely no satisfactory answer can be given. A word from him
would have made some other man Prince Royal of Sweden, but he would
not speak. With apathetic scorn he looked on while Bernadotte worked
the wires, feeling all the while that Bernadotte's success would be
a misfortune to France. He not only refused to interfere, not only
refused to correct the false representations upon which the Swedes
acted, but gave his formal consent when it was asked, and furnished
Bernadotte with $400,000 to equip himself in a suitable way in setting
out to take possession of his new dignity.
* * * * *
Some months after Napoleon's second marriage, he and the Empress stood
sponsors at the baptism of several infants of his great officers. When
the baptismal ceremony had been finished, the Emperor turned to some of
his intimate friends and said rubbing his hands together as he did when
well pleased, "Before long, gentlemen, I hope we shall have another
baby to baptize."
This joyful intelligence gradually spreading, the whole French nation
began to look forward with a feeling of hope and satisfaction to the
birth of Napoleon's heir.
On March 19, 1811, the Empress felt the first pains, and "the palace
was in a flutter." Next morning early the crisis came. Napoleon
sprang out of his bath, and covered with a dressing-gown hastened
to his wife's room, saying to the excited doctor in charge, "Come,
now, Dubois, don't lose your head." He embraced the suffering Empress
tenderly, but, unable to endure the sight of her anguish, went to
another room, where he stood, pale and trembling, awaiting the event.
When the physician reported that an operation might be necessary, and
that one or the other, mother or child, might have to be sacrificed
Napoleon answered, without hesitation, "Save the mother, it is her
right."
To calm them, he said: "Forget that you are operating upon an Empress.
Treat her as though she were some shopkeeper's wife."
At length the cruel ordeal was over, the child safely delivered, and
the mother relieved. The Emperor sprang to her couch and covered
her with caresses. He was overwhelmed with joy; his face shone with
delight. "Well, Constant, we have a big boy!" he cried to his valet;
and to all others as he met them he continued to repeat rapturously,
"We have a big boy!" Very, very human was this "Corsican ogre,"
Napoleon Bonaparte.
If words and looks go for evidence, the warrior of Austerlitz, the
giver of crowns and kingdoms, was never so happy as when he took
his son in his arms, kissed it tenderly, and holding it toward his
courtiers, said proudly, "Gentlemen, the King of Rome!"
All Paris listened, eagerly attentive, to the great bells of Notre
Dame; steeple answered steeple, until every church had joined in
the chorus. All Paris hearkened to the cannon, counting report
after report: for if the child were a girl, the shots would stop at
twenty-one; if a boy, there would be one hundred. At the sound of
the twenty-second gun there burst out a universal shout of joy and
congratulation. "Hats flew up into the air, people ran to meet entire
strangers, and with mutual embraces shouted, _Long live the Emperor!_
Old soldiers shed tears of joy."
Behind a curtain at the window of the palace stood Napoleon, looking
out upon this display of enthusiastic gladness. "His eyes swam with
tears, and he came in that condition to kiss his son."
Never were national rejoicings greater at the birth of an heir to
the throne. Cities, towns, private dwellings, illuminated not only
in France, but throughout the Empire. Couriers rode with the news to
foreign courts. Congratulations poured into the Tuileries from the four
quarters of the earth. The Emperor seemed to be "walking in the midst
of a delicious dream." He was the mightiest monarch of earth; his wife
"a daughter of the Cæsars"; his son, his long-yearned-for son, had
come, was strong and fair,--the "King of Rome!" Napoleon's imagination
was aflame; human grandeur he had pushed to its limit.
His memory may have swept back to far-off Corsica, and to that day
of 1769 when his mother had brought him into the world, lying on the
floor "upon a wretched rug." From that dim period to this, what a march
onward!
If Napoleon had been kind and indulgent to the barren Josephine, what
was his tenderness to the fruitful Maria! He almost smothered her with
caresses, and almost, if not quite, wearied her with attentions. As
to his boy, nothing could have been more touching than his boundless
pride in him, his infinite patience with him, his intense paternal
fondness for him.
Nothing would satisfy the Emperor but that Josephine must see his
boy. Maria must not know; Maria being jealous of the ex-Empress.
One day Napoleon had his child carried privately out to Bagatelle.
Josephine was there. The little King of Rome was presented to her.
Was she envious and jealous? Not so. She took the child in her arms,
pressed it, kissed it, wept over it, prattled "baby talk" to it,
fondling it with "unutterable tenderness" as though it were her own.
Poor Josephine! Sternly truthful historians have told us about the
infidelities and the want of honesty and scruple. With pain and sorrow
we must tell the story of these as it is told to us; but let us turn
the picture as quickly as we may, and look upon the other side--for
there is another and a brighter.
It was true womanhood at its best when the barren, discarded wife
continued to love the husband who had put her away; who loved and
fondled the offspring of the other marriage with a greater tenderness
than the child's own mother ever showed it; who remained faithful to
Napoleon in the dark days when the second wife was false; who grieved
brokenly over his fall, and wished to share his exile.
Evermore will this record speak for Josephine; evermore will it speak
for Napoleon also.
Constant relates: "One day when Bonaparte came back very much fatigued
from hunting, he sent to ask Maria Louisa to come and see him. She
came. The Emperor took her in his arms and gave her a hearty kiss on
the cheek. Maria took her handkerchief and wiped it off.
"'Well, Louise,' said the Emperor, 'so I disgust thee?'
"'No,' replied the Empress, 'I have a habit of wiping myself like that.
I do the same with the King of Rome.' The Emperor seemed dissatisfied."
A wife and mother wiping off the kisses of husband and child reveals
her own character so fully by the act that comment is unnecessary.
CHAPTER XXXV
"My taskmaster has no bowels; it is the nature of things." This remark,
made by Napoleon long prior to the divorce, was now to be verified with
results calamitous to Europe and to himself. The war of 1812 was one
for which he had no enthusiasm, and into which he was drawn by almost
irresistible circumstances. To Metternich he said, "I shall have war
with Russia on grounds which lie beyond human possibilities, because
they are rooted in the case itself."
The French Emperor felt himself committed to his Continental system.
His pride, his pledge, his self-preservation, were at stake. As long as
England could make war upon him, and league against him the kings and
cabinets of the Continent, his empire would never be secure. He might
weather the storm for his own life; but the same endless antagonism,
the same implacable hatred, would pursue his successor. To steady his
throne, he must have peace with Great Britain: this peace he could not
get till he conquered it; having no navy, he could only "conquer the
sea on the land," and his only hope of doing this was to make good the
Continental boycott against English manufactures. If he could close all
Continental ports to British goods, he would starve England into peace.
But as long as Continental ports were but partially closed, his policy
would be a failure. Command of the seaboard was his great aim, hence
the invasion of Spain and Portugal, the annexation of Holland, the
Illyrian provinces, and the Duchy of Oldenberg.
The motive of Napoleon in granting Alexander such liberal terms
at Tilsit was to get another adherent to the Continental system.
The Czar took the benefits of the treaty and shirked its burdens.
His coöperation with Napoleon in the war of 1809 was nothing less
than a mockery, and when the Russian landlords clamored against the
Continental system, Alexander began to relax it. When the Emperor
complained of this violation of the treaty, the Czar retorted that
Napoleon himself did not enforce his system, that he licensed
violations of it--a retort in which there was truth enough to sting.
By a vast system of smuggling, misuse of the neutral flag, and the
forging of neutral papers, English goods continued to pour into the
Continent. Unless Napoleon could put a stop to this, he might as well
give up the contest. In October, 1810, he wrote to the Czar urging
him to seize these so-called neutral ships, alleging that they were
English. "Whatever papers they carry, your Majesty may be sure they are
English." It is now admitted that this statement of the Emperor was
substantially correct. The Czar refused, and, to make his refusal the
more galling, he issued a ukase, allowing the admission of colonial
goods while it virtually prohibited French wines and silks. A plainer
declaration of commercial war he could not have made. That it would
lead to a clash of arms, he must have known. At any rate the Czar's
entire line of conduct from 1810 was that of a monarch preparing for
a great war. It was in 1810 he sounded the Poles, seeking to know
whether they would side with Russia in a contest with Napoleon. His
armies were increased, his fortresses strengthened, and he made secret
approaches to England and to Austria.
In addition to the Continental system there were other grievances.
Napoleon had added Galicia to the Grand Duchy of Warsaw, after the
Treaty of Vienna in 1809, in violation of his agreement with the
Czar. He had taken possession of Oldenberg, whose Duke had married a
sister of the Czar. In each of these cases the Emperor had offered
explanations, and he had offered an equivalent in Germany for
Oldenberg; but the transactions themselves rankled in the Russian
memory--although she had really no right to object to Napoleon's
treatment of Oldenberg which was a member of his Confederation of the
Rhine; and although she had accepted at his hands a valuable increase
of territory as the price of her lukewarm support in the war of 1809.
In the matter of the marriage, there had been irritation, Napoleon
suspecting that Alexander meant to procrastinate and then refuse, while
the Czar believed that the Emperor was wooing two princesses at the
same time, and coolly balancing the Russian against the Austrian. This
was not the truth, but was near it. A Napoleonic family council had
debated the two alliances, upon the assumption that the Emperor could
choose either, and had decided in favor of the Hapsburg. Alexander,
the Romanoff, therefore felt insulted. In fact, after this second
marriage of Napoleon, the Czar had believed that war was inevitable.
Nevertheless, the fault even here was with the Czar. Napoleon had asked
for his sister, and was entitled to a positive answer. Indefinite
adjournment, without a promise, was, to a man in Napoleon's position,
a polite way of refusing.
Still there was no rupture. Diplomatic relations were strained, war
began to be talked of, preparations got under way, but diplomacy yet
hoped to solve the problem. The final quarrel seems to have taken place
over the wording of a new treaty. Alexander wanted Napoleon to say that
"Poland shall never be restored." How could the Emperor guarantee such
a thing? He was not Destiny. He could not foresee what might be done
by others and by Time. He was willing to promise that _he_ would never
restore Poland, nor aid in its restoration. He wrote this promise in
the strongest terms. The Czar struck out the amendment, rewrote the
original, "Poland shall never be restored," and demanded Napoleon's
signature.
Was this an affront, or not? There the case, so far as the actual
rupture goes, rests. Napoleon considered it a humiliation to sign such
an indefinite, peremptory guarantee; he thought it an insult for the
Czar to show so plainly that he doubted his word.
England, of course, was buzzing at the Russian ear all this while.
Her agents moved heaven and earth to make the "two bullies" fight. No
matter which was worsted, Great Britain would be the gainer. She feared
France on the Continent, Russia on the Indian frontier. A duel between
these colossal powers would exhaust both, leaving England all the
stronger by comparison.
Russia and Turkey were at war on the Danube. The Christians were doing
their utmost to relieve the heathen of several thousand square miles of
land. England exerted herself to bring about peace between Turk and
Russian, in order that the Czar might not have a war in his rear as
Napoleon had in Spain.
It is said that a forged letter, in which Napoleon was made to state
that he agreed to a partition of Turkey, was shown at Constantinople.
The Turk had his suspicions of this letter; but an Englishman swore
that he recognized Napoleon's writing. By some strange neglect, France
had no ambassador in Turkey at this critical moment. Andréossy had been
appointed, had set out, but had waited at Laybach for his credentials.
When they at length arrived, and he proceeded to Constantinople, it was
too late.
Before any declaration of war, and while diplomatic relations were
still maintained by the two governments, the Czar sent an agent to
Paris to pose as envoy and to work as spy. This man, Czernischeff,
bribed a clerk in the French war office to steal a complete statement
of the French forces, dispositions, equipments, etc. The clerk was
shot; the noble Russian escaped by sudden, secret, and rapid flight.
At practically the same time, Napoleon was equally well served at St.
Petersburg by a spy who stole the "states" of the Russian armies, and
the plates from which the great maps of Russia were printed. From
these plates Napoleon furnished his generals with maps for the Russian
campaign.
Napoleon fully realized the nature of the task he had before him in
a contest with Russia. To defend himself in Italy, Germany, or even
Poland against the Czar was one thing; to invade that vast empire with
the purpose of seizing its capital and compelling it to sign such
treaties as he had imposed upon Austria and Prussia, was another task
altogether--a task colossal, if not appalling. No one knew this better
than Napoleon, and his preparations were made on a scale such as Europe
had never seen.
In advance of the work of the soldier came that of the diplomat. Both
Russia and France sought alliances. Great Britain was, of course,
heartily with the Czar. Sweden, controlled by Bernadotte, took the same
side. He had demanded, as the price of his alliance, that Napoleon give
him Norway, thus despoiling the Danes. The Emperor refused, but offered
Finland, which Russia had seized. The Czar promised Norway, and thus
the Frenchman, Bernadotte, who probably had not yet spent all the money
Napoleon had supplied him with when he went to Sweden, pledged his
support to the enemies of France. For all practical purposes, Russia
likewise made an ally of Turkey. So utterly improbable did it seem that
Turkey would make peace with its hereditary enemy at the very moment
when it had the best opportunity fate had ever offered in all the long
struggle, that Napoleon had not even calculated upon such an event. It
took him completely by surprise.
Turkish recollections of Tilsit and Erfurth, Turkish fears of other
bargains of the same sort, and Turkish dread of an English bombardment
of Constantinople, which was threatened, brought about the unlooked-for
treaty which gave Russia an army to throw upon Napoleon's flank.
In addition to these advantages the Czar had another, and of vast
importance--the war in Spain. Three hundred thousand French troops were
held in the peninsula, and scores of the best officers the Empire could
boast.
To Alexander it must have seemed that it would indeed be a miracle if
Napoleon could sustain two such immense contests so far apart, one at
the extreme south the other in the extreme north. Even Napoleon had
appeared to grow weary of his huge tasks, and had been heard to say,
"The bow is overbent."
But in getting ready for the contest he certainly accomplished
wonders. So imposing were his armaments that Austria and Prussia both
believed he would succeed, and they cast in their lot with the French.
Each agreed to furnish contingents: the Emperor Francis assured his
son-in-law that he might "fully rely upon Austria for the triumph of
the common cause," and the King of Prussia pledged his "unswerving
fidelity." Upon these broken reeds the astute Emperor did not, in all
probability, intend to lean very heavily. Events were soon to prove
that they would bear no weight at all.
Before putting himself at the head of his army, Napoleon held a grand
assemblage of his allies at Dresden (May, 1812). It was the most
imposing, as it was the last, of the Napoleonic pageants, wherein
vassal princes gathered about him and did him homage. Accompanied by
the Empress Maria Louisa, he left St. Cloud May 9, reached Mayence
on the 14th, and from thence made a triumphal progress to the Saxon
capital. Princes of the Confederation of the Rhine hastened to receive
their suzerain; "many even came to wait for them on the road, amongst
others the King of Würtemberg and the Grand Duke of Baden." The King
and Queen of Saxony came forth from Dresden to meet them; and a
torchlight procession escorted them into the city. On the morrow came
the Emperor and Empress of Austria, and the archdukes; following these
came the King and Crown Prince of Prussia, the Queen of Westphalia,
and scores of princes, noblemen, and dignitaries. "The splendor of the
Court," says an eye-witness, "gave Napoleon the air of some legendary
Grand Mogul. As at Tilsit, he showered magnificent presents on all
sides. At his levees, reigning princes danced attendance for hours in
the hope of being honored with an audience. Every country sent its
contingent. There were no eyes but for Napoleon. The populace gathered
in crowds outside the palaces, following his every movement, and
dogging his progress through the streets, in hourly expectation of some
great event."
The Crown Prince of Prussia begged for the privilege of serving on
the Emperor's staff, and was denied. Napoleon doubtless thought the
campaign before him was risky enough without the presence of a possible
spy in his military family.
Napoleon was no longer the man he had been in his earlier campaigns. He
had grown fat, subject to fits of lassitude, and to a painful disease,
dysuria. His plans were as fine as ever, but the execution was nothing
like what it had been. He no longer gave such personal attention to
detail; irresolution sometimes paralyzed his combinations.
Nor were his generals up to their former standard. He had made them
too rich. They had pampered themselves and grown lazy. They had no
stomach for the Russian war, joined their commands reluctantly, and
worked without zeal. Neither was the army to be compared to those of
Austerlitz, Jena, and Wagram. In his host of six hundred thousand,
there were but two hundred thousand Frenchmen, the remainder being
composed of Germans from the Confederation of the Rhine, Prussians,
Austrians, Italians, Poles, Swiss, Dutch, and even Spaniards and
Portuguese. In such a motley array there could be no cohesion, no
strength of common purpose which could stand a serious strain. Even the
French soldiers, splendid as they undoubtedly were, were not animated
by the same spirit as formerly. The causes of the war were beyond their
grasp, even the generals felt that the Continental system was not worth
fighting about. England, on the verge of commercial ruin, might know
better: Napoleon certainly knew better; but to the average Frenchman
the grievances on both sides were too vague and abstract to justify so
huge a conflict.
No declaration of war had been published, neither Czar nor Emperor
had yet fully committed himself, and hopes were entertained that even
yet terms might be arranged. But when the travel-stained carriage of
Count Narbonne rolled into Dresden, and he announced that Alexander had
refused to make any change in his attitude, it became with Napoleon a
question of back down or fight. The Czar was determined not to begin
the war; he was equally determined not to keep the contract made at
Tilsit. Just as England had held Malta after pledging herself to give
it up, Russia was resolved to repudiate and oppose the Continental
system which she had promised to support.
At St. Helena Napoleon said that he and Alexander were like two
bullies, each trying to frighten the other, and neither wishing to
fight. From the manner in which Napoleon continued to hesitate and to
send messengers, after all his preparations were complete, it would
seem that he, at least, had hoped to the last that an accommodation
might be reached. Narbonne's report put an end to doubt.
Either Alexander's breach of the Continental system must be borne, to
the ruin of Napoleon's whole policy, or there must be war. The Emperor
had gone too far to stop. What would the world say if, after having
made such gigantic preparations, he abandoned the enterprise without
having extorted a single concession? The very "nature of things" drove
him on, and, dismissing the Dresden conference, he put his host in
motion for the Niemen.
Says General Marbot: "When the sun rose on June 24 we witnessed a most
imposing spectacle. On the highest point near the left bank were seen
the Emperor's tents. Around them the <DW72>s of every hill, and the
valleys between, were gay with men and horses flashing with arms."
Amid strains of music from the military bands, the eagles were borne
forward, and, under the eye of the master, a quarter of a million
soldiers began to tramp over the bridges, shouting, "Live the Emperor!"
Soon Napoleon himself crossed the bridge, and galloped through the
forest at full speed on his Arab, as though it exhilarated him to be
upon Russian soil.
The Russians made no attempt to check the invaders. Deceived as to
Napoleon's plan of campaign, their armies were scattered, and soon
became involved in the gravest peril. Had it not been for the terrible
blunders of Jerome Bonaparte and Junot, the Russian force under Barclay
de Tolly must have been cut off and destroyed. Had this been done, it
might, like Ulm, have proved decisive. But Napoleon found it impossible
to perfect his combinations: the Russian armies escaped, united, and
the long campaign began.
Crops had failed in this part of Russia the year before, and the
land was scantily supplied with provisions. The troops of the Czar
laid waste the country as they retreated; hence the invaders almost
immediately began to suffer, for their commissariat could not sustain
so tremendous a burden as the feeding of the half million men and one
hundred thousand horses. The summer heat was stifling. Men and horses
sank under it. One writer gives us a picture of Napoleon himself,
stripped to his shirt and lying across a bed, panting and inert with
heat. Torrents of rain followed. The roads were cut up, becoming mere
sinks of mud. Desertions, straggling, mortalities, marauding, became
frightful, so much so that an officer who came up with reserves stated
that the route over which the Grand Army had passed looked like that
of a defeated foe. Ten thousand horses died for want of forage between
the Niemen and Wilna. After the floods came sultry weather again and
the suffocating dust of the roads. The hospitals were crowded with the
sick. Discipline was lax, movements slow and uncertain. There was a
babel of languages, growing confusion, quarrels among officers, and
much vacillation in the Emperor himself.
At Wilna the Polish question faced him again. Once more he temporized.
He had mortally offended the Czar by enlarging the Grand Duchy of
Warsaw, perpetually menacing Russia with a resurrected and vengeful
Poland. He now froze the ardor of the Poles by indefinitely postponing
the day of their deliverance. When he afterward realized how
tremendously effective a united Poland would have been in the death
struggle with the Czar, he must have inwardly cursed the bonds which
tied his hands--the alliances with Prussia and Austria. Very frankly,
very honorably, he told the Polish delegation that his engagements
with these two powers made it impossible for him to reëstablish their
national independence.
While at Wilna Napoleon received an envoy from the Czar, who proposed
that if the French would recross the Niemen, terms of peace might be
agreed on. Such an offer seemed to be altogether one-sided, giving
substantial advantages to Alexander, and assuring nothing to Napoleon.
Therefore it was rejected.
After having lingered at Wilna from June 28 to July 16, a loss of time
which Lord Wolseley thinks "it is impossible to explain away when we
remember how late it was in the year when he opened the campaign," the
Emperor marched upon Vitebsk. It was here that he learned that Russia
had come to terms with Sweden and Turkey.
It was at this place that, according to Ségur, the Emperor exclaimed,
"Here I am, and here I will stay," taking off his sword and throwing
it upon the table. He had pursued the Russians some distance beyond
the town, had failed to force them into a pitched battle, and had now
returned to headquarters. "I will stay here for the winter, complete my
army, give it a rest, and organize Poland. The campaign of 1812 is at
an end." Turning to the King of Naples, he continued: "Murat, the first
Russian campaign is over. We will plant our standards here. We will
intrench and quarter the troops. The year 1813 will see us in Moscow;
1814 in St. Petersburg--the war with Russia is one of three years!"
But he soon became irresolute. The thought of eight months of inaction,
with the Grand Army on the defensive, became unbearable. What would
the world say? "Europe will say, 'He stayed at Vitebsk because he
_dared_ not advance.' Am I to give Russia time to arm? How can we go
into winter quarters in July? Let us forestall the winter! Peace is at
Moscow. Why should we remain here eight months, idle and exposed to
treacherous intrigues in the rear, when we can reach our goal in twenty
days?"
He did not convince his marshals; they opposed the advance; but he
angrily swept their objections aside.
To Duroc he said he would go to Smolensk and there winter. Complaining
that his generals were sick of war, that he had made them too rich,
that they could think of nothing but the pleasures of the chase on
their estates, and the display of themselves in fine carriages in
Paris, he ordered the advance upon Smolensk. Once more he failed to
secure his much-desired pitched battle. The Russians fought his advance
guard stubbornly, and inflicted heavy losses, but during the night they
continued their retreat. The French found Smolensk a heap of smoking
ruins; French shells and Russian patriots had fired it.
Much has been said about the alleged plan of Russia to lure Napoleon
into the country and to destroy him by starvation. The fact seems to
be that the Russians retreated because they could not help it. They
fought often and desperately. The Czar himself came to the army for the
express purpose of inspiring it to fight. Outnumbered and beaten, it
fell back, desolating the country as it went; but the plain facts show
that the Russians did all that was in their power to put a stop to the
invasion. The alleged campaign policy of "luring Napoleon to his doom"
is fiction.
At Smolensk, Napoleon was no more willing to stop than he had been at
Vitebsk. Peace was at Moscow; he must press on; he must beat the enemy
in a great pitched battle, and give his friend, the Czar, the excuse
to his people without which he would not dare to come to terms. Again
there were hot words between the Emperor and his marshals. Murat, in
great anger, predicted that if the army was forced on to Moscow, it
would be lost. But the order was imperative: "On to Moscow!"--and the
army marched.
The Czar, or those who controlled him, were dissatisfied with the
manner in which their side of the campaign had been conducted. There
had been too much retreat, and not enough fight. Kutusoff was put in
command with the understanding that he must give battle--a fact which,
of itself, would seem to dispose of the theory that Napoleon was
"lured" into the interior as a matter of policy.
At Borodino the Russians barred the road to "Mother Moscow": and here
the pitched battle was fought. With a cannonade that was heard for
eighty miles, a quarter of a million men here butchered each other all
day long on September 7, until seventy thousand lay dead or wounded.
Night ended the carnage, and next morning the Russians were again in
retreat.
During this famous battle, Napoleon remained sitting, or slowly
walking up and down at one place, where he received reports and sent
orders. He spoke but little, and seemed ill. In fact, he was a sick
man, suffering with a severe cold and with his bladder complaint. He
showed no activity, and left the battle to his marshals. At three in
the afternoon the Russians had put in their last reserves, and were in
distress everywhere--driven from their intrenchment, and threatened
with ruin should the French reserves now attack. Ney, Murat, Davoust,
all clamored for the Guard, the Emperor's reserve. He hesitated. They
sent again, and still he wavered. "Sire!" said Bessières, commander
of the Guard, "remember that you are eight hundred leagues from your
capital." Napoleon refused the Guard. Ney was amazed, furious: "What
does this mean? What is the Emperor doing in the rear? If he is tired
of fighting, let him go back to his d--d Tuileries, and leave us to do
what is necessary!"
Thus the Guard never fired a shot, the battle remained unfinished,
and the Russians retired in good order, when they might have been
destroyed. Military critics say that the Emperor made two capital
blunders at Borodino: first, in vetoing Davoust's offer to turn the
Russian flank and come upon their rear; and, second, in not using his
reserves.
That night the Emperor tried to dictate orders, but could not. He was
too hoarse to talk. He was obliged to write; and he fell to it, writing
rapidly, and throwing the scraps of paper on the table. Secretaries
deciphered these scrawls slowly, and copied them, as fast as they
could. As the papers accumulated, Napoleon would rap on his table for
the secretaries to remove them. For twelve hours he labored, not a
sound to be heard save the scratching of Napoleon's pen and the rapping
of his hammer.
The French continued their march onward, and at last neared Moscow.
Napoleon left his carriage, mounted his horse, and rode forward. "In
the distance could be seen the long columns of Russian cavalry retiring
in good order before the French troops." The French marched on,
and at last Moscow was in sight. It was a proud moment for Napoleon
when he stood on Pilgrim's Hill, surrounded by a brilliant staff,
and gazed upon the towers, the golden domes of the vast city, while
his lieutenants and his troops shouted, in wild enthusiasm, "Moscow!
Moscow!"
The Emperor was heard to mutter, "It was time." Apparently his greatest
enterprise had been crowned with success. His long triumphant march
toward Asia would rank with Alexander's. Russia would now sue for
peace, terms would be easily arranged, Continental unity would follow,
and England would find herself an island once more--not an empire.
But it was soon apparent that Moscow was not like Berlin or Vienna.
Here were no crowds of spectators to gaze upon the victors. The
streets were silent, empty. The houses were deserted. Here was a vast
city without citizens. The French were dumfounded. Napoleon refused
at first to believe: "the thing was preposterous." The conquerors
marched through the streets, the military bands playing, "To us is the
victory," but the vast solitude awed them as they marched.
The sight of the Kremlin, however, gave the conqueror a thrill of
exultation. "Here I am at last! Here I am in Moscow, in the ancient
palace of the Czars! in the Kremlin itself!"
Almost immediately, and in spite of all Napoleon could do, commenced
the wholesale pillage of the city. Discipline relaxed, and marauders
stormed the vacant houses on the hunt for loot. In the middle of the
night of the 16th of September, the sleeping Napoleon was roused and
brought running to the window of the Kremlin by the cry of "Fire!"
The flames, feeding on wooden houses and fanned by high winds, defied
control, and struck the conquerors with terror. As described by
Napoleon himself, at St. Helena, "It was the spectacle of a sea and
billows of fire, a sky and clouds of fire, mountains of red, rolling
fire, like immense ocean waves, alternately bursting forth and lifting
themselves to skies of fire, and then sinking into an ocean of fire
below. Oh, it was the grandest, sublimest, most terrible sight the
world ever saw!"
Russians say that the French burnt the city; the French say the
Russians did it. French officers allege most positively that Russian
incendiaries were caught in the act. It is certain that numbers of
persons so taken were shot, as a punishment. On the other hand, so
eminent a Russian as Tolstoï maintains that the carelessness of the
French soldiers was the cause of the fires. The Russians who had burned
Smolensk to deprive the French of its use, who made the line of their
retreat a desert to deprive the French of supplies, were probably the
burners of Moscow. They burnt it as they burnt Smolensk and every
village on their line of march, as a war measure which would injure the
invaders. The fact that Rostopchin, the mayor, had carried away all
appliances for putting out fires, would seem to be a conclusive piece
of circumstantial evidence.
This awful calamity, unexpected, unexampled, upset Napoleon's
calculations. To destroy a town like Smolensk was one thing, to make
of Moscow, one of the great cities of the world, an ocean of flame, a
desert of ashes, was quite another. It was appalling: it stupefied,
benumbed, bewildered Napoleon as no event in his career had done. He
realized the frightful extent of the disaster, and saw himself hurled
from the pinnacle to the abyss.
Indecision had already made sad havoc in the campaign: indecision now
completed the ruin. Napoleon had loitered at Wilna eighteen days;
had halted sixteen days at Vitebsk. He had hesitated at Borodino,
practically leaving the battle to his marshals, refusing them the
reserves. Now at Moscow, he dawdled for five weeks, when every day
brought nearer the march of two enemies that hitherto had not hindered
him,--the Russian army, from the Danube, and _Winter!_
At the Kremlin was the most wretched man in existence. The Emperor had
reached his Moscow only to find it a prison. Inexorable conditions shut
him in with unpitying grip. He could not rest, could not sleep, would
not talk, lingered long at table, lolled for hours on a sofa,--in his
hand a novel which he did not read. He, the profoundest of calculators,
who had from boyhood calculated everything, had for once miscalculated
in everything. He had misjudged his friends and his foes; had erred
as to the Russian temper; had fatally misconceived the character of
the Czar. He knew Alexander to be weak, vain, vacillating; he did not
allow for the strength which strong advisers like Stein and Sir Robert
Wilson and dozens of others might give to this wavering monarch. He had
calculated upon finding peace at Moscow, and had not found it. He had
felt assured that, at the worst, Moscow would furnish abundant food
and excellent winter quarters. It did neither. At fault in so many
matters of vital concern, the Emperor was a prey to the most gloomy
reflections. He set up a theatre for his troops, but did not attend it.
He rode daily through the streets on his little white Arab, but spoke
to no one. Sometimes in the evening he would play a game of cards with
Duroc. There were a few concerts at the palace; some singing by Italian
artists, some piano music; but the Emperor listened moodily, "with
heavy heart." He held his reviews, distributed rewards, but looked pale
and stern, saying almost nothing. He duped himself with hopes of peace.
He sent envoys and letters to Alexander--envoys who were not received,
letters which were not answered. With an obstinacy which was fatal,
he refused to see the truth of his situation. A lethargy, a failure
of power to decide, mastered him. Even a light fall of snow was not
warning sufficient to rouse him.
"At the Kremlin," says Constant, "the days were long and tedious." The
Emperor was waiting for the Czar's answer, which never came. His morbid
irritability was stirred by the great flocks of crows and jackdaws that
hovered about the city. "My God," he cried, "do they mean to follow us
everywhere!"
On October 3 he summoned a council of his marshals and proposed to
march upon St. Petersburg. His officers listened coldly, and opposed
him.
In a sort of desperation he then sent Lauriston to Kutusoff to ask for
an interview with Alexander, saying to his envoy: "I want peace; you
hear me. Get me peace. But save my honor if you can!"
The wily Kutusoff humored Lauriston, and Lauriston, in turn, nursed the
infatuation of the Emperor. Thus precious days slipped away, the French
were still at Moscow, winter was coming, and two other Russian armies,
one from the north and one from the south, were marching steadily on to
strike the French line of communication.
Napoleon wished to attack Kutusoff, drive him or destroy him, and then
fall back on Smolensk. His officers counselled against this.
"Then what am I to do?"
"Stay here," advised Count Daru. "Turn Moscow into a fortified camp,
and so pass the winter. There is plenty of bread and salt. We can
forage, we can salt down the horses which we cannot feed. As for
quarters, if there are not houses enough here, there are plenty of
cellars. We can hold out till spring, when our reënforcements, backed
by Lithuania in arms, will come to the rescue and complete our success."
"Counsel of the lion!" exclaimed the Emperor. "But what will Paris say?
what will they do? No; France is not accustomed to my absence. Prussia
and Austria will take advantage of it."
At length a rabbit, fleeing for dear life from a Cossack, put an end to
hesitation, and put two great armies in motion.
Tolstoï relates: "On October 14 a Cossack, Shapovalof, while on patrol
duty, shot at a rabbit, and, entering the woods in pursuit of the
wounded animal, stumbled upon the unguarded left flank of Murat's
army"--Napoleon's advance guard.
Shapovalof, on his return to camp, told what he had seen, the news
reached headquarters, a reconnoissance confirmed the statement, and the
Russians, sorely tempted, broke the armistice, fell upon the unwary
Murat, and did him immense damage. But for a difference between the
Russian generals, it appears that Murat's entire force might have been
captured.
The Emperor was holding a review in the courtyard of the Kremlin when
members of his suite began to say to one another that they heard
cannon firing in the direction of the advance guard. At first no one
dared speak of it to Napoleon. Duroc finally did so, and the Emperor
was seen to be seriously disturbed. The review had not been recommenced
before an aide-de-camp from Murat came at full speed to report that the
truce had been broken, the French taken by surprise, and routed with
heavy loss.
This was October 18. At last Napoleon was a soldier again: the news of
the battle had roused him to action. His decision was taken, orders
flew, and before night the whole army was in motion.
CHAPTER XXXVI
Encumbered by a vast amount of booty, a host of camp-followers, and
a huge train of vehicles of all sorts, the Grand Army left Moscow,
upward of one hundred thousand strong and with some fifty thousand
horses. Neither men nor horses had been shod for a winter campaign. The
clothing worn by the troops was mostly that of summer. The movement
of the troops was slow, because of the enormous baggage. The Emperor
wished to retreat by the Kalouga road which would carry him over a
country able to support him with provisions. The Russians barred the
way, and at Malo-Yaroslavitz the French, under Eugène Beauharnais,
attacked and beat them. Falling back to a stronger position, the
Russians still barred the way. Military critics say that had not
Napoleon's retreat been so sluggish, he would have outstripped these
Russians in their efforts to head him off. Had he burned all that
plunder which his army was carrying away, he might have saved his army.
Marshal Bessières and others, sent forward to reconnoitre, reported
that the enemy was too strongly intrenched to be dislodged; the army
must get back to the old road by which it had come. Napoleon hesitated,
listened to reports and advice, lost time, and finally gave the word
to retreat by the old route--a fatal decision. What Bessières had seen,
according to some authorities, was but a rear-guard: Kutusoff had
retreated, and the new route by Kalouga could have been taken by the
French.
With heavy heart the Emperor led the way to the other road--that which
had already been swept bare in the advance to Moscow.
The Russians did not press the pursuit with any great vigor, but the
Grand Army, nevertheless, melted like snow. Men and horses died of
starvation, demoralization set in, bands of stragglers were cut off by
Cossacks, so that after a battle at Wiasma, and previous to any snow or
severe cold, only fifty-five thousand men and twelve thousand horses
were fit for active service.
On November 6 the weather changed, and wintry horrors accumulated. The
snow, the freezing winds, the icy rains, the lack of food, the want
of shelter, the ferocity of pursuing foes, the inhumanity of comrades
and friends, the immense plains to be crossed, the deep rivers to be
bridged, the enormous burden of despair to be borne,--these were the
factors of the most hideous drama war ever presented.
The Grand Army reeled in tattered fragments toward home, fighting,
starving, freezing, meeting death in every shape known to man. The
French marched in four divisions, commanded by the Emperor, Eugène,
Davoust, and Ney. Terrible as was the daily loss by disease, death,
and straggling, each of these divisions held its formation, and never
failed to stand and fight when the Russians attacked. The unbending
courage shown by these commanders, the steadiness of subordinate
officers, the despairing gallantry of the remnants of the Grand Army,
stand out in bold relief to the general gloom of this mightiest of
shipwrecks. Much of the time Napoleon was on foot, clad in furs, staff
in hand to help him through the drifts, marching stolidly, silently,
with his men. Nothing that he could do was left undone; but that which
he could do had little influence on general results as they tramped
along. Until they reached Smolensk, he was almost as powerless as the
others; after that his superiority saved what was left of the army.
The hardships of the retreat increased after November 14, when Smolensk
was left behind. Men fell by the road exhausted, men were blinded by
the glare of the light on limitless fields of snow, men were maddened
by the intolerable anxieties and woes of the march. In the day the
ice cut their rag-covered or naked feet, the wind and freezing rain
tortured their hungry, tattered bodies. At night--nights of sixteen
fearful hours--bivouac fires were scant and insufficient, and when
morning dawned, the circle of sleeping forms around these dismal
bivouacs would sometimes remain forever unbroken--the sleep of the
soldier was the long one, the final one.
In October the Russian prisoners had said to the French, "In a
fortnight the nails will drop from your fingers; you will not be
able to hold your guns." The cold was even worse; not only did nails
drop off, the hands dropped off. The time soon came when a benumbed
Frenchman, who had fallen into a ditch, and who had piteously begged a
passing comrade to lend a helping hand, was answered, "I haven't any!"
There were only the stumps of the arms; the poor fellow's hands had
been frozen off. "But here, catch hold of my cloak," he continued, and
the man in the ditch having caught hold, was dragged to his feet.
Conditions like these made savages of the men. In the rush for food
and fire and shelter, the strong tramped down the weak. Frantic
with cold and hunger, they fought each other like wolves for place
and provisions. The weaker were shut out and died. Horse-flesh was
common diet; it is even said that cannibalism occurred. For warmth,
artillerymen could be seen holding their hands at the noses of their
horses; for food, a soldier was considered lucky who found a little
flour, half dirt and chaff, in the cracks of a floor. But in the
worst stages of this awful retreat there was human heroism; there was
human sympathy and unselfishness. There is nothing finer in the fine
character of Eugène Beauharnais than the gallantry with which he set
the good example of patience, courage, loyalty, and self-sacrifice.
From the time he beat Kutusoff in the first fight after Moscow, to
his taking the chief command, which Murat abandoned, his conduct was
heroic. Rugged Davoust, the best of the marshals now serving, who would
have saved his master at Borodino, and who did snatch him from the
burning streets of Moscow, was a tower of strength after the retreat
began.
Other marshals did not love Davoust; they quarrelled with him, said he
was slow, and accused him of not maintaining discipline. On the retreat
Ney, whom Davoust had left behind, charged him with something like
treachery. But Napoleon knew the value of Davoust, and history knows
it. To the careful student of this eventful epoch the conclusion comes
home, irresistibly, that Napoleon might have remained till his death
the mightiest monarch of the world had he listened to two men,--in
civil affairs, Cambacérès; in military matters, Davoust.
As to Murat, he fought all along the front with such conspicuous
gallantry, superbly mounted and gorgeously dressed, that he extorted
the admiration of the Russians themselves. The Cossacks, especially,
looked upon him as the bravest, the most martial of men. Murat fought
the cavalry till the horses were all dead, and then he spent most of
his time in Napoleon's carriage.
But Ney, rugged, lionlike Ney, surpassed them all, winning in this
campaign the Emperor's proud title, "The brave of the braves." Such
grandeur of courage, such steadiness, such loyalty, the world never
surpassed. Separated from Davoust, beset by overwhelming numbers, he
seemed a lost man. The Emperor, hard pressed himself, but determined
to make a final effort to save his marshals, halted at Krasnoi, facing
sixty thousand Russians with six thousand French. Nothing in Napoleon's
own career is finer than this. Russian shells began to fly, screaming
through the air and along the snow. Lebrun spoke of it as of something
unusually terrible. "Bah!" said the Emperor with contempt; "balls
have been whistling about our legs these twenty years." His desperate
courage in standing at bay so impressed Kutusoff that he drew back,
and Davoust came through. But Ney was still behind, and in the face of
the tremendous odds the French were forced onward. In deep grief for
his marshal, the Emperor reproached himself for having exposed Ney too
much. From time to time he would inquire if any one had heard from him.
On the 20th of November General Gourgand came in haste to announce that
Ney was only a few leagues away and would soon join. With a cry of joy,
Napoleon exclaimed, "Is it true?" When Gourgand explained how Ney had
marched and fought: how he had defied a beleaguring host ten times his
own number; how, summoned to surrender, he had replied, "A marshal of
France has never surrendered!" and how he had, partly by stratagem, and
partly by force, escaped with a small remnant of his command, Napoleon
was delighted. "There are 200,000,000 francs in my vaults in the
Tuileries, and I would give them all to have Ney at my side!"
When the heroic survivors of this column joined the main army, there
were shouts and tears of joy.
It was Ney who held the Cossacks at bay toward the final stages of the
retreat; it was Ney who fired the last shot of the war as he recrossed
the Niemen: it was Ney who became almost literally the rear-guard of
the Grand Army.
Well might the Bourbon Duchess of Angoulême say, in 1815, when told the
story of this man's antique heroism in the Russian campaign, "Had we
known all that, we would not have had him shot!"
In the disorder, savagery, elemental chaos of this historic retreat,
human nature flew to the extremes. There were soldiers who slew each
other in struggles for food, and soldiers who risked starvation to
share with others. In some instances comradeship was mocked, in some
it was stronger than ever. There were instances where the strong
laughed at the weak who pleaded for aid. There were cases where the
strong braved all to save the weak. Wounded officers were seen drawn
on sledges to which their comrades had harnessed themselves, brother
officers taking the place of horses. A child, abandoned by its mother,
was saved by Marshal Ney, and escaped all the hardships of the
retreat. Another mother drowning in the Beresina held her babe aloft in
her arms, the child alive, the mother as good as dead.
One of the most touching and purely unselfish acts of devotion was that
of the Hessian contingent in its protection of their hereditary prince.
The people of Hesse had little cause to reverence their rulers--petty
tyrants who had sold them into military servitude at so much a head to
England, and who had misgoverned them with the worst of feudal methods.
But on the coldest night of the retreat, when it seemed that the young
Prince Emil would freeze to death, the remnant of the Hessians closed
around him, "wrapped in their great white cloaks pressed tightly
against one another, protecting him from wind and cold. The next
morning three-fourths of them were dead, and buried beneath the snow."
By the time the French came near the Beresina, the two Russian armies,
which had been released by the treaties the Czar had made with Turkey
and Sweden, had reached the scene of war, and threatened the line of
retreat. Kutusoff in overwhelming force in the rear, Wittgenstein and
Tchitchagoff in front and flank, the French seemed doomed. When the
Russians were driven by Oudinot from Borissow, they burnt the bridge
over the Beresina. The ice had melted, the river was swollen, it was
wide and deep, and the Russians were on the opposite bank ready to
dispute the passage. To bridge and cross the river in the face of these
Russians--such was the French necessity: either that or surrender, for
Kutusoff was close behind.
Already the Emperor had destroyed his papers and burned his eagles to
save them from capture; already had provided himself with poison,
resolved to die rather than be taken prisoner.
Standing up to their lips in the freezing current of the river,
soldiers worked all night, fixing the timbers for the bridge. It was a
terrible labor, and several lost their lives, drowned or frozen. Those
who toiled on, had to keep the masses of ice pushed away while they
worked.
The Emperor sat in a wretched hovel, waiting for day. Great tears
rolled down his cheeks. "Berthier, how are we to get out of this?"
Murat urged him to take an escort of a few Poles, cross the river
higher up, and escape. The Emperor silently shook his head, and Murat
said no more.
Suddenly came news that was almost too good for belief: the Russians
had disappeared! Tchitchagoff, deceived by Napoleon's feint to cross
elsewhere, or misled by Kutusoff's despatches, had led his army away.
The line of retreat was now open, the bridges were rapidly finished,
and with shouts of "Live the Emperor!" the jubilant French began to
cross. When in their hurry a jam occurred in the passage, and artillery
teams got blocked, Napoleon himself sprang on the bridge, caught the
horses, and helped to free the pieces.
The bridges, constructed under so many difficulties and in such haste,
were frail, the crush of the crowd in going over became greater and
greater. Finally the bridges gave way. They were repaired, but broke
again. Beginning with this, the tumult, the terror, the frantic
struggle for place, the loss of life, became frightful. The weak fell,
they were trampled by men and horses, and ground to pulp by wheels.
Some perished on the bridges, others were pushed off and drowned
in the river. There were no side-rails or ledges, nothing to keep
those on the outer edge from being crowded off--and they went over by
hundreds, by thousands. The Russians under Wittgenstein having come up,
a fierce battle ensued between them and the French rear-guard. Amid
wild confusion, the passage of the river continued, while a storm raged
and the cannon roared. In the evening the large bridge, crushed by the
weight upon it, gave way, and with a fearful cry, which rose above the
storm and the battle, the multitude that was crossing sank forever.
Next day the battle raged again, while the crossing continued. Early in
the night, Victor's rear-guard began to cross, the Russians cannonading
the bridge, and covering it with the dead. Next morning the bridge was
burned, and all the thousands of stragglers and camp-followers were cut
off, and perished miserably.
Beyond the Beresina, the regulars of the Russian army did not press the
pursuit, but the Cossacks hung on, inflicting heavy losses. From cold,
from hunger, from disease, the French continued to lose fearfully; but
the broken remnant of the Grand Army was now comparatively safe from
the enemy.
Full details of the Malet conspiracy having reached Napoleon, he became
anxious and restless. He believed he could render greater service to
himself and the Empire by being in Paris. Turning over the command to
Murat, at Smorgoni, the Emperor entered a covered sleigh, and set out
for France.
Accompanied by Duroc, Caulaincourt and Lobau, Roustan the Mameluke,
and a Polish officer, the Emperor sped across the snow on his way
homeward. Almost captured by Cossacks, he reached Warsaw on the 15th
of December, 1812, where he put up at the English Hotel, and sent for
the Abbé de Pradt, his minister to the Grand Duchy. Here, in a small
room of the hotel, moving about restlessly, stamping his feet for
circulation while a servant girl bent over the hearth trying to make
a fire from green wood, he gave his instructions to his treacherous
minister, and announced that in the following spring he would be back
in the Niemen at the head of three hundred thousand men. Then he sped
onward toward Saxony.
Late at night, December 14, 1812, the sledge of the flying Emperor
reached Dresden, where there was a brief conference between Napoleon
and his faithful ally. Bitter beyond description must have been the
reflections of the lonely fugitive in hurrying through those streets,
where a few months before kings had crowded to his antechamber!
Escaping the conspiracies aimed at his life in Germany, he safely
entered France, and reached Paris, late at night, December 18, 1812,
arriving at the Tuileries almost alone, in a hackney coach.
There was an outburst of indignation in the Grand Army remnants when it
was known that the Emperor had gone. "The same trick he played us in
Egypt," said one General to another. Murat had on his hands a thankless
task at best, and under his management the situation did not improve.
At Wilna the Cossack "Hourra!" stampeded the French, who fled, loosing
six thousand prisoners. At the steep hill, a few miles beyond, the
horses could not drag the artillery up the ice-covered road, and it was
abandoned.
Sick of such a responsibility, Murat bethought himself that he also
had a kingdom that might need his presence, and on January 16, 1813, he
made over the command to Eugène Beauharnais.
There were seventeen thousand men in the army when Murat left it;
Eugène increased its numbers until, by the 9th of March, 1813, it was
an effective force of forty thousand. Taking a strong position, his
line stretching from Magdeburg to Dresden, the loyal Eugène waited for
his Emperor to bring up reënforcements.
CHAPTER XXXVII
There is no convincing evidence that the Russian war of 1812 was
generally unpopular in France. There is no proof whatever that any
national calamity growing out of it was expected or feared. So great
was the confidence which the Emperor's uninterrupted success had
inspired, that the current belief was that Russia would be beaten and
brought to terms. The glamour of the Dresden conference was sufficient
to dazzle the French people, and the magnificent host which gathered
under the eagles of the Empire left them no room for doubts. Led by
such a captain as Napoleon, this army of half a million men would bear
down all opposition. Bulletins from the front, dictated by the Emperor,
did not fail to produce the impression desired; and when at length
the victory of Borodino was followed by the French entry into Moscow,
national enthusiasm and pride reached its height.
The first shadow that fell upon France, the first thrill of fear, was
caused by the news that the Russians had given their capital to the
flames. Still, when it became known that the Emperor was quartering
the army amid the ruins, that there was shelter and food for all, that
communications between Paris and Moscow were so well guarded that not
a courier or convoy had been cut off, that Napoleon, seemingly quite
at ease, was giving his attention to the internal affairs of France,
was drawing up regulations for schools and theatres, was corresponding
with his son's governess upon the subject of the child's teething,
the French convinced themselves that the invasion had proved another
triumph. They could not put their eyes upon that sombre figure in
the Kremlin, the chief who had not a word to say to those about
him, who lay listless upon the sofa day by day,--a leader without a
plan,--wrapping himself in the delusion that even yet the Czar would
accept his peaceful overtures.
So strong was the system which Napoleon had organized in France that
it went on in his absence just as regularly as when he was present.
Even when the daring General Malet, encouraged by the Emperor's great
distance from his capital, conspired with the priest, Abbé Lafon,
to overthrow the government, the attempts never had the slightest
chance of success. By means of a forged decree of the Senate, and the
announcement that the Emperor was dead, the conspirators were for a
moment enabled to secure control of a small body of troops, arrest
the minister and the prefect of police, and to take possession of the
city hall. But almost immediately the authorities asserted themselves,
seized the conspirators, and put them to death.
The true significance of this episode lay in the fact that so violent
a revolutionist as Malet, who had plotted to kill Napoleon because of
the Concordat, was found in league with the Abbé Lafon, a royalist and
clerical fanatic, and that they had agreed upon a programme which was
so eminently sane as to be formidable.
According to their plan, Napoleon's family were to be set aside, the
conscription abolished, and the most oppressive taxes lifted. The Pope
was to be restored to his temporal power, and France was to secure
peace with the world by consenting to be reduced to her old boundaries
of Rhine, Alps, and Pyrenees. Those who had purchased the confiscated
property of the Church and the nobles were to be quieted with the
assurance that their titles should not be questioned.
When we remember that peace was finally established in France upon
substantially the same lines as those marked out by the Abbé Lafon,
it becomes evident that he was in touch with those royalist clericals
who, failing miserably in 1812, succeeded completely two years later.
Napoleon's uneasiness when he heard of the conspiracy, and his
curiosity in asking for the minutest details, can well be understood.
* * * * *
The twenty-fifth bulletin from the Grand Army told France that the
retreat from Moscow had begun. The twenty-eighth bulletin, dated from
Smolensk, and made public in Paris on November 29, 1812, announced
that winter had set in. After this, France was left for eighteen days
without news--eighteen days filled with dread. Then on December 17 came
the avalanche. The twenty-ninth bulletin, revealing much, suggested
all--the Grand Army was no more! The consternation, the dismay, the
stupor of grief and terror which overspread the stricken land, can be
imagined; it passes the power of words.
And the home-coming of the Emperor--what was it like, this time?
It was midnight in Paris, the 18th of December, 1812. The Empress Maria
Louisa, at the Tuileries, sad and unwell, had gone to bed. The imperial
babe, the infant King of Rome, was asleep. It was a mournful time
in France. Where was the hut from one end of the Empire to the other
which did not hear sobs this bitter, bitter night? How many women,
at cheerless firesides, wept and prayed for sons, husbands, lovers,
shrouded in motionless snow on far Russian plains! Even the Empress
was sorrowful. She knew nothing of the fate of the army or its chief.
Napoleon himself might get rest for his unresting spirit from Cossack
lance or Russian gun--in which event the Empress Maria might find
untold calamity for her imperial self.
A common cab rolled into the courtyard below, and steps were heard
hastily ascending the stairs. Two men hooded and wrapped up in furs,
pushed their way into the anteroom to the Empress's bedchamber. Voices
were heard in this anteroom, and the Empress, frightened, was just
getting out of bed, when Napoleon burst in, rushed up to her, and
caught her in his arms.
On the following day, according to Pasquier, the Emperor admitted no
one but his archchancellor, his ministers, and his intimates. On the
20th, which was Sunday, he attended divine service, and then held
the usual levee; after which he formally received the Senate and the
Council. Seated upon his throne, enveloped in his robes of state, this
wonderful man, so recently a fugitive fleeing almost alone through
the wilds of Poland, never presented a serener face to the world, nor
looked down upon the grandees who bowed before him with haughtier
glance, than upon this memorable Sabbath. Loyal addresses were listened
to with dignity and composure; imperial responses were made in a tone
which convinced France and Europe that Napoleon remained unconquered.
Such was the grandeur of his attitude, so powerfully did his fortitude,
courage, magnetic audacity appeal to this gallant nation, that it
rallied to him with almost universal sympathy and enthusiasm. Towns,
cities, corporate bodies, imperial dependencies, sent in loyal
addresses, offers of cordial support. From Italy, Holland, the Rhine
provinces, poured in warm expressions of attachment and fidelity. Rome,
Milan, Florence, Turin, Hamburg, Amsterdam, Mayence, testified their
sense of the benefits his rule had conferred upon them, and tendered
him "arms, armies, gold, fidelity, and constancy."
Napoleon had said that he would be back in Germany in the spring with
three hundred thousand men. He lost no time in getting ready to keep
his promise. It was an awful task--this creation of a new army; but
he set about it with a grim resolution, a patient persistence, which
accomplished wonders. Skeleton regiments of veterans were filled in
with youthful recruits, and hurriedly drilled. The twelve hundred
cannon lost in Russia were replaced by old guns from the arsenals, or
new ones from the foundries. The enormous loss of war material was made
good from the reserves in the military depots. But where could the
Emperor get horses to supply the mighty number frozen or starved in
Russia? He could not get them. His utmost exertions could but supply
teams for the artillery. Of cavalry he could mount almost none.
Meditate a moment on the situation. The civilized world stood arrayed
against one man, one people. England on the seas, in Portugal, in
Spain; Russia marching on with a victorious host; Sweden (having been
promised Norway and English money) uniting with the Czar; Prussia and
Austria leaving the side of France,--Prussia joining in the crusade,
and Austria preparing to do so,--smaller German powers threatened
with ruin if they did not declare war upon Napoleon; Murat at Naples
betraying the man who had given him the crown; the Pope doing his
utmost to sow disaffection by troubling the conscience of Catholics
throughout the Empire; royalists in France beginning to stir, covertly
and stealthily, in the tortuous ways of intrigue and conspiracy. All
this we see upon one side. And upon the other, what? One man of supreme
genius and courage,--backed by one gallant nation,--preparing to lead
forth, to meet a world in arms, an army composed largely of boys,
almost without cavalry, and almost without drill.
"I noticed at this epoch," says Constant, "that the Emperor had never
hunted so frequently." Two or three times a week the hunting suit was
donned, and the imperial party would seek the pleasures of the chase.
As Napoleon had no real fondness for hunting, his valet was surprised.
One day he learned the explanation. English newspapers, as the Emperor
told Duroc, had been repeating that he was ill, could not stir, and
was no longer good for anything. "I'll soon make them see that I am as
sound in body as in mind!"
One of these hunts, Napoleon endeavored to turn to a particularly
good account. The Pope was at Fontainebleau, to which place he had
been removed from Savona at the opening of the Russian campaign. His
quarrel with the Emperor had become most annoying in its consequences.
Disaffection, because of it, had found its way into the very Council
of State. All attempt at negotiation had been fruitless. On the eve of
another great war, here was a question which demanded settlement; and
the Emperor determined to go in person to the Pope.
On January 19, 1813, the hunt was directed to Grosbois, the fine estate
which had belonged to Barras, then to Moreau, and then to Berthier,
Prince of Neufchâtel. At Grosbois, accordingly, the imperial party
hunted. "But what was the surprise of all his suite when, at the moment
of reëntering the carriages, his Majesty ordered them to be driven
toward Fontainebleau."
The Empress and the ladies, having no raiment with them other than
hunting costumes, were in some confusion at the prospect. The Emperor
teased them for a while, and then let them know that by his orders the
necessary change of clothes had been sent from Paris beforehand and
would be ready for them at Fontainebleau. Taking up his quarters in the
ancient palace, Napoleon and Maria Louisa went informally to call upon
the Pope. The meeting was affectionate. Again there were huggings and
kissings; again it was "My father!" "My son!" And again the magnetism,
the adroit winsomness of Napoleon, swept the aged pontiff off his feet.
He signed a new compact with his "son"; and once more there came to
them both the bliss due to the peacemakers.
Radiant with pleasure, Napoleon returned to Paris; and, quick as
couriers could speed, went the good news to all parts of the Empire.
But he had been too fast. He had given permission that the rebellious
cardinals--"the black cardinals," who, refusing to attend the
celebration of the religious marriage with Maria Louisa, had been
forbidden to wear the red robes--might attend the Pope. And these black
cardinals had not changed their color,--were still black,--and they
began immediately to urge the Holy Father to break his plighted word.
The Holy Father did so, pleading by way of excuse, that the paper he
had signed was not a contract or treaty, but only the basis of one;
and that Napoleon had acted in bad faith in making it public. But the
Emperor inserted the treaty in the official gazette, keeping up the
pretence that all was peace between him and the Pope; so that the
French people at large knew no better until a much later date.
There are critics who say that Napoleon was too hasty in setting out
to join his army in April, 1813. But the plain facts of the case would
seem to show that Napoleon knew what he was about. Prussia had issued
her declaration of war on March 17, 1813, and Blücher pushed forward to
the Elbe. Russian troops had likewise reached the Elbe, and Cossacks
raided in the vicinity of Dresden, which the French, under Davoust,
evacuated. Blücher entered the Saxon capitol; the Saxon king was a
fugitive; and the Prussians passed on toward Leipsic.
By the 24th of April the Czar of Russia and the King of Prussia were in
Dresden. Bernadotte, at the head of thirty thousand Swedes, had joined
Bülow, and was covering Berlin.
In view of these events, how can it be said with assurance that
Napoleon was overhasty in taking the field?
Remembering that the Allies had threatened war upon those minor
German powers who would not join them, and that Saxony was already
in their grasp, it seems that Napoleon's conduct admits of easy
explanation. Unless he checked the Allies, and that speedily, the Rhine
Confederation would go to pieces; the French garrisons in various
German cities would be lost. Eugène and his army would be cut off at
Magdeburg, and the fabric of Napoleonic Empire would fall without a
blow having been struck in its defence.
To accomplish these very purposes, the Allies had pressed forward;
and great must have been the confusion in both armies; for Napoleon,
as well as his enemies, was surprised when the two armies struck each
other at Lützen, May 2, 1813. A bloody struggle followed; the Allies
were outgeneralled, and they retreated from the field. Having no
cavalry, the Emperor lost the usual fruits of victory; but the mere
fact that he, so recently the fugitive from a lost army, now appeared
at the head of another host, and had driven Russians and Prussians
back in defeat, produced a moral effect which was immense. The enemy
was driven beyond the Elbe; all hopes of breaking up the Rhine
Confederation were at an end; Eugène and Napoleon would now unite;
Saxony was redeemed. Napoleon entered Dresden in triumph. His friend
and ally, the Saxon king, returned to his capital. The French army was
full of confidence: the Allies made no effort to stand their ground
till they reached Bautzen, on the Spree. Here, on May 21 and 22, they
were assailed by the French, and again overthrown.
So competent a judge as Lord Wolseley is of the opinion that a mistake
of Marshal Ney in this battle saved the allied army from total ruin.
The Russians and Prussians held a strong fortified position resting on
the Bohemian Mountains, from which there was only one line of retreat.
Napoleon's quick eye took in the situation, and he sent Ney to the rear
of the enemy with seventy thousand men, while he assailed their front
with eighty thousand. In executing this turning movement, Ney became
engaged with a small force of Prussians, which Blücher had detached to
protect his rear. "Instead of pressing his march along the rear of the
allied army to cut off its retreat, and attack it in the rear, whilst
Napoleon assailed it in front, Ney allowed his movements to be checked,
and his direction diverted by this insignificant Prussian detachment.
This fighting soon roused Blücher to a sense of his extreme danger, and
he at once fell back and made good his retreat." The Russians made the
best of a bad situation till dark, and then escaped during the night.
"Ney had, in fact, only succeeded in manœuvring the Allies out of a
position in which Napoleon intended to destroy them, and where they
must have been destroyed had his orders been skilfully obeyed."
As it was, the Allies drew off without losing a gun, and Napoleon,
looking over the thousands of dead that cumbered the field, exclaimed
in rage and grief, "What a massacre for nothing!"
It was at this stage of the campaign that Napoleon is thought to have
made the crowning mistake of his later years. He halted his victorious
columns, and signed the armistice of Pleiswitz (June 4, 1813).
Austria had, since her defeats in 1809, fully recovered her strength.
Her armies reorganized, her people animated by a patriotic spirit which
had been intensified by promises of constitutional reforms, she had
come unhurt out of the war of 1812, and was now determined to recover
her lost provinces and her position as an independent power of the
first class. With Russia and France both severely crippled by the
late struggle, Austria realized her advantage too well to allow the
opportunity to pass. Either from Napoleon or the Allies the position
lost in 1809 must be recovered. With this end in view, Metternich
negotiated with all parties,--Prussia, England, France, and Russia. The
amount of lying this able and eminent Christian did at this critical
time would probably have taxed the conscience of even such veterans in
deception as Fouché and Talleyrand.
Whether Napoleon could have won the friendship of Austria by frankly
surrendering to her demands for the restitution of her lost territory,
must always remain a matter of doubt. Inasmuch as the Austrian army
was not quite ready to take the field, and her treasury was empty, and
she had no complaint against Napoleon, excepting that she had made an
unprovoked attack upon him in 1809 and had been thoroughly whipped,
the probability is that a prompt concession of her demands would have
gained her neutrality in the war of 1813. But this is by no means
certain. When we remember the strength of dynastic prejudices, the
influence of British money, the rising tide of German nationality and
of hatred of Napoleon, the intense antagonism to French principles, the
activity of royalist and clerical intrigue--it is difficult to escape
the conclusion that had Napoleon yielded up what he had taken from
Austria, he could have stopped at nothing short of a full surrender all
along the line. And had he returned to France shorn of all that French
blood had won, the storm of indignation there would have driven him
from the throne. Napoleon himself expressed substantially this view at
St. Helena; it may have been sound. Why, then; did he grant the truce?
What did he mean by saying, after he had signed it, "If the Allies do
not sincerely wish for peace, this armistice may prove our ruin"? No
one can say. There are facts which appear to prove conclusively that
he ardently wished for an honorable peace. Other facts seem to indicate
that he was playing for time, that he never did mean to give up
anything, and that he was beaten in a grand game of duplicity, where,
intending to deceive, he was duped.
CHAPTER XXXVIII
The guiding hand of Austrian diplomacy at this time being Metternich's,
and that astute person having left behind him certain _Memoirs_ which
his family have arranged and published, it may be fairly presumed that
any revelation of Metternich's own perfidy made in these _Memoirs_ can
be credited.
According to his own story, Metternich sought an interview with the
Czar (June 17, 1813) and urged him to trust implicitly to the Austrian
mediation which had been tendered to the belligerents. Alexander had
his misgivings, and inquired:--
"What will become of _our cause_ if Napoleon accepts the mediation?"
Metternich replied:--
"If he declines, the truce will come to an end, and you will find us
among the number of your allies; if he accepts, _the negotiations will
most certainly_ show that Napoleon is neither wise nor just, and then
_the result will be the same_. In any case, we shall have gained time
to bring up our armies for combined attack."
What did Alexander mean by "our cause," which might be ruined by
Napoleon's consent to allow Austria to mediate? If peace was all that
the Allies wanted, why demur to Austria's offer?
And what did Metternich mean by assuring the Czar that it made no
difference whether Napoleon declined or accepted, the results would be
the same?
Evidently he meant to convince Alexander that "our cause" was as dear
to Austria as to Russia; and that if Napoleon trusted to Austrian
mediation, he would be deceived and despoiled. The Czar so understood
it, and he "seemed exceedingly well pleased."
The political meaning of "our cause" was this: English diplomats had
been unusually busy, and had (June 14 and 15, 1813) negotiated new
treaties with Russia and Prussia whereby Great Britain agreed to pay
heavy subsidies to those powers to prosecute the war, which was not to
be ended without England's consent.
Inasmuch as England was no party to the negotiations then pending
between Napoleon and the Allies, one of two things is obvious: the
Allies were intent upon betraying England, or of duping France. As
to which of the two it was meant to deceive, the language used by
Metternich to Alexander, and by Alexander to Metternich, leaves no
doubt.
What, on the other hand, were the thoughts of Napoleon? On June 2,
1813, he wrote to Eugène, who had been sent back to Italy, "I shall
grant a truce on account of the armaments of Austria, and in order to
gain time to bring up the Italian army to Laybach to threaten Vienna."
There are those who see in this a proof that Napoleon did not desire
peace. Read in the light of the surrounding circumstances, it is just
as easy to see in the letter an evidence that Napoleon merely wished to
escape Austrian dictation.
He had already offered to treat for peace with Russia and Prussia;
and they, controlled by English influence, had refused to treat, save
through Austria.
Anxious, suspicious, harassed by all sorts of cares, Napoleon summoned
Metternich to Dresden.
Napoleon understood Metternich thoroughly, and despised him. With this
man, as with Fouché, Talleyrand, and Bernadotte, the proud Corsican had
too lightly indulged in the perilous license of contempt.
"Sire, why do you not send Metternich away?" Duroc inquired one day at
the Tuileries.
"Ah, well," answered Napoleon, "if Austria sent me a new minister, I
should have him to study; as to Metternich, he can no longer deceive
me."
Summoned to Dresden, the Austrian diplomat went, and on June 27, 1813,
held his famous interview with Napoleon. It was not then known to any
save the parties to the treaty that Lord Aberdeen, acting for England,
had already made his bargain with Austria, whereby the latter power
agreed to accept an enormous bribe to enter the coalition against
France. On the very day of Metternich's interview with Napoleon,
Austria was actually signing the Reichenbach treaty which, affirmed by
the Emperor Francis on August 1, 1813, placed Austria's two hundred
thousand men at the service of "our cause."
Napoleon knew nothing of this; he suspected it, dreaded it, desperately
sought to avert it. Hence his call to Metternich.
In his _Memoirs_, the Austrian statesman relates that he found the
French Emperor at the Marcolini Garden, near the Elster meadows. "The
French army sighed for peace. The generals had little confidence in
the issue of the war." "The appearance of the Austrian minister at
Napoleon's headquarters could only be regarded by the French generals
as decisive in its results." Bursting with self-importance was this
Metternich, of whom Napoleon said that he was always believing that he
controlled everything, whereas he was eternally being controlled by
others. In this instance he walked toward Napoleon's rooms with the
majestic port of an arbiter of nations, whereas the whole thing had
already been determined by Lord Aberdeen's negotiations at Vienna, not
to mention the masterful influence of Sir Charles Stewart and Lord
Cathcart in the counsels of Russia and Prussia.
"It would be difficult to describe," says Metternich, "the expression
of painful anxiety shown on the faces of the crowd of men in uniform
who were assembled in the waiting rooms of the Emperor. The Prince of
Neufchâtel (Berthier) said to me in a low voice, "Do not forget that
Europe requires peace, and especially France, which will have nothing
but peace."
Of Berthier, Napoleon himself said that, in anything outside his
specialty of writing despatches, "he was a mere goose." If Berthier
made at this juncture any such remark to Metternich as that important
man records, it would be a charity to let Berthier escape with so light
a reproach as that of being a mere goose. Such a remark to such a man,
by such a man, and at such a time is rankly odorous of disaffection,
disloyalty, and the incipient treason which broke out openly a few
months later.
Metternich, referring to Berthier's remark, complacently states,
"Not seeing myself called upon to answer this, I at once entered the
Emperor's reception room." Great was Metternich in this crisis, too
great to bandy words with a mere mushroom, Prince de Neufchâtel!
"Napoleon waited for me, standing in the middle of the room with his
sword at his side, and his hat under his arm. He came up in a studied
manner and inquired after the health of the Emperor Francis. His
countenance soon clouded over, and he spoke, standing in front of me,
as follows:--
"'So you _too_ want war; well, you shall have it. Three times have I
replaced the Emperor Francis on his throne. I have promised always to
live in peace with him. I have married his daughter. To-day I repent of
it.'"
Metternich says that at this crisis he felt himself the representative
of all European society. He felt the strength of his position, felt
that the mighty Napoleon lay in the hollow of his hand.
"If I may say so, Napoleon seemed to me small!"
"If I may say so"--why the modest doubt? Where is the limit of what one
may say in one's _Memoirs_? Do the writers of _Memoirs_ ever by any
possibility get worsted in discussion, or fail to say and do the very
best thing that could have been said and done?
Metternich proceeds to relate how he read Napoleon a paternal lecture;
how he explained to the French Emperor that France as well as Europe
required peace; how he intimated that Austria would throw her aid to
the coalition; how he predicted that the French army would be swept
away, and how he asked the Emperor, "If this juvenile army that you
levied but yesterday should be destroyed, what then?" "When Napoleon
heard these words he was overcome with rage, he turned pale, and his
features were distorted. 'You are no soldier,' said he, 'and you do not
know what goes on in the mind of a soldier. I was brought up in the
field, and a man such as I am does not concern himself much about the
lives of a million of men.' With this exclamation he threw his hat into
the corner of the room."
Of course the _Memoirs_ represent Metternich as promptly taking
advantage of this imprudent outbreak, and as throwing Napoleon
quite upon the defensive. It is noticeable that in the _Memoirs_ of
Napoleon's enemies, the authors invariably got the better of him in
trials of wit. Some very dull people gave him some very crushing
conversational blows--in their _Memoirs_.
But this much is known of the Dresden interview,--it lasted half a day,
and Metternich reports less than half an hour's talk. The Austrian
does not record how unerringly Napoleon guessed the riddle, and how
directly he put the question,--"Metternich, how much has England paid
you to act this part against me?" Nor does he record the fact that
Napoleon, in his extremity, offered to buy Austria off by ceding the
Illyrian provinces, and that the bargain could not be made because the
Emperor Francis advanced his demands as often as Napoleon enlarged
his concessions. Austria, sold to England, was perfectly willing to
be bought by France; but the price demanded was so excessive, that
Napoleon indignantly cried out, "I will die under the ruins of my
throne before I will consent to strip France of all her possessions,
and dishonor myself in the eyes of the world!"
Metternich records that he said to Napoleon: "You are lost. I thought
it when I came here; now I know it." The Emperor's reply to this
remarkable observation is not on the Metternich tablets. The writers of
_Memoirs_ have a habit of getting in the last word.
Not satisfied with having crushed Napoleon, Metternich dealt a parting
blow to Berthier, the Emperor's goose.
"In the anterooms I found the same generals whom I had seen on
entering. They crowded round me to read in my face the impression of
nearly nine hours' conversation. I did not stop, and I do not think
I satisfied their curiosity. Berthier accompanied me to my carriage.
He seized a moment when no one was near to ask me whether I had been
satisfied with the Emperor." To this humblest of questions, "Were you
satisfied with the Emperor?" the important Metternich replied, with a
loftiness which must have painfully bruised the Emperor's goose:--
"Yes, yes! It is all over with the man. He has lost his wits."
It is all over with the man; he has lost his mind--great Metternich,
small Napoleon, and poor Berthier, the Emperor's assiduous goose!
One other important fact the Metternich _Memoirs_ record: the Archduke
Charles needed twenty additional days to bring up the Austrian
reserves, and Metternich undertook to decoy Napoleon into an extension
of the armistice. The _Memoirs_ record how Napoleon vainly endeavored
through the Duke of Bassano to come to terms of peace; how Metternich
stubbornly stood his ground, refusing to budge an inch; how Napoleon
kept up the contest until the Austrian ordered his carriage and was
about to leave Dresden; how Napoleon then yielded, calling Metternich
back, and signing an agreement to accept Austrian mediation, to prolong
the armistice till August 10, and to submit the issues to a congress of
the powers to be assembled at Prague on the 10th of July.
In Thiers's _History of the Consulate and Empire_ we read that
Napoleon by his cleverness and diplomacy lured the Allies into granting
him precious delays most necessary to his welfare. In Metternich's
_Memoirs_ we read that the Austrian, by his adroitness and implied
threats, led Napoleon to the exact time which the Archduke Charles said
was needed to get his forces just where he wanted them. Which of these
contradictory stories is the truth? which is history?
The Congress of Prague assembled, and it soon became apparent that
peace would not be made. British influence dominated it from the first.
By consenting, once for all, to surrender his empire and become King of
France,--France with the old boundaries,--Napoleon could doubtless have
rid himself of the Allies. But what then? Could he have held the throne
in France after so complete a submission to foreign dictation? Could he
thus have secured internal peace for France itself? Would not England
have pressed home the advantage, restored the Bourbons, and destroyed
the work of the Revolution?
When we recall what took place in 1814 and afterward,--the steady
progress of reaction and counter-revolution until absolutism and
aristocratic privilege had completely triumphed again throughout
Europe,--we can but honor the sagacity and the unquailing courage of
Napoleon in standing his ground, indomitably, against combinations
without and disaffection within, rather than make craven surrender to a
coalition which meant nothing less than death to democratic principles
and institutions, as well as to his own supremacy.
In Spain the fortunes of war were going heavily against France.
King Joseph was in everybody's way, hampering military movements by
his absurdities; the marshals were at odds with each other, and no
coöperation could be had. Wellington, whose progress in the peninsula
had been slow and fluctuating, now advanced into Spain, and won a
decisive battle. Just as the victory of Salamanca had influenced
Russian councils in 1812, that of Vittoria bore heavily against
Napoleon at the Congress of Prague.
Napoleon himself had no confidence in the negotiations, and was
painfully aware of the manifold perils which beset him. He returned to
Mayence, and bent all his energies to the improvement of his situation.
One day he called upon Beugnot to write at his dictation, and Beugnot,
flurried at the unexpected summons, twice took the Emperor's chair.
Napoleon said: "So you are determined to sit in my seat! You have
chosen a bad time for it."
Soult was sent off to Spain to hold Wellington in check, Fouché and
Talleyrand were summoned to aid in fathoming the Austrian intrigue, and
influences were set to work to bring Murat back to the army.
CHAPTER XXXIX
To Mayence the Empress Maria Louisa came, to spend a few days pending
the peace negotiations. If Napoleon cherished the belief that her
presence would have any bearing upon her father's policy, the illusion
soon vanished. Austrian diplomats were already saying, "Politics made
the marriage; politics can unmake it."
So confident was Austria that the Congress at Prague would accomplish
nothing, that she had drawn up her declaration of war and held it
ready, as the last day of the truce wore on toward midnight. At the
stroke of the clock, the paper was delivered for publication, and the
war signals were lit along the Bohemian mountains. When Napoleon's
courier arrived, a few hours later, bringing to the French envoys
authority to sign the terms demanded, the Allies declined to consider
the matter at all. It was too late. Technically they were acting
within their rights; but if we really wish to know the truth about the
negotiations, the conduct of those diplomats, watching the midnight
clock, sending out midnight declarations of war, and lighting midnight
fires to proclaim the failure of the Congress, belongs to the class of
actions which speaks louder than words. If their real purpose had been
to stop the shedding of blood and to liberate Europe from Napoleon's
"cruel yoke," they would never have made so great a difference between
midnight of the 10th and early morning of the 11th. Nothing was to be
gained by such extreme rigor, beyond the ending of the Congress; for,
by the terms of the treaty, six days' notice was necessary before the
resumption of hostilities.
Says Metternich: "As the clock struck twelve on the night of August 10,
I despatched the declaration of war. Then I had the beacons lighted
which had been prepared from Prague to the Silesian frontier, as a sign
of the breach of the negotiations."
* * * * *
Pasquier relates an interesting story which he had from Daru.
One day toward the end of July, Sébastiani, a Corsican, and a life-long
friend of Napoleon, came to make a report, and was asked by the Emperor
what was being said about the military situation. Sébastiani replied
that the current opinion was that Austria would join the Allies, in
which event Dresden could no longer be made the central point of the
French line of defence.
"You are all right," said Napoleon, "and my mind is made up. I am going
to return to the banks of the Saale; I will gather there some three
hundred thousand men, and, with my rear resting on Mayence, my right
flank covered by the extremity of the mountains of Bohemia, I will show
the enemy the bull's horns. He will seek to manœuvre under my eyes; no
sooner has he committed his first mistake than I will fall upon him,
crush him, and the coalition will vanish more quickly than it appeared."
Daru was sent for and told to go at once and prepare the necessary
orders for this retrograde movement. As Daru was leaving the room,
Bassano entered, and the Emperor put to him the usual question, "What
is being said?" Bassano replied that certain persons who pretended to
know everything were speaking of a backward movement, saying: "That
your Majesty cannot remain here. They forget that the great Frederick,
with forces vastly inferior to your own, held out all winter in the
same position against the combined armies of Austria and Russia."
This comparison made so deep an impression upon Napoleon that when Daru
returned a few hours later with all the orders he had been told to
prepare, he found the Emperor in a pensive mood, and was dismissed with
these words, "The matter requires more thought."
The result of this new meditation was that he persisted in his first
system of operations: Dresden remained the central point of his line.
Napoleon's position at the renewal of hostilities was well-nigh
desperate. He had grossly deceived himself. Keenly aware of the
demoralized condition of his own forces, he had not realized how
much worse had been the condition of the Allies. Calculating upon
the reënforcements he could muster, he had not rightly estimated the
strength which Russia and Austria could add to their resources. As to
Austria, particularly, it seems that he miscalculated to the extent of
one hundred thousand men.
In other important respects, the allied position became stronger.
Marshal Ney's chief of staff, Jomini, deserted, and carried over to
the enemy the general knowledge he had gained in Napoleonic warfare,
as well as the special information he had obtained in the present
campaign. General Moreau, leaving Baltimore in the United States,
had landed at Stralsund, where Bernadotte received him with the
highest military honors; and he was now in position to direct the
allied forces. Thus with Bernadotte, Jomini, and Moreau to guide their
counsels, the Allies would be able to combat Napoleon with advantages
they had never possessed before. They would be advised by men who
understood his system, men who could anticipate his plans and defeat
his combinations.
"We are teaching them how to beat us!" Napoleon himself had already
said, speaking to Lannes of the improved Russian tactics. In this
campaign his enemies had agreed upon the best of policies,--to avoid
battle when he commanded in person, and to crush his lieutenants
wherever found.
In yet another respect events were telling heavily against the French.
Marshal Bessières, commander of the cavalry of the Imperial Guard, had
been killed in one of the first skirmishes; and, after Bautzen, a spent
cannon ball had mortally wounded Duroc. Both these were officers of
the highest merit, devotedly attached to the Emperor, and possessing
his implicit confidence. He had singled them out at the beginning of
his career, had lifted them from the ranks, and had raised them to
imperial peerages. Their loss he felt to be irreparable, and his grief
was almost overwhelming. For the first time in his career he was so
prostrated, on the evening of Duroc's death, that he was unable to give
orders. Alone in his tent, his head bowed to his breast, he sat in a
stupor of sorrow; and to his officers coming for instructions, he said,
"Everything to-morrow." Next morning, at breakfast, Constant noticed
the big tears which rolled down his cheeks and fell upon his plate.
The Allies, having tricked the great trickster in the matter of the
armistice, broke it to effect the junction between the Russian and
Austrian forces. This much more won by fraud, the war began again.
Napoleon made a dash at Blücher, who did not forget to fall back out
of reach, as agreed among the Allies. The dreaded Emperor, being at a
distance, vainly chasing Blücher, the main army of the Allies marched
upon Dresden, where St. Cyr was in command of the defence.
On the 25th of August, 1813, some two hundred thousand of the allied
troops invested the city, whose garrison was about twenty thousand. If
the French should lose it, ruin to their campaign would follow. In vain
Jomini urged the Austrian commander, Schwarzenberg, to attack at once,
while Napoleon was away. No. The leisurely Prince, being fatigued, or
something else, must await the morning of another day; for Napoleon was
in Silesia, too far off to be a source of disquiet. On August 26 the
assault began, St. Cyr meeting it with heroism, but steadily losing
ground.
Three hundred pieces of artillery rained shot and shell upon the
crowded city. The dying and the dead, men, women, and children
strewed the streets. The inhabitants of the town implored the French
to surrender. Two regiments of Westphalian hussars, from Jerome
Bonaparte's kingdom, went over to the enemy. But the Emperor had not
lost sight of Dresden. When the news reached him that the allied army
was crossing the Bohemian frontier, he guessed the point threatened,
and hurried to its relief. As he marched, courier after courier from
St. Cyr galloped up to hasten the coming of succor. Napoleon's horses
were spurred on to their highest speed, till he reached the outskirts
of the city, from which, with his field-glass, he could survey the
battle. The road over which he must enter Dresden was swept by such a
fire from the Austrian guns that it is said Napoleon went down upon
all fours to crawl past. As he entered the city, its defenders went
wild with joy. "There he is! There he is!" was shouted by thousands,
as the Old Guard rushed forward to meet him. "Nothing was heard," says
Caulaincourt, "but clapping of hands and shouts of enthusiasm. Men,
women, and children mingled with the troops and escorted us to the
palace. The consternation and alarm which had hitherto prevailed, were
now succeeded by boundless joy and confidence."
The Emperor had marched his army one hundred and twenty miles in
four days over roads which heavy rains had turned into bogs. He had
arrived in time; those who had strained their eyes to catch the first
glimpse of the relief columns had not looked in vain. "There he is!
There he is!" roused all drooping spirits, gave life to dead hope, so
mysteriously irresistible is the influence of a great man. The date was
August, 1813. Just a few months were to roll by before the good city of
Paris would find itself beleagued by these same Allies. Napoleon would
again be away, but would again be devouring distance, moving heaven and
earth to get back in time. Again anxious eyes would look out over walls
and battlements, scanning the horizon to catch a glimpse of the white
horse and the stunted rider, flying to the relief. Ardent patriots,
seeing what they long to see, will mistake some other figure for his,
and will raise the cry. "There he is!" But traitors and cowards will be
busy in the great captain's chief city, his own brother will act the
craven and fly, his best-beloved of the surviving marshals will fight
the feeble fight of the dastard, his son will be torn screaming and
struggling from the palace, and while the haggard eye of the war-worn
Emperor, almost there, will strain to see the towers of Notre Dame, the
white flag will fly over a surrendered town.
Too late! Just a few hours too late.
* * * * *
That night in Dresden, after having reconnoitred and made all his
dispositions, Napoleon was walking up and down his room. Stopping
suddenly, he turned to Caulaincourt and said:--
"Murat has arrived."
This brilliant soldier had wavered until the battles of Lützen and
Bautzen had been gained; but he had now come to lead a few more
matchless charges of cavalry, meteoric in splendor, before he should
lose heart again, forsake Napoleon utterly, and take his wilful course
to utter and shameful ruin.
"Murat has come. I have given him command of my guard. As long as I am
successful, he will follow my fortune."
The Allies were not aware that either Napoleon or Murat had arrived.
It is said that the battle had not been long in progress before
Schwarzenberg turned to the Czar and remarked, "The Emperor must
certainly be in Dresden."
Holding the allied centre in check by a concentrated fire of heavy
artillery, Napoleon launched Ney at their right and Murat at their
left. Both attacks were completely successful. The allied army broke at
all points, and retreated toward Bohemia, leaving some twenty thousand
prisoners in the hands of the French.
Torrents of rain had poured down during the whole day, and as Napoleon
came riding back into the city that evening by the side of Murat, his
clothes dripped water, and a stream poured from his soaked hat. As
Constant undressed him he had a slight chill, followed by fever, and he
took his bed.
Worn out as he was, the Emperor must have felt profoundly relieved. He
had won a victory of the first magnitude, infinitely greater than those
of Lützen and Bautzen, for he now had cavalry. His mistake in having
granted the armistice had perhaps been redeemed. If his lieutenants now
served him well, the coalition which had put him in such extreme peril
would dissolve. He would emerge from the danger with glory undimmed,
empire strengthened. "This is nothing!" he said, referring to his
triumph at Dresden. "Wait till we hear from Vandamme. He is in their
rear. It is there we must look for the great results."
Alas for such calculations! His lieutenants were ruining the campaign
faster than he could repair it. The Prussians, led by Bülow (nominally
under Bernadotte), had beaten Oudinot at Grossbeeren, on August 23,
driving the French back upon the Elbe. Blücher had caught Macdonald in
the act of crossing a swollen river in Silesia, had fallen upon him
and destroyed him, in the battle of Katzbach, August 26; and, to crown
the climax of disaster, Vandamme, from whom so much had been expected,
was, partly through a false movement of his own, and partly through
the failure of Napoleon to support him, crushed and captured at Kulm
(August 29 and 30).
Thus, Dresden proved a barren triumph. The Czar of Russia and the King
of Prussia should have been taken prisoners; the allied army should
have been annihilated; the war should have ended with a glorious peace
for France. How did it happen that the wrecked army escaped, and made
havoc with Vandamme at Kulm?
The story goes that the Emperor, pressing eagerly forward in pursuit
of the vanquished foe, was suddenly stricken with severe sickness; and
instead of being carried on to Pirna, was hurried back to Dresden. The
army, left without leadership, slackened in the pursuit; the Allies
were left undisturbed; and when they came upon Vandamme, that rash
officer, taken front and rear, was overwhelmed by superior numbers.
As to the cause of Napoleon's sudden illness, accounts differ widely.
General Marbot states that it was "the result of the fatigue caused by
five days in the saddle under incessant rain."
According to the Emperor himself, as reported by Daru to Pasquier,
the illness was "nothing but an attack of indigestion caused by a
wretched stew seasoned with garlic, which I cannot endure." But he had
at the time believed himself to be poisoned. "And on such trifles,"
said he to Daru, "the greatest events hang! The present one is perhaps
irreparable."
Virtually the same explanation of his sudden return to Dresden, and the
abandonment of the pursuit, was given by Napoleon at St. Helena.
It is significant that Constant's _Memoirs_ represent the Emperor as
vomiting and having a chill, accompanied by utter exhaustion, upon his
return from the battle-field on the evening of the 27th. Overwork,
exposure, mental anxiety, the continual strain of mind and body
had evidently brought on a collapse. The illness which recalled him
back from Pirna may have originated in the same natural causes. The
"stew seasoned with garlic," or the "leg of mutton stuffed with sage"
(for each statement occurs), may have been merely the thing which
precipitated the breakdown which was already inevitable.
Whatever the cause, the results were decisive. As at Borodino, he
lost all control of events, let the campaign drift as it would, and
recovered himself when it was too late to repair the mischief.
Dresden was to prove the last imperial victory. When Napoleon, drenched
and dripping, his fine beaver aflop on his shoulder, was taken into
the arms of the grateful King of Saxony, on the return from the
battle-field of Dresden, he was receiving the last congratulation which
he as Emperor would ever hear from subject monarch. To this limit had
already shrunk the fortunes of the conqueror who, a few months back,
had summoned Talma from Paris to play "to a parquet of kings."
A stray dog wandering about the battle-field of Dresden, with a collar
on its neck, attracted some curiosity, and it was soon known in the
French army that the collar bore the inscription, "I belong to General
Moreau." It was soon known, likewise, that this misguided soldier had
been mortally wounded early in the action, and had died amidst the
enemies of his country.
Napoleon believed that he himself had directed the fatal shot; but one
who was in Moreau's party at the time contended that the ball came from
a different battery.
Remaining in the vicinity of Dresden till the last days of September,
Napoleon found himself gradually growing weaker. His army was
crumbling away through hardships, disease, and battle. Reënforcements
as steadily added to the strength of the Allies. Operating in a country
hostile to him as it had never been before, Napoleon had the utmost
difficulty in keeping himself advised of the numbers and movements
of the forces opposed to him. So intense was the patriotic spirit in
Germany that the spy could do almost nothing for the French, while the
Allies were kept informed of everything.
It was Blücher who took the offensive for the Allies, and boldly
crossed the Elbe at Wartenburg. Napoleon rushed from Dresden to throw
himself upon the Prussians; but as soon as Blücher learned that
Napoleon was in his front he shunned battle and went to join Bernadotte
(October 7, 1813). The huge iron girdle of the allied armies was slowly
being formed around the French; it became evident that the line of the
Elbe must be abandoned.
But before taking this decision it seems that Napoleon had contemplated
a bold forward march upon Berlin, and had been thwarted by the
opposition of his generals. Ever since the Russian disasters had broken
the spell of his influence, the Emperor had encountered more or less
surliness and independence among his higher officers. The marshals had
taken a tone which was almost insubordinate, and the great captain was
no longer able to ignore their opinions.
When it became known that he intended to make a dash at Berlin,
regardless of the possibility that armies double the size of his
own might throw themselves between him and France, there was almost
universal dissatisfaction among the troops. Moscow was recalled. Nobody
wanted a repetition of that hideous experience. "Have not enough of us
been killed? Must we all be left here?"
To add to Napoleon's embarrassment, news came that Bavaria had deserted
and gone over to the Allies. Says Constant, "An unheard-of thing
happened: his staff went in a body to the Emperor, entreating him to
abandon his plans on Berlin and march on Leipsic."
For two days the Emperor did nothing. Quartered in the dismal château
of Düben, he became as inert, as apathetic, as he had been at Borodino
and at Moscow. "I saw him," writes Constant, "during nearly an entire
day, lying on a sofa, with a table in front of him covered with maps
and papers which he did not look at, with no other occupation for hours
together than that of slowly tracing large letters on sheets of white
paper."
The Emperor yielded to the pressure of his officers, and "the order to
depart was given. There was an outburst of almost immoderate joy. Every
face was radiant. Throughout the army could be heard the cry, 'We are
going to see France again, to embrace our children, our parents, our
friends.'"
Falling back upon Leipsic, Napoleon found Murat already engaged with
the Austrians. In the hope that he could crush Schwarzenberg before
Blücher and Bernadotte came up, the Emperor prepared for battle. There
were about one hundred and fifty thousand of the Austrians, while the
French numbered about one hundred and seventy thousand; but it was
necessary to place the divisions of Ney and Marmont on the north, where
the Russians and Prussians and Swedes were expected. The great "Battle
of the Nations" began on the morning of the 16th of October, 1813, and
raged all day. The advantage was with the French, for they fought from
positions more or less sheltered; but the Emperor appears to have made
one serious mistake. Blücher not having yet arrived, Ney and Marmont
were ordered to Napoleon's aid in the effort to destroy the Austrians
before the coming of reënforcements. Ney moved, but Marmont was already
engaged with Blücher when he received the Emperor's order. Holding
his ground and assaulted by overwhelming numbers, Marmont's corps was
almost destroyed; while Ney, divided between his old position and the
new, rendered no effective service in either place. Just as d'Erlon's
corps, swinging like a pendulum between Quatre-Bras and Ligny did not
strike at either point, so Ney lost his force on the fatal field of
Leipsic.
General Marbot states, moreover, that Ney left his original position
without orders from the Emperor. Blücher, getting up before Napoleon
expected him, and worsting the French on the north, turned the scales
in favor of the Allies.
Why it was that Napoleon had not called St. Cyr from Dresden, and
thus added thirty thousand to his own forces, cannot now be known. He
himself said at St. Helena that he sent despatches to this effect, but
that they were intercepted. Taking into account the swarms of Cossacks
and Bashkirs which were flying over the country, and also the intensely
hostile spirit of the native populations, the capture of a French
courier would seem to have been a natural event.
However, there are those who say that St. Cyr was left at Dresden on
purpose, because Napoleon was unwilling that the Saxon capital should
fall into the hands of the enemy. In other words, he left his garrison
caged at Dresden, just as he left cooped up within similar fortresses
a sufficient number of veteran troops to have made his army as large as
that of the Allies.
In the year 1797 the young Napoleon had driven the Austrian armies from
Italy, had chased them through the mountains of the Tyrol, and had come
almost in sight of Vienna. Austria sent Count Meerfeldt into the French
lines to sue for peace, and her prayer was granted. In 1805 this same
Napoleon had shattered the Russo-Austrian forces at Austerlitz, and was
about to capture both Czar and Emperor. Again Count Meerfeldt was sent
to Napoleon's tent to beg for mercy, and again the plea was heard. Now
it was 1813, the tide had turned, and it was Napoleon's time to ask
for peace. His messenger was a released captive, Count Meerfeldt, he
of Leoben and Austerlitz; and to the message neither Czar nor Austrian
emperor returned any answer whatever.
During the 17th there was no fighting, and the French made no movement.
They could probably have retired unmolested, but Napoleon was awaiting
a reply to his propositions.
During the night, rockets blazed in the sky on the north--the signal to
Schwarzenberg and Blücher that Bernadotte and Bennigsen had come. The
Swedes, the German bands, the Russian reserves, were all up, and the
Allies would now outnumber the French two to one.
With the light of the 18th began "the greatest battle in all authentic
history." Nearly half a million men threw themselves upon each other
with a fury like that of maniacs. Men from every quarter of Europe were
there, from Spain to Turkey, from the northern seas to the Adriatic and
Mediterranean, men from palaces and men from huts, men who flashed
like Murat in the gaudiest uniforms of modern Europe, and men like the
Bashkirs who wore the dress and carried the bow and arrow of ancient
Scythia.
The French never fought better than on this day, nor did the Allies;
but the French soldier was not what he had been, nor were French
officers the same. Shortly before this the Emperor had said to
Augereau, "You are no longer the Augereau of Castiglione;" and the
answer was, "Nor have I the troops of Castiglione." Ney had written,
after his overthrow at Dennewitz: "I have been totally defeated, and do
not know whether my army has reassembled. The spirit of the generals
and officers is shattered. I had rather be a grenadier than to command
under such conditions." Napoleon had exclaimed in bitterness of spirit,
"The deserters will be my ruin."
Bavaria, threatened by the Allies and carried along by the torrent
of German patriotism, was threatening Napoleon's rear. The King of
Würtemberg had honorably given notice that he also would be compelled
to turn against the French. Saxony was moved by the same influences,
and, in spite of the presence of her king in Leipsic, the Saxon troops
felt the impulse of national passion. In the very hottest of the
fight on the great day of the 18th, the Saxon infantry went over to
Bernadotte, and turned their batteries upon the French. The Würtemberg
cavalry followed. Then all was lost. The courage of the bravest, the
skill of the ablest, sink before such odds as these. One account
represents Napoleon as lifting a rage-swept face to heaven, with a
cry of "Infamous!" and then rushing at the head of the Old Guard to
restore the broken line. Another story is that he sank into a wooden
chair which some one handed him, and fell into the deep sleep of utter
exhaustion.
Bernadotte had commanded the Saxon troops for Napoleon in the campaign
of 1809. He had issued a proclamation, on his own motion, claiming
credit for the victory of Wagram for these Saxons, and the Emperor
reproved him for the untruth and the impertinence. Operating now
against Napoleon, and in Saxony, Bernadotte had broadcasted the country
with a proclamation calling upon the Saxons to join him. It is quite
possible that the coincidence of these circumstances influenced the
wavering troops, who had used half their ammunition against the Allies,
to spend the other half against the French.
This desertion of about twenty-five thousand men furnished one
imperative reason for retreat; but there seems to have been a second,
equally good. Constant says, "In the evening the Emperor was sitting
on a red morocco camp-stool amidst the bivouac fires, dictating orders
for the night to Berthier, when two artillery commanders presented
themselves to his Majesty, and told him that they were nearly out of
ammunition." Some two hundred and twenty-five thousand cannon balls had
been fired, the reserves were exhausted, and the nearest magazines were
out of reach.
The retreat began that night; and troops continued to pour across the
one bridge of the Elster as fast as they could go. Why was there but
one bridge? No satisfactory answer can be made, unless we adopt the
theory of sheer neglect. The stream was so small that any number of
bridges might have been built during the idle day of the 17th; but no
orders were issued, and the French army was left to fight awful odds,
with a river at its back, over which lay the only line of retreat,
and across which there was a single bridge. Did the Emperor forget the
terrible experience of Aspern? Was he no longer the Napoleon of Rivoli,
as Augereau was no longer the Augereau of Castiglione?
"Ordener is worn out," Napoleon remarked at Austerlitz. "One has but a
short time for war. I am good for another six years, and then I shall
have to stop."
Austerlitz was fought at the close of 1805; Leipsic toward the end of
1813: the great captain had already gone two years beyond his limit.
The lean, wiry, tireless young general of the Italian campaign, who
had fought Alvinczy five days without closing his eyes or taking off
his boots, could never be identified in the dull-faced, slow-moving,
corpulent, and soon-wearied Emperor of 1813.
Next morning, October 19, the Allies discovered that the French were
in retreat, and this attack was renewed at all points with passionate
energy. Napoleon left his bivouac, came into Leipsic, took up quarters
in the hotel called _The Prussian Arms_. He went to the palace to
take leave of the King and Queen of Saxony, who wished to follow
his fortunes still. He advised them to stay and make the best terms
possible with the Allies. He released his remaining Saxon troops. All
day the retreat went on, the battle raging at the same time, the French
rear-guard maintaining itself with superb courage.
The magistrates of the town, fearing its utter destruction, begged
the Allies to suspend the cannonade till the French could get away.
"Let Leipsic perish," answered the "Saviors of Germany"; and the guns
continued to roar.
To protect his rear while the retreat was in progress, Napoleon was
urged to fire the suburbs next to the allied lines. He nobly refused.
What a horrible day it must have been! The steady thunder of a thousand
cannon; the crackle of four hundred thousand muskets; the shouts of
onset; the shrieks of the wounded; the fierce crash of caissons and
wagons; the stormlike hurly-burly of countless men and horses, all wild
with passion, all excited to the highest pitch of action, all crowding
desperately toward the maddened town, the gorged, blood-stained
streets--to reach the all-important bridge!
The world seemed ablaze with hatred for the fleeing French. The very
body-guard of the Saxon king whirled upon their stricken allies, and
poured deadly volleys into the retreating ranks. Even the cowardly
Baden troop, which had been left in Leipsic by the French, to chop wood
for the bakehouses, now laid aside their axes, and from the shelter of
the bakeries shot down the French soldiers as they passed.
The Emperor with difficulty had crossed the river, and given personal
direction to the reunion of the various corps. The rear-guard was
making heroic efforts to save the army; and all was going as well as
defeats and retreats can be expected to go, when suddenly there came a
deafening explosion which, for a moment, drowned the noise of battle.
It roused Napoleon, who had fallen asleep; and when Murat and Augereau
came running to tell him that the bridge had been blown up and the
rear-guard cut off, he seized his head convulsively in his hands,
stunned by the awful news.
The French officer, charged with the duty of destroying the bridge
when the rear-guard should have passed, had touched off the mine too
soon.
The twenty odd thousand heroes who had been protecting the retreat,
found themselves hemmed in--a swollen river in front, and three hundred
thousand of the enemy in flank and rear. Some few dashed into the water
and swam across, among them Marshal Macdonald. Some in attempting to
swim were drowned, among them the golden-hearted, hero-patriot of
Poland, Poniatowski. But the bulk of the rear-guard laid down their
arms to the enemy.
In the three days at Leipsic Napoleon lost 40,000 killed, 30,000
prisoners, and 260 guns. The Allies lost in killed and wounded 54,000.
The retreat from Leipsic was less horrible than that from Moscow, but
it was dismal enough. Men died like flies from camp diseases; and those
who kept the ranks were demoralized.
At Erfurth, Murat left the army. The brothers-in-law embraced each
other in the fervid French fashion, which looks so much and means so
little. In this case it meant considerably less than nothing, for Murat
had already decided to join the Allies, and Napoleon had issued orders
to his minister of police to clap Murat into prison if he should set
foot in France. Murat avoided the danger by getting to Naples by way of
the right bank of the Rhine, and through Switzerland.
Sadly shorn of his strength, Napoleon wended his way homeward, doing
what he could to save the remnants of his army. So woe-begone was the
condition of the French that Bavaria, upon which Napoleon had heaped
immense favors, found itself unable to resist the temptation to give
the ass's kick to the expiring lion. At Hanau the kick was delivered,
with sorry results for the ass. The mortally wounded lion swept the
Bavarians out of his path and passed on, dragging himself across the
Rhine at Mayence, November 2, 1813.
CHAPTER XL
From the Rhine to the Vistula the retreat of the French caused an
outburst of joy. Nationalities and dynasties drew a mighty breath of
relief. Peoples, as well as kings, had warred against French domination
in 1813; and peoples, rather than kings, had been Napoleon's ruin.
Quickened into life by the French Revolution, Germany had partially
thrown feudalism off; and, whereas in 1807 there had been no such
political factor as a German people, in 1813 it was the all-powerful
element of resistance to Napoleon. The German statesman outlined a
people's programme, the German pamphleteer and agitator propagated it,
the German poet inspired it, the German pulpit consecrated it, the
German secret society organized it. There was the weapon; Spain had
shown what could be done with it; the kings had but to grasp and use
it. Under its blows, Napoleon's strength steadily sank.
Inspired by the German spirit, the allied armies rose after each defeat
ready to fight again. Carried away by the current, Napoleon's German
allies left his ranks and turned their guns upon him. Intimidated by
its power, his trusty officers lost heart, lost nerve, lost judgment.
Buoyed by its confidence, the kings had no fears, and rejected all
compromise. Napoleon was barely across the Rhine before his Rhenish
confederation was a thing of the past, the kingdom of Westphalia a
recollection, Jerome Bonaparte a fugitive without a crown, the Saxon
monarch a prisoner, Holland a revolted province, Polish independence
and the Grand Duchy of Warsaw a vanished dream.
The "Saviors of Europe" had saved it. Napoleon's "cruel yoke" would vex
Germany no more. To emphasize the fact, the "Saviors" levied upon the
country a tribute of men and money, which just about doubled the weight
of Napoleon's cruel yoke.
Very heavy had been the hand of France during her ascendency. Very
freely Napoleon had helped himself to such things in Germany as he
needed. Very harshly had he put down all opposition to his will. And
the French officers, imitating their chief, had plundered the land with
insolent disregard of moderation or morality. From Jerome Bonaparte
downward, Napoleon's representatives in Germany had been, as a rule,
a scandal, a burden, an intolerable offence to German pride, German
patriotism, and German pockets. It was with a furious explosion of
pent-up wrath that Germany at last arose and drove them out.
Who was there to warn the peoples of the European states that they
were blindly beating back the pioneers of progress, blindly combating
the cause of liberalism, blindly doing the work of absolutism and
privilege? Who would have hearkened to such a warning, had there been
those wise enough and brave enough to have spoken? Viewed upon the
surface, the work Napoleon had done could not be separated from his
mode of doing it. The methods were rough, sometimes brutal, always
dictatorial.
People could see this, feel it, and resent it--just as they saw, felt,
and resented his exactions of men, money, and war material. They could
not, or did not, make due allowance for the man's ultimate purpose.
They could not, or would not, realize how profoundly his code of
laws and his system of administration worked for the final triumph
of liberal principles. They could not, or would not, understand that
there was _then_ no way under heaven by which he could subdue the
forces of feudalism, break the strength of aristocracy, and establish
the equality of all men before the law, other than the method which he
pursued.
So the peoples in their folly made common cause with the kings,
who promised them constitutions, civil and political liberty, and
representative government. In their haste and their zeal, they ran to
arms and laid their treasures at the feet of the kings. In their ardor
and devotion, they marched and fought, endured and persisted, with
an unselfish constancy which no trials, sufferings, or defeats could
vanquish.
They advanced to the attack with fierce shouts of joy; on the retreat
they were not cast down; reverses did not dampen their hopes nor
shake their resolution. When the truce of Pleiswitz was granted, they
welcomed it only as it gave them time to recuperate. When the Congress
of Prague convened, they regarded it with dread, fearing that peace
might be made and Napoleon left part-master of Germany. When the beacon
lights blazed along the heights at midnight of August 10, they were
hailed as slaves might hail the signals of deliverance.
In his _Memoirs_, Metternich relates that when, after the battle of
Leipsic, he entered the palace of the King of Saxony to notify him
of the pleasure of the Allies, the Queen reproached him bitterly for
having deserted Napoleon's "sacred cause." Metternich states that he
informed her that he had not come there to argue the question with her.
And yet, if Metternich had any reply to make, then was the time to make
it. The Queen's side of the case was weaker then than it would ever
be again; Metternich's stronger. Perfect as may have been the Queen's
faith, it was beyond her power to pierce the curtain of the years, and
see what lay in the future. Had the spirit of prophecy touched her
lips, she would have been taken for a maniac, for this would have been
her revelation:--
"The promises the kings have made to the people will be broken; the
hope of the patriot will be dashed to the ground; counter-revolution
will set in; and the shadow of absolutism will deepen over the world.
The noble will again put on his boots and his spurs; the peasant will
once more dread the frown of his lord. The king will follow no law but
that of his pleasure; the priest will again avow that Jehovah is a
Tory and a Jesuit. Reactionaries will drive out Napoleon's Code, and
the revolutionary principles of civil equality. The prisons will be
gorged with liberals; on hundreds of gibbets democrats will rot. The
Inquisition will come again, and the shrieks of the heretic will soothe
the troubled conscience of the orthodox. Constitutions promised to
peoples, and solemnly sworn to by kings, will be coldly set aside, and
the heroes who demanded them will, by way of traitor's deaths, become
martyrs to liberty.
"Mediævalism will return; statues of the Virgin will weep, or wink, or
sweat; and miracles will refresh the faith of the righteous, bringing
death to the scoffer who too boldly doubts. The press will be gagged,
free speech denied, public assemblies made penal. The Jesuits will
swarm as never before, monasteries and convents fill to overflowing,
church wealth will multiply, and neither priest nor noble will pay
tribute to the state. Clerical papers will demand the gallows for
liberals, clericals will seize the schools, clericals will forbid all
political writings.
"The time will come when the European doctrine will again be proclaimed
that the sovereign has full power over the lives and the property of
his subjects. The time will come when this same Emperor Francis will
publicly admonish the Laybach professors that they are not to teach the
youth of Germany too much:--'I do not want learned men! I want obedient
men!'
"The time will come when in Bourbon France the work of the Revolution
will be set aside by the stroke of the pen, and absolute government
decreed again. Even in England, free speech attempted at a public
meeting will bring out the troops who will charge upon a mixed and
unarmed multitude, wounding and slaying with a brutality born of
bigoted royalism and class-tyranny. The cry for reform there will
challenge such resistance that Wellington will hold his army ready to
massacre English people.
"The time will come when these three kings--Alexander, Francis, and
Frederick William--will form their Holy Alliance in the interest of
aristocracy, hereditary privilege, clerical tyranny, and absolute
royalty. By force of arms they will crush democracy wherever it
appears; they will bring upon Europe a reign of terror; and the cause
of human progress will seem to be lost forever.
"And as for you, Prince Metternich, the time will come when you will
have been so identified with the oppressors of the people, so well
known as their busy tool, their heartless advocate, their pitiless
executioner, their polished liar, hypocrite, and comprehensive knave,
that a minister of state will proclaim amid universal applause, 'I sum
up the infamy of the last decades in the name of Metternich!'"
All this might the Queen of Saxony have said to her insolent tormentor;
for all this is literal truth. In the light of history the woman was
right: Napoleon's was the "sacred cause."
* * * * *
When the Emperor reached Paris, his situation was as trying as any
mortal was ever called upon to face. Not a legitimate king like
Alexander, Frederick William, or Francis, his power could not rally
from shocks which theirs had so easily survived. Great as had been his
genius for construction, he could not give to his empire the solidity
and sanctity which comes from age. He could create orders of nobility,
and judicial, legislative, and executive systems; he could erect a
throne, establish a dynasty, and surround it with a court; but he could
not so consecrate it with the mysterious benediction of time that it
would defy adversity, and stand of its own strength amid storms which
levelled all around it.
The great Frederick and the small Frederick William remained the centre
of Prussian hopes, Prussian loyalty, Prussian efforts even when Berlin
was in the hands of the enemy, the army scattered in defeat, and the
King almost a fugitive. Prussia, in all her battles, fought for the
King; in her defeats, mourned with the King; in her resurrection from
disaster, rallied round the King.
Austria had done the same. Her Emperor Francis had as little real
manhood in him as any potentate that ever complacently repeated the
formula of "God and I." He was weak in war and in peace; in the head,
empty; in the heart, waxy and cold; in the spirit, selfish, false,
cowardly, and unscrupulous. Yet when this man's unprovoked attacks
upon Napoleon had brought Austria to her shame and sorrow,--cities
burnt, fields wasted, armies destroyed, woe in every house for lives
lost in battle,--Austria knew no rallying-point other than Francis;
and when the poor creature came back to Vienna, after Napoleon had
granted him peace, all classes met him with admiration, love, loyalty,
and enthusiasm. Napoleon, returning to France victorious, was not more
joyously acclaimed by the French than was this defeated and despoiled
Francis applauded in Vienna.
The one was a legitimate king, the other was not. On the side of
Francis and the Fredericks were time, training, habit, and system.
Germans were born into the system, educated to it, practised in it, and
died out of it--to be succeeded by generations who knew nothing but to
follow in the footsteps of those that had gone before.
In France the old order had been overthrown and the new had not so
completely identified itself with Napoleon that he could exert the
tremendous force which antiquity and custom lend to institutions.
Nevertheless, the truth seems to be that in his last struggles Napoleon
had the masses with him. Had he made a direct appeal to the peasantry
and to the workmen of the cities, there is every reason to believe
that he could have enrolled a million men. The population in France
was not at a standstill then as it is now. It was steadily on the
increase; and it was fairly prosperous, and fairly contented. The
Emperor had given special attention to agriculture and manufactures. In
every possible way he had encouraged both, and his efforts had borne
fruit. He had not increased the taxes, he had not burdened the State
with loans, he had not issued paper money, he had not even changed the
conscription laws. In some of his campaigns he had called for recruits
before they were legally due; but, as the Senate had sanctioned the
call, the nation had acquiesced. It is true that men and boys had
dodged the enrolling officers, and that the numbers of those who defied
and resisted the conscriptions had increased to many thousands; but the
meaning of this was nothing more than that the people were tired of
distant wars.
A pledge from the Emperor that soldiers should not be sent out of
France would apparently have rallied to him the full military support
of the nation. But Napoleon could not get his own consent to arm the
peasants and the artisans. Both in 1814 and in 1815 that one chance of
salvation was offered to him; in each year he rejected it.
The awful scenes of the Revolution which he had witnessed had left him
the legacy of morbid dread of mobs. The soldier who could gaze stolidly
upon the frightful rout at Leipsic, where men were perishing in the
wild storm of battle by the tens of thousands, could never free himself
from the recollection of the Parisian rabble which had slaughtered a
few hundreds. At Moscow he refused to arm the serfs against their
masters; in France he as deliberately rejected all proposals to appeal
to the lower orders to support his throne.
The secret is revealed by his question, "Who can tell me what spirit
will animate these men?" He feared for his dynasty, dreading a republic
in which free elections would control the choice of the executive.
But while the mass of the French people remained loyal to Napoleon,
the upper classes were divided. There had always been a leaven of
royalism in the land, and Napoleon himself had immensely strengthened
its influence. Bringing back the émigrés, restoring hereditary estates,
creating orders of nobility anew, and establishing royal forms, he
had been educating the country up to monarchy as no one else could
have done--had been "making up the bed for the Bourbons." The ancient
nobility, as a rule, had secretly scorned him as a Corsican parvenu,
even while crowding his antechambers and loading themselves with his
favors. Now that reverses had commenced, their eyes began to turn to
their old masters, the Bourbons, and the hopes of a restoration and a
counter-revolution began to take distinct shape in Paris itself.
To the royalists, also, went the support of a large number of the
rich--men who resented the income tax of twenty-five per cent, which
Napoleon at this time felt it necessary to impose upon them. Another
grudge, they, the rich, had against him: he would not allow them to
loot his treasury, as the rich were doing in England. Nor would he
grant exemptions from any sort of public burden, special privilege
being in his eyes a thing utterly abominable. Hence, such men as the
great banker Laffitte were not his friends.
There was another element of opposition which made itself felt at this
crisis. There were various contractors, and other public employees,
who had taken advantage of the decline of Napoleon's power to plunder,
embezzle, and cheat. The Emperor was on the track of numbers of these
men, and in his wrath had sworn to bring them to judgment. "Never will
I pardon those who squander public funds!" These men moved in upper
circles, and had many social, political, and financial allies. Dreading
punishment if Napoleon held his throne, they became active partisans
of the Bourbon restoration. Even his old schoolmate, Bourrienne, his
private secretary of many years, betrayed him shamelessly. The Emperor
had detected the fact that Bourrienne had been using his official
position for private gain, and had dismissed him; but on account of old
association had softened the fall by appointing him Consul at Hamburg.
At this place Bourrienne amassed a fortune by violating the Continental
system, and he now hated the man he had betrayed, and from whom he
feared punishment. This was but one case among hundreds.
Then, there was the Talleyrand, Fouché, Rémusat, Abbé Louis, Abbé
Montesquieu, Duc de Dalberg sort. Talleyrand had been enriched,
ennobled, imperially pampered, but never trusted. Napoleon had borne
with his venalities and treacheries until men marvelled at his
forbearance. This minister of France was in the pay of Austria, of
Russia, of England, of any foe of France who could pay the price.
It was probably he who sold to England the secret of Tilsit. It was
certainly he who conspired with the Czar against Napoleon, and took a
bribe from Austria every time she needed mercy from France. It was he
who extorted tribute from Napoleon's allies at the same time that he
sold state secrets to Napoleon's foes. Denounced and dismissed, and
then employed again, this man was ripe for a greater betrayal than he
had yet made, and he now believed that the opportunity was close at
hand.
Fouché, also, had been Napoleon's minister, Napoleon's Duke of Otranto.
Dabbling in conspiracies of all sorts, and venturing upon a direct
intrigue with England, Napoleon had disgraced him, instead of having
him shot. Needing him again, the Emperor had reëmployed him, thereby
affording another rancorous foe his chance to strike when the time
should come.
In the army there was the same grand division of sentiment,--the rank
and file being devoted to Napoleon, the officers divided.
The marshals were tired of war, there being nothing further in it
for them. They had been lifted as high as they could go; they had
been enriched to satiety; their fame was established. Why should they
continue to fight? Were they never to be left in peace? What was the
good of having wealth if they were never to enjoy it?
The marshals were human; their grumblings and growlings most natural.
They honestly believed that peace depended upon the Emperor alone, that
he only had to stretch forth his hand to get it.
He himself knew better; but it almost maddened him to realize that so
few understood this as he did.
"Peace! peace!" he cried impatiently, to Berthier the goose. "You
miserable----! Don't you know that I want peace more than any one? How
am I to get it? The more I concede, the more they demand!"
This brings us squarely to the question: Did the Allies, in good faith,
offer Napoleon peace, and did he recklessly refuse it?
Then and afterward he contended that he had done everything in his
power to secure honorable terms. Almost with his dying breath he
repeated this statement at St. Helena. What is the truth about it?
Let any one who wishes to know, study the _Memoirs_ of the period; let
him further study the despatches and treaties of the Allies; let him
give due weight to the influence upon these Allies of the Bourbons,
the ancient nobility, the higher priests of the Catholic Church, the
dynastic prejudices of the allied kings, and the intense personal
hatreds of such powerful counsellors of kings as Pozzo di Borgo, Stein,
Bernadotte, Castlereagh, and Talleyrand. In addition to this, let such
a student consider how the Allies violated the armistice of Pleiswitz,
the capitulations of Dantzic and Dresden, the treaties they made with
Napoleon in 1812, and that which they made with him at his abdication
in 1814.
Let such a student furthermore consider that these Allies not only
broke the treaty they made with Napoleon in 1814, but likewise violated
the pledges which they had made to their own peoples in drawing them
into the war.
If, after the study of these evidences of the bad faith of the Allies,
there still remains doubt, the _Memoirs_ of Metternich will remove
it--if it be removable.
The world knows that the only avowed purpose of the Allies was to
liberate Europe by driving Napoleon back beyond the Rhine, and that
this end had now been attained. Hence, if the real objects the Allies
had in view were those which had been made public, why should not
the war have ceased? Europe was free, Napoleon's empire shattered,
nothing remained to him but France--why should the Allies follow him
there? It was necessary to hoodwink the world upon this point, and it
was Metternich's task to do it;--for the allied kings were determined
to invade France and put an end to Napoleon's political existence.
Metternich avows this himself; yet he persuaded them to make to
Napoleon the celebrated Frankfort Proposals. All the world knows that
the allied kings, with an apparent excess of magnanimity, offered
even then to come to such terms with Napoleon as would have left him
in possession of the France of 1792, a larger realm than the greatest
of Bourbon kings had ever ruled. What the world did not know was that
these Frankfort Proposals were not sincere, and were made for effect
only. It was necessary to the Allies to cover their own designs, to
justify their departure from the declarations of 1813, to create the
impression that they themselves favored peace while Napoleon persisted
in war. Succeeding in this, they would cut the ground from under his
feet, divide the French, and deprive him of enthusiastic and united
national support. With profound policy and duplicity, they sought to
create in France itself the impression that Napoleon was the only
obstacle to peace, and that their efforts were aimed at him, and not
at France, her institutions, her principles, or her glory. Not for a
moment was France given cause to suspect that the Bourbons were to be
forced upon her, and the great work of the Revolution partially undone.
Not for a moment was she allowed to realize that offers of peace to
Napoleon were deceptive--intended only to embarrass him and to divide
his people. Yet Metternich himself admits that the Frankfort Proposals
were made for effect--not only admits it, but takes credit for it. He
states that he was compelled to exert all his influence with the allied
sovereigns to secure their consent to these proposals, and that he
overcame their resistance, as he had overcome Alexander's in 1813, by
assuring them that the offers would come to nothing.
CHAPTER XLI
Had Napoleon promptly accepted the Frankfort Proposal as they were
made, would he have secured peace? Manifestly not, for Metternich had
put two conditions to his offer which do not look pacific. First, the
war was not to be suspended during negotiations. Second, the Frankfort
Proposals were only to be taken as _bases_ upon which diplomats could
work. Does this look like a _bona fide_ offer of peace? Napoleon
thought not, and impartial history must hesitate long before saying
he erred. When in December, 1813, he sent his envoy to the Allies,
agreeing to all they demanded, he was once more told that he should
have consented sooner. The Allies had gained their point in having made
the offer, and their active interest in the matter was at an end. The
French envoy was kept in hand, seeking audiences and positive replies,
while the allied armies marched into France.
France in 1814 was a nation of about thirty million souls. During the
years 1812 and 1813 she had furnished nearly six hundred thousand
soldiers to Napoleon's armies. Of these about half were prisoners in
Russia and Germany, or were shut up in distant garrisons; about two
hundred thousands were dead or missing; about one hundred thousand
remained subject to the Emperor's call. It was his hope that further
conscription would yield him three hundred thousand recruits; but it
failed to do so.
So much war material had been lost in the campaigns in Russia and
Saxony that he could not furnish muskets to volunteers; some went to
war armed with shot-guns. Neither could he mount any large force of
cavalry; horses could not be had. Nor were there uniforms for all; some
went to the front in sabots and blouse. Money was lacking, and the
Emperor took more than $10,000,000 from his own private funds (saved
from his Civil List), and threw them into the equipment of the troops,
calling also upon the rich for voluntary contributions, on a sliding
scale which he was thoughtful enough to furnish. A few of the taxes
were increased, the communal lands taken for the public service, and
paper money issued against the value of this particular property.
Competent judges have expressed the opinion that had Napoleon at
this time liberated the Pope and Ferdinand of Spain, and done so
unconditionally, he might have won in the campaign which was about to
open. The release of the Pope might have brought back to allegiance
many of the disaffected; the release of Ferdinand might have made it
necessary for the English to quit Spain, and in this manner Napoleon
would have drawn to his own support the veterans he still kept there.
The Duke of Wellington is quoted as saying that had Ferdinand appeared
in Spain in December, 1813, the English would have had to evacuate it.
He, of all men, should have known.
But Napoleon would not consent to make unconditional surrender to the
Pope or to Ferdinand. He patched up a peace with the latter, which,
being a halfway measure, yielded no benefit; and as to the Pope, the
Holy Father refused to treat on any terms with his "son in Christ
Jesus." Restore him to Rome first; then he would treat.
From the time Napoleon returned from Saxony till he left Paris to take
charge of his last campaign, less than three months passed.
There was never a time when he labored with greater patience or
exhibited greater fortitude, courage, and determination. But the
evidence seems to indicate that he had lost hope, that he was conscious
of the fact that nothing less than a miracle could save him.
Ever since the Russian campaign, he had not had the same confidence
in his star. As he set out from St. Cloud for his campaign in Saxony
he said to Caulaincourt: "I envy the lot of the meanest peasant of
my empire. At my age he has discharged his debts to the country and
remains at home, enjoying the society of his wife and children; while
I--I must fly to the camp and throw myself into the struggles of war."
Méneval states that in private he found the Emperor "careworn, though
he did his best to hide his anxiety."
"But in public his face was calm and reassured. In our conversations he
used to complain of feeling tired of war and of no longer being able to
endure horse exercise. He reproached me in jest with having fine times,
whilst he painfully dragged his plough."
Is there anything which is more pathetic and which shows how grandly
Napoleon towered above the small men who were tugging to pull him down
than his rebuke to the intriguers of the legislative body?
At the head of a disloyal faction there, M. Lainé--an old Girondin,
now a royalist, who was soon to set up the Bourbon standard at
Bordeaux--started a movement which was meant to give aid to the Allies
by showing that divisions existed in France, and by forming a nucleus
of Bourbon opposition. A committee, which Lainé controlled, made a
report in which Napoleon's government was impliedly censured, and
reforms demanded. Following this lead, others in the legislative body
clamored for the acceptance of the Frankfort Proposals.
This movement of opposition in the legislative body, at a time when
half a million men were on the march to invade France, was nothing
short of treason. At such a crisis, the dullest of Frenchmen must have
understood that obstruction to Napoleon was comfort to the enemy.
Even the cold Pasquier admits that the Emperor's words to these men
were "somewhat touching."
Having reproved the committee for allowing Lainé, the royalist, to lead
them astray, Napoleon said: "I stood in need of something to console
me, and you have sought to dishonor me. I was expecting that you would
unite in mind and deed to drive out the foreigner. You have bidden him
come! Indeed, had I lost two battles, it would not have done France
greater harm."
Somewhat touching, Chancellor Pasquier? Ah, if ever the great man was
heard to sob in public, it was here! A nobler grief, and a nobler
expression of it, history has seldom recorded.
In the course of the same talk, the indignant Emperor reminded the
legislators that whatever differences existed between him and them
should have been discussed in private. "Dirty linen should not be
washed in public." Then hurried away by angry impatience at those
who were forever prating about the sacrifices he exacted of France,
he exclaimed, "France has more need of me than I of France." This
was true, but the statement was imprudent; and his enemies at once
misconstrued his meaning, and used the remark to his damage. He
dismissed the legislative body fearing, doubtless, that while he was at
the head of the army the royalists of the chamber might become a danger
in his rear.
Blow after blow fell upon the defeated Emperor during the closing weeks
of 1813. St. Cyr gave up Dresden, and Rapp surrendered Dantzic, upon
condition that their troops should be allowed to return to France. The
Allies set aside the conditions, and held the garrisons as prisoners of
war.
Constant relates two incidents which reveal Napoleon's melancholy more
fully than his words to Méneval or to the legislative body.
The Emperor went about Paris more informally than he had ever done.
Sometimes on horseback, sometimes on foot, he went to inspect his
public works, schools, and hospitals. Apparently he was curious to feel
the public pulse. Constant says that the people cheered him, and that
sometimes great multitudes followed him back to the Tuileries. The time
had been when the Emperor had not paid any special heed to the shouts
of a street mob. Now the cry of enthusiasm was music to his ears. After
one of these episodes the Emperor would return to the palace in high
spirits, would have much to say to his valet that night, and would be
"very gay."
In his visits to Saint-Denis (Girl's School of the Legion of Honor)
the Emperor was usually accompanied by two pages. "Now it happened in
the evening," writes Constant, "that the Emperor, after returning from
Saint-Denis, said to me with a laugh on entering his chamber, where I
was waiting to undress him, 'Well, well, here are my pages trying to
resemble the ancient pages. The little rogues! Do you know what they
do? When I go to Saint-Denis they wrangle with each other as to who
shall go with me.' As he spoke, the Emperor was laughing and rubbing
his hands, and repeated in the same tone a number of times, 'The little
rogues.'"
Would Chancellor Pasquier admit that this was also "somewhat touching"?
The greatest man of all history had said with proud mournfulness, "I
stood in need of something to console me," and we do not realize how
infinitely sad he was till we read in Constant's artless narrative that
the shouts of the mob made him "very gay," and that the dispute of the
boys in the palace as to which two should go out into the town with him
made him rub his hands with pleasure, and repeat time and again, "Ah,
the little rogues."
* * * * *
At the beginning of 1814 positive information came that Murat had made
a treaty with Austria, and had promised an army of thirty thousand men
to coöperate with the Allies against France. Much as this defection
must have wounded the Emperor, the worst part of it was that he knew
his sister Caroline to be more to blame than Murat. She did not believe
that the Allies meant to dethrone Napoleon; she believed he could make
peace on the basis of the Frankfort Proposals; and to save her own
crown she believed that a treaty with the Allies was necessary. To this
extent her treachery can be palliated--excuse for it there is none.
[Illustration: LETTER TO COUNTESS WALEWSKI, APRIL 16, 1814.*]
This defection was the cruelest blow of all; for Murat had been
promising his support, and the Emperor had based his plan of campaign
upon it. He had intended that Eugène should unite his forces to those
of Murat, and that the two should fall upon the Austrian line of
communications, threatening Vienna. From this plan he had expected the
happiest results.
Murat had been negotiating with England and Austria, but had not
definitely made terms. It is said that he was driven to a decision by a
wound which Napoleon inflicted upon his vanity. Murat, having written
the Emperor that he could bring thirty thousand men to the field to aid
France, was told to send the troops to Pavia, where they would receive
"the Emperor's orders." The King of Naples received this letter on a
day when, with the Queen and others, he was making a visit to Pompeii.
He was so much hurt by Napoleon's tone that he tore the despatch in
pieces, trampled on the fragments, and returned to Naples to close with
the Austrian offers.
One must pity this brave, vain, fickle Murat, urged on to his shame and
ruin by his innate levity of character, the sting of wounded vanity,
the selfish promptings of an ambitious wife, and the temptings of
professional diplomats.
England dug the grave for Murat as she did for Napoleon, her agent at
Naples being Lord Bentinck. Murat having sent the Englishman a sword of
honor, the latter wrote to his government:--
"It is a severe violence to my feelings to incur any degree of
obligation to an individual whom I so deeply despise."
On the same day he wrote to Murat: "The sword of a great captain is
the most flattering compliment which a soldier can receive. It is with
the highest gratitude that I accept, sire, the gift which you have done
me the honor to send."
Lord Bentinck belonged, we must presume, to what Lord Wolseley calls
"the highest type of English gentleman"; hence his duplicity must not
be spoken of in the terms we use in denouncing the vulgar.
Another piece of bad luck had happened to the Emperor since the
Saxon campaign--his two brothers, Joseph and Jerome, were in France.
Wellington had not left the former much to resign in Spain; but
whatever there was, Joseph had surrendered it, and he had come away.
He was now in Paris, confident as ever of his own great merits, and
most unfortunately exercising his former evil influence. Napoleon made
this imbecile Lieutenant-General of the kingdom, and having made the
Empress regent, Joseph became President of the Council of Regency. The
disastrous consequences of putting such power into Joseph's hands will
be seen presently.
At length everything which human effort and human genius could achieve
for the national defence, in so short a time, was done; and it became
imperative that the Emperor should join his army.
On Sunday of January 23, 1814, it being known that he would leave Paris
in a few hours, the officers of the twelve legions of the National
Guard assembled in the hall of the marshals, at the Tuileries, to be
presented as the Emperor should return from Mass. Presently he came;
and while the Empress stood at his side, he took his little son in his
arms, and presented him to the brilliant throng. In a voice which
revealed his deep feeling, he told them that he was about to leave
Paris to put himself at the head of the army to drive the invaders from
France, and he reckoned on the zeal of all good citizens. He appealed
to them to be united, and to repel all insinuations which would tend to
divisions. "Efforts will not be lacking to shake your fidelity to your
duties; I rely on you to reject these perfidious attempts. Gentlemen,
officers of the National Guard, I put under your protection what, next
to France, is dearest to me in all the world,--my wife and my son!"
Even Pasquier records that these words were uttered in tones which
went to the heart, and with an expression of face that was noble
and touching. "I saw tears course down many a cheek. All swore by
acclamation to be worthy of the confidence with which they were being
honored, and every one of them took this oath in all sincerity."
Warming up a little, in spite of himself, the Chancellor adds, "This
powerful sovereign in the toils of adversity, this glorious soldier
bearing up against the buffets of fortune, could but deeply stir souls
when, appealing to the most cherished affections of the human heart, he
placed himself under their protection." The learned Chancellor frostily
adds that "the capital did not remain indifferent to this scene, and
was more deeply moved by it than one might expect."
Let us get out of this draught of wind from the frozen summits of
eminent respectability, and turn to a man whose heart-beat had not been
chilled in any social or judicial ice-box.
Constant writes:--
"... The Emperor's glance rested on the Empress and on the King of
Rome. He added in a voice that betrayed emotion, indicating by look and
gesture his son, 'I confide him to you, gentlemen!' At these words, a
thousand cries, a thousand arms arose, swearing to guard this precious
trust. The Empress, bathed in tears, would have fallen if the Emperor
had not caught her in his arms. At this sight the enthusiasm reached
its climax; tears fell from every eye, and there was not one of the
spectators who did not seem ready to shed his blood for the imperial
family."
* * * * *
At the beginning of 1814 France was threatened by four armies,
aggregating half a million men. Wellington was at the Pyrenees in
the south, Bernadotte was in the Netherlands, while Blücher and
Schwarzenberg, crossing the Rhine higher up, but at different points,
were marching upon Paris by the Seine and the Marne.
With a confidence which events justified, the Emperor left Soult to
oppose Wellington. As to Bernadotte, he was neither trusted by the
Allies nor feared by Napoleon. The recreant Frenchman had merely come
to terms with the Allies because they had promised to take Norway from
Denmark and give it to Sweden. In addition to this, the Czar of Russia
had dangled before Bernadotte's eyes, as a tempting bait, the crown of
France--a fact which of itself proves the hollowness of the overtures
made to Napoleon from Frankfort. So well was the crafty Prince-Royal
of Sweden understood by those who had bought him, that he was kept
under strict personal surveillance by each of the four great allied
powers,--Russia, Austria, Prussia, and Great Britain. From an army
led by such a man, Napoleon had little to fear; and he gave his whole
personal energies to Blücher and Schwarzenberg, especially to Blücher.
This old hussar who had served under Frederick the Great, and who was
now more than seventy years of age, was the most energetic of all the
officers arrayed against France; and he gave Napoleon more trouble than
all the others put together. He could easily be outgeneralled, he could
be beaten any number of times by such a captain as Napoleon; but there
was no such thing as conquering him. Routed one day, he was ready to
fight again the next. Outmanœuvred at one point, he turned up ready for
battle at another. His marches were swift, his resources inexhaustible,
his pluck and determination an inspiration, not only to the Prussians,
but to all the allied armies. He was not much of a general, was a
good deal of a brute; but he was about as well fitted for the task of
wearing down Napoleon's strength as any officer Europe could have put
into the field.
Moving slowly from the Rhine toward Paris, meeting no resistance which
could hinder their march, the Allies, who were making war upon Napoleon
alone, and who had no grudge against France, and whose wish it was, as
they proclaimed, to see France "great, prosperous, and happy," gave
rein to such license, committed such havoc upon property, and such
riotous outrage upon man, woman, and child, that the details cannot be
printed. In Spain, Napoleon had shot his own soldiers to put an end
to pillage; in Russia he had done the same. At Leipsic he had refused
to burn the suburbs to save his army. In his invasions of Prussia and
Austria he had held his men so well in hand that non-combatants were
almost as safe, personally, as they had been under their own king.
At Berlin the French Emperor publicly disgraced a prominent French
officer for having written an insulting letter to a German lady.
In France the sovereigns whose every proclamation and treaty ran under
the sanctimonious heading, "In the name of the Holy and Indivisible
Trinity," let loose upon the country savage hordes of Cossacks, Croats,
and Prussian fanatics who wreaked their vengeance upon the non-combatant
peasantry and villagers until the invasion of the "Saviors of Society"
became a saturnalia of lust and blood and arson, which no language fit
for books can describe.
The Prussians had almost reached Brienne when the Emperor took the
field with a small force, and drove them from St. Dizier. He then came
upon Blücher at Brienne, suddenly, while the Prussian general was
feasting at the château, and captured one of the higher officers at the
foot of the stairs. The Emperor believed he had nabbed Blücher himself,
and he shouted, "We will hold on to that old fighter; the campaign will
not last long!"
But Blücher had fled through the back door, and had escaped. The battle
raged over the school grounds and the park where Napoleon had read and
meditated in his boyhood. During the fight he found himself storming
the school buildings, where the Prussians were posted; and he pointed
out to his companions the tree in the park under which he had read
_Jerusalem Delivered_.
One of the guides in the movement about Brienne was a curé who had been
a regent of the college while Napoleon was there. They recognized each
other, the Emperor exclaiming: "What! is this you, my dear master? Then
you have never quitted this region? So much the better; you will be
more able to serve the country's cause."
The curé saddled his mare and took his place cheerfully in the imperial
staff, saying, "Sire, I could find my way over the neighborhood with my
eyes shut."
The Emperor drove the Prussians from Brienne with heavy loss; but when
Blücher joined Schwarzenberg, and Napoleon with his slender force
attacked this huge mass at La Rothière, he was beaten off, after a
desperate combat.
Riding back to the château of Brienne to spend the night, the Emperor
was suddenly assailed by a swarm of Cossacks, and for a moment he was
in great personal danger; so much so that he drew his sword to defend
himself. A Cossack lunged at him with a lance, and was shot down by
General Gourgaud.
This incident gave Gourgaud a claim upon Napoleon which was heard of
frequently afterward,--rather too frequently, as the Emperor thought.
At St. Helena Gourgaud, a fretful man and a jealous, tortured himself
and his master by too many complaints of neglect; and reminded the
Emperor once too often of the pistol-shot which had slain the Cossack.
"I saw nothing of it," said Napoleon, thus putting a quietus to that
particularly frequent conversational nuisance.
It was now the 1st of February, 1814; the Emperor fell back to Nogent,
the Austrians following. Blücher separated from Schwarzenberg, divided
his army into small detachments, and made straight for Paris. In a
flash Napoleon saw his advantage, and acted. At Champ-Aubert he fell
upon one of these scattered divisions and destroyed it. At Montmirail
he crushed another; and hurling his victorious little army upon
Blücher himself, drove that astonished old warrior back upon Châlons.
Putting his guard into carts and carriages, and posting at the highest
speed night and day, Napoleon united with Marshals Oudinot, Victor,
and Macdonald at Guignes. On February 18 he fell upon the huge army
of Schwarzenberg at Montereau and actually drove it back toward
Troyes,--the Austrians as they retired calling upon old Blücher to come
and give them help!
When Caulaincourt, early in December, 1813, had appeared at Frankfort
ready to accept those famous proposals unconditionally, Metternich
had shuffled, evaded, and procrastinated. Finally, a Peace Congress
was assembled at Châtillon (February 6, 1814); and while the soldiers
marched and fought, the diplomats ate, drank and made themselves merry
in the farce of trying to arrange a treaty. Caulaincourt, gallant and
hospitable, supplied his brother diplomats at Châtillon with all the
good things which Paris could furnish,--good eatables, good drinkables,
and gay women. Hence, the Peace Congress was a very enjoyable affair,
indeed. It was not expected to do anything, and it fully came up to
expectations. As the tide of success veered, so shifted the diplomats.
When the Allies won a victory, their demands advanced; when Napoleon
won, the demands moderated. There was no such thing as a coming
together.
CHAPTER XLII
After his defeat at La Rothière, the Emperor authorized Bassano to
make peace, giving to Caulaincourt unlimited powers. But before the
necessary papers could be signed, Blücher had made his false movement,
and Napoleon's hopes had risen. Bassano, entering his room on the
morning of February 9, found the Emperor lying on his map and planting
his wax-headed pins.
"Ah, it is you, is it?" cried he to Bassano, who held the papers in
his hands ready for signing. "There is no more question of that. See
here, I want to thrash Blücher. He has taken the Montmirail road. I
shall fight him to-morrow and next day. The face of affairs is about to
change. We will wait."
In the movements which followed the Bonaparte of the Italian campaign
was seen again, and for the last time. He was everywhere, he was
tireless, he was inspiring, he was faultless, he was a terror to his
foes. We see him heading charges with reckless dash, see him aiming
cannon in the batteries, see him showing his recruits how to build
bridges, see him check a panic by spurring his own horse up to a live
shell and holding him there till the bomb exploded, see him rallying
fugitives, on foot and sword in hand. We hear him appeal to his tardy
marshals to "Pull on the boots and the resolution of 1793"; we hear
him address the people and the troops with the military eloquence of
his best days; we see him writing all night after marching or fighting
all day--his care and his efforts embracing everything, and achieving
all that was possible to man.
That was a pretty picture at the crossing of the river Aube, where
Napoleon was making a hasty bridge out of ladders spliced together,
floored with blinds taken from the houses near by. Balls were tearing
up the ground where the Emperor stood; but yet when he was about to
quench his extreme thirst by dipping up in his hands the water of the
river, a little girl of the village, seeing his need, ran to him with
a glass of wine. Empire was slipping away from him, and his mind must
have been weighed down by a thousand cares; but he was so touched by
the gallantry of the little maid that he smiled down upon her, as he
gratefully drank, and he said:--
"Mademoiselle, you would make a brave soldier!"
Then he added playfully, "Will you take the epaulets? Will you be my
aide-de-camp?" He gave her his hand, which she kissed, and as she
turned to go he added, "Come to Paris when the war is over, and remind
me of what you did to-day; you will feel my gratitude."
He was no gentleman; he had not a spark of generosity in his nature; he
was mean and cruel; he was a superlatively bad man. So his enemies say,
beginning at Lewis Goldsmith and ending at Viscount Wolseley. It may be
so; but it is a little hard on the average citizen who would like to
love the good men and hate the bad ones that a "superlatively evil man"
like Napoleon Bonaparte should be endowed by Providence with qualities
which make such men as Wellington, Metternich, Talleyrand, Czar
Alexander, Emperor Francis, or Bourbon Louis seem small, seem paltry,
seem prosaic and sordid beside him.
Another glimpse of the Emperor fixes attention in these last struggles.
He was at the village of Méry where he rapidly reconnoitred over the
marshy ground bordering the Aube. Getting out of the saddle, he sat
down upon a bundle of reeds, resting his back against the hut of a
night-watchman, and unrolled his map. Studying this a few moments, he
sprang upon his horse, set off at a gallop, crying to his staff, "This
time we have got them!"
It did indeed seem that Blücher was entrapped and would be annihilated;
but after very heavy losses he managed to get across the marsh and the
river. It is said that a sudden frost, hardening the mud, was all that
saved him.
Having been reënforced by the corps of Bülow and Woronzoff, which
England had compelled Bernadotte to send, Blücher advanced against
Marmont on the Marne. The French fell back upon the position of Marshal
Mortier; and the two French generals, with about twelve thousand,
checked one hundred thousand Prussians.
Napoleon, with twenty-five thousand, hurried to the support of his
marshals, and was in Blücher's rear by March 1. Once more the Prussian
seemed doomed. His only line of retreat lay through Soissons and across
the Aisne. With Napoleon hot upon his track, and in his rear a French
fortress, how was he to escape destruction? A French weakling, or
traitor, had opened the way by surrendering Soissons. Had he but held
the town for a day longer, the war might have ended by a brilliant
triumph of the French. Moreau was the name of the commandant at
Soissons--a name of ill-omen to Napoleon, whose fury was extreme.
"Have that wretch arrested," he wrote, "and also the members of the
council of defence; have them arraigned before a military commission
composed of general officers, and, in God's name, see that they are
shot in twenty-four hours."
Here was lost the most splendid opportunity which came to the French
during the campaign. Blücher safely crossed the Aisne (March 3)
in the night, and was attacked by Marmont on March 9. During the
day the French were successful; but Blücher launched at the unwary
Marmont a night attack which was completely successful. The French
lost forty-five guns and twenty-five hundred prisoners. In a sort
of desperation, Napoleon gave battle at Laon, but was so heavily
outnumbered that he was forced to retreat.
Almost immediately, however, he fell upon the Russians at Rheims, March
13, killed their general, St. Priest, and destroyed their force. It was
at this time that Langeron, one of Blücher's high officers, wrote: "We
expect to see this terrible man everywhere. He has beaten us all, one
after another; we dread the audacity of his enterprises, the swiftness
of his movements, and the ability of his combinations. One has scarcely
conceived any scheme of operations before he has destroyed it."
This tribute from an enemy is very significant of what "this terrible
man" might have accomplished had he been seconded. Suppose Murat and
Eugène had been operating on the allied line of communications! Or
suppose Augereau had done his duty in Switzerland, in the rear of the
Allies! Spite of the odds, it seems certain that Napoleon would have
beaten the entire array had he not been shamefully betrayed--abandoned
by creatures of his own making.
As if the stars in their courses were fighting against this struggling
Titan, he learned that the relations between his wife and his brother
Joseph were becoming suspicious. Chancellor Pasquier states that he
himself saw the letters written by Napoleon on leaving Rheims in which
Savary, minister of police, was censured for not having made known
the facts to the Emperor, and in which Savary was ordered to watch
closely the suspected parties. Pasquier adds that at first he thought
the Emperor must be deranged; but that information which came to him
afterward caused him to believe that Napoleon's suspicions "were only
too well founded."
Did ever a tragedy show darker lines than this? All Europe marching
against one man, his people divided, his lieutenants mutinous and
inclining to treason, his senators ready to depose him, a sister and a
brother-in-law stabbing him to the vitals, members of his Council of
Regency in communication with the enemy, nobles whom he had restored
and enriched plotting his destruction, and his favorite brother, his
Lieutenant-General of the kingdom, using the opportunity which the
trust afforded to debauch his wife!
Is it any wonder that even this indomitable spirit sometimes bent under
the strain?
Referring to the battle of Craonne, Constant writes:--
"The Emperor who had fought bravely in this battle as in all others,
and incurred the dangers of a common soldier, transferred his
headquarters to Bray. Hardly had he entered the room when he called me,
took his boots off while leaning on my shoulder, but without saying
a word, threw his sword and hat on the table, and stretched himself
on the bed with a sound which left one in doubt whether it was the
profound sigh of fatigue or the groan of utter despair. His Majesty's
countenance was sorrowful and anxious. He slept for several hours the
sleep of exhaustion."
After the Emperor's repulse at Laon, Schwarzenberg took heart and
advanced toward Paris; but Napoleon, leaving Rheims, marched to
Épernay, and the Austrians fell back, pursued by the French. The allied
armies, however, concentrated at Arcis on the Aube, and, with one
hundred thousand men, beat off the Emperor when he attacked them with
thirty thousand.
Napoleon now made his fatal mistake--fatal because he could count on
no one but himself. He moved his army to the rear of the Allies to cut
their line of communications. This was a move ruinous to them, if the
French armies in front should do their duty. The despatches in which
Napoleon explained his march to the Empress Regent at Paris fell into
the hands of the enemy, owing to Marmont's disobedience of orders
in abandoning the line of communications. They hesitated painfully,
they had even turned and made a day's march following Napoleon, when
the capture of a bundle of letters from Paris, and the receipt of
invitations from traitors and royalists in Paris, revealed the true
situation there, and convinced them that by a swift advance they could
capture the city and end the war. Accordingly they turned about,
detaching a trifling force to harass and deceive the Emperor.
These movements, Napoleon to the rear and the Allies toward Paris,
decided the campaign. The small force of eight or ten thousand, which
the Allies had sent to follow the Emperor, was cut to pieces by him
at St. Dizier, and from the prisoners taken in the action he learned
of rumors that the Allies were in full march upon Paris. He soon
learned, also, that through Marmont's disobedience of orders a severe
defeat had been inflicted upon the two marshals, and that Blücher and
Schwarzenberg had united.
What should Napoleon now do? Should he continue his march, gather up
the garrisons of his fortresses, enroll recruits, and, having cut the
enemy's communications, return to give him battle? He wished to do
so, urged it upon the council of war, and at St. Helena repeated his
belief that this course would have saved him. It might have done so.
The army of the Allies, when it reached Paris, only numbered about
one hundred and twenty thousand. Half that number of troops were
almost within the Emperor's reach, and there were indications that the
peasantry, infuriated by the brutality of the invaders, were about to
rise in mass. At this time they could have been armed, for Napoleon had
captured muskets by the thousand from the enemy. If Marmont and Mortier
would but exhaust the policy of obstruction and resistance; if Joseph
and War-minister Clarke, at Paris, would but do their duty, the Allies
would be caught between two fires, for the Emperor would not be long in
marshalling his strength and coming back.
But the older and higher officers were opposed to the plan. They told
Napoleon that he must march at once to the relief of Paris. After
a night of meditation and misery at St. Dizier, he set out on the
return (March 28, 1814). At Doulevent he received cipher despatches
from Lavalette, postmaster-general in Paris, warning him that if
he would save the capital he had not a moment to lose. This message
aroused him for the first time to the extremity of the peril. He had
expected a stubborner resistance from Marmont, had relied upon greater
effectiveness in Joseph and Clarke. But even now he did not realize
the awful truth, the absolute necessity for his immediate presence to
save Paris--else he would have mounted horse and spurred across France
as he had once done, to smaller purpose, across Spain: as he had done
the year before when Dresden was beleaguered. In this connection let
us remember what he had told Méneval,--that he was no longer able to
endure horse exercise. For a cause which may have been physical, he did
not mount a horse himself, for the long life-and-death ride, but he
sent General Dejean. Through this messenger he told Joseph that he was
coming at full speed, and would reach Paris in two days. Let the Allies
be resisted for only two days--he would answer for the balance. Away
sped Dejean, and he reached the goal in time.
The Empress and the King of Rome had been sent from the capital by
Joseph, and Joseph had taken horse to follow; but Dejean spurred after
him, and caught him up in the Bois de Boulogne. Brother's message was
delivered to brother, Napoleon's appeal made to Joseph; and the answer,
coldly given and stubbornly repeated, was, "Too late."
The Allies had marched, dreading every hour to hear the returning
Emperor come thundering on their rear; Marmont had made one of the
worst managed of retreats, and had allowed the enemy to advance
far more rapidly than they had dared to hope; Parisians had vainly
clamored for arms, that they might defend their city; and while
thousands of citizens stood on the heights of Montmartre, looking
expectantly for the Emperor, who was known to be coming, and while the
cry, "It is he! It is he!" occasionally broke out as some figure on a
white horse was seen in the distance, the imbecile Joseph wrote to the
traitorous Marmont the permission to capitulate. This note had not been
delivered, the fight was still going on, and Dejean prayed Joseph to
recall the note. "The Emperor will be here to-morrow! For God's sake,
give him one day!"
With a sullen refusal to wait, Joseph put spurs to his horse, and set
out to rejoin Maria Louisa.
In the dark corridors of human passion and prejudice, who can read the
truth? The rebukes of the outraged husband to a recreant brother may
have swayed Joseph, just as the reproofs of an indignant chief to a
disobedient subordinate may have controlled Marmont.
The note from Joseph did its work. The defence ceased, the French army
marched out, and the chief city of France fell, almost undefended.
Talleyrand and his clique had invited the Allies to march upon the
capital, and the same party of traitors had paralyzed the spirit of
the defence as far as they were able. They had found unconscious but
powerful accomplices in Napoleon's brothers.
That night the French troops marching away from Paris, according to
the terms of the capitulation, were met, only a few miles from the
city, by Napoleon. After having sent Dejean, he had hurried his troops
on to Doulaincourt, where more bad news was picked up; and, by double
marches, he reached Troyes (March 29), where he rested. At daybreak
he left his army to continue its march, while he, with a small escort,
flew on to Villeneuve. There he threw himself into a coach and,
followed by a handful of officers, dashed forward--to Sens, where he
learned that the Allies were before Paris,--to Fontainebleau, where he
was told of the flight of the Empress,--to Essonnes, where they said
that the fight of Paris was raging,--and to La Cour de France, only ten
miles from his capital, where at midnight (March 30), as he waited for
a fresh team to be put to his carriage, he heard the tramp of horses
and the clank of arms. It was a squadron of cavalry on the highroad
from Paris. He shouted to them from the dark, and to his challenge came
the terrible response, "Paris has fallen."
The scene which followed is one of those which haunt the memory. The
chilly gloom of the night, the little wayside inn, the halted cavalry,
the horseless carriage, the rage of the maddened Emperor, his hoarse
call for fresh horses, his furious denunciation of those who had
betrayed him, his desperate efforts to hurry the post-boys at the
stables, the passion which carried him forward on foot a mile along the
road to Paris, and the remonstrances of his few friends who urged him
to go back--make a weird and tragic picture one does not forget.
It was not until he met a body of French infantry, also leaving
Paris, that the frenzied Emperor would stop, and even then he would
not retrace his steps. He sent Caulaincourt to make a last appeal to
Alexander of Russia, he who had risen in the theatre at Erfurth to take
Napoleon's hand when the actor recited, "The friendship of a great man
is a gift of the gods."
A messenger was sent also to Marmont, and the Emperor waited in the
road to receive his answer; nine miles, and not much more than an hour,
being the tantalizing margin upon which, again, fate had traced the
words, "Too late." Only the river separated him from the outposts of
the enemy; their campfires could be seen by reflection in the distance,
and yonder to the west was the dull glare hanging over Paris--Paris
where a hundred thousand men were ready to fight, if only a leader
would show them how!
Leaden must have been the feet of those hours, infinite the woe of that
most impatient of men, that haughtiest of men, that self-consciously
ablest of men, as he tramped restlessly back and forth on the bleak
hill in the dark, awaiting the answers from his messengers.
At last he was almost forced into his carriage and driven back to
Fontainebleau. Making his way to one of the humblest rooms, he fell
upon the bed, exhausted, heart-broken.
You go to France to-day, and you see around you everywhere, Napoleon.
You hear, on all sides, Napoleon. Ask a Frenchman about other historic
names, and he will reply with extravagant politeness. Leave him to
speak for himself, and his raptures run to Napoleon. _He_ is the Man;
_he_ is the ideal soldier, statesman, financier, developer, the creator
of institutions, organizer of society, the inspiration of patriotism.
What Frenchman speaks of the little men who pulled Napoleon down? Who
remembers them but to curse their infamous names? Who does not know
that the very soul of French memory and veneration for the past centres
at the Invalides, where the dead warrior lies in state?
We see this now. Time works its reversals of judgment. The pamphlet
gives way to the book; the caricature to the portrait; the discordant
cry of passion to the calm voice of reason. Angels roll away sepulchral
stones; and posterity sees the resurrected Cromwells, the Dantons, the
Napoleons, just as they were. Great is the power of lies--lies boldly
told and stubbornly maintained, but great, also, is the reaction of
truth. The cause, and the man of the cause, may have been slain by the
falsehood, and Truth may serve merely to show posterity where the grave
is; but sometimes--not always--she does more; sometimes the cause, and
the man of the cause, are called back into the battle-field of the
living; sometimes the great issues are joined again; sometimes the
martyr remains triumphant, the victim holds the victory.
CHAPTER XLIII
The final resurrection and triumph of Napoleon no one could foresee on
March 31, 1814, when he lay in a stupor of weariness and soul-sickness
at Fontainebleau, while the Allies were entering Paris.
It was a sad day out there at the old palace; in the capital was
spasmodic jubilation. Talleyrand, of the Council of Regency, had
managed to remain in Paris when the Empress fled. Talleyrand became the
moving spirit of royalist intrigue. He may not have intended the return
of the Bourbons, may have been tricked by Vitrolles as Lord Holland
relates; but he had meant all the while to overthrow Napoleon, and had
countenanced, if not suggested, plans for his assassination.
To prove to Czar Alexander that France hungered and thirsted for
the Bourbons, Talleyrand got up cavalcades of young aristocrats who
rode about shouting, "Down with the tyrant! Long live Louis XVIII.!"
High-born ladies, also, began to take active part in the business, it
being an axiom with Talleyrand that if you wish to accomplish anything
important, you "must set the women going." Ladies of the old nobility,
elegantly dressed, were in the streets, distributing white cockades,
and drumming up recruits. Royalism and clericalism bugled for all their
forces; and while Napoleon's friends, disorganized, awaited leaders,
the day was carried for the Bourbons.
So that when the Allies marched into Paris, as masters, on March 31,
1814, the royalist faction welcomed the invaders as "Liberators."
How had these royalists got back to France, to freedom, and to wealth?
Through the magnanimity of "the tyrant" whom it was now so easy to
abuse. How had those high-priests of the Church, who were Talleyrand's
aides in treachery, regained their places, their influence, their
splendid importance? Through the leniency of the man who was now
abandoned, denounced, sold to the enemies of France.
And how had the wars commenced which Napoleon had inherited, and
which he had never been able to end? By the determination of kings
and aristocracies to check the spread of French principles, to crush
democracy in its birth, and to restore to its old place organized
superstition, class-privilege, and the divine right of kings. In the
long fight, the new doctrine had gone down; and the old had risen
again. Royalists, clericals, class-worshippers, fell into transports
of joy. Glorious Easter, with a sun-burst, flooded them with light.
They thronged the streets in gala dress; they filled the air with glad
outcry; they kissed the victor's bloody hand, and hailed him as a god.
They followed Czar Alexander through the streets to Talleyrand's house,
with such extravagance of joyful demonstration that you might have
thought him a French hero fresh from victories won over foreign foes.
Cossacks, driving before them French prisoners, were enthusiastically
cheered as they passed through the streets. Aristocratic women, by
the hundred, trooped after the foreigners who led the parade, threw
themselves with embraces upon the horses, and kissed the very boots of
the riders. And these troops, mark you, were those who had made havoc
in the provinces of France, with a ferocity and a lust which had not
only wreaked its fill upon helpless maid and matron, but had revelled
in the sport of compelling fathers, husbands, and sons to witness what
they could neither prevent nor revenge, and which had coldly slain the
victims after the bestial appetite had been glutted.
Cheer the Cossack bands as they <DW8> with lances the bleeding French
captives who have seen their homes burnt, and their wives and
daughters violated and butchered! Hug the horses, and kiss the feet
of the foreigners who have come to beat down your people, change your
government, quell your democracy, force back into power a king and a
system that had led the nation to misery and shame!
Do all this, O high-born ladies of France, for the triumph of to-day
is yours! But when passion has cooled and reason returned; when
overwhelming pressure from without has been removed and France has
become herself again, your excesses of servility to-day will but have
hastened the speed of the To-morrow in which your precious Bourbons,
and your precious feudalism will be driven forever forth from the land
into which foreign bayonets have brought them. The man who lingers
at Fontainebleau is to-day no longer Emperor to the high and mighty
ones in Paris. To confederated monarchs he is "Bonaparte"; to banded
conspirators he is "Bonaparte"; to recreant marshals, ungrateful
nobles, grasping clericals, treacherous Dalbergs and Talleyrands, he
is "Bonaparte." Foreign and domestic foes make their appointment at his
triumphal column in the Place Vendome, tugging and pulling to drag his
statue down, as they have dragged _him_ down.
The Empire is a wreck, the Napoleonic spell broken for all time to
come. Down with the Corsican and his works! Up with the Bourbon lilies,
and the glories of the Old Régime!
So runs the current--the shouts of the honest devotee and of the
time-server whose only aim in life is to find out which is the
winning side. Far-seeing, indeed, would be the sage,--wise as well as
brave,--who, in this hour of national degradation, should dare to say
that all this carnival of royalism would pass like a dream;--would dare
to say that the fallen Emperor would rise again and would sweep his
enemies from his path, and would come once more to rule the land--with
the majesty and the permanence which belongs to none but the immortal
dead.
* * * * *
Troops had collected in the neighborhood of Fontainebleau to the
number of forty or fifty thousand. The younger officers and the men
of the rank and file were still devoted to the Emperor. Whenever he
appeared he was met with the same old acclamations; and shouts of
"To Paris" indicated the readiness of the army for the great battle
which it was thought he would fight under the walls of Paris. After
his first torpor, Napoleon had recovered himself, had formed his
plans, and had convinced himself that the allied army could be cut
off and destroyed. But in order for him to succeed it was necessary
that treason in Paris should give him a chance to win, and treason
gave him no such chance. The high-priests and the nobles whose hands
Napoleon had strengthened by his Concordat and the recall of the
émigrés, made the streets of Paris hot with the hurry of their feet
as they ran here, there, and yonder, marshalling their partisans. The
Abbés Montesquieu and Louis, the Archbishop of Malines, cordially
working with Talleyrand and Dalberg, and assisted by banker Laffitte
and others of that kind, honeycombed the Senate and the various public
bodies with conspiracy, drawing into one common net those who merely
wished to end the war by getting rid of Napoleon, as well as those who
were original Bourbonites. In this crisis there was none to take the
lead for Napoleon. He had deprived the masses of the people of all
initiative; had given them civil liberty, but had taken away from them
all political importance. Into the hands of the nobles and the priests
he had replaced power, wealth, influence, class organization. When
the Church and the aristocracy turned upon him, where was the power
of resistance to come from? The army was a tower of strength to the
Emperor, it is true; but even here there was mortal weakness, for the
higher officers, who had been ennobled, were imbued with the spirit
of their class. If the Senate, and the Church, and the aristocracy
should declare against Napoleon, it soon became evident that his
marshals would declare against him also. He had so bedizened them with
titles, loaded them with honors, and gorged them with riches, that
they could get nothing more by remaining loyal, even though he should
finally triumph. Upon the other hand, should he fail, they would lose
everything; hence to desert him was plainly the safe thing to do.
Napoleon was holding a review of his troops at Fontainebleau when
Caulaincourt was seen to approach him, and whisper something in his
ear. He drew back as though he had been struck, and bit his lips, while
a slight flush passed over his face. Recovering himself at once, he
continued the review. Caulaincourt's whispered news had been that the
Senate had deposed him.
"The allied sovereigns will no longer treat with Bonaparte nor any
member of his family." This declaration had cleared the way for the
creation (April 1) of a provisional government by the French Senate,
which provisional government was composed of Talleyrand and four other
clerical and aristocratic conspirators.
The beginning having been made, the rest was easy. On April 3 the
Senate decreed the Emperor's deposition, alleging against him
certain breaches of the Constitution, which breaches the Senate had
unmurmuringly sanctioned at the time of their commission. Various
public bodies in and around Paris began to declare against him, having
no more right to depose him than the Senate possessed, but adding very
sensibly to the demoralization of his supporters. Even yet the army was
true; even yet when he appealed to the troops, the answering cry was,
"Live the Emperor!" Thus while in Paris his petted civil functionaries,
his restored clericals, and his nobles were jostling one another in
the tumultuous rush of desertion, and while the swelling stream of the
great treason was rolling onward as smoothly as Talleyrand could wish,
there was one cause of anxiety to the traitors,--the attitude of the
French army.
On April 4 the Emperor held his usual review; it proved to be the last.
The younger officers and the troops were as enthusiastic as ever, but
the marshals were cold. After the parade they followed Napoleon to his
room. Only in a general way is known what passed at this conference.
The marshals were tired of the war, and were determined that it should
come to an end. Napoleon had formed his plans to march upon Paris and
fight a great battle to save his crown. Marshal Macdonald had approved
the plan and was ready to second his chief; the others would listen
to no plans, and were resolute in their purpose to get rid of this
chief. It seems to be certain that if a surrender could not be got from
Napoleon by fair means, the marshals were ready to try those that were
foul. If he could not be persuaded, he was to be intimidated; and if
threats failed, he was to be assassinated. Talleyrand's provisional
government was equally determined and unscrupulous. Napoleon was to
be killed if he could not otherwise be managed. Foremost among the
marshals demanding his abdication, and apparently threatening his life,
was Marshal Ney, whose tone and bearing to his chief are said to have
been brutally harsh.
After having exhausted argument and persuasion upon these officers,
Napoleon dismissed them, and drew up his declaration that he resigned
the throne in favor of his son.
"Here is my abdication!" he said to Caulaincourt; "carry it to Paris."
He appeared to be laboring to control intense emotion, and Caulaincourt
burst into tears as he took the paper.
As long as the French army appeared to be devoted to the Emperor, the
Allies had not openly declared for the Bourbons. They had encouraged
the idea that they would favor a regency in favor of Napoleon's son,
conceding to its fullest extent the right of the French people to
select their own rulers. It was by the skilful use of this pretence
that many of the French officers had been led astray. It was by this
mingling of the sweet with the bitter that Napoleon's first act of
abdication had been wrung from him by the marshals. Succeeded by
the son he adored, France would not be wholly lost to him, since it
remained to his dynasty.
But here again Marmont ruined all. Played upon by Laffitte and
Talleyrand's clique,--flattered, cajoled, and adroitly seduced,--this
marshal of France made a secret bargain with the Allies which took from
the Emperor the strongest body of troops then at hand.
Thus it happened that when the Ney-Macdonald delegation, bearing the
conditional abdication, returned to Paris, and were urging upon the
Czar the claims of Napoleon's son, the conference was interrupted by an
excited messenger who had come to announce to Alexander that Marmont's
corps had been led into the allied lines. This astounding intelligence
ended the negotiations. The Czar promptly dropped the veil, and
disclosed the real policy of the Allies. The marshals went back to
Fontainebleau to demand an abdication freed from conditions.
Marmont had dealt the final blow to a tottering cause--"Marmont, the
friend of my youth, who was brought up in my tent, whom I have loaded
with honors and riches!" as the fallen Emperor exclaimed, in accents of
profound amazement and grief. Yes, when the miserable renegade sat down
to plot with Talleyrand the complete ruin of the Empire, it was in a
luxurious palace which Napoleon had given him.
What officer had ruined a campaign in Spain and thereby done grievous
injury to the Emperor in Russia? Who had disobeyed orders, brought on
the night surprise at Laon, and wrecked Napoleon's pursuit of Blücher?
Who had lost the line of communications, by movements against orders,
and had let Napoleon's most important despatches fall into the hands
of the enemy? Who had caused the defeat at Fère-Champenoise; who had
so feebly resisted the allied advance upon Paris that their progress
astonished themselves? Who had surrendered a vast city of eight hundred
thousand souls to foreigners, when he must have known that Napoleon
was coming to the rescue as fast as horse could run? Marmont, the
spoiled favorite; Marmont, the vainglorious weakling; Marmont, the
false-hearted traitor! Verily he reaped his reward. To the Bourbons
he became a hero, and so remained for a season. But France--the real
France--hated him as North America hates Benedict Arnold. The time came
when he who had betrayed Napoleon for the Bourbons, betrayed the elder
Bourbons for the House of Orleans. Despised by all parties, he wandered
about Europe as wretched as he deserved to be. And the day came when
the gondoliers at Venice pointed him out scornfully to each other, and
refused to bend an oar for the miscreant.
"You see him yonder! That is Marmont. Well, he was Napoleon's friend,
and he betrayed him!"
* * * * *
Undaunted even by Marmont's defection, Napoleon issued a proclamation,
and began his preparations to retire beyond the Loire, and fight it
out. His conditional abdication rejected, war could not be worse than
peace, and he explained his plan of campaign to his marshals. They cut
him short, brusquely, menacingly. The Emperor stood alone, forsaken by
all his lieutenants, and made an imploring address to them, pleading
with them to make one final effort for France. His words fell on hearts
that were turned to stone. They harshly declared that the confidence
of the army was gone. Macdonald said that they must have unconditional
abdication.
The Emperor promised to reply next day, and, as his marshals filed
out, he said, in bitterness of spirit,--"Those men have neither heart
nor bowels; I am conquered less by fortune than by the egotism and
ingratitude of my companions-in-arms."
Who has not read of that panic of apostasy which now ran like a
torrent? From the setting sun at Fontainebleau to that which was
rising in Paris, all turned--turned with the haste of panic-stricken
pardon-seekers, or of greed-devoured place-hunters. From the highest to
the lowest, the fallen Emperor's attendants left him. Princes, dukes,
marshals, generals,--all creations of his,--fled from him as from the
contagion of pestilence. Even Berthier, the favorite, the confidant,
the pampered and petted--even Berthier bit his nails for a brief season
of hesitancy, and then abandoned his friend to his misery. Marmont's
treason had hurt, had wrung a cry of amazement and pain from that
tortured spirit; but Berthier's was a crueller stab. "Berthier, you see
that I have need of consolation, that my true friends should surround
me. Will you come back?" Berthier went, and he did not come back.
They left him, singly and in squads, till he and his faithful guard
were almost all that remained. His very valets, the Mameluke he
brought from Egypt, and Constant whose _Memoirs_ portray his master so
lovingly, could not resist the panic of the hour; they turned their
backs upon their master, and, according to that master's statements in
his instructions to his executors, they robbed him before they fled.
But there were some who did not go, a few who stood the storm. May
their glorious names live forever! Among these it is pleasant to find
the name of his old schoolmate, Colonel Bussy.
Bertrand, Gourgaud, Montholon, Bassano, Cambronne, Caulaincourt,
Lavalette, Druot, and some others did not blanch. Nor did the Old Guard
falter. The "growlers" had followed the chief--murmuring sometimes,
but following--all through the terrors of the last campaign; they were
ready to follow him again.
And there were womanly hearts that warmed to the lonely monarch, and
would have consoled him--first of all, Josephine. She had watched
his every movement though the campaign with an agony of interest and
apprehension. His name was ever in her thoughts and on her lips. Of
all who came from the army she would ask: How does he look? Is he
pale? Does he sleep? Does he believe his star has deserted him? Often
the harassed Emperor found time to write to her, brief notes full of
kindness and confidence. These she would take to her privacy, read, and
weep over. She understood the great man, at the last; she had not done
so at first. From Brienne he wrote her, "I have sought death in many
battles, but could not find it. I would now hail it as a boon. Yet I
should like to see Josephine once more." This note she carried in her
bosom.
When she heard of the abdication, she was frantic with grief, and
she would have flown to his side, only she thought of one who had
the better right,--Maria Louisa. As the broken monarch sat in the
gloom, his great head sunk on his breast, two other noble-hearted
women appeared at Fontainebleau. One of them was the beautiful Polish
lady, Madame Walewski; the name of the other is not given. They
were announced, and the Emperor promised to see them. After waiting
many hours, they went away. Napoleon had fallen into revery again
and had forgotten they were there. It is said that he took poison,
intending to kill himself. This has been questioned; but it is certain
that he swallowed some drug which brought on a sudden and alarming
illness, during which he said he was going to die. "I cannot endure
the torments I experience. They have dragged my eagles in the dirt!
They have misunderstood me! Marmont gave me the last blow! I loved
him. Berthier's desertion has broken my heart! My old friends, my old
companions-in-arms!"
Says Constant: "What a night! what a night! While I live I shall never
think of it without a shudder."
On the morning after this attempted suicide, Napoleon "appeared much
as usual," and met his marshals to give them his answer to their
demand for unconditional abdication. Even yet he made one more attempt
to inspire them to effort, to infuse into them something of his own
courage. It was all in vain. Then he scrawled the few lines in which he
laid down his great office, and handed them the paper.
"You claim that you need rest! Very well, then, take it!"
"What shall we demand of the Allies in your behalf?" the marshals
inquired.
"Nothing. Do the best you can for France; for myself, I ask nothing."
They went away upon their errand, and once more the Emperor sank into
a stupor of despondency. Much of the time he spent seated upon a stone
bench, near the fountain, in the English garden which he had himself
laid out at the back of the palace. Just as he had lain, novel in hand,
upon the sofa at Moscow, silent and moody day by day; and just as he
had sat in the château of Düben, in 1813, idly tracing big letters on
white paper; so he now sat by the hour on the stone bench in the garden
at Fontainebleau, saying nothing, and kicking his heel into the gravel
until his boot had made a hole a foot deep in the earth.
Deserted as he had been, Napoleon was yet a man to be dreaded; and the
Allies were most anxious to come to terms with him, and to get him
out of the country. Partly from fear of what he might do if driven
to despair, and partly out of generosity to a fallen foe, the Czar
influenced the other powers to sign the treaty of Fontainebleau with
Napoleon, whereby he was to retain his title of Emperor, to receive
a yearly pension of $400,000 from France, and remain undisturbed as
Emperor of Elba. His son, as successor to his wife, was to have a realm
composed of Parma, Placentia, and Guastalla.
Resigning himself to his fate, Napoleon received the Commissioners whom
the Allies sent to take charge of his journey to his new empire, and
busied himself in the selection of the books and baggage he intended to
take with him.
With assumed gayety he said to Constant, whom the Emperor evidently
believed would follow him, "Eh, well, my son, get your cart ready: we
will go and plant our cabbages."
But every now and then the full sweep of bitter reality would come over
him, and he would clap his hand to his forehead, crying:--
"Great God! Is it possible?"
His departure was fixed for April 20, 1814. The Imperial Guard formed
in the White Horse Court of the palace. The Emperor appeared upon the
stairs, pale and firm. A dozen or more stanch friends waited to bid
him farewell. He shook hands with them all. The line of carriages
was waiting; but he passed hastily by them, and advanced toward the
soldiers drawn up in the court.
It was seen then that he would speak to the troops, and dead silence
reigned. The old, proud bearing was there again,--pride softened by
unutterable sadness,--and the voice was full and sonorous as he spoke
the few words which reached all hearts that day, reach them now, and
will reach them as long as human blood is warm.
"Soldiers of the Old Guard, I bid you farewell! For twenty years I
have led you in the path of honor and glory. In these last days, as
in the days of our prosperity, you have never ceased to be models of
fidelity and courage. With men such as you, our cause could never have
been lost; we could have maintained a civil war for years. But it would
have rendered our country unhappy. I have therefore sacrificed all my
interests to those of France. Her happiness is my only thought. It will
still be the object of my wishes. Do not regret my fate. If I have
consented to live, it is in order to promote your glory. I trust to
write the deeds we have achieved together. Adieu, my children! I would
that I could press you all to my heart. Let me embrace your general and
your eagle!"
He took General Petit, commander of the Guard, in his arms, and he
pressed the eagle to his lips.
The soldiers sobbed, even the Commissioners were touched; and Napoleon,
hurrying through the group which had gathered round him, reached his
carriage, fell back on the cushions, and covered his face with his
hands.
There was the word of command, the crunching and grinding of wheels,
and the carriages were soon lost to sight.
CHAPTER XLIV
The Count of Provence was living in England when Napoleon's Senate
called him to the throne. He was one of those who had "digged the pit"
for his brother, Louis XVI.; and who, when that brother was falling
into it, discreetly ran away to foreign lands. After several changes
of asylum on the Continent, he had gone to England as a last refuge.
France had well-nigh forgotten him. A generation of Frenchmen who knew
not the Bourbons had grown up; and the abuses of the Old Order were
known to the younger generation only as an almost incredible story,
told in the evenings by older people, as the family circled about the
hearthstone. So completely had the Revolution swept away the foul
wrongs of the Bourbon system, that the younger generation could never
be made to understand why their fathers hated it with such bitterness.
Reined in by the iron hand of Napoleon, the nobles and the clericals of
the Empire seemed to be harmless enough. Why should the noble and the
priest of the Old Order have been so much worse than these?
The graybeards in France knew; but the younger people could no more
realize the former situation than could the children of Daniel Boone,
George Rogers Clarke, John Sevier, or of the New England pioneers,
understand the horrors of Indian warfare. The story of Bourbon
misrule, class tyranny, and church greed fell upon the ear with a sound
deadened by the lapse of twenty odd years.
Bourbon emissaries had pledges and soft words for all parties. To
Napoleon's nobles were given the assurance that they should remain
noble; to his generals, that they should retain their honors and their
wealth. To the priests it was not necessary to say that they should
have even more than the Concordat gave, for the priests knew how dearly
the Bourbons loved the old pact between Church and State. To pacify men
of liberal ideas, promises were made that the restored Bourbons would
rule as constitutional kings, recognizing in good faith the changes
wrought by the Revolution. Napoleon's Senate was not so forgetful of
its own safety, and of the interests of France, that it failed to put
the contract in writing. The Constitution of a limited monarchy was
formulated, and the Count of Artois, brother and representative of
Louis XVIII., accepted its conditions.
In England the new King was given an ovation upon his departure for
France, and he took occasion to write to the Prince Regent that, next
to God, he owed his crown to Great Britain. This statement was not
good policy, for neither in France nor among the potentates of the
Continent did it tend to popularize the speaker; but it was the truth,
nevertheless. The settled purpose of Pitt had been the restoration
of the Bourbons, and upon this basis it is now known that he built
the first European coalition against republican France. Canning and
Castlereagh had but inherited the principles of the abler Pitt. In a
speech in Parliament (April 7, 1814), Lord Castlereagh proclaimed that
his "object had long been to restore Europe to that ancient social
system which her late convulsions had disjointed and overthrown."
As Hobhouse says, "When he talks so plainly, even Lord Castlereagh can
be understood; when he professes such principles, even Lord Castlereagh
may be believed."
Fresh from his London ovation, and full of his ideas of divine right,
Louis met the French legislative body at Compiègne, and evaded their
request for a declaration of the royal policy. It became evident that
he intended to set aside the pledges made in his name, and to rule as
absolute sovereign. To this purpose he was urged by clericals, nobles,
and his own inclinations, for, as Napoleon said, "the Bourbons had
learned nothing and forgotten nothing." With a royal disregard of
facts, he had mentally abolished Napoleon's empire, all of its glories,
all of its shame, and had appropriated the entire era to himself. In
his own mind he had become King of France at the death of the boy,
Louis XVII.; and the year 1814 was the nineteenth year of his reign!
Here, indeed, was cause for tribulation among the eminent turncoats who
had exchanged Napoleon for the Bourbon! If the Empire had been but a
hallucination, what would become of the nobles created by the Emperor,
the honors conferred by him, the lands whose titles had been granted by
him, the great institutions which had been founded by him? What would
become of his peers, his judges, his marshals, his schools, hospitals,
and public charities? Where would the Legion of Honor be? What was to
become of the revolutionary principle that all Frenchmen were equals
in law, and that all careers were open to merit? Questions like these
buzzed throughout the land, and the hum of inquiry soon grew into the
murmurs of alarm, of anger. If Bourbons came back to power in any
such temper as that, what would become of eminent statesmen who had
overturned the ancient monarchy, abolished the nobility, confiscated
the wealth of the Church, and guillotined the King? What would be the
fate of Talleyrand, Fouché, and Company? Aghast at such a prospect as
unhampered and vengeful Bourbonism threatened, eminent renegades who
had negotiated Napoleon's downfall with the Czar Alexander appealed to
the Russian monarch to stand between themselves and the danger. Like
most mortals, the Czar had a strict code of morals for his neighbors.
Ready to break pledges himself, it shocked him to see Louis ignore the
conditions upon which he had been summoned to France. In courtly phrase
the Bourbon was notified that until he confirmed the promises Artois
had made to the Senate, there should be no royal entry into Paris. Even
under this pressure, Louis would not yield an iota of the precious
dogma of divine right. Refusing to concede that the people had any
inherent powers whatever, and stubbornly maintaining that all power,
privilege, and sovereignty rested in him alone, he graciously published
a proclamation in which he granted to the people, of his own free will,
certain civil and political rights, ignoring the Senate altogether.
This "Charter" having been signed, the King made his triumphal entry
into Paris, May 3, 1814.
On the evening of the same day, as the sun was sinking in the
Mediterranean, the mountains of the island of Elba rose upon the sight
of the crew of the British vessel, the _Undaunted_, and Napoleon had
his first glimpse of his little realm in the sea.
His journey from Fontainebleau to Fréjus, on the French coast, had
been, at first, soothed by many expressions of kindness and of sympathy
from the people who thronged the line of travel; but as the fallen
Emperor reached the province where the White Terror had once raged, and
was to rage again, popular expressions underwent a complete change.
Mobs of hooting royalists surrounded his carriage, and dinned into his
ears the most brutal insults. Only his escort saved him from being torn
to pieces. At Avignon he missed, almost by miracle, the dreadful fate
which overtook Marshal Brune there, after Waterloo. Napoleon believed
that these royalist mobs were set upon him by Talleyrand's provisional
government, and perhaps his suspicion was correct. It is certain that a
certain nobleman, Maubreuil by name, afterward charged Talleyrand with
having employed him to kill Napoleon; and when Talleyrand denied the
story, Maubreuil took the first occasion to beat him--a beating which
Talleyrand was wise enough not to endeavor to punish by prosecution.
Surrounded by savage mobs who jeered him, insulted him, threatened
him, and made desperate efforts to seize him, Napoleon is said to
have lost his nerve. Unfriendly witnesses allege that he trembled,
paled, shed tears, and cowered behind Bertrand, seeking to hide. What
is more certain, is that he disguised himself in coat and cap of the
Austrian uniform, mounted the horse of one of the attendants, and rode
in advance of the carriages to escape recognition. Courage, after all,
seems to be somewhat the slave of habit: a soldier may brave death a
hundred times in battle, and yet become unnerved at the prospect of
being torn to pieces by a lot of maddened human wolves. It should be
remembered, however, that the only real evidence we have of Napoleon's
terror was the wearing of the disguise. If this makes him a coward, he
falls into much distinguished company, for history is full of examples
of similar conduct on the part of men who are admitted to have been
brave.
Napoleon had banished from court his light sister Pauline, because of
some impertinence of the latter to the Empress Maria Louisa. This light
sister was now living at a château which was on his route to the coast,
and he spent a day and a half with her. Shocked to see her imperial
brother in the Austrian uniform, she refused to embrace him until he
had put it off and put on his own.
While Napoleon was staying at the château, a crowd of people from the
surrounding country gathered in the courtyard. He went down and mingled
with them. Soon noticing an old man who wore a red ribbon in his
button-hole, Napoleon went up to him and said:--
"Are you not Jacques Dumont?"
Too much surprised to reply at once, the veteran at length faltered,
"Yes, my lord; yes, General; yes, yes, sire!"
"You were with me in Egypt?"
"Yes, sire!" and the hand was brought to the salute.
"You were wounded; it seems to me a long while ago?"
"At the battle of Trebbia, sire."
The veteran by this time was shaking with emotion, and all the crowd
had clustered thickly about these two.
Taking off his cross of the Legion of Honor, Napoleon put it upon his
old soldier; and while the veteran wept, the crowd shouted, "Live the
Emperor!"
"My name! To remember my name after fifteen years!" the old man
continued to repeat; and so great was the sensation this little
incident was creating that the Commissioners who had charge of the
exile grew alarmed, and hastened to get him back into the house.
The captain and the crew of the British frigate had never seen the
French Emperor save through the glasses of the English editors. Any one
who knows how great is the power of an unbridled press to blacken the
fairest name, distort beyond recognition the loftiest character, and
blast the hopes of the noblest career, can readily comprehend what was
the current British opinion of Napoleon Bonaparte in 1814. Seen through
the eyes of Tory editors and pamphleteers, he was a man contrasted with
whom Lucifer might well hope to become a popular hero.
Great was the surprise of Captain Usher and his sailors to see a
handsome, quiet, polite, and self-controlled gentleman, who talked
easily with everybody, conformed without fuss to all the ship
regulations, gave himself no airs of superhuman loftiness, and took an
intelligent interest in the ship and in the folks about him. So great
was the charm of his manner, and of his conversation, that English
prejudice wore away; and the sailors began to say, "Boney is a good
fellow, after all."
It is amusing to note that Sir Walter Scott records with pride the
fact that there was one sturdy sailor who was not to be softened, who
retained his surliness to the last, and whose gruff comment upon all
the good-humored talk of the Emperor was the word, "_Humbug!_" The
name of this unyielding Briton was Hinton; and both Sir Walter and his
son-in-law Lockhart record his name with a sort of Tory veneration.
In spite of the unyielding Hinton, the sailors of the _Undaunted_ grew
fond enough of Napoleon to accept a handsome gratuity from him at the
journey's end; and the boatswain, addressing him on the quarter-deck in
the name of the crew, "Thanked his honor, and wished him long life and
prosperity in the island of Elba, _and better luck next time_."
Neither Sir Walter Scott nor his son-in-law Lockhart, report Hinton's
remarks upon this occasion; and they leave us in doubt as to whether
his virtue held out against the golden temptation, or whether he
pocketed his share, with a final snort of, "Humbug!"
On May 4, 1814, the Emperor made his official landing in Elba, whose
inhabitants (about thirteen thousand souls) received him well. He made
a thorough investigation of his new empire, its industries, resources,
etc., and sitting his horse upon a height from which he could survey
his whole domain, remarked good-humoredly that he found it rather small.
Soon joined by his mother and by his sister Pauline, also by the
seven hundred troops of the Old Guard assigned him by the Treaty of
Fontainebleau, Napoleon's establishment at Porto Ferrajo resembled
the Tuileries in miniature. Imperial etiquette stiffened most of its
joints, and put on much of its formidable armor. Visitors poured into
Elba by the hundred, and with many of these Napoleon conversed with
easy frankness, speaking of past events with the tone of a man who was
dead to the world.
His restless energies found some employment in the affairs of his
little kingdom, and in the planning of all sorts of improvements upon
which he lavished freely the funds he had brought from France. With
Pauline's money he bought a country-seat, where he spent much time, and
where he could occasionally be seen helping to feed the chickens.
His mother had come and his sister, but where was wife and child? The
allied sovereigns had pledged themselves by formal treaty to send Maria
Louisa to him under escort, and the promise had been broken. Wife and
child had been enveloped with hostile influences, kept well out of his
reach, hastened from France, and carried to Vienna.
Historians gloss over the intrigue which followed--as foul a conspiracy
against human virtue and sacred human relations as ever soiled the
records of the human race.
The Emperor Francis of Austria and Metternich, his minister, were
determined that Maria Louisa should never rejoin her husband, treaty
or no treaty. They knew her character, and for his daughter the royal
father laid the most infamous snare. He deliberately encouraged
Neipperg, an Austrian libertine of high degree; and Napoleon's wife,
entangled in the meshes of this filthy intrigue which had found her all
too ready to yield, no longer wished to return to the husband she had
betrayed.
No wonder the authors who gloat over Napoleon's sins find no comfort
here; and hurry on to other topics. They have made horrible accusations
against him and his sister Pauline, on the mere word of a spiteful
Madame de Rémusat, and of an unscrupulous liar like Fouché. But the
accusations might be true, and nevertheless Napoleon would shine like a
superior being beside such an exemplar of divine right as the Emperor
Francis, who coldly and deliberately, as a matter of state policy,
pushed his own daughter into the arms of a libertine!
We have read of the crimes of the vulgar, the canaille, the Marats,
and the Héberts; does any page of modern history hold a story more
sickening than this? Did any criminal of the vulgar herd stoop to
depths more loathsome than Francis, Emperor "by the grace of God,"
wallowed in?
After having broken their treaty upon the sacred subject of wife and
child, the allied kings found it easy enough to violate it upon matters
less important. They did not respect the property of the Bonaparte
family as they had agreed; they did not pay the Bonaparte pensions;
they did not bestow the principalities promised for Napoleon's son; and
they paid no respect to that provision of the compact which secured
to Napoleon inviolably the island of Elba. Bitter personal enemies
of the fallen Emperor, Pozzo di Borgo, Lord Wellington, Talleyrand,
and others, agreed that he must be removed to a greater distance from
Europe, St. Helena being the place which met with most favor. The fact
that the allied kings had pledged themselves to allow him to remain at
Elba, seems not to have entered into the discussions at all. He who had
broken no treaties was already an outlaw in the counsels of those who
had broken all: they could deal with him as they chose. "In the name
of the most Holy Trinity" they had pledged faith to him; they could as
easily breach the last treaty as its predecessors, being kings by the
grace of God, and owing no fealty to ordinary moralities.
The British ministry began to negotiate with the East India Company for
the island of St. Helena; and the purpose of the allied kings to send
him there as a prisoner of war not only reached Napoleon at Elba, but
actually found its way into the _Moniteur_, the official gazette of
France.
The fact that Louis XVIII. did not pay one cent of the $400,000 which
the Treaty of Fontainebleau had provided for Napoleon's annual revenue,
was of itself a source of serious embarrassment to him, justifying him
in setting aside a contract which his enemies did not regard; but it
had less to do with his movements, perhaps, than any other breach of
the treaty. He cared nothing for money; little for personal luxury. "I
can get along with one horse, and with a dollar a day," he declared
with democratic independence. Besides, he could easily have secured
from Europe the sums he needed, as he himself publicly declared on
his return to France. But when he found that his wife and child would
never be surrendered; that Talleyrand and the Bourbons were still bent
upon having him assassinated; that if he could not be killed he was
to be taken away to a distant rock and held as a prisoner of war, the
impulse became irresistible to make one desperate effort to escape the
impending doom. Those who watched over his personal safety had already
stopped, disarmed, and sent away two would-be assassins: who could tell
whether the third would be stopped? It came to him that the Allies
had agreed to send him to St. Helena: who could say when a British
man-of-war might bear down upon little Elba? Brooding over his wrongs,
and over the perils of his situation, Napoleon gave way to occasional
bursts of anger, declaring that he would die the death of a soldier,
arms in hand, before he would submit to the proposed removal.
A Scotchman of rank who visited Elba at this time wrote: "Bonaparte
is in perfect health, but lodged in a worse house than the worst
description of dwellings appropriated to our clergy in Scotland,
yet still keeping up the state of Emperor, that is, he has certain
officers with grand official names about him. We were first shown into
a room where the only furniture was an old sofa and two rush-bottom
chairs, and a lamp with two burners, only one of which was lighted. An
aide-de-camp received us, who called a servant and said that one of the
lights had gone out. The servant said it had never been lighted. 'Light
it, then,' said the aide-de-camp. Upon which the servant begged to be
excused, saying that the Emperor had given no orders upon the subject.
We were then received by Bonaparte in an inner room. The Emperor wore a
very old French Guard uniform with three orders, and had on very dirty
boots, being just come in from his country house."
Then the writer describes a conversation in which Napoleon spoke
without apparent reserve of his past life. Referring to the doings of
the Bourbons in France, he remarked that they had better mind what
they were about, as there were still five hundred thousand excellent
soldiers there. "But what is all that to me?" he exclaimed with a rapid
turn; "I am to all intents and purposes dead."
"His manner," says the Scotchman, "was that of a blunt, honest,
good-hearted soldier's, his smile, when he chose it, very insinuating.
He never has anybody to dinner. Bertrand says that they are in the
greatest distress for money, as the French court does not pay the
stipulated salary to Bonaparte.
"The following day the Emperor set off for his country house. He was in
an old coach with four half-starved horses; on the wheel-horse sat a
coachman of the ordinary size, and the bridles had the imperial eagle
on them; on the leaders there was a mere child, and the bridles had the
coronet of a British viscount on them. He had General Bertrand in the
carriage, and two or three officers behind on small ponies, which could
not, by all the exertions of their riders, keep up with the carriage,
emaciated as those poor horses were."
The Scotchman contrasts the wretched little establishment at Elba with
the splendor of the Tuileries where he went to see Louis XVIII. dine in
public,--separate table for king, separate tables for princes of the
blood-royal; attendant courtiers standing in full dress, duchesses only
being permitted to sit; everything served on gold plate; the dining
hall, a hundred feet long, brilliantly lighted and hung with gobelin
tapestries, "and a very fine concert going on all the time."
The contrast between these two pictures, striking as it was to the
Scotchman, was no less so to Napoleon, who felt the squalor of Elba
and longed for the lost grandeur of France. If there had been a secret
bargain between the fallen Emperor and the Bourbons that they should
prepare the country for his speedy return, they could hardly have gone
to work in a more effective manner to accomplish that result. They had
not been in possession of the throne six months before the nation was
fairly seething with discontent.
NOTE.--While the Congress of Vienna was in session, Dr. Richard
Bright, an Englishman, was visiting the city and saw the
pageant. He describes many of the august sovereigns who were in
attendance, and gives an account of the festivities, amusements,
and polite dissipations which were in progress. But perhaps the
most interesting page the Doctor wrote was that in which he
relates his visit to Napoleon's son, who was then with his mother
at the palace of Schönbrunn. "We found that all the servants
about the palace were Frenchmen, who still wore the liveries of
Napoleon.... We ... were ushered into a room where the infant
[King of Rome] was sitting on the floor amusing himself amidst
a profuse collection of playthings.... He was at that moment
occupied with a toy which imitated a well-furnished kitchen. He
was the sweetest child I ever beheld; his complexion light, with
fine, white, silky hair, falling in curls upon his neck. He was
dressed in the embroidered uniform of an hussar, and seemed to
pay little attention to us as we entered, continuing to arrange
the dishes in his little kitchen. I believe he was the least
embarrassed of the party. He was rather too old to admit of
loud praise of his beauty, and rather too young to enter into
conversation. His appearance was so engaging that I longed to
take him in my arms, but his situation forbade such familiarity.
Under these circumstances, we contrived a few trifling questions,
to which he gave such arch and bashful answers as we have all
often received from children of his age."
Madame Montesquieu was still with the child, but, after a while,
she and all the other French attendants were dismissed. The
effort was made to wean the poor boy of all things French, and to
transform him into an Austrian.
It may be proper here to add that he died of consumption at
the early age of twenty-one. It is darkly hinted that the same
malevolent influences which destroyed the respectability of
Napoleon's wife led the son into excesses which undermined his
constitution. To the last he was passionately fond of his father,
and when Marmont visited Vienna in 1831 the Duke de Reichstadt
(as the boy was called in Austria) eagerly drew from him all that
he would tell of the great Emperor.
The cage in which Napoleon's only legitimate son was kept was
gilded with pension and title and outward show of deference, but
it was a cage, nevertheless, and he died in it (1832).
CHAPTER XLV
The ink was hardly dry upon the Charter before Louis XVIII. began to
break its conditions. It had served its purpose, he had ridden into
office upon it: what further use had he for it? Why should he trammel
his actions by treaty when the other kings of Europe were freeing
themselves from such fetters? To the south of him was Spain, where
the liberals had framed a constitution which Ferdinand, released
by Napoleon early in 1814, had sworn to respect, and which he had
set aside the moment he had taken again into his hands the reins
of power. Instead of reform and limited monarchy on the peninsula,
there was now a full restoration of the Old Order, feudalism, tithes,
local tyrannies, clerical and royal absolutism, the jails full of
democrats, and the Inquisition hungry for heretics. Nobles and priests
struck their ancient bargain, mastered a willing king, and with the
resistless strength of self-interest, class-prejudice, and corporate
unity of purpose, acting upon the ignorance, the superstition, and the
cultivated hatreds of the people, carried Spain back with a rush to the
good old times of Bourbon and Roman absolutism.
Not only in the south was counter-revolution triumphant; in the north
it was equally so. In Jerome Bonaparte's kingdom of Westphalia,
where the people had driven out the system of Napoleon, and called
in their former rulers, old laws and customs rattled back to their
rusty grooves; the Code Napoléon vanished; equality of civil right was
seen no more, feudalism fell like a chain upon the astounded peasant,
purchasers of state lands were ousted without compensation, special
privilege and tax exemptions again gladdened the elect, aristocracy
and clericalism swept away every vestige of Jerome's brief rule,
the torture chamber again rang with the shrieks of victims, and the
punishment of death by breaking upon the wheel emphasized the desperate
efforts nobles and priests were making to stem the torrent of modern
liberalism.
And the Holy Father at Rome, loosed by Napoleon from Fontainebleau at
about the same time that Ferdinand of Spain had been released from
Valençay, had wended his way back to Italy as Ferdinand had to Spain,
and, seated again in St. Peter's chair, had laid his pious hands to the
same work in Rome which Ferdinand was busy with in Madrid.
With absolutism and feudalism triumphing all around him, why should
not Louis XVIII. follow the glorious examples? Did he not owe it to
God and the ancient Bourbon kings to cast out from France the devil
of democracy which had rended her, and to clothe her once more in
her right mind--in the docile obedience to kingly word and clerical
admonition? Apparently he did; and apparently he believed that the
quicker he set about it the better.
He had guaranteed freedom of the press in his Charter; but this was a
promise he could not venture to keep. He meant to violate the Charter
and to restore the Old Order; and he knew that this could not be done
if the press remained free. He had lived in England where he may have
heard Richard Brinsley Sheridan when he thrilled the House of Commons
with that famous burst of eloquence, "Give them a corrupt House of
Lords, give them a venal House of Commons, give them a tyrannical
Prince, give them a truckling Court, and let me have but an unfettered
Press, I will defy them to encroach a hair's-breadth upon the liberties
of England!" Therefore, one of his first acts was to gag the press with
a censorship. With indecent haste, this royal ordinance breaching the
Charter was published just six days after the official publication of
the Charter itself.
Unbridled criticism by those organs which in our modern system control
public opinion being thus made impossible, other measures of similar
tendency followed swiftly.
Loudly condemning Napoleon's toleration of heretics, Jews, and
non-believers, the clericals induced the King to compel Frenchmen of
all creeds and races to suspend business not only on the Christian
Sabbath, but on the festival days of the Catholic Church.
Not satisfied with a grand religious ceremony to "purify" the spot upon
which Louis XVI. had been guillotined, nor with having dug up bones
supposed to be his and given them magnificent sepulture, Louis solemnly
devoted France to the Virgin Mary, and her image was borne through the
streets in formal procession, wherein the great dignitaries ambled
along with lighted candles in their hands.
By the Charter, the army had been specially protected. Napoleon's
soldiers still had guns in their hands and rage in their hearts when
Talleyrand was writing out the pledges with which the returning
Bourbons were to be fettered. It was highly important to soothe these
troops, or to remove their fear that the Bourbons would deal with them
unjustly. Hence the sixty-ninth article of the Charter, which declared
that soldiers in active service, the officers and soldiers in retreat,
the widows, the officers and soldiers on the pension list, should
preserve their rank, honors, and pensions.
By royal ordinance (December 16, 1814) this clause of the Charter was
violated.
Fourteen thousand officers and sergeants were dismissed on half-pay;
and the places of these battle-scarred heroes of the Empire were filled
by five thousand nobles who had never seen service save with the
enemies of France. Naval officers who had deserted the ships of their
own country, and had served against their native land, were put back
into the French navy, and given the rank they had won abroad. Veterans
who had fought for the French Republic and the French Empire, from
Valmy and Jemappes to Laon and Montmirail, found themselves officered
by insolent little noblemen who had never smelt gunpowder. General
Dupont, known principally for his capitulation at Baylen, was made
minister of war. The tricolor flag which French soldiers had borne
victoriously into every capital on the Continent was put away. Many of
the bullet-shredded banners were destroyed--they and their splendid
memories being hateful to the Bourbon soul.
The white flag of the old monarchy--a flag which living French soldiers
knew only as the rallying-point of treason and rebellion in La
Vendée--was made the national standard. The numbers of the regiments
were changed, and the veterans of a dozen historic campaigns lost the
names by which they were known, and which they had made glorious in the
arduous test of battle. The Imperial Guard was banished from Paris; the
Swiss were again enrolled to defend the palace, and clad in the uniform
of 1792; a Bourbon military household was organized, filled with young
nobles who had never fired a shot, who were paid fancy salaries, and
decked out in a livery which made all Paris titter. To complete the
burlesque, they resurrected and made chief officer of the palace the
old Marquis of Chansenets, who had been Governor of the Tuileries on
August 10, 1792, and had escaped massacre that day by hiding under
piles of dead.
The young Bourbon dukes, Berry and Angoulême, knew nothing whatever of
war, practically or otherwise; yet they were put in highest military
command; and they gave themselves airs which neither Wellington,
Blücher, or Napoleon ever assumed. These young princes of the
blood-royal told French veterans on parade that their twenty years of
service under the Republic and under the Empire were but twenty years
of brigandage. When Napoleon's Old Guard failed to manœuvre as the
youthful Duke of Angoulême would have them do, they were sneeringly
advised to go to England to learn their drill. Does a colonel so
displease the Duke of Berry that he must be cashiered, disgraced?
The haughty Bourbon tears off the epaulets with his own hand! At
another time the same doughty warrior strikes a soldier on parade.
Word goes out that a monument is to be raised to the invading émigrés
whom English vessels had landed at Quiberon in 1795, and whom the
republicans had slaughtered there. Honors to these being granted,
Pichegru and Georges Cadoudal were not forgotten. Their names were
mentioned with honor, masses recited for the repose of their souls, and
a patent of nobility granted to Cadoudal's family.
By the Charter, laws were to be made by king, peers, and deputies
acting together. In actual practice the King made his own laws.
From the mouths of such men as Lainé, whom Napoleon had thoroughly
understood and denounced, the gospel of non-resistance was heard in all
its ancient simplicity, "If the King wills it, the law wills it."
Incredible as it may seem, the members of the old Parliament of Paris
met at a private house, and drew up a protest against the Charter.
With one accord nobles and priests began to speak of the return of
feudalism, of seignorial rights, of tithes, of benefices, of exclusive
chase, and of the confiscated lands. The clergy of Paris, in their
address to the King (August, 1814), expressed their earnest desire
for the restoration of "that old France, in which were intermingled,
without distinction, in every heart, those two sacred names,--God and
King."
At least one sermon was preached in which those citizens who did not
restore to the nobles and the Church the lands which the Revolution
had taken away were threatened with the doom of Jezebel--_and they
should be devoured by dogs_. Three hundred petitions were found at one
time lying upon the table of the Bourbon minister of the interior,
sent there by distressed Catholics who declared that their priests
refused them absolution on account of their being owners of national
properties. To the trembling devotee, the poor slave of superstition,
the priest said, "Surrender to Church and nobles the land you bought
and paid for, else the gates of heaven shall remain shut to you!" Under
the spell of clerical duress many a middle-class and peasant proprietor
swapped good land for a verbal free passage to the new Jerusalem. Many
nobles, imitating a king who had mentally abolished all changes since
1789, began to claim forgotten dues and to exercise offensive feudal
privileges. The Duke of Wellington himself acted the _grand seigneur_
of the Old Régime; and with a cavalcade of friends and a pack of hounds
went charging at his pleasure over the crops of the farmers around
Paris, trampling their young grain with serene disregard of peasant
rights. These nobles of old France, who had fled from the dangers of
the Revolution, and who had been restored by Napoleon, or by foreign
bayonets, were as proud, as intolerant, as though they had accomplished
the Bourbon restoration by themselves. They regarded the nobles of
Napoleon's creation with unconcealed contempt. The wives of men whose
fathers had been ennobled for shady services to shadier Bourbon kings,
looked with lofty scorn upon the ladies of such men as Marshal Ney,
whom Napoleon had ennobled for service as gallant as any soldier
ever rendered to France. To mark beyond all mistake the dividing
line between the old nobility and the new, the military schools were
reëstablished, in which a hundred years of nobility were necessary for
admission--another violation of the Charter.
Louis XVIII. was not devoid of talent, nor of worldly wisdom; but
he was not the man to contrast favorably with Napoleon. It was his
misfortune to be personally repulsive. Like his brother, Louis XVI.
he was swinish in tastes and habits. So fat that he could not mount a
horse, so unwieldy that he could only waddle about in velvet gaiters,
he was no man's hero--nor woman's either. Those who loved the ancient
system were compelled to use him, not because they loved _him_, but
because they adored the system.
Gifted with small talent for governing, how could he bring order out
of the chaos Napoleon's fall had left? How could he reconcile the
intemperate greed of the partisans of the Old Order with the advocates
of liberal ideas in France? How could he harmonize emancipated peasants
with lords of Church and State who were clamorous to reënslave them?
How could he restore prosperity to the French manufacturer suddenly
ruined by the flood of English goods, which flood Napoleon had so long
dammed with his Continental system? And when the curé of St. Roch
refused holy burial to an actress, how could the feeble Louis control
either arrogant priest or indignant, riotous friends of the actress?
And how could he prevent all France from remembering that once before
when this same priest had refused Christian burial to an opera dancer,
the iron hand of Napoleon Bonaparte had fallen upon the unchristian
curé, inflicting chastisement, and the reproof that "Jesus Christ
commanded us to pray even for our enemies"?
No wonder, then, that when Carnot published a memorial, arraigning
the government for its breaches of faith, and pointing out its rapid
progress to absolutism, the book had a vast circulation. Chateaubriand
was brought forward to write a reply, and he wrote it; but even
Chateaubriand could not slay facts with a pen, though the courtiers at
the palace seem to have believed that he had done so.
Such was the Bourbon restoration. Undoing much of the work of the
Revolution, it menaced all. Apparently it was only a question of time
when France would be clothed again in the political and religious garb
of 1789. Those who had flattered themselves that they were getting
constitutional monarchy in exchange of Napoleon's despotism, soon
realized that the Bourbon system had most of Napoleon's vices and
none of his virtues. Talleyrand, Fouché, and Company had expected to
rule the kingdom as constitutional ministers. They found that their
influence was nothing when opposed by such royalist courtiers as the
empty-headed Blacas. Three months did not elapse after Talleyrand and
Fouché had plotted the downfall of Napoleon before they were plotting
the overthrow of Louis XVIII.
* * * * *
At length the Congress of Nations assembled at Vienna (September,
1814), and a very grand gathering of notabilities it was. The Czar
of Russia, the kings of Prussia, Denmark, Bavaria, and Würtemberg,
the Emperor Francis of Austria, were present in person; the kings of
England and France were represented by Lord Castlereagh and Prince
Talleyrand, respectively; Saxony, Naples, and other small states were
represented by delegations more or less official, and more or less
recognized.
Statesmen of many countries, diplomats, envoys, agents, male and
female, attended in great numbers; and in fêtes, banquets, balls,
excursions, and miscellaneous amusements some $50,000 each day were
gayly consumed.
Faithless in their dealings with Napoleon, the allied kings had been
distrustful of each other; behind public treaties secret agreements had
lurked, and now at the Congress of Vienna these underhand dealings
began to crop out. Ostensibly Napoleon had been overthrown by a grand,
brotherly coöperation of all the European monarchs. Ostensibly the
motive of this grand, brotherly coöperation had been to liberate the
people of Europe from the grinding tyranny of Napoleonic government.
No sooner had eminently wise heads begun to wag at this congress,
loosening eminently sage tongues, than it appeared that Russia,
Prussia, Austria, and England had made a secret bargain, quite a while
ago, to divide at their own pleasure the territories of which they had
stripped the too ambitious Emperor of the French. Consequently, the
representatives of these four Christian powers began to hold little
meetings of their own, to readjust the map of Europe, shutting the door
in the face of the eminent Talleyrand and lesser lights who had come
there to wield influence on a variety of subjects. This concert of the
four Christian powers, to the utter ignoring of other powers, likewise
Christian, would have resulted in a new map of Europe, just suited to
their own views but for one thing. In reaching their secret agreement
to shut out the other powers, they had failed to come to an agreement
among themselves.
If four royal and Christian victors secretly agree to monopolize the
spoils, it is obviously of the utmost importance that they should
not fall out while dividing the loot. Russia, Austria, Prussia, and
England were in harmony so far as agreeing that those four should take
everything which Napoleon had lost; but the Congress of Vienna had
barely passed the stage of mutual congratulations, and a solemn return
of thanks to God, before the row between the four robber powers began.
The Czar demanded all of Poland; Prussia all of Saxony; Austria's
eager eyes were fixed upon Italy, and England stiffened her grip on
colonies generally.
A great deal has been said in praise of the masterly manner in which
Talleyrand forced open the door, and led France again to the council
board of nations. His boasted diplomacy seems to have amounted to no
more than this: the four powers mentioned quarrelled among themselves,
and France found her opportunity to take sides. Talleyrand made good
the opening thus offered, but surely he was not the only Frenchman who
could have done so. France had not been obliterated: she was still the
France of 1792, which had successfully resisted all Europe. If the four
great powers found themselves about to fight, two against two, was it
owing to Talleyrand's genius alone that France was courted by one party
to the feud? Surely not. It was owing to the greatness of France--not
the greatness of Talleyrand.
Louis XVIII. could have brought into the field not only the remnants
of Napoleon's army in the late campaign, but also the army with which
Soult had fought Wellington, as well as the troops which the Treaty of
Paris had released from northern prisons and garrison towns.
In a war which enlisted the support of the French people, half a
million men could easily have been armed; hence we can readily
understand why Austria and England, enraged by the greed of Russia and
Prussia, signed a secret treaty with France in January 1815.
However, the spirit of compromise worked with the Congress of Vienna;
and to avoid such a dreadful war as was on the eve of breaking out
among the allied kings, the Czar was allowed to take nearly all of
Poland; and Prussia had her way with Saxony; for while they gave her
only half of Saxony itself, they made up for the other half by giving
her more than an equivalent on the Rhine.
Juggling with the doctrine of "legitimacy," and claiming that all
thrones must be restored to princes who were rulers "by the grace of
God," and not by the choice of the people, Talleyrand seems to have
brought the powers to agree that Murat should be ousted from Naples,
and the Bourbons restored. Bernadotte could not be treated likewise,
because he was the adopted son of the legitimate King of Sweden!
He was not only confirmed in his high office, but the English fleet had
been sent to aid him in seizing the prey which had been promised him
as the price of his waging war upon his mother-country. Norway, which
Napoleon had refused to promise him, and which the Czar had promised,
was torn from Denmark by force, and handed over to Sweden, in spite of
all the Norwegians themselves could do.
* * * * *
Informed of all that was passing in France, in Italy, and at the Vienna
Congress, Napoleon prepared to make a bold dash for his throne. He
communicated secretly with Murat, with various Italian friends, with
various friends in France. Vague rumors began to circulate among his
old soldiers that he would reappear in the spring.
Did he make a secret treaty with Austria, detaching her from the
European alliance? There is some reason to believe that he did. He
repeatedly declared at St. Helena that such a treaty had been made;
and the author of the _Private Memoirs of the Court of Louis XVIII._
corroborates him. In that curious, interesting book a copy of the
alleged treaty is given.
Napoleon himself is reported to have said that the conspiracy which
Fouché had been organizing among the army officers forced him to leave
Elba three months earlier than he had intended. This is important,
if true, for it is conceded that had he waited three months longer
his chances of success would have been immensely improved--provided
that he had not in the meantime been seized as a prisoner of war or
assassinated.
Concealing his design to the last moment, Napoleon gathered up his
little army of eleven hundred men, went on board a small flotilla at
Porto Ferrajo, February 15, 1815, and set sail for France. His mother
and his sister looked on in tears while the troops were embarking, and
the Emperor himself was deeply affected. As he embraced his mother and
bade her farewell, he said, "I must go now, or I shall never go."
* * * * *
At the Tuileries on the night of March 2, 1815, a curious scene was
witnessed in the saloon of the Abbé d'André, director-general of the
royal police.
Quite a number of people being present, conversation fell upon certain
ugly rumors concerning Elba. A gentleman just from Italy spoke of the
active movements of Napoleon's agents. It was said that the Emperor
was engaged in some hostile preparations. The gentleman from Italy
evidently made an impression upon the company, and created a feeling
of uneasiness. The mere thought of Napoleon Bonaparte breaking loose
from Elba, and landing in France, was enough of itself to materially
increase the chilliness of a night in March to the Bourbon group.
But the Abbé d'André was equal to the emergency. As director-general of
police it was his business to know what Napoleon was doing, and he knew.
Rising from his chair, and striding to the fireplace, he faced the
company, and harangued them thus:--
"It is certainly a very extraordinary thing that right-thinking
people should be the first to find fault with the government. For
heaven's sake, ladies and gentlemen, do give the ministers credit for
common sense! If you think them indifferent to passing events, you
are strangely mistaken. They watch everything, see everything, and
take precautions against everything. Do not be alarmed about Elba.
Every step Bonaparte takes is carefully noted. Elba is surrounded by
numerous cruisers. All who come and all who go are carefully examined.
Government receives a daily report of all that takes place there. Now,
to convince you that your alarms are silly, I will read you the report
we received yesterday."
With this the complacent police minister drew from his pocket the
official bulletin, and read it. His agent represented that Napoleon
was reduced to a very low state of health, that he had the scurvy, and
was assailed by the infirmities of premature old age; that he rarely
went out, and that he would sometimes be seen on the seashore amusing
himself by tossing pebbles into the sea--a sure sign of approaching
lunacy. And so forth.
Having read this valuable report, d'André looked down upon his
auditors with a glance of triumph. He had demonstrated to his complete
satisfaction that Napoleon was not only in Elba, but that he was
pitching idle pebbles into a listless sea, and was on the direct route
to the lunatic asylum.
This was March 2; on the day previous Napoleon had landed at Cannes,
and was marching upon Paris!
The shock which Europe felt when the signal telegraph flashed the news
that the lion was loose again, was such as Europe had probably never
felt before, and will probably never feel again. It paralyzed the
King and the court at the Tuileries; it created consternation among
the kings and statesmen at the Congress of Vienna. The royalist lady
who wrote the _Memoirs of the Court of Louis XVIII._, declares that
the King's ministers looked like men who had seen a ghost. They were
frightened into such imbecility that they were incapable of forming any
plan or giving any sane advice.
On the other hand, Wellington's belief was that Napoleon had acted
on false information, and that the King would "destroy him without
difficulty, and in a short time."
How Wellington ever managed to conjure up the mental picture of
Napoleon being destroyed by Louis XVIII. is one of the psychological
mysteries.
The man who, of all men, best knew that Louis XVIII. could never
stand his ground against Napoleon was Louis himself; and he began to
arrange to go out at one gate while Napoleon came in at the other.
Proclamations he issued, but no man read them. A price he set on
Napoleon's head, but no man was eager to earn it. Generals and troops
he sent to stop the daring intruder, but the troops cried "Live
the Emperor!" and the officers had to flee, or join the Napoleonic
procession. The Duchess of Angoulême, daughter of Louis XVI., exhorted
the soldiers at Bordeaux, but even her appeals fell flat. The Count
of Artois and Marshal Macdonald were equally unsuccessful at Lyons;
their troops deserted them, and they were forced to gallop away.
Marshal Ney was quite sure that he could manage the soldiers committed
to him, and that he could cage the monster from Elba. Pledging his
word to the quaking King, he set forth upon his errand, drew up his
troops, harangued them, and proposed the capture of Napoleon. They
laughed at him, drowned his voice in cries of "Live the Emperor!" and
the inconstant Ney fell into the current, surrendered to his men,
proclaimed his adherence to the man he had been sent to capture, and
went in person to lay his offer of service at the feet of his old
master!
Sadly Louis XVIII. turned to Blacas upon whom he had too trustfully
leaned for guidance and counsel. "Blacas, you are a good fellow, but I
was grievously deceived when I mistook your devotedness for talent."
With nobody to fight for him, it was time he was leaving; and on the
night of March 19 he left. With him on his doleful way to the frontier
went a terror-stricken renegade, who dreaded of all things that
Napoleon should lay hands upon him,--Marmont, the Arnold of France.
CHAPTER XLVI
During the voyage from Elba to France, Napoleon had been in the best
of spirits, moving about familiarly among his men, and chatting freely
upon all subjects. He had not told them where they were going, but
probably they little needed telling. All must have felt that they were
bound for France.
The passage was full of peril, for French cruisers were often in
sight. One of these came quite near, so much so that Napoleon ordered
his guards to take off their bearskin caps and to lie down upon the
deck. The commander of the French vessel hailed Napoleon's brig, and
recognizing it as from Elba, asked, "How's the Emperor?" Napoleon
himself seized the speaking-trumpet and replied, "He is wonderfully
well."
At length the companions of the Emperor were told that they were bound
for France, and those who could write were called around him to copy
two proclamations he intended to scatter abroad upon landing. He had
himself written these in Elba, but nobody present could read them--not
even himself.
Casting these into the sea, he dictated two others,--one for his old
soldiers, the other for the nation at large. He revised these papers
ten times before they satisfied him, and then he set all hands making
copies. Engaged thus, they came within sight of France, and they
greeted the shores with enthusiastic shouts.
It was about five o'clock in the evening of March 1, 1815, that
Napoleon and his little army landed near Cannes, and bivouacked in a
meadow surrounded by olive trees, close to the shore. A captain and
twenty-five men, sent to Antibes to rouse the garrison and bring it
over to Napoleon, entered the town crying, "Live the Emperor!" without
explanation or further statement; and the people of the place, knowing
nothing of Napoleon's landing, took these men, who had suddenly
come screaming through their quiet town, to be lunatics. The royal
commandant had sufficient presence of mind to shut the town gates;
and so the gallant twenty-six, who went to surprise and capture, got
surprised and captured.
"We have made a bad beginning," said Napoleon, when news of this mishap
reached him. "We have nothing to do but to march as fast as we can, and
get to the mountain passes before the news of our arrival."
The moon rose, and at midnight the Emperor began his march. He had
brought a few horses from Elba, had bought a few more from peasants
after landing, and thus some of his officers were mounted, while he
himself rode in a carriage given him by his sister Pauline, and which
he had brought from Elba. They marched all night, passing through
silent, moonlit villages, where the people, roused by reports of
something unusual afoot,--the pirates had come, some said,--stood
gaping at the marching troops, responding with shrugs of the shoulders
to the shouts of "Live the Emperor!" It was not until the column had
passed through Grasse, a town of six thousand inhabitants, and had
halted on a hill beyond, that the people seemed to realize what was
happening. The pirate alarm disappeared, the fires of enthusiasm began
to glow, and with glad shout of "Live the Emperor!" the town-folk came
running toward the camp, bearing provisions for the troops. From this
time the country people were certain that Napoleon had really come
back, and his march became one of triumph. Leaving cannon and carriage
at Grasse, the column pressed on toward Cérénon by mountain paths still
covered with snow, the Emperor marching on foot among his grenadiers.
When he stumbled and fell on the rough road, they laughed at him; and
he could hear them calling him, among themselves, "Our little monk."
Reaching Gap on the 5th, he printed his proclamations; and he began
to scatter them by thousands. And never before did proclamations find
such willing readers, or win such popular favor. Advancing toward
Grenoble, the advance guard under Cambronne encountered a battalion
of six thousand troops, sent to stop the march of the invaders. The
royalist commander refused to parley with Napoleon's officers, and
threatened to fire. Cambronne sent to inform the Emperor of what had
occurred. Napoleon was riding in an old carriage, picked up at Gap,
when this report reached him. Mounting his horse, he galloped forward
to within a hundred yards of the hostile battalion. Not a cheer greeted
him. Turning to Bertrand, the disappointed Emperor remarked, "They have
deceived me, but no matter. Forward march!" Throwing the bridle of his
horse to Bertrand, he went on foot toward the royal troops.
"Fire!" shouted the officer, drawing his sword. And then Napoleon,
unbuttoning that familiar gray overcoat, and fronting them with that
familiar cocked hat, made the famous address which broke down all
military opposition between Grenoble and Paris, sweeping thousands of
bayonets out of his way with a word.
"What! My children, do you not recognize me? It is your Emperor. If
there be one among you who would kill his general, he can do it. Here I
am!"
"Live the Emperor!" came the answer of six thousand men, as they melted
into tears, broke ranks, and crowded around him to fall at his feet,
kiss his hands, and touch the hem of his garment.
The officer who had ordered them to fire had a good horse and a fair
start; hence he managed to escape.
The six thousand who had come to capture Napoleon turned and marched
with him. By this time the country was aroused on all sides, and crowds
flocked around the column, shouting "Live the Emperor!" Advancing
beyond Vizille, the Emperor was met by Colonel Labédoyère, who had
brought his regiment to join Napoleon's ranks. With cries of joy the
troops mingled, and Napoleon took the ardent young colonel in his arms,
pressing him to his breast, and saying, "Colonel, it is you who replace
me upon the throne!" Onward then to Grenoble, where the gates had been
closed, and the defences manned to resist the invader.
It was dark when Napoleon arrived before the walls. He ordered
Labédoyère to address the troops within. This was done, and there
were cries of "Live the Emperor!" from within the city. But the royal
commandant had the keys, and the gates could not be opened. "Room!
room!" came the cry from within. It was the shout of citizens of the
town coming with beams to batter down the gates.
The work was soon done, the way was open, and the Emperor's column
found itself surrounded by a multitude as enthusiastic as any they had
met. With uncontrollable transports they laid hold of Napoleon, pulled
him from his horse, and bore him forward in their arms.
That night was one long festival for soldiers, citizens, and peasants;
and next morning a great crowd followed him when he set out for Lyons.
There, upon an immenser scale, was repeated the ovation of Grenoble.
Royal officers lost all control of their troops. Marshal Macdonald
and the Count of Artois were utterly abandoned; and when they fled,
were followed by a solitary trooper, to whom Napoleon afterward gave
the cross of the Legion of Honor. For four days, this great city of
southern France testified in every possible way its unbounded joy at
the Emperor's return. It is said that twenty thousand people were
constantly under his windows. It is certain that he never forgot these
glorious days--almost the last days which he might name glorious.
His journey was now no longer an adventure; once more he was a great
power among the nations of earth. He had committed no violence, had
shed no blood. The love and the admiration of a gallant people were
his again--balm for all those wounds of last year. In his address, at
his departure, his closing words were simple and touching, "People of
Lyons, I love you!" and there can be no doubt that he did.
Moving onward, he came to Auxerre on the 17th; and in the evening came
Marshal Ney, with something in word and manner which suggests that he
felt what nothing so well describes as the term "sheepish." Very rude
had he been to his Emperor in 1814--rude, brutal, threatening. Now
there was a change. Ney was contrite, apologetic, explanatory. He had
been misrepresented, it seems; and the newspapers had told lies about
him. But Napoleon relieved him with: "Embrace me, my dear Ney. To me
you are still the _Bravest of the brave_."
Halting briefly at Fontainebleau on March 20, Napoleon spent some
solitary hours in the room where he had suffered such agonies the
year before; and he went again into the garden which had been his
Gethsemane. Pushing on to Paris, he arrived after dark and entered
the Tuileries at nine o'clock, borne on the shoulders of his wildly
enthusiastic friends. Five thousand young nobles of the royal
body-guard had left Paris that morning to head the royal army, and
oppose Napoleon's advance. The troops they expected to command joined
their Emperor near Paris; and the noble officers, left without
commands, were heard in the Parisian saloons that evening plausibly
explaining the cause of their failure to stop the usurper's progress.
The great city of Paris did not go out to meet the returning Emperor
as Grenoble and Lyons had done. Paris was rather indifferent. "They
let me come as they let the other fellows go," remarked Napoleon that
night. Thousands of soldiers had cheered him as he entered the capital,
adoring friends had pressed him so ardently at the Tuileries that he
had cried out, "My friends, you smother me!" Elegant ladies of the
imperial court, Hortense in the lead, had made ready to welcome him to
the palace; they had thrown arms about his neck and kissed him. But as
the wifeless, childless Emperor sat by the fireside late in the night,
almost alone, his feet up, resting on the mantelpiece, he looked very
tired and very sad. Many old friends had met him; many had stayed
away. Paris had not been so warm as Lyons. France was not so unanimous
as he had hoped. Confidence in him, and his fortune and final success,
was very far indeed from being universal.
Bourrienne records that one of the Paris newspapers made note of the
various stages of Napoleon's return in this wise:--
"A report is circulated that the Corsican brigand has landed at
Cannes;" a few days later the same pen wrote: "Do you know what news is
circulated? They say the rash usurper has been received at Grenoble;"
then later came the announcement, "I have it from a good source that
General Bonaparte has entered Lyons;" then, after a few days, it was,
"Napoleon, it appears, is at Fontainebleau;" and on March 20 came the
final, "His Majesty the Emperor and King alighted this evening at his
palace of the Tuileries."
CHAPTER XLVII
While it is true that the return of the Emperor had not pleased the
nobles, the ultramontane priests, the capitalists, and the intriguers
who had been working for the Duke of Orleans, there appears to be
no doubt that the army and the masses of the people were sincerely
rejoiced. The only thing which had a tendency to cool the general
enthusiasm was the apprehension of war. But Napoleon having taken
great pains to make it known that he wished for peace, that he meant
to respect the Treaty of Paris, and that he intended to rule as a
constitutional king, the French could not fully realize the certainty
of war. They had heard the allied kings declare that France had the
right to choose her own ruler, and had been told that the Bourbons were
restored simply because the Senate and other organs of public opinion
had deposed Napoleon and selected Louis XVIII. If the allied kings were
telling the truth in making such declarations, then the French, who
had put Napoleon aside for the Bourbon, had as much right to put the
Bourbon aside for Napoleon. Neither to the French people, nor to Louis
XVIII., did it appear certain that the allied kings would march their
armies back into France to drive out an emperor the nation had welcomed.
Consequently the beginning of the Hundred Days was marked with what
General Thiébault calls a "boundless enthusiasm." He was present on
the night of Napoleon's entry into Paris; he was one of the officers
sent by the King to stop the Emperor's advance; and Thiébault says
that "at least twenty thousand persons were crowding about the
Tuileries. Suddenly Napoleon reappeared. There was an instantaneous and
irresistible outburst. At sight of him the transports rose to such a
pitch that you would have thought the ceilings were coming down; then,
as after a thunder-clap, every man came to himself, quivering with
ecstasy, and stammering like a man intoxicated."
This first night of his return had barely passed before Napoleon was
hard at work reorganizing his government; and he continued to labor
sixteen hours a day, almost without rest, to create an administration,
an army, and a thorough system of national defence.
As Dumas tersely states, "At his voice, France was covered with
manufactories, workshops, founderies; and the armorers of the capital
alone furnished as many as three thousand guns in twenty-four hours;
whilst the tailors made in the same time as many as fifteen and even
eighteen hundred coats. At the same time the lists of the regiments
of the line were increased from two battalions to five; those of the
cavalry were reënforced by two squadrons; two hundred battalions of
the National Guard were organized; twenty marine regiments and forty
regiments of the Young Guard were put in condition for service; the old
disbanded soldiers were recalled to the standard; the conscriptions of
1814 and 1815 were raised; soldiers and officers in retirement were
engaged to reënter the line. Six armies were formed under the names
of the Army of the North, of the Moselle, of the Rhine, of the Jura,
of the Alps, and of the Pyrenees; whilst a seventh, the Army of the
Reserve, collected under the walls of Paris and of Lyons, which cities
were to be fortified."
Politically, Napoleon's position in France itself was full of trouble.
Though they had cast out the Bourbons, the people had no intention of
returning to imperial despotism. Liberal ideas prevailed everywhere,
and Napoleon himself must not now hope to rule by personal sway. He
must become the mouthpiece and the public agent of the nation, else he
would become king of a minority faction, with the bulk of the nation
against him.
As an evidence of his good faith in accepting limited power, Napoleon
called to his counsels Benjamin Constant, leader of the French
liberals, a friend of Madame de Staël, and a very bitter enemy to
the Emperor. Constant responded to the invitation, and prepared an
amendment to the constitution of the Empire, which Madame de Staël
believed was precisely the thing needed to rally all France to
Napoleon's support, and to make certain the future of the cause of
liberalism.
This famous document, known as "The Act Additional," did not vindicate
Madame de Staël's judgment. It angered all parties, more or less, for
it was what modern politicians would call "a straddle." It contained
enough democracy to offend the imperialists; and enough imperialism to
disgust the democrats.
Let it be remembered that the rallying cry of the people who had
flocked to the returning Emperor had been: "Down with the nobles! Down
with the priests!" So intense had been this feeling, this terrible
antagonism to the abuses of the Old Order, that Napoleon himself, at
Lyons, had whispered, "This is madness." In Paris he had found the
same spirit. Nobles and priests were furiously hated, not so much on
personal grounds, as because they stood for an abominable system.
By tens of thousands the workmen of Paris had paraded before the
Tuileries, making the air ring with the old war cries of the
Revolution, and chanting fiercely the song whose burden is "With the
guts of the last of the priests we will strangle the last of the kings!"
Now, of all men, Napoleon was the least likely to throw himself into
the arms of men like these. He had no objection to nobles if they
were _his_ nobles; nor to priests if they were _his_ priests; nor,
indeed, to kings if they were _his_ kings. Perfectly willing that the
opportunities of life should be offered to all men alike, whether
peasants or princes, and democrat enough to wish that all men should
be equal in the eye of the law,--free to choose their vocations, their
religion, and their political creed,--he had not the slightest idea
of opening the flood-gates of that pent-up democracy, socialism, and
communism which had horrified him in the days of his youth.
In the "Act Additional" provisions were made for a representative
government and for the responsibility of ministers. Freedom of
religion, freedom of the press, security for person and property, were
also guaranteed.
The good effects of these concessions were nullified by the creation of
a hereditary House of Lords, which, it is said, Napoleon opposed, but
which was adopted in spite of him. General Thiébault thought that this
unpopular feature of the new Constitution lost the Emperor two hundred
thousand men, who, otherwise, would have joined his army.
This "Act Additional" was submitted to the people, and adopted, but the
vote was light.
By a decree which he had issued from Lyons, he had abolished the Senate
and the legislative body. In their place was to be put the new House
of Lords, and a legislative assembly. Urged by Lafayette, and other
Liberals whose support he could not throw away, Napoleon ordered the
elections much earlier than he had intended--and much earlier than was
good for him, as it afterward appeared.
One by one grievous disappointments fell upon Napoleon and his people.
It became evident that his return meant war. The Congress of Vienna
declared that he had broken the Treaty of Fontainebleau, and declared
him an outlaw. The armies of the kings were ordered to halt in their
homeward march, and to set out for France again. Napoleon's letters to
the Allies could not even be delivered; his couriers were turned back
at the frontier.
If Austria had made a secret agreement with him, it became apparent
that nothing was to be hoped for in that quarter.
Murat had ruined everything by madly plunging into the papal states,
proclaiming Italian unity and independence, and dashing himself to
pieces in an attempt far beyond his means and his ability. Austria
believed that Murat was acting at the instigation of Napoleon, and this
unfounded suspicion led her to think, as Napoleon said, that he had
played her false.
Murat's army melted away in the face of Austrian and English
opposition; the Italians did not rise as he had hoped; and the rash,
unfortunate King of Naples fled to France, and hid himself near Toulon.
From this place of concealment he sent to Napoleon the offer of his
services; but the great man who had forgiven Ney, and reëmployed
Fouché, drew the line at Murat. More's the pity! In an army which had
a general's place for the infamous Bourmont, there surely might have
been found room for the finest cavalry leader in the world--a man who
had sinned, but had bitterly repented; a man whose splendid sword might
have made Ligny another Jena, and Waterloo another Dresden.
As it was, Murat's failure strengthened the Allies, and cast a gloom
over France.
Two things Napoleon needed above all others,--time and money. He had
only a few weeks in which to create means of defence against a world
in arms; and the lack of money made it impossible for him to utilize
to the best advantage even these few weeks. Supported only by silver
and gold (arrant cowards in times of war), and the note currency of
the Bank of France, he was combating nations which redoubled their
resources by the issue of paper money. He received liberal voluntary
contributions; Hobhouse relates that it was a frequent occurrence for
rolls of bank notes to be handed the Emperor while he was reviewing the
troops. But, after all, such a resource yields comparatively little;
and the scarcity of money seriously crippled the great captain in
preparing for his last fight.
Before he sets out to join the army we see Napoleon in two characters
which will never fade from the memory: one as the successor of
Charlemagne and Emperor of the French; the other as the private citizen
with his personal griefs.
Time being so short, it was decided that the electoral colleges of
France should have a grand open-air meeting as in the days of Charles
the Great--a _Champ de Mai_, to be held in the Field of Mars.
On the 1st of June, 1815, deputations from all the constituencies of
the Empire, together with those from the army, and every public body,
assembled in that historic amphitheatre where the first Festival of the
Federation had been held twenty odd years before. Sixty thousand troops
added to the pomp of the ceremony, and countless throngs of Parisians
crowded the field. There was inspiring music, impressive religious
forms, and a great taking of oaths to the new Constitution. Napoleon
himself took the oath, distributed the eagles to his enthusiastic
soldiers, and in a far-reaching, sharply pitched voice delivered one of
his masterly addresses.
"Emperor, consul, soldier, I owe everything to the people. In
prosperity, in adversity, on the field of battle, in the council room,
on the throne, in exile, France has been the soul and constant object
of my thought and my efforts."
How could Frenchmen listen to words like these and not burst into
cheers? Had he been dressed that day in simple uniform instead of
absurd court costume; had he kept his baleful brothers--Joseph, Lucien,
and Jerome--in the background instead of at the forefront; had he made
his appeal and trusted his cause more unreservedly to the people, the
_Champ de Mai_ might have been a colossal repetition of his triumph at
Grenoble and Lyons. As it was, Paris regarded it as a fine spectacle,
an exhibition to be seen and applauded--nothing more. It touched the
heart of the army; it did not touch the larger heart of the French
people.
When the chambers met, the Emperor delivered still a more successful
speech. Hobhouse, who was present, says that when he had finished with
the sentence, pronounced in a louder tone and with a flourish of the
right hand, "The sacred cause of country will triumph!" he rose quickly
from his throne, "bowed to the assembly, and retired amidst thunders
of applause, which accompanied him from the throne to the door, and
obliged him several times to turn round and salute the assembly as he
was ascending the stairs of the area. He appeared highly delighted.
Indeed, nothing could exceed the enthusiasm, which was the more
gratifying as it proceeded from such an assembly." When we remember
that this assembly of notables was already hostile to Napoleon, was
already cut up into factions, only one of which was devoted to him, and
that it was an open secret that these notables would openly oppose him
the moment the fortunes of war should go against him, his oratorical
triumph becomes all the more remarkable.
So much for the Emperor, his labors, his speeches, his dangers, his
mighty efforts to conquer an impossible situation; we can admire it
all, marvel at his genius, courage, resources, and versatility; but
it is only when we go with him to Malmaison that we draw near to the
_man_, feel for him, feel with him, and realize how greatly he has
been misunderstood. He had always been a good son; he had been but too
affectionate, too generous, to his sisters and brothers; he had been to
both his wives one of the most tenderly indulgent of husbands.
It seems that he had continued to hope, almost to the last, that
Maria Louisa would come to him at Elba, and bring his boy. A lot of
fireworks, we are told, had fallen into his possession, and he had
kept them carefully, ready to be used when wife and child should come.
He knew, at length, that neither would ever see him again. He had been
told of Neipperg, and the true reason why Maria Louisa had ceased to
write. "Méva, tell papa I am still very fond of him!" and this message,
sent almost by stealth, was all that Méneval could bring to the father
from the little son who was held at Vienna. No wonder that Napoleon
should be found sitting before a portrait of his son, with tears
coursing down his cheeks.
Josephine was dead. The fall of the Emperor, her hero, her Cid, had
bewildered and unnerved her. Frightened at the din of war that shook
the whole realm, she had lived in terror at Malmaison. The allied
kings paid her every attention, and in showing the King of Prussia
over her lovely grounds when she was ill, broken out with an eruption,
she had, it is said, brought on a fatal relapse. Murmuring the words
"Elba"--"Bonaparte"--she died, while her hero was yet in exile. It
is a revelation of his true character that before setting out on his
last campaign he should claim one day out of the few fate gave him,
and devote it to memories, to regrets, to recollections of the frail,
but tender-hearted woman who had warmed to him when all the world was
growing cold. He went to Malmaison, almost alone, and, with Hortense,
walked over the grounds, seeing the old familiar places, and thinking
of the "old familiar faces." He lingered in the garden he himself had
made, and in which he used to love to work when he was First Consul,
surrounded by trees and flowers, and inhaling the breath of nature.
He used to say that he could work better there than anywhere else. He
wandered through the park, looking out on the trees he had planted in
those brilliant days long ago. Every spot had its silent reminder of
glories that were gone, of friends he would see no more.
He had asked to be told everything about Josephine,--her last days,
her sickness, her dying hours; no details were too trivial to escape
him. And as they told the story he would break in with exclamations
of interest, of fondness, of sorrow. On this visit to the château he
wanted to see everything that could remind him of her, and of their old
life together--the death-chamber at the last. Here he would have no
companion. "My daughter, let me go in here alone!" and he put Hortense
back, entered, and closed the door. He remained a long while, and when
he came out his eyes showed that he had been weeping.
* * * * *
His personal appearance at this time is thus described by Hobhouse, who
saw him at a military review at the Tuileries: "His face was deadly
pale; his jaws overhung, but not so much as I had heard; his lips
thin, but partially curling, so as to give his mouth an inexpressible
sweetness. He had the habit of retracting the lips and apparently
chewing. His hair was dusky brown, scattered thinly over his temples;
the crown of his head was bald. One of the names of affection given him
of late by his soldiers is 'Our little monk.' He was not fat in the
upper part of his body, but projected considerably in the abdomen, so
much so, that his linen appeared beneath his waistcoat. He generally
stood with his hands knit behind him, or folded before him, but
sometimes unfolded them, played with his nose, took snuff three or four
times, and looked at his watch. He seemed to have a laboring in his
chest, sighing or swallowing. He very seldom spoke, but when he did,
smiled, in some sort, agreeably. He looked about him, not knitting but
joining his eyebrows, as if to see more minutely, and went through the
whole tedious ceremony with an air of sedate impatience."
Hobhouse speaks of Napoleon's reception at the opera where Talma was to
play Hector. "The house was choked with spectators, who crowded into
the orchestra. The airs of La Victoire and the Marseillaise were called
for, and performed amidst thunders of applause, the spectators joining
in the burden of the song.... Napoleon entered at the third scene.
The whole mass rose with a shout which still thunders in my ears. The
vivats continued until the Emperor, bowing right and left, seated
himself, and the play recommenced. The audience received every speech
which had the least reference to their returned hero with unnumbered
plaudits."
General Thiébault in his _Memoirs_ declares that Napoleon was no longer
the same man he had once been; that his face wore a greenish tinge
and had lost its expression; that his mouth had lost its witchery;
"his very head no longer had the pose which used to characterize the
conqueror of the world; and his gait was as perplexed as his demeanor
and gestures were undecided. Everything about him seemed to have lost
its nature and to be broken up."
The lady who composed the _Memoirs of the Court of Louis XVIII._ saw
Napoleon holding a review at the Tuileries, and had a conversation with
him afterward.
"Bonaparte was dressed that day in a green uniform. I have been told
that it was the same which he afterward wore at Waterloo, and which he
wore, almost in tatters, at St. Helena. He had been reviewing some
troops that morning at the Champ-de-Mars, and his coat, hat, and boots
were still dusty.... I looked in vain for the fire which once beamed
in his eyes. He stooped more than usual; his head almost hung upon
his breast; his complexion was yellow, his countenance melancholy and
thoughtful, and his little hat drawn almost over his eyes, gave him a
gloomy expression. His movements were still abrupt, but this seemed
merely the effect of habit.... He had altogether a wearied, harassed
appearance, which seemed to indicate a great man extinct."
To the same effect is the testimony of Chancellor Pasquier.
Carnot said: "I do not know him again. He talks instead of acting,
he the man of rapid decisions; he asks opinions, he the imperious
dictator, who seemed insulted by advice; his mind wanders, though he
used to have the power of attending to everything, when and as he
would; he is sleepy, and he used to sleep and wake at pleasure."
CHAPTER XLVIII
All had been done that could be done--all that it was in his nature to
do. He had equipped two hundred thousand men in arms, and had filled
them with martial fire. He had called back to the service every officer
who would come, saving Augereau, who had betrayed Lyons in 1814,
and Murat, who had joined the Allies. He had courted the liberals,
temporized with the Jacobins, tolerated the royalists, and shut his
eyes to incipient treason. To the Constants and La Fayettes he had
said, "Gentlemen, don't waste time in debates on constitutional law
while the nation is in danger; unite with me to save her"; but he knew
that his appeal was wasted. To the dangerous traitor Fouché he had
said, "I ought to have you shot"; but he left him minister, and knew
that if battles were lost, Fouché would be the first to plot for the
return of the Bourbons.
He listened to Jacobin songs, appreciated Jacobin strength, and
believed that he could win the fight if he would put on the red bonnet.
But he would not. In Brumaire, 1799, he had said, "If I conquer with
the Jacobins, I would then have to conquer against them." His opinions
had not changed. If he put on the red cap of the Jacobins, and put guns
into their hands, he might save his own crown; but how about his son?
Democracy once unchained, who would ever bind it again? Thus he would
not nationalize the war--his one chance of success.
With two hundred thousand men, the Emperor, who might have enrolled
a million, turned to face all Europe. The allied kings already had a
million men in arms, and England was supplying $55,000,000 a month to
pay them. In quality, Napoleon had led few better armies than that of
his last campaign; but while the troops were passionately devoted to
the Emperor, they had lost confidence in many of the higher officers,
and went to the front dreading treachery in their leaders.
The Russians and Austrians could not reach the Rhine before July;
but the armies of Blücher and Wellington, about one hundred thousand
each, were already in Belgium. Napoleon could strike at these with
only about one hundred and twenty-five thousand. But as the enemy was
widely scattered, and was not expecting immediate attack, he believed
that he might best open the war by throwing himself between Wellington
and Blücher, preventing their junction, crushing them in detail, and
thus discourage the coalition to such an extent that he might detach at
least some of its members.
Had he waited two weeks longer, he could have taken with him the twelve
thousand troops who were putting down the royalists in La Vendée; but
he could not foresee that the revolt would be quelled so soon. Other
errors, however, were committed, for which he alone was responsible.
He left his best officer, Davoust, in Paris, instead of employing him
in the field. Had Davoust been put in Grouchy's place, the result of
the campaign would almost certainly have been different. Again, he had
given no confidence to Ney, had not even notified the marshal whether
he was to be employed. It was so late when Ney got his orders that the
campaign had already opened, and the fighting begun before he could
arrive from Paris, without his horses, and accompanied by a single
aide-de-camp.
Another thing: the Emperor gave the command of his right wing,
which was to act independently, to an officer untried in that
capacity,--Grouchy; and he did it over the protest of Soult and other
general officers, who warned him that Grouchy was not the man for such
a place.
A gross blunder was made as to Bourmont. This man had been one of the
Chouan chiefs of 1800, to whom Napoleon extended clemency. Pardoned,
then, by the First Consul, he had afterwards been implicated in
the Georges conspiracy, and had fled to Portugal. Junot picked him
up there, took a fancy to him, got him employed; and the man being
a good officer, won rapid promotion. In 1814 he had been one of
the traitors, and had gone over to the Bourbons. In 1815 he fell
in with the Napoleonic tide, and professed the zeal of a sincere
imperialist. Seeking employment in the army, he was contemptuously
refused by Davoust, who told him that he must perform quarantine. Most
unfortunately, Labédoyère and Gérard had faith in Bourmont, and the
matter was carried to the Emperor. To Labédoyère, Napoleon could refuse
nothing, and Bourmont was appointed to the command of one of the finest
divisions.
Concentrating his army swiftly, Napoleon was near Charleroi, on the
evening of June 14, 1815, and next day crossed the Sambre.
At daybreak, on the morning of the 15th, General Bourmont, two officers
of his staff, and eight soldiers deserted. As Bourmont had been
present at the Council of War, he knew the secrets of the French, and
these he carried with him to the Allies. This treason, on the eve
of battle, demoralized, for a time, the entire division, and had a
depressing effect throughout the army.
Another "deplorable mischance" happened on this morning. An order to
Vandamme to advance was sent by a single courier, whose leg was broken
by a fall of his horse. The order was not delivered, Vandamme did not
make the movement, and Napoleon's manœuvre, by which he had expected to
cut off and capture the Prussian corps of Ziethen, failed.
Blücher, acting much more promptly than Wellington, concentrated his
army at Fleurus, from which he retired on Ligny. Wellington and many
of his officers were at the Duchess of Richmond's ball, in Brussels,
on the night of June 15, when Napoleon's guns were heard. At eleven
o'clock a despatch arrived which told of the French capture of
Charleroi and advance upon Brussels. Although Wellington knew that
Napoleon's army was in motion, he was taken by surprise at the nearness
of his approach. Withdrawing into a private room with the Duke of
Richmond, he called for a map, saying, "That damned rascal Bonaparte
has humbugged me!"
From midnight on to dawn, the English army was hurrying to the front,
to concentrate and fight. Without waiting for Wellington or his orders,
Prince Bernard, of Saxe-Wiemar, had already occupied Quatre-Bras. When
Wellington arrived there, June 16, he passed on at once to a conference
with Blücher, to whom he had written a letter which Blücher had
received at noon. In this letter, Wellington had seemed to promise aid
to Blücher if he would fight at Ligny,--mentioning the positions which
the troops of the Anglo-Belgian army then occupied.
The curious feature of the case is that Wellington's troops were
not where his letter said they were, and that he remarked to one of
his staff as he was leaving Blücher, "If he fights here, he will be
damnably whipped."
This letter in which Wellington promised to help Blücher only came to
light in 1876, and Lord Wolseley says that Wellington, "an English
gentleman of the highest type, wholly and absolutely incapable of
anything bordering on untruth or deceit, must have been misled by
his inefficient staff." Perhaps so. But it looks marvellously like a
case where the English gentleman of the highest type had been caught
napping by "that damned rascal Bonaparte," and wanted "old Blücher" to
fight, in order that the British army might have time to concentrate.
Blücher's chief of staff, Gneisenau, held this view at the time, and
died in that belief. So little did the opening events of the campaign
depend upon any generalship of Wellington, that some of his officers
had to violate his orders before they could reach the positions which
it was absolutely necessary they should occupy.
It was near five o'clock on the evening of June 15 that Ney, who had
come from Paris to Beaumont in a post-chaise, and from Beaumont had
travelled to Avesnes in a peasant's cart, bought horses from Marshal
Mortier. At that late hour he was given command of the left wing of
the French army, with verbal orders from Napoleon himself. Just what
these orders were is a matter of dispute. The partisans of Ney contend
that the Emperor said, "Go and drive back the enemy." Napoleon and
his sympathizers allege that the orders were to seize Quatre-Bras,
and hold it. That the Emperor meant to give such orders, there can
hardly be a doubt. On his way to Quatre-Bras, Ney encountered some
Nassau troops at Frasnes, who fell back at once. Instead of advancing
upon Quatre-Bras, Ney halted some two or three miles short of it,
and reported to Napoleon for further orders. A small force of French
cavalry actually entered Quatre-Bras, and then retired.
The Emperor, worn out with fatigue, and suffering from urinary,
hemorrhoidal, and other ailments, had gone back to Charleroi to sleep
and rest.
For reasons not fully explained, it was nine o'clock on the morning
of the 16th before Ney was ordered positively to advance and capture
Quatre-Bras. Had he moved promptly, he could even then have taken the
place, for it was held by a few thousand Nassauers only. It was not
until 2 P.M. that Ney attacked. A still greater delay marked Napoleon's
own movements. It was between two and three o'clock in the evening
before he struck the Prussians at Ligny.
Here, then, were two battles raging on the same day only a few miles
apart. Ney was making a desperate onset at Quatre-Bras, which he
could easily have taken on the 15th, or early on the 16th, but which
was now held by ever increasing numbers of the enemy. And Napoleon
was straining every nerve to defeat the Prussians, who had profited
enormously by his delays.
It was at this crisis of his fortunes that he was tantalized by one of
the most remarkable of military mishaps. A corps of twenty thousand
men under D'Erlon, intended to act with Ney, was on its march to
Quatre-Bras, when a staff-officer, Colonel de Forbin-Janson, delivered
a pencilled order from Napoleon to D'Erlon, which was totally
misconstrued, and which led D'Erlon to march to the French left, when
he should have struck the Prussians cross-wise, while the Emperor
pressed them in front. D'Erlon set out, came in sight of Ligny, and
created consternation among the French, who thought it a Prussian
reënforcement. Napoleon, not expecting troops on his left, was forced
to suspend his movements until he could ascertain the facts, thus
losing precious time. Strange to say, this French corps, now that it
was on the field, was not used at Ligny, but was countermanded by Ney,
whom Forbin-Janson should have informed of the Emperor's order, and was
marched back to Quatre-Bras, where it arrived too late to help Ney. Had
it gone into action at either place, its aid must have been decisive.
As it was, these twenty thousand troops were as completely lost to the
French "as though the earth had swallowed them up."
Night found the Prussians beaten; and a vigorous pursuit, such
as Murat, or La Salle, or Bessières could have made, might have
disorganized them for the campaign. But there was no pursuit. They
rallied at their leisure, and the French did not even know next day
what route their retreat had taken.
After the battle Napoleon was again exhausted, and nothing was done
to improve the victory. The Emperor slept, and the army waited.
Next morning at seven his generals stood around, idle, grumbling,
discouraged. Vandamme was saying: "Gentlemen, the Napoleon of the
Italian campaign no longer lives. Our victory of yesterday will lead to
nothing. You will see."
Mr. Houssaye contends that the Emperor was not in poor condition,
physically or mentally; and he enumerates facts to prove what he says.
It all depends upon what his standard of comparison is. Does he compare
the French general with the English chief,--the one launching a host of
men so swiftly and surely that they were upon the enemy before it was
known that they had moved; and the other idling in a ballroom, issuing
late and confused orders, naming the wrong place for concentration, and
saved only by the initiative of Prince Bernard, the disobedience of
his own officers, and the bad luck which dogged the movements of the
French? If you compare Napoleon to Wellington, one must say that the
former was _not_ in poor condition. But if we compare the Bonaparte of
1815 with Blücher, the admission must be made that in sustained energy
and unwavering tenacity of purpose, the German far exceeded his great
antagonist. And if we contrast the Bonaparte of 1815 with the Bonaparte
of 1796, we at once exclaim with Vandamme,--"The Napoleon we knew in
Italy no longer lives."
Mr. Houssaye himself states that late in the morning of June 17 the
Emperor did not know what had taken place at Quatre-Bras the day
before; did not know the true situation there; did not know that
by swiftly moving to the aid of Ney he would envelop Wellington
with overwhelming numbers and crush him! Even the Napoleon of 1814
would have missed no such chance as that. When the facts at length
became known to him he realized what he had lost, dashed on with the
vanguard to Quatre-Bras, and led the headlong pursuit of the English
rear-guard--but it was too late. Wellington was well on his way to Mont
St. Jean, and Lord Uxbridge was desperately hurrying the last of the
British cavalry out of the danger, with his "Gallop! for God's sake
gallop, or you will be captured!"
Furthermore, Mr. Houssaye relates an incident which corroborates
Carnot, Pasquier, and others who say that the Emperor was no longer
able to endure prolonged labor:--
"It was now (June 14) a little past noon. The Emperor, amid the cheers
of the inhabitants, passed through Charleroi, and halted at the foot of
the crumbling glacis, near the little public-house called La Belle-Vue.
He got off his horse, sent for a chair, and sat down by the side of
the road. The troops defiled past him, cheering him lustily as they
marched, their shouts deadening the roll of the drums and the shrill
calls of the bugles. The enthusiasm of the troops bordered on frenzy;
they broke ranks to embrace the horse of their Emperor."
And what of Napoleon amid this splendid ovation--an ovation spontaneous
and thrilling like that of the eve of Austerlitz?
He sat there dozing, the cheers of the troops, which deadened churns
and bugles, being powerless to rouse him! It was only noon, he had
only been in the saddle half a day--was _this_ the man of Eckmühl, of
Friedland, of Wagram? Was _this_ the chief who used to ride and ride
till horse after horse fell in its tracks?
Turn from this dozing chief, exhausted by half a day's work, and look
at old Blücher. At the age of seventy-three, he is full of pluck and
dash and persistence. He hurries up his divisions to fight as soon as
he knows that the French are moving. He is in the thick of the combat
at Ligny. He heads charges like a common hussar. His horse is shot and
he falls under the feet of rushing squadrons, is drawn out almost
dead and borne off the field unconscious. Bruised and battered, the
old man no sooner "comes to himself" than he is up again, beating down
the cautious counsels of his chief-of-staff, and determined to go to
the help of Wellington,--who had not come to _his_ help,--although the
chief-of-staff, Gneisenau, believing Wellington to be a "master knave,"
wished the Prussians to leave the English to take care of themselves at
Waterloo, as the Prussians had been left to take care of _themselves_
at Ligny. And on the ever memorable 18th, while Napoleon will be
waiting, hour by hour, for the ground to dry so that he can move his
artillery, old Blücher will be coming as fast as he can hurry his
troops through the mud, as fast as he can drag _his_ artillery; and the
net result will be that, while miry ground stops the great Napoleon, it
does not stop the impetuous and indomitable Blücher.
CHAPTER XLIX
When Napoleon finally awoke on the 17th, he spent the morning talking
politics to Gérard and Grouchy. It was midday when he gave the latter
some thirty-three thousand men, and sent him after the Prussians. The
spirit, if not the letter, of his instructions was that he was to
penetrate Blücher's intentions: "whether he was separating from the
English, or meant to unite, and fight again!" Davoust would have known
how to interpret such an order, and how to act upon it; Grouchy, it
seems, did not. For thirty years there was a dispute about the order
itself, but at length it came to light; and since its text has been
known there has been little difference of opinion on the subject of
Grouchy's conduct. Detached from the main army to take care of Blücher,
and to prevent the Prussians from coming to the aid of the English, he
failed miserably to perform the task intrusted to him, and was of no
more service to Napoleon in the movement which decided the campaign
than D'Erlon had been at Ligny.
Through torrents of rain, through the mud and slush of the cut-up
roads, the French followed the English toward Brussels.
On the crests of Mont St. Jean, with the forest of Soignes behind him,
Wellington drew up his men for battle, relying upon Blücher's promise
to arrive in time to coöperate. There were eighteen thousand troops at
Hal, which might have been called up to his support; but Wellington,
entirely misconceiving Napoleon's plans, had expected an attack upon
his right, and this large force at Hal was left there in idleness to
guard against an imaginary danger. By two o'clock in the morning of
the 18th, Blücher sent a courier to Wellington, promising the support
without which the English army would have continued its retreat.
When Napoleon's vanguard reached La Belle Alliance, and he saw that
Wellington's army was in position on the opposite heights, he was
happy. He had feared that the English would retire behind the forest of
Soignes, unite with the Prussians, and thus be too strong for him. If
he could but fight Wellington while Blücher was away, he did not doubt
his ability to "give the Englishman a lesson": for while the French
numbered 74,000, there were but 67,000 of the Anglo-Belgian army.
The French army floundered through the mud of the soaked wheat-fields,
the miry lowlands of the Dyle, and were late in the night of the 17th
in reaching their positions at La Belle Alliance. Indeed, some of the
troops did not reach the battle-field till late next morning. The
floods of rain had rendered it impossible for the provision trains to
keep up. The exhausted French lay down with empty stomachs, to rest as
well as they could on the wet ground, without shelter or fire, whilst
the English army, comfortably fed, kept themselves warm by campfires.
At dawn the rain ceased. Napoleon again reconnoitred, the ground being
so soft that in places he "mired up," requiring help to lift his
feet out of his tracks. Unconscious that even then old Blücher was
wading through the bogs, across country, to get from Wavre to the
English left at St. Lambert, Napoleon allowed hour after hour to slip
by, stealing from him every chance of victory. The natural line of
Prussian retreat was on Namur: he did not know that while Blücher lay
unconscious, on the 16th, Gneisenau, chief of staff, had directed the
retreat on Wavre. Therefore, Napoleon took his breakfast leisurely,
chatting cheerfully with his general officers; and when he rode along
the lines, saw all the splendor of his magnificent array, heard the
bugles and the bands, and the sweeter music of seventy thousand voices
shouting "Live the Emperor!" the great captain's face glowed with pride
and joy. To him such a spectacle, such a greeting, was the nectar of
the gods; he drank it now for the very last time.
It was eight o'clock when he made his plan of battle, nine when he
issued orders, at ten he lay down and slept an hour.
Napoleon mounted his horse at eleven, and rode along the Brussels
highroad to the farmhouse of La Belle Alliance; then he returned to
the height of Rossomme. Between the crest upon which he sat his white
Arabian mare, "Désirée," and that upon which Wellington awaited his
attack, stretched the <DW72>s of the ridges and the grain-covered
valley between, about a mile in width. The Emperor was as calm and as
confident as he had ever been in his life. Sitting his horse on the
heights where all his army could see him, see the old gray overcoat
and little cocked hat, see the square, pale face and the squat, sturdy
figure, he swept every part of the field and of the horizon with his
glass, and then gave the word. It was near noon on this fateful Sabbath
day when the signal guns were heard; and the Prussians of Bülow's
corps were already approaching St. Lambert. The battle commenced with
an attack on the château of Hougomont, a stone building on the British
right, protected by walls and moat and hedge. The French corps of
Reillé, in the three divisions of Foy, Bachelu, and Jerome Bonaparte,
threw itself furiously against this fortress; and desperate fighting,
attack, and defence made the place literally run with blood--but the
English, though driven from the woods, held the château.
The attack on Hougomont was a feint which the rash Jerome carried too
far. The real attack was to be on the English centre, and to prepare
for this the Emperor formed a battery of eighty guns. It was about one
o'clock when Ney, who was to lead the charge, sent word that all was
ready.
Before giving the signal, Napoleon swept the horizon with his glass,
long and carefully. Away to the northeast he saw something which fixed
his attention: it might be a clump of trees; it might be a column of
soldiers. Staff officers followed the Emperor's gaze, levelled their
glasses, gave various opinions. "Trees," said some; "Troops," said
others. If troops, what troops--Blücher's or Grouchy's? Such an awful
doubt demanded instant action. Napoleon called for General Domon
and ordered him to take a division of light cavalry and ride to St.
Lambert; if the troops were Prussians, he must stop them.
Dumas describes the movement of the light cavalry: "Three thousand
horsemen moved to the right, four abreast, unrolled themselves like
an immense ribbon, winding a moment in the lines of the army, then
breaking loose through our extreme right, rode rapidly and re-formed
like a parade nearly three thousand toises from its extremity."
Soon the Emperor's fearful doubt became a terrible certainty. Not
trees, but troops, stood over there in the distance; and the troops
were Prussians!
Where was Grouchy?
A Prussian prisoner taken in the territory where no Prussians should
have been, was brought to the Emperor, and at his replies to the
questions asked him, the imperial staff was panic-stricken; and
Napoleon himself filled with a storm of impotent rage. No French troops
had been seen where Grouchy should have been, and the Prussian host was
crowding toward the field of battle!
From this time onward the doomed Emperor was fighting two battles:
Wellington at Mont St. Jean, and the Prussians at Plancenoit. About
seven thousand of the best troops were sent to hold the Prussians off,
while the attack on Wellington was being renewed. This was toward three
o'clock in the afternoon.
With two battles on his hands, Napoleon in his despair sent another
messenger to Grouchy. Bitterly remarking upon the conduct of his
lieutenant, who had been "amusing himself at Gembloux," the Emperor
exclaimed that if Grouchy but repaired his "horrible fault," and
marched promptly, all would yet be well; for, be it remembered, Grouchy
was only ten or twelve miles to the right.
Suffering from local ailment which made the saddle painful to him, the
Emperor dismounted and seated himself at a small table upon which his
maps were spread. Sometimes he got up and paced back and forth with his
hands crossed behind him. Sometimes he folded his arms on the table
and there rested his head,--in pain or slumber. The management of the
actual fighting which was going on all this while, was left almost
entirely to Ney and D'Erlon, but especially to Ney, whose rashness
at Waterloo was as ruinous to the French as his caution had been at
Quatre-Bras.
Wellington, on the contrary, was as anxious a man as ever bravely faced
a foe. He had not believed himself equal to the combat with Napoleon,
man to man, and had only resolved to give battle after having been
assured of Blücher's aid. Whether the Prussians could arrive in time,
was Wellington's great doubt. He felt that his only salvation lay just
there; and it was not until Bülow's corps, at 4.30 P.M., had drawn
away from Napoleon at least sixteen thousand of his best troops, that
Wellington, feeling the French onset in his front relax, exclaimed: "By
God! I believe we will whip them yet." Stronger evidence than that of
the Prussian military expert, Muffling, is this Wellington exclamation,
that he was a lost man had not "Old Blücher" come.
Against Wellington's left the corps of D'Erlon was hurled; and at
Papelotte and La Haye Sainte the struggle was as bloody, as desperate,
as full of quick turns of fortune, ebb and flow, success mingled with
failure, as any known to history. The English line was terribly shaken,
the losses frightful, but the French finally were driven back.
The Emperor had intended to support Reillé with Lobau's corps; that
corps had been sent from the field to meet the Prussians.
Ney asked for a cavalry division to support the renewed attack he was
about to make with D'Erlon's corps. Owing to some mistake, Ney got
not only the cavalry division which he had asked for, but the entire
cavalry reserve, so that he took with him some twelve thousand horse.
This mighty mass was not launched at the weakened English left, but at
the centre. How the French host rode down into the valley, up the hill,
and charged upon the English guns and the English squares, repeating
the assault time and time again, all readers know. Made with a heroism
which the world can but admire, these charges were repulsed with a
courage which nothing could shake. The English squares stood unbroken
against French horse, as the French themselves had stood against the
Mamelukes. Twice, thrice, the British cannoneers were driven from their
guns; twice the British artillery was in the hands of the French. Why
were not the guns spiked? Why at least, were not the sponges broken,
or the caissons destroyed? In the melée no one gave the order. So the
cannon and its ammunition and its rammer was left there ready for the
British gunner, when the retreat of the French cavalry made it possible
for him to return to his battery. The attack had been premature. The
Emperor himself exclaimed, "This is an hour too soon, but as it has
been done I must support it. The day may be lost by this mistake."
It is true that Wellington's army was fearfully battered; that, between
his rear and Brussels, the road was full of panic-stricken fugitives,
not all of whom were Belgians or Hanoverians. It is true that English
officers had almost despaired, and that frantic riders flew to Bülow
imploring him to save the British army. It is true that there was a
gap in the English line into which Ney frantically sought to throw
infantry, and so win the day. But Napoleon had already been forced to
send ten thousand other veteran troops to hold in check the thirty
thousand Prussians. When, therefore, Ney's messenger came, asking for
infantry, the Emperor petulantly answered, "Infantry! Where does he
expect me to get them? Can I make them?" There are those who say that
had he thrown in the few reserve battalions of the Guard, the day might
have been won.
So the great opportunity passed. La Haye Sainte was taken; but the
English line was mended by reënforcements where it had been broken, and
the Prussians, under Ziethen, joined Wellington on his left. It was now
seven o'clock. The French were about to be taken in the flank by the
entire Prussian army. Napoleon might have drawn off in good order, but
the junction of Blücher and Wellington would spoil all his plans. There
was a chance yet for him to crush the English by a final charge into
which every available man should be thrown. If it succeeded, all was
won; if it failed, all was lost. It was the superb risk of the daring
gambler: everything upon a single cast.
The orders flew, lines were formed, the great captain rode among
his men, and spoke to them. The sound of their shouts of "Live the
Emperor!" reached the English lines where the charge was expected, a
deserter from the French ranks having brought warning. Ney was put at
the head of the columns, and the march began. Through the mud of the
valley, and up the slippery hill they went, under the murderous fire of
all the English guns. Through the dense ranks, too closely crowded in
that small space, great lines were cut by cannon balls, and so hot was
the musket fire that they could not deploy. Ziethen's Prussians were
now in the fight, coming with full force on the right. Ney's men, taken
front and flank, had yet advanced to within fifty yards of the English
line; but unable to open their ranks and charge, under such a terrific
fire, they fell into confusion. The Emperor was watching them through
his glass. "They are all mixed up; for the present, all is lost." At
the moment when Napoleon was saying this, Wellington was ordering the
advance of his whole line; the Prussian guns were thundering on the
French flank; and over the lost field ran the cry: "The Guard recoils!
We are betrayed! Save himself who can!"
In vain Ney struggled to hold the rout; in vain the Emperor hoarsely
shouted to his men to rally: it was dark; confusion was everywhere; and
the French army, a mighty wreck, was swept from its moorings. English
cavalry made furious charges, crying "No quarter!" and Napoleon had no
cavalry reserves to meet the shock.
NOTE.--In reference to the disputed incident of the British
demand for the surrender of the Old Guard, and Cambronne's reply,
the truth seems to be, that such a demand was made, and that
Cambronne did reply, defiantly, though nastily; and that his
language shot out in the disgust and exasperation of the moment,
can more accurately be rendered into the English phrase, "Go to
hell!" than in the classic terms, "The Guard dies: it does not
surrender!"
Immediately after his scornful response, the heroic Cambronne was
shot full in the face, and was left for dead on the field.
Readers of Thackeray will remember how he jeers and laughs at
the defiance of the Old Guard; just as they will remember how he
jeers and mocks at the second funeral of Napoleon,--so sure is
the professional fun-maker to overreach himself, now and then.
The truth is, that the French troops were badly handled in the
actual fighting at Waterloo; and that Napoleon stated no more
than the fact when he charged Ney with having acted like a madman.
The troops, cavalry, and infantry were massed in such dense
formation, on such contracted area, that they were in each
other's way, had no fair chance to do what they should have done,
and were sacrificed horribly to the British artillery. At the
very moment when Ney was clamoring for reënforcements, he had
forgotten a part of his own troops,--who were not engaged, who
could have been used, and who might have decided the day in his
favor.
The mismanagement of the troops still further demoralized them,
as it tended to confirm their suspicions that they were being
betrayed.
It has been claimed that Napoleon intentionally deceived his own
troops, toward the last, by sending word along the line that
Grouchy had come. This is by no means certain. The Emperor could
hear the guns of Grouchy, who was engaged at Wavre, just as
Grouchy had heard, during the afternoon, the guns at Waterloo.
Napoleon doubtless believed that Grouchy was at last going to
show up on his extreme right.
The old road of Ohain seems not to have wrecked the French
cavalry in the tragic manner Victor Hugo alleges. Romance,
tradition, and patriotic painting represents the Emperor's
squadrons as being engulfed in the ravine made by the road where
it passed through the high ground--over which ground the cavalry
is alleged to have charged, in ignorance that the ravine, or
"hollow way," was there. Mr. Houssaye who has studied the matter
thoroughly says that there is no historic foundation for the
story.
The remnants of the Old Guard formed squares, and for a while held
off their pursuers; but the barrier was too frail, and it soon melted
away. Napoleon, dazed and despairing, spurred his horse toward the
English guns, but Soult, according to Gourgaud, caught the bridle
reins, and the Emperor was forced off the field, protected by the last
of the Old Guard squares. With a few horsemen he rode away, so crushed,
so tired, that Bertrand and Monthyon had to hold him upright in the
saddle. Several times on the retreat he attempted vainly to rally the
fugitives: the panic was too complete.
The English rested at La Belle Alliance; and Wellington, after meeting
and hugging Blücher, rode to Waterloo to write his despatches. A
Rothschild agent had already gone at speed to the coast, to reach
England ahead of the news, and make additional millions for that
enterprising house.
The Prussians pressed the pursuit with relentless vigor; and the
summer moon lit as wild a man-hunt as this blood-soaked planet ever
knew.
* * * * *
What should Napoleon do,--stay, and attempt to rally the army, or
hasten to Paris to check intriguers and organize resistance to the
invaders? He did not know what had become of Grouchy, did not know
how much of his own army was left. He dreaded the betrayal and the
deposition of 1814, not fully realizing the deeper pits of 1815. As
a matter of fact, Grouchy's army was intact. He had led it in most
leisurely fashion to Wavre, and it had listened all day to the guns
of Waterloo. Gérard, Vandamme, Exelmans, felt that the Emperor was in
the midst of a great battle, and with the instinct of soldiers urged
that they should "March to the guns!" They pleaded with Grouchy to go,
Gérard insisting with such temper that Grouchy's precious self-love was
pricked. In vain was all remonstrance; Grouchy would not move. He went
to Wavre, fought the rear-guard which Blücher had left there to detain
him, made himself as utterly useless to his chief as though he had not
existed, and then, after Waterloo, fell back, in admirable order, to
Namur. Pluming himself upon the safety of his corps, the loss of the
Empire did not ruffle his self-complacent satisfaction.
There was chaos in Paris when it was known that the army was no more,
and that the Emperor was at the Élysée palace. The tongue of faction
fiercely wagged, and conspiracy stalked unmasked wherever it would.
Lafayette babbled of constitutions and guarantees for liberty, when
France needed every strong arm and every gun. Fouché, duping both
imperialists and republicans, plotted for the Bourbons, and opened
communications with Wellington. Lucien Bonaparte gave wings to his
conceit, and dreamed of a new government in which he should be chief
and Napoleon lieutenant!
Carnot alone kept his head and saw clearly what was needed. "Give
Napoleon all he wants, make him temporary dictator, hold up the man's
hands, and let him save the country!"
Grand old republican! History puts upon his memory, as a wreath,
Napoleon's own sad words, uttered in these days of trial, "Carnot, I
have known you too late!"
Fouché sowed distrust in the chambers, making them believe that
Napoleon meant to dissolve them. This the Emperor was advised to do;
and should, perhaps, have done. When they refused to vote him supplies,
they ceased to be of service; became, instead, a source of weakness and
danger. Why not cut down such a tree? Why tolerate politicians who at
such a moment prated of constitutional limitations?
Napoleon ordered his carriage to go to the chambers; but after the
horses had idly pawed the ground for hours, he changed his mind. He
would not go.
Ney returned in a fury from the army. Napoleon's bulletins of the
battle had censured him. The marshal angrily replied in the _Moniteur_,
and he now from his place in the House of Peers struck back at his
late master. When Labédoyère, Davoust, and others told the chambers
that Grouchy's army was intact, and that thirty or forty thousand of
Napoleon's own troops had rallied,--all of which was true,--Ney hotly
denied it. Passionate and positive, he declared that the army no
longer existed; that all talk of defence was idle; that terms must be
made with the enemy. Unfortunate man, whom Bourbon hatred had marked
for a traitor's death! His one chance for life was to continue the
fight for the Emperor; his headstrong folly and falsehood ruined both
Napoleon and himself.
Nothing would satisfy the Lafayette party but Napoleon's abdication.
The ground must be cleared for a republic or a limited monarchy. Freed
of Napoleon, Lafayette believed that France could make peace with the
Allies, and would be suffered to choose her own ruler and form of
government. Fouché slyly encouraged this dream of the man whom Napoleon
justly termed "a political ninny." No one knew better than Fouché that
Napoleon's vacant throne would be filled by the king whom Napoleon had
driven from it.
The plots that were at work became known throughout Paris, and created
an immense sensation. The masses of the people wanted no Bourbons, no
Lafayette experiments. In the face of such national danger, they wanted
Napoleon. Great crowds began to collect, and the streets rang with
cries of "Live the Emperor!" The multitude thronged the avenues to the
Élysée palace, and clamored for Napoleon to assert himself.
But at last the great man's energy was dead. He cared no longer for
anything. He was sick in mind and body, disgusted, worn out, utterly
discouraged. The enemies of France he could fight--yes, a world full
of them!--but France itself he would not fight. He would head no
faction; would wage no civil war for his crown. It had come to that,
and his heart failed him. Let the factions rage, let his French
enemies combine: he would not stoop to such a combat. At last he was
vanquished: this greater Percy's spur was cold.
Behind the armies of Blücher and Wellington blazed the campfires of
more than five hundred thousand soldiers marching under their kings
upon France: how could any human being combat half of France and the
whole of Europe besides? The great head sank upon his breast, and the
beaten Emperor muttered, "Let them do as they will."
He gave in his abdication in favor of his son, when abdication was
demanded. He submitted when his son was set aside. He made no effort
to prevent the formation of Fouché's provisional government. He warned
the erring statesmen that they were playing Fouché's game, and were
making a huge mistake; but he lifted no hand to check the movement.
Soldiers as well as citizens clamored for him to lead them; he answered
their shouts with lifted hat and bowed head, but in no other way. When
Fouché, fearing him, ordered him away, he went.
Stopping at Malmaison, it was the same. He took no interest in
anything, was apathetic, slept much, talked at random, and strolled
idly about the grounds. Soldiers, passing in the road, cheered him with
as much enthusiasm as ever, but he merely said, "It would have been
better had they stood and fought at Waterloo."
There was one flash of his old spirit. The armies of Wellington and
Blücher, marching upon Paris, had become widely separated. He saw
that they could be beaten in detail, and he offered his services as a
general to the Fouché government to drive back the invaders. The offer
was refused.
The army which had been operating in La Vendée clamored for him to
put himself at its head; the army of the Loire sent envoys; citizens
thronged about him and besought him to rouse himself and fight. "No. It
would only be civil war. I will not shed the blood of the French in a
purely personal cause."
He formed no plans. He lingered at Malmaison when he could have
escaped. Finally he went to the coast, and again he wasted time in
uncertainty when he might have safely taken ship to America.[4]
[4] Talma was present at the last parting, at Malmaison,
between the Emperor and his mother, and he said it was one
of the most tragic scenes he ever witnessed. When the last
moment arrived, the Empress-mother, prostrated with grief,
and with tears streaming from her eyes, could only utter
in a tremulous voice, "Adieu, my son! Adieu." And Napoleon
was so affected that he caught hold of both her hands and
cried, "Adieu, my mother!" and burst into tears as he left
her.--(Gronow's _Anecdotes_.)
When almost every other chance was gone, he trusted himself to Captain
Maitland of the British navy, whom Napoleon had understood to promise
asylum for him in England.
* * * * *
The armies of Wellington and Blücher continued their advance. There
was some fighting before Paris; then came capitulation; and then came
the Bourbons, skulking back to the throne in the rear of the enemies
of France. Lafayette and the provisional government were quietly swept
into the outer darkness. In after years he lamented his error of 1815,
and in 1830 he did what he could to square accounts with his friends,
the elder Bourbons.
CHAPTER L
Whatever legal right Great Britain had to treat the French Emperor
as prisoner of war, must necessarily have grown out of the manner in
which she got possession of his person. In regard to this, the actual
facts are that Lord Castlereagh in 1814 had suggested that he come to
England, where he would be well received; and Captain Maitland of the
_Bellerophon_, while disclaiming any authority to bind his government,
had certainly not said anything which would warn the Emperor not to
expect such treatment as Castlereagh, an English minister, had seemed
to offer in 1814. Upon the contrary, Napoleon was received on board
Captain Maitland's ship with formal honors; and when Napoleon said, "I
come to place myself under the protection of the British laws," Captain
Maitland gave him no hint that those laws had no protection for him. If
Great Britain did not intend to accept him in the spirit in which he
offered himself, should she have received him without giving him notice
that he was acting under a delusion? Was it honorable, was it right? If
she considered him a captive, why not tell him so? Why receive him on
board with formal demonstrations of honor; why invite him to banquets
where British admirals treated him as a sovereign? Why wait till the
fleet was on the English coast before reading to him the cold lines
which consigned him to St. Helena?
The entire episode reeks with dishonor. It will not do to say that he
was certain to have been captured anyhow; for that statement cannot be
true. There were three vessels offered him at Rochefort, in either of
which he might have escaped to America; or he could have placed himself
at the head of some of the French troops, near by, and have recommenced
the war. With Napoleon's standard once more up, his sword in his hand,
who can doubt that he could have wrung from his enemies some settlement
better than hopeless captivity upon a barren rock? At all events, it
seems a shocking thing to open one's door to a vanquished foe, after he
has knocked thereon with the plea of a guest; and then, after having
let him enter as a guest, to bar the door upon him as a prisoner. No
amount of argument can hide the shame of such a transaction.
When Napoleon came on board Captain Maitland's ship, there is no doubt
whatever that he was sincere in his belief that he would be permitted
to live in England as a private citizen. Nor is there any doubt that
Maitland thought so too. When Admiral Hotham, of the British man of
war, _Superb_, visited the _Bellerophon_, Maitland's ship, on the
evening of Napoleon's going on board, he asked permission to see, not a
prisoner, but an Emperor. And the breakfast he gave in Napoleon's honor
next morning on the _Superb_ was given, not to a captive, but to a
sovereign. Not only the admiral, but all the officers of the squadron,
paid to the distinguished visitor every honor; and he was invited to
continue his journey in the more commodious vessel, the _Superb_. He
declined, out of regard for Maitland's feelings; and it was Napoleon's
preference, and not Hotham's, which prevailed.
These things being considered, who can doubt that Napoleon and the
naval squadron which had possession of him were honestly acting in the
belief that he was on his way to England as a guest, as a great man in
misfortune, who was seeking asylum in the magnanimity of a great people?
The time had been when the word "chivalry" counted for something in
Great Britain, though, to be sure, its influence had been fitful. A
king like Edward III. and a prince like Edward's son, who were knights,
might exhaust generosity in their dealings with a captive king of
France, who was likewise a knight; but the severed limbs and gory
head of Scottish Wallace were quite enough to have caused Napoleon to
doubt whether John of France received the benefit of a rule or of an
exception.
Between the Black Prince, to whom John trusted, and the Prince Regent,
to whom Napoleon wrote his manly and touching appeal, the difference
in character was considerably wider than the chasm of the years which
separated them. To this Prince Regent, known to history as King George
IV., the fallen Emperor of the French wrote: "My political career is
ended, and I come to sit down at the fireside of the British people.
I place myself under the protection of their laws, and I claim this
protection from your Royal Highness as the most powerful, most
constant, most generous of my foes!"
Surely a manly appeal! Surely a noble confidence! The soldier who had
wielded what an Englishman has recently called "the most splendid of
human swords," turned to the chief of his foes and said, "The battle
has gone against me; my public life is at an end; I offer you my
sword; let me sit down under your protection and spend the evening of
my life in peace!"
He was a broken man; he had refused to make any further strife in
France when thousands of the people implored him, to the moment of
his departure, to stay and fight again. "No. I am tired out--tired of
myself and of the world." He was ill, could no longer ride horseback in
comfort, could no longer concentrate his mind for prolonged effort. And
he who had been so restless now lay abed, or lolled with a novel in his
hand, and gossiped or dozed by the hour.
Never in Napoleon's career had the prayer of a vanquished foe fallen
upon ears which heard not. The battle ended; he was ready for peace.
He bore no malice, took no revenge. Splendid acts of generosity lit
his progress from first to last. During the Hundred Days when he was
so much occupied and in such straits for money, he had sought out the
Dowager-Duchess of Orleans, and renewed her large pension; she had
delivered him a prize when he was a schoolboy. In the dreadful strain
of the hours between Ligny and Waterloo, he had remarked the critical
condition of a captive English officer, Colonel Elphinstone, and had
sent his own surgeon to give immediate attention to the wounded man,
thus saving his life. To the Belgian peasants he had threatened the
terrors of hell if they neglected to succor the Prussian wounded.
It is folly to say that noble deeds like these spring from hearts
that are base. Natural kindness, inborn nobility, must be the source
from which such conduct flows. Generous himself to the vanquished,
magnanimous to those who threw themselves upon his generosity, it is
easy to understand how it was that Napoleon trusted confidently to the
liberality of Great Britain. Just as the pallid face of the dead is the
flag of truce which hushes the angry voice of feud, just as the lowered
point of lance or sword threw around the weaker man the invisible armor
which no gallant knight would ever pierce, so this greatest captain of
modern times believed that he had only to say to England: "Enough! I
am beaten! I throw myself on your clemency!" in order to win the same
immunity from insult, harsh treatment, and continued warfare.
So, when British officials at length came on board the ship and read
to him the decision of the English ministry, that he was to be taken
to St. Helena as prisoner of war; when British officials searched his
trunks, took charge of his cash, and demanded his sword, his amazement,
grief, horror, and indignation were profound. He had made for himself a
Fool's Paradise; he had seen himself living in England, at one of her
quiet, lovely homes; had surrounded himself with books and friends, and
was to spend the remainder of life as a private gentleman whose passion
was literature. When the horrible reality came upon him, he seemed
desperate, and contemplated suicide.
Lord Liverpool, English Prime Minister, had, in official despatches,
expressed the opinion that the very best way to deal with Napoleon
was to treat him as a rebel and have him hanged or shot. Lord
Wellington's opinion ran along on parallel lines to this, he being one
of those warriors to whom generosity was a myth. In this spirit the
British government conveyed Napoleon to St. Helena; in this spirit
he was treated as long as he lived; and in this spirit his dead body
was pursued to the grave. In the same spirit men who never met him
personally, and who studied him from the point of view of Toryism
only, have blackened his memory from that day to this, seeing his
faults, and nothing but his faults; trumpeting his sins, and nothing
but his sins, just as though Napoleon Bonaparte were not a son of Adam,
like any other, and wonderfully made out of the mixed elements of good
and bad.
Even yet, royalism, absolutism, fetichism in Church and State, have a
horror of Napoleon Bonaparte, so rudely did he smash their idols, so
truly did he clear the way for modern liberalism. One can hardly escape
the conclusion that even yet books of a certain type, written against
Napoleon, are little more than briefs for the defendants in the case
which the modern world makes against the kings, the nobles, and the
priests for the manner in which they crushed democracy for a time on
the false plea of crushing Napoleon.
Passing from the custody of Captain Maitland to that of Sir George
Cockburn, Napoleon was made to feel the change of status as well as the
change of ship. Sir George was a typical commander of a battle-ship,--a
small monarch, a despot on a limited scale. His own _Diary_ exhibits
him as no other writing could. It shows him to have felt that he must
make "Bonaparte" know his real position; make "Bonaparte" come down
from his lofty perch and look up to the eminence of Sir George. If
"Bonaparte" presumed to put on airs around Sir George, Sir George would
soon teach him better. If "Bonaparte" showed the slightest inclination
to act the Emperor, Sir George would promptly convince him that "I
cannot allow it." If "Bonaparte" grew tired of sitting at the dinner
table an hour and a half, having never been accustomed to spend more
than twenty minutes in that manner, Sir George would resent his
leaving the table while the others guzzled wine; and would, as Napoleon
left the room, make sneering remarks to "Bonaparte's" friends about
"Bonaparte's" manners.
One of the things of which Sir George said "I cannot allow it," was the
proposed gift of a handsome gratuity from "Bonaparte" to the sailors
of the ship. Sir George evidently feared that such a gift, adding to
"Bonaparte's" already great popularity with the crew, might bear fruit
unpleasant to the taste of Sir George.
Indeed, the manner in which all those who came in contact with
Napoleon found their prejudice melt away, is very remarkable. Fouché
had selected General Becker as Napoleon's custodian in France for the
reason that Becker bore the Emperor a grudge; yet by the time Napoleon
went on board Maitland's ship, Becker had become an ardent friend, and
the parting between them left Becker in tears.
Captain Maitland liked him, Lord Keith liked him, the crews of the
English ships liked him. Even Sir George Cockburn ceased to hate him.
"Damn the fellow!" exclaimed Lord Keith; "I believe that if he and the
Prince Regent should meet, the two would be the best of friends in half
an hour."
One incident of the voyage to St. Helena could not be told in words
more vivid than those of Lord Rosebery:--
"Once only in that voyage did his apathy forsake him. At dawn
one morning when the ship was making Ushant, the watch, to their
unspeakable surprise, saw the Emperor issue from his cabin and make
his way, with some difficulty, to the poop. Arrived there, he asked
the officer on duty if the coast were indeed Ushant, and then taking
a telescope, he gazed fixedly at the land. From seven till near noon
he thus remained motionless. Neither the officers of the ship nor his
staff as they watched him, durst disturb that agony. At last, as the
outlines faded from his sight, he turned his ghastly face, concealing
it as best he could, and clutched at the arm of Bertrand, who supported
him back to his cabin. It was his last sight of France."
Landed at St. Helena, he was given shabby quarters in a renovated,
repaired, and amplified cow-house. The walls of it were thin, the rooms
small; the rain and the wind pierced it, the heat made an oven of it,
the rats infested it; no shade trees cast grateful shade about it; no
fruits or flowers relieved its dismal repulsiveness.
To make sure that Napoleon should not escape from the isolated,
precipitous rock of St. Helena, a considerable fleet of cruisers
girdled the island, and nearly three thousand troops watched the
prisoner. The eye could not range in any direction without resting upon
a sentinel. During the daytime the Emperor had continual reminders
of his fallen condition; and when night came on the line of sentries
closed in, and no one could pass.
The prisoner and his friends were allowed to have books to read; and if
Sir Hudson Lowe in browsing among the European newspapers and magazines
happened upon some peculiarly bitter weed of abuse of Napoleon, that
particular paper or magazine was sure to be sent up to Longwood,
Napoleon's residence. If books, papers, or magazines arrived in which
the captive was tenderly handled, such articles became contraband,
upon one plea or another, and rarely reached the lonely man they would
have cheered. The prisoner and his companions were given enough to
eat, generally, and a sufficiency of fuel and water. It was only
occasionally that Napoleon had to feed the fire in his damp room by
breaking up his furniture; nor was it often that the quality of the
food was such that appetites were lost because of grave suspicions as
to the manner in which the cow or sheep which supplied the beef or
mutton had come to its death.
Excepting the bare necessities of life, the prisoner was given nothing
to make captivity reasonably comfortable. Ditches and trenches were
dug all about him, guns planted, soldiers posted, and absurdly minute,
vexatious regulations made. If Napoleon rode, a British soldier must
attend him; if he stayed in the house, a British soldier must have
sight of him every day. No letter could come or go without having
been opened and read by his jailer, Sir Hudson Lowe. Books sent him,
pictures, and everything else had to come through the same channel.
If any article sent him were addressed to him as Emperor, it was
impounded relentlessly. A Mr. Barber who had come to live in the island
had brought with him two portraits of Napoleon's son, intending, as a
kindness which would certainly be appreciated, to present them to the
bereaved father. Sir Hudson Lowe forbade the gift, and the Emperor
never laid eyes upon the treasures. It was only through Eugène that
Napoleon finally received a portrait of his son: it came packed in a
box of books. A marble bust of the King of Rome came also, and this was
long held by Lowe, who threatened to break it in pieces. A letter from
Napoleon's mother, in which she offered to share his lot though blind
and bending with age, was torn open and read by the governor before its
delivery. The captive refused to consent that either his mother or his
sister Pauline should come: he was unwilling to see them subjected to
the insolence of his jailers.
The question of title gave more trouble at St. Helena than almost
any other. It was vexatious, it was met at every turn, and it could
never be settled. It angered Napoleon excessively when Sir Hudson Lowe
persistently continued to shut off from him all letters, books, or
other articles which came addressed to "The Emperor." Great Britain was
resolved that he should not be known by the title he had worn so long,
which a vote of the French people had confirmed, which the Pope had
consecrated so far as a pope can consecrate, which every king on the
Continent had recognized, and which England herself had recognized at
the Congress of Châtillon, if not under the ministry of Charles Fox.
"General Bonaparte" was the highest title that Great Britain could
now allow; and her prisoner resisted her as stubbornly on this point
as General George Washington resisted her right to send him letters
addressed "Mr. George Washington."
A small thing in itself, the refusal of his title became important to
him because of the spirit which actuated those who refused it. They
meant to degrade him in the eyes of the world, to wound his pride by an
exertion of authority; and he resented it as all self-respecting men
must resent the smallest of affronts when inflicted with the meanest of
motives.
"Let us compromise," urged Napoleon; "call me General Duroc or Colonel
Muiron." "No!" said Great Britain; "we will call you General Bonaparte,
for _that_ hurts you." In simple words, such was England's attitude
throughout his captivity to this lonely, broken, most wretched man.
A book which an Englishman, Byron's friend Hobhouse, wrote on the
Hundred Days, and which would have given the exile immense pleasure,
was not delivered because in sending it the author had written on the
fly-leaf "To the Emperor Napoleon." And when the prisoner died, and
his friends wished to inscribe on his coffin-lid the word, "Napoleon,"
Great Britain, speaking through Sir Hudson Lowe, refused the
privilege,--Napoleon was the imperial name; it could not be permitted.
The white face of the dead man, the folded hands, the frozen sleep of
Death, made no appeal to his captor which could soften this inexorable
enmity. Hounding him to his very grave they demanded that "Bonaparte"
be added to "Napoleon," to prove to all the world that England,
ungenerous to the living captive who had come to her for generosity,
had been implacable even unto death, and after death. So it was that
the coffin of this greatest of men went unmarked to the tomb. Save in
anonymous burial there was no escape from the malignancy which had made
his last years one long period of torture.
* * * * *
Napoleon's household at St. Helena consisted of General Bertrand
and wife and children, Count Montholon and wife, Las Casas and son,
General Gourgaud, and Doctor O'Meara, the Irish surgeon of the
English battleship _Bellerophon_, who had asked and been granted by
his government permission to attach himself to the Emperor as his
physician. Besides these, there was a staff of domestics, and, toward
the end, a Corsican doctor Antommarchi and a couple of priests.
Organizing his little establishment with the same love of system which
he had shown throughout his career, Napoleon preserved at St. Helena
the etiquette of the Tuileries. He had his great household officers,
as at Elba; his servants wore the imperial livery; intercourse between
himself and the friends who attended him was as ceremonious as it had
ever been. Nobody was admitted to his presence save after audience
asked and granted. In his shabby little room this fallen monarch
imposed his will upon those about him to such an extent that none of
his friends entered until summoned, or left until dismissed. Not till
general conversation was in full current did any of his companions
address him unless first spoken to by him. No matter how long he
might feel inclined to talk, they stood throughout, never daring to
sit unless he graciously invited them to do so. He would read to the
company, and they were expected to listen attentively. A yawn was an
offence, and was rebuked on the spot. A nod was an aggravation, and it
would be broken into by such prompt admonitions as, "Madame Montholon,
you sleep!"
Those were dreary days at St. Helena, and the nights were drearier
still. He ceased to ride, so hateful was the sight of his jailers. He
tried to get some amusement out of planting trees, making a garden, and
digging a fish pond. Sometimes he romped with the children; often he
played chess, and cards, and billiards. In the pathetic attempt to get
the benefit of horseback exercise without having to ride out in custody
of an English officer, he rigged up a wooden contrivance in the house
and worked away on this make-believe horse for a while.
But books and composition were his great resources. He read much,
dictated a great deal; and when these tired him, he called in his
companions and tried conversation.
As was natural, his talk touched every epoch of his past,--his home and
family in Corsica, his childhood, his school days, his early struggles,
his first triumphs, his campaigns and battles, his numberless plans
and undertakings, his mistakes and failures. He spoke of himself,
generally, in the third person, as of one long since dead; and spoke of
the events of his career as some one, seated upon a mountain top, might
calmly describe the panorama below.
In alluding to those who had served him, in any capacity, his was the
tone of a chemist reporting the result of some analysis.
He rarely showed much temper either way, for or against, but spoke
with a curious indifference, as of remote historical characters. Even
when stating his bad opinion of Fouché, Talleyrand, Augereau, Emperor
Francis, or Czar Alexander, he manifested no rancor.
Without any trace of bitterness, he referred to the harm his brothers
and sisters had done him; of Marmont, Berthier, Murat, Ney, he spoke
with as much absence of malice as was possible under the circumstances.
He took to himself all the blame for his great errors,--his Russian
campaign and the attempt on Spain.
More inclined to be severe on those who had failed him during the
Hundred Days, he put the burden where history must say it belongs,--on
Bourmont, on Ney, on the false movement of D'Erlon's column, on
Grouchy, and on Fouché and Lafayette.
The anniversary of Waterloo was a yearly affliction. It was a day that
oppressed him, a day which wrung from him anguished regrets.
"Ah, if it were to be done over again!"
How did it happen? why was it that his left failed him at Ligny, and
his right at Waterloo? Was there treachery, or merely misfortune?
Over this problem he would ponder, with a face which revealed deep
emotion; a feeling akin to that which had caused him to raise his hand
and strike his forehead on the day when he heard the guns of Blücher's
army where he had expected to hear Grouchy's.
Wellington he frankly hated: partly because Wellington had commanded
at Waterloo, and partly because Wellington had sent him to St. Helena.
In his Will, the dying Emperor left an unworthy trace of this bitter
feeling by devising a sum of money to a man who was charged with having
attempted to assassinate the English duke. True, the Emperor states
that the man had been acquitted, but the Will asserts that Cantillon
had as much right to kill Wellington as the latter had "to send me to
die on this rock." Here is vindictiveness and a departure from good
morals; but if ever circumstances justified such an offence, it was in
the case of Napoleon.
But the time, hard as he tried to kill it, hung heavy on his hands.
He would lie in bed till late in the day, spend hours in the bath,
lounge in undress on the sofa. If he could by any means keep himself
pleasantly occupied till midnight, he was overjoyed: "We have got
through one more day!" "When I wake at night, do you think my thoughts
are pleasant, remembering what I have been, and what I am?" "How long
the nights are!" was an exclamation which reveals an ocean of misery.
With more to grieve over than all of his companions put together,
he made it a point to set an example of cheerfulness, of amiable
comradeship, of intelligent consideration for others. "We are a little
group, a little family, condemned to pass dreary years of exile here
on this bleak rock; let us try make the time pass as agreeably as
possible." When there were jealousies and bickerings between members
of his little court, it was the Emperor who soothed them away. When a
fretful Gourgaud would take offence at something Napoleon had said or
done, he was coaxed out of his ill-humor, or paternally sent to bed to
sleep it off.
NOTE.--Lord Rosebery in his "Napoleon," says, "As to his
habitation, Longwood was a collection of huts which had been
constructed as a cattle-shed. It was swept by an eternal wind; it
was shadeless, and it was damp. Lowe himself can say no good of
it, and may have felt the strange play of fortune by which he was
allotted the one delightful residence on the island with twelve
thousand a year [about $60,000], while Napoleon was living in an
old cow-house on eight."
CHAPTER LI
Many visitors, passengers in English vessels, called to see him.
Generally, but not always, he received them. Generally, but not always,
visitors so received went away converted into sympathetic friends,
sometimes enthusiastic partisans. Only a few days ago (April, 1901)
there died in London an aged man who, when a lad, saw the Emperor at
St. Helena. The boy had been fascinated; never ceased to recall the
placid countenance, gentle, sonorous voice, and wonderfully expressive
eye; and spoke of Napoleon with enthusiasm to the last.
If the world possessed a faithful record of Napoleon's conversation
at St. Helena, no book would be more interesting, for he discoursed
freely on almost every subject of human interest, and on most topics he
touched he said something worth hearing. But we have only an imperfect,
fragmentary, unreliable record. Long conversations extending through
several hours, and jotted down by a secretary afterward, necessarily
lose most of their flavor. It would be a miracle if such a method of
reporting so rapid a talker as Napoleon were accurate.
On the subjects of death, religion, the soul, the hereafter, he is
differently reported,--or, rather, he held two lines of expression.
When thinking of political effect and the interests of his son, he
would of course remember the Catholic Church, its power, its creed,
and would say things which put him on the plane of the Concordat--the
restorer of religion, the believer in Christ. But when he was not
posing for effect, when he blurted out his real thoughts, all this
disappeared. He did not believe in the modern doctrine about the
soul, and scouted the idea of immortality. "When we are dead, my dear
Gourgaud, we are altogether dead."
Again he would ask: "What is a soul? Where is the soul of a sleeper,
a madman, a babe?" In spite of that old-time pointing to the stars in
the heavens and the oft-quoted question which we are told dumfounded
the materialists, "Can you tell me who made all that?" Napoleon at
St. Helena proclaimed himself a materialist. Long before Darwin's
great book appeared, Napoleon announced his belief in the principle
of evolution. His great difficulty in reconciling the dogma of a
benevolent and just God with the universe as it exists, was that the
facts seemed all against the dogma. In the days of his power he had
said scornfully, "God fights on the side of the heavy battalions;"
at St. Helena he declared that he could not believe in a just God
punishing and rewarding, for good people are always unfortunate and
scoundrels are always lucky. "Look at Talleyrand; he is sure to die
in his bed!" And so he did; and if the Pope's blessing was a passport
to heaven, this most villanous of all Frenchmen reached heaven by
the best and shortest route. The manner in which the weak--no matter
how good--go down before the strong,--no matter how bad,--in human
affairs, as in the realms of animal life, staggered his belief in
the benevolence of the plan of creation. "Were I obliged to have a
religion, I would worship the Sun--the source of all life, the real god
of earth."
"Why should punishment be eternal?" Why damn a man who was brought
into the world, not of his own will, and who was stamped with certain
qualities which almost inevitably determined his character and
conduct--why punish such a man with the eternal torments of hell
because of a few years of sin? What good could it accomplish to torture
poor human beings forever and forever? Would God _never_ grow sorry?
No? Then he was crueller than the savagest of the human race. Justice!
Could it be just to create men with certain passions, turn them loose
for a few years to see what they would do, and then when they had done
what the law of their nature made it almost inevitable that they would
do,--and what God knew they would do before he created them,--was it
just to burn these helpless wretches forever in the slow fires of hell?
Napoleon could not bring himself to think so.
He said that, when in Egypt, the sheiks had disturbed him considerably
by alleging that he was a pagan because he worshipped three gods. These
sheiks, with tantalizing persistence, maintained that God the Father,
God the Son, and God the Spirit made three gods. Of course Napoleon
endeavored to explain to these benighted Arabs that our three gods
were only one. The sheiks of Cairo, however, being men of primitive
mind and stubborn habit, would not open their eyes to the truth, and
they continued to say that Mahomet's creed was better than Christ's,
because Mahometans believe in one God, only. All other celestial beings
are angels, lower than God. Human beings, men born of women, may be
prophets, martyrs, sublimely missioned reformers, but they are not gods.
"As for me," exclaimed Napoleon, on one occasion, "I do not believe in
the divinity of Christ. He was put to death like any other fanatic who
professed to be a prophet or a messiah. There were constantly people of
this kind." As, indeed, there are. England crushed the last one in the
Soudan a few years ago.
The great sorrow of Napoleon in his captivity was the absence of his
wife and son. He believed, or pretended to believe, that Maria Louisa
was still faithful to him. He had been told of her shame, he had even
hotly denounced the infamous manner in which her father had put her
into the power of Neipperg, but with singular persistency he would
return to the idea that she yet loved him, and would join him if the
Allies would permit. He could not know that the mother of his child had
declared that she did not love him, and never had loved him.
* * * * *
A striking refrain, running through all the discussions of those acts
of his reign which had been under hottest fire, is this, "History
will do me justice." Time and again, after stating his explanations,
reasons, motives, or justification, he comes back to the words,
"History will do me justice."
Considering all the circumstances, the confidence was sublime. His was
a blasted name throughout the world. In France it was bad taste to
mention him. By formal enactment of combined Europe he was an outlaw,
beyond the pale of humanity, a pariah whom all were privileged to
stone. Only one newspaper of the free press of England had dared to
say a word for him when the government was making a prisoner out of a
man it had not captured; only two members of Parliament dared protest
against the wrong.
[Illustration: THE KING OF ROME
From the painting by Sir T. Lawrence]
In France his followers, Ney and Labédoyère, had been shot, and
Lavalette condemned. Reaction was rushing like an avalanche, and
sweeping all before it. Royalist Catholics were outdoing in the White
Terror the atrocities of the Red. Italy was her old self again, and
Murat had looked into the muzzles of the Bourbon muskets, and had
said, with the last flash of the old courage and pride, "Save my face,
aim at my heart--fire!" Every pander who could distort or create was
adding to the piles of books in which the Corsican monster was devoted
to damnation here and hereafter. Yet, in spite of all, the captive was
serenely at ease about his future.
"History will do me justice. My work will speak for itself. I shall
soon be gone; but what I did, and what I attempted, will live for
ages. My public improvements, my canals, harbors, roads, monuments,
churches, hospitals, my school system, my code, my organization of the
civil service, my system of finance, the manufactures that sprang up
at my touch, the arts and sciences encouraged, the libraries founded,
the triumphs of democracy which I organized and made permanent--these
are my witnesses, and to posterity they will testify. Your Wellingtons
and your Metternichs may dam the stream of liberal ideas, checking the
current for the time; but the torrent will be only the stronger when it
breaks.
"From the passions of to-day, I appeal to the sober judgment of
to-morrow. Future generations will remember my intentions, consider my
difficulties, and judge me leniently."
This superb confidence sustained him so buoyantly that he was never
more imperial in his pose than at St. Helena. When Lowe threatened to
have his room forcibly entered each day in order that the jailer might
know his prisoner was still there, the indomitable Corsican said, "I'll
kill the first man that tries it!" and before that courage of despair
even Hudson Lowe drew back. When England demanded his sword, he had
placed his hand upon it and looked the British officer in the eye with
an expression that could not be misunderstood. The brave and generous
Lord Keith, more chivalrous than his government, bowed to his captive,
and retired without the sword.
"Let him" (Lowe) "send all my friends away, if he will; let him plant
sentinels at the doors and windows, and give me nothing but bread and
water: I care not. My soul is free. I am as independent as when I was
at the head of six hundred thousand men; as free as when I gave laws to
Europe!"
Mr. Taine with painstaking malevolence traces Napoleon back to Cæsar
Borgia; but this granite formation of character was not Italian, it
was Corsican. The spirit which here nerved the solitary captive to
brave a world in arms was not that of his Italian father who bent the
courtier's knee to the conquerors of his country; it was that of his
Corsican mother, whose firmness of character resisted all fears and all
temptations. In Napoleon, Italy may have reached her highest type; but
in him, also, Corsica saw the last and the greatest of the heroic race
of Sampiero.
"The atmosphere of modern ideas stifles the old feudalists, for
henceforth nothing can destroy or deface the grand principles of our
revolution. These great truths can never cease to exist. Created in
the French Tribune, cemented by the blood of battles, adorned by the
laurels of victory, hailed by the acclamations of the people, they
can never be turned backward. They live in Great Britain, illuminate
America, they are nationalized in France. Behold the tripod from whence
issues the light of the world! They will yet triumph. They will be the
faith, the religion, the morality of all peoples, and this era will
be connected with my name. For, after all, I kindled the torch and
consecrated the principle, and now persecution makes me the Messiah
of those principles. Friends and foes must acknowledge that of these
principles I am the chief soldier, the grand representative. Thus, when
I am in my grave, I shall still be, for the people, the polar star of
their rights. My name will be the war-cry of their efforts."
Scores of other quotations might be made to the same effect, and they
go far to explain why modern liberalism regarded Napoleon as The Man.
He grew to hate democracy? Yes. He crushed opposition to his will
rigorously, pitilessly? Yes. He stifled free speech and smothered
representative government? Yes. He was more despotic than any Bourbon?
Yes. Then how dared he predict that his name would become the war-cry
of the people in their struggle for civil rights?
Because he knew that posterity would see at work, within the body of
his despotism, the spirit of democracy. He knew that with his system
of civil and social equality, and the absolute privilege of every
citizen, however humbly born, to rise to the loftiest positions, no
real despotism could be possible; and that history would say so. When
he, the Emperor, chosen by the people, stood up in his carriage on the
streets of Paris and pointed out to his Austrian bride the window of
the room in which he had lodged when he came up from Brienne,--a poor
boy with his career to make,--his pride in pointing to that mile-post
on the toilsome route of his promotion was that of all self-made men,
was that of the man who scorns to win where he has not fought, was that
of the robust conqueror who wants nothing for which he has not paid the
price of manly effort.
It was the same spirit which flashed out of him when Metternich
presented from the Emperor of Austria, in 1809, the proofs that he was
descended from the nobility of Florence.
"I will have none of such tomfoolery. My patent of nobility dates from
the battle of Montenotte!"
It was the same spirit which moved him to chide Duroc, his beloved
Duroc, when that highest officer of the palace had been rude to
Constant, the valet, Constant being in tears about it.
The same spirit was on him when he stopped to talk with poor Toby,
the Malay slave of St. Helena, and to give him money; the same when
he rebuked Madame Balcombe, who with angry voice ordered some heavily
burdened slaves to give way to her, in a steep, narrow path,--"Respect
the burden, Madame!"
Thought, feelings, deeds like these are not born in hearts barren
of human sympathy, dead to the sense of fraternity, or alien to the
sentiment which inspires the mystic to strive for the good of all.
* * * * *
Bertrand states that after 1820 Napoleon was a confirmed invalid.
Sitting in his chair, clad in dressing-gown, he spent the days reading,
being no longer able to work or dictate.
"What a delightful thing rest is. The bed has become for me a place of
luxury. How fallen am I. Once my activity was boundless; my mind never
slumbered; I sometimes dictated to four or five secretaries, who wrote
as fast as words could be uttered. But then I was Napoleon. Now I am
nothing. I am sunk into a stupor, I can hardly raise my eyelids, my
faculties forsake me. I do not live; I merely exist."
Through March and April, 1821, he was slowly dying, and suffering
torments from his ailment--cancer of the stomach. His patience and his
kindness to those around him were perfect.
On one of the last days of April he said to Montholon, early in the
morning on awakening from sleep: "I have just seen the good Josephine.
I reached out my arms to embrace her, and she disappeared. She was
seated there. It seemed to me that I had seen her yesterday evening.
She is not changed; she loves me yet. Did you see her?"
Burning fever and delirium marked these final days; but in the lucid
intervals he was calm, fearless, and thoughtful for the friends about
him. On May 4 Bertrand asked him if he would have a priest. "No, I
want no man to teach me how to die." Nevertheless, he accepted the
usual clerical services. And the picture of a densely ignorant and
dull-minded priest, taking possession of Napoleon Bonaparte, hearing
his confessions and granting him heavenly passports, is one of those
things which makes the vocabulary of amazement seem to need enlargement
and intensification.
It would not, perhaps, be difficult to explain why Napoleon, in his
last illness, accepted the services of a priest, and died in the arms
of the Church; but it puzzles one to understand why he embalmed in
his Will his delusion as to Maria Louisa. He had long known of her
infidelity, he received no line or message from her during the whole
time of his captivity; yet he speaks of her in his will as though she
had ever been the true and loving wife. Was this done from personal
pride? Or did he do it for the sake of his son? Both motives may have
influenced him, especially the latter.
A storm was raging over the island on May 4. "The rain fell in
torrents, and a fierce gale howled over the drenched crags of St.
Helena. Napoleon's favorite willow was torn up by the roots, and every
tree he had planted at Longwood was blown down.
"The night was very bad," says Montholon. "Toward two o'clock delirium
set in, accompanied by nervous contractions. Twice I thought I heard
the words, _France--armée--tête d'armée--Josephine_, at the same time
the Emperor sprang from the bed, in spite of my efforts to restrain
him. His strength was so great that he threw me down, heavily falling
to the floor."
Others, hearing the noise, ran in, and the Emperor was put back
upon the bed, where he became calm again. At six in the morning the
death-rattle was heard. As Montholon approached the bed, the dying man
made a sign that he wanted water. He was past swallowing; his thirst
could only be allayed by a sponge pressed to his lips. He then lay all
day with his eyes fixed, seemingly in deep meditation. As the sun was
setting, he died--the evening gun of the English fort booming across
the sea as his life went out.
"Ah," said Marchand, "he died in the arms of victory! He called for
Desaix, Lannes, Duroc. I heard him order up the artillery, and then he
cried: 'Deploy the eagles! Onward!'"
"I shall never forget," says Stewart, "Marshal Bertrand coming out of
the room and announcing, in a hollow voice, 'The Emperor is dead,' the
last word being accompanied by a deafening peal of thunder."
Napoleon had made his preparations for death with the composure of an
ancient pagan. He had given minute instructions to all about him as to
their duties when he should be gone, and had directed an autopsy of his
body in order that the true character of his disease might be known,
for the benefit of his son. He inquired of the young priest whether
he knew how to arrange the death chapel; and he dictated the form of
notice which should be sent Sir Hudson Lowe when he, Napoleon, should
be dead. In his Will, written by his own hand, he set out an elaborate
list of legacies, including those who had befriended his boyhood, and
those who had been loyal to him in the days of his power, as well as
those whose fidelity had been the comfort of his captivity and dying
hours. From his mother and nurse to his teachers and schoolfellows, his
companions-in-arms and the children of those who had died in battle
at his side, to the Old Guard and the faithful few at St. Helena, he
swelled the debt of gratitude, and honored himself in remembering
others. In regard to this Will, it may be of interest to state that
only a small portion of the vast assets Napoleon claimed to have left
in Europe could be found by his executors, and that during the second
Empire the State voted $1,600,000 toward the unpaid legacies.
Given the funeral of a general officer, his unmarked coffin was borne
by soldiers down into the little valley, where was the willow, under
which he often rested, and the spring whose waters had so refreshed him
in the fever of his long decline. Here he was buried, May 8, 1821.
* * * * *
One day, at St. Helena, there was a stormy interview between prisoner
and jailer, between Napoleon and Sir Hudson Lowe. The book from
Hobhouse had been kept by the governor, and this and many other things
the captive resented.
"I detained the book because it was addressed to the _Emperor_," said
Lowe.
"And who gave _you_ the right to dispute that title?" cried Napoleon,
indignantly.
"In a few years your Lord Castlereagh and all the others, and you
yourself, will be buried in the dust of oblivion; or, if your names be
remembered at all, it will be only on account of the indignity with
which you have treated me; but the Emperor Napoleon will continue
forever the subject, the ornament of history, and the star of civilized
nations. Your libels are of no avail against me. You have expended
millions on them; what have they produced? Truth pierces through the
clouds; it shines like the sun, and like the sun it cannot perish!"
To which proud boast, Sir Hudson Lowe replied, as he records, "You make
me smile, sir."
Sir Hudson may have smiled then, and may have kept on smirking as
long as Napoleon lived. Nothing seemed less likely than that the
prophetic words of the prisoner would come true. But there came a time
when Sir Hudson did not smile. When death had released the prisoner,
and the faithful companions of his years of misery went home and
told their story,--O'Meara in England, Las Casas and Montholon in
France,--Sir Hudson did not smile; for all Europe rang with his name,
and all generous hearts condemned him. He turned to British courts for
vindication, and did not get it. He applied to the English ministers
for high, permanent employment and liberal pension, and he got neither
the one nor the other. Young Las Casas invited him to fight, and he
did not fight. He dropped into a contempt which was so deep and so
universal that even Wellington, in effect, turned his back upon the
creature he had used, having no further need for just such a man.
"You make me smile, sir," said amused Sir Hudson, when the shabbily
clad, prematurely decrepit man, standing on the hearth of his dismal
room, prophesied his political resurrection and his final triumph over
his enemies. Had Castlereagh heard, he also would have smiled, not
foreseeing that ghastly climax to political prostitution, when, after
a lifetime of truckling to royalism, and of doing its foulest work, he
should find the whole world turn black, should cut his own throat, and
be followed to his tomb by the hoots of an English mob!
Wellington, too, would have been amused at hearing the prisoner's
prophecy; would have thought Napoleon insane, not foreseeing the
perilous times in England when the progress of liberalism would break
the line of his Tory opposition; would win triumphs for reform in
spite of his threat that he would have his dragoons "sharp grind their
sabres as at Waterloo." With the windows of his London home smashed
by a British mob, with millions of liberals shouting demands for
better laws, so fiercely that even Wellington gave up trust in those
sharp-ground swords, there came a day when the Iron Duke may have
remembered the prophet of St. Helena, and read the words again--without
the smile.
"In a few years you and all the others will be buried in the dust of
oblivion; but the Emperor will live forever, the ornament of history,
the star of civilized nations!"
It was a proud boast, and proudly has time made it good. In a few years
the Bourbons had played out their shabby parts on the throne of France,
and had gone into final and hopeless exile, "unwept, unhonored, and
unsung."
Liberalism had risen from defeats, and made its will supreme. Both in
England and in France the Old Order had passed away, principles more
enlightened prevailed. A new day had dawned, not cloudless nor free
from storm, but better and brighter than 1815 or 1821. In the year of
our Lord 1840, the thought of the two great nations turned to the grave
at St. Helena. France asked, and England gave--whom? The Emperor! Not
"Bonaparte" nor "General Bonaparte," save in the minds of the very
small and the exceedingly venomous; but Napoleon, "the Emperor and
king."
The grave at St. Helena was opened; the perfectly preserved face,
beautiful in death, uncovered amid sighs and tears; and then the body,
taken away to be entombed "upon the banks of the Seine in the midst
of the people I have so much loved," was received on board a royal
ship, by a prince of the Bourbon house of Orleans, with masts squared,
flags flying, cannon booming, drums beating, and every note of triumph
swelling the pomp of that imperial reception. With a vast outpouring of
the people, France welcomed the greatest Frenchman home.
"Truth cuts through the clouds; shines like the sun; and like the sun
it is immortal!" Sublime confidence, sublimely justified!
"You make me smile, sir," said Lowe; but that was many years since. It
is 1840 now, and Napoleon's turn has come.
From king to peasant, all France starts up to meet her returning
hero. He comes back to a throne which none dispute. He comes back to
a dominion no Marmont can betray. Allied kings will league themselves
in vain to break that imperial supremacy. No Talleyrand or Fouché or
Bourmont can find for treachery a leverage to overthrow that majestic
power. No. It is secure in a realm which envy and malice and ignoble
passion may invade, but cannot conquer. It has linked itself with
things immortal; and for this imperial career and fame there can be no
death.
Let Cherbourg's thousand guns salute! Let triumphal arches span the
Seine as he passes on his way! Let hill and <DW72> and river bank hold
their gazing hosts! Let flowers and garlands shower down on the bier
from every bridge. Let aged peasants drop on reverent knees, fire the
old musket in humble salute, and then cover the weeping faces with
trembling hands! Cold is this December day; but winter cannot chill
this vast enthusiasm. From the quay, where the funeral barge moors, to
the Church of the Invalides, where the tomb waits, a million people
throng the route. Streets, avenues, squares, balconies, windows, roofs,
trees--all are full of people. Cannons, drums, military bands, the
tramp of men and war-horses, the glitter of endless lines of soldiers,
the songs which rouse the passions and the memories, the shouts of
dense crowds stirred by electrical emotions--all these mark this
December day as the gorgeous funeral car bears Napoleon to his final
rest. There is the white war-horse, not Marengo, but one like him; and
upon the horse is the saddle and the bridle Napoleon had used. There
are his old Marshals Moncey, and Soult, and Oudinot; there is Bertrand
and Gourgaud and Las Casas, the faithful companions of his long exile.
But above all there are the relics of his ancient wars to come weeping
around the bier; and there is a remnant of his Old Guard to march with
him to his tomb. Oh, the magic of the mighty dead! No freezing December
air can keep down the fervor which makes the great city ring with cries
of "Live the Emperor!"
Sixteen black horses, plumed and draped, draw the lofty funeral
car over which lies the purple velvet robe, and in which is the
coffin--marked, at last, in letters of gold, "Napoleon." Princes of
the Church come forth to meet the body; a king and his court and the
proudest notables of France wait within to receive it.
"The Emperor!" cries the herald at the door; and the brilliant assembly
rises, as one man, and makes the reverent bow to the dead man who
enters.
Over all is the spell of a master spirit; over all the spell of a
deathless past.
The sword of Austerlitz is handed to King Louis Philippe by Soult;
and the King gives it to the faithful Bertrand; and Bertrand lays it,
reverently, upon his master's coffin. The awful stillness of the great
temple is broken by the sobs of gray-haired soldiers.
With a grand _Requiem_ chant, the funeral ends; but the silent
procession of mourners coming in endless lines to view the coffin
lasts more than a week, bringing people from all parts of France, from
Belgium, and from other lands.
Nor has that procession ended yet. Around the great man, lying there in
his splendid tomb, with his marshals near him and the battle-flags he
made famous drooping about him, still flows the homage of the world.
The steps of those who travel, like the thoughts of those who are
students of human affairs, turn from the four quarters of the earth to
the tomb of this mightiest of men.
His impress lies upon France forever, in her laws, her institutions,
her individual and national life; but his empire does not stop with
France,--is cramped by no "natural limits" of Rhine and Alps and
Pyrenees.
By force of genius and of character, by superior fitness to do great
things, he was the chief usurper of his time. He is the usurper
yet, and for the same reasons. He did the work kings ought to have
done,--doing it in spite of the kings. He does it yet, in spite of the
kings.
His hand, as organizer of the Revolution, which was greater even than
he, is at the loom where the life-garments of nations are woven. Listen
to this voice, coming out of Italy: "Within the space of ten years we
had made [under Napoleon] more progress than our ancestors had done
in three centuries. We had acquired the French civil, criminal, and
commercial codes; we had abolished the feudal system, and justice
was administered with improved methods." So wrote General Pépé; and
what he said of Italy was equally true of every other portion of
Continental Europe which had come under the imperial sway. It was this
work Napoleon was doing from the very first day he grasped the reins
of power; it was this work the allied kings dreaded; it was this work
they meant to stop.
In that he strove for himself and his dynasty, Napoleon failed
miserably, for to that extent he betrayed his trust, was false to his
mission, wandered from the road. But so far as his toil was for others,
for correct principles, for better laws, better conditions, productive
of happier homes and better men and women, he did not fail. No Leipsic
or Waterloo could destroy what was best in his career: no William Pitt
could pile up sufficient gold to bribe into the field kings strong
enough to chain peoples as they had once been chained. In vain was
Metternich's Holy Alliance, his armed resistance to liberal ideas; his
savage laws, his inhuman dragoonings:--the immortal could not be made
to die.
INDEX
A
Abensberg, battle of, 440.
Aboukir, battle of, 219–220.
Acre, siege of, 215.
"Act Additional"--amendment to Constitution, 1814, 637–639.
Adige, French defence, 156–167.
Ajaccio--
Birthplace of Napoleon, 17.
Paoli, _see that title_.
Reception of Napoleon, 1799, 230–232.
Revolutionary movements, 1789, 49–60.
[_See also_ Corsica.]
Alexander, Czar of Russia--
Erfurth conference, 428.
Successor of Paul, 291.
Vienna Congress, 620–623.
[_See also_ Russia.]
Alexandria taken by Napoleon, 203.
Alps crossed, 1800, 280.
Alvinczy, General, defeated by Napoleon, 162–168.
Amiens, Peace of, 293;
ruptured, 312.
Amnesty to political offenders during Consulate, 258.
Ancients, council of, _see_ Council of Ancients.
André, Abbé d', rumors as to movements of Napoleon at Elba, 624–625.
Antommarchi, death mask of Napoleon, 388.
Aragon, aid in Corsican struggle for independence, 3, 4.
Arcis on the Aube, battle of, 576.
Army of France--
Creation of new army by Napoleon, 1800, 279–282;
1813, 506.
Destruction in Russia, retreat from Moscow, 1812, 493–499, 504.
Napoleon in--
Commander, 112–114, 126.
Loss of position, name struck from list of generals, 60–64, 104.
Western transfer, order evaded, 94–96, 104.
Reorganization by Napoleon, 264, 636.
Artois, Count of, conspiracy against Napoleon, 317–328.
Aspern, battle of, 442–443, 450.
Aube River crossing, incident, 572.
Aubrey--
Exile, 258, 259.
Napoleon transferred to army of the West, 95, 96.
Auerstädt, battle of, 362, 364.
Augereau, General--
_Coup d'état_ of 18th Brumaire, 245, 251.
Directory supported by, during royalist movement, 182–184, 236.
Italian campaign, 162–164, 168.
Austerlitz, battle of, 347, 349.
Austria--
1793, French booty, bargain with England, 83.
1796, Napoleon's Italian Campaign, 144–186.
1799–1800, operations in Italy, peace of Lunéville, 224, 279–290.
1805, coalition of powers, defeat at Austerlitz, 339–347, 355–357.
1809, renewal of war, Wagram, etc., 439–449.
1812, ally of France, 476, 477.
1813, rising in Germany, mediation offered, 507–521, 554–556.
1813–15, coalition of powers and fall of Napoleon, 523–648.
1814, Vienna Congress, 620–623.
Secret treaty with Napoleon alleged, 623, 639.
[_See also_ Charles, Archduke, and Francis, Emperor.]
Avignon, Girondin revolt, 70, 71.
B
Barras, General--
Character, and misgovernment as Director, 125–128.
Directory, movement against, and fall of, 106, 182, 237–247.
_Memoirs_ of Napoleon, 82.
Bassano, peace treaty, 1814, 571.
"Battle of the Nations," 1813, 534.
Bautzen, battle of, 510.
Bavaria--
Deserts Napoleon in 1813, 534, 537, 541.
Refusal to enter coalition against France, 1806, 349.
Baylen, capitulation of, 427.
Bayonne, Napoleon at, 419–421.
Beauharnais, Eugène--
Jaffa massacre, 213.
Moscow retreat, 491, 494.
Viceroy of Italy, 336.
Beauharnais, Josephine, _see_ Josephine.
Beauharnais, Stephanie, dancing anecdote, 32.
Beaulieu, Austrian general, defeated by Napoleon, 144, 154, 155, 159.
_Bellerophon_, British ship, Napoleon sent to St. Helena, 672, 673.
Bennigsen, Russian general, campaign against Napoleon, 381–383.
Bentinck, Lord, duplicity of, 563.
Beresina, crossed by French troops, 1812, 497–499.
Berg, Grand Duchy of, created, 1806, 351.
Berlin--
Entered by Napoleon, 1806, 366–369.
March abandoned, 1813, 533–534.
Berlin Decree, 369–371, 416.
Bernadotte, General--
Desertion of Napoleon, 1812–14, 475, 526, 538, 566–573.
Italian campaign, 175, 176.
Norway transferred to Swedish dominion, 623.
Policy, 18th Brumaire, 243, 248, 249.
Sweden, Prince-Royal of, 1810, 463–465.
Berthier, General--
Austrian campaign, 1809, mismanagement, 439, 440.
Commander-in-chief of army in Italy, 1800, 280.
Desertion of Napoleon, 1814, 592–594.
Metternich's interview with Napoleon, 1813, 517.
Bessières, commander of Imperial Guard, 155;
death of, 526.
Blücher, Prussian general--
Germany, rising in, 1813, 509.
Hostilities of 1813, battle of Leipsic, etc., 527, 533, 535.
War of 1814–15, battle of Waterloo, etc., 566–577, 648–671.
Bohemia, Congress of Prague, 521–523, 545.
Bonaparte, Caroline, wife of Murat, Berg, Grand Duchy of, created
1806, 350–351.
Treachery of, 562, 563.
Bonaparte, Charles, father of Napoleon, 19–27, 41.
Bonaparte, Jerome, king of Westphalia, _see_ Westphalia.
Bonaparte, Joseph--
Italy, crown refused, 336.
Naples, King of, 350, 421.
President of Council of Regency in Paris, betrayal of Napoleon,
1814, 564, 575, 578–579.
Spain, King of, 421.
Complaint of interference of Napoleon, 435.
Driven from throne, 430, 564.
Bonaparte, Letitia R., mother of Napoleon, 19–21.
Absence at coronation, 333.
Life at Elba, 605, 624.
Bonaparte, Louis--
Holland, king of, 350.
Complaint as to interference of Napoleon, 435.
Vacates throne, 462–464.
Maintenance and ingratitude during boyhood, 53, 57.
Bonaparte, Lucien--
Pamphlet issued by, 289.
President of Council of Five Hundred on 18th Brumaire, 235, 252–253.
Refuses bribe offered by Napoleon, 351.
Bonaparte, Napoleon, _see_ Napoleon.
Bonaparte, Pauline, Life at Elba, 603, 605, 624.
Borodino, battle of, 483.
Bourbon restoration, 1814, 583–586, 598–627.
Bourmont, rise and treason in army of Napoleon, 649.
Bourrienne--
Anecdotes of Napoleon, 27, 218, 220, 235, 242, 255, 283.
Betrayal of Napoleon, 552.
Brienne--
College, unpopularity of Napoleon, 26–33.
Visit to, 1804, 334.
War of 1814, 335, 568.
Brougham, Lord, anecdote of Napoleon, 405.
Brueys, French admiral, defeat by Nelson, 208.
Brumaire, _coup d'état_ of 18th Brumaire, 241–255.
Brunswick, Duke of, wounded at Auerstädt, 364.
Busca, Cardinal, French campaign, 170.
Bussey, schoolmate of Napoleon, 31, 32, 593.
Buttafuoco, Corsican representative in France, Napoleon's "open
letter," 52, 53, 54.
C
Cadoudal conspiracy, 318–328.
Caffarelli, General, French capture of Malta, 202.
Cairo--
March to, 203.
Retreat, 217–219.
Revolt, war principles of Napoleon, 211.
Cambacérès, consul, opposition to arrest of Duke d'Enghien, 324.
Cambronne, royalist commander, return of Napoleon from Elba, 1814, 630.
Campo Formio, treaty of, 178–187.
Cannes, landing of Napoleon from Elba, 1814, 626, 629.
Carnot, _Memoirs_ of, 646, 668.
Carraccioli, Admiral, murder of, 225, 226.
Carteaux, abandonment of Toulon command to Napoleon, 73–78.
Castlereagh, Lord, Vienna Congress, 1814, 620.
Caulaincourt--
Abdication of Napoleon, 588–589.
Peace negotiations, 1813–14, 570–571.
Cavour, statecraft policy, confession, 374.
Censorship of the Press, 1814, 614.
Ceracchi conspiracy, 288.
Cervoni, Corsican general, Napoleon and Toulon, 75, 76.
_Champ de Mai_, 1815, 641.
Champ-Aubert, battle of, 569.
Charles, Archduke of Austria--
Austerlitz defeat, treaty of Presburg, 344, 347.
Defeat of Jourdan and Masséna, 224.
Italian campaign, defeated by Napoleon, 162, 175–177.
Opinion of Napoleon, 1814, 6.
Renewal of war, 1809, 439–449.
Charles, Captain Hypolite, and Josephine, 193, 209, 235.
Charles IV. of Spain, abdication, 418–419, 425.
"Charter," issued and violated by Louis XVIII, 1814, 601, 612–618.
Châtillon Peace Congress, 570.
Chinese massacres, comparison with Jaffa massacre, etc., 215, 218.
Choiseul, French minister, purchase of Corsica, 14, 15, 26.
Church, Concordat of 1801, 302–309, 453.
Church atrocities, Bourbon restoration, 1814, 614–619.
Cisalpine Republic--
Creation of, 195.
Italian Republic formed, 329.
Reorganization, 286.
Coalitions of European powers--
1793, 83, 115–121.
1798, peace of Lunéville, 222–290.
1805, Austerlitz, peace of Presburg, 339–347.
1806, Jena, Treaty of Tilsit, 355–385.
1813, Dresden, etc., 523–582.
Armistice, 511–556.
Desperate position of Napoleon, 525–526, 548–553.
Determination of Allies to crush Napoleon, 554–557.
Support of nation weakened by illegitimacy of Napoleon's
kingdom, 548–549.
1814–15, 635–670.
[_See also_ names of Powers, England, Russia, etc.]
Cobentzel, Austrian diplomat, Campo Formio treaty, 184–187.
Cockburn, Sir George, treatment of Napoleon during voyage to St.
Helena, 677–678.
Codification of laws--the Code Napoléon, 300–302, 412, 413.
Commercial war, _see_ Continental system.
Concordat, work of the First Consul, 302–309, 453.
Confederation of the Rhine--
Formation, 350, 352.
Overthrow, 544.
Prussian army against, 364.
Rising in Germany, 1813, 509, 510.
Constant, valet of Napoleon, anecdotes, 390, 400, 456, 457, 458, 466,
468, 488, 507, 526, 531, 534, 538, 561, 565, 575, 594, 596.
Constitution, _see_ Consulate, Empire, Republic, etc.
Consulate--Napoleon as First Consul, 257–271, 280.
Life tenure of consulship, 310.
Peace overtures during, 275–278.
Reforms in the republic, 256–273, 295–302.
Continental system, 369–371, 385, 416.
Holland, aid to Great Britain in violating system, 436.
Tilsit treaty with Russia, violation, 470–478.
Convention, adjournment and new Constitution, 104–112.
Corsica--
Ajaccio, _see that title_.
British occupation, failure of French expedition, 92–94.
British withdrawal, 1796, 195.
Description, situation, etc., 1.
Early patriotism of Napoleon, 24–30.
Incorporation with France, organization of governments, 1789, 50, 51.
History of foreign supremacy and struggle for independence, 1–16.
Napoleon's activity in favor of French Revolution, 49–52.
Napoleon's ambition to achieve independence of Corsica, 45, 64.
National Guard election, arrest of French commissioner, 58, 59.
Paoli, _see that title_.
"Corsican ogre," name given to Napoleon, 419, 466.
Corunna, battle of, 433.
Council of Ancients, fall of the Directory, 18th Brumaire, 241–251.
Council of Five Hundred--
Directory, fall of, 18th Brumaire, 241–253.
Lucien Bonaparte, deputy and president, 235, 252–253.
Councils, removal of, 236–241.
Craonne, battle of, 575.
Cumberland, Duke of, massacre of Highlanders after Culloden, 214.
Czernischeff, Russian general, spy on French army, 1812, 474.
D
Danube--
Cession of provinces to Russia, 1808, 429.
Crossed by French forces, 1809, 441–446.
War between Russia and Turkey, 1812, 473, 475, 481.
D'Argenteau, Napoleon's victory of Montenotte, 138–140.
Daru, coalition of 1813, 524–525.
Davidovitch, defeat of, 161–168.
Davoust, French general--
Austrian campaign, 1809, Wagram, 440–448.
Berlin, entry into, 1806, 366.
Campaign of 1814, Napoleon's error in overlooking Davoust, 648, 657.
Defeat of Prussian forces, 362.
Moscow retreat, 494.
De Barrin--French Revolution, Napoleon's movements, 49, 50.
Dejean, General, messenger to Joseph Bonaparte, fall of Paris,
1814, 578–579.
Della Rocca, A., G., and R., Corsican struggle, 3, 5.
D'Enghien, Duke, execution of, 322–327.
Denmark, British seizure of fleet, 415–416.
D'Erlon, mistake at Ligny, 652–653.
Des Mazis, aid to Napoleon, 101.
Desaix, death of, 285.
Desgenettes, surgeon of French army in Egypt, 218.
Directory--
Napoleon's success and power feared, 147, 193, 194.
Misgovernment under Barras and others, 123–125, 135.
Organization of, 112.
Supported by Napoleon during royalist insurrection, 182–184.
Weakness and overthrow of, 236–255, 273.
Djezzar, Napoleon's campaign in Egypt, 213, 216–217.
Dolgorouki, demands surrender of Italy, etc. from Napoleon, 344.
Doria, S., Corsican struggle, 7.
Dresden--
Battle of, 1813, 527–532.
Conferences, 1812, 1813, 476–479, 516–519.
Dubois de Crancé, warning to Directory against Napoleon, 243, 246.
Dugomier, General, siege of Toulon, 78.
Dumas--reforms by Napoleon, 1814, 636.
Dumont, J., recognition by Napoleon, 1814, 603.
Duroc, General, death of, 526.
Dutch delegation, congratulations on Jena victory, 379–380.
E
Eckmühl, battle of, 440, 441.
Education reform during Consulate, 295, 298.
Egypt--
British conquest, 292.
French invasion, 199–227.
Napoleonic improvements, 207, 411.
Religious observances, 206, 689.
Elba, Napoleon's exile--
Departure for, 596.
Journey, 601–602;
landing, 605.
Life at, 605–610.
Return of Napoleon, 623–628.
Political position in France, 627.
Reception in France, 623–636.
War with Allies, 635, 639–640.
Terms of Treaty of Fontainebleau, 595, 608.
Elbe, concentration of French forces, 1813, 530, 533.
Elchingen, battle of, 341.
Elster bridge, French retreat, 1813, 538, 540.
Émigrés, release of, 258, 587.
Empire, French--
Dreams of empire, 305.
Napoleon proclaimed Emperor, coronation, 331–333;
anniversary of coronation, 346.
Enghien, Duke d', execution of, 322–327.
England--
Austerlitz, battle of, consternation at result of, 349.
Coalitions, 1793, 83, 115–121;
1798, 222;
1805, 339;
1813, 523;
1814, 566;
1815, 648.
Continental system, _see that title_.
Corsica, occupation of, 92–94;
withdrawal, 195.
Danish fleet seized by, 415–416.
Egypt and Malta taken, 292, 312.
Encouragement to Austria to war against France, 290, 439.
French Invasion of England, 1805, preparations and defeat of
Napoleon, 339–340.
Napoleon's hatred of, 83–85.
Nelson, _see that title_.
Newspaper abuse of Napoleon, 314.
Northern confederation against, treaty of Tilsit, 385.
Peace offered by Napoleon, and rejected, 275–277, 339, 430.
Portugal, British defeat of French, 427.
St. Helena, Napoleon as prisoner of war, 672–676.
Vienna Congress, 1814, dispute as to division of territory, 620–623.
War declared, 1804, seizures of French property, 315.
War loans and paper currency, 353.
Waterloo, battle of, 660–667.
Wellington, _see that title_.
Enzersdorf, battle of, 446.
Erfurth conference, 428.
Essling, battle of, 442.
Eylau, battle of, 381.
F
Ferdinand of Naples, entry into Rome, 1798, 222, 223.
Ferdinand of Spain--
Disputes with Charles IV, 418–419, 425.
Proclaimed king of Spain, surrender of crown to Napoleon, 418–421.
Release refused, 1813, 558;
granted, 1814, 612, 613.
Financial reforms, 297, 352–354.
First Consul, _see_ Consulate.
Five Hundred, Council of, _see_ Council of Five Hundred.
Fleury, Cardinal, Corsican struggle, 12.
Fontainebleau--
Abdication of Napoleon, 1814, 588–594.
Conference with Pope, 1813, 508.
Departure for Elba, 1814, 596.
Napoleon at, 1814, news of fall of Paris, 581, 583.
Fontainebleau, Treaty of, terms and violation of, 595, 606–608.
Fouché--
Betrayal of Napoleon, 553.
Provisional government after Waterloo, 668–670.
Fox, British ministry, 1806, 359, 363.
Francis, Emperor of Austria--
Centre of Austrian loyalty, 549.
Conduct regarding Maria Louisa, 606, 607.
Frankfort proposals, insincerity of, 555–562.
Frederick the Great, tomb of, sash and sword taken by Napoleon, 368, 369.
Frederick, King of Prussia, centre of Prussian loyalty, 548.
French revolution--
Foreign intervention feared, 1791, 56.
Napoleon sides with nation, activity in Corsica, 47–52.
Swiss defence and Westermann attack, Napoleon's attitude, 61–63.
Valence ceremonies, new oath of allegiance, 1791, 55.
Friedland, battle of, 383.
Fructidor, _coup d'état_ of, 183, 258.
Fulton steamboat invention, 402.
G
Gaffori, Corsican chief, fall of, 13.
Gap, return of Napoleon from Elba, 1814, 630.
Genoa--
Annexation to France, 1804, 338.
Corsican struggle, 2–14.
Disturbances, 1796, 156.
Napoleon's mission in, 1794, 88.
George IV. of England, Napoleon's appeal for British protection,
1815, 674.
Georges conspiracy, 318–328, 417.
Germany--
Aid to Corsica, 10.
Confederation of the Rhine, _see that title_.
Hatred of French principles by feudal powers, origin of Prussian
war, 364.
Redistribution of lands, 329–331.
Rising against France, 1813, 506–522, 543–545.
Giampolo, Corsican independence, 5.
Girondin revolt, 70, 71.
Godoy, Spanish minister, fall of, 417–421.
Gohier, fall of the Directory, 239–247.
Gourgand, General, complaints of neglect, 569.
Government of France--
Legislative body, _see that title_.
Louis XVIII, _see that title_.
Provisional government, 1815, 667–671.
Reorganizations, 256–273, 636–641.
[_See also_ Consulate, Directory, etc.]
Great Britain, _see_ England.
Great St. Bernard, crossed 1800, 280.
Grenoble, reception of Napoleon in 1814, 630–631.
Grenville, Lord, Napoleon's peace overtures, 276.
Grossbeeren, battle of, 530.
Grouchy, conduct of, 1814–15, 648–667.
Guadamara mountains, crossed, 1808, 432.
H
Hanau, battle of, 542.
Hanover, ceded to Prussia, 1806, 357, 359, 363.
Hatzfeldt, Prince, treachery of, 367.
Haugwitz, Prussian envoy to Napoleon, 357.
Hautefort, Marquis de--Thellusson ball, 133.
Heilsberg, battle of, 383.
Helvetic republic established, 222.
Hinton, sailor on board the _Undaunted_, 604–605.
Hobhouse, writings of, 642, 682.
Hoche, General--
Directory, support to, 182.
Italian campaign, 177.
Hohenlinden, Moreau's victory, 290.
Hohenlohe, Prussian general, defeated at Jena, 361.
Holland, monarchy under Louis Bonaparte, 1806, 350.
Dependency on France, complaint, 435.
Throne vacated, Holland annexed to France, 1810, 462–464.
Honors, distribution of, enthronement of members of Bonaparte
family, 350–352.
Hougomont fortress, British defence, 1815, 660.
House of Lords, created 1814, 638–639.
Houssaye incidents of Napoleon, 1815, 653–655.
Hundred Days of Napoleon, 1814, 635, 675, 684.
I
Imperial guard formed, 155.
Inquisition, 173, 612.
Invasion of France, 1813, and fall of Paris, 1814, 557–582.
Inventions ignored by Napoleon, 402.
Italy--
Army, Napoleon in, 86, 103.
Commander-in-chief, 132, 136–138.
Transfer order, evasion of, 94–96.
Campaigns of Napoleon, 87, 138–195, 278–290.
Coalition against French republic, 221–227.
Monarchy under Napoleon, 335–338.
Reforms by Napoleon, 410.
Republic created, 171, 194, 195.
Troops in Paris favorable to Napoleon, 18th Brumaire, 242.
J
Jaffa massacre, 213–215.
Jena, battle of, 361, 403.
Jomini, desertion to allied forces, 525.
Josephine, wife of Napoleon--
Character and infidelity of, 127–134, 191–193, 209–210.
Coronation, 333.
Death of, Napoleon's visit to Malmaison, 643–644.
Divorce, 130, 455–457.
Fall of Napoleon, attitude of Josephine, 593–594.
First meeting, 109–110.
Italy, Josephine joins Napoleon in 1796, 192.
Marrac, château of, life at, 419–420.
Marriage, 130, 132.
Napoleon's return from Egypt, 234–235.
Son of Napoleon secretly shown to, 468.
Joubert, defeat of Austrians in Italy, 167, 168.
Jourdan, defeated by Archduke Charles, 224.
Junot--
Anecdotes of Napoleon, 79, 209, 292, 345, 346, 393–395.
Portugal, French invasion, 418, 427.
K
Katzbach, battle of, 530.
Keralio, de, impression of Napoleon, 30, 33.
Kléber, General, assassination in Egypt, 207, 216, 291.
Knights of St. John, capture of Malta by Napoleon, 201–202.
Kremlin of Moscow, Napoleon at, 485–488.
Kulm, battle of, 530, 531.
Kubusoff, Russian general, French retreat from Moscow, 488,
492, 495, 497.
L
Labédoyère, Colonel--
Execution of, 691.
Napoleon's return from Elba, 631.
La Belle Alliance, British position in, 1815, 658, 666.
Lafayette provisional government, abdication of Napoleon, 1815,
667, 669, 671.
Lafayette, release of, 186.
Lafon conspiracy, 503.
Lainé, opposition to Napoleon, 1813, 559–560.
Landshut, battle of, 440.
Lannes, General--
Death of, at Essling, 443–445.
Hostilities of, 1805, 343–343.
Italian campaign, 170.
Montebello victory, 283.
Laon, battle of, 574, 576.
La Rothière, battle of, 569.
La Vendée, pacification of, 265, 275.
Leclerc, invasion of St. Domingo, 311.
Lefebvre won over to Napoleon's side against Directory, 246, 247.
Leghorn, seizure of English goods, 158.
Legislative body of France--
Abolition, creation of House of Lords, 1814, 638–639.
Deposition of Napoleon by Senate, 1814, 588.
Opposition to Napoleon, 1813, 560.
Sieyès' plan of government, 1800, 266.
Leipsic, battle of, 534–541.
Lepelletier Section insurrection, 105, 107.
Ligny, battle of, 651–653.
Limited Monarchy under Louis XVIII, 599, 611.
"Little Corporal"--nickname of Napoleon, 146, 191, 420.
Lodi--victory of Napoleon, 144–146.
Lombardy--
Invasion of, 146, 150.
Italian republic formed, Napoleon as president, 329.
Republic formed, 194.
Lonato, battle of, 190.
Loretto, shrines, 171.
Louis XVIII, king of France--
Called from England to France, 1814, 596, 599.
Consternation at return of Napoleon from Elba, 626–627.
Government of, violations of the "Charter" and departure from
France, 600, 601, 612–627.
Limited monarchy, 599, 611.
Louisa, queen of Prussia, activity in war of 1806, 360–366, 384–385.
Louisiana, sale to United States, 316, 317.
Lowe, Sir Hudson, treatment of Napoleon at St. Helena, 679–701.
Lucca, republic of, gift from Napoleon to his sister, 338.
Lunéville, Peace of, 290.
Lützen, battle of, 510.
Lyons, reception of Napoleon, 1799, 232, 286;
1814, 632.
M
Macdonald, Marshal, abdication of Napoleon, 589, 592.
Mack, Austrian general, campaign against French republic, 222.
Madrid, riot, 425. [_See also_ Spain.]
Mahometans, Napoleon's policy in Egypt, 205–207.
Maida, battle of, 349.
Maitland, Captain, Napoleon on board the _Bellerophon_, 671–677.
Malet conspiracy, 503.
Malmaison--
Anecdotes of Napoleon, 396–399.
Death of Josephine--Napoleon's visit in 1815, 643–644.
Napoleon at, after Waterloo, 670, 671.
Malta--
British conquest, 292.
Rupture of Peace of Amiens, 312.
Capture by Napoleon, 201–202.
Mamelukes, rulers of Egypt, defeated by Napoleon, 200–205, 216.
Mantua, siege and capitulation, 160–169.
Marbeuf, General, friendship during boyhood of Napoleon, 24, 30.
Marbois, mismanagement of finances, 352–354.
Marbot, General--
Madrid riot, 425.
_Memoirs_, 232, 233, 278, 347.
Marengo, battle of, 278–287, 404.
Marguerite, peasant at Brienne, visit to, 334.
Maria Louisa, wife of Napoleon--
Character of, 460–461, 468.
Desertion of Napoleon, 606, 611, 642, 690, 696.
Empress Regent in 1814, betrayal of Napoleon, 564, 575.
King of Rome born, 1811, 465–467.
Marriage, 457–460, 472.
Marmont, General--
Leipsic, battle of, 535.
Operations in 1814, 573–578.
Treachery of, 590–591.
Marrac, château of, anecdotes of life at, 1808, 419–420.
Masséna, General--
Austrian campaign, 1809, Wagram, 410–448.
Genoa, siege and evacuation, 279, 282, 283.
Italian campaign, 162, 163, 168, 175, 176.
Melas, defeated at Marengo, 280–286.
Menou, General--
English conquest of Egypt, 291.
Revolt of the Sections, 106.
Méry village, Napoleon at, 1814, 573.
Metternich, Austrian diplomat--
Austrian mediation--policy, and interview with Napoleon,
524, 554–562.
_Memoirs_, 512–521, 545.
Milan--
Claim on Corsica, 4.
French occupation of, 151–153.
Josephine joins Napoleon, 1796, 192.
Napoleon crowned King of Italy, 336.
Milan Decree, 416.
Military of France, _see_ Army.
Miot de Melito--designs of Napoleon, 181, 182.
Modena, union with papal legations and Cisalpine, 195.
Modena, Duke of, peace terms offered to Napoleon, 151, 152, 182.
Monarchy, French--
Empire, _see that title_.
Limited monarchy under Louis XVIII, 599, 611.
Montebello, Lannes's victory, 283.
Montenotte victory, 139–140.
Montmirail, battle of, 570.
Mont St. Jean, battle of, 657.
Moore, Sir J., retreat and death at Corunna, 432, 433.
Moreau, General--
Conspiracy against Napoleon, 319–328.
_Coup d'état_ of 18th Brumaire, 243.
Death of, 532.
Defeated by Archduke Charles, 161, 162.
Desertion of Napoleon, 525–532.
Pichegru's arrest by Augereau, captured despatches, 183.
Soissons surrender, 563.
War with Austria, Hohenlinden victory, 279, 290.
Moscow--
Fire, 486.
Retreat of French army, 482–499, 504.
Moulins, fall of Directory, 18th Brumaire, 239–247.
Muiron, saves life of Napoleon, 164.
Murad Bey, Mameluke chief, defeat of, 204.
Murat, General--
Bourbon restoration, 1814, 624.
Cavalry leader, qualities as, 155, 640.
Desertion and betrayal of Napoleon, 507, 541, 562, 563.
Discontent of, desire to become king, 426, 437, 461.
Dresden, battle of, 1813, 529.
Execution of, 691.
Eylau, battle of, 381.
Grand Duchy of Berg created, 1806, 351.
Italian colors conveyed to France, 1796, 144, 147.
Italian independence proclaimed by, failure of, 639–640.
Madrid riot, 425.
Moscow, advance and retreat, 483–499.
Naples, king of, 437.
Russians, defeat of, 1805, 343–345.
Spain, campaign in, 1808, 419, 421.
Turkish commander Mustapha, defeat of, 219.
Warsaw gayeties, 375–380.
Mustapha defeated by Murat, 219.
N
Naples--
Joseph Bonaparte as King of, 350.
Murat succeeds Joseph as King, 437.
Napoleon's policy in 1796, 157.
Parthenopean republic proclaimed, 223.
Napoleon--
Abdication, 589–594, 669–670.
Ajaccio, _see that title_.
Army of France, _see that title_.
Arrest, overthrow of Robespierre, 1794, 89–91.
Birth and parentage, 17–22.
Birth of King of Rome, 465–467.
Boyhood, anecdotes of, 22–42.
Brienne, _see that title_.
Campaigns, _see_ names of countries, Italy, Egypt, etc.
Coalitions, _see that title_.
Comparison with rulers, etc., of same period, 289, 423, 430, 654.
Consulate, _see that title_.
Coronation, 331–333;
anniversary of, 346.
Corsica, _see that title_.
Death, 696–697.
Deserted and betrayed, 587, 590–595.
Directory, _see that title_.
Education, 22–38.
Elba, _see that title_.
Empire, _see that title_.
England, _see that title_.
Europe, Napoleon's relations with, conditions existing at
commencement of career, 121, 122.
European monarchs, antagonism of, 355–358.
Exhaustion, 653–656, 666, 669–670, 675.
Family affairs 41, 65, 70, 87.
French Revolution, _see that title_.
Funeral at St. Helena, 1821, 697–698;
Paris ceremonies, 1840, 700–703.
Germany, _see that title_.
Habits and characteristics, 196–199, 294–295, 389–411, 683–694.
High-water mark of power, 412.
Honors, distribution, 350.
Hundred days, 635, 675, 684.
Hunting, 507.
Illness, 530, 531, 694–696.
Immortality, 18, 690–704.
Italy, _see that title_.
Jacobin denunciation of Napoleon, 86.
Josephine, _see that title_.
Maria Louisa, _see that title_.
Marriage with Josephine, 130–132, 198;
divorce, 455–457.
Marriage with Maria Louisa, 457–460, 472.
Paoli, _see that title_.
Paris, _see that title_.
Personal appearance, 1785, 39, 40;
1795, 100;
1807, 386–388;
1814, 644–646.
Plots against life of Napoleon, 197, 288–289, 317–328, 451.
Poverty and economy, 53, 54, 61.
Prussia, _see that title_.
Religious views at St. Helena, 687–690.
Republic, _see that title_.
Results of victories of Napoleon, 413.
Russia, _see that title_.
St. Helena, _see that title_.
Spain, _see that title_.
Studies and writings, 34–45, 53, 54, 65, 67, 72.
Succession, speculations as to, 451.
Turkey, _see that title_.
Valence, _see that title_.
Will, 696–697.
[_See also_ names of countries, and political events.]
Napoleon, son of Hortense and Louis Bonaparte, death of, 452, 463.
Napoleon II, _see_ Rome, king of.
Narbonne, Count, French invasion of Russia, 1812, 478.
Neipperg and Maria Louisa, 606, 643, 690.
Nelson, Lord--
Death at Trafalgar, 342.
Hatred of the French, 84.
Italy, murder of Carraccioli, 226.
Napoleon's Egyptian expedition, battle of the Nile, etc., 201, 208.
Neuhoff, T. de, King of Corsica, 11–13.
Ney, General--
Abdication of Napoleon, 589–590.
Dresden, battle of, 529.
Campaign of 1814–15, battle of Waterloo, etc., 649, 651–669.
Elchingen, battle of, 343.
Execution of, 691.
Germany, rising in, 1813, 510.
Marshal, 332.
Moscow retreat, 495, 496.
Return of Napoleon from Elba, 627, 632, 633.
Russian campaign, 1807, 381, 383.
Niemen--
Interview with Czar of Russia, 1807, 383.
Passage across, 1812, 479, 481.
Nile, battle of, 208.
Norway, transference to Swedish rule, 623.
O
Oldenburg taken by Napoleon, 472.
Orezzo, Corsican general assembly, 51, 52.
Oudinot, Marshal, _Memoirs_, Erfurth conference, 428.
P
Paoli, Corsican general--
British protectorate plan for Corsica, 92.
First meeting with Napoleon, 52.
Independence struggle, 12–16.
Quarrel and struggle with Napoleon, 60–68, 198.
Return to Corsica, 1790, after exile, 51.
"Parallel between Cæsar, Cromwell, Monk, and Bonaparte," pamphlet, 289.
Paris--
Bourbon restoration, 1814, 583–586.
Coronation of Napoleon, 333.
Exile of Napoleon from Corsica, 61–63.
Fall of, 1814, 576–581.
Farewell of Napoleon to National Guard, 1814, 564.
Funeral of Napoleon, 1840, 700–703.
Military school, Napoleon at, 33–35.
Reception of Napoleon, 1800, 287;
return from Elba, 633.
Return of Napoleon from Russia, 1812, 499–500, 504.
Parma, Duke of, contribution to Napoleon, 146, 147.
Parthenopean republic proclaimed, 223.
Pasquier records, 560, 565.
Peninsular war, 417–434.
Permon family, early intimacy with Napoleon, 33–36, 64, 98–100,
113, 337, 406.
Phélippeaux, aid to Turks against Napoleon, 212.
Pichegru--
Banishment of, 183, 258.
Brienne college, 30.
Conspiracy against Napoleon, 318–328.
Suicide of, 328.
Piedmont, invasion of, 87, 138–143, 146, 150.
Pisa, war with Genoa over Corsica, 2.
Pitt, W.--
Administration and policy, 116, 117.
Death of, 359.
Plague among troops in Egypt, 217, 218.
Pleiswitz, armistice of, 511, 545, 554.
Poland--
Aid to Napoleon in Spain, etc., 374–377, 431.
Independence, Napoleon's policy, 372–377, 473, 480–481.
Napoleon at Warsaw, 372–381.
Princess Potocka, _memoirs_, 375–380.
Russian possession--Vienna Congress, 1814, 622, 623.
Walewski, Mme., _see that title_.
Pope--
Concordat sanctioned, 302–309.
Coronation of Napoleon, 333.
Loosed from Fontainebleau, 1814, 613.
Quarrel with Napoleon, 337, 453–455;
reconciliation, 508–509.
Temporal power abolished, 222, 453, 454, 558.
Terms with Napoleon, 1796, violation, 157–173.
Portugal--
English invasion, 1808, defeat of the French, 427.
French invasion, 1808, 417–418.
Pouzet, General, death of, 444–445.
Pozzo di Borgo--
British occupation of Corsica, 92, 93.
Enmity to Napoleon, 58–60.
Prague, Congress of, 521–523, 545.
Presburg, treaty of, 347.
Press censorship, 1814, 614.
Provera, Austrian general--Italian defeat, 167–169.
Prussia--
Ally of France in war of 1812, 476.
Berlin entered by Napoleon, 1806, 366–369.
Hanover ceded to, 357, 359, 363.
Neutrality of, 1799, 277.
Policy denounced, 363.
Reorganization, 413.
Tilsit, Treaty of, 384.
Vienna Congress, 1814, dispute as to division of territory, 620–623.
War threatened, 1804, 357.
War with Napoleon, 1806, overthrow of Prussian monarchy, battle of
Jena, 359–366, 403.
War of 1814–15, battle of Waterloo, etc., 566, 648–671.
Pultusk, battle of, 378, 383.
Pyramids, battle of, 204–205.
Q
Quasdanovitch, Austrian general, defeat of, 160.
Quatre-Bras, battle of, 650–654.
R
Rampon, Napoleon's victory of Montenotte, 139–140.
Rastadt, Congress of, 330.
Ratisbonne, battle of, 440, 451.
Red sea incident, 207.
Reichenbach, treaty of, 516.
Republic of France--
Consulate, Directory, etc., _see those titles_.
European leagues to restore Old Order in France, 115–121.
First organized, 13th Vendémiaire, 107.
Reorganization, 256–273, 295–302.
Rheims, battle of, 574.
Rhine, _see_ Confederation of the Rhine.
Robespierre, Napoleon denounced as friend of, 71, 89, 90.
Rocca, _see_ Della Rocca.
Roman Catholic Church, _see_ Church.
Rome--
Neapolitan army in, 222–223.
Pope, _see that title_.
Republic, 221–224.
Rome, King of, Napoleon's son--
Abdication of Napoleon in favor of, 589–592.
Austrian treatment of, palace of Schönbrunn, 611.
Birth of, 465–467.
Message to Napoleon at Elba, 643.
Terms of treaty of Fontainebleau violated by Allies, 606–607.
Rose, J. H., Napoleon's seizures of British ships, 316.
Ruffo, attack on republicans of Naples, treaty of peace, 225–226.
Russia--
Alexander, _see that title_.
Alliance to Prussia, 358, 429.
Bourbon restoration in France, 1814, 583–586.
Coalitions, 1799, 224;
1805, 339–348;
1813, 525–541;
1814–15, 566–648.
Continental system opposed, 470–478.
Erfurth conference, 428.
French invasion, Moscow, etc., 1812, 470–504.
Lukewarm support to Napoleon in war of 1809, 441, 472.
Rising in Germany against France, 1813, 507–514.
Tilsit, Treaty of, 1807, 383–385, 470–478.
Vienna Congress, 1814, dispute as to division of territories, 620–623.
War with Turkey on the Danube, 473, 475, 481.
S
St. Cloud, _coup d'état_ of 18th Brumaire, 241–255.
St. Cyr, Dresden defence and Leipsic defeat, 1813, 527, 535.
Saint-Denis school, visit to, 561.
St. Dizier, battle of, 568, 577.
St. Domingo, <DW64> revolt, failure of French expedition, 310.
St. Helena, Napoleon's exile--
British deception, 672–676.
Death and funeral of Napoleon, 696–698.
Farewell of Napoleon at Malmaison, 671.
Life at St. Helena, 679–699.
Negotiations for removal of Napoleon from Elba, 1814, 607, 608.
St. Jean, battle of, 657.
St. Jean d'Acre, siege of, 215.
Salamanca, battle of, 522.
Salicetti, intimacy with Napoleon, 71, 77, 87, 89, 91, 93, 98, 99.
Sambuccio, Corsican leader, organization of village confederation, 2.
Sampiero, Corsican leader, 5–8, 692.
San Marino, rights of, respected by Napoleon, 173.
Sardinia, French invasion of, 66, 138–143.
Saxony--
Desertion to enemies of Napoleon, 1813, 537.
Prussian possession, Vienna Congress, 1814, 622, 623.
Saxony, Queen of, reproaches Metternich for deserting Napoleon, 546.
Schérer, in command of army of Italy, succeeded by Napoleon, 135, 136.
Schwarzenberg, Austrian Prince--
Dresden hostilities, 1813, 527, 529, 534, 536.
Invasion of France, 1814, 566–577.
Paris fête in honor of Napoleon and Maria Louisa, 460.
Scotchman's story of Napoleon at Elba, 608–610.
Sébastiani, General--
Military situation, 1813, 524.
Turkey refuses to join coalition against France, 415.
Sections, revolt and disarmament, 105–109.
Ségur--
_Memoirs_ of Napoleon, 341.
Wounded in Spain, 431.
Seine overflow, Napoleon's embankment, 410.
Sémonville, French commissioner,--
Napoleon's defence of France in Corsica, 68.
Senate, French--
Deposition of Napoleon, 1814, 588.
Sieyès' plan of government, 1800, 266.
Sérurier, Italian campaign, 169, 170.
Sheridan, R. B., speech in British House of Commons, 614.
Sieyès' new constitution after overthrow of Directory, 237–253, 265–270.
Smolensk, advance on, 482.
Smith, Sir S., aid to Arabs against Napoleon, 212, 215, 220.
Social conditions in France--
Reform of, 295.
Thellusson ball, 132–134.
Soissons surrender--treachery of Moreau, 573.
Sommo Sierra mountain pass, blockade by Spanish bands, 431.
Spain--
Alliance with France violated, 1807, 417.
Bonaparte, Joseph, _see that title_.
Ferdinand, _see that title_.
French invasion, 1807–8, 419–434.
Crown surrendered to Napoleon, 419–424.
Progress of the war, neglect of Napoleon, 452, 455.
Unpopularity of the war in France, 437.
Improvements by Napoleon, 410.
Internal disputes, Godoy and Ferdinand, 418–421.
Madrid, riot, 425.
Reorganization of government by Napoleon, complaint of Joseph
Bonaparte, 1809, 435.
Staël, Mme. de, banishment of, 399, 408, 414
"Supper of Beaucaire," pamphlet by Napoleon, 65, 72.
Suwarow, Russian general, victories in Italy, 224.
Sweden--
Bernadotte, _see that title_.
Coalition of 1805 against France, 339.
Switzerland, Helvetic republic proclaimed, 222.
Syria, invasion of, 213.
T
Talleyrand, French diplomat--
Betrayal of Napoleon and conspiracy against, 437–439, 552, 579.
Bourbon restoration, abdication of Napoleon, 1814, 583–588.
Death of, 688.
Execution of Duke d'Enghien, 324–327.
Germany, reorganization, 330.
Turkish mission proposal, 200.
Vienna Congress, 1814, 620–623.
Warsaw gayeties, 377.
Tallien, Mme., character of, 127, 128, 130, 134.
Tariff, _see_ Continental system.
Taxation reforms during Consulate, 261–262, 271.
Thames embankment, Napoleon's suggestion, 410.
Thellusson ball, society conditions, 132–134.
Theodore, King of Corsica, 11–13.
Theosophy, sect, 260.
Thiébault, _Memoirs_ of, 108, 110, 434, 645.
Tilsit, Treaty of, 1807, 383–385.
Continental system supported by Russia, 385;
violation, 470–478.
Tolentino, treaty of, 1797, 173.
Toulon, siege of, military genius of Napoleon, 72–83.
Toussaint L'Ouverture--
Revolt of St. Domingo against France, 311.
Treatment of, by Napoleon, 408.
Trafalgar, battle of, 342.
Transpadane republic established, 194.
Turkey--
Coalition, refusal to join in, 1807, 415.
Defeated by Napoleon in Egypt, 212–220.
Invasion of Corsica, 6.
Military system reorganized, 103, 104.
War with Russia on the Danube, 473, 475, 481.
Turreau, wife of, battle incident, 92.
Tyrolese revolt, 450.
U
Ulm campaign, 341.
_Undaunted_, British ship, conveyance of Napoleon to Elba,
601, 604–605.
United States, sale of Louisiana to, 316, 317.
Ushant, Napoleon's last sight of France, 678, 679.
V
Valeggio, narrow escape of Napoleon from Austrians, 154.
Valence--
Napoleon joins regiment of La Fère, social life, etc., 35.
National oath ceremonies, 1791, 55.
Reception of Napoleon, 1799, 233.
Valette, General, troops condemned by Napoleon, 189.
Valladolid, Napoleon's ride to Bayonne, 1809, 433, 434.
Vandamme, defeated at Kulm, 530, 531.
Vannina, wife of Sampiero, 6, 7.
Vaubois, defeat of, 162, 166.
Vendémiaire [13th] Napoleon acting chief in, 107.
Venice, Napoleon's policy, disturbances in Venetia, 155, 156, 178–180.
Victor, General, captured by Prussians, 379.
Vienna--
Fall of, 1809, 441.
Marriage of Napoleon and Maria Louisa by proxy, 1810, 458.
Vienna Congress, 620–626.
Consternation at return of Napoleon from Elba, 626, 639.
Dispute between four powers, 620–623.
Vienna, Treaty of, 357, 472.
Villeneuve, Admiral, failure of expedition to England, 340.
Vimeiro, battle of, 427.
Vincentello, Corsican struggle, 3, 4.
Vitebsk, delay at, war of 1812, 481, 482.
Vittolo, Corsican struggle, 8.
Vittoria, battle of, 430, 522.
W
Wagram, battle of, 447–448.
Walewski, Mme., favorite of Napoleon, 378–383.
Visit to Napoleon at Fontainebleau, 1814, 594.
Warsaw--
Grand Duchy of, 374, 472, 480.
Napoleon at, 1806–7, 372–381.
Waterloo, battle of, 660–667.
Regrets at St. Helena, 634–685.
Wellington, Duke of--
Canova's statue of Napoleon, anecdote, 368.
Invasion of France, 1814, 566.
Napoleon's hatred of, 685.
Vimeiro, battle of, 427.
Waterloo, battle of, Blücher's coöperation in war of 1814–15, 648–671.
Westphalia, monarchy under Jerome Bonaparte, 351, 384.
Napoleon's policy and advice to Jerome, 412, 413.
Old Order restored, 1814, 612, 613.
Whitworth, Lord, British ambassador to Paris, 1804, 313.
Wilna, delay at--French invasion of Russia, 1812, 481.
Wolseley, Lord, opinion of Napoleon, 411.
Wurmser, Austrian general, defeated by Napoleon, 159–169.
Transcriber's Notes
Punctuation and spelling were made consistent when a predominant
preference was found in this book; otherwise they were not changed.
(Exception: "Kleber" was changed to "Kléber", even though the former
occured more often than the latter, because the accented form is the
correct one.)
Simple typographical errors were corrected; occasional unbalanced
quotation marks retained.
Ambiguous hyphens at the ends of lines were retained; occurrences of
inconsistent hyphenation have not been changed.
Index not checked for proper alphabetization or correct page references.
Page 127: "Idealogists" was printed that way.
Page 301: "colaborers" was printed that way.
Page 569: "a fretful man and a jealous" was printed that way.
Illustration facing page 562: the caption ends with an asterisk.
End of the Project Gutenberg EBook of Napoleon, by Thomas E. Watson
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Q: create single perceptron with scikits MLPregressor I use sklearn.neural_networks MLPRegressor
Do I understand it right, that by choosing hidden_layer_sizes=(1, ) I create a single perceptron because the first "hidden layer" is nothing else than the neurons that learn from the input layer?
A: When you set hidden_layer_size=(1,) you create a network with 1 hidden layer with size 1 neuron. It means instead of a Single-Layer Perceptron which has no hidden layer, you create a Multi-Layer Perceptron with 1 hidden layer with size 1 neuron.
you can read it from here: http://scikit-learn.org/stable/modules/generated/sklearn.neural_network.MLPRegressor.html
hidden_layer_sizes : tuple, length = n_layers - 2, default (100,)
n-layers - 2 means the value in hidden_layer_size is not included the first layer (input layer) and the last layer (output layer)
To create a Single Layer Perceptron, set it to empty: hidden_layer_size=()
| {
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{"url":"https:\/\/kb.osu.edu\/dspace\/handle\/1811\/13833","text":"# WATER ON THE SUN: A NEW SPECTROSCOPIC PARADIGM\n\nPlease use this identifier to cite or link to this item: http:\/\/hdl.handle.net\/1811\/13833\n\nFiles Size Format View\n1997-MF-01.jpg 165.5Kb JPEG image\n\n Title: WATER ON THE SUN: A NEW SPECTROSCOPIC PARADIGM Creators: Polyansky, Oleg L.; Zobov, N. F.; Viti, Serena; Tennyson, Jonathan; Bernath, P. F.; Wallace, Lloyd Issue Date: 1997 Publisher: Ohio State University Abstract: Sunspot infrared absorption spectra with $T \\sim 3000^\\circ$ and $750 \\leq \\bar{\\nu} \\leq 1010 cm^{-1}$ have recently been $reported^{a}$. The spectra are highly congested ($\\sim$ 50 lines per $cm^{-1}$) with spectral lines thought to be due to water. Traditional perturbation theory is inadequate for analysing this problem. Instead we employ full variational solutions of the problem which go beyond the standard Born-Oppenheimer approximation. This treatment leads to vibration-rotation quantum number assignments for individual lines (none of which had been previously assigned). Furthermore we attribute many more spectral lines to water than could be achieved using previous theory or $experiment^{g}$. In particular we assign transitions involving rotational levels in the ground state and first few vibrational states up to 22,000 $cm^{-1}$ above the ground state, about double that previously known and approximately halfway to dissociation. In addition we assign levels with $K_{a}$ as high as 32 compared to the previous maximum of 20. We find previously unobserved and unanticipated spectroscope characteristics of water. These characteristics will be present in other hot water spectra found in flames, rocket plumes, cool stellar atmospheres and elsewhere, as well as in the spectra of other hot molecules. The approach applied here thus represent a paradigm shift in the theory of polyatomic molecular spectroscopy which we expect will be widely followed in all future treatments of the spectra of hot molecules. Description: $^{g}$L. Wallace, et al Science 268, 1155-1158 (1995). Author Institution: Department of Physics Astronomy, University College London; Department of Chemistry, University of Waterloo; National Optical Observatories, POBOX 26732 Tucson, AZ URI: http:\/\/hdl.handle.net\/1811\/13833 Other Identifiers: 1997-MF-01","date":"2015-11-26 14:19:24","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\": 0.4968435764312744, \"perplexity\": 2862.5043760141925}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-48\/segments\/1448398447729.93\/warc\/CC-MAIN-20151124205407-00143-ip-10-71-132-137.ec2.internal.warc.gz\"}"} | null | null |
Grocery Outlet's new location in Maryland is now open; new Pennsylvania branch coming next week
Grocery Outlet's new Maryland store is located at 801 East Pulaski Highway in Elkton. / Photo Courtesy: Grocery Store
Located in Emeryville, California, the Grocery Outlet continues its East Coast expansion with the opening of a new store in Maryland earlier this month. The new store, located at 801 East Pulaski Highway in Elkton, will bring nearly 30 new jobs to the Northeast Maryland community.
"We are so thrilled to be part of the Elkton community and make big savings on quality groceries," independent operator Scott Hines said in a statement. "This partnership with Grocery Outlet gives me the opportunity to grow my business, create new jobs and, more importantly, give back to the local community."
Independent operator Scott Hines. / Photo Courtesy: Grocery Store
As part of Grocery Outlet's community outreach, Hines donated $1,000 to Youth Empowerment Source (YES), whose mission is to empower children, youth and families in Cecil County, Maryland, and Upper Bay Counseling & Support Services, Inc. Hines also donated $2,500 to the Elkton Vet Center to support veterans, service members and their families.
grocery store, that reported strong traffic trends for the third quarter, will also be opening a new location in Lebanon, Pennsylvania at 1301 Quentin Rd. on December 8th.
"We are so thrilled to be a part of the Lebanese community and make big savings on quality groceries," independent operators Bob and Kimberlie Jackson said in a statement. "This partnership with Grocery Outlet gives us the opportunity to grow our business, create new jobs and, more importantly, give back to the local community."
Grocery Outlet shoppers offer the same brands as traditional grocery stores, but at lower prices, and "scour the country to find the top manufacturers with excess inventory and seasonal closeouts, allowing Grocery Outlet 'wow savings' on thousands of branded products." ' can offer," the company said in a statement.
The budget grocery retailer operates over 430 locations in California, Idaho, New Jersey, Nevada, Oregon, Pennsylvania, Washington and Maryland. Grocery outlet stores are owned by independent operators based in the communities in which they operate.
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Thousands of sandhill cranes migrate across northwest…
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Tags: New business, news, retailers
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January 27 Playbook: Expired
King of Prussia's wife sentenced to 12 years in federal prison for drug trafficking and COVID fraud | USAO-DE | {
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Teen Creates App To Help Care For Grandmother With Dementia, Releases Free For Millions Of Caregivers
A high school student in Lexington, Massachusetts, developed an app that makes it easier for people to care for loved ones with dementia.
Logan Wells / Credit: Boston Herald
Logan Wells was 15 when his grandmother was diagnosed with the disease.
"The effect that it's had on my grandmother has been terrible, but it was also really hard on my parents and other family members," he told Best Life. "It became really hard to stay on the same page, because we had to have multiple group chats."
So, he came up with the idea for CareZare, which allows caregivers to easily work as a team through a communication portal.
Logan did the coding while his father, Eric, helped him create the original prototype and coordinated the marketing.
The free app allows users to create a profile centered around the individual with dementia and invite other people to join and receive notifications.
With the app, you can schedule events, confirm completed tasks, and even add a "heads up" such as the current mood of the patient or poor weather conditions.
Logan says the app is currently being used by over 600 families, and he's hoping it will grow.
"Our users have been great about giving us feedback so we can tailor the app to their needs," he said. "Caregiving is such an important issue for them because it's so personal for them, just as it is for me." | {
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The Possession of Hannah Grace
Sony Pictures // R // $34.99 // February 26, 2019
Review by William Harrison | posted March 26, 2019
THE FILM:
The opening reel of Diederik Van Rooijen's The Possession of Hannah Grace shows glimpses of promise. The film opens mid exorcism, as Hannah Grace (Kirby Johnson) writhes and moans before levitating, killing a priest and taunting her father, Grainger (Louis Herthum). The man then takes a pillow and suffocates Hannah, revealing the woman beneath, as the evil seems to evaporate from her body. Said body then makes its way to a city morgue, where former law enforcement officer Megan Reed (Shay Mitchell) has recently begun a job on the graveyard shift. The film then offers a few minutes of creepy, moody suspense as the evil reappears, before completely unraveling into an abrupt, unsatisfying ending.
Reed left the force after freezing in the line of duty, during which time her partner was shot and killed. She has flashbacks and hallucinations related to the events, and begins boozing and popping pills to cope. Her sponsor helps get that under control, and encourages Reed to apply for the morgue position, despite her having to work completely alone in the basement of a city hospital. Reed is hired and starts work, assuring her former boyfriend and current officer Andrew Kurtz (Grey Damon) that she is mentally stable enough to do the job. The twisted, burned body of Hannah Grace comes in late one night, and Reed places the body in one of the morgue's drawers. Soon, strange things begin happening around Reed.
In its opening minutes, The Possession of Hannah Grace manages to maintain some decent atmosphere. One neat trick Director Rooijen employs is having the morgue's lights cycle on and off based on motion sensors. The soundtrack includes the accompanying hum of LED-light interference, which becomes a foreboding warning that evil is afoot. The morgue itself is plenty creepy, but not necessarily in the way you might assume. This is not some haunted mental asylum; it is a modern facility in a modern city hospital, complete with plenty of steel, sharp tools and cutting-edge technology. Reed starts hearing footsteps and clanging doors, and notices that Hannah Grace's body, initially still in the drawer, appears to show signs of healing. A manic Grainger soon shows up and is willing to hurt anyone who attempts to stop him from making sure the evil inside Hannah Grace does not survive.
The movie soon shows its hand, and becomes a collection of fungible horror beats. The film relies too often on grainy surveillance footage and CGI trickery to evoke fear, and each interaction with the obviously-not-dead-dead Hannah Grace is the same. Practical effects like her twisted, lifeless body and a bouncing rubber band ball eclipse silly, CGI spider walking, and the filmmakers should have learned from penultimate possession thriller The Exorcist why less is often more. Worse yet is the insanely abrupt ending, which comes out of nowhere. Even when the scares do not work, the majority of The Possession of Hannah Grace tries to build suspense. The jump into the finale feels like the filmmakers cut a solid 30 minutes of material (and maybe they did) and is tremendously underwhelming. This demonic-possession rehash offers little to recommend.
THE BLU-RAY:
Sony's 2.39:1/1080p/AVC-encoded image looks pretty good despite the film's lower budget. Fine-object detail impresses, and textures on costumes and set dressings are abundant. Black levels are good, and shadow detail is abundant amid the frequently low-light set pieces. Digital noise is kept to a minimum, skin tones are correct and colors are appropriately saturated. This image is not the most flashy you will see, but it is certainly competent.
The 5.1 DTS-HD Master Audio mix makes the most of the film's occasionally effective atmospheric effects. There are plenty of moans, creeks, pitter-patters and thumps to surround the viewer, and the LFE kicks in during more hectic sequences. Dialogue is crisp and the score is appropriately integrated. A host of lossy dub soundtracks and subtitle options are included.
PACKAGING AND EXTRAS:
This single-disc release comes in an Elite case that is wrapped in a slipcover. A digital copy is included. Extras include The Killer Cast (6:31/HD); An Autopsy of Hannah (6:36/HD), which looks at the make-up effects; Megan's Diaries (1:34/HD); and a Deleted Scene (0:44/HD).
Despite some early promise, The Possession of Hannah Grace devolves into another generic possession thriller with cheap scares and a lousy ending. Skip It. | {
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\section{Introduction to the results}
\indent
Given a locally Lipschitz real-valued function $f$ on $\mathbb R$, called a flux,
we consider the scalar conservation law
\begin{eqnarray} \label{cons law}
\left\{ \begin{array}{ll}
u_t + f(u)_x \, = \, 0 \, , \qquad t > 0, \, \, x \in \mathbb R, \\
u(0,.) \, =\, u^{0},
\end{array}
\right.
\end{eqnarray}
with unknown $u=u(t,x) \in \mathbb R$ and initial datum $u^{0} \in L^{\infty}(\mathbb R)$, and where the subscripts stand for derivation.
\medskip
We shall consider solutions that are called {\it entropy solutions} (see \cite{S} for instance) and are
defined as follows:
a function $u=u(t,x) \in L^{\infty}( [0,+\infty[ \times \mathbb R )$ is said to be an entropy solution of (\ref
{cons law})
on $ [0,+\infty[ \times \mathbb R$ if the entropy inequality
\begin{eqnarray}\label{entropy}
E(u)_t \, + \, F(u)_x \, \leq \, 0
\end{eqnarray}
holds in the sense of distributions for all convex Lipschitz function $E$ on $\mathbb R$, and with associated
flux $F$ defined by
\begin{equation}\label{fluxF}
F(u) \, = \, \int_{0}^{u} f'(v) \, E'(v) \, dv.
\end{equation}
This means that
$$
\int_{0}^{+ \infty} \! \! \int_{\mathbb R} \bigl( E(u) \, \varphi_t + F(u) \, \varphi_x \bigr) \, dt\, dx \, + \,
\int_{\mathbb R} E(u^0(x))\, \varphi(0,x) \, dx \, \geq 0
$$
for all nonnegative $\varphi$ in the space ${\cal C}_{c}^{\infty}([0 , +\infty[ \times \mathbb R)$ of
${\cal C}^{\infty}$ functions on $[0 , +\infty[ \times \mathbb R$ with compact support.
\medskip
We shall also consider {\it classical solutions}, that is, functions $u=u(t,x)$ in
${\cal C}^{1}(]0,+\infty[ \times \mathbb R) \cap \cal{C}([0,+\infty[ \times \mathbb R)$ satisfying
\eqref{cons law} pointwise.
In particular any classical solution to \eqref{cons law} satisfies \eqref{entropy}, i.e. is an
entropy solution,
and conversely any entropy solution satisfies \eqref {cons law} in the distribution sense.
\medskip
For entropy solutions, the following result is due to Kru$\mathrm {\check z}$kov (see \cite{K}):
\begin{theo} \label{Kruzkov}
For every $u^{0} \in L^{\infty}(\mathbb R)$, there exists a unique entropy solution $u$
to $(\ref{cons law})$ in
$L^{\infty}([0,+\infty[ \times \mathbb R) \cap \cal C ([0,+\infty[, L_{loc}^{1}(\mathbb R))$.
\end{theo}
Moreover for classical solutions, we have (see \cite{S} for instance):
\begin{theo} \label{Kruzkovclassique}
Given a ${\cal C}^{2}$ flux $f$ and a ${\cal C}^1$ bounded initial datum $u^0$ such that
$f' \circ u^0$ is nondecreasing on $\mathbb R$, the unique entropy solution $u$ to
$(\ref{cons law})$ is a classical solution.
\end{theo}
In this work we shall consider initial data in the subset
${\cal U}$ of $L^{\infty}(\mathbb R)$ defined by
\begin{defi}
A function $v : \mathbb R \rightarrow \mathbb R$ belongs to ${\cal U}$ if it is nondecreasing,
right-continuous,
and has limits $0$ and $1$ at $-\infty$ and $+\infty$ respectively.
\end{defi}
The following proposition expresses that this set is
preserved by the conservation law \eqref{cons law}:
\begin{prop}\label{Uconserve}
Given an initial datum $u^0 \in {\cal U}$, the entropy solution $u$ given by
Theorem \ref{Kruzkov} is such that $u(t,.)$ belongs to
${\cal U}$ for all $t \geq 0$.
\end{prop}
More precisely, given any $t \geq 0$, the $L^{\infty}(\mathbb R)$ function $u(t,.)$ is $a.e.$ equal to an element
of the set ${\cal U}$, which on the other hand is characterized by
\begin{prop}\label{charact}
The distributional derivative $v_x$ of any $v \in {\cal U}$ is a
Borel probability measure on $\mathbb R$, and for any $x \in \mathbb R$,
$$
v(x) \, = \, v_x(]-\infty,x]).
$$
Conversely, if $\mu$ is a probability measure on $\mathbb R$, then $v$ defined on $\mathbb R$ as
$$
v(x) \, = \, \mu(]-\infty,x])
$$
belongs to ${\cal U}$, and $v_x = \mu$.
\end{prop}
Consequently the map $ v \mapsto v_x$ is one-to-one from ${\cal U}$ onto the set ${\cal P}$ of
probability measures on $\mathbb R$ (and ${\cal U}$ can be seen as the set of repartition functions
of real-valued random variables).
Propositions \ref{Uconserve} and \ref{charact} allow us to characterize at any time the distance between
two solutions (with initial datum in ${\cal U}$) in terms of their
space derivatives, in particular by means of the Wasserstein distances: given
any real number $p \geq 1$, the Wasserstein distance of order $p$ is defined on the set of
probability measures on $\mathbb R$ by
$$
W_p(\mu,\tilde \mu)=\, \inf_{\pi} \,
\Bigl( \,\int_{\mathbb R^2} \vert x-y \vert ^p \, d\pi(x,y)\, \Bigr)^{1/p}
$$
where $\pi$ runs over the set of probability measures on $\mathbb R^2$
with marginals $\mu$ and
$\tilde \mu$; these distances are considered here in a broad sense with possibly infinite values.
\medskip
This paper aims at proving that the Wasserstein distances between the space derivatives of any two such entropy
solutions is a nonincreasing function of time:
\begin{theo} \label{theoreme}
Given a locally Lipschitz real-valued function $f$ on $\mathbb R$ and two initial data $u^0$ and ${\tilde u}^0$
in ${\cal U}$, let $u$ and
${\tilde u}$ be the associated entropy solutions to \eqref{cons law}. Then, for any
$t \geq 0$ and $p \geq 1$, we have (with possibly infinite values)
$$
W_p(u_{x}(t,.), {\tilde u}_{x}(t,.)) \, \leq \, W_p(u_{x}^{0}, {\tilde u}_{x}^{0}).
$$
\end{theo}
We shall see in Section \ref{section wasserstein} that for $p=1$ the distance $W_1$ satisfies
$$
W_1(v_x,{\tilde v}_x) \, = \, \Vert v-{\tilde v} \Vert_{L^1(\mathbb R)}
$$
for all $v,{\tilde v} \in {\cal U}$. Hence Theorem \ref{theoreme} reads in the case $p=1$:
$$
\Vert u(t,.) - {\tilde u}(t,.) \Vert_{L^1(\mathbb R)} \, \leq \, \Vert u^0 - {\tilde u}^0 \Vert_{L^1(\mathbb R)}.
$$
Thus, for initial profiles in ${\cal U}$, we recover the $L^1$-contraction property given by
Kru$ {\check z}$kov.
\medskip
In the case of classical solutions, the result of Theorem \ref{theoreme} is improved, since the Wasserstein
distance between two solutions is conserved:
\begin{theo}\label{theoremeclassique}
Given a ${\cal C}^1$ real-valued function $f$ on $\mathbb R$, let $u^0$ and ${\tilde u}^0$ in ${\cal U}$ be
two initial data such that the associated entropy solutions
$u$ and ${\tilde u}$ to \eqref{cons law} are classical solutions, increasing in $x$ for all $t\geq 0$.
Then for any $t \geq 0$ and $p \geq 1$ we have (with possibly infinite values)
$$
W_p(u_{x}(t,.), {\tilde u}_{x}(t,.)) \, = \, W_p(u_{x}^{0}, {\tilde u}_{x}^{0}).
$$
\end{theo}
\medskip
>From these general results can be induced some corollaries in the case of initial data in the subsets
${\cal U}_p$ of ${\cal U}$ defined as:
\begin{defi}
Let $p \geq 1$. A function $v$ in ${\cal U}$ belongs to ${\cal U}_p$ if its distributional
derivative $v_x$ has finite moment of order $p$, that is, if $\displaystyle \int_{\mathbb R} \vert x \vert^p \, dv_x(x)$
is finite.
\end{defi}
As in Proposition \ref{charact} the map $ v \mapsto v_x$ is one-to-one from ${\cal U}_p$ onto the set
${\cal P}_p$ of probability measures on $\mathbb R$ with finite moment of order $p$. But we shall note in
Section \ref{section wasserstein} that the map $W_p$ on ${\cal P}_p \times {\cal P}_p$
defines a distance on ${\cal P}_p$.
Then the real-valued map $d_p$ defined on ${\cal U}_p \times {\cal U}_p$ by
$$
d_p(v, {\tilde v}) \, = \, W_p(v_x, {\tilde v}_x)
$$
induces a distance on ${\cal U}_p$, and for the associated topology we have
\begin{cor}\label{corsolutionUp}
Given a locally Lipschitz function $f$ on $\mathbb R$, $p \geq 1$ and $u^0 \in {\cal U}_p$, the entropy solution $u$ to
\eqref{cons law} belongs to ${\cal C}([0,+\infty[,{\cal U}_p).$
\end{cor}
In particular for $p=1$
$$
d_1(v,{\tilde v}) = W_1(v_x,{\tilde v}_x) = \Vert v- {\tilde v} \Vert_{L^1(\mathbb R)},
$$
and the previous result can be precised by
\begin{cor}\label{corsolutionU1}
Given a locally Lipschitz function $f$ on $\mathbb R$ and $u^0 \in {\cal U}_1$, the entropy solution $u$ to \eqref{cons law} is such that
$$
\Vert u(t,.) - u(s,.) \Vert_{L^1(\mathbb R)} \leq \vert t-s \vert \, \Vert f' \Vert_{L^{\infty}([0,1])}.
$$
\end{cor}
This known result holds under weaker assumptions (for $u^0$ with bounded variation, see \cite{S}), but in
our case it will be recovered in a straightforward way.
\medskip
Finally Theorem \ref{theoremeclassique} can be precised in the ${\cal U}_p$ framework in
the following way:
\begin{cor}\label{corclassique}
Given a ${\cal C}^2$ convex flux $f$ and two ${\cal C}^1$ increasing initial data $u^0$ and ${\tilde u}^0$
in ${\cal U}_p$
for some $p \geq 1$, the following three properties hold:
1. the associated entropy solutions $u$ and ${\tilde u}$ are classical solutions;
2. $u(t,.)$ and ${\tilde u}(t,.)$ belong to ${\cal U}_p$ and are increasing for all $t \geq 0$;
3. for all $t \geq 0$, we have (with finite values)
$$
W_p(u_{x}(t,.), {\tilde u}_{x}(t,.)) \, = \, W_p(u_{x}^{0}, {\tilde u}_{x}^{0}).
$$
\end{cor}
\medskip
The paper is organized as follows.
The definition and some properties of Wasserstein distances are discussed in greater detail in Section
\ref{section wasserstein}. In Section \ref{sectionpreuveclassique} we consider the case of
classical solutions, proving Theorem \ref{theoremeclassique} and
Corollary \ref{corclassique}. Then the general case of entropy solutions is studied
in Sections \ref{sectiondiscretisation} and \ref{sectionpreuve}:
more precisely in Section \ref{sectiondiscretisation} we introduce a time-discretized scheme, show
the $W_p$ contraction property for this discretized evolution and prove the convergence of the corresponding approximate solution toward the
entropy solution;
Theorem \ref{theoreme} and its corollaries follow from this in Section \ref{sectionpreuve}. In Section
\ref{sectionviscous} we shall finally see how such results extend to viscous conservation laws.
\section {Wasserstein distances}\label{section wasserstein}
\indent
In this section $p$ is a real number with $p\geq 1$, ${\cal P}$ (resp. ${\cal P}_p$) stands for the
set of probability measures on $\mathbb R$ (resp. with finite moment of order $p$) and $dx$
for the Lebesgue measure on $\mathbb R$.
The Wasserstein distance of order $p$, valued in $\mathbb R \cup \{+\infty\}$, is defined on
${\cal P} \times {\cal P}$ by
\begin{eqnarray}\label{defwas1}
W_p(\mu,{\tilde \mu}) \, = \, \inf_{\pi} \,
\Bigl( \,\int_{\mathbb R^2} \vert x-y \vert ^p \, d\pi(x,y)\, \Bigr)^{1/p}
\end{eqnarray}
where $\pi$ runs over the set of probability measures on $\mathbb R^2$ with marginals
$\mu$ and ${\tilde \mu}$. It is equivalently defined by
\begin{eqnarray}\label{defwas2}
W_p(\mu, {\tilde \mu})=
\inf_{X_{\mu},X_{{\tilde \mu}}}
\Bigl(\int_{0}^{1}\left|X_{\mu}(w)-X_{{\tilde \mu}}(w)\right|^p \, dw
\Bigr)^{1/p}
\end{eqnarray}
where the infimum is taken over all random variables $X_{\mu}$ and $X_{{\tilde \mu}}$ on
the probability space $(]0,1[,dw)$
with respective laws $\mu$ and ${\tilde \mu}$.
It takes finite values on ${\cal P}_p \times {\cal P}_p$
and indeed defines a distance on ${\cal P}_p$.
For complete references about the Wasserstein distances and related topics the reader
can refer to \cite{V}. We only mention that both infima in (\ref{defwas1}) and (\ref{defwas2})
are achieved, and
for the second definition we shall precise some random variables that achieve the infimum. For this
purpose we introduce the notion of generalized inverse:
\begin{defi}\label{ginverse}
Let $v$ belong to ${\cal U}$. Then its generalized inverse is the function $v^{-1}$
defined on $]0,1[$ by
\begin{eqnarray*}
v^{-1}(w) \, = \, \inf \{x \in \mathbb R; \, v(x) > w\}.
\end{eqnarray*}
\end{defi}
Then $v^{-1}$ is a nondecreasing random variable on $(]0,1[, dw)$ by definition,
with law $v_x$ since
\begin{eqnarray*}
\int_{0}^{1} f(v^{-1}(w)) \ dw
&=&
\int_{0}^{1} \Bigl( \int_{\mathbb R} f'(s) {\bf 1}_{\{s \leq v^{-1}(w)\}} \, ds \Bigr) \, dw\\
&=&
\int_{\mathbb R} \Bigl( \int_{0}^{1} f'(s) {\bf 1}_{\{v(s) \leq w\}} \, dw \Bigr) \, ds \\
&=&
\int_{\mathbb R} f'(s)(1-v(s)) \ ds \\
&=& \int_{\mathbb R} f(s) \ dv_x(s)
\end{eqnarray*}
for all $f$ in ${\cal C}^{1}_{c}(\mathbb R)$. In particular its repartition function is $v$.
Moreover this generalized inverse achieves the infimum in (\ref{defwas2}):
\begin{prop}\label{propertyW_p}
Let $v$ and ${\tilde v}$ in ${\cal U}$. Then we have
(with possibly infinite values)
\begin{eqnarray*}
W_p(v_x,{\tilde v}_x) \, = \, \Bigl( \int_{0}^{1} \vert v^{-1}(w) -
{\tilde v}^{-1}(w) \vert^p \, dw \Bigr)^{1/p}
\end{eqnarray*}
for all $p \geq 1$. In particular for $p=1$ we also have
\begin{eqnarray*}
W_1(v_x,{\tilde v}_x) \, = \, \Vert v - {\tilde v} \Vert_{L^1(\mathbb R)}.
\end{eqnarray*}
\end{prop}
\medskip
{\it Proof.}
The general result is proved in \cite{V}. The result specific to the case $p=1$ follows
by introducing, for a given $v \in {\cal U}$, the map defined on $\mathbb R \times ]0,1[$ by
$$
jv (x,w) = \left\{ \begin{array}{ll}
1 & \mbox{if $v(x) > w$}\\
0 & \mbox{if $v(x) \leq w,$}
\end{array}
\right.
$$
for which we have
$$
|v^{-1}-\tilde v^{-1}|(w) = \int_{\mathbb R}|jv - j\tilde v|(x,w) \ dx
$$
for almost every $ w \in \, ]0,1[$, and
$$
\int_{0}^{1}|jv - j\tilde v|(x,w) \ dw\, = \, \vert v-\tilde v \vert(x)
$$
for almost every $x \in \mathbb R$. Integrating the first equality on $w$ in $]0,1[$ and the second one on $x$
in $\mathbb R$, we deduce
$$
\int_{0}^{1}|v^{-1}-\tilde v^{-1}|(w) \ dw = \int_{\mathbb R}|v-\tilde v|(x) \ dx.
$$
$\hfill\Box$
\bigskip
Given $v \in {\cal U}$, its generalized inverse $v^{-1}$ is actually the a.e. unique nondecreasing
random variable on $(]0,1[, dw)$ with law $v_x$. Given any other random variable $X$ on $(]0,1[, dw)$
with law $v_x$, $v^{-1}$ is called the (a.e. unique) nondecreasing rearrangement of $X$ (see \cite{V}).
\medskip
We conclude this section recalling a result relative to the convergence of probability measures.
A sequence $(\mu_n)$ of probability measures on $\mathbb R$ is said to converge weakly toward
a probability measure $\mu$ if, as $n$ goes to $+\infty$,
$\displaystyle \int_{\mathbb R} \varphi \, d\mu_n$ tends to
$\displaystyle \int_{\mathbb R} \varphi \, d\mu$ for all bounded continuous real-valued functions
$\varphi$ on $\mathbb R$ (or equivalently for all ${\cal C}^{\infty}$ functions $\varphi$ with compact
support, that is, if $\mu_n$ converges to $\mu$ in the distribution sense). Given $p\geq 1$ this convergence
is metrized on ${\cal P}_p$ by the distance $W_p$ as shown by the following proposition (see \cite{V}):
\begin{prop}\label{cvWp/weak}
Let $p \geq 1$, $(\mu_n)$ a sequence of probability measures in ${\cal P}_p$ and $\mu \in {\cal P}.$
Then the following statements are equivalent:
i) $(W_p(\mu_n,\mu))$ converges to $0$;
ii) $(\mu_n)$ converges weakly to $\mu$ and $\displaystyle \sup_{n} \int_{\vert x \vert \geq R}
\vert x \vert^p \, d\mu_n(x)$ tends to $0$ as $R$ goes to infinity.
\end{prop}
In this proposition we do not a priori assume that $\mu$ belongs to ${\cal P}_p$, but it can be noted that
this property is actually induced by any of both hypotheses $i)$ and $ii)$.
For measures in $\cal P$ we have the weaker result:
\begin{prop}\label{weakcv}
Let $p \geq 1$, $(\mu_n)$ and $(\nu_n)$ two sequences in ${\cal P}$
converging weakly to $\mu$ and $\nu$ in ${\cal P}$ respectively. Then
(with possibly infinite values)
$$
W_p(\mu,\nu) \leq \liminf_{n \to +\infty} W_p(\mu_n,\nu_n).
$$
\end{prop}
\section{The case of classical solutions: Theorem \ref{theoremeclassique}
and corollary}\label{sectionpreuveclassique}
\indent
\subsection{Proof of Theorem \ref{theoremeclassique}}
\indent
We consider two
classical solutions $u$ and ${\tilde u}$ to (\ref{cons law}) such that
$u(t,.)$ and ${\tilde u}(t,.)$ belong to ${\cal U}$ and are increasing for all $t \geq 0$, and we shall
prove that
$$
W_p(u_{x}(t,.), {\tilde u}_{x}(t,.)) \, = \, W_p(u_{x}^{0}, {\tilde u}_{x}^{0})
$$
as a consequence of Proposition \ref{propertyW_p}.
The map $u^0$ is increasing from $0$ to $1$, so has a (true) inverse
$X(0,.)$ defined on $]0,1[$ by
$$
u^0(X(0,w)) \, = \, w.
$$
Then, given $w \in \, ]0,1[$, we consider a characteristic curve $t \mapsto X(t,w)$ solution of
\begin{equation}\label{caracteristiques}
X_t(t,w) = f'\bigl(u(t,X(t,w))\bigr)
\end{equation}
for $t \geq 0$, and taking value $X(0,w)$ at $t=0$.
Since $f$ is ${\cal C}^1$ and $u$ is bounded there exists a (non necessarily unique) solution
$X(.,w)$ to
\eqref{caracteristiques} by Peano Theorem (see \cite{H} for instance);
moreover by a classical
computation from \eqref{cons law} it is known to satisfy
\begin{equation}\label{inverse}
u(t,X(t,w)) \, = \, w
\end{equation}
for all $t \geq 0$, from which it follows that
$$
X_t(t,w) \, \Bigl( = f'(u(t,X(t,w))) \Bigr)= f'(w)
$$
and hence
\begin{equation}\label{X(t)classique}
X(t,w) \, = \, X(0,w) \, + \, tf'(w).
\end{equation}
In particular there exists a unique
solution $X(.,w)$ to \eqref{caracteristiques}. Now given $t \geq 0$, $X(t,.)$ is the (true) inverse of the increasing function $u(t,.)$
(by \eqref{inverse}), and Proposition \ref{propertyW_p} writes
$$
W_{p}(u_{x}(t,.),{\tilde u}_{x}(t,.)) \, = \, \Bigl( \int_{0}^{1} \vert X(t,w) -
{\tilde X}(t,w) \vert^{p} \, dw \Bigr)^{1/p}.
$$
But from \eqref{X(t)classique} we obtain
\begin{equation}\label{cst}
X(t,w) \, - \, {\tilde X}(t,w) \, = \, X(0,w) \, - \, {\tilde X}(0,w).
\end{equation}
This result ensures in particular that $\displaystyle W_p(u_{x}(t,.),{\tilde u}_{x}(t,.))$
remains constant in time, may its initial value be finite or not; note however
that \eqref{cst} is actually much stronger that
Theorem \ref{theoremeclassique}.
\bigskip
\subsection{Proof of Corollary \ref{corclassique}}
\indent
We assume that $f$ is a ${\cal C}^2$ convex function on $\mathbb R$, and $u^0$ is
a ${\cal C}^1$ increasing initial profile in ${\cal U}_p$.
First of all we note that the associated entropy solutions $u$ is a classical solution
in view of Theorem \ref{Kruzkovclassique}: this result is proved in \cite{S} for instance,
and its proof also ensures that $u(t,.)$ is increasing for all $t \geq 0$.
Then we check that the moment property is preserved by the conservation law, that is, that
$u(t,.)$ also belongs to ${\cal U}_p$ for any $t \geq 0$. Indeed, given $t \geq 0$, we have by the
change of variable $w = [u(t,.)](x)$:
\begin{eqnarray*}
\int_{\mathbb R} \vert x \vert^p \, u_{x}(t,x) \, dx
& = & \int_{0}^{1} \vert X(t,w) \vert^p \, dw \\
& = & \int_{0}^{1} \vert X(0,w) + t f'(w) \vert^p \, dw \\
& \leq & 2^{p-1} \left[ \int_{0}^{1} \vert X(0,w) \vert^p \, dw \, +
t^p \Vert f' \Vert^p_{L^{\infty}(]0,1[)}
\right]
\end{eqnarray*}
which is finite since
$$
\int_{0}^{1} \vert X(0,w)\vert^p \, dw = \int_{\mathbb R} \vert x \vert^p \, u_{x}^{0}(x) \, dx
$$
is finite by assumption.
This ends the proof of Corollary \ref{corclassique}. $\hfill\Box$
\section{Time discretization of the conservation law}\label{sectiondiscretisation}
\indent
In the previous section we have seen that the classical
solutions are obtained through the method of characteristics, that we now summarize in our case:
given an
initial profile $u^0$ in ${\cal U}$ such that the corresponding solution $u$ is ${\cal C}^{1}$ and
increasing
in $x$ for all $t \geq 0$, let $X(0,.)$ be its inverse, defined by
$$
u^0(X(0,w)) \, = \, w
$$
for all $w \in \, ]0,1[$. Let then $X(0,w)$ evolve into
\begin{equation}\label{X(t)}
X(t,w) \, = \, X(0,w) + t f'(w)
\end{equation}
for all $ t \geq 0$ and $w \in \, ]0,1[$ (see \eqref{X(t)classique}).
The solution $u(t,.)$ is then the inverse of the increasing map $X(t,.)$, that is, is
the unique solution of
$$
X(t,u(t,x)) \, = \, x.
$$
\medskip
In the general case, defining $X(0,.)$ in some similar way, there is no hope for
the function $X(t,.)$
defined by \eqref{X(t)}
to be increasing for $t > 0$; inverting it would thus lead to a multivalued function, and
no more to the
entropy solution of the conservation law, as in the particular case discussed above.
However, averaging (or "collapsing") this multivalued function into a single-valued function, Y. Brenier showed in
\cite{B} how to build an approximate solution to the conservation law.
We now precisely describe this so-called Transport-Collapse method in our case.
\subsection{Definition and $W_p$ contraction property of the discretized solution}\label{Time discretization
of the problem}
\indent
Let $u^{0} \in {\cal U}$ be some fixed initial profile, with generalized inverse
$X(0,.)$ given as in Definition \ref{ginverse} by
$$
X(0,w) \, = \, \inf \{x \in \mathbb R; u^{0}(x) > w \}
$$
for all $w \in \, ]0,1[$. $X(0,.)$ can be seen as a random variable on the
probability space $]0,1[$ equipped with the Lebesgue measure $dw$; its law is
$u^{0}_x$, as pointed out after Definition \ref{ginverse}.
We let then $X(0,.)$ evolve according to the method of
characteristics, denoting
$$
X(h,w) \, = \, X(0,w) \, + \, hf'(w)
$$
for all $h \geq 0$ and almost every $w \in \, ]0,1[$. Again, given $h \geq 0$, $X(h,.)$ can be seen as a random variable on
$]0,1[$; let then
$T_h u^0$ be its repartition function, that is, the function belonging to ${\cal U}$ and defined at any $x \in \mathbb R$
as the Lebesgue measure of the set $\{w\in \, ]0,1[; \, X(h,w) \leq x \}$.
It is given by
$$
T_h u^0(x) \, = \, \int_{0}^{1} {\bf 1}_{\{X(h,w) \leq x\}}(w) \, dw.
$$
\medskip
We summarize this construction in the following definition:
\begin{defi}\label{defiTh}
Let $v\in{\cal U}$ with generalized inverse $X(0,.)$ defined on $]0,1[$ by
$$
X(0,w) \, = \, \inf \{x \in \mathbb R; v(x) > w \}.
$$
Then, given $ h \geq 0$, and letting
$$
X(h,w) \, = \, X(0,w) \, + \, hf'(w)
$$
for almost every $w \in \, ]0,1[$, we define the ${\cal U}$ function $T_hv$ on $\mathbb R$ by
$$
T_h v(x) \, = \, \int_{0}^{1} {\bf 1}_{\{X(h,w) \leq x\}}(w) \, dw.
$$
\end{defi}
\medskip
In the case of Section \ref{sectionpreuveclassique} (see \eqref{X(t)classique}),
it turns out that $X(h,.)$ is the (true) inverse of $T_hu^0,$ and $(h,x) \mapsto T_hu^{0}(x)$ is
exactly
the entropy solution to equation $(\ref {cons law})$ with initial datum $u^{0}$ in $\cal U$.
This does not hold anymore in the general case,
but will allow us to build an approximate solution $S_hu^0$ by iterating the operator $T_h$. Let us first give two important properties of $T_h$:
\begin{prop}\label{propTh}
Let $h\geq 0$, $T_h$ defined as above and $p \geq 1$. Then
i) $T_hv$ belongs to ${\cal U}_p$ if so does $v$.
ii) For any $v$ and ${\tilde v}$ in ${\cal U}$ we have (with possibly infinite values unless
$v$ and ${\tilde v} \in {\cal U}_p$)
$$
W_p([T_h v ]_x, [T_h {\tilde v} ]_x) \, \leq
\, W_p(v_x, {\tilde v}_x).
$$
\end{prop}
\medskip
{\it Proof.} It is really similar to what has been done in Section
\ref{sectionpreuveclassique}
as for Corollary \ref{corclassique}.
$i)$ $T_h v$ belongs to ${\cal U}$ as a repartition function of a random variable, and we have
\begin{eqnarray*}
\int_{\mathbb R} \vert x \vert^p \, d[T_hv]_x(x)
& = & \int_{0}^{1} \vert X(h,w) \vert^p \, dw \\
&= &\int_{0}^{1} \vert X(0,w) \, + \, hf'(w) \vert^p \, dw \\
&\leq & 2^{p-1} \int_{0}^{1} \vert X(0,w) \vert^p + \vert h f'(w) \vert^p \, dw \\
&\leq & 2^{p-1} \left[ \int_{\mathbb R} \vert x \vert^p \, dv_{x}(x) +
h^p \Vert f' \Vert^p_{L^{\infty}(]0,1[)}
\right],
\end{eqnarray*}
which ensures that $[T_hv]_x$ has finite moment of order $p$ if so does $v_{x}$.
\bigskip
$ii)$ On one hand the generalized inverses $X(0,.)$
and $\tilde{X}(0,.)$ of $v$
and ${\tilde v}$ respectively satisfy
\begin{equation}\label{time0}
W_{p}(v_x, {\tilde v}_x) \, = \, \Bigl( \int_{0}^{1} \vert X(0,w) - \tilde{X}(0,w) \vert^p
\, dw \Bigr)^{1/p}
\end{equation}
by Proposition \ref {propertyW_p} (with finite values if both $v$ and ${\tilde v}$ belong to
${\cal U}_p$, and possibly infinite otherwise).
On the other hand
$X(h,.)$ and $\tilde{X}(h,.)$ have respective
law $[T_h v]_x$ and $[T_h {\tilde v}]_x$, so
\begin{equation}\label{timet}
W_{p}([T_h u^{0}]_x, [T_h {\tilde u}^{0}]_x) \,
\leq \, \Bigl(\int_{0}^{1} \vert X(h,w) - \tilde{X}(h,w) \vert^p \, dw \Bigr)^{1/p}
\end{equation}
by definition of the Wasserstein distance.
But
$$
X(h,w) - \, \tilde{X}(h,w) \, = \, X(0,w) \, - \, \tilde{X}(0,w)
$$
for almost every $w \in \, ]0,1[$ by definition, which concludes the argument by
\eqref{time0} and \eqref{timet}.
Note again that \eqref{timet} holds only as an inequality since $X(h,.)$ and ${\tilde X}(h,.)$ are
not necessarily nondecreasing, which was the case in the example
discussed in Section \ref{sectionpreuveclassique}.
$\hfill\Box$
\medskip
We now use the operator $T_h$ defined above to build an approximate solution $S_hu^0$
to the conservation law
$(\ref {cons law})$:
\begin{defi}\label{defiSh}
Let $h$ be some positive number and $v \in {\cal U}$.
For any $t \geq 0$ decomposed as $t = (N+s)h$ with $N \in \mathbb N$ and $0 \leq s < 1$,
we let
$$
S_hv(t,.) \, = \, (1-s) \, T_{h}^{N} v(.) \, + \, s \, T_{h}^{N+1} v(.)
$$
where $T_{h}^{0}v = v$ and $T_{h}^{N+1}v = T_h(T_{h}^{N}v)$.
\end{defi}
These iterations make sense because $T_hv\in{\cal U}$ if $v\in {\cal U}$,
$S_hv(t,.) \in {\cal U}$ (resp. ${\cal U}_p$) for any $h, t \geq 0$ and
$v \in {\cal U}$ (resp. ${\cal U}_p$).
We now prove two contractions properties on these approximate solutions. We first have the $L^1(\mathbb R)$
contraction property:
\begin{prop}\label{contractL1}
Let $h$ be some fixed positive number and $S_h$ defined as above. Then, for any $v \in {\cal U}$ and
$s,t \geq 0$ we have
$$
\Vert S_hv(t,.) - S_hv(s,.) \Vert_{L^1(\mathbb R)} \, \leq \, \vert t-s \vert \, \Vert f' \Vert_{L^{\infty}([0,1])}.
$$
\end{prop}
\medskip
{\it Proof.}
As in \cite{B} we first observe that $\|T_hV -V\|_{L^1(\mathbb R)}\leq h \Vert f' \Vert_{L^{\infty}(]0,1[)}$
for any $V \in {\cal U}$, then let
$t=(M+\mu)h$ and $s= (N+\nu)h$ with $M, N \in \mathbb N$ and $0 \leq \mu, \nu <1$,
and, for instance assuming that $M>N$, prove the proposition by applying this first bound
to $V = S_hv(kh,.) = T_{h}^{k}v$ for $k=N+1, \dots, M-1$.
$\hfill \Box$
\medskip
Then we have the $W_p$ contraction property:
\begin{prop}\label{Shcontract}
Let $h$ be some fixed positive number and $S_h$ defined as above. Then,
given $v$ and ${\tilde v}$ in
${\cal U}$, we have for any $t \geq 0$:
$$
W_p([S_h v]_x(t,.), [S_h{\tilde v}]_x(t,.)) \, \leq
\, W_p(v_x, {\tilde v}_x).
$$
\end{prop}
\medskip
{\it Proof.}
It follows from Proposition \ref{propTh} (about $T_h$) and to the convexity of the $W_p$ distance
to the power $p$, in the sense that
$$
W_{p}^{p}(\alpha \mu_1 + (1-\alpha) \mu_2, \alpha \nu_1 + (1-\alpha) \nu_2) \, \leq \,
\alpha W_{p}^{p}(\mu_1 , \nu_1 ) + ( 1-\alpha) W_{p}^{p}(\mu_2, \nu_2)
$$
for all real number $\alpha \in [0,1]$ and probability measures $\mu_1, \mu_2, \nu_1$ and $\nu_2$
(see \cite{V} for instance).
$\hfill\Box$
\bigskip
We shall now recall the convergence of the scheme toward the entropy solution of the conservation
law.
\subsection{Convergence of the scheme in the $L^{1}_{loc}(\mathbb R)$ sense}\label{cvL1loc}
\indent
In this section we consider the space $\cal C([0,+\infty[, L^1_{loc}(\mathbb R))$ equipped with the topology
defined by the semi-norms
$$
q_{nm}(f) \, = \, \sup_{t \in [0,n]} \, \int_{-m}^{m} \vert f(x) \vert \, dx
$$
for any integers $n$ and $m$ and $f \in {\cal C}([0,+\infty[, L^1_{loc}(\mathbb R))$. Then we have
\begin{prop} \label{schemeconvergence}
Let $u^0 \in {\cal U}$. Then, as $h$ goes to $0$, the function
$S_{h}u^0$ converges in ${\cal C}([0,+\infty[, L^1_{loc}(\mathbb R))$ to the entropy solution
of (\ref{cons law}) with initial datum $u^0$.
\end{prop}
We briefly give the steps of the proof, which follows the one of Brenier in \cite{B}, adapted
to functions of ${\cal U}$ instead of $L^1(\mathbb R)$.
We first prove that the family $(S_hu^0)_h$ is
relatively compact in ${\cal C}([0,+\infty[, L^1_{loc}(\mathbb R))$ by means of
Proposition \ref{contractL1}, and Helly and Ascoli-Arzela Theorems. Then we check that the
limit of any sequence of $(S_hu^0)_h$ converging in
${\cal C}([0,+\infty[, L^1_{loc}(\mathbb R))$ is an entropy solution to the conservation law
\eqref{cons law} with initial datum $u^0$. By the uniqueness of this solution
ensured by Theorem \ref{Kruzkov}, this concludes the proof of Proposition \ref{schemeconvergence}.
\subsection{Convergence of the scheme in $W_p$ distance sense}\label{subsectionpreuveconvergenceWp}
\indent
We first prove a uniform equiintegrability result on the approximate solutions:
\begin{prop}\label{equiintegrable}
Let $S_h$ be defined as above, $v\in {\cal U}_p$ and $T \geq 0$. Then
\begin{eqnarray*}
\sup_{0 \leq h \leq T} \sup_{0 \leq t \leq T} \int_{|x|\geq R} |x|^p d[S_hv]_x(t,x)
\end{eqnarray*}
tends to $0$ as $R$ goes to infinity.
\end{prop}
{\it Proof.}
We again denote $\displaystyle M = \Vert f' \Vert_{L^{\infty}(]0,1[)}$, and first consider $T_h$ itself, writing
\begin{eqnarray*}
\int_{\vert x\vert \geq R} \vert x \vert^p d[T_hv]_x(x)
& =& \int_{0}^{1} \vert v^{-1}(w) +hf'(w) \vert^p \, {\bf 1}_{\{\vert v^{-1}(w) +hf'(w) \vert \geq R\}} \, dw \\
& \leq & \int_{\mathbb R} (\vert x \vert +hM)^p {\bf 1}_{\{\vert x \vert +hM \geq R\}} \, dv_x(x) \\
& \leq & \left( 1+\frac{hM}{R-hM} \right)^p \int_{\vert x \vert \geq R-hM} \vert x \vert^p \, dv_x(x)
\end{eqnarray*}
for $R >hM$. From this computation we deduce by iteration
$$
\int_{\vert x\vert \geq R} \vert x \vert^p d[T_{h}^{N}v]_x(x)
\leq \, \prod_{j=1}^{N} \left( 1 + \frac{hM}{R-jhM} \right)^p \int_{\vert x \vert \geq R-NhM}
\vert x \vert^p \, dv_x(x)
$$
for $R > NhM$, with
$$
\prod_{j=1}^{N} \left( 1 + \frac{hM}{R-jhM} \right) \leq \left( 1 + \frac{hM}{R-NhM} \right)^{N} \leq
\exp \left( \frac{NhM}{R-NhM} \right).
$$
Thus
$$
\int_{\vert x\vert \geq R} \vert x \vert^p d[S_{h}v]_x(Nh,x)
\leq \exp \left( \frac{pTM}{R-TM} \right) \int_{\vert x \vert \geq R-TM}
\vert x \vert^p \, dv_x(x)
$$
for any $N$ and $h$ such that $Nh \leq T$.
>From this we get for instance
$$
\int_{\vert x\vert \geq R} \vert x \vert^p d[S_{h}v]_x(t,x)
\leq \exp \left( \frac{2pTM}{R-2TM} \right) \int_{\vert x \vert \geq R-2TM}
\vert x \vert^p \, dv_x(x)
$$
for any $t$ and $h$ smaller than $T$. This concludes the argument since the last integral tends to $0$ as
$R$ goes to infinity.
$\hfill\Box$
\bigskip
>From this we deduce the convergence of the scheme in $W_p$ distance sense:
\begin{prop}\label{convergenceWp}
Let $u^0 \in {\cal U}_p$ and
$u$ be the entropy solution
to (\ref{cons law}) with initial datum $u^0$.
Then, for any $t \geq 0$,
$W_p([S_h u^0]_x(t,.), u_x(t,.) )$ converges to $0$ as $h$ goes to $0$.
\end{prop}
\medskip
{\it Proof.}
Given $t \geq 0$, $S_hu^0(t,.)$ converges to $u(t,.)$ in $L^{1}_{loc}(\mathbb R)$ as $h$ goes to $0$ (by Proposition
\ref{schemeconvergence}), so $[S_hu]_x(t,.)$ converges to the probability measure $u_x(t,.)$, first
in the distribution sense, then in the weak sense of probability measures, and finally in $W_p$ distance by
Propositions \ref{equiintegrable} and \ref{cvWp/weak}.
Note in particular that $u_x(t,.)$ has finite moment of order $p$ for any $ t \geq 0$, that is,
$u(t,.)$ belongs to ${\cal U}_p$.
$\hfill\Box$
\section{The general case of entropy solutions: Theorem \ref {theoreme} and corollaries}\label{sectionpreuve}
\subsection{Proof of Theorem \ref {theoreme}}\label{soussectionpreuve}
\indent
We let $p \geq 1$ and consider two initial data $u^0$ and ${\tilde u}^0$ in ${\cal U}$ with
associated entropy solutions $u$ and $\tilde u$.
Given $t \geq 0$, Proposition
\ref{schemeconvergence} yields again the convergence of $[S_h u^0]_x(t,.)$ to $u_x(t,.)$
in the weak sense of probability measures. Since this holds also
for $\tilde u^0$, we obtain
$$
W_p(u_x(t,.), {\tilde u}_x(t,.)) \leq \liminf_{h \to 0}
W_p([S_h u^0]_x(t,.), [S_h {\tilde u}^0]_x(t,.))
$$
by Proposition \ref{weakcv}. But, for each $h$,
$$
W_p([S_h u^0]_x(t,.), [S_h {\tilde u}^0]_x(t,.)) \leq W_p(u_x^0, {\tilde u}_x^0)
$$
by Proposition \ref{Shcontract}, so finally
$$
W_p(u_x(t,.), {\tilde u}_x(t,.)) \leq W_p(u_x^0, {\tilde u}_x^0).
$$
This concludes the argument.
\subsection{Proof of Corollary \ref{corsolutionUp}}
\indent
We recall that in the introduction we have defined a distance on each ${\cal U}_p$ by letting
$$
d_p(u, {\tilde u}) \, = \, W_p(u_x, {\tilde u}_x),
$$
and we now prove that, given $p \geq 1$ and $u^0 \in {\cal U}_p$, the entropy solution $u$ to the
conservation law \eqref{cons law} belongs to ${\cal C}([0,+\infty[, {\cal U}_p)$.
We first note, in view of the proof of Proposition \ref{convergenceWp}, that $u(t,.)$ indeed belongs to
${\cal U}_p$ for all $t \geq 0$.
Then, given $s \geq 0$, we need to prove that $d_p(u(t,.),u(s,.))\, (=W_p(u_x(t,.),u_x(s,.)))$ tends to $0$
as $t$ goes to $s$. Indeed, on one hand $u(t,.)$ tends to $u(s,.)$ in $L^{1}_{loc}(\mathbb R)$ by Theorem \ref{Kruzkov}, so $u_x(t,.)$ tends to
$u_x(s,.)$, first in the distribution sense, then in the weak sense of probability measures.
On the other hand, given $T > s$, we now prove that
$\displaystyle \sup_{0 \leq t \leq T} \int_{\vert x \vert \geq R} \vert x \vert^p \, du_x(t,x)$ goes to $0$ as $R$ goes
to infinity. For this, given $\varepsilon > 0$, let $R$ such that
$$
\sup_{0 \leq h \leq T} \sup_{0 \leq t \leq T} \int_{\vert x \vert \geq R} \vert x \vert^p \, d[S_hu^0]_x(t,x)
\leq \varepsilon
$$
by Proposition \ref{equiintegrable}. Let then $ \varphi \in {\cal C}^{\infty}_{c}(\mathbb R)$ such that
$0 \leq \varphi \leq 1$ and $\varphi(x) =0$ if $\vert x \vert \leq R$.
On one hand
$$
\int_{\mathbb R} \varphi(x) \vert x \vert^p \, d[S_hu^0]_x(t,x) \,
\to \int_{\mathbb R} \varphi(x) \vert x \vert^p \, du_x(t,x)
$$
as $h$ goes to $0$ since $\varphi(x) \vert x \vert^p \in {\cal C}^{\infty}_{c}(\mathbb R)$ and $[S_hu^0]_x(t,.)$ tends
to $u_x(t,.)$ in distribution sense.
On the other hand
$$
\int_{\mathbb R} \varphi(x) \vert x \vert^p \, d[S_hu^0]_x(t,x) \, \leq \, \varepsilon
$$
for all $0 \leq h,t \leq T$. Hence at the limit
$$
\int_{\mathbb R} \varphi(x) \vert x \vert^p \, du_x(t,x) \, \leq \, \varepsilon
$$
for all $t \leq T$, from which it follows that
$$
\sup_{0 \leq t \leq T} \int_{\vert x \vert \geq R} \vert x \vert^p \, du_x(t,x) \, \leq \, \varepsilon,
$$
which means that indeed $\displaystyle \sup_{0 \leq t \leq T} \int_{\vert x \vert \geq R} \vert x \vert^p \, du_x(t,x)$ goes to $0$
as $R$ goes to infinity.
\medskip
From these two results we deduce the continuity result by Proposition \ref{cvWp/weak}.
\subsection{Proof of Corollary \ref{corsolutionU1}}
\indent
Given $t \geq 0$, $S_hu^0(t,.)$ converges to $u(t,.)$ in $L^{1}_{loc}(\mathbb R)$ by Proposition \ref{schemeconvergence},
so for all $s,t, n \geq 0$ we have
$$
\Vert u(t,.) - u(s,.) \Vert_{L^1([-n,n])} = \lim_{h \to 0} \Vert S_hu^0(t,.) - S_hu^0(s,.) \Vert_{L^1([-n,n])}.
$$
But
$$
\Vert S_hu^0(t,.) - S_hu^0(s,.) \Vert_{L^1([-n,n])} \leq \Vert S_hu^0(t,.) - S_hu^0(s,.) \Vert_{L^1(\mathbb R)}
\leq \vert t-s \vert \, \Vert f' \Vert_{L^{\infty}(\mathbb R)}
$$
for all $h \geq 0$ by Proposition \ref{contractL1}, so letting $h$ go to $0$ we get
$$
\Vert u(t,.) - u(s,.) \Vert_{L^1([-n,n])} \leq \vert t-s \vert \, \Vert f' \Vert_{L^{\infty}(\mathbb R)}.
$$
Since this holds for all $n \geq 0$, we obtain Corollary \ref{corsolutionU1}.
\section{Extension to viscous conservation laws}\label{sectionviscous}
\indent
In this section we let $\nu$ be a positive number and consider the viscous conservation law
\begin{equation}\label{viscouscl}
u_t + f(u)_x = \nu \, u_{xx} \qquad t> 0, \; x \in \mathbb R
\end{equation}
with initial datum $u^0 \in L^{\infty}(\mathbb R)$.
Assuming that $f$ is a locally Lipschitz real-valued function on $\mathbb R$, and calling
{\it solution}
a function $u$ in $L^{\infty}([0,+\infty[ \times \mathbb R)$ such that \eqref{viscouscl} holds
in the sense of
distributions, it is known that, given $u^0 \in L^{\infty}(\mathbb R)$, there exists a unique
solution $u$ to \eqref{viscouscl}. If
moreover $u^0 \in \cal U$, then $u(t,.)$ also belongs to $\cal U$
for all $t \geq 0$, and the $W_p$ contraction property stated in Theorem \ref{theoreme}
in the inviscid case $\nu = 0$ still holds:
\begin{theo}\label{theoremevisqueux}
Given a locally Lipschitz real-valued function $f$ on $\mathbb R$ and two initial data $u^0$ and ${\tilde u}^0$
in ${\cal U}$, let $u$ and
${\tilde u}$ be the associated solutions to \eqref{viscouscl}. Then, for any
$t \geq 0$ and $p \geq 1$, we have (with possibly infinite values)
$$
W_p(u_{x}(t,.), {\tilde u}_{x}(t,.)) \, \leq \, W_p(u_{x}^{0}, {\tilde u}_{x}^{0}).
$$
\end{theo}
\medskip
We briefly mention how this contraction property for the viscous conservation law allows to
recover the same property for the inviscid equation, given in Theorem \ref{theoreme}. Given
some initial datum $u^0$ in $\cal U$ and $\nu >0$, let indeed $u_{\nu}$ be the corresponding
solution to the viscous equation \eqref{viscouscl}. Then it is known (see \cite{S} for instance)
that $u_{\nu}(t,.)$ converges in $L^{1}_{loc}(\mathbb R)$ to the solution $u(t,.)$ to the
inviscid conservation law \eqref{cons law} with initial datum $u^0$. From this the argument
already used in Section \ref{soussectionpreuve} (with $S_hu^0(t,.)$ intead of $u_{\nu}(t,.)$)
enables to recover Theorem \ref{theoreme}.
\medskip
The proof of Theorem \ref{theoremevisqueux} follows the lines of Sections
\ref{sectiondiscretisation} and \ref{sectionpreuve}
and makes use of a time-discretization of equation \eqref{viscouscl} based on the discretization
of the inviscid conservation law
previously discussed. More precisely, given a time step $h > 0$, we first
map $u^0 \in {\cal U}$ to $T_hu^0$ as in section 4.1, and then let $T_hu^0$ evolve along the heat
equation on a time
interval $h$, that is, map it to
$$
\cal T_hu^0 = K_h * T_hu^0
$$
where $K_h$ is the heat kernel defined on $\mathbb R$ by
$$
K_h(z) = \frac{1}{\sqrt{4 \pi h}} \, e^{-\frac{z^2}{4h}}.
$$
Then, defining an approximate solution $\cal S_hu^0$ by iterating the $\cal T_h$ operator as in Definition
\ref{defiSh}, we prove that Propositions \ref{propTh} and \ref{Shcontract} still hold for the
new $\cal T_h$ and $\cal S_h$ operators (Note that the convolution with the heat kernel is a contraction for the Wasserstein distance of any finite order).
Proposition \ref{contractL1} only holds
assuming that $v$ is twice derivable with $v''$ in $L^1(\mathbb R)$: it more precisely reads
$$
\Vert \cal S_hv(t,.) - \cal S_hv(s,.) \Vert_{L^1(\mathbb R)} \leq \,
\vert t-s \vert \, [\Vert f' \Vert_{L^{\infty}(]0,1[)} + \Vert v'' \Vert_{L^1(\mathbb R)}].
$$
As in Section \ref{cvL1loc}, this enables to prove that, given $u^0$ in $\cal U$, twice derivable with
$(u^0)''$ in $L^1(\mathbb R)$, the family $(\cal S_hu^0)_h$ converges in $\cal C([0,+\infty[,L^{1}_{loc}(\mathbb R))$
to the solution of \eqref{viscouscl} with initial datum $u^0$.
With this convergence result in hand we follow the lines of Section \ref{soussectionpreuve} to prove
Theorem \ref{theoremevisqueux} in the case of twice derivable initial data, with $L^1$ second derivative,
while the general case follows by a density argument.
\bigskip
\bigskip
\noindent
{\bf Acknowledgments:}
This work has been partly supported by the European network Hyke, funded by the EC contract
HPRN-CT-2002-00282.
\medskip
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 765 |
Mérigny – miejscowość i gmina we Francji, w Regionie Centralnym, w departamencie Indre.
Według danych na rok 1990 gminę zamieszkiwały 563 osoby, a gęstość zaludnienia wynosiła 18 osób/km² (wśród 1842 gmin Regionu Centralnego Mérigny plasuje się na 632. miejscu pod względem liczby ludności, natomiast pod względem powierzchni na miejscu 322.).
Bibliografia
Miejscowości w departamencie Indre | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,148 |
Événements
Janvier
Samedi , : un accident de ballon fait 11 morts. C'est le second accident de ballon le plus meurtrier de l'histoire.
Février
Mars
Vendredi , : dernier vol aux couleurs de Continental Airlines, absorbée par United Airlines. La compagnie avait été créée en 1934.
Mardi , : un commandant de bord de la compagnie JetBlue panique en plein vol et le copilote choisit de s'enfermer seul dans le cockpit pour terminer le vol. L'événement relance le débat sur les conditions de stress des pilotes.
Avril
Lundi , : un ATR-72 de la compagnie UTair s'écrase près de Tioumen, causant la mort de 29 des 43 personnes à bord.
Mai
Vendredi ', : dernier vol d'un Boeing 720.
Jeudi , : découverte de l'épave d'un Soukhoï Superjet 100 au Mont Salak.
Juin
Dimanche : accident d'hélicoptère de la police au Kenya, où périssent six personnes, dont le ministre de l'Intérieur George Saitoti.
Juillet
Vendredi , : un bi-réacteur s'écrase à l'aéroport du Castellet, dans le Var.
Août
Septembre
Samedi : le pilote suisse Carlo Schmid achève son tour du monde sur Cessna 210 commencé le à l'aéroport de Dübendorf, dans le canton de Zurich. À 22 ans, il est le plus jeune pilote à avoir accompli un tel vol en solitaire.
Octobre
Mardi , : décès de l'as français Roland de la Poype.
Novembre
Décembre
, : premier vol du Dassault nEUROn depuis la base aérienne d'Istres.
Notes et références
Voir aussi
Articles connexes
Liste des accidents aériens en 2012 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,406 |
Politics, Social Media
Social Media: A tool of Segregation and Ghettoization that Is Ruining Politics
Social networks are out to be more encompassing and controlling, more totalizing, than earlier media ever was.
Emotional appeals can be good for politics. They can spur civic involvement and they can galvanize public attention, focusing it on injustices and abuses of power. But there's a dark side to social media's emotionalism. Trump's popularity took off only after, playing to the public's frustrations and fears, demonizing Mexican immigrants and it worked.
The fact that experienced politicians are having trouble fitting themselves into the new mold is not unusual. Whenever a new medium upends the game, veteran politicians struggle. They go on playing by the old medium's rules. They continue to follow the conventions of broadcast TV. They assume that television will establish the campaign's talking points, package the race as a series of tidy stories and shape the way voters see the contestants. They may have teams of digital representatives tending to their online messaging, but they still view social media as a complement to TV coverage, a means of reinforcing their messages and images, rather than as the campaign's driving force.
News organizations, too, tend to be slow to adapt to the arrival of a new medium. In the past, television, gave a theatrical rhythm to political campaigns. Each day was an act in a broader drama. Political campaigns were "narratives," they had "story lines." Social media is different. There is no narrative; there is no story line. There is no context. As a result, today's political campaign reports are often out of sync with the public's opinion and reaction and to events.
As an example, In July 2015, when Trump kicked dirt on John McCain's reputation saying, "He's not a war hero, I like people who weren't captured," in print and on TV, this comment received ample saturation coverage, but the narrative never advanced and far from apologizing, Trump kept attacking. While the tweets piled up, the public's attention buzzed to newer things, and the story died even before it became a story. With Social media, we are entering a post-narrative world of campaigning greatly circumscribing and overtaking the power of traditional media in stage-managing political races.
Rather than narrating stories, newscasters are now reading tweets.
The Internet was intended as a participative tool, as a force for democratization. Early digital enthusiasts expected that the web would engender a deeper national conversation. This was absolutely wishful thinking and daydreaming. Already in the early days of the Social networks there were signs that online media were to promote and encourage a restless mob mentality. People were skimming headlines and posts, seeking information to reinforce their biases while rejecting any contrary perspectives and viewpoints contradicting their opinions. Even today and more ever than ever, public information gathering is still further tribalistic than pluralistic. Blog authors and blog readers, even more than ever, are now exclusively gravitating toward digital content that will reinforce their biases, their opinions and convictions. Originally intended to be a force for participation and democratization, the Internet is now the perfect tool for discrimination, segregation and ghettoization.
If there is one thing that the Internet achieved and Social media reinforced, it is the polarizing effect that broadcast media, particularly talk radio and cable news, had been having for many years. Today, Social media is turning out to be more encompassing and controlling, more totalizing, than earlier media ever was. Today, social networks like Facebook, Twitter and Google do not only regulate the messages people receive, they also regulate their responses thus seriously influencing public opinion.
Social networks and media are now shaping the forms of our discourse.
Facebook feeds us with a cascade of messages selected by their News Feed algorithm, and we are provided with a set of prescribed ways to react to each one of these messages. We can click a Like button; share the message with our friends or comment. On Twitter, we can either reply, retweet or favorite and, any thought we express has to fit a tight text limit. Google News also presents us a series of headlines underlining the latest trending stories. It then provides a row of buttons for sharing the headlines either on Google Plus, Twitter or Facebook.
All social networks without exception are now imposing these formal constraints and limitations on what we see, what we read and on how we can respond, none of these restrictions having anything to do with promoting public interest. All these constraints and limitations only reflect the commercial interests of the companies and service providers operating the Social network as well as the specific protocols of their software programming. While the systematic formulaic quality of the Social media is well suited to the chitchat and gossiping that takes place among friends, when applied to politics and the political speech, these same constraints are nothing else than pernicious, inspiring insignificance rather than wisdom and enlightenment.
JMD is an enthusiastic writer, columnist and social activist who most enjoys evolving in complex interactive situations.
http://jmdonline.tumblr.com/
http://lefuturistedailynews.com/
http://news.thefuturistdailynews.com/
https://about.me/jmdlive/ | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,446 |
Mazama bororo (Мазама бороро) — вид ссавців з родини Оленеві (Cervidae).
Опис
Хоча розмір і структура M. bororo найбільш схожа на Mazama nana, його забарвлення дуже схоже на Mazama americana. Вид зовні нагадує гібрид між цими двома видами, але відрізняється від обох і їх гібридів каріотипом.
Поширення
Перша популяція диких тварин була виявлена в Національному парку Intervales в період між 2000 і 2002 роками. З тих пір він був описаний тільки з дев'ять ділянок проживання. M. bororo, здається, обмежується біомом атлантичного лісу, між паралелями 23° і 26° південної широти і меридіанами 47° і 50° з.д. Цей діапазон простягається вздовж південної частини штату Сан-Паулу, на сході Парани і крайньому північному сході штату Санта-Катаріна (Бразилія). Єдине придатне дослідження населення проведене в Національному парку Intervales, де оцінена щільність 1,5 особин/км ² (вважається оптимальною в добре захищених областях). Зниження щільності (0,5 особи/км²) були віднесені до інших районів. Ці значення генерують оцінки загального числа 8500 дорослих особин (Vogliotti and Duarte 2010, 2012). Вид є ендеміком тропічних і субтропічних вологих широколистяних лісів атлантичного лісу. Рельєф варіюється від рівня моря прибережних рівнин до місцевості крутого рельєфу і пагорбів вище 1200 метрів. Клімат в регіоні вологий субтропічний, з переходом на високогірний вологий субтропічний.
Поведінка
Веде сутінковий і нічний спосіб життя і, здається, більш активний протягом літнього сезону дощів. Деякі докази плодоїдності забезпечуються фотопастками.
Відтворення
Оленята були записані в період з вересня по лютий.
Загрози та охорона
Основні загрози: браконьєрство, втрата середовища проживання і фрагментація, пов'язані зі змінами в землекористуванні, хижацтва домашніми і дикими собаками. Можлива загроза: інфекційні хвороби великої рогатої худоби.
Тварина перебуває в Національному офіційному списку зникаючих видів фауни і списку штату Парана.
Джерела
Тварини, описані 1996
Оленеві | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,142 |
Q: jHipsterProperties getXXX value not changed when value of spring-cloud-config in jhipster-register xxx was changed jHipsterProperties getXXX value not changed when value of spring-cloud-config in jhipster-register xxx was changed
java version "1.8.0_144"
Java(TM) SE Runtime Environment (build 1.8.0_144-b01)
Java HotSpot(TM) 64-Bit Server VM (build 25.144-b01, mixed mode)
git version 2.14.3 (Apple Git-98)
node: v9.4.0
npm: 5.6.0
bower: 1.8.2
gulp:
[23:45:31] CLI version 2.0.0
yeoman: 2.0.0
yarn: 1.3.2
Docker version 17.12.0-ce, build c97c6d6
docker-compose version 1.18.0, build 8dd22a9
A: This is not specific to JHipster, this is how Spring Cloud Config works.
Unless you use Spring Cloud Bus, it's not automatic you must send a POST request to /management/refresh (JHipster configuration) in your microservice in order to force it to refresh itself and load the new value in. Also, you should check whether this endpoint is configured to require authentication as it is a rather sensitive endpoint.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 290 |
{"url":"http:\/\/planetmath.org\/Measurepreserving","text":"# measure-preserving\n\n## 1 Definition\n\nLet $(X_{1},\\mathfrak{B}_{1},\\mu_{1})$ and $(X_{2},\\mathfrak{B}_{2},\\mu_{2})$ be measure spaces, and $T:X_{1}\\to X_{2}$ be a measurable transformation. The transformation $T$ is said to be measure-preserving if for all $A\\in\\mathfrak{B}_{2}$ we have that\n\n $\\mu_{1}(T^{-1}(A))=\\mu_{2}(A),$\n\nwhere $T^{-1}(A)$ is, as usual, the set of points $x\\in X_{1}$ such that $T(x)\\in A$.\n\n\u2022 If $T$ is bijective, measure-preserving, and its inverse $T^{-1}$ is also measure-preserving, then $T$ is said to be an measure-preserving transformation.\n\n\u2022 Measure-preserving transformations between the same measure space are sometimes called of the measure space.\n\nRemarks:\n\n\u2022 The fact that a map $T:X_{1}\\longrightarrow X_{2}$ is measure-preserving depends heavily on the sigma-algebras $\\mathfrak{B}_{i}$ and measures $\\mu_{i}$ involved. If other measures or sigma-algebras are also in consideration, one should make clear to which measure space is $T:X_{1}\\longrightarrow X_{2}$ measure-preserving.\n\n\u2022 Measure-preserving maps are the morphisms on the category whose objects are measure spaces. This should be clear from the next results and examples.\n\n## 2 Properties\n\n\u2022 The composition of measure-preserving maps is again measure-preserving. Of course, we are supposing that the domains and codomains of the maps are such that the composition is possible.\n\n\u2022 Let $(X_{1},\\mathfrak{B}_{1},\\mu_{1})$ and $(X_{2},\\mathfrak{B}_{2},\\mu_{2})$ be measure spaces and $(X_{1},\\overline{\\mathfrak{B}_{1}},\\overline{\\mu_{1}})$ and $(X_{2},\\overline{\\mathfrak{B}_{2}},\\overline{\\mu_{2}})$ their completions. If $T:(X_{1},\\mathfrak{B}_{1},\\mu_{1})\\longrightarrow(X_{2},\\mathfrak{B}_{2},\\mu_{% 2})$ is measure-preserving, then so is $T:(X_{1},\\overline{\\mathfrak{B}_{1}},\\overline{\\mu_{1}})\\longrightarrow(X_{2},% \\overline{\\mathfrak{B}_{2}},\\overline{\\mu_{2}})$.\n\n\u2022 Let $(X_{1},\\mathfrak{B}_{1},\\mu_{1})$ and $(X_{2},\\mathfrak{B}_{2},\\mu_{2})$ be measure spaces and $T_{1}:X_{1}\\longrightarrow X_{1}$, $T_{2}:X_{2}\\longrightarrow X_{2}$ be measure-preserving maps. Then, the product map $T_{1}\\times T_{2}:X_{1}\\times X_{2}\\longrightarrow X_{1}\\times X_{2}$, defined by\n\n $\\displaystyle T_{1}\\times T_{2}\\;(x_{1},x_{2}):=(T_{1}(x_{1}),T_{2}(x_{2}))$\n\nis a measure-preserving transformation of $(T_{1}\\times T_{2},\\mathfrak{B}_{1}\\times\\mathfrak{B}_{1},\\mu_{1}\\times\\mu_{2})$.\n\n## 3 Examples\n\n\u2022 The identity map of a measure space $(X,\\mathfrak{B},\\mu)$ is always measure-preserving.\n\n\u2022 Let $G$ be a locally compact group (http:\/\/planetmath.org\/TopologicalGroup). For each $a\\in G$, the transformation $T(g):=ag$ is measure-preserving relatively to any left Haar measure. Similarly, any right translation on $G$ any right Haar measure.\n\n\u2022 Every continuous surjective homomorphism between compact Hausdorff is measure-preserving relatively to the normalized Haar measure (see this entry (http:\/\/planetmath.org\/ContinuousEpimorphismOfCompactGroupsPreservesHaarMeasure)).\n\n Title measure-preserving Canonical name Measurepreserving Date of creation 2013-03-22 12:19:41 Last modified on 2013-03-22 12:19:41 Owner asteroid (17536) Last modified by asteroid (17536) Numerical id 17 Author asteroid (17536) Entry type Definition Classification msc 28D05 Classification msc 37A05 Synonym measure preserving Synonym measure-preserving transformation Synonym measure-preserving map Related topic ErgodicTransformation Defines invertible measure-preserving transformation Defines endomorphism of a measure space","date":"2018-03-24 10:20:16","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 34, \"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\": 0.9551412463188171, \"perplexity\": 553.010548764671}, \"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-2018-13\/segments\/1521257650188.31\/warc\/CC-MAIN-20180324093251-20180324113251-00351.warc.gz\"}"} | null | null |
{{Info/Santos
|nome =Santo Eusébio de Vercelli
|data_nascimento =
|local_nascimento =Sardenha
|data_morte =
|local_morte =Vercelli, Piemonte, Itália
|dia_consagrado =2 de agosto; 16 de dezembro
|venerado_em =Igreja Católica
|imagem =File:Sebastiano Ricci 049.jpg
|tamanho =250px
|legenda =A Vírgem Maria na glória com o Arcanjo Gabriel, e os Santos "Eusébio de Vercelli" (sentado), São Sebastião, e São Roque, Sebastiano Ricci.
|títulos =Bispo de Vercelli, Confessor
|patrono =Vercelli}}
Eusébio de Vercelli (; Sardenha, c. 283 - Vercelli, 1 de agosto de 371) foi o primeiro bispo da antiga diocese de Vercelli e foi um dos principais expoentes da luta contra a difusão da heresia ariana, é venerado como santo pela Igreja Católica.
Biografia
Segundo a tradição mudou-se com a mãe e a irmã menor para Roma após o martírio de seu pai. Na "Urbe" foi primeiro "leitor" e depois ordenado presbítero pelo Papa Marcos e consagrado bispo pelo Papa Júlio I em 15 de dezembro de 345. Todavia não há notícia de seu episcopado anteriormente a 354 quando, em uma carta do bispo Ambrósio de Milão, ele é elogiado por ter imposto ao clero de sua diocese vida comum, como para o monges, de acordo com o modelo das igrejas orientais: por este motivo, também é homenageado como o co-fundador de sua ordem por Cônegos Regulares de Santo Agostinho.
Ele dedicou-se com grande empenho à evangelização das zonas rurais e em grande parte pagãs. Fundou uma sociedade sacerdotal inspirada no modelo monástico da qual saíram importantes bispos e santos.
Eusébio defendeu a tese da "plena divindade de Jesus Cristo" frente à política ariana do imperador Constâncio II, para quem a fé ariana era politicamente mais interessante. Esta atitude custou-lhe o desterro e exílio primeiro para Citópolis, na Palestina, depois para a Capadócia e Tebaida, no Egito.
Este foi um momento difícil para a Igreja. Constâncio parecia esquecido há muito tempo era de tolerância e de paz iniciado por seu pai Constantino com o Edito de Milão. O Arianisno, condenado no Concílio de Niceia (325), sem o apoio do Imperador, havia desaparecido mas, no Sínodo de Arles (353), novamente triunfaria em seus conceitos. O Papa Libério recusara-se, no entanto, a adoção de um forma pacífica de resolver o problema vexatório.
O papa Libério, então envia-o junto com Lúcifer, bispo de Cagliari (início de 354), em uma missão junto ao Imperador Constâncio II para solicitar a convocação de um concílio para por fim à disputa entre os arianos (apoiado pelo próprio imperador ) e os seguidores da ortodoxia. Constâncio cedeu ao apelo e o concílio foi convocado em Milão em 355. Havia dois problemas básicos: o reconhecimento do credo adotado em Niceia e a defesa de Atanásio de Alexandria. Todavia o grupo ariano formado e dirigido por Valente de Mursa e Ursácio de Singiduno conseguiu que o concílio adotasse seus pré estabelecidos critérios. Assim como os bispos arianos, eram a maioria, Eusébio se recusou a assinar os decretos do concílio. Ele e outros resistentes como Ósio de Córdoba e Lúcifer de Cagliari, foram banidos. Eusébio foi confinado em Citópolis na Palestina (Betel St.), sob a supervisão do bispo ariano Patrófilo de Citópolis.
Apesar de tudo manteve sempre correspondência epistolar com a comunidade dos seus fiéis e nas suas cartas lhes pede que "saúdem também aqueles que estão fora da Igreja e que se dignam de nutrir por nós sentimentos de amor". A sua relação com a sua diocese não se limitava aos cristãos mas se estendia a todos os que de alguma forma reconheciam a sua autoridade espiritual ou o respeitavam como homem exemplar. Em suas correspondência relata aos fiéis pateticamente as lesões, violência e o abuso com que era tratado. Posteriormente foi transferido para a Capadócia e Tebaida superior, no Egito, onde pode conhecer melhor a alma do Oriente e seus estilos de vida.
Em fins de 361, com o morte de Constâncio II e o ascenso de Juliano, o Apóstata, os exilados puderam retornar ao local onde viviam anteriormente. Eusébio retorna à sua diocese. No ano seguinte 362, auxilia no Concílio de Alexandria, convocado por Atanásio, que decide por perdoar os bispos arianos que retornassem ao estado laical. Em seguida, nome da diocese, Eusébio partiu para uma visitação à Palestina e Síria para relatar sobre as decisões do Concílio de 362, decretar suas decisões e restaurar a fé. No ano de 363 ele retorna a Vercelli. Ele educou o clero de sua diocese com observância de regras monásticas, embora vivessem no meio da cidade, porque "o bispo e o clero deve compartilhar os problemas dos cidadãos de forma crível, cultivando ao mesmo tempo uma cidadania diversa: a do céu". Nos anos que se seguem, à frente do episcopado, juntamente com Hilário de Poitiers, ele enfrenta o semiarianismo (a doutrina homoianosiana) de Auxêncio de Milão, bispo de Mediolano que defendia a fórmula cristológica de Valente de Mursa e Ursácio de Singiduno, na qual o "... Filho era similar ao Pai, tanto "em todas as coisas" ou "de acordo com as escrituras..." Formula também defendida pelos acacianos, pelos prelados Demófilo de Constantinopla, bispo de Bereia (?-370) e Constantinopla (370-380) Germínio de Sirmio, Acácio de Cesareia, bispo de Cesareia (340-366), e aceita por Ósio de Córdoba e Aécio, patriarca de Antioquia.
Eusébio morreu nos primeiros dias de agosto, 371.
Obras
A luta contra o Arianismo preenchido toda a sua vida, mas não impediu que ele também foi um grande promotor do monaquismo no Ocidente. Ele próprio viveu como um membro de sua comunidade de sacerdotes.
A Enciclopédia Católica afirma o seguinte: Três curtas cartas de Eusébio foram publicadas na Pat. Lat de Migne. Jerônimo, em sua De Viris Illustribus (cap. 96 ) atribui a ele uma tradução para o latim dos comentários sobre os salmos, escrito originalmente em grego por Eusébio de Cesareia, obra que se perdeu. O Codex Vercellensis, preservado na catedral de Vercelli, é considerado o mais antigo manuscrito dos evangelhos em Latim antigo ("Codex A") e, acredita-se, foi escrito por Eusébio. Ele foi publicado por Irico (Milão 1748) e Bianchini (Roma 1749), foi reimpresso por Migne. E, por fim, uma nova edição foi publicada por Belsheim (Christiania 1894).
Das três cartas, reconhecidas como autênticas, são: a primeira ao imperador Constâncio, dando a conhecer o recebimento da notificação do Sínodo e anunciando que vai para Milão, a outra, já mencionada, é dirigida aos presbíteros e ao povo da Itália; segue junta desta o Exemplar libelli facti ad Patrophilum. A terceira a Gregório de Elvira. Parece que as informações recebidas a partir desta levou ao seu julgamento errôneo sobre a conduta de Ósio.
Se lhe atribui também o manuscrito dos Evangelhos (s. IV), que é preservado na catedral de Vercelli, de seis e uma tradução latina do Comentario a los Salmos de Eusébio de Cesareia. Da mesma forma, embora nenhuma base sólida, o Símbolo Quicumque ou Credo de Atanásio onde se afirma que Jesus "desceu ao inferno" também atribuída a Vicente de Lérins, Hilário de Poitiers e outros; uma extensa confissão de fé; os doze livros De Trinitate, que decorreu sob o nome de Santo Atanásio e que J. P. Migne atribue a Vigilio Thapse. M. Simonetti, contrário à hipótese Bulhart V. P. Schepens, nega que este trabalho seja anterior a Agostinho de Hipona.
Tempos modernos
Bento XVI sobre ele disse: O pastor e os fiéis da Igreja estão no mundo mas não são do mundo. Por isso, os pastores devem exortar a seus fiéis a não considerar as cidades do mundo como sua morada estável, mas a buscar a definitiva (…) Jerusalém celestial (…) Esta decisão permite aos pastores e aos fiéis a salvaguardar a escala justa de valores, sem dobrar-se nunca às modas do momento e às injustas pretensões do poder político. (…) Por isto, eusébio recomendava sempre aos seus fiéis "guardar com especial esmero a fé, manter a concórdia e a ser assíduos na oração".'' (Alocução de 17 de outubro de 2007, praça de S. Pedro - VISnews 071017)
A Igreja Católica celebrava a sua memória litúrgica em 16 de dezembro, mas o Papa Paulo VI em 1969, com a reforma do calendário litúrgico, transferiu a sua comemoração para o dia 2 de agosto como memória facultativa.
Ligações externas
Eusébio de Vercelli
Bispos católicos da Itália
Opositores ao arianismo
Santos do Império Romano
Romanos antigos do século III
Romanos antigos do século IV
Escritores em latim
Bispos do século IV | {
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L'édition 1998 du Trophée des champions est la édition du Trophée des champions. Le match oppose le Racing Club de Lens, champion de France 1997-1998 au Paris Saint-Germain Football Club, vainqueur de la Coupe de France 1997-1998 en battant en finale ces mêmes Lensois.
Le match arbitré par Gilles Chéron se déroule le au Stade de la Vallée du Cher à Tours devant spectateurs. Les Parisiens s'imposent sur le score de 1 à 0 grâce à un but de Yann Lachuer à la cinquante-quatrième minute, s'adjugeant ainsi leur deuxième Trophée des champions.
Feuille de match
Les règles du match sont les suivantes : la durée de la rencontre est de 90 minutes. S'il y a toujours match nul, une séance de tirs au but est réalisée. Trois remplacements sont autorisés pour chaque équipe.
Notes et références
1998
Événement sportif à Tours
Football en France en 1998
Sport en juillet 1998
Face-à-face du Paris Saint-Germain
Racing Club de Lens | {
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} | 9,226 |
\section{Introduction}
Let $f:X\to S$ be a proper, flat and finitely presented curve over an
arbitrary scheme (over $\operatorname{Spec}(\Bbb{Z})$) $S$. Let $G$ be
a split reductive group scheme over $\operatorname{Spec}(\Bbb{Z})$,
base changed to $S$, and $B$ a Borel subgroup of $G$. Let $D\subset X$
be a relatively ample effective Cartier divisor which is flat over
$S$, and set ${U}=X\setminus D$. Generalizing results of Drinfeld and
Simpson \cite{DS} for the case of smooth $f$, the following result was
proved in \cite[Theorem 1.4]{BF} without any conditions on the
singularities of $f$:
\begin{theorem}\label{triv3}
Let $P$ be a principal $G$-bundle on $X$ with $G$ semisimple and
simply connected. Then, after a surjective \'{e}tale base change
$S'\to S$, $P$ is trivial on $U_{S'}$.
\end{theorem}
Now suppose $G$ is semisimple, but not necessarily simply connected.
and. Triviality statements similar to the above are proved in
\cite[Theorem 1.5]{BF} but with stronger hypotheses: for example, in
characteristic zero, the Cartier divisor $D$ is not allowed to pass
through the singular locus of $f$, and $D$ is also assumed to be set
theoretically a union of sections of $f$ (and some other mild
conditions).
In this note, motivated in part by the article \cite{Sol}, we study
the analogue of Theorem \ref{triv3} for non-simply connected $G$. In
this case there is a natural obstruction to local triviality
constructed as follows:
Let $\widetilde{G}$ be the simply connected cover of $G$ and denote by
$\pi_1{(G)}$ the scheme theoretic kernel o the covering map
$\widetilde{G} \to G$. The central exact sequence of sheaves of groups
(on the fppf site of $X$),
$$1\to \pi_1(G)_X \to
\widetilde{G}_X \to {G}_X \to 1$$ gives
rise to a boundary map in fppf cohomology
\begin{equation} \label{bound}
H^1_{\fl}(X,G)\to
H^2_{\fl}(X, \pi_1(G)) \, .
\end{equation}
Therefore, from $P\in H^1_{\fl}(X,G)$, we get an element
$\alpha_P\in H^2_{\fl}(X, \pi_1(G))$\footnote{We note that for a
smooth group scheme, fppf cohomology is the same as etale
cohomology. In particular, if $|\pi_1(G)|$ is invertible in
$\mathcal{O}_S$, we may replace fppf cohomology by etale cohomology
throughout this paper.}. It is clear that if $P$ is trivial on $U$,
then $\alpha_P$ maps to zero in $H^2_{\fl}(U, \pi_1(G))$. Thus, for
the generalization of Theorem \ref{triv3} to hold for $P$, the
following property (L) must hold: \vspace{0.1in}
\begin{enumerate}
\item[(L)]There exists a surjective \'{e}tale morphism $S'\to S$
such that $\alpha_P$ maps to zero in $H^2_{\fl}(U_{S'}, \pi_1(G))$.
\end{enumerate}
\vspace{0.05in} We show that this property is nontrivial: For
$G=\operatorname{PGL}(m)$, we construct principal $G$-bundles on
families of curves $X\to S$ with nodal singularities, and $D$ passing
through the singularities of $f$, where property (L), so also the
direct generalization of Theorem \ref{triv3}, fails (Proposition
\ref{one}). These examples include cases when $S$ is a smooth curve,
and $X\to S$ is a family of smooth curves degenerating to curve with a
single nodal singularity and the divisor $D$ passes through the
node. Examples for other classical groups $G$ can be constructed using
similar methods.
Even though condition (L) is not always satisfied, we show in Lemma
\ref{lem:ff} that the weaker condition (L$'$) below often holds,
e.g., when $S$ is a smooth curve and $U$ is smooth over $S$:
\vspace{0.1in}
\begin{enumerate}
\item[(L$'$)]There exists a faithfully flat morphism $S'\to S$
such that $\alpha_P$ maps to zero in $H^2_{\fl}(U_{S'}, \pi_1(G))$.
\end{enumerate}
\vspace{0.05in}
We are thus faced with:
\begin{question}
Does condition (L$'$) always hold? If so, does there always exist a
faithfully flat morphism $S' \to S$ such that $P$ becomes trivial on
$U_{S'}$?
\end{question}
We do not know the answer to this in full generality. However, we
prove (Theorem \ref{thm:dim1}):
\begin{theorem} Let $f:X \to S$ be flat projective
curve, $D \subset X$ a relatively ample Cartier divisor which is
flat over $S$ and set $U = X \backslash D$. Let $G$ be a semisimple
group and let $P$ be a principal $G$-bundle on $X$. Assume further
that
\begin{enumerate}
\item $S$ is an excellent regular (purely) one dimensional scheme and
\item $U$ is smooth over $S$.
\end{enumerate}
Then there is a faithfully flat morphism $S' \to S$ such that $P$
becomes trivial on $U_{S'}$.
\end{theorem}
We also show in Proposition \ref{extensio} that for $G=\operatorname{PGL}(m)$,
and $P$ satisfying a condition weaker than (L), and $S$ smooth, $P$
lifts to a principal $\operatorname{GL}(m)$-bundle on $X$ (after an \'{e}tale
base change in $S$). This result generalizes to arbitrary groups, see
Remark \ref{marigold}.
\section{Consequences of condition (L)}
\subsection{The case $S$ is regular of dimension one}
\begin{lemma} \label{lem:pure} Let $U$ be a regular Noetherian scheme
and $D \subset U$ a closed subscheme. Let $V = U \backslash D$ and
let $\{D_i\}$ be the irreducible components of $D$ of codimension
one. Then for any integer $n > 0$, the kernel of the restriction
map $H^2_{\fl}(U, \mu_n) \to H^2_{\fl}(V, \mu_n)$ is the subgroup
generated by the first Chern classes of all $\mathcal{O}_U(D_i)$.
\end{lemma}
The lemma is well-known for etale cohomology, but we do not know a
reference for fppf cohomology so we give a proof.
\begin{proof}
We first note that for any scheme $U$, $H^1_{\fl}(U, \mathbb{G}_m)
= \Pic(U)$, and if $U$ is regular then $H^2_{\fl}(U, \mathbb{G}_m) =
\mathrm{Br}(U)$.
Consider the commutative diagram
\[
\xymatrix{ H^0_{\fl}(U, \mathbb{G}_m) \ar[r] \ar[d] & H^0_{\fl}(V,
\mathbb{G}_m) \ar[r] \ar[d] & H^1_{D,\fl}(U, \mathbb{G}_m) \ar[r]^{g_1}
\ar[d]^{c} & H^1_{\fl}(U, \mathbb{G}_m) \ar[r]^{g_2} \ar[d]^{c_U} &
H^1_{\fl}(V, \mathbb{G}_m) \ar[d]^{c_V} \\
H^1_{\fl}(U, \mu_n) \ar[r] \ar[d] & H^1_{\fl}(V, \mu_n) \ar[r]
\ar[d] & H^2_{D,\fl}(U, \mu_n) \ar[r] \ar[d] & H^2_{\fl}(U, \mu_n)
\ar[r] \ar[d] & H^2_{\fl}(V, \mu_n)
\ar[d] \\
H^1_{\fl}(U, \mathbb{G}_m) \ar[r]^{f_1} & H^1_{\fl}(V, \mathbb{G}_m)
\ar[r] & H^2_{D,\fl}(U, \mathbb{G}_m) \ar[r] & H^2_{\fl}(U,
\mathbb{G}_m) \ar[r]^{f_2} &
H^2_{\fl}(V, \mathbb{G}_m) \\
}
\]
where the rows come from the long exact sequence of cohomology with
supports and the columns from the Kummer sequence.
The map $f_1$ is surjective because $U$ is regular and the map $f_2$
is injective by \cite[Corollaire 1.10]{GBII}. This implies that $
H^2_{D,\fl}(U, \mathbb{G}_m) = 0$ so the map $c$ is surjective. The
claim then follows by a simple diagram chase, noting that the map
$c_U$ gives, by definition, the first Chern class of a line bundle on
$U$ and the kernel of $g_2$ (equal to the image of $g_1$) is precisely
the subgroup of $\Pic(U)$ generated by the $\mathcal{O}_U(D_i)$.
\end{proof}
\begin{lemma} \label{lem:ff} Let $f: U \to S$ be a smooth
morphism of relative dimension one with $S$ the spectrum of a
henselian dvr $R$ with quotient field $K$ and residue field
$k$. Given any element $\alpha \in H^2_{\fl}(U, \mu_n)$ there
exists a faithfully flat morphism $S' \to S$, with $S'$ also the
spectrum of a dvr, such that the pullback of $\alpha$ in $U_{S'}$ is
$0$.
\end{lemma}
If $R$ is excellent, or $n$ is invertible in $\mathcal{O}_S$, the proof
shows that $S' \to S$ can be chosen to be finite.
\begin{proof}
Let $U_0$ be the closed fibre of $f$ and set $V = U \backslash U_0$.
Since $V$ is an affine curve over $K$,
$H^2_{\fl}(V_{\overline{K}},\mu_n) = 0$. This follows from the
Kummer sequence, and the following facts for smooth curves $Y$ over an
algebraically closed field: The vanishing of $\mathrm{Br}(Y)$ (Tsen's theorem)
and, if $Y$ is affine, the surjectivity of multiplication by $n$ map on
$\Pic(Y)$ for $n>0$. It follows that there exists a
finite extension $K_1$ of $K$ so that the image of $\alpha$ in
$H^2_{\fl}(V,\mu_n)$ becomes $0$ in $H^2_{\fl}(V_{K_1},\mu_n)$. By
replacing $R$ by its integral closure $R_1$ in $K_1$ (which is still
a dvr), functoriality implies that we may assume $\alpha$ is in the
kernel of the restriction map
$ r: H^2_{\fl}(U,\mu_n) \to H^2_{\fl}(V,\mu_n) $.
Since $f$ is smooth, $U$ is regular, so by Lemma \ref{lem:pure} the
kernel of $r$ is spanned by the fundamental classes of the
irreducible components of $U_0$. Let $R \to R'$ be a finite map,
with $R'$ a dvr, such that the ramification degree is divisible by
$n$ and set $S' = \Spec(R')$. The
pullbacks of the Chern classes of all the components of $U_0$ become
divisible by $n$, hence are all $0$ in
$H^2_{\fl}(U_{S'},\mu_n)$. We conclude that $\alpha$ also becomes
$0$ in $H^2_{\fl}(U_{S'},\mu_n)$.
\end{proof}
Let $f:X\to S$ and $D$ be as in the introduction, $G$ an
arbitrary semisimple group and $P$ a principal $G$-bundle on $X$.
\begin{proposition}\label{afterT}
Assume
\begin{enumerate}
\item $S$ is an excellent regular (purely) one dimensional scheme
(e.g., a smooth curve over a field).
\item $X$ is reduced.
\item The closure of the non-regular locus of $U=X-D$ does not
intersect $D$; this is equivalent to assuming that the non-regular
locus of $U$ is finite over $S$, e.g., $U$ has isolated
singularities.
\item $\alpha_P$ is zero when restricted to $U$.
\end{enumerate}
Then there is a surjective \'{e}tale morphism
$S'\to S$ such that $P$ is trivial on $U_{S'}$.
\end{proposition}
\begin{proof}
For the sake of clarity we first deal with the case $U$ is regular. Let
$g:\widetilde{X}\to X$ be a resolution of singularities of $X$
\cite{Lipman}. By our assumptions $U$ is regular so we can assume
$U\subset \widetilde{X}$. Note that $\widetilde{X}\to S$ is flat
since $S$ is regular and one-dimensional.
We first show that $\widetilde{X}-U$ supports a relatively ample
Cartier divisor $\widetilde{D}$ (possibly non-effective). By
assumption $D$ supports a relatively ample divisor $D'$. A
resolution of singularities for $X$ can be obtained by iterating the
process of normalization and then blowing up the singular locus
(cf. \cite{Lipman}, and $X$ is excellent). Let the resulting
schemes be denoted by $X_0=X,X_1,\dots, X_s=\widetilde{X}$. We
build relatively ample Cartier divisors $D_r$ at each step of this
resolution $X_r$, $D_0=D'$, and finally set $\widetilde{D}=D_s$. For
the normalization step, we just pull back the Cartier divisor from
the previous step. For a resolution step $g:X_{r+1}\to X_r$, let
$E_{r+1}$ be the exceptional divisor of the blow up $g$. It is easy
to see that then ${D}_{r+1}=g^*(n{D}_r) - E_{r+1}$ is relatively
ample for $n$ sufficiently large (use \cite[Proposition
II.7.10]{Hartshorne}: We may assume that $D'$, and hence each $D_r$,
is actually ample since $S$ is affine).
Therefore, $\widetilde{X}-U$ supports a relatively ample Cartier
divisor $\widetilde{D}$ (possibly non-effective). Let
$L=\mathcal{O}_{\widetilde{X}}(\widetilde{D})$ be the corresponding
relatively ample line bundle on $\widetilde{X}$; it is trivial on
$U$.
Assume that $S$ is affine. By replacing $S$ by an \'{e}tale cover we
may assume that $P$ has a $B$-reduction, where $B$ is a Borel subgroup
of $G$, and then we may also assume (as in \S 3.2.2 of \cite{BF}) that
$P$ is induced from an $H$-bundle $E$, where $H$ is a maximal torus of
$B$.
Let $\widetilde{G}$ be the simply connected cover of $G$ and and let
$Z \cong \pi_1(G)$ be the kernel of the covering map
$\widetilde{G} \to G$. Let $\widetilde{H}$ be the maximal torus in
$\widetilde{G}$ mapping onto $H$, so $Z \subset \widetilde{H}$. We
have a commutative diagram
\[
\xymatrix{
1 \ar[r] & Z \ar[r] \ar[d] & \widetilde{H} \ar[r] \ar[d] & H \ar[r] \ar[d]
& 1 \\
1 \ar[r] & Z \ar[r] & \widetilde{G} \ar[r] & G \ar[r] & 1
}
\]
whose rows are exact sequences of group schemes. Since we have
assumed that $\alpha_P$ becomes $0$ on $U$, by the commutativity of
the diagram it follows that $E|_U$ lifts to a $\widetilde{H}$-bundle
$\tilde{E}_U$ on $U$. Since $\widetilde{H}$ is a torus and
$\widetilde{X}$ is regular, $\tilde{E}_U$ extends to a
$\widetilde{H}$-bundle $\widetilde{E}$ on $\widetilde{X}$ (this
follows from the fact that line bundles on $U$ extend to
$\widetilde{X}$).
Let $\widetilde{P}$ be the induced $\widetilde{G}$-bundle on
$\widetilde{X}$. Since $\widetilde{G}$ is simply connected, and
$\widetilde{X}-U$ supports a relatively ample Cartier divisor
$\widetilde{D}$, by (almost) the same argument as in \S 3.2.2 of
\cite{BF} (see Remark \ref{improv} below) we see that
$\widetilde{P}|_U$ is trivial, hence $P|_U$ is also trivial.
If $U$ is not regular, we employ the following strategy: We
choose a partial desingularization $\widetilde{X}\to X$ which is an
isomorphism over $U$, such that $\widetilde{X}$ is regular in a
neighborhood of $\widetilde{X}-U$. To see that such a partial
desingularization exists, first consider a full desingularization
$Q\to X$. We just carry out only those blow ups with support over
${X}-U$, and normalize only in neighbourhoods of inverse images of
$X-U$, and obtain $\widetilde{X}\to X$ which is an isomorphism over
$U$, with $\widetilde{X}$ regular on the complement of $U$.
\end{proof}
\iffalse
\begin{remark}
The proof actually shows a stronger result: Let $P$ be a principal
$\operatorname{PGL}(m)$-bundle on $U$ (and not on $X$). As before
$P$ gives a class in $H^2_{et}(U, \mu_m)$, assume this class is
zero. Also, assume that the singular locus of the surface $U$ is
finite over the smooth curve $S$. Then, locally in the Zariski
topology on $S$, $P$ is trivial on $U$.
\end{remark}
\fi
\begin{remark}\label{improv}
\cite[Theorem 1.4]{BF} can be generalized as follows: Let $S$ be an
arbitrary scheme over $\operatorname{Spec}(\Bbb{Z})$ and let
$f:X\to S$ be a proper, flat and finitely presented curve over
$S$. Let $E$ be a principal $G$-bundle on $X$ with $G$ semisimple
and simply connected. Let $U\subset X$ be an open subset, affine
over $S$, such that $X-U$ supports a relatively ample Cartier
divisor $D$ for $X\to S$ (possibly non-effective, whose components
need not be flat over $S$). Then, after a surjective \'{e}tale base
change $S'\to S$, $E$ is trivial on $U_{S'}$.
To prove this we need to slightly modify the proof of
\cite[Proposition 3.2]{BF} as follows: Assume $S$ is affine. We
twist by tensor powers of $L=\mathcal{O}(D)$ to find subbundles
$\mathcal{O}\subset E_i\tensor L^{\tensor{r}}$ with corresponding
quotients $T_i$, $i=1,2$. On the affine open subset
$U\subseteq {X}$, these extensions of vector bundles split, and $L$
is trivial. Therefore, restricted to $U$ we get
$E_i=\mathcal{O}\oplus T_i$, with $T_i$ a line bundle. But $T_i$ is
the determinant of $E_i$, hence $T_1$ and $T_2$ are isomorphic on
$U$.
\end{remark}
By combining Lemma \ref{lem:ff} and Proposition \ref{afterT} we
obtain:
\begin{theorem} \label{thm:dim1} Let $f:X \to S$ be flat projective
curve, $D \subset X$ a relatively ample Cartier divisor which is
flat over $S$ and set $U = X \backslash D$. Let $G$ be a semisimple
group and let $P$ be a principal $G$-bundle on $X$. Assume further
that
\begin{enumerate}
\item $S$ is an excellent regular (purely) one dimensional scheme and
\item $U$ is smooth over $S$.
\end{enumerate}
Then there is a faithfully flat morphism $S' \to S$ such that $P$
becomes trivial on $U_{S'}$.
\end{theorem}
\begin{proof}
Since $\pi_1(G)$ is a finite group scheme of multiplicative type, by
applying Lemma \ref{lem:ff} we may find a faithfully flat finite
type cover $S_1 \to S$, with $S_1$ also excellent regular and one
dimensional, such that $\alpha_P$ becomes $0$ on $U_{S_1}$. We then
apply Proposition \ref{afterT} to the induced morphism
$X_1^{red} \to S_1$, where $X_1:= X \times_S S_1$, to get an
\'{e}tale cover $S' \to S_1$ so that $P$ becomes trivial on
$U_{S'}$. The composition of the maps $S' \to S_1 \to S$ is the
desired faithfully flat map
\end{proof}
\subsection{Lifting to vector bundles}
A principal $\operatorname{PGL}(m)$-bundle $P$ on $X$ gives rise to a cohomology
class $\alpha_P\in H^2_{\fl}(X, \mu_m)$ as well a cohomology class
$\beta_P\in H^2_{et}(X, \Bbb{G}_m)$ ($= H^2_{\fl}(X, \Bbb{G}_m)$), by
considering the exact sequence of group schemes
$$1\to \Bbb{G}_{m} \to
{\operatorname{GL}}(m) \to {\operatorname{PGL}}(m)\to 1 \ .$$
Clearly $\alpha_P$ maps to $\beta_P$ under the natural map
$H^2_{\fl}(X, \mu_m)\to H^2_{et}(X, \Bbb{G}_m)$. It is easy to see
that $\beta_P$ represents the obstruction to lifting $P$
to a principal ${\operatorname{GL}}(m)$-bundle, i.e., a
vector bundle on $X$.
Condition (L) implies that $\beta_P$ maps to zero in
$H^2_{et}(U, \Bbb{G}_m)$, i.e., $P$ can be lifted to a vector
bundle on $U$. In fact, under somewhat mild conditions, $P$ can be
lifted to a vector bundle on $X$ after a surjective \'{e}tale base
change of $S$:
\begin{proposition}\label{extensio}
Assume $S$ is smooth, and the smooth locus of $X\to S$ is dense in
every fiber. If $\beta_P$ maps to zero in $H^2_{et}(U, \Bbb{G}_m)$,
then after an \'{e}tale base change in $S$, $P$ comes from a vector
bundle on $X$ and hence $\beta_P\in H^2_{et}(X, \Bbb{G}_m)$ becomes
zero.
\end{proposition}
\begin{proof}
After an \'{e}tale base change in $S$, we can find sections of
$X\to S$ such that their union is disjoint from $D$ and contained in
the smooth locus of $X\to S$. We can also assume that the union of
these sections is relatively ample. Let $U'\subset X$ be the
complement of these sections. Using \cite[Theorem 1.5]{BF}, we may
assume that $P$ is trivial on $U'$ after an \'{e}tale base change in
$S$. Lift this trivial $\operatorname{PGL}(m)$-bundle to a vector bundle $W$
on $U'$.
By assumption, $P$ comes from a vector bundle $V$ on $U$. Thus, we
have two $\operatorname{GL}(m)$-bundles $W$ and $V$ on $U'\cap U$ which
coincide as $\operatorname{PGL}(m)$-bundles. Let $L^*$ be the sheaf of
isomorphisms $V\to W$ which induce identity on the underlying
$\operatorname{PGL}(m)$-bundle. Clearly $L^*$ is a $\Bbb{G}_m$-bundle, let $L$
be the corresponding line bundle. Hence $W$ is isomorphic to
$V\tensor L$ on $U'\cap U$. Extend $L$ to a line bundle on $U$ ($U$
is smooth along $U-U'\cap U$ since $S$ is smooth and the sections
have images in the smooth locus of $X\to S$). Now glue the vector
bundle $V\tensor L$ (a vector bundle on $U$) with $W$ (a vector
bundle on $U'$) over $U'\cap U$, to get a vector bundle $A$ on $X$.
The $\operatorname{PGL}(m)$-bundle induced from $A$ equals $P$ which completes
the proof.
\end{proof}
The examples in Section \ref{cordes} all had $\beta_P=0$, i.e., came
from vector bundles on $X$. So $\beta_P=0$ is a lot weaker than
$\alpha_P=0$.
\begin{remark}\label{marigold}
The proof of Prop \ref{extensio} works more generally: For $G$ any
semisimple group (replacing $\operatorname{PGL}(m)$) let $G'$ be as in Lemma
\ref{lem:cover} below. For $P$ a principal $G$-bundle on $X$ we
get, as above, elements $\alpha_P\in H^2_{\fl}(X, \pi_1(G))$ and
$\beta_P\in H^2_{et}(X, K)$. Suppose $\beta_P$ maps to zero in
$H^2_{et}(U, K)$, which would be the case if $\alpha_P$ maps to zero
in $H^2_{\fl}(U, \pi_1(G))$ (i.e., if condition (L) holds). Then,
after an \'{e}tale base change in $S$, $P$ comes from a principal
$G'$-bundle on $X$ and hence $\beta_P\in H^2_{et}(X, K)$ becomes
zero.
\end{remark}
The following lemma is well-known, we give a proof for the convenience
of the reader.
\begin{lem} \label{lem:cover} For any semisimple group $G$ there
exists a reductive group $G'$ mapping surjectively to $G$ with
kernel a central torus $K$, and such that the derived group of $G'$
is simply connected.
\end{lem}
\begin{proof}
Let $\widetilde{G}$ be the simply connected cover of $G$ and let
$\widetilde{T}$ be any torus in $\widetilde{G}$ containing the
kernel $Z \cong \pi_1(G)$ of the covering map $\widetilde{G} \to G$.
Then we may take $G'$ to be
$(\widetilde{G} \times \widetilde{T}/Z)$, where $Z$ is embedded
diagonally. There is a natural map $G' \to G$ induced by projection
to the first factor and the kernel of this is $\tilde{T}$ (embedded
in $G'$ via the second factor). Moreover, the derived group of $G'$
is equal to $\widetilde{G}$ (embedded via the first factor). One
gets a somewhat canonical construction by taking $\widetilde{T}$ to
be a maximal torus
\end{proof}
\begin{remark}
There are many choices for $G'$, e.g., for $G = \mathrm{PGL}(m)$
(resp.~$\mathrm{PGSp}(2m)$) one may also take $G'$ to be
$\mathrm{GL}(m)$ (resp.~$\mathrm{GSp}(2m)$).
\end{remark}
\section{The examples}\label{cordes}
\subsection{}
By constructing examples where property (L) does not hold, we show
that Theorem \ref{triv3} fails if $G$ is not assumed to be simply
connected.
Let $S$ be a smooth curve over a field of characteristic zero (for
simplicity) and let $X \to S$ a family of projective curves with a
unique singular fibre over the point $s_0 \in S$ having an ordinary
double point at the point $x_0$ over $s_0$. Locally in the \'{e}tale
topology at $x_0$, the family looks like the surface with equation
$xy - z^{n+1} = 0$, for some $n >0$, with the map given by
$(x,y,z) \mapsto z$.
We assume that the family has a section $\sigma: S \to X$ not passing
through $x_0$ and we also assume that there is a section
$\tau:S \to X$ with $\tau(s_0) = x_0$. Such families with sections can
be constructed by base changing any family as above by a suitable map
$S' \to S$, with $S'$ also a smooth curve, factoring through $X$. Note
that the local class group at $x_0$ is $\Bbb{Z}/(n+1)\Bbb{Z}$ (use the
method of proof of \cite[Example II.6.5.2]{Hartshorne}), so
$D=(n+1)\tau(S)$ is a Cartier divisor which is flat and, as is easily
seen, relatively ample over $S$. Set $U=X-D$.
Let $L=\mathcal{O}_X(\sigma(S))$; for any positive integer $m$, the
first Chern class of $L$ gives a cohomology class
$c_1(L) \in H_{et}^2(X,\mu_m)$. Let $P$ be the
$\operatorname{PGL}(m)$ bundle on $X$ induced from the
$\operatorname{GL}(m)$-bundle $L\oplus
\mathcal{O}^{\oplus(m-1)}$.
Using the identification $\pi_1(G)= \mu_m$, it is easy to see that
$\alpha_P=c_1(L)\in H^2_{et}(X, \mu_m)$.
\begin{proposition}\label{one}
For suitable $m$ and $n$, $P$ is not trivial on $U_{S'}$ for any
\'{e}tale neighborhood $S'$ of $s_0$.
\end{proposition}
Let $S'$ be an \'{e}tale neighbourhood of $s_0\in S$. By functoriality of
the boundary map \eqref{bound} Proposition \ref{one} follows from
\begin{clm}\label{two}
For suitable $m$ and $n$, the class $c_1(L)$ restricts to a non-zero
class in $H_{et}^2(X_{S'}-\tau(S'),\mu_m)$.
\end{clm}
It suffices to prove this for $S = S'$, since \'{e}tale base change
does not alter any of the properties of the family $X \to S$.
\subsection{}
The singularity of $X$ at $x_0$ is \'{e}tale locally equivalent to
$xy -z^{n+1} = 0$, so of type $A_n$. The exceptional divisor of the
minimal resolution $Q$ consists of a chain of $n$ smooth rational
curves $E_1,E_2,\dots, E_n$, each with self-intersection $-2$ and with
$E_i$ intersecting $E_{i+1}$ transversely, $i= 1, \dots, n-1$; see
for example, \cite[III.7]{BPV}. The fibre $F$ over $s_0$, hence its
strict transform $\tilde{F}$, may or may not be irreducible; in the
latter case we write $\tilde{F_1}$ and $\tilde{F_2}$ for the
components. Locally the fibre corresponds to the curve $xy = 0$,
$z=0$, so its strict transform intersects $E_1$ and $E_n$
transversely (in a single point each). The strict transform
$\tilde{D}$ of $D = \tau(S)$ intersects the exceptional divisor in a
single point which must be smooth (since $Q$ is smooth), so lies on a
unique exceptional divisor $E_t$. Note that $t$ can be arbitrary:
if $S'$ is a smooth curve in $Q$ which intersects $E_t$ transversely
at a point $s_0'$ then $X' = S' \times_S X$ has a singular fibre over
$s_0'$ and a section which on the corresponding desingularization $Q'$
passes through $E_t'$. By considering tangent directions, one sees
that $\tilde{D}$ does not intersect $\tilde{F}$; $F$ and $D$ become
disjoint after a single blowup.
Let $C = \sigma(S)$ and $\tilde{C}$ its strict transform in $Q$. Let
$E = \cup_i E_i$, so we have $X - D = Q- \tilde{D}\cup E$. Note that
$H^2_{ \tilde{D}\cup E, et}(Q,\mu_m)$ is freely generated by the classes of
$\tilde{D}$ and all the $E_i$. Thus, using the Gysin sequence, it
suffices to show that the class of $\tilde{C}$ in $H_{et}^2(Q,\mu_m)$ is
not in the span of the classes of $\tilde{D}$ and the $E_i$. Assume
that we have an equation
\begin{equation}\label{class} [\tilde{C}] = a [\tilde{D}] + \sum_i
b_i[E_i]\in H_{et}^2(Q,\mu_m)
\end{equation}
We will get a contradiction, in certain cases, by using elementary
intersection theory. Each irreducible component $G$ of $E \cup \tilde{F}$
is a proper curve, so we have maps
\[
H_{et}^2(Q, \mu_m) \to H_{et}^2(G, \mu_m) \to \Bbb{Z}/m\Bbb{Z} ,
\]
where the first map is pullback and the second is the degree map
(which is an isomorphism). Moreover, the pullback map is compatible
with the restriction of line bundles or, equivalently, intersections
of divisors.
\subsubsection{}
Suppose $\tilde{F}$ is reducible. We may assume that $\tilde{C}$
passes through $\tilde{F}_1$, $\tilde{F}_1$ intersects $E_1$
and $\tilde{F}_2$ intersects $E_n$. Restricting both sides of
\eqref{class} to each of $\tilde{F}_1$, $\tilde{F}_2$ and all the
$E_i$ and using the degree isomorphisms, we get $n+2$ equations in
$n+1$ unknowns. We show below that this leads to a contradiction if
$m$ does not divide $t$, which will certainly be the case if $m>n$.
\begin{itemize}
\item Intersecting \eqref{class} with $\tilde{F}_1$, we get
$b_1=1$. Intersecting with $\tilde{F}_2$ gives $b_n=0$.
\item By induction, we may prove that if $i\leq t$, $b_i=i b_1$. These
equations are obtained by intersecting the two sides of
\eqref{class} by $E_1,\dots,E_{t-1}$. Therefore $b_t=tb_1$.
\item By descending induction from $i=n$, we can prove
that $b_{i}=0$ if $i\geq t$: The case $i=n$ is already
known. Intersecting with $E_n$ (if $t<n$) gives $b_{n-1}=2b_n$.
Intersect \eqref{class} with $E_{i}$ (if $i>t$) to get $b_{i-1}
-2b_i +b_{i+1}=0$, and hence $b_{i-1}=0$.
\end{itemize}
Therefore we have $b_t=tb_1=0\in \Bbb{Z}/m\Bbb{Z}$, and hence $t=0\in
\Bbb{Z}/m\Bbb{Z}$.
\subsubsection{}
Now suppose $\tilde{F}$ is irreducible.
We now intersect both sides of \eqref{class} with the classes of
$\tilde{F}$ and all the $E_i$ and then apply the degree isomorphisms,
getting $n+1$ equations in $n+1$ unknowns. As we show below these
equations imply that $t$ is a linear combination of $n+1$ and
$m$. Therefore, if the gcd of $n+1$ and $m$ does not divide $t$ (for
example, if $n+1$ divides $m$), we reach a contradiction.
\begin{itemize}
\item Intersecting \eqref{class} with $\tilde{F}$, we get
$b_1+b_n=1$.
\item By induction, we may prove that if $i\leq t$, $b_i=i b_1$. These
equations are obtained by intersecting the two sides of
\eqref{class} by $E_1,\dots,E_{t-1}$. Therefore $b_t=tb_1$.
\item By descending induction from $i=n$, we can prove that
that $b_{i}=(n-i+1)b_n$ if $i\geq t$: The case $i=n$ is already
known. Intersecting with $E_n$ (if $t<n$) gives $b_{n-1}=2b_n$.
Intersect \eqref{class} with $E_{i}$ (if $i>t$) to get $b_{i-1}
-2b_i +b_{i+1}=0$, and hence $b_{i-1}=(n-(i-1)-1)b_n$.
\end{itemize}
Therefore $b_t=tb_1= (n-t+1)b_n$, so $t(1-b_n)= (n-t+1)b_n$, hence
$b_n(n+1)=t$. We thus see that $t$ is a linear combination of $n+1$
and $m$.
\subsection{}
Let $X \to S$ be a family of curves as at the beginning of this
section and let $f: Q \to S$ be the minimal desingularization of
$X$. Let $S^{sh}$ be the strict henselisation of $S$ at $s_0$ and
$Q^{sh} = Q \times_S S^{sh}$. By the proper base change theorem, the
restriction map $H_{et}^2(Q^{sh}, \mu_m) = H_{et}^2(X_0, \mu_m)$ is an
isomorphism, where $X_0$ is the (geometric) fibre of $f$ over
$s_0$. Now $H_{et}^2(X_0, \mu_m)$ is a free $\Bbb{Z}/m\Bbb{Z}$-module
with basis the irreducible components of $X_0$, i.e., the $E_i$ and
$\tilde{F}$ (or $\tilde{F}_1$ and $\tilde{F}_2$). It follows from this
that for any $\alpha \in H_{et}^2(Q, \mu_m)$, if the numerical
equations obtained by intersecting both sides of an equality
\begin{equation}
\label{class2} \alpha = a [\tilde{D}] + \sum_i
b_i[E_i]\in H_{et}^2(Q,\mu_m)
\end{equation}
with the $E_i$ and $\tilde{F}$ (or $\tilde{F}_1$ and $\tilde{F}_2)$)
can be solved, then in fact \eqref{class2} itself can be solved (for
the pullbacks) in $H_{et}^2(Q^{sh}, \mu_m)$, so also when pulled back
to some \'{e}tale neighbourhood $S'$ of $s_0 \in S$. In particular,
this applies to $[\tilde{C}]$ as above.
\section{Acknowledgements}
We thank P.~ Solis for useful communication
(in 2016).
\begin{bibdiv}
\begin{biblist}
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EDITION = {Second},
PUBLISHER = {Springer-Verlag, Berlin},
YEAR = {2004}
PAGES = {xii+436},
}
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}
\bib{DS} {article}{
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}
\bib{Hartshorne}{book} {
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PAGES = {xvi+496},
}
\bib{Lipman}{article} {
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PAGES = {151--207},
}
\iffalse
\bib{L}{article} {
AUTHOR = {Lieblich, M.},
TITLE = {Twisted sheaves and the period-index problem},
JOURNAL = {Compos. Math.},
FJOURNAL = {Compositio Mathematica},
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\fi
\bib{Sol}{article}{
AUTHOR = {Solis, P.},
TITLE = {Nodal Uniformization of G-bundles},
NOTE ={arXiv:1608.05681},
}
\end{biblist}
\end{bibdiv}
\vspace{0.05 in}
\noindent
P.B.: Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599, USA\\
{{email: belkale@email.unc.edu}}
\vspace{0.08 cm}
\noindent
N.F.: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India\\
{{email: naf@math.tifr.res.in}}
\vspace{0.08 cm}
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 119 |
Here's your chance to make that conviction go up in smoke.
Chittenden and Windsor counties will both hold expungement clinics next month to help wipe clean the records of people who have been convicted of misdemeanor marijuana possession.
The events — June 9 in South Royalton and June 12 in Burlington — come weeks before possessing and growing small amounts of marijuana becomes legal in Vermont. Volunteers with the Center for Justice Reform at the Vermont Law School will help attendees fill out an expungement petition, which both Chittenden County State's Attorney Sarah George and Windsor County State's Attorney David Cahill have vowed to support.
"This does not apply to felony-level offenses, convictions for sale of marijuana, or any offenses that took place outside of Windsor or Chittenden County," Vermont Law School spokesperson Ben Jervey said in a press release.
A bill in the Vermont legislature this year would have "fast-tracked" such expungements, but it died in committee.
Robert Sand, director of the Vermont Law School's Center for Justice Reform, mentioned in February the possibility of a running an expungement clinic on the county level with George and Cahill. The plan has the endorsement of Vermont Attorney General T.J. Donovan.
Expungement Day for Windsor County convictions will be held from 9 a.m. to noon, Saturday, June 9, in Oakes Hall, Room 012 at VLS. Expungement Day for Chittenden County convictions will be held from 9 a.m. to 4 p.m., Tuesday, June 12, in Courtroom 2C of the Costello Courthouse at 32 Cherry Street in Burlington. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,887 |
Subalaya is a town in the Birmaharajpur subdivision of Subarnapur district, Odisha, India. It is located on an island in size at the confluence of the Mahanadi river and Surubalijora.
This town is home to Subalaya High School and Subalaya College.
References
Cities and towns in Subarnapur district
Islands of Odisha | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,341 |
Borne out of Arts and Health in 2009, the Express Your Voice Choir met weekly, September through June for over six years. Almost 200 older adults from various cultural backgrounds, speaking many different languages and from all walks of life, raised their voices in this project. Under the direction of vocalist and composer DB Boyko, the choir performed their original collaborative work for the VOICE OVER mind Festival, The Memory Festival, Music on Main's Modulus Festival, Tiny Talent Biltmore Cabaret, Sound of Dragon Festival and, of course, at the Arts and Health Project Gala every year.
Many choir members had no previous musical experience, but as they worked together, they came to understand the importance of sharing life stories as a way to build community through the power and connectivity of music. The group explored their bodies as vessels for sound production. They came to know their creative capacities – articulating their personal stories with nuance to become universal ideas in poetry and song. They became opinionated about their work and confident in their ideas. Unabashed about expressing their voices in song and laughter, they learned to whisper and they learned to roar.
Express Your Voice culminated in 2015 with the production of a CD of their work made in collaboration with Vancouver's Now Orchestra and a concert/CD Launch in June 2015. You can listen to this today on the headset available in the exhibit. The concert and recording were made possible thru support from BC Arts Council, Canada Council, Roundhouse Community Centre Association, Western Front New Music and NOW Society.
Singing has continued with Arts & Health at the Roundhouse with Backpocket Songs. If you are interested in participating in seniors arts programming at Roundhouse Community Centre, please contact Diana Vanderveen.
"I have talked to many participants over the years and I know that this workshop improves their mental health. It makes them happier; it brings socialization in to their lives."
"Participants are gaining an enormous amount of confidence within themselves through this workshop and gaining confidence can only benefit your health."
"Someone recommended the program to me but I said well I can't go because I can't sing but they said don't worry about it, this isn't about singing…we learn about breathing and being aware of your body. So my friends persuaded me to come and I love it. In terms of health…my mother had COPD (chronic obstructive pulmonary disorder) and this is wonderful in terms of learning how to breathe properly …it's just terrific because I can feel my whole body filling up with oxygen and it also relieves a lot of my muscle and joint pain."
"This class is very interactive and it involves not just singing. At one point I remember we were taking our blood pressure and comparing our blood pressure before and after our class. I find it affects my health greatly because I walk to this class from my house so it allows me to be active physically as well."
"I never sang in my life. I'm 86 so it's rather late to start something like this. Maybe it will help me to last a little longer! At this stage of my life it's very enjoyable to experience something new." | {
"redpajama_set_name": "RedPajamaC4"
} | 8,671 |
Q: While loops - python new to python and need some help with while loop that causing me some issues.
I am creating a simple converter.
def converter():
x = 1
while x == 1:
q_1 = input ('please choose the currency you wish to convert: \
a) US Dollar\
b) Euro\
c) Shekel ')
if q_1.lower() is ('a' or 'b' or 'c'):
x += 1
x = 1
q_2 = False
while q_2 is False:
q_2 = input ('please choose the currency you wish to convert to:\
a) US Dollar\
b) Euro\
c) Shekel ')
if q_2.lower() is not ('a' or 'b' or 'c'):
q_2 = False
print ('end for now')
For some reason the first loop is not working. Whatever I input, whether its a,b,c lower or upper or a wrong answer (for example: d,e,f...) it returns the same q_1, Its not moving on to the next block of code even if the input is correct (=a,b,c).
Thanks
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,026 |
{"url":"https:\/\/www.encyclopediaofmath.org\/index.php?title=Affix_of_a_complex_number&oldid=30622","text":"Affix of a complex number\n\n(diff) \u2190 Older revision | Latest revision (diff) | Newer revision \u2192 (diff)\n\nLet $z=a+ib$ in its geometric representation. Affix is the point in the complex plane corresponding to this number, i.e. the point with Cartesian coordinates $(a,b)$. The affix is sometimes identified with the complex number itself.\n\nHow to Cite This Entry:\nAffix of a complex number. Encyclopedia of Mathematics. URL: http:\/\/www.encyclopediaofmath.org\/index.php?title=Affix_of_a_complex_number&oldid=30622","date":"2019-09-18 07:50:23","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\": 0.8878916501998901, \"perplexity\": 2274.709620299293}, \"config\": {\"markdown_headings\": false, \"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-2019-39\/segments\/1568514573258.74\/warc\/CC-MAIN-20190918065330-20190918091330-00476.warc.gz\"}"} | null | null |
\section{Introduction}
Each object-oriented programming language offers its own set of objects, classes, types, functions, constants, traits, templates, and so on, which programmers can use off-the-shelf to model their specific use cases:
``Development Kit'' in Java,
``Standard Library'' in C++, Python, Swift, Rust, and Ruby,
``.NET Standard'' in C\#,
``Built-in Objects'' in JavaScript,
and so on.
Each Standard Library (SL) freely defines its own principles of abstraction. For example, to get an absolute value of a numeric object \ff{x} in Java, one has to call a static method of another class \ff{Math.abs(x)}, while in Ruby it would be a property of the same object \ff{x.abs}. For example, in Java, an attempt to get a value from a hash map by a key will produce \ff{null} in case of its absence, while in C++ it will return an empty iterator. There are many similar examples demonstrating the absence of common ground between SLs.
As a humble attempt to create such a common ground for the world of objects, we suggest our own taxonomy of objects for EO\footnote{\url{https://www.eolang.org}}, a strictly formal~\citep{kudasov2021} object-oriented programming language with an intentionally reduced feature set~\citep{bugayenko2021eolang}. All objects are grouped as such:
\begin{itemize}
\item Primitives (\cref{sec:primitives})
\item Array (\cref{sec:array})
\item Error handling (\cref{sec:errors})
\item Flow control abstractions (\cref{sec:flow})
\item Non-standard bit-width numbers (\cref{sec:digits})
\item Memory abstractions (\cref{sec:memory})
\item Math functions and algorithms (\cref{sec:math})
\item String manipulations (\cref{sec:strings})
\item Collections (\cref{sec:collections})
\item I/O Streams (\cref{sec:streams})
\item File System abstractions (\cref{sec:fs})
\item Net Sockets (\cref{sec:sockets})
\item HTTP request and response (\cref{sec:http})
\item Synchronization in multi-threading (\cref{sec:synchronization})
\end{itemize}
An object in EO is either a composition of other objects or an atom, which is a foreign function interface to a lower-level runtime such as, for example, JVM or Assembly. In this paper, we denote atoms by a star, for example: \aff{times}.
Everywhere in the paper we use dark blue color to highlight an object when it's mentioned for the first time.
In this paper\footnote{%
\LaTeX{} sources of this paper are maintained in
\href{https://github.com/objectionary/on-the-origin-of-objects}{objectionary/on-the-origin-of-objects} GitHub repository,
the rendered version is \href{https://github.com/objectionary/on-the-origin-of-objects/releases/tag/0.3.0}{\ff{0.3.0}}.}
we don't provide exact specification of each object, in order to avoid
conflicts with their exact definitions in Objectionary\footnote{\url{https://www.objectionary.com}}.
\section{Principles}
We adhere to a few principles:
\begin{itemize}
\item We tend to minimize the global scope, keeping the number of global objects to the absolute possible minimum.
\item Wherever possible, objects must be implemented in EO, instead of being atoms.
\item There should be no functionality implemented two or more times in the entire taxonomy.
\item Object names must not be abbreviated and must constitute an English sentence when being used through dot notation, for example:
\begin{ffcode}
x.times.y > z
\end{ffcode}
means ``$x$ times $y$ is $z$.''
There are a few exceptions though, like \ff{eq}, \ff{seq}, \ff{lt}, and a few others.
\end{itemize}
In case of any runtime error, an object is supposed to ``return'' an error object, with \ff{message} attribute present (as \ff{string}) and \ff{@} attribute absent.
\section{Primitives}\label{sec:primitives}
There are five primitive data objects described below. All of them have \adeff{as-bytes} attribute, which is an abstraction of their representation as a sequence of bytes.
All primitives also have \deff{as-hash} attribute, which, being an \ff{int}, is their own implementation of a hash function.
They also have \deff{eq} attribute, which is \ff{TRUE} if the primitive is equal to another object, through the use of \ff{\^{}.as-bytes.eq}.
\subsection{Bytes}
The center of the taxonomy is \deff{bytes} data object, which is an abstraction of an sequence of bytes. The sequence can either be empty or contain an theoretically unlimited number of bytes. A byte is a unit of information that consists of eight adjacent binary digits (bits), each of which consists of a 0 or 1. In EO syntax a sequence of bytes is denoted as either \eohex{--} (double dash) for an empty one or as a concatenation of \eohex{xx-}, where \ff{xx} is a hexadecimal representation of a byte.
The object \ff{bytes} has these four attributes, to turn itself into one of four primitive data objects:
\adeff{as-int},
\adeff{as-bool},
\adeff{as-float},
and
\adeff{as-string}. The attribute \aff{as-int} expects the size of the sequence to be less or equal to eight. The attribute \aff{as-bool} is \ff{FALSE} only if all bytes equal to zero. The attribute \aff{as-float} expects exactly eight bytes.
There are also attributes for bitwise operations:
\adeff{and},
\adeff{or},
\adeff{xor},
\adeff{not},
\adeff{left},
and
\adeff{right}.
The object also has attribute \adeff{eq} for comparing itself with another sequence of bytes.
The attribute \adeff{size} is the total number of bytes in the sequence.
The attribute \adeff{slice} represents a sub-sequence inside the current one.
The attribute \adeff{concat} is a new sequence, which is a concatenation of two byte sequences: the current and the provided one.
\subsection{Int}
The object \deff{int} is an eight-bytes abstraction of a two's complement signed integer in a big-endian order.
The attribute \adeff{plus} is a summary of this number and another \ff{int}.
The attribute \deff{minus} is a subtraction of another \ff{int} from this number.
The attributes \adeff{times} and \adeff{div} are a multiplication and a division of this number and another \ff{int}.
The attribute \deff{neg} is the same number with a different sign.
The attribute \adeff{lt} is a \ff{bool} object \ff{TRUE} if it's ``less than'' another \ff{int} and \ff{FALSE} otherwise. Attributes \deff{gt}, \deff{lte}, and \deff{gte} are ``greater than,'' ``less than or equal,'' and ``greater than or equal'' comparisons respectively.
Integers with a different bit-width are explained in \cref{sec:digits}.
All other manipulations with integers can be done in their decorators. Some of them are explained in \cref{sec:math}.
\subsection{Bool}
The object \deff{bool} is a one-bit abstraction of a Boolean value. Its \aff{as-bytes} is either \eohex{00-} or \eohex{01-}.
There are two pre-defined objects \deff{TRUE} and \deff{FALSE}.
The attribute \deff{not} is a Boolean inversion. Attributes \deff{and}, \deff{or}, \deff{xor} are logical conjunction, disjunction, and exclusive disjunction of the object itself with an a array of other Boolean values; they use \aff{and}, \aff{or}, and \aff{xor} from \ff{\^{}.as-bytes} respectively.
The attribute \adeff{if} is a branching mechanism, expecting three arguments: a condition as \ff{bool}, a ``positive'' object, and a ``negative'' object. When being dataized, the object \aff{if} first dataizes the condition and then, according to the result obtained, either dataizes the positive object or the negative one, returning the result as a result of its own dataization. Both positive and negative objects must be copies of the same abstract object. This code give a title to a random number:
\begin{ffcode}
QQ.io.stdout
QQ.txt.sprintf
"Coin toss:
if.
QQ.math.random.pseudo.gte 0.5
"heads"
"tail"
\end{ffcode}
The attribute \adeff{while} is an iterating mechanism, expecting two attributes: a condition as \ff{bool} and an abstract object with one free attribute. When being dataized, the object \aff{while} first dataizes the condition and then either stops if it is \ff{FALSE} or dataizes the abstract object with an \ff{int} equal to the number of the iterating cycle. This code makes a few attempts to find a random number that is smaller than 0.1:
\begin{ffcode}
while.
QQ.math.random.pseudo.gte 0.1
[i]
QQ.io.stdout > @
QQ.txt.sprintf
"Attempt
\end{ffcode}
\subsection{Float}
The object \deff{float} is an abstraction of a floating point number, which takes eight bytes and fills them up according to the format suggested by \citet{ieee754}.
The attribute \adeff{plus} is a summary of this number and another \ff{float}.
The attribute \deff{minus} is a subtraction of another \ff{float} from this number.
The attributes \adeff{times} and \adeff{div} are a multiplication and a division of this number and another \ff{float}.
The attribute \deff{neg} is the same number with a different sign.
The attribute \adeff{lt} is a \ff{bool} object \ff{TRUE} if it's ``less than'' another \ff{float} and \ff{FALSE} otherwise. Attributes \deff{gt}, \deff{lte}, and \deff{gte} are ``greater than,'' ``less than or equal,'' and ``greater than or equal'' comparisons respectively.
Floating-point numbers with a different bit-width are explained in \cref{sec:digits}.
All other manipulations with floating-point numbers can be done in their decorators. Some of them are explained in \cref{sec:math}.
\subsection{String}
The object \deff{string} is an abstraction of a piece of Unicode text in UTF-8 encoding, according to \citet{unicode}. UTF-8 uses one byte for the first 128 code points, and up to 4 bytes for other characters.
The attribute \adeff{slice} takes a piece of a string as another \ff{string}. The attribute \adeff{length} is a total count of characters in the string.
Strings in other encodings, such as UTF-16 or CP1251, may be implemented through direct manipulations with \ff{bytes}.
All other manipulations with strings are explained in \cref{sec:strings}.
\section{Array}\label{sec:array}
The object \deff{array} is an abstraction of an immutable sequence of objects. For example, this code represents a two-dimensional array \ff{x} of numbers and strings:
\begin{ffcode}
* > x
* "green" 0x0D1
* "red" 0xF21
* "blue" 0x11C
\end{ffcode}
The attribute \adeff{with} is a new \ff{array} with all elements from the current array and a new element added to the end of it.
The attribute \adeff{at} is the $i$-th element of the array.
The attribute \adeff{length} is the total amount of elements in the array.
All other manipulations with arrays can be implemented in their decorators. Some of them are explained in \cref{sec:collections}.
\section{Error Handling}\label{sec:errors}
Here we define objects that help handle errors and exceptional situations.
The object \adeff{error} causes program termination at the first attempt to dataize it.
It encapsulates any other object, which can play the role of an exception that is
floating to the upper level:
\begin{ffcode}
[x] > d
if.
x.eq 0
error "Can't divide by zero"
42.div x
\end{ffcode}
The object \adeff{try} enables catching of \aff{error} objects and extracting exceptions from them.
For example, the following code prints "division by zero" and then "finally":
\begin{ffcode}
try
[]
42.div 0 > @
[e]
QQ.io.stdout > @
e
[]
QQ.io.stdout > @
"finally"
\end{ffcode}
\section{Flow Control}\label{sec:flow}
Here we define objects that help control dataization flow.
The object \adeff{seq} is an abstraction of sequence of objects to be dataized sequentially. For example, this code prints one message to the console and then terminates the program due to the inability to dataize the division by zero in the middle:
\begin{ffcode}
seq
QQ.io.stdout "Hello, world!
42.div 0
QQ.io.stdout "Bye!"
\end{ffcode}
The object \adeff{goto} enables forward and backward ``jumps'' either immediately finishing dataization or restarting it. For example, this code won't print a message to the console if \ff{x} is equal to zero:
\begin{ffcode}
goto
[g]
seq > @
if. > y
x.eq 0
g.forward 0
42.div x
QQ.io.stdout
QQ.txt.sprintf "42/x =
\end{ffcode}
In this example, the number will be read from the console again, if it's equal to zero:
\begin{ffcode}
goto
[g]
seq > @
as-int. > x
QQ.txt.parsed
QQ.io.stdin
if.
x.eq 0
g.backward
QQ.io.stdout
QQ.txt.sprintf
"Number
\end{ffcode}
The object \deff{switch} is an abstraction of a multi-case branching that encapsulates $(k, v)$ pairs and the dataization result is equal to $v$ of the first pair where $k$ is \ff{TRUE}, while the last pair is the one to be used if no other pairs match:
\begin{ffcode}
QQ.io.stdout
switch
*
password.eq "swordfish"
"password is correct!"
*
password.eq ""
"empty password is not allowed"
*
FALSE
"password is wrong"
\end{ffcode}
\section{Digits}\label{sec:digits}
Here we define objects that represent numbers with smaller or larger bitwise width comparing with the default 64-bits convention.
All objects presented in this Section belong to \ff{QQ.digits} package.
Objects \deff{int8}, \deff{int16}, \deff{int32}, and \deff{int128} are decorators of \ff{bytes} with a predefined size. They implement the same numeric operations as \ff{int}.
Objects \deff{float16}, \deff{float32}, and \deff{float128} are also decorators of \ff{bytes}, implementing the same operations as \ff{float}.
\section{Memory}\label{sec:memory}
Here we define objects that manage memory.
The object \adeff{memory} is an abstraction of a read-write memory capable of storing one of five primitive data objects mentioned in \cref{sec:primitives}. The attribute \adeff{write} implements writing operation, while the object \aff{memory} itself decorates the data object stored in it. This code writes a number into memory and then reads it back and prints:
\begin{ffcode}
memory 0 > m
seq
m.write 42
QQ.io.stdout
QQ.txt.sprintf "Memory contains
\end{ffcode}
The object \adeff{cage} is similar to \aff{memory}, but it can store any object, not only five primitives. The use of \aff{cage} is strongly discouraged. The following code stores a ``book'' in a \aff{cage}, then retrieves it back, and prints one of its attribute:
\begin{ffcode}
[] > book
title > "Object Thinking"
author > "David West"
cage 0 > c
seq
c.write book
QQ.io.stdout
QQ.txt.sprintf
"Title is
\end{ffcode}
The object \deff{ram} is an abstraction of a random-access memory of certain size. It behaves like \ff{bytes}, but has an additional attribute \adeff{write}. In this example, one kilobyte of memory with random data is allocated when a copy of \ff{ram} is created, a non-copying slice \ff{s} of 13 bytes is made starting with the 200-th byte, data is written into it, then a non-copying sub-slice is created of only five bytes, and finally a string is read back and \ff{"Hello"} is printed:
\begin{ffcode}
ram 1024 > r
seq
write.
r.slice 200 13 > s
"Hello, world!".as-bytes
QQ.io.stdout
as-string.
s.slice 0 5
\end{ffcode}
The object \deff{heap} encapsulates a copy of \ff{ram} and is an abstraction of a memory management as it exists in \citet{posix}. There are two attributes \deff{malloc} and \deff{free}, which allocate and free memory blocks respectively. An allocation of a memory block creates a copy of \deff{heap.pointer} object, which is a decorator of \ff{int} with two additional attributes \deff{write} and \deff{read}.
In this code, 13 bytes are allocated, a string is stored into them, then read and printed, and then the bytes are freed:
\begin{ffcode}
heap (ram 1024) > h
seq
h.malloc > p
p.write "Hello, world!"
QQ.io.stdout
(p.read 13).as-string
h.free p
\end{ffcode}
\section{Math}\label{sec:math}
Here we define objects that represent math functions and algorithms.
All objects in this Section belong to \ff{QQ.math} package.
The object \deff{random} is a abstraction of a random \ff{float} between zero and one inclusively. It has an additional attribute \adeff{pseudo} that makes \ff{random} with a pseudorandom seed.
The object \deff{angle} is a decorator of \ff{float}. It assumes that the angle is in radians and has the following attributes for trigonometric functions:
\deff{sine}, \deff{cosine}, and \deff{tangent}. There are attributes \deff{as-degrees} and \deff{as-radians} for switching from radians to degrees and backwards.
The object \deff{number} is a decorator of \ff{int} and \ff{float} with the following additional attributes:
\begin{itemize}
\item \deff{abs}: absolute value of itself ($|\rho|$)
\item \deff{ceil}: round itself up
\item \deff{floor}: round itself down
\item \deff{ln}: natural logarithm ($\ln \rho$)
\item \deff{log}: logarithm ($\log_x \rho$)
\item \deff{max}: the greater of itself and another number
\item \deff{min}: the smaller of itself and another number
\item \deff{power}: itself raised to the power ($\rho^x$)
\item \deff{signum}: the sign of itself
\item \deff{sqrt}: square root of itself ($\sqrt\rho$)
\end{itemize}
\section{Strings}\label{sec:strings}
All objects presented in this Section belong to \ff{QQ.txt} package.
The object \deff{sscanf} encapsulates a format \ff{string} and a content \ff{string}. It behaves like an array of scanned data objects. For example, this code parses a hexadecimal number from the console:
\begin{ffcode}
at.
QQ.txt.sscanf
QQ.io.stdin
0
\end{ffcode}
The object \deff{sprintf} builds a string according to the format provided and compliant with \citet[Chapter 5]{posix}, for example:
\begin{ffcode}
QQ.txt.sprintf
"Hi,
"Jeff"
3.14
\end{ffcode}
The object \deff{text} is a decorator of a \ff{string}, it has the following attributes:
\begin{itemize}
\item \deff{contains}: checks whether it contains $x$
\item \deff{ends-with}: checks whether it ends with $x$
\item \deff{index-of}: finds the first occurence of a sub-string
\item \deff{join}: joins an array with this one as a glue
\item \deff{lower-case}: makes it lower case
\item \deff{last-index-of}: finds the last occurence of a sub-string
\item \deff{left-trim}: removes leading spaces
\item \deff{replace}: finds and replaces a sub-string
\item \deff{right-trim}: removes trailing spaces
\item \deff{split}: breaks it into an array of strings
\item \deff{starts-with}: checks whether it starts with $x$
\item \deff{trim}: removes both leading and trailing spaces
\item \deff{upper-case}: makes it upper case
\end{itemize}
The object \deff{regex} is an abstraction of a regular expression, in accordance with \citet[Part~2]{posix} (Extended Regular Expressions) and full support of Unicode. The attribute \deff{match} is a split of the \ff{string} into parts:
\begin{ffcode}
QQ.txt.regex "/(и([^ ]+))/i" > r
r.match > m
"Из искры возгорится пламя"
eq.
m
*
*
"Из"
0
*
"И"
* "з" 1 *
* " "
*
"искры"
3
*
"и"
* "скры" 4 *
* " возгор"
*
"ится"
15
*
"и"
"тся" 16 *
* " пламя"
\end{ffcode}
\section{Collections}\label{sec:collections}
Here we discuss abstractions of lists, maps, sets, and other ``collections.'' All objects presented in this Section belong to \ff{QQ.collections} package.
\subsection{List}
The object \deff{list} is a decorator of \ff{array}.
The attribute \deff{is-empty} is \ff{TRUE} if the length of the array is zero.
The attribute \deff{eq} is \ff{TRUE} if each element of the array is equal to the corresponding element of another array and the lengths of both arrays are the same.
The attribute \deff{without} is a new array with the $i$-th element removed.
The attributes \deff{each}, \deff{reduced}, \deff{found}, \deff{filtered}, and \deff{mapped} are respectively similar to \ff{forEach}, \ff{reduce}, \ff{find}, \ff{reduce}, and \ff{map} methods of \ff{Array} object in JavaScript~\citep{EcmaScript}. A few ``twin'' attributes \deff{eachi}, \deff{reducedi}, \deff{filteredi}, \deff{foundi}, and \deff{mappedi} are semantically the same, but with an extra \ff{int} argument as a counter of a cycle.
The attribute \deff{slice} is a part of the array.
The attribute \deff{sorted} is a new array with elements sorted using given comparison abstract object with two free attributes.
The attribute \deff{reversed} is a new array with elements positioned in a reverse order.
\subsection{Map}
The object \deff{map} is a decorator of \ff{array} of pairs $(k, v)$. The \ff{map} ensures that all $k$ are always unique. It is expected that each $k$ has \ff{as-hash} attribute that behaves as \ff{int}.
The attributes \ff{with}, \ff{without}, \ff{found}, and \ff{foundi} are reimplemented in \ff{map}.
\subsection{Set}
The object \deff{set} is a decorator of \ff{array}. The \ff{set} ensures that all elements in the array are always unique. It is expected that each $k$ has \ff{as-hash} attribute that behaves as \ff{int}.
The attributes \ff{with}, \ff{without}, \ff{found}, and \ff{foundi} are reimplemented in \ff{set}.
\subsection{Mutable Arrays}
The objects \deff{array-list} and \deff{linked-list} are the abstractions of mutable lists that behave like \ff{array}. They have three additional attributes: \deff{inject}, \deff{replace}, and \deff{extract}. They encapsulate \aff{cage} object.
\section{I/O Streams}\label{sec:streams}
Here we define manipulations with input and output streams. All objects presented in this Section belong to \ff{QQ.io} package.
It is expected that an input stream has the following interface:
\begin{ffcode}
[] > input
data > @
[max-count] > read /input
[] > close
\end{ffcode}
It is expected that an output stream has the following interface:
\begin{ffcode}
[] > output
[bytes-to-write] > write /input
[] > close
\end{ffcode}
The object \adeff{stdout} is an ``output'' that prints a \ff{string} to the standard output stream, while the object \adeff{stderr} is an ``output'' that prints to the standard error stream.
The object \adeff{stdin} is an abstraction of a \ff{string} currently available in the standard input stream until the EOL character (\ff{\char`\\n}) and is an ``input.'' If there is no string in the stream, the object blocks dataization and waits. This code endlessly reads strings from the console and immediately prints them back:
\begin{ffcode}
TRUE.while
[i]
QQ.io.stdout > @
QQ.io.stdin
\end{ffcode}
The object \adeff{bytes-as-input} is an ``input'' made from \ff{bytes}.
The object \adeff{memory-as-output} is an ``output'' directed towards a copy of \ff{memory}.
The object \adeff{copied} is channel between an ``input'' and an ``output,'' which moves all available bytes from the former to the latter when being dataized. For example, this code write a text to a temporary file:
\begin{ffcode}
QQ.io.copied
QQ.io.bytes-as-input
as-bytes.
"Hello, world!"
as-output.
QQ.fs.file "/tmp/foo.txt"
"w+"
\end{ffcode}
The object \deff{content} is a \ff{string} representation of the entire content of an ``input.''
\section{File System}\label{sec:fs}
Here we define manipulations with files and directories.
All objects presented in this Section belong to \ff{QQ.fs} package.
The object \deff{file} is an abstraction of a file and is a decorator of \ff{string}, which is the path of the file.
The attribute \adeff{exists} is \ff{TRUE} if the file exists.
The attribute \adeff{is-dir} is \ff{TRUE} if the file is a directory.
The attribute \adeff{touch} makes sure the file exists.
The attribute \adeff{rm} removes the file.
The attribute \adeff{mv} renames or moves the file to a new place.
The attribute \adeff{size} is the size of the file in bytes.
The attribute \adeff{as-output} is an output stream for this file, while the attribute \adeff{as-input} is an input stream.
The object \deff{directory} is an abstraction of a directory.
The attribute \deff{mkdir} creates the directory with all its parent directories.
The attribute \deff{rm-rf} deletes the directory recursively with all its subdirectories.
The attribute \deff{walk} finds files in the directory using glob pattern matching.
The attribute \deff{tmpfile} is a temporary file in the directory.
The object \adeff{tmpdir} is a system \ff{directory} of temporary files.
The object \deff{path} is a decorator of a \ff{string} and is a path of a file.
The attribute \adeff{resolve} is a new path with a suffix appended to the current one.
The attribute \adeff{dir-name} is the name of the directory in the path.
The attribute \adeff{ext-name} is the extension in the path.
The attribute \adeff{base-name} is the name of the file in the path.
\section{Sockets}\label{sec:sockets}
Here we define objects used for both server-side and client-side TCP sockets in accordance with \citet{posix}.
All objects presented in this Section belong to \ff{QQ.net} package.
The object \deff{socket} is an abstraction of a TCP socket. The attribute \adeff{connect} establishes a connection and makes a copy of the socket object. Then, its attributes \adeff{as-input} and \adeff{as-output} may be used for reading from the socket and for writing to it. For example, this code opens a connection to the 80th TCP port of \ff{google.com} and then reads the entire stream as a Unicode string:
\begin{ffcode}
connect. > s
QQ.net.socket
"google.com"
80
QQ.io.stdout
QQ.io.content
s.as-input
s.close
\end{ffcode}
The attribute \adeff{listen} makes a copy of the socket and establishes a server connection. Then, the attribute \adeff{accept} can be used to wait for an incoming connection and then make a copy when it arrives. For example, this code binds to the 8080th port on a ``localhost'' and when a connection arrives, prints a message into it:
\begin{ffcode}
listen. > s
QQ.net.socket
"127.0.0.1"
8080
QQ.io.copied
QQ.io.bytes-as-input
"Hello, world!".as-bytes
s.accept.as-output
s.close
\end{ffcode}
The attribute \adeff{close} terminates the connection and makes the
closed \aff{socket} object impossible to use anymore.
\section{HTTP}\label{sec:http}
Here we define objects used for parsing and printing of HTTP requests and responses in accordance with \citet{rfc2616}.
All objects presented in this Section belong to \ff{QQ.http} package.
The objects \deff{http-request} and \deff{http-response} are abstractions of HTTP request and response respectively. They have attributes that help building them; they both have \deff{as-string} attribute to turn them into a \ff{string}:
\begin{ffcode}
http-request
.with-method 'GET'
.with-address '/index.html'
.with-header 'Accept-Encoding' 'utf-8'
.with-cookie 'Session-Id' '8F09A4E438C'
.with-content-type 'plain/text'
.as-string > r
\end{ffcode}
They both have \deff{from-string} attribute to create objects from a \ff{string}.
They also have attributes that represent the pieces, which request and response are built of:
\begin{ffcode}
http-response.from-string "..." > r
r.status
r.header 'Content-Type'
r.cookie 'Session-Id'
\end{ffcode}
\section{Synchronization}\label{sec:synchronization}
Here we define objects used for explicit synchronization between threads.
All objects presented in this Section belong to \ff{QQ.sync} package.
The object \deff{semaphore} is a counting semaphore with two attributes: \adeff{capture} and \adeff{release}.
The object \deff{atomic-memory} is a synchronized decorator of \ff{memory} with a binary \ff{semaphore} encapsulated.
\printbibliography
\clearpage
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,502 |
HomePosts tagged 'UN'
Biden's coming China headache: Climate change and "Developing Countries"
December 9, 2020 December 8, 2020 usissuescom Foreign Policy China, Climate, Paris, UN
By Roland Gross – Re-Blogtged From Climate Science Press
Regime survival, China's red line, is predicated on meeting the material aspirations of ordinary citizens, the only source of legitimacy afforded to unelected governments throughout history.
A Biden presidency, which now seems most likely, will have plenty on its foreign policy plate, ranging from relations with Russia, China and Europe to the Iran question in the Middle East. But it is likely that global climate change policy, especially in relation to China's position in it, will be among the most contentious challenges it will face in international diplomacy.
Weekly Climate and Energy News Roundup # 417
July 28, 2020 usissuescom CAGW Alarmism, Energy Policy, Regulation CAGW, Climate Change, Climate Models, CO2, global warming, IPCC, Paris, UN, water vapor
The Week That Was: July 25, 2020
By Ken Haapala, President, SEPP
Quote of the Week: "When we are planning for posterity, we ought to remember that virtue is not hereditary." —Thomas Paine (1776)
Number of the Week: 12 datasets of evidence
July Summary Part III; Models and Observations: Two weeks ago TWTW reviewed Richard Lindzen's new paper summarizing what we know with reasonable certainty, what we suspect, and what we know is incorrect about climate change, the greenhouse effect, temperature trends, climate modeling, ocean chemistry, and sea level rise. Key parts included:
1) The climate system is never in equilibrium.
Faulty Forecasts and False Climate Narrative Hold Nations Hostage
July 21, 2020 July 22, 2020 usissuescom CAGW Alarmism, Foreign Policy, Regulation CAGW, Climate Change, Climate Models, CMIP6, global warming, India, IPCC, UN
By Vijay Jayaraj – Re4-Blogged From WUWT
The United States is the only major Western country that is not part of the Paris climate agreement, which seeks to restrict and reduce fossil fuel consumption across the world. But the country is not immune from the impacts of the restrictive energy policies the agreement imposes on its trade partners. One of those is my own country, India.
India imports large amounts of coal, oil, and natural gas from the U.S., mostly to generate affordable power for its electric grid. That grid must grow rapidly to meet the needs of over 1.3 billion people. Over 300 million of them—comparable to the whole U.S. population—currently have no electricity. But they need it desperately for their health and their escape from severe poverty.
Financiers of Poverty, Malnutrition and Death – Part 1
April 28, 2020 April 30, 2020 usissuescom Foreign Policy Agriculture, Colonialism, Foundations, Kenya, NGOs, Pesticides, Socialism, UN
By Paul Driessen – Re-Blogged From WUWT
Private 'philanthropic' foundations join government agencies in funding anti-technology NGOs
The UN Food and Agriculture Organization, anti-development banks, the Agency for International Development (USAID), NGO (non-government organization) pressure groups and other eco-imperialists are properly condemned for using their money, power, and control over trade and lending to keep millions of African, Asian and Latin American families from having access to reliable, affordable energy, pesticides and spatial insect repellants to prevent disease, and modern agricultural technologies.
Those outfits perpetuate poverty, disease, malnutrition and death. Yet the eco-manslaughter continues.
Keeping Africa on the Brink of Starvation
March 2, 2020 February 24, 2020 usissuescom Foreign Policy Africa, Eritrea, Ethiopia, FAO, Locust, NGOs, Somalia, UN
UN and EU government agencies – and tax-exempt NGOs – have brought a plague of locusts
Billions of desert locusts have descended again on East Africa. Crawling first, then sprouting wings and flying in hungry hoards of 40-150 million or more, they are devastating crops and threatening tens of millions of people with lost livelihoods and starvation. This latest locust plague, says the United Nations, is the worst in 70 years for Kenya, the worst in 25 years for Ethiopia, Eritrea, Djibouti and Somalia.
Locust swarms can blanket scores or hundreds of square miles at a time, travel 80 miles a day, and consume more than 400 million pounds of vegetation daily, Africa Fighting Malaria cofounder Richard Tren notes. The insects increase their numbers logarithmically, meaning numbers can be 500 times higher in six months. In Ethiopia, on January 9, a massive swarm nearly brought down a Boeing 737 jetliner.
The Globalists' Race Against Time on China
October 30, 2019 October 27, 2019 usissuescom Uncategorized Afghanistan, China, Globalism, Islam, Russia, UN
To recap briefly, most of the communist countries collapsed by 1991 and the Western democratic tradition was seen as the winner of an existential battle that had waged since the Russian Revolution of 1917. Historian Francis Fukuyama called it "the end of history" because only good things would happen thereafter. Mankind's ideological evolution had ended and Western liberal democracy would be the final form of government.
In response to that wishful thinking, Harvard historian Samuel Huntington wrote a paper, and subsequently a book, entitled The Clash of Civilizations and the Remaking of the World Order in which he predicted that with the end of ideological conflict the world would revert to a normal state of affairs characterized by cultural conflict. In particular, Professor Huntington predicted an attack by Islamists on the United States. That attack duly happened five years later. Huntington had identified China and Islam as "challenger civilizations."
October 7, 2019 October 4, 2019 usissuescom CAGW Alarmism Climate, EPA, IPCC, Science, Socialism, UN
By Dr Paul Rossiter – Re-Blogged From WUWT
In an earlier posting (WUWT https://wattsupwiththat.com/2019/09/26/understanding-the-climate-movement-the-impotence-of-science/) I referred to the work of Douglas Murray (The Madness of Crowds) in helping to understand how the climate debate was just a Trojan horse being exploited for a much wider social change agenda being pursued by globalists and the socialist Left. In that article I alluded to some of the drivers that are enabling the movement, including Noble Cause Corruption and personal or corporate financial gain. Here I explore further the role of Noble Cause Corruption. While regular followers of WUWT will be familiar with some of the content, I think that pulling it together makes a compelling case.
Weekly Climate and Energy News Roundup #378
October 1, 2019 usissuescom CAGW Alarmism, Energy Policy, Foreign Policy CAGW, Climate Change, Climate Models, Coal, EPA, Gas, global warming, IPCC, Solar, UN, Wind
The Week That Was: September 28, 2019, Brought to You by www.SEPP.org
By Ken Haapala, President, Science and Environmental Policy Project (SEPP)
Quote of the Week – "Sometimes people hold a core belief that is very strong. When they are presented with evidence that works against that belief, the new evidence cannot be accepted. It would create a feeling that is extremely uncomfortable, called cognitive dissonance. And because it is so important to protect the core belief, they will rationalize, ignore and even deny anything that doesn't fit in with the core belief."— Frantz Fanon, French West Indian psychiatrist, political philosopher, revolutionary, [H/t William Readdy]
Number of the Week: 30% fewer labor hours
UN Children's Climate Circus: The conditions for most of the world's population are improving significantly. Although wars are ongoing, there is no major world war, killing millions. There are no major famines, other than those created by government policies. World grain reserves are full, and production is increasing greatly in tropical countries, which were once considered too hot, with too thin, too acidic soils to be major grain producers. There is still much to do, particularly in Africa, South America and Asia, but, based on the World Bank. the numbers of people living in extreme poverty are declining significantly, with major reductions in Asia. So based on mathematical computer models, the UN and many international organizations are declaring we are in a "climate crisis" – based on projections of the future that are not validated by physical evidence today.
Environmentalism: Evidence Suggests it Was Always and Only About Achieving World Government
June 14, 2019 June 13, 2019 usissuescom CAGW Alarmism CAGW, Climate Change, CO2, global warming, One World, Socialism, UN
By Dr. Tim Ball – Re-Blogged From WUWT
It is common sense to protect our environment, but what has occurred for 50 years is exploitation of that idea for a socialist agenda. We wasted 50 years believing that humans are not natural, and everything they do is destructive. We wasted and continue to waste trillions of dollars on unnecessary policies and useless technologies, all based on false assumptions, pseudoscience, and emotional bullying.
We now know 50 years later that every single prediction concerning the environmental demise of the Earth and the people made in the original Earth Day Report was wrong. We also know that every additional claim, such as overpopulation, global warming, sea level rise, desertification, deforestation, and sea ice collapse, among many others, were wrong. I challenge anyone to produce empirical evidence that proves anything happening today is outside any long-term record of natural activity.
U.N. Told Us We'd Have 'Disaster' By Year 2000
March 8, 2019 March 7, 2019 usissuescom CAGW Alarmism CAGW, Climate Change, Disaster, Fear Mongering, global warming, UN
By Anthony Watts – Re-Blogged From WUWT
I must have slept through that event, thankfully, I'm still here. Global Warming zealots have been predicting doom for years, the latest being that we now have only 12 years left.
But, back in 1989, we were told we have only 11 years left, till the year 2000. If we didn't act, "entire nations could be wiped off the face of the Earth by rising sea levels".
That date came and went. Yet here we are again, with the same old doom-mongering.
Don't believe me? AP archived the story here:
https://www.apnews.com/bd45c372caf118ec99964ea547880cd0
And, I've saved it as a PDF, since things like this tend to get "disappeared".
Climate Summit Language Reveals Real But Hidden Agenda
December 26, 2018 December 19, 2018 usissuescom CAGW Alarmism, Foreign Policy CAGW, Climate Change, Katowice, New World Order, Poland, UN, Wealth Transfer
By David Wojick, Ph.D. – Re-Blogged From WUWT
The goal isn't saving Earth from climate disaster – it's changing the world order
People complain all the time about UN jargon. But the technical language of the Katowice, Poland climate summit is actually very revealing. It is all about changing the world order.
Words exist because there is something important to talk about. Words also embody basic beliefs. In this context, it is very useful that the ever-green Climate Change News has published a Glossary of the 32 technical terms they think are most important in Katowice.
Cherry Picking & ClimateGate
December 23, 2018 December 23, 2018 usissuescom CAGW Alarmism, Foreign Policy Anthony Watts, Charles Rotter, ClimateGate, CRU, Skeptics, Steve McIntyre, STteve Mosher, UEA, UN
Re-Blogged From Red Pilled America
Why did Donald Trump say a lot of global warming was a hoax? We follow the biggest science heist in history to find the answer.
Red Pilled America is designed to be listened to, not read. Please reference and use the audio version for exact quotes.
Patrick Courrielche: Like every year at about this time, world leaders are meeting to discuss global warming.
The topic has been a popular political football since at least Al Gore's 2006 documentary "An Inconvenient Truth."
Al Gore: Within the decade there will be no more snows of Kilimanjaro.
Italy's Interior Minister Begins Deporting Migrants
September 19, 2018 September 16, 2018 usissuescom Foreign Policy Deportation, Immigrants, Italy, Libya, Nigeria, UN
By Robert Spencer – Re-Blogged From Freedom Outpost
Salvini is right, but he will be excoriated as a "racist" anyway.
The political and media elites expect, and indeed demand, that the countries of the West commit national suicide.
Anything short of that is "racist" and "neo-Nazi."
Trump's Paris Decision One Year Later: Looking Better and Better
June 6, 2018 June 3, 2018 usissuescom CAGW Alarmism, Energy Policy, Foreign Policy CAGW, China, Climate Change, Coal, Fracking, Gas, global warming, India, Oil, Paris, Regulation, UN
By Robert Bradley Jr. – Re-Blogged From http://www.WattsUpWithThat.com
As of today, the United States will cease all implementation of the non-binding Paris Accord and the draconian financial and economic burdens the agreement imposes on our country. This includes ending the implementation of the nationally determined contribution and, very importantly, the Green Climate Fund which is costing the United States a vast fortune.
-President Trump on the Paris Climate Agreement, June 1, 2017
Now or Never: Israel Makes Its Move Against Iran
May 29, 2018 May 25, 2018 usissuescom Foreign Policy Iran, Israel, Middle East, Rusia, Syria, UN
By Reva Goujon – Re-Blogged From Stratfor
An unusual set of circumstances is enabling Israel to scale up attacks against Iran in Syria and risk a broader confrontation in the process.
As Israel raises the stakes in its conflict with Iran, it will look to lock in U.S. security commitments in the region for the long haul.
The White House's decision to withdraw from the Iran nuclear deal is a long-shot bet on regime change at odds with U.S. attempts to reduce its military burden in the region.
Russia's bark is often worse than its bite, but it will retain the clout to narrow the scope of U.S. and Israeli ambitions against Iran.
Will Congress Finally Get Tough on Junk Science?
March 13, 2018 March 6, 2018 usissuescom Regulation Cancer, ChemicalsGlyphosate, Congress Committee on Scince, IARC, Regulation, UN
By Paul Driessen – Re-Blogged From http://www.WattsUpWithThat.com
House hearing investigates a UN cancer agency accused of misusing US taxpayer funds
A growing problem for modern industrialized Western societies is the legion of government agencies and unelected bureaucrats and allied nongovernmental organizations that seem impervious to transparency, accountability or reform. Their expansive power often controls public perceptions and public policies.
Prominent among them are those involved in climate change research and energy policy. In recent years, they have adjusted data to fit the dangerous manmade climate chaos narrative, while doling out billions of taxpayer dollars for research that supports this perspective, and basing dire predictions and policy demands primarily on climate models that assume carbon dioxide now drives climate and weather (and the sun, water vapor, ocean currents and other powerful natural forces have been relegated to minor roles).
Taking the Temperature of the Ukraine Conflict
March 1, 2018 February 23, 2018 usissuescom Foreign Policy Peacekeepers, Russia, Sanctions, Ukraine, UN
Re-Blogged From Stratfor
As highlighted in the 2018 Annual Forecast, progress toward a deal to deploy U.N. peacekeepers to intervene in the conflict in Eastern Ukraine is distinctly possible. Recent signs of compromise over other aspects of that conflict, such as prisoner exchanges, indicate that the forecast is on track.
See 2018 Annual Forecast
The idea of deploying U.N. peacekeepers to Eastern Ukraine was broached several months ago amid growing intensity in diplomacy surrounding the conflict between Russian-backed separatists and pro-government forces there. This weekend's Munich Security Conference will offer a chance for more talks over the issue, but given the differences of opinion over the size, scope and mission of any U.N. force, there's no guarantee that an agreement will be struck. But some signs of compromise over the peacekeepers issue — and the opportunity offered by the security gathering that will attract representatives from key powers — make real movement on the issue a possibility.
(MYKOLA LAZARENKO/AFP/Getty Images)
On the Precautionary Principle
January 31, 2018 January 28, 2018 usissuescom CAGW Alarmism, Regulation CAGW, Climate Change, EPA, global warming, IPCC, Regulation, UN
By Neil Lock – Re-Blogged From http://www.WattsUpWithThat.com
Today, I'm going to look at a mantra much trumpeted by environmentalists; the precautionary principle. I'll seek to make a case that, since the early 1980s, this idea has been perverted. To such an extent, that the principle now has an effect all but opposite to its true intention. I'll trace how this happened, and try to outline how we might fix the resulting mess.
What is the precautionary principle?
South Korea Seizes Second Ship Suspected of Providing Oil to North Korea
January 5, 2018 December 31, 2017 usissuescom Energy Policy, Foreign Policy China, North Korea, Oil, Sanctions, South Korea, UN
By Yuna Park & Hyunjoo Jin – Re-Blogged From Reuters
SEOUL () – South Korean authorities have seized a Panama-flagged vessel suspected of transferring oil products to North Korea in violation of international sanctions, a customs official said on Sunday.
The seizure was the second to be revealed by South Korea within a few days, as the United Nations steps up efforts to squeeze essential oil supplies to the reclusive North following its nuclear or ballistic missile tests.
President Trump and Ambassador Haley Cut United Nations Funding by Almost $300 Million, Globalists Explode
December 26, 2017 usissuescom Foreign Policy budget, UN, US
Re-Blogged From iPatriot
U.S. Ambassador to the UN Nikki Haley is having the week of her career, and inspiring many patriotic Americans while she's at it.
Haley has an undoubtedly difficult job. Her role as a liaison between the increasingly populist Trump administration and the evermore globalism-based United Nations puts the ambassador between a rock and a hard place. Filled with glass. And bees. Barefoot.
December 17, 2017 December 16, 2017 usissuescom CAGW Alarmism, Energy Policy CAGW, Climate Change, Climate Models, Food Production, Four Fears, Four Freedoms, global warming, UN
By Ken Haapala, President, The Science and Environmental Policy Project
Brought to You by www.SEPP.org
UN – Protection of Four Freedoms: On December 10, 1948, the three-year old-UN adopted its Universal Declaration of Human Rights. Among others, Eleanor Roosevelt lobbied heavily for this declaration, invoking what was called the Four Freedoms. On January 6, 1941, President Roosevelt articulated these concepts in his State of the Union address. At the time, the US was formally neutral about the war occurring in Europe and in Asia, though Roosevelt was trying to convince the reluctant Congress and public to join the side of Great Britain.
The 1970s Global Cooling Scare
December 16, 2017 December 13, 2017 usissuescom CAGW Alarmism CAGW, Climate Change, Climate Models, Global Cooling, global warming, IPCC, UN
By Bernie Lewin – Re-Blogged From http://www.WattsUpWithThat.com
This is the second post drawing on themes raised in the book Searching for the Catastrophe Signal. See a previous post on WUWT here.
Forty-five years ago today, two geologists penned a letter to the president of the United States warning that the rocky decent into the next ice age might have already begun.
TUCSON, July 31 (UPI) — Scientists confirmed Thursday that water, considered an essential building block of life, does indeed exist on the planet Mars.An analysis of a soil sample collected by the Phoenix lander detected traces of water, which exists as ice just below the red soil on the Martian surface.
"We've seen evidence for this water ice before in observations by the Mars Odyssey orbiter and in disappearing chunks observed by Phoenix last month," scientist William Boynton said in a written statement released by NASA and the Jet Propulsion Lab, "but this is the first time Martian water has been touched and tasted."
Boynton is lead scientist for the Thermal and Evolved-Gas Analyzer team based at the University of Arizona.
Details of the composition of the water were not immediately released. The sample came from a 2-inch deep trench carefully carved by the lander's robotic arm.
The presence of water is one of more dramatic discoveries made by the Phoenix since it touched down on Mars near the pole May 24. NASA announced it had secured funding to extend the Phoenix mission through Sept. 30.
More here: http://phoenix.lpl.arizona.edu/
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UN Agency to US Congress: Drop Dead
December 15, 2017 December 12, 2017 usissuescom Foreign Policy, Regulation Corruption, Glyphosate, IARC, Roundup, UN
IARC takes US money, manipulates scientific studies, colludes with activists – and snubs Congress
The International Agency for Research on Cancer (IARC) in France has received over $48 million from America's National Institutes of Health (NIH), to determine whether various chemicals cause cancer in humans. Of more than 900 chemicals it has reviewed, only one was ever found non-carcinogenic. The latest substance to face IARC scrutiny is glyphosate, the active ingredient in the herbicide RoundUp.
Stop hyping Harvey and Irma!
October 1, 2017 September 28, 2017 usissuescom CAGW Alarmism, Foreign Policy, Statistics CAGW, China, Climate Change, EU, Germany, global warming, Harvey, Hurricanes, Irma, Japan, Paris, UN
By Dr. Neil Frank, former Director National Hurricane Center
Over the past several weeks numerous articles suggest Harvey and Irma were the result of global warming. The concept is a warmer earth will generate stronger and wetter hurricanes. A number of people have said Irma was the most intense hurricane in the history of the Atlantic while Harvey was the wettest and both were good examples of what we can expect in the future because of global warming. What does a fact check reveal about these two hurricanes?
Irma was indeed a very powerful Cat 5 hurricane when it moved across the Leeward Islands and the 185 mph winds reported by a recon plane at 10,000 ft. were among the strongest recorded in Atlantic hurricanes. How does Irma compare to other intense Atlantic hurricanes? To answer that question, we must first look at the history of the methods used to determine the strength of a hurricane because it changed early this century.
Now That Trump Has Defeated Paris, He's Taking on Montreal!
June 13, 2017 June 10, 2017 usissuescom CAGW Alarmism, Foreign Policy, Regulation Antarctica, CFCs, Montreal, Ozone, UN
By David Middleton – Re-Blogged From http://www.WattsUpWithThat.com
Sacré bleu !
Trump Budget Attacks Montreal Protocol, Reagan's Crown Jewel
May 24, 2017 David Doniger
The Trump FY18 budget proposal slashes funding to support compliance with the Montreal Protocol, Ronald Reagan's treaty to save the ozone layer.
The cut—which appears to be on the order of 40 percent—welches on U.S. international commitments and will imperil the global phase-out of ozone-destroying chemicals.
The Montreal Protocol—widely considered the world's most successful environmental treaty—was negotiated under President Ronald Reagan in 1987 and is his crowning environmental achievement. It has been strengthened repeatedly under both Republican and Democratic presidents.
Is Climate Alarmism Governance at War with the USA?
January 10, 2017 usissuescom CAGW Alarmism, Energy Policy, Foreign Policy, GDP & Employment, Regulation CAGW, Climate Change, Communism, EPA, global warming, Greenpeace, IPCC, UN, War, War on US
[This is an IMPORTANT article – especially Section III. Please take the time to read. Thanks. – Bob]
By Leo Goldstein – Re-Blogged From http://www.WattsUpWithThat.com
My essay The Command & Control Center of Climate Alarmism discussed the centralized structure of climate alarmism, and introduced the term Climate Alarmism Governance (CAG) to define its command & control center. The fact that most alarmist groups and their multiple activities are centrally coordinated or even directed raises a natural question about their central motives and goals. The impression that these groups believe in the IPCC theory of catastrophic anthropogenic global warming is contradicted by their widespread opposition to the use of nuclear power and to building new hydro power plants. Hydropower is obviously a renewable energy source.
The same groups oppose natural gas power, which emits 3-4 times less carbon dioxide per kWh compared with coal power. There are many more contradictions in the CAG's statements and actions. It seems to be aware that its "scientific base" is fake, and purposefully makes illogical and impossible demands to thwart any serious consideration of technological or economic solutions for the alleged problem. Each time such economic or technological actions are seriously contemplated, somebody takes another look at the so-called "climate science" and finds a striking lack of actual science. Then it takes 5-8 years to explain the fraud away, and to raise alarm to new heights.
Ban Ki-Moon to Trump: Action on Climate Change is "Unstoppable"
November 18, 2016 November 16, 2016 usissuescom CAGW Alarmism, Energy Policy, Foreign Policy Ban Ki Moon, China, CO2, Fossil Fuels, France, Morocco, Paris, Solar, UN, Wind
UN Secretary General Ban Ki-Moon has warned President-elect Trump that he will not have the power to derail climate programmes, even climate programmes in the USA.
France, U.N. tell Trump action on climate change unstoppable
France and the United Nations on Tuesday stepped up warnings to U.S. President-elect Donald Trump about the risks of quitting a 2015 global plan to combat climate change, saying a historic shift from fossil fuels is unstoppable.
French President Francois Hollande, addressing almost 200 nations meeting in Morocco on ways to slow global warming, said that inaction would be "disastrous for future generations and it would be dangerous for peace".
Possible United States Climate Change Action Plan
November 13, 2016 November 10, 2016 usissuescom CAGW Alarmism, Energy Policy, Regulation CAGW, Climate Change, EPA, global warming, IPCC, UN, UNFCCC
By Anthony Watts – Re-Blogged From http://www.WattsUpWithThat.com
Last night, there was this tweet:
The fellow works for Buzzfeed, and highly liberal and pro-climate outfit. It was quite an admission. Since existing climate plans are almost certain to be on the scrap heap now, here's a new plan from Christopher Monckton.
UN Brokers New Global Green Tax on Air Travel
October 12, 2016 October 10, 2016 usissuescom CAGW Alarmism, Energy Policy, Foreign Policy Air Travel, Air Travel Tax, CAGW, Carbon Tax, Climate Alarmism, UN
The United Nations has brokered a new international agreement which forces airlines to pay for "green" projects. By 2035, the UN expects the deal will siphon $24 billion / annum from the pockets of air travellers.
Aviation pact on global warming wins go-ahead
Airlines back UN accord to offset emissions growth by funding green projects.
Delegates from nearly 200 nations approved the accord at the UN's International Civil Aviation Organisation in Montreal in a step the agency's head, Fang Liu, described as a "historic first".
USexit Bill Introduced in Congress
July 2, 2016 usissuescom Foreign Policy UN, UNEPPA, UNESCO, US, USexit, WHO
By Onan Coca – Re-Blogged From Freedom Outpost
In the wake of the wonderful decision by the people of the United Kingdom to #Brexit, some conservatives in Congress have decided to seize the moment and push for an #Amexit (American Exit) from the United Nations! It's an idea that conservatives have long supported and may now grab the national imagination, as Americans seek new ways to disconnect themselves from the corrupt establishment that runs our political world.
Bill sponsors Thomas Massie (R-KY), Mike Rogers (R-MI), Tim Huelskamp (R-KS), Jeff Duncan (R-SC), Lynn Westmoreland (R-GA), and Ted Yoho (R-FL) recently released the text of their bill hoping to convince Americans to embrace Independence and leave the U.N.
January 15, 2016 usissuescom CAGW Alarmism CAGW, Climate Alarmists, Climate Change, Climate Models, EPA, Flooding, IPCC, Mississippi River, UN
The Week That Was: January 9, 2016 – Brought to You by www.SEPP.org
By Ken Haapala, President, Science and Environmental Policy Project
Paris Agreement – Treaty or Not? The December 26 TWTW emphasized that from a scientific and practical viewpoint the Agreement in Paris reached at the conclusion of the Conference of Parties (COP-21) of the United Nations' Framework Convention on Climate Change (UNFCCC), "Paris Agreement" is largely smoke and mirrors. It does not obligate countries to reduce Carbon Dioxide (CO2) emissions or countries to contribute to the "Green Climate Fund. Further, the climate science on which the fear of global warming/climate change is based is not robust and far from complete. The models used by the UN Intergovernmental Panel on Climate Change (IPCC) fail to properly account for natural climate change and past warming periods including the one from about 1910 to 1940. These models consistently overestimate the warming of the lower atmosphere. It is here where greenhouse gas warming, chiefly from human emissions of CO2, should occur. Yet, since 1979 satellites have provided the most comprehensive data of global warming and cooling in existence. For the lower atmosphere the data show no significant warming for over a decade. As John Christy has demonstrated, lower atmospheric temperatures are calculated by three independent groups and are confirmed by independent measurements of temperatures by four sets of weather balloon data.
The recent effort by the US National Oceanic and Atmospheric Administration (NOAA) to alter the historic surface temperature record to show recent warming has been severely criticized and has little merit. It can be considered to be a desperate act to continue fear of global warming.
Obama Is Correct, Climate Change Is Biggest Threat, But Only Because Official IPCC Climate Science Is Completely Wrong
December 1, 2015 usissuescom CAGW Alarmism, Foreign Policy, GDP & Employment, Regulation CAGW, Climate Alarmists, Climate Change, Environmentalism, global warming, Green, IPCC, Maurice Strong, NIPCC, Socialism, UN
By Dr Tim Ball – Re-Blogged From http://www.WattsUpWithThat.com
Kafkaesque is one word that encapsulates the entire Paris Conference. It is defined as:
A nightmarish situation which most people can somehow relate to, although strongly surreal. With an ethereal, "evil", omnipotent power floating just beyond the senses.
There are insufficient superlatives to describe the disaster that is the UN COP21 Climate Conference in Paris. None of the superlatives are the ones used by the organizers and their lackeys. It is the largest, most political conference ever, based on completely false claims deliberately created in the greatest science deception in history. It will cost more socially in direct damage to individual lives, communities, and social structures. It will cost more in economic damage to jobs, businesses, and industry. In addition, besides destroying lives it will remove freedom and actually cost lives. It will weaken economies preventing resistance to terrorism. This far exceeds any potential damage from terrorism and is much worse because it is self-inflicted (Figure 1).
UN: We Should Switch to Eating Insects
May 9, 2015 May 9, 2015 usissuescom CAGW Alarmism, Regulation CAGW, Cattle, Climate Change, CO2, global warming, greenhouse gases, Insects, Methane, Protein, UN
Former UN secretary general Kofi Annan has suggested in an interview with The Guardian, that people should switch to eating insects, to reduce the need for traditional cattle farming. | {
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{"url":"https:\/\/indico.fnal.gov\/contributionListDisplay.py?confId=6662","text":"# 2013 User's Meeting Poster Session\n\nJune 12, 2013\nFermi National Accelerator Laboratory Batavia, IL 60510\nUS\/Central timezone\nHome > Contribution List\nDisplaying 32 contributions out of 32\nNOvA is a long-baseline neutrino oscillation experiment that will use the NuMI beam originating at Fermilab. NOvA enables the study of two oscillation channels: $\\nu_{\\mu}$ disappearance and $\\nu_{e}$ appearance. It consists of two functionally identical detectors, the Near Detector (ND) at FNAL and the Far Detector (FD) near International Falls in Northern Minnesota. The ND will be used to study ... More\nPresented by Ms. Kanika SACHDEV\nAt MuCool Test Area (MTA) of Fermilab, an experiment has been performed with an RF cavity filled with high pressure hydrogen gas to study beam loading effects. In this experiment a 400 MeV proton beam is used with an external magnetic field of B=3 T. Quantitative information about the number of protons passing through the cavity is an essential requirement of the beam test. We have developed beam ... More\nPresented by Dr. MUKTI RANJAN JANA\nThe CMS Hadron Calorimeter (Hcal) is an integral part of the particle flow and tracking of the CMS detector. A new design is to be implemented during the Phase 1 upgrade of the LHC, this design will implement multiple layers to the Hcal in order to reveal various physical properties of the incoming tracks. These layers bring new challenges to the framework of the DAQ and analysis from the Hcal por ... More\nPresented by Mr. Josh KAISEN\nMINERvA (Main Injector Experiment for v-A) is a neutrino scattering experiment in the 1-10 GeV energy range in the NuMI high-intensity neutrino beam at Fermi National Accelerator Laboratory. MINERvA is measuring neutrino\/antineutrino scattering off a variety of different nuclear materials (C, Fe, Pb, He, H2O). This poster will describe the current analysis on charged current coherent pion pro ... More\nPresented by Aaron HIGUERA\nMINERvA has recently submitted two papers to PRL with its first results for charged-current quasi-elastic neutrino scattering from scintillator. The poster shows our results.\nPresented by Ms. Cheryl PATRICK\nThe MiniBooNE experiment is sensitive to sub-GeV weakly interacting massive particles (WIMPs) due to the large number of protons on target (POT) and by virtue of the large detector mass. The ongoing search in MiniBooNE neutral current elastic scattering (NCE) sample is reported, looking at both the energy distribution and also exploiting the excellent timing resolution. We also discuss an idea to ... More\nPresented by Ranjan DHARMAPALAN\nThe NO\u03bdA experiment is a long baseline neutrino experiment designed to measure the appearance of electron neutrinos in the Fermilab NuMI muon neutrino beam. The experiment has two segmented liquid scintillator detectors located 14 mrad off the beam axis, with a Near Detector located at Fermilab, and a Far Detector 810 km away. NO\u03bdA will measure the 13 neutrino mixing angle and it will have excel ... More\nPresented by Mr. Gareth KAFKA\nThe NOvA long-baseline neutrino experiment has been designed to study electron neutrino appearance in a muon neutrino beam using a totally active, segmented, liquid scintillator detector located off the Fermilab NuMI beam axis. NOvA will observe electron neutrino appearance with a baseline of 810 km subject to significant matter effects. It will thus have excellent sensitivity to the neutrino mass ... More\nPresented by Tian XIN, Dr. Gavin DAVIES\nPrecision calibration of optical fiber\u2019s activities is crucial for the liquid scintillation detectors of the NOvA experiment. Stability test and calibration study of optical detector are necessary for a successful physics outcome of the detector.\u00a0 We present the stability test of the fiber-loop-transmissions \u00a0(FLT) quality assurance device, and the calibration results of various detector modul ... More\nPresented by Ms. Kuldeep Kaur MAAN\nWe develop a field-programmable gate array (FPGA) TDC module for Fermilab SeaQuest (E906) experiment. This 64-channel TDC is made of a 6U VMEbus unit equipping with a Microsemi ProASIC3 Flash based FPGA of low power and high radiation tolerance. The TDC firmware could digitize multiple hits of both polarities and possesses a multiple-hit elimination functionality which could be turned on to remove ... More\nPresented by Ms. Su-Yin WANG\nA high pressure hydrogen gas-filled RF (HPRF) cavity can operate in the multi-Tesla magnetic fields required for a muon accelerator cooling channel. A beam test was performed at the Fermilab MuCool Test Area by sending a 400 MeV proton beam through an 805 MHz cavity and quantifying the effects of the resulting plasma within the cavity. The resulting energy loss per electron-ion pair produced has ... More\nPresented by Mr. Ben FREEMIRE\nThe Main Injector Particle Production (MIPP) experiment at Fermilab is a full acceptance spectrometer to measure hadronic particle production using beams of $\\pi^{\\pm}$, $\\rm{K^{\\pm}}$, p and $\\rm{\\bar{p}}$ ranging in momentum from 5 to 120 GeV\/c incident on Liquid-Hydrogen, Beryllium, Carbon, Bismuth, Uranium and NuMI targets. The experiment has excellent charged particle identification using ... More\nPresented by Mr. Amandeep SINGH\nAt the core of the CMS all-silicon tracking system is the silicon pixel detector, comprising three barrel layers and two pixel disks in the forward and backward regions, accounting for a total of 66 million channels. The pixel detector provides high-resolution 3D coordinates of the tracks produced in high energy pp collisions. Under the combined action of electric and magnetic fields, the charged ... More\nPresented by Andrew GODSHALK\nThe MINOS detectors are used to collect data from the NuMI neutrino beam as well as atmospheric neutrino data. The atmospheric data taken by the Far Detector, located underground at a depth of 2070 meters-water-equivalent and at 735 km from the neutrino production target, is combined with beam data from both Near and Far Detectors to measure the neutrino and antineutrino mixing parameters. Because ... More\nPresented by Ms. Michelle MESQUITA DE MEDEIROS\nThe study of $Z$ boson production processes in association with $b$ quarks provide important tests of perturbative QCD calculations. We measure the ratio of cross sections, $\\sigma(p\\bar{p}\\rightarrow Z+b)$\/$\\sigma(p\\bar{p}\\rightarrow Z+jets)$, for associated production of a $Z$ boson with jets as a function of the jet transverse momentum, jet pseudorapidity, $Z$ boson transverse momentum, an ... More\nPresented by Mr. Joseph ZENNAMO\nThe NO\u03bdA experiment is a next generation long-baseline, accelerator-based neutrino oscillation experiment, currently under construction at Fermilab and northern Minnesota. NO\u03bdA will improve the existing constraints on electron neutrino appearance by more than an order of magnitude by comparing electron neutrino rates observed by two totally active liquid scintillator detectors, located 14 mrad o ... More\nPresented by Dr. Raphael SCHROETER\nThe Main Injector Particle Production (MIPP) experiment at Fermilab is a fixed target hadron production experiment. It measures particle production in interactions of 120 GeV\/c primary protons from the Main Injector and secondary beams of $\\pi^{\\pm}, \\rm{K}^{\\pm}$, p and $\\bar{\\rm{p}}$ from 5 to 90 GeV\/c on nuclear targets which include H, Be, C, Bi and U, and a dedicated run with the NuMI target. ... More\nPresented by Ms. Sonam MAHAJAN\nThe Compact Muon Solenoid (CMS) Hadron Calorimeter (HCAL) is scheduled to be upgraded in order to increase longitudinal depth segmentation in the Barrel and Endcap regions and to improve anomalous signal rejection efficiency in the Forward Region. In order to achieve these goals, the phototransducers and the front-end and back-end electronics of the HCAL will be upgraded in stages over the next se ... More\nPresented by Elliot HUGHES, Mr. Hector HERNANDEZ ROJAS, Ms. Diana Patricia MENDEZ MENDEZ\nThe production rate of pions\/kasons, which decay into neutrino incident at NOvA, in iron and helium relative to that in carbon is shown as a function of xF and pT. Simulations are done with the medium energy horn configuration in G4NuMI for neutrinos incident at NOvA Near Detector. Results are shown for Forward Horn Current(Focus-Positive) vs Reverse Horn Current for two hadron cross secti ... More\nPresented by Ms. Kuldeep Kaur MAAN\nWhen relativistic electrons propagate parallel to planar channels in a crystal lattice, they can oscillate about the crystal planes emitting an undulator like radiation known as Channeling Radiation. We plan to use our novel photo and field emission cathodes to generate very small emittance electron beams to make a channeling radiation X-ray source. This experiment is currently under construction ... More\nPresented by Mr. Ben BLOMBERG\nProton computed tomography (pCT) is a new medical imaging technique that offers many advantages over conventional X-ray CT, especially when used in conjunction with proton therapy treatment. The pCT scanner consists of two fiber trackers in front of the object, two fiber trackers behind the object, and a range detector behind the rear fiber trackers. The residual proton energy is measured in the ... More\nPresented by Andrew GEARHART\nThe High Brightness Electron Source Lab (HBESL) at Fermilab was reconfigured from the previous A0 facility to develop novel techniques to produce and diagnose high brightness electron beams whose applications are found in many fields. In this poster we present the recent developments at HBESL in regards to the new results on photo- and field emission studies from different cathodes. We also discus ... More\nPresented by Mr. Harsha PANUGANTI\nThe MINOS experiment makes precision measurement of the atmospheric neutrino mixing parameters using neutrinos at the Main Injector(NuMI) and by employing two detectors separated by long base line. The normalized energy response at the each detector is obtained by a comprehensive calibration procedure to correct for the detector affects using cosmic ray muons . As part of the calibration procedure ... More\nPresented by Mr. Navaneeth Poonthottathil POONTHOTTATHIL\nSince Paul Dirac first put forward the idea of the magnetic monopole in 1931, there have been many experimental and theoretical efforts to find this elusive particle, but so far without any success. The NOvA experiment at Fermilab, is also trying to observe this mysterious particle. As we wait for the first data to be delivered by the NO\u03bdA far detector, we have made great strides in monopole simu ... More\nPresented by Mr. Zukai WANG\nA search for heavy resonances decaying into $\\tau^{+}\\tau^{-}$ has been performed using 4.94 fb$^{-1}$ of proton-proton collision data at 7 TeV recorded by the CMS detector during LHC Run2011. Estimation of major backgrounds has been performed using data-driven methods wherever possible. In the absence of any excess of observed data events over the Standard Model background prediction, an upper li ... More\nPresented by Dr. Nitish DHINGRA\nMINOS is a long-baseline neutrino oscillation experiment composed of two detectors along Fermilab's high-intensity NuMI neutrino beam. In addition to studying oscillation between different flavours of neutrinos, MINOS is also capable of studying the possibility of oscillations between neutrinos and antineutrinos. The observation of such a signal would indicate the violation of Lorentz and CPT symm ... More\nPresented by Ms. Richa SHARMA\nI will present a new theory, explaining what dark matter is, what dark energy is,and why gravity works. This theory also explains why relativity happens and why particles are solid. The theory also defines what light is, and what matter is and comes to a different conclusion about what is inside a black hole and the way that a black hole radiates it's mass without any information being lost.\nPresented by Mr. Joseph OCLON\nThe NOvA experiment will study neutrino oscillations using the NuMI beam produced at Fermilab. The experiment is currently under construction and will consist of a near detector at the Fermilab site, and a far detector, located 810 km away in Ash River, Minnesota, both 14 mrad off of the beam axis. The fully active liquid scintillator detectors are designed to identify the interaction of neu ... More\nPresented by Dr. Satish DESAI\nA variable-dispersion bunch compressor chicane with a transverse-deflecting cavity (TDC) may serve as a transverse-to-longitudinal emittance exchangers (EEX). In this paper, we present a design and simulations of a chicane-based EEX for eventual implementation at Fermilab's Advanced Superconducting Test Accelerator (ASTA). Such a beamline is foreseen to enable bunch current profile shaping, bunch ... More\nPresented by Chris PROKOP\nArgoNeuT, a 175 liter Liquid Argon Time Projection Chamber (LArTPC), exposed to NUMI beamline at Fermilab (2009-2010), has recently collected thousands of neutrino and anti-neutrino events between 0.1 and 10 GeV. ArgoNeuT is the first LArTPC exposed to a low energy neutrino beam, first ever in the US in neutrino beam and the second LArTPC exposed to a neutrino beam ever. The project is part of the ... More\nPresented by Saima FAROOQ\nThe CMS pixel detector is a tracking device located closest to the interaction point. The present detector was designed for a maximum luminosity of 1\u00d71034 cm\u22122s\u22121. Following the Phase 1 upgrade of the LHC, the peak luminosity is foreseen to reach 2\u00d71034 cm\u22122s\u22121. Due to the radiation damage and significant data losses in the readout chip, the present pixel system must be replaced by ... More\nPresented by Dr. Ashish KUMAR\nThe next generation of neutrino experiments will require massive and\/or high resolution detectors to reach the sensitivity needed to measure CP violation in the lepton sector and the neutrino mass hierarchy. The Large-Area Picosecond Photo Detector (LAPPD) Collaboration is developing new methods to fabricate 8in-square thin planar micro channel plate photosensors, which have shown to have excellen ... 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>Profile>Company Profile>FENC History
Selected FENC Overview FENC History
In February, FENC, through its subsidiary "Far Eastern Investment (H) Ltd." acquired Mossi & Ghisolfi's (M&G) assets of PET plant in West Virginia and R&D center in Ohio, USA.
In May, FENC won the "CSR Annual Survey – Grand Prize in the Traditional Industrial Group" of the 14th Annual Corporate Social Responsibility Award by Global Views Magazine.
In April, FENC was in the top 5% of the listed companies in the third "Corporate Governance Evaluation" conducted by Taiwan Stock Exchange
In May, FENC won the "Corporate Social Responsibility Award" as the Role Model in the manufacturing industry category from Global View Magazine.
In November, FENC was included as a constituent of the MSCI ESG Leaders Indexes and assessed of MSCI ESG Rating – Industrial Conglomerates: A.
In February, DynaFeed, a FENC revolutionary smart garment system with bio-sensing technology and IoT platform, was awarded the ISPO Asian Gold Winner at the globally prestigious ISPO Textrends Exhibition.
In May, FENC won the "Corporate Social Responsibility Award", ranking first in the manufacturing industry category from Global View Magazine due to conserving energy and protecting the environment.
In June, FENC won Enterprise Asia's "2016 Asia Responsible Entrepreneurship Award" in the category of green leadership for developing the world's first Bio-PET bottle.
In November, FENC received three "2016 Taiwan Corporate Sustainability Awards", held by Taiwan Institute for Sustainable Energy, including the "CSR Report of the Year", "Corporate Sustainability Award" as well as "Growth through Innovation Award"(for the smart clothing in remote health care project)
In December, FENC earned the 13th "National Innovation Award" in Taiwan in developing the 100% bio-PET polyester shirt. The 100% bio-PET polyester shirt made entirely from plant-based material, which reduces the carbon footprints by 30% compared to the petrochemical based one, was developed by FE Group R&D Center.
In April, FENC was awarded the highest "A++" ranking in the 12th Annual Information Disclosure and Transparency Rankings Evaluation among Listed Companies.
In June, FENC, through its subsidiary "Far Eastern Investment (H) Ltd.", has established Far Eastern Polytex (Vietnam) Ltd. for a new vertically integrated polyester and textiles production base.
In November, FENC won a Gold Award from Taiwan Institute for Sustainable Energy (TAISE) in "Taiwan Top 50 Corporate Sustainability Report Awards," ranking first in the Traditional Manufacturing category and also received the "Growth Through Innovation Award" in "Corporate Sustainable Performances" category for developing the world's first 100% bio-based PET bottle.
In April, FENC was awarded the "10th Annual Corporate Social Responsibility Awards - Global Views Excellent Service Awards" for the project "The Greenest Bottle, starts with a Genuine Heart"
In April, FENC, through its subsidiary "Far Eastern Polychem Industries Ltd.", has entered into a joint venture with Ishizuka Glass Co., Ltd.("IGC"), to establish Far Eastern Ishizuka Green PET Corporation in Japan to conduct R-PET production and distribution business
In May, 1st Global Sustainable Procurement (GSP) supplier awards was launched by Coca-Cola and FENC was awarded "2013 Supplier of the Year" out of 900 suppliers.
In May, Far Eastern New Century (China) Investment Co., Ltd., the subsidiary of Far Eastern New Century, obtained the right to the use of land through public auction for RMB 978 million(equivalent to NT$ 4.67biilion). The land is located at plot A09B – 02, World Expo Zone, Pudong New Area, Shanghai.
In May, FENC issued Formosa and Yen bonds in the Gre Tai Securities Market, successfully being the first manufacturing company in Taiwan to issue bonds denominated in both RMB and Yen.
In October, Far EasTone won three 4G frequency bands and is the only operator offering the 20MHZ contiguous spectrum in the telecom industry
In May, FENC founded Far Eastern Industries (Yangzhou) Ltd. and Far Eastern Union Petrochemical (Yangzhou) Ltd., via indirect investments and plans to build a new production site for polyester and ethylene glycol.
In March, FENC has constructed, operated and sponsored EcoARK, a exhibition hall composed of 100% recycled plastic bottles, at the Taipei International Flora Exposition. This green construction created several firsts in the world and the National Geographic Channel (NGC) produced a documentary "Megastructures EcoARK" on EcoARK as well. The show was broadcasted throughout 168 countries in 34 languages.
In April, the first commercial office building of T-Park, TPKA, officially put into operation.
In November, FENC and Sinopec Yizheng Chemical Fiber Company established Far Eastern Yizheng Petrochemical (Yanzhou) Company Ltd. via joint-investmnt.
In December, a wholly owned subsidiary of FENC has entered a joint venture with Sinopec Yizheng Chemical Fibre Company Limited to establish Far Eastern Yihua Petrochemical (Yanzhou) Corporation to conduct purified terephthalic acid (PTA) production.
In January, new shares of FENC were listed in Taiwan Stock Exchange.
In December, FENC and Sinopec Yizheng Chemical Fibre Company Limited (YCF) have agreed to form a joint-venture company to construct a green-field purified terepthatic acid (PTA) plant located in the Yangzhou Chemical Industrial Park. Three parties aforesaid signed a "Letter of Intent (LOI)"
In April, FETL built a pavilion named "Far Eastern EcoARK" for the International Flora Expo held by the Taipei City Government. Such pavilion built by recycled PET bricks helped promote the awaress of conserving the environment.
In October, in the Company's Extraordinary Shareholders' Meeting held on 13 October 2009, shareholders presented had resolved and approved to rename the company, from Far Eastern Textile Limited (FETL) to Far Eastern New Century Corporation (FENC), effective on the same date.
In March, Sino Belgium Beer (Suzhou) Ltd was established and invested by FETL. The factory was completed in April. In October, a beer "Martens 1758" , manufactured for Belgium Martens beer company, was marketed in Shanghai area.
In October, FETL has obtained all shares of "Invista Far Eastern Petrochemicals Ltd."& "Far Eastern Investa Ltd" and renamed them to " Oriental Petrochemical (Taiwan) Co. Ltd." & " Far Eastern Fibertech Co., Ltd" respectively.
In January, Far Eastern Resources Development Co. which is fully owned by FETL proposed a change to the government on the urban development plan from production factory into a telecommunication-related specialized zone combined with a medical service center. The government has already approved such proposal after a three-year evaluation. This land re-zoning plan was officially announced on 23 January 2007.
In June, Far Eastern (China) Investment Holding Ltd which is invested by FETL obtained operating license.
In July, the long term and short term credit rating of FETL has been rated as "twA+" and "twA-" respectively by Taiwan Rating's Corp for the first time.
In February, The public highway electronic toll collection system is officially activated, this system is built by FETL invested company "Far Eastern Electronic Toll Collection Co. Ltd.".
In April, Oriental Petrochemical (Shanghai) Corporation which is invested by FETL is announced to production, with PTA annual production capacity of 600 thousand tons to support the synthetic fiber business under Far Eastern group and other producers.
In February, a development project " Taipei Far Eastern Telecom Park" (T-Park) conducted by FERD was approved by Ministry of Economic Affairs as "national major investment and major public constructions".
In April, Far Eastone Telecommunications Ltd which is invested by FETL is passed by Taiwan Stock Exchange Corporation to become as a public listed company.
In October, FETL is awarded by Taiwan CommonWealth Magazine as the number one "The benchmark Enterprise with best reputation" in 2005 survey of benchmark enterprises.
In April, FETL invested company "Far Eastern Electronic Toll Collection Co. Ltd." has signed BOT contract with National Freeway Bureau.
In September, Far Eastern Resources Development Company ("FERD") which is 100% owned by FETL was established to transfer the book value of existing property development related businesses to FERD in order to elaborate the related specialty and actively developing the existing land resources.
In September, FETL is awarded by Taiwan CommonWealth Magazine as the number one "The benchmark Enterprise with best reputation" in 2003 survey of benchmark enterprises.
In May, FETL started the installation of SAP R/3 as the ERP system with PricewaterhorseCoopers. This project will be completed and put on line in early 2003 to help promoting internal processing re-engineering, cost reduction and management of financial information.
In, June, permission was received from the Investment Commission, Ministry of Economic Affairs for an investment by FETL's wholly-owned subsidiary Yuan Ding Investment Corp. to establish Far Eastern Industries (Wuxi) Ltd.
In October, a joint investment by FETL's owned subsidiaries and Far Eastern Department Stores ("FEDS") was completed to acquaire the controlling interest of the SOGO Depoartment Stores.
In March, FETL-invested New Century InfoComm Tech Co., Ltd. (NCIC) launched its variable voice and data services with "速博sparq" as the brand name. Best quality services of NCIC helps customers surf in an era of keen competition and rapid changes.
In May, Far EasTone Telecommunications Ltd. (FET), consortium headed by the Far Eastern Group and AT&T plus other members, successfully became a public listed company in Taiwan Stock Exchange in December. FET is the 2nd public listed company of mobile phone services in Taiwan.
Far Eastern Polychem Industries Limited (FEPI), the parent company of Far Eastern Industries (Shanghai) Ltd., was successfully listed on the Growth Enterprise Market (GEM) of the Stock Exchange of Hong Kong on January 31. The money raised was used for the expansion of Far Eastern Industries (Shanghai) Ltd. for strengthening its competitiveness.
FETL-invested New Century InfoComm Tech Co., Ltd. (NCIC) was awarded one of the three fixed line info-comm licenses in March. This became another big step for FETL in telecommunications business.
Mr. Y. Z. Hsu, Far Eastern Group founder, passed away at the age of 90 in December and left behind the most valuable and cherished founding spirit of "Sincerity, Diligence, Thrift, and Diligence" as the guiding principles.
FETL issued new common shares in October. Along with shares held by Asia Cement and Far Eastern Department Stores, the total number of shares is 14,400,000 and issued for NT$44.5/share as GDR. This issuance not only raised the capital but also directed FETL to the international capital market.
The FETL-invested Far Eastern Textile Industrial (Shanghai) Co. Ltd.began trial production in September. Since this was the last chemical fiber company to be issued a license by the mainland Chinese authorities,after the plant begins mass production it is expected to become a major source of reinvestment profit for FETL.
Production by the ring-spindle machines at Hukou Plant No. 8 began in November, easily absorbing the post-expansion demand for cotton yarn materials by domestic yarn-dyed fabric plants.
In January Far EasTone Telecommunications Ltd., which is 62.4% owned by FETL subsidiary Yuan Ding Investment Corp., obtained island-wide DCS and northern-region GSM mobile phone licenses from the Directorate General of Telecommunications. This new high-tech enterprise is a powerful stimulative force in FETL's transition into the new century, and it provides a new model for growth as well.
Permission was received in July from the Investment Commission,Ministry of Economic Affairs for a joint investment of US$30 million by FETL and its wholly-owned subsidiary Yuan Ding Investment Corp. in the establishment of a holding company in a third area to establish Far Eastern Industries (Shanghai) Ltd. for the production and sale of polyester yarn, polyester filament, and other chemical fiber products.
The first domestic convertible corporate bonds were issued in July, in the amount of NT$1.5 billion and with a face interest rate of 0%. The holders of these bonds can choose to exchange them for shares in two Far Eastern Group companies, Far Eastern Department Stores or U-Ming Marine Transport Corp.
DuPont-Far Eastern Co. Ltd. was established in cooperation with DuPont of the United States, with a projected investment of US$100 million in the production of high-tech nylon 66.
A contract was signed with ICI for the establishment of ICI Far Eastern Ltd. to construct a PTA plant at Kuanyin in Taoyuan County.
The Yilan and Panchiao plants of the Apparel Division, and the Neili and Hukou plants of the Textile Division, won ISO-9002 certification.
The Hsinpu Synthetic Fiber Plant of the Fiber Division passed evaluation by the DNVI company to become the first chemical fiber plant in Taiwan to win ISO-9001 certification.
Completion of the various elements of the Taipei Metro Complex began in October and the headquarters of FETL as well as of Asia Cement and other related enterprises moved into the complex on Oct. 16 and 17,making this the locus of the Far Eastern Group.
Permission was received to carry out the first issuance of overseas corporate bonds in the amount of US$50 million. The bonds were fully subscribed in October that year.
Convertible bonds were issued in the amount of NT$1.5 billion and carrying an interest rate of 4.25%. These were the first convertible bonds to be issued in Taiwan.
To strengthen the development of uses for polyester long-fiber cloth, a joint investment of NT$1 billion was made together with Hong Ho Precision Textile Co. in the establishment of Everest Textile Co. to produce fine woven fabrics as a means of heightening the added value of FETL products.
A joint investment of NT$360 million was made together with Canada's London Life Insurance Co., Global Investment Holding Co., Chiao Tung Bank, and Central Investment Holding Co. in the establishment of China Investment Development Co. to engage in high-tech, real estate,and natural resources investment.
In line with the government's environmental protection policy, an investment was made jointly with the Shin Kong Group to establish the Taiwan Resources Recycling Co. to engage in the recycling and handling of wastes.
The Hukou textile factory was developed, and yarn and fabric plants were constructed there.
Ground-breaking for the Taipei Metro Complex took place in August;these mixed-use towers, with 41 stories above ground and five below,contain offices, a shopping center, and a tourist hotel.
A joint investment of NT$1 billion was carried out with Card Freudenberg of Germany and Vilene of Japan in the establishment of Freudenberg Far Eastern Spunweb Co. to engage in the production of non-woven industrial fabrics and related high-tech polyester fiber products.
Production technology was acquired from L'Air Liquide International of France and a joint investment of NT$230 million was made in the establishment of Liquid Air Far East Ltd. to produce nitrogen and other industrial gases.
To boost FETL's share of the Southeast Asian market for PET bottles,joint investments were carried out in October with Hong Kong and Thai companies for the establishment of P.E.T. Packaging (HK) Ltd. and P.E.T. (Thailand) Co., respectively.
Permission was received to merge Orient Chemical Fiber into FETL and establish the Eastman Division, which in July the following year was merged into the Textile Division.
A textile plant belonging to the former Jung Lung Textile was acquired and renamed the Taishan Textile Plant.
The Chungchou textile plant at Kuanyin in Taoyuan County was purchased and renamed the Kuanyin Textile Factory.
Permission was received to acquire and merge Orient Chemical Fiber and establish a chemical fiber plant.
The Yilan apparel plant was built.
The Panchiao textile factory of Taiwan Textile and the Neili textile plant of Yunghsing Industries were procured and added as FETL's Panchiao and Neili textile plants.
A new spinning plant was built at Hsinpu to produce polyethylene and acrylic fiber.
A new garment factory was constructed at Hsinpu.
Permission for stock market listing was received in April.
The headquarters was moved to Paoching Rd. in Taipei in July.
The third synthetic fiber textile plant was established, completing the vertical integration of FETL's processes from spinning to weaving,dyeing and finishing, and apparel production.
The second textile plant was established to supply yarn for FETL's own needs.
Cotton and chemical fiber facilities were installed in response to the needs of society and the synthetic fiber industry.
An advanced apparel plant was established.
Far Eastern Knitting and Taiwan Far Eastern Textile were merged to form Far Eastern Textile Ltd., which was located on Yungsui Rd. in Taipei.
The name of the company was changed to Far Eastern Knitting Co., Ltd.;at the same time, the Taiwan Far Eastern Textile Co., Ltd. was set up in Panchiao for the purpose of establishing a weaving mill.
Far Eastern moved to Taiwan and installed its knitting factory in the Taipei suburb of Panchiao, where it continued producing and marketing knitted products.
Yu-Ziang Hsu founded Far Eastern Knitting Factory Co., Ltd. in Shanghai to produce "Skyscraper"-brand underwear for sale throughout the world.
Spokesperson - Humphrey Cheng
Corporate Management President
Tel:+886-2-27338000 #8969
csostaff@feg.com.tw
Acting Spokesperson - David Wang
ccwang@feg.com.tw
SITEMAP Home
Far Eastern New Century Corporation
36F, Taipei Metro Tower, 207, Tun Hwa South Road, Sec. 2, Taipei, Taiwan, R.O.C. | TEL:886-2-27338000
Copyright © 2020 Far Eastern New Century Corporation All Rights Reserved.
Web Designed by PAVI. | {
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Das Contract Law Englands und Wales' ist der Teil der Rechtsordnung Englands und Wales', der sich mit den Voraussetzungen und Wirkungen von Verträgen beschäftigt. Er beinhaltet somit größtenteils Rechtsgebiete, die ihre funktionalen Äquivalente in der allgemeinen Zivilrechtslehre und im allgemeinen Schuldrecht der Rechtsordnungen des deutschen Rechtskreises finden. Eine Besonderheit des common law ist die Forderung von Consideration (etwa 'Gegenleistung') für die Wirksamkeit eines Vertrages.
Literatur | {
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Q: primary shards in mongodb I am trying to go through the documents for mongodb sharding and I am a bit confused about how the primary shards are assigned and the meaning of primary shards
As per the documentation it stats that
Every database has a primary shard that holds all the un-sharded
collections for a database. The primary shard has no relation to the
primary in a replica set.
does this mean that a primary shard is the shard (or the collection of servers) in the shard where the database was first created ?
Say I have 3 shards s0, s1 and s2. In each shard i have 3 servers
*
*s0 Server 1 (Primary)
*s0 Server 2 (Secondary)
*s0 - Server 3 (Secondary)
*s1 - Server 4 (Primary)
*s1 - Server 5(Secondary)
*s1 - Server 6(Secondary)
*s2 - Server 7(Primary)
*s2 - Server 8(Secondary)
*s2 - Server 9(Secondary)
Now when I create a new database via a mongoclient and via mongos . Now say that request goes to the shard 1 (s1). Since create database is a write operation it would go to the server 4 in shard 1 and thus s1 becomes by primary shard ?
If on the other hand the request would have traversed to s2 shard then server 7 would being primary would have created the collection and then s2 would have been my primary shard ?
Is this understanding correct or I am going wrong some where ?
A: Yes, you are right! And you understanded concept.
As long as you don't shard individual collection, collection must have primary location, at one of the replica sets. So, think those individual shards as individual RS's.
So, one DB is located to one shard and if you shard collection inside DB, collection is "balanced" to multiple shards. With TAG's you can decide where that collection is spread. Normal situation is spread it to all shards evenly.
And you can always make decision what is DB's primary location. After creating, you can "move" it, when DB is still empty or quite small, it's fast operation. movePrimary
| {
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Edu Enin-Okut
Do I need a patent?
To begin to answer this question, you should familiarize yourself with what a patent is, who can get one, and if you decide that you need a patent, how to get it.
A patent allows its owner to prevent others from using, making, and selling an invention protected by it, within the jurisdiction of the government who granted the patent, for a limited period of time. The patent contains a description of the invention and a set of claims that legally define the scope of protection the patent provides. The government granting patent protection to the invention does so as an exchange. The inventor provides a disclosure of the invention made available to the public to serve as a "springboard" for other innovation, and in exchange for disclosure, the governmental authority provides marketplace protection via the patent.
Here in the U.S., the United States Patent & Trademark Office (USPTO) reviews applications made for patents. Either the inventor, or the entity an inventor is employed by (e.g., a corporation), can apply for a patent. Timing of the filing of the application is simply, in a best-case scenario, as soon as the inventor fully understands the invention and how it is made and/or used.
Upon examination of the claims in an application, if the USPTO determines that the invention is patentable, the applicant will be granted a patent. How is this determination made? Patentability of an invention is determined via Title 35 of the U.S. Code (35 USC). In particular, the applicant must show that the invention is an eligible process, machine, manufacture, or composition of matter (35 U.S.C. 101); novel (35 U.S.C. § 102); and non-obvious (35 U.S.C. § 103).
To determine if the invention of a patent application is novel and non-obvious, a search is conducted to identify references that describe all, or parts, of the invention as it is claimed in the application. Generally speaking, if a reference both describes all of the elements described in the application's claims and was available to the public before the filing date of the application, the invention is not patentable under 35 U.S.C. 102 because it lacks novelty. However, even if the invention is found to be novel, references can be combined to demonstrate that the claimed invention would have been obvious to the ordinary, skilled artisan. That is, if two or more references available to the public before the application's filing date, by means of their combination, describe all of the elements described in the application's claims, and can be combined as they are in the claims, then the invention may not be patentable under 35 U.S.C. 103 for being obvious.
The statutory requirements of these federal statutes can be likened to "hurdles" to be cleared by the invention described in the application. If the claims of the application clear all of the hurdles, the USPTO will grant a patent that can be used in a variety of beneficial ways for the patent owner. | {
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Høgskavlpiggen Peak () is a peak rising from the western part of Høgskavlen Mountain, in the Borg Massif of Queen Maud Land, Antarctica. It was mapped by Norwegian cartographers from surveys and air photos by the Norwegian–British–Swedish Antarctic Expedition (1949–52) and named Høgskavlpiggen (the high snowdrift peak).
References
Mountains of Queen Maud Land
Princess Martha Coast | {
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{"url":"https:\/\/www.physicsforums.com\/threads\/ac-household-generators.848751\/","text":"# AC household generators\n\n1. Dec 17, 2015\n\n### deckart\n\nI'm only familiar with a gas powered generator that I use at home when the power is out. But I'm designing a contraption that will be able to spin a generator with considerable torque. But the RPM will not be consistent. I can limit the upper end but it will often be below max RPM.\n\nAm I correct in assuming that lower RPM will affect the 60 Hz frequency generation? If so, are there ways to maintain 60 Hz with a varying input RPM?\n\n2. Dec 17, 2015\n\n### Staff: Mentor\n\nGenerate a DC voltage and use an inverter to make the appropriate 60Hz AC Mains output voltage.\n\n3. Dec 17, 2015\n\n### deckart\n\nAha, that's the way to do it! Thanks.\n\n4. Dec 18, 2015\n\n### CWatters\n\nHow will your \"contraption\" regulate it's output power?\n\nMy understanding is that when the load on a generator increases (because someone turned on a light) they open the throttle to increase power\/torque and maintain rpm. If your contraption can't do this then perhaps consider using a battery to decouple the load from the generator?\n\n5. Dec 18, 2015\n\n### deckart\n\nFrom what I understand, excess power can be put back into the grid. This is one of the benefits of household solar. If the home owner isn't using the excess his meter actually begins to go backwards.\n\n6. Dec 18, 2015\n\n### dlgoff\n\nI wouldn't consider selling power back due to the equipment cost. As it is, here in the US, you'll need a Automatic Transfer Switch (ATS).\n\nLast edited by a moderator: May 7, 2017\n7. Dec 19, 2015\n\n### deckart\n\n\"But why would utilities go through the trouble of purchasing this energy?\nWell, because the government says so. In the U.S., the Public Utility Regulatory Policy Act (PURPA)dictates that electric utilities on the traditional power grid must purchase the excess electricity that renewable energy systems generate. It's a way of encouraging renewable energy production without requiring utilities to invest in expensive renewable systems themselves.\" http:\/\/science.howstuffworks.com\/environmental\/energy\/sell-electricity-back-grid.htm\n\nI don't believe I need to purchase an ATS.\n\n8. Dec 19, 2015\n\n### dlgoff\n\nI don't think you can get around this. Yes utilities are required to purchase excess when the equipment is properly attached to the grid; that and they're not going to pay you at the same rate as they are selling it for and usually for quite a bit less than selling price.\n\n9. Dec 19, 2015\n\n### deckart\n\nI understand that you get paid at a lesser rate, but there are also rebates, tax incentives, etc.\nAs far as the hardware required, I'm asking a buddy who is an electrical contractor. He installs solar array systems and knows details. I'll post what he has to say on it.\n\n10. Dec 19, 2015\n\nCaution: Be SURE to check the 'fine print' in your local power companies regulations or rules or whatnot regarding what you actually have to do to sell power back to them. I looked into this once but decided not to go this route because not only did they pay very little per kWh, they also charged a $75 monthly fee for this service. I'd have had to generate several times my homes power consumption just to break even with that fee. 11. Dec 19, 2015 ### deckart Ok, so if I sell power back to the grid, it could cost me more than if I didn't? 12. Dec 19, 2015 ### Drakkith ### Staff: Mentor It's possible, yes. Like I said, check with your power company. 13. Dec 19, 2015 ### CWatters That's certainly possible here in the UK. The meter doesn't go backwards (most are digital these days) you either have a separate export meter or they assume that 50% of what you generate will be exported. 14. Dec 19, 2015 ### Nugatory ### Staff: Mentor The ATS requirement is a bit of a red herring here. An ATS automatically and completely disconnects your house from the grid whenever your generator is working, so it's not part of the solution if you're planning to return excess power to the grid. To connect your generator to the grid, you need the power conditioning equipment to ensure that not only are you generating at 60 Hz (North America), but also that it is in phase (the peaks and valleys of your 60 Hz power match up with those of the grid) and the waveform is at least vaguely sinusoidal and spike-free (the output of some light-duty farm\/home\/shop generators can be amazingly dirty). There also has to be an automatic lockout so that the power company can shut you down whenever they need to work on the power lines in your neighborhood. This equipment is becoming increasingly available and affordable when you're starting with the DC output of photovoltaic cells, but I'm not sure that there's a commercially available solution for a repurposed home generator, let alone one that would be acceptable to the local power company. 15. Dec 19, 2015 ### russ_watters ### Staff: Mentor It might. Have you calculated how much it will cost for you to generate your own electricity? It shouldn't be hard to find out the price per kWh the utility will pay you and compare with what it is costing you to make it. There's a reason people don't do this very often and I'm not sure you understand what you are getting yourself into (or even what it is that you are going to be doing). In general though, when you buy electricity, you are paying for three separate things: the generation at the plant, the transmission from the plant to the local grid and the distribution of the power from the local grid to your house. Each of those is about a third of the cost, so if, for example, you pay 15 cents for your electricity, you'd only be able to sell it back for about 5 cents because the only thing you are doing for the utility is the generation. 16. Dec 19, 2015 ### anorlunda Phrasing it that way makes it sound like there must be a back channel communication from the utility to your house. That's not reliable enough for safety purposes. It also sounds like disconnect is used only when the utility truck is in your neighborhood. That's insufficient In addition to protecting utility workers you must not attempt to power your whole neighborhood, because that could put neighbors at risk. The same disconnect must also protect you from galvanic DC currents that could fry all your stuff when an unbalanced fault exists. That means ground fault detection on the customer side. For safety purposes, the disconnect automation must use only local information, and it must act instantaneously when the grid point you connect to loses voltage. Only devices certified to meet applicable standards may be used to interconnect a home to the grid. 17. Dec 19, 2015 ### deckart It may cost an excess of$20-30k USD to get this project up fired up. And that's just a very early estimation. It's a prototype and there will be a lot of refinements to be worked out after it is already up and running. I don't expect it to pay for itself, actually, if it does it will likely be more than a decade of use before it does. But, it will be capable of generating far more power than your typical home based solar array.\n\nThe generator will be DC and convert to AC using an appropriate inverter.\n\nI'm researching the details with my local utility company and there is a limit to the amount of power you are allowed to put back on the grid. But you do get a good rate from them: \"If your system generates more electricity than you use, the excess power delivered to the PUD\u2019s distribution system is credited to your account at the same rate class at which you would buy power from the PUD. Other requirements of the rate schedule apply, including the daily system charge. Unused credits carry over each month until April 30 of each year. If any net metering credits remain, they will be granted to the PUD as described in Washington State Law. (RCW 80.60)\"\n\n18. Dec 19, 2015\n\n### deckart\n\nHowever, at this utility company you only receive a credit. No money to be made from this power company out of a home based generator. But there are other incentives.\n\nLast edited: Dec 19, 2015\n19. Dec 19, 2015\n\n### dlgoff\n\nMy thought concerning the need for the ATS was: During power outages, times when you start the generator, you certainly don't want it attached to the grid. This is what's dangerous for anyone working to restore the power.\n\n20. Dec 19, 2015\n\n### deckart\n\nIt's required and would be part of the system.\n\u2022 A disconnect switch with a lockout function, allowing PUD 3 linemen to disconnect your solar array from the electric grid so that they can work on utility lines without fear of energy back-feeding from your system into the grid.\nThe electric company has complete access to shut it down without notice.","date":"2017-11-23 08:35:35","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\": 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\": 0.28671759366989136, \"perplexity\": 1688.1810347940643}, \"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-2017-47\/segments\/1510934806760.43\/warc\/CC-MAIN-20171123070158-20171123090158-00115.warc.gz\"}"} | null | null |
Graceworks Ministries: Donating from the Heart
Healing for the Soul
Article Linda Dohse | Photography Teresa Ginn
Tucked away in two small buildings in south Franklin, and one in Fairview, is an organization providing so much care, compassion and love for its neighbors in Williamson County, it can literally take your breath away. Yes, Williamson County, the seventh richest county in the United States and also the wealthiest when it comes to helping neighbors in need.
Meet GraceWorks Ministries, founded in 1995 when concerned area residents and faith leaders came together and decided Williamson County needed a central place where people could go for help with food, clothing and financial assistance. Church resources combined with private and public sectors, and GraceWorks was born.
Today, GraceWorks has expanded upon these relationships to establish a referral network with other agencies providing help for immediate and long-term needs. GraceWorks consists of four programs making up the acronym F.I.S.H. — Family Support, Instructional Programs, Seasonal Needs and Hunger Prevention. 9,722 Williamson County neighbors were served by the GraceWorks program this past fiscal year (July 2017 – June 2018).
516 households in threat of eviction received financial assistance
1,534 households received financial assistance to keep heat, water and other essentials on
197 homeless neighbors were provided temporary shelter or transportation to a shelter
60-plus families received multiple weeks of free financial guidance mentoring
183 mentor instructional hours provided to families in need
Seasonal Needs
4,021 people received Christmas gifts through the holiday program, the Manger
2,400 children given backpacks filled with school supplies
446 families received free tax preparation, providing $304,983 in returns
Hunger Prevention
8,665 neighbors received food
5,081 food carts left GraceWorks for food pantries to fill neighbors' kitchens
10 community mobile food pantries filled 6,900 trunks of food for neighbors in Franklin, Fairview, Cottage Grove and other communities
"GraceWorks formed because we had a problem to solve. A person had to go to many different churches and service organizations to get help," says Alicia Bell, GraceWorks' director of development. "We are blessed to inherit the wise solution our founders imagined nearly 25 years ago. Now we have two community centers where someone in need can access many different resources simultaneously. This type of wraparound care is now recognized as some of the most effective and preventative work we can do to alleviate poverty, and our community had been doing it for 24 years."
GraceWorks West opened its doors five years ago, with a poverty rate more than double that of Williamson County; 8.3 percent and 3.9 percent, respectively.
GraceWorks Thrift Stores raised more than $1 million for GraceWorks programs this past fiscal year. Every item purchased helps change the lives of your Williamson County neighbors.
"GraceWorks is a place where neighbors who can help walk alongside neighbors in need of help. It truly is Williamson County's community resource center, connecting your time, your resources and your financial donations with those in our community who need it most. We are so grateful to serve this community with GraceWorks," says Valencia Breckenridge, GraceWorks' president and CEO.
GraceWorks is a United Way of Williamson County agency and a member of Community Foundation of Middle TN, Second Harvest Food Bank of Middle TN, Williamson County Chamber of Commerce and the Center for Nonprofit Management. GraceWorks Ministries received a four-star rating from Charity Navigator, the most-utilized charity evaluator in America. It has also earned the 2018 Platinum Seal of Transparency from GuideStar, which provides information on 2.5 million nonprofit organizations. Both ratings are the highest awarded.
Eighty-nine percent of every donation to GraceWorks went directly into programs this past year, thanks in large part to the generous work of volunteers who donated 88,678 hours, changing not only the lives of neighbors, but their own lives as well.
For more information, visit GraceWorksMinistries.net.
104 Southeast Parkway, Franklin, 615.794.9055
2382 Fairview Blvd., Fairview, 615.799.0006
Thrift store hours
Franklin: 9 a.m.–4 p.m. Monday through Saturday
Fairview: 9:30 a.m. –2:30 p.m. Monday through Friday and 10 a.m.– p.m. Saturday | {
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package org.dukecon.server.core;
import org.springframework.web.filter.ShallowEtagHeaderFilter;
import javax.servlet.FilterChain;
import javax.servlet.ServletException;
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpServletRequestWrapper;
import javax.servlet.http.HttpServletResponse;
import java.io.IOException;
/**
* The Apache web server we run in front of this application compresses the responses with gzip. It also modifies the etag.
* This is a workaround to strip the additional etag from the header when the clients sends a request for this resource.
*
* @author Alexander Schwartz 2017
*/
public class MyShallowEtagHeaderFilter extends ShallowEtagHeaderFilter {
@Override
protected void doFilterInternal(HttpServletRequest request, HttpServletResponse response, FilterChain filterChain) throws ServletException, IOException {
HttpServletRequestWrapper wrapper = new HttpServletRequestWrapper(request) {
@Override
public String getHeader(String name) {
String value = super.getHeader(name);
if (name.equalsIgnoreCase("If-None-Match") && value != null) {
value = value.replaceAll("-gzip", "");
}
return value;
}
};
super.doFilterInternal(wrapper, response, filterChain);
}
}
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President Buhari Takes First 2020 Foreign Trip To London For African Investment Summit
Tobias Sylvester
President Muhammadu Buhari has taken his first foreign trip this year to london for the inaugural UK-Africa investment summit scheduled for Monday, January 20, 2020.
The President's Special Adviser on Media and Publicity, Femi Adesina, who disclosed this in a statement, said Buhari departed Abuja for the event on Friday, and would be hosted by the British Prime Minister, Boris Johnson.
Adesina said said the summit is expected to bring African leaders, international business chief executives, heads of international organisations together "to create new partnerships that will deliver more investments and jobs" in Africa and the UK.
"Apart from highlighting new perspectives on UK-Africa Partnership for Prosperity, issues of Sustainable Finance and Infrastructure; Trade and Investment; Future African Growth Sectors and Clean Energy and Climate, are expected to dominate presentations and discussions during the Summit, " he said in a statement.
"With the expected take-off of the African Continental Free Trade Area (AfCFTA) in mid-2020, the London investment summit will provide Nigeria with the opportunity to project itself as a leading investment destination for new industries.
"In addition, the summit will deepen Nigeria-United Kingdom investment ties post-Brexit given that Africa currently represents just two percent of British trade activity, with Nigeria accounting for only 10 percent of that total.
"The Nigerian delegation to the investment meeting will further showcase what the Federal Government has done through policies and legislations to improve the investment and business climate in the country."
According to the statement, Buhari will also hold a meeting with Prince Charles, head of the Commonwealth, in Glasgow, Scotland, as well as a bilateral meeting with Prime Minister Boris Johnson and heads of multilateral organisations.
Among the governors who will accompany the president are Yahaya Bello (Kogi), Muhammad Yahaya (Gombe) and Okezie Ikpeazu (Abia).
The ministers are Geoffrey Onyeama (foreign affairs), Nìyí Adebayo (industry, trade and investment), Zainab Ahmed (finance, budget and national planning).
The remaining people in the president's delegation are: Babagana Monguno, national security adviser and Ahmed Abubakar, director-general of the National Intelligence Agency.
The president is expected back in Abuja next week Thursday.
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Federal Government Plans To Provide Alternative Fuel A Common Man Can Buy At N97 Per Litre
News1 hour ago | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,138 |
Q: How to simulate the WatchOS on Xcode 7.0.1 I recently updated my Xcode to Version 7.0.1 and I built my first Apple Watch app.
I would like to test it but it seems like I need the actual device to be able to simulate it?
I went to Hardware > External Devices > and I do not see the Apple Watch option anywhere.
*
*Anybody else has experience this?
*What can I do to fix it?
A: It is not the same simulator but another one called 'Simulator (Watch)'.
If you select the target for the Watch project, you end up with this (menu selection):
which will launch the two simulators
A: Select scheme for Apple Watch in XCode and display should appear after running the project.
A: My case is worse, there is even no simulator option under "Project WatchKit App" scheme.
However I am able to bring it up by adding new simulator paring with watch simulator from device management window.
*
*Start any iOS simulator.
*Go to Hardware -> Device -> Manage Devices...
*Click the + button under the bottom left corner.
Then you will be able to add new iphone simulators paired with apple watch. Sorry, I do not have enough reputation to post image here.
Although I still can't find the watch simulator under the external displays dropdown, I can run the watch app from the "Project WatchKit App" scheme anyway.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,145 |
\section{#1} \setcounter{equation}{0}}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{conj}{Conjecture}[section]
\newtheorem{lemma}{Lemma}[section]
\newtheorem{remark}{Remark}[section]
\newtheorem{coro}{Corollary}[section]
\newtheorem{ques}{Question}[section]
\newtheorem{prop}{Proposition}[section]
\def{\mathrm R}{{\mathrm R}}
\def{\mathrm W}{{\mathrm W}}
\def{\mathrm E}{{\mathrm E}}
\def{\mathrm {Rc}}{{\mathrm {Rc}}}
\def{\RRR}{{\RRR}}
\def{\mathrm S}{{\mathrm S}}
\def{\mathrm C}{{\mathrm C}}
\def{\mathrm {Rm}}{{\mathrm {Rm}}}
\def\mathrm{Diag}{\mathrm{Diag}}
\def\mathrm{Id}{\mathrm{Id}}
\def\dotfill{\dotfill}
\setlength{\oddsidemargin}{0.25in}
\setlength{\evensidemargin}{0.25in}
\setlength{\topmargin}{0.0in}
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\begin{document}
\title{Einstein four-manifolds of Pinched Sectional Curvature}
\author{Xiaodong Cao}
\address{Department of Mathematics,
Cornell University, Ithaca, NY 14853-4201}
\email{cao@math.cornell.edu}
\author{Hung Tran}
\address{Department of Mathematics,
University of California at Irvine, Irvine, CA 92697}
\email{hungtt1@uci.edu}
\renewcommand{\subjclassname}{%
\textup{2010} Mathematics Subject Classification}
\subjclass[2010]{Primary 53C25}
\date{ \today}
\begin{abstract} In this paper, we obtain classification of four-dimensional Einstein manifolds with positive Ricci curvature and pinched sectional curvature. In particular, the first result concerns with an upper bound of sectional curvature, improving a theorem of E. Costa. The second is a generalization of D. Yang's result assuming an upper bound on the difference between sectional curvatures.
\end{abstract}
\maketitle
\section{Introduction}
A Riemannian manifold $(M,g)$ is called Einstein if it satisfies
\begin{equation}
\label{einstein}
{\mathrm {Rc}}=\lambda g,
\end{equation}
where ${\mathrm {Rc}}$ is its Ricci curvature and $\lambda$ is a constant. A fundamental question in differential geometry is to determine whether a smooth manifold admits an Einstein metric or not. In dimension four, the Hitchin-Thorpe inequality gives a topological obstruction to the existence of such a structure. Currently, there is no known topological obstruction in higher dimensions. Thus, a generally crucial problem is to classify Einstein manifolds with suitable curvature assumptions.
Furthermore, it is known that if $\lambda>0$ then $M$ is compact and has finite fundamental group by Myer's theorem \cite{myer41}. Again, in dimension four, there are not many examples. The well-known ones (irreducible and reducible symmetric spaces) are the sphere $\mathbb{S}^4$ with round metric $g_0$, the complex protective space $\mathbb{CP}_2$ with Fubini-Study metric $g_{FS}$, the product of two spheres with same curvature $\mathbb{S}^2\times \mathbb{S}^2$, and their quotients. They all have non-negative sectional curvature and are only known examples with that condition. This motivates the following folk conjecture (see, for example, \cite{yangdg00}):
\begin{conj} An Einstein four manifold with $\lambda>0$ and non-negative sectional curvature must be either $\mathbb{S}^4$, $\mathbb{CP}_2$, $\mathbb{S}^2\times \mathbb{S}^2$ or quotient.
\end{conj}
For convenience, one can normalize the metric such that ${\mathrm {Rc}}=g$. M. Berger first obtained classification under the condition that the sectional curvature is $1/4$-pinched \cite{berger61}. In the last decades, there have been many attempts to completely solve this conjecture; for example, see \cite{gl99, yangdg00, costa04, cao14einstein} and the references therein. In particular, one interesting approach is to assume a positive lower bound on the sectional curvature, i.e., $K_{min}\geq \epsilon>0$; this immediately implies that $K_{max}\leq 1-2\epsilon$, so the sectional curvature is $(\frac{\epsilon}{1-2\epsilon})$-pinched. That is, Berger's result implies classification for Einstein manifolds provided $K_{min}\geq \frac{1}{6}$. There have been various results in this direction. The lower bound has been improved from $\frac{1}{120}(\sqrt{1249}-23)$ by D. Yang \cite{yangdg00} to $\frac16 (2-\sqrt{2})$ by E. Costa \cite{costa04} to $\frac{1}{12}$ by the first author and P. Wu \cite{cao14einstein}. There are also classification results under related conditions such as $K\geq 0$ and positive intersection form \cite{gl99}, non-negative curvature operator \cite{tachibana}, nonnegative isotropic curvature \cite{brendle10einstein}, and 3-nonnegative curvature operator \cite{cao14einstein}. \\
It is noted that $K\geq 0$ implies $K\leq 1$. So it is also interesting to consider upper bounds on the sectional curvature (say $K\leq 1$) instead of lower bound. Costa \cite{costa04} observed that if $K\leq \frac{2}{3}$ then the Einstein manifold must be $\mathbb{S}^4$, $\mathbb{CP}_2$ or their quotients. Note that without assuming non-negativity of sectional curvature, an upper bound on $K$ gives, due to the algebraic structure, \textit{a priori} lower bound on $K$. For instance if $K\leq 1$ implies $K\geq -2$. But a careful analysis of the differential structure would give a better bound. In particular, using \cite[Proposition 2.4(3)]{cao14einstein}, one can show that the condition $K< 1$ is equivalent to the Riemannian curvature operator being 4-positive; hence, it follows that \[K> \frac{1}{28}(7-\sqrt{105})\approx -.11596.\]
That's our motivation to derive the following improvements.
\begin{theorem}
Let $(M,g)$ be a complete smooth 4-manifold such that ${\mathrm {Rc}}=g$. Assume the sectional curvature satisfies either one of the following conditions:
\begin{itemize}
\label{maineinstein}
\item[a.]$K\leq \frac{14-\sqrt{19}}{12}\approx .8034.$
\item[b.] At each point $q\in M$, for every orthonormal basis $\{e_i\}_{i=1}^4 \in T_qM$ which satisfies $K(e_1,e_2)\geq K(e_1,e_3)$,
\[2K(e_1,e_2)+K(e_1,e_3)\geq \frac{\sqrt{19}-3}{4}\approx .3397247.\]
\end{itemize}
Then $(M,g)$ is isometric to either $(S^4,g_{0})$, $(\mathbb{RP}^4, g_0)$, or $(\mathbb{CP}^2,\ g_{FS})$ up to rescaling.
\end{theorem}
\begin{remark} Condition (a) is an improvement of Costa's result where the upper bound is $\frac{2}{3}\approx .6666$. Condition (b) generalizes a result of \cite{yangdg00} where the lower bound is $9/14\approx .642857$. As explained in Section \ref{classify}, this is essentially an upper bound on the difference between two highest sectional curvatures; see Berger's decomposition in Section 2.
\end{remark}
Here is a sketch of the proof. The main idea is to make use of elliptic equations, which arise from Ricci flow computation, to study a static metric (see \cite{brendle10einstein, caotran1, cao14einstein, tran16weyl} for similar exploitation of this approach). In particular, Brendle first observed a Bochner formula for the Riemannian curvature on an Einstein manifold. Considering this formula at point $p$, which realizes the minimal sectional sectional curvature, yields an inequality involving only zero order terms. Thus, either condition leads to a lower bound of $K$, which improves the \textit{a priori} bound. The rest of the proof is an adaptation of arguments in \cite{yangdg00, cao14einstein}: integrating a Bochner-Weitzenb\"ock identity of the Weyl tensor and pinched sectional curvature imply the manifold is half-conformally flat. Then Hitchin's classification theorem of such manifolds completes our proof. \\
The organization of the paper is as follows. The next section collects preliminaries including Berger's curvature decomposition, the inequality at point $p$ realizing the minimal sectional sectional curvature, and classifications by a condition on the Weyl tensor. Section \ref{sectionestimate} derives estimates from the algebraic structure of the curvature and the inequality resulted from the differential structure. Finally, the last section provides proof of the main theorem.
\section{Preliminaries}
\subsection{\textbf{Curvature decomposition for Einstein four-manifolds}}
On an oriented four-manifold $(M,\ g)$, let ${\mathrm R}, K, {\mathrm {Rc}}, {\mathrm S}, {\mathrm W}$ denote the Riemann curvature, sectional curvature, Ricci curvature, scalar curvature and Weyl curvature respectively. Also $\chi$ and $\tau$ denote the Euler characteristic and topological signature. The Hodge star operator induces a natural decomposition of the vector bundle of 2-forms
$\wedge^2 TM$
\begin{equation*}
\wedge^2 TM =\wedge^+ M \oplus \wedge^- M,
\end{equation*}
where $\wedge^{\pm} M$ are the eigenspaces of $\pm 1$ respectively.
Elements of $\wedge^+ M$ and $\wedge^- M$ are called self-dual and
anti-self-dual.
Furthermore, it leads a decomposition for the curvature operator ${\mathrm R}: \wedge^2 TM
\rightarrow \wedge^2 TM$:
\begin{equation*}
{\mathrm R} =\left( \begin{array}{cc}
\frac{{\mathrm S}}{12}\mathrm{Id}+{\mathrm W}^+ & {\mathrm {Rc}}-\frac{{\mathrm S}}{4}\mathrm{Id} \\
{\mathrm {Rc}}-\frac{{\mathrm S}}{4}\mathrm{Id} & \frac{{\mathrm S}}{12}\mathrm{Id}+{\mathrm W}^-
\end{array} \right),
\end{equation*}
for ${\mathrm W}^{\pm}$ the restriction of ${\mathrm W}$ to $\wedge^{\pm}M$. Here ${\mathrm E}={\mathrm {Rc}}-\frac{{\mathrm S}}{4}\mathrm{Id}$ is the traceless Ricci part. If the manifold is closed, then the Gauss-Bonnet-Chern formula for the Euler characteristic and Hirzebruch formulas for the signature (cf. \cite{Besse} for more details) are,
\begin{align}
\label{Euler}
8\pi^2 \chi(M) &= \int_{M}(|{\mathrm W}|^2-\frac{1}{2}|{\mathrm E}|^2+\frac{S^2}{24}) dv;\\
\label{signature}
12 \pi^2 \tau(M) &=\int_{M}(|{\mathrm W}^{+}|^2-|{\mathrm W}^{-}|^2)dv.
\end{align}
\begin{remark} It follows immediately that if M admits an Einsterin metric then ${\mathrm E}=0$,
\begin{equation}
\label{dual}
{\mathrm R} =\left( \begin{array}{cc}
{\mathrm R}^+ & 0 \\
0 & {\mathrm R}^-
\end{array} \right)=\left( \begin{array}{cc}
\frac{{\mathrm S}}{12}\mathrm{Id}+{\mathrm W}^+ & 0 \\
0 & \frac{{\mathrm S}}{12}\mathrm{Id}+{\mathrm W}^-
\end{array} \right).
\end{equation}
Also as a direct consequence of (\ref{Euler}) and (\ref{signature}), we have the Hitchin-Thorpe inequality
\begin{equation*}
|\tau(M)|\leq \frac{2}{3}\chi(M).
\end{equation*}
\end{remark}
For instance, the curvature of $\mathbb{S}^4$ ($\chi=2,\tau=0$) with standard metric $g_0$ is:
\begin{equation}
{\mathrm R}=\left( \begin{array}{cc}
\frac{{\mathrm S}}{12}\mathrm{Id} & \\
& \frac{{\mathrm S}}{12}\mathrm{Id}
\end{array} \right)
\end{equation}
$(\mathbb{RP}^4, g_0)$ is the quotient of $(\mathbb{S}^4,g_0)$. The curvature of $\mathbb{CP}^2$ ($\chi=3,\tau=1$) with Fubini-Study metric $g_{FS}$ is:
\begin{equation}
{\mathrm R}=\left( \begin{array}{cc}
\mathrm{Diag} \{0,\ 0, \ \frac{{\mathrm S}}{4}\}& \\
& \frac{{\mathrm S}}{12}\mathrm{Id}
\end{array} \right).
\end{equation}
The self-dual part of Weyl tensor ${\mathrm W}^+=\mathrm{Diag}\{-\frac{{\mathrm S}}{12}, \ -\frac{{\mathrm S}}{12}, \ \frac{{\mathrm S}}{6}\}$ and anti-self-dual part ${\mathrm W}^{-}=0$.
The curvature of $\mathbb{S}^2\times \mathbb{S}^2$ ($\chi=4,\tau=0$) with the product metric is
\begin{equation}
{\mathrm R}=\left( \begin{array}{cc}
A & 0\\
0 & A
\end{array} \right)
\end{equation}
for $A=\mathrm{Diag}\{0,\ 0,\ \frac{{\mathrm S}}{4}\}$. The self-dual part and anti-self-dual part of the Weyl tensor are
${\mathrm W}^{\pm}=\mathrm{Diag}\{-\frac{{\mathrm S}}{12},\ -\frac{{\mathrm S}}{12},\ \frac{{\mathrm S}}{6}\}$. \\
The duality decomposition also implies that, ${\mathrm R},{\mathrm R}^{\pm},{\mathrm W},{\mathrm W}^{\pm}$ of an Einstein four-manifold are all harmonic.
Using the harmonicity of ${\mathrm W}^{\pm}$, A. Derdzi\'nski \cite{Derd83}
derived the following Weitzenb\"ock formula (also see A. Besse
\cite[Prop. 16.73]{Besse}),
\begin{prop}
Let $(M,\ g)$ be an Einstein four-manifold, then
\begin{equation}
\label{weitzenbock}
\Delta|W^{\pm}|^2 = 2|\nabla W^{\pm}|^2
+{\mathrm S} |W^{\pm}|^2 -36\det W^{\pm}.
\end{equation}
\end{prop}
It was observed by Gursky-LeBrun \cite{gl99} and Yang
\cite{yangdg00} that ${\mathrm W}^{\pm}$ satisfies the following refined Kato inequality (proven to be
optimal by \cite{branson00, CGH00weight}),
\begin{prop}
Let $(M,\ g)$ be an Einstein four-manifold, then
\begin{equation}
\label{Kato}
|\nabla W^{\pm}|^2\geq \frac{5}{3}|\nabla|W^{\pm}||^2.
\end{equation}
\end{prop}
On the other hand, Berger \cite{berger61} has another curvature
decomposition for Einstein four-manifolds (also see
\cite{st69}).
\begin{prop}
\label{berger}
Let $(M,\ g)$ be an Einstein four-manifold with ${\mathrm {Rc}}=\lambda g$. For
any $p\in M$, there exists an orthonormal basis $\{e_i\}_{1\leq i\leq
4}$ of $T_p M$, such that relative to the corresponding basis
$\{e_i\wedge e_j\}_{1\leq i<j\leq 4}$ of $\wedge^2 T_pM$,
${\mathrm R}$ takes the form
\begin{equation}
\label{abba}
{\mathrm R}=\left( \begin{array}{cc}
A & B\\
B & A
\end{array}\right),
\end{equation}
where $A=\mathrm{Diag}\{a_1,\ a_2,\ a_3\}$, $B=\mathrm{Diag} \{b_1,\ b_2,\ b_3\}$.
Moreover, we have the followings:
\begin{enumerate}
\item $a_1=K(e_1, e_2)=K(e_3, e_4)=\min\{K(\sigma): \sigma\in\wedge^2 T_p M,||\sigma||=1\}$,\\
$a_3=K(e_1,e_4)=K(e_2,e_3)=\max\{K(\sigma):\sigma\in\wedge^2 T_p M, ||\sigma||=1\}$,\\
$a_2=K(e_1, e_3)=K(e_2, e_4)$, and $a_1+a_2+a_3=\lambda$;
\item $b_1=R_{1234},\ b_2=R_{1342},\ b_3=R_{1423}$,
\item $|b_2-b_1|\leq a_2-a_1,\ |b_3-b_1|\leq a_3-a_1,\ |b_3-b_2|\leq
a_3-a_2$.
\end{enumerate}
\end{prop}
One can easily observe that, for
Einstein four-manifolds, diagonalization of (\ref{abba}) becomes (\ref{dual}). As a consequence, eigenvalues of the curvature operator are ordered,
\begin{equation}
\label{eigenvalue}
\begin{cases}
a_1+b_1 \leq a_2+b_2 \leq a_3+b_3, &\\
a_1-b_1 \leq a_2-b_2 \leq a_3-b_3. &
\end{cases}
\end{equation}
Here
$a_i+b_i\ (1\leq i\leq 3)$ are eigenvectors of self-dual $2$-forms, and $a_i-b_i\ (1\leq i\leq 3)$ are eigenvectors
of anti-self-dual $2$-forms. Furthermore, ${\mathrm W}^{\pm}$ are given by,
\begin{equation}\label{eigenvalueW}
\begin{cases}
{\mathrm W}^+(\omega^+_i,\omega^+_j) = [(a_i+b_i)-\frac{s}{12}]\delta_{ij}, &\\
{\mathrm W}^-(\omega^-_i,\omega^-_j) = [(a_i-b_i)-\frac{s}{12}]\delta_{ij}, &
\end{cases}
\end{equation}
where $\{\omega^\pm_i\}_{1\leq i\leq 3}$ are the corresponding orthonormal bases of $\wedge^\pm M$ using Prop \ref{berger}.\\
In the following, we normalize the metric such that ${\mathrm {Rc}}=g$. Recall that for Einstein manifolds (see \cite{H3} or
\cite{brendle10einstein}),
\begin{equation*} \Delta
R(e_i,e_j,e_k,e_l) +2(B_{ijkl}-B_{ijlk}+B_{ikjl}-B_{iljk})
=2R_{ijkl},
\end{equation*}
where $B_{ijkl}=g^{mn}g^{pq}R_{imjp}R_{knlq}$. Berger's
curvature decomposition yields explicitly that
\begin{equation*}
\Delta R(e_1,e_2,e_1,e_2) +2(a_1^2+b_1^2+2a_2a_3+2b_2b_3) = 2a_1.
\end{equation*}
Let \textbf{$p$} be the point that realizes the minimum of the sectional curvature of $(M^4,g)$ by the tangent plane spanned by $\{e_1,e_2\}\subset T_p M$. For
any $v\in T_p M$ and geodesic $\gamma(t)$ with $\gamma(0)=p,\
\gamma'(0)=v$, let $\{e_1,\ e_2,\ e_3,\ e_4\}$ be a parallel
orthornormal frame along $\gamma(t)$, then we have
\begin{equation*}
\begin{split}
(D^2_{v,v}R)(e_1,e_2,e_1,e_2)(p)=D^2_{v,v}(R(e_1,e_2,e_1,e_2))(p)\geq0.
\end{split}
\end{equation*}
Hence it follows that $(\Delta R)(e_1,e_2,e_1,e_2)(p) \geq 0$. Thus, at $p$, the following holds
\begin{equation}
\begin{split}
a_1^2+b_1^2+2(a_2a_3+b_2b_3)&\leq a_1.
\end{split} \label{Hamilton}
\end{equation}
\subsection{\textbf{Classification by estimates on ${\mathrm W}^\pm$.}}
We also need the following, which is implicit in \cite{cao14einstein}. A proof is provided for completeness.
\begin{prop}
\label{propWpm}
Let $(M, g)$ be an Einstein four-manifold $Rc=g$
such that,
\[|{\mathrm W}^+|+|{\mathrm W}^-|\leq \sqrt{\frac{3}{2}}\]
Then it is isometric to either $(S^4,g_{0})$, $(\mathbb{RP}^4, g_0)$, or $(\mathbb{CP}^2,\ g_{FS})$ up to rescaling.
\end{prop}
\begin{proof}
If the manifold is half-conformally flat, then, by Hitchin's classification \cite[Theorem 13.30]{Besse}, the result follows. If not, then for some $\alpha>0$ to be determined later, and any $\epsilon>0$, there exists
$t=t(\alpha,\epsilon)\in \mathbb{R}^{+}$, such that
\begin{equation*}
\int_M
(|W^+|^2+\epsilon)^{\frac{\alpha}{2}}-t(|W^-|^2+\epsilon)^{\frac{\alpha}{2}}
dv=0.
\end{equation*}
Also $t(\alpha,\epsilon)\rightarrow t(\alpha, 0)$ as
$\epsilon\rightarrow 0$.
\
Applying Weitzenb\"ock formula (\ref{weitzenbock}) and refined Kato inequality (\ref{Kato}) yields,
\begin{align*}
& \Delta[(|W^+|^2+\epsilon)^\alpha+t^2(|W^-|^2+\epsilon)^\alpha]\\
=& \alpha(|W^+|^2+\epsilon)^{\alpha-2}[(|W^+|^2+\epsilon)(2|\nabla W^+|^2+{\mathrm S}|W^+|^2-36\det W^+)+(\alpha-1)|\nabla|W^+|^2|^2]\nonumber \\
+& t^2\alpha(|W^-|^2+\epsilon)^{\alpha-2}[(|W^-|^2+\epsilon)(2|\nabla W^-|^2+{\mathrm S}|W^-|^2-36\det W^-)+(\alpha-1)|\nabla|W^-|^2|^2] \nonumber\\
\geq& [(4-\frac{2}{3\alpha})|\nabla(|W^+|^2+\epsilon)^{\frac{\alpha}{2}}|^2+\alpha(|W^+|^2+\epsilon)^{\alpha-1}({\mathrm S}|W^+|^2-36\det W^+)]\nonumber \\
+&
t^2[(4-\frac{2}{3\alpha})|\nabla(|W^-|^2+\epsilon)^{\frac{\alpha}{2}}|^2+\alpha(|W^-|^2+\epsilon)^{\alpha-1}({\mathrm S}|W^-|^2-36\det W^-)]. (*)\\
\end{align*}
Using the Poincar\'e inequality, we have
\begin{equation*}
\begin{split}
&(4-\frac{2}{3\alpha})\int_M
(|\nabla(|W^+|^2+\epsilon)^{\frac{\alpha}{2}}|^2+t^2|\nabla(|W^-|^2+\epsilon)^{\frac{\alpha}{2}}|^2)
dv\\
&\geq (2-\frac{1}{3\alpha})\int_M|\nabla[(|W^+|^2+\epsilon)^{\frac{\alpha}{2}}-t(|W^-|^2+\epsilon)^{\frac{\alpha}{2}}]|^2 dv\\
&\geq (2-\frac{1}{3\alpha})\lambda_1 \int_M
[(|W^+|^2+\epsilon)^{\frac{\alpha}{2}}-t(|W^-|^2+\epsilon)^{\frac{\alpha}{2}}]^2dv,
\end{split}
\end{equation*}
where $\lambda_1$ is the lowest positive eigenvalue of the Laplace
operator. In our case that $\text{Ric}=g$, we have $\lambda_1 \geq
\frac{4}{3}$ (see, for example, \cite{Lich58}).
Picking $\alpha=\frac{1}{3}$, which maximizes the value of
$\frac{1}{\alpha}(2-\frac{1}{3\alpha})$, substituting ${\mathrm S}=4$, and integrating the above
inequality (*), we obtain
\begin{equation*}
\begin{split}
0\geq \frac13 \int_M&
\Big(4\Big[(|W^+|^2+\epsilon)^{\frac{1}{6}}-t(|W^-|^2+\epsilon)^{\frac{1}{6}}\Big]^2+t^2(|W^-|^2+\epsilon)^{-2/3}(4|W^-|^2-36\det
W^-)\\
&+(|W^+|^2+\epsilon)^{-2/3}(4|W^+|^2-36\det W^+)\Big)dv.
\end{split}
\end{equation*}
Recall the algebraic inequalities,
\[36\text{det}(W^{\pm})\leq 2\sqrt{6}|W^{\pm}|^3.\]
Now let $\epsilon\rightarrow 0$, we get
\begin{align*}
0\geq & \int_M \Big(t^2|W^-|^{-4/3}({\mathrm S}|W^-|^2-36\det
W^-)+4(|W^+|^{1/3}-t|W^-|^{1/3})^2\\
&+|W^+|^{-4/3}(4|W^+|^2-36\det W^+)\Big)dv,\\
\geq & \int_M \Big(t^2|W^-|^{2/3}(4-2\sqrt{6}|W^-|)+4(|W^+|^{1/3}-t|W^-|^{1/3})^2\\
&+|W^+|^{2/3}(4-2\sqrt{6}|W^+|)\Big)dv\\
\geq & \int_M \Big(t^2 |W^-|^{2/3}(8-2\sqrt{6}|W^-|)-8t|W^+|^{1/3}|W^-|^{1/3}+|W^+|^{2/3}(8-2\sqrt{6}|W^+|)\Big)dv.
\end{align*}
The integrand is a quadratic function of $t$, with positive leading
coefficient and discriminant
\[
D=|W^+|^{2/3}|W^-|^{2/3}(16-64+16\sqrt{6}(|W^+|+|W^-|)-24|W^+||W^-|\leq 0.
\]
So equality must happen at each point and so either $|{\mathrm W}^+|$ or $|{\mathrm W}^-|$ must vanish at each point. As both are analytic functions, one of them must be vanishing at every point. So the manifold is half-conformally flat, a contradiction.
\end{proof}
\section{Estimates}
\label{sectionestimate}
In this section, we derive estimates from the algebraic structure of ${\mathrm W}^{\pm}$ and the differential inequality (\ref{Hamilton}).
\subsection{Algebraic Estimates}
The technical lemma below estimates the norm of ${\mathrm W}^{\pm}$ by pinching of sectional curvature.
\begin{lemma}
\label{k3k1}
Using the Berger's decomposition Prop. \ref{berger}, suppose
\begin{align*}
a_3-a_2 &= \frac{\delta}{2}\geq 0,\\
a_3+a_2 &= \alpha>0.
\end{align*}
Then
\begin{align*} \delta &\leq 6\alpha-4;\\
|W^{+}|+|W^{-}| &\leq \frac{6\alpha-4+\delta}{\sqrt{6}},\\
|W^{+}|^2+|W^{-}|^2 &\leq \frac{1}{2}(12\alpha^2-16\alpha+\frac{16}{3}+\delta^2)\\
&= 8(a_3^2-(1-a_1)(1-a_2)+\frac{1}{3}).
\end{align*}
\end{lemma}
\begin{proof} We'll prove the first estimate while the second one follows from the same method. Let $\{\lambda_i, \mu_i\}_{i=1}^3$ be eigenvalues of ${\mathrm W}^\pm$. By (\ref{eigenvalueW}) the assumptions above translate to
\begin{align*}
\lambda_3+\lambda_2+\mu_3+\mu_2 =\alpha_1=2(\alpha-\frac{2}{3}),\\
\lambda_3-\lambda_2+\mu_3-\mu_2 &= \delta,\\
-\frac{\lambda_3}{2}\leq \lambda_2\leq \lambda_3,\\
-\frac{\mu_3}{2}\leq \mu_2\leq \mu_3.
\end{align*}
Then
\begin{align*}
|W^{+}|+|W^{-}|&= \sqrt{2}(\sqrt{\lambda_3^2+\lambda_2^2+\lambda_3\lambda_2}+\sqrt{\mu_3^2+\mu_2^2+\mu_3\mu_2},\\
&=\sqrt{2}(\sqrt{\frac{3}{4}(\lambda_3+\lambda_2)^2+\frac{1}{4}((\lambda_3-\lambda_2)^2}+\sqrt{\frac{3}{4}(\mu_3+\mu_2)^2+\frac{1}{4}((\mu_3-\mu_2)^2}).
\end{align*}
So we consider the following problem.
For,
\begin{align*}
\lambda_3+\lambda_2 &=p,\\
\lambda_3-\lambda_2 &=q,\\
\mu_3+\mu_2 &=m,\\
\mu_3-\mu_2 &=n.
\end{align*}
The constraints become:
\begin{align*}
p+m &= \alpha_1,\\
q+n &= \delta,\\
0 &\leq q\leq 3p,\\
0 &\leq n\leq 3m.
\end{align*}
The goal is to maximize
\[f(p,q,m,n)=\sqrt{3p^2+q^2}+\sqrt{3m^2+n^2}.\]
First, since the constraint is a closed set, the maximum exists.
Next, we consider the problem with 2 variables $m, n$. The constraints become,
\begin{align*}
0 &\leq 3m-n=\ell \leq 3\alpha_1-\delta,\\
0 &\leq n\leq \delta.
\end{align*}
The function to maximize is
\begin{align*}
f(m,n) &= \sqrt{3(\alpha_1-m)^2+(\delta-n)^2}+\sqrt{3m^2+n^2},\\
\sqrt{3}f(m,n) &=\sqrt{(3\alpha_1-\ell-n)^2+3(\delta-n)^2}+\sqrt{(\ell+n)^2+3n^2},\\
&=g(\ell,n).
\end{align*}
We consider the following cases.
\textbf{Case 1:} $n=0$ then
\begin{align*}
g(\ell,0)
&=\sqrt{(\ell-3\alpha_1)^2+3\delta^2}+\ell.
\end{align*}
Since the function $f(x)=\sqrt{x^2+a^2}+x$, $a>0$, is strictly increasing,
\[g(\ell,0)\leq 3\alpha_1+\delta.\]
\textbf{Case 2:} $\ell=0$ then
\begin{align*}
g(n,0) &= \sqrt{4n^2-6(\alpha_1+\delta)n+ 9\alpha_1^2+3\delta^2}+2n,\\
&=\sqrt{(2n-\frac{3}{2}(\alpha_1+\delta))^2+(\frac{3\sqrt{3}}{2}\alpha_1-\frac{\sqrt{3}}{2}\delta)^2}+2n\\
& \leq 3\alpha_1+\delta.
\end{align*}
\textbf{Case 3:} $n=\delta$ then
\begin{align*}
g(\ell,\delta)
&=(3\alpha_1-\delta)-\ell+\sqrt{(\ell+\delta)^2+3\delta^2},\\
&\leq 3\alpha_1+\delta.
\end{align*}
\textbf{Case 4:} $\ell=3\alpha_1-\delta$ then
\begin{align*}
g(3\alpha_1-\delta,n) &= 2(\delta-n)+\sqrt{(2n+\frac{1}{2}(3\alpha_1-\delta))^2+\frac{3}{4}(3\alpha_1-\delta)^2}\\
&\leq 3\alpha_1+\delta.
\end{align*}
\textbf{Case 5:} At a critical point,
\begin{align*}
0=\partial_\ell g &=-\frac{3\alpha_1-\ell-n}{\sqrt{(3\alpha_1-\ell-n)^2+3(\delta-n)^2}}+\frac{\ell+n}{\sqrt{(\ell+n)^2+3n^2}},\\
0=\partial_n g &=-\frac{3\alpha_1+3\delta-\ell-4n}{\sqrt{(3\alpha_1-\ell-n)^2+3(\delta-n)^2}}+\frac{4n+\ell}{\sqrt{(\ell+n)^2+3n^2}}
\end{align*}
Therefore, at that point,
\begin{align*}
\frac{\ell+n}{(3\alpha_1-\delta-\ell)+(\delta-n)} &=\frac{4n+\ell}{(3\alpha_1-\delta-\ell)+4(\delta-n)}\\
&=\frac{n}{\delta-n}=\frac{\ell}{3\alpha_1-\delta-\ell}=\frac{1}{x}.
\end{align*}
Then,
\begin{align*}
g(\ell,n)&=(x+1)\sqrt{(\frac{3\alpha_1-\delta}{x+1}+\frac{\delta}{x+1})^2+(\frac{\delta}{x+1})^2}\\
&=\sqrt{9\alpha_1^2+\delta^2}\leq 3\alpha_1+\delta.
\end{align*}
\end{proof}
\begin{remark} The first estimate generalizes and unifies \cite[Lemma 4.1]{yangdg00} which treats the case $\alpha\leq 1-\epsilon$, $\delta\leq 2(1-3\epsilon)$ in part (a.) and $\alpha\leq 1$, $\delta \leq 1-6\epsilon$ in part (b.).
\end{remark}
\begin{remark}
The condition that $6\alpha+\delta-4\leq 3$ implies $3$-non-negative curvature.
\end{remark}
\begin{coro}
\label{eulerestimate}Let $(M, g)$ be an Einstein four-manifold ${\mathrm {Rc}}=g$
such that at each point, $\alpha\leq a_1\leq a_3\leq \beta$, then
\[8\pi^2 \chi(M) \leq \Big(8(\beta^2-(1-\alpha)(\alpha+\beta)+\frac{10}{3}\Big)\text{Vol}(M).\]
\end{coro}
\begin{proof}
Recall,
\[8\pi^2 \chi(M)=\int_M (|{\mathrm W}^+|^2+|{\mathrm W}^-|^2+\frac{{\mathrm S}^2}{24}) d\mu.\]
By Lemma \ref{k3k1}, at each point,
\[|W^{+}|^2+|W^{-}|^2 \leq 8(a_3^2-(1-a_1)(1-a_2)+\frac{1}{3}).\]
So it remains to maximize, given the pinching condition on $a_1, ~a_3$,
\[f(a_1, a_3)=a_3^2-(1-a_1)(a_1+a_3).\]
By the algebraic properties of $a_1, ~a_3$, the domain here is a quadrilateral determined by lines $x=\alpha, y=\beta, 2x+y=1, 2y+x=1$ (which is already within the half-plane $y\geq x$). So standard technique yields,
\[|W^{+}|^2+|W^{-}|^2 \leq 8(\beta^2-(1-\alpha)(\alpha+\beta)+\frac{1}{3}).\]
The result then follows.
\end{proof}
\begin{remark}
In \cite{gl99}, the authors show that if ${\mathrm W}^+\not \equiv 0$ then,
\[\int_M |{\mathrm W}^+|^2 dv\geq \frac{2}{3}\text{Vol}(M).\]
That is, if the Einstein 4-manifold is not half-conformally flat then,
\[8\pi^2 \chi(M) \geq 2 \text{Vol}(M).\]
They also observe that if $a_1\geq 0$ then,
\[8\pi^2 \chi(M) \leq \frac{10}{3}\text{Vol}(M).\]
As a consequence, it follows that \[9\geq \chi(M)>\frac{15}{4}|\tau(M)|.\]
Therefore, there are only finitely many homeomorphism types for an Einstein 4-manifold with non-negative sectional curvature and not half-conformally flat. Corollary \ref{eulerestimate} then gives a more precise description of the relation between the topology type and bound on the sectional curvature. For instance, if $a_1> \alpha=\frac{2-\sqrt{3}}{6}\approx .04466$ then we could choose $\beta=1-2\alpha$ and then $(|\tau|, \chi)$ could only be one of the following choices $(1, 5), (1,7),$ $(0, 2), (0,4), (0,6)$.
\end{remark}
\subsection{Differential Estimates} Here we derive several consequences of (\ref{Hamilton}). First we observe the following.
\begin{lemma}
\label{algebraic2}
Let $xy\leq 0$ and assume
\begin{align*}
|2x+y| &\leq a,\\
|x-y| &\leq b.
\end{align*}
If $2a<b$ then \[4xy+x^2+y^2\geq \frac{1}{3}(2a^2-2ab-b^2).\]
If $2a\geq b$ then \[4xy+x^2+y^2\geq -\frac{1}{2}b^2.\]
\end{lemma}
\begin{proof}
Let $m=2x+y$ and $n=x-y$ then
\begin{align*}
9(4xy+x^2+y^2) &=(m+n)^2+(m-2n)^2+4(m+n)(m-2n)\\
&=6m^2-3n^2-6mn\:=f(m,n).
\end{align*}
Consider the region $D=\{-a\leq m\leq a; -b\leq n\leq b\}$. The only critical point of $f(m,n)$ is $(0,0)$ and $f(0,0)=0$. So we consider the function along the boundary of $D$ and the result follows.
\end{proof}
Recall that \textbf{$p$} is the point that realizes the minimum of the sectional curvature of $(M^4,g)$ by the tangent plane spanned by $\{e_1,e_2\}$. At point $p$, we get:
\begin{equation*}
\begin{split}
a_1^2+b_1^2+2(a_2a_3+b_2b_3)&\leq a_1.
\end{split}
\end{equation*}
Also by Prop \ref{berger} we observe,
\begin{align*}
|b_2-b_3| &\leq a_3-a_2=b,\\
|b_2-b_1|=|2b_2+b_3|&\leq a_2-a_1=a,\\
b_1^2+2b_2b_3 &=b_2^2+b_3^2+4b_2b_3.
\end{align*}
So Lemma \ref{algebraic2} implies the followings:
\begin{itemize}
\item If $2a<b$ or $a_1+1\geq 4a_2$ then
\[b_1^2+2b_2b_3\leq (a_2-a_1)^2 -\frac{1}{3}(a_3-a_1)^2.\]
\item If $2a\geq b$ or $a_1+1\leq 4a_2$ then
\[b_1^2+2b_2b_3\leq -\frac{1}{2}(a_3-a_2)^2.\]
\end{itemize}
Consequently, it is possible to obtain a lower bound for sectional curvature given an upper bound.
\begin{lemma}
\label{Kupper}
At point $p$, suppose $a_3=\alpha\leq 1$ then we have:
\begin{align*}
4a_2 &\leq a_1+1,\\
a_1 & \geq \frac{1}{28}(15-8\alpha-\sqrt{3}\sqrt{96\alpha^2-80\alpha+19}).
\end{align*}
\end{lemma}
\begin{proof}
Let $\delta=a_1=\min K$ at point $p$ then we have
\begin{align*}
a_3 &=\alpha,\\
a_1 &=\delta,\\
a_2 &= 1-\alpha-\delta,\\
a_2+a_3 &=1-\delta,\\
a_2a_3 &= (1-\alpha-\delta)\alpha.
\end{align*}
If $b_2b_3\geq 0$ then equation (\ref{Hamilton}) becomes
\[\delta=a_1\geq a_1^2+2a_2a_3\geq \delta^2+2\delta(1-2\delta)=2\delta-3\delta^2.\]
If $a_1< 0$ then $a_2< 0$ and, consequently $a_3> 1$, a contradiction. So either $a_1=a_2=0$ or $a_1=a_2=\frac{1}{3}$. \\
If $b_2b_3< 0$ then we consider two cases.
\textbf{Case 1:} $4a_2 > 1+a_1$ and, by the discussion following Lemma \ref{algebraic2}, we have
\begin{align*}
\delta=a_1 &\geq a_1^2+2a_2a_3+b_2^2+b_3^2+4b_2 b_3\\
\delta &\geq \delta^2+2(1-\alpha-\delta)\alpha-\frac{( 2\alpha-1+\delta)^2}{2};\\
0 &\geq \delta^2- 8\alpha\delta+8\alpha-8\alpha^2-1\\
0 &\geq \delta^2-8\alpha\delta+\alpha_1.
\end{align*}
As a consequence,
\[4\alpha-\sqrt{16\alpha^2-\alpha_1}\geq \delta\geq 4\alpha-\sqrt{16\alpha^2-\alpha_1}.\]
So,
\begin{align*}
1 &=a_1+a_2+a_3\\
&> a_1+\frac{1}{4}(1+a_1)+\alpha,\\
\frac{3}{4}&> \frac{5}{4}(4\alpha-\sqrt{24\alpha^2+1-8\alpha}+\alpha\\
&> 6\alpha -\frac{5}{4}\sqrt{24\alpha^2+1-8\alpha}.
\end{align*}
But that is a contradiction for $\frac{1}{3}\leq \alpha\leq 1$. Thus this case does not hold.
\textbf{Case 2:} $4a_2 \leq 1+a_1$ and, by the discussion following Lemma \ref{algebraic2}, we have
\begin{align*}
\delta=a_1 &\geq a_1^2+2a_2a_3+b_2^2+b_3^2+4b_2 b_3\\
\delta &\geq \delta^2+2(1-\alpha-\delta)\alpha + (1-\alpha-2\delta)^2-\frac{(\alpha-\delta)^2}{3};\\
0 &\geq 14\delta^2+(8\alpha-15)\delta+3-4\alpha^2.
\end{align*}
As a consequence,
\[\frac{1}{28}(15-8\alpha+\sqrt{3}\sqrt{96\alpha^2-80\alpha+19}\geq \delta\geq \frac{1}{28}(15-8\alpha-\sqrt{3}\sqrt{96\alpha^2-80\alpha+19}.\]
\end{proof}
\begin{coro}
\label{possec}
At $p$, if $a_3\leq \frac{\sqrt{3}}{2}\approx .866025$ then $K\geq 0$.
\end{coro}
\begin{proof}
Let $a_3=\alpha$ at point p. Then by Lemma \ref{Kupper},
\begin{align*}
a_1 &\geq 0\\
15-8\alpha &\geq \sqrt{3}\sqrt{96\alpha^2-80\alpha+19} \\
\leftrightarrow -\frac{\sqrt{3}}{2} \leq \alpha &\leq \frac{\sqrt{3}}{2}.
\end{align*}
\end{proof}
\begin{remark}
Z. Zhang \cite{zhang2016four} obtains a similar result but we fail to follow the proof.
\end{remark}
\begin{lemma}
\label{Kdiffbound}
At point $p$ suppose $0\leq a_3-a_2=\alpha<2$ then
\begin{align*}
4a_2&\leq a_1+1,\\
a_1 &\geq \beta=\frac{1}{6}(3-2\alpha-\sqrt{1+8\alpha^2-4\alpha}).
\end{align*}
\end{lemma}
\begin{proof}
Let $\delta=a_1=\min K$ at point $p$ then we have
\begin{align*}
a_2+a_3 &=1-\delta,\\
a_3-a_2 &= \alpha,\\
a_2-a_1 &=\frac{1-\alpha-3\delta}{2},\\
4a_2a_3=(a_2+a_3)^2-(a_2-a_3)^2 &= (1-\delta)^2-\alpha^2.
\end{align*}
If $b_2b_3\geq 0$ then equation (\ref{Hamilton}) yields
\begin{align*}
\delta=a_1 &\geq a_1^2+2a_2a_3\geq \delta^2+\frac{1}{2}((1-\delta)^2-\alpha^2);\\
0 &\geq \frac{3}{2}\delta^2-2\delta+\frac{1}{2}(1+\alpha^2)
\end{align*}
Therefore if $\alpha>\frac{1}{\sqrt{3}}$ there is a contradiction. For $0\leq \alpha\leq \frac{1}{\sqrt{3}}$, we have,
\[\frac{1}{3}\leq \frac{1}{3}(2-\sqrt{1-3\alpha^2})\leq \delta \leq \frac{1}{3}(2+\sqrt{1-3\alpha^2}). \]
Therefore, $a_1=a_2=a_3=\frac{1}{3}$. \\
If $b_2b_3< 0$ then we consider two cases.
\textbf{Case 1:} If $4a_2> a_1+1$ then, by the discussion following Lemma \ref{algebraic2}, equation (\ref{Hamilton}) becomes
\begin{align*}
\delta=a_1 &\geq a_1^2+2a_2a_3+b_2^2+b_3^2+4b_2 b_3\\
\delta &\geq \delta^2+\frac{1}{2}((1-\delta)^2-\alpha^2)-\frac{\alpha^2}{2};\\
0 &\geq 3\delta^2- 4\delta+1-2\alpha^2\\
&\geq 3\delta^2-4\delta+\alpha_1.
\end{align*}
As a consequence,
\[\frac{2+\sqrt{4-3\alpha_1}}{3}\geq \delta\geq \frac{2-\sqrt{4-3\alpha_1}}{3}.\]
So,
\begin{align*}
1 &=a_1+a_2+a_3,\\
&=a_1+2a_2+\alpha \geq \frac{1}{2}+\frac{3}{2}a_1+\alpha;\\
\frac{1}{2}&\geq \alpha+1-\frac{1}{2}\sqrt{1+6\alpha^2}.
\end{align*}
For $0\leq \alpha<2$, the inequality above is possible only if $\alpha=0$. That implies $\delta\geq \frac{1}{3}$. So $a_1=a_2=a_3=\frac{1}{3}$, a contradiction to $4a_2> a_1+1$.
\textbf{Case 2:} If $4a_2\leq a_1+1$ then, by the discussion following Lemma \ref{algebraic2}, equation (\ref{Hamilton}) becomes
\begin{align*}
\delta=a_1 &\geq a_1^2+2a_2a_3+b_2^2+b_3^2+4b_2 b_3\\
\delta &\geq \delta^2+\frac{1}{2}((1-\delta)^2-\alpha^2)+(\frac{1-\alpha-3\delta}{2})^2-\frac{1}{3}(\frac{1+\alpha-3\delta}{2})^2;\\
0 &\geq 3\delta^2- \delta(3-2\alpha)+\frac{2}{3}-\frac{2\alpha}{3}-\frac{\alpha^2}{3}.
\end{align*}
As a consequence,
\[\frac{1}{6}(3-2\alpha+\sqrt{1+8\alpha^2-4\alpha})\geq \delta\geq \frac{1}{6}(3-2\alpha-\sqrt{1+8\alpha^2-4\alpha}).\]
\end{proof}
\begin{coro}
\label{possec1}
At $p$, if $a_3-a_2\leq \sqrt{3}-1$ then $K\geq 0$.
\end{coro}
\begin{proof}
Let $a_3-a_2=\alpha$ at point p. Then by Lemma \ref{Kupper},
\begin{align*}
a_1 &\geq 0\\
\leftrightarrow 3-2\alpha &\geq \sqrt{1+8\alpha^2-4\alpha},\\
\leftrightarrow -1-\sqrt{3} &\leq \alpha\leq \sqrt{3}-1.
\end{align*}
As $\alpha\geq 0$ the result follows.
\end{proof}
Lemmas \ref{Kupper} and \ref{Kdiffbound} imply that, at p, $a_2$ and $a_1$ are closed to each other if there is an upper bound on $a_3$ or $a_3-a_2$. The next result estimates $a_2-a_1$ by $a_1$.
\begin{lemma}
\label{a2a1}
Suppose at point $p$,
\begin{align*}
a_1 &=\delta\geq 0,\\
a_2 &=x+\delta\leq \frac{1}{4}+\frac{\delta}{4}.
\end{align*}
Then \[0\leq x\leq 1-3\delta -\frac{1}{2}\sqrt{3+18\delta^2-15\delta}.\]
\end{lemma}
\begin{proof}
We have \[a_3 =\alpha=1-2\delta-x.\]
If $b_2b_3\geq 0$ then equation (\ref{Hamilton}) yields
\begin{align*}
\delta=a_1 &\geq a_1^2+2a_2a_3\geq \delta^2+2(x+\delta)(1-2\delta-x);\\
0 &\leq 2x^2 +x(6\delta-2)+3\delta^2-\delta.
\end{align*}
Therefore,
\[\delta\geq \frac{1}{6}(1-6x+\sqrt{12x^2+12x+1}).\]
So, for $0\leq x\leq 1$,
\[a_1+a_2=2a_1+x\geq x+ \frac{1}{3}(1-6x+\sqrt{12x^2+12x+1})\geq \frac{2}{3}.\]
Thus, $x=0$. \\
We consider $b_2b_3<0$.
Then equation (\ref{Hamilton}) becomes
\begin{align*}
\delta =a_1 &\geq \delta^2+2(x+\delta)\alpha+(b_2^2+b_3^2+4b_2b_3).
\end{align*}
Since $4a_2\leq 1+a_1$, applying the discussion after Lemma \ref{algebraic2} into equation (\ref{Hamilton}) yields
\begin{align*}
\delta =a_1 &\geq \delta^2+2(x+\delta)\alpha+(b_2^2+b_3^2+4b_2b_3),\\
\delta =a_1 &\geq \delta^2+2(x+\delta)\alpha+\frac{1}{3}(2x^2-2x(\alpha-x-\delta)-(\alpha-x-\delta)^2),\\
&\geq \delta^2+2(x+\delta)\alpha+x^2-\frac{1}{3}(\alpha-\delta)^2;\\
0 &\geq x^2+2x\alpha+2\delta\alpha+\delta^2-\delta-\frac{1}{3}(\alpha-\delta)^2.
\end{align*}
Substituting $\alpha=1-2\delta-x$ then yields,
\begin{align*}
0 &\leq 4x^2-8x(1-3\delta)+(1-9\delta+18\delta^2).
\end{align*}
This quadratic has the discriminant
\[D=48(1-5\delta+6\delta^2)=48(1-2\delta)(1-3\delta)\geq 0.\]
As a consequence,
\[ x\leq 1-3\delta -\frac{1}{2}\sqrt{3+18\delta^2-15\delta}.\]
Then the result follows.
\end{proof}
\begin{remark}
For $0\leq \delta\leq \frac{1}{3}$,
\[1-3\delta -\frac{1}{2}\sqrt{3+18\delta^2-15\delta}<\frac{1}{4}(1-3\delta).\]
\end{remark}
\section{Classification}
\label{classify}
This section proves the main result.
\begin{theorem}
\label{mainupper}
Let $(M, g)$ be an Einstein four-manifold ${\mathrm {Rc}}=g$
such that at each point, \[K\leq \beta=\frac{14-\sqrt{19}}{12}\approx .8034.\]
Then it is isometric to either $(S^4,g_{0})$, $(\mathbb{RP}^4, g_0)$, or $(\mathbb{CP}^2,\ g_{FS})$ up to rescaling.
\end{theorem}
\begin{proof}
We consider Berger's decomposition Prop \ref{berger} at point $p$ realizing the minimum of sectional curvature. Let $\alpha=a_3$. By Lemma \ref{Kupper},
\[a_1\geq \alpha_1=\frac{1}{28}(15-8\alpha-\sqrt{3}\sqrt{96\alpha^2-80\alpha+19}).\]
Since this function of $\alpha$ is decreasing for $\alpha\geq \frac{1}{3}$, we conclude that,
\[a_1\geq \beta_1=\frac{1}{28}(15-8\beta-\sqrt{3}\sqrt{96\beta^2-80\beta+19}).\]
By the choice of $p$, the sectional curvature is at least $\beta_1$ at each point.
By Lemma \ref{k3k1}, then at each point
\begin{align*}
|W^+|+|W^-|&\leq \frac{6(K_3+K_2)+2(K_3-K_2)-4}{\sqrt{6}},\\
&\leq \frac{8K_3+4K_2-4}{\sqrt{6}}=\frac{4K_3-4K_1}{\sqrt{6}},\\
&\leq \frac{4\beta-4\beta_1}{\sqrt{6}}.
\end{align*}
Substituting $\beta=\frac{14-\sqrt{19}}{12}$ yields,
\[|W^+|+|W^-|\leq \frac{3}{\sqrt{6}}=\sqrt{\frac{3}{2}}.\]
The theorem then follows from Prop \ref{propWpm}.
\end{proof}
Similarly, we have the following.
\begin{theorem}
\label{maindiff}
Let $(M, g)$ be an Einstein four-manifold ${\mathrm {Rc}}=g$
such that at each point, \[a_3-a_2\leq \beta=\frac{7-\sqrt{19}}{4}\approx .660275.\]
Then it is isometric to either $(S^4,g_{0})$, $(\mathbb{RP}^4, g_0)$, or $(\mathbb{CP}^2,\ g_{FS})$ up to rescaling.
\end{theorem}
\begin{proof}
We consider Berger's decomposition Prop \ref{berger} at point $p$ realizing the minimum of sectional curvature. Let $\alpha=a_3-a_2$. By Lemma \ref{Kdiffbound},
\[a_1\geq \alpha_1=\frac{1}{6}(3-2\alpha-\sqrt{1+8\alpha^2-4\alpha}).\]
Since this function of $\alpha$ is decreasing for $\alpha\geq 0$, we conclude that,
\[a_1\geq \beta_1=\frac{1}{6}(3-2\beta-\sqrt{1+8\beta^2-4\beta}).\]
By the choice of $p$, the sectional curvature is at least $\beta_1$ at each point.
By Lemma \ref{k3k1}, then at each point
\begin{align*}
|W^+|+|W^-|&\leq \frac{6(a_3+a_2)+2(a_3-a_2)-4}{\sqrt{6}},\\
&\leq \frac{2-6a_1+2(a_3-a_2)}{\sqrt{6}}\\
&\leq \frac{2+2\beta-6\beta_1}{\sqrt{6}}.
\end{align*}
Substituting $\beta=\frac{7-\sqrt{19}}{4}$ yields,
\[|W^+|+|W^-|\leq \frac{3}{\sqrt{6}}=\sqrt{\frac{3}{2}}.\]
The theorem then follows from Prop \ref{propWpm}.
\end{proof}
Now the proof of Theorem \ref{maineinstein} follows immediately.
\begin{proof}
Condition (a.) is considered in Theorem \ref{mainupper}.
Condition (b.) implies that
\begin{align*}
2a_2+a_1 &\geq \frac{\sqrt{19}-3}{4},\\
a_2-a_3 &\geq \frac{\sqrt{19}-7}{4}.
\end{align*}
This is exactly the condition of Theorem \ref{maindiff} so the result follows.
\end{proof}
\def$'${$'$}
\bibliographystyle{plain}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 248 |
\section{INTRODUCTION}
\label{sec:intro}
\input{blast-tng_model}
The Balloon-borne Large Aperture Submillimeter Telescope - The Next Generation (BLAST-TNG)\cite{Galitzki2014b} consists of a 2.5\,m Cassegrain telescope with three microwave kinetic inductance detector (MKID) arrays operating over 30\% bandwidths centered on 250, 350, and 500\,$\mu$m, which have 1836, 950, 460 detectors with diffraction limited resolution of 25$^{\prime\prime}$, 35$^{\prime\prime}$, and 50$^{\prime\prime}$, respectively. It will be flown on a stratospheric balloon as part of NASA's long duration balloon program. An overview of the instrument design is shown in Figure \ref{fig:model}.
The primary science goal of BLAST-TNG is to probe polarized thermal emission from dust in Galactic star forming regions in order to detect the local magnetic field orientation as projected on to the plane of the sky. The Antarctic flights in 2010\cite{Pascale2012} and 2012\cite{Galitzki2014} of the previous instrument, BLASTPol, produced maps of magnetic field morphology in star forming regions with unprecedented levels of detail\cite{Matthews2014, Gandilo2016, Fissel2016, Santos2016, Soler2016, Galitzki2016, Shariff2016}. The demonstrated scientific potential of submillimeter polarimetry observations prompted the design and construction of BLAST-TNG, which will have 16 times the BLASTPol mapping speed as well as better resolution.
The increased collecting area, sensitivity, and resolution will allow for the mapping of more clouds than the 2012 flight and enable observations of diffuse galactic dust emission. BLAST-TNG will allow us to investigate the role magnetic fields play in the formation and evolution of molecular clouds and their associated sub-structures including filaments, cores, and protostars as well as furthering our understanding of dust grain emission and alignment mechanisms. Additionally, BLAST-TNG provides a unique platform for observations which link the large-scale {\it Planck}\cite{PlanckI2015} polarimetry maps to the small scale, but high resolution, polarimetry maps made by interferometers such as ALMA\cite{ALMA2016}.
\section{Magnetic Fields in Star-Forming Regions}
\label{sec:magfield}
In order to create a complete theory of star formation we must understand the processes that regulate the star formation rate in molecular clouds. Recent progress includes using observations of dust emission and extinction, which shows how core mass distribution correlates with observed stellar mass distribution\cite{Nutter2007}. {\it Herschel} data has yielded many important results relevant to the star formation process such as observations that filamentary structures show a tendency for the densest filaments to be perpendicular to the local magnetic field, while faint, low density sub-filaments tend to be parallel to the local magnetic field\cite{Palmeirim2013}. Additionally, {\it Planck}'s all-sky maps of polarized dust emission have greatly increased our understanding of the role magnetic fields play in our galaxy. From these maps, strong evidence has been found that magnetic field orientation is correlated with molecular cloud structure and the degree of this alignment depends on the magnetic field strength and turbulent properties of the cloud being observed\cite{PlanckXXXV2016}.
However, there are many questions concerning the star-formation process and the evolution of cloud structure that remain to be addressed\cite{McKee2007}. Examples include whether the lifetimes of molecular clouds and their internal structures are equal\cite{Vazquez2006} to or larger\cite{Netterfield2009,Blitz2007,Goldsmith2008} than the turbulent crossing time. To have lifetimes longer than crossing times would require a supporting mechanism to counteract gravity. Magnetic fields could provide such support and numerical simulations have shown magnetic fields in clouds can drastically alter star formation efficiencies and the lifetimes of molecular clouds\cite{Li2010,Hennebelle2011}. However, knowledge of magnetic fields and their interaction with molecular cloud structure is still fairly limited. Zeeman splitting observations have produced measurements of the field strength along the line of sight, but are limited to bright regions, and optical extinction polarization observations have produced a small number of magnetic field pseudo-vectors, but only in areas of low extinction\cite{Crutcher2010,Falgarone2008}.
The most promising method for detecting magnetic fields over large ranges of dust column density is with far-IR and submillimeter polarimetry\cite{Hildebrand2000,WardThompson2000,WardThompson2009}. Spinning dust grains preferentially align with short axes parallel to the local magnetic field through the process of radiative alignment torques\cite{Andersson2015}. The grains emit modified blackbody radiation that peaks in the far-IR/submillimeter and is polarized orthogonally to the local magnetic field. BLAST-TNG will have the unique capability to create degree-scale polarization maps of molecular clouds with sub-arcminute resolution with a mapping speed that will allow it to cover multiple targets during each flight. BLAST-TNG data will build on the results of BLASTPol, enabling additional and more detailed comparisons between polarization maps and numerical simulations\cite{WardThompson2000}.
BLAST-TNG observations will target the following three key questions in star formation:\emph{
}i) \emph{Is core morphology and evolution determined by large-scale magnetic fields?} ii) \emph{Does filamentary structure have
a magnetic origin? iii) What is the field strength, and how does it vary from cloud to cloud?} as further discussed in Ref. \citenum{Fissel2010}.
\section{Instrument}
\label{sec:instrument}
\input{fgr_optic_v1}
BLAST-TNG will continue the legacy of BLASTPol with the construction of a new instrument that incorporates many successful elements from previous ballooning experiments. The optical layout of BLAST-TNG is shown in Figure \ref{fig:optics} with the optical component parameters listed in Table \ref{tab:optica}. A 2.5\,m diameter carbon fiber primary mirror\footnote{Vanguard Space Technologies: 9431 Dowdy Drive, San Diego, CA 92126} provides diffraction-limited observations. The telescope uses a Cassegrain configuration with the primary mirror illuminating a 56\,cm diameter aluminum secondary mirror. The secondary mirror is actuated to allow for refocusing during the flight to adjust to the differential thermal contraction of the support structure. The beam is then re-imaged by the 4\,K cold optics which use a modified Offner relay configuration. The light is split by two dichroic filters\cite{Ade2006} into the science bands at 250, 350, and 500\,$\mu$m\ to allow for simultaneous observations of the same patch of sky. The cold optics have been installed in the flight cryostat and will be characterized concurrently with the detector performance. The primary and secondary mirrors and supporting structure are on schedule for a July 2016 delivery.
Achieving a circular, 22$^{\prime}$\ diameter, field of view (FOV) requires re-imaging optics significantly larger than those of BLASTPol. The size constraints necessitated the construction of a new cryostat which was also designed to have a longer hold time of $\sim$28 days, versus the previous 13 day hold time of BLASTPol. The BLAST-TNG cryostat has a 250 liter liquid helium bath to provide cooling to 4\,K and utilizes two vapor-cooled shields (VCS) to provide additional thermal isolation. The arrays are kept at 270\,mK by a closed-cycle \textsuperscript{3}He refrigerator with a 1\,K intercept stage provided by an open cycle \textsuperscript{4}He pumped pot that is fed off the main Helium tank and vents to atmosphere during flight. The detector arrays and cold optics are contained within an Amuneal\footnote{Amuneal Manufacturing Corp., 4737 Darrah Street, Philadelphia, PA 19124} enclosure which provides shielding from ambient magnetic fields. The light is coupled to the detectors with an aluminum feedhorn block with a three step Potter\cite{Potter1963} style profile to provide a more symmetric beam in both polarization directions than previously achieved with conical feedhorns\cite{Rownd2003}. Each feedhorn pixel contains two orthogonally oriented MKIDs (See Fig. \ref{fig:horn_layouts}). BLAST-TNG will serve as a pathfinder instrument for MKIDs \cite{Day2003}, which have never been flown before. The development of MKID arrays for astronomy is an extremely active area of detector research, and flight testing them will be a significant milestone.
Additional details of the instrument design including the electronics, pointing system, control system, and detector readout can be found in Ref. \citenum{Galitzki2014b}.
\input{HornArrays_v1}
\subsection{Cryogenic Performance}
The BLAST-TNG cryostat\footnote{Precision Cryogenic Systems Inc., 7804 Rockville Rd., Indianapolis, IN 46214} was delivered to the University of Pennsylvania (UPenn) in February 2015. Over the following year the thermometry, refrigerator systems, re-imaging optics, and the 250\,$\mu$m\ detector array were integrated and tested in increments to allow us to characterize the performance of the cryogenic system and debug systems as they were added. The cross section of the cryostat can be seen in Figure \ref{fig:cryostat}. A thermal model was developed to describe the expected steady-state thermal load on each temperature stage. The thermal model took into account radiative loading as well as conduction through the G10 mechanical supports, cabling, motor axles, the helium fill tube, and the 1\,K refrigerator exhaust tube (See Table \ref{tab:therm_model}).
During testing, the VCSs were observed to reach a steady temperature of $\sim$65\,K and $\sim$165\,K. The steady state load on the 4\,K cold plate was measured to be $\sim$340\,mW, as determined by the measured helium boil-off rate of the cryostat. The loading corresponds to a 22.5 day hold time for the 250 liter tank with an approximate boil-off rate of 11 liters of liquid helium per day. The observed loading is approximately 40\% larger than the predicted loading of 240\,mW from the thermal model used in the design of the cryostat. We believe our excess loading is due in part to un-modeled light leaks in the MLI blanket around fixtures and feedthroughs, as suggested by SPIDER\cite{Gudmundsson2015}, but also due to unexpected complexities in the thermal behavior of G10 material, which provides the mechanical support in the BLAST-TNG cryostat.
\input{cryostat}
By adjusting the conductive model of the G10 we can account for most of the additional loading observed. This observation has prompted us to replace the G10 sections between the 165\,K and 65\,K stages and between the 65\,K and 4\,K stages with thinner walled material. The change will decrease the effective loading on the 4\,K stage to bring the performance in line with our target 28 day hold time. It should also be noted from Ref. \citenum{Gudmundsson2015} that the thermal loading at balloon flight altitudes is observed to be less due to the cooler temperature of the cryogenic vessel and the reduced optical loading through the window which can increase the hold times of cryostats during flight.
As a baseline for comparing cryostat performance a figure of merit was developed in Ref. \citenum{Holmes2001} that divides the radiative loading, $H$, by the cryogen depletion rate, $R$. For the SPIDER cryostat along with many satellite cryostats, $H/R \approx 60$\,W\,Days/L whereas the BLAST-TNG cryostat ranks slightly higher with $H/R\approx 230$\,W\,Days/L using the 250\,L cryogenic volume, a hold time of 22.5 days, and the approximately 6\,m$^2$ surface area of the 4\,K shield.
\subsection{Detector Performance}
The 250\,$\mu$m\ MKID detectors have been shown to be photon noise limited in a 7 pixel test array that was feedhorn coupled to a variable blackbody source. Additional details of the tests and results can be found in Ref. \citenum{Hubmayr2015}. The noise equivalent power (NEP) of the detectors was fit using a three component noise model that included recombination noise and the photon noise on top of a flat background noise level. The fit determined that the detectors were limited by photon noise in the range 1\,pW to 20\,pW, which comfortably encompasses the expected BLAST-TNG flight loading on the detectors of $\sim$5 to $\sim$14\,pW. The fit to the noise model also produces an estimate of the optical coupling efficiency which was determined to be $\sim 70\%$.
The 250\,$\mu$m\ (1.2\,THz) array is designed to have a bandpass from 325 to 175\,$\mu$m\ (1.0 to 1.4\,THz) which is defined on the long wavelength end by the feedhorn profile and on the short wavelength end, by a low pass filter mounted in front of the feedhorn block. The bandpass was tested using a hot $1050^\circ$\,C thermal source coupled to a Fourier Transform Spectrometer (FTS) that filled the feedhorn beam. The tests determined that the edges of the bandpass for both polarization directions in a single pixel to be in agreement with the design of the filters and feedhorns\cite{Dober2015}.
The MKID's polarization performance has also been tested and is described in detail in Ref. \citenum{Dober2015}. The tests were performed with a source chopped between $1050^\circ$\,C and $20^\circ$\,C with a wire grid polarizer mounted between the source and the detectors. The polarizing grid is then rotated to produce a sinusoidal response at the detectors with orthogonal detectors 90 degrees out of phase. Fits to these measurements determined the cross-polar signal for both detector directions in a pixel to be $<$3\%, demonstrating the effectiveness of feedhorn coupled MKIDs for submillimeter polarimetry measurements.
Additional details of the MKID design and performance can be found in Ref. \citenum{McKenney2016}.
\subsection{Readout Electronics}
The BLAST-TNG readout is a highly multiplexed 1024 channel digital spectrometer which is the first of its kind to have been developed for the second generation Reconfigurable Open Architecture Computing Hardware (ROACH-2)\cite{Werthimer2011}. The ROACH-2 architecture is based on a field programmable gate array (FPGA), and is a product of the Collaboration for Astronomy Signal Processing and Electronics Research (CASPER). The ROACH is used in conjunction with a DAC/ADC board that was designed for ARCONS\cite{McHugh2012}. Building on the legacy of previous KID readouts created for the ROACH platform, the BLAST-TNG firmware performs coarse and fine channelization of 512\,MHz of RF bandwidth. The resulting channels are $\sim$100\,kHz wide and can be read out at rates of 200\,Hz to 500\,kHz. BLAST-TNG uses five ROACH-2 boards, three for the 250\,$\mu$m\ array and one each for the 350 and 500\,$\mu$m\ arrays, along with a suite of IF components and single board computers. The readout hardware is housed in the `ROACH-2 Motel', a custom enclosure designed for BLAST-TNG. Control software is written in Python, and will be ported to C for integration into the flight software. Details of the system's overall performance are forthcoming.
\subsection{Polarimetry}
\label{sec:polarimetry}
\input{hwpr_v1}
The primary scanning strategy during flight will be a slow raster scan, which works well for extended sources. A typical BLAST-TNG raster will scan across targets in azimuth at a speed of approximately $ 0.5^\circ{\rm s}^{-1}$ with an elevation scan speed calculated to change the elevation by 1/3 the array FOV in one crossing of the target in azimuth. A Half Wave Plate (HWP) is used to modulate the polarization signal, so that each pixel samples {\it I}, {\it Q}, and {\it U} multiple times during the course of a scan which allows us to control for polarization systematics. The HWP is stepped between four set angles (0$^\circ$, 22.5$^\circ$, 45$^\circ$, and 67.5$^\circ$) after each completed scan of a source in elevation. The HWP used in BLASTPol\cite{Moncelsi2014} had a 10\,cm diameter aperture and was made from five layers of 500\,$\mu$m\ thick sapphire with an anti-reflective coating. However, the technology did not scale easily to larger apertures necessitating a new approach. The HWP developed for BLAST-TNG uses metal mesh filter technology\cite{Ade2006} to make a large diameter, $\sim$18\,cm, HWP (See Fig. \ref{fig:hwpr}). These types of HWP have demonstrated broad-band transmission at THz frequencies\cite{Pisano2012, Pisano2014}.
The detector rows are oriented parallel to the nominal scan direction with the MKID orientation rotated by 45 degrees in adjacent pixels along the scan direction. This alignment allows for sampling of both {\it Q} and {\it U} Stokes parameter on a timescale that is shorter than the array's common-mode $1/f$ noise, creating a redundant polarization modulation feature. The sampling timescale of the Stokes parameter is $\sim$0.025 s, which is determined by the detector separation, $\sim$45$^{\prime\prime}$\ at 250\,$\mu$m, and typical scan speed, $\sim 0.5^\circ{\rm s}^{-1}$.
\section{Conclusion}
\label{sec:conclusion}
BLASTPol successfully demonstrated the viability of balloon-borne telescopes to explore the polarization of the submillimeter sky and has led directly to the development of BLAST-TNG. Progress in the construction of the new instrument is on schedule and is proceeding rapidly. The cryogenics system has been thoroughly tested and is in a near flight ready status. Additionally, the detector technology is well understood and has undergone extensive testing at NIST prior to delivery to UPenn. The 250\,$\mu$m\ array has been installed in the cryostat and has been successfully incorporated into the readout architecture with observed optical sensitivity during cryogenic operations. We expect to demonstrate the detector's target sensitivity in the flight cryostat during the summer of 2016. The 350 and 500\,$\mu$m\ arrays and feedhorn blocks are being fabricated for testing and installation by fall 2016. The new BLAST-TNG instrument will give us magnetic field morphology maps at unprecedented resolution that span entire molecular cloud structures, allowing us to link the full-sky polarimetry maps of {\it Planck} with the high-resolution, small-area polarimetry maps, of telescopes such as ALMA. This will provide strong constraints on models of magnetic fields and turbulent interaction within magnetic fields as well as increasing our understanding of dust grain models.
\section{Acknowledgments}
BLAST is funded by NASA through grant number NNX13AE50G S08. Detector development is supported in part by NASA through NNH13ZDA001N-APRA. Brad Dober was funded by a NASA Earth and Space Science Fellowship NNX12AL58H S02. The BLAST-TNG collaboration would like to acknowledge the Xilinx University Program for their generous donation of five Virtex-6 FPGAs for use in our ROACH-2 readout electronics.
Peter Ashton was supported through Reach for the Stars, a GK-12 program supported by the National Science Foundation under grant DGE-0948017.
We would also like to thank the Columbia Scientic Balloon Facility (CSBF) staff for their continued outstanding work.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,489 |
De Plantin-Moretusprijs was een Vlaamse literatuurprijs.
De prijs werd toegekend aan boeken die zich onderscheiden door verzorgde vormgeving, illustratie, en grafisch-technische productie. Het was een initiatief van de Vereniging van Uitgevers van Nederlandstalige Boeken, nu bekend als de Vlaamse Uitgevers Vereniging (VUV) en het Plantin Genootschap.
Elk jaar werden boeken in verschillende categorieën, waaronder kinder- en jeugdboeken, kunstboeken en educatieve en wetenschappelijke uitgaven, door een jury uitgekozen en bekroond. In de categorie Het Beste Boekomslag werd door het publiek uit tien omslagen gekozen via een online stempagina.
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Vlaamse literatuurprijs | {
"redpajama_set_name": "RedPajamaWikipedia"
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\section{Introduction}
\label{sec:introduction}
There has been excellent progress towards gravitational wave astronomy
over recent years. The first generation of large scale gravitational
wave interferometers reached unprecedented sensitivities and have
undertaken extended science runs. The U.S. \ac{LIGO}
\cite{Abbott:2009li}, the French--Italian Virgo \cite{Acernese:2006bj}
and the German--British GEO600 \cite{Willke:2007zz} detectors now form a
collaborative network of interferometers. The data from these detectors
has been analyzed for gravitational waves from compact binary
coalescence \cite{Abadie:2010yba}, stochastic background
\cite{Abbott:2009ws}, unmodelled burst \cite{Abadie:2010mt} and pulsar
\cite{Collaboration:2009rfa} sources. \ac{S6} and \ac{VSR23} ended in
October 2010 and yielded the most sensitive data yet taken; the analysis
of this data is ongoing. In the meantime, the detectors are being
upgraded to their advanced configurations \cite{Harry:2010zz,avlligowebsite,
advvirgowebsite}, with the expectation of a ten fold improvement in
sensitivity. With these sensitivities, it is expected that
gravitational waves will be observed regularly \cite{Temp:2010cfa}.
Furthermore, with a proposed advanced detector in Japan
\cite{lcgtwebsite}, a possible detector in Australia \cite{aigowebsite},
and 3rd generation detectors on the horizon \cite{Hild:2008ng}, future
prospects are promising.
As the gravitational wave community matures it is essential that a
relationship is built between \ac{GW} and \ac{EM} astronomers. The
\ac{GW} emission from a source is likely to provide complementary
information to emission in various \ac{EM} bands, and a joint
observation is significantly more likely to answer outstanding
astrophysical questions. Already this relationship is beginning to
mature. A number of \ac{EM} transients have already been followed up in
\ac{GW} data \cite{Abbott:2007rh, Abadie:2010uf, Collaboration:2009kk}.
Additionally, infrastructure is also being put in place to allow for
\ac{EM} follow-up of \ac{GW} observations \cite{Kanner:2008zh}.
\ac{CBC} are one of the most promising sources of gravitational waves,
and also an ideal candidate for joint \ac{GW}-\ac{EM} astronomy. During
the late stages of inspiral and merger, a compact binary emits a
distinctive, ``chirping'' gravitational wave signal. Furthermore,
\ac{CBC}s containing at least one \ac{NS} are expected to emit
electromagnetically. Specifically, \ac{BNS} and \ac{NSBH} mergers are
the preferred progenitor model for the short \ac{GRB}
\cite{nakar:2007,Shibata:2007zm}. It is also possible that
these mergers will be observable electromagnetically as orphan
afterglows \cite{nakar:2007}, optical \cite{Metzger:2010sy} or radio
transients \cite{Predoi:2009af}. Since \ac{GRB}s are well localized
both in time and on the sky by \ac{EM} observations, the corresponding
\ac{GW} search can be simplified
by reducing the volume of parameter space relative to an all-sky,
all-time search. Targeted searches for \ac{CBC} waveforms associated
to short \ac{GRB}s were performed using data from \ac{S5} and \ac{VSR1}
\cite{Abbott:2007rh, Abadie:2010uf}.
In this paper, we introduce a targeted, coherent search algorithm for
detecting \ac{GW} from \ac{CBC}. This targeted search is designed as a
follow-up to \ac{EM} transients, and in particular \ac{GRB}s.
Previous searches for this source have made
use of a coincidence requirement --- namely that a signal with
consistent parameters is observed in two or more detectors in the
network. The analysis introduced here makes use of the data from all
operational detectors, and combines the data in a coherent manner before
matched filtering against \ac{CBC} template waveforms. In a
coherent analysis, it is straightforward to restrict the signal
model to only two independent polarizations. This allows for the
rejection of incoherent background noise, and consequently increases the
sensitivity of the search if more than two detectors are operating.
The data output by gravitational wave interferometers is neither
stationary nor Gaussian, but is contaminated by noise transients of
instrumental and environmental origin. This makes the task of doing
data analysis a complex one, and matched filtering alone is not
sufficient to distinguish signal from noise. Regardless of whether a
coincident or coherent search is performed, the most significant events
by \ac{SNR} would always be dominated by non-Gaussian transients, or
``glitches'', in the data. A significant effort goes into understanding
the cause of these glitches \cite{Blackburn:2008ah} and removing times
of poor data quality from the analysis. While these efforts greatly
reduce the number of glitches they cannot remove them entirely.
Therefore the analysis must also employ methods to distinguish signal
from noise transients. In previous \ac{CBC} searches, signal
consistency tests \cite{Allen:2004gu, Hanna:2008} have proved very
effective at removing the non-Gaussian background. We extend these
tests to the coherent analysis described in this paper and demonstrate
their continued effectiveness. In addition, coherent analyses naturally
lend themselves to multi-detector consistency tests, such as the null
stream \cite{Guersel:1989th}. We describe a number of such consistency
tests for this templated \ac{CBC} search and again demonstrate their
efficacy. Finally, we are able to show that the various signal
consistency tests are sufficient to remove the majority of non-Gaussian
transients and render the search almost as sensitive as if the data were
Gaussian and stationary.
The layout of this paper is as follows. In section
\ref{sec:coh_matched_filter}, we describe the formulation of a targeted
coherent triggered search for \ac{CBC} signals. In section
\ref{sec:snr_cont_consistency} we discuss an implementation of the null
stream formalism and other multi-detector consistency tests. In section
\ref{sec:chi2tests} we describe a number of $\chi^{2}$ tests than can be
applied in a coherent search to try to separate and veto glitches.
Finally, in \ref{sec:s4data} we outline an implementation of a
targetted, coherent search for \ac{CBC} and present results on both
simulated, Gaussian data and real detector data taken from \ac{S4}.
\section{Coherent Matched filtering}
\label{sec:coh_matched_filter}
In this section, we describe the coherent
matched-filtering search for a gravitational wave signal from a
coalescing binary in data from a network of detectors. We restrict attention to
binaries where the component spin can be neglected. The description is
primarily tailored towards searches where the sky location of the
gravitational wave event is known a priori, as is appropriate when
performing a followup of an \ac{EM} transient such as a \ac{GRB}
\cite{nakar:2007, Abadie:2010uf}. Finally, since all previously
published \ac{CBC} search results \cite{Abadie:2010yba, Abbott:2009qj,
Abbott:2009tt} have used a coincidence search between detectors, we
compare the coherent analysis with the multi-detector coincident
analysis.
The coherent analysis for coalescing binary
systems has been derived previously using a similar method
in \cite{Pai:2000zt, Bose:1999pj,Bose:1999bp,Bose:2011}.
Our presentation makes use of the $\mathcal{F}$-statistic formalism,
introduced in \cite{Jaranowski:1998qm}. This was originally defined as a
method for performing searches for continuous wave searches and has been
regularly used for this task (see for example \cite{Abbott:2009nc}).
It was noted in \cite{Cutler:2005hc} that the $\mathcal{F}$-statistic and
the multiple detector inspiral statistic derived in \cite{Bose:1999pj}
are similar and the $\mathcal{F}$-statistic was adapted to searches
for \ac{CBC} signals in \cite{Cornish:2006ms}.
\subsection{The binary coalescence waveform}
\label{ssec:binary_waveform}
The generic binary coalescence waveform depends upon as many as
seventeen parameters. However, we restrict attention to binaries on
circular orbits with non-spinning components. This reduces the
parameter space to nine dimensions: the two component masses $M_{1}$ and
$M_{2}$; the sky location of the signal ($\theta$, $\phi$); the
distance, D, to the signal; the coalescence time of the signal, $t_{o}$;
the orientation of the binary, given by the inclination $\iota$, the
polarization angle $\psi$ and the coalescence phase $\phi_{o}$.
We also assume that the sky location ($\theta$, $\phi$) of
the signal is known, thereby reducing the number of unkown parameters to
seven.
In the radiation frame, where the gravitational wave propagates in the
$\mathbf{e}_{z}^{R}$-direction, the gravitational waveform is given by
\begin{equation}
\mathbf{h} = h_{+} \mathbf{e}_{+} + h_{\times} \mathbf{e}_{\times}
\end{equation}
where
\begin{eqnarray}
\mathbf{e}_{+} &=& \mathbf{e}^{R}_{x} \otimes \mathbf{e}^{R}_{x} -
\mathbf{e}^{R}_{y} \otimes \mathbf{e}^{R}_{y} \, , \nonumber \\
\mathbf{e}_{\times} &=& \mathbf{e}^{R}_{x} \otimes \mathbf{e}^{R}_{y} +
\mathbf{e}^{R}_{y} \otimes \mathbf{e}^{R}_{x} \, ,
\end{eqnarray}
and the waveforms $h_{+, \times}$ depend upon
seven parameters ($M_{1}, M_{2}, t_{o}, D, \iota, \psi, \phi_{o}$). The
three remaining angles $(\iota, \psi, \phi_{o})$ give the relationship
between the radiation frame and the source frame (in which
$\mathbf{e}^{S}_{z}$ lies in the direction of the binary's angular
momentum and $\mathbf{e}^{S}_{x}$ along the separation between the
binary components at $t_{o}$). Even for a known sky location, it is
necessary to search a seven dimensional parameter space of signals.
Naively covering this space with a grid of templates would be
prohibitively costly \cite{OwenSathyaprakash98}. However, the analysis
is greatly simplified by the observation that the last four parameters
enter only as amplitude parameters which can be analytically maximized
over at minimal cost.%
\footnote{This was observed for the inspiral signal in
\cite{Bose:1999pj} and independently for continuous wave signals in
\cite{Jaranowski:1998qm}.}
Specifically, the two polarizations of the waveform can be expressed as
\begin{eqnarray}\label{eq:h_plus_cross}
h_{+}(t) &=& \mathcal{A}^{1} h_{0}(t) + \mathcal{A}^{3}
h_{\frac{\pi}{2}}(t)
\nonumber \\
h_{\times}(t) &=& \mathcal{A}^{2} h_{0}(t) +
\mathcal{A}^{4} h_{\frac{\pi}{2}}(t) \, .
\end{eqnarray}
The two phases of the waveform are written as $h_{0}$ and
$h_{\frac{\pi}{2}}$. These depend upon the physical parameters of the
system (in this case just the masses) as well as the coalescence time
$t_{o}$.%
\footnote{This decomposition is actually valid for all binaries in which
the plane of the orbit does not precess. Thus, binary coalescence
waveforms in which the spins are aligned with the orbital angular
momentum can also be expressed in this form. However, for generic spin
configurations, the orbit will precess and this simple decomposition is
no longer applicable}
$\mathcal{A}^{i}$ are constant amplitude terms and are given
explicitly as \cite{Cornish:2006ms,Bose:2011}
\begin{eqnarray} \label{eq:amplitude_def}
\mathcal{A}^{1} &=&
A_{+} \cos 2 \phi_{o} \cos 2 \psi - A_{\times}\sin 2 \phi_{o} \sin 2 \psi
\\
\mathcal{A}^{2} &=&
A_{+} \cos 2 \phi_{o} \sin 2 \psi + A_{\times} \sin 2 \phi_{o} \cos 2 \psi
\nonumber \\
\mathcal{A}^{3} &=&
- A_{+} \sin 2 \phi_{o} \cos 2 \psi - A_{\times} \cos 2 \phi_{o} \sin 2 \psi
\nonumber \\
\mathcal{A}^{4} &=&
- A_{+} \sin 2 \phi_{o} \sin 2 \psi + A_{\times} \cos 2 \phi_{o}
\cos 2 \psi \, , \nonumber
\end{eqnarray}
where
\begin{eqnarray}\label{eq:aplus_across}
A_{+} &=& \frac{D_{o}}{D}\frac{(1 + \cos^{2} \iota)}{2} \nonumber \\
A_{\times} &=& \frac{D_{o}}{D}\cos \iota \, ,
\end{eqnarray}
and $D_{o}$ is a fiducial distance which is used to scale
the amplitudes $\mathcal{A}^{i}$ and waveforms $h_{0, \frac{\pi}{2}}$.
Thus, the amplitudes $\mathcal{A}^{i}$ depend upon the distance to the
source and the binary orientation as encoded in the three angles
($\iota$, $\psi$, $\phi_{0}$). For \textit{any} set of
values $\mathcal{A}^{i}$, the expressions (\ref{eq:amplitude_def}) can
be inverted to obtain the physical parameters, unique up to reflection
symmetry of the system \cite{Cornish:2006ms}.
The gravitational waveform observed in a detector $X$ is
\begin{equation}
h^{X} = h^{ij} D^{X}_{ij}
\end{equation}
where $D^{X}_{ij}$ denotes the detector response tensor. For an
interferometric detector, the response tensor is given by
\begin{equation}
\mathbf{D}^{X} = (\mathbf{e}^{X}_{x} \otimes \mathbf{e}^{X}_{x}
- \mathbf{e}^{X}_{y} \otimes \mathbf{e}^{X}_{y})
\end{equation}
where the basis vectors $\mathbf{e}^{X}_{x}$ and $\mathbf{e}^{X}_{y}$
point in the directions of the arms of the detector. It is often
convenient to re-express the gravitational wave signal observed in a
given detector as
\begin{equation}
h^{X}(t) = F_{+}(\theta^{X}, \phi^{X}, \chi^{X}) h_{+}(t)
+ F_{\times}(\theta^{X}, \phi^{X}, \chi^{X}) h_{\times}(t) \, ,
\end{equation}
where the detector response to the two polarizations of the
gravitational wave is encoded in the functions
\begin{eqnarray}\label{eq:det_response}
F_{+}(\theta, \phi, \chi) =
&-& \frac{1}{2} ( 1 + \cos^{2} \theta) \cos 2\phi \cos 2\chi \nonumber \\
&-& \cos \theta \sin 2\phi \sin 2\chi \, , \\
F_{\times}(\theta, \phi, \chi) =&&
\frac{1}{2} ( 1 + \cos^{2} \theta) \cos 2\phi \sin 2\chi \nonumber \\
&-& \cos \theta \sin 2\phi \cos 2\chi.
\end{eqnarray}
These response functions depend upon the three angles ($\theta^{X},
\phi^{X}, \chi^{X}$) which relate the detector frame to the radiation
frame: $\theta^{X}$ and $\phi^{X}$ give the sky location relative to the
detector, while $\chi^{X}$ is the polarization angle between the
detector and the radiation frames. We have, somewhat unconventionally,
allowed for a polarization angle in transforming from source to
radiation \textit{and} radiation to detector coordinates. In what
follows, we will often find it convenient to fix the angle $\chi^{X}$ by
explicitly tying it to the detector (or geocentric) frame; for example,
by maximizing the detector (or network) sensitivity to the $+$
polarization. The angle $\psi$ then describes the orientation of the
source with respect to this preferred radiation frame.
Since we are considering \ac{CBC} observed in ground-based detectors,
the time that a potential signal would spend in the sensitivity band of
any detector will be short (less than 60s for the initial detectors).
Thus the change in the source's sky location over the observation time
may be neglected, and the angles ($\theta^{X}, \phi^{X}, \chi^{X}$)
can be treated as constants. When working with a network
of detectors, it is often useful to work in the geocentric frame. The
location of the source $(\theta, \phi, \chi)$ is measured relative to
this frame, and coalescence time is measured at the Earth's centre. In
this case, the location and orientation of the detector $X$ are specified
by three angles, which we denote $\vec{\alpha}^{X}$, and the detector
response will depend upon six angles $(\vec{\alpha}^{X}, \theta, \phi,
\chi)$. Then, the observed signal in a given detector is%
\footnote{We do not give the explicit formula for the response function
dependent on the six angles $(\vec{\alpha}^{X}, \theta, \phi, \chi)$, as
the expression is somewhat lengthy. It can be obtained by performing
six successive rotations to the detector response tensor to transform
from the detector frame, via the geocentric frame, to the radiation
frame. The calculation is detailed in \cite{livas87a}.}
\begin{equation}\label{eq:hx_t}
h^X(t) = F_{+}(\vec{\alpha}^{X},\theta, \phi, \chi)
h_{+}(t^{X} )
+ F_{\times}(\vec{\alpha}^{X},\theta, \phi, \chi)
h_{\times}(t^{X}) \, ,
\end{equation}
where $t^{X}$ is the time of arrival of the signal at detector X,
\begin{equation}
t^X = t - dt(\vec{\alpha}^{X},\theta,\phi,\chi)
\end{equation}
and $dt$ gives the difference in arrival time of the signal between the
geocenter and detector, for the given sky position.
Combining the final expressions for the binary coalescence waveform
(\ref{eq:h_plus_cross}) and the detector response (\ref{eq:hx_t}), we
can express the gravitational waveform observed in a given detector as
\begin{equation}\label{eq:inspiral_wave}
h^{X}(t) = \sum_{\mu=1}^{4} \mathcal{A}^{\mu}(D, \psi, \phi_{o}, \iota)
h^{X}_{\mu}(t)
\end{equation}
where the $\mathcal{A}^{\mu}$ are defined in (\ref{eq:amplitude_def})
and $h^{X}_{\mu}$ are given by
\begin{eqnarray} \label{eq:fourh_def}
h^{X}_{1}(t) &=& F_{+}^{X} h_{0}(t^{X}) \nonumber\\
h^{X}_{2}(t) &=& F_{\times}^{X} h_{0}(t^{X}) \nonumber\\
h^{X}_{3}(t) &=& F_{+}^{X} h_{\frac{\pi}{2}}(t^{X}) \nonumber \\
h^{X}_{4}(t) &=& F_{\times}^{X} h_{\frac{\pi}{2}}(t^{X}) \, . \label{eq:hmu}
\end{eqnarray}
\subsection{Multi detector binary coalescence search}
\label{ssec:inspiral_fstat}
Matched filtering theory \cite{Wainstein} provides a method for
determining whether the signal $h(t, \xi)$, parametrized by the time
and other parameters $\xi$, is present in a noisy data stream. The
data output by a detector is
\begin{equation}
s^{X}(t) = n^{X}(t) + h^{X}(t, \xi)
\end{equation}
where $n^{X}(t)$ is the noise, taken to be Gaussian and stationary. The
noise $n^{X}(t)$ of the detectors is characterized by the noise \ac{PSD}
$S^{X}_{h}(f)$ as
\begin{equation}
\langle \tilde{n}^{X}(f) [\tilde{n}^{X} (f^{\prime})]^{\star} \rangle =
\delta(f - f^{\prime}) S^{X}_{h}(f) \, .
\end{equation}
With this, we define the single detector inner product between two time
series $a(t)$ and $b(t)$ as
\begin{equation}\label{eq:inner_product}
(a^{X} | b^{X}) = 4 \, \mathrm{Re} \int_{0}^{\infty}
\, \frac{\tilde{a}^{X}(f) [\tilde{b}^{X}(f)]^{\star}}{ S^{X}_{h}(f) } \, .
\end{equation}
Then, the likelihood ratio of there being a signal $h$ present in the
data is given by:
\begin{equation}\label{eq:likelihood}
\Lambda(h) = \frac{P(s|h)}{P(s|0)} = \frac{e^{- (s^{X} - h^{X} | s^{X}
- h^{X})
/2}}{e^{-(s^{X}| s^{X}) /2}} \, ,
\end{equation}
and the log-likelihood can be written as
\begin{equation}
\log \Lambda = (s|h) - \frac{1}{2} (h|h) \, .
\end{equation}
The likelihood ratio for multiple detectors is a straightforward
generalization of the single detector expression (\ref{eq:likelihood}).
Assuming that the noise in different detectors are independent, in the
sense that
\begin{equation}
\langle \tilde{n}^{X}(f) [\tilde{n}^{Y}(f^{\prime}]^{\star}) \rangle =
\delta^{XY} \delta(f - f^{\prime}) S^{X}_{h}(f) \, ,
\end{equation}
the multi-detector inner product is simply given by the sum of the
single detector contributions
\begin{equation}\label{eq:multi_inner}
(\mathbf{a} | \mathbf{b} ) := \sum_{X} ( a^{X} | b^{X} ) \, .
\end{equation}
The multi-detector likelihood is given by
\begin{equation}\label{eq:multi_log_lambda}
\ln \Lambda = (\mathbf{s} | \mathbf{h} ) - \frac{1}{2}(\mathbf{h} |
\mathbf{h}) \, .
\end{equation}
This is the optimal statistic for signal detection in Gaussian noise: the larger
the value of $\ln \Lambda$, the more likely that a signal is present.
It is not, however, an optimal statistic if the noise is not Gaussian, as we will
explore in more detail in sections \ref{sec:snr_cont_consistency} and \ref{sec:chi2tests}.
Specializing to the case of binary coalescence, we can substitute the
known waveform parametrization (\ref{eq:inspiral_wave}) into the general
matched filter likelihood (\ref{eq:multi_log_lambda}). The
multi-detector likelihood becomes
\begin{equation}\label{eq:multi_det_lambda}
\ln \Lambda = \mathcal{A}^{\mu} (\mathbf{s} | \mathbf{h}_{\mu} )
- \frac{1}{2} \mathcal{A}^{\mu} \mathcal{M}_{\mu \nu} \mathcal{A}^{\nu}
\end{equation}
where the matrix $\mathcal{M}_{\mu \nu}$ is defined as
\begin{equation}
\mathcal{M}_{\mu \nu} := ( \mathbf{h}_{\mu} | \mathbf{h}_{\nu} ) \, .
\end{equation}
The derivative of (\ref{eq:multi_det_lambda}) with respect to
$\mathcal{A}^{\mu}$ provides the values of $\mathcal{A}^{\mu}$ which
maximize the likelihood as
\begin{equation}
\hat{A}^{\mu} = \mathcal{M}^{\mu \nu} (\mathbf{s} | \mathbf{h}_{\nu} ) \, ,
\end{equation}
where, following \cite{Prix:2007rb}, we take $\mathcal{M}^{\mu \nu }$ to
be the inverse of $\mathcal{M}_{\mu \nu}$. We then define the coherent \ac{SNR}
via the maximum likelihood as
\begin{equation}\label{eq:multi_det_max_lambda}
\rho^2_{\mathrm{coh}} = 2 \ln \Lambda |_{\rm{max}} =
(\mathbf{s} | \mathbf{h}_{\mu} ) \mathcal{M}^{\mu \nu}
(\mathbf{s} | \mathbf{h}_{\nu} ) \, .
\end{equation}
It is not difficult to show that $\rho^2_{\mathrm{coh}}$ follows a
$\chi^{2}$ distribution with four degrees of freedom in the absence of a
signal, and a non-central $\chi^{2}$ distribution (again with 4 degrees
of freedom) when a signal is present. See, for example, \cite{Prix:2007rb} for
more details. Furthermore, $\rho^2_{\mathrm{coh}}$ is now a function of
only the waveform components $h_{\mu}$ and no longer the
$\mathcal{A}^{\mu}$ parameters. Thus four of the original seven
waveform parameters have been analytically maximized, leaving three to
be searched over.
Calculating the maximized likelihood, as well as estimating the
parameters $\hat{\mathcal{A}}^{\mu}$ requires an inversion of the matrix
$\mathcal{M}_{\mu \nu}$. \ac{CBC} signals will spend a large number of
cycles in the sensitive band of the detector and consequently the $0$
and $\frac{\pi}{2}$ phases will be (close to) orthogonal. Since the
frequency evolves slowly, the amplitudes of the two phases
will be close to equal,%
\footnote{Indeed, several \ac{CBC} waveforms are generated directly in
the frequency domain \cite{Damour:2000zb}, making these equalities exact.}
i.e.
\begin{eqnarray}
( h^{X}_{0} | h^{X}_{\frac{\pi}{2}} ) &\approx& 0 \, \\
( h^{X}_{\frac{\pi}{2}} | h^{X}_{\frac{\pi}{2}} ) &\approx&
( h^{X}_{0} | h^{X}_{0} ) =: (\sigma^{X})^{2}\, .
\end{eqnarray}
Therefore, the matrix $\mathcal{M}$ simplifies to
\begin{equation}
\mathcal{M}_{\mu \nu} = \left( \begin{array}{cccc}
A & C & 0 & 0 \\
C & B & 0 & 0 \\
0 & 0 & A & C \\
0 & 0 & C & B \end{array}
\right)
\end{equation}
where
\begin{equation}\label{eq:ab}
\begin{array}{l}
A = \sum_{X} (\sigma^{X} F^{X}_{+})^2 \\
B = \sum_{X} (\sigma^{X} F^{X}_{\times})^2 \\
C = \sum_{X} (\sigma^{X} F^{X}_{+})(\sigma^{X} F^{X}_{\times}) \, .
\end{array}
\end{equation}
In this form the detection statistic is almost identical to the $\mathcal{F}$-statistic
for detecting rotating neutron stars, as described in
\cite{Jaranowski:1998qm}, in the case where the neutron star has a small wobble angle.
\subsubsection*{Dominant Polarization}
Since we have included a polarization angle in both the transformation
between geocentric and radiation frame ($\chi$) and between radiation
and source frame ($\psi$), we have the freedom to specify one of these
without placing any physical restriction on the signal. The coherent
\ac{SNR} is further simplified by introducing a dominant polarization
frame which renders $\mathcal{M}_{\mu \nu}$ diagonal.
Under a rotation of the radiation frame by an angle $\chi^{\mathrm{DP}}$, the
detector response functions transform as
\begin{eqnarray}
F^{X}_{+} &\rightarrow& F^{\mathrm{DP}, X}_{+} =
F^{X}_{+} \cos 2 \chi^{\mathrm{DP}} +
F^{X}_{\times} \sin 2 \chi^{\mathrm{DP}} \\ \nonumber
F^{X}_{\times} &\rightarrow& F^{\mathrm{DP}, X}_{\times} =
- F^{X}_{+} \sin 2 \chi^{\mathrm{DP}} +
F^{X}_{\times} \cos 2 \chi^{\mathrm{DP}} \label{eq:f_transformation}.
\end{eqnarray}
The rotation through $\chi^{\mathrm{DP}}$ will have an identical effect
on all detectors. Thus, there exists a polarization angle
$\chi^{\mathrm{DP}}$ which satisfies
\begin{equation}
C^{\mathrm{DP}} =
\sum_{X} (\sigma^{X} F^{\mathrm{DP},X}_{+})
(\sigma^{X} F^{\mathrm{DP},X}_{\times}) = 0 \, .
\end{equation}
This can be solved to give $\chi^{\mathrm{DP}}$ as
\begin{equation}
\tan 4 \chi^{\mathrm{DP}} = \frac{2 \sum_{X}
(\sigma^{X} F^{X}_{+})(\sigma^{X} F^{X}_{\times})
}{\sum_{X} \left[ (\sigma^{X} F^{X}_{+})^{2} -
(\sigma^{X} F^{X}_{\times})^{2} \right]} \, .
\end{equation}
This choice serves to diagonalize the matrix
$\mathcal{M}$. To uniquely determine $\chi^{\mathrm{DP}}$, we impose an additional
requirement that the network be more sensitive to the $+$
polarization than to the $\times$ polarization.
The value of $\chi^{\mathrm{DP}}$ is a function of the
detector network, the source location and waveform; in particular it
depends upon $F_{+, \times}^{X}$ and $\sigma^{X}$. From now on, we
assume that we are working in the dominant polarization frame and drop
the DP superscript from our expressions.
The concept of the dominant polarization frame has been introduced previously in
un-modelled burst searches \cite{KlMoRaMi:05, KlMoRaMi:06,
1367-2630-12-5-053034}. While the idea is very similar, the actual
implementation is somewhat different.
In the case that both $A$ and $B$ are non-zero, i.e.~that the detector
has some sensitivity to both polarizations, the coherent \ac{SNR}
can be written, in the dominant polarization, as
\begin{eqnarray}\label{eq:fstat_dp}
\rho_{\mathrm{coh}}^{2} &=&
\frac{\mathbf{(s|F_{+} h_{0})}^{2}
+ \mathbf{(s|F_{+} h_{\frac{\pi}{2}})}^{2}}{
\mathbf{ (F_{+} h_{0} | F_{+} h_{0}) }} + \\
&& \, \frac{\mathbf{(s|F_{\times} h_{0})}^{2} +
\mathbf{(s|F_{\times} h_{\frac{\pi}{2}})}^{2}}{
\mathbf{ (F_{\times} h_{0} | F_{\times} h_{0}) } } . \nonumber
\end{eqnarray}
The coherent \ac{SNR} can then be seen to arise as the quadrature sum of
the power in the two phases of the waveform ($0$ and $\frac{\pi}{2}$) in
the two gravitational wave polarizations ($+$ and $\times$).
\subsubsection*{Network Degeneracy}
In many cases, a detector network is much more
sensitive to one gravitational wave polarization than the other. In the
extreme limit (e.g. co-located and co-aligned detectors such as those at
the Hanford site) the network is entirely insensitive to the second
polarization. In the dominant polarization frame, the network becomes
degenerate as $B \rightarrow 0$ or equivalently
\begin{equation}
\sum_{X} (\sigma^{X} F^{X}_{\times})^2 \rightarrow 0 \, .
\end{equation}
Thus the network will only be degenerate if $F^{X}_{\times} = 0$ for all
detectors X. If the network is degenerate then it is easy to see that the
detection statistic will be degenerate as well. In this case it is logical
to remove the $\times$ terms from the detection statistic reducing it to
\begin{equation}\label{eq:fstat_degenerate}
\rho_{\mathrm{coh}}^{2} =
\frac{\mathbf{(s|F_{+} h_{0})}^{2} + \mathbf{(s|F_{+} h_{\frac{\pi}{2}})}^{2}}{
\mathbf{ (F_{+} h_{0} | F_{+} h_{0}) }},
\end{equation}
which is $\chi^{2}$ distributed with two degrees of freedom.
In this formalism the coherent \ac{SNR} changes abruptly from (\ref{eq:fstat_degenerate})
to (\ref{eq:fstat_dp}). If there is any sensitivity, no matter how
small, to the $\times$ polarization, there is an entirely different
detection statistic. This arises due to maximization over the
$\mathcal{A}^{\mu}$ parameters, allowing them to take any value. Thus,
even though a network may have very little sensitivity to the $\times$
polarization, and consequently there be little chance of observing the
waveform in the $\times$ polarization, this is not taken into account in
the derivation. A possible modification is to place an astrophysical
prior on the parameters $(D, \iota, \psi, \phi_{0})$ and propagate this
to the distribution of the $\mathcal{A}^{\mu}$ \cite{Prix:2009tq}. This
would provide a smooth transition from the degenerate to non-degenerate
search.
\subsection{Comparison with Coincident Search}
\label{sec:coinc_vs_coherent}
The single detector search is a special case of the degenerate network
(\ref{eq:fstat_degenerate}) and can be written as
\begin{equation} \label{eq:sngl_det_snr}
\rho_{X}^{2} = \frac{ (s^{X}| h_{0})^2 + (s^{X} | h_{\frac{\pi}{2}})^2}{
(\sigma^{X})^{2}} \, .
\end{equation}
A coincidence search requires a signal to be observed in two or more
detectors, without requiring consistency of the measured waveform
amplitudes in the different detectors. In many cases, coincidence
searches have made use of different template banks in the different
detectors \cite{Abadie:2010uf, Abadie:2010yba, Abbott:2009qj} and
required coincidence between the recovered mass parameters
\cite{Robinson:2008}. A comparison with the coherent analysis discussed
above is facilitated if we consider a coincident search where an
identical template is used in all detectors, as was done in an analysis
of early LIGO data \cite{Abbott:2005pe}. In this case, the
multi-detector coincident \ac{SNR} is given by
\begin{equation} \label{eq:coinc_snr}
\rho^{2}_{\mathrm{coinc}} = \sum_{X} \rho_X^2 =\sum_{X}
\frac{ (s^{X} | h_{0})^2 + (s^{X} | h_{\frac{\pi}{2}})^2}{(\sigma^{X})^{2}}
\, .
\end{equation}
This is not immediately comparable to the coherent \ac{SNR} given in
(\ref{eq:fstat_dp}). However, both can be re-cast into similar forms by
writing the coincident \ac{SNR} as
\begin{equation} \label{eq:coinc_xy}
\rho^{2}_{\mathrm{coinc}} = \sum_{X,Y} \sum_{i = 0, \frac{\pi}{2}}
\Big( s^{X} \Big| \frac{h_{i}}{\sigma^{X}}\Big)
\left[ \delta^{XY} \right]
\Big( s^{Y} \Big| \frac{h_{i}}{\sigma^{Y}}\Big)
\end{equation}
Similarly, the coherent \ac{SNR} can be written as
\begin{equation} \label{eq:coherent_xy}
\rho^{2}_{\mathrm{coh}} = \sum_{X,Y} \sum_{i = 0, \frac{\pi}{2}}
\Big( s^{X} \Big| \frac{h_{i}}{\sigma^{X}}\Big)
\left[ f_{+}^{X} f_{+}^{Y} + f_{\times}^{X} f_{\times}^{Y} \right]
\Big( s^{Y} \Big| \frac{h_{i}}{\sigma^{Y}}\Big)
\end{equation}
where we have defined the orthogonal unit vectors (in detector space)
$f_{+}^{X}, f_{\times}^{X}$ as
\begin{equation}
f_{+,\times}^{X} = \frac{\sigma^{X} F_{+,\times}^{X}}{\sqrt{\sum_{Y}
(\sigma^{Y} F_{+,\times}^{Y})^{2}}} \, .
\end{equation}
The \ac{SNR} of the coincident search (\ref{eq:coinc_xy}) is simply the
sum of all power consistent with the template waveform in each detector.
The coherent \ac{SNR} (\ref{eq:coherent_xy}) makes use of the fact that
gravitational waves have only two polarizations to restrict the
accumulated \ac{SNR} to the physical subspace spanned by $f^{+}$ and
$f^{\times}$. For a signal, the power will lie entirely in this
subspace, while noise in the detectors will contribute to all
components of the coincident \ac{SNR}. Thus, the coherent analysis
obtains precisely the same signal \ac{SNR} but reduces the noise
background. Specifically, the coherent \ac{SNR} acquires contributions
from four noise degrees of freedom, while the coincident \ac{SNR} has
$2N$ noise degrees of freedom, where $N$ indicates the number of active
detectors. For a non-degenerate two detector
network, the coincident and coherent \ac{SNR}s are equal as in this case
$f_{+}^{X} f_{+}^{Y} + f_{\times}^{X} f_{\times}^{Y} = \delta^{XY}$.
In the case where a network is sensitive to only one
polarization, the coherent \ac{SNR} is constructed solely from the
$f^{X}_{+}$ direction and coherent \ac{SNR} is $\chi^{2}$ distributed with 2
degrees of freedom.
Finally, we note that restricting to the coherent \ac{SNR} can help to
separate transients from gravitational wave signals as those transients
which do not contribute power to the signal space will be ignored.
However, many noise transients will contribute to the coherent \ac{SNR}
and more active methods of removing them are required. These methods
are the focus of sections \ref{sec:snr_cont_consistency} and
\ref{sec:chi2tests}.
\subsection{Synthetic + and $\times$ detectors}
\label{sec:plus_cross_dets}
In the dominant polarization the coherent \ac{SNR} is comprised of
separate $+$ and $\times$ components, with no cross terms.
We can go one step further and interpret the coherent \ac{SNR} as
arising from two synthetic detectors, one
sensitive to only the $+$ polarization and one sensitive to only the
$\times$ polarization. These synthetic detectors are most easily formed
by combining the ``overwhitened'' data streams $o^{X}$ from the various
detectors, where
\begin{equation}
o^X(f) = \frac{s^X(f)}{S_h^X(f)} \, .
\end{equation}
The overwhitened synthetic data streams are simply
\begin{equation}
o_{+,\times}(f) = \sum F^{X}_{+,\times} o^X(f) \, ;
\end{equation}
and the power spectra for these overwhitened data streams are
\begin{equation} \label{eq:psds}
S_{+,\times} = \left(\sum_X
\frac{(F_{+,\times}^X)^2}{S_h^X(f)}\right)^{-1} \, .
\end{equation}
Using this, the un-whitened synthetic data streams are given as%
\footnote{There is some ambiguity in fixing the overall normalization of
the synthetic detectors. We require that our synthetic detectors have
the same sensitivity to the two polarizations as the original network
did by requiring $(h_{0}^{+,\times} | h_{0}^{+,\times} )_{+, \times}
= \sum_{X} (F^{X}_{+,\times} \sigma^{X})^{2}$.}
\begin{equation}\label{eq:splus_cross_def}
s_{+,\times}(f) = \sum_X \frac{F_{+,\times}^X s^X(f)}{S_h^X(f)}
\left(\sum_Y \frac{(F_{+,\times}^Y)^2}{S_h^Y(f)}\right)^{-1} \, .
\end{equation}
In terms of these synthetic detectors the detection statistic becomes
\begin{equation}\label{eq:fstat_plus_cross}
\rho_{\mathrm{coh}}^{2} =
\frac{ (s_+|h_{0})_{+}^{2} + (s_+| h_{\frac{\pi}{2}})_{+}^{2}}{
( h_{0} | h_{0})_{+} } +
\frac{(s_{\times}| h_{0})_{\times}^{2} +
(s_{\times}| h_{\frac{\pi}{2}})_{\times}^{2}}{
( h_{0} | h_{0})_{\times} } \, ,
\end{equation}
where the subscripts $+, \times$ on the inner products denote the fact
that the power spectrum of the synthetic detectors is used in their
evaluation.
\section{Signal consistency between detectors}
\label{sec:snr_cont_consistency}
As discussed in the introduction, due to the presence of non-Gaussian
noise transients, it is essential to make use of signal
consistency requirements within search algorithms to distinguish
glitches from gravitational wave signals.
Multi-detector analyses have made good use of signal consistency between
detectors (see e.g. \cite{1367-2630-12-5-053034}). A particularly
powerful test is the use of a ``null stream'' \cite{Guersel:1989th}
which, by construction, contains no gravitational wave signal. Many
noise transients will contribute power to the null stream and can
therefore be eliminated as candidate events. In addition, requiring
that the gravitational wave signal is recovered consistently between
detectors can eliminate other noise transients, in our case this is
equivalent to imposing restrictions on the recovered values of the
parameters, $\hat{\mathcal{A}}^{\mu}$. These two methods will be
considered in turn. For matched filtering searches, requiring
consistency between the observed signal and template waveform has also
proven very powerful \cite{Allen:2004gu}. A full description of
waveform consistency tests is presented in the next section.
\subsection{Null Stream Consistency}
\label{sec:nullstream}
The gravitational waveform consists of two polarizations. Thus for
networks comprising three or more detectors it is possible to construct
one or more null data streams which contain no gravitational wave signal
\cite{Guersel:1989th}. In the context of a coherent search for \ac{CBC}
signals, the null consistency tests arise quite naturally. In section
\ref{sec:coinc_vs_coherent}, we noted that the coherent \ac{SNR} can be
thought of as a projection of the coincident multi-detector \ac{SNR}
onto a four dimensional signal subspace. The remaining
dimensions in the coincident search do not contain any gravitational
wave signal, but will be subject to both Gaussian and non-Gaussian
noise. Thus, we can define the null \ac{SNR} as
\begin{eqnarray}\label{eq:null_overwhite}
\rho_{\mathrm{N}}^{2} &=& \rho^{2}_{\mathrm{coinc}} -
\rho^{2}_{\mathrm{coh}} \\
&=& \sum_{X,Y} \sum_{i = 0 , \frac{\pi}{2}}
\Big( s^{X} \Big| \frac{h_{i}}{\sigma^{X}}\Big)
\left[ N^{XY} \right]
\Big( s^{Y} \Big| \frac{h_{i}}{\sigma^{Y}}\Big)
\nonumber \, ,
\end{eqnarray}
where
\begin{equation} \label{eq:null_cont}
N^{XY} = \delta^{XY} - f_{+}^{X} f_{+}^{Y} - f_{\times}^{X}
f_{\times}^{Y} \, .
\end{equation}
A gravitational wave signal matching the template $h$ will provide no
contribution to the null \ac{SNR}, so we expect that, for signals, this
statistic will be $\chi^{2}$ distributed with $(2N - 4)$ degrees of
freedom. A noise transient that is incoherent across the data
streams, may give a large coherent \ac{SNR}, but it is likely to also give a
large null \ac{SNR}. Thus requiring a \textit{small} null \ac{SNR} will prove
effective at distinguishing incoherent noise transients from real
gravitational wave signals. Since the definition of the null \ac{SNR}
(\ref{eq:null_overwhite}) makes use of the template waveform,
gravitational waveforms which do not match the template $h$ can
contribute to the null \ac{SNR}.
We can go one step further and introduce synthetic null detectors in
analogy with the synthetic $+$ and $\times$ detectors. For
concreteness, we describe the three detector case, but this can be
extended in a straightforward manner to larger networks. To do so, we
introduce the null direction
\begin{equation}
n^{X} = \epsilon^{XYZ} f_{+}^{Y} f_{\times}^{Z}.
\end{equation}
such that $N^{XY} = n^{X} n^{Y}$.
Then, the over-whitened synthetic null detector is
\begin{equation}
o_{N}(f) = \sum \frac{n^{X}}{\sigma^{X}} o^X(f) \, .
\end{equation}
The power spectrum of the null stream is%
\footnote{In this case, there is a normalization ambiguity. For the
synthetic plus and cross streams, it was natural to require that the
synthetic detectors have the same sensitivities as the original
network. For the null stream this is not feasible as the network has
zero sensitivity to a signal in the null stream, so we normalize such
that $(h_{0} | h_{0})_{N} = 1$.}
\begin{equation} \label{eq:nullpsds}
S_{N}(f) = \left(\sum_X \frac{(n^X)^2}{(\sigma^{X})^{2} S_h^X(f)}\right)^{-1}
\end{equation}
and the un-whitened null stream is%
\begin{equation}\label{eq:sn}
s_{N}(f) = \left( \sum_X \frac{n^{X} s^X(f)}{\sigma^{X} S_h^X(f)}
\right) \cdot S_{N}(f) \, .
\end{equation}
Finally, the null \ac{SNR} can be written as
\begin{equation}
\rho_{\mathrm{N}}^{2} = \frac{
\left( s_{N} | h_{0} \right)_{N}^{2} +
\left( s_{N} | h_{\frac{\pi}{2}} \right)_{N}^{2} }{ (h_{0} | h_{0})_{N} } \, .
\end{equation}
The null \ac{SNR} described above differs from the multi-detector null
stream formalism introduced in \cite{Guersel:1989th} and used by several
other authors. A null stream is constructed to be a data stream which
contains no contribution from the $h_{+}$ and $h_{\times}$ gravitational
waveforms, regardless of the details of the waveform. To provide a
concrete comparison between the null stream and null \ac{SNR}, we
restrict attention to a three detector network. The null stream is
explicitly constructed as
\begin{equation} \label{eq:snormalnull}
\mathrm{s_{\mathrm{Null}}}(f) = \epsilon_{XYZ} F^{X}_{+} F^{Y}_{\times}
s^{Z}(f) \, .
\end{equation}
By comparing the null stream in (\ref{eq:snormalnull}) with the
synthetic null detector (\ref{eq:sn}), it is clear that these will
generically differ. To get an insight into the differences, consider a
network with two co-located detectors $A$ and $B$, with power spectra
$S^{A}_{h}(f)$ and $S^{B}_{h}(f)$ respectively, and a third detector $C$
which is sensitive to the other polarization of gravitational waves.
For this network, the null stream will be a combination of only the $A$
and $B$ detector data. The power spectrum of the null stream is
\begin{equation}
S_{\mathrm{Null}}(f) = S^{A}(f) + S^{B}(f).
\end{equation}
while for the synthetic null detector, it is
\begin{equation}
\frac{1}{S_{\mathrm{N}}(f)} =
\frac{1}{(\sigma^{A})^{2} S^{A}(f)} + \frac{1}{(\sigma^{B})^{2} S^{B}(f)} \, .
\end{equation}
Thus, if the power spectra of detectors $A$ and $B$ are identical, then
the two null streams are also identical. In the extreme case that the
sensitivity bands of the two detectors do not overlap at all, then there
is no null stream ($S_{\mathrm{Null}} \rightarrow \infty$). However,
the null \ac{SNR} need not vanish and is similar to a two bin version of
the $\chi^{2}$ test described in section \ref{ssec:standard_chisq}.
Thus, it is possible to construct scenarios in which these two null
stream formulations differ significantly.
For the most part, the power spectra of the ground based detectors are
rather comparable. So, in general there will not be a significant
difference between these two forms. There are advantages to both
methods. The null stream is designed to cancel all gravitational wave
signals from the data, thus making it more robust when the signal is not
well known. However, by making use of the template signal, there are
instances in which the null \ac{SNR} provides a more powerful
consistency test. Furthermore, it has a computational benefit in that
it does not require the production of a null stream --- all
manipulations are performed on the single detector \ac{SNR} data
streams which are subsequently separated into coherent and null
componenets. In practice we have found very little difference in
performance, and choose to compute the null \ac{SNR}
(\ref{eq:null_overwhite}) for computational simplicity.
Finally, we note that both null stream formalisms will perform optimally
only if the three detectors have similar sensitivities. In the case
where one detector is significantly less sensitive than the others, the
null stream will generally tend to the data of that less sensitive
detector. Also, the null formalisms described here will only completely
cancel a gravitational wave signal provided that the calibration of the
data streams is accurate, any error in calibration will lead to a signal
surviving in the null stream data.
\subsection{Amplitude Consistency}
\label{sec:ampcons}
The four amplitude parameters $\mathcal{A}^{i}$, encoding the distance
to and orientation of the binary system, can take any values. Indeed,
any set of $\mathcal{A}^{i}$ corresponds to unique values of the
distance, inclination angle, coalescence phase and polarization angle,
up to symmetries of the system. However, some of these values will be
significantly more likely to occur astrophysically than others.
For example, the number of binary coalescence events is expected to be
approximately proportional to star formation rate \cite{Temp:2010cfa} and
consequently should be roughly uniform in volume. Thus, events are more
likely to occur at a greater distance. Similarly, the gravitational
wave amplitude, at a fixed distance, is greater for face on signals than
edge on ones, as is clear from (\ref{eq:aplus_across}). Thus,
approximately face on signals at a large distance are more likely
signals than nearby, edge on ones.
The distribution of noise events will follow its own characteristic
distribution. For Gaussian noise, this distribution can be evaluated
and the signal and noise distributions incorporated into the ranking
statistic \cite{Prix:2009tq}. Non-stationarities in the data will again
produce a different distribution of amplitudes. Specifically, the
majority of transients are caused by a disturbance or glitch in a single
detector with little or no signal in the other detectors. For networks
with three or more detectors, this will typically be inconsistent with a
coherent signal across the network, leading to a large value of the null
\ac{SNR}. In certain scenarios, most notably for two detector networks,
there will be a consistent set of values for the $\mathcal{A}^{i}$.
However, these values carry the characteristic signature of a glitch.
Specifically, the \ac{SNR} contributions will typically be consistent
with a nearby, close to edge on system ($A_{\times} \approx 0$), with a
very specific orientation to provide essentially no response in all but
one detector. Thus, the glitch distribution of the $\mathcal{A}^{i}$
parameters, will be significantly different from the distribution
expected for gravitational wave signals. In the remainder of this
section, we explore the possibility of making use of the extracted
$\mathcal{A}^{i}$ parameters to distinguish between glitches and
signals. Unlike the null stream, amplitude consistency tests are
available for two detector networks. They should be especially useful
in the case of the two 4km LIGO instruments, which have similar
sensitivities to the majority of points on the sky.
\begin{figure}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_1a}
\end{minipage}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_1b}
\end{minipage}
\caption{\label{fig:sim_inc_injs}
The distribution of the recovered inclination angle plotted against
coherent \ac{SNR} for optimally oriented signals (unfilled circles),
uniformly distributed orientations (blue crosses) and simulated glitches
(red circles). The top figure shows a network configuration where we are
equally sensitive to both gravitational wave polarizations. The bottom
figure shows a configuration where we are 5 times more sensitive to the
$+$ polarization than to the $\times$.}
\end{figure}
We have argued that the majority of gravitational wave signals will
originate from (close to) face on binaries while the majority of noise
transients will mimic (close to) edge on binaries. The recovered value
of the inclination angle $\iota$ should then serve to separate signals
from noise. To investigate this, we simulated a large number of
simulated \ac{CBC} signals and a large number of noise glitches; added
Gaussian noise and plotted the recovered inclination angle in Figure
\ref{fig:sim_inc_injs}. The glitches were generated as events with a
large \ac{SNR} in one detector coincident with Gaussian noise in a
second detector. The signals were separated into two groups: the first
with only face on binaries ($|\cos \iota| = 1$) and the second a uniform
distribution over the two sphere (uniform in $\cos \iota$ and $\psi$) of
the binary orientation. In both cases, they were distributed uniformly
in volume and orbital phase. We also consider different network
configurations, both containing two equally sensitive detectors. In the
first case one detector is sensitive to $+$ and the other to $\times$
polarization ; in the second case both detectors have strong and equal
sensitivity to the $+$ polarization and weak but opposite sensitivity to
the $\times$ polarization --- rather typical for the Hanford, Livingston
network. For both sets of signals and choices of network, there is a
clear distinction between signal and glitch distribution. However,
there is a clear downwards bias on the recovered values of $\iota$.
This can be understood by looking at the expressions for $A_{+}$ and
$A_{\times}$. For face on binaries, these will be equal but, in the
presence of noise, $A_{\times}$ will be reconstructed to be somewhat
smaller than $A_{+}$. A relative difference of only $5\%$ leads to a
recovered inclination of $45^{\circ}$, so even for loud signals there
can be large discrepancy between the actual and recovered inclination
angle.
Despite the difference in distribution between signal and noise, there
is also a significant overlap of the populations at low SNRs. Consequently, any
threshold imposed on the recovered inclination angle is liable to
either reject a fraction of signals or pass a fraction of glitches. It
is, however, quite possible that knowledge of these expected
distributions could be folded into the detection statistic in a Bayesian
manner.
\begin{figure}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_2a}
\end{minipage}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_2b}
\end{minipage}
\caption{\label{fig:sim_snr_injs}
The distribution of single detector \ac{SNR} plotted against coherent
\ac{SNR} for optimally oriented signals (unfilled circles), uniformly
oriented signals (blue crosses) and glitches (red circles). The top
figure shows a two equally sensitive detector network configuration
where one detector sees only the $+$ polarization and the second
detector sees only the $\times$ polarization. The bottom figure shows a
two detector network configuration where both detectors have strong and
equal sensitivity to the $+$ polarization and weak but opposite
sensitivity to the $\times$ polarization. This is meant to emulate a
typical instance for the Hanford, Livingston network. The diagonal solid
black line shows the expected \ac{SNR} for the optimally oriented
signals. The horizontal dashed black line indicates an \ac{SNR} of 4.}
\end{figure}
We have found that using the observed \ac{SNR} in the individual
instruments to be a more effective discriminator of signal and noise.
To demonstrate the efficacy of such an approach, in Figure
\ref{fig:sim_snr_injs} we plot the single detector \ac{SNR} as a
function of the coherent \ac{SNR} for the same population of glitches
and the two classes of signals (face on and uniformly distributed
orientation) described above. The glitches fall into two groups
depending upon which detector suffered the glitch. Since our model
detectors are equally sensitive, then on average one expects each
detector to accrue $1/\sqrt{2}$ of the coherent \ac{SNR}. Even allowing
for non-optimally oriented signals and the addition of Gaussian noise,
the signals follow this expectation. Only a small number of signals
are found with \ac{SNR}s inconsistent with the expected values, these
are ones that have very specific orientations. Overall, the
signal and glitch populations are very well separated, at least until
the coherent \ac{SNR} becomes rather small.
The most effective strategy we have found is to require that all events
have an \ac{SNR} above 4 in the two most sensitive detectors in the
network. The cut is illustrated in Figure \ref{fig:sim_snr_injs}. This
strategy removes the majority of glitch signals while having a negligible
effect on the signal population at large \ac{SNR}. For lower \ac{SNR}
the signals which are lost due to this cut would be unlikely to be
detection candidates as Gaussian noise alone produces similar events.
\section{Coherent $\chi^2$ tests}
\label{sec:chi2tests}
Data from gravitational wave detectors contain numerous
non-stationarities due to both instrumental and environmental causes.
These non-stationarities, or glitches, typically do not
match well with the \ac{CBC} waveform. However, they often contain enough power
that, even though the match with the template is poor, a large \ac{SNR}
is observed. In the previous section, we have seen how the use of
various coherent consistency tests can mitigate this problem.
Additionally, a number of other signal consistency tests have been
implemented \cite{Allen:2004gu, Hanna:2008} and used in searches for CBC
signals \cite{Abadie:2010yba, Abbott:2009qj, Abbott:2009tt}. These
tests are all designed to eliminate glitches which have a different
signal morphology than the template waveform. This is essentially done
by testing whether the detector data orthogonal to the signal is well
described as Gaussian and stationary --- for a glitch, there will be
residual power which does not match the template waveform. These tests
are commonly known as ``$\chi^2$ tests'' as they construct a statistic
which is $\chi^{2}$ distributed in the presence of Gaussian noise plus a
signal matching the template waveform. If the data contains a glitch,
the $\chi^{2}$ statistic will generally have a large value, thereby
allowing for differentiation of signal from non-stationary noise. In
this section, we briefly review the general formulation of $\chi^{2}$
tests before presenting a detailed description of three such tests which
have been implemented for the coherent search described in section
\ref{sec:coh_matched_filter}.
\subsection{A general framework for $\chi^{2}$ tests}
\label{sec:gen_chi}
Consider the data from a gravitational wave detector at a time $t$ which
has produced a large \ac{SNR} when filtered against a template $h(t)$.
Generically, the data $s(t)$ can be decomposed as
\begin{equation}\label{eq:signal_model}
s(t) = n(t) + A h(t) + B g(t)
\end{equation}
where $n(t)$ represents a Gaussian noise component, $h(t)$ is the
template waveform, $g(t)$ is an additional non-Gaussian noise
contribution to the data stream and $A$ and $B$ are amplitude factors.
The glitch contribution $g(t)$ is taken to be the power orthogonal to
$h(t)$ and both $g(t)$ and $h(t)$ are normalized,
so that
\begin{equation}
( g | g ) = 1 \, , (h | h) = 1 \, , ( g | h ) = 0 \, .
\end{equation}
In order to construct a $\chi^{2}$ test, we must introduce an additional
set of waveforms $T^{i}$. These waveforms are required to be
orthonormal and orthogonal to $h$,
\begin{equation}
(h|T^i) = 0 \, , (T^i | T^j) = \delta^{ij} \, .
\end{equation}
Furthermore, for the $\chi^{2}$ test to be effective, the $T^{i}$ must
have a good overlap with the glitch waveform $g(t)$.
The $\chi^{2}$ discriminator is constructed as
\begin{equation}\label{eq:chi2}
\chi^2 = \sum_{i=1}^{N} (T^i | s)^2 \, .
\end{equation}
When the data comprises only signal plus Gaussian noise, i.e. $B=0$ in
equation (\ref{eq:signal_model}),
\begin{equation}
\chi^2 = \sum_{i=1}^{N} (T^i | n)^2.
\end{equation}
and the statistic is the sum of squares of independent Gaussian
variables with zero mean and unit variance. Thus the test is $\chi^{2}$
distributed with $N$ degrees of freedom, with a mean and variance of
\begin{equation}
\langle\chi^2\rangle = N \, ,
\quad
{\rm Var}(\chi^2) = 2N \, .
\end{equation}
This is true for \emph{any} set of waveforms $T^i$ given the above
assumptions.
In the case where the data are not an exact match to the signal, we take
both $A$ and $B$ non-zero, i.e. any signal or glitch can be decomposed
into a part $A h(t)$ proportional to the template under consideration
plus a second orthogonal contribution $B g(t)$. Clearly, for different
glitches, the waveform $g(t)$ as well as the amplitude factor $B$ will
be different. In this case the $\chi^{2}$ test takes the form
\begin{equation}
\chi^2 = \sum_{i=1}^N \left[ (T^i | n)^2 + 2 B (T^i | n)(T^i | g) +
B^{2} (T^i|g)^2 \right] \, .
\end{equation}
This has a mean
\begin{equation}
\langle\chi^2\rangle = N + B^{2} \sum_i^N (T^i | g)^2
\end{equation}
and a variance
\begin{equation}
{\rm Var}(\chi^2) = 2N + 4 B^{2} \sum_i(T^i|g)^{2} \, .
\end{equation}
The $\chi^{2}$ test is distributed as a non-central $\chi^{2}$
distribution with $N$ degrees of freedom and a non-centrality parameter
\cite{Allen:2004gu}
\begin{equation}
\lambda = B^{2} \sum_{i=1}^N (T^i | g)^2 \, .
\end{equation}
The challenge in constructing a $\chi^{2}$ test is to select the basis
waveforms $T^{i}$ such they have large overlaps with the observed
glitches in the data. If this is done successfully, then any glitch
producing a large \ac{SNR} will also give a large value of $\chi^{2}$,
inconsistent with a signal in Gaussian noise.
In many cases, there is some uncertainty in the template waveform. For
example, the post-Newtonian (PN) expansion used in generating \ac{CBC}
waveforms is truncated at a finite (typically 3 or 3.5 PN
\cite{Bliving}) order and there will be differences between this
analytically calculated waveform and the one provided by nature. There
are similar uncertainties in waveforms obtained from numerical
relativity simulations \cite{Hannam:2009hh}. Additionally, to search
the full parameter space of coalescing binaries, a discrete template
bank is used which allows for some mismatch between the templates and
any potential signal within the parameter space
\cite{OwenSathyaprakash98}. Normally the template bank is created so
that the mismatch is no larger than $3\%$ at any point in the parameter
space. Finally, there are uncertainties in instrumental calibration
\cite{Abadie:2010px} which will affect the match between signal and
template.
We model these effects by parametrizing the signal as
\begin{equation}\label{eq:mismatch_sig}
H(t) = A ( \sqrt{1 - \epsilon^{2}}\, h(t) + \epsilon \, m(t) ) \, ,
\end{equation}
where $m(t)$ is the component of $H$ that is orthogonal to $h$
[$(m|h) = 0$] and $\epsilon$ encodes the mismatch between signal and
template in the sense that
\begin{equation}\label{eq:mismatch}
1 - \frac{(H | h)}{\sqrt{(H | H) (h |h)}}
= 1 - \sqrt{1 - \epsilon^{2}} \approx \epsilon\, .
\end{equation}
In most cases, it is reasonable to assume a mismatch of less than $5\%$.
The obvious counter-example is when searching for highly spinning
systems using non-spinning waveforms, see e.g.
\cite{Vandenbroeck:2009cv,Fazi:2009}.
Since (\ref{eq:mismatch_sig}) is a special case of
(\ref{eq:signal_model}) it follows directly that the mean and variance
of the $\chi^{2}$ test in the presence of a mis-matched signal are
\begin{eqnarray}
\langle\chi^2\rangle &=& N + A^2 \epsilon^2 \sum_{i=1}^N (T^i | m)^2
\nonumber \\
{\rm Var}(\chi^2) &=& 2N + 4A^2\epsilon^2\sum_{i=1}^{N} (T^i | m)^2.
\end{eqnarray}
Since the \ac{SNR} of the signal is proportional to $A$, the expected
$\chi^{2}$ value for a mis-matched signal increases with the strength of
the signal. However, for mismatched signals $\chi^{2} \propto
\epsilon^{2} A^2$ while for glitches $\chi^{2} \propto B^{2}$ and
provided $\epsilon A \ll B$ the two can be separated. See
\cite{Allen:2004gu} for a more detailed discussion.
When introducing the $\chi^{2}$ test, we assumed that the $T^{i}$ were
orthonormal and orthogonal to the template waveform $h$. In practice,
this can be difficult to guarantee. The signal consistency tests
discussed in the remainder of this section are constructed from
gravitational waveforms. If one picks a set of gravitational waveforms,
$t^i$, there is no guarantee that they will be either orthonormal or
orthogonal to $h$. We can, at least, construct waveforms which are
orthogonal to $h$ by introducing
\begin{equation}
T^i = \frac{t^i - (t^i | h) h }{\sqrt{ 1 - (t^i | h)^2} }.
\end{equation}
While this ensures $(h|T^i)=0$ it does not guarantee
orthonormality of the $T^{i}$, $(T^i|T^j) = \delta^{ij}$. Thus this
method will not produce a $\chi^{2}$ distribution, and will instead form
a generalized $\chi^{2}$ distribution. The mean of the distribution
remains $N$ but the variance is increased,
\begin{equation}
{\rm Var}(\chi^2) = 2N + 2 \sum_{i \neq j}
(T^{i} | T^{j})^{2}.
\end{equation}
It has been found, however, that this does not present a significant
obstacle to using these tests, especially as the thresholds are
tuned empirically \cite{LIGOS3S4Tuning}.
\subsubsection*{Multi-detector $\chi^{2}$ tests}
\label{sec:cohchi2test}
In section \ref{sec:coh_matched_filter}, we derived a coherent
multi-detector search for coalescing binaries. The search involves
filtering four waveform components $h_{\mu}$ against the multi-detector
data stream. Our initial discussion of $\chi^{2}$ tests was
limited to the description of a single phase template waveform $h$ and
test waveforms $T^{i}$. The extension to a two phase waveform has been
described previously \cite{Allen:2004gu} and here we extend that to a
four component waveform across multiple detectors, as is appropriate for
this search. We begin by noting that the four waveform components
$h_{\mu}$ are orthogonal in the dominant polarization basis. They are,
however, not generally normalized, as
\begin{equation}
( \mathbf{h}_{\mu} | \mathbf{h}_{\nu} ) = \mathcal{M}_{\mu \nu} =
\mathrm{diag} (A, B, A, B) \, ,
\end{equation}
where $A$ and $B$ are defined in (\ref{eq:ab}). Thus, we first
normalize so that
\begin{equation}
( \hat{\mathbf{h}}_{\mu} | \hat{\mathbf{h}}_{\nu} ) = \delta_{\mu \nu}.
\end{equation}
To construct a network $\chi^{2}$ test, we require a set of
(4-component) normalized, test waveforms $\hat{t}_{\mu}^{i}$. The
components
\begin{equation} \label{eq:genchisq}
T^{i}_{\mu} = \frac{\hat{t}^i_{\mu}
- \sum_{\nu} (\hat{\mathbf{t}}^i_{\mu}|\hat{\mathbf{h}}_{\nu}) \hat{h}_{\nu}}
{\sqrt{1 - \sum_{\sigma}
(\hat{\mathbf{t}}^i_{\sigma}|\hat{\mathbf{h}}_{\sigma})^2}} \, ,
\end{equation}
constructed to be orthogonal to $h_{\mu}$, are used in the $\chi^{2}$
test. Thus, the coherent, multi-detector $\chi^2$ test is
\begin{equation} \label{eq:cohchi2}
\chi^2 = \sum_{\mu=1}^4 \sum_{i=1}^N (\mathbf{T}^i_{\mu} | \mathbf{s})^2 \, .
\end{equation}
Provided the test waveforms are orthonormal, in the sense that
\begin{equation}\label{eq:template_orth}
(\mathbf{T}^{i}_{\mu} | \mathbf{T}^{j}_{\nu}) = \delta^{ij}
\delta_{\mu\nu} \, ,
\end{equation}
the distribution for a signal matching $h_{\mu}$ plus Gaussian noise
will be $\chi^{2}$ distributed with $4N$ degrees of freedom. As for the
single phase filter, we cannot always guarantee (\ref{eq:template_orth})
is satisfied, although it is relatively simple to ensure the four
components of a given template \textit{are} orthogonal. This means that
the statistic will not, in general, be $\chi^{2}$ distributed: The mean
remains $4N$ but the variance increases to
\begin{equation}
{\rm Var}(\chi^2) = 8N +
2 \sum_{i,j=1}^N \sum_{\mu,\nu=1}^{4}
\left[ (T^{i}_{\mu} | T^{j}_{\nu})^{2} - \delta^{ij}\delta_{\mu\nu} \right].
\end{equation}
\subsection{The coherent bank $\chi^{2}$ test}
\label{sec:bank_chi}
The bank $\chi^{2}$ test was designed to test the consistency of the
observed \ac{SNR} across different templates in the bank at the time of
a candidate signal. It was first described in \cite{Hanna:2008} for the
case of a single detector. A glitch will typically cause a high
\ac{SNR} in many templates across the bank, while a real signal will
give a well prescribed distribution of \ac{SNR} across the template
bank.
\begin{figure}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_3}
\end{minipage}
\caption{\label{fig:bank_hist}
The distribution of the bank $\chi^{2}$ test for a single template $h$,
with a bank of size $10$. The plot shows the distribution of the bank
veto calculated for every time sample in $128 s$ of simulated Gaussian
data (with no signal present). In the case that the ten bank templates
are orthogonal, the expected distribution is $\chi^{2}$ with 40 degrees
of freedom (shown as the solid black line). As can be seen, the actual
distribution follows the expected one closely.}
\end{figure}
The bank $\chi^{2}$ makes use of other CBC templates as the waveforms
$t^{i}$ to construct the $\chi^{2}$ test. These $N$ templates are taken
from different points across the mass space. In implementing the bank
$\chi^{2}$, we choose a \textit{fixed} set of template waveforms $t^{i}$
which remain the same for every template $h$ in the search template
bank. The bank $\chi^{2}$ statistic is then constructed following
(\ref{eq:genchisq}) and (\ref{eq:cohchi2}). The test is most effective
when the set of $T_{\mu}^{i}$ is close to orthogonal \cite{Hanna:2008}
so we select templates which are well distributed across the mass space,
ensuring the overlaps $(T_{\mu}^{i} | T_{\nu}^{j})$ are small for $i
\neq j$. Figure \ref{fig:bank_hist} shows the distribution of the bank
$\chi^{2}$ for a single template filtered against Gaussian noise. The
set of fixed bank waveforms consisted of ten waveforms distributed over
the full mass parameter space. Using these waveforms, the deviation
from a $\chi^{2}$ distribution is negligible.
For the bank $\chi^{2}$ to be effective, glitches in the data must have
a good overlap with a reasonable fraction of the templates $t^{i}$.
While, in general, it is difficult to predict the composition of
glitches in the data, it seems reasonable to assume that glitches which
produce a large \ac{SNR} for the template $h$ will also have a good
overlap with other waveforms in the template space. Thus, the set of
templates which is spread across the parameter space is suitable.
\subsection{The coherent autocorrelation $\chi^{2}$ test}
\label{sec:auto_chi}
Filtering a gravitational wave template against data containing a
matching signal produces a peak in the \ac{SNR} at the time of
the signal. Furthermore, there is a characteristic shape of this peak
which depends upon the template waveform and also the noise power
spectrum of the data. An example of this ``autocorrelation''
for a binary neutron star template is shown in Figure
\ref{fig:auto_corr}. A noise transient in the data will produce a peak
in the \ac{SNR} but it will typically lack the characteristic shape
produced by a genuine \ac{CBC} signal.
\begin{figure}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_4}
\end{minipage}
\caption{\label{fig:auto_corr}
The single detector auto-correlation of a gravitational wave inspiral signal from a
1.4,1.4 solar mass binary neutron star. Both phases of the waveform are
shown. }
\end{figure}
The ``auto'' $\chi^{2}$ test was designed to test the consistency of the
\ac{SNR} peak \cite{Hanna:2008}. It is a similar test to the bank
$\chi^{2}$, but where the bank $\chi^{2}$ investigates consistency in
\ac{SNR} across the mass space, the auto $\chi^{2}$ tests for
consistency of the \ac{SNR} time series. The set of templates $t^{i}$
are chosen to be the original template $h$ with time shifts $\delta
t^{i}$ applied. The values of $\delta t^{i}$ are all unique and chosen
to be of the same time-scale as the auto-correlation of the template
waveform (typically $0.1s$ or less) and the duration of
non-stationarities in the data, which is similar.
In Figure \ref{fig:auto_hist}, we show the distribution of the auto
$\chi^{2}$ for a single template waveform filtered in Gaussian data.
For this result, forty waveforms $t^{i}$ were used, equally spaced with
a $1$ ms spacing, and all with coalescence times prior to that of
$h$. Thus, the auto $\chi^{2}$ is testing the consistency of the \ac{SNR}
time series for $0.04$ seconds prior to the \ac{SNR} peak. The overlap
$(t^{i}| t^{j})$ depends only upon the difference $\delta t^{i} - \delta
t^{j}$ and Figure \ref{fig:auto_corr} shows clearly that a significant
fraction of the overlaps are far from zero. Consequently, the auto
$\chi^{2}$ test has a distribution with a large deviation from a
$\chi^{2}$ distribution with $4N$ degrees of freedom.
\begin{figure}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_5}
\end{minipage}
\caption{\label{fig:auto_hist}
The distribution of the auto $\chi^{2}$ test for a single template $h$,
generated with 40 time shifted templates, with shifts between $0.001$ and
$0.04$ seconds. The plot shows the distribution of the auto veto
calculated for every time sample in $128 s$ of simulated Gaussian data
(with no signal present). In the case that the forty time shifted
templates are orthogonal, the expected distribution is $\chi^{2}$ with
160 degrees of freedom (shown in black). As can be seen, the actual
distribution differs significantly from this due to the
non-orthogonality of the $t^{i}$ waveforms.}
\end{figure}
\subsection{The coherent $\chi^2$ test}
\label{ssec:standard_chisq}
The ``standard'' $\chi^{2}$ test originally proposed in
\cite{Allen:2004gu} has been used as a discriminator in many
gravitational wave searches for CBCs. Given the template waveforms and
the detector sensitivity, it is possible to predict the accumulation of
\ac{SNR} as a function of frequency. By calculating the observed
\ac{SNR} contribution from a number of frequency bins, and comparing to
the predicted value, one can construct a $\chi^{2}$ consistency test.
Formally, given a template $h$ which produced a candidate signal with an
\ac{SNR} of $\rho$, calculate $N$ non-overlapping frequency windows such
that the expected \ac{SNR} is $\rho/N$ in each. Then, calculate the
actual \ac{SNR} $\rho^{i}$ in each of these frequency bins and compare
with the expected value by calculating
\begin{equation}\label{eq:standard_chisq}
\chi^2 = N \sum_i^N (\rho^i - \rho/N)^2 \, .
\end{equation}
For a gravitational wave signal matching the template $h$ plus Gaussian
noise, this statistic will be $\chi^2$ distributed with $N-1$ degrees of
freedom. Written in the form (\ref{eq:standard_chisq}) it appears
different from the general case we discussed earlier. In
\cite{Allen:2004gu} it was shown that it can be re-expressed in the form
(\ref{eq:chi2}).
This $\chi^{2}$ test can be extended to coherent, multi-detector
searches. Indeed, in \cite{Itoh:2004zd}, the construction was
applied to a coherent search for continuous
gravitational waves. Here, we present the extension to a coherent CBC
search. First, define
\begin{equation}
\rho_{\mu}^i =
\frac{\mathbf{(s | h_{\mu}^i})}{\mathbf{\sqrt{(h_{\mu} | h_{\mu})}}}
\end{equation}
to be the \ac{SNR} contribution in the $i$th frequency bin to the
\ac{SNR}.%
\footnote{Strictly speaking the frequency bins for the $F_+$ and
$F_{\times}$ components will be different because, as we have noted in
equation (\ref{eq:psds}), the \ac{PSD}s for the synthetic $+$ and $\times$
detectors are not equal. However, usually the difference between the two
is small enough that it can be safely ignored to avoid computing twice
the number of filters. Alternatively, in \cite{Allen:2004gu} a method
was presented for calculating the standard $\chi^2$ test using unequal
frequency bins, that method could easily be incorporated into a coherent
search.}
The coherent $\chi^{2}$ statistic is then
constructed as
\begin{equation}
\chi^2 = N \sum_{i=1}^N \sum_{\mu = 1}^4 (\rho_{\mu}^i - \rho_{\mu}/N)^2.
\end{equation}
As all the components are orthogonal it is easy to see that this
statistic will be exactly $\chi^{2}$ distributed with $4N - 4$ degrees
of freedom. One can interpret this as the sum of the single detector
$\chi^{2}$ values for the $h_{0}$ and $h_{\frac{\pi}{2}}$ waveforms in the
synthetic $+$ and $\times$ detectors. Figure \ref{fig:chi_hist} shows
the distribution of the ``standard''
$\chi^{2}$, using 16 frequency bins. The distribution matches the
expected $\chi^{2}$ with 60 degrees of freedom.
\begin{figure}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_6}
\end{minipage}
\caption{\label{fig:chi_hist}
The distribution of the $\chi^{2}$ test for a single template $h$, split
into 16 non-overlapping frequency bins. The plot shows the distribution
of the $\chi^{2}$ test calculated for every time sample in $128 s$ of
simulated Gaussian data (with no signal present). The observed
distribution of values shows (shown in grey) is an excellent match with the
expected $\chi^{2}$ distribution with sixty degrees of freedom (shown in
black). }
\end{figure}
An alternative approach to applying the $\chi^2$ test to a coherent search
was proposed in \cite{Pai:2000zt}. This approach involves calculating the
$\chi^2$ values for each of the active detectors and using these values
to veto glitches.
\section{Implementation and Performance of a Coherent Search}
\label{sec:s4data}
In the previous sections we have presented a method for detecting
gravitational waves from CBCs in a network of detectors. The coherent
\ac{SNR} described in \ref{sec:coh_matched_filter} is ideal for
distinguishing signals in Gaussian data and, in sections
\ref{sec:snr_cont_consistency} and \ref{sec:chi2tests}, we have
introduced a number of strategies for discriminating between signal and
noise in non-Gaussian, non-stationary data. Here, we describe an
implementation of the targeted, coherent search for gravitational waves
from \ac{CBC}. In addition, we demonstrate its efficacy by performing
test analyses of simulated data and real data taken from \ac{S4}.
\subsection{Implementation of a coherent triggered search for CBCs}
\label{sec:searchimplementation}
Here, we describe the main steps by which the algorithms described in
sections \ref{sec:coh_matched_filter}, \ref{sec:snr_cont_consistency}
and \ref{sec:chi2tests} have been implemented. The analysis is
available in the \ac{LIGO} Scientific Collaboration Applications Library
(LAL) suite \cite{lalsuite}, and makes use of a large number of tools
and methods previously implemented in that library.
\subsubsection{Analysis setup}
\label{sec:searchsetup}
A targeted, coincident search for gravitational waves from \ac{CBC}
associated to \ac{GRB}s has been implemented, and used in a search of
\ac{S5} and \ac{VSR1} data \cite{Abadie:2010uf}. The
coherent search pipeline uses many of the same definitions, and much of
the same architecture to determine the analysis details. Specifically,
``onsource'' time is [-5,+1) seconds around the reported time of the
GRB; this is when a gravitational wave signal would be expected
\cite{Shibata:2007zm,DavLevKing04}. The noise background is estimated using 1,944 seconds of
``offsource'' data split into 324 trials of 6 second length each. These
are used to calculated the significance of any event occuring in the
onsource. As in Ref.~\cite{Abadie:2010uf} we impose a 48s buffer zone
between the onsource and offsource regions. To obtain an accurate
estimate of the detectors' power spectra, we only analyse data from a
detector if it has taken at least 2190s of continuous data around the
time of the GRB. Modulo this restriction, the coherent analysis is
designed to make use of data from all detectors that were on at the time
of the GRB.
\subsubsection{Template bank generation}
\label{sec:templategeneration}
The problem of placing a template bank for a single detector has been
extensively studied \cite{Owen96, OwenSathyaprakash98, Bank06,
Cokelaer:2007kx}. However, less thought has been given to the problem
of placing an appropriate bank for a coherent analysis. Our current
method is to use a template bank generated for one of the detectors in
the network. In the results presented later, we have made use of a bank
generated with the initial \ac{LIGO} design spectrum, with a maximum
total mass of 40$M_{\odot}$ and a minimum component mass of
1$M_{\odot}$, these are the same values as used in \cite{Abadie:2010uf}.
This method enables us to demonstrate the efficiency of this coherent
search it is not the optimal solution. A simple improvement would
involve placing a template bank appropriate for the (maximally
sensitive) synthetic $+$ detector defined in equation (\ref{eq:psds}).
In many cases, a network is significantly more sensitive to one GW
polarization and, in these cases, this template bank would perform well.
\subsubsection{Coherent SNR and Null Streams}
\label{sec:cohsnrproduction}
The data are first read in and conditioned using the methods and
algorithms developed for the \ac{S4} search for post-merger ringdowns from
CBCs \cite{Abbott:2009km, Goggin:2008dz}. The data are downsampled to a
frequency of 4096Hz and split into overlapping 256 second segments for
analysis. The noise \ac{PSD}s are calculated using the same method as in
\cite{Abbott:2009km}.
Each template of the bank is filtered against the data from each
detector to generate the single detector filters
$(s^{X}|h^{X}_{0,\frac{\pi}{2}})$ and sensitivities $\sigma^X$. The
algorithms used are taken from the LAL FindChirp library
\cite{Allen:2005fk}, specifically those written to perform a search for
spinning waveforms \cite{Fazi:2009} using the physical template family
(PTF) waveforms \cite{PBCV04}.%
\footnote{This choice stems from the desire to extend this search to
incorporate a single spin. This is particularly appropriate for
\ac{NSBH} binaries where the spin of the \ac{NS} can be safely
neglected.}
The waveform templates are generated using the TaylorT4 post--Newtonian
approximant \cite{Damour:2000zb}. The single detector filter outputs are
shifted in time to account for the relative delays from the given
\ac{GRB} sky location. They are then combined to form the coherent and
the null \ac{SNR}s as described by (\ref{eq:coherent_xy}) and
(\ref{eq:null_overwhite}). A ``trigger'' is recorded at any time the
coherent \ac{SNR} is greater than 6, and no louder event occurred in
any template in the bank within $0.1$ seconds.
\subsubsection{Calculating the $\chi^{2}$ tests}
\label{sec:sbvproduction}
The analysis calculates signal based vetoes in the same manner that it
does the coherent \ac{SNR}: The necessary single detector filters are
constructed and then these are combined together to create the
$\chi^{2}$ tests as described in the earlier sections.
Calculating the ``standard'' $\chi^2$ test is computationally expensive.
Therefore this veto is only calculated for a segment if there is at
least one event within that segment with \ac{SNR} larger than the
threshold and with values of bank $\chi^2$, auto $\chi^2$ and null
\ac{SNR} that do not immediately lead to it being dismissed as a glitch.
\subsubsection{Simulated Signals}
\label{sec:softwareinjs}
The sensitivity of the analysis to gravitational wave signals from
\ac{CBC} is assessed by adding simulated signals to the data stream
before performing the search. The analysis uses the architecture from
\cite{Abbott:2009km} to perform these simulations. A simulation is
deemed to have been recovered by the analysis is there is an event
within $0.1$ seconds of the signal time; no attempt is made to guarantee
a good match between simulated and recovered parameters. While this
does mean that, in principle, signals may be found due to a nearby
glitch, the effect is minimal, particularly when considering detection
candidates which are louder than all background.
The results shown in the remainder of the section are based on a set of
simulated signals comprised of binary neutron stars (component masses
limited to be between 1 and 3 $M_{\odot}$) at appropriate distances to
be observable by the detector network. All of these binaries are
oriented face on to the detectors. These choices are motivated by the
fact that the current implementation is designed as a search for
gravitational waves associated with \ac{GRB}s.
\subsection{Analysis of simulated data}
\label{sec:gaussiannoise}
The analysis was first run on simulated data for the initial \ac{LIGO}
network (H1, H2, L1). Data were simulated to be Gaussian and
stationary, with no noise transients. Specifically, the coherent
analysis pipeline was run on 2190 sections of
Gaussian data as if a GRB had occurred in the middle of the data
stretch. This provides a benchmark with which to compare results when
running on real data.
\begin{figure}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_7}
\end{minipage}
\caption{\label{fig:S4gaussiansnr}
The distribution of \ac{SNR} triggers in the offsource region plotted
against time for an analysis of simulated Gaussian noise in the initial
\ac{LIGO} (H1, H2, L1) network. }
\end{figure}
Figure \ref{fig:S4gaussiansnr} shows all the triggers produced by the
pipeline in the off source time. The loudest event in the approximately
2000 seconds of off-source data has an \ac{SNR} of 7.24.
Ideally, the various signal consistency tests described previously will
reduce the amplitude of the loudest surviving event in real data to
something similar to this.
\subsection{Analysis of real data}
\label{sec:realdata}
\begin{figure}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_8}
\end{minipage}
\caption{\label{fig:S4snrtime}
The distribution of \ac{SNR} triggers in the offsource region plotted against
time for an analysis of a mock S4 GRB. The axes on the plot are chosen to be
identical to those for figure \ref{fig:S4gaussiansnr} to make the plots easier
to compare. The S4 data has a large number of non-Gaussian features. The
largest of these peaks extends to a coherent \ac{SNR} of 40, although
non-Gaussian structure is visible at \ac{SNR}s as low as 7.}
\end{figure}
A test analysis was performed on real data taken from \ac{S4}. We chose
an arbitrary block of 2190 seconds of data for which all three of the
\ac{LIGO} detectors were operating and ran the analysis as if a GRB had
occurred during this time. The simulated sky location of the GRB was
(184.623\textdegree,42.294\textdegree) in right ascension and
declination respectively. For this chosen time and sky location the
sensitivity of the H1 and L1 detectors were roughly equal and the H2
detector was half as sensitive as the other two.
\subsubsection*{Coherent SNR}
\label{sec:coh_snr}
Figure \ref{fig:S4snrtime} shows the coherent \ac{SNR} of triggers
produced during the analysis of the S4 data. It clearly demonstrates
that this data is not well characterized by Gaussian noise alone. A
number of loud transients are present in the data which show up as short
duration peaks of large \ac{SNR}. The loudest of these has an
\ac{SNR} of almost 40. If events were only ranked on \ac{SNR}, a signal
would have to be very loud to show against this non-Gaussian background.
In addition to the loud peaks there are also a large number of
quieter peaks that show up at all times in the data. If the search
is to begin to approach the efficiency of the Gaussian case then the
signal consistency tests must allow us to reject the quieter noise
transients, as well as the loud ones.
In the remainder of this subsection we demonstrate the performance of
the signal consistency tests introduced in sections
\ref{sec:snr_cont_consistency} and \ref{sec:chi2tests}. Finally, we
formulate a detection statistic, which arises as a combination of the
coherent \ac{SNR} and signal consistency tests, and demonstrate that
with it the majority of the non-Gaussian background can be removed.
\subsubsection*{Null SNR}
\label{sec:s4null}
\begin{figure}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_9}
\end{minipage}
\caption{\label{fig:S4null}
The distribution of the null \ac{SNR} plotted against coherent \ac{SNR}.
The solid line at null \ac{SNR} of 5.5 is the line above which
triggers are vetoed. The dashed line at 3.5 is the line above which
triggers are downweighted (see section \ref{sec:detstats4}). }
\end{figure}
Figure \ref{fig:S4null} shows the performance of the null stream for
both simulated signals and background noise. The ability of the null
\ac{SNR} to distinguish signal from noise is relatively poor in this
example. The mock GRB analysis uses data from the two Hanford detectors
and the detector at Livingston. Thus, the null stream is
derived from a combination of the H1 and H2 detectors; the Livingston
detector does not contribute. The loudest glitches during the time
of this analysis originated in L1, and therefore do not have significant
null \ac{SNR}. However, quieter glitches in the Hanford detectors at an
\ac{SNR} around 10 do produce a large null \ac{SNR}. Any trigger with a
null \ac{SNR} greater than 5 is eliminated from the analysis.
\subsubsection*{Single detector SNR}
\label{sec:S4snglsnrs}
\begin{figure}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_10a}
\end{minipage}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_10b}
\end{minipage}
\caption{\label{fig:S4h1l1snr}
The distribution of single detector \ac{SNR} for the more sensitive H1
and L1 detectors, plotted against coherent \ac{SNR}. The top figure
shows the H1 \ac{SNR}, the bottom figure shows the L1 \ac{SNR}. The
horizontal line indicates \ac{SNR}=4. Below this line triggers
will be vetoed. The inclined dark gray line indicates the expected
\ac{SNR} of these face on simulated signals.}
\end{figure}
The most straightforward, and most effective amplitude consistency test
we have found is the requirement of a single detector \ac{SNR} greater
than 4 in the two most sensitive detectors; In this analysis, the L1
and H1 detectors. Figure \ref{fig:S4h1l1snr} demonstrates that this is
a particularly effective strategy for removing noise glitches. Triggers
arising due to glitches in the L1 detector have large coherent \ac{SNR}
but a negligible contribution from H1 and are consequently discarded.
\subsubsection*{$\chi^2$ tests}
\label{sec:s4chi2}
\begin{figure}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_11}
\end{minipage}
\caption{\label{fig:S4bank_hist}
The distribution of the bank $\chi^{2}$ test for a single template $h$,
with a bank of size $10$. The plot shows the distribution of the bank
veto calculated for every time sample in $128 s$ of data. The observed
distribution is inconsistent with the expected result in Gaussian noise
(the black curve).}
\end{figure}
In section \ref{sec:chi2tests} we introduced three $\chi^2$ tests
designed to separate signals from noise glitches in the data. Figure
\ref{fig:S4bank_hist} shows the distribution of the bank $\chi^2$ for
every time sample for a single template. This is directly comparable to
Figure \ref{fig:bank_hist} which shows the same for Gaussian data. The
deviation from the predicted $\chi^{2}$ distribution is due to the
non-Gaussianity of the data.
\begin{figure}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_12a}
\end{minipage}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_12b}
\end{minipage}
\caption{\label{fig:S4bank_auto trig}
The distribution of bank and auto $\chi^{2}$ test plotted
against \ac{SNR}. The results for the off-source data triggers are
plotted in blue, with simulated signals in red.
The solid line shows the line of \textit{newSNR} = 6,
defined in section \ref{sec:detstats4}.
Triggers with \textit{newSNR} $ < 6$ are vetoed.}
\end{figure}
The distribution of bank and auto $\chi^{2}$ for both simulated signals
and noise triggers is shown in Figure \ref{fig:S4bank_auto trig}. Both
of these tests are effective at separating the simulated signals from
noise transients. In order to quantify this, we make use of the
\textit{newSNR} formalism that is being used in the latest
coincident searches for CBCs \cite{s6allsky,s6grb}. The idea is to
downweight the significance of noise triggers with large $\chi^{2}$
values relative to signals. This is achieved by introducing the ``\textit{newSNR}'':
\begin{equation}
\rho_{\mathrm{new}} = \left\{
\begin{array}{cl}
\displaystyle \rho, & \chi^2 \le n_{\mathrm{dof}} \\[0.1in]
\displaystyle \frac{\rho}{\left[\left(1 +
\frac{\chi^2}{n_{dof}}^{4/3}\right)/2\right]^{1/4}}, & \chi^2 >
n_{\mathrm{dof}}
\end{array}
\right.
\end{equation}
where $n_{\mathrm{dof}}$ is the number of degrees of freedom of the
$\chi^{2}$ test.
For a signal, the mean $\chi^{2}$ value is one per degree of freedom and
consequently the \textit{newSNR} will be similar to the SNR. Noise
transients with a large $\chi^{2}$ value are significantly downweighted.
The \textit{newSNR} is calculated using both the auto and bank $\chi^{2}$
values. Any trigger with \textit{either} an auto \textit{newSNR} or bank \textit{newSNR}
less than 6 is discarded. The curves on Figure \ref{fig:S4bank_auto
trig} show this \textit{newSNR} threshold for the two $\chi^{2}$ tests.
\begin{figure}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_13}
\end{minipage}
\caption{\label{fig:S4chisq}
The distribution of standard $\chi^{2}$ test plotted
against \ac{SNR}. The results for the off-source data triggers are
plotted in blue, with simulated signals in red. The dashed lines show
contours of \textit{newSNR}, defined in section
\ref{sec:detstats4}, the solid line shows the line of \textit{newSNR} = 6.
Triggers with \textit{newSNR} $< 6$ are vetoed.}
\end{figure}
Finally, we turn to the standard $\chi^{2}$ test. As this is rather
costly to compute, we only do so for triggers which have passed all of
the previously described thresholds (on coherent, null and single
detector \ac{SNR}, the bank and auto $\chi^{2}$). Figure
\ref{fig:S4chisq} shows the distribution of the standard $\chi^{2}$ test
for simulated signals and noise. The preceding tests have succeeded in
removing the vast majority of non-Gaussian triggers from the data. A
threshold of 6 on \textit{newSNR} serves to eliminate a few more. We have
found that the standard $\chi^{2}$ is the most effective at separating
signal from background so we also make use of it in the final ranking of
events. Figure \ref{fig:S4chisq}, shows contours of constant \textit{newSNR}
which will be used in the final ranking.
\subsubsection*{Detection statistic}
\label{sec:detstats4}
In the preceeding discussion, we have imposed a number of cuts on the
initial candidate events produced by the analysis pipeline. Let us
briefly recap those cuts:
\begin{itemize}
\item Generate a trigger at any time for which $\rho > 6$. Only keep
the loudest one in each 0.1 seconds.
\item Discard any triggers with $\rho_{N} > 5$.
\item Discard any triggers for which $\rho_{H1} < 4$ or $\rho_{L1} < 4$.
\item Discard any triggers for which $\rho_{new} < 6$ for the bank or
auto $\chi^{2}$.
\end{itemize}
Finally, we rank the remaining triggers based upon the \textit{newSNR}
calculated using the standard $\chi^{2}$ as well as the null SNR as:
\begin{itemize}
\item Rank remaining triggers using a detection statistic $\rho_{det}$
given by
\begin{equation}\label{eq:rho_det}
\rho_{\mathrm{det}} = \left\{
\begin{array}{ll}
\displaystyle \rho_{\mathrm{new}} , & \rho_{N} \le 3.5 \\[0.1in]
\displaystyle \frac{\rho_{\mathrm{new}}}{\rho_{\mathrm{Null}} - 2.5} ,
& 3.5 < \rho_{N} < 5.0
\end{array}
\right.
\end{equation}
\end{itemize}
The length of time a \ac{CBC} spends in the sensitive band of the
detector varies greatly with the mass, and it has been found that the
shorter, high mass templates are more susceptible to occuring with large
\ac{SNR} at the time of glitches \cite{abbott:122001}. Also, the
various signal consistency tests are less effective for these short
templates. Therefore, we follow Ref.~\cite{abbott:122001} and split
the template bank into three regions based on the chirp mass of the
template. The false alarm probability for a given trigger is based on a
comparison of the detection statistic to off source triggers \textit{in
the same mass bin}.
\subsubsection*{Performance of search}
\begin{figure}
\begin{minipage}[t]{0.95\linewidth}
\includegraphics[width=\linewidth]{Figure_14}
\end{minipage}
\caption{\label{fig:S4injrec}
Efficiency of recovery of simulated signals in real data. The
efficiency is shown for four different cases: i) signals found above an
\ac{SNR} of 7.24, the loudest background trigger in Gaussian noise
(black solid line); ii) signals found above an \ac{SNR} of 12.88, the
loudest background trigger in real noise (red dashed line); iii) signals
found with a value of the detection statistic (\ref{eq:rho_det}) above
7.41, the loudest background event; iv) signals found
louder than all background in an H1-L1 search (green dotted line).}
\end{figure}
The sensitivity of the analysis can be assessed by examining the
performance of recovering simulated signals. The signal population was
\ac{BNS} with optimal orientation originating from the location of the
fake GRB. For these purposes we will only consider an signal found
if its associated trigger is louder than the loudest event that occured
in the low mass bin during the offsource time --- this ensures that the
false alarm probability is less than one in 324 (the number of offsource
trials). At this level, a candidate event starts to be interesting but
realisitically a false alarm probability closer to $10^{-4}$ or
$10^{-5}$ would be required for a detection candidate.
Figure \ref{fig:S4injrec} shows the efficiency with which simulated
signals are recovered as a function of the distance. Recall that the
largest \ac{SNR} recorded in the analysis of simulated, Gaussian data
was $7.24$. We show the efficiency of the search at finding simulations
with an \ac{SNR} greater than this. If the data were Gaussian, or the
signal consistency tests were able to remove all non-Gaussianities, then
the real search would match this sensitivity. By using \textit{only}
\ac{SNR} to rank events, the sensitivity of the search is substantially
worse than in Gaussian data. Although the offsource contained events
with an \ac{SNR} up to 39, the loudest low mass trigger had a coherent
\ac{SNR} of 12.88. This is almost double the loudest Gaussian noise and
thus the sensitivity of the search is reduced by about a factor of two
--- illustrated by the 50\% efficiency moving down from 20 Mpc to 10
Mpc. The signal consistency tests --- null stream, $\chi^{2}$ tests and
single detector \ac{SNR} threshold --- are designed to bring the
sensitivity closer to the Gaussian case. The simulated signals are
considered found if they are recovered with a detection \ac{SNR} greater
than $7.41$ (the loudest off-source event) and all signal consistency
tests. The efficiency of the detection search is only about 10\% less
than it would be in Gaussian noise. The 10\% loss in
sensitivity can be attributed to having a slightly louder offsource
event ($7.41$ rather than $7.24$) and a \textit{small} loss of
efficiency due to the various signal consistency checks.
To illustrate the benefits of a coherent search, we would like to
compare the performance with a coincidence search. For the initial LIGO
network, signals close to detection threshold would be unlikely to have
passed any SNR threshold placed on the H2 detector. Specifically, for a
signal with a coherent \ac{SNR} of 7.5, the expected \ac{SNR} in H2
would be around 2.5 which is a prohibitively low threshold. Therefore
it is reasonable to compare the coherent search to a two detector, H1-L1
coincidence search. For a two detector search, the coherent and
coincident \ac{SNR}s are equal, and the null stream test is not
available. Consequently, the performance of two detector coherent and
concident searches should be comparable. Therefore, we present the
results of an H1-L1 detector coherent search to give an indication of
the performance of a coincidence search. The efficiency of this two
detector search is also shown in Figure \ref{fig:S4injrec}. The
sensitivity of the two detector search is about a factor of 10\% lower
than the three detector coherent search. For a network of three
approximately equally sensitive detectors, we would expect an even
greater sensitivity improvement from employing coherent techniques.
\section{Discussion}
We have presented a formulation of a targeted coherent search for
compact binary coalescences. For Gaussian noise, the
coherent \ac{SNR} would be ideal for separating signals from the noise
background. However, since data from gravitational wave interferometers
is neither Gaussian nor stationary, we have also discussed a number of
methods of separating the non-stationary noise background from the
signal population. These tests include various $\chi^{2}$ tests, which
were originally designed for use in single detectors. We have extended
them to the network analysis and demonstrated their continued efficacy.
Additionally, the coherent analysis allows for some additional tests
which are not readily available in the coincidence case. The most
significant of these is the null \ac{SNR} which can be used to reject
events which are not consistent with two gravitational wave
polarizations. Additionally, we explored consistency tests between the
recovered amplitudes of the gravitational wave and found that a simple
\ac{SNR} threshold on the two most sensitive detectors gave excellent
results.
The analysis described in this paper has been implemented and in the
final section we showed results of a test run. This made use of the
\ac{S4} data from the LIGO detectors. Although the data was far from
Gaussian, after the application of all of the signal consistency tests
the results were remarkably close to what would be expected in Gaussian
noise. This analysis is available to be used in searches for GW inspiral
signals associated with GRBs in more recent LIGO and Virgo data,
such as S6 and VSR2 and VSR3.
There are a number of ways in which this analysis could be enhanced to
broaden its use and increase its sensitivity. First, a number of
\ac{GRB}s, particularly those observed by Fermi \cite{fermiwebsite} and
IPN \cite{ipnwebsite} are not localized sufficiently accurately that the
error box can be treated as a point on the sky. Thus, it would be nice
to extend this analysis to allow for a region of the sky to be covered.
This would require looping over the relevant sky points; incorporating
the correct detector sensitivities $F_{+,\times}$ and time delays. In
principle, this would not greatly slow down the analysis as the majority
of time is taken in performing the single detector filters and these
would \textit{not} need to be re-calculated. As well as looking at a
patch on the sky, the analysis could be extended to cover the whole sky,
as appropriate for an un-triggered search. This brings in a host of new
complications which have been met and dealt with by other coherent
search methods \cite{1367-2630-12-5-053034, Klimenko:2008fu}. In order
to obtain a good estimate of the background for an all sky, un-triggered
search we would need to implement background estimation and time
shifting the data would likely be the best way to do this.
Since \ac{GRB}s are thought to be rather tightly beamed, it is
reasonable to take them as being face on, or close to. In this case,
the gravitational waves are circularly polarized and there is, in
effect, only a single polarization. This opens the possibility of
limiting the signal space to just this one polarization and adding an
extra ``null'' test. Alternatively, it should be possible to perform a
Bayesian marginalization over the astrophysically expected distributions
of the various parameters.
The progenitors of short \ac{GRB}s are thought to be \ac{BNS} or
\ac{NSBH}. The search we have described is ideal for the \ac{BNS} case
as the spins of the neutron stars are unlikely to have a significant
effect on the waveform. However, when one of the components of the
binary is a black hole, the spin could be large. Furthermore, the mass
ratio is likely to be relatively large. In this case, the spin of the
black hole can have a significant effect on the observed waveform
\cite{PBCV04}. Consequently, we would like to extend this search to
incorporate spin effects. The infrastructure described in this paper
can already accept spinning waveforms, but the implementation of signal
based vetoes proves somewhat more complex. Work is underway on this
\cite{HFspin}.
\section*{Acknowledgements}
The authors would like to thank Sukanta Bose, Duncan Brown, James Clark, Alex Dietz,
Tom Dent, Nick Fotopolous, Phil Hall, Ioannis Kamaretsos, Duncan Macleod, Laura Nuttall,
Valeriu Predoi, Patrick Sutton, Bangalore Sathyaprakash, John Veitch and Alan
Weinstein for useful discussion and helpful comments about this work.
In this work
IWH was supported by the Science and Technology Facilities Council, UK,
studentship ST/F005954/1, SF was supported by the Royal Society.
This paper has been given the internal \ac{LSC} document number
P1000104.
\\
\\
\\
\\
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 92 |
NOKIA Posts on XDA
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\section{Introduction}
A truly comprehensive understanding of magnetism at the nanoscale
is still lacking.
From a theoretical point of view the problem of magnetization
decay in nanosystems is difficult to treat:
nanoscopic systems are
too big to be solved by brute force calculation and too small
to be tackled by the tools of
statistical mechanics at the equilibrium.
Indeed, the problem of magnetization decay is a typical
example of out of equilibrium phenomenon, which is the decay out
of a metastable state.
On the other hand, nanomagnetism
has also important consequences
in the technology of memory and information processing devices.
The quest for improving magneto-storage density
calls for the realization of smaller and smaller magnetic units.
Significant improvements in experimental techniques
allowed investigations
of magnetic properties in nanoparticles and nanowires\cite{barbara}.
In particular, recently, there has been great interest in
Single Chain Magnets (SCM)~\cite{vindigni1,vindigni2,nowak1,gambardella,carbone},
which are possible candidates for nanoscopic memory units.
Nanoscopic systems can also
show ferromagnetic behavior at low but
finite temperature, even if a ferromagnetic phase transition is theoretically
forbidden~\cite{mermin}, due to large magnetic decay times.
The modelization of the magnetization decay, through an on--site
anisotropic barrier is quite typical in literature, even if,
mainly short-range
interactions have been considered.
Nevertheless, in many realistic situations,
one needs to go beyond nearest neighbor coupling,
taking into account the long range nature of the interaction
defined by a two--body spin interaction constant decaying at large
distance with a power law exponent $\alpha $ not
larger than the embedding
spatial dimension $d$\cite{libroruffo}.
It is the case, for instance, of the dipolar interaction
in 3--d systems,
or of the so--called
RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction,
which decays as $r^{-d}$, where
$r$ is the distance between spins, and $d$ is
the dimension of the lattice system.
In particular, the latter
might be responsible for the ferromagnetic behavior of
Diluted Magnetic Semiconductors (DMS) \cite{dms} and
Diluted Magnetic Oxides (DMO) \cite{coey}, promising
materials for the realization of spintronics devices.
One of the first attempts to understand magnetic
decay times in nanoparticles is due to Ne\'el\cite{neel}
and Brown \cite{brown}, who considered that all the spins in
a magnetic particle move coherently, so that they can be considered
as a single spin and described magnetization decay as
due to thermal activation over a single energy barrier.
In Brown's theory this time, $\tau$,
is shown to follow an Arrhenius Law :
\begin{equation}
\tau \propto e^{\beta \Delta E}
\label{al}
\end{equation}
where
$\beta = 1/ k_B T$ is the
inverse temperature and $\Delta E \propto V $ is the anisotropic energy
barrier proportional to the particle volume $V$ .
A step forward Brown's theory has been realized by Braun \cite{braun}.
In his theoretical approach
a sufficiently elongated system of short range interacting spins
with an on--site anisotropy barrier,
have been shown to reverse their magnetic moments (thus
producing an average magnetization decay) through
a process called nucleation, energetically convenient
with respect to coherent rotation.
In this mechanism, accomplished by the formation
of a soliton-antisoliton domain wall,
the magnetic anisotropic energy to be overcome
turns out to be proportional
to the {\it cross sectional area} of the particle,
$\Delta E \propto A$ and not to its volume $V$.
Studies of different mechanisms of magnetic
decay have been the objective of intense investigation\cite{nowak2}
until recently, where also 3--d spherical samples with short range interactions
and on--site anisotropy are shown
to produce nucleation for sufficiently large radius\cite{nowak3}.
Thus, for short range interaction, Brown's theory, and a consequent
Arrhenius Law with an exponent proportional to the volume $V$
of the particle is valid only for very small
particles, while in general, for large or elongated particles,
the exponent is given by the cross sectional area of the particle.
A smaller exponent means smaller decay
times for the same temperature.
The size and shape dependence of the magnetic anisotropy barrier,
and consequently of the decay times, have been also
confirmed experimentally in Ref.~\cite{bode}.
The consequences of long range interaction on magnetic decay
is much less investigated.
Long range interaction can affect the decay out of a metastable
state in a significant way; in the seminal paper \cite{griffiths}
it was shown that the decay time out of a metastable state
in a toy model with infinite range interaction
is given by the Arrhenius Law with an
exponent proportional to the squared volume of the particle.
The main goal of this paper is to analyze magnetic decay
beyond nearest-neighbor interaction, focusing on realistic
long range interacting systems.
In order to estimate the dependence of magnetic decay times on
temperature, we propose a different point of view,
which turns out to be independent of the decay mechanism and related
to the recently found Topological Non-connectivity Threshold (TNT)
in anisotropic spin systems~\cite{jsp,tntruffo}.
\section{Topological Non-Connectivity Threshold and Magnetization decay time}
In this Section, following Ref.~\cite{jsp}, we briefly review the Topological Non-Connectivity Threshold.
Let us consider
a generic anisotropic spin system, with an easy axis of magnetization,
(the direction $ \hat{n}_{easy}$ of the magnetization in the ground
state), with a microcanonical
energy $$H( \vec{S}_1,\ldots,\vec{S}_N)=E.$$
Let us also set
\begin{equation}
m = (1/N) \sum_k \vec{S}_k \cdot \hat{n}_{easy},
\label{m}
\end{equation}
as the magnetization along the easy axis. Note that in our paper
it will be $\hat{n}_{easy}=\hat{z} $.
It was proven~\cite{jsp} that below a suitable threshold, $E_{tnt}$, given by the minimal
energy attainable under the constraint
of zero magnetization $m$ along the easy axis:
\begin{equation}
E_{tnt}= {\rm Min } (H (...\vec{S}_i... )\
| \ m =0),
\label{Etnt}
\end{equation}
the constant energy surface is disconnected in two portions,
characterized by a different sign of the magnetization.
From the dynamical point of view one has a case of
ergodicity breaking: a trajectory
at fixed energy cannot change the sign of
magnetization since it is confined forever in one region of the
phase space.
It was also demonstrated that in case of long range
interaction among the spins\cite {musesti},
the disconnected energy portion
determined by the TNT, remains finite,
when the number of particles becomes infinite.
While for isolated systems, the magnetization cannot reverse its
sign if its microcanonical energy $E$ is below the energy
threshold $E_{tnt}$, when the system
is put in contact with a heat bath this may happen
for any (even extremely low) temperature. Question arise whether
the TNT dictates in some way the magnetization decay.
This is exactly what we have found (see Sections below), namely
$\Delta E_{tnt}=E_{tnt}-E_{min}$, represents an effective energy barrier
for magnetic decay and the decay time depends
exponentially on such energy barrier:
\begin{equation}
\tau = \tau_0 \ e^{\beta (E_{tnt}-E_{min}) } =
\tau_0 \ e^{\beta \Delta E_{tnt} },
\label{tau}
\end{equation}
where, $\tau_0$ is a factor, that may depend
on temperature too, $E_{min}$ is the ground state
energy and $\beta=1/k_BT$. While this was confirmed in
simple toy models with all-to-all interaction among the spins
\cite{spadafora}, here our aim is to generalize
these results to realistic spin systems.
It is possible to give a heuristic justification of Eq.~(\ref{tau}).
Magnetic decay occurs through fluctuations of the magnetization
around its equilibrium value.
The probability a magnetization fluctuation
is determined by the
free energy barrier, $\Delta F = \Delta E - k_B T \Delta S,$
through the Arrhenius factor, $e^{-\beta\Delta F}$.
Since the entropic barrier, $\Delta S$, is usually negligible
at low temperature,
the accessible spin configurations can be determined minimizing the
energy only.
In order to reverse its sign, the value of the magnetization has to
go, say, from a magnetization $m=1$ to $m=0$.
Since for $m=1$ the system is in its minimal
energy, it is clear that $\Delta E_{tnt}$ represents the minimal
energy barrier found by the system while reversing its magnetization.
\section{The Model : Isotropic $\alpha-$Ranged plus On--Site Interaction}
Let us now focus on spin systems with isotropic
long--range exchange interaction and on--site anisotropy,
described by the following Hamiltonian:
\begin{equation}
H = -J \sum_{i>j}
\frac{ \vec {S}_i \vec {S }_j}{r_{i,j}^{\alpha}} - D \sum_i (S^z_i)^2,
\label{isoD}
\end{equation}
where, $ \vec {S_i}$ are the spin vectors with unit length,
$\alpha$ determines the range of the interaction
among the spins, $J>0$ is the exchange coupling
and $D>0$ is the on--site energy anisotropy.
The minimal energy for this class of spin systems is attained
when all the spins are alligned along the $\hat{z}$ direction,
which thus defines the easy axis of the magnetization.
In the following we will mainly focus on the ``critical'' case $\alpha=d$,
since it is relevant for realistic applications (dipole interaction
in $3$-D and RKKY interactions);
here critical is referred
to the fact that interaction is defined as long--ranged for $\alpha<d$,
while it is short ranged for $\alpha>d$~\cite{libroruffo}.
Moreover, we choose Hamiltonian~(\ref{isoD})
for sake of generality since we would like to consider
not a single specific interaction, but a class of interactions
depending as some power of distance among spins.
For this class of systems,
the energy $E_{tnt}$, see Eq.~(\ref{Etnt}), can be computed numerically
using a minimizing constrained algorithm.
We can also estimate analytically $E_{tnt}$
for a generic range of the interaction $\alpha$.
To this purpose let us consider two configurations with
$m=0$:
\begin{itemize}
\item the first one with all
spins aligned perpendicular to the easy axis.
The energy difference of this configuration
from the one having minimal energy is $DN$,
which is the energy barrier due to the coherent rotation of all
spins;
\item
a configuration, labelled $\uparrow\downarrow$,
consisting ot two neighbors identical blocks with opposite magnetization
along the easy axis.
This configuration roughly corresponds
to what is called nucleation configuration in literature.
The energy difference of this configuration from the minimal energy
in the case $\alpha \leq d$, is given by~\cite{musesti}:
\begin{equation}
\label{tnt}
\Delta E_{\uparrow\downarrow} = J C_{\alpha, d} N^{2-\alpha/d},
\end{equation}
where $C_{\alpha, d}$ is a suitable constant, for instance,
$C_{1,1} \simeq 4 \ln 2 $.
\end{itemize}
Following similar reasoning as in Ref.~\cite{musesti},
it can be shown that the energy of these two configurations is a good
approximation of $E_{tnt}$, so that we can write
\begin{equation}
\Delta E_{tnt} \equiv E_{tnt} -E_{min} \approx {\rm Min} (DN, \Delta E_{\uparrow\downarrow}),
\label{ddee}
\end{equation}
Note that Eq.~(\ref{ddee}), valid whenever $DN$ is not close to
$\Delta E_{\uparrow \downarrow}$,
gives an estimation of the anisotropic energy barrier, which
can be used in Eq.~(\ref{tau}) to get magnetic decay times.
Eq.~(\ref{ddee}) has been confirmed numerically in Fig.~(\ref{tntfig}),
for the case $\alpha=d=1$, and we have found coherent rotation
for $D \ll D_{cr}= 4J \ln 2 $
and nucleation for $D \gg D_{cr}$, where the $D_{cr}$ has been obtained
comparing Eqs.~(\ref{tnt}) and (\ref{ddee})~\footnote{
Even if it not obvious, a priori, that for long range
interactions, the mechanism of magnetization decay can be
described by the process of nucleation and coherent rotation, we
assume them to be true and we verify, in the last Section,
that they really occurs in our case.}.
In this figure we compute numerically the energy barrier $\Delta E_{tnt}$
using a minimizing constrained algorithm (symbols) and we compare it with
the approximation
(\ref{ddee}) for one dimensional chains with
different number of spins.
As one can see, the agreement is fairly good.
\begin{figure}[!ht]
\vspace{0cm}
\includegraphics[width=8cm]{fig0.pdf}
\caption{Energy barrier as a function of the anisotropy
barrier $D$ for the $\alpha=d=1$.
Different symbols indicate different number of spins in the linear array,
as indicated in the legend.
Dashed lines indicate the approximation Eq.~(\ref{ddee}).
The vertical black line indicates $D=D_{cr}$, and
separates the region of coherent rotation (CR, left),
from the region of nucleation (NU, right).
}
\label{tntfig}
\end{figure}
Note that in case of nucleation
($DN > \Delta E_{\uparrow\downarrow}$),
the effective energy barrier $\Delta E_{tnt}$
to be put in the Arrhenius Law
should be increased by a term $D$, called single-spin
flip. This extra term should be added only for
continuous models,
as the modified Heisenberg model we are considering,
so that, $\tau_0 \propto e^{D \beta}$ \cite{vindigni2}.
This should be done since a single
spin can continuously change from $S=1$ to $S=-1$
only passing the state $S=0$.
While the two extreme states have the same magnetic
anisotropy (since it is proportional to $DS^2$) the intermediate state $S=0$
has a barrier higher by a factor $D$.
This additional spin-flip does not occur, for instance,
in the Ising--like models,
since there are no intermediate states between $S=1$ and $S=-1$.
In the following
we analyzed the magnetic decay time in the canonical ensemble, using
a modified Monte Carlo
simulation \cite{metropolis,nowak2}.
As initial condition we choose all spins aligned along the easy axis,
and from the exponential decay of the average magnetization,
$\langle m(t) \rangle \propto e^{- t/ \tau}$, we
computed the magnetic decay time, $\tau$.
\section{Enhanced Barrier}
In this Section, we show our numerical results for the magnetization
decay. They will clearly give evidence of the enhancement of
the magnetization decay time due to long range interaction.
\subsection{ One dimensional case }
Here we focus on the one dimensional critical case.
\begin{figure}[!ht]
\vspace{0cm}
\includegraphics[width=7cm]{fig1.pdf}
\caption{Magnetic decay times, $\tau$ {\it vs} the rescaled inverse
temperature, $\beta/\beta_{stat} $ for $\alpha=d=1$ and different numbers
of spins $N$ as indicated in the legend.
Upper panel is characterized by
coherent rotation with parameters $J=1$ and $D=0.05$ , while the lower by
nucleation with $J=1/16$ and $D=0.5$.
Different symbols refer
to numerical results,
while
full lines in are the theoretical predictions
$\exp (\beta \Delta E_{tnt} )$. Specifically for coherent
rotation, we have $\Delta E_{tnt}=DN$, while
for nucleation, we have
$\Delta E_{tnt}= \Delta E_{\uparrow\downarrow} +D$
(see text for explanations).
Vertical dashed lines refer to the inverse rescaled
statistical temperature $\beta=\beta_{stat}$ obtained by
a standard mean field approach.
}
\label{uno}
\end{figure}
Our results for the magnetic decay time, are collected in Fig.~\ref{uno},
where we consider the case $\alpha=d=1$: magnetic decay times
are shown in the upper panel
for coherent rotation ($D \ll D_{cr}$)
and in the lower panel for nucleation ($D \gg D_{cr}$).
Samples with different
number of particles experience different anisotropy energy barriers. As one
can see the numerical results indicated by symbols well agree with the
theoretical prediction given by Eq.~(\ref{ddee}), shown as full lines.
Our results for coherent rotation, Fig.~\ref{uno} (upper panel),
clearly indicates
that Brown's theory of coherent rotation with an anisotropy energy barrier
proportional to the particle volume ($V \propto N$ ) is still at work
even for long range interacting systems.
In Fig.~\ref{uno} (lower panel),
the case of nucleation is shown. Also in this case
the anisotropy energy barrier is proportional to the particle volume.
Let us remark that this behaviour is different
for short range interacting systems,
where in the one dimensional case, the anisotropic energy barrier is
independent from the size of the system~\cite{vindigni2,carbone}.
Note that for high temperature (small $\beta $ values)
symbols with different number of spins lye upon the same curve, that turns
out to be almost independent of $N$.
\subsection{Multidimensional case}
Our results can be extended to higher dimensions.
In particular we will show that for large enough particle,
the anisotropic energy barrier is always proportional
to the volume of the particle. Moreover we point out
that for finite sized systems, the anisotropic energy barrier can
grow even faster than the volume.
From Eqs~(\ref{tnt}) and~(\ref{ddee}), we have that
while for coherent rotation, the anisotropy energy is always proportional
to the volume of the particle, for nucleation the anisotropy energy
can grow even faster than the volume of the particle,
$\Delta E_{\uparrow\downarrow} \propto N^{2-\alpha/d}$.
Since the anisotropy energy barrier is determined by the smallest of the two barriers, it follows that
for sufficiently large particles the energy
barrier will always be proportional to the particle volume
since $V \propto N$.
In particular, this means that even in the case of 3--d elongated particles,
differently with what happens in the short range case,
the energy barrier {\it does not
depend on the cross sectional area but on the whole
particle volume.}
This theoretical prediction has been numerically confirmed in Fig.~\ref{fin},
where we study the case of nucleation in thin parallelepipeds
$L \times L \times \epsilon L $, in presence of a `` critical'' interaction $\alpha=d=3$.
We chose the aspect ratio $\epsilon = 10 $.
\begin{figure}[!ht]
\vspace{0cm}
\includegraphics[width=7cm]{com.pdf}
\caption{Energy barrier $\Delta E$ as a function
of the side $L$ of the parallelepiped, obtained
by an exponential fitting of the decay time {\it vs} the inverse temperature $\beta$.
Here is
$\alpha=3$,
$J=1/20$ and $D=0.5$ (nucleation).
}
\label{fin}
\end{figure}
The energy barrier $\Delta E$ extracted from the numerical fit of the
Arrhenius Law $\tau = \tau_0 \exp(\beta \Delta E)$
has been plot as a function of the side $L$
of the parallelepiped. For sake of comparison
the lines proportional to the cross section
($L^2$) and to the volume ($L^3$) has been
drawn. As one can see without any doubt the barrier grows as the volume.
\begin{figure}[!ht]
\vspace{0cm}
\includegraphics[width=7cm]{fig2.pdf}
\caption{Decay time $\tau$
{\it vs} the rescaled inverse temperature $\beta/\beta_{stat}$ for a
square lattice ($d=2$) with $\alpha=1$.
for $J=1$ and $D=0.025$ (upper panel, coherent rotation);
and for $J=1/40$ and
$D=1/2$ (lower panel, nucleation).
Symbols refer to numerical data, while full lines are the
analytical prediction Eq.~(\ref{ddee}).
Vertical dashed lines represent the rescaled inverse
statistical temperature $\beta/\beta_{stat}=1$.
Note that in case of coherent rotation (upper panel),
the anisotropy energy is proportional to $DN$, while in the case of nucleation
(lower panel), the anisotropy energy is proportional to $JN^{3/2}$.
Lattice dimensions have been indicated in the legend}
\label{fisoD}
\end{figure}
From Eqs~(\ref{tnt}) and~(\ref{ddee}), it also follows
that, when $\alpha < d$ the
anisotropy barrier can grow even faster than the volume of the particle.
This can happen up to a critical value of the particle volume, for which $DN=\Delta E_{\uparrow \downarrow}$.
Such an effect is a distinguished feature
of long--range interaction
and it is forbidden in the case of short range interactions.
To confirme such theoretical prediction let us consider a square lattice
($d=2$) characterized by an exchange interaction decaying as $1/r$ ($\alpha=1$).
Even in this case we can distinguish between the regime of coherent rotation
(large anisotropy barriers $D$) from that of nucleation
(small $D$ values).
The results of our simulation have been shown
in Fig.~\ref{fisoD}.
In the lower panel the theoretical predictions have been indicated
as full lines while symbols represents numerical results from
Montecarlo simulation. As one can see the agreement with the theory,
which predicts an energy barrier $\Delta E_{tnt} \propto J N^{3/2}$
is fairly good. For sake of comparison, the regime of coherent
rotation (Fig.~\ref{fisoD}, upper panel) is also shown, indicating that,
in this case,
the energy barrier is proportional to the volume of the particle, namely $\Delta E_{tnt} \propto D N$.
Another important point to be discussed is in which temperature range the Arrhenius Law
with the exponent given by Eq.~(\ref{ddee}) holds.
In the cases of coherent rotation and nucleation,
see also Ref.~{\cite{brown}}, we might expect that the Arrhenius Law
is valid only when $k_B T \ll \Delta E_{tnt}$.
Clearly this gives an upper bound for the
temperature for which Eq.~(\ref{tau})
is valid. Moreover it should be $T \ll T_{stat}$,
where the latter is the temperature at which the barrier at $m=0$
in the free energy vanishes (and it coincides with the
temperature at which a phase transition occurs in the thermodynamic
limit). It is very interesting that, computing
$T_{stat}= 1/k_B \beta_{stat}$ by means of
a standard mean field approach, one gets a very nice estimate
of the validity range of the Arrhenius Law (see dashed vertical lines in Figs.
\ref{uno} and \ref{fisoD}). Nevertheless we stress that this delicate point
needs further analysis to be clarified.
\section{Coherent Rotation and Nucleation}
\label{sec:Pm}
Let us notice that the use of the words coherent rotation
and nucleation, are not only ways to label two different mechanisms taken
from the short range models, but correspond to the spin dynamics.
To prove that we first consider in Fig.~\ref{last} two different situations
taken from the upper (coherent rotation) and the lower panel (nucleation)
of Fig.~\ref{fisoD}. In particular we consider one single Montecarlo trajectory
and we plot, in Fig.~\ref{last} the value of $M = |\frac{1}{N} \sum_{i=1}^N \vec{S}_i|$ and $m=\frac{1}{N} \sum_{i=1}^N S^z_i$,
as a function of the Metropolis time. It is clear that while in the case
of coherent rotation (upper panel of Fig.~\ref{last})
$M \approx 1 $ and $m$ change its sign,
for nucleation (lower panel of Fig.~\ref{last})
one has $M \simeq |m|$.
\begin{figure}[!ht]
\vspace{0cm}
\includegraphics[scale=0.5]{fig3.pdf}
\caption{Upper panel (coherent rotation) for a square lattice
$6 \times 6$, $\beta=5$.
Lower panel (nucleation) for a square lattice $8 \times 8$
and $\beta=4.5$. In both panels
the red curve refers to $M$, while the black one to $m$.
}
\label{last}
\end{figure}
As an interesting consequences of the coherent motion of the spins
during the magnetic reversal, we show here,
focusing on the one dimensional case, that one can
estimate the whole probability distribution of the
magnetization in the canonical ensemble, $P_T(m)$ at low temperature
and around $m=0$.
Note that the knowledge of the probability distribution of
the magnetization allows one to compute
the magnetic decay time:
\begin{equation}
\tau \propto e^{\beta\Delta F} = \frac{P_T(m_{max})}{P_T(m_{min})},
\label{ddf}
\end{equation}
where
$P_T(m_{max,min})$ stands for the maximum/minimum
value of the probability distribution.
Due to the coherent motion of all spins it is
possible to express the energy of the system as a function
of the total magnetization along the easy axis; from the
knowledge of $E(m)$ we can compute $P_T(m)$ since:
$$
P_T(m) \ dm= P_T(E) \ dE = e^{-E(m)/k_B T} \rho(E) \ dE
$$
where $\rho(E)$ is the density of states at fixed energy.
Using the fact that
$\rho(E) dE= \rho(m) dm$, where $\rho(m)$ is the density of
states at fixed magnetization,
we have:
\begin{equation}
P_T(m) \ dm = e^{-E(m)/k_B T}\ \rho(m) \ dm.
\label{pTm}
\end{equation}
Let us compute $E(m)$ for coherent rotation and nucleation.
When the decay of the magnetization occurs through
coherent rotation we have $\vec{S}_i \vec{S}_j=1$, and
$S_i^z= \langle S^z \rangle=m$
so that, from Eq.~(\ref{isoD}) we have:
\begin{equation}
E (m) = -J/2 \sum 1/r_{i,j}^{\alpha} -DNm^2.
\label{Ecr}
\end{equation}
Since all spins move coherently on a sphere,
the density of states at fixed magnetization along any axis is constant,
$\rho(m)= const.$ Moreover
the first term in the r.h.s. of Eq.~(\ref{Ecr})
is independent of $m$ and we have (for coherent rotations):
\begin{equation}
P_T(m) \propto e^{\beta DNm^2} .
\label{Pcr}
\end{equation}
We verified numerically that Eq.~(\ref{Pcr}) gives
an excellent approximation of the probability distribution of the
magnetization around $m=0$ in the
coherent rotation regime, see Fig.~\ref{unob} (upper panel).
In case of nucleation the possible configurations which the system can visit
can be obtained assuming that magnetic decay occurs
by first reversing one of the edge spins, then its nearest neighbor,
and then the spin immediately after until
all spins are reversed.
If we have $k$ spins on the left pointing upwards and $N-k$ spins
pointing downwards, we can write the energy of this configuration
as
\begin{equation}
\label{ebb}
E(k,N)= E_{min}(k) + E_{min}(N-k)+W(k,N-k),
\end{equation}
where $W(k,N-k)$ is the
interaction energy between the two neighbors
blocks of $k$ and $N-k$ spins and
\begin{equation}
\label{ebb1}
E_{min}(k)= -J/2 \sum^k_{i=1} \sum^k_{j \ne i} 1/r_{i,j}^{\alpha} -Dk,
\end{equation}
is the minimal energy for a system of $k$ spins.
The minimal energy of a system of $N$ spins can be easily obtained
from (\ref{ebb}) by changing the sign of $W(k,N-k)$,
\begin{equation}
E_{min}(N)=E_{min}(k) + E_{min}(N-k)-W(k,N-k).
\end{equation}
Taking into account that $m=(2k-N)/N$ is the magnetization of
a system composed
by $k$ spins along the easy axis and $N-k$ opposite to it,
one gets,
\begin{equation}
E(m) = 2E_{min}(N_+) +2E_{min}(N_-) - E_{min}(N),
\label{newen}
\end{equation}
where $N_{\pm}= N(1-m)/2$.
In this case it is more difficult
to estimate $\rho(m)$. Assuming, also in this case
$\rho(m)=const.$, from
the knowledge of $E(m)$ (Eq.~(\ref{newen})),
we obtain $P_T(m) \propto e^{-\beta E(m)} $
which agrees very well (apart close to $m= \pm 1$)
with numerical results in the nucleation regime,
see Fig.~\ref{unob} (lower panel).
\begin{figure}[!ht]
\vspace{0cm}
\includegraphics[width=7cm]{fig1b.pdf}
\caption{
Probability distribution of the magnetization $P_T(m)$ {\it vs}
the magnetization $m$ for $\alpha=d=1$, $N=20$ and
different temperatures $\beta=1/k_{B}T$.
Upper panel is for $J=1$ and $D=0.05$ (coherent rotation regime)
and
$\beta=6$ (upper red hystogram), $\beta=9$ (lower black hystogram).
The lower panel is
for $J=1/16$ and $D=0.5$ (nucleation)
and
$\beta=8$ (upper red hystogram), $\beta=11$
(lower black hystogram).
Hystograms represent
numerical data, while smooth curves analytical results.
}
\label{unob}
\end{figure}
The validity of Eq.~(\ref{tau}) and of our method
to approximate $P_T(m)$ at low temperature, have been
tested for a wide range of values of $\alpha$
(even for short range interactions) and
a detailed study will be reported elsewhere \cite{fausto}.
\section{Conclusions}
In conclusion we propose a general method to determine
the anisotropic energy barrier in spin systems.
The barrier, which determines magnetic decay times, can be computed
from the topological non-connectivity energy threshold in the corresponding
isolated systems. Our analysis shows that for long
range interaction two different regimes can be identifyied, coherent
rotation and nucleation.
In the first regime we have predicted and numerically confirmed
that magnetic decay time depends exponentially on the volume of the
particle.
Nevertheless, in the regime of nucleation, the magnetic barrier
depends on a suitable power of the volume, $V^{2-\alpha/d}$,
where $\alpha < d $ is the range of interaction and $d$
is the lattice dimension.
These facts have two remarkable consequences. The first one is that
magnetic decay times depend exponentially on the volume of the
particle and not on its cross sectional area, as happens
for short range interactions.
The second one is that, the fast growth of the magnetic barrier
with the volume, gives rise to the possibility
to observe long-lived metastable ferromagnetism in finite systems
at high temperature which
is ruled out for short range interaction.
\hspace{1.cm}
We acknowledge useful discussion with B. Goncalves, D.~Mukamel,
S.~Ruffo, R.~Trasarti-Battistoni and A.~Vindigni.
This work has been supported by Regione Lombardia and CILEA Consortium
through a Laboratory for Interdisciplinary Advanced Simulation (LISA)
Initiative (2010)
grant [link:http://lisa.cilea.it] ". Support by the grant D.2.2 2010
(Calcolo ad alte prestazioni) from Universit\'a Cattolica
is also acknowledged.
| {
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} | 3,794 |
Shops, Spas & Casino
ASIA'S NEW ENTERTAINMENT CAPTITAL
WELCOME TO THE STUDIO CITY MEDIA PORTAL
STUDIO CITY NEW YEAR'S EVE COUNTDOWN PARTY – THOUSANDS OF REVELERS CELEBRATE THE ARRIVAL OF 2016 AT TIMES SQUARE MACAU
Macau – January 1, 2016 – A huge crowd of over 1,000 revelers joined the free 'I ♥ New York Times Square NYE Countdown' at Studio City's Time Square Macau to take in a never-seen-before party atmosphere in Macau, and to cheer in the arrival of 2016!
From early evening, the dynamic, cinematically-themed Times Square Macau was transformed into a vibrant dance floor filled with jubilant partygoers and Studio City special hotel guests. Live music and dance performances featuring 6 mirror ball themed dancers and the stylish dancers from Studio City's own Pacha Nightclub had the house jumping all night and the atmosphere was electrified by amazing vocal performance of internationally acclaimed New York-born singer-songwriter Kelis, supported by pumping beats of UK DJ Nikki 'Beatnik'. Together they turned Times Square Macau into a huge dance floor with a stunning audio visual feast, with guests raising their glasses and enjoying New York style culinary treats while interacting with street performers who roamed about delighting children and adults alike.
Right on cue, as midnight approached, snow started falling on guests as New York City's iconic New Year Eve's celebration was brought to life when a 1.5-meter mirror ball began its travel down New York Boulevard before descending during the final countdown seconds of 2015 sung in with a surprise reappearance of Kelis to sing Auld Lang Syne with spectacular visual effects and virtual fireworks and 2,000 balloons raining down on guests to mark the start of a glamorous new year filled with hopes, challenges, changes and dreams.
Studio City – This is Entertainment.
For further information on Studio City, please visit: www.studiocity-macau.com, follow us on Sina Weibo at www.weibo.com/studiocity and like us on Facebook athttp://www.facebook.com/studiocitymacau
For our latest press releases, visuals and multimedia, please visit: www.studiocitymacaumedia.com
This press release contains forward-looking statements. These statements are made under the "safe harbor" provisions of the U.S. Private Securities Litigation Reform Act of 1995. The Company may also make written or oral forward-looking statements in its periodic reports to the U.S. Securities and Exchange Commission (the "SEC"), in its annual report to shareholders, in press releases and other written materials and in oral statements made by its officers, directors or employees to third parties. Statements that are not historical facts, including statements about the Company's beliefs and expectations, are forward-looking statements. Forward-looking statements involve inherent risks and uncertainties, and a number of factors could cause actual results to differ materially from those contained in any forward-looking statement. These factors include, but are not limited to, (i) growth of the gaming market and visitation in Macau and the Philippines, (ii) capital and credit market volatility, (iii) local and global economic conditions, (iv) our anticipated growth strategies, (v) gaming authority and other governmental approvals and regulations, and (vi) our future business development, results of operations and financial condition. In some cases, forward-looking statements can be identified by words or phrases such as "may", "will", "expect", "anticipate", "target", "aim", "estimate", "intend", "plan", "believe", "potential", "continue", "is/are likely to" or other similar expressions. Further information regarding these and other risks, uncertainties or factors is included in the Company's filings with the SEC. All information provided in this press release is as of the date of this press release, and the Company undertakes no duty to update such information, except as required under applicable law.
About Melco Crown Entertainment Limited
Melco Crown Entertainment, with its American depositary shares listed on the NASDAQ Global Select Market (NASDAQ: MPEL), is a developer, owner and operator of casino gaming and entertainment casino resort facilities in Asia. Melco Crown Entertainment currently operates Altira Macau (www.altiramacau.com), a casino hotel located at Taipa, Macau and City of Dreams (www.cityofdreamsmacau.com), an integrated urban casino resort located in Cotai, Macau. Melco Crown Entertainment's business also includes the Mocha Clubs (www.mochaclubs.com), which comprise the largest non-casino based operations of electronic gaming machines in Macau. The Company is also developing the planned Studio City (www.studiocity-macau.com), a cinematically-themed integrated entertainment, retail and gaming resort in Cotai, Macau. In the Philippines, Melco Crown (Philippines) Resorts Corporation's subsidiary, MCE Leisure (Philippines) Corporation, currently operates and manages City of Dreams Manila (www.cityofdreams.com.ph), a casino, hotel, retail and entertainment integrated resort in the Entertainment City complex in Manila. For more information about Melco Crown Entertainment, please visit www.melco-crown.com.
Melco Crown Entertainment has strong support from both of its major shareholders, Melco International Development Limited ("Melco") and Crown Resorts Limited ("Crown"). Melco is a listed company on the Stock Exchange and is substantially owned and led by Mr. Lawrence Ho, who is Co-Chairman, an Executive Director and the Chief Executive Officer of Melco Crown Entertainment. Crown is a top-50 company listed on the Australian Securities Exchange and led by Chairman Mr. James Packer, who is also Co-Chairman and a Non-executive Director of Melco Crown Entertainment.
About Studio City
Studio City, when it opens, is set to take Macau's entertainment destination proposition to unprecedented new levels, by providing a 'next generation' of outstanding entertainment-driven leisure destination experiences that will help the territory's evolution into a truly international tourism center.
The Hollywood-themed studio-concept resort is a thrilling new cinematic inspired entertainment and leisure destination and is designed to be the most diversified entertainment offering in Macau. Ideally located on Cotai, close to the Lotus Bridge immigration point connecting Hengqin Island and a future station-point for the Macau Light Rapid Transit, Studio City will deliver more world-class entertainment amenities than any integrated resort in the market.
Studio City's stunning Art Deco facade includes the "Golden Reel", the world's highest figure-8 Ferris wheel which straddles the resort's two-tower hotel at a height of some 130 meters. The integrated resort will provide the ultimate in sophisticated leisure entertainment, hotel, retail, dining and lifestyle experiences.
The resort's innovative entertainment offerings include "Studio City Event Center", a 5,000-seat multi-purpose entertainment center designed to host live concerts, theatrical and sporting events; and "Studio 8", a 300-seat live-audience TV broadcast studio for reality and game-show productions distributed in the Asia region. The entertainment experiences also include a magic theater "The House of Magic" and a Warner Bros. Batman-themed 4D flight simulation "Batman Dark Flight", a 40,000-square-foot family entertainment center "Warner Bros. Fun Zone" for kids filled with Warner Bros.' and DC Comics' franchise characters and play-rides, together with "Pacha Macau" which will bring Ibiza-style nightlife to Macau.
Studio City is destined to deliver an unparalleled leisure entertainment and hospitality experience, strengthening the depth and diversity of Macau's leisure, business and tourism proposition as a leading visitor destination in Asia.
For further information on Studio City visit: www.studiocity-macau.com and follow us on Sina Weibo at www.weibo.com/studiocity.
Melco Crown Entertainment
Ms. Natalie Leung
Manager, Public Relations
Email: natalieleung@melco-crown.com
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Assistant Manager, Public Relations
Email: emilymsng@melco-crown.com
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{"url":"https:\/\/bookdown.org\/content\/50286a34-7e39-4500-8dd2-62bf686c1710\/one-sample-inferential-statistics.html","text":"# 10 One Sample Inferential Statistics\n\nThe general question at hand with one-sample inferential tests, is that we wish to test the probability that our one sample of data comes from a population that has a true population mean $$\\mu$$ that is equal to, greater than, or less than, some specific value. We will look at two ways of doing this - firstly using a z-test and then using t-tests.\n\n## 10.1 One-sample z-tests\n\n### 10.1.1 Sampling Distribution Recap\n\nIn one-sample z-tests we are provided with the population mean $$\\mu$$ and standard deviation $$\\sigma$$. We then collect or are given one sample of data of size $$n$$. From this sample, we calculate the sample mean $$\\overline{x}$$. The question then becomes, how likely were we to get a sample mean as large or as small as the sample that we got?\n\nTo answer this, we need to think in terms of the sampling distribution of sample means. We need to recognize that our one observed sample mean $$\\overline{x}$$ is just one sample mean that we could have got from a sampling distribution of sample means.\n\nFor instance, look at the population below. This is a normally distributed population of IQ scores, with a population mean $$\\mu = 100$$ and a population standard deviation $$\\sigma = 15$$.\n\nLet\u2019s take a sample of size $$n=25$$ from this population, round the individual scores to 1dp, and get the mean of the sample:\n\nset.seed(1)\nsamp1 <- round(rnorm(n=25, mean=100, sd=15),1)\nsamp1\n## [1] 90.6 102.8 87.5 123.9 104.9 87.7 107.3 111.1 108.6 95.4 122.7 105.8\n## [13] 90.7 66.8 116.9 99.3 99.8 114.2 112.3 108.9 113.8 111.7 101.1 70.2\n## [25] 109.3\nmean(samp1)\n## [1] 102.532\n\nOur one observed sample has a sample mean of $$\\overline{x}=102.5$$\n\nIf we repeated this step and got a second sample of $$n=25$$, we could get another sample mean $$\\overline{x}$$:\n\nsamp2 <- round(rnorm(n=25, mean=100, sd=15),1)\nsamp2\n## [1] 99.2 97.7 77.9 92.8 106.3 120.4 98.5 105.8 99.2 79.3 93.8 94.1\n## [13] 99.1 116.5 111.4 97.5 96.2 110.5 108.3 89.7 89.4 105.5 111.5 98.3\n## [25] 113.2\nmean(samp2)\n## [1] 100.484\n\nThis time the sample mean is $$\\overline{x}=100.5$$.\n\nIf you remember back to section 7.2, if we were to repeat this process thousands and thousands of times, we would get a sampling distribution of sample means. We could visualize all of our sample means from many thousands of samples in a histogram, which shows the shape of the sampling distribution:\n\nBecause of Central Limit Theorem (see section 7.3) then this sampling distribution is normally distributed and it\u2019s mean $$\\mu_{\\overline{x}}$$ is equal to the population mean $$\\mu$$. Therefore $$\\mu_{\\overline{x}}=10.0$$. We also know the standard deviation of this sampling distribution, also known as the standard error as it can be calculated by: $$\\Large \\sigma_{\\overline{x}} = \\frac{\\sigma}{\\sqrt{n}}$$. Therefore, the sampling distribution standard deviation is $$\\sigma_{\\overline{x}}=3.0$$:\n\nsem <- 15 \/ sqrt(25)\nsem\n## [1] 3\n\nBecause this sampling distribution is normally distributed, we can determine how far away from the mean any sample mean is in terms of how many standard deviations from the mean they are. For instance, our first sample we got a mean of $$\\overline{x}=102.5$$. How many sampling distribution standard deviations is this from the mean of the sampling distribution? We can use an amended z-score formula (see section 7.1) to determine this:\n\n$$z = \\frac{\\overline{x} - \\mu_{\\overline{x}}}{\\sigma_{\\overline{x}}}$$\n\n(102.5 - 100.0) \/ 3\n## [1] 0.8333333\n\nSo, our sample mean of $$\\overline{x}=102.5$$ is 0.833 standard deviations above the mean. Because our sampling distribution is normally distributed, then we can visualize how far above the mean this value is on the standard normal curve as well as on the sampling distribution:\n\nIf we were asked what proportion of sample means were at least as big as 102.5, then we\u2019d be interested in knowing what proportion of sample means are to the right of the red lines above. We can calculate the area under a standard normal curve to the left of any z value in R using pnorm():\n\npnorm(0.833)\n## [1] 0.7975776\n\nTo find the proportion of the curve to the right of the red line (i.e.\u00a0the proportion of sample means that are greater than 102.5), we just subtract this value from 1.\n\n1 - pnorm(0.833)\n## [1] 0.2024224\n\nSo 20.2% of samples have a sample mean greater than 102.5. In this situation, our one sample mean was not therefore that unusual or surprising.\n\n### 10.1.2 Calculating p-values for z-test\n\nOne-tailed tests\n\nWe can calculate the proportion of sample means that are greater or less than any value. For instance, if we were interested in whether a new reading program in a school boosted the IQ of subjects. We might take a sample of 25 of these students and measure their IQ. If we got a sample mean of $$\\overline{x}= 105.7$$, we may wish to test whether this value is surprisingly large given that the population of IQ has a $$\\mu=100.0$$ and $$\\sigma=15.0$$.\n\nIf we were to formally write this in hypothesis terms, it would look like this:\n\n$$H_{0}: \\mu \\le 100.0$$\n$$H_{1}: \\mu > 100.0$$\n\nThis is saying that the alternative hypothesis $$H_{1}$$ is that our sample of 25 come from a population whose mean is greater than 100.0. The null hypothesis that we are testing is that they come from a population whose mean is equal to or less than 100.0.\n\nFor the test, we assume with the null hypothesis that our sample did indeed come from a population with $$\\mu=100.0$$ and $$\\sigma=15.0$$. We already calculated above that the sampling distribution of sample means for $$n=25$$ has a $$\\mu_{\\overline{x}}=100.0$$ and $$\\sigma_{\\overline{x}}=3.0$$. How unusual is our one observed sample mean of $$\\overline{x}=105.7$$? We need to calculate this in terms of z:\n\n$$\\Large z = \\frac{\\overline{x} - \\mu_{\\overline{x}}}{\\sigma_{\\overline{x}}}$$\n\n(105.7 - 100.0) \/ 3\n## [1] 1.9\n\nThis suggests that our observed sample mean is 1.9 sampling distribution standard deviations away from the mean of the sampling distribution. We next need to work out what proportion of sample means are greater than this. That is akin to the red shaded area below:\n\nWe can do this with pnorm():\n\n1 - pnorm(1.9)\n## [1] 0.02871656\n\nThis shows that only 2.9% of sample means are greater than our observed sample mean, given the population data of $$\\mu=100.0$$ and $$\\sigma=15.0$$. Therefore, our observed sample mean is quite surprising. We can write the likelihood of getting this sample mean as p = 0.029. Because we a priori had a prediction as to the direction of the mean in our sample (we predicted it to be higher than the population mean of 100.0), then we have in fact just done a one-tailed test. If we decide that any p-values that are below p=0.05 are \u2018significant\u2019, then we can say that our reading program in the school has a \u2018significant effect\u2019 on improving IQ scores.\n\nTwo-tailed tests\n\nWhat instead we had implement a reading program that was quite radical, and we were not sure whether it would be successful or not. We were interested in seeing whether it could increase or decrease IQ? In this situation, we do not have a direction of prediction, and we set up our hypotheses slightly differently:\n\n$$H_{0}: \\mu = 100.0$$\n$$H_{1}: \\mu \\ne 100.0$$\n\nHere, we are interested in whether our observed sample mean of $$\\mu=105.7$$ could have come from a sampling distribution with a population mean of $_{=100.0} or not. The initial steps are the same. We calculate how unusual our observed sample mean was in terms of standard deviations away from the mean of the sampling distribution: (105.7 - 100.0) \/ 3 ## [1] 1.9 It\u2019s still 1.9 standard deviations away. What we have to now thing about, is that because we did not predict the direction of the difference, we have to double our p-value. This is to account for the fact that in terms of \u2018surprising\u2019 results, we are interested in results that are more extreme than 1.9 standard deviations either side of the mean - i.e. the sum of the shaded area below: Therefore, our p-value for this test is: 2 * (1 - pnorm(1.9)) ## [1] 0.05743312 Which is p=0.057. This would suggest that our reading program did not sufficiently shift the population IQ scores in our school away from 100.0, as our p-value is greater than 0.05. But is this really true? It is important to consider two things here. One, it is important what initial hypothesis that you set up. If you have a strong a priori belief in the directionality of the hypothesis, then you are justified in doing a one-tailed z-test and using that p-value from that. Secondly, the difference between p=0.029 and p=0.057 in this case isn\u2019t that great. We shouldn\u2019t be overly focused on the cut-off value of p=0.05 as the criteria as to whether our results are significant or not significant. We should see the bigger picture, that our p-value is just one piece of information as to how different our sample of data is from the population that we believe it came from. ### 10.1.3 Using critical values In the preceding section, we ran one-tailed and two-tailed z-tests and calculated exact p-values. It is reasonably straightforward to do this in R. There is no reason not to use that approach. We prefer it. However, most often in introductory textbooks, a different approach is used. In this approach, the step of calculating the p-value is missed out. Instead, you are asked to just determine whether your observed z-value is more extreme than you\u2019d expect by chance. \u201cBy chance\u201d in this context means, that your observed z-value is less than 5% likely to occur. One-tailed z-test The population mean for SAT scores is $$\\mu=500$$ with a population standard deviation $$\\sigma=100$$. A tutoring company says that they improve SAT scores. A random sample of 12 students who took the tutoring program had a sample mean of $$\\overline(x)=551$$. Let\u2019s test whether this sample mean came from the population. $$H_{0}: \\mu \\le 500.0$$ $$H_{1}: \\mu > 500.0$$ Next, we calculate the mean and standard deviation of the sampling distribution for a sample size $$n=12$$. For the test, we assume that the sampling distribution mean $$\\mu_{\\overline{x}}=500.0$$ - i.e. is the same as the population mean. The standard deviation of the sampling distribution $$\\sigma_{\\overline{x}} = 28.87$$: 100 \/ sqrt(12) ## [1] 28.86751 Next, we work out how many sampling distribution standard deviations from the sampling distribution mean is our observed sample: (551 - 500) \/ 28.86751 ## [1] 1.766692 This shows that our observed sample mean of $$\\overline{x}=551$$ is 1.77 standard deviations above the mean of the sampling distribution. We could convert this to a p-value and calculate precisely how many sample means are larger than this in the sampling distribution. Instead, we\u2019ll take a different approach: Because this sampling distribution is approximately normal, we can determine how many standard deviations above the mean you\u2019d have to be to be larger than 95% of all samples. It turns out that $$z=1.645$$ is the value of $$z$$ that leaves 5% in the right hand tail. Therefore, any value of $$z$$ greater than $$z=1.645$$ will be \u2018unusually\u2019 large and have a p-value of less than 0.05. If we were dealing with sample means that were surprisingly small (so a one-tailed test where we are predicting that the sample mean comes from a population with a mean that is smaller than the population mean), then we are looking for $$z$$ values that are lower than $$z=-1.645$$. We can work out where these \u2018critical values\u2019 are in R using the qnorm() function: qnorm(0.95) # leaves 5% in right of tail ## [1] 1.644854 qnorm(0.05) # leaves 5% in left of tail ## [1] -1.644854 If we get back to our observed $$z$$ value of $$z=1.77$$, we can overlay this over the graph above like this: As you can see, our observed $$z$$ value is more extreme than the \u2018critical value\u2019 of $$z=1.645$$. We say that our observed value is therefore in the \u2018region of rejection\u2019 and we can therefore reject the null hypothesis with a p-value of $$p<0.05$$ and accept the alternate hypothesis that our sample comes from a population with a population mean that is greater than 500. In other words, the tutoring program appears to have a population mean of SAT scores greater than 500. Two-tailed z-test With the one-tailed z-test, we see that our critical values of z are $$z=1.645$$ for situations in which we are testing whether our sample mean is unexpectedly large, or $$z=-1.645$$ for situations in which we are testing that our sample mean is unexpectedly small. In a two-tailed situation, we are testing whether our sample mean is unexpectedly large or small. Because we still want only 5% of sample means to be in this \u2018unexpectedly\u2019 large or small category, this time we need a value of $$z$$ that leaves a total of 5% in the ends of both tails of the normal distribution. This is the same as leaving 2.5% in each tail: qnorm(.975) # leaves 2.5% in right tail ## [1] 1.959964 qnorm(.025) # leaves 2.5% in left tail ## [1] -1.959964 Let\u2019s illustrate this a bit further with the following example. Say we have a bakery that makes cupcakes. The population mean weight of cupcakes is $$\\mu=6.5$$ ounces, with a standard deviation of $$\\sigma=0.15$$ ounces. A customer wants to test if a new cupcake variety is heavier or lighter than 6.5 ounces. They purchase a random sample of 10 cupcakes and find that the sample mean is $$\\overline(x)=6.42$$ ounces. If we were to conduct a two-tailed test, to test if the population mean that our sample come from is equal to 6.5 ounces or not, then our hypotheses would be: $$H_{0}: \\mu = 6.5$$ $$H_{1}: \\mu \\ne 6.5$$ We need to calculate the z-score for our sample mean, to determine how many standard deviations of the sampling distribution it is away from the mean. sem <- 0.15 \/ sqrt(10) #standard deviation of the sampling distribution z <- (6.42 - 6.5) \/ sem # how many SD away from the mean is our sample z ## [1] -1.686548 We can overlay this observed value of $$z$$ onto our standard normal curve like this: Our value of $$z=-1.69$$ is therefore not inside either of the regions of rejection. This means that we do not have sufficient evidence to reject the null hypothesis that our sample comes from a population with mean of equal to 6.5. ## 10.2 One-sample t-tests As with confidence intervals based on the $$z$$-distribution (the standard normal curve), the major issue with z-tests is that they require you to know the population mean $$\\sigma$$ to perform the calculations. This is almost never the case - with exceptions like standardized tests including IQ and SAT that are designed to have specific means and standard deviations. If you wish to test whether your observed sample mean is likely or not to come from a population with a given mean, what approach should you take when you do not know $$\\sigma$$? As with confidence intervals, the approach we take is to use the $$t$$-distribution. In this situation, because we don\u2019t know our population standard deviation $$\\sigma$$, we have to estimate it using the sample standard deviation $$s$$. Further, because our sampling distribution may not be precisely normal given this estimation, we say that it comes from a $$t$$-distribution. $$t$$-distributions have slightly heavier tails than the normal distribution. One-tailed t-test example Let\u2019s illustrate the steps we take in a one-sample t-test with an example. These steps are identical to the two-tailed t-test up until we calculate the p-value. The population mean number of words spoken by two year olds by their 2nd birthday is $$\\mu=50$$ words and this is normally distributed. We don\u2019t know the population standard deviation $$\\sigma$$. A researcher wanted to investigate if reading to children increases their word knowledge. They collected data from 12 children ($$n=12$$) who were read to for at least two hours every day. These are the number of words spoken by the 12 children: x <- c(45, 53, 71, 35, 51, 59, 49, 55, 78, 27, 66, 59) x ## [1] 45 53 71 35 51 59 49 55 78 27 66 59 mean(x) ## [1] 54 Our one observed sample mean $$\\overline{x}=54$$. This is higher than 50, but is it meaningfully higher? If we were to formalize our hypothesis for this test, we would write: $$H_{0}: \\mu \\le 50.0$$ $$H_{1}: \\mu > 50.0$$ We are testing whether our sample was likely to have come from a population with mean 50 or less (null hypothesis), or if it was more likely to come from a population with a mean of greater than 50. The first step is to think about the sampling distribution. We need to recognize that our one observed sample mean is just one sample mean that we theoretically could have got from a sample distribution. Under the null hypothesis, we are going to assume that the mean of our sampling distribution $$\\mu_{\\overline{x}}$$ is equivalent to the population mean $$\\mu$$. Therefore, $$\\mu_{\\overline{x}}=50.0$$ Next, we need to calculate the standard deviation of the sampling distribution of sample means for n=12 (i.e. the standard error). As we do not know the population standard deviation $$\\sigma$$, we estimate this by using the following formula: $$\\Large \\sigma_{\\overline{x}} = \\frac{s}{\\sqrt{n}}$$ Therefore, our estimate of the standard error is $$\\sigma_{\\overline{x}}=4.14$$: sem <- sd(x) \/ sqrt(12) sem ## [1] 4.143268 Now that we know both the mean and standard deviation of the t-shaped sampling distribution, next we need to calculate how many standard deviations from this mean is our one observed sample mean. We calculate that using the formula that is similar to the $$z$$ formula: $$\\Large t = \\frac{\\overline{x} - \\mu_{\\overline{x}}}{\\sigma_{\\overline{x}}}$$ Our sample mean of $$\\overline{x}=54$$ has a $$t$$ value of $$t = 0.965$$: (54-50) \/ sem ## [1] 0.9654216 This means that it is approximately 0.965 standard deviations higher than the mean. We can calculate the proportion of sample means in the sampling distribution that are higher than our one observed sample mean by calculating the area under the curve to the right of our $$t$$-value. Remember, that our sampling distribution is $$t$$-shaped and has 11 degrees of freedom. The degrees of freedom are $$df = n-1$$ for a one-sample t-test. To determine what proportion of the curve lies to the right of $$t=0.965$$ we can use pt() which calculates the proportion to the left of the given value. pt(0.965, df=11) ## [1] 0.8223595 So, this tells us that for a $$t$$-distribution with 11 degrees of freedom, that 82.2% of values are to the left (lower than) of this value. That means that 17.8% of values are to the right, or 17.8% of sample means that could be drawn from the sampling distribution with a mean of 54 and standard deviation of 4.14 will be higher than our observed sample mean. 1 - pt(0.965, df=11) ## [1] 0.1776405 We can also get this value by setting lower.tail = FALSE: pt(0.965, df=11, lower.tail = FALSE) ## [1] 0.1776405 Because we made a prediction as to the direction of the hypothesis - i.e. we predicted that reading to children would increase the population mean, we are effectively running a one-tailed test. Our p-value is simply $$p=0.177$$. As we use an alpha level of 0.05 (a p-value of 0.05 as our critical value), this suggests that we do not have sufficient evidence to suggest that our sample of 12 children have a mean value that comes from a population with a mean that is greater than 50. We do not reject our null hypothesis. Two-tailed t-test example There are 20 psychology students in Dr. Zeppo\u2019s class. Here are their scores on a test, as well as their sample mean $$\\overline{x}$$ and sample standard deviation $$s$$: zeppo <- c(50,60,60,64,66,66,67,69,70,74,76,76,77,79,79,79,81,82,82,89) zeppo ## [1] 50 60 60 64 66 66 67 69 70 74 76 76 77 79 79 79 81 82 82 89 length(zeppo) # 20 - there are 20 students in the sample. ## [1] 20 mean(zeppo) # the mean of the sample is 72.3 ## [1] 72.3 sd(zeppo) # the sample SD is 9.52 ## [1] 9.520615 Historically, students in this class get a score of 65 points on this test - that is the population mean $$\\mu$$. Dr Zeppo wishes to test if this one sample (one class) has a mean (technically \u2018comes from a population with a mean\u2019) that is different to 65. We would write out this hypothesis like this: $$H_{0}: \\mu = 65.0$$ $$H_{1}: \\mu \\ne 65.0$$ As with all of these tests, our first job is to recognize that our one sample mean is just one sample mean that we \u2018theoretically\u2019 could have got from lots of samples of size $$n=20$$. All of those sample means together are referred to as the sampling distribution of sample means. Under the null hypothesis, we assume that the mean of the sampling distribution of sample means $$\\mu_{\\overline{x}}=65$$, i.e. it is equivalent to the population mean $$\\mu$$. Next, we have to estimate the standard deviation of the sampling distribution of sample means, i.e. the standard error $$\\sigma_{\\overline{x}}$$. We do this using the same formula as before: $$\\large \\sigma_{\\overline{x}} = \\frac{s}{\\sqrt{n}}$$ So, our standard error is $$\\sigma_{\\overline{x}} = 2.13$$: sem <- sd(zeppo) \/ sqrt(20) sem ## [1] 2.128874 Following this, we need to calculate how expected or unexpected our one sample mean $$\\overline{x}$$ was. We do this by calculating it in terms of how many sampling distribution standard deviations is it away from the sampling distribution mean. We use the formula: $$\\Large t = \\frac{\\overline{x} - \\mu_{\\overline{x}}}{\\sigma_{\\overline{x}}}$$ (mean(zeppo) - 65) \/ sem ## [1] 3.429042 Our observed sample mean of $$\\overline{x} = 72.3$$ is 3.43 sampling distribution standard deviations from the sampling distribution mean. We can picture this as follows: To calculate our p-value for our 2-tailed t-test, we need to calculate not just the area underneath the curve with values of $$t$$ greater than our observed $$t=3.43$$, but also the values under the curve with $$t$$ values that are more negative than $$t=-3.43$$. This is because in a 2-tailed test, we need to test for the probability of getting a $$t$$-value as large in both directions. Our p-value can be calculated using pt(): pt(3.43, df = 19, lower.tail = F) + pt(-3.43, df = 19) ## [1] 0.002807258 Or alternatively, we could just multiply those values greater than $$t=3.43$$ by 2: pt(3.43, df = 19, lower.tail = F) * 2 ## [1] 0.002807258 Either way, we can see that our p-values is $$p = 0.003$$, which tells us that our observed mean of $$\\overline{x}=72.3$$ is quite unlikely to have come from a distribution with a population mean $$\\mu=65$$. This leads us to rejecting our null hypothesis and accepting the alternative, that these psychology students come from a population with a mean that is greater than 65. ### 10.2.1 Critical values for the one-sample t-test As with the z-test (see section ??, instead of calculating the p-values for our observed values of $$t$$, you can simply test whether your value of $$t$$ exceeds (in either the positive or negative direction) some \u2018critical value\u2019 of $$t$$. Again, this approach was more often taken when it wasn\u2019t as easy to run computers to do these tests, so it seems a bit obsolete to do it this way. We recommend just doing it the way outlined above. Nevertheless, just for completeness, here is how to calculate these critical values of $$t$$. We\u2019ll use data from a different dataset. Here, we have the times taken to complete a crossword puzzle. We have a sample of $$n=10$$ subjects. library(tidyverse) xt <- read_csv(\"data\/crosstimes.csv\") xt$time3\n## [1] 15.04036 15.38213 15.70967 14.71215 12.18972 19.90511 20.00015 12.45357\n## [9] 12.86255 12.82682\n\nLet\u2019s say we wish to test whether this sample comes from a population with a mean of less than 16.0. We would be doing a one-tailed test and our hypotheses would look like this:\n\n$$H_{0}: \\mu \\ge 16.0$$\n$$H_{1}: \\mu < 16.0$$\n\nWhen using critical values, all the steps up to completing the observed $$t$$-value are the same as before. So, we assume that our one sample mean $$\\overline{x}$$ comes from a sampling distribution of sample means that has a mean equivalent to the population mean of 16. The standard deviation of this sampling distribution is:\n\nsem <- sd(xt$time3) \/ sqrt(10) sem ## [1] 0.9027857 Next, we calculate our observed $$t$$ which is a measure of how many sampling deviation standard deviations our observed sample mean is away from the mean of the sampling distribution: (mean(xt$time3) - 16) \/ sem\n## [1] -0.9878071\n\nOur observed $$t$$ values is $$t = -0.99$$.\n\nAs we are conducting a one-tailed t-test, we need to think in terms of what value of $$t$$ leaves 5% in the tail for a t-distribution with 9 degrees of freedom. This is visualized below:\n\nIf our observed sample mean with a $$t$$-value of -0.99 was unexpectedly small, then it would need to be in the region of rejection (red shaded area). This would mean that it was in the bottom 5% of sample means from such a distribution. The value of $$t$$ that is the boundary of the the lower 5% can be calculated using the qt() function like this:\n\nqt(0.05, df=9)\n## [1] -1.833113\n\nTwo-tailed tests\n\nFor this example, let\u2019s use the penguins data. Say we are interested in the flipper length of male Adelie penguins on Biscoe island (a bit specific, but let\u2019s go with it), and wanted to know if their mean length was different from $$\\mu = 188$$. Our hypotheses would be:\n\n$$H_{0}: \\mu = 188.0$$\n$$H_{1}: \\mu \\ne 188.0$$\n\nFrom our data, we can calculate our $$n$$ and sample mean $$\\overline{x}$$:\n\n### Read in the Data Penguins\n\n# just look at the females.\nadelie <- penguins %>% filter(species == \"Adelie\", sex == \"MALE\", island == \"Biscoe\")\n\nnrow(adelie)\n## [1] 22\nmean(adelie$flipper_length_mm) ## [1] 190.4091 We can also represent these data as a boxplot: ggplot(adelie, aes(x = 0, y = flipper_length_mm)) + geom_boxplot() + geom_jitter(width = .1, size=2)+ theme(axis.title.y=element_blank(), axis.text.y=element_blank(), axis.ticks.y=element_blank()) + coord_flip() + geom_hline(yintercept = 187, color=\"red\") Our sample of penguins has a sample size of $$n=22$$, with a sample mean of $$\\overline{x}=190.4$$. Let\u2019s calculate our observed value of $$t$$ for this sample: sem <- sd(adelie$flipper_length_mm) \/ sqrt(22)\n\ntobs <- (mean(adelie$flipper_length_mm) - 188) \/ sem tobs ## [1] 1.748218 This means that our observed sample mean is 1.75 sample standard deviations above the sampling distribution mean. In terms of critical regions, for a 2-tailed test, we need to know the values of $$t$$ that leave 2.5% in each tail for a $$t$$-distribution with 21 degrees of freedom. qt(.975, df = 21) ## [1] 2.079614 qt(.025, df = 21) ## [1] -2.079614 For a $$t$$-distribution with 21 degrees of freedom, the top 2.5% of t-values are greater than $$t=2.08$$, whilst the lowest 2.5% of t-values are below $$t=-2.08$$. Therefore, for us to reject the null hypothesis, our observed t-value needs to be higher than 2.08 or lower than -2.08. That would leave it in the region of rejection (red shaded areas above). Our observed t-value is $$t=1.75$$ which is not in these areas, so we cannot reject the null hypothesis. We do not have sufficient evidence to suggest that our penguins come from a population with a mean of $$\\mu = 188$$. ## 10.3 Conducting one-sample t-tests in R Conducting one-sample t-tests in R is very straightforward. First, let\u2019s consider the sample of 12 two-year olds and their word scores. x <- c(45, 53, 71, 35, 51, 59, 49, 55, 78, 27, 66, 59) mean(x) ## [1] 54 To test whether this sample mean is likely to have come from a population with a mean greater than 50, we use t.test() in the following way: t.test(x, mu = 50, alternative = \"greater\") # one-tailed test ## ## One Sample t-test ## ## data: x ## t = 0.96542, df = 11, p-value = 0.1775 ## alternative hypothesis: true mean is greater than 50 ## 95 percent confidence interval: ## 46.55917 Inf ## sample estimates: ## mean of x ## 54 mu specifies the mean that we are testing against. alternative = \"greater\" states that it is a one-tailed test, where we are testing the prediction that the population mean is greater than 50. The output gives us the same observed t-value that we calculated by hand $$t=0.97$$, the degrees of freedom and the p-value. To conduct a two-tailed test, where we just make the prediction that the population mean that the sample came from is not equal to some value, we just drop the alternative argument. For instance, we can test whether the zeppo data come from a population with a mean equal to 65: t.test(zeppo, mu = 65) # two tailed test ## ## One Sample t-test ## ## data: zeppo ## t = 3.429, df = 19, p-value = 0.002813 ## alternative hypothesis: true mean is not equal to 65 ## 95 percent confidence interval: ## 67.84422 76.75578 ## sample estimates: ## mean of x ## 72.3 Again, we see the same t-value, degrees of freedom and p-value as we calculated by hand. Also with a two-tailed t-test we get the 95% confidence interval of the true population mean (see section @ref(calculating -a-t-distribution-confidence-interval). Finally, if we wished to do a one-tailed t-test where we were testing whether the sample came from a population with a population mean of less than some value, we would use alternative = \"less\". For example, to test if the sample of puzzle competitors came from a population that completed their puzzles in less than 16 minutes: t.test(xt$time3, mu = 16, alternative = \"less\")\n##\n## One Sample t-test\n##\n## data: xt$time3 ## t = -0.98781, df = 9, p-value = 0.1745 ## alternative hypothesis: true mean is less than 16 ## 95 percent confidence interval: ## -Inf 16.76313 ## sample estimates: ## mean of x ## 15.10822 ## 10.4 Assumptions of the one-sample t-test The main assumptions of the one-sample t-test are that the observations should be independent of each other, and the values should be approximately normally distributed. We can more formally test if our data come from a population that is approximately normally distributed using a Shapiro-Wilk test. This test essentially examines the distribution of our data, and determines the probability that it came from a normal distribution. We can perform this test in R using shapiro.test(). shapiro.test(x) ## ## Shapiro-Wilk normality test ## ## data: x ## W = 0.98341, p-value = 0.9938 shapiro.test(zeppo) ## ## Shapiro-Wilk normality test ## ## data: zeppo ## W = 0.96205, p-value = 0.5856 shapiro.test(xt$time3)\n##\n## Shapiro-Wilk normality test\n##\n## data: xt$time3 ## W = 0.84497, p-value = 0.0506 shapiro.test(adelie$flipper_length_mm)\n##\n## Shapiro-Wilk normality test\n##\n## data: adelie$flipper_length_mm ## W = 0.96541, p-value = 0.6056 As you can see, all four of the datasets that we have performed one-sample t-tests on have p-values for this test that are greater than p=0.05. This suggests that our data are approximately normally distributed. The p-value for the crossword puzzle times is very low p=0.0501 which probably suggests that we should look at that data in more detail to be sure that our data are normally distributed. If your data are not normally distributed, then one option is to perform a non-parametric alternative to the one-sample t-test. This test is called the one-sample Wilcoxon signed rank test. We will not go into the details of the test, but effectively it tests whether your sample is likely to have come from a population with a median of a specified value. It is run like this in R: wilcox.test(xt$time3, mu = 16, alternative = \"less\")\n##\n## Wilcoxon signed rank exact test\n##\n## data: xt\\$time3\n## V = 19, p-value = 0.2158\n## alternative hypothesis: true location is less than 16\n\nAgain, with this test, we are looking for a p-value lower than 0.05 to reject the null hypothesis and accept the alternative that our sample comes from a population with a median of less than 16.","date":"2022-05-16 07:52:21","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"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\": 0.8143813014030457, \"perplexity\": 485.71337552740755}, \"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\/1652662510097.3\/warc\/CC-MAIN-20220516073101-20220516103101-00171.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.vedantu.com\/question-answer\/three-coins-are-tossed-together-to-find-the-class-11-maths-cbse-5f5d004a68d6b37d16426af3","text":"Question\n\n# Three coins are tossed together to find the probability of getting:(i) exactly two heads (ii) at most two heads (iii) at least one head and one tail(iv) no tails\n\nHint: Before attempting this question one should have prior knowledge about the concept of probability and also remember that Probability of happening of an event= $\\dfrac{{Total{\\text{ }}number{\\text{ }}of{\\text{ }}favourable{\\text{ }}cases}}{{Total{\\text{ }}Number{\\text{ }}of{\\text{ }}possible{\\text{ }}outcomes}}$, using this information can help you to approach the solution of the problem.\n\nComplete step-by-step solution:\nAccording to the given information, we know that 3 coins are tossed together\nAlso, we know that when three coins are tossed simultaneously, the total number of outcomes = 8 i.e., (HHH, HHT, HTH, THH, TTH, THT, HTT, TTT)\nLet X be the event of getting exactly two heads.\nSo, the number of favorable cases is (HHT, HTH, THH)\nTherefore n(X) = 3\nWe know that Probability of happening of an event = $\\dfrac{{Total{\\text{ }}number{\\text{ }}of{\\text{ }}favourable{\\text{ }}cases}}{{Total{\\text{ }}Number{\\text{ }}of{\\text{ }}possible{\\text{ }}outcomes}}$\nSo, probability of exactly two heads i.e. P (X) =$\\dfrac{{Total{\\text{ }}number{\\text{ }}of{\\text{ }}favourable{\\text{ }}cases}}{{Total{\\text{ }}Number{\\text{ }}of{\\text{ }}possible{\\text{ }}outcomes}}$\nSubstituting the given values in the above formula we get\nP(X)= $\\dfrac{3}{8}$\nProbability of at most two heads\nLet Y be the event of getting at most two heads\nTherefore, no. of favorable cases is (HHT, HTH, TTT, THH, TTH, THT, HTT)\nSo, n(Y)=7\nWe know that Probability of happening of an event = $\\dfrac{{Total{\\text{ }}number{\\text{ }}of{\\text{ }}favourable{\\text{ }}cases}}{{Total{\\text{ }}Number{\\text{ }}of{\\text{ }}possible{\\text{ }}outcomes}}$\nSo, probability of exactly two heads i.e. P (Y) =$\\dfrac{{Total{\\text{ }}number{\\text{ }}of{\\text{ }}favourable{\\text{ }}cases}}{{Total{\\text{ }}Number{\\text{ }}of{\\text{ }}possible{\\text{ }}outcomes}}$\nSubstituting the given values in the above formula we get\nP(Y) = $\\dfrac{7}{8}$\nProbability for at least one head and one tail\nLet Z be the event of getting at least one head and one tail\nTherefore, no. of favorable events, = (HHT, HTH, THH, TTH, THT, HTT)\nSo, n(Z)=6\nWe know that Probability of happening of an event = $\\dfrac{{Total{\\text{ }}number{\\text{ }}of{\\text{ }}favourable{\\text{ }}cases}}{{Total{\\text{ }}Number{\\text{ }}of{\\text{ }}possible{\\text{ }}outcomes}}$\nSo, probability of exactly two heads i.e. P (Z) =$\\dfrac{{Total{\\text{ }}number{\\text{ }}of{\\text{ }}favourable{\\text{ }}cases}}{{Total{\\text{ }}Number{\\text{ }}of{\\text{ }}possible{\\text{ }}outcomes}}$\nSubstituting the given values in the above formula we get\nP (Z) =$\\dfrac{6}{8} = \\dfrac{3}{4}$\nProbability for no tails\nLet A be the event of getting no tails\nTherefore, no. of favorable events = (HHH)\nSo, n(A)=1\nWe know that Probability of happening of an event = $\\dfrac{{Total{\\text{ }}number{\\text{ }}of{\\text{ }}favourable{\\text{ }}cases}}{{Total{\\text{ }}Number{\\text{ }}of{\\text{ }}possible{\\text{ }}outcomes}}$\nSo, probability of exactly two heads i.e. P (A) =$\\dfrac{{Total{\\text{ }}number{\\text{ }}of{\\text{ }}favourable{\\text{ }}cases}}{{Total{\\text{ }}Number{\\text{ }}of{\\text{ }}possible{\\text{ }}outcomes}}$\nSubstituting the given values in the above formula we get\nP(A) = $\\dfrac{1}{8}$\n\nNote: In the above question we knew that three coins are tossed also we know that when we toss one coin there are only two outcomes either head or tails since in this case we have to toss three coins simultaneously we found the total outcomes possible in this case which we found that 8 are the total outcomes by using the basic reasoning language that one coin can show only head or tail at a time so the outcomes we got for the three coins was (HHH, HHT, HTH, THH, TTH, THT, HTT, TTT) then for each given case we used the formula of Probability of happening of an event which is given by $\\dfrac{{Total{\\text{ }}number{\\text{ }}of{\\text{ }}favourable{\\text{ }}cases}}{{Total{\\text{ }}Number{\\text{ }}of{\\text{ }}possible{\\text{ }}outcomes}}$.","date":"2021-03-01 16:43:31","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 2, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8680207133293152, \"perplexity\": 477.1178689999725}, \"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\/1614178362741.28\/warc\/CC-MAIN-20210301151825-20210301181825-00471.warc.gz\"}"} | null | null |
\section{Introduction}
Galaxy interactions and mergers have been advocated as one of the principal actors in galaxy evolution. \cite{Toomre_77} proposed mergers as responsible for the fast morphological transformation of disc galaxies into spheroids or, in less dramatic cases, for the growth of massive classical bulges \citep{Hopkins_09c, Hopkins_09d}. Although this is still a debated result \citep{Fensch_17, Lofthouse_17}, gas-rich mergers have been proposed as triggers of intense bursts of star formation \citep{Barnes_91, Mihos_96, Cox_08, Calabro_19} resulting in luminous and ultra-luminous infrared galaxies \citep[][]{Sanders_88, Duc_97, Elbaz_03}, as well as triggers of high luminosity single and double active galactic nuclei \citep[AGNs,][]{DiMatteo_05, Capelo_15} possibly responsible for the quenching of star formation in the remnant \citep{Sijacki_06, DiMatteo_08, Booth_09, Dubois_13}. Mergers can also lead to galaxy spin flip (from aligned to perpendicular) along filaments, therefore they bring diversity in the intrinsic alignment pattern \citep[\emph{e.g.}][]{Welker_14,Welker_19}. Finally, mergers of massive galaxies are the natural path to the formation of massive black hole pairs and binaries \citep[][]{Begelman_80, Tremmel_15, Tremmel_17, Tremmel_18, Bellovary_19, Pfister_17, Pfister_19a}.
If the interaction with their complex environment leads the two black holes to \hugo{separation} of $10^{-3} (M_{\rm binary}/10^6 \ensuremath{\, \mathrm{M}_{\odot}})^{0.75}$ pc\footnote{This estimate applies to close to equal mass circular binaries, for the discussion on the actual dependencies on the eccentricity and mass ratio see Eq.~(2) in \protect{\cite{Dotti_12}}.}, with $M_{\rm binary}$ the total mass of the black hole binary, it can further shrink and finally coalesce in less than an Hubble time, while emitting gravitational waves detectable by current and future observational campaigns \citep{Hobbs_10, AmaroSeoane_13, AmaroSeoane_17, Babak_16}.
For all these reasons, galaxy mergers and their consequences have been explored thoroughly from a theoretical point of view, both analyzing and post--processing the outcomes of coarse but large cosmological simulations \citep[\emph{e.g.}][]{Steinborg_16, Volonteri_16}, as well as higher resolution isolated mergers starting from idealized initial conditions \citep[\emph{e.g.}][]{Capelo_15}.
In order to confirm these results from an observational perspective, it is required to know which galaxies are going to merge. Two main methods have been used to obtain this information. The first relies on identifying perturbations in galaxy morphology due to mergers \citep{LeFevre_00, Conselice_03, Lotz_08, Goulding_18}. The second method, which we will study in more detail in this paper, is pair counting \citep{Zepf_89, LeFevre_00, Snyder_17, Snyder_18, Ventou_19, Duncan_19}: a pair is selected as ``merging'' if the relative projected distance ($d$) and redshift difference ($\Delta z$) of the two galaxies are smaller than given thresholds $d_\textrm{th}$ and $\Delta z_\textrm{th}$. Both methods have their advantages and drawbacks, in principle, the first one uses all the information in the images, but it requires very high resolution and therefore cannot be applied at high redshift. Pair counting uses ``less'' information and can be applied to higher redshift, but pairs with a large real 3D separations, which will not merge nor interact within a Hubble time, could be selected. The last point naturally raises the question of the optimal thresholds as well as the dependence of these thresholds with other parameters such as the masses, the mass ratio etc...
In this study we take full advantage of the results of the {\sc Horizon-AGN} cosmological simulation \citep{Dubois_14a} to build mock catalogues of observationally selected galaxy pairs and define the best technique to select merging pairs. In \S \ref{sec:BuildTheCatalog}, we detail how we construct this catalog and compare it with similar catalogs \citep{Snyder_17}; in \S \ref{sec:DetectionOfRealGalaxyMerger} we test three different algorithms to detect pairs and compare their efficiency; we finally give our conclusions in \S \ref{sec:conclusions}.
\begin{figure}
\begin{center}
\includegraphics[width=\columnwidth]{Figure1a.pdf} \\
\rule{\columnwidth}{0.1cm}
\includegraphics[width=\columnwidth]{Figure1b.pdf}
\caption{\textbf{Top:} Sketch of the construction of a lightcone. Squares on the top line represent the simulated box, which is evolved in time. Slices of the box are stored at each timestep and are then stacked to form the lightcone (bottom line). Note that some galaxies are present at all time in the box, but not in the lightcone, and that some galaxies (the black one here) can be in the box without being in the lightcone. \textbf{Bottom:} Merger tree associated with the simulation sketched, some galaxies merge (blue-red pair), some remain isolated for a long time (yellow, black and green) and some ``dissolve'' as they have no child identified (grey).}
\label{fig:lightcone}
\end{center}
\end{figure}
\section{Build a numerical catalog}
\label{sec:BuildTheCatalog}
Our aim is to build a catalog of galaxy pairs, as an observer would do, but knowing, for a given pair, if it will merge or not. Here we detail how we build this catalog\footnote{Please contact the corresponding author if you are interested in obtaining the catalog.}. In \S \ref{sec:AvailableData}, we present the different data available we used; we then describe our method to build the catalog in \S \ref{sec:CompilingData}; finally, in \S \ref{sec:ValidationOfTheCatalog}, we compare this catalogs with results from \cite{Snyder_17} to verify its behavior.
\subsection{Available data}
\label{sec:AvailableData}
We use the data from the {\sc Horizon-AGN} simulation \citep{Dubois_14a}. This is one of the largest hydrodynamical cosmological simulation available, the box size is 140\ensuremath{\, \mathrm{ Mpc}}\, at $z=0$, with 1 kpc resolution in the most refined regions and a dark matter particle mass of $8\times 10^7 \ensuremath{\, \mathrm{M}_{\odot}}$. It has been run with the adaptive mesh refinement code {\sc Ramses} \citep{Teyssier_02}, and contains state-of-the-art galaxy formation subgrid physics: cooling \citep{Sutherland_93}, background UV heating~\citep{Haardt_96}, star formation \citep{Rasera_06} resulting in a stellar particle mass of $2\times 10^6 \ensuremath{\, \mathrm{M}_{\odot}}$, feedback (stellar winds, type II and type Ia supernovae) and black hole formation, accretion and feedback~\citep{Dubois_12}. \textsc{Horizon-AGN} reproduces many properties of real galaxies \citep{Dubois_16, Volonteri_16, Kaviraj_17}, therefore we can use it to produce mock catalogs, from which we can derive realistic methods observers could use to interpret the data they collect.
\subsubsection{Galaxies in the lightcone}
Concentric shells centered on a fiducial observer located at the origin of the simulation box at $z=0$, and containing particles (dark matter, stars and black holes) as well as gas cells, have been extracted on the fly at each coarse time step of the simulation. This allows the creation of a lightcone \citep{Pichon_10,Gouin_19} as sketched in Fig.~\ref{fig:lightcone} (top). The opening angle is 2.25 deg from $z=0$ to $z=1$, corresponding to the angular size of the full simulation box at $z=1$.
A catalog of galaxies has been extracted from this lightcone~\citep{Laigle_17} containing, in particular, the following information for each galaxy:
\begin{itemize}
\item stellar mass $M$;
\item star formation rate $SFR$;
\item \hugo{aspect ratio $\gamma$ as seen in the lightcone, defined as the ratio between the semi-minor and semi-major axis;}
\item location on the sky with right ascension and declination;
\item observed redshift, $z$, corresponding to the redshift an observer would measure from a spectroscopic dataset.
\end{itemize}
\subsubsection{Galaxies in the box}
Galaxies in the box have been identified with \textsc{AdaptaHOP} \citep{Aubert_04}. The algorithm detects gravitationally bound structures containing at least 50 stellar particles, therefore having a minimum mass of $10^8$ \ensuremath{\, \mathrm{M}_{\odot}}. Using again the sketch in Fig.~\ref{fig:lightcone} (bottom), the blue, red, green, grey and yellow dots (galaxies) are now identified both in the box and in the lightcone. However, initially, galaxies in the lightcone and in snapshots are not matched. This matching is important because, for galaxies in the lightcone, similarly to galaxies in the sky, we have only an image at one particular time. Galaxies in the box are instead consistently evolved from $z = 100$ down to $z = 0$, therefore we know their history, \emph{e.g.} we know how they move or how their mass evolves (as represented by the enhancement of the size of the dots). Each galaxy that can be observed in the lightcone has been associated to the same galaxy in the box~\citep{Laigle_17}, connecting the ``observational view'' to how a galaxy actually evolves over cosmic time.
\subsubsection{Merger tree}
The merger tree of galaxies in the box has been produced with \textsc{TreeMaker} \citep{Tweed_09}. Galaxies containing particles with the same ID at different times are matched to form the history of each galaxy. With this we can follow galaxies from their birth down to $z=0$. This is sketched in Fig.~\ref{fig:lightcone} (bottom) where galaxies are followed with time, some merging (blue-red pair), some remaining isolated (black, yellow and green dots) and some ``dissolving'' (grey dot, see \S \ref{sec:CompilingData}).
\subsection{Combining data}
\label{sec:CompilingData}
With all the data presented in the previous Sections, for a pair of galaxies in the lightcone, we have a pair of galaxies in the box, which we can follow down to $z=0$ with the merger tree to see if they merge, or not, and how long it takes if it is actually the case. We select all the pairs (in the lightcone) fulfilling the following criteria:
\begin{itemize}
\item Both galaxies must be observed at redshift $0.05<z<1$, this is the redshift range from which the lightcone of {\sc Horizon-AGN} with angular opening $2.25\deg$ has been produced;
\item The mass of the most massive galaxy has to be larger than $10^9 \ensuremath{\, \mathrm{M}_{\odot}}$, so that it is defined with at least 500 stellar particles, and lower that $10^{11}\ensuremath{\, \mathrm{M}_{\odot}}$, so that there are more than 10 of those galaxies in the catalog. We also impose a stellar mass ratio between galaxies of $0.1<q<1$;
\item The projected distance between the two galaxies, $d$, measured with the angular distance assuming that the redshift is the one of the primary galaxy, has to be lower than $5 \ensuremath{\, \mathrm{ Mpc}}$. Similarly, the redshift difference between the two galaxies, $\Delta z$, has to be lower than $0.05$. These criteria are intentionally extremely loose to ensure that most merging pairs are included. Consistently with the simulation, we assume a $\Lambda$CDM cosmology with \emph{WMAP7} parameters \citep{Komatsu_11}.
\end{itemize}
We end up with $\sim 9\times 10^8$ pairs of galaxies, for which we know the following observational quantities: the mass of the primary and mass ratio, $M_\mathrm{pri}$ and $q$; the redshift difference, $\Delta z$; the projected distance, $d$; their SFR, \ensuremath{\, SFR_\textrm{pri}} and \ensuremath{\, SFR_\textrm{sec}}; \hugo{and their aspect ratios, $\gamma_\mathrm{pri}$ and $\gamma_\mathrm{sec}$}. We also know the associated pair in the snapshots, which we can follow in the merger tree. We use the sketch in Fig.~\ref{fig:lightcone} (bottom) to list the possible cases:
\begin{enumerate}
\item The two galaxies live at the same time, \emph{i.e.}\, they are in the same snapshot. We can then follow their history in the merger tree and see if the two galaxies merge, and how long it takes (\ensuremath{\, \tau_\mathrm{merger}}). For instance, the blue-red pair merges, while the blue-green pair has not merged by $z=0$ ($\ensuremath{\, \tau_\mathrm{merger}} = \infty$).
\item The two galaxies do not live at the same time, \emph{i.e.}\, they are not in the same snapshot. We then follow the history of the galaxy with higher redshift until the two galaxies are at the same snapshot, and then apply case (i). For instance we would trace the blue galaxy in the blue-grey pair until time $t+\d t$ and then apply case (i). In this particular example, an additional feature happens: the grey galaxy ``dissolves'', this can happen if the galaxy \hugo{loses} enough stars, or is so perturbed, that it is not recognized by \textsc{AdaptaHOP} in one snapshot. As it is difficult to differentiate between a numerical and a physical disruption, pairs in which a galaxy ``dissolves'' are discarded (this represents $\sim 3\times 10^7$ pairs, a small fraction of the total).
\end{enumerate}
\subsection{Validation of the catalog}
\label{sec:ValidationOfTheCatalog}
To confirm that our catalog is coherent with previous studies, we perform a similar analysis as done for Fig.~2 in \cite{Snyder_17}: at a given redshift $\ensuremath{\, z_\textrm{pri}}$ for the primary, we estimate how many pairs fulfill the criterion observers use to define a merger, \emph{i.e.} $\Delta z < 0.02(1+\ensuremath{\, z_\textrm{pri}}) = \Delta z_\textrm{th} $ and $d<75 \ensuremath{\, \mathrm{kpc}}=d_\textrm{th}$. Given this selection process, we can count how many selected pairs actually merge (true positive, $TP$) and how many selected pairs actually do not merge by $z=0$ (false positive, $FP$). From this, we compute the purity $P$ in $[0,1]$, corresponding to the fraction of selected pairs that actually merge:
\begin{eqnarray}
P=\frac{TP}{TP+FP} \, .
\end{eqnarray}
We show our results in Fig.~\ref{fig:FracMergerByzEqualZero}. Similarly to \cite{Snyder_17}, we find that, for $\ensuremath{\, z_\textrm{pri}}<1$, about 50\% of the pairs selected with $\Delta z < 0.02(1+\ensuremath{\, z_\textrm{pri}})= \Delta z_\textrm{th} $ and $d<75 \ensuremath{\, \mathrm{kpc}}=d_\textrm{th}$ will not have merged by $z=0$. This confirms the robustness of this results, the goodness of our catalog, and at the same time, shows that there is room from improvement in detecting true mergers from galaxy pairs \citep{Cibinel_15,Snyder_18}.
\begin{figure}
\begin{center}
\includegraphics[width=\columnwidth]{Figure2.pdf}
\caption{\textbf{Left axis, histograms}: Total number of seletected pairs (blue) and number of pairs actually merging by $z=0$ (orange). We show in the top left corner the criterion to define a pair. \textbf{Right axis, markers}: purity of the selection in our catalog and in \protect\cite{Snyder_17}.}
\label{fig:FracMergerByzEqualZero}
\end{center}
\end{figure}
\section{Detection of real galaxy mergers}
\label{sec:DetectionOfRealGalaxyMerger}
In this Section, we test three algorithms to detect real galaxy mergers from the available properties of each pairs in the catalog. We first show in \S \ref{sec:TwoExtremeCases} what are the main problems that must be overcome to build a faithful catalog without \hugo{losing} too many real pairs; we then discuss the metric we will use to judge the quality of the algorithm in \S \ref{sec:Goodness}; and we finally detail the algorithms in \S \ref{sec:OptimalParametersForDetectingPairs} and \S \ref{sec:NN}.
From now on, we will not consider the ``number of pairs which have merged by $z=0$'', since it is is not representative of the instantaneous merger rate, we consider instead the ``number of pairs which merge within 3 Gyr'', meaning that $\ensuremath{\, \tau_\mathrm{merger}}~<~3 \ensuremath{\, \mathrm{Gyr}}~=~\tau_{\rm merger, max}$. Note that for pairs with $z<0.25$, the time left before $z=0$ is less than 3 Gyr, in that case we consider indeed ``pairs which have merged by $z=0$''. The value of $\tau_{\rm merger, max}=3 \ensuremath{\, \mathrm{Gyr}}$ has been chosen because it is in agreement with typical merger timescales obtained in numerical simulations \citep{Capelo_15}, but we stress that its exact value is rather arbitrary, and partially affects the results as shown in Appendix \ref{sec:ChangingOurDefitionOfMerger}.
\subsection{A difficult exercise}
\label{sec:TwoExtremeCases}
Of the $9\times 10^8$ pairs, only $\sim 10^5$, \emph{i.e.}\, only $\sim 0.01\%$, merge: the problem of detecting merging pairs is extremely unbalanced. This fraction depends on the particular parameters we used to select pairs (we do not expect to have mergers for $d\sim5\ensuremath{\, \mathrm{ Mpc}}$...), but it is expected to be always low, as most pairs in the sky do not merge.
In addition, the problem is also extremely degenerate. For instance, we show in Table~\ref{table:ExtremePairs} the details and fate of four specific pairs:
\begin{itemize}
\item Pairs 1 and 2 consist in two pairs, with similar properties in terms of projected distance and redshift difference, but, given our definition of ``merger'', one of them merges and the other does not;
\item Pairs 3 and 4 consist in two pairs with, in both cases, two galaxies very close in redshift space ($\Delta z \lesssim 10^{-3}$) but, in one case, the two galaxies are far given the projected threshold usually used (projected distance $d$ is 349 \ensuremath{\, \mathrm{kpc}}) and, in the other case, they are close ($d$ is 37 \ensuremath{\, \mathrm{kpc}}); nonetheless, the distant pair merges whereas the close one does not.
\end{itemize}
We show in Fig.~\ref{fig:distances} the 3D distance (solid line), as measured in the simulation, between the two galaxies in the four pairs described in Table~\ref{table:ExtremePairs}, as a function of time. We also indicate at which time the pair is ``seen'' in the lightcone (marker). Pairs 1 and 2 have the same observed $d$ and $\Delta z$ but have in reality different orbital parameters. Galaxies in Pair 1 are separated by indeed $\sim100 \ensuremath{\, \mathrm{kpc}}$ and a relative speed of 100 km/s, but galaxies in Pair 2 are in fact separated by 400 kpc and a relative speed of 800 km/s. These different orbital parameters lead to a different fate, and a different merger timescale. Pair 3 is seen at the apocententer of a very eccentric orbit resulting in a fast merger, while Pair 4 is more circular, explaining why the merger takes a longer time.
From these simple examples, it is clear that using only thresholds on projected distance and redshift difference cannot be 100\% accurate, other quantities such as the masses (see \S\ref{sec:DependanceInMpri}), the shapes, the colors etc... or relations between all these quantities (see \S \ref{sec:NN}) should be used \citep[see also][]{Snyder_17,Goulding_18,Snyder_18}.
\begin{table}
\begin{center}
\begin{tabular}{ccccccc}
\hline
Pair ID & \ensuremath{\, z_\textrm{pri}} & \ensuremath{\, M_\textrm{pri}} & \ensuremath{\, M_\textrm{sec}} & $d$ & $\Delta z$ & \ensuremath{\, \tau_\mathrm{merger}} \\
&& $10^{10}$ \ensuremath{\, \mathrm{M}_{\odot}} & $10^{10}$ \ensuremath{\, \mathrm{M}_{\odot}} & \ensuremath{\, \mathrm{kpc}} & $10^{-4}$ & \ensuremath{\, \mathrm{Gyr}}\\
\hline
\hline
1 & 0.4578 & 2.307 & 2.05& 123& 0.4 & 1.977 \\
2 & 0.8996 & 1.293 & 0.485 & 125& 0.4 & $\infty$ \\
3 & 0.711 & 3.588 & 0.412 & 349 & 0.4 & 0.738 \\
4 & 0.7542 & 1.554 & 0.503 & 37& 2.0 & 6.427 \\
\hline
\end{tabular}
\caption{Four pairs, with similar properties but different behaviors.}
\label{table:ExtremePairs}
\end{center}
\end{table}
\begin{figure}
\begin{center}
\includegraphics[width=\columnwidth]{Figure3.pdf}
\caption{3D distance as a function of time between the two galaxies of the four pairs described in Table~\ref{table:ExtremePairs}. Markers indicate the time at which the pair is seen in the lightcone.}
\label{fig:distances}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width=\columnwidth]{Figure4.pdf}
\caption{Estimate of the $MCC$ as a function of the thresholds on redshift difference $\Delta z_\mathrm{th}$ and projected distance $d_\mathrm{th}$.}
\label{fig:PCMCCF1}
\end{center}
\end{figure}
\subsection{Goodness of the detection method}
\label{sec:Goodness}
To compare two selection methods, and judge which one is the best, we need a metric. Purity (see \S\ref{sec:ValidationOfTheCatalog}) only is not a good metric, as a very restrictive threshold (very small $d_\textrm{th}$ and $\Delta z_\textrm{th}$) would result in a purity of 100\%, but would miss many true mergers. This is why we also consider the completeness $C$ in $[0,1]$ corresponding to \hugo{the fraction of true mergers selected}:
\begin{eqnarray}
C=\frac{TP}{TP+FN} \, ,
\end{eqnarray}
where $FN$ (false negative) corresponds to the number of true mergers not selected.
Clearly, purity and completeness vary in opposite directions: if the thresholds are very restrictive, as we already said, purity will be high, but completeness will be low, and vice versa. For this reason, we need a combination of $P$ and $C$ or, similarly, of $FP$, $FN$, $TP$ and $TN$, where $TN$ (true negative) corresponds to the number of non mergers non selected. We use the \emph{Matthews correlation coefficient}, $MCC$ \citep{MCC}, defined as:
\begin{eqnarray}
MCC &=& \frac{TP\times TN - FP\times FN}{\sqrt{(TP+FP)(TP+FN)(TN+FP)(TN+FN)}} \nonumber \, .\end{eqnarray}
The $MCC$ is in $[-1,1]$, 1 meaning that the algorithm gives perfect predictions, 0 meaning that it is random and -1 meaning it is always wrong.
\subsection{Using simple thresholds on $d_\textrm{th}$ and $\Delta z_\textrm{th}$}
\label{sec:OptimalParametersForDetectingPairs}
\subsubsection{Starting point}
\label{sec:DependanceInDandZ}
We begin with a simple detection method: a pair is selected and (observationally) defined as merging if its projected distance and redshift difference are lower than the thresholds $\Delta z_\textrm{th}$ and $d_\textrm{th}$. As discussed in \S \ref{sec:TwoExtremeCases} this method cannot be 100\% accurate but it still is a reasonable (and frequently used) starting point.
In this Section, we search for the best $\Delta z_\textrm{th}$ and $d_\textrm{th}$ that optimize the $MCC$. For this purpose, we vary the two parameters and compute the $MCC$.
In Fig.~\ref{fig:PCMCCF1}, we show the $MCC$ given the thresholds used. We marked with a dashed-black line when this metric is at maximum. We find $\Delta z_\textrm{th}=7\times10^{-4}\sim 10^{-3}$ and $d_\textrm{th} = 86 \ensuremath{\, \mathrm{kpc}} \sim 100 \ensuremath{\, \mathrm{kpc}}$. The value of $100 \ensuremath{\, \mathrm{kpc}}$ is similar to the threshold used by observers, and it is of the order of magnitude expected: galaxies separated by 10 kpc are very likely to undergo a merging process \citep[the typical scale length of the disc of the Milky-Way is 3.5 kpc,][]{BT_87}; and 1000 kpc would correspond to very distant, probably non interacting, pairs. The value of $10^{-3}$ for the redshift difference, hardly achievable with current photometric redshift, is however about one order of magnitude lower than the threshold usually chosen, typically $10^{-2}(1+\ensuremath{\, z_\textrm{pri}})$. Note that \cite{Pasquet_19} suggested a method allowing to reach $10^{-3}$ uncertainty on photometric redshift measurement, which is encouraging for the future surveys.
The best thresholds give $P=0.36$ and $C=0.41$. This again confirms our first guess of \S\ref{sec:TwoExtremeCases}: using only $d$ and $\Delta z$ is too degenerate to properly distinguish between mergers and non mergers. While the value of $P=0.36$ might seems extremely low, we recall here that the catalog is extremely unbalanced and degenerate, with only 0.01\% of pairs actually merging, therefore this selection method is actually three orders of magnitude better than random selection. The maximal $MCC=0.38$ is surprisingly good given the simplicity of the method. For example, \cite{Snyder_18}, using Random Forest on 10 parameters on pairs from the \textsc{Illustris} simulation \citep{Vogelsberger_14}, find a $MCC$ of about 0.4, with the difference that they considered pairs up to $z \sim 9$.
It is interesting to note that, at the time we were writing this paper, \cite{Ventou_19} performed a similar independent analysis to determine the optimal thresholds to detect merging pairs. They use a different simulation \citep[\textsc{Illustris}, ][]{Vogelsberger_14}, a different redshift range (up to $z=5$ but with lower redshift resolution as they use 6 snapshots), and a different metric to chose their threshold (completeness of 30\%), nonetheless, they found similar values, with pairs selected as merging if $d<50\ensuremath{\, \mathrm{kpc}}$ and $\Delta z < 10^{-3}$ or $50\ensuremath{\, \mathrm{kpc}} < d < 100 \ensuremath{\, \mathrm{kpc}}$ and $d<3\times 10^{-4}$. This supports our and their findings.
\begin{figure}
\begin{center}
\includegraphics[width=\columnwidth]{Figure5a.pdf}
\hfill
\includegraphics[width=\columnwidth]{Figure5b.pdf}\\
\caption{\textbf{Top:} Estimate of the $MCC$ as a function of the thresholds on redshift difference $\Delta z_\mathrm{th}$ and projected distance $d_\mathrm{th}$. In this example, $\ensuremath{\, M_\textrm{pri}}$ is in between $10^{10}$ and $10^{10.25}$ \ensuremath{\, \mathrm{M}_{\odot}}. \textbf{Bottom:} Evolution of the optimal $d_\mathrm{th}$ (blue dots) and $\Delta z_\mathrm{th}$ (orange squares) for $M_\textrm{pri}$ within different mass intervals equally spaced by 0.25 dex, as well as their fits reported in Eq.~\eqref{eq:dthOfMpri} and Eq.~\eqref{eq:dzthOfMpri}. The larger the dots the larger the $MCC$ (min: 0.28, max: 0.54).}
\label{fig:PCofdr}
\end{center}
\end{figure}
\subsubsection{Including the dependence on $M_\mathrm{pri}$}
\label{sec:DependanceInMpri}
More massive galaxies are expected to merge more frequently \hugo{than} low mass galaxies \citep{Fakhouri_10}. This is why we expect the thresholds $\Delta z_\textrm{th}$ and $d_\textrm{th}$ to depend on the masses of galaxies.
We explore this with our second selection method: a pair is selected and (observationally) defined as merging if its projected distance and redshift difference are lower than the \ensuremath{\, M_\textrm{pri}}\, dependent thresholds $\Delta z_\textrm{th}(\ensuremath{\, M_\textrm{pri}})$ and $d_\textrm{th}(\ensuremath{\, M_\textrm{pri}})$.
With this idea in mind, we split the catalog in sub-catalogs in which \ensuremath{\, M_\textrm{pri}}\, is in $[M_\mathrm{min}, M_\mathrm{max}]$, where $M_\textrm{min}$ ($M_\textrm{max}$) varies in equal logarithmic bins (0.25 dex) in between $10^9$ and $10^{11}$ \ensuremath{\, \mathrm{M}_{\odot}}. We then vary $d_\mathrm{th}$ and $\Delta z_\mathrm{th}$, and compute the $MCC$, as shown on the example in Fig.~\ref{fig:PCofdr} (top). In this example, for a primary mass within $10^{10}$ and $10^{10.25}$ \ensuremath{\, \mathrm{M}_{\odot}}, the $MCC$ peaks at 0.46 for $d_\mathrm {th}= 86 \ensuremath{\, \mathrm{kpc}}$ and $\Delta z_\mathrm {th}= 6\times 10^{-4} $: the classification is much better than using only $d_\mathrm{th}$ and $\Delta z_\mathrm{th}$. However, both the $MCC$ and the thresholds depend on \ensuremath{\, M_\textrm{pri}}. We show this dependence in Fig.~\ref{fig:PCofdr} as well as a simple power law fit for the evolution of the thresholds:
\begin{eqnarray}
d_\mathrm{th} &=& 84 \ensuremath{\, \mathrm{kpc}} \left( \frac{\ensuremath{\, M_\textrm{pri}}}{10^{10}\ensuremath{\, \mathrm{M}_{\odot}}} \right)^{0.20} \label{eq:dthOfMpri} \\
\Delta z_\mathrm{th} &=& 6\times 10^{-4} \left( \frac{\ensuremath{\, M_\textrm{pri}}}{10^{10}\ensuremath{\, \mathrm{M}_{\odot}}} \right)^{0.28} \, . \label{eq:dzthOfMpri}
\end{eqnarray}
Both thresholds logarithmically scale as $\sim 1/3 \times \log(\ensuremath{\, M_\textrm{pri}})$. This is expected, indeed, using Eq.~(12) from \cite{Taffoni_03}, the dynamical friction timescale \citep{Chandrasekhar_43, BT_87}, which we use as a proxy for $\ensuremath{\, \tau_\mathrm{merger}}$, scales as:
\begin{eqnarray}
\ensuremath{\, \tau_\mathrm{merger}} = \frac{r^2 v_{c,\mathrm{pri}}}{\ensuremath{\, M_\textrm{sec}}}\, ,
\end{eqnarray}
where $v_{c,\mathrm{pri}}$ is the circular velocity at the virial radius of the primary and $r$ the real 3D distance between the galaxies. Considering constant density $\tilde{\rho}$ ($\ensuremath{\, M_\textrm{pri}} \sim \tilde{\rho} R^3_\mathrm{pri}$) and virialized galaxies ($v_{c,\mathrm{pri}} \propto \ensuremath{\, M_\textrm{pri}}^{1/2} R^{-1/2}_\mathrm{pri}$ ) immediately leads to $\ensuremath{\, \tau_\mathrm{merger}} \propto \ensuremath{\, M_\textrm{pri}}^{-2/3}q^{-1}r^2$. In conclusions, for similar mass ratios ($q$ is between 0.1 and 1 in our catalog), and for a fixed dynamical friction timescale ($\ensuremath{\, \tau_\mathrm{merger}} < \tau_{\rm merger, max} =3 \ensuremath{\, \mathrm{Gyr}}$), we have $r\propto \ensuremath{\, M_\textrm{pri}}^{1/3}$.
The $MCC$ is higher ($\sim 0.6$) for massive galaxies than for low mass galaxies ($\sim 0.3$): it is easier to detect real mergers of massive pairs. However, overall, if we chose $\Delta z_\mathrm{th}$ and $d_\mathrm{th}$ given by Eqs.~\eqref{eq:dthOfMpri} and~\eqref{eq:dzthOfMpri}, we find $P=0.43$, $C=0.36$ and $MCC=0.40$. \hugo{Note that we have optimistically assumed that $M_\mathrm{pri}$ is perfectly known, which is not true for real catalogs \citep[uncertainty on mass is typically 0.3~dex, ][]{Davidzon_17}}. In conclusions, including \ensuremath{\, M_\textrm{pri}}\, results in a minor improvement of the classification compared with selection using only $\Delta z $ and $d$.
\subsection{Using a neural network}
\label{sec:NN}
We have shown in \S \ref{sec:DependanceInMpri} that using additional information than the projected distance or redshift difference can marginally improve the quality of the detection method. Similarly, non-linear relations between all properties of each pair could improve the quality of the detection method.
We explore this with our third selection method: we build a simple neural network with {\sc keras} \citep{Keras}, which we train so that it detects merging pairs from the properties available in our catalog. Below we describe the main features of the network and the parameters used to ensure the reproducibility of our test. The architecture of the network is \hugo{somewhat} similar to the one from \cite{Marchetti_17}, with:
\begin{itemize}
\item \hugo{An input layer with the 9 parameters of each pairs ($d_\mathrm{th}$, $\Delta z_\mathrm{th}$, \ensuremath{\, M_\textrm{pri}}, $q$, $z_\mathrm{pri}$, $SFR_\mathrm{pri}$, $SFR_\mathrm{sec}$, $\gamma_\mathrm{pri}$, $\gamma_\mathrm{sec}$)};
\item a first hidden layer in which 5 neurons, \emph{i.e.}\, 5 linear combinations of the \hugo{9 parameters resulting in 45 weights and 5 bias}. In order to introduce non-linearities, the results of these linear combinations are passed to an activation function for which we chose a hyperbolic tangent;\footnote{We tested a sigmoid activation function as well and found that the neural network behaved best with the hyperbolic tangent.}
\item A second hidden layer, again with 5 neurons\footnote{In both hidden layers, we also tried with 10, 20, 50 and 100 neurons, which resulted in no significant improvement. Above 20 neurons the results actually becomes worse due to overfitting. For these reasons we finally opted for 5 neurons.}, \emph{i.e.}\, 5 linear combinations of the 5 outputs of the previous layer resulting in 30 new free parameters. Again, the results are passed to a hyperbolic tangent;
\item An output layer with one neuron, \emph{i.e.}\, a linear combination of the 5 outputs of the previous layer resulting in 6 new free parameters. In order to obtain a number that could be interpreted as a merging probability, the activation function chosen here is a sigmoid returning a real number $f$ in [0,1], where objects that the neural network considers secure non-mergers correspond to 0 while secure mergers are labeled 1.
\end{itemize}
The first step is the training of the network. For this task we used a sub-catalog (referred as \textit{training set}, with 1\% of the catalog, \emph{i.e.}\, $10^7$ pairs). The training proceeds running through this catalog multiple times (epochs), and evolving the \hugo{86} parameters of the 11 linear combinations computed in the hidden layers. As "loss function" (the metric used to evaluated how well each set of coefficients performs) we use the binary cross-entropy:
\begin{eqnarray}
L(y,\hat{y}) = -\frac{1}{N}\sum_{i=0}^N\left( y_i\log(\hat{y}_i) + (1-y_i)\log(1-\hat{y}_i) \right) \, ,
\end{eqnarray}
where $y$ corresponds to the real labels of the $N=10^7$ pairs of the \textit{training set}, $\hat{y}$ to the predicted label by the network, and index $i$ refer to a given pair. If a pair is merging (non merging) then its true label is 1 (0), if the predicted label is 1 (0) then $L$ will be null and if it is 0 (1) then the loss will be infinite. During the training, the network searches for the minimum of the loss using the Adam optimizer \citep{Adam}, with an initial learning rate (the parameter that determines the size of the steps in the free parameter space) of 0.01. If the loss varies by less than $10^{-4}$ during 10 epochs, we divide the learning rate by 5 down to a minimum of $10^{-4}$, and the training ends when the loss has varied by less than $10^{-4}$ during 50 epochs.
The second step is the "validation" of the network, performed on a second \textit{validation set} of 0.5\% of the catalog ($5\times10^6$ pairs). During this phase the network defines a threshold $f_\mathrm{th}$: every pair resulting in $f>f_\mathrm{th}$ are considered as merging, while pairs with $f<f_\mathrm{th}$ are dubbed as chance superpositions. The value of $f_\mathrm{th}$ is defined by maximizing the $MCC$ on the validation set, consistently with the analysis discussed in the previous Sections.
Finally, once the network is trained and validated, we run it on a third \textit{test set} of 0.5\% of the catalog ($5\times10^6$ pairs\footnote{The network has not been run on the whole sample because of the computational cost of the test. Note however that the number of pairs used is large enough for this kind of architecture, \cite{Marchetti_17} typically had a sample with $2.5\times10^6$ objects.}). The test run performed results in a very low $MCC$ ($\sim 0.1$), due to the extreme unbalance of the catalog (see \S\ref{sec:TwoExtremeCases}), that "teaches" the neural network to typically answer that pairs never merge.
To overcome this issue, we build a new \textit{balanced training set} ($2\times10^5$ pairs) containing 50\% of merging pairs and 50\% of non merging pairs. In order to check the good behavior of our network on a balanced catalog, we also build a \textit{balanced test set} ($3\times10^4$ pairs).
\begin{figure}
\begin{center}
\includegraphics[width=\columnwidth]{Figure6.pdf}
\caption{Histogram of outputs from the network of mergers (solid lines) and non mergers (dashed lines) when applied to the balanced (thick line) and unbalanced (thin line) dataset. In most of cases, the network is able to classify correctly the pair, but a small fraction, which in is dominant (as the problem is unbalanced), of non merging pairs are identified as ``merging'' (as the problem is degenerate) which results in poor classification.}
\label{fig:histNN}
\end{center}
\end{figure}
After training on the new balanced set and optimizing the threshold on the unbalanced validation set, we obtain a $MCC$ on the unbalanced test set of 0.41. This is again not much of an improvement compared with naive selection using only $\Delta z $ and $d$. The reason is that, among the large number of non merging pairs, a small fraction have similar properties than merging pairs (we recall that the problem is degenerate, see \S\ref{sec:TwoExtremeCases}). However, as the problem is also unbalanced, although this fraction is small, the resulting number of false positive can be larger than the number of merging pairs itself. We show for instance in Fig.~\ref{fig:histNN} the histogram of outputs of the network, $f$, on mergers (solid lines) and non mergers (dashed lines) in the case of the balanced (thick line) and unbalanced (thin line) test sets. In both cases more than 90\% of mergers (non mergers) have $f>0.95$ ($f<0.05$): the network is perfectly capable of classifying most of pairs. In the case of the balanced test set, where degeneracy is minimized due to balancing, the network is excellent ($MCC=0.97$), however, in the case of the real dataset, the 0.35\% of non merging pairs with $f>0.95$, \emph{i.e.}\, classified as ``mergers'', outnumber the total number of pairs, resulting in a $MCC$ of 0.41. \hugo{This problem is inherent to the small number of input parameters in the network and, to obtain better results, more inputs should be used: one could think of parameters linked to morphology and/or disturbances, such as the $\phi$-asymmetries \citep{Conselice_00}, the Gini coefficient \citep{Lotz_08} or other reduced quantities to describe the image. However, given the large size of the dataset, using all the pixels of the images as input parameters in a more complex network would probably be the most efficient way of greatly improve the classification. We postpone such analysis to a future study.}
\section{Conclusions}
\label{sec:conclusions}
In this paper, using the {\sc Horizon-AGN} simulation, we build a mock catalog of galaxy pairs in order to infer the optimal way to determine true merging pairs. We summarize our finding below:
\begin{itemize}
\item Using only the projected distance and redshift difference cannot be 100\% accurate: we found two pairs with similar projected properties but with different behaviors, some merging some not;
\item Nonetheless, the optimal parameters when using only the projected distance and redshift difference are $d_\mathrm{th}=86\ensuremath{\, \mathrm{kpc}}$ and $\Delta z_\mathrm{th} = 7\times 10^{-4}$. This result is in excellent agreemenet with the recent results of \cite{Ventou_19}. Note that the resulting $MCC$ (the metric we use in this paper) is only 0.38. This is due to a combination of both the degeneracy and unbalancing of the problem;
\item More detailed classifiers including the mass of the primary marginally improve the $MCC$ to 0.40. The improvement is much better for massive galaxies, because massive galaxies merge more frequently;
\item Including non-linear relations between the \hugo{9} parameters of each pair in the catalog (projected distance, redshift difference, masses, redshift, SFRs \hugo{and aspect ratios}) through a neural network again marginally improve the $MCC$ to 0.41. This confirms that the most relevant parameters to detect merging pairs are the projected distance and redshift difference. It also shows that, in order to be more predictive, future detection methods will need to use the full image instead of reduced quantities.
\end{itemize}
These new selection criteria can be used in large survey to refine the estimates of the evolution of the galaxy merger rate \citep[\emph{e.g.}][]{Ventou_19}, but also to study statistically the effects of mergers on the SFR \citep[\emph{e.g.}][]{Calabro_19} or AGNs \citep[\emph{e.g.}][]{Koss_12}.
\section*{Acknowledgments}
\hugo{HP is indebted to the Danish National Research Foundation (DNRF132) for support. HP, MV and YD acknowledge support from the European Research Council (Project no. 614199, `BLACK'). This work has made use of the Horizon Cluster hosted by the Institut d'Astrophysique de Paris; we thank Stephane Rouberol for running smoothly this cluster for us. HP thank A. Szenicer for insightful discussions. We thank the referee, Jon Loveday, for carefully reading the manuscript and providing useful comments.}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,373 |
Cindy Sherman (Glen Ridge, Nueva Jersey; 19 de enero de 1954), nacida con el nombre de Cynthia Morris Sherman, es una fotógrafa y directora de cine estadounidense. Una de las mayores representantes de la fotografía de posguerra, exhibió más de tres décadas de su trabajo en el MoMA de Nueva York.
A pesar de que en la mayoría de sus fotografías aparece ella misma, no las considera autorretratos. Sherman se utiliza a sí misma como vehículo para representar una gran variedad de temas del mundo contemporáneo, como el papel de la mujer o el papel del artista. A través de una serie de diferentes obras, Sherman ha planteado difíciles e importantes preguntas sobre el papel y la representación de las mujeres en la sociedad, los medios de comunicación y la naturaleza de la creación del arte. En 2020 fue galardonada con el Premio de la Fundación Wolf de las Artes.
Biografía
Inicios
Cindy Sherman nació en Glen Ridge, un suburbio del área metropolitana de Nueva York, sin embargo su familia se mudó poco después de su nacimiento a Huntington, en Long Island, donde Sherman creció siendo la más joven de cinco hermanos. A diferencia de otros artistas, Sherman no estaba particularmente involucrada en las artes cuando era joven, su padre se ganaba la vida como ingeniero y su madre trabajaba como maestra de lectura. Sherman dice que no sabía lo que era el mundo del arte hasta que fue a la universidad. A pesar de que sus padres carecen de interés artístico, apoyaron su decisión de entrar en la escuela de arte después de terminar la escuela secundaria.
Cindy Sherman se empezó a interesar por las Artes Visuales en la Universidad de Buffalo. La carrera de Sherman en Buffalo comenzó muy diferente de como acabó. En su primer año, Sherman empezó a trabajar la pintura hasta que un día, se dio cuenta de que no era suficiente. Frustrada por las limitaciones de la pintura y la sensación de que había hecho todo lo que pudo, se dio por vencida. Sherman dijo que sentía que "... no había nada más que decir [a través de la pintura ] Estaba meticulosamente copiando otro arte y entonces me di cuenta de que sólo podía usar la cámara y desarrollar mis ideas con ella", y esto es lo que hizo. Sherman reconoce que nunca podría haber tenido éxito como pintora. Al carecer de la conexión crítica que necesitan para continuar con la pintura, Sherman volvió a la fotografía, que fue lo que estudió durante el resto de su tiempo en Buffalo. Durante este tiempo, conoció a Robert Longo un artista que será muy importante en su vida. Junto con Longo y su compañero de estudios Charles Clough, Sherman formó Hallwalls, un espacio de artistas independientes donde ella y otros artistas exponían.
Carrera artística
Después de su graduación, en 1976, decidió mudarse a Nueva York para embarcarse de lleno en su carrera artística, en un loft en Fulton Street en el bajo Manhattan. Fue entonces cuando comenzó a tomar fotografías de sí misma. Estas fotografías, autorretratos conceptuales, vendrían a ser conocidas como Complete Untitled Film Stills (1977-1980),. en los que escenifica situaciones con vestuario y utilería para dar a las fotografías la apariencia de un fotograma cinematográfico, usando estética y planos propios del Cine negro.
En otra conocida serie "Retratos históricos", Sherman personifica protagonistas masculinos de pinturas clásicas de la historia del arte de Occidente, tales como "Baco enfermo" de Caravaggio, entre otros.
Si bien Sherman aparece en las fotografías, ella no las considera propiamente autorretratos: en Untitled Film Stills, tal vez uno de los trabajos más conocidos de la carrera de Sherman hasta el momento. En estas fotografías, que empezaron en 1977, Sherman se pone a sí misma en el papel de actriz de películas clase B. Sus fotografías muestran personajes construidos con pelucas, sombreros, vestidos, ropa diferente a la suya. Estas fotografías pueden confundirse con retratos pero son algo muy diferente. En cada una de estas fotografías, Sherman juega un rol, una ficción autofabricada en la que posa adoptando roles femeninos estereotípicos: ama de casa, prostituta, mujer en peligro, mujer llorando, bailarina y actriz.
La época en la que Sherman se dio a conocer como fotógrafa había muchas mujeres artistas cuyo trabajo respondía a la mirada lasciva de un público masculino. La artista neoyorquina de performance Hannah Wilke era un peso pesado durante este periodo, a menudo posaba desnuda y disfrutaba abiertamente de su atractivo erótico. Resultaba en parte un personaje voluntarioso y en parte una verdad física. Al contrario que el exhibicionismo de Wilke, que empleaba el desnudo como una liberación, Sherman ha sido siempre una artista del ocultamiento, disfrazándose desde mediados de los setenta para emular fantasías pop. El desnudo no formaba parte de su trabajo a pesar de que en los años ochenta, tras los éxitos de sus fotogramas, adoptó en su fotografías pechos sintéticos y vulvas artificiales que añadían un divertimento vicioso a la fantasía masculina.
Durante los años setenta, Sherman jugó un papel preponderante en la reestructuración feminista del cuerpo, movimiento originado y mantenido por las mujeres. Esta generación creía que "lo personal es político" y los artistas de performance, en su mayoría mujeres, se apropiaron de este axioma y lo transformaron, a la vista de sus logros, en algo asombrosamente real basado en la disforia existente entre los sexos. La propia Sherman, especialmente en sus comienzos, creó infinidad de personajes con los que quedar apabullado por la cantidad de rostros y cuerpos que era capaz de construir usando su propio cuerpo. Su importancia como artista reside en este apabullamiento. En su deliberado intento de revelar la naturaleza interpretativa de la psique femenina, Sherman adquiere múltiples y variados rostros. Los seres que emergen de sus brillantes transformaciones pertenecen al glamour de la industria cinematográfica de los años 30 y 40, cuando la belleza femenina era la clave para vender entradas.
Para algunos resultaría fácil calificar las fotografías de Sherman como arbitrarias; su efecto teatral respondería a su naturaleza esencialmente artificial. Vistas de este modo, las imágenes pierden su extravagante intensidad y se convierten en crítica a la femineidad tal como Hollywood la representa. Aunque el artificio es una estratagema importante en los trucajes de Sherman, también intenta expresar la verdad de la pose. Esto crea una dialéctica, presente de una manera más poderosa en sus primeros trabajos. Como veremos, en su última obra la artista sucumbe al rencor y a una visión negativa de la mujer. Sherman conjuga la verdad y el artificio al mismo tiempo. Hace hincapié en el momento que surge cuando una mujer ya no sabe si está interpretando un papel o revelando su propio ser.
La colección de fotogramas de Sherman implica, de un modo bastante obvio, una redirección imaginaria de la mujer en una sociedad gobernada por hombres. Sorprendentemente y de un modo muy efectivo, mantiene el decoro en los fotogramas de pequeñas dimensiones por los que es más conocida. Pero la modestia tiene un precio. La artista interpreta a su género de modo que llama la atención sobre el papel subordinado de la mujer. A partir de los años ochenta Sherman evoluciona como "fotografista". La conciencia de la subordinación se convierte en impulso para una serie de fotografías cuyo contenido destila una rabia abrumadora, como si la imagen encantadora que adoptó en sus primeros trabajos quisiera vengarse de la acusación de que las mujeres interpretan su femineidad para agradar a los hombres
Dada la enorme diferencia entre su primer trabajo y sus últimos esfuerzos, resulta necesario separar ambas etapas como mejor podamos. A pesar de la astucia evidente con la que Sherman interpreta el papel protagonista en sus primeras colecciones de fotogramas, estos contienen la inocencia de la juventud; es joven y atractiva, así que las fotografías que toma de sí misma agradan desde el punto de vista erótico y al mismo tiempo, de manera implícita, resultan edificantes. En las propias imágenes de pequeñas dimensiones en blanco y negro al comienzo de la exhibición del Museo de Arte moderno se aprecia el alcance del mencionado equilibrio.
En general las fotografías funcionan como alternativas a lo ordinario, ese ser pedestre en el que la mayoría nos apoyamos para pasar los días. Hay una fotografía extraordinariamente sexi, Fotograma sin título#13 (1978) que muestra a una rubia y voluptuosa Sherman cogiendo un libro de arte del estante de una biblioteca. A pesar de que sostiene el libro, su mirada no está en el estante sino que se dirige hacia algo que no podemos ver. Su cabello aparece derramado sobre su frente, mientras una cinta de pelo trata de mantenerlo en orden. Aunque no es una fotografía para Playboy, sí posee una atracción genuina al mostrar el contorno (vestido) del cuerpo de Sherman. La falta de espontaneidad, la certeza de que se ha posado para la foto, introduce la noción de artificio, que extrañamente contiene al mismo tiempo cierto sentimiento de autenticidad.
Una de las diferencias más importantes entre Nan Goldin, la otra fotógrafa americana, y Sherman radica en que la llamada autenticidad de Goldin es consecuencia de una realidad producida por su propio interés en el sexo, mientras que Sherman es una artista cuyas recreaciones dan como resultado algo mucho más creíble. El aura de fantasía de Sherman nos lleva de alguna manera a aceptar su contrario, es decir, aceptar que lo que vemos es real. Esto puede ocurrir porque estamos tan acostumbrados a ver fotogramas que los consideramos como algo más real que la propia realidad que nos circunda. La transformación resulta básica en la personalidad artística de Sherman. Transforma su ropaje psicológico desde una ingenuidad supuestamente inocente hasta las imágenes que muestran, en un proceso de enojo ascendente, a una mujer cuyas interpretaciones alcanzan una ferocidad prácticamente mitológica.
Primeros trabajos
Sus primeros trabajos atestiguan un erotismo más sencillo. Fotograma sin título#14 (1978) presenta a Sherman con un vestido negro y collar de perlas en una habitación con un tocador y una mesa. Vemos la espalda de Sherman y un reflejo de la mesa, con un vaso de vino y una silla, en el espejo directamente detrás de ella. Su aspecto, intensificado por su mano apoyada en la mejilla, parece alerta, incluso ligeramente aprensivo. De nuevo su mirada se dirige hacia alguien o algo que no vemos. Su atractivo físico define la fotografía, en modo que hace justicia con los amoríos de las películas hechas una o dos generaciones antes que sus fotogramas. Las poses románticas se incluyen en un buen número de sus primeras fotos, pero no abruman al espectador. Forman parte de un conjunto de posibilidades emocionales capturadas en el momento en que expresan la femineidad sin resaltar necesariamente el feminismo. Debido a que carecen de ideología en sentido tradicional, tratan más sobre los sentimientos, sobre la psicología. Por lo tanto no pertenecen al arte más politizado de su época, aunque quede claro que los asuntos que trata pertenecen a la personificación del género, visto por una mujer interpretando para el placer de los hombres.
La imaginería en sí misma está aislada, ya que Sherman aparece casi siempre sola en las fotografías, lo cual intensifica y acentúa las circunstancias mórbidas de no tener amigos o familiares con los que interactuar. Sin embargo el acompañamiento por otra persona echaría por tierra el aislamiento mítico de la mayoría de las fotografías, que después de todo existen como demostración del artista alienado, posmoderno. Encontramos cierta resistencia en estas imágenes que van más allá de los estilizados accesorios de la coquetería, hacia un lugar donde ocurre algo más profundo. Aunque muchas de estas fotos tratan sobre las emociones, en muchas de ellas el afecto es falso, señalando de alguna manera las consecuencias, básicamente irreales o surreales, de la supuesta verdad de la cámara. Al estar hablando de las imágenes de una mujer joven, deducimos con facilidad que aún no habían hecho mella en ella las penalidades de la experiencia. Esto significa que el arte –el arte de las fotografías- es suficiente para rescatar al ser que se tornaría tan airado en su proceso de maduración. La razón de que esto ocurra parece tener pocas explicaciones o justificaciones. Simplemente es así. La experiencia de sus últimas fotos, decidida como está a interpretar a la mujer desde una óptica muy severa, no deja pistas para que su público pueda entender su trabajo. Es como si, tras la fealdad de sus vaginas de goma o bajo el maquillaje de las sexys rubias de bote, todavía cupiera una indignación más grande. ¿Qué le haría a Sherman trabajar de este modo?
ARTIFICIALIDAD:
Las fotografías más lóbregas se dan a finales de los ochenta y principios de los noventa: son espantosas y grotescas. Hay una brecha enorme entre sus fotogramas y los trabajos hechos con partes del cuerpo sintéticas. La fealdad deliberada en el arte tiene una larga historia, sin embargo en el caso de Sherman la desfiguración es tan extrema que de alguna manera pierde la capacidad de sorprender. Sherman está sobreactuando al mostrar su sentido del decoro destrozado, donde las imágenes se convierten en ejemplos de una malformación extrema, hasta el punto de que ya no son terroríficas sino absurdas.
Siempre ha existido un componente surreal en su sensibilidad –los fotogramas invierten la expectación al sugerir una realidad que finalmente es producto de la imaginación-. La imagen de un par de traseros con enormes furúnculos –Sin título#177 (1987)- quiere deliberadamente ofender nuestra idea de la dignidad física, nuestra propia dignidad, así como la de la gente en general. Mucha de la fuerza estética de Sherman proviene de la idea de que nosotros también formamos parte de la debacle general de la humanidad, aunque resulte fácil distanciarse de estas fotografías alienadas y ordinarias.
A pesar del mal gusto casi cómico de las fotos, queda claro que se basan más en la construcción de la imaginación de Sherman, que en revelaciones de su psique. En el primer caso, Sherman apenas muestra su cuerpo en estas imágenes, por lo tanto es difícil afirmar que está hablando sobre ella. Y en el segundo, el uso de partes artificiales contribuye a una lectura distanciada de su significado. Aun así, la piel ulcerosa y el extremismo sexual de estas imágenes nos lleva a la pregunta del por qué alguien querría siquiera mirarlas, incluso teniendo en cuenta que se basan en lo absurdo de la condición humana, concretamente de la mujer. En Sin título#250 (1992) el rostro de una vieja y horrorosa mujer, con unos cuantos pelos rubios sintéticos que salpican una cabeza prácticamente calva, mira directamente al espectador. Los brazos que sostienen la cabeza están claramente hechos de madera, mientras los pechos con unos pezones rojos enormes y un vientre embarazado conducen a una enorme vagina sin piernas. El cuerpo descansa sobre marañas de pelo, y resulta extremadamente desagradable de afrontar, como si Sherman estuviera decidida a que esta fase de su trabajo tuviera una función de catarsis de alguna clase. Pero la monstruosidad de estas partes no molestan tanto, más bien resultan ridículas, una cualidad que Sherman investiga a lo largo de su carrera.
Uno no puede imaginar trabajo más distante del de sus inicios que la hizo famosa. Cuando tenía 20 años parecía haber resuelto el eterno dilema de la mujer, forzada como está a interpretar su género. Hay un grupo de fotos de los ochenta en los que Sherman representa, en color, una gran variedad de poses: la idea parece haber sido tomada de los fotogramas cinematográficos, casi todo su trabajo posterior debe su tenacidad y poderío a las innovaciones de su primer proyecto, pero con un ligero sentimiento de acritud que después se convertiría en auténtica furia. En una estupenda imagen, Sin título#119(1983), Sherman se retrata como una cantante de medio pelo, lleva pendientes de plástico de los que cuelgan perlas artificiales, los brazos extendidos y la boca completamente abierta. Carece del desprecio de género de otras fotografías del mismo periodo, razón por la cual resulta más sugerente. Se trata de una representación de tipo conmovedor en la que el papel que interpreta no es alienante sino que más bien apacigua a través de cierta vulnerabilidad medio absurda. Otra imagen de 1984, Sin título#132, nos muestra a Sherman en un traje a rayas rojas y amarillas, con un cigarrillo en su mano izquierda y una lata de cerveza en la derecha. Su rostro, aunque parcialmente ensombrecido, parece asustado a pesar de su sonrisa a medias. De nuevo se trata de una imagen de una vulnerabilidad evidente, aunque empieza a configurarse la idea de la desfiguración física como muestra de angustia psíquica o a un nivel más amplio, de penuria cultural. El público de Sherman no sabe las razones de este cambio, puede simplemente que el artista se haya cansado de mantener una pose de buena persona, ya que su incidencia en lo grotesco comienza ya en 1985, cuando en una imagen Sherman se apropia de una peluca de hombre y un hocico de cerdo a la luz del atardecer.
TRANSGRESIÓN
Desde el punto de vista de la conducta, la tensión entre la Cindy Sherman buena y la mala demuestra que la interpretación de distintos papeles tiene consecuencias, no solamente para el espectador sino también para la propia artista.
La transgresión tiene lugar para recordarnos el valor del performance, que desde mediados de los años ochenta hasta los primeros noventa llega a ser abiertamente absurdo, caricaturizado hasta el punto de convertirse en ridículo. A finales de los años ochenta, Sherman incorpora la imaginería de los grandes maestros, imaginería renacentista que se apoya en la desfiguración como una manera de censurar la autoridad de la historia del arte.Sin título#215 (1989) nos muestra a un joven sacerdote ataviado con la vestimenta de su profesión; vemos de nuevo una mirada insulsa en la distancia, el símbolo de la cruz apenas visible en el dobladillo del faldón. En otro trabajo, Sin título#183 (1988) Sherman interpreta el papel de una matrona renacentista, su profundo escote permite apreciar unos enormes pechos falsos. Su vestido color marfil contrasta con los labios rojos de Sherman, que es la única nota de color en la fotografía. En Sin título#224(1990), emula a Caravaggio. Una engalanada Sherman ataviada con toga sostiene uvas verdes en la mano y frente a ella sobre una mesa hay un racimo de uvas rojas. Estas descripciones nos dan una idea de cuan variados son los disfraces de Sherman, así como de su capacidad creativa, cuyo repertorio parece infinito.
Para el año 2000, Sherman deja claro que el travestismo y la ironía profunda serían sus grandes temas, fundamentados en su relación con la figura y la psique de la mujer. Las imágenes de payasos que utiliza desde el comienzo del nuevo siglo y hasta la mitad de la primera década del siglo XXI resultan agresivas y espeluznantes hasta el punto de parecer peligrosas. Su exagerado maquillaje en colores primarios coincide con miradas de auténtica malevolencia. Dicha aspereza domina su trabajo de la pasada década, decidido a atacar de modo implacable la dignidad de la mujer. Se trata de una misoginia de un tipo extraño, perpetuada por una mujer que aparentemente duda del valor de las mujeres. Una de las imágenes más horribles parte, de nuevo, del sentimiento de vulnerabilidad. Por ejemplo, en una fotografía del año 2000, Sin título#359, vemos a una mujer de mediana edad con maquillaje blanco alrededor de su ojos y encima de los labios las pestañas falsas son tan altas que le llegan hasta la frente. Decora su cuello un variopinto conjunto de cadenas. La artista, con labios rojos, mira a la cámara con la determinación de agradar. Esta emoción se repite imagen tras imagen, lo que inevitablemente, a pesar de la evidente brillantez de Sherman en crear nuevas formas, se ríe de la ansiedad de la mujer provocada al reconocerse como un objeto que ya no resulta atractivo al hombre. El grotesco maquillaje distribuido en gruesas capas la convierten en una caricatura aparentemente quemada por el sol, que llega al extremo de resultar irreconocible.
Trabajo actual
En sus trabajos más recientes, los últimos cinco años, vemos a una artista entrada en años que continúa agitando el arquetipo de la mujer en sociedad. La idea de una belleza pasada, muerta en la actualidad, aparece con frecuencia; la vulnerabilidad en muchas de sus fotografías llega a ser repugnante. Por ejemplo en Sin título#465 (2008), Sherman se presenta como una gran dama en las afueras de Central Park; lleva un vestido palabra de honor y un collar de perlas. Se ve también un pendiente enorme. Podemos apreciar las arrugas bajo el colorete de sus mejillas y sobre los labios. Su cuerpo girado a medias apunta intensamente al espectador, con tal mirada que a su lado la de Medusa parecería inofensiva. La idea de amargura no parece muy lejana y el papel que representa Sherman resulta desagradable; está muy enfadada y dispuesta a comunicar ese enfado.
En otra fotografía, Sin título#476 (2008), Sherman interpreta el papel de una mujer rica vestida con un traje largo de color rojo, sentada con un perrito terrier gris en su regazo. Su peluca es plateada y tras ella vemos una vista marítima completamente banal. La imagen nos muestra a una persona atrapada en el propio confort de su éxito y tal vez no sea ir demasiado lejos si apreciamos un cierto toque alegórico aplicable a nosotros y a la propia artista. Aparte de sus disfraces imaginarios, Sherman no demuestra gran interés en el arte, sin embargo en su trabajo de los dos últimos años se ha manifestado en contra del trabajo gráfico, normalmente de la naturaleza. En una imagen sin título de 2010 lleva un disfraz que recuerda vagamente a un cosaco, un ojo negro y tres cadenas unidas colgando de su chaqueta. Esto sucede en el lado izquierdo de la fotografía, en el derecho la vemos con un largo cabello moreno y ataviada con una falda marrón hasta los pies. Tras ambas figuras encontramos la impresión de un camino decorado con árboles a ambos lados. La imagen es en blanco y negro. En ambos casos, la mirada de Sherman está perdida, no registra nada mientras mira al espectador.
En una construcción similar, también de 2010, la figura de la izquierda lleva una túnica transparente sobre un vestido azul con flores blancas. En la fotografía parece cansada, visiblemente envejecida. En el lado derecho, Sherman lleva un disfraz color carne que ofrece la desnudez como una especie de entretenimiento absurdo: el disfraz incluye unos pechos desmesurados y un triángulo de pelo púbico. Con un corte de pelo de chico de los recados, Sherman sostiene una espada descaradamente falsa. Tras la figura hallamos lo que parece ser una escena del siglo XIX, un lago rodeado por un frondoso bosque. La imaginería gráfica vuelve a estar en blanco y negro. La idea del mito toma cuerpo, nos damos cuenta de que Sherman pretende representar una mitología risible del ser.
En estos últimos trabajos, parece como si Sherman no estuviera terminando con estrépito, sino más bien con un quejido. Pero Sherman no ha llegado todavía a los sesenta años, así que sería prematuro caracterizar esto como su despedida del arte. En su prodigiosa producción de cerca de 500 imágenes la artista captura la historia de la femineidad sin sucumbir a ideologías. O eso parece. Bajo los disfraces, bajo esa mirada imperiosa, parece que las ideas de Sherman sobre el deseo de ser amada y aceptada poseen cierta cualidad subversiva. Las mujeres aprenden la clase de comportamiento del que Sherman se mofa, no es como si estuvieran genéticamente preparadas para agradar. En cierto sentido, este arte se radicaliza por la idea de vulnerabilidad que lleva consigo, por lo tanto no puede decirse que Sherman se limita a disfrazarse. Ella interpreta y personifica al mismo tiempo el comportamiento de su género. Se trata de un teatro que llega a ser tan auténtico que el realismo político surge dentro de la fotografía. No se trata de la obviedad del arte de Sherman, sino de su contenido más profundo. De hecho es algo que el espectador debe intuir, ya que el contexto nunca queda claro. El enfado del que las fotografías de Sherman están imbuidas es mucho más accesible, sin embargo es un efecto distante. La Sherman real se encuentra en algún lugar entre la charlatanería de sus disfraces y la vulnerabilidad de sus míticos personajes, alguien que pertenece claramente a los anales de la historia del arte contemporáneo.
Bibliografía
Elcuerpo mutilado (la angustia de muerte en el arte) José Miguel G. Cortés.
Mujeres artistas (2005) Thaschen GmbH ISBM 978-3-8228-4120-4
(2007) Cindy Sherman: A Play of Selves.Hatje Cantz. ISBN 978-3-7757-1942-1.
(2006) Cindy Sherman: Working Girl.Contemporary Art Museum, St. Louis. ISBN 978-0-9712195-8-8.
(2004) Cindy Sherman: Centerfolds. Skarstedt Fine Art. ISBN 0-9709090-2-0.
(2003) Cindy Sherman: The Complete Untitled Film Stills. Museum of Modern Art. ISBN 0-87070-507-5.
(2002) Elisabeth Bronfen, et al. Cindy Sherman: Photographic Works 1975-1995 (Paperback). Schirmer/Mosel. ISBN 3-88814-809-X.
(2001) Early Work of Cindy Sherman. Glenn Horowitz Bookseller. ISBN 0-9654020-3-7.
(2000) Leslie Sills, et al. In Real Life: Six Women Photographers. Holiday House. ISBN 0-8234-1498-1.
(2000) Amanda Cruz, et al. Cindy Sherman: Retrospective (Paperback). Thames & Hudson, ISBN 0-500-27987-X.
(1999) Essential, The: Cindy Sherman. Harry N. Abrams, Inc., ISBN 0-8109-5808-2.
(1999) Shelley Rice (ed.) Inverted Odysseys: Claude Cahun, Maya Deren, Cindy Sherman. MIT Press. ISBN 0-262-68106-4.
Filmografía
Cindy Sherman [videorecording]: Transformations. by Paul Tschinkel; Marc H Miller; Sarah Berry; Stan Harrison; Cindy Sherman; Helen Winer; Peter Schjeldahl; Inner-Tube Video. 2002, 28 minutes, Color. NY: Inner-Tube Video.
''Office Killer (1997) Directora: Cindy Sherman | Escritores: Tom Kalin, Elise MacAdam, Elise MacAdam, Cindy Sherman | Elenco: Carol Kane, Molly Ringwald, Jeanne Tripplehorn. Duración: 82 min, 95 min edición Argentina. Video color pornografíca
Referencias
Enlaces externos
Directores de cine de Estados Unidos
Miembros de la Academia Estadounidense de las Artes y las Letras
Longislandeses
Fotógrafos retratistas
Fotógrafas de Estados Unidos
Artistas contemporáneos
Premio internacional de la Fundación Hasselblad
Becarios MacArthur
Directoras de cine de Estados Unidos
Premio Wolf en Artes | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,021 |
\section{Conjugacy classes density}
\paragraph{Preliminaries.}
Invertible measure-preserving transformation $T$ acting on a standard non-atomic probability space\footnote{Standard non-atomic probability space is a probability
space isomorphic $mod$ $0$ to unit interval with Lebesgue measure. We consider transformations and other relations equal if they differ on zero measure set.}
$(X, \Sigma, \mu)$ is called {\em mixing} if for any measurable sets $A$, $B$
$$\lim_{n\to\infty}\mu(T^nA\cap B)=\mu(A)\mu(B).$$
Let $\{A_i\}$ be a countable collection of sets generating $\sigma$\nd algebra $\Sigma$.
Each one of the metrics
$$d(T,S) = \sum_{i\in\mathbb{N}}\frac 1 {2^i}(\mu(TA_i\triangle SA_i) + \mu(T^{-1}A_i\triangle S^{-1}A_i))$$
and
$$a(T,S) = \sum_{i,j\in\mathbb{N}}\frac 1 {2^{i+j}}|\mu(TA_i\cap A_j) - \mu(SA_i\cap A_j) |$$
generates weak topology in the space~$\mathcal M$ of mixing transformations.
None of these metrics is complete in~$\mathcal M$. To make~$\mathcal M$ a complete metric space
Tikhonov introduced the metric
$$\tau(T,S) = d(T,S) + \sup_{i\in\mathbb{Z}} a(T^n, S^n)$$
in his paper~\cite{tikhonov0}. This metric generates a different topology called {\em leash-topology}. The collection of neighborhoods of form
$$\mathcal U(T, q, \varepsilon) = \{S\in\mathcal M\mid\forall n\in\mathbb{Z}\;\forall A,B\in q\;|\mu(T^nA\cap B) - \mu(S^nA\cap B)|<\varepsilon\}$$
form a base of this topology. Each neighborhood of this form is defined by its center $T$, a collection $q$ of measurable sets and a positive number $\varepsilon$.
One can explore generic properties of mixings in the space~$\mathcal M$, equipped with the metric $\tau(T,S)$.
A subset of metric space is called a {\em $G_\delta$ set} if it can be represented as a countable intersection of open sets.
A superset of a dense $G_\delta$ set is called {\em residual}. If a set of transformations having some property is residual, the property is called {\em generic}.
Term ``generic'' explains itself with the following facts: countable intersection of residual sets is residual, a superset of a residual set is residual.
The main result of this paper is
\begin{theorem}\label{main}
Conjugacy class of any mixing transformation $S$ is dense in~$\mathcal M$.
\end{theorem}
\paragraph{Bernoulli shift with entropy $1$.}
Let us define a mixing called {\em Bernoulli shift with entropy\footnote{For notational convenience we use binary entropy function. If one uses natural logarithm, entropy of
this transformation would be $\ln 2$}~$1$}.
Its phase space $X$ is a Cartesian product of countably many copies of space $\{0, 1\}$:
$$X=\{0,1\}^\mathbb{Z}, \mu(\{0\})=\mu(\{1\})=\frac 1 2.$$
$X$ is a standard non-atomic probability space. Its elements are bidirectionally infinite zero-one sequences, and the transformation acts on them by right shift.
We will write points of the space as $$x=(\dots x_{-2}, x_{-1}, x_0, x_1, x_2, \dots).$$
Let us denote the sets $\{x\in X\mid x_0 = 0\}$ and $\{x\in X\mid x_0 = 1\}$ as $D_0$ and $D_1$ respectively. Let us denote the partition $X=D_0\sqcup D_1$ as $\xi$.
This partition is generating: the intersection $$\bigvee_{i\in\mathbb{Z}}T^i\xi$$ of its images is the partition into points.
This implies every measurable set $C\subset X$ can be approximated by sets $\{C_k\}_{k\in\mathbb{N}}$, where $C_k$ is measurable with respect to $$\bigvee_{|i|\le k}T^i\xi.$$
Tikhonov showed~(\cite{tikhonov1}) that Bernoulli shifts with entropy~$1$ are dense in~$\mathcal M$.
It follows from a more general statement by Tikhonov: transformations conjugate to any fixed Cartesian product are dense in $\mathcal M$.
Bernoulli shift is always a Cartesian product of another Bernoulli shifts with lesser entropy.
Thus, to prove that conjugacy class of any mixing transformation is dense in $\mathcal M$ it is enough to show that
in every neighborhood of any Bernoulli shift with entropy $1$ there exists an element of this conjugacy class.
\paragraph{Passing to smaller neighborhoods.}
Let us fix $T$~--- a Bernoulli shift with entropy~$1$, and its neghtbourhood $\mathcal U(T, q, \varepsilon)$.
Let us denote the elements of the collection $q$ by $A_1, A_2, \dots A_n$.
For every $A_j$ let $\tilde A_j$ be measurable with respect to some finite intersection
$$\bigvee_{|i|\le k_j}T^i\xi$$
and let $\tilde A_j$ approximate $A_j$ with precision $\frac\varepsilon 5$.
Denote the collection $\{\tilde A_1, \tilde A_2, \dots \tilde A_n\}$ as $\tilde q$, and the maximum of $k_j$ as $k$.
Every~$\tilde A_i$ is measurable with respect to $$\bigvee_{|i|\le k}T^i\xi,$$ and for every $j$ the sets $A_j$ and $\tilde A_j$ are close to each other:
$\mu(\tilde A_j\triangle A_j)<\frac\varepsilon 5$.
Let us show that $$\mathcal U(T, \tilde q, \frac\varepsilon 5)\subset\mathcal U(T, q, \varepsilon).$$
Indeed, if $P\in\mathcal U(T, \tilde q, \frac\varepsilon 5)$, then for any $r, s$ and $m$
$$|\mu(P^m\tilde A_r\cap\tilde A_s) - \mu(T^p\tilde A_r\cap \tilde A_s)|<\frac\varepsilon 5.$$
This implies that for any $r, s$ and $m$
\begin{multline*}
|\mu(P^mA_r\cap A_s) - \mu(T^mA_r\cap A_s)|\le\\\le
|\mu(P^mA_r\cap A_s) - \mu(P^m\tilde A_r\cap A_s)| + |\mu(P^m\tilde A_r\cap A_s) - \mu(P^m\tilde A_r\cap\tilde A_s)| +\\+
|\mu(P^m\tilde A_r\cap\tilde A_s) - \mu(T^m\tilde A_r\cap \tilde A_s)| +\\+
|\mu(T^m\tilde A_r\cap\tilde A_s) - \mu(T^m\tilde A_r\cap A_s)| + |\mu(T^m\tilde A_r\cap A_s) - \mu(T^mA_r\cap A_s)|\le\\\le
\frac\varepsilon 5 + \frac\varepsilon 5 + \frac\varepsilon 5 + \frac\varepsilon 5 + \frac\varepsilon 5 =\varepsilon,
\end{multline*}
that is $P\in\mathcal U(T, q, \varepsilon)$.
Let us consider now a collection $\hat q$, consisting of all atoms of partition $$\bigvee_{|i|\le k}T^i\xi.$$
Every atom is of the form $$B_{(b_{-k}, b_{-k+1}, \dots b_k)} = \bigcap_{|i|\le k} T^iD_{b_i} =
\{x\in X\mid(x_{-k}=b_{-k}, x_{-k+1}=b_{-k+1}, \dots x_k=b_k\}$$
Let us show that $$\mathcal U(T, \hat q, \frac\varepsilon{5\cdot 2^{4k+2}})\subset\mathcal U(T, \tilde q, \frac\varepsilon 5).$$
Indeed, let $P\in\mathcal U(T, \hat q, \frac\varepsilon{5\cdot 2^{4k+2}})$, that is for all $u, v$ and $m$
$$|\mu(P^mB_u\cap B_v) - \mu(T^mB_u\cap B_v)|<\frac\varepsilon{5\cdot 2^{4k+2}}.$$
Here $u$ and $v$ are any one-zero sequences of length $2k+1$.
To estimate the difference $|\mu(P^m\tilde A_r\cap\tilde A_s) - \mu(T^m\tilde A_r\cap\tilde A_s)|$ notice that $\tilde A_r$
can be pieced out of some $C_{u_1}, C_{u_2}, \ldots\in\hat q$, and the number of the pieces cannot exceed $2^{2k+1}$.
Similarly decompose $\tilde A_s$ into pieces $C_{v_1}, C_{v_2}, \ldots\in\hat q$.
\begin{multline*}
|\mu(P^m\tilde A_r\cap\tilde A_s) - \mu(T^m\tilde A_r\cap\tilde A_s)| = \Bigl|\sum_{l,w}\mu(P^mC_{u_l}\cap C_{v_w}) - \sum_{l,w}\mu(T^mC_{u_l}\cap C_{v_w})\Bigr|\le\\\le
\sum_{l,w}|\mu(P^mC_{u_l}\cap C_{v_w}) - \mu(T^mC_{u_l}\cap C_{v_w})|<\sum_{l,w}\frac\varepsilon{5\cdot 2^{4k+2}}\le\\\le
2^{2k+1}\cdot 2^{2k+1}\cdot \frac\varepsilon{5\cdot 2^{4k+2}}=\frac\varepsilon 5.
\end{multline*}
\paragraph{Images almost-independence.}
Recall $S$ is an arbitrary mixing.
Let $S$ act on standard non-atomic probability space~$Y$. Let us show that in the neigbourhood $\mathcal U(T, \hat q, \frac\varepsilon{5\cdot 2^{4k+2}})$
there is a transformation $V$ acting on $X$ and conjugate to $S$. According to~\cite{bashtanov} for every $\delta>0$ there exists such a set $A\subset Y$ of measure~$\frac 1 2$ that
sets $T^mA, m\in\mathbb{Z}$ are collectionwise $\delta$\nd independent. Condition of collectionwise {\em $\delta$\nd independence} of sets $E_1, E_2, \dots$ means that
the measure of any finite intersection of form
\begin{equation}
\label{indep}
E_{m_1}\cap E_{m_2}\cap\dots E_{m_p}
\end{equation}
differs from $$\prod_{i=1}^p\mu(E_{m_i})$$ less than by $\delta$ in assumption that $m_i$ are different.
To build such a set in~\cite{bashtanov} author uses the method offered by V.~V.~Ryzhikov in~\cite{ryzhikovPairwise}:
one builds an approximating sequence of Rokhlin castles, random union of cells of sufficiently big castle satisfies the conditions with positive probability.
Let us call sets $E_1, E_2, \ldots \subset Y$ {\em well collectionwise $\delta$\nd independent}, if
the measure of any finite intersection of form
\begin{equation}
\label{full_indep}
E_{m_1}\cap E_{m_2}\cap\dots E_{m_{p_0}}\cap(Y\setminus E_{n_1})\cap(Y\setminus E_{n_2})\cap\dots(Y\setminus E_{n_{p_1}})
\end{equation}
differs from $$\prod_{i=1}^{p_0}\mu(E_{m_i})\prod_{i=1}^{p_1}\mu(Y\setminus E_{n_i})$$ less than by $\delta$ in assumption that none of $m_i$ and $n_i$ coincide. It is not hard to show that if a collection of sets
is $\delta$\nd independent, than every its finite subcollection of cardinality $c$ will be well collectionwise $c\delta$\nd independent. This follows from the fact that
any intersection of form \eqref{full_indep} and length~$c$ can be expressed by
$c$ intersections of form~\eqref{indep} using operations of disjoint union and set-theoretical difference.
Notice that using the methods of~\cite{ryzhikovPairwise, bashtanov} one can directly prove well collectionwise $\delta$\nd independence of all images of the set $A$.
\paragraph{Building the conjugate transformation.}
Let us take $\delta = \frac 1{4k+2}\cdot\frac\varepsilon{15\cdot 2^{4k+2}}$.
Then every $4k+2$ images of set $A$ will be well $\frac\varepsilon{15\cdot 2^{4k+2}}$\nd independent.
Denote $A$ as $F_0$, $X\setminus A$ as $F_1$, and the partition $Y = F_0\sqcup F_1$ as $\eta$. Consider atoms of partitions $$\eta_k = \bigvee_{|i|\le k}T^i\eta.$$
The measure of each of them differs from $\frac 1{2^{2k+1}}$ less than by $\frac\varepsilon{15\cdot 2^{4k+2}}$.
In $X$ there exists a partition $$\xi_k = \bigvee_{|i|\le k}T^i\xi,$$ and the measure of each its atom is exactly $\frac 1{2^{2k+1}}$.
The desired transformation is $V = Q^{-1}SQ$, where $Q\colon X\to Y$ is an arbitrary measure-preserving invertible transformation, that maps atoms of partition
$\xi_k$ onto the correspondent atoms of $\eta_k$ with a gap less than $\frac\varepsilon{15\cdot 2^{4k+2}}$ for each atom.
\paragraph{Estimates for the transformation built.}
Let us prove that the transformation $V$ is situated in the neighborhood $\mathcal U(T, \hat q, \frac\varepsilon{5\cdot 2^{4k+2}})$.
For this it is necessary for every $u, v$ and $m$ the following condition to satisfy:
$$|\mu(V^mB_u\cap B_v) - \mu(T^mB_u\cap B_v)|<\frac\varepsilon{5\cdot 2^{4k+2}}.$$
Let us represent $B_u$ and $B_v$ in such a form:
$$B_u = \bigcap_{|i|\le k} T^iD_{u_i},\quad B_v = \bigcap_{|i|\le k} T^iD_{v_i}.$$
Then $T^mB_u\cap B_v$ and $V^mB_u\cap B_v$ will take form
$$\bigl(\bigcap_{|i|\le k} T^{i+m}D_{u_i}\bigr)\cap\bigl(\bigcap_{|i|\le k} T^iD_{v_i}\bigr)
\quad\mbox{and}\quad
\bigl(\bigcap_{|i|\le k} V^mT^iD_{u_i}\bigr)\cap\bigl(\bigcap_{|i|\le k} T^iD_{v_i}\bigl)$$
respectively. Estimate the difference of measures:
\begin{multline*}
\biggl|\mu\Bigl(\bigl(\bigcap_{|i|\le k} T^{i+m}D_{u_i}\bigr)\cap\bigl(\bigcap_{|i|\le k} T^iD_{v_i}\bigr)\Bigr) -
\mu\Bigl(\bigl(\bigcap_{|i|\le k} V^mT^iD_{u_i}\bigr)\cap\bigl(\bigcap_{|i|\le k} T^iD_{v_i}\bigr)\Bigr)\biggr| \le\\\le
\biggl|\mu\Bigl(\bigl(\bigcap_{|i|\le k} T^{i+m}D_{u_i}\bigr)\cap\bigl(\bigcap_{|i|\le k} T^iD_{v_i}\bigr)\Bigr) -
\mu\Bigl(\bigl(\bigcap_{|i|\le k} S^{i+m}F_{u_i}\bigr)\cap\bigl(\bigcap_{|i|\le k} S^iF_{v_i}\bigr)\Bigr)\biggr| +\\+
\biggl|\mu\Bigl(\bigl(\bigcap_{|i|\le k} S^{i+m}F_{u_i}\bigr)\cap\bigl(\bigcap_{|i|\le k} S^iF_{v_i}\bigr)\Bigr) -
\mu\Bigl(V^m\bigl(\bigcap_{|i|\le k} T^iD_{u_i}\bigr)\cap\bigl(\bigcap_{|i|\le k} T^iD_{v_i}\bigl)\Bigl)\biggl|.
\end{multline*}
Let us estimate the first item. Its left side is some intersection of $D_0$, $D_1$ and their images under action by powers of $T$, not more than
$4k+2$ sets are intersected.
They are collectionwise independent, or, what is the same, well collectionwise $0$\nd independent.
The right side is the similar intersection of $F_0$, $F_1$ and their images under action by powers of $S$. They are well
collectionwise $\frac\varepsilon{15\cdot 2^{4k+2}}$\nd independent.
Hence the difference between the left and the right sides does not exceed $\frac\varepsilon{15\cdot 2^{4k+2}}$ in modulus.
It can happen that some sets of the left side coincide. In this case the correspondent sets on the right also coincide and we have the intersection of less number of sets.
Also there can be an intersection of form $$\cdots\cap T^zD_0\cap\cdots\cap T^zD_1\cap\cdots$$ on the left. Then there is a similar intersection
$$\cdots\cap S^zF_0\cap\cdots\cap S^zF_1\cap\cdots$$
on the right. In this case both left and right sides equal $0$.
Let us estimate the second item.
\begin{multline*}
\biggl|\mu\Bigl(\bigl(\bigcap_{|i|\le k} S^{i+m}F_{u_i}\bigr)\cap\bigl(\bigcap_{|i|\le k} S^iF_{v_i}\bigr)\Bigr) -
\mu\Bigl(V^m\bigl(\bigcap_{|i|\le k} T^iD_{u_i}\bigr)\cap\bigl(\bigcap_{|i|\le k} T^iD_{v_i}\bigl)\Bigl)\biggl|=\\=
\biggl|\mu\Bigl(S^m\bigl(\bigcap_{|i|\le k} S^iF_{u_i}\bigr)\cap\bigl(\bigcap_{|i|\le k} S^iF_{v_i}\bigr)\Bigr) -
\mu\Bigl(S^mQ\bigl(\bigcap_{|i|\le k} T^iD_{u_i}\bigr)\cap Q\bigl(\bigcap_{|i|\le k} T^iD_{v_i}\bigl)\Bigl)\biggl|
\end{multline*}
Each of the sets $$\bigcap_{|i|\le k} S^iF_{u_i}\mbox{ and }\bigcap_{|i|\le k} S^iF_{v_i}$$ on the left differs from the corresponding set
$$Q\bigcap_{|i|\le k}T^iD_{u_i}\mbox{ or }Q\bigcap_{|i|\le k}T^iD_{v_i}$$ on the right by a set of measure less than ~$\frac\varepsilon{15\cdot 2^{4k+2}}$.
Therefore the difference between the left and the right sides is not more than $\frac{2\varepsilon}{15\cdot 2^{4k+2}}$.
Sum of the items is less than $\frac\varepsilon{15\cdot 2^{4k+2}} + \frac{2\varepsilon}{15\cdot 2^{4k+2}} = \frac\varepsilon{5\cdot 2^{4k+2}}$, as was to be proved.
We have built a transformation $V$, conjugate to $S$ and situated in the neighborhood $\mathcal U(T, \hat q, \frac\varepsilon{5\cdot 2^{4k+2}})$, and therefore also in $\mathcal U(T, q, \varepsilon)$.
The theorem is proved.
\section{Genericity of rank\nd $1$}
\paragraph{Preliminaries.}
Let the transformation $T$ act on the space $(X, \Sigma, \mu)$. A partition $\xi$ of form
$$X = E\sqcup TE\sqcup\dots\sqcup T^{n-1}E\sqcup D$$
is called a {\em Rokhlin tower of height $n$}.
Sets $E, TE, \dots T^{n-1}E$ are called levels of the tower, and $D$ is called a remainder.
Let us say that {\em a tower approximates} set $A$ with accuracy $\varepsilon > 0$, if there exists such a union $B$ of its levels,
that $\mu(A\triangle B)<\varepsilon$. Let us say that {\em a sequence of towers approximates} set $A$ with accuracy $\varepsilon > 0$,
if all the towers in the sequence starting from a certain index approximate the set with the specified accuracy.
If there exists such a sequence of towers $\{\xi_i\}_{i\in\mathbb{N}}$ that
for every measurable set $A$ and number $\varepsilon>0$ the sequence $\{\xi_i\}$ approximates $A$ with accuracy $\varepsilon$, then
$T$ is said to be {rank\nd $1$}. Rank\nd $1$ mixing transformations were first introduced by D.~Ornstein in~\cite{ornstein}.
\paragraph{Residuality of the set.}
Let us prove the genericity of rank\nd $1$ in mixings.
\begin{theorem}
The set of rank\nd $1$ mixings is a dense $G_\delta$ subset in $\mathcal M$.
\end{theorem}
Let us fix a countable collection of sets $\{A_j\}$, such that every measurable set $A\subset X$ can be approximated by elements of the collection
(such a collection exists due to the properties of standard probability space).
If a sequence of towers approximate $A_j$ with arbitrary little accuracy, then the transformation is rank\nd $1$.
Let us denote the set of mixings, having a Rokhlin tower approximating the sets $A_1, A_2, \dots A_j$ with accuracy $a$, where $a<\frac 1 k$, as $\mathcal R(j, k)$.
Then the intersection $$\bigcap_{j,k}\mathcal R(j, k)$$
is exactly the set of rank\nd $1$ mixing.
Let us show that every $\mathcal R(j, k)$ is open. Let $S\in\mathcal R(j, k)$. It means that there exists such a tower $\xi$,
that for every $i\in\{1, 2, \dots j\}$ the set $A_i$ differs from some union $B_i$ of tower levels by a set of measure $a<\frac 1 k$.
Let $E$ be the downmost level of tower~$\xi$ and $n$ be its height.
Denote $$b=\frac 1{n^2}\left(\frac 1 k - a\right).$$
Let a mixing $V$ be situated in a neighborhood $\mathcal U(S, \{E, SE, \dots S^{n-1}E\}, b)$.
Consider the set $$\tilde E = E\setminus(VE\cup V^2E\cup\dots\cup V^{n-1}E).$$ It differs from $E$ not more than by measure $(n-2)b$.
By construction of $\tilde E$ it is a downmost level of some tower $\eta$: $$X=\tilde E\sqcup V\tilde E\sqcup\dots\sqcup V^{n-1}\tilde E\sqcup \tilde D.$$
As far as the downmost level of the tower $\eta$ differs from the downmost level of tower $\xi$ not more than by measure $(n-2)b$, the other corresponding levels
of these two towers differ not more than by measure $b+(n-2)b = (n-1)b$ one from another, and the corresponding level unions differ not more than by measure $n(n-1)b$.
A union of levels of tower $\eta$ corresponding to some level union $B_i$ in $\xi$ differs from $B_i$ not more than by measure $n(n-1)b$, so
it differs from $A_i$ not more than by measure $n(n-1)b+a < \frac 1 k$.
We achieved that an arbitrary transformation $S$ is included in $\mathcal R(j, k)$ with some its neighborhood. That is, $\mathcal R(j, k)$ is open,
therefore the set of rank\nd $1$ mixings is a $G_\delta$ set.
Conjugacy class of any rank\nd $1$ mixing is dense in $\mathcal M$, so the set of rank\nd $1$ mixing is residual.
\paragraph{Corollaries.}
As far as rank\nd $1$ is generic for mixing, all the properties of rank\nd $1$ mixing are generic.
Expressly minimal self-joinings of all orders, and all its corollaries: trivial centralizer, primeness and absence of roots (see~\cite{king}).
\section{Remarks}
\paragraph{Approximating by conjugates of a non-mixing transformation.}
In paper~\cite{bashtanov} author uses a more weak property than mixing~--- absence of partial rigidity.
Transformation $T$ is called {\em partially rigid with coefficient $a>0$}, if for every measurable set $A\subset X$
$$\limsup_i\mu(A\cap T^iA) \ge a\mu(A).$$
Let us expand the space $\mathcal M$ of mixings to the space $\mathcal A$ of all invertible measure-preserving transformations.
We will use the same metric $\tau(T, S)$.
It is interesting that in this space there exists such an analog to theorem~\ref{main}:
\begin{theorem}
Fix a transformation $S$, not partially rigid. Then in any neighborhood of any mixing $T\in\mathcal A$ there exists a
transformation, conjugate to~$S$.
\end{theorem}
Proof is analogous. Note that the opposite is true: conjugacy class of transformation $S$ cannot approximate mixings if $S$ is partially rigid.
\paragraph{Direct proof of density of rank one.}
Ryzhikov informed author that he knows another proof that rank\nd $1$ mixings are dense in $\mathcal M$. This proof is based neither on Tikhonov theorem about density of
conjugates to a Cartesian product nor on results \cite{ryzhikovPairwise, bashtanov}.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,094 |
\section{Introduction}
\label{intro}
Suggesting a consistent theory for quantum gravity is an ultimate goal of recent research aiming at unifying quantum mechanics (QM) with the theory of general relativity (GR). The quantum nature of gravity is still an open question in physics. It turns to form an enigma occupying the minds of many physicists for many decades, for instance, so--far there is no scientific explanation for the origin of the gravitational fields and how particles behave inside them! This makes the gravity foundamentally different from the other fources of nature. There were various attempts to reconcile some principles of GR in a quantum framework \cite{Rovelli:1989za,Donoghue:1994dn}. The quantum gravity - on one hand - is conjectured to add new elements to GR and QM. On the other hand, the Einstein field equations combine classical geometry with quantum stress--energy--momentum tensor! For QM, we recall the possible modification in the Heisenberg uncertainty principle due to gravitational effects\footnote{They weren't taken into considration in the original Heisenberg uncertainty principle.}, known as generalized uncertainty princile (GUP) \cite{Tawfik:2014zca,Tawfik:2015rva}. The present work introduces some insights on the possible impacts of GUP on the metric tensor and the geodesic equation and their properties.
Couple decades ago, the line element modification and the gravity quantization have been suggested in litrature \cite{Feoli:1999cn,Capozziello:2000gb,Bozza:2001qm}. A review of these models could be found in refs. \cite{Hess:book,Hess:2020ssc,Tawfik:2020zvf}. An extended class of the metric tensors which are functions of a field of an internal vectors $y^{\alpha}(x)$, $g_{\mu\nu}(x^{\alpha}\cdot y^{\alpha}(x))$, was also discussed in litrature \cite{Oliveira:1985cj}. Accordingly, the origin of the gravitational field of spin-1 massless particle could be determined \cite{Oliveira:1985cj}. Regarding the equivalence principle of gravitationan and enirtial mass in extended gravity and non--geodesic motion, a machian request was scratched \cite{Licata:2016qmz}, where a direct coupling between the Ricci curvature scalar and the matter Lagrangian could be fixed in cosmological observations \cite{Licata:2014xgx}.
The present script aims at tackling the long--standing essential puzzle that the Einstein field equations relate {\it non--quantized} semi--Riemannian geometry expressed in Ricci and Einstein tensors, which are basically depending on the metric tensor $g_{\mu\nu}(x^{\alpha})$, with the {\it full--quantized} stress--energy-momentum tensor $T_{\mu\nu}$ \cite{Stephani:624239}. The approach applied here is the finite minimal length uncertainty obtained from GUP. GUP was inspired by black hole physics, doubly special relativity, and string theory \cite{Tawfik:2014zca,Tawfik:2015rva}. It is worthy highligting that GUP is comparable with the Planck length, where quantum fluctuations in {\it quasi--quantized} manifold likely emerge \cite{Karolyhazy1966,Tawfik:2016uhs,Tawfik:2019dda}.
The modifications in the metric tensor and geodesic equation due to GUP shall be introduced. Accordingly, we believe that the present study offers a theoretical framework for the observations that the universe acceleratingly expands. Alongside forces deriving this type of expansion, such as dark energy \cite{Tawfik:2019dda} and cosmological constant \cite{Peebles:2002gy}, we suggest that it might be also originated to interdependence of GR on QM, especially at the Planck scale.
The present paper is organized as follows. Section \ref{sec:gup} reviews the generalized uncertainly principle and minimal length uncertainty. The discretized metric tensor and its properties shall be discussed in section \ref{sec:st}. The discretized geodesic equation and its properties shall be introduced in section \ref{sec:ge}. Section \ref{sec:cncls} is devoted to the final conclusions.
\section{Generalized uncertainly principle and minimal length uncertainty}
\label{sec:gup}
The Heisenberg uncertainty principle (HUP) is a recipe on how the uncertainties are constrained in the quantum non--commutation relations of length and momentum operators, for instance. This was originally suggested in absence of any gravitational field. Analyzing HUP in gravitational fields comes up with modifications, know as GUP. Such a phenomenological aspect can be originated in black hole physics, doubly special relativity, and string theory \cite{Tawfik:2014zca,Tawfik:2015rva}. Phenomenology because so--far there is no theoretical explanation of the gravitational fields origin making gravity substantially different from the other three forces of nature. A finite minimal length was suggested as \cite{Kempf:1994su},
\begin{eqnarray}
\Delta x\, \Delta p\geq \frac{\hbar}{2} \left[1+ \beta (\Delta p)^2 \right], \label{GUP}
\end{eqnarray}
where $\Delta x$ and $\Delta p$ are length and momentum uncertainties, respectively. $\beta = \beta_0 (\ell_p/\hbar)^2 = \beta_0/ (m_p c)^2$, is the GUP parameter with $\ell_p=\sqrt{\hbar G/c^3}=1.977 \times 10^{-16}~$GeV$^{-1}$ the Planck length and $m_p=\sqrt{\hbar c/G}= 1.22 \times 10^{19}~$GeV$/c^2$ the Planck mass. An upper bound on $\beta_0$ is based on astronomical observations, such as, $\beta_0 \lesssim 5.5 \times 10^{60}$ based on recent gravitational waves observations. From Eq. (\ref{GUP}), then the minimum length uncertainty reads
\begin{eqnarray}
\Delta x_{\mbox{min}} \approx \hbar \sqrt{3\beta_0} &=& \ell_p \sqrt{\beta_0}.
\end{eqnarray}
The experimental estimations \cite{Gao:2016fmk} of $\beta_0$ range from $\sim 10^{21}$ to $\sim 10^{39}$. Another GUP approach motivated by quantum deformation of the Pioncarre algebra \cite{Maggiore:1993rv,Maggiore:1993zu} suggests that the minimal length associated with is given as
\begin{eqnarray}
\Delta x_{\mbox{min}} \simeq \frac{\hbar G}{\gamma_0} &=& \frac{\ell_p^2}{\gamma_0},
\end{eqnarray}
where $\gamma_0$ is photon's wavelength sent from infinity to be absorbed in a black hole. Its experimental estimations \cite{Gao:2016fmk} range from $\sim 10^{26}$ to $\sim 10^{34}$.
The UV/IR correspondence can be applied on various phenomena in which short and long distance physics play a characterized role. For example, gravity \cite{Jackson:2005ue} and the {\it ''deformed''} commutation relations have features of UV/IR correspondence \cite{Jackson2005GravityFA}. Therefore, we assume that the minimal length discretization could be analyzed from the UV/IR correspondence \cite{Tawfik:2020zvf}.
Indeed, $\Delta x$ rapidly increases (IR) as the $\Delta p$ increases beyond the Planck scale (UV) \cite{Maldacena:1997re,Gubser:1998bc,Witten:1998qj}.
Analogous to expression (\ref{GUP}), the canonical non--commutation relation of length and momentum quantum operators is given as
\begin{eqnarray}
\left[\hat{x}_i\,, \hat{p}_j\right] \geq \delta_{ij} i\, \hbar \left(1 + \beta p^2 \right), \label{GUP2}
\end{eqnarray}
where $p^2=g_{ij} p^{0i}\, p^{0j}$ and $g_{ij}$ is Minkowski spacetime metric tensor, for instance $(-,+,+,+)$. Both length and momentum operators, respectively, read
\begin{eqnarray}
\hat{x}_i &=& \hat{x}_{0i} (1+\beta p^2), \label{GUP3a}\\
\hat{p}_j &=& \hat{p}_{0j}, \label{GUP3b}
\end{eqnarray}
in which $\hat{x}_{0i}$ and $\hat{p}_{0j}$ can be derived from the corresponding non--communitation relation,
\begin{eqnarray}
[\hat{x}_{0i}, \hat{p}_{0j}]&=&\delta_{ij} i\, \hbar.
\end{eqnarray}
\section{Discretized metric tensor and its properties}
\label{sec:st}
With the quantum non--commutation operations discussed in section \ref{sec:gup} the four--dimensional Minkowskian manifold of the line element can be given as
\begin{eqnarray}
ds^2 &=& g_{\mu\nu} dx^\mu dx^\nu,
\end{eqnarray}
where $\mu$, $\nu$, and $\lambda=0, 1, 2, 3$. This could be extended to eight--dimensional spacetime tangent bundle with coordinates $x^A=(x^\mu(\zeta^a), \beta \dot{x}^\mu(\zeta^a))$, where $\dot{x}^\mu = dx^\mu/d\zeta^\mu$ \cite{Brandt:2000gka}. Obviously, the line element reads
\begin{eqnarray}
d \tilde{s}^{2} = g_{AB} \, dx^A \, dx^B, \label{eq:dS}
\end{eqnarray}
where $x^A= x^A(\zeta^\mu)$, $g_{AB} = g_{\mu_\nu}\otimes g_{\mu\nu}$, and the indices $A$ and $B=0, 1, \cdots, 7$. With some assumptions and approximations, this manifold could be reformulated as an effective four--dimensional spacetime manifold,
\begin{eqnarray}
\tilde{g}_{\mu\nu} &=& g_{AB} \frac{\partial x^A}{\partial \zeta^\mu} \frac{\partial x^B}{\partial \zeta^\nu} \simeq g_{ab} \Big[\frac{\partial x^a}{\partial \zeta^\mu} \frac{\partial x^b}{\partial \zeta^\nu} + \beta \frac{\partial \dot{x}^a}{\partial \zeta^\mu} \frac{\partial \dot{x}^b}{\partial \zeta^\nu} \Big] \simeq \left(1+ \beta \ddot{x}^\lambda \ddot{x}_\lambda \right) g_{\mu\nu}.
\end{eqnarray}
$\ddot{x}^\mu = \partial \dot{x}^\mu/\partial \zeta^\mu$ is four--dimensional acceleration. The indices $a$, and $b=0, 1, \cdots, 7$.
It is now proper to highlight a number of the discretized metric tensor properties. First, we distinguish between flat and curved spacetime:
\begin{itemize}
\item For flat spacetime, $g_{\mu \nu} = \eta_{\mu\nu}$ and the modified metric tensor reads
\begin{eqnarray}
\tilde{g}_{\mu\nu} &\simeq& \eta_{\mu \nu} + \beta \ddot{x}^\lambda \ddot{x}_\lambda \eta_{\mu \nu} \simeq \eta_{\mu \nu} + h_{\mu\nu},
\end{eqnarray}
where $h_{\mu\nu} = \beta \ddot{x}^\lambda \ddot{x}_\lambda \eta_{\mu \nu}$. The quantum fluctuations from which the minimal length uncertainty likely emerges are compassed in $h_{\mu\nu}$. In other words, both GR metric tensor and this modified one are only distinguishable, at finite $h_{\mu\nu}$.
\item For curved spacetime, the modified metric tensor reads
\begin{eqnarray}
\tilde{g}_{\mu\nu} &\simeq & g_{\mu\nu} + \beta \ddot{x}^\lambda \ddot{x}_\lambda g_{\mu\nu}. \label{eq:dmunucurvedtilda}
\end{eqnarray}
Again, $\beta \ddot{x}^\lambda \ddot{x}_\lambda g_{\mu\nu}$ represents the minimal length contributions.
\end{itemize}
The $\tilde{g}_{\mu\nu}$, Eq. (\ref{eq:dmunucurvedtilda}), seems to play the same role as that of $g_{\mu\nu}$, namely it turns a covariant tensor into a contravariant tensor and vice versa. $\tilde{g}_{\mu\nu}$ is apparently symmetric in its indices $\mu$ and $\nu$ as its components are likely equal upon exchanging the indices. The $\tilde{g}_{\mu\nu}$ symmetric properties are invariant upon basis transformation only if its indices are of the same type; variant or covariant. For spacetime represented by a four--dimensional differentiable manifold $\mathcal{M}$, the metric tensor, $\tilde{g}_{\mu\nu}$, Eq. (\ref{eq:dmunucurvedtilda}), is covariant, second--degree, symmetric on $\mathcal{M}$. Such manifold is Lorentzian. In local coordinates $x^{\mu}$, the metric can be expressed in $dx^{\mu}$ (one--form gradients of the scalar coordinate fields $x^{\mu}$), and the coefficients $\tilde{g}_{\mu\nu}$ ($16$ real--valued functions). If the local coordinates are specified, the metric can be written as a $4 \times 4$ symmetric matrix with the coefficients $\tilde{g}_{\mu\nu}$. If the matrix is non--singular having non--vanishing determinant, $\tilde{g}_{\mu\nu}$ is non--degenerate. The Lorentzian signature of $\tilde{g}_{\mu\nu}$ obviously implies that the matrix has one negative and three positive eigenvalues. Under a change of the local coordinates $x^{\mu}\to x^{\bar{\mu}}$, we obtain
\begin{eqnarray}
\tilde{g}_{\bar{\mu}\bar{\nu}} = \frac{\partial x^{\alpha}}{\partial x^{\bar{\mu}}} \, \frac{\partial x^{\beta}}{\partial x^{\bar{\nu}}}\; \tilde{g}_{\alpha \beta} = \Theta^{\alpha}_{\bar{\mu}} \, \Theta^{\beta}_{\bar{\nu}} \; \tilde{g}_{\alpha \beta}
\end{eqnarray}
If $dx^{\mu}$ are regarded as the components of an infinitesimal coordinate displacement four--vector, the metric determines the invariant square of an infinitesimal line element. Also, it is apparent that the principle of the general covariance is satisfied even in absence of gravitational effects on the modified Minkowski metric. Then, the modified four--dimensional line element can be expressed as
\begin{eqnarray}
d \tilde{s}^{2} &=& g_{\mu\nu} \left( dx^\mu dx^\nu+ \beta^2 d\dot{x}^\mu \; d\dot{x}^\nu\right) = ds^2 + \beta^2 \ddot{x}^\lambda \ddot{x}_\lambda \, ds^2,
\end{eqnarray}
and $d \tilde{s}^{2}$ manifests the causal structure of the spacetime. Only timelike four--dimensional line element, $d \tilde{s}^{2}<0$, can physically covered by a massive object. If $d \tilde{s}^{2}=0$ the line element is lightlike (covered by massless photon). On the other hand, for $d \tilde{s}^{2}>0$, the four--dimensional line element is an incremental proper length, i.e., spacelike.
\section{Discretized geodesic equation and its properties}
\label{sec:ge}
The properties of the manifold including geodesics in GR [$\ddot{x}^{\mu}+\Gamma^{\mu}_{\alpha\beta} \dot{x}^{\mu}\dot{x}^{\nu}=0$ with $\dot{x}^{\mu}=\partial x^{\mu}/\partial s$, Christopher symbols $\Gamma^{\mu}_{\alpha\beta}=(g^{\mu\gamma}/2)(\partial g_{\gamma\alpha}/\partial x^{\beta}) + \partial g_{\gamma\beta}/\partial x^{\alpha} - \partial g_{\alpha\beta}/\partial x^{\gamma})$, and $s$ is a scalar parameter of motion such as a proper time] can be generalized. For example, the notion of a {\it ''straight line''} is to be generalized to {\it ''curved spacetime''}. The consequences of the length discretization or minimal length uncertainty based on GUP, generalize the world line of a free particle. GR assumes that gravity couldn't be regarded as a force but it should be emerged from {\it ''classical''} curved spacetime geometry and {\it ''quantized''} stress--energy--momentum tensor is causing the {\it ''classical''} spacetime curvature. The approach utilized here is discretized minimal length, which modifies both metric tensor and line element.
As discussed in ref. \cite{Tawfik:2020zvf}, using the variational principle and extremization of the path $s_{AB}$, the geodesic equation could be derived as follows.
\begin{itemize}
\item In flat spacetime (Minkowski space)
\begin{eqnarray}
\beta {\cal L} \frac{d^2 \dot{x}^{\mu}}{d s^2} - \frac{d x^{\mu}}{d s} + c &=& 0.
\end{eqnarray}
Even if $\beta$, the GUP parameter vanishes, the geodesic equation reduces to that of a straight line, at constant velocity, i.e., both $\beta$ terms disappear.
\item and in curved spacetime
\begin{eqnarray}
\frac{d^2 x^{\mu}}{d s^2} + \Gamma^{\eta}_{\mu \nu} \frac{d x^{\mu}}{d s} \frac{d x^{\nu}}{d s} &=& \beta \Bigg\{ \frac{d}{d s} \Big[ {\cal L} \frac{d^2 \dot{x}^{\mu}}{d s^2} \Big] +\frac{1}{2} g^{\mu \nu} \Bigg(
g_{\mu\nu, \alpha} \frac{d \dot{x}^{\mu}}{d s} \frac{d \dot{x}^{\nu}}{d s} - {\cal L} g_{\mu \alpha, \gamma} \frac{d \dot{x}^{\gamma}}{d s} \frac{d \dot{x}^{\mu}}{d s} \Bigg) \nonumber \\ && {\cal L} g^{\mu \nu} \Bigg(2 g_{\mu \alpha, \gamma} \frac{d}{d s} + g_{\mu\alpha, \gamma, \delta} \frac{d x^{\delta}}{d s} \Bigg) \frac{d x^{\gamma}}{d s} \frac{d \dot{x}^{\mu}}{d s}
\Bigg\} \label{eq:geodsc1}
\end{eqnarray}
where the proper time can be deduced from the Lagrangian, $\tau = \int {\cal L}(s, \dot{x}, \ddot{x})\, ds$,
\begin{eqnarray}
\frac{\partial \tau}{\partial s} &=& {\cal L}(s, \dot{x}, \ddot{x}) = -\left[g_{\mu\nu} \left(\frac{d x^{\mu}}{d s} \frac{d x^{\nu}}{d s} + \beta \frac{d \dot{x}^{\mu}}{d s} \frac{d \dot{x}^{\nu}}{d s} \right)\right]^{1/2}, \nonumber \\
\Gamma^{\eta}_{\mu\nu} &=& \frac{1}{2} g^{\eta\alpha} \left[g_{\mu \alpha, \nu} - g_{\alpha \nu, \mu} + g_{\mu \nu, \alpha}\right], \nonumber \\
g_{\mu\nu, \alpha} &=& \frac{\partial g_{\mu \nu}}{\partial x^{\alpha}}, \nonumber \\
g_{\mu\alpha, \gamma, \delta} &=& \frac{\partial}{\partial x^{\delta}} \left(\frac{\partial g_{\mu \alpha}}{\partial x^{\gamma}}\right). \nonumber
\end{eqnarray}
\end{itemize}
The $\beta$--terms in Eq. (\ref{eq:geodsc1}) distinguish this expression of discretized geodesics from the GR geodesics,
\begin{eqnarray}
\frac{d^2 x^{\mu}}{d s^2} +\Gamma^{\eta}_{\mu\nu} \frac{d x^{\mu}}{d s}\, \frac{d x^{\nu}}{d s}=0,
\end{eqnarray}
which could be solved when, for instance, assuring that the proper time reads $ds^2=g_{\mu\nu} dx^{\mu} dx^{\nu}$. Under the condition that
\begin{eqnarray}
g_{\mu\nu} \frac{d x^{\mu}}{d s}\, \frac{d x^{\nu}}{d s} = \epsilon,
\end{eqnarray}
where $\epsilon=0$ for photon and $\epsilon=1$ for massive particles, the geodesic equation is supplemented. For conserved energy and angular momentum the geodesic equation can be expressed as an ordinary first--order differential equation \cite{Hackmann:2008zza}.
Solving the discretized geodesic equation, Eq. (\ref{eq:geodsc1}), is not a trivial task, because of the finite terms in rhs, which encompass higher--order derivatives.
\section{Conclusions}
\label{sec:cncls}
The approach of minimal length uncertainty conserves both Christoffel connection\footnote{The metric connection characterizes the affine connection to a manifold provided with the metric. This allows lengths, for instance, to be measured on that manifold.} and the equivalence principle of the gravitational and inertial mass. They are not affected. This allows to recover any violations in the equivalence principle, especially as a possible reason of quantum gravity. We highlight that this conclusion contradicts previous studies \cite{Ghosh:2013qra, Scardigli:2007bw}. The reason could be the rigorous procedure implemented in the present study. We have first determined the modified metric tensor. Accordingly, we have obtained the modified line element. Both are key principles of the proposed theory of discretized geometry. We could also derive the corresponding geodesics, in which the appearance of higher--order derivatives substantially distinguishes this expression from the GR geodesics.
The modification to the line element is summarized in the term $\beta^2 \ddot{x}^\lambda \ddot{x}_\lambda$, which highlights the essential contributions added by the acceleration of the test particle. We conclude that the length discretization ensures that the line element wouldn't only expand but apparently accelerates. The metric tensor is also modified by the term $\beta \ddot{x}^\lambda \ddot{x}_\lambda$. The properties of the modified metric tensor has been elaborated.
We find that the modified geodesics is not only providing the acceleration of a test particle inside the gravitational field. Higher--order derivatives are also present \cite{Eager_2016}, namely the jerk, $\dddot{x}^{\mu}$, which in turn is derived from the time derivative of the acceleration. In contract to GR geodesics, solving the modified geodesics isn't a trivial task. The corresponding differential equations are complex and non--linear.
\section*{Acknowledgments}
AT is very grateful to organizers of sixteenth Marcel Grossmann meeting - MG16 for their kind invitation and financial support!
\bibliographystyle{ws-procs961x669}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,491 |
En física teórica, invariancia modular es la invariancia dentro de un grupo como SL(2,Z) de grandes difeomorfismos de un toro. El nombre viene del nombre clásico grupo modular de este grupo, como en la teoría de la forma modular.
En la teoría de cuerdas, la invariancia modular es una exigencia adicional para el diagrama de un lazo, además de algunas anomalías geoidales, a saber la no aparición de anomalías gravitatorias.
Simetría | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,822 |
require 'test_helper'
class Jeweler
module Commands
class TestValidateGemspec < Test::Unit::TestCase
build_command_context 'build context' do
setup do
@command = Jeweler::Commands::ValidateGemspec.build_for(@jeweler)
end
should 'assign gemspec_helper' do
assert_same @gemspec_helper, @command.gemspec_helper
end
should 'assign output' do
assert_same @output, @command.output
end
should 'return Jeweler::Commands::ValidateGemspec' do
assert_kind_of Jeweler::Commands::ValidateGemspec, @command
end
end
end
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,459 |
using System;
namespace jbb
{
public class JBTeam
{
public string Name { get; set;}
public string Title { get; set;}
public string Desc { get; set;}
public string PicURL { get; set;}
public override string ToString ()
{
return String.Format ("{0}, {1}, {2}, {3}", Name, Title, Desc, PicURL);
}
}
public class MyStaffRootObject
{
public JBTeam[] staffs { get; set; }
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 251 |
Poplar Ridge est un hameau (hamlet) du Comté de Brazeau, situé dans la province canadienne d'Alberta.
Démographie
En tant que localité désignée dans le recensement de 2011, Poplar Ridge a une population de habitants dans 186 de ses 194 logements, soit une variation de 0.7% par rapport à la population de 2006. Avec une superficie de , le hameau possède une densité de population de en 2011.
Concernant le recensement de 2006, Poplar Ridge abritait habitants dans 180 de ses 182 logements. Avec une superficie de , le hameau possédait une densité de population de en 2006.
Références
Annexes
Articles connexes
Liste des communautés d'Alberta
Liste des hameaux d'Alberta
Hameau en Alberta
Localité désignée en Alberta | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,692 |
\section{Introduction}
Ever since the heavy ion collision experiments went over the QCD phase transition temperature, the physical property of the quark gluon plasma (QGP) has been one of the most fascinating topics in high energy physics.
The discovery of the large elliptic flow indicates that a kind of collective motion exists in QGP, and
and the success of the hydrodynamic models suggests that the QGP near the critical temperature is in
a strongly coupled liquid state rather than a gas state
(for a review see \cite{Akiba:2015jwa} and references there in).
Furthermore, the comparison between hydrodynamic models and experimental data indicates that
the shear viscosity of the QGP is quite small with $\eta/s\sim0.2$, suggesting that the QGP liquid found is the most perfect fluid we have ever seen
(for a review see Ref.~\cite{Gale:2013da}).
Inspired by the progress of experiment, there have been challenges in the lattice QCD community to calculate viscosities of QGP \cite{Nakamura:2004sy,Meyer:2007ic,Meyer:2009jp,Pasztor:2018yae,Astrakhantsev:2018oue}.
Viscosities can be extracted from the correlation function of the energy-momentum tensor (EMT) applying Kubo's linear response relations.
There are two major difficulties in this procedure to be carried out on the lattice.
Firstly, the lack of translational symmetry on the lattice makes a definition of EMT not trivial.
Secondly, the Kubo's response function is defined in the real time formalism and thus not directly calculable in the Euclidean space time.
We need to use the spectral function to relate the Matsubara Green's function in the imaginary time formalism to the Kubo's response function.
However, a derivation of the continuous spectral function is an ill-posed problem on a finite lattice.
Because of the these difficulties, studies of viscosity on the lattice have been limited to the pure SU(3) theory without quarks.
We solve the first difficulty by adopting the gradient flow method
\cite{Narayanan:2006rf,Luscher:2010iy,Luscher:2013cpa}
as a non-perturbative renormalization scheme for the EMT \cite{Suzuki:2013gza,Makino:2014taa}.
In Ref.~\cite{Taniguchi:2016ofw}, we have computed the one-point function of EMT in $N_{f}=2+1$ full QCD with the gradient flow method,
and found that the results for the diagonal elements of EMT are well consistent with the equation of state evaluated previously with the conventional $T$-integration method.
We now compute two-point functions of diagonal as well as off-diagonal elements of EMT.
For the second difficulty, we try a couple of ans\"atze for the spectral function to fit the correlation functions in this study.
By virtue of the gradient flow the correlation function is evaluated with a good precision and the fit works well.
\section{Viscosities}
The shear viscosity $\eta$ is given by a proportional coefficient in the stress tensor (spatial components of EMT) against a gradient of the velocity field $u_{i}$ for sufficiently long wavelength and slow mode
\begin{eqnarray}
&&
\langle T_{ij}\rangle_{\beta}=-\eta\partial_{i}u_{j},\quad
(i\neq j),
\end{eqnarray}
where
\begin{eqnarray}
&&
\vev{T_{ij}}_{\beta}=\frac{{\rm Tr}\left(\exp\left(-\beta{H}\right)T_{ij}\right)}
{{\rm Tr}\exp\left(-\beta{H}\right)}
\end{eqnarray}
with $\beta$ the inverse temperature and $H$ the Hamiltonian.
The bulk viscosity $\zeta$ is given in a similar manner, $\langle T_{ii}\rangle_{\beta}=-\zeta\partial_{i}u_{i}$
where $i$ is not summed over.
In thermal equilibrium, however, the medium is isotropic and we have $\langle T_{ij}\rangle_{\beta}=0$ for $i\neq j$.
This is consistent with a fact that hydrodynamics is a non-equilibrium phenomenon.
We thus introduce velocity field $u_{l}(\vec{x})$ to study a relaxation process due to local fluctuation of the momentum density $T^{0l}$ interns of time dependent stress tensor
\begin{eqnarray}
&&
\langle{T}_{ij}(t,\vec{x})\rangle_{u}
=\frac{1}{Z_{u}}{\rm Tr}\left(
\exp\left(-\beta{H}+\beta\int d^{3}x\,{T^{0l}}(\vec{x})u_{l}(\vec{x})\right){T}_{ij}(t,\vec{x})\right),
\\&&
Z_{u}={{\rm Tr}\exp\left(-\beta{H}+\beta\int d^{3}x\,{T^{0l}}(\vec{x})u_{l}(\vec{x})\right)},
\end{eqnarray}
where $(t,\vec{x})$ is a coordinate of the Minkowski space-time with $\eta_{\mu\nu}=(+---)$.
Using a relation
\begin{eqnarray*}
&&
\exp\left(-\beta{H}+\beta\int d^{3}x\,{T^{0l}}(\vec{x})\,u_{l}(\vec{x})\right)
=\exp\left(-\beta{H}\right)
T_{\tau}\exp\left(\int_{0}^{\beta}d\tau \int d^{3}x\,{T^{0l}}(-i\tau,\vec{x})\,u_{l}(\vec{x})\right)
\end{eqnarray*}
with
${T^{0l}}(-i\tau,\vec{x})=e^{\tau{H}}{T^{0l}}(\vec{x})e^{-\tau{H}}$
and $T_\tau$ for the $\tau$-ordered product operation,
we expand the expectation value to the leading order in $u_{l}$,
\begin{eqnarray}
\langle{T}_{ij}(t,\vec{x})\rangle_{u}&=&
\int_0^{\beta}d\tau \int d^{3}x'
\vev{
\Delta{T}_{ij}(t-i\tau,\vec{x})\,
\Delta{T^{0l}}(0,\vec{x}')
}_\beta
u_{l}(\vec{x}'),
\end{eqnarray}
where
$\Delta T_{ij}=T_{ij}-\vev{T_{ij}}_{\beta}$.
Making use of the conservation of EMT,
the translation invariance and the time reversal symmetry in real time, we have
\begin{eqnarray}
\langle{T}_{ij}(t,\vec{x})\rangle_{u}&=&
-\int_{0}^{t}ds \int d^{3}x'\int_{0}^{\beta}d\tau
\langle\Delta{T}_{ij}(s-i\tau,\vec{x})\,
\Delta{T}^{kl}(0,\vec{x}')\rangle_{\beta}\,\partial_{k}u_{l}(\vec{x}').
\end{eqnarray}
Assuming a uniform gradient for the velocity field $u_{l}(\vec{x})$ we extract the viscosity.
Further applying the translational invariance in space-time we finally get linear response relations for the viscosities
\begin{eqnarray}
&&
\eta=
\int_{0}^{\infty}dt \int d^{3}x\int_{0}^{\beta}d\tau\,
\langle\Delta{T}_{ij}(t-i\tau,\vec{x})\,
\Delta{T}_{ij}(0,\vec{0})\rangle_{\beta},
\label{eq:eta}
\\&&
\zeta=
\int_{0}^{\infty}dt \int d^{3}x\int_{0}^{\beta}d\tau
\langle\Delta{T}_{ii}(t-i\tau,\vec{x})\,
\Delta{T}_{ii}(0,\vec{0})\rangle_{\beta},
\label{eq:zeta}
\end{eqnarray}
where sum is not taken over spatial indices.
The Kubo's canonical correlation in the right hand sides of \eqn{eq:eta} and \eqn{eq:zeta} is defined in the real time formalism and is not simply available on the lattice with Euclidean time.
We use the spectral function to relate Kubo's response function to the Matsubara Green function in Euclidean time.
The spectral function is defined as usual
\begin{eqnarray}
&&
\rho_{ij;kl}(k)\equiv\int d^{4}x\,e^{ikx}\left\langle\left[{T_{ij}}(x),{T_{kl}}(0)\right]\right\rangle_\beta.
\end{eqnarray}
It is easy to show that both the Kubo and Matsubara Green functions are related with the spectral function as follows
\begin{eqnarray}
&&
\int d^{3}x\,\langle{T_{ij}}(-i\tau,\vec{x}){T_{kl}}(0,\vec{0})\rangle_{\beta}
=\int_{0}^{\infty}\frac{dk_{0}}{2\pi}\frac{\cosh k_{0}\left(\tau-\frac{\beta}{2}\right)}{\sinh k_{0}\frac{\beta}{2}}\rho_{ij;kl}(k_{0},\vec{0}),
\label{euclidean-spectral-function}
\\&&
\int_{0}^{\beta}d\tau \int_{-\infty}^\infty dt\,e^{ik_{0}t}
\int d^{3}x\,e^{-i\vec{k}\vec{x}}
\langle{T_{ij}}(t-i\tau,\vec{x})\,{T_{kl}}(0,\vec{0})\rangle_{\beta}
=\frac{\rho_{ij;kl}(k)}{k_{0}}.
\end{eqnarray}
When the spectral function is derived from the Euclidean correlation functions according to \eqn{euclidean-spectral-function}, the viscosities are given by
\begin{eqnarray}
\eta=\lim_{k_0\to0}\frac{\rho_{ij;ij}(k_0,,\vec{0})}{2k_0},
\quad\quad
\zeta=\lim_{k_0\to0}\frac{\rho_{ii;ii}(k_0,,\vec{0})}{2k_0}.
\end{eqnarray}
\section{Lattice calculation}
\label{sec-gradient-flow}
We compute nonperturbatively renormalized EMT by the gradient flow method of Refs.~\cite{Suzuki:2013gza,Makino:2014taa}.
We adopt the flow equations given in Refs.~\cite{Luscher:2010iy,Luscher:2013cpa}
for the gauge and quark fields
\begin{eqnarray}
&&
\partial_tB_\mu(t,x)=D_\nu G_{\nu\mu}(t,x),
\quad
B_\mu(t=0,x)=A_\mu(x),
\label{eq:(2.1)}
\\&&
\partial_t\chi_f(t,x)=D_\mu D_\mu\chi_f(t,x),
\quad
\chi_f(t=0,x)=\psi_f(x),
\label{eq:(2.4)}
\\&&
\partial_t\ovl{\chi}_f(t,x)
=\ovl{\chi}_f(t,x)\overleftarrow{D}_\mu\overleftarrow{D}_\mu,
\quad
\ovl{\chi}_f(t=0,x)=\ovl{\psi}_f(x),
\label{eq:(2.5)}
\end{eqnarray}
where the field strength $G_{\mu\nu}$ and the covariant derivative $D_\mu$ are given in terms of the flowed gauge field $B_\mu$,
and $f=u$, $d$, $s$, denotes the flavor index.
The properly normalized EMT which satisfies the Ward-Takahashi identity in the continuum limit is given by two steps.
First, we make a flowed tensor operator $T_{\mu\nu}(t,x)$ using flowed fields \eqn{eq:(2.1)}-\eqn{eq:(2.5)}
by a linear combination of five operators $\tilde{O}_{i\mu\nu}(t,x)$
multiplied with matching coefficients $c_{i}(t)$ defined in Refs.~\cite{Suzuki:2013gza,Makino:2014taa}.
Then, we take the limit $T_{\mu\nu}(x)=\lim_{t\to0}T_{\mu\nu}(t,x)$
to resolve mixing with irrelevant dimension six operators.
To carry out the $t\to0$ extrapolation on finite lattices avoiding $O(a^2/t)$ singularities at small $t$, we adopt the strategy of Ref.~\cite{Taniguchi:2016ofw},
\textit{i.e.}, we first identify a region of $t$ (linear window) in which a linear behavior is visible, and then extrapolate the data by a linear fit in the linear window.
Some numerical techniques to calculate the correlation function
$\langle{T_{ij}}(t,{x}){T_{kl}}(t,0)\rangle_{\beta}$ at flow time $t$ are explained in Ref.~\cite{Taniguchi:2017ibr}.
The spectral function $\rho_{ij;kl}(k)$ is a continuous function in four momentum $k$.
It is an ill-posed problem to derive it from finite-number data of lattice correlation function obtained on a lattice with finite volume.
In this study, we try to get the spectral function by a fit to the correlation function using two types of fit ans\"atze.
One is the Breit-Wigner form for the spectral function \cite{Nakamura:2004sy}
\begin{eqnarray}
&&
\frac{\rho_{\rm BW}(k_{0})}{k_{0}}=\frac{F}{1+b^{2}(k_{0}-\omega_{0})^{2}}
+\frac{F}{1+b^{2}(k_{0}+\omega_{0})^{2}},
\label{BW-model}
\end{eqnarray}
where $F$, $b$ and $\omega_0$ are fit parameters.
The other is the hard thermal loop ansatz which uses a combination of the hydrodynamical model and perturbative prediction
\begin{eqnarray}
&&
\frac{\rho_{\rm HTL}(k_{0})}{k_{0}}=\frac{a}{1+b^{2}k_{0}^{2}}
+\theta(k_{0}-\omega_{0})\frac{Ak_{0}^{3}}{\tanh\frac{k_{0}}{4T}},
\label{HTL-model}
\end{eqnarray}
where $a$, $b$, $\omega_0$ and $A$ are fit parameters.
\section{Numerical results}
Measurements of EMT with the gradient flow method are performed on the $N_f=2+1$ gauge
configurations generated for Ref.~\cite{Umeda:2012er}.
The zero-temperature gauge configurations were generated for Ref.~\cite{Ishikawa:2007nn}.
The nonperturbatively $O(a)$-improved Wilson quark action and
the renormalization-group improved Iwasaki gauge action are adopted.
The bare coupling constant is set to $\beta=2.05$, which corresponds
to~$a=0.0701(29)\,\mathrm{fm}$ ($1/a\simeq2.79\,\mathrm{GeV}$).
The hopping parameters are set to $\kappa_u=\kappa_d\equiv\kappa_{ud}=0.1356$
and $\kappa_s=0.1351$, which correspond to heavy $u$ and $d$ quarks,
$m_\pi/m_\rho\simeq0.63$, and almost physical $s$ quark, $m_{\eta_{ss}}/m_\phi\simeq0.74$.
We adopt the fixed-scale approach~\cite{Umeda:2008bd} in which the temperature $T=1/(aN_t)$ is varied by changing the temporal lattice size $N_t$ with a fixed lattice spacing $a$.
The temperature varies $174\le T\le464$ MeV with temporal length $16\ge N_{t}\ge6$.
See Ref.~\cite{Taniguchi:2016ofw} for a detailed explanation of numerical parameters.
\begin{figure}[tb]
\centering
\includegraphics[width=4.9cm,trim=-20mm -10mm 0mm 0mm,clip]{figs/TT_tcorr_clover_imp_3216_ovS_ijij_BreitWigner.eps}
\includegraphics[width=4.9cm,trim=-20mm -10mm 0mm 0mm,clip]{figs/TT_tcorr_clover_imp_3214_ovS_ijij_BreitWigner.eps}
\includegraphics[width=4.9cm,trim=-20mm -10mm 0mm 0mm,clip]{figs/TT_tcorr_clover_imp_3212_ovS_ijij_BreitWigner.eps}
\includegraphics[width=4.9cm,trim=-20mm -20mm 0mm 0mm,clip]{figs/TT_tcorr_clover_imp_3210_ovS_ijij_BreitWigner.eps}
\includegraphics[width=4.9cm,trim=-20mm -20mm 0mm 0mm,clip]{figs/TT_tcorr_clover_imp_3208_ovS_ijij_BreitWigner.eps}
\includegraphics[width=4.9cm,trim=-20mm -20mm 0mm 0mm,clip]{figs/TT_tcorr_clover_imp_3206_ovS_ijij_BreitWigner.eps}
\vspace*{-3em}
\caption{EMT correlation function $\sum_{\vec{x}}\vev{T_{ij}(t;\vec{x},x_{4})\,T_{ij}(t;0)}$ as function of Euclidean time $x_{4}$ at flow time $t/a^{2}=0.5$ (blue square), $1.0$ (green circle), $1.5$ (orange up triangle) and $2.0$ (red down triangle).
From the top left to the bottom the temperature is $T\simeq174$, $199$, $232$, $279$, $348$ and $464$ MeV ($N_t=16$, $14$, $12$, $10$, $8$ and $6$, respectively).
Solid lines are the fits with the Breit-Wigner fit ansatz using data between two dotted vertical lines.
}
\label{TTijij-x4-BW}
\end{figure}
\begin{figure}[tb]
\centering
\includegraphics[width=4.9cm,trim=-20mm -10mm 5mm 0mm,clip]{figs/TT_tcorr_clover_imp_3216_ovS_ijij_BreitWigner_fit.eps}
\includegraphics[width=4.9cm,trim=-20mm -10mm 5mm 0mm,clip]{figs/TT_tcorr_clover_imp_3214_ovS_ijij_BreitWigner_fit.eps}
\includegraphics[width=4.8cm,trim=-20mm -10mm 5mm 0mm,clip]{figs/TT_tcorr_clover_imp_3212_ovS_ijij_BreitWigner_fit.eps}
\includegraphics[width=4.9cm,trim=-20mm -20mm 5mm 0mm,clip]{figs/TT_tcorr_clover_imp_3210_ovS_ijij_BreitWigner_fit.eps}
\includegraphics[width=4.9cm,trim=-20mm -20mm 5mm 0mm,clip]{figs/TT_tcorr_clover_imp_3208_ovS_ijij_BreitWigner_fit.eps}
\includegraphics[width=4.9cm,trim=-20mm -20mm 5mm 0mm,clip]{figs/TT_tcorr_clover_imp_3206_ovS_ijij_BreitWigner_fit.eps}
\vspace*{-3em}
\caption{The shear viscosity divided by the entropy density $\eta/s$ as a function of the flow time.
$\eta/s$ is extracted by fitting the correlation function with the Breit-Wigner ansatz.
We take the $t\to0$ limit with a linear fit using the fit range indicated by two dotted vertical lines.
}
\label{etaovers1}
\end{figure}
\begin{figure}[tb]
\centering
\includegraphics[width=6.2cm,trim=-20mm -20mm 0mm 0mm,clip]{figs/eta_ov_s_vs_T.eps}
\hspace{5mm}
\includegraphics[width=6.2cm,trim=-20mm -20mm 0mm 0mm,clip]{figs/eta_ov_s_vs_T_larger.eps}
\vspace*{-3em}
\caption{Preliminary results for the shear viscosity divided by the entropy density, $\eta/s$, as a function of the temperature.
The viscosity is extracted by fitting the correlation function with the Breit-Wigner ansatz (black circles) and the hard thermal loop ansatz (red triangles).
The blue solid line is $1/4\pi$ from the AdS/CFT correspondence.
The right panel is the same but differs in vertical scale.
}
\label{etaovers-T}
\end{figure}
\begin{table}[b]
\caption{Preliminary results for the shear viscosity divided by the entropy density, $\eta/s$, at each temperature given by Breit-Wigner (BW) fit ansatz and hard thermal loop (HTL) fit ansatz.}
\label{table1}
\centering
\vspace*{0.5em}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
T[MeV] & $174$ & $199$ & $232$ & $279$ & $348$ & $464$ \cr
\hline
BW ansatz
& $2.3(2.7)$ & $0.00(23)$ & $0.145(51)$ & $0.240(47)$ & $0.1753(53)$ & $0.175(11)$ \cr
HTL ansatz
& $2.52(47)$ & $0.59(16)$ & $0.208(38)$ & $0.24(10)$ & $0.05(12)$ & $0.061(11)$ \cr
\hline
\end{tabular}
\label{default}
\end{table}%
In Fig.\ref{TTijij-x4-BW} we plot the shear correlation function $\sum_{\vec{x}}\vev{T_{ij}(t;\vec{x},x_{4})T_{ij}(t;0)}$ as function of Euclidean time $x_{4}$ at four different flow times $t$ for six different temperatures $T$ shown in each panel.
Spatial indices are averaged over all $i\neq j$ combinations.
Within the fit range indicated by the vertical dotted lines, the Breit-Wigner ansatz \eqn{BW-model} fits the data well with $\chi^{2}/{\rm dof}<2$ at low temperatures $T\le279$ MeV.
On the other hand, $\chi^{2}/{\rm dof}$ exceeds ten at higher temperatures.
The results for the shear viscosity divided by the entropy density, $\eta/s$, is plotted in Fig.~\ref{etaovers1} as a function of the flow time at six temperatures.
We take the $t\to0$ limit by using data within the region shown by two vertical dotted lines.
Our preliminary results for $\eta/s$ by the Breit-Wigner ansatz at each temperature are summarized in the first row of Table~\ref{table1}, and are plotted in Fig.~\ref{etaovers-T} by black circles.
The same procedure works well also with the hard thermal loop fit ansatz \eqn{HTL-model}.
Our preliminary results for $\eta/s$ by the hard thermal loop ansatz are summarized in the second row of Table~\ref{table1}, and are plotted in Fig.~\ref{etaovers-T} by red triangles.
For the bulk viscosity $\zeta$, we find that our diagonal correlation function
$\sum_{\vec{x}}\vev{T_{ii}(t;\vec{x},x_{4})\,T_{ii}(t;0)}$ is statistically not fine enough to extract a non-trivial value of $\zeta/s$.
Both with Breit-Wigner and hard thermal loop fit ans\"atze, we find large $\chi^{2}/{\rm dof}$ above five.
The resultant values of $\zeta/s$ are consistent with zero with large statistical error for all temperatures we studied.
\section{Conclusion}
We calculated two point correlation functions of the energy-momentum tensor (EMT) in lattice QCD with $(2+1)$-flavors at finite temperature, $174\le T\le464$ MeV.
Nonperturbatively renormalized EMT is calculated by applying the gradient flow renormalization scheme.
By virtue of the gradient flow, statistical error is suppressed at finite flow time and the correlation functions are evaluated with a good precision.
We apply two types of model fit for the correlation function to extract the spectral function.
The procedure works well for the shear correlation function $\sum_{\vec{x}}\vev{T_{ij}(t;\vec{x},x_{4})\,T_{ij}(t;0)}$.
Our preliminary results for the shear viscosity are given in Fig.~\ref{etaovers-T} and Table~\ref{table1} as a function of temperature.
The resultant shear viscosity seems to be consistent with the small experimental value given in Ref.~\cite{Gale:2013da} well above the pseudo-critical temperature $T_{\mathrm{pc}}\approx190\,\mathrm{MeV}$.
On the other hand, we need a higher statistics for the bulk viscosity.
\vspace{2mm}
This work was in part supported by JSPS KAKENHI Grant Numbers JP18K03607, JP17K05442, JP16H03982, JP15K05041,
JP26400251, JP26400244, and JP26287040.
This research used computational resources of COMA and Oakforest-PACS provided by the Interdisciplinary Computational Science Program of Center for Computational Sciences, University of Tsukuba,
Oakforest-PACS at JCAHPC through the HPCI System Research Project (Project ID:hp17208), OCTOPUS at Cybermedia Center, Osaka University, and ITO at R.I.I.T., Kyushu University.
The simulations were in part based on the Lattice QCD code set Bridge++ \cite{bridge}.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,337 |
Q: How to start a script at a specified point in Powershell I have a powershell script I want to be able to define different starting points for. Once the starting point is hit the script would pick up from that point and continue through the remaining code in the script. I don't believe that a case statement will work since I don't think that will just let the script flow through from whatever starting point is defined.
I would expect to see something like this when the script was started.
Please choose your starting point:
*
*Beginning
*Start at step 2
*Start at step 3 etc.....
When the selection is made the script jumps to that point then will run through the remainder of the script.
Answer: The code is going to end up looking something like this:
#steps
$stepChoice = read-host 'Where would you like to start.'
switch($stepChoice)
{
1{Step1}
2{Step2}
3{Step3}
}
function Step1 {
'Step 1'
Step2
}
function Step2 {
'Step 2'
Step3
}
function Step3 {
'Step 3'
'Done!'
}
Thanks for your help
A: AFAIK, there is nothing like this in PowerShell. If you need something simple this might work for you:
*) Create a script with steps defined as functions. Each function in the end calls the next step-function:
# Steps.ps1
function Step1 {
'Step 1'
Step2
}
function Step2 {
'Step 2'
Step3
}
function Step3 {
'Step 3'
'Done!'
}
*) If you want to start with step 1: dot-source the Steps.ps1 and call Step1:
. .\Steps.ps1
Step1
*) If you want to start with step 2: dot-source the Steps.ps1 and call Step2:
. .\Steps.ps1
Step2
A: This extra answer is probably too much for this particular task.
But it may be useful to know about the tool.
It can be used for similar and more convoluted tasks.
The tool is Invoke-Build.ps1.
It is a standalone script, just put it anywhere in the path, this is it.
Then use the code like this:
Steps.ps1
# Invoke-Build task is a sequence of scripts and other tasks.
# This task does its job and then calls the task Step2.
task Step1 {
'Step 1'
},
Step2
# This task does its job and then calls the task Step3.
task Step2 {
'Step 2'
},
Step3
# The last task, just its name and code.
task Step3 {
'Step 3'
}
Test.ps1
Invoke-Build step1 Steps.ps1 # do steps 1, 2, 3
Invoke-Build step2 Steps.ps1 # do steps 2, 3
Invoke-Build step3 Steps.ps1 # do just step 3
The difference between this and previous answer is that with task approach
actual step code blocks do not have to be explicitly dependent, that is to call
some other steps. It is the task infrastructure that glues the actions together.
A: PowerShell doesn't contain a GOTO type command, so you must encapsulate each of the logic steps (Beginning, step2, step3, ...) in a procedure/code block of some kind and call as appropriate. While a switch statement won't scale well if you need a lot of choices, for three it would be fairly simple - here is an idea, though I am sure this idea can be implemented better:
function Begin () { "Starting" }
function Step-1 () { "One" }
function Step-2 () { "Two" }
function Take-Action() {
param([string]$choice);
switch ($choice) {
"Start" { & Begin ; Take-Action "One" }
"One" { & Step-1; Take-Action "Two" }
"Two" { & Step-2 }
}
}
& Take-Action "Start"
Output:
Starting
One
Two
A: A more direct approach would be to use a series of if statements, so that any helper functions can be used independently without having to cross-reference other steps.
[int]$stepChoice = read-host 'Where would you like to start.'
if( $stepChoice -le 1 ) {
'Step 1'
}
if( $stepChoice -le 2 ) {
'Step 2'
}
if( $stepChoice -le 3 ) {
'Step 3'
}
'Done!'
Also note that a switch statement will continue to evaluate conditions until it encounters a break statement, so this form will also work:
switch( $stepChoice ) {
{ $_ -le 1 } { 'Step 1' }
{ $_ -le 2 } { 'Step 2' }
{ $_ -le 3 } { 'Step 3' }
}
'Done!'
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 637 |
Алакарга́ () — посёлок городского типа в Яккабагском районе Кашкадарьинской области Республики Узбекистан.
Высота центра населённого пункта — около 620—630 м. Алакарга располагается между отходящими от Яккабагдарьи каналами Бешарык (протекает по южной окраине посёлка) и Правобережный (течёт с севера посёлка). Через северную часть посёлка проходит автодорога Р-84 (Яккабаг — Эски-Яккабаг). Территория смыкается с расположенным по другую сторону данной автодороги населённым пунктом Джаманата.
По состоянию на 1985 года население Алакарги составляло 1100 человек. Постановлением Кабинета министров Республики Узбекистан от 13 марта 2009 года присвоен статус посёлка городского типа.
Примечания
Посёлки городского типа Яккабагского района | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,698 |
Engineering Bust May Be Over
After four-year decline, civil and environmental fields are gaining popularity. TECHNICAL EDUCATION IN THE US
By Laurent Belsie Staff writer of The Christian Science Monitor
@CSMecon
THE highly publicized decline in young American engineers appears to be ending, buoying hopes that the nation won't lose its technological edge. After a four-year drop, the number of undergraduate engineering students in the United States stabilized last year and may increase this year. Many of the top engineering schools are seeing an unexpected increase in applicants for the fall.
An informal Monitor survey of more than one dozen universities found nine with a rising number of applications, two holding steady, and one declining. This rise is taking place even though the total number of college freshmen is declining.
The finding is important because technology and science experts have worried that the US was producing too few engineers to meet its future needs.
"Something is clearly going on, but we're not sure what," says Diane Shinberg, educational survey manager of the Engineering Manpower Commission. "We had expected the numbers to continue to decline and they didn't."
The commission, which provides statistics on the engineering work force, found that overall enrollment of undergraduate engineers went up very slightly last year - from 338,529 in 1989 to 338,842 in 1990. That ended a steady decline that started in 1986, when total enrollments stood at 369,520.
The number of freshmen entering engineering programs continued to decline last year - by 1.1 percent. But that was less than the commission had expected. The number could turn up this year, since applications are up.
The rise in applications is broad and deep. It is taking place at small and large schools, state universities and private colleges.
Purdue University's engineering school received a record 6,250 applications for the 1991 fall semester. Texas A&M got so many applicants for engineering it stopped accepting them March 1 - its earliest cutoff date ever.
Lehigh University in Bethlehem, Pa., is up 7.5 percent for the fall; Cooper Union in New York City, up 14 percent; Georgia Tech, up 18.5 percent; Michigan State University, up 20 percent. Carnegie Mellon University in Pittsburgh, Cornell University in Ithaca, N.Y., and Harvey Mudd College in Claremont, Calif., also report increases.
A few schools held steady, such as the Massachusetts Institute of Technology. Caltech is showing a slight increase in applicants. Among those surveyed by the Monitor, only Penn State University showed a decrease.
The rise in applications flies in the face of the overall decline in college students. There are 1 million fewer 18-year-olds this year according to US Census projections than in 1979 - the peak year, with 4.3 million. The pool of 18-year-olds should reach a low of 3.2 million in 1993 before rising again.
This phenomenon of rising applications is so new that most admissions directors and engineering deans were surprised by it. Many are hesitant to forecast a turnaround just yet.
"It would be a dramatic change," says George Van Dusen, assistant dean at Michigan State University's engineering college.
One possible explanation is that the students are applying to many schools simultaneously, says Phil Wankat, head of Purdue's freshman engineering department. He says the engineering school's in-state applications stayed level while out-of-state applications went up.
Officials at other universities suggest that there are more students interested in engineering. But they say the turnaround may be short term.
"It could be related to the recession, where parents and students realize that it's going to be harder to get jobs out there," says Paul Christiano, dean of engineering at Carnegie Mellon University.
Engineering traditionally has provided larger salaries and better-than-average job security. A recent survey of US employers found that engineering and computer-science graduates this year will command the highest entry-level salaries.
Some engineering specialties are going through difficult times as defense- and computer-related companies retrench. But other specialties, such as civil and environmental engineering, are becoming suddenly popular.
"I don't think we are going to see the trough that we thought," says Barbara Arena of Lehigh's engineering school. "People are really going out and they're talking up engineering."
Schools such as Lehigh have increased their financial-aid packages. Engineering schools around the country have started programs in junior-high and high schools to attract female and minority students.
Some schools are even trying to change themselves to attract more students. Cornell's engineering school is hiring its first-ever coordinator of women for next fall. And Georgia Tech, instead of its traditional sink-or-swim approach, is trying to ensure success for the most students possible, says Jim Langley, the university's vice president for external affairs.
So, a turnaround? The preliminary evidence suggests one is under way.
"If we are not able to say that, I fear that we are going to be in big trouble" in a few years, says Mr. Christiano of Carnegie Mellon. "It implies that our economy will have shrunk."
US universities see decreased enrollment from China
How one engineering program used storytelling to recruit more women
For women in science, busting barriers is just part of the job | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,825 |
Sabaton's film - "The War To End All Wars' set to be released in 2023
The time has come for Sabaton to reveal some BIG NEWS. The band is beyond proud to announce that for the last two years, they have been busy working on an exciting, large-scale project.
In 2023, Sabaton will release The War To End All Wars movie, a full-length musical motion picture featuring songs from the band's 10th studio album, The War To End All Wars. This movie vividly tells the stories of World War I by way of animation and live action. It will give the viewer a better understanding of what the band's songs on the album are about -- it is a musical and historical adventure.
Currently in post-production, the movie is being made in collaboration with Yarnhub Animation Studio. Sabaton previously worked with them on other projects, including their most recent animated story video for 'The Red Baron'. The War To End All Wars movie is on a completely different scale that neither the band nor Yarnhub have ever attempted before. As the band has said, you're going to want to see this!
"We premiered an early version of this movie to journalists during a preview session for our latest album, 'The War To End All Wars,' at the Royal Military Museum in Brussels. Witnessing their reaction to it was priceless - they were speechless - so we decided to take it to the next level and push the boundaries even further for a global audience." // Pär Sundström
"When Sabaton asked us to go beyond anything we had produced before and jointly create a film for their new album, we were filled with excitement and trepidation. It was a massive undertaking that required new people, technology, and skills. But we couldn't miss the opportunity. We often say our mission is to harvest Goosebumps, and our work with Sabaton has always been the most successful in that regard. It's been two years in the making, but after spending many late nights and weekends in meetings with the band, the end result is something unique. A new way to listen to the album; a deeper understanding that helps the viewer experience the bravery and tragedy that was the inspiration for Sabaton's latest masterwork." // David Webb, Yarnhub
The War To End All Wars movie is a cohesive, thought-provoking and emotionally charged piece with a heavy focus on storytelling. It features members of the band, both in real life and animated, and a lot of research and effort has been put into it to ensure it depicts history in the most accurate way possible – this is something that the band is very passionate about. Sabaton had a dream of creating something that's entertaining but with great educational value, and that dream has become a reality after two years of hard work.
There is so much more to tell you about this movie and Sabaton will reveal more in time, but know that they are very excited to present this to you next year. Watch this space.
In the meantime, we hope you enjoy this teaser… - https://youtube.com/shorts/uYFWmUZagT4
Yarnhub is an independent animation studio that was founded in 2019. Yarnhub looks to captivate and thrill audiences by recreating history with epic storytelling using iconic cinematography and animated visuals.
Sabaton climbed the international charts with their album The War To End All Wars, securing #1 positions in Germany, Austria, Sweden, Poland, Hungary and Finland. Having achieved the top position for the second time in Germany, Sweden and Finland, the album peaked at #1 in Poland, Hungary and Austria for the first time in the band's career. This and additional outstanding results in other territories have made The War To End All Wars Sabaton's most successful album so far.
www.sabaton.net
www.facebook.com/sabaton
www.instagram.com/sabatonofficial
www.nuclearblast.de/sabaton
www.twitter.com/sabaton
www.youtube.com/c/Sabaton
If you enjoy reading this content, please consider a donation
© 2011-2022 Global Metal Apocalypse
Christmas Guide 2021
Releases Of The Year
Single Release | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,026 |
\section{Introduction}
Many applications of quantum systems are placed in a realm close to
classical behavior, where nevertheless quantum properties need to be
taken into account. In view of the more complicated structure of
quantum systems, both of a conceptual as well as technical nature, it
is then often helpful to work with equations of classical type, i.e.\
systems of ordinary differential equations for mechanical systems,
which are amended by correction terms resulting from quantum
theory. From a mathematical point of view, the question arises how
well the behavior of a (wave) function subject to a partial
differential equation can be approximated by finitely many variables
subject to a system of coupled but ordinary differential equations.
One very powerful method is that of effective actions
\cite{PositronEffAc,VacPolEffAc} which have been
developed and are widely used for quantum field theories. The
effective action of a free field theory is identical to the classical
action, while interacting theories receive quantum corrections ``from
integrating out irrelevant degrees of freedom.'' The language is
suggestive for the physical intuition behind the formalism, but the
technical details and the mathematical relation between classical and
quantum theories remain less clear.
In this article we develop, building on earlier work
\cite{GeomQuantMech,ClassQuantMech,Schilling,Perturb,Josh}, a
geometrical picture of effective equations of motion for a quantum
mechanical system with a clear-cut relation between the classical and
quantum system: as a manifold, a classical phase space of the form
${\mathbb R}^{2n}$ can literally be embedded into the quantum
system.\footnote{Using the geometrical picture of
\cite{GeomQuantMech,ClassQuantMech} for this purpose and the idea of
horizontality as well as the appearance of additional quantum degrees
of freedom in this context were suggested to us by Abhay Ashtekar.}
Also the Scchr\"odinger equation can be formulated as Hamiltonian
equations of motion for quantum phase space variables, and
self-adjoint operators as observables in quantum theory select special
functions on the quantum phase space which can be considered as
observables of the classical type. We discuss several examples and
show that, in the regime where effective action techniques can be
used, they coincide with our method.
\section{Effective Actions}
For any system with classical action $S[q]$ as a functional of the
classical coordinates $q$, thus satisfying
\begin{equation}
\frac{\delta S}{\delta q}=-J
\end{equation}
in the presence of an external source $J$, one can formally define the
effective action $\Gamma[q]$ satisfying the same relation
\begin{equation}\label{EffEq}
\frac{\delta \Gamma}{\delta q}=-J
\end{equation}
but containing $\hbar$-dependent quantum corrections. If the
generating functional $Z[J]$ of Greens functions is known, $\Gamma$ is
obtained as the Legendre transform of $-i\hbar\log Z[J]$
\cite{EffAcQFT}.
This procedure is well-motivated from particle physics where
additional contributions to $\Gamma$ can be understood as resulting
from perturbative quantum interactions (``exchange of virtual
particles''). Indeed, effective actions are mostly used in
perturbative settings where the generating functional $Z$ can be
computed by perturbing around free theories, using e.g.\ Gaussian path
integrations.
For other systems, or quantum mechanical applications,
Eq.~(\ref{EffEq}) can, however, be seen at best as a formal
justification. The effective action can rarely be derived in general,
but its properties can make an interpretation very complicated. First,
$\Gamma$ is in general complex and so are the effective equations
(\ref{EffEq}) as well as their solutions. In fact, $q$ in
(\ref{EffEq}) is not the classical $q$ and not even the expectation
value of $\hat{q}$ in a suitable state of the quantum system. Instead,
in general it is related to non-diagonal matrix elements of $\hat{q}$
\cite{VariationalEffAc}. Secondly, $\Gamma$ is in general a non-local
functional of $q$ which cannot be written as the time integral of a
function of $q$ and its derivatives. In most applications, one employs
a derivative expansion assuming that higher derivatives of $q$ are
small. In this case, each new derivative order introduces additional
degrees of freedom into the effective action which are not classical,
but whose relation to quantum properties of, e.g., the wave function
is not clear either. Indeed, in this perturbative scheme, not all
solutions of the higher derivative effective action are consistent
perturbatively as many depend non-analytically on the perturbation
parameter $\hbar$ \cite{Simon}. For those solutions, it is then not
guaranteed that they capture the correct perturbative behavior
considering that next order corrections, non-analytical in the
perturbation parameter, can dominate the leading order. Such
non-analytical solutions have to be excluded in a perturbative
treatment, which usually brings down the number of solutions to the
classical value even if perturbative corrections are of higher
derivative form \cite{Simon}. The description, even in a local
approximation, can thus be quite complicated, given by higher
derivative equations with many general solutions subject to the
additional condition that only solutions analytic in the perturbation
parameter are to be retained. The formulation is thus very redundant
if higher derivative terms are used. Moreover, where there seem to be
additional (quantum) degrees of freedom associated with higher
derivative corrections, their role remains dubious given that many
solutions have to be excluded.
There are other technical difficulties if one tries to generalize
beyond the usual realm of perturbing around the ground state of a free
field theory or, in quantum mechanics, the ground state of a harmonic
oscillator. In the latter case, for a system with classical
action
\begin{equation}
S[q(t)]=\frac{1}{2}m\dot{q}^2-\frac{1}{2}m\omega^2q^2-U(q)
\end{equation}
one can derive the effective action \cite{EffAcQM} (see also
Ref.~\cite{SymmBreakEffAc} for the effective potential)
\begin{equation} \label{EffAc}
\Gamma_{{\rm eff}}[q(t)]=\int
{\mathrm{d}} t\left[\frac{1}{2}\left(m+\frac{\hbar U'''(q)^2}
{2^5m^2\left(\omega^2+m^{-1}U''(q)\right)^{\frac{5}{2}}}\right)\dot
q^2
-U(q)-\frac{\hbar\omega}{2} \left(1+\frac{U''(q)}{m\omega^2}
\right)^{\frac{1}{2}}\right]
\end{equation}
to first order in $\hbar$ and in the derivative expansion, using path
integral techniques. The quantum system is here described effectively
in an expansion around the ground state of the Harmonic oscillator. On
the other hand, a quantum system allows more freedom and one could,
e.g., want to find an effective formulation for a quantum system which
is prepared to be initially close to a squeezed state, or a state of
non-minimal uncertainty. This freedom is not allowed by the usual
definition of an effective action.
Other problems include the presence of ``infrared problems'': In the
free particle limit, corresponding to a massless field theory, one has
$U(q)=-\frac{1}{2}m\omega^2q^2$ for which (\ref{EffAc}) becomes
meaningless. Still, at least for some time the free particle should be
possible to be described in an effective classical manner. Other
generalizations, such as for systems to be perturbed around a
Hamiltonian non-quadratic in momenta as they occur, e.g., in quantum
cosmology, look even more complicated since one could not rely on
Gaussian path integrations.
For all these reasons it is of interest to develop a scheme for
deriving effective equations of a quantum system based on a
geometrical formulation of quantum mechanics. This has been used
already in the context of quantum cosmology \cite{Perturb,Josh} where
usual techniques fail. As we show here, it reduces to the effective
action result (\ref{EffAc}) in the common range of applicability, but
is much more general. Moreover, it provides a clear, geometrical
picture for the relation between the dynamics of classical and quantum
systems, the role of quantum degrees of freedom and the effective
approximation.
\section{A Geometrical Formulation of Quantum Mechanics}
The formalism of quantum theory has been studied for almost a century
already and a prominent understanding of its structure, based mainly
on functional analysis, has been achieved. From this perspective,
quantum mechanics appears very different from classical mechanics not
only conceptually but also mathematically. While in classical physics
the viewpoint is geometrical, employing symplectic or Poisson
structures on a phase space, quantum theory is analytical and based on
Hilbert space structures and operator algebras. There are, however,
some contributions which develop and pursue a purely geometrical
picture of quantum mechanics, in which the process of quantization and
kinematical as well as dynamical considerations are generalizations of
classical structures. The process of quantization is described in a
geometrical, though not always constructive, manner in geometric
quantization \cite{Woodhouse}, employing line bundles with
connections, but the picture of the resulting theory remains
analytical based on function spaces and operators
thereon. Independently, a geometrical formulation of quantum mechanics
has been developed which, irrespective of the quantization procedure,
provides a geometrical viewpoint for all the ingredients necessary for
the basic formulation of quantum physics
\cite{GeomQuantMech,ClassQuantMech}. It is the latter which will be
crucial for our purposes of developing a geometrical theory of
effective equations of motion and the classical limit.
Let us assume that we are given a quantum system, specified by a
Hilbert space ${\cal H}=({\cal V},\langle\cdot,\cdot\rangle)$ with
underlying vector space ${\cal V}$ equipped with inner product
$\langle\cdot,\cdot\rangle$, together with an algebra of basic
operators and a Hamiltonian $\hat{H}$. The Hamiltonian defines a flow
on ${\cal H}$ by $\frac{{\mathrm{d}}\Psi}{{\mathrm{d}} t}=-i\hbar^{-1}\hat{H}\Psi$.
\begin{lemma}
Let $({\cal V},\langle\cdot,\cdot\rangle)$ be a Hilbert space. The
inner product $\langle\cdot,\cdot\rangle$ on ${\cal H}$ defines a
K\"ahler structure on ${\cal V}$.
\end{lemma}
\begin{proof}
To start with we note that the inner product can be decomposed as
\begin{equation}
\langle\Phi, \Psi
\rangle=\frac{1}{2\hbar}G(\Phi,\Psi)+\frac{i}{2\hbar}\Omega(\Phi,\Psi)
\end{equation}
where $G(\Phi,\Psi)$ and $\Omega(\Phi,\Psi)$ denote the real and
complex parts of $2\hbar\langle\Phi, \Psi\rangle$, respectively. It
follows from the properties of an inner product that $G$ is a metric
and $\Omega$ a symplectic structure on the vector space
${\cal V}$, identified with its tangent space in any of its
points. Also by definition, the metric and symplectic structure are
related to each other by
\[
G(\Phi,\Psi)=\Omega(\Phi,i\Psi)\,.
\]
With the obvious complex structure, $({\cal V},G,\Omega)$ is thus
K\"ahler.
\end{proof}
As used in the proof, points and tangent vectors of the K\"ahler
manifold ${\cal K}=({\cal V},G,\Omega)$ correspond to states in the
Hilbert space, and functions densely defined on ${\cal V}$ can be
associated to mean values of operators acting on ${\cal H}$: Any
operator $\hat{F}$ on ${\cal H}$ defines a function $F:=\langle\hat
F\rangle$ on ${\cal K}$ taking values $F(\Psi)=\langle\Psi,\hat
F\Psi\rangle$ in points $\Psi$ of its domain of definition.
Any state $\eta\in{\cal H}$ defines a constant vector field on ${\cal
K}$, which can be used to compute the Lie derivative
\begin{equation}
\pounds_\eta F(\Psi):=\frac{{\mathrm{d}}}{{\mathrm{d}} t}F(\Psi+t\eta)|_{t=0}\,.
\end{equation}
This allows us to show
\begin{lemma}
Let $F=\langle\hat{F}\rangle$ be a function on ${\cal K}$ associated
with a self-adjoint operator $\hat{F}$ on ${\cal H}$. Its Hamiltonian
vector field is given by
\[
X_F(\Psi):=\frac{1}{i\hbar}\hat F\Psi\,.
\]
\end{lemma}
\begin{proof}
Using the definition of a Lie derivative and self-adjointness of
$\hat{F}$ we have
\begin{eqnarray}
\pounds_\eta F(\Psi)&=&\frac{{\mathrm{d}}}{{\mathrm{d}} t}\langle\Psi+t\eta,\hat
F(\Psi+t\eta)\rangle|_{t=0}=\langle\eta,\hat
F\Psi\rangle+\langle\Psi,\hat
F\eta\rangle\\\nonumber&=&-i\hbar\left(\langle-i\hbar^{-1}\hat
F\Psi,\eta\rangle-\langle\eta,-i\hbar^{-1}\hat
F\Psi\rangle\right)=\Omega\left(-i\hbar^{-1}\hat
F\Psi,\eta\right)
\end{eqnarray}
for any vector $\eta$, from which $X_F$ can immediately be read off.
\end{proof}
\begin{rem}
Such vector fields are also known as Schr\"odinger vector fields, as
their flow is generated on ${\cal H}$ by a Schr\"odinger equation
\begin{equation}
\frac{{\mathrm{d}}}{{\mathrm{d}} t}|\Psi\rangle=\frac{1}{i\hbar}\hat
F|\Psi\rangle\,.
\end{equation}
The flow is a family of unitary transformations, i.e.\ automorphisms
of the Hilbert space which preserve the Hilbert space
structure. Therefore, the flow preserves not only the symplectic
structure of ${\cal K}$, as any Hamiltonian vector field does, but
also the metric. Hamiltonian vector fields thus are Killing vector
fields, and since each tangent space has a basis of Killing vectors
the K\"ahler space is maximally symmetric.
\end{rem}
For two functions $F=\langle \hat F\rangle$ and $K=\langle\hat
K\rangle$ the symplectic structure defines the Poisson bracket
\begin{equation}
\left\{F,K\right\}:=\Omega(X_F,X_G)=\frac{1}{i\hbar}
\langle[\hat{F},\hat{K}]\rangle\,.
\end{equation}
For, e.g., $q:=\langle\hat q\rangle$ and $p:=\langle \hat p\rangle$ we
have $\left\{q,p\right\}=1$ from $[\hat q,\hat p]=i\hbar$.
Of physical significance in quantum theory are only vectors of the
Hilbert space up to multiplication with a non-zero complex
number. Physical information is then not contained in the vector space
${\cal V}$ but in the projective space ${\cal V}/{\mathbb C}^*$.
From now on we will take this into account by working only with norm
one states and norm-preserving vector fields..
\section{Classical and Quantum Variables}
For any quantum system, the algebra of basic operators, which is a
representation of the classical algebra of basic phase space variables
defined by Poisson brackets, plays an important role. We will assume
mainly, for simplicity, that this basic algebra is given by a set of
position and momentum operators, $\hat{q}^i$ and $\hat{p}_i$ for
$1\leq i\leq N$, with canonical commutation relations. This
distinguished set of operators leads to further structure on ${\cal
K}$:
\begin{defi}
The set of fundamental operators $(\hat{q}^i,\hat{p}_i)$ on ${\cal
H}$ defines a fiber bundle structure on ${\cal V}$ where the bundle
projection identifies all points $\Phi$, $\Psi$ for which
$\langle\Psi,\hat{q}^i\Psi\rangle=\langle\Phi,\hat{q}^i\Phi\rangle$
and {$\langle\Psi,\hat p_i\Psi\rangle=\langle\Phi,\hat
p_i\Phi\rangle$} for all $i$. The base manifold can be identified
with the classical phase space as a manifold.
\end{defi}
\begin{rem}
The Hilbert space used for the quantization of a classical system is
always infinite dimensional, which implies that the fibers of the
bundle are infinite dimensional. For instance, for an analytic wave
function one can consider the collection of numbers associated to the
mean values of products of the fundamental operators,
$a_n=\langle\Psi,\hat{q}^n\Psi\rangle$ and $b_n=\langle\Psi,\hat{q}^n
\hat p\Psi\rangle$ for all $n\geq 0$. Usually denominated by the
name of Hamburger momenta \cite{ReedSimon}, the $(a_n,b_n)$ are a
complete set in the sense that they uniquely determine the wave
function. Indeed, from linear combinations $c_n$ of the Hamburger
momenta with coefficients corresponding to some orthogonal
polynomials, taking Hermite polynomials $\{H_n(q)=\sum_lh_{n,l}q^l\}$
for definiteness, we have
\begin{equation}
c_n=\sum_lh_{n,l}a_l=\int dq|\Psi(q)|^2H_n(q)
\end{equation}
giving the absolute value of the wave function as
\begin{equation}
|\Psi(q)|^2=e^{-q^2}\sum_n \frac{c_nH_n(q)}{2^n\pi n!}\,.
\end{equation}
The $b_n$, on the other hand, provide information about
the phase $\alpha(q)$ of the wave function up to a constant:
\begin{equation}
b_n=-\int dq\Psi(q)^*{q}^n
i\partial_q\Psi(q)=-\int {\mathrm{d}} q|\Psi(q)|{q}^n i\partial_q|\Psi(q)|-\int
{\mathrm{d}} q|\Psi(q)|^2{q}^n i\partial_q\alpha(q)
\end{equation}
from which $\partial_q\alpha(q)$ is determined as before, using the
already known norm of $\Psi$.
\end{rem}
One could thus use Hamburger momenta as coordinates on the fiber
bundle, but for practical purposes it is more helpful to choose
coordinates which are not only adapted to the bundle structure but
also to the symplectic structure. We thus require that, in addition to
the classical variables $q^i$ and $p_i$, coordinates of the fibers
generate Hamiltonian vector fields symplectically orthogonal to
$\partial/\partial q^i$ and $\partial/\partial p_i$.
\begin{defi}
The {\em quantum variables} of a Hilbert space ${\cal H}$ are defined as
\begin{equation}
G^{i_1 \ldots i_n}\!:=\! \langle(\hat{x}^{(i_1}\!-x^{(i_1}) \cdots
(\hat{x}^{i_n)}\!-x^{i_n)})\rangle
=\sum_{k=0}^{n}(-)^k(_k^n)x^{(i_1}\!\! \cdots x^{i_k}
\langle\hat{x}^{i_{k+1}}\!\! \cdots \hat{x}^{i_n)}\rangle
\end{equation}
with respect to fundamental operators
$\{\hat{x}^i\}_{1\leq i\leq 2N}:=\{\hat{q}^k,\hat{p}_k\}_{1\leq i\leq N}$
where round brackets on indices denote symmetrization.
\end{defi}
Variables of this type have been considered in quantum field theories;
see, e.g., \cite{EffAcComp}. Together with the classical variables,
they provide in particular local trivializations of the quantum phase
space as a fiber bundle.
\begin{lemma}
The fiber coordinates $G^{i_1 \ldots i_n}$ on ${\cal K}$ are
symplectically orthogonal to the classical coordinates
$x^i$.
\end{lemma}
\begin{proof}
We compute the Poisson bracket with $x^j$ to obtain
\begin{eqnarray}
\left\{x^j,G^{i_1 \cdots i_n}\right\} &=&
\sum^{n}_{k=0}(-)^k(^n_k)\left[\left\{x^j,x^{(i_1} \cdots
x^{i_k}\right\} \langle\hat x^{i_{k+1}} \cdots \hat x^{i_n)}\rangle
+x^{(i_1} \cdots x^{i_k}\left\{x^j, \langle\hat x^{i_{k+1}} \cdots
\hat x^{i_n)}\rangle\right\}\right]\nonumber\\
&=&\sum_{k=0}^n
(-)^k(^n_k)\left[k\epsilon^{j(i_n}x^{i_1}\!\! \cdots x^{i_{k-1}}
\langle\hat{x}^{i_{k}}\!\! \cdots \hat{x}^{i_{n-1})}\rangle+
(n-k)\epsilon^{j(i_n}x^{i_1}\!\! \cdots x^{i_k}
\langle\hat{x}^{i_{k+1}}\!\! \cdots
\hat{x}^{i_{n-1})}\rangle\right]\nonumber\\
&=&\sum_{l=0}^{n-1}
(-)^{(l+1)}(^n_l) (n-l)\epsilon^{j(i_n}x^{i_1}\!\! \cdots x^{i_l}
\langle\hat{x}^{i_{l+1}}\!\! \cdots
\hat{x}^{i_{n-1})}\rangle\nonumber\\
&&+\sum_{k=0}^{n} (-)^k(^n_k)
(n-k)\epsilon^{j(i_n}x^{i_1}\!\! \cdots x^{i_k}
\langle\hat{x}^{i_{k+1}}\!\! \cdots \hat{x}^{i_{n-1})}\rangle=0
\end{eqnarray}
where we used repeatedly the
Leibnitz rule and introduced
$\epsilon^{ij}=\left\{x^i,x^j\right\}$.
\end{proof}
\begin{rem}
An alternative proof proceeds by computing the Poisson bracket
between the function $\langle e^{\alpha_i(\hat x^i-x^i)}\rangle$ and
$x^j$, restricting to the dense subspace in which such functions are
analytic in $\{\alpha_i\}$, and expanding.
\end{rem}
Since the fibers are symplectic, $\Omega$ defines a natural
decomposition of tangent spaces of ${\cal K}$ as a direct sum of a
vertical space tangent to the fibers and a horizontal space ${\rm
Hor}^{\Omega}{\cal K}$ as the symplectic complement:
\begin{corr}
$({\cal K},\pi,{\cal B})$ is a fiber bundle with connection over the
classical phase space ${\cal B}$ as base manifold.
\end{corr}
We now know the Poisson relation between the classical variables $x^i$
and between $x^i$ and the $G^{j_1,\ldots, j_m}$. In order to compute
the remaining Poisson brackets $\left\{G^{i_1, \ldots,
i_n},G^{j_1,\ldots, j_m}\right\}$ for $N$ canonical degrees of freedom
we introduce a new notation
\begin{equation}
G^{a_{k_1},\dots ,a_{k_N}}_{b_{k_1},\dots, b_{k_N}}= \langle(\hat
q^{k_1}-q^{k_1})^{a_{k_1}}\cdots(\hat q^{k_N}-q^{k_N})^{a_{k_N}}(\hat
p_{k_1}-p_{k_1})^{b_{k_1}}\cdots(\hat
p_{k_N}-p_{k_N})^{b_{k_N}}\rangle_{\rm Weyl}\nonumber
\end{equation}
the label ``Weyl'' meaning that the product of operators is Weyl or
fully symmetric ordered. The notation allows us to drop indices whose
values are zero so whenever we are dealing with a single pair of
degrees of freedom we use the notation where $G^{a,n}:=G^{n-a}_a$.
\begin{lemma}
The Poisson brackets for the variables above are
\begin{eqnarray}\nonumber\left\{G^{a_{k_1},\dots
,a_{k_N}}_{b_{k_1},\dots,b_{k_N}},G^{c_{k_1},\dots,c_{k_N}}_{d_{k_1},
\dots,d_{k_N}}\right\}\!\!
=\!\!-\!\!\!\!\!\!\!\!\sum_{r,s,{e_1,\dots,e_N}}\!\!\!\!\!\!
(-)^{r+s}({\textstyle\frac{1}{2}}\hbar)^{2r}
\delta_{e_1+\dots+e_N,2r+1}K_{r,s,\{e\}}^{\{a\}\{b\}\{c\}\{d\}}
G^{a_{k_1}+c_{k_1}-e_1,
\dots,a_{k_N}+c_{k_N}-e_N}_{b_{k_1}+d_{k_1}-e_1,\dots,b_{k_N}+
d_{k_N}-e_N}&&\\\nonumber-\sum_{f=1}^N\!\!
\left( a_{k_{\!f}}d_{k_{\!f}}G^{a_{k_1},\dots, a_{k_{\!f}}-1,\dots,
a_{k_N}}_{b_{k_1},\dots,b_{k_N}}G^{c_{k_1},\dots,c_{k_N}}_{d_{k_1},\dots,
d_{k_{\!f}}-1,\dots, d_{k_N}}\!\!\!-\!
b_{k_{\!f}}c_{k_{\!f}}G^{a_{k_1},\dots,a_{k_N}}_{b_{k_1},\dots,b_{k_{\!f}}-1
,\dots,b_{k_N}}G^{c_{k_1},\dots,c_{k_{\!f}}-1,\dots,c_{k_N}}_{d_{k_1},\dots,
d_{k_N}}\right)&&
\end{eqnarray}with indices running as
\begin{eqnarray}&1\leq
2r+1\leq\sum_{f=1}^N\left(\min(a_{\!f},d_{\!f})+
\min(b_{\!f},c_{\!f})\right),&\nonumber
\\&0\leq s\leq\min\left(r,\sum_{f=1}^N\min(b_{\!f},c_{\!f})\right),&\nonumber\\
&0\leq
e_{\!f}\leq\min(a_{\!f},d_{\!f},s)+\min(b_{\!f},c_{\!f},2r+1-s).&
\nonumber\end{eqnarray} and coefficients given by
\begin{equation}
K_{r,s,\{e\}}^{\{a\}\{b\}\{c\}\{d\}}=
\sum_{g_1,\dots,g_n}
\frac{\delta_{g_1+\dots+g_N,2r+1-s}}{s!(2r+1-s)!}\prod_f\frac{
\left(^{\ \ a_{\!f}}_{e_{\!f}-g_{\!f}}\right)
\left(^{b_{\!f}}_{g_{\!f}}\right)\left(^{c_{\!f}}_{g_{\!f}}\right)\left(^{\
\ d_{\!f}}_{e_{\!f}-g_{\!f}}\right)}{\left(^{ 2r+1-s}_{\ \
g_{\!f}}\right)\left(^{\ \ s}_{e_{\!f}-g_{\!f}}\right)}
\end{equation}
where
\[
\max(e_{\!f}-s,e_{\!f}-a_{\!f},e_{\!f}-d_{\!f},0)\leq g_{\!f}\leq
\min(b_{\!f},c_{\!f},2r+1-s,e_{\!f})\,.
\]
\end{lemma}
\begin{proof}
Consider first the Poisson bracket between functions of the form
$D(\alpha)=\langle e^{\alpha_i(\hat x^i -x^i)}\rangle$. For
analytical wave functions in the mean values, $D(\alpha)$ is an
analytical function and so is the Poisson bracket between two such
functions $D(\alpha)$ and $D(\beta)$. We can therefore take the
coefficients in a Taylor expansion for all orders in $\alpha_i$ and
$\beta_j$. Using the relation $[e^{\alpha_i\hat x^i}, e^{\beta_j\hat
x^j}]=2 i
\sin(\frac{\hbar}{2}\alpha_j\beta_k\epsilon^{jk})e^{(\alpha+\beta)_i\hat
x^i}$, which follows from the Baker--Campbell--Hausdorff formula and
the commutator $[\alpha_i\hat{x}^i,\beta_j\hat{x}^j]=
i\hbar\epsilon^{ij} \alpha_i\beta_j$, we find that
\begin{equation}\label{symplecticstructureD}
\left\{D(\alpha),D(\beta)\right\}=\frac{2}{\hbar}
\sin({\textstyle\frac{1}{2}}\hbar\alpha_j\beta_k\epsilon^{jk})D(\alpha+\beta)
-\alpha_j\beta_k\epsilon^{jk}D(\alpha)D(\beta)\,.
\end{equation}
Now, we use $D(\alpha)=\langle e^{\alpha_i(\hat x^i -x^i)}\rangle=
\underset{\{a\},\{b\}}{\sum}G^{a_1\cdots a_N}_{b_1\cdots b_N}
\prod_{i=1}^N\alpha_{q^i}^{a_i}\alpha_{p_i}^{b_i}(a_i!b_i!)^{-1}$,
and substitute
\begin{eqnarray}
\frac{2}{\hbar}\sin({\textstyle\frac{1}{2}}\hbar\alpha_j\beta_k\epsilon^{jk})
D(\alpha+\beta)&=&
-\sum(-)^{r+s}({\textstyle\frac{1}{2}\hbar})^{2r}G^{a_1+c_1,\cdots
,a_N+c_N}_{b_1+d_1,\cdots,b_N+d_N}\\
&&\times\prod_{f=1}^N\frac{\alpha_{q^f}^{a_f+g_f}\alpha_{p_f}^{b_f+e_f}
\beta_{q^f}^{c_f+e_f}\beta_{p_f}^{d_f+g_f}
}{a_f!b_f!c_f!d_f!e_f!g_f!(2r+1-s-e_f)!(s-g_f)!}
\nonumber
\end{eqnarray}
where we sum over all collections of numbers $a_f$, $b_f$, $c_f$,
$d_f$, $e_f$, $g_f$, $r$ and $s$ such that $\sum_f g_f=s$, $\sum_f
e_f=2r-s$ and $s\leq 2r+1$. Since the equality
(\ref{symplecticstructureD}) holds for any $\alpha$ and $\beta$,
coefficients in the expansion have to fulfill the equality.
\end{proof}
\section{Uncertainty Principle}
The fibers of ${\cal K}$ as a fiber bundle over the classical phase
space are not vector spaces, and the quantum variables $G^{i_1,\ldots,
i_n}$ are not allowed to take arbitrary values. Similarly, not any
collection of numbers is a collection of Hamburger momenta. With
${\cal K}$ being a K\"ahler space, the fibers are bounded by relations
following from Schwarz inequalities. A special case of this fact is
well-known and commonly written as the uncertainty relation
\begin{equation}
(\triangle
q )^2(\triangle p)^2\geq\frac{\hbar^2}{4}+\langle(\hat q\hat
p+\hat p\hat q)/2-qp\rangle^2\geq \frac{\hbar^2}{4}
\end{equation}
where $(\triangle a)^2=\langle(\hat a -a)^2\rangle$, or in our
notation
\begin{equation} \label{UncertG2}
G^{0,2}G^{2,2}\geq\frac{\hbar^2}{4}+(G^{1,2})^2\,.
\end{equation}
More generally, the Schwarz inequality for a K\"ahler manifold with
metric $g$ and symplectic structure $\omega$ is
\begin{equation}
g(u,u)g(v,v)\geq
\left|g(u,v)\right|^2+\left|\omega(u,v)\right|^2
\end{equation}
for all tangent vectors $u$ and $v$.
This results in bounds to be imposed on the quantum variables.
\begin{lemma}
The function $D(\alpha)=\langle e^{\alpha_i(\hat{x}^i-x^i)}\rangle$
is subject to
\begin{equation}\label{uncertainty}
\left(\!D(2\alpha)\!\!-\!\!D(\!\alpha)^2\right)\!\left(\!D(2\beta)\!-\!
D(\beta)^2\!\right)\geq
D(\!\alpha+\!\beta)^2\!-\!2\cos({\textstyle\frac{1}{2}\hbar}
\alpha\times\beta)
D(\!\alpha+\beta)D(\!\alpha)D(\beta)+D(\!\alpha)^2D(\beta)^2\,.
\end{equation}
\end{lemma}
\begin{proof}
For the Schwarz inequality we need to know the metric and
pre-symplectic structure on the space of states of unit norm, which
we compute by evaluating them on vector fields that generate
transformations only along the submanifold of unit vectors in the
Hilbert space. To an arbitrary vector $X_F=\frac{1}{i\hbar}\hat
F\Psi$ we associate the vector given by $\tilde X_F=\left(1-
|\Psi\rangle \langle\Psi|\right)X_F = \frac{1}{i\hbar}(\hat F-
F)\Psi$.
This ensures that the transformation
generated by $\tilde X_F$ maps normalized states to normalized
states, which is most easily seen infinitesimally using
$|(1+\epsilon\tilde{X}_F)\Psi|^2=|\Psi|^2-2i\hbar^{-1}\epsilon
\langle\Psi,(\hat{F}-F)\Psi\rangle+O(\epsilon^2)=|\Psi|^2+O(\epsilon^2)$.
The metric on the space of physical states evaluated in Hamiltonian
vector fields induces a symmetric bracket
\begin{equation}
(F,K)=g(X_F,X_K)=G(\left(1-
|\Psi\rangle \langle\Psi|\right)X_F,\left(1- |\Psi\rangle
\langle\Psi|\right)X_K)\,.
\end{equation}
The symplectic structure is as before,
$\omega(X_F,X_K)=\Omega(X_F,X_K)$.
For the corresponding operators, $g$ and $\omega$
result in the anticommutator $[\cdot,\cdot]_+$ and commutator
$[\cdot,\cdot]$, respectively.
For functions $\langle e^{\alpha.\hat x}\rangle$ and $\langle
e^{\beta.\hat x}\rangle$ (parameterized by $\alpha_i$ and $\beta_i$)
the Schwarz inequality implies
\begin{equation}
(\langle e^{2\alpha.\hat x}\rangle-\langle
e^{\alpha.\hat x}\rangle^2)(\langle e^{2\beta.\hat x}\rangle-\langle
e^{\beta.\hat
x}\rangle^2)\geq\left|\frac{1}{2}
\langle[e^{\alpha.\hat x},e^{\beta.\hat x}]_+\rangle-\langle
e^{\alpha.\hat x}\rangle\langle e^{\beta.\hat x}\rangle\right|^2
+\frac{1}{4}\left|\langle[e^{\alpha.\hat
x},e^{\beta.\hat x}]\rangle\right|^2
\end{equation}
which upon using, as before, the Baker--Campbell--Hausdorff formula
for the commutator and anticommutator and multiplying both sides with
$e^{-2(\alpha+\beta).x}$ proves the lemma.
\end{proof}
This gives us a large class of inequalities thus specifying bounds
on the variables $G^{i_1,\ldots, i_n}$. The boundary, obtained through
saturation of the inequalities, is characterized by relations which
result from the lemma order by order in $\alpha$ and $\beta$.
\section{Quantum Evolution}
The dynamical flow of the quantum system is given as the unitary
Schr\"odinger flow on ${\cal H}$ of a self-adjoint Hamiltonian
operator $\hat{H}$. As before, this flow is also Hamiltonian when
viewed on the K\"ahler space ${\cal K}$. It is generated by the
Hamiltonian function obtained as the mean value of the Hamiltonian
operator. In terms of coordinates on the manifold the Hamiltonian
function is obtained by Taylor expanding the mean value of the
Hamiltonian operator which in our convention is taken to be Weyl
ordered:
\begin{defi}
The {\em quantum Hamiltonian}\footnote{This is the basic object for
an effective theory, playing a similar role in the effective
potential \cite{EffPotExp}.} on ${\cal K}$ is the function
\begin{equation} \label{HQ}
H_Q:=\langle H(\hat{x}^i)\rangle_{\rm Weyl}=\langle
H(x^i+(\hat{x}^i-x^i))\rangle =\sum_{n=0}^{\infty} \sum_{a=0}^n
\frac{1}{n!}\binom{n}{a}\frac{\partial^n
H(q,p)}{\partial p^a\partial q^{n-a}}G^{a,n}
\end{equation}
generating {\em Hamiltonian equations of motion}
\begin{eqnarray}
\dot{x}^i=&\{x^i,H_Q\}\nonumber\\
\dot{G}^{a,n}=&\{G^{a,n},H_Q\}\,.
\end{eqnarray}
\end{defi}
This Hamiltonian flow is equivalent to the Schr\"odinger equation of
the Hamiltonian operator. As such, it is an equivalent description of
the quantum dynamics and only superficially takes a classical form,
albeit for infinitely many variables, in its mathematical
structure. Nevertheless, the reformulation makes it possible to
analyze the classical limit in a direct manner, and to derive
effective equations in appropriate regimes. Classical dynamics is to
arise in the limit of ``small" quantum fluctuations which, when the
fluctuations are completely ignored or switched off by $\hbar\to0$,
should give rise to classical equations of motion. In practice, this
limit is not easy to define, and the most direct way is to derive
first effective equations of motion, which still contain $\hbar$, and
then take the limit $\hbar\to0$.
In this procedure, the main problem is to reduce the infinite set of
coupled quantum equations of motion to a set of differential
equations for only a finite set of variables. Additional degrees of
freedom without classical analogs carry information about, e.g., the
spreading of the wave function around the peak, which itself is
captured by expectation values. For a formulation of classical type,
taking into account only a finite number of degrees of freedom, a
system has to allow a {\em finite-dimensional} \,submanifold of the
quantum space ${\cal K}$ which is preserved by the quantum flow. We
start by generalizing the situation encountered in \cite{Schilling}:
\begin{defi} \label{StrongEff}
A {\em strong effective classical system} $({\cal P},H_{\rm eff})$
for a quantum system $({\cal H},\hat{H})$ is given by a finite
dimensional pre-symplectic subspace ${\cal P}$ of the K\"ahler space
${\cal K}$ associated with ${\cal H}$ satisfying the following two
conditions:
\begin{enumerate}
\item For each $p\in{\cal P}\subset{\cal K}$ the tangent space
$T_p{\cal P}$ contains the horizontal subspace ${\rm
Hor}_p^{\Omega}{\cal K}$ of $p$ in ${\cal K}$ defined by the
symplectic structure: ${\rm Hor}_p^{\Omega}{\cal K}\subset T_p{\cal
P}$ for all $p\in {\cal P}$ {\em (base horizontality)}.
\item ${\cal P}$ is fixed under the
Schr\"odinger flow of $\hat{H}$ and, if ${\cal P}$ is symplectic, the
restriction of the flow to ${\cal P}$ agrees with the Hamiltonian
flow generated by the {\em effective Hamiltonian} $H_{\rm eff}$.
\end{enumerate}
\end{defi}
\begin{rem}
A strong effective classical system agrees with the quantum system
both at the kinematical and quantum level since its symplectic
structure as well as the Hamiltonian flow are induced by the
embedding. As such, the conditions are very strong since they require
a quantum system to be described {\em exactly} in terms of a {\em finite
dimensional} system ${\cal P}$. In addition to agreement between the
strong effective and the quantum dynamics, the first condition
ensures that the classical variables are contained in ${\cal P}$ and
fulfill the classical Poisson relations.
\end{rem}
In the simplest case we require the effective system to have the same
dimension as the classical system, such that potentially only
correction terms will appear in $H_{\rm eff}$ (to be discussed further
in Theorem~\ref{StrongEffHam} below) but no additional degrees of
freedom. Quantum variables, in general, cannot simply be ignored
since they evolve and back react on the classical variables. Sometimes
one may be forced to keep an odd number of quantum variables, such as
the three $G^{a,2}$, in the system which we allow by requiring the
effective phase space ${\cal P}$ to be only pre-symplectic. For a
strong effective system of the classical dimension, however, the
dynamics of the quantum variables in the embedding space occurs only
as a functional dependence through the classical coordinates:
\begin{equation}
\dot{G}^{a,n}=\dot{x}^i\partial_{x^i}G^{a,n}(x^j)\,.
\end{equation}
The effective equations of motion, generated by $H_{\rm eff}$ are then
obtained by inserting solutions
$G^{a,n}(x)$ in the equations for $x^i$:
\begin{equation}
\dot{x}^i=\{x^i,H_Q\}|_{G^{a,n}(x)}=\sum_{n=0}^{\infty}
\frac{1}{n!}\{x^i,H(x^i),_{i_1\dots i_n}\}G^{i_1,\ldots, i_n}(x)\,.
\end{equation}
\section{Examples}
We now demonstrate the applicability of the general procedure by
presenting examples, which will then lead the way to a weakened
definition and, in the following section, a proof that the results
coincide with standard effective action techniques when both can be
applied.
\begin{excount}{Harmonic Oscillator}
The quantum Hamiltonian (\ref{HQ}) for a harmonic
oscillator is
\begin{equation}
H_Q=\frac{1}{2m}p^2+\frac{1}{2}m\omega^2q^2
+\frac{1}{2}m\omega^2G^{0,2}+\frac{1}{2m}G^{2,2}
\end{equation}
giving equations of motion
\begin{eqnarray}
\nonumber \dot{p}=&\{p,H_Q\}&=-m\omega^2 q\\
\dot{q}=&\{q,H_Q\}&=\frac{1}{m} p\\\nonumber
\dot{G}^{a,n}=&\{{G}^{a,n},H_Q\}&=\frac{1}{m}(n-a)G^{a+1,n}-m\omega^2
aG^{a-1,n}\,.
\end{eqnarray}
In this case, the set of infinitely many coupled equations splits into
an infinite number of sets, for each $n$ as well as the classical
variables, each having a finite number of coupled
equations. Independently of the solutions for the $G^{a,n}$ we obtain
the same set of effective equations for $q$ and $p$ agreeing with the
classical ones. Therefore the effective Hamiltonian for a system of
the classical dimension is here identical to the classical one (up to a
constant which can be added freely). We can also define higher
dimensional (but non-symplectic) systems by including the variables
$G^{a,n}$ for a finite set of values for $n$.
Along the classical evolution, the evolution of the additional
parameters is then given by linear differential equations which we
write down in a dimensionless form, defining
\begin{equation} \label{Gtilde}
\tilde G^{a,n}=\hbar^{-n/2}(m\omega)^{n/2-a}G^{a,n}\,.
\end{equation}
The requirement that
dynamics be restricted to the classical subspace parameterized by
$q$ and $p$ implies
\begin{equation} \label{M}
\frac{1}{\omega}\left(\frac{1}{m}p\partial_q-
m\omega^2q\partial_p\right) \tilde{G}^{a,n}=(n-a)\tilde{G}^{a+1,n}-
a\tilde{G}^{a-1,n}=:{}^{(n)}\!M^a_{\ b}\tilde{G}^{b,n}
\end{equation}
whose solution is
\begin{equation}
\tilde{G}^{a,n}(r,\theta)=(\exp\theta{}^{(n)}\!M)^a_{\ b}A^b(r)
\end{equation}
where $r=\sqrt{\frac{1}{m}p^2+m\omega^2 q^2}$, $\tan
(\theta)=m\omega q/p$ and $A^{a,n}(r)$ are $n+1$ arbitrary functions
of $r$. For, e.g., $n=2$ we have
\begin{eqnarray}
\tilde{G}^{0,2}(r,\theta)&=&A^{0,2}(r)-e^{2i\theta}A^{2, 2}(r)-
e^{-2i\theta}A^{-2, 2}(r) \label{HOG02}\\
\tilde{G}^{1,2}(r,\theta)&=&-ie^{2i\theta}A^{2,2}(r)+ie^{-2i\theta}
A^{-2,2}(r)\label{HOG12}\\
\tilde{G}^{2,2}(r,\theta)&=&A^{0,2}(r)+e^{2i\theta}A^{2,2}(r)+
e^{-2i\theta}A^{-2,2}(r)\label{HOG22}
\end{eqnarray}
In terms of the constants $A^{a,n}$, the uncertainty relation
(\ref{UncertG2}) reads:
\begin{equation}
(A^{0,2}(r))^2-4A^{2,2}(r)A^{-2,2}(r)\geq\frac{1}{4}
\end{equation}
We are thus allowed to choose $A^{2,2}=0=A^{-2,2}$ and
$A^{0,2}=\frac{1}{2}$ which saturates the uncertainty bound and
makes the $G^{a,2}$ constant. In fact, these values arise from
quantum evolution given by coherent states $|\alpha\rangle
=e^{\alpha\hat a^\dagger-\bar{\alpha}\hat a}|0\rangle$ which
corresponds to trajectories of {\em constant} quantum variables
\begin{equation}\label{freemoments}
\tilde{G}^{a,n}=\frac{1}{2^n}\frac{a!}{(a/2)!}\frac{(n-a)!}{((n-a)/2)!}
\end{equation}
for even $a$ and $n$, and $\tilde{G}^{a,n}=0$ otherwise. This implies
that any truncation of the system by including only a finite set of
values for $n$, which as already seen is consistent with the dynamical
equations, and choosing initial conditions to be that of a
coherent state gives a base horizontal subspace as required by
Def.~\ref{StrongEff}. In other words, the harmonic oscillator allows
an infinite set of strong effective classical systems, including one
of the classical dimension. The last case is symplectic, with
effective Hamiltonian $H_{\rm eff}=H+{\rm const}$.
In particular, for $n=2$ we see that the uncertainty relations are
saturated. For other states, the quantum variables will in general
vary during evolution, which means that the spreading of states
changes in time. Nevertheless, the variables remain bounded and the
system will stay in a semiclassical regime of small uncertainties if
it starts there. With varying $G$, we will not obtain a strong
effective system as horizontality will be violated. Nevertheless, such
states are often of interest and suitable for an effective
description, which we will provide in a weakened form later on.
\end{excount}
\begin{excount}{Linear systems}
The harmonic oscillator is a special case of systems, where a complete
set of functions on the classical phase space exists such that they
form a Lie algebra with the Hamiltonian. For such systems, which we
call linear, semiclassical aspects can be analyzed in an elegant
manner using {\em generalized coherent states}: a family of states ---
of the dimension of the algebra minus the dimension of its subalgebra
that generates the stability subgroup of a given, so-called extremal
state --- with respect to which the mean values of operators can be
approximated very well by their classical expressions \cite{CohStates}.
In this example we assume that basic variables of the quantum system
are not necessarily canonical but given by the Lie algebra elements
$\hat{L}^i$ of a linear quantum system. Thus, our classical
variables are mean values $L^i:=\langle\hat L^i\rangle$, and quantum
variables are
\[
G_L^{i_1,\ldots, i_n}=\langle(\hat L^{(i_1}-L^{i_1})\cdots(\hat
L^{i_n}-L^{i_n)})\rangle\,.
\]
Poisson brackets between these
functions on the infinite dimensional K\"ahler manifold ${\cal K}$
can easily be found to be
\[
\{L^i,L^j\}=f^{ij}{}_{k}L^k
\]
and
\[
\{L^i,G_L^{i_1,\ldots, i_n}\}=\sum_{r,j} f^{ii_r}{}_{j}
G_L^{i_1,\ldots, i_{r-1}ji_{r+1},\ldots, i_n}\,.
\]
It is then immediately seen that the Hamiltonian dynamics of all
degrees of freedom is linear, the $L^i$ decouple from the quantum
variables, and that the dynamics of any $G_L^{i_1,\ldots, i_n}$
depends only on other $G_L^{j_1,\ldots, j_n}$ with the same $n$. As in
the harmonic oscillator case, the dynamics of infinitely many
degrees of freedom thus decouples into infinitely many sectors
containing only finitely many variables. This shows
\begin{corr} \label{IntegrableCorr}
Any linear quantum system admits a class of finite dimensional
subspaces preserved by the quantum flow, including one of the
classical dimension.
\end{corr}
This is not sufficient for the existence of a strong effective system,
for which we also have to discuss base horizontality. As in the
harmonic oscillator example, one can try to use coherent states which
have been widely analyzed in this context. Nevertheless, the issue of
base horizontality, i.e.\ finding coherent states for which all $G$
are constant, in general is more complicated.
A special family of states is generated by acting with the Lie
algebra on an extremal state, i.e.\ a lowest weight of a module
representation, which can thus be seen to be in one-to-one
correspondence with the factor space of the Lie algebra by the
stabilizer of the state. More explicitly those states are of the
form
\[
|\eta\rangle_{\Lambda,\Omega} =e^{\sum_\alpha\eta_\alpha E_\alpha-H.c.}|{\rm
ext}\rangle
=N(\tau(\eta),\tau(\eta)^*)^{-1}e^{\sum_\alpha\tau_\alpha(\eta)
E_\alpha}|{\rm ext}\rangle\,,
\]
where $\Lambda$ is a representation of the Lie algebra, $\Omega$ is
the quotient of the Group manifold by its stabilizer, $|{\rm
ext}\rangle$ is an extremal state, $E_{-\alpha}|{\rm ext}\rangle=0$
for all positive roots $\alpha$ and $\eta_\alpha$ or $\tau_\alpha$
are coordinate charts of the homogeneous space. Since the flow is
generated by an element of the Lie algebra, generalized coherent
states define a preserved manifold according to the
Baker--Campbell--Hausdorff formula.
In this situation one can compute the mean values of elements $L^i$ of
the Lie algebra and the quantum variables $G_L^{i_1,\ldots, i_n}$ as
functions over the classical phase space. With this construction of
coherent states, the semiclassical phase space associated to the Lie
algebra and the dimension of the classical theories would differ
depending on the choice of the extremal state and each of these would
provide us with diffeomorphisms from the set of $L^i$ to the
$\tau_\alpha$, these last ones being the only dynamical variables of
this subspace (when all conditions are satisfied, we have by definition
{\em dynamical coherent states}).
We can notice as well that a natural emergence of a K\"ahler structure
for this submanifold of the space of states, as observed within the
context of the geometrical formulation of quantum mechanics, is also
justified in Gilmore's construction.
We are not aware of general expressions for the $G$ or special choices
of constant values as they exist for the harmonic oscillator. It is,
however, clear that such constant choices are not possible in general
for a linear system as the counter-example of the free particle
demonstrates.
\end{excount}
\begin{excount}{Free Particle}
The free particle is an example for a linear system and can be
obtained as the limit of a harmonic oscillator for
$\omega\to0$. However, the limit is non-trivial and the semiclassical
behavior changes significantly. If we re-instate units into the
uncertainty formulas of the harmonic oscillator, we obtain in the
case of constant $G^{a,2}$:
\[
G^{0,2}=\frac{\hbar}{2m\omega}\quad,\quad G^{1,2}=0\quad,\quad
G^{2,2}=\frac{\hbar{m\omega}}{2}\,.
\]
The fixed point of the evolution of quantum variables which exists
for the harmonic oscillator thus moves out to infinity in the free
particle limit and disappears. Moreover, the closed classical orbits
break open and become unbounded. Even non-constant bounded solutions
for the $G$ then cease to exist, a fact well-known from quantum
mechanics where the wave function of a free particle has a strictly
growing spread, while harmonic oscillator states always have bounded
spread as follows from (\ref{HOG02}), (\ref{HOG12}) and
(\ref{HOG22}). For a free particle, one can thus not expect to have a
valid semiclassical approximation for all times.
One can see this explicitly by computing eigenvalues of the matrices
${}^{(n)}\!M$ in (\ref{M}) for arbitrary $n$ which in the limit of
vanishing frequency become degenerate. More precisely, the solutions of
\begin{equation}
\frac{p}{m}\partial_qG^{a,n}=\frac{n-a}{m}G^{a+1,n}
\end{equation}
are given by
\begin{equation}
G^{a,n}(q,p)=p^a\sum_{i=0}^{n-a}\frac{c_{i,n}(n-a)!}{(n-a-i)!}q^{n-a-i}
\end{equation}
with integration constants $c_{i,n}$, $i=0,\ldots,n$. Minimal
uncertainty requires for $n=2$ that
$2c_0c_2-c_1^2=\frac{\hbar^2}{4p^2}$. Initial conditions could be
chosen by requiring the initial state to be a Harmonic oscillator
coherent state at the point $(q_0,p_0)$. Since, due to the degeneracy
of eigenvalues, solutions for the $G$ are now polynomials in $q$ and
the classical trajectories are unbounded, the spread is unbounded
when the whole evolution is considered. In particular, no constant
choice and so no strong effective system exists. With unbounded
quantum variables, the system cannot be considered semiclassical for
all times, but for limited amounts of time this can be reasonable. If
this is done, the equations of motion for the classical variables $q$
and $p$ are unmodified such that there is no need for introducing an
effective Hamiltonian different from the classical one if one is
interested only in an effective system of the classical dimension.
\end{excount}
\begin{excount}{Quantum Cosmology}
So far we have mainly reproduced known results in a different
language. To illustrate the generality of the procedure we now
compute effective equations for an unbounded Hamiltonian which
generally occurs in quantum cosmology. Here, one considers the
quantized metric of a homogeneous and isotropic space-time whose sole
dynamical parameter is the scale factor $a$ determining the change of
size of space in time. The canonical structure as well as Hamiltonian
follow from the Einstein--Hilbert action specialized to such an
isotropic metric. The momentum is then given by
$p_a=3a\dot{a}/\kappa$ with the gravitational constant $\kappa$, and
the Hamiltonian is equivalent to the Friedmann equation. There are
different sets of canonical variables, all related to the spatial
metric and extrinsic curvature of spatial slices, some of which are
better adapted to quantization. Here, we use the example of isotropic
quantum cosmology coupled to matter in the form of dust (constant
matter energy $E$) in Ashtekar variables \cite{AshVar} which in the
isotropic case are $(c,p)$ with $\{c,p\}=\frac{1}{3}\gamma\kappa$
where $\gamma$ is a real constant, the so-called Barbero--Immirzi
parameter\cite{AshVarReell,Immirzi}, and give a Hamiltonian
$H=-3\gamma^{-2}\kappa^{-1}c^2\sqrt{p}+E$. (This is formally similar
to a system with varying mass as discussed in \cite{EffAcVarMass}.)
For details of the variables $(c,p)$ used we refer to
\cite{IsoCosmo,Bohr}. The geometrical meaning can be seen from
$|p|=a^2$ and $c=\frac{1}{2}\gamma\dot{a}$ in terms of the scale
factor $a$. For a semiclassical universe, we thus have $c\ll1$ and
$p\gg \ell_{\rm P}^2=\hbar\kappa$ In contrast to $a$, $p$ can also be
negative in general with the sign corresponding to spatial
orientation, but we will assume $p>0$ in this example. The
Hamiltonian $H$ is actually a constraint in this case, but we will
not discuss aspects of constrained systems in the geometric
formulation here.
To simplify calculations we already weaken the notion of a strong
effective system and require agreement between quantum and effective
dynamics only up to corrections of the order $\hbar$. Performing the
$\hbar$ expansion of the mean value of the Hamiltonian we obtain
\begin{equation}
H_Q=H+\frac{1}{2}\hbar\kappa H,_{ij}\tilde{G}^{ij}+O(\hbar^{\frac{3}{2}})=
H-\frac{3\hbar}{\gamma^2}\left(\sqrt{p}\tilde{G}^{0,2}+
\frac{c}{\sqrt{p}}\tilde{G}^{1,2}-\frac{c^2}{8\sqrt{p^3}}
\tilde{G}^{2,2}\right)+O(\hbar^{\frac{3}{2}})\,.
\end{equation}
in terms of $\tilde G^{a,n}=\ell_{\rm P}^{-n}{G}^{a,n}$. These
variables are motivated by the uncertainty relations, with for the
symplectic structure in this example read
$G^{0,2}G^{2,2}-(G^{1,2})^2\geq \frac{1}{36}\gamma^2\ell_{\rm
P}^4$. Thus, one can expect that for minimal uncertainty the
$\tilde{G}$ (which are not dimensionless) do not contribute further
factors of $\hbar$. We will now perform a more detailed analysis.
{}From the commutation relation $[c,p]=\frac{1}{3}i\gamma\ell_{\rm
P}^2$ we obtain
\[
\dot G^{a,n}=(\dot c\partial_c+\dot p\partial_p)G^{a,n}=
-\frac{1}{\gamma\sqrt{p^3}}
\left(-2ap^2G^{a-1,n}+(n-2a)cpG^{a,n}-\frac{(n-a)c^2}{4}G^{a+1,n}\right)\,.
\]
At this point it is useful to define $G^{a,n}=:c^{n-a}p^ag^{a,n}$ with
dimensionless $g$, leading to
\[
({\textstyle\frac{1}{2}}c\partial_c-2p\partial_p)g^{a,n}=-ag^{a-1,
n}+\frac{1}{4}(n+a)g^{a,n}-\frac{1}{8}(n-a)g^{a+1,n}\,.
\]
This system of partial differential equations can be simplified by
introducing coordinates $(x,y)$ by $e^{2x}=\ell c^2/\sqrt{p}$ and
$y:=c^2\sqrt{p}/\ell$ with a constant $\ell$ of dimension length,
e.g.\ $\ell=\kappa E$ as the only classically available length scale
independent of the canonical variables, such that
$\frac{1}{2}c\partial_c-2p\partial_p=\partial_x$ and
$(\frac{1}{2}c\partial_c-2p\partial_p)f(y)=0$ for any function $f$
independent of $x$.
The general solution for $n=2$ then is
\begin{eqnarray}
g^{0,2}&=&g_0(y)+g_{\frac{3}{2}}(y)e^{\frac{3}{2}x}+g_{3}(y)e^{3x}\nonumber\\
g^{1,2}&=&2g_0(y)-g_{\frac{3}{2}}(y)e^{\frac{3}{2}x}-4g_{3}(y)e^{3x}\nonumber\\
g^{2,2}&=&4g_0(y)-8g_{\frac{3}{2}}(y)e^{\frac{3}{2}x}+16g_{3}(y)e^{3x}\nonumber
\end{eqnarray}
subject to the uncertainty relation
\begin{equation}\label{QCuncert}
4g_0g_3-g_{\frac{3}{2}}^2\geq
\frac{\gamma^2\ell_{\rm P}^4}{2^23^4\ell^{\frac{3}{2}}(c^2\sqrt{p})^{\frac
{5}{2}}}\,.
\end{equation}
Since $H$ is a constraint, $y$ will be constant physically such that
we can also consider $g_0$, $g_{\frac{3}{2}}$ and $g_{3}$ as
constants. On the constraint surface, the right hand side of the
uncertainty relation is then of the order $(\ell_{\rm P}/\kappa E)^4$
for the above choice of $\ell$ and thus very small.
Note first that, unlike the free particle and the harmonic
oscillator examples, solutions for the $G^{a,n}$ do not leave
unaffected the effective system. In this example, provided that it
allows an effective Hamiltonian description, we would thus encounter
an effective Hamiltonian different from the classical one. Spreading
back-reacts on the dynamics according to the effective equations
\begin{eqnarray}
\gamma\dot c &=&-c^2p^{-\frac{1}{2}}\left(1+
\frac{1}{2}g_0-g_{\frac{3}{2}}(\ell c^2p^{-\frac{1}{2}})^{3/4}
+11g_3(\ell c^2p^{-\frac{1}{2}})^{3/2}
+\cdots\right)
\\\gamma\dot p&=&c\sqrt{p}\left(4+
2g_0+
2g_{\frac{3}{2}}(\ell c^2p^{-\frac{1}{2}})^{3/4}
-16g_3(\ell c^2p^{-\frac{1}{2}})^{3/2}
+\cdots\right)
\end{eqnarray}
There is no explicit $\hbar$ in the correction terms because we use
dimensionless variables, but the uncertainty relation shows that for
constants close to minimal uncertainty the corrections are of higher
order in the Planck length.
Moreover, as in the free particle case no constant solutions for the
$G^{a,n}$ exist. We thus have to weaken not only the condition of a
preserved embedding, but also its horizontality. Since we are
interested in effective equations only up to a certain order in
$\hbar$, which we already used in the dynamics of this example, it is
reasonable to require constant $G$ also only up to terms of some
order in $\hbar$. This means that the quantum variables do not need to
be strictly constant, but change only slowly. In this example, we have
\begin{eqnarray*}
\dot{G}^{0,2} &=& -\gamma^{-1}
c^3 p^{-1/2}
(g_0+{\textstyle\frac{5}{2}}g_{\frac{3}{2}}e^{\frac{3}{2}x}+
4g_3e^{3x})\\
\dot{G}^{1,2} &=& 3\gamma^{-1}
c^2 p^{1/2}
(g_0+ 2g_3e^{3x})\\
\dot{G}^{2,2} &=& 4\gamma^{-1}
c p^{3/2}
(2g_0+5g_{\frac{3}{2}}e^{\frac{3}{2}x}+ 2g_3e^{3x})
\end{eqnarray*}
where $e^x$ is small for a large, semiclassical universe and the
dominant terms are given by $g_0$. For large $p$, $\dot{G}^{2,2}$
grows most strongly, but we can ensure that it is small by using small
$g_0$. It is easy to see that the uncertainty relation allows $g_0$ to
be small enough such that the $\dot{G}^{a,2}$ are small and at most of
the order $\hbar$. For instance, $g_{\frac{3}{2}}=0$, $g_3=1$ and
$g_0\sim \ell_{\rm P}^4 \ell^{-3/2} (c^2\sqrt{p})^{-5/2}$ is a
suitable choice where correction terms to the classical equations are
small and the strongest growth of the second order quantum variables,
given by $\dot{G}^{2,2}\sim \ell_{\rm P}^4 \ell^{-3/2} c^{-4}p^{1/4}$
is small on the constraint surface and using $\ell\sim \kappa E$:
$\dot{G}^{2,2}\sim \ell_{\rm P}^4 (\kappa E)^{-7/2} p^{5/4}$. To the
$\hbar$-order of the equations derived here the system is thus almost
preserved, and quantum variables do not grow strongly for some time of
the evolution provided that the integration constants $g_a$ are chosen
appropriately. (Similar results, without using explicit quantum
variables $G$, have been obtained in \cite{Josh,Perturb}.)
\end{excount}
In the following section we will
formalize the weakened conditions on an effective system and show
that this allows one to reproduce standard effective action results.
\section{An-Harmonic oscillator}
We now come to the main part of this paper. As motivated by the
preceding examples, we first weaken the effective equation scheme
developed so far and then show that it reproduces the standard
effective action results when quantum dynamics is expanded around the
ground state of a harmonic oscillator. From what we discussed so far,
one can already see that basic properties are the same: First, the
harmonic oscillator ground state (or any coherent state) gives a
quantum dynamics with constant quantum variables such that the quantum
Hamiltonian differs from the classical one only by a
constant. Effective equations of motion are then identical to the
classical ones, which agrees with the usual result. If there is an
anharmonic contribution to the potential, however, the evolution of
classical variables depends on the quantum variables, and moreover
there is no finite set of decoupled quantum variables. Thus, for an
exact solution all infinitely many quantum variables have to be taken
into account, and in general {\em no strong effective system
exists}. This is the analog of the non-locality of the standard
effective action which in general cannot be written as a time integral
of a functional of the $q^i$ and finitely many of their time
derivatives. In standard effective actions, a derivative expansion is
an important approximation, and similarly we have to weaken our
definition of effective systems by introducing approximate notions.
The classical Hamiltonian is now given by $H=
\frac{1}{2m}p^2+\frac{1}{2}m\omega^2q^2+U(q)$, and the quantum
Hamiltonian in terms of dimensionless quantum variables (\ref{Gtilde}),
dropping the tilde from now on, is
\begin{equation} \label{HQexpand}
H_Q=\frac{1}{2m}p^2+\frac{1}{2}m\omega^2q^2+U(q)
+\frac{\hbar\omega}{2}(G^{0,2}+G^{2,2})+\sum_n\frac{1}{n!}
(\hbar/m\omega)^{n/2}U^{(n)}(q)G^{0,n}\,.
\end{equation}
This generates equations of motion
\begin{eqnarray}
\nonumber \dot{q}&=& m^{-1}p\label{eom}\\
\dot{p}&=&-m\omega^2q -U'(q)-\sum_n\frac{1}{n!}(m^{-1}\omega^{-1}
\hbar)^{n/2}U^{(n+1)}(q)G^{0,n}\\
\nonumber \dot{G}^{a,n}&=&-a\omega
G^{a-1,n}+(n-a)\omega G^{a+1,n}
-\frac{aU''}{m\omega}G^{a-1,n}\\
\nonumber&&+
\frac{\sqrt{\hbar}aU'''(q)}{2(m\omega)^{\frac{3}{2}}}G^{a-1,n-1}G^{0,2}
+\frac{\hbar aU''''(q)}{3!(m\omega)^2}G^{a-1,n-1}G^{0,3}\\
\nonumber&&
-\frac{a}{2}\left(
\frac{\sqrt{\hbar}U'''(q)}{(m\omega)^{\frac{3}{2}}}G^{a-1,n+1}+\frac{\hbar
U''''(q)}{3(m\omega)^2}G^{a-1,n+2}\right)\\
\nonumber&&
+\frac{a(a-1)(a-2)}{3\cdot2^3}\left(
\frac{\sqrt{\hbar}U'''(q)}{(m\omega)^{\frac{3}{2}}}G^{a-3,n-3}+\frac{\hbar
U''''(q)}{(m\omega)^2}G^{a-3,n-2}\right)+\cdots
\end{eqnarray}
showing explicitly that a potential of order higher than two makes
the equations of motion for the $G^{a,n}$ involve $G^{a,n+1}$,
$G^{a,n+2}$ and so on, therefore requiring one to solve an infinite
set of coupled non-linear equations. However, for semiclassical
dynamics the $G^{a,n}$ should be small as they are related to the
spreading of the wave function. This allows the implementation of a
perturbative expansion in $\hbar^{1/2}$ powers to solve the equations
for $G$, where the number of degrees of freedom involved to calculate
the equations of motion for the classical variables up to a given
order is finite.
We emphasize that corrections appear at half-integer powers in
$\hbar$, except for the linear order. This is in contrast to what is
often intuitively expected for quantum theories, where only
corrections in powers of $\hbar$ are supposed to appear. (Correction
terms of half-integer order do not appear only if the classical
Hamiltonian is even in all canonical variables.) However, this is much
more natural from a quantum gravity point of view where not $\hbar$
but the Planck length $\ell_{\rm P}=\sqrt{\kappa\hbar}$ is the basic
parameter, which is a fractional power of $\hbar$ (see the quantum
cosmology example).
To solve the equations, we expand $G^{a,n}=\sum_e
G^{a,n}_e\hbar^{e/2}$. If we want to find a solution up to $k$th order
we have to calculate the solutions to (\ref{eom}) for $G^{0,2}$ up to
the order $k-2$ and $G^{0,3}$ to the order $k-3$. At the same time,
these will be functions of the $G^{a,n}$ to all orders up to
$G^{a,3+2(k-3)-l}_l$ for all positive integer $l\leq 2k-3$.
\begin{ex}
For $U(q)=\frac{\delta}{4!} q^4$ we have equations of motion
\begin{eqnarray} \nonumber\dot
G^{a,n}_0&=&\!-a\omega G_0^{a-1,n}\!\! +\!\!(n\!-\!a)\omega
G_0^{a+1,n} \!\! -\!\!\frac{\delta
q^2a}{2m\omega}G_0^{a-1,n}\!\!\\
\nonumber\dot {G}^{a,n}_1&=&\!-a\omega G_1^{a-1,n}\!\!
+\!\!(n\!-\!a)\omega G_1^{a+1,n} \!\! -\!\!\frac{\delta
q^2a}{2m\omega} G_1^{a-1,n}\!\!+\!\!\frac{\delta
aq}{2(m\omega)^{\frac{3}{2}}} G_0^{0,2} G_0^{a-1,n-1}\\\nonumber&&
-\frac{\delta a
q}{2(m\omega)^{\frac{3}{2}}}\left(G_0^{a-1,n+1}-
\frac{(a-1)(a-2)}{12} G_0^{a-3,n-3}\right)\\
\nonumber\dot { G}^{a,n}_2&=&\!-a\omega G_2^{a-1,n}\!\!
+\!\!(n\!-\!a)\omega G_2^{a+1,n} \!\! -\!\!\frac{\delta
q^2a}{2m\omega}G_2^{a-1,n}\!\!+\!\!\frac{\delta
aq}{2(m\omega)^{\frac{3}{2}}}( G_1^{0,2} G_0^{a-1,n-1}+ G_0^{0,2}
G_1^{a-1,n-1})\\\nonumber&& -\frac{\delta a
q}{2(m\omega)^{\frac{3}{2}}}\left(G_1^{a-1,n+1}-\frac{(a-1)(a-2)}{12}
G_1^{a-3,n-3}\right)\\\nonumber&& +\frac{\delta a}{3!(m\omega)^2}
G_0^{0,3} G_0^{a-1,n-1}-\frac{\delta a q}{6(m\omega)^2}\left(
G_0^{a-1,n+2}-\frac{(a-1)(a-2)}{4(m\omega)^2}G_0^{a-3,n-2}\right)
\end{eqnarray}
up to second order.
\end{ex}
Now, in order to construct a strong effective theory of the system we
would again have to find a submanifold which is invariant under the
action of the Hamiltonian. The only dynamics contained in our quantum
degrees of freedom then comes via the submanifold: $\dot
G^{a,n}=\dot{x}^i\partial_iG^{a,n}$, e.g.\ for a potential
$U(q)=\frac{\delta}{4!} q^4$
\begin{equation}\label{G=section}
\dot
G^{a,n}=\left(\frac{1}{m}p\partial_q-\left(m\omega^2q
+\frac{\delta}{3!}q^3 +\frac{\hbar\delta q}{2m\omega}G^{0,2}
+\frac{\hbar^{3/2}\delta
}{3!(m\omega)^{\frac{3}{2}}}G^{0,3}\right)\partial_p\right)G^{a,n}\,.
\end{equation}
It seems convenient to perform an expansion in $\delta$ in addition to
$\hbar$ in order to solve the system of equations. However, solutions
of these equations, perturbative or exact, are in general not single
valued functions of the classical variables and therefore an exactly
preserved semiclassical submanifold does not exist. In fact, we have
\begin{lemma}
Let $({\cal H}, \hat{H})$ be a quantum mechanical system such that
$\hat{H}=\frac{1}{2m}\hat{p}^2+V(\hat{q})$. If
$({\cal H},\hat{H})$ admits a strong effective system of the
classical dimension then
$({\cal H}, \hat{H})$ is linear.
\end{lemma}
\begin{proof}
By assumption, we have an embedding of the classical phase space into
the quantum phase space such that the quantum flow is everywhere
tangential to the embedding and the classical symplectic structure is
induced. We can thus take the quantum Hamiltonian vector field and
choose additional horizontal vector fields generated by functions
$L^i$ on ${\cal K}$ such that they span the tangent space to ${\cal
P}$ in each point $p\in{\cal P}$. Since, by construction, the
collection of all those vector fields can be integrated to a
manifold, they are in involution. Vector fields on the bundle,
finally, correspond to linear operators on the Hilbert space having
the same commutation relations as the Poisson relations of the
generating functions. There is thus a complete set of operators of
the quantum system which includes the Hamiltonian and is in
involution.
\end{proof}
The notion of a strong effective system then does not allow enough
freedom to include many physically interesting systems. Indeed, the
dynamics of a strong effective system does not significantly differ
from the classical one:
\begin{theo} \label{StrongEffHam}
For any strong effective system of classical dimension, $H_{\rm
eff}=H+{\rm const}$ differs from the classical Hamiltonian only by a
constant of order $\hbar$.
\end{theo}
\begin{proof}
{}From the preceding lemma it follows that a strong effective system
can exist only when the Hamiltonian is at most quadratic in the
complete classical phase space functions $L^i$. In an expansion as in
(\ref{HQexpand}) we then have only the linear order in $\hbar$
containing $G^{a,2}$. Since by assumption the strong effective system
is of the classical dimension, horizontality implies that the
$G^{a,2}$ are constant. Thus, $H_Q-H=\hbar c$ with a constant $c$,
and $H_Q$ directly gives the effective Hamiltonian.
\end{proof}
If quantum degrees of freedom are included in a strong effective
system of dimension higher than the classical one, they are then only
added onto the classical system without interactions, which is not of
much interest. On the other hand, for effective equations one is not
necessarily interested in precisely describing whole orbits of the
system, for which single valued solutions $G(q,p)$ would be required,
but foremost in understanding the local behavior compared to the
classical one, i.e.\ modifications of time derivatives of the
classical variables. The conditions for a strong effective system,
however, are requirements on the whole set of orbits of the system.
Thus, as noted before, we have to weaken our definition of effective
systems. We first do so in a manner which focuses on the finite
dimensionality of classical systems but ignores more refined notions
of semiclassicality:
\begin{defi} \label{EffSys}
An {\em effective system of order $k$} for a quantum system $({\cal
H},\hat{H})$ is a dynamical system $({\cal M},X_{\rm eff})$, i.e.\ a
finite-dimensional manifold ${\cal M}$ together with an effective flow
defined by the vector field $X_{\rm eff}$, which can locally be
embedded in the K\"ahler manifold ${\cal K}$ associated with ${\cal
H}$ such that it is {\em almost preserved}: for any $p\in{\cal M}$
there is an embedding $\iota_p$ of a neighborhood of $p$ in ${\cal K}$
such that $X_H(p)-\iota_{p*}X_{\rm eff}(p)$ is of the order $\hbar^{k+1}$
with the vector field $X_H$ generated by the quantum Hamiltonian.
\end{defi}
An effective system in this sense allows one to describe a quantum
system by a set of finitely many equations of motion, as we
encountered it before in the examples. The only concept of
classicality is the finite dimensionality, while otherwise the quantum
variables included in the effective system can change rapidly and grow
large even if an initial state has small fluctuations. Moreover, the
finite dimensional space of an effective system is not required to be
of even dimension or, even if it is of even dimension, to be a
symplectic space. In general, it is only equipped locally with a
pre-symplectic form through the pull-back of $\Omega$ on ${\cal K}$. A
stronger notion, taking these issues into account, is
\begin{defi} \label{HamEffSys}
A {\em Hamiltonian effective system $({\cal P},H_{\rm eff})$ of order
$k$} for a quantum system $({\cal H},\hat{H})$ is a
finite-dimensional subspace ${\cal P}$ of the K\"ahler
manifold ${\cal K}$ associated with ${\cal H}$ which is
\begin{enumerate}
\item {\em symplectic}, i.e.\ equipped with a symplectic structure
$\Omega_{\cal P}=\iota^*\Omega_{\cal K}+O(\hbar^{k+1})$ agreeing up to
order $\hbar^{k+1}$ with the pull back of the full symplectic
structure, and
\item {\em almost preserved and Hamiltonian}, i.e.\
there is a Hamiltonian vector field $X_{\rm eff}$ generated by the
{\em effective Hamiltonian} $H_{\rm eff}$ on ${\cal P}$ such that for
any $p\in{\cal P}$ the vector $X_H(p)-X_{\rm eff}(p)$ is of the order
$\hbar^{k+1}$ with the vector field $X_H$ generated by the quantum
Hamiltonian.
\end{enumerate}
\end{defi}
By using a symplectic subspace we ensure that the commutator algebra
of the quantum system, which determines the symplectic structure on
${\cal K}$, is reflected in the symplectic structure of the effective
system. Moreover, as in the previous definition the dynamics of the
effective system is close to the quantum dynamics. Still, the
effective Hamiltonian is not directly related to the quantum
Hamiltonian: one generally expands the quantum Hamiltonian in powers
of $\hbar$, solves some of the equations of motion for $G^{a,n}$ and
reinserts solutions into the expansion. Nevertheless, to low orders in
$\hbar$ most fluctuations can be ignored and it is often possible to
work directly with the quantum Hamiltonian as the expectation value in
suitably peaked states. This is the case for effective equations of
quantum cosmology \cite{Inflation, Perturb, Josh} where this procedure
has been suggested first.
In this definition, we still do not include any reference to the
corresponding classical system. In general, its dynamics will not be
close to the effective dynamics, but there are usually regimes where
this can be ensured for at least some time starting with appropriate
initial states. Also the symplectic structure $\Omega_{\cal P}$ can
differ from the classical one. This is realized also for effective
actions such as (\ref{EffAc}), where the symplectic structure also
receives correction terms of the same order in $\hbar$ as the
Hamiltonian. The effective and classical symplectic structures are
close if the embedding of ${\cal P}$ in ${\cal K}$ is ``almost
horizontal'' which can be formalized by requiring that for any $p\in
{\cal P}$ and $v\in{\rm Hor}_p^{\Omega}{\cal K}$ there is a $w\in
T_p{\cal P}$ such that $w-v\in T_p{\cal K}$ is of some appropriate
order in $\hbar$.
We do not make this definition of almost horizontality more precise
since it turns out not to be needed to reproduce usual effective
action results. Moreover, its practical implementation can be rather
complicated: The quantum cosmology example showed that the order to
which one can ensure almost horizontality is not directly related to
the order in $\hbar$ to which equations of motion are expanded. If one
has an almost horizontal embedding, ignored quantum degrees of freedom
remain almost constant such that they do not much influence the
evolution for an appropriately prepared initial state. But not any
system can be approximated in this manner, and so the condition of
almost horizontality implies that for some systems only higher
dimensional Hamiltonian effective systems exist. In such a case there
are some quantum degrees of freedom which can by no means be ignored
for the effective dynamics. On the other hand, in such a case it may
be difficult to guarantee the existence of a symplectic
structure. This happens, for instance, if the $G^{a,2}$ change too
rapidly, but not higher $G$. One can then use a 5-dimensional
effective system with variables $(q,p,G^{0,2},G^{1,2},G^{2,2})$ which
can only be pre-symplectic and thus not Hamiltonian. Alternatively,
one can drop the condition of almost horizontality, but then has to
accept a new (pre-)symplectic structure which is not necessarily
related to the classical one by only correction terms. These
constraints show that a discussion of quantum variables in
higher-dimensional effective systems can be complicated if one insists
on the presence of a canonical structure. Moreover, computing the
symplectic structure on the K\"ahler space and its pull-back to the
effective manifold in an explicit manner is usually complicated (see,
however, Sec.~\ref{DynCohStates} for a brief discussion).
We thus present a final definition which does not require
an explicit form of the quantum symplectic structure but is sufficient
for the usual setting of effective actions:
\begin{defi}
An {\em adiabatic effective system of order $(e,k)$} for a quantum
system $({\cal H},\hat{H})$ is an effective system $({\cal M},X_{\rm
eff})$ of order $k$ in the sense of Def.~\ref{EffSys} such that the
local embeddings are given by solutions up to order $e$ in an
adiabatic expansion of those quantum variables not included as variables of
the effective system.
\end{defi}
Here, adiabaticity intuitively captures the physical property of a
weak influence of quantum degrees of freedom on the classical ones: in
the adiabatic approximation they change only slowly compared to the
classical variables. Provided that a semiclassical initial state is
chosen it is then guaranteed that the system remains semiclassical for
some time.
This viewpoint is still much more general than the usual definition of an
effective action, and it allows much more freedom by choosing
different finite-dimensional subspaces. For an explicit derivation of
effective equations, of course, one has to find solutions
$G^{a,n}(x^i)$ as they appear in the quantum Hamiltonian, which
requires one to solve an infinite set of coupled differential
equations for infinitely many variables. Only in exceptional cases,
such as integrable systems, can this be done without
approximations. Moreover, general solutions for $G^{a,n}(x^i)$ contain
infinitely many constants of integration which then also appear in the
effective equations after inserting the $G^{a,n}(x^i)$. On the one
hand, this allows much more freedom in choosing the states, such as
squeezed or of non-minimal uncertainty, to perturb around. But it also
means that one needs criteria to fix the integration constants in
situations of interest. One such situation is that of
\begin{theo}
A system with classical Hamiltonian
$H=\frac{1}{2m}p^2+\frac{1}{2}m\omega^2q^2+U(q)$ admits an adiabatic
effective system of order $(2,1)$ whose dynamics is governed by the
effective action (\ref{EffAc}).
\end{theo}
\begin{proof}
In order to find the subspace ${\cal P}$ and the dynamics on it we
expand the quantum Hamiltonian in powers of $\hbar$ and solve the
equations of motion for $G^{a,n}$ in an adiabatic approximation.
The adiabatic approximation of slowly varying fields in the equations
of motion is an expansion in a parameter $\lambda$ introduced for the
sake of the calculation, but in the end set to
$\lambda=1$. Derivatives with respect to time are scaled as
$\frac{{\mathrm{d}}}{{\mathrm{d}} t}\rightarrow\lambda\frac{{\mathrm{d}}}{{\mathrm{d}} t}$ and, expanding
$G^{a,n}=\sum_eG^{a,n}_e\lambda^e$, the equations of motion
\[
\dot x^i\partial_iG^{a,n}=\{G^{a,n},H_Q\}_Q
\]
imply
\[
\dot x^i\partial_iG_{e-1}^{a,n}=\{G_e^{a,n},H_Q\}_Q\,.
\]
In addition to the adiabatic approximation we also perform a
semiclassical expansion in powers of $\hbar$. In what follows, we
will calculate the first order in $\hbar$ and go to
second order in $\lambda$ for $G^{a,2}$.
To zeroth order in $\lambda$ the equations to solve are
\[
0=\{G^{a,n}_0,H_Q\}_Q=\omega\left((n-a)G_0^{a+1,n}-a
\left(1+\frac{U''}{m\omega^2}\right)G_0^{a-1,n}\right)
\]
with general solution
\[
G_0^{a,n}=(^{n/2}_{a/2})(^n_a)^{-1}\left(
1+\frac{U''}{m\omega^2}\right)^{a/2}G^{0,n}_0
\]
for even $a$ and $n$, and $G_0^{a,n}=0$ whenever $a$ or $n$ are
odd. This still leaves the value of $G_0^{0,n}$ free, which will be
fixed shortly. To first order in $\lambda$,
\[
(n-a)G_1^{a+1,n}-a\left(1+\frac{U''}{m\omega^2}\right)
G_1^{a-1,n}=\frac{1}{\omega}\dot{G}_0^{a,n}
\]
implies
\begin{lemma}
\[
\sum_{a\:{\rm even}}(^{n/2}_{a/2})\left(1+\frac{U''}{m\omega^2}\right)^\frac{n-a}{2}\dot{G}_0^{a,n}=0
\]
\end{lemma}
\begin{proof}
{}From the equation above\[\sum_{a}(^{n/2}_{a/2})\left(1+\frac{U''}
{m\omega^2}\right)^\frac{n-a}{2}\!\!\dot{G}_0^{a,n}=\sum_{a}(^{n/2}_{a/2})\left(1+\frac{U''}
{m\omega^2}\right)^\frac{n-a}{2}\!\!\left(
(n-a)G_1^{a+1,n}-a\left(1+\frac{U''}{m\omega^2}\right)
G_1^{a-1,n}\right)\]
manipulating the first term of the right hand side expression we
shift $a\to a-2$ leaving the limits for $a$ unaffected in the
summation to obtain
\[\sum_{a}\frac{(n/2)!\left(1+\frac{U''}
{m\omega^2}\right)^\frac{n-a+2}{2}}{((a-2)/2)!((n-a+2)/2)!}
(n-a+2)G_1^{a-1,n}=\sum_{a}(^{n/2}_{a/2})a\left(1+\frac{U''}{m\omega^2}\right)^\frac{n-a+2}{2}
G_1^{a-1,n}\] which cancels then the second term to finish the
proof.
\end{proof}
This imposes a constraint on $G_0^{0,n}$ solved by setting
$G^{0,n}_0=C_n(1+\frac{U''}{m\omega^2})^{-n/4}$. The remaining
constants $C_n$ are fixed to $C_n=\frac{n!}{2^n(n/2)!}$ by requiring
that the limit $U\rightarrow 0$ reproduces the quantum variables of
coherent states of the free theory (\ref{freemoments}) or equivalently
by requiring the perturbative vacuum of the quantum theory to be
associated to the vacuum of the effective system. Therefore,
\[
G_0^{a,n}=\frac{(n-a)!a!}{2^n((n-a)/2)!(a/2)!}
\left(1+\frac{U''}{m\omega^2}\right)^{\frac{2a-n}{4}}\,.
\]
We will need only the $n=2$ corrections to first order in $\hbar$,
and the solution to the first order equations becomes trivial:
$G^{1,2}_1=\frac{1}{2\omega}\dot G^{0,2}_0$, the rest being zero. To
second order we have
\[
G^{2,2}_2-\left(1+\frac{U''}{m\omega^2}\right)
G^{0,2}_2=\frac{1}{\omega} \dot{G}_1^{1,2}=\frac{1}{2\omega^2}\ddot G^{0,2}_0
\]
again leaving free parameters in the general solution to be fixed by
the next, third order from which we obtain
\[
\left(1+\frac{U''}{m\omega^2}\right)\dot
G^{0,2}_2+\dot G^{2,2}_2=0
\]
as in the Lemma before. The previous two equations can be combined to
a first order differential equations for $G_2^{0,2}$ in terms of known
solutions at lower orders:
\[
\dot{G}_2^{0,2}- \frac{\dot{G}_0^{0,2}}{G_0^{0,2}} G_2^{0,2}+
\frac{1}{\omega^2} (G_0^{0,2})^2 \dddot{G}^{0,2}_0=0\,.
\]
Its general solution is
\[
G_2^{0,2}= \left( c-2\omega^{-2} (G_0^{0,2})^{3/2}
\frac{{\mathrm{d}}^2}{{\mathrm{d}} t^2}(G_0^{0,2})^{1/2}\right) G_0^{0,2}
\]
where the integration constant $c$ can be fixed to $c=0$ by requiring
the correct free limit $U=0$ (for which the original two differential
equations imply $G_2^{2,2}=-G_2^{0,2}=0$). From this, the solution to
the system is
\[
G_2^{0,2}=-\frac{2}{\omega^2} (G^{0,2}_0)^{\frac{5}{2}}
\frac{{\mathrm{d}}^2}{{\mathrm{d}} t^2}(G^{0,2}_0)^{1/2}=\frac{\left(
1+\frac{U''}{m\omega^2}\right)^{-\frac{7}{2}}}
{4\omega^2}\left(\left(1+\frac{U''}{m\omega^2}\right)\frac{U'''\ddot
q+U''''\dot q^2}{4m\omega^2}-5\left(\frac{U'''\dot
q}{4m\omega^2}\right)^2\right)\,.
\]
Finally, putting our approximate expressions for the quantum variables
back into the equations of the classical variables (\ref{eom}), we obtain
\begin{eqnarray}
&&\nonumber\left(m+\frac{\lambda^2\hbar(U''')^2}{2^5m^2\omega^5\left(
1+\frac{U''}{m\omega^2}\right)
^{\frac{5}{2}}}\right)\ddot q+\frac{\lambda^2\hbar\dot
q^2\left(4m\omega^2U'''U''''\left(1+\frac{U''}{m\omega^2}\right)-
5(U''')^3\right)}
{2^7m^3\omega^7\left(1+\frac{U''}{m\omega^2}\right)^{\frac{7}{2}}}\\
&&+m\omega^2q+U'+\frac{\hbar
U'''}{4m\omega\left(1+\frac{U''}{m\omega^2}\right)^{\frac{1}{2}}}=0
\end{eqnarray}
as it also follows from the effective action (\ref{EffAc}) after setting
$\lambda=1$.
\end{proof}
The proof demonstrates the role of the harmonic oscillator ground
state and its importance for fixing constants in the effective
equations. If there is no distinguished state, effective equations
contain free parameters incorporating the freedom of choosing an
initial state in which the system is prepared.
The role of adiabaticity here is the same as in the derivative
expansion of low energy effective actions, but even for an an-harmonic
oscillator are the effective systems defined here more general: we are
not forced to expand around a vacuum state but can make other choices
depending on the physical situation at hand. The vacuum state was used
here in order to fix the constants $C_n$ which appear when integrating
equations of motion for quantum variables. One can just as well choose
different constants, for instance those corresponding to a squeezed
state, and obtain the corresponding effective equations. Note,
however, that not every choice is consistent with the adiabatic
approximation. For instance, the proff showed that $G_0^{a,2}$ had to
be zero to leading order in $\hbar$. Thus, one cannot allow arbitrary
squeezing since the parameter $G_0^{1,2}$ is restricted. This can
become non-zero only at higher orders in the expansion.
Or, while one would always include the classical variables in the
effective system, they can be accompanied by some of the quantum
variables which are not treated as adiabatic. One can include such
quantum degrees of freedom directly as defined on the quantum phase
space, or introduce them by perturbing quantum variables around the
adiabatic solution, $G^{a,n}=G^{a,n}_{\rm adiabatic}+g^{a,n}(t)$. New
degrees of freedom given by $g^{a,n}(t)$ are then independent of the
classical variables and describe quantum corrections on top of the
adiabatic one.
There are also situations where no distinguished state such as the
vacuum is known, as it happens in the example of quantum cosmology
discussed earlier. General effective equations can then still be
formulated but contain free parameters incorporating the freedom of
choosing an initial state in which the system is prepared. The
constants $C_n$ in the above proof, for instance, would then remain
unspecified and appear in effective equations. To the same order as
considered here, only the constant $C_2$ enters which will appear in
general equations of motion. Following the lines of the proof above
without fixing $C_2$ is easily seen to lead to an effective action of
the form (\ref{EffAc}) with mass term
\[
m+C_2^3\frac{\hbar U'''(q)^2}
{2^5m^2\left(\omega^2+m^{-1}U''(q)\right)^{\frac{5}{2}}}
\]
and effective potential
\[
-\frac{1}{2}m\omega^2q^2
-U(q)-C_2\frac{\hbar\omega}{2} \left(1+\frac{U''(q)}{m\omega^2}
\right)^{\frac{1}{2}}\,.
\]
\begin{rem}
Knowing the effective action, one can derive the corresponding
momentum and compute the effective symplectic structure. Corrections
to the canonical symplectic structure can then occur if one uses a
momentum variable $p$ that matches the dynamics of the mean value of
$\hat p$. Still, this does not necessarily imply that the system is
a Hamiltonian effective system of first order as per
Def.~\ref{HamEffSys} because we did not relate this symplectic
structure to that following from pull-back from the quantum
symplectic structure.
\end{rem}
\section{Dynamical coherent states}
\label{DynCohStates}
In addition to the effective dynamical behavior of classical and
quantum degrees of freedom it is also of interest to know
approximate states whose dynamics corresponds to the effective
evolution. Under the name of dynamical coherent states
\cite{CohStates}, they can be obtained by collecting the information
contained in the mean values of the fundamental operators and the
spreading as well as higher order distortions of the state of the
system. In this section, we only collect results related to the
previous discussion without going into further details.
As we already stated, the task could be achieved by summing
up the Hermite polynomial modes obtained through the Hamburger
momenta, but a short cut to the answer is possible using Moyal's
formula \cite{MoyalFormula} by which four arbitrary normalizable
vectors $|\Psi_1\rangle$, $|\Psi_2\rangle$, $|\Psi_3\rangle$ and
$|\Psi_4\rangle$ satisfy
\begin{equation}\label{moyal's}
\int\frac{{\mathrm{d}}^2z}{2\pi}\langle\Psi_1|e^{z\hat
a^\dagger-\bar{z}\hat a}|\Psi_2\rangle \langle\Psi_3|e^{-z\hat
a^\dagger+\bar{z}\hat
a}|\Psi_4\rangle=\langle\Psi_1|\Psi_4
\rangle\langle\Psi_3|\Psi_2\rangle
\end{equation}
where $z=\frac{1}{\sqrt{2}}(z^q+iz^p)$ and $\hat a=
\frac{1}{\sqrt{2\hbar}}(\hat q+i\hat p)$. For a bounded operator
$\hat F$, (\ref{moyal's}) can be rewritten as
\begin{equation}
\int\frac{{\mathrm{d}}^2z}{2\pi}\langle\Psi_1|e^{z\hat
a^\dagger-\bar{z}\hat a}|\Psi_2\rangle {\rm Tr}\left\{\hat F e^{-z\hat
a^\dagger+\bar{z}\hat a}
\right\} =\langle\Psi_1|\hat
F|\Psi_2\rangle\,.
\end{equation}
For given solutions $G^{a,n}$, the reconstruction of a dynamical
coherent state is completed by performing the integral with
arbitrary $|\Psi_1\rangle$, $|\Psi_2\rangle$ after inserting for
$\hat{F}$ the probability density operator $\hat\rho(q,p)$ and
assuming that the state is analytical such that
\[
{\rm Tr}\left\{\hat\rho(q,p)e^{-z\hat a^\dagger+\bar{z}\hat a}
\right\}=e^{\frac{i}{\sqrt\hbar}(z^qp-z^pq)}
\sum_{n=0}^{\infty}\sum_{a=0}^{n}\frac{(-)^{n-a}i^n}{n!}(^n_a)
(z^q)^{a}(z^p)^{n-a}G^{a,n}(q,p)
\]
produce the matrix elements of $\hat\rho(q,p)$ in a basis of
operators $e^{z\hat a^\dagger-\bar{z}\hat a}$. For the anharmonic
oscillator to $0th$ order in $\hbar$ we have $G^{i_1,\ldots,
i_n}=\frac{n!}{(n/2)!}G^{(i_1i_2}\cdots
G^{i_{n-1}i_n)}$ for $n$ even, implying
\[
{\rm Tr}\left\{\hat
\rho_{_U}\!(q,p)e^{-z\hat a^\dagger+\bar{z}\hat a}
\right\}=\exp\left(\frac{i}{\sqrt\hbar}(z^i\epsilon_{ij}x^j)-\frac{1}{2}z^{i
}z^{j}\epsilon_{ik}\epsilon_{jl} G^{kl}(q,p)\right)\,.
\]
In order to perform the integral above, we choose to work with
Harmonic oscillator coherent states
$|\alpha\rangle=e^{\alpha\hat{a}^\dagger-\bar\alpha\hat{a}}|0\rangle$
for which the matrix elements of the exponential
operator are $\langle\alpha|e^{z\hat
a^\dagger-\bar{z}\hat{a}}|\alpha'\rangle=\exp(-\frac{1}{4\hbar}
({\alpha'}^i-\alpha^i)
\delta_{ij}({\alpha'}^j-\alpha^j)+\frac{i}{4\hbar}
({\alpha'}^i+\alpha^i)\epsilon_{ij}
({\alpha'}^j-\alpha^j+2z^j))$. Finally, defining
$S_i=\delta_{ij}({\alpha'}^j-\alpha^j)+
i\epsilon_{ij}({\alpha'}^i+\alpha^i-2x^i),$ the matrix elements of
the probability density operator are
\begin{eqnarray}\label{rho}
\langle
\alpha|\hat\rho_{_U}\!(q,p)|\alpha'
\rangle &=& \frac{1}{\sqrt{\det(\frac{1}{2}\delta^{ij}+G^{ij})}}
\exp\left(-\frac{1}{4\hbar}S_{i_1}\epsilon^{i_1j_1}(2G^{ij}+
\delta^{ij})^{-1}_{j_1j_2}\epsilon^{j_2i_2}S_{i_2}
\right)\\
&&\times \exp\left(-\frac{i}{4\hbar}
({\alpha'}^i-\alpha^i)\epsilon_{ij}({\alpha'}^j+\alpha^j)
-\frac{1}{4\hbar}({\alpha'}^i-\alpha^i)\delta_{ij}({\alpha'}^j-\alpha^j)
\right).\nonumber
\end{eqnarray}
The trace of the operator above can now be computed to equal one
whenever $G^{ij}$ is a non-degenerate matrix. In order to be sure that
$\rho$ is a density matrix, we need to show its positivity. We do not
have a complete proof for arbitrary systems, but using the fact that
the assumption of the state being semi-classical requires the mean
values of operators to be given by their classical expressions up to
$\hbar$ corrections, a case by case study leads to the conclusion that
the positive mean values above lead to positivity of the
operator.
Furthermore, the state of the quantum system as given above is not in
general a pure state, but if
$G^{ij}=\frac{\hbar}{2}(e^{g\epsilon})^i_k(e^{g\epsilon})^j_l\delta^{kl},$
also $\hat\rho_{_U}(x)^2$ has trace one and thus gives a pure state which
can be realized as a squeezed coherent state labeled by the symmetric
matrix $g_{ij}$ through
\begin{equation}|x,g\rangle=\exp\left(\frac{i}{2\hbar}g_{ij}(\hat x^i-x^i)(\hat
x^j-x^j)\right)
\exp\left(-\frac{i}{\hbar}x^i\epsilon_{ij}\hat x^j\right)|0\rangle.
\end{equation}
With the help of $e^{-\frac{i}{2\hbar}g_{ij}\hat x^i\hat x^j}\hat
x^ke^{\frac{i}{2\hbar}g_{ij}\hat x^i\hat x^j}=
(e^{g\epsilon})^k_l\hat x^l$, the remaining fiber coordinates become
\begin{equation}
G^{i_1,\ldots, i_n}(g_{ij})=\frac{\hbar^{n/2}n!}
{2^{n}(n/2)!}(e^{g\epsilon})^{i_1}_{j_1}
\cdots(e^{g\epsilon})^{i_n}_{j_n}\delta^{(j_1j_2}\cdots
\delta^{j_{n-1}j_n)}
\end{equation}
Reconstructing a dynamical coherent state from the quantum variables
$G^{a,n}$ also provides means to compute the symplectic structure on
the effective space, as needed for a Hamiltonian effective system as
per Def.~\ref{HamEffSys}. For the evaluation of the symplectic
structure on the vector fields we obtain the pull-back $\Omega(Y,Z)=
2\hbar{\rm Im}\langle Y,Z\rangle$ where $Y$ and $Z$
are tangent vectors to the embedded effective manifold. Given a
dynamical coherent state $|\psi(f^i)\rangle$ as a function of
classical variables $f^i$, we can define a basis of the tangent space
spanned by $|i\rangle:=\partial{|\psi\rangle}/\partial f^i$. Expanding
$Y=\sum_i Y_i|i\rangle$ and $Z=\sum_i Z_i|i\rangle$, we have
\[
\langle Y|Z\rangle= \sum_{i,j} \bar{Y}^iZ^j
\frac{\partial\langle\psi|}{\partial
f^i}\frac{\partial|\psi\rangle}{\partial f^j}
\]
such that we can formally write
\begin{equation}
\Omega
=-2i\hbar\,{\mathrm{d}}(\langle x_1,\ldots,x_n|)\wedge
{\mathrm{d}}(|x_1,\ldots,x_n\rangle)\,.
\end{equation}
Thus, the pull-back of the symplectic structure to the subspace of
squeezed states is
\begin{equation} \label{OmegaSqueezed}
\Omega_{|x,g\rangle}= 2\epsilon_{ij}{\mathrm{d}} x^i\wedge {\mathrm{d}}
x^j+2^{-5}\hbar \delta^{i_1i_2} \epsilon^{i_3i_4}
(\delta^{j_1}_{i_1}+ (e^{g\epsilon})^{j_1}_{i_1})\cdots
(\delta^{j_4}_{i_4}+ (e^{g\epsilon})^{j_4}_{i_4}){\mathrm{d}}
g_{j_1j_3}\wedge{\mathrm{d}} g_{j_2j_4}\,.
\end{equation}
For an effective system of the classical dimension, corresponding to a
set of solutions $g_{ij}(x^k)$, we can further pull back
(\ref{OmegaSqueezed}) to the classical manifold and obtain the quantum
symplectic structure there. This shows that the classical symplectic
structure is reproduced up to corrections of order $\hbar$ if the $g$
do not change strongly (adiabaticity or almost horizontality), and
provides means to compute those correction terms.
\section{Conclusions}
Comparison with common effective action techniques applicable to
an-harmonic oscillators demonstrates how effective systems can be
formulated more generally for any quantum system. We have extracted
several definitions which have different strengths and use different
mathematical structures:
\[
\includegraphics[width=6.0cm]{diagrama.eps}
\]
Here, the strengths of each of our
definitions are compared in a condensed diagram by use of
implication arrows and abbreviations in which the initial S holds
for strong, H for Hamiltonian, A for adiabatic and ES for effective
system. The only definition not provided before is that of a strong
Hamiltonian effective system which is a Hamiltonian effective system
which is {\em exactly} preserved and whose symplectic structure is
{\em exactly} the pull-back of the quantum symplectic structure. It is
clear from the discussions before that any strong effective system is
also strong Hamiltonian, and examples lead to the conjecture that the
converse is also true. Still, since we are not aware of a proof, we
include strong Hamiltonian effective systems in this diagram.
While the definition of Hamiltonian effective systems is most
geometrical, adiabatic effective systems turn out to be more
practical and are more directly related to path integral techniques.
The weakest notion of an effective system can be applied to any
system but does not incorporate many classical aspects except for
finite dimensionality for mechanical systems. As the examples
showed, in particular that of quantum cosmology, the general
definitions provided here are more widely applicable and also
present a more intuitive understanding of possible quantum degrees
of freedom. Moreover, they are always switched on perturbatively,
and no non-analyticity in perturbation parameters as with higher
derivative effective actions arises.
The expansion of the quantum Hamiltonian also showed that in general
half-integer powers of $\hbar$ have to be expected in correction terms
and not just integer powers as often stated. The only exception is the
first order in $\hbar^{1/2}$ which does not appear because the
expectation value of variables $G^1$ would be zero by
definition. Half-integer powers do not appear only if one has a system
with a Hamiltonian even in all canonical variables, such as an
an-harmonic oscillator with an even potential, as it often occurs in
quantum field theories. These observations are relevant for quantum
gravity phenomenology because an expansion in the Planck length
$\ell_{\rm P}=\sqrt{\kappa\hbar}$ naturally involves half-integer
powers in $\hbar$. From the perspective provided here one can expect
all integer powers of the Planck length except for the linear one.
Other advantages are that the effective equations have a geometrical
interpretation where only real variables, unlike $q(t)$ in the usual
definition, occur. We are dealing directly with equations of motion
displaying only the relevant degrees of freedom, which are
automatically provided with an interpretation as properties of the
wave function, and can directly deal with canonical formulations in
which the scheme indeed arises most naturally. The techniques are
general enough for arbitrary initial states and systems with unbounded
Hamiltonians, as demonstrated by our quantum cosmology example. The
infrared problem of (\ref{EffAc}) for $m\to0$ is seen to arise only in
the adiabatic approximation, but can easily be treated by using more
general notions of effectivity such as by including the spreading
parameters $G^{a,2}$ in a pre-symplectic effective system.
As discussed briefly in the preceding section, techniques introduced
here can also be used directly at the quantum level and not just for
effective semiclassical approximations. In this context, we have
presented only first steps, but this already shows that the techniques
can give information on dynamical coherent states. This will then also
have helpful implications for the effective equation scheme itself
from which such states arise, as they can give a handle on computing
the pull-back of the full symplectic structure.
\section*{Acknowledgements}
We thank Abhay Ashtekar for several discussions and suggestions in the
early stages of this work. We are grateful to Emil Akhmedov, Benjamin
Bahr, Oscar Castillo, H\'ector Hern\'andez, Mikolaj Korzynski, Angel
Mu\~noz, Hanno Sahlmann and Thomas Thiemann for fruitful discussions
on different aspects of this work. MB is grateful to the Isaac Newton
Institute for Mathematical Sciences, Cambridge for hospitality during
the workshop ``Global Problems in Mathematical Relativity,'' where
this paper was completed, and thanks the organizers Piotr Chrusciel
and Helmut Friedrich for an invitation.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 794 |
\section{Introduction}
\label{sec:introduction}
Known stellar-mass and intermediate-mass black hole candidates accrete through mass transfer from a
stellar companion without exception.
Rapidly-accreting massive black hole candidates, such as in Seyfert
galaxies and quasars, appear to be situated
close to dusty, molecular, and highly inhomogeneous gas
reservoirs, where cold, dense clumps are in free fall or
are embedded in a hot, ionized, and tenuous
confining medium. In neither case does the accretion flow
resemble the laminar flow of the Bondi-Hoyle-Littleton solution.
There is a distinct possibility, however,
that massive black hole progenitor ``seeds,'' with masses $M_{\rm
bh}\gtrsim 100~M_\odot$ \citep{Madau:01}, did pass through an early
phase of quasiradial accretion in protogalaxies, prior to significant
dust enrichment and the emergence of a pervasive cold phase in the
interstellar medium \citep[e.g.,][]{Volonteri:05,Alvarez:06,Alvarez:09,Johnson:07,Pelupessy:07,DiMatteo:08,Greif:08}. This was the period immediately following the
onset of atomic cooling, the epoch when protogalaxies experienced rapid growth
due to cosmic infall and yet had potential wells too shallow to
retain all of their newly synthesized metals.
Since the accretion rate in quasiradial, Bondi-like accretion is
proportional to gas density, Bondi-like accretion presents an appealing
formation process for massive black holes: given the presence of
sufficiently dense gas in a protogalactic nucleus,
Eddington-limited accretion and mass exponentiation on a Salpeter
time scale would proceed; stellar-size seed black holes would
reach masses $\gtrsim 10^9 M_\odot$
inferred in high-redshift quasars in the cosmic time
available to them \citep[e.g.,][]{Haiman:01,Volonteri:03,Tanaka:08}. A potential flaw in this reasoning was noticed early,
namely, that in the event of radiatively-efficient accretion,
radiative heating and radiation pressure may reduce
the accretion rate \citep{Shvartsman:71,Buff:74,Hatchett:76,Ostriker:76,Cowie:78,Stellingwerf:82,Begelman:85,Ricotti:08,Alvarez:09}. The possibility of a transition to
radiative-feedback-driven temporal intermittency,
which has been evident in one-dimensional simulations of
Compton-heated accretion onto massive black holes in
galaxy clusters \citep{Ciotti:01,Ciotti:07,Sazonov:05},
has further complicated the assessment of quasiradial accretion's
viability as a massive black hole formation process. If the accretion
is indeed intermittent and episodic,
how long is the duty cycle, how large is the
average accretion rate, and does it permit evolution
of seed black holes into quasars? Does episodic accretion proceed
in bursts, where episodes of Eddington-limited rapid accretion
alternate with near-complete radiative quenching and outflow, as
one-dimensional models appear to suggest, or does the multidimensional
nature of realistic irradiated accretion flows imply a damping of the
fluctuations and convergence to a quasi-steady state characterized by a reduced accretion rate?
Here, we present the first results from our program to
investigate radiatively-efficient
accretion onto black holes embedded in a realistic galactic gaseous
medium with the help of high-resolution hydrodynamic simulations. We
do not attempt to simulate fluid flow and radiation emission
mechanisms near the event horizon of the black
hole; instead, we simply fix the shape of the
spectral energy distribution of the radiation produced
near the event horizon and simulate the irradiated fluid flow on radial
scales spanning the sonic radius, where the photoheated fluid falls supersonically toward the black hole, and a much larger
radius in the gas cloud that is entirely unaffected by the black
hole's radiative output, where boundary conditions for the accretion
flow are set. This work is organized as follows. In
\S~\ref{sec:numerical} we concisely describe our numerical algorithm.
A more detailed description and a suite of tests will be
provided in a longer follow-up paper (Couch et al., in preparation).
In \S~\ref{sec:results} we
describe our results with particular focus on the
intermittency of the accretion flow. In \S~\ref{sec:conclusions} we
compare our results to analytical models \citep[][and references
therein]{Milosavljevic:08} and discuss the outlook for massive black hole
formation through quasiradial accretion.
\section{Numerical Algorithm}
\label{sec:numerical}
Here we describe numerical methodologies that we have implemented in
the parallel adaptive-mesh-refinement (AMR) code FLASH \citep{Fryxell:00},
version 2.5, to facilitate our
simulations of low-angular momentum accretion
flow with a central ionizing source. The hydrodynamic solver
used was the piecewise parabolic method (PPM), which is a higher-order
Godunov method. Contact steepening that sharpens contact
discontinuities in the PPM module was disabled after we noticed that
it led to spurious flow near stationary ionization fronts. By default, FLASH does not conserve
angular momentum in 2D cylindrical simulations. To simulate fluid
motion in the azimuthal direction, we
introduce the specific angular momentum $l\equiv rv_\phi$ as an
additional conserved ``mass
scalar'' quantity that is advected with the fluid. Equivalence with
3D cylindrically symmetric equations of fluid dynamics is achieved by
adding the centrifugal force to the total acceleration, ${\bf a}={\bf
a}_{\rm grav} + {\bf a}_{\rm rad} + l^2\hat {\bf R}/R^3$.
\subsection{The Central Hole and the Central Ionizing Source}
\label{sec:hole}
The simulations were carried out in cylindrical symmetry on a
rectangular $(R,z)$ grid in two spatial dimensions, where $R$ is the distance from the axis of
symmetry. In what follows, $r$ will denote the
distance from the origin, $r^2=R^2+z^2$. A small spherical region
$r<r_{\rm hole}$ was excluded from the hydrodynamical update; we refer
to this region as the ``hole.'' A unidirectional
``outflow'' boundary condition, allowing only outflow from the simulated spatial domain and inflow into the central hole, was imposed at
$r=r_{\rm hole}$. The gravitational acceleration was set to that of a Newtonian point mass located at the origin of the grid ${\bf a}_{\rm grav}=-G M_{\rm hole}\hat {\bf r}/ r^2$.
The mass of the material flowing into the hole was added
to the point mass $M_{\rm hole}$. Self gravity of the fluid was ignored because, typically, the mass of the photoionized gas around the black hole was less than $1\%$ of the mass of the black hole.
An isotropic source of ionizing radiation was placed at the origin of
the grid. The total luminosity of the ionizing source between
energies $h\nu_{\rm min}=13.6\textrm{ eV}$ and $h\nu_{\rm
max}=100\textrm{ keV}$ was set to be proportional to the accretion
rate into the hole,
\begin{equation}
\int_{\nu_{\rm min}}^{\nu_{\rm max}} L_\nu d\nu = \epsilon \dot M_{\rm
hole} c^2 ,
\end{equation}
where $\epsilon$ is a radiative efficiency which was uniformly
set to $0.1$. The radiative spectral energy distribution was set
to the power law $L_\nu \propto \nu^{-3/2}$ and was calculated in 40
logarithmically-spaced energy bins.
\subsection{Composition, Chemistry, and Thermodynamics}
\label{sec:chemistry}
We simulated a six-species primordial fluid containing hydrogen
and helium and their ions: H,
H$^+$, He, He$^+$, He$^{++}$, and $e^{-}$. Abundances
of the six species were integrated in time with a chemical network
that includes collisional ionization of H, He, and He$^+$, ``case B''
recombination of H$^+$, He$^+$, and He$^{++}$, bidirectional charge exchange between H
(H$^+$) and He$^+$ (He), as well as primary and secondary
photoionization of H and He. Secondary photoionization and heating by
fast photoelectrons were implemented in accordance with the results of
\citet{Shull:85} and \citet{Dalgarno:99}. Photoionization and photoheating rates were calculated in
a photon-conserving manner (see \S~\ref{sec:radiation}) from the local,
extincted radiative fluxes.
Photoionization heating and collisional cooling of the fluid were
operator-split from the hydrodynamic update. Cooling processes that
were taken into account include Bremsstrahlung, collisional ionization
cooling of H, He, and He$^+$, recombination cooling of H$^+$, He$^+$,
and He$^{++}$, dielectronic recombination cooling of He$^+$,
collisional excitation cooling of H and He$^+$, and Compton cooling to
the cosmic microwave background. At the high gas densities in the
simulations, the Compton cooling was negligible.
Number densities of all six species and the temperature of the gas
were advanced
simultaneously during the chemical and thermodynamic update
with the Bulirsch-Stoer-type semi-implicit extrapolation mid-point method
of \citet{Bader:83}. Our implementation of the method closely
follows that provided in the GNU Scientific Library \citep{Galassi:06}.
This method utilizes the Jacobian matrix
of the partial derivatives of the right-hand side of our seven coupled
ordinary differential equations. We evaluate the partial derivatives
analytically. Special care was taken to accurately integrate the
abundance of the neutral and partially ionized fraction in a
strongly photoionized gas. We carried the Richardson extrapolation
sequence to four points,
which was sufficient for numerical stability.
In the operator-split alternating hydrodynamical and
chemothermodynamic update, the hydrodynamic step was globally
constrained to not exceed $10\%$ of the minimum electron abundance
change time scale, $\Delta t_{\rm hydro}\leq 0.1\ n_e /|\dot n_e|$, in
combination with the usual Courant limit. The chemothermodynamic update is
carried out in single or in multiple and possibly much shorter
Bader-Deuflhard steps. The latter are individually
limited in every cell by the time
scale on which any of the six abundances and the temperature evolves,
$\Delta t_{\rm BD}\leq \min \{ 0.1\ n_i/|\dot n_i| , 0.1\ T/\dot T,
\Delta t_{\rm hydro}\}$, where $i={\rm H},...,e^-$ \citep[cf. e.g.,][]{Whalen:06}.
\subsection{Line-of-Sight Radiative Transfer and Radiation Pressure}
\label{sec:radiation}
Here, we discuss our implementation of
multifrequency photon-conserving line-of-sight radiative transfer and the resulting
radiation pressure force. We calculate the line-of-sight optical
depth $\tau_\nu^{(k)}$ from the central source to the faces of any
rectangular zone along $N_{\rm ray}=4$ separate rays, $k=1,...,N_{\rm ray}$; the rays are equally
spaced in angle as seen from the central source. We also calculate the
optical depth to absorption within the zone along each of the rays
$\hat \tau_\nu^{(k)}$. The effective flux at the zone center is
calculated via \citep[see, e.g.,][and references therein]{Mellema:06}
\begin{equation}
\label{eq:photon_conserving}
F_\nu = \frac{L_\nu}{4\pi r^2}
\frac{\sum_{k=1}^{N_{\rm rays}} \exp (-\tau_\nu^{(k)}) [1-\exp (-\hat
\tau_\nu^{(k)})]}{\sum_{k=1}^{N_{\rm rays}} \hat \tau_\nu^{(k)}} .
\end{equation}
The total photon absorption rates per chemical species $i$
within the zone are then calculated via
$\Gamma_{i,\nu} = \sigma_{i,\nu} n_i V F_\nu/h\nu$, where $V$ is
the zone volume.
In the limit in which the zone is very optically thick, $\hat
\tau_\nu^{(k)}\gg 1$, we obtain
\begin{equation}
\label{eq:optically_thick}
\sum_i \Gamma_{i,\nu} \approx (h\nu)^{-1} F_\nu \langle
\exp(-\tau_\nu^{(k)})\rangle \Omega ,
\end{equation}
where $\Omega$ is the angular size of the zone as seen from the central
source, and the extinction external to the zone is averaged over
rays. The approximation in equation (\ref{eq:optically_thick}) becomes exact in the
limit $N_{\rm rays}\rightarrow \infty$, as it has to be to conserve
photons.
We calculate radiation pressure associated with photoionization and
Thomson scattering. The radiation pressure force is added to the
gravitational force of the central point mass. We ignore line resonance radiation altogether and also ignore any diffusion of ionizing radiation \citep[see, e.g.,][]{Ritzerveld:05}.
\subsection{Mesh Refinement and Initial Conditions}
\label{sec:amr_initial}
We simulate a cylindrical domain in the upper hemisphere $0 < (R,z) <
1\textrm{ pc}$ with 18 levels of mesh refinement. Since each AMR block
contains $8\times8$ zones, the maximum spatial resolution in the
simulation is $\Delta x\sim 3\times10^{12}\textrm{ cm}$. We require that the
central hole, with radius $r_{\rm hole}=10^{14}\textrm{ cm}$, is
always resolved at the highest level of mesh refinement. We achieve
pseudo-logarithmic gridding by capping the resolution at radius $r$ with
$\Delta x > \frac{1}{8} \eta r$ where we choose $\eta=0.1$; this
prevents use of excessive resolution far from the central hole.
The simulation domain initially contained uniform-density partially
ionized gas, with initial electron abundance of $\chi_e=0.5$, at temperature $10^4\textrm{ K}$ and density $n_{\rm H}=10^7\textrm{ cm}^{-3}$. The initial value for the central point
mass was $100~M_\odot$.
\begin{figure}
\begin{center}
\includegraphics[width=3.5in]{f1.pdf}
\end{center}
\caption{Central accretion rate and radiative luminosity as a function
of time for radiative efficiency $\epsilon=0.1$.}
\label{fig:accretion_rate_luminosity}
\end{figure}
\section{Results}
\label{sec:results}
The central accretion rate, shown in Figure
\ref{fig:accretion_rate_luminosity}, oscillates between values close
to, and occasionally mildly exceeding the Eddington
limit, $\dot M_{\rm max}\sim \dot M_{\rm Edd}\sim
2\times10^{-6}M_\odot\textrm{ yr}^{-1}$, and a rate lower by an order of
magnitude, $\dot M_{\rm min}\sim 2\times10^{-7} M_\odot\textrm{ yr}^{-1}$. The
accretion is approximately periodic with a mild trend toward an
increasing period separating consecutive peak episodes; the period
varies between $250\textrm{ yr}$ and $350\textrm{ yr}$. Accretion
rate falloff following a maximum is roughly exponential, as is
expected since photoionization radiation pressure in the
ionized region surrounding the black hole evacuates the accreting gas
and drives down the accretion rate \citep[see \S~3
in][]{Milosavljevic:08}. The average accretion rate and luminosity are $\langle \dot M\rangle = 4.6\times10^{19} \textrm{ g cm}^{-3}$ and $\langle L\rangle=4.2\times10^{39}\textrm{ erg s}^{-1}$, which says that on average, the black hole accretes at $32\%$ of the Eddington limit. The average accretion rate is still only $\sim 1\%$ of the adiabatic
``Bondi'' accretion rate $\dot M_{\rm Bondi} =\pi (GM_{\rm bh})^2 n m_p/c_{\rm s}^{3}(\infty)$, calculated ignoring radiative feedback, for an ambient sound speed of $c_{\rm s}(\infty)=14\textrm{ km s}^{-1}$.
During a central accretion maximum, photoionization radiation pressure drives
an outflow in the ionized gas within the \ion{H}{2} region that has
neutral fractions $\chi_{\rm H}\sim 10^{-4}-10^{-5}$
(Fig.~\ref{fig:color_figure}, \emph{lower panels}). This leads to
rarefaction and exponential drop in central accretion. Meanwhile, as
radiation pressure subsides, gas near the edge of the \ion{H}{2}
region accelerates inward. This acceleration is driven by a gas pressure imbalance near the edge; the imbalance was inherited from the preceding accretion maximum when an outward radiation pressure force balanced an inward gas pressure gradient force.
The outflow intersects with the
inflow, and the inflowing gas ultimately arrives at the edge of the
central hole and gives rise to a new accretion maximum. The longest
timescale in the cycle is the inward acceleration time, which is here a
factor of $\sim 3$ times shorter than the radial sound crossing time of the
\ion{H}{2} region with typical temperature $T_{\rm HII}\sim
4\times10^4\textrm{ K}$.
\begin{figure}
\begin{center}
\includegraphics[width=3.5in]{f2.pdf}
\end{center}
\caption{Gas number density $n$ (\emph{upper panels}) and neutral fraction
$\chi_{\rm H}$
(\emph{lower panels}) at two separate instances around
$t\sim 4,000\textrm{ yr}$. The
left panels show the flow during a central accretion
minimum; infalling gas is clearly visible at $r\sim
1.5\times10^{16}\textrm{ cm}$. The right panels show the flow
during a central accretion maximum. The structure near the central axis, in the conical region marked by dashed lines, is an artifact of our having set the optical depth to zero along the axis, for $R/|z|<\tan5^\circ$, to avoid numerical issues arising from the coordinate singularity. }
\label{fig:color_figure}
\end{figure}
Figure \ref{fig:radii}\emph{a} shows that the radius of the \ion{H}{2} region surrounding the black hole reaches an
asymptotic value of $r_{\rm ion}\sim 6\times 10^{16}\textrm{ cm}$. This only somewhat smaller, by $40\%$, than the crude estimate obtained for hydrogen-only cloud in equation (4) of \citet{Milosavljevic:08}. The region
$r< r_{\rm ion}$ is not entirely free of neutral gas; during accretion
minima, as seen in the two left panels of Figure
\ref{fig:color_figure}, dense clumps form in the gas that has been
expelled by radiation pressure and is now falling back toward the
black hole, and the regions in the dense clumps' shadows recombine.
The range of radii that is shaded in Figure \ref{fig:radii}\emph{a}
contains a multiphase medium. The densest neutral clumps that form near
the edges of the \ion{H}{2} region are six times
denser than the ambient gas, but this density is not sufficient to resist
photoevaporation during accretion maxima. Figure \ref{fig:radii}\emph{b} shows that the flow into the central
hole is typically supersonic with sonic radius located at $r_{\rm
s}\sim 2\times10^{14}\textrm{ cm}$, but during accretion maxima, shock
heating in the infalling gas drives subsonic flow to the brink of
the excised hole at $r_{\rm hole}=10^{14}\textrm{ cm}$.
\begin{figure}
\begin{center}
\includegraphics[width=3.5in]{f3.pdf}
\end{center}
\caption{Minimum radius at which neutral gas, with ionization fraction
$\chi_{\rm H^+}<\frac{1}{2}$ is found (lower boundary of the shaded
region in panel [\emph{a}]) and maximum radius at which ionized gas, with $\chi_{\rm
H^+}>\frac{1}{2}$, is found (upper boundary of the shaded region).
Panel (\emph{b}) shows the minimum radius at which the radial inflow
is subsonic. Because of transient shock heating in the flow, the
sonic radius, which normally resides at $r_{\rm s}\sim
2.2\times10^{14}\textrm{ cm}$, shrinks to the edge of the hole at
$r_{\rm hole}=10^{14} \textrm{ cm}$.}
\label{fig:radii}
\end{figure}
\section{Conclusions and Discussion}
\label{sec:conclusions}
We have simulated accretion from a uniform, high-density ($10^7\textrm{ cm}^{-3}$)\footnote{Atomic densities have been found to reach comparable high levels in simulations of protogalactic collapse \citep[e.g.,][]{Bromm:03,Wise:07,Wise:08}.} metal-free protogalactic cloud onto an intermediate-mass black hole. At radii from the black hole smaller than the size of the excised region, $10^{14}\textrm{ cm}$, the accretion was assumed to be radiatively efficient. We find that a compact \ion{H}{2} region forms around the black hole. The accretion is intermittent due to alternating photoionization radiation pressure-driven expulsion and external pressure-driven fallback. The average accretion rate is $\lesssim 1\%$ of the Bondi accretion rate calculated ignoring the radiation's influence, and $\sim \frac{1}{3}$ of the Eddington-limited rate.
The numerical results are consistent with the predictions of our toy model for episodic quasiradial accretion \citep{Milosavljevic:08}, where we suggested that photoionization heating and photoionization radiation pressure within the compact \ion{H}{2} region are the dominant accretion-suppression mechanisms. We also suggested that Ly$\alpha$ line resonance radiation pressure, which we do not account for in the simulations presented here, should further reduce the accretion rate. The intermittency is qualitatively similar to that seen in one-dimensional simulations of the accretion of hot irradiated intergalactic medium onto black holes in central cluster galaxies by \citet{Sazonov:05} and \citet{Ciotti:07}, with the notable caveat that photoionization radiation pressure was unimportant in that context.
The simulation in which the accreting fluid was endowed with small angular momentum corresponding to maximum circularization radius equal to $r_{\rm hole}$ exhibited similar intermittency and only a slightly reduced average accretion rate, consistent with \citet[and references therein]{Krumholz:05}. In contrast with the nonrotating simulations that did not contain axial outflows, narrow polar outflows form that resemble some of those found by \citet{Proga:07} and \citet{Proga:08} in simulations of accretion flows irradiated by a quasar. The accretion intermittency and inflow-outflow behavior that we observe is qualitatively similar to that seen in Proga et al., but
additional tests are needed to ascertain whether out axial outflows are physical.
The overall goal is to combine the highly-resolved simulations presented here with large-scale cosmological simulations of how the first galaxies formed at the end of the cosmic dark ages \citep[e.g.,][]{Greif:08}. Those simulations can resolve the central gas flows to within $\sim 0.01\textrm{ pc}$, where we can implement sub-grid prescriptions based on the calculations done here. An important challenge will be to derive prescriptions for the feedback from black hole accretion that are applicable to a wide range of protogalactic conditions. We will report on these efforts elsewhere (Couch et al., in preparation).
\acknowledgements
We acknowledge valuable discussions with Daniel Proga.
The software used in this work was in part developed by the DOE-supported
ASC/Alliance Center for Astrophysical Thermonuclear Flashes at the
University of Chicago. The authors acknowledge the Texas Advanced
Advanced Computing Center (TACC) at the University of Texas at Austin
for providing high-performance computing resources that have
contributed to this research. V.~B. and M.~M.
acknowledge support from NSF grant AST-0708795.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,500 |
This fortnight we have been discussing the latest Facebook update that claims it will allow users to control who they most frequently see updates from in their News Feed. As well as this, Google again clarifies its position on links, Twitter gets rid of three Twitter Cards and Pinterest launches third-party integration.
For friends and pages you have chosen to see more of, Facebook will highlight new stories they have shared since you last logged into Facebook. This will appeal to those still desperately trying to only see updates from their actual friends on Facebook.
However, so brands are not neglected, Facebook has added the 'Discover New Pages' option. This will give a user suggestions of publishers, artists and businesses based on the types of pages that you have liked in the past.
These were rolled out on iOS on Thursday 9 July and will be on Android and desktop in the coming weeks.
Jacob Frantz, Product Manager at Facebook, explains further in this newsroom post.
This week, SEOs and digital marketers were in much discussion about a post on the Google Portuguese webmaster blog that stated it was unnatural to even ask for links.
A few days later, Google retracted this statement and corrected it to read 'not buy, sell or ask for links that may violate our linking webmaster guidelines', according to this post by Barry Schwartz on Search Engine Roundtable.
So you can ask for links, as long as you go about it in the right way, which to be clear, is the Google way.
Read the industry's reaction in the comments of Barry's post.
Twitter Cards allow media experiences to be attached to tweets. By adding specific HTML code to webpages, any users who tweets a link from the brand website will have what is known as a card attached to the tweet that is visible to all their followers.
For most blog content and product pages, the 'Summary Card' and 'Summary Card with Large Image' will be the most relevant. Using Twitter Cards on your tweets can dramatically improve engagement, as well as drive more traffic to your website.
Not using Twitter Cards yet? Visit Twitter's Developer guide. Already got Twitter Cards? Find out how to analyse their performance with the Twitter Card Analytics guide.
The above tweet shows an example of a 'Summary Card' attached to a Fresh Egg tweet.
On Wednesday 8 July Pinterest switched on its developer platform. It introduced Polyvore and IFTTT as the first third-party integrations and announced these will be followed by more.
"If you use IFTTT, logging in with Pinterest lets you automatically save any photo you like on Instagram as a Pin. It also works with actions in other apps, like Reddit upvotes, Etsy favorites or any other Pinterest "Recipe" you create on IFTTT.
IFTTT allows users to automate actions between online platforms; each automation is called a 'recipe'. Brands that are struggling to find the time to use Pinterest can create recipes to minimise time spent searching for images to pin.
This is currently available on iOS or desktop and will be on Android soon.
Will instant messaging be banned in the UK? | {
"redpajama_set_name": "RedPajamaC4"
} | 6,580 |
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\section{Introduction} Problems of Waring-type involving mixed sums of powers provide convenient specimens on which to test analytic methods that one hopes subsequently to apply more generally. Let $t\ge 2$ and $2\le k_1\le \ldots \le k_t$ be fixed integers, and let $n$ be a natural number sufficiently large in terms of $t$ and $\bfk$. We refer to the problem of establishing the existence of solutions $\bfx\in \dbN^t$ of the Diophantine equation
\begin{equation}\label{1.1}
n=x_1^{k_1}+x_2^{k_2}+\ldots +x_t^{k_t}
\end{equation}
as the {\it Waring problem} corresponding to the exponent $t$-tuple $\bfk$. Associated with this problem is the parameter $\bet(\bfk)=k_1^{-1}+\ldots +k_t^{-1}$ that determines the difficulty of obtaining solutions. Aficionados of the Hardy-Littlewood method will recognise that when $k_t\ge 3$, the intrinsic convexity barrier prevents the circle method from establishing the existence of solutions to (\ref{1.1}) when $\bet(\bfk)\le 2$. The goal of this paper is to resolve a wide class of such problems of Waring-type, if necessary by assuming the truth of the Generalised Riemann Hypothesis. Henceforth we abbreviate the latter hypothesis to GRH, by which we mean the Riemann Hypothesis for all $L$-functions associated with Dirichlet characters. Our first result illustrates what we have in mind, and concerns the exponent tuple $\bfk=(2,2,3,3,6,6)$, for which $\bet(\bfk)=2$.
\begin{theorem}\label{theorem1.1}
Assume the truth of GRH. Then all sufficiently large natural numbers $n$ are represented in the form
\begin{equation}\label{1.2}
x_1^2+x_2^2+x_3^3+x_4^3+x_5^6+x_6^6=n,
\end{equation}
with $x_i\in \dbN$ $(1\le i\le 6)$.
\end{theorem}
As a consequence of recent work of the author \cite{Woo2012} concerning the anticipated asymptotic formula associated with this representation problem, it follows without condition that the number of integers $n$ with $1\le n\le X$, which fail to be represented in the shape (\ref{1.2}), is at most $O((\log X)^{3+\eps})$. The closest analogue to Theorem \ref{theorem1.1} thus far achieved in the literature is the implicit resolution by Vaughan \cite{Vau1980} of the Waring problem associated to the tuple $\bfk=(2,2,3,3,5,5)$, although it would not be difficult to extract from this result a conclusion for the tuple $\bfk=(2,2,3,3,5,6)$. There are very few instances in which the Waring problem corresponding to exponent $\bfk$ has been resolved when $\bet(\bfk)\le 2$. Subject to natural conditions of congruential type, Gauss \cite{Gau1801} tackled the case $\bfk=(2,2,2)$ with $\bet(\bfk)=\tfrac{3}{2}$, and more recently Linnik \cite{Lin1972} and Hooley \cite{Hoo1981b} successfully considered $\bfk=(2,2,3,3,3)$ with $\bet(\bfk)=2$. Also, work of Golubeva \cite{Gol1996, Gol2008} addresses the mixed exponent $\bfk=(2,2,3,3,4,16,4k+1)$ with $\bet(\bfk)=2-\tfrac{1}{48}+\tfrac{1}{4k+1}$. Most recently of all, subject to the validity of the Elliott-Halberstam conjecture together with GRH, work of Friedlander and the author \cite{FW2012} resolves the Waring problem corresponding to the exponent tuple $\bfk=(2,2,4,4,4,k)$, with $\bet(\bfk)=2-\tfrac{1}{4}+\tfrac{1}{k}$. Here, the final $k$th power may be deleted if one is prepared to accommodate certain congruence conditions modulo $48$.\par
Rather than apply the circle method to establish Theorem \ref{theorem1.1}, which as we have noted is limited to situations with $\bet(\bfk)>2$ by the convexity barrier, we instead apply a method of Golubeva involving the theory of ternary quadratic forms \cite{Gol1996, Gol2008}. In applying this method, we avoid in this paper certain difficulties arising from auxiliary congruences by assuming where necessary the truth of GRH. Following some preliminary discussion in \S2, we establish in \S3 the more widely applicable conclusion contained in the following theorem. Here and in \S3, we write
\begin{equation}\label{1.3}
\gam(\bfk)=\prod_{j=1}^t\left(1-\frac{1}{k_i}\right)\quad \text{and}\quad \gamtil(\bfk)=\left( 1-\frac{1}{k_t}\right)\prod_{j=1}^{t-2}\left(1-\frac{1}{k_i}\right).
\end{equation}
We emphasise that throughout this paper, except where otherwise indicated, we assume that $2\le k_1\le \ldots \le k_t$.
\begin{theorem}\label{theorem1.2}
Assume the truth of GRH. Then provided that $\gam(\bfk)<\frac{12}{17}$, all sufficiently large natural numbers $n$ are represented in the form
\begin{equation}\label{1.4}
x_1^2+x_2^2+x_3^3+x_4^3+\sum_{j=1}^ty_j^{k_j}=n,
\end{equation}
with $\bfx\in \dbN^4$ and $\bfy\in \dbN^t$. The same conclusion holds without the assumption of GRH if either (i) one has $t\ge 2$ and $\gamtil(\bfk)<\frac{74}{105}$, or (ii) one has $\gam(\bfk)<\frac{74}{105}$ and the exponents $k_1,\ldots ,k_t$ are not all even.
\end{theorem}
The conclusion of Theorem \ref{theorem1.1} follows at once on noting that $\gam(6,6)=\frac{25}{36}<\frac{12}{17}$. Further corollaries follow likewise with a modicum of computation.
\begin{corollary}\label{corollary1.4}
All sufficiently large natural numbers $n$ are represented as a sum of positive integral powers in the form
$$x_1^2+x_2^2+x_3^3+x_4^3+x_5^5+x_6^8=n,$$
and also in the form
$$x_1^2+x_2^2+x_3^3+x_4^3+x_5^9+x_6^9+x_7^9=n.$$
\end{corollary}
\begin{corollary}\label{corollary1.3}
Assume the truth of GRH. Then all sufficiently large natural numbers $n$ are represented as a sum of positive integral powers in the form
$$x_1^2+x_2^2+x_3^3+x_4^3+x_5^6+x_6^{12}+x_7^{12}=n.$$
\end{corollary}
If one is prepared to assume the Ramanujan Conjecture concerning the Fourier coefficients of cusp forms of weight $\tfrac{3}{2}$, then further progress is possible, as we demonstrate in \S4.
\begin{theorem}\label{theorem1.5}
Assume the truth of GRH and the Ramanujan Conjecture. Then provided that $\gam(\bfk)<\frac{5}{6}$, all sufficiently large natural numbers $n$ are represented in the form (\ref{1.4}) with $\bfx\in \dbN^4$ and $\bfy\in \dbN^t$. The same conclusion holds without the assumption of GRH if either (i) one has $t\ge 2$ and $\gamtil(\bfk)<\frac{5}{6}$, or (ii) one has $\gam(\bfk)<\frac{5}{6}$ and the exponents $k_1,\ldots ,k_t$ are not all even.
\end{theorem}
We record two immediate consequences of Theorem \ref{theorem1.5} which require no further explanation.
\begin{corollary}\label{corollary1.6}
Assume the truth of the Ramanujan Conjecture. Then all sufficiently large natural numbers $n$ are represented as a sum of positive integral powers in the form
$$x_1^2+x_2^2+x_3^3+x_4^3+x_5^5=n,$$
and also in the form
$$x_1^2+x_2^2+x_3^3+x_4^3+x_5^6+x_6^{2k+1}=n.$$
\end{corollary}
\begin{corollary}\label{corollary1.7}
Assume the truth of GRH and the Ramanujan Conjecture. Then all sufficiently large natural numbers $n$ are represented as a sum of positive integral powers in the form
$$x_1^2+x_2^2+x_3^3+x_4^3+x_5^4=n.$$
\end{corollary}
We finish by remarking that several authors have considered Waring's problem in the general setting (\ref{1.1}) with mixed powers $k_1,\ldots ,k_t$. The reader will locate a representative slice of this literature in the sources Br\"udern \cite{Bru1987}, Hooley \cite{Hoo1981a} and Vaughan \cite{Vau1971}.\par
It is a pleasure to record here my gratitude to Elena Golubeva and Valentin Blomer for correspondence and conversations several years ago concerning Golubeva's theorem on ternary quadratic forms and its proof, here reported as Theorem \ref{theorem2.1} below.
\section{Golubeva's method: preliminaries}
Our goal in this section and the next is the proof of Theorem \ref{theorem1.2}, together with the conclusion of Theorem \ref{theorem1.1} which essentially amounts to a corollary of the former theorem. Here we make use of a method originating in work of Linnik \cite{Lin1943}, and much enhanced by the level-lowering procedure of Golubeva \cite{Gol1996, Gol2008}. We seek to establish the solubility of the equation (\ref{1.4}) when $n$ is large by putting $x_3=A+x_0$ and $x_4=A-x_0$, with $A\in \dbN$ of size nearly $n^{1/3}$ and $|x_0|<A$. Notice here that when $A$ and $x_0$ are both integers, then $x_3$ and $x_4$ are necessarily of the same parity. In this way, the representation problem (\ref{1.4}) is transformed into the related one
\begin{equation}\label{2.1}
x_1^2+x_2^2+6Ax_0^2=n-2A^3-\sum_{j=1}^ty_j^{k_j},
\end{equation}
in which we seek a solution with $A\in \dbN$, $|x_0|<A$ and $\bfy\in \dbN^t$. Were $A$ to be very small compared to the integer on the right hand side of (\ref{2.1}), for fixed $\bfy$, and $x_0$ unconstrained, then such a problem would be well within the scope of the theory of ternary quadratic forms. The large size of $A$ obstructs such an approach. In order to bypass this difficulty, we instead seek to choose $y_1,\ldots ,y_t$ in such a way that
$$n-\sum_{j=1}^ty_j^{k_j}$$
is divisible by $q^{6h}$, for some natural numbers $q$ and $h$. If $q^{2h}$ is reasonably close in size to $n^{1/3}$, then one may substitute
$$A=q^{6h}B,\quad x_0=z_0,\quad x_i=q^{3h}z_i\quad (i=1,2),$$
$$N=q^{-6h}\Bigl( n-\sum_{j=1}^ty_j^{k_j}\Bigr) -2q^{12h}B^3.$$
This transforms the representation problem (\ref{2.1}) into the shape
$$z_1^2+z_2^2+6Bz_0^2=N,$$
with $N$ now relatively large compared to $B$. In this way, the level of the modular forms involved in the analysis of the ternary quadratic form $z_1^2+z_2^2+6Bz_0^2$ is lowered to the point that a successful analysis again becomes feasible. This level lowering approach of Golubeva is further enhanced by choosing $B$ in such a manner that $N$ contains a sizeable square factor, this innovation also having been devised by Golubeva.\par
The key ingredient from the theory of ternary quadratic forms of which we make use is the following result of Golubeva.
\begin{theorem}\label{theorem2.1}
For each $\del>0$, there exists a positive number $C(\del)$ with the property that, whenever $n\in \dbN$ and $p$ is a prime number satisfying the following conditions:
\item{(i)} one has $(n,6p)=1$;
\item{(ii)} the congruence $n\equiv x^2+y^2+6pz^2\mmod{16}$ is soluble;
\item{(iii)} the integer $n$ may be written in the form $n=tm^2$ with $(t,m)=1$, and one has $nm^{12}>C(\del)p^{21+\del}$;
\vskip.1cm \noindent then the equation
\begin{equation}\label{2.2}
n=x^2+y^2+6pz^2
\end{equation}
has a solution in natural numbers $x$, $y$ and $z$.
\end{theorem}
\begin{proof} This is in all essentials \cite[Theorem 2]{Gol2008}. We have modified the conclusion to assert that the integers $x$, $y$ and $z$ are natural numbers. Such follows from the argument of the proof of \cite[Theorem 2]{Gol2008}, on noting that the number of representations of $n$ in the shape (\ref{2.2}) with $xyz=0$ is plainly $O_\eps(n^\eps)$. Meanwhile, for each $\eps>0$, the total number of solutions delivered by Golubeva's argument is at least $C_\eps n^{1/2-\eps}p^{-1/2}$, for a positive constant $C_\eps$ depending at most on $\eps$.\par
It may be helpful to the reader examining the proof of \cite[Theorem 2]{Gol2008} to think of $m^2$ as the largest square divisor of $n$, so that $t$ is squarefree. The bounds for the $n$-th Fourier coefficients of eigenforms, for arbitrary $n$, reported by Golubeva are then discussed in detail in \cite[Lemma 1]{Blo2008}. See the sketch proof of Theorem \ref{theorem4.1} below for more on this matter.\end{proof}
We next set up the machinery to construct the integer $q$ that plays a key role in the above sketch. This rests on the existence of small primes $p_j$ having the property that a given integer $m$ is a $k_j$-th power residue modulo $p_j$. Current technology fails to deliver such a conclusion in general without appeal to a suitable Riemann Hypothesis.
\begin{lemma}\label{lemma2.2} Let $k,D\in \dbN$, and suppose that $m$ is a large natural number with $m\gg D^A$, for some fixed $A>0$. Then there exists a prime $\varpi$ with $(mD,\varpi)=1$ having the property that the congruence $y^k\equiv m\mmod{\varpi^h}$ is soluble for every natural number $h$. When $k$ is odd, one may choose $\varpi$ with $\varpi\ll_k \log m$. When $k$ is even, meanwhile, provided that the Riemann Hypothesis holds for the Dedekind zeta function $\zet_L(s)$, where $L=\dbQ(e^{2\pi i/k},\sqrt[k]{m})$, one may choose $\varpi$ with $\varpi\ll_{k,\eps} (\log m)^{2+\eps}$.
\end{lemma}
\begin{proof} Consider first the situation in which $k$ is odd. We take $\varpi$ to be any prime number with $\varpi\equiv 2\mmod{k}$ and $\varpi\nmid mD$. Since the number of prime divisors of $mD$ is $O(\log m/\log \log m)$, it follows from the Prime Number Theorem in arithmetic progressions that such a prime exists with $\varpi\ll_k \log m$. Since $(\varpi-1,k)=1$, it follows from Fermat's Little Theorem that the congruence $y^k\equiv m\mmod{\varpi}$ is soluble, and then an application of Hensel's Lemma reveals that for every integer $h$, the congruence $y^k\equiv m\mmod{\varpi^h}$ is soluble. This completes the proof of the lemma when $k$ is odd.\par
When $k$ is even, we must resort to higher reciprocity laws (see Milne \cite[Chapter V, especially p.162]{Mil2011} and Pollack \cite{Pol2012} for suitable background material). Let $\zet_k=e^{2\pi i/k}$, and write $K=\dbQ(\zet_k)$ and $L=\dbQ(\zet_k,\sqrt[k]{m})$. Write $d_L$ for the discriminant of $L$ over $\dbQ$. Then it follows from the Dedekind-Kummer splitting criterion that for any prime ideal $\grp$ of $K$ relatively prime to $k$ and $m$, so that $\grp$ is unramified in $L$, the $k$th power residue symbol $\left({\displaystyle{\frac{m}{\grp}}}\right)_k$ is equal to $1$ if and only if $\grp$ splits in $L$. The latter in turn happens if and only if the Artin symbol $\left( {\displaystyle{\frac{L/K}{\grp}}}\right)$ is the identity in $\text{Gal}(L/K)$. Assuming the Riemann Hypothesis for the Dedekind zeta function $\zet_L(s)$, it follows from work of Lagarias and Odlyzko \cite{LO1977} that there exists a prime ideal $\grp$ of $K$, unramified in $L$, with $\left( {\displaystyle{\frac{L/K}{\grp}}}\right)$ equal to the identity and satisfying
$$N_{K/\dbQ}(\grp)\ll (\log d_L)^2(\log \log d_L)^4\ll_\eps (\log m)^{2+\eps}.$$
This work shows, moreover, that $N_{K/\dbQ}(\grp)$ may be chosen to be a rational prime, say $\varpi$, with $(\varpi,kmD)=1$. Thus we deduce that the congruence $y^k\equiv m\mmod{\varpi}$ is soluble for some rational prime $\varpi$ satisfying
$$\varpi\ll_\eps (\log m)^{2+\eps}\quad \text{and}\quad (kmD,\varpi)=1.$$
An application of Hensel's Lemma again now shows that the congruence $y^k\equiv m\mmod{\varpi^h}$ is soluble for every natural number $h$. This completes the proof of the lemma.
\end{proof}
We note that the Riemann Hypothesis for the Dedekind zeta function $\zet_L(s)$ occurring in the statement of Lemma \ref{lemma2.2} follows from GRH.\par
We next make some preparations which facilitate the application of Lemma \ref{lemma2.2} in the level-lowering procedure of Golubeva. The first observation that we must keep in mind is that in order to apply Theorem \ref{theorem2.1}, one must ensure that the conditions (i) and (ii) are met. It transpires that some slightly delicate footwork is required as we proceed through the argument so as to ensure that such remains possible. In order to motivate some of this manoeuvring, we note that a modicum of computation confirms that when $p$ is an odd prime, then for any integer $\lam$ the expression
$$x^2+y^2+6pz^2+2\lam^2p^3$$
represents all of the odd residue classes modulo $16$, with one at least of $x$ and $y$ odd. It follows as a consequence of this observation that we may concentrate on condition (i) of Theorem \ref{theorem2.1} in what follows.\par
We now briefly describe the setting for the next lemma. We suppose throughout that $n$ is a sufficiently large natural number. It is convenient to adopt the notation of writing $K$ for the product $k_1\ldots k_{t-1}$. We consider fixed distinct prime numbers $\varpi_1,\ldots ,\varpi_{t-1}$ satisfying the conditions $(30K,\varpi_i)=1$ $(1\le i\le t-1)$ and $\varpi_{t-1}\nmid n$. Since the number of distinct prime divisors of $n$ is $O(\log n/\log \log n)$, we may suppose in addition that
\begin{equation}\label{2.3}
K^{10}<\varpi_{t-1}\ll_K \log n\quad \text{and}\quad K^{10}<\varpi_i\ll_K 1\quad (1\le i\le t-2).
\end{equation}
Finally, we write $\Ome_u=\varpi_1\ldots \varpi_u$, with the familiar convention that $\Ome_0=1$.
\begin{lemma}\label{lemma2.3}
Assume the truth of GRH. Then there exist $y,h\in \dbN$, and a prime number $\varpi$ with $\varpi\le (\log n)^3$, having the following properties:
\item{(a)} $(30n\Ome_{t-1},\varpi)=1$ and $y^{k_t}\equiv n\mmod{\varpi^{6Kh}}$;
\item{(b)} $n^{1/k_t}(\log n)^{-20tK}\le \varpi^{6Kh}\le y\le n^{1/k_t}(\log n)^{-t}$;
\item{(c)} $(n-y^{k_t}, 10\Ome_{t-1})=1$ and $n-y^{k_t}\not\equiv 2\mmod{3}$;
\item{(d)} when $t\ge 2$, then the integer $\varpi^{-6Kh}(n-y^{k_t})$ is a $k_{t-1}$-th power residue modulo $\varpi_{t-1}$.\vskip.1cm
\noindent When $k_t$ is odd, this conclusion is independent of GRH.
\end{lemma}
\begin{proof} When $k_t$ is even, assume the truth of GRH. Then it follows from Lemma \ref{lemma2.2} that when $n$ is sufficiently large, then there exists a prime number $\varpi$ with $\varpi\le (\log n)^3$ and $(30n\Ome_{t-1},\varpi)=1$ such that, for any $l\in \dbN$, there exists a solution of the congruence
\begin{equation}\label{2.4}
z^{k_t}\equiv n\mmod{\varpi^l}.
\end{equation}
We choose $l$ to be the largest multiple of $6K$, say $l=6Kh$, having the property that
$$\varpi^l\le n^{1/k_t}(\log n)^{-t-2}.$$
\par Let $z$ denote any solution of (\ref{2.4}) with $1\le z\le \varpi^l$. Also, define the integer $g_3(n)$ by putting
$$g_3(n)=\begin{cases} 0,&\text{when $n\not\equiv 2\mmod{3}$,}\\
1,&\text{when $n\equiv 2\mmod{3}$.}\end{cases}$$
When $t\ge 2$ it follows from Weil \cite{Wei1949} that, since $(n\varpi,\varpi_{t-1})=1$, the congruence
$$\varpi^{-l}n\equiv w^{k_{t-1}}+\varpi^{-l}v^{k_t}\mmod{\varpi_{t-1}}$$
possesses a solution $w,v$ with $\varpi_{t-1}\nmid wv$. When $t\ge 2$, fix any one such solution $w,v$. In addition, when $q\in \{2,5,\varpi_1,\ldots ,\varpi_{t-2}\}$, put
$$g_q(n)=\begin{cases} 0,&\text{when $(n,q)=1$,}\\
1,&\text{when $q|n$.}\end{cases}$$
Then since $(30\Ome_{t-1},\varpi)=1$, it follows from the Chinese Remainder Theorem that there exists an integer $g$ with $1\le g\le 30\Ome_{t-1}$ having the property that
$$z+g\varpi^l\equiv g_q(n)\mmod{q}\quad (q=2,3,5,\varpi_1,\ldots ,\varpi_{t-2}),$$
and such that when $t\ge 2$ one has
$$z+g\varpi^l\equiv v\mmod{\varpi_{t-1}}.$$
We consequently have
$$(n-(z+g\varpi^l)^{k_t},10\Ome_{t-1})=1\quad \text{and}\quad n-(z+g\varpi^l)^{k_t}\not\equiv 2\mmod{3}.$$
In addition, when $t\ge 2$ the congruence
$$\varpi^{-l}(n-(z+g\varpi^l)^{k_t})\equiv w^{k_{t-1}}\mmod{\varpi_{t-1}}$$
is soluble with $\varpi_{t-1}\nmid w$.\par
We now take $y=z+g\varpi^l$, and note that from (\ref{2.3}) we have the bounds
$$y\le 31\Ome_{t-1}\varpi^l\le (\log n)^2(n^{1/k_t}(\log n)^{-t-2})\le n^{1/k_t}(\log n)^{-t}$$
and
$$y\ge \varpi^l\ge n^{1/k_t}(\log n)^{-t-2-18K}\ge n^{1/k_t}(\log n)^{-20tK}.$$
The conclusion of the lemma is now immediate.
\end{proof}
An application of Lemma \ref{lemma2.3} sows the seeds for the iteration of a result with a similar flavour.
\begin{lemma}\label{lemma2.4}
Let $u$ be a natural number with $1\le u\le t-1$, and let $m\in \dbN$ satisfy $\log m\gg \log n$. Suppose that $m$ is a $k_u$-th power residue modulo $\varpi_u$, and in particular that $\varpi_u\nmid m$. In addition, when $u\ge 2$ suppose that $\varpi_{u-1}\nmid m$. Then there exist natural numbers $y$ and $h$ having the following properties:
\item{(a)} $y^{k_u}\equiv m \mmod{\varpi_u^{6Kh}}$;
\item{(b)} $m^{1/k_u}(\log m)^{-20uk}\le \varpi_u^{6Kh}\le y\le m^{1/k_u}(\log m)^{-u}$;
\item{(c)} $(m-y^{k_u},10\Ome_{u-1})=1$ and $m-y^{k_u}\not\equiv 2\mmod{3}$;
\item{(d)} when $u\ge 2$, then the integer $\varpi_u^{-6Kh}(m-y^{k_u})$ is a $k_{u-1}$-th power residue modulo $\varpi_{u-1}$.
\end{lemma}
\begin{proof} Since $ m$ is a $k_u$-th power residue modulo $\varpi_u$ and $(\varpi_u,k_u)=1$, it follows from an application of Hensel's Lemma that, for any $l\in \dbN$, there exists a solution of the congruence
\begin{equation}\label{2.5}
z^{k_u}\equiv m\mmod{\varpi_u^l}.
\end{equation}
We choose $l$ to be the largest multiple of $6K$, say $l=6Kh$, having the property that
$$\varpi_u^l\le m^{1/k_u}(\log m)^{-u-1}.$$
\par Let $z$ denote any solution of (\ref{2.5}) with $1\le z\le \varpi_u^l$. We define the integers $g_q(m)$ just as in the argument of the proof of Lemma \ref{lemma2.3} when $q=2,3,5,\varpi_1,\ldots ,\varpi_{u-2}$, mutatis mutandis. When $u\ge 2$ it follows from Weil \cite{Wei1949} that, since $(m\varpi_u,\varpi_{u-1})=1$, the congruence
$$\varpi_u^{-l}m\equiv w^{k_{u-1}}+\varpi_u^{-l}v^{k_u}\mmod{\varpi_{u-1}}$$
possesses a solution $w,v$ with $\varpi_{u-1}\nmid wv$. When $u\ge 2$, we fix any one such solution $w,v$. Since $(30\Ome_{u-1},\varpi_u)=1$, it follows from the Chinese Remainder Theorem that there exists an integer $g$ with $1\le g\le 30\Ome_{u-1}$ having the property that
$$z+g\varpi_u^l\equiv g_q(m)\mmod{q}\quad (q=2,3,5,\varpi_1,\ldots ,\varpi_{u-2})$$
and such that when $u\ge 2$ one has
$$z+g\varpi_u^l\equiv v\mmod{\varpi_{u-1}}.$$
We consequently have
$$(m-(z+g\varpi_u^l)^{k_u},10\Ome_{u-1})=1\quad \text{and}\quad m-(z+g\varpi_u^l)^{k_u}\not\equiv 2\mmod{3}.$$
In addition, when $u\ge 2$, the congruence
$$\varpi_u^{-l}(m-(z+g\varpi_u^l)^{k_u})\equiv w^{k_{u-1}}\mmod{\varpi_{u-1}}$$
is soluble with $\varpi_{u-1}\nmid w$.\par
We now take $y=z+g\varpi_u^l$, and note that from (\ref{2.3}) we have the bounds
$$y\le 31\Ome_{u-1}\varpi_u^l\le (\log m)(m^{1/k_u}(\log m)^{-u-1})\le m^{1/k_u}(\log m)^{-1}$$
and
$$y\ge \varpi_u^l\ge m^{1/k_u}(\log m)^{-u-1-K}\ge m^{1/k_u}(\log m)^{-20uK}.$$
The conclusion of the lemma now follows.
\end{proof}
Finally, in order to avoid the assumption of GRH when the exponents $k_1,\ldots ,k_t$ are all even, we require an additional device. We recall our implicit assumption that $k_{t-1}\le k_t$.
\begin{lemma}\label{lemma2.5} Suppose that $t\ge 2$, and let $n$ be a sufficiently large natural number with $\varpi_{t-1}\nmid n$. Then there exist natural numbers $y_1$, $y_2$ and $h$ having the following properties:
\item{(a)} $y_1^{k_{t-1}}+y_2^{k_t}\equiv n\mmod{\varpi_{t-1}^{6Kh}}$;
\item{(b)} $n^{1/k_t}(\log n)^{-20tK}\le \varpi_{t-1}^{6Kh}\le \min\{y_1,y_2\}\le \max\{y_1,y_2\}\le n^{1/k_t}(\log n)^{-t}$;
\item{(c)} $(n-y_1^{k_{t-1}}-y_2^{k_t},10\Ome_{t-2})=1$ and $n-y_1^{k_{t-1}}-y_2^{k_t}\not\equiv 2\mmod{3}$;
\item{(d)} when $t\ge 3$, then the integer $\varpi_{t-1}^{-6Kh}(n-y_1^{k_{t-1}}-y_2^{k_t})$ is a $k_{t-2}$-th power residue modulo $\varpi_{t-2}$.\vskip.1cm
\end{lemma}
\begin{proof} Since $\varpi_{t-1}\nmid n$, it follows from Weil \cite{Wei1949} that the congruence
$$n\equiv u^{k_{t-1}}+v^{k_t}\mmod{\varpi_{t-1}}$$
possesses a solution $u,v$ with $\varpi_{t-1}\nmid uv$. Since $(k_{t-1},\varpi_{t-1})=1$, an application of Hensel's Lemma with $v$ fixed shows that, for any $l\in \dbN$, there exists a solution of the congruence
\begin{equation}\label{2.6}
n\equiv z^{k_{t-1}}+w^{k_t}\mmod{\varpi_{t-1}^l},
\end{equation}
with
$$z\equiv u\mmod{\varpi_{t-1}}\quad \text{and}\quad w\equiv v\mmod{\varpi_{t-1}}.$$
We choose $l$ to be the largest multiple of $6K$, say $l=6Kh$, having the property that
$$\varpi_{t-1}^l\le n^{1/k_t}(\log n)^{-t-2}.$$
Let $z,w$ denote any solution of (\ref{2.6}) with $\varpi_{t-1}^l<z,w\le 2\varpi_{t-1}^l$. When $t\ge 3$, we may proceed as in the argument of the proof of Lemma \ref{lemma2.3} to show that the congruence
$$\varpi_{t-1}^{-l}(n-w^{k_t})\equiv x^{k_{t-2}}+\varpi_{t-1}^{-l}y^{k_{t-1}}\mmod{\varpi_{t-2}}$$
possesses a solution $x,y$ with $\varpi_{t-2}\nmid xy$. Note here that
$$(n-w^{k_t},\varpi_{t-1})=(z^{k_{t-1}},\varpi_{t-1})=(u^{k_{t-1}},\varpi_{t-1})=1.$$
\par When $t\ge 3$, fix any one such solution $x,y$. In addition, when $1\le i<t-2$, define
$$g_{\varpi_i}(n)=\begin{cases} 0,&\text{when $(n-w^{k_t},\varpi_i)=1$,}\\
1,&\text{when $\varpi_i|(n-w^{k_t})$,}\end{cases}$$
and define $g_q(n)$ likewise when $q=2,5$. When $q=3$ we define $g_3(n)$ by putting
$$g_3(n)=\begin{cases} 0,&\text{when $n-w^{k_t}\not\equiv 2\mmod{3}$,}\\
1,&\text{when $n-w^{k_t}\equiv 2\mmod{3}$.}\end{cases}$$
Then since $(30\Ome_{t-2},\varpi_{t-1})=1$, it follows from the Chinese Remainder Theorem that there exists an integer $g$ with $1\le g\le 30\Ome_{t-2}$ having the property that
$$z+g\varpi_{t-1}^l\equiv g_q(n)\mmod{q}\quad (q=2,3,5,\varpi_1,\ldots ,\varpi_{t-3}),$$
and such that when $t\ge 3$ one has
$$z+g\varpi_{t-1}^l\equiv y\mmod{\varpi_{t-2}}.$$
We consequently have
$$(n-w^{k_t}-(z+g\varpi_{t-1}^l)^{k_{t-1}},10\Ome_{t-2})=1$$
and
$$n-w^{k_t}-(z+g\varpi_{t-1}^l)^{k_{t-1}}\not\equiv 2\mmod{3}.$$
In addition, when $t\ge 3$, the congruence
$$\varpi_{t-1}^{-l}(n-w^{k_t}-(z+g\varpi_{t-1}^l)^{k_{t-1}})\equiv u^{k_{t-2}}\mmod{\varpi_{t-2}}$$
is soluble with $\varpi_{t-2}\nmid u$.\par
We now take $y_1=z+g\varpi_{t-1}^l$ and $y_2=w$, and note that
$$\max\{y_1,y_2\}\le 31\Ome_{t-2}\varpi_{t-1}^l\le (\log n)^2(n^{1/k_t}(\log n)^{-t-2})=n^{1/k_t}(\log n)^{-t}$$
and
$$\min\{y_1,y_2\}\ge \varpi_{t-1}^l\ge n^{1/k_t}(\log n)^{-t-2-6K}\ge n^{1/k_t}(\log n)^{-20tK}.$$
The conclusion of the lemma is now immediate.
\end{proof}
\section{Golubeva's method: an iterative process}
We now proceed in an iterative fashion. We focus in our main discussion on the most interesting situations in which $\gam(\bfk)>\tfrac{2}{3}$, though later we sketch how to modify this central argument so as to handle the easier cases in which $\gam(\bfk)\le \tfrac{2}{3}$. In addition, our initial focus is on the situation where either (i) not all of the exponents $k_1,\ldots ,k_t$ are even, or (ii) one assumes the truth of GRH. In the first situation, we relabel exponents so that $k_t$ is odd, so that in our application of Lemma \ref{lemma2.3} we are able to avoid the assumption of GRH.\par
Consider the representation problem
\begin{equation}\label{3.1}
m_t=v_t^2+w_t^2+(A_t+z)^2+(A_t-z)^2+\sum_{j=1}^ty_{jt}^{k_j},
\end{equation}
which we seek to solve in natural numbers $v_t$, $w_t$, $A_t$, $z$, $\bfy$ subject to the condition $A_t>(n/6)^{1/3}$, whenever $m_t=n$ is sufficiently large. Given such a solution of (\ref{3.1}), one has
$$m_t=v_t^2+w_t^2+6A_tz^2+2A_t^3+\sum_{j=1}^ty_{jt}^{k_j},$$
and hence
$$z<(\tfrac{1}{6}n/A_t)^{1/2}<(n/6)^{1/3}<A_t,$$
so that (\ref{3.1}) exhibits a solution of the Waring problem (\ref{1.4}) in natural numbers $\bfx,\bfy$.\par
Recall that $K=k_1\ldots k_{t-1}$, and consider fixed distinct prime numbers $\varpi_1,\ldots ,\varpi_{t-1}$ with $(30K,\varpi_i)=1$ $(1\le i\le t-1)$ and $\varpi_{t-1}\nmid n$, and satisfying (\ref{2.3}). From Lemma \ref{lemma2.3}, we find that there exist natural numbers $y=y_{tt}$ and $h=h_t$, and a prime number $\varpi_t$ with $\varpi_t\le (\log n)^3$, having the properties (a) to (d) of the conclusion of that lemma. Here, we assume GRH only in circumstances in which $k_t$ (and indeed every exponent $k_i$) is even.\par
We introduce some notation in order to assist with the iteration to come. When $0\le r\le t$, define $\gam_r$ and $\Ups_r=\Ups_r(\bfh)$ by
$$\gam_r=\prod_{r<l\le t}\left(1-\frac{1}{k_l}\right) \quad \text{and}\quad \Ups_r=\prod_{r<l\le t}\varpi_l^{6Kh_l}.$$
Then with the integers $y_{tt}$ and $h_t$, and the prime number $\varpi_t$, fixed as above, we find that the representation problem (\ref{3.1}) may be solved whenever the derived representation problem
\begin{align}
m_t-y_{tt}^{k_t}=(\varpi_t^{3Kh_t}v_{t-1})^2+&(\varpi_t^{3Kh_t}w_{t-1})^2+
6(\varpi_t^{6Kh_t}A_{t-1})z^2\notag \\
&+2(\varpi_t^{6Kh_t}A_{t-1})^3+\sum_{j=1}^{t-1}(\varpi_t^{6h_tK/k_j}y_{j,t-1})^{k_j}\label{3.2}
\end{align}
is soluble in natural numbers $v_{t-1},w_{t-1},A_{t-1},z$ and $y_{j,t-1}$ $(1\le j\le t-1)$, in which we impose the condition
$$\varpi_t^{6Kh_t}A_{t-1}>(n/6)^{1/3}.$$
\par Write
$$m_{t-1}=\varpi_t^{-6Kh_t}(m_t-y_{tt}^{k_t}).$$
Then in view of property (a) of Lemma \ref{lemma2.3}, the representation problem (\ref{3.2}) is equivalent to
\begin{equation}\label{3.3}
m_r=v_r^2+w_r^2+6A_rz^2+2\Ups_r^2A_r^3+\sum_{j=1}^ry_{jr}^{k_j},
\end{equation}
subject to
\begin{equation}\label{3.4}
\Ups_rA_r>(n/6)^{1/3},
\end{equation}
in the special case $r=t-1$. Notice here, again in the special case $r=t-1$, that property (b) of Lemma \ref{lemma2.3} ensures that
\begin{equation}\label{3.5}
n^{1-\gam_r}(\log n)^{-20(t-r)tK}\le \Ups_r\le n^{1-\gam_r}(\log n)^{20(t-r)tK}
\end{equation}
and
\begin{equation}\label{3.6}
n(1-2(t-r)(\log n)^{-1})\le \Ups_rm_r\le n.
\end{equation}
Thus, in particular, one has
\begin{equation}\label{3.7}
\tfrac{1}{2}n^{\gam_r}(\log n)^{-20(t-r)tK}\le m_r\le n^{\gam_r}(\log n)^{20(t-r)tK}.
\end{equation}
On noting that $\varpi_{r+1}^{6Kh_{r+1}}\equiv 1\mmod{3}$, properties (a) and (c) furnish the relations
\begin{equation}\label{3.8}
(m_r,10\Ome_r)=1\quad \text{and}\quad m_r\not\equiv 2\mmod{3}.
\end{equation}
In addition, property (d) shows that when $t\ge 2$, the congruence
\begin{equation}\label{3.9}
m_r\equiv y^{k_r}\mmod{\varpi_r}
\end{equation}
is soluble for some integer $y$ with $(y,\varpi_r)=1$.\par
We have shown that the Waring problem (\ref{1.4}) is soluble whenever, for $r=t-1$, the representation problem (\ref{3.3}) is soluble subject to the conditions (\ref{3.4}) to (\ref{3.9}). We now show by induction that the same is true for $0\le r<t-1$. Let $u$ be an integer with $1\le u\le t-1$, and suppose that the inductive hypothesis holds for $r=u$. The condition (\ref{3.7}) ensures that $\log m_u\gg \log n$, and (\ref{3.8}) ensures that $(m_u,\varpi_{u-1}\varpi_u)=1$. In addition, it follows from (\ref{3.9}) that $m_u$ is a $k_u$-th power residue modulo $\varpi_u$. Then we deduce from Lemma \ref{lemma2.4} that there exist natural numbers $y=y_{uu}$ and $h=h_u$, having the properties (a) to (d) of the conclusion of that lemma. As in the discussion corresponding to the case $r=t$, it follows that with the integers $y_{uu}$ and $h_u$ fixed, the representation problem (\ref{3.3}) may be solved when $r=u$ provided that the problem
\begin{align}
m_u-y_{uu}^{k_u}=(\varpi_u^{3Kh_u}&v_{u-1})^2+(\varpi_u^{3Kh_u}w_{u-1})^2+
6(\varpi_u^{6Kh_u}A_{u-1})z^2\notag \\
&+2\Ups_u^2(\varpi_u^{6Kh_u}A_{u-1})^3+\sum_{j=1}^{u-1}(\varpi_u^{6h_uK/k_j}y_{j,u-1})^{k_j}\label{3.10}
\end{align}
is soluble in natural numbers $v_{u-1},w_{u-1},A_{u-1},z$ and $y_{j,u-1}$ $(1\le j\le u-1)$, in which we impose the condition
$$\Ups_{u-1}A_{u-1}>(n/6)^{1/3}.$$
\par Write
\begin{equation}\label{3.11}
m_{u-1}=\varpi_u^{-6Kh_u}(m_u-y_{uu}^{k_u}).
\end{equation}
Then by property (a) of Lemma \ref{lemma2.4}, the representation problem (\ref{3.10}) is equivalent to (\ref{3.3}) subject to (\ref{3.4}) in the special case $r=u-1$. Continuing our restriction to the special case $r=u-1$, property (b) of Lemma \ref{lemma2.4} combines with the bounds (\ref{3.6}) and (\ref{3.7}) to deliver the estimates
\begin{align*}
\Ups_{u-1}&=\varpi_u^{6Kh_u}\Ups_u\le m_u^{1/k_u}(\log m_u)^{-u}\Ups_u\le m_u^{1/k_u-1}(\log m_u)^{-u}(m_u\Ups_u)\\
&\le n\left( \tfrac{1}{2}n^{\gam_u}(\log n)^{-20(t-u)tK}\right)^{1/k_u-1}\le 2n^{1-\gam_{u-1}}(\log n)^{20(t-u)tK}\\
&\le n^{1-\gam_{u-1}}(\log n)^{20(t-u+1)tK}
\end{align*}
and
\begin{align*}
\Ups_{u-1}&=\varpi_u^{6Kh_u}\Ups_u\ge m_u^{1/k_u-1}(\log m_u)^{-20uK}(m_u\Ups_u)\\
&\ge \tfrac{1}{2}n\left( n^{\gam_u}(\log n)^{20(t-u)tK}\right)^{1/k_u-1}(\log n)^{-20uK}\\
&\ge n^{1-\gam_{u-1}}(\log n)^{-20(t-u+1)tK},
\end{align*}
so that (\ref{3.5}) holds with $r=u-1$. Likewise, one finds that property (b) in combination with (\ref{3.6}) and (\ref{3.11}) shows that
$$\Ups_{u-1}m_{u-1}\le \Ups_um_u\le n$$
and
$$\Ups_{u-1}m_{u-1}\ge \Ups_um_u(1-(\log m_u)^{-u})\ge n(1-2(t-u+1)(\log n)^{-1}),$$
so that (\ref{3.6}) holds with $r=u-1$. Finally, property (c) ensures that (\ref{3.8}) holds with $r=u-1$, and property (d) shows that when $u\ge 2$, then (\ref{3.9}) holds with $r=u-1$. We have therefore confirmed the inductive hypothesis with $r=u-1$, and this completes the inductive step.\par
At this stage we have shown that the Waring problem (\ref{1.4}) is soluble provided that the representation problem (\ref{3.3}) is soluble when $r=0$ subject to the conditions (\ref{3.4}) to (\ref{3.8}). Simplifying notation in the obvious manner, it therefore suffices to consider the representation problem
\begin{equation}\label{3.12}
m=v^2+w^2+6Bz^2+2\lam^2B^3,
\end{equation}
where $m$ is a sufficiently large positive integer with $(m,10)=1$ and $m\not\equiv 2\mmod{3}$. We may suppose further that $(\lam,30m)=1$, that $\lam$ is an odd square, and that
\begin{equation}\label{3.13}
\lam^{-1}n(1-2t(\log n)^{-1})\le m\le \lam^{-1}n,
\end{equation}
and
\begin{equation}\label{3.14}
n^{1-\gam_0}(\log n)^{-20t^2K}\le \lam\le n^{1-\gam_0}(\log n)^{20t^2K}.
\end{equation}
Finally, our goal is to find a solution satisfying the condition $\lam B>(n/6)^{1/3}$.\par
Consider the congruence
$$2\lam^2B^3\equiv m\mmod{5}.$$
Since $5\nmid m$, and $5$ is distinct from $2,\varpi_1,\ldots ,\varpi_t$, and is congruent to $2$ modulo $3$, the congruence
$$B^3\equiv (2\lam^2)^{-1}m\mmod{5}$$
is soluble with $(B,m)=1$. An application of Hensel's Lemma consequently shows that the congruence
\begin{equation}\label{3.15}
2\lam^2B^3\equiv m\mmod{5^{2h}}
\end{equation}
is soluble for every natural number $h$. Let $\eps$ be a sufficiently small positive number, and take $c=2+2\eps$ when GRH holds, and otherwise put $c=\tfrac{12}{5}+2\eps$. We take $h$ to be the largest integer for which one has
$$\lam (5^{2h+1})^c<(n/6)^{1/3},$$
so that
\begin{equation}\label{3.16}
5^{-2c}(n/6)^{1/3}\le \lam (5^{2h+1})^c<(n/6)^{1/3}.
\end{equation}
Thus from (\ref{3.14}) we have
$$n^{(\gam_0-2/3)/(2c)}(\log n)^{-10t^2K}<5^h<n^{(\gam_0-2/3)/(2c)}(\log n)^{10t^2K}.$$
\par Let $B$ be any fixed solution of (\ref{3.15}) with $1\le B\le 5^{2h}$. Then with $\nu$ either equal to $0$ or to $1$, one has
$$2\lam^2(B+5^{2h}\nu)^3-m\not\equiv 0\mmod{5^{2h+1}}.$$
The methods of Iwaniec \cite{Iwa1974}, Huxley \cite{Hux1975} and Gallagher \cite{Gal1972} may be employed to show that, whenever $Q>(5^{2h+1})^{12/5+\eps}$, then there is a prime number $p$ with $Q<p\le 2^{1/3}Q$, and satisfying
$$p\nmid m,\quad p\equiv B+5^{2h}\nu \mmod{5^{2h+1}}\quad \text{and}\quad p\equiv 1\mmod{3}.$$
We direct the reader to the discussion in the preamble to \cite[Theorem 2.1]{AGP1994}, as it relates to \cite[equation (0.3)]{AGP1994}, for an account of a suitable lower bound for this purpose. In addition, by virtue of the opening discussion of Heath-Brown \cite{HB1992}, on GRH such a prime exists whenever $Q>(5^{2h+1})^{2+\eps}$. We take $Q=\lam^{-1}(n/6)^{1/3}$, and observe from (\ref{3.16}) and the definition of $c$ that there is an $\eps$ to spare in the exponent of $5^{2h+1}$ to guarantee that $Q$ satisfies the respective lower bounds just cited. In this way we see that a suitable prime number $p$ exists with
\begin{equation}\label{3.17}
(n/6)^{1/3}<\lam p<(n/3)^{1/3},
\end{equation}
and with
$$p\equiv 1\mmod{3},\quad 2\lam^2p^3\equiv m\mmod{5^{2h}}\quad \text{and}\quad 2\lam^2p^3\not\equiv m\mmod{5^{2h+1}},$$
in which
\begin{equation}\label{3.18}
n^{(\gam_0-2/3)/c}(\log n)^{-20t^2K}<5^{2h}<n^{(\gam_0-2/3)/c}(\log n)^{20t^2K}.
\end{equation}
\par Write $N=TM^2$, where
$$T=5^{-2h}(m-2\lam^2p^3)\quad \text{and}\quad M=5^h.$$
Then we have $(T,M)=1$, and in view of (\ref{3.12}) we have yet only to solve the representation problem
$$N=x^2+y^2+6pz^2,$$
subject to the condition $\lam p>(n/6)^{1/3}$. Here, we may suppose that
$$N=m-2\lam^2p^3\equiv m\mmod{2},\quad N=m-2\lam^2p^3\equiv m-2\mmod{3}$$
and
$$(N,p)=(m-2\lam^2p^3,p)=(m,p)=1.$$
Since $m$ is odd, it follows that the congruence
$$N\equiv x^2+y^2+6pz^2\mmod{16}$$
is soluble. Moreover, we have $3\nmid (m-2)$ and $2\nmid m$, so that $(N,6p)=1$. Then it follows from Theorem \ref{theorem2.1} that this representation problem is soluble provided only that
$$NM^{12}>C(\eps)p^{21+\eps}\quad \text{and}\quad \lam p>(n/6)^{1/3}.$$
The second of these conditions is satisfied by virtue of (\ref{3.17}), whilst from (\ref{3.13}), (\ref{3.17}) and (\ref{3.18}) in combination with the latter constraint, we have
\begin{align*}
NM^{12}&>(m-2\lam^2p^3)(5^h)^{12}\\
&\ge \lam^{-1}n(1-2t(\log n)^{-1}-\tfrac{2}{3})(n^{(\gam_0-2/3)/c-\eps/8})^6.
\end{align*}
On recalling (\ref{3.14}), we discern that
\begin{equation}\label{3.19}
NM^{12}\ge n^{\gam_0+6(\gam_0-2/3)/c-\eps}.
\end{equation}
Meanwhile, from (\ref{3.17}) in combination with (\ref{3.14}) we find that
\begin{equation}\label{3.20}
p^{21+\eps}<(n^{1/3}\lam^{-1})^{21+\eps}<n^{21\gam_0-14+\eps}.
\end{equation}
Provided that
\begin{equation}\label{3.21}
\gam_0(6/c+1)-4/c-\eps>21\gam_0-14+\eps,
\end{equation}
then a comparison of (\ref{3.19}) and (\ref{3.20}) reveals that $NM^{12}>C(\eps)p^{21+\eps}$, and so it follows from the discussion of the last paragraph that we have a representation of $m$ in the shape (\ref{3.12}). This in turn implies that $m_t$ is represented in the form (\ref{3.1}), and hence that the Waring problem (\ref{1.4}) is indeed soluble. The inequality (\ref{3.21}) yields the condition
$$\gam_0<\frac{14-4/c-2\eps}{21-6/c-1}=\frac{7c-2-c\eps}{10c-3}.$$
Provided that $\gam_0<\tfrac{12}{17}$ and $\eps$ is chosen sufficiently small, therefore, this condition is satisfied with $c=2+2\eps$, which is the above choice of $c$ that follows from the assumption of GRH. Alternatively, as long as $\gam_0<\tfrac{74}{105}$ and $\eps$ is taken to be sufficiently small, this condition is satisfied with $c=\tfrac{12}{5}+2\eps$, which is our earlier choice for $c$ relevant when GRH is not assumed to hold. Thus, on recalling (\ref{1.3}) we find that when GRH holds and $\gam(\bfk)<\tfrac{12}{17}$, then we are able to solve the equation $N=x^2+y^2+6pz^2$, whence all sufficiently large natural numbers $n$ have a representation in the form (\ref{1.4}). The same conclusion holds independent of GRH when the $k_i$ are not all even and $\gam(\bfk)<\tfrac{74}{105}$. This completes our discussion of the central argument required to prove Theorem \ref{theorem1.2} when either the validity of GRH is assumed, or else when the exponents $k_1,\ldots ,k_t$ are not all even.\par
We now briefly sketch the modifications required to deliver the conclusion of Theorem \ref{theorem1.2} when $t\ge 2$ and $\gamtil(\bfk)<\tfrac{74}{105}$. In this instance, we modify the argument above following (\ref{3.3}) by applying Lemma \ref{lemma2.5} in place of Lemma \ref{lemma2.3}. We consider fixed distinct primes $\varpi_1,\ldots ,\varpi_{t-1}$ as before. It follows from the former lemma that there exist natural numbers $y_1=y_{t-1,t-1}$, $y_2=y_{t,t-1}$ and $h=h_{t-1}$ having the properties (a) to (d) of its conclusion. With the integers $y_{t-1,t-1}$, $y_{t,t-1}$ and $h_{t-1}$ fixed, we find that the representation problem (\ref{3.1}) may be solved whenever the representation problem
\begin{align*}
m_t-y_{t-1,t-1}^{k_{t-1}}-y_{t,t-1}^{k_t}=(\varpi_{t-1}^{3Kh_{t-1}}&v_{t-2})^2+(\varpi_{t-1}^{3Kh_{t-1}}w_{t-2})^2+
6(\varpi_{t-1}^{6Kh_{t-1}}A_{t-2})z^2\\
&+2(\varpi_{t-1}^{6Kh_{t-1}}A_{t-2})^3+\sum_{j=1}^{t-2}(\varpi_{t-1}^{6h_{t-1}K/k_j}y_{j,t-2})^{k_j}
\end{align*}
is soluble in natural numbers $v_{t-2},w_{t-2},A_{t-2},z$ and $y_{j,t-2}$ $(1\le j\le t-2)$, in which we impose the condition
$$\varpi_{t-1}^{6Kh_{t-1}}A_{t-2}>(n/6)^{1/3}.$$
\par Write
$$m_{t-2}=\varpi_{t-1}^{-6Kh_{t-1}}(m_t-y_{t-1,t-1}^{k_{t-1}}-y_{t,t-1}^{k_t}).$$
Then in view of property (a) of Lemma \ref{lemma2.5}, this representation problem is equivalent to (\ref{3.3}) subject to (\ref{3.4}) in the special case $r=t-2$, where we now write
$$\Ups_r=\prod_{r<l\le t-1}\varpi_l^{6Kh_l}.$$
Properties (a) to (d) of Lemma \ref{lemma2.5} deliver the relations (\ref{3.5}) to (\ref{3.9}), though one must now replace the exponents $\gam_r$ with the modified exponent
$$\gamtil_r=\left( 1-\frac{1}{k_t}\right) \prod_{r<l\le t-2}\left( 1-\frac{1}{k_l}\right).$$
The problem now assumes the form treated above, save that the exponents $\gam_r$ must be decorated by tildes throughout. The reader should experience no difficulty in completing the argument as before, concluding that Theorem \ref{theorem1.2} holds when $t\ge 2$ and $\gamtil(\bfk)<\frac{74}{105}$.\par
It now remains only to note that when $\gam(\bfk)<\tfrac{2}{3}$ (or indeed $\gamtil(\bfk)<\tfrac{2}{3}$), the above argument can of course be modified so that the exponents $h_i$ are made smaller. In this way, in the conclusion of Lemma \ref{lemma2.3}, one may ensure that property (b) is replaced by a condition of the type
$$n^{\ome/k_t}(\log n)^{-20tK}\le \varpi^{6Kh}\le y\le n^{\ome/k_t}(\log n)^{-t},$$
with similar modifications in Lemmata \ref{lemma2.4} and \ref{lemma2.5}. We choose $\ome=\ome(\nu)$ to be the positive number with $0<\ome<1$ for which the modified exponent
$$\gam(\bfk;\ome)=\prod_{j=1}^t\left( 1-\frac{\ome}{k_j}\right)$$
satisfies $\gam(\bfk;\ome)=\tfrac{2}{3}+\nu$, for a suitably small positive number $\nu$. By modifying in this way the central argument applied above, one derives the same conclusion save with $\gam(\bfk)$ replaced by $\gam(\bfk;\ome)$. Since $\tfrac{2}{3}<\gam(\bfk;\ome)=\tfrac{2}{3}+\nu$, the desired conclusion follows. Similar comments apply also in the situation discussed in the previous paragraph.\par
Theorem \ref{theorem1.1} follows immediately from Theorem \ref{theorem1.2} on noting that $(\tfrac{5}{6})^2<\tfrac{12}{17}$. Likewise, Corollaries \ref{corollary1.4} and \ref{corollary1.3} follow on noting that
$$\gam(5,8)=\left(\frac{4}{5}\right)\left(\frac{7}{8}\right)<\frac{74}{105},\quad \gam(9,9,9)=\left(\frac{8}{9}\right)^3<\frac{74}{105},$$
$$\gam(6,12,12)=\left(\frac{5}{6}\right)\left(\frac{11}{12}\right)^2<\frac{12}{17}.$$
\section{Consequences of the Ramanujan Conjecture}
In this section we refine the conclusion of Theorem \ref{theorem2.1}, assuming the truth of the Ramanujan Conjecture concerning Fourier coefficients of cusp forms of weight $\tfrac{3}{2}$.
\begin{theorem}\label{theorem4.1}
Assume the truth of the Ramanujan Conjecture. For each $\del>0$, there exists a positive number $C(\del)$ with the property that whenever $n\in \dbN$ and $p$ is a prime number satisfying the following conditions:
\item{(i)} one has $(n,6p)=1$;
\item{(ii)} the congruence $n\equiv x^2+y^2+6pz^2\mmod{16}$ is soluble;
\item{(iii)} one has $n>C(\del)p^{5+\del}$;
\vskip.1cm \noindent then the equation (\ref{2.2}) has a solution in natural numbers $x$, $y$ and $z$.
\end{theorem}
\begin{proof} We follow the argument of \cite[\S2]{Gol2008}, mutatis mutandis. Write $r(n)$ for the number of representations of the integer $n$ in the shape (\ref{2.2}) with $x,y,z\in \dbN$. Denote by $S_{3/2}^{(1)}(24p,\chi)$ the space of cusp forms of weight $\tfrac{3}{2}$ and level $24p$ which, under the Shimura lift, are taken into cusp forms of weight $2$. Let $K$ denote the dimension of $S_{3/2}^{(1)}(24p,\chi)$, so that $K\ll p^{1+\eps}$, and let $(\varphi_k(z))_{k=1}^K$ be an orthonormal basis for this space.\par
Let $\fhat(n)$ be the $n$-th Fourier coefficient of a cusp form $f(z)$, so that
$$f(z)=\sum_{n=0}^\infty \fhat(n)e(nz).$$
We write $n$ in the shape $n=tm^2$ with $t$ squarefree. Note that the condition $(n,6p)=1$ ensures that both $t$ and $m$ are coprime to the level. Then by combining Deligne's estimates for the eigenvalues of Hecke operators of weight $2$, together with Shimura's lift, one finds that
$$\phihat_k(n)\ll |\phihat_k(t)|m^{1/2+\eps}.$$
This estimate is employed in the argument of the proof of \cite[Theorem 2]{Gol2008}. We direct the reader to \cite[Lemma 1]{Blo2008} for a discussion of this conclusion. The Ramanujan Conjecture asserts that when $f\in S_{3/2}^{(1)}(24p,\chi)$, then for squarefree integers $r$ one should have
$$|\fhat(r)|\ll r^{1/4+\eps}.$$
We apply this estimate trivially to obtain
$$\sum_{k=1}^K|\phihat_k(t)|^2\ll Kt^{1/2+2\eps}\ll p^{1+\eps}t^{1/2+2\eps}.$$
Recall that $n=tm^2$. Then on substituting this bound for Golubeva's use of the Duke-Iwaniec estimate
$$\sum_{k=1}^K|\phihat_k(t)|^2\ll t^{13/14+\eps},$$
the reader will have no difficulty in following the argument of \cite[\S2]{Gol2008} so as to establish that
$$r(n)\gg_\eps n^{1/2-\eps}p^{-1/2}+O\left(p^{1/4+\eps}m^{1/2+\eps}(p^{1+\eps}t^{1/2+2\eps})^{1/2}\right).$$
Consequently, one has $r(n)\gg_\eps n^{1/2-2\eps}p^{-1/2}$ provided only that
$$n^{1/2-2\eps}p^{-1/2}\gg p^{3/4+2\eps}(tm^2)^{1/4+\eps},$$
or equivalently,
$$n^{1/4-3\eps}\gg p^{5/4+2\eps}.$$
Then, whenever $\del>0$, and $\eps>0$ is taken sufficiently small in terms of $\del$, one finds that
$r(n)\gg_\eps n^{1/2-2\eps}p^{-1/2}$ provided only that $n\gg p^{5+\del}$. This completes the
proof of the theorem.
\end{proof}
The conclusion of Theorem \ref{theorem4.1} may be substituted into the argument of \S3 without any great difficulty. The lower bound (\ref{3.19}) is replaced by $N\ge n^{\gam_0-\eps}$, whilst (\ref{3.20}) becomes
$$p^{5+\eps}<(n^{1/3}\lam^{-1})^{5+\eps}<n^{5\gam_0-10/3+\eps}.$$
Hence, provided that
\begin{equation}\label{4.1}
\gam_0-\eps>5\gam_0-\tfrac{10}{3}+\eps,
\end{equation}
a comparison reveals that $N>p^{5+\eps}$, and so it follows as before that the Waring problem (\ref{1.4})
is soluble, but now subject to the truth of the Ramanujan Conjecture. The inequality (\ref{4.1}) yields the condition
$$\gam_0<\tfrac{1}{4}(\tfrac{10}{3}-2\eps)=\tfrac{5}{6}-\tfrac{1}{2}\eps.$$
Provided that $\gam_0<\tfrac{5}{6}$ and $\eps$ is chosen sufficiently small, therefore, this condition is satisfied. All that remains is to note that in the suppressed argument leading to this point in our discussion
we find it necessary to assume GRH only when all the exponents $k_1,\ldots ,k_t$ are even. The variants sketched at the end of \S3 follow with obvious modifications that need not detain us here. This completes the proof of Theorem \ref{theorem1.5}.\par
We finish by noting that a more optimistic enhancement of Theorem \ref{theorem4.1} might be expected to hold with the condition (iii) replaced by the constraint that $n>C(\del)p^{3+\del}$. If true, such would replace the condition (\ref{4.1}) by
$$\gam_0-\eps>3(\gam_0-\tfrac{2}{3})+\eps.$$
This condition is satisfied provided that $\gam_0<1$ and $\eps$ is chosen sufficiently small. Such a conclusion would imply that when $n$ is sufficiently large, the Waring problem (\ref{1.4}) is soluble whenever either $t\ge 2$, or the exponents $k_1,\ldots ,k_t$ are not all even. When $t=1$ and $k_1$ is even, the Waring problem (\ref{1.4}) would remain soluble provided that GRH holds.
\bibliographystyle{amsbracket}
\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,960 |
Q: Как правильно внести значение просмотров в лист тренируюсь в написании html парсера суть работы в том что бы вытащить с сайта инфу о сериалах а именно Названия / URL постера / Просмотры, с названием и URL постера все прошло гладко но на просмотрах у меня всё встало не получается занести их в список.
сделал как смог, но все просмотры съехали на одну позицию вниз, как можно поправить?
using HtmlAgilityPack;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Net;
using System.Text;
using System.Threading;
using System.Threading.Tasks;
namespace ConsoleSimpleHTMLParser
{
#region
// Базовый класс, в котором храняться название тайтла, ссылки на постер и колличество просмотров.
class SeriesData
{
public SeriesData(string t, string up, string v)
{
Title = t;
UrlPoster = up;
View = v;
}
public string Title { get; set; }
public string UrlPoster { get; set; }
public string View { get; set; }
}
class Series : SeriesData
{
public Series(string t, string up, string v) : base(t, up, v)
{
// ...
}
}
// Класс SeriesList способен управлять любым видом списков сериалов.
// при условии, что он является производным от класса SeriesData.
class SeriesList<T> where T : SeriesData
{
T[] serList;
int end;
public SeriesList()
{
serList = new T[10000];
end = 0;
}
// Добавить элемент в список.
public bool Add(T newEntry)
{
if (end == 10000)
{
return false;
}
serList[end] = newEntry;
end++;
return true;
}
public void Insert(string inst, int count)
{
try
{
serList[count].View = inst;
}
catch (Exception exc)
{
count--;
serList[count].View = inst;
}
}
public void ShowList()
{
for (int i = 0; i < end; i++)
{
Console.WriteLine("Название: {0} \nURL Постера: {1}\nПросмотры: {2}\n", serList[i].Title, serList[i].UrlPoster, serList[i].View);
}
}
}
#endregion
class Program
{
static string LoadPage(string url)
{
var result = "";
var request = (HttpWebRequest)WebRequest.Create(url);
var response = (HttpWebResponse)request.GetResponse();
if (response.StatusCode == HttpStatusCode.OK)
{
var receiveStream = response.GetResponseStream();
if (receiveStream != null)
{
StreamReader readStream;
if (response.CharacterSet == null)
readStream = new StreamReader(receiveStream);
else
readStream = new StreamReader(receiveStream, Encoding.GetEncoding(response.CharacterSet));
result = readStream.ReadToEnd();
readStream.Close();
}
response.Close();
}
return result;
}
static void Main()
{
SeriesList<Series> serieslist = new SeriesList<Series>();
// Загрузить html из сети интернет
var pageContent = LoadPage(@"https://web.archive.org/web/20190926110623/https://animevost.org/");
var document = new HtmlDocument();
document.LoadHtml(pageContent);
// Загрузить html локально
//HtmlDocument document2 = new HtmlDocument();
//document2.Load(@"H:\sample.txt");
HtmlNodeCollection infoSeriesTitleURLPoster = document.DocumentNode.SelectNodes(".//td/div/a/img");
HtmlNodeCollection infoSeriesView = document.DocumentNode.SelectNodes(".//div/div[2]/div[2]/span[1]");
foreach (HtmlNode item in infoSeriesTitleURLPoster)
{
serieslist.Add(new Series(item.GetAttributeValue("title", "").Replace(""", ""), // название
item.GetAttributeValue("src", ""), // url постера
item.GetAttributeValue("span", ""))); // просмотры
}
int count = 0;
foreach (HtmlNode item in infoSeriesView)
{
serieslist.Insert(item.InnerText, count++);
}
serieslist.ShowList();
Console.ReadKey(true);
}
}
}
A: Давно не пробовал Html agility pack, но что-то типа такого:
var series = document.DocumentNode.SelectNodes(".//div[@class='shortstory']");
foreach (HtmlNode item in series)
{
var title = item.SelectSingleNode(".//div[@class='shortstoryHead']/h2/a")?.InnerText;
var posterUrl = item.SelectSingleNode(".//img[@class='imgRadius']")?.GetAttributeValue("src", "");
var views = item.SelectSingleNode(".//span[@class='staticInfoRightSmotr']")?.InnerText;
var element = new Series(title, posterUrl, views);
serieslist.Add(element);
}
Выводит без сдвигов:
Название: Кандагава: Девушки на гидроциклах / Kandagawa Jet Girls [1 из 12+] [2 серия - 15 октября]
URL Постера: /web/20190926110623im_/https://animevost.org/uploads/posts/2019-09/1569439519_1.jpg
Просмотры: 15138
Название: Маг-обманщик из другого мира / Isekai Cheat Magician [1-12 из 12]
URL Постера: /web/20190926110623im_/https://animevost.org/uploads/posts/2019-07/1563784705_01-1.jpg
Просмотры: 3578543
Название: Рыцари усердия / Try Knights [1-9 из 12+]
URL Постера: /web/20190926110623im_/https://animevost.org/uploads/posts/2019-08/1565134513_1.jpg
Просмотры: 310173
Название: Рыцари усердия / Try Knights [1-9 из 12+]
URL Постера: poster_url
Просмотры: 310173
Как работает — смотрите объяснения в комментариях EvgeniyZ, он всё правильно вам сказал.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,131 |
Q: Does the stellar MK classification fix the apparent luminosity? Introduction
Let say we have some stars and their spectral classification in the MK index. (not all HD stars)
*
*HD xxxx - B3
*HD yyyy - O7
*HD zzzz - F0
*....
If the stars share the same spectral type, then they share the same superficial temperature $T$. Also, the $LRT$ relation holds
$$\boxed{L=4\pi \sigma R^2 T^4} $$
for $L$ absolute luminosity, $\sigma$ the Stefan-Boltzmann constant and $R$ the stellar radius. By definition of $L$
$$L=\ell 4\pi r^2$$
where $\ell$ is the apparent luminosity and $r$ is the distance of the star from the Earth. Let's take a look at the distance
$$r^2=\frac{L}{\ell 4 \pi}=\frac{4\pi \sigma R^2T^4}{\ell 4 \pi}=\frac{\sigma R^2 T^4}{\ell}$$
Question
Do I need further information to say anything about the distance and the apparent magnitude of the stars, in the form of their stellar radius $R$ and the apparent luminosity $\ell$.
A: In general, your relation among $r$, $R$, $T$, and $\ell$ holds. Knowing any three can determine the fourth.
That said, I've never seen "apparent luminosity" defined like that, where it doesn't have the same units as luminosity. Really I've never seen "apparent luminosity" defined. In fact, the flux matches that definition:
$$ F = \frac{L}{4\pi r^2}. $$
Then your relation could be written
$$ r^2 = \frac{\sigma R^2T^4}{F}. $$
$F$ is measured from photometry and $T$ is measured from spectroscopy. $R$ can be determined from the spectrum with stellar modeling, but those models are calibrated on stars with known values of $r$ obtained from parallax.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 500 |
That was my affirmation for the day. It was a nice thought until I had to deal with a lady I perceived was being rude, and then all compassion and joy went out the door as I vented my frustrations upon this government worker. In my mind, she became the barrier to hindering me from accomplishing a very important task that day. And maybe she was the barrier. Maybe if I would've gotten a different clerk they would have been more compassionate or understanding about my situation. Who knows. What I do know is that I am disstraught that I allowed my own lack of compassion for her to steal my joy. Even more daunting is that I lost an opportunity to influence her and everyone else in that office in a positive way since I'm sure everyone heard my words of irritation and saw me storm out the door in my anger.
In that moment I became just like every other person this lady had to deal with every day that took their frustrations out on her. If you heard the full story you may think my actions were justified, and I could justify them in my own mind if I allowed myself. On the other hand, I could have really taken advantage of this aggravating situation if I had only looked beyond my own agenda and saw her as an individual with feelings, a family to support, and a soul to save. This is why I will not let myself off the hook on this. I know in my heart that my intentions were selfish and inconsiderate of her regardless of how she was treating me. I did not plant the seeds of love that would have promoted joy for both of us that day.
There are times in our life where it's appropriate to make blatant, bold statements against things that are evil, unfair, or unjust, but we need to be choosy about those moments and the influence they will have on others. To do this, I am working diligently to make it my habit to lead with compassion first. This means in circumstances of perceived offense where initial safety and virtue aren't being threatened, I will give people the benefit of the doubt and treat them in the same manner I would want to be treated while remembering my own weaknesses. After this primary reaction of empathy, I can then decide if I want to evaluate the situation further, and take additional action based upon confirmed facts only if my intentions are noble.
We are all people with feelings, agendas, and souls scarred by sin. How much more joy would we experience in our lives if we habitually recognized this and led with compassion? How much more joy would we give to others around us? Yes, people do have evil intentions without regret in the way they treat others, and it is heartbreaking if we find this out. However, without really knowing the true intentions of someone's heart, we can decide to control the assumptions we make and the stories we tell ourselves to mold the perspectives that will influence how we treat people. Practicing compassion through sympathetic, considerate thoughts and actions is a tool to train us in loving souls as Christ does. By unselfishly looking out for the best interest of others in this way, we can protect the joy in our heart as we let go of our ineffective rants of frustration by replacing them with compassion first.
I am grateful that You are compassionate of my faults, my merciful Lord. Forgive me when I do not bestow this same compassion upon others and squander the opportunities I am given to show love. I understand it's okay for me to be frustrated and angry, but I need to use these moments wisely. Teach me to be discerning in using these emotions in a godly manner as Your Son did. Teach me to love as Christ with compassion that draws others to You and promotes joy within the heart. Through Him is all compassion and joy, amen.
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